LMFDB - Embedded newform 504.4.s.h.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,4,Mod(289,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("504.289");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	504.s (of order $3$, degree $2$, 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:	$29.7369626429$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.11163123.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 14x^{4} + 49x^{2} + 27 $ x^6 + 14x^4 + 49x^2 + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.2
Root			$0.821510i$ of defining polynomial
Character	$\chi$	$=$	504.289
Dual form			504.4.s.h.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.34580 + 5.79509i) q^{5} +(-8.65024 - 16.3760i) q^{7} +O(q^{10})$	$q+(-3.34580 + 5.79509i) q^{5} +(-8.65024 - 16.3760i) q^{7} +(15.7441 + 27.2695i) q^{11} +18.6837 q^{13} +(-43.9769 - 76.1703i) q^{17} +(-6.54850 + 11.3423i) q^{19} +(-4.68840 + 8.12055i) q^{23} +(40.1113 + 69.4748i) q^{25} +5.11923 q^{29} +(128.706 + 222.925i) q^{31} +(123.842 + 4.66183i) q^{35} +(190.107 - 329.276i) q^{37} +217.959 q^{41} +377.049 q^{43} +(-178.855 + 309.786i) q^{47} +(-193.347 + 283.313i) q^{49} +(382.195 + 661.981i) q^{53} -210.706 q^{55} +(-225.336 - 390.293i) q^{59} +(87.0388 - 150.756i) q^{61} +(-62.5117 + 108.273i) q^{65} +(248.617 + 430.617i) q^{67} -350.238 q^{71} +(531.343 + 920.312i) q^{73} +(310.375 - 493.712i) q^{77} +(-280.224 + 485.363i) q^{79} +1105.27 q^{83} +588.551 q^{85} +(603.357 - 1045.04i) q^{89} +(-161.618 - 305.964i) q^{91} +(-43.8199 - 75.8983i) q^{95} +1442.99 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 4 q^{7}+O(q^{10}) $ 6 * q - 3 * q^5 - 4 * q^7	$ 6 q - 3 q^{5} - 4 q^{7} - 3 q^{11} - 52 q^{13} - 31 q^{17} + 89 q^{19} - 201 q^{23} - 300 q^{25} - 380 q^{29} + 339 q^{31} + 473 q^{35} + 535 q^{37} - 116 q^{41} + 536 q^{43} - 205 q^{47} - 1530 q^{49} + 757 q^{53} - 3306 q^{55} - 1799 q^{59} - 625 q^{61} - 1750 q^{65} + 495 q^{67} - 1280 q^{71} + 443 q^{73} + 1131 q^{77} - 79 q^{79} + 4744 q^{83} - 1954 q^{85} + 821 q^{89} - 1352 q^{91} - 1327 q^{95} - 684 q^{97}+O(q^{100}) $ 6 * q - 3 * q^5 - 4 * q^7 - 3 * q^11 - 52 * q^13 - 31 * q^17 + 89 * q^19 - 201 * q^23 - 300 * q^25 - 380 * q^29 + 339 * q^31 + 473 * q^35 + 535 * q^37 - 116 * q^41 + 536 * q^43 - 205 * q^47 - 1530 * q^49 + 757 * q^53 - 3306 * q^55 - 1799 * q^59 - 625 * q^61 - 1750 * q^65 + 495 * q^67 - 1280 * q^71 + 443 * q^73 + 1131 * q^77 - 79 * q^79 + 4744 * q^83 - 1954 * q^85 + 821 * q^89 - 1352 * q^91 - 1327 * q^95 - 684 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$5$	−3.34580	+	5.79509i	−0.299257	+	0.518328i	−0.975966	−	0.217922i	$-0.930072\pi$
$5$	−3.34580	+	5.79509i	−0.299257	+	0.518328i	0.676709	+	0.736250i	$0.263405\pi$
$6$		0			0
$7$	−8.65024	−	16.3760i	−0.467069	−	0.884221i
$7$	−8.65024	−	16.3760i	−0.467069	−	0.884221i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	15.7441	+	27.2695i	0.431546	+	0.747460i	0.997007	−	0.0773151i	$-0.0246348\pi$
$11$	15.7441	+	27.2695i	0.431546	+	0.747460i	−0.565460	+	0.824776i	$0.691301\pi$
$12$		0			0
$13$	18.6837			0.398609			0.199304	−	0.979938i	$-0.436132\pi$
$13$	18.6837			0.398609			0.199304	+	0.979938i	$0.436132\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−43.9769	−	76.1703i	−0.627410	−	1.08671i	−0.988070	−	0.154008i	$-0.950782\pi$
$17$	−43.9769	−	76.1703i	−0.627410	−	1.08671i	0.360660	−	0.932698i	$-0.382552\pi$
$18$		0			0
$19$	−6.54850	+	11.3423i	−0.0790700	+	0.136953i	−0.902849	−	0.429958i	$-0.858528\pi$
$19$	−6.54850	+	11.3423i	−0.0790700	+	0.136953i	0.823779	+	0.566911i	$0.191862\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.68840	+	8.12055i	−0.0425043	+	0.0736197i	−0.886495	−	0.462738i	$-0.846867\pi$
$23$	−4.68840	+	8.12055i	−0.0425043	+	0.0736197i	0.843991	+	0.536358i	$0.180200\pi$
$24$		0			0
$25$	40.1113	+	69.4748i	0.320890	+	0.555799i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.11923			0.0327799			0.0163900	−	0.999866i	$-0.494783\pi$
$29$	5.11923			0.0327799			0.0163900	+	0.999866i	$0.494783\pi$
$30$		0			0
$31$	128.706	+	222.925i	0.745685	+	1.29156i	0.949874	+	0.312633i	$0.101211\pi$
$31$	128.706	+	222.925i	0.745685	+	1.29156i	−0.204189	+	0.978932i	$0.565456\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	123.842	+	4.66183i	0.598090	+	0.0225141i
$36$		0			0
$37$	190.107	−	329.276i	0.844688	−	1.46304i	−0.0412040	−	0.999151i	$-0.513119\pi$
$37$	190.107	−	329.276i	0.844688	−	1.46304i	0.885892	−	0.463892i	$-0.153547\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	217.959			0.830230			0.415115	−	0.909769i	$-0.363741\pi$
$41$	217.959			0.830230			0.415115	+	0.909769i	$0.363741\pi$
$42$		0			0
$43$	377.049			1.33720			0.668598	−	0.743624i	$-0.266895\pi$
$43$	377.049			1.33720			0.668598	+	0.743624i	$0.266895\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−178.855	+	309.786i	−0.555079	+	0.961425i	0.442818	+	0.896611i	$0.353979\pi$
$47$	−178.855	+	309.786i	−0.555079	+	0.961425i	−0.997897	+	0.0648137i	$0.979355\pi$
$48$		0			0
$49$	−193.347	+	283.313i	−0.563693	+	0.825984i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	382.195	+	661.981i	0.990538	+	1.71566i	0.614122	+	0.789211i	$0.289510\pi$
$53$	382.195	+	661.981i	0.990538	+	1.71566i	0.376415	+	0.926451i	$0.377157\pi$
$54$		0			0
$55$	−210.706			−0.516573
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−225.336	−	390.293i	−0.497224	−	0.861216i	0.502771	−	0.864419i	$-0.332314\pi$
$59$	−225.336	−	390.293i	−0.497224	−	0.861216i	−0.999995	+	0.00320303i	$0.998980\pi$
$60$		0			0
$61$	87.0388	−	150.756i	0.182691	−	0.316431i	−0.760105	−	0.649801i	$-0.774852\pi$
$61$	87.0388	−	150.756i	0.182691	−	0.316431i	0.942796	+	0.333370i	$0.108186\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−62.5117	+	108.273i	−0.119287	+	0.206610i
$66$		0			0
$67$	248.617	+	430.617i	0.453334	+	0.785198i	0.998591	−	0.0530711i	$-0.0169010\pi$
$67$	248.617	+	430.617i	0.453334	+	0.785198i	−0.545256	+	0.838269i	$0.683568\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−350.238			−0.585432			−0.292716	−	0.956199i	$-0.594559\pi$
