LMFDB - Embedded newform 1620.4.i.j.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,4,Mod(541,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1620.541");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1620.i (of order $3$, 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:	$95.5830942093$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1620.541
Dual form			1620.4.i.j.1081.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.50000 + 4.33013i) q^{5} +(8.00000 - 13.8564i) q^{7} +O(q^{10})$	$q+(2.50000 + 4.33013i) q^{5} +(8.00000 - 13.8564i) q^{7} +(-30.0000 + 51.9615i) q^{11} +(-43.0000 - 74.4782i) q^{13} -18.0000 q^{17} +44.0000 q^{19} +(24.0000 + 41.5692i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-93.0000 + 161.081i) q^{29} +(-88.0000 - 152.420i) q^{31} +80.0000 q^{35} +254.000 q^{37} +(93.0000 + 161.081i) q^{41} +(50.0000 - 86.6025i) q^{43} +(84.0000 - 145.492i) q^{47} +(43.5000 + 75.3442i) q^{49} +498.000 q^{53} -300.000 q^{55} +(-126.000 - 218.238i) q^{59} +(29.0000 - 50.2295i) q^{61} +(215.000 - 372.391i) q^{65} +(518.000 + 897.202i) q^{67} -168.000 q^{71} +506.000 q^{73} +(480.000 + 831.384i) q^{77} +(-136.000 + 235.559i) q^{79} +(474.000 - 820.992i) q^{83} +(-45.0000 - 77.9423i) q^{85} +1014.00 q^{89} -1376.00 q^{91} +(110.000 + 190.526i) q^{95} +(383.000 - 663.375i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 5 q^{5} + 16 q^{7}+O(q^{10}) $ 2 * q + 5 * q^5 + 16 * q^7	$ 2 q + 5 q^{5} + 16 q^{7} - 60 q^{11} - 86 q^{13} - 36 q^{17} + 88 q^{19} + 48 q^{23} - 25 q^{25} - 186 q^{29} - 176 q^{31} + 160 q^{35} + 508 q^{37} + 186 q^{41} + 100 q^{43} + 168 q^{47} + 87 q^{49} + 996 q^{53} - 600 q^{55} - 252 q^{59} + 58 q^{61} + 430 q^{65} + 1036 q^{67} - 336 q^{71} + 1012 q^{73} + 960 q^{77} - 272 q^{79} + 948 q^{83} - 90 q^{85} + 2028 q^{89} - 2752 q^{91} + 220 q^{95} + 766 q^{97}+O(q^{100}) $ 2 * q + 5 * q^5 + 16 * q^7 - 60 * q^11 - 86 * q^13 - 36 * q^17 + 88 * q^19 + 48 * q^23 - 25 * q^25 - 186 * q^29 - 176 * q^31 + 160 * q^35 + 508 * q^37 + 186 * q^41 + 100 * q^43 + 168 * q^47 + 87 * q^49 + 996 * q^53 - 600 * q^55 - 252 * q^59 + 58 * q^61 + 430 * q^65 + 1036 * q^67 - 336 * q^71 + 1012 * q^73 + 960 * q^77 - 272 * q^79 + 948 * q^83 - 90 * q^85 + 2028 * q^89 - 2752 * q^91 + 220 * q^95 + 766 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	8.00000	−	13.8564i	0.431959	−	0.748176i	−0.565083	−	0.825034i	$-0.691156\pi$
$7$	8.00000	−	13.8564i	0.431959	−	0.748176i	0.997042	+	0.0768587i	$0.0244890\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−30.0000	+	51.9615i	−0.822304	+	1.42427i	0.0816590	+	0.996660i	$0.473978\pi$
$11$	−30.0000	+	51.9615i	−0.822304	+	1.42427i	−0.903963	+	0.427611i	$0.859355\pi$
$12$		0			0
$13$	−43.0000	−	74.4782i	−0.917389	−	1.58896i	−0.803366	−	0.595486i	$-0.796960\pi$
$13$	−43.0000	−	74.4782i	−0.917389	−	1.58896i	−0.114023	−	0.993478i	$-0.536374\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−18.0000			−0.256802			−0.128401	−	0.991722i	$-0.540985\pi$
$17$	−18.0000			−0.256802			−0.128401	+	0.991722i	$0.540985\pi$
$18$		0			0
$19$	44.0000			0.531279			0.265639	−	0.964072i	$-0.414417\pi$
$19$	44.0000			0.531279			0.265639	+	0.964072i	$0.414417\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	24.0000	+	41.5692i	0.217580	+	0.376860i	0.954068	−	0.299591i	$-0.0968503\pi$
$23$	24.0000	+	41.5692i	0.217580	+	0.376860i	−0.736487	+	0.676451i	$0.763517\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−93.0000	+	161.081i	−0.595506	+	1.03145i	0.397970	+	0.917399i	$0.369715\pi$
$29$	−93.0000	+	161.081i	−0.595506	+	1.03145i	−0.993475	+	0.114048i	$0.963618\pi$
$30$		0			0
$31$	−88.0000	−	152.420i	−0.509847	−	0.883081i	−0.999935	−	0.0114083i	$-0.996369\pi$
$31$	−88.0000	−	152.420i	−0.509847	−	0.883081i	0.490088	−	0.871673i	$-0.336965\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	80.0000			0.386356
$36$		0			0
$37$	254.000			1.12858			0.564288	−	0.825578i	$-0.309151\pi$
$37$	254.000			1.12858			0.564288	+	0.825578i	$0.309151\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	93.0000	+	161.081i	0.354248	+	0.613575i	0.986989	−	0.160788i	$-0.0514036\pi$
$41$	93.0000	+	161.081i	0.354248	+	0.613575i	−0.632741	+	0.774363i	$0.718070\pi$
$42$		0			0
$43$	50.0000	−	86.6025i	0.177324	−	0.307134i	−0.763639	−	0.645643i	$-0.776589\pi$
$43$	50.0000	−	86.6025i	0.177324	−	0.307134i	0.940963	+	0.338509i	$0.109923\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	84.0000	−	145.492i	0.260695	−	0.451537i	−0.705732	−	0.708479i	$-0.749382\pi$
$47$	84.0000	−	145.492i	0.260695	−	0.451537i	0.966427	+	0.256942i	$0.0827150\pi$
$48$		0			0
$49$	43.5000	+	75.3442i	0.126822	+	0.219662i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	498.000			1.29067			0.645335	−	0.763899i	$-0.276718\pi$
$53$	498.000			1.29067			0.645335	+	0.763899i	$0.276718\pi$
$54$		0			0
$55$	−300.000			−0.735491
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−126.000	−	218.238i	−0.278031	−	0.481563i	0.692865	−	0.721068i	$-0.256348\pi$
$59$	−126.000	−	218.238i	−0.278031	−	0.481563i	−0.970895	+	0.239505i	$0.923015\pi$
$60$		0			0
$61$	29.0000	−	50.2295i	0.0608700	−	0.105430i	−0.833985	−	0.551788i	$-0.813946\pi$
$61$	29.0000	−	50.2295i	0.0608700	−	0.105430i	0.894855	+	0.446358i	$0.147279\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	215.000	−	372.391i	0.410269	−	0.710606i
$66$		0			0
$67$	518.000	+	897.202i	0.944534	+	1.63598i	0.756682	+	0.653783i	$0.226819\pi$
$67$	518.000	+	897.202i	0.944534	+	1.63598i	0.187852	+	0.982197i	$0.439847\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−168.000			−0.280816			−0.140408	−	0.990094i	$-0.544841\pi$
$71$	−168.000			−0.280816			−0.140408	+	0.990094i	$0.544841\pi$
$72$		0			0
$73$	506.000			0.811272			0.405636	−	0.914035i	$-0.367050\pi$
$73$	506.000			0.811272			0.405636	+	0.914035i	$0.367050\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	480.000	+	831.384i	0.710404	+	1.23046i
$78$		0			0
$79$	−136.000	+	235.559i	−0.193686	+	0.335474i	−0.946469	−	0.322795i	$-0.895378\pi$
