LMFDB - Embedded newform 3024.2.cc.d.881.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(881,3024)]

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([0, 0, 5, 3]))

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

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

chi := DirichletCharacter("3024.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cc (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.19
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.d.2897.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16173 - 2.01217i) q^{5} +(1.25073 + 2.33145i) q^{7} +O(q^{10})$	$q+(1.16173 - 2.01217i) q^{5} +(1.25073 + 2.33145i) q^{7} +(-2.17784 + 1.25738i) q^{11} +(0.244656 + 0.141252i) q^{13} +2.01033 q^{17} +2.93904i q^{19} +(-4.32546 - 2.49731i) q^{23} +(-0.199225 - 0.345068i) q^{25} +(-4.02448 + 2.32353i) q^{29} +(8.91154 + 5.14508i) q^{31} +(6.14429 + 0.191820i) q^{35} +3.93132 q^{37} +(3.44915 - 5.97410i) q^{41} +(5.66183 + 9.80657i) q^{43} +(1.84396 + 3.19383i) q^{47} +(-3.87133 + 5.83205i) q^{49} +0.845432i q^{53} +5.84293i q^{55} +(-7.27908 + 12.6077i) q^{59} +(-9.59760 + 5.54118i) q^{61} +(0.568447 - 0.328193i) q^{65} +(5.59936 - 9.69838i) q^{67} -7.67879i q^{71} -6.37515i q^{73} +(-5.65542 - 3.50489i) q^{77} +(-3.71484 - 6.43430i) q^{79} +(4.73177 + 8.19566i) q^{83} +(2.33546 - 4.04513i) q^{85} +5.12467 q^{89} +(-0.0233229 + 0.747071i) q^{91} +(5.91385 + 3.41436i) q^{95} +(4.49852 - 2.59722i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) $ 48 * q + 12 * q^23 - 24 * q^25 + 36 * q^29 - 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 + 12 * q^79 + 12 * q^91 - 108 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.16173	−	2.01217i	0.519541	−	0.899871i	−0.480201	−	0.877158i	$-0.659436\pi$
$5$	1.16173	−	2.01217i	0.519541	−	0.899871i	0.999742	−	0.0227126i	$-0.00723025\pi$
$6$		0			0
$7$	1.25073	+	2.33145i	0.472733	+	0.881206i
$7$	1.25073	+	2.33145i	0.472733	+	0.881206i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.17784	+	1.25738i	−0.656645	+	0.379114i	−0.790997	−	0.611820i	$-0.790438\pi$
$11$	−2.17784	+	1.25738i	−0.656645	+	0.379114i	0.134353	+	0.990934i	$0.457105\pi$
$12$		0			0
$13$	0.244656	+	0.141252i	0.0678552	+	0.0391762i	0.533544	−	0.845772i	$-0.320860\pi$
$13$	0.244656	+	0.141252i	0.0678552	+	0.0391762i	−0.465689	+	0.884949i	$0.654193\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.01033			0.487577			0.243788	−	0.969828i	$-0.421610\pi$
$17$	2.01033			0.487577			0.243788	+	0.969828i	$0.421610\pi$
$18$		0			0
$19$			2.93904i			0.674261i	0.941458	+	0.337130i	$0.109456\pi$
$19$			2.93904i			0.674261i	−0.941458	+	0.337130i	$0.890544\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.32546	−	2.49731i	−0.901921	−	0.520724i	−0.0240979	−	0.999710i	$-0.507671\pi$
$23$	−4.32546	−	2.49731i	−0.901921	−	0.520724i	−0.877823	+	0.478985i	$0.841005\pi$
$24$		0			0
$25$	−0.199225	−	0.345068i	−0.0398450	−	0.0690136i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.02448	+	2.32353i	−0.747326	+	0.431469i	−0.824727	−	0.565531i	$-0.808671\pi$
$29$	−4.02448	+	2.32353i	−0.747326	+	0.431469i	0.0774007	+	0.997000i	$0.475338\pi$
$30$		0			0
$31$	8.91154	+	5.14508i	1.60056	+	0.924083i	0.991375	+	0.131054i	$0.0418362\pi$
$31$	8.91154	+	5.14508i	1.60056	+	0.924083i	0.609184	+	0.793029i	$0.291497\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.14429	+	0.191820i	1.03858	+	0.0324234i
$36$		0			0
$37$	3.93132			0.646305			0.323153	−	0.946347i	$-0.395257\pi$
$37$	3.93132			0.646305			0.323153	+	0.946347i	$0.395257\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.44915	−	5.97410i	0.538666	−	0.932997i	−0.460310	−	0.887758i	$-0.652262\pi$
$41$	3.44915	−	5.97410i	0.538666	−	0.932997i	0.998976	−	0.0452389i	$-0.0144049\pi$
$42$		0			0
$43$	5.66183	+	9.80657i	0.863421	+	1.49549i	0.868607	+	0.495502i	$0.165016\pi$
$43$	5.66183	+	9.80657i	0.863421	+	1.49549i	−0.00518640	+	0.999987i	$0.501651\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.84396	+	3.19383i	0.268969	+	0.465869i	0.968596	−	0.248640i	$-0.0799836\pi$
$47$	1.84396	+	3.19383i	0.268969	+	0.465869i	−0.699627	+	0.714509i	$0.746650\pi$
$48$		0			0
$49$	−3.87133	+	5.83205i	−0.553047	+	0.833150i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			0.845432i			0.116129i	0.998313	+	0.0580645i	$0.0184929\pi$
$53$			0.845432i			0.116129i	−0.998313	+	0.0580645i	$0.981507\pi$
$54$		0			0
$55$			5.84293i			0.787860i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.27908	+	12.6077i	−0.947656	+	1.64139i	−0.197312	+	0.980341i	$0.563221\pi$
$59$	−7.27908	+	12.6077i	−0.947656	+	1.64139i	−0.750344	+	0.661048i	$0.770112\pi$
$60$		0			0
$61$	−9.59760	+	5.54118i	−1.22885	+	0.709475i	−0.966789	−	0.255577i	$-0.917735\pi$
$61$	−9.59760	+	5.54118i	−1.22885	+	0.709475i	−0.262058	+	0.965052i	$0.584401\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.568447	−	0.328193i	0.0705071	−	0.0407073i
$66$		0			0
$67$	5.59936	−	9.69838i	0.684071	−	1.18485i	−0.289657	−	0.957130i	$-0.593541\pi$
$67$	5.59936	−	9.69838i	0.684071	−	1.18485i	0.973728	−	0.227715i	$-0.0731253\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.67879i		−	0.911304i	−0.890158	−	0.455652i	$-0.849406\pi$
$71$		−	7.67879i		−	0.911304i	0.890158	−	0.455652i	$-0.150594\pi$
$72$		0			0
$73$		−	6.37515i		−	0.746155i	−0.927800	−	0.373077i	$-0.878303\pi$
$73$		−	6.37515i		−	0.746155i	0.927800	−	0.373077i	$-0.121697\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.65542	−	3.50489i	−0.644495	−	0.399419i
$78$		0			0
$79$	−3.71484	−	6.43430i	−0.417953	−	0.723915i	0.577781	−	0.816192i	$-0.303919\pi$
$79$	−3.71484	−	6.43430i	−0.417953	−	0.723915i	−0.995733	+	0.0922769i	$0.970585\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.73177	+	8.19566i	0.519379	+	0.899591i	0.999746	+	0.0225236i	$0.00717008\pi$
$83$	4.73177	+	8.19566i	0.519379	+	0.899591i	−0.480367	+	0.877067i	$0.659497\pi$
