LMFDB - Embedded newform 735.3.e.a.244.14

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			244.14
Character	$\chi$	$=$	735.244
Dual form			735.3.e.a.244.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.40813i q^{2} -1.73205 q^{3} -7.61537 q^{4} +(1.24390 - 4.84280i) q^{5} -5.90306i q^{6} -12.3217i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+3.40813i q^{2} -1.73205 q^{3} -7.61537 q^{4} +(1.24390 - 4.84280i) q^{5} -5.90306i q^{6} -12.3217i q^{8} +3.00000 q^{9} +(16.5049 + 4.23938i) q^{10} -1.38932 q^{11} +13.1902 q^{12} -3.78639 q^{13} +(-2.15450 + 8.38798i) q^{15} +11.5324 q^{16} +31.7072 q^{17} +10.2244i q^{18} +14.8188i q^{19} +(-9.47278 + 36.8797i) q^{20} -4.73498i q^{22} +22.6176i q^{23} +21.3418i q^{24} +(-21.9054 - 12.0479i) q^{25} -12.9045i q^{26} -5.19615 q^{27} -42.9485 q^{29} +(-28.5873 - 7.34283i) q^{30} +32.3468i q^{31} -9.98266i q^{32} +2.40637 q^{33} +108.062i q^{34} -22.8461 q^{36} +8.42148i q^{37} -50.5046 q^{38} +6.55822 q^{39} +(-59.6714 - 15.3270i) q^{40} -46.3613i q^{41} +9.92743i q^{43} +10.5802 q^{44} +(3.73170 - 14.5284i) q^{45} -77.0837 q^{46} -54.5621 q^{47} -19.9747 q^{48} +(41.0610 - 74.6566i) q^{50} -54.9184 q^{51} +28.8348 q^{52} +85.9468i q^{53} -17.7092i q^{54} +(-1.72817 + 6.72818i) q^{55} -25.6670i q^{57} -146.374i q^{58} +92.8967i q^{59} +(16.4073 - 63.8776i) q^{60} +1.63810i q^{61} -110.242 q^{62} +80.1519 q^{64} +(-4.70990 + 18.3367i) q^{65} +8.20122i q^{66} -43.7671i q^{67} -241.462 q^{68} -39.1748i q^{69} -60.9268 q^{71} -36.9650i q^{72} -64.6485 q^{73} -28.7015 q^{74} +(37.9413 + 20.8676i) q^{75} -112.851i q^{76} +22.3513i q^{78} -1.48987 q^{79} +(14.3452 - 55.8492i) q^{80} +9.00000 q^{81} +158.006 q^{82} -13.6731 q^{83} +(39.4406 - 153.551i) q^{85} -33.8340 q^{86} +74.3891 q^{87} +17.1187i q^{88} +127.089i q^{89} +(49.5147 + 12.7181i) q^{90} -172.241i q^{92} -56.0262i q^{93} -185.955i q^{94} +(71.7647 + 18.4332i) q^{95} +17.2905i q^{96} +119.276 q^{97} -4.16795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			3.40813i			1.70407i	0.523487	+	0.852033i	$0.324631\pi$
$2$			3.40813i			1.70407i	−0.523487	+	0.852033i	$0.675369\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−7.61537			−1.90384
$5$	1.24390	−	4.84280i	0.248780	−	0.968560i
$5$	1.24390	−	4.84280i	0.248780	−	0.968560i
$6$		−	5.90306i		−	0.983843i
$7$		0			0
$7$		0			0
$8$		−	12.3217i		−	1.54021i
$9$	3.00000			0.333333
$10$	16.5049	+	4.23938i	1.65049	+	0.423938i
$11$	−1.38932			−0.126302			−0.0631508	−	0.998004i	$-0.520115\pi$
$11$	−1.38932			−0.126302			−0.0631508	+	0.998004i	$0.520115\pi$
$12$	13.1902			1.09918
$13$	−3.78639			−0.291261			−0.145630	−	0.989339i	$-0.546521\pi$
$13$	−3.78639			−0.291261			−0.145630	+	0.989339i	$0.546521\pi$
$14$		0			0
$15$	−2.15450	+	8.38798i	−0.143633	+	0.559198i
$16$	11.5324			0.720777
$17$	31.7072			1.86513			0.932563	−	0.361006i	$-0.117567\pi$
$17$	31.7072			1.86513			0.932563	+	0.361006i	$0.117567\pi$
$18$			10.2244i			0.568022i
$19$			14.8188i			0.779939i	0.920828	+	0.389970i	$0.127514\pi$
$19$			14.8188i			0.779939i	−0.920828	+	0.389970i	$0.872486\pi$
$20$	−9.47278	+	36.8797i	−0.473639	+	1.84399i
$21$		0			0
$22$		−	4.73498i		−	0.215226i
$23$			22.6176i			0.983372i	0.870773	+	0.491686i	$0.163619\pi$
$23$			22.6176i			0.983372i	−0.870773	+	0.491686i	$0.836381\pi$
$24$			21.3418i			0.889241i
$25$	−21.9054	−	12.0479i	−0.876217	−	0.481917i
$26$		−	12.9045i		−	0.496328i
$27$	−5.19615			−0.192450
$28$		0			0
$29$	−42.9485			−1.48098			−0.740492	−	0.672065i	$-0.765407\pi$
$29$	−42.9485			−1.48098			−0.740492	+	0.672065i	$0.765407\pi$
$30$	−28.5873	−	7.34283i	−0.952911	−	0.244761i
$31$			32.3468i			1.04344i	0.853116	+	0.521722i	$0.174710\pi$
$31$			32.3468i			1.04344i	−0.853116	+	0.521722i	$0.825290\pi$
$32$		−	9.98266i		−	0.311958i
$33$	2.40637			0.0729202
$34$			108.062i			3.17830i
$35$		0			0
$36$	−22.8461			−0.634615
$37$			8.42148i			0.227608i	0.993503	+	0.113804i	$0.0363035\pi$
$37$			8.42148i			0.227608i	−0.993503	+	0.113804i	$0.963696\pi$
$38$	−50.5046			−1.32907
$39$	6.55822			0.168160
$40$	−59.6714	−	15.3270i	−1.49179	−	0.383174i
$41$		−	46.3613i		−	1.13076i	−0.824829	−	0.565382i	$-0.808729\pi$
$41$		−	46.3613i		−	1.13076i	0.824829	−	0.565382i	$-0.191271\pi$
$42$		0			0
$43$			9.92743i			0.230871i	0.993315	+	0.115435i	$0.0368263\pi$
$43$			9.92743i			0.230871i	−0.993315	+	0.115435i	$0.963174\pi$
$44$	10.5802			0.240458
$45$	3.73170	−	14.5284i	0.0829268	−	0.322853i
$46$	−77.0837			−1.67573
$47$	−54.5621			−1.16090			−0.580448	−	0.814297i	$-0.697123\pi$
$47$	−54.5621			−1.16090			−0.580448	+	0.814297i	$0.697123\pi$
$48$	−19.9747			−0.416141
$49$		0			0
$50$	41.0610	−	74.6566i	0.821219	−	1.49313i
$51$	−54.9184			−1.07683
$52$	28.8348			0.554515
$53$			85.9468i			1.62164i	0.585297	+	0.810819i	$0.300978\pi$
$53$			85.9468i			1.62164i	−0.585297	+	0.810819i	$0.699022\pi$
$54$		−	17.7092i		−	0.327948i
$55$	−1.72817	+	6.72818i	−0.0314213	+	0.122331i
$56$		0			0
$57$		−	25.6670i		−	0.450298i
$58$		−	146.374i		−	2.52370i
$59$			92.8967i			1.57452i	0.616621	+	0.787260i	$0.288501\pi$
$59$			92.8967i			1.57452i	−0.616621	+	0.787260i	$0.711499\pi$
$60$	16.4073	−	63.8776i	0.273455	−	1.06463i
$61$			1.63810i			0.0268540i	0.999910	+	0.0134270i	$0.00427408\pi$
$61$			1.63810i			0.0268540i	−0.999910	+	0.0134270i	$0.995726\pi$
$62$	−110.242			−1.77810
$63$		0			0
$64$	80.1519			1.25237
$65$	−4.70990	+	18.3367i	−0.0724600	+	0.282104i
$66$			8.20122i			0.124261i
$67$		−	43.7671i		−	0.653240i	−0.945156	−	0.326620i	$-0.894090\pi$
$67$		−	43.7671i		−	0.653240i	0.945156	−	0.326620i	$-0.105910\pi$
$68$	−241.462			−3.55091
$69$		−	39.1748i		−	0.567750i
$70$		0			0
$71$	−60.9268			−0.858124			−0.429062	−	0.903275i	$-0.641156\pi$
$71$	−60.9268			−0.858124			−0.429062	+	0.903275i	$0.641156\pi$
$72$		−	36.9650i		−	0.513403i
$73$	−64.6485			−0.885596			−0.442798	−	0.896621i	$-0.646014\pi$
$73$	−64.6485			−0.885596			−0.442798	+	0.896621i	$0.646014\pi$
$74$	−28.7015			−0.387858
$75$	37.9413	+	20.8676i	0.505884	+	0.278235i
$76$		−	112.851i		−	1.48488i
$77$		0			0
$78$			22.3513i			0.286555i
$79$	−1.48987			−0.0188591			−0.00942957	−	0.999956i	$-0.503002\pi$
$79$	−1.48987			−0.0188591			−0.00942957	+	0.999956i	$0.503002\pi$
$80$	14.3452	−	55.8492i	0.179315	−	0.698115i
$81$	9.00000			0.111111
$82$	158.006			1.92690
$83$	−13.6731			−0.164736			−0.0823681	−	0.996602i	$-0.526248\pi$
