LMFDB - Embedded newform 735.3.e.a.244.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,3,Mod(244,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("735.244");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	735.e (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:	$20.0272994305$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			244.4
Character	$\chi$	$=$	735.244
Dual form			735.3.e.a.244.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.98186i q^{2} -1.73205 q^{3} +0.0722490 q^{4} +(4.19079 + 2.72714i) q^{5} -3.43267i q^{6} +8.07061i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.98186i q^{2} -1.73205 q^{3} +0.0722490 q^{4} +(4.19079 + 2.72714i) q^{5} -3.43267i q^{6} +8.07061i q^{8} +3.00000 q^{9} +(-5.40480 + 8.30553i) q^{10} +6.60248 q^{11} -0.125139 q^{12} +21.3701 q^{13} +(-7.25866 - 4.72355i) q^{15} -15.7058 q^{16} +15.9983 q^{17} +5.94557i q^{18} -20.0104i q^{19} +(0.302780 + 0.197033i) q^{20} +13.0852i q^{22} -1.83294i q^{23} -13.9787i q^{24} +(10.1254 + 22.8577i) q^{25} +42.3524i q^{26} -5.19615 q^{27} -4.58193 q^{29} +(9.36139 - 14.3856i) q^{30} -60.6581i q^{31} +1.15584i q^{32} -11.4358 q^{33} +31.7063i q^{34} +0.216747 q^{36} +10.8338i q^{37} +39.6577 q^{38} -37.0141 q^{39} +(-22.0097 + 33.8222i) q^{40} +18.1160i q^{41} +19.8864i q^{43} +0.477022 q^{44} +(12.5724 + 8.18143i) q^{45} +3.63263 q^{46} +87.6996 q^{47} +27.2032 q^{48} +(-45.3007 + 20.0671i) q^{50} -27.7099 q^{51} +1.54397 q^{52} +13.3831i q^{53} -10.2980i q^{54} +(27.6696 + 18.0059i) q^{55} +34.6590i q^{57} -9.08072i q^{58} +3.82911i q^{59} +(-0.524431 - 0.341272i) q^{60} +36.0133i q^{61} +120.216 q^{62} -65.1138 q^{64} +(89.5574 + 58.2792i) q^{65} -22.6642i q^{66} +28.8911i q^{67} +1.15586 q^{68} +3.17475i q^{69} -98.4282 q^{71} +24.2118i q^{72} -120.525 q^{73} -21.4710 q^{74} +(-17.5377 - 39.5908i) q^{75} -1.44573i q^{76} -73.3565i q^{78} -34.4977 q^{79} +(-65.8196 - 42.8319i) q^{80} +9.00000 q^{81} -35.9034 q^{82} -70.9960 q^{83} +(67.0454 + 43.6296i) q^{85} -39.4119 q^{86} +7.93613 q^{87} +53.2860i q^{88} +133.790i q^{89} +(-16.2144 + 24.9166i) q^{90} -0.132428i q^{92} +105.063i q^{93} +173.808i q^{94} +(54.5711 - 83.8592i) q^{95} -2.00198i q^{96} -119.662 q^{97} +19.8074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} + 96 q^{9}+O(q^{10}) $ 32 * q - 64 * q^4 + 96 * q^9	$ 32 q - 64 q^{4} + 96 q^{9} + 56 q^{11} - 24 q^{15} + 80 q^{16} + 68 q^{25} - 88 q^{29} - 192 q^{36} - 72 q^{39} - 640 q^{44} + 120 q^{46} - 24 q^{51} + 396 q^{60} - 400 q^{64} + 92 q^{65} + 344 q^{71} - 1800 q^{74} + 40 q^{79} + 288 q^{81} + 304 q^{85} - 288 q^{86} + 684 q^{95} + 168 q^{99}+O(q^{100}) $ 32 * q - 64 * q^4 + 96 * q^9 + 56 * q^11 - 24 * q^15 + 80 * q^16 + 68 * q^25 - 88 * q^29 - 192 * q^36 - 72 * q^39 - 640 * q^44 + 120 * q^46 - 24 * q^51 + 396 * q^60 - 400 * q^64 + 92 * q^65 + 344 * q^71 - 1800 * q^74 + 40 * q^79 + 288 * q^81 + 304 * q^85 - 288 * q^86 + 684 * q^95 + 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			1.98186i			0.990928i	0.868629	+	0.495464i	$0.165002\pi$
$2$			1.98186i			0.990928i	−0.868629	+	0.495464i	$0.834998\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	0.0722490			0.0180622
$5$	4.19079	+	2.72714i	0.838157	+	0.545428i
$5$	4.19079	+	2.72714i	0.838157	+	0.545428i
$6$		−	3.43267i		−	0.572112i
$7$		0			0
$7$		0			0
$8$			8.07061i			1.00883i
$9$	3.00000			0.333333
$10$	−5.40480	+	8.30553i	−0.540480	+	0.830553i
$11$	6.60248			0.600225			0.300113	−	0.953904i	$-0.402976\pi$
$11$	6.60248			0.600225			0.300113	+	0.953904i	$0.402976\pi$
$12$	−0.125139			−0.0104282
$13$	21.3701			1.64385			0.821926	−	0.569594i	$-0.192900\pi$
$13$	21.3701			1.64385			0.821926	+	0.569594i	$0.192900\pi$
$14$		0			0
$15$	−7.25866	−	4.72355i	−0.483910	−	0.314903i
$16$	−15.7058			−0.981612
$17$	15.9983			0.941076			0.470538	−	0.882380i	$-0.344060\pi$
$17$	15.9983			0.941076			0.470538	+	0.882380i	$0.344060\pi$
$18$			5.94557i			0.330309i
$19$		−	20.0104i		−	1.05318i	−0.850120	−	0.526589i	$-0.823471\pi$
$19$		−	20.0104i		−	1.05318i	0.850120	−	0.526589i	$-0.176529\pi$
$20$	0.302780	+	0.197033i	0.0151390	+	0.00985166i
$21$		0			0
$22$			13.0852i			0.594780i
$23$		−	1.83294i		−	0.0796932i	−0.999206	−	0.0398466i	$-0.987313\pi$
$23$		−	1.83294i		−	0.0796932i	0.999206	−	0.0398466i	$-0.0126869\pi$
$24$		−	13.9787i		−	0.582446i
$25$	10.1254	+	22.8577i	0.405016	+	0.914310i
$26$			42.3524i			1.62894i
$27$	−5.19615			−0.192450
$28$		0			0
$29$	−4.58193			−0.157997			−0.0789987	−	0.996875i	$-0.525172\pi$
$29$	−4.58193			−0.157997			−0.0789987	+	0.996875i	$0.525172\pi$
$30$	9.36139	−	14.3856i	0.312046	−	0.479520i
$31$		−	60.6581i		−	1.95671i	−0.206923	−	0.978357i	$-0.566345\pi$
$31$		−	60.6581i		−	1.95671i	0.206923	−	0.978357i	$-0.433655\pi$
$32$			1.15584i			0.0361200i
$33$	−11.4358			−0.346540
$34$			31.7063i			0.932538i
$35$		0			0
$36$	0.216747			0.00602075
$37$			10.8338i			0.292806i	0.989225	+	0.146403i	$0.0467696\pi$
$37$			10.8338i			0.292806i	−0.989225	+	0.146403i	$0.953230\pi$
$38$	39.6577			1.04362
$39$	−37.0141			−0.949078
$40$	−22.0097	+	33.8222i	−0.550242	+	0.845555i
$41$			18.1160i			0.441854i	0.975290	+	0.220927i	$0.0709083\pi$
$41$			18.1160i			0.441854i	−0.975290	+	0.220927i	$0.929092\pi$
$42$		0			0
$43$			19.8864i			0.462474i	0.972897	+	0.231237i	$0.0742772\pi$
$43$			19.8864i			0.462474i	−0.972897	+	0.231237i	$0.925723\pi$
$44$	0.477022			0.0108414
$45$	12.5724	+	8.18143i	0.279386	+	0.181809i
$46$	3.63263			0.0789702
$47$	87.6996			1.86595			0.932974	−	0.359944i	$-0.117204\pi$
$47$	87.6996			1.86595			0.932974	+	0.359944i	$0.117204\pi$
$48$	27.2032			0.566734
$49$		0			0
$50$	−45.3007	+	20.0671i	−0.906015	+	0.401341i
$51$	−27.7099			−0.543330
$52$	1.54397			0.0296917
$53$			13.3831i			0.252511i	0.991998	+	0.126256i	$0.0402960\pi$
$53$			13.3831i			0.252511i	−0.991998	+	0.126256i	$0.959704\pi$
$54$		−	10.2980i		−	0.190704i
$55$	27.6696	+	18.0059i	0.503083	+	0.327380i
$56$		0			0
$57$			34.6590i			0.608053i
$58$		−	9.08072i		−	0.156564i
$59$			3.82911i			0.0649001i	0.999473	+	0.0324501i	$0.0103310\pi$
$59$			3.82911i			0.0649001i	−0.999473	+	0.0324501i	$0.989669\pi$
$60$	−0.524431	−	0.341272i	−0.00874051	−	0.00568786i
$61$			36.0133i			0.590381i	0.955438	+	0.295191i	$0.0953831\pi$
$61$			36.0133i			0.590381i	−0.955438	+	0.295191i	$0.904617\pi$
$62$	120.216			1.93896
$63$		0			0
$64$	−65.1138			−1.01740
$65$	89.5574	+	58.2792i	1.37781	+	0.896604i
$66$		−	22.6642i		−	0.343396i
$67$			28.8911i			0.431210i	0.976481	+	0.215605i	$0.0691723\pi$
$67$			28.8911i			0.431210i	−0.976481	+	0.215605i	$0.930828\pi$
$68$	1.15586			0.0169979
$69$			3.17475i			0.0460109i
$70$		0			0
