LMFDB - Embedded newform 1183.2.c.h.337.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 96x^{8} + 266x^{6} + 332x^{4} + 141x^{2} + 1 $ x^12 + 16x^10 + 96x^8 + 266x^6 + 332x^4 + 141*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.9
Root			$0.0849355i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.h.337.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.90785i q^{2} -1.08494 q^{3} -1.63989 q^{4} -1.10591i q^{5} -2.06989i q^{6} -1.00000i q^{7} +0.687029i q^{8} -1.82292 q^{9} +O(q^{10})$	\(q+1.90785i q^{2} -1.08494 q^{3} -1.63989 q^{4} -1.10591i q^{5} -2.06989i q^{6} -1.00000i q^{7} +0.687029i q^{8} -1.82292 q^{9} +2.10992 q^{10} +0.799816i q^{11} +1.77918 q^{12} +1.90785 q^{14} +1.19984i q^{15} -4.59054 q^{16} -2.63979 q^{17} -3.47785i q^{18} -1.84186i q^{19} +1.81358i q^{20} +1.08494i q^{21} -1.52593 q^{22} +3.82692 q^{23} -0.745382i q^{24} +3.77696 q^{25} +5.23255 q^{27} +1.63989i q^{28} -7.54322 q^{29} -2.28912 q^{30} -7.86730i q^{31} -7.38400i q^{32} -0.867749i q^{33} -5.03633i q^{34} -1.10591 q^{35} +2.98939 q^{36} -3.45786i q^{37} +3.51399 q^{38} +0.759794 q^{40} -10.9578i q^{41} -2.06989 q^{42} +2.63910 q^{43} -1.31161i q^{44} +2.01599i q^{45} +7.30119i q^{46} -5.22430i q^{47} +4.98044 q^{48} -1.00000 q^{49} +7.20587i q^{50} +2.86401 q^{51} +6.15957 q^{53} +9.98293i q^{54} +0.884527 q^{55} +0.687029 q^{56} +1.99830i q^{57} -14.3913i q^{58} -5.10250i q^{59} -1.96762i q^{60} +3.31543 q^{61} +15.0096 q^{62} +1.82292i q^{63} +4.90649 q^{64} +1.65553 q^{66} -13.9305i q^{67} +4.32898 q^{68} -4.15196 q^{69} -2.10992i q^{70} +6.69004i q^{71} -1.25240i q^{72} -15.0774i q^{73} +6.59708 q^{74} -4.09775 q^{75} +3.02045i q^{76} +0.799816 q^{77} -8.10529 q^{79} +5.07673i q^{80} -0.208236 q^{81} +20.9059 q^{82} +15.6338i q^{83} -1.77918i q^{84} +2.91938i q^{85} +5.03501i q^{86} +8.18390 q^{87} -0.549497 q^{88} +2.27897i q^{89} -3.84620 q^{90} -6.27574 q^{92} +8.53552i q^{93} +9.96718 q^{94} -2.03694 q^{95} +8.01116i q^{96} +16.4949i q^{97} -1.90785i q^{98} -1.45800i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{3} - 16 q^{4}+O(q^{10}) $ 12 * q - 8 * q^3 - 16 * q^4	$ 12 q - 8 q^{3} - 16 q^{4} + 28 q^{10} + 46 q^{12} - 4 q^{14} + 46 q^{17} - 8 q^{22} + 36 q^{23} + 20 q^{25} - 20 q^{27} - 30 q^{29} - 28 q^{30} - 4 q^{35} - 44 q^{36} + 22 q^{38} - 28 q^{40} + 16 q^{42} + 36 q^{43} - 22 q^{48} - 12 q^{49} - 28 q^{51} - 50 q^{53} + 6 q^{56} + 32 q^{61} + 18 q^{62} + 14 q^{64} + 32 q^{66} - 68 q^{68} + 2 q^{69} - 28 q^{74} - 30 q^{75} + 16 q^{77} + 4 q^{79} - 12 q^{81} + 20 q^{82} + 26 q^{87} + 96 q^{88} - 64 q^{92} - 28 q^{94} + 14 q^{95}+O(q^{100}) $ 12 * q - 8 * q^3 - 16 * q^4 + 28 * q^10 + 46 * q^12 - 4 * q^14 + 46 * q^17 - 8 * q^22 + 36 * q^23 + 20 * q^25 - 20 * q^27 - 30 * q^29 - 28 * q^30 - 4 * q^35 - 44 * q^36 + 22 * q^38 - 28 * q^40 + 16 * q^42 + 36 * q^43 - 22 * q^48 - 12 * q^49 - 28 * q^51 - 50 * q^53 + 6 * q^56 + 32 * q^61 + 18 * q^62 + 14 * q^64 + 32 * q^66 - 68 * q^68 + 2 * q^69 - 28 * q^74 - 30 * q^75 + 16 * q^77 + 4 * q^79 - 12 * q^81 + 20 * q^82 + 26 * q^87 + 96 * q^88 - 64 * q^92 - 28 * q^94 + 14 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.90785i	1.34905i	0.738250	+	0.674527i	$0.235652\pi$
$2$	1.90785i	1.34905i	−0.738250	+	0.674527i	$0.764348\pi$
$3$	−1.08494	−0.626388	−0.313194	−	0.949689i	$-0.601399\pi$
$3$	−1.08494	−0.626388	−0.313194	+	0.949689i	$0.601399\pi$
$4$	−1.63989	−0.819947
$5$	− 1.10591i	− 0.494579i	−0.968942	−	0.247290i	$-0.920460\pi$
$5$	− 1.10591i	− 0.494579i	0.968942	−	0.247290i	$-0.0795399\pi$
$6$	− 2.06989i	− 0.845031i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	0.687029i	0.242902i
$9$	−1.82292	−0.607638
$10$	2.10992	0.667214
$11$	0.799816i	0.241154i	0.992704	+	0.120577i	$0.0384744\pi$
$11$	0.799816i	0.241154i	−0.992704	+	0.120577i	$0.961526\pi$
$12$	1.77918	0.513605
$13$	0	0
$13$	0	0
$14$	1.90785	0.509894
$15$	1.19984i	0.309798i
$16$	−4.59054	−1.14763
$17$	−2.63979	−0.640244	−0.320122	−	0.947376i	$-0.603724\pi$
$17$	−2.63979	−0.640244	−0.320122	+	0.947376i	$0.603724\pi$
$18$	− 3.47785i	− 0.819737i
$19$	− 1.84186i	− 0.422552i	−0.977426	−	0.211276i	$-0.932238\pi$
$19$	− 1.84186i	− 0.422552i	0.977426	−	0.211276i	$-0.0677618\pi$
$20$	1.81358i	0.405529i
$21$	1.08494i	0.236752i
$22$	−1.52593	−0.325329
$23$	3.82692	0.797968	0.398984	−	0.916958i	$-0.369363\pi$
$23$	3.82692	0.797968	0.398984	+	0.916958i	$0.369363\pi$
$24$	− 0.745382i	− 0.152151i
$25$	3.77696	0.755391
$26$	0	0
$27$	5.23255	1.00701
$28$	1.63989i	0.309911i
$29$	−7.54322	−1.40074	−0.700370	−	0.713780i	$-0.746982\pi$
$29$	−7.54322	−1.40074	−0.700370	+	0.713780i	$0.746982\pi$
$30$	−2.28912	−0.417935
$31$	− 7.86730i	− 1.41301i	−0.707708	−	0.706505i	$-0.750271\pi$
$31$	− 7.86730i	− 1.41301i	0.707708	−	0.706505i	$-0.249729\pi$
$32$	− 7.38400i	− 1.30532i
$33$	− 0.867749i	− 0.151056i
$34$	− 5.03633i	− 0.863724i
$35$	−1.10591	−0.186933
$36$	2.98939	0.498231
$37$	− 3.45786i	− 0.568469i	−0.958755	−	0.284234i	$-0.908261\pi$
$37$	− 3.45786i	− 0.568469i	0.958755	−	0.284234i	$-0.0917394\pi$
$38$	3.51399	0.570045
$39$	0	0
$40$	0.759794	0.120134
$41$	− 10.9578i	− 1.71133i	−0.517532	−	0.855664i	$-0.673149\pi$
$41$	− 10.9578i	− 1.71133i	0.517532	−	0.855664i	$-0.326851\pi$
$42$	−2.06989	−0.319392
$43$	2.63910	0.402459	0.201230	−	0.979544i	$-0.435506\pi$
$43$	2.63910	0.402459	0.201230	+	0.979544i	$0.435506\pi$
$44$	− 1.31161i	− 0.197733i
$45$	2.01599i	0.300525i
$46$	7.30119i	1.07650i
$47$	− 5.22430i	− 0.762043i	−0.924566	−	0.381021i	$-0.875572\pi$
$47$	− 5.22430i	− 0.762043i	0.924566	−	0.381021i	$-0.124428\pi$
$48$	4.98044	0.718864
$49$	−1.00000	−0.142857
$50$	7.20587i	1.01906i
$51$	2.86401	0.401041
$52$	0	0
$53$	6.15957	0.846082	0.423041	−	0.906111i	$-0.360963\pi$
$53$	6.15957	0.846082	0.423041	+	0.906111i	$0.360963\pi$
$54$	9.98293i	1.35850i
$55$	0.884527	0.119270
$56$	0.687029	0.0918081
$57$	1.99830i	0.264681i
$58$	− 14.3913i	− 1.88967i
