LMFDB - Embedded newform 294.4.d.a.293.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,4,Mod(293,294)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("294.293"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 $ x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 - 24x^11 + 714x^10 - 1940x^9 - 2834x^8 - 17460x^7 + 57834x^6 - 17496x^5 + 59049x^4 - 118098x^3 - 531441x^2 - 9565938x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{8}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			293.3
Root			$2.99617 + 0.151487i$ of defining polynomial
Character	$\chi$	$=$	294.293
Dual form			294.4.d.a.293.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000i q^{2} +(-2.36753 + 4.62545i) q^{3} -4.00000 q^{4} +4.49068 q^{5} +(9.25090 + 4.73506i) q^{6} +8.00000i q^{8} +(-15.7896 - 21.9018i) q^{9} -8.98135i q^{10} -23.4214i q^{11} +(9.47012 - 18.5018i) q^{12} +5.91384i q^{13} +(-10.6318 + 20.7714i) q^{15} +16.0000 q^{16} +116.084 q^{17} +(-43.8036 + 31.5792i) q^{18} -9.26685i q^{19} -17.9627 q^{20} -46.8428 q^{22} +124.386i q^{23} +(-37.0036 - 18.9402i) q^{24} -104.834 q^{25} +11.8277 q^{26} +(138.688 - 21.1808i) q^{27} +207.807i q^{29} +(41.5428 + 21.2636i) q^{30} +141.756i q^{31} -32.0000i q^{32} +(108.335 + 55.4509i) q^{33} -232.167i q^{34} +(63.1584 + 87.6072i) q^{36} +299.675 q^{37} -18.5337 q^{38} +(-27.3542 - 14.0012i) q^{39} +35.9254i q^{40} +508.379 q^{41} +391.127 q^{43} +93.6856i q^{44} +(-70.9060 - 98.3539i) q^{45} +248.771 q^{46} -80.5151 q^{47} +(-37.8805 + 74.0072i) q^{48} +209.668i q^{50} +(-274.832 + 536.939i) q^{51} -23.6554i q^{52} -298.718i q^{53} +(-42.3617 - 277.376i) q^{54} -105.178i q^{55} +(42.8634 + 21.9396i) q^{57} +415.614 q^{58} +204.552 q^{59} +(42.5273 - 83.0856i) q^{60} +627.877i q^{61} +283.512 q^{62} -64.0000 q^{64} +26.5572i q^{65} +(110.902 - 216.669i) q^{66} -102.779 q^{67} -464.335 q^{68} +(-575.340 - 294.487i) q^{69} +46.9785i q^{71} +(175.214 - 126.317i) q^{72} -263.482i q^{73} -599.351i q^{74} +(248.197 - 484.904i) q^{75} +37.0674i q^{76} +(-28.0024 + 54.7084i) q^{78} -1067.27 q^{79} +71.8508 q^{80} +(-230.377 + 691.641i) q^{81} -1016.76i q^{82} +270.436 q^{83} +521.294 q^{85} -782.254i q^{86} +(-961.201 - 491.990i) q^{87} +187.371 q^{88} +887.530 q^{89} +(-196.708 + 141.812i) q^{90} -497.543i q^{92} +(-655.685 - 335.612i) q^{93} +161.030i q^{94} -41.6144i q^{95} +(148.014 + 75.7610i) q^{96} +219.564i q^{97} +(-512.971 + 369.815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 64 q^{4} - 36 q^{9} + 256 q^{16} + 96 q^{18} + 24 q^{22} + 388 q^{25} - 720 q^{30} + 144 q^{36} + 1924 q^{37} - 1188 q^{39} + 1732 q^{43} - 336 q^{46} - 3276 q^{51} - 2664 q^{57} + 1560 q^{58} - 1024 q^{64}+ \cdots - 4284 q^{99}+O(q^{100}) $ 16 * q - 64 * q^4 - 36 * q^9 + 256 * q^16 + 96 * q^18 + 24 * q^22 + 388 * q^25 - 720 * q^30 + 144 * q^36 + 1924 * q^37 - 1188 * q^39 + 1732 * q^43 - 336 * q^46 - 3276 * q^51 - 2664 * q^57 + 1560 * q^58 - 1024 * q^64 + 1412 * q^67 - 384 * q^72 + 2832 * q^78 + 5312 * q^79 - 252 * q^81 + 5232 * q^85 - 96 * q^88 - 4032 * q^93 - 4284 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$	−2.36753	+	4.62545i	−0.455632	+	0.890168i
