LMFDB - Embedded newform 1050.6.g.h.799.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,6,Mod(799,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("1050.799");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1050.g (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:	$168.403010804$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1050.799
Dual form			1050.6.g.h.799.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} -36.0000 q^{6} +49.0000i q^{7} +64.0000i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} -36.0000 q^{6} +49.0000i q^{7} +64.0000i q^{8} -81.0000 q^{9} +650.000 q^{11} +144.000i q^{12} +762.000i q^{13} +196.000 q^{14} +256.000 q^{16} +556.000i q^{17} +324.000i q^{18} +2452.00 q^{19} +441.000 q^{21} -2600.00i q^{22} -2950.00i q^{23} +576.000 q^{24} +3048.00 q^{26} +729.000i q^{27} -784.000i q^{28} +674.000 q^{29} -3024.00 q^{31} -1024.00i q^{32} -5850.00i q^{33} +2224.00 q^{34} +1296.00 q^{36} -7730.00i q^{37} -9808.00i q^{38} +6858.00 q^{39} -17016.0 q^{41} -1764.00i q^{42} +21836.0i q^{43} -10400.0 q^{44} -11800.0 q^{46} +23940.0i q^{47} -2304.00i q^{48} -2401.00 q^{49} +5004.00 q^{51} -12192.0i q^{52} +15594.0i q^{53} +2916.00 q^{54} -3136.00 q^{56} -22068.0i q^{57} -2696.00i q^{58} -5608.00 q^{59} +150.000 q^{61} +12096.0i q^{62} -3969.00i q^{63} -4096.00 q^{64} -23400.0 q^{66} +43784.0i q^{67} -8896.00i q^{68} -26550.0 q^{69} -39178.0 q^{71} -5184.00i q^{72} -23570.0i q^{73} -30920.0 q^{74} -39232.0 q^{76} +31850.0i q^{77} -27432.0i q^{78} +17892.0 q^{79} +6561.00 q^{81} +68064.0i q^{82} +38972.0i q^{83} -7056.00 q^{84} +87344.0 q^{86} -6066.00i q^{87} +41600.0i q^{88} -6024.00 q^{89} -37338.0 q^{91} +47200.0i q^{92} +27216.0i q^{93} +95760.0 q^{94} -9216.00 q^{96} -108430. i q^{97} +9604.00i q^{98} -52650.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{4} - 72 q^{6} - 162 q^{9}+O(q^{10}) $ 2 * q - 32 * q^4 - 72 * q^6 - 162 * q^9	$ 2 q - 32 q^{4} - 72 q^{6} - 162 q^{9} + 1300 q^{11} + 392 q^{14} + 512 q^{16} + 4904 q^{19} + 882 q^{21} + 1152 q^{24} + 6096 q^{26} + 1348 q^{29} - 6048 q^{31} + 4448 q^{34} + 2592 q^{36} + 13716 q^{39} - 34032 q^{41} - 20800 q^{44} - 23600 q^{46} - 4802 q^{49} + 10008 q^{51} + 5832 q^{54} - 6272 q^{56} - 11216 q^{59} + 300 q^{61} - 8192 q^{64} - 46800 q^{66} - 53100 q^{69} - 78356 q^{71} - 61840 q^{74} - 78464 q^{76} + 35784 q^{79} + 13122 q^{81} - 14112 q^{84} + 174688 q^{86} - 12048 q^{89} - 74676 q^{91} + 191520 q^{94} - 18432 q^{96} - 105300 q^{99}+O(q^{100}) $ 2 * q - 32 * q^4 - 72 * q^6 - 162 * q^9 + 1300 * q^11 + 392 * q^14 + 512 * q^16 + 4904 * q^19 + 882 * q^21 + 1152 * q^24 + 6096 * q^26 + 1348 * q^29 - 6048 * q^31 + 4448 * q^34 + 2592 * q^36 + 13716 * q^39 - 34032 * q^41 - 20800 * q^44 - 23600 * q^46 - 4802 * q^49 + 10008 * q^51 + 5832 * q^54 - 6272 * q^56 - 11216 * q^59 + 300 * q^61 - 8192 * q^64 - 46800 * q^66 - 53100 * q^69 - 78356 * q^71 - 61840 * q^74 - 78464 * q^76 + 35784 * q^79 + 13122 * q^81 - 14112 * q^84 + 174688 * q^86 - 12048 * q^89 - 74676 * q^91 + 191520 * q^94 - 18432 * q^96 - 105300 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 4.00000i	− 0.707107i
$2$	− 4.00000i	− 0.707107i
$3$	− 9.00000i	− 0.577350i
$3$	− 9.00000i	− 0.577350i
$4$	−16.0000	−0.500000
$5$	0	0
$5$	0	0
$6$	−36.0000	−0.408248
$7$	49.0000i	0.377964i
$7$	49.0000i	0.377964i
$8$	64.0000i	0.353553i
$9$	−81.0000	−0.333333
$10$	0	0
$11$	650.000	1.61969	0.809845	−	0.586645i	$-0.199551\pi$
$11$	650.000	1.61969	0.809845	+	0.586645i	$0.199551\pi$
$12$	144.000i	0.288675i
$13$	762.000i	1.25054i	0.780410	+	0.625269i	$0.215011\pi$
$13$	762.000i	1.25054i	−0.780410	+	0.625269i	$0.784989\pi$
$14$	196.000	0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	556.000i	0.466608i	0.972404	+	0.233304i	$0.0749538\pi$
$17$	556.000i	0.466608i	−0.972404	+	0.233304i	$0.925046\pi$
$18$	324.000i	0.235702i
$19$	2452.00	1.55825	0.779124	−	0.626870i	$-0.215664\pi$
$19$	2452.00	1.55825	0.779124	+	0.626870i	$0.215664\pi$
$20$	0	0
$21$	441.000	0.218218
$22$	− 2600.00i	− 1.14529i
$23$	− 2950.00i	− 1.16279i	−0.813620	−	0.581397i	$-0.802507\pi$
$23$	− 2950.00i	− 1.16279i	0.813620	−	0.581397i	$-0.197493\pi$
$24$	576.000	0.204124
$25$	0	0
$26$	3048.00	0.884263
$27$	729.000i	0.192450i
$28$	− 784.000i	− 0.188982i
$29$	674.000	0.148821	0.0744106	−	0.997228i	$-0.476292\pi$
$29$	674.000	0.148821	0.0744106	+	0.997228i	$0.476292\pi$
$30$	0	0
$31$	−3024.00	−0.565168	−0.282584	−	0.959243i	$-0.591192\pi$
$31$	−3024.00	−0.565168	−0.282584	+	0.959243i	$0.591192\pi$
$32$	− 1024.00i	− 0.176777i
$33$	− 5850.00i	− 0.935128i
$34$	2224.00	0.329942
$35$	0	0
$36$	1296.00	0.166667
$37$	− 7730.00i	− 0.928272i	−0.885764	−	0.464136i	$-0.846365\pi$
$37$	− 7730.00i	− 0.928272i	0.885764	−	0.464136i	$-0.153635\pi$
$38$	− 9808.00i	− 1.10185i
$39$	6858.00	0.721998
$40$	0	0
$41$	−17016.0	−1.58088	−0.790438	−	0.612542i	$-0.790147\pi$
$41$	−17016.0	−1.58088	−0.790438	+	0.612542i	$0.790147\pi$
$42$	− 1764.00i	− 0.154303i
$43$	21836.0i	1.80095i	0.434907	+	0.900476i	$0.356781\pi$
$43$	21836.0i	1.80095i	−0.434907	+	0.900476i	$0.643219\pi$
$44$	−10400.0	−0.809845
$45$	0	0
$46$	−11800.0	−0.822219
$47$	23940.0i	1.58081i	0.612585	+	0.790405i	$0.290130\pi$
$47$	23940.0i	1.58081i	−0.612585	+	0.790405i	$0.709870\pi$
$48$	− 2304.00i	− 0.144338i
$49$	−2401.00	−0.142857
$50$	0	0
$51$	5004.00	0.269396
$52$	− 12192.0i	− 0.625269i
$53$	15594.0i	0.762549i	0.924462	+	0.381275i	$0.124515\pi$
$53$	15594.0i	0.762549i	−0.924462	+	0.381275i	$0.875485\pi$
$54$	2916.00	0.136083
$55$	0	0
$56$	−3136.00	−0.133631
$57$	− 22068.0i	− 0.899655i
$58$	− 2696.00i	− 0.105233i
$59$	−5608.00	−0.209738	−0.104869	−	0.994486i	$-0.533442\pi$
$59$	−5608.00	−0.209738	−0.104869	+	0.994486i	$0.533442\pi$
$60$	0	0
$61$	150.000	0.00516139	0.00258069	−	0.999997i	$-0.499179\pi$
$61$	150.000	0.00516139	0.00258069	+	0.999997i	$0.499179\pi$
