LMFDB - Embedded newform 700.3.o.a.649.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,3,Mod(549,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.549"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	700.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.0736185052$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	700.649
Dual form			700.3.o.a.549.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.50000i) q^{3} +7.00000i q^{7} +(3.00000 - 5.19615i) q^{9} +(-7.50000 - 12.9904i) q^{11} -13.8564 q^{13} +(-14.7224 - 25.5000i) q^{17} +(-13.5000 - 7.79423i) q^{19} +(-10.5000 + 6.06218i) q^{21} +(7.79423 + 4.50000i) q^{23} +25.9808 q^{27} +6.00000 q^{29} +(-10.5000 + 6.06218i) q^{31} +(12.9904 - 22.5000i) q^{33} +(26.8468 + 15.5000i) q^{37} +(-12.0000 - 20.7846i) q^{39} -55.4256i q^{41} +10.0000i q^{43} +(21.6506 - 37.5000i) q^{47} -49.0000 q^{49} +(25.5000 - 44.1673i) q^{51} +(-49.3634 + 28.5000i) q^{53} -27.0000i q^{57} +(70.5000 - 40.7032i) q^{59} +(-70.5000 - 40.7032i) q^{61} +(36.3731 + 21.0000i) q^{63} +(42.4352 - 24.5000i) q^{67} +15.5885i q^{69} -126.000 q^{71} +(-12.9904 - 22.5000i) q^{73} +(90.9327 - 52.5000i) q^{77} +(-36.5000 + 63.2199i) q^{79} +(-4.50000 - 7.79423i) q^{81} +13.8564 q^{83} +(5.19615 + 9.00000i) q^{87} +(-49.5000 - 28.5788i) q^{89} -96.9948i q^{91} +(-18.1865 - 10.5000i) q^{93} +27.7128 q^{97} -90.0000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{9} - 30 q^{11} - 54 q^{19} - 42 q^{21} + 24 q^{29} - 42 q^{31} - 48 q^{39} - 196 q^{49} + 102 q^{51} + 282 q^{59} - 282 q^{61} - 504 q^{71} - 146 q^{79} - 18 q^{81} - 198 q^{89} - 360 q^{99}+O(q^{100}) $ 4 * q + 12 * q^9 - 30 * q^11 - 54 * q^19 - 42 * q^21 + 24 * q^29 - 42 * q^31 - 48 * q^39 - 196 * q^49 + 102 * q^51 + 282 * q^59 - 282 * q^61 - 504 * q^71 - 146 * q^79 - 18 * q^81 - 198 * q^89 - 360 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			7.00000i			1.00000i
$7$			7.00000i			1.00000i
$8$		0			0
$9$	3.00000	−	5.19615i	0.333333	−	0.577350i
$10$		0			0
$11$	−7.50000	−	12.9904i	−0.681818	−	1.18094i	−0.974425	−	0.224711i	$-0.927856\pi$
$11$	−7.50000	−	12.9904i	−0.681818	−	1.18094i	0.292607	−	0.956233i	$-0.405477\pi$
$12$		0			0
$13$	−13.8564			−1.06588			−0.532939	−	0.846154i	$-0.678912\pi$
$13$	−13.8564			−1.06588			−0.532939	+	0.846154i	$0.678912\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−14.7224	−	25.5000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$17$	−14.7224	−	25.5000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$18$		0			0
$19$	−13.5000	−	7.79423i	−0.710526	−	0.410223i	0.100730	−	0.994914i	$-0.467882\pi$
$19$	−13.5000	−	7.79423i	−0.710526	−	0.410223i	−0.811256	+	0.584691i	$0.801216\pi$
$20$		0			0
$21$	−10.5000	+	6.06218i	−0.500000	+	0.288675i
$22$		0			0
$23$	7.79423	+	4.50000i	0.338880	+	0.195652i	0.659776	−	0.751462i	$-0.270651\pi$
$23$	7.79423	+	4.50000i	0.338880	+	0.195652i	−0.320897	+	0.947114i	$0.603984\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	25.9808			0.962250
$28$		0			0
$29$	6.00000			0.206897			0.103448	−	0.994635i	$-0.467012\pi$
$29$	6.00000			0.206897			0.103448	+	0.994635i	$0.467012\pi$
$30$		0			0
$31$	−10.5000	+	6.06218i	−0.338710	+	0.195554i	−0.659701	−	0.751528i	$-0.729317\pi$
$31$	−10.5000	+	6.06218i	−0.338710	+	0.195554i	0.320992	+	0.947082i	$0.395984\pi$
$32$		0			0
$33$	12.9904	−	22.5000i	0.393648	−	0.681818i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	26.8468	+	15.5000i	0.725589	+	0.418919i	0.816806	−	0.576912i	$-0.195742\pi$
$37$	26.8468	+	15.5000i	0.725589	+	0.418919i	−0.0912174	+	0.995831i	$0.529076\pi$
$38$		0			0
$39$	−12.0000	−	20.7846i	−0.307692	−	0.532939i
$40$		0			0
$41$		−	55.4256i		−	1.35184i	−0.736973	−	0.675922i	$-0.763745\pi$
$41$		−	55.4256i		−	1.35184i	0.736973	−	0.675922i	$-0.236255\pi$
$42$		0			0
$43$			10.0000i			0.232558i	0.993217	+	0.116279i	$0.0370967\pi$
$43$			10.0000i			0.232558i	−0.993217	+	0.116279i	$0.962903\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	21.6506	−	37.5000i	0.460652	−	0.797872i	−0.538342	−	0.842727i	$-0.680949\pi$
$47$	21.6506	−	37.5000i	0.460652	−	0.797872i	0.998994	+	0.0448543i	$0.0142824\pi$
$48$		0			0
$49$	−49.0000			−1.00000
$50$		0			0
$51$	25.5000	−	44.1673i	0.500000	−	0.866025i
$52$		0			0
$53$	−49.3634	+	28.5000i	−0.931386	+	0.537736i	−0.887250	−	0.461290i	$-0.847387\pi$
$53$	−49.3634	+	28.5000i	−0.931386	+	0.537736i	−0.0441362	+	0.999026i	$0.514054\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	27.0000i		−	0.473684i
$58$		0			0
$59$	70.5000	−	40.7032i	1.19492	−	0.689885i	0.235498	−	0.971875i	$-0.424328\pi$
$59$	70.5000	−	40.7032i	1.19492	−	0.689885i	0.959417	+	0.281990i	$0.0909946\pi$
$60$		0			0
$61$	−70.5000	−	40.7032i	−1.15574	−	0.667265i	−0.205459	−	0.978666i	$-0.565869\pi$
$61$	−70.5000	−	40.7032i	−1.15574	−	0.667265i	−0.950279	+	0.311400i	$0.899202\pi$
$62$		0			0
$63$	36.3731	+	21.0000i	0.577350	+	0.333333i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	42.4352	−	24.5000i	0.633362	−	0.365672i	−0.148691	−	0.988884i	$-0.547506\pi$
$67$	42.4352	−	24.5000i	0.633362	−	0.365672i	0.782053	+	0.623212i	$0.214173\pi$
$68$		0			0
$69$			15.5885i			0.225920i
$70$		0			0
$71$	−126.000			−1.77465			−0.887324	−	0.461147i	$-0.847438\pi$
$71$	−126.000			−1.77465			−0.887324	+	0.461147i	$0.847438\pi$
$72$		0			0
$73$	−12.9904	−	22.5000i	−0.177950	−	0.308219i	0.763228	−	0.646129i	$-0.223613\pi$
$73$	−12.9904	−	22.5000i	−0.177950	−	0.308219i	−0.941178	+	0.337910i	$0.890280\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	90.9327	−	52.5000i	1.18094	−	0.681818i
$78$		0			0
$79$	−36.5000	+	63.2199i	−0.462025	+	0.800251i	−0.999062	−	0.0433077i	$-0.986210\pi$
$79$	−36.5000	+	63.2199i	−0.462025	+	0.800251i	0.537036	+	0.843559i	$0.319544\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	13.8564			0.166945			0.0834723	−	0.996510i	$-0.473399\pi$
$83$	13.8564			0.166945			0.0834723	+	0.996510i	$0.473399\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.19615	+	9.00000i	0.0597259	+	0.103448i
$88$		0			0
$89$	−49.5000	−	28.5788i	−0.556180	−	0.321111i	0.195431	−	0.980717i	$-0.437389\pi$
