LMFDB - Embedded newform 1152.2.w.b.431.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(143,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4]))

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

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

chi := DirichletCharacter("1152.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.w (of order $8$, degree $4$, 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			431.5
Character	$\chi$	$=$	1152.431
Dual form			1152.2.w.b.719.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0505677 + 0.0209458i) q^{5} +(-1.44150 - 1.44150i) q^{7} +O(q^{10})$	$q+(-0.0505677 + 0.0209458i) q^{5} +(-1.44150 - 1.44150i) q^{7} +(-0.320987 + 0.132957i) q^{11} +(0.623666 - 1.50566i) q^{13} -5.65026 q^{17} +(-4.13118 - 1.71119i) q^{19} +(3.03457 + 3.03457i) q^{23} +(-3.53342 + 3.53342i) q^{25} +(-0.721807 + 1.74260i) q^{29} -5.26441i q^{31} +(0.103087 + 0.0427001i) q^{35} +(-1.32038 - 3.18767i) q^{37} +(-6.90990 + 6.90990i) q^{41} +(-3.40135 - 8.21159i) q^{43} +3.23039i q^{47} -2.84413i q^{49} +(0.579972 + 1.40018i) q^{53} +(0.0134467 - 0.0134467i) q^{55} +(-4.21939 - 10.1865i) q^{59} +(-12.1464 - 5.03120i) q^{61} +0.0892011i q^{65} +(-3.34709 + 8.08060i) q^{67} +(-9.36679 + 9.36679i) q^{71} +(-1.72215 - 1.72215i) q^{73} +(0.654363 + 0.271046i) q^{77} +15.1224 q^{79} +(2.48612 - 6.00202i) q^{83} +(0.285721 - 0.118349i) q^{85} +(2.70367 + 2.70367i) q^{89} +(-3.06943 + 1.27140i) q^{91} +0.244747 q^{95} +6.43802 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95}+O(q^{100}) $ 32 * q + 8 * q^11 - 16 * q^29 - 24 * q^35 - 16 * q^53 + 32 * q^55 - 32 * q^59 + 32 * q^61 + 16 * q^67 - 16 * q^71 - 16 * q^77 + 32 * q^79 + 40 * q^83 + 48 * q^91 + 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.0505677	+	0.0209458i	−0.0226146	+	0.00936726i	−0.393962	−	0.919127i	$-0.628896\pi$
$5$	−0.0505677	+	0.0209458i	−0.0226146	+	0.00936726i	0.371347	+	0.928494i	$0.378896\pi$
$6$		0			0
$7$	−1.44150	−	1.44150i	−0.544837	−	0.544837i	0.380106	−	0.924943i	$-0.375888\pi$
$7$	−1.44150	−	1.44150i	−0.544837	−	0.544837i	−0.924943	+	0.380106i	$0.875888\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.320987	+	0.132957i	−0.0967813	+	0.0400881i	−0.430549	−	0.902567i	$-0.641680\pi$
$11$	−0.320987	+	0.132957i	−0.0967813	+	0.0400881i	0.333767	+	0.942655i	$0.391680\pi$
$12$		0			0
$13$	0.623666	−	1.50566i	0.172974	−	0.417595i	−0.813489	−	0.581580i	$-0.802435\pi$
$13$	0.623666	−	1.50566i	0.172974	−	0.417595i	0.986463	+	0.163985i	$0.0524347\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.65026			−1.37039			−0.685195	−	0.728360i	$-0.740283\pi$
$17$	−5.65026			−1.37039			−0.685195	+	0.728360i	$0.740283\pi$
$18$		0			0
$19$	−4.13118	−	1.71119i	−0.947758	−	0.392574i	−0.145370	−	0.989377i	$-0.546437\pi$
$19$	−4.13118	−	1.71119i	−0.947758	−	0.392574i	−0.802388	+	0.596803i	$0.796437\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.03457	+	3.03457i	0.632752	+	0.632752i	0.948757	−	0.316006i	$-0.102342\pi$
$23$	3.03457	+	3.03457i	0.632752	+	0.632752i	−0.316006	+	0.948757i	$0.602342\pi$
$24$		0			0
$25$	−3.53342	+	3.53342i	−0.706683	+	0.706683i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.721807	+	1.74260i	−0.134036	+	0.323592i	−0.976620	−	0.214973i	$-0.931034\pi$
$29$	−0.721807	+	1.74260i	−0.134036	+	0.323592i	0.842584	+	0.538565i	$0.181034\pi$
$30$		0			0
$31$		−	5.26441i		−	0.945516i	−0.881192	−	0.472758i	$-0.843258\pi$
$31$		−	5.26441i		−	0.945516i	0.881192	−	0.472758i	$-0.156742\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.103087	+	0.0427001i	0.0174249	+	0.00721763i
$36$		0			0
$37$	−1.32038	−	3.18767i	−0.217069	−	0.524050i	0.777409	−	0.628995i	$-0.216533\pi$
$37$	−1.32038	−	3.18767i	−0.217069	−	0.524050i	−0.994478	+	0.104945i	$0.966533\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.90990	+	6.90990i	−1.07915	+	1.07915i	−0.0825597	+	0.996586i	$0.526310\pi$
$41$	−6.90990	+	6.90990i	−1.07915	+	1.07915i	−0.996586	+	0.0825597i	$0.973690\pi$
$42$		0			0
$43$	−3.40135	−	8.21159i	−0.518701	−	1.25226i	−0.938701	−	0.344731i	$-0.887970\pi$
$43$	−3.40135	−	8.21159i	−0.518701	−	1.25226i	0.420000	−	0.907524i	$-0.362030\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			3.23039i			0.471201i	0.971850	+	0.235600i	$0.0757057\pi$
$47$			3.23039i			0.471201i	−0.971850	+	0.235600i	$0.924294\pi$
$48$		0			0
$49$		−	2.84413i		−	0.406305i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.579972	+	1.40018i	0.0796653	+	0.192329i	0.958694	−	0.284440i	$-0.0918077\pi$
$53$	0.579972	+	1.40018i	0.0796653	+	0.192329i	−0.879029	+	0.476769i	$0.841808\pi$
$54$		0			0
$55$	0.0134467	−	0.0134467i	0.00181315	−	0.00181315i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.21939	−	10.1865i	−0.549317	−	1.32617i	−0.917988	−	0.396609i	$-0.870187\pi$
$59$	−4.21939	−	10.1865i	−0.549317	−	1.32617i	0.368671	−	0.929560i	$-0.379813\pi$
$60$		0			0
$61$	−12.1464	−	5.03120i	−1.55519	−	0.644180i	−0.570942	−	0.820990i	$-0.693422\pi$
$61$	−12.1464	−	5.03120i	−1.55519	−	0.644180i	−0.984245	+	0.176811i	$0.943422\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			0.0892011i			0.0110640i
$66$		0			0
$67$	−3.34709	+	8.08060i	−0.408913	+	0.987203i	0.576512	+	0.817089i	$0.304414\pi$
$67$	−3.34709	+	8.08060i	−0.408913	+	0.987203i	−0.985424	+	0.170114i	$0.945586\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.36679	+	9.36679i	−1.11163	+	1.11163i	−0.118704	+	0.992930i	$0.537874\pi$
$71$	−9.36679	+	9.36679i	−1.11163	+	1.11163i	−0.992930	+	0.118704i	$0.962126\pi$
$72$		0			0
$73$	−1.72215	−	1.72215i	−0.201562	−	0.201562i	0.599107	−	0.800669i	$-0.295522\pi$
$73$	−1.72215	−	1.72215i	−0.201562	−	0.201562i	−0.800669	+	0.599107i	$0.795522\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.654363	+	0.271046i	0.0745716	+	0.0308886i
$78$		0			0
$79$	15.1224			1.70140			0.850702	−	0.525648i	$-0.176177\pi$