$3$	−2.36753	+	4.62545i	−0.455632	+	0.890168i
$4$	−4.00000			−0.500000
$5$	4.49068			0.401658			0.200829	−	0.979626i	$-0.435636\pi$
$5$	4.49068			0.401658			0.200829	+	0.979626i	$0.435636\pi$
$6$	9.25090	+	4.73506i	0.629444	+	0.322180i
$7$		0			0
$7$		0			0
$8$			8.00000i			0.353553i
$9$	−15.7896	−	21.9018i	−0.584800	−	0.811178i
$10$		−	8.98135i		−	0.284015i
$11$		−	23.4214i		−	0.641984i	−0.947082	−	0.320992i	$-0.895984\pi$
$11$		−	23.4214i		−	0.641984i	0.947082	−	0.320992i	$-0.104016\pi$
$12$	9.47012	−	18.5018i	0.227816	−	0.445084i
$13$			5.91384i			0.126170i	0.998008	+	0.0630848i	$0.0200939\pi$
$13$			5.91384i			0.126170i	−0.998008	+	0.0630848i	$0.979906\pi$
$14$		0			0
$15$	−10.6318	+	20.7714i	−0.183008	+	0.357544i
$16$	16.0000			0.250000
$17$	116.084			1.65614			0.828071	−	0.560623i	$-0.189438\pi$
$17$	116.084			1.65614			0.828071	+	0.560623i	$0.189438\pi$
$18$	−43.8036	+	31.5792i	−0.573589	+	0.413516i
$19$		−	9.26685i		−	0.111893i	−0.998434	−	0.0559464i	$-0.982182\pi$
$19$		−	9.26685i		−	0.111893i	0.998434	−	0.0559464i	$-0.0178176\pi$
$20$	−17.9627			−0.200829
$21$		0			0
$22$	−46.8428			−0.453951
$23$			124.386i			1.12766i	0.825891	+	0.563830i	$0.190673\pi$
$23$			124.386i			1.12766i	−0.825891	+	0.563830i	$0.809327\pi$
$24$	−37.0036	−	18.9402i	−0.314722	−	0.161090i
$25$	−104.834			−0.838671
$26$	11.8277			0.0892154
$27$	138.688	−	21.1808i	0.988538	−	0.150972i
$28$		0			0
$29$			207.807i			1.33065i	0.746555	+	0.665324i	$0.231707\pi$
$29$			207.807i			1.33065i	−0.746555	+	0.665324i	$0.768293\pi$
$30$	41.5428	+	21.2636i	0.252821	+	0.129406i
$31$			141.756i			0.821294i	0.911794	+	0.410647i	$0.134697\pi$
$31$			141.756i			0.821294i	−0.911794	+	0.410647i	$0.865303\pi$
$32$		−	32.0000i		−	0.176777i
$33$	108.335	+	55.4509i	0.571474	+	0.292508i
$34$		−	232.167i		−	1.17107i
$35$		0			0
$36$	63.1584	+	87.6072i	0.292400	+	0.405589i
$37$	299.675			1.33152			0.665761	−	0.746165i	$-0.268107\pi$
$37$	299.675			1.33152			0.665761	+	0.746165i	$0.268107\pi$
$38$	−18.5337			−0.0791201
$39$	−27.3542	−	14.0012i	−0.112312	−	0.0574868i
$40$			35.9254i			0.142008i
$41$	508.379			1.93647			0.968237	−	0.250032i	$-0.0804412\pi$
$41$	508.379			1.93647			0.968237	+	0.250032i	$0.0804412\pi$
$42$		0			0
$43$	391.127			1.38712			0.693562	−	0.720397i	$-0.256041\pi$
$43$	391.127			1.38712			0.693562	+	0.720397i	$0.256041\pi$
$44$			93.6856i			0.320992i
$45$	−70.9060	−	98.3539i	−0.234890	−	0.325816i
$46$	248.771			0.797377
$47$	−80.5151			−0.249879			−0.124940	−	0.992164i	$-0.539874\pi$
$47$	−80.5151			−0.249879			−0.124940	+	0.992164i	$0.539874\pi$
$48$	−37.8805	+	74.0072i	−0.113908	+	0.222542i
$49$		0			0
$50$			209.668i			0.593030i
$51$	−274.832	+	536.939i	−0.754591	+	1.47425i
$52$		−	23.6554i		−	0.0630848i
$53$		−	298.718i		−	0.774189i	−0.922040	−	0.387094i	$-0.873479\pi$
$53$		−	298.718i		−	0.774189i	0.922040	−	0.387094i	$-0.126521\pi$
