LMFDB - Embedded newform 1950.2.f.p.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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			649.1
Root			$1.56155i$ of defining polynomial
Character	$\chi$	$=$	1950.649
Dual form			1950.2.f.p.649.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} +0.438447 q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} +0.438447 q^{7} +1.00000 q^{8} -1.00000 q^{9} +1.56155i q^{11} -1.00000i q^{12} +(0.561553 + 3.56155i) q^{13} +0.438447 q^{14} +1.00000 q^{16} +6.68466i q^{17} -1.00000 q^{18} +7.68466i q^{19} -0.438447i q^{21} +1.56155i q^{22} -3.12311i q^{23} -1.00000i q^{24} +(0.561553 + 3.56155i) q^{26} +1.00000i q^{27} +0.438447 q^{28} +1.00000 q^{29} +5.56155i q^{31} +1.00000 q^{32} +1.56155 q^{33} +6.68466i q^{34} -1.00000 q^{36} +4.56155 q^{37} +7.68466i q^{38} +(3.56155 - 0.561553i) q^{39} -4.56155i q^{41} -0.438447i q^{42} -11.1231i q^{43} +1.56155i q^{44} -3.12311i q^{46} +8.12311 q^{47} -1.00000i q^{48} -6.80776 q^{49} +6.68466 q^{51} +(0.561553 + 3.56155i) q^{52} -5.00000i q^{53} +1.00000i q^{54} +0.438447 q^{56} +7.68466 q^{57} +1.00000 q^{58} +9.56155i q^{59} -0.684658 q^{61} +5.56155i q^{62} -0.438447 q^{63} +1.00000 q^{64} +1.56155 q^{66} -4.12311 q^{67} +6.68466i q^{68} -3.12311 q^{69} -13.9309i q^{71} -1.00000 q^{72} +7.12311 q^{73} +4.56155 q^{74} +7.68466i q^{76} +0.684658i q^{77} +(3.56155 - 0.561553i) q^{78} +2.31534 q^{79} +1.00000 q^{81} -4.56155i q^{82} +14.9309 q^{83} -0.438447i q^{84} -11.1231i q^{86} -1.00000i q^{87} +1.56155i q^{88} +5.12311i q^{89} +(0.246211 + 1.56155i) q^{91} -3.12311i q^{92} +5.56155 q^{93} +8.12311 q^{94} -1.00000i q^{96} -13.1231 q^{97} -6.80776 q^{98} -1.56155i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 10 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 10 * q^7 + 4 * q^8 - 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{4} + 10 q^{7} + 4 q^{8} - 4 q^{9} - 6 q^{13} + 10 q^{14} + 4 q^{16} - 4 q^{18} - 6 q^{26} + 10 q^{28} + 4 q^{29} + 4 q^{32} - 2 q^{33} - 4 q^{36} + 10 q^{37} + 6 q^{39} + 16 q^{47} + 14 q^{49} + 2 q^{51} - 6 q^{52} + 10 q^{56} + 6 q^{57} + 4 q^{58} + 22 q^{61} - 10 q^{63} + 4 q^{64} - 2 q^{66} + 4 q^{69} - 4 q^{72} + 12 q^{73} + 10 q^{74} + 6 q^{78} + 34 q^{79} + 4 q^{81} + 2 q^{83} - 32 q^{91} + 14 q^{93} + 16 q^{94} - 36 q^{97} + 14 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 10 * q^7 + 4 * q^8 - 4 * q^9 - 6 * q^13 + 10 * q^14 + 4 * q^16 - 4 * q^18 - 6 * q^26 + 10 * q^28 + 4 * q^29 + 4 * q^32 - 2 * q^33 - 4 * q^36 + 10 * q^37 + 6 * q^39 + 16 * q^47 + 14 * q^49 + 2 * q^51 - 6 * q^52 + 10 * q^56 + 6 * q^57 + 4 * q^58 + 22 * q^61 - 10 * q^63 + 4 * q^64 - 2 * q^66 + 4 * q^69 - 4 * q^72 + 12 * q^73 + 10 * q^74 + 6 * q^78 + 34 * q^79 + 4 * q^81 + 2 * q^83 - 32 * q^91 + 14 * q^93 + 16 * q^94 - 36 * q^97 + 14 * 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
$7$	0.438447			0.165717			0.0828587	−	0.996561i	$-0.473595\pi$
$7$	0.438447			0.165717			0.0828587	+	0.996561i	$0.473595\pi$
$8$	1.00000			0.353553
$9$	−1.00000			−0.333333
$10$		0			0
$11$			1.56155i			0.470826i	0.971895	+	0.235413i	$0.0756443\pi$
$11$			1.56155i			0.470826i	−0.971895	+	0.235413i	$0.924356\pi$
$12$		−	1.00000i		−	0.288675i
$13$	0.561553	+	3.56155i	0.155747	+	0.987797i
$13$	0.561553	+	3.56155i	0.155747	+	0.987797i
$14$	0.438447			0.117180
$15$		0			0
$16$	1.00000			0.250000
$17$			6.68466i			1.62127i	0.585553	+	0.810634i	$0.300877\pi$
$17$			6.68466i			1.62127i	−0.585553	+	0.810634i	$0.699123\pi$
$18$	−1.00000			−0.235702
$19$			7.68466i			1.76298i	0.472201	+	0.881491i	$0.343460\pi$
$19$			7.68466i			1.76298i	−0.472201	+	0.881491i	$0.656540\pi$
$20$		0			0
$21$		−	0.438447i		−	0.0956770i
$22$			1.56155i			0.332924i
$23$		−	3.12311i		−	0.651213i	−0.945505	−	0.325606i	$-0.894432\pi$
$23$		−	3.12311i		−	0.651213i	0.945505	−	0.325606i	$-0.105568\pi$
$24$		−	1.00000i		−	0.204124i
$25$		0			0
$26$	0.561553	+	3.56155i	0.110130	+	0.698478i
$27$			1.00000i			0.192450i
$28$	0.438447			0.0828587
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$			5.56155i			0.998884i	0.866347	+	0.499442i	$0.166462\pi$
$31$			5.56155i			0.998884i	−0.866347	+	0.499442i	$0.833538\pi$
$32$	1.00000			0.176777
$33$	1.56155			0.271831
$34$			6.68466i			1.14641i
$35$		0			0
$36$	−1.00000			−0.166667
$37$	4.56155			0.749915			0.374957	−	0.927042i	$-0.377657\pi$
$37$	4.56155			0.749915			0.374957	+	0.927042i	$0.377657\pi$
$38$			7.68466i			1.24662i
$39$	3.56155	−	0.561553i	0.570305	−	0.0899204i
$40$		0			0
$41$		−	4.56155i		−	0.712395i	−0.934411	−	0.356197i	$-0.884073\pi$
$41$		−	4.56155i		−	0.712395i	0.934411	−	0.356197i	$-0.115927\pi$
$42$		−	0.438447i		−	0.0676539i
$43$		−	11.1231i		−	1.69626i	−0.529790	−	0.848129i	$-0.677729\pi$
$43$		−	11.1231i		−	1.69626i	0.529790	−	0.848129i	$-0.322271\pi$
$44$			1.56155i			0.235413i
$45$		0			0
$46$		−	3.12311i		−	0.460477i
$47$	8.12311			1.18488			0.592438	−	0.805616i	$-0.298165\pi$
$47$	8.12311			1.18488			0.592438	+	0.805616i	$0.298165\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−6.80776			−0.972538
$50$		0			0
$51$	6.68466			0.936039
$52$	0.561553	+	3.56155i	0.0778734	+	0.493899i
$53$		−	5.00000i		−	0.686803i	−0.939189	−	0.343401i	$-0.888421\pi$
$53$		−	5.00000i		−	0.686803i	0.939189	−	0.343401i	$-0.111579\pi$
$54$			1.00000i			0.136083i
$55$		0			0
$56$	0.438447			0.0585900
$57$	7.68466			1.01786
$58$	1.00000			0.131306
$59$			9.56155i			1.24481i	0.782696	+	0.622404i	$0.213844\pi$
$59$			9.56155i			1.24481i	−0.782696	+	0.622404i	$0.786156\pi$
$60$		0			0
$61$	−0.684658			−0.0876615			−0.0438308	−	0.999039i	$-0.513956\pi$
$61$	−0.684658			−0.0876615			−0.0438308	+	0.999039i	$0.513956\pi$
$62$			5.56155i			0.706318i
$63$	−0.438447			−0.0552392
$64$	1.00000			0.125000
$65$		0			0
$66$	1.56155			0.192214
$67$	−4.12311			−0.503718			−0.251859	−	0.967764i	$-0.581042\pi$
$67$	−4.12311			−0.503718			−0.251859	+	0.967764i	$0.581042\pi$
$68$			6.68466i			0.810634i
$69$	−3.12311			−0.375978
$70$		0			0
$71$		−	13.9309i		−	1.65329i	−0.562724	−	0.826645i	$-0.690247\pi$
$71$		−	13.9309i		−	1.65329i	0.562724	−	0.826645i	$-0.309753\pi$
$72$	−1.00000			−0.117851
