LMFDB - Embedded newform 1950.2.b.h.1351.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1351,1950)]

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, 0, 1]))

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

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

chi := DirichletCharacter("1950.1351");

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.b (of order $2$, degree $1$, 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			1351.1
Root			$-2.56155i$ of defining polynomial
Character	$\chi$	$=$	1950.1351
Dual form			1950.2.b.h.1351.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{6} -5.12311i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{6} -5.12311i q^{7} +1.00000i q^{8} +1.00000 q^{9} +3.12311i q^{11} +1.00000 q^{12} +(0.561553 + 3.56155i) q^{13} -5.12311 q^{14} +1.00000 q^{16} -2.00000 q^{17} -1.00000i q^{18} +6.00000i q^{19} +5.12311i q^{21} +3.12311 q^{22} -3.12311 q^{23} -1.00000i q^{24} +(3.56155 - 0.561553i) q^{26} -1.00000 q^{27} +5.12311i q^{28} +2.00000 q^{29} +5.12311i q^{31} -1.00000i q^{32} -3.12311i q^{33} +2.00000i q^{34} -1.00000 q^{36} +3.12311i q^{37} +6.00000 q^{38} +(-0.561553 - 3.56155i) q^{39} -9.12311i q^{41} +5.12311 q^{42} +10.2462 q^{43} -3.12311i q^{44} +3.12311i q^{46} +10.2462i q^{47} -1.00000 q^{48} -19.2462 q^{49} +2.00000 q^{51} +(-0.561553 - 3.56155i) q^{52} -11.3693 q^{53} +1.00000i q^{54} +5.12311 q^{56} -6.00000i q^{57} -2.00000i q^{58} -7.12311i q^{59} +10.0000 q^{61} +5.12311 q^{62} -5.12311i q^{63} -1.00000 q^{64} -3.12311 q^{66} +13.1231i q^{67} +2.00000 q^{68} +3.12311 q^{69} +6.24621i q^{71} +1.00000i q^{72} -4.87689i q^{73} +3.12311 q^{74} -6.00000i q^{76} +16.0000 q^{77} +(-3.56155 + 0.561553i) q^{78} +8.00000 q^{79} +1.00000 q^{81} -9.12311 q^{82} +10.2462i q^{83} -5.12311i q^{84} -10.2462i q^{86} -2.00000 q^{87} -3.12311 q^{88} +5.12311i q^{89} +(18.2462 - 2.87689i) q^{91} +3.12311 q^{92} -5.12311i q^{93} +10.2462 q^{94} +1.00000i q^{96} -4.87689i q^{97} +19.2462i q^{98} +3.12311i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 4 * q^4 + 4 * q^9	$ 4 q - 4 q^{3} - 4 q^{4} + 4 q^{9} + 4 q^{12} - 6 q^{13} - 4 q^{14} + 4 q^{16} - 8 q^{17} - 4 q^{22} + 4 q^{23} + 6 q^{26} - 4 q^{27} + 8 q^{29} - 4 q^{36} + 24 q^{38} + 6 q^{39} + 4 q^{42} + 8 q^{43} - 4 q^{48} - 44 q^{49} + 8 q^{51} + 6 q^{52} + 4 q^{53} + 4 q^{56} + 40 q^{61} + 4 q^{62} - 4 q^{64} + 4 q^{66} + 8 q^{68} - 4 q^{69} - 4 q^{74} + 64 q^{77} - 6 q^{78} + 32 q^{79} + 4 q^{81} - 20 q^{82} - 8 q^{87} + 4 q^{88} + 40 q^{91} - 4 q^{92} + 8 q^{94}+O(q^{100}) $ 4 * q - 4 * q^3 - 4 * q^4 + 4 * q^9 + 4 * q^12 - 6 * q^13 - 4 * q^14 + 4 * q^16 - 8 * q^17 - 4 * q^22 + 4 * q^23 + 6 * q^26 - 4 * q^27 + 8 * q^29 - 4 * q^36 + 24 * q^38 + 6 * q^39 + 4 * q^42 + 8 * q^43 - 4 * q^48 - 44 * q^49 + 8 * q^51 + 6 * q^52 + 4 * q^53 + 4 * q^56 + 40 * q^61 + 4 * q^62 - 4 * q^64 + 4 * q^66 + 8 * q^68 - 4 * q^69 - 4 * q^74 + 64 * q^77 - 6 * q^78 + 32 * q^79 + 4 * q^81 - 20 * q^82 - 8 * q^87 + 4 * q^88 + 40 * q^91 - 4 * q^92 + 8 * q^94

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$		−	5.12311i		−	1.93635i	−0.250270	−	0.968176i	$-0.580520\pi$
$7$		−	5.12311i		−	1.93635i	0.250270	−	0.968176i	$-0.419480\pi$
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$		0			0
$11$			3.12311i			0.941652i	0.882226	+	0.470826i	$0.156044\pi$
$11$			3.12311i			0.941652i	−0.882226	+	0.470826i	$0.843956\pi$
$12$	1.00000			0.288675
$13$	0.561553	+	3.56155i	0.155747	+	0.987797i
$13$	0.561553	+	3.56155i	0.155747	+	0.987797i
$14$	−5.12311			−1.36921
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		−	1.00000i		−	0.235702i
$19$			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
$21$			5.12311i			1.11795i
$22$	3.12311			0.665848
$23$	−3.12311			−0.651213			−0.325606	−	0.945505i	$-0.605568\pi$
$23$	−3.12311			−0.651213			−0.325606	+	0.945505i	$0.605568\pi$
$24$		−	1.00000i		−	0.204124i
$25$		0			0
$26$	3.56155	−	0.561553i	0.698478	−	0.110130i
$27$	−1.00000			−0.192450
$28$			5.12311i			0.968176i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$			5.12311i			0.920137i	0.887883	+	0.460068i	$0.152175\pi$
$31$			5.12311i			0.920137i	−0.887883	+	0.460068i	$0.847825\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	3.12311i		−	0.543663i
$34$			2.00000i			0.342997i
$35$		0			0
$36$	−1.00000			−0.166667
$37$			3.12311i			0.513435i	0.966486	+	0.256718i	$0.0826411\pi$
$37$			3.12311i			0.513435i	−0.966486	+	0.256718i	$0.917359\pi$
$38$	6.00000			0.973329
$39$	−0.561553	−	3.56155i	−0.0899204	−	0.570305i
$40$		0			0
$41$		−	9.12311i		−	1.42479i	−0.701779	−	0.712395i	$-0.747611\pi$
$41$		−	9.12311i		−	1.42479i	0.701779	−	0.712395i	$-0.252389\pi$
$42$	5.12311			0.790512
$43$	10.2462			1.56253			0.781266	−	0.624198i	$-0.214574\pi$
$43$	10.2462			1.56253			0.781266	+	0.624198i	$0.214574\pi$
$44$		−	3.12311i		−	0.470826i
$45$		0			0
$46$			3.12311i			0.460477i
$47$			10.2462i			1.49456i	0.664507	+	0.747282i	$0.268641\pi$
$47$			10.2462i			1.49456i	−0.664507	+	0.747282i	$0.731359\pi$
$48$	−1.00000			−0.144338
$49$	−19.2462			−2.74946
$50$		0			0
$51$	2.00000			0.280056
$52$	−0.561553	−	3.56155i	−0.0778734	−	0.493899i
$53$	−11.3693			−1.56170			−0.780848	−	0.624721i	$-0.785213\pi$
$53$	−11.3693			−1.56170			−0.780848	+	0.624721i	$0.785213\pi$
$54$			1.00000i			0.136083i
$55$		0			0
$56$	5.12311			0.684604
$57$		−	6.00000i		−	0.794719i
$58$		−	2.00000i		−	0.262613i
$59$		−	7.12311i		−	0.927349i	−0.886006	−	0.463675i	$-0.846531\pi$
$59$		−	7.12311i		−	0.927349i	0.886006	−	0.463675i	$-0.153469\pi$
$60$		0			0
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	5.12311			0.650635
$63$		−	5.12311i		−	0.645451i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−3.12311			−0.384428
$67$			13.1231i			1.60324i	0.597832	+	0.801621i	$0.296029\pi$
$67$			13.1231i			1.60324i	−0.597832	+	0.801621i	$0.703971\pi$
$68$	2.00000			0.242536
$69$	3.12311			0.375978
$70$		0			0
$71$			6.24621i			0.741289i	0.928775	+	0.370644i	$0.120863\pi$
$71$			6.24621i			0.741289i	−0.928775	+	0.370644i	$0.879137\pi$
