LMFDB - Embedded newform 1014.4.b.d.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,4,Mod(337,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1014.337");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1014.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$59.8279367458$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1014.337
Dual form			1014.4.b.d.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -3.00000 q^{3} -4.00000 q^{4} +6.00000i q^{5} +6.00000i q^{6} +16.0000i q^{7} +8.00000i q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} -3.00000 q^{3} -4.00000 q^{4} +6.00000i q^{5} +6.00000i q^{6} +16.0000i q^{7} +8.00000i q^{8} +9.00000 q^{9} +12.0000 q^{10} -12.0000i q^{11} +12.0000 q^{12} +32.0000 q^{14} -18.0000i q^{15} +16.0000 q^{16} +126.000 q^{17} -18.0000i q^{18} +20.0000i q^{19} -24.0000i q^{20} -48.0000i q^{21} -24.0000 q^{22} -168.000 q^{23} -24.0000i q^{24} +89.0000 q^{25} -27.0000 q^{27} -64.0000i q^{28} +30.0000 q^{29} -36.0000 q^{30} -88.0000i q^{31} -32.0000i q^{32} +36.0000i q^{33} -252.000i q^{34} -96.0000 q^{35} -36.0000 q^{36} -254.000i q^{37} +40.0000 q^{38} -48.0000 q^{40} +42.0000i q^{41} -96.0000 q^{42} +52.0000 q^{43} +48.0000i q^{44} +54.0000i q^{45} +336.000i q^{46} +96.0000i q^{47} -48.0000 q^{48} +87.0000 q^{49} -178.000i q^{50} -378.000 q^{51} +198.000 q^{53} +54.0000i q^{54} +72.0000 q^{55} -128.000 q^{56} -60.0000i q^{57} -60.0000i q^{58} +660.000i q^{59} +72.0000i q^{60} -538.000 q^{61} -176.000 q^{62} +144.000i q^{63} -64.0000 q^{64} +72.0000 q^{66} +884.000i q^{67} -504.000 q^{68} +504.000 q^{69} +192.000i q^{70} +792.000i q^{71} +72.0000i q^{72} -218.000i q^{73} -508.000 q^{74} -267.000 q^{75} -80.0000i q^{76} +192.000 q^{77} -520.000 q^{79} +96.0000i q^{80} +81.0000 q^{81} +84.0000 q^{82} -492.000i q^{83} +192.000i q^{84} +756.000i q^{85} -104.000i q^{86} -90.0000 q^{87} +96.0000 q^{88} -810.000i q^{89} +108.000 q^{90} +672.000 q^{92} +264.000i q^{93} +192.000 q^{94} -120.000 q^{95} +96.0000i q^{96} +1154.00i q^{97} -174.000i q^{98} -108.000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 6 q^{3} - 8 q^{4} + 18 q^{9}+O(q^{10}) $ 2 * q - 6 * q^3 - 8 * q^4 + 18 * q^9	$ 2 q - 6 q^{3} - 8 q^{4} + 18 q^{9} + 24 q^{10} + 24 q^{12} + 64 q^{14} + 32 q^{16} + 252 q^{17} - 48 q^{22} - 336 q^{23} + 178 q^{25} - 54 q^{27} + 60 q^{29} - 72 q^{30} - 192 q^{35} - 72 q^{36} + 80 q^{38} - 96 q^{40} - 192 q^{42} + 104 q^{43} - 96 q^{48} + 174 q^{49} - 756 q^{51} + 396 q^{53} + 144 q^{55} - 256 q^{56} - 1076 q^{61} - 352 q^{62} - 128 q^{64} + 144 q^{66} - 1008 q^{68} + 1008 q^{69} - 1016 q^{74} - 534 q^{75} + 384 q^{77} - 1040 q^{79} + 162 q^{81} + 168 q^{82} - 180 q^{87} + 192 q^{88} + 216 q^{90} + 1344 q^{92} + 384 q^{94} - 240 q^{95}+O(q^{100}) $ 2 * q - 6 * q^3 - 8 * q^4 + 18 * q^9 + 24 * q^10 + 24 * q^12 + 64 * q^14 + 32 * q^16 + 252 * q^17 - 48 * q^22 - 336 * q^23 + 178 * q^25 - 54 * q^27 + 60 * q^29 - 72 * q^30 - 192 * q^35 - 72 * q^36 + 80 * q^38 - 96 * q^40 - 192 * q^42 + 104 * q^43 - 96 * q^48 + 174 * q^49 - 756 * q^51 + 396 * q^53 + 144 * q^55 - 256 * q^56 - 1076 * q^61 - 352 * q^62 - 128 * q^64 + 144 * q^66 - 1008 * q^68 + 1008 * q^69 - 1016 * q^74 - 534 * q^75 + 384 * q^77 - 1040 * q^79 + 162 * q^81 + 168 * q^82 - 180 * q^87 + 192 * q^88 + 216 * q^90 + 1344 * q^92 + 384 * q^94 - 240 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 2.00000i	− 0.707107i
$2$	− 2.00000i	− 0.707107i
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−4.00000	−0.500000
$5$	6.00000i	0.536656i	0.963328	+	0.268328i	$0.0864711\pi$
$5$	6.00000i	0.536656i	−0.963328	+	0.268328i	$0.913529\pi$
$6$	6.00000i	0.408248i
$7$	16.0000i	0.863919i	0.901893	+	0.431959i	$0.142178\pi$
$7$	16.0000i	0.863919i	−0.901893	+	0.431959i	$0.857822\pi$
$8$	8.00000i	0.353553i
$9$	9.00000	0.333333
$10$	12.0000	0.379473
$11$	− 12.0000i	− 0.328921i	−0.986384	−	0.164461i	$-0.947412\pi$
$11$	− 12.0000i	− 0.328921i	0.986384	−	0.164461i	$-0.0525884\pi$
$12$	12.0000	0.288675
$13$	0	0
$13$	0	0
$14$	32.0000	0.610883
$15$	− 18.0000i	− 0.309839i
$16$	16.0000	0.250000
$17$	126.000	1.79762	0.898808	−	0.438342i	$-0.144434\pi$
$17$	126.000	1.79762	0.898808	+	0.438342i	$0.144434\pi$
$18$	− 18.0000i	− 0.235702i
$19$	20.0000i	0.241490i	0.992684	+	0.120745i	$0.0385284\pi$
$19$	20.0000i	0.241490i	−0.992684	+	0.120745i	$0.961472\pi$
$20$	− 24.0000i	− 0.268328i
$21$	− 48.0000i	− 0.498784i
$22$	−24.0000	−0.232583
$23$	−168.000	−1.52306	−0.761531	−	0.648129i	$-0.775552\pi$
$23$	−168.000	−1.52306	−0.761531	+	0.648129i	$0.775552\pi$
$24$	− 24.0000i	− 0.204124i
$25$	89.0000	0.712000
$26$	0	0
$27$	−27.0000	−0.192450
$28$	− 64.0000i	− 0.431959i
$29$	30.0000	0.192099	0.0960493	−	0.995377i	$-0.469379\pi$
$29$	30.0000	0.192099	0.0960493	+	0.995377i	$0.469379\pi$
$30$	−36.0000	−0.219089
$31$	− 88.0000i	− 0.509847i	−0.966961	−	0.254924i	$-0.917950\pi$
$31$	− 88.0000i	− 0.509847i	0.966961	−	0.254924i	$-0.0820503\pi$
$32$	− 32.0000i	− 0.176777i
$33$	36.0000i	0.189903i
$34$	− 252.000i	− 1.27111i
$35$	−96.0000	−0.463627
$36$	−36.0000	−0.166667
$37$	− 254.000i	− 1.12858i	−0.825578	−	0.564288i	$-0.809151\pi$
$37$	− 254.000i	− 1.12858i	0.825578	−	0.564288i	$-0.190849\pi$
$38$	40.0000	0.170759
$39$	0	0
$40$	−48.0000	−0.189737
$41$	42.0000i	0.159983i	0.996796	+	0.0799914i	$0.0254893\pi$
$41$	42.0000i	0.159983i	−0.996796	+	0.0799914i	$0.974511\pi$
$42$	−96.0000	−0.352693
$43$	52.0000	0.184417	0.0922084	−	0.995740i	$-0.470607\pi$
$43$	52.0000	0.184417	0.0922084	+	0.995740i	$0.470607\pi$
$44$	48.0000i	0.164461i
$45$	54.0000i	0.178885i
$46$	336.000i	1.07697i
$47$	96.0000i	0.297937i	0.988842	+	0.148969i	$0.0475953\pi$
$47$	96.0000i	0.297937i	−0.988842	+	0.148969i	$0.952405\pi$
$48$	−48.0000	−0.144338
$49$	87.0000	0.253644
$50$	− 178.000i	− 0.503460i
$51$	−378.000	−1.03785
$52$	0	0
$53$	198.000	0.513158	0.256579	−	0.966523i	$-0.417405\pi$
$53$	198.000	0.513158	0.256579	+	0.966523i	$0.417405\pi$
$54$	54.0000i	0.136083i
$55$	72.0000	0.176518
$56$	−128.000	−0.305441
$57$	− 60.0000i	− 0.139424i
$58$	− 60.0000i	− 0.135834i
$59$	660.000i	1.45635i	0.685391	+	0.728175i	$0.259631\pi$
$59$	660.000i	1.45635i	−0.685391	+	0.728175i	$0.740369\pi$
$60$	72.0000i	0.154919i
$61$	−538.000	−1.12924	−0.564622	−	0.825350i	$-0.690978\pi$