$54$	−42.3617	−	277.376i	−0.106754	−	0.699002i
$55$		−	105.178i		−	0.257858i
$56$		0			0
$57$	42.8634	+	21.9396i	0.0996034	+	0.0509818i
$58$	415.614			0.940910
$59$	204.552			0.451363			0.225682	−	0.974201i	$-0.427539\pi$
$59$	204.552			0.451363			0.225682	+	0.974201i	$0.427539\pi$
$60$	42.5273	−	83.0856i	0.0915041	−	0.178772i
$61$			627.877i			1.31789i	0.752190	+	0.658946i	$0.228997\pi$
$61$			627.877i			1.31789i	−0.752190	+	0.658946i	$0.771003\pi$
$62$	283.512			0.580743
$63$		0			0
$64$	−64.0000			−0.125000
$65$			26.5572i			0.0506771i
$66$	110.902	−	216.669i	0.206834	−	0.404093i
$67$	−102.779			−0.187410			−0.0937048	−	0.995600i	$-0.529871\pi$
$67$	−102.779			−0.187410			−0.0937048	+	0.995600i	$0.529871\pi$
$68$	−464.335			−0.828071
$69$	−575.340	−	294.487i	−1.00381	−	0.513798i
$70$		0			0
$71$			46.9785i			0.0785256i	0.999229	+	0.0392628i	$0.0125010\pi$
$71$			46.9785i			0.0785256i	−0.999229	+	0.0392628i	$0.987499\pi$
$72$	175.214	−	126.317i	0.286795	−	0.206758i
$73$		−	263.482i		−	0.422442i	−0.977438	−	0.211221i	$-0.932256\pi$
$73$		−	263.482i		−	0.422442i	0.977438	−	0.211221i	$-0.0677439\pi$
$74$		−	599.351i		−	0.941528i
$75$	248.197	−	484.904i	0.382125	−	0.746558i
$76$			37.0674i			0.0559464i
$77$		0			0
$78$	−28.0024	+	54.7084i	−0.0406493	+	0.0794167i
$79$	−1067.27			−1.51996			−0.759981	−	0.649945i	$-0.774792\pi$
$79$	−1067.27			−1.51996			−0.759981	+	0.649945i	$0.774792\pi$
$80$	71.8508			0.100415
$81$	−230.377	+	691.641i	−0.316018	+	0.948753i
$82$		−	1016.76i		−	1.36929i
$83$	270.436			0.357642			0.178821	−	0.983882i	$-0.442772\pi$
$83$	270.436			0.357642			0.178821	+	0.983882i	$0.442772\pi$
$84$		0			0
$85$	521.294			0.665203
$86$		−	782.254i		−	0.980844i
$87$	−961.201	−	491.990i	−1.18450	−	0.606285i
$88$	187.371			0.226976
$89$	887.530			1.05706			0.528528	−	0.848916i	$-0.322744\pi$
$89$	887.530			1.05706			0.528528	+	0.848916i	$0.322744\pi$
$90$	−196.708	+	141.812i	−0.230387	+	0.166092i
$91$		0			0
$92$		−	497.543i		−	0.563830i
$93$	−655.685	−	335.612i	−0.731090	−	0.374207i
$94$			161.030i			0.176691i
$95$		−	41.6144i		−	0.0449426i
$96$	148.014	+	75.7610i	0.157361	+	0.0805450i
$97$			219.564i			0.229828i	0.993375	+	0.114914i	$0.0366593\pi$
$97$			219.564i			0.229828i	−0.993375	+	0.114914i	$0.963341\pi$
$98$		0			0
$99$	−512.971	+	369.815i	−0.520763	+	0.375432i
$100$	419.335			0.419335
$101$	985.067			0.970473			0.485237	−	0.874383i	$-0.338733\pi$
$101$	985.067			0.970473			0.485237	+	0.874383i	$0.338733\pi$
$102$	1073.88	+	549.663i	1.04245	+	0.533576i
$103$			1285.03i			1.22930i	0.788800	+	0.614650i	$0.210703\pi$
$103$			1285.03i			1.22930i	−0.788800	+	0.614650i	$0.789297\pi$
$104$	−47.3107			−0.0446077
$105$		0			0
$106$	−597.435			−0.547434
$107$			182.915i			0.165262i	0.996580	+	0.0826311i	$0.0263323\pi$
$107$			182.915i			0.165262i	−0.996580	+	0.0826311i	$0.973668\pi$
$108$	−554.752	+	84.7233i	−0.494269	+	0.0754862i
$109$	−582.942			−0.512254			−0.256127	−	0.966643i	$-0.582447\pi$