$72$			1.00000i			0.117851i
$73$		−	4.87689i		−	0.570797i	−0.958409	−	0.285399i	$-0.907874\pi$
$73$		−	4.87689i		−	0.570797i	0.958409	−	0.285399i	$-0.0921260\pi$
$74$	3.12311			0.363054
$75$		0			0
$76$		−	6.00000i		−	0.688247i
$77$	16.0000			1.82337
$78$	−3.56155	+	0.561553i	−0.403266	+	0.0635833i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−9.12311			−1.00748
$83$			10.2462i			1.12467i	0.826910	+	0.562334i	$0.190096\pi$
$83$			10.2462i			1.12467i	−0.826910	+	0.562334i	$0.809904\pi$
$84$		−	5.12311i		−	0.558977i
$85$		0			0
$86$		−	10.2462i		−	1.10488i
$87$	−2.00000			−0.214423
$88$	−3.12311			−0.332924
$89$			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
$91$	18.2462	−	2.87689i	1.91272	−	0.301580i
$92$	3.12311			0.325606
$93$		−	5.12311i		−	0.531241i
$94$	10.2462			1.05682
$95$		0			0
$96$			1.00000i			0.102062i
$97$		−	4.87689i		−	0.495174i	−0.968866	−	0.247587i	$-0.920362\pi$
$97$		−	4.87689i		−	0.495174i	0.968866	−	0.247587i	$-0.0796375\pi$
$98$			19.2462i			1.94416i
$99$			3.12311i			0.313884i
$100$		0			0
$101$	4.24621			0.422514			0.211257	−	0.977431i	$-0.432244\pi$
$101$	4.24621			0.422514			0.211257	+	0.977431i	$0.432244\pi$
$102$		−	2.00000i		−	0.198030i
$103$	4.87689			0.480535			0.240267	−	0.970707i	$-0.422765\pi$
$103$	4.87689			0.480535			0.240267	+	0.970707i	$0.422765\pi$
$104$	−3.56155	+	0.561553i	−0.349239	+	0.0550648i
$105$		0			0
$106$			11.3693i			1.10429i
$107$	8.00000			0.773389			0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000			0.773389			0.386695	+	0.922208i	$0.373617\pi$
$108$	1.00000			0.0962250
$109$		−	11.1231i		−	1.06540i	−0.846304	−	0.532700i	$-0.821177\pi$
$109$		−	11.1231i		−	1.06540i	0.846304	−	0.532700i	$-0.178823\pi$
$110$		0			0
$111$		−	3.12311i		−	0.296432i
$112$		−	5.12311i		−	0.484088i
$113$	4.24621			0.399450			0.199725	−	0.979852i	$-0.435995\pi$
$113$	4.24621			0.399450			0.199725	+	0.979852i	$0.435995\pi$
$114$	−6.00000			−0.561951
$115$		0			0
$116$	−2.00000			−0.185695
$117$	0.561553	+	3.56155i	0.0519156	+	0.329266i
$118$	−7.12311			−0.655735
$119$			10.2462i			0.939269i
$120$		0			0
$121$	1.24621			0.113292
$122$		−	10.0000i		−	0.905357i
$123$			9.12311i			0.822603i
$124$		−	5.12311i		−	0.460068i
$125$		0			0
$126$	−5.12311			−0.456403
$127$	4.87689			0.432754			0.216377	−	0.976310i	$-0.430576\pi$
$127$	4.87689			0.432754			0.216377	+	0.976310i	$0.430576\pi$
$128$			1.00000i			0.0883883i
$129$	−10.2462			−0.902129
$130$		0			0
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$			3.12311i			0.271831i
$133$	30.7386			2.66538
$134$	13.1231			1.13366
$135$		0			0
$136$		−	2.00000i		−	0.171499i
$137$			22.4924i			1.92166i	0.277143	+	0.960829i	$0.410612\pi$
$137$			22.4924i			1.92166i	−0.277143	+	0.960829i	$0.589388\pi$
$138$		−	3.12311i		−	0.265856i
$139$	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
$141$		−	10.2462i		−	0.862887i
$142$	6.24621			0.524170
$143$	−11.1231	+	1.75379i	−0.930161	+	0.146659i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−4.87689			−0.403615
$147$	19.2462			1.58740
$148$		−	3.12311i		−	0.256718i
$149$			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
$151$			11.3693i			0.925222i	0.886561	+	0.462611i	$0.153087\pi$
$151$			11.3693i			0.925222i	−0.886561	+	0.462611i	$0.846913\pi$
$152$	−6.00000			−0.486664
$153$	−2.00000			−0.161690
$154$		−	16.0000i		−	1.28932i
$155$		0			0
$156$	0.561553	+	3.56155i	0.0449602	+	0.285152i
$157$	3.36932			0.268901			0.134450	−	0.990920i	$-0.457073\pi$
$157$	3.36932			0.268901			0.134450	+	0.990920i	$0.457073\pi$
$158$		−	8.00000i		−	0.636446i
$159$	11.3693			0.901645
$160$		0			0
$161$			16.0000i			1.26098i
$162$		−	1.00000i		−	0.0785674i
$163$			1.12311i			0.0879684i	0.999032	+	0.0439842i	$0.0140051\pi$
$163$			1.12311i			0.0879684i	−0.999032	+	0.0439842i	$0.985995\pi$
$164$			9.12311i			0.712395i
$165$		0			0
$166$	10.2462			0.795260
$167$		−	5.75379i		−	0.445242i	−0.974905	−	0.222621i	$-0.928539\pi$
$167$		−	5.75379i		−	0.445242i	0.974905	−	0.222621i	$-0.0714612\pi$
$168$	−5.12311			−0.395256
$169$	−12.3693	+	4.00000i	−0.951486	+	0.307692i
$170$		0			0
$171$			6.00000i			0.458831i
$172$	−10.2462			−0.781266
$173$	−14.8769			−1.13107			−0.565535	−	0.824725i	$-0.691330\pi$
$173$	−14.8769			−1.13107			−0.565535	+	0.824725i	$0.691330\pi$
$174$			2.00000i			0.151620i
$175$		0			0
$176$			3.12311i			0.235413i
$177$			7.12311i			0.535405i
$178$	5.12311			0.383993
$179$	−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
$181$	−3.75379			−0.279017			−0.139508	−	0.990221i	$-0.544552\pi$
$181$	−3.75379			−0.279017			−0.139508	+	0.990221i	$0.544552\pi$
$182$	−2.87689	−	18.2462i	−0.213250	−	1.35250i
$183$	−10.0000			−0.739221
$184$		−	3.12311i		−	0.230238i
$185$		0			0
$186$	−5.12311			−0.375644
$187$		−	6.24621i		−	0.456768i
$188$		−	10.2462i		−	0.747282i
$189$			5.12311i			0.372651i
$190$		0			0
$191$	−16.4924			−1.19335			−0.596675	−	0.802483i	$-0.703512\pi$
$191$	−16.4924			−1.19335			−0.596675	+	0.802483i	$0.703512\pi$
$192$	1.00000			0.0721688
$193$		−	16.8769i		−	1.21483i	−0.794386	−	0.607413i	$-0.792207\pi$
$193$		−	16.8769i		−	1.21483i	0.794386	−	0.607413i	$-0.207793\pi$
$194$	−4.87689			−0.350141
$195$		0			0
$196$	19.2462			1.37473
$197$		−	0.246211i		−	0.0175418i	−0.999962	−	0.00877091i	$-0.997208\pi$
$197$		−	0.246211i		−	0.0175418i	0.999962	−	0.00877091i	$-0.00279190\pi$
$198$	3.12311			0.221949
$199$	1.75379			0.124323			0.0621614	−	0.998066i	$-0.480201\pi$
$199$	1.75379			0.124323			0.0621614	+	0.998066i	$0.480201\pi$
$200$		0			0
$201$		−	13.1231i		−	0.925633i
$202$		−	4.24621i		−	0.298762i
$203$		−	10.2462i		−	0.719143i
$204$	−2.00000			−0.140028
$205$		0			0
$206$		−	4.87689i		−	0.339789i
$207$	−3.12311			−0.217071
$208$	0.561553	+	3.56155i	0.0389367	+	0.246949i
$209$	−18.7386			−1.29618
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	11.3693			0.780848
$213$		−	6.24621i		−	0.427983i
$214$		−	8.00000i		−	0.546869i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	26.2462			1.78171
$218$	−11.1231			−0.753352