$61$	−538.000	−1.12924	−0.564622	+	0.825350i	$0.690978\pi$
$62$	−176.000	−0.360516
$63$	144.000i	0.287973i
$64$	−64.0000	−0.125000
$65$	0	0
$66$	72.0000	0.134282
$67$	884.000i	1.61191i	0.591979	+	0.805954i	$0.298347\pi$
$67$	884.000i	1.61191i	−0.591979	+	0.805954i	$0.701653\pi$
$68$	−504.000	−0.898808
$69$	504.000	0.879340
$70$	192.000i	0.327834i
$71$	792.000i	1.32385i	0.749572	+	0.661923i	$0.230260\pi$
$71$	792.000i	1.32385i	−0.749572	+	0.661923i	$0.769740\pi$
$72$	72.0000i	0.117851i
$73$	− 218.000i	− 0.349520i	−0.984611	−	0.174760i	$-0.944085\pi$
$73$	− 218.000i	− 0.349520i	0.984611	−	0.174760i	$-0.0559150\pi$
$74$	−508.000	−0.798024
$75$	−267.000	−0.411073
$76$	− 80.0000i	− 0.120745i
$77$	192.000	0.284161
$78$	0	0
$79$	−520.000	−0.740564	−0.370282	−	0.928919i	$-0.620739\pi$
$79$	−520.000	−0.740564	−0.370282	+	0.928919i	$0.620739\pi$
$80$	96.0000i	0.134164i
$81$	81.0000	0.111111
$82$	84.0000	0.113125
$83$	− 492.000i	− 0.650651i	−0.945602	−	0.325325i	$-0.894526\pi$
$83$	− 492.000i	− 0.650651i	0.945602	−	0.325325i	$-0.105474\pi$
$84$	192.000i	0.249392i
$85$	756.000i	0.964703i
$86$	− 104.000i	− 0.130402i
$87$	−90.0000	−0.110908
$88$	96.0000	0.116291
$89$	− 810.000i	− 0.964717i	−0.875974	−	0.482359i	$-0.839780\pi$
$89$	− 810.000i	− 0.964717i	0.875974	−	0.482359i	$-0.160220\pi$
$90$	108.000	0.126491
$91$	0	0
$92$	672.000	0.761531
$93$	264.000i	0.294360i
$94$	192.000	0.210673
$95$	−120.000	−0.129597
$96$	96.0000i	0.102062i
$97$	1154.00i	1.20795i	0.797004	+	0.603974i	$0.206417\pi$
$97$	1154.00i	1.20795i	−0.797004	+	0.603974i	$0.793583\pi$
$98$	− 174.000i	− 0.179354i
$99$	− 108.000i	− 0.109640i
$100$	−356.000	−0.356000
$101$	618.000	0.608845	0.304422	−	0.952537i	$-0.401537\pi$
$101$	618.000	0.608845	0.304422	+	0.952537i	$0.401537\pi$
$102$	756.000i	0.733874i
$103$	−128.000	−0.122449	−0.0612243	−	0.998124i	$-0.519501\pi$
$103$	−128.000	−0.122449	−0.0612243	+	0.998124i	$0.519501\pi$
$104$	0	0
$105$	288.000	0.267675
$106$	− 396.000i	− 0.362858i
$107$	−1476.00	−1.33355	−0.666777	−	0.745257i	$-0.732327\pi$
$107$	−1476.00	−1.33355	−0.666777	+	0.745257i	$0.732327\pi$
$108$	108.000	0.0962250
$109$	1190.00i	1.04570i	0.852425	+	0.522850i	$0.175131\pi$
$109$	1190.00i	1.04570i	−0.852425	+	0.522850i	$0.824869\pi$
$110$	− 144.000i	− 0.124817i
$111$	762.000i	0.651584i
$112$	256.000i	0.215980i
$113$	−462.000	−0.384613	−0.192307	−	0.981335i	$-0.561597\pi$
$113$	−462.000	−0.384613	−0.192307	+	0.981335i	$0.561597\pi$
$114$	−120.000	−0.0985880
$115$	− 1008.00i	− 0.817361i
$116$	−120.000	−0.0960493
$117$	0	0
$118$	1320.00	1.02980
$119$	2016.00i	1.55300i
$120$	144.000	0.109545
$121$	1187.00	0.891811
$122$	1076.00i	0.798496i
$123$	− 126.000i	− 0.0923662i
$124$	352.000i	0.254924i
$125$	1284.00i	0.918756i
$126$	288.000	0.203628
$127$	2536.00	1.77192	0.885959	−	0.463763i	$-0.153501\pi$
$127$	2536.00	1.77192	0.885959	+	0.463763i	$0.153501\pi$
$128$	128.000i	0.0883883i
$129$	−156.000	−0.106473
$130$	0	0
$131$	2292.00	1.52865	0.764324	−	0.644832i	$-0.223073\pi$
$131$	2292.00	1.52865	0.764324	+	0.644832i	$0.223073\pi$
$132$	− 144.000i	− 0.0949514i
$133$	−320.000	−0.208628
$134$	1768.00	1.13979
$135$	− 162.000i	− 0.103280i
$136$	1008.00i	0.635554i
$137$	726.000i	0.452747i	0.974041	+	0.226374i	$0.0726870\pi$
$137$	726.000i	0.452747i	−0.974041	+	0.226374i	$0.927313\pi$
$138$	− 1008.00i	− 0.621787i
$139$	380.000	0.231879	0.115939	−	0.993256i	$-0.463012\pi$
$139$	380.000	0.231879	0.115939	+	0.993256i	$0.463012\pi$
$140$	384.000	0.231814
$141$	− 288.000i	− 0.172014i
$142$	1584.00	0.936101
$143$	0	0
$144$	144.000	0.0833333
$145$	180.000i	0.103091i
$146$	−436.000	−0.247148
$147$	−261.000	−0.146442
$148$	1016.00i	0.564288i
$149$	1590.00i	0.874214i	0.899410	+	0.437107i	$0.143997\pi$
$149$	1590.00i	0.874214i	−0.899410	+	0.437107i	$0.856003\pi$
$150$	534.000i	0.290673i
$151$	− 2432.00i	− 1.31068i	−0.755332	−	0.655342i	$-0.772524\pi$
$151$	− 2432.00i	− 1.31068i	0.755332	−	0.655342i	$-0.227476\pi$
$152$	−160.000	−0.0853797
$153$	1134.00	0.599206
$154$	− 384.000i	− 0.200932i
$155$	528.000	0.273613
$156$	0	0
$157$	614.000	0.312118	0.156059	−	0.987748i	$-0.450121\pi$
$157$	614.000	0.312118	0.156059	+	0.987748i	$0.450121\pi$
$158$	1040.00i	0.523658i
$159$	−594.000	−0.296272
$160$	192.000	0.0948683
$161$	− 2688.00i	− 1.31580i
$162$	− 162.000i	− 0.0785674i
$163$	1852.00i	0.889938i	0.895546	+	0.444969i	$0.146785\pi$
$163$	1852.00i	0.889938i	−0.895546	+	0.444969i	$0.853215\pi$
$164$	− 168.000i	− 0.0799914i
$165$	−216.000	−0.101913
$166$	−984.000	−0.460080
$167$	2136.00i	0.989752i	0.868964	+	0.494876i	$0.164787\pi$
$167$	2136.00i	0.989752i	−0.868964	+	0.494876i	$0.835213\pi$
$168$	384.000	0.176347
$169$	0	0
$170$	1512.00	0.682148
$171$	180.000i	0.0804967i
$172$	−208.000	−0.0922084
$173$	−1758.00	−0.772591	−0.386296	−	0.922375i	$-0.626246\pi$
$173$	−1758.00	−0.772591	−0.386296	+	0.922375i	$0.626246\pi$
$174$	180.000i	0.0784239i
$175$	1424.00i	0.615110i
$176$	− 192.000i	− 0.0822304i
$177$	− 1980.00i	− 0.840824i
$178$	−1620.00	−0.682158
$179$	540.000	0.225483	0.112742	−	0.993624i	$-0.464037\pi$
$179$	540.000	0.225483	0.112742	+	0.993624i	$0.464037\pi$
$180$	− 216.000i	− 0.0894427i
$181$	−1982.00	−0.813928	−0.406964	−	0.913444i	$-0.633412\pi$
$181$	−1982.00	−0.813928	−0.406964	+	0.913444i	$0.633412\pi$
$182$	0	0
$183$	1614.00	0.651969
$184$	− 1344.00i	− 0.538484i
$185$	1524.00	0.605658
$186$	528.000	0.208144
$187$	− 1512.00i	− 0.591275i
$188$	− 384.000i	− 0.148969i
$189$	− 432.000i	− 0.166261i
$190$	240.000i	0.0916391i
$191$	−2688.00	−1.01831	−0.509154	−	0.860675i	$-0.670042\pi$
$191$	−2688.00	−1.01831	−0.509154	+	0.860675i	$0.670042\pi$
$192$	192.000	0.0721688
$193$	2302.00i	0.858557i	0.903172	+	0.429279i	$0.141232\pi$
$193$	2302.00i	0.858557i	−0.903172	+	0.429279i	$0.858768\pi$
$194$	2308.00	0.854148
$195$	0	0
$196$	−348.000	−0.126822
$197$	4374.00i	1.58190i	0.611880	+	0.790951i	$0.290414\pi$
$197$	4374.00i	1.58190i	−0.611880	+	0.790951i	$0.709586\pi$
$198$	−216.000	−0.0775275
$199$	1600.00	0.569955	0.284977	−	0.958534i	$-0.408014\pi$
$199$	1600.00	0.569955	0.284977	+	0.958534i	$0.408014\pi$
$200$	712.000i	0.251730i
$201$	− 2652.00i	− 0.930635i
$202$	− 1236.00i	− 0.430518i
$203$	480.000i	0.165958i
$204$	1512.00	0.518927
$205$	−252.000	−0.0858558