$89$	−49.5000	−	28.5788i	−0.556180	−	0.321111i	−0.751611	+	0.659607i	$0.770723\pi$
$90$		0			0
$91$		−	96.9948i		−	1.06588i
$92$		0			0
$93$	−18.1865	−	10.5000i	−0.195554	−	0.112903i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	27.7128			0.285699			0.142850	−	0.989744i	$-0.454373\pi$
$97$	27.7128			0.285699			0.142850	+	0.989744i	$0.454373\pi$
$98$		0			0
$99$	−90.0000			−0.909091
$100$		0			0
$101$	85.5000	−	49.3634i	0.846535	−	0.488747i	−0.0129455	−	0.999916i	$-0.504121\pi$
$101$	85.5000	−	49.3634i	0.846535	−	0.488747i	0.859480	+	0.511169i	$0.170787\pi$
$102$		0			0
$103$	−35.5070	+	61.5000i	−0.344729	+	0.597087i	−0.985304	−	0.170808i	$-0.945362\pi$
$103$	−35.5070	+	61.5000i	−0.344729	+	0.597087i	0.640576	+	0.767895i	$0.278696\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	33.7750	+	19.5000i	0.315654	+	0.182243i	0.649454	−	0.760401i	$-0.274998\pi$
$107$	33.7750	+	19.5000i	0.315654	+	0.182243i	−0.333800	+	0.942644i	$0.608331\pi$
$108$		0			0
$109$	51.5000	+	89.2006i	0.472477	+	0.818354i	0.999504	−	0.0314943i	$-0.0100266\pi$
$109$	51.5000	+	89.2006i	0.472477	+	0.818354i	−0.527027	+	0.849849i	$0.676693\pi$
$110$		0			0
$111$			53.6936i			0.483726i
$112$		0			0
$113$		−	78.0000i		−	0.690265i	−0.938554	−	0.345133i	$-0.887834\pi$
$113$		−	78.0000i		−	0.690265i	0.938554	−	0.345133i	$-0.112166\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−41.5692	+	72.0000i	−0.355292	+	0.615385i
$118$		0			0
$119$	178.500	−	103.057i	1.50000	−	0.866025i
$120$		0			0
$121$	−52.0000	+	90.0666i	−0.429752	+	0.744352i
$122$		0			0
$123$	83.1384	−	48.0000i	0.675922	−	0.390244i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	50.0000i		−	0.393701i	−0.980434	−	0.196850i	$-0.936929\pi$
$127$		−	50.0000i		−	0.393701i	0.980434	−	0.196850i	$-0.0630713\pi$
$128$		0			0
$129$	−15.0000	+	8.66025i	−0.116279	+	0.0671338i
$130$		0			0
$131$	85.5000	+	49.3634i	0.652672	+	0.376820i	0.789479	−	0.613777i	$-0.210351\pi$
$131$	85.5000	+	49.3634i	0.652672	+	0.376820i	−0.136807	+	0.990598i	$0.543684\pi$
$132$		0			0
$133$	54.5596	−	94.5000i	0.410223	−	0.710526i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−54.5596	+	31.5000i	−0.398245	+	0.229927i	−0.685727	−	0.727859i	$-0.740515\pi$
$137$	−54.5596	+	31.5000i	−0.398245	+	0.229927i	0.287481	+	0.957786i	$0.407182\pi$
$138$		0			0
$139$		−	235.559i		−	1.69467i	−0.531060	−	0.847334i	$-0.678206\pi$
$139$		−	235.559i		−	1.69467i	0.531060	−	0.847334i	$-0.321794\pi$
$140$		0			0
$141$	75.0000			0.531915
$142$		0			0
$143$	103.923	+	180.000i	0.726735	+	1.25874i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−42.4352	−	73.5000i	−0.288675	−	0.500000i
$148$		0			0
$149$	−88.5000	+	153.286i	−0.593960	+	1.02877i	0.399733	+	0.916632i	$0.369103\pi$
$149$	−88.5000	+	153.286i	−0.593960	+	1.02877i	−0.993693	+	0.112137i	$0.964231\pi$
$150$		0			0
$151$	−27.5000	−	47.6314i	−0.182119	−	0.315440i	0.760483	−	0.649358i	$-0.224962\pi$
$151$	−27.5000	−	47.6314i	−0.182119	−	0.315440i	−0.942602	+	0.333918i	$0.891629\pi$
$152$		0			0
$153$	−176.669			−1.15470
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−49.3634	−	85.5000i	−0.314417	−	0.544586i	0.664897	−	0.746935i	$-0.268476\pi$
$157$	−49.3634	−	85.5000i	−0.314417	−	0.544586i	−0.979313	+	0.202350i	$0.935142\pi$
$158$		0			0
$159$	−85.5000	−	49.3634i	−0.537736	−	0.310462i
$160$		0			0
$161$	−31.5000	+	54.5596i	−0.195652	+	0.338880i
$162$		0			0
$163$	−19.9186	−	11.5000i	−0.122200	−	0.0705521i	0.437654	−	0.899143i	$-0.355809\pi$
$163$	−19.9186	−	11.5000i	−0.122200	−	0.0705521i	−0.559854	+	0.828591i	$0.689143\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−277.128			−1.65945			−0.829725	−	0.558172i	$-0.811503\pi$
$167$	−277.128			−1.65945			−0.829725	+	0.558172i	$0.811503\pi$
$168$		0			0
$169$	23.0000			0.136095
$170$		0			0
$171$	−81.0000	+	46.7654i	−0.473684	+	0.273482i
$172$		0			0
$173$	−70.1481	+	121.500i	−0.405480	+	0.702312i	−0.994377	−	0.105896i	$-0.966229\pi$
$173$	−70.1481	+	121.500i	−0.405480	+	0.702312i	0.588897	+	0.808208i	$0.299562\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	122.110	+	70.5000i	0.689885	+	0.398305i
$178$		0			0
$179$	31.5000	+	54.5596i	0.175978	+	0.304802i	0.940499	−	0.339796i	$-0.110358\pi$
$179$	31.5000	+	54.5596i	0.175978	+	0.304802i	−0.764522	+	0.644598i	$0.777025\pi$
$180$		0			0
$181$			124.708i			0.688993i	0.938788	+	0.344496i	$0.111950\pi$
$181$			124.708i			0.688993i	−0.938788	+	0.344496i	$0.888050\pi$
$182$		0			0
$183$		−	141.000i		−	0.770492i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−220.836	+	382.500i	−1.18094	+	2.04545i
$188$		0			0
$189$			181.865i			0.962250i
$190$		0			0
$191$	28.5000	−	49.3634i	0.149215	−	0.258447i	−0.781723	−	0.623626i	$-0.785659\pi$
$191$	28.5000	−	49.3634i	0.149215	−	0.258447i	0.930937	+	0.365179i	$0.118992\pi$
$192$		0			0
$193$	−180.999	+	104.500i	−0.937820	+	0.541451i	−0.889276	−	0.457370i	$-0.848791\pi$
$193$	−180.999	+	104.500i	−0.937820	+	0.541451i	−0.0485439	+	0.998821i	$0.515458\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			150.000i			0.761421i	0.924694	+	0.380711i	$0.124321\pi$
$197$			150.000i			0.761421i	−0.924694	+	0.380711i	$0.875679\pi$
$198$		0			0
$199$	178.500	−	103.057i	0.896985	−	0.517874i	0.0207642	−	0.999784i	$-0.493390\pi$
$199$	178.500	−	103.057i	0.896985	−	0.517874i	0.876221	+	0.481910i	$0.160057\pi$
$200$		0			0
$201$	73.5000	+	42.4352i	0.365672	+	0.211121i
$202$		0			0
$203$			42.0000i			0.206897i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	46.7654	−	27.0000i	0.225920	−	0.130435i
$208$		0			0
$209$			233.827i			1.11879i
$210$		0			0
$211$	346.000			1.63981			0.819905	−	0.572499i	$-0.194026\pi$
$211$	346.000			1.63981			0.819905	+	0.572499i	$0.194026\pi$
$212$		0			0
$213$	−109.119	−	189.000i	−0.512297	−	0.887324i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−42.4352	−	73.5000i	−0.195554	−	0.338710i
$218$		0			0
$219$	22.5000	−	38.9711i	0.102740	−	0.177950i
$220$		0			0
$221$	204.000	+	353.338i	0.923077	+	1.59882i
$222$		0			0
$223$	332.554			1.49127			0.745636	−	0.666353i	$-0.232146\pi$
