LMFDB - Embedded newform 1900.2.i.b.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(201,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1900.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.i (of order $3$, degree $2$, 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:	$15.1715763840$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1900.201
Dual form			1900.2.i.b.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{3} +4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	$q+(1.00000 - 1.73205i) q^{3} +4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} -3.00000 q^{11} +(3.00000 + 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{17} +(3.50000 + 2.59808i) q^{19} +(4.00000 - 6.92820i) q^{21} +(2.00000 + 3.46410i) q^{23} +4.00000 q^{27} +(-0.500000 - 0.866025i) q^{29} -5.00000 q^{31} +(-3.00000 + 5.19615i) q^{33} +4.00000 q^{37} +12.0000 q^{39} +(-1.00000 + 1.73205i) q^{41} +(3.00000 + 5.19615i) q^{47} +9.00000 q^{49} +(-2.00000 - 3.46410i) q^{51} +(-3.00000 - 5.19615i) q^{53} +(8.00000 - 3.46410i) q^{57} +(0.500000 - 0.866025i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-2.00000 - 3.46410i) q^{63} +(-7.00000 - 12.1244i) q^{67} +8.00000 q^{69} +(-7.50000 + 12.9904i) q^{71} +(6.00000 - 10.3923i) q^{73} -12.0000 q^{77} +(0.500000 - 0.866025i) q^{79} +(5.50000 - 9.52628i) q^{81} -16.0000 q^{83} -2.00000 q^{87} +(-8.50000 - 14.7224i) q^{89} +(12.0000 + 20.7846i) q^{91} +(-5.00000 + 8.66025i) q^{93} +(6.00000 - 10.3923i) q^{97} +(1.50000 + 2.59808i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 8 q^{7} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 8 * q^7 - q^9	$ 2 q + 2 q^{3} + 8 q^{7} - q^{9} - 6 q^{11} + 6 q^{13} + 2 q^{17} + 7 q^{19} + 8 q^{21} + 4 q^{23} + 8 q^{27} - q^{29} - 10 q^{31} - 6 q^{33} + 8 q^{37} + 24 q^{39} - 2 q^{41} + 6 q^{47} + 18 q^{49} - 4 q^{51} - 6 q^{53} + 16 q^{57} + q^{59} + 7 q^{61} - 4 q^{63} - 14 q^{67} + 16 q^{69} - 15 q^{71} + 12 q^{73} - 24 q^{77} + q^{79} + 11 q^{81} - 32 q^{83} - 4 q^{87} - 17 q^{89} + 24 q^{91} - 10 q^{93} + 12 q^{97} + 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 8 * q^7 - q^9 - 6 * q^11 + 6 * q^13 + 2 * q^17 + 7 * q^19 + 8 * q^21 + 4 * q^23 + 8 * q^27 - q^29 - 10 * q^31 - 6 * q^33 + 8 * q^37 + 24 * q^39 - 2 * q^41 + 6 * q^47 + 18 * q^49 - 4 * q^51 - 6 * q^53 + 16 * q^57 + q^59 + 7 * q^61 - 4 * q^63 - 14 * q^67 + 16 * q^69 - 15 * q^71 + 12 * q^73 - 24 * q^77 + q^79 + 11 * q^81 - 32 * q^83 - 4 * q^87 - 17 * q^89 + 24 * q^91 - 10 * q^93 + 12 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	−0.418432	−	0.908248i	$-0.637420\pi$
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	0.995782	−	0.0917517i	$-0.0292466\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.00000			1.51186			0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000			1.51186			0.755929	+	0.654654i	$0.227186\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$		0			0
$13$	3.00000	+	5.19615i	0.832050	+	1.44115i	0.896410	+	0.443227i	$0.146166\pi$
$13$	3.00000	+	5.19615i	0.832050	+	1.44115i	−0.0643593	+	0.997927i	$0.520500\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$		0			0
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$20$		0			0
$21$	4.00000	−	6.92820i	0.872872	−	1.51186i
$22$		0			0
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.00000			0.769800
$28$		0			0
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	0.815861	−	0.578249i	$-0.196264\pi$
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	−0.908708	+	0.417432i	$0.862930\pi$
$30$		0			0
$31$	−5.00000			−0.898027			−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000			−0.898027			−0.449013	+	0.893525i	$0.648224\pi$
$32$		0			0
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$		0			0
$39$	12.0000			1.92154
$40$		0			0
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	−0.933486	−	0.358614i	$-0.883249\pi$
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	0.777312	+	0.629115i	$0.216583\pi$
$42$		0			0
$43$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$43$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	9.00000			1.28571
$50$		0			0
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$		0			0
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	8.00000	−	3.46410i	1.05963	−	0.458831i
$58$		0			0
$59$	0.500000	−	0.866025i	0.0650945	−	0.112747i	−0.831641	−	0.555313i	$-0.812598\pi$
$59$	0.500000	−	0.866025i	0.0650945	−	0.112747i	0.896736	+	0.442566i	$0.145932\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$		0			0
$63$	−2.00000	−	3.46410i	−0.251976	−	0.436436i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	0.0212861	−	0.999773i	$-0.493224\pi$
$68$		0			0
$69$	8.00000			0.963087
$70$		0			0
$71$	−7.50000	+	12.9904i	−0.890086	+	1.54167i	−0.0503155	+	0.998733i	$0.516023\pi$
$71$	−7.50000	+	12.9904i	−0.890086	+	1.54167i	−0.839771	+	0.542941i	$0.817311\pi$
$72$		0			0
$73$	6.00000	−	10.3923i	0.702247	−	1.21633i	−0.265429	−	0.964130i	$-0.585514\pi$
$73$	6.00000	−	10.3923i	0.702247	−	1.21633i	0.967676	−	0.252197i	$-0.0811531\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.0000			−1.36753
$78$		0			0
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	−16.0000			−1.75623			−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000			−1.75623			−0.878114	+	0.478451i	$0.841198\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.00000			−0.214423
