LMFDB - Embedded newform 3024.2.q.l.2305.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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, 2, 2]))

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.q (of order $3$, 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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2305.10
Character	$\chi$	$=$	3024.2305
Dual form			3024.2.q.l.2881.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.59750 + 2.76695i) q^{5} +(1.66645 - 2.05498i) q^{7} +O(q^{10})$	$q+(1.59750 + 2.76695i) q^{5} +(1.66645 - 2.05498i) q^{7} +(1.14139 - 1.97695i) q^{11} +(-0.675051 + 1.16922i) q^{13} +(-2.21425 - 3.83519i) q^{17} +(3.69214 - 6.39497i) q^{19} +(3.23479 + 5.60283i) q^{23} +(-2.60400 + 4.51026i) q^{25} +(1.06167 + 1.83887i) q^{29} +0.632308 q^{31} +(8.34818 + 1.32814i) q^{35} +(1.92885 - 3.34087i) q^{37} +(5.05124 - 8.74900i) q^{41} +(-4.24701 - 7.35603i) q^{43} +6.53173 q^{47} +(-1.44591 - 6.84904i) q^{49} +(-2.39950 - 4.15606i) q^{53} +7.29349 q^{55} +6.20383 q^{59} -8.91093 q^{61} -4.31357 q^{65} +3.01570 q^{67} -15.3791 q^{71} +(4.36577 + 7.56173i) q^{73} +(-2.16053 - 5.64002i) q^{77} +1.87610 q^{79} +(-3.00140 - 5.19857i) q^{83} +(7.07451 - 12.2534i) q^{85} +(-2.65390 + 4.59668i) q^{89} +(1.27780 + 3.33566i) q^{91} +23.5927 q^{95} +(7.44539 + 12.8958i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{5} - 5 q^{7}+O(q^{10}) $ 22 * q - q^5 - 5 * q^7	$ 22 q - q^{5} - 5 q^{7} + 3 q^{11} + 7 q^{13} + q^{17} - 13 q^{19} - 22 q^{25} + 7 q^{29} + 12 q^{31} + 2 q^{35} + 6 q^{37} - 4 q^{41} - 2 q^{43} - 34 q^{47} - 25 q^{49} - q^{53} - 2 q^{55} + 42 q^{59} - 62 q^{61} - 6 q^{65} - 52 q^{67} - 32 q^{71} + 17 q^{73} + q^{77} - 32 q^{79} - 36 q^{83} + 28 q^{85} + 2 q^{89} - 15 q^{91} + 48 q^{95} + 19 q^{97}+O(q^{100}) $ 22 * q - q^5 - 5 * q^7 + 3 * q^11 + 7 * q^13 + q^17 - 13 * q^19 - 22 * q^25 + 7 * q^29 + 12 * q^31 + 2 * q^35 + 6 * q^37 - 4 * q^41 - 2 * q^43 - 34 * q^47 - 25 * q^49 - q^53 - 2 * q^55 + 42 * q^59 - 62 * q^61 - 6 * q^65 - 52 * q^67 - 32 * q^71 + 17 * q^73 + q^77 - 32 * q^79 - 36 * q^83 + 28 * q^85 + 2 * q^89 - 15 * q^91 + 48 * q^95 + 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.59750	+	2.76695i	0.714423	+	1.23742i	0.963182	+	0.268851i	$0.0866441\pi$
$5$	1.59750	+	2.76695i	0.714423	+	1.23742i	−0.248759	+	0.968566i	$0.580023\pi$
$6$		0			0
$7$	1.66645	−	2.05498i	0.629857	−	0.776711i
$7$	1.66645	−	2.05498i	0.629857	−	0.776711i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.14139	−	1.97695i	0.344143	−	0.596073i	−0.641055	−	0.767495i	$-0.721503\pi$
$11$	1.14139	−	1.97695i	0.344143	−	0.596073i	0.985198	+	0.171422i	$0.0548362\pi$
$12$		0			0
$13$	−0.675051	+	1.16922i	−0.187225	+	0.324284i	−0.944324	−	0.329017i	$-0.893283\pi$
$13$	−0.675051	+	1.16922i	−0.187225	+	0.324284i	0.757099	+	0.653300i	$0.226616\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.21425	−	3.83519i	−0.537033	−	0.930169i	−0.999062	−	0.0433042i	$-0.986212\pi$
$17$	−2.21425	−	3.83519i	−0.537033	−	0.930169i	0.462028	−	0.886865i	$-0.347122\pi$
$18$		0			0
$19$	3.69214	−	6.39497i	0.847034	−	1.46711i	−0.0368084	−	0.999322i	$-0.511719\pi$
$19$	3.69214	−	6.39497i	0.847034	−	1.46711i	0.883843	−	0.467784i	$-0.154948\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.23479	+	5.60283i	0.674501	+	1.16827i	0.976614	+	0.214999i	$0.0689747\pi$
$23$	3.23479	+	5.60283i	0.674501	+	1.16827i	−0.302113	+	0.953272i	$0.597692\pi$
$24$		0			0
$25$	−2.60400	+	4.51026i	−0.520800	+	0.902053i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.06167	+	1.83887i	0.197148	+	0.341470i	0.947602	−	0.319452i	$-0.103499\pi$
$29$	1.06167	+	1.83887i	0.197148	+	0.341470i	−0.750455	+	0.660922i	$0.770166\pi$
$30$		0			0
$31$	0.632308			0.113566			0.0567830	−	0.998387i	$-0.481916\pi$
$31$	0.632308			0.113566			0.0567830	+	0.998387i	$0.481916\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	8.34818	+	1.32814i	1.41110	+	0.224496i
$36$		0			0
$37$	1.92885	−	3.34087i	0.317102	−	0.549236i	−0.662780	−	0.748814i	$-0.730624\pi$
$37$	1.92885	−	3.34087i	0.317102	−	0.549236i	0.979882	+	0.199578i	$0.0639570\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.05124	−	8.74900i	0.788871	−	1.36636i	−0.137788	−	0.990462i	$-0.543999\pi$
$41$	5.05124	−	8.74900i	0.788871	−	1.36636i	0.926659	−	0.375903i	$-0.122667\pi$
$42$		0			0
$43$	−4.24701	−	7.35603i	−0.647663	−	1.12178i	−0.983680	−	0.179929i	$-0.942413\pi$
$43$	−4.24701	−	7.35603i	−0.647663	−	1.12178i	0.336017	−	0.941856i	$-0.390920\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.53173			0.952751			0.476375	−	0.879242i	$-0.341950\pi$
$47$	6.53173			0.952751			0.476375	+	0.879242i	$0.341950\pi$
$48$		0			0
$49$	−1.44591	−	6.84904i	−0.206559	−	0.978434i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.39950	−	4.15606i	−0.329597	−	0.570879i	0.652835	−	0.757500i	$-0.273580\pi$
$53$	−2.39950	−	4.15606i	−0.329597	−	0.570879i	−0.982432	+	0.186621i	$0.940246\pi$
$54$		0			0
$55$	7.29349			0.983454
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.20383			0.807670			0.403835	−	0.914832i	$-0.367677\pi$
$59$	6.20383			0.807670			0.403835	+	0.914832i	$0.367677\pi$
$60$		0			0
$61$	−8.91093			−1.14093			−0.570464	−	0.821323i	$-0.693236\pi$
$61$	−8.91093			−1.14093			−0.570464	+	0.821323i	$0.693236\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.31357			−0.535033
$66$		0			0
$67$	3.01570			0.368426			0.184213	−	0.982886i	$-0.441026\pi$
$67$	3.01570			0.368426			0.184213	+	0.982886i	$0.441026\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−15.3791			−1.82516			−0.912580	−	0.408899i	$-0.865913\pi$
$71$	−15.3791			−1.82516			−0.912580	+	0.408899i	$0.865913\pi$
$72$		0			0
$73$	4.36577	+	7.56173i	0.510974	+	0.885033i	0.999919	+	0.0127186i	$0.00404857\pi$
$73$	4.36577	+	7.56173i	0.510974	+	0.885033i	−0.488945	+	0.872315i	$0.662618\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.16053	−	5.64002i	−0.246215	−	0.642740i
