LMFDB - Embedded newform 1600.2.q.h.849.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(49,1600)]

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, 1, 2]))

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

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

chi := DirichletCharacter("1600.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.q (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:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 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			849.4
Root			$-0.296075 - 1.38287i$ of defining polynomial
Character	$\chi$	$=$	1600.849
Dual form			1600.2.q.h.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.120009 + 0.120009i) q^{3} -2.66881 q^{7} +2.97120i q^{9} +O(q^{10})$	$q+(-0.120009 + 0.120009i) q^{3} -2.66881 q^{7} +2.97120i q^{9} +(3.49714 - 3.49714i) q^{11} +(-2.94072 + 2.94072i) q^{13} -1.85116i q^{17} +(-3.44856 - 3.44856i) q^{19} +(0.320281 - 0.320281i) q^{21} -0.707288 q^{23} +(-0.716597 - 0.716597i) q^{27} +(3.49909 + 3.49909i) q^{29} -6.84272 q^{31} +0.839377i q^{33} +(0.0975060 + 0.0975060i) q^{37} -0.705826i q^{39} -10.2052i q^{41} +(-4.43844 - 4.43844i) q^{43} -1.89428i q^{47} +0.122561 q^{49} +(0.222155 + 0.222155i) q^{51} +(-7.43897 - 7.43897i) q^{53} +0.827717 q^{57} +(0.959574 - 0.959574i) q^{59} +(6.49825 + 6.49825i) q^{61} -7.92956i q^{63} +(-3.49691 + 3.49691i) q^{67} +(0.0848809 - 0.0848809i) q^{69} -7.86777i q^{71} -15.6564 q^{73} +(-9.33322 + 9.33322i) q^{77} -6.70212 q^{79} -8.74159 q^{81} +(-3.87327 + 3.87327i) q^{83} -0.839845 q^{87} -10.5055i q^{89} +(7.84824 - 7.84824i) q^{91} +(0.821187 - 0.821187i) q^{93} -4.79937i q^{97} +(10.3907 + 10.3907i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 8 q^{11} - 8 q^{19} + 24 q^{23} + 24 q^{27} + 16 q^{29} + 16 q^{37} - 8 q^{43} + 16 q^{49} + 32 q^{51} + 16 q^{53} - 8 q^{59} + 16 q^{61} - 40 q^{67} - 16 q^{69} + 16 q^{77} + 16 q^{79} - 16 q^{81} + 40 q^{83} - 32 q^{91} + 48 q^{93} - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^7 + 8 * q^11 - 8 * q^19 + 24 * q^23 + 24 * q^27 + 16 * q^29 + 16 * q^37 - 8 * q^43 + 16 * q^49 + 32 * q^51 + 16 * q^53 - 8 * q^59 + 16 * q^61 - 40 * q^67 - 16 * q^69 + 16 * q^77 + 16 * q^79 - 16 * q^81 + 40 * q^83 - 32 * q^91 + 48 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$577$	$901$	$1151$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−0.120009	+	0.120009i	−0.0692872	+	0.0692872i	−0.740901	−	0.671614i	$-0.765601\pi$
$3$	−0.120009	+	0.120009i	−0.0692872	+	0.0692872i	0.671614	+	0.740901i	$0.265601\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.66881			−1.00872			−0.504358	−	0.863495i	$-0.668271\pi$
$7$	−2.66881			−1.00872			−0.504358	+	0.863495i	$0.668271\pi$
$8$		0			0
$9$			2.97120i			0.990399i
$10$		0			0
$11$	3.49714	−	3.49714i	1.05443	−	1.05443i	0.0559977	−	0.998431i	$-0.482166\pi$
$11$	3.49714	−	3.49714i	1.05443	−	1.05443i	0.998431	−	0.0559977i	$-0.0178339\pi$
$12$		0			0
$13$	−2.94072	+	2.94072i	−0.815610	+	0.815610i	−0.985468	−	0.169858i	$-0.945669\pi$
$13$	−2.94072	+	2.94072i	−0.815610	+	0.815610i	0.169858	+	0.985468i	$0.445669\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	1.85116i		−	0.448971i	−0.974477	−	0.224486i	$-0.927930\pi$
$17$		−	1.85116i		−	0.448971i	0.974477	−	0.224486i	$-0.0720702\pi$
$18$		0			0
$19$	−3.44856	−	3.44856i	−0.791155	−	0.791155i	0.190527	−	0.981682i	$-0.438980\pi$
$19$	−3.44856	−	3.44856i	−0.791155	−	0.791155i	−0.981682	+	0.190527i	$0.938980\pi$
$20$		0			0
$21$	0.320281	−	0.320281i	0.0698911	−	0.0698911i
$22$		0			0
$23$	−0.707288			−0.147480			−0.0737399	−	0.997278i	$-0.523493\pi$
$23$	−0.707288			−0.147480			−0.0737399	+	0.997278i	$0.523493\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.716597	−	0.716597i	−0.137909	−	0.137909i
$28$		0			0
$29$	3.49909	+	3.49909i	0.649766	+	0.649766i	0.952936	−	0.303171i	$-0.0980452\pi$
$29$	3.49909	+	3.49909i	0.649766	+	0.649766i	−0.303171	+	0.952936i	$0.598045\pi$
$30$		0			0
$31$	−6.84272			−1.22899			−0.614494	−	0.788921i	$-0.710640\pi$
$31$	−6.84272			−1.22899			−0.614494	+	0.788921i	$0.710640\pi$
$32$		0			0
$33$			0.839377i			0.146117i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.0975060	+	0.0975060i	0.0160299	+	0.0160299i	0.715076	−	0.699046i	$-0.246392\pi$
$37$	0.0975060	+	0.0975060i	0.0160299	+	0.0160299i	−0.699046	+	0.715076i	$0.746392\pi$
$38$		0			0
$39$		−	0.705826i		−	0.113023i
$40$		0			0
$41$		−	10.2052i		−	1.59379i	−0.604117	−	0.796896i	$-0.706474\pi$
$41$		−	10.2052i		−	1.59379i	0.604117	−	0.796896i	$-0.293526\pi$
$42$		0			0
$43$	−4.43844	−	4.43844i	−0.676855	−	0.676855i	0.282432	−	0.959287i	$-0.408859\pi$
$43$	−4.43844	−	4.43844i	−0.676855	−	0.676855i	−0.959287	+	0.282432i	$0.908859\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	1.89428i		−	0.276310i	−0.990411	−	0.138155i	$-0.955883\pi$
$47$		−	1.89428i		−	0.276310i	0.990411	−	0.138155i	$-0.0441172\pi$
$48$		0			0
$49$	0.122561			0.0175087
$50$		0			0
$51$	0.222155	+	0.222155i	0.0311079	+	0.0311079i
$52$		0			0
$53$	−7.43897	−	7.43897i	−1.02182	−	1.02182i	−0.999757	−	0.0220650i	$-0.992976\pi$
$53$	−7.43897	−	7.43897i	−1.02182	−	1.02182i	−0.0220650	−	0.999757i	$-0.507024\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.827717			0.109634
$58$		0			0
$59$	0.959574	−	0.959574i	0.124926	−	0.124926i	−0.641880	−	0.766805i	$-0.721845\pi$
$59$	0.959574	−	0.959574i	0.124926	−	0.124926i	0.766805	+	0.641880i	$0.221845\pi$
$60$		0			0
$61$	6.49825	+	6.49825i	0.832015	+	0.832015i	0.987792	−	0.155777i	$-0.0497881\pi$
$61$	6.49825	+	6.49825i	0.832015	+	0.832015i	−0.155777	+	0.987792i	$0.549788\pi$
$62$		0			0
$63$		−	7.92956i		−	0.999031i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.49691	+	3.49691i	−0.427216	+	0.427216i	−0.887679	−	0.460463i	$-0.847683\pi$
$67$	−3.49691	+	3.49691i	−0.427216	+	0.427216i	0.460463	+	0.887679i	$0.347683\pi$
$68$		0			0
$69$	0.0848809	−	0.0848809i	0.0102185	−	0.0102185i
$70$		0			0
$71$		−	7.86777i		−	0.933733i	−0.884328	−	0.466866i	$-0.845383\pi$