$71$	−350.238			−0.585432			−0.292716	+	0.956199i	$0.594559\pi$
$72$		0			0
$73$	531.343	+	920.312i	0.851903	+	1.47554i	0.879488	+	0.475920i	$0.157885\pi$
$73$	531.343	+	920.312i	0.851903	+	1.47554i	−0.0275851	+	0.999619i	$0.508782\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	310.375	−	493.712i	0.459358	−	0.730698i
$78$		0			0
$79$	−280.224	+	485.363i	−0.399085	+	0.691235i	−0.993613	−	0.112839i	$-0.964005\pi$
$79$	−280.224	+	485.363i	−0.399085	+	0.691235i	0.594528	+	0.804075i	$0.297339\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1105.27			1.46168			0.730840	−	0.682549i	$-0.239129\pi$
$83$	1105.27			1.46168			0.730840	+	0.682549i	$0.239129\pi$
$84$		0			0
$85$	588.551			0.751027
$86$		0			0
$87$		0			0
$88$		0			0
$89$	603.357	−	1045.04i	0.718604	−	1.24466i	−0.242950	−	0.970039i	$-0.578115\pi$
$89$	603.357	−	1045.04i	0.718604	−	1.24466i	0.961553	−	0.274619i	$-0.0885517\pi$
$90$		0			0
$91$	−161.618	−	305.964i	−0.186178	−	0.352458i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−43.8199	−	75.8983i	−0.0473245	−	0.0819684i
$96$		0			0
$97$	1442.99			1.51045			0.755226	−	0.655465i	$-0.227527\pi$
$97$	1442.99			1.51045			0.755226	+	0.655465i	$0.227527\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	155.961	+	270.133i	0.153651	+	0.266131i	0.932567	−	0.360997i	$-0.117564\pi$
$101$	155.961	+	270.133i	0.153651	+	0.266131i	−0.778916	+	0.627128i	$0.784230\pi$
$102$		0			0
$103$	290.816	−	503.708i	0.278203	−	0.481862i	−0.692735	−	0.721192i	$-0.743594\pi$
$103$	290.816	−	503.708i	0.278203	−	0.481862i	0.970938	+	0.239330i	$0.0769278\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−587.738	+	1017.99i	−0.531016	+	0.919748i	0.468328	+	0.883555i	$0.344856\pi$
$107$	−587.738	+	1017.99i	−0.531016	+	0.919748i	−0.999345	+	0.0361930i	$0.988477\pi$
$108$		0			0
$109$	−168.526	−	291.896i	−0.148091	−	0.256500i	0.782431	−	0.622737i	$-0.213979\pi$
$109$	−168.526	−	291.896i	−0.148091	−	0.256500i	−0.930522	+	0.366237i	$0.880646\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1168.16			0.972487			0.486243	−	0.873823i	$-0.338367\pi$
$113$	1168.16			0.972487			0.486243	+	0.873823i	$0.338367\pi$
$114$		0			0
$115$	−31.3729	−	54.3394i	−0.0254394	−	0.0440624i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−866.953	+	1379.06i	−0.667844	+	1.06234i
$120$		0			0
$121$	169.749	−	294.015i	0.127535	−	0.220898i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1373.27			−0.982629
$126$		0			0
$127$	23.4734			0.0164010			0.00820049	−	0.999966i	$-0.497390\pi$
$127$	23.4734			0.0164010			0.00820049	+	0.999966i	$0.497390\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−186.991	+	323.878i	−0.124713	+	0.216010i	−0.921621	−	0.388091i	$-0.873135\pi$
$131$	−186.991	+	323.878i	−0.124713	+	0.216010i	0.796907	+	0.604101i	$0.206468\pi$
$132$		0			0
$133$	242.388	+	9.12429i	0.158028	+	0.00594870i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	569.069	+	985.656i	0.354882	+	0.614674i	0.987098	−	0.160119i	$-0.0511877\pi$
$137$	569.069	+	985.656i	0.354882	+	0.614674i	−0.632216	+	0.774792i	$0.717854\pi$
$138$		0			0
$139$	−1229.46			−0.750224			−0.375112	−	0.926979i	$-0.622396\pi$
$139$	−1229.46			−0.750224			−0.375112	+	0.926979i	$0.622396\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	294.157	+	509.494i	0.172018	+	0.297944i
$144$		0			0
$145$	−17.1279	+	29.6664i	−0.00980962	+	0.0169908i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1481.38	−	2565.82i	0.814492	−	1.41074i	−0.0952006	−	0.995458i	$-0.530349\pi$
$149$	1481.38	−	2565.82i	0.814492	−	1.41074i	0.909692	−	0.415283i	$-0.136317\pi$
$150$		0			0
$151$	1298.85	+	2249.68i	0.699993	+	1.21242i	0.968468	+	0.249137i	$0.0801471\pi$
$151$	1298.85	+	2249.68i	0.699993	+	1.21242i	−0.268475	+	0.963287i	$0.586520\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1722.49			−0.892606
$156$		0			0
$157$	−682.492	−	1182.11i	−0.346935	−	0.600909i	0.638768	−	0.769399i	$-0.279444\pi$
$157$	−682.492	−	1182.11i	−0.346935	−	0.600909i	−0.985703	+	0.168490i	$0.946111\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	173.538	+	6.53254i	0.0849485	+	0.00319774i
$162$		0			0
$163$	−1658.74	+	2873.02i	−0.797071	+	1.38057i	0.124445	+	0.992227i	$0.460285\pi$
$163$	−1658.74	+	2873.02i	−0.797071	+	1.38057i	−0.921516	+	0.388341i	$0.873048\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3803.96			−1.76263			−0.881315	−	0.472530i	$-0.843341\pi$
$167$	−3803.96			−1.76263			−0.881315	+	0.472530i	$0.843341\pi$
$168$		0			0
$169$	−1847.92			−0.841111
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1261.15	−	2184.37i	0.554239	−	0.959970i	−0.443723	−	0.896164i	$-0.646343\pi$
$173$	1261.15	−	2184.37i	0.554239	−	0.959970i	0.997962	−	0.0638064i	$-0.0203240\pi$
$174$		0			0
$175$	790.747	−	1257.84i	0.341571	−	0.543334i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−93.5182	−	161.978i	−0.0390496	−	0.0676359i	0.845840	−	0.533437i	$-0.179100\pi$
$179$	−93.5182	−	161.978i	−0.0390496	−	0.0676359i	−0.884890	+	0.465801i	$0.845766\pi$
$180$		0			0
$181$	−457.654			−0.187940			−0.0939701	−	0.995575i	$-0.529956\pi$
$181$	−457.654			−0.187940			−0.0939701	+	0.995575i	$0.529956\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1272.12	+	2203.38i	0.505558	+	0.875652i
$186$		0			0
$187$	1384.75	−	2398.46i	0.541513	−	0.937928i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1445.80	−	2504.19i	0.547719	−	0.948676i	−0.450712	−	0.892670i	$-0.648830\pi$
$191$	1445.80	−	2504.19i	0.547719	−	0.948676i	0.998430	−	0.0560069i	$-0.0178369\pi$
$192$		0			0
$193$	−573.946	−	994.104i	−0.214060	−	0.370762i	0.738922	−	0.673791i	$-0.235335\pi$
$193$	−573.946	−	994.104i	−0.214060	−	0.370762i	−0.952981	+	0.303029i	$0.902002\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1638.22			−0.592481			−0.296240	−	0.955113i	$-0.595733\pi$
$197$	−1638.22			−0.592481			−0.296240	+	0.955113i	$0.595733\pi$
$198$		0			0