$88$		0			0
$89$	−8.50000	−	14.7224i	−0.900998	−	1.56057i	−0.826201	−	0.563376i	$-0.809502\pi$
$89$	−8.50000	−	14.7224i	−0.900998	−	1.56057i	−0.0747975	−	0.997199i	$-0.523831\pi$
$90$		0			0
$91$	12.0000	+	20.7846i	1.25794	+	2.17882i
$92$		0			0
$93$	−5.00000	+	8.66025i	−0.518476	+	0.898027i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	6.00000	−	10.3923i	0.609208	−	1.05518i	−0.382164	−	0.924095i	$-0.624821\pi$
$97$	6.00000	−	10.3923i	0.609208	−	1.05518i	0.991371	−	0.131084i	$-0.0418458\pi$
$98$		0			0
$99$	1.50000	+	2.59808i	0.150756	+	0.261116i
$100$		0			0
$101$	−5.50000	−	9.52628i	−0.547270	−	0.947900i	−0.998460	−	0.0554722i	$-0.982334\pi$
$101$	−5.50000	−	9.52628i	−0.547270	−	0.947900i	0.451190	−	0.892428i	$-0.351000\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	−0.983531	−	0.180741i	$-0.942150\pi$
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	0.648292	+	0.761392i	$0.275484\pi$
$110$		0			0
$111$	4.00000	−	6.92820i	0.379663	−	0.657596i
$112$		0			0
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.00000	−	5.19615i	0.277350	−	0.480384i
$118$		0			0
$119$	4.00000	−	6.92820i	0.366679	−	0.635107i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$	2.00000	+	3.46410i	0.180334	+	0.312348i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	9.00000	+	15.5885i	0.798621	+	1.38325i	0.920514	+	0.390709i	$0.127770\pi$
$127$	9.00000	+	15.5885i	0.798621	+	1.38325i	−0.121894	+	0.992543i	$0.538897\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.0155672	−	0.999879i	$-0.495045\pi$
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.858137	−	0.513421i	$-0.171622\pi$
$132$		0			0
$133$	14.0000	+	10.3923i	1.21395	+	0.901127i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$		0			0
$139$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$139$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$140$		0			0
$141$	12.0000			1.01058
$142$		0			0
$143$	−9.00000	−	15.5885i	−0.752618	−	1.30357i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	9.00000	−	15.5885i	0.742307	−	1.28571i
$148$		0			0
$149$	8.50000	−	14.7224i	0.696347	−	1.20611i	−0.273377	−	0.961907i	$-0.588141\pi$
$149$	8.50000	−	14.7224i	0.696347	−	1.20611i	0.969724	−	0.244202i	$-0.0785259\pi$
$150$		0			0
$151$	3.00000			0.244137			0.122068	−	0.992522i	$-0.461047\pi$
$151$	3.00000			0.244137			0.122068	+	0.992522i	$0.461047\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.00000	−	15.5885i	0.718278	−	1.24409i	−0.243403	−	0.969925i	$-0.578264\pi$
$157$	9.00000	−	15.5885i	0.718278	−	1.24409i	0.961681	−	0.274169i	$-0.0884028\pi$
$158$		0			0
$159$	−12.0000			−0.951662
$160$		0			0
$161$	8.00000	+	13.8564i	0.630488	+	1.09204i
$162$		0			0
$163$	−18.0000			−1.40987			−0.704934	−	0.709273i	$-0.749024\pi$
$163$	−18.0000			−1.40987			−0.704934	+	0.709273i	$0.749024\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	0.978259	−	0.207385i	$-0.0664952\pi$
$167$	4.00000	+	6.92820i	0.309529	+	0.536120i	−0.668730	+	0.743505i	$0.733162\pi$
$168$		0			0
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$		0			0
$171$	0.500000	−	4.33013i	0.0382360	−	0.331133i
$172$		0			0
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.00000	−	1.73205i	−0.0751646	−	0.130189i
$178$		0			0
$179$	−15.0000			−1.12115			−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000			−1.12115			−0.560576	+	0.828103i	$0.689420\pi$
$180$		0			0
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	0.826465	−	0.562988i	$-0.190348\pi$
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	−0.900794	+	0.434246i	$0.857015\pi$
$182$		0			0
$183$	14.0000			1.03491
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$		0			0
$189$	16.0000			1.16383
$190$		0			0
$191$	−13.0000			−0.940647			−0.470323	−	0.882494i	$-0.655863\pi$
$191$	−13.0000			−0.940647			−0.470323	+	0.882494i	$0.655863\pi$
$192$		0			0
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	−0.420096	−	0.907480i	$-0.638004\pi$
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	0.995948	−	0.0899262i	$-0.0286631\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	−11.5000	−	19.9186i	−0.815213	−	1.41199i	−0.909175	−	0.416415i	$-0.863286\pi$
$199$	−11.5000	−	19.9186i	−0.815213	−	1.41199i	0.0939612	−	0.995576i	$-0.470047\pi$
$200$		0			0
$201$	−28.0000			−1.97497
$202$		0			0
$203$	−2.00000	−	3.46410i	−0.140372	−	0.243132i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.00000	−	3.46410i	0.139010	−	0.240772i
$208$		0			0
$209$	−10.5000	−	7.79423i	−0.726300	−	0.539138i
$210$		0			0
$211$	0.500000	−	0.866025i	0.0344214	−	0.0596196i	−0.848301	−	0.529514i	$-0.822374\pi$
$211$	0.500000	−	0.866025i	0.0344214	−	0.0596196i	0.882723	+	0.469894i	$0.155708\pi$
$212$		0			0
$213$	15.0000	+	25.9808i	1.02778	+	1.78017i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−20.0000			−1.35769
$218$		0			0
$219$	−12.0000	−	20.7846i	−0.810885	−	1.40449i
$220$		0			0
$221$	12.0000			0.807207
$222$		0			0
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	−0.700449	−	0.713702i	$-0.747017\pi$
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	0.968309	+	0.249756i	$0.0803503\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.00000			0.265489			0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000			0.265489			0.132745	+	0.991150i	$0.457621\pi$
$228$		0			0