$79$	−136.000	+	235.559i	−0.193686	+	0.335474i	0.752783	+	0.658269i	$0.228711\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	474.000	−	820.992i	0.626846	−	1.08573i	−0.361334	−	0.932436i	$-0.617679\pi$
$83$	474.000	−	820.992i	0.626846	−	1.08573i	0.988181	−	0.153294i	$-0.0489880\pi$
$84$		0			0
$85$	−45.0000	−	77.9423i	−0.0574228	−	0.0994592i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1014.00			1.20768			0.603841	−	0.797104i	$-0.293636\pi$
$89$	1014.00			1.20768			0.603841	+	0.797104i	$0.293636\pi$
$90$		0			0
$91$	−1376.00			−1.58510
$92$		0			0
$93$		0			0
$94$		0			0
$95$	110.000	+	190.526i	0.118797	+	0.205763i
$96$		0			0
$97$	383.000	−	663.375i	0.400905	−	0.694387i	−0.592931	−	0.805254i	$-0.702029\pi$
$97$	383.000	−	663.375i	0.400905	−	0.694387i	0.993835	+	0.110866i	$0.0353625\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−657.000	+	1137.96i	−0.647267	+	1.12110i	0.336506	+	0.941681i	$0.390755\pi$
$101$	−657.000	+	1137.96i	−0.647267	+	1.12110i	−0.983773	+	0.179418i	$0.942579\pi$
$102$		0			0
$103$	224.000	+	387.979i	0.214285	+	0.371153i	0.953051	−	0.302809i	$-0.0979245\pi$
$103$	224.000	+	387.979i	0.214285	+	0.371153i	−0.738766	+	0.673962i	$0.764591\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1548.00			−1.39861			−0.699303	−	0.714826i	$-0.746506\pi$
$107$	−1548.00			−1.39861			−0.699303	+	0.714826i	$0.746506\pi$
$108$		0			0
$109$	278.000			0.244290			0.122145	−	0.992512i	$-0.461023\pi$
$109$	278.000			0.244290			0.122145	+	0.992512i	$0.461023\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−279.000	−	483.242i	−0.232266	−	0.402297i	0.726208	−	0.687475i	$-0.241281\pi$
$113$	−279.000	−	483.242i	−0.232266	−	0.402297i	−0.958475	+	0.285177i	$0.907947\pi$
$114$		0			0
$115$	−120.000	+	207.846i	−0.0973048	+	0.168537i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−144.000	+	249.415i	−0.110928	+	0.192133i
$120$		0			0
$121$	−1134.50	−	1965.01i	−0.852367	−	1.47634i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−125.000			−0.0894427
$126$		0			0
$127$	344.000			0.240355			0.120177	−	0.992752i	$-0.461654\pi$
$127$	344.000			0.240355			0.120177	+	0.992752i	$0.461654\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	390.000	+	675.500i	0.260110	+	0.450524i	0.966271	−	0.257527i	$-0.0829077\pi$
$131$	390.000	+	675.500i	0.260110	+	0.450524i	−0.706161	+	0.708052i	$0.749574\pi$
$132$		0			0
$133$	352.000	−	609.682i	0.229491	−	0.397490i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	333.000	−	576.773i	0.207665	−	0.359686i	−0.743314	−	0.668943i	$-0.766747\pi$
$137$	333.000	−	576.773i	0.207665	−	0.359686i	0.950979	+	0.309257i	$0.100080\pi$
$138$		0			0
$139$	−442.000	−	765.566i	−0.269712	−	0.467155i	0.699075	−	0.715048i	$-0.253595\pi$
$139$	−442.000	−	765.566i	−0.269712	−	0.467155i	−0.968787	+	0.247893i	$0.920262\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5160.00			3.01749
$144$		0			0
$145$	−930.000			−0.532637
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−57.0000	−	98.7269i	−0.0313397	−	0.0542820i	0.849930	−	0.526895i	$-0.176644\pi$
$149$	−57.0000	−	98.7269i	−0.0313397	−	0.0542820i	−0.881270	+	0.472613i	$0.843311\pi$
$150$		0			0
$151$	20.0000	−	34.6410i	0.0107787	−	0.0186692i	−0.860586	−	0.509306i	$-0.829902\pi$
$151$	20.0000	−	34.6410i	0.0107787	−	0.0186692i	0.871364	+	0.490636i	$0.163236\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	440.000	−	762.102i	0.228011	−	0.394926i
$156$		0			0
$157$	77.0000	+	133.368i	0.0391418	+	0.0677957i	0.884933	−	0.465719i	$-0.154204\pi$
$157$	77.0000	+	133.368i	0.0391418	+	0.0677957i	−0.845791	+	0.533515i	$0.820871\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	768.000			0.375943
$162$		0			0
$163$	2180.00			1.04755			0.523775	−	0.851856i	$-0.324523\pi$
$163$	2180.00			1.04755			0.523775	+	0.851856i	$0.324523\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1848.00	+	3200.83i	0.856303	+	1.48316i	0.875431	+	0.483343i	$0.160577\pi$
$167$	1848.00	+	3200.83i	0.856303	+	1.48316i	−0.0191287	+	0.999817i	$0.506089\pi$
$168$		0			0
$169$	−2599.50	+	4502.47i	−1.18320	+	2.04937i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	651.000	−	1127.57i	0.286096	−	0.495533i	−0.686778	−	0.726867i	$-0.740976\pi$
$173$	651.000	−	1127.57i	0.286096	−	0.495533i	0.972874	+	0.231334i	$0.0743090\pi$
$174$		0			0
$175$	200.000	+	346.410i	0.0863919	+	0.149635i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4308.00			1.79885			0.899427	−	0.437070i	$-0.143984\pi$
$179$	4308.00			1.79885			0.899427	+	0.437070i	$0.143984\pi$
$180$		0			0
$181$	1550.00			0.636523			0.318261	−	0.948003i	$-0.396901\pi$
$181$	1550.00			0.636523			0.318261	+	0.948003i	$0.396901\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	635.000	+	1099.85i	0.252357	+	0.437096i
$186$		0			0
$187$	540.000	−	935.307i	0.211170	−	0.365756i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	24.0000	−	41.5692i	0.00909204	−	0.0157479i	−0.861444	−	0.507853i	$-0.830439\pi$
$191$	24.0000	−	41.5692i	0.00909204	−	0.0157479i	0.870536	+	0.492105i	$0.163773\pi$
$192$		0			0
$193$	−529.000	−	916.255i	−0.197297	−	0.341728i	0.750354	−	0.661036i	$-0.229883\pi$
$193$	−529.000	−	916.255i	−0.197297	−	0.341728i	−0.947651	+	0.319308i	$0.896550\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3714.00			1.34321			0.671603	−	0.740911i	$-0.265606\pi$
$197$	3714.00			1.34321			0.671603	+	0.740911i	$0.265606\pi$
$198$		0			0
$199$	−1768.00			−0.629800			−0.314900	−	0.949125i	$-0.601971\pi$
$199$	−1768.00			−0.629800			−0.314900	+	0.949125i	$0.601971\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1488.00	+	2577.29i	0.514469	+	0.891086i
$204$		0			0
$205$	−465.000	+	805.404i	−0.158424	+	0.274399i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1320.00	+	2286.31i	−0.436872	+	0.756685i
$210$		0			0
$211$	2018.00	+	3495.28i	0.658412	+	1.14040i	0.981027	+	0.193872i	$0.0621047\pi$
$211$	2018.00	+	3495.28i	0.658412	+	1.14040i	−0.322615	+	0.946530i	$0.604562\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	500.000			0.158603