$199$	−2655.64	−	4599.70i	−0.945996	−	1.63851i	−0.753745	−	0.657167i	$-0.771755\pi$
$199$	−2655.64	−	4599.70i	−0.945996	−	1.63851i	−0.192251	−	0.981346i	$-0.561579\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−44.2826	−	83.8325i	−0.0153105	−	0.0289847i
$204$		0			0
$205$	−729.245	+	1263.09i	−0.248452	+	0.430332i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−412.400			−0.136489
$210$		0			0
$211$	−1505.74			−0.491277			−0.245639	−	0.969361i	$-0.578998\pi$
$211$	−1505.74			−0.491277			−0.245639	+	0.969361i	$0.578998\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1261.53	+	2185.03i	−0.400165	+	0.693107i
$216$		0			0
$217$	2537.28	−	4036.04i	0.793742	−	1.26260i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−821.650	−	1423.14i	−0.250091	−	0.433171i
$222$		0			0
$223$	−2520.23			−0.756802			−0.378401	−	0.925642i	$-0.623526\pi$
$223$	−2520.23			−0.756802			−0.378401	+	0.925642i	$0.623526\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−769.019	−	1331.98i	−0.224853	−	0.389456i	0.731423	−	0.681925i	$-0.238857\pi$
$227$	−769.019	−	1331.98i	−0.224853	−	0.389456i	−0.956275	+	0.292468i	$0.905523\pi$
$228$		0			0
$229$	−285.842	+	495.092i	−0.0824845	+	0.142867i	−0.904317	−	0.426863i	$-0.859619\pi$
$229$	−285.842	+	495.092i	−0.0824845	+	0.142867i	0.821832	+	0.569730i	$0.192952\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−802.101	+	1389.28i	−0.225525	+	0.390621i	−0.956477	−	0.291808i	$-0.905743\pi$
$233$	−802.101	+	1389.28i	−0.225525	+	0.390621i	0.730952	+	0.682429i	$0.239077\pi$
$234$		0			0
$235$	−1196.83	−	2072.96i	−0.332223	−	0.575426i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4699.38			1.27187			0.635936	−	0.771742i	$-0.280614\pi$
$239$	4699.38			1.27187			0.635936	+	0.771742i	$0.280614\pi$
$240$		0			0
$241$	436.304	+	755.700i	0.116617	+	0.201987i	0.918425	−	0.395595i	$-0.129462\pi$
$241$	436.304	+	755.700i	0.116617	+	0.201987i	−0.801808	+	0.597582i	$0.796128\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−994.923	−	2068.37i	−0.259442	−	0.539360i
$246$		0			0
$247$	−122.350	+	211.916i	−0.0315180	+	0.0545908i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−3126.30			−0.786176			−0.393088	−	0.919501i	$-0.628593\pi$
$251$	−3126.30			−0.786176			−0.393088	+	0.919501i	$0.628593\pi$
$252$		0			0
$253$	−295.258			−0.0733704
$254$		0			0
$255$		0			0
$256$		0			0
$257$	452.007	−	782.900i	0.109710	−	0.190023i	−0.805943	−	0.591993i	$-0.798341\pi$
$257$	452.007	−	782.900i	0.109710	−	0.190023i	0.915653	+	0.401970i	$0.131674\pi$
$258$		0			0
$259$	−7036.69	−	264.884i	−1.68818	−	0.0635487i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−46.3184	−	80.2258i	−0.0108598	−	0.0188096i	0.860544	−	0.509375i	$-0.170124\pi$
$263$	−46.3184	−	80.2258i	−0.0108598	−	0.0188096i	−0.871404	+	0.490566i	$0.836790\pi$
$264$		0			0
$265$	−5114.98			−1.18570
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2025.89	−	3508.94i	−0.459184	−	0.795330i	0.539734	−	0.841836i	$-0.318525\pi$
$269$	−2025.89	−	3508.94i	−0.459184	−	0.795330i	−0.998918	+	0.0465054i	$0.985192\pi$
$270$		0			0
$271$	−1395.65	+	2417.34i	−0.312840	+	0.541855i	−0.978976	−	0.203975i	$-0.934614\pi$
$271$	−1395.65	+	2417.34i	−0.312840	+	0.541855i	0.666136	+	0.745830i	$0.267947\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1263.03	+	2187.63i	−0.276958	+	0.479706i
$276$		0			0
$277$	1290.33	+	2234.92i	0.279886	+	0.484777i	0.971356	−	0.237628i	$-0.0763699\pi$
$277$	1290.33	+	2234.92i	0.279886	+	0.484777i	−0.691470	+	0.722405i	$0.743037\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	919.487			0.195203			0.0976014	−	0.995226i	$-0.468883\pi$
$281$	919.487			0.195203			0.0976014	+	0.995226i	$0.468883\pi$
$282$		0			0
$283$	4136.00	+	7163.77i	0.868762	+	1.50474i	0.863262	+	0.504756i	$0.168417\pi$
$283$	4136.00	+	7163.77i	0.868762	+	1.50474i	0.00550035	+	0.999985i	$0.498249\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1885.39	−	3569.29i	−0.387775	−	0.734107i
$288$		0			0
$289$	−1411.44	+	2444.68i	−0.287286	+	0.497595i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2859.38			0.570126			0.285063	−	0.958509i	$-0.407986\pi$
$293$	2859.38			0.570126			0.285063	+	0.958509i	$0.407986\pi$
$294$		0			0
$295$	3015.71			0.595191
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−87.5965	+	151.722i	−0.0169426	+	0.0293455i
$300$		0			0
$301$	−3261.56	−	6174.55i	−0.624563	−	1.18238i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	582.428	+	1008.79i	0.109343	+	0.189388i
$306$		0			0
$307$	−3542.86			−0.658638			−0.329319	−	0.944219i	$-0.606819\pi$
$307$	−3542.86			−0.658638			−0.329319	+	0.944219i	$0.606819\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−311.274	−	539.143i	−0.0567548	−	0.0983022i	0.836252	−	0.548345i	$-0.184742\pi$
$311$	−311.274	−	539.143i	−0.0567548	−	0.0983022i	−0.893007	+	0.450043i	$0.851409\pi$
$312$		0			0
$313$	3532.42	−	6118.34i	0.637905	−	1.10488i	−0.347986	−	0.937500i	$-0.613134\pi$
$313$	3532.42	−	6118.34i	0.637905	−	1.10488i	0.985892	−	0.167385i	$-0.0535322\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3229.60	+	5593.84i	−0.572217	+	0.991108i	0.424121	+	0.905605i	$0.360583\pi$
$317$	−3229.60	+	5593.84i	−0.572217	+	0.991108i	−0.996338	+	0.0855029i	$0.972750\pi$
$318$		0			0
$319$	80.5975	+	139.599i	0.0141461	+	0.0245017i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1151.93			0.198437
$324$		0			0
$325$	749.426	+	1298.04i	0.127910	+	0.221546i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6620.20	+	249.206i	1.10937	+	0.0417604i
$330$		0			0
$331$	4167.61	−	7218.51i	0.692062	−	1.19869i	−0.279099	−	0.960262i	$-0.590036\pi$
$331$	4167.61	−	7218.51i	0.692062	−	1.19869i	0.971161	−	0.238424i	$-0.0766308\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3327.29			−0.542654
$336$		0			0
$337$	5853.18			0.946122			0.473061	−	0.881030i	$-0.343149\pi$
$337$	5853.18			0.946122			0.473061	+	0.881030i	$0.343149\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4052.70	+	7019.49i	−0.643596	+	1.11474i
$342$		0			0