$79$	15.1224			1.70140			0.850702	+	0.525648i	$0.176177\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.48612	−	6.00202i	0.272887	−	0.658807i	−0.726717	−	0.686936i	$-0.758955\pi$
$83$	2.48612	−	6.00202i	0.272887	−	0.658807i	0.999604	+	0.0281294i	$0.00895506\pi$
$84$		0			0
$85$	0.285721	−	0.118349i	0.0309908	−	0.0128368i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.70367	+	2.70367i	0.286588	+	0.286588i	0.835730	−	0.549141i	$-0.185045\pi$
$89$	2.70367	+	2.70367i	0.286588	+	0.286588i	−0.549141	+	0.835730i	$0.685045\pi$
$90$		0			0
$91$	−3.06943	+	1.27140i	−0.321764	+	0.133279i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.244747			0.0251105
$96$		0			0
$97$	6.43802			0.653682			0.326841	−	0.945079i	$-0.394016\pi$
$97$	6.43802			0.653682			0.326841	+	0.945079i	$0.394016\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	17.7633	−	7.35780i	1.76751	−	0.732128i	0.772206	−	0.635372i	$-0.219153\pi$
$101$	17.7633	−	7.35780i	1.76751	−	0.732128i	0.995308	−	0.0967565i	$-0.0308468\pi$
$102$		0			0
$103$	−6.97813	−	6.97813i	−0.687575	−	0.687575i	0.274120	−	0.961695i	$-0.411613\pi$
$103$	−6.97813	−	6.97813i	−0.687575	−	0.687575i	−0.961695	+	0.274120i	$0.911613\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.1509	+	5.44730i	−1.27135	+	0.526611i	−0.913375	−	0.407120i	$-0.866533\pi$
$107$	−13.1509	+	5.44730i	−1.27135	+	0.526611i	−0.357976	+	0.933731i	$0.616533\pi$
$108$		0			0
$109$	6.94514	−	16.7671i	0.665224	−	1.60599i	−0.124280	−	0.992247i	$-0.539662\pi$
$109$	6.94514	−	16.7671i	0.665224	−	1.60599i	0.789504	−	0.613745i	$-0.210338\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.5862			−1.08994			−0.544969	−	0.838456i	$-0.683458\pi$
$113$	−11.5862			−1.08994			−0.544969	+	0.838456i	$0.683458\pi$
$114$		0			0
$115$	−0.217013	−	0.0898897i	−0.0202366	−	0.00838226i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	8.14488	+	8.14488i	0.746640	+	0.746640i
$120$		0			0
$121$	−7.69282	+	7.69282i	−0.699347	+	0.699347i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.209396	−	0.505526i	0.0187289	−	0.0452156i
$126$		0			0
$127$			11.5409i			1.02409i	0.858958	+	0.512045i	$0.171112\pi$
$127$			11.5409i			1.02409i	−0.858958	+	0.512045i	$0.828888\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.46501	−	0.606825i	−0.127998	−	0.0530186i	0.317765	−	0.948169i	$-0.397068\pi$
$131$	−1.46501	−	0.606825i	−0.127998	−	0.0530186i	−0.445763	+	0.895151i	$0.647068\pi$
$132$		0			0
$133$	3.48843	+	8.42181i	0.302485	+	0.730263i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.76283	−	2.76283i	0.236044	−	0.236044i	−0.579166	−	0.815210i	$-0.696622\pi$
$137$	2.76283	−	2.76283i	0.236044	−	0.236044i	0.815210	+	0.579166i	$0.196622\pi$
$138$		0			0
$139$	−2.52007	−	6.08399i	−0.213750	−	0.516037i	0.780244	−	0.625475i	$-0.215095\pi$
$139$	−2.52007	−	6.08399i	−0.213750	−	0.516037i	−0.993994	+	0.109438i	$0.965095\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			0.566219i			0.0473496i
$144$		0			0
$145$		−	0.103238i		−	0.00857345i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.06361	−	4.98199i	−0.169057	−	0.408140i	0.816531	−	0.577301i	$-0.195894\pi$
$149$	−2.06361	−	4.98199i	−0.169057	−	0.408140i	−0.985588	+	0.169161i	$0.945894\pi$
$150$		0			0
$151$	−0.971232	+	0.971232i	−0.0790378	+	0.0790378i	−0.745520	−	0.666483i	$-0.767799\pi$
$151$	−0.971232	+	0.971232i	−0.0790378	+	0.0790378i	0.666483	+	0.745520i	$0.267799\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.110268	+	0.266209i	0.00885690	+	0.0213824i
$156$		0			0
$157$	−10.5849	−	4.38441i	−0.844767	−	0.349914i	−0.0820357	−	0.996629i	$-0.526142\pi$
$157$	−10.5849	−	4.38441i	−0.844767	−	0.349914i	−0.762731	+	0.646715i	$0.776142\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	8.74869i		−	0.689493i
$162$		0			0
$163$	−7.42825	+	17.9334i	−0.581826	+	1.40465i	0.309331	+	0.950955i	$0.399895\pi$
$163$	−7.42825	+	17.9334i	−0.581826	+	1.40465i	−0.891156	+	0.453697i	$0.850105\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.24060	+	6.24060i	−0.482912	+	0.482912i	−0.906060	−	0.423148i	$-0.860925\pi$
$167$	−6.24060	+	6.24060i	−0.482912	+	0.482912i	0.423148	+	0.906060i	$0.360925\pi$
$168$		0			0
$169$	7.31433	+	7.31433i	0.562641	+	0.562641i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.66545	+	4.00356i	0.734850	+	0.304385i	0.718544	−	0.695482i	$-0.244809\pi$
$173$	9.66545	+	4.00356i	0.734850	+	0.304385i	0.0163069	+	0.999867i	$0.494809\pi$
$174$		0			0
$175$	10.1869			0.770055
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.15817	−	7.62449i	0.236053	−	0.569881i	−0.760815	−	0.648969i	$-0.775201\pi$
$179$	3.15817	−	7.62449i	0.236053	−	0.569881i	0.996868	+	0.0790873i	$0.0252006\pi$
$180$		0			0
$181$	10.2651	−	4.25196i	0.763002	−	0.316046i	0.0329681	−	0.999456i	$-0.489504\pi$
$181$	10.2651	−	4.25196i	0.763002	−	0.316046i	0.730034	+	0.683410i	$0.239504\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.133537	+	0.133537i	0.00981782	+	0.00981782i
$186$		0			0
$187$	1.81366	−	0.751244i	0.132628	−	0.0549364i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.11953			0.442794			0.221397	−	0.975184i	$-0.428938\pi$
$191$	6.11953			0.442794			0.221397	+	0.975184i	$0.428938\pi$
$192$		0			0
$193$	14.6513			1.05462			0.527310	−	0.849673i	$-0.323201\pi$
$193$	14.6513			1.05462			0.527310	+	0.849673i	$0.323201\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	20.1664	−	8.35319i	1.43680	−	0.595140i	0.477776	−	0.878482i	$-0.341443\pi$
$197$	20.1664	−	8.35319i	1.43680	−	0.595140i	0.959019	+	0.283341i	$0.0914429\pi$
$198$		0			0
$199$	1.34312	+	1.34312i	0.0952113	+	0.0952113i	0.753108	−	0.657897i	$-0.228554\pi$
$199$	1.34312	+	1.34312i	0.0952113	+	0.0952113i	−0.657897	+	0.753108i	$0.728554\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.55245	−	1.47147i	0.249333	−	0.103277i
$204$		0			0
$205$	0.204684	−	0.494152i	0.0142958	−	0.0345131i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.55357			0.107463
$210$		0			0
