LMFDB - Embedded newform 1600.2.l.f.401.6

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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			401.6
Root			$0.719139 + 1.21772i$ of defining polynomial
Character	$\chi$	$=$	1600.401
Dual form			1600.2.l.f.1201.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66783 + 1.66783i) q^{3} +1.87372i q^{7} +2.56332i q^{9} +O(q^{10})$	$q+(1.66783 + 1.66783i) q^{3} +1.87372i q^{7} +2.56332i q^{9} +(3.29695 - 3.29695i) q^{11} +(-1.90022 - 1.90022i) q^{13} -2.57148 q^{17} +(5.76636 + 5.76636i) q^{19} +(-3.12504 + 3.12504i) q^{21} +7.58574i q^{23} +(0.728312 - 0.728312i) q^{27} +(6.45786 + 6.45786i) q^{29} +0.799135 q^{31} +10.9975 q^{33} +(-2.69652 + 2.69652i) q^{37} -6.33850i q^{39} -0.946984i q^{41} +(0.829986 - 0.829986i) q^{43} +1.52421 q^{47} +3.48919 q^{49} +(-4.28879 - 4.28879i) q^{51} +(-6.97225 + 6.97225i) q^{53} +19.2346i q^{57} +(-6.84418 + 6.84418i) q^{59} +(-6.87247 - 6.87247i) q^{61} -4.80293 q^{63} +(-3.73647 - 3.73647i) q^{67} +(-12.6517 + 12.6517i) q^{69} -9.34417i q^{71} -0.886316i q^{73} +(6.17755 + 6.17755i) q^{77} -3.07575 q^{79} +10.1194 q^{81} +(-0.989393 - 0.989393i) q^{83} +21.5412i q^{87} -10.0942i q^{89} +(3.56048 - 3.56048i) q^{91} +(1.33282 + 1.33282i) q^{93} +7.16829 q^{97} +(8.45113 + 8.45113i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3}+O(q^{10}) $ 12 * q - 2 * q^3	$ 12 q - 2 q^{3} + 2 q^{11} - 4 q^{13} - 8 q^{17} + 14 q^{19} - 20 q^{21} + 10 q^{27} + 4 q^{31} + 28 q^{33} + 8 q^{37} - 8 q^{47} + 4 q^{49} - 10 q^{51} - 16 q^{53} - 20 q^{59} + 4 q^{61} + 8 q^{63} - 50 q^{67} - 8 q^{77} - 12 q^{79} - 8 q^{81} + 2 q^{83} - 44 q^{93} - 12 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 2 * q^11 - 4 * q^13 - 8 * q^17 + 14 * q^19 - 20 * q^21 + 10 * q^27 + 4 * q^31 + 28 * q^33 + 8 * q^37 - 8 * q^47 + 4 * q^49 - 10 * q^51 - 16 * q^53 - 20 * q^59 + 4 * q^61 + 8 * q^63 - 50 * q^67 - 8 * q^77 - 12 * q^79 - 8 * q^81 + 2 * q^83 - 44 * q^93 - 12 * 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
$3$	1.66783	+	1.66783i	0.962922	+	0.962922i	0.999337	−	0.0364144i	$-0.0115936\pi$
$3$	1.66783	+	1.66783i	0.962922	+	0.962922i	−0.0364144	+	0.999337i	$0.511594\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			1.87372i			0.708198i	0.935208	+	0.354099i	$0.115212\pi$
$7$			1.87372i			0.708198i	−0.935208	+	0.354099i	$0.884788\pi$
$8$		0			0
$9$			2.56332i			0.854439i
$10$		0			0
$11$	3.29695	−	3.29695i	0.994068	−	0.994068i	−0.00591443	−	0.999983i	$-0.501883\pi$
$11$	3.29695	−	3.29695i	0.994068	−	0.994068i	0.999983	+	0.00591443i	$0.00188263\pi$
$12$		0			0
$13$	−1.90022	−	1.90022i	−0.527027	−	0.527027i	0.392658	−	0.919685i	$-0.371556\pi$
$13$	−1.90022	−	1.90022i	−0.527027	−	0.527027i	−0.919685	+	0.392658i	$0.871556\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.57148			−0.623675			−0.311838	−	0.950135i	$-0.600944\pi$
$17$	−2.57148			−0.623675			−0.311838	+	0.950135i	$0.600944\pi$
$18$		0			0
$19$	5.76636	+	5.76636i	1.32289	+	1.32289i	0.911422	+	0.411472i	$0.134985\pi$
$19$	5.76636	+	5.76636i	1.32289	+	1.32289i	0.411472	+	0.911422i	$0.365015\pi$
$20$		0			0
$21$	−3.12504	+	3.12504i	−0.681940	+	0.681940i
$22$		0			0
$23$			7.58574i			1.58174i	0.611987	+	0.790868i	$0.290371\pi$
$23$			7.58574i			1.58174i	−0.611987	+	0.790868i	$0.709629\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.728312	−	0.728312i	0.140164	−	0.140164i
$28$		0			0
$29$	6.45786	+	6.45786i	1.19919	+	1.19919i	0.974408	+	0.224787i	$0.0721685\pi$
$29$	6.45786	+	6.45786i	1.19919	+	1.19919i	0.224787	+	0.974408i	$0.427831\pi$
$30$		0			0
$31$	0.799135			0.143529			0.0717644	−	0.997422i	$-0.477137\pi$
$31$	0.799135			0.143529			0.0717644	+	0.997422i	$0.477137\pi$
$32$		0			0
$33$	10.9975			1.91442
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.69652	+	2.69652i	−0.443305	+	0.443305i	−0.893121	−	0.449816i	$-0.851489\pi$
$37$	−2.69652	+	2.69652i	−0.443305	+	0.443305i	0.449816	+	0.893121i	$0.351489\pi$
$38$		0			0
$39$		−	6.33850i		−	1.01497i
$40$		0			0
$41$		−	0.946984i		−	0.147894i	−0.997262	−	0.0739471i	$-0.976440\pi$
$41$		−	0.946984i		−	0.147894i	0.997262	−	0.0739471i	$-0.0235596\pi$
$42$		0			0
$43$	0.829986	−	0.829986i	0.126572	−	0.126572i	−0.640983	−	0.767555i	$-0.721473\pi$
$43$	0.829986	−	0.829986i	0.126572	−	0.126572i	0.767555	+	0.640983i	$0.221473\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.52421			0.222329			0.111165	−	0.993802i	$-0.464542\pi$
$47$	1.52421			0.222329			0.111165	+	0.993802i	$0.464542\pi$
$48$		0			0
$49$	3.48919			0.498456
$50$		0			0
$51$	−4.28879	−	4.28879i	−0.600551	−	0.600551i
$52$		0			0
$53$	−6.97225	+	6.97225i	−0.957712	+	0.957712i	−0.999141	−	0.0414296i	$-0.986809\pi$
$53$	−6.97225	+	6.97225i	−0.957712	+	0.957712i	0.0414296	+	0.999141i	$0.486809\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			19.2346i			2.54769i
$58$		0			0
$59$	−6.84418	+	6.84418i	−0.891036	+	0.891036i	−0.994621	−	0.103585i	$-0.966969\pi$
$59$	−6.84418	+	6.84418i	−0.891036	+	0.891036i	0.103585	+	0.994621i	$0.466969\pi$
$60$		0			0
$61$	−6.87247	−	6.87247i	−0.879930	−	0.879930i	0.113597	−	0.993527i	$-0.463763\pi$
$61$	−6.87247	−	6.87247i	−0.879930	−	0.879930i	−0.993527	+	0.113597i	$0.963763\pi$
$62$		0			0
$63$	−4.80293			−0.605112
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.73647	−	3.73647i	−0.456483	−	0.456483i	0.441016	−	0.897499i	$-0.354618\pi$
$67$	−3.73647	−	3.73647i	−0.456483	−	0.456483i	−0.897499	+	0.441016i	$0.854618\pi$
$68$		0			0
$69$	−12.6517	+	12.6517i	−1.52309	+	1.52309i
$70$		0			0
$71$		−	9.34417i		−	1.10895i	−0.832201	−	0.554475i	$-0.812919\pi$
$71$		−	9.34417i		−	1.10895i	0.832201	−	0.554475i	$-0.187081\pi$
$72$		0			0
$73$		−	0.886316i		−	0.103735i	−0.998654	−	0.0518677i	$-0.983483\pi$
$73$		−	0.886316i		−	0.103735i	0.998654	−	0.0518677i	$-0.0165174\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.17755	+	6.17755i	0.703997	+	0.703997i