$223$	332.554			1.49127			0.745636	+	0.666353i	$0.232146\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−70.1481	−	121.500i	−0.309022	−	0.535242i	0.669126	−	0.743149i	$-0.266668\pi$
$227$	−70.1481	−	121.500i	−0.309022	−	0.535242i	−0.978149	+	0.207906i	$0.933335\pi$
$228$		0			0
$229$	−145.500	−	84.0045i	−0.635371	−	0.366832i	0.147458	−	0.989068i	$-0.452891\pi$
$229$	−145.500	−	84.0045i	−0.635371	−	0.366832i	−0.782829	+	0.622237i	$0.786224\pi$
$230$		0			0
$231$	157.500	+	90.9327i	0.681818	+	0.393648i
$232$		0			0
$233$	236.425	+	136.500i	1.01470	+	0.585837i	0.912564	−	0.408934i	$-0.134099\pi$
$233$	236.425	+	136.500i	1.01470	+	0.585837i	0.102135	+	0.994771i	$0.467433\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−126.440			−0.533501
$238$		0			0
$239$	222.000			0.928870			0.464435	−	0.885607i	$-0.346257\pi$
$239$	222.000			0.928870			0.464435	+	0.885607i	$0.346257\pi$
$240$		0			0
$241$	−190.500	+	109.985i	−0.790456	+	0.456370i	−0.840123	−	0.542396i	$-0.817517\pi$
$241$	−190.500	+	109.985i	−0.790456	+	0.456370i	0.0496668	+	0.998766i	$0.484184\pi$
$242$		0			0
$243$	124.708	−	216.000i	0.513200	−	0.888889i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	187.061	+	108.000i	0.757334	+	0.437247i
$248$		0			0
$249$	12.0000	+	20.7846i	0.0481928	+	0.0834723i
$250$		0			0
$251$			96.9948i			0.386434i	0.981156	+	0.193217i	$0.0618921\pi$
$251$			96.9948i			0.386434i	−0.981156	+	0.193217i	$0.938108\pi$
$252$		0			0
$253$		−	135.000i		−	0.533597i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−96.1288	+	166.500i	−0.374042	+	0.647860i	−0.990183	−	0.139776i	$-0.955362\pi$
$257$	−96.1288	+	166.500i	−0.374042	+	0.647860i	0.616141	+	0.787636i	$0.288695\pi$
$258$		0			0
$259$	−108.500	+	187.928i	−0.418919	+	0.725589i
$260$		0			0
$261$	18.0000	−	31.1769i	0.0689655	−	0.119452i
$262$		0			0
$263$	−132.502	+	76.5000i	−0.503809	+	0.290875i	−0.730285	−	0.683142i	$-0.760613\pi$
$263$	−132.502	+	76.5000i	−0.503809	+	0.290875i	0.226476	+	0.974017i	$0.427280\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	99.0000i		−	0.370787i
$268$		0			0
$269$	394.500	−	227.765i	1.46654	−	0.846709i	0.467243	−	0.884129i	$-0.345247\pi$
$269$	394.500	−	227.765i	1.46654	−	0.846709i	0.999300	+	0.0374200i	$0.0119139\pi$
$270$		0			0
$271$	61.5000	+	35.5070i	0.226937	+	0.131022i	0.609158	−	0.793049i	$-0.291507\pi$
$271$	61.5000	+	35.5070i	0.226937	+	0.131022i	−0.382221	+	0.924071i	$0.624841\pi$
$272$		0			0
$273$	145.492	−	84.0000i	0.532939	−	0.307692i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−310.903	+	179.500i	−1.12239	+	0.648014i	−0.942011	−	0.335582i	$-0.891067\pi$
$277$	−310.903	+	179.500i	−1.12239	+	0.648014i	−0.180383	+	0.983596i	$0.557734\pi$
$278$		0			0
$279$			72.7461i			0.260739i
$280$		0			0
$281$	−222.000			−0.790036			−0.395018	−	0.918673i	$-0.629262\pi$
$281$	−222.000			−0.790036			−0.395018	+	0.918673i	$0.629262\pi$
$282$		0			0
$283$	0.866025	+	1.50000i	0.00306016	+	0.00530035i	0.867551	−	0.497347i	$-0.165693\pi$
$283$	0.866025	+	1.50000i	0.00306016	+	0.00530035i	−0.864491	+	0.502648i	$0.832359\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	387.979			1.35184
$288$		0			0
$289$	−289.000	+	500.563i	−1.00000	+	1.73205i
$290$		0			0
$291$	24.0000	+	41.5692i	0.0824742	+	0.142850i
$292$		0			0
$293$	−235.559			−0.803955			−0.401978	−	0.915649i	$-0.631677\pi$
$293$	−235.559			−0.803955			−0.401978	+	0.915649i	$0.631677\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−194.856	−	337.500i	−0.656080	−	1.13636i
$298$		0			0
$299$	−108.000	−	62.3538i	−0.361204	−	0.208541i
$300$		0			0
$301$	−70.0000			−0.232558
$302$		0			0
$303$	148.090	+	85.5000i	0.488747	+	0.282178i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	96.9948			0.315944			0.157972	−	0.987444i	$-0.449504\pi$
$307$	96.9948			0.315944			0.157972	+	0.987444i	$0.449504\pi$
$308$		0			0
$309$	−123.000			−0.398058
$310$		0			0
$311$	421.500	−	243.353i	1.35531	−	0.782486i	0.366319	−	0.930489i	$-0.380618\pi$
$311$	421.500	−	243.353i	1.35531	−	0.782486i	0.988987	+	0.148003i	$0.0472847\pi$
$312$		0			0
$313$	−111.717	+	193.500i	−0.356924	+	0.618211i	−0.987445	−	0.157961i	$-0.949508\pi$
$313$	−111.717	+	193.500i	−0.356924	+	0.618211i	0.630521	+	0.776172i	$0.282841\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	387.113	+	223.500i	1.22118	+	0.705047i	0.965169	−	0.261627i	$-0.0842591\pi$
$317$	387.113	+	223.500i	1.22118	+	0.705047i	0.256009	+	0.966674i	$0.417592\pi$
$318$		0			0
$319$	−45.0000	−	77.9423i	−0.141066	−	0.244333i
$320$		0			0
$321$			67.5500i			0.210436i
$322$		0			0
$323$			459.000i			1.42105i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−89.2006	+	154.500i	−0.272785	+	0.472477i
$328$		0			0
$329$	262.500	+	151.554i	0.797872	+	0.460652i
$330$		0			0
$331$	−75.5000	+	130.770i	−0.228097	+	0.395075i	−0.957244	−	0.289282i	$-0.906584\pi$
$331$	−75.5000	+	130.770i	−0.228097	+	0.395075i	0.729147	+	0.684357i	$0.239917\pi$
$332$		0			0
$333$	161.081	−	93.0000i	0.483726	−	0.279279i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	274.000i		−	0.813056i	−0.913638	−	0.406528i	$-0.866739\pi$
$337$		−	274.000i		−	0.813056i	0.913638	−	0.406528i	$-0.133261\pi$
$338$		0			0
$339$	117.000	−	67.5500i	0.345133	−	0.199262i
$340$		0			0
$341$	157.500	+	90.9327i	0.461877	+	0.266665i
$342$		0			0
$343$		−	343.000i		−	1.00000i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−470.252	+	271.500i	−1.35519	+	0.782421i	−0.988971	−	0.148107i	$-0.952682\pi$
$347$	−470.252	+	271.500i	−1.35519	+	0.782421i	−0.366221	+	0.930528i	$0.619349\pi$
$348$		0			0
$349$		−	180.133i		−	0.516141i	−0.966126	−	0.258071i	$-0.916913\pi$
$349$		−	180.133i		−	0.516141i	0.966126	−	0.258071i	$-0.0830867\pi$
$350$		0			0
$351$	−360.000			−1.02564
$352$		0			0
$353$	−151.554	−	262.500i	−0.429333	−	0.743626i	0.567481	−	0.823386i	$-0.307918\pi$
$353$	−151.554	−	262.500i	−0.429333	−	0.743626i	−0.996814	+	0.0797602i	$0.974585\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	309.171	+	178.500i	0.866025	+	0.500000i
$358$		0			0
$359$	19.5000	−	33.7750i	0.0543175	−	0.0940808i	−0.837588	−	0.546302i	$-0.816035\pi$
$359$	19.5000	−	33.7750i	0.0543175	−	0.0940808i	0.891906	+	0.452221i	$0.149368\pi$