$71$		−	7.86777i		−	0.933733i	0.884328	−	0.466866i	$-0.154617\pi$
$72$		0			0
$73$	−15.6564			−1.83244			−0.916220	−	0.400675i	$-0.868776\pi$
$73$	−15.6564			−1.83244			−0.916220	+	0.400675i	$0.868776\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.33322	+	9.33322i	−1.06362	+	1.06362i
$78$		0			0
$79$	−6.70212			−0.754047			−0.377024	−	0.926204i	$-0.623052\pi$
$79$	−6.70212			−0.754047			−0.377024	+	0.926204i	$0.623052\pi$
$80$		0			0
$81$	−8.74159			−0.971288
$82$		0			0
$83$	−3.87327	+	3.87327i	−0.425147	+	0.425147i	−0.886971	−	0.461825i	$-0.847195\pi$
$83$	−3.87327	+	3.87327i	−0.425147	+	0.425147i	0.461825	+	0.886971i	$0.347195\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.839845			−0.0900408
$88$		0			0
$89$		−	10.5055i		−	1.11358i	−0.830653	−	0.556790i	$-0.812033\pi$
$89$		−	10.5055i		−	1.11358i	0.830653	−	0.556790i	$-0.187967\pi$
$90$		0			0
$91$	7.84824	−	7.84824i	0.822719	−	0.822719i
$92$		0			0
$93$	0.821187	−	0.821187i	0.0851531	−	0.0851531i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	4.79937i		−	0.487303i	−0.969863	−	0.243651i	$-0.921655\pi$
$97$		−	4.79937i		−	0.487303i	0.969863	−	0.243651i	$-0.0783453\pi$
$98$		0			0
$99$	10.3907	+	10.3907i	1.04430	+	1.04430i
$100$		0			0
$101$	0.372979	−	0.372979i	0.0371128	−	0.0371128i	−0.688307	−	0.725420i	$-0.741646\pi$
$101$	0.372979	−	0.372979i	0.0371128	−	0.0371128i	0.725420	+	0.688307i	$0.241646\pi$
$102$		0			0
$103$	−10.3013			−1.01502			−0.507508	−	0.861647i	$-0.669433\pi$
$103$	−10.3013			−1.01502			−0.507508	+	0.861647i	$0.669433\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.5069	+	14.5069i	1.40244	+	1.40244i	0.792274	+	0.610165i	$0.208897\pi$
$107$	14.5069	+	14.5069i	1.40244	+	1.40244i	0.610165	+	0.792274i	$0.291103\pi$
$108$		0			0
$109$	−0.796284	−	0.796284i	−0.0762701	−	0.0762701i	0.667943	−	0.744213i	$-0.267175\pi$
$109$	−0.796284	−	0.796284i	−0.0762701	−	0.0762701i	−0.744213	+	0.667943i	$0.767175\pi$
$110$		0			0
$111$	−0.0234032			−0.00222133
$112$		0			0
$113$			0.842524i			0.0792580i	0.999214	+	0.0396290i	$0.0126176\pi$
$113$			0.842524i			0.0792580i	−0.999214	+	0.0396290i	$0.987382\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−8.73747	−	8.73747i	−0.807779	−	0.807779i
$118$		0			0
$119$			4.94039i			0.452885i
$120$		0			0
$121$		−	13.4600i		−	1.22364i
$122$		0			0
$123$	1.22472	+	1.22472i	0.110429	+	0.110429i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	21.1693i		−	1.87847i	−0.343277	−	0.939234i	$-0.611537\pi$
$127$		−	21.1693i		−	1.87847i	0.343277	−	0.939234i	$-0.388463\pi$
$128$		0			0
$129$	1.06530			0.0937947
$130$		0			0
$131$	−4.67248	−	4.67248i	−0.408237	−	0.408237i	0.472887	−	0.881123i	$-0.343212\pi$
$131$	−4.67248	−	4.67248i	−0.408237	−	0.408237i	−0.881123	+	0.472887i	$0.843212\pi$
$132$		0			0
$133$	9.20357	+	9.20357i	0.798051	+	0.798051i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.2840			0.878623			0.439312	−	0.898335i	$-0.355222\pi$
$137$	10.2840			0.878623			0.439312	+	0.898335i	$0.355222\pi$
$138$		0			0
$139$	4.98588	−	4.98588i	0.422897	−	0.422897i	−0.463303	−	0.886200i	$-0.653336\pi$
$139$	4.98588	−	4.98588i	0.422897	−	0.422897i	0.886200	+	0.463303i	$0.153336\pi$
$140$		0			0
$141$	0.227331	+	0.227331i	0.0191447	+	0.0191447i
$142$		0			0
$143$			20.5683i			1.72001i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.0147084	+	0.0147084i	−0.00121313	+	0.00121313i
$148$		0			0
$149$	−8.79493	+	8.79493i	−0.720509	+	0.720509i	−0.968709	−	0.248200i	$-0.920161\pi$
$149$	−8.79493	+	8.79493i	−0.720509	+	0.720509i	0.248200	+	0.968709i	$0.420161\pi$
$150$		0			0
$151$			22.1838i			1.80529i	0.430385	+	0.902645i	$0.358378\pi$
$151$			22.1838i			1.80529i	−0.430385	+	0.902645i	$0.641622\pi$
$152$		0			0
$153$	5.50015			0.444661
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.72187	+	3.72187i	−0.297038	+	0.297038i	−0.839852	−	0.542815i	$-0.817359\pi$
$157$	−3.72187	+	3.72187i	−0.297038	+	0.297038i	0.542815	+	0.839852i	$0.317359\pi$
$158$		0			0
$159$	1.78549			0.141598
$160$		0			0
$161$	1.88762			0.148765
$162$		0			0
$163$	2.11630	−	2.11630i	0.165761	−	0.165761i	−0.619352	−	0.785113i	$-0.712605\pi$
$163$	2.11630	−	2.11630i	0.165761	−	0.165761i	0.785113	+	0.619352i	$0.212605\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−18.1604			−1.40530			−0.702648	−	0.711538i	$-0.747999\pi$
$167$	−18.1604			−1.40530			−0.702648	+	0.711538i	$0.747999\pi$
$168$		0			0
$169$		−	4.29572i		−	0.330440i
$170$		0			0
$171$	10.2464	−	10.2464i	0.783559	−	0.783559i
$172$		0			0
$173$	8.53542	−	8.53542i	0.648936	−	0.648936i	−0.303800	−	0.952736i	$-0.598255\pi$
$173$	8.53542	−	8.53542i	0.648936	−	0.648936i	0.952736	+	0.303800i	$0.0982555\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			0.230315i			0.0173115i
$178$		0			0
$179$	−2.42499	−	2.42499i	−0.181252	−	0.181252i	0.610649	−	0.791901i	$-0.290909\pi$
$179$	−2.42499	−	2.42499i	−0.181252	−	0.181252i	−0.791901	+	0.610649i	$0.790909\pi$
$180$		0			0
$181$	4.46593	−	4.46593i	0.331950	−	0.331950i	−0.521377	−	0.853327i	$-0.674581\pi$
$181$	4.46593	−	4.46593i	0.331950	−	0.331950i	0.853327	+	0.521377i	$0.174581\pi$
$182$		0			0
$183$	−1.55970			−0.115296
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−6.47376	−	6.47376i	−0.473408	−	0.473408i
$188$		0			0
$189$	1.91246	+	1.91246i	0.139111	+	0.139111i
$190$		0			0
$191$	−7.75030			−0.560792			−0.280396	−	0.959884i	$-0.590466\pi$
$191$	−7.75030			−0.560792			−0.280396	+	0.959884i	$0.590466\pi$
$192$		0			0
$193$		−	11.3388i		−	0.816181i	−0.912941	−	0.408091i	$-0.866195\pi$
$193$		−	11.3388i		−	0.816181i	0.912941	−	0.408091i	$-0.133805\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.10001	−	1.10001i	−0.0783725	−	0.0783725i	0.666834	−	0.745206i	$-0.267649\pi$
$197$	−1.10001	−	1.10001i	−0.0783725	−	0.0783725i	−0.745206	+	0.666834i	$0.767649\pi$
$198$		0			0
$199$			14.2722i			1.01173i	0.862614	+	0.505864i	$0.168826\pi$
$199$			14.2722i			1.01173i	−0.862614	+	0.505864i	$0.831174\pi$
$200$		0			0
$201$		−	0.839321i		−	0.0592012i
$202$		0			0
