LMFDB - Embedded newform 3024.2.bh.d.2447.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1871,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1, 2]))

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

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

chi := DirichletCharacter("3024.1871");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.bh (of order $6$, degree $2$, 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2447.12
Character	$\chi$	$=$	3024.2447
Dual form			3024.2.bh.d.1871.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.36899i q^{5} +(0.783237 + 2.52716i) q^{7} +O(q^{10})$	$q+2.36899i q^{5} +(0.783237 + 2.52716i) q^{7} -4.14140 q^{11} +(-1.38752 + 2.40326i) q^{13} +(1.58369 + 0.914347i) q^{17} +(2.73242 - 1.57756i) q^{19} -1.02166 q^{23} -0.612123 q^{25} +(-1.59887 + 0.923106i) q^{29} +(-8.06524 + 4.65647i) q^{31} +(-5.98682 + 1.85548i) q^{35} +(3.15039 + 5.45663i) q^{37} +(-8.53919 - 4.93010i) q^{41} +(9.54137 - 5.50871i) q^{43} +(-1.59009 + 2.75412i) q^{47} +(-5.77308 + 3.95873i) q^{49} +(10.2889 + 5.94029i) q^{53} -9.81095i q^{55} +(-1.62351 - 2.81200i) q^{59} +(-0.426723 + 0.739106i) q^{61} +(-5.69329 - 3.28702i) q^{65} +(0.259676 - 0.149924i) q^{67} -15.6672 q^{71} +(-0.419551 + 0.726684i) q^{73} +(-3.24370 - 10.4660i) q^{77} +(-9.69258 - 5.59601i) q^{79} +(-2.64353 - 4.57872i) q^{83} +(-2.16608 + 3.75176i) q^{85} +(1.62851 - 0.940223i) q^{89} +(-7.16017 - 1.62417i) q^{91} +(3.73724 + 6.47308i) q^{95} +(-8.03665 - 13.9199i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{7}+O(q^{10}) $ 30 * q + 2 * q^7	$ 30 q + 2 q^{7} + 6 q^{11} - 12 q^{17} - 9 q^{19} - 24 q^{23} - 36 q^{25} - 27 q^{29} - 6 q^{31} - 6 q^{35} + 6 q^{37} - 9 q^{41} + 21 q^{43} + 12 q^{49} + 3 q^{53} + 3 q^{59} - 3 q^{61} + 39 q^{67} + 18 q^{71} + 21 q^{73} - 36 q^{77} + 33 q^{79} - 15 q^{83} - 3 q^{85} - 6 q^{89} + 26 q^{91} - 27 q^{95} - 6 q^{97}+O(q^{100}) $ 30 * q + 2 * q^7 + 6 * q^11 - 12 * q^17 - 9 * q^19 - 24 * q^23 - 36 * q^25 - 27 * q^29 - 6 * q^31 - 6 * q^35 + 6 * q^37 - 9 * q^41 + 21 * q^43 + 12 * q^49 + 3 * q^53 + 3 * q^59 - 3 * q^61 + 39 * q^67 + 18 * q^71 + 21 * q^73 - 36 * q^77 + 33 * q^79 - 15 * q^83 - 3 * q^85 - 6 * q^89 + 26 * q^91 - 27 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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
$5$			2.36899i			1.05945i	0.848171	+	0.529723i	$0.177704\pi$
$5$			2.36899i			1.05945i	−0.848171	+	0.529723i	$0.822296\pi$
$6$		0			0
$7$	0.783237	+	2.52716i	0.296036	+	0.955177i
$7$	0.783237	+	2.52716i	0.296036	+	0.955177i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.14140			−1.24868			−0.624340	−	0.781153i	$-0.714632\pi$
$11$	−4.14140			−1.24868			−0.624340	+	0.781153i	$0.714632\pi$
$12$		0			0
$13$	−1.38752	+	2.40326i	−0.384829	+	0.666543i	−0.991745	−	0.128222i	$-0.959073\pi$
$13$	−1.38752	+	2.40326i	−0.384829	+	0.666543i	0.606917	+	0.794766i	$0.292406\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.58369	+	0.914347i	0.384102	+	0.221762i	0.679602	−	0.733581i	$-0.262153\pi$
$17$	1.58369	+	0.914347i	0.384102	+	0.221762i	−0.295499	+	0.955343i	$0.595486\pi$
$18$		0			0
$19$	2.73242	−	1.57756i	0.626860	−	0.361918i	−0.152675	−	0.988276i	$-0.548789\pi$
$19$	2.73242	−	1.57756i	0.626860	−	0.361918i	0.779535	+	0.626358i	$0.215455\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.02166			−0.213031			−0.106516	−	0.994311i	$-0.533969\pi$
$23$	−1.02166			−0.213031			−0.106516	+	0.994311i	$0.533969\pi$
$24$		0			0
$25$	−0.612123			−0.122425
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.59887	+	0.923106i	−0.296902	+	0.171417i	−0.641050	−	0.767499i	$-0.721501\pi$
$29$	−1.59887	+	0.923106i	−0.296902	+	0.171417i	0.344148	+	0.938915i	$0.388168\pi$
$30$		0			0
$31$	−8.06524	+	4.65647i	−1.44856	+	0.836327i	−0.998396	−	0.0566188i	$-0.981968\pi$
$31$	−8.06524	+	4.65647i	−1.44856	+	0.836327i	−0.450165	+	0.892946i	$0.648635\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.98682	+	1.85548i	−1.01196	+	0.313634i
$36$		0			0
$37$	3.15039	+	5.45663i	0.517920	+	0.897064i	0.999783	+	0.0208175i	$0.00662691\pi$
$37$	3.15039	+	5.45663i	0.517920	+	0.897064i	−0.481863	+	0.876246i	$0.660040\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.53919	−	4.93010i	−1.33360	−	0.769953i	−0.347748	−	0.937588i	$-0.613054\pi$
$41$	−8.53919	−	4.93010i	−1.33360	−	0.769953i	−0.985849	+	0.167635i	$0.946387\pi$
$42$		0			0
$43$	9.54137	−	5.50871i	1.45505	−	0.840071i	0.456284	−	0.889834i	$-0.349180\pi$
$43$	9.54137	−	5.50871i	1.45505	−	0.840071i	0.998761	+	0.0497632i	$0.0158467\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.59009	+	2.75412i	−0.231939	+	0.401729i	−0.958379	−	0.285500i	$-0.907840\pi$
$47$	−1.59009	+	2.75412i	−0.231939	+	0.401729i	0.726440	+	0.687230i	$0.241174\pi$
$48$		0			0
$49$	−5.77308	+	3.95873i	−0.824726	+	0.565533i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	10.2889	+	5.94029i	1.41329	+	0.815962i	0.995697	−	0.0926733i	$-0.0295412\pi$
$53$	10.2889	+	5.94029i	1.41329	+	0.815962i	0.417591	+	0.908635i	$0.362875\pi$
$54$		0			0
$55$		−	9.81095i		−	1.32291i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.62351	−	2.81200i	−0.211363	−	0.366092i	0.740778	−	0.671750i	$-0.234457\pi$
$59$	−1.62351	−	2.81200i	−0.211363	−	0.366092i	−0.952141	+	0.305658i	$0.901124\pi$
$60$		0			0
$61$	−0.426723	+	0.739106i	−0.0546363	+	0.0946328i	−0.892050	−	0.451937i	$-0.850733\pi$
$61$	−0.426723	+	0.739106i	−0.0546363	+	0.0946328i	0.837414	+	0.546570i	$0.184067\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.69329	−	3.28702i	−0.706166	−	0.407705i
$66$		0			0
$67$	0.259676	−	0.149924i	0.0317245	−	0.0183161i	−0.484054	−	0.875038i	$-0.660836\pi$
$67$	0.259676	−	0.149924i	0.0317245	−	0.0183161i	0.515778	+	0.856722i	$0.327503\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−15.6672			−1.85936			−0.929678	−	0.368373i	$-0.879915\pi$
$71$	−15.6672			−1.85936			−0.929678	+	0.368373i	$0.879915\pi$
$72$		0			0