$78$		0			0
$79$	1.87610			0.211078			0.105539	−	0.994415i	$-0.466343\pi$
$79$	1.87610			0.211078			0.105539	+	0.994415i	$0.466343\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.00140	−	5.19857i	−0.329446	−	0.570617i	0.652956	−	0.757396i	$-0.273529\pi$
$83$	−3.00140	−	5.19857i	−0.329446	−	0.570617i	−0.982402	+	0.186779i	$0.940195\pi$
$84$		0			0
$85$	7.07451	−	12.2534i	0.767338	−	1.32907i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.65390	+	4.59668i	−0.281313	+	0.487248i	−0.971708	−	0.236184i	$-0.924103\pi$
$89$	−2.65390	+	4.59668i	−0.281313	+	0.487248i	0.690396	+	0.723432i	$0.257436\pi$
$90$		0			0
$91$	1.27780	+	3.33566i	0.133949	+	0.349673i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	23.5927			2.42056
$96$		0			0
$97$	7.44539	+	12.8958i	0.755965	+	1.30937i	0.944893	+	0.327378i	$0.106165\pi$
$97$	7.44539	+	12.8958i	0.755965	+	1.30937i	−0.188929	+	0.981991i	$0.560502\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.00299	+	12.1295i	−0.696824	+	1.20693i	0.272738	+	0.962088i	$0.412071\pi$
$101$	−7.00299	+	12.1295i	−0.696824	+	1.20693i	−0.969562	+	0.244846i	$0.921263\pi$
$102$		0			0
$103$	8.03055	+	13.9093i	0.791274	+	1.37053i	0.925179	+	0.379532i	$0.123915\pi$
$103$	8.03055	+	13.9093i	0.791274	+	1.37053i	−0.133905	+	0.990994i	$0.542752\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.26820	−	2.19658i	0.122601	−	0.212352i	−0.798191	−	0.602404i	$-0.794210\pi$
$107$	1.26820	−	2.19658i	0.122601	−	0.212352i	0.920793	+	0.390052i	$0.127543\pi$
$108$		0			0
$109$	8.10946	+	14.0460i	0.776746	+	1.34536i	0.933808	+	0.357775i	$0.116464\pi$
$109$	8.10946	+	14.0460i	0.776746	+	1.34536i	−0.157062	+	0.987589i	$0.550202\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.61499	+	2.79725i	−0.151926	+	0.263143i	−0.931935	−	0.362625i	$-0.881881\pi$
$113$	−1.61499	+	2.79725i	−0.151926	+	0.263143i	0.780010	+	0.625767i	$0.215214\pi$
$114$		0			0
$115$	−10.3352	+	17.9010i	−0.963759	+	1.66928i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−11.5712	−	1.84089i	−1.06073	−	0.168754i
$120$		0			0
$121$	2.89445	+	5.01333i	0.263131	+	0.455757i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.664575			−0.0594414
$126$		0			0
$127$	12.6429			1.12187			0.560936	−	0.827859i	$-0.310441\pi$
$127$	12.6429			1.12187			0.560936	+	0.827859i	$0.310441\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.53430	−	16.5139i	−0.833015	−	1.44282i	−0.895636	−	0.444787i	$-0.853279\pi$
$131$	−9.53430	−	16.5139i	−0.833015	−	1.44282i	0.0626210	−	0.998037i	$-0.480054\pi$
$132$		0			0
$133$	−6.98881	−	18.2442i	−0.606007	−	1.58197i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.38236	−	5.85842i	0.288975	−	0.500519i	−0.684591	−	0.728928i	$-0.740019\pi$
$137$	3.38236	−	5.85842i	0.288975	−	0.500519i	0.973565	+	0.228409i	$0.0733523\pi$
$138$		0			0
$139$	6.57218	−	11.3834i	0.557445	−	0.965524i	−0.440263	−	0.897869i	$-0.645115\pi$
$139$	6.57218	−	11.3834i	0.557445	−	0.965524i	0.997709	−	0.0676550i	$-0.0215517\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.54100	+	2.66908i	0.128865	+	0.223200i
$144$		0			0
$145$	−3.39204	+	5.87518i	−0.281693	+	0.487907i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.140257	+	0.242932i	0.0114903	+	0.0199018i	0.871713	−	0.490016i	$-0.163009\pi$
$149$	0.140257	+	0.242932i	0.0114903	+	0.0199018i	−0.860223	+	0.509918i	$0.829676\pi$
$150$		0			0
$151$	4.42899	−	7.67123i	0.360426	−	0.624276i	−0.627605	−	0.778532i	$-0.715965\pi$
$151$	4.42899	−	7.67123i	0.360426	−	0.624276i	0.988031	+	0.154256i	$0.0492980\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.01011	+	1.74956i	0.0811341	+	0.140528i
$156$		0			0
$157$	−1.92894			−0.153946			−0.0769731	−	0.997033i	$-0.524526\pi$
$157$	−1.92894			−0.153946			−0.0769731	+	0.997033i	$0.524526\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	16.9043	+	2.68936i	1.33225	+	0.211952i
$162$		0			0
$163$	12.1983	−	21.1281i	0.955446	−	1.65488i	0.222100	−	0.975024i	$-0.428709\pi$
$163$	12.1983	−	21.1281i	0.955446	−	1.65488i	0.733345	−	0.679856i	$-0.237958\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.75658	−	4.77453i	0.213310	−	0.369464i	−0.739438	−	0.673224i	$-0.764909\pi$
$167$	2.75658	−	4.77453i	0.213310	−	0.369464i	0.952749	+	0.303760i	$0.0982421\pi$
$168$		0			0
$169$	5.58861	+	9.67976i	0.429893	+	0.744597i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−12.6052			−0.958355			−0.479178	−	0.877718i	$-0.659065\pi$
$173$	−12.6052			−0.958355			−0.479178	+	0.877718i	$0.659065\pi$
$174$		0			0
$175$	4.92909	+	12.8673i	0.372604	+	0.972676i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.10472	+	8.84164i	0.381545	+	0.660855i	0.991283	−	0.131747i	$-0.0420588\pi$
$179$	5.10472	+	8.84164i	0.381545	+	0.660855i	−0.609738	+	0.792603i	$0.708725\pi$
$180$		0			0
$181$	−16.2398			−1.20710			−0.603548	−	0.797327i	$-0.706247\pi$
$181$	−16.2398			−1.20710			−0.603548	+	0.797327i	$0.706247\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	12.3254			0.906179
$186$		0			0
$187$	−10.1093			−0.739265
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.94120			−0.285175			−0.142587	−	0.989782i	$-0.545542\pi$
$191$	−3.94120			−0.285175			−0.142587	+	0.989782i	$0.545542\pi$
$192$		0			0
$193$	−5.74112			−0.413255			−0.206627	−	0.978420i	$-0.566249\pi$
$193$	−5.74112			−0.413255			−0.206627	+	0.978420i	$0.566249\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.67480			0.546807			0.273403	−	0.961899i	$-0.411851\pi$
$197$	7.67480			0.546807			0.273403	+	0.961899i	$0.411851\pi$
$198$		0			0
$199$	2.26928	+	3.93050i	0.160865	+	0.278626i	0.935179	−	0.354175i	$-0.115238\pi$
$199$	2.26928	+	3.93050i	0.160865	+	0.278626i	−0.774314	+	0.632801i	$0.781905\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.54807	+	0.882659i	0.389398	+	0.0619505i
$204$		0			0
$205$	32.2774			2.25435
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.42836	−	14.5983i	−0.583002	−	1.00979i