$203$	−9.33843	−	9.33843i	−0.655429	−	0.655429i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	2.10149i		−	0.146064i
$208$		0			0
$209$	−24.1203			−1.66843
$210$		0			0
$211$	12.4716	+	12.4716i	0.858577	+	0.858577i	0.991171	−	0.132593i	$-0.0423305\pi$
$211$	12.4716	+	12.4716i	0.858577	+	0.858577i	−0.132593	+	0.991171i	$0.542330\pi$
$212$		0			0
$213$	0.944203	+	0.944203i	0.0646957	+	0.0646957i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	18.2619			1.23970
$218$		0			0
$219$	1.87890	−	1.87890i	0.126965	−	0.126965i
$220$		0			0
$221$	5.44374	+	5.44374i	0.366186	+	0.366186i
$222$		0			0
$223$		−	3.08673i		−	0.206703i	−0.994645	−	0.103351i	$-0.967043\pi$
$223$		−	3.08673i		−	0.206703i	0.994645	−	0.103351i	$-0.0329566\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.31678	+	8.31678i	−0.552004	+	0.552004i	−0.927019	−	0.375015i	$-0.877638\pi$
$227$	−8.31678	+	8.31678i	−0.552004	+	0.552004i	0.375015	+	0.927019i	$0.377638\pi$
$228$		0			0
$229$	9.98910	−	9.98910i	0.660098	−	0.660098i	−0.295305	−	0.955403i	$-0.595421\pi$
$229$	9.98910	−	9.98910i	0.660098	−	0.660098i	0.955403	+	0.295305i	$0.0954212\pi$
$230$		0			0
$231$		−	2.24014i		−	0.147390i
$232$		0			0
$233$	13.9015			0.910718			0.455359	−	0.890308i	$-0.349511\pi$
$233$	13.9015			0.910718			0.455359	+	0.890308i	$0.349511\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.804314	−	0.804314i	0.0522458	−	0.0522458i
$238$		0			0
$239$	−10.7687			−0.696569			−0.348284	−	0.937389i	$-0.613236\pi$
$239$	−10.7687			−0.696569			−0.348284	+	0.937389i	$0.613236\pi$
$240$		0			0
$241$	−12.4707			−0.803305			−0.401653	−	0.915792i	$-0.631564\pi$
$241$	−12.4707			−0.803305			−0.401653	+	0.915792i	$0.631564\pi$
$242$		0			0
$243$	3.19886	−	3.19886i	0.205207	−	0.205207i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	20.2826			1.29055
$248$		0			0
$249$		−	0.929654i		−	0.0589144i
$250$		0			0
$251$	−3.69093	+	3.69093i	−0.232969	+	0.232969i	−0.813931	−	0.580962i	$-0.802677\pi$
$251$	−3.69093	+	3.69093i	−0.232969	+	0.232969i	0.580962	+	0.813931i	$0.302677\pi$
$252$		0			0
$253$	−2.47349	+	2.47349i	−0.155507	+	0.155507i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	3.11011i		−	0.194003i	−0.995284	−	0.0970016i	$-0.969075\pi$
$257$		−	3.11011i		−	0.194003i	0.995284	−	0.0970016i	$-0.0309252\pi$
$258$		0			0
$259$	−0.260225	−	0.260225i	−0.0161696	−	0.0161696i
$260$		0			0
$261$	−10.3965	+	10.3965i	−0.643527	+	0.643527i
$262$		0			0
$263$	17.9512			1.10692			0.553458	−	0.832877i	$-0.313308\pi$
$263$	17.9512			1.10692			0.553458	+	0.832877i	$0.313308\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.26075	+	1.26075i	0.0771568	+	0.0771568i
$268$		0			0
$269$	−1.62436	−	1.62436i	−0.0990392	−	0.0990392i	0.655851	−	0.754890i	$-0.272310\pi$
$269$	−1.62436	−	1.62436i	−0.0990392	−	0.0990392i	−0.754890	+	0.655851i	$0.772310\pi$
$270$		0			0
$271$	−18.1808			−1.10440			−0.552201	−	0.833711i	$-0.686212\pi$
$271$	−18.1808			−1.10440			−0.552201	+	0.833711i	$0.686212\pi$
$272$		0			0
$273$			1.88372i			0.114008i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	13.8675	+	13.8675i	0.833218	+	0.833218i	0.987956	−	0.154737i	$-0.0494531\pi$
$277$	13.8675	+	13.8675i	0.833218	+	0.833218i	−0.154737	+	0.987956i	$0.549453\pi$
$278$		0			0
$279$		−	20.3310i		−	1.21719i
$280$		0			0
$281$			10.7377i			0.640556i	0.947324	+	0.320278i	$0.103776\pi$
$281$			10.7377i			0.640556i	−0.947324	+	0.320278i	$0.896224\pi$
$282$		0			0
$283$	16.3679	+	16.3679i	0.972971	+	0.972971i	0.999644	−	0.0266735i	$-0.00849143\pi$
$283$	16.3679	+	16.3679i	0.972971	+	0.972971i	−0.0266735	+	0.999644i	$0.508491\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			27.2359i			1.60768i
$288$		0			0
$289$	13.5732			0.798425
$290$		0			0
$291$	0.575968	+	0.575968i	0.0337638	+	0.0337638i
$292$		0			0
$293$	−4.22052	−	4.22052i	−0.246566	−	0.246566i	0.572994	−	0.819560i	$-0.305782\pi$
$293$	−4.22052	−	4.22052i	−0.246566	−	0.246566i	−0.819560	+	0.572994i	$0.805782\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−5.01208			−0.290831
$298$		0			0
$299$	2.07994	−	2.07994i	0.120286	−	0.120286i
$300$		0			0
$301$	11.8454	+	11.8454i	0.682755	+	0.682755i
$302$		0			0
$303$			0.0895217i			0.00514289i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	12.6363	−	12.6363i	0.721190	−	0.721190i	−0.247658	−	0.968848i	$-0.579661\pi$
$307$	12.6363	−	12.6363i	0.721190	−	0.721190i	0.968848	+	0.247658i	$0.0796608\pi$
$308$		0			0
$309$	1.23625	−	1.23625i	0.0703276	−	0.0703276i
$310$		0			0
$311$			8.56815i			0.485855i	0.970044	+	0.242928i	$0.0781078\pi$
$311$			8.56815i			0.485855i	−0.970044	+	0.242928i	$0.921892\pi$
$312$		0			0
$313$	19.1825			1.08426			0.542129	−	0.840295i	$-0.317618\pi$
$313$	19.1825			1.08426			0.542129	+	0.840295i	$0.317618\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.41764	+	9.41764i	−0.528947	+	0.528947i	−0.920258	−	0.391311i	$-0.872022\pi$
$317$	−9.41764	+	9.41764i	−0.528947	+	0.528947i	0.391311	+	0.920258i	$0.372022\pi$
$318$		0			0
$319$	24.4737			1.37026
$320$		0			0
$321$	−3.48193			−0.194342
$322$		0			0
$323$	−6.38383	+	6.38383i	−0.355206	+	0.355206i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.191122			0.0105691
$328$		0			0
$329$			5.05549i			0.278718i
$330$		0			0
$331$	−12.8579	+	12.8579i	−0.706733	+	0.706733i	−0.965847	−	0.259114i	$-0.916569\pi$
$331$	−12.8579	+	12.8579i	−0.706733	+	0.706733i	0.259114	+	0.965847i	$0.416569\pi$
$332$		0			0
$333$	−0.289709	+	0.289709i	−0.0158760	+	0.0158760i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	3.31961i		−	0.180831i	−0.995904	−	0.0904153i	$-0.971181\pi$
$337$		−	3.31961i		−	0.180831i	0.995904	−	0.0904153i	$-0.0288194\pi$
$338$		0			0
$339$	−0.101110	−	0.101110i	−0.00549156	−	0.00549156i
$340$		0			0
$341$	−23.9300	+	23.9300i	−1.29588	+	1.29588i
$342$		0			0
$343$	18.3546			0.991055
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.8860	+	17.8860i	0.960171	+	0.960171i	0.999237	−	0.0390656i	$-0.0124381\pi$
$347$	17.8860	+	17.8860i	0.960171	+	0.960171i	−0.0390656	+	0.999237i	$0.512438\pi$
$348$		0			0