$84$		0			0
$85$	2.33546	−	4.04513i	0.253316	−	0.438756i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.12467			0.543214			0.271607	−	0.962408i	$-0.412445\pi$
$89$	5.12467			0.543214			0.271607	+	0.962408i	$0.412445\pi$
$90$		0			0
$91$	−0.0233229	+	0.747071i	−0.00244491	+	0.0783143i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.91385	+	3.41436i	0.606748	+	0.350306i
$96$		0			0
$97$	4.49852	−	2.59722i	0.456755	−	0.263708i	−0.253924	−	0.967224i	$-0.581721\pi$
$97$	4.49852	−	2.59722i	0.456755	−	0.263708i	0.710679	+	0.703517i	$0.248388\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.08122	+	7.06888i	0.406096	+	0.703379i	0.994448	−	0.105225i	$-0.0335564\pi$
$101$	4.08122	+	7.06888i	0.406096	+	0.703379i	−0.588352	+	0.808605i	$0.700223\pi$
$102$		0			0
$103$	7.91895	+	4.57201i	0.780278	+	0.450493i	0.836529	−	0.547923i	$-0.184581\pi$
$103$	7.91895	+	4.57201i	0.780278	+	0.450493i	−0.0562511	+	0.998417i	$0.517915\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			9.91633i			0.958648i	0.877638	+	0.479324i	$0.159118\pi$
$107$			9.91633i			0.958648i	−0.877638	+	0.479324i	$0.840882\pi$
$108$		0			0
$109$	7.55063			0.723220			0.361610	−	0.932330i	$-0.382227\pi$
$109$	7.55063			0.723220			0.361610	+	0.932330i	$0.382227\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.89485	−	2.82604i	−0.460469	−	0.265852i	0.251773	−	0.967786i	$-0.418987\pi$
$113$	−4.89485	−	2.82604i	−0.460469	−	0.265852i	−0.712241	+	0.701935i	$0.752320\pi$
$114$		0			0
$115$	−10.0500	+	5.80238i	−0.937169	+	0.541075i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.51439	+	4.68698i	0.230494	+	0.429655i
$120$		0			0
$121$	−2.33800	+	4.04953i	−0.212545	+	0.368139i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.6915			0.956277
$126$		0			0
$127$	−10.6289			−0.943160			−0.471580	−	0.881823i	$-0.656316\pi$
$127$	−10.6289			−0.943160			−0.471580	+	0.881823i	$0.656316\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.74685	−	4.75768i	0.239993	−	0.415681i	−0.720719	−	0.693228i	$-0.756188\pi$
$131$	2.74685	−	4.75768i	0.239993	−	0.415681i	0.960712	+	0.277547i	$0.0895214\pi$
$132$		0			0
$133$	−6.85222	+	3.67595i	−0.594163	+	0.318745i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	17.8601	−	10.3115i	1.52589	−	0.880973i	0.526361	−	0.850261i	$-0.323556\pi$
$137$	17.8601	−	10.3115i	1.52589	−	0.880973i	0.999528	−	0.0307114i	$-0.00977729\pi$
$138$		0			0
$139$	4.80013	+	2.77136i	0.407142	+	0.235064i	0.689561	−	0.724228i	$-0.257804\pi$
$139$	4.80013	+	2.77136i	0.407142	+	0.235064i	−0.282419	+	0.959291i	$0.591137\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.710429			−0.0594090
$144$		0			0
$145$			10.7973i			0.896663i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.99945	+	2.30908i	0.327648	+	0.189167i	0.654796	−	0.755805i	$-0.272754\pi$
$149$	3.99945	+	2.30908i	0.327648	+	0.189167i	−0.327149	+	0.944973i	$0.606088\pi$
$150$		0			0
$151$	−3.38911	−	5.87011i	−0.275802	−	0.477703i	0.694535	−	0.719459i	$-0.255610\pi$
$151$	−3.38911	−	5.87011i	−0.275802	−	0.477703i	−0.970337	+	0.241756i	$0.922277\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	20.7056	−	11.9544i	1.66311	−	0.960198i
$156$		0			0
$157$	6.42189	+	3.70768i	0.512522	+	0.295905i	0.733870	−	0.679290i	$-0.237712\pi$
$157$	6.42189	+	3.70768i	0.512522	+	0.295905i	−0.221347	+	0.975195i	$0.571045\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.412344	−	13.2081i	0.0324973	−	1.04094i
$162$		0			0
$163$	−12.0227			−0.941689			−0.470844	−	0.882216i	$-0.656051\pi$
$163$	−12.0227			−0.941689			−0.470844	+	0.882216i	$0.656051\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.4096	−	18.0300i	0.805521	−	1.39520i	−0.110419	−	0.993885i	$-0.535219\pi$
$167$	10.4096	−	18.0300i	0.805521	−	1.39520i	0.915939	−	0.401317i	$-0.131448\pi$
$168$		0			0
$169$	−6.46010	−	11.1892i	−0.496930	−	0.860709i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.68149	−	6.37652i	−0.279898	−	0.484798i	0.691461	−	0.722414i	$-0.256967\pi$
$173$	−3.68149	−	6.37652i	−0.279898	−	0.484798i	−0.971359	+	0.237616i	$0.923634\pi$
$174$		0			0
$175$	0.555331	−	0.896072i	0.0419791	−	0.0677367i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			16.8136i			1.25670i	0.777929	+	0.628352i	$0.216270\pi$
$179$			16.8136i			1.25670i	−0.777929	+	0.628352i	$0.783730\pi$
$180$		0			0
$181$		−	4.02239i		−	0.298982i	−0.988763	−	0.149491i	$-0.952236\pi$
$181$		−	4.02239i		−	0.298982i	0.988763	−	0.149491i	$-0.0477635\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.56713	−	7.91050i	0.335782	−	0.581591i
$186$		0			0
$187$	−4.37818	+	2.52775i	−0.320165	+	0.184847i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.42466	+	2.55458i	−0.320157	+	0.184843i	−0.651463	−	0.758681i	$-0.725844\pi$
$191$	−4.42466	+	2.55458i	−0.320157	+	0.184843i	0.331306	+	0.943524i	$0.392511\pi$
$192$		0			0
$193$	−3.54994	+	6.14868i	−0.255531	+	0.442592i	−0.965039	−	0.262105i	$-0.915583\pi$
$193$	−3.54994	+	6.14868i	−0.255531	+	0.442592i	0.709509	+	0.704696i	$0.248917\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			15.6086i			1.11206i	0.831161	+	0.556032i	$0.187677\pi$
$197$			15.6086i			1.11206i	−0.831161	+	0.556032i	$0.812323\pi$
$198$		0			0
$199$			26.8155i			1.90090i	0.310875	+	0.950451i	$0.399378\pi$
$199$			26.8155i			1.90090i	−0.310875	+	0.950451i	$0.600622\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−10.4508	−	6.47675i	−0.733499	−	0.454578i
$204$		0			0
$205$	−8.01394	−	13.8806i	−0.559718	−	0.969460i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.69548	−	6.40076i	−0.255622	−	0.442750i
$210$		0			0
$211$	1.15444	−	1.99955i	0.0794748	−	0.137654i	−0.823549	−	0.567246i	$-0.808009\pi$
$211$	1.15444	−	1.99955i	0.0794748	−	0.137654i	0.903023	+	0.429591i	$0.141342\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	26.3100			1.79433
$216$		0			0