$83$	−13.6731			−0.164736			−0.0823681	+	0.996602i	$0.526248\pi$
$84$		0			0
$85$	39.4406	−	153.551i	0.464007	−	1.80649i
$86$	−33.8340			−0.393419
$87$	74.3891			0.855047
$88$			17.1187i			0.194531i
$89$			127.089i			1.42796i	0.700164	+	0.713982i	$0.253110\pi$
$89$			127.089i			1.42796i	−0.700164	+	0.713982i	$0.746890\pi$
$90$	49.5147	+	12.7181i	0.550164	+	0.141313i
$91$		0			0
$92$		−	172.241i		−	1.87219i
$93$		−	56.0262i		−	0.602433i
$94$		−	185.955i		−	1.97825i
$95$	71.7647	+	18.4332i	0.755418	+	0.194034i
$96$			17.2905i			0.180109i
$97$	119.276			1.22965			0.614824	−	0.788664i	$-0.289227\pi$
$97$	119.276			1.22965			0.614824	+	0.788664i	$0.289227\pi$
$98$		0			0
$99$	−4.16795			−0.0421005
$100$	166.818	+	91.7495i	1.66818	+	0.917495i
$101$		−	119.732i		−	1.18546i	−0.805400	−	0.592732i	$-0.798050\pi$
$101$		−	119.732i		−	1.18546i	0.805400	−	0.592732i	$-0.201950\pi$
$102$		−	187.169i		−	1.83499i
$103$	62.3773			0.605605			0.302802	−	0.953053i	$-0.402078\pi$
$103$	62.3773			0.605605			0.302802	+	0.953053i	$0.402078\pi$
$104$			46.6547i			0.448603i
$105$		0			0
$106$	−292.918			−2.76338
$107$			120.327i			1.12455i	0.826951	+	0.562275i	$0.190074\pi$
$107$			120.327i			1.12455i	−0.826951	+	0.562275i	$0.809926\pi$
$108$	39.5706			0.366395
$109$	−65.0596			−0.596877			−0.298439	−	0.954429i	$-0.596466\pi$
$109$	−65.0596			−0.596877			−0.298439	+	0.954429i	$0.596466\pi$
$110$	−22.9305	−	5.88985i	−0.208459	−	0.0535440i
$111$		−	14.5864i		−	0.131409i
$112$		0			0
$113$			133.463i			1.18109i	0.807005	+	0.590545i	$0.201087\pi$
$113$			133.463i			1.18109i	−0.807005	+	0.590545i	$0.798913\pi$
$114$	87.4765			0.767338
$115$	109.532	+	28.1340i	0.952455	+	0.244644i
$116$	327.069			2.81956
$117$	−11.3592			−0.0970869
$118$	−316.604			−2.68309
$119$		0			0
$120$	103.354	+	26.5471i	0.861283	+	0.221226i
$121$	−119.070			−0.984048
$122$	−5.58285			−0.0457611
$123$			80.3002i			0.652847i
$124$		−	246.333i		−	1.98655i
$125$	−85.5939	+	91.0971i	−0.684751	+	0.728777i
$126$		0			0
$127$			187.969i			1.48007i	0.672570	+	0.740034i	$0.265191\pi$
$127$			187.969i			1.48007i	−0.672570	+	0.740034i	$0.734809\pi$
$128$			233.238i			1.82217i
$129$		−	17.1948i		−	0.133293i
$130$	−62.4940	−	16.0520i	−0.480723	−	0.123477i
$131$			71.2441i			0.543848i	0.962319	+	0.271924i	$0.0876599\pi$
$131$			71.2441i			0.543848i	−0.962319	+	0.271924i	$0.912340\pi$
$132$	−18.3254			−0.138829
$133$		0			0
$134$	149.164			1.11316
$135$	−6.46350	+	25.1639i	−0.0478778	+	0.186399i
$136$		−	390.685i		−	2.87269i
$137$			37.9813i			0.277236i	0.990346	+	0.138618i	$0.0442660\pi$
$137$			37.9813i			0.277236i	−0.990346	+	0.138618i	$0.955734\pi$
$138$	133.513			0.967484
$139$		−	98.4179i		−	0.708042i	−0.935237	−	0.354021i	$-0.884814\pi$
$139$		−	98.4179i		−	0.708042i	0.935237	−	0.354021i	$-0.115186\pi$
$140$		0			0
$141$	94.5044			0.670244
$142$		−	207.647i		−	1.46230i
$143$	5.26050			0.0367867
$144$	34.5973			0.240259
$145$	−53.4238	+	207.991i	−0.368440	+	1.43442i
$146$		−	220.331i		−	1.50911i
$147$		0			0
$148$		−	64.1327i		−	0.433329i
$149$	−178.688			−1.19925			−0.599625	−	0.800281i	$-0.704683\pi$
$149$	−178.688			−1.19925			−0.599625	+	0.800281i	$0.704683\pi$
$150$	−71.1197	+	129.309i	−0.474131	+	0.862060i
$151$	241.553			1.59969			0.799846	−	0.600205i	$-0.204915\pi$
$151$	241.553			1.59969			0.799846	+	0.600205i	$0.204915\pi$
$152$	182.593			1.20127
$153$	95.1215			0.621709
$154$		0			0
$155$	156.649	+	40.2362i	1.01064	+	0.259588i
$156$	−49.9433			−0.320149
$157$	41.3247			0.263215			0.131607	−	0.991302i	$-0.457986\pi$
$157$	41.3247			0.263215			0.131607	+	0.991302i	$0.457986\pi$
$158$		−	5.07768i		−	0.0321372i
$159$		−	148.864i		−	0.936253i
$160$	−48.3440	−	12.4174i	−0.302150	−	0.0776090i
$161$		0			0
$162$			30.6732i			0.189341i
$163$			69.8733i			0.428670i	0.976760	+	0.214335i	$0.0687585\pi$
$163$			69.8733i			0.428670i	−0.976760	+	0.214335i	$0.931242\pi$
$164$			353.059i			2.15280i
$165$	2.99328	−	11.6536i	0.0181411	−	0.0706276i
$166$		−	46.5998i		−	0.280722i
$167$	−32.7058			−0.195843			−0.0979217	−	0.995194i	$-0.531219\pi$
$167$	−32.7058			−0.195843			−0.0979217	+	0.995194i	$0.531219\pi$
$168$		0			0
$169$	−154.663			−0.915167
$170$	523.324	+	134.419i	3.07837	+	0.790699i
$171$			44.4565i			0.259980i
$172$		−	75.6011i		−	0.439541i
$173$	−24.8488			−0.143635			−0.0718173	−	0.997418i	$-0.522880\pi$
$173$	−24.8488			−0.143635			−0.0718173	+	0.997418i	$0.522880\pi$
$174$			253.528i			1.45706i
$175$		0			0
$176$	−16.0222			−0.0910352
$177$		−	160.902i		−	0.909050i
$178$	−433.135			−2.43335
$179$	−140.125			−0.782821			−0.391411	−	0.920216i	$-0.628013\pi$
$179$	−140.125			−0.782821			−0.391411	+	0.920216i	$0.628013\pi$
$180$	−28.4183	+	110.639i	−0.157880	+	0.614662i
$181$		−	281.086i		−	1.55296i	−0.630142	−	0.776480i	$-0.717003\pi$
$181$		−	281.086i		−	1.55296i	0.630142	−	0.776480i	$-0.282997\pi$
$182$		0			0
$183$		−	2.83727i		−	0.0155042i
$184$	278.686			1.51460
$185$	40.7835	+	10.4755i	0.220452	+	0.0566243i
$186$	190.945			1.02659
$187$	−44.0513			−0.235568
$188$	415.511			2.21017
$189$		0			0
$190$	−62.8227	+	244.584i	−0.330646	+	1.28728i
$191$	−102.376			−0.535998			−0.267999	−	0.963419i	$-0.586362\pi$
$191$	−102.376			−0.535998			−0.267999	+	0.963419i	$0.586362\pi$
$192$	−138.827			−0.723059
$193$		−	2.68202i		−	0.0138965i	−0.999976	−	0.00694825i	$-0.997788\pi$
$193$		−	2.68202i		−	0.0138965i	0.999976	−	0.00694825i	$-0.00221171\pi$
$194$			406.508i			2.09540i
$195$	8.15778	−	31.7602i	0.0418348	−	0.162873i
$196$		0			0
$197$			32.0387i			0.162633i	0.996688	+	0.0813164i	$0.0259124\pi$
$197$			32.0387i			0.162633i	−0.996688	+	0.0813164i	$0.974088\pi$
$198$		−	14.2049i		−	0.0717421i
$199$		−	16.3169i		−	0.0819945i	−0.999159	−	0.0409973i	$-0.986947\pi$
$199$		−	16.3169i		−	0.0819945i	0.999159	−	0.0409973i	$-0.0130535\pi$
$200$	−148.451	+	269.912i	−0.742254	+	1.34956i
$201$			75.8068i			0.377148i
$202$	408.062			2.02011
$203$		0			0
$204$	418.224			2.05012
$205$	−224.519	−	57.6689i	−1.09521	−	0.281312i
$206$			212.590i			1.03199i
$207$			67.8527i			0.327791i
$208$	−43.6663			−0.209934
$209$		−	20.5881i		−	0.0985075i
$210$		0			0
$211$	−311.474			−1.47618			−0.738091	−	0.674701i	$-0.764272\pi$
$211$	−311.474			−1.47618			−0.738091	+	0.674701i	$0.764272\pi$
$212$		−	654.517i		−	3.08735i
$213$	105.528			0.495438
$214$	−410.090			−1.91631
$215$	48.0766	+	12.3488i	0.223612	+	0.0574361i
$216$			64.0253i			0.296414i
$217$		0			0