$59$	− 5.10250i	− 0.664288i	−0.943229	−	0.332144i	$-0.892228\pi$
$59$	− 5.10250i	− 0.664288i	0.943229	−	0.332144i	$-0.107772\pi$
$60$	− 1.96762i	− 0.254018i
$61$	3.31543	0.424498	0.212249	−	0.977216i	$-0.431921\pi$
$61$	3.31543	0.424498	0.212249	+	0.977216i	$0.431921\pi$
$62$	15.0096	1.90623
$63$	1.82292i	0.229666i
$64$	4.90649	0.613312
$65$	0	0
$66$	1.65553	0.203782
$67$	− 13.9305i	− 1.70188i	−0.525260	−	0.850942i	$-0.676032\pi$
$67$	− 13.9305i	− 1.70188i	0.525260	−	0.850942i	$-0.323968\pi$
$68$	4.32898	0.524966
$69$	−4.15196	−0.499837
$70$	− 2.10992i	− 0.252183i
$71$	6.69004i	0.793962i	0.917827	+	0.396981i	$0.129942\pi$
$71$	6.69004i	0.793962i	−0.917827	+	0.396981i	$0.870058\pi$
$72$	− 1.25240i	− 0.147596i
$73$	− 15.0774i	− 1.76467i	−0.470619	−	0.882336i	$-0.655969\pi$
$73$	− 15.0774i	− 1.76467i	0.470619	−	0.882336i	$-0.344031\pi$
$74$	6.59708	0.766895
$75$	−4.09775	−0.473168
$76$	3.02045i	0.346470i
$77$	0.799816	0.0911475
$78$	0	0
$79$	−8.10529	−0.911916	−0.455958	−	0.890001i	$-0.650703\pi$
$79$	−8.10529	−0.911916	−0.455958	+	0.890001i	$0.650703\pi$
$80$	5.07673i	0.567596i
$81$	−0.208236	−0.0231373
$82$	20.9059	2.30867
$83$	15.6338i	1.71603i	0.513623	+	0.858016i	$0.328303\pi$
$83$	15.6338i	1.71603i	−0.513623	+	0.858016i	$0.671697\pi$
$84$	− 1.77918i	− 0.194124i
$85$	2.91938i	0.316651i
$86$	5.03501i	0.542939i
$87$	8.18390	0.877407
$88$	−0.549497	−0.0585766
$89$	2.27897i	0.241570i	0.992679	+	0.120785i	$0.0385412\pi$
$89$	2.27897i	0.241570i	−0.992679	+	0.120785i	$0.961459\pi$
$90$	−3.84620	−0.405425
$91$	0	0
$92$	−6.27574	−0.654291
$93$	8.53552i	0.885092i
$94$	9.96718	1.02804
$95$	−2.03694	−0.208985
$96$	8.01116i	0.817636i
$97$	16.4949i	1.67481i	0.546585	+	0.837404i	$0.315927\pi$
$97$	16.4949i	1.67481i	−0.546585	+	0.837404i	$0.684073\pi$
$98$	− 1.90785i	− 0.192722i
$99$	− 1.45800i	− 0.146534i
$100$	−6.19381	−0.619381
$101$	14.0686	1.39988	0.699940	−	0.714201i	$-0.253210\pi$
$101$	14.0686	1.39988	0.699940	+	0.714201i	$0.253210\pi$
$102$	5.46409i	0.541026i
$103$	−0.110230	−0.0108613	−0.00543063	−	0.999985i	$-0.501729\pi$
$103$	−0.110230	−0.0108613	−0.00543063	+	0.999985i	$0.501729\pi$
$104$	0	0
$105$	1.19984	0.117093
$106$	11.7515i	1.14141i
$107$	−13.8071	−1.33478	−0.667389	−	0.744709i	$-0.732588\pi$
$107$	−13.8071	−1.33478	−0.667389	+	0.744709i	$0.732588\pi$
$108$	−8.58083	−0.825691
$109$	− 2.17385i	− 0.208217i	−0.994566	−	0.104108i	$-0.966801\pi$
$109$	− 2.17385i	− 0.208217i	0.994566	−	0.104108i	$-0.0331989\pi$
$110$	1.68754i	0.160901i
$111$	3.75156i	0.356082i
$112$	4.59054i	0.433765i
$113$	−16.2026	−1.52421	−0.762105	−	0.647453i	$-0.775834\pi$
$113$	−16.2026	−1.52421	−0.762105	+	0.647453i	$0.775834\pi$
$114$	−3.81245	−0.357069
$115$	− 4.23224i	− 0.394658i
$116$	12.3701	1.14853
$117$	0	0
$118$	9.73480	0.896161
$119$	2.63979i	0.241989i
$120$	−0.824328	−0.0752505
$121$	10.3603	0.941845
$122$	6.32535i	0.572670i
$123$	11.8886i	1.07195i
$124$	12.9015i	1.15859i
$125$	− 9.70655i	− 0.868180i
$126$	−3.47785	−0.309831
$127$	−19.9799	−1.77293	−0.886463	−	0.462800i	$-0.846845\pi$
$127$	−19.9799	−1.77293	−0.886463	+	0.462800i	$0.846845\pi$
$128$	− 5.40714i	− 0.477928i
$129$	−2.86325	−0.252095
$130$	0	0
$131$	−18.3019	−1.59905	−0.799524	−	0.600634i	$-0.794915\pi$
$131$	−18.3019	−1.59905	−0.799524	+	0.600634i	$0.794915\pi$
$132$	1.42302i	0.123858i
$133$	−1.84186	−0.159709
$134$	26.5773	2.29593
$135$	− 5.78675i	− 0.498044i
$136$	− 1.81362i	− 0.155516i
$137$	− 1.03858i	− 0.0887322i	−0.999015	−	0.0443661i	$-0.985873\pi$
$137$	− 1.03858i	− 0.0887322i	0.999015	−	0.0443661i	$-0.0141268\pi$
$138$	− 7.92132i	− 0.674307i
$139$	16.0516	1.36148	0.680738	−	0.732527i	$-0.261659\pi$
$139$	16.0516	1.36148	0.680738	+	0.732527i	$0.261659\pi$
$140$	1.81358	0.153275
$141$	5.66803i	0.477334i
$142$	−12.7636	−1.07110
$143$	0	0
$144$	8.36816	0.697346
$145$	8.34214i	0.692777i
$146$	28.7654	2.38064
$147$	1.08494	0.0894840
$148$	5.67052i	0.466114i
$149$	− 0.376052i	− 0.0308074i	−0.999881	−	0.0154037i	$-0.995097\pi$
$149$	− 0.376052i	− 0.0308074i	0.999881	−	0.0154037i	$-0.00490334\pi$
$150$	− 7.81790i	− 0.638329i
$151$	0.149749i	0.0121864i	0.999981	+	0.00609321i	$0.00193954\pi$
$151$	0.149749i	0.0121864i	−0.999981	+	0.00609321i	$0.998060\pi$
$152$	1.26541	0.102638
$153$	4.81212	0.389037
$154$	1.52593i	0.122963i
$155$	−8.70055	−0.698845
$156$	0	0
$157$	−7.22397	−0.576536	−0.288268	−	0.957550i	$-0.593079\pi$
$157$	−7.22397	−0.576536	−0.288268	+	0.957550i	$0.593079\pi$
$158$	− 15.4637i	− 1.23022i
$159$	−6.68274	−0.529976
$160$	−8.16606	−0.645584
$161$	− 3.82692i	− 0.301603i
$162$	− 0.397282i	− 0.0312134i
$163$	− 3.83171i	− 0.300123i	−0.988677	−	0.150062i	$-0.952053\pi$
$163$	− 3.83171i	− 0.300123i	0.988677	−	0.150062i	$-0.0479472\pi$
$164$	17.9697i	1.40320i
$165$	−0.959654	−0.0747090
$166$	−29.8269	−2.31502
$167$	− 1.83270i	− 0.141819i	−0.997483	−	0.0709094i	$-0.977410\pi$
$167$	− 1.83270i	− 0.141819i	0.997483	−	0.0709094i	$-0.0225901\pi$
$168$	−0.745382	−0.0575075
$169$	0	0
$170$	−5.56974	−0.427180
$171$	3.35755i	0.256759i
$172$	−4.32784	−0.329995
$173$	22.0343	1.67524	0.837618	−	0.546256i	$-0.183947\pi$
$173$	22.0343	1.67524	0.837618	+	0.546256i	$0.183947\pi$
$174$	15.6137i	1.18367i
$175$	− 3.77696i	− 0.285511i
$176$	− 3.67158i	− 0.276756i
$177$	5.53588i	0.416102i
$178$	−4.34793	−0.325891
$179$	−5.62164	−0.420181	−0.210091	−	0.977682i	$-0.567376\pi$
$179$	−5.62164	−0.420181	−0.210091	+	0.977682i	$0.567376\pi$
$180$	− 3.30600i	− 0.246415i
$181$	4.44007	0.330028	0.165014	−	0.986291i	$-0.447233\pi$
$181$	4.44007	0.330028	0.165014	+	0.986291i	$0.447233\pi$
$182$	0	0
$183$	−3.59703	−0.265900
$184$	2.62920i	0.193828i
$185$	−3.82409	−0.281153
$186$	−16.2845	−1.19404
$187$	− 2.11135i	− 0.154397i
$188$	8.56730i	0.624834i
$189$	− 5.23255i	− 0.380612i
$190$	− 3.88617i	− 0.281932i
$191$	−4.39741	−0.318186	−0.159093	−	0.987264i	$-0.550857\pi$
$191$	−4.39741	−0.318186	−0.159093	+	0.987264i	$0.550857\pi$