$206$	256.000i	0.0865843i
$207$	−1512.00	−0.507687
$208$	0	0
$209$	240.000	0.0794313
$210$	− 576.000i	− 0.189275i
$211$	3332.00	1.08713	0.543565	−	0.839367i	$-0.317074\pi$
$211$	3332.00	1.08713	0.543565	+	0.839367i	$0.317074\pi$
$212$	−792.000	−0.256579
$213$	− 2376.00i	− 0.764323i
$214$	2952.00i	0.942965i
$215$	312.000i	0.0989685i
$216$	− 216.000i	− 0.0680414i
$217$	1408.00	0.440467
$218$	2380.00	0.739422
$219$	654.000i	0.201796i
$220$	−288.000	−0.0882589
$221$	0	0
$222$	1524.00	0.460740
$223$	2648.00i	0.795171i	0.917565	+	0.397586i	$0.130152\pi$
$223$	2648.00i	0.795171i	−0.917565	+	0.397586i	$0.869848\pi$
$224$	512.000	0.152721
$225$	801.000	0.237333
$226$	924.000i	0.271963i
$227$	2244.00i	0.656121i	0.944657	+	0.328061i	$0.106395\pi$
$227$	2244.00i	0.656121i	−0.944657	+	0.328061i	$0.893605\pi$
$228$	240.000i	0.0697122i
$229$	5650.00i	1.63040i	0.579177	+	0.815202i	$0.303374\pi$
$229$	5650.00i	1.63040i	−0.579177	+	0.815202i	$0.696626\pi$
$230$	−2016.00	−0.577961
$231$	−576.000	−0.164061
$232$	240.000i	0.0679171i
$233$	−4698.00	−1.32093	−0.660464	−	0.750858i	$-0.729640\pi$
$233$	−4698.00	−1.32093	−0.660464	+	0.750858i	$0.729640\pi$
$234$	0	0
$235$	−576.000	−0.159890
$236$	− 2640.00i	− 0.728175i
$237$	1560.00	0.427565
$238$	4032.00	1.09813
$239$	− 1200.00i	− 0.324776i	−0.986727	−	0.162388i	$-0.948080\pi$
$239$	− 1200.00i	− 0.324776i	0.986727	−	0.162388i	$-0.0519197\pi$
$240$	− 288.000i	− 0.0774597i
$241$	718.000i	0.191911i	0.995386	+	0.0959553i	$0.0305906\pi$
$241$	718.000i	0.191911i	−0.995386	+	0.0959553i	$0.969409\pi$
$242$	− 2374.00i	− 0.630605i
$243$	−243.000	−0.0641500
$244$	2152.00	0.564622
$245$	522.000i	0.136120i
$246$	−252.000	−0.0653127
$247$	0	0
$248$	704.000	0.180258
$249$	1476.00i	0.375653i
$250$	2568.00	0.649658
$251$	−6012.00	−1.51185	−0.755924	−	0.654659i	$-0.772812\pi$
$251$	−6012.00	−1.51185	−0.755924	+	0.654659i	$0.772812\pi$
$252$	− 576.000i	− 0.143986i
$253$	2016.00i	0.500968i
$254$	− 5072.00i	− 1.25294i
$255$	− 2268.00i	− 0.556971i
$256$	256.000	0.0625000
$257$	2046.00	0.496599	0.248300	−	0.968683i	$-0.420128\pi$
$257$	2046.00	0.496599	0.248300	+	0.968683i	$0.420128\pi$
$258$	312.000i	0.0752879i
$259$	4064.00	0.974999
$260$	0	0
$261$	270.000	0.0640329
$262$	− 4584.00i	− 1.08092i
$263$	−6072.00	−1.42363	−0.711817	−	0.702365i	$-0.752127\pi$
$263$	−6072.00	−1.42363	−0.711817	+	0.702365i	$0.752127\pi$
$264$	−288.000	−0.0671408
$265$	1188.00i	0.275390i
$266$	640.000i	0.147522i
$267$	2430.00i	0.556980i
$268$	− 3536.00i	− 0.805954i
$269$	−6930.00	−1.57074	−0.785371	−	0.619025i	$-0.787528\pi$
$269$	−6930.00	−1.57074	−0.785371	+	0.619025i	$0.787528\pi$
$270$	−324.000	−0.0730297
$271$	− 1352.00i	− 0.303056i	−0.988453	−	0.151528i	$-0.951581\pi$
$271$	− 1352.00i	− 0.303056i	0.988453	−	0.151528i	$-0.0484194\pi$
$272$	2016.00	0.449404
$273$	0	0
$274$	1452.00	0.320141
$275$	− 1068.00i	− 0.234192i
$276$	−2016.00	−0.439670
$277$	1186.00	0.257256	0.128628	−	0.991693i	$-0.458943\pi$
$277$	1186.00	0.257256	0.128628	+	0.991693i	$0.458943\pi$
$278$	− 760.000i	− 0.163963i
$279$	− 792.000i	− 0.169949i
$280$	− 768.000i	− 0.163917i
$281$	− 2442.00i	− 0.518425i	−0.965820	−	0.259213i	$-0.916537\pi$
$281$	− 2442.00i	− 0.518425i	0.965820	−	0.259213i	$-0.0834630\pi$
$282$	−576.000	−0.121632
$283$	−2828.00	−0.594018	−0.297009	−	0.954875i	$-0.595989\pi$
$283$	−2828.00	−0.594018	−0.297009	+	0.954875i	$0.595989\pi$
$284$	− 3168.00i	− 0.661923i
$285$	360.000	0.0748230
$286$	0	0
$287$	−672.000	−0.138212
$288$	− 288.000i	− 0.0589256i
$289$	10963.0	2.23143
$290$	360.000	0.0728963
$291$	− 3462.00i	− 0.697409i
$292$	872.000i	0.174760i
$293$	− 4758.00i	− 0.948687i	−0.880340	−	0.474344i	$-0.842685\pi$
$293$	− 4758.00i	− 0.948687i	0.880340	−	0.474344i	$-0.157315\pi$
$294$	522.000i	0.103550i
$295$	−3960.00	−0.781560
$296$	2032.00	0.399012
$297$	324.000i	0.0633010i
$298$	3180.00	0.618163
$299$	0	0
$300$	1068.00	0.205537
$301$	832.000i	0.159321i
$302$	−4864.00	−0.926794
$303$	−1854.00	−0.351517
$304$	320.000i	0.0603726i
$305$	− 3228.00i	− 0.606016i
$306$	− 2268.00i	− 0.423702i
$307$	8476.00i	1.57574i	0.615844	+	0.787868i	$0.288815\pi$
$307$	8476.00i	1.57574i	−0.615844	+	0.787868i	$0.711185\pi$
$308$	−768.000	−0.142081
$309$	384.000	0.0706958
$310$	− 1056.00i	− 0.193473i
$311$	−4632.00	−0.844555	−0.422278	−	0.906467i	$-0.638769\pi$
$311$	−4632.00	−0.844555	−0.422278	+	0.906467i	$0.638769\pi$
$312$	0	0
$313$	−4822.00	−0.870785	−0.435392	−	0.900241i	$-0.643390\pi$
$313$	−4822.00	−0.870785	−0.435392	+	0.900241i	$0.643390\pi$
$314$	− 1228.00i	− 0.220701i
$315$	−864.000	−0.154542
$316$	2080.00	0.370282
$317$	− 3426.00i	− 0.607014i	−0.952829	−	0.303507i	$-0.901842\pi$
$317$	− 3426.00i	− 0.607014i	0.952829	−	0.303507i	$-0.0981575\pi$
$318$	1188.00i	0.209496i
$319$	− 360.000i	− 0.0631854i
$320$	− 384.000i	− 0.0670820i
$321$	4428.00	0.769928
$322$	−5376.00	−0.930412
$323$	2520.00i	0.434107i
$324$	−324.000	−0.0555556
$325$	0	0
$326$	3704.00	0.629281
$327$	− 3570.00i	− 0.603735i
$328$	−336.000	−0.0565625
$329$	−1536.00	−0.257393
$330$	432.000i	0.0720631i
$331$	− 2788.00i	− 0.462968i	−0.972839	−	0.231484i	$-0.925642\pi$
$331$	− 2788.00i	− 0.462968i	0.972839	−	0.231484i	$-0.0743581\pi$
$332$	1968.00i	0.325325i
$333$	− 2286.00i	− 0.376192i
$334$	4272.00	0.699861
$335$	−5304.00	−0.865040
$336$	− 768.000i	− 0.124696i
$337$	−434.000	−0.0701528	−0.0350764	−	0.999385i	$-0.511167\pi$
$337$	−434.000	−0.0701528	−0.0350764	+	0.999385i	$0.511167\pi$
$338$	0	0
$339$	1386.00	0.222057
$340$	− 3024.00i	− 0.482351i
$341$	−1056.00	−0.167700
$342$	360.000	0.0569198
$343$	6880.00i	1.08305i
$344$	416.000i	0.0652012i
$345$	3024.00i	0.471903i
$346$	3516.00i	0.546304i
$347$	6684.00	1.03405	0.517026	−	0.855970i	$-0.327039\pi$
$347$	6684.00	1.03405	0.517026	+	0.855970i	$0.327039\pi$
$348$	360.000	0.0554541
$349$	− 2630.00i	− 0.403383i	−0.979449	−	0.201692i	$-0.935356\pi$
$349$	− 2630.00i	− 0.403383i	0.979449	−	0.201692i	$-0.0646438\pi$
$350$	2848.00	0.434949
$351$	0	0
$352$	−384.000	−0.0581456
$353$	− 7422.00i	− 1.11907i	−0.828805	−	0.559537i	$-0.810979\pi$
$353$	− 7422.00i	− 1.11907i	0.828805	−	0.559537i	$-0.189021\pi$
$354$	−3960.00	−0.594553
$355$	−4752.00	−0.710451
$356$	3240.00i	0.482359i
$357$	− 6048.00i	− 0.896622i
$358$	− 1080.00i	− 0.159441i
