LMFDB - Embedded newform 525.3.h.d.76.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(76,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("525.76");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.h (of order $2$, degree $1$, 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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 21x^10 - 26x^9 + 295x^8 - 372x^7 + 1704x^6 - 1074x^5 + 5613x^4 - 5472x^3 + 4950x^2 - 1638*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.7
Root			$-1.01714 + 1.76174i$ of defining polynomial
Character	$\chi$	$=$	525.76
Dual form			525.3.h.d.76.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.71214 q^{2} -1.73205i q^{3} -1.06857 q^{4} -2.96552i q^{6} +(3.33344 + 6.15534i) q^{7} -8.67811 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.71214 q^{2} -1.73205i q^{3} -1.06857 q^{4} -2.96552i q^{6} +(3.33344 + 6.15534i) q^{7} -8.67811 q^{8} -3.00000 q^{9} +17.0001 q^{11} +1.85082i q^{12} +16.3319i q^{13} +(5.70733 + 10.5388i) q^{14} -10.5839 q^{16} +13.4266i q^{17} -5.13643 q^{18} -13.7499i q^{19} +(10.6614 - 5.77369i) q^{21} +29.1066 q^{22} +16.6179 q^{23} +15.0309i q^{24} +27.9626i q^{26} +5.19615i q^{27} +(-3.56202 - 6.57741i) q^{28} +32.1793 q^{29} +6.74366i q^{31} +16.5913 q^{32} -29.4450i q^{33} +22.9883i q^{34} +3.20571 q^{36} +69.2141 q^{37} -23.5418i q^{38} +28.2878 q^{39} +39.7391i q^{41} +(18.2538 - 9.88538i) q^{42} -43.2210 q^{43} -18.1658 q^{44} +28.4522 q^{46} +40.1384i q^{47} +18.3318i q^{48} +(-26.7763 + 41.0369i) q^{49} +23.2556 q^{51} -17.4518i q^{52} -22.5002 q^{53} +8.89655i q^{54} +(-28.9280 - 53.4167i) q^{56} -23.8155 q^{57} +55.0956 q^{58} -81.6005i q^{59} -14.9859i q^{61} +11.5461i q^{62} +(-10.0003 - 18.4660i) q^{63} +70.7422 q^{64} -50.4141i q^{66} -72.0872 q^{67} -14.3473i q^{68} -28.7831i q^{69} -25.7338 q^{71} +26.0343 q^{72} +75.0647i q^{73} +118.504 q^{74} +14.6927i q^{76} +(56.6689 + 104.641i) q^{77} +48.4327 q^{78} +80.0480 q^{79} +9.00000 q^{81} +68.0389i q^{82} -102.112i q^{83} +(-11.3924 + 6.16959i) q^{84} -74.0005 q^{86} -55.7362i q^{87} -147.529 q^{88} +128.381i q^{89} +(-100.529 + 54.4416i) q^{91} -17.7574 q^{92} +11.6804 q^{93} +68.7227i q^{94} -28.7371i q^{96} -159.448i q^{97} +(-45.8449 + 70.2610i) q^{98} -51.0003 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9	$ 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} - 12 q^{18} + 36 q^{21} + 88 q^{22} + 64 q^{23} - 88 q^{28} + 104 q^{29} + 228 q^{32} - 132 q^{36} - 32 q^{37} - 24 q^{39} + 60 q^{42} - 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 24 q^{51} - 176 q^{53} - 368 q^{56} + 240 q^{57} + 400 q^{58} - 24 q^{63} - 20 q^{64} - 168 q^{67} + 32 q^{71} + 12 q^{72} + 184 q^{74} - 8 q^{77} - 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 400 q^{86} + 536 q^{88} + 24 q^{91} - 192 q^{92} - 48 q^{93} - 884 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 - 12 * q^18 + 36 * q^21 + 88 * q^22 + 64 * q^23 - 88 * q^28 + 104 * q^29 + 228 * q^32 - 132 * q^36 - 32 * q^37 - 24 * q^39 + 60 * q^42 - 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 24 * q^51 - 176 * q^53 - 368 * q^56 + 240 * q^57 + 400 * q^58 - 24 * q^63 - 20 * q^64 - 168 * q^67 + 32 * q^71 + 12 * q^72 + 184 * q^74 - 8 * q^77 - 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 400 * q^86 + 536 * q^88 + 24 * q^91 - 192 * q^92 - 48 * q^93 - 884 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.71214			0.856071			0.428035	−	0.903762i	$-0.359206\pi$
$2$	1.71214			0.856071			0.428035	+	0.903762i	$0.359206\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−1.06857			−0.267143
$5$		0			0
$5$		0			0
$6$		−	2.96552i		−	0.494253i
$7$	3.33344	+	6.15534i	0.476206	+	0.879334i
$7$	3.33344	+	6.15534i	0.476206	+	0.879334i
$8$	−8.67811			−1.08476
$9$	−3.00000			−0.333333
$10$		0			0
$11$	17.0001			1.54546			0.772732	−	0.634732i	$-0.218890\pi$
$11$	17.0001			1.54546			0.772732	+	0.634732i	$0.218890\pi$
$12$			1.85082i			0.154235i
$13$			16.3319i			1.25630i	0.778091	+	0.628152i	$0.216188\pi$
$13$			16.3319i			1.25630i	−0.778091	+	0.628152i	$0.783812\pi$
$14$	5.70733	+	10.5388i	0.407666	+	0.752772i
$15$		0			0
$16$	−10.5839			−0.661492
$17$			13.4266i			0.789801i	0.918724	+	0.394900i	$0.129221\pi$
$17$			13.4266i			0.789801i	−0.918724	+	0.394900i	$0.870779\pi$
$18$	−5.13643			−0.285357
$19$		−	13.7499i		−	0.723679i	−0.932240	−	0.361839i	$-0.882149\pi$
$19$		−	13.7499i		−	0.723679i	0.932240	−	0.361839i	$-0.117851\pi$
$20$		0			0
$21$	10.6614	−	5.77369i	0.507684	−	0.274938i
$22$	29.1066			1.32303
$23$	16.6179			0.722518			0.361259	−	0.932466i	$-0.382347\pi$
$23$	16.6179			0.722518			0.361259	+	0.932466i	$0.382347\pi$
$24$			15.0309i			0.626289i
$25$		0			0
$26$			27.9626i			1.07548i
$27$			5.19615i			0.192450i
$28$	−3.56202	−	6.57741i	−0.127215	−	0.234907i
$29$	32.1793			1.10963			0.554816	−	0.831973i	$-0.312789\pi$
$29$	32.1793			1.10963			0.554816	+	0.831973i	$0.312789\pi$
$30$		0			0
$31$			6.74366i			0.217538i	0.994067	+	0.108769i	$0.0346908\pi$
$31$			6.74366i			0.217538i	−0.994067	+	0.108769i	$0.965309\pi$
$32$	16.5913			0.518480
$33$		−	29.4450i		−	0.892274i
$34$			22.9883i			0.676125i
$35$		0			0
$36$	3.20571			0.0890475
$37$	69.2141			1.87065			0.935325	−	0.353789i	$-0.115107\pi$
$37$	69.2141			1.87065			0.935325	+	0.353789i	$0.115107\pi$
$38$		−	23.5418i		−	0.619520i
$39$	28.2878			0.725327
$40$		0			0
$41$			39.7391i			0.969246i	0.874723	+	0.484623i	$0.161043\pi$
$41$			39.7391i			0.969246i	−0.874723	+	0.484623i	$0.838957\pi$
$42$	18.2538	−	9.88538i	0.434613	−	0.235366i
$43$	−43.2210			−1.00514			−0.502570	−	0.864537i	$-0.667612\pi$
$43$	−43.2210			−1.00514			−0.502570	+	0.864537i	$0.667612\pi$
$44$	−18.1658			−0.412859
$45$		0			0
$46$	28.4522			0.618526
$47$			40.1384i			0.854009i	0.904249	+	0.427005i	$0.140431\pi$
$47$			40.1384i			0.854009i	−0.904249	+	0.427005i	$0.859569\pi$
$48$			18.3318i			0.381913i
$49$	−26.7763	+	41.0369i	−0.546456	+	0.837488i
$50$		0			0
$51$	23.2556			0.455992
$52$		−	17.4518i		−	0.335612i
$53$	−22.5002			−0.424533			−0.212266	−	0.977212i	$-0.568084\pi$
$53$	−22.5002			−0.424533			−0.212266	+	0.977212i	$0.568084\pi$
$54$			8.89655i			0.164751i
$55$		0			0
$56$	−28.9280	−	53.4167i	−0.516571	−	0.953869i
$57$	−23.8155			−0.417816
$58$	55.0956			0.949924
$59$		−	81.6005i		−	1.38306i	−0.722348	−	0.691529i	$-0.756937\pi$
$59$		−	81.6005i		−	1.38306i	0.722348	−	0.691529i	$-0.243063\pi$
$60$		0			0