$349$	3.68796	+	3.68796i	0.197412	+	0.197412i	0.798890	−	0.601478i	$-0.205421\pi$
$349$	3.68796	+	3.68796i	0.197412	+	0.197412i	−0.601478	+	0.798890i	$0.705421\pi$
$350$		0			0
$351$	4.21463			0.224960
$352$		0			0
$353$			33.0951i			1.76148i	0.473604	+	0.880738i	$0.342953\pi$
$353$			33.0951i			1.76148i	−0.473604	+	0.880738i	$0.657047\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.592891	−	0.592891i	−0.0313791	−	0.0313791i
$358$		0			0
$359$		−	6.52522i		−	0.344388i	−0.985063	−	0.172194i	$-0.944914\pi$
$359$		−	6.52522i		−	0.344388i	0.985063	−	0.172194i	$-0.0550856\pi$
$360$		0			0
$361$			4.78519i			0.251852i
$362$		0			0
$363$	1.61532	+	1.61532i	0.0847825	+	0.0847825i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	11.0338i		−	0.575959i	−0.957636	−	0.287980i	$-0.907016\pi$
$367$		−	11.0338i		−	0.575959i	0.957636	−	0.287980i	$-0.0929836\pi$
$368$		0			0
$369$	30.3218			1.57849
$370$		0			0
$371$	19.8532	+	19.8532i	1.03073	+	1.03073i
$372$		0			0
$373$	6.84468	+	6.84468i	0.354404	+	0.354404i	0.861745	−	0.507341i	$-0.169372\pi$
$373$	6.84468	+	6.84468i	0.354404	+	0.354404i	−0.507341	+	0.861745i	$0.669372\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−20.5797			−1.05991
$378$		0			0
$379$	−10.1072	+	10.1072i	−0.519171	+	0.519171i	−0.917321	−	0.398150i	$-0.869653\pi$
$379$	−10.1072	+	10.1072i	−0.519171	+	0.519171i	0.398150	+	0.917321i	$0.369653\pi$
$380$		0			0
$381$	2.54050	+	2.54050i	0.130154	+	0.130154i
$382$		0			0
$383$		−	29.5283i		−	1.50883i	−0.656400	−	0.754413i	$-0.727922\pi$
$383$		−	29.5283i		−	1.50883i	0.656400	−	0.754413i	$-0.272078\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	13.1875	−	13.1875i	0.670356	−	0.670356i
$388$		0			0
$389$	−0.990949	+	0.990949i	−0.0502431	+	0.0502431i	−0.731782	−	0.681539i	$-0.761311\pi$
$389$	−0.990949	+	0.990949i	−0.0502431	+	0.0502431i	0.681539	+	0.731782i	$0.261311\pi$
$390$		0			0
$391$			1.30930i			0.0662142i
$392$		0			0
$393$	1.12148			0.0565711
$394$		0			0
$395$		0			0
$396$		0			0
$397$	17.0024	−	17.0024i	0.853326	−	0.853326i	−0.137216	−	0.990541i	$-0.543815\pi$
$397$	17.0024	−	17.0024i	0.853326	−	0.853326i	0.990541	+	0.137216i	$0.0438153\pi$
$398$		0			0
$399$	−2.20902			−0.110589
$400$		0			0
$401$	26.7791			1.33728			0.668642	−	0.743585i	$-0.266876\pi$
$401$	26.7791			1.33728			0.668642	+	0.743585i	$0.266876\pi$
$402$		0			0
$403$	20.1225	−	20.1225i	1.00238	−	1.00238i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.681985			0.0338048
$408$		0			0
$409$			13.1970i			0.652550i	0.945275	+	0.326275i	$0.105794\pi$
$409$			13.1970i			0.652550i	−0.945275	+	0.326275i	$0.894206\pi$
$410$		0			0
$411$	−1.23417	+	1.23417i	−0.0608773	+	0.0608773i
$412$		0			0
$413$	−2.56092	+	2.56092i	−0.126015	+	0.126015i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			1.19670i			0.0586026i
$418$		0			0
$419$	−9.92468	−	9.92468i	−0.484852	−	0.484852i	0.421825	−	0.906677i	$-0.361390\pi$
$419$	−9.92468	−	9.92468i	−0.484852	−	0.484852i	−0.906677	+	0.421825i	$0.861390\pi$
$420$		0			0
$421$	15.7930	−	15.7930i	0.769702	−	0.769702i	−0.208352	−	0.978054i	$-0.566810\pi$
$421$	15.7930	−	15.7930i	0.769702	−	0.769702i	0.978054	+	0.208352i	$0.0668100\pi$
$422$		0			0
$423$	5.62829			0.273657
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−17.3426	−	17.3426i	−0.839268	−	0.839268i
$428$		0			0
$429$	−2.46838	−	2.46838i	−0.119174	−	0.119174i
$430$		0			0
$431$	0.285215			0.0137383			0.00686917	−	0.999976i	$-0.497813\pi$
$431$	0.285215			0.0137383			0.00686917	+	0.999976i	$0.497813\pi$
$432$		0			0
$433$		−	18.1101i		−	0.870318i	−0.900354	−	0.435159i	$-0.856692\pi$
$433$		−	18.1101i		−	0.870318i	0.900354	−	0.435159i	$-0.143308\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.43913	+	2.43913i	0.116679	+	0.116679i
$438$		0			0
$439$			11.5931i			0.553308i	0.960970	+	0.276654i	$0.0892256\pi$
$439$			11.5931i			0.553308i	−0.960970	+	0.276654i	$0.910774\pi$
$440$		0			0
$441$			0.364153i			0.0173406i
$442$		0			0
$443$	22.6855	+	22.6855i	1.07782	+	1.07782i	0.996705	+	0.0811145i	$0.0258479\pi$
$443$	22.6855	+	22.6855i	1.07782	+	1.07782i	0.0811145	+	0.996705i	$0.474152\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	2.11094i		−	0.0998440i
$448$		0			0
$449$	−12.1999			−0.575747			−0.287873	−	0.957669i	$-0.592948\pi$
$449$	−12.1999			−0.575747			−0.287873	+	0.957669i	$0.592948\pi$
$450$		0			0
$451$	−35.6892	−	35.6892i	−1.68054	−	1.68054i
$452$		0			0
$453$	−2.66225	−	2.66225i	−0.125083	−	0.125083i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.70660			−0.0798314			−0.0399157	−	0.999203i	$-0.512709\pi$
$457$	−1.70660			−0.0798314			−0.0399157	+	0.999203i	$0.512709\pi$
$458$		0			0
$459$	−1.32653	+	1.32653i	−0.0619172	+	0.0619172i
$460$		0			0
$461$	−4.74710	−	4.74710i	−0.221094	−	0.221094i	0.587865	−	0.808959i	$-0.299969\pi$
$461$	−4.74710	−	4.74710i	−0.221094	−	0.221094i	−0.808959	+	0.587865i	$0.799969\pi$
$462$		0			0
$463$			11.1761i			0.519398i	0.965690	+	0.259699i	$0.0836234\pi$
$463$			11.1761i			0.519398i	−0.965690	+	0.259699i	$0.916377\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.06471	+	2.06471i	−0.0955435	+	0.0955435i	−0.753263	−	0.657719i	$-0.771521\pi$
$467$	−2.06471	+	2.06471i	−0.0955435	+	0.0955435i	0.657719	+	0.753263i	$0.271521\pi$
$468$		0			0
$469$	9.33260	−	9.33260i	0.430940	−	0.430940i
$470$		0			0
$471$		−	0.893315i		−	0.0411618i
$472$		0			0
$473$	−31.0437			−1.42739
$474$		0			0
$475$		0			0
$476$		0			0
$477$	22.1026	−	22.1026i	1.01201	−	1.01201i
$478$		0			0
$479$	−41.6214			−1.90173			−0.950864	−	0.309608i	$-0.899802\pi$
$479$	−41.6214			−1.90173			−0.950864	+	0.309608i	$0.899802\pi$
$480$		0			0
$481$	−0.573477			−0.0261483
$482$		0			0
$483$	−0.226531	+	0.226531i	−0.0103075	+	0.0103075i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.25627			−0.374127			−0.187064	−	0.982348i	$-0.559897\pi$
$487$	−8.25627			−0.374127			−0.187064	+	0.982348i	$0.559897\pi$
$488$		0			0
$489$			0.507950i			0.0229703i
$490$		0			0
$491$	−4.28512	+	4.28512i	−0.193385	+	0.193385i	−0.797157	−	0.603772i	$-0.793664\pi$
