LMFDB - Embedded newform 1600.2.l.h.1201.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(401,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("1600.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.l (of order $4$, degree $2$, 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1201.7
Root			$-1.40501 - 0.161069i$ of defining polynomial
Character	$\chi$	$=$	1600.1201
Dual form			1600.2.l.h.401.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86033 - 1.86033i) q^{3} -3.61392i q^{7} -3.92163i q^{9} +O(q^{10})$	$q+(1.86033 - 1.86033i) q^{3} -3.61392i q^{7} -3.92163i q^{9} +(0.0947876 + 0.0947876i) q^{11} +(2.59462 - 2.59462i) q^{13} -1.89939 q^{17} +(-2.16418 + 2.16418i) q^{19} +(-6.72307 - 6.72307i) q^{21} -5.08251i q^{23} +(-1.71452 - 1.71452i) q^{27} +(-1.25896 + 1.25896i) q^{29} +1.27453 q^{31} +0.352672 q^{33} +(2.25207 + 2.25207i) q^{37} -9.65368i q^{39} +8.52451i q^{41} +(1.61439 + 1.61439i) q^{43} -2.53884 q^{47} -6.06040 q^{49} +(-3.53349 + 3.53349i) q^{51} +(-5.67100 - 5.67100i) q^{53} +8.05215i q^{57} +(-7.81785 - 7.81785i) q^{59} +(3.46410 - 3.46410i) q^{61} -14.1724 q^{63} +(6.29856 - 6.29856i) q^{67} +(-9.45512 - 9.45512i) q^{69} -11.3074i q^{71} +16.1786i q^{73} +(0.342555 - 0.342555i) q^{77} +1.13575 q^{79} +5.38573 q^{81} +(3.75489 - 3.75489i) q^{83} +4.68417i q^{87} +3.98203i q^{89} +(-9.37674 - 9.37674i) q^{91} +(2.37103 - 2.37103i) q^{93} +10.3042 q^{97} +(0.371721 - 0.371721i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{19} - 16 q^{21} + 16 q^{29} - 16 q^{31} - 16 q^{49} + 16 q^{51} - 24 q^{59} - 32 q^{69} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 88 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^19 - 16 * q^21 + 16 * q^29 - 16 * q^31 - 16 * q^49 + 16 * q^51 - 24 * q^59 - 32 * q^69 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.86033	−	1.86033i	1.07406	−	1.07406i	0.0770310	−	0.997029i	$-0.475456\pi$
$3$	1.86033	−	1.86033i	1.07406	−	1.07406i	0.997029	−	0.0770310i	$-0.0245441\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	3.61392i		−	1.36593i	−0.730450	−	0.682966i	$-0.760690\pi$
$7$		−	3.61392i		−	1.36593i	0.730450	−	0.682966i	$-0.239310\pi$
$8$		0			0
$9$		−	3.92163i		−	1.30721i
$10$		0			0
$11$	0.0947876	+	0.0947876i	0.0285795	+	0.0285795i	0.721252	−	0.692673i	$-0.243567\pi$
$11$	0.0947876	+	0.0947876i	0.0285795	+	0.0285795i	−0.692673	+	0.721252i	$0.743567\pi$
$12$		0			0
$13$	2.59462	−	2.59462i	0.719618	−	0.719618i	−0.248909	−	0.968527i	$-0.580072\pi$
$13$	2.59462	−	2.59462i	0.719618	−	0.719618i	0.968527	+	0.248909i	$0.0800720\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.89939			−0.460671			−0.230335	−	0.973111i	$-0.573982\pi$
$17$	−1.89939			−0.460671			−0.230335	+	0.973111i	$0.573982\pi$
$18$		0			0
$19$	−2.16418	+	2.16418i	−0.496496	+	0.496496i	−0.910345	−	0.413849i	$-0.864184\pi$
$19$	−2.16418	+	2.16418i	−0.496496	+	0.496496i	0.413849	+	0.910345i	$0.364184\pi$
$20$		0			0
$21$	−6.72307	−	6.72307i	−1.46709	−	1.46709i
$22$		0			0
$23$		−	5.08251i		−	1.05978i	−0.848068	−	0.529888i	$-0.822234\pi$
$23$		−	5.08251i		−	1.05978i	0.848068	−	0.529888i	$-0.177766\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.71452	−	1.71452i	−0.329960	−	0.329960i
$28$		0			0
$29$	−1.25896	+	1.25896i	−0.233784	+	0.233784i	−0.814270	−	0.580486i	$-0.802863\pi$
$29$	−1.25896	+	1.25896i	−0.233784	+	0.233784i	0.580486	+	0.814270i	$0.302863\pi$
$30$		0			0
$31$	1.27453			0.228912			0.114456	−	0.993428i	$-0.463488\pi$
$31$	1.27453			0.228912			0.114456	+	0.993428i	$0.463488\pi$
$32$		0			0
$33$	0.352672			0.0613923
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.25207	+	2.25207i	0.370237	+	0.370237i	0.867564	−	0.497326i	$-0.165685\pi$
$37$	2.25207	+	2.25207i	0.370237	+	0.370237i	−0.497326	+	0.867564i	$0.665685\pi$
$38$		0			0
$39$		−	9.65368i		−	1.54583i
$40$		0			0
$41$			8.52451i			1.33130i	0.746262	+	0.665652i	$0.231847\pi$
$41$			8.52451i			1.33130i	−0.746262	+	0.665652i	$0.768153\pi$
$42$		0			0
$43$	1.61439	+	1.61439i	0.246192	+	0.246192i	0.819406	−	0.573214i	$-0.194304\pi$
$43$	1.61439	+	1.61439i	0.246192	+	0.246192i	−0.573214	+	0.819406i	$0.694304\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.53884			−0.370328			−0.185164	−	0.982708i	$-0.559282\pi$
$47$	−2.53884			−0.370328			−0.185164	+	0.982708i	$0.559282\pi$
$48$		0			0
$49$	−6.06040			−0.865772
$50$		0			0
$51$	−3.53349	+	3.53349i	−0.494788	+	0.494788i
$52$		0			0
$53$	−5.67100	−	5.67100i	−0.778971	−	0.778971i	0.200684	−	0.979656i	$-0.435683\pi$
$53$	−5.67100	−	5.67100i	−0.778971	−	0.778971i	−0.979656	+	0.200684i	$0.935683\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			8.05215i			1.06653i
$58$		0			0
$59$	−7.81785	−	7.81785i	−1.01780	−	1.01780i	−0.999839	−	0.0179591i	$-0.994283\pi$
$59$	−7.81785	−	7.81785i	−1.01780	−	1.01780i	−0.0179591	−	0.999839i	$-0.505717\pi$
$60$		0			0
$61$	3.46410	−	3.46410i	0.443533	−	0.443533i	−0.449665	−	0.893197i	$-0.648457\pi$
$61$	3.46410	−	3.46410i	0.443533	−	0.443533i	0.893197	+	0.449665i	$0.148457\pi$
$62$		0			0
$63$	−14.1724			−1.78556
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.29856	−	6.29856i	0.769491	−	0.769491i	−0.208526	−	0.978017i	$-0.566866\pi$
$67$	6.29856	−	6.29856i	0.769491	−	0.769491i	0.978017	+	0.208526i	$0.0668665\pi$
$68$		0			0
$69$	−9.45512	−	9.45512i	−1.13826	−	1.13826i
$70$		0			0
$71$		−	11.3074i		−	1.34194i	−0.741486	−	0.670968i	$-0.765879\pi$
$71$		−	11.3074i		−	1.34194i	0.741486	−	0.670968i	$-0.234121\pi$
$72$		0			0
$73$			16.1786i			1.89356i	0.321885	+	0.946779i	$0.395684\pi$
$73$			16.1786i			1.89356i	−0.321885	+	0.946779i	$0.604316\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.342555	−	0.342555i	0.0390377	−	0.0390377i
$78$		0			0
$79$	1.13575			0.127782			0.0638908	−	0.997957i	$-0.479649\pi$
$79$	1.13575			0.127782			0.0638908	+	0.997957i	$0.479649\pi$
$80$		0			0
$81$	5.38573			0.598414
$82$		0			0