$219$			4.87689i			0.329550i
$220$		0			0
$221$	−1.12311	−	7.12311i	−0.0755483	−	0.479152i
$222$	−3.12311			−0.209609
$223$		−	15.3693i		−	1.02921i	−0.857429	−	0.514603i	$-0.827939\pi$
$223$		−	15.3693i		−	1.02921i	0.857429	−	0.514603i	$-0.172061\pi$
$224$	−5.12311			−0.342302
$225$		0			0
$226$		−	4.24621i		−	0.282454i
$227$			8.00000i			0.530979i	0.964114	+	0.265489i	$0.0855335\pi$
$227$			8.00000i			0.530979i	−0.964114	+	0.265489i	$0.914466\pi$
$228$			6.00000i			0.397360i
$229$		−	3.12311i		−	0.206381i	−0.994662	−	0.103190i	$-0.967095\pi$
$229$		−	3.12311i		−	0.206381i	0.994662	−	0.103190i	$-0.0329051\pi$
$230$		0			0
$231$	−16.0000			−1.05272
$232$			2.00000i			0.131306i
$233$	24.2462			1.58842			0.794211	−	0.607642i	$-0.207884\pi$
$233$	24.2462			1.58842			0.794211	+	0.607642i	$0.207884\pi$
$234$	3.56155	−	0.561553i	0.232826	−	0.0367099i
$235$		0			0
$236$			7.12311i			0.463675i
$237$	−8.00000			−0.519656
$238$	10.2462			0.664163
$239$			28.4924i			1.84302i	0.388353	+	0.921511i	$0.373044\pi$
$239$			28.4924i			1.84302i	−0.388353	+	0.921511i	$0.626956\pi$
$240$		0			0
$241$		−	2.24621i		−	0.144691i	−0.997380	−	0.0723456i	$-0.976952\pi$
$241$		−	2.24621i		−	0.144691i	0.997380	−	0.0723456i	$-0.0230485\pi$
$242$		−	1.24621i		−	0.0801095i
$243$	−1.00000			−0.0641500
$244$	−10.0000			−0.640184
$245$		0			0
$246$	9.12311			0.581668
$247$	−21.3693	+	3.36932i	−1.35970	+	0.214384i
$248$	−5.12311			−0.325318
$249$		−	10.2462i		−	0.649327i
$250$		0			0
$251$	9.75379			0.615654			0.307827	−	0.951442i	$-0.400398\pi$
$251$	9.75379			0.615654			0.307827	+	0.951442i	$0.400398\pi$
$252$			5.12311i			0.322725i
$253$		−	9.75379i		−	0.613215i
$254$		−	4.87689i		−	0.306004i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.24621			−0.264871			−0.132436	−	0.991192i	$-0.542280\pi$
$257$	−4.24621			−0.264871			−0.132436	+	0.991192i	$0.542280\pi$
$258$			10.2462i			0.637901i
$259$	16.0000			0.994192
$260$		0			0
$261$	2.00000			0.123797
$262$		−	4.00000i		−	0.247121i
$263$	2.63068			0.162215			0.0811074	−	0.996705i	$-0.474154\pi$
$263$	2.63068			0.162215			0.0811074	+	0.996705i	$0.474154\pi$
$264$	3.12311			0.192214
$265$		0			0
$266$		−	30.7386i		−	1.88471i
$267$		−	5.12311i		−	0.313529i
$268$		−	13.1231i		−	0.801621i
$269$	0.246211			0.0150118			0.00750588	−	0.999972i	$-0.497611\pi$
$269$	0.246211			0.0150118			0.00750588	+	0.999972i	$0.497611\pi$
$270$		0			0
$271$		−	14.8769i		−	0.903707i	−0.892092	−	0.451853i	$-0.850763\pi$
$271$		−	14.8769i		−	0.903707i	0.892092	−	0.451853i	$-0.149237\pi$
$272$	−2.00000			−0.121268
$273$	−18.2462	+	2.87689i	−1.10431	+	0.174118i
$274$	22.4924			1.35882
$275$		0			0
$276$	−3.12311			−0.187989
$277$	−27.8617			−1.67405			−0.837025	−	0.547165i	$-0.815707\pi$
$277$	−27.8617			−1.67405			−0.837025	+	0.547165i	$0.815707\pi$
$278$		−	16.4924i		−	0.989150i
$279$			5.12311i			0.306712i
$280$		0			0
$281$		−	5.12311i		−	0.305619i	−0.988256	−	0.152809i	$-0.951168\pi$
$281$		−	5.12311i		−	0.305619i	0.988256	−	0.152809i	$-0.0488321\pi$
$282$	−10.2462			−0.610153
$283$	4.00000			0.237775			0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000			0.237775			0.118888	+	0.992908i	$0.462067\pi$
$284$		−	6.24621i		−	0.370644i
$285$		0			0
$286$	1.75379	+	11.1231i	0.103704	+	0.657723i
$287$	−46.7386			−2.75889
$288$		−	1.00000i		−	0.0589256i
$289$	−13.0000			−0.764706
$290$		0			0
$291$			4.87689i			0.285889i
$292$			4.87689i			0.285399i
$293$		−	20.7386i		−	1.21156i	−0.795631	−	0.605782i	$-0.792860\pi$
$293$		−	20.7386i		−	1.21156i	0.795631	−	0.605782i	$-0.207140\pi$
$294$		−	19.2462i		−	1.12246i
$295$		0			0
$296$	−3.12311			−0.181527
$297$		−	3.12311i		−	0.181221i
$298$	14.0000			0.810998
$299$	−1.75379	−	11.1231i	−0.101424	−	0.643266i
$300$		0			0
$301$		−	52.4924i		−	3.02561i
$302$	11.3693			0.654231
$303$	−4.24621			−0.243938
$304$			6.00000i			0.344124i
$305$		0			0
$306$			2.00000i			0.114332i
$307$			22.8769i			1.30565i	0.757507	+	0.652827i	$0.226417\pi$
$307$			22.8769i			1.30565i	−0.757507	+	0.652827i	$0.773583\pi$
$308$	−16.0000			−0.911685
$309$	−4.87689			−0.277437
$310$		0			0
$311$	−24.4924			−1.38884			−0.694419	−	0.719571i	$-0.744339\pi$
$311$	−24.4924			−1.38884			−0.694419	+	0.719571i	$0.744339\pi$
$312$	3.56155	−	0.561553i	0.201633	−	0.0317917i
$313$	0.246211			0.0139167			0.00695834	−	0.999976i	$-0.497785\pi$
$313$	0.246211			0.0139167			0.00695834	+	0.999976i	$0.497785\pi$
$314$		−	3.36932i		−	0.190142i
$315$		0			0
$316$	−8.00000			−0.450035
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$		−	11.3693i		−	0.637560i
$319$			6.24621i			0.349721i
$320$		0			0
$321$	−8.00000			−0.446516
$322$	16.0000			0.891645
$323$		−	12.0000i		−	0.667698i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	1.12311			0.0622031
$327$			11.1231i			0.615109i
$328$	9.12311			0.503739
$329$	52.4924			2.89400
$330$		0			0
$331$			24.2462i			1.33269i	0.745643	+	0.666346i	$0.232143\pi$
$331$			24.2462i			1.33269i	−0.745643	+	0.666346i	$0.767857\pi$
$332$		−	10.2462i		−	0.562334i
$333$			3.12311i			0.171145i
$334$	−5.75379			−0.314833
$335$		0			0
$336$			5.12311i			0.279488i
$337$	−6.00000			−0.326841			−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000			−0.326841			−0.163420	+	0.986557i	$0.552253\pi$
$338$	4.00000	+	12.3693i	0.217571	+	0.672802i
$339$	−4.24621			−0.230623
$340$		0			0
$341$	−16.0000			−0.866449
$342$	6.00000			0.324443
$343$			62.7386i			3.38757i
$344$			10.2462i			0.552439i
$345$		0			0
$346$			14.8769i			0.799787i
$347$	−2.24621			−0.120583			−0.0602915	−	0.998181i	$-0.519203\pi$
$347$	−2.24621			−0.120583			−0.0602915	+	0.998181i	$0.519203\pi$
$348$	2.00000			0.107211
$349$			5.36932i			0.287413i	0.989620	+	0.143706i	$0.0459021\pi$
$349$			5.36932i			0.287413i	−0.989620	+	0.143706i	$0.954098\pi$
$350$		0			0
$351$	−0.561553	−	3.56155i	−0.0299735	−	0.190102i
$352$	3.12311			0.166462
$353$			4.24621i			0.226003i	0.993595	+	0.113002i	$0.0360465\pi$
$353$			4.24621i			0.226003i	−0.993595	+	0.113002i	$0.963954\pi$
$354$	7.12311			0.378589