$73$	7.12311			0.833696			0.416848	−	0.908976i	$-0.363135\pi$
$73$	7.12311			0.833696			0.416848	+	0.908976i	$0.363135\pi$
$74$	4.56155			0.530270
$75$		0			0
$76$			7.68466i			0.881491i
$77$			0.684658i			0.0780241i
$78$	3.56155	−	0.561553i	0.403266	−	0.0635833i
$79$	2.31534			0.260496			0.130248	−	0.991481i	$-0.458423\pi$
$79$	2.31534			0.260496			0.130248	+	0.991481i	$0.458423\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		−	4.56155i		−	0.503739i
$83$	14.9309			1.63888			0.819438	−	0.573168i	$-0.194286\pi$
$83$	14.9309			1.63888			0.819438	+	0.573168i	$0.194286\pi$
$84$		−	0.438447i		−	0.0478385i
$85$		0			0
$86$		−	11.1231i		−	1.19944i
$87$		−	1.00000i		−	0.107211i
$88$			1.56155i			0.166462i
$89$			5.12311i			0.543048i	0.962432	+	0.271524i	$0.0875277\pi$
$89$			5.12311i			0.543048i	−0.962432	+	0.271524i	$0.912472\pi$
$90$		0			0
$91$	0.246211	+	1.56155i	0.0258100	+	0.163695i
$92$		−	3.12311i		−	0.325606i
$93$	5.56155			0.576706
$94$	8.12311			0.837834
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	−13.1231			−1.33245			−0.666225	−	0.745751i	$-0.732091\pi$
$97$	−13.1231			−1.33245			−0.666225	+	0.745751i	$0.732091\pi$
$98$	−6.80776			−0.687688
$99$		−	1.56155i		−	0.156942i
$100$		0			0
$101$	−12.4384			−1.23767			−0.618836	−	0.785520i	$-0.712395\pi$
$101$	−12.4384			−1.23767			−0.618836	+	0.785520i	$0.712395\pi$
$102$	6.68466			0.661880
$103$		−	7.12311i		−	0.701860i	−0.936402	−	0.350930i	$-0.885865\pi$
$103$		−	7.12311i		−	0.701860i	0.936402	−	0.350930i	$-0.114135\pi$
$104$	0.561553	+	3.56155i	0.0550648	+	0.349239i
$105$		0			0
$106$		−	5.00000i		−	0.485643i
$107$		−	0.315342i		−	0.0304852i	−0.999884	−	0.0152426i	$-0.995148\pi$
$107$		−	0.315342i		−	0.0304852i	0.999884	−	0.0152426i	$-0.00485206\pi$
$108$			1.00000i			0.0962250i
$109$			20.5616i			1.96944i	0.174146	+	0.984720i	$0.444283\pi$
$109$			20.5616i			1.96944i	−0.174146	+	0.984720i	$0.555717\pi$
$110$		0			0
$111$		−	4.56155i		−	0.432963i
$112$	0.438447			0.0414294
$113$			4.24621i			0.399450i	0.979852	+	0.199725i	$0.0640049\pi$
$113$			4.24621i			0.399450i	−0.979852	+	0.199725i	$0.935995\pi$
$114$	7.68466			0.719734
$115$		0			0
$116$	1.00000			0.0928477
$117$	−0.561553	−	3.56155i	−0.0519156	−	0.329266i
$118$			9.56155i			0.880212i
$119$			2.93087i			0.268672i
$120$		0			0
$121$	8.56155			0.778323
$122$	−0.684658			−0.0619861
$123$	−4.56155			−0.411301
$124$			5.56155i			0.499442i
$125$		0			0
$126$	−0.438447			−0.0390600
$127$			11.4384i			1.01500i	0.861652	+	0.507499i	$0.169430\pi$
$127$			11.4384i			1.01500i	−0.861652	+	0.507499i	$0.830570\pi$
$128$	1.00000			0.0883883
$129$	−11.1231			−0.979335
$130$		0			0
$131$	−6.31534			−0.551774			−0.275887	−	0.961190i	$-0.588972\pi$
$131$	−6.31534			−0.551774			−0.275887	+	0.961190i	$0.588972\pi$
$132$	1.56155			0.135916
$133$			3.36932i			0.292157i
$134$	−4.12311			−0.356182
$135$		0			0
$136$			6.68466i			0.573205i
$137$	6.56155			0.560591			0.280296	−	0.959914i	$-0.409567\pi$
$137$	6.56155			0.560591			0.280296	+	0.959914i	$0.409567\pi$
$138$	−3.12311			−0.265856
$139$	−16.4924			−1.39887			−0.699435	−	0.714697i	$-0.746565\pi$
$139$	−16.4924			−1.39887			−0.699435	+	0.714697i	$0.746565\pi$
$140$		0			0
$141$		−	8.12311i		−	0.684089i
$142$		−	13.9309i		−	1.16905i
$143$	−5.56155	+	0.876894i	−0.465080	+	0.0733296i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	7.12311			0.589512
$147$			6.80776i			0.561495i
$148$	4.56155			0.374957
$149$		−	19.3693i		−	1.58680i	−0.608703	−	0.793398i	$-0.708310\pi$
$149$		−	19.3693i		−	1.58680i	0.608703	−	0.793398i	$-0.291690\pi$
$150$		0			0
$151$		−	3.31534i		−	0.269799i	−0.990859	−	0.134899i	$-0.956929\pi$
$151$		−	3.31534i		−	0.269799i	0.990859	−	0.134899i	$-0.0430711\pi$
$152$			7.68466i			0.623308i
$153$		−	6.68466i		−	0.540423i
$154$			0.684658i			0.0551713i
$155$		0			0
$156$	3.56155	−	0.561553i	0.285152	−	0.0449602i
$157$		−	10.6847i		−	0.852729i	−0.904552	−	0.426364i	$-0.859794\pi$
$157$		−	10.6847i		−	0.852729i	0.904552	−	0.426364i	$-0.140206\pi$
$158$	2.31534			0.184199
$159$	−5.00000			−0.396526
$160$		0			0
$161$		−	1.36932i		−	0.107917i
$162$	1.00000			0.0785674
$163$	16.4924			1.29179			0.645893	−	0.763428i	$-0.276485\pi$
$163$	16.4924			1.29179			0.645893	+	0.763428i	$0.276485\pi$
$164$		−	4.56155i		−	0.356197i
$165$		0			0
$166$	14.9309			1.15886
$167$	13.4384			1.03990			0.519949	−	0.854197i	$-0.325951\pi$
$167$	13.4384			1.03990			0.519949	+	0.854197i	$0.325951\pi$
$168$		−	0.438447i		−	0.0338269i
$169$	−12.3693	+	4.00000i	−0.951486	+	0.307692i
$170$		0			0
$171$		−	7.68466i		−	0.587661i
$172$		−	11.1231i		−	0.848129i
$173$			0.123106i			0.00935955i	0.999989	+	0.00467977i	$0.00148962\pi$
$173$			0.123106i			0.00935955i	−0.999989	+	0.00467977i	$0.998510\pi$
$174$		−	1.00000i		−	0.0758098i
$175$		0			0
$176$			1.56155i			0.117706i
$177$	9.56155			0.718690
$178$			5.12311i			0.383993i
$179$	19.1231			1.42933			0.714664	−	0.699468i	$-0.246580\pi$
$179$	19.1231			1.42933			0.714664	+	0.699468i	$0.246580\pi$
$180$		0			0
$181$	0.192236			0.0142888			0.00714439	−	0.999974i	$-0.497726\pi$
$181$	0.192236			0.0142888			0.00714439	+	0.999974i	$0.497726\pi$
$182$	0.246211	+	1.56155i	0.0182504	+	0.115750i
$183$			0.684658i			0.0506114i
$184$		−	3.12311i		−	0.230238i
$185$		0			0
$186$	5.56155			0.407793
$187$	−10.4384			−0.763335
$188$	8.12311			0.592438
$189$			0.438447i			0.0318923i
$190$		0			0
$191$	−16.4924			−1.19335			−0.596675	−	0.802483i	$-0.703512\pi$
$191$	−16.4924			−1.19335			−0.596675	+	0.802483i	$0.703512\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	−4.87689			−0.351047			−0.175523	−	0.984475i	$-0.556162\pi$
$193$	−4.87689			−0.351047			−0.175523	+	0.984475i	$0.556162\pi$
$194$	−13.1231			−0.942184
$195$		0			0
$196$	−6.80776			−0.486269
$197$	12.2462			0.872506			0.436253	−	0.899824i	$-0.356305\pi$
$197$	12.2462			0.872506			0.436253	+	0.899824i	$0.356305\pi$
$198$		−	1.56155i		−	0.110975i
$199$	5.93087			0.420428			0.210214	−	0.977655i	$-0.432584\pi$
$199$	5.93087			0.420428			0.210214	+	0.977655i	$0.432584\pi$
$200$		0			0
$201$			4.12311i			0.290821i
$202$	−12.4384			−0.875166
$203$	0.438447			0.0307730
$204$	6.68466			0.468020