$216$		0			0
$217$	−2816.00			−0.880933
$218$		0			0
$219$		0			0
$220$		0			0
$221$	774.000	+	1340.61i	0.235588	+	0.408050i
$222$		0			0
$223$	−340.000	+	588.897i	−0.102099	+	0.176841i	−0.912549	−	0.408967i	$-0.865889\pi$
$223$	−340.000	+	588.897i	−0.102099	+	0.176841i	0.810450	+	0.585807i	$0.199223\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1194.00	−	2068.07i	0.349113	−	0.604681i	−0.636979	−	0.770881i	$-0.719816\pi$
$227$	1194.00	−	2068.07i	0.349113	−	0.604681i	0.986092	+	0.166200i	$0.0531497\pi$
$228$		0			0
$229$	1937.00	+	3354.98i	0.558954	+	0.968137i	0.997584	+	0.0694695i	$0.0221307\pi$
$229$	1937.00	+	3354.98i	0.558954	+	0.968137i	−0.438630	+	0.898668i	$0.644536\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3162.00			−0.889054			−0.444527	−	0.895766i	$-0.646628\pi$
$233$	−3162.00			−0.889054			−0.444527	+	0.895766i	$0.646628\pi$
$234$		0			0
$235$	840.000			0.233173
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2712.00	+	4697.32i	0.733995	+	1.27132i	0.955163	+	0.296080i	$0.0956796\pi$
$239$	2712.00	+	4697.32i	0.733995	+	1.27132i	−0.221169	+	0.975236i	$0.570987\pi$
$240$		0			0
$241$	1943.00	−	3365.37i	0.519335	−	0.899514i	−0.480413	−	0.877042i	$-0.659513\pi$
$241$	1943.00	−	3365.37i	0.519335	−	0.899514i	0.999747	−	0.0224714i	$-0.00715348\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−217.500	+	376.721i	−0.0567166	+	0.0982360i
$246$		0			0
$247$	−1892.00	−	3277.04i	−0.487389	−	0.844182i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5100.00			1.28251			0.641253	−	0.767329i	$-0.278415\pi$
$251$	5100.00			1.28251			0.641253	+	0.767329i	$0.278415\pi$
$252$		0			0
$253$	−2880.00			−0.715668
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1089.00	+	1886.20i	0.264319	+	0.457814i	0.967385	−	0.253311i	$-0.0815195\pi$
$257$	1089.00	+	1886.20i	0.264319	+	0.457814i	−0.703066	+	0.711125i	$0.748186\pi$
$258$		0			0
$259$	2032.00	−	3519.53i	0.487499	−	0.844374i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3072.00	+	5320.86i	−0.720257	+	1.24752i	0.240639	+	0.970615i	$0.422643\pi$
$263$	−3072.00	+	5320.86i	−0.720257	+	1.24752i	−0.960897	+	0.276907i	$0.910690\pi$
$264$		0			0
$265$	1245.00	+	2156.40i	0.288603	+	0.499875i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−822.000			−0.186313			−0.0931566	−	0.995651i	$-0.529696\pi$
$269$	−822.000			−0.186313			−0.0931566	+	0.995651i	$0.529696\pi$
$270$		0			0
$271$	8480.00			1.90082			0.950412	−	0.310994i	$-0.100662\pi$
$271$	8480.00			1.90082			0.950412	+	0.310994i	$0.100662\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−750.000	−	1299.04i	−0.164461	−	0.284854i
$276$		0			0
$277$	569.000	−	985.537i	0.123422	−	0.213773i	−0.797693	−	0.603064i	$-0.793946\pi$
$277$	569.000	−	985.537i	0.123422	−	0.213773i	0.921115	+	0.389291i	$0.127280\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2853.00	−	4941.54i	0.605679	−	1.04907i	−0.386265	−	0.922388i	$-0.626235\pi$
$281$	2853.00	−	4941.54i	0.605679	−	1.04907i	0.991944	−	0.126678i	$-0.0404316\pi$
$282$		0			0
$283$	1514.00	+	2622.32i	0.318014	+	0.550816i	0.980074	−	0.198635i	$-0.0636508\pi$
$283$	1514.00	+	2622.32i	0.318014	+	0.550816i	−0.662060	+	0.749451i	$0.730317\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2976.00			0.612083
$288$		0			0
$289$	−4589.00			−0.934053
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1695.00	+	2935.83i	0.337962	+	0.585368i	0.984049	−	0.177896i	$-0.0569290\pi$
$293$	1695.00	+	2935.83i	0.337962	+	0.585368i	−0.646087	+	0.763264i	$0.723596\pi$
$294$		0			0
$295$	630.000	−	1091.19i	0.124339	−	0.215362i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2064.00	−	3574.95i	0.399211	−	0.691454i
$300$		0			0
$301$	−800.000	−	1385.64i	−0.153193	−	0.265339i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	290.000			0.0544438
$306$		0			0
$307$	−4156.00			−0.772624			−0.386312	−	0.922368i	$-0.626251\pi$
$307$	−4156.00			−0.772624			−0.386312	+	0.922368i	$0.626251\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3276.00	+	5674.20i	0.597315	+	1.03458i	0.993216	+	0.116286i	$0.0370990\pi$
$311$	3276.00	+	5674.20i	0.597315	+	1.03458i	−0.395901	+	0.918293i	$0.629568\pi$
$312$		0			0
$313$	683.000	−	1182.99i	0.123340	−	0.213631i	−0.797743	−	0.602998i	$-0.793973\pi$
$313$	683.000	−	1182.99i	0.123340	−	0.213631i	0.921083	+	0.389367i	$0.127306\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1299.00	−	2249.93i	0.230155	−	0.398640i	−0.727699	−	0.685897i	$-0.759410\pi$
$317$	1299.00	−	2249.93i	0.230155	−	0.398640i	0.957854	+	0.287257i	$0.0927434\pi$
$318$		0			0
$319$	−5580.00	−	9664.84i	−0.979373	−	1.69632i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−792.000			−0.136434
$324$		0			0
$325$	2150.00			0.366956
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1344.00	−	2327.88i	−0.225219	−	0.390091i
$330$		0			0
$331$	1646.00	−	2850.96i	0.273330	−	0.473422i	−0.696382	−	0.717671i	$-0.745208\pi$
$331$	1646.00	−	2850.96i	0.273330	−	0.473422i	0.969713	+	0.244249i	$0.0785415\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2590.00	+	4486.01i	−0.422408	+	0.731633i
$336$		0			0
$337$	−3097.00	−	5364.16i	−0.500606	−	0.867076i	−1.00000		0.000700294i	$-0.999777\pi$
$337$	−3097.00	−	5364.16i	−0.500606	−	0.867076i	0.499393	−	0.866375i	$-0.333556\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	10560.0			1.67700
$342$		0			0
$343$	6880.00			1.08305
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5010.00	−	8677.57i	−0.775075	−	1.34247i	−0.934753	−	0.355299i	$-0.884379\pi$
$347$	−5010.00	−	8677.57i	−0.775075	−	1.34247i	0.159678	−	0.987169i	$-0.448954\pi$
$348$		0			0
$349$	1565.00	−	2710.66i	0.240036	−	0.415754i	−0.720688	−	0.693259i	$-0.756174\pi$
$349$	1565.00	−	2710.66i	0.240036	−	0.415754i	0.960724	+	0.277505i	$0.0895074\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2097.00	−	3632.11i	0.316181	−	0.547642i	−0.663506	−	0.748171i	$-0.730932\pi$
$353$	2097.00	−	3632.11i	0.316181	−	0.547642i	0.979688	+	0.200528i	$0.0642658\pi$