$355$		0			0
$356$		−	5.12311i		−	0.271524i
$357$		−	10.2462i		−	0.542287i
$358$			16.4924i			0.871652i
$359$		−	34.2462i		−	1.80745i	−0.428118	−	0.903723i	$-0.640823\pi$
$359$		−	34.2462i		−	1.80745i	0.428118	−	0.903723i	$-0.359177\pi$
$360$		0			0
$361$	−17.0000			−0.894737
$362$			3.75379i			0.197295i
$363$	−1.24621			−0.0654091
$364$	−18.2462	+	2.87689i	−0.956361	+	0.150790i
$365$		0			0
$366$			10.0000i			0.522708i
$367$	−33.3693			−1.74186			−0.870932	−	0.491403i	$-0.836484\pi$
$367$	−33.3693			−1.74186			−0.870932	+	0.491403i	$0.836484\pi$
$368$	−3.12311			−0.162803
$369$		−	9.12311i		−	0.474930i
$370$		0			0
$371$			58.2462i			3.02399i
$372$			5.12311i			0.265621i
$373$	1.12311			0.0581522			0.0290761	−	0.999577i	$-0.490743\pi$
$373$	1.12311			0.0581522			0.0290761	+	0.999577i	$0.490743\pi$
$374$	−6.24621			−0.322984
$375$		0			0
$376$	−10.2462			−0.528408
$377$	1.12311	+	7.12311i	0.0578429	+	0.366859i
$378$	5.12311			0.263504
$379$			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
$381$	−4.87689			−0.249851
$382$			16.4924i			0.843826i
$383$			18.2462i			0.932338i	0.884696	+	0.466169i	$0.154366\pi$
$383$			18.2462i			0.932338i	−0.884696	+	0.466169i	$0.845634\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		0			0
$386$	−16.8769			−0.859011
$387$	10.2462			0.520844
$388$			4.87689i			0.247587i
$389$	16.2462			0.823716			0.411858	−	0.911248i	$-0.364880\pi$
$389$	16.2462			0.823716			0.411858	+	0.911248i	$0.364880\pi$
$390$		0			0
$391$	6.24621			0.315884
$392$		−	19.2462i		−	0.972080i
$393$	−4.00000			−0.201773
$394$	−0.246211			−0.0124039
$395$		0			0
$396$		−	3.12311i		−	0.156942i
$397$			9.36932i			0.470233i	0.971967	+	0.235116i	$0.0755471\pi$
$397$			9.36932i			0.470233i	−0.971967	+	0.235116i	$0.924453\pi$
$398$		−	1.75379i		−	0.0879095i
$399$	−30.7386			−1.53886
$400$		0			0
$401$		−	23.3693i		−	1.16701i	−0.812110	−	0.583504i	$-0.801681\pi$
$401$		−	23.3693i		−	1.16701i	0.812110	−	0.583504i	$-0.198319\pi$
$402$	−13.1231			−0.654521
$403$	−18.2462	+	2.87689i	−0.908909	+	0.143308i
$404$	−4.24621			−0.211257
$405$		0			0
$406$	−10.2462			−0.508511
$407$	−9.75379			−0.483477
$408$			2.00000i			0.0990148i
$409$			24.4924i			1.21107i	0.795818	+	0.605536i	$0.207041\pi$
$409$			24.4924i			1.21107i	−0.795818	+	0.605536i	$0.792959\pi$
$410$		0			0
$411$		−	22.4924i		−	1.10947i
$412$	−4.87689			−0.240267
$413$	−36.4924			−1.79567
$414$			3.12311i			0.153492i
$415$		0			0
$416$	3.56155	−	0.561553i	0.174619	−	0.0275324i
$417$	−16.4924			−0.807637
$418$			18.7386i			0.916537i
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$		0			0
$421$			25.3693i			1.23642i	0.786011	+	0.618212i	$0.212143\pi$
$421$			25.3693i			1.23642i	−0.786011	+	0.618212i	$0.787857\pi$
$422$		−	4.00000i		−	0.194717i
$423$			10.2462i			0.498188i
$424$		−	11.3693i		−	0.552143i
$425$		0			0
$426$	−6.24621			−0.302630
$427$		−	51.2311i		−	2.47924i
$428$	−8.00000			−0.386695
$429$	11.1231	−	1.75379i	0.537029	−	0.0846737i
$430$		0			0
$431$		−	0.492423i		−	0.0237192i	−0.999930	−	0.0118596i	$-0.996225\pi$
$431$		−	0.492423i		−	0.0237192i	0.999930	−	0.0118596i	$-0.00377511\pi$
$432$	−1.00000			−0.0481125
$433$	18.0000			0.865025			0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000			0.865025			0.432512	+	0.901628i	$0.357627\pi$
$434$		−	26.2462i		−	1.25986i
$435$		0			0
$436$			11.1231i			0.532700i
$437$		−	18.7386i		−	0.896390i
$438$	4.87689			0.233027
$439$	−3.50758			−0.167408			−0.0837038	−	0.996491i	$-0.526675\pi$
$439$	−3.50758			−0.167408			−0.0837038	+	0.996491i	$0.526675\pi$
$440$		0			0
$441$	−19.2462			−0.916486
$442$	−7.12311	+	1.12311i	−0.338812	+	0.0534207i
$443$	36.4924			1.73381			0.866904	−	0.498476i	$-0.166107\pi$
$443$	36.4924			1.73381			0.866904	+	0.498476i	$0.166107\pi$
$444$			3.12311i			0.148216i
$445$		0			0
$446$	−15.3693			−0.727758
$447$		−	14.0000i		−	0.662177i
$448$			5.12311i			0.242044i
$449$			37.1231i			1.75195i	0.482359	+	0.875974i	$0.339780\pi$
$449$			37.1231i			1.75195i	−0.482359	+	0.875974i	$0.660220\pi$
$450$		0			0
$451$	28.4924			1.34166
$452$	−4.24621			−0.199725
$453$		−	11.3693i		−	0.534177i
$454$	8.00000			0.375459
$455$		0			0
$456$	6.00000			0.280976
$457$			6.63068i			0.310170i	0.987901	+	0.155085i	$0.0495652\pi$
$457$			6.63068i			0.310170i	−0.987901	+	0.155085i	$0.950435\pi$
$458$	−3.12311			−0.145933
$459$	2.00000			0.0933520
$460$		0			0
$461$			14.4924i			0.674979i	0.941329	+	0.337490i	$0.109578\pi$
$461$			14.4924i			0.674979i	−0.941329	+	0.337490i	$0.890422\pi$
$462$			16.0000i			0.744387i
$463$			35.8617i			1.66664i	0.552794	+	0.833318i	$0.313562\pi$
$463$			35.8617i			1.66664i	−0.552794	+	0.833318i	$0.686438\pi$
$464$	2.00000			0.0928477
$465$		0			0
$466$		−	24.2462i		−	1.12318i
$467$	5.75379			0.266254			0.133127	−	0.991099i	$-0.457498\pi$
$467$	5.75379			0.266254			0.133127	+	0.991099i	$0.457498\pi$
$468$	−0.561553	−	3.56155i	−0.0259578	−	0.164633i
$469$	67.2311			3.10444
$470$		0			0
$471$	−3.36932			−0.155250
$472$	7.12311			0.327868
$473$			32.0000i			1.47136i
$474$			8.00000i			0.367452i
$475$		0			0
$476$		−	10.2462i		−	0.469634i
$477$	−11.3693			−0.520565
$478$	28.4924			1.30321
$479$		−	20.4924i		−	0.936323i	−0.883643	−	0.468161i	$-0.844917\pi$
$479$		−	20.4924i		−	0.936323i	0.883643	−	0.468161i	$-0.155083\pi$
$480$		0			0
$481$	−11.1231	+	1.75379i	−0.507170	+	0.0799659i
$482$	−2.24621			−0.102312
$483$		−	16.0000i		−	0.728025i
$484$	−1.24621			−0.0566460
$485$		0			0
$486$			1.00000i			0.0453609i
$487$		−	7.36932i		−	0.333936i	−0.985962	−	0.166968i	$-0.946602\pi$
$487$		−	7.36932i		−	0.333936i	0.985962	−	0.166968i	$-0.0533976\pi$
$488$			10.0000i			0.452679i
$489$		−	1.12311i		−	0.0507886i
$490$		0			0
$491$	−10.7386			−0.484628			−0.242314	−	0.970198i	$-0.577906\pi$
$491$	−10.7386			−0.484628			−0.242314	+	0.970198i	$0.577906\pi$
$492$		−	9.12311i		−	0.411301i
$493$	−4.00000			−0.180151
$494$	3.36932	+	21.3693i	0.151593	+	0.961451i
$495$		0			0
$496$			5.12311i			0.230034i
$497$	32.0000			1.43540
$498$	−10.2462			−0.459144