$62$	12096.0i	0.399634i
$63$	− 3969.00i	− 0.125988i
$64$	−4096.00	−0.125000
$65$	0	0
$66$	−23400.0	−0.661235
$67$	43784.0i	1.19159i	0.803135	+	0.595797i	$0.203164\pi$
$67$	43784.0i	1.19159i	−0.803135	+	0.595797i	$0.796836\pi$
$68$	− 8896.00i	− 0.233304i
$69$	−26550.0	−0.671339
$70$	0	0
$71$	−39178.0	−0.922351	−0.461176	−	0.887309i	$-0.652572\pi$
$71$	−39178.0	−0.922351	−0.461176	+	0.887309i	$0.652572\pi$
$72$	− 5184.00i	− 0.117851i
$73$	− 23570.0i	− 0.517669i	−0.965922	−	0.258835i	$-0.916662\pi$
$73$	− 23570.0i	− 0.517669i	0.965922	−	0.258835i	$-0.0833385\pi$
$74$	−30920.0	−0.656387
$75$	0	0
$76$	−39232.0	−0.779124
$77$	31850.0i	0.612185i
$78$	− 27432.0i	− 0.510530i
$79$	17892.0	0.322546	0.161273	−	0.986910i	$-0.448440\pi$
$79$	17892.0	0.322546	0.161273	+	0.986910i	$0.448440\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	68064.0i	1.11785i
$83$	38972.0i	0.620951i	0.950581	+	0.310476i	$0.100488\pi$
$83$	38972.0i	0.620951i	−0.950581	+	0.310476i	$0.899512\pi$
$84$	−7056.00	−0.109109
$85$	0	0
$86$	87344.0	1.27346
$87$	− 6066.00i	− 0.0859220i
$88$	41600.0i	0.572647i
$89$	−6024.00	−0.0806139	−0.0403070	−	0.999187i	$-0.512834\pi$
$89$	−6024.00	−0.0806139	−0.0403070	+	0.999187i	$0.512834\pi$
$90$	0	0
$91$	−37338.0	−0.472659
$92$	47200.0i	0.581397i
$93$	27216.0i	0.326300i
$94$	95760.0	1.11780
$95$	0	0
$96$	−9216.00	−0.102062
$97$	− 108430.i	− 1.17009i	−0.811000	−	0.585046i	$-0.801076\pi$
$97$	− 108430.i	− 1.17009i	0.811000	−	0.585046i	$-0.198924\pi$
$98$	9604.00i	0.101015i
$99$	−52650.0	−0.539896
$100$	0	0
$101$	−70424.0	−0.686938	−0.343469	−	0.939164i	$-0.611602\pi$
$101$	−70424.0	−0.686938	−0.343469	+	0.939164i	$0.611602\pi$
$102$	− 20016.0i	− 0.190492i
$103$	− 31552.0i	− 0.293045i	−0.989207	−	0.146522i	$-0.953192\pi$
$103$	− 31552.0i	− 0.293045i	0.989207	−	0.146522i	$-0.0468080\pi$
$104$	−48768.0	−0.442132
$105$	0	0
$106$	62376.0	0.539204
$107$	− 108282.i	− 0.914317i	−0.889385	−	0.457159i	$-0.848867\pi$
$107$	− 108282.i	− 0.914317i	0.889385	−	0.457159i	$-0.151133\pi$
$108$	− 11664.0i	− 0.0962250i
$109$	72146.0	0.581629	0.290814	−	0.956779i	$-0.406074\pi$
$109$	72146.0	0.581629	0.290814	+	0.956779i	$0.406074\pi$
$110$	0	0
$111$	−69570.0	−0.535938
$112$	12544.0i	0.0944911i
$113$	220906.i	1.62746i	0.581240	+	0.813732i	$0.302568\pi$
$113$	220906.i	1.62746i	−0.581240	+	0.813732i	$0.697432\pi$
$114$	−88272.0	−0.636152
$115$	0	0
$116$	−10784.0	−0.0744106
$117$	− 61722.0i	− 0.416846i
$118$	22432.0i	0.148307i
$119$	−27244.0	−0.176361
$120$	0	0
$121$	261449.	1.62339
$122$	− 600.000i	− 0.00364965i
$123$	153144.i	0.912719i
$124$	48384.0	0.282584
$125$	0	0
$126$	−15876.0	−0.0890871
$127$	239652.i	1.31847i	0.751935	+	0.659237i	$0.229121\pi$
$127$	239652.i	1.31847i	−0.751935	+	0.659237i	$0.770879\pi$
$128$	16384.0i	0.0883883i
$129$	196524.	1.03978
$130$	0	0
$131$	−274172.	−1.39587	−0.697935	−	0.716161i	$-0.745897\pi$
$131$	−274172.	−1.39587	−0.697935	+	0.716161i	$0.745897\pi$
$132$	93600.0i	0.467564i
$133$	120148.i	0.588962i
$134$	175136.	0.842584
$135$	0	0
$136$	−35584.0	−0.164971
$137$	391154.i	1.78052i	0.455455	+	0.890259i	$0.349477\pi$
$137$	391154.i	1.78052i	−0.455455	+	0.890259i	$0.650523\pi$
$138$	106200.i	0.474708i
$139$	−339364.	−1.48980	−0.744901	−	0.667175i	$-0.767503\pi$
$139$	−339364.	−1.48980	−0.744901	+	0.667175i	$0.767503\pi$
$140$	0	0
$141$	215460.	0.912681
$142$	156712.i	0.652201i
$143$	495300.i	2.02548i
$144$	−20736.0	−0.0833333
$145$	0	0
$146$	−94280.0	−0.366047
$147$	21609.0i	0.0824786i
$148$	123680.i	0.464136i
$149$	29334.0	0.108244	0.0541222	−	0.998534i	$-0.482764\pi$
$149$	29334.0	0.108244	0.0541222	+	0.998534i	$0.482764\pi$
$150$	0	0
$151$	71608.0	0.255575	0.127788	−	0.991802i	$-0.459212\pi$
$151$	71608.0	0.255575	0.127788	+	0.991802i	$0.459212\pi$
$152$	156928.i	0.550924i
$153$	− 45036.0i	− 0.155536i
$154$	127400.	0.432880
$155$	0	0
$156$	−109728.	−0.360999
$157$	− 296318.i	− 0.959420i	−0.877427	−	0.479710i	$-0.840742\pi$
$157$	− 296318.i	− 0.959420i	0.877427	−	0.479710i	$-0.159258\pi$
$158$	− 71568.0i	− 0.228074i
$159$	140346.	0.440258
$160$	0	0
$161$	144550.	0.439494
$162$	− 26244.0i	− 0.0785674i
$163$	− 480400.i	− 1.41623i	−0.706097	−	0.708115i	$-0.749546\pi$
$163$	− 480400.i	− 1.41623i	0.706097	−	0.708115i	$-0.250454\pi$
$164$	272256.	0.790438
$165$	0	0
$166$	155888.	0.439079
$167$	− 160180.i	− 0.444444i	−0.974996	−	0.222222i	$-0.928669\pi$
$167$	− 160180.i	− 0.444444i	0.974996	−	0.222222i	$-0.0713310\pi$
$168$	28224.0i	0.0771517i
$169$	−209351.	−0.563843
$170$	0	0
$171$	−198612.	−0.519416
$172$	− 349376.i	− 0.900476i
$173$	− 8984.00i	− 0.0228220i	−0.999935	−	0.0114110i	$-0.996368\pi$
$173$	− 8984.00i	− 0.0228220i	0.999935	−	0.0114110i	$-0.00363232\pi$
$174$	−24264.0	−0.0607560
$175$	0	0
$176$	166400.	0.404922
$177$	50472.0i	0.121093i
$178$	24096.0i	0.0570026i
$179$	−182886.	−0.426627	−0.213313	−	0.976984i	$-0.568425\pi$
$179$	−182886.	−0.426627	−0.213313	+	0.976984i	$0.568425\pi$
$180$	0	0
$181$	138330.	0.313848	0.156924	−	0.987611i	$-0.449842\pi$
$181$	138330.	0.313848	0.156924	+	0.987611i	$0.449842\pi$
$182$	149352.i	0.334220i
$183$	− 1350.00i	− 0.00297993i
$184$	188800.	0.411109
$185$	0	0
$186$	108864.	0.230729
$187$	361400.i	0.755760i
$188$	− 383040.i	− 0.790405i
$189$	−35721.0	−0.0727393
$190$	0	0
$191$	327222.	0.649021	0.324511	−	0.945882i	$-0.394800\pi$
$191$	327222.	0.649021	0.324511	+	0.945882i	$0.394800\pi$
$192$	36864.0i	0.0721688i
$193$	786902.i	1.52064i	0.649547	+	0.760322i	$0.274959\pi$
$193$	786902.i	1.52064i	−0.649547	+	0.760322i	$0.725041\pi$
$194$	−433720.	−0.827380
$195$	0	0
$196$	38416.0	0.0714286
$197$	− 423098.i	− 0.776740i	−0.921504	−	0.388370i	$-0.873038\pi$
$197$	− 423098.i	− 0.776740i	0.921504	−	0.388370i	$-0.126962\pi$
$198$	210600.i	0.381764i
$199$	−1.02392e6	−1.83288	−0.916439	−	0.400175i	$-0.868949\pi$
