LMFDB - Embedded newform 1950.2.f.o.649.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(649,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("1950.649");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.f (of order $2$, degree $1$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9x^{2} + 16 $ x^4 + 9*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			649.1
Root			$2.56155i$ of defining polynomial
Character	$\chi$	$=$	1950.649
Dual form			1950.2.f.o.649.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} -3.12311 q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} -3.12311 q^{7} +1.00000 q^{8} -1.00000 q^{9} +5.12311i q^{11} -1.00000i q^{12} +(-0.561553 - 3.56155i) q^{13} -3.12311 q^{14} +1.00000 q^{16} +2.00000i q^{17} -1.00000 q^{18} +6.00000i q^{19} +3.12311i q^{21} +5.12311i q^{22} +5.12311i q^{23} -1.00000i q^{24} +(-0.561553 - 3.56155i) q^{26} +1.00000i q^{27} -3.12311 q^{28} -2.00000 q^{29} +3.12311i q^{31} +1.00000 q^{32} +5.12311 q^{33} +2.00000i q^{34} -1.00000 q^{36} +5.12311 q^{37} +6.00000i q^{38} +(-3.56155 + 0.561553i) q^{39} +0.876894i q^{41} +3.12311i q^{42} -6.24621i q^{43} +5.12311i q^{44} +5.12311i q^{46} +6.24621 q^{47} -1.00000i q^{48} +2.75379 q^{49} +2.00000 q^{51} +(-0.561553 - 3.56155i) q^{52} +13.3693i q^{53} +1.00000i q^{54} -3.12311 q^{56} +6.00000 q^{57} -2.00000 q^{58} +1.12311i q^{59} +10.0000 q^{61} +3.12311i q^{62} +3.12311 q^{63} +1.00000 q^{64} +5.12311 q^{66} -4.87689 q^{67} +2.00000i q^{68} +5.12311 q^{69} +10.2462i q^{71} -1.00000 q^{72} -13.1231 q^{73} +5.12311 q^{74} +6.00000i q^{76} -16.0000i q^{77} +(-3.56155 + 0.561553i) q^{78} -8.00000 q^{79} +1.00000 q^{81} +0.876894i q^{82} -6.24621 q^{83} +3.12311i q^{84} -6.24621i q^{86} +2.00000i q^{87} +5.12311i q^{88} -3.12311i q^{89} +(1.75379 + 11.1231i) q^{91} +5.12311i q^{92} +3.12311 q^{93} +6.24621 q^{94} -1.00000i q^{96} +13.1231 q^{97} +2.75379 q^{98} -5.12311i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8 - 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8} - 4 q^{9} + 6 q^{13} + 4 q^{14} + 4 q^{16} - 4 q^{18} + 6 q^{26} + 4 q^{28} - 8 q^{29} + 4 q^{32} + 4 q^{33} - 4 q^{36} + 4 q^{37} - 6 q^{39} - 8 q^{47} + 44 q^{49} + 8 q^{51} + 6 q^{52} + 4 q^{56} + 24 q^{57} - 8 q^{58} + 40 q^{61} - 4 q^{63} + 4 q^{64} + 4 q^{66} - 36 q^{67} + 4 q^{69} - 4 q^{72} - 36 q^{73} + 4 q^{74} - 6 q^{78} - 32 q^{79} + 4 q^{81} + 8 q^{83} + 40 q^{91} - 4 q^{93} - 8 q^{94} + 36 q^{97} + 44 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8 - 4 * q^9 + 6 * q^13 + 4 * q^14 + 4 * q^16 - 4 * q^18 + 6 * q^26 + 4 * q^28 - 8 * q^29 + 4 * q^32 + 4 * q^33 - 4 * q^36 + 4 * q^37 - 6 * q^39 - 8 * q^47 + 44 * q^49 + 8 * q^51 + 6 * q^52 + 4 * q^56 + 24 * q^57 - 8 * q^58 + 40 * q^61 - 4 * q^63 + 4 * q^64 + 4 * q^66 - 36 * q^67 + 4 * q^69 - 4 * q^72 - 36 * q^73 + 4 * q^74 - 6 * q^78 - 32 * q^79 + 4 * q^81 + 8 * q^83 + 40 * q^91 - 4 * q^93 - 8 * q^94 + 36 * q^97 + 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$		−	1.00000i		−	0.408248i
$7$	−3.12311			−1.18042			−0.590211	−	0.807249i	$-0.700956\pi$
$7$	−3.12311			−1.18042			−0.590211	+	0.807249i	$0.700956\pi$
$8$	1.00000			0.353553
$9$	−1.00000			−0.333333
$10$		0			0
$11$			5.12311i			1.54467i	0.635213	+	0.772337i	$0.280912\pi$
$11$			5.12311i			1.54467i	−0.635213	+	0.772337i	$0.719088\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−0.561553	−	3.56155i	−0.155747	−	0.987797i
$13$	−0.561553	−	3.56155i	−0.155747	−	0.987797i
$14$	−3.12311			−0.834685
$15$		0			0
$16$	1.00000			0.250000
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$	−1.00000			−0.235702
$19$			6.00000i			1.37649i	0.725476	+	0.688247i	$0.241620\pi$
$19$			6.00000i			1.37649i	−0.725476	+	0.688247i	$0.758380\pi$
$20$		0			0
$21$			3.12311i			0.681518i
$22$			5.12311i			1.09225i
$23$			5.12311i			1.06824i	0.845408	+	0.534121i	$0.179357\pi$
$23$			5.12311i			1.06824i	−0.845408	+	0.534121i	$0.820643\pi$
$24$		−	1.00000i		−	0.204124i
$25$		0			0
$26$	−0.561553	−	3.56155i	−0.110130	−	0.698478i
$27$			1.00000i			0.192450i
$28$	−3.12311			−0.590211
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$			3.12311i			0.560926i	0.959865	+	0.280463i	$0.0904881\pi$
$31$			3.12311i			0.560926i	−0.959865	+	0.280463i	$0.909512\pi$
$32$	1.00000			0.176777
$33$	5.12311			0.891818
$34$			2.00000i			0.342997i
$35$		0			0
$36$	−1.00000			−0.166667
$37$	5.12311			0.842233			0.421117	−	0.907006i	$-0.361638\pi$
$37$	5.12311			0.842233			0.421117	+	0.907006i	$0.361638\pi$
$38$			6.00000i			0.973329i
$39$	−3.56155	+	0.561553i	−0.570305	+	0.0899204i
$40$		0			0
$41$			0.876894i			0.136948i	0.997653	+	0.0684739i	$0.0218130\pi$
$41$			0.876894i			0.136948i	−0.997653	+	0.0684739i	$0.978187\pi$
$42$			3.12311i			0.481906i
$43$		−	6.24621i		−	0.952538i	−0.879300	−	0.476269i	$-0.841989\pi$
$43$		−	6.24621i		−	0.952538i	0.879300	−	0.476269i	$-0.158011\pi$
$44$			5.12311i			0.772337i
$45$		0			0
$46$			5.12311i			0.755361i
$47$	6.24621			0.911104			0.455552	−	0.890209i	$-0.349442\pi$
$47$	6.24621			0.911104			0.455552	+	0.890209i	$0.349442\pi$
$48$		−	1.00000i		−	0.144338i
$49$	2.75379			0.393398
$50$		0			0
$51$	2.00000			0.280056
$52$	−0.561553	−	3.56155i	−0.0778734	−	0.493899i
$53$			13.3693i			1.83642i	0.396098	+	0.918208i	$0.370364\pi$
$53$			13.3693i			1.83642i	−0.396098	+	0.918208i	$0.629636\pi$
$54$			1.00000i			0.136083i
$55$		0			0
$56$	−3.12311			−0.417343
$57$	6.00000			0.794719
$58$	−2.00000			−0.262613
$59$			1.12311i			0.146216i	0.997324	+	0.0731079i	$0.0232918\pi$
$59$			1.12311i			0.146216i	−0.997324	+	0.0731079i	$0.976708\pi$
$60$		0			0
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$			3.12311i			0.396635i
$63$	3.12311			0.393474
$64$	1.00000			0.125000
$65$		0			0
$66$	5.12311			0.630611
$67$	−4.87689			−0.595807			−0.297904	−	0.954596i	$-0.596287\pi$
$67$	−4.87689			−0.595807			−0.297904	+	0.954596i	$0.596287\pi$
$68$			2.00000i			0.242536i
$69$	5.12311			0.616749
$70$		0			0
$71$			10.2462i			1.21600i	0.793936	+	0.608001i	$0.208028\pi$
$71$			10.2462i			1.21600i	−0.793936	+	0.608001i	$0.791972\pi$
$72$	−1.00000			−0.117851