$73$	−0.419551	+	0.726684i	−0.0491048	+	0.0850520i	−0.889533	−	0.456871i	$-0.848970\pi$
$73$	−0.419551	+	0.726684i	−0.0491048	+	0.0850520i	0.840428	+	0.541923i	$0.182303\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.24370	−	10.4660i	−0.369654	−	1.19271i
$78$		0			0
$79$	−9.69258	−	5.59601i	−1.09050	−	0.629601i	−0.156791	−	0.987632i	$-0.550115\pi$
$79$	−9.69258	−	5.59601i	−1.09050	−	0.629601i	−0.933710	+	0.358031i	$0.883448\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.64353	−	4.57872i	−0.290165	−	0.502580i	0.683684	−	0.729778i	$-0.260377\pi$
$83$	−2.64353	−	4.57872i	−0.290165	−	0.502580i	−0.973849	+	0.227198i	$0.927043\pi$
$84$		0			0
$85$	−2.16608	+	3.75176i	−0.234944	+	0.406936i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.62851	−	0.940223i	0.172622	−	0.0996635i	−0.411200	−	0.911545i	$-0.634890\pi$
$89$	1.62851	−	0.940223i	0.172622	−	0.0996635i	0.583822	+	0.811882i	$0.301557\pi$
$90$		0			0
$91$	−7.16017	−	1.62417i	−0.750590	−	0.170259i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.73724	+	6.47308i	0.383432	+	0.664124i
$96$		0			0
$97$	−8.03665	−	13.9199i	−0.815999	−	1.41335i	−0.908609	−	0.417649i	$-0.862854\pi$
$97$	−8.03665	−	13.9199i	−0.815999	−	1.41335i	0.0926100	−	0.995702i	$-0.470479\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		−	9.65156i		−	0.960366i	−0.877168	−	0.480183i	$-0.840570\pi$
$101$		−	9.65156i		−	0.960366i	0.877168	−	0.480183i	$-0.159430\pi$
$102$		0			0
$103$		−	9.51229i		−	0.937274i	−0.883391	−	0.468637i	$-0.844745\pi$
$103$		−	9.51229i		−	0.937274i	0.883391	−	0.468637i	$-0.155255\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.53673	−	7.85784i	−0.438582	−	0.759646i	0.558998	−	0.829169i	$-0.311186\pi$
$107$	−4.53673	−	7.85784i	−0.438582	−	0.759646i	−0.997580	+	0.0695224i	$0.977852\pi$
$108$		0			0
$109$	−6.96808	+	12.0691i	−0.667421	+	1.15601i	0.311202	+	0.950344i	$0.399268\pi$
$109$	−6.96808	+	12.0691i	−0.667421	+	1.15601i	−0.978623	+	0.205663i	$0.934065\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.4701	+	7.19961i	1.17309	+	0.677282i	0.954405	−	0.298514i	$-0.0964909\pi$
$113$	12.4701	+	7.19961i	1.17309	+	0.677282i	0.218682	+	0.975796i	$0.429824\pi$
$114$		0			0
$115$		−	2.42031i		−	0.225695i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.07029	+	4.71840i	−0.0981136	+	0.432535i
$120$		0			0
$121$	6.15122			0.559202
$122$		0			0
$123$		0			0
$124$		0			0
$125$			10.3948i			0.929743i
$126$		0			0
$127$		−	17.3111i		−	1.53611i	−0.640383	−	0.768056i	$-0.721224\pi$
$127$		−	17.3111i		−	1.53611i	0.640383	−	0.768056i	$-0.278776\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	14.5663			1.27266			0.636331	−	0.771417i	$-0.280451\pi$
$131$	14.5663			1.27266			0.636331	+	0.771417i	$0.280451\pi$
$132$		0			0
$133$	6.12689	+	5.66966i	0.531269	+	0.491622i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			8.44753i			0.721721i	0.932620	+	0.360861i	$0.117517\pi$
$137$			8.44753i			0.721721i	−0.932620	+	0.360861i	$0.882483\pi$
$138$		0			0
$139$	−2.44796	−	1.41333i	−0.207633	−	0.119877i	0.392578	−	0.919719i	$-0.371583\pi$
$139$	−2.44796	−	1.41333i	−0.207633	−	0.119877i	−0.600211	+	0.799842i	$0.704917\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.74628	−	9.95285i	0.480528	−	0.832299i
$144$		0			0
$145$	−2.18683	−	3.78770i	−0.181606	−	0.314552i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			19.0143i			1.55771i	0.627205	+	0.778854i	$0.284199\pi$
$149$			19.0143i			1.55771i	−0.627205	+	0.778854i	$0.715801\pi$
$150$		0			0
$151$			2.82893i			0.230215i	0.993353	+	0.115107i	$0.0367212\pi$
$151$			2.82893i			0.230215i	−0.993353	+	0.115107i	$0.963279\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−11.0311	−	19.1065i	−0.886043	−	1.53467i
$156$		0			0
$157$	−1.26644	−	2.19354i	−0.101073	−	0.175063i	0.811054	−	0.584971i	$-0.198894\pi$
$157$	−1.26644	−	2.19354i	−0.101073	−	0.175063i	−0.912127	+	0.409908i	$0.865561\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.800204	−	2.58191i	−0.0630649	−	0.203483i
$162$		0			0
$163$	7.47930	−	4.31818i	0.585824	−	0.338226i	−0.177620	−	0.984099i	$-0.556840\pi$
$163$	7.47930	−	4.31818i	0.585824	−	0.338226i	0.763445	+	0.645873i	$0.223507\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.35289	+	11.0035i	−0.491602	+	0.851479i	−0.999953	−	0.00967054i	$-0.996922\pi$
$167$	−6.35289	+	11.0035i	−0.491602	+	0.851479i	0.508352	+	0.861150i	$0.330255\pi$
$168$		0			0
$169$	2.64957	+	4.58920i	0.203813	+	0.353015i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.0225933	+	0.0130443i	0.00171774	+	0.000991738i	0.500859	−	0.865529i	$-0.333018\pi$
$173$	0.0225933	+	0.0130443i	0.00171774	+	0.000991738i	−0.499141	+	0.866521i	$0.666351\pi$
$174$		0			0
$175$	−0.479437	−	1.54693i	−0.0362420	−	0.116937i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.11673	+	7.13038i	−0.307699	+	0.532950i	−0.977859	−	0.209267i	$-0.932892\pi$
$179$	−4.11673	+	7.13038i	−0.307699	+	0.532950i	0.670160	+	0.742217i	$0.266226\pi$
$180$		0			0
$181$	−9.49775			−0.705962			−0.352981	−	0.935630i	$-0.614832\pi$
$181$	−9.49775			−0.705962			−0.352981	+	0.935630i	$0.614832\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.9267	+	7.46324i	−0.950390	+	0.548708i
$186$		0			0
$187$	−6.55872	−	3.78668i	−0.479621	−	0.276909i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.96530	−	8.60015i	0.359276	−	0.622285i	−0.628564	−	0.777758i	$-0.716357\pi$
$191$	4.96530	−	8.60015i	0.359276	−	0.622285i	0.987840	+	0.155473i	$0.0496902\pi$
$192$		0			0
$193$	−7.83098	−	13.5637i	−0.563686	−	0.976333i	−0.997171	−	0.0751721i	$-0.976049\pi$
$193$	−7.83098	−	13.5637i	−0.563686	−	0.976333i	0.433484	−	0.901161i	$-0.357284\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			12.1289i			0.864148i	0.901838	+	0.432074i	$0.142218\pi$
$197$			12.1289i			0.864148i	−0.901838	+	0.432074i	$0.857782\pi$
$198$		0			0
$199$	−10.5404	−	6.08552i	−0.747191	−	0.431391i	0.0774869	−	0.996993i	$-0.475310\pi$