$360$		0			0
$361$	−59.0000	−	102.191i	−0.163435	−	0.283078i
$362$		0			0
$363$	−180.133			−0.496235
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−174.071	−	301.500i	−0.474308	−	0.821526i	0.525259	−	0.850942i	$-0.323968\pi$
$367$	−174.071	−	301.500i	−0.474308	−	0.821526i	−0.999567	+	0.0294165i	$0.990635\pi$
$368$		0			0
$369$	−288.000	−	166.277i	−0.780488	−	0.450615i
$370$		0			0
$371$	−199.500	−	345.544i	−0.537736	−	0.931386i
$372$		0			0
$373$	−331.688	−	191.500i	−0.889243	−	0.513405i	−0.0155484	−	0.999879i	$-0.504949\pi$
$373$	−331.688	−	191.500i	−0.889243	−	0.513405i	−0.873695	+	0.486474i	$0.838283\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−83.1384			−0.220526
$378$		0			0
$379$	230.000			0.606860			0.303430	−	0.952854i	$-0.401868\pi$
$379$	230.000			0.606860			0.303430	+	0.952854i	$0.401868\pi$
$380$		0			0
$381$	75.0000	−	43.3013i	0.196850	−	0.113652i
$382$		0			0
$383$	−160.215	+	277.500i	−0.418315	+	0.724543i	−0.995770	−	0.0918794i	$-0.970713\pi$
$383$	−160.215	+	277.500i	−0.418315	+	0.724543i	0.577455	+	0.816423i	$0.304046\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	51.9615	+	30.0000i	0.134268	+	0.0775194i
$388$		0			0
$389$	−100.500	−	174.071i	−0.258355	−	0.447484i	0.707447	−	0.706767i	$-0.249847\pi$
$389$	−100.500	−	174.071i	−0.258355	−	0.447484i	−0.965801	+	0.259283i	$0.916514\pi$
$390$		0			0
$391$		−	265.004i		−	0.677759i
$392$		0			0
$393$			171.000i			0.435115i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−26.8468	+	46.5000i	−0.0676241	+	0.117128i	−0.897855	−	0.440291i	$-0.854875\pi$
$397$	−26.8468	+	46.5000i	−0.0676241	+	0.117128i	0.830231	+	0.557420i	$0.188209\pi$
$398$		0			0
$399$	189.000			0.473684
$400$		0			0
$401$	88.5000	−	153.286i	0.220698	−	0.382261i	−0.734322	−	0.678801i	$-0.762500\pi$
$401$	88.5000	−	153.286i	0.220698	−	0.382261i	0.955020	+	0.296541i	$0.0958331\pi$
$402$		0			0
$403$	145.492	−	84.0000i	0.361023	−	0.208437i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	465.000i		−	1.14251i
$408$		0			0
$409$	−289.500	+	167.143i	−0.707824	+	0.408662i	−0.810255	−	0.586078i	$-0.800671\pi$
$409$	−289.500	+	167.143i	−0.707824	+	0.408662i	0.102431	+	0.994740i	$0.467338\pi$
$410$		0			0
$411$	−94.5000	−	54.5596i	−0.229927	−	0.132748i
$412$		0			0
$413$	284.922	+	493.500i	0.689885	+	1.19492i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	353.338	−	204.000i	0.847334	−	0.489209i
$418$		0			0
$419$		−	595.825i		−	1.42202i	−0.703183	−	0.711009i	$-0.748239\pi$
$419$		−	595.825i		−	1.42202i	0.703183	−	0.711009i	$-0.251761\pi$
$420$		0			0
$421$	−22.0000			−0.0522565			−0.0261283	−	0.999659i	$-0.508318\pi$
$421$	−22.0000			−0.0522565			−0.0261283	+	0.999659i	$0.508318\pi$
$422$		0			0
$423$	−129.904	−	225.000i	−0.307101	−	0.531915i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	284.922	−	493.500i	0.667265	−	1.15574i
$428$		0			0
$429$	−180.000	+	311.769i	−0.419580	+	0.726735i
$430$		0			0
$431$	−163.500	−	283.190i	−0.379350	−	0.657054i	0.611618	−	0.791154i	$-0.290519\pi$
$431$	−163.500	−	283.190i	−0.379350	−	0.657054i	−0.990968	+	0.134100i	$0.957186\pi$
$432$		0			0
$433$	−27.7128			−0.0640019			−0.0320009	−	0.999488i	$-0.510188\pi$
$433$	−27.7128			−0.0640019			−0.0320009	+	0.999488i	$0.510188\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−70.1481	−	121.500i	−0.160522	−	0.278032i
$438$		0			0
$439$	−517.500	−	298.779i	−1.17882	−	0.680589i	−0.223075	−	0.974801i	$-0.571610\pi$
$439$	−517.500	−	298.779i	−1.17882	−	0.680589i	−0.955740	+	0.294212i	$0.904943\pi$
$440$		0			0
$441$	−147.000	+	254.611i	−0.333333	+	0.577350i
$442$		0			0
$443$	631.333	+	364.500i	1.42513	+	0.822799i	0.996731	−	0.0807907i	$-0.0257445\pi$
$443$	631.333	+	364.500i	1.42513	+	0.822799i	0.428399	+	0.903590i	$0.359078\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−306.573			−0.685846
$448$		0			0
$449$	270.000			0.601336			0.300668	−	0.953729i	$-0.402790\pi$
$449$	270.000			0.601336			0.300668	+	0.953729i	$0.402790\pi$
$450$		0			0
$451$	−720.000	+	415.692i	−1.59645	+	0.921712i
$452$		0			0
$453$	47.6314	−	82.5000i	0.105147	−	0.182119i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	691.954	+	399.500i	1.51412	+	0.874179i	0.999863	+	0.0165451i	$0.00526672\pi$
$457$	691.954	+	399.500i	1.51412	+	0.874179i	0.514260	+	0.857634i	$0.328067\pi$
$458$		0			0
$459$	−382.500	−	662.509i	−0.833333	−	1.44338i
$460$		0			0
$461$		−	429.549i		−	0.931776i	−0.884844	−	0.465888i	$-0.845735\pi$
$461$		−	429.549i		−	0.931776i	0.884844	−	0.465888i	$-0.154265\pi$
$462$		0			0
$463$		−	814.000i		−	1.75810i	−0.476730	−	0.879050i	$-0.658178\pi$
$463$		−	814.000i		−	1.75810i	0.476730	−	0.879050i	$-0.341822\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−200.052	+	346.500i	−0.428377	+	0.741970i	−0.996729	−	0.0808151i	$-0.974248\pi$
$467$	−200.052	+	346.500i	−0.428377	+	0.741970i	0.568353	+	0.822785i	$0.307581\pi$
$468$		0			0
$469$	171.500	+	297.047i	0.365672	+	0.633362i
$470$		0			0
$471$	85.5000	−	148.090i	0.181529	−	0.314417i
$472$		0			0
$473$	129.904	−	75.0000i	0.274638	−	0.158562i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			342.000i			0.716981i
$478$		0			0
$479$	466.500	−	269.334i	0.973904	−	0.562284i	0.0734798	−	0.997297i	$-0.476590\pi$
$479$	466.500	−	269.334i	0.973904	−	0.562284i	0.900424	+	0.435013i	$0.143256\pi$
$480$		0			0
$481$	−372.000	−	214.774i	−0.773389	−	0.446516i
$482$		0			0
$483$	−109.119			−0.225920
$484$		0			0
$485$		0			0
$486$		0			0
$487$	742.184	−	428.500i	1.52399	−	0.879877i	0.524395	−	0.851475i	$-0.324292\pi$
$487$	742.184	−	428.500i	1.52399	−	0.879877i	0.999597	−	0.0284015i	$-0.00904169\pi$
$488$		0			0
$489$		−	39.8372i		−	0.0814666i
$490$		0			0
$491$	570.000			1.16090			0.580448	−	0.814297i	$-0.302877\pi$
$491$	570.000			1.16090			0.580448	+	0.814297i	$0.302877\pi$
$492$		0			0
$493$	−88.3346	−	153.000i	−0.179178	−	0.310345i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		−	882.000i		−	1.77465i
$498$		0			0
$499$	−212.500	+	368.061i	−0.425852	+	0.737597i	−0.996500	−	0.0835981i	$-0.973359\pi$
$499$	−212.500	+	368.061i	−0.425852	+	0.737597i	0.570648	+	0.821195i	$0.306692\pi$