$210$		0			0
$211$	−9.84097	+	17.0451i	−0.677480	+	1.17343i	0.298257	+	0.954486i	$0.403595\pi$
$211$	−9.84097	+	17.0451i	−0.677480	+	1.17343i	−0.975737	+	0.218944i	$0.929739\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	13.5692	−	23.5025i	0.925410	−	1.60286i
$216$		0			0
$217$	1.05371	−	1.29938i	0.0715304	−	0.0882079i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.97891			0.402185
$222$		0			0
$223$	−6.63518	−	11.4925i	−0.444324	−	0.769592i	0.553681	−	0.832729i	$-0.313223\pi$
$223$	−6.63518	−	11.4925i	−0.444324	−	0.769592i	−0.998005	+	0.0631368i	$0.979890\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.0305	+	19.1053i	−0.732118	+	1.26807i	0.223858	+	0.974622i	$0.428135\pi$
$227$	−11.0305	+	19.1053i	−0.732118	+	1.26807i	−0.955976	+	0.293445i	$0.905198\pi$
$228$		0			0
$229$	8.92359	+	15.4561i	0.589688	+	1.02137i	0.994273	+	0.106869i	$0.0340825\pi$
$229$	8.92359	+	15.4561i	0.589688	+	1.02137i	−0.404585	+	0.914500i	$0.632584\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.84409	−	13.5864i	0.513883	−	0.890072i	−0.485987	−	0.873966i	$-0.661540\pi$
$233$	7.84409	−	13.5864i	0.513883	−	0.890072i	0.999870	−	0.0161061i	$-0.00512696\pi$
$234$		0			0
$235$	10.4344	+	18.0730i	0.680667	+	1.17895i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.0639656	+	0.110792i	−0.00413759	+	0.00716652i	−0.868087	−	0.496412i	$-0.834650\pi$
$239$	−0.0639656	+	0.110792i	−0.00413759	+	0.00716652i	0.863949	+	0.503579i	$0.167984\pi$
$240$		0			0
$241$	−7.54343	+	13.0656i	−0.485915	+	0.841630i	−0.999869	−	0.0161883i	$-0.994847\pi$
$241$	−7.54343	+	13.0656i	−0.485915	+	0.841630i	0.513954	+	0.857818i	$0.328180\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	16.6411	−	14.9421i	1.06316	−	0.954616i
$246$		0			0
$247$	4.98476	+	8.63386i	0.317173	+	0.549359i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.3738			0.781030			0.390515	−	0.920596i	$-0.372297\pi$
$251$	12.3738			0.781030			0.390515	+	0.920596i	$0.372297\pi$
$252$		0			0
$253$	14.7687			0.928499
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.0433	+	19.1276i	0.688865	+	1.19315i	0.972205	+	0.234130i	$0.0752240\pi$
$257$	11.0433	+	19.1276i	0.688865	+	1.19315i	−0.283340	+	0.959019i	$0.591443\pi$
$258$		0			0
$259$	−3.65111	−	9.53115i	−0.226869	−	0.592237i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.89678	−	6.74943i	0.240286	−	0.416187i	−0.720510	−	0.693445i	$-0.756092\pi$
$263$	3.89678	−	6.74943i	0.240286	−	0.416187i	0.960796	+	0.277257i	$0.0894255\pi$
$264$		0			0
$265$	7.66641	−	13.2786i	0.470944	−	0.815698i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.85738	+	6.68119i	0.235189	+	0.407359i	0.959328	−	0.282295i	$-0.0910958\pi$
$269$	3.85738	+	6.68119i	0.235189	+	0.407359i	−0.724139	+	0.689654i	$0.757762\pi$
$270$		0			0
$271$	−12.5744	+	21.7795i	−0.763839	+	1.32301i	0.177019	+	0.984207i	$0.443355\pi$
$271$	−12.5744	+	21.7795i	−0.763839	+	1.32301i	−0.940858	+	0.338801i	$0.889979\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.94438	+	10.2960i	0.358460	+	0.620870i
$276$		0			0
$277$	3.98137	−	6.89593i	0.239217	−	0.414336i	−0.721273	−	0.692651i	$-0.756443\pi$
$277$	3.98137	−	6.89593i	0.239217	−	0.414336i	0.960490	+	0.278315i	$0.0897759\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.3385	−	23.1030i	−0.795710	−	1.37821i	−0.922388	−	0.386266i	$-0.873765\pi$
$281$	−13.3385	−	23.1030i	−0.795710	−	1.37821i	0.126678	−	0.991944i	$-0.459569\pi$
$282$		0			0
$283$	−14.4399			−0.858364			−0.429182	−	0.903218i	$-0.641198\pi$
$283$	−14.4399			−0.858364			−0.429182	+	0.903218i	$0.641198\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.56144	−	24.9600i	−0.564394	−	1.47334i
$288$		0			0
$289$	−1.30577	+	2.26166i	−0.0768099	+	0.133039i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.27703	−	14.3362i	0.483549	−	0.837532i	−0.516272	−	0.856424i	$-0.672681\pi$
$293$	8.27703	−	14.3362i	0.483549	−	0.837532i	0.999822	+	0.0188927i	$0.00601408\pi$
$294$		0			0
$295$	9.91061	+	17.1657i	0.577018	+	0.999424i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−8.73460			−0.505135
$300$		0			0
$301$	−22.1939	−	3.53090i	−1.27924	−	0.203518i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−14.2352	−	24.6561i	−0.815105	−	1.41180i
$306$		0			0
$307$	−10.9233			−0.623425			−0.311713	−	0.950176i	$-0.600903\pi$
$307$	−10.9233			−0.623425			−0.311713	+	0.950176i	$0.600903\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.25360			−0.297904			−0.148952	−	0.988844i	$-0.547590\pi$
$311$	−5.25360			−0.297904			−0.148952	+	0.988844i	$0.547590\pi$
$312$		0			0
$313$	21.5184			1.21629			0.608145	−	0.793826i	$-0.291914\pi$
$313$	21.5184			1.21629			0.608145	+	0.793826i	$0.291914\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.5323			0.984710			0.492355	−	0.870394i	$-0.336136\pi$
$317$	17.5323			0.984710			0.492355	+	0.870394i	$0.336136\pi$
$318$		0			0
$319$	4.84714			0.271388
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−32.7012			−1.81954
$324$		0			0
$325$	−3.51567	−	6.08932i	−0.195014	−	0.337774i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	10.8848	−	13.4226i	0.600097	−	0.740012i
$330$		0			0
$331$	−6.27589			−0.344954			−0.172477	−	0.985014i	$-0.555177\pi$
$331$	−6.27589			−0.344954			−0.172477	+	0.985014i	$0.555177\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4.81757	+	8.34428i	0.263212	+	0.455897i
$336$		0			0
$337$	13.5924	−	23.5427i	0.740426	−	1.28246i	−0.211876	−	0.977297i	$-0.567957\pi$
$337$	13.5924	−	23.5427i	0.740426	−	1.28246i	0.952302	−	0.305159i	$-0.0987095\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.721712	−	1.25004i	0.0390829	−	0.0676936i
$342$		0			0
$343$	−16.4842	−	8.44222i	−0.890063	−	0.455837i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−19.1808			−1.02968			−0.514840	−	0.857286i	$-0.672149\pi$
$347$	−19.1808			−1.02968			−0.514840	+	0.857286i	$0.672149\pi$
$348$		0			0
$349$	10.1028	+	17.4985i	0.540789	+	0.936675i	0.998859	+	0.0477584i	$0.0152078\pi$