$199$	−10.5404	−	6.08552i	−0.747191	−	0.431391i	−0.824678	+	0.565602i	$0.808644\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.58513	−	3.31758i	−0.251627	−	0.232849i
$204$		0			0
$205$	11.6794	−	20.2293i	0.815723	−	1.41287i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−11.3161	+	6.53333i	−0.782748	+	0.451920i
$210$		0			0
$211$	7.33542	+	4.23511i	0.504991	+	0.291557i	0.730772	−	0.682621i	$-0.239160\pi$
$211$	7.33542	+	4.23511i	0.504991	+	0.291557i	−0.225781	+	0.974178i	$0.572493\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	13.0501	+	22.6034i	0.890009	+	1.54154i
$216$		0			0
$217$	−18.0846	−	16.7350i	−1.22767	−	1.13605i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.39482	+	2.53735i	−0.295627	+	0.170681i
$222$		0			0
$223$	7.76299	−	4.48197i	0.519848	−	0.300135i	−0.217024	−	0.976166i	$-0.569635\pi$
$223$	7.76299	−	4.48197i	0.519848	−	0.300135i	0.736873	+	0.676032i	$0.236302\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−17.9514			−1.19148			−0.595738	−	0.803179i	$-0.703140\pi$
$227$	−17.9514			−1.19148			−0.595738	+	0.803179i	$0.703140\pi$
$228$		0			0
$229$	−2.21449			−0.146338			−0.0731689	−	0.997320i	$-0.523311\pi$
$229$	−2.21449			−0.146338			−0.0731689	+	0.997320i	$0.523311\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.98834	+	1.72532i	−0.195773	+	0.113029i	−0.594682	−	0.803961i	$-0.702722\pi$
$233$	−2.98834	+	1.72532i	−0.195773	+	0.113029i	0.398910	+	0.916990i	$0.369389\pi$
$234$		0			0
$235$	−6.52448	−	3.76691i	−0.425610	−	0.245726i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.67035	−	6.35723i	0.237415	−	0.411215i	−0.722557	−	0.691312i	$-0.757033\pi$
$239$	3.67035	−	6.35723i	0.237415	−	0.411215i	0.959972	+	0.280097i	$0.0903665\pi$
$240$		0			0
$241$	−17.3446			−1.11726			−0.558631	−	0.829416i	$-0.688673\pi$
$241$	−17.3446			−1.11726			−0.558631	+	0.829416i	$0.688673\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−9.37820	−	13.6764i	−0.599151	−	0.873752i
$246$		0			0
$247$			8.75561i			0.557106i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−13.9816			−0.882511			−0.441255	−	0.897382i	$-0.645467\pi$
$251$	−13.9816			−0.882511			−0.441255	+	0.897382i	$0.645467\pi$
$252$		0			0
$253$	4.23112			0.266008
$254$		0			0
$255$		0			0
$256$		0			0
$257$			28.0261i			1.74822i	0.485730	+	0.874109i	$0.338554\pi$
$257$			28.0261i			1.74822i	−0.485730	+	0.874109i	$0.661446\pi$
$258$		0			0
$259$	−11.3223	+	12.2354i	−0.703532	+	0.760268i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−16.9791			−1.04697			−0.523487	−	0.852034i	$-0.675369\pi$
$263$	−16.9791			−1.04697			−0.523487	+	0.852034i	$0.675369\pi$
$264$		0			0
$265$	−14.0725	+	24.3743i	−0.864467	+	1.49730i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	23.7601	+	13.7179i	1.44868	+	0.836396i	0.998403	−	0.0564933i	$-0.0179920\pi$
$269$	23.7601	+	13.7179i	1.44868	+	0.836396i	0.450277	+	0.892889i	$0.351325\pi$
$270$		0			0
$271$	−3.93599	+	2.27244i	−0.239094	+	0.138041i	−0.614760	−	0.788714i	$-0.710747\pi$
$271$	−3.93599	+	2.27244i	−0.239094	+	0.138041i	0.375666	+	0.926755i	$0.377414\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.53505			0.152869
$276$		0			0
$277$	6.58357			0.395568			0.197784	−	0.980246i	$-0.436625\pi$
$277$	6.58357			0.395568			0.197784	+	0.980246i	$0.436625\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	23.0468	−	13.3061i	1.37486	−	0.793775i	0.383324	−	0.923614i	$-0.374779\pi$
$281$	23.0468	−	13.3061i	1.37486	−	0.793775i	0.991535	+	0.129839i	$0.0414461\pi$
$282$		0			0
$283$	−26.7323	+	15.4339i	−1.58907	+	0.917449i	−0.595607	+	0.803276i	$0.703088\pi$
$283$	−26.7323	+	15.4339i	−1.58907	+	0.917449i	−0.993461	+	0.114173i	$0.963578\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.77095	−	25.4413i	0.340649	−	1.50175i
$288$		0			0
$289$	−6.82794	−	11.8263i	−0.401644	−	0.695667i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.92535	+	2.84365i	0.287742	+	0.166128i	0.636923	−	0.770927i	$-0.280207\pi$
$293$	4.92535	+	2.84365i	0.287742	+	0.166128i	−0.349181	+	0.937055i	$0.613540\pi$
$294$		0			0
$295$	6.66162	−	3.84609i	0.387854	−	0.223928i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.41758	−	2.45532i	0.0819806	−	0.141995i
$300$		0			0
$301$	21.3946	+	19.7979i	1.23316	+	1.14113i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.75094	−	1.01090i	−0.100258	−	0.0578842i
$306$		0			0
$307$			27.9000i			1.59234i	0.605075	+	0.796168i	$0.293143\pi$
$307$			27.9000i			1.59234i	−0.605075	+	0.796168i	$0.706857\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	14.5572	+	25.2138i	0.825463	+	1.42974i	0.901565	+	0.432644i	$0.142419\pi$
$311$	14.5572	+	25.2138i	0.825463	+	1.42974i	−0.0761021	+	0.997100i	$0.524247\pi$
$312$		0			0
$313$	−14.2072	+	24.6075i	−0.803037	+	1.39090i	0.114572	+	0.993415i	$0.463450\pi$
$313$	−14.2072	+	24.6075i	−0.803037	+	1.39090i	−0.917608	+	0.397486i	$0.869883\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.3899	−	12.3495i	−1.20138	−	0.693615i	−0.240515	−	0.970645i	$-0.577316\pi$
$317$	−21.3899	−	12.3495i	−1.20138	−	0.693615i	−0.960861	+	0.277030i	$0.910650\pi$
$318$		0			0
$319$	6.62155	−	3.82296i	0.370736	−	0.214044i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	5.76976			0.321038
$324$		0			0
$325$	0.849332	−	1.47109i	0.0471125	−	0.0816012i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−8.20552	−	1.86129i	−0.452385	−	0.102616i
$330$		0			0
$331$	12.8194	+	7.40130i	0.704620	+	0.406812i	0.809066	−	0.587718i	$-0.199974\pi$
$331$	12.8194	+	7.40130i	0.704620	+	0.406812i	−0.104446	+	0.994531i	$0.533307\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.355169	+	0.615170i	0.0194049	+	0.0336103i
$336$		0			0
$337$	14.3380	−	24.8342i	0.781042	−	1.35280i	−0.150293	−	0.988642i	$-0.548022\pi$
$337$	14.3380	−	24.8342i	0.781042	−	1.35280i	0.931335	−	0.364163i	$-0.118645\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	33.4014	−	19.2843i	1.80879	−	1.04430i
$342$		0			0
$343$	−14.5260	−	11.4889i	−0.784332	−	0.620341i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.31831	+	16.1398i	0.500233	+	0.866429i	1.00000		0.000269083i	$8.56516e-5\pi$