$61$		−	14.9859i		−	0.245671i	−0.992427	−	0.122836i	$-0.960801\pi$
$61$		−	14.9859i		−	0.245671i	0.992427	−	0.122836i	$-0.0391988\pi$
$62$			11.5461i			0.186228i
$63$	−10.0003	−	18.4660i	−0.158735	−	0.293111i
$64$	70.7422			1.10535
$65$		0			0
$66$		−	50.4141i		−	0.763850i
$67$	−72.0872			−1.07593			−0.537964	−	0.842968i	$-0.680806\pi$
$67$	−72.0872			−1.07593			−0.537964	+	0.842968i	$0.680806\pi$
$68$		−	14.3473i		−	0.210989i
$69$		−	28.7831i		−	0.417146i
$70$		0			0
$71$	−25.7338			−0.362448			−0.181224	−	0.983442i	$-0.558006\pi$
$71$	−25.7338			−0.362448			−0.181224	+	0.983442i	$0.558006\pi$
$72$	26.0343			0.361588
$73$			75.0647i			1.02828i	0.857705	+	0.514142i	$0.171890\pi$
$73$			75.0647i			1.02828i	−0.857705	+	0.514142i	$0.828110\pi$
$74$	118.504			1.60141
$75$		0			0
$76$			14.6927i			0.193325i
$77$	56.6689	+	104.641i	0.735959	+	1.35898i
$78$	48.4327			0.620931
$79$	80.0480			1.01327			0.506633	−	0.862162i	$-0.330890\pi$
$79$	80.0480			1.01327			0.506633	+	0.862162i	$0.330890\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$			68.0389i			0.829743i
$83$		−	102.112i		−	1.23027i	−0.788421	−	0.615135i	$-0.789101\pi$
$83$		−	102.112i		−	1.23027i	0.788421	−	0.615135i	$-0.210899\pi$
$84$	−11.3924	+	6.16959i	−0.135624	+	0.0734476i
$85$		0			0
$86$	−74.0005			−0.860471
$87$		−	55.7362i		−	0.640646i
$88$	−147.529			−1.67646
$89$			128.381i			1.44248i	0.692683	+	0.721242i	$0.256429\pi$
$89$			128.381i			1.44248i	−0.692683	+	0.721242i	$0.743571\pi$
$90$		0			0
$91$	−100.529	+	54.4416i	−1.10471	+	0.598259i
$92$	−17.7574			−0.193015
$93$	11.6804			0.125595
$94$			68.7227i			0.731092i
$95$		0			0
$96$		−	28.7371i		−	0.299344i
$97$		−	159.448i		−	1.64379i	−0.569636	−	0.821897i	$-0.692916\pi$
$97$		−	159.448i		−	1.64379i	0.569636	−	0.821897i	$-0.307084\pi$
$98$	−45.8449	+	70.2610i	−0.467805	+	0.716949i
$99$	−51.0003			−0.515155
$100$		0			0
$101$			24.1380i			0.238990i	0.992835	+	0.119495i	$0.0381276\pi$
$101$			24.1380i			0.238990i	−0.992835	+	0.119495i	$0.961872\pi$
$102$	39.8168			0.390361
$103$			87.3469i			0.848028i	0.905656	+	0.424014i	$0.139379\pi$
$103$			87.3469i			0.848028i	−0.905656	+	0.424014i	$0.860621\pi$
$104$		−	141.730i		−	1.36279i
$105$		0			0
$106$	−38.5236			−0.363430
$107$	−168.359			−1.57344			−0.786722	−	0.617307i	$-0.788224\pi$
$107$	−168.359			−1.57344			−0.786722	+	0.617307i	$0.788224\pi$
$108$		−	5.55245i		−	0.0514116i
$109$	−155.570			−1.42725			−0.713624	−	0.700529i	$-0.752947\pi$
$109$	−155.570			−1.42725			−0.713624	+	0.700529i	$0.752947\pi$
$110$		0			0
$111$		−	119.882i		−	1.08002i
$112$	−35.2807	−	65.1473i	−0.315007	−	0.581672i
$113$	20.9965			0.185810			0.0929050	−	0.995675i	$-0.470385\pi$
$113$	20.9965			0.185810			0.0929050	+	0.995675i	$0.470385\pi$
$114$	−40.7756			−0.357680
$115$		0			0
$116$	−34.3859			−0.296430
$117$		−	48.9958i		−	0.418768i
$118$		−	139.712i		−	1.18400i
$119$	−82.6453	+	44.7568i	−0.694498	+	0.376108i
$120$		0			0
$121$	168.004			1.38846
$122$		−	25.6581i		−	0.210312i
$123$	68.8301			0.559594
$124$		−	7.20608i		−	0.0581135i
$125$		0			0
$126$	−17.1220	−	31.6164i	−0.135889	−	0.250924i
$127$	59.8712			0.471427			0.235713	−	0.971823i	$-0.424257\pi$
$127$	59.8712			0.471427			0.235713	+	0.971823i	$0.424257\pi$
$128$	54.7554			0.427776
$129$			74.8609i			0.580317i
$130$		0			0
$131$			166.868i			1.27380i	0.770947	+	0.636899i	$0.219783\pi$
$131$			166.868i			1.27380i	−0.770947	+	0.636899i	$0.780217\pi$
$132$			31.4641i			0.238364i
$133$	84.6352	−	45.8345i	0.636355	−	0.344620i
$134$	−123.423			−0.921071
$135$		0			0
$136$		−	116.518i		−	0.856747i
$137$	−126.139			−0.920726			−0.460363	−	0.887731i	$-0.652281\pi$
$137$	−126.139			−0.920726			−0.460363	+	0.887731i	$0.652281\pi$
$138$		−	49.2807i		−	0.357106i
$139$		−	211.650i		−	1.52266i	−0.648365	−	0.761330i	$-0.724547\pi$
$139$		−	211.650i		−	1.52266i	0.648365	−	0.761330i	$-0.275453\pi$
$140$		0			0
$141$	69.5218			0.493062
$142$	−44.0599			−0.310281
$143$			277.645i			1.94157i
$144$	31.7516			0.220497
$145$		0			0
$146$			128.521i			0.880284i
$147$	71.0780	+	46.3780i	0.483524	+	0.315496i
$148$	−73.9601			−0.499730
$149$	−64.1825			−0.430755			−0.215377	−	0.976531i	$-0.569098\pi$
$149$	−64.1825			−0.430755			−0.215377	+	0.976531i	$0.569098\pi$
$150$		0			0
$151$	110.915			0.734538			0.367269	−	0.930115i	$-0.380293\pi$
$151$	110.915			0.734538			0.367269	+	0.930115i	$0.380293\pi$
$152$			119.323i			0.785021i
$153$		−	40.2798i		−	0.263267i
$154$	97.0252	+	179.161i	0.630033	+	1.16338i
$155$		0			0
$156$	−30.2275			−0.193766
$157$		−	290.451i		−	1.85001i	−0.379956	−	0.925004i	$-0.624061\pi$
$157$		−	290.451i		−	1.85001i	0.379956	−	0.925004i	$-0.375939\pi$
$158$	137.053			0.867427
$159$			38.9716i			0.245104i
$160$		0			0
$161$	55.3948	+	102.289i	0.344067	+	0.635334i
$162$	15.4093			0.0951190
$163$	53.8559			0.330404			0.165202	−	0.986260i	$-0.447172\pi$
$163$	53.8559			0.330404			0.165202	+	0.986260i	$0.447172\pi$
$164$		−	42.4640i		−	0.258927i
$165$		0			0
$166$		−	174.831i		−	1.05320i
$167$			41.7927i			0.250255i	0.992141	+	0.125128i	$0.0399341\pi$
$167$			41.7927i			0.250255i	−0.992141	+	0.125128i	$0.960066\pi$
$168$	−92.5204	+	50.1047i	−0.550717	+	0.298242i
$169$	−97.7324			−0.578298
$170$		0			0
$171$			41.2497i			0.241226i
$172$	46.1847			0.268515
$173$		−	130.344i		−	0.753434i	−0.926328	−	0.376717i	$-0.877053\pi$
$173$		−	130.344i		−	0.753434i	0.926328	−	0.376717i	$-0.122947\pi$
$174$		−	95.4283i		−	0.548439i
$175$		0			0
$176$	−179.927			−1.02231
$177$	−141.336			−0.798509
$178$			219.807i			1.23487i
$179$	44.9934			0.251360			0.125680	−	0.992071i	$-0.459889\pi$
$179$	44.9934			0.251360			0.125680	+	0.992071i	$0.459889\pi$
$180$		0			0
$181$		−	17.8944i		−	0.0988640i	−0.998777	−	0.0494320i	$-0.984259\pi$
$181$		−	17.8944i		−	0.0988640i	0.998777	−	0.0494320i	$-0.0157411\pi$
$182$	−172.119	+	93.2117i	−0.945710	+	0.512152i
$183$	−25.9564			−0.141838
$184$	−144.212			−0.783761
$185$		0			0
$186$	19.9985			0.107519
$187$			228.254i			1.22061i
$188$		−	42.8907i		−	0.228142i
$189$	−31.9841	+	17.3211i	−0.169228	+	0.0916459i
$190$		0			0
$191$	178.314			0.933583			0.466791	−	0.884367i	$-0.345410\pi$
$191$	178.314			0.933583			0.466791	+	0.884367i	$0.345410\pi$
$192$		−	122.529i		−	0.638173i
$193$	336.283			1.74240			0.871200	−	0.490928i	$-0.163342\pi$
$193$	336.283			1.74240			0.871200	+	0.490928i	$0.163342\pi$
$194$		−	272.998i		−	1.40720i
$195$		0			0
$196$	28.6124	−	43.8508i	0.145982	−	0.223729i