$211$	14.6312	+	6.06043i	1.00725	+	0.417217i	0.824451	−	0.565933i	$-0.191484\pi$
$211$	14.6312	+	6.06043i	1.00725	+	0.417217i	0.182800	+	0.983150i	$0.441484\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.343997	+	0.343997i	0.0234604	+	0.0234604i
$216$		0			0
$217$	−7.58867	+	7.58867i	−0.515153	+	0.515153i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.52387	+	8.50739i	−0.237041	+	0.572269i
$222$		0			0
$223$			0.0733906i			0.00491460i	0.999997	+	0.00245730i	$0.000782183\pi$
$223$			0.0733906i			0.00491460i	−0.999997	+	0.00245730i	$0.999218\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	14.3718	+	5.95299i	0.953888	+	0.395114i	0.804691	−	0.593694i	$-0.202331\pi$
$227$	14.3718	+	5.95299i	0.953888	+	0.395114i	0.149198	+	0.988807i	$0.452331\pi$
$228$		0			0
$229$	10.0229	+	24.1975i	0.662333	+	1.59901i	0.794138	+	0.607737i	$0.207923\pi$
$229$	10.0229	+	24.1975i	0.662333	+	1.59901i	−0.131806	+	0.991276i	$0.542077\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.88581	+	4.88581i	−0.320080	+	0.320080i	−0.848798	−	0.528718i	$-0.822673\pi$
$233$	−4.88581	+	4.88581i	−0.320080	+	0.320080i	0.528718	+	0.848798i	$0.322673\pi$
$234$		0			0
$235$	−0.0676632	−	0.163353i	−0.00441386	−	0.0106560i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	24.3341i		−	1.57404i	−0.616928	−	0.787020i	$-0.711623\pi$
$239$		−	24.3341i		−	1.57404i	0.616928	−	0.787020i	$-0.288377\pi$
$240$		0			0
$241$			3.20992i			0.206769i	0.994641	+	0.103384i	$0.0329672\pi$
$241$			3.20992i			0.206769i	−0.994641	+	0.103384i	$0.967033\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.0595727	+	0.143821i	0.00380596	+	0.00918841i
$246$		0			0
$247$	−5.15295	+	5.15295i	−0.327875	+	0.327875i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−8.63734	−	20.8524i	−0.545184	−	1.31619i	−0.921024	−	0.389506i	$-0.872646\pi$
$251$	−8.63734	−	20.8524i	−0.545184	−	1.31619i	0.375840	−	0.926685i	$-0.377354\pi$
$252$		0			0
$253$	−1.37753	−	0.570590i	−0.0866043	−	0.0358727i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	11.4338i		−	0.713221i	−0.934253	−	0.356611i	$-0.883932\pi$
$257$		−	11.4338i		−	0.713221i	0.934253	−	0.356611i	$-0.116068\pi$
$258$		0			0
$259$	−2.69171	+	6.49837i	−0.167255	+	0.403789i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.2028	−	10.2028i	0.629129	−	0.629129i	−0.318720	−	0.947849i	$-0.603253\pi$
$263$	10.2028	−	10.2028i	0.629129	−	0.629129i	0.947849	+	0.318720i	$0.103253\pi$
$264$		0			0
$265$	−0.0586557	−	0.0586557i	−0.00360319	−	0.00360319i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−24.4000	−	10.1068i	−1.48770	−	0.616223i	−0.516881	−	0.856057i	$-0.672907\pi$
$269$	−24.4000	−	10.1068i	−1.48770	−	0.616223i	−0.970814	+	0.239834i	$0.922907\pi$
$270$		0			0
$271$	23.0385			1.39949			0.699746	−	0.714392i	$-0.253297\pi$
$271$	23.0385			1.39949			0.699746	+	0.714392i	$0.253297\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.664388	−	1.60397i	0.0400641	−	0.0967233i
$276$		0			0
$277$	0.872254	−	0.361300i	0.0524087	−	0.0217084i	−0.356325	−	0.934362i	$-0.615970\pi$
$277$	0.872254	−	0.361300i	0.0524087	−	0.0217084i	0.408734	+	0.912654i	$0.365970\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	15.0398	+	15.0398i	0.897197	+	0.897197i	0.995187	−	0.0979901i	$-0.0312413\pi$
$281$	15.0398	+	15.0398i	0.897197	+	0.897197i	−0.0979901	+	0.995187i	$0.531241\pi$
$282$		0			0
$283$	25.3592	−	10.5041i	1.50745	−	0.624405i	0.532417	−	0.846482i	$-0.321284\pi$
$283$	25.3592	−	10.5041i	1.50745	−	0.624405i	0.975029	+	0.222077i	$0.0712838\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	19.9213			1.17592
$288$		0			0
$289$	14.9255			0.877970
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−17.2872	+	7.16058i	−1.00993	+	0.418326i	−0.825428	−	0.564507i	$-0.809066\pi$
$293$	−17.2872	+	7.16058i	−1.00993	+	0.418326i	−0.184499	+	0.982833i	$0.559066\pi$
$294$		0			0
$295$	0.426729	+	0.426729i	0.0248451	+	0.0248451i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.46159	−	2.67648i	0.373684	−	0.154785i
$300$		0			0
$301$	−6.93397	+	16.7401i	−0.399668	+	0.964883i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.719598			0.0412041
$306$		0			0
$307$	−0.389197	−	0.161211i	−0.0222126	−	0.00920078i	0.371549	−	0.928413i	$-0.378827\pi$
$307$	−0.389197	−	0.161211i	−0.0222126	−	0.00920078i	−0.393762	+	0.919212i	$0.628827\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.59481	+	3.59481i	0.203843	+	0.203843i	0.801644	−	0.597801i	$-0.203959\pi$
$311$	3.59481	+	3.59481i	0.203843	+	0.203843i	−0.597801	+	0.801644i	$0.703959\pi$
$312$		0			0
$313$	−16.1765	+	16.1765i	−0.914351	+	0.914351i	−0.996611	−	0.0822596i	$-0.973786\pi$
$313$	−16.1765	+	16.1765i	−0.914351	+	0.914351i	0.0822596	+	0.996611i	$0.473786\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.85103	−	4.46879i	0.103964	−	0.250992i	−0.863334	−	0.504632i	$-0.831628\pi$
$317$	1.85103	−	4.46879i	0.103964	−	0.250992i	0.967299	+	0.253640i	$0.0816280\pi$
$318$		0			0
$319$		−	0.655321i		−	0.0366909i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	23.3423	+	9.66869i	1.29880	+	0.537980i
$324$		0			0
$325$	3.11646	+	7.52380i	0.172870	+	0.417345i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.65662	−	4.65662i	0.256728	−	0.256728i
$330$		0			0
$331$	−6.31236	−	15.2394i	−0.346959	−	0.837632i	−0.996976	−	0.0777129i	$-0.975238\pi$
$331$	−6.31236	−	15.2394i	−0.346959	−	0.837632i	0.650017	−	0.759920i	$-0.274762\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	0.478725i		−	0.0261556i
$336$		0			0
$337$		−	13.9550i		−	0.760179i	−0.924950	−	0.380089i	$-0.875893\pi$
$337$		−	13.9550i		−	0.760179i	0.924950	−	0.380089i	$-0.124107\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.699942	+	1.68981i	0.0379040	+	0.0915083i
$342$		0			0
$343$	−14.1904	+	14.1904i	−0.766207	+	0.766207i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.72778	+	16.2423i	0.361166	+	0.871932i	0.995130	+	0.0985697i	$0.0314267\pi$