$349$	10.1028	+	17.4985i	0.540789	+	0.936675i	−0.458069	+	0.888916i	$0.651459\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.2499	+	24.6816i	−0.758448	+	1.31367i	0.185193	+	0.982702i	$0.440709\pi$
$353$	−14.2499	+	24.6816i	−0.758448	+	1.31367i	−0.943642	+	0.330969i	$0.892624\pi$
$354$		0			0
$355$	−24.5680	−	42.5531i	−1.30394	−	2.25848i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	15.4572	−	26.7727i	0.815802	−	1.41301i	−0.0929489	−	0.995671i	$-0.529629\pi$
$359$	15.4572	−	26.7727i	0.815802	−	1.41301i	0.908751	−	0.417339i	$-0.137037\pi$
$360$		0			0
$361$	−17.7638	−	30.7677i	−0.934934	−	1.61935i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−13.9486	+	24.1597i	−0.730103	+	1.26458i
$366$		0			0
$367$	−3.41547	+	5.91577i	−0.178286	+	0.308801i	−0.941294	−	0.337589i	$-0.890389\pi$
$367$	−3.41547	+	5.91577i	−0.178286	+	0.308801i	0.763007	+	0.646390i	$0.223722\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−12.5393	−	1.99491i	−0.651007	−	0.103571i
$372$		0			0
$373$	−3.38245	−	5.85858i	−0.175137	−	0.303346i	0.765072	−	0.643945i	$-0.222703\pi$
$373$	−3.38245	−	5.85858i	−0.175137	−	0.303346i	−0.940209	+	0.340599i	$0.889370\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.86673			−0.147644
$378$		0			0
$379$	7.62967			0.391910			0.195955	−	0.980613i	$-0.437219\pi$
$379$	7.62967			0.391910			0.195955	+	0.980613i	$0.437219\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.21132	+	5.56217i	0.164091	+	0.284214i	0.936332	−	0.351116i	$-0.114198\pi$
$383$	3.21132	+	5.56217i	0.164091	+	0.284214i	−0.772241	+	0.635329i	$0.780864\pi$
$384$		0			0
$385$	12.1542	−	14.9880i	0.619436	−	0.763860i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.92675	+	13.7295i	−0.401902	+	0.696115i	−0.993955	−	0.109784i	$-0.964984\pi$
$389$	−7.92675	+	13.7295i	−0.401902	+	0.696115i	0.592053	+	0.805899i	$0.298317\pi$
$390$		0			0
$391$	14.3253	−	24.8121i	0.724460	−	1.25480i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.99707	+	5.19107i	0.150799	+	0.261191i
$396$		0			0
$397$	−8.56287	+	14.8313i	−0.429758	+	0.744363i	−0.996852	−	0.0792903i	$-0.974735\pi$
$397$	−8.56287	+	14.8313i	−0.429758	+	0.744363i	0.567093	+	0.823654i	$0.308068\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.8845	+	20.5846i	0.593486	+	1.02795i	0.993759	+	0.111552i	$0.0355821\pi$
$401$	11.8845	+	20.5846i	0.593486	+	1.02795i	−0.400273	+	0.916396i	$0.631085\pi$
$402$		0			0
$403$	−0.426840	+	0.739309i	−0.0212624	+	0.0368276i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.40316	−	7.62649i	−0.218256	−	0.378031i
$408$		0			0
$409$	15.1189			0.747582			0.373791	−	0.927513i	$-0.378058\pi$
$409$	15.1189			0.747582			0.373791	+	0.927513i	$0.378058\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.3383	−	12.7488i	0.508717	−	0.627326i
$414$		0			0
$415$	9.58945	−	16.6094i	0.470728	−	0.815324i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.82673	−	4.89604i	0.138095	−	0.239187i	−0.788681	−	0.614803i	$-0.789236\pi$
$419$	2.82673	−	4.89604i	0.138095	−	0.239187i	0.926775	+	0.375616i	$0.122569\pi$
$420$		0			0
$421$	−12.5088	−	21.6658i	−0.609640	−	1.05593i	−0.991300	−	0.131625i	$-0.957981\pi$
$421$	−12.5088	−	21.6658i	−0.609640	−	1.05593i	0.381660	−	0.924303i	$-0.375353\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	23.0636			1.11875
$426$		0			0
$427$	−14.8496	+	18.3118i	−0.718622	+	0.886171i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.4514	+	18.1024i	0.503428	+	0.871962i	0.999992	+	0.00396247i	$0.00126130\pi$
$431$	10.4514	+	18.1024i	0.503428	+	0.871962i	−0.496564	+	0.868000i	$0.665405\pi$
$432$		0			0
$433$	−21.2708			−1.02221			−0.511104	−	0.859519i	$-0.670763\pi$
$433$	−21.2708			−1.02221			−0.511104	+	0.859519i	$0.670763\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	47.7732			2.28530
$438$		0			0
$439$	−17.1817			−0.820040			−0.410020	−	0.912077i	$-0.634478\pi$
$439$	−17.1817			−0.820040			−0.410020	+	0.912077i	$0.634478\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.7436			−0.605467			−0.302734	−	0.953075i	$-0.597899\pi$
$443$	−12.7436			−0.605467			−0.302734	+	0.953075i	$0.597899\pi$
$444$		0			0
$445$	−16.9584			−0.803905
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−31.5913			−1.49088			−0.745442	−	0.666570i	$-0.767762\pi$
$449$	−31.5913			−1.49088			−0.745442	+	0.666570i	$0.767762\pi$
$450$		0			0
$451$	−11.5309	−	19.9721i	−0.542969	−	0.940449i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.18833	+	8.86432i	−0.336994	+	0.415566i
$456$		0			0
$457$	−7.30486			−0.341707			−0.170853	−	0.985296i	$-0.554652\pi$
$457$	−7.30486			−0.341707			−0.170853	+	0.985296i	$0.554652\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.3651	+	23.1491i	0.622477	+	1.07816i	0.989023	+	0.147761i	$0.0472068\pi$
$461$	13.3651	+	23.1491i	0.622477	+	1.07816i	−0.366546	+	0.930400i	$0.619460\pi$
$462$		0			0
$463$	1.75608	−	3.04161i	0.0816117	−	0.141356i	−0.822331	−	0.569010i	$-0.807327\pi$
$463$	1.75608	−	3.04161i	0.0816117	−	0.141356i	0.903942	+	0.427654i	$0.140660\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.80239	+	13.5141i	−0.361052	+	0.625360i	−0.988134	−	0.153593i	$-0.950915\pi$
$467$	−7.80239	+	13.5141i	−0.361052	+	0.625360i	0.627083	+	0.778953i	$0.284249\pi$
$468$		0			0
$469$	5.02550	−	6.19721i	0.232056	−	0.286161i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−19.3900			−0.891554
$474$		0			0
$475$	19.2287	+	33.3050i	0.882272	+	1.52814i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.54444	−	14.7994i	0.390405	−	0.676202i	−0.602098	−	0.798422i	$-0.705668\pi$
$479$	8.54444	−	14.7994i	0.390405	−	0.676202i	0.992503	+	0.122221i	$0.0390015\pi$
$480$		0			0
$481$	2.60415	+	4.51052i	0.118739	+	0.205662i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−23.7880	+	41.2020i	−1.08016	+	1.87089i
$486$		0			0
$487$	12.9335	+	22.4014i	0.586072	+	1.01511i	0.994741	+	0.102423i	$0.0326597\pi$