$499$		−	1.50758i		−	0.0674884i	−0.999431	−	0.0337442i	$-0.989257\pi$
$499$		−	1.50758i		−	0.0674884i	0.999431	−	0.0337442i	$-0.0107432\pi$
$500$		0			0
$501$			5.75379i			0.257060i
$502$		−	9.75379i		−	0.435333i
$503$	−10.6307			−0.473999			−0.236999	−	0.971510i	$-0.576164\pi$
$503$	−10.6307			−0.473999			−0.236999	+	0.971510i	$0.576164\pi$
$504$	5.12311			0.228201
$505$		0			0
$506$	−9.75379			−0.433609
$507$	12.3693	−	4.00000i	0.549341	−	0.177646i
$508$	−4.87689			−0.216377
$509$		−	15.7538i		−	0.698274i	−0.937072	−	0.349137i	$-0.886475\pi$
$509$		−	15.7538i		−	0.698274i	0.937072	−	0.349137i	$-0.113525\pi$
$510$		0			0
$511$	−24.9848			−1.10526
$512$		−	1.00000i		−	0.0441942i
$513$		−	6.00000i		−	0.264906i
$514$			4.24621i			0.187292i
$515$		0			0
$516$	10.2462			0.451064
$517$	−32.0000			−1.40736
$518$		−	16.0000i		−	0.703000i
$519$	14.8769			0.653023
$520$		0			0
$521$	−16.2462			−0.711759			−0.355880	−	0.934532i	$-0.615819\pi$
$521$	−16.2462			−0.711759			−0.355880	+	0.934532i	$0.615819\pi$
$522$		−	2.00000i		−	0.0875376i
$523$	−22.7386			−0.994291			−0.497146	−	0.867667i	$-0.665618\pi$
$523$	−22.7386			−0.994291			−0.497146	+	0.867667i	$0.665618\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$		−	2.63068i		−	0.114703i
$527$		−	10.2462i		−	0.446332i
$528$		−	3.12311i		−	0.135916i
$529$	−13.2462			−0.575922
$530$		0			0
$531$		−	7.12311i		−	0.309116i
$532$	−30.7386			−1.33269
$533$	32.4924	−	5.12311i	1.40740	−	0.221906i
$534$	−5.12311			−0.221698
$535$		0			0
$536$	−13.1231			−0.566832
$537$	16.4924			0.711701
$538$		−	0.246211i		−	0.0106149i
$539$		−	60.1080i		−	2.58903i
$540$		0			0
$541$		−	19.1231i		−	0.822167i	−0.911598	−	0.411083i	$-0.865151\pi$
$541$		−	19.1231i		−	0.822167i	0.911598	−	0.411083i	$-0.134849\pi$
$542$	−14.8769			−0.639017
$543$	3.75379			0.161090
$544$			2.00000i			0.0857493i
$545$		0			0
$546$	2.87689	+	18.2462i	0.123120	+	0.780866i
$547$	44.9848			1.92341			0.961707	−	0.274081i	$-0.0883737\pi$
$547$	44.9848			1.92341			0.961707	+	0.274081i	$0.0883737\pi$
$548$		−	22.4924i		−	0.960829i
$549$	10.0000			0.426790
$550$		0			0
$551$			12.0000i			0.511217i
$552$			3.12311i			0.132928i
$553$		−	40.9848i		−	1.74285i
$554$			27.8617i			1.18373i
$555$		0			0
$556$	−16.4924			−0.699435
$557$			28.2462i			1.19683i	0.801186	+	0.598415i	$0.204203\pi$
$557$			28.2462i			1.19683i	−0.801186	+	0.598415i	$0.795797\pi$
$558$	5.12311			0.216878
$559$	5.75379	+	36.4924i	0.243359	+	1.54347i
$560$		0			0
$561$			6.24621i			0.263715i
$562$	−5.12311			−0.216105
$563$	−32.9848			−1.39015			−0.695073	−	0.718939i	$-0.744628\pi$
$563$	−32.9848			−1.39015			−0.695073	+	0.718939i	$0.744628\pi$
$564$			10.2462i			0.431443i
$565$		0			0
$566$		−	4.00000i		−	0.168133i
$567$		−	5.12311i		−	0.215150i
$568$	−6.24621			−0.262085
$569$	36.7386			1.54016			0.770082	−	0.637945i	$-0.220215\pi$
$569$	36.7386			1.54016			0.770082	+	0.637945i	$0.220215\pi$
$570$		0			0
$571$	24.4924			1.02498			0.512488	−	0.858694i	$-0.328724\pi$
$571$	24.4924			1.02498			0.512488	+	0.858694i	$0.328724\pi$
$572$	11.1231	−	1.75379i	0.465080	−	0.0733296i
$573$	16.4924			0.688981
$574$			46.7386i			1.95083i
$575$		0			0
$576$	−1.00000			−0.0416667
$577$			2.63068i			0.109517i	0.998500	+	0.0547584i	$0.0174389\pi$
$577$			2.63068i			0.109517i	−0.998500	+	0.0547584i	$0.982561\pi$
$578$			13.0000i			0.540729i
$579$			16.8769i			0.701380i
$580$		0			0
$581$	52.4924			2.17775
$582$	4.87689			0.202154
$583$		−	35.5076i		−	1.47057i
$584$	4.87689			0.201807
$585$		0			0
$586$	−20.7386			−0.856705
$587$			16.4924i			0.680715i	0.940296	+	0.340358i	$0.110548\pi$
$587$			16.4924i			0.680715i	−0.940296	+	0.340358i	$0.889452\pi$
$588$	−19.2462			−0.793700
$589$	−30.7386			−1.26656
$590$		0			0
$591$			0.246211i			0.0101278i
$592$			3.12311i			0.128359i
$593$		−	38.4924i		−	1.58069i	−0.612659	−	0.790347i	$-0.709900\pi$
$593$		−	38.4924i		−	1.58069i	0.612659	−	0.790347i	$-0.290100\pi$
$594$	−3.12311			−0.128143
$595$		0			0
$596$		−	14.0000i		−	0.573462i
$597$	−1.75379			−0.0717778
$598$	−11.1231	+	1.75379i	−0.454858	+	0.0717178i
$599$	−3.50758			−0.143316			−0.0716579	−	0.997429i	$-0.522829\pi$
$599$	−3.50758			−0.143316			−0.0716579	+	0.997429i	$0.522829\pi$
$600$		0			0
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$	−52.4924			−2.13943
$603$			13.1231i			0.534414i
$604$		−	11.3693i		−	0.462611i
$605$		0			0
$606$			4.24621i			0.172491i
$607$	9.36932			0.380289			0.190144	−	0.981756i	$-0.439104\pi$
$607$	9.36932			0.380289			0.190144	+	0.981756i	$0.439104\pi$
$608$	6.00000			0.243332
$609$			10.2462i			0.415197i
$610$		0			0
$611$	−36.4924	+	5.75379i	−1.47633	+	0.232773i
$612$	2.00000			0.0808452
$613$			14.6307i			0.590928i	0.955354	+	0.295464i	$0.0954742\pi$
$613$			14.6307i			0.590928i	−0.955354	+	0.295464i	$0.904526\pi$
$614$	22.8769			0.923236
$615$		0			0
$616$			16.0000i			0.644658i
$617$			8.73863i			0.351804i	0.984408	+	0.175902i	$0.0562842\pi$
$617$			8.73863i			0.351804i	−0.984408	+	0.175902i	$0.943716\pi$
$618$			4.87689i			0.196177i
$619$			26.9848i			1.08461i	0.840181	+	0.542306i	$0.182449\pi$
$619$			26.9848i			1.08461i	−0.840181	+	0.542306i	$0.817551\pi$
$620$		0			0
$621$	3.12311			0.125326
$622$			24.4924i			0.982057i
$623$	26.2462			1.05153
$624$	−0.561553	−	3.56155i	−0.0224801	−	0.142576i
$625$		0			0
$626$		−	0.246211i		−	0.00984058i
$627$	18.7386			0.748349
$628$	−3.36932			−0.134450
$629$		−	6.24621i		−	0.249053i
$630$		0			0
$631$		−	5.61553i		−	0.223551i	−0.993734	−	0.111775i	$-0.964346\pi$
$631$		−	5.61553i		−	0.223551i	0.993734	−	0.111775i	$-0.0356537\pi$
$632$			8.00000i			0.318223i
$633$	−4.00000			−0.158986
$634$	6.00000			0.238290
$635$		0			0
$636$	−11.3693			−0.450823
$637$	−10.8078	−	68.5464i	−0.428219	−	2.71591i
$638$	6.24621			0.247290
$639$			6.24621i			0.247096i
$640$		0			0
$641$	−2.00000			−0.0789953			−0.0394976	−	0.999220i	$-0.512576\pi$
$641$	−2.00000			−0.0789953			−0.0394976	+	0.999220i	$0.512576\pi$
$642$			8.00000i			0.315735i
$643$		−	7.36932i		−	0.290617i	−0.989386	−	0.145309i	$-0.953582\pi$