$83$	3.75489	−	3.75489i	0.412153	−	0.412153i	−0.470335	−	0.882488i	$-0.655867\pi$
$83$	3.75489	−	3.75489i	0.412153	−	0.412153i	0.882488	+	0.470335i	$0.155867\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			4.68417i			0.502196i
$88$		0			0
$89$			3.98203i			0.422094i	0.977476	+	0.211047i	$0.0676874\pi$
$89$			3.98203i			0.422094i	−0.977476	+	0.211047i	$0.932313\pi$
$90$		0			0
$91$	−9.37674	−	9.37674i	−0.982950	−	0.982950i
$92$		0			0
$93$	2.37103	−	2.37103i	0.245865	−	0.245865i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	10.3042			1.04623			0.523117	−	0.852261i	$-0.324769\pi$
$97$	10.3042			1.04623			0.523117	+	0.852261i	$0.324769\pi$
$98$		0			0
$99$	0.371721	−	0.371721i	0.0373594	−	0.0373594i
$100$		0			0
$101$	1.25896	+	1.25896i	0.125272	+	0.125272i	0.766963	−	0.641691i	$-0.221767\pi$
$101$	1.25896	+	1.25896i	0.125272	+	0.125272i	−0.641691	+	0.766963i	$0.721767\pi$
$102$		0			0
$103$			10.8655i			1.07061i	0.844658	+	0.535306i	$0.179804\pi$
$103$			10.8655i			1.07061i	−0.844658	+	0.535306i	$0.820196\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.48167	+	9.48167i	0.916628	+	0.916628i	0.996782	−	0.0801549i	$-0.0255415\pi$
$107$	9.48167	+	9.48167i	0.916628	+	0.916628i	−0.0801549	+	0.996782i	$0.525541\pi$
$108$		0			0
$109$	8.57530	−	8.57530i	0.821365	−	0.821365i	−0.164939	−	0.986304i	$-0.552743\pi$
$109$	8.57530	−	8.57530i	0.821365	−	0.821365i	0.986304	+	0.164939i	$0.0527427\pi$
$110$		0			0
$111$	8.37915			0.795314
$112$		0			0
$113$	−12.5286			−1.17860			−0.589298	−	0.807916i	$-0.700595\pi$
$113$	−12.5286			−1.17860			−0.589298	+	0.807916i	$0.700595\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−10.1751	−	10.1751i	−0.940691	−	0.940691i
$118$		0			0
$119$			6.86425i			0.629245i
$120$		0			0
$121$		−	10.9820i		−	0.998366i
$122$		0			0
$123$	15.8584	+	15.8584i	1.42990	+	1.42990i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.94200			−0.261061			−0.130530	−	0.991444i	$-0.541668\pi$
$127$	−2.94200			−0.261061			−0.130530	+	0.991444i	$0.541668\pi$
$128$		0			0
$129$	6.00658			0.528850
$130$		0			0
$131$	−6.54333	+	6.54333i	−0.571693	+	0.571693i	−0.932601	−	0.360908i	$-0.882467\pi$
$131$	−6.54333	+	6.54333i	−0.571693	+	0.571693i	0.360908	+	0.932601i	$0.382467\pi$
$132$		0			0
$133$	7.82116	+	7.82116i	0.678180	+	0.678180i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	1.82513i		−	0.155931i	−0.996956	−	0.0779657i	$-0.975158\pi$
$137$		−	1.82513i		−	0.155931i	0.996956	−	0.0779657i	$-0.0248425\pi$
$138$		0			0
$139$	−5.36931	−	5.36931i	−0.455419	−	0.455419i	0.441729	−	0.897148i	$-0.354365\pi$
$139$	−5.36931	−	5.36931i	−0.455419	−	0.455419i	−0.897148	+	0.441729i	$0.854365\pi$
$140$		0			0
$141$	−4.72307	+	4.72307i	−0.397754	+	0.397754i
$142$		0			0
$143$	0.491875			0.0411327
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−11.2743	+	11.2743i	−0.929891	+	0.929891i
$148$		0			0
$149$	−4.37915	−	4.37915i	−0.358754	−	0.358754i	0.504600	−	0.863354i	$-0.331640\pi$
$149$	−4.37915	−	4.37915i	−0.358754	−	0.358754i	−0.863354	+	0.504600i	$0.831640\pi$
$150$		0			0
$151$			12.9610i			1.05475i	0.849631	+	0.527377i	$0.176824\pi$
$151$			12.9610i			1.05475i	−0.849631	+	0.527377i	$0.823176\pi$
$152$		0			0
$153$			7.44871i			0.602193i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.12723	−	9.12723i	0.728432	−	0.728432i	−0.241875	−	0.970307i	$-0.577762\pi$
$157$	9.12723	−	9.12723i	0.728432	−	0.728432i	0.970307	+	0.241875i	$0.0777624\pi$
$158$		0			0
$159$	−21.0998			−1.67332
$160$		0			0
$161$	−18.3678			−1.44758
$162$		0			0
$163$	−6.15099	+	6.15099i	−0.481783	+	0.481783i	−0.905701	−	0.423918i	$-0.860654\pi$
$163$	−6.15099	+	6.15099i	−0.481783	+	0.481783i	0.423918	+	0.905701i	$0.360654\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			0.710173i			0.0549548i	0.999622	+	0.0274774i	$0.00874743\pi$
$167$			0.710173i			0.0549548i	−0.999622	+	0.0274774i	$0.991253\pi$
$168$		0			0
$169$		−	0.464102i		−	0.0357001i
$170$		0			0
$171$	8.48709	+	8.48709i	0.649024	+	0.649024i
$172$		0			0
$173$	14.1773	−	14.1773i	1.07788	−	1.07788i	0.0811779	−	0.996700i	$-0.474132\pi$
$173$	14.1773	−	14.1773i	1.07788	−	1.07788i	0.996700	−	0.0811779i	$-0.0258682\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−29.0875			−2.18635
$178$		0			0
$179$	9.00502	−	9.00502i	0.673067	−	0.673067i	−0.285355	−	0.958422i	$-0.592111\pi$
$179$	9.00502	−	9.00502i	0.673067	−	0.673067i	0.958422	+	0.285355i	$0.0921115\pi$
$180$		0			0
$181$	14.1872	+	14.1872i	1.05452	+	1.05452i	0.998425	+	0.0560986i	$0.0178661\pi$
$181$	14.1872	+	14.1872i	1.05452	+	1.05452i	0.0560986	+	0.998425i	$0.482134\pi$
$182$		0			0
$183$		−	12.8887i		−	0.952761i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.180039	−	0.180039i	−0.0131657	−	0.0131657i
$188$		0			0
$189$	−6.19615	+	6.19615i	−0.450704	+	0.450704i
$190$		0			0
$191$	−18.9282			−1.36960			−0.684798	−	0.728733i	$-0.740110\pi$
$191$	−18.9282			−1.36960			−0.684798	+	0.728733i	$0.740110\pi$
$192$		0			0
$193$	21.3880			1.53954			0.769772	−	0.638319i	$-0.220370\pi$
$193$	21.3880			1.53954			0.769772	+	0.638319i	$0.220370\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.39341	+	6.39341i	0.455511	+	0.455511i	0.897179	−	0.441667i	$-0.145613\pi$
$197$	6.39341	+	6.39341i	0.455511	+	0.455511i	−0.441667	+	0.897179i	$0.645613\pi$
$198$		0			0
$199$			5.85641i			0.415150i	0.978219	+	0.207575i	$0.0665570\pi$
$199$			5.85641i			0.415150i	−0.978219	+	0.207575i	$0.933443\pi$
$200$		0			0
$201$		−	23.4347i		−	1.65296i
$202$		0			0
$203$	4.54979	+	4.54979i	0.319333	+	0.319333i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−19.9317			−1.38535
$208$		0			0
$209$	−0.410274			−0.0283793
$210$		0			0
$211$	19.2640	−	19.2640i	1.32619	−	1.32619i	0.417520	−	0.908668i	$-0.362900\pi$
$211$	19.2640	−	19.2640i	1.32619	−	1.32619i	0.908668	−	0.417520i	$-0.137100\pi$
$212$		0			0
$213$	−21.0354	−	21.0354i	−1.44132	−	1.44132i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	4.60603i		−	0.312678i