$71$	−98.4282			−1.38631			−0.693157	−	0.720787i	$-0.743781\pi$
$71$	−98.4282			−1.38631			−0.693157	+	0.720787i	$0.743781\pi$
$72$			24.2118i			0.336275i
$73$	−120.525			−1.65103			−0.825515	−	0.564380i	$-0.809115\pi$
$73$	−120.525			−1.65103			−0.825515	+	0.564380i	$0.809115\pi$
$74$	−21.4710			−0.290149
$75$	−17.5377	−	39.5908i	−0.233836	−	0.527877i
$76$		−	1.44573i		−	0.0190228i
$77$		0			0
$78$		−	73.3565i		−	0.940468i
$79$	−34.4977			−0.436680			−0.218340	−	0.975873i	$-0.570064\pi$
$79$	−34.4977			−0.436680			−0.218340	+	0.975873i	$0.570064\pi$
$80$	−65.8196	−	42.8319i	−0.822745	−	0.535399i
$81$	9.00000			0.111111
$82$	−35.9034			−0.437846
$83$	−70.9960			−0.855373			−0.427686	−	0.903927i	$-0.640671\pi$
$83$	−70.9960			−0.855373			−0.427686	+	0.903927i	$0.640671\pi$
$84$		0			0
$85$	67.0454	+	43.6296i	0.788770	+	0.513289i
$86$	−39.4119			−0.458278
$87$	7.93613			0.0912199
$88$			53.2860i			0.605523i
$89$			133.790i			1.50326i	0.659587	+	0.751628i	$0.270731\pi$
$89$			133.790i			1.50326i	−0.659587	+	0.751628i	$0.729269\pi$
$90$	−16.2144	+	24.9166i	−0.180160	+	0.276851i
$91$		0			0
$92$		−	0.132428i		−	0.00143944i
$93$			105.063i			1.12971i
$94$			173.808i			1.84902i
$95$	54.5711	−	83.8592i	0.574433	−	0.882729i
$96$		−	2.00198i		−	0.0208539i
$97$	−119.662			−1.23363			−0.616814	−	0.787109i	$-0.711577\pi$
$97$	−119.662			−1.23363			−0.616814	+	0.787109i	$0.711577\pi$
$98$		0			0
$99$	19.8074			0.200075
$100$	0.731550	+	1.65145i	0.00731550	+	0.0165145i
$101$		−	57.3546i		−	0.567867i	−0.958844	−	0.283934i	$-0.908360\pi$
$101$		−	57.3546i		−	0.567867i	0.958844	−	0.283934i	$-0.0916395\pi$
$102$		−	54.9169i		−	0.538401i
$103$	65.6923			0.637789			0.318895	−	0.947790i	$-0.396688\pi$
$103$	65.6923			0.637789			0.318895	+	0.947790i	$0.396688\pi$
$104$			172.470i			1.65836i
$105$		0			0
$106$	−26.5234			−0.250221
$107$		−	127.254i		−	1.18929i	−0.803989	−	0.594644i	$-0.797293\pi$
$107$		−	127.254i		−	1.18929i	0.803989	−	0.594644i	$-0.202707\pi$
$108$	−0.375417			−0.00347608
$109$	−65.1457			−0.597667			−0.298833	−	0.954305i	$-0.596597\pi$
$109$	−65.1457			−0.597667			−0.298833	+	0.954305i	$0.596597\pi$
$110$	−35.6851	+	54.8371i	−0.324410	+	0.498519i
$111$		−	18.7647i		−	0.169051i
$112$		0			0
$113$			92.2637i			0.816493i	0.912872	+	0.408246i	$0.133860\pi$
$113$			92.2637i			0.816493i	−0.912872	+	0.408246i	$0.866140\pi$
$114$	−68.6891			−0.602536
$115$	4.99870	−	7.68148i	0.0434669	−	0.0667955i
$116$	−0.331040			−0.00285379
$117$	64.1102			0.547951
$118$	−7.58874			−0.0643113
$119$		0			0
$120$	38.1219	−	58.5818i	0.317683	−	0.488181i
$121$	−77.4073			−0.639729
$122$	−71.3731			−0.585025
$123$		−	31.3779i		−	0.255105i
$124$		−	4.38249i		−	0.0353427i
$125$	−19.9029	+	123.405i	−0.159223	+	0.987243i
$126$		0			0
$127$			106.233i			0.836481i	0.908336	+	0.418241i	$0.137353\pi$
$127$			106.233i			0.836481i	−0.908336	+	0.418241i	$0.862647\pi$
$128$		−	124.423i		−	0.972054i
$129$		−	34.4442i		−	0.267009i
$130$	−115.501	+	177.490i	−0.888469	+	1.36531i
$131$		−	120.025i		−	0.916218i	−0.888896	−	0.458109i	$-0.848527\pi$
$131$		−	120.025i		−	0.916218i	0.888896	−	0.458109i	$-0.151473\pi$
$132$	−0.826227			−0.00625930
$133$		0			0
$134$	−57.2579			−0.427298
$135$	−21.7760	−	14.1706i	−0.161303	−	0.104968i
$136$			129.116i			0.949382i
$137$		−	233.552i		−	1.70476i	−0.522923	−	0.852380i	$-0.675159\pi$
$137$		−	233.552i		−	1.70476i	0.522923	−	0.852380i	$-0.324841\pi$
$138$	−6.29190			−0.0455935
$139$			63.8054i			0.459031i	0.973305	+	0.229516i	$0.0737142\pi$
$139$			63.8054i			0.459031i	−0.973305	+	0.229516i	$0.926286\pi$
$140$		0			0
$141$	−151.900			−1.07731
$142$		−	195.071i		−	1.37374i
$143$	141.095			0.986682
$144$	−47.1174			−0.327204
$145$	−19.2019	−	12.4956i	−0.132427	−	0.0861763i
$146$		−	238.864i		−	1.63605i
$147$		0			0
$148$			0.782732i			0.00528873i
$149$	212.801			1.42820			0.714098	−	0.700045i	$-0.246837\pi$
$149$	212.801			1.42820			0.714098	+	0.700045i	$0.246837\pi$
$150$	78.4632	−	34.7572i	0.523088	−	0.231715i
$151$	189.222			1.25312			0.626562	−	0.779372i	$-0.284462\pi$
$151$	189.222			1.25312			0.626562	+	0.779372i	$0.284462\pi$
$152$	161.496			1.06247
$153$	47.9949			0.313692
$154$		0			0
$155$	165.423	−	254.205i	1.06725	−	1.64003i
$156$	−2.67423			−0.0171425
$157$	−76.4882			−0.487186			−0.243593	−	0.969878i	$-0.578326\pi$
$157$	−76.4882			−0.487186			−0.243593	+	0.969878i	$0.578326\pi$
$158$		−	68.3695i		−	0.432719i
$159$		−	23.1802i		−	0.145788i
$160$	−3.15214	+	4.84389i	−0.0197009	+	0.0302743i
$161$		0			0
$162$			17.8367i			0.110103i
$163$			158.090i			0.969876i	0.874549	+	0.484938i	$0.161158\pi$
$163$			158.090i			0.969876i	−0.874549	+	0.484938i	$0.838842\pi$
$164$			1.30887i			0.00798088i
$165$	−47.9251	−	31.1871i	−0.290455	−	0.189013i
$166$		−	140.704i		−	0.847613i
$167$	51.2715			0.307015			0.153507	−	0.988147i	$-0.450943\pi$
$167$	51.2715			0.307015			0.153507	+	0.988147i	$0.450943\pi$
$168$		0			0
$169$	287.680			1.70225
$170$	−86.4676	+	132.874i	−0.508633	+	0.781614i
$171$		−	60.0311i		−	0.351059i
$172$			1.43677i			0.00835331i
$173$	−90.1962			−0.521366			−0.260683	−	0.965425i	$-0.583948\pi$
$173$	−90.1962			−0.521366			−0.260683	+	0.965425i	$0.583948\pi$
$174$			15.7283i			0.0903923i
$175$		0			0
$176$	−103.697			−0.589188
$177$		−	6.63221i		−	0.0374701i
$178$	−265.152			−1.48962
$179$	−98.5521			−0.550570			−0.275285	−	0.961363i	$-0.588772\pi$
$179$	−98.5521			−0.550570			−0.275285	+	0.961363i	$0.588772\pi$
$180$	0.908340	+	0.591100i	0.00504634	+	0.00328389i
$181$		−	251.131i		−	1.38746i	−0.720234	−	0.693731i	$-0.755966\pi$
$181$		−	251.131i		−	1.38746i	0.720234	−	0.693731i	$-0.244034\pi$
$182$		0			0
$183$		−	62.3768i		−	0.340857i
$184$	14.7930			0.0803966
$185$	−29.5453	+	45.4022i	−0.159705	+	0.245417i
$186$	−208.220			−1.11946
$187$	105.628			0.564858
$188$	6.33620			0.0337032
$189$		0			0
$190$	166.197	+	108.152i	0.874721	+	0.569222i
$191$	105.389			0.551777			0.275888	−	0.961190i	$-0.411028\pi$
$191$	105.389			0.551777			0.275888	+	0.961190i	$0.411028\pi$
$192$	112.780			0.587398
$193$		−	69.6991i		−	0.361135i	−0.983563	−	0.180568i	$-0.942207\pi$
$193$		−	69.6991i		−	0.361135i	0.983563	−	0.180568i	$-0.0577935\pi$
$194$		−	237.153i		−	1.22244i
$195$	−155.118	−	100.943i	−0.795477	−	0.517654i
$196$		0			0
$197$		−	84.6930i		−	0.429914i	−0.976624	−	0.214957i	$-0.931039\pi$
$197$		−	84.6930i		−	0.429914i	0.976624	−	0.214957i	$-0.0689611\pi$
$198$			39.2555i			0.198260i
$199$		−	164.195i		−	0.825103i	−0.910934	−	0.412551i	$-0.864638\pi$
$199$		−	164.195i		−	0.825103i	0.910934	−	0.412551i	$-0.135362\pi$
$200$	−184.476	+	81.7181i	−0.922379	+	0.408591i
$201$		−	50.0408i		−	0.248959i