$205$		0			0
$206$		−	7.12311i		−	0.496290i
$207$			3.12311i			0.217071i
$208$	0.561553	+	3.56155i	0.0389367	+	0.246949i
$209$	−12.0000			−0.830057
$210$		0			0
$211$	−17.3693			−1.19575			−0.597877	−	0.801588i	$-0.703989\pi$
$211$	−17.3693			−1.19575			−0.597877	+	0.801588i	$0.703989\pi$
$212$		−	5.00000i		−	0.343401i
$213$	−13.9309			−0.954527
$214$		−	0.315342i		−	0.0215563i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$			2.43845i			0.165533i
$218$			20.5616i			1.39260i
$219$		−	7.12311i		−	0.481335i
$220$		0			0
$221$	−23.8078	+	3.75379i	−1.60148	+	0.252507i
$222$		−	4.56155i		−	0.306151i
$223$	15.3693			1.02921			0.514603	−	0.857429i	$-0.327939\pi$
$223$	15.3693			1.02921			0.514603	+	0.857429i	$0.327939\pi$
$224$	0.438447			0.0292950
$225$		0			0
$226$			4.24621i			0.282454i
$227$	−3.31534			−0.220047			−0.110023	−	0.993929i	$-0.535093\pi$
$227$	−3.31534			−0.220047			−0.110023	+	0.993929i	$0.535093\pi$
$228$	7.68466			0.508929
$229$			7.19224i			0.475276i	0.971354	+	0.237638i	$0.0763732\pi$
$229$			7.19224i			0.475276i	−0.971354	+	0.237638i	$0.923627\pi$
$230$		0			0
$231$	0.684658			0.0450472
$232$	1.00000			0.0656532
$233$		−	3.12311i		−	0.204601i	−0.994754	−	0.102301i	$-0.967380\pi$
$233$		−	3.12311i		−	0.204601i	0.994754	−	0.102301i	$-0.0326204\pi$
$234$	−0.561553	−	3.56155i	−0.0367099	−	0.232826i
$235$		0			0
$236$			9.56155i			0.622404i
$237$		−	2.31534i		−	0.150398i
$238$			2.93087i			0.189980i
$239$		−	6.93087i		−	0.448321i	−0.974552	−	0.224160i	$-0.928036\pi$
$239$		−	6.93087i		−	0.448321i	0.974552	−	0.224160i	$-0.0719639\pi$
$240$		0			0
$241$			20.2462i			1.30417i	0.758145	+	0.652087i	$0.226106\pi$
$241$			20.2462i			1.30417i	−0.758145	+	0.652087i	$0.773894\pi$
$242$	8.56155			0.550357
$243$		−	1.00000i		−	0.0641500i
$244$	−0.684658			−0.0438308
$245$		0			0
$246$	−4.56155			−0.290834
$247$	−27.3693	+	4.31534i	−1.74147	+	0.274579i
$248$			5.56155i			0.353159i
$249$		−	14.9309i		−	0.946205i
$250$		0			0
$251$	11.4384			0.721988			0.360994	−	0.932568i	$-0.382437\pi$
$251$	11.4384			0.721988			0.360994	+	0.932568i	$0.382437\pi$
$252$	−0.438447			−0.0276196
$253$	4.87689			0.306608
$254$			11.4384i			0.717712i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	15.8078i		−	0.986061i	−0.870012	−	0.493031i	$-0.835889\pi$
$257$		−	15.8078i		−	0.986061i	0.870012	−	0.493031i	$-0.164111\pi$
$258$	−11.1231			−0.692494
$259$	2.00000			0.124274
$260$		0			0
$261$	−1.00000			−0.0618984
$262$	−6.31534			−0.390163
$263$		−	24.7386i		−	1.52545i	−0.646723	−	0.762725i	$-0.723861\pi$
$263$		−	24.7386i		−	1.52545i	0.646723	−	0.762725i	$-0.276139\pi$
$264$	1.56155			0.0961069
$265$		0			0
$266$			3.36932i			0.206586i
$267$	5.12311			0.313529
$268$	−4.12311			−0.251859
$269$	9.49242			0.578763			0.289382	−	0.957214i	$-0.406550\pi$
$269$	9.49242			0.578763			0.289382	+	0.957214i	$0.406550\pi$
$270$		0			0
$271$			4.19224i			0.254660i	0.991860	+	0.127330i	$0.0406408\pi$
$271$			4.19224i			0.254660i	−0.991860	+	0.127330i	$0.959359\pi$
$272$			6.68466i			0.405317i
$273$	1.56155	−	0.246211i	0.0945095	−	0.0149014i
$274$	6.56155			0.396398
$275$		0			0
$276$	−3.12311			−0.187989
$277$		−	15.6155i		−	0.938246i	−0.883133	−	0.469123i	$-0.844570\pi$
$277$		−	15.6155i		−	0.938246i	0.883133	−	0.469123i	$-0.155430\pi$
$278$	−16.4924			−0.989150
$279$		−	5.56155i		−	0.332961i
$280$		0			0
$281$		−	5.93087i		−	0.353806i	−0.984228	−	0.176903i	$-0.943392\pi$
$281$		−	5.93087i		−	0.353806i	0.984228	−	0.176903i	$-0.0566079\pi$
$282$		−	8.12311i		−	0.483724i
$283$			7.36932i			0.438060i	0.975718	+	0.219030i	$0.0702893\pi$
$283$			7.36932i			0.438060i	−0.975718	+	0.219030i	$0.929711\pi$
$284$		−	13.9309i		−	0.826645i
$285$		0			0
$286$	−5.56155	+	0.876894i	−0.328862	+	0.0518519i
$287$		−	2.00000i		−	0.118056i
$288$	−1.00000			−0.0589256
$289$	−27.6847			−1.62851
$290$		0			0
$291$			13.1231i			0.769290i
$292$	7.12311			0.416848
$293$	0.630683			0.0368449			0.0184225	−	0.999830i	$-0.494136\pi$
$293$	0.630683			0.0368449			0.0184225	+	0.999830i	$0.494136\pi$
$294$			6.80776i			0.397037i
$295$		0			0
$296$	4.56155			0.265135
$297$	−1.56155			−0.0906105
$298$		−	19.3693i		−	1.12203i
$299$	11.1231	−	1.75379i	0.643266	−	0.101424i
$300$		0			0
$301$		−	4.87689i		−	0.281100i
$302$		−	3.31534i		−	0.190776i
$303$			12.4384i			0.714570i
$304$			7.68466i			0.440745i
$305$		0			0
$306$		−	6.68466i		−	0.382136i
$307$	2.06913			0.118092			0.0590458	−	0.998255i	$-0.481194\pi$
$307$	2.06913			0.118092			0.0590458	+	0.998255i	$0.481194\pi$
$308$			0.684658i			0.0390120i
$309$	−7.12311			−0.405219
$310$		0			0
$311$	14.8769			0.843591			0.421796	−	0.906691i	$-0.361400\pi$
$311$	14.8769			0.843591			0.421796	+	0.906691i	$0.361400\pi$
$312$	3.56155	−	0.561553i	0.201633	−	0.0317917i
$313$		−	24.8617i		−	1.40527i	−0.711551	−	0.702634i	$-0.752007\pi$
$313$		−	24.8617i		−	1.40527i	0.711551	−	0.702634i	$-0.247993\pi$
$314$		−	10.6847i		−	0.602970i
$315$		0			0
$316$	2.31534			0.130248
$317$	−30.0000			−1.68497			−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000			−1.68497			−0.842484	+	0.538721i	$0.818908\pi$
$318$	−5.00000			−0.280386
$319$			1.56155i			0.0874302i
$320$		0			0
$321$	−0.315342			−0.0176006
$322$		−	1.36932i		−	0.0763090i
$323$	−51.3693			−2.85827
$324$	1.00000			0.0555556
$325$		0			0
$326$	16.4924			0.913431
$327$	20.5616			1.13706
$328$		−	4.56155i		−	0.251870i
$329$	3.56155			0.196355
$330$		0			0
$331$			24.4924i			1.34623i	0.739540	+	0.673113i	$0.235043\pi$
$331$			24.4924i			1.34623i	−0.739540	+	0.673113i	$0.764957\pi$
$332$	14.9309			0.819438
$333$	−4.56155			−0.249972
$334$	13.4384			0.735319
$335$		0			0
$336$		−	0.438447i		−	0.0239193i
$337$		−	10.6847i		−	0.582030i	−0.956718	−	0.291015i	$-0.906007\pi$
$337$		−	10.6847i		−	0.582030i	0.956718	−	0.291015i	$-0.0939930\pi$
$338$	−12.3693	+	4.00000i	−0.672802	+	0.217571i
$339$	4.24621			0.230623
$340$		0			0
$341$	−8.68466			−0.470301
$342$		−	7.68466i		−	0.415539i
$343$	−6.05398			−0.326884
$344$		−	11.1231i		−	0.599718i
$345$		0			0
$346$			0.123106i			0.00661820i
$347$			18.5616i			0.996436i	0.867052	+	0.498218i	$0.166012\pi$
$347$			18.5616i			0.996436i	−0.867052	+	0.498218i	$0.833988\pi$
