LMFDB - Embedded newform 3024.2.cj.c.1439.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(1439,3024)]

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, 4]))

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

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

chi := DirichletCharacter("3024.1439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cj (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			1439.12
Character	$\chi$	$=$	3024.1439
Dual form			3024.2.cj.c.2879.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05161 + 1.18450i) q^{5} +(1.79697 - 1.94188i) q^{7} +O(q^{10})$	$q+(2.05161 + 1.18450i) q^{5} +(1.79697 - 1.94188i) q^{7} +(-2.07070 - 3.58656i) q^{11} +(-1.38752 - 2.40326i) q^{13} +(-1.58369 - 0.914347i) q^{17} +(2.73242 - 1.57756i) q^{19} +(-0.510831 + 0.884786i) q^{23} +(0.306061 + 0.530114i) q^{25} +(-1.59887 - 0.923106i) q^{29} -9.31294i q^{31} +(5.98682 - 1.85548i) q^{35} +(3.15039 + 5.45663i) q^{37} +(-8.53919 + 4.93010i) q^{41} +(-9.54137 - 5.50871i) q^{43} -3.18018 q^{47} +(-0.541821 - 6.97900i) q^{49} +(-10.2889 - 5.94029i) q^{53} -9.81095i q^{55} -3.24702 q^{59} +0.853446 q^{61} -6.57405i q^{65} +0.299848i q^{67} +15.6672 q^{71} +(-0.419551 + 0.726684i) q^{73} +(-10.6857 - 2.42387i) q^{77} +11.1920i q^{79} +(2.64353 - 4.57872i) q^{83} +(-2.16608 - 3.75176i) q^{85} +(-1.62851 + 0.940223i) q^{89} +(-7.16017 - 1.62417i) q^{91} +7.47447 q^{95} +(-8.03665 + 13.9199i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{5} - 7 q^{7}+O(q^{10}) $ 30 * q - 3 * q^5 - 7 * q^7	$ 30 q - 3 q^{5} - 7 q^{7} + 3 q^{11} + 12 q^{17} - 9 q^{19} - 12 q^{23} + 18 q^{25} - 27 q^{29} + 6 q^{35} + 6 q^{37} - 9 q^{41} - 21 q^{43} - 3 q^{49} - 3 q^{53} + 6 q^{59} + 6 q^{61} - 18 q^{71} + 21 q^{73} - 72 q^{77} + 15 q^{83} - 3 q^{85} + 6 q^{89} + 26 q^{91} - 54 q^{95} - 6 q^{97}+O(q^{100}) $ 30 * q - 3 * q^5 - 7 * q^7 + 3 * q^11 + 12 * q^17 - 9 * q^19 - 12 * q^23 + 18 * q^25 - 27 * q^29 + 6 * q^35 + 6 * q^37 - 9 * q^41 - 21 * q^43 - 3 * q^49 - 3 * q^53 + 6 * q^59 + 6 * q^61 - 18 * q^71 + 21 * q^73 - 72 * q^77 + 15 * q^83 - 3 * q^85 + 6 * q^89 + 26 * q^91 - 54 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	2.05161	+	1.18450i	0.917507	+	0.529723i	0.882839	−	0.469676i	$-0.155629\pi$
$5$	2.05161	+	1.18450i	0.917507	+	0.529723i	0.0346679	+	0.999399i	$0.488963\pi$
$6$		0			0
$7$	1.79697	−	1.94188i	0.679190	−	0.733963i
$7$	1.79697	−	1.94188i	0.679190	−	0.733963i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.07070	−	3.58656i	−0.624340	−	1.08139i	−0.988668	−	0.150118i	$-0.952035\pi$
$11$	−2.07070	−	3.58656i	−0.624340	−	1.08139i	0.364328	−	0.931271i	$-0.381299\pi$
$12$		0			0
$13$	−1.38752	−	2.40326i	−0.384829	−	0.666543i	0.606917	−	0.794766i	$-0.292406\pi$
$13$	−1.38752	−	2.40326i	−0.384829	−	0.666543i	−0.991745	+	0.128222i	$0.959073\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.58369	−	0.914347i	−0.384102	−	0.221762i	0.295499	−	0.955343i	$-0.404514\pi$
$17$	−1.58369	−	0.914347i	−0.384102	−	0.221762i	−0.679602	+	0.733581i	$0.737847\pi$
$18$		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
$23$	−0.510831	+	0.884786i	−0.106516	+	0.184491i	−0.914356	−	0.404910i	$-0.867303\pi$
$23$	−0.510831	+	0.884786i	−0.106516	+	0.184491i	0.807841	+	0.589401i	$0.200636\pi$
$24$		0			0
$25$	0.306061	+	0.530114i	0.0612123	+	0.106023i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.59887	−	0.923106i	−0.296902	−	0.171417i	0.344148	−	0.938915i	$-0.388168\pi$
$29$	−1.59887	−	0.923106i	−0.296902	−	0.171417i	−0.641050	+	0.767499i	$0.721501\pi$
$30$		0			0
$31$		−	9.31294i		−	1.67265i	−0.548231	−	0.836327i	$-0.684699\pi$
$31$		−	9.31294i		−	1.67265i	0.548231	−	0.836327i	$-0.315301\pi$
$32$		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	−0.985849	−	0.167635i	$-0.946387\pi$
$41$	−8.53919	+	4.93010i	−1.33360	+	0.769953i	−0.347748	+	0.937588i	$0.613054\pi$
$42$		0			0
$43$	−9.54137	−	5.50871i	−1.45505	−	0.840071i	−0.456284	−	0.889834i	$-0.650820\pi$
$43$	−9.54137	−	5.50871i	−1.45505	−	0.840071i	−0.998761	+	0.0497632i	$0.984153\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.18018			−0.463877			−0.231939	−	0.972730i	$-0.574507\pi$
$47$	−3.18018			−0.463877			−0.231939	+	0.972730i	$0.574507\pi$
$48$		0			0
$49$	−0.541821	−	6.97900i	−0.0774030	−	0.997000i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.2889	−	5.94029i	−1.41329	−	0.815962i	−0.417591	−	0.908635i	$-0.637125\pi$
$53$	−10.2889	−	5.94029i	−1.41329	−	0.815962i	−0.995697	+	0.0926733i	$0.970459\pi$
$54$		0			0
$55$		−	9.81095i		−	1.32291i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.24702			−0.422726			−0.211363	−	0.977408i	$-0.567790\pi$
$59$	−3.24702			−0.422726			−0.211363	+	0.977408i	$0.567790\pi$
$60$		0			0
$61$	0.853446			0.109273			0.0546363	−	0.998506i	$-0.482600\pi$