$218$		−	221.732i		−	1.01712i
$219$	111.974			0.511299
$220$	13.1607	−	51.2376i	0.0598213	−	0.232898i
$221$	−120.056			−0.543238
$222$	49.7125			0.223930
$223$	111.515			0.500068			0.250034	−	0.968237i	$-0.419558\pi$
$223$	111.515			0.500068			0.250034	+	0.968237i	$0.419558\pi$
$224$		0			0
$225$	−65.7163	−	36.1438i	−0.292072	−	0.160639i
$226$	−454.860			−2.01266
$227$	−85.2730			−0.375652			−0.187826	−	0.982202i	$-0.560144\pi$
$227$	−85.2730			−0.375652			−0.187826	+	0.982202i	$0.560144\pi$
$228$			195.464i			0.857297i
$229$		−	69.7692i		−	0.304669i	−0.988329	−	0.152334i	$-0.951321\pi$
$229$		−	69.7692i		−	0.304669i	0.988329	−	0.152334i	$-0.0486791\pi$
$230$	−95.8845	+	373.301i	−0.416889	+	1.62305i
$231$		0			0
$232$			529.198i			2.28103i
$233$			173.573i			0.744949i	0.928042	+	0.372475i	$0.121491\pi$
$233$			173.573i			0.744949i	−0.928042	+	0.372475i	$0.878509\pi$
$234$		−	38.7136i		−	0.165443i
$235$	−67.8699	+	264.234i	−0.288808	+	1.12440i
$236$		−	707.443i		−	2.99764i
$237$	2.58053			0.0108883
$238$		0			0
$239$	−108.916			−0.455717			−0.227858	−	0.973694i	$-0.573172\pi$
$239$	−108.916			−0.455717			−0.227858	+	0.973694i	$0.573172\pi$
$240$	−24.8466	+	96.7337i	−0.103528	+	0.403057i
$241$			103.710i			0.430333i	0.976577	+	0.215167i	$0.0690294\pi$
$241$			103.710i			0.430333i	−0.976577	+	0.215167i	$0.930971\pi$
$242$		−	405.806i		−	1.67688i
$243$	−15.5885			−0.0641500
$244$		−	12.4747i		−	0.0511259i
$245$		0			0
$246$	−273.674			−1.11249
$247$		−	56.1099i		−	0.227166i
$248$	398.566			1.60712
$249$	23.6825			0.0951105
$250$	−310.471	−	291.715i	−1.24188	−	1.16686i
$251$			231.368i			0.921787i	0.887456	+	0.460893i	$0.152471\pi$
$251$			231.368i			0.921787i	−0.887456	+	0.460893i	$0.847529\pi$
$252$		0			0
$253$		−	31.4230i		−	0.124201i
$254$	−640.622			−2.52213
$255$	−68.3131	+	265.959i	−0.267894	+	1.04298i
$256$	−474.298			−1.85273
$257$	92.3044			0.359161			0.179581	−	0.983743i	$-0.442526\pi$
$257$	92.3044			0.359161			0.179581	+	0.983743i	$0.442526\pi$
$258$	58.6022			0.227140
$259$		0			0
$260$	35.8676	−	139.641i	0.137952	−	0.537081i
$261$	−128.846			−0.493661
$262$	−242.809			−0.926753
$263$		−	150.781i		−	0.573312i	−0.958034	−	0.286656i	$-0.907456\pi$
$263$		−	150.781i		−	0.573312i	0.958034	−	0.286656i	$-0.0925437\pi$
$264$		−	29.6505i		−	0.112312i
$265$	416.223	+	106.909i	1.57065	+	0.403432i
$266$		0			0
$267$		−	220.124i		−	0.824435i
$268$			333.303i			1.24367i
$269$			110.336i			0.410171i	0.978744	+	0.205086i	$0.0657473\pi$
$269$			110.336i			0.410171i	−0.978744	+	0.205086i	$0.934253\pi$
$270$	−85.7620	−	22.0285i	−0.317637	−	0.0815870i
$271$		−	99.2649i		−	0.366291i	−0.983086	−	0.183145i	$-0.941372\pi$
$271$		−	99.2649i		−	0.366291i	0.983086	−	0.183145i	$-0.0586279\pi$
$272$	365.660			1.34434
$273$		0			0
$274$	−129.445			−0.472428
$275$	30.4336	+	16.7384i	0.110667	+	0.0608669i
$276$			298.330i			1.08091i
$277$			389.295i			1.40540i	0.711488	+	0.702699i	$0.248022\pi$
$277$			389.295i			1.40540i	−0.711488	+	0.702699i	$0.751978\pi$
$278$	335.421			1.20655
$279$			97.0403i			0.347815i
$280$		0			0
$281$	307.374			1.09386			0.546928	−	0.837180i	$-0.315797\pi$
$281$	307.374			1.09386			0.546928	+	0.837180i	$0.315797\pi$
$282$			322.084i			1.14214i
$283$	449.080			1.58686			0.793428	−	0.608665i	$-0.208294\pi$
$283$	449.080			1.58686			0.793428	+	0.608665i	$0.208294\pi$
$284$	463.980			1.63373
$285$	−124.300	−	31.9272i	−0.436141	−	0.112025i
$286$			17.9285i			0.0626870i
$287$		0			0
$288$		−	29.9480i		−	0.103986i
$289$	716.344			2.47870
$290$	−708.862	−	182.075i	−2.44435	−	0.627846i
$291$	−206.592			−0.709938
$292$	492.323			1.68604
$293$	73.8439			0.252027			0.126013	−	0.992029i	$-0.459782\pi$
$293$	73.8439			0.252027			0.126013	+	0.992029i	$0.459782\pi$
$294$		0			0
$295$	449.880	+	115.554i	1.52502	+	0.391710i
$296$	103.767			0.350563
$297$	7.21910			0.0243067
$298$		−	608.993i		−	2.04360i
$299$		−	85.6389i		−	0.286418i
$300$	−288.937	−	158.915i	−0.963124	−	0.529716i
$301$		0			0
$302$			823.246i			2.72598i
$303$			207.382i			0.684427i
$304$			170.897i			0.562162i
$305$	7.93297	+	2.03763i	0.0260098	+	0.00668076i
$306$			324.187i			1.05943i
$307$	−162.912			−0.530659			−0.265330	−	0.964158i	$-0.585481\pi$
$307$	−162.912			−0.530659			−0.265330	+	0.964158i	$0.585481\pi$
$308$		0			0
$309$	−108.041			−0.349646
$310$	−137.130	+	533.880i	−0.442356	+	1.72219i
$311$		−	39.6656i		−	0.127542i	−0.997965	−	0.0637711i	$-0.979687\pi$
$311$		−	39.6656i		−	0.127542i	0.997965	−	0.0637711i	$-0.0203128\pi$
$312$		−	80.8083i		−	0.259001i
$313$	148.263			0.473684			0.236842	−	0.971548i	$-0.423888\pi$
$313$	148.263			0.473684			0.236842	+	0.971548i	$0.423888\pi$
$314$			140.840i			0.448536i
$315$		0			0
$316$	11.3459			0.0359049
$317$			51.9340i			0.163830i	0.996639	+	0.0819149i	$0.0261036\pi$
$317$			51.9340i			0.163830i	−0.996639	+	0.0819149i	$0.973896\pi$
$318$	507.349			1.59544
$319$	59.6691			0.187051
$320$	99.7011	−	388.160i	0.311566	−	1.21300i
$321$		−	208.412i		−	0.649259i
$322$		0			0
$323$			469.863i			1.45469i
$324$	−68.5384			−0.211538
$325$	82.9425	+	45.6182i	0.255208	+	0.140364i
$326$	−238.137			−0.730483
$327$	112.687			0.344607
$328$	−571.249			−1.74161
$329$		0			0
$330$	39.7169	+	10.2015i	0.120354	+	0.0309137i
$331$	387.031			1.16928			0.584639	−	0.811293i	$-0.301236\pi$
$331$	387.031			1.16928			0.584639	+	0.811293i	$0.301236\pi$
$332$	104.126			0.313632
$333$			25.2644i			0.0758692i
$334$		−	111.466i		−	0.333730i
$335$	−211.955	−	54.4419i	−0.632702	−	0.162513i
$336$		0			0
$337$		−	574.984i		−	1.70618i	−0.521761	−	0.853092i	$-0.674725\pi$
$337$		−	574.984i		−	1.70618i	0.521761	−	0.853092i	$-0.325275\pi$
$338$		−	527.113i		−	1.55951i
$339$		−	231.165i		−	0.681902i
$340$	−300.355	+	1169.35i	−0.883396	+	3.43927i
$341$		−	44.9399i		−	0.131789i
$342$	−151.514			−0.443023
$343$		0			0
$344$	122.323			0.355589
$345$	−189.716	−	48.7296i	−0.549900	−	0.141245i
$346$		−	84.6879i		−	0.244763i
$347$		−	24.4571i		−	0.0704816i	−0.999379	−	0.0352408i	$-0.988780\pi$
$347$		−	24.4571i		−	0.0704816i	0.999379	−	0.0352408i	$-0.0112198\pi$
$348$	−566.500			−1.62787
$349$			162.352i			0.465193i	0.972573	+	0.232597i	$0.0747222\pi$
$349$			162.352i			0.465193i	−0.972573	+	0.232597i	$0.925278\pi$
$350$		0			0
$351$	19.6747			0.0560532
$352$			13.8691i			0.0394008i
$353$	390.651			1.10666			0.553331	−	0.832962i	$-0.313357\pi$