$78$		0			0
$79$	−3.07575			−0.346049			−0.173024	−	0.984918i	$-0.555354\pi$
$79$	−3.07575			−0.346049			−0.173024	+	0.984918i	$0.555354\pi$
$80$		0			0
$81$	10.1194			1.12437
$82$		0			0
$83$	−0.989393	−	0.989393i	−0.108600	−	0.108600i	0.650719	−	0.759319i	$-0.274468\pi$
$83$	−0.989393	−	0.989393i	−0.108600	−	0.108600i	−0.759319	+	0.650719i	$0.774468\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			21.5412i			2.30946i
$88$		0			0
$89$		−	10.0942i		−	1.06998i	−0.844859	−	0.534990i	$-0.820316\pi$
$89$		−	10.0942i		−	1.06998i	0.844859	−	0.534990i	$-0.179684\pi$
$90$		0			0
$91$	3.56048	−	3.56048i	0.373239	−	0.373239i
$92$		0			0
$93$	1.33282	+	1.33282i	0.138207	+	0.138207i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.16829			0.727830			0.363915	−	0.931432i	$-0.381440\pi$
$97$	7.16829			0.727830			0.363915	+	0.931432i	$0.381440\pi$
$98$		0			0
$99$	8.45113	+	8.45113i	0.849371	+	0.849371i
$100$		0			0
$101$	−1.05091	+	1.05091i	−0.104570	+	0.104570i	−0.757456	−	0.652886i	$-0.773558\pi$
$101$	−1.05091	+	1.05091i	−0.104570	+	0.104570i	0.652886	+	0.757456i	$0.273558\pi$
$102$		0			0
$103$		−	8.20690i		−	0.808649i	−0.914616	−	0.404325i	$-0.867507\pi$
$103$		−	8.20690i		−	0.808649i	0.914616	−	0.404325i	$-0.132493\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.85743	+	2.85743i	−0.276238	+	0.276238i	−0.831605	−	0.555367i	$-0.812578\pi$
$107$	−2.85743	+	2.85743i	−0.276238	+	0.276238i	0.555367	+	0.831605i	$0.312578\pi$
$108$		0			0
$109$	−11.3735	−	11.3735i	−1.08939	−	1.08939i	−0.995592	−	0.0937940i	$-0.970100\pi$
$109$	−11.3735	−	11.3735i	−1.08939	−	1.08939i	−0.0937940	−	0.995592i	$-0.529900\pi$
$110$		0			0
$111$	−8.99467			−0.853736
$112$		0			0
$113$	3.54221			0.333223			0.166611	−	0.986023i	$-0.446717\pi$
$113$	3.54221			0.333223			0.166611	+	0.986023i	$0.446717\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	4.87088	−	4.87088i	0.450313	−	0.450313i
$118$		0			0
$119$		−	4.81822i		−	0.441685i
$120$		0			0
$121$		−	10.7398i		−	0.976343i
$122$		0			0
$123$	1.57941	−	1.57941i	0.142411	−	0.142411i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	18.0693			1.60339			0.801693	−	0.597735i	$-0.203933\pi$
$127$	18.0693			1.60339			0.801693	+	0.597735i	$0.203933\pi$
$128$		0			0
$129$	2.76855			0.243757
$130$		0			0
$131$	6.39614	+	6.39614i	0.558834	+	0.558834i	0.928975	−	0.370142i	$-0.120691\pi$
$131$	6.39614	+	6.39614i	0.558834	+	0.558834i	−0.370142	+	0.928975i	$0.620691\pi$
$132$		0			0
$133$	−10.8045	+	10.8045i	−0.936871	+	0.936871i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	10.7357i		−	0.917212i	−0.888640	−	0.458606i	$-0.848349\pi$
$137$		−	10.7357i		−	0.917212i	0.888640	−	0.458606i	$-0.151651\pi$
$138$		0			0
$139$	2.31086	−	2.31086i	0.196005	−	0.196005i	−0.602280	−	0.798285i	$-0.705741\pi$
$139$	2.31086	−	2.31086i	0.196005	−	0.196005i	0.798285	+	0.602280i	$0.205741\pi$
$140$		0			0
$141$	2.54213	+	2.54213i	0.214086	+	0.214086i
$142$		0			0
$143$	−12.5299			−1.04780
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.81938	+	5.81938i	0.479974	+	0.479974i
$148$		0			0
$149$	1.38743	−	1.38743i	0.113663	−	0.113663i	−0.647988	−	0.761651i	$-0.724389\pi$
$149$	1.38743	−	1.38743i	0.113663	−	0.113663i	0.761651	+	0.647988i	$0.224389\pi$
$150$		0			0
$151$		−	5.68590i		−	0.462712i	−0.972869	−	0.231356i	$-0.925684\pi$
$151$		−	5.68590i		−	0.462712i	0.972869	−	0.231356i	$-0.0743163\pi$
$152$		0			0
$153$		−	6.59152i		−	0.532892i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.48874	+	2.48874i	0.198623	+	0.198623i	0.799409	−	0.600787i	$-0.205146\pi$
$157$	2.48874	+	2.48874i	0.198623	+	0.198623i	−0.600787	+	0.799409i	$0.705146\pi$
$158$		0			0
$159$	−23.2571			−1.84440
$160$		0			0
$161$	−14.2135			−1.12018
$162$		0			0
$163$	12.7091	+	12.7091i	0.995451	+	0.995451i	0.999990	−	0.00453842i	$-0.00144463\pi$
$163$	12.7091	+	12.7091i	0.995451	+	0.995451i	−0.00453842	+	0.999990i	$0.501445\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			5.00982i			0.387672i	0.981034	+	0.193836i	$0.0620929\pi$
$167$			5.00982i			0.387672i	−0.981034	+	0.193836i	$0.937907\pi$
$168$		0			0
$169$		−	5.77830i		−	0.444485i
$170$		0			0
$171$	−14.7810	+	14.7810i	−1.13033	+	1.13033i
$172$		0			0
$173$	−6.19546	−	6.19546i	−0.471032	−	0.471032i	0.431216	−	0.902249i	$-0.358085\pi$
$173$	−6.19546	−	6.19546i	−0.471032	−	0.471032i	−0.902249	+	0.431216i	$0.858085\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−22.8299			−1.71600
$178$		0			0
$179$	5.51628	+	5.51628i	0.412306	+	0.412306i	0.882541	−	0.470235i	$-0.155831\pi$
$179$	5.51628	+	5.51628i	0.412306	+	0.412306i	−0.470235	+	0.882541i	$0.655831\pi$
$180$		0			0
$181$	11.8993	−	11.8993i	0.884470	−	0.884470i	−0.109515	−	0.993985i	$-0.534930\pi$
$181$	11.8993	−	11.8993i	0.884470	−	0.884470i	0.993985	+	0.109515i	$0.0349298\pi$
$182$		0			0
$183$		−	22.9242i		−	1.69461i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−8.47804	+	8.47804i	−0.619976	+	0.619976i
$188$		0			0
$189$	1.36465	+	1.36465i	0.0992637	+	0.0992637i
$190$		0			0
$191$	−11.1278			−0.805180			−0.402590	−	0.915380i	$-0.631890\pi$
$191$	−11.1278			−0.805180			−0.402590	+	0.915380i	$0.631890\pi$
$192$		0			0
$193$	−20.7821			−1.49593			−0.747965	−	0.663738i	$-0.768969\pi$
$193$	−20.7821			−1.49593			−0.747965	+	0.663738i	$0.768969\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.0309	−	14.0309i	0.999663	−	0.999663i	−0.000337236	−	1.00000i	$-0.500107\pi$
$197$	14.0309	−	14.0309i	0.999663	−	0.999663i	1.00000		0.000337236i	$0.000107346\pi$
$198$		0			0
$199$		−	3.24727i		−	0.230193i	−0.993354	−	0.115096i	$-0.963282\pi$
$199$		−	3.24727i		−	0.230193i	0.993354	−	0.115096i	$-0.0367177\pi$
$200$		0			0
$201$		−	12.4636i		−	0.879115i
$202$		0			0
$203$	−12.1002	+	12.1002i	−0.849267	+	0.849267i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−19.4447			−1.35150