$491$	−4.28512	+	4.28512i	−0.193385	+	0.193385i	0.603772	+	0.797157i	$0.293664\pi$
$492$		0			0
$493$	6.47737	−	6.47737i	0.291726	−	0.291726i
$494$		0			0
$495$		0			0
$496$		0			0
$497$			20.9976i			0.941871i
$498$		0			0
$499$	−15.1287	−	15.1287i	−0.677253	−	0.677253i	0.282125	−	0.959378i	$-0.408961\pi$
$499$	−15.1287	−	15.1287i	−0.677253	−	0.677253i	−0.959378	+	0.282125i	$0.908961\pi$
$500$		0			0
$501$	2.17941	−	2.17941i	0.0973689	−	0.0973689i
$502$		0			0
$503$	18.6439			0.831291			0.415646	−	0.909527i	$-0.363556\pi$
$503$	18.6439			0.831291			0.415646	+	0.909527i	$0.363556\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.515524	+	0.515524i	0.0228952	+	0.0228952i
$508$		0			0
$509$	−11.6243	−	11.6243i	−0.515239	−	0.515239i	0.400888	−	0.916127i	$-0.368702\pi$
$509$	−11.6243	−	11.6243i	−0.515239	−	0.515239i	−0.916127	+	0.400888i	$0.868702\pi$
$510$		0			0
$511$	41.7839			1.84841
$512$		0			0
$513$			4.94246i			0.218215i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−6.62459	−	6.62459i	−0.291349	−	0.291349i
$518$		0			0
$519$			2.04865i			0.0899259i
$520$		0			0
$521$			36.9052i			1.61684i	0.588603	+	0.808422i	$0.299678\pi$
$521$			36.9052i			1.61684i	−0.588603	+	0.808422i	$0.700322\pi$
$522$		0			0
$523$	−6.04158	−	6.04158i	−0.264180	−	0.264180i	0.562570	−	0.826750i	$-0.309813\pi$
$523$	−6.04158	−	6.04158i	−0.264180	−	0.264180i	−0.826750	+	0.562570i	$0.809813\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			12.6669i			0.551780i
$528$		0			0
$529$	−22.4997			−0.978250
$530$		0			0
$531$	2.85108	+	2.85108i	0.123726	+	0.123726i
$532$		0			0
$533$	30.0108	+	30.0108i	1.29991	+	1.29991i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.582041			0.0251169
$538$		0			0
$539$	0.428614	−	0.428614i	0.0184617	−	0.0184617i
$540$		0			0
$541$	−28.4222	−	28.4222i	−1.22197	−	1.22197i	−0.966932	−	0.255035i	$-0.917913\pi$
$541$	−28.4222	−	28.4222i	−1.22197	−	1.22197i	−0.255035	−	0.966932i	$-0.582087\pi$
$542$		0			0
$543$			1.07190i			0.0459997i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−23.3562	+	23.3562i	−0.998640	+	0.998640i	−0.999999	−	0.00135902i	$-0.999567\pi$
$547$	−23.3562	+	23.3562i	−0.998640	+	0.998640i	0.00135902	+	0.999999i	$0.499567\pi$
$548$		0			0
$549$	−19.3076	+	19.3076i	−0.824027	+	0.824027i
$550$		0			0
$551$		−	24.1337i		−	1.02813i
$552$		0			0
$553$	17.8867			0.760620
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.89520	+	4.89520i	−0.207416	+	0.207416i	−0.803168	−	0.595752i	$-0.796854\pi$
$557$	−4.89520	+	4.89520i	−0.207416	+	0.207416i	0.595752	+	0.803168i	$0.296854\pi$
$558$		0			0
$559$	26.1044			1.10410
$560$		0			0
$561$	1.55382			0.0656022
$562$		0			0
$563$	1.28613	−	1.28613i	0.0542040	−	0.0542040i	−0.679485	−	0.733689i	$-0.737797\pi$
$563$	1.28613	−	1.28613i	0.0542040	−	0.0542040i	0.733689	+	0.679485i	$0.237797\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	23.3297			0.979754
$568$		0			0
$569$			11.4799i			0.481261i	0.970617	+	0.240631i	$0.0773543\pi$
$569$			11.4799i			0.481261i	−0.970617	+	0.240631i	$0.922646\pi$
$570$		0			0
$571$	−28.7069	+	28.7069i	−1.20134	+	1.20134i	−0.227587	+	0.973758i	$0.573083\pi$
$571$	−28.7069	+	28.7069i	−1.20134	+	1.20134i	−0.973758	+	0.227587i	$0.926917\pi$
$572$		0			0
$573$	0.930105	−	0.930105i	0.0388557	−	0.0388557i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			20.3419i			0.846842i	0.905933	+	0.423421i	$0.139171\pi$
$577$			20.3419i			0.846842i	−0.905933	+	0.423421i	$0.860829\pi$
$578$		0			0
$579$	1.36075	+	1.36075i	0.0565509	+	0.0565509i
$580$		0			0
$581$	10.3370	−	10.3370i	0.428852	−	0.428852i
$582$		0			0
$583$	−52.0303			−2.15488
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−25.8136	−	25.8136i	−1.06544	−	1.06544i	−0.997703	−	0.0677360i	$-0.978422\pi$
$587$	−25.8136	−	25.8136i	−1.06544	−	1.06544i	−0.0677360	−	0.997703i	$-0.521578\pi$
$588$		0			0
$589$	23.5975	+	23.5975i	0.972320	+	0.972320i
$590$		0			0
$591$	0.264022			0.0108604
$592$		0			0
$593$			4.02945i			0.165470i	0.996572	+	0.0827349i	$0.0263655\pi$
$593$			4.02945i			0.165470i	−0.996572	+	0.0827349i	$0.973635\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.71279	−	1.71279i	−0.0700997	−	0.0700997i
$598$		0			0
$599$		−	31.6701i		−	1.29400i	−0.762489	−	0.647002i	$-0.776023\pi$
$599$		−	31.6701i		−	1.29400i	0.762489	−	0.647002i	$-0.223977\pi$
$600$		0			0
$601$			19.4667i			0.794065i	0.917805	+	0.397032i	$0.129960\pi$
$601$			19.4667i			0.794065i	−0.917805	+	0.397032i	$0.870040\pi$
$602$		0			0
$603$	−10.3900	−	10.3900i	−0.423114	−	0.423114i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			13.6128i			0.552528i	0.961082	+	0.276264i	$0.0890965\pi$
$607$			13.6128i			0.552528i	−0.961082	+	0.276264i	$0.910904\pi$
$608$		0			0
$609$	2.24139			0.0908257
$610$		0			0
$611$	5.57057	+	5.57057i	0.225361	+	0.225361i
$612$		0			0
$613$	−11.1480	−	11.1480i	−0.450265	−	0.450265i	0.445177	−	0.895442i	$-0.353141\pi$
$613$	−11.1480	−	11.1480i	−0.450265	−	0.450265i	−0.895442	+	0.445177i	$0.853141\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.96695			0.0791863			0.0395932	−	0.999216i	$-0.487394\pi$
$617$	1.96695			0.0791863			0.0395932	+	0.999216i	$0.487394\pi$
$618$		0			0
$619$	7.84144	−	7.84144i	0.315174	−	0.315174i	−0.531736	−	0.846910i	$-0.678460\pi$
$619$	7.84144	−	7.84144i	0.315174	−	0.315174i	0.846910	+	0.531736i	$0.178460\pi$
$620$		0			0
$621$	0.506840	+	0.506840i	0.0203388	+	0.0203388i
$622$		0			0
$623$			28.0372i			1.12329i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	2.89464	−	2.89464i	0.115601	−	0.115601i
$628$		0			0
$629$	0.180499	−	0.180499i	0.00719696	−	0.00719696i
$630$		0			0
$631$		−	0.220729i		−	0.00878708i	−0.999990	−	0.00439354i	$-0.998601\pi$
$631$		−	0.220729i		−	0.00878708i	0.999990	−	0.00439354i	$-0.00139851\pi$
$632$		0			0
$633$	−2.99339			−0.118977
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.360418	+	0.360418i	−0.0142803	+	0.0142803i
$638$		0			0
$639$	23.3767			0.924767
$640$		0			0
$641$	−19.2037			−0.758502			−0.379251	−	0.925294i	$-0.623818\pi$