$353$	390.651			1.10666			0.553331	+	0.832962i	$0.313357\pi$
$354$	548.375			1.54908
$355$	−75.7870	+	295.056i	−0.213484	+	0.831145i
$356$		−	967.828i		−	2.71862i
$357$		0			0
$358$		−	477.565i		−	1.33398i
$359$	336.069			0.936126			0.468063	−	0.883695i	$-0.344952\pi$
$359$	336.069			0.936126			0.468063	+	0.883695i	$0.344952\pi$
$360$	−179.014	−	45.9809i	−0.497262	−	0.127725i
$361$	141.402			0.391695
$362$	957.978			2.64635
$363$	206.235			0.568140
$364$		0			0
$365$	−80.4164	+	313.080i	−0.220319	+	0.857753i
$366$	9.66978			0.0264202
$367$	349.017			0.951000			0.475500	−	0.879716i	$-0.342267\pi$
$367$	349.017			0.951000			0.475500	+	0.879716i	$0.342267\pi$
$368$			260.835i			0.708792i
$369$		−	139.084i		−	0.376921i
$370$	−35.7019	+	138.996i	−0.0964916	+	0.375664i
$371$		0			0
$372$			426.661i			1.14694i
$373$		−	164.385i		−	0.440710i	−0.975420	−	0.220355i	$-0.929278\pi$
$373$		−	164.385i		−	0.440710i	0.975420	−	0.220355i	$-0.0707216\pi$
$374$		−	150.133i		−	0.401424i
$375$	148.253	−	157.785i	0.395341	−	0.420760i
$376$			672.297i			1.78802i
$377$	162.620			0.431353
$378$		0			0
$379$	172.731			0.455755			0.227878	−	0.973690i	$-0.426821\pi$
$379$	172.731			0.455755			0.227878	+	0.973690i	$0.426821\pi$
$380$	−546.515	−	140.376i	−1.43820	−	0.369409i
$381$		−	325.571i		−	0.854518i
$382$		−	348.910i		−	0.913376i
$383$	−222.360			−0.580573			−0.290287	−	0.956940i	$-0.593751\pi$
$383$	−222.360			−0.580573			−0.290287	+	0.956940i	$0.593751\pi$
$384$		−	403.980i		−	1.05203i
$385$		0			0
$386$	9.14070			0.0236806
$387$			29.7823i			0.0769569i
$388$	−908.331			−2.34106
$389$	−485.992			−1.24934			−0.624668	−	0.780890i	$-0.714766\pi$
$389$	−485.992			−1.24934			−0.624668	+	0.780890i	$0.714766\pi$
$390$	108.243	+	27.8028i	0.277546	+	0.0712893i
$391$			717.139i			1.83411i
$392$		0			0
$393$		−	123.398i		−	0.313991i
$394$	−109.192			−0.277137
$395$	−1.85325	+	7.21515i	−0.00469178	+	0.0182662i
$396$	31.7405			0.0801528
$397$	−395.590			−0.996448			−0.498224	−	0.867048i	$-0.666014\pi$
$397$	−395.590			−0.996448			−0.498224	+	0.867048i	$0.666014\pi$
$398$	55.6102			0.139724
$399$		0			0
$400$	−252.623	−	138.942i	−0.631557	−	0.347355i
$401$	378.849			0.944761			0.472380	−	0.881395i	$-0.343395\pi$
$401$	378.849			0.944761			0.472380	+	0.881395i	$0.343395\pi$
$402$	−258.360			−0.642686
$403$		−	122.477i		−	0.303914i
$404$			911.802i			2.25694i
$405$	11.1951	−	43.5852i	0.0276423	−	0.107618i
$406$		0			0
$407$		−	11.7001i		−	0.0287472i
$408$			676.687i			1.65855i
$409$		−	778.837i		−	1.90425i	−0.305713	−	0.952124i	$-0.598895\pi$
$409$		−	778.837i		−	1.90425i	0.305713	−	0.952124i	$-0.401105\pi$
$410$	196.543	−	765.190i	0.479374	−	1.86632i
$411$		−	65.7856i		−	0.160062i
$412$	−475.026			−1.15298
$413$		0			0
$414$	−231.251			−0.558577
$415$	−17.0080	+	66.2161i	−0.0409831	+	0.159557i
$416$			37.7983i			0.0908612i
$417$			170.465i			0.408788i
$418$	70.1669			0.167863
$419$		−	350.942i		−	0.837571i	−0.908085	−	0.418785i	$-0.862456\pi$
$419$		−	350.942i		−	0.837571i	0.908085	−	0.418785i	$-0.137544\pi$
$420$		0			0
$421$	175.760			0.417482			0.208741	−	0.977971i	$-0.433063\pi$
$421$	175.760			0.417482			0.208741	+	0.977971i	$0.433063\pi$
$422$		−	1061.55i		−	2.51551i
$423$	−163.686			−0.386966
$424$	1059.01			2.49766
$425$	−694.559	−	382.006i	−1.63426	−	0.898837i
$426$			359.655i			0.844260i
$427$		0			0
$428$		−	916.334i		−	2.14097i
$429$	−9.11145			−0.0212388
$430$	−42.0862	+	163.851i	−0.0978749	+	0.381050i
$431$	855.322			1.98450			0.992252	−	0.124239i	$-0.0396489\pi$
$431$	855.322			1.98450			0.992252	+	0.124239i	$0.0396489\pi$
$432$	−59.9242			−0.138714
$433$	67.4511			0.155776			0.0778881	−	0.996962i	$-0.475182\pi$
$433$	67.4511			0.155776			0.0778881	+	0.996962i	$0.475182\pi$
$434$		0			0
$435$	92.5327	−	360.251i	0.212719	−	0.828164i
$436$	495.453			1.13636
$437$	−335.166			−0.766970
$438$			381.624i			0.871288i
$439$			280.295i			0.638484i	0.947673	+	0.319242i	$0.103428\pi$
$439$			280.295i			0.638484i	−0.947673	+	0.319242i	$0.896572\pi$
$440$	82.9025	+	21.2940i	0.188415	+	0.0483954i
$441$		0			0
$442$		−	409.166i		−	0.925715i
$443$			462.556i			1.04414i	0.852901	+	0.522072i	$0.174841\pi$
$443$			462.556i			1.04414i	−0.852901	+	0.522072i	$0.825159\pi$
$444$			111.081i			0.250183i
$445$	615.465	+	158.086i	1.38307	+	0.355249i
$446$			380.058i			0.852149i
$447$	309.497			0.692387
$448$		0			0
$449$	−502.561			−1.11929			−0.559644	−	0.828733i	$-0.689062\pi$
$449$	−502.561			−1.11929			−0.559644	+	0.828733i	$0.689062\pi$
$450$	123.183	−	223.970i	0.273740	−	0.497711i
$451$			64.4106i			0.142817i
$452$		−	1016.37i		−	2.24861i
$453$	−418.383			−0.923582
$454$		−	290.622i		−	0.640136i
$455$		0			0
$456$	−316.260			−0.693553
$457$		−	624.598i		−	1.36674i	−0.730074	−	0.683368i	$-0.760515\pi$
$457$		−	624.598i		−	1.36674i	0.730074	−	0.683368i	$-0.239485\pi$
$458$	237.783			0.519176
$459$	−164.755			−0.358944
$460$	−834.130	−	214.251i	−1.81333	−	0.465763i
$461$		−	68.1722i		−	0.147879i	−0.997263	−	0.0739395i	$-0.976443\pi$
$461$		−	68.1722i		−	0.147879i	0.997263	−	0.0739395i	$-0.0235572\pi$
$462$		0			0
$463$		−	231.353i		−	0.499682i	−0.968287	−	0.249841i	$-0.919622\pi$
$463$		−	231.353i		−	0.499682i	0.968287	−	0.249841i	$-0.0803784\pi$
$464$	−495.301			−1.06746
$465$	−271.324	−	69.6911i	−0.583492	−	0.149873i
$466$	−591.560			−1.26944
$467$	492.263			1.05410			0.527048	−	0.849836i	$-0.323299\pi$
$467$	492.263			1.05410			0.527048	+	0.849836i	$0.323299\pi$
$468$	86.5044			0.184838
$469$		0			0
$470$	−900.543	−	231.310i	−1.91605	−	0.492149i
$471$	−71.5765			−0.151967
$472$	1144.64			2.42509
$473$		−	13.7924i		−	0.0291593i
$474$			8.79481i			0.0185544i
$475$	178.536	−	324.613i	0.375866	−	0.683396i
$476$		0			0
$477$			257.841i			0.540546i
$478$		−	371.201i		−	0.776572i
$479$		−	717.478i		−	1.49787i	−0.662646	−	0.748933i	$-0.730566\pi$
$479$		−	717.478i		−	1.49787i	0.662646	−	0.748933i	$-0.269434\pi$
$480$	83.7343	+	21.5076i	0.174446	+	0.0448076i
$481$		−	31.8870i		−	0.0662932i
$482$	−353.458			−0.733316
$483$		0			0
$484$	906.761			1.87347
$485$	148.368	−	577.629i	0.305912	−	1.19099i
$486$		−	53.1275i		−	0.109316i
$487$			400.941i			0.823288i	0.911345	+	0.411644i	$0.135045\pi$
$487$			400.941i			0.823288i	−0.911345	+	0.411644i	$0.864955\pi$
$488$	20.1841			0.0413609
$489$		−	121.024i		−	0.247493i
$490$		0			0
$491$	894.115			1.82101			0.910505	−	0.413499i	$-0.135693\pi$
$491$	894.115			1.82101			0.910505	+	0.413499i	$0.135693\pi$