$643$		−	7.36932i		−	0.290617i	0.989386	−	0.145309i	$-0.0464175\pi$
$644$		−	16.0000i		−	0.630488i
$645$		0			0
$646$	−12.0000			−0.472134
$647$	11.6155			0.456654			0.228327	−	0.973585i	$-0.426675\pi$
$647$	11.6155			0.456654			0.228327	+	0.973585i	$0.426675\pi$
$648$			1.00000i			0.0392837i
$649$	22.2462			0.873240
$650$		0			0
$651$	−26.2462			−1.02867
$652$		−	1.12311i		−	0.0439842i
$653$	−43.8617			−1.71644			−0.858221	−	0.513280i	$-0.828430\pi$
$653$	−43.8617			−1.71644			−0.858221	+	0.513280i	$0.828430\pi$
$654$	11.1231			0.434948
$655$		0			0
$656$		−	9.12311i		−	0.356197i
$657$		−	4.87689i		−	0.190266i
$658$		−	52.4924i		−	2.04637i
$659$	−38.2462			−1.48986			−0.744930	−	0.667142i	$-0.767517\pi$
$659$	−38.2462			−1.48986			−0.744930	+	0.667142i	$0.767517\pi$
$660$		0			0
$661$		−	0.876894i		−	0.0341072i	−0.999855	−	0.0170536i	$-0.994571\pi$
$661$		−	0.876894i		−	0.0341072i	0.999855	−	0.0170536i	$-0.00542860\pi$
$662$	24.2462			0.942356
$663$	1.12311	+	7.12311i	0.0436178	+	0.276638i
$664$	−10.2462			−0.397630
$665$		0			0
$666$	3.12311			0.121018
$667$	−6.24621			−0.241854
$668$			5.75379i			0.222621i
$669$			15.3693i			0.594212i
$670$		0			0
$671$			31.2311i			1.20566i
$672$	5.12311			0.197628
$673$	38.9848			1.50276			0.751378	−	0.659872i	$-0.229390\pi$
$673$	38.9848			1.50276			0.751378	+	0.659872i	$0.229390\pi$
$674$			6.00000i			0.231111i
$675$		0			0
$676$	12.3693	−	4.00000i	0.475743	−	0.153846i
$677$	−21.1231			−0.811827			−0.405913	−	0.913912i	$-0.633047\pi$
$677$	−21.1231			−0.811827			−0.405913	+	0.913912i	$0.633047\pi$
$678$			4.24621i			0.163075i
$679$	−24.9848			−0.958830
$680$		0			0
$681$		−	8.00000i		−	0.306561i
$682$			16.0000i			0.612672i
$683$			48.9848i			1.87435i	0.348856	+	0.937177i	$0.386570\pi$
$683$			48.9848i			1.87435i	−0.348856	+	0.937177i	$0.613430\pi$
$684$		−	6.00000i		−	0.229416i
$685$		0			0
$686$	62.7386			2.39537
$687$			3.12311i			0.119154i
$688$	10.2462			0.390633
$689$	−6.38447	−	40.4924i	−0.243229	−	1.54264i
$690$		0			0
$691$			20.7386i			0.788935i	0.918910	+	0.394467i	$0.129071\pi$
$691$			20.7386i			0.788935i	−0.918910	+	0.394467i	$0.870929\pi$
$692$	14.8769			0.565535
$693$	16.0000			0.607790
$694$			2.24621i			0.0852650i
$695$		0			0
$696$		−	2.00000i		−	0.0758098i
$697$			18.2462i			0.691125i
$698$	5.36932			0.203232
$699$	−24.2462			−0.917076
$700$		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
$703$	−18.7386			−0.706741
$704$		−	3.12311i		−	0.117706i
$705$		0			0
$706$	4.24621			0.159808
$707$		−	21.7538i		−	0.818135i
$708$		−	7.12311i		−	0.267703i
$709$		−	39.6155i		−	1.48779i	−0.668295	−	0.743896i	$-0.732976\pi$
$709$		−	39.6155i		−	1.48779i	0.668295	−	0.743896i	$-0.267024\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	−5.12311			−0.191997
$713$		−	16.0000i		−	0.599205i
$714$	−10.2462			−0.383455
$715$		0			0
$716$	16.4924			0.616351
$717$		−	28.4924i		−	1.06407i
$718$	−34.2462			−1.27806
$719$	−20.0000			−0.745874			−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000			−0.745874			−0.372937	+	0.927857i	$0.621649\pi$
$720$		0			0
$721$		−	24.9848i		−	0.930484i
$722$			17.0000i			0.632674i
$723$			2.24621i			0.0835375i
$724$	3.75379			0.139508
$725$		0			0
$726$			1.24621i			0.0462512i
$727$	37.8617			1.40421			0.702107	−	0.712071i	$-0.252243\pi$
$727$	37.8617			1.40421			0.702107	+	0.712071i	$0.252243\pi$
$728$	2.87689	+	18.2462i	0.106625	+	0.676250i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−20.4924			−0.757940
$732$	10.0000			0.369611
$733$			10.6307i			0.392653i	0.980539	+	0.196327i	$0.0629013\pi$
$733$			10.6307i			0.392653i	−0.980539	+	0.196327i	$0.937099\pi$
$734$			33.3693i			1.23168i
$735$		0			0
$736$			3.12311i			0.115119i
$737$	−40.9848			−1.50970
$738$	−9.12311			−0.335826
$739$		−	45.2311i		−	1.66385i	−0.554887	−	0.831926i	$-0.687239\pi$
$739$		−	45.2311i		−	1.66385i	0.554887	−	0.831926i	$-0.312761\pi$
$740$		0			0
$741$	21.3693	−	3.36932i	0.785021	−	0.123775i
$742$	58.2462			2.13829
$743$		−	16.0000i		−	0.586983i	−0.955962	−	0.293492i	$-0.905183\pi$
$743$		−	16.0000i		−	0.586983i	0.955962	−	0.293492i	$-0.0948173\pi$
$744$	5.12311			0.187822
$745$		0			0
$746$		−	1.12311i		−	0.0411198i
$747$			10.2462i			0.374889i
$748$			6.24621i			0.228384i
$749$		−	40.9848i		−	1.49755i
$750$		0			0
$751$	−9.75379			−0.355921			−0.177960	−	0.984038i	$-0.556950\pi$
$751$	−9.75379			−0.355921			−0.177960	+	0.984038i	$0.556950\pi$
$752$			10.2462i			0.373641i
$753$	−9.75379			−0.355448
$754$	7.12311	−	1.12311i	0.259408	−	0.0409011i
$755$		0			0
$756$		−	5.12311i		−	0.186326i
$757$	−5.12311			−0.186202			−0.0931012	−	0.995657i	$-0.529678\pi$
$757$	−5.12311			−0.186202			−0.0931012	+	0.995657i	$0.529678\pi$
$758$	6.00000			0.217930
$759$			9.75379i			0.354040i
$760$		0			0
$761$		−	5.12311i		−	0.185712i	−0.995680	−	0.0928562i	$-0.970400\pi$
$761$		−	5.12311i		−	0.185712i	0.995680	−	0.0928562i	$-0.0295997\pi$
$762$			4.87689i			0.176671i
$763$	−56.9848			−2.06299
$764$	16.4924			0.596675
$765$		0			0
$766$	18.2462			0.659262
$767$	25.3693	−	4.00000i	0.916033	−	0.144432i
$768$	−1.00000			−0.0360844
$769$		−	32.9848i		−	1.18946i	−0.803924	−	0.594732i	$-0.797258\pi$
$769$		−	32.9848i		−	1.18946i	0.803924	−	0.594732i	$-0.202742\pi$
$770$		0			0
$771$	4.24621			0.152924
$772$			16.8769i			0.607413i
$773$			0.246211i			0.00885560i	0.999990	+	0.00442780i	$0.00140942\pi$
$773$			0.246211i			0.00885560i	−0.999990	+	0.00442780i	$0.998591\pi$
$774$		−	10.2462i		−	0.368292i
$775$		0			0
$776$	4.87689			0.175070
$777$	−16.0000			−0.573997
$778$		−	16.2462i		−	0.582455i
$779$	54.7386			1.96122
$780$		0			0
$781$	−19.5076			−0.698036
$782$		−	6.24621i		−	0.223364i
$783$	−2.00000			−0.0714742
$784$	−19.2462			−0.687365
$785$		0			0
$786$			4.00000i			0.142675i
$787$		−	53.6155i		−	1.91119i	−0.294688	−	0.955594i	$-0.595216\pi$
$787$		−	53.6155i		−	1.91119i	0.294688	−	0.955594i	$-0.404784\pi$
$788$			0.246211i			0.00877091i
$789$	−2.63068			−0.0936548
$790$		0			0
$791$		−	21.7538i		−	0.773476i