$229$	21.0000			1.38772			0.693860	−	0.720110i	$-0.255909\pi$
$229$	21.0000			1.38772			0.693860	+	0.720110i	$0.255909\pi$
$230$		0			0
$231$	−12.0000	+	20.7846i	−0.789542	+	1.36753i
$232$		0			0
$233$	−5.00000	+	8.66025i	−0.327561	+	0.567352i	−0.982027	−	0.188739i	$-0.939560\pi$
$233$	−5.00000	+	8.66025i	−0.327561	+	0.567352i	0.654466	+	0.756091i	$0.272893\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.00000	−	1.73205i	−0.0649570	−	0.112509i
$238$		0			0
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$		0			0
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	0.774202	−	0.632938i	$-0.218151\pi$
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	−0.935242	+	0.354010i	$0.884818\pi$
$242$		0			0
$243$	−5.00000	−	8.66025i	−0.320750	−	0.555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.00000	+	25.9808i	−0.190885	+	1.65312i
$248$		0			0
$249$	−16.0000	+	27.7128i	−1.01396	+	1.75623i
$250$		0			0
$251$	−15.5000	−	26.8468i	−0.978351	−	1.69455i	−0.668400	−	0.743802i	$-0.733021\pi$
$251$	−15.5000	−	26.8468i	−0.978351	−	1.69455i	−0.309951	−	0.950753i	$-0.600313\pi$
$252$		0			0
$253$	−6.00000	−	10.3923i	−0.377217	−	0.653359i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$		0			0
$259$	16.0000			0.994192
$260$		0			0
$261$	−0.500000	+	0.866025i	−0.0309492	+	0.0536056i
$262$		0			0
$263$	5.00000	−	8.66025i	0.308313	−	0.534014i	−0.669680	−	0.742650i	$-0.733569\pi$
$263$	5.00000	−	8.66025i	0.308313	−	0.534014i	0.977993	+	0.208635i	$0.0669022\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−34.0000			−2.08077
$268$		0			0
$269$	0.500000	−	0.866025i	0.0304855	−	0.0528025i	−0.850380	−	0.526169i	$-0.823628\pi$
$269$	0.500000	−	0.866025i	0.0304855	−	0.0528025i	0.880866	+	0.473366i	$0.156961\pi$
$270$		0			0
$271$	−8.50000	+	14.7224i	−0.516338	+	0.894324i	0.483482	+	0.875354i	$0.339372\pi$
$271$	−8.50000	+	14.7224i	−0.516338	+	0.894324i	−0.999820	+	0.0189696i	$0.993961\pi$
$272$		0			0
$273$	48.0000			2.90509
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−16.0000			−0.961347			−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000			−0.961347			−0.480673	+	0.876900i	$0.659608\pi$
$278$		0			0
$279$	2.50000	+	4.33013i	0.149671	+	0.259238i
$280$		0			0
$281$	13.0000	+	22.5167i	0.775515	+	1.34323i	0.934505	+	0.355951i	$0.115843\pi$
$281$	13.0000	+	22.5167i	0.775515	+	1.34323i	−0.158990	+	0.987280i	$0.550824\pi$
$282$		0			0
$283$	−13.0000	+	22.5167i	−0.772770	+	1.33848i	0.163270	+	0.986581i	$0.447796\pi$
$283$	−13.0000	+	22.5167i	−0.772770	+	1.33848i	−0.936039	+	0.351895i	$0.885537\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.00000	+	6.92820i	−0.236113	+	0.408959i
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	−12.0000	−	20.7846i	−0.703452	−	1.21842i
$292$		0			0
$293$	−16.0000			−0.934730			−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000			−0.934730			−0.467365	+	0.884064i	$0.654797\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−12.0000			−0.696311
$298$		0			0
$299$	−12.0000	+	20.7846i	−0.693978	+	1.20201i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−22.0000			−1.26387
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−7.00000	+	12.1244i	−0.399511	+	0.691974i	−0.993666	−	0.112377i	$-0.964153\pi$
$307$	−7.00000	+	12.1244i	−0.399511	+	0.691974i	0.594154	+	0.804351i	$0.297487\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	17.0000	+	29.4449i	0.960897	+	1.66432i	0.720257	+	0.693708i	$0.244024\pi$
$313$	17.0000	+	29.4449i	0.960897	+	1.66432i	0.240640	+	0.970614i	$0.422643\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$		0			0
$319$	1.50000	+	2.59808i	0.0839839	+	0.145464i
$320$		0			0
$321$	12.0000	−	20.7846i	0.669775	−	1.16008i
$322$		0			0
$323$	8.00000	−	3.46410i	0.445132	−	0.192748i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	7.00000	+	12.1244i	0.387101	+	0.670478i
$328$		0			0
$329$	12.0000	+	20.7846i	0.661581	+	1.14589i
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$		0			0
$333$	−2.00000	−	3.46410i	−0.109599	−	0.189832i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	2.00000	−	3.46410i	0.108947	−	0.188702i	−0.806397	−	0.591375i	$-0.798585\pi$
$337$	2.00000	−	3.46410i	0.108947	−	0.188702i	0.915344	+	0.402673i	$0.131919\pi$
$338$		0			0
$339$	−14.0000	+	24.2487i	−0.760376	+	1.31701i
$340$		0			0
$341$	15.0000			0.812296
$342$		0			0
$343$	8.00000			0.431959
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	12.0000	+	20.7846i	0.640513	+	1.10940i
$352$		0			0
$353$	36.0000			1.91609			0.958043	−	0.286623i	$-0.0925328\pi$
$353$	36.0000			1.91609			0.958043	+	0.286623i	$0.0925328\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−8.00000	−	13.8564i	−0.423405	−	0.733359i
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$		0			0
$363$	−2.00000	+	3.46410i	−0.104973	+	0.181818i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	−0.956544	−	0.291587i	$-0.905817\pi$
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	0.225750	−	0.974185i	$-0.427517\pi$
$368$		0			0
$369$	2.00000			0.104116
$370$		0			0
$371$	−12.0000	−	20.7846i	−0.623009	−	1.07908i
$372$		0			0
$373$	12.0000			0.621336			0.310668	−	0.950518i	$-0.399447\pi$
$373$	12.0000			0.621336			0.310668	+	0.950518i	$0.399447\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.00000	−	5.19615i	0.154508	−	0.267615i
$378$		0			0
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$		0			0