$208$		0			0
$209$	38.0228			2.63009
$210$		0			0
$211$	10.1821	+	10.1821i	0.700964	+	0.700964i	0.964617	−	0.263654i	$-0.0849276\pi$
$211$	10.1821	+	10.1821i	0.700964	+	0.700964i	−0.263654	+	0.964617i	$0.584928\pi$
$212$		0			0
$213$	15.5845	−	15.5845i	1.06783	−	1.06783i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			1.49735i			0.101647i
$218$		0			0
$219$	1.47822	−	1.47822i	0.0998892	−	0.0998892i
$220$		0			0
$221$	4.88638	+	4.88638i	0.328694	+	0.328694i
$222$		0			0
$223$	24.0469			1.61030			0.805151	−	0.593070i	$-0.202084\pi$
$223$	24.0469			1.61030			0.805151	+	0.593070i	$0.202084\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.9863	−	11.9863i	−0.795562	−	0.795562i	0.186830	−	0.982392i	$-0.440179\pi$
$227$	−11.9863	−	11.9863i	−0.795562	−	0.795562i	−0.982392	+	0.186830i	$0.940179\pi$
$228$		0			0
$229$	−20.1972	+	20.1972i	−1.33467	+	1.33467i	−0.433529	+	0.901140i	$0.642732\pi$
$229$	−20.1972	+	20.1972i	−1.33467	+	1.33467i	−0.901140	+	0.433529i	$0.857268\pi$
$230$		0			0
$231$			20.6062i			1.35579i
$232$		0			0
$233$			10.0655i			0.659410i	0.944084	+	0.329705i	$0.106949\pi$
$233$			10.0655i			0.659410i	−0.944084	+	0.329705i	$0.893051\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−5.12983	−	5.12983i	−0.333218	−	0.333218i
$238$		0			0
$239$	−0.992801			−0.0642189			−0.0321095	−	0.999484i	$-0.510223\pi$
$239$	−0.992801			−0.0642189			−0.0321095	+	0.999484i	$0.510223\pi$
$240$		0			0
$241$	14.1229			0.909738			0.454869	−	0.890558i	$-0.349686\pi$
$241$	14.1229			0.909738			0.454869	+	0.890558i	$0.349686\pi$
$242$		0			0
$243$	14.6924	+	14.6924i	0.942520	+	0.942520i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		−	21.9148i		−	1.39440i
$248$		0			0
$249$		−	3.30028i		−	0.209147i
$250$		0			0
$251$	−1.56681	+	1.56681i	−0.0988961	+	0.0988961i	−0.754824	−	0.655928i	$-0.772278\pi$
$251$	−1.56681	+	1.56681i	−0.0988961	+	0.0988961i	0.655928	+	0.754824i	$0.272278\pi$
$252$		0			0
$253$	25.0098	+	25.0098i	1.57235	+	1.57235i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.2593			−0.639960			−0.319980	−	0.947424i	$-0.603676\pi$
$257$	−10.2593			−0.639960			−0.319980	+	0.947424i	$0.603676\pi$
$258$		0			0
$259$	−5.05251	−	5.05251i	−0.313948	−	0.313948i
$260$		0			0
$261$	−16.5535	+	16.5535i	−1.02464	+	1.02464i
$262$		0			0
$263$		−	19.0630i		−	1.17548i	−0.809051	−	0.587739i	$-0.800018\pi$
$263$		−	19.0630i		−	1.17548i	0.809051	−	0.587739i	$-0.199982\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	16.8354	−	16.8354i	1.03031	−	1.03031i
$268$		0			0
$269$	3.48459	+	3.48459i	0.212459	+	0.212459i	0.805311	−	0.592852i	$-0.201998\pi$
$269$	3.48459	+	3.48459i	0.212459	+	0.212459i	−0.592852	+	0.805311i	$0.701998\pi$
$270$		0			0
$271$	30.0045			1.82264			0.911322	−	0.411695i	$-0.135063\pi$
$271$	30.0045			1.82264			0.911322	+	0.411695i	$0.135063\pi$
$272$		0			0
$273$	11.8765			0.718801
$274$		0			0
$275$		0			0
$276$		0			0
$277$	8.43732	−	8.43732i	0.506949	−	0.506949i	−0.406639	−	0.913589i	$-0.633299\pi$
$277$	8.43732	−	8.43732i	0.506949	−	0.506949i	0.913589	+	0.406639i	$0.133299\pi$
$278$		0			0
$279$			2.04844i			0.122637i
$280$		0			0
$281$			6.44714i			0.384604i	0.981336	+	0.192302i	$0.0615954\pi$
$281$			6.44714i			0.384604i	−0.981336	+	0.192302i	$0.938405\pi$
$282$		0			0
$283$	−2.61000	+	2.61000i	−0.155148	+	0.155148i	−0.780413	−	0.625264i	$-0.784991\pi$
$283$	−2.61000	+	2.61000i	−0.155148	+	0.155148i	0.625264	+	0.780413i	$0.284991\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.77438			0.104738
$288$		0			0
$289$	−10.3875			−0.611029
$290$		0			0
$291$	11.9555	+	11.9555i	0.700844	+	0.700844i
$292$		0			0
$293$	−7.52428	+	7.52428i	−0.439573	+	0.439573i	−0.891868	−	0.452295i	$-0.850605\pi$
$293$	−7.52428	+	7.52428i	−0.439573	+	0.439573i	0.452295	+	0.891868i	$0.350605\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	4.80242i		−	0.278665i
$298$		0			0
$299$	14.4146	−	14.4146i	0.833618	−	0.833618i
$300$		0			0
$301$	1.55516	+	1.55516i	0.0896377	+	0.0896377i
$302$		0			0
$303$	−3.50549			−0.201385
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−12.7130	−	12.7130i	−0.725571	−	0.725571i	0.244163	−	0.969734i	$-0.421487\pi$
$307$	−12.7130	−	12.7130i	−0.725571	−	0.725571i	−0.969734	+	0.244163i	$0.921487\pi$
$308$		0			0
$309$	13.6877	−	13.6877i	0.778667	−	0.778667i
$310$		0			0
$311$		−	11.9313i		−	0.676563i	−0.941045	−	0.338281i	$-0.890154\pi$
$311$		−	11.9313i		−	0.676563i	0.941045	−	0.338281i	$-0.109846\pi$
$312$		0			0
$313$		−	34.3458i		−	1.94134i	−0.240414	−	0.970670i	$-0.577283\pi$
$313$		−	34.3458i		−	1.94134i	0.240414	−	0.970670i	$-0.422717\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.1112	−	17.1112i	−0.961060	−	0.961060i	0.0382097	−	0.999270i	$-0.487835\pi$
$317$	−17.1112	−	17.1112i	−0.961060	−	0.961060i	−0.999270	+	0.0382097i	$0.987835\pi$
$318$		0			0
$319$	42.5825			2.38416
$320$		0			0
$321$	−9.53141			−0.531992
$322$		0			0
$323$	−14.8281	−	14.8281i	−0.825056	−	0.825056i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	37.9382i		−	2.09799i
$328$		0			0
$329$			2.85594i			0.157453i
$330$		0			0
$331$	−9.80246	+	9.80246i	−0.538792	+	0.538792i	−0.923174	−	0.384382i	$-0.874415\pi$
$331$	−9.80246	+	9.80246i	−0.538792	+	0.538792i	0.384382	+	0.923174i	$0.374415\pi$
$332$		0			0
$333$	−6.91203	−	6.91203i	−0.378777	−	0.378777i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	6.07501			0.330927			0.165463	−	0.986216i	$-0.447088\pi$
$337$	6.07501			0.330927			0.165463	+	0.986216i	$0.447088\pi$
$338$		0			0
$339$	5.90780	+	5.90780i	0.320868	+	0.320868i
$340$		0			0
$341$	2.63471	−	2.63471i	0.142677	−	0.142677i
$342$		0			0
$343$			19.6538i			1.06120i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.77231	+	5.77231i	−0.309874	+	0.309874i	−0.844860	−	0.534987i	$-0.820317\pi$
$347$	−5.77231	+	5.77231i	−0.309874	+	0.309874i	0.534987	+	0.844860i	$0.320317\pi$