$202$	113.668			0.562715
$203$		0			0
$204$	−2.00201			−0.00981377
$205$	−49.4050	+	75.9204i	−0.241000	+	0.370344i
$206$			130.193i			0.632003i
$207$		−	5.49883i		−	0.0265644i
$208$	−335.634			−1.61362
$209$		−	132.118i		−	0.632144i
$210$		0			0
$211$	−180.173			−0.853903			−0.426951	−	0.904275i	$-0.640412\pi$
$211$	−180.173			−0.853903			−0.426951	+	0.904275i	$0.640412\pi$
$212$			0.966916i			0.00456092i
$213$	170.483			0.800388
$214$	252.199			1.17850
$215$	−54.2330	+	83.3395i	−0.252246	+	0.387626i
$216$		−	41.9361i		−	0.194149i
$217$		0			0
$218$		−	129.109i		−	0.592245i
$219$	208.756			0.953223
$220$	1.99910	+	1.30091i	0.00908682	+	0.00591322i
$221$	341.885			1.54699
$222$	37.1889			0.167518
$223$	−254.131			−1.13960			−0.569801	−	0.821783i	$-0.692980\pi$
$223$	−254.131			−1.13960			−0.569801	+	0.821783i	$0.692980\pi$
$224$		0			0
$225$	30.3762	+	68.5732i	0.135005	+	0.304770i
$226$	−182.853			−0.809085
$227$	164.507			0.724699			0.362349	−	0.932042i	$-0.381975\pi$
$227$	164.507			0.724699			0.362349	+	0.932042i	$0.381975\pi$
$228$			2.50408i			0.0109828i
$229$			109.229i			0.476983i	0.971145	+	0.238492i	$0.0766529\pi$
$229$			109.229i			0.476983i	−0.971145	+	0.238492i	$0.923347\pi$
$230$	15.2236	+	9.90670i	0.0661895	+	0.0430726i
$231$		0			0
$232$		−	36.9789i		−	0.159392i
$233$			18.3754i			0.0788642i	0.999222	+	0.0394321i	$0.0125549\pi$
$233$			18.3754i			0.0788642i	−0.999222	+	0.0394321i	$0.987445\pi$
$234$			127.057i			0.542980i
$235$	367.530	+	239.169i	1.56396	+	1.01774i
$236$			0.276649i			0.00117224i
$237$	59.7518			0.252117
$238$		0			0
$239$	83.6340			0.349933			0.174966	−	0.984574i	$-0.444018\pi$
$239$	83.6340			0.349933			0.174966	+	0.984574i	$0.444018\pi$
$240$	114.003	+	74.1870i	0.475012	+	0.309113i
$241$			90.9956i			0.377575i	0.982018	+	0.188788i	$0.0604558\pi$
$241$			90.9956i			0.377575i	−0.982018	+	0.188788i	$0.939544\pi$
$242$		−	153.410i		−	0.633926i
$243$	−15.5885			−0.0641500
$244$			2.60192i			0.0106636i
$245$		0			0
$246$	62.1864			0.252790
$247$		−	427.623i		−	1.73127i
$248$	489.548			1.97398
$249$	122.969			0.493850
$250$	−244.572	−	39.4447i	−0.978286	−	0.157779i
$251$		−	405.829i		−	1.61685i	−0.588601	−	0.808424i	$-0.700321\pi$
$251$		−	405.829i		−	1.61685i	0.588601	−	0.808424i	$-0.299679\pi$
$252$		0			0
$253$		−	12.1020i		−	0.0478339i
$254$	−210.539			−0.828893
$255$	−116.126	−	75.5687i	−0.455396	−	0.296348i
$256$	−13.8673			−0.0541690
$257$	−46.2245			−0.179862			−0.0899309	−	0.995948i	$-0.528665\pi$
$257$	−46.2245			−0.179862			−0.0899309	+	0.995948i	$0.528665\pi$
$258$	68.2634			0.264587
$259$		0			0
$260$	6.47043	+	4.21062i	0.0248863	+	0.0161947i
$261$	−13.7458			−0.0526658
$262$	237.871			0.907906
$263$			431.893i			1.64218i	0.570800	+	0.821089i	$0.306633\pi$
$263$			431.893i			1.64218i	−0.570800	+	0.821089i	$0.693367\pi$
$264$		−	92.2941i		−	0.349599i
$265$	−36.4976	+	56.0858i	−0.137727	+	0.211644i
$266$		0			0
$267$		−	231.731i		−	0.867905i
$268$			2.08735i			0.00778862i
$269$		−	141.299i		−	0.525277i	−0.964894	−	0.262638i	$-0.915407\pi$
$269$		−	141.299i		−	0.525277i	0.964894	−	0.262638i	$-0.0845926\pi$
$270$	28.0842	−	43.1568i	0.104015	−	0.159840i
$271$		−	7.47081i		−	0.0275676i	−0.999905	−	0.0137838i	$-0.995612\pi$
$271$		−	7.47081i		−	0.0275676i	0.999905	−	0.0137838i	$-0.00438765\pi$
$272$	−251.266			−0.923771
$273$		0			0
$274$	462.866			1.68929
$275$	66.8527	+	150.918i	0.243101	+	0.548792i
$276$			0.229373i			0.000831060i
$277$		−	27.0477i		−	0.0976451i	−0.998807	−	0.0488225i	$-0.984453\pi$
$277$		−	27.0477i		−	0.0976451i	0.998807	−	0.0488225i	$-0.0155469\pi$
$278$	−126.453			−0.454867
$279$		−	181.974i		−	0.652238i
$280$		0			0
$281$	498.278			1.77323			0.886617	−	0.462505i	$-0.153049\pi$
$281$	498.278			1.77323			0.886617	+	0.462505i	$0.153049\pi$
$282$		−	301.044i		−	1.06753i
$283$	−355.941			−1.25774			−0.628870	−	0.777510i	$-0.716482\pi$
$283$	−355.941			−1.25774			−0.628870	+	0.777510i	$0.716482\pi$
$284$	−7.11134			−0.0250399
$285$	−94.5200	+	145.248i	−0.331649	+	0.509644i
$286$			279.631i			0.977730i
$287$		0			0
$288$			3.46752i			0.0120400i
$289$	−33.0547			−0.114376
$290$	24.7644	−	38.0553i	0.0853945	−	0.131225i
$291$	207.260			0.712235
$292$	−8.70782			−0.0298213
$293$	−11.1221			−0.0379593			−0.0189797	−	0.999820i	$-0.506042\pi$
$293$	−11.1221			−0.0379593			−0.0189797	+	0.999820i	$0.506042\pi$
$294$		0			0
$295$	−10.4425	+	16.0470i	−0.0353984	+	0.0543965i
$296$	−87.4354			−0.295390
$297$	−34.3075			−0.115513
$298$			421.742i			1.41524i
$299$		−	39.1702i		−	0.131004i
$300$	−1.26708	−	2.86039i	−0.00422360	−	0.00953464i
$301$		0			0
$302$			375.010i			1.24176i
$303$			99.3410i			0.327858i
$304$			314.279i			1.03381i
$305$	−98.2132	+	150.924i	−0.322011	+	0.494832i
$306$			95.1189i			0.310846i
$307$	369.947			1.20504			0.602519	−	0.798105i	$-0.294164\pi$
$307$	369.947			1.20504			0.602519	+	0.798105i	$0.294164\pi$
$308$		0			0
$309$	−113.782			−0.368228
$310$	503.798	+	327.845i	1.62516	+	1.05757i
$311$		−	289.207i		−	0.929927i	−0.885330	−	0.464963i	$-0.846067\pi$
$311$		−	289.207i		−	0.929927i	0.885330	−	0.464963i	$-0.153933\pi$
$312$		−	298.726i		−	0.957455i
$313$	206.263			0.658987			0.329493	−	0.944158i	$-0.393122\pi$
$313$	206.263			0.658987			0.329493	+	0.944158i	$0.393122\pi$
$314$		−	151.589i		−	0.482766i
$315$		0			0
$316$	−2.49243			−0.00788743
$317$			64.1430i			0.202344i	0.994869	+	0.101172i	$0.0322592\pi$
$317$			64.1430i			0.202344i	−0.994869	+	0.101172i	$0.967741\pi$
$318$	45.9398			0.144465
$319$	−30.2521			−0.0948341
$320$	−272.878	−	177.575i	−0.852745	−	0.554921i
$321$			220.410i			0.686636i
$322$		0			0
$323$		−	320.132i		−	0.991120i
$324$	0.650241			0.00200692
$325$	216.380	+	488.472i	0.665786	+	1.50299i
$326$	−313.311			−0.961077
$327$	112.836			0.345063
$328$	−146.207			−0.445754
$329$		0			0
$330$	61.8084	−	94.9807i	0.187298	−	0.287820i
$331$	160.954			0.486265			0.243133	−	0.969993i	$-0.421825\pi$
$331$	160.954			0.486265			0.243133	+	0.969993i	$0.421825\pi$
$332$	−5.12939			−0.0154500
$333$			32.5014i			0.0976019i
$334$			101.613i			0.304229i
$335$	−78.7900	+	121.076i	−0.235194	+	0.361422i
$336$		0			0
$337$			262.731i			0.779616i	0.920896	+	0.389808i	$0.127459\pi$
$337$			262.731i			0.779616i	−0.920896	+	0.389808i	$0.872541\pi$
$338$			570.140i			1.68681i
$339$		−	159.805i		−	0.471402i
$340$	4.84396	+	3.15219i	0.0142470	+	0.00927116i
$341$		−	400.494i		−	1.17447i
$342$	118.973			0.347874
$343$		0			0
$344$	−160.495			−0.466556
$345$	−8.65800	+	13.3047i	−0.0250957	+	0.0385644i
$346$		−	178.756i		−	0.516636i
$347$		−	372.867i		−	1.07454i	−0.843409	−	0.537272i	$-0.819455\pi$
$347$		−	372.867i		−	1.07454i	0.843409	−	0.537272i	$-0.180545\pi$
