LMFDB - Embedded newform 105.3.h.a.76.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(76,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, 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("105.76");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.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:	$2.86104277578$
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^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.6
Root			$-1.01714 - 1.76174i$ of defining polynomial
Character	$\chi$	$=$	105.76
Dual form			105.3.h.a.76.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71214 q^{2} +1.73205i q^{3} -1.06857 q^{4} -2.23607i q^{5} -2.96552i q^{6} +(-3.33344 - 6.15534i) q^{7} +8.67811 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-1.71214 q^{2} +1.73205i q^{3} -1.06857 q^{4} -2.23607i q^{5} -2.96552i q^{6} +(-3.33344 - 6.15534i) q^{7} +8.67811 q^{8} -3.00000 q^{9} +3.82847i q^{10} +17.0001 q^{11} -1.85082i q^{12} -16.3319i q^{13} +(5.70733 + 10.5388i) q^{14} +3.87298 q^{15} -10.5839 q^{16} -13.4266i q^{17} +5.13643 q^{18} -13.7499i q^{19} +2.38940i q^{20} +(10.6614 - 5.77369i) q^{21} -29.1066 q^{22} -16.6179 q^{23} +15.0309i q^{24} -5.00000 q^{25} +27.9626i q^{26} -5.19615i q^{27} +(3.56202 + 6.57741i) q^{28} +32.1793 q^{29} -6.63110 q^{30} +6.74366i q^{31} -16.5913 q^{32} +29.4450i q^{33} +22.9883i q^{34} +(-13.7637 + 7.45380i) q^{35} +3.20571 q^{36} -69.2141 q^{37} +23.5418i q^{38} +28.2878 q^{39} -19.4048i q^{40} +39.7391i q^{41} +(-18.2538 + 9.88538i) q^{42} +43.2210 q^{43} -18.1658 q^{44} +6.70820i q^{45} +28.4522 q^{46} -40.1384i q^{47} -18.3318i q^{48} +(-26.7763 + 41.0369i) q^{49} +8.56071 q^{50} +23.2556 q^{51} +17.4518i q^{52} +22.5002 q^{53} +8.89655i q^{54} -38.0134i q^{55} +(-28.9280 - 53.4167i) q^{56} +23.8155 q^{57} -55.0956 q^{58} -81.6005i q^{59} -4.13855 q^{60} -14.9859i q^{61} -11.5461i q^{62} +(10.0003 + 18.4660i) q^{63} +70.7422 q^{64} -36.5193 q^{65} -50.4141i q^{66} +72.0872 q^{67} +14.3473i q^{68} -28.7831i q^{69} +(23.5655 - 12.7620i) q^{70} -25.7338 q^{71} -26.0343 q^{72} -75.0647i q^{73} +118.504 q^{74} -8.66025i q^{75} +14.6927i q^{76} +(-56.6689 - 104.641i) q^{77} -48.4327 q^{78} +80.0480 q^{79} +23.6663i q^{80} +9.00000 q^{81} -68.0389i q^{82} +102.112i q^{83} +(-11.3924 + 6.16959i) q^{84} -30.0228 q^{85} -74.0005 q^{86} +55.7362i q^{87} +147.529 q^{88} +128.381i q^{89} -11.4854i q^{90} +(-100.529 + 54.4416i) q^{91} +17.7574 q^{92} -11.6804 q^{93} +68.7227i q^{94} -30.7457 q^{95} -28.7371i q^{96} +159.448i q^{97} +(45.8449 - 70.2610i) q^{98} -51.0003 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 60 q^{25} + 88 q^{28} + 104 q^{29} - 228 q^{32} + 60 q^{35} - 132 q^{36} + 32 q^{37} - 24 q^{39} - 60 q^{42} + 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 20 q^{50} + 24 q^{51} + 176 q^{53} - 368 q^{56} - 240 q^{57} - 400 q^{58} + 24 q^{63} - 20 q^{64} - 240 q^{65} + 168 q^{67} - 60 q^{70} + 32 q^{71} - 12 q^{72} + 184 q^{74} + 8 q^{77} + 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 120 q^{85} + 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 - 60 * q^25 + 88 * q^28 + 104 * q^29 - 228 * q^32 + 60 * q^35 - 132 * q^36 + 32 * q^37 - 24 * q^39 - 60 * q^42 + 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 20 * q^50 + 24 * q^51 + 176 * q^53 - 368 * q^56 - 240 * q^57 - 400 * q^58 + 24 * q^63 - 20 * q^64 - 240 * q^65 + 168 * q^67 - 60 * q^70 + 32 * q^71 - 12 * q^72 + 184 * q^74 + 8 * q^77 + 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 120 * q^85 + 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$-1$	$1$

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	$-0.640794\pi$
$2$	−1.71214			−0.856071			−0.428035	+	0.903762i	$0.640794\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−1.06857			−0.267143
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$		−	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
$10$			3.82847i			0.382847i
$11$	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	$-0.783812\pi$
$13$		−	16.3319i		−	1.25630i	0.778091	−	0.628152i	$-0.216188\pi$
$14$	5.70733	+	10.5388i	0.407666	+	0.752772i
$15$	3.87298			0.258199
$16$	−10.5839			−0.661492
$17$		−	13.4266i		−	0.789801i	−0.918724	−	0.394900i	$-0.870779\pi$
$17$		−	13.4266i		−	0.789801i	0.918724	−	0.394900i	$-0.129221\pi$
$18$	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	$-0.117851\pi$
$20$			2.38940i			0.119470i
$21$	10.6614	−	5.77369i	0.507684	−	0.274938i
$22$	−29.1066			−1.32303
$23$	−16.6179			−0.722518			−0.361259	−	0.932466i	$-0.617653\pi$
$23$	−16.6179			−0.722518			−0.361259	+	0.932466i	$0.617653\pi$
$24$			15.0309i			0.626289i
$25$	−5.00000			−0.200000
$26$			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	$0.312789\pi$
$30$	−6.63110			−0.221037
$31$			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
$35$	−13.7637	+	7.45380i	−0.393250	+	0.212966i
$36$	3.20571			0.0890475
$37$	−69.2141			−1.87065			−0.935325	−	0.353789i	$-0.884893\pi$
$37$	−69.2141			−1.87065			−0.935325	+	0.353789i	$0.884893\pi$
$38$			23.5418i			0.619520i
$39$	28.2878			0.725327
$40$		−	19.4048i		−	0.485121i
$41$			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	$-0.332388\pi$
$43$	43.2210			1.00514			0.502570	+	0.864537i	$0.332388\pi$
$44$	−18.1658			−0.412859
$45$			6.70820i			0.149071i
$46$	28.4522			0.618526
$47$		−	40.1384i		−	0.854009i	−0.904249	−	0.427005i	$-0.859569\pi$
$47$		−	40.1384i		−	0.854009i	0.904249	−	0.427005i	$-0.140431\pi$
$48$		−	18.3318i		−	0.381913i