$348$		−	1.00000i		−	0.0536056i
$349$		−	22.0000i		−	1.17763i	−0.808267	−	0.588817i	$-0.799594\pi$
$349$		−	22.0000i		−	1.17763i	0.808267	−	0.588817i	$-0.200406\pi$
$350$		0			0
$351$	−3.56155	+	0.561553i	−0.190102	+	0.0299735i
$352$			1.56155i			0.0832310i
$353$	−15.4384			−0.821706			−0.410853	−	0.911702i	$-0.634769\pi$
$353$	−15.4384			−0.821706			−0.410853	+	0.911702i	$0.634769\pi$
$354$	9.56155			0.508191
$355$		0			0
$356$			5.12311i			0.271524i
$357$	2.93087			0.155118
$358$	19.1231			1.01069
$359$		−	3.87689i		−	0.204615i	−0.994753	−	0.102307i	$-0.967377\pi$
$359$		−	3.87689i		−	0.204615i	0.994753	−	0.102307i	$-0.0326225\pi$
$360$		0			0
$361$	−40.0540			−2.10810
$362$	0.192236			0.0101037
$363$		−	8.56155i		−	0.449365i
$364$	0.246211	+	1.56155i	0.0129050	+	0.0818476i
$365$		0			0
$366$			0.684658i			0.0357877i
$367$			19.6847i			1.02753i	0.857931	+	0.513765i	$0.171750\pi$
$367$			19.6847i			1.02753i	−0.857931	+	0.513765i	$0.828250\pi$
$368$		−	3.12311i		−	0.162803i
$369$			4.56155i			0.237465i
$370$		0			0
$371$		−	2.19224i		−	0.113815i
$372$	5.56155			0.288353
$373$			32.4384i			1.67960i	0.542897	+	0.839800i	$0.317328\pi$
$373$			32.4384i			1.67960i	−0.542897	+	0.839800i	$0.682672\pi$
$374$	−10.4384			−0.539759
$375$		0			0
$376$	8.12311			0.418917
$377$	0.561553	+	3.56155i	0.0289214	+	0.183429i
$378$			0.438447i			0.0225513i
$379$		−	7.31534i		−	0.375764i	−0.982192	−	0.187882i	$-0.939838\pi$
$379$		−	7.31534i		−	0.375764i	0.982192	−	0.187882i	$-0.0601622\pi$
$380$		0			0
$381$	11.4384			0.586009
$382$	−16.4924			−0.843826
$383$	13.9309			0.711834			0.355917	−	0.934518i	$-0.384169\pi$
$383$	13.9309			0.711834			0.355917	+	0.934518i	$0.384169\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		0			0
$386$	−4.87689			−0.248227
$387$			11.1231i			0.565419i
$388$	−13.1231			−0.666225
$389$	6.80776			0.345167			0.172584	−	0.984995i	$-0.444788\pi$
$389$	6.80776			0.345167			0.172584	+	0.984995i	$0.444788\pi$
$390$		0			0
$391$	20.8769			1.05579
$392$	−6.80776			−0.343844
$393$			6.31534i			0.318567i
$394$	12.2462			0.616955
$395$		0			0
$396$		−	1.56155i		−	0.0784710i
$397$	−35.0540			−1.75931			−0.879654	−	0.475614i	$-0.842226\pi$
$397$	−35.0540			−1.75931			−0.879654	+	0.475614i	$0.842226\pi$
$398$	5.93087			0.297288
$399$	3.36932			0.168677
$400$		0			0
$401$		−	22.0000i		−	1.09863i	−0.835616	−	0.549314i	$-0.814889\pi$
$401$		−	22.0000i		−	1.09863i	0.835616	−	0.549314i	$-0.185111\pi$
$402$			4.12311i			0.205642i
$403$	−19.8078	+	3.12311i	−0.986695	+	0.155573i
$404$	−12.4384			−0.618836
$405$		0			0
$406$	0.438447			0.0217598
$407$			7.12311i			0.353079i
$408$	6.68466			0.330940
$409$		−	27.6155i		−	1.36550i	−0.730652	−	0.682750i	$-0.760784\pi$
$409$		−	27.6155i		−	1.36550i	0.730652	−	0.682750i	$-0.239216\pi$
$410$		0			0
$411$		−	6.56155i		−	0.323658i
$412$		−	7.12311i		−	0.350930i
$413$			4.19224i			0.206286i
$414$			3.12311i			0.153492i
$415$		0			0
$416$	0.561553	+	3.56155i	0.0275324	+	0.174619i
$417$			16.4924i			0.807637i
$418$	−12.0000			−0.586939
$419$	5.68466			0.277714			0.138857	−	0.990312i	$-0.455657\pi$
$419$	5.68466			0.277714			0.138857	+	0.990312i	$0.455657\pi$
$420$		0			0
$421$			4.63068i			0.225686i	0.993613	+	0.112843i	$0.0359957\pi$
$421$			4.63068i			0.225686i	−0.993613	+	0.112843i	$0.964004\pi$
$422$	−17.3693			−0.845525
$423$	−8.12311			−0.394959
$424$		−	5.00000i		−	0.242821i
$425$		0			0
$426$	−13.9309			−0.674953
$427$	−0.300187			−0.0145270
$428$		−	0.315342i		−	0.0152426i
$429$	0.876894	+	5.56155i	0.0423369	+	0.268514i
$430$		0			0
$431$			8.17708i			0.393876i	0.980416	+	0.196938i	$0.0630998\pi$
$431$			8.17708i			0.393876i	−0.980416	+	0.196938i	$0.936900\pi$
$432$			1.00000i			0.0481125i
$433$			5.05398i			0.242879i	0.992599	+	0.121439i	$0.0387510\pi$
$433$			5.05398i			0.242879i	−0.992599	+	0.121439i	$0.961249\pi$
$434$			2.43845i			0.117049i
$435$		0			0
$436$			20.5616i			0.984720i
$437$	24.0000			1.14808
$438$		−	7.12311i		−	0.340355i
$439$	27.3002			1.30297			0.651483	−	0.758663i	$-0.274147\pi$
$439$	27.3002			1.30297			0.651483	+	0.758663i	$0.274147\pi$
$440$		0			0
$441$	6.80776			0.324179
$442$	−23.8078	+	3.75379i	−1.13242	+	0.178550i
$443$		−	28.5616i		−	1.35700i	−0.734600	−	0.678500i	$-0.762630\pi$
$443$		−	28.5616i		−	1.35700i	0.734600	−	0.678500i	$-0.237370\pi$
$444$		−	4.56155i		−	0.216482i
$445$		0			0
$446$	15.3693			0.727758
$447$	−19.3693			−0.916137
$448$	0.438447			0.0207147
$449$			5.43845i			0.256656i	0.991732	+	0.128328i	$0.0409611\pi$
$449$			5.43845i			0.256656i	−0.991732	+	0.128328i	$0.959039\pi$
$450$		0			0
$451$	7.12311			0.335414
$452$			4.24621i			0.199725i
$453$	−3.31534			−0.155768
$454$	−3.31534			−0.155597
$455$		0			0
$456$	7.68466			0.359867
$457$	−28.7386			−1.34434			−0.672168	−	0.740398i	$-0.734637\pi$
$457$	−28.7386			−1.34434			−0.672168	+	0.740398i	$0.734637\pi$
$458$			7.19224i			0.336071i
$459$	−6.68466			−0.312013
$460$		0			0
$461$			22.2462i			1.03611i	0.855348	+	0.518055i	$0.173344\pi$
$461$			22.2462i			1.03611i	−0.855348	+	0.518055i	$0.826656\pi$
$462$	0.684658			0.0318532
$463$	−11.5616			−0.537311			−0.268655	−	0.963236i	$-0.586579\pi$
$463$	−11.5616			−0.537311			−0.268655	+	0.963236i	$0.586579\pi$
$464$	1.00000			0.0464238
$465$		0			0
$466$		−	3.12311i		−	0.144675i
$467$		−	40.8078i		−	1.88836i	−0.329433	−	0.944179i	$-0.606857\pi$
$467$		−	40.8078i		−	1.88836i	0.329433	−	0.944179i	$-0.393143\pi$
$468$	−0.561553	−	3.56155i	−0.0259578	−	0.164633i
$469$	−1.80776			−0.0834748
$470$		0			0
$471$	−10.6847			−0.492323
$472$			9.56155i			0.440106i
$473$	17.3693			0.798642
$474$		−	2.31534i		−	0.106347i
$475$		0			0
$476$			2.93087i			0.134336i
$477$			5.00000i			0.228934i
$478$		−	6.93087i		−	0.317011i
$479$		−	32.1231i		−	1.46774i	−0.679289	−	0.733871i	$-0.737712\pi$
$479$		−	32.1231i		−	1.46774i	0.679289	−	0.733871i	$-0.262288\pi$
$480$		0			0
$481$	2.56155	+	16.2462i	0.116797	+	0.740763i
$482$			20.2462i			0.922190i
$483$	−1.36932			−0.0623061
$484$	8.56155			0.389161
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−6.68466			−0.302911			−0.151455	−	0.988464i	$-0.548396\pi$