$348$	0.573377			0.00164764
$349$		−	522.429i		−	1.49693i	−0.663173	−	0.748466i	$-0.730791\pi$
$349$		−	522.429i		−	1.49693i	0.663173	−	0.748466i	$-0.269209\pi$
$350$		0			0
$351$	−111.042			−0.316359
$352$			7.63142i			0.0216802i
$353$	−440.081			−1.24669			−0.623344	−	0.781948i	$-0.714226\pi$
$353$	−440.081			−1.24669			−0.623344	+	0.781948i	$0.714226\pi$
$354$	13.1441			0.0371302
$355$	−412.492	−	268.428i	−1.16195	−	0.756134i
$356$			9.66617i			0.0271522i
$357$		0			0
$358$		−	195.316i		−	0.545576i
$359$	−226.055			−0.629679			−0.314839	−	0.949145i	$-0.601951\pi$
$359$	−226.055			−0.629679			−0.314839	+	0.949145i	$0.601951\pi$
$360$	−66.0291	+	101.467i	−0.183414	+	0.281852i
$361$	−39.4153			−0.109184
$362$	497.704			1.37487
$363$	134.073			0.369348
$364$		0			0
$365$	−505.095	−	328.689i	−1.38382	−	0.900519i
$366$	123.622			0.337764
$367$	−143.694			−0.391537			−0.195768	−	0.980650i	$-0.562720\pi$
$367$	−143.694			−0.391537			−0.195768	+	0.980650i	$0.562720\pi$
$368$			28.7878i			0.0782278i
$369$			54.3481i			0.147285i
$370$	−89.9806	−	58.5546i	−0.243191	−	0.158256i
$371$		0			0
$372$			7.59069i			0.0204051i
$373$		−	605.640i		−	1.62370i	−0.583867	−	0.811849i	$-0.698461\pi$
$373$		−	605.640i		−	1.62370i	0.583867	−	0.811849i	$-0.301539\pi$
$374$			209.340i			0.559733i
$375$	34.4729	−	213.744i	0.0919277	−	0.569985i
$376$			707.789i			1.88242i
$377$	−97.9161			−0.259724
$378$		0			0
$379$	−620.928			−1.63833			−0.819167	−	0.573555i	$-0.805564\pi$
$379$	−620.928			−1.63833			−0.819167	+	0.573555i	$0.805564\pi$
$380$	3.94271	−	6.05875i	0.0103756	−	0.0159441i
$381$		−	184.001i		−	0.482943i
$382$			208.867i			0.546771i
$383$	−204.855			−0.534870			−0.267435	−	0.963576i	$-0.586176\pi$
$383$	−204.855			−0.534870			−0.267435	+	0.963576i	$0.586176\pi$
$384$			215.507i			0.561215i
$385$		0			0
$386$	138.134			0.357859
$387$			59.6591i			0.154158i
$388$	−8.64545			−0.0222821
$389$	−237.270			−0.609948			−0.304974	−	0.952361i	$-0.598648\pi$
$389$	−237.270			−0.609948			−0.304974	+	0.952361i	$0.598648\pi$
$390$	200.054	−	307.422i	0.512958	−	0.788260i
$391$		−	29.3240i		−	0.0749974i
$392$		0			0
$393$			207.889i			0.528979i
$394$	167.849			0.426014
$395$	−144.573	−	94.0802i	−0.366007	−	0.238178i
$396$	1.43107			0.00361381
$397$	665.531			1.67640			0.838200	−	0.545363i	$-0.183608\pi$
$397$	665.531			1.67640			0.838200	+	0.545363i	$0.183608\pi$
$398$	325.412			0.817617
$399$		0			0
$400$	−159.027	−	358.999i	−0.397568	−	0.897497i
$401$	−378.396			−0.943630			−0.471815	−	0.881697i	$-0.656401\pi$
$401$	−378.396			−0.943630			−0.471815	+	0.881697i	$0.656401\pi$
$402$	99.1736			0.246700
$403$		−	1296.27i		−	3.21655i
$404$		−	4.14381i		−	0.0102570i
$405$	37.7171	+	24.5443i	0.0931286	+	0.0606032i
$406$		0			0
$407$			71.5300i			0.175749i
$408$		−	223.635i		−	0.548126i
$409$		−	381.014i		−	0.931574i	−0.884897	−	0.465787i	$-0.845771\pi$
$409$		−	381.014i		−	0.931574i	0.884897	−	0.465787i	$-0.154229\pi$
$410$	−150.463	−	97.9136i	−0.366984	−	0.238814i
$411$			404.524i			0.984243i
$412$	4.74620			0.0115199
$413$		0			0
$414$	10.8979			0.0263234
$415$	−297.529	−	193.616i	−0.716937	−	0.466545i
$416$			24.7004i			0.0593760i
$417$		−	110.514i		−	0.265022i
$418$	261.839			0.626409
$419$			368.460i			0.879379i	0.898150	+	0.439690i	$0.144912\pi$
$419$			368.460i			0.879379i	−0.898150	+	0.439690i	$0.855088\pi$
$420$		0			0
$421$	294.472			0.699457			0.349729	−	0.936851i	$-0.386274\pi$
$421$	294.472			0.699457			0.349729	+	0.936851i	$0.386274\pi$
$422$		−	357.078i		−	0.846156i
$423$	263.099			0.621983
$424$	−108.010			−0.254740
$425$	161.989	+	365.685i	0.381151	+	0.860435i
$426$			337.872i			0.793127i
$427$		0			0
$428$		−	9.19396i		−	0.0214812i
$429$	−244.385			−0.569661
$430$	−165.167	−	107.482i	−0.384109	−	0.249958i
$431$	−436.943			−1.01379			−0.506895	−	0.862008i	$-0.669207\pi$
$431$	−436.943			−1.01379			−0.506895	+	0.862008i	$0.669207\pi$
$432$	81.6096			0.188911
$433$	−678.283			−1.56647			−0.783237	−	0.621724i	$-0.786433\pi$
$433$	−678.283			−1.56647			−0.783237	+	0.621724i	$0.786433\pi$
$434$		0			0
$435$	33.2586	+	21.6430i	0.0764566	+	0.0497539i
$436$	−4.70671			−0.0107952
$437$	−36.6779			−0.0839311
$438$			413.724i			0.944575i
$439$		−	327.430i		−	0.745853i	−0.927861	−	0.372927i	$-0.878354\pi$
$439$		−	327.430i		−	0.745853i	0.927861	−	0.372927i	$-0.121646\pi$
$440$	−145.319	+	223.310i	−0.330269	+	0.507524i
$441$		0			0
$442$			677.566i			1.53295i
$443$			378.133i			0.853573i	0.904352	+	0.426787i	$0.140354\pi$
$443$			378.133i			0.853573i	−0.904352	+	0.426787i	$0.859646\pi$
$444$		−	1.35573i		−	0.00305345i
$445$	−364.864	+	560.684i	−0.819918	+	1.25996i
$446$		−	503.651i		−	1.12926i
$447$	−368.583			−0.824570
$448$		0			0
$449$	−84.0926			−0.187289			−0.0936444	−	0.995606i	$-0.529852\pi$
$449$	−84.0926			−0.187289			−0.0936444	+	0.995606i	$0.529852\pi$
$450$	−135.902	+	60.2012i	−0.302005	+	0.133780i
$451$			119.611i			0.265212i
$452$			6.66596i			0.0147477i
$453$	−327.742			−0.723491
$454$			326.028i			0.718124i
$455$		0			0
$456$	−279.719			−0.613419
$457$		−	241.486i		−	0.528415i	−0.964466	−	0.264207i	$-0.914890\pi$
$457$		−	241.486i		−	0.528415i	0.964466	−	0.264207i	$-0.0851104\pi$
$458$	−216.476			−0.472656
$459$	−83.1296			−0.181110
$460$	0.361151	−	0.554979i	0.000785111	−	0.00120648i
$461$			576.884i			1.25137i	0.780074	+	0.625687i	$0.215181\pi$
$461$			576.884i			1.25137i	−0.780074	+	0.625687i	$0.784819\pi$
$462$		0			0
$463$			535.082i			1.15568i	0.816149	+	0.577842i	$0.196105\pi$
$463$			535.082i			1.15568i	−0.816149	+	0.577842i	$0.803895\pi$
$464$	71.9627			0.155092
$465$	−286.522	+	440.297i	−0.616176	+	0.946874i
$466$	−36.4173			−0.0781487
$467$	32.5216			0.0696394			0.0348197	−	0.999394i	$-0.488914\pi$
$467$	32.5216			0.0696394			0.0348197	+	0.999394i	$0.488914\pi$
$468$	4.63190			0.00989722
$469$		0			0
$470$	−473.999	+	728.392i	−1.00851	+	1.54977i
$471$	132.482			0.281277
$472$	−30.9032			−0.0654729
$473$			131.299i			0.277588i
$474$			118.420i			0.249830i
$475$	457.392	−	202.613i	0.962931	−	0.426554i
$476$		0			0
$477$			40.1493i			0.0841705i
$478$			165.750i			0.346758i
$479$		−	271.055i		−	0.565876i	−0.959138	−	0.282938i	$-0.908691\pi$
$479$		−	271.055i		−	0.565876i	0.959138	−	0.282938i	$-0.0913091\pi$
$480$	5.45967	−	8.38986i	0.0113743	−	0.0174789i
$481$			231.519i			0.481329i
$482$	−180.340			−0.374150
$483$		0			0
$484$	−5.59260			−0.0115550
$485$	−501.477	−	326.335i	−1.03397	−	0.672856i
$486$		−	30.8941i		−	0.0635680i
$487$		−	517.812i		−	1.06327i	−0.846974	−	0.531635i	$-0.821578\pi$
$487$		−	517.812i		−	1.06327i	0.846974	−	0.531635i	$-0.178422\pi$