$381$	36.0000			1.84434
$382$		0			0
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	−0.998954	−	0.0457244i	$-0.985440\pi$
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	0.539076	+	0.842257i	$0.318774\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	10.5000	+	18.1865i	0.532371	+	0.922094i	0.999286	+	0.0377914i	$0.0120322\pi$
$389$	10.5000	+	18.1865i	0.532371	+	0.922094i	−0.466915	+	0.884302i	$0.654634\pi$
$390$		0			0
$391$	8.00000			0.404577
$392$		0			0
$393$	−20.0000	−	34.6410i	−1.00887	−	1.74741i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	−0.948772	−	0.315963i	$-0.897673\pi$
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	0.748017	+	0.663679i	$0.231006\pi$
$398$		0			0
$399$	32.0000	−	13.8564i	1.60200	−	0.693688i
$400$		0			0
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	−0.990257	−	0.139253i	$-0.955530\pi$
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	0.615725	+	0.787961i	$0.288863\pi$
$402$		0			0
$403$	−15.0000	−	25.9808i	−0.747203	−	1.29419i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−12.0000			−0.594818
$408$		0			0
$409$	0.500000	+	0.866025i	0.0247234	+	0.0428222i	0.878122	−	0.478436i	$-0.158796\pi$
$409$	0.500000	+	0.866025i	0.0247234	+	0.0428222i	−0.853399	+	0.521258i	$0.825463\pi$
$410$		0			0
$411$	24.0000			1.18383
$412$		0			0
$413$	2.00000	−	3.46410i	0.0984136	−	0.170457i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−5.00000			−0.244266			−0.122133	−	0.992514i	$-0.538973\pi$
$419$	−5.00000			−0.244266			−0.122133	+	0.992514i	$0.538973\pi$
$420$		0			0
$421$	−12.5000	+	21.6506i	−0.609213	+	1.05519i	0.382158	+	0.924097i	$0.375181\pi$
$421$	−12.5000	+	21.6506i	−0.609213	+	1.05519i	−0.991370	+	0.131090i	$0.958152\pi$
$422$		0			0
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	14.0000	+	24.2487i	0.677507	+	1.17348i
$428$		0			0
$429$	−36.0000			−1.73810
$430$		0			0
$431$	−13.5000	−	23.3827i	−0.650272	−	1.12630i	−0.983057	−	0.183301i	$-0.941322\pi$
$431$	−13.5000	−	23.3827i	−0.650272	−	1.12630i	0.332785	−	0.943003i	$-0.392012\pi$
$432$		0			0
$433$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$433$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.00000	+	17.3205i	−0.0956730	+	0.828552i
$438$		0			0
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	−0.877711	−	0.479191i	$-0.840930\pi$
$439$	−0.500000	+	0.866025i	−0.0238637	+	0.0413331i	0.853847	+	0.520524i	$0.174263\pi$
$440$		0			0
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−17.0000	−	29.4449i	−0.804072	−	1.39269i
$448$		0			0
$449$	−1.00000			−0.0471929			−0.0235965	−	0.999722i	$-0.507512\pi$
$449$	−1.00000			−0.0471929			−0.0235965	+	0.999722i	$0.507512\pi$
$450$		0			0
$451$	3.00000	−	5.19615i	0.141264	−	0.244677i
$452$		0			0
$453$	3.00000	−	5.19615i	0.140952	−	0.244137i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.00000			0.0935561			0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000			0.0935561			0.0467780	+	0.998905i	$0.485105\pi$
$458$		0			0
$459$	4.00000	−	6.92820i	0.186704	−	0.323381i
$460$		0			0
$461$	−17.5000	+	30.3109i	−0.815056	+	1.41172i	0.0942312	+	0.995550i	$0.469961\pi$
$461$	−17.5000	+	30.3109i	−0.815056	+	1.41172i	−0.909288	+	0.416169i	$0.863373\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	20.0000			0.925490			0.462745	−	0.886492i	$-0.346865\pi$
$467$	20.0000			0.925490			0.462745	+	0.886492i	$0.346865\pi$
$468$		0			0
$469$	−28.0000	−	48.4974i	−1.29292	−	2.23940i
$470$		0			0
$471$	−18.0000	−	31.1769i	−0.829396	−	1.43656i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−3.00000	+	5.19615i	−0.137361	+	0.237915i
$478$		0			0
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	0.898257	−	0.439470i	$-0.144834\pi$
$479$	1.50000	+	2.59808i	0.0685367	+	0.118709i	−0.829721	+	0.558179i	$0.811500\pi$
$480$		0			0
$481$	12.0000	+	20.7846i	0.547153	+	0.947697i
$482$		0			0
$483$	32.0000			1.45605
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−34.0000			−1.54069			−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000			−1.54069			−0.770344	+	0.637629i	$0.779915\pi$
$488$		0			0
$489$	−18.0000	+	31.1769i	−0.813988	+	1.40987i
$490$		0			0
$491$	12.5000	−	21.6506i	0.564117	−	0.977079i	−0.433014	−	0.901387i	$-0.642550\pi$
$491$	12.5000	−	21.6506i	0.564117	−	0.977079i	0.997131	−	0.0756923i	$-0.0241167\pi$
$492$		0			0
$493$	−2.00000			−0.0900755
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−30.0000	+	51.9615i	−1.34568	+	2.33079i
$498$		0			0
$499$	−18.0000	+	31.1769i	−0.805791	+	1.39567i	0.109965	+	0.993935i	$0.464926\pi$
$499$	−18.0000	+	31.1769i	−0.805791	+	1.39567i	−0.915756	+	0.401735i	$0.868407\pi$
$500$		0			0
$501$	16.0000			0.714827
$502$		0			0
$503$	11.0000	+	19.0526i	0.490466	+	0.849512i	0.999940	−	0.0109744i	$-0.00349334\pi$
$503$	11.0000	+	19.0526i	0.490466	+	0.849512i	−0.509474	+	0.860486i	$0.670160\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	23.0000	+	39.8372i	1.02147	+	1.76923i
$508$		0			0
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$	24.0000	−	41.5692i	1.06170	−	1.83891i
$512$		0			0
$513$	14.0000	+	10.3923i	0.618115	+	0.458831i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−9.00000	−	15.5885i	−0.395820	−	0.685580i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−45.0000			−1.97149			−0.985743	−	0.168259i	$-0.946186\pi$