$487$	−6.68466			−0.302911			−0.151455	+	0.988464i	$0.548396\pi$
$488$	−0.684658			−0.0309930
$489$		−	16.4924i		−	0.745813i
$490$		0			0
$491$	38.7386			1.74825			0.874125	−	0.485701i	$-0.161436\pi$
$491$	38.7386			1.74825			0.874125	+	0.485701i	$0.161436\pi$
$492$	−4.56155			−0.205651
$493$			6.68466i			0.301062i
$494$	−27.3693	+	4.31534i	−1.23140	+	0.194156i
$495$		0			0
$496$			5.56155i			0.249721i
$497$		−	6.10795i		−	0.273979i
$498$		−	14.9309i		−	0.669068i
$499$			28.1231i			1.25896i	0.777015	+	0.629482i	$0.216733\pi$
$499$			28.1231i			1.25896i	−0.777015	+	0.629482i	$0.783267\pi$
$500$		0			0
$501$		−	13.4384i		−	0.600386i
$502$	11.4384			0.510523
$503$		−	8.73863i		−	0.389636i	−0.980839	−	0.194818i	$-0.937588\pi$
$503$		−	8.73863i		−	0.389636i	0.980839	−	0.194818i	$-0.0624117\pi$
$504$	−0.438447			−0.0195300
$505$		0			0
$506$	4.87689			0.216804
$507$	4.00000	+	12.3693i	0.177646	+	0.549341i
$508$			11.4384i			0.507499i
$509$		−	22.4924i		−	0.996959i	−0.866901	−	0.498480i	$-0.833892\pi$
$509$		−	22.4924i		−	0.996959i	0.866901	−	0.498480i	$-0.166108\pi$
$510$		0			0
$511$	3.12311			0.138158
$512$	1.00000			0.0441942
$513$	−7.68466			−0.339286
$514$		−	15.8078i		−	0.697251i
$515$		0			0
$516$	−11.1231			−0.489667
$517$			12.6847i			0.557871i
$518$	2.00000			0.0878750
$519$	0.123106			0.00540374
$520$		0			0
$521$	−16.2462			−0.711759			−0.355880	−	0.934532i	$-0.615819\pi$
$521$	−16.2462			−0.711759			−0.355880	+	0.934532i	$0.615819\pi$
$522$	−1.00000			−0.0437688
$523$		−	0.630683i		−	0.0275778i	−0.999905	−	0.0137889i	$-0.995611\pi$
$523$		−	0.630683i		−	0.0275778i	0.999905	−	0.0137889i	$-0.00438929\pi$
$524$	−6.31534			−0.275887
$525$		0			0
$526$		−	24.7386i		−	1.07866i
$527$	−37.1771			−1.61946
$528$	1.56155			0.0679579
$529$	13.2462			0.575922
$530$		0			0
$531$		−	9.56155i		−	0.414936i
$532$			3.36932i			0.146078i
$533$	16.2462	−	2.56155i	0.703702	−	0.110953i
$534$	5.12311			0.221698
$535$		0			0
$536$	−4.12311			−0.178091
$537$		−	19.1231i		−	0.825223i
$538$	9.49242			0.409247
$539$		−	10.6307i		−	0.457896i
$540$		0			0
$541$		−	32.2462i		−	1.38637i	−0.720758	−	0.693186i	$-0.756206\pi$
$541$		−	32.2462i		−	1.38637i	0.720758	−	0.693186i	$-0.243794\pi$
$542$			4.19224i			0.180072i
$543$		−	0.192236i		−	0.00824963i
$544$			6.68466i			0.286602i
$545$		0			0
$546$	1.56155	−	0.246211i	0.0668283	−	0.0105369i
$547$			7.12311i			0.304562i	0.988337	+	0.152281i	$0.0486619\pi$
$547$			7.12311i			0.304562i	−0.988337	+	0.152281i	$0.951338\pi$
$548$	6.56155			0.280296
$549$	0.684658			0.0292205
$550$		0			0
$551$			7.68466i			0.327377i
$552$	−3.12311			−0.132928
$553$	1.01515			0.0431688
$554$		−	15.6155i		−	0.663440i
$555$		0			0
$556$	−16.4924			−0.699435
$557$	41.8617			1.77374			0.886869	−	0.462020i	$-0.152875\pi$
$557$	41.8617			1.77374			0.886869	+	0.462020i	$0.152875\pi$
$558$		−	5.56155i		−	0.235439i
$559$	39.6155	−	6.24621i	1.67556	−	0.264187i
$560$		0			0
$561$			10.4384i			0.440712i
$562$		−	5.93087i		−	0.250179i
$563$		−	43.3002i		−	1.82489i	−0.409205	−	0.912443i	$-0.634194\pi$
$563$		−	43.3002i		−	1.82489i	0.409205	−	0.912443i	$-0.365806\pi$
$564$		−	8.12311i		−	0.342044i
$565$		0			0
$566$			7.36932i			0.309755i
$567$	0.438447			0.0184131
$568$		−	13.9309i		−	0.584526i
$569$	7.31534			0.306675			0.153338	−	0.988174i	$-0.450998\pi$
$569$	7.31534			0.306675			0.153338	+	0.988174i	$0.450998\pi$
$570$		0			0
$571$	27.1231			1.13507			0.567533	−	0.823350i	$-0.307898\pi$
$571$	27.1231			1.13507			0.567533	+	0.823350i	$0.307898\pi$
$572$	−5.56155	+	0.876894i	−0.232540	+	0.0366648i
$573$			16.4924i			0.688981i
$574$		−	2.00000i		−	0.0834784i
$575$		0			0
$576$	−1.00000			−0.0416667
$577$	−8.63068			−0.359300			−0.179650	−	0.983731i	$-0.557497\pi$
$577$	−8.63068			−0.359300			−0.179650	+	0.983731i	$0.557497\pi$
$578$	−27.6847			−1.15153
$579$			4.87689i			0.202677i
$580$		0			0
$581$	6.54640			0.271590
$582$			13.1231i			0.543970i
$583$	7.80776			0.323365
$584$	7.12311			0.294756
$585$		0			0
$586$	0.630683			0.0260533
$587$	18.9309			0.781361			0.390680	−	0.920526i	$-0.372240\pi$
$587$	18.9309			0.781361			0.390680	+	0.920526i	$0.372240\pi$
$588$			6.80776i			0.280747i
$589$	−42.7386			−1.76101
$590$		0			0
$591$		−	12.2462i		−	0.503742i
$592$	4.56155			0.187479
$593$	−24.8078			−1.01873			−0.509366	−	0.860550i	$-0.670120\pi$
$593$	−24.8078			−1.01873			−0.509366	+	0.860550i	$0.670120\pi$
$594$	−1.56155			−0.0640713
$595$		0			0
$596$		−	19.3693i		−	0.793398i
$597$		−	5.93087i		−	0.242734i
$598$	11.1231	−	1.75379i	0.454858	−	0.0717178i
$599$	22.9848			0.939135			0.469568	−	0.882896i	$-0.344410\pi$
$599$	22.9848			0.939135			0.469568	+	0.882896i	$0.344410\pi$
$600$		0			0
$601$	11.7386			0.478829			0.239414	−	0.970917i	$-0.423045\pi$
$601$	11.7386			0.478829			0.239414	+	0.970917i	$0.423045\pi$
$602$		−	4.87689i		−	0.198767i
$603$	4.12311			0.167906
$604$		−	3.31534i		−	0.134899i
$605$		0			0
$606$			12.4384i			0.505277i
$607$			47.0540i			1.90986i	0.296828	+	0.954931i	$0.404071\pi$
$607$			47.0540i			1.90986i	−0.296828	+	0.954931i	$0.595929\pi$
$608$			7.68466i			0.311654i
$609$		−	0.438447i		−	0.0177668i
$610$		0			0
$611$	4.56155	+	28.9309i	0.184541	+	1.17042i
$612$		−	6.68466i		−	0.270211i
$613$	−39.3693			−1.59011			−0.795056	−	0.606536i	$-0.792559\pi$
$613$	−39.3693			−1.59011			−0.795056	+	0.606536i	$0.792559\pi$
$614$	2.06913			0.0835033
$615$		0			0
$616$			0.684658i			0.0275857i
$617$	−27.6847			−1.11454			−0.557271	−	0.830331i	$-0.688152\pi$
$617$	−27.6847			−1.11454			−0.557271	+	0.830331i	$0.688152\pi$
$618$	−7.12311			−0.286533
$619$			2.24621i			0.0902829i	0.998981	+	0.0451414i	$0.0143738\pi$
$619$			2.24621i			0.0902829i	−0.998981	+	0.0451414i	$0.985626\pi$
$620$		0			0
$621$	3.12311			0.125326
$622$	14.8769			0.596509
$623$			2.24621i			0.0899926i
$624$	3.56155	−	0.561553i	0.142576	−	0.0224801i
$625$		0			0
$626$		−	24.8617i		−	0.993675i
$627$			12.0000i			0.479234i
$628$		−	10.6847i		−	0.426364i
$629$			30.4924i			1.21581i
$630$		0			0
$631$			22.8769i			0.910715i	0.890309	+	0.455357i	$0.150489\pi$
$631$			22.8769i			0.910715i	−0.890309	+	0.455357i	$0.849511\pi$
$632$	2.31534			0.0920993