$199$	−1.02392e6	−1.83288	−0.916439	+	0.400175i	$0.868949\pi$
$200$	0	0
$201$	394056.	0.687967
$202$	281696.i	0.485738i
$203$	33026.0i	0.0562491i
$204$	−80064.0	−0.134698
$205$	0	0
$206$	−126208.	−0.207214
$207$	238950.i	0.387598i
$208$	195072.i	0.312634i
$209$	1.59380e6	2.52388
$210$	0	0
$211$	461516.	0.713642	0.356821	−	0.934173i	$-0.383861\pi$
$211$	461516.	0.713642	0.356821	+	0.934173i	$0.383861\pi$
$212$	− 249504.i	− 0.381275i
$213$	352602.i	0.532520i
$214$	−433128.	−0.646520
$215$	0	0
$216$	−46656.0	−0.0680414
$217$	− 148176.i	− 0.213613i
$218$	− 288584.i	− 0.411274i
$219$	−212130.	−0.298877
$220$	0	0
$221$	−423672.	−0.583511
$222$	278280.i	0.378965i
$223$	995048.i	1.33993i	0.742393	+	0.669965i	$0.233691\pi$
$223$	995048.i	1.33993i	−0.742393	+	0.669965i	$0.766309\pi$
$224$	50176.0	0.0668153
$225$	0	0
$226$	883624.	1.15079
$227$	95568.0i	0.123097i	0.998104	+	0.0615486i	$0.0196039\pi$
$227$	95568.0i	0.123097i	−0.998104	+	0.0615486i	$0.980396\pi$
$228$	353088.i	0.449827i
$229$	1.04409e6	1.31567	0.657836	−	0.753161i	$-0.271472\pi$
$229$	1.04409e6	1.31567	0.657836	+	0.753161i	$0.271472\pi$
$230$	0	0
$231$	286650.	0.353445
$232$	43136.0i	0.0526163i
$233$	− 1.16941e6i	− 1.41116i	−0.708629	−	0.705581i	$-0.750686\pi$
$233$	− 1.16941e6i	− 1.41116i	0.708629	−	0.705581i	$-0.249314\pi$
$234$	−246888.	−0.294754
$235$	0	0
$236$	89728.0	0.104869
$237$	− 161028.i	− 0.186222i
$238$	108976.i	0.124706i
$239$	27342.0	0.0309625	0.0154812	−	0.999880i	$-0.495072\pi$
$239$	27342.0	0.0309625	0.0154812	+	0.999880i	$0.495072\pi$
$240$	0	0
$241$	−907714.	−1.00671	−0.503357	−	0.864078i	$-0.667902\pi$
$241$	−907714.	−1.00671	−0.503357	+	0.864078i	$0.667902\pi$
$242$	− 1.04580e6i	− 1.14791i
$243$	− 59049.0i	− 0.0641500i
$244$	−2400.00	−0.00258069
$245$	0	0
$246$	612576.	0.645390
$247$	1.86842e6i	1.94865i
$248$	− 193536.i	− 0.199817i
$249$	350748.	0.358506
$250$	0	0
$251$	44088.0	0.0441709	0.0220854	−	0.999756i	$-0.492969\pi$
$251$	44088.0	0.0441709	0.0220854	+	0.999756i	$0.492969\pi$
$252$	63504.0i	0.0629941i
$253$	− 1.91750e6i	− 1.88336i
$254$	958608.	0.932302
$255$	0	0
$256$	65536.0	0.0625000
$257$	829200.i	0.783117i	0.920153	+	0.391558i	$0.128064\pi$
$257$	829200.i	0.783117i	−0.920153	+	0.391558i	$0.871936\pi$
$258$	− 786096.i	− 0.735235i
$259$	378770.	0.350854
$260$	0	0
$261$	−54594.0	−0.0496071
$262$	1.09669e6i	0.987029i
$263$	1.31947e6i	1.17627i	0.808761	+	0.588137i	$0.200139\pi$
$263$	1.31947e6i	1.17627i	−0.808761	+	0.588137i	$0.799861\pi$
$264$	374400.	0.330618
$265$	0	0
$266$	480592.	0.416459
$267$	54216.0i	0.0465425i
$268$	− 700544.i	− 0.595797i
$269$	783788.	0.660416	0.330208	−	0.943908i	$-0.392881\pi$
$269$	783788.	0.660416	0.330208	+	0.943908i	$0.392881\pi$
$270$	0	0
$271$	955080.	0.789981	0.394990	−	0.918685i	$-0.370748\pi$
$271$	955080.	0.789981	0.394990	+	0.918685i	$0.370748\pi$
$272$	142336.i	0.116652i
$273$	336042.i	0.272890i
$274$	1.56462e6	1.25902
$275$	0	0
$276$	424800.	0.335669
$277$	− 1.91273e6i	− 1.49780i	−0.662682	−	0.748901i	$-0.730582\pi$
$277$	− 1.91273e6i	− 1.49780i	0.662682	−	0.748901i	$-0.269418\pi$
$278$	1.35746e6i	1.05345i
$279$	244944.	0.188389
$280$	0	0
$281$	−1.02620e6	−0.775295	−0.387648	−	0.921808i	$-0.626712\pi$
$281$	−1.02620e6	−0.775295	−0.387648	+	0.921808i	$0.626712\pi$
$282$	− 861840.i	− 0.645363i
$283$	1.74668e6i	1.29642i	0.761461	+	0.648211i	$0.224482\pi$
$283$	1.74668e6i	1.29642i	−0.761461	+	0.648211i	$0.775518\pi$
$284$	626848.	0.461176
$285$	0	0
$286$	1.98120e6	1.43223
$287$	− 833784.i	− 0.597515i
$288$	82944.0i	0.0589256i
$289$	1.11072e6	0.782277
$290$	0	0
$291$	−975870.	−0.675553
$292$	377120.i	0.258835i
$293$	2.23212e6i	1.51897i	0.650526	+	0.759484i	$0.274548\pi$
$293$	2.23212e6i	1.51897i	−0.650526	+	0.759484i	$0.725452\pi$
$294$	86436.0	0.0583212
$295$	0	0
$296$	494720.	0.328194
$297$	473850.i	0.311709i
$298$	− 117336.i	− 0.0765404i
$299$	2.24790e6	1.45412
$300$	0	0
$301$	−1.06996e6	−0.680696
$302$	− 286432.i	− 0.180719i
$303$	633816.i	0.396604i
$304$	627712.	0.389562
$305$	0	0
$306$	−180144.	−0.109981
$307$	− 1.85324e6i	− 1.12224i	−0.827735	−	0.561119i	$-0.810371\pi$
$307$	− 1.85324e6i	− 1.12224i	0.827735	−	0.561119i	$-0.189629\pi$
$308$	− 509600.i	− 0.306092i
$309$	−283968.	−0.169189
$310$	0	0
$311$	−450956.	−0.264383	−0.132191	−	0.991224i	$-0.542201\pi$
$311$	−450956.	−0.264383	−0.132191	+	0.991224i	$0.542201\pi$
$312$	438912.i	0.255265i
$313$	1.60263e6i	0.924642i	0.886713	+	0.462321i	$0.152983\pi$
$313$	1.60263e6i	0.924642i	−0.886713	+	0.462321i	$0.847017\pi$
$314$	−1.18527e6	−0.678413
$315$	0	0
$316$	−286272.	−0.161273
$317$	20862.0i	0.0116602i	0.999983	+	0.00583012i	$0.00185580\pi$
$317$	20862.0i	0.0116602i	−0.999983	+	0.00583012i	$0.998144\pi$
$318$	− 561384.i	− 0.311309i
$319$	438100.	0.241044
$320$	0	0
$321$	−974538.	−0.527881
$322$	− 578200.i	− 0.310770i
$323$	1.36331e6i	0.727091i
$324$	−104976.	−0.0555556
$325$	0	0
$326$	−1.92160e6	−1.00143
$327$	− 649314.i	− 0.335804i
$328$	− 1.08902e6i	− 0.558924i
$329$	−1.17306e6	−0.597490
$330$	0	0
$331$	2.07621e6	1.04160	0.520801	−	0.853678i	$-0.325633\pi$
$331$	2.07621e6	1.04160	0.520801	+	0.853678i	$0.325633\pi$
$332$	− 623552.i	− 0.310476i
$333$	626130.i	0.309424i
$334$	−640720.	−0.314269
$335$	0	0
$336$	112896.	0.0545545
$337$	− 1.20508e6i	− 0.578019i	−0.957326	−	0.289009i	$-0.906674\pi$
$337$	− 1.20508e6i	− 0.578019i	0.957326	−	0.289009i	$-0.0933259\pi$
$338$	837404.i	0.398697i
$339$	1.98815e6	0.939617
$340$	0	0
$341$	−1.96560e6	−0.915396
$342$	794448.i	0.367282i
$343$	− 117649.i	− 0.0539949i
$344$	−1.39750e6	−0.636732
$345$	0	0
$346$	−35936.0	−0.0161376
$347$	876642.i	0.390840i	0.980720	+	0.195420i	$0.0626069\pi$
$347$	876642.i	0.390840i	−0.980720	+	0.195420i	$0.937393\pi$
$348$	97056.0i	0.0429610i
$349$	1.29593e6	0.569532	0.284766	−	0.958597i	$-0.408084\pi$
$349$	1.29593e6	0.569532	0.284766	+	0.958597i	$0.408084\pi$
