LMFDB - Embedded newform 2340.2.fo.b.1601.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2340,2,Mod(1241,2340)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2340, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2340.1241"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2340.fo (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.6849940730$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1601.10
Character	$\chi$	$=$	2340.1601
Dual form			2340.2.fo.b.2321.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{5} +(4.91520 - 1.31702i) q^{7} +(-3.41018 - 0.913756i) q^{11} +(3.41097 - 1.16846i) q^{13} +(-3.88518 + 6.72932i) q^{17} +(1.75838 + 6.56236i) q^{19} +(3.13407 + 5.42838i) q^{23} +1.00000i q^{25} +(1.62296 - 0.937019i) q^{29} +(-1.00592 + 1.00592i) q^{31} +(4.40685 + 2.54429i) q^{35} +(-1.83424 + 6.84546i) q^{37} +(1.55232 - 5.79335i) q^{41} +(-6.96335 - 4.02029i) q^{43} +(6.57647 - 6.57647i) q^{47} +(16.3624 - 9.44686i) q^{49} +10.5138i q^{53} +(-1.76524 - 3.05749i) q^{55} +(-2.73047 - 10.1903i) q^{59} +(-0.963040 + 1.66803i) q^{61} +(3.23815 + 1.58569i) q^{65} +(14.0158 + 3.75552i) q^{67} +(0.328790 - 0.0880990i) q^{71} +(-1.98760 - 1.98760i) q^{73} -17.9652 q^{77} -5.53894 q^{79} +(9.81723 + 9.81723i) q^{83} +(-7.50558 + 2.01112i) q^{85} +(-6.68489 - 1.79121i) q^{89} +(15.2267 - 10.2355i) q^{91} +(-3.39693 + 5.88365i) q^{95} +(-4.47916 - 16.7164i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{7} + 12 q^{13} + 28 q^{19} + 36 q^{31} - 40 q^{37} - 72 q^{43} - 36 q^{49} - 32 q^{61} + 16 q^{67} + 28 q^{73} + 48 q^{79} - 20 q^{85} + 132 q^{91} + 48 q^{97}+O(q^{100}) $ 40 * q + 8 * q^7 + 12 * q^13 + 28 * q^19 + 36 * q^31 - 40 * q^37 - 72 * q^43 - 36 * q^49 - 32 * q^61 + 16 * q^67 + 28 * q^73 + 48 * q^79 - 20 * q^85 + 132 * q^91 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$.

$n$	$937$	$1081$	$1171$	$2081$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$	4.91520	−	1.31702i	1.85777	−	0.497788i	0.857899	−	0.513819i	$-0.171770\pi$
$7$	4.91520	−	1.31702i	1.85777	−	0.497788i	0.999872	+	0.0160306i	$0.00510292\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.41018	−	0.913756i	−1.02821	−	0.275508i	−0.294990	−	0.955500i	$-0.595316\pi$
$11$	−3.41018	−	0.913756i	−1.02821	−	0.275508i	−0.733219	+	0.679993i	$0.761983\pi$
$12$		0			0
$13$	3.41097	−	1.16846i	0.946032	−	0.324073i
$13$	3.41097	−	1.16846i	0.946032	−	0.324073i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.88518	+	6.72932i	−0.942294	+	1.63210i	−0.181212	+	0.983444i	$0.558002\pi$
$17$	−3.88518	+	6.72932i	−0.942294	+	1.63210i	−0.761081	+	0.648656i	$0.775331\pi$
$18$		0			0
$19$	1.75838	+	6.56236i	0.403400	+	1.50551i	0.806988	+	0.590568i	$0.201096\pi$
$19$	1.75838	+	6.56236i	0.403400	+	1.50551i	−0.403588	+	0.914941i	$0.632237\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.13407	+	5.42838i	0.653500	+	1.13189i	0.982268	+	0.187484i	$0.0600332\pi$
$23$	3.13407	+	5.42838i	0.653500	+	1.13189i	−0.328768	+	0.944411i	$0.606633\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.62296	−	0.937019i	0.301377	−	0.174000i	−0.341684	−	0.939815i	$-0.610997\pi$
$29$	1.62296	−	0.937019i	0.301377	−	0.174000i	0.643061	+	0.765815i	$0.277664\pi$
$30$		0			0
$31$	−1.00592	+	1.00592i	−0.180668	+	0.180668i	−0.791647	−	0.610979i	$-0.790776\pi$
$31$	−1.00592	+	1.00592i	−0.180668	+	0.180668i	0.610979	+	0.791647i	$0.290776\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.40685	+	2.54429i	0.744893	+	0.430064i
$36$		0			0
$37$	−1.83424	+	6.84546i	−0.301547	+	1.12539i	0.634331	+	0.773062i	$0.281276\pi$
$37$	−1.83424	+	6.84546i	−0.301547	+	1.12539i	−0.935877	+	0.352326i	$0.885391\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.55232	−	5.79335i	0.242432	−	0.904769i	−0.732225	−	0.681063i	$-0.761518\pi$
$41$	1.55232	−	5.79335i	0.242432	−	0.904769i	0.974657	−	0.223706i	$-0.0718155\pi$
$42$		0			0
$43$	−6.96335	−	4.02029i	−1.06190	−	0.613089i	−0.135943	−	0.990717i	$-0.543406\pi$
$43$	−6.96335	−	4.02029i	−1.06190	−	0.613089i	−0.925957	+	0.377628i	$0.876740\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.57647	−	6.57647i	0.959277	−	0.959277i	−0.0399256	−	0.999203i	$-0.512712\pi$
$47$	6.57647	−	6.57647i	0.959277	−	0.959277i	0.999203	+	0.0399256i	$0.0127121\pi$
$48$		0			0
$49$	16.3624	−	9.44686i	2.33749	−	1.34955i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			10.5138i			1.44418i	0.691799	+	0.722090i	$0.256818\pi$
$53$			10.5138i			1.44418i	−0.691799	+	0.722090i	$0.743182\pi$
$54$		0			0
$55$	−1.76524	−	3.05749i	−0.238025	−	0.412271i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.73047	−	10.1903i	−0.355477	−	1.32666i	−0.879883	−	0.475190i	$-0.842379\pi$
$59$	−2.73047	−	10.1903i	−0.355477	−	1.32666i	0.524406	−	0.851468i	$-0.324287\pi$
$60$		0			0
$61$	−0.963040	+	1.66803i	−0.123305	+	0.213570i	−0.921069	−	0.389400i	$-0.872683\pi$
$61$	−0.963040	+	1.66803i	−0.123305	+	0.213570i	0.797764	+	0.602969i	$0.206016\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.23815	+	1.58569i	0.401642	+	0.196681i
$66$		0			0
$67$	14.0158	+	3.75552i	1.71230	+	0.458810i	0.975987	−	0.217829i	$-0.0698975\pi$
$67$	14.0158	+	3.75552i	1.71230	+	0.458810i	0.736315	+	0.676639i	$0.236564\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.328790	−	0.0880990i	0.0390202	−	0.0104554i	−0.239256	−	0.970956i	$-0.576904\pi$
$71$	0.328790	−	0.0880990i	0.0390202	−	0.0104554i	0.278276	+	0.960501i	$0.410237\pi$
$72$		0			0
$73$	−1.98760	−	1.98760i	−0.232631	−	0.232631i	0.581159	−	0.813790i	$-0.302599\pi$
$73$	−1.98760	−	1.98760i	−0.232631	−	0.232631i	−0.813790	+	0.581159i	$0.802599\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−17.9652			−2.04732
$78$		0			0
$79$	−5.53894			−0.623180			−0.311590	−	0.950217i	$-0.600862\pi$
$79$	−5.53894			−0.623180			−0.311590	+	0.950217i	$0.600862\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	9.81723	+	9.81723i	1.07758	+	1.07758i	0.996726	+	0.0808547i	$0.0257650\pi$