$61$	0.853446			0.109273			0.0546363	+	0.998506i	$0.482600\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	6.57405i		−	0.815410i
$66$		0			0
$67$			0.299848i			0.0366322i	0.999832	+	0.0183161i	$0.00583053\pi$
$67$			0.299848i			0.0366322i	−0.999832	+	0.0183161i	$0.994169\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	15.6672			1.85936			0.929678	−	0.368373i	$-0.120085\pi$
$71$	15.6672			1.85936			0.929678	+	0.368373i	$0.120085\pi$
$72$		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
$77$	−10.6857	−	2.42387i	−1.21774	−	0.276226i
$78$		0			0
$79$			11.1920i			1.25920i	0.776919	+	0.629601i	$0.216782\pi$
$79$			11.1920i			1.25920i	−0.776919	+	0.629601i	$0.783218\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.64353	−	4.57872i	0.290165	−	0.502580i	−0.683684	−	0.729778i	$-0.739623\pi$
$83$	2.64353	−	4.57872i	0.290165	−	0.502580i	0.973849	+	0.227198i	$0.0729565\pi$
$84$		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	−0.583822	−	0.811882i	$-0.698443\pi$
$89$	−1.62851	+	0.940223i	−0.172622	+	0.0996635i	0.411200	+	0.911545i	$0.365110\pi$
$90$		0			0
$91$	−7.16017	−	1.62417i	−0.750590	−	0.170259i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.47447			0.766865
$96$		0			0
$97$	−8.03665	+	13.9199i	−0.815999	+	1.41335i	0.0926100	+	0.995702i	$0.470479\pi$
$97$	−8.03665	+	13.9199i	−0.815999	+	1.41335i	−0.908609	+	0.417649i	$0.862854\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.35849	−	4.82578i	0.831701	−	0.480183i	−0.0227335	−	0.999742i	$-0.507237\pi$
$101$	8.35849	−	4.82578i	0.831701	−	0.480183i	0.854435	+	0.519559i	$0.173904\pi$
$102$		0			0
$103$	8.23789	+	4.75615i	0.811703	+	0.468637i	0.847547	−	0.530720i	$-0.178079\pi$
$103$	8.23789	+	4.75615i	0.811703	+	0.468637i	−0.0358439	+	0.999357i	$0.511412\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.53673	+	7.85784i	0.438582	+	0.759646i	0.997580	−	0.0695224i	$-0.0221475\pi$
$107$	4.53673	+	7.85784i	0.438582	+	0.759646i	−0.558998	+	0.829169i	$0.688814\pi$
$108$		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	0.218682	−	0.975796i	$-0.429824\pi$
$113$	12.4701	−	7.19961i	1.17309	−	0.677282i	0.954405	+	0.298514i	$0.0964909\pi$
$114$		0			0
$115$	−2.09605	+	1.21016i	−0.195458	+	0.112848i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.62140	+	1.43230i	−0.423643	+	0.131299i
$120$		0			0
$121$	−3.07561	+	5.32711i	−0.279601	+	0.484283i
$122$		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
$131$	7.28314	−	12.6148i	0.636331	−	1.10216i	−0.349901	−	0.936787i	$-0.613785\pi$
$131$	7.28314	−	12.6148i	0.636331	−	1.10216i	0.986232	−	0.165370i	$-0.0528819\pi$
$132$		0			0
$133$	1.84663	−	8.14087i	0.160123	−	0.705903i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.31578	+	4.22377i	−0.625029	+	0.360861i	−0.778824	−	0.627242i	$-0.784184\pi$
$137$	−7.31578	+	4.22377i	−0.625029	+	0.360861i	0.153795	+	0.988103i	$0.450850\pi$
$138$		0			0
$139$	2.44796	−	1.41333i	0.207633	−	0.119877i	−0.392578	−	0.919719i	$-0.628417\pi$
$139$	2.44796	−	1.41333i	0.207633	−	0.119877i	0.600211	+	0.799842i	$0.295083\pi$
$140$		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
$149$	16.4668	+	9.50713i	1.34902	+	0.778854i	0.988110	−	0.153748i	$-0.0491345\pi$
$149$	16.4668	+	9.50713i	1.34902	+	0.778854i	0.360905	+	0.932603i	$0.382468\pi$
$150$		0			0
$151$	2.44992	−	1.41446i	0.199372	−	0.115107i	−0.396991	−	0.917823i	$-0.629945\pi$
$151$	2.44992	−	1.41446i	0.199372	−	0.115107i	0.596362	+	0.802715i	$0.296612\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	11.0311	−	19.1065i	0.886043	−	1.53467i
$156$		0			0
$157$	2.53288			0.202146			0.101073	−	0.994879i	$-0.467773\pi$
$157$	2.53288			0.202146			0.101073	+	0.994879i	$0.467773\pi$
$158$		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	$-0.00307828\pi$
$167$	6.35289	+	11.0035i	0.491602	+	0.851479i	−0.508352	+	0.861150i	$0.669745\pi$
$168$		0			0
$169$	2.64957	−	4.58920i	0.203813	−	0.353015i
$170$		0			0
$171$		0			0
$172$		0			0
$173$			0.0260885i			0.00198348i	1.00000		0.000991738i	$0.000315680\pi$
$173$			0.0260885i			0.00198348i	−1.00000		0.000991738i	$0.999684\pi$
$174$		0			0
$175$	1.57940	+	0.358261i	0.119391	+	0.0270820i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.11673	−	7.13038i	0.307699	−	0.532950i	−0.670160	−	0.742217i	$-0.733774\pi$
$179$	4.11673	−	7.13038i	0.307699	−	0.532950i	0.977859	+	0.209267i	$0.0671078\pi$
$180$		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
$185$			14.9265i			1.09742i
$186$		0			0
$187$			7.57336i			0.553819i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.93060			0.718553			0.359276	−	0.933231i	$-0.383024\pi$
$191$	9.93060			0.718553			0.359276	+	0.933231i	$0.383024\pi$
$192$		0			0
$193$	15.6620			1.12737			0.563686	−	0.825989i	$-0.309383\pi$