$359$	10440.0i	1.53482i	0.641154	+	0.767412i	$0.278456\pi$
$359$	10440.0i	1.53482i	−0.641154	+	0.767412i	$0.721544\pi$
$360$	−432.000	−0.0632456
$361$	6459.00	0.941682
$362$	3964.00i	0.575534i
$363$	−3561.00	−0.514887
$364$	0	0
$365$	1308.00	0.187572
$366$	− 3228.00i	− 0.461012i
$367$	10424.0	1.48264	0.741319	−	0.671153i	$-0.234200\pi$
$367$	10424.0	1.48264	0.741319	+	0.671153i	$0.234200\pi$
$368$	−2688.00	−0.380765
$369$	378.000i	0.0533276i
$370$	− 3048.00i	− 0.428265i
$371$	3168.00i	0.443327i
$372$	− 1056.00i	− 0.147180i
$373$	3278.00	0.455036	0.227518	−	0.973774i	$-0.426939\pi$
$373$	3278.00	0.455036	0.227518	+	0.973774i	$0.426939\pi$
$374$	−3024.00	−0.418094
$375$	− 3852.00i	− 0.530444i
$376$	−768.000	−0.105337
$377$	0	0
$378$	−864.000	−0.117564
$379$	6140.00i	0.832165i	0.909327	+	0.416083i	$0.136597\pi$
$379$	6140.00i	0.832165i	−0.909327	+	0.416083i	$0.863403\pi$
$380$	480.000	0.0647986
$381$	−7608.00	−1.02302
$382$	5376.00i	0.720053i
$383$	− 3072.00i	− 0.409848i	−0.978778	−	0.204924i	$-0.934305\pi$
$383$	− 3072.00i	− 0.409848i	0.978778	−	0.204924i	$-0.0656948\pi$
$384$	− 384.000i	− 0.0510310i
$385$	1152.00i	0.152497i
$386$	4604.00	0.607092
$387$	468.000	0.0614723
$388$	− 4616.00i	− 0.603974i
$389$	−6150.00	−0.801587	−0.400794	−	0.916168i	$-0.631266\pi$
$389$	−6150.00	−0.801587	−0.400794	+	0.916168i	$0.631266\pi$
$390$	0	0
$391$	−21168.0	−2.73788
$392$	696.000i	0.0896768i
$393$	−6876.00	−0.882566
$394$	8748.00	1.11857
$395$	− 3120.00i	− 0.397428i
$396$	432.000i	0.0548202i
$397$	106.000i	0.0134005i	0.999978	+	0.00670024i	$0.00213277\pi$
$397$	106.000i	0.0134005i	−0.999978	+	0.00670024i	$0.997867\pi$
$398$	− 3200.00i	− 0.403019i
$399$	960.000	0.120451
$400$	1424.00	0.178000
$401$	1758.00i	0.218929i	0.993991	+	0.109464i	$0.0349135\pi$
$401$	1758.00i	0.218929i	−0.993991	+	0.109464i	$0.965086\pi$
$402$	−5304.00	−0.658058
$403$	0	0
$404$	−2472.00	−0.304422
$405$	486.000i	0.0596285i
$406$	960.000	0.117350
$407$	−3048.00	−0.371213
$408$	− 3024.00i	− 0.366937i
$409$	− 3670.00i	− 0.443691i	−0.975082	−	0.221846i	$-0.928792\pi$
$409$	− 3670.00i	− 0.443691i	0.975082	−	0.221846i	$-0.0712081\pi$
$410$	504.000i	0.0607092i
$411$	− 2178.00i	− 0.261394i
$412$	512.000	0.0612243
$413$	−10560.0	−1.25817
$414$	3024.00i	0.358989i
$415$	2952.00	0.349176
$416$	0	0
$417$	−1140.00	−0.133875
$418$	− 480.000i	− 0.0561664i
$419$	−9660.00	−1.12631	−0.563153	−	0.826353i	$-0.690412\pi$
$419$	−9660.00	−1.12631	−0.563153	+	0.826353i	$0.690412\pi$
$420$	−1152.00	−0.133838
$421$	8462.00i	0.979602i	0.871834	+	0.489801i	$0.162931\pi$
$421$	8462.00i	0.979602i	−0.871834	+	0.489801i	$0.837069\pi$
$422$	− 6664.00i	− 0.768717i
$423$	864.000i	0.0993123i
$424$	1584.00i	0.181429i
$425$	11214.0	1.27990
$426$	−4752.00	−0.540458
$427$	− 8608.00i	− 0.975575i
$428$	5904.00	0.666777
$429$	0	0
$430$	624.000	0.0699813
$431$	9792.00i	1.09435i	0.837019	+	0.547174i	$0.184296\pi$
$431$	9792.00i	1.09435i	−0.837019	+	0.547174i	$0.815704\pi$
$432$	−432.000	−0.0481125
$433$	7342.00	0.814859	0.407430	−	0.913237i	$-0.366425\pi$
$433$	7342.00	0.814859	0.407430	+	0.913237i	$0.366425\pi$
$434$	− 2816.00i	− 0.311457i
$435$	− 540.000i	− 0.0595196i
$436$	− 4760.00i	− 0.522850i
$437$	− 3360.00i	− 0.367805i
$438$	1308.00	0.142691
$439$	−10640.0	−1.15676	−0.578382	−	0.815766i	$-0.696316\pi$
$439$	−10640.0	−1.15676	−0.578382	+	0.815766i	$0.696316\pi$
$440$	576.000i	0.0624085i
$441$	783.000	0.0845481
$442$	0	0
$443$	−17412.0	−1.86742	−0.933712	−	0.358024i	$-0.883451\pi$
$443$	−17412.0	−1.86742	−0.933712	+	0.358024i	$0.883451\pi$
$444$	− 3048.00i	− 0.325792i
$445$	4860.00	0.517722
$446$	5296.00	0.562271
$447$	− 4770.00i	− 0.504728i
$448$	− 1024.00i	− 0.107990i
$449$	1710.00i	0.179732i	0.995954	+	0.0898662i	$0.0286440\pi$
$449$	1710.00i	0.179732i	−0.995954	+	0.0898662i	$0.971356\pi$
$450$	− 1602.00i	− 0.167820i
$451$	504.000	0.0526218
$452$	1848.00	0.192307
$453$	7296.00i	0.756724i
$454$	4488.00	0.463948
$455$	0	0
$456$	480.000	0.0492940
$457$	− 646.000i	− 0.0661239i	−0.999453	−	0.0330619i	$-0.989474\pi$
$457$	− 646.000i	− 0.0661239i	0.999453	−	0.0330619i	$-0.0105259\pi$
$458$	11300.0	1.15287
$459$	−3402.00	−0.345952
$460$	4032.00i	0.408680i
$461$	− 6018.00i	− 0.607996i	−0.952673	−	0.303998i	$-0.901678\pi$
$461$	− 6018.00i	− 0.607996i	0.952673	−	0.303998i	$-0.0983216\pi$
$462$	1152.00i	0.116008i
$463$	6712.00i	0.673722i	0.941554	+	0.336861i	$0.109365\pi$
$463$	6712.00i	0.673722i	−0.941554	+	0.336861i	$0.890635\pi$
$464$	480.000	0.0480247
$465$	−1584.00	−0.157970
$466$	9396.00i	0.934037i
$467$	−5364.00	−0.531512	−0.265756	−	0.964040i	$-0.585622\pi$
$467$	−5364.00	−0.531512	−0.265756	+	0.964040i	$0.585622\pi$
$468$	0	0
$469$	−14144.0	−1.39256
$470$	1152.00i	0.113059i
$471$	−1842.00	−0.180201
$472$	−5280.00	−0.514898
$473$	− 624.000i	− 0.0606587i
$474$	− 3120.00i	− 0.302334i
$475$	1780.00i	0.171941i
$476$	− 8064.00i	− 0.776498i
$477$	1782.00	0.171053
$478$	−2400.00	−0.229652
$479$	− 9840.00i	− 0.938624i	−0.883032	−	0.469312i	$-0.844502\pi$
$479$	− 9840.00i	− 0.938624i	0.883032	−	0.469312i	$-0.155498\pi$
$480$	−576.000	−0.0547723
$481$	0	0
$482$	1436.00	0.135701
$483$	8064.00i	0.759678i
$484$	−4748.00	−0.445905
$485$	−6924.00	−0.648253
$486$	486.000i	0.0453609i
$487$	1424.00i	0.132500i	0.997803	+	0.0662501i	$0.0211035\pi$
$487$	1424.00i	0.132500i	−0.997803	+	0.0662501i	$0.978896\pi$
$488$	− 4304.00i	− 0.399248i
$489$	− 5556.00i	− 0.513806i
$490$	1044.00	0.0962513
$491$	4548.00	0.418021	0.209011	−	0.977913i	$-0.432976\pi$
$491$	4548.00	0.418021	0.209011	+	0.977913i	$0.432976\pi$
$492$	504.000i	0.0461831i
$493$	3780.00	0.345320
$494$	0	0
$495$	648.000	0.0588393
$496$	− 1408.00i	− 0.127462i
$497$	−12672.0	−1.14370
$498$	2952.00	0.265627
$499$	6500.00i	0.583126i	0.956552	+	0.291563i	$0.0941753\pi$
$499$	6500.00i	0.583126i	−0.956552	+	0.291563i	$0.905825\pi$
$500$	− 5136.00i	− 0.459378i
$501$	− 6408.00i	− 0.571434i
$502$	12024.0i	1.06904i
$503$	12168.0	1.07862	0.539308	−	0.842108i	$-0.318686\pi$
$503$	12168.0	1.07862	0.539308	+	0.842108i	$0.318686\pi$
$504$	−1152.00	−0.101814
$505$	3708.00i	0.326740i
$506$	4032.00	0.354238
$507$	0	0
$508$	−10144.0	−0.885959
$509$	− 21090.0i	− 1.83654i	−0.395957	−	0.918269i	$-0.629587\pi$
$509$	− 21090.0i	− 1.83654i	0.395957	−	0.918269i	$-0.370413\pi$