$83$	9.81723	+	9.81723i	1.07758	+	1.07758i	0.0808547	+	0.996726i	$0.474235\pi$
$84$		0			0
$85$	−7.50558	+	2.01112i	−0.814095	+	0.218136i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.68489	−	1.79121i	−0.708597	−	0.189868i	−0.113519	−	0.993536i	$-0.536212\pi$
$89$	−6.68489	−	1.79121i	−0.708597	−	0.189868i	−0.595078	+	0.803668i	$0.702879\pi$
$90$		0			0
$91$	15.2267	−	10.2355i	1.59619	−	1.07298i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.39693	+	5.88365i	−0.348517	+	0.603650i
$96$		0			0
$97$	−4.47916	−	16.7164i	−0.454790	−	1.69730i	−0.688706	−	0.725041i	$-0.741821\pi$
$97$	−4.47916	−	16.7164i	−0.454790	−	1.69730i	0.233916	−	0.972257i	$-0.424846\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.886502	+	1.53547i	0.0882102	+	0.152785i	0.906755	−	0.421659i	$-0.138552\pi$
$101$	0.886502	+	1.53547i	0.0882102	+	0.152785i	−0.818544	+	0.574443i	$0.805219\pi$
$102$		0			0
$103$			9.63862i			0.949721i	0.880061	+	0.474861i	$0.157502\pi$
$103$			9.63862i			0.949721i	−0.880061	+	0.474861i	$0.842498\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.97946	−	2.29754i	0.384709	−	0.222112i	−0.295156	−	0.955449i	$-0.595372\pi$
$107$	3.97946	−	2.29754i	0.384709	−	0.222112i	0.679865	+	0.733337i	$0.262038\pi$
$108$		0			0
$109$	−2.16464	+	2.16464i	−0.207335	+	0.207335i	−0.803134	−	0.595799i	$-0.796835\pi$
$109$	−2.16464	+	2.16464i	−0.207335	+	0.207335i	0.595799	+	0.803134i	$0.296835\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.81298	−	1.62408i	−0.264623	−	0.152780i	0.361818	−	0.932249i	$-0.382156\pi$
$113$	−2.81298	−	1.62408i	−0.264623	−	0.152780i	−0.626442	+	0.779468i	$0.715489\pi$
$114$		0			0
$115$	−1.62232	+	6.05457i	−0.151282	+	0.564591i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−10.2337	+	38.1928i	−0.938125	+	3.50113i
$120$		0			0
$121$	1.26812	+	0.732149i	0.115284	+	0.0665590i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	9.82773	−	5.67404i	0.872070	−	0.503490i	0.00403443	−	0.999992i	$-0.498716\pi$
$127$	9.82773	−	5.67404i	0.872070	−	0.503490i	0.868036	+	0.496502i	$0.165382\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$			1.30632i			0.114134i	0.998370	+	0.0570670i	$0.0181749\pi$
$131$			1.30632i			0.114134i	−0.998370	+	0.0570670i	$0.981825\pi$
$132$		0			0
$133$	17.2856	+	29.9395i	1.49885	+	2.59608i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.81041	−	6.75655i	−0.154674	−	0.577251i	−0.999133	−	0.0416311i	$-0.986745\pi$
$137$	−1.81041	−	6.75655i	−0.154674	−	0.577251i	0.844459	−	0.535620i	$-0.179922\pi$
$138$		0			0
$139$	4.67361	−	8.09494i	0.396411	−	0.686603i	−0.596869	−	0.802338i	$-0.703589\pi$
$139$	4.67361	−	8.09494i	0.396411	−	0.686603i	0.993280	+	0.115735i	$0.0369223\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−12.6997	+	0.867877i	−1.06200	+	0.0725755i
$144$		0			0
$145$	1.81018	+	0.485037i	0.150327	+	0.0402801i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.1927	−	2.73112i	0.835018	−	0.223742i	0.184116	−	0.982904i	$-0.441058\pi$
$149$	10.1927	−	2.73112i	0.835018	−	0.223742i	0.650902	+	0.759162i	$0.274391\pi$
$150$		0			0
$151$	−0.397738	−	0.397738i	−0.0323675	−	0.0323675i	0.690738	−	0.723105i	$-0.257286\pi$
$151$	−0.397738	−	0.397738i	−0.0323675	−	0.0323675i	−0.723105	+	0.690738i	$0.757286\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.42258			−0.114265
$156$		0			0
$157$	4.16188			0.332154			0.166077	−	0.986113i	$-0.446890\pi$
$157$	4.16188			0.332154			0.166077	+	0.986113i	$0.446890\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	22.5539	+	22.5539i	1.77750	+	1.77750i
$162$		0			0
$163$	−2.29310	+	0.614433i	−0.179609	+	0.0481261i	−0.347503	−	0.937679i	$-0.612970\pi$
$163$	−2.29310	+	0.614433i	−0.179609	+	0.0481261i	0.167893	+	0.985805i	$0.446304\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.36269	−	1.16898i	−0.337595	−	0.0904584i	0.0860388	−	0.996292i	$-0.472579\pi$
$167$	−4.36269	−	1.16898i	−0.337595	−	0.0904584i	−0.423634	+	0.905833i	$0.639246\pi$
$168$		0			0
$169$	10.2694	−	7.97117i	0.789953	−	0.613167i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.31182	−	2.27214i	0.0997360	−	0.172748i	−0.811839	−	0.583881i	$-0.801534\pi$
$173$	1.31182	−	2.27214i	0.0997360	−	0.172748i	0.911575	+	0.411133i	$0.134867\pi$
$174$		0			0
$175$	1.31702	+	4.91520i	0.0995576	+	0.371554i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.25552	+	5.63872i	0.243329	+	0.421458i	0.961660	−	0.274243i	$-0.0884273\pi$
$179$	3.25552	+	5.63872i	0.243329	+	0.421458i	−0.718332	+	0.695701i	$0.755094\pi$
$180$		0			0
$181$			9.87330i			0.733876i	0.930245	+	0.366938i	$0.119594\pi$
$181$			9.87330i			0.733876i	−0.930245	+	0.366938i	$0.880406\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.13747	+	3.54347i	−0.451236	+	0.260521i
$186$		0			0
$187$	19.3981	−	19.3981i	1.41853	−	1.41853i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.92073	+	5.72774i	0.717839	+	0.414444i	0.813957	−	0.580926i	$-0.197309\pi$
$191$	9.92073	+	5.72774i	0.717839	+	0.414444i	−0.0961179	+	0.995370i	$0.530643\pi$
$192$		0			0
$193$	3.56621	−	13.3093i	0.256702	−	0.958023i	−0.710434	−	0.703764i	$-0.751501\pi$
$193$	3.56621	−	13.3093i	0.256702	−	0.958023i	0.967136	−	0.254260i	$-0.0818319\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.72023	−	21.3482i	0.407549	−	1.52099i	−0.391756	−	0.920069i	$-0.628132\pi$
$197$	5.72023	−	21.3482i	0.407549	−	1.52099i	0.799305	−	0.600926i	$-0.205201\pi$
$198$		0			0
$199$	5.45174	+	3.14756i	0.386463	+	0.223125i	0.680627	−	0.732630i	$-0.261708\pi$
$199$	5.45174	+	3.14756i	0.386463	+	0.223125i	−0.294163	+	0.955755i	$0.595041\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.74311	−	6.74311i	0.473274	−	0.473274i
$204$		0			0
$205$	5.19417	−	2.99886i	0.362777	−	0.209449i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	23.9856i		−	1.65912i
$210$		0			0
$211$	8.67159	+	15.0196i	0.596977	+	1.03399i	0.993265	+	0.115868i	$0.0369649\pi$