$521$	−45.0000			−1.97149			−0.985743	+	0.168259i	$0.946186\pi$
$522$		0			0
$523$	−5.00000	−	8.66025i	−0.218635	−	0.378686i	0.735756	−	0.677247i	$-0.236827\pi$
$523$	−5.00000	−	8.66025i	−0.218635	−	0.378686i	−0.954391	+	0.298560i	$0.903494\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.00000	+	8.66025i	−0.217803	+	0.377247i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	−1.00000			−0.0433963
$532$		0			0
$533$	−12.0000			−0.519778
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−15.0000	+	25.9808i	−0.647298	+	1.12115i
$538$		0			0
$539$	−27.0000			−1.16297
$540$		0			0
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$		0			0
$543$	−4.00000			−0.171656
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	0.767752	−	0.640747i	$-0.221375\pi$
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	−0.938779	+	0.344519i	$0.888042\pi$
$548$		0			0
$549$	3.50000	−	6.06218i	0.149376	−	0.258727i
$550$		0			0
$551$	0.500000	−	4.33013i	0.0213007	−	0.184470i
$552$		0			0
$553$	2.00000	−	3.46410i	0.0850487	−	0.147309i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−20.0000	−	34.6410i	−0.847427	−	1.46779i	−0.883497	−	0.468438i	$-0.844817\pi$
$557$	−20.0000	−	34.6410i	−0.847427	−	1.46779i	0.0360693	−	0.999349i	$-0.488516\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	6.00000	+	10.3923i	0.253320	+	0.438763i
$562$		0			0
$563$	−10.0000			−0.421450			−0.210725	−	0.977545i	$-0.567582\pi$
$563$	−10.0000			−0.421450			−0.210725	+	0.977545i	$0.567582\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	22.0000	−	38.1051i	0.923913	−	1.60026i
$568$		0			0
$569$	−17.0000			−0.712677			−0.356339	−	0.934357i	$-0.615975\pi$
$569$	−17.0000			−0.712677			−0.356339	+	0.934357i	$0.615975\pi$
$570$		0			0
$571$	−17.0000			−0.711428			−0.355714	−	0.934595i	$-0.615762\pi$
$571$	−17.0000			−0.711428			−0.355714	+	0.934595i	$0.615762\pi$
$572$		0			0
$573$	−13.0000	+	22.5167i	−0.543083	+	0.940647i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	20.0000			0.832611			0.416305	−	0.909225i	$-0.363325\pi$
$577$	20.0000			0.832611			0.416305	+	0.909225i	$0.363325\pi$
$578$		0			0
$579$	−16.0000	−	27.7128i	−0.664937	−	1.15171i
$580$		0			0
$581$	−64.0000			−2.65517
$582$		0			0
$583$	9.00000	+	15.5885i	0.372742	+	0.645608i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.00000	+	10.3923i	−0.247647	+	0.428936i	−0.962872	−	0.269957i	$-0.912990\pi$
$587$	−6.00000	+	10.3923i	−0.247647	+	0.428936i	0.715226	+	0.698893i	$0.246324\pi$
$588$		0			0
$589$	−17.5000	−	12.9904i	−0.721075	−	0.535259i
$590$		0			0
$591$	−2.00000	+	3.46410i	−0.0822690	+	0.142494i
$592$		0			0
$593$	−2.00000	−	3.46410i	−0.0821302	−	0.142254i	0.822035	−	0.569438i	$-0.192839\pi$
$593$	−2.00000	−	3.46410i	−0.0821302	−	0.142254i	−0.904165	+	0.427184i	$0.859506\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−46.0000			−1.88265
$598$		0			0
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$		0			0
$601$	17.0000			0.693444			0.346722	−	0.937968i	$-0.387295\pi$
$601$	17.0000			0.693444			0.346722	+	0.937968i	$0.387295\pi$
$602$		0			0
$603$	−7.00000	+	12.1244i	−0.285062	+	0.493742i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	14.0000			0.568242			0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000			0.568242			0.284121	+	0.958788i	$0.408298\pi$
$608$		0			0
$609$	−8.00000			−0.324176
$610$		0			0
$611$	−18.0000	+	31.1769i	−0.728202	+	1.26128i
$612$		0			0
$613$	−11.0000	+	19.0526i	−0.444286	+	0.769526i	−0.998002	−	0.0631797i	$-0.979876\pi$
$613$	−11.0000	+	19.0526i	−0.444286	+	0.769526i	0.553716	+	0.832705i	$0.313209\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.00000	−	6.92820i	−0.161034	−	0.278919i	0.774206	−	0.632934i	$-0.218150\pi$
$617$	−4.00000	−	6.92820i	−0.161034	−	0.278919i	−0.935240	+	0.354015i	$0.884816\pi$
$618$		0			0
$619$	−20.0000			−0.803868			−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000			−0.803868			−0.401934	+	0.915669i	$0.631662\pi$
$620$		0			0
$621$	8.00000	+	13.8564i	0.321029	+	0.556038i
$622$		0			0
$623$	−34.0000	−	58.8897i	−1.36218	−	2.35937i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−24.0000	+	10.3923i	−0.958468	+	0.415029i
$628$		0			0
$629$	4.00000	−	6.92820i	0.159490	−	0.276246i
$630$		0			0
$631$	16.5000	+	28.5788i	0.656855	+	1.13771i	0.981425	+	0.191844i	$0.0614468\pi$
$631$	16.5000	+	28.5788i	0.656855	+	1.13771i	−0.324571	+	0.945861i	$0.605220\pi$
$632$		0			0
$633$	−1.00000	−	1.73205i	−0.0397464	−	0.0688428i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	27.0000	+	46.7654i	1.06978	+	1.85291i
$638$		0			0
$639$	15.0000			0.593391
$640$		0			0
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	−0.941106	−	0.338112i	$-0.890212\pi$
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	0.763367	+	0.645966i	$0.223545\pi$
$642$		0			0
$643$	−1.00000	+	1.73205i	−0.0394362	+	0.0683054i	−0.885070	−	0.465458i	$-0.845890\pi$
$643$	−1.00000	+	1.73205i	−0.0394362	+	0.0683054i	0.845634	+	0.533764i	$0.179223\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	30.0000			1.17942			0.589711	−	0.807614i	$-0.299242\pi$
$647$	30.0000			1.17942			0.589711	+	0.807614i	$0.299242\pi$
$648$		0			0
$649$	−1.50000	+	2.59808i	−0.0588802	+	0.101983i
$650$		0			0
$651$	−20.0000	+	34.6410i	−0.783862	+	1.35769i
$652$		0			0