$218$		0			0
$219$	30.0974	+	30.0974i	2.03379	+	2.03379i
$220$		0			0
$221$	−4.92820	+	4.92820i	−0.331507	+	0.331507i
$222$		0			0
$223$	−20.1117			−1.34678			−0.673390	−	0.739287i	$-0.735163\pi$
$223$	−20.1117			−1.34678			−0.673390	+	0.739287i	$0.735163\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.21430	−	4.21430i	0.279713	−	0.279713i	−0.553282	−	0.832994i	$-0.686625\pi$
$227$	4.21430	−	4.21430i	0.279713	−	0.279713i	0.832994	+	0.553282i	$0.186625\pi$
$228$		0			0
$229$	18.0304	+	18.0304i	1.19148	+	1.19148i	0.976651	+	0.214833i	$0.0689207\pi$
$229$	18.0304	+	18.0304i	1.19148	+	1.19148i	0.214833	+	0.976651i	$0.431079\pi$
$230$		0			0
$231$		−	1.27453i		−	0.0838577i
$232$		0			0
$233$			4.57839i			0.299941i	0.988691	+	0.149970i	$0.0479178\pi$
$233$			4.57839i			0.299941i	−0.988691	+	0.149970i	$0.952082\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2.11286	−	2.11286i	0.137245	−	0.137245i
$238$		0			0
$239$	18.3104			1.18440			0.592200	−	0.805791i	$-0.298259\pi$
$239$	18.3104			1.18440			0.592200	+	0.805791i	$0.298259\pi$
$240$		0			0
$241$	−9.31393			−0.599963			−0.299982	−	0.953945i	$-0.596981\pi$
$241$	−9.31393			−0.599963			−0.299982	+	0.953945i	$0.596981\pi$
$242$		0			0
$243$	15.1628	−	15.1628i	0.972693	−	0.972693i
$244$		0			0
$245$		0			0
$246$		0			0
$247$			11.2304i			0.714575i
$248$		0			0
$249$		−	13.9706i		−	0.885353i
$250$		0			0
$251$	14.2156	+	14.2156i	0.897281	+	0.897281i	0.995195	−	0.0979143i	$-0.0312171\pi$
$251$	14.2156	+	14.2156i	0.897281	+	0.897281i	−0.0979143	+	0.995195i	$0.531217\pi$
$252$		0			0
$253$	0.481758	−	0.481758i	0.0302879	−	0.0302879i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	17.1347			1.06883			0.534416	−	0.845222i	$-0.320532\pi$
$257$	17.1347			1.06883			0.534416	+	0.845222i	$0.320532\pi$
$258$		0			0
$259$	8.13878	−	8.13878i	0.505719	−	0.505719i
$260$		0			0
$261$	4.93719	+	4.93719i	0.305604	+	0.305604i
$262$		0			0
$263$		−	5.11593i		−	0.315462i	−0.987482	−	0.157731i	$-0.949582\pi$
$263$		−	5.11593i		−	0.315462i	0.987482	−	0.157731i	$-0.0504179\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	7.40788	+	7.40788i	0.453355	+	0.453355i
$268$		0			0
$269$	−19.1506	+	19.1506i	−1.16763	+	1.16763i	−0.184870	+	0.982763i	$0.559186\pi$
$269$	−19.1506	+	19.1506i	−1.16763	+	1.16763i	−0.982763	+	0.184870i	$0.940814\pi$
$270$		0			0
$271$	−4.72066			−0.286760			−0.143380	−	0.989668i	$-0.545797\pi$
$271$	−4.72066			−0.286760			−0.143380	+	0.989668i	$0.545797\pi$
$272$		0			0
$273$	−34.8876			−2.11149
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−12.8887	−	12.8887i	−0.774408	−	0.774408i	0.204466	−	0.978874i	$-0.434454\pi$
$277$	−12.8887	−	12.8887i	−0.774408	−	0.774408i	−0.978874	+	0.204466i	$0.934454\pi$
$278$		0			0
$279$		−	4.99822i		−	0.299235i
$280$		0			0
$281$			16.4934i			0.983913i	0.870620	+	0.491956i	$0.163718\pi$
$281$			16.4934i			0.983913i	−0.870620	+	0.491956i	$0.836282\pi$
$282$		0			0
$283$	−7.69771	−	7.69771i	−0.457581	−	0.457581i	0.440279	−	0.897861i	$-0.354879\pi$
$283$	−7.69771	−	7.69771i	−0.457581	−	0.457581i	−0.897861	+	0.440279i	$0.854879\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	30.8069			1.81847
$288$		0			0
$289$	−13.3923			−0.787783
$290$		0			0
$291$	19.1692	−	19.1692i	1.12372	−	1.12372i
$292$		0			0
$293$	5.75538	+	5.75538i	0.336233	+	0.336233i	0.854947	−	0.518715i	$-0.173589\pi$
$293$	5.75538	+	5.75538i	0.336233	+	0.336233i	−0.518715	+	0.854947i	$0.673589\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	0.325031i		−	0.0188602i
$298$		0			0
$299$	−13.1872	−	13.1872i	−0.762634	−	0.762634i
$300$		0			0
$301$	5.83427	−	5.83427i	0.336282	−	0.336282i
$302$		0			0
$303$	4.68417			0.269098
$304$		0			0
$305$		0			0
$306$		0			0
$307$	9.60547	−	9.60547i	0.548213	−	0.548213i	−0.377711	−	0.925924i	$-0.623289\pi$
$307$	9.60547	−	9.60547i	0.548213	−	0.548213i	0.925924	+	0.377711i	$0.123289\pi$
$308$		0			0
$309$	20.2134	+	20.2134i	1.14990	+	1.14990i
$310$		0			0
$311$			20.3415i			1.15346i	0.816934	+	0.576731i	$0.195672\pi$
$311$			20.3415i			1.15346i	−0.816934	+	0.576731i	$0.804328\pi$
$312$		0			0
$313$		−	25.6414i		−	1.44934i	−0.689097	−	0.724669i	$-0.741993\pi$
$313$		−	25.6414i		−	1.44934i	0.689097	−	0.724669i	$-0.258007\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.945994	+	0.945994i	−0.0531323	+	0.0531323i	−0.733174	−	0.680041i	$-0.761962\pi$
$317$	−0.945994	+	0.945994i	−0.0531323	+	0.0531323i	0.680041	+	0.733174i	$0.261962\pi$
$318$		0			0
$319$	−0.238668			−0.0133629
$320$		0			0
$321$	35.2780			1.96903
$322$		0			0
$323$	4.11062	−	4.11062i	0.228721	−	0.228721i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	31.9057i		−	1.76439i
$328$		0			0
$329$			9.17515i			0.505843i
$330$		0			0
$331$	−6.16418	−	6.16418i	−0.338814	−	0.338814i	0.517107	−	0.855921i	$-0.327009\pi$
$331$	−6.16418	−	6.16418i	−0.338814	−	0.338814i	−0.855921	+	0.517107i	$0.827009\pi$
$332$		0			0
$333$	8.83176	−	8.83176i	0.483977	−	0.483977i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	28.2333			1.53797			0.768983	−	0.639269i	$-0.220763\pi$
$337$	28.2333			1.53797			0.768983	+	0.639269i	$0.220763\pi$
$338$		0			0
$339$	−23.3074	+	23.3074i	−1.26588	+	1.26588i
$340$		0			0
$341$	0.120809	+	0.120809i	0.00654219	+	0.00654219i
$342$		0			0
$343$		−	3.39562i		−	0.183346i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.0548	−	13.0548i	−0.700816	−	0.700816i	0.263770	−	0.964586i	$-0.415034\pi$
$347$	−13.0548	−	13.0548i	−0.700816	−	0.700816i	−0.964586	+	0.263770i	$0.915034\pi$
$348$		0			0
$349$	20.3080	−	20.3080i	1.08706	−	1.08706i	0.0912314	−	0.995830i	$-0.470920\pi$
$349$	20.3080	−	20.3080i	1.08706	−	1.08706i	0.995830	−	0.0912314i	$-0.0290803\pi$
$350$		0			0
$351$	−8.89708			−0.474891
$352$		0			0
$353$	18.6814			0.994310			0.497155	−	0.867662i	$-0.334378\pi$