$350$	0	0
$351$	−555498.	−0.240666
$352$	− 665600.i	− 0.286323i
$353$	− 3.99040e6i	− 1.70443i	−0.523192	−	0.852215i	$-0.675259\pi$
$353$	− 3.99040e6i	− 1.70443i	0.523192	−	0.852215i	$-0.324741\pi$
$354$	201888.	0.0856253
$355$	0	0
$356$	96384.0	0.0403070
$357$	245196.i	0.101822i
$358$	731544.i	0.301671i
$359$	−4.06452e6	−1.66446	−0.832229	−	0.554432i	$-0.812936\pi$
$359$	−4.06452e6	−1.66446	−0.832229	+	0.554432i	$0.812936\pi$
$360$	0	0
$361$	3.53620e6	1.42814
$362$	− 553320.i	− 0.221924i
$363$	− 2.35304e6i	− 0.937266i
$364$	597408.	0.236329
$365$	0	0
$366$	−5400.00	−0.00210713
$367$	1.67243e6i	0.648162i	0.946029	+	0.324081i	$0.105055\pi$
$367$	1.67243e6i	0.648162i	−0.946029	+	0.324081i	$0.894945\pi$
$368$	− 755200.i	− 0.290698i
$369$	1.37830e6	0.526959
$370$	0	0
$371$	−764106.	−0.288216
$372$	− 435456.i	− 0.163150i
$373$	3.16769e6i	1.17888i	0.807812	+	0.589441i	$0.200652\pi$
$373$	3.16769e6i	1.17888i	−0.807812	+	0.589441i	$0.799348\pi$
$374$	1.44560e6	0.534403
$375$	0	0
$376$	−1.53216e6	−0.558901
$377$	513588.i	0.186106i
$378$	142884.i	0.0514344i
$379$	4.20388e6	1.50332	0.751662	−	0.659548i	$-0.229252\pi$
$379$	4.20388e6	1.50332	0.751662	+	0.659548i	$0.229252\pi$
$380$	0	0
$381$	2.15687e6	0.761222
$382$	− 1.30889e6i	− 0.458927i
$383$	− 342616.i	− 0.119347i	−0.998218	−	0.0596734i	$-0.980994\pi$
$383$	− 342616.i	− 0.119347i	0.998218	−	0.0596734i	$-0.0190059\pi$
$384$	147456.	0.0510310
$385$	0	0
$386$	3.14761e6	1.07526
$387$	− 1.76872e6i	− 0.600317i
$388$	1.73488e6i	0.585046i
$389$	3.83959e6	1.28650	0.643252	−	0.765654i	$-0.277585\pi$
$389$	3.83959e6	1.28650	0.643252	+	0.765654i	$0.277585\pi$
$390$	0	0
$391$	1.64020e6	0.542569
$392$	− 153664.i	− 0.0505076i
$393$	2.46755e6i	0.805906i
$394$	−1.69239e6	−0.549238
$395$	0	0
$396$	842400.	0.269948
$397$	− 3.43894e6i	− 1.09509i	−0.836777	−	0.547543i	$-0.815563\pi$
$397$	− 3.43894e6i	− 1.09509i	0.836777	−	0.547543i	$-0.184437\pi$
$398$	4.09568e6i	1.29604i
$399$	1.08133e6	0.340038
$400$	0	0
$401$	−3.89421e6	−1.20937	−0.604684	−	0.796466i	$-0.706701\pi$
$401$	−3.89421e6	−1.20937	−0.604684	+	0.796466i	$0.706701\pi$
$402$	− 1.57622e6i	− 0.486466i
$403$	− 2.30429e6i	− 0.706764i
$404$	1.12678e6	0.343469
$405$	0	0
$406$	132104.	0.0397741
$407$	− 5.02450e6i	− 1.50351i
$408$	320256.i	0.0952460i
$409$	1.64679e6	0.486778	0.243389	−	0.969929i	$-0.421741\pi$
$409$	1.64679e6	0.486778	0.243389	+	0.969929i	$0.421741\pi$
$410$	0	0
$411$	3.52039e6	1.02798
$412$	504832.i	0.146522i
$413$	− 274792.i	− 0.0792737i
$414$	955800.	0.274073
$415$	0	0
$416$	780288.	0.221066
$417$	3.05428e6i	0.860138i
$418$	− 6.37520e6i	− 1.78465i
$419$	1.67659e6	0.466544	0.233272	−	0.972412i	$-0.425057\pi$
$419$	1.67659e6	0.466544	0.233272	+	0.972412i	$0.425057\pi$
$420$	0	0
$421$	−566742.	−0.155840	−0.0779202	−	0.996960i	$-0.524828\pi$
$421$	−566742.	−0.155840	−0.0779202	+	0.996960i	$0.524828\pi$
$422$	− 1.84606e6i	− 0.504621i
$423$	− 1.93914e6i	− 0.526936i
$424$	−998016.	−0.269602
$425$	0	0
$426$	1.41041e6	0.376548
$427$	7350.00i	0.00195082i
$428$	1.73251e6i	0.457159i
$429$	4.45770e6	1.16941
$430$	0	0
$431$	6.68468e6	1.73335	0.866677	−	0.498870i	$-0.166251\pi$
$431$	6.68468e6	1.73335	0.866677	+	0.498870i	$0.166251\pi$
$432$	186624.i	0.0481125i
$433$	6.91337e6i	1.77203i	0.463661	+	0.886013i	$0.346536\pi$
$433$	6.91337e6i	1.77203i	−0.463661	+	0.886013i	$0.653464\pi$
$434$	−592704.	−0.151047
$435$	0	0
$436$	−1.15434e6	−0.290814
$437$	− 7.23340e6i	− 1.81192i
$438$	848520.i	0.211338i
$439$	4.56281e6	1.12998	0.564990	−	0.825098i	$-0.308880\pi$
$439$	4.56281e6	1.12998	0.564990	+	0.825098i	$0.308880\pi$
$440$	0	0
$441$	194481.	0.0476190
$442$	1.69469e6i	0.412605i
$443$	4.59760e6i	1.11307i	0.830825	+	0.556534i	$0.187869\pi$
$443$	4.59760e6i	1.11307i	−0.830825	+	0.556534i	$0.812131\pi$
$444$	1.11312e6	0.267969
$445$	0	0
$446$	3.98019e6	0.947473
$447$	− 264006.i	− 0.0624950i
$448$	− 200704.i	− 0.0472456i
$449$	−1.70658e6	−0.399494	−0.199747	−	0.979848i	$-0.564012\pi$
$449$	−1.70658e6	−0.399494	−0.199747	+	0.979848i	$0.564012\pi$
$450$	0	0
$451$	−1.10604e7	−2.56053
$452$	− 3.53450e6i	− 0.813732i
$453$	− 644472.i	− 0.147557i
$454$	382272.	0.0870428
$455$	0	0
$456$	1.41235e6	0.318076
$457$	6.93916e6i	1.55423i	0.629356	+	0.777117i	$0.283319\pi$
$457$	6.93916e6i	1.55423i	−0.629356	+	0.777117i	$0.716681\pi$
$458$	− 4.17634e6i	− 0.930320i
$459$	−405324.	−0.0897988
$460$	0	0
$461$	−2.61805e6	−0.573753	−0.286877	−	0.957968i	$-0.592617\pi$
$461$	−2.61805e6	−0.573753	−0.286877	+	0.957968i	$0.592617\pi$
$462$	− 1.14660e6i	− 0.249923i
$463$	7.13602e6i	1.54705i	0.633767	+	0.773524i	$0.281508\pi$
$463$	7.13602e6i	1.54705i	−0.633767	+	0.773524i	$0.718492\pi$
$464$	172544.	0.0372053
$465$	0	0
$466$	−4.67764e6	−0.997843
$467$	2.17398e6i	0.461278i	0.973039	+	0.230639i	$0.0740816\pi$
$467$	2.17398e6i	0.461278i	−0.973039	+	0.230639i	$0.925918\pi$
$468$	987552.i	0.208423i
$469$	−2.14542e6	−0.450380
$470$	0	0
$471$	−2.66686e6	−0.553922
$472$	− 358912.i	− 0.0741537i
$473$	1.41934e7i	2.91698i
$474$	−644112.	−0.131679
$475$	0	0
$476$	435904.	0.0881807
$477$	− 1.26311e6i	− 0.254183i
$478$	− 109368.i	− 0.0218938i
$479$	4.63294e6	0.922609	0.461305	−	0.887242i	$-0.347381\pi$
$479$	4.63294e6	0.922609	0.461305	+	0.887242i	$0.347381\pi$
$480$	0	0
$481$	5.89026e6	1.16084
$482$	3.63086e6i	0.711855i
$483$	− 1.30095e6i	− 0.253742i
$484$	−4.18318e6	−0.811696
$485$	0	0
$486$	−236196.	−0.0453609
$487$	4.56645e6i	0.872481i	0.899830	+	0.436241i	$0.143690\pi$
$487$	4.56645e6i	0.872481i	−0.899830	+	0.436241i	$0.856310\pi$
$488$	9600.00i	0.00182483i
$489$	−4.32360e6	−0.817661
$490$	0	0
$491$	−5.31429e6	−0.994813	−0.497407	−	0.867518i	$-0.665714\pi$
$491$	−5.31429e6	−0.994813	−0.497407	+	0.867518i	$0.665714\pi$
$492$	− 2.45030e6i	− 0.456360i
$493$	374744.i	0.0694412i
$494$	7.47370e6	1.37790
$495$	0	0