$487$	12.9335	+	22.4014i	0.586072	+	1.01511i	−0.408669	+	0.912683i	$0.634007\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.51452	+	13.0155i	−0.339126	+	0.587383i	−0.984269	−	0.176679i	$-0.943465\pi$
$491$	−7.51452	+	13.0155i	−0.339126	+	0.587383i	0.645143	+	0.764062i	$0.276798\pi$
$492$		0			0
$493$	4.70160	−	8.14342i	0.211750	−	0.366761i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−25.6284	+	31.6037i	−1.14959	+	1.41762i
$498$		0			0
$499$	7.62094	+	13.1999i	0.341160	+	0.590907i	0.984648	−	0.174549i	$-0.0558468\pi$
$499$	7.62094	+	13.1999i	0.341160	+	0.590907i	−0.643488	+	0.765456i	$0.722513\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18.6284			0.830599			0.415299	−	0.909685i	$-0.363677\pi$
$503$	18.6284			0.830599			0.415299	+	0.909685i	$0.363677\pi$
$504$		0			0
$505$	−44.7491			−1.99131
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.72333	−	6.44899i	−0.165034	−	0.285847i	0.771634	−	0.636067i	$-0.219440\pi$
$509$	−3.72333	−	6.44899i	−0.165034	−	0.285847i	−0.936667	+	0.350221i	$0.886107\pi$
$510$		0			0
$511$	22.8145	+	3.62964i	1.00926	+	0.160566i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−25.6576	+	44.4402i	−1.13061	+	1.95827i
$516$		0			0
$517$	7.45527	−	12.9129i	0.327882	−	0.567909i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.3853	+	19.7200i	0.498800	+	0.863947i	0.999999	−	0.00138491i	$-0.000440830\pi$
$521$	11.3853	+	19.7200i	0.498800	+	0.863947i	−0.501199	+	0.865332i	$0.667107\pi$
$522$		0			0
$523$	−16.5092	+	28.5949i	−0.721899	+	1.25037i	0.238339	+	0.971182i	$0.423397\pi$
$523$	−16.5092	+	28.5949i	−0.721899	+	1.25037i	−0.960238	+	0.279184i	$0.909936\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.40009	−	2.42502i	−0.0609887	−	0.105636i
$528$		0			0
$529$	−9.42780	+	16.3294i	−0.409904	+	0.709975i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.81969	+	11.8120i	0.295393	+	0.511636i
$534$		0			0
$535$	8.10378			0.350357
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−15.1906	−	4.95894i	−0.654304	−	0.213597i
$540$		0			0
$541$	8.53464	−	14.7824i	0.366933	−	0.635546i	−0.622151	−	0.782897i	$-0.713741\pi$
$541$	8.53464	−	14.7824i	0.366933	−	0.635546i	0.989084	+	0.147351i	$0.0470745\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−25.9097	+	44.8769i	−1.10985	+	1.92232i
$546$		0			0
$547$	−16.3574	−	28.3318i	−0.699390	−	1.21138i	−0.968678	−	0.248319i	$-0.920122\pi$
$547$	−16.3574	−	28.3318i	−0.699390	−	1.21138i	0.269288	−	0.963060i	$-0.413212\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	15.6794			0.667963
$552$		0			0
$553$	3.12642	−	3.85536i	0.132949	−	0.163946i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.0783	−	29.5806i	−0.723633	−	1.25337i	−0.959534	−	0.281592i	$-0.909138\pi$
$557$	−17.0783	−	29.5806i	−0.723633	−	1.25337i	0.235902	−	0.971777i	$-0.424196\pi$
$558$		0			0
$559$	11.4678			0.485036
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.67074			−0.407573			−0.203786	−	0.979015i	$-0.565325\pi$
$563$	−9.67074			−0.407573			−0.203786	+	0.979015i	$0.565325\pi$
$564$		0			0
$565$	−10.3198			−0.434157
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−11.1274			−0.466484			−0.233242	−	0.972419i	$-0.574933\pi$
$569$	−11.1274			−0.466484			−0.233242	+	0.972419i	$0.574933\pi$
$570$		0			0
$571$	−0.729305			−0.0305205			−0.0152602	−	0.999884i	$-0.504858\pi$
$571$	−0.729305			−0.0305205			−0.0152602	+	0.999884i	$0.504858\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−33.6937			−1.40512
$576$		0			0
$577$	9.49359	+	16.4434i	0.395223	+	0.684547i	0.993130	−	0.117019i	$-0.0373338\pi$
$577$	9.49359	+	16.4434i	0.395223	+	0.684547i	−0.597906	+	0.801566i	$0.704001\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−15.6846	−	2.49532i	−0.650709	−	0.103523i
$582$		0			0
$583$	−10.9551			−0.453714
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.30535	−	2.26093i	−0.0538775	−	0.0933185i	0.837829	−	0.545933i	$-0.183825\pi$
$587$	−1.30535	−	2.26093i	−0.0538775	−	0.0933185i	−0.891706	+	0.452615i	$0.850491\pi$
$588$		0			0
$589$	2.33457	−	4.04359i	0.0961942	−	0.166613i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.92622	−	13.7286i	0.325491	−	0.563767i	−0.656121	−	0.754656i	$-0.727804\pi$
$593$	7.92622	−	13.7286i	0.325491	−	0.563767i	0.981612	+	0.190889i	$0.0611371\pi$
$594$		0			0
$595$	−13.3913	−	34.9576i	−0.548988	−	1.43312i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15.8610			0.648063			0.324032	−	0.946046i	$-0.394962\pi$
$599$	15.8610			0.648063			0.324032	+	0.946046i	$0.394962\pi$
$600$		0			0
$601$	0.834141	+	1.44477i	0.0340253	+	0.0589336i	0.882537	−	0.470244i	$-0.155834\pi$
$601$	0.834141	+	1.44477i	0.0340253	+	0.0589336i	−0.848511	+	0.529177i	$0.822501\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−9.24774	+	16.0176i	−0.375974	+	0.651207i
$606$		0			0
$607$	−18.2555	−	31.6194i	−0.740968	−	1.28339i	−0.952055	−	0.305926i	$-0.901034\pi$
$607$	−18.2555	−	31.6194i	−0.740968	−	1.28339i	0.211088	−	0.977467i	$-0.432299\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.40925	+	7.63705i	−0.178379	+	0.308962i
$612$		0			0
$613$	18.2957	+	31.6891i	0.738958	+	1.27991i	0.952965	+	0.303080i	$0.0980150\pi$
$613$	18.2957	+	31.6891i	0.738958	+	1.27991i	−0.214007	+	0.976832i	$0.568652\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.10936	−	8.84967i	0.205695	−	0.356274i	−0.744659	−	0.667445i	$-0.767388\pi$
$617$	5.10936	−	8.84967i	0.205695	−	0.356274i	0.950354	+	0.311171i	$0.100721\pi$
$618$		0			0
$619$	−12.3664	+	21.4193i	−0.497049	+	0.860914i	−0.999994	−	0.00340432i	$-0.998916\pi$
$619$	−12.3664	+	21.4193i	−0.497049	+	0.860914i	0.502945	+	0.864318i	$0.332250\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	5.02353	+	13.1138i	0.201264	+	0.525395i
$624$		0			0
$625$	11.9584	+	20.7125i	0.478334	+	0.828499i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−17.0838			−0.681177
$630$		0			0
$631$	−42.1420			−1.67765			−0.838823	−	0.544404i	$-0.816756\pi$