$353$	18.6814			0.994310			0.497155	+	0.867662i	$0.334378\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	12.7697	+	12.7697i	0.675847	+	0.675847i
$358$		0			0
$359$			16.4072i			0.865937i	0.901409	+	0.432968i	$0.142534\pi$
$359$			16.4072i			0.865937i	−0.901409	+	0.432968i	$0.857466\pi$
$360$		0			0
$361$			9.63268i			0.506983i
$362$		0			0
$363$	−20.4302	−	20.4302i	−1.07231	−	1.07231i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−3.58049			−0.186900			−0.0934500	−	0.995624i	$-0.529790\pi$
$367$	−3.58049			−0.186900			−0.0934500	+	0.995624i	$0.529790\pi$
$368$		0			0
$369$	33.4299			1.74029
$370$		0			0
$371$	−20.4945	+	20.4945i	−1.06402	+	1.06402i
$372$		0			0
$373$	−8.72985	−	8.72985i	−0.452015	−	0.452015i	0.444008	−	0.896023i	$-0.353556\pi$
$373$	−8.72985	−	8.72985i	−0.452015	−	0.452015i	−0.896023	+	0.444008i	$0.853556\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			6.53307i			0.336470i
$378$		0			0
$379$	6.11276	+	6.11276i	0.313991	+	0.313991i	0.846454	−	0.532462i	$-0.178733\pi$
$379$	6.11276	+	6.11276i	0.313991	+	0.313991i	−0.532462	+	0.846454i	$0.678733\pi$
$380$		0			0
$381$	−5.47309	+	5.47309i	−0.280395	+	0.280395i
$382$		0			0
$383$	7.31434			0.373745			0.186873	−	0.982384i	$-0.440165\pi$
$383$	7.31434			0.373745			0.186873	+	0.982384i	$0.440165\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.33103	−	6.33103i	0.321824	−	0.321824i
$388$		0			0
$389$	9.74166	+	9.74166i	0.493922	+	0.493922i	0.909539	−	0.415618i	$-0.136435\pi$
$389$	9.74166	+	9.74166i	0.493922	+	0.493922i	−0.415618	+	0.909539i	$0.636435\pi$
$390$		0			0
$391$			9.65368i			0.488207i
$392$		0			0
$393$			24.3454i			1.22807i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.04203	+	8.04203i	−0.403618	+	0.403618i	−0.879506	−	0.475888i	$-0.842127\pi$
$397$	−8.04203	+	8.04203i	−0.403618	+	0.403618i	0.475888	+	0.879506i	$0.342127\pi$
$398$		0			0
$399$	29.0998			1.45681
$400$		0			0
$401$	−6.77627			−0.338391			−0.169195	−	0.985583i	$-0.554117\pi$
$401$	−6.77627			−0.338391			−0.169195	+	0.985583i	$0.554117\pi$
$402$		0			0
$403$	3.30691	−	3.30691i	0.164729	−	0.164729i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			0.426936i			0.0211624i
$408$		0			0
$409$			16.2601i			0.804010i	0.915637	+	0.402005i	$0.131687\pi$
$409$			16.2601i			0.804010i	−0.915637	+	0.402005i	$0.868313\pi$
$410$		0			0
$411$	−3.39534	−	3.39534i	−0.167480	−	0.167480i
$412$		0			0
$413$	−28.2531	+	28.2531i	−1.39024	+	1.39024i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−19.9773			−0.978295
$418$		0			0
$419$	−10.1408	+	10.1408i	−0.495409	+	0.495409i	−0.910005	−	0.414596i	$-0.863923\pi$
$419$	−10.1408	+	10.1408i	−0.495409	+	0.495409i	0.414596	+	0.910005i	$0.363923\pi$
$420$		0			0
$421$	−13.5849	−	13.5849i	−0.662088	−	0.662088i	0.293784	−	0.955872i	$-0.405085\pi$
$421$	−13.5849	−	13.5849i	−0.662088	−	0.662088i	−0.955872	+	0.293784i	$0.905085\pi$
$422$		0			0
$423$			9.95637i			0.484095i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−12.5190	−	12.5190i	−0.605836	−	0.605836i
$428$		0			0
$429$	0.915049	−	0.915049i	0.0441790	−	0.0441790i
$430$		0			0
$431$	−1.37612			−0.0662853			−0.0331427	−	0.999451i	$-0.510552\pi$
$431$	−1.37612			−0.0662853			−0.0331427	+	0.999451i	$0.510552\pi$
$432$		0			0
$433$	19.9307			0.957810			0.478905	−	0.877867i	$-0.341034\pi$
$433$	19.9307			0.957810			0.478905	+	0.877867i	$0.341034\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10.9994	+	10.9994i	0.526175	+	0.526175i
$438$		0			0
$439$			25.4133i			1.21291i	0.795117	+	0.606455i	$0.207409\pi$
$439$			25.4133i			1.21291i	−0.795117	+	0.606455i	$0.792591\pi$
$440$		0			0
$441$			23.7666i			1.13174i
$442$		0			0
$443$	24.7208	+	24.7208i	1.17452	+	1.17452i	0.981120	+	0.193402i	$0.0619522\pi$
$443$	24.7208	+	24.7208i	1.17452	+	1.17452i	0.193402	+	0.981120i	$0.438048\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−16.2933			−0.770646
$448$		0			0
$449$	−5.62743			−0.265575			−0.132787	−	0.991145i	$-0.542393\pi$
$449$	−5.62743			−0.265575			−0.132787	+	0.991145i	$0.542393\pi$
$450$		0			0
$451$	−0.808017	+	0.808017i	−0.0380481	+	0.0380481i
$452$		0			0
$453$	24.1117	+	24.1117i	1.13287	+	1.13287i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			26.6040i			1.24448i	0.782825	+	0.622241i	$0.213778\pi$
$457$			26.6040i			1.24448i	−0.782825	+	0.622241i	$0.786222\pi$
$458$		0			0
$459$	3.25656	+	3.25656i	0.152003	+	0.152003i
$460$		0			0
$461$	11.9468	−	11.9468i	0.556418	−	0.556418i	−0.371868	−	0.928286i	$-0.621283\pi$
$461$	11.9468	−	11.9468i	0.556418	−	0.556418i	0.928286	+	0.371868i	$0.121283\pi$
$462$		0			0
$463$	−0.530134			−0.0246374			−0.0123187	−	0.999924i	$-0.503921\pi$
$463$	−0.530134			−0.0246374			−0.0123187	+	0.999924i	$0.503921\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.4219	+	11.4219i	−0.528542	+	0.528542i	−0.920138	−	0.391595i	$-0.871923\pi$
$467$	−11.4219	+	11.4219i	−0.528542	+	0.528542i	0.391595	+	0.920138i	$0.371923\pi$
$468$		0			0
$469$	−22.7625	−	22.7625i	−1.05107	−	1.05107i
$470$		0			0
$471$		−	33.9592i		−	1.56476i
$472$		0			0
$473$			0.306048i			0.0140721i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−22.2395	+	22.2395i	−1.01828	+	1.01828i
$478$		0			0
$479$	6.37434			0.291251			0.145625	−	0.989340i	$-0.453481\pi$
$479$	6.37434			0.291251			0.145625	+	0.989340i	$0.453481\pi$
$480$		0			0
$481$	11.6865			0.532859
$482$		0			0
$483$	−34.1700	+	34.1700i	−1.55479	+	1.55479i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			31.3203i			1.41926i	0.704575	+	0.709629i	$0.251138\pi$
$487$			31.3203i			1.41926i	−0.704575	+	0.709629i	$0.748862\pi$
$488$		0			0
$489$			22.8857i			1.03493i
$490$		0			0
$491$	−14.0893	−	14.0893i	−0.635843	−	0.635843i	0.313684	−	0.949527i	$-0.398437\pi$
$491$	−14.0893	−	14.0893i	−0.635843	−	0.635843i	−0.949527	+	0.313684i	$0.898437\pi$
$492$		0			0
$493$	2.39127	−	2.39127i	0.107697	−	0.107697i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−40.8639			−1.83299
$498$		0			0