$488$	−290.649			−0.595592
$489$		−	273.819i		−	0.559958i
$490$		0			0
$491$	700.753			1.42719			0.713597	−	0.700556i	$-0.247065\pi$
$491$	700.753			1.42719			0.713597	+	0.700556i	$0.247065\pi$
$492$		−	2.26702i		−	0.00460777i
$493$	−73.3030			−0.148688
$494$	847.488			1.71556
$495$	83.0088	+	54.0177i	0.167694	+	0.109127i
$496$			952.684i			1.92073i
$497$		0			0
$498$			243.706i			0.489369i
$499$	212.715			0.426282			0.213141	−	0.977021i	$-0.431631\pi$
$499$	212.715			0.426282			0.213141	+	0.977021i	$0.431631\pi$
$500$	−1.43797	+	8.91591i	−0.00287593	+	0.0178318i
$501$	−88.8048			−0.177255
$502$	804.294			1.60218
$503$	614.027			1.22073			0.610365	−	0.792120i	$-0.291023\pi$
$503$	614.027			1.22073			0.610365	+	0.792120i	$0.291023\pi$
$504$		0			0
$505$	156.414	−	240.361i	0.309731	−	0.475962i
$506$	23.9844			0.0473999
$507$	−498.277			−0.982794
$508$			7.67524i			0.0151087i
$509$			619.612i			1.21731i	0.793434	+	0.608656i	$0.208291\pi$
$509$			619.612i			1.21731i	−0.793434	+	0.608656i	$0.791709\pi$
$510$	149.766	−	230.145i	0.293659	−	0.451265i
$511$		0			0
$512$		−	525.174i		−	1.02573i
$513$			103.977i			0.202684i
$514$		−	91.6103i		−	0.178230i
$515$	275.303	+	179.152i	0.534568	+	0.347868i
$516$		−	2.48856i		−	0.00482279i
$517$	579.035			1.11999
$518$		0			0
$519$	156.224			0.301011
$520$	−470.349	+	722.783i	−0.904517	+	1.38997i
$521$			1032.03i			1.98086i	0.138032	+	0.990428i	$0.455922\pi$
$521$			1032.03i			1.98086i	−0.138032	+	0.990428i	$0.544078\pi$
$522$		−	27.2421i		−	0.0521880i
$523$	−60.7467			−0.116150			−0.0580752	−	0.998312i	$-0.518496\pi$
$523$	−60.7467			−0.116150			−0.0580752	+	0.998312i	$0.518496\pi$
$524$		−	8.67165i		−	0.0165490i
$525$		0			0
$526$	−855.949			−1.62728
$527$		−	970.427i		−	1.84142i
$528$	179.609			0.340168
$529$	525.640			0.993649
$530$	−111.154	−	72.3330i	−0.209724	−	0.136477i
$531$			11.4873i			0.0216334i
$532$		0			0
$533$			387.141i			0.726343i
$534$	459.257			0.860031
$535$	347.039	−	533.294i	0.648671	−	0.996811i
$536$	−233.168			−0.435016
$537$	170.697			0.317872
$538$	280.035			0.520511
$539$		0			0
$540$	−1.57329	−	1.02381i	−0.00291350	−	0.00189595i
$541$	−129.943			−0.240190			−0.120095	−	0.992762i	$-0.538320\pi$
$541$	−129.943			−0.240190			−0.120095	+	0.992762i	$0.538320\pi$
$542$	14.8061			0.0273175
$543$			434.971i			0.801051i
$544$			18.4915i			0.0339917i
$545$	−273.012	−	177.661i	−0.500939	−	0.325984i
$546$		0			0
$547$		−	269.262i		−	0.492252i	−0.969238	−	0.246126i	$-0.920842\pi$
$547$		−	269.262i		−	0.492252i	0.969238	−	0.246126i	$-0.0791577\pi$
$548$		−	16.8739i		−	0.0307918i
$549$			108.040i			0.196794i
$550$	−299.097	+	132.492i	−0.543813	+	0.240895i
$551$			91.6861i			0.166399i
$552$	−25.6222			−0.0464170
$553$		0			0
$554$	53.6046			0.0967592
$555$	51.1740	−	78.6389i	0.0922055	−	0.141692i
$556$			4.60987i			0.00829114i
$557$			185.560i			0.333142i	0.986029	+	0.166571i	$0.0532695\pi$
$557$			185.560i			0.333142i	−0.986029	+	0.166571i	$0.946730\pi$
$558$	360.647			0.646321
$559$			424.973i			0.760238i
$560$		0			0
$561$	−182.954			−0.326121
$562$			987.516i			1.75715i
$563$	−512.836			−0.910899			−0.455449	−	0.890262i	$-0.650521\pi$
$563$	−512.836			−0.910899			−0.455449	+	0.890262i	$0.650521\pi$
$564$	−10.9746			−0.0194586
$565$	−251.616	+	386.657i	−0.445338	+	0.684349i
$566$		−	705.423i		−	1.24633i
$567$		0			0
$568$		−	794.376i		−	1.39855i
$569$	115.153			0.202379			0.101189	−	0.994867i	$-0.467735\pi$
$569$	115.153			0.202379			0.101189	+	0.994867i	$0.467735\pi$
$570$	−287.861	−	187.325i	−0.505020	−	0.328640i
$571$	−770.720			−1.34977			−0.674886	−	0.737922i	$-0.735807\pi$
$571$	−770.720			−1.34977			−0.674886	+	0.737922i	$0.735807\pi$
$572$	10.1940			0.0178217
$573$	−182.540			−0.318569
$574$		0			0
$575$	41.8970	−	18.5593i	0.0728643	−	0.0322770i
$576$	−195.342			−0.339135
$577$	506.978			0.878645			0.439322	−	0.898330i	$-0.355219\pi$
$577$	506.978			0.878645			0.439322	+	0.898330i	$0.355219\pi$
$578$		−	65.5097i		−	0.113339i
$579$			120.722i			0.208502i
$580$	−1.38732	−	0.902792i	−0.00239192	−	0.00155654i
$581$		0			0
$582$			410.760i			0.705774i
$583$			88.3617i			0.151564i
$584$		−	972.712i		−	1.66560i
$585$	268.672	+	174.838i	0.459269	+	0.298868i
$586$		−	22.0424i		−	0.0376149i
$587$	958.495			1.63287			0.816435	−	0.577437i	$-0.195947\pi$
$587$	958.495			1.63287			0.816435	+	0.577437i	$0.195947\pi$
$588$		0			0
$589$	−1213.79			−2.06077
$590$	−31.8028	−	20.6956i	−0.0539030	−	0.0350772i
$591$			146.693i			0.248211i
$592$		−	170.153i		−	0.287421i
$593$	63.0346			0.106298			0.0531489	−	0.998587i	$-0.483074\pi$
$593$	63.0346			0.106298			0.0531489	+	0.998587i	$0.483074\pi$
$594$		−	67.9925i		−	0.114465i
$595$		0			0
$596$	15.3747			0.0257964
$597$			284.395i			0.476373i
$598$	77.6296			0.129815
$599$	−457.791			−0.764259			−0.382129	−	0.924109i	$-0.624809\pi$
$599$	−457.791			−0.764259			−0.382129	+	0.924109i	$0.624809\pi$
$600$	319.522	−	141.540i	0.532536	−	0.235900i
$601$			774.741i			1.28909i	0.764568	+	0.644543i	$0.222952\pi$
$601$			774.741i			1.28909i	−0.764568	+	0.644543i	$0.777048\pi$
$602$		0			0
$603$			86.6732i			0.143737i
$604$	13.6711			0.0226342
$605$	−324.397	−	211.101i	−0.536194	−	0.348927i
$606$	−196.880			−0.324884
$607$	−512.551			−0.844401			−0.422200	−	0.906503i	$-0.638742\pi$
$607$	−512.551			−0.844401			−0.422200	+	0.906503i	$0.638742\pi$
$608$	23.1288			0.0380408
$609$		0			0
$610$	−299.109	−	194.644i	−0.490343	−	0.319089i
$611$	1874.15			3.06734
$612$	3.46758			0.00566598
$613$			152.334i			0.248505i	0.992251	+	0.124252i	$0.0396533\pi$
$613$			152.334i			0.248505i	−0.992251	+	0.124252i	$0.960347\pi$
$614$			733.181i			1.19411i
$615$	85.5720	−	131.498i	0.139141	−	0.213818i
$616$		0			0
$617$			440.775i			0.714384i	0.934031	+	0.357192i	$0.116266\pi$
$617$			440.775i			0.714384i	−0.934031	+	0.357192i	$0.883734\pi$
$618$		−	225.500i		−	0.364887i
$619$			39.9571i			0.0645510i	0.999479	+	0.0322755i	$0.0102754\pi$
$619$			39.9571i			0.0645510i	−0.999479	+	0.0322755i	$0.989725\pi$
$620$	11.9517	−	18.3661i	0.0192769	−	0.0296227i
$621$			9.52426i			0.0153370i
$622$	573.167			0.921490
$623$		0			0
$624$	581.335			0.931626
$625$	−419.953	+	462.887i	−0.671924	+	0.740620i
$626$			408.783i			0.653008i
$627$			228.835i			0.364969i
$628$	−5.52620			−0.00879968
$629$			173.322i			0.275552i
$630$		0			0
$631$	384.003			0.608562			0.304281	−	0.952582i	$-0.401584\pi$
$631$	384.003			0.608562			0.304281	+	0.952582i	$0.401584\pi$
$632$		−	278.418i		−	0.440534i
$633$	312.070			0.493001
$634$	−127.122			−0.200508
$635$	−289.713	+	445.200i	−0.456241	+	0.701103i
$636$		−	1.67475i		−	0.00263325i
$637$		0			0
$638$		−	59.9552i		−	0.0939737i