$653$	−12.0000			−0.469596			−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000			−0.469596			−0.234798	+	0.972044i	$0.575443\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−12.0000			−0.468165
$658$		0			0
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	−20.5000	−	35.5070i	−0.797358	−	1.38106i	−0.921331	−	0.388778i	$-0.872897\pi$
$661$	−20.5000	−	35.5070i	−0.797358	−	1.38106i	0.123974	−	0.992286i	$-0.460436\pi$
$662$		0			0
$663$	12.0000	−	20.7846i	0.466041	−	0.807207i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.00000	−	3.46410i	0.0774403	−	0.134131i
$668$		0			0
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$		0			0
$671$	−10.5000	−	18.1865i	−0.405348	−	0.702083i
$672$		0			0
$673$	28.0000			1.07932			0.539660	−	0.841883i	$-0.318553\pi$
$673$	28.0000			1.07932			0.539660	+	0.841883i	$0.318553\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	32.0000			1.22986			0.614930	−	0.788582i	$-0.289184\pi$
$677$	32.0000			1.22986			0.614930	+	0.788582i	$0.289184\pi$
$678$		0			0
$679$	24.0000	−	41.5692i	0.921035	−	1.59528i
$680$		0			0
$681$	4.00000	−	6.92820i	0.153280	−	0.265489i
$682$		0			0
$683$	−6.00000			−0.229584			−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000			−0.229584			−0.114792	+	0.993390i	$0.536620\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	21.0000	−	36.3731i	0.801200	−	1.38772i
$688$		0			0
$689$	18.0000	−	31.1769i	0.685745	−	1.18775i
$690$		0			0
$691$	37.0000			1.40755			0.703773	−	0.710425i	$-0.251497\pi$
$691$	37.0000			1.40755			0.703773	+	0.710425i	$0.251497\pi$
$692$		0			0
$693$	6.00000	+	10.3923i	0.227921	+	0.394771i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	2.00000	+	3.46410i	0.0757554	+	0.131212i
$698$		0			0
$699$	10.0000	+	17.3205i	0.378235	+	0.655122i
$700$		0			0
$701$	21.0000	−	36.3731i	0.793159	−	1.37379i	−0.130843	−	0.991403i	$-0.541768\pi$
$701$	21.0000	−	36.3731i	0.793159	−	1.37379i	0.924002	−	0.382389i	$-0.124898\pi$
$702$		0			0
$703$	14.0000	+	10.3923i	0.528020	+	0.391953i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−22.0000	−	38.1051i	−0.827395	−	1.43309i
$708$		0			0
$709$	−2.50000	−	4.33013i	−0.0938895	−	0.162621i	0.815255	−	0.579102i	$-0.196597\pi$
$709$	−2.50000	−	4.33013i	−0.0938895	−	0.162621i	−0.909145	+	0.416481i	$0.863263\pi$
$710$		0			0
$711$	−1.00000			−0.0375029
$712$		0			0
$713$	−10.0000	−	17.3205i	−0.374503	−	0.648658i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	15.0000	−	25.9808i	0.560185	−	0.970269i
$718$		0			0
$719$	−14.5000	+	25.1147i	−0.540759	+	0.936622i	0.458102	+	0.888900i	$0.348529\pi$
$719$	−14.5000	+	25.1147i	−0.540759	+	0.936622i	−0.998861	+	0.0477220i	$0.984804\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−10.0000			−0.371904
$724$		0			0
$725$		0			0
$726$		0			0
$727$	13.0000	−	22.5167i	0.482143	−	0.835097i	−0.517647	−	0.855595i	$-0.673192\pi$
$727$	13.0000	−	22.5167i	0.482143	−	0.835097i	0.999790	+	0.0204978i	$0.00652512\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$		0			0
$732$		0			0
$733$	12.0000			0.443230			0.221615	−	0.975134i	$-0.428867\pi$
$733$	12.0000			0.443230			0.221615	+	0.975134i	$0.428867\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	21.0000	+	36.3731i	0.773545	+	1.33982i
$738$		0			0
$739$	9.50000	−	16.4545i	0.349463	−	0.605288i	−0.636691	−	0.771119i	$-0.719697\pi$
$739$	9.50000	−	16.4545i	0.349463	−	0.605288i	0.986154	+	0.165831i	$0.0530307\pi$
$740$		0			0
$741$	42.0000	+	31.1769i	1.54291	+	1.14531i
$742$		0			0
$743$	26.0000	−	45.0333i	0.953847	−	1.65211i	0.216864	−	0.976202i	$-0.430417\pi$
$743$	26.0000	−	45.0333i	0.953847	−	1.65211i	0.736984	−	0.675910i	$-0.236249\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	8.00000	+	13.8564i	0.292705	+	0.506979i
$748$		0			0
$749$	48.0000			1.75388
$750$		0			0
$751$	−9.50000	−	16.4545i	−0.346660	−	0.600433i	0.638994	−	0.769212i	$-0.279351\pi$
$751$	−9.50000	−	16.4545i	−0.346660	−	0.600433i	−0.985654	+	0.168779i	$0.946018\pi$
$752$		0			0
$753$	−62.0000			−2.25941
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−7.00000	+	12.1244i	−0.254419	+	0.440667i	−0.964738	−	0.263213i	$-0.915218\pi$
$757$	−7.00000	+	12.1244i	−0.254419	+	0.440667i	0.710318	+	0.703881i	$0.248551\pi$
$758$		0			0
$759$	−24.0000			−0.871145
$760$		0			0
$761$	54.0000			1.95750			0.978749	−	0.205061i	$-0.0657392\pi$
$761$	54.0000			1.95750			0.978749	+	0.205061i	$0.0657392\pi$
$762$		0			0
$763$	−14.0000	+	24.2487i	−0.506834	+	0.877862i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.00000			0.216647
$768$		0			0
$769$	−6.50000	−	11.2583i	−0.234396	−	0.405986i	0.724701	−	0.689063i	$-0.241978\pi$
$769$	−6.50000	−	11.2583i	−0.234396	−	0.405986i	−0.959097	+	0.283078i	$0.908645\pi$
$770$		0			0
$771$	36.0000			1.29651
$772$		0			0
$773$	−27.0000	−	46.7654i	−0.971123	−	1.68203i	−0.692179	−	0.721726i	$-0.743349\pi$
$773$	−27.0000	−	46.7654i	−0.971123	−	1.68203i	−0.278944	−	0.960307i	$-0.589984\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	16.0000	−	27.7128i	0.573997	−	0.994192i
$778$		0			0
$779$	−8.00000	+	3.46410i	−0.286630	+	0.124114i
$780$		0			0
$781$	22.5000	−	38.9711i	0.805113	−	1.39450i
$782$		0			0
$783$	−2.00000	−	3.46410i	−0.0714742	−	0.123797i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−38.0000			−1.35455			−0.677277	−	0.735728i	$-0.736840\pi$
$787$	−38.0000			−1.35455			−0.677277	+	0.735728i	$0.736840\pi$
$788$		0			0
$789$	−10.0000	−	17.3205i	−0.356009	−	0.616626i