$49$	−26.7763	+	41.0369i	−0.546456	+	0.837488i
$50$	8.56071			0.171214
$51$	23.2556			0.455992
$52$			17.4518i			0.335612i
$53$	22.5002			0.424533			0.212266	−	0.977212i	$-0.431916\pi$
$53$	22.5002			0.424533			0.212266	+	0.977212i	$0.431916\pi$
$54$			8.89655i			0.164751i
$55$		−	38.0134i		−	0.691153i
$56$	−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	$-0.243063\pi$
$60$	−4.13855			−0.0689759
$61$		−	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
$65$	−36.5193			−0.561836
$66$		−	50.4141i		−	0.763850i
$67$	72.0872			1.07593			0.537964	−	0.842968i	$-0.319194\pi$
$67$	72.0872			1.07593			0.537964	+	0.842968i	$0.319194\pi$
$68$			14.3473i			0.210989i
$69$		−	28.7831i		−	0.417146i
$70$	23.5655	−	12.7620i	0.336650	−	0.182314i
$71$	−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	$-0.828110\pi$
$73$		−	75.0647i		−	1.02828i	0.857705	−	0.514142i	$-0.171890\pi$
$74$	118.504			1.60141
$75$		−	8.66025i		−	0.115470i
$76$			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	$0.330890\pi$
$80$			23.6663i			0.295828i
$81$	9.00000			0.111111
$82$		−	68.0389i		−	0.829743i
$83$			102.112i			1.23027i	0.788421	+	0.615135i	$0.210899\pi$
$83$			102.112i			1.23027i	−0.788421	+	0.615135i	$0.789101\pi$
$84$	−11.3924	+	6.16959i	−0.135624	+	0.0734476i
$85$	−30.0228			−0.353210
$86$	−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	$0.743571\pi$
$90$		−	11.4854i		−	0.127616i
$91$	−100.529	+	54.4416i	−1.10471	+	0.598259i
$92$	17.7574			0.193015
$93$	−11.6804			−0.125595
$94$			68.7227i			0.731092i
$95$	−30.7457			−0.323639
$96$		−	28.7371i		−	0.299344i
$97$			159.448i			1.64379i	0.569636	+	0.821897i	$0.307084\pi$
$97$			159.448i			1.64379i	−0.569636	+	0.821897i	$0.692916\pi$
$98$	45.8449	−	70.2610i	0.467805	−	0.716949i
$99$	−51.0003			−0.515155
$100$	5.34285			0.0534285
$101$			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	$-0.860621\pi$
$103$		−	87.3469i		−	0.848028i	0.905656	−	0.424014i	$-0.139379\pi$
$104$		−	141.730i		−	1.36279i
$105$	−12.9104	−	23.8395i	−0.122956	−	0.227043i
$106$	−38.5236			−0.363430
$107$	168.359			1.57344			0.786722	−	0.617307i	$-0.211776\pi$
$107$	168.359			1.57344			0.786722	+	0.617307i	$0.211776\pi$
$108$			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	$0.752947\pi$
$110$			65.0843i			0.591676i
$111$		−	119.882i		−	1.08002i
$112$	35.2807	+	65.1473i	0.315007	+	0.581672i
$113$	−20.9965			−0.185810			−0.0929050	−	0.995675i	$-0.529615\pi$
$113$	−20.9965			−0.185810			−0.0929050	+	0.995675i	$0.529615\pi$
$114$	−40.7756			−0.357680
$115$			37.1588i			0.323120i
$116$	−34.3859			−0.296430
$117$			48.9958i			0.418768i
$118$			139.712i			1.18400i
$119$	−82.6453	+	44.7568i	−0.694498	+	0.376108i
$120$	33.6102			0.280085
$121$	168.004			1.38846
$122$			25.6581i			0.210312i
$123$	−68.8301			−0.559594
$124$		−	7.20608i		−	0.0581135i
$125$			11.1803i			0.0894427i
$126$	−17.1220	−	31.6164i	−0.135889	−	0.250924i
$127$	−59.8712			−0.471427			−0.235713	−	0.971823i	$-0.575743\pi$
$127$	−59.8712			−0.471427			−0.235713	+	0.971823i	$0.575743\pi$
$128$	−54.7554			−0.427776
$129$			74.8609i			0.580317i
$130$	62.5263			0.480971
$131$			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
$135$	−11.6190			−0.0860663
$136$		−	116.518i		−	0.856747i
$137$	126.139			0.920726			0.460363	−	0.887731i	$-0.347719\pi$
$137$	126.139			0.920726			0.460363	+	0.887731i	$0.347719\pi$
$138$			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	$-0.275453\pi$
$140$	14.7075	−	7.96491i	0.105054	−	0.0568922i
$141$	69.5218			0.493062
$142$	44.0599			0.310281
$143$		−	277.645i		−	1.94157i
$144$	31.7516			0.220497
$145$		−	71.9552i		−	0.496243i
$146$			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	$0.569098\pi$
$150$			14.8276i			0.0988506i
$151$	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
$155$	15.0793			0.0972858
$156$	−30.2275			−0.193766
$157$			290.451i			1.85001i	0.379956	+	0.925004i	$0.375939\pi$
$157$			290.451i			1.85001i	−0.379956	+	0.925004i	$0.624061\pi$
$158$	−137.053			−0.867427
$159$			38.9716i			0.245104i
$160$			37.0994i			0.231871i
$161$	55.3948	+	102.289i	0.344067	+	0.635334i
$162$	−15.4093			−0.0951190
$163$	−53.8559			−0.330404			−0.165202	−	0.986260i	$-0.552828\pi$
$163$	−53.8559			−0.330404			−0.165202	+	0.986260i	$0.552828\pi$
$164$		−	42.4640i		−	0.258927i
$165$	65.8411			0.399037
$166$		−	174.831i		−	1.05320i
$167$		−	41.7927i		−	0.250255i	−0.992141	−	0.125128i	$-0.960066\pi$
$167$		−	41.7927i		−	0.250255i	0.992141	−	0.125128i	$-0.0399341\pi$
$168$	92.5204	−	50.1047i	0.550717	−	0.298242i
$169$	−97.7324			−0.578298
$170$	51.4033			0.302372
$171$			41.2497i			0.241226i
$172$	−46.1847			−0.268515
$173$			130.344i			0.753434i	0.926328	+	0.376717i	$0.122947\pi$
$173$			130.344i			0.753434i	−0.926328	+	0.376717i	$0.877053\pi$
$174$		−	95.4283i		−	0.548439i
$175$	16.6672	+	30.7767i	0.0952412	+	0.175867i
$176$	−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	$0.459889\pi$
$180$		−	7.16819i		−	0.0398233i
$181$		−	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
$185$			154.767i			0.836581i
$186$	19.9985			0.107519
$187$		−	228.254i		−	1.22061i
$188$			42.8907i			0.228142i
$189$	−31.9841	+	17.3211i	−0.169228	+	0.0916459i
$190$	52.6410			0.277058
$191$	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	$-0.836658\pi$
$193$	−336.283			−1.74240			−0.871200	+	0.490928i	$0.836658\pi$
$194$		−	272.998i		−	1.40720i
$195$		−	63.2534i		−	0.324376i
$196$	28.6124	−	43.8508i	0.145982	−	0.223729i
$197$	49.2082			0.249788			0.124894	−	0.992170i	$-0.460141\pi$