$343$	6312.02	+	715.521i	0.993636	+	0.112637i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3587.90	+	6214.43i	0.555069	+	0.961407i	0.997898	+	0.0648013i	$0.0206414\pi$
$347$	3587.90	+	6214.43i	0.555069	+	0.961407i	−0.442830	+	0.896606i	$0.646025\pi$
$348$		0			0
$349$	−10302.4			−1.58016			−0.790081	−	0.613003i	$-0.789961\pi$
$349$	−10302.4			−1.58016			−0.790081	+	0.613003i	$0.789961\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	550.560	+	953.599i	0.0830124	+	0.143782i	0.904543	−	0.426383i	$-0.140213\pi$
$353$	550.560	+	953.599i	0.0830124	+	0.143782i	−0.821530	+	0.570165i	$0.806879\pi$
$354$		0			0
$355$	1171.83	−	2029.66i	0.175195	−	0.303446i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2816.47	+	4878.26i	−0.414060	+	0.717172i	−0.995329	−	0.0965388i	$-0.969223\pi$
$359$	−2816.47	+	4878.26i	−0.414060	+	0.717172i	0.581270	+	0.813711i	$0.302556\pi$
$360$		0			0
$361$	3343.73	+	5791.52i	0.487496	+	0.844368i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7111.05			−1.01975
$366$		0			0
$367$	−1598.23	−	2768.22i	−0.227322	−	0.393733i	0.729692	−	0.683776i	$-0.239664\pi$
$367$	−1598.23	−	2768.22i	−0.227322	−	0.393733i	−0.957013	+	0.290044i	$0.906330\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7534.52	−	11985.1i	1.05437	−	1.67719i
$372$		0			0
$373$	−457.697	+	792.755i	−0.0635353	+	0.110046i	−0.896043	−	0.443967i	$-0.853571\pi$
$373$	−457.697	+	792.755i	−0.0635353	+	0.110046i	0.832508	+	0.554013i	$0.186904\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	95.6460			0.0130664
$378$		0			0
$379$	11767.5			1.59487			0.797437	−	0.603402i	$-0.206188\pi$
$379$	11767.5			1.59487			0.797437	+	0.603402i	$0.206188\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4207.56	−	7287.71i	0.561348	−	0.972283i	−0.436031	−	0.899932i	$-0.643616\pi$
$383$	4207.56	−	7287.71i	0.561348	−	0.972283i	0.997379	−	0.0723518i	$-0.0230504\pi$
$384$		0			0
$385$	1822.65	+	3450.51i	0.241275	+	0.456765i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1681.19	−	2911.91i	−0.219125	−	0.379536i	0.735415	−	0.677616i	$-0.236987\pi$
$389$	−1681.19	−	2911.91i	−0.219125	−	0.379536i	−0.954541	+	0.298080i	$0.903654\pi$
$390$		0			0
$391$	824.726			0.106671
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1875.15	−	3247.85i	−0.238858	−	0.413714i
$396$		0			0
$397$	2431.72	−	4211.86i	0.307417	−	0.532462i	−0.670380	−	0.742018i	$-0.733869\pi$
$397$	2431.72	−	4211.86i	0.307417	−	0.532462i	0.977797	+	0.209557i	$0.0672020\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1869.43	−	3237.94i	0.232805	−	0.403229i	−0.725828	−	0.687876i	$-0.758543\pi$
$401$	1869.43	−	3237.94i	0.232805	−	0.403229i	0.958632	+	0.284647i	$0.0918764\pi$
$402$		0			0
$403$	2404.70	+	4165.06i	0.297237	+	0.514829i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	11972.2			1.45809
$408$		0			0
$409$	7006.64	+	12135.9i	0.847081	+	1.46719i	0.883802	+	0.467862i	$0.154976\pi$
$409$	7006.64	+	12135.9i	0.847081	+	1.46719i	−0.0367205	+	0.999326i	$0.511691\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4442.22	+	7066.22i	−0.529268	+	0.841903i
$414$		0			0
$415$	−3698.01	+	6405.15i	−0.437418	+	0.757630i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8043.46			0.937826			0.468913	−	0.883244i	$-0.344646\pi$
$419$	8043.46			0.937826			0.468913	+	0.883244i	$0.344646\pi$
$420$		0			0
$421$	1832.27			0.212112			0.106056	−	0.994360i	$-0.466178\pi$
$421$	1832.27			0.212112			0.106056	+	0.994360i	$0.466178\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3527.94	−	6110.58i	0.402660	−	0.697427i
$426$		0			0
$427$	−3221.68	−	121.275i	−0.365124	−	0.0137445i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1431.63	+	2479.65i	0.159998	+	0.277124i	0.934868	−	0.354997i	$-0.115518\pi$
$431$	1431.63	+	2479.65i	0.159998	+	0.277124i	−0.774870	+	0.632121i	$0.782185\pi$
$432$		0			0
$433$	−6856.23			−0.760946			−0.380473	−	0.924792i	$-0.624239\pi$
$433$	−6856.23			−0.760946			−0.380473	+	0.924792i	$0.624239\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−61.4040	−	106.355i	−0.00672163	−	0.0116422i
$438$		0			0
$439$	2037.21	−	3528.55i	0.221482	−	0.383618i	−0.733776	−	0.679391i	$-0.762244\pi$
$439$	2037.21	−	3528.55i	0.221482	−	0.383618i	0.955258	+	0.295773i	$0.0955772\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1248.96	+	2163.27i	−0.133950	+	0.232009i	−0.925196	−	0.379490i	$-0.876100\pi$
$443$	−1248.96	+	2163.27i	−0.133950	+	0.232009i	0.791246	+	0.611498i	$0.209433\pi$
$444$		0			0
$445$	4037.42	+	6993.01i	0.430094	+	0.744945i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−9529.68			−1.00163			−0.500817	−	0.865553i	$-0.666967\pi$
$449$	−9529.68			−1.00163			−0.500817	+	0.865553i	$0.666967\pi$
$450$		0			0
$451$	3431.55	+	5943.62i	0.358283	+	0.620564i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2313.83	+	87.1001i	0.238404	+	0.00897432i
$456$		0			0
$457$	−5275.95	+	9138.22i	−0.540041	+	0.935379i	0.458860	+	0.888509i	$0.348258\pi$
$457$	−5275.95	+	9138.22i	−0.540041	+	0.935379i	−0.998901	+	0.0468699i	$0.985075\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−13103.5			−1.32384			−0.661922	−	0.749573i	$-0.730259\pi$
$461$	−13103.5			−1.32384			−0.661922	+	0.749573i	$0.730259\pi$
$462$		0			0
$463$	−816.035			−0.0819101			−0.0409550	−	0.999161i	$-0.513040\pi$
$463$	−816.035			−0.0819101			−0.0409550	+	0.999161i	$0.513040\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2294.16	+	3973.61i	−0.227326	+	0.393740i	−0.957015	−	0.290039i	$-0.906332\pi$
$467$	−2294.16	+	3973.61i	−0.227326	+	0.393740i	0.729689	+	0.683779i	$0.239665\pi$
$468$		0			0
$469$	4901.19	−	7796.30i	0.482550	−	0.767590i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5936.28	+	10281.9i	0.577062	+	0.999501i
$474$		0			0
$475$	−1050.68			−0.101491
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8690.77	+	15052.9i	0.829001	+	1.43587i	0.898822	+	0.438313i	$0.144424\pi$
$479$	8690.77	+	15052.9i	0.829001	+	1.43587i	−0.0698212	+	0.997560i	$0.522243\pi$
$480$		0			0