$193$	15.6620			1.12737			0.563686	+	0.825989i	$0.309383\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	12.1289i		−	0.864148i	−0.901838	−	0.432074i	$-0.857782\pi$
$197$		−	12.1289i		−	0.864148i	0.901838	−	0.432074i	$-0.142218\pi$
$198$		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
$203$	−4.66568	+	1.44602i	−0.327466	+	0.101491i
$204$		0			0
$205$	−23.3587			−1.63145
$206$		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	$-0.760840\pi$
$211$	−7.33542	+	4.23511i	−0.504991	+	0.291557i	0.225781	+	0.974178i	$0.427507\pi$
$212$		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
$221$			5.07470i			0.341361i
$222$		0			0
$223$	−7.76299	−	4.48197i	−0.519848	−	0.300135i	0.217024	−	0.976166i	$-0.430365\pi$
$223$	−7.76299	−	4.48197i	−0.519848	−	0.300135i	−0.736873	+	0.676032i	$0.763698\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.97570	−	15.5464i	−0.595738	−	1.03185i	−0.993442	−	0.114335i	$-0.963526\pi$
$227$	−8.97570	−	15.5464i	−0.595738	−	1.03185i	0.397704	−	0.917514i	$-0.369807\pi$
$228$		0			0
$229$	1.10725	−	1.91781i	0.0731689	−	0.126732i	−0.827120	−	0.562026i	$-0.810022\pi$
$229$	1.10725	−	1.91781i	0.0731689	−	0.126732i	0.900289	+	0.435294i	$0.143355\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.98834	−	1.72532i	0.195773	−	0.113029i	−0.398910	−	0.916990i	$-0.630611\pi$
$233$	2.98834	−	1.72532i	0.195773	−	0.113029i	0.594682	+	0.803961i	$0.297278\pi$
$234$		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	$-0.242967\pi$
$239$	−3.67035	−	6.35723i	−0.237415	−	0.411215i	−0.959972	+	0.280097i	$0.909633\pi$
$240$		0			0
$241$	8.67228	+	15.0208i	0.558631	+	0.967577i	0.997611	+	0.0690802i	$0.0220064\pi$
$241$	8.67228	+	15.0208i	0.558631	+	0.967577i	−0.438980	+	0.898497i	$0.644660\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7.15499	−	14.9599i	0.457116	−	0.955756i
$246$		0			0
$247$	−7.58258	−	4.37780i	−0.482468	−	0.278553i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	13.9816			0.882511			0.441255	−	0.897382i	$-0.354533\pi$
$251$	13.9816			0.882511			0.441255	+	0.897382i	$0.354533\pi$
$252$		0			0
$253$	4.23112			0.266008
$254$		0			0
$255$		0			0
$256$		0			0
$257$	24.2713	+	14.0130i	1.51400	+	0.874109i	0.999866	+	0.0164002i	$0.00522058\pi$
$257$	24.2713	+	14.0130i	1.51400	+	0.874109i	0.514136	+	0.857709i	$0.328113\pi$
$258$		0			0
$259$	16.2573	+	3.68770i	1.01018	+	0.229142i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.48953	−	14.7043i	−0.523487	−	0.906706i	−0.999626	−	0.0273363i	$-0.991298\pi$
$263$	−8.48953	−	14.7043i	−0.523487	−	0.906706i	0.476139	−	0.879370i	$-0.342036\pi$
$264$		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	−0.450277	−	0.892889i	$-0.648675\pi$
$269$	−23.7601	−	13.7179i	−1.44868	−	0.836396i	−0.998403	+	0.0564933i	$0.982008\pi$
$270$		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
$275$	1.26752	−	2.19541i	0.0764345	−	0.132388i
$276$		0			0
$277$	−3.29179	−	5.70154i	−0.197784	−	0.342572i	0.750025	−	0.661409i	$-0.230041\pi$
$277$	−3.29179	−	5.70154i	−0.197784	−	0.342572i	−0.947810	+	0.318837i	$0.896708\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	23.0468	+	13.3061i	1.37486	+	0.793775i	0.991535	−	0.129839i	$-0.0414461\pi$
$281$	23.0468	+	13.3061i	1.37486	+	0.793775i	0.383324	+	0.923614i	$0.374779\pi$
$282$		0			0
$283$		−	30.8678i		−	1.83490i	−0.397854	−	0.917449i	$-0.630245\pi$
$283$		−	30.8678i		−	1.83490i	0.397854	−	0.917449i	$-0.369755\pi$
$284$		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	−0.349181	−	0.937055i	$-0.613540\pi$
$293$	4.92535	−	2.84365i	0.287742	−	0.166128i	0.636923	+	0.770927i	$0.280207\pi$
$294$		0			0
$295$	−6.66162	−	3.84609i	−0.387854	−	0.223928i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.83516			0.163961
$300$		0			0
$301$	−27.8428	+	8.62925i	−1.60483	+	0.497382i
$302$		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
$311$	29.1144			1.65093			0.825463	−	0.564456i	$-0.190914\pi$
$311$	29.1144			1.65093			0.825463	+	0.564456i	$0.190914\pi$
$312$		0			0
$313$	28.4143			1.60607			0.803037	−	0.595929i	$-0.203216\pi$
$313$	28.4143			1.60607			0.803037	+	0.595929i	$0.203216\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	24.6989i		−	1.38723i	−0.720346	−	0.693615i	$-0.756017\pi$
$317$		−	24.6989i		−	1.38723i	0.720346	−	0.693615i	$-0.243983\pi$
$318$		0			0
$319$			7.64591i			0.428089i
$320$		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
$329$	−5.71468	+	6.17554i	−0.315061	+	0.340469i
$330$		0			0
$331$		−	14.8026i		−	0.813625i	−0.913512	−	0.406812i	$-0.866640\pi$
$331$		−	14.8026i		−	0.813625i	0.913512	−	0.406812i	$-0.133360\pi$
$332$		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	0.931335	+	0.364163i	$0.118645\pi$
$337$	14.3380	+	24.8342i	0.781042	+	1.35280i	−0.150293	+	0.988642i	$0.548022\pi$
$338$		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