$192$	−5.32323	−0.384171
$193$	− 25.2708i	− 1.81903i	−0.415669	−	0.909516i	$-0.636452\pi$
$193$	− 25.2708i	− 1.81903i	0.415669	−	0.909516i	$-0.363548\pi$
$194$	−31.4699	−2.25941
$195$	0	0
$196$	1.63989	0.117135
$197$	6.91860i	0.492930i	0.969152	+	0.246465i	$0.0792691\pi$
$197$	6.91860i	0.492930i	−0.969152	+	0.246465i	$0.920731\pi$
$198$	2.78164	0.197683
$199$	−17.3958	−1.23315	−0.616577	−	0.787295i	$-0.711481\pi$
$199$	−17.3958	−1.23315	−0.616577	+	0.787295i	$0.711481\pi$
$200$	2.59488i	0.183486i
$201$	15.1137i	1.06604i
$202$	26.8408i	1.88851i
$203$	7.54322i	0.529430i
$204$	−4.69666	−0.328832
$205$	−12.1184	−0.846387
$206$	− 0.210302i	− 0.0146524i
$207$	−6.97615	−0.484876
$208$	0	0
$209$	1.47315	0.101900
$210$	2.28912i	0.157964i
$211$	7.50167	0.516436	0.258218	−	0.966087i	$-0.416865\pi$
$211$	7.50167	0.516436	0.258218	+	0.966087i	$0.416865\pi$
$212$	−10.1010	−0.693742
$213$	− 7.25826i	− 0.497328i
$214$	− 26.3418i	− 1.80069i
$215$	− 2.91862i	− 0.199048i
$216$	3.59492i	0.244603i
$217$	−7.86730	−0.534067
$218$	4.14738	0.280896
$219$	16.3580i	1.10537i
$220$	−1.45053	−0.0977947
$221$	0	0
$222$	−7.15741	−0.480374
$223$	− 25.8645i	− 1.73201i	−0.500032	−	0.866007i	$-0.666678\pi$
$223$	− 25.8645i	− 1.73201i	0.500032	−	0.866007i	$-0.333322\pi$
$224$	−7.38400	−0.493364
$225$	−6.88507	−0.459005
$226$	− 30.9121i	− 2.05624i
$227$	5.19695i	0.344933i	0.985015	+	0.172467i	$0.0551737\pi$
$227$	5.19695i	0.344933i	−0.985015	+	0.172467i	$0.944826\pi$
$228$	− 3.27700i	− 0.217024i
$229$	− 5.03722i	− 0.332869i	−0.986053	−	0.166434i	$-0.946775\pi$
$229$	− 5.03722i	− 0.332869i	0.986053	−	0.166434i	$-0.0532254\pi$
$230$	8.07448	0.532415
$231$	−0.867749	−0.0570937
$232$	− 5.18241i	− 0.340242i
$233$	16.2022	1.06144	0.530721	−	0.847546i	$-0.321921\pi$
$233$	16.2022	1.06144	0.530721	+	0.847546i	$0.321921\pi$
$234$	0	0
$235$	−5.77762	−0.376890
$236$	8.36755i	0.544681i
$237$	8.79372	0.571213
$238$	−5.03633	−0.326457
$239$	3.22405i	0.208546i	0.994549	+	0.104273i	$0.0332516\pi$
$239$	3.22405i	0.208546i	−0.994549	+	0.104273i	$0.966748\pi$
$240$	− 5.50793i	− 0.355535i
$241$	17.2522i	1.11131i	0.831413	+	0.555655i	$0.187532\pi$
$241$	17.2522i	1.11131i	−0.831413	+	0.555655i	$0.812468\pi$
$242$	19.7659i	1.27060i
$243$	−15.4717	−0.992512
$244$	−5.43696	−0.348065
$245$	1.10591i	0.0706542i
$246$	−22.6816	−1.44613
$247$	0	0
$248$	5.40507	0.343222
$249$	− 16.9617i	− 1.07490i
$250$	18.5186	1.17122
$251$	−17.3864	−1.09742	−0.548711	−	0.836012i	$-0.684881\pi$
$251$	−17.3864	−1.09742	−0.548711	+	0.836012i	$0.684881\pi$
$252$	− 2.98939i	− 0.188314i
$253$	3.06083i	0.192433i
$254$	− 38.1186i	− 2.39177i
$255$	− 3.16734i	− 0.198347i
$256$	20.1290	1.25806
$257$	14.6189	0.911901	0.455950	−	0.890005i	$-0.349299\pi$
$257$	14.6189	0.911901	0.455950	+	0.890005i	$0.349299\pi$
$258$	− 5.46266i	− 0.340090i
$259$	−3.45786	−0.214861
$260$	0	0
$261$	13.7506	0.851143
$262$	− 34.9174i	− 2.15720i
$263$	7.41229	0.457061	0.228531	−	0.973537i	$-0.426608\pi$
$263$	7.41229	0.457061	0.228531	+	0.973537i	$0.426608\pi$
$264$	0.596169	0.0366916
$265$	− 6.81195i	− 0.418455i
$266$	− 3.51399i	− 0.215457i
$267$	− 2.47253i	− 0.151317i
$268$	22.8446i	1.39545i
$269$	−4.58385	−0.279482	−0.139741	−	0.990188i	$-0.544627\pi$
$269$	−4.58385	−0.279482	−0.139741	+	0.990188i	$0.544627\pi$
$270$	11.0402	0.671888
$271$	3.62768i	0.220366i	0.993911	+	0.110183i	$0.0351437\pi$
$271$	3.62768i	0.220366i	−0.993911	+	0.110183i	$0.964856\pi$
$272$	12.1181	0.734766
$273$	0	0
$274$	1.98146	0.119705
$275$	3.02087i	0.182165i
$276$	6.80877	0.409840
$277$	−23.6739	−1.42242	−0.711212	−	0.702978i	$-0.751853\pi$
$277$	−23.6739	−1.42242	−0.711212	+	0.702978i	$0.751853\pi$
$278$	30.6240i	1.83670i
$279$	14.3414i	0.858599i
$280$	− 0.759794i	− 0.0454064i
$281$	25.5415i	1.52368i	0.647768	+	0.761838i	$0.275703\pi$
$281$	25.5415i	1.52368i	−0.647768	+	0.761838i	$0.724297\pi$
$282$	−10.8138	−0.643950
$283$	2.95356	0.175571	0.0877855	−	0.996139i	$-0.472021\pi$
$283$	2.95356	0.175571	0.0877855	+	0.996139i	$0.472021\pi$
$284$	− 10.9710i	− 0.651006i
$285$	2.20994	0.130906
$286$	0	0
$287$	−10.9578	−0.646821
$288$	13.4604i	0.793162i
$289$	−10.0315	−0.590088
$290$	−15.9156	−0.934594
$291$	− 17.8959i	− 1.04908i
$292$	24.7253i	1.44694i
$293$	− 22.6667i	− 1.32420i	−0.749414	−	0.662102i	$-0.769665\pi$
$293$	− 22.6667i	− 1.32420i	0.749414	−	0.662102i	$-0.230335\pi$
$294$	2.06989i	0.120719i
$295$	−5.64291	−0.328543
$296$	2.37565	0.138082
$297$	4.18508i	0.242843i
$298$	0.717451	0.0415608
$299$	0	0
$300$	6.71988	0.387973
$301$	− 2.63910i	− 0.152115i
$302$	−0.285699	−0.0164401
$303$	−15.2636	−0.876868
$304$	8.45512i	0.484934i
$305$	− 3.66658i	− 0.209948i
$306$	9.18080i	0.524832i
$307$	− 2.04932i	− 0.116961i	−0.998289	−	0.0584805i	$-0.981374\pi$
$307$	− 2.04932i	− 0.116961i	0.998289	−	0.0584805i	$-0.0186255\pi$
$308$	−1.31161	−0.0747361
$309$	0.119592	0.00680336
$310$	− 16.5994i	− 0.942780i
$311$	15.4445	0.875776	0.437888	−	0.899030i	$-0.355727\pi$
$311$	15.4445	0.875776	0.437888	+	0.899030i	$0.355727\pi$
$312$	0	0
$313$	−6.59184	−0.372593	−0.186296	−	0.982494i	$-0.559648\pi$
$313$	−6.59184	−0.372593	−0.186296	+	0.982494i	$0.559648\pi$
$314$	− 13.7823i	− 0.777778i
$315$	2.01599	0.113588
$316$	13.2918	0.747723
$317$	− 17.6182i	− 0.989536i	−0.869025	−	0.494768i	$-0.835253\pi$
$317$	− 17.6182i	− 0.989536i	0.869025	−	0.494768i	$-0.164747\pi$
$318$	− 12.7497i	− 0.714966i
$319$	− 6.03319i	− 0.337794i
$320$	− 5.42615i	− 0.303331i
$321$	14.9798	0.836089
$322$	7.30119	0.406879
$323$	4.86213i	0.270536i
$324$	0.341484	0.0189713
$325$	0	0
$326$	7.31034	0.404882
$327$	2.35848i	0.130424i
$328$	7.52836	0.415684
$329$	−5.22430	−0.288025
$330$	− 1.83088i	− 0.100786i
$331$	− 14.0822i	− 0.774027i	−0.922074	−	0.387014i	$-0.873507\pi$
$331$	− 14.0822i	− 0.774027i	0.922074	−	0.387014i	$-0.126493\pi$
$332$	− 25.6378i	− 1.40706i
$333$	6.30339i	0.345423i
$334$	3.49652	0.191321
$335$	−15.4059	−0.841716