$197$	49.2082			0.249788			0.124894	+	0.992170i	$0.460141\pi$
$198$	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	$-0.142062\pi$
$200$	−43.3906			−0.216953
$201$			124.859i			0.621187i
$202$		−	41.3277i		−	0.204592i
$203$	−107.268	−	198.075i	−0.528414	−	0.975737i
$204$	−24.8502			−0.121815
$205$	88.8593			0.433460
$206$			149.550i			0.725972i
$207$	49.8537			0.240839
$208$			172.855i			0.831035i
$209$		−	233.750i		−	1.11842i
$210$	22.1044	+	40.8166i	0.105259	+	0.194365i
$211$	−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
$215$		−	96.6451i		−	0.449512i
$216$		−	45.0928i		−	0.208763i
$217$	41.5095	−	22.4796i	0.191288	−	0.103593i
$218$	266.358			1.22183
$219$	130.016			0.593680
$220$			40.6200i			0.184636i
$221$	−219.283			−0.992229
$222$			205.256i			0.924574i
$223$			310.066i			1.39043i	0.718802	+	0.695215i	$0.244691\pi$
$223$			310.066i			1.39043i	−0.718802	+	0.695215i	$0.755309\pi$
$224$	55.3063	+	102.125i	0.246903	+	0.455917i
$225$	15.0000			0.0666667
$226$	35.9490			0.159067
$227$			108.558i			0.478228i	0.970991	+	0.239114i	$0.0768570\pi$
$227$			108.558i			0.478228i	−0.970991	+	0.239114i	$0.923143\pi$
$228$	−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	$-0.172706\pi$
$230$		−	63.6211i		−	0.276613i
$231$	181.244	−	98.1534i	0.784607	−	0.424906i
$232$	279.256			1.20369
$233$	151.290			0.649312			0.324656	−	0.945832i	$-0.394751\pi$
$233$	151.290			0.649312			0.324656	+	0.945832i	$0.394751\pi$
$234$		−	83.8878i		−	0.358495i
$235$	−89.7523			−0.381925
$236$			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	$0.467784\pi$
$240$	−40.9912			−0.170797
$241$		−	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
$245$	91.7613	+	59.8737i	0.374536	+	0.244382i
$246$	117.847			0.479053
$247$	−224.563			−0.909160
$248$			58.5223i			0.235977i
$249$	−176.864			−0.710297
$250$		−	19.1423i		−	0.0765693i
$251$			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
$255$		−	52.0010i		−	0.203926i
$256$	−189.220			−0.739141
$257$			141.110i			0.549065i	0.961578	+	0.274532i	$0.0885231\pi$
$257$			141.110i			0.549065i	−0.961578	+	0.274532i	$0.911477\pi$
$258$		−	128.173i		−	0.496793i
$259$	230.721	+	426.036i	0.890815	+	1.64493i
$260$	39.0235			0.150090
$261$	−96.5380			−0.369877
$262$		−	285.701i		−	1.09046i
$263$	38.0901			0.144829			0.0724147	−	0.997375i	$-0.476930\pi$
$263$	38.0901			0.144829			0.0724147	+	0.997375i	$0.476930\pi$
$264$			255.527i			0.967907i
$265$		−	50.3121i		−	0.189857i
$266$	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	$0.680031\pi$
$270$	19.8933			0.0736789
$271$		−	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
$275$	−85.0005			−0.309093
$276$			30.7567i			0.111437i
$277$	−85.3396			−0.308085			−0.154043	−	0.988064i	$-0.549229\pi$
$277$	−85.3396			−0.308085			−0.154043	+	0.988064i	$0.549229\pi$
$278$			362.374i			1.30350i
$279$		−	20.2310i		−	0.0725125i
$280$	−119.443	+	64.6849i	−0.426583	+	0.231018i
$281$	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	$0.0851390\pi$
$283$			149.591i			0.528588i	−0.964442	+	0.264294i	$0.914861\pi$
$284$	27.4984			0.0968252
$285$		−	53.2531i		−	0.186853i
$286$			475.367i			1.66212i
$287$	244.607	−	132.468i	0.852291	−	0.461561i
$288$	49.7740			0.172827
$289$	108.726			0.376215
$290$			123.197i			0.424819i
$291$	−276.172			−0.949045
$292$			80.2119i			0.274698i
$293$		−	145.805i		−	0.497627i	−0.968551	−	0.248813i	$-0.919959\pi$
$293$		−	145.805i		−	0.497627i	0.968551	−	0.248813i	$-0.0800406\pi$
$294$	121.696	+	79.4056i	0.413931	+	0.270087i
$295$	−182.464			−0.618523
$296$	−600.648			−2.02921
$297$		−	88.3351i		−	0.297425i
$298$	109.889			0.368757
$299$			271.403i			0.907701i
$300$			9.25409i			0.0308470i
$301$	−144.075	−	266.040i	−0.478653	−	0.883853i
$302$	−189.903			−0.628817
$303$	−41.8082			−0.137981
$304$			145.527i			0.478708i
$305$	−33.5096			−0.109868
$306$		−	68.9648i		−	0.225375i
$307$			205.594i			0.669686i	0.942274	+	0.334843i	$0.108683\pi$
$307$			205.594i			0.669686i	−0.942274	+	0.334843i	$0.891317\pi$
$308$	60.5547	+	111.817i	0.196606	+	0.363041i
$309$	151.289			0.489609
$310$	−25.8179			−0.0832835
$311$		−	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	$-0.802788\pi$
$313$		−	363.503i		−	1.16135i	0.814135	−	0.580676i	$-0.197212\pi$
$314$		−	497.294i		−	1.58374i
$315$	41.2912	−	22.3614i	0.131083	−	0.0709886i
$316$	−85.5369			−0.270686
$317$	441.407			1.39245			0.696226	−	0.717822i	$-0.254861\pi$
$317$	441.407			1.39245			0.696226	+	0.717822i	$0.254861\pi$
$318$		−	66.7248i		−	0.209827i
$319$	547.052			1.71490
$320$		−	158.184i		−	0.494326i
$321$			291.606i			0.908429i
$322$	−94.8438	−	175.133i	−0.294546	−	0.543891i
$323$	−184.615			−0.571562
$324$	−9.61713			−0.0296825
$325$			81.6597i			0.251261i
$326$	92.2089			0.282849
$327$		−	269.455i		−	0.824022i
$328$			344.860i			1.05140i
$329$	−247.066	+	133.799i	−0.750959	+	0.406684i
$330$	−112.729			−0.341604
$331$	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
$335$		−	161.192i		−	0.481170i
$336$	−112.838	+	61.1080i	−0.335829	+	0.181869i
$337$	442.557			1.31323			0.656613	−	0.754228i	$-0.271988\pi$
$337$	442.557			1.31323			0.656613	+	0.754228i	$0.271988\pi$
$338$	167.332			0.495064
$339$		−	36.3671i		−	0.107277i
$340$	32.0815			0.0943573
$341$			114.643i			0.336197i
$342$		−	70.6253i		−	0.206507i
$343$	341.853	+	28.0231i	0.996657	+	0.0816999i
$344$	375.077			1.09034
$345$	−64.3609			−0.186553
$346$		−	223.167i		−	0.644993i
$347$	−493.763			−1.42295			−0.711475	−	0.702712i	$-0.751972\pi$