$217$	−0.849533	+	27.2119i	−0.0576701	+	1.84727i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.491838	+	0.283963i	0.0330846	+	0.0191014i
$222$		0			0
$223$	16.6900	−	9.63599i	1.11765	−	0.645274i	0.176847	−	0.984238i	$-0.443410\pi$
$223$	16.6900	−	9.63599i	1.11765	−	0.645274i	0.940799	+	0.338965i	$0.110077\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.124385	+	0.215441i	0.00825572	+	0.0142993i	0.870124	−	0.492833i	$-0.164039\pi$
$227$	0.124385	+	0.215441i	0.00825572	+	0.0142993i	−0.861868	+	0.507133i	$0.830705\pi$
$228$		0			0
$229$	18.2102	+	10.5137i	1.20336	+	0.694762i	0.961302	−	0.275498i	$-0.0888429\pi$
$229$	18.2102	+	10.5137i	1.20336	+	0.694762i	0.242062	+	0.970261i	$0.422176\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			23.5168i			1.54064i	0.637659	+	0.770318i	$0.279903\pi$
$233$			23.5168i			1.54064i	−0.637659	+	0.770318i	$0.720097\pi$
$234$		0			0
$235$	8.56873			0.558962
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.6889	−	6.17125i	−0.691409	−	0.399185i	0.112731	−	0.993626i	$-0.464040\pi$
$239$	−10.6889	−	6.17125i	−0.691409	−	0.399185i	−0.804140	+	0.594441i	$0.797374\pi$
$240$		0			0
$241$	4.62278	−	2.66896i	0.297780	−	0.171923i	−0.343665	−	0.939092i	$-0.611669\pi$
$241$	4.62278	−	2.66896i	0.297780	−	0.171923i	0.641445	+	0.767169i	$0.278335\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7.23766	+	14.5650i	0.462397	+	0.930526i
$246$		0			0
$247$	−0.415144	+	0.719051i	−0.0264150	+	0.0457521i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−21.7872			−1.37520			−0.687599	−	0.726091i	$-0.741335\pi$
$251$	−21.7872			−1.37520			−0.687599	+	0.726091i	$0.741335\pi$
$252$		0			0
$253$	12.5602			0.789655
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.0603	+	22.6211i	−0.814679	+	1.41106i	0.0948796	+	0.995489i	$0.469753\pi$
$257$	−13.0603	+	22.6211i	−0.814679	+	1.41106i	−0.909558	+	0.415576i	$0.863580\pi$
$258$		0			0
$259$	4.91704	+	9.16568i	0.305530	+	0.569528i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	17.1035	−	9.87469i	1.05464	−	0.608899i	0.130699	−	0.991422i	$-0.458278\pi$
$263$	17.1035	−	9.87469i	1.05464	−	0.608899i	0.923946	+	0.382523i	$0.124945\pi$
$264$		0			0
$265$	1.70115	+	0.982162i	0.104501	+	0.0603337i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	26.7501			1.63098			0.815492	−	0.578769i	$-0.196467\pi$
$269$	26.7501			1.63098			0.815492	+	0.578769i	$0.196467\pi$
$270$		0			0
$271$		−	27.3379i		−	1.66066i	−0.557274	−	0.830329i	$-0.688153\pi$
$271$		−	27.3379i		−	1.66066i	0.557274	−	0.830329i	$-0.311847\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.867762	+	0.501003i	0.0523280	+	0.0302116i
$276$		0			0
$277$	−7.06241	−	12.2325i	−0.424339	−	0.734977i	0.572019	−	0.820240i	$-0.306160\pi$
$277$	−7.06241	−	12.2325i	−0.424339	−	0.734977i	−0.996358	+	0.0852630i	$0.972827\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	22.0291	−	12.7185i	1.31415	−	0.758723i	0.331366	−	0.943502i	$-0.392490\pi$
$281$	22.0291	−	12.7185i	1.31415	−	0.758723i	0.982780	+	0.184780i	$0.0591571\pi$
$282$		0			0
$283$	−18.2802	−	10.5541i	−1.08664	−	0.627374i	−0.153963	−	0.988077i	$-0.549204\pi$
$283$	−18.2802	−	10.5541i	−1.08664	−	0.627374i	−0.932681	+	0.360703i	$0.882537\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	18.2423	+	0.569508i	1.07681	+	0.0336170i
$288$		0			0
$289$	−12.9586			−0.762269
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.36260	+	11.0204i	−0.371707	+	0.643816i	−0.989828	−	0.142267i	$-0.954561\pi$
$293$	−6.36260	+	11.0204i	−0.371707	+	0.643816i	0.618121	+	0.786083i	$0.287894\pi$
$294$		0			0
$295$	16.9126	+	29.2935i	0.984692	+	1.70554i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.705499	−	1.22196i	−0.0408000	−	0.0706677i
$300$		0			0
$301$	−15.7821	+	25.4657i	−0.909665	+	1.46782i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			25.7494i			1.47440i
$306$		0			0
$307$		−	7.12625i		−	0.406717i	−0.979104	−	0.203358i	$-0.934814\pi$
$307$		−	7.12625i		−	0.406717i	0.979104	−	0.203358i	$-0.0651856\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.67348	+	2.89855i	−0.0948944	+	0.164362i	−0.909565	−	0.415563i	$-0.863585\pi$
$311$	−1.67348	+	2.89855i	−0.0948944	+	0.164362i	0.814670	+	0.579925i	$0.196918\pi$
$312$		0			0
$313$	3.49029	−	2.01512i	0.197283	−	0.113901i	−0.398105	−	0.917340i	$-0.630332\pi$
$313$	3.49029	−	2.01512i	0.197283	−	0.113901i	0.595388	+	0.803439i	$0.296999\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.9601	+	6.90518i	−0.671748	+	0.387834i	−0.796739	−	0.604324i	$-0.793443\pi$
$317$	−11.9601	+	6.90518i	−0.671748	+	0.387834i	0.124991	+	0.992158i	$0.460110\pi$
$318$		0			0
$319$	5.84312	−	10.1206i	0.327152	−	0.566644i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			5.90843i			0.328754i
$324$		0			0
$325$		−	0.112564i		−	0.00624391i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.13996	+	8.29374i	−0.283375	+	0.457249i
$330$		0			0
$331$	−2.71627	−	4.70472i	−0.149300	−	0.258595i	0.781669	−	0.623693i	$-0.214369\pi$
$331$	−2.71627	−	4.70472i	−0.149300	−	0.258595i	−0.930969	+	0.365099i	$0.881035\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.0099	−	22.5338i	−0.710805	−	1.23115i
$336$		0			0
$337$	−8.45417	+	14.6431i	−0.460528	+	0.797658i	−0.998987	−	0.0449936i	$-0.985673\pi$
$337$	−8.45417	+	14.6431i	−0.460528	+	0.797658i	0.538459	+	0.842652i	$0.319007\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−25.8772			−1.40133
$342$		0			0
$343$	−18.4391	−	1.73146i	−0.995620	−	0.0934903i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.1375	−	8.73962i	−0.812622	−	0.469168i	0.0352435	−	0.999379i	$-0.488779\pi$
$347$	−15.1375	−	8.73962i	−0.812622	−	0.469168i	−0.847866	+	0.530211i	$0.822113\pi$
$348$		0			0
$349$	27.5413	−	15.9010i	1.47425	−	0.851159i	0.474672	−	0.880163i	$-0.342567\pi$