$347$	18.6366			1.00047			0.500233	−	0.865891i	$-0.333248\pi$
$347$	18.6366			1.00047			0.500233	+	0.865891i	$0.333248\pi$
$348$		0			0
$349$	−8.10052	+	14.0305i	−0.433611	+	0.751036i	−0.997181	−	0.0750321i	$-0.976094\pi$
$349$	−8.10052	+	14.0305i	−0.433611	+	0.751036i	0.563570	+	0.826068i	$0.309427\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9.94346	+	5.74086i	−0.529237	+	0.305555i	−0.740706	−	0.671830i	$-0.765509\pi$
$353$	−9.94346	+	5.74086i	−0.529237	+	0.305555i	0.211469	+	0.977385i	$0.432175\pi$
$354$		0			0
$355$	32.1430	+	18.5578i	1.70597	+	0.984943i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.31363	−	14.3996i	−0.438777	−	0.759983i	0.558819	−	0.829290i	$-0.311255\pi$
$359$	−8.31363	−	14.3996i	−0.438777	−	0.759983i	−0.997595	+	0.0693065i	$0.977921\pi$
$360$		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
$367$	17.4096	−	10.0514i	0.908772	−	0.524680i	0.0287361	−	0.999587i	$-0.490852\pi$
$367$	17.4096	−	10.0514i	0.908772	−	0.524680i	0.880036	+	0.474907i	$0.157518\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−30.0241	+	9.30531i	−1.55878	+	0.483108i
$372$		0			0
$373$	−16.7149	+	28.9511i	−0.865465	+	1.49903i	0.00111918	+	0.999999i	$0.499644\pi$
$373$	−16.7149	+	28.9511i	−0.865465	+	1.49903i	−0.866584	+	0.499030i	$0.833690\pi$
$374$		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
$383$	−9.60092	+	16.6293i	−0.490584	+	0.849716i	−0.999941	−	0.0108387i	$-0.996550\pi$
$383$	−9.60092	+	16.6293i	−0.490584	+	0.849716i	0.509357	+	0.860555i	$0.329883\pi$
$384$		0			0
$385$	−19.0517	−	17.6300i	−0.970966	−	0.898506i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	11.4890	−	6.63319i	0.582517	−	0.336316i	−0.179616	−	0.983737i	$-0.557486\pi$
$389$	11.4890	−	6.63319i	0.582517	−	0.336316i	0.762133	+	0.647421i	$0.224152\pi$
$390$		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
$401$	−3.65064	−	2.10770i	−0.182304	−	0.105253i	0.406071	−	0.913842i	$-0.366899\pi$
$401$	−3.65064	−	2.10770i	−0.182304	−	0.105253i	−0.588375	+	0.808588i	$0.700232\pi$
$402$		0			0
$403$	−22.3814	+	12.9219i	−1.11490	+	0.643685i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	13.0470	−	22.5981i	0.646717	−	1.12015i
$408$		0			0
$409$	16.5900			0.820325			0.410163	−	0.912012i	$-0.365472\pi$
$409$	16.5900			0.820325			0.410163	+	0.912012i	$0.365472\pi$
$410$		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	$-0.215711\pi$
$419$	−3.14140	−	5.44107i	−0.153467	−	0.265813i	−0.932500	+	0.361170i	$0.882377\pi$
$420$		0			0
$421$	14.9372	−	25.8720i	0.727995	−	1.26092i	−0.229735	−	0.973253i	$-0.573786\pi$
$421$	14.9372	−	25.8720i	0.727995	−	1.26092i	0.957729	−	0.287670i	$-0.0928808\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		−	1.11938i		−	0.0542981i
$426$		0			0
$427$	1.53361	−	1.65729i	0.0742168	−	0.0802020i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.76371	+	11.7151i	−0.325796	+	0.564296i	−0.981673	−	0.190572i	$-0.938966\pi$
$431$	−6.76371	+	11.7151i	−0.325796	+	0.564296i	0.655877	+	0.754868i	$0.272299\pi$
$432$		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
$437$			3.22348i			0.154200i
$438$		0			0
$439$		−	16.2021i		−	0.773283i	−0.922230	−	0.386642i	$-0.873635\pi$
$439$		−	16.2021i		−	0.773283i	0.922230	−	0.386642i	$-0.126365\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−27.2200			−1.29326			−0.646630	−	0.762804i	$-0.723822\pi$
$443$	−27.2200			−1.29326			−0.646630	+	0.762804i	$0.723822\pi$
$444$		0			0
$445$	−4.45476			−0.211176
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	17.8656i		−	0.843130i	−0.906798	−	0.421565i	$-0.861481\pi$
$449$		−	17.8656i		−	0.843130i	0.906798	−	0.421565i	$-0.138519\pi$
$450$		0			0
$451$	35.3642	+	20.4175i	1.66524	+	0.961425i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−12.7660	−	11.8133i	−0.598481	−	0.553818i
$456$		0			0
$457$	14.2480			0.666493			0.333246	−	0.942840i	$-0.391856\pi$
$457$	14.2480			0.666493			0.333246	+	0.942840i	$0.391856\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.37315	+	1.94749i	0.157103	+	0.0907036i	0.576491	−	0.817104i	$-0.304422\pi$
$461$	3.37315	+	1.94749i	0.157103	+	0.0907036i	−0.419387	+	0.907807i	$0.637755\pi$
$462$		0			0
$463$	−4.28829	+	2.47585i	−0.199294	+	0.115062i	−0.596326	−	0.802742i	$-0.703373\pi$
$463$	−4.28829	+	2.47585i	−0.199294	+	0.115062i	0.397032	+	0.917805i	$0.370040\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.3358	+	17.9021i	0.478282	+	0.828409i	0.999690	−	0.0248989i	$-0.00792638\pi$
$467$	10.3358	+	17.9021i	0.478282	+	0.828409i	−0.521408	+	0.853307i	$0.674593\pi$
$468$		0			0
$469$	0.582270	+	0.538817i	0.0268867	+	0.0248802i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			45.6276i			2.09796i
$474$		0			0
$475$	1.67258	+	0.965663i	0.0767431	+	0.0443076i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.2174	+	22.8933i	0.603920	+	1.04602i	0.992221	+	0.124488i	$0.0397288\pi$