$336$	− 4.98044i	− 0.271705i
$337$	−2.73318	−0.148886	−0.0744429	−	0.997225i	$-0.523718\pi$
$337$	−2.73318	−0.148886	−0.0744429	+	0.997225i	$0.523718\pi$
$338$	0	0
$339$	17.5788	0.954747
$340$	− 4.78747i	− 0.259637i
$341$	6.29240	0.340752
$342$	−6.40571	−0.346381
$343$	1.00000i	0.0539949i
$344$	1.81314i	0.0977579i
$345$	4.59171i	0.247209i
$346$	42.0382i	2.25999i
$347$	−2.90684	−0.156047	−0.0780236	−	0.996952i	$-0.524861\pi$
$347$	−2.90684	−0.156047	−0.0780236	+	0.996952i	$0.524861\pi$
$348$	−13.4207	−0.719427
$349$	− 7.10583i	− 0.380366i	−0.981749	−	0.190183i	$-0.939092\pi$
$349$	− 7.10583i	− 0.380366i	0.981749	−	0.190183i	$-0.0609082\pi$
$350$	7.20587	0.385170
$351$	0	0
$352$	5.90584	0.314782
$353$	− 6.18844i	− 0.329378i	−0.986346	−	0.164689i	$-0.947338\pi$
$353$	− 6.18844i	− 0.329378i	0.986346	−	0.164689i	$-0.0526620\pi$
$354$	−10.5616	−0.561344
$355$	7.39860	0.392677
$356$	− 3.73726i	− 0.198075i
$357$	− 2.86401i	− 0.151579i
$358$	− 10.7253i	− 0.566847i
$359$	25.8517i	1.36440i	0.731165	+	0.682201i	$0.238977\pi$
$359$	25.8517i	1.36440i	−0.731165	+	0.682201i	$0.761023\pi$
$360$	−1.38504	−0.0729981
$361$	15.6076	0.821450
$362$	8.47099i	0.445225i
$363$	−11.2403	−0.589960
$364$	0	0
$365$	−16.6743	−0.872770
$366$	− 6.86260i	− 0.358714i
$367$	−34.7499	−1.81393	−0.906964	−	0.421207i	$-0.861606\pi$
$367$	−34.7499	−1.81393	−0.906964	+	0.421207i	$0.861606\pi$
$368$	−17.5676	−0.915775
$369$	19.9752i	1.03987i
$370$	− 7.29580i	− 0.379290i
$371$	− 6.15957i	− 0.319789i
$372$	− 13.9973i	− 0.725728i
$373$	−26.1368	−1.35331	−0.676656	−	0.736299i	$-0.736572\pi$
$373$	−26.1368	−1.35331	−0.676656	+	0.736299i	$0.736572\pi$
$374$	4.02814	0.208290
$375$	10.5310i	0.543817i
$376$	3.58925	0.185101
$377$	0	0
$378$	9.98293	0.513466
$379$	18.1562i	0.932623i	0.884621	+	0.466311i	$0.154417\pi$
$379$	18.1562i	0.932623i	−0.884621	+	0.466311i	$0.845583\pi$
$380$	3.34036	0.171357
$381$	21.6769	1.11054
$382$	− 8.38961i	− 0.429250i
$383$	− 7.68219i	− 0.392541i	−0.980550	−	0.196271i	$-0.937117\pi$
$383$	− 7.68219i	− 0.392541i	0.980550	−	0.196271i	$-0.0628831\pi$
$384$	5.86640i	0.299368i
$385$	− 0.884527i	− 0.0450797i
$386$	48.2129	2.45397
$387$	−4.81086	−0.244550
$388$	− 27.0499i	− 1.37325i
$389$	9.23745	0.468357	0.234179	−	0.972194i	$-0.424760\pi$
$389$	9.23745	0.468357	0.234179	+	0.972194i	$0.424760\pi$
$390$	0	0
$391$	−10.1023	−0.510894
$392$	− 0.687029i	− 0.0347002i
$393$	19.8564	1.00162
$394$	−13.1997	−0.664989
$395$	8.96374i	0.451015i
$396$	2.39096i	0.120150i
$397$	16.7052i	0.838410i	0.907892	+	0.419205i	$0.137691\pi$
$397$	16.7052i	0.838410i	−0.907892	+	0.419205i	$0.862309\pi$
$398$	− 33.1885i	− 1.66359i
$399$	1.99830	0.100040
$400$	−17.3383	−0.866913
$401$	28.3934i	1.41790i	0.705258	+	0.708950i	$0.250831\pi$
$401$	28.3934i	1.41790i	−0.705258	+	0.708950i	$0.749169\pi$
$402$	−28.8347	−1.43814
$403$	0	0
$404$	−23.0710	−1.14783
$405$	0.230290i	0.0114432i
$406$	−14.3913	−0.714230
$407$	2.76565	0.137088
$408$	1.96766i	0.0974135i
$409$	− 25.8721i	− 1.27929i	−0.768669	−	0.639647i	$-0.779081\pi$
$409$	− 25.8721i	− 1.27929i	0.768669	−	0.639647i	$-0.220919\pi$
$410$	− 23.1201i	− 1.14182i
$411$	1.12680i	0.0555808i
$412$	0.180765	0.00890565
$413$	−5.10250	−0.251077
$414$	− 13.3094i	− 0.654124i
$415$	17.2896	0.848714
$416$	0	0
$417$	−17.4149	−0.852811
$418$	2.81055i	0.137468i
$419$	−6.55673	−0.320317	−0.160158	−	0.987091i	$-0.551201\pi$
$419$	−6.55673	−0.320317	−0.160158	+	0.987091i	$0.551201\pi$
$420$	−1.96762	−0.0960099
$421$	− 14.4100i	− 0.702300i	−0.936319	−	0.351150i	$-0.885791\pi$
$421$	− 14.4100i	− 0.702300i	0.936319	−	0.351150i	$-0.114209\pi$
$422$	14.3121i	0.696700i
$423$	9.52346i	0.463046i
$424$	4.23181i	0.205515i
$425$	−9.97039	−0.483635
$426$	13.8477	0.670922
$427$	− 3.31543i	− 0.160445i
$428$	22.6421	1.09445
$429$	0	0
$430$	5.56828	0.268526
$431$	14.7027i	0.708204i	0.935207	+	0.354102i	$0.115213\pi$
$431$	14.7027i	0.708204i	−0.935207	+	0.354102i	$0.884787\pi$
$432$	−24.0202	−1.15567
$433$	20.6178	0.990830	0.495415	−	0.868656i	$-0.335016\pi$
$433$	20.6178	0.990830	0.495415	+	0.868656i	$0.335016\pi$
$434$	− 15.0096i	− 0.720486i
$435$	− 9.05068i	− 0.433947i
$436$	3.56488i	0.170727i
$437$	− 7.04865i	− 0.337182i
$438$	−31.2086	−1.49120
$439$	−20.3424	−0.970892	−0.485446	−	0.874267i	$-0.661343\pi$
$439$	−20.3424	−0.970892	−0.485446	+	0.874267i	$0.661343\pi$
$440$	0.607696i	0.0289708i
$441$	1.82292	0.0868055
$442$	0	0
$443$	13.8195	0.656582	0.328291	−	0.944577i	$-0.393527\pi$
$443$	13.8195	0.656582	0.328291	+	0.944577i	$0.393527\pi$
$444$	− 6.15215i	− 0.291968i
$445$	2.52034	0.119476
$446$	49.3456	2.33658
$447$	0.407992i	0.0192974i
$448$	− 4.90649i	− 0.231810i
$449$	18.2060i	0.859193i	0.903021	+	0.429596i	$0.141344\pi$
$449$	18.2060i	0.859193i	−0.903021	+	0.429596i	$0.858656\pi$
$450$	− 13.1357i	− 0.619222i
$451$	8.76426	0.412693
$452$	26.5705	1.24977
$453$	− 0.162468i	− 0.00763342i
$454$	−9.91500	−0.465334
$455$	0	0
$456$	−1.37289	−0.0642914
$457$	− 8.94689i	− 0.418518i	−0.977860	−	0.209259i	$-0.932895\pi$
$457$	− 8.94689i	− 0.418518i	0.977860	−	0.209259i	$-0.0671051\pi$
$458$	9.61025	0.449058
$459$	−13.8129	−0.644729
$460$	6.94042i	0.323599i
$461$	8.68811i	0.404645i	0.979319	+	0.202323i	$0.0648490\pi$
$461$	8.68811i	0.404645i	−0.979319	+	0.202323i	$0.935151\pi$
$462$	− 1.65553i	− 0.0770225i
$463$	− 20.2019i	− 0.938864i	−0.882969	−	0.469432i	$-0.844459\pi$
$463$	− 20.2019i	− 0.938864i	0.882969	−	0.469432i	$-0.155541\pi$
$464$	34.6274	1.60754
$465$	9.43954	0.437748
$466$	30.9114i	1.43194i
$467$	10.5588	0.488601	0.244300	−	0.969700i	$-0.421442\pi$
$467$	10.5588	0.488601	0.244300	+	0.969700i	$0.421442\pi$
$468$	0	0
$469$	−13.9305	−0.643252
$470$	− 11.0228i	− 0.508446i
$471$	7.83754	0.361135
$472$	3.50556	0.161357
$473$	2.11079i	0.0970545i
$474$	16.7771i	0.770597i
$475$	− 6.95662i	− 0.319192i
$476$	− 4.32898i	− 0.198418i
$477$	−11.2284	−0.514112
$478$	−6.15100	−0.281340