$349$	27.5413	−	15.9010i	1.47425	−	0.851159i	0.999579	+	0.0290038i	$0.00923350\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	16.0034	+	27.7187i	0.851775	+	1.47532i	0.879605	+	0.475705i	$0.157807\pi$
$353$	16.0034	+	27.7187i	0.851775	+	1.47532i	−0.0278304	+	0.999613i	$0.508860\pi$
$354$		0			0
$355$	−15.4510	−	8.92066i	−0.820056	−	0.473460i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			5.86805i			0.309704i	0.987938	+	0.154852i	$0.0494901\pi$
$359$			5.86805i			0.309704i	−0.987938	+	0.154852i	$0.950510\pi$
$360$		0			0
$361$	10.3621			0.545372
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−12.8279	−	7.40619i	−0.671443	−	0.387658i
$366$		0			0
$367$	−20.8681	+	12.0482i	−1.08931	+	0.628912i	−0.933392	−	0.358858i	$-0.883166\pi$
$367$	−20.8681	+	12.0482i	−1.08931	+	0.628912i	−0.155916	+	0.987770i	$0.549833\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.97108	+	1.05741i	−0.102334	+	0.0548980i
$372$		0			0
$373$	15.1182	−	26.1855i	0.782790	−	1.35583i	−0.147521	−	0.989059i	$-0.547129\pi$
$373$	15.1182	−	26.1855i	0.782790	−	1.35583i	0.930311	−	0.366773i	$-0.119537\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.31281			−0.0676133
$378$		0			0
$379$	−24.6188			−1.26458			−0.632292	−	0.774730i	$-0.717886\pi$
$379$	−24.6188			−1.26458			−0.632292	+	0.774730i	$0.717886\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	14.7429	−	25.5354i	0.753326	−	1.30480i	−0.192876	−	0.981223i	$-0.561782\pi$
$383$	14.7429	−	25.5354i	0.753326	−	1.30480i	0.946202	−	0.323576i	$-0.104885\pi$
$384$		0			0
$385$	−13.6225	+	7.30795i	−0.694267	+	0.372448i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.19930	−	4.73387i	0.415721	−	0.240017i	−0.277524	−	0.960719i	$-0.589514\pi$
$389$	8.19930	−	4.73387i	0.415721	−	0.240017i	0.693245	+	0.720702i	$0.256180\pi$
$390$		0			0
$391$	−8.69560	−	5.02041i	−0.439755	−	0.253893i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−17.2626			−0.868573
$396$		0			0
$397$		−	0.430822i		−	0.0216223i	−0.999942	−	0.0108112i	$-0.996559\pi$
$397$		−	0.430822i		−	0.0216223i	0.999942	−	0.0108112i	$-0.00344137\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−19.1407	−	11.0509i	−0.955842	−	0.551856i	−0.0609515	−	0.998141i	$-0.519413\pi$
$401$	−19.1407	−	11.0509i	−0.955842	−	0.551856i	−0.894891	+	0.446285i	$0.852747\pi$
$402$		0			0
$403$	1.45350	+	2.51754i	0.0724042	+	0.125408i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.56181	+	4.94316i	−0.424393	+	0.245023i
$408$		0			0
$409$	−19.6278	−	11.3321i	−0.970535	−	0.560338i	−0.0711355	−	0.997467i	$-0.522662\pi$
$409$	−19.6278	−	11.3321i	−0.970535	−	0.560338i	−0.899399	+	0.437128i	$0.855996\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−38.4985	−	1.20189i	−1.89439	−	0.0591412i
$414$		0			0
$415$	21.9881			1.07935
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.69489	+	11.5959i	−0.327067	+	0.566496i	−0.981928	−	0.189252i	$-0.939394\pi$
$419$	−6.69489	+	11.5959i	−0.327067	+	0.566496i	0.654862	+	0.755749i	$0.272727\pi$
$420$		0			0
$421$	13.6383	+	23.6223i	0.664691	+	1.15128i	0.979369	+	0.202080i	$0.0647702\pi$
$421$	13.6383	+	23.6223i	0.664691	+	1.15128i	−0.314678	+	0.949199i	$0.601896\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.400508	−	0.693700i	−0.0194275	−	0.0336494i
$426$		0			0
$427$	−24.9230	−	15.4458i	−1.20611	−	0.747475i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			30.2430i			1.45675i	0.685177	+	0.728377i	$0.259725\pi$
$431$			30.2430i			1.45675i	−0.685177	+	0.728377i	$0.740275\pi$
$432$		0			0
$433$			8.03211i			0.385999i	0.981199	+	0.192999i	$0.0618215\pi$
$433$			8.03211i			0.385999i	−0.981199	+	0.192999i	$0.938178\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.33967	−	12.7127i	0.351104	−	0.608130i
$438$		0			0
$439$	25.7082	−	14.8426i	1.22699	−	0.708401i	0.260588	−	0.965450i	$-0.416084\pi$
$439$	25.7082	−	14.8426i	1.22699	−	0.708401i	0.966398	+	0.257050i	$0.0827504\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.67730	−	2.12309i	0.174714	−	0.100871i	−0.410093	−	0.912044i	$-0.634504\pi$
$443$	3.67730	−	2.12309i	0.174714	−	0.100871i	0.584807	+	0.811173i	$0.301170\pi$
$444$		0			0
$445$	5.95347	−	10.3117i	0.282222	−	0.488822i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	11.2597i		−	0.531376i	−0.964059	−	0.265688i	$-0.914401\pi$
$449$		−	11.2597i		−	0.531376i	0.964059	−	0.265688i	$-0.0855991\pi$
$450$		0			0
$451$			17.3475i			0.816863i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.47614	+	0.914823i	0.0692025	+	0.0428876i
$456$		0			0
$457$	8.81254	+	15.2638i	0.412233	+	0.714009i	0.995134	−	0.0985348i	$-0.0314156\pi$
$457$	8.81254	+	15.2638i	0.412233	+	0.714009i	−0.582900	+	0.812544i	$0.698082\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.7014	−	28.9277i	−0.777862	−	1.34730i	−0.933172	−	0.359430i	$-0.882971\pi$
$461$	−16.7014	−	28.9277i	−0.777862	−	1.34730i	0.155310	−	0.987866i	$-0.450362\pi$
$462$		0			0
$463$	7.91102	−	13.7023i	0.367656	−	0.636799i	−0.621543	−	0.783380i	$-0.713494\pi$
$463$	7.91102	−	13.7023i	0.367656	−	0.636799i	0.989199	+	0.146581i	$0.0468270\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.88148			−0.364711			−0.182356	−	0.983233i	$-0.558372\pi$
$467$	−7.88148			−0.364711			−0.182356	+	0.983233i	$0.558372\pi$
$468$		0			0
$469$	29.6146	+	0.924542i	1.36748	+	0.0426914i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−24.6612	−	14.2381i	−1.13392	−	0.654670i
$474$		0			0
$475$	1.01417	−	0.585529i	0.0465332	−	0.0268659i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.64131	−	4.57489i	−0.120685	−	0.209032i	0.799353	−	0.600861i	$-0.205176\pi$
$479$	−2.64131	−	4.57489i	−0.120685	−	0.209032i	−0.920038	+	0.391830i	$0.871842\pi$
$480$		0			0
$481$	0.961820	+	0.555307i	0.0438552	+	0.0253198i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	12.0691i		−	0.548027i
$486$		0			0
$487$	−3.90074			−0.176760			−0.0883798	−	0.996087i	$-0.528169\pi$