$197$	−49.2082			−0.249788			−0.124894	−	0.992170i	$-0.539859\pi$
$197$	−49.2082			−0.249788			−0.124894	+	0.992170i	$0.539859\pi$
$198$	−87.3198			−0.441009
$199$		−	171.789i		−	0.863262i	−0.902050	−	0.431631i	$-0.857938\pi$
$199$		−	171.789i		−	0.863262i	0.902050	−	0.431631i	$-0.142062\pi$
$200$		0			0
$201$			124.859i			0.621187i
$202$			41.3277i			0.204592i
$203$	107.268	+	198.075i	0.528414	+	0.975737i
$204$	−24.8502			−0.121815
$205$		0			0
$206$			149.550i			0.725972i
$207$	−49.8537			−0.240839
$208$		−	172.855i		−	0.831035i
$209$		−	233.750i		−	1.11842i
$210$		0			0
$211$	−5.09458			−0.0241449			−0.0120725	−	0.999927i	$-0.503843\pi$
$211$	−5.09458			−0.0241449			−0.0120725	+	0.999927i	$0.503843\pi$
$212$	24.0431			0.113411
$213$			44.5722i			0.209259i
$214$	−288.254			−1.34698
$215$		0			0
$216$		−	45.0928i		−	0.208763i
$217$	−41.5095	+	22.4796i	−0.191288	+	0.103593i
$218$	−266.358			−1.22183
$219$	130.016			0.593680
$220$		0			0
$221$	−219.283			−0.992229
$222$		−	205.256i		−	0.924574i
$223$		−	310.066i		−	1.39043i	−0.718802	−	0.695215i	$-0.755309\pi$
$223$		−	310.066i		−	1.39043i	0.718802	−	0.695215i	$-0.244691\pi$
$224$	55.3063	+	102.125i	0.246903	+	0.455917i
$225$		0			0
$226$	35.9490			0.159067
$227$		−	108.558i		−	0.478228i	−0.970991	−	0.239114i	$-0.923143\pi$
$227$		−	108.558i		−	0.478228i	0.970991	−	0.239114i	$-0.0768570\pi$
$228$	25.4486			0.111616
$229$		−	236.483i		−	1.03268i	−0.856384	−	0.516339i	$-0.827294\pi$
$229$		−	236.483i		−	1.03268i	0.856384	−	0.516339i	$-0.172706\pi$
$230$		0			0
$231$	181.244	−	98.1534i	0.784607	−	0.424906i
$232$	−279.256			−1.20369
$233$	−151.290			−0.649312			−0.324656	−	0.945832i	$-0.605249\pi$
$233$	−151.290			−0.649312			−0.324656	+	0.945832i	$0.605249\pi$
$234$		−	83.8878i		−	0.358495i
$235$		0			0
$236$			87.1958i			0.369474i
$237$		−	138.647i		−	0.585009i
$238$	−141.500	+	76.6300i	−0.594540	+	0.321975i
$239$	48.2956			0.202074			0.101037	−	0.994883i	$-0.467784\pi$
$239$	48.2956			0.202074			0.101037	+	0.994883i	$0.467784\pi$
$240$		0			0
$241$		−	230.735i		−	0.957406i	−0.877977	−	0.478703i	$-0.841107\pi$
$241$		−	230.735i		−	0.957406i	0.877977	−	0.478703i	$-0.158893\pi$
$242$	287.646			1.18862
$243$		−	15.5885i		−	0.0641500i
$244$			16.0135i			0.0656292i
$245$		0			0
$246$	117.847			0.479053
$247$	224.563			0.909160
$248$		−	58.5223i		−	0.235977i
$249$	−176.864			−0.710297
$250$		0			0
$251$			86.6812i			0.345343i	0.984979	+	0.172672i	$0.0552399\pi$
$251$			86.6812i			0.345343i	−0.984979	+	0.172672i	$0.944760\pi$
$252$	10.6861	+	19.7322i	0.0424050	+	0.0783025i
$253$	282.506			1.11663
$254$	102.508			0.403575
$255$		0			0
$256$	−189.220			−0.739141
$257$		−	141.110i		−	0.549065i	−0.961578	−	0.274532i	$-0.911477\pi$
$257$		−	141.110i		−	0.549065i	0.961578	−	0.274532i	$-0.0885231\pi$
$258$			128.173i			0.496793i
$259$	230.721	+	426.036i	0.890815	+	1.64493i
$260$		0			0
$261$	−96.5380			−0.369877
$262$			285.701i			1.09046i
$263$	−38.0901			−0.144829			−0.0724147	−	0.997375i	$-0.523070\pi$
$263$	−38.0901			−0.144829			−0.0724147	+	0.997375i	$0.523070\pi$
$264$			255.527i			0.967907i
$265$		0			0
$266$	144.908	−	78.4752i	0.544765	−	0.295019i
$267$	222.363			0.832819
$268$	77.0302			0.287426
$269$			454.220i			1.68855i	0.535909	+	0.844275i	$0.319969\pi$
$269$			454.220i			1.68855i	−0.535909	+	0.844275i	$0.680031\pi$
$270$		0			0
$271$		−	78.7098i		−	0.290442i	−0.989399	−	0.145221i	$-0.953611\pi$
$271$		−	78.7098i		−	0.290442i	0.989399	−	0.145221i	$-0.0463893\pi$
$272$		−	142.106i		−	0.522447i
$273$	94.2956	+	174.121i	0.345405	+	0.637805i
$274$	−215.969			−0.788207
$275$		0			0
$276$			30.7567i			0.111437i
$277$	85.3396			0.308085			0.154043	−	0.988064i	$-0.450771\pi$
$277$	85.3396			0.308085			0.154043	+	0.988064i	$0.450771\pi$
$278$		−	362.374i		−	1.30350i
$279$		−	20.2310i		−	0.0725125i
$280$		0			0
$281$	167.376			0.595643			0.297821	−	0.954622i	$-0.403740\pi$
$281$	167.376			0.595643			0.297821	+	0.954622i	$0.403740\pi$
$282$	119.031			0.422096
$283$		−	149.591i		−	0.528588i	−0.964442	−	0.264294i	$-0.914861\pi$
$283$		−	149.591i		−	0.528588i	0.964442	−	0.264294i	$-0.0851390\pi$
$284$	27.4984			0.0968252
$285$		0			0
$286$			475.367i			1.66212i
$287$	−244.607	+	132.468i	−0.852291	+	0.461561i
$288$	−49.7740			−0.172827
$289$	108.726			0.376215
$290$		0			0
$291$	−276.172			−0.949045
$292$		−	80.2119i		−	0.274698i
$293$			145.805i			0.497627i	0.968551	+	0.248813i	$0.0800406\pi$
$293$			145.805i			0.497627i	−0.968551	+	0.248813i	$0.919959\pi$
$294$	121.696	+	79.4056i	0.413931	+	0.270087i
$295$		0			0
$296$	−600.648			−2.02921
$297$			88.3351i			0.297425i
$298$	−109.889			−0.368757
$299$			271.403i			0.907701i
$300$		0			0
$301$	−144.075	−	266.040i	−0.478653	−	0.883853i
$302$	189.903			0.628817
$303$	41.8082			0.137981
$304$			145.527i			0.478708i
$305$		0			0
$306$		−	68.9648i		−	0.225375i
$307$		−	205.594i		−	0.669686i	−0.942274	−	0.334843i	$-0.891317\pi$
$307$		−	205.594i		−	0.669686i	0.942274	−	0.334843i	$-0.108683\pi$
$308$	−60.5547	−	111.817i	−0.196606	−	0.363041i
$309$	151.289			0.489609
$310$		0			0
$311$		−	424.383i		−	1.36458i	−0.731084	−	0.682288i	$-0.760985\pi$
$311$		−	424.383i		−	1.36458i	0.731084	−	0.682288i	$-0.239015\pi$
$312$	−245.484			−0.786809
$313$			363.503i			1.16135i	0.814135	+	0.580676i	$0.197212\pi$
$313$			363.503i			1.16135i	−0.814135	+	0.580676i	$0.802788\pi$
$314$		−	497.294i		−	1.58374i
$315$		0			0
$316$	−85.5369			−0.270686
$317$	−441.407			−1.39245			−0.696226	−	0.717822i	$-0.745139\pi$
$317$	−441.407			−1.39245			−0.696226	+	0.717822i	$0.745139\pi$
$318$			66.7248i			0.209827i
$319$	547.052			1.71490
$320$		0			0
$321$			291.606i			0.908429i
$322$	94.8438	+	175.133i	0.294546	+	0.543891i
$323$	184.615			0.571562
$324$	−9.61713			−0.0296825
$325$		0			0
$326$	92.2089			0.282849
$327$			269.455i			0.824022i
$328$		−	344.860i		−	1.05140i
$329$	−247.066	+	133.799i	−0.750959	+	0.406684i
$330$		0			0
$331$	509.327			1.53875			0.769376	−	0.638796i	$-0.220567\pi$
$331$	509.327			1.53875			0.769376	+	0.638796i	$0.220567\pi$
$332$			109.114i			0.328658i
$333$	−207.642			−0.623550
$334$			71.5550i			0.214236i
$335$		0			0
$336$	−112.838	+	61.1080i	−0.335829	+	0.181869i
$337$	−442.557			−1.31323			−0.656613	−	0.754228i	$-0.728012\pi$
$337$	−442.557			−1.31323			−0.656613	+	0.754228i	$0.728012\pi$
$338$	−167.332			−0.495064
$339$		−	36.3671i		−	0.107277i
$340$		0			0