$73$	−13.1231			−1.53594			−0.767972	−	0.640484i	$-0.778734\pi$
$73$	−13.1231			−1.53594			−0.767972	+	0.640484i	$0.778734\pi$
$74$	5.12311			0.595549
$75$		0			0
$76$			6.00000i			0.688247i
$77$		−	16.0000i		−	1.82337i
$78$	−3.56155	+	0.561553i	−0.403266	+	0.0635833i
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$			0.876894i			0.0968368i
$83$	−6.24621			−0.685611			−0.342805	−	0.939406i	$-0.611377\pi$
$83$	−6.24621			−0.685611			−0.342805	+	0.939406i	$0.611377\pi$
$84$			3.12311i			0.340759i
$85$		0			0
$86$		−	6.24621i		−	0.673546i
$87$			2.00000i			0.214423i
$88$			5.12311i			0.546125i
$89$		−	3.12311i		−	0.331049i	−0.986206	−	0.165524i	$-0.947068\pi$
$89$		−	3.12311i		−	0.331049i	0.986206	−	0.165524i	$-0.0529316\pi$
$90$		0			0
$91$	1.75379	+	11.1231i	0.183847	+	1.16602i
$92$			5.12311i			0.534121i
$93$	3.12311			0.323851
$94$	6.24621			0.644247
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	13.1231			1.33245			0.666225	−	0.745751i	$-0.267909\pi$
$97$	13.1231			1.33245			0.666225	+	0.745751i	$0.267909\pi$
$98$	2.75379			0.278175
$99$		−	5.12311i		−	0.514891i
$100$		0			0
$101$	−12.2462			−1.21854			−0.609272	−	0.792961i	$-0.708538\pi$
$101$	−12.2462			−1.21854			−0.609272	+	0.792961i	$0.708538\pi$
$102$	2.00000			0.198030
$103$			13.1231i			1.29306i	0.762889	+	0.646529i	$0.223780\pi$
$103$			13.1231i			1.29306i	−0.762889	+	0.646529i	$0.776220\pi$
$104$	−0.561553	−	3.56155i	−0.0550648	−	0.349239i
$105$		0			0
$106$			13.3693i			1.29854i
$107$		−	8.00000i		−	0.773389i	−0.922208	−	0.386695i	$-0.873617\pi$
$107$		−	8.00000i		−	0.773389i	0.922208	−	0.386695i	$-0.126383\pi$
$108$			1.00000i			0.0962250i
$109$		−	2.87689i		−	0.275557i	−0.990463	−	0.137778i	$-0.956004\pi$
$109$		−	2.87689i		−	0.275557i	0.990463	−	0.137778i	$-0.0439961\pi$
$110$		0			0
$111$		−	5.12311i		−	0.486264i
$112$	−3.12311			−0.295106
$113$		−	12.2462i		−	1.15203i	−0.817440	−	0.576013i	$-0.804608\pi$
$113$		−	12.2462i		−	1.15203i	0.817440	−	0.576013i	$-0.195392\pi$
$114$	6.00000			0.561951
$115$		0			0
$116$	−2.00000			−0.185695
$117$	0.561553	+	3.56155i	0.0519156	+	0.329266i
$118$			1.12311i			0.103390i
$119$		−	6.24621i		−	0.572589i
$120$		0			0
$121$	−15.2462			−1.38602
$122$	10.0000			0.905357
$123$	0.876894			0.0790669
$124$			3.12311i			0.280463i
$125$		0			0
$126$	3.12311			0.278228
$127$		−	13.1231i		−	1.16449i	−0.813014	−	0.582244i	$-0.802175\pi$
$127$		−	13.1231i		−	1.16449i	0.813014	−	0.582244i	$-0.197825\pi$
$128$	1.00000			0.0883883
$129$	−6.24621			−0.549948
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$	5.12311			0.445909
$133$		−	18.7386i		−	1.62485i
$134$	−4.87689			−0.421300
$135$		0			0
$136$			2.00000i			0.171499i
$137$	10.4924			0.896428			0.448214	−	0.893926i	$-0.352060\pi$
$137$	10.4924			0.896428			0.448214	+	0.893926i	$0.352060\pi$
$138$	5.12311			0.436108
$139$	16.4924			1.39887			0.699435	−	0.714697i	$-0.253435\pi$
$139$	16.4924			1.39887			0.699435	+	0.714697i	$0.253435\pi$
$140$		0			0
$141$		−	6.24621i		−	0.526026i
$142$			10.2462i			0.859843i
$143$	18.2462	−	2.87689i	1.52582	−	0.240578i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−13.1231			−1.08608
$147$		−	2.75379i		−	0.227129i
$148$	5.12311			0.421117
$149$			14.0000i			1.14692i	0.819232	+	0.573462i	$0.194400\pi$
$149$			14.0000i			1.14692i	−0.819232	+	0.573462i	$0.805600\pi$
$150$		0			0
$151$			13.3693i			1.08798i	0.839092	+	0.543990i	$0.183087\pi$
$151$			13.3693i			1.08798i	−0.839092	+	0.543990i	$0.816913\pi$
$152$			6.00000i			0.486664i
$153$		−	2.00000i		−	0.161690i
$154$		−	16.0000i		−	1.28932i
$155$		0			0
$156$	−3.56155	+	0.561553i	−0.285152	+	0.0449602i
$157$			21.3693i			1.70546i	0.522354	+	0.852729i	$0.325054\pi$
$157$			21.3693i			1.70546i	−0.522354	+	0.852729i	$0.674946\pi$
$158$	−8.00000			−0.636446
$159$	13.3693			1.06026
$160$		0			0
$161$		−	16.0000i		−	1.26098i
$162$	1.00000			0.0785674
$163$	−7.12311			−0.557925			−0.278962	−	0.960302i	$-0.589990\pi$
$163$	−7.12311			−0.557925			−0.278962	+	0.960302i	$0.589990\pi$
$164$			0.876894i			0.0684739i
$165$		0			0
$166$	−6.24621			−0.484800
$167$	22.2462			1.72146			0.860732	−	0.509059i	$-0.170006\pi$
$167$	22.2462			1.72146			0.860732	+	0.509059i	$0.170006\pi$
$168$			3.12311i			0.240953i
$169$	−12.3693	+	4.00000i	−0.951486	+	0.307692i
$170$		0			0
$171$		−	6.00000i		−	0.458831i
$172$		−	6.24621i		−	0.476269i
$173$		−	23.1231i		−	1.75802i	−0.476806	−	0.879009i	$-0.658206\pi$
$173$		−	23.1231i		−	1.75802i	0.476806	−	0.879009i	$-0.341794\pi$
$174$			2.00000i			0.151620i
$175$		0			0
$176$			5.12311i			0.386169i
$177$	1.12311			0.0844178
$178$		−	3.12311i		−	0.234087i
$179$	−16.4924			−1.23270			−0.616351	−	0.787472i	$-0.711390\pi$
$179$	−16.4924			−1.23270			−0.616351	+	0.787472i	$0.711390\pi$
$180$		0			0
$181$	−20.2462			−1.50489			−0.752445	−	0.658656i	$-0.771125\pi$
$181$	−20.2462			−1.50489			−0.752445	+	0.658656i	$0.771125\pi$
$182$	1.75379	+	11.1231i	0.129999	+	0.824499i
$183$		−	10.0000i		−	0.739221i
$184$			5.12311i			0.377680i
$185$		0			0
$186$	3.12311			0.228997
$187$	−10.2462			−0.749277
$188$	6.24621			0.455552
$189$		−	3.12311i		−	0.227173i
$190$		0			0
$191$	16.4924			1.19335			0.596675	−	0.802483i	$-0.296488\pi$
$191$	16.4924			1.19335			0.596675	+	0.802483i	$0.296488\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	−25.1231			−1.80840			−0.904200	−	0.427109i	$-0.859532\pi$
$193$	−25.1231			−1.80840			−0.904200	+	0.427109i	$0.859532\pi$
$194$	13.1231			0.942184
$195$		0			0
$196$	2.75379			0.196699
$197$	−16.2462			−1.15749			−0.578747	−	0.815507i	$-0.696458\pi$
$197$	−16.2462			−1.15749			−0.578747	+	0.815507i	$0.696458\pi$
$198$		−	5.12311i		−	0.364083i
$199$	−18.2462			−1.29344			−0.646720	−	0.762728i	$-0.723860\pi$
$199$	−18.2462			−1.29344			−0.646720	+	0.762728i	$0.723860\pi$
$200$		0			0
$201$			4.87689i			0.343990i
$202$	−12.2462			−0.861640
$203$	6.24621			0.438398
$204$	2.00000			0.140028
$205$		0			0
$206$			13.1231i			0.914330i
$207$		−	5.12311i		−	0.356080i
$208$	−0.561553	−	3.56155i	−0.0389367	−	0.246949i
$209$	−30.7386			−2.12624