$641$	−19.2037			−0.758502			−0.379251	+	0.925294i	$0.623818\pi$
$642$		0			0
$643$	−7.17110	+	7.17110i	−0.282801	+	0.282801i	−0.834225	−	0.551424i	$-0.814085\pi$
$643$	−7.17110	+	7.17110i	−0.282801	+	0.282801i	0.551424	+	0.834225i	$0.314085\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	26.4735			1.04078			0.520391	−	0.853928i	$-0.325786\pi$
$647$	26.4735			1.04078			0.520391	+	0.853928i	$0.325786\pi$
$648$		0			0
$649$		−	6.71153i		−	0.263451i
$650$		0			0
$651$	−2.19159	+	2.19159i	−0.0858953	+	0.0858953i
$652$		0			0
$653$	−10.5746	+	10.5746i	−0.413815	+	0.413815i	−0.883065	−	0.469250i	$-0.844524\pi$
$653$	−10.5746	+	10.5746i	−0.413815	+	0.413815i	0.469250	+	0.883065i	$0.344524\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	46.5182i		−	1.81485i
$658$		0			0
$659$	24.1291	+	24.1291i	0.939937	+	0.939937i	0.998296	−	0.0583584i	$-0.0185866\pi$
$659$	24.1291	+	24.1291i	0.939937	+	0.939937i	−0.0583584	+	0.998296i	$0.518587\pi$
$660$		0			0
$661$	23.4294	−	23.4294i	0.911299	−	0.911299i	−0.0850756	−	0.996374i	$-0.527113\pi$
$661$	23.4294	−	23.4294i	0.911299	−	0.911299i	0.996374	+	0.0850756i	$0.0271132\pi$
$662$		0			0
$663$	−1.30659			−0.0507439
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.47487	−	2.47487i	−0.0958273	−	0.0958273i
$668$		0			0
$669$	0.370435	+	0.370435i	0.0143218	+	0.0143218i
$670$		0			0
$671$	45.4506			1.75460
$672$		0			0
$673$		−	41.8069i		−	1.61154i	−0.592230	−	0.805769i	$-0.701752\pi$
$673$		−	41.8069i		−	1.61154i	0.592230	−	0.805769i	$-0.298248\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	22.7350	+	22.7350i	0.873776	+	0.873776i	0.992882	−	0.119106i	$-0.0380027\pi$
$677$	22.7350	+	22.7350i	0.873776	+	0.873776i	−0.119106	+	0.992882i	$0.538003\pi$
$678$		0			0
$679$			12.8086i			0.491550i
$680$		0			0
$681$		−	1.99617i		−	0.0764936i
$682$		0			0
$683$	−34.4402	−	34.4402i	−1.31782	−	1.31782i	−0.915501	−	0.402315i	$-0.868206\pi$
$683$	−34.4402	−	34.4402i	−1.31782	−	1.31782i	−0.402315	−	0.915501i	$-0.631794\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			2.39756i			0.0914727i
$688$		0			0
$689$	43.7519			1.66682
$690$		0			0
$691$	−16.0991	−	16.0991i	−0.612438	−	0.612438i	0.331143	−	0.943581i	$-0.392566\pi$
$691$	−16.0991	−	16.0991i	−0.612438	−	0.612438i	−0.943581	+	0.331143i	$0.892566\pi$
$692$		0			0
$693$	−27.7308	−	27.7308i	−1.05341	−	1.05341i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−18.8915			−0.715567
$698$		0			0
$699$	−1.66830	+	1.66830i	−0.0631010	+	0.0631010i
$700$		0			0
$701$	−30.0507	−	30.0507i	−1.13500	−	1.13500i	−0.989334	−	0.145666i	$-0.953467\pi$
$701$	−30.0507	−	30.0507i	−1.13500	−	1.13500i	−0.145666	−	0.989334i	$-0.546533\pi$
$702$		0			0
$703$		−	0.672512i		−	0.0253643i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.995412	+	0.995412i	−0.0374363	+	0.0374363i
$708$		0			0
$709$	12.9188	−	12.9188i	0.485176	−	0.485176i	−0.421604	−	0.906780i	$-0.638533\pi$
$709$	12.9188	−	12.9188i	0.485176	−	0.485176i	0.906780	+	0.421604i	$0.138533\pi$
$710$		0			0
$711$		−	19.9133i		−	0.746807i
$712$		0			0
$713$	4.83977			0.181251
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.29234	−	1.29234i	0.0482633	−	0.0482633i
$718$		0			0
$719$	17.0356			0.635319			0.317659	−	0.948205i	$-0.397103\pi$
$719$	17.0356			0.635319			0.317659	+	0.948205i	$0.397103\pi$
$720$		0			0
$721$	27.4922			1.02386
$722$		0			0
$723$	1.49659	−	1.49659i	0.0556588	−	0.0556588i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−31.7051			−1.17588			−0.587939	−	0.808905i	$-0.700061\pi$
$727$	−31.7051			−1.17588			−0.587939	+	0.808905i	$0.700061\pi$
$728$		0			0
$729$		−	25.4570i		−	0.942852i
$730$		0			0
$731$	−8.21624	+	8.21624i	−0.303888	+	0.303888i
$732$		0			0
$733$	−3.87657	+	3.87657i	−0.143184	+	0.143184i	−0.775065	−	0.631881i	$-0.782283\pi$
$733$	−3.87657	+	3.87657i	−0.143184	+	0.143184i	0.631881	+	0.775065i	$0.282283\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			24.4584i			0.900937i
$738$		0			0
$739$	11.3024	+	11.3024i	0.415766	+	0.415766i	0.883742	−	0.467975i	$-0.155016\pi$
$739$	11.3024	+	11.3024i	0.415766	+	0.415766i	−0.467975	+	0.883742i	$0.655016\pi$
$740$		0			0
$741$	−2.43409	+	2.43409i	−0.0894184	+	0.0894184i
$742$		0			0
$743$	−30.7210			−1.12704			−0.563521	−	0.826102i	$-0.690554\pi$
$743$	−30.7210			−1.12704			−0.563521	+	0.826102i	$0.690554\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−11.5082	−	11.5082i	−0.421065	−	0.421065i
$748$		0			0
$749$	−38.7163	−	38.7163i	−1.41466	−	1.41466i
$750$		0			0
$751$	−16.4695			−0.600981			−0.300491	−	0.953785i	$-0.597150\pi$
$751$	−16.4695			−0.600981			−0.300491	+	0.953785i	$0.597150\pi$
$752$		0			0
$753$		−	0.885888i		−	0.0322836i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−21.9737	−	21.9737i	−0.798649	−	0.798649i	0.184233	−	0.982883i	$-0.441020\pi$
$757$	−21.9737	−	21.9737i	−0.798649	−	0.798649i	−0.982883	+	0.184233i	$0.941020\pi$
$758$		0			0
$759$		−	0.593681i		−	0.0215493i
$760$		0			0
$761$		−	5.91749i		−	0.214509i	−0.994232	−	0.107254i	$-0.965794\pi$
$761$		−	5.91749i		−	0.214509i	0.994232	−	0.107254i	$-0.0342060\pi$
$762$		0			0
$763$	2.12513	+	2.12513i	0.0769349	+	0.0769349i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			5.64368i			0.203782i
$768$		0			0
$769$	−10.7206			−0.386596			−0.193298	−	0.981140i	$-0.561918\pi$
$769$	−10.7206			−0.386596			−0.193298	+	0.981140i	$0.561918\pi$
$770$		0			0
$771$	0.373240	+	0.373240i	0.0134419	+	0.0134419i
$772$		0			0
$773$	−16.8329	−	16.8329i	−0.605438	−	0.605438i	0.336312	−	0.941750i	$-0.390820\pi$
$773$	−16.8329	−	16.8329i	−0.605438	−	0.605438i	−0.941750	+	0.336312i	$0.890820\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.0624587			0.00224069
$778$		0			0
$779$	−35.1934	+	35.1934i	−1.26094	+	1.26094i
$780$		0			0
$781$	−27.5147	−	27.5147i	−0.984554	−	0.984554i
$782$		0			0
$783$		−	5.01488i		−	0.179217i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	25.4619	−	25.4619i	0.907619	−	0.907619i	−0.0884603	−	0.996080i	$-0.528195\pi$
$787$	25.4619	−	25.4619i	0.907619	−	0.907619i	0.996080	+	0.0884603i	$0.0281946\pi$