$211$	8.67159	+	15.0196i	0.596977	+	1.03399i	−0.396288	+	0.918126i	$0.629702\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.08106	−	7.76661i	−0.141927	−	0.529678i
$216$		0			0
$217$	−3.61947	+	6.26911i	−0.245706	+	0.425575i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.38925	+	27.4932i	−0.362520	+	1.84939i
$222$		0			0
$223$	−2.48941	−	0.667035i	−0.166703	−	0.0446679i	0.174502	−	0.984657i	$-0.444168\pi$
$223$	−2.48941	−	0.667035i	−0.166703	−	0.0446679i	−0.341205	+	0.939989i	$0.610835\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−21.0657	+	5.64454i	−1.39818	+	0.374641i	−0.877691	−	0.479227i	$-0.840917\pi$
$227$	−21.0657	+	5.64454i	−1.39818	+	0.374641i	−0.520489	+	0.853868i	$0.674250\pi$
$228$		0			0
$229$	−3.71218	−	3.71218i	−0.245308	−	0.245308i	0.573734	−	0.819042i	$-0.305494\pi$
$229$	−3.71218	−	3.71218i	−0.245308	−	0.245308i	−0.819042	+	0.573734i	$0.805494\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.1730			0.731968			0.365984	−	0.930621i	$-0.380733\pi$
$233$	11.1730			0.731968			0.365984	+	0.930621i	$0.380733\pi$
$234$		0			0
$235$	9.30054			0.606700
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−14.2925	−	14.2925i	−0.924505	−	0.924505i	0.0728388	−	0.997344i	$-0.476794\pi$
$239$	−14.2925	−	14.2925i	−0.924505	−	0.924505i	−0.997344	+	0.0728388i	$0.976794\pi$
$240$		0			0
$241$	−5.79026	+	1.55149i	−0.372983	+	0.0999405i	−0.440441	−	0.897782i	$-0.645178\pi$
$241$	−5.79026	+	1.55149i	−0.372983	+	0.0999405i	0.0674578	+	0.997722i	$0.478511\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	18.2499	+	4.89006i	1.16595	+	0.312414i
$246$		0			0
$247$	13.6656	+	20.3294i	0.869524	+	1.29353i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−8.47750	+	14.6835i	−0.535095	+	0.926812i	0.464064	+	0.885802i	$0.346391\pi$
$251$	−8.47750	+	14.6835i	−0.535095	+	0.926812i	−0.999159	+	0.0410100i	$0.986942\pi$
$252$		0			0
$253$	−5.72756	−	21.3755i	−0.360088	−	1.34387i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.06559	+	12.2380i	0.440739	+	0.763383i	0.997745	−	0.0671261i	$-0.0213830\pi$
$257$	7.06559	+	12.2380i	0.440739	+	0.763383i	−0.557005	+	0.830509i	$0.688050\pi$
$258$		0			0
$259$			36.0625i			2.24082i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.74258	+	3.89283i	−0.415765	+	0.240042i	−0.693264	−	0.720684i	$-0.743828\pi$
$263$	−6.74258	+	3.89283i	−0.415765	+	0.240042i	0.277499	+	0.960726i	$0.410495\pi$
$264$		0			0
$265$	−7.43437	+	7.43437i	−0.456690	+	0.456690i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.34421	−	5.39488i	−0.569726	−	0.328932i	0.187314	−	0.982300i	$-0.440022\pi$
$269$	−9.34421	−	5.39488i	−0.569726	−	0.328932i	−0.757040	+	0.653368i	$0.773355\pi$
$270$		0			0
$271$	−6.59816	+	24.6247i	−0.400810	+	1.49584i	0.410846	+	0.911705i	$0.365234\pi$
$271$	−6.59816	+	24.6247i	−0.400810	+	1.49584i	−0.811655	+	0.584137i	$0.801433\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.913756	−	3.41018i	0.0551015	−	0.205642i
$276$		0			0
$277$	−27.4764	−	15.8635i	−1.65090	−	0.953145i	−0.976705	−	0.214587i	$-0.931160\pi$
$277$	−27.4764	−	15.8635i	−1.65090	−	0.953145i	−0.674190	−	0.738558i	$-0.735507\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	8.57802	−	8.57802i	0.511722	−	0.511722i	−0.403332	−	0.915054i	$-0.632148\pi$
$281$	8.57802	−	8.57802i	0.511722	−	0.511722i	0.915054	+	0.403332i	$0.132148\pi$
$282$		0			0
$283$	−4.18008	+	2.41337i	−0.248480	+	0.143460i	−0.619068	−	0.785337i	$-0.712489\pi$
$283$	−4.18008	+	2.41337i	−0.248480	+	0.143460i	0.370588	+	0.928797i	$0.379156\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	30.5199i		−	1.80153i
$288$		0			0
$289$	−21.6892	−	37.5668i	−1.27583	−	2.20981i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.72872	−	13.9158i	−0.217834	−	0.812969i	−0.985150	−	0.171699i	$-0.945074\pi$
$293$	−3.72872	−	13.9158i	−0.217834	−	0.812969i	0.767315	−	0.641270i	$-0.221592\pi$
$294$		0			0
$295$	5.27487	−	9.13633i	0.307115	−	0.531938i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	17.0331	+	14.8540i	0.985048	+	0.859027i
$300$		0			0
$301$	−39.5211	−	10.5896i	−2.27796	−	0.610376i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.86045	+	0.498506i	−0.106529	+	0.0285444i
$306$		0			0
$307$	−2.35939	−	2.35939i	−0.134657	−	0.134657i	0.636565	−	0.771223i	$-0.280355\pi$
$307$	−2.35939	−	2.35939i	−0.134657	−	0.134657i	−0.771223	+	0.636565i	$0.780355\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	19.6010			1.11147			0.555736	−	0.831359i	$-0.312437\pi$
$311$	19.6010			1.11147			0.555736	+	0.831359i	$0.312437\pi$
$312$		0			0
$313$	−15.2645			−0.862798			−0.431399	−	0.902161i	$-0.641980\pi$
$313$	−15.2645			−0.862798			−0.431399	+	0.902161i	$0.641980\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.7945	+	10.7945i	0.606277	+	0.606277i	0.941971	−	0.335694i	$-0.108971\pi$
$317$	10.7945	+	10.7945i	0.606277	+	0.606277i	−0.335694	+	0.941971i	$0.608971\pi$
$318$		0			0
$319$	−6.39081	+	1.71241i	−0.357817	+	0.0958767i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−50.9919	−	13.6632i	−2.83726	−	0.760242i
$324$		0			0
$325$	1.16846	+	3.41097i	0.0648146	+	0.189206i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	23.6633	−	40.9860i	1.30460	−	2.25963i
$330$		0			0
$331$	3.58052	+	13.3627i	0.196803	+	0.734479i	0.991793	+	0.127856i	$0.0408096\pi$
$331$	3.58052	+	13.3627i	0.196803	+	0.734479i	−0.794990	+	0.606623i	$0.792524\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	7.25511	+	12.5662i	0.396389	+	0.686566i
$336$		0			0
$337$		−	14.8786i		−	0.810490i	−0.914208	−	0.405245i	$-0.867186\pi$
$337$		−	14.8786i		−	0.810490i	0.914208	−	0.405245i	$-0.132814\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.34953	−	2.51120i	0.235540	−	0.135989i
$342$		0			0
$343$	42.7957	−	42.7957i	2.31075	−	2.31075i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−27.8810	−	16.0971i	−1.49673	−	0.864138i	−0.496737	−	0.867901i	$-0.665469\pi$