$487$	−3.90074			−0.176760			−0.0883798	+	0.996087i	$0.528169\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−15.6506	−	9.03585i	−0.706300	−	0.407782i	0.103390	−	0.994641i	$-0.467031\pi$
$491$	−15.6506	−	9.03585i	−0.706300	−	0.407782i	−0.809689	+	0.586859i	$0.800364\pi$
$492$		0			0
$493$	−8.09052	+	4.67106i	−0.364379	+	0.210374i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	17.9027	−	9.60412i	0.803047	−	0.430804i
$498$		0			0
$499$	1.95896	−	3.39301i	0.0876949	−	0.151892i	−0.818841	−	0.574020i	$-0.805383\pi$
$499$	1.95896	−	3.39301i	0.0876949	−	0.151892i	0.906536	+	0.422128i	$0.138717\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	0.565207			0.0252013			0.0126007	−	0.999921i	$-0.495989\pi$
$503$	0.565207			0.0252013			0.0126007	+	0.999921i	$0.495989\pi$
$504$		0			0
$505$	18.9651			0.843934
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.68974	−	9.85492i	0.252193	−	0.436812i	−0.711936	−	0.702244i	$-0.752181\pi$
$509$	5.68974	−	9.85492i	0.252193	−	0.436812i	0.964129	+	0.265433i	$0.0855148\pi$
$510$		0			0
$511$	14.8633	−	7.97361i	0.657516	−	0.352732i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	18.3993	−	10.6229i	0.810772	−	0.468099i
$516$		0			0
$517$	−8.03172	−	4.63711i	−0.353235	−	0.203940i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.78433			−0.297227			−0.148613	−	0.988895i	$-0.547481\pi$
$521$	−6.78433			−0.297227			−0.148613	+	0.988895i	$0.547481\pi$
$522$		0			0
$523$		−	43.4601i		−	1.90038i	−0.311672	−	0.950190i	$-0.600889\pi$
$523$		−	43.4601i		−	1.90038i	0.311672	−	0.950190i	$-0.399111\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	17.9151	+	10.3433i	0.780395	+	0.450561i
$528$		0			0
$529$	0.973072	+	1.68541i	0.0423075	+	0.0732787i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.68771	−	0.974397i	0.0731026	−	0.0422058i
$534$		0			0
$535$	19.9534	+	11.5201i	0.862659	+	0.498057i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.09805	−	17.5690i	0.0472963	−	0.756751i
$540$		0			0
$541$	−34.1486			−1.46816			−0.734082	−	0.679061i	$-0.762387\pi$
$541$	−34.1486			−1.46816			−0.734082	+	0.679061i	$0.762387\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.77179	−	15.1932i	0.375742	−	0.650804i
$546$		0			0
$547$	−17.5029	−	30.3159i	−0.748369	−	1.29621i	−0.948604	−	0.316466i	$-0.897504\pi$
$547$	−17.5029	−	30.3159i	−0.748369	−	1.29621i	0.200234	−	0.979748i	$-0.435830\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6.82894	−	11.8281i	−0.290923	−	0.503893i
$552$		0			0
$553$	10.3550	−	16.7086i	0.440338	−	0.710521i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	1.61299i		−	0.0683444i	−0.999416	−	0.0341722i	$-0.989121\pi$
$557$		−	1.61299i		−	0.0683444i	0.999416	−	0.0341722i	$-0.0108795\pi$
$558$		0			0
$559$			3.19898i			0.135302i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−16.6209	+	28.7883i	−0.700488	+	1.21328i	0.267808	+	0.963472i	$0.413701\pi$
$563$	−16.6209	+	28.7883i	−0.700488	+	1.21328i	−0.968295	+	0.249808i	$0.919633\pi$
$564$		0			0
$565$	−11.3730	+	6.56619i	−0.478465	+	0.276242i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.49511	+	3.74995i	−0.272289	+	0.157206i	−0.629927	−	0.776654i	$-0.716915\pi$
$569$	−6.49511	+	3.74995i	−0.272289	+	0.157206i	0.357638	+	0.933860i	$0.383582\pi$
$570$		0			0
$571$	−15.7805	+	27.3327i	−0.660395	+	1.14384i	0.320117	+	0.947378i	$0.396278\pi$
$571$	−15.7805	+	27.3327i	−0.660395	+	1.14384i	−0.980512	+	0.196459i	$0.937056\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			1.99010i			0.0829931i
$576$		0			0
$577$		−	26.3137i		−	1.09545i	−0.836658	−	0.547726i	$-0.815494\pi$
$577$		−	26.3137i		−	1.09545i	0.836658	−	0.547726i	$-0.184506\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−13.1896	+	21.2825i	−0.547197	+	0.882946i
$582$		0			0
$583$	−1.06303	−	1.84122i	−0.0440261	−	0.0762555i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.8116	−	25.6545i	−0.611341	−	1.05887i	−0.991015	−	0.133753i	$-0.957297\pi$
$587$	−14.8116	−	25.6545i	−0.611341	−	1.05887i	0.379674	−	0.925120i	$-0.376036\pi$
$588$		0			0
$589$	−15.1216	+	26.1913i	−0.623073	+	1.07919i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.8344			−0.444916			−0.222458	−	0.974942i	$-0.571408\pi$
$593$	−10.8344			−0.444916			−0.222458	+	0.974942i	$0.571408\pi$
$594$		0			0
$595$	12.3521	+	0.385621i	0.506385	+	0.0158089i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−21.3274	−	12.3134i	−0.871413	−	0.503111i	−0.00359567	−	0.999994i	$-0.501145\pi$
$599$	−21.3274	−	12.3134i	−0.871413	−	0.503111i	−0.867818	+	0.496883i	$0.834478\pi$
$600$		0			0
$601$	34.8096	−	20.0973i	1.41991	−	0.819786i	0.423621	−	0.905840i	$-0.360759\pi$
$601$	34.8096	−	20.0973i	1.41991	−	0.819786i	0.996291	+	0.0860533i	$0.0274255\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.43223	+	9.40891i	0.220852	+	0.382526i
$606$		0			0
$607$	20.5906	+	11.8880i	0.835747	+	0.482519i	0.855816	−	0.517280i	$-0.173055\pi$
$607$	20.5906	+	11.8880i	0.835747	+	0.482519i	−0.0200693	+	0.999799i	$0.506389\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			1.04185i			0.0421488i
$612$		0			0
$613$	−26.0354			−1.05156			−0.525780	−	0.850620i	$-0.676227\pi$
$613$	−26.0354			−1.05156			−0.525780	+	0.850620i	$0.676227\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4.94660	−	2.85592i	−0.199143	−	0.114975i	0.397113	−	0.917770i	$-0.370012\pi$
$617$	−4.94660	−	2.85592i	−0.199143	−	0.114975i	−0.596256	+	0.802795i	$0.703345\pi$
$618$		0			0
$619$	−39.4955	+	22.8027i	−1.58746	+	0.916520i	−0.593734	+	0.804661i	$0.702347\pi$
$619$	−39.4955	+	22.8027i	−1.58746	+	0.916520i	−0.993724	+	0.111859i	$0.964320\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	6.40960	+	11.9479i	0.256795	+	0.478683i
$624$		0			0
$625$	13.4167	−	23.2385i	0.536670	−	0.929539i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	7.90325			0.315123
$630$		0			0
$631$	39.5756			1.57548			0.787739	−	0.616009i	$-0.211252\pi$