$633$			17.3693i			0.690368i
$634$	−30.0000			−1.19145
$635$		0			0
$636$	−5.00000			−0.198263
$637$	−3.82292	−	24.2462i	−0.151470	−	0.960670i
$638$			1.56155i			0.0618225i
$639$			13.9309i			0.551097i
$640$		0			0
$641$	−19.4233			−0.767174			−0.383587	−	0.923505i	$-0.625311\pi$
$641$	−19.4233			−0.767174			−0.383587	+	0.923505i	$0.625311\pi$
$642$	−0.315342			−0.0124455
$643$	15.6847			0.618543			0.309271	−	0.950974i	$-0.399915\pi$
$643$	15.6847			0.618543			0.309271	+	0.950974i	$0.399915\pi$
$644$		−	1.36932i		−	0.0539586i
$645$		0			0
$646$	−51.3693			−2.02110
$647$		−	10.8769i		−	0.427615i	−0.976876	−	0.213807i	$-0.931413\pi$
$647$		−	10.8769i		−	0.427615i	0.976876	−	0.213807i	$-0.0685865\pi$
$648$	1.00000			0.0392837
$649$	−14.9309			−0.586088
$650$		0			0
$651$	2.43845			0.0955703
$652$	16.4924			0.645893
$653$			46.3002i			1.81187i	0.423421	+	0.905933i	$0.360829\pi$
$653$			46.3002i			1.81187i	−0.423421	+	0.905933i	$0.639171\pi$
$654$	20.5616			0.804020
$655$		0			0
$656$		−	4.56155i		−	0.178099i
$657$	−7.12311			−0.277899
$658$	3.56155			0.138844
$659$	12.5616			0.489329			0.244664	−	0.969608i	$-0.421322\pi$
$659$	12.5616			0.489329			0.244664	+	0.969608i	$0.421322\pi$
$660$		0			0
$661$			15.3002i			0.595108i	0.954705	+	0.297554i	$0.0961709\pi$
$661$			15.3002i			0.595108i	−0.954705	+	0.297554i	$0.903829\pi$
$662$			24.4924i			0.951925i
$663$	3.75379	+	23.8078i	0.145785	+	0.924617i
$664$	14.9309			0.579430
$665$		0			0
$666$	−4.56155			−0.176757
$667$		−	3.12311i		−	0.120927i
$668$	13.4384			0.519949
$669$		−	15.3693i		−	0.594212i
$670$		0			0
$671$		−	1.06913i		−	0.0412733i
$672$		−	0.438447i		−	0.0169135i
$673$		−	22.1231i		−	0.852783i	−0.904539	−	0.426392i	$-0.859785\pi$
$673$		−	22.1231i		−	0.852783i	0.904539	−	0.426392i	$-0.140215\pi$
$674$		−	10.6847i		−	0.411558i
$675$		0			0
$676$	−12.3693	+	4.00000i	−0.475743	+	0.153846i
$677$		−	36.2462i		−	1.39306i	−0.717530	−	0.696528i	$-0.754727\pi$
$677$		−	36.2462i		−	1.39306i	0.717530	−	0.696528i	$-0.245273\pi$
$678$	4.24621			0.163075
$679$	−5.75379			−0.220810
$680$		0			0
$681$			3.31534i			0.127044i
$682$	−8.68466			−0.332553
$683$	35.6695			1.36486			0.682428	−	0.730953i	$-0.260924\pi$
$683$	35.6695			1.36486			0.682428	+	0.730953i	$0.260924\pi$
$684$		−	7.68466i		−	0.293830i
$685$		0			0
$686$	−6.05398			−0.231142
$687$	7.19224			0.274401
$688$		−	11.1231i		−	0.424064i
$689$	17.8078	−	2.80776i	0.678422	−	0.106967i
$690$		0			0
$691$		−	35.0000i		−	1.33146i	−0.746191	−	0.665731i	$-0.768120\pi$
$691$		−	35.0000i		−	1.33146i	0.746191	−	0.665731i	$-0.231880\pi$
$692$			0.123106i			0.00467977i
$693$		−	0.684658i		−	0.0260080i
$694$			18.5616i			0.704587i
$695$		0			0
$696$		−	1.00000i		−	0.0379049i
$697$	30.4924			1.15498
$698$		−	22.0000i		−	0.832712i
$699$	−3.12311			−0.118127
$700$		0			0
$701$	26.6847			1.00787			0.503933	−	0.863743i	$-0.331886\pi$
$701$	26.6847			1.00787			0.503933	+	0.863743i	$0.331886\pi$
$702$	−3.56155	+	0.561553i	−0.134422	+	0.0211944i
$703$			35.0540i			1.32209i
$704$			1.56155i			0.0588532i
$705$		0			0
$706$	−15.4384			−0.581034
$707$	−5.45360			−0.205104
$708$	9.56155			0.359345
$709$			6.49242i			0.243828i	0.992541	+	0.121914i	$0.0389032\pi$
$709$			6.49242i			0.243828i	−0.992541	+	0.121914i	$0.961097\pi$
$710$		0			0
$711$	−2.31534			−0.0868321
$712$			5.12311i			0.191997i
$713$	17.3693			0.650486
$714$	2.93087			0.109685
$715$		0			0
$716$	19.1231			0.714664
$717$	−6.93087			−0.258838
$718$		−	3.87689i		−	0.144684i
$719$	−25.3693			−0.946116			−0.473058	−	0.881031i	$-0.656850\pi$
$719$	−25.3693			−0.946116			−0.473058	+	0.881031i	$0.656850\pi$
$720$		0			0
$721$		−	3.12311i		−	0.116311i
$722$	−40.0540			−1.49065
$723$	20.2462			0.752965
$724$	0.192236			0.00714439
$725$		0			0
$726$		−	8.56155i		−	0.317749i
$727$		−	0.384472i		−	0.0142593i	−0.999975	−	0.00712964i	$-0.997731\pi$
$727$		−	0.384472i		−	0.0142593i	0.999975	−	0.00712964i	$-0.00226945\pi$
$728$	0.246211	+	1.56155i	0.00912520	+	0.0578750i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	74.3542			2.75009
$732$			0.684658i			0.0253057i
$733$	39.6847			1.46579			0.732893	−	0.680344i	$-0.238170\pi$
$733$	39.6847			1.46579			0.732893	+	0.680344i	$0.238170\pi$
$734$			19.6847i			0.726574i
$735$		0			0
$736$		−	3.12311i		−	0.115119i
$737$		−	6.43845i		−	0.237163i
$738$			4.56155i			0.167913i
$739$		−	47.4924i		−	1.74704i	−0.486791	−	0.873519i	$-0.661833\pi$
$739$		−	47.4924i		−	1.74704i	0.486791	−	0.873519i	$-0.338167\pi$
$740$		0			0
$741$	4.31534	+	27.3693i	0.158528	+	1.00544i
$742$		−	2.19224i		−	0.0804795i
$743$	26.3693			0.967396			0.483698	−	0.875235i	$-0.339293\pi$
$743$	26.3693			0.967396			0.483698	+	0.875235i	$0.339293\pi$
$744$	5.56155			0.203896
$745$		0			0
$746$			32.4384i			1.18766i
$747$	−14.9309			−0.546292
$748$	−10.4384			−0.381667
$749$		−	0.138261i		−	0.00505193i
$750$		0			0
$751$	−14.8078			−0.540343			−0.270171	−	0.962812i	$-0.587080\pi$
$751$	−14.8078			−0.540343			−0.270171	+	0.962812i	$0.587080\pi$
$752$	8.12311			0.296219
$753$		−	11.4384i		−	0.416840i
$754$	0.561553	+	3.56155i	0.0204505	+	0.129704i
$755$		0			0
$756$			0.438447i			0.0159462i
$757$		−	2.93087i		−	0.106524i	−0.998581	−	0.0532621i	$-0.983038\pi$
$757$		−	2.93087i		−	0.106524i	0.998581	−	0.0532621i	$-0.0169619\pi$
$758$		−	7.31534i		−	0.265705i
$759$		−	4.87689i		−	0.177020i
$760$		0			0
$761$		−	42.6695i		−	1.54677i	−0.633938	−	0.773384i	$-0.718562\pi$
$761$		−	42.6695i		−	1.54677i	0.633938	−	0.773384i	$-0.281438\pi$
$762$	11.4384			0.414371
$763$			9.01515i			0.326371i
$764$	−16.4924			−0.596675
$765$		0			0
$766$	13.9309			0.503343
$767$	−34.0540	+	5.36932i	−1.22962	+	0.193875i
$768$		−	1.00000i		−	0.0360844i
$769$		−	2.24621i		−	0.0810004i	−0.999180	−	0.0405002i	$-0.987105\pi$
$769$		−	2.24621i		−	0.0810004i	0.999180	−	0.0405002i	$-0.0128951\pi$
$770$		0			0
$771$	−15.8078			−0.569303
$772$	−4.87689			−0.175523
$773$	−31.2311			−1.12330			−0.561652	−	0.827374i	$-0.689834\pi$
$773$	−31.2311			−1.12330			−0.561652	+	0.827374i	$0.689834\pi$
$774$			11.1231i			0.399812i
$775$		0			0
$776$	−13.1231			−0.471092
$777$		−	2.00000i		−	0.0717496i
$778$	6.80776			0.244070