$341$			114.643i			0.336197i
$342$			70.6253i			0.206507i
$343$	−341.853	−	28.0231i	−0.996657	−	0.0816999i
$344$	375.077			1.09034
$345$		0			0
$346$		−	223.167i		−	0.644993i
$347$	493.763			1.42295			0.711475	−	0.702712i	$-0.248028\pi$
$347$	493.763			1.42295			0.711475	+	0.702712i	$0.248028\pi$
$348$			59.5581i			0.171144i
$349$		−	324.460i		−	0.929686i	−0.885393	−	0.464843i	$-0.846111\pi$
$349$		−	324.460i		−	0.929686i	0.885393	−	0.464843i	$-0.153889\pi$
$350$		0			0
$351$	−84.8633			−0.241776
$352$	282.055			0.801292
$353$			529.424i			1.49979i	0.661559	+	0.749893i	$0.269895\pi$
$353$			529.424i			1.49979i	−0.661559	+	0.749893i	$0.730105\pi$
$354$	−241.988			−0.683581
$355$		0			0
$356$		−	137.184i		−	0.385349i
$357$	77.5211	+	143.146i	0.217146	+	0.400969i
$358$	77.0351			0.215182
$359$	64.2261			0.178903			0.0894514	−	0.995991i	$-0.471489\pi$
$359$	64.2261			0.178903			0.0894514	+	0.995991i	$0.471489\pi$
$360$		0			0
$361$	171.940			0.476289
$362$		−	30.6377i		−	0.0846346i
$363$		−	290.991i		−	0.801627i
$364$	107.422	−	58.1747i	0.295115	−	0.159821i
$365$		0			0
$366$	−44.4411			−0.121424
$367$		−	10.8172i		−	0.0294747i	−0.999891	−	0.0147373i	$-0.995309\pi$
$367$		−	10.8172i		−	0.0294747i	0.999891	−	0.0147373i	$-0.00469121\pi$
$368$	−175.882			−0.477940
$369$		−	119.217i		−	0.323082i
$370$		0			0
$371$	−75.0033	−	138.497i	−0.202165	−	0.373306i
$372$	−12.4813			−0.0335519
$373$	−532.850			−1.42855			−0.714276	−	0.699864i	$-0.753244\pi$
$373$	−532.850			−1.42855			−0.714276	+	0.699864i	$0.753244\pi$
$374$			390.803i			1.04493i
$375$		0			0
$376$		−	348.326i		−	0.926398i
$377$			525.551i			1.39403i
$378$	−54.7613	+	29.6561i	−0.144871	+	0.0784554i
$379$	516.003			1.36149			0.680743	−	0.732523i	$-0.261657\pi$
$379$	516.003			1.36149			0.680743	+	0.732523i	$0.261657\pi$
$380$		0			0
$381$		−	103.700i		−	0.272178i
$382$	305.299			0.799213
$383$			415.069i			1.08373i	0.840465	+	0.541866i	$0.182282\pi$
$383$			415.069i			1.08373i	−0.840465	+	0.541866i	$0.817718\pi$
$384$		−	94.8391i		−	0.246977i
$385$		0			0
$386$	575.765			1.49162
$387$	129.663			0.335046
$388$			170.381i			0.439127i
$389$	54.8032			0.140882			0.0704411	−	0.997516i	$-0.477559\pi$
$389$	54.8032			0.140882			0.0704411	+	0.997516i	$0.477559\pi$
$390$		0			0
$391$			223.122i			0.570645i
$392$	232.368	−	356.123i	0.592775	−	0.908477i
$393$	289.023			0.735428
$394$	−84.2514			−0.213836
$395$		0			0
$396$	54.4974			0.137620
$397$			19.9434i			0.0502352i	0.999685	+	0.0251176i	$0.00799602\pi$
$397$			19.9434i			0.0502352i	−0.999685	+	0.0251176i	$0.992004\pi$
$398$		−	294.127i		−	0.739013i
$399$	−79.3877	−	146.593i	−0.198967	−	0.367400i
$400$		0			0
$401$	−239.505			−0.597269			−0.298634	−	0.954368i	$-0.596531\pi$
$401$	−239.505			−0.597269			−0.298634	+	0.954368i	$0.596531\pi$
$402$			213.776i			0.531781i
$403$	−110.137			−0.273293
$404$		−	25.7931i		−	0.0638444i
$405$		0			0
$406$	183.658	+	339.132i	0.452359	+	0.835300i
$407$	1176.65			2.89102
$408$	−201.814			−0.494643
$409$			663.541i			1.62235i	0.584804	+	0.811175i	$0.301171\pi$
$409$			663.541i			1.62235i	−0.584804	+	0.811175i	$0.698829\pi$
$410$		0			0
$411$			218.480i			0.531581i
$412$		−	93.3363i		−	0.226544i
$413$	502.278	−	272.010i	1.21617	−	0.658621i
$414$	−85.3566			−0.206175
$415$		0			0
$416$			270.969i			0.651368i
$417$	−366.588			−0.879108
$418$		−	400.213i		−	0.957447i
$419$		−	110.648i		−	0.264077i	−0.991245	−	0.132039i	$-0.957848\pi$
$419$		−	110.648i		−	0.264077i	0.991245	−	0.132039i	$-0.0421523\pi$
$420$		0			0
$421$	−521.325			−1.23830			−0.619151	−	0.785272i	$-0.712523\pi$
$421$	−521.325			−1.23830			−0.619151	+	0.785272i	$0.712523\pi$
$422$	−8.72264			−0.0206698
$423$		−	120.415i		−	0.284670i
$424$	195.260			0.460518
$425$		0			0
$426$			76.3140i			0.179141i
$427$	92.2435	−	49.9548i	0.216027	−	0.116990i
$428$	179.903			0.420334
$429$	480.895			1.12097
$430$		0			0
$431$	573.019			1.32951			0.664755	−	0.747062i	$-0.268536\pi$
$431$	573.019			1.32951			0.664755	+	0.747062i	$0.268536\pi$
$432$		−	54.9954i		−	0.127304i
$433$		−	429.740i		−	0.992472i	−0.868188	−	0.496236i	$-0.834715\pi$
$433$		−	429.740i		−	0.992472i	0.868188	−	0.496236i	$-0.165285\pi$
$434$	−71.0702	+	38.4883i	−0.163756	+	0.0886827i
$435$		0			0
$436$	166.237			0.381279
$437$		−	228.495i		−	0.522871i
$438$	222.606			0.508232
$439$		−	83.0494i		−	0.189179i	−0.995516	−	0.0945893i	$-0.969846\pi$
$439$		−	83.0494i		−	0.189179i	0.995516	−	0.0945893i	$-0.0301538\pi$
$440$		0			0
$441$	80.3290	−	123.111i	0.182152	−	0.279163i
$442$	−375.443			−0.849419
$443$	410.010			0.925530			0.462765	−	0.886481i	$-0.346857\pi$
$443$	410.010			0.925530			0.462765	+	0.886481i	$0.346857\pi$
$444$			128.103i			0.288520i
$445$		0			0
$446$		−	530.876i		−	1.19031i
$447$			111.167i			0.248696i
$448$	235.815	+	435.442i	0.526373	+	0.971969i
$449$	−205.948			−0.458682			−0.229341	−	0.973346i	$-0.573657\pi$
$449$	−205.948			−0.458682			−0.229341	+	0.973346i	$0.573657\pi$
$450$		0			0
$451$			675.569i			1.49793i
$452$	−22.4363			−0.0496378
$453$		−	192.111i		−	0.424086i
$454$		−	185.866i		−	0.409397i
$455$		0			0
$456$	206.674			0.453232
$457$	640.868			1.40234			0.701169	−	0.712995i	$-0.252662\pi$
$457$	640.868			1.40234			0.701169	+	0.712995i	$0.252662\pi$
$458$		−	404.893i		−	0.884046i
$459$	−69.7667			−0.151997
$460$		0			0
$461$		−	166.085i		−	0.360272i	−0.983642	−	0.180136i	$-0.942346\pi$
$461$		−	166.085i		−	0.360272i	0.983642	−	0.180136i	$-0.0576538\pi$
$462$	310.316	−	168.052i	0.671679	−	0.363750i
$463$	10.4409			0.0225505			0.0112753	−	0.999936i	$-0.496411\pi$
$463$	10.4409			0.0225505			0.0112753	+	0.999936i	$0.496411\pi$
$464$	−340.582			−0.734013
$465$		0			0
$466$	−259.029			−0.555857
$467$		−	269.736i		−	0.577592i	−0.957391	−	0.288796i	$-0.906745\pi$
$467$		−	269.736i		−	0.577592i	0.957391	−	0.288796i	$-0.0932550\pi$
$468$			52.3555i			0.111871i
$469$	−240.298	−	443.721i	−0.512364	−	0.946100i
$470$		0			0
$471$	−503.077			−1.06810
$472$			708.138i			1.50029i
$473$	−734.761			−1.55341
$474$		−	237.384i		−	0.500809i
$475$		0			0
$476$	88.3123	−	47.8258i	0.185530	−	0.100474i
$477$	67.5007			0.141511
$478$	82.6889			0.172989
$479$			649.820i			1.35662i	0.734777	+	0.678309i	$0.237287\pi$
$479$			649.820i			1.35662i	−0.734777	+	0.678309i	$0.762713\pi$
$480$		0			0
$481$			1130.40i			2.35011i
$482$		−	395.051i		−	0.819608i
$483$	177.169	−	95.9467i	0.366810	−	0.198647i
$484$	−179.524			−0.370917
$485$		0			0