$499$	−2.30233	+	2.30233i	−0.103067	+	0.103067i	−0.756760	−	0.653693i	$-0.773219\pi$
$499$	−2.30233	+	2.30233i	−0.103067	+	0.103067i	0.653693	+	0.756760i	$0.273219\pi$
$500$		0			0
$501$	1.32115	+	1.32115i	0.0590248	+	0.0590248i
$502$		0			0
$503$			14.7556i			0.657921i	0.944344	+	0.328961i	$0.106698\pi$
$503$			14.7556i			0.657921i	−0.944344	+	0.328961i	$0.893302\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.863380	−	0.863380i	−0.0383441	−	0.0383441i
$508$		0			0
$509$	8.03042	−	8.03042i	0.355942	−	0.355942i	−0.506373	−	0.862315i	$-0.669014\pi$
$509$	8.03042	−	8.03042i	0.355942	−	0.355942i	0.862315	+	0.506373i	$0.169014\pi$
$510$		0			0
$511$	58.4680			2.58647
$512$		0			0
$513$	7.42107			0.327648
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.240650	−	0.240650i	−0.0105838	−	0.0105838i
$518$		0			0
$519$		−	52.7487i		−	2.31541i
$520$		0			0
$521$			13.7417i			0.602033i	0.953619	+	0.301017i	$0.0973259\pi$
$521$			13.7417i			0.602033i	−0.953619	+	0.301017i	$0.902674\pi$
$522$		0			0
$523$	−6.77116	−	6.77116i	−0.296082	−	0.296082i	0.543395	−	0.839477i	$-0.317139\pi$
$523$	−6.77116	−	6.77116i	−0.296082	−	0.296082i	−0.839477	+	0.543395i	$0.817139\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.42083			−0.105453
$528$		0			0
$529$	−2.83186			−0.123124
$530$		0			0
$531$	−30.6587	+	30.6587i	−1.33047	+	1.33047i
$532$		0			0
$533$	22.1179	+	22.1179i	0.958030	+	0.958030i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		−	33.5046i		−	1.44583i
$538$		0			0
$539$	−0.574451	−	0.574451i	−0.0247434	−	0.0247434i
$540$		0			0
$541$	7.82599	−	7.82599i	0.336465	−	0.336465i	−0.518570	−	0.855035i	$-0.673535\pi$
$541$	7.82599	−	7.82599i	0.336465	−	0.336465i	0.855035	+	0.518570i	$0.173535\pi$
$542$		0			0
$543$	52.7855			2.26524
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−16.1263	+	16.1263i	−0.689511	+	0.689511i	−0.962124	−	0.272613i	$-0.912112\pi$
$547$	−16.1263	+	16.1263i	−0.689511	+	0.689511i	0.272613	+	0.962124i	$0.412112\pi$
$548$		0			0
$549$	−13.5849	−	13.5849i	−0.579790	−	0.579790i
$550$		0			0
$551$		−	5.44924i		−	0.232146i
$552$		0			0
$553$		−	4.10450i		−	0.174541i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.7333	−	13.7333i	0.581897	−	0.581897i	−0.353527	−	0.935424i	$-0.615018\pi$
$557$	13.7333	−	13.7333i	0.581897	−	0.581897i	0.935424	+	0.353527i	$0.115018\pi$
$558$		0			0
$559$	8.37745			0.354328
$560$		0			0
$561$	−0.669862			−0.0282816
$562$		0			0
$563$	−13.2023	+	13.2023i	−0.556412	+	0.556412i	−0.928284	−	0.371872i	$-0.878716\pi$
$563$	−13.2023	+	13.2023i	−0.556412	+	0.556412i	0.371872	+	0.928284i	$0.378716\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	19.4636i		−	0.817393i
$568$		0			0
$569$			7.32481i			0.307072i	0.988143	+	0.153536i	$0.0490661\pi$
$569$			7.32481i			0.307072i	−0.988143	+	0.153536i	$0.950934\pi$
$570$		0			0
$571$	22.1916	+	22.1916i	0.928688	+	0.928688i	0.997621	−	0.0689332i	$-0.0219595\pi$
$571$	22.1916	+	22.1916i	0.928688	+	0.928688i	−0.0689332	+	0.997621i	$0.521960\pi$
$572$		0			0
$573$	−35.2126	+	35.2126i	−1.47103	+	1.47103i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	9.39473			0.391108			0.195554	−	0.980693i	$-0.437350\pi$
$577$	9.39473			0.391108			0.195554	+	0.980693i	$0.437350\pi$
$578$		0			0
$579$	39.7887	−	39.7887i	1.65356	−	1.65356i
$580$		0			0
$581$	−13.5699	−	13.5699i	−0.562973	−	0.562973i
$582$		0			0
$583$		−	1.07508i		−	0.0445253i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	10.7246	+	10.7246i	0.442650	+	0.442650i	0.892902	−	0.450252i	$-0.148666\pi$
$587$	10.7246	+	10.7246i	0.442650	+	0.442650i	−0.450252	+	0.892902i	$0.648666\pi$
$588$		0			0
$589$	−2.75830	+	2.75830i	−0.113654	+	0.113654i
$590$		0			0
$591$	23.7876			0.978493
$592$		0			0
$593$	−38.2253			−1.56973			−0.784863	−	0.619670i	$-0.787267\pi$
$593$	−38.2253			−1.56973			−0.784863	+	0.619670i	$0.787267\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	10.8948	+	10.8948i	0.445896	+	0.445896i
$598$		0			0
$599$			41.5801i			1.69892i	0.527656	+	0.849458i	$0.323071\pi$
$599$			41.5801i			1.69892i	−0.527656	+	0.849458i	$0.676929\pi$
$600$		0			0
$601$		−	23.1081i		−	0.942599i	−0.881973	−	0.471299i	$-0.843785\pi$
$601$		−	23.1081i		−	0.942599i	0.881973	−	0.471299i	$-0.156215\pi$
$602$		0			0
$603$	−24.7006	−	24.7006i	−1.00589	−	1.00589i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	15.1150			0.613500			0.306750	−	0.951790i	$-0.400759\pi$
$607$	15.1150			0.613500			0.306750	+	0.951790i	$0.400759\pi$
$608$		0			0
$609$	16.9282			0.685965
$610$		0			0
$611$	−6.58732	+	6.58732i	−0.266494	+	0.266494i
$612$		0			0
$613$	1.18710	+	1.18710i	0.0479466	+	0.0479466i	0.730674	−	0.682727i	$-0.239206\pi$
$613$	1.18710	+	1.18710i	0.0479466	+	0.0479466i	−0.682727	+	0.730674i	$0.739206\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			5.23711i			0.210838i	0.994428	+	0.105419i	$0.0336184\pi$
$617$			5.23711i			0.210838i	−0.994428	+	0.105419i	$0.966382\pi$
$618$		0			0
$619$	−6.52847	−	6.52847i	−0.262401	−	0.262401i	0.563628	−	0.826029i	$-0.309405\pi$
$619$	−6.52847	−	6.52847i	−0.262401	−	0.262401i	−0.826029	+	0.563628i	$0.809405\pi$
$620$		0			0
$621$	−8.71408	+	8.71408i	−0.349684	+	0.349684i
$622$		0			0
$623$	14.3907			0.576553
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.763244	+	0.763244i	−0.0304810	+	0.0304810i
$628$		0			0
$629$	−4.27756	−	4.27756i	−0.170557	−	0.170557i
$630$		0			0
$631$		−	21.7193i		−	0.864633i	−0.901722	−	0.432316i	$-0.857696\pi$
$631$		−	21.7193i		−	0.864633i	0.901722	−	0.432316i	$-0.142304\pi$
$632$		0			0
$633$		−	71.6746i		−	2.84881i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−15.7244	+	15.7244i	−0.623025	+	0.623025i
$638$		0			0
$639$	−44.3432			−1.75419
$640$		0			0
$641$	−45.3927			−1.79291			−0.896453	−	0.443139i	$-0.853865\pi$
$641$	−45.3927			−1.79291			−0.896453	+	0.443139i	$0.853865\pi$
$642$		0			0
$643$	20.5408	−	20.5408i	0.810049	−	0.810049i	−0.174592	−	0.984641i	$-0.555861\pi$