$788$		0			0
$789$	−2.15430	+	2.15430i	−0.0766951	+	0.0766951i
$790$		0			0
$791$		−	2.24854i		−	0.0799489i
$792$		0			0
$793$	−38.2191			−1.35720
$794$		0			0
$795$		0			0
$796$		0			0
$797$	7.14518	−	7.14518i	0.253095	−	0.253095i	−0.569143	−	0.822238i	$-0.692725\pi$
$797$	7.14518	−	7.14518i	0.253095	−	0.253095i	0.822238	+	0.569143i	$0.192725\pi$
$798$		0			0
$799$	−3.50662			−0.124055
$800$		0			0
$801$	31.2139			1.10289
$802$		0			0
$803$	−54.7526	+	54.7526i	−1.93218	+	1.93218i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.389876			0.0137243
$808$		0			0
$809$		−	12.4413i		−	0.437412i	−0.975791	−	0.218706i	$-0.929817\pi$
$809$		−	12.4413i		−	0.437412i	0.975791	−	0.218706i	$-0.0701835\pi$
$810$		0			0
$811$	30.6494	−	30.6494i	1.07624	−	1.07624i	0.0794022	−	0.996843i	$-0.474699\pi$
$811$	30.6494	−	30.6494i	1.07624	−	1.07624i	0.996843	−	0.0794022i	$-0.0253011\pi$
$812$		0			0
$813$	2.18185	−	2.18185i	0.0765210	−	0.0765210i
$814$		0			0
$815$		0			0
$816$		0			0
$817$			30.6125i			1.07099i
$818$		0			0
$819$	23.3187	+	23.3187i	0.814820	+	0.814820i
$820$		0			0
$821$	8.84907	−	8.84907i	0.308835	−	0.308835i	−0.535623	−	0.844457i	$-0.679923\pi$
$821$	8.84907	−	8.84907i	0.308835	−	0.308835i	0.844457	+	0.535623i	$0.179923\pi$
$822$		0			0
$823$	11.7501			0.409583			0.204792	−	0.978806i	$-0.434348\pi$
$823$	11.7501			0.409583			0.204792	+	0.978806i	$0.434348\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.40407	−	3.40407i	−0.118371	−	0.118371i	0.645440	−	0.763811i	$-0.276674\pi$
$827$	−3.40407	−	3.40407i	−0.118371	−	0.118371i	−0.763811	+	0.645440i	$0.776674\pi$
$828$		0			0
$829$	−24.8718	−	24.8718i	−0.863834	−	0.863834i	0.127947	−	0.991781i	$-0.459161\pi$
$829$	−24.8718	−	24.8718i	−0.863834	−	0.863834i	−0.991781	+	0.127947i	$0.959161\pi$
$830$		0			0
$831$	−3.32845			−0.115463
$832$		0			0
$833$		−	0.226880i		−	0.00786092i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	4.90347	+	4.90347i	0.169489	+	0.169489i
$838$		0			0
$839$			3.26196i			0.112615i	0.998413	+	0.0563076i	$0.0179328\pi$
$839$			3.26196i			0.112615i	−0.998413	+	0.0563076i	$0.982067\pi$
$840$		0			0
$841$		−	4.51268i		−	0.155610i
$842$		0			0
$843$	−1.28862	−	1.28862i	−0.0443823	−	0.0443823i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			35.9223i			1.23430i
$848$		0			0
$849$	−3.92859			−0.134829
$850$		0			0
$851$	−0.0689649	−	0.0689649i	−0.00236409	−	0.00236409i
$852$		0			0
$853$	4.02276	+	4.02276i	0.137737	+	0.137737i	0.772613	−	0.634877i	$-0.218949\pi$
$853$	4.02276	+	4.02276i	0.137737	+	0.137737i	−0.634877	+	0.772613i	$0.718949\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−44.6563			−1.52543			−0.762714	−	0.646736i	$-0.776134\pi$
$857$	−44.6563			−1.52543			−0.762714	+	0.646736i	$0.776134\pi$
$858$		0			0
$859$	5.22864	−	5.22864i	0.178399	−	0.178399i	−0.612259	−	0.790658i	$-0.709739\pi$
$859$	5.22864	−	5.22864i	0.178399	−	0.178399i	0.790658	+	0.612259i	$0.209739\pi$
$860$		0			0
$861$	−3.26855	−	3.26855i	−0.111392	−	0.111392i
$862$		0			0
$863$		−	36.9653i		−	1.25831i	−0.777278	−	0.629157i	$-0.783400\pi$
$863$		−	36.9653i		−	1.25831i	0.777278	−	0.629157i	$-0.216600\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.62891	+	1.62891i	−0.0553206	+	0.0553206i
$868$		0			0
$869$	−23.4383	+	23.4383i	−0.795089	+	0.795089i
$870$		0			0
$871$		−	20.5669i		−	0.696883i
$872$		0			0
$873$	14.2599			0.482624
$874$		0			0
$875$		0			0
$876$		0			0
$877$	9.40192	−	9.40192i	0.317480	−	0.317480i	−0.530318	−	0.847799i	$-0.677928\pi$
$877$	9.40192	−	9.40192i	0.317480	−	0.317480i	0.847799	+	0.530318i	$0.177928\pi$
$878$		0			0
$879$	1.01300			0.0341677
$880$		0			0
$881$	−10.3069			−0.347248			−0.173624	−	0.984812i	$-0.555548\pi$
$881$	−10.3069			−0.347248			−0.173624	+	0.984812i	$0.555548\pi$
$882$		0			0
$883$	34.3375	−	34.3375i	1.15555	−	1.15555i	0.170128	−	0.985422i	$-0.445582\pi$
$883$	34.3375	−	34.3375i	1.15555	−	1.15555i	0.985422	−	0.170128i	$-0.0544182\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.79523			−0.228161			−0.114081	−	0.993471i	$-0.536392\pi$
$887$	−6.79523			−0.228161			−0.114081	+	0.993471i	$0.536392\pi$
$888$		0			0
$889$			56.4968i			1.89484i
$890$		0			0
$891$	−30.5706	+	30.5706i	−1.02415	+	1.02415i
$892$		0			0
$893$	−6.53256	+	6.53256i	−0.218604	+	0.218604i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			0.499223i			0.0166686i
$898$		0			0
$899$	−23.9433	−	23.9433i	−0.798554	−	0.798554i
$900$		0			0
$901$	−13.7707	+	13.7707i	−0.458769	+	0.458769i
$902$		0			0
$903$	−2.84310			−0.0946123
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−3.82391	−	3.82391i	−0.126971	−	0.126971i	0.640766	−	0.767737i	$-0.278617\pi$
$907$	−3.82391	−	3.82391i	−0.126971	−	0.126971i	−0.767737	+	0.640766i	$0.778617\pi$
$908$		0			0
$909$	1.10819	+	1.10819i	0.0367565	+	0.0367565i
$910$		0			0
$911$	18.9169			0.626743			0.313372	−	0.949631i	$-0.398541\pi$
$911$	18.9169			0.626743			0.313372	+	0.949631i	$0.398541\pi$
$912$		0			0
$913$			27.0908i			0.896574i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.4700	+	12.4700i	0.411795	+	0.411795i
$918$		0			0
$919$			48.9075i			1.61331i	0.591022	+	0.806655i	$0.298724\pi$
$919$			48.9075i			1.61331i	−0.591022	+	0.806655i	$0.701276\pi$
$920$		0			0
$921$			3.03293i			0.0999384i
$922$		0			0
$923$	23.1369	+	23.1369i	0.761562	+	0.761562i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		−	30.6071i		−	1.00527i
$928$		0			0
$929$	−35.4660			−1.16360			−0.581801	−	0.813331i	$-0.697652\pi$
$929$	−35.4660			−1.16360			−0.581801	+	0.813331i	$0.697652\pi$
$930$		0			0
$931$	−0.422660	−	0.422660i	−0.0138521	−	0.0138521i
$932$		0			0
$933$	−1.02825	−	1.02825i	−0.0336635	−	0.0336635i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−56.4991			−1.84575			−0.922873	−	0.385105i	$-0.874165\pi$
$937$	−56.4991			−1.84575			−0.922873	+	0.385105i	$0.874165\pi$
$938$		0			0
$939$	−2.30207	+	2.30207i	−0.0751252	+	0.0751252i
$940$		0			0
$941$	−2.86034	−	2.86034i	−0.0932445	−	0.0932445i	0.658946	−	0.752190i	$-0.271003\pi$