$354$		0			0
$355$	−420.000	−	727.461i	−0.0627924	−	0.108760i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4104.00			0.603345			0.301672	−	0.953412i	$-0.402455\pi$
$359$	4104.00			0.603345			0.301672	+	0.953412i	$0.402455\pi$
$360$		0			0
$361$	−4923.00			−0.717743
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1265.00	+	2191.04i	0.181406	+	0.314204i
$366$		0			0
$367$	−3748.00	+	6491.73i	−0.533090	+	0.923339i	0.466163	+	0.884699i	$0.345636\pi$
$367$	−3748.00	+	6491.73i	−0.533090	+	0.923339i	−0.999253	+	0.0386401i	$0.987697\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3984.00	−	6900.49i	0.557517	−	0.965649i
$372$		0			0
$373$	2921.00	+	5059.32i	0.405479	+	0.702310i	0.994377	−	0.105897i	$-0.0337714\pi$
$373$	2921.00	+	5059.32i	0.405479	+	0.702310i	−0.588898	+	0.808207i	$0.700438\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15996.0			2.18524
$378$		0			0
$379$	−412.000			−0.0558391			−0.0279195	−	0.999610i	$-0.508888\pi$
$379$	−412.000			−0.0558391			−0.0279195	+	0.999610i	$0.508888\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1284.00	+	2223.95i	0.171304	+	0.296707i	0.938876	−	0.344256i	$-0.111869\pi$
$383$	1284.00	+	2223.95i	0.171304	+	0.296707i	−0.767572	+	0.640963i	$0.778535\pi$
$384$		0			0
$385$	−2400.00	+	4156.92i	−0.317702	+	0.550276i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6543.00	−	11332.8i	0.852810	−	1.47711i	−0.0258510	−	0.999666i	$-0.508230\pi$
$389$	6543.00	−	11332.8i	0.852810	−	1.47711i	0.878662	−	0.477445i	$-0.158437\pi$
$390$		0			0
$391$	−432.000	−	748.246i	−0.0558751	−	0.0967786i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1360.00			−0.173238
$396$		0			0
$397$	10454.0			1.32159			0.660795	−	0.750566i	$-0.270219\pi$
$397$	10454.0			1.32159			0.660795	+	0.750566i	$0.270219\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5415.00	−	9379.06i	−0.674345	−	1.16800i	−0.976660	−	0.214791i	$-0.931093\pi$
$401$	−5415.00	−	9379.06i	−0.674345	−	1.16800i	0.302315	−	0.953208i	$-0.402240\pi$
$402$		0			0
$403$	−7568.00	+	13108.2i	−0.935456	+	1.62026i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7620.00	+	13198.2i	−0.928033	+	1.60740i
$408$		0			0
$409$	4283.00	+	7418.37i	0.517801	+	0.896858i	0.999786	+	0.0206786i	$0.00658267\pi$
$409$	4283.00	+	7418.37i	0.517801	+	0.896858i	−0.481985	+	0.876180i	$0.660084\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4032.00			−0.480392
$414$		0			0
$415$	4740.00			0.560669
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6942.00	+	12023.9i	0.809401	+	1.40192i	0.913280	+	0.407333i	$0.133541\pi$
$419$	6942.00	+	12023.9i	0.809401	+	1.40192i	−0.103879	+	0.994590i	$0.533125\pi$
$420$		0			0
$421$	−2143.00	+	3711.78i	−0.248084	+	0.429694i	−0.962994	−	0.269522i	$-0.913134\pi$
$421$	−2143.00	+	3711.78i	−0.248084	+	0.429694i	0.714910	+	0.699216i	$0.246468\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	225.000	−	389.711i	0.0256802	−	0.0444795i
$426$		0			0
$427$	−464.000	−	803.672i	−0.0525867	−	0.0910829i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6336.00			−0.708108			−0.354054	−	0.935225i	$-0.615197\pi$
$431$	−6336.00			−0.708108			−0.354054	+	0.935225i	$0.615197\pi$
$432$		0			0
$433$	−8974.00			−0.995988			−0.497994	−	0.867180i	$-0.665930\pi$
$433$	−8974.00			−0.995988			−0.497994	+	0.867180i	$0.665930\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1056.00	+	1829.05i	0.115596	+	0.200218i
$438$		0			0
$439$	1484.00	−	2570.36i	0.161338	−	0.279446i	−0.774011	−	0.633173i	$-0.781752\pi$
$439$	1484.00	−	2570.36i	0.161338	−	0.279446i	0.935349	+	0.353727i	$0.115086\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6186.00	+	10714.5i	−0.663444	+	1.14912i	0.316261	+	0.948672i	$0.397573\pi$
$443$	−6186.00	+	10714.5i	−0.663444	+	1.14912i	−0.979705	+	0.200446i	$0.935761\pi$
$444$		0			0
$445$	2535.00	+	4390.75i	0.270046	+	0.467734i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−11394.0			−1.19759			−0.598793	−	0.800904i	$-0.704353\pi$
$449$	−11394.0			−1.19759			−0.598793	+	0.800904i	$0.704353\pi$
$450$		0			0
$451$	−11160.0			−1.16520
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3440.00	−	5958.25i	−0.354439	−	0.613906i
$456$		0			0
$457$	179.000	−	310.037i	0.0183222	−	0.0317351i	−0.856719	−	0.515784i	$-0.827501\pi$
$457$	179.000	−	310.037i	0.0183222	−	0.0317351i	0.875041	+	0.484049i	$0.160834\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3765.00	+	6521.17i	−0.380376	+	0.658831i	−0.991116	−	0.133000i	$-0.957539\pi$
$461$	−3765.00	+	6521.17i	−0.380376	+	0.658831i	0.610740	+	0.791832i	$0.290872\pi$
$462$		0			0
$463$	6884.00	+	11923.4i	0.690986	+	1.19682i	0.971515	+	0.236978i	$0.0761568\pi$
$463$	6884.00	+	11923.4i	0.690986	+	1.19682i	−0.280529	+	0.959846i	$0.590510\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13380.0			−1.32581			−0.662904	−	0.748704i	$-0.730676\pi$
$467$	−13380.0			−1.32581			−0.662904	+	0.748704i	$0.730676\pi$
$468$		0			0
$469$	16576.0			1.63200
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3000.00	+	5196.15i	0.291628	+	0.505115i
$474$		0			0
$475$	−550.000	+	952.628i	−0.0531279	+	0.0920201i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3168.00	+	5487.14i	−0.302191	+	0.523411i	−0.976632	−	0.214918i	$-0.931051\pi$
$479$	−3168.00	+	5487.14i	−0.302191	+	0.523411i	0.674441	+	0.738329i	$0.264385\pi$
$480$		0			0
$481$	−10922.0	−	18917.5i	−1.03534	−	1.79327i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3830.00			0.358580
$486$		0			0
$487$	−5008.00			−0.465984			−0.232992	−	0.972479i	$-0.574852\pi$
$487$	−5008.00			−0.465984			−0.232992	+	0.972479i	$0.574852\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6450.00	+	11171.7i	0.592840	+	1.02683i	0.993848	+	0.110754i	$0.0353267\pi$
$491$	6450.00	+	11171.7i	0.592840	+	1.02683i	−0.401008	+	0.916075i	$0.631340\pi$
$492$		0			0
$493$	1674.00	−	2899.45i	0.152927	−	0.264878i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1344.00	+	2327.88i	−0.121301	+	0.210100i
$498$		0			0
