LMFDB - Embedded newform 1008.3.cd.f.415.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,3,Mod(415,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1008.415");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1008.cd (of order $6$, 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:	$27.4660106475$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.2
Root			$2.13746 - 0.656712i$ of defining polynomial
Character	$\chi$	$=$	1008.415
Dual form			1008.3.cd.f.991.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63746 - 2.83616i) q^{5} +(-6.77492 + 1.76082i) q^{7} +O(q^{10})$	$q+(1.63746 - 2.83616i) q^{5} +(-6.77492 + 1.76082i) q^{7} +(-16.1873 + 9.34574i) q^{11} +10.2749 q^{13} +(-12.5498 - 21.7370i) q^{17} +(26.7870 + 15.4655i) q^{19} +(-4.54983 - 2.62685i) q^{23} +(7.13746 + 12.3624i) q^{25} +42.0241 q^{29} +(45.1495 - 26.0671i) q^{31} +(-6.09967 + 22.0980i) q^{35} +(-17.9622 + 31.1115i) q^{37} +38.7492 q^{41} -31.5380i q^{43} +(21.0000 + 12.1244i) q^{47} +(42.7990 - 23.8589i) q^{49} +(-32.8127 - 56.8333i) q^{53} +61.2130i q^{55} +(38.8368 - 22.4224i) q^{59} +(31.5498 - 54.6459i) q^{61} +(16.8248 - 29.1413i) q^{65} +(-19.2371 + 11.1066i) q^{67} +97.5703i q^{71} +(-45.8625 - 79.4363i) q^{73} +(93.2114 - 91.8196i) q^{77} +(8.02575 + 4.63367i) q^{79} -51.1976i q^{83} -82.1993 q^{85} +(-26.7251 + 46.2892i) q^{89} +(-69.6117 + 18.0923i) q^{91} +(87.7251 - 50.6481i) q^{95} +129.522 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{5} - 12 q^{7}+O(q^{10}) $ 4 * q - q^5 - 12 * q^7	$ 4 q - q^{5} - 12 q^{7} - 27 q^{11} + 26 q^{13} - 20 q^{17} + 9 q^{19} + 12 q^{23} + 21 q^{25} + 2 q^{29} + 90 q^{31} + 36 q^{35} - 19 q^{37} + 4 q^{41} + 84 q^{47} - 10 q^{49} - 169 q^{53} + 27 q^{59} + 96 q^{61} + 22 q^{65} - 9 q^{67} - 191 q^{73} + 169 q^{77} + 168 q^{79} - 208 q^{85} - 122 q^{89} - 135 q^{91} + 366 q^{95} + 50 q^{97}+O(q^{100}) $ 4 * q - q^5 - 12 * q^7 - 27 * q^11 + 26 * q^13 - 20 * q^17 + 9 * q^19 + 12 * q^23 + 21 * q^25 + 2 * q^29 + 90 * q^31 + 36 * q^35 - 19 * q^37 + 4 * q^41 + 84 * q^47 - 10 * q^49 - 169 * q^53 + 27 * q^59 + 96 * q^61 + 22 * q^65 - 9 * q^67 - 191 * q^73 + 169 * q^77 + 168 * q^79 - 208 * q^85 - 122 * q^89 - 135 * q^91 + 366 * q^95 + 50 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.63746	−	2.83616i	0.327492	−	0.567232i	−0.654522	−	0.756043i	$-0.727130\pi$
$5$	1.63746	−	2.83616i	0.327492	−	0.567232i	0.982013	+	0.188811i	$0.0604633\pi$
$6$		0			0
$7$	−6.77492	+	1.76082i	−0.967845	+	0.251546i
$7$	−6.77492	+	1.76082i	−0.967845	+	0.251546i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−16.1873	+	9.34574i	−1.47157	+	0.849613i	−0.999490	−	0.0319419i	$-0.989831\pi$
$11$	−16.1873	+	9.34574i	−1.47157	+	0.849613i	−0.472082	+	0.881554i	$0.656498\pi$
$12$		0			0
$13$	10.2749			0.790378			0.395189	−	0.918600i	$-0.370679\pi$
$13$	10.2749			0.790378			0.395189	+	0.918600i	$0.370679\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−12.5498	−	21.7370i	−0.738226	−	1.27864i	−0.953294	−	0.302045i	$-0.902331\pi$
$17$	−12.5498	−	21.7370i	−0.738226	−	1.27864i	0.215068	−	0.976599i	$-0.431003\pi$
$18$		0			0
$19$	26.7870	+	15.4655i	1.40984	+	0.813972i	0.995372	−	0.0960925i	$-0.0306345\pi$
$19$	26.7870	+	15.4655i	1.40984	+	0.813972i	0.414468	+	0.910064i	$0.363968\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.54983	−	2.62685i	−0.197819	−	0.114211i	0.397819	−	0.917464i	$-0.369767\pi$
$23$	−4.54983	−	2.62685i	−0.197819	−	0.114211i	−0.595638	+	0.803253i	$0.703101\pi$
$24$		0			0
$25$	7.13746	+	12.3624i	0.285498	+	0.494498i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	42.0241			1.44911			0.724553	−	0.689219i	$-0.242046\pi$
$29$	42.0241			1.44911			0.724553	+	0.689219i	$0.242046\pi$
$30$		0			0
$31$	45.1495	−	26.0671i	1.45644	−	0.840873i	0.457602	−	0.889157i	$-0.348708\pi$
$31$	45.1495	−	26.0671i	1.45644	−	0.840873i	0.998834	+	0.0482837i	$0.0153752\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.09967	+	22.0980i	−0.174276	+	0.631372i
$36$		0			0
$37$	−17.9622	+	31.1115i	−0.485465	+	0.840850i	−0.999860	−	0.0167029i	$-0.994683\pi$
$37$	−17.9622	+	31.1115i	−0.485465	+	0.840850i	0.514395	+	0.857553i	$0.328016\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	38.7492			0.945102			0.472551	−	0.881303i	$-0.343333\pi$
$41$	38.7492			0.945102			0.472551	+	0.881303i	$0.343333\pi$
$42$		0			0
$43$		−	31.5380i		−	0.733442i	−0.930331	−	0.366721i	$-0.880480\pi$
$43$		−	31.5380i		−	0.733442i	0.930331	−	0.366721i	$-0.119520\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	21.0000	+	12.1244i	0.446809	+	0.257965i	0.706481	−	0.707732i	$-0.250281\pi$
$47$	21.0000	+	12.1244i	0.446809	+	0.257965i	−0.259673	+	0.965697i	$0.583615\pi$
$48$		0			0
$49$	42.7990	−	23.8589i	0.873449	−	0.486915i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−32.8127	−	56.8333i	−0.619108	−	1.07233i	−0.989649	−	0.143510i	$-0.954161\pi$
$53$	−32.8127	−	56.8333i	−0.619108	−	1.07233i	0.370541	−	0.928816i	$-0.379172\pi$
$54$		0			0
$55$			61.2130i			1.11296i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	38.8368	−	22.4224i	0.658251	−	0.380041i	−0.133359	−	0.991068i	$-0.542576\pi$
$59$	38.8368	−	22.4224i	0.658251	−	0.380041i	0.791610	+	0.611026i	$0.209243\pi$
$60$		0			0
$61$	31.5498	−	54.6459i	0.517210	−	0.895835i	−0.482590	−	0.875846i	$-0.660304\pi$
$61$	31.5498	−	54.6459i	0.517210	−	0.895835i	0.999800	−	0.0199882i	$-0.00636287\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	16.8248	−	29.1413i	0.258842	−	0.448328i
$66$		0			0
$67$	−19.2371	+	11.1066i	−0.287121	+	0.165770i	−0.636643	−	0.771159i	$-0.719677\pi$
$67$	−19.2371	+	11.1066i	−0.287121	+	0.165770i	0.349522	+	0.936928i	$0.386344\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			97.5703i			1.37423i	0.726549	+	0.687115i	$0.241123\pi$
$71$			97.5703i			1.37423i	−0.726549	+	0.687115i	$0.758877\pi$
$72$		0			0
$73$	−45.8625	−	79.4363i	−0.628254	−	1.08817i	−0.987902	−	0.155080i	$-0.950437\pi$