$496$	−774144.	−0.141292
$497$	− 1.91972e6i	− 0.348616i
$498$	− 1.40299e6i	− 0.253502i
$499$	2.46314e6	0.442831	0.221415	−	0.975180i	$-0.428932\pi$
$499$	2.46314e6	0.442831	0.221415	+	0.975180i	$0.428932\pi$
$500$	0	0
$501$	−1.44162e6	−0.256600
$502$	− 176352.i	− 0.0312335i
$503$	2.79924e6i	0.493310i	0.969103	+	0.246655i	$0.0793315\pi$
$503$	2.79924e6i	0.493310i	−0.969103	+	0.246655i	$0.920669\pi$
$504$	254016.	0.0445435
$505$	0	0
$506$	−7.67000e6	−1.33174
$507$	1.88416e6i	0.325535i
$508$	− 3.83443e6i	− 0.659237i
$509$	−1.99914e6	−0.342018	−0.171009	−	0.985269i	$-0.554703\pi$
$509$	−1.99914e6	−0.342018	−0.171009	+	0.985269i	$0.554703\pi$
$510$	0	0
$511$	1.15493e6	0.195661
$512$	− 262144.i	− 0.0441942i
$513$	1.78751e6i	0.299885i
$514$	3.31680e6	0.553747
$515$	0	0
$516$	−3.14438e6	−0.519890
$517$	1.55610e7i	2.56042i
$518$	− 1.51508e6i	− 0.248091i
$519$	−80856.0	−0.0131763
$520$	0	0
$521$	3.52160e6	0.568390	0.284195	−	0.958767i	$-0.408274\pi$
$521$	3.52160e6	0.568390	0.284195	+	0.958767i	$0.408274\pi$
$522$	218376.i	0.0350775i
$523$	2.60685e6i	0.416737i	0.978050	+	0.208369i	$0.0668153\pi$
$523$	2.60685e6i	0.416737i	−0.978050	+	0.208369i	$0.933185\pi$
$524$	4.38675e6	0.697935
$525$	0	0
$526$	5.27786e6	0.831752
$527$	− 1.68134e6i	− 0.263712i
$528$	− 1.49760e6i	− 0.233782i
$529$	−2.26616e6	−0.352088
$530$	0	0
$531$	454248.	0.0699128
$532$	− 1.92237e6i	− 0.294481i
$533$	− 1.29662e7i	− 1.97694i
$534$	216864.	0.0329105
$535$	0	0
$536$	−2.80218e6	−0.421292
$537$	1.64597e6i	0.246313i
$538$	− 3.13515e6i	− 0.466985i
$539$	−1.56065e6	−0.231384
$540$	0	0
$541$	−1.37441e6	−0.201894	−0.100947	−	0.994892i	$-0.532187\pi$
$541$	−1.37441e6	−0.201894	−0.100947	+	0.994892i	$0.532187\pi$
$542$	− 3.82032e6i	− 0.558601i
$543$	− 1.24497e6i	− 0.181200i
$544$	569344.	0.0824855
$545$	0	0
$546$	1.34417e6	0.192962
$547$	8.78398e6i	1.25523i	0.778524	+	0.627614i	$0.215968\pi$
$547$	8.78398e6i	1.25523i	−0.778524	+	0.627614i	$0.784032\pi$
$548$	− 6.25846e6i	− 0.890259i
$549$	−12150.0	−0.00172046
$550$	0	0
$551$	1.65265e6	0.231900
$552$	− 1.69920e6i	− 0.237354i
$553$	876708.i	0.121911i
$554$	−7.65092e6	−1.05911
$555$	0	0
$556$	5.42982e6	0.744901
$557$	− 6.29262e6i	− 0.859396i	−0.902973	−	0.429698i	$-0.858620\pi$
$557$	− 6.29262e6i	− 0.859396i	0.902973	−	0.429698i	$-0.141380\pi$
$558$	− 979776.i	− 0.133211i
$559$	−1.66390e7	−2.25216
$560$	0	0
$561$	3.25260e6	0.436338
$562$	4.10481e6i	0.548216i
$563$	4.86582e6i	0.646971i	0.946233	+	0.323485i	$0.104855\pi$
$563$	4.86582e6i	0.646971i	−0.946233	+	0.323485i	$0.895145\pi$
$564$	−3.44736e6	−0.456340
$565$	0	0
$566$	6.98670e6	0.916709
$567$	321489.i	0.0419961i
$568$	− 2.50739e6i	− 0.326100i
$569$	4.46383e6	0.577998	0.288999	−	0.957329i	$-0.406678\pi$
$569$	4.46383e6	0.577998	0.288999	+	0.957329i	$0.406678\pi$
$570$	0	0
$571$	8.17054e6	1.04872	0.524361	−	0.851496i	$-0.324304\pi$
$571$	8.17054e6	1.04872	0.524361	+	0.851496i	$0.324304\pi$
$572$	− 7.92480e6i	− 1.01274i
$573$	− 2.94500e6i	− 0.374713i
$574$	−3.33514e6	−0.422507
$575$	0	0
$576$	331776.	0.0416667
$577$	5.50343e6i	0.688167i	0.938939	+	0.344084i	$0.111810\pi$
$577$	5.50343e6i	0.688167i	−0.938939	+	0.344084i	$0.888190\pi$
$578$	− 4.44288e6i	− 0.553153i
$579$	7.08212e6	0.877944
$580$	0	0
$581$	−1.90963e6	−0.234697
$582$	3.90348e6i	0.477688i
$583$	1.01361e7i	1.23509i
$584$	1.50848e6	0.183024
$585$	0	0
$586$	8.92848e6	1.07407
$587$	− 8.14251e6i	− 0.975356i	−0.873024	−	0.487678i	$-0.837844\pi$
$587$	− 8.14251e6i	− 0.975356i	0.873024	−	0.487678i	$-0.162156\pi$
$588$	− 345744.i	− 0.0412393i
$589$	−7.41485e6	−0.880672
$590$	0	0
$591$	−3.80788e6	−0.448451
$592$	− 1.97888e6i	− 0.232068i
$593$	− 2.73136e6i	− 0.318964i	−0.987201	−	0.159482i	$-0.949018\pi$
$593$	− 2.73136e6i	− 0.318964i	0.987201	−	0.159482i	$-0.0509824\pi$
$594$	1.89540e6	0.220412
$595$	0	0
$596$	−469344.	−0.0541222
$597$	9.21528e6i	1.05821i
$598$	− 8.99160e6i	− 1.02822i
$599$	−1.23733e6	−0.140902	−0.0704510	−	0.997515i	$-0.522444\pi$
$599$	−1.23733e6	−0.140902	−0.0704510	+	0.997515i	$0.522444\pi$
$600$	0	0
$601$	−1.59756e7	−1.80414	−0.902071	−	0.431587i	$-0.857954\pi$
$601$	−1.59756e7	−1.80414	−0.902071	+	0.431587i	$0.857954\pi$
$602$	4.27986e6i	0.481324i
$603$	− 3.54650e6i	− 0.397198i
$604$	−1.14573e6	−0.127788
$605$	0	0
$606$	2.53526e6	0.280441
$607$	1.88275e6i	0.207406i	0.994608	+	0.103703i	$0.0330692\pi$
$607$	1.88275e6i	0.207406i	−0.994608	+	0.103703i	$0.966931\pi$
$608$	− 2.51085e6i	− 0.275462i
$609$	297234.	0.0324755
$610$	0	0
$611$	−1.82423e7	−1.97686
$612$	720576.i	0.0777681i
$613$	− 9.82804e6i	− 1.05637i	−0.849130	−	0.528185i	$-0.822873\pi$
$613$	− 9.82804e6i	− 1.05637i	0.849130	−	0.528185i	$-0.177127\pi$
$614$	−7.41294e6	−0.793542
$615$	0	0
$616$	−2.03840e6	−0.216440
$617$	8.21262e6i	0.868498i	0.900793	+	0.434249i	$0.142986\pi$
$617$	8.21262e6i	0.868498i	−0.900793	+	0.434249i	$0.857014\pi$
$618$	1.13587e6i	0.119635i
$619$	−6.98465e6	−0.732686	−0.366343	−	0.930480i	$-0.619390\pi$
$619$	−6.98465e6	−0.732686	−0.366343	+	0.930480i	$0.619390\pi$
$620$	0	0
$621$	2.15055e6	0.223780
$622$	1.80382e6i	0.186947i
$623$	− 295176.i	− 0.0304692i
$624$	1.75565e6	0.180499
$625$	0	0
$626$	6.41054e6	0.653820
$627$	− 1.43442e7i	− 1.45716i
$628$	4.74109e6i	0.479710i
$629$	4.29788e6	0.433139
$630$	0	0
$631$	1.26789e7	1.26767	0.633837	−	0.773467i	$-0.281479\pi$
$631$	1.26789e7	1.26767	0.633837	+	0.773467i	$0.281479\pi$
$632$	1.14509e6i	0.114037i
$633$	− 4.15364e6i	− 0.412022i
$634$	83448.0	0.00824504
$635$	0	0
$636$	−2.24554e6	−0.220129
$637$	− 1.82956e6i	− 0.178648i
$638$	− 1.75240e6i	− 0.170444i
$639$	3.17342e6	0.307450
$640$	0	0
$641$	−1.40324e7	−1.34892	−0.674460	−	0.738311i	$-0.735624\pi$
$641$	−1.40324e7	−1.34892	−0.674460	+	0.738311i	$0.735624\pi$
$642$	3.89815e6i	0.373268i
$643$	1.30368e6i	0.124349i	0.998065	+	0.0621745i	$0.0198035\pi$
$643$	1.30368e6i	0.124349i	−0.998065	+	0.0621745i	$0.980196\pi$