$486$		−	26.6897i		−	0.0549170i
$487$	−597.640			−1.22719			−0.613593	−	0.789622i	$-0.710277\pi$
$487$	−597.640			−1.22719			−0.613593	+	0.789622i	$0.710277\pi$
$488$			130.050i			0.266495i
$489$		−	93.2811i		−	0.190759i
$490$		0			0
$491$	−107.625			−0.219195			−0.109598	−	0.993976i	$-0.534956\pi$
$491$	−107.625			−0.219195			−0.109598	+	0.993976i	$0.534956\pi$
$492$	−73.5498			−0.149491
$493$			432.059i			0.876388i
$494$	384.483			0.778306
$495$		0			0
$496$		−	71.3741i		−	0.143899i
$497$	−85.7821	−	158.400i	−0.172600	−	0.318713i
$498$	−302.816			−0.608065
$499$	−420.611			−0.842908			−0.421454	−	0.906850i	$-0.638480\pi$
$499$	−420.611			−0.842908			−0.421454	+	0.906850i	$0.638480\pi$
$500$		0			0
$501$	72.3870			0.144485
$502$			148.410i			0.295638i
$503$		−	837.716i		−	1.66544i	−0.553694	−	0.832720i	$-0.686782\pi$
$503$		−	837.716i		−	1.66544i	0.553694	−	0.832720i	$-0.313218\pi$
$504$	86.7840	+	160.250i	0.172190	+	0.317956i
$505$		0			0
$506$	483.691			0.955910
$507$			169.278i			0.333881i
$508$	−63.9766			−0.125938
$509$		−	511.304i		−	1.00453i	−0.864715	−	0.502264i	$-0.832501\pi$
$509$		−	511.304i		−	1.00453i	0.864715	−	0.502264i	$-0.167499\pi$
$510$		0			0
$511$	−462.049	+	250.224i	−0.904205	+	0.489675i
$512$	−542.993			−1.06053
$513$	71.4466			0.139272
$514$		−	241.600i		−	0.470038i
$515$		0			0
$516$		−	79.9942i		−	0.155027i
$517$			682.358i			1.31984i
$518$	395.027	+	729.434i	0.762601	+	1.40817i
$519$	−225.762			−0.434995
$520$		0			0
$521$		−	958.401i		−	1.83954i	−0.392455	−	0.919771i	$-0.628374\pi$
$521$		−	958.401i		−	1.83954i	0.392455	−	0.919771i	$-0.371626\pi$
$522$	−165.287			−0.316641
$523$		−	152.860i		−	0.292275i	−0.989264	−	0.146138i	$-0.953316\pi$
$523$		−	152.860i		−	0.292275i	0.989264	−	0.146138i	$-0.0466843\pi$
$524$		−	178.310i		−	0.340286i
$525$		0			0
$526$	−65.2157			−0.123984
$527$	−90.5445			−0.171811
$528$			311.643i			0.590232i
$529$	−252.845			−0.477968
$530$		0			0
$531$			244.801i			0.461020i
$532$	−90.4387	+	48.9774i	−0.169998	+	0.0920627i
$533$	−649.017			−1.21767
$534$	380.716			0.712952
$535$		0			0
$536$	625.581			1.16713
$537$		−	77.9309i		−	0.145123i
$538$			777.689i			1.44552i
$539$	−455.200	+	697.632i	−0.844527	+	1.29431i
$540$		0			0
$541$	−285.016			−0.526832			−0.263416	−	0.964682i	$-0.584849\pi$
$541$	−285.016			−0.526832			−0.263416	+	0.964682i	$0.584849\pi$
$542$		−	134.762i		−	0.248639i
$543$	−30.9940			−0.0570791
$544$			222.766i			0.409495i
$545$		0			0
$546$	161.447	+	298.119i	0.295691	+	0.546006i
$547$	195.330			0.357092			0.178546	−	0.983932i	$-0.442861\pi$
$547$	195.330			0.357092			0.178546	+	0.983932i	$0.442861\pi$
$548$	134.789			0.245965
$549$			44.9578i			0.0818904i
$550$		0			0
$551$		−	442.463i		−	0.803017i
$552$			249.783i			0.452505i
$553$	266.835	+	492.722i	0.482523	+	0.890999i
$554$	146.113			0.263743
$555$		0			0
$556$			226.163i			0.406767i
$557$	27.9390			0.0501598			0.0250799	−	0.999685i	$-0.492016\pi$
$557$	27.9390			0.0501598			0.0250799	+	0.999685i	$0.492016\pi$
$558$		−	34.6383i		−	0.0620759i
$559$		−	705.883i		−	1.26276i
$560$		0			0
$561$	395.347			0.704719
$562$	286.571			0.509912
$563$		−	459.585i		−	0.816314i	−0.912912	−	0.408157i	$-0.866172\pi$
$563$		−	459.585i		−	0.816314i	0.912912	−	0.408157i	$-0.133828\pi$
$564$	−74.2889			−0.131718
$565$		0			0
$566$		−	256.120i		−	0.452509i
$567$	30.0010	+	55.3980i	0.0529118	+	0.0977037i
$568$	223.321			0.393170
$569$	−635.353			−1.11661			−0.558306	−	0.829635i	$-0.688549\pi$
$569$	−635.353			−1.11661			−0.558306	+	0.829635i	$0.688549\pi$
$570$		0			0
$571$	205.282			0.359513			0.179757	−	0.983711i	$-0.442469\pi$
$571$	205.282			0.359513			0.179757	+	0.983711i	$0.442469\pi$
$572$		−	296.683i		−	0.518676i
$573$		−	308.849i		−	0.539004i
$574$	−418.803	+	226.804i	−0.729621	+	0.395129i
$575$		0			0
$576$	−212.227			−0.368449
$577$		−	185.464i		−	0.321429i	−0.987001	−	0.160714i	$-0.948620\pi$
$577$		−	185.464i		−	0.321429i	0.987001	−	0.160714i	$-0.0513798\pi$
$578$	186.155			0.322067
$579$		−	582.460i		−	1.00598i
$580$		0			0
$581$	628.537	−	340.386i	1.08182	−	0.585862i
$582$	−472.846			−0.812450
$583$	−382.506			−0.656100
$584$		−	651.420i		−	1.11545i
$585$		0			0
$586$			249.638i			0.426004i
$587$		−	673.958i		−	1.14814i	−0.818806	−	0.574070i	$-0.805364\pi$
$587$		−	673.958i		−	1.14814i	0.818806	−	0.574070i	$-0.194636\pi$
$588$	−75.9519	−	49.5581i	−0.129170	−	0.0842825i
$589$	92.7247			0.157427
$590$		0			0
$591$			85.2311i			0.144215i
$592$	−732.553			−1.23742
$593$		−	0.486694i		−	0.000820731i	−1.00000		0.000410366i	$-0.999869\pi$
$593$		−	0.486694i		−	0.000820731i	1.00000		0.000410366i	$-0.000130623\pi$
$594$			151.242i			0.254617i
$595$		0			0
$596$	68.5835			0.115073
$597$	−297.547			−0.498404
$598$			464.680i			0.777057i
$599$	580.285			0.968756			0.484378	−	0.874859i	$-0.339046\pi$
$599$	580.285			0.968756			0.484378	+	0.874859i	$0.339046\pi$
$600$		0			0
$601$		−	781.851i		−	1.30092i	−0.759542	−	0.650459i	$-0.774577\pi$
$601$		−	781.851i		−	1.30092i	0.759542	−	0.650459i	$-0.225423\pi$
$602$	−246.676	−	455.498i	−0.409761	−	0.756641i
$603$	216.262			0.358643
$604$	−118.521			−0.196226
$605$		0			0
$606$	71.5816			0.118121
$607$		−	907.211i		−	1.49458i	−0.664498	−	0.747290i	$-0.731354\pi$
$607$		−	907.211i		−	1.49458i	0.664498	−	0.747290i	$-0.268646\pi$
$608$		−	228.129i		−	0.375213i
$609$	343.075	−	185.794i	0.563342	−	0.305080i
$610$		0			0
$611$	−655.539			−1.07289
$612$			43.0418i			0.0703298i
$613$	911.642			1.48718			0.743590	−	0.668636i	$-0.233121\pi$
$613$	911.642			1.48718			0.743590	+	0.668636i	$0.233121\pi$
$614$		−	352.006i		−	0.573299i
$615$		0			0
$616$	−491.779	−	908.089i	−0.798342	−	1.47417i
$617$	−637.918			−1.03390			−0.516951	−	0.856015i	$-0.672933\pi$
$617$	−637.918			−1.03390			−0.516951	+	0.856015i	$0.672933\pi$
$618$	259.029			0.419140
$619$			862.604i			1.39354i	0.717292	+	0.696772i	$0.245381\pi$
$619$			862.604i			1.39354i	−0.717292	+	0.696772i	$0.754619\pi$
$620$		0			0
$621$			86.3492i			0.139049i
$622$		−	726.604i		−	1.16817i
$623$	−790.229	+	427.951i	−1.26843	+	0.686920i
$624$	−299.394			−0.479798
$625$		0			0
$626$			622.369i			0.994200i
$627$	−404.866			−0.645720
$628$			310.368i			0.494216i
$629$			929.310i			1.47744i
$630$		0			0
$631$	−601.057			−0.952547			−0.476273	−	0.879297i	$-0.658013\pi$
$631$	−601.057			−0.952547			−0.476273	+	0.879297i	$0.658013\pi$
$632$	−694.665			−1.09915
$633$			8.82406i			0.0139401i