$790$		0			0
$791$	−56.0000			−1.99113
$792$		0			0
$793$	−21.0000	+	36.3731i	−0.745732	+	1.29165i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	22.0000			0.779280			0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000			0.779280			0.389640	+	0.920967i	$0.372599\pi$
$798$		0			0
$799$	12.0000			0.424529
$800$		0			0
$801$	−8.50000	+	14.7224i	−0.300333	+	0.520192i
$802$		0			0
$803$	−18.0000	+	31.1769i	−0.635206	+	1.10021i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.00000	−	1.73205i	−0.0352017	−	0.0609711i
$808$		0			0
$809$	45.0000			1.58212			0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000			1.58212			0.791058	+	0.611741i	$0.209531\pi$
$810$		0			0
$811$	6.50000	+	11.2583i	0.228246	+	0.395333i	0.957288	−	0.289135i	$-0.0933677\pi$
$811$	6.50000	+	11.2583i	0.228246	+	0.395333i	−0.729042	+	0.684468i	$0.760034\pi$
$812$		0			0
$813$	17.0000	+	29.4449i	0.596216	+	1.03268i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	12.0000	−	20.7846i	0.419314	−	0.726273i
$820$		0			0
$821$	−12.5000	−	21.6506i	−0.436253	−	0.755612i	0.561144	−	0.827718i	$-0.310361\pi$
$821$	−12.5000	−	21.6506i	−0.436253	−	0.755612i	−0.997397	+	0.0721058i	$0.977028\pi$
$822$		0			0
$823$	13.0000	+	22.5167i	0.453152	+	0.784881i	0.998580	−	0.0532760i	$-0.0169663\pi$
$823$	13.0000	+	22.5167i	0.453152	+	0.784881i	−0.545428	+	0.838157i	$0.683633\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.00000	−	15.5885i	−0.312961	−	0.542064i	0.666041	−	0.745915i	$-0.267987\pi$
$827$	−9.00000	−	15.5885i	−0.312961	−	0.542064i	−0.979002	+	0.203851i	$0.934654\pi$
$828$		0			0
$829$	−30.0000			−1.04194			−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000			−1.04194			−0.520972	+	0.853574i	$0.674430\pi$
$830$		0			0
$831$	−16.0000	+	27.7128i	−0.555034	+	0.961347i
$832$		0			0
$833$	9.00000	−	15.5885i	0.311832	−	0.540108i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−20.0000			−0.691301
$838$		0			0
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$		0			0
$843$	52.0000			1.79098
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−8.00000			−0.274883
$848$		0			0
$849$	26.0000	+	45.0333i	0.892318	+	1.54554i
$850$		0			0
$851$	8.00000	+	13.8564i	0.274236	+	0.474991i
$852$		0			0
$853$	19.0000	−	32.9090i	0.650548	−	1.12678i	−0.332443	−	0.943123i	$-0.607873\pi$
$853$	19.0000	−	32.9090i	0.650548	−	1.12678i	0.982990	−	0.183658i	$-0.0587939\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	0.874429	−	0.485153i	$-0.161236\pi$
$859$	0.500000	+	0.866025i	0.0170598	+	0.0295484i	−0.857369	+	0.514701i	$0.827903\pi$
$860$		0			0
$861$	8.00000	+	13.8564i	0.272639	+	0.472225i
$862$		0			0
$863$	18.0000			0.612727			0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000			0.612727			0.306364	+	0.951915i	$0.400888\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	26.0000			0.883006
$868$		0			0
$869$	−1.50000	+	2.59808i	−0.0508840	+	0.0881337i
$870$		0			0
$871$	42.0000	−	72.7461i	1.42312	−	2.46491i
$872$		0			0
$873$	−12.0000			−0.406138
$874$		0			0
$875$		0			0
$876$		0			0
$877$	20.0000	−	34.6410i	0.675352	−	1.16974i	−0.301014	−	0.953620i	$-0.597325\pi$
$877$	20.0000	−	34.6410i	0.675352	−	1.16974i	0.976366	−	0.216124i	$-0.0693416\pi$
$878$		0			0
$879$	−16.0000	+	27.7128i	−0.539667	+	0.934730i
$880$		0			0
$881$	−7.00000			−0.235836			−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000			−0.235836			−0.117918	+	0.993023i	$0.537622\pi$
$882$		0			0
$883$	4.00000	+	6.92820i	0.134611	+	0.233153i	0.925449	−	0.378873i	$-0.123688\pi$
$883$	4.00000	+	6.92820i	0.134611	+	0.233153i	−0.790838	+	0.612026i	$0.790355\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.0000	+	24.2487i	0.470074	+	0.814192i	0.999414	−	0.0342175i	$-0.0108939\pi$
$887$	14.0000	+	24.2487i	0.470074	+	0.814192i	−0.529340	+	0.848410i	$0.677561\pi$
$888$		0			0
$889$	36.0000	+	62.3538i	1.20740	+	2.09128i
$890$		0			0
$891$	−16.5000	+	28.5788i	−0.552771	+	0.957427i
$892$		0			0
$893$	−3.00000	+	25.9808i	−0.100391	+	0.869413i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	24.0000	+	41.5692i	0.801337	+	1.38796i
$898$		0			0
$899$	2.50000	+	4.33013i	0.0833797	+	0.144418i
$900$		0			0
$901$	−12.0000			−0.399778
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	16.0000	−	27.7128i	0.531271	−	0.920189i	−0.468063	−	0.883695i	$-0.655048\pi$
$907$	16.0000	−	27.7128i	0.531271	−	0.920189i	0.999334	−	0.0364935i	$-0.0116188\pi$
$908$		0			0
$909$	−5.50000	+	9.52628i	−0.182423	+	0.315967i
$910$		0			0
$911$	7.00000			0.231920			0.115960	−	0.993254i	$-0.463006\pi$
$911$	7.00000			0.231920			0.115960	+	0.993254i	$0.463006\pi$
$912$		0			0
$913$	48.0000			1.58857
$914$		0			0
$915$		0			0
$916$		0			0
$917$	40.0000	−	69.2820i	1.32092	−	2.28789i
$918$		0			0
$919$	8.00000			0.263896			0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000			0.263896			0.131948	+	0.991257i	$0.457877\pi$
$920$		0			0
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$		0			0
$923$	−90.0000			−2.96239
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	−0.640768	−	0.767735i	$-0.721384\pi$
$929$	10.5000	−	18.1865i	0.344494	−	0.596681i	0.985262	+	0.171054i	$0.0547172\pi$
$930$		0			0
$931$	31.5000	+	23.3827i	1.03237	+	0.766337i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	1.00000	+	1.73205i	0.0326686	+	0.0565836i	0.881897	−	0.471441i	$-0.156266\pi$