$479$	13.2174	+	22.8933i	0.603920	+	1.04602i	−0.388301	+	0.921533i	$0.626938\pi$
$480$		0			0
$481$	8.74245	−	15.1424i	0.398621	−	0.690432i
$482$		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	$-0.113258\pi$
$491$	3.70049	+	6.40944i	0.167001	+	0.289254i	−0.770363	+	0.637605i	$0.779925\pi$
$492$		0			0
$493$	1.68808	+	2.92384i	0.0760272	+	0.131683i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	28.1535	−	30.4239i	1.26286	−	1.36470i
$498$		0			0
$499$	−8.73491	−	5.04310i	−0.391028	−	0.225760i	0.291577	−	0.956547i	$-0.405820\pi$
$499$	−8.73491	−	5.04310i	−0.391028	−	0.225760i	−0.682606	+	0.730787i	$0.739153\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−2.11362			−0.0942416			−0.0471208	−	0.998889i	$-0.515005\pi$
$503$	−2.11362			−0.0942416			−0.0471208	+	0.998889i	$0.515005\pi$
$504$		0			0
$505$	22.8645			1.01746
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−25.9327	−	14.9723i	−1.14945	−	0.663633i	−0.200694	−	0.979654i	$-0.564320\pi$
$509$	−25.9327	−	14.9723i	−1.14945	−	0.663633i	−0.948752	+	0.316021i	$0.897653\pi$
$510$		0			0
$511$	0.657216	+	2.12055i	0.0290735	+	0.0938075i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	11.2673	+	19.5155i	0.496495	+	0.859955i
$516$		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	0.992740	−	0.120278i	$-0.0383786\pi$
$521$	31.6120	+	18.2512i	1.38495	+	0.799599i	0.392206	+	0.919877i	$0.371712\pi$
$522$		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
$527$	−8.51526	+	14.7489i	−0.370930	+	0.642470i
$528$		0			0
$529$	10.9781	+	19.0146i	0.477309	+	0.826723i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	23.6966	+	13.6812i	1.02641	+	0.592600i
$534$		0			0
$535$			21.4949i			0.929307i
$536$		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	−0.997346	−	0.0728131i	$-0.976802\pi$
$547$	−36.4637	−	21.0523i	−1.55908	−	0.900133i	−0.561731	−	0.827320i	$-0.689864\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.82504			−0.248155
$552$		0			0
$553$	21.7336	+	20.1117i	0.924207	+	0.855237i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−3.87538	−	2.23745i	−0.164205	−	0.0948039i	0.415645	−	0.909527i	$-0.363556\pi$
$557$	−3.87538	−	2.23745i	−0.164205	−	0.0948039i	−0.579851	+	0.814723i	$0.696889\pi$
$558$		0			0
$559$			30.5738i			1.29313i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10.7503			0.453070			0.226535	−	0.974003i	$-0.427260\pi$
$563$	10.7503			0.453070			0.226535	+	0.974003i	$0.427260\pi$
$564$		0			0
$565$	34.1116			1.43509
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	22.9334i		−	0.961420i	−0.876880	−	0.480710i	$-0.840379\pi$
$569$		−	22.9334i		−	0.961420i	0.876880	−	0.480710i	$-0.159621\pi$
$570$		0			0
$571$			16.9289i			0.708451i	0.935160	+	0.354226i	$0.115256\pi$
$571$			16.9289i			0.708451i	−0.935160	+	0.354226i	$0.884744\pi$
$572$		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
$581$	−4.14102	−	13.3612i	−0.171798	−	0.554317i
$582$		0			0
$583$			49.2023i			2.03775i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−20.2944	+	35.1509i	−0.837638	+	1.45083i	0.0542266	+	0.998529i	$0.482731\pi$
$587$	−20.2944	+	35.1509i	−0.837638	+	1.45083i	−0.891864	+	0.452303i	$0.850603\pi$
$588$		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	−0.647218	−	0.762305i	$-0.724068\pi$
$593$	−7.56487	+	4.36758i	−0.310652	+	0.179355i	0.336566	+	0.941660i	$0.390734\pi$
$594$		0			0
$595$	−11.1779	−	2.53551i	−0.458247	−	0.103946i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.6289			−0.516002			−0.258001	−	0.966145i	$-0.583064\pi$
$599$	−12.6289			−0.516002			−0.258001	+	0.966145i	$0.583064\pi$
$600$		0			0
$601$	11.3142	−	19.5968i	0.461516	−	0.799369i	−0.537521	−	0.843250i	$-0.680639\pi$
$601$	11.3142	−	19.5968i	0.461516	−	0.799369i	0.999037	+	0.0438818i	$0.0139725\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−12.6199	+	7.28610i	−0.513071	+	0.296222i
$606$		0			0
$607$	−27.8354	−	16.0708i	−1.12980	−	0.652292i	−0.185918	−	0.982565i	$-0.559526\pi$
$607$	−27.8354	−	16.0708i	−1.12980	−	0.652292i	−0.943885	+	0.330273i	$0.892859\pi$
$608$		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	0.323575	−	0.946203i	$-0.395115\pi$
$617$	32.4105	−	18.7122i	1.30480	−	0.753325i	0.981223	+	0.192877i	$0.0617819\pi$
$618$		0			0
$619$	29.4038	−	16.9763i	1.18184	−	0.682335i	0.225400	−	0.974266i	$-0.427631\pi$
$619$	29.4038	−	16.9763i	1.18184	−	0.682335i	0.956439	+	0.291931i	$0.0942977\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.10058	+	4.85193i	−0.0440939	+	0.194389i
$624$		0			0
$625$	13.8430	−	23.9767i	0.553718	−	0.959068i
$626$		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
$635$	20.5049	−	35.5156i	0.813713	−	1.40939i
$636$		0			0