$631$	39.5756			1.57548			0.787739	+	0.616009i	$0.211252\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.3479	+	21.3871i	−0.490010	+	0.848722i
$636$		0			0
$637$	−1.77093	+	0.880011i	−0.0701668	+	0.0348673i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−19.1080	+	11.0320i	−0.754719	+	0.435737i	−0.827396	−	0.561618i	$-0.810179\pi$
$641$	−19.1080	+	11.0320i	−0.754719	+	0.435737i	0.0726775	+	0.997355i	$0.476846\pi$
$642$		0			0
$643$	−17.9250	−	10.3490i	−0.706894	−	0.408126i	0.103016	−	0.994680i	$-0.467151\pi$
$643$	−17.9250	−	10.3490i	−0.706894	−	0.408126i	−0.809910	+	0.586554i	$0.800484\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.6007			−0.534697			−0.267348	−	0.963600i	$-0.586147\pi$
$647$	−13.6007			−0.534697			−0.267348	+	0.963600i	$0.586147\pi$
$648$		0			0
$649$		−	36.6103i		−	1.43708i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	33.8994	+	19.5718i	1.32659	+	0.765905i	0.984770	−	0.173862i	$-0.0556246\pi$
$653$	33.8994	+	19.5718i	1.32659	+	0.765905i	0.341816	+	0.939767i	$0.388958\pi$
$654$		0			0
$655$	−6.38218	−	11.0543i	−0.249373	−	0.431926i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.36427	+	4.82911i	−0.325826	+	0.188116i	−0.653986	−	0.756506i	$-0.726905\pi$
$659$	−8.36427	+	4.82911i	−0.325826	+	0.188116i	0.328161	+	0.944622i	$0.393571\pi$
$660$		0			0
$661$	−11.2955	−	6.52145i	−0.439343	−	0.253655i	0.263976	−	0.964529i	$-0.414966\pi$
$661$	−11.2955	−	6.52145i	−0.439343	−	0.253655i	−0.703319	+	0.710874i	$0.748299\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.563765	+	18.0583i	−0.0218618	+	0.700271i
$666$		0			0
$667$	23.2103			0.898706
$668$		0			0
$669$		0			0
$670$		0			0
$671$	13.9347	−	24.1356i	0.537944	−	0.931746i
$672$		0			0
$673$	−10.2742	−	17.7955i	−0.396042	−	0.685965i	0.597192	−	0.802099i	$-0.296283\pi$
$673$	−10.2742	−	17.7955i	−0.396042	−	0.685965i	−0.993234	+	0.116134i	$0.962950\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.3014	−	21.3067i	−0.472782	−	0.818882i	0.526733	−	0.850031i	$-0.323417\pi$
$677$	−12.3014	−	21.3067i	−0.472782	−	0.818882i	−0.999515	+	0.0311486i	$0.990084\pi$
$678$		0			0
$679$	11.6817	+	7.23964i	0.448304	+	0.277832i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	34.7249i		−	1.32871i	−0.747416	−	0.664357i	$-0.768706\pi$
$683$		−	34.7249i		−	1.32871i	0.747416	−	0.664357i	$-0.231294\pi$
$684$		0			0
$685$		−	47.9167i		−	1.83080i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.119419	+	0.206840i	−0.00454950	+	0.00787996i
$690$		0			0
$691$	12.5120	−	7.22382i	0.475980	−	0.274807i	−0.242760	−	0.970086i	$-0.578053\pi$
$691$	12.5120	−	7.22382i	0.475980	−	0.274807i	0.718740	+	0.695279i	$0.244719\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	11.1529	−	6.43913i	0.423054	−	0.244250i
$696$		0			0
$697$	6.93392	−	12.0099i	0.262641	−	0.454907i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	30.9550i		−	1.16915i	−0.811338	−	0.584577i	$-0.801261\pi$
$701$		−	30.9550i		−	1.16915i	0.811338	−	0.584577i	$-0.198739\pi$
$702$		0			0
$703$			11.5543i			0.435778i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−11.3762	+	18.3564i	−0.427847	+	0.690365i
$708$		0			0
$709$	2.64988	+	4.58973i	0.0995184	+	0.172371i	0.911485	−	0.411332i	$-0.134936\pi$
$709$	2.64988	+	4.58973i	0.0995184	+	0.172371i	−0.811967	+	0.583703i	$0.801603\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−25.6977	−	44.5097i	−0.962385	−	1.66690i
$714$		0			0
$715$	−0.825325	+	1.42951i	−0.0308654	+	0.0534605i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−23.8427			−0.889184			−0.444592	−	0.895733i	$-0.646651\pi$
$719$	−23.8427			−0.889184			−0.444592	+	0.895733i	$0.646651\pi$
$720$		0			0
$721$	−0.754911	+	24.1810i	−0.0281143	+	0.900548i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.60355	+	0.925812i	0.0595545	+	0.0343838i
$726$		0			0
$727$	41.8426	−	24.1579i	1.55186	−	0.895965i	0.553866	−	0.832606i	$-0.313152\pi$
$727$	41.8426	−	24.1579i	1.55186	−	0.895965i	0.997991	−	0.0633594i	$-0.0201814\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	11.3821	+	19.7144i	0.420984	+	0.729165i
$732$		0			0
$733$	−14.9281	−	8.61872i	−0.551381	−	0.318340i	0.198298	−	0.980142i	$-0.436459\pi$
$733$	−14.9281	−	8.61872i	−0.551381	−	0.318340i	−0.749679	+	0.661802i	$0.769792\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			28.1621i			1.03736i
$738$		0			0
$739$	11.0251			0.405567			0.202783	−	0.979224i	$-0.435001\pi$
$739$	11.0251			0.405567			0.202783	+	0.979224i	$0.435001\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−14.2819	−	8.24567i	−0.523953	−	0.302504i	0.214598	−	0.976703i	$-0.431156\pi$
$743$	−14.2819	−	8.24567i	−0.523953	−	0.302504i	−0.738550	+	0.674198i	$0.764489\pi$
$744$		0			0
$745$	9.29254	−	5.36505i	0.340452	−	0.196560i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−23.1194	+	12.4027i	−0.844766	+	0.453185i
$750$		0			0
$751$	−7.08239	+	12.2671i	−0.258440	+	0.447631i	−0.965824	−	0.259198i	$-0.916542\pi$
$751$	−7.08239	+	12.2671i	−0.258440	+	0.447631i	0.707384	+	0.706829i	$0.249875\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−15.7489			−0.573161
$756$		0			0
$757$	−24.3048			−0.883374			−0.441687	−	0.897169i	$-0.645620\pi$
$757$	−24.3048			−0.883374			−0.441687	+	0.897169i	$0.645620\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.29941	−	12.6429i	0.264603	−	0.458306i	−0.702856	−	0.711332i	$-0.748092\pi$
$761$	7.29941	−	12.6429i	0.264603	−	0.458306i	0.967460	+	0.253025i	$0.0814256\pi$
$762$		0			0
$763$	9.44384	+	17.6039i	0.341890	+	0.637305i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.56174	+	2.05637i	−0.128607	+	0.0742512i
$768$		0			0
$769$	−20.5263	−	11.8509i	−0.740198	−	0.427353i	0.0819433	−	0.996637i	$-0.473887\pi$
$769$	−20.5263	−	11.8509i	−0.740198	−	0.427353i	−0.822141	+	0.569284i	$0.807221\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	33.3407			1.19918			0.599591	−	0.800307i	$-0.295330\pi$