$644$	−2.31280e6	−0.219747
$645$	0	0
$646$	5.45325e6	0.514131
$647$	− 1.57110e6i	− 0.147551i	−0.997275	−	0.0737757i	$-0.976495\pi$
$647$	− 1.57110e6i	− 0.147551i	0.997275	−	0.0737757i	$-0.0235049\pi$
$648$	419904.i	0.0392837i
$649$	−3.64520e6	−0.339711
$650$	0	0
$651$	−1.33358e6	−0.123330
$652$	7.68640e6i	0.708115i
$653$	− 8.34115e6i	− 0.765496i	−0.923853	−	0.382748i	$-0.874978\pi$
$653$	− 8.34115e6i	− 0.765496i	0.923853	−	0.382748i	$-0.125022\pi$
$654$	−2.59726e6	−0.237449
$655$	0	0
$656$	−4.35610e6	−0.395219
$657$	1.90917e6i	0.172556i
$658$	4.69224e6i	0.422489i
$659$	−6.18334e6	−0.554638	−0.277319	−	0.960778i	$-0.589446\pi$
$659$	−6.18334e6	−0.554638	−0.277319	+	0.960778i	$0.589446\pi$
$660$	0	0
$661$	928966.	0.0826982	0.0413491	−	0.999145i	$-0.486834\pi$
$661$	928966.	0.0826982	0.0413491	+	0.999145i	$0.486834\pi$
$662$	− 8.30485e6i	− 0.736524i
$663$	3.81305e6i	0.336890i
$664$	−2.49421e6	−0.219539
$665$	0	0
$666$	2.50452e6	0.218796
$667$	− 1.98830e6i	− 0.173048i
$668$	2.56288e6i	0.222222i
$669$	8.95543e6	0.773609
$670$	0	0
$671$	97500.0	0.00835985
$672$	− 451584.i	− 0.0385758i
$673$	1.79131e7i	1.52452i	0.647272	+	0.762259i	$0.275910\pi$
$673$	1.79131e7i	1.52452i	−0.647272	+	0.762259i	$0.724090\pi$
$674$	−4.82033e6	−0.408721
$675$	0	0
$676$	3.34962e6	0.281922
$677$	4.96397e6i	0.416253i	0.978102	+	0.208126i	$0.0667366\pi$
$677$	4.96397e6i	0.416253i	−0.978102	+	0.208126i	$0.933263\pi$
$678$	− 7.95262e6i	− 0.664409i
$679$	5.31307e6	0.442253
$680$	0	0
$681$	860112.	0.0710701
$682$	7.86240e6i	0.647283i
$683$	89526.0i	0.00734340i	0.999993	+	0.00367170i	$0.00116874\pi$
$683$	89526.0i	0.00734340i	−0.999993	+	0.00367170i	$0.998831\pi$
$684$	3.17779e6	0.259708
$685$	0	0
$686$	−470596.	−0.0381802
$687$	− 9.39677e6i	− 0.759603i
$688$	5.59002e6i	0.450238i
$689$	−1.18826e7	−0.953596
$690$	0	0
$691$	−142396.	−0.0113450	−0.00567248	−	0.999984i	$-0.501806\pi$
$691$	−142396.	−0.0113450	−0.00567248	+	0.999984i	$0.501806\pi$
$692$	143744.i	0.0114110i
$693$	− 2.57985e6i	− 0.204062i
$694$	3.50657e6	0.276365
$695$	0	0
$696$	388224.	0.0303780
$697$	− 9.46090e6i	− 0.737650i
$698$	− 5.18372e6i	− 0.402720i
$699$	−1.05247e7	−0.814735
$700$	0	0
$701$	1.03935e7	0.798852	0.399426	−	0.916765i	$-0.369209\pi$
$701$	1.03935e7	0.798852	0.399426	+	0.916765i	$0.369209\pi$
$702$	2.22199e6i	0.170177i
$703$	− 1.89540e7i	− 1.44648i
$704$	−2.66240e6	−0.202461
$705$	0	0
$706$	−1.59616e7	−1.20521
$707$	− 3.45078e6i	− 0.259638i
$708$	− 807552.i	− 0.0605463i
$709$	−4.65503e6	−0.347782	−0.173891	−	0.984765i	$-0.555634\pi$
$709$	−4.65503e6	−0.347782	−0.173891	+	0.984765i	$0.555634\pi$
$710$	0	0
$711$	−1.44925e6	−0.107515
$712$	− 385536.i	− 0.0285013i
$713$	8.92080e6i	0.657173i
$714$	980784.	0.0719992
$715$	0	0
$716$	2.92618e6	0.213313
$717$	− 246078.i	− 0.0178762i
$718$	1.62581e7i	1.17695i
$719$	6.72134e6	0.484880	0.242440	−	0.970166i	$-0.422052\pi$
$719$	6.72134e6	0.484880	0.242440	+	0.970166i	$0.422052\pi$
$720$	0	0
$721$	1.54605e6	0.110760
$722$	− 1.41448e7i	− 1.00984i
$723$	8.16943e6i	0.581227i
$724$	−2.21328e6	−0.156924
$725$	0	0
$726$	−9.41216e6	−0.662747
$727$	1.24076e7i	0.870670i	0.900269	+	0.435335i	$0.143370\pi$
$727$	1.24076e7i	0.870670i	−0.900269	+	0.435335i	$0.856630\pi$
$728$	− 2.38963e6i	− 0.167110i
$729$	−531441.	−0.0370370
$730$	0	0
$731$	−1.21408e7	−0.840339
$732$	21600.0i	0.00148996i
$733$	1.35958e7i	0.934641i	0.884088	+	0.467321i	$0.154781\pi$
$733$	1.35958e7i	0.934641i	−0.884088	+	0.467321i	$0.845219\pi$
$734$	6.68973e6	0.458319
$735$	0	0
$736$	−3.02080e6	−0.205555
$737$	2.84596e7i	1.93001i
$738$	− 5.51318e6i	− 0.372616i
$739$	−2.56819e6	−0.172988	−0.0864941	−	0.996252i	$-0.527566\pi$
$739$	−2.56819e6	−0.172988	−0.0864941	+	0.996252i	$0.527566\pi$
$740$	0	0
$741$	1.68158e7	1.12505
$742$	3.05642e6i	0.203800i
$743$	− 2.02133e7i	− 1.34327i	−0.740880	−	0.671637i	$-0.765591\pi$
$743$	− 2.02133e7i	− 1.34327i	0.740880	−	0.671637i	$-0.234409\pi$
$744$	−1.74182e6	−0.115364
$745$	0	0
$746$	1.26707e7	0.833595
$747$	− 3.15673e6i	− 0.206984i
$748$	− 5.78240e6i	− 0.377880i
$749$	5.30582e6	0.345579
$750$	0	0
$751$	7.04813e6	0.456010	0.228005	−	0.973660i	$-0.426780\pi$
$751$	7.04813e6	0.456010	0.228005	+	0.973660i	$0.426780\pi$
$752$	6.12864e6i	0.395202i
$753$	− 396792.i	− 0.0255021i
$754$	2.05435e6	0.131597
$755$	0	0
$756$	571536.	0.0363696
$757$	2.04120e7i	1.29463i	0.762223	+	0.647315i	$0.224108\pi$
$757$	2.04120e7i	1.29463i	−0.762223	+	0.647315i	$0.775892\pi$
$758$	− 1.68155e7i	− 1.06301i
$759$	−1.72575e7	−1.08736
$760$	0	0
$761$	−5.07974e6	−0.317965	−0.158983	−	0.987281i	$-0.550821\pi$
$761$	−5.07974e6	−0.317965	−0.158983	+	0.987281i	$0.550821\pi$
$762$	− 8.62747e6i	− 0.538265i
$763$	3.53515e6i	0.219835i
$764$	−5.23555e6	−0.324511
$765$	0	0
$766$	−1.37046e6	−0.0843909
$767$	− 4.27330e6i	− 0.262286i
$768$	− 589824.i	− 0.0360844i
$769$	−2.33898e7	−1.42630	−0.713149	−	0.701012i	$-0.752732\pi$
$769$	−2.33898e7	−1.42630	−0.713149	+	0.701012i	$0.752732\pi$
$770$	0	0
$771$	7.46280e6	0.452133
$772$	− 1.25904e7i	− 0.760322i
$773$	− 1.11253e6i	− 0.0669672i	−0.999439	−	0.0334836i	$-0.989340\pi$
$773$	− 1.11253e6i	− 0.0669672i	0.999439	−	0.0334836i	$-0.0106602\pi$
$774$	−7.07486e6	−0.424488
$775$	0	0
$776$	6.93952e6	0.413690
$777$	− 3.40893e6i	− 0.202566i
$778$	− 1.53584e7i	− 0.909696i
$779$	−4.17232e7	−2.46340
$780$	0	0
$781$	−2.54657e7	−1.49392
$782$	− 6.56080e6i	− 0.383654i
$783$	491346.i	0.0286407i
$784$	−614656.	−0.0357143
$785$	0	0
$786$	9.87019e6	0.569861
$787$	− 2.00812e6i	− 0.115572i	−0.998329	−	0.0577859i	$-0.981596\pi$
$787$	− 2.00812e6i	− 0.115572i	0.998329	−	0.0577859i	$-0.0184041\pi$
$788$	6.76957e6i	0.388370i
$789$	1.18752e7	0.679123
$790$	0	0
$791$	−1.08244e7	−0.615124
$792$	− 3.36960e6i	− 0.190882i
$793$	114300.i	0.00645451i
$794$	−1.37558e7	−0.774343
$795$	0	0
$796$	1.63827e7	0.916439