$481$	3551.90	−	6152.07i	0.336700	−	0.583182i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4827.96	+	8362.28i	−0.452013	+	0.782910i
$486$		0			0
$487$	8176.24	+	14161.7i	0.760781	+	1.31771i	0.942448	+	0.334352i	$0.108517\pi$
$487$	8176.24	+	14161.7i	0.760781	+	1.31771i	−0.181667	+	0.983360i	$0.558149\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13094.7			1.20358			0.601789	−	0.798655i	$-0.294455\pi$
$491$	13094.7			1.20358			0.601789	+	0.798655i	$0.294455\pi$
$492$		0			0
$493$	−225.128	−	389.933i	−0.0205664	−	0.0356221i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3029.65	+	5735.50i	0.273437	+	0.517651i
$498$		0			0
$499$	4880.53	−	8453.32i	0.437840	−	0.758362i	−0.559682	−	0.828707i	$-0.689077\pi$
$499$	4880.53	−	8453.32i	0.437840	−	0.758362i	0.997523	+	0.0703455i	$0.0224102\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−14229.0			−1.26131			−0.630657	−	0.776061i	$-0.717215\pi$
$503$	−14229.0			−1.26131			−0.630657	+	0.776061i	$0.717215\pi$
$504$		0			0
$505$	−2087.26			−0.183924
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10160.2	−	17597.9i	0.884757	−	1.53244i	0.0387650	−	0.999248i	$-0.487658\pi$
$509$	10160.2	−	17597.9i	0.884757	−	1.53244i	0.845992	−	0.533196i	$-0.179009\pi$
$510$		0			0
$511$	10474.8	−	16662.2i	0.906805	−	1.44245i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1946.02	+	3370.61i	0.166509	+	0.288401i
$516$		0			0
$517$	−11263.6			−0.958170
$518$		0			0
$519$		0			0
$520$		0			0
$521$	10092.7	+	17481.0i	0.848692	+	1.46998i	0.882376	+	0.470544i	$0.155942\pi$
$521$	10092.7	+	17481.0i	0.848692	+	1.46998i	−0.0336847	+	0.999433i	$0.510724\pi$
$522$		0			0
$523$	1355.34	−	2347.51i	0.113317	−	0.196271i	−0.803789	−	0.594915i	$-0.797186\pi$
$523$	1355.34	−	2347.51i	0.113317	−	0.196271i	0.917106	+	0.398644i	$0.130519\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	11320.2	−	19607.1i	0.935701	−	1.62068i
$528$		0			0
$529$	6039.54	+	10460.8i	0.496387	+	0.859767i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4072.27			0.330937
$534$		0			0
$535$	−3932.90	−	6811.99i	−0.317821	−	0.550482i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10769.9	−	811.977i	−0.860650	−	0.0648874i
$540$		0			0
$541$	−1828.34	+	3166.77i	−0.145298	+	0.251664i	−0.929484	−	0.368862i	$-0.879747\pi$
$541$	−1828.34	+	3166.77i	−0.145298	+	0.251664i	0.784186	+	0.620526i	$0.213081\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2255.42			0.177269
$546$		0			0
$547$	787.130			0.0615269			0.0307635	−	0.999527i	$-0.490206\pi$
$547$	787.130			0.0615269			0.0307635	+	0.999527i	$0.490206\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−33.5233	+	58.0640i	−0.00259191	+	0.00448931i
$552$		0			0
$553$	10372.3	+	390.448i	0.797605	+	0.0300245i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6228.68	−	10788.4i	−0.473820	−	0.820680i	0.525731	−	0.850651i	$-0.323792\pi$
$557$	−6228.68	−	10788.4i	−0.473820	−	0.820680i	−0.999551	+	0.0299707i	$0.990459\pi$
$558$		0			0
$559$	7044.66			0.533018
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7959.35	−	13786.0i	−0.595820	−	1.03199i	−0.993431	−	0.114436i	$-0.963494\pi$
$563$	−7959.35	−	13786.0i	−0.595820	−	1.03199i	0.397611	−	0.917554i	$-0.369839\pi$
$564$		0			0
$565$	−3908.42	+	6769.57i	−0.291023	+	0.504067i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3908.25	+	6769.28i	−0.287948	+	0.498740i	−0.973320	−	0.229453i	$-0.926306\pi$
$569$	−3908.25	+	6769.28i	−0.287948	+	0.498740i	0.685372	+	0.728193i	$0.259640\pi$
$570$		0			0
$571$	10918.9	+	18912.1i	0.800248	+	1.38607i	0.919453	+	0.393200i	$0.128632\pi$
$571$	10918.9	+	18912.1i	0.800248	+	1.38607i	−0.119206	+	0.992870i	$0.538035\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−752.232			−0.0545569
$576$		0			0
$577$	−7592.30	−	13150.3i	−0.547785	−	0.948791i	−0.998426	−	0.0560856i	$-0.982138\pi$
$577$	−7592.30	−	13150.3i	−0.547785	−	0.948791i	0.450641	−	0.892705i	$-0.351195\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−9560.87	−	18099.9i	−0.682705	−	1.29245i
$582$		0			0
$583$	−12034.6	+	20844.5i	−0.854926	+	1.48078i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21861.6			1.53718			0.768591	−	0.639740i	$-0.220958\pi$
$587$	21861.6			1.53718			0.768591	+	0.639740i	$0.220958\pi$
$588$		0			0
$589$	−3371.32			−0.235845
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−136.751	+	236.860i	−0.00946997	+	0.0164025i	−0.870722	−	0.491776i	$-0.836348\pi$
$593$	−136.751	+	236.860i	−0.00946997	+	0.0164025i	0.861252	+	0.508179i	$0.169681\pi$
$594$		0			0
$595$	−5091.11	−	9638.11i	−0.350782	−	0.664074i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1221.81	−	2116.24i	−0.0833421	−	0.144353i	0.821341	−	0.570437i	$-0.193226\pi$
$599$	−1221.81	−	2116.24i	−0.0833421	−	0.144353i	−0.904684	+	0.426084i	$0.859893\pi$
$600$		0			0
$601$	−1107.14			−0.0751431			−0.0375716	−	0.999294i	$-0.511962\pi$
$601$	−1107.14			−0.0751431			−0.0375716	+	0.999294i	$0.511962\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1135.89	+	1967.43i	0.0763317	+	0.132210i
$606$		0			0
$607$	709.429	−	1228.77i	0.0474379	−	0.0821649i	−0.841331	−	0.540520i	$-0.818228\pi$
$607$	709.429	−	1228.77i	0.0474379	−	0.0821649i	0.888769	+	0.458355i	$0.151561\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3341.67	+	5787.94i	−0.221259	+	0.383233i
$612$		0			0
$613$	−4701.49	−	8143.22i	−0.309774	−	0.536544i	0.668539	−	0.743677i	$-0.266920\pi$
$613$	−4701.49	−	8143.22i	−0.309774	−	0.536544i	−0.978313	+	0.207133i	$0.933587\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11223.0			0.732284			0.366142	−	0.930559i	$-0.380678\pi$
$617$	11223.0			0.732284			0.366142	+	0.930559i	$0.380678\pi$
$618$		0			0
$619$	−7939.57	−	13751.7i	−0.515538	−	0.892938i	−0.999837	−	0.0180360i	$-0.994259\pi$
$619$	−7939.57	−	13751.7i	−0.515538	−	0.892938i	0.484299	−	0.874903i	$-0.339075\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−22332.8	−	840.682i	−1.43619	−	0.0540629i
$624$		0			0
$625$	−419.247	+	726.156i	−0.0268318	+	0.0464740i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−33441.3			−2.11986