$479$	38.1404i	1.74268i	0.490680	+	0.871340i	$0.336748\pi$
$479$	38.1404i	1.74268i	−0.490680	+	0.871340i	$0.663252\pi$
$480$	8.85965	0.404386
$481$	0	0
$482$	−32.9146	−1.49922
$483$	4.15196i	0.188921i
$484$	−16.9898	−0.772263
$485$	18.2420	0.828325
$486$	− 29.5178i	− 1.33895i
$487$	− 4.23947i	− 0.192109i	−0.995376	−	0.0960544i	$-0.969378\pi$
$487$	− 4.23947i	− 0.192109i	0.995376	−	0.0960544i	$-0.0306223\pi$
$488$	2.27780i	0.103111i
$489$	4.15716i	0.187993i
$490$	−2.10992	−0.0953163
$491$	−16.0662	−0.725057	−0.362529	−	0.931973i	$-0.618087\pi$
$491$	−16.0662	−0.725057	−0.362529	+	0.931973i	$0.618087\pi$
$492$	− 19.4960i	− 0.878946i
$493$	19.9125	0.896815
$494$	0	0
$495$	−1.61242	−0.0724728
$496$	36.1151i	1.62162i
$497$	6.69004	0.300089
$498$	32.3603	1.45010
$499$	28.9437i	1.29570i	0.761769	+	0.647848i	$0.224331\pi$
$499$	28.9437i	1.29570i	−0.761769	+	0.647848i	$0.775669\pi$
$500$	15.9177i	0.711862i
$501$	1.98837i	0.0888336i
$502$	− 33.1707i	− 1.48048i
$503$	−26.9087	−1.19980	−0.599901	−	0.800075i	$-0.704793\pi$
$503$	−26.9087	−1.19980	−0.599901	+	0.800075i	$0.704793\pi$
$504$	−1.25240	−0.0557861
$505$	− 15.5587i	− 0.692352i
$506$	−5.83961	−0.259602
$507$	0	0
$508$	32.7648	1.45370
$509$	20.0963i	0.890755i	0.895343	+	0.445377i	$0.146930\pi$
$509$	20.0963i	0.890755i	−0.895343	+	0.445377i	$0.853070\pi$
$510$	6.04281	0.267580
$511$	−15.0774	−0.666984
$512$	27.5888i	1.21927i
$513$	− 9.63762i	− 0.425511i
$514$	27.8906i	1.23020i
$515$	0.121904i	0.00537175i
$516$	4.69543	0.206705
$517$	4.17848	0.183769
$518$	− 6.59708i	− 0.289859i
$519$	−23.9058	−1.04935
$520$	0	0
$521$	30.2678	1.32605	0.663027	−	0.748595i	$-0.269271\pi$
$521$	30.2678	1.32605	0.663027	+	0.748595i	$0.269271\pi$
$522$	26.2342i	1.14824i
$523$	41.6444	1.82098	0.910491	−	0.413529i	$-0.135704\pi$
$523$	41.6444	1.82098	0.910491	+	0.413529i	$0.135704\pi$
$524$	30.0132	1.31113
$525$	4.09775i	0.178841i
$526$	14.1415i	0.616600i
$527$	20.7681i	0.904671i
$528$	3.98343i	0.173357i
$529$	−8.35469	−0.363248
$530$	12.9962	0.564518
$531$	9.30142i	0.403647i
$532$	3.02045	0.130953
$533$	0	0
$534$	4.71722	0.204134
$535$	15.2694i	0.660154i
$536$	9.57067	0.413390
$537$	6.09912	0.263196
$538$	− 8.74531i	− 0.377037i
$539$	− 0.799816i	− 0.0344505i
$540$	9.48965i	0.408369i
$541$	− 9.64131i	− 0.414512i	−0.978287	−	0.207256i	$-0.933547\pi$
$541$	− 9.64131i	− 0.414512i	0.978287	−	0.207256i	$-0.0664534\pi$
$542$	−6.92107	−0.297285
$543$	−4.81719	−0.206725
$544$	19.4922i	0.835723i
$545$	−2.40409	−0.102980
$546$	0	0
$547$	−21.0811	−0.901362	−0.450681	−	0.892685i	$-0.648819\pi$
$547$	−21.0811	−0.901362	−0.450681	+	0.892685i	$0.648819\pi$
$548$	1.70317i	0.0727557i
$549$	−6.04375	−0.257941
$550$	−5.76337	−0.245751
$551$	13.8935i	0.591885i
$552$	− 2.85252i	− 0.121411i
$553$	8.10529i	0.344672i
$554$	− 45.1662i	− 1.91893i
$555$	4.14889	0.176111
$556$	−26.3228	−1.11634
$557$	− 16.5044i	− 0.699313i	−0.936878	−	0.349657i	$-0.886298\pi$
$557$	− 16.5044i	− 0.699313i	0.936878	−	0.349657i	$-0.113702\pi$
$558$	−27.3613	−1.15830
$559$	0	0
$560$	5.07673	0.214531
$561$	2.29068i	0.0967125i
$562$	−48.7293	−2.05552
$563$	10.7950	0.454954	0.227477	−	0.973784i	$-0.426952\pi$
$563$	10.7950	0.454954	0.227477	+	0.973784i	$0.426952\pi$
$564$	− 9.29496i	− 0.391389i
$565$	17.9186i	0.753843i
$566$	5.63495i	0.236855i
$567$	0.208236i	0.00874507i
$568$	−4.59625	−0.192854
$569$	39.8672	1.67132	0.835660	−	0.549247i	$-0.185085\pi$
$569$	39.8672	1.67132	0.835660	+	0.549247i	$0.185085\pi$
$570$	4.21624i	0.176599i
$571$	−42.8074	−1.79143	−0.895717	−	0.444624i	$-0.853337\pi$
$571$	−42.8074	−1.79143	−0.895717	+	0.444624i	$0.853337\pi$
$572$	0	0
$573$	4.77091	0.199308
$574$	− 20.9059i	− 0.872597i
$575$	14.4541	0.602778
$576$	−8.94412	−0.372672
$577$	0.199664i	0.00831211i	0.999991	+	0.00415606i	$0.00132292\pi$
$577$	0.199664i	0.00831211i	−0.999991	+	0.00415606i	$0.998677\pi$
$578$	− 19.1386i	− 0.796060i
$579$	27.4172i	1.13942i
$580$	− 13.6802i	− 0.568040i
$581$	15.6338	0.648599
$582$	34.1428	1.41526
$583$	4.92652i	0.204036i
$584$	10.3586	0.428642
$585$	0	0
$586$	43.2447	1.78642
$587$	1.12962i	0.0466244i	0.999728	+	0.0233122i	$0.00742117\pi$
$587$	1.12962i	0.0466244i	−0.999728	+	0.0233122i	$0.992579\pi$
$588$	−1.77918	−0.0733721
$589$	−14.4905	−0.597069
$590$	− 10.7658i	− 0.443223i
$591$	− 7.50624i	− 0.308765i
$592$	15.8734i	0.652394i
$593$	− 16.5142i	− 0.678158i	−0.940758	−	0.339079i	$-0.889885\pi$
$593$	− 16.5142i	− 0.678158i	0.940758	−	0.339079i	$-0.110115\pi$
$594$	−7.98450	−0.327608
$595$	2.91938	0.119683
$596$	0.616685i	0.0252604i
$597$	18.8733	0.772432
$598$	0	0
$599$	7.44907	0.304361	0.152180	−	0.988353i	$-0.451371\pi$
$599$	7.44907	0.304361	0.152180	+	0.988353i	$0.451371\pi$
$600$	− 2.81528i	− 0.114933i
$601$	−20.8286	−0.849618	−0.424809	−	0.905283i	$-0.639659\pi$
$601$	−20.8286	−0.849618	−0.424809	+	0.905283i	$0.639659\pi$
$602$	5.03501	0.205212
$603$	25.3942i	1.03413i
$604$	− 0.245573i	− 0.00999221i
$605$	− 11.4576i	− 0.465817i
$606$	− 29.1206i	− 1.18294i
$607$	35.4304	1.43808	0.719038	−	0.694970i	$-0.244583\pi$
$607$	35.4304	1.43808	0.719038	+	0.694970i	$0.244583\pi$
$608$	−13.6003	−0.551564
$609$	− 8.18390i	− 0.331628i
$610$	6.99529	0.283231
$611$	0	0
$612$	−7.89136	−0.318989
$613$	19.1451i	0.773263i	0.922234	+	0.386632i	$0.126362\pi$
$613$	19.1451i	0.773263i	−0.922234	+	0.386632i	$0.873638\pi$
$614$	3.90980	0.157787
$615$	13.1477	0.530167
$616$	0.549497i	0.0221399i
$617$	3.52481i	0.141904i	0.997480	+	0.0709518i	$0.0226036\pi$
$617$	3.52481i	0.141904i	−0.997480	+	0.0709518i	$0.977396\pi$
$618$	0.228164i	0.00917810i
$619$	− 40.1768i	− 1.61484i	−0.589976	−	0.807421i	$-0.700863\pi$
$619$	− 40.1768i	− 1.61484i	0.589976	−	0.807421i	$-0.299137\pi$
$620$	14.2680	0.573016
$621$	20.0245	0.803557
$622$	29.4657i	1.18147i
$623$	2.27897	0.0913049
$624$	0	0
$625$	8.15019	0.326008
$626$	− 12.5762i	− 0.502648i
$627$	−1.59827	−0.0638288
$628$	11.8465	0.472728
$629$	9.12804i	0.363959i