$500$		0			0
$501$	−240.000	−	415.692i	−0.479042	−	0.829725i
$502$		0			0
$503$	−193.990			−0.385665			−0.192833	−	0.981232i	$-0.561767\pi$
$503$	−193.990			−0.385665			−0.192833	+	0.981232i	$0.561767\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	19.9186	+	34.5000i	0.0392871	+	0.0680473i
$508$		0			0
$509$	334.500	+	193.124i	0.657171	+	0.379418i	0.791198	−	0.611560i	$-0.209458\pi$
$509$	334.500	+	193.124i	0.657171	+	0.379418i	−0.134027	+	0.990978i	$0.542791\pi$
$510$		0			0
$511$	157.500	−	90.9327i	0.308219	−	0.177950i
$512$		0			0
$513$	−350.740	−	202.500i	−0.683704	−	0.394737i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−649.519			−1.25632
$518$		0			0
$519$	−243.000			−0.468208
$520$		0			0
$521$	−214.500	+	123.842i	−0.411708	+	0.237700i	−0.691523	−	0.722354i	$-0.743060\pi$
$521$	−214.500	+	123.842i	−0.411708	+	0.237700i	0.279815	+	0.960054i	$0.409727\pi$
$522$		0			0
$523$	−395.774	+	685.500i	−0.756737	+	1.31071i	0.187769	+	0.982213i	$0.439874\pi$
$523$	−395.774	+	685.500i	−0.756737	+	1.31071i	−0.944506	+	0.328494i	$0.893459\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	309.171	+	178.500i	0.586662	+	0.338710i
$528$		0			0
$529$	−224.000	−	387.979i	−0.423440	−	0.733420i
$530$		0			0
$531$		−	488.438i		−	0.919846i
$532$		0			0
$533$			768.000i			1.44090i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−54.5596	+	94.5000i	−0.101601	+	0.175978i
$538$		0			0
$539$	367.500	+	636.529i	0.681818	+	1.18094i
$540$		0			0
$541$	360.500	−	624.404i	0.666359	−	1.15417i	−0.312556	−	0.949899i	$-0.601185\pi$
$541$	360.500	−	624.404i	0.666359	−	1.15417i	0.978915	−	0.204268i	$-0.0654813\pi$
$542$		0			0
$543$	−187.061	+	108.000i	−0.344496	+	0.198895i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			118.000i			0.215722i	0.994166	+	0.107861i	$0.0344002\pi$
$547$			118.000i			0.215722i	−0.994166	+	0.107861i	$0.965600\pi$
$548$		0			0
$549$	−423.000	+	244.219i	−0.770492	+	0.444844i
$550$		0			0
$551$	−81.0000	−	46.7654i	−0.147005	−	0.0848736i
$552$		0			0
$553$	−442.539	−	255.500i	−0.800251	−	0.462025i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	548.194	−	316.500i	0.984190	−	0.568223i	0.0806578	−	0.996742i	$-0.474298\pi$
$557$	548.194	−	316.500i	0.984190	−	0.568223i	0.903533	+	0.428519i	$0.140965\pi$
$558$		0			0
$559$		−	138.564i		−	0.247878i
$560$		0			0
$561$	−765.000			−1.36364
$562$		0			0
$563$	−137.698	−	238.500i	−0.244579	−	0.423623i	0.717434	−	0.696626i	$-0.245316\pi$
$563$	−137.698	−	238.500i	−0.244579	−	0.423623i	−0.962013	+	0.273003i	$0.911983\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	54.5596	−	31.5000i	0.0962250	−	0.0555556i
$568$		0			0
$569$	223.500	−	387.113i	0.392794	−	0.680340i	−0.600023	−	0.799983i	$-0.704842\pi$
$569$	223.500	−	387.113i	0.392794	−	0.680340i	0.992817	+	0.119643i	$0.0381751\pi$
$570$		0			0
$571$	−263.500	−	456.395i	−0.461471	−	0.799291i	0.537563	−	0.843223i	$-0.319345\pi$
$571$	−263.500	−	456.395i	−0.461471	−	0.799291i	−0.999035	+	0.0439319i	$0.986012\pi$
$572$		0			0
$573$	98.7269			0.172298
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−84.0045	−	145.500i	−0.145588	−	0.252166i	0.784004	−	0.620756i	$-0.213174\pi$
$577$	−84.0045	−	145.500i	−0.145588	−	0.252166i	−0.929592	+	0.368589i	$0.879841\pi$
$578$		0			0
$579$	−313.500	−	180.999i	−0.541451	−	0.312607i
$580$		0			0
$581$			96.9948i			0.166945i
$582$		0			0
$583$	740.452	+	427.500i	1.27007	+	0.733276i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	956.092			1.62878			0.814388	−	0.580320i	$-0.197073\pi$
$587$	956.092			1.62878			0.814388	+	0.580320i	$0.197073\pi$
$588$		0			0
$589$	189.000			0.320883
$590$		0			0
$591$	−225.000	+	129.904i	−0.380711	+	0.219803i
$592$		0			0
$593$	151.554	−	262.500i	0.255572	−	0.442664i	−0.709478	−	0.704727i	$-0.751069\pi$
$593$	151.554	−	262.500i	0.255572	−	0.442664i	0.965051	+	0.262063i	$0.0844027\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	309.171	+	178.500i	0.517874	+	0.298995i
$598$		0			0
$599$	403.500	+	698.883i	0.673623	+	1.16675i	0.976869	+	0.213837i	$0.0685960\pi$
$599$	403.500	+	698.883i	0.673623	+	1.16675i	−0.303247	+	0.952912i	$0.598071\pi$
$600$		0			0
$601$			387.979i			0.645556i	0.946475	+	0.322778i	$0.104617\pi$
$601$			387.979i			0.645556i	−0.946475	+	0.322778i	$0.895383\pi$
$602$		0			0
$603$		−	294.000i		−	0.487562i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−366.329	+	634.500i	−0.603507	+	1.04530i	0.388779	+	0.921331i	$0.372897\pi$
$607$	−366.329	+	634.500i	−0.603507	+	1.04530i	−0.992286	+	0.123974i	$0.960436\pi$
$608$		0			0
$609$	−63.0000	+	36.3731i	−0.103448	+	0.0597259i
$610$		0			0
$611$	−300.000	+	519.615i	−0.490998	+	0.850434i
$612$		0			0
$613$	435.611	−	251.500i	0.710621	−	0.410277i	−0.100670	−	0.994920i	$-0.532099\pi$
$613$	435.611	−	251.500i	0.710621	−	0.410277i	0.811291	+	0.584643i	$0.198765\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	930.000i		−	1.50729i	−0.657280	−	0.753647i	$-0.728293\pi$
$617$		−	930.000i		−	1.50729i	0.657280	−	0.753647i	$-0.271707\pi$
$618$		0			0
$619$	−457.500	+	264.138i	−0.739095	+	0.426717i	−0.821740	−	0.569862i	$-0.806997\pi$
$619$	−457.500	+	264.138i	−0.739095	+	0.426717i	0.0826450	+	0.996579i	$0.473663\pi$
$620$		0			0
$621$	202.500	+	116.913i	0.326087	+	0.188266i
$622$		0			0
$623$	200.052	−	346.500i	0.321111	−	0.556180i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−350.740	+	202.500i	−0.559394	+	0.322967i
$628$		0			0
$629$		−	912.791i		−	1.45118i
$630$		0			0
$631$	194.000			0.307448			0.153724	−	0.988114i	$-0.450873\pi$
$631$	194.000			0.307448			0.153724	+	0.988114i	$0.450873\pi$
$632$		0			0
$633$	299.645	+	519.000i	0.473372	+	0.819905i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	678.964			1.06588
$638$		0			0
$639$	−378.000	+	654.715i	−0.591549	+	1.02459i
$640$		0			0
$641$	16.5000	+	28.5788i	0.0257410	+	0.0445848i	0.878609	−	0.477542i	$-0.158472\pi$
$641$	16.5000	+	28.5788i	0.0257410	+	0.0445848i	−0.852868	+	0.522127i	$0.825139\pi$
$642$		0			0
$643$	346.410			0.538741			0.269370	−	0.963037i	$-0.413184\pi$