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$			13.3693i			0.918208i
$213$	10.2462			0.702059
$214$		−	8.00000i		−	0.546869i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$		−	9.75379i		−	0.662130i
$218$		−	2.87689i		−	0.194848i
$219$			13.1231i			0.886777i
$220$		0			0
$221$	7.12311	−	1.12311i	0.479152	−	0.0755483i
$222$		−	5.12311i		−	0.343840i
$223$	9.36932			0.627416			0.313708	−	0.949520i	$-0.398429\pi$
$223$	9.36932			0.627416			0.313708	+	0.949520i	$0.398429\pi$
$224$	−3.12311			−0.208671
$225$		0			0
$226$		−	12.2462i		−	0.814606i
$227$	−8.00000			−0.530979			−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000			−0.530979			−0.265489	+	0.964114i	$0.585534\pi$
$228$	6.00000			0.397360
$229$			5.12311i			0.338544i	0.985569	+	0.169272i	$0.0541417\pi$
$229$			5.12311i			0.338544i	−0.985569	+	0.169272i	$0.945858\pi$
$230$		0			0
$231$	−16.0000			−1.05272
$232$	−2.00000			−0.131306
$233$			7.75379i			0.507968i	0.967208	+	0.253984i	$0.0817410\pi$
$233$			7.75379i			0.507968i	−0.967208	+	0.253984i	$0.918259\pi$
$234$	0.561553	+	3.56155i	0.0367099	+	0.232826i
$235$		0			0
$236$			1.12311i			0.0731079i
$237$			8.00000i			0.519656i
$238$		−	6.24621i		−	0.404882i
$239$		−	4.49242i		−	0.290591i	−0.989388	−	0.145295i	$-0.953587\pi$
$239$		−	4.49242i		−	0.290591i	0.989388	−	0.145295i	$-0.0464132\pi$
$240$		0			0
$241$		−	14.2462i		−	0.917679i	−0.888519	−	0.458840i	$-0.848265\pi$
$241$		−	14.2462i		−	0.917679i	0.888519	−	0.458840i	$-0.151735\pi$
$242$	−15.2462			−0.980064
$243$		−	1.00000i		−	0.0641500i
$244$	10.0000			0.640184
$245$		0			0
$246$	0.876894			0.0559087
$247$	21.3693	−	3.36932i	1.35970	−	0.214384i
$248$			3.12311i			0.198317i
$249$			6.24621i			0.395838i
$250$		0			0
$251$	26.2462			1.65665			0.828323	−	0.560251i	$-0.189295\pi$
$251$	26.2462			1.65665			0.828323	+	0.560251i	$0.189295\pi$
$252$	3.12311			0.196737
$253$	−26.2462			−1.65009
$254$		−	13.1231i		−	0.823417i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	12.2462i		−	0.763898i	−0.924183	−	0.381949i	$-0.875253\pi$
$257$		−	12.2462i		−	0.763898i	0.924183	−	0.381949i	$-0.124747\pi$
$258$	−6.24621			−0.388872
$259$	−16.0000			−0.994192
$260$		0			0
$261$	2.00000			0.123797
$262$	4.00000			0.247121
$263$			27.3693i			1.68766i	0.536607	+	0.843832i	$0.319706\pi$
$263$			27.3693i			1.68766i	−0.536607	+	0.843832i	$0.680294\pi$
$264$	5.12311			0.315305
$265$		0			0
$266$		−	18.7386i		−	1.14894i
$267$	−3.12311			−0.191131
$268$	−4.87689			−0.297904
$269$	16.2462			0.990549			0.495274	−	0.868737i	$-0.335067\pi$
$269$	16.2462			0.990549			0.495274	+	0.868737i	$0.335067\pi$
$270$		0			0
$271$			23.1231i			1.40463i	0.711867	+	0.702314i	$0.247850\pi$
$271$			23.1231i			1.40463i	−0.711867	+	0.702314i	$0.752150\pi$
$272$			2.00000i			0.121268i
$273$	11.1231	−	1.75379i	0.673201	−	0.106144i
$274$	10.4924			0.633870
$275$		0			0
$276$	5.12311			0.308375
$277$		−	29.8617i		−	1.79422i	−0.441809	−	0.897109i	$-0.645663\pi$
$277$		−	29.8617i		−	1.79422i	0.441809	−	0.897109i	$-0.354337\pi$
$278$	16.4924			0.989150
$279$		−	3.12311i		−	0.186975i
$280$		0			0
$281$		−	3.12311i		−	0.186309i	−0.995652	−	0.0931544i	$-0.970305\pi$
$281$		−	3.12311i		−	0.186309i	0.995652	−	0.0931544i	$-0.0296950\pi$
$282$		−	6.24621i		−	0.371956i
$283$			4.00000i			0.237775i	0.992908	+	0.118888i	$0.0379328\pi$
$283$			4.00000i			0.237775i	−0.992908	+	0.118888i	$0.962067\pi$
$284$			10.2462i			0.608001i
$285$		0			0
$286$	18.2462	−	2.87689i	1.07892	−	0.170114i
$287$		−	2.73863i		−	0.161656i
$288$	−1.00000			−0.0589256
$289$	13.0000			0.764706
$290$		0			0
$291$		−	13.1231i		−	0.769290i
$292$	−13.1231			−0.767972
$293$	28.7386			1.67893			0.839464	−	0.543415i	$-0.182869\pi$
$293$	28.7386			1.67893			0.839464	+	0.543415i	$0.182869\pi$
$294$		−	2.75379i		−	0.160604i
$295$		0			0
$296$	5.12311			0.297774
$297$	−5.12311			−0.297273
$298$			14.0000i			0.810998i
$299$	18.2462	−	2.87689i	1.05521	−	0.166375i
$300$		0			0
$301$			19.5076i			1.12440i
$302$			13.3693i			0.769318i
$303$			12.2462i			0.703526i
$304$			6.00000i			0.344124i
$305$		0			0
$306$		−	2.00000i		−	0.114332i
$307$	−31.1231			−1.77629			−0.888145	−	0.459564i	$-0.848006\pi$
$307$	−31.1231			−1.77629			−0.888145	+	0.459564i	$0.848006\pi$
$308$		−	16.0000i		−	0.911685i
$309$	13.1231			0.746547
$310$		0			0
$311$	8.49242			0.481561			0.240781	−	0.970580i	$-0.422597\pi$
$311$	8.49242			0.481561			0.240781	+	0.970580i	$0.422597\pi$
$312$	−3.56155	+	0.561553i	−0.201633	+	0.0317917i
$313$		−	16.2462i		−	0.918290i	−0.888361	−	0.459145i	$-0.848156\pi$
$313$		−	16.2462i		−	0.918290i	0.888361	−	0.459145i	$-0.151844\pi$
$314$			21.3693i			1.20594i
$315$		0			0
$316$	−8.00000			−0.450035
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$	13.3693			0.749714
$319$		−	10.2462i		−	0.573678i
$320$		0			0
$321$	−8.00000			−0.446516
$322$		−	16.0000i		−	0.891645i
$323$	−12.0000			−0.667698
$324$	1.00000			0.0555556
$325$		0			0
$326$	−7.12311			−0.394512
$327$	−2.87689			−0.159093
$328$			0.876894i			0.0484184i
$329$	−19.5076			−1.07549
$330$		0			0
$331$		−	7.75379i		−	0.426187i	−0.977032	−	0.213093i	$-0.931646\pi$
$331$		−	7.75379i		−	0.426187i	0.977032	−	0.213093i	$-0.0683539\pi$
$332$	−6.24621			−0.342805
$333$	−5.12311			−0.280744
$334$	22.2462			1.21726
$335$		0			0
$336$			3.12311i			0.170379i
$337$			6.00000i			0.326841i	0.986557	+	0.163420i	$0.0522527\pi$
$337$			6.00000i			0.326841i	−0.986557	+	0.163420i	$0.947747\pi$
$338$	−12.3693	+	4.00000i	−0.672802	+	0.217571i
$339$	−12.2462			−0.665123
$340$		0			0
$341$	−16.0000			−0.866449
$342$		−	6.00000i		−	0.324443i
$343$	13.2614			0.716046
$344$		−	6.24621i		−	0.336773i
$345$		0			0
$346$		−	23.1231i		−	1.24311i
$347$		−	14.2462i		−	0.764777i	−0.924002	−	0.382388i	$-0.875102\pi$
$347$		−	14.2462i		−	0.764777i	0.924002	−	0.382388i	$-0.124898\pi$
$348$			2.00000i			0.107211i
$349$		−	19.3693i		−	1.03682i	−0.855133	−	0.518408i	$-0.826525\pi$
$349$		−	19.3693i		−	1.03682i	0.855133	−	0.518408i	$-0.173475\pi$
$350$		0			0
$351$	3.56155	−	0.561553i	0.190102	−	0.0299735i
$352$			5.12311i			0.273062i
$353$	−12.2462			−0.651800			−0.325900	−	0.945404i	$-0.605667\pi$