$73$	−45.8625	−	79.4363i	−0.628254	−	1.08817i	0.359648	−	0.933088i	$-0.382897\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	93.2114	−	91.8196i	1.21054	−	1.19246i
$78$		0			0
$79$	8.02575	+	4.63367i	0.101592	+	0.0586540i	0.549935	−	0.835207i	$-0.314652\pi$
$79$	8.02575	+	4.63367i	0.101592	+	0.0586540i	−0.448343	+	0.893861i	$0.647986\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	51.1976i		−	0.616839i	−0.951250	−	0.308419i	$-0.900200\pi$
$83$		−	51.1976i		−	0.616839i	0.951250	−	0.308419i	$-0.0998000\pi$
$84$		0			0
$85$	−82.1993			−0.967051
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−26.7251	+	46.2892i	−0.300282	+	0.520103i	−0.976200	−	0.216874i	$-0.930414\pi$
$89$	−26.7251	+	46.2892i	−0.300282	+	0.520103i	0.675918	+	0.736977i	$0.263747\pi$
$90$		0			0
$91$	−69.6117	+	18.0923i	−0.764964	+	0.198817i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	87.7251	−	50.6481i	0.923422	−	0.533138i
$96$		0			0
$97$	129.522			1.33528			0.667641	−	0.744483i	$-0.267304\pi$
$97$	129.522			1.33528			0.667641	+	0.744483i	$0.267304\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	26.8488	+	46.5036i	0.265830	+	0.460431i	0.967781	−	0.251794i	$-0.0810206\pi$
$101$	26.8488	+	46.5036i	0.265830	+	0.460431i	−0.701951	+	0.712226i	$0.747687\pi$
$102$		0			0
$103$	−27.8111	−	16.0567i	−0.270010	−	0.155890i	0.358882	−	0.933383i	$-0.383158\pi$
$103$	−27.8111	−	16.0567i	−0.270010	−	0.155890i	−0.628892	+	0.777492i	$0.716491\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	49.5860	+	28.6285i	0.463420	+	0.267556i	0.713481	−	0.700674i	$-0.247117\pi$
$107$	49.5860	+	28.6285i	0.463420	+	0.267556i	−0.250061	+	0.968230i	$0.580451\pi$
$108$		0			0
$109$	70.6873	+	122.434i	0.648507	+	1.12325i	0.983479	+	0.181020i	$0.0579397\pi$
$109$	70.6873	+	122.434i	0.648507	+	1.12325i	−0.334972	+	0.942228i	$0.608727\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	72.1512			0.638506			0.319253	−	0.947670i	$-0.396568\pi$
$113$	72.1512			0.638506			0.319253	+	0.947670i	$0.396568\pi$
$114$		0			0
$115$	−14.9003	+	8.60271i	−0.129568	+	0.0748062i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	123.299	+	125.168i	1.03613	+	1.05183i
$120$		0			0
$121$	114.186	−	197.775i	0.943683	−	1.63451i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	128.622			1.02898
$126$		0			0
$127$			150.887i			1.18809i	0.804433	+	0.594043i	$0.202469\pi$
$127$			150.887i			1.18809i	−0.804433	+	0.594043i	$0.797531\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	121.885	+	70.3703i	0.930420	+	0.537178i	0.886944	−	0.461876i	$-0.152824\pi$
$131$	121.885	+	70.3703i	0.930420	+	0.537178i	0.0434754	+	0.999054i	$0.486157\pi$
$132$		0			0
$133$	−208.711	−	57.6101i	−1.56926	−	0.433159i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−22.5257	−	39.0157i	−0.164421	−	0.284786i	0.772028	−	0.635588i	$-0.219242\pi$
$137$	−22.5257	−	39.0157i	−0.164421	−	0.284786i	−0.936450	+	0.350802i	$0.885909\pi$
$138$		0			0
$139$		−	32.2285i		−	0.231860i	−0.993257	−	0.115930i	$-0.963015\pi$
$139$		−	32.2285i		−	0.231860i	0.993257	−	0.115930i	$-0.0369848\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−166.323	+	96.0267i	−1.16310	+	0.671515i
$144$		0			0
$145$	68.8127	−	119.187i	0.474570	−	0.821980i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	78.5739	−	136.094i	0.527342	−	0.913383i	−0.472150	−	0.881518i	$-0.656522\pi$
$149$	78.5739	−	136.094i	0.527342	−	0.913383i	0.999492	−	0.0318647i	$-0.0101446\pi$
$150$		0			0
$151$	−7.51370	+	4.33804i	−0.0497596	+	0.0287287i	−0.524673	−	0.851304i	$-0.675813\pi$
$151$	−7.51370	+	4.33804i	−0.0497596	+	0.0287287i	0.474914	+	0.880032i	$0.342479\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	170.735i		−	1.10152i
$156$		0			0
$157$	55.0241	+	95.3045i	0.350472	+	0.607035i	0.986332	−	0.164769i	$-0.0526879\pi$
$157$	55.0241	+	95.3045i	0.350472	+	0.607035i	−0.635860	+	0.771804i	$0.719355\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	35.4502	+	9.78523i	0.220187	+	0.0607778i
$162$		0			0
$163$	−127.849	−	73.8136i	−0.784349	−	0.452844i	0.0536205	−	0.998561i	$-0.482924\pi$
$163$	−127.849	−	73.8136i	−0.784349	−	0.452844i	−0.837969	+	0.545717i	$0.816257\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			60.5642i			0.362660i	0.983422	+	0.181330i	$0.0580402\pi$
$167$			60.5642i			0.362660i	−0.983422	+	0.181330i	$0.941960\pi$
$168$		0			0
$169$	−63.4261			−0.375302
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−45.4261	+	78.6803i	−0.262578	+	0.454799i	−0.966926	−	0.255056i	$-0.917906\pi$
$173$	−45.4261	+	78.6803i	−0.262578	+	0.454799i	0.704348	+	0.709855i	$0.251240\pi$
$174$		0			0
$175$	−70.1238	−	71.1867i	−0.400707	−	0.406781i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	275.973	−	159.333i	1.54175	−	0.890128i	0.543018	−	0.839721i	$-0.317282\pi$
$179$	275.973	−	159.333i	1.54175	−	0.890128i	0.998729	−	0.0504063i	$-0.0160516\pi$
$180$		0			0
$181$	31.6769			0.175011			0.0875053	−	0.996164i	$-0.472111\pi$
$181$	31.6769			0.175011			0.0875053	+	0.996164i	$0.472111\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	58.8248	+	101.887i	0.317972	+	0.550743i
$186$		0			0
$187$	406.296	+	234.575i	2.17270	+	1.25441i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−208.722	−	120.506i	−1.09278	−	0.630919i	−0.158468	−	0.987364i	$-0.550655\pi$
$191$	−208.722	−	120.506i	−1.09278	−	0.630919i	−0.934316	+	0.356445i	$0.883989\pi$
$192$		0			0
$193$	170.723	+	295.702i	0.884577	+	1.53213i	0.846197	+	0.532870i	$0.178886\pi$
$193$	170.723	+	295.702i	0.884577	+	1.53213i	0.0383800	+	0.999263i	$0.487780\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	142.550			0.723603			0.361802	−	0.932255i	$-0.382162\pi$
$197$	142.550			0.723603			0.361802	+	0.932255i	$0.382162\pi$
$198$		0			0
$199$	4.54983	−	2.62685i	0.0228635	−	0.0132002i	−0.488525	−	0.872550i	$-0.662465\pi$
$199$	4.54983	−	2.62685i	0.0228635	−	0.0132002i	0.511388	+	0.859350i	$0.329131\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−284.710	+	73.9970i	−1.40251	+	0.364517i