$348$		0			0
$349$	−7.58851	−	7.58851i	−0.406203	−	0.406203i	0.474209	−	0.880412i	$-0.342734\pi$
$349$	−7.58851	−	7.58851i	−0.406203	−	0.406203i	−0.880412	+	0.474209i	$0.842734\pi$
$350$		0			0
$351$	−2.76791			−0.147740
$352$		0			0
$353$	−16.2285			−0.863753			−0.431877	−	0.901933i	$-0.642148\pi$
$353$	−16.2285			−0.863753			−0.431877	+	0.901933i	$0.642148\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	8.03597	−	8.03597i	0.425309	−	0.425309i
$358$		0			0
$359$		−	6.77298i		−	0.357464i	−0.983898	−	0.178732i	$-0.942800\pi$
$359$		−	6.77298i		−	0.357464i	0.983898	−	0.178732i	$-0.0571996\pi$
$360$		0			0
$361$			47.5019i			2.50010i
$362$		0			0
$363$	17.9121	−	17.9121i	0.940142	−	0.940142i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	6.35705			0.331835			0.165918	−	0.986140i	$-0.446941\pi$
$367$	6.35705			0.331835			0.165918	+	0.986140i	$0.446941\pi$
$368$		0			0
$369$	2.42742			0.126367
$370$		0			0
$371$	−13.0640	−	13.0640i	−0.678250	−	0.678250i
$372$		0			0
$373$	9.20937	−	9.20937i	0.476843	−	0.476843i	−0.427278	−	0.904121i	$-0.640527\pi$
$373$	9.20937	−	9.20937i	0.476843	−	0.476843i	0.904121	+	0.427278i	$0.140527\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	24.5428i		−	1.26402i
$378$		0			0
$379$	−5.41600	+	5.41600i	−0.278201	+	0.278201i	−0.832391	−	0.554189i	$-0.813028\pi$
$379$	−5.41600	+	5.41600i	−0.278201	+	0.278201i	0.554189	+	0.832391i	$0.313028\pi$
$380$		0			0
$381$	30.1365	+	30.1365i	1.54394	+	1.54394i
$382$		0			0
$383$	−28.1626			−1.43904			−0.719520	−	0.694472i	$-0.755638\pi$
$383$	−28.1626			−1.43904			−0.719520	+	0.694472i	$0.755638\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.12752	+	2.12752i	0.108148	+	0.108148i
$388$		0			0
$389$	9.59783	−	9.59783i	0.486629	−	0.486629i	−0.420611	−	0.907241i	$-0.638184\pi$
$389$	9.59783	−	9.59783i	0.486629	−	0.486629i	0.907241	+	0.420611i	$0.138184\pi$
$390$		0			0
$391$		−	19.5066i		−	0.986490i
$392$		0			0
$393$			21.3354i			1.07623i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	10.4884	+	10.4884i	0.526399	+	0.526399i	0.919497	−	0.393098i	$-0.128597\pi$
$397$	10.4884	+	10.4884i	0.526399	+	0.526399i	−0.393098	+	0.919497i	$0.628597\pi$
$398$		0			0
$399$	−36.0402			−1.80427
$400$		0			0
$401$	−2.44221			−0.121958			−0.0609791	−	0.998139i	$-0.519422\pi$
$401$	−2.44221			−0.121958			−0.0609791	+	0.998139i	$0.519422\pi$
$402$		0			0
$403$	−1.51853	−	1.51853i	−0.0756436	−	0.0756436i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			17.7806i			0.881350i
$408$		0			0
$409$		−	24.6628i		−	1.21950i	−0.792596	−	0.609748i	$-0.791271\pi$
$409$		−	24.6628i		−	1.21950i	0.792596	−	0.609748i	$-0.208729\pi$
$410$		0			0
$411$	17.9053	−	17.9053i	0.883204	−	0.883204i
$412$		0			0
$413$	−12.8240	−	12.8240i	−0.631030	−	0.631030i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	7.70826			0.377475
$418$		0			0
$419$	−19.1661	−	19.1661i	−0.936326	−	0.936326i	0.0617649	−	0.998091i	$-0.480327\pi$
$419$	−19.1661	−	19.1661i	−0.936326	−	0.936326i	−0.998091	+	0.0617649i	$0.980327\pi$
$420$		0			0
$421$	−7.43469	+	7.43469i	−0.362345	+	0.362345i	−0.864676	−	0.502331i	$-0.832476\pi$
$421$	−7.43469	+	7.43469i	−0.362345	+	0.362345i	0.502331	+	0.864676i	$0.332476\pi$
$422$		0			0
$423$			3.90704i			0.189967i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	12.8771	−	12.8771i	0.623164	−	0.623164i
$428$		0			0
$429$	−20.8977	−	20.8977i	−1.00895	−	1.00895i
$430$		0			0
$431$	−22.5647			−1.08690			−0.543451	−	0.839441i	$-0.682883\pi$
$431$	−22.5647			−1.08690			−0.543451	+	0.839441i	$0.682883\pi$
$432$		0			0
$433$	26.4811			1.27260			0.636301	−	0.771441i	$-0.280464\pi$
$433$	26.4811			1.27260			0.636301	+	0.771441i	$0.280464\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−43.7421	+	43.7421i	−2.09247	+	2.09247i
$438$		0			0
$439$			0.765288i			0.0365252i	0.999833	+	0.0182626i	$0.00581349\pi$
$439$			0.765288i			0.0365252i	−0.999833	+	0.0182626i	$0.994187\pi$
$440$		0			0
$441$			8.94390i			0.425900i
$442$		0			0
$443$	−20.2685	+	20.2685i	−0.962985	+	0.962985i	−0.999339	−	0.0363537i	$-0.988426\pi$
$443$	−20.2685	+	20.2685i	−0.962985	+	0.962985i	0.0363537	+	0.999339i	$0.488426\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	4.62800			0.218897
$448$		0			0
$449$	−35.2717			−1.66457			−0.832287	−	0.554345i	$-0.812969\pi$
$449$	−35.2717			−1.66457			−0.832287	+	0.554345i	$0.812969\pi$
$450$		0			0
$451$	−3.12216	−	3.12216i	−0.147017	−	0.147017i
$452$		0			0
$453$	9.48312	−	9.48312i	0.445556	−	0.445556i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	9.01188i		−	0.421558i	−0.977534	−	0.210779i	$-0.932400\pi$
$457$		−	9.01188i		−	0.421558i	0.977534	−	0.210779i	$-0.0676000\pi$
$458$		0			0
$459$	−1.87284	+	1.87284i	−0.0874167	+	0.0874167i
$460$		0			0
$461$	−22.8247	−	22.8247i	−1.06305	−	1.06305i	−0.997873	−	0.0651807i	$-0.979238\pi$
$461$	−22.8247	−	22.8247i	−1.06305	−	1.06305i	−0.0651807	−	0.997873i	$-0.520762\pi$
$462$		0			0
$463$	−3.72721			−0.173218			−0.0866090	−	0.996242i	$-0.527603\pi$
$463$	−3.72721			−0.173218			−0.0866090	+	0.996242i	$0.527603\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.23477	+	3.23477i	0.149687	+	0.149687i	0.777978	−	0.628291i	$-0.216245\pi$
$467$	3.23477	+	3.23477i	0.149687	+	0.149687i	−0.628291	+	0.777978i	$0.716245\pi$
$468$		0			0
$469$	7.00109	−	7.00109i	0.323280	−	0.323280i
$470$		0			0
$471$			8.30158i			0.382517i
$472$		0			0
$473$		−	5.47284i		−	0.251642i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−17.8721	−	17.8721i	−0.818307	−	0.818307i
$478$		0			0
$479$	11.0636			0.505508			0.252754	−	0.967531i	$-0.418664\pi$
$479$	11.0636			0.505508			0.252754	+	0.967531i	$0.418664\pi$
$480$		0			0
$481$	10.2480			0.467267
$482$		0			0
$483$	−23.7057	−	23.7057i	−1.07865	−	1.07865i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	6.68176i		−	0.302779i	−0.988474	−	0.151390i	$-0.951625\pi$