$630$	3.84620i	0.153236i
$631$	6.33561i	0.252217i	0.992016	+	0.126108i	$0.0402487\pi$
$631$	6.33561i	0.252217i	−0.992016	+	0.126108i	$0.959751\pi$
$632$	− 5.56857i	− 0.221506i
$633$	−8.13883	−0.323489
$634$	33.6129	1.33494
$635$	22.0960i	0.876852i
$636$	10.9590	0.434552
$637$	0	0
$638$	11.5104	0.455702
$639$	− 12.1954i	− 0.482442i
$640$	−5.97983	−0.236373
$641$	27.5697	1.08894	0.544469	−	0.838781i	$-0.316731\pi$
$641$	27.5697	1.08894	0.544469	+	0.838781i	$0.316731\pi$
$642$	28.5792i	1.12793i
$643$	− 15.7718i	− 0.621977i	−0.950414	−	0.310989i	$-0.899340\pi$
$643$	− 15.7718i	− 0.621977i	0.950414	−	0.310989i	$-0.100660\pi$
$644$	6.27574i	0.247299i
$645$	3.16651i	0.124681i
$646$	−9.27621	−0.364968
$647$	−7.55988	−0.297210	−0.148605	−	0.988897i	$-0.547478\pi$
$647$	−7.55988	−0.297210	−0.148605	+	0.988897i	$0.547478\pi$
$648$	− 0.143064i	− 0.00562008i
$649$	4.08106	0.160196
$650$	0	0
$651$	8.53552	0.334533
$652$	6.28360i	0.246085i
$653$	27.2957	1.06816	0.534082	−	0.845432i	$-0.320657\pi$
$653$	27.2957	1.06816	0.534082	+	0.845432i	$0.320657\pi$
$654$	−4.49964	−0.175950
$655$	20.2403i	0.790856i
$656$	50.3024i	1.96398i
$657$	27.4848i	1.07228i
$658$	− 9.96718i	− 0.388561i
$659$	26.4906	1.03193	0.515963	−	0.856611i	$-0.327434\pi$
$659$	26.4906	1.03193	0.515963	+	0.856611i	$0.327434\pi$
$660$	1.57373	0.0612574
$661$	− 9.13946i	− 0.355484i	−0.984077	−	0.177742i	$-0.943121\pi$
$661$	− 9.13946i	− 0.355484i	0.984077	−	0.177742i	$-0.0568792\pi$
$662$	26.8667	1.04420
$663$	0	0
$664$	−10.7409	−0.416827
$665$	2.03694i	0.0789890i
$666$	−12.0259	−0.465995
$667$	−28.8673	−1.11775
$668$	3.00544i	0.116284i
$669$	28.0613i	1.08491i
$670$	− 29.3922i	− 1.13552i
$671$	2.65174i	0.102369i
$672$	8.01116	0.309037
$673$	9.03859	0.348412	0.174206	−	0.984709i	$-0.444264\pi$
$673$	9.03859	0.348412	0.174206	+	0.984709i	$0.444264\pi$
$674$	− 5.21450i	− 0.200855i
$675$	19.7631	0.760683
$676$	0	0
$677$	−6.04397	−0.232289	−0.116144	−	0.993232i	$-0.537054\pi$
$677$	−6.04397	−0.232289	−0.116144	+	0.993232i	$0.537054\pi$
$678$	33.5376i	1.28800i
$679$	16.4949	0.633018
$680$	−2.00570	−0.0769151
$681$	− 5.63835i	− 0.216062i
$682$	12.0050i	0.459693i
$683$	− 43.9978i	− 1.68353i	−0.539846	−	0.841764i	$-0.681518\pi$
$683$	− 43.9978i	− 1.68353i	0.539846	−	0.841764i	$-0.318482\pi$
$684$	− 5.50603i	− 0.210528i
$685$	−1.14858	−0.0438851
$686$	−1.90785	−0.0728421
$687$	5.46505i	0.208505i
$688$	−12.1149	−0.461876
$689$	0	0
$690$	−8.76029	−0.333498
$691$	22.7816i	0.866651i	0.901237	+	0.433326i	$0.142660\pi$
$691$	22.7816i	0.866651i	−0.901237	+	0.433326i	$0.857340\pi$
$692$	−36.1339	−1.37361
$693$	−1.45800	−0.0553847
$694$	− 5.54581i	− 0.210516i
$695$	− 17.7516i	− 0.673357i
$696$	5.62258i	0.213123i
$697$	28.9264i	1.09567i
$698$	13.5569	0.513135
$699$	−17.5784	−0.664875
$700$	6.19381i	0.234104i
$701$	30.4001	1.14820	0.574098	−	0.818786i	$-0.305353\pi$
$701$	30.4001	1.14820	0.574098	+	0.818786i	$0.305353\pi$
$702$	0	0
$703$	−6.36889	−0.240207
$704$	3.92429i	0.147902i
$705$	6.26835	0.236080
$706$	11.8066	0.444348
$707$	− 14.0686i	− 0.529105i
$708$	− 9.07825i	− 0.341182i
$709$	30.0571i	1.12882i	0.825495	+	0.564409i	$0.190896\pi$
$709$	30.0571i	1.12882i	−0.825495	+	0.564409i	$0.809104\pi$
$710$	14.1154i	0.529742i
$711$	14.7753	0.554115
$712$	−1.56572	−0.0586777
$713$	− 30.1075i	− 1.12754i
$714$	5.46409	0.204489
$715$	0	0
$716$	9.21890	0.344526
$717$	− 3.49789i	− 0.130631i
$718$	−49.3212	−1.84065
$719$	−17.5716	−0.655308	−0.327654	−	0.944798i	$-0.606258\pi$
$719$	−17.5716	−0.655308	−0.327654	+	0.944798i	$0.606258\pi$
$720$	− 9.25445i	− 0.344893i
$721$	0.110230i	0.00410517i
$722$	29.7769i	1.10818i
$723$	− 18.7175i	− 0.696111i
$724$	−7.28124	−0.270605
$725$	−28.4904	−1.05811
$726$	− 21.4447i	− 0.795888i
$727$	−24.8988	−0.923446	−0.461723	−	0.887024i	$-0.652769\pi$
$727$	−24.8988	−0.923446	−0.461723	+	0.887024i	$0.652769\pi$
$728$	0	0
$729$	17.4105	0.644835
$730$	− 31.8120i	− 1.17741i
$731$	−6.96668	−0.257672
$732$	5.89875	0.218024
$733$	− 31.8923i	− 1.17797i	−0.808145	−	0.588984i	$-0.799528\pi$
$733$	− 31.8923i	− 1.17797i	0.808145	−	0.588984i	$-0.200472\pi$
$734$	− 66.2976i	− 2.44709i
$735$	− 1.19984i	− 0.0442569i
$736$	− 28.2580i	− 1.04160i
$737$	11.1419	0.410415
$738$	−38.1097	−1.40284
$739$	− 18.0548i	− 0.664157i	−0.943252	−	0.332078i	$-0.892250\pi$
$739$	− 18.0548i	− 0.664157i	0.943252	−	0.332078i	$-0.107750\pi$
$740$	6.27110	0.230530
$741$	0	0
$742$	11.7515	0.431413
$743$	− 43.5109i	− 1.59626i	−0.602486	−	0.798129i	$-0.705823\pi$
$743$	− 43.5109i	− 1.59626i	0.602486	−	0.798129i	$-0.294177\pi$
$744$	−5.86415	−0.214990
$745$	−0.415881	−0.0152367
$746$	− 49.8651i	− 1.82569i
$747$	− 28.4991i	− 1.04273i
$748$	3.46239i	0.126597i
$749$	13.8071i	0.504499i
$750$	−20.0915	−0.733639
$751$	49.5788	1.80916	0.904578	−	0.426307i	$-0.140186\pi$
$751$	49.5788	1.80916	0.904578	+	0.426307i	$0.140186\pi$
$752$	23.9823i	0.874546i
$753$	18.8632	0.687412
$754$	0	0
$755$	0.165610	0.00602715
$756$	8.58083i	0.312082i
$757$	51.8824	1.88570	0.942850	−	0.333218i	$-0.108135\pi$
$757$	51.8824	1.88570	0.942850	+	0.333218i	$0.108135\pi$
$758$	−34.6394	−1.25816
$759$	− 3.32080i	− 0.120538i
$760$	− 1.39943i	− 0.0507628i
$761$	8.00874i	0.290317i	0.989408	+	0.145158i	$0.0463692\pi$
$761$	8.00874i	0.290317i	−0.989408	+	0.145158i	$0.953631\pi$
$762$	41.3562i	1.49818i
$763$	−2.17385	−0.0786986
$764$	7.21129	0.260895
$765$	− 5.32178i	− 0.192410i
$766$	14.6565	0.529560
$767$	0	0
$768$	−21.8387	−0.788035
$769$	22.7156i	0.819147i	0.912277	+	0.409573i	$0.134322\pi$
$769$	22.7156i	0.819147i	−0.912277	+	0.409573i	$0.865678\pi$
$770$	1.68754	0.0608149
$771$	−15.8605	−0.571204
$772$	41.4414i	1.49151i
$773$	− 24.4370i	− 0.878937i	−0.898258	−	0.439468i	$-0.855167\pi$
$773$	− 24.4370i	− 0.878937i	0.898258	−	0.439468i	$-0.144833\pi$
$774$	− 9.17839i	− 0.329911i
$775$	− 29.7145i	− 1.06738i
$776$	−11.3325	−0.406813
$777$	3.75156	0.134586
$778$	17.6237i	0.631839i