$510$	−4536.00	−0.393838
$511$	3488.00	0.301957
$512$	− 512.000i	− 0.0441942i
$513$	− 540.000i	− 0.0464748i
$514$	− 4092.00i	− 0.351149i
$515$	− 768.000i	− 0.0657129i
$516$	624.000	0.0532366
$517$	1152.00	0.0979979
$518$	− 8128.00i	− 0.689428i
$519$	5274.00	0.446056
$520$	0	0
$521$	−5238.00	−0.440462	−0.220231	−	0.975448i	$-0.570681\pi$
$521$	−5238.00	−0.440462	−0.220231	+	0.975448i	$0.570681\pi$
$522$	− 540.000i	− 0.0452781i
$523$	8588.00	0.718025	0.359012	−	0.933333i	$-0.383114\pi$
$523$	8588.00	0.718025	0.359012	+	0.933333i	$0.383114\pi$
$524$	−9168.00	−0.764324
$525$	− 4272.00i	− 0.355134i
$526$	12144.0i	1.00666i
$527$	− 11088.0i	− 0.916510i
$528$	576.000i	0.0474757i
$529$	16057.0	1.31972
$530$	2376.00	0.194730
$531$	5940.00i	0.485450i
$532$	1280.00	0.104314
$533$	0	0
$534$	4860.00	0.393844
$535$	− 8856.00i	− 0.715660i
$536$	−7072.00	−0.569895
$537$	−1620.00	−0.130183
$538$	13860.0i	1.11068i
$539$	− 1044.00i	− 0.0834291i
$540$	648.000i	0.0516398i
$541$	− 3062.00i	− 0.243338i	−0.992571	−	0.121669i	$-0.961175\pi$
$541$	− 3062.00i	− 0.243338i	0.992571	−	0.121669i	$-0.0388246\pi$
$542$	−2704.00	−0.214293
$543$	5946.00	0.469921
$544$	− 4032.00i	− 0.317777i
$545$	−7140.00	−0.561182
$546$	0	0
$547$	−8476.00	−0.662537	−0.331268	−	0.943537i	$-0.607477\pi$
$547$	−8476.00	−0.662537	−0.331268	+	0.943537i	$0.607477\pi$
$548$	− 2904.00i	− 0.226374i
$549$	−4842.00	−0.376414
$550$	−2136.00	−0.165599
$551$	600.000i	0.0463899i
$552$	4032.00i	0.310894i
$553$	− 8320.00i	− 0.639787i
$554$	− 2372.00i	− 0.181907i
$555$	−4572.00	−0.349677
$556$	−1520.00	−0.115939
$557$	12546.0i	0.954383i	0.878799	+	0.477191i	$0.158345\pi$
$557$	12546.0i	0.954383i	−0.878799	+	0.477191i	$0.841655\pi$
$558$	−1584.00	−0.120172
$559$	0	0
$560$	−1536.00	−0.115907
$561$	4536.00i	0.341373i
$562$	−4884.00	−0.366582
$563$	12.0000	0.000898294 0	0.000449147	−	1.00000i	$-0.499857\pi$
$563$	12.0000	0.000898294 0	0.000449147		1.00000i	$0.499857\pi$
$564$	1152.00i	0.0860070i
$565$	− 2772.00i	− 0.206405i
$566$	5656.00i	0.420034i
$567$	1296.00i	0.0959910i
$568$	−6336.00	−0.468050
$569$	−19290.0	−1.42123	−0.710614	−	0.703582i	$-0.751583\pi$
$569$	−19290.0	−1.42123	−0.710614	+	0.703582i	$0.751583\pi$
$570$	− 720.000i	− 0.0529079i
$571$	12148.0	0.890329	0.445165	−	0.895449i	$-0.353145\pi$
$571$	12148.0	0.890329	0.445165	+	0.895449i	$0.353145\pi$
$572$	0	0
$573$	8064.00	0.587920
$574$	1344.00i	0.0977308i
$575$	−14952.0	−1.08442
$576$	−576.000	−0.0416667
$577$	− 10366.0i	− 0.747907i	−0.927447	−	0.373953i	$-0.878002\pi$
$577$	− 10366.0i	− 0.747907i	0.927447	−	0.373953i	$-0.121998\pi$
$578$	− 21926.0i	− 1.57786i
$579$	− 6906.00i	− 0.495688i
$580$	− 720.000i	− 0.0515455i
$581$	7872.00	0.562109
$582$	−6924.00	−0.493143
$583$	− 2376.00i	− 0.168789i
$584$	1744.00	0.123574
$585$	0	0
$586$	−9516.00	−0.670823
$587$	7644.00i	0.537482i	0.963213	+	0.268741i	$0.0866075\pi$
$587$	7644.00i	0.537482i	−0.963213	+	0.268741i	$0.913393\pi$
$588$	1044.00	0.0732208
$589$	1760.00	0.123123
$590$	7920.00i	0.552646i
$591$	− 13122.0i	− 0.913311i
$592$	− 4064.00i	− 0.282144i
$593$	− 8658.00i	− 0.599564i	−0.954008	−	0.299782i	$-0.903086\pi$
$593$	− 8658.00i	− 0.599564i	0.954008	−	0.299782i	$-0.0969139\pi$
$594$	648.000	0.0447605
$595$	−12096.0	−0.833425
$596$	− 6360.00i	− 0.437107i
$597$	−4800.00	−0.329064
$598$	0	0
$599$	25800.0	1.75987	0.879933	−	0.475098i	$-0.157587\pi$
$599$	25800.0	1.75987	0.879933	+	0.475098i	$0.157587\pi$
$600$	− 2136.00i	− 0.145336i
$601$	16202.0	1.09966	0.549828	−	0.835278i	$-0.314693\pi$
$601$	16202.0	1.09966	0.549828	+	0.835278i	$0.314693\pi$
$602$	1664.00	0.112657
$603$	7956.00i	0.537302i
$604$	9728.00i	0.655342i
$605$	7122.00i	0.478596i
$606$	3708.00i	0.248560i
$607$	−24136.0	−1.61392	−0.806960	−	0.590605i	$-0.798889\pi$
$607$	−24136.0	−1.61392	−0.806960	+	0.590605i	$0.798889\pi$
$608$	640.000	0.0426898
$609$	− 1440.00i	− 0.0958157i
$610$	−6456.00	−0.428518
$611$	0	0
$612$	−4536.00	−0.299603
$613$	− 4642.00i	− 0.305854i	−0.988237	−	0.152927i	$-0.951130\pi$
$613$	− 4642.00i	− 0.305854i	0.988237	−	0.152927i	$-0.0488700\pi$
$614$	16952.0	1.11421
$615$	756.000	0.0495689
$616$	1536.00i	0.100466i
$617$	− 6726.00i	− 0.438863i	−0.975628	−	0.219432i	$-0.929580\pi$
$617$	− 6726.00i	− 0.438863i	0.975628	−	0.219432i	$-0.0704203\pi$
$618$	− 768.000i	− 0.0499895i
$619$	21220.0i	1.37787i	0.724821	+	0.688937i	$0.241922\pi$
$619$	21220.0i	1.37787i	−0.724821	+	0.688937i	$0.758078\pi$
$620$	−2112.00	−0.136806
$621$	4536.00	0.293113
$622$	9264.00i	0.597191i
$623$	12960.0	0.833437
$624$	0	0
$625$	3421.00	0.218944
$626$	9644.00i	0.615738i
$627$	−720.000	−0.0458597
$628$	−2456.00	−0.156059
$629$	− 32004.0i	− 2.02875i
$630$	1728.00i	0.109278i
$631$	− 29792.0i	− 1.87956i	−0.341783	−	0.939779i	$-0.611031\pi$
$631$	− 29792.0i	− 1.87956i	0.341783	−	0.939779i	$-0.388969\pi$
$632$	− 4160.00i	− 0.261829i
$633$	−9996.00	−0.627655
$634$	−6852.00	−0.429223
$635$	15216.0i	0.950911i
$636$	2376.00	0.148136
$637$	0	0
$638$	−720.000	−0.0446788
$639$	7128.00i	0.441282i
$640$	−768.000	−0.0474342
$641$	10158.0	0.625923	0.312962	−	0.949766i	$-0.398679\pi$
$641$	10158.0	0.625923	0.312962	+	0.949766i	$0.398679\pi$
$642$	− 8856.00i	− 0.544421i
$643$	29828.0i	1.82940i	0.404138	+	0.914698i	$0.367571\pi$
$643$	29828.0i	1.82940i	−0.404138	+	0.914698i	$0.632429\pi$
$644$	10752.0i	0.657901i
$645$	− 936.000i	− 0.0571395i
$646$	5040.00	0.306960
$647$	−1944.00	−0.118124	−0.0590622	−	0.998254i	$-0.518811\pi$
$647$	−1944.00	−0.118124	−0.0590622	+	0.998254i	$0.518811\pi$
$648$	648.000i	0.0392837i
$649$	7920.00	0.479025
$650$	0	0
$651$	−4224.00	−0.254304
$652$	− 7408.00i	− 0.444969i
$653$	26718.0	1.60116	0.800579	−	0.599227i	$-0.204525\pi$
$653$	26718.0	1.60116	0.800579	+	0.599227i	$0.204525\pi$
$654$	−7140.00	−0.426905
$655$	13752.0i	0.820359i
$656$	672.000i	0.0399957i
$657$	− 1962.00i	− 0.116507i
$658$	3072.00i	0.182005i
$659$	4260.00	0.251815	0.125907	−	0.992042i	$-0.459816\pi$
$659$	4260.00	0.251815	0.125907	+	0.992042i	$0.459816\pi$
$660$	864.000	0.0509563
$661$	− 22862.0i	− 1.34528i	−0.739971	−	0.672639i	$-0.765161\pi$
$661$	− 22862.0i	− 1.34528i	0.739971	−	0.672639i	$-0.234839\pi$
$662$	−5576.00	−0.327368
$663$	0	0
$664$	3936.00	0.230040
$665$	− 1920.00i	− 0.111962i