$630$		0			0
$631$	−9079.04			−0.572791			−0.286395	−	0.958112i	$-0.592457\pi$
$631$	−9079.04			−0.572791			−0.286395	+	0.958112i	$0.592457\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−78.5371	+	136.030i	−0.00490811	+	0.00850110i
$636$		0			0
$637$	−3612.42	+	5293.32i	−0.224693	+	0.329245i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4967.58	+	8604.10i	0.306096	+	0.530174i	0.977505	−	0.210913i	$-0.0676438\pi$
$641$	4967.58	+	8604.10i	0.306096	+	0.530174i	−0.671409	+	0.741087i	$0.734311\pi$
$642$		0			0
$643$	−21282.8			−1.30531			−0.652653	−	0.757657i	$-0.726344\pi$
$643$	−21282.8			−1.30531			−0.652653	+	0.757657i	$0.726344\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3438.07	+	5954.91i	0.208910	+	0.361842i	0.951371	−	0.308046i	$-0.0996752\pi$
$647$	3438.07	+	5954.91i	0.208910	+	0.361842i	−0.742462	+	0.669888i	$0.766342\pi$
$648$		0			0
$649$	7095.39	−	12289.6i	0.429150	−	0.743310i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−701.120	+	1214.38i	−0.0420168	+	0.0727752i	−0.886269	−	0.463171i	$-0.846712\pi$
$653$	−701.120	+	1214.38i	−0.0420168	+	0.0727752i	0.844252	+	0.535946i	$0.180045\pi$
$654$		0			0
$655$	−1251.27	−	2167.26i	−0.0746428	−	0.129285i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19975.7			−1.18079			−0.590395	−	0.807114i	$-0.701028\pi$
$659$	−19975.7			−1.18079			−0.590395	+	0.807114i	$0.701028\pi$
$660$		0			0
$661$	−328.416	−	568.832i	−0.0193251	−	0.0334720i	0.856201	−	0.516643i	$-0.172818\pi$
$661$	−328.416	−	568.832i	−0.0193251	−	0.0334720i	−0.875526	+	0.483171i	$0.839485\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−863.857	+	1374.13i	−0.0503744	+	0.0801302i
$666$		0			0
$667$	−24.0010	+	41.5710i	−0.00139329	+	0.00241325i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5481.37			0.315359
$672$		0			0
$673$	14668.1			0.840140			0.420070	−	0.907492i	$-0.362006\pi$
$673$	14668.1			0.840140			0.420070	+	0.907492i	$0.362006\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9605.04	−	16636.4i	0.545276	−	0.944446i	−0.453314	−	0.891351i	$-0.649758\pi$
$677$	9605.04	−	16636.4i	0.545276	−	0.944446i	0.998589	−	0.0530944i	$-0.0169084\pi$
$678$		0			0
$679$	−12482.2	−	23630.5i	−0.705485	−	1.33557i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9223.01	+	15974.7i	0.516704	+	0.894957i	0.999812	+	0.0193965i	$0.00617449\pi$
$683$	9223.01	+	15974.7i	0.516704	+	0.894957i	−0.483108	+	0.875561i	$0.660492\pi$
$684$		0			0
$685$	−7615.95			−0.424804
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7140.80	+	12368.2i	0.394837	+	0.683878i
$690$		0			0
$691$	12451.0	−	21565.7i	0.685467	−	1.18726i	−0.287822	−	0.957684i	$-0.592931\pi$
$691$	12451.0	−	21565.7i	0.685467	−	1.18726i	0.973290	−	0.229581i	$-0.0737355\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4113.51	−	7124.81i	0.224510	−	0.388863i
$696$		0			0
$697$	−9585.15	−	16602.0i	−0.520894	−	0.902216i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−22637.7			−1.21970			−0.609852	−	0.792515i	$-0.708771\pi$
$701$	−22637.7			−1.21970			−0.609852	+	0.792515i	$0.708771\pi$
$702$		0			0
$703$	2489.84	+	4312.52i	0.133579	+	0.231365i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3074.59	−	4890.73i	0.163553	−	0.260163i
$708$		0			0
$709$	−3.49494	+	6.05341i	−0.000185127	+	0.000320650i	−0.866118	−	0.499840i	$-0.833392\pi$
$709$	−3.49494	+	6.05341i	−0.000185127	+	0.000320650i	0.865933	+	0.500160i	$0.166726\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2413.70			−0.126779
$714$		0			0
$715$	−3936.75			−0.205911
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9509.80	+	16471.5i	−0.493262	+	0.854355i	−0.999970	−	0.00776257i	$-0.997529\pi$
$719$	−9509.80	+	16471.5i	−0.493262	+	0.854355i	0.506708	+	0.862118i	$0.330862\pi$
$720$		0			0
$721$	−10764.3	−	405.206i	−0.556013	−	0.0209302i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	205.339	+	355.658i	0.0105188	+	0.0182190i
$726$		0			0
$727$	−33880.6			−1.72842			−0.864210	−	0.503130i	$-0.832182\pi$
$727$	−33880.6			−1.72842			−0.864210	+	0.503130i	$0.832182\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−16581.5	−	28719.9i	−0.838970	−	1.45314i
$732$		0			0
$733$	5222.71	−	9045.99i	0.263172	−	0.455827i	−0.703911	−	0.710288i	$-0.748565\pi$
$733$	5222.71	−	9045.99i	0.263172	−	0.455827i	0.967083	+	0.254461i	$0.0818980\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7828.48	+	13559.3i	−0.391270	+	0.677699i
$738$		0			0
$739$	12837.3	+	22234.8i	0.639007	+	1.10679i	0.985651	+	0.168796i	$0.0539880\pi$
$739$	12837.3	+	22234.8i	0.639007	+	1.10679i	−0.346644	+	0.937997i	$0.612679\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	30646.2			1.51319			0.756596	−	0.653883i	$-0.226861\pi$
$743$	30646.2			1.51319			0.756596	+	0.653883i	$0.226861\pi$
$744$		0			0
$745$	9912.78	+	17169.4i	0.487485	+	0.844348i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	21754.7	+	818.919i	1.06128	+	0.0399501i
$750$		0			0
$751$	4355.95	−	7544.73i	0.211652	−	0.366593i	−0.740579	−	0.671969i	$-0.765449\pi$
$751$	4355.95	−	7544.73i	0.211652	−	0.366593i	0.952232	+	0.305376i	$0.0987822\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−17382.8			−0.837912
$756$		0			0
$757$	−18830.7			−0.904114			−0.452057	−	0.891989i	$-0.649310\pi$
$757$	−18830.7			−0.904114			−0.452057	+	0.891989i	$0.649310\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	10900.3	−	18879.9i	0.519232	−	0.899336i	−0.480518	−	0.876985i	$-0.659551\pi$
$761$	10900.3	−	18879.9i	0.519232	−	0.899336i	0.999750	−	0.0223513i	$-0.00711523\pi$
$762$		0			0
$763$	−3322.29	+	5284.75i	−0.157634	+	0.250748i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4210.09	−	7292.10i	−0.198198	−	0.343289i
$768$		0			0
$769$	4412.21			0.206903			0.103452	−	0.994634i	$-0.467011\pi$
$769$	4412.21			0.206903			0.103452	+	0.994634i	$0.467011\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−15223.4	−	26367.7i	−0.708342	−	1.22688i	−0.965472	−	0.260507i	$-0.916110\pi$