$347$	9.31831	+	16.1398i	0.500233	+	0.866429i	−0.499767	+	0.866160i	$0.666581\pi$
$348$		0			0
$349$	−8.10052	−	14.0305i	−0.433611	−	0.751036i	0.563570	−	0.826068i	$-0.309427\pi$
$349$	−8.10052	−	14.0305i	−0.433611	−	0.751036i	−0.997181	+	0.0750321i	$0.976094\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			11.4817i			0.611110i	0.952174	+	0.305555i	$0.0988421\pi$
$353$			11.4817i			0.611110i	−0.952174	+	0.305555i	$0.901158\pi$
$354$		0			0
$355$		−	37.1155i		−	1.96989i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.31363	+	14.3996i	0.438777	+	0.759983i	0.997595	−	0.0693065i	$-0.0220786\pi$
$359$	8.31363	+	14.3996i	0.438777	+	0.759983i	−0.558819	+	0.829290i	$0.688745\pi$
$360$		0			0
$361$	−4.52258	+	7.83334i	−0.238031	+	0.412281i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.72151	−	0.993914i	−0.0901079	−	0.0520238i
$366$		0			0
$367$			20.1028i			1.04936i	0.851300	+	0.524680i	$0.175815\pi$
$367$			20.1028i			1.04936i	−0.851300	+	0.524680i	$0.824185\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.95344	+	30.6543i	−0.361004	+	1.59149i
$372$		0			0
$373$	33.4298			1.73093			0.865465	−	0.500969i	$-0.167023\pi$
$373$	33.4298			1.73093			0.865465	+	0.500969i	$0.167023\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	5.12331i		−	0.263864i
$378$		0			0
$379$			15.2571i			0.783704i	0.920028	+	0.391852i	$0.128166\pi$
$379$			15.2571i			0.783704i	−0.920028	+	0.391852i	$0.871834\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−19.2018			−0.981168			−0.490584	−	0.871394i	$-0.663217\pi$
$383$	−19.2018			−0.981168			−0.490584	+	0.871394i	$0.663217\pi$
$384$		0			0
$385$	24.7938	−	7.68430i	1.26361	−	0.391628i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	13.2664i		−	0.672632i	−0.941749	−	0.336316i	$-0.890819\pi$
$389$		−	13.2664i		−	0.672632i	0.941749	−	0.336316i	$-0.109181\pi$
$390$		0			0
$391$	−1.61800	−	0.934154i	−0.0818259	−	0.0472422i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	13.2569	−	22.9616i	0.667028	−	1.15533i
$396$		0			0
$397$	5.15559	+	8.92974i	0.258752	+	0.448171i	0.965908	−	0.258887i	$-0.0833556\pi$
$397$	5.15559	+	8.92974i	0.258752	+	0.448171i	−0.707156	+	0.707057i	$0.750022\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	4.21540i		−	0.210507i	−0.994445	−	0.105253i	$-0.966435\pi$
$401$		−	4.21540i		−	0.210507i	0.994445	−	0.105253i	$-0.0335654\pi$
$402$		0			0
$403$		−	25.8438i		−	1.28737i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−13.0470	−	22.5981i	−0.646717	−	1.12015i
$408$		0			0
$409$	−8.29502	−	14.3674i	−0.410163	−	0.710422i	0.584745	−	0.811217i	$-0.301195\pi$
$409$	−8.29502	−	14.3674i	−0.410163	−	0.710422i	−0.994907	+	0.100795i	$0.967861\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.83479	−	6.30534i	0.287111	−	0.310266i
$414$		0			0
$415$	10.8470	−	6.26249i	0.532456	−	0.307414i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.14140	−	5.44107i	0.153467	−	0.265813i	−0.779032	−	0.626984i	$-0.784289\pi$
$419$	3.14140	−	5.44107i	0.153467	−	0.265813i	0.932500	+	0.361170i	$0.117623\pi$
$420$		0			0
$421$	14.9372	+	25.8720i	0.727995	+	1.26092i	0.957729	+	0.287670i	$0.0928808\pi$
$421$	14.9372	+	25.8720i	0.727995	+	1.26092i	−0.229735	+	0.973253i	$0.573786\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.969415	−	0.559692i	−0.0470236	−	0.0271491i
$426$		0			0
$427$	−2.20206	−	0.499503i	−0.106565	−	0.0241726i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.76371	−	11.7151i	0.325796	−	0.564296i	−0.655877	−	0.754868i	$-0.727701\pi$
$431$	6.76371	−	11.7151i	0.325796	−	0.564296i	0.981673	+	0.190572i	$0.0610343\pi$
$432$		0			0
$433$	39.5892			1.90254			0.951269	−	0.308363i	$-0.0997813\pi$
$433$	39.5892			1.90254			0.951269	+	0.308363i	$0.0997813\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.79161	+	1.61174i	−0.133541	+	0.0770999i
$438$		0			0
$439$	14.0314	+	8.10104i	0.669683	+	0.386642i	0.795956	−	0.605354i	$-0.206968\pi$
$439$	14.0314	+	8.10104i	0.669683	+	0.386642i	−0.126274	+	0.991995i	$0.540302\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−13.6100	+	23.5732i	−0.646630	+	1.12000i	0.337293	+	0.941400i	$0.390489\pi$
$443$	−13.6100	+	23.5732i	−0.646630	+	1.12000i	−0.983923	+	0.178596i	$0.942845\pi$
$444$		0			0
$445$	2.22738	+	3.85794i	0.105588	+	0.182884i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			17.8656i			0.843130i	0.906798	+	0.421565i	$0.138519\pi$
$449$			17.8656i			0.843130i	−0.906798	+	0.421565i	$0.861481\pi$
$450$		0			0
$451$	35.3642	+	20.4175i	1.66524	+	0.961425i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.84764	−	16.9624i	0.180380	−	0.795209i
$456$		0			0
$457$	−7.12400	+	12.3391i	−0.333246	+	0.577200i	−0.983146	−	0.182820i	$-0.941477\pi$
$457$	−7.12400	+	12.3391i	−0.333246	+	0.577200i	0.649900	+	0.760020i	$0.274811\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.37315	−	1.94749i	0.157103	−	0.0907036i	−0.419387	−	0.907807i	$-0.637755\pi$
$461$	3.37315	−	1.94749i	0.157103	−	0.0907036i	0.576491	+	0.817104i	$0.304422\pi$
$462$		0			0
$463$	4.28829	+	2.47585i	0.199294	+	0.115062i	0.596326	−	0.802742i	$-0.296627\pi$
$463$	4.28829	+	2.47585i	0.199294	+	0.115062i	−0.397032	+	0.917805i	$0.629960\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.3358	−	17.9021i	−0.478282	−	0.828409i	0.521408	−	0.853307i	$-0.325407\pi$
$467$	−10.3358	−	17.9021i	−0.478282	−	0.828409i	−0.999690	+	0.0248989i	$0.992074\pi$
$468$		0			0
$469$	0.582270	+	0.538817i	0.0268867	+	0.0248802i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−39.5147	+	22.8138i	−1.81689	+	1.04898i
$474$		0			0
$475$	−1.67258	+	0.965663i	−0.0767431	+	0.0443076i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	26.4349			1.20784			0.603920	−	0.797045i	$-0.293605\pi$
$479$	26.4349			1.20784			0.603920	+	0.797045i	$0.293605\pi$
$480$		0			0
$481$	−17.4849			−0.797243
$482$		0			0
$483$		0			0
$484$		0			0