$347$	−27.8810	−	16.0971i	−1.49673	−	0.864138i	−0.999993	+	0.00376328i	$0.998802\pi$
$348$		0			0
$349$	−9.13898	+	34.1071i	−0.489198	+	1.82571i	0.0711640	+	0.997465i	$0.477329\pi$
$349$	−9.13898	+	34.1071i	−0.489198	+	1.82571i	−0.560362	+	0.828248i	$0.689338\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.89877	−	22.0145i	0.313960	−	1.17171i	−0.610994	−	0.791635i	$-0.709230\pi$
$353$	5.89877	−	22.0145i	0.313960	−	1.17171i	0.924954	−	0.380079i	$-0.124103\pi$
$354$		0			0
$355$	0.294785	+	0.170194i	0.0156456	+	0.00903297i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.83163	+	6.83163i	−0.360560	+	0.360560i	−0.864019	−	0.503459i	$-0.832060\pi$
$359$	−6.83163	+	6.83163i	−0.360560	+	0.360560i	0.503459	+	0.864019i	$0.332060\pi$
$360$		0			0
$361$	−23.5182	+	13.5782i	−1.23780	+	0.714644i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	2.81089i		−	0.147129i
$366$		0			0
$367$	−5.52736	−	9.57367i	−0.288526	−	0.499742i	0.684932	−	0.728607i	$-0.259832\pi$
$367$	−5.52736	−	9.57367i	−0.288526	−	0.499742i	−0.973458	+	0.228865i	$0.926499\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	13.8469	+	51.6774i	0.718896	+	2.68295i
$372$		0			0
$373$	11.6015	−	20.0944i	0.600703	−	1.04045i	−0.392012	−	0.919960i	$-0.628221\pi$
$373$	11.6015	−	20.0944i	0.600703	−	1.04045i	0.992715	−	0.120488i	$-0.0384459\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.44101	−	5.09251i	0.228723	−	0.262278i
$378$		0			0
$379$	−13.5502	−	3.63077i	−0.696029	−	0.186500i	−0.106578	−	0.994304i	$-0.533989\pi$
$379$	−13.5502	−	3.63077i	−0.696029	−	0.186500i	−0.589451	+	0.807804i	$0.700656\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.5614	−	4.43760i	0.846246	−	0.226751i	0.190457	−	0.981695i	$-0.439003\pi$
$383$	16.5614	−	4.43760i	0.846246	−	0.226751i	0.655789	+	0.754944i	$0.272336\pi$
$384$		0			0
$385$	−12.7033	−	12.7033i	−0.647420	−	0.647420i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−5.68999			−0.288494			−0.144247	−	0.989542i	$-0.546076\pi$
$389$	−5.68999			−0.288494			−0.144247	+	0.989542i	$0.546076\pi$
$390$		0			0
$391$	−48.7057			−2.46315
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.91662	−	3.91662i	−0.197067	−	0.197067i
$396$		0			0
$397$	−5.64065	+	1.51141i	−0.283096	+	0.0758553i	−0.397573	−	0.917571i	$-0.630147\pi$
$397$	−5.64065	+	1.51141i	−0.283096	+	0.0758553i	0.114477	+	0.993426i	$0.463481\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.50765	+	2.01167i	0.374914	+	0.100458i	0.441355	−	0.897332i	$-0.354498\pi$
$401$	7.50765	+	2.01167i	0.374914	+	0.100458i	−0.0664412	+	0.997790i	$0.521164\pi$
$402$		0			0
$403$	−2.25578	+	4.60653i	−0.112368	+	0.229468i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	12.5102	−	21.6682i	0.620106	−	1.07405i
$408$		0			0
$409$	−7.51693	−	28.0536i	−0.371688	−	1.38716i	−0.858124	−	0.513443i	$-0.828370\pi$
$409$	−7.51693	−	28.0536i	−0.371688	−	1.38716i	0.486436	−	0.873716i	$-0.338297\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−26.8416	−	46.4910i	−1.32079	−	2.28767i
$414$		0			0
$415$			13.8837i			0.681522i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−17.1629	+	9.90900i	−0.838462	+	0.484086i	−0.856741	−	0.515746i	$-0.827515\pi$
$419$	−17.1629	+	9.90900i	−0.838462	+	0.484086i	0.0182789	+	0.999833i	$0.494181\pi$
$420$		0			0
$421$	−8.01546	+	8.01546i	−0.390650	+	0.390650i	−0.874919	−	0.484269i	$-0.839086\pi$
$421$	−8.01546	+	8.01546i	−0.390650	+	0.390650i	0.484269	+	0.874919i	$0.339086\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.72932	−	3.88518i	−0.326420	−	0.188459i
$426$		0			0
$427$	−2.53669	+	9.46706i	−0.122759	+	0.458143i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.62197	−	6.05329i	0.0781278	−	0.291577i	−0.915797	−	0.401643i	$-0.868439\pi$
$431$	1.62197	−	6.05329i	0.0781278	−	0.291577i	0.993924	+	0.110066i	$0.0351061\pi$
$432$		0			0
$433$	−26.0659	−	15.0492i	−1.25265	−	0.723217i	−0.281014	−	0.959704i	$-0.590671\pi$
$433$	−26.0659	−	15.0492i	−1.25265	−	0.723217i	−0.971635	+	0.236486i	$0.924004\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−30.1121	+	30.1121i	−1.44046	+	1.44046i
$438$		0			0
$439$	13.6256	−	7.86674i	0.650314	−	0.375459i	−0.138262	−	0.990396i	$-0.544152\pi$
$439$	13.6256	−	7.86674i	0.650314	−	0.375459i	0.788577	+	0.614937i	$0.210818\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	14.6529i		−	0.696180i	−0.937461	−	0.348090i	$-0.886830\pi$
$443$		−	14.6529i		−	0.696180i	0.937461	−	0.348090i	$-0.113170\pi$
$444$		0			0
$445$	−3.46035	−	5.99351i	−0.164037	−	0.284120i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−8.84623	−	33.0146i	−0.417480	−	1.55805i	−0.779817	−	0.626008i	$-0.784688\pi$
$449$	−8.84623	−	33.0146i	−0.417480	−	1.55805i	0.362337	−	0.932047i	$-0.381979\pi$
$450$		0			0
$451$	−10.5874	+	18.3379i	−0.498542	+	0.863500i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	18.0045	+	3.52927i	0.844065	+	0.165455i
$456$		0			0
$457$	3.08340	+	0.826195i	0.144236	+	0.0386478i	0.330214	−	0.943906i	$-0.392879\pi$
$457$	3.08340	+	0.826195i	0.144236	+	0.0386478i	−0.185979	+	0.982554i	$0.559546\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.54114	+	1.48474i	−0.258077	+	0.0691514i	−0.385537	−	0.922692i	$-0.625984\pi$
$461$	−5.54114	+	1.48474i	−0.258077	+	0.0691514i	0.127461	+	0.991844i	$0.459317\pi$
$462$		0			0
$463$	26.1825	+	26.1825i	1.21680	+	1.21680i	0.968745	+	0.248060i	$0.0797930\pi$
$463$	26.1825	+	26.1825i	1.21680	+	1.21680i	0.248060	+	0.968745i	$0.420207\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.6072			−0.953586			−0.476793	−	0.879016i	$-0.658201\pi$
$467$	−20.6072			−0.953586			−0.476793	+	0.879016i	$0.658201\pi$
$468$		0			0
$469$	73.8365			3.40945
$470$		0			0
$471$		0			0
$472$		0			0
$473$	20.0727	+	20.0727i	0.922945	+	0.922945i
$474$		0			0
$475$	−6.56236	+	1.75838i	−0.301102	+	0.0806800i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	33.8617	+	9.07322i	1.54718	+	0.414566i	0.928578	−	0.371137i	$-0.121032\pi$