$773$	−15223.4	−	26367.7i	−0.708342	−	1.22688i	0.257130	−	0.966377i	$-0.417223\pi$
$774$		0			0
$775$	−10325.1	+	17883.6i	−0.478567	+	0.828902i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1427.30	+	2472.16i	−0.0656462	+	0.113703i
$780$		0			0
$781$	−5514.17	−	9550.83i	−0.252641	−	0.437587i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	9133.92			0.415291
$786$		0			0
$787$	5606.01	+	9709.90i	0.253917	+	0.439797i	0.964601	−	0.263714i	$-0.0849476\pi$
$787$	5606.01	+	9709.90i	0.253917	+	0.439797i	−0.710684	+	0.703512i	$0.751614\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−10104.8	−	19129.7i	−0.454219	−	0.859893i
$792$		0			0
$793$	1626.20	−	2816.67i	0.0728224	−	0.126132i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11809.3			0.524852			0.262426	−	0.964952i	$-0.415477\pi$
$797$	11809.3			0.524852			0.262426	+	0.964952i	$0.415477\pi$
$798$		0			0
$799$	31462.0			1.39305
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−16731.0	+	28978.9i	−0.735272	+	1.27353i
$804$		0			0
$805$	−618.479	+	983.811i	−0.0270789	+	0.0430743i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	7163.83	+	12408.1i	0.311331	+	0.539241i	0.978651	−	0.205530i	$-0.0658919\pi$
$809$	7163.83	+	12408.1i	0.311331	+	0.539241i	−0.667320	+	0.744771i	$0.732559\pi$
$810$		0			0
$811$	−32413.9			−1.40346			−0.701730	−	0.712443i	$-0.747589\pi$
$811$	−32413.9			−1.40346			−0.701730	+	0.712443i	$0.747589\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−11099.6	−	19225.1i	−0.477058	−	0.826289i
$816$		0			0
$817$	−2469.11	+	4276.62i	−0.105732	+	0.183133i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1203.08	−	2083.80i	0.0511423	−	0.0885810i	−0.839321	−	0.543636i	$-0.817047\pi$
$821$	1203.08	−	2083.80i	0.0511423	−	0.0885810i	0.890463	+	0.455055i	$0.150380\pi$
$822$		0			0
$823$	980.182	+	1697.72i	0.0415152	+	0.0719064i	0.886036	−	0.463616i	$-0.153448\pi$
$823$	980.182	+	1697.72i	0.0415152	+	0.0719064i	−0.844521	+	0.535522i	$0.820115\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−17517.2			−0.736557			−0.368278	−	0.929716i	$-0.620053\pi$
$827$	−17517.2			−0.736557			−0.368278	+	0.929716i	$0.620053\pi$
$828$		0			0
$829$	−16749.4	−	29010.8i	−0.701724	−	1.21542i	−0.967861	−	0.251487i	$-0.919080\pi$
$829$	−16749.4	−	29010.8i	−0.701724	−	1.21542i	0.266136	−	0.963935i	$-0.414253\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	30082.8	+	2268.05i	1.25127	+	0.0943375i
$834$		0			0
$835$	12727.3	−	22044.3i	0.527479	−	0.913621i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1609.45			0.0662268			0.0331134	−	0.999452i	$-0.489458\pi$
$839$	1609.45			0.0662268			0.0331134	+	0.999452i	$0.489458\pi$
$840$		0			0
$841$	−24362.8			−0.998925
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6182.76	−	10708.9i	0.251708	−	0.435972i
$846$		0			0
$847$	−6283.16	−	236.519i	−0.254890	−	0.00959490i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1782.60	+	3087.55i	0.0718058	+	0.124371i
$852$		0			0
$853$	−20446.9			−0.820739			−0.410369	−	0.911919i	$-0.634600\pi$
$853$	−20446.9			−0.820739			−0.410369	+	0.911919i	$0.634600\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2892.11	−	5009.28i	−0.115277	−	0.199666i	0.802613	−	0.596500i	$-0.203442\pi$
$857$	−2892.11	−	5009.28i	−0.115277	−	0.199666i	−0.917891	+	0.396834i	$0.870109\pi$
$858$		0			0
$859$	−16180.7	+	28025.7i	−0.642697	+	1.11318i	0.342131	+	0.939652i	$0.388851\pi$
$859$	−16180.7	+	28025.7i	−0.642697	+	1.11318i	−0.984828	+	0.173532i	$0.944482\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−14415.6	+	24968.6i	−0.568614	+	0.984868i	0.428089	+	0.903736i	$0.359187\pi$
$863$	−14415.6	+	24968.6i	−0.568614	+	0.984868i	−0.996703	+	0.0811320i	$0.974146\pi$
$864$		0			0
$865$	8439.09	+	14616.9i	0.331720	+	0.574556i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−17647.5			−0.688895
$870$		0			0
$871$	4645.08	+	8045.51i	0.180703	+	0.312987i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	11879.1	+	22488.6i	0.458956	+	0.868861i
$876$		0			0
$877$	6552.70	−	11349.6i	0.252302	−	0.437000i	−0.711857	−	0.702324i	$-0.752146\pi$
$877$	6552.70	−	11349.6i	0.252302	−	0.437000i	0.964159	+	0.265324i	$0.0854790\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	3089.10			0.118132			0.0590661	−	0.998254i	$-0.481188\pi$
$881$	3089.10			0.118132			0.0590661	+	0.998254i	$0.481188\pi$
$882$		0			0
$883$	1601.96			0.0610536			0.0305268	−	0.999534i	$-0.490282\pi$
$883$	1601.96			0.0610536			0.0305268	+	0.999534i	$0.490282\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−11285.2	+	19546.6i	−0.427194	+	0.739921i	−0.996622	−	0.0821197i	$-0.973831\pi$
$887$	−11285.2	+	19546.6i	−0.427194	+	0.739921i	0.569429	+	0.822041i	$0.307164\pi$
$888$		0			0
$889$	−203.050	−	384.400i	−0.00766039	−	0.0145021i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2342.47	−	4057.27i	−0.0877801	−	0.152040i
$894$		0			0
$895$	1251.57			0.0467435
$896$		0			0
$897$		0			0
$898$		0			0
$899$	658.875	+	1141.20i	0.0244435	+	0.0423374i
$900$		0			0
$901$	33615.5	−	58223.8i	1.24295	−	2.15285i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1531.22	−	2652.15i	0.0562424	−	0.0974147i
$906$		0			0
$907$	−24172.1	−	41867.4i	−0.884920	−	1.53273i	−0.845805	−	0.533492i	$-0.820880\pi$
$907$	−24172.1	−	41867.4i	−0.884920	−	1.53273i	−0.0391146	−	0.999235i	$-0.512454\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−14697.9			−0.534539			−0.267269	−	0.963622i	$-0.586121\pi$
$911$	−14697.9			−0.534539			−0.267269	+	0.963622i	$0.586121\pi$
$912$		0			0
$913$	17401.5	+	30140.2i	0.630783	+	1.09255i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6921.34	+	260.542i	0.249250	+	0.00938261i
$918$		0			0
$919$	−7665.28	+	13276.7i	−0.275141	+	0.476558i	−0.970171	−	0.242423i	$-0.922058\pi$
$919$	−7665.28	+	13276.7i	−0.275141	+	0.476558i	0.695030	+	0.718981i	$0.255391\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6543.74			−0.233358
$924$		0			0
$925$	30501.8			1.08421
$926$		0			0
$927$		0			0
$928$		0			0
$929$	27955.2	−	48419.7i	0.987275	−	1.71001i	0.355922	−	0.934516i	$-0.384167\pi$