$779$	35.0540			1.25594
$780$		0			0
$781$	21.7538			0.778412
$782$	20.8769			0.746556
$783$			1.00000i			0.0357371i
$784$	−6.80776			−0.243134
$785$		0			0
$786$			6.31534i			0.225261i
$787$	30.9309			1.10257			0.551283	−	0.834318i	$-0.314138\pi$
$787$	30.9309			1.10257			0.551283	+	0.834318i	$0.314138\pi$
$788$	12.2462			0.436253
$789$	−24.7386			−0.880719
$790$		0			0
$791$			1.86174i			0.0661958i
$792$		−	1.56155i		−	0.0554874i
$793$	−0.384472	−	2.43845i	−0.0136530	−	0.0865918i
$794$	−35.0540			−1.24402
$795$		0			0
$796$	5.93087			0.210214
$797$		−	48.5464i		−	1.71960i	−0.510630	−	0.859801i	$-0.670588\pi$
$797$		−	48.5464i		−	1.71960i	0.510630	−	0.859801i	$-0.329412\pi$
$798$	3.36932			0.119273
$799$			54.3002i			1.92100i
$800$		0			0
$801$		−	5.12311i		−	0.181016i
$802$		−	22.0000i		−	0.776847i
$803$			11.1231i			0.392526i
$804$			4.12311i			0.145411i
$805$		0			0
$806$	−19.8078	+	3.12311i	−0.697699	+	0.110007i
$807$		−	9.49242i		−	0.334149i
$808$	−12.4384			−0.437583
$809$	7.12311			0.250435			0.125218	−	0.992129i	$-0.460037\pi$
$809$	7.12311			0.250435			0.125218	+	0.992129i	$0.460037\pi$
$810$		0			0
$811$			33.1771i			1.16500i	0.812829	+	0.582502i	$0.197926\pi$
$811$			33.1771i			1.16500i	−0.812829	+	0.582502i	$0.802074\pi$
$812$	0.438447			0.0153865
$813$	4.19224			0.147028
$814$			7.12311i			0.249665i
$815$		0			0
$816$	6.68466			0.234010
$817$	85.4773			2.99047
$818$		−	27.6155i		−	0.965554i
$819$	−0.246211	−	1.56155i	−0.00860332	−	0.0545651i
$820$		0			0
$821$		−	11.6155i		−	0.405385i	−0.979242	−	0.202692i	$-0.935031\pi$
$821$		−	11.6155i		−	0.405385i	0.979242	−	0.202692i	$-0.0649691\pi$
$822$		−	6.56155i		−	0.228860i
$823$			28.8078i			1.00418i	0.864817	+	0.502088i	$0.167435\pi$
$823$			28.8078i			1.00418i	−0.864817	+	0.502088i	$0.832565\pi$
$824$		−	7.12311i		−	0.248145i
$825$		0			0
$826$			4.19224i			0.145867i
$827$	41.3153			1.43668			0.718338	−	0.695695i	$-0.244903\pi$
$827$	41.3153			1.43668			0.718338	+	0.695695i	$0.244903\pi$
$828$			3.12311i			0.108535i
$829$	21.8078			0.757415			0.378707	−	0.925516i	$-0.376369\pi$
$829$	21.8078			0.757415			0.378707	+	0.925516i	$0.376369\pi$
$830$		0			0
$831$	−15.6155			−0.541697
$832$	0.561553	+	3.56155i	0.0194683	+	0.123475i
$833$		−	45.5076i		−	1.57674i
$834$			16.4924i			0.571086i
$835$		0			0
$836$	−12.0000			−0.415029
$837$	−5.56155			−0.192235
$838$	5.68466			0.196373
$839$			40.0000i			1.38095i	0.723355	+	0.690477i	$0.242599\pi$
$839$			40.0000i			1.38095i	−0.723355	+	0.690477i	$0.757401\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$			4.63068i			0.159584i
$843$	−5.93087			−0.204270
$844$	−17.3693			−0.597877
$845$		0			0
$846$	−8.12311			−0.279278
$847$	3.75379			0.128982
$848$		−	5.00000i		−	0.171701i
$849$	7.36932			0.252914
$850$		0			0
$851$		−	14.2462i		−	0.488354i
$852$	−13.9309			−0.477264
$853$	−28.8078			−0.986359			−0.493180	−	0.869928i	$-0.664165\pi$
$853$	−28.8078			−0.986359			−0.493180	+	0.869928i	$0.664165\pi$
$854$	−0.300187			−0.0102722
$855$		0			0
$856$		−	0.315342i		−	0.0107782i
$857$		−	31.6155i		−	1.07997i	−0.841676	−	0.539983i	$-0.818431\pi$
$857$		−	31.6155i		−	1.07997i	0.841676	−	0.539983i	$-0.181569\pi$
$858$	0.876894	+	5.56155i	0.0299367	+	0.189868i
$859$	−12.7386			−0.434637			−0.217318	−	0.976101i	$-0.569731\pi$
$859$	−12.7386			−0.434637			−0.217318	+	0.976101i	$0.569731\pi$
$860$		0			0
$861$	−2.00000			−0.0681598
$862$			8.17708i			0.278512i
$863$	−44.8617			−1.52711			−0.763556	−	0.645742i	$-0.776548\pi$
$863$	−44.8617			−1.52711			−0.763556	+	0.645742i	$0.776548\pi$
$864$			1.00000i			0.0340207i
$865$		0			0
$866$			5.05398i			0.171741i
$867$			27.6847i			0.940220i
$868$			2.43845i			0.0827663i
$869$			3.61553i			0.122648i
$870$		0			0
$871$	−2.31534	−	14.6847i	−0.0784524	−	0.497571i
$872$			20.5616i			0.696302i
$873$	13.1231			0.444150
$874$	24.0000			0.811812
$875$		0			0
$876$		−	7.12311i		−	0.240667i
$877$	32.1771			1.08654			0.543271	−	0.839557i	$-0.317185\pi$
$877$	32.1771			1.08654			0.543271	+	0.839557i	$0.317185\pi$
$878$	27.3002			0.921337
$879$		−	0.630683i		−	0.0212724i
$880$		0			0
$881$	−51.0388			−1.71954			−0.859771	−	0.510680i	$-0.829394\pi$
$881$	−51.0388			−1.71954			−0.859771	+	0.510680i	$0.829394\pi$
$882$	6.80776			0.229229
$883$			17.6155i			0.592810i	0.955062	+	0.296405i	$0.0957878\pi$
$883$			17.6155i			0.592810i	−0.955062	+	0.296405i	$0.904212\pi$
$884$	−23.8078	+	3.75379i	−0.800742	+	0.126254i
$885$		0			0
$886$		−	28.5616i		−	0.959544i
$887$			39.6155i			1.33016i	0.746772	+	0.665080i	$0.231602\pi$
$887$			39.6155i			1.33016i	−0.746772	+	0.665080i	$0.768398\pi$
$888$		−	4.56155i		−	0.153076i
$889$			5.01515i			0.168203i
$890$		0			0
$891$			1.56155i			0.0523140i
$892$	15.3693			0.514603
$893$			62.4233i			2.08892i
$894$	−19.3693			−0.647807
$895$		0			0
$896$	0.438447			0.0146475
$897$	−1.75379	−	11.1231i	−0.0585573	−	0.371390i
$898$			5.43845i			0.181483i
$899$			5.56155i			0.185488i
$900$		0			0
$901$	33.4233			1.11349
$902$	7.12311			0.237173
$903$	−4.87689			−0.162293
$904$			4.24621i			0.141227i
$905$		0			0
$906$	−3.31534			−0.110145
$907$		−	14.3845i		−	0.477629i	−0.971065	−	0.238814i	$-0.923241\pi$
$907$		−	14.3845i		−	0.477629i	0.971065	−	0.238814i	$-0.0767587\pi$
$908$	−3.31534			−0.110023
$909$	12.4384			0.412557
$910$		0			0
$911$	−22.6307			−0.749788			−0.374894	−	0.927068i	$-0.622321\pi$
$911$	−22.6307			−0.749788			−0.374894	+	0.927068i	$0.622321\pi$
$912$	7.68466			0.254464
$913$			23.3153i			0.771625i
$914$	−28.7386			−0.950590
$915$		0			0
$916$			7.19224i			0.237638i
$917$	−2.76894			−0.0914386
$918$	−6.68466			−0.220627
$919$	18.5616			0.612289			0.306145	−	0.951985i	$-0.400961\pi$
$919$	18.5616			0.612289			0.306145	+	0.951985i	$0.400961\pi$
$920$		0			0
$921$		−	2.06913i		−	0.0681802i
$922$			22.2462i			0.732640i
$923$	49.6155	−	7.82292i	1.63312	−	0.257495i
$924$	0.684658			0.0225236
$925$		0			0
$926$	−11.5616			−0.379936
$927$			7.12311i			0.233953i
$928$	1.00000			0.0328266
$929$			50.4233i			1.65433i	0.561956	+	0.827167i	$0.310049\pi$
$929$			50.4233i			1.65433i	−0.561956	+	0.827167i	$0.689951\pi$
$930$		0			0
$931$		−	52.3153i		−	1.71457i