$347$	6.72778	+	16.2423i	0.361166	+	0.871932i	−0.633964	+	0.773363i	$0.718573\pi$
$348$		0			0
$349$	18.1387	+	7.51328i	0.970940	+	0.402177i	0.811062	−	0.584960i	$-0.198890\pi$
$349$	18.1387	+	7.51328i	0.970940	+	0.402177i	0.159878	+	0.987137i	$0.448890\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			1.36137i			0.0724586i	0.999344	+	0.0362293i	$0.0115347\pi$
$353$			1.36137i			0.0724586i	−0.999344	+	0.0362293i	$0.988465\pi$
$354$		0			0
$355$	0.277462	−	0.669853i	0.0147262	−	0.0355521i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.43099	+	1.43099i	−0.0755246	+	0.0755246i	−0.743860	−	0.668335i	$-0.767007\pi$
$359$	−1.43099	+	1.43099i	−0.0755246	+	0.0755246i	0.668335	+	0.743860i	$0.267007\pi$
$360$		0			0
$361$	0.703464	+	0.703464i	0.0370244	+	0.0370244i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.123157	+	0.0510132i	0.00644632	+	0.00267015i
$366$		0			0
$367$	−4.44867			−0.232219			−0.116109	−	0.993236i	$-0.537042\pi$
$367$	−4.44867			−0.232219			−0.116109	+	0.993236i	$0.537042\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.18233	−	2.85439i	0.0613834	−	0.148193i
$372$		0			0
$373$	−15.1942	+	6.29364i	−0.786726	+	0.325873i	−0.739626	−	0.673018i	$-0.764998\pi$
$373$	−15.1942	+	6.29364i	−0.786726	+	0.325873i	−0.0470995	+	0.998890i	$0.514998\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.17359	+	2.17359i	0.111946	+	0.111946i
$378$		0			0
$379$	−7.31677	+	3.03071i	−0.375837	+	0.155677i	−0.562602	−	0.826728i	$-0.690200\pi$
$379$	−7.31677	+	3.03071i	−0.375837	+	0.155677i	0.186765	+	0.982405i	$0.440200\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−37.8805			−1.93560			−0.967801	−	0.251716i	$-0.919005\pi$
$383$	−37.8805			−1.93560			−0.967801	+	0.251716i	$0.919005\pi$
$384$		0			0
$385$	−0.0387669			−0.00197575
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−11.3365	+	4.69571i	−0.574781	+	0.238082i	−0.651088	−	0.759002i	$-0.725687\pi$
$389$	−11.3365	+	4.69571i	−0.574781	+	0.238082i	0.0763069	+	0.997084i	$0.475687\pi$
$390$		0			0
$391$	−17.1461	−	17.1461i	−0.867117	−	0.867117i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.764706	+	0.316752i	−0.0384765	+	0.0159375i
$396$		0			0
$397$	2.58068	−	6.23031i	0.129520	−	0.312690i	−0.845794	−	0.533509i	$-0.820873\pi$
$397$	2.58068	−	6.23031i	0.129520	−	0.312690i	0.975315	+	0.220819i	$0.0708730\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.816119			−0.0407550			−0.0203775	−	0.999792i	$-0.506487\pi$
$401$	−0.816119			−0.0407550			−0.0203775	+	0.999792i	$0.506487\pi$
$402$		0			0
$403$	−7.92642	−	3.28323i	−0.394843	−	0.163549i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.847648	+	0.847648i	0.0420164	+	0.0420164i
$408$		0			0
$409$	17.3208	−	17.3208i	0.856460	−	0.856460i	−0.134459	−	0.990919i	$-0.542930\pi$
$409$	17.3208	−	17.3208i	0.856460	−	0.856460i	0.990919	+	0.134459i	$0.0429297\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.60162	+	20.7661i	−0.423258	+	1.02183i
$414$		0			0
$415$			0.355582i			0.0174548i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−11.8029	−	4.88890i	−0.576607	−	0.238839i	0.0752697	−	0.997163i	$-0.476018\pi$
$419$	−11.8029	−	4.88890i	−0.576607	−	0.238839i	−0.651877	+	0.758325i	$0.726018\pi$
$420$		0			0
$421$	0.806753	+	1.94767i	0.0393187	+	0.0949238i	0.942319	−	0.334716i	$-0.108640\pi$
$421$	0.806753	+	1.94767i	0.0393187	+	0.0949238i	−0.903000	+	0.429640i	$0.858640\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	19.9647	−	19.9647i	0.968432	−	0.968432i
$426$		0			0
$427$	10.2566	+	24.7616i	0.496351	+	1.19830i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	33.1877i		−	1.59860i	−0.600934	−	0.799299i	$-0.705205\pi$
$431$		−	33.1877i		−	1.59860i	0.600934	−	0.799299i	$-0.294795\pi$
$432$		0			0
$433$		−	14.0761i		−	0.676453i	−0.941065	−	0.338227i	$-0.890173\pi$
$433$		−	14.0761i		−	0.676453i	0.941065	−	0.338227i	$-0.109827\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.34363	−	17.7291i	−0.351293	−	0.848098i
$438$		0			0
$439$	−1.50704	+	1.50704i	−0.0719273	+	0.0719273i	−0.742155	−	0.670228i	$-0.766196\pi$
$439$	−1.50704	+	1.50704i	−0.0719273	+	0.0719273i	0.670228	+	0.742155i	$0.266196\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.4760	+	25.2913i	0.497731	+	1.20163i	0.950703	+	0.310103i	$0.100364\pi$
$443$	10.4760	+	25.2913i	0.497731	+	1.20163i	−0.452972	+	0.891525i	$0.649636\pi$
$444$		0			0
$445$	−0.193349	−	0.0800878i	−0.00916562	−	0.00379652i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	13.5428i		−	0.639126i	−0.947565	−	0.319563i	$-0.896464\pi$
$449$		−	13.5428i		−	0.639126i	0.947565	−	0.319563i	$-0.103536\pi$
$450$		0			0
$451$	1.29927	−	3.13671i	0.0611802	−	0.147702i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.128584	−	0.128584i	0.00602810	−	0.00602810i
$456$		0			0
$457$	−14.4316	−	14.4316i	−0.675084	−	0.675084i	0.283800	−	0.958884i	$-0.408405\pi$
$457$	−14.4316	−	14.4316i	−0.675084	−	0.675084i	−0.958884	+	0.283800i	$0.908405\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.33454	+	3.86649i	0.434753	+	0.180080i	0.589316	−	0.807902i	$-0.299397\pi$
$461$	9.33454	+	3.86649i	0.434753	+	0.180080i	−0.154564	+	0.987983i	$0.549397\pi$
$462$		0			0
$463$	−33.3750			−1.55107			−0.775534	−	0.631306i	$-0.782519\pi$
$463$	−33.3750			−1.55107			−0.775534	+	0.631306i	$0.782519\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.5324	+	32.6702i	−0.626207	+	1.51180i	0.218095	+	0.975928i	$0.430016\pi$
$467$	−13.5324	+	32.6702i	−0.626207	+	1.51180i	−0.844301	+	0.535869i	$0.819984\pi$
$468$		0			0
$469$	16.4731	−	6.82337i	0.760656	−	0.315074i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.18358	+	2.18358i	0.100401	+	0.100401i
$474$		0			0
$475$	20.6435	−	8.55083i	0.947190	−	0.392339i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	16.4726			0.752653			0.376326	−	0.926487i	$-0.377187\pi$
$479$	16.4726			0.752653			0.376326	+	0.926487i	$0.377187\pi$
$480$		0			0