$666$	−4572.00	−0.266008
$667$	−5040.00	−0.292578
$668$	− 8544.00i	− 0.494876i
$669$	− 7944.00i	− 0.459092i
$670$	10608.0i	0.611676i
$671$	6456.00i	0.371432i
$672$	−1536.00	−0.0881733
$673$	32542.0	1.86390	0.931948	−	0.362592i	$-0.118108\pi$
$673$	32542.0	1.86390	0.931948	+	0.362592i	$0.118108\pi$
$674$	868.000i	0.0496055i
$675$	−2403.00	−0.137024
$676$	0	0
$677$	14214.0	0.806925	0.403463	−	0.914996i	$-0.367807\pi$
$677$	14214.0	0.806925	0.403463	+	0.914996i	$0.367807\pi$
$678$	− 2772.00i	− 0.157018i
$679$	−18464.0	−1.04357
$680$	−6048.00	−0.341074
$681$	− 6732.00i	− 0.378812i
$682$	2112.00i	0.118582i
$683$	7092.00i	0.397317i	0.980069	+	0.198659i	$0.0636585\pi$
$683$	7092.00i	0.397317i	−0.980069	+	0.198659i	$0.936341\pi$
$684$	− 720.000i	− 0.0402484i
$685$	−4356.00	−0.242970
$686$	13760.0	0.765830
$687$	− 16950.0i	− 0.941314i
$688$	832.000	0.0461042
$689$	0	0
$690$	6048.00	0.333686
$691$	− 13228.0i	− 0.728244i	−0.931351	−	0.364122i	$-0.881369\pi$
$691$	− 13228.0i	− 0.728244i	0.931351	−	0.364122i	$-0.118631\pi$
$692$	7032.00	0.386296
$693$	1728.00	0.0947205
$694$	− 13368.0i	− 0.731185i
$695$	2280.00i	0.124439i
$696$	− 720.000i	− 0.0392120i
$697$	5292.00i	0.287588i
$698$	−5260.00	−0.285235
$699$	14094.0	0.762638
$700$	− 5696.00i	− 0.307555i
$701$	−28062.0	−1.51196	−0.755982	−	0.654592i	$-0.772840\pi$
$701$	−28062.0	−1.51196	−0.755982	+	0.654592i	$0.772840\pi$
$702$	0	0
$703$	5080.00	0.272540
$704$	768.000i	0.0411152i
$705$	1728.00	0.0923124
$706$	−14844.0	−0.791305
$707$	9888.00i	0.525992i
$708$	7920.00i	0.420412i
$709$	27250.0i	1.44343i	0.692188	+	0.721717i	$0.256647\pi$
$709$	27250.0i	1.44343i	−0.692188	+	0.721717i	$0.743353\pi$
$710$	9504.00i	0.502364i
$711$	−4680.00	−0.246855
$712$	6480.00	0.341079
$713$	14784.0i	0.776529i
$714$	−12096.0	−0.634008
$715$	0	0
$716$	−2160.00	−0.112742
$717$	3600.00i	0.187510i
$718$	20880.0	1.08529
$719$	14400.0	0.746912	0.373456	−	0.927648i	$-0.378173\pi$
$719$	14400.0	0.746912	0.373456	+	0.927648i	$0.378173\pi$
$720$	864.000i	0.0447214i
$721$	− 2048.00i	− 0.105786i
$722$	− 12918.0i	− 0.665870i
$723$	− 2154.00i	− 0.110800i
$724$	7928.00	0.406964
$725$	2670.00	0.136774
$726$	7122.00i	0.364080i
$727$	−17984.0	−0.917455	−0.458727	−	0.888577i	$-0.651695\pi$
$727$	−17984.0	−0.917455	−0.458727	+	0.888577i	$0.651695\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	− 2616.00i	− 0.132634i
$731$	6552.00	0.331511
$732$	−6456.00	−0.325984
$733$	16598.0i	0.836373i	0.908361	+	0.418186i	$0.137334\pi$
$733$	16598.0i	0.836373i	−0.908361	+	0.418186i	$0.862666\pi$
$734$	− 20848.0i	− 1.04838i
$735$	− 1566.00i	− 0.0785888i
$736$	5376.00i	0.269242i
$737$	10608.0	0.530191
$738$	756.000	0.0377083
$739$	− 1460.00i	− 0.0726752i	−0.999340	−	0.0363376i	$-0.988431\pi$
$739$	− 1460.00i	− 0.0726752i	0.999340	−	0.0363376i	$-0.0115692\pi$
$740$	−6096.00	−0.302829
$741$	0	0
$742$	6336.00	0.313480
$743$	− 30072.0i	− 1.48484i	−0.669936	−	0.742419i	$-0.733678\pi$
$743$	− 30072.0i	− 1.48484i	0.669936	−	0.742419i	$-0.266322\pi$
$744$	−2112.00	−0.104072
$745$	−9540.00	−0.469152
$746$	− 6556.00i	− 0.321759i
$747$	− 4428.00i	− 0.216884i
$748$	6048.00i	0.295637i
$749$	− 23616.0i	− 1.15208i
$750$	−7704.00	−0.375080
$751$	18088.0	0.878882	0.439441	−	0.898271i	$-0.355177\pi$
$751$	18088.0	0.878882	0.439441	+	0.898271i	$0.355177\pi$
$752$	1536.00i	0.0744843i
$753$	18036.0	0.872866
$754$	0	0
$755$	14592.0	0.703387
$756$	1728.00i	0.0831306i
$757$	24734.0	1.18755	0.593773	−	0.804633i	$-0.297638\pi$
$757$	24734.0	1.18755	0.593773	+	0.804633i	$0.297638\pi$
$758$	12280.0	0.588430
$759$	− 6048.00i	− 0.289234i
$760$	− 960.000i	− 0.0458196i
$761$	22278.0i	1.06120i	0.847621	+	0.530602i	$0.178034\pi$
$761$	22278.0i	1.06120i	−0.847621	+	0.530602i	$0.821966\pi$
$762$	15216.0i	0.723383i
$763$	−19040.0	−0.903400
$764$	10752.0	0.509154
$765$	6804.00i	0.321568i
$766$	−6144.00	−0.289806
$767$	0	0
$768$	−768.000	−0.0360844
$769$	16130.0i	0.756388i	0.925726	+	0.378194i	$0.123455\pi$
$769$	16130.0i	0.756388i	−0.925726	+	0.378194i	$0.876545\pi$
$770$	2304.00	0.107832
$771$	−6138.00	−0.286712
$772$	− 9208.00i	− 0.429279i
$773$	29718.0i	1.38277i	0.722486	+	0.691386i	$0.242999\pi$
$773$	29718.0i	1.38277i	−0.722486	+	0.691386i	$0.757001\pi$
$774$	− 936.000i	− 0.0434675i
$775$	− 7832.00i	− 0.363011i
$776$	−9232.00	−0.427074
$777$	−12192.0	−0.562916
$778$	12300.0i	0.566808i
$779$	−840.000	−0.0386343
$780$	0	0
$781$	9504.00	0.435442
$782$	42336.0i	1.93597i
$783$	−810.000	−0.0369694
$784$	1392.00	0.0634111
$785$	3684.00i	0.167500i
$786$	13752.0i	0.624068i
$787$	− 9524.00i	− 0.431377i	−0.976462	−	0.215689i	$-0.930800\pi$
$787$	− 9524.00i	− 0.431377i	0.976462	−	0.215689i	$-0.0691996\pi$
$788$	− 17496.0i	− 0.790951i
$789$	18216.0	0.821935
$790$	−6240.00	−0.281024
$791$	− 7392.00i	− 0.332275i
$792$	864.000	0.0387638
$793$	0	0
$794$	212.000	0.00947556
$795$	− 3564.00i	− 0.158996i
$796$	−6400.00	−0.284977
$797$	33906.0	1.50692	0.753458	−	0.657496i	$-0.228384\pi$
$797$	33906.0	1.50692	0.753458	+	0.657496i	$0.228384\pi$
$798$	− 1920.00i	− 0.0851720i
$799$	12096.0i	0.535577i
$800$	− 2848.00i	− 0.125865i
$801$	− 7290.00i	− 0.321572i
$802$	3516.00	0.154806
$803$	−2616.00	−0.114965
$804$	10608.0i	0.465318i
$805$	16128.0	0.706133
$806$	0	0
$807$	20790.0	0.906868
$808$	4944.00i	0.215259i
$809$	−630.000	−0.0273790	−0.0136895	−	0.999906i	$-0.504358\pi$
$809$	−630.000	−0.0273790	−0.0136895	+	0.999906i	$0.504358\pi$
$810$	972.000	0.0421637
$811$	− 20788.0i	− 0.900081i	−0.893008	−	0.450040i	$-0.851410\pi$
$811$	− 20788.0i	− 0.900081i	0.893008	−	0.450040i	$-0.148590\pi$
$812$	− 1920.00i	− 0.0829788i
$813$	4056.00i	0.174969i
$814$	6096.00i	0.262487i
$815$	−11112.0	−0.477591
$816$	−6048.00	−0.259464
$817$	1040.00i	0.0445349i
$818$	−7340.00	−0.313737
$819$	0	0
$820$	1008.00	0.0429279
$821$	− 43098.0i	− 1.83207i	−0.401097	−	0.916036i	$-0.631371\pi$
$821$	− 43098.0i	− 1.83207i	0.401097	−	0.916036i	$-0.368629\pi$
$822$	−4356.00	−0.184833
$823$	14272.0	0.604484	0.302242	−	0.953231i	$-0.402265\pi$
$823$	14272.0	0.604484	0.302242	+	0.953231i	$0.402265\pi$
$824$	− 1024.00i	− 0.0432921i
$825$	3204.00i	0.135211i
$826$	21120.0i	0.889660i
$827$	− 13644.0i	− 0.573698i	−0.957976	−	0.286849i	$-0.907392\pi$
$827$	− 13644.0i	− 0.573698i	0.957976	−	0.286849i	$-0.0926078\pi$