$492$		−	611.516i		−	1.24292i
$493$	−1361.78			−2.76222
$494$	191.230			0.387106
$495$	−5.18452	+	20.1845i	−0.0104738	+	0.0407769i
$496$			373.037i			0.752090i
$497$		0			0
$498$			80.7132i			0.162075i
$499$	−522.546			−1.04719			−0.523593	−	0.851968i	$-0.675409\pi$
$499$	−522.546			−1.04719			−0.523593	+	0.851968i	$0.675409\pi$
$500$	651.830	−	693.739i	1.30366	−	1.38748i
$501$	56.6482			0.113070
$502$	−788.535			−1.57079
$503$	−849.283			−1.68844			−0.844218	−	0.536000i	$-0.819935\pi$
$503$	−849.283			−1.68844			−0.844218	+	0.536000i	$0.819935\pi$
$504$		0			0
$505$	−579.837	−	148.935i	−1.14819	−	0.294920i
$506$	107.094			0.211647
$507$	267.885			0.528372
$508$		−	1431.45i		−	2.81782i
$509$		−	680.863i		−	1.33765i	−0.743420	−	0.668824i	$-0.766798\pi$
$509$		−	680.863i		−	1.33765i	0.743420	−	0.668824i	$-0.233202\pi$
$510$	−906.423	−	232.820i	−1.77730	−	0.456510i
$511$		0			0
$512$		−	683.520i		−	1.33500i
$513$		−	77.0010i		−	0.150099i
$514$			314.586i			0.612034i
$515$	77.5912	−	302.081i	0.150663	−	0.586564i
$516$			130.945i			0.253769i
$517$	75.8041			0.146623
$518$		0			0
$519$	43.0393			0.0829274
$520$	225.939	+	58.0338i	0.434499	+	0.111604i
$521$			75.6935i			0.145285i	0.997358	+	0.0726425i	$0.0231432\pi$
$521$			75.6935i			0.145285i	−0.997358	+	0.0726425i	$0.976857\pi$
$522$		−	439.123i		−	0.841232i
$523$	178.870			0.342008			0.171004	−	0.985270i	$-0.445299\pi$
$523$	178.870			0.342008			0.171004	+	0.985270i	$0.445299\pi$
$524$		−	542.550i		−	1.03540i
$525$		0			0
$526$	513.882			0.976963
$527$			1025.62i			1.94616i
$528$	27.7513			0.0525592
$529$	17.4459			0.0329791
$530$	−364.362	+	1418.54i	−0.687475	+	2.67650i
$531$			278.690i			0.524840i
$532$		0			0
$533$			175.542i			0.329347i
$534$	750.213			1.40489
$535$	582.719	+	149.675i	1.08919	+	0.279766i
$536$	−539.284			−1.00613
$537$	242.704			0.451962
$538$	−376.040			−0.698959
$539$		0			0
$540$	49.2220	−	191.633i	0.0911518	−	0.354875i
$541$	714.783			1.32123			0.660613	−	0.750727i	$-0.270296\pi$
$541$	714.783			1.32123			0.660613	+	0.750727i	$0.270296\pi$
$542$	338.308			0.624184
$543$			486.855i			0.896602i
$544$		−	316.522i		−	0.581842i
$545$	−80.9278	+	315.071i	−0.148491	+	0.578111i
$546$		0			0
$547$			422.685i			0.772734i	0.922345	+	0.386367i	$0.126270\pi$
$547$			422.685i			0.772734i	−0.922345	+	0.386367i	$0.873730\pi$
$548$		−	289.242i		−	0.527814i
$549$			4.91429i			0.00895135i
$550$	−57.0467	+	103.722i	−0.103721	+	0.188585i
$551$		−	636.448i		−	1.15508i
$552$	−482.699			−0.874454
$553$		0			0
$554$	−1326.77			−2.39489
$555$	−70.6392	−	18.1441i	−0.127278	−	0.0326920i
$556$			749.489i			1.34800i
$557$		−	494.051i		−	0.886986i	−0.896278	−	0.443493i	$-0.853739\pi$
$557$		−	494.051i		−	0.886986i	0.896278	−	0.443493i	$-0.146261\pi$
$558$	−330.726			−0.592699
$559$		−	37.5891i		−	0.0672436i
$560$		0			0
$561$	76.2991			0.136005
$562$			1047.57i			1.86400i
$563$	−242.801			−0.431263			−0.215632	−	0.976475i	$-0.569181\pi$
$563$	−242.801			−0.431263			−0.215632	+	0.976475i	$0.569181\pi$
$564$	−719.686			−1.27604
$565$	646.335	+	166.015i	1.14396	+	0.293832i
$566$			1530.52i			2.70411i
$567$		0			0
$568$			750.721i			1.32169i
$569$	−478.349			−0.840684			−0.420342	−	0.907366i	$-0.638090\pi$
$569$	−478.349			−0.840684			−0.420342	+	0.907366i	$0.638090\pi$
$570$	108.812	−	423.631i	0.190899	−	0.743213i
$571$	108.277			0.189626			0.0948131	−	0.995495i	$-0.469775\pi$
$571$	108.277			0.189626			0.0948131	+	0.995495i	$0.469775\pi$
$572$	−40.0606			−0.0700361
$573$	177.320			0.309459
$574$		0			0
$575$	272.495	−	495.447i	0.473904	−	0.861647i
$576$	240.456			0.417458
$577$	99.3599			0.172201			0.0861004	−	0.996286i	$-0.472559\pi$
$577$	99.3599			0.172201			0.0861004	+	0.996286i	$0.472559\pi$
$578$			2441.40i			4.22387i
$579$			4.64540i			0.00802315i
$580$	406.842	−	1583.93i	0.701452	−	2.73091i
$581$		0			0
$582$		−	704.093i		−	1.20978i
$583$		−	119.407i		−	0.204815i
$584$			796.578i			1.36400i
$585$	−14.1297	+	55.0102i	−0.0241533	+	0.0940345i
$586$			251.670i			0.429471i
$587$	−3.32500			−0.00566440			−0.00283220	−	0.999996i	$-0.500902\pi$
$587$	−3.32500			−0.00566440			−0.00283220	+	0.999996i	$0.500902\pi$
$588$		0			0
$589$	−479.342			−0.813823
$590$	−393.825	+	1533.25i	−0.667499	+	2.59873i
$591$		−	55.4926i		−	0.0938961i
$592$			97.1201i			0.164054i
$593$	−467.783			−0.788841			−0.394421	−	0.918930i	$-0.629055\pi$
$593$	−467.783			−0.788841			−0.394421	+	0.918930i	$0.629055\pi$
$594$			24.6037i			0.0414203i
$595$		0			0
$596$	1360.78			2.28318
$597$			28.2617i			0.0473396i
$598$	291.869			0.488075
$599$	−528.905			−0.882980			−0.441490	−	0.897266i	$-0.645550\pi$
$599$	−528.905			−0.882980			−0.441490	+	0.897266i	$0.645550\pi$
$600$	257.124	−	467.500i	0.428540	−	0.779167i
$601$			490.357i			0.815901i	0.913004	+	0.407951i	$0.133756\pi$
$601$			490.357i			0.815901i	−0.913004	+	0.407951i	$0.866244\pi$
$602$		0			0
$603$		−	131.301i		−	0.217747i
$604$	−1839.52			−3.04556
$605$	−148.111	+	576.631i	−0.244812	+	0.953109i
$606$	−706.784			−1.16631
$607$	99.3369			0.163652			0.0818261	−	0.996647i	$-0.473925\pi$
$607$	99.3369			0.163652			0.0818261	+	0.996647i	$0.473925\pi$
$608$	147.931			0.243308
$609$		0			0
$610$	−6.94452	+	27.0366i	−0.0113845	+	0.0443224i
$611$	206.594			0.338124
$612$	−724.386			−1.18364
$613$		−	286.370i		−	0.467161i	−0.972337	−	0.233581i	$-0.924956\pi$
$613$		−	286.370i		−	0.467161i	0.972337	−	0.233581i	$-0.0750443\pi$
$614$		−	555.227i		−	0.904279i
$615$	388.878	+	99.8855i	0.632321	+	0.162415i
$616$		0			0
$617$			335.855i			0.544336i	0.962250	+	0.272168i	$0.0877406\pi$
$617$			335.855i			0.544336i	−0.962250	+	0.272168i	$0.912259\pi$
$618$		−	368.217i		−	0.595820i
$619$		−	622.672i		−	1.00593i	−0.864306	−	0.502966i	$-0.832242\pi$
$619$		−	622.672i		−	1.00593i	0.864306	−	0.502966i	$-0.167758\pi$
$620$	−1192.94	−	306.414i	−1.92410	−	0.494215i
$621$		−	117.524i		−	0.189250i
$622$	135.186			0.217340
$623$		0			0
$624$	75.6322			0.121205
$625$	334.695	+	527.830i	0.535511	+	0.844528i
$626$			505.300i			0.807189i
$627$			35.6596i			0.0568733i
$628$	−314.703			−0.501120
$629$			267.021i			0.424517i
$630$		0			0
$631$	−342.555			−0.542876			−0.271438	−	0.962456i	$-0.587499\pi$
$631$	−342.555			−0.542876			−0.271438	+	0.962456i	$0.587499\pi$
$632$			18.3577i			0.0290470i
$633$	539.489			0.852274
$634$	−176.998			−0.279177
$635$	910.294	+	233.814i	1.43353	+	0.368212i