$347$	−493.763			−1.42295			−0.711475	+	0.702712i	$0.751972\pi$
$348$		−	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	$-0.153889\pi$
$350$	−28.5366	−	52.6940i	−0.0815332	−	0.150554i
$351$	−84.8633			−0.241776
$352$	−282.055			−0.801292
$353$		−	529.424i		−	1.49979i	−0.661559	−	0.749893i	$-0.730105\pi$
$353$		−	529.424i		−	1.49979i	0.661559	−	0.749893i	$-0.269895\pi$
$354$	−241.988			−0.683581
$355$			57.5425i			0.162092i
$356$		−	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	$0.471489\pi$
$360$			58.2145i			0.161707i
$361$	171.940			0.476289
$362$			30.6377i			0.0846346i
$363$			290.991i			0.801627i
$364$	107.422	−	58.1747i	0.295115	−	0.159821i
$365$	−167.850			−0.459863
$366$	−44.4411			−0.121424
$367$			10.8172i			0.0294747i	0.999891	+	0.0147373i	$0.00469121\pi$
$367$			10.8172i			0.0294747i	−0.999891	+	0.0147373i	$0.995309\pi$
$368$	175.882			0.477940
$369$		−	119.217i		−	0.323082i
$370$		−	264.984i		−	0.716172i
$371$	−75.0033	−	138.497i	−0.202165	−	0.373306i
$372$	12.4813			0.0335519
$373$	532.850			1.42855			0.714276	−	0.699864i	$-0.246756\pi$
$373$	532.850			1.42855			0.714276	+	0.699864i	$0.246756\pi$
$374$			390.803i			1.04493i
$375$	−19.3649			−0.0516398
$376$		−	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	$0.261657\pi$
$380$	32.8539			0.0864578
$381$		−	103.700i		−	0.272178i
$382$	−305.299			−0.799213
$383$		−	415.069i		−	1.08373i	−0.840465	−	0.541866i	$-0.817718\pi$
$383$		−	415.069i		−	1.08373i	0.840465	−	0.541866i	$-0.182282\pi$
$384$		−	94.8391i		−	0.246977i
$385$	−233.985	+	126.715i	−0.607754	+	0.329131i
$386$	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	$0.477559\pi$
$390$			108.299i			0.277689i
$391$			223.122i			0.570645i
$392$	−232.368	+	356.123i	−0.592775	+	0.908477i
$393$	−289.023			−0.735428
$394$	−84.2514			−0.213836
$395$		−	178.993i		−	0.453146i
$396$	54.4974			0.137620
$397$		−	19.9434i		−	0.0502352i	−0.999685	−	0.0251176i	$-0.992004\pi$
$397$		−	19.9434i		−	0.0502352i	0.999685	−	0.0251176i	$-0.00799602\pi$
$398$			294.127i			0.739013i
$399$	−79.3877	−	146.593i	−0.198967	−	0.367400i
$400$	52.9194			0.132298
$401$	−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
$405$		−	20.1246i		−	0.0496904i
$406$	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	$0.698829\pi$
$410$	−152.140			−0.371072
$411$			218.480i			0.531581i
$412$			93.3363i			0.226544i
$413$	−502.278	+	272.010i	−1.21617	+	0.658621i
$414$	−85.3566			−0.206175
$415$	228.330			0.550194
$416$			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	$-0.0421523\pi$
$420$	13.7956	+	25.4742i	0.0328467	+	0.0606528i
$421$	−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
$425$			67.1330i			0.157960i
$426$			76.3140i			0.179141i
$427$	−92.2435	+	49.9548i	−0.216027	+	0.116990i
$428$	−179.903			−0.420334
$429$	480.895			1.12097
$430$			165.470i			0.384814i
$431$	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	$0.165285\pi$
$433$			429.740i			0.992472i	−0.868188	+	0.496236i	$0.834715\pi$
$434$	−71.0702	+	38.4883i	−0.163756	+	0.0886827i
$435$	124.630			0.286506
$436$	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	$-0.0301538\pi$
$440$		−	329.884i		−	0.749737i
$441$	80.3290	−	123.111i	0.182152	−	0.279163i
$442$	375.443			0.849419
$443$	−410.010			−0.925530			−0.462765	−	0.886481i	$-0.653143\pi$
$443$	−410.010			−0.925530			−0.462765	+	0.886481i	$0.653143\pi$
$444$			128.103i			0.288520i
$445$	287.069			0.645099
$446$		−	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	$0.573657\pi$
$450$	−25.6821			−0.0570714
$451$			675.569i			1.49793i
$452$	22.4363			0.0496378
$453$			192.111i			0.424086i
$454$		−	185.866i		−	0.409397i
$455$	121.735	+	224.789i	0.267550	+	0.494041i
$456$	206.674			0.453232
$457$	−640.868			−1.40234			−0.701169	−	0.712995i	$-0.747338\pi$
$457$	−640.868			−1.40234			−0.701169	+	0.712995i	$0.747338\pi$
$458$			404.893i			0.884046i
$459$	−69.7667			−0.151997
$460$		−	39.7068i		−	0.0863190i
$461$		−	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	$-0.503589\pi$
$463$	−10.4409			−0.0225505			−0.0112753	+	0.999936i	$0.503589\pi$
$464$	−340.582			−0.734013
$465$			26.1181i			0.0561680i
$466$	−259.029			−0.555857
$467$			269.736i			0.577592i	0.957391	+	0.288796i	$0.0932550\pi$
$467$			269.736i			0.577592i	−0.957391	+	0.288796i	$0.906745\pi$
$468$		−	52.3555i		−	0.111871i
$469$	−240.298	−	443.721i	−0.512364	−	0.946100i
$470$	153.669			0.326954
$471$	−503.077			−1.06810
$472$		−	708.138i		−	1.50029i
$473$	734.761			1.55341
$474$		−	237.384i		−	0.500809i
$475$			68.7495i			0.144736i
$476$	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	$0.762713\pi$
$480$	−64.2580			−0.133871
$481$			1130.40i			2.35011i
$482$			395.051i			0.819608i
$483$	−177.169	+	95.9467i	−0.366810	+	0.198647i
$484$	−179.524			−0.370917
$485$	356.537			0.735127
$486$		−	26.6897i		−	0.0549170i
$487$	597.640			1.22719			0.613593	−	0.789622i	$-0.289723\pi$
$487$	597.640			1.22719			0.613593	+	0.789622i	$0.289723\pi$
$488$		−	130.050i		−	0.266495i
$489$		−	93.2811i		−	0.190759i
$490$	−157.108	−	102.512i	−0.320629	−	0.209209i
$491$	−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
$495$			114.040i			0.230384i
$496$		−	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	$0.638480\pi$
$500$		−	11.9470i		−	0.0238940i
$501$	72.3870			0.144485
$502$		−	148.410i		−	0.295638i
$503$			837.716i			1.66544i	0.553694	+	0.832720i	$0.313218\pi$
$503$			837.716i			1.66544i	−0.553694	+	0.832720i	$0.686782\pi$