$204$		0			0
$205$	63.4502	−	109.899i	0.309513	−	0.536092i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−578.145			−2.76624
$210$		0			0
$211$		−	271.267i		−	1.28563i	−0.766023	−	0.642814i	$-0.777767\pi$
$211$		−	271.267i		−	1.28563i	0.766023	−	0.642814i	$-0.222233\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−89.4469	−	51.6422i	−0.416032	−	0.240196i
$216$		0			0
$217$	−259.985	+	256.103i	−1.19809	+	1.18020i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−128.949	−	223.345i	−0.583477	−	1.01061i
$222$		0			0
$223$		−	76.8907i		−	0.344801i	−0.985027	−	0.172401i	$-0.944848\pi$
$223$		−	76.8907i		−	0.344801i	0.985027	−	0.172401i	$-0.0551524\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−119.765	+	69.1461i	−0.527597	+	0.304608i	−0.740037	−	0.672566i	$-0.765192\pi$
$227$	−119.765	+	69.1461i	−0.527597	+	0.304608i	0.212440	+	0.977174i	$0.431859\pi$
$228$		0			0
$229$	−67.1856	+	116.369i	−0.293387	+	0.508161i	−0.974608	−	0.223916i	$-0.928116\pi$
$229$	−67.1856	+	116.369i	−0.293387	+	0.508161i	0.681221	+	0.732078i	$0.261449\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−35.9244	+	62.2229i	−0.154182	+	0.267051i	−0.932761	−	0.360496i	$-0.882608\pi$
$233$	−35.9244	+	62.2229i	−0.154182	+	0.267051i	0.778579	+	0.627547i	$0.215941\pi$
$234$		0			0
$235$	68.7733	−	39.7063i	0.292652	−	0.168963i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			331.308i			1.38623i	0.720829	+	0.693113i	$0.243761\pi$
$239$			331.308i			1.38623i	−0.720829	+	0.693113i	$0.756239\pi$
$240$		0			0
$241$	−53.2629	−	92.2540i	−0.221008	−	0.382797i	0.734106	−	0.679034i	$-0.237601\pi$
$241$	−53.2629	−	92.2540i	−0.221008	−	0.382797i	−0.955114	+	0.296238i	$0.904268\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.41403	−	160.453i	0.00985319	−	0.654909i
$246$		0			0
$247$	275.234	+	158.906i	1.11431	+	0.643345i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	251.100i		−	1.00040i	−0.865910	−	0.500199i	$-0.833260\pi$
$251$		−	251.100i		−	1.00040i	0.865910	−	0.500199i	$-0.166740\pi$
$252$		0			0
$253$	98.1993			0.388140
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−203.199	+	351.952i	−0.790659	+	1.36946i	0.134901	+	0.990859i	$0.456928\pi$
$257$	−203.199	+	351.952i	−0.790659	+	1.36946i	−0.925559	+	0.378602i	$0.876405\pi$
$258$		0			0
$259$	66.9107	−	242.406i	0.258343	−	0.935930i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−48.8696	+	28.2149i	−0.185816	+	0.107281i	−0.590022	−	0.807387i	$-0.700881\pi$
$263$	−48.8696	+	28.2149i	−0.185816	+	0.107281i	0.404206	+	0.914668i	$0.367548\pi$
$264$		0			0
$265$	−214.918			−0.811011
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−68.2355	−	118.187i	−0.253663	−	0.439358i	0.710868	−	0.703325i	$-0.248302\pi$
$269$	−68.2355	−	118.187i	−0.253663	−	0.439358i	−0.964532	+	0.263967i	$0.914969\pi$
$270$		0			0
$271$	−0.534478	−	0.308581i	−0.00197225	−	0.00113868i	0.499014	−	0.866594i	$-0.333696\pi$
$271$	−0.534478	−	0.308581i	−0.00197225	−	0.00113868i	−0.500986	+	0.865456i	$0.667029\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−231.072	−	133.410i	−0.840263	−	0.485126i
$276$		0			0
$277$	−195.632	−	338.845i	−0.706254	−	1.22327i	−0.966237	−	0.257655i	$-0.917050\pi$
$277$	−195.632	−	338.845i	−0.706254	−	1.22327i	0.259982	−	0.965613i	$-0.416283\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	534.248			1.90124			0.950618	−	0.310362i	$-0.100450\pi$
$281$	534.248			1.90124			0.950618	+	0.310362i	$0.100450\pi$
$282$		0			0
$283$	−55.4639	+	32.0221i	−0.195985	+	0.113152i	−0.594782	−	0.803887i	$-0.702761\pi$
$283$	−55.4639	+	32.0221i	−0.195985	+	0.113152i	0.398796	+	0.917040i	$0.369428\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−262.522	+	68.2304i	−0.914712	+	0.237737i
$288$		0			0
$289$	−170.497	+	295.309i	−0.589954	+	1.02183i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−88.6703			−0.302629			−0.151314	−	0.988486i	$-0.548351\pi$
$293$	−88.6703			−0.302629			−0.151314	+	0.988486i	$0.548351\pi$
$294$		0			0
$295$		−	146.863i		−	0.497841i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−46.7492	−	26.9906i	−0.156352	−	0.0902697i
$300$		0			0
$301$	55.5328	+	213.667i	0.184494	+	0.709858i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−103.323	−	178.961i	−0.338764	−	0.586757i
$306$		0			0
$307$		−	147.004i		−	0.478841i	−0.970916	−	0.239421i	$-0.923043\pi$
$307$		−	147.004i		−	0.478841i	0.970916	−	0.239421i	$-0.0769575\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−159.526	+	92.1022i	−0.512945	+	0.296149i	−0.734043	−	0.679103i	$-0.762369\pi$
$311$	−159.526	+	92.1022i	−0.512945	+	0.296149i	0.221099	+	0.975251i	$0.429036\pi$
$312$		0			0
$313$	111.521	−	193.160i	0.356296	−	0.617123i	−0.631043	−	0.775748i	$-0.717373\pi$
$313$	111.521	−	193.160i	0.356296	−	0.617123i	0.987339	+	0.158625i	$0.0507060\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−310.359	+	537.558i	−0.979051	+	1.69577i	−0.313191	+	0.949690i	$0.601398\pi$
$317$	−310.359	+	537.558i	−0.979051	+	1.69577i	−0.665861	+	0.746076i	$0.731935\pi$
$318$		0			0
$319$	−680.256	+	392.746i	−2.13246	+	1.23118i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	776.356i		−	2.40358i
$324$		0			0
$325$	73.3368	+	127.023i	0.225652	+	0.390840i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−163.622	−	45.1642i	−0.497332	−	0.137277i
$330$		0			0
$331$	−314.787	−	181.742i	−0.951018	−	0.549071i	−0.0576210	−	0.998339i	$-0.518351\pi$
$331$	−314.787	−	181.742i	−0.951018	−	0.549071i	−0.893397	+	0.449268i	$0.851685\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			72.7461i			0.217153i
$336$		0			0
$337$	−322.093			−0.955766			−0.477883	−	0.878424i	$-0.658596\pi$
$337$	−322.093			−0.955766			−0.477883	+	0.878424i	$0.658596\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−487.232	+	843.911i	−1.42883	+	2.47481i
$342$		0			0