$636$			1133.66i			1.78248i
$637$		0			0
$638$			203.360i			0.318747i
$639$	−182.780			−0.286041
$640$	1129.52	+	290.125i	1.76488	+	0.453320i
$641$	−972.615			−1.51734			−0.758670	−	0.651475i	$-0.774150\pi$
$641$	−972.615			−1.51734			−0.758670	+	0.651475i	$0.774150\pi$
$642$	710.296			1.10638
$643$	−986.446			−1.53413			−0.767065	−	0.641569i	$-0.778284\pi$
$643$	−986.446			−1.53413			−0.767065	+	0.641569i	$0.778284\pi$
$644$		0			0
$645$	−83.2711	−	21.3887i	−0.129102	−	0.0331607i
$646$	−1601.36			−2.47888
$647$	−80.9953			−0.125186			−0.0625930	−	0.998039i	$-0.519937\pi$
$647$	−80.9953			−0.125186			−0.0625930	+	0.998039i	$0.519937\pi$
$648$		−	110.895i		−	0.171134i
$649$		−	129.063i		−	0.198864i
$650$	−155.473	+	282.679i	−0.239189	+	0.434891i
$651$		0			0
$652$		−	532.111i		−	0.816121i
$653$		−	379.966i		−	0.581877i	−0.956742	−	0.290938i	$-0.906033\pi$
$653$		−	379.966i		−	0.581877i	0.956742	−	0.290938i	$-0.0939675\pi$
$654$			384.051i			0.587234i
$655$	345.021	+	88.6206i	0.526749	+	0.135299i
$656$		−	534.659i		−	0.815028i
$657$	−193.946			−0.295199
$658$		0			0
$659$	409.417			0.621269			0.310635	−	0.950529i	$-0.399458\pi$
$659$	409.417			0.621269			0.310635	+	0.950529i	$0.399458\pi$
$660$	−22.7950	+	88.7462i	−0.0345378	+	0.134464i
$661$			453.064i			0.685421i	0.939441	+	0.342711i	$0.111345\pi$
$661$			453.064i			0.685421i	−0.939441	+	0.342711i	$0.888655\pi$
$662$			1319.05i			1.99253i
$663$	207.943			0.313639
$664$			168.476i			0.253728i
$665$		0			0
$666$	−86.1046			−0.129286
$667$		−	971.391i		−	1.45636i
$668$	249.067			0.372855
$669$	−193.150			−0.288714
$670$	185.545	−	722.372i	0.276933	−	1.07817i
$671$		−	2.27584i		−	0.00339171i
$672$		0			0
$673$			1044.13i			1.55145i	0.631071	+	0.775725i	$0.282616\pi$
$673$			1044.13i			1.55145i	−0.631071	+	0.775725i	$0.717384\pi$
$674$	1959.62			2.90745
$675$	113.824	+	62.6029i	0.168628	+	0.0927450i
$676$	1177.82			1.74234
$677$	−1322.03			−1.95277			−0.976386	−	0.216034i	$-0.930688\pi$
$677$	−1322.03			−1.95277			−0.976386	+	0.216034i	$0.930688\pi$
$678$	787.841			1.16201
$679$		0			0
$680$	−1892.01	−	485.974i	−2.78237	−	0.714668i
$681$	147.697			0.216883
$682$	153.161			0.224576
$683$			825.663i			1.20888i	0.796652	+	0.604438i	$0.206602\pi$
$683$			825.663i			1.20888i	−0.796652	+	0.604438i	$0.793398\pi$
$684$		−	338.553i		−	0.494961i
$685$	183.936	+	47.2450i	0.268520	+	0.0689708i
$686$		0			0
$687$			120.844i			0.175901i
$688$			114.487i			0.166406i
$689$		−	325.428i		−	0.472320i
$690$	166.077	−	646.576i	0.240691	−	0.937067i
$691$		−	253.870i		−	0.367394i	−0.982983	−	0.183697i	$-0.941193\pi$
$691$		−	253.870i		−	0.367394i	0.982983	−	0.183697i	$-0.0588066\pi$
$692$	189.233			0.273458
$693$		0			0
$694$	83.3531			0.120105
$695$	−476.618	−	122.422i	−0.685782	−	0.176147i
$696$		−	916.598i		−	1.31695i
$697$		−	1469.99i		−	2.10902i
$698$	−553.319			−0.792720
$699$		−	300.637i		−	0.430097i
$700$		0			0
$701$	304.585			0.434500			0.217250	−	0.976116i	$-0.430291\pi$
$701$	304.585			0.434500			0.217250	+	0.976116i	$0.430291\pi$
$702$			67.0539i			0.0955184i
$703$	−124.797			−0.177520
$704$	−111.356			−0.158177
$705$	117.554	−	457.666i	0.166744	−	0.649171i
$706$			1331.39i			1.88582i
$707$		0			0
$708$			1225.33i			1.73069i
$709$	46.9749			0.0662552			0.0331276	−	0.999451i	$-0.489453\pi$
$709$	46.9749			0.0662552			0.0331276	+	0.999451i	$0.489453\pi$
$710$	−1005.59	−	258.292i	−1.41633	−	0.363792i
$711$	−4.46962			−0.00628638
$712$	1565.95			2.19936
$713$	−731.605			−1.02609
$714$		0			0
$715$	6.54354	−	25.4755i	0.00915180	−	0.0356301i
$716$	1067.10			1.49037
$717$	188.649			0.263108
$718$			1145.37i			1.59522i
$719$			319.584i			0.444484i	0.974992	+	0.222242i	$0.0713374\pi$
$719$			319.584i			0.444484i	−0.974992	+	0.222242i	$0.928663\pi$
$720$	43.0356	−	167.548i	0.0597717	−	0.232705i
$721$		0			0
$722$			481.916i			0.667474i
$723$		−	179.631i		−	0.248453i
$724$			2140.57i			2.95659i
$725$	940.806	+	517.441i	1.29766	+	0.713712i
$726$			702.876i			0.968149i
$727$	1192.80			1.64071			0.820354	−	0.571855i	$-0.193776\pi$
$727$	1192.80			1.64071			0.820354	+	0.571855i	$0.193776\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$	−1067.02	−	274.070i	−1.46167	−	0.375438i
$731$			314.771i			0.430603i
$732$			21.6068i			0.0295176i
$733$	−35.3288			−0.0481975			−0.0240988	−	0.999710i	$-0.507672\pi$
$733$	−35.3288			−0.0481975			−0.0240988	+	0.999710i	$0.507672\pi$
$734$			1189.50i			1.62057i
$735$		0			0
$736$	225.783			0.306771
$737$			60.8063i			0.0825052i
$738$	474.017			0.642299
$739$	−785.334			−1.06270			−0.531349	−	0.847153i	$-0.678315\pi$
$739$	−785.334			−1.06270			−0.531349	+	0.847153i	$0.678315\pi$
$740$	−310.582	−	79.7748i	−0.419705	−	0.107804i
$741$			97.1853i			0.131154i
$742$		0			0
$743$			419.098i			0.564062i	0.959405	+	0.282031i	$0.0910082\pi$
$743$			419.098i			0.564062i	−0.959405	+	0.282031i	$0.908992\pi$
$744$	−690.337			−0.927872
$745$	−222.270	+	865.351i	−0.298350	+	1.16154i
$746$	560.245			0.750999
$747$	−41.0193			−0.0549121
$748$	335.467			0.448485
$749$		0			0
$750$	537.752	+	505.266i	0.717002	+	0.673688i
$751$	−119.704			−0.159393			−0.0796963	−	0.996819i	$-0.525395\pi$
$751$	−119.704			−0.159393			−0.0796963	+	0.996819i	$0.525395\pi$
$752$	−629.234			−0.836747
$753$		−	400.742i		−	0.532194i
$754$			554.231i			0.735054i
$755$	300.469	−	1169.79i	0.397972	−	1.54940i
$756$		0			0
$757$		−	995.970i		−	1.31568i	−0.753157	−	0.657840i	$-0.771470\pi$
$757$		−	995.970i		−	1.31568i	0.753157	−	0.657840i	$-0.228530\pi$
$758$			588.691i			0.776637i
$759$			54.4262i			0.0717077i
$760$	227.128	−	884.261i	0.298852	−	1.16350i
$761$			273.721i			0.359686i	0.983695	+	0.179843i	$0.0575591\pi$
$761$			273.721i			0.359686i	−0.983695	+	0.179843i	$0.942441\pi$
$762$	1109.59			1.45615
$763$		0			0
$764$	779.629			1.02046
$765$	118.322	−	460.654i	0.154669	−	0.602162i
$766$		−	757.831i		−	0.989336i
$767$		−	351.743i		−	0.458596i
$768$	821.508			1.06967
$769$		−	694.742i		−	0.903435i	−0.892161	−	0.451718i	$-0.850811\pi$
$769$		−	694.742i		−	0.903435i	0.892161	−	0.451718i	$-0.149189\pi$
$770$		0			0
$771$	−159.876			−0.207362
$772$			20.4246i			0.0264568i
$773$	−621.693			−0.804260			−0.402130	−	0.915583i	$-0.631730\pi$
$773$	−621.693			−0.804260			−0.402130	+	0.915583i	$0.631730\pi$
$774$	−101.502			−0.131140
$775$	389.712	−	708.569i	0.502854	−	0.914283i
$776$		−	1469.68i		−	1.89392i