$634$	−755.752			−1.19204
$635$		0			0
$636$		−	41.6438i		−	0.0654777i
$637$	−670.213	−	437.309i	−1.05214	−	0.686514i
$638$	936.631			1.46807
$639$	77.2014			0.120816
$640$		0			0
$641$	−884.432			−1.37977			−0.689885	−	0.723919i	$-0.742339\pi$
$641$	−884.432			−1.37977			−0.689885	+	0.723919i	$0.742339\pi$
$642$			499.270i			0.777680i
$643$			385.448i			0.599453i	0.954025	+	0.299726i	$0.0968954\pi$
$643$			385.448i			0.599453i	−0.954025	+	0.299726i	$0.903105\pi$
$644$	−59.1933	−	109.303i	−0.0919150	−	0.169725i
$645$		0			0
$646$	316.086			0.489298
$647$			1096.93i			1.69540i	0.530473	+	0.847702i	$0.322014\pi$
$647$			1096.93i			1.69540i	−0.530473	+	0.847702i	$0.677986\pi$
$648$	−78.1030			−0.120529
$649$		−	1387.22i		−	2.13747i
$650$		0			0
$651$	38.9358	+	71.8966i	0.0598093	+	0.110440i
$652$	−57.5488			−0.0882650
$653$	556.888			0.852814			0.426407	−	0.904531i	$-0.359779\pi$
$653$	556.888			0.852814			0.426407	+	0.904531i	$0.359779\pi$
$654$			461.345i			0.705421i
$655$		0			0
$656$		−	420.594i		−	0.641149i
$657$		−	225.194i		−	0.342761i
$658$	−423.011	+	229.083i	−0.642874	+	0.348151i
$659$	−715.578			−1.08585			−0.542927	−	0.839780i	$-0.682684\pi$
$659$	−715.578			−1.08585			−0.542927	+	0.839780i	$0.682684\pi$
$660$		0			0
$661$		−	280.365i		−	0.424152i	−0.977253	−	0.212076i	$-0.931978\pi$
$661$		−	280.365i		−	0.424152i	0.977253	−	0.212076i	$-0.0680225\pi$
$662$	872.040			1.31728
$663$			379.809i			0.572864i
$664$			886.143i			1.33455i
$665$		0			0
$666$	−355.513			−0.533803
$667$	534.753			0.801729
$668$		−	44.6584i		−	0.0668539i
$669$	−537.050			−0.802765
$670$		0			0
$671$		−	254.763i		−	0.379676i
$672$	176.886	−	95.7933i	0.263224	−	0.142550i
$673$	−1067.08			−1.58556			−0.792781	−	0.609506i	$-0.791368\pi$
$673$	−1067.08			−1.58556			−0.792781	+	0.609506i	$0.791368\pi$
$674$	−757.721			−1.12421
$675$		0			0
$676$	104.434			0.154488
$677$		−	313.071i		−	0.462439i	−0.972902	−	0.231219i	$-0.925728\pi$
$677$		−	313.071i		−	0.462439i	0.972902	−	0.231219i	$-0.0742715\pi$
$678$		−	62.2656i		−	0.0918371i
$679$	981.456	−	531.511i	1.44544	−	0.782785i
$680$		0			0
$681$	−188.028			−0.276105
$682$			196.285i			0.287808i
$683$	−505.514			−0.740138			−0.370069	−	0.929004i	$-0.620666\pi$
$683$	−505.514			−0.740138			−0.370069	+	0.929004i	$0.620666\pi$
$684$		−	44.0782i		−	0.0644418i
$685$		0			0
$686$	−585.301	−	47.9795i	−0.853209	−	0.0699409i
$687$	−409.601			−0.596217
$688$	457.446			0.664892
$689$		−	367.473i		−	0.533342i
$690$		0			0
$691$			276.726i			0.400472i	0.979748	+	0.200236i	$0.0641709\pi$
$691$			276.726i			0.400472i	−0.979748	+	0.200236i	$0.935829\pi$
$692$			139.282i			0.201274i
$693$	−170.007	−	313.924i	−0.245320	−	0.452993i
$694$	845.393			1.21815
$695$		0			0
$696$			483.685i			0.694950i
$697$	−533.561			−0.765511
$698$		−	555.522i		−	0.795877i
$699$			262.041i			0.374880i
$700$		0			0
$701$	854.178			1.21851			0.609256	−	0.792973i	$-0.291468\pi$
$701$	854.178			1.21851			0.609256	+	0.792973i	$0.291468\pi$
$702$	−145.298			−0.206977
$703$		−	951.687i		−	1.35375i
$704$	1202.63			1.70828
$705$		0			0
$706$			906.450i			1.28392i
$707$	−148.577	+	80.4626i	−0.210152	+	0.113809i
$708$	151.028			0.213316
$709$	−452.996			−0.638922			−0.319461	−	0.947599i	$-0.603502\pi$
$709$	−452.996			−0.638922			−0.319461	+	0.947599i	$0.603502\pi$
$710$		0			0
$711$	−240.144			−0.337755
$712$		−	1114.11i		−	1.56476i
$713$			112.066i			0.157175i
$714$	132.727	+	245.086i	0.185892	+	0.343258i
$715$		0			0
$716$	−48.0786			−0.0671489
$717$		−	83.6504i		−	0.116667i
$718$	109.964			0.153153
$719$			840.685i			1.16924i	0.811306	+	0.584621i	$0.198757\pi$
$719$			840.685i			1.16924i	−0.811306	+	0.584621i	$0.801243\pi$
$720$		0			0
$721$	−537.650	+	291.166i	−0.745700	+	0.403836i
$722$	294.386			0.407737
$723$	−399.645			−0.552759
$724$			19.1214i			0.0264108i
$725$		0			0
$726$		−	498.217i		−	0.686250i
$727$			1339.58i			1.84262i	0.388829	+	0.921310i	$0.372880\pi$
$727$			1339.58i			1.84262i	−0.388829	+	0.921310i	$0.627120\pi$
$728$	872.398	−	472.450i	1.19835	−	0.648970i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$		−	580.311i		−	0.793860i
$732$	27.7363			0.0378911
$733$		−	536.275i		−	0.731616i	−0.930690	−	0.365808i	$-0.880793\pi$
$733$		−	536.275i		−	0.731616i	0.930690	−	0.365808i	$-0.119207\pi$
$734$		−	18.5206i		−	0.0252324i
$735$		0			0
$736$	275.713			0.374611
$737$	−1225.49			−1.66281
$738$		−	204.117i		−	0.276581i
$739$	−898.552			−1.21590			−0.607951	−	0.793974i	$-0.708008\pi$
$739$	−898.552			−1.21590			−0.607951	+	0.793974i	$0.708008\pi$
$740$		0			0
$741$		−	388.954i		−	0.524904i
$742$	−128.416	−	237.126i	−0.173068	−	0.319576i
$743$	−532.720			−0.716985			−0.358493	−	0.933533i	$-0.616709\pi$
$743$	−532.720			−0.716985			−0.358493	+	0.933533i	$0.616709\pi$
$744$	−101.364			−0.136241
$745$		0			0
$746$	−912.314			−1.22294
$747$			306.337i			0.410090i
$748$		−	243.905i		−	0.326076i
$749$	−561.214	−	1036.30i	−0.749284	−	1.38358i
$750$		0			0
$751$	342.085			0.455506			0.227753	−	0.973719i	$-0.426862\pi$
$751$	342.085			0.455506			0.227753	+	0.973719i	$0.426862\pi$
$752$		−	424.820i		−	0.564921i
$753$	150.136			0.199384
$754$			899.818i			1.19339i
$755$		0			0
$756$	34.1772	−	18.5088i	0.0452080	−	0.0244825i
$757$	−405.961			−0.536276			−0.268138	−	0.963381i	$-0.586408\pi$
$757$	−405.961			−0.536276			−0.268138	+	0.963381i	$0.586408\pi$
$758$	883.470			1.16553
$759$		−	489.315i		−	0.644684i
$760$		0			0
$761$			577.340i			0.758660i	0.925261	+	0.379330i	$0.123845\pi$
$761$			577.340i			0.758660i	−0.925261	+	0.379330i	$0.876155\pi$
$762$		−	177.549i		−	0.233004i
$763$	−518.584	−	957.586i	−0.679664	−	1.25503i
$764$	−190.541			−0.249400
$765$		0			0
$766$			710.657i			0.927751i
$767$	1332.69			1.73754
$768$			327.739i			0.426743i
$769$		−	828.522i		−	1.07740i	−0.842497	−	0.538701i	$-0.818915\pi$
$769$		−	828.522i		−	1.07740i	0.842497	−	0.538701i	$-0.181085\pi$
$770$		0			0
$771$	−244.409			−0.317003
$772$	−359.342			−0.465469
$773$			438.991i			0.567906i	0.958838	+	0.283953i	$0.0916460\pi$
$773$			438.991i			0.567906i	−0.958838	+	0.283953i	$0.908354\pi$
$774$	222.001			0.286824
$775$		0			0
$776$			1383.71i			1.78313i
$777$	737.916	−	399.621i	0.949699	−	0.514312i
$778$	93.8308			0.120605
$779$	546.408			0.701423
$780$		0			0
$781$	−437.477			−0.560150
$782$			382.017i			0.488512i
$783$			167.209i			0.213549i
$784$	283.397	−	434.330i	0.361476	−	0.553992i