$637$	−16.0205	+	10.9856i	−0.634757	+	0.435267i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	32.0278	−	18.4912i	1.26502	−	0.730360i	0.290979	−	0.956729i	$-0.406019\pi$
$641$	32.0278	−	18.4912i	1.26502	−	0.730360i	0.974042	+	0.226369i	$0.0726857\pi$
$642$		0			0
$643$	−7.41539	+	4.28128i	−0.292435	+	0.168837i	−0.639039	−	0.769174i	$-0.720668\pi$
$643$	−7.41539	+	4.28128i	−0.292435	+	0.168837i	0.346605	+	0.938011i	$0.387335\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.8126	+	27.3882i	−0.621658	+	1.07674i	0.367519	+	0.930016i	$0.380207\pi$
$647$	−15.8126	+	27.3882i	−0.621658	+	1.07674i	−0.989177	+	0.146727i	$0.953126\pi$
$648$		0			0
$649$	6.72362	+	11.6456i	0.263925	+	0.457132i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−23.6987	−	13.6824i	−0.927400	−	0.535435i	−0.0414116	−	0.999142i	$-0.513185\pi$
$653$	−23.6987	−	13.6824i	−0.927400	−	0.535435i	−0.885988	+	0.463708i	$0.846519\pi$
$654$		0			0
$655$	29.8843	−	17.2537i	1.16767	−	0.674157i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−17.2635	+	29.9012i	−0.672489	+	1.16478i	0.304707	+	0.952446i	$0.401441\pi$
$659$	−17.2635	+	29.9012i	−0.672489	+	1.16478i	−0.977196	+	0.212339i	$0.931892\pi$
$660$		0			0
$661$	−10.8755			−0.423008			−0.211504	−	0.977377i	$-0.567836\pi$
$661$	−10.8755			−0.423008			−0.211504	+	0.977377i	$0.567836\pi$
$662$		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	−0.518332	−	0.855179i	$-0.673447\pi$
$673$	12.4897	−	21.6327i	0.481441	−	0.833880i	0.999773	+	0.0212993i	$0.00678029\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			31.9133i			1.22653i	0.789878	+	0.613263i	$0.210144\pi$
$677$			31.9133i			1.22653i	−0.789878	+	0.613263i	$0.789856\pi$
$678$		0			0
$679$	12.5892	+	40.6198i	0.483129	+	1.55885i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.154508	+	0.267616i	−0.00591210	+	0.0102401i	−0.868966	−	0.494871i	$-0.835215\pi$
$683$	−0.154508	+	0.267616i	−0.00591210	+	0.0102401i	0.863054	+	0.505111i	$0.168549\pi$
$684$		0			0
$685$	−20.0121			−0.764624
$686$		0			0
$687$		0			0
$688$		0			0
$689$			32.9691i			1.25602i
$690$		0			0
$691$		−	2.73646i		−	0.104100i	−0.998644	−	0.0520499i	$-0.983425\pi$
$691$		−	2.73646i		−	0.104100i	0.998644	−	0.0520499i	$-0.0165755\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.69633			0.254006
$696$		0			0
$697$	18.0313			0.682984
$698$		0			0
$699$		0			0
$700$		0			0
$701$			34.1114i			1.28837i	0.764869	+	0.644185i	$0.222803\pi$
$701$			34.1114i			1.28837i	−0.764869	+	0.644185i	$0.777197\pi$
$702$		0			0
$703$	17.2164	+	9.93987i	0.649327	+	0.374889i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.64884	−	24.9030i	0.212446	−	0.936573i
$708$		0			0
$709$	−5.73655			−0.215441			−0.107720	−	0.994181i	$-0.534355\pi$
$709$	−5.73655			−0.215441			−0.107720	+	0.994181i	$0.534355\pi$
$710$		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	$-0.984506\pi$
$719$	−14.5211	−	25.1513i	−0.541545	−	0.937983i	0.457271	−	0.889328i	$-0.348827\pi$
$720$		0			0
$721$	24.0391	−	7.45038i	0.895262	−	0.277467i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		−	1.13011i		−	0.0419712i
$726$		0			0
$727$	10.3221	+	5.95949i	0.382827	+	0.221025i	0.679048	−	0.734094i	$-0.262393\pi$
$727$	10.3221	+	5.95949i	0.382827	+	0.221025i	−0.296220	+	0.955120i	$0.595726\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	10.0737	+	17.4482i	0.372591	+	0.645347i
$732$		0			0
$733$	3.94962	−	6.84094i	0.145883	−	0.252676i	−0.783819	−	0.620989i	$-0.786731\pi$
$733$	3.94962	−	6.84094i	0.145883	−	0.252676i	0.929702	+	0.368313i	$0.120065\pi$
$734$		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	$-0.180296\pi$
$743$	−1.16678	−	2.02092i	−0.0428050	−	0.0741404i	−0.886634	+	0.462472i	$0.846963\pi$
$744$		0			0
$745$	22.5223	+	39.0098i	0.825154	+	1.42921i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	23.4114	+	5.31049i	0.855433	+	0.194041i
$750$		0			0
$751$	−28.5621	−	16.4903i	−1.04224	−	0.601740i	−0.121776	−	0.992558i	$-0.538859\pi$
$751$	−28.5621	−	16.4903i	−1.04224	−	0.601740i	−0.920468	+	0.390818i	$0.872192\pi$
$752$		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
$761$	42.6425	+	24.6197i	1.54579	+	0.892463i	0.998456	+	0.0555491i	$0.0176909\pi$
$761$	42.6425	+	24.6197i	1.54579	+	0.892463i	0.547335	+	0.836914i	$0.315642\pi$
$762$		0			0
$763$	10.9153	+	35.2189i	0.395161	+	1.27501i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.50531	+	7.80343i	0.162677	+	0.281765i
$768$		0			0
$769$	24.2219	+	41.9536i	0.873465	+	1.51289i	0.858389	+	0.512999i	$0.171466\pi$
$769$	24.2219	+	41.9536i	0.873465	+	1.51289i	0.0150758	+	0.999886i	$0.495201\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	10.8701	+	6.27584i	0.390970	+	0.225726i	0.682580	−	0.730811i	$-0.260858\pi$
$773$	10.8701	+	6.27584i	0.390970	+	0.225726i	−0.291611	+	0.956537i	$0.594191\pi$
$774$		0			0