$109$	−582.942			−0.512254			−0.256127	+	0.966643i	$0.582447\pi$
$110$	−210.356			−0.182333
$111$	−709.490	+	1386.13i	−0.606683	+	1.18528i
$112$		0			0
$113$		−	2283.94i		−	1.90137i	−0.310152	−	0.950687i	$-0.600380\pi$
$113$		−	2283.94i		−	1.90137i	0.310152	−	0.950687i	$-0.399620\pi$
$114$	43.8791	−	85.7267i	0.0360496	−	0.0704302i
$115$			558.576i			0.452934i
$116$		−	831.228i		−	0.665324i
$117$	129.524	−	93.3772i	0.102346	−	0.0737840i
$118$		−	409.104i		−	0.319162i
$119$		0			0
$120$	−166.171	−	85.0545i	−0.126411	−	0.0647032i
$121$	782.438			0.587857
$122$	1255.75			0.931890
$123$	−1203.60	+	2351.48i	−0.882319	+	1.72379i
$124$		−	567.024i		−	0.410647i
$125$	−1032.11			−0.738517
$126$		0			0
$127$	−1554.48			−1.08613			−0.543064	−	0.839692i	$-0.682736\pi$
$127$	−1554.48			−1.08613			−0.543064	+	0.839692i	$0.682736\pi$
$128$			128.000i			0.0883883i
$129$	−926.005	+	1809.14i	−0.632017	+	1.23477i
$130$	53.1143			0.0358341
$131$	−2094.93			−1.39721			−0.698605	−	0.715508i	$-0.746195\pi$
$131$	−2094.93			−1.39721			−0.698605	+	0.715508i	$0.746195\pi$
$132$	−433.338	−	221.804i	−0.285737	−	0.146254i
$133$		0			0
$134$			205.558i			0.132519i
$135$	622.803	−	95.1162i	0.397054	−	0.0606393i
$136$			928.669i			0.585535i
$137$		−	610.839i		−	0.380931i	−0.981694	−	0.190465i	$-0.939000\pi$
$137$		−	610.839i		−	0.380931i	0.981694	−	0.190465i	$-0.0609997\pi$
$138$	−588.974	+	1150.68i	−0.363310	+	0.709799i
$139$			1806.61i			1.10241i	0.834370	+	0.551204i	$0.185831\pi$
$139$			1806.61i			1.10241i	−0.834370	+	0.551204i	$0.814169\pi$
$140$		0			0
$141$	190.622	−	372.419i	0.113853	−	0.222435i
$142$	93.9569			0.0555260
$143$	138.511			0.0809988
$144$	−252.634	−	350.429i	−0.146200	−	0.202794i
$145$			933.194i			0.534466i
$146$	−526.964			−0.298711
$147$		0			0
$148$	−1198.70			−0.665761
$149$		−	2704.02i		−	1.48673i	−0.668888	−	0.743363i	$-0.733229\pi$
$149$		−	2704.02i		−	1.48673i	0.668888	−	0.743363i	$-0.266771\pi$
$150$	−969.807	−	496.395i	−0.527896	−	0.270203i
$151$	1540.70			0.830336			0.415168	−	0.909745i	$-0.363723\pi$
$151$	1540.70			0.830336			0.415168	+	0.909745i	$0.363723\pi$
$152$	74.1348			0.0395601
$153$	−1832.91	−	2542.44i	−0.968512	−	1.34343i
$154$		0			0
$155$			636.580i			0.329880i
$156$	109.417	+	56.0048i	0.0561561	+	0.0287434i
$157$			551.367i			0.280280i	0.990132	+	0.140140i	$0.0447552\pi$
$157$			551.367i			0.280280i	−0.990132	+	0.140140i	$0.955245\pi$
$158$			2134.54i			1.07478i
$159$	1381.70	+	707.223i	0.689158	+	0.352745i
$160$		−	143.702i		−	0.0710038i
$161$		0			0
$162$	1383.28	+	460.755i	0.670870	+	0.223459i
$163$	−2311.64			−1.11081			−0.555403	−	0.831581i	$-0.687436\pi$
$163$	−2311.64			−1.11081			−0.555403	+	0.831581i	$0.687436\pi$
$164$	−2033.52			−0.968237
$165$	486.496	+	249.012i	0.229537	+	0.117488i
$166$		−	540.873i		−	0.252891i
$167$	2580.87			1.19589			0.597944	−	0.801538i	$-0.295984\pi$
$167$	2580.87			1.19589			0.597944	+	0.801538i	$0.295984\pi$
$168$		0			0
$169$	2162.03			0.984081
$170$		−	1042.59i		−	0.470370i
$171$	−202.961	+	146.320i	−0.0907649	+	0.0654348i