$485$	32.9761	−	19.0388i	1.49737	−	0.864506i
$486$		0			0
$487$	13.9150	+	8.03383i	0.630549	+	0.364048i	0.780965	−	0.624575i	$-0.214728\pi$
$487$	13.9150	+	8.03383i	0.630549	+	0.364048i	−0.150415	+	0.988623i	$0.548061\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.70049	+	6.40944i	−0.167001	+	0.289254i	−0.937364	−	0.348351i	$-0.886742\pi$
$491$	−3.70049	+	6.40944i	−0.167001	+	0.289254i	0.770363	+	0.637605i	$0.220075\pi$
$492$		0			0
$493$	−3.37616			−0.152054
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.2711	−	39.5936i	−0.550436	−	1.77601i
$498$		0			0
$499$			10.0862i			0.451521i	0.974183	+	0.225760i	$0.0724866\pi$
$499$			10.0862i			0.451521i	−0.974183	+	0.225760i	$0.927513\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	2.11362			0.0942416			0.0471208	−	0.998889i	$-0.484995\pi$
$503$	2.11362			0.0942416			0.0471208	+	0.998889i	$0.484995\pi$
$504$		0			0
$505$	22.8645			1.01746
$506$		0			0
$507$		0			0
$508$		0			0
$509$		−	29.9445i		−	1.32727i	−0.748058	−	0.663633i	$-0.769014\pi$
$509$		−	29.9445i		−	1.32727i	0.748058	−	0.663633i	$-0.230986\pi$
$510$		0			0
$511$	−2.16506	−	0.491108i	−0.0957764	−	0.0217253i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	22.5345			0.992990
$516$		0			0
$517$	6.58521	−	11.4059i	0.289617	−	0.501632i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−31.6120	−	18.2512i	−1.38495	−	0.799599i	−0.392206	−	0.919877i	$-0.628288\pi$
$521$	−31.6120	−	18.2512i	−1.38495	−	0.799599i	−0.992740	+	0.120278i	$0.961621\pi$
$522$		0			0
$523$	−9.22636	+	5.32684i	−0.403440	+	0.232926i	−0.687967	−	0.725742i	$-0.741497\pi$
$523$	−9.22636	+	5.32684i	−0.403440	+	0.232926i	0.284527	+	0.958668i	$0.408163\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−17.0305			−0.741861
$528$		0			0
$529$	−21.9562			−0.954618
$530$		0			0
$531$		0			0
$532$		0			0
$533$	23.6966	−	13.6812i	1.02641	−	0.592600i
$534$		0			0
$535$	18.6152	−	10.7475i	0.804804	−	0.464654i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	23.9087	−	16.3947i	1.02982	−	0.706170i
$540$		0			0
$541$	−14.8060	−	25.6447i	−0.636558	−	1.10255i	−0.986183	−	0.165661i	$-0.947024\pi$
$541$	−14.8060	−	25.6447i	−0.636558	−	1.10255i	0.349625	−	0.936890i	$-0.386309\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−28.5915	−	16.5073i	−1.22473	−	0.707096i
$546$		0			0
$547$	36.4637	−	21.0523i	1.55908	−	0.900133i	0.561731	−	0.827320i	$-0.310136\pi$
$547$	36.4637	−	21.0523i	1.55908	−	0.900133i	0.997346	−	0.0728131i	$-0.0231977\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.91252	+	5.04463i	−0.124077	+	0.214909i
$552$		0			0
$553$	6.55044	−	28.8777i	0.278553	−	1.22801i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.87538	+	2.23745i	0.164205	+	0.0948039i	0.579851	−	0.814723i	$-0.303111\pi$
$557$	3.87538	+	2.23745i	0.164205	+	0.0948039i	−0.415645	+	0.909527i	$0.636444\pi$
$558$		0			0
$559$			30.5738i			1.29313i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	5.37514	+	9.31001i	0.226535	+	0.392370i	0.956779	−	0.290816i	$-0.0939269\pi$
$563$	5.37514	+	9.31001i	0.226535	+	0.392370i	−0.730244	+	0.683187i	$0.760594\pi$
$564$		0			0
$565$	−17.0558	+	29.5415i	−0.717544	+	1.24282i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−19.8609	−	11.4667i	−0.832614	−	0.480710i	0.0221329	−	0.999755i	$-0.492954\pi$
$569$	−19.8609	−	11.4667i	−0.832614	−	0.480710i	−0.854747	+	0.519045i	$0.826288\pi$
$570$		0			0
$571$	14.6608	−	8.46444i	0.613537	−	0.354226i	−0.160812	−	0.986985i	$-0.551411\pi$
$571$	14.6608	−	8.46444i	0.613537	−	0.354226i	0.774348	+	0.632759i	$0.218078\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.625383			0.0260803
$576$		0			0
$577$	−9.14015	+	15.8312i	−0.380509	+	0.659062i	−0.991135	−	0.132858i	$-0.957585\pi$
$577$	−9.14015	+	15.8312i	−0.380509	+	0.659062i	0.610626	+	0.791919i	$0.290918\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	9.50066	−	10.2668i	0.394154	−	0.425940i
$582$		0			0
$583$	−42.6104	−	24.6011i	−1.76474	−	1.01888i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.2944	+	35.1509i	0.837638	+	1.45083i	0.891864	+	0.452303i	$0.149397\pi$
$587$	20.2944	+	35.1509i	0.837638	+	1.45083i	−0.0542266	+	0.998529i	$0.517269\pi$
$588$		0			0
$589$	−14.6918	+	25.4469i	−0.605364	+	1.04852i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.56487	−	4.36758i	0.310652	−	0.179355i	−0.336566	−	0.941660i	$-0.609266\pi$
$593$	7.56487	−	4.36758i	0.310652	−	0.179355i	0.647218	+	0.762305i	$0.275932\pi$
$594$		0			0
$595$	−11.1779	−	2.53551i	−0.458247	−	0.103946i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.31444	−	10.9369i	−0.258001	−	0.446871i	0.707705	−	0.706508i	$-0.249731\pi$
$599$	−6.31444	−	10.9369i	−0.258001	−	0.446871i	−0.965706	+	0.259637i	$0.916397\pi$
$600$		0			0
$601$	11.3142	+	19.5968i	0.461516	+	0.799369i	0.999037	−	0.0438818i	$-0.0139725\pi$
$601$	11.3142	+	19.5968i	0.461516	+	0.799369i	−0.537521	+	0.843250i	$0.680639\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$			14.5722i			0.592444i
$606$		0			0
$607$			32.1415i			1.30458i	0.757968	+	0.652292i	$0.226192\pi$
$607$			32.1415i			1.30458i	−0.757968	+	0.652292i	$0.773808\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.41257	−	7.64279i	−0.178513	−	0.309194i
$612$		0			0
$613$	6.49677	−	11.2527i	0.262402	−	0.454494i	−0.704478	−	0.709726i	$-0.748819\pi$
$613$	6.49677	−	11.2527i	0.262402	−	0.454494i	0.966880	+	0.255232i	$0.0821520\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	32.4105	+	18.7122i	1.30480	+	0.753325i	0.981223	−	0.192877i	$-0.0617819\pi$
$617$	32.4105	+	18.7122i	1.30480	+	0.753325i	0.323575	+	0.946203i	$0.395115\pi$
$618$		0			0
$619$			33.9526i			1.36467i	0.731039	+	0.682335i	$0.239036\pi$
$619$			33.9526i			1.36467i	−0.731039	+	0.682335i	$0.760964\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.65161	+	3.37910i	0.146299	+	0.135381i
$624$		0			0
$625$	−27.6859			−1.10744
$626$		0			0
$627$		0			0
$628$		0			0
$629$			11.5222i			0.459419i
$630$		0			0
$631$			20.5424i			0.817780i	0.912584	+	0.408890i	$0.134084\pi$