$479$	33.8617	+	9.07322i	1.54718	+	0.414566i	0.618603	+	0.785703i	$0.287699\pi$
$480$		0			0
$481$	1.74214	+	25.4929i	0.0794348	+	1.16238i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.65307	−	14.9876i	0.392916	−	0.680550i
$486$		0			0
$487$	3.08456	+	11.5117i	0.139775	+	0.521646i	0.999933	+	0.0116181i	$0.00369823\pi$
$487$	3.08456	+	11.5117i	0.139775	+	0.521646i	−0.860158	+	0.510028i	$0.829635\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.20961	+	14.2195i	0.370494	+	0.641715i	0.989642	−	0.143560i	$-0.0458549\pi$
$491$	8.20961	+	14.2195i	0.370494	+	0.641715i	−0.619147	+	0.785275i	$0.712522\pi$
$492$		0			0
$493$			14.5619i			0.655836i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.50004	−	0.866048i	0.0672860	−	0.0388476i
$498$		0			0
$499$	16.3880	−	16.3880i	0.733625	−	0.733625i	−0.237711	−	0.971336i	$-0.576397\pi$
$499$	16.3880	−	16.3880i	0.733625	−	0.733625i	0.971336	+	0.237711i	$0.0763970\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	37.2392	+	21.5001i	1.66041	+	0.958641i	0.972517	+	0.232834i	$0.0747998\pi$
$503$	37.2392	+	21.5001i	1.66041	+	0.958641i	0.687898	+	0.725807i	$0.258534\pi$
$504$		0			0
$505$	−0.458887	+	1.71259i	−0.0204202	+	0.0762093i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.90063	+	10.8253i	−0.128568	+	0.479824i	−0.999942	−	0.0107968i	$-0.996563\pi$
$509$	−2.90063	+	10.8253i	−0.128568	+	0.479824i	0.871373	+	0.490621i	$0.163230\pi$
$510$		0			0
$511$	−12.3872	−	7.15174i	−0.547976	−	0.316374i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.81553	+	6.81553i	−0.300328	+	0.300328i
$516$		0			0
$517$	−28.4363	+	16.4177i	−1.25063	+	0.722049i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	0.421232i		−	0.0184545i	−0.999957	−	0.00922726i	$-0.997063\pi$
$521$		−	0.421232i		−	0.0184545i	0.999957	−	0.00922726i	$-0.00293717\pi$
$522$		0			0
$523$	14.2808	+	24.7350i	0.624454	+	1.08159i	0.988646	+	0.150262i	$0.0480118\pi$
$523$	14.2808	+	24.7350i	0.624454	+	1.08159i	−0.364192	+	0.931324i	$0.618655\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.86098	−	10.6773i	−0.124626	−	0.465112i
$528$		0			0
$529$	−8.14484	+	14.1073i	−0.354124	+	0.613360i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.47438	−	21.5748i	−0.0638626	−	0.934506i
$534$		0			0
$535$	4.43851	+	1.18930i	0.191894	+	0.0514178i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−64.4311	+	17.2643i	−2.77524	+	0.743624i
$540$		0			0
$541$	−6.18704	−	6.18704i	−0.266002	−	0.266002i	0.561485	−	0.827487i	$-0.310230\pi$
$541$	−6.18704	−	6.18704i	−0.266002	−	0.266002i	−0.827487	+	0.561485i	$0.810230\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.06126			−0.131130
$546$		0			0
$547$	−5.98071			−0.255717			−0.127858	−	0.991792i	$-0.540810\pi$
$547$	−5.98071			−0.255717			−0.127858	+	0.991792i	$0.540810\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.00284	+	9.00284i	0.383534	+	0.383534i
$552$		0			0
$553$	−27.2250	+	7.29492i	−1.15772	+	0.310211i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.6228	−	3.11431i	−0.492472	−	0.131957i	0.00403211	−	0.999992i	$-0.498717\pi$
$557$	−11.6228	−	3.11431i	−0.492472	−	0.131957i	−0.496504	+	0.868034i	$0.665383\pi$
$558$		0			0
$559$	−28.4493	−	5.57668i	−1.20328	−	0.235868i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5.15030	+	8.92058i	−0.217059	+	0.375958i	−0.953908	−	0.300100i	$-0.902980\pi$
$563$	−5.15030	+	8.92058i	−0.217059	+	0.375958i	0.736848	+	0.676058i	$0.236313\pi$
$564$		0			0
$565$	−0.840684	−	3.13748i	−0.0353678	−	0.131995i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.0379	−	24.3144i	−0.588501	−	1.01931i	−0.994429	−	0.105409i	$-0.966385\pi$
$569$	−14.0379	−	24.3144i	−0.588501	−	1.01931i	0.405928	−	0.913905i	$-0.366948\pi$
$570$		0			0
$571$		−	17.9916i		−	0.752924i	−0.926432	−	0.376462i	$-0.877140\pi$
$571$		−	17.9916i		−	0.752924i	0.926432	−	0.376462i	$-0.122860\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−5.42838	+	3.13407i	−0.226379	+	0.130700i
$576$		0			0
$577$	−2.85046	+	2.85046i	−0.118666	+	0.118666i	−0.763946	−	0.645280i	$-0.776741\pi$
$577$	−2.85046	+	2.85046i	−0.118666	+	0.118666i	0.645280	+	0.763946i	$0.276741\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	61.1831	+	35.3241i	2.53830	+	1.46549i
$582$		0			0
$583$	9.60704	−	35.8539i	0.397883	−	1.48492i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.08005	+	7.76284i	−0.0858527	+	0.320407i	−0.995474	−	0.0950312i	$-0.969705\pi$
$587$	−2.08005	+	7.76284i	−0.0858527	+	0.320407i	0.909622	+	0.415438i	$0.136372\pi$
$588$		0			0
$589$	−8.36999	−	4.83242i	−0.344879	−	0.199116i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−19.9507	+	19.9507i	−0.819276	+	0.819276i	−0.986003	−	0.166727i	$-0.946680\pi$
$593$	−19.9507	+	19.9507i	−0.819276	+	0.819276i	0.166727	+	0.986003i	$0.446680\pi$
$594$		0			0
$595$	−34.2427	+	19.7701i	−1.40382	+	0.810493i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	5.01691i		−	0.204986i	−0.994734	−	0.102493i	$-0.967318\pi$
$599$		−	5.01691i		−	0.204986i	0.994734	−	0.102493i	$-0.0326819\pi$
$600$		0			0
$601$	−11.4153	−	19.7719i	−0.465641	−	0.806514i	0.533589	−	0.845744i	$-0.320843\pi$
$601$	−11.4153	−	19.7719i	−0.465641	−	0.806514i	−0.999230	+	0.0392296i	$0.987510\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.378988	+	1.41440i	0.0154081	+	0.0575037i
$606$		0			0
$607$	11.5814	−	20.0596i	0.470074	−	0.814193i	−0.529340	−	0.848410i	$-0.677560\pi$
$607$	11.5814	−	20.0596i	0.470074	−	0.814193i	0.999414	+	0.0342171i	$0.0108938\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	14.7478	−	30.1165i	0.596631	−	1.21838i
$612$		0			0
$613$	5.92571	+	1.58779i	0.239337	+	0.0641302i	0.376494	−	0.926419i	$-0.377130\pi$
$613$	5.92571	+	1.58779i	0.239337	+	0.0641302i	−0.137157	+	0.990549i	$0.543796\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	45.0349	−	12.0671i	1.81304	−	0.485802i	0.817152	−	0.576422i	$-0.195552\pi$