$785$		0			0
$786$	494.849			0.629579
$787$		−	285.209i		−	0.362400i	−0.983446	−	0.181200i	$-0.942002\pi$
$787$		−	285.209i		−	0.362400i	0.983446	−	0.181200i	$-0.0579982\pi$
$788$	52.5824			0.0667289
$789$			65.9740i			0.0836172i
$790$		0			0
$791$	69.9907	+	129.241i	0.0884838	+	0.163389i
$792$	442.586			0.558821
$793$	244.750			0.308638
$794$			34.1459i			0.0430049i
$795$		0			0
$796$			183.569i			0.230614i
$797$		−	1243.03i		−	1.55964i	−0.626006	−	0.779818i	$-0.715311\pi$
$797$		−	1243.03i		−	1.55964i	0.626006	−	0.779818i	$-0.284689\pi$
$798$	−135.923	−	250.987i	−0.170330	−	0.314520i
$799$	−538.923			−0.674497
$800$		0			0
$801$		−	385.143i		−	0.480828i
$802$	−410.066			−0.511304
$803$			1276.11i			1.58918i
$804$		−	133.420i		−	0.165946i
$805$		0			0
$806$	−188.570			−0.233958
$807$	786.732			0.974885
$808$		−	209.472i		−	0.259248i
$809$	−630.338			−0.779157			−0.389578	−	0.920993i	$-0.627379\pi$
$809$	−630.338			−0.779157			−0.389578	+	0.920993i	$0.627379\pi$
$810$		0			0
$811$		−	1121.08i		−	1.38234i	−0.722692	−	0.691170i	$-0.757095\pi$
$811$		−	1121.08i		−	1.38234i	0.722692	−	0.691170i	$-0.242905\pi$
$812$	−114.623	−	211.657i	−0.141162	−	0.260661i
$813$	−136.329			−0.167687
$814$	2014.59			2.47492
$815$		0			0
$816$	−246.134			−0.301635
$817$			594.284i			0.727398i
$818$			1136.08i			1.38885i
$819$	301.586	−	163.325i	0.368237	−	0.199420i
$820$		0			0
$821$	544.285			0.662954			0.331477	−	0.943463i	$-0.392453\pi$
$821$	544.285			0.662954			0.331477	+	0.943463i	$0.392453\pi$
$822$			374.069i			0.455071i
$823$	−83.7611			−0.101775			−0.0508877	−	0.998704i	$-0.516205\pi$
$823$	−83.7611			−0.101775			−0.0508877	+	0.998704i	$0.516205\pi$
$824$		−	758.006i		−	0.919911i
$825$		0			0
$826$	859.972	−	465.721i	1.04113	−	0.563826i
$827$	957.378			1.15765			0.578826	−	0.815451i	$-0.303511\pi$
$827$	957.378			1.15765			0.578826	+	0.815451i	$0.303511\pi$
$828$	53.2722			0.0643384
$829$			9.08184i			0.0109552i	0.999985	+	0.00547759i	$0.00174358\pi$
$829$			9.08184i			0.0109552i	−0.999985	+	0.00547759i	$0.998256\pi$
$830$		0			0
$831$		−	147.812i		−	0.177873i
$832$			1155.36i			1.38865i
$833$	−550.987	−	359.515i	−0.661449	−	0.431591i
$834$	−627.651			−0.752579
$835$		0			0
$836$			249.778i			0.298778i
$837$	−35.0411			−0.0418651
$838$		−	189.446i		−	0.226069i
$839$			492.860i			0.587437i	0.955892	+	0.293719i	$0.0948929\pi$
$839$			492.860i			0.587437i	−0.955892	+	0.293719i	$0.905107\pi$
$840$		0			0
$841$	194.509			0.231283
$842$	−892.583			−1.06007
$843$		−	289.903i		−	0.343894i
$844$	5.44391			0.00645013
$845$		0			0
$846$		−	206.168i		−	0.243697i
$847$	560.030	+	1034.12i	0.661193	+	1.22092i
$848$	238.140			0.280825
$849$	−259.098			−0.305181
$850$		0			0
$851$	1150.19			1.35158
$852$		−	47.6286i		−	0.0559021i
$853$			519.198i			0.608672i	0.952565	+	0.304336i	$0.0984346\pi$
$853$			519.198i			0.608672i	−0.952565	+	0.304336i	$0.901565\pi$
$854$	157.934	−	85.5297i	0.184934	−	0.100152i
$855$		0			0
$856$	1461.03			1.70682
$857$			479.468i			0.559473i	0.960077	+	0.279736i	$0.0902470\pi$
$857$			479.468i			0.559473i	−0.960077	+	0.279736i	$0.909753\pi$
$858$	823.360			0.959627
$859$			1667.63i			1.94136i	0.240378	+	0.970679i	$0.422729\pi$
$859$			1667.63i			1.94136i	−0.240378	+	0.970679i	$0.577271\pi$
$860$		0			0
$861$	229.441	+	423.672i	0.266482	+	0.492070i
$862$	981.089			1.13815
$863$	−1217.16			−1.41039			−0.705193	−	0.709016i	$-0.749139\pi$
$863$	−1217.16			−1.41039			−0.705193	+	0.709016i	$0.749139\pi$
$864$			86.2112i			0.0997814i
$865$		0			0
$866$		−	735.776i		−	0.849626i
$867$		−	188.319i		−	0.217208i
$868$	44.3558	−	24.0211i	0.0511012	−	0.0276740i
$869$	1360.82			1.56597
$870$		0			0
$871$		−	1177.32i		−	1.35169i
$872$	1350.05			1.54823
$873$			478.344i			0.547931i
$874$		−	391.215i		−	0.447615i
$875$		0			0
$876$	−138.931			−0.158597
$877$	1027.18			1.17125			0.585623	−	0.810583i	$-0.300850\pi$
$877$	1027.18			1.17125			0.585623	+	0.810583i	$0.300850\pi$
$878$		−	142.192i		−	0.161950i
$879$	252.541			0.287305
$880$		0			0
$881$			149.054i			0.169187i	0.996416	+	0.0845937i	$0.0269592\pi$
$881$			149.054i			0.169187i	−0.996416	+	0.0845937i	$0.973041\pi$
$882$	137.535	−	210.783i	0.155935	−	0.238983i
$883$	−201.243			−0.227908			−0.113954	−	0.993486i	$-0.536352\pi$
$883$	−201.243			−0.227908			−0.113954	+	0.993486i	$0.536352\pi$
$884$	234.319			0.265067
$885$		0			0
$886$	701.995			0.792319
$887$			951.252i			1.07244i	0.844079	+	0.536219i	$0.180148\pi$
$887$			951.252i			1.07244i	−0.844079	+	0.536219i	$0.819852\pi$
$888$			1040.35i			1.17157i
$889$	199.577	+	368.527i	0.224496	+	0.414542i
$890$		0			0
$891$	153.001			0.171718
$892$			331.327i			0.371443i
$893$	551.899			0.618028
$894$			190.334i			0.212902i
$895$		0			0
$896$	182.524	+	337.038i	0.203710	+	0.376158i
$897$	470.083			0.524062
$898$	−352.613			−0.392664
$899$			217.007i			0.241387i
$900$		0			0
$901$		−	302.102i		−	0.335296i
$902$			1156.67i			1.28234i
$903$	−460.794	+	249.545i	−0.510293	+	0.276351i
$904$	−182.210			−0.201560
$905$		0			0
$906$		−	328.921i		−	0.363047i
$907$	559.990			0.617409			0.308705	−	0.951158i	$-0.400105\pi$
$907$	559.990			0.617409			0.308705	+	0.951158i	$0.400105\pi$
$908$			116.002i			0.127755i
$909$		−	72.4140i		−	0.0796633i
$910$		0			0
$911$	−674.618			−0.740525			−0.370262	−	0.928927i	$-0.620732\pi$
$911$	−674.618			−0.740525			−0.370262	+	0.928927i	$0.620732\pi$
$912$	252.061			0.276382
$913$		−	1735.92i		−	1.90134i
$914$	1097.26			1.20050
$915$		0			0
$916$			252.699i			0.275872i
$917$	−1027.13	+	556.244i	−1.12009	+	0.606591i
$918$	−119.450			−0.130120
$919$	982.395			1.06898			0.534491	−	0.845174i	$-0.320503\pi$
$919$	982.395			1.06898			0.534491	+	0.845174i	$0.320503\pi$
$920$		0			0
$921$	−356.099			−0.386644
$922$		−	284.362i		−	0.308419i
$923$		−	420.283i		−	0.455345i
$924$	−193.672	+	104.884i	−0.209602	+	0.113511i
$925$		0			0
$926$	17.8763			0.0193049
$927$		−	262.041i		−	0.282676i
$928$	533.898			0.575322
$929$		−	344.774i		−	0.371124i	−0.982633	−	0.185562i	$-0.940589\pi$
$929$		−	344.774i		−	0.371124i	0.982633	−	0.185562i	$-0.0594105\pi$
$930$		0			0
$931$	564.253	+	368.172i	0.606072	+	0.395458i
$932$	161.664			0.173459
$933$	−735.053			−0.787838
$934$		−	461.826i		−	0.494460i
$935$		0			0
$936$			425.191i			0.454264i
$937$		−	635.256i		−	0.677967i	−0.940792	−	0.338984i	$-0.889917\pi$
$937$		−	635.256i		−	0.677967i	0.940792	−	0.338984i	$-0.110083\pi$