$631$			20.5424i			0.817780i	−0.912584	+	0.408890i	$0.865916\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	41.0099			1.62743
$636$		0			0
$637$	−1.50357	−	19.3670i	−0.0595738	−	0.767349i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	36.9825i		−	1.46072i	−0.683062	−	0.730360i	$-0.739352\pi$
$641$		−	36.9825i		−	1.46072i	0.683062	−	0.730360i	$-0.260648\pi$
$642$		0			0
$643$	7.41539	+	4.28128i	0.292435	+	0.168837i	0.639039	−	0.769174i	$-0.279332\pi$
$643$	7.41539	+	4.28128i	0.292435	+	0.168837i	−0.346605	+	0.938011i	$0.612665\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	15.8126	−	27.3882i	0.621658	−	1.07674i	−0.367519	−	0.930016i	$-0.619793\pi$
$647$	15.8126	−	27.3882i	0.621658	−	1.07674i	0.989177	−	0.146727i	$-0.0468739\pi$
$648$		0			0
$649$	6.72362	+	11.6456i	0.263925	+	0.457132i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	27.3648i		−	1.07087i	−0.844577	−	0.535435i	$-0.820148\pi$
$653$		−	27.3648i		−	1.07087i	0.844577	−	0.535435i	$-0.179852\pi$
$654$		0			0
$655$			34.5074i			1.34831i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17.2635	+	29.9012i	0.672489	+	1.16478i	0.977196	+	0.212339i	$0.0681081\pi$
$659$	17.2635	+	29.9012i	0.672489	+	1.16478i	−0.304707	+	0.952446i	$0.598559\pi$
$660$		0			0
$661$	5.43775	+	9.41846i	0.211504	+	0.366336i	0.952185	−	0.305521i	$-0.0988305\pi$
$661$	5.43775	+	9.41846i	0.211504	+	0.366336i	−0.740681	+	0.671856i	$0.765497\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−13.4314	+	14.5146i	−0.520847	+	0.562850i
$666$		0			0
$667$	1.63350	−	0.943103i	0.0632495	−	0.0365171i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.76723	−	3.06094i	0.0682232	−	0.118166i
$672$		0			0
$673$	12.4897	+	21.6327i	0.481441	+	0.833880i	0.999773	−	0.0212993i	$-0.00678029\pi$
$673$	12.4897	+	21.6327i	0.481441	+	0.833880i	−0.518332	+	0.855179i	$0.673447\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	27.6377	+	15.9566i	1.06220	+	0.613263i	0.926041	−	0.377423i	$-0.123190\pi$
$677$	27.6377	+	15.9566i	1.06220	+	0.613263i	0.136162	+	0.990687i	$0.456523\pi$
$678$		0			0
$679$	28.8832	−	31.2125i	1.10844	−	1.19783i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.154508	−	0.267616i	0.00591210	−	0.0102401i	−0.863054	−	0.505111i	$-0.831451\pi$
$683$	0.154508	−	0.267616i	0.00591210	−	0.0102401i	0.868966	+	0.494871i	$0.164785\pi$
$684$		0			0
$685$	−20.0121			−0.764624
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−28.5521	+	16.4846i	−1.08775	+	0.628011i
$690$		0			0
$691$	2.36984	+	1.36823i	0.0901530	+	0.0520499i	0.544399	−	0.838827i	$-0.316758\pi$
$691$	2.36984	+	1.36823i	0.0901530	+	0.0520499i	−0.454246	+	0.890876i	$0.650091\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.34816	−	5.79919i	0.127003	−	0.219976i
$696$		0			0
$697$	−9.01565	−	15.6156i	−0.341492	−	0.591481i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	34.1114i		−	1.28837i	−0.764869	−	0.644185i	$-0.777197\pi$
$701$		−	34.1114i		−	1.28837i	0.764869	−	0.644185i	$-0.222803\pi$
$702$		0			0
$703$	17.2164	+	9.93987i	0.649327	+	0.374889i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	24.3910	−	7.55946i	0.917319	−	0.284303i
$708$		0			0
$709$	2.86828	−	4.96800i	0.107720	−	0.186577i	−0.807126	−	0.590379i	$-0.798978\pi$
$709$	2.86828	−	4.96800i	0.107720	−	0.186577i	0.914846	+	0.403802i	$0.132312\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.23996	−	4.75734i	0.308589	−	0.178164i
$714$		0			0
$715$	23.5782	+	13.6129i	0.881776	+	0.509093i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	14.5211	+	25.1513i	0.541545	+	0.937983i	0.998816	+	0.0486559i	$0.0154938\pi$
$719$	14.5211	+	25.1513i	0.541545	+	0.937983i	−0.457271	+	0.889328i	$0.651173\pi$
$720$		0			0
$721$	24.0391	−	7.45038i	0.895262	−	0.277467i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.978703	−	0.565054i	0.0363481	−	0.0209856i
$726$		0			0
$727$	−10.3221	+	5.95949i	−0.382827	+	0.221025i	−0.679048	−	0.734094i	$-0.737607\pi$
$727$	−10.3221	+	5.95949i	−0.382827	+	0.221025i	0.296220	+	0.955120i	$0.404274\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	20.1475			0.745182
$732$		0			0
$733$	−7.89924			−0.291765			−0.145883	−	0.989302i	$-0.546602\pi$
$733$	−7.89924			−0.291765			−0.145883	+	0.989302i	$0.546602\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.07542	+	0.620895i	−0.0396137	+	0.0228710i
$738$		0			0
$739$	−20.6202	−	11.9051i	−0.758525	−	0.437934i	0.0702410	−	0.997530i	$-0.477623\pi$
$739$	−20.6202	−	11.9051i	−0.758525	−	0.437934i	−0.828766	+	0.559596i	$0.810956\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.16678	−	2.02092i	0.0428050	−	0.0741404i	−0.843829	−	0.536612i	$-0.819704\pi$
$743$	1.16678	−	2.02092i	0.0428050	−	0.0741404i	0.886634	+	0.462472i	$0.153037\pi$
$744$		0			0
$745$	−45.0446			−1.65031
$746$		0			0
$747$		0			0
$748$		0			0
$749$	16.3047	−	17.6196i	0.595761	−	0.643806i
$750$		0			0
$751$			32.9806i			1.20348i	0.798692	+	0.601740i	$0.205526\pi$
$751$			32.9806i			1.20348i	−0.798692	+	0.601740i	$0.794474\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.70170			−0.243900
$756$		0			0
$757$	46.1289			1.67658			0.838291	−	0.545223i	$-0.183555\pi$
$757$	46.1289			1.67658			0.838291	+	0.545223i	$0.183555\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			49.2394i			1.78493i	0.451121	+	0.892463i	$0.351024\pi$
$761$			49.2394i			1.78493i	−0.451121	+	0.892463i	$0.648976\pi$
$762$		0			0
$763$	−35.9581	−	8.15652i	−1.30177	−	0.295286i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.01062			0.325355
$768$		0			0
$769$	24.2219	−	41.9536i	0.873465	−	1.51289i	0.0150758	−	0.999886i	$-0.495201\pi$
$769$	24.2219	−	41.9536i	0.873465	−	1.51289i	0.858389	−	0.512999i	$-0.171466\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.8701	−	6.27584i	−0.390970	−	0.225726i	0.291611	−	0.956537i	$-0.405809\pi$
$773$	−10.8701	−	6.27584i	−0.390970	−	0.225726i	−0.682580	+	0.730811i	$0.739142\pi$
$774$		0			0