$643$	20.5408	−	20.5408i	0.810049	−	0.810049i	0.984641	+	0.174592i	$0.0558607\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	31.7472i		−	1.24811i	−0.781379	−	0.624056i	$-0.785484\pi$
$647$		−	31.7472i		−	1.24811i	0.781379	−	0.624056i	$-0.214516\pi$
$648$		0			0
$649$		−	1.48207i		−	0.0581764i
$650$		0			0
$651$	−8.56873	−	8.56873i	−0.335835	−	0.335835i
$652$		0			0
$653$	4.30078	−	4.30078i	0.168302	−	0.168302i	−0.617930	−	0.786233i	$-0.712029\pi$
$653$	4.30078	−	4.30078i	0.168302	−	0.168302i	0.786233	+	0.617930i	$0.212029\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	63.4463			2.47527
$658$		0			0
$659$	−18.2156	+	18.2156i	−0.709579	+	0.709579i	−0.966447	−	0.256868i	$-0.917310\pi$
$659$	−18.2156	+	18.2156i	−0.709579	+	0.709579i	0.256868	+	0.966447i	$0.417310\pi$
$660$		0			0
$661$	−19.7679	−	19.7679i	−0.768883	−	0.768883i	0.209027	−	0.977910i	$-0.432970\pi$
$661$	−19.7679	−	19.7679i	−0.768883	−	0.768883i	−0.977910	+	0.209027i	$0.932970\pi$
$662$		0			0
$663$			18.3361i			0.712116i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	6.39869	+	6.39869i	0.247758	+	0.247758i
$668$		0			0
$669$	−37.4144	+	37.4144i	−1.44652	+	1.44652i
$670$		0			0
$671$	0.656708			0.0253519
$672$		0			0
$673$	−8.43246			−0.325047			−0.162524	−	0.986705i	$-0.551963\pi$
$673$	−8.43246			−0.325047			−0.162524	+	0.986705i	$0.551963\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−20.8693	−	20.8693i	−0.802073	−	0.802073i	0.181346	−	0.983419i	$-0.441954\pi$
$677$	−20.8693	−	20.8693i	−0.802073	−	0.802073i	−0.983419	+	0.181346i	$0.941954\pi$
$678$		0			0
$679$		−	37.2386i		−	1.42909i
$680$		0			0
$681$		−	15.6799i		−	0.600856i
$682$		0			0
$683$	−16.4398	−	16.4398i	−0.629051	−	0.629051i	0.318778	−	0.947829i	$-0.396728\pi$
$683$	−16.4398	−	16.4398i	−0.629051	−	0.629051i	−0.947829	+	0.318778i	$0.896728\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	67.0849			2.55945
$688$		0			0
$689$	−29.4282			−1.12112
$690$		0			0
$691$	−17.4076	+	17.4076i	−0.662216	+	0.662216i	−0.955902	−	0.293686i	$-0.905118\pi$
$691$	−17.4076	+	17.4076i	−0.662216	+	0.662216i	0.293686	+	0.955902i	$0.405118\pi$
$692$		0			0
$693$	−1.34337	−	1.34337i	−0.0510304	−	0.0510304i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	16.1914i		−	0.613293i
$698$		0			0
$699$	8.51731	+	8.51731i	0.322154	+	0.322154i
$700$		0			0
$701$	−25.3888	+	25.3888i	−0.958920	+	0.958920i	−0.999189	−	0.0402687i	$-0.987179\pi$
$701$	−25.3888	+	25.3888i	−0.958920	+	0.958920i	0.0402687	+	0.999189i	$0.487179\pi$
$702$		0			0
$703$	−9.74773			−0.367643
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.54979	−	4.54979i	0.171113	−	0.171113i
$708$		0			0
$709$	−17.6201	−	17.6201i	−0.661738	−	0.661738i	0.294051	−	0.955790i	$-0.404996\pi$
$709$	−17.6201	−	17.6201i	−0.661738	−	0.661738i	−0.955790	+	0.294051i	$0.904996\pi$
$710$		0			0
$711$		−	4.45398i		−	0.167037i
$712$		0			0
$713$		−	6.47779i		−	0.242595i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	34.0633	−	34.0633i	1.27212	−	1.27212i
$718$		0			0
$719$	−42.6068			−1.58896			−0.794482	−	0.607287i	$-0.792258\pi$
$719$	−42.6068			−1.58896			−0.794482	+	0.607287i	$0.792258\pi$
$720$		0			0
$721$	39.2671			1.46238
$722$		0			0
$723$	−17.3269	+	17.3269i	−0.644396	+	0.644396i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			50.5830i			1.87602i	0.346609	+	0.938010i	$0.387333\pi$
$727$			50.5830i			1.87602i	−0.346609	+	0.938010i	$0.612667\pi$
$728$		0			0
$729$		−	40.2583i		−	1.49105i
$730$		0			0
$731$	−3.06636	−	3.06636i	−0.113413	−	0.113413i
$732$		0			0
$733$	6.17299	−	6.17299i	0.228005	−	0.228005i	−0.583854	−	0.811859i	$-0.698456\pi$
$733$	6.17299	−	6.17299i	0.228005	−	0.228005i	0.811859	+	0.583854i	$0.198456\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.19405			0.0439834
$738$		0			0
$739$	22.8974	−	22.8974i	0.842293	−	0.842293i	−0.146864	−	0.989157i	$-0.546918\pi$
$739$	22.8974	−	22.8974i	0.842293	−	0.842293i	0.989157	+	0.146864i	$0.0469178\pi$
$740$		0			0
$741$	20.8923	+	20.8923i	0.767497	+	0.767497i
$742$		0			0
$743$		−	11.8975i		−	0.436478i	−0.975895	−	0.218239i	$-0.929969\pi$
$743$		−	11.8975i		−	0.436478i	0.975895	−	0.218239i	$-0.0700312\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−14.7253	−	14.7253i	−0.538770	−	0.538770i
$748$		0			0
$749$	34.2660	−	34.2660i	1.25205	−	1.25205i
$750$		0			0
$751$	−23.4102			−0.854250			−0.427125	−	0.904193i	$-0.640474\pi$
$751$	−23.4102			−0.854250			−0.427125	+	0.904193i	$0.640474\pi$
$752$		0			0
$753$	52.8913			1.92747
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−11.3218	−	11.3218i	−0.411496	−	0.411496i	0.470763	−	0.882260i	$-0.343979\pi$
$757$	−11.3218	−	11.3218i	−0.411496	−	0.411496i	−0.882260	+	0.470763i	$0.843979\pi$
$758$		0			0
$759$		−	1.79246i		−	0.0650620i
$760$		0			0
$761$		−	8.53590i		−	0.309426i	−0.987959	−	0.154713i	$-0.950555\pi$
$761$		−	8.53590i		−	0.309426i	0.987959	−	0.154713i	$-0.0494453\pi$
$762$		0			0
$763$	−30.9904	−	30.9904i	−1.12193	−	1.12193i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−40.5687			−1.46485
$768$		0			0
$769$	17.8384			0.643270			0.321635	−	0.946864i	$-0.395768\pi$
$769$	17.8384			0.643270			0.321635	+	0.946864i	$0.395768\pi$
$770$		0			0
$771$	31.8761	−	31.8761i	1.14799	−	1.14799i
$772$		0			0
$773$	−23.9457	−	23.9457i	−0.861267	−	0.861267i	0.130219	−	0.991485i	$-0.458432\pi$
$773$	−23.9457	−	23.9457i	−0.861267	−	0.861267i	−0.991485	+	0.130219i	$0.958432\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		−	30.2816i		−	1.08635i
$778$		0			0
$779$	−18.4485	−	18.4485i	−0.660988	−	0.660988i
$780$		0			0
$781$	1.07180	−	1.07180i	0.0383519	−	0.0383519i
$782$		0			0
$783$	4.31705			0.154279
$784$		0			0
$785$		0			0
$786$		0			0
$787$	32.3914	−	32.3914i	1.15463	−	1.15463i	0.169014	−	0.985614i	$-0.445942\pi$
$787$	32.3914	−	32.3914i	1.15463	−	1.15463i	0.985614	−	0.169014i	$-0.0540582\pi$