$639$	−295.285			−0.462104
$640$	339.319	−	521.430i	0.530186	−	0.814734i
$641$	1144.75			1.78588			0.892938	−	0.450179i	$-0.148640\pi$
$641$	1144.75			1.78588			0.892938	+	0.450179i	$0.148640\pi$
$642$	−436.821			−0.680406
$643$	−501.070			−0.779269			−0.389634	−	0.920970i	$-0.627399\pi$
$643$	−501.070			−0.779269			−0.389634	+	0.920970i	$0.627399\pi$
$644$		0			0
$645$	93.9342	−	144.348i	0.145634	−	0.223796i
$646$	634.455			0.982129
$647$	644.427			0.996024			0.498012	−	0.867170i	$-0.334064\pi$
$647$	644.427			0.996024			0.498012	+	0.867170i	$0.334064\pi$
$648$			72.6355i			0.112092i
$649$			25.2816i			0.0389547i
$650$	−968.080	+	428.835i	−1.48935	+	0.659746i
$651$		0			0
$652$			11.4218i			0.0175181i
$653$			991.859i			1.51893i	0.650550	+	0.759464i	$0.274538\pi$
$653$			991.859i			1.51893i	−0.650550	+	0.759464i	$0.725462\pi$
$654$			223.624i			0.341933i
$655$	327.324	−	502.997i	0.499731	−	0.767935i
$656$		−	284.527i		−	0.433729i
$657$	−361.576			−0.550343
$658$		0			0
$659$	−973.378			−1.47705			−0.738527	−	0.674224i	$-0.764478\pi$
$659$	−973.378			−1.47705			−0.738527	+	0.674224i	$0.764478\pi$
$660$	−3.46254	−	2.25324i	−0.00524628	−	0.00341400i
$661$		−	990.821i		−	1.49897i	−0.662020	−	0.749486i	$-0.730301\pi$
$661$		−	990.821i		−	1.49897i	0.662020	−	0.749486i	$-0.269699\pi$
$662$			318.987i			0.481854i
$663$	−592.162			−0.893155
$664$		−	572.981i		−	0.862923i
$665$		0			0
$666$	−64.4131			−0.0967164
$667$			8.39842i			0.0125913i
$668$	3.70431			0.00554538
$669$	440.168			0.657949
$670$	−239.956	−	156.150i	−0.358143	−	0.233060i
$671$			237.777i			0.354362i
$672$		0			0
$673$		−	218.787i		−	0.325092i	−0.986701	−	0.162546i	$-0.948029\pi$
$673$		−	218.787i		−	0.325092i	0.986701	−	0.162546i	$-0.0519706\pi$
$674$	−520.694			−0.772543
$675$	−52.6131	−	118.772i	−0.0779453	−	0.175959i
$676$	20.7846			0.0307464
$677$	−92.6444			−0.136845			−0.0684227	−	0.997656i	$-0.521797\pi$
$677$	−92.6444			−0.136845			−0.0684227	+	0.997656i	$0.521797\pi$
$678$	316.711			0.467125
$679$		0			0
$680$	−352.117	+	541.097i	−0.517820	+	0.795732i
$681$	−284.934			−0.418405
$682$	793.722			1.16381
$683$			987.640i			1.44603i	0.690831	+	0.723016i	$0.257245\pi$
$683$			987.640i			1.44603i	−0.690831	+	0.723016i	$0.742755\pi$
$684$		−	4.33719i		−	0.00634092i
$685$	636.930	−	978.767i	0.929824	−	1.42886i
$686$		0			0
$687$		−	189.190i		−	0.275386i
$688$		−	312.331i		−	0.453970i
$689$			285.998i			0.415091i
$690$	−26.3680	−	17.1589i	−0.0382145	−	0.0248680i
$691$		−	715.038i		−	1.03479i	−0.855747	−	0.517394i	$-0.826902\pi$
$691$		−	715.038i		−	1.03479i	0.855747	−	0.517394i	$-0.173098\pi$
$692$	−6.51659			−0.00941703
$693$		0			0
$694$	738.968			1.06480
$695$	−174.006	+	267.395i	−0.250369	+	0.384741i
$696$			64.0494i			0.0920250i
$697$			289.826i			0.415819i
$698$	1035.38			1.48335
$699$		−	31.8271i		−	0.0455323i
$700$		0			0
$701$	157.215			0.224272			0.112136	−	0.993693i	$-0.464231\pi$
$701$	157.215			0.224272			0.112136	+	0.993693i	$0.464231\pi$
$702$		−	220.070i		−	0.313489i
$703$	216.789			0.308376
$704$	−429.913			−0.610672
$705$	−636.581	−	414.253i	−0.902952	−	0.587593i
$706$		−	872.177i		−	1.23538i
$707$		0			0
$708$		−	0.479170i		−	0.000676794i
$709$	−862.220			−1.21611			−0.608054	−	0.793896i	$-0.708049\pi$
$709$	−862.220			−1.21611			−0.608054	+	0.793896i	$0.708049\pi$
$710$	531.985	−	817.499i	0.749275	−	1.15141i
$711$	−103.493			−0.145560
$712$	−1079.76			−1.51652
$713$	−111.183			−0.155937
$714$		0			0
$715$	591.301	+	384.787i	0.826995	+	0.538164i
$716$	−7.12029			−0.00994454
$717$	−144.858			−0.202034
$718$		−	448.008i		−	0.623966i
$719$		−	581.643i		−	0.808961i	−0.914547	−	0.404481i	$-0.867452\pi$
$719$		−	581.643i		−	0.808961i	0.914547	−	0.404481i	$-0.132548\pi$
$720$	−197.459	−	128.496i	−0.274248	−	0.178466i
$721$		0			0
$722$		−	78.1155i		−	0.108193i
$723$		−	157.609i		−	0.217993i
$724$		−	18.1439i		−	0.0250607i
$725$	−46.3938	−	104.732i	−0.0639915	−	0.144459i
$726$			265.714i			0.365997i
$727$	−621.129			−0.854372			−0.427186	−	0.904164i	$-0.640495\pi$
$727$	−621.129			−0.854372			−0.427186	+	0.904164i	$0.640495\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$	651.415	−	1001.03i	0.892349	−	1.37127i
$731$			318.148i			0.435223i
$732$		−	4.50666i		−	0.00615664i
$733$	731.003			0.997275			0.498638	−	0.866811i	$-0.333834\pi$
$733$	731.003			0.997275			0.498638	+	0.866811i	$0.333834\pi$
$734$		−	284.781i		−	0.387985i
$735$		0			0
$736$	2.11859			0.00287852
$737$			190.753i			0.258823i
$738$	−107.710			−0.145949
$739$	−639.011			−0.864696			−0.432348	−	0.901707i	$-0.642315\pi$
$739$	−639.011			−0.864696			−0.432348	+	0.901707i	$0.642315\pi$
$740$	−2.13462	+	3.28026i	−0.00288462	+	0.00443279i
$741$			740.665i			0.999548i
$742$		0			0
$743$			486.795i			0.655175i	0.944821	+	0.327588i	$0.106236\pi$
$743$			486.795i			0.655175i	−0.944821	+	0.327588i	$0.893764\pi$
$744$	−847.922			−1.13968
$745$	891.805	+	580.339i	1.19705	+	0.778979i
$746$	1200.29			1.60897
$747$	−212.988			−0.285124
$748$	7.63154			0.0102026
$749$		0			0
$750$	423.610	+	68.3203i	0.564814	+	0.0910937i
$751$	608.062			0.809670			0.404835	−	0.914390i	$-0.367329\pi$
$751$	608.062			0.809670			0.404835	+	0.914390i	$0.367329\pi$
$752$	−1377.39			−1.83164
$753$			702.916i			0.933487i
$754$		−	194.056i		−	0.257368i
$755$	792.988	+	516.034i	1.05031	+	0.683489i
$756$		0			0
$757$		−	889.150i		−	1.17457i	−0.809380	−	0.587285i	$-0.800197\pi$
$757$		−	889.150i		−	1.17457i	0.809380	−	0.587285i	$-0.199803\pi$
$758$		−	1230.59i		−	1.62347i
$759$			20.9612i			0.0276169i
$760$	676.795	+	440.422i	0.890520	+	0.579503i
$761$			1060.70i			1.39382i	0.717158	+	0.696910i	$0.245442\pi$
$761$			1060.70i			1.39382i	−0.717158	+	0.696910i	$0.754558\pi$
$762$	364.664			0.478561
$763$		0			0
$764$	7.61428			0.00996633
$765$	201.136	+	130.889i	0.262923	+	0.171096i
$766$		−	405.993i		−	0.530018i
$767$			81.8283i			0.106686i
$768$	24.0188			0.0312745
$769$		−	1226.40i		−	1.59480i	−0.603448	−	0.797402i	$-0.706207\pi$
$769$		−	1226.40i		−	1.59480i	0.603448	−	0.797402i	$-0.293793\pi$
$770$		0			0
$771$	80.0632			0.103843
$772$		−	5.03569i		−	0.00652291i
$773$	693.996			0.897795			0.448898	−	0.893583i	$-0.351817\pi$
$773$	693.996			0.897795			0.448898	+	0.893583i	$0.351817\pi$
$774$	−118.236			−0.152759
$775$	1386.51	−	614.188i	1.78904	−	0.792500i
$776$		−	965.744i		−	1.24452i
$777$		0			0
$778$		−	470.235i		−	0.604415i
$779$	362.509			0.465351
$780$	−11.2071	−	7.29300i	−0.0143681	−	0.00935000i
$781$	−649.870			−0.832100
$782$	58.1159			0.0743170
$783$	23.8084			0.0304066
$784$		0			0
$785$	−320.546	−	208.594i	−0.408339	−	0.265725i
$786$	−412.005			−0.524180