$343$	−247.949	+	237.003i	−0.722882	+	0.690972i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	305.093	−	176.146i	0.879231	−	0.507624i	0.00882601	−	0.999961i	$-0.497191\pi$
$347$	305.093	−	176.146i	0.879231	−	0.507624i	0.870405	+	0.492337i	$0.163857\pi$
$348$		0			0
$349$	221.395			0.634371			0.317185	−	0.948364i	$-0.397262\pi$
$349$	221.395			0.634371			0.317185	+	0.948364i	$0.397262\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−28.8729	−	50.0094i	−0.0817930	−	0.141670i	0.822227	−	0.569159i	$-0.192731\pi$
$353$	−28.8729	−	50.0094i	−0.0817930	−	0.141670i	−0.904020	+	0.427490i	$0.859398\pi$
$354$		0			0
$355$	276.725	+	159.767i	0.779507	+	0.450049i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	243.117	+	140.364i	0.677207	+	0.390985i	0.798802	−	0.601594i	$-0.205468\pi$
$359$	243.117	+	140.364i	0.677207	+	0.390985i	−0.121595	+	0.992580i	$0.538801\pi$
$360$		0			0
$361$	297.861	+	515.910i	0.825099	+	1.42911i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−300.392			−0.822992
$366$		0			0
$367$	−80.2974	+	46.3597i	−0.218794	+	0.126321i	−0.605392	−	0.795928i	$-0.706984\pi$
$367$	−80.2974	+	46.3597i	−0.218794	+	0.126321i	0.386598	+	0.922248i	$0.373650\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	322.377	+	327.263i	0.868940	+	0.882112i
$372$		0			0
$373$	78.4365	−	135.856i	0.210285	−	0.364225i	−0.741518	−	0.670933i	$-0.765894\pi$
$373$	78.4365	−	135.856i	0.210285	−	0.364225i	0.951804	+	0.306707i	$0.0992273\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	431.794			1.14534
$378$		0			0
$379$		−	466.559i		−	1.23103i	−0.788127	−	0.615513i	$-0.788949\pi$
$379$		−	466.559i		−	1.23103i	0.788127	−	0.615513i	$-0.211051\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	429.625	+	248.044i	1.12174	+	0.647635i	0.941844	−	0.336051i	$-0.109091\pi$
$383$	429.625	+	248.044i	1.12174	+	0.647635i	0.179893	+	0.983686i	$0.442425\pi$
$384$		0			0
$385$	−107.785	−	414.713i	−0.279962	−	1.07718i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	324.148	+	561.441i	0.833285	+	1.44329i	0.895419	+	0.445224i	$0.146876\pi$
$389$	324.148	+	561.441i	0.833285	+	1.44329i	−0.0621342	+	0.998068i	$0.519791\pi$
$390$		0			0
$391$			131.866i			0.337253i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	26.2837	−	15.1749i	0.0665409	−	0.0384174i
$396$		0			0
$397$	−156.210	+	270.563i	−0.393475	+	0.681519i	−0.992905	−	0.118908i	$-0.962061\pi$
$397$	−156.210	+	270.563i	−0.393475	+	0.681519i	0.599430	+	0.800427i	$0.295394\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	16.0000	−	27.7128i	0.0399002	−	0.0691093i	−0.845386	−	0.534156i	$-0.820629\pi$
$401$	16.0000	−	27.7128i	0.0399002	−	0.0691093i	0.885286	+	0.465047i	$0.153963\pi$
$402$		0			0
$403$	463.907	−	267.837i	1.15114	−	0.664608i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	671.480i		−	1.64983i
$408$		0			0
$409$	−305.370	−	528.916i	−0.746625	−	1.29319i	−0.949432	−	0.313974i	$-0.898340\pi$
$409$	−305.370	−	528.916i	−0.746625	−	1.29319i	0.202807	−	0.979219i	$-0.434994\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−223.634	+	220.295i	−0.541487	+	0.533402i
$414$		0			0
$415$	−145.205	−	83.8340i	−0.349891	−	0.202010i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	674.432i		−	1.60962i	−0.593530	−	0.804812i	$-0.702266\pi$
$419$		−	674.432i		−	1.60962i	0.593530	−	0.804812i	$-0.297734\pi$
$420$		0			0
$421$	−97.9792			−0.232730			−0.116365	−	0.993207i	$-0.537124\pi$
$421$	−97.9792			−0.232730			−0.116365	+	0.993207i	$0.537124\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	179.148	−	310.293i	0.421524	−	0.730102i
$426$		0			0
$427$	−117.526	+	425.775i	−0.275236	+	0.997132i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.13038	−	1.22998i	0.00494288	−	0.00285377i	−0.497527	−	0.867449i	$-0.665758\pi$
$431$	2.13038	−	1.22998i	0.00494288	−	0.00285377i	0.502469	+	0.864595i	$0.332425\pi$
$432$		0			0
$433$	475.670			1.09855			0.549273	−	0.835643i	$-0.314905\pi$
$433$	475.670			1.09855			0.549273	+	0.835643i	$0.314905\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−81.2508	−	140.731i	−0.185929	−	0.322038i
$438$		0			0
$439$	−118.686	−	68.5232i	−0.270355	−	0.156089i	0.358694	−	0.933455i	$-0.383222\pi$
$439$	−118.686	−	68.5232i	−0.270355	−	0.156089i	−0.629049	+	0.777366i	$0.716555\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	139.459	+	80.5166i	0.314806	+	0.181753i	0.649075	−	0.760724i	$-0.275156\pi$
$443$	139.459	+	80.5166i	0.314806	+	0.181753i	−0.334269	+	0.942478i	$0.608489\pi$
$444$		0			0
$445$	87.5224	+	151.593i	0.196680	+	0.340659i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−279.643			−0.622813			−0.311406	−	0.950277i	$-0.600800\pi$
$449$	−279.643			−0.622813			−0.311406	+	0.950277i	$0.600800\pi$
$450$		0			0
$451$	−627.244	+	362.140i	−1.39079	+	0.802970i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−62.6736	+	227.055i	−0.137744	+	0.499023i
$456$		0			0
$457$	−234.675	+	406.469i	−0.513513	+	0.889430i	0.486365	+	0.873756i	$0.338323\pi$
$457$	−234.675	+	406.469i	−0.513513	+	0.889430i	−0.999877	+	0.0156739i	$0.995011\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−234.440			−0.508547			−0.254274	−	0.967132i	$-0.581836\pi$
$461$	−234.440			−0.508547			−0.254274	+	0.967132i	$0.581836\pi$
$462$		0			0
$463$		−	515.120i		−	1.11257i	−0.830992	−	0.556285i	$-0.812226\pi$
$463$		−	515.120i		−	1.11257i	0.830992	−	0.556285i	$-0.187774\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	121.677	+	70.2502i	0.260550	+	0.150429i	0.624585	−	0.780956i	$-0.285268\pi$
$467$	121.677	+	70.2502i	0.260550	+	0.150429i	−0.364035	+	0.931385i	$0.618601\pi$
$468$		0			0
$469$	110.773	−	109.119i	0.236190	−	0.232664i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	294.746	+	510.515i	0.623141	+	1.07931i
$474$		0			0
$475$			441.536i			0.929550i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−785.564	+	453.546i	−1.64001	+	0.946859i	−0.659180	+	0.751985i	$0.729097\pi$
$479$	−785.564	+	453.546i	−1.64001	+	0.946859i	−0.980828	+	0.194874i	$0.937570\pi$