$487$		−	6.68176i		−	0.302779i	0.988474	−	0.151390i	$-0.0483748\pi$
$488$		0			0
$489$			42.3932i			1.91708i
$490$		0			0
$491$	18.4274	−	18.4274i	0.831618	−	0.831618i	−0.156120	−	0.987738i	$-0.549899\pi$
$491$	18.4274	−	18.4274i	0.831618	−	0.831618i	0.987738	+	0.156120i	$0.0498986\pi$
$492$		0			0
$493$	−16.6063	−	16.6063i	−0.747908	−	0.747908i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	17.5083			0.785356
$498$		0			0
$499$	−8.84615	−	8.84615i	−0.396008	−	0.396008i	0.480814	−	0.876822i	$-0.340341\pi$
$499$	−8.84615	−	8.84615i	−0.396008	−	0.396008i	−0.876822	+	0.480814i	$0.840341\pi$
$500$		0			0
$501$	−8.35554	+	8.35554i	−0.373298	+	0.373298i
$502$		0			0
$503$			16.8746i			0.752401i	0.926538	+	0.376201i	$0.122770\pi$
$503$			16.8746i			0.752401i	−0.926538	+	0.376201i	$0.877230\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	9.63723	−	9.63723i	0.428004	−	0.428004i
$508$		0			0
$509$	20.5691	+	20.5691i	0.911707	+	0.911707i	0.996407	−	0.0846994i	$-0.0269930\pi$
$509$	20.5691	+	20.5691i	0.911707	+	0.911707i	−0.0846994	+	0.996407i	$0.526993\pi$
$510$		0			0
$511$	1.66070			0.0734652
$512$		0			0
$513$	8.39943			0.370844
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.02526	−	5.02526i	0.221011	−	0.221011i
$518$		0			0
$519$		−	20.6660i		−	0.907135i
$520$		0			0
$521$		−	12.6708i		−	0.555118i	−0.960709	−	0.277559i	$-0.910475\pi$
$521$		−	12.6708i		−	0.555118i	0.960709	−	0.277559i	$-0.0895253\pi$
$522$		0			0
$523$	27.8509	−	27.8509i	1.21784	−	1.21784i	0.249448	−	0.968388i	$-0.419751\pi$
$523$	27.8509	−	27.8509i	1.21784	−	1.21784i	0.968388	−	0.249448i	$-0.0802491\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.05496			−0.0895154
$528$		0			0
$529$	−34.5435			−1.50189
$530$		0			0
$531$	−17.5438	−	17.5438i	−0.761336	−	0.761336i
$532$		0			0
$533$	−1.79948	+	1.79948i	−0.0779442	+	0.0779442i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			18.4005i			0.794038i
$538$		0			0
$539$	11.5037	−	11.5037i	0.495499	−	0.495499i
$540$		0			0
$541$	−23.4122	−	23.4122i	−1.00657	−	1.00657i	−0.999978	−	0.00659048i	$-0.997902\pi$
$541$	−23.4122	−	23.4122i	−1.00657	−	1.00657i	−0.00659048	−	0.999978i	$-0.502098\pi$
$542$		0			0
$543$	39.6921			1.70335
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−17.3745	−	17.3745i	−0.742878	−	0.742878i	0.230253	−	0.973131i	$-0.426045\pi$
$547$	−17.3745	−	17.3745i	−0.742878	−	0.742878i	−0.973131	+	0.230253i	$0.926045\pi$
$548$		0			0
$549$	17.6163	−	17.6163i	0.751846	−	0.751846i
$550$		0			0
$551$			74.4767i			3.17282i
$552$		0			0
$553$		−	5.76308i		−	0.245071i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	22.8889	+	22.8889i	0.969832	+	0.969832i	0.999558	−	0.0297261i	$-0.00946351\pi$
$557$	22.8889	+	22.8889i	0.969832	+	0.969832i	−0.0297261	+	0.999558i	$0.509464\pi$
$558$		0			0
$559$	−3.15432			−0.133413
$560$		0			0
$561$	−28.2799			−1.19398
$562$		0			0
$563$	−19.2489	−	19.2489i	−0.811246	−	0.811246i	0.173574	−	0.984821i	$-0.444468\pi$
$563$	−19.2489	−	19.2489i	−0.811246	−	0.811246i	−0.984821	+	0.173574i	$0.944468\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			18.9608i			0.796278i
$568$		0			0
$569$		−	34.4274i		−	1.44327i	−0.692273	−	0.721635i	$-0.743391\pi$
$569$		−	34.4274i		−	1.44327i	0.692273	−	0.721635i	$-0.256609\pi$
$570$		0			0
$571$	−5.85059	+	5.85059i	−0.244840	+	0.244840i	−0.818849	−	0.574009i	$-0.805387\pi$
$571$	−5.85059	+	5.85059i	−0.244840	+	0.244840i	0.574009	+	0.818849i	$0.305387\pi$
$572$		0			0
$573$	−18.5593	−	18.5593i	−0.775326	−	0.775326i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	32.5042			1.35317			0.676585	−	0.736365i	$-0.263459\pi$
$577$	32.5042			1.35317			0.676585	+	0.736365i	$0.263459\pi$
$578$		0			0
$579$	−34.6611	−	34.6611i	−1.44047	−	1.44047i
$580$		0			0
$581$	1.85384	−	1.85384i	0.0769103	−	0.0769103i
$582$		0			0
$583$			45.9743i			1.90406i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.7519	−	14.7519i	0.608875	−	0.608875i	−0.333777	−	0.942652i	$-0.608323\pi$
$587$	14.7519	−	14.7519i	0.608875	−	0.608875i	0.942652	+	0.333777i	$0.108323\pi$
$588$		0			0
$589$	4.60810	+	4.60810i	0.189873	+	0.189873i
$590$		0			0
$591$	46.8024			1.92520
$592$		0			0
$593$	−20.5310			−0.843108			−0.421554	−	0.906803i	$-0.638515\pi$
$593$	−20.5310			−0.843108			−0.421554	+	0.906803i	$0.638515\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.41590	−	5.41590i	0.221658	−	0.221658i
$598$		0			0
$599$			12.3998i			0.506644i	0.967382	+	0.253322i	$0.0815232\pi$
$599$			12.3998i			0.506644i	−0.967382	+	0.253322i	$0.918477\pi$
$600$		0			0
$601$		−	12.3980i		−	0.505723i	−0.967502	−	0.252862i	$-0.918628\pi$
$601$		−	12.3980i		−	0.505723i	0.967502	−	0.252862i	$-0.0813718\pi$
$602$		0			0
$603$	9.57777	−	9.57777i	0.390037	−	0.390037i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.90398			−0.199046			−0.0995232	−	0.995035i	$-0.531732\pi$
$607$	−4.90398			−0.199046			−0.0995232	+	0.995035i	$0.531732\pi$
$608$		0			0
$609$	−40.3621			−1.63556
$610$		0			0
$611$	−2.89635	−	2.89635i	−0.117174	−	0.117174i
$612$		0			0
$613$	−0.408547	+	0.408547i	−0.0165011	+	0.0165011i	−0.715309	−	0.698808i	$-0.753714\pi$
$613$	−0.408547	+	0.408547i	−0.0165011	+	0.0165011i	0.698808	+	0.715309i	$0.253714\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			6.17186i			0.248470i	0.992253	+	0.124235i	$0.0396476\pi$
$617$			6.17186i			0.248470i	−0.992253	+	0.124235i	$0.960352\pi$
$618$		0			0
$619$	−18.5138	+	18.5138i	−0.744132	+	0.744132i	−0.973370	−	0.229238i	$-0.926377\pi$
$619$	−18.5138	+	18.5138i	−0.744132	+	0.744132i	0.229238	+	0.973370i	$0.426377\pi$
$620$		0			0
$621$	5.52479	+	5.52479i	0.221702	+	0.221702i
$622$		0			0
$623$	18.9136			0.757757
$624$		0			0
$625$		0			0
$626$		0			0
$627$	63.4156	+	63.4156i	2.53258	+	2.53258i
$628$		0			0
$629$	6.93404	−	6.93404i	0.276478	−	0.276478i
$630$		0			0