$777$		0			0
$778$		−	1656.32i		−	2.12895i
$779$	687.021			0.881927
$780$	−62.1246	+	241.865i	−0.0796469	+	0.310084i
$781$	84.6466			0.108382
$782$	−2444.10			−3.12545
$783$	223.167			0.285016
$784$		0			0
$785$	51.4039	−	200.127i	0.0654827	−	0.254939i
$786$	420.558			0.535061
$787$	−23.3233			−0.0296357			−0.0148179	−	0.999890i	$-0.504717\pi$
$787$	−23.3233			−0.0296357			−0.0148179	+	0.999890i	$0.504717\pi$
$788$		−	243.987i		−	0.309628i
$789$			261.161i			0.331002i
$790$	−24.5902	−	6.31614i	−0.0311268	−	0.00799511i
$791$		0			0
$792$			51.3561i			0.0648436i
$793$		−	6.20247i		−	0.00782153i
$794$		−	1348.22i		−	1.69801i
$795$	−720.920	−	185.173i	−0.906818	−	0.232921i
$796$			124.259i			0.156105i
$797$	−140.581			−0.176388			−0.0881941	−	0.996103i	$-0.528110\pi$
$797$	−140.581			−0.176388			−0.0881941	+	0.996103i	$0.528110\pi$
$798$		0			0
$799$	−1730.01			−2.16522
$800$	−120.270	+	218.674i	−0.150338	+	0.273343i
$801$			381.266i			0.475988i
$802$			1291.17i			1.60994i
$803$	89.8172			0.111852
$804$		−	577.297i		−	0.718031i
$805$		0			0
$806$	417.420			0.517890
$807$		−	191.108i		−	0.236812i
$808$	−1475.30			−1.82586
$809$	−185.799			−0.229665			−0.114832	−	0.993385i	$-0.536633\pi$
$809$	−185.799			−0.229665			−0.114832	+	0.993385i	$0.536633\pi$
$810$	148.544	+	38.1544i	0.183388	+	0.0471043i
$811$		−	683.280i		−	0.842516i	−0.906941	−	0.421258i	$-0.861589\pi$
$811$		−	683.280i		−	0.842516i	0.906941	−	0.421258i	$-0.138411\pi$
$812$		0			0
$813$			171.932i			0.211478i
$814$	39.8755			0.0489871
$815$	338.382	+	86.9155i	0.415193	+	0.106645i
$816$	−633.343			−0.776155
$817$	−147.113			−0.180065
$818$	2654.38			3.24496
$819$		0			0
$820$	1709.79	+	439.171i	2.08511	+	0.535574i
$821$	−765.524			−0.932429			−0.466214	−	0.884672i	$-0.654382\pi$
$821$	−765.524			−0.932429			−0.466214	+	0.884672i	$0.654382\pi$
$822$	224.206			0.272757
$823$		−	1543.68i		−	1.87567i	−0.347078	−	0.937836i	$-0.612826\pi$
$823$		−	1543.68i		−	1.87567i	0.347078	−	0.937836i	$-0.387174\pi$
$824$		−	768.593i		−	0.932758i
$825$	−52.7125	−	28.9917i	−0.0638939	−	0.0351415i
$826$		0			0
$827$		−	794.814i		−	0.961081i	−0.876973	−	0.480540i	$-0.840441\pi$
$827$		−	794.814i		−	0.961081i	0.876973	−	0.480540i	$-0.159559\pi$
$828$		−	516.724i		−	0.624062i
$829$			792.208i			0.955619i	0.878464	+	0.477809i	$0.158569\pi$
$829$			792.208i			0.955619i	−0.878464	+	0.477809i	$0.841431\pi$
$830$	−225.673	−	57.9655i	−0.271896	−	0.0698380i
$831$		−	674.279i		−	0.811407i
$832$	−303.487			−0.364768
$833$		0			0
$834$	−580.967			−0.696603
$835$	−40.6829	+	158.388i	−0.0487220	+	0.189686i
$836$			156.786i			0.187543i
$837$		−	168.079i		−	0.200811i
$838$	1196.06			1.42728
$839$			1167.54i			1.39159i	0.718241	+	0.695795i	$0.244948\pi$
$839$			1167.54i			1.39159i	−0.718241	+	0.695795i	$0.755052\pi$
$840$		0			0
$841$	1003.58			1.19331
$842$			599.013i			0.711417i
$843$	−532.387			−0.631538
$844$	2371.99			2.81042
$845$	−192.386	+	749.003i	−0.227676	+	0.886394i
$846$		−	557.865i		−	0.659415i
$847$		0			0
$848$			991.176i			1.16884i
$849$	−777.829			−0.916171
$850$	1301.93	−	2367.15i	1.53168	−	2.78488i
$851$	−190.473			−0.223823
$852$	−803.638			−0.943237
$853$	−1146.86			−1.34450			−0.672251	−	0.740324i	$-0.734672\pi$
$853$	−1146.86			−1.34450			−0.672251	+	0.740324i	$0.734672\pi$
$854$		0			0
$855$	215.294	+	55.2995i	0.251806	+	0.0646778i
$856$	1482.63			1.73204
$857$	−214.914			−0.250775			−0.125387	−	0.992108i	$-0.540017\pi$
$857$	−214.914			−0.250775			−0.125387	+	0.992108i	$0.540017\pi$
$858$		−	31.0530i		−	0.0361923i
$859$			1139.27i			1.32627i	0.748499	+	0.663136i	$0.230775\pi$
$859$			1139.27i			1.32627i	−0.748499	+	0.663136i	$0.769225\pi$
$860$	−366.121	−	94.0404i	−0.425722	−	0.109349i
$861$		0			0
$862$			2915.05i			3.38173i
$863$			544.040i			0.630405i	0.949024	+	0.315203i	$0.102073\pi$
$863$			544.040i			0.630405i	−0.949024	+	0.315203i	$0.897927\pi$
$864$			51.8714i			0.0600364i
$865$	−30.9094	+	120.338i	−0.0357334	+	0.139119i
$866$			229.882i			0.265453i
$867$	−1240.74			−1.43108
$868$		0			0
$869$	2.06990			0.00238194
$870$	1227.78	+	315.364i	1.41125	+	0.362487i
$871$			165.719i			0.190263i
$872$			801.644i			0.919316i
$873$	357.828			0.409883
$874$		−	1142.29i		−	1.30697i
$875$		0			0
$876$	−852.728			−0.973433
$877$		−	526.622i		−	0.600481i	−0.953863	−	0.300241i	$-0.902933\pi$
$877$		−	526.622i		−	0.600481i	0.953863	−	0.300241i	$-0.0970670\pi$
$878$	−955.282			−1.08802
$879$	−127.901			−0.145508
$880$	−19.9300	+	77.5923i	−0.0226478	+	0.0881730i
$881$		−	121.399i		−	0.137797i	−0.997624	−	0.0688983i	$-0.978052\pi$
$881$		−	121.399i		−	0.137797i	0.997624	−	0.0688983i	$-0.0219484\pi$
$882$		0			0
$883$		−	243.586i		−	0.275862i	−0.990442	−	0.137931i	$-0.955955\pi$
$883$		−	243.586i		−	0.275862i	0.990442	−	0.137931i	$-0.0440453\pi$
$884$	914.269			1.03424
$885$	−779.215	−	200.146i	−0.880469	−	0.226154i
$886$	−1576.45			−1.77929
$887$	1273.89			1.43618			0.718092	−	0.695948i	$-0.245016\pi$
$887$	1273.89			1.43618			0.718092	+	0.695948i	$0.245016\pi$
$888$	−179.729			−0.202398
$889$		0			0
$890$	−538.778	+	2097.59i	−0.605368	+	2.35684i
$891$	−12.5039			−0.0140335
$892$	−849.229			−0.952051
$893$		−	808.548i		−	0.905429i
$894$			1054.81i			1.17987i
$895$	−174.302	+	678.597i	−0.194751	+	0.758209i
$896$		0			0
$897$			148.331i			0.165363i
$898$		−	1712.79i		−	1.90734i
$899$		−	1389.25i		−	1.54532i
$900$	500.454	+	275.249i	0.556060	+	0.305832i
$901$			2725.13i			3.02456i
$902$	−219.520			−0.243370
$903$		0			0
$904$	1644.49			1.81913
$905$	−1361.24	−	349.643i	−1.50414	−	0.386346i
$906$		−	1425.90i		−	1.57385i
$907$			566.444i			0.624525i	0.949996	+	0.312262i	$0.101087\pi$
$907$			566.444i			0.624525i	−0.949996	+	0.312262i	$0.898913\pi$
$908$	649.386			0.715182
$909$		−	359.195i		−	0.395154i
$910$		0			0
$911$	−1468.26			−1.61170			−0.805850	−	0.592120i	$-0.798291\pi$
$911$	−1468.26			−1.61170			−0.805850	+	0.592120i	$0.798291\pi$
$912$		−	296.003i		−	0.324564i
$913$	18.9963			0.0208064
$914$	2128.71			2.32901
$915$	−13.7403	−	3.52928i	−0.0150167	−	0.00385714i
$916$			531.318i			0.580042i
$917$		0			0
$918$		−	561.508i		−	0.611664i
$919$	1028.43			1.11907			0.559535	−	0.828807i	$-0.310980\pi$
$919$	1028.43			1.11907			0.559535	+	0.828807i	$0.310980\pi$
$920$	346.658	−	1349.62i	0.376803	−	1.46698i
$921$	282.172			0.306376
$922$	232.340			0.251996
$923$	230.693			0.249938
$924$		0			0