$932$		−	3.12311i		−	0.102301i
$933$		−	14.8769i		−	0.487048i
$934$		−	40.8078i		−	1.33527i
$935$		0			0
$936$	−0.561553	−	3.56155i	−0.0183549	−	0.116413i
$937$		−	11.0691i		−	0.361613i	−0.983519	−	0.180806i	$-0.942129\pi$
$937$		−	11.0691i		−	0.361613i	0.983519	−	0.180806i	$-0.0578707\pi$
$938$	−1.80776			−0.0590256
$939$	−24.8617			−0.811332
$940$		0			0
$941$			40.7386i			1.32804i	0.747714	+	0.664021i	$0.231151\pi$
$941$			40.7386i			1.32804i	−0.747714	+	0.664021i	$0.768849\pi$
$942$	−10.6847			−0.348125
$943$	−14.2462			−0.463920
$944$			9.56155i			0.311202i
$945$		0			0
$946$	17.3693			0.564725
$947$	−16.9309			−0.550179			−0.275090	−	0.961419i	$-0.588708\pi$
$947$	−16.9309			−0.550179			−0.275090	+	0.961419i	$0.588708\pi$
$948$		−	2.31534i		−	0.0751988i
$949$	4.00000	+	25.3693i	0.129845	+	0.823523i
$950$		0			0
$951$			30.0000i			0.972817i
$952$			2.93087i			0.0949900i
$953$		−	1.80776i		−	0.0585592i	−0.999571	−	0.0292796i	$-0.990679\pi$
$953$		−	1.80776i		−	0.0585592i	0.999571	−	0.0292796i	$-0.00932132\pi$
$954$			5.00000i			0.161881i
$955$		0			0
$956$		−	6.93087i		−	0.224160i
$957$	1.56155			0.0504778
$958$		−	32.1231i		−	1.03785i
$959$	2.87689			0.0928998
$960$		0			0
$961$	0.0691303			0.00223001
$962$	2.56155	+	16.2462i	0.0825878	+	0.523799i
$963$			0.315342i			0.0101617i
$964$			20.2462i			0.652087i
$965$		0			0
$966$	−1.36932			−0.0440570
$967$	−43.6695			−1.40432			−0.702158	−	0.712021i	$-0.747780\pi$
$967$	−43.6695			−1.40432			−0.702158	+	0.712021i	$0.747780\pi$
$968$	8.56155			0.275179
$969$			51.3693i			1.65022i
$970$		0			0
$971$	1.93087			0.0619646			0.0309823	−	0.999520i	$-0.490136\pi$
$971$	1.93087			0.0619646			0.0309823	+	0.999520i	$0.490136\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−7.23106			−0.231817
$974$	−6.68466			−0.214190
$975$		0			0
$976$	−0.684658			−0.0219154
$977$	31.3693			1.00359			0.501797	−	0.864986i	$-0.332673\pi$
$977$	31.3693			1.00359			0.501797	+	0.864986i	$0.332673\pi$
$978$		−	16.4924i		−	0.527370i
$979$	−8.00000			−0.255681
$980$		0			0
$981$		−	20.5616i		−	0.656480i
$982$	38.7386			1.23620
$983$	9.06913			0.289260			0.144630	−	0.989486i	$-0.453801\pi$
$983$	9.06913			0.289260			0.144630	+	0.989486i	$0.453801\pi$
$984$	−4.56155			−0.145417
$985$		0			0
$986$			6.68466i			0.212883i
$987$		−	3.56155i		−	0.113365i
$988$	−27.3693	+	4.31534i	−0.870734	+	0.137289i
$989$	−34.7386			−1.10462
$990$		0			0
$991$	−25.6847			−0.815900			−0.407950	−	0.913004i	$-0.633756\pi$
$991$	−25.6847			−0.815900			−0.407950	+	0.913004i	$0.633756\pi$
$992$			5.56155i			0.176579i
$993$	24.4924			0.777244
$994$		−	6.10795i		−	0.193732i
$995$		0			0
$996$		−	14.9309i		−	0.473103i
$997$		−	53.6695i		−	1.69973i	−0.527000	−	0.849865i	$-0.676683\pi$
$997$		−	53.6695i		−	1.69973i	0.527000	−	0.849865i	$-0.323317\pi$
$998$			28.1231i			0.890221i
$999$			4.56155i			0.144321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.f.p.649.1		4
5.2	odd	4		1950.2.b.i.1351.3	yes	4
5.3	odd	4		1950.2.b.j.1351.2	yes	4
5.4	even	2		1950.2.f.k.649.4		4
13.12	even	2		1950.2.f.k.649.2		4
65.12	odd	4		1950.2.b.i.1351.2	✓	4
65.38	odd	4		1950.2.b.j.1351.3	yes	4
65.64	even	2	inner	1950.2.f.p.649.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.b.i.1351.2	✓	4	65.12	odd	4
1950.2.b.i.1351.3	yes	4	5.2	odd	4
1950.2.b.j.1351.2	yes	4	5.3	odd	4
1950.2.b.j.1351.3	yes	4	65.38	odd	4
1950.2.f.k.649.2		4	13.12	even	2
1950.2.f.k.649.4		4	5.4	even	2
1950.2.f.p.649.1		4	1.1	even	1	trivial
1950.2.f.p.649.3		4	65.64	even	2	inner

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} +0.438447 q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.00000i q^{6} +0.438447 q^{7} +1.00000 q^{8} -1.00000 q^{9} +1.56155i q^{11} -1.00000i q^{12} +(0.561553 + 3.56155i) q^{13} +0.438447 q^{14} +1.00000 q^{16} +6.68466i q^{17} -1.00000 q^{18} +7.68466i q^{19} -0.438447i q^{21} +1.56155i q^{22} -3.12311i q^{23} -1.00000i q^{24} +(0.561553 + 3.56155i) q^{26} +1.00000i q^{27} +0.438447 q^{28} +1.00000 q^{29} +5.56155i q^{31} +1.00000 q^{32} +1.56155 q^{33} +6.68466i q^{34} -1.00000 q^{36} +4.56155 q^{37} +7.68466i q^{38} +(3.56155 - 0.561553i) q^{39} -4.56155i q^{41} -0.438447i q^{42} -11.1231i q^{43} +1.56155i q^{44} -3.12311i q^{46} +8.12311 q^{47} -1.00000i q^{48} -6.80776 q^{49} +6.68466 q^{51} +(0.561553 + 3.56155i) q^{52} -5.00000i q^{53} +1.00000i q^{54} +0.438447 q^{56} +7.68466 q^{57} +1.00000 q^{58} +9.56155i q^{59} -0.684658 q^{61} +5.56155i q^{62} -0.438447 q^{63} +1.00000 q^{64} +1.56155 q^{66} -4.12311 q^{67} +6.68466i q^{68} -3.12311 q^{69} -13.9309i q^{71} -1.00000 q^{72} +7.12311 q^{73} +4.56155 q^{74} +7.68466i q^{76} +0.684658i q^{77} +(3.56155 - 0.561553i) q^{78} +2.31534 q^{79} +1.00000 q^{81} -4.56155i q^{82} +14.9309 q^{83} -0.438447i q^{84} -11.1231i q^{86} -1.00000i q^{87} +1.56155i q^{88} +5.12311i q^{89} +(0.246211 + 1.56155i) q^{91} -3.12311i q^{92} +5.56155 q^{93} +8.12311 q^{94} -1.00000i q^{96} -13.1231 q^{97} -6.80776 q^{98} -1.56155i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 10 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 10 * q^7 + 4 * q^8 - 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{4} + 10 q^{7} + 4 q^{8} - 4 q^{9} - 6 q^{13} + 10 q^{14} + 4 q^{16} - 4 q^{18} - 6 q^{26} + 10 q^{28} + 4 q^{29} + 4 q^{32} - 2 q^{33} - 4 q^{36} + 10 q^{37} + 6 q^{39} + 16 q^{47} + 14 q^{49} + 2 q^{51} - 6 q^{52} + 10 q^{56} + 6 q^{57} + 4 q^{58} + 22 q^{61} - 10 q^{63} + 4 q^{64} - 2 q^{66} + 4 q^{69} - 4 q^{72} + 12 q^{73} + 10 q^{74} + 6 q^{78} + 34 q^{79} + 4 q^{81} + 2 q^{83} - 32 q^{91} + 14 q^{93} + 16 q^{94} - 36 q^{97} + 14 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 10 * q^7 + 4 * q^8 - 4 * q^9 - 6 * q^13 + 10 * q^14 + 4 * q^16 - 4 * q^18 - 6 * q^26 + 10 * q^28 + 4 * q^29 + 4 * q^32 - 2 * q^33 - 4 * q^36 + 10 * q^37 + 6 * q^39 + 16 * q^47 + 14 * q^49 + 2 * q^51 - 6 * q^52 + 10 * q^56 + 6 * q^57 + 4 * q^58 + 22 * q^61 - 10 * q^63 + 4 * q^64 - 2 * q^66 + 4 * q^69 - 4 * q^72 + 12 * q^73 + 10 * q^74 + 6 * q^78 + 34 * q^79 + 4 * q^81 + 2 * q^83 - 32 * q^91 + 14 * q^93 + 16 * q^94 - 36 * q^97 + 14 * q^98

Introduction

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