$481$	−5.62303			−0.256388
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.325556	+	0.134850i	−0.0147827	+	0.00612321i
$486$		0			0
$487$	3.20291	+	3.20291i	0.145138	+	0.145138i	0.775942	−	0.630804i	$-0.217275\pi$
$487$	3.20291	+	3.20291i	0.145138	+	0.145138i	−0.630804	+	0.775942i	$0.717275\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−36.4450	+	15.0960i	−1.64474	+	0.681274i	−0.996764	−	0.0803853i	$-0.974385\pi$
$491$	−36.4450	+	15.0960i	−1.64474	+	0.681274i	−0.647977	+	0.761660i	$0.724385\pi$
$492$		0			0
$493$	4.07840	−	9.84613i	0.183682	−	0.443447i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	27.0045			1.21132
$498$		0			0
$499$	17.7901	+	7.36890i	0.796395	+	0.329877i	0.743511	−	0.668723i	$-0.233159\pi$
$499$	17.7901	+	7.36890i	0.796395	+	0.329877i	0.0528833	+	0.998601i	$0.483159\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−24.4309	−	24.4309i	−1.08932	−	1.08932i	−0.995598	−	0.0937240i	$-0.970123\pi$
$503$	−24.4309	−	24.4309i	−1.08932	−	1.08932i	−0.0937240	−	0.995598i	$-0.529877\pi$
$504$		0			0
$505$	−0.744134	+	0.744134i	−0.0331135	+	0.0331135i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.742577	+	1.79274i	−0.0329141	+	0.0794618i	−0.939482	−	0.342599i	$-0.888693\pi$
$509$	−0.742577	+	1.79274i	−0.0329141	+	0.0794618i	0.906568	+	0.422060i	$0.138693\pi$
$510$		0			0
$511$			4.96496i			0.219637i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.499031	+	0.206705i	0.0219899	+	0.00910852i
$516$		0			0
$517$	−0.429504	−	1.03691i	−0.0188896	−	0.0456034i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.94706	+	9.94706i	−0.435788	+	0.435788i	−0.890592	−	0.454803i	$-0.849710\pi$
$521$	−9.94706	+	9.94706i	−0.435788	+	0.435788i	0.454803	+	0.890592i	$0.349710\pi$
$522$		0			0
$523$	−12.9517	−	31.2681i	−0.566338	−	1.36726i	−0.904621	−	0.426216i	$-0.859846\pi$
$523$	−12.9517	−	31.2681i	−0.566338	−	1.36726i	0.338284	−	0.941044i	$-0.390154\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			29.7453i			1.29573i
$528$		0			0
$529$		−	4.58277i		−	0.199251i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.09451	+	14.7134i	0.263983	+	0.637310i
$534$		0			0
$535$	0.550915	−	0.550915i	0.0238181	−	0.0238181i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.378148	+	0.912930i	0.0162880	+	0.0393227i
$540$		0			0
$541$	−24.6347	−	10.2040i	−1.05913	−	0.438705i	−0.215986	−	0.976396i	$-0.569296\pi$
$541$	−24.6347	−	10.2040i	−1.05913	−	0.438705i	−0.843142	+	0.537692i	$0.819296\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			0.993343i			0.0425502i
$546$		0			0
$547$	5.59032	−	13.4962i	0.239025	−	0.577057i	−0.758158	−	0.652071i	$-0.773900\pi$
$547$	5.59032	−	13.4962i	0.239025	−	0.577057i	0.997182	+	0.0750145i	$0.0239003\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.96383	−	5.96383i	0.254068	−	0.254068i
$552$		0			0
$553$	−21.7990	−	21.7990i	−0.926989	−	0.926989i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−32.9643	−	13.6543i	−1.39674	−	0.578549i	−0.447838	−	0.894115i	$-0.647806\pi$
$557$	−32.9643	−	13.6543i	−1.39674	−	0.578549i	−0.948904	+	0.315565i	$0.897806\pi$
$558$		0			0
$559$	−14.4852			−0.612658
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11.6660	+	28.1642i	−0.491663	+	1.18698i	0.462211	+	0.886770i	$0.347056\pi$
$563$	−11.6660	+	28.1642i	−0.491663	+	1.18698i	−0.953873	+	0.300209i	$0.902944\pi$
$564$		0			0
$565$	0.585887	−	0.242683i	0.0246485	−	0.0102097i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.70810	−	2.70810i	−0.113529	−	0.113529i	0.648060	−	0.761589i	$-0.275581\pi$
$569$	−2.70810	−	2.70810i	−0.113529	−	0.113529i	−0.761589	+	0.648060i	$0.775581\pi$
$570$		0			0
$571$	−13.3976	+	5.54948i	−0.560673	+	0.232238i	−0.644977	−	0.764202i	$-0.723133\pi$
$571$	−13.3976	+	5.54948i	−0.560673	+	0.232238i	0.0843044	+	0.996440i	$0.473133\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−21.4448			−0.894310
$576$		0			0
$577$	−31.1960			−1.29871			−0.649354	−	0.760486i	$-0.724961\pi$
$577$	−31.1960			−1.29871			−0.649354	+	0.760486i	$0.724961\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−12.2357	+	5.06818i	−0.507622	+	0.210264i
$582$		0			0
$583$	−0.372327	−	0.372327i	−0.0154202	−	0.0154202i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.0976	−	8.32471i	0.829518	−	0.343598i	0.0728061	−	0.997346i	$-0.476805\pi$
$587$	20.0976	−	8.32471i	0.829518	−	0.343598i	0.756712	+	0.653749i	$0.226805\pi$
$588$		0			0
$589$	−9.00842	+	21.7482i	−0.371185	+	0.896121i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.4216			0.551158			0.275579	−	0.961278i	$-0.411130\pi$
$593$	13.4216			0.551158			0.275579	+	0.961278i	$0.411130\pi$
$594$		0			0
$595$	−0.582469	−	0.241267i	−0.0238789	−	0.00989097i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−18.3224	−	18.3224i	−0.748635	−	0.748635i	0.225588	−	0.974223i	$-0.427570\pi$
$599$	−18.3224	−	18.3224i	−0.748635	−	0.748635i	−0.974223	+	0.225588i	$0.927570\pi$
$600$		0			0
$601$	7.64445	−	7.64445i	0.311824	−	0.311824i	−0.533792	−	0.845616i	$-0.679234\pi$
$601$	7.64445	−	7.64445i	0.311824	−	0.311824i	0.845616	+	0.533792i	$0.179234\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.227876	−	0.550141i	0.00926447	−	0.0223664i
$606$		0			0
$607$		−	13.1965i		−	0.535628i	−0.963471	−	0.267814i	$-0.913699\pi$
$607$		−	13.1965i		−	0.535628i	0.963471	−	0.267814i	$-0.0863013\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.86387	+	2.01468i	0.196771	+	0.0815053i
$612$		0			0
$613$	−7.87596	−	19.0142i	−0.318107	−	0.767978i	−0.999354	−	0.0359251i	$-0.988562\pi$
$613$	−7.87596	−	19.0142i	−0.318107	−	0.767978i	0.681247	−	0.732053i	$-0.261438\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.36409	−	2.36409i	0.0951748	−	0.0951748i	−0.657916	−	0.753091i	$-0.728562\pi$
$617$	2.36409	−	2.36409i	0.0951748	−	0.0951748i	0.753091	+	0.657916i	$0.228562\pi$
$618$		0			0
$619$	9.55563	+	23.0693i	0.384073	+	0.927235i	0.991169	+	0.132606i	$0.0423346\pi$