$631$	−42.1420			−1.67765			−0.838823	+	0.544404i	$0.816756\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	20.1969	+	34.9821i	0.801491	+	1.38822i
$636$		0			0
$637$	8.98411	+	2.93285i	0.355964	+	0.116204i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.16519	+	2.01817i	−0.0460222	+	0.0797128i	−0.888119	−	0.459614i	$-0.847988\pi$
$641$	−1.16519	+	2.01817i	−0.0460222	+	0.0797128i	0.842097	+	0.539327i	$0.181321\pi$
$642$		0			0
$643$	−16.5035	+	28.5850i	−0.650836	+	1.12728i	0.332085	+	0.943250i	$0.392248\pi$
$643$	−16.5035	+	28.5850i	−0.650836	+	1.12728i	−0.982920	+	0.184031i	$0.941085\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.4187	−	18.0458i	−0.409603	−	0.709452i	0.585243	−	0.810858i	$-0.300999\pi$
$647$	−10.4187	−	18.0458i	−0.409603	−	0.709452i	−0.994845	+	0.101406i	$0.967666\pi$
$648$		0			0
$649$	7.08101	−	12.2647i	0.277954	−	0.481430i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−24.4176	−	42.2925i	−0.955534	−	1.65503i	−0.733142	−	0.680075i	$-0.761947\pi$
$653$	−24.4176	−	42.2925i	−0.955534	−	1.65503i	−0.222391	−	0.974958i	$-0.571386\pi$
$654$		0			0
$655$	30.4620	−	52.7618i	1.19025	−	2.06157i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.272662	+	0.472265i	0.0106214	+	0.0183968i	0.871287	−	0.490773i	$-0.163286\pi$
$659$	0.272662	+	0.472265i	0.0106214	+	0.0183968i	−0.860666	+	0.509170i	$0.829952\pi$
$660$		0			0
$661$	−46.4250			−1.80572			−0.902861	−	0.429933i	$-0.858537\pi$
$661$	−46.4250			−1.80572			−0.902861	+	0.429933i	$0.858537\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	39.3160	−	48.4827i	1.52461	−	1.88008i
$666$		0			0
$667$	−6.86858	+	11.8967i	−0.265953	+	0.460643i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.1709	+	17.6165i	−0.392642	+	0.680076i
$672$		0			0
$673$	−16.9838	−	29.4168i	−0.654677	−	1.13393i	−0.981975	−	0.189013i	$-0.939471\pi$
$673$	−16.9838	−	29.4168i	−0.654677	−	1.13393i	0.327298	−	0.944921i	$-0.393862\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−31.2851			−1.20238			−0.601191	−	0.799105i	$-0.705307\pi$
$677$	−31.2851			−1.20238			−0.601191	+	0.799105i	$0.705307\pi$
$678$		0			0
$679$	38.9080	+	6.18999i	1.49315	+	0.237550i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.289712	+	0.501795i	0.0110855	+	0.0192007i	0.871515	−	0.490369i	$-0.163138\pi$
$683$	0.289712	+	0.501795i	0.0110855	+	0.0192007i	−0.860429	+	0.509570i	$0.829805\pi$
$684$		0			0
$685$	21.6133			0.825801
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.47915			0.246836
$690$		0			0
$691$	−2.21565			−0.0842872			−0.0421436	−	0.999112i	$-0.513419\pi$
$691$	−2.21565			−0.0842872			−0.0421436	+	0.999112i	$0.513419\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	41.9962			1.59301
$696$		0			0
$697$	−44.7387			−1.69460
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−4.74299			−0.179140			−0.0895702	−	0.995981i	$-0.528549\pi$
$701$	−4.74299			−0.179140			−0.0895702	+	0.995981i	$0.528549\pi$
$702$		0			0
$703$	−14.2432	−	24.6699i	−0.537192	−	0.930444i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	13.2559	+	34.6043i	0.498539	+	1.30143i
$708$		0			0
$709$	−23.3765			−0.877923			−0.438962	−	0.898506i	$-0.644654\pi$
$709$	−23.3765			−0.877923			−0.438962	+	0.898506i	$0.644654\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.04539	+	3.54272i	0.0766004	+	0.132676i
$714$		0			0
$715$	−4.92348	+	8.52771i	−0.184128	+	0.318918i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	13.0256	−	22.5610i	0.485772	−	0.841382i	−0.514094	−	0.857734i	$-0.671872\pi$
$719$	13.0256	−	22.5610i	0.485772	−	0.841382i	0.999866	+	0.0163516i	$0.00520511\pi$
$720$		0			0
$721$	41.9659	+	6.67649i	1.56289	+	0.248645i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−11.0584			−0.410698
$726$		0			0
$727$	−5.79712	−	10.0409i	−0.215003	−	0.372396i	0.738270	−	0.674505i	$-0.235643\pi$
$727$	−5.79712	−	10.0409i	−0.215003	−	0.372396i	−0.953274	+	0.302108i	$0.902310\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−18.8078	+	32.5761i	−0.695633	+	1.20487i
$732$		0			0
$733$	17.6743	+	30.6128i	0.652816	+	1.13071i	0.982436	+	0.186597i	$0.0597459\pi$
$733$	17.6743	+	30.6128i	0.652816	+	1.13071i	−0.329620	+	0.944114i	$0.606921\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.44210	−	5.96189i	0.126791	−	0.219609i
$738$		0			0
$739$	−4.66968	−	8.08812i	−0.171777	−	0.297526i	0.767264	−	0.641331i	$-0.221617\pi$
$739$	−4.66968	−	8.08812i	−0.171777	−	0.297526i	−0.939041	+	0.343805i	$0.888284\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−14.6308	+	25.3412i	−0.536750	+	0.929679i	0.462326	+	0.886710i	$0.347015\pi$
$743$	−14.6308	+	25.3412i	−0.536750	+	0.929679i	−0.999076	+	0.0429687i	$0.986318\pi$
$744$		0			0
$745$	−0.448120	+	0.776167i	−0.0164179	+	0.0284366i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.40056	−	6.26662i	−0.0877146	−	0.228977i
$750$		0			0
$751$	13.3106	+	23.0547i	0.485712	+	0.841278i	0.999865	−	0.0164202i	$-0.00522696\pi$
$751$	13.3106	+	23.0547i	0.485712	+	0.841278i	−0.514153	+	0.857699i	$0.671894\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	28.3012			1.02999
$756$		0			0
$757$	−35.3183			−1.28367			−0.641833	−	0.766845i	$-0.721826\pi$
$757$	−35.3183			−1.28367			−0.641833	+	0.766845i	$0.721826\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	15.7824	+	27.3359i	0.572112	+	0.990927i	0.996349	+	0.0853760i	$0.0272091\pi$
$761$	15.7824	+	27.3359i	0.572112	+	0.990927i	−0.424237	+	0.905551i	$0.639458\pi$
$762$		0			0
$763$	42.3783	+	6.74210i	1.53420	+	0.244080i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.18790	+	7.25366i	−0.151216	+	0.261914i
$768$		0			0
$769$	−23.8477	+	41.3055i	−0.859972	+	1.48951i	0.0119829	+	0.999928i	$0.496186\pi$
$769$	−23.8477	+	41.3055i	−0.859972	+	1.48951i	−0.871955	+	0.489587i	$0.837148\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−20.7219	−	35.8914i	−0.745314	−	1.29092i	−0.950048	−	0.312105i	$-0.898966\pi$