$631$		−	20.7940i		−	0.827795i	−0.910323	−	0.413897i	$-0.864167\pi$
$631$		−	20.7940i		−	0.827795i	0.910323	−	0.413897i	$-0.135833\pi$
$632$		0			0
$633$			33.9640i			1.34995i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−6.63024	−	6.63024i	−0.262700	−	0.262700i
$638$		0			0
$639$	23.9521			0.947530
$640$		0			0
$641$	16.1179			0.636620			0.318310	−	0.947987i	$-0.396885\pi$
$641$	16.1179			0.636620			0.318310	+	0.947987i	$0.396885\pi$
$642$		0			0
$643$	−10.3733	−	10.3733i	−0.409082	−	0.409082i	0.472336	−	0.881419i	$-0.343411\pi$
$643$	−10.3733	−	10.3733i	−0.409082	−	0.409082i	−0.881419	+	0.472336i	$0.843411\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	32.5724i		−	1.28055i	−0.768145	−	0.640276i	$-0.778820\pi$
$647$		−	32.5724i		−	1.28055i	0.768145	−	0.640276i	$-0.221180\pi$
$648$		0			0
$649$			45.1298i			1.77150i
$650$		0			0
$651$	−2.49733	+	2.49733i	−0.0978780	+	0.0978780i
$652$		0			0
$653$	4.31962	+	4.31962i	0.169040	+	0.169040i	0.786557	−	0.617517i	$-0.211861\pi$
$653$	4.31962	+	4.31962i	0.169040	+	0.169040i	−0.617517	+	0.786557i	$0.711861\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.27191			0.0886356
$658$		0			0
$659$	4.19711	+	4.19711i	0.163496	+	0.163496i	0.784114	−	0.620617i	$-0.213118\pi$
$659$	4.19711	+	4.19711i	0.163496	+	0.163496i	−0.620617	+	0.784114i	$0.713118\pi$
$660$		0			0
$661$	21.2310	−	21.2310i	0.825790	−	0.825790i	−0.161141	−	0.986931i	$-0.551518\pi$
$661$	21.2310	−	21.2310i	0.825790	−	0.825790i	0.986931	+	0.161141i	$0.0515175\pi$
$662$		0			0
$663$			16.2993i			0.633013i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−48.9877	+	48.9877i	−1.89681	+	1.89681i
$668$		0			0
$669$	40.1062	+	40.1062i	1.55060	+	1.55060i
$670$		0			0
$671$	−45.3164			−1.74942
$672$		0			0
$673$	−6.08317			−0.234489			−0.117244	−	0.993103i	$-0.537406\pi$
$673$	−6.08317			−0.234489			−0.117244	+	0.993103i	$0.537406\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.42443	+	8.42443i	−0.323777	+	0.323777i	−0.850214	−	0.526437i	$-0.823528\pi$
$677$	−8.42443	+	8.42443i	−0.323777	+	0.323777i	0.526437	+	0.850214i	$0.323528\pi$
$678$		0			0
$679$			13.4313i			0.515447i
$680$		0			0
$681$		−	39.9824i		−	1.53213i
$682$		0			0
$683$	−14.7609	+	14.7609i	−0.564812	+	0.564812i	−0.930670	−	0.365859i	$-0.880775\pi$
$683$	−14.7609	+	14.7609i	−0.564812	+	0.564812i	0.365859	+	0.930670i	$0.380775\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−67.3710			−2.57036
$688$		0			0
$689$	26.4977			1.00948
$690$		0			0
$691$	4.06268	+	4.06268i	0.154552	+	0.154552i	0.780147	−	0.625596i	$-0.215144\pi$
$691$	4.06268	+	4.06268i	0.154552	+	0.154552i	−0.625596	+	0.780147i	$0.715144\pi$
$692$		0			0
$693$	−15.8350	+	15.8350i	−0.601523	+	0.601523i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			2.43515i			0.0922379i
$698$		0			0
$699$	−16.7875	+	16.7875i	−0.634961	+	0.634961i
$700$		0			0
$701$	11.1049	+	11.1049i	0.419428	+	0.419428i	0.885007	−	0.465578i	$-0.154154\pi$
$701$	11.1049	+	11.1049i	0.419428	+	0.419428i	−0.465578	+	0.885007i	$0.654154\pi$
$702$		0			0
$703$	−31.0982			−1.17289
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.96911	−	1.96911i	−0.0740561	−	0.0740561i
$708$		0			0
$709$	13.0114	−	13.0114i	0.488652	−	0.488652i	−0.419229	−	0.907881i	$-0.637700\pi$
$709$	13.0114	−	13.0114i	0.488652	−	0.488652i	0.907881	+	0.419229i	$0.137700\pi$
$710$		0			0
$711$		−	7.88412i		−	0.295678i
$712$		0			0
$713$			6.06203i			0.227025i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.65582	−	1.65582i	−0.0618378	−	0.0618378i
$718$		0			0
$719$	50.0570			1.86681			0.933406	−	0.358821i	$-0.116821\pi$
$719$	50.0570			1.86681			0.933406	+	0.358821i	$0.116821\pi$
$720$		0			0
$721$	15.3774			0.572684
$722$		0			0
$723$	23.5547	+	23.5547i	0.876007	+	0.876007i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			27.7141i			1.02786i	0.857832	+	0.513930i	$0.171811\pi$
$727$			27.7141i			1.02786i	−0.857832	+	0.513930i	$0.828189\pi$
$728$		0			0
$729$			18.6509i			0.690775i
$730$		0			0
$731$	−2.13429	+	2.13429i	−0.0789396	+	0.0789396i
$732$		0			0
$733$	16.8860	+	16.8860i	0.623698	+	0.623698i	0.946475	−	0.322777i	$-0.104616\pi$
$733$	16.8860	+	16.8860i	0.623698	+	0.623698i	−0.322777	+	0.946475i	$0.604616\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−24.6379			−0.907550
$738$		0			0
$739$	23.6286	+	23.6286i	0.869193	+	0.869193i	0.992383	−	0.123190i	$-0.0393124\pi$
$739$	23.6286	+	23.6286i	0.869193	+	0.869193i	−0.123190	+	0.992383i	$0.539312\pi$
$740$		0			0
$741$	36.5501	−	36.5501i	1.34270	−	1.34270i
$742$		0			0
$743$		−	6.53356i		−	0.239693i	−0.992792	−	0.119846i	$-0.961760\pi$
$743$		−	6.53356i		−	0.239693i	0.992792	−	0.119846i	$-0.0382402\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.53613	−	2.53613i	0.0927921	−	0.0927921i
$748$		0			0
$749$	−5.35401	−	5.35401i	−0.195631	−	0.195631i
$750$		0			0
$751$	22.8483			0.833746			0.416873	−	0.908965i	$-0.363126\pi$
$751$	22.8483			0.833746			0.416873	+	0.908965i	$0.363126\pi$
$752$		0			0
$753$	−5.22634			−0.190459
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−24.0190	+	24.0190i	−0.872985	+	0.872985i	−0.992797	−	0.119811i	$-0.961771\pi$
$757$	−24.0190	+	24.0190i	−0.872985	+	0.872985i	0.119811	+	0.992797i	$0.461771\pi$
$758$		0			0
$759$			83.4243i			3.02811i
$760$		0			0
$761$			5.51772i			0.200017i	0.994987	+	0.100009i	$0.0318871\pi$
$761$			5.51772i			0.200017i	−0.994987	+	0.100009i	$0.968113\pi$
$762$		0			0
$763$	21.3107	−	21.3107i	0.771501	−	0.771501i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	26.0109			0.939200
$768$		0			0
$769$	14.0124			0.505299			0.252649	−	0.967558i	$-0.418698\pi$
$769$	14.0124			0.505299			0.252649	+	0.967558i	$0.418698\pi$
$770$		0			0
$771$	−17.1108	−	17.1108i	−0.616231	−	0.616231i
$772$		0			0
$773$	0.753043	−	0.753043i	0.0270851	−	0.0270851i	−0.693435	−	0.720520i	$-0.743903\pi$