$353$	−12.2462			−0.651800			−0.325900	+	0.945404i	$0.605667\pi$
$354$	1.12311			0.0596924
$355$		0			0
$356$		−	3.12311i		−	0.165524i
$357$	−6.24621			−0.330585
$358$	−16.4924			−0.871652
$359$		−	17.7538i		−	0.937009i	−0.883461	−	0.468505i	$-0.844793\pi$
$359$		−	17.7538i		−	0.937009i	0.883461	−	0.468505i	$-0.155207\pi$
$360$		0			0
$361$	−17.0000			−0.894737
$362$	−20.2462			−1.06412
$363$			15.2462i			0.800219i
$364$	1.75379	+	11.1231i	0.0919235	+	0.583009i
$365$		0			0
$366$		−	10.0000i		−	0.522708i
$367$			8.63068i			0.450518i	0.974299	+	0.225259i	$0.0723228\pi$
$367$			8.63068i			0.450518i	−0.974299	+	0.225259i	$0.927677\pi$
$368$			5.12311i			0.267060i
$369$		−	0.876894i		−	0.0456493i
$370$		0			0
$371$		−	41.7538i		−	2.16775i
$372$	3.12311			0.161925
$373$		−	7.12311i		−	0.368820i	−0.982849	−	0.184410i	$-0.940963\pi$
$373$		−	7.12311i		−	0.368820i	0.982849	−	0.184410i	$-0.0590375\pi$
$374$	−10.2462			−0.529819
$375$		0			0
$376$	6.24621			0.322124
$377$	1.12311	+	7.12311i	0.0578429	+	0.366859i
$378$		−	3.12311i		−	0.160635i
$379$			6.00000i			0.308199i	0.988055	+	0.154100i	$0.0492477\pi$
$379$			6.00000i			0.308199i	−0.988055	+	0.154100i	$0.950752\pi$
$380$		0			0
$381$	−13.1231			−0.672317
$382$	16.4924			0.843826
$383$	1.75379			0.0896144			0.0448072	−	0.998996i	$-0.485733\pi$
$383$	1.75379			0.0896144			0.0448072	+	0.998996i	$0.485733\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		0			0
$386$	−25.1231			−1.27873
$387$			6.24621i			0.317513i
$388$	13.1231			0.666225
$389$	0.246211			0.0124834			0.00624170	−	0.999981i	$-0.498013\pi$
$389$	0.246211			0.0124834			0.00624170	+	0.999981i	$0.498013\pi$
$390$		0			0
$391$	−10.2462			−0.518173
$392$	2.75379			0.139087
$393$		−	4.00000i		−	0.201773i
$394$	−16.2462			−0.818472
$395$		0			0
$396$		−	5.12311i		−	0.257446i
$397$	15.3693			0.771364			0.385682	−	0.922632i	$-0.373966\pi$
$397$	15.3693			0.771364			0.385682	+	0.922632i	$0.373966\pi$
$398$	−18.2462			−0.914600
$399$	−18.7386			−0.938105
$400$		0			0
$401$		−	1.36932i		−	0.0683804i	−0.999415	−	0.0341902i	$-0.989115\pi$
$401$		−	1.36932i		−	0.0683804i	0.999415	−	0.0341902i	$-0.0108852\pi$
$402$			4.87689i			0.243237i
$403$	11.1231	−	1.75379i	0.554081	−	0.0873624i
$404$	−12.2462			−0.609272
$405$		0			0
$406$	6.24621			0.309994
$407$			26.2462i			1.30098i
$408$	2.00000			0.0990148
$409$		−	8.49242i		−	0.419923i	−0.977710	−	0.209962i	$-0.932666\pi$
$409$		−	8.49242i		−	0.419923i	0.977710	−	0.209962i	$-0.0673339\pi$
$410$		0			0
$411$		−	10.4924i		−	0.517553i
$412$			13.1231i			0.646529i
$413$		−	3.50758i		−	0.172597i
$414$		−	5.12311i		−	0.251787i
$415$		0			0
$416$	−0.561553	−	3.56155i	−0.0275324	−	0.174619i
$417$		−	16.4924i		−	0.807637i
$418$	−30.7386			−1.50348
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$		−	0.630683i		−	0.0307376i	−0.999882	−	0.0153688i	$-0.995108\pi$
$421$		−	0.630683i		−	0.0307376i	0.999882	−	0.0153688i	$-0.00489224\pi$
$422$	4.00000			0.194717
$423$	−6.24621			−0.303701
$424$			13.3693i			0.649271i
$425$		0			0
$426$	10.2462			0.496431
$427$	−31.2311			−1.51138
$428$		−	8.00000i		−	0.386695i
$429$	−2.87689	−	18.2462i	−0.138898	−	0.880935i
$430$		0			0
$431$		−	32.4924i		−	1.56510i	−0.622585	−	0.782552i	$-0.713917\pi$
$431$		−	32.4924i		−	1.56510i	0.622585	−	0.782552i	$-0.286083\pi$
$432$			1.00000i			0.0481125i
$433$			18.0000i			0.865025i	0.901628	+	0.432512i	$0.142373\pi$
$433$			18.0000i			0.865025i	−0.901628	+	0.432512i	$0.857627\pi$
$434$		−	9.75379i		−	0.468197i
$435$		0			0
$436$		−	2.87689i		−	0.137778i
$437$	−30.7386			−1.47043
$438$			13.1231i			0.627046i
$439$	36.4924			1.74169			0.870844	−	0.491559i	$-0.163573\pi$
$439$	36.4924			1.74169			0.870844	+	0.491559i	$0.163573\pi$
$440$		0			0
$441$	−2.75379			−0.131133
$442$	7.12311	−	1.12311i	0.338812	−	0.0534207i
$443$			3.50758i			0.166650i	0.996522	+	0.0833250i	$0.0265540\pi$
$443$			3.50758i			0.166650i	−0.996522	+	0.0833250i	$0.973446\pi$
$444$		−	5.12311i		−	0.243132i
$445$		0			0
$446$	9.36932			0.443650
$447$	14.0000			0.662177
$448$	−3.12311			−0.147553
$449$			28.8769i			1.36278i	0.731918	+	0.681392i	$0.238625\pi$
$449$			28.8769i			1.36278i	−0.731918	+	0.681392i	$0.761375\pi$
$450$		0			0
$451$	−4.49242			−0.211540
$452$		−	12.2462i		−	0.576013i
$453$	13.3693			0.628145
$454$	−8.00000			−0.375459
$455$		0			0
$456$	6.00000			0.280976
$457$	−31.3693			−1.46739			−0.733697	−	0.679476i	$-0.762207\pi$
$457$	−31.3693			−1.46739			−0.733697	+	0.679476i	$0.762207\pi$
$458$			5.12311i			0.239387i
$459$	−2.00000			−0.0933520
$460$		0			0
$461$			18.4924i			0.861278i	0.902524	+	0.430639i	$0.141712\pi$
$461$			18.4924i			0.861278i	−0.902524	+	0.430639i	$0.858288\pi$
$462$	−16.0000			−0.744387
$463$	−21.8617			−1.01600			−0.508001	−	0.861357i	$-0.669615\pi$
$463$	−21.8617			−1.01600			−0.508001	+	0.861357i	$0.669615\pi$
$464$	−2.00000			−0.0928477
$465$		0			0
$466$			7.75379i			0.359187i
$467$		−	22.2462i		−	1.02943i	−0.857361	−	0.514716i	$-0.827897\pi$
$467$		−	22.2462i		−	1.02943i	0.857361	−	0.514716i	$-0.172103\pi$
$468$	0.561553	+	3.56155i	0.0259578	+	0.164633i
$469$	15.2311			0.703305
$470$		0			0
$471$	21.3693			0.984646
$472$			1.12311i			0.0516951i
$473$	32.0000			1.47136
$474$			8.00000i			0.367452i
$475$		0			0
$476$		−	6.24621i		−	0.286295i
$477$		−	13.3693i		−	0.612139i
$478$		−	4.49242i		−	0.205479i
$479$			12.4924i			0.570793i	0.958409	+	0.285397i	$0.0921253\pi$
$479$			12.4924i			0.570793i	−0.958409	+	0.285397i	$0.907875\pi$
$480$		0			0
$481$	−2.87689	−	18.2462i	−0.131175	−	0.831956i
$482$		−	14.2462i		−	0.648897i
$483$	−16.0000			−0.728025
$484$	−15.2462			−0.693010
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−17.3693			−0.787079			−0.393539	−	0.919308i	$-0.628750\pi$
$487$	−17.3693			−0.787079			−0.393539	+	0.919308i	$0.628750\pi$
$488$	10.0000			0.452679
$489$			7.12311i			0.322118i
$490$		0			0
$491$	38.7386			1.74825			0.874125	−	0.485701i	$-0.161436\pi$
$491$	38.7386			1.74825			0.874125	+	0.485701i	$0.161436\pi$
$492$	0.876894			0.0395335
$493$		−	4.00000i		−	0.180151i
$494$	21.3693	−	3.36932i	0.961451	−	0.151593i