$775$	4.93692	−	2.85033i	0.177339	−	0.102387i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−31.1102			−1.11464
$780$		0			0
$781$	64.8843			2.32174
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.19647	−	3.00018i	0.185470	−	0.107081i
$786$		0			0
$787$	−14.2967	+	8.25421i	−0.509623	+	0.294231i	−0.732678	−	0.680575i	$-0.761730\pi$
$787$	−14.2967	+	8.25421i	−0.509623	+	0.294231i	0.223056	+	0.974806i	$0.428397\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−8.42754	+	37.1529i	−0.299649	+	1.32101i
$792$		0			0
$793$	−1.18417	−	2.05105i	−0.0420512	−	0.0728349i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.09669	−	1.21053i	−0.0742687	−	0.0428791i	0.462406	−	0.886668i	$-0.346986\pi$
$797$	−2.09669	−	1.21053i	−0.0742687	−	0.0428791i	−0.536674	+	0.843789i	$0.680320\pi$
$798$		0			0
$799$	−5.03644	+	2.90779i	−0.178176	+	0.102870i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.73753	−	3.00949i	0.0613162	−	0.106203i
$804$		0			0
$805$	6.11651	−	1.89568i	0.215579	−	0.0668138i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	27.8540	+	16.0815i	0.979293	+	0.565395i	0.902057	−	0.431618i	$-0.142057\pi$
$809$	27.8540	+	16.0815i	0.979293	+	0.565395i	0.0772364	+	0.997013i	$0.475390\pi$
$810$		0			0
$811$		−	31.5999i		−	1.10962i	−0.831976	−	0.554812i	$-0.812790\pi$
$811$		−	31.5999i		−	1.10962i	0.831976	−	0.554812i	$-0.187210\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.2297	+	17.7184i	0.358332	+	0.620649i
$816$		0			0
$817$	17.3807	−	30.1043i	0.608074	−	1.05321i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−34.8215	−	20.1042i	−1.21528	−	0.701642i	−0.251375	−	0.967890i	$-0.580883\pi$
$821$	−34.8215	−	20.1042i	−1.21528	−	0.701642i	−0.963905	+	0.266248i	$0.914216\pi$
$822$		0			0
$823$	20.2108	−	11.6687i	0.704505	−	0.406746i	−0.104518	−	0.994523i	$-0.533330\pi$
$823$	20.2108	−	11.6687i	0.704505	−	0.406746i	0.809023	+	0.587777i	$0.199997\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	32.8733			1.14312			0.571558	−	0.820561i	$-0.306339\pi$
$827$	32.8733			1.14312			0.571558	+	0.820561i	$0.306339\pi$
$828$		0			0
$829$	−9.89105	+	17.1318i	−0.343530	+	0.595012i	−0.985086	−	0.172065i	$-0.944956\pi$
$829$	−9.89105	+	17.1318i	−0.343530	+	0.595012i	0.641555	+	0.767077i	$0.278289\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−12.7625	+	0.990824i	−0.442193	+	0.0343300i
$834$		0			0
$835$	−26.0673	−	15.0500i	−0.902096	−	0.520825i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.16013	+	15.8658i	0.316243	+	0.547748i	0.979701	−	0.200465i	$-0.0642453\pi$
$839$	9.16013	+	15.8658i	0.316243	+	0.547748i	−0.663458	+	0.748213i	$0.730912\pi$
$840$		0			0
$841$	−12.7957	+	22.1629i	−0.441233	+	0.764238i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−10.8718	+	6.27682i	−0.374000	+	0.215929i
$846$		0			0
$847$	4.81786	+	15.5451i	0.165544	+	0.534137i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.21863	−	5.57483i	−0.110333	−	0.191103i
$852$		0			0
$853$	−22.1236	−	38.3192i	−0.757498	−	1.31203i	−0.944123	−	0.329594i	$-0.893088\pi$
$853$	−22.1236	−	38.3192i	−0.757498	−	1.31203i	0.186625	−	0.982431i	$-0.440245\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			50.7367i			1.73313i	0.499063	+	0.866566i	$0.333678\pi$
$857$			50.7367i			1.73313i	−0.499063	+	0.866566i	$0.666322\pi$
$858$		0			0
$859$			4.30738i			0.146966i	0.997296	+	0.0734829i	$0.0234114\pi$
$859$			4.30738i			0.146966i	−0.997296	+	0.0734829i	$0.976589\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.42163	+	16.3187i	0.320716	+	0.555496i	0.980636	−	0.195840i	$-0.0627432\pi$
$863$	9.42163	+	16.3187i	0.320716	+	0.555496i	−0.659920	+	0.751336i	$0.729410\pi$
$864$		0			0
$865$	−0.0309018	+	0.0535234i	−0.00105069	+	0.00181985i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	40.1409	+	23.1754i	1.36169	+	0.786170i
$870$		0			0
$871$			0.832090i			0.0281943i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−26.2694	+	8.14163i	−0.888069	+	0.275237i
$876$		0			0
$877$	29.1118			0.983037			0.491519	−	0.870867i	$-0.336442\pi$
$877$	29.1118			0.983037			0.491519	+	0.870867i	$0.336442\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	21.7911i		−	0.734161i	−0.930189	−	0.367081i	$-0.880357\pi$
$881$		−	21.7911i		−	0.734161i	0.930189	−	0.367081i	$-0.119643\pi$
$882$		0			0
$883$		−	8.18321i		−	0.275387i	−0.990475	−	0.137693i	$-0.956031\pi$
$883$		−	8.18321i		−	0.275387i	0.990475	−	0.137693i	$-0.0439689\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.61322			−0.121320			−0.0606600	−	0.998158i	$-0.519321\pi$
$887$	−3.61322			−0.121320			−0.0606600	+	0.998158i	$0.519321\pi$
$888$		0			0
$889$	43.7479	−	13.5587i	1.46726	−	0.454744i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			10.0339i			0.335771i
$894$		0			0
$895$	−16.8918	−	9.75249i	−0.564631	−	0.325990i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	8.59683	−	14.8902i	0.286720	−	0.496614i
$900$		0			0
$901$	10.8630	+	18.8152i	0.361898	+	0.626826i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	22.5001i		−	0.747928i
$906$		0			0
$907$			50.8788i			1.68940i	0.535237	+	0.844702i	$0.320222\pi$
$907$			50.8788i			1.68940i	−0.535237	+	0.844702i	$0.679778\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−29.4958	−	51.0882i	−0.977238	−	1.69263i	−0.672342	−	0.740240i	$-0.734712\pi$
$911$	−29.4958	−	51.0882i	−0.977238	−	1.69263i	−0.304896	−	0.952386i	$-0.598622\pi$
$912$		0			0
$913$	10.9479	+	18.9623i	0.362323	+	0.627562i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	11.4088	+	36.8113i	0.376753	+	1.21562i
$918$		0			0
$919$	−26.6301	+	15.3749i	−0.878447	+	0.507172i	−0.870146	−	0.492794i	$-0.835976\pi$
$919$	−26.6301	+	15.3749i	−0.878447	+	0.507172i	−0.00830118	+	0.999966i	$0.502642\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	21.7386	−	37.6523i	0.715534	−	1.23934i
$924$		0			0
$925$	−1.92842	−	3.34012i	−0.0634061	−	0.109823i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	5.13839	+	2.96665i	0.168585	+	0.0973327i	0.581919	−	0.813247i	$-0.302302\pi$