$797$	− 3.00897e7i	− 1.67792i	−0.544191	−	0.838961i	$-0.683163\pi$
$797$	− 3.00897e7i	− 1.67792i	0.544191	−	0.838961i	$-0.316837\pi$
$798$	− 4.32533e6i	− 0.240443i
$799$	−1.33106e7	−0.737619
$800$	0	0
$801$	487944.	0.0268713
$802$	1.55768e7i	0.855152i
$803$	− 1.53205e7i	− 0.838463i
$804$	−6.30490e6	−0.343984
$805$	0	0
$806$	−9.21715e6	−0.499757
$807$	− 7.05409e6i	− 0.381292i
$808$	− 4.50714e6i	− 0.242869i
$809$	1.88207e6	0.101103	0.0505515	−	0.998721i	$-0.483902\pi$
$809$	1.88207e6	0.101103	0.0505515	+	0.998721i	$0.483902\pi$
$810$	0	0
$811$	4.88220e6	0.260654	0.130327	−	0.991471i	$-0.458397\pi$
$811$	4.88220e6	0.260654	0.130327	+	0.991471i	$0.458397\pi$
$812$	− 528416.i	− 0.0281246i
$813$	− 8.59572e6i	− 0.456096i
$814$	−2.00980e7	−1.06314
$815$	0	0
$816$	1.28102e6	0.0673491
$817$	5.35419e7i	2.80633i
$818$	− 6.58718e6i	− 0.344204i
$819$	3.02438e6	0.157553
$820$	0	0
$821$	8.37096e6	0.433429	0.216714	−	0.976235i	$-0.430466\pi$
$821$	8.37096e6	0.433429	0.216714	+	0.976235i	$0.430466\pi$
$822$	− 1.40815e7i	− 0.726893i
$823$	− 2.02090e7i	− 1.04003i	−0.854157	−	0.520015i	$-0.825926\pi$
$823$	− 2.02090e7i	− 1.04003i	0.854157	−	0.520015i	$-0.174074\pi$
$824$	2.01933e6	0.103607
$825$	0	0
$826$	−1.09917e6	−0.0560549
$827$	1.31059e7i	0.666352i	0.942865	+	0.333176i	$0.108120\pi$
$827$	1.31059e7i	0.666352i	−0.942865	+	0.333176i	$0.891880\pi$
$828$	− 3.82320e6i	− 0.193799i
$829$	−3.18667e7	−1.61046	−0.805232	−	0.592960i	$-0.797959\pi$
$829$	−3.18667e7	−1.61046	−0.805232	+	0.592960i	$0.797959\pi$
$830$	0	0
$831$	−1.72146e7	−0.864756
$832$	− 3.12115e6i	− 0.156317i
$833$	− 1.33496e6i	− 0.0666583i
$834$	1.22171e7	0.608209
$835$	0	0
$836$	−2.55008e7	−1.26194
$837$	− 2.20450e6i	− 0.108767i
$838$	− 6.70637e6i	− 0.329896i
$839$	−9.94742e6	−0.487872	−0.243936	−	0.969791i	$-0.578439\pi$
$839$	−9.94742e6	−0.487872	−0.243936	+	0.969791i	$0.578439\pi$
$840$	0	0
$841$	−2.00569e7	−0.977852
$842$	2.26697e6i	0.110196i
$843$	9.23582e6i	0.447617i
$844$	−7.38426e6	−0.356821
$845$	0	0
$846$	−7.75656e6	−0.372600
$847$	1.28110e7i	0.613585i
$848$	3.99206e6i	0.190637i
$849$	1.57201e7	0.748489
$850$	0	0
$851$	−2.28035e7	−1.07939
$852$	− 5.64163e6i	− 0.266260i
$853$	− 6.52611e6i	− 0.307102i	−0.988141	−	0.153551i	$-0.950929\pi$
$853$	− 6.52611e6i	− 0.307102i	0.988141	−	0.153551i	$-0.0490709\pi$
$854$	29400.0	0.00137944
$855$	0	0
$856$	6.93005e6	0.323260
$857$	8.76238e6i	0.407540i	0.979019	+	0.203770i	$0.0653194\pi$
$857$	8.76238e6i	0.407540i	−0.979019	+	0.203770i	$0.934681\pi$
$858$	− 1.78308e7i	− 0.826899i
$859$	−6.47942e6	−0.299608	−0.149804	−	0.988716i	$-0.547864\pi$
$859$	−6.47942e6	−0.299608	−0.149804	+	0.988716i	$0.547864\pi$
$860$	0	0
$861$	−7.50406e6	−0.344975
$862$	− 2.67387e7i	− 1.22567i
$863$	− 1.83417e7i	− 0.838323i	−0.907912	−	0.419162i	$-0.862324\pi$
$863$	− 1.83417e7i	− 0.838323i	0.907912	−	0.419162i	$-0.137676\pi$
$864$	746496.	0.0340207
$865$	0	0
$866$	2.76535e7	1.25301
$867$	− 9.99649e6i	− 0.451648i
$868$	2.37082e6i	0.106807i
$869$	1.16298e7	0.522424
$870$	0	0
$871$	−3.33634e7	−1.49013
$872$	4.61734e6i	0.205637i
$873$	8.78283e6i	0.390031i
$874$	−2.89336e7	−1.28122
$875$	0	0
$876$	3.39408e6	0.149438
$877$	− 2.69065e7i	− 1.18129i	−0.806930	−	0.590647i	$-0.798873\pi$
$877$	− 2.69065e7i	− 1.18129i	0.806930	−	0.590647i	$-0.201127\pi$
$878$	− 1.82512e7i	− 0.799017i
$879$	2.00891e7	0.876976
$880$	0	0
$881$	−1.52174e7	−0.660542	−0.330271	−	0.943886i	$-0.607140\pi$
$881$	−1.52174e7	−0.660542	−0.330271	+	0.943886i	$0.607140\pi$
$882$	− 777924.i	− 0.0336718i
$883$	− 2.61520e7i	− 1.12877i	−0.825513	−	0.564383i	$-0.809114\pi$
$883$	− 2.61520e7i	− 1.12877i	0.825513	−	0.564383i	$-0.190886\pi$
$884$	6.77875e6	0.291756
$885$	0	0
$886$	1.83904e7	0.787058
$887$	1.08021e7i	0.460997i	0.973073	+	0.230499i	$0.0740357\pi$
$887$	1.08021e7i	0.460997i	−0.973073	+	0.230499i	$0.925964\pi$
$888$	− 4.45248e6i	− 0.189483i
$889$	−1.17429e7	−0.498337
$890$	0	0
$891$	4.26465e6	0.179965
$892$	− 1.59208e7i	− 0.669965i
$893$	5.87009e7i	2.46329i
$894$	−1.05602e6	−0.0441906
$895$	0	0
$896$	−802816.	−0.0334077
$897$	− 2.02311e7i	− 0.839534i
$898$	6.82631e6i	0.282485i
$899$	−2.03818e6	−0.0841090
$900$	0	0
$901$	−8.67026e6	−0.355812
$902$	4.42416e7i	1.81057i
$903$	9.62968e6i	0.393000i
$904$	−1.41380e7	−0.575395
$905$	0	0
$906$	−2.57789e6	−0.104338
$907$	9.84167e6i	0.397238i	0.980077	+	0.198619i	$0.0636456\pi$
$907$	9.84167e6i	0.397238i	−0.980077	+	0.198619i	$0.936354\pi$
$908$	− 1.52909e6i	− 0.0615486i
$909$	5.70434e6	0.228979
$910$	0	0
$911$	2.72509e7	1.08789	0.543945	−	0.839121i	$-0.316930\pi$
$911$	2.72509e7	1.08789	0.543945	+	0.839121i	$0.316930\pi$
$912$	− 5.64941e6i	− 0.224914i
$913$	2.53318e7i	1.00575i
$914$	2.77566e7	1.09901
$915$	0	0
$916$	−1.67054e7	−0.657836
$917$	− 1.34344e7i	− 0.527589i
$918$	1.62130e6i	0.0634974i
$919$	−2.86432e7	−1.11875	−0.559374	−	0.828916i	$-0.688958\pi$
$919$	−2.86432e7	−1.11875	−0.559374	+	0.828916i	$0.688958\pi$
$920$	0	0
$921$	−1.66791e7	−0.647924
$922$	1.04722e7i	0.405705i
$923$	− 2.98536e7i	− 1.15343i
$924$	−4.58640e6	−0.176723
$925$	0	0
$926$	2.85441e7	1.09393
$927$	2.55571e6i	0.0976816i
$928$	− 690176.i	− 0.0263081i
$929$	−6.78492e6	−0.257932	−0.128966	−	0.991649i	$-0.541166\pi$
$929$	−6.78492e6	−0.257932	−0.128966	+	0.991649i	$0.541166\pi$
$930$	0	0
$931$	−5.88725e6	−0.222607
$932$	1.87106e7i	0.705581i
$933$	4.05860e6i	0.152641i
$934$	8.69590e6	0.326173
$935$	0	0
$936$	3.95021e6	0.147377
$937$	− 3.00308e7i	− 1.11742i	−0.829362	−	0.558712i	$-0.811296\pi$
$937$	− 3.00308e7i	− 1.11742i	0.829362	−	0.558712i	$-0.188704\pi$
$938$	8.58166e6i	0.318467i
$939$	1.44237e7	0.533842
$940$	0	0
$941$	2.30725e7	0.849415	0.424707	−	0.905331i	$-0.360377\pi$
$941$	2.30725e7	0.849415	0.424707	+	0.905331i	$0.360377\pi$
$942$	1.06674e7i	0.391682i
$943$	5.01972e7i	1.83823i
$944$	−1.43565e6	−0.0524346
$945$	0	0