$499$	4058.00	+	7028.66i	0.364050	+	0.630553i	0.988623	−	0.150413i	$-0.0480603\pi$
$499$	4058.00	+	7028.66i	0.364050	+	0.630553i	−0.624573	+	0.780966i	$0.714727\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	4944.00			0.438255			0.219127	−	0.975696i	$-0.429679\pi$
$503$	4944.00			0.438255			0.219127	+	0.975696i	$0.429679\pi$
$504$		0			0
$505$	−6570.00			−0.578933
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2733.00	−	4733.69i	−0.237992	−	0.412215i	0.722146	−	0.691741i	$-0.243156\pi$
$509$	−2733.00	−	4733.69i	−0.237992	−	0.412215i	−0.960138	+	0.279526i	$0.909823\pi$
$510$		0			0
$511$	4048.00	−	7011.34i	0.350436	−	0.606974i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1120.00	+	1939.90i	−0.0958313	+	0.165985i
$516$		0			0
$517$	5040.00	+	8729.54i	0.428741	+	0.742601i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10074.0			−0.847121			−0.423560	−	0.905868i	$-0.639220\pi$
$521$	−10074.0			−0.847121			−0.423560	+	0.905868i	$0.639220\pi$
$522$		0			0
$523$	−13828.0			−1.15613			−0.578065	−	0.815991i	$-0.696192\pi$
$523$	−13828.0			−1.15613			−0.578065	+	0.815991i	$0.696192\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1584.00	+	2743.57i	0.130930	+	0.226777i
$528$		0			0
$529$	4931.50	−	8541.61i	0.405318	−	0.702031i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7998.00	−	13852.9i	0.649966	−	1.12577i
$534$		0			0
$535$	−3870.00	−	6703.04i	−0.312738	−	0.541678i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5220.00			−0.417145
$540$		0			0
$541$	−15226.0			−1.21001			−0.605006	−	0.796221i	$-0.706829\pi$
$541$	−15226.0			−1.21001			−0.605006	+	0.796221i	$0.706829\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	695.000	+	1203.78i	0.0546248	+	0.0946130i
$546$		0			0
$547$	6614.00	−	11455.8i	0.516991	−	0.895455i	−0.482814	−	0.875723i	$-0.660385\pi$
$547$	6614.00	−	11455.8i	0.516991	−	0.895455i	0.999805	−	0.0197322i	$-0.00628137\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−4092.00	+	7087.55i	−0.316379	+	0.547985i
$552$		0			0
$553$	2176.00	+	3768.94i	0.167329	+	0.289822i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8490.00			0.645840			0.322920	−	0.946426i	$-0.395336\pi$
$557$	8490.00			0.645840			0.322920	+	0.946426i	$0.395336\pi$
$558$		0			0
$559$	−8600.00			−0.650700
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5142.00	−	8906.21i	−0.384919	−	0.666699i	0.606839	−	0.794825i	$-0.292437\pi$
$563$	−5142.00	−	8906.21i	−0.384919	−	0.666699i	−0.991758	+	0.128125i	$0.959104\pi$
$564$		0			0
$565$	1395.00	−	2416.21i	0.103873	−	0.179913i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	885.000	−	1532.86i	0.0652041	−	0.112937i	−0.831580	−	0.555404i	$-0.812563\pi$
$569$	885.000	−	1532.86i	0.0652041	−	0.112937i	0.896785	+	0.442468i	$0.145897\pi$
$570$		0			0
$571$	−3034.00	−	5255.04i	−0.222362	−	0.385143i	0.733162	−	0.680054i	$-0.238043\pi$
$571$	−3034.00	−	5255.04i	−0.222362	−	0.385143i	−0.955525	+	0.294911i	$0.904710\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1200.00			−0.0870321
$576$		0			0
$577$	21506.0			1.55166			0.775829	−	0.630943i	$-0.217332\pi$
$577$	21506.0			1.55166			0.775829	+	0.630943i	$0.217332\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7584.00	−	13135.9i	−0.541544	−	0.937983i
$582$		0			0
$583$	−14940.0	+	25876.8i	−1.06132	+	1.83827i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6054.00	−	10485.8i	0.425682	−	0.737303i	−0.570802	−	0.821088i	$-0.693368\pi$
$587$	6054.00	−	10485.8i	0.425682	−	0.737303i	0.996484	+	0.0837850i	$0.0267009\pi$
$588$		0			0
$589$	−3872.00	−	6706.50i	−0.270871	−	0.469162i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15474.0			−1.07157			−0.535785	−	0.844354i	$-0.679984\pi$
$593$	−15474.0			−1.07157			−0.535785	+	0.844354i	$0.679984\pi$
$594$		0			0
$595$	−1440.00			−0.0992172
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1260.00	−	2182.38i	−0.0859469	−	0.148864i	0.819847	−	0.572582i	$-0.194058\pi$
$599$	−1260.00	−	2182.38i	−0.0859469	−	0.148864i	−0.905794	+	0.423718i	$0.860725\pi$
$600$		0			0
$601$	6395.00	−	11076.5i	0.434039	−	0.751778i	−0.563178	−	0.826336i	$-0.690421\pi$
$601$	6395.00	−	11076.5i	0.434039	−	0.751778i	0.997217	+	0.0745581i	$0.0237546\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5672.50	−	9825.06i	0.381190	−	0.660240i
$606$		0			0
$607$	−5788.00	−	10025.1i	−0.387031	−	0.670357i	0.605018	−	0.796212i	$-0.293166\pi$
$607$	−5788.00	−	10025.1i	−0.387031	−	0.670357i	−0.992049	+	0.125855i	$0.959833\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−14448.0			−0.956634
$612$		0			0
$613$	20126.0			1.32607			0.663035	−	0.748588i	$-0.269268\pi$
$613$	20126.0			1.32607			0.663035	+	0.748588i	$0.269268\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13971.0	−	24198.5i	−0.911590	−	1.57892i	−0.811818	−	0.583911i	$-0.801522\pi$
$617$	−13971.0	−	24198.5i	−0.911590	−	1.57892i	−0.0997725	−	0.995010i	$-0.531811\pi$
$618$		0			0
$619$	11270.0	−	19520.2i	0.731792	−	1.26750i	−0.224324	−	0.974515i	$-0.572017\pi$
$619$	11270.0	−	19520.2i	0.731792	−	1.26750i	0.956116	−	0.292987i	$-0.0946493\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8112.00	−	14050.4i	0.521670	−	0.903559i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4572.00			−0.289821
$630$		0			0
$631$	−5128.00			−0.323522			−0.161761	−	0.986830i	$-0.551717\pi$
$631$	−5128.00			−0.323522			−0.161761	+	0.986830i	$0.551717\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	860.000	+	1489.56i	0.0537450	+	0.0930890i
$636$		0			0
$637$	3741.00	−	6479.60i	0.232690	−	0.403032i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−6399.00	+	11083.4i	−0.394298	+	0.682945i	−0.993011	−	0.118019i	$-0.962346\pi$
$641$	−6399.00	+	11083.4i	−0.394298	+	0.682945i	0.598713	+	0.800964i	$0.295679\pi$
$642$		0			0
$643$	10574.0	+	18314.7i	0.648519	+	1.12327i	0.983477	+	0.181035i	$0.0579447\pi$
$643$	10574.0	+	18314.7i	0.648519	+	1.12327i	−0.334957	+	0.942233i	$0.608722\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16464.0			−1.00041			−0.500206	−	0.865906i	$-0.666742\pi$