$828$	6048.00	0.253844
$829$	2410.00	0.100968	0.0504842	−	0.998725i	$-0.483924\pi$
$829$	2410.00	0.100968	0.0504842	+	0.998725i	$0.483924\pi$
$830$	− 5904.00i	− 0.246905i
$831$	−3558.00	−0.148527
$832$	0	0
$833$	10962.0	0.455955
$834$	2280.00i	0.0946642i
$835$	−12816.0	−0.531157
$836$	−960.000	−0.0397157
$837$	2376.00i	0.0981202i
$838$	19320.0i	0.796418i
$839$	− 23160.0i	− 0.953006i	−0.879173	−	0.476503i	$-0.841904\pi$
$839$	− 23160.0i	− 0.953006i	0.879173	−	0.476503i	$-0.158096\pi$
$840$	2304.00i	0.0946376i
$841$	−23489.0	−0.963098
$842$	16924.0	0.692684
$843$	7326.00i	0.299313i
$844$	−13328.0	−0.543565
$845$	0	0
$846$	1728.00	0.0702244
$847$	18992.0i	0.770452i
$848$	3168.00	0.128290
$849$	8484.00	0.342957
$850$	− 22428.0i	− 0.905028i
$851$	42672.0i	1.71889i
$852$	9504.00i	0.382162i
$853$	− 32078.0i	− 1.28761i	−0.765190	−	0.643804i	$-0.777355\pi$
$853$	− 32078.0i	− 1.28761i	0.765190	−	0.643804i	$-0.222645\pi$
$854$	−17216.0	−0.689835
$855$	−1080.00	−0.0431991
$856$	− 11808.0i	− 0.471483i
$857$	14406.0	0.574212	0.287106	−	0.957899i	$-0.407307\pi$
$857$	14406.0	0.574212	0.287106	+	0.957899i	$0.407307\pi$
$858$	0	0
$859$	30620.0	1.21623	0.608115	−	0.793849i	$-0.291926\pi$
$859$	30620.0	1.21623	0.608115	+	0.793849i	$0.291926\pi$
$860$	− 1248.00i	− 0.0494842i
$861$	2016.00	0.0797969
$862$	19584.0	0.773821
$863$	17568.0i	0.692957i	0.938058	+	0.346478i	$0.112623\pi$
$863$	17568.0i	0.692957i	−0.938058	+	0.346478i	$0.887377\pi$
$864$	864.000i	0.0340207i
$865$	− 10548.0i	− 0.414616i
$866$	− 14684.0i	− 0.576192i
$867$	−32889.0	−1.28831
$868$	−5632.00	−0.220233
$869$	6240.00i	0.243587i
$870$	−1080.00	−0.0420867
$871$	0	0
$872$	−9520.00	−0.369711
$873$	10386.0i	0.402649i
$874$	−6720.00	−0.260077
$875$	−20544.0	−0.793730
$876$	− 2616.00i	− 0.100898i
$877$	− 21706.0i	− 0.835758i	−0.908503	−	0.417879i	$-0.862774\pi$
$877$	− 21706.0i	− 0.835758i	0.908503	−	0.417879i	$-0.137226\pi$
$878$	21280.0i	0.817956i
$879$	14274.0i	0.547725i
$880$	1152.00	0.0441294
$881$	14958.0	0.572018	0.286009	−	0.958227i	$-0.407671\pi$
$881$	14958.0	0.572018	0.286009	+	0.958227i	$0.407671\pi$
$882$	− 1566.00i	− 0.0597845i
$883$	32812.0	1.25052	0.625261	−	0.780415i	$-0.284992\pi$
$883$	32812.0	1.25052	0.625261	+	0.780415i	$0.284992\pi$
$884$	0	0
$885$	11880.0	0.451234
$886$	34824.0i	1.32047i
$887$	−38856.0	−1.47086	−0.735432	−	0.677598i	$-0.763021\pi$
$887$	−38856.0	−1.47086	−0.735432	+	0.677598i	$0.763021\pi$
$888$	−6096.00	−0.230370
$889$	40576.0i	1.53079i
$890$	− 9720.00i	− 0.366084i
$891$	− 972.000i	− 0.0365468i
$892$	− 10592.0i	− 0.397586i
$893$	−1920.00	−0.0719489
$894$	−9540.00	−0.356896
$895$	3240.00i	0.121007i
$896$	−2048.00	−0.0763604
$897$	0	0
$898$	3420.00	0.127090
$899$	− 2640.00i	− 0.0979410i
$900$	−3204.00	−0.118667
$901$	24948.0	0.922462
$902$	− 1008.00i	− 0.0372092i
$903$	− 2496.00i	− 0.0919841i
$904$	− 3696.00i	− 0.135981i
$905$	− 11892.0i	− 0.436799i
$906$	14592.0	0.535085
$907$	28276.0	1.03516	0.517579	−	0.855635i	$-0.326833\pi$
$907$	28276.0	1.03516	0.517579	+	0.855635i	$0.326833\pi$
$908$	− 8976.00i	− 0.328061i
$909$	5562.00	0.202948
$910$	0	0
$911$	8112.00	0.295019	0.147510	−	0.989061i	$-0.452874\pi$
$911$	8112.00	0.295019	0.147510	+	0.989061i	$0.452874\pi$
$912$	− 960.000i	− 0.0348561i
$913$	−5904.00	−0.214013
$914$	−1292.00	−0.0467566
$915$	9684.00i	0.349883i
$916$	− 22600.0i	− 0.815202i
$917$	36672.0i	1.32063i
$918$	6804.00i	0.244625i
$919$	−26080.0	−0.936126	−0.468063	−	0.883695i	$-0.655048\pi$
$919$	−26080.0	−0.936126	−0.468063	+	0.883695i	$0.655048\pi$
$920$	8064.00	0.288981
$921$	− 25428.0i	− 0.909751i
$922$	−12036.0	−0.429918
$923$	0	0
$924$	2304.00	0.0820303
$925$	− 22606.0i	− 0.803547i
$926$	13424.0	0.476393
$927$	−1152.00	−0.0408162
$928$	− 960.000i	− 0.0339586i
$929$	49170.0i	1.73651i	0.496120	+	0.868254i	$0.334757\pi$
$929$	49170.0i	1.73651i	−0.496120	+	0.868254i	$0.665243\pi$
$930$	3168.00i	0.111702i
$931$	1740.00i	0.0612526i
$932$	18792.0	0.660464
$933$	13896.0	0.487604
$934$	10728.0i	0.375836i
$935$	9072.00	0.317311
$936$	0	0
$937$	48314.0	1.68447	0.842236	−	0.539110i	$-0.181239\pi$
$937$	48314.0	1.68447	0.842236	+	0.539110i	$0.181239\pi$
$938$	28288.0i	0.984687i
$939$	14466.0	0.502748
$940$	2304.00	0.0799449
$941$	34782.0i	1.20495i	0.798137	+	0.602477i	$0.205819\pi$
$941$	34782.0i	1.20495i	−0.798137	+	0.602477i	$0.794181\pi$
$942$	3684.00i	0.127422i
$943$	− 7056.00i	− 0.243664i
$944$	10560.0i	0.364088i
$945$	2592.00	0.0892251
$946$	−1248.00	−0.0428922
$947$	25116.0i	0.861838i	0.902391	+	0.430919i	$0.141810\pi$
$947$	25116.0i	0.861838i	−0.902391	+	0.430919i	$0.858190\pi$
$948$	−6240.00	−0.213782
$949$	0	0
$950$	3560.00	0.121581
$951$	10278.0i	0.350460i
$952$	−16128.0	−0.549067
$953$	15462.0	0.525565	0.262782	−	0.964855i	$-0.415360\pi$
$953$	15462.0	0.525565	0.262782	+	0.964855i	$0.415360\pi$
$954$	− 3564.00i	− 0.120953i
$955$	− 16128.0i	− 0.546481i
$956$	4800.00i	0.162388i
$957$	1080.00i	0.0364801i
$958$	−19680.0	−0.663708
$959$	−11616.0	−0.391137
$960$	1152.00i	0.0387298i
$961$	22047.0	0.740056
$962$	0	0
$963$	−13284.0	−0.444518
$964$	− 2872.00i	− 0.0959553i
$965$	−13812.0	−0.460750
$966$	16128.0	0.537174
$967$	− 736.000i	− 0.0244759i	−0.999925	−	0.0122379i	$-0.996104\pi$
$967$	− 736.000i	− 0.0244759i	0.999925	−	0.0122379i	$-0.00389555\pi$
$968$	9496.00i	0.315303i
$969$	− 7560.00i	− 0.250632i
$970$	13848.0i	0.458384i
$971$	−29268.0	−0.967307	−0.483653	−	0.875260i	$-0.660690\pi$
$971$	−29268.0	−0.967307	−0.483653	+	0.875260i	$0.660690\pi$
$972$	972.000	0.0320750
$973$	6080.00i	0.200325i
$974$	2848.00	0.0936918
$975$	0	0
$976$	−8608.00	−0.282311
$977$	16674.0i	0.546007i	0.962013	+	0.273003i	$0.0880170\pi$
$977$	16674.0i	0.546007i	−0.962013	+	0.273003i	$0.911983\pi$
$978$	−11112.0	−0.363316
$979$	−9720.00	−0.317316
$980$	− 2088.00i	− 0.0680599i
$981$	10710.0i	0.348567i
$982$	− 9096.00i	− 0.295586i
$983$	31272.0i	1.01467i	0.861749	+	0.507336i	$0.169370\pi$
$983$	31272.0i	1.01467i	−0.861749	+	0.507336i	$0.830630\pi$
$984$	1008.00	0.0326564
$985$	−26244.0	−0.848937
$986$	− 7560.00i	− 0.244178i
$987$	4608.00	0.148606
$988$	0	0
$989$	−8736.00	−0.280878
$990$	− 1296.00i	− 0.0416056i
$991$	−15928.0	−0.510565	−0.255282	−	0.966867i	$-0.582168\pi$
$991$	−15928.0	−0.510565	−0.255282	+	0.966867i	$0.582168\pi$