$941$	−2.86034	−	2.86034i	−0.0932445	−	0.0932445i	−0.752190	+	0.658946i	$0.771003\pi$
$942$		0			0
$943$			7.21805i			0.235052i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.86681	+	5.86681i	−0.190646	+	0.190646i	−0.795975	−	0.605329i	$-0.793041\pi$
$947$	−5.86681	+	5.86681i	−0.190646	+	0.190646i	0.605329	+	0.795975i	$0.293041\pi$
$948$		0			0
$949$	46.0411	−	46.0411i	1.49456	−	1.49456i
$950$		0			0
$951$		−	2.26040i		−	0.0732985i
$952$		0			0
$953$	25.0238			0.810599			0.405299	−	0.914184i	$-0.367167\pi$
$953$	25.0238			0.810599			0.405299	+	0.914184i	$0.367167\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.93706	+	2.93706i	−0.0949416	+	0.0949416i
$958$		0			0
$959$	−27.4461			−0.886281
$960$		0			0
$961$	15.8228			0.510412
$962$		0			0
$963$	−43.1030	+	43.1030i	−1.38897	+	1.38897i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	16.6523			0.535502			0.267751	−	0.963488i	$-0.413720\pi$
$967$	16.6523			0.535502			0.267751	+	0.963488i	$0.413720\pi$
$968$		0			0
$969$		−	1.53223i		−	0.0492224i
$970$		0			0
$971$	30.6552	−	30.6552i	0.983771	−	0.983771i	−0.0160991	−	0.999870i	$-0.505125\pi$
$971$	30.6552	−	30.6552i	0.983771	−	0.983771i	0.999870	+	0.0160991i	$0.00512472\pi$
$972$		0			0
$973$	−13.3064	+	13.3064i	−0.426583	+	0.426583i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			13.4307i			0.429687i	0.976648	+	0.214844i	$0.0689242\pi$
$977$			13.4307i			0.429687i	−0.976648	+	0.214844i	$0.931076\pi$
$978$		0			0
$979$	−36.7392	−	36.7392i	−1.17419	−	1.17419i
$980$		0			0
$981$	2.36591	−	2.36591i	0.0755378	−	0.0755378i
$982$		0			0
$983$	−7.94549			−0.253422			−0.126711	−	0.991940i	$-0.540442\pi$
$983$	−7.94549			−0.253422			−0.126711	+	0.991940i	$0.540442\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.606704	−	0.606704i	−0.0193116	−	0.0193116i
$988$		0			0
$989$	3.13925	+	3.13925i	0.0998225	+	0.0998225i
$990$		0			0
$991$	25.0787			0.796652			0.398326	−	0.917244i	$-0.369591\pi$
$991$	25.0787			0.796652			0.398326	+	0.917244i	$0.369591\pi$
$992$		0			0
$993$		−	3.08612i		−	0.0979350i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−36.1819	−	36.1819i	−1.14589	−	1.14589i	−0.987353	−	0.158539i	$-0.949322\pi$
$997$	−36.1819	−	36.1819i	−1.14589	−	1.14589i	−0.158539	−	0.987353i	$-0.550678\pi$
$998$		0			0
$999$		−	0.139745i		−	0.00442134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.q.h.849.4		16
4.3	odd	2		400.2.q.g.349.3		16
5.2	odd	4		320.2.l.a.81.5		16
5.3	odd	4		1600.2.l.i.401.4		16
5.4	even	2		1600.2.q.g.849.5		16
15.2	even	4		2880.2.t.c.721.6		16
16.5	even	4		1600.2.q.g.49.5		16
16.11	odd	4		400.2.q.h.149.6		16
20.3	even	4		400.2.l.h.301.2		16
20.7	even	4		80.2.l.a.61.7	yes	16
20.19	odd	2		400.2.q.h.349.6		16
40.27	even	4		640.2.l.b.161.5		16
40.37	odd	4		640.2.l.a.161.4		16
60.47	odd	4		720.2.t.c.541.2		16
80.27	even	4		80.2.l.a.21.7	✓	16
80.37	odd	4		320.2.l.a.241.5		16
80.43	even	4		400.2.l.h.101.2		16
80.53	odd	4		1600.2.l.i.1201.4		16
80.59	odd	4		400.2.q.g.149.3		16
80.67	even	4		640.2.l.b.481.5		16
80.69	even	4	inner	1600.2.q.h.49.4		16
80.77	odd	4		640.2.l.a.481.4		16
160.27	even	8		5120.2.a.s.1.5		8
160.37	odd	8		5120.2.a.u.1.4		8
160.107	even	8		5120.2.a.v.1.4		8
160.117	odd	8		5120.2.a.t.1.5		8
240.107	odd	4		720.2.t.c.181.2		16
240.197	even	4		2880.2.t.c.2161.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.7	✓	16	80.27	even	4
80.2.l.a.61.7	yes	16	20.7	even	4
320.2.l.a.81.5		16	5.2	odd	4
320.2.l.a.241.5		16	80.37	odd	4
400.2.l.h.101.2		16	80.43	even	4
400.2.l.h.301.2		16	20.3	even	4
400.2.q.g.149.3		16	80.59	odd	4
400.2.q.g.349.3		16	4.3	odd	2
400.2.q.h.149.6		16	16.11	odd	4
400.2.q.h.349.6		16	20.19	odd	2
640.2.l.a.161.4		16	40.37	odd	4
640.2.l.a.481.4		16	80.77	odd	4
640.2.l.b.161.5		16	40.27	even	4
640.2.l.b.481.5		16	80.67	even	4
720.2.t.c.181.2		16	240.107	odd	4
720.2.t.c.541.2		16	60.47	odd	4
1600.2.l.i.401.4		16	5.3	odd	4
1600.2.l.i.1201.4		16	80.53	odd	4
1600.2.q.g.49.5		16	16.5	even	4
1600.2.q.g.849.5		16	5.4	even	2
1600.2.q.h.49.4		16	80.69	even	4	inner
1600.2.q.h.849.4		16	1.1	even	1	trivial
2880.2.t.c.721.6		16	15.2	even	4
2880.2.t.c.2161.7		16	240.197	even	4
5120.2.a.s.1.5		8	160.27	even	8
5120.2.a.t.1.5		8	160.117	odd	8
5120.2.a.u.1.4		8	160.37	odd	8
5120.2.a.v.1.4		8	160.107	even	8

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.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.120009 + 0.120009i) q^{3} -2.66881 q^{7} +2.97120i q^{9} +O(q^{10})\)	\(q+(-0.120009 + 0.120009i) q^{3} -2.66881 q^{7} +2.97120i q^{9} +(3.49714 - 3.49714i) q^{11} +(-2.94072 + 2.94072i) q^{13} -1.85116i q^{17} +(-3.44856 - 3.44856i) q^{19} +(0.320281 - 0.320281i) q^{21} -0.707288 q^{23} +(-0.716597 - 0.716597i) q^{27} +(3.49909 + 3.49909i) q^{29} -6.84272 q^{31} +0.839377i q^{33} +(0.0975060 + 0.0975060i) q^{37} -0.705826i q^{39} -10.2052i q^{41} +(-4.43844 - 4.43844i) q^{43} -1.89428i q^{47} +0.122561 q^{49} +(0.222155 + 0.222155i) q^{51} +(-7.43897 - 7.43897i) q^{53} +0.827717 q^{57} +(0.959574 - 0.959574i) q^{59} +(6.49825 + 6.49825i) q^{61} -7.92956i q^{63} +(-3.49691 + 3.49691i) q^{67} +(0.0848809 - 0.0848809i) q^{69} -7.86777i q^{71} -15.6564 q^{73} +(-9.33322 + 9.33322i) q^{77} -6.70212 q^{79} -8.74159 q^{81} +(-3.87327 + 3.87327i) q^{83} -0.839845 q^{87} -10.5055i q^{89} +(7.84824 - 7.84824i) q^{91} +(0.821187 - 0.821187i) q^{93} -4.79937i q^{97} +(10.3907 + 10.3907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 8 q^{11} - 8 q^{19} + 24 q^{23} + 24 q^{27} + 16 q^{29} + 16 q^{37} - 8 q^{43} + 16 q^{49} + 32 q^{51} + 16 q^{53} - 8 q^{59} + 16 q^{61} - 40 q^{67} - 16 q^{69} + 16 q^{77} + 16 q^{79} - 16 q^{81} + 40 q^{83} - 32 q^{91} + 48 q^{93} - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^7 + 8 * q^11 - 8 * q^19 + 24 * q^23 + 24 * q^27 + 16 * q^29 + 16 * q^37 - 8 * q^43 + 16 * q^49 + 32 * q^51 + 16 * q^53 - 8 * q^59 + 16 * q^61 - 40 * q^67 - 16 * q^69 + 16 * q^77 + 16 * q^79 - 16 * q^81 + 40 * q^83 - 32 * q^91 + 48 * q^93 - 8 * q^99

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