$929$	5.13839	+	2.96665i	0.168585	+	0.0973327i	−0.413333	+	0.910580i	$0.635636\pi$
$930$		0			0
$931$	−9.52934	+	19.9243i	−0.312311	+	0.652993i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	8.97061	−	15.5376i	0.293370	−	0.508132i
$936$		0			0
$937$	−6.00231			−0.196087			−0.0980435	−	0.995182i	$-0.531258\pi$
$937$	−6.00231			−0.196087			−0.0980435	+	0.995182i	$0.531258\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−39.8847	+	23.0275i	−1.30020	+	0.750674i	−0.980439	−	0.196823i	$-0.936938\pi$
$941$	−39.8847	+	23.0275i	−1.30020	+	0.750674i	−0.319766	+	0.947497i	$0.603604\pi$
$942$		0			0
$943$	8.72417	+	5.03690i	0.284098	+	0.164024i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.27908	+	12.6077i	−0.236538	+	0.409696i	−0.959719	−	0.280963i	$-0.909346\pi$
$947$	−7.27908	+	12.6077i	−0.236538	+	0.409696i	0.723180	+	0.690659i	$0.242680\pi$
$948$		0			0
$949$	−1.16427	−	2.01658i	−0.0377939	−	0.0654609i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	29.0894i		−	0.942297i	−0.882054	−	0.471149i	$-0.843840\pi$
$953$		−	29.0894i		−	0.942297i	0.882054	−	0.471149i	$-0.156160\pi$
$954$		0			0
$955$	20.3737	+	11.7628i	0.659277	+	0.380634i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−21.3483	+	6.61642i	−0.689371	+	0.213655i
$960$		0			0
$961$	27.8654	−	48.2644i	0.898885	−	1.55691i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	32.1322	−	18.5515i	1.03437	−	0.597195i
$966$		0			0
$967$	5.25768	+	3.03552i	0.169075	+	0.0976158i	0.582150	−	0.813082i	$-0.302212\pi$
$967$	5.25768	+	3.03552i	0.169075	+	0.0976158i	−0.413074	+	0.910697i	$0.635545\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−28.5315	−	49.4180i	−0.915619	−	1.58590i	−0.805992	−	0.591927i	$-0.798368\pi$
$971$	−28.5315	−	49.4180i	−0.915619	−	1.58590i	−0.109627	−	0.993973i	$-0.534966\pi$
$972$		0			0
$973$	1.65438	−	7.29335i	0.0530369	−	0.233814i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	16.6568	−	9.61682i	0.532899	−	0.307669i	−0.209297	−	0.977852i	$-0.567118\pi$
$977$	16.6568	−	9.61682i	0.532899	−	0.307669i	0.742196	+	0.670183i	$0.233784\pi$
$978$		0			0
$979$	−6.74433	+	3.89384i	−0.215550	+	0.124448i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−27.1792			−0.866883			−0.433441	−	0.901182i	$-0.642701\pi$
$983$	−27.1792			−0.866883			−0.433441	+	0.901182i	$0.642701\pi$
$984$		0			0
$985$	−28.7332			−0.915517
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.74806	+	5.62805i	−0.309970	+	0.178961i
$990$		0			0
$991$	29.2381	+	16.8806i	0.928778	+	0.536230i	0.886425	−	0.462873i	$-0.153181\pi$
$991$	29.2381	+	16.8806i	0.928778	+	0.536230i	0.0423529	+	0.999103i	$0.486515\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	14.4165	−	24.9702i	0.457035	−	0.791608i
$996$		0			0
$997$	−2.85134			−0.0903028			−0.0451514	−	0.998980i	$-0.514377\pi$
$997$	−2.85134			−0.0903028			−0.0451514	+	0.998980i	$0.514377\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.bh.d.2447.12		30
3.2	odd	2		1008.2.bh.d.95.12	yes	30
4.3	odd	2		3024.2.bh.c.2447.12		30
7.2	even	3		3024.2.cj.d.2879.12		30
9.2	odd	6		3024.2.cj.c.1439.12		30
9.7	even	3		1008.2.cj.c.767.14	yes	30
12.11	even	2		1008.2.bh.c.95.4	✓	30
21.2	odd	6		1008.2.cj.d.527.2	yes	30
28.23	odd	6		3024.2.cj.c.2879.12		30
36.7	odd	6		1008.2.cj.d.767.2	yes	30
36.11	even	6		3024.2.cj.d.1439.12		30
63.2	odd	6		3024.2.bh.c.1871.4		30
63.16	even	3		1008.2.bh.c.191.4	yes	30
84.23	even	6		1008.2.cj.c.527.14	yes	30
252.79	odd	6		1008.2.bh.d.191.12	yes	30
252.191	even	6	inner	3024.2.bh.d.1871.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bh.c.95.4	✓	30	12.11	even	2
1008.2.bh.c.191.4	yes	30	63.16	even	3
1008.2.bh.d.95.12	yes	30	3.2	odd	2
1008.2.bh.d.191.12	yes	30	252.79	odd	6
1008.2.cj.c.527.14	yes	30	84.23	even	6
1008.2.cj.c.767.14	yes	30	9.7	even	3
1008.2.cj.d.527.2	yes	30	21.2	odd	6
1008.2.cj.d.767.2	yes	30	36.7	odd	6
3024.2.bh.c.1871.4		30	63.2	odd	6
3024.2.bh.c.2447.12		30	4.3	odd	2
3024.2.bh.d.1871.4		30	252.191	even	6	inner
3024.2.bh.d.2447.12		30	1.1	even	1	trivial
3024.2.cj.c.1439.12		30	9.2	odd	6
3024.2.cj.c.2879.12		30	28.23	odd	6
3024.2.cj.d.1439.12		30	36.11	even	6
3024.2.cj.d.2879.12		30	7.2	even	3

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.36899i q^{5} +(0.783237 + 2.52716i) q^{7} +O(q^{10})\)	\(q+2.36899i q^{5} +(0.783237 + 2.52716i) q^{7} -4.14140 q^{11} +(-1.38752 + 2.40326i) q^{13} +(1.58369 + 0.914347i) q^{17} +(2.73242 - 1.57756i) q^{19} -1.02166 q^{23} -0.612123 q^{25} +(-1.59887 + 0.923106i) q^{29} +(-8.06524 + 4.65647i) q^{31} +(-5.98682 + 1.85548i) q^{35} +(3.15039 + 5.45663i) q^{37} +(-8.53919 - 4.93010i) q^{41} +(9.54137 - 5.50871i) q^{43} +(-1.59009 + 2.75412i) q^{47} +(-5.77308 + 3.95873i) q^{49} +(10.2889 + 5.94029i) q^{53} -9.81095i q^{55} +(-1.62351 - 2.81200i) q^{59} +(-0.426723 + 0.739106i) q^{61} +(-5.69329 - 3.28702i) q^{65} +(0.259676 - 0.149924i) q^{67} -15.6672 q^{71} +(-0.419551 + 0.726684i) q^{73} +(-3.24370 - 10.4660i) q^{77} +(-9.69258 - 5.59601i) q^{79} +(-2.64353 - 4.57872i) q^{83} +(-2.16608 + 3.75176i) q^{85} +(1.62851 - 0.940223i) q^{89} +(-7.16017 - 1.62417i) q^{91} +(3.73724 + 6.47308i) q^{95} +(-8.03665 - 13.9199i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{7}+O(q^{10}) \) 30 * q + 2 * q^7	\( 30 q + 2 q^{7} + 6 q^{11} - 12 q^{17} - 9 q^{19} - 24 q^{23} - 36 q^{25} - 27 q^{29} - 6 q^{31} - 6 q^{35} + 6 q^{37} - 9 q^{41} + 21 q^{43} + 12 q^{49} + 3 q^{53} + 3 q^{59} - 3 q^{61} + 39 q^{67} + 18 q^{71} + 21 q^{73} - 36 q^{77} + 33 q^{79} - 15 q^{83} - 3 q^{85} - 6 q^{89} + 26 q^{91} - 27 q^{95} - 6 q^{97}+O(q^{100}) \) 30 * q + 2 * q^7 + 6 * q^11 - 12 * q^17 - 9 * q^19 - 24 * q^23 - 36 * q^25 - 27 * q^29 - 6 * q^31 - 6 * q^35 + 6 * q^37 - 9 * q^41 + 21 * q^43 + 12 * q^49 + 3 * q^53 + 3 * q^59 - 3 * q^61 + 39 * q^67 + 18 * q^71 + 21 * q^73 - 36 * q^77 + 33 * q^79 - 15 * q^83 - 3 * q^85 - 6 * q^89 + 26 * q^91 - 27 * q^95 - 6 * q^97

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