$792$	−3.12311			−0.110975
$793$	5.61553	+	35.6155i	0.199413	+	1.26474i
$794$	9.36932			0.332505
$795$		0			0
$796$	−1.75379			−0.0621614
$797$	31.8617			1.12860			0.564300	−	0.825570i	$-0.309146\pi$
$797$	31.8617			1.12860			0.564300	+	0.825570i	$0.309146\pi$
$798$			30.7386i			1.08814i
$799$		−	20.4924i		−	0.724970i
$800$		0			0
$801$			5.12311i			0.181016i
$802$	−23.3693			−0.825199
$803$	15.2311			0.537492
$804$			13.1231i			0.462816i
$805$		0			0
$806$	2.87689	+	18.2462i	0.101334	+	0.642695i
$807$	−0.246211			−0.00866705
$808$			4.24621i			0.149381i
$809$	−46.4924			−1.63459			−0.817293	−	0.576222i	$-0.804526\pi$
$809$	−46.4924			−1.63459			−0.817293	+	0.576222i	$0.804526\pi$
$810$		0			0
$811$			44.2462i			1.55369i	0.629689	+	0.776847i	$0.283182\pi$
$811$			44.2462i			1.55369i	−0.629689	+	0.776847i	$0.716818\pi$
$812$			10.2462i			0.359572i
$813$			14.8769i			0.521755i
$814$			9.75379i			0.341870i
$815$		0			0
$816$	2.00000			0.0700140
$817$			61.4773i			2.15082i
$818$	24.4924			0.856357
$819$	18.2462	−	2.87689i	0.637574	−	0.100527i
$820$		0			0
$821$		−	27.7538i		−	0.968614i	−0.874898	−	0.484307i	$-0.839072\pi$
$821$		−	27.7538i		−	0.968614i	0.874898	−	0.484307i	$-0.160928\pi$
$822$	−22.4924			−0.784513
$823$	51.1231			1.78204			0.891020	−	0.453965i	$-0.149991\pi$
$823$	51.1231			1.78204			0.891020	+	0.453965i	$0.149991\pi$
$824$			4.87689i			0.169895i
$825$		0			0
$826$			36.4924i			1.26973i
$827$			50.7386i			1.76436i	0.470917	+	0.882178i	$0.343923\pi$
$827$			50.7386i			1.76436i	−0.470917	+	0.882178i	$0.656077\pi$
$828$	3.12311			0.108535
$829$	−7.75379			−0.269300			−0.134650	−	0.990893i	$-0.542991\pi$
$829$	−7.75379			−0.269300			−0.134650	+	0.990893i	$0.542991\pi$
$830$		0			0
$831$	27.8617			0.966513
$832$	−0.561553	−	3.56155i	−0.0194683	−	0.123475i
$833$	38.4924			1.33368
$834$			16.4924i			0.571086i
$835$		0			0
$836$	18.7386			0.648089
$837$		−	5.12311i		−	0.177080i
$838$			28.0000i			0.967244i
$839$		−	2.73863i		−	0.0945481i	−0.998882	−	0.0472741i	$-0.984947\pi$
$839$		−	2.73863i		−	0.0945481i	0.998882	−	0.0472741i	$-0.0150534\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	25.3693			0.874284
$843$			5.12311i			0.176449i
$844$	−4.00000			−0.137686
$845$		0			0
$846$	10.2462			0.352272
$847$		−	6.38447i		−	0.219373i
$848$	−11.3693			−0.390424
$849$	−4.00000			−0.137280
$850$		0			0
$851$		−	9.75379i		−	0.334356i
$852$			6.24621i			0.213992i
$853$		−	21.8617i		−	0.748532i	−0.927321	−	0.374266i	$-0.877895\pi$
$853$		−	21.8617i		−	0.748532i	0.927321	−	0.374266i	$-0.122105\pi$
$854$	−51.2311			−1.75309
$855$		0			0
$856$			8.00000i			0.273434i
$857$	−2.49242			−0.0851395			−0.0425698	−	0.999093i	$-0.513554\pi$
$857$	−2.49242			−0.0851395			−0.0425698	+	0.999093i	$0.513554\pi$
$858$	−1.75379	−	11.1231i	−0.0598734	−	0.379737i
$859$	−12.0000			−0.409435			−0.204717	−	0.978821i	$-0.565628\pi$
$859$	−12.0000			−0.409435			−0.204717	+	0.978821i	$0.565628\pi$
$860$		0			0
$861$	46.7386			1.59285
$862$	−0.492423			−0.0167720
$863$			10.2462i			0.348785i	0.984676	+	0.174393i	$0.0557962\pi$
$863$			10.2462i			0.348785i	−0.984676	+	0.174393i	$0.944204\pi$
$864$			1.00000i			0.0340207i
$865$		0			0
$866$		−	18.0000i		−	0.611665i
$867$	13.0000			0.441503
$868$	−26.2462			−0.890854
$869$			24.9848i			0.847553i
$870$		0			0
$871$	−46.7386	+	7.36932i	−1.58368	+	0.249700i
$872$	11.1231			0.376676
$873$		−	4.87689i		−	0.165058i
$874$	−18.7386			−0.633844
$875$		0			0
$876$		−	4.87689i		−	0.164775i
$877$		−	27.1231i		−	0.915882i	−0.888983	−	0.457941i	$-0.848587\pi$
$877$		−	27.1231i		−	0.915882i	0.888983	−	0.457941i	$-0.151413\pi$
$878$			3.50758i			0.118375i
$879$			20.7386i			0.699497i
$880$		0			0
$881$	11.7538			0.395995			0.197998	−	0.980203i	$-0.436556\pi$
$881$	11.7538			0.395995			0.197998	+	0.980203i	$0.436556\pi$
$882$			19.2462i			0.648054i
$883$	26.2462			0.883255			0.441628	−	0.897198i	$-0.354401\pi$
$883$	26.2462			0.883255			0.441628	+	0.897198i	$0.354401\pi$
$884$	1.12311	+	7.12311i	0.0377741	+	0.239576i
$885$		0			0
$886$		−	36.4924i		−	1.22599i
$887$	27.1231			0.910705			0.455352	−	0.890311i	$-0.349513\pi$
$887$	27.1231			0.910705			0.455352	+	0.890311i	$0.349513\pi$
$888$	3.12311			0.104805
$889$		−	24.9848i		−	0.837965i
$890$		0			0
$891$			3.12311i			0.104628i
$892$			15.3693i			0.514603i
$893$	−61.4773			−2.05726
$894$	−14.0000			−0.468230
$895$		0			0
$896$	5.12311			0.171151
$897$	1.75379	+	11.1231i	0.0585573	+	0.371390i
$898$	37.1231			1.23881
$899$			10.2462i			0.341730i
$900$		0			0
$901$	22.7386			0.757534
$902$		−	28.4924i		−	0.948694i
$903$			52.4924i			1.74684i
$904$			4.24621i			0.141227i
$905$		0			0
$906$	−11.3693			−0.377720
$907$	−42.2462			−1.40276			−0.701381	−	0.712786i	$-0.747433\pi$
$907$	−42.2462			−1.40276			−0.701381	+	0.712786i	$0.747433\pi$
$908$		−	8.00000i		−	0.265489i
$909$	4.24621			0.140838
$910$		0			0
$911$	4.00000			0.132526			0.0662630	−	0.997802i	$-0.478892\pi$
$911$	4.00000			0.132526			0.0662630	+	0.997802i	$0.478892\pi$
$912$		−	6.00000i		−	0.198680i
$913$	−32.0000			−1.05905
$914$	6.63068			0.219324
$915$		0			0
$916$			3.12311i			0.103190i
$917$		−	20.4924i		−	0.676719i
$918$		−	2.00000i		−	0.0660098i
$919$	−38.2462			−1.26163			−0.630813	−	0.775935i	$-0.717279\pi$
$919$	−38.2462			−1.26163			−0.630813	+	0.775935i	$0.717279\pi$
$920$		0			0
$921$		−	22.8769i		−	0.753819i
$922$	14.4924			0.477283
$923$	−22.2462	+	3.50758i	−0.732243	+	0.115453i
$924$	16.0000			0.526361
$925$		0			0
$926$	35.8617			1.17849
$927$	4.87689			0.160178
$928$		−	2.00000i		−	0.0656532i
$929$			46.1080i			1.51275i	0.654137	+	0.756376i	$0.273032\pi$
$929$			46.1080i			1.51275i	−0.654137	+	0.756376i	$0.726968\pi$
$930$		0			0
$931$		−	115.477i		−	3.78461i
$932$	−24.2462			−0.794211
$933$	24.4924			0.801846
$934$		−	5.75379i		−	0.188270i
$935$		0			0
$936$	−3.56155	+	0.561553i	−0.116413	+	0.0183549i
$937$	3.75379			0.122631			0.0613155	−	0.998118i	$-0.480470\pi$
$937$	3.75379			0.122631			0.0613155	+	0.998118i	$0.480470\pi$
$938$		−	67.2311i		−	2.19517i