$773$	−20.7219	−	35.8914i	−0.745314	−	1.29092i	0.204733	−	0.978818i	$-0.434367\pi$
$774$		0			0
$775$	−1.64653	+	2.85188i	−0.0591452	+	0.102442i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−37.2997	−	64.6050i	−1.33640	−	2.31472i
$780$		0			0
$781$	−17.5536	+	30.4036i	−0.628116	+	1.08793i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.08148	−	5.33728i	−0.109983	−	0.190496i
$786$		0			0
$787$	26.3177			0.938125			0.469063	−	0.883165i	$-0.344592\pi$
$787$	26.3177			0.938125			0.469063	+	0.883165i	$0.344592\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.05700	+	7.98024i	0.108694	+	0.283745i
$792$		0			0
$793$	6.01533	−	10.4189i	0.213611	−	0.369984i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.42109	+	14.5858i	−0.298290	+	0.516654i	−0.975745	−	0.218911i	$-0.929750\pi$
$797$	−8.42109	+	14.5858i	−0.298290	+	0.516654i	0.677455	+	0.735565i	$0.263083\pi$
$798$		0			0
$799$	−14.4629	−	25.0504i	−0.511659	−	0.886220i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	19.9322			0.703392
$804$		0			0
$805$	19.5633	+	51.0697i	0.689516	+	1.79997i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	11.8734	+	20.5653i	0.417445	+	0.723036i	0.995682	−	0.0928330i	$-0.0295923\pi$
$809$	11.8734	+	20.5653i	0.417445	+	0.723036i	−0.578237	+	0.815869i	$0.696259\pi$
$810$		0			0
$811$	−21.9596			−0.771107			−0.385553	−	0.922686i	$-0.625989\pi$
$811$	−21.9596			−0.771107			−0.385553	+	0.922686i	$0.625989\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	77.9471			2.73037
$816$		0			0
$817$	−62.7221			−2.19437
$818$		0			0
$819$		0			0
$820$		0			0
$821$	21.2208			0.740610			0.370305	−	0.928910i	$-0.379253\pi$
$821$	21.2208			0.740610			0.370305	+	0.928910i	$0.379253\pi$
$822$		0			0
$823$	−13.0785			−0.455890			−0.227945	−	0.973674i	$-0.573201\pi$
$823$	−13.0785			−0.455890			−0.227945	+	0.973674i	$0.573201\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−25.8079			−0.897427			−0.448714	−	0.893676i	$-0.648118\pi$
$827$	−25.8079			−0.897427			−0.448714	+	0.893676i	$0.648118\pi$
$828$		0			0
$829$	−6.21392	−	10.7628i	−0.215818	−	0.373808i	0.737707	−	0.675121i	$-0.235909\pi$
$829$	−6.21392	−	10.7628i	−0.215818	−	0.373808i	−0.953525	+	0.301313i	$0.902575\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−23.0657	+	20.7108i	−0.799180	+	0.717587i
$834$		0			0
$835$	17.6145			0.609575
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.492155	+	0.852437i	0.0169911	+	0.0294294i	0.874396	−	0.485213i	$-0.161258\pi$
$839$	0.492155	+	0.852437i	0.0169911	+	0.0294294i	−0.857405	+	0.514643i	$0.827925\pi$
$840$		0			0
$841$	12.2457	−	21.2102i	0.422266	−	0.731386i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−17.8556	+	30.9268i	−0.614251	+	1.06391i
$846$		0			0
$847$	15.1257	+	2.40640i	0.519727	+	0.0826849i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	24.9578			0.855542
$852$		0			0
$853$	−4.66990	−	8.08850i	−0.159894	−	0.276945i	0.774936	−	0.632040i	$-0.217782\pi$
$853$	−4.66990	−	8.08850i	−0.159894	−	0.276945i	−0.934830	+	0.355095i	$0.884449\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.78991	+	10.0284i	−0.197779	+	0.342564i	−0.947808	−	0.318841i	$-0.896706\pi$
$857$	−5.78991	+	10.0284i	−0.197779	+	0.342564i	0.750029	+	0.661405i	$0.230040\pi$
$858$		0			0
$859$	−26.8214	−	46.4560i	−0.915134	−	1.58506i	−0.806705	−	0.590954i	$-0.798751\pi$
$859$	−26.8214	−	46.4560i	−0.915134	−	1.58506i	−0.108429	−	0.994104i	$-0.534582\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.80485	+	8.32225i	−0.163559	+	0.283293i	−0.936143	−	0.351620i	$-0.885631\pi$
$863$	−4.80485	+	8.32225i	−0.163559	+	0.283293i	0.772584	+	0.634913i	$0.218964\pi$
$864$		0			0
$865$	−20.1368	−	34.8779i	−0.684671	−	1.18588i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.14137	−	3.70896i	0.0726409	−	0.125818i
$870$		0			0
$871$	−2.03575	+	3.52602i	−0.0689788	+	0.119475i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.10748	+	1.36569i	−0.0374396	+	0.0461687i
$876$		0			0
$877$	0.532415	+	0.922170i	0.0179784	+	0.0311395i	0.874875	−	0.484349i	$-0.160944\pi$
$877$	0.532415	+	0.922170i	0.0179784	+	0.0311395i	−0.856896	+	0.515489i	$0.827610\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	20.7526			0.699171			0.349586	−	0.936904i	$-0.386322\pi$
$881$	20.7526			0.699171			0.349586	+	0.936904i	$0.386322\pi$
$882$		0			0
$883$	8.80560			0.296332			0.148166	−	0.988963i	$-0.452663\pi$
$883$	8.80560			0.296332			0.148166	+	0.988963i	$0.452663\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.0074	−	17.3334i	−0.336017	−	0.581998i	0.647663	−	0.761927i	$-0.275746\pi$
$887$	−10.0074	−	17.3334i	−0.336017	−	0.581998i	−0.983680	+	0.179929i	$0.942413\pi$
$888$		0			0
$889$	21.0686	−	25.9809i	0.706619	−	0.871370i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	24.1160	−	41.7702i	0.807013	−	1.39779i
$894$		0			0
$895$	−16.3096	+	28.2490i	−0.545169	+	0.944260i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.671304	+	1.16273i	0.0223892	+	0.0387793i
$900$		0			0
$901$	−10.6262	+	18.4051i	−0.354009	+	0.613162i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−25.9431	−	44.9347i	−0.862377	−	1.49368i
$906$		0			0
$907$	12.5307	−	21.7039i	0.416076	−	0.720665i	−0.579465	−	0.814997i	$-0.696738\pi$
$907$	12.5307	−	21.7039i	0.416076	−	0.720665i	0.995541	+	0.0943323i	$0.0300716\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	4.86265	+	8.42236i	0.161107	+	0.279045i	0.935266	−	0.353946i	$-0.115160\pi$
$911$	4.86265	+	8.42236i	0.161107	+	0.279045i	−0.774159	+	0.632991i	$0.781827\pi$
$912$		0			0
$913$	−13.7031			−0.453506
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−49.8241	−	7.92668i	−1.64534	−	0.261762i
$918$		0			0
$919$	23.2582	−	40.2844i	0.767217	−	1.32886i	−0.171849	−	0.985123i	$-0.554974\pi$
$919$	23.2582	−	40.2844i	0.767217	−	1.32886i	0.939066	−	0.343736i	$-0.111692\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	10.3817	−	17.9815i	0.341716	−	0.591870i