$619$	9.55563	+	23.0693i	0.384073	+	0.927235i	−0.607095	+	0.794629i	$0.707665\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	7.79470i		−	0.312288i
$624$		0			0
$625$		−	24.9551i		−	0.998203i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	7.46048	+	18.0112i	0.297469	+	0.718153i
$630$		0			0
$631$	1.69280	−	1.69280i	0.0673892	−	0.0673892i	−0.672609	−	0.739998i	$-0.734826\pi$
$631$	1.69280	−	1.69280i	0.0673892	−	0.0673892i	0.739998	+	0.672609i	$0.234826\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.241734	−	0.583598i	−0.00959292	−	0.0231594i
$636$		0			0
$637$	−4.28230	−	1.77379i	−0.169671	−	0.0702800i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			39.0060i			1.54065i	0.637654	+	0.770323i	$0.279905\pi$
$641$			39.0060i			1.54065i	−0.637654	+	0.770323i	$0.720095\pi$
$642$		0			0
$643$	8.76787	−	21.1675i	0.345771	−	0.834765i	−0.651339	−	0.758787i	$-0.725792\pi$
$643$	8.76787	−	21.1675i	0.345771	−	0.834765i	0.997110	−	0.0759778i	$-0.0242078\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−17.6444	+	17.6444i	−0.693674	+	0.693674i	−0.963038	−	0.269364i	$-0.913186\pi$
$647$	−17.6444	+	17.6444i	−0.693674	+	0.693674i	0.269364	+	0.963038i	$0.413186\pi$
$648$		0			0
$649$	2.70874	+	2.70874i	0.106327	+	0.106327i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.16105	−	1.30935i	−0.123701	−	0.0512387i	0.319974	−	0.947426i	$-0.396326\pi$
$653$	−3.16105	−	1.30935i	−0.123701	−	0.0512387i	−0.443676	+	0.896187i	$0.646326\pi$
$654$		0			0
$655$	0.0867924			0.00339126
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.00896	−	21.7495i	0.350939	−	0.847242i	−0.645565	−	0.763705i	$-0.723378\pi$
$659$	9.00896	−	21.7495i	0.350939	−	0.847242i	0.996505	−	0.0835372i	$-0.0266217\pi$
$660$		0			0
$661$	−27.2013	+	11.2672i	−1.05801	+	0.438242i	−0.842744	−	0.538314i	$-0.819061\pi$
$661$	−27.2013	+	11.2672i	−1.05801	+	0.438242i	−0.215265	+	0.976556i	$0.569061\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.352804	−	0.352804i	−0.0136811	−	0.0136811i
$666$		0			0
$667$	−7.47840	+	3.09766i	−0.289565	+	0.119942i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.56777			0.176337
$672$		0			0
$673$	−40.2867			−1.55294			−0.776469	−	0.630155i	$-0.782991\pi$
$673$	−40.2867			−1.55294			−0.776469	+	0.630155i	$0.782991\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−20.8698	+	8.64457i	−0.802093	+	0.332238i	−0.745794	−	0.666176i	$-0.767930\pi$
$677$	−20.8698	+	8.64457i	−0.802093	+	0.332238i	−0.0562986	+	0.998414i	$0.517930\pi$
$678$		0			0
$679$	−9.28043	−	9.28043i	−0.356150	−	0.356150i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−13.3957	+	5.54867i	−0.512572	+	0.212314i	−0.623950	−	0.781464i	$-0.714473\pi$
$683$	−13.3957	+	5.54867i	−0.512572	+	0.212314i	0.111379	+	0.993778i	$0.464473\pi$
$684$		0			0
$685$	−0.0818402	+	0.197580i	−0.00312695	+	0.00754913i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.46990			0.0940957
$690$		0			0
$691$	−4.05430	−	1.67935i	−0.154233	−	0.0638854i	0.304232	−	0.952598i	$-0.401600\pi$
$691$	−4.05430	−	1.67935i	−0.154233	−	0.0638854i	−0.458464	+	0.888713i	$0.651600\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.254868	+	0.254868i	0.00966771	+	0.00966771i
$696$		0			0
$697$	39.0428	−	39.0428i	1.47885	−	1.47885i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−8.00533	+	19.3266i	−0.302357	+	0.729954i	0.697553	+	0.716533i	$0.254272\pi$
$701$	−8.00533	+	19.3266i	−0.302357	+	0.729954i	−0.999910	+	0.0134211i	$0.995728\pi$
$702$		0			0
$703$			15.4283i			0.581888i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−36.2122	−	14.9996i	−1.36190	−	0.564117i
$708$		0			0
$709$	−7.37340	−	17.8010i	−0.276914	−	0.668529i	0.722833	−	0.691022i	$-0.242839\pi$
$709$	−7.37340	−	17.8010i	−0.276914	−	0.668529i	−0.999747	+	0.0224936i	$0.992839\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	15.9752	−	15.9752i	0.598277	−	0.598277i
$714$		0			0
$715$	−0.0118599	−	0.0286324i	−0.000443536	−	0.00107079i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			14.6223i			0.545320i	0.962110	+	0.272660i	$0.0879035\pi$
$719$			14.6223i			0.545320i	−0.962110	+	0.272660i	$0.912097\pi$
$720$		0			0
$721$			20.1180i			0.749233i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.60687	−	8.70776i	−0.133956	−	0.323398i
$726$		0			0
$727$	20.9235	−	20.9235i	0.776011	−	0.776011i	−0.203139	−	0.979150i	$-0.565114\pi$
$727$	20.9235	−	20.9235i	0.776011	−	0.776011i	0.979150	+	0.203139i	$0.0651144\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	19.2185	+	46.3976i	0.710823	+	1.71608i
$732$		0			0
$733$	23.8873	+	9.89446i	0.882299	+	0.365460i	0.777388	−	0.629021i	$-0.216544\pi$
$733$	23.8873	+	9.89446i	0.882299	+	0.365460i	0.104911	+	0.994482i	$0.466544\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	3.03879i		−	0.111935i
$738$		0			0
$739$	12.2087	−	29.4745i	0.449106	−	1.08424i	−0.523552	−	0.851994i	$-0.675393\pi$
$739$	12.2087	−	29.4745i	0.449106	−	1.08424i	0.972658	−	0.232243i	$-0.0746065\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	6.80000	−	6.80000i	0.249468	−	0.249468i	−0.571284	−	0.820752i	$-0.693555\pi$
$743$	6.80000	−	6.80000i	0.249468	−	0.249468i	0.820752	+	0.571284i	$0.193555\pi$
$744$		0			0
$745$	0.208704	+	0.208704i	0.00764632	+	0.00764632i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	26.8095	+	11.1048i	0.979596	+	0.405762i
$750$		0			0
$751$	−44.9473			−1.64015			−0.820074	−	0.572257i	$-0.806068\pi$
$751$	−44.9473			−1.64015			−0.820074	+	0.572257i	$0.806068\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.0287697	−	0.0694563i	0.00104704	−	0.00252777i
$756$		0			0
$757$	−1.70690	+	0.707023i	−0.0620385	+	0.0256972i	−0.413487	−	0.910510i	$-0.635689\pi$
$757$	−1.70690	+	0.707023i	−0.0620385	+	0.0256972i	0.351448	+	0.936207i	$0.385689\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−12.7724	−	12.7724i	−0.463001	−	0.463001i	0.436637	−	0.899638i	$-0.356169\pi$