$787$	−374.619			−0.476008			−0.238004	−	0.971264i	$-0.576493\pi$
$787$	−374.619			−0.476008			−0.238004	+	0.971264i	$0.576493\pi$
$788$		−	6.11899i		−	0.00776521i
$789$		−	748.061i		−	0.948112i
$790$	186.453	−	286.522i	0.236017	−	0.362686i
$791$		0			0
$792$			159.858i			0.201841i
$793$			769.606i			0.970499i
$794$			1318.99i			1.66119i
$795$	63.2158	−	97.1434i	0.0795167	−	0.122193i
$796$		−	11.8630i		−	0.0149032i
$797$	−1102.96			−1.38389			−0.691947	−	0.721948i	$-0.743247\pi$
$797$	−1102.96			−1.38389			−0.691947	+	0.721948i	$0.743247\pi$
$798$		0			0
$799$	1403.04			1.75600
$800$	−26.4199	+	11.7034i	−0.0330249	+	0.0146292i
$801$			401.369i			0.501085i
$802$		−	749.926i		−	0.935069i
$803$	−795.765			−0.990990
$804$		−	3.61539i		−	0.00449676i
$805$		0			0
$806$	2569.02			3.18737
$807$			244.738i			0.303269i
$808$	462.886			0.572879
$809$	79.2510			0.0979617			0.0489808	−	0.998800i	$-0.484403\pi$
$809$	79.2510			0.0979617			0.0489808	+	0.998800i	$0.484403\pi$
$810$	−48.6432	+	74.7498i	−0.0600533	+	0.0922837i
$811$			561.470i			0.692318i	0.938176	+	0.346159i	$0.112514\pi$
$811$			561.470i			0.692318i	−0.938176	+	0.346159i	$0.887486\pi$
$812$		0			0
$813$			12.9398i			0.0159161i
$814$	−141.762			−0.174155
$815$	−431.133	+	662.520i	−0.528998	+	0.812908i
$816$	435.205			0.533339
$817$	397.934			0.487067
$818$	755.114			0.923122
$819$		0			0
$820$	−3.56946	+	5.48517i	−0.00435300	+	0.00668924i
$821$	−403.814			−0.491857			−0.245928	−	0.969288i	$-0.579093\pi$
$821$	−403.814			−0.491857			−0.245928	+	0.969288i	$0.579093\pi$
$822$	−801.708			−0.975314
$823$		−	1370.46i		−	1.66520i	−0.553878	−	0.832598i	$-0.686853\pi$
$823$		−	1370.46i		−	1.66520i	0.553878	−	0.832598i	$-0.313147\pi$
$824$			530.177i			0.643419i
$825$	−115.792	−	261.397i	−0.140354	−	0.316845i
$826$		0			0
$827$			297.863i			0.360173i	0.983651	+	0.180086i	$0.0576378\pi$
$827$			297.863i			0.360173i	−0.983651	+	0.180086i	$0.942362\pi$
$828$		−	0.397285i		−	0.000479813i
$829$			407.339i			0.491362i	0.969351	+	0.245681i	$0.0790116\pi$
$829$			407.339i			0.491362i	−0.969351	+	0.245681i	$0.920988\pi$
$830$	383.719	−	589.659i	0.462312	−	0.710433i
$831$			46.8480i			0.0563754i
$832$	−1391.49			−1.67246
$833$		0			0
$834$	219.023			0.262618
$835$	214.868	+	139.825i	0.257327	+	0.167455i
$836$		−	9.54540i		−	0.0114179i
$837$			315.189i			0.376570i
$838$	−730.234			−0.871401
$839$			1238.46i			1.47611i	0.674739	+	0.738056i	$0.264256\pi$
$839$			1238.46i			1.47611i	−0.674739	+	0.738056i	$0.735744\pi$
$840$		0			0
$841$	−820.006			−0.975037
$842$			583.600i			0.693112i
$843$	−863.044			−1.02378
$844$	−13.0173			−0.0154234
$845$	1205.61	+	784.545i	1.42675	+	0.928455i
$846$			521.424i			0.616340i
$847$		0			0
$848$		−	210.192i		−	0.247868i
$849$	616.507			0.726157
$850$	−724.734	+	321.039i	−0.852629	+	0.377693i
$851$	19.8578			0.0233346
$852$	12.3172			0.0144568
$853$	−243.147			−0.285049			−0.142525	−	0.989791i	$-0.545522\pi$
$853$	−243.147			−0.285049			−0.142525	+	0.989791i	$0.545522\pi$
$854$		0			0
$855$	163.713	−	251.578i	0.191478	−	0.294243i
$856$	1027.02			1.19978
$857$	152.099			0.177478			0.0887392	−	0.996055i	$-0.471716\pi$
$857$	152.099			0.177478			0.0887392	+	0.996055i	$0.471716\pi$
$858$		−	484.335i		−	0.564493i
$859$		−	1235.53i		−	1.43833i	−0.694839	−	0.719165i	$-0.744525\pi$
$859$		−	1235.53i		−	1.43833i	0.694839	−	0.719165i	$-0.255475\pi$
$860$	−3.91828	+	6.02120i	−0.00455613	+	0.00700139i
$861$		0			0
$862$		−	865.959i		−	1.00459i
$863$		−	903.581i		−	1.04702i	−0.852019	−	0.523512i	$-0.824622\pi$
$863$		−	903.581i		−	1.04702i	0.852019	−	0.523512i	$-0.175378\pi$
$864$		−	6.00593i		−	0.00695131i
$865$	−377.993	−	245.978i	−0.436986	−	0.284368i
$866$		−	1344.26i		−	1.55226i
$867$	57.2524			0.0660351
$868$		0			0
$869$	−227.771			−0.262107
$870$	−42.8932	+	65.9138i	−0.0493025	+	0.0757630i
$871$			617.404i			0.708845i
$872$		−	525.765i		−	0.602942i
$873$	−358.986			−0.411209
$874$		−	72.6903i		−	0.0831697i
$875$		0			0
$876$	15.0824			0.0172173
$877$		−	635.566i		−	0.724705i	−0.932041	−	0.362352i	$-0.881974\pi$
$877$		−	635.566i		−	0.724705i	0.932041	−	0.362352i	$-0.118026\pi$
$878$	648.918			0.739087
$879$	19.2640			0.0219158
$880$	−434.573	−	282.797i	−0.493832	−	0.321360i
$881$		−	1453.08i		−	1.64935i	−0.565605	−	0.824677i	$-0.691357\pi$
$881$		−	1453.08i		−	1.64935i	0.565605	−	0.824677i	$-0.308643\pi$
$882$		0			0
$883$		−	279.559i		−	0.316601i	−0.987391	−	0.158301i	$-0.949399\pi$
$883$		−	279.559i		−	0.316601i	0.987391	−	0.158301i	$-0.0506015\pi$
$884$	24.7008			0.0279421
$885$	18.0870	−	27.7942i	0.0204373	−	0.0314058i
$886$	−749.405			−0.845830
$887$	−482.497			−0.543965			−0.271983	−	0.962302i	$-0.587679\pi$
$887$	−482.497			−0.543965			−0.271983	+	0.962302i	$0.587679\pi$
$888$	151.443			0.170544
$889$		0			0
$890$	−1111.20	−	723.107i	−1.24853	−	0.812480i
$891$	59.4223			0.0666917
$892$	−18.3607			−0.0205838
$893$		−	1754.90i		−	1.96518i
$894$		−	730.478i		−	0.817089i
$895$	−413.011	−	268.766i	−0.461465	−	0.300297i
$896$		0			0
$897$			67.8447i			0.0756351i
$898$		−	166.659i		−	0.185590i
$899$			277.931i			0.309156i
$900$	2.19465	+	4.95435i	0.00243850	+	0.00550483i
$901$			214.107i			0.237632i
$902$	−237.051			−0.262806
$903$		0			0
$904$	−744.624			−0.823699
$905$	684.869	−	1052.43i	0.756761	−	1.16291i
$906$		−	649.536i		−	0.716928i
$907$			1200.83i			1.32396i	0.749524	+	0.661978i	$0.230283\pi$
$907$			1200.83i			1.32396i	−0.749524	+	0.661978i	$0.769717\pi$
$908$	11.8854			0.0130897
$909$		−	172.064i		−	0.189289i
$910$		0			0
$911$	1298.64			1.42551			0.712753	−	0.701415i	$-0.247448\pi$
$911$	1298.64			1.42551			0.712753	+	0.701415i	$0.247448\pi$
$912$		−	544.347i		−	0.596871i
$913$	−468.749			−0.513417
$914$	478.590			0.523621
$915$	170.110	−	261.408i	0.185913	−	0.285692i
$916$			7.89169i			0.00861539i
$917$		0			0
$918$		−	164.751i		−	0.179467i
$919$	325.805			0.354521			0.177260	−	0.984164i	$-0.443277\pi$
$919$	325.805			0.354521			0.177260	+	0.984164i	$0.443277\pi$
$920$	61.9942	+	40.3425i	0.0673850	+	0.0438506i
$921$	−640.766			−0.695729
$922$	−1143.30			−1.24002
$923$	−2103.42			−2.27889
$924$		0			0
$925$	−247.636	+	109.697i	−0.267715	+	0.118591i
$926$	−1060.45			−1.14520
$927$	197.077			0.212596
$928$		−	5.29598i		−	0.00570688i
$929$		−	1497.76i		−	1.61223i	−0.591760	−	0.806114i	$-0.701567\pi$
$929$		−	1497.76i		−	1.61223i	0.591760	−	0.806114i	$-0.298433\pi$
$930$	−872.604	−	567.845i	−0.938284	−	0.610586i
$931$		0			0
$932$			1.32760i			0.00142446i
$933$			500.922i			0.536894i
$934$			64.4531i			0.0690076i
$935$	442.666	+	288.064i	0.473440	+	0.308089i
$936$			517.409i			0.552787i
$937$	1375.13			1.46759			0.733796	−	0.679370i	$-0.237747\pi$