$924$		0			0
$925$	10.0455	+	17.3993i	0.330293	+	0.572085i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−34.4680			−1.13086			−0.565429	−	0.824797i	$-0.691289\pi$
$929$	−34.4680			−1.13086			−0.565429	+	0.824797i	$0.691289\pi$
$930$		0			0
$931$	−49.1379	−	16.0410i	−1.61043	−	0.525723i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−16.1496	−	27.9719i	−0.528148	−	0.914779i
$936$		0			0
$937$	27.1376			0.886547			0.443274	−	0.896386i	$-0.353817\pi$
$937$	27.1376			0.886547			0.443274	+	0.896386i	$0.353817\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.0390			0.327262			0.163631	−	0.986522i	$-0.447679\pi$
$941$	10.0390			0.327262			0.163631	+	0.986522i	$0.447679\pi$
$942$		0			0
$943$	65.3589			2.12838
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.0977			−0.555599			−0.277800	−	0.960639i	$-0.589605\pi$
$947$	−17.0977			−0.555599			−0.277800	+	0.960639i	$0.589605\pi$
$948$		0			0
$949$	−11.7885			−0.382669
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2.79843			0.0906500			0.0453250	−	0.998972i	$-0.485568\pi$
$953$	2.79843			0.0906500			0.0453250	+	0.998972i	$0.485568\pi$
$954$		0			0
$955$	−6.29605	−	10.9051i	−0.203736	−	0.352880i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−6.40244	−	16.7134i	−0.206746	−	0.539705i
$960$		0			0
$961$	−30.6002			−0.987103
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.17143	−	15.8854i	−0.295239	−	0.511369i
$966$		0			0
$967$	−4.97799	+	8.62213i	−0.160081	+	0.277269i	−0.934898	−	0.354917i	$-0.884509\pi$
$967$	−4.97799	+	8.62213i	−0.160081	+	0.277269i	0.774816	+	0.632186i	$0.217842\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.13634	+	1.96819i	−0.0364668	+	0.0631623i	−0.883683	−	0.468086i	$-0.844944\pi$
$971$	−1.13634	+	1.96819i	−0.0364668	+	0.0631623i	0.847216	+	0.531249i	$0.178277\pi$
$972$		0			0
$973$	−12.4404	−	32.4755i	−0.398822	−	1.04112i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−16.8466			−0.538971			−0.269485	−	0.963004i	$-0.586854\pi$
$977$	−16.8466			−0.538971			−0.269485	+	0.963004i	$0.586854\pi$
$978$		0			0
$979$	6.05828	+	10.4932i	0.193623	+	0.335366i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.7661	−	18.6475i	0.343386	−	0.594762i	−0.641673	−	0.766978i	$-0.721759\pi$
$983$	10.7661	−	18.6475i	0.343386	−	0.594762i	0.985059	+	0.172216i	$0.0550928\pi$
$984$		0			0
$985$	12.2605	+	21.2358i	0.390651	+	0.676628i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	27.4764	−	47.5905i	0.873699	−	1.51329i
$990$		0			0
$991$	16.8227	+	29.1378i	0.534392	+	0.925594i	0.999193	+	0.0401785i	$0.0127927\pi$
$991$	16.8227	+	29.1378i	0.534392	+	0.925594i	−0.464801	+	0.885415i	$0.653874\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.25033	+	12.5579i	−0.229851	+	0.398113i
$996$		0			0
$997$	−6.99406	+	12.1141i	−0.221504	+	0.383656i	−0.955265	−	0.295752i	$-0.904430\pi$
$997$	−6.99406	+	12.1141i	−0.221504	+	0.383656i	0.733761	+	0.679408i	$0.237763\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.l.2305.10		22
3.2	odd	2		1008.2.q.l.625.10		22
4.3	odd	2		1512.2.q.d.793.10		22
7.4	even	3		3024.2.t.k.1873.2		22
9.2	odd	6		1008.2.t.l.961.3		22
9.7	even	3		3024.2.t.k.289.2		22
12.11	even	2		504.2.q.c.121.2	yes	22
21.11	odd	6		1008.2.t.l.193.3		22
28.11	odd	6		1512.2.t.c.361.2		22
36.7	odd	6		1512.2.t.c.289.2		22
36.11	even	6		504.2.t.c.457.9	yes	22
63.11	odd	6		1008.2.q.l.529.10		22
63.25	even	3	inner	3024.2.q.l.2881.10		22
84.11	even	6		504.2.t.c.193.9	yes	22
252.11	even	6		504.2.q.c.25.2	✓	22
252.151	odd	6		1512.2.q.d.1369.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.2	✓	22	252.11	even	6
504.2.q.c.121.2	yes	22	12.11	even	2
504.2.t.c.193.9	yes	22	84.11	even	6
504.2.t.c.457.9	yes	22	36.11	even	6
1008.2.q.l.529.10		22	63.11	odd	6
1008.2.q.l.625.10		22	3.2	odd	2
1008.2.t.l.193.3		22	21.11	odd	6
1008.2.t.l.961.3		22	9.2	odd	6
1512.2.q.d.793.10		22	4.3	odd	2
1512.2.q.d.1369.10		22	252.151	odd	6
1512.2.t.c.289.2		22	36.7	odd	6
1512.2.t.c.361.2		22	28.11	odd	6
3024.2.q.l.2305.10		22	1.1	even	1	trivial
3024.2.q.l.2881.10		22	63.25	even	3	inner
3024.2.t.k.289.2		22	9.7	even	3
3024.2.t.k.1873.2		22	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.59750 + 2.76695i) q^{5} +(1.66645 - 2.05498i) q^{7} +O(q^{10})\)	\(q+(1.59750 + 2.76695i) q^{5} +(1.66645 - 2.05498i) q^{7} +(1.14139 - 1.97695i) q^{11} +(-0.675051 + 1.16922i) q^{13} +(-2.21425 - 3.83519i) q^{17} +(3.69214 - 6.39497i) q^{19} +(3.23479 + 5.60283i) q^{23} +(-2.60400 + 4.51026i) q^{25} +(1.06167 + 1.83887i) q^{29} +0.632308 q^{31} +(8.34818 + 1.32814i) q^{35} +(1.92885 - 3.34087i) q^{37} +(5.05124 - 8.74900i) q^{41} +(-4.24701 - 7.35603i) q^{43} +6.53173 q^{47} +(-1.44591 - 6.84904i) q^{49} +(-2.39950 - 4.15606i) q^{53} +7.29349 q^{55} +6.20383 q^{59} -8.91093 q^{61} -4.31357 q^{65} +3.01570 q^{67} -15.3791 q^{71} +(4.36577 + 7.56173i) q^{73} +(-2.16053 - 5.64002i) q^{77} +1.87610 q^{79} +(-3.00140 - 5.19857i) q^{83} +(7.07451 - 12.2534i) q^{85} +(-2.65390 + 4.59668i) q^{89} +(1.27780 + 3.33566i) q^{91} +23.5927 q^{95} +(7.44539 + 12.8958i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{5} - 5 q^{7}+O(q^{10}) \) 22 * q - q^5 - 5 * q^7	\( 22 q - q^{5} - 5 q^{7} + 3 q^{11} + 7 q^{13} + q^{17} - 13 q^{19} - 22 q^{25} + 7 q^{29} + 12 q^{31} + 2 q^{35} + 6 q^{37} - 4 q^{41} - 2 q^{43} - 34 q^{47} - 25 q^{49} - q^{53} - 2 q^{55} + 42 q^{59} - 62 q^{61} - 6 q^{65} - 52 q^{67} - 32 q^{71} + 17 q^{73} + q^{77} - 32 q^{79} - 36 q^{83} + 28 q^{85} + 2 q^{89} - 15 q^{91} + 48 q^{95} + 19 q^{97}+O(q^{100}) \) 22 * q - q^5 - 5 * q^7 + 3 * q^11 + 7 * q^13 + q^17 - 13 * q^19 - 22 * q^25 + 7 * q^29 + 12 * q^31 + 2 * q^35 + 6 * q^37 - 4 * q^41 - 2 * q^43 - 34 * q^47 - 25 * q^49 - q^53 - 2 * q^55 + 42 * q^59 - 62 * q^61 - 6 * q^65 - 52 * q^67 - 32 * q^71 + 17 * q^73 + q^77 - 32 * q^79 - 36 * q^83 + 28 * q^85 + 2 * q^89 - 15 * q^91 + 48 * q^95 + 19 * q^97

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