$504$	86.7840	+	160.250i	0.172190	+	0.317956i
$505$	53.9742			0.106880
$506$	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	$-0.167499\pi$
$510$			89.0331i			0.174575i
$511$	−462.049	+	250.224i	−0.904205	+	0.489675i
$512$	542.993			1.06053
$513$	−71.4466			−0.139272
$514$		−	241.600i		−	0.470038i
$515$	−195.314			−0.379250
$516$		−	79.9942i		−	0.155027i
$517$		−	682.358i		−	1.31984i
$518$	−395.027	−	729.434i	−0.762601	−	1.40817i
$519$	−225.762			−0.434995
$520$	−316.919			−0.609459
$521$		−	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	$0.0466843\pi$
$523$			152.860i			0.292275i	−0.989264	+	0.146138i	$0.953316\pi$
$524$		−	178.310i		−	0.340286i
$525$	−53.3068	+	28.8685i	−0.101537	+	0.0549875i
$526$	−65.2157			−0.123984
$527$	90.5445			0.171811
$528$		−	311.643i		−	0.590232i
$529$	−252.845			−0.477968
$530$			86.1414i			0.162531i
$531$			244.801i			0.461020i
$532$	90.4387	−	48.9774i	0.169998	−	0.0920627i
$533$	649.017			1.21767
$534$	380.716			0.712952
$535$		−	376.461i		−	0.703666i
$536$	625.581			1.16713
$537$			77.9309i			0.145123i
$538$		−	777.689i		−	1.44552i
$539$	−455.200	+	697.632i	−0.844527	+	1.29431i
$540$	12.4157			0.0229920
$541$	−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
$545$			347.865i			0.638285i
$546$	161.447	+	298.119i	0.295691	+	0.546006i
$547$	−195.330			−0.357092			−0.178546	−	0.983932i	$-0.557139\pi$
$547$	−195.330			−0.357092			−0.178546	+	0.983932i	$0.557139\pi$
$548$	−134.789			−0.245965
$549$			44.9578i			0.0818904i
$550$	145.533			0.264605
$551$		−	442.463i		−	0.803017i
$552$		−	249.783i		−	0.452505i
$553$	−266.835	−	492.722i	−0.482523	−	0.890999i
$554$	146.113			0.263743
$555$	−268.065			−0.483000
$556$			226.163i			0.406767i
$557$	−27.9390			−0.0501598			−0.0250799	−	0.999685i	$-0.507984\pi$
$557$	−27.9390			−0.0501598			−0.0250799	+	0.999685i	$0.507984\pi$
$558$			34.6383i			0.0620759i
$559$		−	705.883i		−	1.26276i
$560$	145.674	−	78.8901i	0.260132	−	0.140875i
$561$	395.347			0.704719
$562$	−286.571			−0.509912
$563$			459.585i			0.816314i	0.912912	+	0.408157i	$0.133828\pi$
$563$			459.585i			0.816314i	−0.912912	+	0.408157i	$0.866172\pi$
$564$	−74.2889			−0.131718
$565$			46.9497i			0.0830968i
$566$		−	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	$0.688549\pi$
$570$			91.1769i			0.159959i
$571$	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
$575$	83.0895			0.144504
$576$	−212.227			−0.368449
$577$			185.464i			0.321429i	0.987001	+	0.160714i	$0.0513798\pi$
$577$			185.464i			0.321429i	−0.987001	+	0.160714i	$0.948620\pi$
$578$	−186.155			−0.322067
$579$		−	582.460i		−	1.00598i
$580$			76.8892i			0.132568i
$581$	628.537	−	340.386i	1.08182	−	0.585862i
$582$	472.846			0.812450
$583$	382.506			0.656100
$584$		−	651.420i		−	1.11545i
$585$	109.558			0.187279
$586$			249.638i			0.426004i
$587$			673.958i			1.14814i	0.818806	+	0.574070i	$0.194636\pi$
$587$			673.958i			1.14814i	−0.818806	+	0.574070i	$0.805364\pi$
$588$	75.9519	+	49.5581i	0.129170	+	0.0842825i
$589$	92.7247			0.157427
$590$	312.405			0.529499
$591$			85.2311i			0.144215i
$592$	732.553			1.23742
$593$			0.486694i			0.000820731i	1.00000		0.000410366i	$0.000130623\pi$
$593$			0.486694i			0.000820731i	−1.00000		0.000410366i	$0.999869\pi$
$594$			151.242i			0.254617i
$595$	100.079	+	184.800i	0.168201	+	0.310589i
$596$	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	$0.339046\pi$
$600$		−	75.1546i		−	0.125258i
$601$		−	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
$605$		−	375.667i		−	0.620938i
$606$	71.5816			0.118121
$607$			907.211i			1.49458i	0.664498	+	0.747290i	$0.268646\pi$
$607$			907.211i			1.49458i	−0.664498	+	0.747290i	$0.731354\pi$
$608$			228.129i			0.375213i
$609$	343.075	−	185.794i	0.563342	−	0.305080i
$610$	57.3732			0.0940544
$611$	−655.539			−1.07289
$612$		−	43.0418i		−	0.0703298i
$613$	−911.642			−1.48718			−0.743590	−	0.668636i	$-0.766879\pi$
$613$	−911.642			−1.48718			−0.743590	+	0.668636i	$0.766879\pi$
$614$		−	352.006i		−	0.573299i
$615$			153.909i			0.250258i
$616$	−491.779	−	908.089i	−0.798342	−	1.47417i
$617$	637.918			1.03390			0.516951	−	0.856015i	$-0.327067\pi$
$617$	637.918			1.03390			0.516951	+	0.856015i	$0.327067\pi$
$618$	−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	$0.754619\pi$
$620$	−16.1133			−0.0259892
$621$			86.3492i			0.139049i
$622$			726.604i			1.16817i
$623$	790.229	−	427.951i	1.26843	−	0.686920i
$624$	−299.394			−0.479798
$625$	25.0000			0.0400000
$626$			622.369i			0.994200i
$627$	404.866			0.645720
$628$		−	310.368i		−	0.494216i
$629$			929.310i			1.47744i
$630$	−70.6965	+	38.2859i	−0.112217	+	0.0607713i
$631$	−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
$635$			133.876i			0.210828i
$636$		−	41.6438i		−	0.0654777i
$637$	670.213	+	437.309i	1.05214	+	0.686514i
$638$	−936.631			−1.46807
$639$	77.2014			0.120816
$640$			122.437i			0.191307i
$641$	−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	$-0.903105\pi$
$643$		−	385.448i		−	0.599453i	0.954025	−	0.299726i	$-0.0968954\pi$
$644$	−59.1933	−	109.303i	−0.0919150	−	0.169725i
$645$	167.394			0.259526
$646$	316.086			0.489298
$647$		−	1096.93i		−	1.69540i	−0.530473	−	0.847702i	$-0.677986\pi$
$647$		−	1096.93i		−	1.69540i	0.530473	−	0.847702i	$-0.322014\pi$
$648$	78.1030			0.120529
$649$		−	1387.22i		−	2.13747i
$650$		−	139.813i		−	0.215097i
$651$	38.9358	+	71.8966i	0.0598093	+	0.110440i
$652$	57.5488			0.0882650
$653$	−556.888			−0.852814			−0.426407	−	0.904531i	$-0.640221\pi$
$653$	−556.888			−0.852814			−0.426407	+	0.904531i	$0.640221\pi$