$929$	27955.2	−	48419.7i	0.987275	−	1.71001i	0.631353	−	0.775495i	$-0.282500\pi$
$930$		0			0
$931$	−1947.30	−	4048.28i	−0.0685500	−	0.142510i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	9266.18	+	16049.5i	0.324103	+	0.561363i
$936$		0			0
$937$	18627.7			0.649457			0.324728	−	0.945807i	$-0.394727\pi$
$937$	18627.7			0.649457			0.324728	+	0.945807i	$0.394727\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20282.3	+	35130.0i	0.702641	+	1.21701i	0.967536	+	0.252732i	$0.0813292\pi$
$941$	20282.3	+	35130.0i	0.702641	+	1.21701i	−0.264896	+	0.964277i	$0.585337\pi$
$942$		0			0
$943$	−1021.88	+	1769.94i	−0.0352884	+	0.0611212i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13345.1	−	23114.3i	0.457926	−	0.793151i	−0.540925	−	0.841071i	$-0.681926\pi$
$947$	13345.1	−	23114.3i	0.457926	−	0.793151i	0.998851	+	0.0479196i	$0.0152591\pi$
$948$		0			0
$949$	9927.43	+	17194.8i	0.339576	+	0.588163i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	7182.06			0.244123			0.122062	−	0.992523i	$-0.461049\pi$
$953$	7182.06			0.244123			0.122062	+	0.992523i	$0.461049\pi$
$954$		0			0
$955$	9674.69	+	16757.0i	0.327817	+	0.567796i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	11218.5	−	17845.2i	0.377753	−	0.600889i
$960$		0			0
$961$	−18234.9	+	31583.7i	−0.612093	+	1.06018i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	7681.22			0.256236
$966$		0			0
$967$	18129.4			0.602898			0.301449	−	0.953482i	$-0.402530\pi$
$967$	18129.4			0.602898			0.301449	+	0.953482i	$0.402530\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−10488.0	+	18165.8i	−0.346629	+	0.600378i	−0.985648	−	0.168812i	$-0.946007\pi$
$971$	−10488.0	+	18165.8i	−0.346629	+	0.600378i	0.639020	+	0.769190i	$0.279340\pi$
$972$		0			0
$973$	10635.1	+	20133.6i	0.350407	+	0.663364i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−22347.4	−	38706.8i	−0.731786	−	1.26749i	−0.956119	−	0.292979i	$-0.905354\pi$
$977$	−22347.4	−	38706.8i	−0.731786	−	1.26749i	0.224333	−	0.974513i	$-0.427980\pi$
$978$		0			0
$979$	37997.1			1.24044
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7713.11	+	13359.5i	0.250265	+	0.433471i	0.963599	−	0.267353i	$-0.0861490\pi$
$983$	7713.11	+	13359.5i	0.250265	+	0.433471i	−0.713334	+	0.700824i	$0.752816\pi$
$984$		0			0
$985$	5481.17	−	9493.66i	0.177304	−	0.307100i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1767.76	+	3061.85i	−0.0568366	+	0.0984439i
$990$		0			0
$991$	−14124.0	−	24463.5i	−0.452739	−	0.784167i	0.545816	−	0.837905i	$-0.316220\pi$
$991$	−14124.0	−	24463.5i	−0.452739	−	0.784167i	−0.998555	+	0.0537377i	$0.982887\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	35540.9			1.13238
$996$		0			0
$997$	18560.8	+	32148.2i	0.589594	+	1.02121i	0.994285	+	0.106754i	$0.0340457\pi$
$997$	18560.8	+	32148.2i	0.589594	+	1.02121i	−0.404691	+	0.914453i	$0.632621\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.4.s.h.289.2		6
3.2	odd	2		56.4.i.b.9.1	✓	6
7.4	even	3	inner	504.4.s.h.361.2		6
12.11	even	2		112.4.i.e.65.3		6
21.2	odd	6		392.4.a.i.1.3		3
21.5	even	6		392.4.a.l.1.1		3
21.11	odd	6		56.4.i.b.25.1	yes	6
21.17	even	6		392.4.i.m.361.3		6
21.20	even	2		392.4.i.m.177.3		6
24.5	odd	2		448.4.i.j.65.3		6
24.11	even	2		448.4.i.m.65.1		6
84.11	even	6		112.4.i.e.81.3		6
84.23	even	6		784.4.a.be.1.1		3
84.47	odd	6		784.4.a.bb.1.3		3
168.11	even	6		448.4.i.m.193.1		6
168.53	odd	6		448.4.i.j.193.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.4.i.b.9.1	✓	6	3.2	odd	2
56.4.i.b.25.1	yes	6	21.11	odd	6
112.4.i.e.65.3		6	12.11	even	2
112.4.i.e.81.3		6	84.11	even	6
392.4.a.i.1.3		3	21.2	odd	6
392.4.a.l.1.1		3	21.5	even	6
392.4.i.m.177.3		6	21.20	even	2
392.4.i.m.361.3		6	21.17	even	6
448.4.i.j.65.3		6	24.5	odd	2
448.4.i.j.193.3		6	168.53	odd	6
448.4.i.m.65.1		6	24.11	even	2
448.4.i.m.193.1		6	168.11	even	6
504.4.s.h.289.2		6	1.1	even	1	trivial
504.4.s.h.361.2		6	7.4	even	3	inner
784.4.a.bb.1.3		3	84.47	odd	6
784.4.a.be.1.1		3	84.23	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	504.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.34580 + 5.79509i) q^{5} +(-8.65024 - 16.3760i) q^{7} +O(q^{10})\)	\(q+(-3.34580 + 5.79509i) q^{5} +(-8.65024 - 16.3760i) q^{7} +(15.7441 + 27.2695i) q^{11} +18.6837 q^{13} +(-43.9769 - 76.1703i) q^{17} +(-6.54850 + 11.3423i) q^{19} +(-4.68840 + 8.12055i) q^{23} +(40.1113 + 69.4748i) q^{25} +5.11923 q^{29} +(128.706 + 222.925i) q^{31} +(123.842 + 4.66183i) q^{35} +(190.107 - 329.276i) q^{37} +217.959 q^{41} +377.049 q^{43} +(-178.855 + 309.786i) q^{47} +(-193.347 + 283.313i) q^{49} +(382.195 + 661.981i) q^{53} -210.706 q^{55} +(-225.336 - 390.293i) q^{59} +(87.0388 - 150.756i) q^{61} +(-62.5117 + 108.273i) q^{65} +(248.617 + 430.617i) q^{67} -350.238 q^{71} +(531.343 + 920.312i) q^{73} +(310.375 - 493.712i) q^{77} +(-280.224 + 485.363i) q^{79} +1105.27 q^{83} +588.551 q^{85} +(603.357 - 1045.04i) q^{89} +(-161.618 - 305.964i) q^{91} +(-43.8199 - 75.8983i) q^{95} +1442.99 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 4 q^{7}+O(q^{10}) \) 6 * q - 3 * q^5 - 4 * q^7	\( 6 q - 3 q^{5} - 4 q^{7} - 3 q^{11} - 52 q^{13} - 31 q^{17} + 89 q^{19} - 201 q^{23} - 300 q^{25} - 380 q^{29} + 339 q^{31} + 473 q^{35} + 535 q^{37} - 116 q^{41} + 536 q^{43} - 205 q^{47} - 1530 q^{49} + 757 q^{53} - 3306 q^{55} - 1799 q^{59} - 625 q^{61} - 1750 q^{65} + 495 q^{67} - 1280 q^{71} + 443 q^{73} + 1131 q^{77} - 79 q^{79} + 4744 q^{83} - 1954 q^{85} + 821 q^{89} - 1352 q^{91} - 1327 q^{95} - 684 q^{97}+O(q^{100}) \) 6 * q - 3 * q^5 - 4 * q^7 - 3 * q^11 - 52 * q^13 - 31 * q^17 + 89 * q^19 - 201 * q^23 - 300 * q^25 - 380 * q^29 + 339 * q^31 + 473 * q^35 + 535 * q^37 - 116 * q^41 + 536 * q^43 - 205 * q^47 - 1530 * q^49 + 757 * q^53 - 3306 * q^55 - 1799 * q^59 - 625 * q^61 - 1750 * q^65 + 495 * q^67 - 1280 * q^71 + 443 * q^73 + 1131 * q^77 - 79 * q^79 + 4744 * q^83 - 1954 * q^85 + 821 * q^89 - 1352 * q^91 - 1327 * q^95 - 684 * q^97

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