$480$		0			0
$481$	−184.560	+	319.668i	−0.383701	+	0.664590i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	212.088	−	367.347i	0.437294	−	0.757416i
$486$		0			0
$487$	251.153	−	145.003i	0.515714	−	0.297748i	−0.219465	−	0.975620i	$-0.570431\pi$
$487$	251.153	−	145.003i	0.515714	−	0.297748i	0.735179	+	0.677873i	$0.237098\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	353.412i		−	0.719779i	−0.932995	−	0.359890i	$-0.882814\pi$
$491$		−	353.412i		−	0.719779i	0.932995	−	0.359890i	$-0.117186\pi$
$492$		0			0
$493$	−527.395	−	913.476i	−1.06977	−	1.85289i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−171.804	−	661.031i	−0.345682	−	1.33004i
$498$		0			0
$499$	−284.543	−	164.281i	−0.570226	−	0.329220i	0.187014	−	0.982357i	$-0.440119\pi$
$499$	−284.543	−	164.281i	−0.570226	−	0.329220i	−0.757240	+	0.653137i	$0.773452\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			791.625i			1.57381i	0.617076	+	0.786904i	$0.288317\pi$
$503$			791.625i			1.57381i	−0.617076	+	0.786904i	$0.711683\pi$
$504$		0			0
$505$	175.855			0.348229
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−217.637	+	376.959i	−0.427579	+	0.740588i	−0.996657	−	0.0816953i	$-0.973967\pi$
$509$	−217.637	+	376.959i	−0.427579	+	0.740588i	0.569079	+	0.822283i	$0.307300\pi$
$510$		0			0
$511$	450.588	+	457.418i	0.881777	+	0.895143i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−91.0789	+	52.5844i	−0.176852	+	0.102106i
$516$		0			0
$517$	−453.244			−0.876681
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−129.378	−	224.089i	−0.248326	−	0.430113i	0.714735	−	0.699395i	$-0.246547\pi$
$521$	−129.378	−	224.089i	−0.248326	−	0.430113i	−0.963062	+	0.269282i	$0.913214\pi$
$522$		0			0
$523$	−809.523	−	467.378i	−1.54784	−	0.893649i	−0.998306	−	0.0581805i	$-0.981470\pi$
$523$	−809.523	−	467.378i	−1.54784	−	0.893649i	−0.549539	−	0.835468i	$-0.685197\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1133.24	−	654.275i	−2.15036	−	1.24151i
$528$		0			0
$529$	−250.699	−	434.224i	−0.473912	−	0.820839i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	398.145			0.746988
$534$		0			0
$535$	162.390	−	93.7559i	0.303533	−	0.175245i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−469.821	+	786.199i	−0.871654	+	1.45862i
$540$		0			0
$541$	−53.4572	+	92.5907i	−0.0988119	+	0.171147i	−0.911193	−	0.411979i	$-0.864838\pi$
$541$	−53.4572	+	92.5907i	−0.0988119	+	0.171147i	0.812381	+	0.583127i	$0.198171\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	462.990			0.849523
$546$		0			0
$547$		−	33.5534i		−	0.0613408i	−0.999530	−	0.0306704i	$-0.990236\pi$
$547$		−	33.5534i		−	0.0613408i	0.999530	−	0.0306704i	$-0.00976422\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1125.70	+	649.922i	2.04301	+	1.17953i
$552$		0			0
$553$	−62.5328	−	17.2608i	−0.113079	−	0.0312130i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−484.954	−	839.965i	−0.870653	−	1.50802i	−0.861322	−	0.508059i	$-0.830363\pi$
$557$	−484.954	−	839.965i	−0.870653	−	1.50802i	−0.00933136	−	0.999956i	$-0.502970\pi$
$558$		0			0
$559$		−	324.050i		−	0.579696i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	99.2629	−	57.3094i	0.176311	−	0.101793i	−0.409247	−	0.912423i	$-0.634209\pi$
$563$	99.2629	−	57.3094i	0.176311	−	0.101793i	0.585558	+	0.810630i	$0.300875\pi$
$564$		0			0
$565$	118.145	−	204.632i	0.209105	−	0.362181i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	152.275	−	263.748i	0.267618	−	0.463529i	−0.700628	−	0.713527i	$-0.747097\pi$
$569$	152.275	−	263.748i	0.267618	−	0.463529i	0.968246	+	0.249998i	$0.0804300\pi$
$570$		0			0
$571$	709.636	−	409.708i	1.24279	−	0.717528i	0.273132	−	0.961976i	$-0.411940\pi$
$571$	709.636	−	409.708i	1.24279	−	0.717528i	0.969662	+	0.244449i	$0.0786069\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	74.9961i		−	0.130428i
$576$		0			0
$577$	517.895	+	897.021i	0.897566	+	1.55463i	0.830597	+	0.556874i	$0.187999\pi$
$577$	517.895	+	897.021i	0.897566	+	1.55463i	0.0669688	+	0.997755i	$0.478667\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	90.1500	+	346.860i	0.155163	+	0.597005i
$582$		0			0
$583$	1062.30	+	613.318i	1.82212	+	1.05200i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	991.224i		−	1.68863i	−0.535850	−	0.844313i	$-0.680009\pi$
$587$		−	991.224i		−	1.68863i	0.535850	−	0.844313i	$-0.319991\pi$
$588$		0			0
$589$	1612.56			2.73779
$590$		0			0
$591$		0			0
$592$		0			0
$593$	273.368	−	473.487i	0.460992	−	0.798461i	−0.538019	−	0.842933i	$-0.680827\pi$
$593$	273.368	−	473.487i	0.460992	−	0.798461i	0.999011	+	0.0444719i	$0.0141605\pi$
$594$		0			0
$595$	556.894	−	144.738i	0.935956	−	0.243258i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	389.474	−	224.863i	0.650207	−	0.375397i	−0.138328	−	0.990386i	$-0.544173\pi$
$599$	389.474	−	224.863i	0.650207	−	0.375397i	0.788536	+	0.614989i	$0.210840\pi$
$600$		0			0
$601$	−392.106			−0.652423			−0.326212	−	0.945297i	$-0.605772\pi$
$601$	−392.106			−0.652423			−0.326212	+	0.945297i	$0.605772\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−373.949	−	647.698i	−0.618097	−	1.07057i
$606$		0			0
$607$	657.040	+	379.342i	1.08244	+	0.624946i	0.931553	−	0.363605i	$-0.118454\pi$
$607$	657.040	+	379.342i	1.08244	+	0.624946i	0.150885	+	0.988551i	$0.451788\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	215.773	+	124.577i	0.353148	+	0.203890i
$612$		0			0
$613$	217.670	+	377.016i	0.355090	+	0.615034i	0.987133	−	0.159899i	$-0.0511168\pi$
$613$	217.670	+	377.016i	0.355090	+	0.615034i	−0.632043	+	0.774933i	$0.717783\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	145.189			0.235315			0.117658	−	0.993054i	$-0.462461\pi$
$617$	145.189			0.235315			0.117658	+	0.993054i	$0.462461\pi$
$618$		0			0
$619$	442.399	−	255.419i	0.714700	−	0.412632i	−0.0980990	−	0.995177i	$-0.531276\pi$
$619$	442.399	−	255.419i	0.714700	−	0.412632i	0.812799	+	0.582545i	$0.197943\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	99.5531	−	360.664i	0.159796	−	0.578914i