$495$		0			0
$496$			3.12311i			0.140232i
$497$		−	32.0000i		−	1.43540i
$498$			6.24621i			0.279899i
$499$		−	34.4924i		−	1.54409i	−0.635566	−	0.772046i	$-0.719233\pi$
$499$		−	34.4924i		−	1.54409i	0.635566	−	0.772046i	$-0.280767\pi$
$500$		0			0
$501$		−	22.2462i		−	0.993887i
$502$	26.2462			1.17143
$503$		−	35.3693i		−	1.57704i	−0.615009	−	0.788520i	$-0.710848\pi$
$503$		−	35.3693i		−	1.57704i	0.615009	−	0.788520i	$-0.289152\pi$
$504$	3.12311			0.139114
$505$		0			0
$506$	−26.2462			−1.16679
$507$	4.00000	+	12.3693i	0.177646	+	0.549341i
$508$		−	13.1231i		−	0.582244i
$509$		−	32.2462i		−	1.42929i	−0.699488	−	0.714644i	$-0.746589\pi$
$509$		−	32.2462i		−	1.42929i	0.699488	−	0.714644i	$-0.253411\pi$
$510$		0			0
$511$	40.9848			1.81306
$512$	1.00000			0.0441942
$513$	−6.00000			−0.264906
$514$		−	12.2462i		−	0.540157i
$515$		0			0
$516$	−6.24621			−0.274974
$517$			32.0000i			1.40736i
$518$	−16.0000			−0.703000
$519$	−23.1231			−1.01499
$520$		0			0
$521$	0.246211			0.0107867			0.00539336	−	0.999985i	$-0.498283\pi$
$521$	0.246211			0.0107867			0.00539336	+	0.999985i	$0.498283\pi$
$522$	2.00000			0.0875376
$523$			26.7386i			1.16920i	0.811322	+	0.584599i	$0.198748\pi$
$523$			26.7386i			1.16920i	−0.811322	+	0.584599i	$0.801252\pi$
$524$	4.00000			0.174741
$525$		0			0
$526$			27.3693i			1.19336i
$527$	−6.24621			−0.272089
$528$	5.12311			0.222955
$529$	−3.24621			−0.141140
$530$		0			0
$531$		−	1.12311i		−	0.0487386i
$532$		−	18.7386i		−	0.812423i
$533$	3.12311	−	0.492423i	0.135277	−	0.0213292i
$534$	−3.12311			−0.135150
$535$		0			0
$536$	−4.87689			−0.210650
$537$			16.4924i			0.711701i
$538$	16.2462			0.700424
$539$			14.1080i			0.607672i
$540$		0			0
$541$			10.8769i			0.467634i	0.972281	+	0.233817i	$0.0751217\pi$
$541$			10.8769i			0.467634i	−0.972281	+	0.233817i	$0.924878\pi$
$542$			23.1231i			0.993222i
$543$			20.2462i			0.868848i
$544$			2.00000i			0.0857493i
$545$		0			0
$546$	11.1231	−	1.75379i	0.476025	−	0.0750552i
$547$			20.9848i			0.897247i	0.893721	+	0.448624i	$0.148086\pi$
$547$			20.9848i			0.897247i	−0.893721	+	0.448624i	$0.851914\pi$
$548$	10.4924			0.448214
$549$	−10.0000			−0.426790
$550$		0			0
$551$		−	12.0000i		−	0.511217i
$552$	5.12311			0.218054
$553$	24.9848			1.06246
$554$		−	29.8617i		−	1.26870i
$555$		0			0
$556$	16.4924			0.699435
$557$	−11.7538			−0.498024			−0.249012	−	0.968500i	$-0.580106\pi$
$557$	−11.7538			−0.498024			−0.249012	+	0.968500i	$0.580106\pi$
$558$		−	3.12311i		−	0.132212i
$559$	−22.2462	+	3.50758i	−0.940914	+	0.148355i
$560$		0			0
$561$			10.2462i			0.432595i
$562$		−	3.12311i		−	0.131740i
$563$			32.9848i			1.39015i	0.718939	+	0.695073i	$0.244628\pi$
$563$			32.9848i			1.39015i	−0.718939	+	0.695073i	$0.755372\pi$
$564$		−	6.24621i		−	0.263013i
$565$		0			0
$566$			4.00000i			0.168133i
$567$	−3.12311			−0.131158
$568$			10.2462i			0.429921i
$569$	12.7386			0.534031			0.267016	−	0.963692i	$-0.413962\pi$
$569$	12.7386			0.534031			0.267016	+	0.963692i	$0.413962\pi$
$570$		0			0
$571$	−8.49242			−0.355397			−0.177698	−	0.984085i	$-0.556865\pi$
$571$	−8.49242			−0.355397			−0.177698	+	0.984085i	$0.556865\pi$
$572$	18.2462	−	2.87689i	0.762912	−	0.120289i
$573$		−	16.4924i		−	0.688981i
$574$		−	2.73863i		−	0.114308i
$575$		0			0
$576$	−1.00000			−0.0416667
$577$	−27.3693			−1.13940			−0.569700	−	0.821853i	$-0.692941\pi$
$577$	−27.3693			−1.13940			−0.569700	+	0.821853i	$0.692941\pi$
$578$	13.0000			0.540729
$579$			25.1231i			1.04408i
$580$		0			0
$581$	19.5076			0.809311
$582$		−	13.1231i		−	0.543970i
$583$	−68.4924			−2.83667
$584$	−13.1231			−0.543038
$585$		0			0
$586$	28.7386			1.18718
$587$	16.4924			0.680715			0.340358	−	0.940296i	$-0.389452\pi$
$587$	16.4924			0.680715			0.340358	+	0.940296i	$0.389452\pi$
$588$		−	2.75379i		−	0.113564i
$589$	−18.7386			−0.772112
$590$		0			0
$591$			16.2462i			0.668280i
$592$	5.12311			0.210558
$593$	−5.50758			−0.226169			−0.113085	−	0.993585i	$-0.536073\pi$
$593$	−5.50758			−0.226169			−0.113085	+	0.993585i	$0.536073\pi$
$594$	−5.12311			−0.210204
$595$		0			0
$596$			14.0000i			0.573462i
$597$			18.2462i			0.746768i
$598$	18.2462	−	2.87689i	0.746143	−	0.117645i
$599$	36.4924			1.49104			0.745520	−	0.666483i	$-0.232201\pi$
$599$	36.4924			1.49104			0.745520	+	0.666483i	$0.232201\pi$
$600$		0			0
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$			19.5076i			0.795070i
$603$	4.87689			0.198602
$604$			13.3693i			0.543990i
$605$		0			0
$606$			12.2462i			0.497468i
$607$			15.3693i			0.623821i	0.950111	+	0.311911i	$0.100969\pi$
$607$			15.3693i			0.623821i	−0.950111	+	0.311911i	$0.899031\pi$
$608$			6.00000i			0.243332i
$609$		−	6.24621i		−	0.253109i
$610$		0			0
$611$	−3.50758	−	22.2462i	−0.141901	−	0.899985i
$612$		−	2.00000i		−	0.0808452i
$613$	39.3693			1.59011			0.795056	−	0.606536i	$-0.207441\pi$
$613$	39.3693			1.59011			0.795056	+	0.606536i	$0.207441\pi$
$614$	−31.1231			−1.25603
$615$		0			0
$616$		−	16.0000i		−	0.644658i
$617$	40.7386			1.64008			0.820038	−	0.572309i	$-0.193952\pi$
$617$	40.7386			1.64008			0.820038	+	0.572309i	$0.193952\pi$
$618$	13.1231			0.527889
$619$		−	38.9848i		−	1.56693i	−0.621434	−	0.783467i	$-0.713450\pi$
$619$		−	38.9848i		−	1.56693i	0.621434	−	0.783467i	$-0.286550\pi$
$620$		0			0
$621$	−5.12311			−0.205583
$622$	8.49242			0.340515
$623$			9.75379i			0.390777i
$624$	−3.56155	+	0.561553i	−0.142576	+	0.0224801i
$625$		0			0
$626$		−	16.2462i		−	0.649329i
$627$			30.7386i			1.22758i
$628$			21.3693i			0.852729i
$629$			10.2462i			0.408543i
$630$		0			0
$631$		−	35.6155i		−	1.41783i	−0.705293	−	0.708916i	$-0.749185\pi$
$631$		−	35.6155i		−	1.41783i	0.705293	−	0.708916i	$-0.250815\pi$
$632$	−8.00000			−0.318223
$633$		−	4.00000i		−	0.158986i
$634$	−6.00000			−0.238290
$635$		0			0
$636$	13.3693			0.530128
$637$	−1.54640	−	9.80776i	−0.0612705	−	0.388598i
$638$		−	10.2462i		−	0.405651i
$639$		−	10.2462i		−	0.405334i
$640$		0			0
$641$	−2.00000			−0.0789953			−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000			−0.0789953			−0.0394976	+	0.999220i	$0.512576\pi$
$642$	−8.00000			−0.315735