$938$	−411.425	−	759.713i	−0.438620	−	0.809929i
$939$	629.606			0.670507
$940$		0			0
$941$			1207.78i			1.28351i	0.766909	+	0.641756i	$0.221794\pi$
$941$			1207.78i			1.28351i	−0.766909	+	0.641756i	$0.778206\pi$
$942$	−861.338			−0.914372
$943$			660.380i			0.700297i
$944$			863.649i			0.914883i
$945$		0			0
$946$	−1258.02			−1.32983
$947$	254.133			0.268356			0.134178	−	0.990957i	$-0.457161\pi$
$947$	254.133			0.268356			0.134178	+	0.990957i	$0.457161\pi$
$948$			148.154i			0.156281i
$949$	−1225.95			−1.29184
$950$		0			0
$951$			764.540i			0.803933i
$952$	717.205	−	388.405i	0.753367	−	0.407988i
$953$	−424.523			−0.445460			−0.222730	−	0.974880i	$-0.571497\pi$
$953$	−424.523			−0.445460			−0.222730	+	0.974880i	$0.571497\pi$
$954$	115.571			0.121143
$955$		0			0
$956$	−51.6072			−0.0539824
$957$		−	947.522i		−	0.990096i
$958$			1112.58i			1.16136i
$959$	−420.479	−	776.431i	−0.438455	−	0.809625i
$960$		0			0
$961$	915.523			0.952677
$962$			1935.41i			2.01186i
$963$	505.076			0.524482
$964$			246.557i			0.255764i
$965$		0			0
$966$	303.339	−	164.274i	0.314016	−	0.170056i
$967$	46.7338			0.0483286			0.0241643	−	0.999708i	$-0.492308\pi$
$967$	46.7338			0.0483286			0.0241643	+	0.999708i	$0.492308\pi$
$968$	−1457.95			−1.50615
$969$		−	319.762i		−	0.329991i
$970$		0			0
$971$			1724.03i			1.77552i	0.460303	+	0.887762i	$0.347741\pi$
$971$			1724.03i			1.77552i	−0.460303	+	0.887762i	$0.652259\pi$
$972$			16.6574i			0.0171372i
$973$	1302.77	−	705.522i	1.33893	−	0.725100i
$974$	−1023.24			−1.05056
$975$		0			0
$976$			158.609i			0.162510i
$977$	1613.20			1.65118			0.825589	−	0.564271i	$-0.190843\pi$
$977$	1613.20			1.65118			0.825589	+	0.564271i	$0.190843\pi$
$978$		−	159.711i		−	0.163303i
$979$			2182.49i			2.22931i
$980$		0			0
$981$	466.710			0.475749
$982$	−184.269			−0.187647
$983$		−	31.6909i		−	0.0322389i	−0.999870	−	0.0161195i	$-0.994869\pi$
$983$		−	31.6909i		−	0.0322389i	0.999870	−	0.0161195i	$-0.00513121\pi$
$984$	−597.315			−0.607028
$985$		0			0
$986$			739.747i			0.750250i
$987$	231.747	+	427.930i	0.234799	+	0.433566i
$988$	−239.961			−0.242875
$989$	−718.242			−0.726231
$990$		0			0
$991$	−236.475			−0.238623			−0.119311	−	0.992857i	$-0.538069\pi$
$991$	−236.475			−0.238623			−0.119311	+	0.992857i	$0.538069\pi$
$992$			111.886i			0.112789i
$993$		−	882.180i		−	0.888399i
$994$	−146.871	−	271.204i	−0.147758	−	0.272841i
$995$		0			0
$996$	188.992			0.189751
$997$		−	948.441i		−	0.951295i	−0.879636	−	0.475648i	$-0.842214\pi$
$997$		−	948.441i		−	0.951295i	0.879636	−	0.475648i	$-0.157786\pi$
$998$	−720.146			−0.721589
$999$			359.647i			0.360007i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.h.d.76.7		12
5.2	odd	4		525.3.e.c.349.2		24
5.3	odd	4		525.3.e.c.349.15		24
5.4	even	2		105.3.h.a.76.6	yes	12
7.6	odd	2	inner	525.3.h.d.76.8		12
15.14	odd	2		315.3.h.d.181.8		12
20.19	odd	2		1680.3.s.c.1441.2		12
35.13	even	4		525.3.e.c.349.1		24
35.27	even	4		525.3.e.c.349.16		24
35.34	odd	2		105.3.h.a.76.5	✓	12
105.104	even	2		315.3.h.d.181.7		12
140.139	even	2		1680.3.s.c.1441.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.5	✓	12	35.34	odd	2
105.3.h.a.76.6	yes	12	5.4	even	2
315.3.h.d.181.7		12	105.104	even	2
315.3.h.d.181.8		12	15.14	odd	2
525.3.e.c.349.1		24	35.13	even	4
525.3.e.c.349.2		24	5.2	odd	4
525.3.e.c.349.15		24	5.3	odd	4
525.3.e.c.349.16		24	35.27	even	4
525.3.h.d.76.7		12	1.1	even	1	trivial
525.3.h.d.76.8		12	7.6	odd	2	inner
1680.3.s.c.1441.2		12	20.19	odd	2
1680.3.s.c.1441.11		12	140.139	even	2

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.71214 q^{2} -1.73205i q^{3} -1.06857 q^{4} -2.96552i q^{6} +(3.33344 + 6.15534i) q^{7} -8.67811 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.71214 q^{2} -1.73205i q^{3} -1.06857 q^{4} -2.96552i q^{6} +(3.33344 + 6.15534i) q^{7} -8.67811 q^{8} -3.00000 q^{9} +17.0001 q^{11} +1.85082i q^{12} +16.3319i q^{13} +(5.70733 + 10.5388i) q^{14} -10.5839 q^{16} +13.4266i q^{17} -5.13643 q^{18} -13.7499i q^{19} +(10.6614 - 5.77369i) q^{21} +29.1066 q^{22} +16.6179 q^{23} +15.0309i q^{24} +27.9626i q^{26} +5.19615i q^{27} +(-3.56202 - 6.57741i) q^{28} +32.1793 q^{29} +6.74366i q^{31} +16.5913 q^{32} -29.4450i q^{33} +22.9883i q^{34} +3.20571 q^{36} +69.2141 q^{37} -23.5418i q^{38} +28.2878 q^{39} +39.7391i q^{41} +(18.2538 - 9.88538i) q^{42} -43.2210 q^{43} -18.1658 q^{44} +28.4522 q^{46} +40.1384i q^{47} +18.3318i q^{48} +(-26.7763 + 41.0369i) q^{49} +23.2556 q^{51} -17.4518i q^{52} -22.5002 q^{53} +8.89655i q^{54} +(-28.9280 - 53.4167i) q^{56} -23.8155 q^{57} +55.0956 q^{58} -81.6005i q^{59} -14.9859i q^{61} +11.5461i q^{62} +(-10.0003 - 18.4660i) q^{63} +70.7422 q^{64} -50.4141i q^{66} -72.0872 q^{67} -14.3473i q^{68} -28.7831i q^{69} -25.7338 q^{71} +26.0343 q^{72} +75.0647i q^{73} +118.504 q^{74} +14.6927i q^{76} +(56.6689 + 104.641i) q^{77} +48.4327 q^{78} +80.0480 q^{79} +9.00000 q^{81} +68.0389i q^{82} -102.112i q^{83} +(-11.3924 + 6.16959i) q^{84} -74.0005 q^{86} -55.7362i q^{87} -147.529 q^{88} +128.381i q^{89} +(-100.529 + 54.4416i) q^{91} -17.7574 q^{92} +11.6804 q^{93} +68.7227i q^{94} -28.7371i q^{96} -159.448i q^{97} +(-45.8449 + 70.2610i) q^{98} -51.0003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9	\( 12 q + 4 q^{2} + 44 q^{4} + 8 q^{7} - 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} - 12 q^{18} + 36 q^{21} + 88 q^{22} + 64 q^{23} - 88 q^{28} + 104 q^{29} + 228 q^{32} - 132 q^{36} - 32 q^{37} - 24 q^{39} + 60 q^{42} - 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 24 q^{51} - 176 q^{53} - 368 q^{56} + 240 q^{57} + 400 q^{58} - 24 q^{63} - 20 q^{64} - 168 q^{67} + 32 q^{71} + 12 q^{72} + 184 q^{74} - 8 q^{77} - 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 400 q^{86} + 536 q^{88} + 24 q^{91} - 192 q^{92} - 48 q^{93} - 884 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 44 * q^4 + 8 * q^7 - 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 - 12 * q^18 + 36 * q^21 + 88 * q^22 + 64 * q^23 - 88 * q^28 + 104 * q^29 + 228 * q^32 - 132 * q^36 - 32 * q^37 - 24 * q^39 + 60 * q^42 - 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 24 * q^51 - 176 * q^53 - 368 * q^56 + 240 * q^57 + 400 * q^58 - 24 * q^63 - 20 * q^64 - 168 * q^67 + 32 * q^71 + 12 * q^72 + 184 * q^74 - 8 * q^77 - 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 400 * q^86 + 536 * q^88 + 24 * q^91 - 192 * q^92 - 48 * q^93 - 884 * q^98 + 48 * q^99

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