$654$			461.345i			0.705421i
$655$	373.127			0.569660
$656$		−	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	$0.682684\pi$
$660$	−70.3559			−0.106600
$661$		−	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
$665$	102.489	+	189.250i	0.154119	+	0.284587i
$666$	−355.513			−0.533803
$667$	−534.753			−0.801729
$668$			44.6584i			0.0668539i
$669$	−537.050			−0.802765
$670$			275.983i			0.411915i
$671$		−	254.763i		−	0.379676i
$672$	−176.886	+	95.7933i	−0.263224	+	0.142550i
$673$	1067.08			1.58556			0.792781	−	0.609506i	$-0.208632\pi$
$673$	1067.08			1.58556			0.792781	+	0.609506i	$0.208632\pi$
$674$	−757.721			−1.12421
$675$			25.9808i			0.0384900i
$676$	104.434			0.154488
$677$			313.071i			0.462439i	0.972902	+	0.231219i	$0.0742715\pi$
$677$			313.071i			0.462439i	−0.972902	+	0.231219i	$0.925728\pi$
$678$			62.2656i			0.0918371i
$679$	981.456	−	531.511i	1.44544	−	0.782785i
$680$	−260.541			−0.383149
$681$	−188.028			−0.276105
$682$		−	196.285i		−	0.287808i
$683$	505.514			0.740138			0.370069	−	0.929004i	$-0.379334\pi$
$683$	505.514			0.740138			0.370069	+	0.929004i	$0.379334\pi$
$684$		−	44.0782i		−	0.0644418i
$685$		−	282.056i		−	0.411761i
$686$	−585.301	−	47.9795i	−0.853209	−	0.0699409i
$687$	409.601			0.596217
$688$	−457.446			−0.664892
$689$		−	367.473i		−	0.533342i
$690$	110.195			0.159703
$691$			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
$695$	−473.263			−0.680954
$696$			483.685i			0.694950i
$697$	533.561			0.765511
$698$			555.522i			0.795877i
$699$			262.041i			0.374880i
$700$	−17.8101	−	32.8870i	−0.0254430	−	0.0469815i
$701$	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
$705$		−	155.455i		−	0.220504i
$706$			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	$0.603502\pi$
$710$		−	98.5210i		−	0.138762i
$711$	−240.144			−0.337755
$712$			1114.11i			1.56476i
$713$		−	112.066i		−	0.157175i
$714$	132.727	+	245.086i	0.185892	+	0.343258i
$715$	−620.833			−0.868297
$716$	−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	$0.801243\pi$
$720$		−	70.9988i		−	0.0986095i
$721$	−537.650	+	291.166i	−0.745700	+	0.403836i
$722$	−294.386			−0.407737
$723$	399.645			0.552759
$724$			19.1214i			0.0264108i
$725$	−160.897			−0.221926
$726$		−	498.217i		−	0.686250i
$727$		−	1339.58i		−	1.84262i	−0.388829	−	0.921310i	$-0.627120\pi$
$727$		−	1339.58i		−	1.84262i	0.388829	−	0.921310i	$-0.372880\pi$
$728$	−872.398	+	472.450i	−1.19835	+	0.648970i
$729$	−27.0000			−0.0370370
$730$	287.383			0.393675
$731$		−	580.311i		−	0.793860i
$732$	−27.7363			−0.0378911
$733$			536.275i			0.731616i	0.930690	+	0.365808i	$0.119207\pi$
$733$			536.275i			0.731616i	−0.930690	+	0.365808i	$0.880793\pi$
$734$		−	18.5206i		−	0.0252324i
$735$	−103.704	+	158.935i	−0.141094	+	0.216238i
$736$	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	$0.708008\pi$
$740$		−	165.380i		−	0.223486i
$741$		−	388.954i		−	0.524904i
$742$	128.416	+	237.126i	0.173068	+	0.319576i
$743$	532.720			0.716985			0.358493	−	0.933533i	$-0.383291\pi$
$743$	532.720			0.716985			0.358493	+	0.933533i	$0.383291\pi$
$744$	−101.364			−0.136241
$745$			143.516i			0.192639i
$746$	−912.314			−1.22294
$747$		−	306.337i		−	0.410090i
$748$			243.905i			0.326076i
$749$	−561.214	−	1036.30i	−0.749284	−	1.38358i
$750$	33.1555			0.0442073
$751$	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
$755$		−	248.014i		−	0.328495i
$756$	34.1772	−	18.5088i	0.0452080	−	0.0244825i
$757$	405.961			0.536276			0.268138	−	0.963381i	$-0.413592\pi$
$757$	405.961			0.536276			0.268138	+	0.963381i	$0.413592\pi$
$758$	−883.470			−1.16553
$759$		−	489.315i		−	0.644684i
$760$	−266.815			−0.351072
$761$			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
$765$	90.0684			0.117737
$766$			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	$-0.181085\pi$
$770$	400.616	−	216.955i	0.520280	−	0.281760i
$771$	−244.409			−0.317003
$772$	359.342			0.465469
$773$		−	438.991i		−	0.567906i	−0.958838	−	0.283953i	$-0.908354\pi$
$773$		−	438.991i		−	0.567906i	0.958838	−	0.283953i	$-0.0916460\pi$
$774$	222.001			0.286824
$775$		−	33.7183i		−	0.0435075i
$776$			1383.71i			1.78313i
$777$	−737.916	+	399.621i	−0.949699	+	0.514312i
$778$	−93.8308			−0.120605
$779$	546.408			0.701423
$780$			67.5906i			0.0866547i
$781$	−437.477			−0.560150
$782$		−	382.017i		−	0.488512i
$783$		−	167.209i		−	0.213549i
$784$	283.397	−	434.330i	0.361476	−	0.553992i
$785$	649.469			0.827349
$786$	494.849			0.629579
$787$			285.209i			0.362400i	0.983446	+	0.181200i	$0.0579982\pi$
$787$			285.209i			0.362400i	−0.983446	+	0.181200i	$0.942002\pi$
$788$	−52.5824			−0.0667289
$789$			65.9740i			0.0836172i
$790$			306.461i			0.387925i
$791$	69.9907	+	129.241i	0.0884838	+	0.163389i
$792$	−442.586			−0.558821
$793$	−244.750			−0.308638
$794$			34.1459i			0.0430049i
$795$	87.1431			0.109614
$796$			183.569i			0.230614i
$797$			1243.03i			1.55964i	0.626006	+	0.779818i	$0.284689\pi$
$797$			1243.03i			1.55964i	−0.626006	+	0.779818i	$0.715311\pi$
$798$	135.923	+	250.987i	0.170330	+	0.314520i
$799$	−538.923			−0.674497
$800$	82.9567			0.103696
$801$		−	385.143i		−	0.480828i
$802$	410.066			0.511304
$803$		−	1276.11i		−	1.58918i
$804$		−	133.420i		−	0.165946i
$805$	228.725	−	123.867i	0.284130	−	0.153872i
$806$	−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	$0.627379\pi$
$810$			34.4562i			0.0425385i
$811$		−	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
$815$			120.425i			0.147761i
$816$	−246.134			−0.301635
$817$		−	594.284i		−	0.727398i