$925$	101.461	−	184.476i	0.109688	−	0.199434i
$926$	788.482			0.851492
$927$	187.132			0.201868
$928$			428.741i			0.462005i
$929$		−	636.285i		−	0.684914i	−0.939533	−	0.342457i	$-0.888741\pi$
$929$		−	636.285i		−	0.684914i	0.939533	−	0.342457i	$-0.111259\pi$
$930$	237.517	−	924.708i	0.255394	−	0.994309i
$931$		0			0
$932$		−	1321.82i		−	1.41827i
$933$			68.7029i			0.0736365i
$934$			1677.70i			1.79625i
$935$	−54.7955	+	213.332i	−0.0586048	+	0.228162i
$936$			139.964i			0.149534i
$937$	1396.05			1.48991			0.744956	−	0.667113i	$-0.232470\pi$
$937$	1396.05			1.48991			0.744956	+	0.667113i	$0.232470\pi$
$938$		0			0
$939$	−256.799			−0.273482
$940$	516.855	−	2012.24i	0.549846	−	2.14068i
$941$			386.686i			0.410931i	0.978664	+	0.205466i	$0.0658709\pi$
$941$			386.686i			0.410931i	−0.978664	+	0.205466i	$0.934129\pi$
$942$		−	243.942i		−	0.258962i
$943$	1048.58			1.11196
$944$			1071.32i			1.13488i
$945$		0			0
$946$	47.0062			0.0496894
$947$			576.403i			0.608662i	0.952566	+	0.304331i	$0.0984329\pi$
$947$			576.403i			0.608662i	−0.952566	+	0.304331i	$0.901567\pi$
$948$	−19.6517			−0.0207297
$949$	244.785			0.257939
$950$	1106.32	+	608.476i	1.16455	+	0.640501i
$951$		−	89.9524i		−	0.0945872i
$952$		0			0
$953$		−	1080.91i		−	1.13421i	−0.823644	−	0.567107i	$-0.808063\pi$
$953$		−	1080.91i		−	1.13421i	0.823644	−	0.567107i	$-0.191937\pi$
$954$	−878.755			−0.921127
$955$	−127.345	+	495.785i	−0.133346	+	0.519146i
$956$	829.438			0.867613
$957$	−103.350			−0.107994
$958$	2445.26			2.55246
$959$		0			0
$960$	−172.687	+	672.313i	−0.179883	+	0.700326i
$961$	−85.3127			−0.0887750
$962$	108.675			0.112968
$963$			360.980i			0.374850i
$964$		−	789.793i		−	0.819287i
$965$	−12.9885	−	3.33617i	−0.0134596	−	0.00345718i
$966$		0			0
$967$			785.695i			0.812508i	0.913760	+	0.406254i	$0.133165\pi$
$967$			785.695i			0.812508i	−0.913760	+	0.406254i	$0.866835\pi$
$968$			1467.14i			1.51564i
$969$		−	813.827i		−	0.839863i
$970$	1968.64	+	505.656i	2.02952	+	0.521295i
$971$		−	925.267i		−	0.952901i	−0.879201	−	0.476450i	$-0.841923\pi$
$971$		−	925.267i		−	0.952901i	0.879201	−	0.476450i	$-0.158077\pi$
$972$	118.712			0.122132
$973$		0			0
$974$	−1366.46			−1.40294
$975$	−143.661	−	79.0130i	−0.147344	−	0.0810390i
$976$			18.8912i			0.0193558i
$977$			321.667i			0.329240i	0.986357	+	0.164620i	$0.0526397\pi$
$977$			321.667i			0.329240i	−0.986357	+	0.164620i	$0.947360\pi$
$978$	412.466			0.421744
$979$		−	176.567i		−	0.180354i
$980$		0			0
$981$	−195.179			−0.198959
$982$			3047.26i			3.10312i
$983$	1426.09			1.45076			0.725379	−	0.688350i	$-0.241665\pi$
$983$	1426.09			1.45076			0.725379	+	0.688350i	$0.241665\pi$
$984$	989.433			1.00552
$985$	155.157	+	39.8530i	0.157520	+	0.0404599i
$986$		−	4641.11i		−	4.70701i
$987$		0			0
$988$			427.298i			0.432488i
$989$	−224.534			−0.227032
$990$	−68.7916	−	17.6695i	−0.0694865	−	0.0178480i
$991$	1709.84			1.72537			0.862683	−	0.505744i	$-0.168782\pi$
$991$	1709.84			1.72537			0.862683	+	0.505744i	$0.168782\pi$
$992$	322.907			0.325511
$993$	−670.358			−0.675083
$994$		0			0
$995$	−79.0195	−	20.2966i	−0.0794166	−	0.0203986i
$996$	−180.351			−0.181076
$997$	−1374.11			−1.37824			−0.689122	−	0.724645i	$-0.742004\pi$
$997$	−1374.11			−1.37824			−0.689122	+	0.724645i	$0.742004\pi$
$998$		−	1780.91i		−	1.78448i
$999$		−	43.7593i		−	0.0438031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.3.e.a.244.14		32
5.4	even	2	inner	735.3.e.a.244.5		32
7.2	even	3		105.3.r.a.94.15	yes	32
7.3	odd	6		105.3.r.a.19.2	✓	32
7.6	odd	2	inner	735.3.e.a.244.6		32
21.2	odd	6		315.3.bi.e.199.2		32
21.17	even	6		315.3.bi.e.19.15		32
35.2	odd	12		525.3.o.p.451.8		16
35.3	even	12		525.3.o.q.376.1		16
35.9	even	6		105.3.r.a.94.2	yes	32
35.17	even	12		525.3.o.p.376.8		16
35.23	odd	12		525.3.o.q.451.1		16
35.24	odd	6		105.3.r.a.19.15	yes	32
35.34	odd	2	inner	735.3.e.a.244.13		32
105.44	odd	6		315.3.bi.e.199.15		32
105.59	even	6		315.3.bi.e.19.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.2	✓	32	7.3	odd	6
105.3.r.a.19.15	yes	32	35.24	odd	6
105.3.r.a.94.2	yes	32	35.9	even	6
105.3.r.a.94.15	yes	32	7.2	even	3
315.3.bi.e.19.2		32	105.59	even	6
315.3.bi.e.19.15		32	21.17	even	6
315.3.bi.e.199.2		32	21.2	odd	6
315.3.bi.e.199.15		32	105.44	odd	6
525.3.o.p.376.8		16	35.17	even	12
525.3.o.p.451.8		16	35.2	odd	12
525.3.o.q.376.1		16	35.3	even	12
525.3.o.q.451.1		16	35.23	odd	12
735.3.e.a.244.5		32	5.4	even	2	inner
735.3.e.a.244.6		32	7.6	odd	2	inner
735.3.e.a.244.13		32	35.34	odd	2	inner
735.3.e.a.244.14		32	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+3.40813i q^{2} -1.73205 q^{3} -7.61537 q^{4} +(1.24390 - 4.84280i) q^{5} -5.90306i q^{6} -12.3217i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+3.40813i q^{2} -1.73205 q^{3} -7.61537 q^{4} +(1.24390 - 4.84280i) q^{5} -5.90306i q^{6} -12.3217i q^{8} +3.00000 q^{9} +(16.5049 + 4.23938i) q^{10} -1.38932 q^{11} +13.1902 q^{12} -3.78639 q^{13} +(-2.15450 + 8.38798i) q^{15} +11.5324 q^{16} +31.7072 q^{17} +10.2244i q^{18} +14.8188i q^{19} +(-9.47278 + 36.8797i) q^{20} -4.73498i q^{22} +22.6176i q^{23} +21.3418i q^{24} +(-21.9054 - 12.0479i) q^{25} -12.9045i q^{26} -5.19615 q^{27} -42.9485 q^{29} +(-28.5873 - 7.34283i) q^{30} +32.3468i q^{31} -9.98266i q^{32} +2.40637 q^{33} +108.062i q^{34} -22.8461 q^{36} +8.42148i q^{37} -50.5046 q^{38} +6.55822 q^{39} +(-59.6714 - 15.3270i) q^{40} -46.3613i q^{41} +9.92743i q^{43} +10.5802 q^{44} +(3.73170 - 14.5284i) q^{45} -77.0837 q^{46} -54.5621 q^{47} -19.9747 q^{48} +(41.0610 - 74.6566i) q^{50} -54.9184 q^{51} +28.8348 q^{52} +85.9468i q^{53} -17.7092i q^{54} +(-1.72817 + 6.72818i) q^{55} -25.6670i q^{57} -146.374i q^{58} +92.8967i q^{59} +(16.4073 - 63.8776i) q^{60} +1.63810i q^{61} -110.242 q^{62} +80.1519 q^{64} +(-4.70990 + 18.3367i) q^{65} +8.20122i q^{66} -43.7671i q^{67} -241.462 q^{68} -39.1748i q^{69} -60.9268 q^{71} -36.9650i q^{72} -64.6485 q^{73} -28.7015 q^{74} +(37.9413 + 20.8676i) q^{75} -112.851i q^{76} +22.3513i q^{78} -1.48987 q^{79} +(14.3452 - 55.8492i) q^{80} +9.00000 q^{81} +158.006 q^{82} -13.6731 q^{83} +(39.4406 - 153.551i) q^{85} -33.8340 q^{86} +74.3891 q^{87} +17.1187i q^{88} +127.089i q^{89} +(49.5147 + 12.7181i) q^{90} -172.241i q^{92} -56.0262i q^{93} -185.955i q^{94} +(71.7647 + 18.4332i) q^{95} +17.2905i q^{96} +119.276 q^{97} -4.16795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 96 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more