$775$	4.93692	−	2.85033i	0.177339	−	0.102387i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−15.5551	+	26.9422i	−0.557320	+	0.965306i
$780$		0			0
$781$	−32.4421	−	56.1914i	−1.16087	−	2.01069i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.19647	+	3.00018i	0.185470	+	0.107081i
$786$		0			0
$787$		−	16.5084i		−	0.588461i	−0.955734	−	0.294231i	$-0.904937\pi$
$787$		−	16.5084i		−	0.588461i	0.955734	−	0.294231i	$-0.0950634\pi$
$788$		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	−0.536674	−	0.843789i	$-0.680320\pi$
$797$	−2.09669	+	1.21053i	−0.0742687	+	0.0428791i	0.462406	+	0.886668i	$0.346986\pi$
$798$		0			0
$799$	5.03644	+	2.90779i	0.178176	+	0.102870i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.47506			0.122632
$804$		0			0
$805$	−1.41655	+	6.24489i	−0.0499269	+	0.220104i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−27.8540	−	16.0815i	−0.979293	−	0.565395i	−0.0772364	−	0.997013i	$-0.524610\pi$
$809$	−27.8540	−	16.0815i	−0.979293	−	0.565395i	−0.902057	+	0.431618i	$0.857943\pi$
$810$		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
$815$	20.4595			0.716664
$816$		0			0
$817$	−34.7614			−1.21615
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	40.2084i		−	1.40328i	−0.712530	−	0.701642i	$-0.752451\pi$
$821$		−	40.2084i		−	1.40328i	0.712530	−	0.701642i	$-0.247549\pi$
$822$		0			0
$823$			23.3374i			0.813492i	0.913541	+	0.406746i	$0.133337\pi$
$823$			23.3374i			0.813492i	−0.913541	+	0.406746i	$0.866663\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−32.8733			−1.14312			−0.571558	−	0.820561i	$-0.693661\pi$
$827$	−32.8733			−1.14312			−0.571558	+	0.820561i	$0.693661\pi$
$828$		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
$833$	−5.52315	+	11.5480i	−0.191366	+	0.400115i
$834$		0			0
$835$			30.0999i			1.04165i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−9.16013	+	15.8658i	−0.316243	+	0.547748i	−0.979701	−	0.200465i	$-0.935755\pi$
$839$	−9.16013	+	15.8658i	−0.316243	+	0.547748i	0.663458	+	0.748213i	$0.269088\pi$
$840$		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
$851$	−6.43726			−0.220666
$852$		0			0
$853$	−22.1236	+	38.3192i	−0.757498	+	1.31203i	0.186625	+	0.982431i	$0.440245\pi$
$853$	−22.1236	+	38.3192i	−0.757498	+	1.31203i	−0.944123	+	0.329594i	$0.893088\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−43.9393	+	25.3683i	−1.50094	+	0.866566i	−0.500937	+	0.865484i	$0.667011\pi$
$857$	−43.9393	+	25.3683i	−1.50094	+	0.866566i	−0.999999	+	0.00108213i	$0.999656\pi$
$858$		0			0
$859$	−3.73030	−	2.15369i	−0.127276	−	0.0734829i	0.435010	−	0.900426i	$-0.356745\pi$
$859$	−3.73030	−	2.15369i	−0.127276	−	0.0734829i	−0.562286	+	0.826943i	$0.690078\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.42163	−	16.3187i	−0.320716	−	0.555496i	0.659920	−	0.751336i	$-0.270590\pi$
$863$	−9.42163	−	16.3187i	−0.320716	−	0.555496i	−0.980636	+	0.195840i	$0.937257\pi$
$864$		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
$871$	0.720611	−	0.416045i	0.0244170	−	0.0140971i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−20.1856	−	18.6792i	−0.682397	−	0.631472i
$876$		0			0
$877$	−14.5559	+	25.2116i	−0.491519	+	0.851335i	−0.999952	−	0.00976596i	$-0.996891\pi$
$877$	−14.5559	+	25.2116i	−0.491519	+	0.851335i	0.508434	+	0.861101i	$0.330225\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			21.7911i			0.734161i	0.930189	+	0.367081i	$0.119643\pi$
$881$			21.7911i			0.734161i	−0.930189	+	0.367081i	$0.880357\pi$
$882$		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
$887$	−1.80661	+	3.12914i	−0.0606600	+	0.105066i	−0.894761	−	0.446546i	$-0.852654\pi$
$887$	−1.80661	+	3.12914i	−0.0606600	+	0.105066i	0.834101	+	0.551612i	$0.185987\pi$
$888$		0			0
$889$	−33.6161	−	31.1075i	−1.12745	−	1.04331i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.68960	+	5.01694i	−0.290786	+	0.167886i
$894$		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
$905$	−19.4856	−	11.2500i	−0.647725	−	0.373964i
$906$		0			0
$907$	44.0624	−	25.4394i	1.46307	−	0.844702i	0.463915	−	0.885880i	$-0.346444\pi$
$907$	44.0624	−	25.4394i	1.46307	−	0.844702i	0.999152	+	0.0411775i	$0.0131109\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	29.4958	−	51.0882i	0.977238	−	1.69263i	0.304896	−	0.952386i	$-0.401378\pi$
$911$	29.4958	−	51.0882i	0.977238	−	1.69263i	0.672342	−	0.740240i	$-0.265288\pi$
$912$		0			0
$913$	−21.8958			−0.724646
$914$		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
$929$			5.93330i			0.194665i	0.995252	+	0.0973327i	$0.0310311\pi$
$929$			5.93330i			0.194665i	−0.995252	+	0.0973327i	$0.968969\pi$
$930$		0			0
$931$	−12.4903	−	18.2148i	−0.409353	−	0.596966i
$932$		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
$941$			46.0549i			1.50135i	0.660673	+	0.750674i	$0.270271\pi$
$941$			46.0549i			1.50135i	−0.660673	+	0.750674i	$0.729729\pi$
$942$		0			0