$172$	−1564.51			−0.693562
$173$	−1002.10			−0.440395			−0.220197	−	0.975455i	$-0.570670\pi$
$173$	−1002.10			−0.440395			−0.220197	+	0.975455i	$0.570670\pi$
$174$	−983.979	+	1922.40i	−0.428708	+	0.837569i
$175$		0			0
$176$		−	374.743i		−	0.160496i
$177$	−484.284	+	946.146i	−0.205655	+	0.401789i
$178$		−	1775.06i		−	0.747452i
$179$		−	3000.33i		−	1.25282i	−0.779493	−	0.626411i	$-0.784523\pi$
$179$		−	3000.33i		−	1.25282i	0.779493	−	0.626411i	$-0.215477\pi$
$180$	283.624	+	393.416i	0.117445	+	0.162908i
$181$			967.850i			0.397457i	0.980055	+	0.198729i	$0.0636812\pi$
$181$			967.850i			0.397457i	−0.980055	+	0.198729i	$0.936319\pi$
$182$		0			0
$183$	−2904.21	−	1486.52i	−1.17315	−	0.600473i
$184$	−995.085			−0.398688
$185$	1345.74			0.534817
$186$	−671.223	+	1311.37i	−0.264605	+	0.516959i
$187$		−	2718.84i		−	1.06322i
$188$	322.060			0.124940
$189$		0			0
$190$	−83.2289			−0.0317792
$191$			411.321i			0.155823i	0.996960	+	0.0779113i	$0.0248251\pi$
$191$			411.321i			0.155823i	−0.996960	+	0.0779113i	$0.975175\pi$
$192$	151.522	−	296.029i	0.0569539	−	0.111271i
$193$	816.423			0.304494			0.152247	−	0.988342i	$-0.451349\pi$
$193$	816.423			0.304494			0.152247	+	0.988342i	$0.451349\pi$
$194$	439.128			0.162513
$195$	−122.839	−	62.8749i	−0.0451111	−	0.0230901i
$196$		0			0
$197$		−	633.331i		−	0.229051i	−0.993420	−	0.114525i	$-0.963465\pi$
$197$		−	633.331i		−	0.229051i	0.993420	−	0.114525i	$-0.0365347\pi$
$198$	739.629	+	1025.94i	0.265471	+	0.368235i
$199$		−	3423.08i		−	1.21938i	−0.792641	−	0.609688i	$-0.791295\pi$
$199$		−	3423.08i		−	1.21938i	0.792641	−	0.609688i	$-0.208705\pi$
$200$		−	838.671i		−	0.296515i
$201$	243.332	−	475.399i	0.0853897	−	0.166826i
$202$		−	1970.13i		−	0.686228i
$203$		0			0
$204$	1099.33	−	2147.76i	0.377295	−	0.737123i
$205$	2282.97			0.777801
$206$	2570.06			0.869247
$207$	2724.27	−	1964.00i	0.914733	−	0.659456i
$208$			94.6215i			0.0315424i
$209$	−217.043			−0.0718333
$210$		0			0
$211$	1023.65			0.333986			0.166993	−	0.985958i	$-0.446594\pi$
$211$	1023.65			0.333986			0.166993	+	0.985958i	$0.446594\pi$
$212$			1194.87i			0.387094i
$213$	−217.297	−	111.223i	−0.0699010	−	0.0357787i
$214$	365.830			0.116858
$215$	1756.42			0.557150
$216$	169.447	+	1109.50i	0.0533768	+	0.349501i
$217$		0			0
$218$			1165.88i			0.362219i
$219$	1218.72	+	623.802i	0.376044	+	0.192478i
$220$			420.712i			0.128929i
$221$			686.501i			0.208955i
$222$	2772.27	+	1418.98i	0.838119	+	0.428990i
$223$			1521.32i			0.456840i	0.973563	+	0.228420i	$0.0733559\pi$
$223$			1521.32i			0.456840i	−0.973563	+	0.228420i	$0.926644\pi$
$224$		0			0
$225$	1655.28	+	2296.05i	0.490454	+	0.680311i
$226$	−4567.88			−1.34447
$227$	1459.15			0.426640			0.213320	−	0.976982i	$-0.431572\pi$
$227$	1459.15			0.426640			0.213320	+	0.976982i	$0.431572\pi$
$228$	−171.453	−	87.7582i	−0.0498017	−	0.0254909i
$229$		−	4794.52i		−	1.38354i	−0.722118	−	0.691770i	$-0.756831\pi$
$229$		−	4794.52i		−	1.38354i	0.722118	−	0.691770i	$-0.243169\pi$
$230$	1117.15			0.320273