$773$	33.3407			1.19918			0.599591	+	0.800307i	$0.295330\pi$
$774$		0			0
$775$		−	4.10011i		−	0.147280i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	17.5581	+	10.1372i	0.629083	+	0.363202i
$780$		0			0
$781$	9.65514	+	16.7232i	0.345488	+	0.598403i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	14.9210	−	8.61463i	0.532552	−	0.307469i
$786$		0			0
$787$	−9.81353	−	5.66584i	−0.349815	−	0.201966i	0.314789	−	0.949162i	$-0.398066\pi$
$787$	−9.81353	−	5.66584i	−0.349815	−	0.201966i	−0.664604	+	0.747196i	$0.731400\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.466624	−	14.9467i	0.0165912	−	0.531445i
$792$		0			0
$793$	−3.13081			−0.111178
$794$		0			0
$795$		0			0
$796$		0			0
$797$	16.3604	−	28.3370i	0.579515	−	1.00375i	−0.416020	−	0.909356i	$-0.636575\pi$
$797$	16.3604	−	28.3370i	0.579515	−	1.00375i	0.995535	−	0.0943942i	$-0.0300914\pi$
$798$		0			0
$799$	3.70697	+	6.42066i	0.131143	+	0.227147i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.01597	+	13.8841i	0.282878	+	0.489958i
$804$		0			0
$805$	−26.0979	−	16.1739i	−0.919829	−	0.570055i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			24.6586i			0.866951i	0.901165	+	0.433475i	$0.142713\pi$
$809$			24.6586i			0.866951i	−0.901165	+	0.433475i	$0.857287\pi$
$810$		0			0
$811$		−	24.8675i		−	0.873216i	−0.899652	−	0.436608i	$-0.856180\pi$
$811$		−	24.8675i		−	0.873216i	0.899652	−	0.436608i	$-0.143820\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−13.9671	+	24.1917i	−0.489246	+	0.847398i
$816$		0			0
$817$	−28.8219	+	16.6403i	−1.00835	+	0.582171i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	41.7660	−	24.1136i	1.45764	−	0.841570i	0.458747	−	0.888567i	$-0.348299\pi$
$821$	41.7660	−	24.1136i	1.45764	−	0.841570i	0.998895	+	0.0469972i	$0.0149652\pi$
$822$		0			0
$823$	−24.1616	+	41.8492i	−0.842221	+	1.45877i	0.0457915	+	0.998951i	$0.485419\pi$
$823$	−24.1616	+	41.8492i	−0.842221	+	1.45877i	−0.888013	+	0.459819i	$0.847914\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			50.5791i			1.75881i	0.476078	+	0.879403i	$0.342058\pi$
$827$			50.5791i			1.75881i	−0.476078	+	0.879403i	$0.657942\pi$
$828$		0			0
$829$		−	14.9456i		−	0.519082i	−0.965732	−	0.259541i	$-0.916429\pi$
$829$		−	14.9456i		−	0.519082i	0.965732	−	0.259541i	$-0.0835713\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.78264	+	11.7243i	−0.269653	+	0.406224i
$834$		0			0
$835$	−24.1863	−	41.8919i	−0.837001	−	1.44973i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.25434	−	5.63669i	−0.112352	−	0.194600i	0.804366	−	0.594134i	$-0.202505\pi$
$839$	−3.25434	−	5.63669i	−0.112352	−	0.194600i	−0.916718	+	0.399534i	$0.869172\pi$
$840$		0			0
$841$	−3.70240	+	6.41274i	−0.127669	+	0.221129i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−30.0195			−1.03270
$846$		0			0
$847$	−12.3655	−	0.386040i	−0.424883	−	0.0132645i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−17.0048	−	9.81771i	−0.582916	−	0.336547i
$852$		0			0
$853$	−14.8966	+	8.60053i	−0.510049	+	0.294477i	−0.732854	−	0.680386i	$-0.761812\pi$
$853$	−14.8966	+	8.60053i	−0.510049	+	0.294477i	0.222805	+	0.974863i	$0.428479\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−20.2073	−	35.0001i	−0.690269	−	1.19558i	−0.971750	−	0.236014i	$-0.924159\pi$
$857$	−20.2073	−	35.0001i	−0.690269	−	1.19558i	0.281481	−	0.959567i	$-0.409174\pi$
$858$		0			0
$859$	20.1957	+	11.6600i	0.689068	+	0.397834i	0.803263	−	0.595625i	$-0.203095\pi$
$859$	20.1957	+	11.6600i	0.689068	+	0.397834i	−0.114195	+	0.993458i	$0.536429\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			9.03284i			0.307481i	0.988111	+	0.153741i	$0.0491320\pi$
$863$			9.03284i			0.307481i	−0.988111	+	0.153741i	$0.950868\pi$
$864$		0			0
$865$	−17.1076			−0.581674
$866$		0			0
$867$		0			0
$868$		0			0
$869$	16.1807	+	9.34193i	0.548893	+	0.316903i
$870$		0			0
$871$	2.73983	−	1.58184i	0.0928356	−	0.0535986i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	13.3722	+	24.9267i	0.452064	+	0.842677i
$876$		0			0
$877$	8.21638	−	14.2312i	0.277447	−	0.480553i	−0.693302	−	0.720647i	$-0.743845\pi$
$877$	8.21638	−	14.2312i	0.277447	−	0.480553i	0.970750	+	0.240094i	$0.0771782\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−20.8143			−0.701252			−0.350626	−	0.936516i	$-0.614031\pi$
$881$	−20.8143			−0.701252			−0.350626	+	0.936516i	$0.614031\pi$
$882$		0			0
$883$	−29.8412			−1.00424			−0.502119	−	0.864799i	$-0.667446\pi$
$883$	−29.8412			−1.00424			−0.502119	+	0.864799i	$0.667446\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.25876	−	14.3046i	0.277302	−	0.480301i	−0.693411	−	0.720542i	$-0.743893\pi$
$887$	8.25876	−	14.3046i	0.277302	−	0.480301i	0.970713	+	0.240241i	$0.0772264\pi$
$888$		0			0
$889$	−13.2939	−	24.7807i	−0.445863	−	0.831118i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−9.38679	+	5.41947i	−0.314117	+	0.181356i
$894$		0			0
$895$	33.8318	+	19.5328i	1.13087	+	0.652909i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−47.8190			−1.59485
$900$		0			0
$901$			1.69960i			0.0566218i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.09375	−	4.67293i	−0.269045	−	0.155333i
$906$		0			0
$907$	9.12715	+	15.8087i	0.303062	+	0.524919i	0.976828	−	0.214026i	$-0.0686577\pi$
$907$	9.12715	+	15.8087i	0.303062	+	0.524919i	−0.673766	+	0.738945i	$0.735324\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	2.75798	−	1.59232i	0.0913758	−	0.0527559i	−0.453616	−	0.891197i	$-0.649866\pi$
$911$	2.75798	−	1.59232i	0.0913758	−	0.0527559i	0.544992	+	0.838441i	$0.316533\pi$
$912$		0			0
$913$	−20.6101	−	11.8993i	−0.682095	−	0.393808i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	14.5279	+	0.453548i	0.479753	+	0.0149775i
$918$		0			0
$919$	13.7624			0.453980			0.226990	−	0.973897i	$-0.427111\pi$
$919$	13.7624			0.453980			0.226990	+	0.973897i	$0.427111\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.08464	−	1.87866i	0.0357015	−	0.0618368i