$939$	−0.246211			−0.00803480
$940$		0			0
$941$			14.0000i			0.456387i	0.973616	+	0.228193i	$0.0732819\pi$
$941$			14.0000i			0.456387i	−0.973616	+	0.228193i	$0.926718\pi$
$942$			3.36932i			0.109778i
$943$			28.4924i			0.927841i
$944$		−	7.12311i		−	0.231837i
$945$		0			0
$946$	32.0000			1.04041
$947$		−	24.4924i		−	0.795897i	−0.917408	−	0.397948i	$-0.869722\pi$
$947$		−	24.4924i		−	0.795897i	0.917408	−	0.397948i	$-0.130278\pi$
$948$	8.00000			0.259828
$949$	17.3693	−	2.73863i	0.563832	−	0.0888998i
$950$		0			0
$951$		−	6.00000i		−	0.194563i
$952$	−10.2462			−0.332082
$953$	42.9848			1.39242			0.696208	−	0.717840i	$-0.254869\pi$
$953$	42.9848			1.39242			0.696208	+	0.717840i	$0.254869\pi$
$954$			11.3693i			0.368095i
$955$		0			0
$956$		−	28.4924i		−	0.921511i
$957$		−	6.24621i		−	0.201911i
$958$	−20.4924			−0.662080
$959$	115.231			3.72100
$960$		0			0
$961$	4.75379			0.153348
$962$	1.75379	+	11.1231i	0.0565444	+	0.358623i
$963$	8.00000			0.257796
$964$			2.24621i			0.0723456i
$965$		0			0
$966$	−16.0000			−0.514792
$967$		−	6.38447i		−	0.205311i	−0.994717	−	0.102655i	$-0.967266\pi$
$967$		−	6.38447i		−	0.205311i	0.994717	−	0.102655i	$-0.0327339\pi$
$968$			1.24621i			0.0400547i
$969$			12.0000i			0.385496i
$970$		0			0
$971$	54.2462			1.74084			0.870422	−	0.492307i	$-0.163846\pi$
$971$	54.2462			1.74084			0.870422	+	0.492307i	$0.163846\pi$
$972$	1.00000			0.0320750
$973$		−	84.4924i		−	2.70870i
$974$	−7.36932			−0.236128
$975$		0			0
$976$	10.0000			0.320092
$977$			44.7386i			1.43132i	0.698451	+	0.715658i	$0.253873\pi$
$977$			44.7386i			1.43132i	−0.698451	+	0.715658i	$0.746127\pi$
$978$	−1.12311			−0.0359130
$979$	−16.0000			−0.511362
$980$		0			0
$981$		−	11.1231i		−	0.355133i
$982$			10.7386i			0.342684i
$983$		−	27.5076i		−	0.877355i	−0.898644	−	0.438678i	$-0.855447\pi$
$983$		−	27.5076i		−	0.877355i	0.898644	−	0.438678i	$-0.144553\pi$
$984$	−9.12311			−0.290834
$985$		0			0
$986$			4.00000i			0.127386i
$987$	−52.4924			−1.67085
$988$	21.3693	−	3.36932i	0.679849	−	0.107192i
$989$	−32.0000			−1.01754
$990$		0			0
$991$	18.7386			0.595252			0.297626	−	0.954682i	$-0.403805\pi$
$991$	18.7386			0.595252			0.297626	+	0.954682i	$0.403805\pi$
$992$	5.12311			0.162659
$993$		−	24.2462i		−	0.769430i
$994$		−	32.0000i		−	1.01498i
$995$		0			0
$996$			10.2462i			0.324664i
$997$	52.3542			1.65807			0.829036	−	0.559195i	$-0.188890\pi$
$997$	52.3542			1.65807			0.829036	+	0.559195i	$0.188890\pi$
$998$	−1.50758			−0.0477215
$999$		−	3.12311i		−	0.0988107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.b.h.1351.1		4
5.2	odd	4		1950.2.f.o.649.4		4
5.3	odd	4		1950.2.f.l.649.1		4
5.4	even	2		390.2.b.d.181.4	yes	4
13.12	even	2	inner	1950.2.b.h.1351.4		4
15.14	odd	2		1170.2.b.f.181.2		4
20.19	odd	2		3120.2.g.o.961.1		4
65.12	odd	4		1950.2.f.l.649.3		4
65.34	odd	4		5070.2.a.bd.1.2		2
65.38	odd	4		1950.2.f.o.649.2		4
65.44	odd	4		5070.2.a.bh.1.1		2
65.64	even	2		390.2.b.d.181.1	✓	4
195.194	odd	2		1170.2.b.f.181.3		4
260.259	odd	2		3120.2.g.o.961.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.b.d.181.1	✓	4	65.64	even	2
390.2.b.d.181.4	yes	4	5.4	even	2
1170.2.b.f.181.2		4	15.14	odd	2
1170.2.b.f.181.3		4	195.194	odd	2
1950.2.b.h.1351.1		4	1.1	even	1	trivial
1950.2.b.h.1351.4		4	13.12	even	2	inner
1950.2.f.l.649.1		4	5.3	odd	4
1950.2.f.l.649.3		4	65.12	odd	4
1950.2.f.o.649.2		4	65.38	odd	4
1950.2.f.o.649.4		4	5.2	odd	4
3120.2.g.o.961.1		4	20.19	odd	2
3120.2.g.o.961.4		4	260.259	odd	2
5070.2.a.bd.1.2		2	65.34	odd	4
5070.2.a.bh.1.1		2	65.44	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{6} -5.12311i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{6} -5.12311i q^{7} +1.00000i q^{8} +1.00000 q^{9} +3.12311i q^{11} +1.00000 q^{12} +(0.561553 + 3.56155i) q^{13} -5.12311 q^{14} +1.00000 q^{16} -2.00000 q^{17} -1.00000i q^{18} +6.00000i q^{19} +5.12311i q^{21} +3.12311 q^{22} -3.12311 q^{23} -1.00000i q^{24} +(3.56155 - 0.561553i) q^{26} -1.00000 q^{27} +5.12311i q^{28} +2.00000 q^{29} +5.12311i q^{31} -1.00000i q^{32} -3.12311i q^{33} +2.00000i q^{34} -1.00000 q^{36} +3.12311i q^{37} +6.00000 q^{38} +(-0.561553 - 3.56155i) q^{39} -9.12311i q^{41} +5.12311 q^{42} +10.2462 q^{43} -3.12311i q^{44} +3.12311i q^{46} +10.2462i q^{47} -1.00000 q^{48} -19.2462 q^{49} +2.00000 q^{51} +(-0.561553 - 3.56155i) q^{52} -11.3693 q^{53} +1.00000i q^{54} +5.12311 q^{56} -6.00000i q^{57} -2.00000i q^{58} -7.12311i q^{59} +10.0000 q^{61} +5.12311 q^{62} -5.12311i q^{63} -1.00000 q^{64} -3.12311 q^{66} +13.1231i q^{67} +2.00000 q^{68} +3.12311 q^{69} +6.24621i q^{71} +1.00000i q^{72} -4.87689i q^{73} +3.12311 q^{74} -6.00000i q^{76} +16.0000 q^{77} +(-3.56155 + 0.561553i) q^{78} +8.00000 q^{79} +1.00000 q^{81} -9.12311 q^{82} +10.2462i q^{83} -5.12311i q^{84} -10.2462i q^{86} -2.00000 q^{87} -3.12311 q^{88} +5.12311i q^{89} +(18.2462 - 2.87689i) q^{91} +3.12311 q^{92} -5.12311i q^{93} +10.2462 q^{94} +1.00000i q^{96} -4.87689i q^{97} +19.2462i q^{98} +3.12311i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 4 * q^4 + 4 * q^9	\( 4 q - 4 q^{3} - 4 q^{4} + 4 q^{9} + 4 q^{12} - 6 q^{13} - 4 q^{14} + 4 q^{16} - 8 q^{17} - 4 q^{22} + 4 q^{23} + 6 q^{26} - 4 q^{27} + 8 q^{29} - 4 q^{36} + 24 q^{38} + 6 q^{39} + 4 q^{42} + 8 q^{43} - 4 q^{48} - 44 q^{49} + 8 q^{51} + 6 q^{52} + 4 q^{53} + 4 q^{56} + 40 q^{61} + 4 q^{62} - 4 q^{64} + 4 q^{66} + 8 q^{68} - 4 q^{69} - 4 q^{74} + 64 q^{77} - 6 q^{78} + 32 q^{79} + 4 q^{81} - 20 q^{82} - 8 q^{87} + 4 q^{88} + 40 q^{91} - 4 q^{92} + 8 q^{94}+O(q^{100}) \) 4 * q - 4 * q^3 - 4 * q^4 + 4 * q^9 + 4 * q^12 - 6 * q^13 - 4 * q^14 + 4 * q^16 - 8 * q^17 - 4 * q^22 + 4 * q^23 + 6 * q^26 - 4 * q^27 + 8 * q^29 - 4 * q^36 + 24 * q^38 + 6 * q^39 + 4 * q^42 + 8 * q^43 - 4 * q^48 - 44 * q^49 + 8 * q^51 + 6 * q^52 + 4 * q^53 + 4 * q^56 + 40 * q^61 + 4 * q^62 - 4 * q^64 + 4 * q^66 + 8 * q^68 - 4 * q^69 - 4 * q^74 + 64 * q^77 - 6 * q^78 + 32 * q^79 + 4 * q^81 - 20 * q^82 - 8 * q^87 + 4 * q^88 + 40 * q^91 - 4 * q^92 + 8 * q^94

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