$231$		0			0
$232$	−1662.46			−0.470455
$233$			1669.42i			0.469386i	0.972069	+	0.234693i	$0.0754086\pi$
$233$			1669.42i			0.469386i	−0.972069	+	0.234693i	$0.924591\pi$
$234$	−186.754	−	259.048i	−0.0521731	−	0.0723695i
$235$	−361.567			−0.100366
$236$	−818.209			−0.225682
$237$	2526.79	−	4936.60i	0.692543	−	1.35302i
$238$		0			0
$239$			3529.25i			0.955181i	0.878583	+	0.477590i	$0.158490\pi$
$239$			3529.25i			0.955181i	−0.878583	+	0.477590i	$0.841510\pi$
$240$	−170.109	+	332.342i	−0.0457520	+	0.0893859i
$241$		−	4929.59i		−	1.31761i	−0.752316	−	0.658803i	$-0.771063\pi$
$241$		−	4929.59i		−	1.31761i	0.752316	−	0.658803i	$-0.228937\pi$
$242$		−	1564.88i		−	0.415678i
$243$	−2653.73	−	2703.08i	−0.700562	−	0.713591i
$244$		−	2511.51i		−	0.658946i
$245$		0			0
$246$	4702.97	+	2407.21i	1.21890	+	0.623894i
$247$	54.8027			0.0141175
$248$	−1134.05			−0.290371
$249$	−640.267	+	1250.89i	−0.162953	+	0.318361i
$250$			2064.22i			0.522211i
$251$	1294.99			0.325652			0.162826	−	0.986655i	$-0.447939\pi$
$251$	1294.99			0.325652			0.162826	+	0.986655i	$0.447939\pi$
$252$		0			0
$253$	2913.29			0.723940
$254$			3108.97i			0.768008i
$255$	−1234.18	+	2411.22i	−0.303088	+	0.592143i
$256$	256.000			0.0625000
$257$	−1456.08			−0.353415			−0.176708	−	0.984263i	$-0.556545\pi$
$257$	−1456.08			−0.353415			−0.176708	+	0.984263i	$0.556545\pi$
$258$	3618.28	+	1852.01i	0.873117	+	0.446904i
$259$		0			0
$260$		−	106.229i		−	0.0253385i
$261$	4551.35	−	3281.19i	1.07939	−	0.778163i
$262$			4189.85i			0.987976i
$263$		−	2136.55i		−	0.500932i	−0.968125	−	0.250466i	$-0.919416\pi$
$263$		−	2136.55i		−	0.500932i	0.968125	−	0.250466i	$-0.0805839\pi$
$264$	−443.607	+	866.677i	−0.103417	+	0.202046i
$265$		−	1341.44i		−	0.310959i
$266$		0			0
$267$	−2101.26	+	4105.23i	−0.481628	+	0.940958i
$268$	411.115			0.0937048
$269$	−2887.45			−0.654465			−0.327233	−	0.944944i	$-0.606116\pi$
$269$	−2887.45			−0.654465			−0.327233	+	0.944944i	$0.606116\pi$
$270$	−190.232	−	1245.61i	−0.0428784	−	0.280760i
$271$			5857.70i			1.31303i	0.754315	+	0.656513i	$0.227969\pi$
$271$			5857.70i			1.31303i	−0.754315	+	0.656513i	$0.772031\pi$
$272$	1857.34			0.414036
$273$		0			0
$274$	−1221.68			−0.269359
$275$			2455.36i			0.538413i
$276$	2301.36	+	1177.95i	0.501904	+	0.256899i
$277$	−2803.03			−0.608006			−0.304003	−	0.952671i	$-0.598323\pi$
$277$	−2803.03			−0.608006			−0.304003	+	0.952671i	$0.598323\pi$
$278$	3613.22			0.779520
$279$	3104.71	−	2238.27i	0.666215	−	0.480293i
$280$		0			0
$281$			4665.53i			0.990469i	0.868759	+	0.495235i	$0.164918\pi$
$281$			4665.53i			0.990469i	−0.868759	+	0.495235i	$0.835082\pi$
$282$	−744.837	−	381.244i	−0.157285	−	0.0805062i
$283$			5374.59i			1.12893i	0.825458	+	0.564463i	$0.190917\pi$
$283$			5374.59i			1.12893i	−0.825458	+	0.564463i	$0.809083\pi$
$284$		−	187.914i		−	0.0392628i
$285$	192.486	+	98.5235i	0.0400065	+	0.0204773i
$286$		−	277.021i		−	0.0572748i
$287$		0			0
$288$	−700.857	+	505.267i	−0.143397	+	0.103379i
$289$	8562.42			1.74281
$290$	1866.39			0.377924