$617$	45.0349	−	12.0671i	1.81304	−	0.485802i	0.995886	+	0.0906201i	$0.0288849\pi$
$618$		0			0
$619$	−4.91074	−	4.91074i	−0.197379	−	0.197379i	0.601496	−	0.798876i	$-0.294571\pi$
$619$	−4.91074	−	4.91074i	−0.197379	−	0.197379i	−0.798876	+	0.601496i	$0.794571\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−35.2166			−1.41092
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−38.9390	−	38.9390i	−1.55260	−	1.55260i
$630$		0			0
$631$	−15.7564	+	4.22192i	−0.627252	+	0.168072i	−0.558423	−	0.829557i	$-0.688593\pi$
$631$	−15.7564	+	4.22192i	−0.627252	+	0.168072i	−0.0688299	+	0.997628i	$0.521927\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	10.9614	+	2.93710i	0.434990	+	0.116555i
$636$		0			0
$637$	44.7735	−	51.3418i	1.77399	−	2.03424i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	21.2110	−	36.7385i	0.837784	−	1.45108i	−0.0539589	−	0.998543i	$-0.517184\pi$
$641$	21.2110	−	36.7385i	0.837784	−	1.45108i	0.891743	−	0.452542i	$-0.149483\pi$
$642$		0			0
$643$	4.87370	+	18.1889i	0.192200	+	0.717300i	0.992974	+	0.118334i	$0.0377552\pi$
$643$	4.87370	+	18.1889i	0.192200	+	0.717300i	−0.800774	+	0.598967i	$0.795578\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−17.1488	−	29.7025i	−0.674188	−	1.16773i	−0.976706	−	0.214583i	$-0.931161\pi$
$647$	−17.1488	−	29.7025i	−0.674188	−	1.16773i	0.302518	−	0.953144i	$-0.402173\pi$
$648$		0			0
$649$			37.2456i			1.46202i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.9677	−	8.06426i	0.546598	−	0.315579i	−0.201150	−	0.979560i	$-0.564468\pi$
$653$	13.9677	−	8.06426i	0.546598	−	0.315579i	0.747749	+	0.663982i	$0.231135\pi$
$654$		0			0
$655$	−0.923710	+	0.923710i	−0.0360923	+	0.0360923i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.23701	+	1.29154i	0.0871417	+	0.0503113i	0.542938	−	0.839773i	$-0.317312\pi$
$659$	2.23701	+	1.29154i	0.0871417	+	0.0503113i	−0.455796	+	0.890084i	$0.650645\pi$
$660$		0			0
$661$	12.8478	−	47.9485i	0.499720	−	1.86498i	−0.00208455	−	0.999998i	$-0.500664\pi$
$661$	12.8478	−	47.9485i	0.499720	−	1.86498i	0.501804	−	0.864981i	$-0.332670\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.94767	+	33.3931i	−0.346976	+	1.29493i
$666$		0			0
$667$	10.1730	+	5.87337i	0.393899	+	0.227418i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.80832	−	4.80832i	0.185623	−	0.185623i
$672$		0			0
$673$	−33.4345	+	19.3034i	−1.28881	+	0.744092i	−0.978441	−	0.206526i	$-0.933784\pi$
$673$	−33.4345	+	19.3034i	−1.28881	+	0.744092i	−0.310364	+	0.950618i	$0.600451\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	17.9996i		−	0.691782i	−0.938275	−	0.345891i	$-0.887577\pi$
$677$		−	17.9996i		−	0.691782i	0.938275	−	0.345891i	$-0.112423\pi$
$678$		0			0
$679$	−44.0319	−	76.2655i	−1.68979	−	2.92680i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.4871	−	39.1383i	−0.401277	−	1.49759i	−0.810820	−	0.585296i	$-0.800978\pi$
$683$	−10.4871	−	39.1383i	−0.401277	−	1.49759i	0.409543	−	0.912291i	$-0.365688\pi$
$684$		0			0
$685$	3.49745	−	6.05776i	0.133631	−	0.231455i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.2850	+	35.8622i	0.468020	+	1.36624i
$690$		0			0
$691$	−11.9737	−	3.20834i	−0.455501	−	0.122051i	0.0237713	−	0.999717i	$-0.492433\pi$
$691$	−11.9737	−	3.20834i	−0.455501	−	0.122051i	−0.479272	+	0.877666i	$0.659099\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	9.02873	−	2.41924i	0.342479	−	0.0917670i
$696$		0			0
$697$	32.9543	+	32.9543i	1.24823	+	1.24823i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−46.7452			−1.76554			−0.882772	−	0.469802i	$-0.844325\pi$
$701$	−46.7452			−1.76554			−0.882772	+	0.469802i	$0.844325\pi$
$702$		0			0
$703$	−48.1477			−1.81592
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.37958	+	6.37958i	0.239929	+	0.239929i
$708$		0			0
$709$	−33.9244	+	9.09001i	−1.27406	+	0.341382i	−0.831584	−	0.555399i	$-0.812565\pi$
$709$	−33.9244	+	9.09001i	−1.27406	+	0.341382i	−0.442473	+	0.896782i	$0.645899\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−8.61313	−	2.30788i	−0.322564	−	0.0864308i
$714$		0			0
$715$	−9.59373	−	8.36637i	−0.358785	−	0.312885i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	16.7948	−	29.0895i	0.626341	−	1.08485i	−0.361939	−	0.932202i	$-0.617885\pi$
$719$	16.7948	−	29.0895i	0.626341	−	1.08485i	0.988280	−	0.152652i	$-0.0487814\pi$
$720$		0			0
$721$	12.6943	+	47.3757i	0.472760	+	1.76436i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.937019	+	1.62296i	0.0348000	+	0.0602754i
$726$		0			0
$727$		−	25.3263i		−	0.939300i	−0.882853	−	0.469650i	$-0.844380\pi$
$727$		−	25.3263i		−	0.939300i	0.882853	−	0.469650i	$-0.155620\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	54.1077	−	31.2391i	2.00124	−	1.15542i
$732$		0			0
$733$	−36.4588	+	36.4588i	−1.34664	+	1.34664i	−0.457352	+	0.889286i	$0.651202\pi$
$733$	−36.4588	+	36.4588i	−1.34664	+	1.34664i	−0.889286	+	0.457352i	$0.848798\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−44.3648	−	25.6140i	−1.63420	−	0.943505i
$738$		0			0
$739$	1.09790	−	4.09742i	0.0403869	−	0.150726i	−0.942788	−	0.333393i	$-0.891806\pi$
$739$	1.09790	−	4.09742i	0.0403869	−	0.150726i	0.983175	+	0.182667i	$0.0584731\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.1045	−	37.7106i	0.370699	−	1.38347i	−0.488828	−	0.872380i	$-0.662576\pi$
$743$	10.1045	−	37.7106i	0.370699	−	1.38347i	0.859528	−	0.511089i	$-0.170758\pi$
$744$		0			0
$745$	9.13852	+	5.27613i	0.334809	+	0.193302i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	16.5339	−	16.5339i	0.604137	−	0.604137i
$750$		0			0
$751$	−15.0174	+	8.67029i	−0.547992	+	0.316383i	−0.748312	−	0.663347i	$-0.769135\pi$
$751$	−15.0174	+	8.67029i	−0.547992	+	0.316383i	0.200320	+	0.979731i	$0.435802\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	0.562487i		−	0.0204710i
$756$		0			0
$757$	−14.0002	−	24.2491i	−0.508847	−	0.881349i	−0.999948	−	0.0102463i	$-0.996738\pi$