$946$	5.67736e7	2.06262
$947$	− 2.71433e7i	− 0.983531i	−0.870728	−	0.491765i	$-0.836352\pi$
$947$	− 2.71433e7i	− 0.983531i	0.870728	−	0.491765i	$-0.163648\pi$
$948$	2.57645e6i	0.0931109i
$949$	1.79603e7	0.647365
$950$	0	0
$951$	187758.	0.00673205
$952$	− 1.74362e6i	− 0.0623532i
$953$	− 1.61552e7i	− 0.576209i	−0.957599	−	0.288104i	$-0.906975\pi$
$953$	− 1.61552e7i	− 0.576209i	0.957599	−	0.288104i	$-0.0930250\pi$
$954$	−5.05246e6	−0.179735
$955$	0	0
$956$	−437472.	−0.0154812
$957$	− 3.94290e6i	− 0.139167i
$958$	− 1.85318e7i	− 0.652383i
$959$	−1.91665e7	−0.672973
$960$	0	0
$961$	−1.94846e7	−0.680585
$962$	− 2.35610e7i	− 0.820837i
$963$	8.77084e6i	0.304772i
$964$	1.45234e7	0.503357
$965$	0	0
$966$	−5.20380e6	−0.179423
$967$	3.80323e7i	1.30793i	0.756523	+	0.653967i	$0.226897\pi$
$967$	3.80323e7i	1.30793i	−0.756523	+	0.653967i	$0.773103\pi$
$968$	1.67327e7i	0.573956i
$969$	1.22698e7	0.419786
$970$	0	0
$971$	−2.23104e7	−0.759379	−0.379689	−	0.925114i	$-0.623969\pi$
$971$	−2.23104e7	−0.759379	−0.379689	+	0.925114i	$0.623969\pi$
$972$	944784.i	0.0320750i
$973$	− 1.66288e7i	− 0.563093i
$974$	1.82658e7	0.616937
$975$	0	0
$976$	38400.0	0.00129035
$977$	− 3.06930e7i	− 1.02873i	−0.857570	−	0.514367i	$-0.828027\pi$
$977$	− 3.06930e7i	− 1.02873i	0.857570	−	0.514367i	$-0.171973\pi$
$978$	1.72944e7i	0.578174i
$979$	−3.91560e6	−0.130569
$980$	0	0
$981$	−5.84383e6	−0.193876
$982$	2.12572e7i	0.703439i
$983$	− 1.52706e7i	− 0.504048i	−0.967721	−	0.252024i	$-0.918904\pi$
$983$	− 1.52706e7i	− 0.504048i	0.967721	−	0.252024i	$-0.0810961\pi$
$984$	−9.80122e6	−0.322695
$985$	0	0
$986$	1.49898e6	0.0491024
$987$	1.05575e7i	0.344961i
$988$	− 2.98948e7i	− 0.974323i
$989$	6.44162e7	2.09413
$990$	0	0
$991$	3.16279e7	1.02303	0.511513	−	0.859276i	$-0.329085\pi$
$991$	3.16279e7	1.02303	0.511513	+	0.859276i	$0.329085\pi$
$992$	3.09658e6i	0.0999085i
$993$	− 1.86859e7i	− 0.601369i
$994$	−7.67889e6	−0.246509
$995$	0	0
$996$	−5.61197e6	−0.179253
$997$	3.55842e7i	1.13376i	0.823802	+	0.566878i	$0.191849\pi$
$997$	3.55842e7i	1.13376i	−0.823802	+	0.566878i	$0.808151\pi$
$998$	− 9.85256e6i	− 0.313129i
$999$	5.63517e6	0.178646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.6.g.h.799.1		2
5.2	odd	4		42.6.a.e.1.1	✓	1
5.3	odd	4		1050.6.a.f.1.1		1
5.4	even	2	inner	1050.6.g.h.799.2		2
15.2	even	4		126.6.a.a.1.1		1
20.7	even	4		336.6.a.q.1.1		1
35.2	odd	12		294.6.e.d.67.1		2
35.12	even	12		294.6.e.c.67.1		2
35.17	even	12		294.6.e.c.79.1		2
35.27	even	4		294.6.a.k.1.1		1
35.32	odd	12		294.6.e.d.79.1		2
60.47	odd	4		1008.6.a.d.1.1		1
105.62	odd	4		882.6.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.a.e.1.1	✓	1	5.2	odd	4
126.6.a.a.1.1		1	15.2	even	4
294.6.a.k.1.1		1	35.27	even	4
294.6.e.c.67.1		2	35.12	even	12
294.6.e.c.79.1		2	35.17	even	12
294.6.e.d.67.1		2	35.2	odd	12
294.6.e.d.79.1		2	35.32	odd	12
336.6.a.q.1.1		1	20.7	even	4
882.6.a.j.1.1		1	105.62	odd	4
1008.6.a.d.1.1		1	60.47	odd	4
1050.6.a.f.1.1		1	5.3	odd	4
1050.6.g.h.799.1		2	1.1	even	1	trivial
1050.6.g.h.799.2		2	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1050.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} -36.0000 q^{6} +49.0000i q^{7} +64.0000i q^{8} -81.0000 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} -36.0000 q^{6} +49.0000i q^{7} +64.0000i q^{8} -81.0000 q^{9} +650.000 q^{11} +144.000i q^{12} +762.000i q^{13} +196.000 q^{14} +256.000 q^{16} +556.000i q^{17} +324.000i q^{18} +2452.00 q^{19} +441.000 q^{21} -2600.00i q^{22} -2950.00i q^{23} +576.000 q^{24} +3048.00 q^{26} +729.000i q^{27} -784.000i q^{28} +674.000 q^{29} -3024.00 q^{31} -1024.00i q^{32} -5850.00i q^{33} +2224.00 q^{34} +1296.00 q^{36} -7730.00i q^{37} -9808.00i q^{38} +6858.00 q^{39} -17016.0 q^{41} -1764.00i q^{42} +21836.0i q^{43} -10400.0 q^{44} -11800.0 q^{46} +23940.0i q^{47} -2304.00i q^{48} -2401.00 q^{49} +5004.00 q^{51} -12192.0i q^{52} +15594.0i q^{53} +2916.00 q^{54} -3136.00 q^{56} -22068.0i q^{57} -2696.00i q^{58} -5608.00 q^{59} +150.000 q^{61} +12096.0i q^{62} -3969.00i q^{63} -4096.00 q^{64} -23400.0 q^{66} +43784.0i q^{67} -8896.00i q^{68} -26550.0 q^{69} -39178.0 q^{71} -5184.00i q^{72} -23570.0i q^{73} -30920.0 q^{74} -39232.0 q^{76} +31850.0i q^{77} -27432.0i q^{78} +17892.0 q^{79} +6561.00 q^{81} +68064.0i q^{82} +38972.0i q^{83} -7056.00 q^{84} +87344.0 q^{86} -6066.00i q^{87} +41600.0i q^{88} -6024.00 q^{89} -37338.0 q^{91} +47200.0i q^{92} +27216.0i q^{93} +95760.0 q^{94} -9216.00 q^{96} -108430. i q^{97} +9604.00i q^{98} -52650.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{4} - 72 q^{6} - 162 q^{9}+O(q^{10}) \) 2 * q - 32 * q^4 - 72 * q^6 - 162 * q^9	\( 2 q - 32 q^{4} - 72 q^{6} - 162 q^{9} + 1300 q^{11} + 392 q^{14} + 512 q^{16} + 4904 q^{19} + 882 q^{21} + 1152 q^{24} + 6096 q^{26} + 1348 q^{29} - 6048 q^{31} + 4448 q^{34} + 2592 q^{36} + 13716 q^{39} - 34032 q^{41} - 20800 q^{44} - 23600 q^{46} - 4802 q^{49} + 10008 q^{51} + 5832 q^{54} - 6272 q^{56} - 11216 q^{59} + 300 q^{61} - 8192 q^{64} - 46800 q^{66} - 53100 q^{69} - 78356 q^{71} - 61840 q^{74} - 78464 q^{76} + 35784 q^{79} + 13122 q^{81} - 14112 q^{84} + 174688 q^{86} - 12048 q^{89} - 74676 q^{91} + 191520 q^{94} - 18432 q^{96} - 105300 q^{99}+O(q^{100}) \) 2 * q - 32 * q^4 - 72 * q^6 - 162 * q^9 + 1300 * q^11 + 392 * q^14 + 512 * q^16 + 4904 * q^19 + 882 * q^21 + 1152 * q^24 + 6096 * q^26 + 1348 * q^29 - 6048 * q^31 + 4448 * q^34 + 2592 * q^36 + 13716 * q^39 - 34032 * q^41 - 20800 * q^44 - 23600 * q^46 - 4802 * q^49 + 10008 * q^51 + 5832 * q^54 - 6272 * q^56 - 11216 * q^59 + 300 * q^61 - 8192 * q^64 - 46800 * q^66 - 53100 * q^69 - 78356 * q^71 - 61840 * q^74 - 78464 * q^76 + 35784 * q^79 + 13122 * q^81 - 14112 * q^84 + 174688 * q^86 - 12048 * q^89 - 74676 * q^91 + 191520 * q^94 - 18432 * q^96 - 105300 * q^99

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