$643$	17.3693			0.684979			0.342489	−	0.939522i	$-0.388730\pi$
$643$	17.3693			0.684979			0.342489	+	0.939522i	$0.388730\pi$
$644$		−	16.0000i		−	0.630488i
$645$		0			0
$646$	−12.0000			−0.472134
$647$			29.6155i			1.16431i	0.813079	+	0.582153i	$0.197790\pi$
$647$			29.6155i			1.16431i	−0.813079	+	0.582153i	$0.802210\pi$
$648$	1.00000			0.0392837
$649$	−5.75379			−0.225856
$650$		0			0
$651$	−9.75379			−0.382281
$652$	−7.12311			−0.278962
$653$			13.8617i			0.542452i	0.962516	+	0.271226i	$0.0874290\pi$
$653$			13.8617i			0.542452i	−0.962516	+	0.271226i	$0.912571\pi$
$654$	−2.87689			−0.112495
$655$		0			0
$656$			0.876894i			0.0342370i
$657$	13.1231			0.511981
$658$	−19.5076			−0.760485
$659$	21.7538			0.847407			0.423704	−	0.905801i	$-0.360730\pi$
$659$	21.7538			0.847407			0.423704	+	0.905801i	$0.360730\pi$
$660$		0			0
$661$			9.12311i			0.354848i	0.984135	+	0.177424i	$0.0567763\pi$
$661$			9.12311i			0.354848i	−0.984135	+	0.177424i	$0.943224\pi$
$662$		−	7.75379i		−	0.301360i
$663$	−1.12311	−	7.12311i	−0.0436178	−	0.276638i
$664$	−6.24621			−0.242400
$665$		0			0
$666$	−5.12311			−0.198516
$667$		−	10.2462i		−	0.396735i
$668$	22.2462			0.860732
$669$		−	9.36932i		−	0.362239i
$670$		0			0
$671$			51.2311i			1.97775i
$672$			3.12311i			0.120476i
$673$		−	26.9848i		−	1.04019i	−0.854109	−	0.520095i	$-0.825897\pi$
$673$		−	26.9848i		−	1.04019i	0.854109	−	0.520095i	$-0.174103\pi$
$674$			6.00000i			0.231111i
$675$		0			0
$676$	−12.3693	+	4.00000i	−0.475743	+	0.153846i
$677$			12.8769i			0.494899i	0.968901	+	0.247450i	$0.0795925\pi$
$677$			12.8769i			0.494899i	−0.968901	+	0.247450i	$0.920408\pi$
$678$	−12.2462			−0.470313
$679$	−40.9848			−1.57285
$680$		0			0
$681$			8.00000i			0.306561i
$682$	−16.0000			−0.612672
$683$	−16.9848			−0.649907			−0.324954	−	0.945730i	$-0.605349\pi$
$683$	−16.9848			−0.649907			−0.324954	+	0.945730i	$0.605349\pi$
$684$		−	6.00000i		−	0.229416i
$685$		0			0
$686$	13.2614			0.506321
$687$	5.12311			0.195459
$688$		−	6.24621i		−	0.238135i
$689$	47.6155	−	7.50758i	1.81401	−	0.286016i
$690$		0			0
$691$			28.7386i			1.09327i	0.837371	+	0.546635i	$0.184091\pi$
$691$			28.7386i			1.09327i	−0.837371	+	0.546635i	$0.815909\pi$
$692$		−	23.1231i		−	0.879009i
$693$			16.0000i			0.607790i
$694$		−	14.2462i		−	0.540779i
$695$		0			0
$696$			2.00000i			0.0758098i
$697$	−1.75379			−0.0664295
$698$		−	19.3693i		−	0.733139i
$699$	7.75379			0.293275
$700$		0			0
$701$	−14.0000			−0.528773			−0.264386	−	0.964417i	$-0.585169\pi$
$701$	−14.0000			−0.528773			−0.264386	+	0.964417i	$0.585169\pi$
$702$	3.56155	−	0.561553i	0.134422	−	0.0211944i
$703$			30.7386i			1.15933i
$704$			5.12311i			0.193084i
$705$		0			0
$706$	−12.2462			−0.460892
$707$	38.2462			1.43840
$708$	1.12311			0.0422089
$709$			1.61553i			0.0606724i	0.999540	+	0.0303362i	$0.00965780\pi$
$709$			1.61553i			0.0606724i	−0.999540	+	0.0303362i	$0.990342\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$		−	3.12311i		−	0.117043i
$713$	−16.0000			−0.599205
$714$	−6.24621			−0.233759
$715$		0			0
$716$	−16.4924			−0.616351
$717$	−4.49242			−0.167773
$718$		−	17.7538i		−	0.662566i
$719$	20.0000			0.745874			0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000			0.745874			0.372937	+	0.927857i	$0.378351\pi$
$720$		0			0
$721$		−	40.9848i		−	1.52636i
$722$	−17.0000			−0.632674
$723$	−14.2462			−0.529822
$724$	−20.2462			−0.752445
$725$		0			0
$726$			15.2462i			0.565840i
$727$			19.8617i			0.736631i	0.929701	+	0.368316i	$0.120065\pi$
$727$			19.8617i			0.736631i	−0.929701	+	0.368316i	$0.879935\pi$
$728$	1.75379	+	11.1231i	0.0649997	+	0.412250i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	12.4924			0.462049
$732$		−	10.0000i		−	0.369611i
$733$	35.3693			1.30640			0.653198	−	0.757187i	$-0.273427\pi$
$733$	35.3693			1.30640			0.653198	+	0.757187i	$0.273427\pi$
$734$			8.63068i			0.318564i
$735$		0			0
$736$			5.12311i			0.188840i
$737$		−	24.9848i		−	0.920329i
$738$		−	0.876894i		−	0.0322789i
$739$			37.2311i			1.36957i	0.728747	+	0.684783i	$0.240103\pi$
$739$			37.2311i			1.36957i	−0.728747	+	0.684783i	$0.759897\pi$
$740$		0			0
$741$	−3.36932	−	21.3693i	−0.123775	−	0.785021i
$742$		−	41.7538i		−	1.53283i
$743$	−16.0000			−0.586983			−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000			−0.586983			−0.293492	+	0.955962i	$0.594817\pi$
$744$	3.12311			0.114499
$745$		0			0
$746$		−	7.12311i		−	0.260795i
$747$	6.24621			0.228537
$748$	−10.2462			−0.374639
$749$			24.9848i			0.912926i
$750$		0			0
$751$	−26.2462			−0.957738			−0.478869	−	0.877886i	$-0.658953\pi$
$751$	−26.2462			−0.957738			−0.478869	+	0.877886i	$0.658953\pi$
$752$	6.24621			0.227776
$753$		−	26.2462i		−	0.956465i
$754$	1.12311	+	7.12311i	0.0409011	+	0.259408i
$755$		0			0
$756$		−	3.12311i		−	0.113586i
$757$		−	3.12311i		−	0.113511i	−0.998388	−	0.0567556i	$-0.981924\pi$
$757$		−	3.12311i		−	0.113511i	0.998388	−	0.0567556i	$-0.0180756\pi$
$758$			6.00000i			0.217930i
$759$			26.2462i			0.952677i
$760$		0			0
$761$		−	3.12311i		−	0.113212i	−0.998397	−	0.0566062i	$-0.981972\pi$
$761$		−	3.12311i		−	0.113212i	0.998397	−	0.0566062i	$-0.0180280\pi$
$762$	−13.1231			−0.475400
$763$			8.98485i			0.325273i
$764$	16.4924			0.596675
$765$		0			0
$766$	1.75379			0.0633670
$767$	4.00000	−	0.630683i	0.144432	−	0.0227726i
$768$		−	1.00000i		−	0.0360844i
$769$			32.9848i			1.18946i	0.803924	+	0.594732i	$0.202742\pi$
$769$			32.9848i			1.18946i	−0.803924	+	0.594732i	$0.797258\pi$
$770$		0			0
$771$	−12.2462			−0.441037
$772$	−25.1231			−0.904200
$773$	−16.2462			−0.584336			−0.292168	−	0.956367i	$-0.594377\pi$
$773$	−16.2462			−0.584336			−0.292168	+	0.956367i	$0.594377\pi$
$774$			6.24621i			0.224515i
$775$		0			0
$776$	13.1231			0.471092
$777$			16.0000i			0.573997i
$778$	0.246211			0.00882710
$779$	−5.26137			−0.188508
$780$		0			0
$781$	−52.4924			−1.87833
$782$	−10.2462			−0.366404
$783$		−	2.00000i		−	0.0714742i
$784$	2.75379			0.0983496
$785$		0			0
$786$		−	4.00000i		−	0.142675i
$787$	12.3845			0.441459			0.220729	−	0.975335i	$-0.429156\pi$
$787$	12.3845			0.441459			0.220729	+	0.975335i	$0.429156\pi$
$788$	−16.2462			−0.578747