$624$		0			0
$625$	32.1769	−	55.7320i	0.0514830	−	0.0891713i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	901.691			1.43353
$630$		0			0
$631$			345.666i			0.547807i	0.961757	+	0.273904i	$0.0883150\pi$
$631$			345.666i			0.547807i	−0.961757	+	0.273904i	$0.911685\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	427.940	+	247.071i	0.673921	+	0.389088i
$636$		0			0
$637$	439.756	−	245.148i	0.690355	−	0.384847i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	452.072	+	783.012i	0.705261	+	1.22155i	0.966597	+	0.256300i	$0.0825035\pi$
$641$	452.072	+	783.012i	0.705261	+	1.22155i	−0.261336	+	0.965248i	$0.584163\pi$
$642$		0			0
$643$			265.621i			0.413096i	0.978436	+	0.206548i	$0.0662230\pi$
$643$			265.621i			0.413096i	−0.978436	+	0.206548i	$0.933777\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−306.807	+	177.135i	−0.474200	+	0.273779i	−0.717996	−	0.696047i	$-0.754940\pi$
$647$	−306.807	+	177.135i	−0.474200	+	0.273779i	0.243796	+	0.969826i	$0.421607\pi$
$648$		0			0
$649$	−419.108	+	725.917i	−0.645776	+	1.11852i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	390.483	−	676.336i	0.597983	−	1.03574i	−0.395135	−	0.918623i	$-0.629302\pi$
$653$	390.483	−	676.336i	0.597983	−	1.03574i	0.993118	−	0.117114i	$-0.0373644\pi$
$654$		0			0
$655$	399.163	−	230.457i	0.609409	−	0.351843i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			309.905i			0.470265i	0.971963	+	0.235133i	$0.0755524\pi$
$659$			309.905i			0.470265i	−0.971963	+	0.235133i	$0.924448\pi$
$660$		0			0
$661$	345.059	+	597.659i	0.522025	+	0.904174i	0.999672	+	0.0256219i	$0.00815660\pi$
$661$	345.059	+	597.659i	0.522025	+	0.904174i	−0.477647	+	0.878552i	$0.658510\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−505.148	+	497.605i	−0.759621	+	0.748278i
$666$		0			0
$667$	−191.203	−	110.391i	−0.286661	−	0.165504i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			1179.43i			1.75771i
$672$		0			0
$673$	714.238			1.06127			0.530637	−	0.847599i	$-0.321953\pi$
$673$	714.238			1.06127			0.530637	+	0.847599i	$0.321953\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	589.205	−	1020.53i	0.870317	−	1.50743i	0.00864841	−	0.999963i	$-0.497247\pi$
$677$	589.205	−	1020.53i	0.870317	−	1.50743i	0.861669	−	0.507471i	$-0.169420\pi$
$678$		0			0
$679$	−877.504	+	228.066i	−1.29235	+	0.335885i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−732.226	+	422.751i	−1.07207	+	0.618961i	−0.928747	−	0.370714i	$-0.879113\pi$
$683$	−732.226	+	422.751i	−1.07207	+	0.618961i	−0.143326	+	0.989676i	$0.545780\pi$
$684$		0			0
$685$	−147.540			−0.215387
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−337.148	−	583.957i	−0.489329	−	0.847543i
$690$		0			0
$691$	871.598	+	503.218i	1.26136	+	0.728245i	0.973337	−	0.229379i	$-0.0736694\pi$
$691$	871.598	+	503.218i	1.26136	+	0.728245i	0.288021	+	0.957624i	$0.407003\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−91.4053	−	52.7729i	−0.131518	−	0.0759322i
$696$		0			0
$697$	−486.296	−	842.289i	−0.697698	−	1.20845i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1047.00			1.49358			0.746791	−	0.665059i	$-0.231594\pi$
$701$	1047.00			1.49358			0.746791	+	0.665059i	$0.231594\pi$
$702$		0			0
$703$	−962.306	+	555.588i	−1.36886	+	0.790310i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−263.783	−	267.782i	−0.373102	−	0.378758i
$708$		0			0
$709$	664.485	−	1150.92i	0.937215	−	1.62330i	0.166578	−	0.986028i	$-0.446728\pi$
$709$	664.485	−	1150.92i	0.937215	−	1.62330i	0.770637	−	0.637275i	$-0.219938\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−273.897			−0.384147
$714$		0			0
$715$			628.959i			0.879663i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1126.85	+	650.586i	1.56724	+	0.904849i	0.996489	+	0.0837294i	$0.0266831\pi$
$719$	1126.85	+	650.586i	1.56724	+	0.904849i	0.570756	+	0.821120i	$0.306650\pi$
$720$		0			0
$721$	216.691	+	59.8126i	0.300542	+	0.0829578i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	299.945	+	519.520i	0.413718	+	0.716580i
$726$		0			0
$727$		−	951.043i		−	1.30817i	−0.756419	−	0.654087i	$-0.773053\pi$
$727$		−	951.043i		−	1.30817i	0.756419	−	0.654087i	$-0.226947\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−685.540	+	395.797i	−0.937811	+	0.541445i
$732$		0			0
$733$	−365.313	+	632.740i	−0.498380	+	0.863220i	−0.999998	−	0.00186934i	$-0.999405\pi$
$733$	−365.313	+	632.740i	−0.498380	+	0.863220i	0.501618	+	0.865089i	$0.332738\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	207.598	−	359.570i	0.281680	−	0.487884i
$738$		0			0
$739$	−197.107	+	113.800i	−0.266721	+	0.153991i	−0.627397	−	0.778700i	$-0.715879\pi$
$739$	−197.107	+	113.800i	−0.266721	+	0.153991i	0.360676	+	0.932691i	$0.382546\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	1129.94i		−	1.52078i	−0.649470	−	0.760388i	$-0.725009\pi$
$743$		−	1129.94i		−	1.52078i	0.649470	−	0.760388i	$-0.274991\pi$
$744$		0			0
$745$	−257.323	−	445.697i	−0.345400	−	0.598251i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−386.350	−	106.643i	−0.515822	−	0.142381i
$750$		0			0
$751$	−858.755	−	495.802i	−1.14348	−	0.660190i	−0.196192	−	0.980566i	$-0.562857\pi$
$751$	−858.755	−	495.802i	−1.14348	−	0.660190i	−0.947290	+	0.320376i	$0.896191\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			28.4134i			0.0376337i
$756$		0			0
$757$	−373.286			−0.493112			−0.246556	−	0.969129i	$-0.579299\pi$
$757$	−373.286			−0.493112			−0.246556	+	0.969129i	$0.579299\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	113.106	−	195.906i	0.148629	−	0.257432i	−0.782092	−	0.623163i	$-0.785847\pi$
$761$	113.106	−	195.906i	0.148629	−	0.257432i	0.930721	+	0.365730i	$0.119181\pi$
$762$		0			0
$763$	−694.485	−	705.012i	−0.910203	−	0.924000i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	399.045	−	230.389i	0.520267	−	0.300376i
$768$		0			0
$769$	100.836			0.131126			0.0655628	−	0.997848i	$-0.479116\pi$