$773$	0.753043	−	0.753043i	0.0270851	−	0.0270851i	0.720520	+	0.693435i	$0.243903\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		−	16.8535i		−	0.604614i
$778$		0			0
$779$	5.46066	−	5.46066i	0.195648	−	0.195648i
$780$		0			0
$781$	−30.8073	−	30.8073i	−1.10237	−	1.10237i
$782$		0			0
$783$	9.40668			0.336167
$784$		0			0
$785$		0			0
$786$		0			0
$787$	29.2752	+	29.2752i	1.04355	+	1.04355i	0.999008	+	0.0445395i	$0.0141821\pi$
$787$	29.2752	+	29.2752i	1.04355	+	1.04355i	0.0445395	+	0.999008i	$0.485818\pi$
$788$		0			0
$789$	31.7939	−	31.7939i	1.13189	−	1.13189i
$790$		0			0
$791$			6.63709i			0.235988i
$792$		0			0
$793$			26.1185i			0.927494i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.09658	−	6.09658i	−0.215952	−	0.215952i	0.590838	−	0.806790i	$-0.298797\pi$
$797$	−6.09658	−	6.09658i	−0.215952	−	0.215952i	−0.806790	+	0.590838i	$0.798797\pi$
$798$		0			0
$799$	−3.91948			−0.138661
$800$		0			0
$801$	25.8745			0.914232
$802$		0			0
$803$	−2.92214	−	2.92214i	−0.103120	−	0.103120i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			11.6234i			0.409163i
$808$		0			0
$809$			31.5083i			1.10777i	0.832592	+	0.553886i	$0.186856\pi$
$809$			31.5083i			1.10777i	−0.832592	+	0.553886i	$0.813144\pi$
$810$		0			0
$811$	−20.2317	+	20.2317i	−0.710431	+	0.710431i	−0.966625	−	0.256194i	$-0.917531\pi$
$811$	−20.2317	+	20.2317i	−0.710431	+	0.710431i	0.256194	+	0.966625i	$0.417531\pi$
$812$		0			0
$813$	50.0424	+	50.0424i	1.75506	+	1.75506i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	9.57200			0.334882
$818$		0			0
$819$	9.12664	+	9.12664i	0.318910	+	0.318910i
$820$		0			0
$821$	−19.1821	+	19.1821i	−0.669459	+	0.669459i	−0.957591	−	0.288132i	$-0.906966\pi$
$821$	−19.1821	+	19.1821i	−0.669459	+	0.669459i	0.288132	+	0.957591i	$0.406966\pi$
$822$		0			0
$823$		−	11.4746i		−	0.399979i	−0.979798	−	0.199989i	$-0.935909\pi$
$823$		−	11.4746i		−	0.399979i	0.979798	−	0.199989i	$-0.0640907\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−17.7573	+	17.7573i	−0.617482	+	0.617482i	−0.944885	−	0.327403i	$-0.893827\pi$
$827$	−17.7573	+	17.7573i	−0.617482	+	0.617482i	0.327403	+	0.944885i	$0.393827\pi$
$828$		0			0
$829$	−20.0071	−	20.0071i	−0.694876	−	0.694876i	0.268424	−	0.963301i	$-0.413497\pi$
$829$	−20.0071	−	20.0071i	−0.694876	−	0.694876i	−0.963301	+	0.268424i	$0.913497\pi$
$830$		0			0
$831$	28.1440			0.976306
$832$		0			0
$833$	−8.97238			−0.310874
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.582020	−	0.582020i	0.0201175	−	0.0201175i
$838$		0			0
$839$			20.3936i			0.704065i	0.935988	+	0.352033i	$0.114509\pi$
$839$			20.3936i			0.704065i	−0.935988	+	0.352033i	$0.885491\pi$
$840$		0			0
$841$			54.4079i			1.87614i
$842$		0			0
$843$	−10.7527	+	10.7527i	−0.370344	+	0.370344i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	20.1233			0.691444
$848$		0			0
$849$	−8.70608			−0.298792
$850$		0			0
$851$	−20.4551	−	20.4551i	−0.701191	−	0.701191i
$852$		0			0
$853$	37.4481	−	37.4481i	1.28220	−	1.28220i	0.342784	−	0.939414i	$-0.388630\pi$
$853$	37.4481	−	37.4481i	1.28220	−	1.28220i	0.939414	−	0.342784i	$-0.111370\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	12.7258i		−	0.434706i	−0.976093	−	0.217353i	$-0.930258\pi$
$857$		−	12.7258i		−	0.434706i	0.976093	−	0.217353i	$-0.0697422\pi$
$858$		0			0
$859$	−17.4318	+	17.4318i	−0.594766	+	0.594766i	−0.938915	−	0.344149i	$-0.888167\pi$
$859$	−17.4318	+	17.4318i	−0.594766	+	0.594766i	0.344149	+	0.938915i	$0.388167\pi$
$860$		0			0
$861$	2.95936	+	2.95936i	0.100855	+	0.100855i
$862$		0			0
$863$	33.6976			1.14708			0.573540	−	0.819178i	$-0.305570\pi$
$863$	33.6976			1.14708			0.573540	+	0.819178i	$0.305570\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−17.3246	−	17.3246i	−0.588374	−	0.588374i
$868$		0			0
$869$	−10.1406	+	10.1406i	−0.343996	+	0.343996i
$870$		0			0
$871$			14.2003i			0.481158i
$872$		0			0
$873$			18.3746i			0.621886i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−21.8386	−	21.8386i	−0.737436	−	0.737436i	0.234645	−	0.972081i	$-0.424607\pi$
$877$	−21.8386	−	21.8386i	−0.737436	−	0.737436i	−0.972081	+	0.234645i	$0.924607\pi$
$878$		0			0
$879$	−25.0985			−0.846550
$880$		0			0
$881$	−39.3274			−1.32497			−0.662487	−	0.749073i	$-0.730499\pi$
$881$	−39.3274			−1.32497			−0.662487	+	0.749073i	$0.730499\pi$
$882$		0			0
$883$	6.80206	+	6.80206i	0.228907	+	0.228907i	0.812236	−	0.583329i	$-0.198250\pi$
$883$	6.80206	+	6.80206i	0.228907	+	0.228907i	−0.583329	+	0.812236i	$0.698250\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			29.4190i			0.987793i	0.869521	+	0.493897i	$0.164428\pi$
$887$			29.4190i			0.987793i	−0.869521	+	0.493897i	$0.835572\pi$
$888$		0			0
$889$			33.8566i			1.13552i
$890$		0			0
$891$	33.3630	−	33.3630i	1.11770	−	1.11770i
$892$		0			0
$893$	8.78917	+	8.78917i	0.294118	+	0.294118i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	48.0822			1.60542
$898$		0			0
$899$	5.16070	+	5.16070i	0.172119	+	0.172119i
$900$		0			0
$901$	17.9290	−	17.9290i	0.597301	−	0.597301i
$902$		0			0
$903$			5.18748i			0.172628i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−16.6137	+	16.6137i	−0.551649	+	0.551649i	−0.926917	−	0.375267i	$-0.877551\pi$
$907$	−16.6137	+	16.6137i	−0.551649	+	0.551649i	0.375267	+	0.926917i	$0.377551\pi$
$908$		0			0
$909$	−2.69382	−	2.69382i	−0.0893485	−	0.0893485i
$910$		0			0
$911$	−40.7299			−1.34944			−0.674721	−	0.738073i	$-0.735736\pi$
$911$	−40.7299			−1.34944			−0.674721	+	0.738073i	$0.735736\pi$
$912$		0			0
$913$	−6.52396			−0.215912
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11.9846	+	11.9846i	−0.395765	+	0.395765i
$918$		0			0
$919$			35.6125i			1.17475i	0.809316	+	0.587373i	$0.199838\pi$
$919$			35.6125i			1.17475i	−0.809316	+	0.587373i	$0.800162\pi$
$920$		0			0
$921$		−	42.4064i		−	1.39734i
$922$		0			0
$923$	−17.7560	+	17.7560i	−0.584446	+	0.584446i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	21.0369			0.690942