$937$	1.00000	+	1.73205i	0.0326686	+	0.0565836i	−0.849229	+	0.528025i	$0.822933\pi$
$938$		0			0
$939$	68.0000			2.21910
$940$		0			0
$941$	−17.5000	−	30.3109i	−0.570484	−	0.988107i	−0.996516	−	0.0833989i	$-0.973422\pi$
$941$	−17.5000	−	30.3109i	−0.570484	−	0.988107i	0.426033	−	0.904708i	$-0.359911\pi$
$942$		0			0
$943$	−8.00000			−0.260516
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.00000	+	8.66025i	−0.162478	+	0.281420i	−0.935757	−	0.352646i	$-0.885282\pi$
$947$	−5.00000	+	8.66025i	−0.162478	+	0.281420i	0.773279	+	0.634066i	$0.218615\pi$
$948$		0			0
$949$	72.0000			2.33722
$950$		0			0
$951$	−24.0000			−0.778253
$952$		0			0
$953$	−14.0000	+	24.2487i	−0.453504	+	0.785493i	−0.998601	−	0.0528806i	$-0.983160\pi$
$953$	−14.0000	+	24.2487i	−0.453504	+	0.785493i	0.545096	+	0.838373i	$0.316493\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	6.00000			0.193952
$958$		0			0
$959$	24.0000	+	41.5692i	0.775000	+	1.34234i
$960$		0			0
$961$	−6.00000			−0.193548
$962$		0			0
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−6.00000	+	10.3923i	−0.192947	+	0.334194i	−0.946226	−	0.323508i	$-0.895138\pi$
$967$	−6.00000	+	10.3923i	−0.192947	+	0.334194i	0.753279	+	0.657702i	$0.228471\pi$
$968$		0			0
$969$	2.00000	−	17.3205i	0.0642493	−	0.556415i
$970$		0			0
$971$	−30.0000	+	51.9615i	−0.962746	+	1.66752i	−0.247193	+	0.968966i	$0.579508\pi$
$971$	−30.0000	+	51.9615i	−0.962746	+	1.66752i	−0.715553	+	0.698558i	$0.753825\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.0000			−0.383914			−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000			−0.383914			−0.191957	+	0.981403i	$0.561483\pi$
$978$		0			0
$979$	25.5000	+	44.1673i	0.814984	+	1.41159i
$980$		0			0
$981$	7.00000			0.223493
$982$		0			0
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	48.0000			1.52786
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$		0			0
$993$	−20.0000	+	34.6410i	−0.634681	+	1.09930i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	0.775923	−	0.630828i	$-0.217285\pi$
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	−0.934274	+	0.356555i	$0.883951\pi$
$998$		0			0
$999$	16.0000			0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.b.201.1		2
5.2	odd	4		1900.2.s.b.49.1		4
5.3	odd	4		1900.2.s.b.49.2		4
5.4	even	2		380.2.i.a.201.1	yes	2
15.14	odd	2		3420.2.t.b.3241.1		2
19.7	even	3	inner	1900.2.i.b.501.1		2
20.19	odd	2		1520.2.q.g.961.1		2
95.7	odd	12		1900.2.s.b.349.2		4
95.49	even	6		7220.2.a.e.1.1		1
95.64	even	6		380.2.i.a.121.1	✓	2
95.83	odd	12		1900.2.s.b.349.1		4
95.84	odd	6		7220.2.a.a.1.1		1
285.254	odd	6		3420.2.t.b.1261.1		2
380.159	odd	6		1520.2.q.g.881.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.a.121.1	✓	2	95.64	even	6
380.2.i.a.201.1	yes	2	5.4	even	2
1520.2.q.g.881.1		2	380.159	odd	6
1520.2.q.g.961.1		2	20.19	odd	2
1900.2.i.b.201.1		2	1.1	even	1	trivial
1900.2.i.b.501.1		2	19.7	even	3	inner
1900.2.s.b.49.1		4	5.2	odd	4
1900.2.s.b.49.2		4	5.3	odd	4
1900.2.s.b.349.1		4	95.83	odd	12
1900.2.s.b.349.2		4	95.7	odd	12
3420.2.t.b.1261.1		2	285.254	odd	6
3420.2.t.b.3241.1		2	15.14	odd	2
7220.2.a.a.1.1		1	95.84	odd	6
7220.2.a.e.1.1		1	95.49	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:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{3} +4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{3} +4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} -3.00000 q^{11} +(3.00000 + 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{17} +(3.50000 + 2.59808i) q^{19} +(4.00000 - 6.92820i) q^{21} +(2.00000 + 3.46410i) q^{23} +4.00000 q^{27} +(-0.500000 - 0.866025i) q^{29} -5.00000 q^{31} +(-3.00000 + 5.19615i) q^{33} +4.00000 q^{37} +12.0000 q^{39} +(-1.00000 + 1.73205i) q^{41} +(3.00000 + 5.19615i) q^{47} +9.00000 q^{49} +(-2.00000 - 3.46410i) q^{51} +(-3.00000 - 5.19615i) q^{53} +(8.00000 - 3.46410i) q^{57} +(0.500000 - 0.866025i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-2.00000 - 3.46410i) q^{63} +(-7.00000 - 12.1244i) q^{67} +8.00000 q^{69} +(-7.50000 + 12.9904i) q^{71} +(6.00000 - 10.3923i) q^{73} -12.0000 q^{77} +(0.500000 - 0.866025i) q^{79} +(5.50000 - 9.52628i) q^{81} -16.0000 q^{83} -2.00000 q^{87} +(-8.50000 - 14.7224i) q^{89} +(12.0000 + 20.7846i) q^{91} +(-5.00000 + 8.66025i) q^{93} +(6.00000 - 10.3923i) q^{97} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 8 q^{7} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 8 * q^7 - q^9	\( 2 q + 2 q^{3} + 8 q^{7} - q^{9} - 6 q^{11} + 6 q^{13} + 2 q^{17} + 7 q^{19} + 8 q^{21} + 4 q^{23} + 8 q^{27} - q^{29} - 10 q^{31} - 6 q^{33} + 8 q^{37} + 24 q^{39} - 2 q^{41} + 6 q^{47} + 18 q^{49} - 4 q^{51} - 6 q^{53} + 16 q^{57} + q^{59} + 7 q^{61} - 4 q^{63} - 14 q^{67} + 16 q^{69} - 15 q^{71} + 12 q^{73} - 24 q^{77} + q^{79} + 11 q^{81} - 32 q^{83} - 4 q^{87} - 17 q^{89} + 24 q^{91} - 10 q^{93} + 12 q^{97} + 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 8 * q^7 - q^9 - 6 * q^11 + 6 * q^13 + 2 * q^17 + 7 * q^19 + 8 * q^21 + 4 * q^23 + 8 * q^27 - q^29 - 10 * q^31 - 6 * q^33 + 8 * q^37 + 24 * q^39 - 2 * q^41 + 6 * q^47 + 18 * q^49 - 4 * q^51 - 6 * q^53 + 16 * q^57 + q^59 + 7 * q^61 - 4 * q^63 - 14 * q^67 + 16 * q^69 - 15 * q^71 + 12 * q^73 - 24 * q^77 + q^79 + 11 * q^81 - 32 * q^83 - 4 * q^87 - 17 * q^89 + 24 * q^91 - 10 * q^93 + 12 * q^97 + 3 * q^99

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