$769$	100.836			0.131126			0.0655628	+	0.997848i	$0.479116\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−35.8040	−	62.0143i	−0.0463182	−	0.0802255i	0.841937	−	0.539576i	$-0.181415\pi$
$773$	−35.8040	−	62.0143i	−0.0463182	−	0.0802255i	−0.888255	+	0.459351i	$0.848082\pi$
$774$		0			0
$775$	644.505	+	372.105i	0.831620	+	0.480136i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1037.97	+	599.274i	1.33244	+	0.769286i
$780$		0			0
$781$	−911.866	−	1579.40i	−1.16756	−	2.02228i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	360.399			0.459107
$786$		0			0
$787$	−419.619	+	242.267i	−0.533188	+	0.307836i	−0.742314	−	0.670053i	$-0.766272\pi$
$787$	−419.619	+	242.267i	−0.533188	+	0.307836i	0.209126	+	0.977889i	$0.432938\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−488.818	+	127.045i	−0.617975	+	0.160614i
$792$		0			0
$793$	324.172	−	561.482i	0.408792	−	0.708048i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	189.275			0.237484			0.118742	−	0.992925i	$-0.462114\pi$
$797$	189.275			0.237484			0.118742	+	0.992925i	$0.462114\pi$
$798$		0			0
$799$		−	608.635i		−	0.761745i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1484.78	+	857.239i	1.84904	+	1.06754i
$804$		0			0
$805$	85.8007	−	84.5195i	0.106585	−	0.104993i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	558.976	+	968.175i	0.690947	+	1.19675i	0.971528	+	0.236925i	$0.0761394\pi$
$809$	558.976	+	968.175i	0.690947	+	1.19675i	−0.280581	+	0.959830i	$0.590527\pi$
$810$		0			0
$811$			706.070i			0.870616i	0.900282	+	0.435308i	$0.143361\pi$
$811$			706.070i			0.870616i	−0.900282	+	0.435308i	$0.856639\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−418.694	+	241.733i	−0.513735	+	0.296605i
$816$		0			0
$817$	487.750	−	844.807i	0.597001	−	1.03404i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	424.211	−	734.756i	0.516701	−	0.894952i	−0.483111	−	0.875559i	$-0.660493\pi$
$821$	424.211	−	734.756i	0.516701	−	0.894952i	0.999812	−	0.0193930i	$-0.00617338\pi$
$822$		0			0
$823$	29.0930	−	16.7969i	0.0353500	−	0.0204093i	−0.482221	−	0.876050i	$-0.660170\pi$
$823$	29.0930	−	16.7969i	0.0353500	−	0.0204093i	0.517571	+	0.855640i	$0.326836\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1246.59i		−	1.50737i	−0.657236	−	0.753685i	$-0.728275\pi$
$827$		−	1246.59i		−	1.50737i	0.657236	−	0.753685i	$-0.271725\pi$
$828$		0			0
$829$	384.554	+	666.066i	0.463876	+	0.803458i	0.999150	−	0.0412211i	$-0.0131248\pi$
$829$	384.554	+	666.066i	0.463876	+	0.803458i	−0.535274	+	0.844679i	$0.679791\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1055.74	−	630.895i	−1.26739	−	0.757377i
$834$		0			0
$835$	171.770	+	99.1714i	0.205713	+	0.118768i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	244.162i		−	0.291015i	−0.989357	−	0.145508i	$-0.953519\pi$
$839$		−	244.162i		−	0.291015i	0.989357	−	0.145508i	$-0.0464815\pi$
$840$		0			0
$841$	925.024			1.09991
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−103.858	+	179.887i	−0.122908	+	0.212884i
$846$		0			0
$847$	−425.351	+	1540.97i	−0.502185	+	1.81933i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	163.450	−	94.3680i	0.192068	−	0.110891i
$852$		0			0
$853$	−594.722			−0.697212			−0.348606	−	0.937269i	$-0.613345\pi$
$853$	−594.722			−0.697212			−0.348606	+	0.937269i	$0.613345\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	151.172	+	261.837i	0.176397	+	0.305528i	0.940644	−	0.339396i	$-0.110223\pi$
$857$	151.172	+	261.837i	0.176397	+	0.305528i	−0.764247	+	0.644924i	$0.776889\pi$
$858$		0			0
$859$	−507.461	−	292.983i	−0.590758	−	0.341074i	0.174639	−	0.984632i	$-0.444124\pi$
$859$	−507.461	−	292.983i	−0.590758	−	0.341074i	−0.765397	+	0.643558i	$0.777457\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−37.7142	−	21.7743i	−0.0437013	−	0.0252310i	0.477990	−	0.878365i	$-0.341365\pi$
$863$	−37.7142	−	21.7743i	−0.0437013	−	0.0252310i	−0.521691	+	0.853134i	$0.674699\pi$
$864$		0			0
$865$	148.767	+	257.671i	0.171985	+	0.297886i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−173.220			−0.199333
$870$		0			0
$871$	−197.660	+	114.119i	−0.226934	+	0.131021i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−871.404	+	226.481i	−0.995890	+	0.258835i
$876$		0			0
$877$	−702.014	+	1215.92i	−0.800472	+	1.38646i	0.118833	+	0.992914i	$0.462085\pi$
$877$	−702.014	+	1215.92i	−0.800472	+	1.38646i	−0.919306	+	0.393544i	$0.871249\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	507.842			0.576438			0.288219	−	0.957564i	$-0.406937\pi$
$881$	507.842			0.576438			0.288219	+	0.957564i	$0.406937\pi$
$882$		0			0
$883$			438.774i			0.496913i	0.968643	+	0.248457i	$0.0799233\pi$
$883$			438.774i			0.496913i	−0.968643	+	0.248457i	$0.920077\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	178.069	+	102.808i	0.200754	+	0.115905i	0.597007	−	0.802236i	$-0.296356\pi$
$887$	178.069	+	102.808i	0.200754	+	0.115905i	−0.396253	+	0.918141i	$0.629690\pi$
$888$		0			0
$889$	−265.685	−	1022.25i	−0.298858	−	1.14988i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	375.017	+	649.549i	0.419952	+	0.727379i
$894$		0			0
$895$		−	1043.60i		−	1.16604i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1897.37	−	1095.45i	2.11053	−	1.21852i
$900$		0			0
$901$	−823.588	+	1426.50i	−0.914082	+	1.58324i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	51.8696	−	89.8408i	0.0573145	−	0.0992716i
$906$		0			0
$907$	609.240	−	351.745i	0.671709	−	0.387812i	−0.125015	−	0.992155i	$-0.539898\pi$
$907$	609.240	−	351.745i	0.671709	−	0.387812i	0.796724	+	0.604343i	$0.206564\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			372.699i			0.409110i	0.978855	+	0.204555i	$0.0655747\pi$
$911$			372.699i			0.409110i	−0.978855	+	0.204555i	$0.934425\pi$
$912$		0			0
$913$	478.480	+	828.751i	0.524074	+	0.907723i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−949.670	−	262.135i	−1.03563	−	0.285862i
$918$		0			0
$919$	−255.983	−	147.792i	−0.278545	−	0.160818i	0.354219	−	0.935162i	$-0.384747\pi$