$818$		−	1136.08i		−	1.38885i
$819$	301.586	−	163.325i	0.368237	−	0.199420i
$820$	−94.9524			−0.115796
$821$	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	$-0.483795\pi$
$823$	83.7611			0.101775			0.0508877	+	0.998704i	$0.483795\pi$
$824$		−	758.006i		−	0.919911i
$825$		−	147.225i		−	0.178455i
$826$	859.972	−	465.721i	1.04113	−	0.563826i
$827$	−957.378			−1.15765			−0.578826	−	0.815451i	$-0.696489\pi$
$827$	−957.378			−1.15765			−0.578826	+	0.815451i	$0.696489\pi$
$828$	−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	$0.998256\pi$
$830$	−390.934			−0.471005
$831$		−	147.812i		−	0.177873i
$832$		−	1155.36i		−	1.38865i
$833$	550.987	+	359.515i	0.661449	+	0.431591i
$834$	−627.651			−0.752579
$835$	−93.4512			−0.111918
$836$			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	$0.905107\pi$
$840$	−112.038	−	206.882i	−0.133378	−	0.246288i
$841$	194.509			0.231283
$842$	892.583			1.06007
$843$			289.903i			0.343894i
$844$	5.44391			0.00645013
$845$			218.536i			0.258623i
$846$		−	206.168i		−	0.243697i
$847$	−560.030	−	1034.12i	−0.661193	−	1.22092i
$848$	−238.140			−0.280825
$849$	−259.098			−0.305181
$850$		−	114.941i		−	0.135225i
$851$	1150.19			1.35158
$852$			47.6286i			0.0559021i
$853$		−	519.198i		−	0.608672i	−0.952565	−	0.304336i	$-0.901565\pi$
$853$		−	519.198i		−	0.608672i	0.952565	−	0.304336i	$-0.0984346\pi$
$854$	157.934	−	85.5297i	0.184934	−	0.100152i
$855$	92.2371			0.107880
$856$	1461.03			1.70682
$857$		−	479.468i		−	0.559473i	−0.960077	−	0.279736i	$-0.909753\pi$
$857$		−	479.468i		−	0.559473i	0.960077	−	0.279736i	$-0.0902470\pi$
$858$	−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	$0.577271\pi$
$860$			103.272i			0.120084i
$861$	229.441	+	423.672i	0.266482	+	0.492070i
$862$	−981.089			−1.13815
$863$	1217.16			1.41039			0.705193	−	0.709016i	$-0.250861\pi$
$863$	1217.16			1.41039			0.705193	+	0.709016i	$0.250861\pi$
$864$			86.2112i			0.0997814i
$865$	291.458			0.336946
$866$		−	735.776i		−	0.849626i
$867$			188.319i			0.217208i
$868$	−44.3558	+	24.0211i	−0.0511012	+	0.0276740i
$869$	1360.82			1.56597
$870$	−213.384			−0.245269
$871$		−	1177.32i		−	1.35169i
$872$	−1350.05			−1.54823
$873$		−	478.344i		−	0.547931i
$874$		−	391.215i		−	0.447615i
$875$	68.8187	−	37.2690i	0.0786500	−	0.0425932i
$876$	−138.931			−0.158597
$877$	−1027.18			−1.17125			−0.585623	−	0.810583i	$-0.699150\pi$
$877$	−1027.18			−1.17125			−0.585623	+	0.810583i	$0.699150\pi$
$878$			142.192i			0.161950i
$879$	252.541			0.287305
$880$			402.329i			0.457192i
$881$			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	$-0.463648\pi$
$883$	201.243			0.227908			0.113954	+	0.993486i	$0.463648\pi$
$884$	234.319			0.265067
$885$		−	316.037i		−	0.357104i
$886$	701.995			0.792319
$887$		−	951.252i		−	1.07244i	−0.844079	−	0.536219i	$-0.819852\pi$
$887$		−	951.252i		−	1.07244i	0.844079	−	0.536219i	$-0.180148\pi$
$888$		−	1040.35i		−	1.17157i
$889$	199.577	+	368.527i	0.224496	+	0.414542i
$890$	−491.503			−0.552250
$891$	153.001			0.171718
$892$		−	331.327i		−	0.371443i
$893$	−551.899			−0.618028
$894$			190.334i			0.212902i
$895$		−	100.608i		−	0.112412i
$896$	182.524	+	337.038i	0.203710	+	0.376158i
$897$	−470.083			−0.524062
$898$	352.613			0.392664
$899$			217.007i			0.241387i
$900$	−16.0286			−0.0178095
$901$		−	302.102i		−	0.335296i
$902$		−	1156.67i		−	1.28234i
$903$	460.794	−	249.545i	0.510293	−	0.276351i
$904$	−182.210			−0.201560
$905$	−40.0130			−0.0442133
$906$		−	328.921i		−	0.363047i
$907$	−559.990			−0.617409			−0.308705	−	0.951158i	$-0.599895\pi$
$907$	−559.990			−0.617409			−0.308705	+	0.951158i	$0.599895\pi$
$908$		−	116.002i		−	0.127755i
$909$		−	72.4140i		−	0.0796633i
$910$	−208.428	−	384.870i	−0.229042	−	0.422934i
$911$	−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
$915$		−	58.0403i		−	0.0634320i
$916$			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	$0.320503\pi$
$920$			322.468i			0.350509i
$921$	−356.099			−0.386644
$922$			284.362i			0.308419i
$923$			420.283i			0.455345i
$924$	−193.672	+	104.884i	−0.209602	+	0.113511i
$925$	346.070			0.374130
$926$	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	$-0.0594105\pi$
$930$		−	44.7179i		−	0.0480838i
$931$	564.253	+	368.172i	0.606072	+	0.395458i
$932$	−161.664			−0.173459
$933$	735.053			0.787838
$934$		−	461.826i		−	0.494460i
$935$	−510.391			−0.545873
$936$			425.191i			0.454264i
$937$			635.256i			0.677967i	0.940792	+	0.338984i	$0.110083\pi$
$937$			635.256i			0.677967i	−0.940792	+	0.338984i	$0.889917\pi$
$938$	411.425	+	759.713i	0.438620	+	0.809929i
$939$	629.606			0.670507
$940$	95.9066			0.102028
$941$			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
$945$	38.7311	+	71.5185i	0.0409853	+	0.0756810i
$946$	−1258.02			−1.32983
$947$	−254.133			−0.268356			−0.134178	−	0.990957i	$-0.542839\pi$
$947$	−254.133			−0.268356			−0.134178	+	0.990957i	$0.542839\pi$
$948$		−	148.154i		−	0.156281i
$949$	−1225.95			−1.29184
$950$		−	117.709i		−	0.123904i
$951$			764.540i			0.803933i
$952$	−717.205	+	388.405i	−0.753367	+	0.407988i
$953$	424.523			0.445460			0.222730	−	0.974880i	$-0.428503\pi$
$953$	424.523			0.445460			0.222730	+	0.974880i	$0.428503\pi$
$954$	115.571			0.121143
$955$		−	398.723i		−	0.417511i
$956$	−51.6072			−0.0539824
$957$			947.522i			0.990096i
$958$		−	1112.58i		−	1.16136i
$959$	−420.479	−	776.431i	−0.438455	−	0.809625i
$960$	273.984			0.285400
$961$	915.523			0.952677
$962$		−	1935.41i		−	2.01186i
$963$	−505.076			−0.524482
$964$			246.557i			0.255764i
$965$			751.952i			0.779225i