$757$	−14.0002	−	24.2491i	−0.508847	−	0.881349i	0.491100	−	0.871103i	$-0.336595\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.835105	−	3.11666i	−0.0302725	−	0.112979i	0.949136	−	0.314865i	$-0.101959\pi$
$761$	−0.835105	−	3.11666i	−0.0302725	−	0.112979i	−0.979409	+	0.201887i	$0.935293\pi$
$762$		0			0
$763$	−7.78874	+	13.4905i	−0.281971	+	0.488389i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−21.2205	−	31.5682i	−0.766227	−	1.13986i
$768$		0			0
$769$	13.9819	+	3.74644i	0.504201	+	0.135100i	0.501949	−	0.864897i	$-0.332617\pi$
$769$	13.9819	+	3.74644i	0.504201	+	0.135100i	0.00225181	+	0.999997i	$0.499283\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	26.1785	−	7.01452i	0.941576	−	0.252295i	0.244792	−	0.969576i	$-0.421280\pi$
$773$	26.1785	−	7.01452i	0.941576	−	0.252295i	0.696784	+	0.717281i	$0.254614\pi$
$774$		0			0
$775$	−1.00592	−	1.00592i	−0.0361337	−	0.0361337i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	40.7476			1.45993
$780$		0			0
$781$	−1.20174			−0.0430015
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.94289	+	2.94289i	0.105036	+	0.105036i
$786$		0			0
$787$	1.15360	−	0.309107i	0.0411216	−	0.0110185i	−0.238200	−	0.971216i	$-0.576557\pi$
$787$	1.15360	−	0.309107i	0.0411216	−	0.0110185i	0.279321	+	0.960198i	$0.409891\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−15.9653	−	4.27790i	−0.567662	−	0.152104i
$792$		0			0
$793$	−1.33586	+	6.81488i	−0.0474379	+	0.242004i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.2193	−	19.4324i	0.397408	−	0.688331i	−0.595997	−	0.802987i	$-0.703243\pi$
$797$	11.2193	−	19.4324i	0.397408	−	0.688331i	0.993405	+	0.114655i	$0.0365764\pi$
$798$		0			0
$799$	18.7044	+	69.8060i	0.661716	+	2.46956i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.96190	+	8.59427i	0.175102	+	0.303285i
$804$		0			0
$805$			31.8960i			1.12419i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.13097	+	2.38501i	−0.145237	+	0.0838526i	−0.570858	−	0.821049i	$-0.693389\pi$
$809$	−4.13097	+	2.38501i	−0.145237	+	0.0838526i	0.425621	+	0.904902i	$0.360056\pi$
$810$		0			0
$811$	24.0283	−	24.0283i	0.843749	−	0.843749i	−0.145595	−	0.989344i	$-0.546510\pi$
$811$	24.0283	−	24.0283i	0.843749	−	0.843749i	0.989344	+	0.145595i	$0.0465096\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.05593	−	1.18699i	−0.0720162	−	0.0415786i
$816$		0			0
$817$	14.1384	−	52.7652i	0.494640	−	1.84602i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.55836	+	13.2800i	−0.124188	+	0.463474i	−0.999809	−	0.0195230i	$-0.993785\pi$
$821$	−3.55836	+	13.2800i	−0.124188	+	0.463474i	0.875622	+	0.482997i	$0.160452\pi$
$822$		0			0
$823$	−21.9728	−	12.6860i	−0.765923	−	0.442206i	0.0654951	−	0.997853i	$-0.479137\pi$
$823$	−21.9728	−	12.6860i	−0.765923	−	0.442206i	−0.831418	+	0.555647i	$0.812471\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.4353	+	12.4353i	−0.432416	+	0.432416i	−0.889450	−	0.457033i	$-0.848912\pi$
$827$	−12.4353	+	12.4353i	−0.432416	+	0.432416i	0.457033	+	0.889450i	$0.348912\pi$
$828$		0			0
$829$	−7.25977	+	4.19143i	−0.252142	+	0.145574i	−0.620745	−	0.784013i	$-0.713170\pi$
$829$	−7.25977	+	4.19143i	−0.252142	+	0.145574i	0.368603	+	0.929587i	$0.379836\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$			146.811i			5.08670i
$834$		0			0
$835$	−2.25830	−	3.91148i	−0.0781516	−	0.135362i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	7.74456	+	28.9031i	0.267372	+	0.997846i	0.960783	+	0.277303i	$0.0894406\pi$
$839$	7.74456	+	28.9031i	0.267372	+	0.997846i	−0.693411	+	0.720543i	$0.743893\pi$
$840$		0			0
$841$	−12.7440	+	22.0732i	−0.439448	+	0.761146i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	12.8980	+	1.62509i	0.443706	+	0.0559048i
$846$		0			0
$847$	7.19732	+	1.92852i	0.247303	+	0.0662646i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−42.9084	+	11.4973i	−1.47088	+	0.394121i
$852$		0			0
$853$	17.1892	+	17.1892i	0.588546	+	0.588546i	0.937238	−	0.348692i	$-0.113374\pi$
$853$	17.1892	+	17.1892i	0.588546	+	0.588546i	−0.348692	+	0.937238i	$0.613374\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−19.1765			−0.655056			−0.327528	−	0.944842i	$-0.606216\pi$
$857$	−19.1765			−0.655056			−0.327528	+	0.944842i	$0.606216\pi$
$858$		0			0
$859$	11.1892			0.381772			0.190886	−	0.981612i	$-0.438864\pi$
$859$	11.1892			0.381772			0.190886	+	0.981612i	$0.438864\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.6324	+	16.6324i	0.566174	+	0.566174i	0.931055	−	0.364880i	$-0.118890\pi$
$863$	16.6324	+	16.6324i	0.566174	+	0.566174i	−0.364880	+	0.931055i	$0.618890\pi$
$864$		0			0
$865$	2.53425	−	0.679049i	0.0861669	−	0.0230884i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	18.8888	+	5.06124i	0.640759	+	0.171691i
$870$		0			0
$871$	52.1956	−	3.56696i	1.76858	−	0.120862i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.54429	+	4.40685i	−0.0860128	+	0.148979i
$876$		0			0
$877$	9.60712	+	35.8542i	0.324409	+	1.21071i	0.914904	+	0.403671i	$0.132266\pi$
$877$	9.60712	+	35.8542i	0.324409	+	1.21071i	−0.590495	+	0.807041i	$0.701067\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.20525	−	2.08755i	−0.0406059	−	0.0703315i	0.845008	−	0.534753i	$-0.179595\pi$
$881$	−1.20525	−	2.08755i	−0.0406059	−	0.0703315i	−0.885614	+	0.464422i	$0.846262\pi$
$882$		0			0
$883$		−	4.59885i		−	0.154764i	−0.997002	−	0.0773818i	$-0.975344\pi$
$883$		−	4.59885i		−	0.154764i	0.997002	−	0.0773818i	$-0.0246560\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	33.3187	−	19.2366i	1.11873	−	0.645901i	0.177656	−	0.984093i	$-0.443149\pi$
$887$	33.3187	−	19.2366i	1.11873	−	0.645901i	0.941077	+	0.338192i	$0.109815\pi$
$888$		0			0
$889$	40.8324	−	40.8324i	1.36947	−	1.36947i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	54.7211	+	31.5932i	1.83117	+	1.05723i
$894$		0			0
$895$	−1.68518	+	6.28917i	−0.0563293	+	0.210224i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.690005	+	2.57514i	−0.0230130	+	0.0858856i
$900$		0			0