$992$	−2816.00	−0.0901291
$993$	8364.00i	0.267295i
$994$	25344.0i	0.808715i
$995$	9600.00i	0.305870i
$996$	− 5904.00i	− 0.187827i
$997$	42014.0	1.33460	0.667300	−	0.744789i	$-0.267450\pi$
$997$	42014.0	1.33460	0.667300	+	0.744789i	$0.267450\pi$
$998$	13000.0	0.412332
$999$	6858.00i	0.217195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.4.b.d.337.1		2
13.5	odd	4		6.4.a.a.1.1	✓	1
13.8	odd	4		1014.4.a.g.1.1		1
13.12	even	2	inner	1014.4.b.d.337.2		2
39.5	even	4		18.4.a.a.1.1		1
52.31	even	4		48.4.a.c.1.1		1
65.18	even	4		150.4.c.d.49.2		2
65.44	odd	4		150.4.a.i.1.1		1
65.57	even	4		150.4.c.d.49.1		2
91.5	even	12		294.4.e.g.67.1		2
91.18	odd	12		294.4.e.h.79.1		2
91.31	even	12		294.4.e.g.79.1		2
91.44	odd	12		294.4.e.h.67.1		2
91.83	even	4		294.4.a.e.1.1		1
104.5	odd	4		192.4.a.i.1.1		1
104.83	even	4		192.4.a.c.1.1		1
117.5	even	12		162.4.c.c.55.1		2
117.31	odd	12		162.4.c.f.55.1		2
117.70	odd	12		162.4.c.f.109.1		2
117.83	even	12		162.4.c.c.109.1		2
143.109	even	4		726.4.a.f.1.1		1
156.83	odd	4		144.4.a.c.1.1		1
195.44	even	4		450.4.a.h.1.1		1
195.83	odd	4		450.4.c.e.199.1		2
195.122	odd	4		450.4.c.e.199.2		2
208.5	odd	4		768.4.d.n.385.2		2
208.83	even	4		768.4.d.c.385.2		2
208.109	odd	4		768.4.d.n.385.1		2
208.187	even	4		768.4.d.c.385.1		2
221.135	odd	4		1734.4.a.d.1.1		1
247.18	even	4		2166.4.a.i.1.1		1
260.83	odd	4		1200.4.f.j.49.2		2
260.187	odd	4		1200.4.f.j.49.1		2
260.239	even	4		1200.4.a.b.1.1		1
273.5	odd	12		882.4.g.f.361.1		2
273.44	even	12		882.4.g.i.361.1		2
273.83	odd	4		882.4.a.n.1.1		1
273.122	odd	12		882.4.g.f.667.1		2
273.200	even	12		882.4.g.i.667.1		2
312.5	even	4		576.4.a.q.1.1		1
312.83	odd	4		576.4.a.r.1.1		1
364.83	odd	4		2352.4.a.e.1.1		1
429.395	odd	4		2178.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.4.a.a.1.1	✓	1	13.5	odd	4
18.4.a.a.1.1		1	39.5	even	4
48.4.a.c.1.1		1	52.31	even	4
144.4.a.c.1.1		1	156.83	odd	4
150.4.a.i.1.1		1	65.44	odd	4
150.4.c.d.49.1		2	65.57	even	4
150.4.c.d.49.2		2	65.18	even	4
162.4.c.c.55.1		2	117.5	even	12
162.4.c.c.109.1		2	117.83	even	12
162.4.c.f.55.1		2	117.31	odd	12
162.4.c.f.109.1		2	117.70	odd	12
192.4.a.c.1.1		1	104.83	even	4
192.4.a.i.1.1		1	104.5	odd	4
294.4.a.e.1.1		1	91.83	even	4
294.4.e.g.67.1		2	91.5	even	12
294.4.e.g.79.1		2	91.31	even	12
294.4.e.h.67.1		2	91.44	odd	12
294.4.e.h.79.1		2	91.18	odd	12
450.4.a.h.1.1		1	195.44	even	4
450.4.c.e.199.1		2	195.83	odd	4
450.4.c.e.199.2		2	195.122	odd	4
576.4.a.q.1.1		1	312.5	even	4
576.4.a.r.1.1		1	312.83	odd	4
726.4.a.f.1.1		1	143.109	even	4
768.4.d.c.385.1		2	208.187	even	4
768.4.d.c.385.2		2	208.83	even	4
768.4.d.n.385.1		2	208.109	odd	4
768.4.d.n.385.2		2	208.5	odd	4
882.4.a.n.1.1		1	273.83	odd	4
882.4.g.f.361.1		2	273.5	odd	12
882.4.g.f.667.1		2	273.122	odd	12
882.4.g.i.361.1		2	273.44	even	12
882.4.g.i.667.1		2	273.200	even	12
1014.4.a.g.1.1		1	13.8	odd	4
1014.4.b.d.337.1		2	1.1	even	1	trivial
1014.4.b.d.337.2		2	13.12	even	2	inner
1200.4.a.b.1.1		1	260.239	even	4
1200.4.f.j.49.1		2	260.187	odd	4
1200.4.f.j.49.2		2	260.83	odd	4
1734.4.a.d.1.1		1	221.135	odd	4
2166.4.a.i.1.1		1	247.18	even	4
2178.4.a.e.1.1		1	429.395	odd	4
2352.4.a.e.1.1		1	364.83	odd	4

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1014.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -3.00000 q^{3} -4.00000 q^{4} +6.00000i q^{5} +6.00000i q^{6} +16.0000i q^{7} +8.00000i q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} -3.00000 q^{3} -4.00000 q^{4} +6.00000i q^{5} +6.00000i q^{6} +16.0000i q^{7} +8.00000i q^{8} +9.00000 q^{9} +12.0000 q^{10} -12.0000i q^{11} +12.0000 q^{12} +32.0000 q^{14} -18.0000i q^{15} +16.0000 q^{16} +126.000 q^{17} -18.0000i q^{18} +20.0000i q^{19} -24.0000i q^{20} -48.0000i q^{21} -24.0000 q^{22} -168.000 q^{23} -24.0000i q^{24} +89.0000 q^{25} -27.0000 q^{27} -64.0000i q^{28} +30.0000 q^{29} -36.0000 q^{30} -88.0000i q^{31} -32.0000i q^{32} +36.0000i q^{33} -252.000i q^{34} -96.0000 q^{35} -36.0000 q^{36} -254.000i q^{37} +40.0000 q^{38} -48.0000 q^{40} +42.0000i q^{41} -96.0000 q^{42} +52.0000 q^{43} +48.0000i q^{44} +54.0000i q^{45} +336.000i q^{46} +96.0000i q^{47} -48.0000 q^{48} +87.0000 q^{49} -178.000i q^{50} -378.000 q^{51} +198.000 q^{53} +54.0000i q^{54} +72.0000 q^{55} -128.000 q^{56} -60.0000i q^{57} -60.0000i q^{58} +660.000i q^{59} +72.0000i q^{60} -538.000 q^{61} -176.000 q^{62} +144.000i q^{63} -64.0000 q^{64} +72.0000 q^{66} +884.000i q^{67} -504.000 q^{68} +504.000 q^{69} +192.000i q^{70} +792.000i q^{71} +72.0000i q^{72} -218.000i q^{73} -508.000 q^{74} -267.000 q^{75} -80.0000i q^{76} +192.000 q^{77} -520.000 q^{79} +96.0000i q^{80} +81.0000 q^{81} +84.0000 q^{82} -492.000i q^{83} +192.000i q^{84} +756.000i q^{85} -104.000i q^{86} -90.0000 q^{87} +96.0000 q^{88} -810.000i q^{89} +108.000 q^{90} +672.000 q^{92} +264.000i q^{93} +192.000 q^{94} -120.000 q^{95} +96.0000i q^{96} +1154.00i q^{97} -174.000i q^{98} -108.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{3} - 8 q^{4} + 18 q^{9}+O(q^{10}) \) 2 * q - 6 * q^3 - 8 * q^4 + 18 * q^9	\( 2 q - 6 q^{3} - 8 q^{4} + 18 q^{9} + 24 q^{10} + 24 q^{12} + 64 q^{14} + 32 q^{16} + 252 q^{17} - 48 q^{22} - 336 q^{23} + 178 q^{25} - 54 q^{27} + 60 q^{29} - 72 q^{30} - 192 q^{35} - 72 q^{36} + 80 q^{38} - 96 q^{40} - 192 q^{42} + 104 q^{43} - 96 q^{48} + 174 q^{49} - 756 q^{51} + 396 q^{53} + 144 q^{55} - 256 q^{56} - 1076 q^{61} - 352 q^{62} - 128 q^{64} + 144 q^{66} - 1008 q^{68} + 1008 q^{69} - 1016 q^{74} - 534 q^{75} + 384 q^{77} - 1040 q^{79} + 162 q^{81} + 168 q^{82} - 180 q^{87} + 192 q^{88} + 216 q^{90} + 1344 q^{92} + 384 q^{94} - 240 q^{95}+O(q^{100}) \) 2 * q - 6 * q^3 - 8 * q^4 + 18 * q^9 + 24 * q^10 + 24 * q^12 + 64 * q^14 + 32 * q^16 + 252 * q^17 - 48 * q^22 - 336 * q^23 + 178 * q^25 - 54 * q^27 + 60 * q^29 - 72 * q^30 - 192 * q^35 - 72 * q^36 + 80 * q^38 - 96 * q^40 - 192 * q^42 + 104 * q^43 - 96 * q^48 + 174 * q^49 - 756 * q^51 + 396 * q^53 + 144 * q^55 - 256 * q^56 - 1076 * q^61 - 352 * q^62 - 128 * q^64 + 144 * q^66 - 1008 * q^68 + 1008 * q^69 - 1016 * q^74 - 534 * q^75 + 384 * q^77 - 1040 * q^79 + 162 * q^81 + 168 * q^82 - 180 * q^87 + 192 * q^88 + 216 * q^90 + 1344 * q^92 + 384 * q^94 - 240 * q^95

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