$919$	−255.983	−	147.792i	−0.278545	−	0.160818i	−0.632765	+	0.774344i	$0.718080\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			1002.53i			1.08616i
$924$		0			0
$925$	−512.818			−0.554398
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−847.289	+	1467.55i	−0.912044	+	1.57971i	−0.100872	+	0.994899i	$0.532163\pi$
$929$	−847.289	+	1467.55i	−0.912044	+	1.57971i	−0.811172	+	0.584808i	$0.801170\pi$
$930$		0			0
$931$	1515.44	+	22.8000i	1.62776	+	0.0244898i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1330.58	−	768.213i	1.42309	−	0.821619i
$936$		0			0
$937$	−246.691			−0.263278			−0.131639	−	0.991298i	$-0.542024\pi$
$937$	−246.691			−0.263278			−0.131639	+	0.991298i	$0.542024\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	163.858	+	283.810i	0.174131	+	0.301604i	0.939860	−	0.341559i	$-0.110955\pi$
$941$	163.858	+	283.810i	0.174131	+	0.301604i	−0.765729	+	0.643163i	$0.777622\pi$
$942$		0			0
$943$	−176.302	−	101.788i	−0.186959	−	0.107941i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.02078	−	4.63080i	−0.00846967	−	0.00488997i	0.495759	−	0.868460i	$-0.334890\pi$
$947$	−8.02078	−	4.63080i	−0.00846967	−	0.00488997i	−0.504229	+	0.863570i	$0.668223\pi$
$948$		0			0
$949$	−471.234	−	816.201i	−0.496558	−	0.860064i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1300.02			−1.36414			−0.682068	−	0.731289i	$-0.738919\pi$
$953$	−1300.02			−1.36414			−0.682068	+	0.731289i	$0.738919\pi$
$954$		0			0
$955$	−683.547	+	394.646i	−0.715756	+	0.413242i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	221.310	+	224.665i	0.230771	+	0.234270i
$960$		0			0
$961$	878.485	−	1521.58i	0.914136	−	1.58333i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1118.21			1.15877
$966$		0			0
$967$		−	669.581i		−	0.692432i	−0.938155	−	0.346216i	$-0.887466\pi$
$967$		−	669.581i		−	0.692432i	0.938155	−	0.346216i	$-0.112534\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1078.54	−	622.695i	−1.11075	−	0.641292i	−0.171727	−	0.985145i	$-0.554935\pi$
$971$	−1078.54	−	622.695i	−1.11075	−	0.641292i	−0.939024	+	0.343853i	$0.888268\pi$
$972$		0			0
$973$	56.7487	+	218.346i	0.0583235	+	0.224405i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	108.257	+	187.507i	0.110806	+	0.191922i	0.916095	−	0.400960i	$-0.131323\pi$
$977$	108.257	+	187.507i	0.110806	+	0.191922i	−0.805289	+	0.592882i	$0.797990\pi$
$978$		0			0
$979$		−	999.062i		−	1.02049i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	708.832	−	409.245i	0.721091	−	0.416322i	−0.0940632	−	0.995566i	$-0.529986\pi$
$983$	708.832	−	409.245i	0.721091	−	0.416322i	0.815154	+	0.579244i	$0.196652\pi$
$984$		0			0
$985$	233.419	−	404.294i	0.236974	−	0.410451i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−82.8455	+	143.493i	−0.0837670	+	0.145089i
$990$		0			0
$991$	−616.301	+	355.821i	−0.621898	+	0.359053i	−0.777607	−	0.628750i	$-0.783567\pi$
$991$	−616.301	+	355.821i	−0.621898	+	0.359053i	0.155710	+	0.987803i	$0.450234\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	17.2054i		−	0.0172919i
$996$		0			0
$997$	−544.578	−	943.236i	−0.546216	−	0.946074i	−0.998529	−	0.0542152i	$-0.982734\pi$
$997$	−544.578	−	943.236i	−0.546216	−	0.946074i	0.452313	−	0.891859i	$-0.350599\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.3.cd.f.415.2		4
3.2	odd	2		336.3.be.b.79.1	yes	4
4.3	odd	2		1008.3.cd.g.415.2		4
7.4	even	3		1008.3.cd.g.991.2		4
12.11	even	2		336.3.be.a.79.1	✓	4
21.2	odd	6		2352.3.m.g.1471.4		4
21.5	even	6		2352.3.m.h.1471.1		4
21.11	odd	6		336.3.be.a.319.1	yes	4
28.11	odd	6	inner	1008.3.cd.f.991.2		4
84.11	even	6		336.3.be.b.319.1	yes	4
84.23	even	6		2352.3.m.g.1471.2		4
84.47	odd	6		2352.3.m.h.1471.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.be.a.79.1	✓	4	12.11	even	2
336.3.be.a.319.1	yes	4	21.11	odd	6
336.3.be.b.79.1	yes	4	3.2	odd	2
336.3.be.b.319.1	yes	4	84.11	even	6
1008.3.cd.f.415.2		4	1.1	even	1	trivial
1008.3.cd.f.991.2		4	28.11	odd	6	inner
1008.3.cd.g.415.2		4	4.3	odd	2
1008.3.cd.g.991.2		4	7.4	even	3
2352.3.m.g.1471.2		4	84.23	even	6
2352.3.m.g.1471.4		4	21.2	odd	6
2352.3.m.h.1471.1		4	21.5	even	6
2352.3.m.h.1471.3		4	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63746 - 2.83616i) q^{5} +(-6.77492 + 1.76082i) q^{7} +O(q^{10})\)	\(q+(1.63746 - 2.83616i) q^{5} +(-6.77492 + 1.76082i) q^{7} +(-16.1873 + 9.34574i) q^{11} +10.2749 q^{13} +(-12.5498 - 21.7370i) q^{17} +(26.7870 + 15.4655i) q^{19} +(-4.54983 - 2.62685i) q^{23} +(7.13746 + 12.3624i) q^{25} +42.0241 q^{29} +(45.1495 - 26.0671i) q^{31} +(-6.09967 + 22.0980i) q^{35} +(-17.9622 + 31.1115i) q^{37} +38.7492 q^{41} -31.5380i q^{43} +(21.0000 + 12.1244i) q^{47} +(42.7990 - 23.8589i) q^{49} +(-32.8127 - 56.8333i) q^{53} +61.2130i q^{55} +(38.8368 - 22.4224i) q^{59} +(31.5498 - 54.6459i) q^{61} +(16.8248 - 29.1413i) q^{65} +(-19.2371 + 11.1066i) q^{67} +97.5703i q^{71} +(-45.8625 - 79.4363i) q^{73} +(93.2114 - 91.8196i) q^{77} +(8.02575 + 4.63367i) q^{79} -51.1976i q^{83} -82.1993 q^{85} +(-26.7251 + 46.2892i) q^{89} +(-69.6117 + 18.0923i) q^{91} +(87.7251 - 50.6481i) q^{95} +129.522 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{5} - 12 q^{7}+O(q^{10}) \) 4 * q - q^5 - 12 * q^7	\( 4 q - q^{5} - 12 q^{7} - 27 q^{11} + 26 q^{13} - 20 q^{17} + 9 q^{19} + 12 q^{23} + 21 q^{25} + 2 q^{29} + 90 q^{31} + 36 q^{35} - 19 q^{37} + 4 q^{41} + 84 q^{47} - 10 q^{49} - 169 q^{53} + 27 q^{59} + 96 q^{61} + 22 q^{65} - 9 q^{67} - 191 q^{73} + 169 q^{77} + 168 q^{79} - 208 q^{85} - 122 q^{89} - 135 q^{91} + 366 q^{95} + 50 q^{97}+O(q^{100}) \) 4 * q - q^5 - 12 * q^7 - 27 * q^11 + 26 * q^13 - 20 * q^17 + 9 * q^19 + 12 * q^23 + 21 * q^25 + 2 * q^29 + 90 * q^31 + 36 * q^35 - 19 * q^37 + 4 * q^41 + 84 * q^47 - 10 * q^49 - 169 * q^53 + 27 * q^59 + 96 * q^61 + 22 * q^65 - 9 * q^67 - 191 * q^73 + 169 * q^77 + 168 * q^79 - 208 * q^85 - 122 * q^89 - 135 * q^91 + 366 * q^95 + 50 * q^97

Introduction

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