$789$	27.3693			0.974373
$790$		0			0
$791$			38.2462i			1.35988i
$792$		−	5.12311i		−	0.182042i
$793$	−5.61553	−	35.6155i	−0.199413	−	1.26474i
$794$	15.3693			0.545437
$795$		0			0
$796$	−18.2462			−0.646720
$797$			25.8617i			0.916070i	0.888934	+	0.458035i	$0.151447\pi$
$797$			25.8617i			0.916070i	−0.888934	+	0.458035i	$0.848553\pi$
$798$	−18.7386			−0.663340
$799$			12.4924i			0.441950i
$800$		0			0
$801$			3.12311i			0.110350i
$802$		−	1.36932i		−	0.0483523i
$803$		−	67.2311i		−	2.37253i
$804$			4.87689i			0.171995i
$805$		0			0
$806$	11.1231	−	1.75379i	0.391795	−	0.0617746i
$807$		−	16.2462i		−	0.571894i
$808$	−12.2462			−0.430820
$809$	13.5076			0.474901			0.237451	−	0.971400i	$-0.423688\pi$
$809$	13.5076			0.474901			0.237451	+	0.971400i	$0.423688\pi$
$810$		0			0
$811$		−	27.7538i		−	0.974567i	−0.873244	−	0.487284i	$-0.837988\pi$
$811$		−	27.7538i		−	0.974567i	0.873244	−	0.487284i	$-0.162012\pi$
$812$	6.24621			0.219199
$813$	23.1231			0.810963
$814$			26.2462i			0.919929i
$815$		0			0
$816$	2.00000			0.0700140
$817$	37.4773			1.31116
$818$		−	8.49242i		−	0.296931i
$819$	−1.75379	−	11.1231i	−0.0612823	−	0.388673i
$820$		0			0
$821$			44.2462i			1.54420i	0.635499	+	0.772102i	$0.280794\pi$
$821$			44.2462i			1.54420i	−0.635499	+	0.772102i	$0.719206\pi$
$822$		−	10.4924i		−	0.365965i
$823$			42.8769i			1.49459i	0.664490	+	0.747297i	$0.268649\pi$
$823$			42.8769i			1.49459i	−0.664490	+	0.747297i	$0.731351\pi$
$824$			13.1231i			0.457165i
$825$		0			0
$826$		−	3.50758i		−	0.122044i
$827$	−1.26137			−0.0438620			−0.0219310	−	0.999759i	$-0.506981\pi$
$827$	−1.26137			−0.0438620			−0.0219310	+	0.999759i	$0.506981\pi$
$828$		−	5.12311i		−	0.178040i
$829$	24.2462			0.842106			0.421053	−	0.907036i	$-0.361661\pi$
$829$	24.2462			0.842106			0.421053	+	0.907036i	$0.361661\pi$
$830$		0			0
$831$	−29.8617			−1.03589
$832$	−0.561553	−	3.56155i	−0.0194683	−	0.123475i
$833$			5.50758i			0.190826i
$834$		−	16.4924i		−	0.571086i
$835$		0			0
$836$	−30.7386			−1.06312
$837$	−3.12311			−0.107950
$838$	28.0000			0.967244
$839$			46.7386i			1.61360i	0.590827	+	0.806798i	$0.298802\pi$
$839$			46.7386i			1.61360i	−0.590827	+	0.806798i	$0.701198\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		−	0.630683i		−	0.0217348i
$843$	−3.12311			−0.107565
$844$	4.00000			0.137686
$845$		0			0
$846$	−6.24621			−0.214749
$847$	47.6155			1.63609
$848$			13.3693i			0.459104i
$849$	4.00000			0.137280
$850$		0			0
$851$			26.2462i			0.899709i
$852$	10.2462			0.351029
$853$	35.8617			1.22788			0.613941	−	0.789352i	$-0.289583\pi$
$853$	35.8617			1.22788			0.613941	+	0.789352i	$0.289583\pi$
$854$	−31.2311			−1.06870
$855$		0			0
$856$		−	8.00000i		−	0.273434i
$857$		−	30.4924i		−	1.04160i	−0.853678	−	0.520801i	$-0.825633\pi$
$857$		−	30.4924i		−	1.04160i	0.853678	−	0.520801i	$-0.174367\pi$
$858$	−2.87689	−	18.2462i	−0.0982156	−	0.622915i
$859$	12.0000			0.409435			0.204717	−	0.978821i	$-0.434372\pi$
$859$	12.0000			0.409435			0.204717	+	0.978821i	$0.434372\pi$
$860$		0			0
$861$	−2.73863			−0.0933324
$862$		−	32.4924i		−	1.10670i
$863$	−6.24621			−0.212624			−0.106312	−	0.994333i	$-0.533904\pi$
$863$	−6.24621			−0.212624			−0.106312	+	0.994333i	$0.533904\pi$
$864$			1.00000i			0.0340207i
$865$		0			0
$866$			18.0000i			0.611665i
$867$		−	13.0000i		−	0.441503i
$868$		−	9.75379i		−	0.331065i
$869$		−	40.9848i		−	1.39032i
$870$		0			0
$871$	2.73863	+	17.3693i	0.0927951	+	0.588537i
$872$		−	2.87689i		−	0.0974239i
$873$	−13.1231			−0.444150
$874$	−30.7386			−1.03975
$875$		0			0
$876$			13.1231i			0.443389i
$877$	18.8769			0.637427			0.318714	−	0.947851i	$-0.396749\pi$
$877$	18.8769			0.637427			0.318714	+	0.947851i	$0.396749\pi$
$878$	36.4924			1.23156
$879$		−	28.7386i		−	0.969330i
$880$		0			0
$881$	28.2462			0.951639			0.475820	−	0.879543i	$-0.342152\pi$
$881$	28.2462			0.951639			0.475820	+	0.879543i	$0.342152\pi$
$882$	−2.75379			−0.0927249
$883$			9.75379i			0.328241i	0.986440	+	0.164121i	$0.0524786\pi$
$883$			9.75379i			0.328241i	−0.986440	+	0.164121i	$0.947521\pi$
$884$	7.12311	−	1.12311i	0.239576	−	0.0377741i
$885$		0			0
$886$			3.50758i			0.117839i
$887$		−	18.8769i		−	0.633824i	−0.948455	−	0.316912i	$-0.897354\pi$
$887$		−	18.8769i		−	0.633824i	0.948455	−	0.316912i	$-0.102646\pi$
$888$		−	5.12311i		−	0.171920i
$889$			40.9848i			1.37459i
$890$		0			0
$891$			5.12311i			0.171630i
$892$	9.36932			0.313708
$893$			37.4773i			1.25413i
$894$	14.0000			0.468230
$895$		0			0
$896$	−3.12311			−0.104336
$897$	−2.87689	−	18.2462i	−0.0960567	−	0.609223i
$898$			28.8769i			0.963634i
$899$		−	6.24621i		−	0.208323i
$900$		0			0
$901$	−26.7386			−0.890793
$902$	−4.49242			−0.149581
$903$	19.5076			0.649172
$904$		−	12.2462i		−	0.407303i
$905$		0			0
$906$	13.3693			0.444166
$907$			25.7538i			0.855141i	0.903982	+	0.427570i	$0.140630\pi$
$907$			25.7538i			0.855141i	−0.903982	+	0.427570i	$0.859370\pi$
$908$	−8.00000			−0.265489
$909$	12.2462			0.406181
$910$		0			0
$911$	4.00000			0.132526			0.0662630	−	0.997802i	$-0.478892\pi$
$911$	4.00000			0.132526			0.0662630	+	0.997802i	$0.478892\pi$
$912$	6.00000			0.198680
$913$		−	32.0000i		−	1.05905i
$914$	−31.3693			−1.03760
$915$		0			0
$916$			5.12311i			0.169272i
$917$	−12.4924			−0.412536
$918$	−2.00000			−0.0660098
$919$	21.7538			0.717591			0.358796	−	0.933416i	$-0.383187\pi$
$919$	21.7538			0.717591			0.358796	+	0.933416i	$0.383187\pi$
$920$		0			0
$921$			31.1231i			1.02554i
$922$			18.4924i			0.609016i
$923$	36.4924	−	5.75379i	1.20116	−	0.189388i
$924$	−16.0000			−0.526361
$925$		0			0
$926$	−21.8617			−0.718421
$927$		−	13.1231i		−	0.431019i
$928$	−2.00000			−0.0656532
$929$		−	28.1080i		−	0.922192i	−0.887350	−	0.461096i	$-0.847456\pi$
$929$		−	28.1080i		−	0.922192i	0.887350	−	0.461096i	$-0.152544\pi$
$930$		0			0
$931$			16.5227i			0.541511i
$932$			7.75379i			0.253984i
$933$		−	8.49242i		−	0.278029i
$934$		−	22.2462i		−	0.727918i
$935$		0			0
$936$	0.561553	+	3.56155i	0.0183549	+	0.116413i
$937$		−	20.2462i		−	0.661415i	−0.943733	−	0.330707i	$-0.892713\pi$
$937$		−	20.2462i		−	0.661415i	0.943733	−	0.330707i	$-0.107287\pi$
$938$	15.2311			0.497312