$291$	−1015.58	−	519.825i	−0.204586	−	0.104717i
$292$			1053.93i			0.211221i
$293$	−1302.13			−0.259630			−0.129815	−	0.991538i	$-0.541438\pi$
$293$	−1302.13			−0.259630			−0.129815	+	0.991538i	$0.541438\pi$
$294$		0			0
$295$	918.578			0.181294
$296$			2397.40i			0.470764i
$297$	−496.085	−	3248.27i	−0.0969218	−	0.634625i
$298$	−5408.05			−1.05127
$299$	−735.597			−0.142277
$300$	−992.789	+	1939.61i	−0.191062	+	0.373279i
$301$		0			0
$302$		−	3081.41i		−	0.587136i
$303$	−2332.18	+	4556.38i	−0.442178	+	0.863885i
$304$		−	148.270i		−	0.0279732i
$305$			2819.59i			0.529342i
$306$	−5084.88	+	3665.83i	−0.949946	+	0.684841i
$307$		−	644.894i		−	0.119889i	−0.998202	−	0.0599447i	$-0.980908\pi$
$307$		−	644.894i		−	0.119889i	0.998202	−	0.0599447i	$-0.0190924\pi$
$308$		0			0
$309$	−5943.85	−	3042.35i	−1.09428	−	0.560108i
$310$	1273.16			0.233260
$311$	1336.84			0.243747			0.121873	−	0.992546i	$-0.461110\pi$
$311$	1336.84			0.243747			0.121873	+	0.992546i	$0.461110\pi$
$312$	112.010	−	218.834i	0.0203247	−	0.0397084i
$313$			1685.48i			0.304373i	0.988352	+	0.152187i	$0.0486315\pi$
$313$			1685.48i			0.304373i	−0.988352	+	0.152187i	$0.951369\pi$
$314$	1102.73			0.198188
$315$		0			0
$316$	4269.07			0.759981
$317$			3013.71i			0.533965i	0.963701	+	0.266982i	$0.0860265\pi$
$317$			3013.71i			0.533965i	−0.963701	+	0.266982i	$0.913973\pi$
$318$	1414.45	−	2763.41i	0.249428	−	0.487309i
$319$	4867.13			0.854254
$320$	−287.403			−0.0502073
$321$	−846.064	−	433.057i	−0.147111	−	0.0752987i
$322$		0			0
$323$		−	1075.73i		−	0.185310i
$324$	921.509	−	2766.56i	0.158009	−	0.474377i
$325$		−	619.971i		−	0.105815i
$326$			4623.27i			0.785458i
$327$	1380.13	−	2696.37i	0.233399	−	0.455993i
$328$			4067.03i			0.684647i
$329$		0			0
$330$	498.024	−	972.991i	0.0830768	−	0.162307i
$331$	−788.920			−0.131006			−0.0655030	−	0.997852i	$-0.520865\pi$
$331$	−788.920			−0.131006			−0.0655030	+	0.997852i	$0.520865\pi$
$332$	−1081.75			−0.178821
$333$	−4731.75	−	6563.43i	−0.778674	−	1.08010i
$334$		−	5161.73i		−	0.845621i
$335$	−461.547			−0.0752746
$336$		0			0
$337$	1906.16			0.308116			0.154058	−	0.988062i	$-0.450766\pi$
$337$	1906.16			0.308116			0.154058	+	0.988062i	$0.450766\pi$
$338$		−	4324.05i		−	0.695851i
$339$	10564.3	+	5407.30i	1.69254	+	0.866326i
$340$	−2085.18			−0.332602
$341$	3320.12			0.527257
$342$	292.640	+	405.921i	0.0462694	+	0.0641805i
$343$		0			0
$344$			3129.02i			0.490422i
$345$	−2583.66	−	1322.44i	−0.403188	−	0.206371i
$346$			2004.20i			0.311406i
$347$			5241.16i			0.810836i	0.914131	+	0.405418i	$0.132874\pi$
$347$			5241.16i			0.810836i	−0.914131	+	0.405418i	$0.867126\pi$
$348$	3844.81	+	1967.96i	0.592251	+	0.303143i
$349$		−	4502.54i		−	0.690588i	−0.938495	−	0.345294i	$-0.887779\pi$
$349$		−	4502.54i		−	0.690588i	0.938495	−	0.345294i	$-0.112221\pi$
$350$		0			0
$351$	125.260	+	820.179i	0.0190481	+	0.124723i
$352$	−749.485			−0.113488
$353$	−9599.40			−1.44738			−0.723689	−	0.690126i	$-0.757555\pi$
$353$	−9599.40			−1.44738			−0.723689	+	0.690126i	$0.757555\pi$