$966$	303.339	−	164.274i	0.314016	−	0.170056i
$967$	−46.7338			−0.0483286			−0.0241643	−	0.999708i	$-0.507692\pi$
$967$	−46.7338			−0.0483286			−0.0241643	+	0.999708i	$0.507692\pi$
$968$	1457.95			1.50615
$969$		−	319.762i		−	0.329991i
$970$	−610.441			−0.629321
$971$			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
$975$	−141.439			−0.145065
$976$			158.609i			0.162510i
$977$	−1613.20			−1.65118			−0.825589	−	0.564271i	$-0.809157\pi$
$977$	−1613.20			−1.65118			−0.825589	+	0.564271i	$0.809157\pi$
$978$			159.711i			0.163303i
$979$			2182.49i			2.22931i
$980$	−98.0534	−	63.9792i	−0.100055	−	0.0652849i
$981$	466.710			0.475749
$982$	184.269			0.187647
$983$			31.6909i			0.0322389i	0.999870	+	0.0161195i	$0.00513121\pi$
$983$			31.6909i			0.0322389i	−0.999870	+	0.0161195i	$0.994869\pi$
$984$	−597.315			−0.607028
$985$		−	110.033i		−	0.111708i
$986$			739.747i			0.750250i
$987$	−231.747	−	427.930i	−0.234799	−	0.433566i
$988$	239.961			0.242875
$989$	−718.242			−0.726231
$990$		−	195.253i		−	0.197225i
$991$	−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
$995$	−384.132			−0.386062
$996$	188.992			0.189751
$997$			948.441i			0.951295i	0.879636	+	0.475648i	$0.157786\pi$
$997$			948.441i			0.951295i	−0.879636	+	0.475648i	$0.842214\pi$
$998$	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	105.3.h.a.76.6	yes	12
3.2	odd	2		315.3.h.d.181.8		12
4.3	odd	2		1680.3.s.c.1441.2		12
5.2	odd	4		525.3.e.c.349.15		24
5.3	odd	4		525.3.e.c.349.2		24
5.4	even	2		525.3.h.d.76.7		12
7.6	odd	2	inner	105.3.h.a.76.5	✓	12
21.20	even	2		315.3.h.d.181.7		12
28.27	even	2		1680.3.s.c.1441.11		12
35.13	even	4		525.3.e.c.349.16		24
35.27	even	4		525.3.e.c.349.1		24
35.34	odd	2		525.3.h.d.76.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.5	✓	12	7.6	odd	2	inner
105.3.h.a.76.6	yes	12	1.1	even	1	trivial
315.3.h.d.181.7		12	21.20	even	2
315.3.h.d.181.8		12	3.2	odd	2
525.3.e.c.349.1		24	35.27	even	4
525.3.e.c.349.2		24	5.3	odd	4
525.3.e.c.349.15		24	5.2	odd	4
525.3.e.c.349.16		24	35.13	even	4
525.3.h.d.76.7		12	5.4	even	2
525.3.h.d.76.8		12	35.34	odd	2
1680.3.s.c.1441.2		12	4.3	odd	2
1680.3.s.c.1441.11		12	28.27	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.71214 q^{2} +1.73205i q^{3} -1.06857 q^{4} -2.23607i q^{5} -2.96552i q^{6} +(-3.33344 - 6.15534i) q^{7} +8.67811 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-1.71214 q^{2} +1.73205i q^{3} -1.06857 q^{4} -2.23607i q^{5} -2.96552i q^{6} +(-3.33344 - 6.15534i) q^{7} +8.67811 q^{8} -3.00000 q^{9} +3.82847i q^{10} +17.0001 q^{11} -1.85082i q^{12} -16.3319i q^{13} +(5.70733 + 10.5388i) q^{14} +3.87298 q^{15} -10.5839 q^{16} -13.4266i q^{17} +5.13643 q^{18} -13.7499i q^{19} +2.38940i q^{20} +(10.6614 - 5.77369i) q^{21} -29.1066 q^{22} -16.6179 q^{23} +15.0309i q^{24} -5.00000 q^{25} +27.9626i q^{26} -5.19615i q^{27} +(3.56202 + 6.57741i) q^{28} +32.1793 q^{29} -6.63110 q^{30} +6.74366i q^{31} -16.5913 q^{32} +29.4450i q^{33} +22.9883i q^{34} +(-13.7637 + 7.45380i) q^{35} +3.20571 q^{36} -69.2141 q^{37} +23.5418i q^{38} +28.2878 q^{39} -19.4048i q^{40} +39.7391i q^{41} +(-18.2538 + 9.88538i) q^{42} +43.2210 q^{43} -18.1658 q^{44} +6.70820i q^{45} +28.4522 q^{46} -40.1384i q^{47} -18.3318i q^{48} +(-26.7763 + 41.0369i) q^{49} +8.56071 q^{50} +23.2556 q^{51} +17.4518i q^{52} +22.5002 q^{53} +8.89655i q^{54} -38.0134i q^{55} +(-28.9280 - 53.4167i) q^{56} +23.8155 q^{57} -55.0956 q^{58} -81.6005i q^{59} -4.13855 q^{60} -14.9859i q^{61} -11.5461i q^{62} +(10.0003 + 18.4660i) q^{63} +70.7422 q^{64} -36.5193 q^{65} -50.4141i q^{66} +72.0872 q^{67} +14.3473i q^{68} -28.7831i q^{69} +(23.5655 - 12.7620i) q^{70} -25.7338 q^{71} -26.0343 q^{72} -75.0647i q^{73} +118.504 q^{74} -8.66025i q^{75} +14.6927i q^{76} +(-56.6689 - 104.641i) q^{77} -48.4327 q^{78} +80.0480 q^{79} +23.6663i q^{80} +9.00000 q^{81} -68.0389i q^{82} +102.112i q^{83} +(-11.3924 + 6.16959i) q^{84} -30.0228 q^{85} -74.0005 q^{86} +55.7362i q^{87} +147.529 q^{88} +128.381i q^{89} -11.4854i q^{90} +(-100.529 + 54.4416i) q^{91} +17.7574 q^{92} -11.6804 q^{93} +68.7227i q^{94} -30.7457 q^{95} -28.7371i q^{96} +159.448i q^{97} +(45.8449 - 70.2610i) q^{98} -51.0003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9	\( 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} + 12 q^{18} + 36 q^{21} - 88 q^{22} - 64 q^{23} - 60 q^{25} + 88 q^{28} + 104 q^{29} - 228 q^{32} + 60 q^{35} - 132 q^{36} + 32 q^{37} - 24 q^{39} - 60 q^{42} + 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 20 q^{50} + 24 q^{51} + 176 q^{53} - 368 q^{56} - 240 q^{57} - 400 q^{58} + 24 q^{63} - 20 q^{64} - 240 q^{65} + 168 q^{67} - 60 q^{70} + 32 q^{71} - 12 q^{72} + 184 q^{74} + 8 q^{77} + 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 120 q^{85} + 400 q^{86} - 536 q^{88} + 24 q^{91} + 192 q^{92} + 48 q^{93} + 884 q^{98} + 48 q^{99}+O(q^{100}) \) 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 - 60 * q^25 + 88 * q^28 + 104 * q^29 - 228 * q^32 + 60 * q^35 - 132 * q^36 + 32 * q^37 - 24 * q^39 - 60 * q^42 + 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 20 * q^50 + 24 * q^51 + 176 * q^53 - 368 * q^56 - 240 * q^57 - 400 * q^58 + 24 * q^63 - 20 * q^64 - 240 * q^65 + 168 * q^67 - 60 * q^70 + 32 * q^71 - 12 * q^72 + 184 * q^74 + 8 * q^77 + 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 120 * q^85 + 400 * q^86 - 536 * q^88 + 24 * q^91 + 192 * q^92 + 48 * q^93 + 884 * q^98 + 48 * q^99

Introduction

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