$647$	−16464.0			−1.00041			−0.500206	+	0.865906i	$0.666742\pi$
$648$		0			0
$649$	15120.0			0.914502
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12117.0	−	20987.3i	−0.726148	−	1.25773i	−0.958500	−	0.285094i	$-0.907975\pi$
$653$	−12117.0	−	20987.3i	−0.726148	−	1.25773i	0.232351	−	0.972632i	$-0.425358\pi$
$654$		0			0
$655$	−1950.00	+	3377.50i	−0.116325	+	0.201481i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−11418.0	+	19776.6i	−0.674935	+	1.16902i	0.301553	+	0.953449i	$0.402495\pi$
$659$	−11418.0	+	19776.6i	−0.674935	+	1.16902i	−0.976488	+	0.215572i	$0.930838\pi$
$660$		0			0
$661$	−13159.0	−	22792.1i	−0.774320	−	1.34116i	−0.935176	−	0.354184i	$-0.884759\pi$
$661$	−13159.0	−	22792.1i	−0.774320	−	1.34116i	0.160855	−	0.986978i	$-0.448575\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3520.00			0.205263
$666$		0			0
$667$	−8928.00			−0.518281
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1740.00	+	3013.77i	0.100107	+	0.173391i
$672$		0			0
$673$	−14401.0	+	24943.3i	−0.824841	+	1.42867i	0.0772004	+	0.997016i	$0.475402\pi$
$673$	−14401.0	+	24943.3i	−0.824841	+	1.42867i	−0.902041	+	0.431650i	$0.857931\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1263.00	−	2187.58i	0.0717002	−	0.124188i	−0.827946	−	0.560807i	$-0.810491\pi$
$677$	1263.00	−	2187.58i	0.0717002	−	0.124188i	0.899647	+	0.436619i	$0.143824\pi$
$678$		0			0
$679$	−6128.00	−	10614.0i	−0.346349	−	0.599894i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	23076.0			1.29279			0.646397	−	0.763001i	$-0.276275\pi$
$683$	23076.0			1.29279			0.646397	+	0.763001i	$0.276275\pi$
$684$		0			0
$685$	3330.00			0.185741
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−21414.0	−	37090.1i	−1.18405	−	2.05083i
$690$		0			0
$691$	−3934.00	+	6813.89i	−0.216579	+	0.375127i	−0.953760	−	0.300569i	$-0.902823\pi$
$691$	−3934.00	+	6813.89i	−0.216579	+	0.375127i	0.737181	+	0.675696i	$0.236157\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2210.00	−	3827.83i	0.120619	−	0.208918i
$696$		0			0
$697$	−1674.00	−	2899.45i	−0.0909717	−	0.157568i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−21510.0			−1.15895			−0.579473	−	0.814991i	$-0.696742\pi$
$701$	−21510.0			−1.15895			−0.579473	+	0.814991i	$0.696742\pi$
$702$		0			0
$703$	11176.0			0.599589
$704$		0			0
$705$		0			0
$706$		0			0
$707$	10512.0	+	18207.3i	0.559186	+	0.968538i
$708$		0			0
$709$	−15007.0	+	25992.9i	−0.794922	+	1.37685i	0.127967	+	0.991778i	$0.459155\pi$
$709$	−15007.0	+	25992.9i	−0.794922	+	1.37685i	−0.922889	+	0.385067i	$0.874178\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4224.00	−	7316.18i	0.221865	−	0.384282i
$714$		0			0
$715$	12900.0	+	22343.5i	0.674731	+	1.16867i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	816.000			0.0423250			0.0211625	−	0.999776i	$-0.493263\pi$
$719$	816.000			0.0423250			0.0211625	+	0.999776i	$0.493263\pi$
$720$		0			0
$721$	7168.00			0.370250
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2325.00	−	4027.02i	−0.119101	−	0.206289i
$726$		0			0
$727$	4976.00	−	8618.68i	0.253851	−	0.439683i	−0.710732	−	0.703463i	$-0.751636\pi$
$727$	4976.00	−	8618.68i	0.253851	−	0.439683i	0.964583	+	0.263780i	$0.0849694\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−900.000	+	1558.85i	−0.0455372	+	0.0788728i
$732$		0			0
$733$	16973.0	+	29398.1i	0.855269	+	1.48137i	0.876395	+	0.481592i	$0.159941\pi$
$733$	16973.0	+	29398.1i	0.855269	+	1.48137i	−0.0211266	+	0.999777i	$0.506725\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−62160.0			−3.10677
$738$		0			0
$739$	23420.0			1.16579			0.582895	−	0.812548i	$-0.301920\pi$
$739$	23420.0			1.16579			0.582895	+	0.812548i	$0.301920\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7296.00	−	12637.0i	−0.360248	−	0.623968i	0.627753	−	0.778412i	$-0.283975\pi$
$743$	−7296.00	−	12637.0i	−0.360248	−	0.623968i	−0.988001	+	0.154444i	$0.950641\pi$
$744$		0			0
$745$	285.000	−	493.634i	0.0140156	−	0.0242757i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12384.0	+	21449.7i	−0.604141	+	1.04640i
$750$		0			0
$751$	−4528.00	−	7842.73i	−0.220012	−	0.381072i	0.734799	−	0.678285i	$-0.237276\pi$
$751$	−4528.00	−	7842.73i	−0.220012	−	0.381072i	−0.954811	+	0.297213i	$0.903943\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	200.000			0.00964072
$756$		0			0
$757$	−17554.0			−0.842815			−0.421408	−	0.906871i	$-0.638464\pi$
$757$	−17554.0			−0.842815			−0.421408	+	0.906871i	$0.638464\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−18219.0	−	31556.2i	−0.867856	−	1.50317i	−0.864183	−	0.503177i	$-0.832164\pi$
$761$	−18219.0	−	31556.2i	−0.867856	−	1.50317i	−0.00367239	−	0.999993i	$-0.501169\pi$
$762$		0			0
$763$	2224.00	−	3852.08i	0.105523	−	0.182772i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−10836.0	+	18768.5i	−0.510124	+	0.883561i
$768$		0			0
$769$	4511.00	+	7813.28i	0.211536	+	0.366390i	0.952195	−	0.305490i	$-0.0988203\pi$
$769$	4511.00	+	7813.28i	0.211536	+	0.366390i	−0.740660	+	0.671880i	$0.765487\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1470.00			−0.0683987			−0.0341994	−	0.999415i	$-0.510888\pi$
$773$	−1470.00			−0.0683987			−0.0341994	+	0.999415i	$0.510888\pi$
$774$		0			0
$775$	4400.00			0.203939
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4092.00	+	7087.55i	0.188204	+	0.325979i
$780$		0			0
$781$	5040.00	−	8729.54i	0.230916	−	0.399958i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−385.000	+	666.840i	−0.0175048	+	0.0303191i
$786$		0			0
$787$	−2626.00	−	4548.37i	−0.118941	−	0.206012i	0.800407	−	0.599457i	$-0.204617\pi$
$787$	−2626.00	−	4548.37i	−0.118941	−	0.206012i	−0.919348	+	0.393444i	$0.871283\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−8928.00			−0.401319
$792$		0			0
$793$	−4988.00			−0.223366
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6147.00	+	10646.9i	0.273197	+	0.473191i	0.969679	−	0.244384i	$-0.0785856\pi$
$797$	6147.00	+	10646.9i	0.273197	+	0.473191i	−0.696482	+	0.717575i	$0.745252\pi$
$798$		0			0