$779$	−20.1828	−0.723124
$780$	0	0
$781$	−5.35080	−0.191467
$782$	− 19.2736i	− 0.689224i
$783$	−39.4703	−1.41055
$784$	4.59054	0.163948
$785$	7.98908i	0.285142i
$786$	37.8831i	1.35124i
$787$	− 3.70522i	− 0.132077i	−0.997817	−	0.0660385i	$-0.978964\pi$
$787$	− 3.70522i	− 0.132077i	0.997817	−	0.0660385i	$-0.0210360\pi$
$788$	− 11.3458i	− 0.404176i
$789$	−8.04186	−0.286298
$790$	−17.1015	−0.608443
$791$	16.2026i	0.576097i
$792$	1.00169	0.0355934
$793$	0	0
$794$	−31.8710	−1.13106
$795$	7.39052i	0.262115i
$796$	28.5272	1.01112
$797$	47.2016	1.67197	0.835984	−	0.548754i	$-0.184898\pi$
$797$	47.2016	1.67197	0.835984	+	0.548754i	$0.184898\pi$
$798$	3.81245i	0.134959i
$799$	13.7911i	0.487893i
$800$	− 27.8890i	− 0.986027i
$801$	− 4.15436i	− 0.146787i
$802$	−54.1704	−1.91282
$803$	12.0591	0.425557
$804$	− 24.7849i	− 0.874095i
$805$	−4.23224	−0.149167
$806$	0	0
$807$	4.97319	0.175064
$808$	9.66556i	0.340033i
$809$	−15.3631	−0.540139	−0.270070	−	0.962841i	$-0.587047\pi$
$809$	−15.3631	−0.540139	−0.270070	+	0.962841i	$0.587047\pi$
$810$	−0.439359	−0.0154375
$811$	− 38.2892i	− 1.34452i	−0.740317	−	0.672258i	$-0.765324\pi$
$811$	− 38.2892i	− 1.34452i	0.740317	−	0.672258i	$-0.234676\pi$
$812$	− 12.3701i	− 0.434104i
$813$	− 3.93580i	− 0.138034i
$814$	5.27645i	0.184940i
$815$	−4.23754	−0.148435
$816$	−13.1473	−0.460248
$817$	− 4.86085i	− 0.170060i
$818$	49.3601	1.72584
$819$	0	0
$820$	19.8729	0.693993
$821$	− 18.0178i	− 0.628824i	−0.949287	−	0.314412i	$-0.898193\pi$
$821$	− 18.0178i	− 0.628824i	0.949287	−	0.314412i	$-0.101807\pi$
$822$	−2.14976	−0.0749815
$823$	−12.2209	−0.425995	−0.212998	−	0.977053i	$-0.568323\pi$
$823$	−12.2209	−0.425995	−0.212998	+	0.977053i	$0.568323\pi$
$824$	− 0.0757310i	− 0.00263821i
$825$	− 3.27745i	− 0.114106i
$826$	− 9.73480i	− 0.338717i
$827$	50.2854i	1.74859i	0.485390	+	0.874297i	$0.338677\pi$
$827$	50.2854i	1.74859i	−0.485390	+	0.874297i	$0.661323\pi$
$828$	11.4401	0.397572
$829$	41.3255	1.43530	0.717648	−	0.696407i	$-0.245219\pi$
$829$	41.3255	1.43530	0.717648	+	0.696407i	$0.245219\pi$
$830$	32.9860i	1.14496i
$831$	25.6846	0.890989
$832$	0	0
$833$	2.63979	0.0914634
$834$	− 33.2250i	− 1.15049i
$835$	−2.02681	−0.0701407
$836$	−2.41581	−0.0835524
$837$	− 41.1661i	− 1.42291i
$838$	− 12.5093i	− 0.432125i
$839$	− 44.8612i	− 1.54878i	−0.632708	−	0.774391i	$-0.718057\pi$
$839$	− 44.8612i	− 1.54878i	0.632708	−	0.774391i	$-0.281943\pi$
$840$	0.824328i	0.0284420i
$841$	27.9001	0.962073
$842$	27.4921	0.947441
$843$	− 27.7108i	− 0.954412i
$844$	−12.3019	−0.423450
$845$	0	0
$846$	−18.1693	−0.624674
$847$	− 10.3603i	− 0.355984i
$848$	−28.2757	−0.970993
$849$	−3.20442	−0.109976
$850$	− 19.0220i	− 0.652449i
$851$	− 13.2330i	− 0.453620i
$852$	11.9028i	0.407782i
$853$	38.3749i	1.31393i	0.753920	+	0.656966i	$0.228160\pi$
$853$	38.3749i	1.31393i	−0.753920	+	0.656966i	$0.771840\pi$
$854$	6.32535	0.216449
$855$	3.71316	0.126987
$856$	− 9.48585i	− 0.324220i
$857$	−6.20663	−0.212015	−0.106007	−	0.994365i	$-0.533807\pi$
$857$	−6.20663	−0.212015	−0.106007	+	0.994365i	$0.533807\pi$
$858$	0	0
$859$	43.0183	1.46777	0.733884	−	0.679275i	$-0.237706\pi$
$859$	43.0183	1.46777	0.733884	+	0.679275i	$0.237706\pi$
$860$	4.78622i	0.163209i
$861$	11.8886	0.405161
$862$	−28.0506	−0.955406
$863$	19.4927i	0.663540i	0.943360	+	0.331770i	$0.107646\pi$
$863$	19.4927i	0.663540i	−0.943360	+	0.331770i	$0.892354\pi$
$864$	− 38.6372i	− 1.31446i
$865$	− 24.3680i	− 0.828537i
$866$	39.3358i	1.33668i
$867$	10.8835	0.369624
$868$	12.9015	0.437907
$869$	− 6.48274i	− 0.219912i
$870$	17.2674	0.585418
$871$	0	0
$872$	1.49350	0.0505762
$873$	− 30.0689i	− 1.01768i
$874$	13.4478	0.454877
$875$	−9.70655	−0.328141
$876$	− 26.8253i	− 0.906344i
$877$	− 33.2003i	− 1.12109i	−0.828123	−	0.560547i	$-0.810591\pi$
$877$	− 33.2003i	− 1.12109i	0.828123	−	0.560547i	$-0.189409\pi$
$878$	− 38.8103i	− 1.30979i
$879$	24.5919i	0.829465i
$880$	−4.06045	−0.136878
$881$	−50.5588	−1.70337	−0.851684	−	0.524055i	$-0.824418\pi$
$881$	−50.5588	−1.70337	−0.851684	+	0.524055i	$0.824418\pi$
$882$	3.47785i	0.117105i
$883$	−7.17013	−0.241294	−0.120647	−	0.992695i	$-0.538497\pi$
$883$	−7.17013	−0.241294	−0.120647	+	0.992695i	$0.538497\pi$
$884$	0	0
$885$	6.12220	0.205795
$886$	26.3654i	0.885764i
$887$	−31.0525	−1.04264	−0.521320	−	0.853361i	$-0.674560\pi$
$887$	−31.0525	−1.04264	−0.521320	+	0.853361i	$0.674560\pi$
$888$	−2.57743	−0.0864928
$889$	19.9799i	0.670103i
$890$	4.80843i	0.161179i
$891$	− 0.166550i	− 0.00557964i
$892$	42.4150i	1.42016i
$893$	−9.62243	−0.322002
$894$	−0.778388	−0.0260332
$895$	6.21705i	0.207813i
$896$	−5.40714	−0.180640
$897$	0	0
$898$	−34.7343	−1.15910
$899$	59.3448i	1.97926i
$900$	11.2908	0.376359
$901$	−16.2600	−0.541699
$902$	16.7209i	0.556745i
$903$	2.86325i	0.0952831i
$904$	− 11.1316i	− 0.370233i
$905$	− 4.91033i	− 0.163225i
$906$	0.309965	0.0102979
$907$	21.6888	0.720165	0.360082	−	0.932921i	$-0.382749\pi$
$907$	21.6888	0.720165	0.360082	+	0.932921i	$0.382749\pi$
$908$	− 8.52244i	− 0.282827i
$909$	−25.6459	−0.850621
$910$	0	0
$911$	−28.0626	−0.929756	−0.464878	−	0.885375i	$-0.653902\pi$
$911$	−28.0626	−0.929756	−0.464878	+	0.885375i	$0.653902\pi$
$912$	− 9.17326i	− 0.303757i
$913$	−12.5042	−0.413827
$914$	17.0693	0.564603
$915$	3.97800i	0.131509i
$916$	8.26050i	0.272935i
$917$	18.3019i	0.604383i
$918$	− 26.3529i	− 0.869774i
$919$	−1.09050	−0.0359724	−0.0179862	−	0.999838i	$-0.505725\pi$
$919$	−1.09050	−0.0359724	−0.0179862	+	0.999838i	$0.505725\pi$
$920$	2.90767	0.0958631
$921$	2.22338i	0.0732629i
$922$	−16.5756	−0.545889
$923$	0	0
$924$	1.42302	0.0468138
$925$	− 13.0602i	− 0.429416i
$926$	38.5423	1.26658
$927$	0.200939	0.00659971
$928$	55.6991i	1.82841i
$929$	− 25.7716i	− 0.845540i	−0.906237	−	0.422770i	$-0.861058\pi$
$929$	− 25.7716i	− 0.845540i	0.906237	−	0.422770i	$-0.138942\pi$
$930$	18.0092i	0.590546i
$931$	1.84186i	0.0603645i
$932$	−26.5699	−0.870327
$933$	−16.7563	−0.548575
$934$	20.1445i	0.659149i