$761$	−12.7724	−	12.7724i	−0.463001	−	0.463001i	−0.899638	+	0.436637i	$0.856169\pi$
$762$		0			0
$763$	−34.1812	+	14.1583i	−1.23744	+	0.512566i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−17.9689			−0.648820
$768$		0			0
$769$	19.1995			0.692350			0.346175	−	0.938170i	$-0.387480\pi$
$769$	19.1995			0.692350			0.346175	+	0.938170i	$0.387480\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−23.1310	+	9.58115i	−0.831962	+	0.344610i	−0.757679	−	0.652627i	$-0.773667\pi$
$773$	−23.1310	+	9.58115i	−0.831962	+	0.344610i	−0.0742831	+	0.997237i	$0.523667\pi$
$774$		0			0
$775$	18.6014	+	18.6014i	0.668180	+	0.668180i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	40.3703	−	16.7219i	1.44641	−	0.599124i
$780$		0			0
$781$	1.76124	−	4.25200i	0.0630221	−	0.152149i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.627089			0.0223818
$786$		0			0
$787$	−4.05121	−	1.67807i	−0.144410	−	0.0598166i	0.309308	−	0.950962i	$-0.399903\pi$
$787$	−4.05121	−	1.67807i	−0.144410	−	0.0598166i	−0.453718	+	0.891145i	$0.649903\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	16.7015	+	16.7015i	0.593839	+	0.593839i
$792$		0			0
$793$	−15.1506	+	15.1506i	−0.538013	+	0.538013i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	14.5713	−	35.1783i	0.516144	−	1.24608i	−0.424111	−	0.905610i	$-0.639413\pi$
$797$	14.5713	−	35.1783i	0.516144	−	1.24608i	0.940255	−	0.340471i	$-0.110587\pi$
$798$		0			0
$799$		−	18.2526i		−	0.645729i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.781758	+	0.323815i	0.0275877	+	0.0114272i
$804$		0			0
$805$	0.183249	+	0.442401i	0.00645866	+	0.0155926i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−20.5126	+	20.5126i	−0.721186	+	0.721186i	−0.968847	−	0.247661i	$-0.920338\pi$
$809$	−20.5126	+	20.5126i	−0.721186	+	0.721186i	0.247661	+	0.968847i	$0.420338\pi$
$810$		0			0
$811$	−0.939648	−	2.26851i	−0.0329955	−	0.0796582i	0.906523	−	0.422157i	$-0.138727\pi$
$811$	−0.939648	−	2.26851i	−0.0329955	−	0.0796582i	−0.939518	+	0.342499i	$0.888727\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		−	1.06244i		−	0.0372157i
$816$		0			0
$817$			39.7439i			1.39046i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.2442	−	24.7317i	−0.357526	−	0.863143i	−0.995647	−	0.0932071i	$-0.970288\pi$
$821$	−10.2442	−	24.7317i	−0.357526	−	0.863143i	0.638121	−	0.769936i	$-0.279712\pi$
$822$		0			0
$823$	−8.04412	+	8.04412i	−0.280400	+	0.280400i	−0.833269	−	0.552868i	$-0.813533\pi$
$823$	−8.04412	+	8.04412i	−0.280400	+	0.280400i	0.552868	+	0.833269i	$0.313533\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−14.8516	−	35.8550i	−0.516441	−	1.24680i	−0.940076	−	0.340966i	$-0.889246\pi$
$827$	−14.8516	−	35.8550i	−0.516441	−	1.24680i	0.423634	−	0.905833i	$-0.360754\pi$
$828$		0			0
$829$	48.7703	+	20.2013i	1.69386	+	0.701620i	0.999832	−	0.0183260i	$-0.00583367\pi$
$829$	48.7703	+	20.2013i	1.69386	+	0.701620i	0.694030	+	0.719946i	$0.255834\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			16.0701i			0.556796i
$834$		0			0
$835$	0.184858	−	0.446287i	0.00639728	−	0.0154444i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	36.5267	−	36.5267i	1.26104	−	1.26104i	0.310451	−	0.950589i	$-0.399520\pi$
$839$	36.5267	−	36.5267i	1.26104	−	1.26104i	0.950589	−	0.310451i	$-0.100480\pi$
$840$		0			0
$841$	17.9905	+	17.9905i	0.620361	+	0.620361i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.523074	−	0.216664i	−0.0179943	−	0.00745348i
$846$		0			0
$847$	22.1785			0.762061
$848$		0			0
$849$		0			0
$850$		0			0
$851$	5.66643	−	13.6800i	0.194243	−	0.468944i
$852$		0			0
$853$	8.47051	−	3.50860i	0.290025	−	0.120132i	−0.232928	−	0.972494i	$-0.574831\pi$
$853$	8.47051	−	3.50860i	0.290025	−	0.120132i	0.522952	+	0.852362i	$0.324831\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−30.1040	−	30.1040i	−1.02833	−	1.02833i	−0.999587	−	0.0287458i	$-0.990849\pi$
$857$	−30.1040	−	30.1040i	−1.02833	−	1.02833i	−0.0287458	−	0.999587i	$-0.509151\pi$
$858$		0			0
$859$	25.2414	−	10.4553i	0.861225	−	0.356731i	0.0920383	−	0.995755i	$-0.470662\pi$
$859$	25.2414	−	10.4553i	0.861225	−	0.356731i	0.769186	+	0.639025i	$0.220662\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	37.4443			1.27462			0.637309	−	0.770608i	$-0.280048\pi$
$863$	37.4443			1.27462			0.637309	+	0.770608i	$0.280048\pi$
$864$		0			0
$865$	−0.572618			−0.0194696
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.85410	+	2.01063i	−0.164664	+	0.0682061i
$870$		0			0
$871$	10.0792	+	10.0792i	0.341520	+	0.341520i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.03056	+	0.426873i	−0.0348394	+	0.0144309i
$876$		0			0
$877$	−9.67707	+	23.3625i	−0.326772	+	0.788896i	0.672057	+	0.740500i	$0.265411\pi$
$877$	−9.67707	+	23.3625i	−0.326772	+	0.788896i	−0.998828	+	0.0483966i	$0.984589\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−21.5129			−0.724789			−0.362394	−	0.932025i	$-0.618041\pi$
$881$	−21.5129			−0.724789			−0.362394	+	0.932025i	$0.618041\pi$
$882$		0			0
$883$	−43.7878	−	18.1375i	−1.47358	−	0.610376i	−0.505906	−	0.862589i	$-0.668842\pi$
$883$	−43.7878	−	18.1375i	−1.47358	−	0.610376i	−0.967672	+	0.252213i	$0.918842\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.105277	+	0.105277i	0.00353486	+	0.00353486i	0.708872	−	0.705337i	$-0.249204\pi$
$887$	0.105277	+	0.105277i	0.00353486	+	0.00353486i	−0.705337	+	0.708872i	$0.749204\pi$
$888$		0			0
$889$	16.6363	−	16.6363i	0.557963	−	0.557963i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.52782	−	13.3453i	0.184981	−	0.446584i
$894$		0			0
$895$			0.451704i			0.0150988i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9.17374	+	3.79989i	0.305961	+	0.126733i
$900$		0			0
$901$	−3.27699	−	7.91136i	−0.109173	−	0.263566i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.430024	+	0.430024i	−0.0142945	+	0.0142945i
$906$		0			0
$907$	8.71193	+	21.0325i	0.289275	+	0.698371i	0.999987	−	0.00511165i	$-0.00162709\pi$