$643$	346.410			0.538741			0.269370	+	0.963037i	$0.413184\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−381.917	−	661.500i	−0.590289	−	1.02241i	−0.994193	−	0.107610i	$-0.965680\pi$
$647$	−381.917	−	661.500i	−0.590289	−	1.02241i	0.403904	−	0.914801i	$-0.367653\pi$
$648$		0			0
$649$	−1057.50	−	610.548i	−1.62943	−	0.940752i
$650$		0			0
$651$	73.5000	−	127.306i	0.112903	−	0.195554i
$652$		0			0
$653$	28.5788	+	16.5000i	0.0437654	+	0.0252680i	0.521723	−	0.853115i	$-0.325289\pi$
$653$	28.5788	+	16.5000i	0.0437654	+	0.0252680i	−0.477958	+	0.878383i	$0.658623\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−155.885			−0.237267
$658$		0			0
$659$	870.000			1.32018			0.660091	−	0.751186i	$-0.270518\pi$
$659$	870.000			1.32018			0.660091	+	0.751186i	$0.270518\pi$
$660$		0			0
$661$	877.500	−	506.625i	1.32753	−	0.766452i	0.342616	−	0.939475i	$-0.388687\pi$
$661$	877.500	−	506.625i	1.32753	−	0.766452i	0.984918	+	0.173023i	$0.0553536\pi$
$662$		0			0
$663$	−353.338	+	612.000i	−0.532939	+	0.923077i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	46.7654	+	27.0000i	0.0701130	+	0.0404798i
$668$		0			0
$669$	288.000	+	498.831i	0.430493	+	0.745636i
$670$		0			0
$671$			1221.10i			1.81981i
$672$		0			0
$673$		−	14.0000i		−	0.0208024i	−0.999946	−	0.0104012i	$-0.996689\pi$
$673$		−	14.0000i		−	0.0208024i	0.999946	−	0.0104012i	$-0.00331086\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−137.698	+	238.500i	−0.203394	+	0.352290i	−0.949620	−	0.313404i	$-0.898531\pi$
$677$	−137.698	+	238.500i	−0.203394	+	0.352290i	0.746226	+	0.665693i	$0.231864\pi$
$678$		0			0
$679$			193.990i			0.285699i
$680$		0			0
$681$	121.500	−	210.444i	0.178414	−	0.309022i
$682$		0			0
$683$	−236.425	+	136.500i	−0.346157	+	0.199854i	−0.662991	−	0.748627i	$-0.730713\pi$
$683$	−236.425	+	136.500i	−0.346157	+	0.199854i	0.316835	+	0.948481i	$0.397380\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	291.000i		−	0.423581i
$688$		0			0
$689$	684.000	−	394.908i	0.992743	−	0.573160i
$690$		0			0
$691$	133.500	+	77.0763i	0.193198	+	0.111543i	0.593479	−	0.804850i	$-0.297754\pi$
$691$	133.500	+	77.0763i	0.193198	+	0.111543i	−0.400281	+	0.916393i	$0.631087\pi$
$692$		0			0
$693$		−	630.000i		−	0.909091i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1413.35	+	816.000i	−2.02777	+	1.17073i
$698$		0			0
$699$			472.850i			0.676466i
$700$		0			0
$701$	906.000			1.29244			0.646220	−	0.763151i	$-0.276349\pi$
$701$	906.000			1.29244			0.646220	+	0.763151i	$0.276349\pi$
$702$		0			0
$703$	−241.621	−	418.500i	−0.343700	−	0.595306i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	345.544	+	598.500i	0.488747	+	0.846535i
$708$		0			0
$709$	351.500	−	608.816i	0.495769	−	0.858697i	−0.504219	−	0.863576i	$-0.668220\pi$
$709$	351.500	−	608.816i	0.495769	−	0.858697i	0.999988	+	0.00487903i	$0.00155305\pi$
$710$		0			0
$711$	219.000	+	379.319i	0.308017	+	0.533501i
$712$		0			0
$713$	−109.119			−0.153042
$714$		0			0
$715$		0			0
$716$		0			0
$717$	192.258	+	333.000i	0.268142	+	0.464435i
$718$		0			0
$719$	514.500	+	297.047i	0.715577	+	0.413139i	0.813123	−	0.582092i	$-0.197766\pi$
$719$	514.500	+	297.047i	0.715577	+	0.413139i	−0.0975455	+	0.995231i	$0.531099\pi$
$720$		0			0
$721$	−430.500	−	248.549i	−0.597087	−	0.344729i
$722$		0			0
$723$	−329.956	−	190.500i	−0.456370	−	0.263485i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	27.7128			0.0381194			0.0190597	−	0.999818i	$-0.493933\pi$
$727$	27.7128			0.0381194			0.0190597	+	0.999818i	$0.493933\pi$
$728$		0			0
$729$	351.000			0.481481
$730$		0			0
$731$	255.000	−	147.224i	0.348837	−	0.201401i
$732$		0			0
$733$	484.108	−	838.500i	0.660448	−	1.14393i	−0.320050	−	0.947401i	$-0.603700\pi$
$733$	484.108	−	838.500i	0.660448	−	1.14393i	0.980498	−	0.196529i	$-0.0629668\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−636.529	−	367.500i	−0.863675	−	0.498643i
$738$		0			0
$739$	−288.500	−	499.697i	−0.390392	−	0.676180i	0.602109	−	0.798414i	$-0.294327\pi$
$739$	−288.500	−	499.697i	−0.390392	−	0.676180i	−0.992501	+	0.122235i	$0.960994\pi$
$740$		0			0
$741$			374.123i			0.504889i
$742$		0			0
$743$			162.000i			0.218035i	0.994040	+	0.109017i	$0.0347705\pi$
$743$			162.000i			0.218035i	−0.994040	+	0.109017i	$0.965230\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	41.5692	−	72.0000i	0.0556482	−	0.0963855i
$748$		0			0
$749$	−136.500	+	236.425i	−0.182243	+	0.315654i
$750$		0			0
$751$	−387.500	+	671.170i	−0.515979	+	0.893701i	0.483849	+	0.875151i	$0.339238\pi$
$751$	−387.500	+	671.170i	−0.515979	+	0.893701i	−0.999828	+	0.0185499i	$0.994095\pi$
$752$		0			0
$753$	−145.492	+	84.0000i	−0.193217	+	0.111554i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			950.000i			1.25495i	0.778635	+	0.627477i	$0.215912\pi$
$757$			950.000i			1.25495i	−0.778635	+	0.627477i	$0.784088\pi$
$758$		0			0
$759$	202.500	−	116.913i	0.266798	−	0.154036i
$760$		0			0
$761$	169.500	+	97.8609i	0.222733	+	0.128595i	0.607215	−	0.794537i	$-0.292287\pi$
$761$	169.500	+	97.8609i	0.222733	+	0.128595i	−0.384482	+	0.923133i	$0.625620\pi$
$762$		0			0
$763$	−624.404	+	360.500i	−0.818354	+	0.472477i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−976.877	+	564.000i	−1.27363	+	0.735332i
$768$		0			0
$769$			914.523i			1.18924i	0.804008	+	0.594618i	$0.202697\pi$
$769$			914.523i			1.18924i	−0.804008	+	0.594618i	$0.797303\pi$
$770$		0			0
$771$	−333.000			−0.431907
$772$		0			0
$773$	−89.2006	−	154.500i	−0.115395	−	0.199871i	0.802542	−	0.596595i	$-0.203480\pi$
$773$	−89.2006	−	154.500i	−0.115395	−	0.199871i	−0.917938	+	0.396725i	$0.870147\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−375.855			−0.483726
$778$		0			0
$779$	−432.000	+	748.246i	−0.554557	+	0.960521i
$780$		0			0
$781$	945.000	+	1636.79i	1.20999	+	2.09576i
$782$		0			0
$783$	155.885			0.199086
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−167.143	−	289.500i	−0.212380	−	0.367853i	0.740079	−	0.672520i	$-0.234788\pi$
$787$	−167.143	−	289.500i	−0.212380	−	0.367853i	−0.952459	+	0.304667i	$0.901455\pi$
$788$		0			0
$789$	−229.500	−	132.502i	−0.290875	−	0.167936i
$790$		0			0
$791$	546.000			0.690265
$792$		0			0