$901$	−70.7507	−	40.8479i	−2.35705	−	1.36084i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.98147	+	6.98147i	−0.232072	+	0.232072i
$906$		0			0
$907$	9.70812	−	5.60499i	0.322353	−	0.186111i	−0.330088	−	0.943950i	$-0.607078\pi$
$907$	9.70812	−	5.60499i	0.322353	−	0.186111i	0.652441	+	0.757840i	$0.273745\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			49.4370i			1.63792i	0.573850	+	0.818960i	$0.305449\pi$
$911$			49.4370i			1.63792i	−0.573850	+	0.818960i	$0.694551\pi$
$912$		0			0
$913$	−24.5080	−	42.4491i	−0.811096	−	1.40486i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.72046	+	6.42083i	0.0568145	+	0.212035i
$918$		0			0
$919$	5.53040	−	9.57893i	0.182431	−	0.315980i	−0.760277	−	0.649599i	$-0.774937\pi$
$919$	5.53040	−	9.57893i	0.182431	−	0.315980i	0.942708	+	0.333619i	$0.108270\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.01855	−	0.684681i	0.0335260	−	0.0225366i
$924$		0			0
$925$	−6.84546	−	1.83424i	−0.225077	−	0.0603093i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−22.4548	+	6.01674i	−0.736717	+	0.197403i	−0.607618	−	0.794229i	$-0.707875\pi$
$929$	−22.4548	+	6.01674i	−0.736717	+	0.197403i	−0.129098	+	0.991632i	$0.541208\pi$
$930$		0			0
$931$	90.7651	+	90.7651i	2.97471	+	2.97471i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	27.4331			0.897158
$936$		0			0
$937$	31.9584			1.04404			0.522018	−	0.852935i	$-0.325179\pi$
$937$	31.9584			1.04404			0.522018	+	0.852935i	$0.325179\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	12.9529	+	12.9529i	0.422253	+	0.422253i	0.885979	−	0.463726i	$-0.153488\pi$
$941$	12.9529	+	12.9529i	0.422253	+	0.422253i	−0.463726	+	0.885979i	$0.653488\pi$
$942$		0			0
$943$	36.3136	−	9.73019i	1.18253	−	0.316859i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−30.6968	−	8.22520i	−0.997514	−	0.267283i	−0.277110	−	0.960838i	$-0.589377\pi$
$947$	−30.6968	−	8.22520i	−0.997514	−	0.267283i	−0.720403	+	0.693555i	$0.756043\pi$
$948$		0			0
$949$	−9.10208	−	4.45721i	−0.295466	−	0.144687i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−29.8931	+	51.7765i	−0.968334	+	1.67720i	−0.267957	+	0.963431i	$0.586348\pi$
$953$	−29.8931	+	51.7765i	−0.968334	+	1.67720i	−0.700377	+	0.713773i	$0.746985\pi$
$954$		0			0
$955$	2.96489	+	11.0651i	0.0959417	+	0.358059i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−17.7971	−	30.8254i	−0.574698	−	0.995405i
$960$		0			0
$961$			28.9763i			0.934718i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	11.9328	−	6.88939i	0.384130	−	0.221777i
$966$		0			0
$967$	−3.30610	+	3.30610i	−0.106317	+	0.106317i	−0.758264	−	0.651947i	$-0.773952\pi$
$967$	−3.30610	+	3.30610i	−0.106317	+	0.106317i	0.651947	+	0.758264i	$0.273952\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−28.6405	−	16.5356i	−0.919118	−	0.530653i	−0.0357644	−	0.999360i	$-0.511387\pi$
$971$	−28.6405	−	16.5356i	−0.919118	−	0.530653i	−0.883354	+	0.468707i	$0.844720\pi$
$972$		0			0
$973$	12.3105	−	45.9435i	0.394657	−	1.47288i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.3704	−	38.7030i	0.331780	−	1.23822i	−0.575538	−	0.817775i	$-0.695208\pi$
$977$	10.3704	−	38.7030i	0.331780	−	1.23822i	0.907318	−	0.420444i	$-0.138126\pi$
$978$		0			0
$979$	21.1600	+	12.2167i	0.676276	+	0.390448i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.6658	+	22.6658i	−0.722927	+	0.722927i	−0.969200	−	0.246274i	$-0.920794\pi$
$983$	−22.6658	+	22.6658i	−0.722927	+	0.722927i	0.246274	+	0.969200i	$0.420794\pi$
$984$		0			0
$985$	19.1403	−	11.0506i	0.609859	−	0.352102i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	50.3996i		−	1.60261i
$990$		0			0
$991$	−22.9438	−	39.7398i	−0.728834	−	1.26238i	−0.957377	−	0.288843i	$-0.906729\pi$
$991$	−22.9438	−	39.7398i	−0.728834	−	1.26238i	0.228543	−	0.973534i	$-0.426604\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.62930	+	6.08062i	0.0516522	+	0.192769i
$996$		0			0
$997$	9.14139	−	15.8333i	0.289511	−	0.501447i	−0.684182	−	0.729311i	$-0.739841\pi$
$997$	9.14139	−	15.8333i	0.289511	−	0.501447i	0.973693	+	0.227864i	$0.0731741\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2340.2.fo.b.1601.10	yes	40
3.2	odd	2	inner	2340.2.fo.b.1601.1	✓	40
13.7	odd	12	inner	2340.2.fo.b.2321.1	yes	40
39.20	even	12	inner	2340.2.fo.b.2321.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2340.2.fo.b.1601.1	✓	40	3.2	odd	2	inner
2340.2.fo.b.1601.10	yes	40	1.1	even	1	trivial
2340.2.fo.b.2321.1	yes	40	13.7	odd	12	inner
2340.2.fo.b.2321.10	yes	40	39.20	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.fo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{5} +(4.91520 - 1.31702i) q^{7} +(-3.41018 - 0.913756i) q^{11} +(3.41097 - 1.16846i) q^{13} +(-3.88518 + 6.72932i) q^{17} +(1.75838 + 6.56236i) q^{19} +(3.13407 + 5.42838i) q^{23} +1.00000i q^{25} +(1.62296 - 0.937019i) q^{29} +(-1.00592 + 1.00592i) q^{31} +(4.40685 + 2.54429i) q^{35} +(-1.83424 + 6.84546i) q^{37} +(1.55232 - 5.79335i) q^{41} +(-6.96335 - 4.02029i) q^{43} +(6.57647 - 6.57647i) q^{47} +(16.3624 - 9.44686i) q^{49} +10.5138i q^{53} +(-1.76524 - 3.05749i) q^{55} +(-2.73047 - 10.1903i) q^{59} +(-0.963040 + 1.66803i) q^{61} +(3.23815 + 1.58569i) q^{65} +(14.0158 + 3.75552i) q^{67} +(0.328790 - 0.0880990i) q^{71} +(-1.98760 - 1.98760i) q^{73} -17.9652 q^{77} -5.53894 q^{79} +(9.81723 + 9.81723i) q^{83} +(-7.50558 + 2.01112i) q^{85} +(-6.68489 - 1.79121i) q^{89} +(15.2267 - 10.2355i) q^{91} +(-3.39693 + 5.88365i) q^{95} +(-4.47916 - 16.7164i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{7} + 12 q^{13} + 28 q^{19} + 36 q^{31} - 40 q^{37} - 72 q^{43} - 36 q^{49} - 32 q^{61} + 16 q^{67} + 28 q^{73} + 48 q^{79} - 20 q^{85} + 132 q^{91} + 48 q^{97}+O(q^{100}) \) 40 * q + 8 * q^7 + 12 * q^13 + 28 * q^19 + 36 * q^31 - 40 * q^37 - 72 * q^43 - 36 * q^49 - 32 * q^61 + 16 * q^67 + 28 * q^73 + 48 * q^79 - 20 * q^85 + 132 * q^91 + 48 * q^97

Introduction

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