$907$	8.71193	+	21.0325i	0.289275	+	0.698371i	−0.710712	+	0.703483i	$0.751627\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			45.6074i			1.51104i	0.655125	+	0.755521i	$0.272616\pi$
$911$			45.6074i			1.51104i	−0.655125	+	0.755521i	$0.727384\pi$
$912$		0			0
$913$			2.25712i			0.0746997i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.23707	+	2.98655i	0.0408517	+	0.0986246i
$918$		0			0
$919$	24.4249	−	24.4249i	0.805703	−	0.805703i	−0.178277	−	0.983980i	$-0.557052\pi$
$919$	24.4249	−	24.4249i	0.805703	−	0.805703i	0.983980	+	0.178277i	$0.0570523\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	8.26148	+	19.9450i	0.271930	+	0.656497i
$924$		0			0
$925$	15.9288	+	6.59793i	0.523736	+	0.216938i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			14.0133i			0.459760i	0.973219	+	0.229880i	$0.0738334\pi$
$929$			14.0133i			0.459760i	−0.973219	+	0.229880i	$0.926167\pi$
$930$		0			0
$931$	−4.86686	+	11.7496i	−0.159505	+	0.385079i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.0759774	+	0.0759774i	−0.00248473	+	0.00248473i
$936$		0			0
$937$	13.8787	+	13.8787i	0.453398	+	0.453398i	0.896481	−	0.443083i	$-0.146115\pi$
$937$	13.8787	+	13.8787i	0.453398	+	0.453398i	−0.443083	+	0.896481i	$0.646115\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.58022	−	1.48297i	−0.116712	−	0.0483436i	0.323563	−	0.946206i	$-0.395119\pi$
$941$	−3.58022	−	1.48297i	−0.116712	−	0.0483436i	−0.440275	+	0.897863i	$0.645119\pi$
$942$		0			0
$943$	−41.9372			−1.36566
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.90171	+	4.59114i	−0.0617974	+	0.149192i	−0.951762	−	0.306838i	$-0.900729\pi$
$947$	−1.90171	+	4.59114i	−0.0617974	+	0.149192i	0.889964	+	0.456030i	$0.150729\pi$
$948$		0			0
$949$	−3.66701	+	1.51893i	−0.119036	+	0.0493064i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	16.0973	+	16.0973i	0.521441	+	0.521441i	0.918007	−	0.396565i	$-0.129798\pi$
$953$	16.0973	+	16.0973i	0.521441	+	0.521441i	−0.396565	+	0.918007i	$0.629798\pi$
$954$		0			0
$955$	−0.309451	+	0.128179i	−0.0100136	+	0.00414776i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−7.96526			−0.257212
$960$		0			0
$961$	3.28596			0.105999
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.740881	+	0.306883i	−0.0238498	+	0.00987891i
$966$		0			0
$967$	13.6682	+	13.6682i	0.439540	+	0.439540i	0.891857	−	0.452317i	$-0.149403\pi$
$967$	13.6682	+	13.6682i	0.439540	+	0.439540i	−0.452317	+	0.891857i	$0.649403\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	35.7127	−	14.7927i	1.14608	−	0.474720i	0.272860	−	0.962054i	$-0.412030\pi$
$971$	35.7127	−	14.7927i	1.14608	−	0.474720i	0.873216	+	0.487333i	$0.162030\pi$
$972$		0			0
$973$	−5.13740	+	12.4028i	−0.164698	+	0.397615i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.99623			−0.127851			−0.0639254	−	0.997955i	$-0.520362\pi$
$977$	−3.99623			−0.127851			−0.0639254	+	0.997955i	$0.520362\pi$
$978$		0			0
$979$	−1.22732	−	0.508371i	−0.0392252	−	0.0162476i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5.05054	+	5.05054i	0.161087	+	0.161087i	0.783048	−	0.621961i	$-0.213664\pi$
$983$	5.05054	+	5.05054i	0.161087	+	0.161087i	−0.621961	+	0.783048i	$0.713664\pi$
$984$		0			0
$985$	−0.844804	+	0.844804i	−0.0269177	+	0.0269177i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	14.5970	−	35.2403i	0.464158	−	1.12058i
$990$		0			0
$991$		−	45.1460i		−	1.43411i	−0.697017	−	0.717055i	$-0.745490\pi$
$991$		−	45.1460i		−	1.43411i	0.697017	−	0.717055i	$-0.254510\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.0960513	−	0.0397858i	−0.00304503	−	0.00126129i
$996$		0			0
$997$	−17.6186	−	42.5351i	−0.557987	−	1.34710i	−0.911357	−	0.411616i	$-0.864964\pi$
$997$	−17.6186	−	42.5351i	−0.557987	−	1.34710i	0.353370	−	0.935484i	$-0.385036\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.w.b.431.5		32
3.2	odd	2		1152.2.w.a.431.4		32
4.3	odd	2		288.2.w.a.35.8	✓	32
12.11	even	2		288.2.w.b.35.1	yes	32
32.11	odd	8		1152.2.w.a.719.4		32
32.21	even	8		288.2.w.b.107.1	yes	32
96.11	even	8	inner	1152.2.w.b.719.5		32
96.53	odd	8		288.2.w.a.107.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.8	✓	32	4.3	odd	2
288.2.w.a.107.8	yes	32	96.53	odd	8
288.2.w.b.35.1	yes	32	12.11	even	2
288.2.w.b.107.1	yes	32	32.21	even	8
1152.2.w.a.431.4		32	3.2	odd	2
1152.2.w.a.719.4		32	32.11	odd	8
1152.2.w.b.431.5		32	1.1	even	1	trivial
1152.2.w.b.719.5		32	96.11	even	8	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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.w (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0505677 + 0.0209458i) q^{5} +(-1.44150 - 1.44150i) q^{7} +O(q^{10})\)	\(q+(-0.0505677 + 0.0209458i) q^{5} +(-1.44150 - 1.44150i) q^{7} +(-0.320987 + 0.132957i) q^{11} +(0.623666 - 1.50566i) q^{13} -5.65026 q^{17} +(-4.13118 - 1.71119i) q^{19} +(3.03457 + 3.03457i) q^{23} +(-3.53342 + 3.53342i) q^{25} +(-0.721807 + 1.74260i) q^{29} -5.26441i q^{31} +(0.103087 + 0.0427001i) q^{35} +(-1.32038 - 3.18767i) q^{37} +(-6.90990 + 6.90990i) q^{41} +(-3.40135 - 8.21159i) q^{43} +3.23039i q^{47} -2.84413i q^{49} +(0.579972 + 1.40018i) q^{53} +(0.0134467 - 0.0134467i) q^{55} +(-4.21939 - 10.1865i) q^{59} +(-12.1464 - 5.03120i) q^{61} +0.0892011i q^{65} +(-3.34709 + 8.08060i) q^{67} +(-9.36679 + 9.36679i) q^{71} +(-1.72215 - 1.72215i) q^{73} +(0.654363 + 0.271046i) q^{77} +15.1224 q^{79} +(2.48612 - 6.00202i) q^{83} +(0.285721 - 0.118349i) q^{85} +(2.70367 + 2.70367i) q^{89} +(-3.06943 + 1.27140i) q^{91} +0.244747 q^{95} +6.43802 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{11} - 16 q^{29} - 24 q^{35} - 16 q^{53} + 32 q^{55} - 32 q^{59} + 32 q^{61} + 16 q^{67} - 16 q^{71} - 16 q^{77} + 32 q^{79} + 40 q^{83} + 48 q^{91} + 80 q^{95}+O(q^{100}) \) 32 * q + 8 * q^11 - 16 * q^29 - 24 * q^35 - 16 * q^53 + 32 * q^55 - 32 * q^59 + 32 * q^61 + 16 * q^67 - 16 * q^71 - 16 * q^77 + 32 * q^79 + 40 * q^83 + 48 * q^91 + 80 * q^95

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