$943$		−	10.0738i		−	0.328048i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.5582			−0.473077			−0.236538	−	0.971622i	$-0.576013\pi$
$947$	−14.5582			−0.473077			−0.236538	+	0.971622i	$0.576013\pi$
$948$		0			0
$949$	2.32854			0.0755878
$950$		0			0
$951$		0			0
$952$		0			0
$953$			29.0894i			0.942297i	0.882054	+	0.471149i	$0.156160\pi$
$953$			29.0894i			0.942297i	−0.882054	+	0.471149i	$0.843840\pi$
$954$		0			0
$955$	20.3737	+	11.7628i	0.659277	+	0.380634i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.94415	+	21.7963i	−0.159655	+	0.703841i
$960$		0			0
$961$	−55.7309			−1.79777
$962$		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	$-0.697788\pi$
$967$	−5.25768	+	3.03552i	−0.169075	+	0.0976158i	0.413074	+	0.910697i	$0.364455\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	28.5315	+	49.4180i	0.915619	+	1.58590i	0.805992	+	0.591927i	$0.201632\pi$
$971$	28.5315	+	49.4180i	0.915619	+	1.58590i	0.109627	+	0.993973i	$0.465034\pi$
$972$		0			0
$973$	1.65438	−	7.29335i	0.0530369	−	0.233814i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	19.2336i		−	0.615339i	−0.951493	−	0.307669i	$-0.900451\pi$
$977$		−	19.2336i		−	0.615339i	0.951493	−	0.307669i	$-0.0995491\pi$
$978$		0			0
$979$	6.74433	+	3.89384i	0.215550	+	0.124448i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−13.5896	−	23.5379i	−0.433441	−	0.750742i	0.563726	−	0.825962i	$-0.309368\pi$
$983$	−13.5896	−	23.5379i	−0.433441	−	0.750742i	−0.997167	+	0.0752197i	$0.976034\pi$
$984$		0			0
$985$	14.3666	−	24.8837i	0.457759	−	0.792861i
$986$		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
$997$	1.42567	+	2.46933i	0.0451514	+	0.0782045i	0.887718	−	0.460388i	$-0.152290\pi$
$997$	1.42567	+	2.46933i	0.0451514	+	0.0782045i	−0.842567	+	0.538592i	$0.818956\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cj.c.1439.12		30
3.2	odd	2		1008.2.cj.c.767.14	yes	30
4.3	odd	2		3024.2.cj.d.1439.12		30
7.2	even	3		3024.2.bh.c.1871.4		30
9.4	even	3		1008.2.bh.d.95.12	yes	30
9.5	odd	6		3024.2.bh.d.2447.12		30
12.11	even	2		1008.2.cj.d.767.2	yes	30
21.2	odd	6		1008.2.bh.c.191.4	yes	30
28.23	odd	6		3024.2.bh.d.1871.4		30
36.23	even	6		3024.2.bh.c.2447.12		30
36.31	odd	6		1008.2.bh.c.95.4	✓	30
63.23	odd	6		3024.2.cj.d.2879.12		30
63.58	even	3		1008.2.cj.d.527.2	yes	30
84.23	even	6		1008.2.bh.d.191.12	yes	30
252.23	even	6	inner	3024.2.cj.c.2879.12		30
252.247	odd	6		1008.2.cj.c.527.14	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bh.c.95.4	✓	30	36.31	odd	6
1008.2.bh.c.191.4	yes	30	21.2	odd	6
1008.2.bh.d.95.12	yes	30	9.4	even	3
1008.2.bh.d.191.12	yes	30	84.23	even	6
1008.2.cj.c.527.14	yes	30	252.247	odd	6
1008.2.cj.c.767.14	yes	30	3.2	odd	2
1008.2.cj.d.527.2	yes	30	63.58	even	3
1008.2.cj.d.767.2	yes	30	12.11	even	2
3024.2.bh.c.1871.4		30	7.2	even	3
3024.2.bh.c.2447.12		30	36.23	even	6
3024.2.bh.d.1871.4		30	28.23	odd	6
3024.2.bh.d.2447.12		30	9.5	odd	6
3024.2.cj.c.1439.12		30	1.1	even	1	trivial
3024.2.cj.c.2879.12		30	252.23	even	6	inner
3024.2.cj.d.1439.12		30	4.3	odd	2
3024.2.cj.d.2879.12		30	63.23	odd	6

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.cj (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.05161 + 1.18450i) q^{5} +(1.79697 - 1.94188i) q^{7} +O(q^{10})\)	\(q+(2.05161 + 1.18450i) q^{5} +(1.79697 - 1.94188i) q^{7} +(-2.07070 - 3.58656i) q^{11} +(-1.38752 - 2.40326i) q^{13} +(-1.58369 - 0.914347i) q^{17} +(2.73242 - 1.57756i) q^{19} +(-0.510831 + 0.884786i) q^{23} +(0.306061 + 0.530114i) q^{25} +(-1.59887 - 0.923106i) q^{29} -9.31294i q^{31} +(5.98682 - 1.85548i) q^{35} +(3.15039 + 5.45663i) q^{37} +(-8.53919 + 4.93010i) q^{41} +(-9.54137 - 5.50871i) q^{43} -3.18018 q^{47} +(-0.541821 - 6.97900i) q^{49} +(-10.2889 - 5.94029i) q^{53} -9.81095i q^{55} -3.24702 q^{59} +0.853446 q^{61} -6.57405i q^{65} +0.299848i q^{67} +15.6672 q^{71} +(-0.419551 + 0.726684i) q^{73} +(-10.6857 - 2.42387i) q^{77} +11.1920i q^{79} +(2.64353 - 4.57872i) q^{83} +(-2.16608 - 3.75176i) q^{85} +(-1.62851 + 0.940223i) q^{89} +(-7.16017 - 1.62417i) q^{91} +7.47447 q^{95} +(-8.03665 + 13.9199i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} - 7 q^{7}+O(q^{10}) \) 30 * q - 3 * q^5 - 7 * q^7	\( 30 q - 3 q^{5} - 7 q^{7} + 3 q^{11} + 12 q^{17} - 9 q^{19} - 12 q^{23} + 18 q^{25} - 27 q^{29} + 6 q^{35} + 6 q^{37} - 9 q^{41} - 21 q^{43} - 3 q^{49} - 3 q^{53} + 6 q^{59} + 6 q^{61} - 18 q^{71} + 21 q^{73} - 72 q^{77} + 15 q^{83} - 3 q^{85} + 6 q^{89} + 26 q^{91} - 54 q^{95} - 6 q^{97}+O(q^{100}) \) 30 * q - 3 * q^5 - 7 * q^7 + 3 * q^11 + 12 * q^17 - 9 * q^19 - 12 * q^23 + 18 * q^25 - 27 * q^29 + 6 * q^35 + 6 * q^37 - 9 * q^41 - 21 * q^43 - 3 * q^49 - 3 * q^53 + 6 * q^59 + 6 * q^61 - 18 * q^71 + 21 * q^73 - 72 * q^77 + 15 * q^83 - 3 * q^85 + 6 * q^89 + 26 * q^91 - 54 * q^95 - 6 * q^97

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