$937$	1375.13			1.46759			0.733796	+	0.679370i	$0.237747\pi$
$938$		0			0
$939$	−357.258			−0.380466
$940$	26.5537	+	17.2797i	0.0282486	+	0.0183827i
$941$		−	127.123i		−	0.135093i	−0.997716	−	0.0675465i	$-0.978483\pi$
$941$		−	127.123i		−	0.135093i	0.997716	−	0.0675465i	$-0.0215171\pi$
$942$			262.559i			0.278725i
$943$	33.2057			0.0352128
$944$		−	60.1391i		−	0.0637067i
$945$		0			0
$946$	−260.216			−0.275070
$947$			1227.90i			1.29662i	0.761375	+	0.648311i	$0.224524\pi$
$947$			1227.90i			1.29662i	−0.761375	+	0.648311i	$0.775476\pi$
$948$	4.31701			0.00455381
$949$	−2575.63			−2.71405
$950$	401.550	+	906.485i	0.422684	+	0.954195i
$951$		−	111.099i		−	0.116823i
$952$		0			0
$953$		−	351.252i		−	0.368575i	−0.982872	−	0.184288i	$-0.941002\pi$
$953$		−	351.252i		−	0.368575i	0.982872	−	0.184288i	$-0.0589978\pi$
$954$	−79.5702			−0.0834069
$955$	441.665	+	287.412i	0.462476	+	0.300955i
$956$	6.04247			0.00632057
$957$	52.3981			0.0547525
$958$	537.191			0.560742
$959$		0			0
$960$	472.639	+	307.568i	0.492332	+	0.320384i
$961$	−2718.41			−2.82873
$962$	−458.838			−0.476962
$963$		−	381.761i		−	0.396429i
$964$			6.57434i			0.00681986i
$965$	190.079	−	292.094i	0.196973	−	0.302688i
$966$		0			0
$967$		−	809.550i		−	0.837177i	−0.908176	−	0.418588i	$-0.862525\pi$
$967$		−	809.550i		−	0.837177i	0.908176	−	0.418588i	$-0.137475\pi$
$968$		−	624.724i		−	0.645376i
$969$			554.485i			0.572224i
$970$	646.749	−	993.856i	0.666751	−	1.02459i
$971$		−	985.812i		−	1.01525i	−0.861577	−	0.507627i	$-0.830523\pi$
$971$		−	985.812i		−	1.01525i	0.861577	−	0.507627i	$-0.169477\pi$
$972$	−1.12625			−0.00115869
$973$		0			0
$974$	1026.23			1.05362
$975$	−374.782	−	846.058i	−0.384392	−	0.867752i
$976$		−	565.616i		−	0.579525i
$977$			939.935i			0.962063i	0.876703	+	0.481031i	$0.159738\pi$
$977$			939.935i			0.962063i	−0.876703	+	0.481031i	$0.840262\pi$
$978$	542.671			0.554878
$979$			883.344i			0.902292i
$980$		0			0
$981$	−195.437			−0.199222
$982$			1388.79i			1.41425i
$983$	552.464			0.562018			0.281009	−	0.959705i	$-0.409331\pi$
$983$	552.464			0.562018			0.281009	+	0.959705i	$0.409331\pi$
$984$	253.239			0.257356
$985$	230.970	−	354.930i	0.234487	−	0.360336i
$986$		−	145.276i		−	0.147339i
$987$		0			0
$988$		−	30.8954i		−	0.0312706i
$989$	36.4506			0.0368560
$990$	−107.055	+	164.511i	−0.108137	+	0.166173i
$991$	417.296			0.421085			0.210543	−	0.977585i	$-0.432477\pi$
$991$	417.296			0.421085			0.210543	+	0.977585i	$0.432477\pi$
$992$	70.1112			0.0706766
$993$	−278.780			−0.280745
$994$		0			0
$995$	447.784	−	688.108i	0.450034	−	0.691566i
$996$	8.88436			0.00892004
$997$	1554.49			1.55917			0.779584	−	0.626298i	$-0.215431\pi$
$997$	1554.49			1.55917			0.779584	+	0.626298i	$0.215431\pi$
$998$			421.570i			0.422414i
$999$		−	56.2941i		−	0.0563505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.3.e.a.244.4		32
5.4	even	2	inner	735.3.e.a.244.27		32
7.2	even	3		105.3.r.a.94.12	yes	32
7.3	odd	6		105.3.r.a.19.5	✓	32
7.6	odd	2	inner	735.3.e.a.244.28		32
21.2	odd	6		315.3.bi.e.199.5		32
21.17	even	6		315.3.bi.e.19.12		32
35.2	odd	12		525.3.o.p.451.6		16
35.3	even	12		525.3.o.q.376.3		16
35.9	even	6		105.3.r.a.94.5	yes	32
35.17	even	12		525.3.o.p.376.6		16
35.23	odd	12		525.3.o.q.451.3		16
35.24	odd	6		105.3.r.a.19.12	yes	32
35.34	odd	2	inner	735.3.e.a.244.3		32
105.44	odd	6		315.3.bi.e.199.12		32
105.59	even	6		315.3.bi.e.19.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.5	✓	32	7.3	odd	6
105.3.r.a.19.12	yes	32	35.24	odd	6
105.3.r.a.94.5	yes	32	35.9	even	6
105.3.r.a.94.12	yes	32	7.2	even	3
315.3.bi.e.19.5		32	105.59	even	6
315.3.bi.e.19.12		32	21.17	even	6
315.3.bi.e.199.5		32	21.2	odd	6
315.3.bi.e.199.12		32	105.44	odd	6
525.3.o.p.376.6		16	35.17	even	12
525.3.o.p.451.6		16	35.2	odd	12
525.3.o.q.376.3		16	35.3	even	12
525.3.o.q.451.3		16	35.23	odd	12
735.3.e.a.244.3		32	35.34	odd	2	inner
735.3.e.a.244.4		32	1.1	even	1	trivial
735.3.e.a.244.27		32	5.4	even	2	inner
735.3.e.a.244.28		32	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	735.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.98186i q^{2} -1.73205 q^{3} +0.0722490 q^{4} +(4.19079 + 2.72714i) q^{5} -3.43267i q^{6} +8.07061i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.98186i q^{2} -1.73205 q^{3} +0.0722490 q^{4} +(4.19079 + 2.72714i) q^{5} -3.43267i q^{6} +8.07061i q^{8} +3.00000 q^{9} +(-5.40480 + 8.30553i) q^{10} +6.60248 q^{11} -0.125139 q^{12} +21.3701 q^{13} +(-7.25866 - 4.72355i) q^{15} -15.7058 q^{16} +15.9983 q^{17} +5.94557i q^{18} -20.0104i q^{19} +(0.302780 + 0.197033i) q^{20} +13.0852i q^{22} -1.83294i q^{23} -13.9787i q^{24} +(10.1254 + 22.8577i) q^{25} +42.3524i q^{26} -5.19615 q^{27} -4.58193 q^{29} +(9.36139 - 14.3856i) q^{30} -60.6581i q^{31} +1.15584i q^{32} -11.4358 q^{33} +31.7063i q^{34} +0.216747 q^{36} +10.8338i q^{37} +39.6577 q^{38} -37.0141 q^{39} +(-22.0097 + 33.8222i) q^{40} +18.1160i q^{41} +19.8864i q^{43} +0.477022 q^{44} +(12.5724 + 8.18143i) q^{45} +3.63263 q^{46} +87.6996 q^{47} +27.2032 q^{48} +(-45.3007 + 20.0671i) q^{50} -27.7099 q^{51} +1.54397 q^{52} +13.3831i q^{53} -10.2980i q^{54} +(27.6696 + 18.0059i) q^{55} +34.6590i q^{57} -9.08072i q^{58} +3.82911i q^{59} +(-0.524431 - 0.341272i) q^{60} +36.0133i q^{61} +120.216 q^{62} -65.1138 q^{64} +(89.5574 + 58.2792i) q^{65} -22.6642i q^{66} +28.8911i q^{67} +1.15586 q^{68} +3.17475i q^{69} -98.4282 q^{71} +24.2118i q^{72} -120.525 q^{73} -21.4710 q^{74} +(-17.5377 - 39.5908i) q^{75} -1.44573i q^{76} -73.3565i q^{78} -34.4977 q^{79} +(-65.8196 - 42.8319i) q^{80} +9.00000 q^{81} -35.9034 q^{82} -70.9960 q^{83} +(67.0454 + 43.6296i) q^{85} -39.4119 q^{86} +7.93613 q^{87} +53.2860i q^{88} +133.790i q^{89} +(-16.2144 + 24.9166i) q^{90} -0.132428i q^{92} +105.063i q^{93} +173.808i q^{94} +(54.5711 - 83.8592i) q^{95} -2.00198i q^{96} -119.662 q^{97} +19.8074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 96 q^{9}+O(q^{10}) \) 32 * q - 64 * q^4 + 96 * q^9	\( 32 q - 64 q^{4} + 96 q^{9} + 56 q^{11} - 24 q^{15} + 80 q^{16} + 68 q^{25} - 88 q^{29} - 192 q^{36} - 72 q^{39} - 640 q^{44} + 120 q^{46} - 24 q^{51} + 396 q^{60} - 400 q^{64} + 92 q^{65} + 344 q^{71} - 1800 q^{74} + 40 q^{79} + 288 q^{81} + 304 q^{85} - 288 q^{86} + 684 q^{95} + 168 q^{99}+O(q^{100}) \) 32 * q - 64 * q^4 + 96 * q^9 + 56 * q^11 - 24 * q^15 + 80 * q^16 + 68 * q^25 - 88 * q^29 - 192 * q^36 - 72 * q^39 - 640 * q^44 + 120 * q^46 - 24 * q^51 + 396 * q^60 - 400 * q^64 + 92 * q^65 + 344 * q^71 - 1800 * q^74 + 40 * q^79 + 288 * q^81 + 304 * q^85 - 288 * q^86 + 684 * q^95 + 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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