$788$		0			0
$789$	−9.51731	−	9.51731i	−0.338825	−	0.338825i
$790$		0			0
$791$			45.2775i			1.60988i
$792$		0			0
$793$		−	17.9761i		−	0.638348i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.92658	+	1.92658i	−0.0682428	+	0.0682428i	−0.740404	−	0.672162i	$-0.765366\pi$
$797$	−1.92658	+	1.92658i	−0.0682428	+	0.0682428i	0.672162	+	0.740404i	$0.265366\pi$
$798$		0			0
$799$	4.82225			0.170599
$800$		0			0
$801$	15.6160			0.551765
$802$		0			0
$803$	−1.53353	+	1.53353i	−0.0541170	+	0.0541170i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			71.2527i			2.50822i
$808$		0			0
$809$		−	49.8993i		−	1.75437i	−0.480157	−	0.877183i	$-0.659420\pi$
$809$		−	49.8993i		−	1.75437i	0.480157	−	0.877183i	$-0.340580\pi$
$810$		0			0
$811$	−22.9363	−	22.9363i	−0.805401	−	0.805401i	0.178533	−	0.983934i	$-0.442865\pi$
$811$	−22.9363	−	22.9363i	−0.805401	−	0.805401i	−0.983934	+	0.178533i	$0.942865\pi$
$812$		0			0
$813$	−8.78196	+	8.78196i	−0.307997	+	0.307997i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−6.98764			−0.244467
$818$		0			0
$819$	−36.7721	+	36.7721i	−1.28492	+	1.28492i
$820$		0			0
$821$	10.7321	+	10.7321i	0.374551	+	0.374551i	0.869132	−	0.494581i	$-0.164678\pi$
$821$	10.7321	+	10.7321i	0.374551	+	0.374551i	−0.494581	+	0.869132i	$0.664678\pi$
$822$		0			0
$823$		−	8.56875i		−	0.298688i	−0.988785	−	0.149344i	$-0.952284\pi$
$823$		−	8.56875i		−	0.298688i	0.988785	−	0.149344i	$-0.0477162\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.0841	+	10.0841i	0.350660	+	0.350660i	0.860355	−	0.509695i	$-0.170242\pi$
$827$	10.0841	+	10.0841i	0.350660	+	0.350660i	−0.509695	+	0.860355i	$0.670242\pi$
$828$		0			0
$829$	−0.656708	+	0.656708i	−0.0228084	+	0.0228084i	−0.718419	−	0.695611i	$-0.755134\pi$
$829$	−0.656708	+	0.656708i	−0.0228084	+	0.0228084i	0.695611	+	0.718419i	$0.255134\pi$
$830$		0			0
$831$	−47.9544			−1.66352
$832$		0			0
$833$	11.5111			0.398836
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.18521	−	2.18521i	−0.0755318	−	0.0755318i
$838$		0			0
$839$		−	5.41206i		−	0.186845i	−0.995627	−	0.0934225i	$-0.970219\pi$
$839$		−	5.41206i		−	0.186845i	0.995627	−	0.0934225i	$-0.0297807\pi$
$840$		0			0
$841$			25.8300i			0.890690i
$842$		0			0
$843$	30.6831	+	30.6831i	1.05678	+	1.05678i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−39.6882			−1.36370
$848$		0			0
$849$	−28.6405			−0.982939
$850$		0			0
$851$	11.4461	−	11.4461i	0.392368	−	0.392368i
$852$		0			0
$853$	−17.0301	−	17.0301i	−0.583098	−	0.583098i	0.352655	−	0.935753i	$-0.385279\pi$
$853$	−17.0301	−	17.0301i	−0.583098	−	0.583098i	−0.935753	+	0.352655i	$0.885279\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	53.1079i		−	1.81413i	−0.420988	−	0.907066i	$-0.638317\pi$
$857$		−	53.1079i		−	1.81413i	0.420988	−	0.907066i	$-0.361683\pi$
$858$		0			0
$859$	−10.7609	−	10.7609i	−0.367158	−	0.367158i	0.499282	−	0.866440i	$-0.333597\pi$
$859$	−10.7609	−	10.7609i	−0.367158	−	0.367158i	−0.866440	+	0.499282i	$0.833597\pi$
$860$		0			0
$861$	57.3108	−	57.3108i	1.95315	−	1.95315i
$862$		0			0
$863$	21.2106			0.722016			0.361008	−	0.932563i	$-0.382433\pi$
$863$	21.2106			0.722016			0.361008	+	0.932563i	$0.382433\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−24.9141	+	24.9141i	−0.846126	+	0.846126i
$868$		0			0
$869$	0.107655	+	0.107655i	0.00365194	+	0.00365194i
$870$		0			0
$871$		−	32.6847i		−	1.10748i
$872$		0			0
$873$		−	40.4093i		−	1.36765i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−25.6041	+	25.6041i	−0.864589	+	0.864589i	−0.991867	−	0.127278i	$-0.959376\pi$
$877$	−25.6041	+	25.6041i	−0.864589	+	0.864589i	0.127278	+	0.991867i	$0.459376\pi$
$878$		0			0
$879$	21.4138			0.722268
$880$		0			0
$881$	−13.0675			−0.440255			−0.220128	−	0.975471i	$-0.570647\pi$
$881$	−13.0675			−0.440255			−0.220128	+	0.975471i	$0.570647\pi$
$882$		0			0
$883$	−12.1957	+	12.1957i	−0.410419	+	0.410419i	−0.881884	−	0.471466i	$-0.843725\pi$
$883$	−12.1957	+	12.1957i	−0.410419	+	0.410419i	0.471466	+	0.881884i	$0.343725\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	36.3716i		−	1.22124i	−0.791924	−	0.610619i	$-0.790921\pi$
$887$		−	36.3716i		−	1.22124i	0.791924	−	0.610619i	$-0.209079\pi$
$888$		0			0
$889$			10.6322i			0.356591i
$890$		0			0
$891$	0.510500	+	0.510500i	0.0171024	+	0.0171024i
$892$		0			0
$893$	5.49449	−	5.49449i	0.183866	−	0.183866i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−49.0649			−1.63823
$898$		0			0
$899$	−1.60458	+	1.60458i	−0.0535159	+	0.0535159i
$900$		0			0
$901$	10.7715	+	10.7715i	0.358849	+	0.358849i
$902$		0			0
$903$		−	21.7073i		−	0.722373i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−35.4831	−	35.4831i	−1.17820	−	1.17820i	−0.980203	−	0.197996i	$-0.936557\pi$
$907$	−35.4831	−	35.4831i	−1.17820	−	1.17820i	−0.197996	−	0.980203i	$-0.563443\pi$
$908$		0			0
$909$	4.93719	−	4.93719i	0.163756	−	0.163756i
$910$		0			0
$911$	−22.6536			−0.750547			−0.375274	−	0.926914i	$-0.622451\pi$
$911$	−22.6536			−0.750547			−0.375274	+	0.926914i	$0.622451\pi$
$912$		0			0
$913$	0.711834			0.0235583
$914$		0			0
$915$		0			0
$916$		0			0
$917$	23.6470	+	23.6470i	0.780894	+	0.780894i
$918$		0			0
$919$		−	19.9532i		−	0.658195i	−0.944296	−	0.329097i	$-0.893256\pi$
$919$		−	19.9532i		−	0.658195i	0.944296	−	0.329097i	$-0.106744\pi$
$920$		0			0
$921$		−	35.7386i		−	1.17763i
$922$		0			0
$923$	−29.3383	−	29.3383i	−0.965681	−	0.965681i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	42.6105			1.39951
$928$		0			0
$929$	−11.0293			−0.361859			−0.180929	−	0.983496i	$-0.557911\pi$
$929$	−11.0293			−0.361859			−0.180929	+	0.983496i	$0.557911\pi$
$930$		0			0
$931$	13.1158	−	13.1158i	0.429853	−	0.429853i
$932$		0			0
$933$	37.8418	+	37.8418i	1.23889	+	1.23889i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			36.6851i			1.19845i	0.800581	+	0.599225i	$0.204524\pi$
$937$			36.6851i			1.19845i	−0.800581	+	0.599225i	$0.795476\pi$
$938$		0			0