$793$	976.877	+	564.000i	1.23187	+	0.711223i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−872.954			−1.09530			−0.547650	−	0.836708i	$-0.684477\pi$
$797$	−872.954			−1.09530			−0.547650	+	0.836708i	$0.684477\pi$
$798$		0			0
$799$	−1275.00			−1.59574
$800$		0			0
$801$	−297.000	+	171.473i	−0.370787	+	0.214074i
$802$		0			0
$803$	−194.856	+	337.500i	−0.242660	+	0.420299i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	683.294	+	394.500i	0.846709	+	0.488848i
$808$		0			0
$809$	−232.500	−	402.702i	−0.287392	−	0.497777i	0.685795	−	0.727795i	$-0.259455\pi$
$809$	−232.500	−	402.702i	−0.287392	−	0.497777i	−0.973186	+	0.230018i	$0.926122\pi$
$810$		0			0
$811$			124.708i			0.153770i	0.997040	+	0.0768851i	$0.0244975\pi$
$811$			124.708i			0.153770i	−0.997040	+	0.0768851i	$0.975503\pi$
$812$		0			0
$813$			123.000i			0.151292i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	77.9423	−	135.000i	0.0954006	−	0.165239i
$818$		0			0
$819$	−504.000	−	290.985i	−0.615385	−	0.355292i
$820$		0			0
$821$	376.500	−	652.117i	0.458587	−	0.794296i	−0.540299	−	0.841473i	$-0.681689\pi$
$821$	376.500	−	652.117i	0.458587	−	0.794296i	0.998887	+	0.0471767i	$0.0150224\pi$
$822$		0			0
$823$	−21.6506	+	12.5000i	−0.0263070	+	0.0151883i	−0.513096	−	0.858331i	$-0.671501\pi$
$823$	−21.6506	+	12.5000i	−0.0263070	+	0.0151883i	0.486789	+	0.873520i	$0.338168\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			246.000i			0.297461i	0.988878	+	0.148730i	$0.0475186\pi$
$827$			246.000i			0.297461i	−0.988878	+	0.148730i	$0.952481\pi$
$828$		0			0
$829$	1282.50	−	740.452i	1.54704	−	0.893187i	0.548679	−	0.836033i	$-0.315131\pi$
$829$	1282.50	−	740.452i	1.54704	−	0.893187i	0.998365	−	0.0571537i	$-0.0182025\pi$
$830$		0			0
$831$	−538.500	−	310.903i	−0.648014	−	0.374131i
$832$		0			0
$833$	721.399	+	1249.50i	0.866025	+	1.50000i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−272.798	+	157.500i	−0.325924	+	0.188172i
$838$		0			0
$839$			360.267i			0.429400i	0.976680	+	0.214700i	$0.0688774\pi$
$839$			360.267i			0.429400i	−0.976680	+	0.214700i	$0.931123\pi$
$840$		0			0
$841$	−805.000			−0.957194
$842$		0			0
$843$	−192.258	−	333.000i	−0.228064	−	0.395018i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−630.466	−	364.000i	−0.744352	−	0.429752i
$848$		0			0
$849$	−1.50000	+	2.59808i	−0.00176678	+	0.00306016i
$850$		0			0
$851$	139.500	+	241.621i	0.163925	+	0.283926i
$852$		0			0
$853$	−1205.51			−1.41326			−0.706628	−	0.707585i	$-0.749785\pi$
$853$	−1205.51			−1.41326			−0.706628	+	0.707585i	$0.749785\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−97.8609	−	169.500i	−0.114190	−	0.197783i	0.803266	−	0.595621i	$-0.203094\pi$
$857$	−97.8609	−	169.500i	−0.114190	−	0.197783i	−0.917456	+	0.397838i	$0.869761\pi$
$858$		0			0
$859$	1234.50	+	712.739i	1.43714	+	0.829731i	0.997650	−	0.0685183i	$-0.0218272\pi$
$859$	1234.50	+	712.739i	1.43714	+	0.829731i	0.439486	+	0.898249i	$0.355160\pi$
$860$		0			0
$861$	336.000	+	581.969i	0.390244	+	0.675922i
$862$		0			0
$863$	−740.452	−	427.500i	−0.857997	−	0.495365i	0.00534379	−	0.999986i	$-0.498299\pi$
$863$	−740.452	−	427.500i	−0.857997	−	0.495365i	−0.863341	+	0.504621i	$0.831632\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1001.13			−1.15470
$868$		0			0
$869$	1095.00			1.26007
$870$		0			0
$871$	−588.000	+	339.482i	−0.675086	+	0.389761i
$872$		0			0
$873$	83.1384	−	144.000i	0.0952330	−	0.164948i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−208.712	−	120.500i	−0.237984	−	0.137400i	0.376266	−	0.926512i	$-0.377208\pi$
$877$	−208.712	−	120.500i	−0.237984	−	0.137400i	−0.614250	+	0.789112i	$0.710541\pi$
$878$		0			0
$879$	−204.000	−	353.338i	−0.232082	−	0.401978i
$880$		0			0
$881$		−	1330.22i		−	1.50989i	−0.655787	−	0.754946i	$-0.727663\pi$
$881$		−	1330.22i		−	1.50989i	0.655787	−	0.754946i	$-0.272337\pi$
$882$		0			0
$883$		−	1286.00i		−	1.45640i	−0.685365	−	0.728199i	$-0.740358\pi$
$883$		−	1286.00i		−	1.45640i	0.685365	−	0.728199i	$-0.259642\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−643.457	+	1114.50i	−0.725431	+	1.25648i	0.233366	+	0.972389i	$0.425026\pi$
$887$	−643.457	+	1114.50i	−0.725431	+	1.25648i	−0.958797	+	0.284094i	$0.908307\pi$
$888$		0			0
$889$	350.000			0.393701
$890$		0			0
$891$	−67.5000	+	116.913i	−0.0757576	+	0.131216i
$892$		0			0
$893$	−584.567	+	337.500i	−0.654610	+	0.377940i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	216.000i		−	0.240803i
$898$		0			0
$899$	−63.0000	+	36.3731i	−0.0700779	+	0.0404595i
$900$		0			0
$901$	1453.50	+	839.179i	1.61321	+	0.931386i
$902$		0			0
$903$	−60.6218	−	105.000i	−0.0671338	−	0.116279i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	638.261	−	368.500i	0.703705	−	0.406284i	−0.105021	−	0.994470i	$-0.533491\pi$
$907$	638.261	−	368.500i	0.703705	−	0.406284i	0.808726	+	0.588186i	$0.200158\pi$
$908$		0			0
$909$		−	592.361i		−	0.651663i
$910$		0			0
$911$	1266.00			1.38968			0.694841	−	0.719164i	$-0.255475\pi$
$911$	1266.00			1.38968			0.694841	+	0.719164i	$0.255475\pi$
$912$		0			0
$913$	−103.923	−	180.000i	−0.113826	−	0.197152i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−345.544	+	598.500i	−0.376820	+	0.652672i
$918$		0			0
$919$	−236.500	+	409.630i	−0.257345	+	0.445735i	−0.965530	−	0.260293i	$-0.916181\pi$
$919$	−236.500	+	409.630i	−0.257345	+	0.445735i	0.708185	+	0.706027i	$0.249514\pi$
$920$		0			0
$921$	84.0000	+	145.492i	0.0912052	+	0.157972i
$922$		0			0
$923$	1745.91			1.89156
$924$		0			0
$925$		0			0
$926$		0			0
$927$	213.042	+	369.000i	0.229819	+	0.398058i
$928$		0			0
$929$	−289.500	−	167.143i	−0.311625	−	0.179917i	0.336028	−	0.941852i	$-0.390916\pi$
$929$	−289.500	−	167.143i	−0.311625	−	0.179917i	−0.647654	+	0.761935i	$0.724250\pi$
$930$		0			0
$931$	661.500	+	381.917i	0.710526	+	0.410223i
$932$		0			0
$933$	730.059	+	421.500i	0.782486	+	0.451768i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	859.097			0.916859			0.458430	−	0.888731i	$-0.348412\pi$
$937$	859.097			0.916859			0.458430	+	0.888731i	$0.348412\pi$
$938$		0			0
$939$	−387.000			−0.412141
$940$		0			0
$941$	−106.500	+	61.4878i	−0.113177	+	0.0653430i	−0.555520	−	0.831503i	$-0.687481\pi$