$935$	−2.33497	−0.0763616
$936$	0	0
$937$	−5.39284	−0.176176	−0.0880882	−	0.996113i	$-0.528076\pi$
$937$	−5.39284	−0.176176	−0.0880882	+	0.996113i	$0.528076\pi$
$938$	− 26.5773i	− 0.867781i
$939$	7.15172	0.233388
$940$	9.47468	0.309030
$941$	− 59.3354i	− 1.93428i	−0.254248	−	0.967139i	$-0.581828\pi$
$941$	− 59.3354i	− 1.93428i	0.254248	−	0.967139i	$-0.418172\pi$
$942$	14.9529i	0.487190i
$943$	− 41.9348i	− 1.36558i
$944$	23.4232i	0.762360i
$945$	−5.78675	−0.188243
$946$	−4.02708	−0.130932
$947$	29.0891i	0.945270i	0.881258	+	0.472635i	$0.156697\pi$
$947$	29.0891i	0.945270i	−0.881258	+	0.472635i	$0.843303\pi$
$948$	−14.4208	−0.468364
$949$	0	0
$950$	13.2722	0.430607
$951$	19.1146i	0.619833i
$952$	−1.81362	−0.0587796
$953$	−11.0404	−0.357633	−0.178816	−	0.983882i	$-0.557227\pi$
$953$	−11.0404	−0.357633	−0.178816	+	0.983882i	$0.557227\pi$
$954$	− 21.4221i	− 0.693565i
$955$	4.86315i	0.157368i
$956$	− 5.28710i	− 0.170997i
$957$	6.54562i	0.211590i
$958$	−72.7662	−2.35097
$959$	−1.03858	−0.0335376
$960$	5.88703i	0.190003i
$961$	−30.8945	−0.996596
$962$	0	0
$963$	25.1691	0.811063
$964$	− 28.2917i	− 0.911215i
$965$	−27.9473	−0.899656
$966$	−7.92132	−0.254864
$967$	15.3720i	0.494330i	0.968973	+	0.247165i	$0.0794990\pi$
$967$	15.3720i	0.494330i	−0.968973	+	0.247165i	$0.920501\pi$
$968$	7.11782i	0.228776i
$969$	− 5.27510i	− 0.169460i
$970$	34.8029i	1.11745i
$971$	45.8252	1.47060	0.735300	−	0.677741i	$-0.237041\pi$
$971$	45.8252	1.47060	0.735300	+	0.677741i	$0.237041\pi$
$972$	25.3720	0.813807
$973$	− 16.0516i	− 0.514589i
$974$	8.08828	0.259165
$975$	0	0
$976$	−15.2196	−0.487168
$977$	− 30.9623i	− 0.990572i	−0.868730	−	0.495286i	$-0.835063\pi$
$977$	− 30.9623i	− 0.990572i	0.868730	−	0.495286i	$-0.164937\pi$
$978$	−7.93125	−0.253613
$979$	−1.82275	−0.0582555
$980$	− 1.81358i	− 0.0579327i
$981$	3.96274i	0.126521i
$982$	− 30.6519i	− 0.978142i
$983$	− 27.6460i	− 0.881769i	−0.897564	−	0.440884i	$-0.854665\pi$
$983$	− 27.6460i	− 0.881769i	0.897564	−	0.440884i	$-0.145335\pi$
$984$	−8.16778	−0.260379
$985$	7.65137	0.243793
$986$	37.9901i	1.20985i
$987$	5.66803	0.180415
$988$	0	0
$989$	10.0996	0.321149
$990$	− 3.07625i	− 0.0977697i
$991$	−29.7267	−0.944301	−0.472151	−	0.881518i	$-0.656522\pi$
$991$	−29.7267	−0.944301	−0.472151	+	0.881518i	$0.656522\pi$
$992$	−58.0922	−1.84443
$993$	15.2783i	0.484841i
$994$	12.7636i	0.404837i
$995$	19.2382i	0.609892i
$996$	27.8153i	0.881362i
$997$	24.6552	0.780838	0.390419	−	0.920637i	$-0.372330\pi$
$997$	24.6552	0.780838	0.390419	+	0.920637i	$0.372330\pi$
$998$	−55.2202	−1.74797
$999$	− 18.0934i	− 0.572451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.h.337.9		12
13.5	odd	4		1183.2.a.n.1.5	✓	6
13.8	odd	4		1183.2.a.o.1.2	yes	6
13.12	even	2	inner	1183.2.c.h.337.4		12
91.34	even	4		8281.2.a.cg.1.2		6
91.83	even	4		8281.2.a.cb.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.n.1.5	✓	6	13.5	odd	4
1183.2.a.o.1.2	yes	6	13.8	odd	4
1183.2.c.h.337.4		12	13.12	even	2	inner
1183.2.c.h.337.9		12	1.1	even	1	trivial
8281.2.a.cb.1.5		6	91.83	even	4
8281.2.a.cg.1.2		6	91.34	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.90785i q^{2} -1.08494 q^{3} -1.63989 q^{4} -1.10591i q^{5} -2.06989i q^{6} -1.00000i q^{7} +0.687029i q^{8} -1.82292 q^{9} +O(q^{10})\)	\(q+1.90785i q^{2} -1.08494 q^{3} -1.63989 q^{4} -1.10591i q^{5} -2.06989i q^{6} -1.00000i q^{7} +0.687029i q^{8} -1.82292 q^{9} +2.10992 q^{10} +0.799816i q^{11} +1.77918 q^{12} +1.90785 q^{14} +1.19984i q^{15} -4.59054 q^{16} -2.63979 q^{17} -3.47785i q^{18} -1.84186i q^{19} +1.81358i q^{20} +1.08494i q^{21} -1.52593 q^{22} +3.82692 q^{23} -0.745382i q^{24} +3.77696 q^{25} +5.23255 q^{27} +1.63989i q^{28} -7.54322 q^{29} -2.28912 q^{30} -7.86730i q^{31} -7.38400i q^{32} -0.867749i q^{33} -5.03633i q^{34} -1.10591 q^{35} +2.98939 q^{36} -3.45786i q^{37} +3.51399 q^{38} +0.759794 q^{40} -10.9578i q^{41} -2.06989 q^{42} +2.63910 q^{43} -1.31161i q^{44} +2.01599i q^{45} +7.30119i q^{46} -5.22430i q^{47} +4.98044 q^{48} -1.00000 q^{49} +7.20587i q^{50} +2.86401 q^{51} +6.15957 q^{53} +9.98293i q^{54} +0.884527 q^{55} +0.687029 q^{56} +1.99830i q^{57} -14.3913i q^{58} -5.10250i q^{59} -1.96762i q^{60} +3.31543 q^{61} +15.0096 q^{62} +1.82292i q^{63} +4.90649 q^{64} +1.65553 q^{66} -13.9305i q^{67} +4.32898 q^{68} -4.15196 q^{69} -2.10992i q^{70} +6.69004i q^{71} -1.25240i q^{72} -15.0774i q^{73} +6.59708 q^{74} -4.09775 q^{75} +3.02045i q^{76} +0.799816 q^{77} -8.10529 q^{79} +5.07673i q^{80} -0.208236 q^{81} +20.9059 q^{82} +15.6338i q^{83} -1.77918i q^{84} +2.91938i q^{85} +5.03501i q^{86} +8.18390 q^{87} -0.549497 q^{88} +2.27897i q^{89} -3.84620 q^{90} -6.27574 q^{92} +8.53552i q^{93} +9.96718 q^{94} -2.03694 q^{95} +8.01116i q^{96} +16.4949i q^{97} -1.90785i q^{98} -1.45800i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{3} - 16 q^{4}+O(q^{10}) \) 12 * q - 8 * q^3 - 16 * q^4	\( 12 q - 8 q^{3} - 16 q^{4} + 28 q^{10} + 46 q^{12} - 4 q^{14} + 46 q^{17} - 8 q^{22} + 36 q^{23} + 20 q^{25} - 20 q^{27} - 30 q^{29} - 28 q^{30} - 4 q^{35} - 44 q^{36} + 22 q^{38} - 28 q^{40} + 16 q^{42} + 36 q^{43} - 22 q^{48} - 12 q^{49} - 28 q^{51} - 50 q^{53} + 6 q^{56} + 32 q^{61} + 18 q^{62} + 14 q^{64} + 32 q^{66} - 68 q^{68} + 2 q^{69} - 28 q^{74} - 30 q^{75} + 16 q^{77} + 4 q^{79} - 12 q^{81} + 20 q^{82} + 26 q^{87} + 96 q^{88} - 64 q^{92} - 28 q^{94} + 14 q^{95}+O(q^{100}) \) 12 * q - 8 * q^3 - 16 * q^4 + 28 * q^10 + 46 * q^12 - 4 * q^14 + 46 * q^17 - 8 * q^22 + 36 * q^23 + 20 * q^25 - 20 * q^27 - 30 * q^29 - 28 * q^30 - 4 * q^35 - 44 * q^36 + 22 * q^38 - 28 * q^40 + 16 * q^42 + 36 * q^43 - 22 * q^48 - 12 * q^49 - 28 * q^51 - 50 * q^53 + 6 * q^56 + 32 * q^61 + 18 * q^62 + 14 * q^64 + 32 * q^66 - 68 * q^68 + 2 * q^69 - 28 * q^74 - 30 * q^75 + 16 * q^77 + 4 * q^79 - 12 * q^81 + 20 * q^82 + 26 * q^87 + 96 * q^88 - 64 * q^92 - 28 * q^94 + 14 * q^95

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