$799$	−1512.00	+	2618.86i	−0.0669471	+	0.115956i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−15180.0	+	26292.5i	−0.667112	+	1.15547i
$804$		0			0
$805$	1920.00	+	3325.54i	0.0840635	+	0.145602i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−15546.0			−0.675610			−0.337805	−	0.941216i	$-0.609684\pi$
$809$	−15546.0			−0.675610			−0.337805	+	0.941216i	$0.609684\pi$
$810$		0			0
$811$	19364.0			0.838424			0.419212	−	0.907888i	$-0.362306\pi$
$811$	19364.0			0.838424			0.419212	+	0.907888i	$0.362306\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5450.00	+	9439.68i	0.234239	+	0.405715i
$816$		0			0
$817$	2200.00	−	3810.51i	0.0942084	−	0.163174i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3657.00	+	6334.11i	−0.155457	+	0.269259i	−0.933225	−	0.359292i	$-0.883018\pi$
$821$	−3657.00	+	6334.11i	−0.155457	+	0.269259i	0.777768	+	0.628551i	$0.216352\pi$
$822$		0			0
$823$	−5992.00	−	10378.4i	−0.253789	−	0.439575i	0.710777	−	0.703417i	$-0.248343\pi$
$823$	−5992.00	−	10378.4i	−0.253789	−	0.439575i	−0.964566	+	0.263843i	$0.915010\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−13500.0			−0.567643			−0.283822	−	0.958877i	$-0.591602\pi$
$827$	−13500.0			−0.567643			−0.283822	+	0.958877i	$0.591602\pi$
$828$		0			0
$829$	−44602.0			−1.86863			−0.934313	−	0.356453i	$-0.883986\pi$
$829$	−44602.0			−1.86863			−0.934313	+	0.356453i	$0.883986\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−783.000	−	1356.20i	−0.0325682	−	0.0564098i
$834$		0			0
$835$	−9240.00	+	16004.1i	−0.382950	+	0.663289i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	17724.0	−	30698.9i	0.729321	−	1.26322i	−0.227849	−	0.973696i	$-0.573169\pi$
$839$	17724.0	−	30698.9i	0.729321	−	1.26322i	0.957170	−	0.289525i	$-0.0934973\pi$
$840$		0			0
$841$	−5103.50	−	8839.52i	−0.209254	−	0.362439i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−25995.0			−1.05829
$846$		0			0
$847$	−36304.0			−1.47275
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6096.00	+	10558.6i	0.245556	+	0.425316i
$852$		0			0
$853$	−6295.00	+	10903.3i	−0.252681	+	0.437656i	−0.964263	−	0.264947i	$-0.914646\pi$
$853$	−6295.00	+	10903.3i	−0.252681	+	0.437656i	0.711582	+	0.702603i	$0.247979\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12453.0	−	21569.2i	0.496367	−	0.859733i	−0.503624	−	0.863923i	$-0.668000\pi$
$857$	12453.0	−	21569.2i	0.496367	−	0.859733i	0.999991	+	0.00419015i	$0.00133377\pi$
$858$		0			0
$859$	−11602.0	−	20095.3i	−0.460833	−	0.798185i	0.538170	−	0.842836i	$-0.319116\pi$
$859$	−11602.0	−	20095.3i	−0.460833	−	0.798185i	−0.999003	+	0.0446509i	$0.985782\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−19848.0			−0.782890			−0.391445	−	0.920202i	$-0.628025\pi$
$863$	−19848.0			−0.782890			−0.391445	+	0.920202i	$0.628025\pi$
$864$		0			0
$865$	6510.00			0.255892
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8160.00	−	14133.5i	−0.318537	−	0.551723i
$870$		0			0
$871$	44548.0	−	77159.4i	1.73301	−	3.00166i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1000.00	+	1732.05i	−0.0386356	+	0.0669189i
$876$		0			0
$877$	−13771.0	−	23852.1i	−0.530232	−	0.918389i	−0.999378	−	0.0352683i	$-0.988771\pi$
$877$	−13771.0	−	23852.1i	−0.530232	−	0.918389i	0.469146	−	0.883121i	$-0.344562\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	20718.0			0.792290			0.396145	−	0.918188i	$-0.370348\pi$
$881$	20718.0			0.792290			0.396145	+	0.918188i	$0.370348\pi$
$882$		0			0
$883$	25172.0			0.959349			0.479675	−	0.877446i	$-0.340755\pi$
$883$	25172.0			0.959349			0.479675	+	0.877446i	$0.340755\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6432.00	−	11140.6i	−0.243478	−	0.421717i	0.718224	−	0.695812i	$-0.244955\pi$
$887$	−6432.00	−	11140.6i	−0.243478	−	0.421717i	−0.961703	+	0.274095i	$0.911622\pi$
$888$		0			0
$889$	2752.00	−	4766.60i	0.103824	−	0.179828i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3696.00	−	6401.66i	0.138502	−	0.239892i
$894$		0			0
$895$	10770.0	+	18654.2i	0.402236	+	0.696694i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	32736.0			1.21447
$900$		0			0
$901$	−8964.00			−0.331447
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3875.00	+	6711.70i	0.142331	+	0.246524i
$906$		0			0
$907$	11546.0	−	19998.3i	0.422689	−	0.732118i	−0.573513	−	0.819197i	$-0.694420\pi$
$907$	11546.0	−	19998.3i	0.422689	−	0.732118i	0.996201	+	0.0870783i	$0.0277530\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−7104.00	+	12304.5i	−0.258360	+	0.447493i	−0.965803	−	0.259278i	$-0.916515\pi$
$911$	−7104.00	+	12304.5i	−0.258360	+	0.447493i	0.707443	+	0.706771i	$0.249849\pi$
$912$		0			0
$913$	28440.0	+	49259.5i	1.03092	+	1.78560i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12480.0			0.449428
$918$		0			0
$919$	−26584.0			−0.954217			−0.477108	−	0.878844i	$-0.658315\pi$
$919$	−26584.0			−0.954217			−0.477108	+	0.878844i	$0.658315\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7224.00	+	12512.3i	0.257617	+	0.446206i
$924$		0			0
$925$	−3175.00	+	5499.26i	−0.112858	+	0.195475i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	81.0000	−	140.296i	0.00286063	−	0.00495475i	−0.864592	−	0.502475i	$-0.832423\pi$
$929$	81.0000	−	140.296i	0.00286063	−	0.00495475i	0.867452	+	0.497521i	$0.165756\pi$
$930$		0			0
$931$	1914.00	+	3315.15i	0.0673779	+	0.116702i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5400.00			0.188876
$936$		0			0
$937$	−29734.0			−1.03668			−0.518339	−	0.855175i	$-0.673449\pi$
$937$	−29734.0			−1.03668			−0.518339	+	0.855175i	$0.673449\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	8571.00	+	14845.4i	0.296925	+	0.514290i	0.975431	−	0.220306i	$-0.0707055\pi$
$941$	8571.00	+	14845.4i	0.296925	+	0.514290i	−0.678506	+	0.734595i	$0.737372\pi$
$942$		0			0
$943$	−4464.00	+	7731.87i	−0.154155	+	0.267004i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13218.0	−	22894.2i	0.453566	−	0.785600i	−0.545038	−	0.838411i	$-0.683485\pi$
$947$	13218.0	−	22894.2i	0.453566	−	0.785600i	0.998605	+	0.0528113i	$0.0168182\pi$
$948$		0			0