$941$	−106.500	+	61.4878i	−0.113177	+	0.0653430i	0.442343	+	0.896846i	$0.354147\pi$
$942$		0			0
$943$	249.415	−	432.000i	0.264491	−	0.458112i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−174.071	−	100.500i	−0.183813	−	0.106125i	0.405270	−	0.914197i	$-0.367178\pi$
$947$	−174.071	−	100.500i	−0.183813	−	0.106125i	−0.589083	+	0.808073i	$0.700511\pi$
$948$		0			0
$949$	180.000	+	311.769i	0.189673	+	0.328524i
$950$		0			0
$951$			774.227i			0.814119i
$952$		0			0
$953$			66.0000i			0.0692550i	0.999400	+	0.0346275i	$0.0110245\pi$
$953$			66.0000i			0.0692550i	−0.999400	+	0.0346275i	$0.988976\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	77.9423	−	135.000i	0.0814444	−	0.141066i
$958$		0			0
$959$	−220.500	−	381.917i	−0.229927	−	0.398245i
$960$		0			0
$961$	−407.000	+	704.945i	−0.423517	+	0.733553i
$962$		0			0
$963$	202.650	−	117.000i	0.210436	−	0.121495i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	194.000i		−	0.200620i	−0.994956	−	0.100310i	$-0.968016\pi$
$967$		−	194.000i		−	0.200620i	0.994956	−	0.100310i	$-0.0319835\pi$
$968$		0			0
$969$	−688.500	+	397.506i	−0.710526	+	0.410223i
$970$		0			0
$971$	1285.50	+	742.184i	1.32389	+	0.764350i	0.984347	−	0.176240i	$-0.0563934\pi$
$971$	1285.50	+	742.184i	1.32389	+	0.764350i	0.339546	+	0.940590i	$0.389727\pi$
$972$		0			0
$973$	1648.91			1.69467
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1317.22	−	760.500i	1.34823	−	0.778403i	0.360235	−	0.932862i	$-0.382697\pi$
$977$	1317.22	−	760.500i	1.34823	−	0.778403i	0.987999	+	0.154458i	$0.0493633\pi$
$978$		0			0
$979$			857.365i			0.875756i
$980$		0			0
$981$	618.000			0.629969
$982$		0			0
$983$	562.050	+	973.500i	0.571771	+	0.990336i	0.996384	+	0.0849611i	$0.0270766\pi$
$983$	562.050	+	973.500i	0.571771	+	0.990336i	−0.424614	+	0.905375i	$0.639590\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			525.000i			0.531915i
$988$		0			0
$989$	−45.0000	+	77.9423i	−0.0455005	+	0.0788092i
$990$		0			0
$991$	−411.500	−	712.739i	−0.415237	−	0.719212i	0.580216	−	0.814463i	$-0.302968\pi$
$991$	−411.500	−	712.739i	−0.415237	−	0.719212i	−0.995453	+	0.0952507i	$0.969635\pi$
$992$		0			0
$993$	−261.540			−0.263383
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−63.2199	−	109.500i	−0.0634101	−	0.109829i	0.832578	−	0.553909i	$-0.186864\pi$
$997$	−63.2199	−	109.500i	−0.0634101	−	0.109829i	−0.895988	+	0.444079i	$0.853531\pi$
$998$		0			0
$999$	697.500	+	402.702i	0.698198	+	0.403105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.3.o.a.649.2		4
5.2	odd	4		28.3.h.a.5.1	✓	2
5.3	odd	4		700.3.s.a.201.1		2
5.4	even	2	inner	700.3.o.a.649.1		4
7.3	odd	6	inner	700.3.o.a.549.1		4
15.2	even	4		252.3.z.a.145.1		2
20.7	even	4		112.3.s.a.33.1		2
35.2	odd	12		196.3.b.a.97.2		2
35.3	even	12		700.3.s.a.101.1		2
35.12	even	12		196.3.b.a.97.1		2
35.17	even	12		28.3.h.a.17.1	yes	2
35.24	odd	6	inner	700.3.o.a.549.2		4
35.27	even	4		196.3.h.a.117.1		2
35.32	odd	12		196.3.h.a.129.1		2
40.27	even	4		448.3.s.b.257.1		2
40.37	odd	4		448.3.s.a.257.1		2
60.47	odd	4		1008.3.cg.c.145.1		2
105.2	even	12		1764.3.d.a.685.2		2
105.17	odd	12		252.3.z.a.73.1		2
105.32	even	12		1764.3.z.f.325.1		2
105.47	odd	12		1764.3.d.a.685.1		2
105.62	odd	4		1764.3.z.f.901.1		2
140.27	odd	4		784.3.s.b.705.1		2
140.47	odd	12		784.3.c.a.97.2		2
140.67	even	12		784.3.s.b.129.1		2
140.87	odd	12		112.3.s.a.17.1		2
140.107	even	12		784.3.c.a.97.1		2
280.157	even	12		448.3.s.a.129.1		2
280.227	odd	12		448.3.s.b.129.1		2
420.227	even	12		1008.3.cg.c.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.3.h.a.5.1	✓	2	5.2	odd	4
28.3.h.a.17.1	yes	2	35.17	even	12
112.3.s.a.17.1		2	140.87	odd	12
112.3.s.a.33.1		2	20.7	even	4
196.3.b.a.97.1		2	35.12	even	12
196.3.b.a.97.2		2	35.2	odd	12
196.3.h.a.117.1		2	35.27	even	4
196.3.h.a.129.1		2	35.32	odd	12
252.3.z.a.73.1		2	105.17	odd	12
252.3.z.a.145.1		2	15.2	even	4
448.3.s.a.129.1		2	280.157	even	12
448.3.s.a.257.1		2	40.37	odd	4
448.3.s.b.129.1		2	280.227	odd	12
448.3.s.b.257.1		2	40.27	even	4
700.3.o.a.549.1		4	7.3	odd	6	inner
700.3.o.a.549.2		4	35.24	odd	6	inner
700.3.o.a.649.1		4	5.4	even	2	inner
700.3.o.a.649.2		4	1.1	even	1	trivial
700.3.s.a.101.1		2	35.3	even	12
700.3.s.a.201.1		2	5.3	odd	4
784.3.c.a.97.1		2	140.107	even	12
784.3.c.a.97.2		2	140.47	odd	12
784.3.s.b.129.1		2	140.67	even	12
784.3.s.b.705.1		2	140.27	odd	4
1008.3.cg.c.145.1		2	60.47	odd	4
1008.3.cg.c.577.1		2	420.227	even	12
1764.3.d.a.685.1		2	105.47	odd	12
1764.3.d.a.685.2		2	105.2	even	12
1764.3.z.f.325.1		2	105.32	even	12
1764.3.z.f.901.1		2	105.62	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	700.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{3} +7.00000i q^{7} +(3.00000 - 5.19615i) q^{9} +(-7.50000 - 12.9904i) q^{11} -13.8564 q^{13} +(-14.7224 - 25.5000i) q^{17} +(-13.5000 - 7.79423i) q^{19} +(-10.5000 + 6.06218i) q^{21} +(7.79423 + 4.50000i) q^{23} +25.9808 q^{27} +6.00000 q^{29} +(-10.5000 + 6.06218i) q^{31} +(12.9904 - 22.5000i) q^{33} +(26.8468 + 15.5000i) q^{37} +(-12.0000 - 20.7846i) q^{39} -55.4256i q^{41} +10.0000i q^{43} +(21.6506 - 37.5000i) q^{47} -49.0000 q^{49} +(25.5000 - 44.1673i) q^{51} +(-49.3634 + 28.5000i) q^{53} -27.0000i q^{57} +(70.5000 - 40.7032i) q^{59} +(-70.5000 - 40.7032i) q^{61} +(36.3731 + 21.0000i) q^{63} +(42.4352 - 24.5000i) q^{67} +15.5885i q^{69} -126.000 q^{71} +(-12.9904 - 22.5000i) q^{73} +(90.9327 - 52.5000i) q^{77} +(-36.5000 + 63.2199i) q^{79} +(-4.50000 - 7.79423i) q^{81} +13.8564 q^{83} +(5.19615 + 9.00000i) q^{87} +(-49.5000 - 28.5788i) q^{89} -96.9948i q^{91} +(-18.1865 - 10.5000i) q^{93} +27.7128 q^{97} -90.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{9} - 30 q^{11} - 54 q^{19} - 42 q^{21} + 24 q^{29} - 42 q^{31} - 48 q^{39} - 196 q^{49} + 102 q^{51} + 282 q^{59} - 282 q^{61} - 504 q^{71} - 146 q^{79} - 18 q^{81} - 198 q^{89} - 360 q^{99}+O(q^{100}) \) 4 * q + 12 * q^9 - 30 * q^11 - 54 * q^19 - 42 * q^21 + 24 * q^29 - 42 * q^31 - 48 * q^39 - 196 * q^49 + 102 * q^51 + 282 * q^59 - 282 * q^61 - 504 * q^71 - 146 * q^79 - 18 * q^81 - 198 * q^89 - 360 * q^99

Introduction

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