$939$	−16.2462			−0.530175
$940$		0			0
$941$		−	14.0000i		−	0.456387i	−0.973616	−	0.228193i	$-0.926718\pi$
$941$		−	14.0000i		−	0.456387i	0.973616	−	0.228193i	$-0.0732819\pi$
$942$	21.3693			0.696250
$943$	−4.49242			−0.146293
$944$			1.12311i			0.0365540i
$945$		0			0
$946$	32.0000			1.04041
$947$	−8.49242			−0.275967			−0.137983	−	0.990435i	$-0.544062\pi$
$947$	−8.49242			−0.275967			−0.137983	+	0.990435i	$0.544062\pi$
$948$			8.00000i			0.259828i
$949$	7.36932	+	46.7386i	0.239218	+	1.51720i
$950$		0			0
$951$			6.00000i			0.194563i
$952$		−	6.24621i		−	0.202441i
$953$		−	22.9848i		−	0.744552i	−0.928122	−	0.372276i	$-0.878577\pi$
$953$		−	22.9848i		−	0.744552i	0.928122	−	0.372276i	$-0.121423\pi$
$954$		−	13.3693i		−	0.432848i
$955$		0			0
$956$		−	4.49242i		−	0.145295i
$957$	−10.2462			−0.331213
$958$			12.4924i			0.403612i
$959$	−32.7689			−1.05816
$960$		0			0
$961$	21.2462			0.685362
$962$	−2.87689	−	18.2462i	−0.0927548	−	0.588281i
$963$			8.00000i			0.257796i
$964$		−	14.2462i		−	0.458840i
$965$		0			0
$966$	−16.0000			−0.514792
$967$	47.6155			1.53121			0.765606	−	0.643310i	$-0.222439\pi$
$967$	47.6155			1.53121			0.765606	+	0.643310i	$0.222439\pi$
$968$	−15.2462			−0.490032
$969$			12.0000i			0.385496i
$970$		0			0
$971$	37.7538			1.21158			0.605788	−	0.795626i	$-0.292858\pi$
$971$	37.7538			1.21158			0.605788	+	0.795626i	$0.292858\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−51.5076			−1.65126
$974$	−17.3693			−0.556549
$975$		0			0
$976$	10.0000			0.320092
$977$	4.73863			0.151602			0.0758012	−	0.997123i	$-0.475849\pi$
$977$	4.73863			0.151602			0.0758012	+	0.997123i	$0.475849\pi$
$978$			7.12311i			0.227772i
$979$	16.0000			0.511362
$980$		0			0
$981$			2.87689i			0.0918522i
$982$	38.7386			1.23620
$983$	−60.4924			−1.92941			−0.964704	−	0.263335i	$-0.915177\pi$
$983$	−60.4924			−1.92941			−0.964704	+	0.263335i	$0.915177\pi$
$984$	0.876894			0.0279544
$985$		0			0
$986$		−	4.00000i		−	0.127386i
$987$			19.5076i			0.620933i
$988$	21.3693	−	3.36932i	0.679849	−	0.107192i
$989$	32.0000			1.01754
$990$		0			0
$991$	−30.7386			−0.976445			−0.488222	−	0.872719i	$-0.662355\pi$
$991$	−30.7386			−0.976445			−0.488222	+	0.872719i	$0.662355\pi$
$992$			3.12311i			0.0991587i
$993$	−7.75379			−0.246059
$994$		−	32.0000i		−	1.01498i
$995$		0			0
$996$			6.24621i			0.197919i
$997$			38.3542i			1.21469i	0.794439	+	0.607344i	$0.207765\pi$
$997$			38.3542i			1.21469i	−0.794439	+	0.607344i	$0.792235\pi$
$998$		−	34.4924i		−	1.09184i
$999$			5.12311i			0.162088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.f.o.649.1		4
5.2	odd	4		1950.2.b.h.1351.3		4
5.3	odd	4		390.2.b.d.181.2	✓	4
5.4	even	2		1950.2.f.l.649.4		4
13.12	even	2		1950.2.f.l.649.2		4
15.8	even	4		1170.2.b.f.181.4		4
20.3	even	4		3120.2.g.o.961.3		4
65.8	even	4		5070.2.a.bh.1.2		2
65.12	odd	4		1950.2.b.h.1351.2		4
65.18	even	4		5070.2.a.bd.1.1		2
65.38	odd	4		390.2.b.d.181.3	yes	4
65.64	even	2	inner	1950.2.f.o.649.3		4
195.38	even	4		1170.2.b.f.181.1		4
260.103	even	4		3120.2.g.o.961.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.b.d.181.2	✓	4	5.3	odd	4
390.2.b.d.181.3	yes	4	65.38	odd	4
1170.2.b.f.181.1		4	195.38	even	4
1170.2.b.f.181.4		4	15.8	even	4
1950.2.b.h.1351.2		4	65.12	odd	4
1950.2.b.h.1351.3		4	5.2	odd	4
1950.2.f.l.649.2		4	13.12	even	2
1950.2.f.l.649.4		4	5.4	even	2
1950.2.f.o.649.1		4	1.1	even	1	trivial
1950.2.f.o.649.3		4	65.64	even	2	inner
3120.2.g.o.961.2		4	260.103	even	4
3120.2.g.o.961.3		4	20.3	even	4
5070.2.a.bd.1.1		2	65.18	even	4
5070.2.a.bh.1.2		2	65.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} -3.12311 q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} -3.12311 q^{7} +1.00000 q^{8} -1.00000 q^{9} +5.12311i q^{11} -1.00000i q^{12} +(-0.561553 - 3.56155i) q^{13} -3.12311 q^{14} +1.00000 q^{16} +2.00000i q^{17} -1.00000 q^{18} +6.00000i q^{19} +3.12311i q^{21} +5.12311i q^{22} +5.12311i q^{23} -1.00000i q^{24} +(-0.561553 - 3.56155i) q^{26} +1.00000i q^{27} -3.12311 q^{28} -2.00000 q^{29} +3.12311i q^{31} +1.00000 q^{32} +5.12311 q^{33} +2.00000i q^{34} -1.00000 q^{36} +5.12311 q^{37} +6.00000i q^{38} +(-3.56155 + 0.561553i) q^{39} +0.876894i q^{41} +3.12311i q^{42} -6.24621i q^{43} +5.12311i q^{44} +5.12311i q^{46} +6.24621 q^{47} -1.00000i q^{48} +2.75379 q^{49} +2.00000 q^{51} +(-0.561553 - 3.56155i) q^{52} +13.3693i q^{53} +1.00000i q^{54} -3.12311 q^{56} +6.00000 q^{57} -2.00000 q^{58} +1.12311i q^{59} +10.0000 q^{61} +3.12311i q^{62} +3.12311 q^{63} +1.00000 q^{64} +5.12311 q^{66} -4.87689 q^{67} +2.00000i q^{68} +5.12311 q^{69} +10.2462i q^{71} -1.00000 q^{72} -13.1231 q^{73} +5.12311 q^{74} +6.00000i q^{76} -16.0000i q^{77} +(-3.56155 + 0.561553i) q^{78} -8.00000 q^{79} +1.00000 q^{81} +0.876894i q^{82} -6.24621 q^{83} +3.12311i q^{84} -6.24621i q^{86} +2.00000i q^{87} +5.12311i q^{88} -3.12311i q^{89} +(1.75379 + 11.1231i) q^{91} +5.12311i q^{92} +3.12311 q^{93} +6.24621 q^{94} -1.00000i q^{96} +13.1231 q^{97} +2.75379 q^{98} -5.12311i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8 - 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{4} + 4 q^{7} + 4 q^{8} - 4 q^{9} + 6 q^{13} + 4 q^{14} + 4 q^{16} - 4 q^{18} + 6 q^{26} + 4 q^{28} - 8 q^{29} + 4 q^{32} + 4 q^{33} - 4 q^{36} + 4 q^{37} - 6 q^{39} - 8 q^{47} + 44 q^{49} + 8 q^{51} + 6 q^{52} + 4 q^{56} + 24 q^{57} - 8 q^{58} + 40 q^{61} - 4 q^{63} + 4 q^{64} + 4 q^{66} - 36 q^{67} + 4 q^{69} - 4 q^{72} - 36 q^{73} + 4 q^{74} - 6 q^{78} - 32 q^{79} + 4 q^{81} + 8 q^{83} + 40 q^{91} - 4 q^{93} - 8 q^{94} + 36 q^{97} + 44 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 4 * q^7 + 4 * q^8 - 4 * q^9 + 6 * q^13 + 4 * q^14 + 4 * q^16 - 4 * q^18 + 6 * q^26 + 4 * q^28 - 8 * q^29 + 4 * q^32 + 4 * q^33 - 4 * q^36 + 4 * q^37 - 6 * q^39 - 8 * q^47 + 44 * q^49 + 8 * q^51 + 6 * q^52 + 4 * q^56 + 24 * q^57 - 8 * q^58 + 40 * q^61 - 4 * q^63 + 4 * q^64 + 4 * q^66 - 36 * q^67 + 4 * q^69 - 4 * q^72 - 36 * q^73 + 4 * q^74 - 6 * q^78 - 32 * q^79 + 4 * q^81 + 8 * q^83 + 40 * q^91 - 4 * q^93 - 8 * q^94 + 36 * q^97 + 44 * q^98

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