$928$		0			0
$929$	−0.570971			−0.0187329			−0.00936647	−	0.999956i	$-0.502981\pi$
$929$	−0.570971			−0.0187329			−0.00936647	+	0.999956i	$0.502981\pi$
$930$		0			0
$931$	20.1199	+	20.1199i	0.659404	+	0.659404i
$932$		0			0
$933$	19.8994	−	19.8994i	0.651477	−	0.651477i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			21.3585i			0.697750i	0.937169	+	0.348875i	$0.113436\pi$
$937$			21.3585i			0.697750i	−0.937169	+	0.348875i	$0.886564\pi$
$938$		0			0
$939$	57.2830	−	57.2830i	1.86936	−	1.86936i
$940$		0			0
$941$	33.6914	+	33.6914i	1.09831	+	1.09831i	0.994609	+	0.103700i	$0.0330681\pi$
$941$	33.6914	+	33.6914i	1.09831	+	1.09831i	0.103700	+	0.994609i	$0.466932\pi$
$942$		0			0
$943$	7.18358			0.233929
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.421834	−	0.421834i	−0.0137078	−	0.0137078i	0.700220	−	0.713927i	$-0.253085\pi$
$947$	−0.421834	−	0.421834i	−0.0137078	−	0.0137078i	−0.713927	+	0.700220i	$0.753085\pi$
$948$		0			0
$949$	−1.68420	+	1.68420i	−0.0546714	+	0.0546714i
$950$		0			0
$951$		−	57.0771i		−	1.85085i
$952$		0			0
$953$			27.7261i			0.898137i	0.893497	+	0.449069i	$0.148244\pi$
$953$			27.7261i			0.898137i	−0.893497	+	0.449069i	$0.851756\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	71.0204	+	71.0204i	2.29576	+	2.29576i
$958$		0			0
$959$	20.1156			0.649567
$960$		0			0
$961$	−30.3614			−0.979399
$962$		0			0
$963$	−7.32450	−	7.32450i	−0.236029	−	0.236029i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	41.9640i		−	1.34947i	−0.738060	−	0.674735i	$-0.764258\pi$
$967$		−	41.9640i		−	1.34947i	0.738060	−	0.674735i	$-0.235742\pi$
$968$		0			0
$969$		−	49.4614i		−	1.58893i
$970$		0			0
$971$	−30.0549	+	30.0549i	−0.964508	+	0.964508i	−0.999391	−	0.0348833i	$-0.988894\pi$
$971$	−30.0549	+	30.0549i	−0.964508	+	0.964508i	0.0348833	+	0.999391i	$0.488894\pi$
$972$		0			0
$973$	4.32990	+	4.32990i	0.138810	+	0.138810i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−44.3389			−1.41853			−0.709263	−	0.704944i	$-0.750972\pi$
$977$	−44.3389			−1.41853			−0.709263	+	0.704944i	$0.750972\pi$
$978$		0			0
$979$	−33.2800	−	33.2800i	−1.06363	−	1.06363i
$980$		0			0
$981$	29.1539	−	29.1539i	0.930814	−	0.930814i
$982$		0			0
$983$		−	27.0764i		−	0.863604i	−0.901968	−	0.431802i	$-0.857878\pi$
$983$		−	27.0764i		−	0.863604i	0.901968	−	0.431802i	$-0.142122\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.76323	+	4.76323i	−0.151615	+	0.151615i
$988$		0			0
$989$	6.29606	+	6.29606i	0.200203	+	0.200203i
$990$		0			0
$991$	−19.3780			−0.615564			−0.307782	−	0.951457i	$-0.599587\pi$
$991$	−19.3780			−0.615564			−0.307782	+	0.951457i	$0.599587\pi$
$992$		0			0
$993$	−32.6977			−1.03763
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−8.69453	+	8.69453i	−0.275359	+	0.275359i	−0.831253	−	0.555894i	$-0.812376\pi$
$997$	−8.69453	+	8.69453i	−0.275359	+	0.275359i	0.555894	+	0.831253i	$0.312376\pi$
$998$		0			0
$999$			3.92782i			0.124271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.l.f.401.6		12
4.3	odd	2		400.2.l.g.301.4	yes	12
5.2	odd	4		1600.2.q.e.849.6		12
5.3	odd	4		1600.2.q.f.849.1		12
5.4	even	2		1600.2.l.g.401.1		12
16.5	even	4	inner	1600.2.l.f.1201.6		12
16.11	odd	4		400.2.l.g.101.4	yes	12
20.3	even	4		400.2.q.f.349.5		12
20.7	even	4		400.2.q.e.349.2		12
20.19	odd	2		400.2.l.f.301.3	yes	12
80.27	even	4		400.2.q.f.149.5		12
80.37	odd	4		1600.2.q.f.49.1		12
80.43	even	4		400.2.q.e.149.2		12
80.53	odd	4		1600.2.q.e.49.6		12
80.59	odd	4		400.2.l.f.101.3	✓	12
80.69	even	4		1600.2.l.g.1201.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.3	✓	12	80.59	odd	4
400.2.l.f.301.3	yes	12	20.19	odd	2
400.2.l.g.101.4	yes	12	16.11	odd	4
400.2.l.g.301.4	yes	12	4.3	odd	2
400.2.q.e.149.2		12	80.43	even	4
400.2.q.e.349.2		12	20.7	even	4
400.2.q.f.149.5		12	80.27	even	4
400.2.q.f.349.5		12	20.3	even	4
1600.2.l.f.401.6		12	1.1	even	1	trivial
1600.2.l.f.1201.6		12	16.5	even	4	inner
1600.2.l.g.401.1		12	5.4	even	2
1600.2.l.g.1201.1		12	80.69	even	4
1600.2.q.e.49.6		12	80.53	odd	4
1600.2.q.e.849.6		12	5.2	odd	4
1600.2.q.f.49.1		12	80.37	odd	4
1600.2.q.f.849.1		12	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.66783 + 1.66783i) q^{3} +1.87372i q^{7} +2.56332i q^{9} +O(q^{10})\)	\(q+(1.66783 + 1.66783i) q^{3} +1.87372i q^{7} +2.56332i q^{9} +(3.29695 - 3.29695i) q^{11} +(-1.90022 - 1.90022i) q^{13} -2.57148 q^{17} +(5.76636 + 5.76636i) q^{19} +(-3.12504 + 3.12504i) q^{21} +7.58574i q^{23} +(0.728312 - 0.728312i) q^{27} +(6.45786 + 6.45786i) q^{29} +0.799135 q^{31} +10.9975 q^{33} +(-2.69652 + 2.69652i) q^{37} -6.33850i q^{39} -0.946984i q^{41} +(0.829986 - 0.829986i) q^{43} +1.52421 q^{47} +3.48919 q^{49} +(-4.28879 - 4.28879i) q^{51} +(-6.97225 + 6.97225i) q^{53} +19.2346i q^{57} +(-6.84418 + 6.84418i) q^{59} +(-6.87247 - 6.87247i) q^{61} -4.80293 q^{63} +(-3.73647 - 3.73647i) q^{67} +(-12.6517 + 12.6517i) q^{69} -9.34417i q^{71} -0.886316i q^{73} +(6.17755 + 6.17755i) q^{77} -3.07575 q^{79} +10.1194 q^{81} +(-0.989393 - 0.989393i) q^{83} +21.5412i q^{87} -10.0942i q^{89} +(3.56048 - 3.56048i) q^{91} +(1.33282 + 1.33282i) q^{93} +7.16829 q^{97} +(8.45113 + 8.45113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3}+O(q^{10}) \) 12 * q - 2 * q^3	\( 12 q - 2 q^{3} + 2 q^{11} - 4 q^{13} - 8 q^{17} + 14 q^{19} - 20 q^{21} + 10 q^{27} + 4 q^{31} + 28 q^{33} + 8 q^{37} - 8 q^{47} + 4 q^{49} - 10 q^{51} - 16 q^{53} - 20 q^{59} + 4 q^{61} + 8 q^{63} - 50 q^{67} - 8 q^{77} - 12 q^{79} - 8 q^{81} + 2 q^{83} - 44 q^{93} - 12 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 2 * q^11 - 4 * q^13 - 8 * q^17 + 14 * q^19 - 20 * q^21 + 10 * q^27 + 4 * q^31 + 28 * q^33 + 8 * q^37 - 8 * q^47 + 4 * q^49 - 10 * q^51 - 16 * q^53 - 20 * q^59 + 4 * q^61 + 8 * q^63 - 50 * q^67 - 8 * q^77 - 12 * q^79 - 8 * q^81 + 2 * q^83 - 44 * q^93 - 12 * q^99

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