$924$		0			0
$925$	−0.783218	−	1.35657i	−0.0257520	−	0.0446038i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.638392	+	1.10573i	0.0209450	+	0.0362778i	0.876308	−	0.481751i	$-0.159999\pi$
$929$	0.638392	+	1.10573i	0.0209450	+	0.0362778i	−0.855363	+	0.518029i	$0.826666\pi$
$930$		0			0
$931$	−17.1406	−	11.3780i	−0.561761	−	0.372898i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			11.7462i			0.384142i
$936$		0			0
$937$		−	54.0092i		−	1.76440i	−0.470873	−	0.882201i	$-0.656061\pi$
$937$		−	54.0092i		−	1.76440i	0.470873	−	0.882201i	$-0.343939\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.40019	+	5.88931i	−0.110843	+	0.191986i	−0.916110	−	0.400926i	$-0.868688\pi$
$941$	−3.40019	+	5.88931i	−0.110843	+	0.191986i	0.805267	+	0.592912i	$0.202022\pi$
$942$		0			0
$943$	−29.8383	+	17.2271i	−0.971668	+	0.560993i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−26.2915	+	15.1794i	−0.854359	+	0.493265i	−0.862119	−	0.506705i	$-0.830863\pi$
$947$	−26.2915	+	15.1794i	−0.854359	+	0.493265i	0.00776004	+	0.999970i	$0.497530\pi$
$948$		0			0
$949$	0.900502	−	1.55972i	0.0292315	−	0.0506305i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			36.0446i			1.16760i	0.811897	+	0.583800i	$0.198435\pi$
$953$			36.0446i			1.16760i	−0.811897	+	0.583800i	$0.801565\pi$
$954$		0			0
$955$			11.8709i			0.384133i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	46.3790	+	28.7429i	1.49766	+	0.928157i
$960$		0			0
$961$	37.4436	+	64.8543i	1.20786	+	2.09207i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	8.24814	+	14.2862i	0.265517	+	0.459889i
$966$		0			0
$967$	10.7710	−	18.6560i	0.346373	−	0.599936i	−0.639229	−	0.769016i	$-0.720747\pi$
$967$	10.7710	−	18.6560i	0.346373	−	0.599936i	0.985602	+	0.169081i	$0.0540798\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.00760			0.289068			0.144534	−	0.989500i	$-0.453832\pi$
$971$	9.00760			0.289068			0.144534	+	0.989500i	$0.453832\pi$
$972$		0			0
$973$	−0.457595	+	14.6575i	−0.0146698	+	0.469898i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−19.8654	−	11.4693i	−0.635550	−	0.366935i	0.147348	−	0.989085i	$-0.452926\pi$
$977$	−19.8654	−	11.4693i	−0.635550	−	0.366935i	−0.782898	+	0.622150i	$0.786260\pi$
$978$		0			0
$979$	−11.1607	+	6.44365i	−0.356698	+	0.205940i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	4.18439	+	7.24758i	0.133461	+	0.231162i	0.925009	−	0.379946i	$-0.124057\pi$
$983$	4.18439	+	7.24758i	0.133461	+	0.231162i	−0.791547	+	0.611108i	$0.790724\pi$
$984$		0			0
$985$	31.4071	+	18.1329i	1.00071	+	0.577762i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	56.5573i		−	1.79842i
$990$		0			0
$991$	−26.2476			−0.833781			−0.416891	−	0.908957i	$-0.636880\pi$
$991$	−26.2476			−0.833781			−0.416891	+	0.908957i	$0.636880\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	53.9574	+	31.1523i	1.71057	+	0.987596i
$996$		0			0
$997$	−29.5387	+	17.0542i	−0.935499	+	0.540111i	−0.888547	−	0.458786i	$-0.848284\pi$
$997$	−29.5387	+	17.0542i	−0.935499	+	0.540111i	−0.0469525	+	0.998897i	$0.514951\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.d.881.19		48
3.2	odd	2		1008.2.cc.d.545.16		48
4.3	odd	2		1512.2.bu.a.881.19		48
7.6	odd	2	inner	3024.2.cc.d.881.6		48
9.2	odd	6	inner	3024.2.cc.d.2897.6		48
9.7	even	3		1008.2.cc.d.209.9		48
12.11	even	2		504.2.bu.a.41.9	✓	48
21.20	even	2		1008.2.cc.d.545.9		48
28.27	even	2		1512.2.bu.a.881.6		48
36.7	odd	6		504.2.bu.a.209.16	yes	48
36.11	even	6		1512.2.bu.a.1385.6		48
36.23	even	6		4536.2.k.a.3401.37		48
36.31	odd	6		4536.2.k.a.3401.12		48
63.20	even	6	inner	3024.2.cc.d.2897.19		48
63.34	odd	6		1008.2.cc.d.209.16		48
84.83	odd	2		504.2.bu.a.41.16	yes	48
252.83	odd	6		1512.2.bu.a.1385.19		48
252.139	even	6		4536.2.k.a.3401.38		48
252.167	odd	6		4536.2.k.a.3401.11		48
252.223	even	6		504.2.bu.a.209.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.9	✓	48	12.11	even	2
504.2.bu.a.41.16	yes	48	84.83	odd	2
504.2.bu.a.209.9	yes	48	252.223	even	6
504.2.bu.a.209.16	yes	48	36.7	odd	6
1008.2.cc.d.209.9		48	9.7	even	3
1008.2.cc.d.209.16		48	63.34	odd	6
1008.2.cc.d.545.9		48	21.20	even	2
1008.2.cc.d.545.16		48	3.2	odd	2
1512.2.bu.a.881.6		48	28.27	even	2
1512.2.bu.a.881.19		48	4.3	odd	2
1512.2.bu.a.1385.6		48	36.11	even	6
1512.2.bu.a.1385.19		48	252.83	odd	6
3024.2.cc.d.881.6		48	7.6	odd	2	inner
3024.2.cc.d.881.19		48	1.1	even	1	trivial
3024.2.cc.d.2897.6		48	9.2	odd	6	inner
3024.2.cc.d.2897.19		48	63.20	even	6	inner
4536.2.k.a.3401.11		48	252.167	odd	6
4536.2.k.a.3401.12		48	36.31	odd	6
4536.2.k.a.3401.37		48	36.23	even	6
4536.2.k.a.3401.38		48	252.139	even	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.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.16173 - 2.01217i) q^{5} +(1.25073 + 2.33145i) q^{7} +O(q^{10})\)	\(q+(1.16173 - 2.01217i) q^{5} +(1.25073 + 2.33145i) q^{7} +(-2.17784 + 1.25738i) q^{11} +(0.244656 + 0.141252i) q^{13} +2.01033 q^{17} +2.93904i q^{19} +(-4.32546 - 2.49731i) q^{23} +(-0.199225 - 0.345068i) q^{25} +(-4.02448 + 2.32353i) q^{29} +(8.91154 + 5.14508i) q^{31} +(6.14429 + 0.191820i) q^{35} +3.93132 q^{37} +(3.44915 - 5.97410i) q^{41} +(5.66183 + 9.80657i) q^{43} +(1.84396 + 3.19383i) q^{47} +(-3.87133 + 5.83205i) q^{49} +0.845432i q^{53} +5.84293i q^{55} +(-7.27908 + 12.6077i) q^{59} +(-9.59760 + 5.54118i) q^{61} +(0.568447 - 0.328193i) q^{65} +(5.59936 - 9.69838i) q^{67} -7.67879i q^{71} -6.37515i q^{73} +(-5.65542 - 3.50489i) q^{77} +(-3.71484 - 6.43430i) q^{79} +(4.73177 + 8.19566i) q^{83} +(2.33546 - 4.04513i) q^{85} +5.12467 q^{89} +(-0.0233229 + 0.747071i) q^{91} +(5.91385 + 3.41436i) q^{95} +(4.49852 - 2.59722i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) \) 48 * q + 12 * q^23 - 24 * q^25 + 36 * q^29 - 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 + 12 * q^79 + 12 * q^91 - 108 * q^95

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