$949$	−21758.0	−	37686.0i	−0.744251	−	1.28908i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−27882.0			−0.947730			−0.473865	−	0.880598i	$-0.657142\pi$
$953$	−27882.0			−0.947730			−0.473865	+	0.880598i	$0.657142\pi$
$954$		0			0
$955$	240.000			0.00813217
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5328.00	−	9228.37i	−0.179406	−	0.310740i
$960$		0			0
$961$	−592.500	+	1026.24i	−0.0198886	+	0.0344480i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2645.00	−	4581.27i	0.0882337	−	0.152825i
$966$		0			0
$967$	−6328.00	−	10960.4i	−0.210439	−	0.364491i	0.741413	−	0.671049i	$-0.234156\pi$
$967$	−6328.00	−	10960.4i	−0.210439	−	0.364491i	−0.951852	+	0.306558i	$0.900823\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−2916.00			−0.0963737			−0.0481869	−	0.998838i	$-0.515344\pi$
$971$	−2916.00			−0.0963737			−0.0481869	+	0.998838i	$0.515344\pi$
$972$		0			0
$973$	−14144.0			−0.466018
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3447.00	−	5970.38i	−0.112875	−	0.195506i	0.804053	−	0.594558i	$-0.202673\pi$
$977$	−3447.00	−	5970.38i	−0.112875	−	0.195506i	−0.916928	+	0.399052i	$0.869339\pi$
$978$		0			0
$979$	−30420.0	+	52689.0i	−0.993082	+	1.72007i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22632.0	+	39199.8i	−0.734332	+	1.27190i	0.220683	+	0.975346i	$0.429171\pi$
$983$	−22632.0	+	39199.8i	−0.734332	+	1.27190i	−0.955016	+	0.296555i	$0.904162\pi$
$984$		0			0
$985$	9285.00	+	16082.1i	0.300350	+	0.520221i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4800.00			0.154329
$990$		0			0
$991$	52016.0			1.66735			0.833674	−	0.552256i	$-0.186233\pi$
$991$	52016.0			1.66735			0.833674	+	0.552256i	$0.186233\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4420.00	−	7655.66i	−0.140828	−	0.243920i
$996$		0			0
$997$	6929.00	−	12001.4i	0.220104	−	0.381231i	−0.734735	−	0.678354i	$-0.762694\pi$
$997$	6929.00	−	12001.4i	0.220104	−	0.381231i	0.954839	+	0.297123i	$0.0960270\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.4.i.j.541.1		2
3.2	odd	2		1620.4.i.d.541.1		2
9.2	odd	6		20.4.a.a.1.1	✓	1
9.4	even	3	inner	1620.4.i.j.1081.1		2
9.5	odd	6		1620.4.i.d.1081.1		2
9.7	even	3		180.4.a.a.1.1		1
36.7	odd	6		720.4.a.k.1.1		1
36.11	even	6		80.4.a.c.1.1		1
45.2	even	12		100.4.c.a.49.1		2
45.7	odd	12		900.4.d.k.649.1		2
45.29	odd	6		100.4.a.a.1.1		1
45.34	even	6		900.4.a.m.1.1		1
45.38	even	12		100.4.c.a.49.2		2
45.43	odd	12		900.4.d.k.649.2		2
63.2	odd	6		980.4.i.e.361.1		2
63.11	odd	6		980.4.i.e.961.1		2
63.20	even	6		980.4.a.c.1.1		1
63.38	even	6		980.4.i.n.961.1		2
63.47	even	6		980.4.i.n.361.1		2
72.11	even	6		320.4.a.k.1.1		1
72.29	odd	6		320.4.a.d.1.1		1
99.65	even	6		2420.4.a.d.1.1		1
144.11	even	12		1280.4.d.c.641.2		2
144.29	odd	12		1280.4.d.n.641.2		2
144.83	even	12		1280.4.d.c.641.1		2
144.101	odd	12		1280.4.d.n.641.1		2
180.47	odd	12		400.4.c.j.49.2		2
180.83	odd	12		400.4.c.j.49.1		2
180.119	even	6		400.4.a.o.1.1		1
360.29	odd	6		1600.4.a.bl.1.1		1
360.299	even	6		1600.4.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.4.a.a.1.1	✓	1	9.2	odd	6
80.4.a.c.1.1		1	36.11	even	6
100.4.a.a.1.1		1	45.29	odd	6
100.4.c.a.49.1		2	45.2	even	12
100.4.c.a.49.2		2	45.38	even	12
180.4.a.a.1.1		1	9.7	even	3
320.4.a.d.1.1		1	72.29	odd	6
320.4.a.k.1.1		1	72.11	even	6
400.4.a.o.1.1		1	180.119	even	6
400.4.c.j.49.1		2	180.83	odd	12
400.4.c.j.49.2		2	180.47	odd	12
720.4.a.k.1.1		1	36.7	odd	6
900.4.a.m.1.1		1	45.34	even	6
900.4.d.k.649.1		2	45.7	odd	12
900.4.d.k.649.2		2	45.43	odd	12
980.4.a.c.1.1		1	63.20	even	6
980.4.i.e.361.1		2	63.2	odd	6
980.4.i.e.961.1		2	63.11	odd	6
980.4.i.n.361.1		2	63.47	even	6
980.4.i.n.961.1		2	63.38	even	6
1280.4.d.c.641.1		2	144.83	even	12
1280.4.d.c.641.2		2	144.11	even	12
1280.4.d.n.641.1		2	144.101	odd	12
1280.4.d.n.641.2		2	144.29	odd	12
1600.4.a.p.1.1		1	360.299	even	6
1600.4.a.bl.1.1		1	360.29	odd	6
1620.4.i.d.541.1		2	3.2	odd	2
1620.4.i.d.1081.1		2	9.5	odd	6
1620.4.i.j.541.1		2	1.1	even	1	trivial
1620.4.i.j.1081.1		2	9.4	even	3	inner
2420.4.a.d.1.1		1	99.65	even	6

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1620.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.50000 + 4.33013i) q^{5} +(8.00000 - 13.8564i) q^{7} +O(q^{10})\)	\(q+(2.50000 + 4.33013i) q^{5} +(8.00000 - 13.8564i) q^{7} +(-30.0000 + 51.9615i) q^{11} +(-43.0000 - 74.4782i) q^{13} -18.0000 q^{17} +44.0000 q^{19} +(24.0000 + 41.5692i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-93.0000 + 161.081i) q^{29} +(-88.0000 - 152.420i) q^{31} +80.0000 q^{35} +254.000 q^{37} +(93.0000 + 161.081i) q^{41} +(50.0000 - 86.6025i) q^{43} +(84.0000 - 145.492i) q^{47} +(43.5000 + 75.3442i) q^{49} +498.000 q^{53} -300.000 q^{55} +(-126.000 - 218.238i) q^{59} +(29.0000 - 50.2295i) q^{61} +(215.000 - 372.391i) q^{65} +(518.000 + 897.202i) q^{67} -168.000 q^{71} +506.000 q^{73} +(480.000 + 831.384i) q^{77} +(-136.000 + 235.559i) q^{79} +(474.000 - 820.992i) q^{83} +(-45.0000 - 77.9423i) q^{85} +1014.00 q^{89} -1376.00 q^{91} +(110.000 + 190.526i) q^{95} +(383.000 - 663.375i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 5 q^{5} + 16 q^{7}+O(q^{10}) \) 2 * q + 5 * q^5 + 16 * q^7	\( 2 q + 5 q^{5} + 16 q^{7} - 60 q^{11} - 86 q^{13} - 36 q^{17} + 88 q^{19} + 48 q^{23} - 25 q^{25} - 186 q^{29} - 176 q^{31} + 160 q^{35} + 508 q^{37} + 186 q^{41} + 100 q^{43} + 168 q^{47} + 87 q^{49} + 996 q^{53} - 600 q^{55} - 252 q^{59} + 58 q^{61} + 430 q^{65} + 1036 q^{67} - 336 q^{71} + 1012 q^{73} + 960 q^{77} - 272 q^{79} + 948 q^{83} - 90 q^{85} + 2028 q^{89} - 2752 q^{91} + 220 q^{95} + 766 q^{97}+O(q^{100}) \) 2 * q + 5 * q^5 + 16 * q^7 - 60 * q^11 - 86 * q^13 - 36 * q^17 + 88 * q^19 + 48 * q^23 - 25 * q^25 - 186 * q^29 - 176 * q^31 + 160 * q^35 + 508 * q^37 + 186 * q^41 + 100 * q^43 + 168 * q^47 + 87 * q^49 + 996 * q^53 - 600 * q^55 - 252 * q^59 + 58 * q^61 + 430 * q^65 + 1036 * q^67 - 336 * q^71 + 1012 * q^73 + 960 * q^77 - 272 * q^79 + 948 * q^83 - 90 * q^85 + 2028 * q^89 - 2752 * q^91 + 220 * q^95 + 766 * q^97

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