$939$	−47.7014	−	47.7014i	−1.55668	−	1.55668i
$940$		0			0
$941$	−26.8618	+	26.8618i	−0.875671	+	0.875671i	−0.993083	−	0.117412i	$-0.962540\pi$
$941$	−26.8618	+	26.8618i	−0.875671	+	0.875671i	0.117412	+	0.993083i	$0.462540\pi$
$942$		0			0
$943$	43.3258			1.41088
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−42.0944	+	42.0944i	−1.36788	+	1.36788i	−0.504433	+	0.863451i	$0.668299\pi$
$947$	−42.0944	+	42.0944i	−1.36788	+	1.36788i	−0.863451	+	0.504433i	$0.831701\pi$
$948$		0			0
$949$	41.9772	+	41.9772i	1.36264	+	1.36264i
$950$		0			0
$951$			3.51971i			0.114135i
$952$		0			0
$953$		−	5.32619i		−	0.172532i	−0.996272	−	0.0862661i	$-0.972506\pi$
$953$		−	5.32619i		−	0.172532i	0.996272	−	0.0862661i	$-0.0274935\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−0.444001	+	0.444001i	−0.0143525	+	0.0143525i
$958$		0			0
$959$	−6.59587			−0.212992
$960$		0			0
$961$	−29.3756			−0.947599
$962$		0			0
$963$	37.1836	−	37.1836i	1.19822	−	1.19822i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	29.9668i		−	0.963667i	−0.876263	−	0.481833i	$-0.839971\pi$
$967$		−	29.9668i		−	0.963667i	0.876263	−	0.481833i	$-0.160029\pi$
$968$		0			0
$969$		−	15.2942i		−	0.491320i
$970$		0			0
$971$	−0.750872	−	0.750872i	−0.0240966	−	0.0240966i	0.694956	−	0.719052i	$-0.255424\pi$
$971$	−0.750872	−	0.750872i	−0.0240966	−	0.0240966i	−0.719052	+	0.694956i	$0.755424\pi$
$972$		0			0
$973$	−19.4043	+	19.4043i	−0.622072	+	0.622072i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−26.2513			−0.839854			−0.419927	−	0.907558i	$-0.637944\pi$
$977$	−26.2513			−0.839854			−0.419927	+	0.907558i	$0.637944\pi$
$978$		0			0
$979$	−0.377447	+	0.377447i	−0.0120633	+	0.0120633i
$980$		0			0
$981$	−33.6291	−	33.6291i	−1.07370	−	1.07370i
$982$		0			0
$983$			13.0227i			0.415360i	0.978197	+	0.207680i	$0.0665913\pi$
$983$			13.0227i			0.415360i	−0.978197	+	0.207680i	$0.933409\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	17.0688	+	17.0688i	0.543305	+	0.543305i
$988$		0			0
$989$	8.20514	−	8.20514i	0.260908	−	0.260908i
$990$		0			0
$991$	−44.7487			−1.42149			−0.710744	−	0.703451i	$-0.751642\pi$
$991$	−44.7487			−1.42149			−0.710744	+	0.703451i	$0.751642\pi$
$992$		0			0
$993$	−22.9348			−0.727813
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−21.2387	−	21.2387i	−0.672637	−	0.672637i	0.285686	−	0.958323i	$-0.407778\pi$
$997$	−21.2387	−	21.2387i	−0.672637	−	0.672637i	−0.958323	+	0.285686i	$0.907778\pi$
$998$		0			0
$999$		−	7.72244i		−	0.244327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.l.h.1201.7		16
4.3	odd	2		400.2.l.i.101.6		16
5.2	odd	4		320.2.q.c.49.2		16
5.3	odd	4		320.2.q.c.49.7		16
5.4	even	2	inner	1600.2.l.h.1201.2		16
16.3	odd	4		400.2.l.i.301.6		16
16.13	even	4	inner	1600.2.l.h.401.7		16
20.3	even	4		80.2.q.c.69.7	yes	16
20.7	even	4		80.2.q.c.69.2	yes	16
20.19	odd	2		400.2.l.i.101.3		16
40.3	even	4		640.2.q.e.609.7		16
40.13	odd	4		640.2.q.f.609.2		16
40.27	even	4		640.2.q.e.609.2		16
40.37	odd	4		640.2.q.f.609.7		16
60.23	odd	4		720.2.bm.f.469.2		16
60.47	odd	4		720.2.bm.f.469.7		16
80.3	even	4		80.2.q.c.29.2	✓	16
80.13	odd	4		320.2.q.c.209.2		16
80.19	odd	4		400.2.l.i.301.3		16
80.27	even	4		640.2.q.e.289.7		16
80.29	even	4	inner	1600.2.l.h.401.2		16
80.37	odd	4		640.2.q.f.289.2		16
80.43	even	4		640.2.q.e.289.2		16
80.53	odd	4		640.2.q.f.289.7		16
80.67	even	4		80.2.q.c.29.7	yes	16
80.77	odd	4		320.2.q.c.209.7		16
240.83	odd	4		720.2.bm.f.109.7		16
240.227	odd	4		720.2.bm.f.109.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.2	✓	16	80.3	even	4
80.2.q.c.29.7	yes	16	80.67	even	4
80.2.q.c.69.2	yes	16	20.7	even	4
80.2.q.c.69.7	yes	16	20.3	even	4
320.2.q.c.49.2		16	5.2	odd	4
320.2.q.c.49.7		16	5.3	odd	4
320.2.q.c.209.2		16	80.13	odd	4
320.2.q.c.209.7		16	80.77	odd	4
400.2.l.i.101.3		16	20.19	odd	2
400.2.l.i.101.6		16	4.3	odd	2
400.2.l.i.301.3		16	80.19	odd	4
400.2.l.i.301.6		16	16.3	odd	4
640.2.q.e.289.2		16	80.43	even	4
640.2.q.e.289.7		16	80.27	even	4
640.2.q.e.609.2		16	40.27	even	4
640.2.q.e.609.7		16	40.3	even	4
640.2.q.f.289.2		16	80.37	odd	4
640.2.q.f.289.7		16	80.53	odd	4
640.2.q.f.609.2		16	40.13	odd	4
640.2.q.f.609.7		16	40.37	odd	4
720.2.bm.f.109.2		16	240.227	odd	4
720.2.bm.f.109.7		16	240.83	odd	4
720.2.bm.f.469.2		16	60.23	odd	4
720.2.bm.f.469.7		16	60.47	odd	4
1600.2.l.h.401.2		16	80.29	even	4	inner
1600.2.l.h.401.7		16	16.13	even	4	inner
1600.2.l.h.1201.2		16	5.4	even	2	inner
1600.2.l.h.1201.7		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.86033 - 1.86033i) q^{3} -3.61392i q^{7} -3.92163i q^{9} +O(q^{10})\)	\(q+(1.86033 - 1.86033i) q^{3} -3.61392i q^{7} -3.92163i q^{9} +(0.0947876 + 0.0947876i) q^{11} +(2.59462 - 2.59462i) q^{13} -1.89939 q^{17} +(-2.16418 + 2.16418i) q^{19} +(-6.72307 - 6.72307i) q^{21} -5.08251i q^{23} +(-1.71452 - 1.71452i) q^{27} +(-1.25896 + 1.25896i) q^{29} +1.27453 q^{31} +0.352672 q^{33} +(2.25207 + 2.25207i) q^{37} -9.65368i q^{39} +8.52451i q^{41} +(1.61439 + 1.61439i) q^{43} -2.53884 q^{47} -6.06040 q^{49} +(-3.53349 + 3.53349i) q^{51} +(-5.67100 - 5.67100i) q^{53} +8.05215i q^{57} +(-7.81785 - 7.81785i) q^{59} +(3.46410 - 3.46410i) q^{61} -14.1724 q^{63} +(6.29856 - 6.29856i) q^{67} +(-9.45512 - 9.45512i) q^{69} -11.3074i q^{71} +16.1786i q^{73} +(0.342555 - 0.342555i) q^{77} +1.13575 q^{79} +5.38573 q^{81} +(3.75489 - 3.75489i) q^{83} +4.68417i q^{87} +3.98203i q^{89} +(-9.37674 - 9.37674i) q^{91} +(2.37103 - 2.37103i) q^{93} +10.3042 q^{97} +(0.371721 - 0.371721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{19} - 16 q^{21} + 16 q^{29} - 16 q^{31} - 16 q^{49} + 16 q^{51} - 24 q^{59} - 32 q^{69} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 88 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^19 - 16 * q^21 + 16 * q^29 - 16 * q^31 - 16 * q^49 + 16 * q^51 - 24 * q^59 - 32 * q^69 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 88 * q^99

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