$354$	1892.29	+	968.567i	0.284108	+	0.145420i
$355$			210.965i			0.0315405i
$356$	−3550.12			−0.528528
$357$		0			0
$358$	−6000.66			−0.885879
$359$		−	10165.9i		−	1.49453i	−0.664526	−	0.747265i	$-0.731366\pi$
$359$		−	10165.9i		−	1.49453i	0.664526	−	0.747265i	$-0.268634\pi$
$360$	786.831	−	567.248i	0.115193	−	0.0830461i
$361$	6773.13			0.987480
$362$	1935.70			0.281045
$363$	−1852.44	+	3619.13i	−0.267846	+	0.523292i
$364$		0			0
$365$		−	1183.21i		−	0.169677i
$366$	−2973.04	+	5808.43i	−0.424599	+	0.829540i
$367$			383.989i			0.0546160i	0.999627	+	0.0273080i	$0.00869349\pi$
$367$			383.989i			0.0546160i	−0.999627	+	0.0273080i	$0.991307\pi$
$368$			1990.17i			0.281915i
$369$	−8027.10	−	11134.4i	−1.13245	−	1.57083i
$370$		−	2691.49i		−	0.378173i
$371$		0			0
$372$	2622.74	+	1342.45i	0.365545	+	0.187104i
$373$	−2963.59			−0.411391			−0.205695	−	0.978616i	$-0.565946\pi$
$373$	−2963.59			−0.411391			−0.205695	+	0.978616i	$0.565946\pi$
$374$	−5437.69			−0.751808
$375$	2443.55	−	4773.97i	0.336492	−	0.657405i
$376$		−	644.121i		−	0.0883457i
$377$	−1228.94			−0.167887
$378$		0			0
$379$	−13195.4			−1.78839			−0.894195	−	0.447677i	$-0.852251\pi$
$379$	−13195.4			−1.78839			−0.894195	+	0.447677i	$0.852251\pi$
$380$			166.458i			0.0224713i
$381$	3680.29	−	7190.19i	0.494874	−	0.966836i
$382$	822.641			0.110183
$383$	8951.90			1.19431			0.597155	−	0.802126i	$-0.296298\pi$
$383$	8951.90			1.19431			0.597155	+	0.802126i	$0.296298\pi$
$384$	−592.058	−	303.044i	−0.0786805	−	0.0402725i
$385$		0			0
$386$		−	1632.85i		−	0.215310i
$387$	−6175.74	−	8566.38i	−0.811189	−	1.12520i
$388$		−	878.257i		−	0.114914i
$389$			8769.64i			1.14303i	0.820592	+	0.571515i	$0.193644\pi$
$389$			8769.64i			1.14303i	−0.820592	+	0.571515i	$0.806356\pi$
$390$	−125.750	+	245.678i	−0.0163271	+	0.0318984i
$391$			14439.1i			1.86757i
$392$		0			0
$393$	4959.80	−	9689.97i	0.636613	−	1.24375i
$394$	−1266.66			−0.161963
$395$	−4792.75			−0.610505
$396$	2051.88	−	1479.26i	0.260381	−	0.187716i
$397$			1370.98i			0.173319i	0.996238	+	0.0866594i	$0.0276192\pi$
$397$			1370.98i			0.173319i	−0.996238	+	0.0866594i	$0.972381\pi$
$398$	−6846.17			−0.862229
$399$		0			0
$400$	−1677.34			−0.209668
$401$		−	2762.20i		−	0.343985i	−0.985098	−	0.171992i	$-0.944980\pi$
$401$		−	2762.20i		−	0.343985i	0.985098	−	0.171992i	$-0.0550204\pi$
$402$	−950.797	−	486.664i	−0.117964	−	0.0603796i
$403$	−838.322			−0.103622
$404$	−3940.27			−0.485237
$405$	−1034.55	+	3105.94i	−0.126931	+	0.381075i
$406$		0			0
$407$		−	7018.82i		−	0.854815i
$408$	−4295.51	−	2198.65i	−0.521225	−	0.266788i
$409$			2667.37i			0.322477i	0.986915	+	0.161239i	$0.0515489\pi$
$409$			2667.37i			0.322477i	−0.986915	+	0.161239i	$0.948451\pi$
$410$		−	4565.93i		−	0.549989i
$411$	2825.41	+	1446.18i	0.339093	+	0.173564i
$412$		−	5140.13i		−	0.614650i
$413$		0			0
$414$	−3928.00	−	5448.54i	−0.466306	−	0.646814i
$415$	1214.44			0.143650
$416$	189.243			0.0223038
$417$	−8356.39	−	4277.21i	−0.981329	−	0.502292i
$418$			434.085i			0.0507938i
$419$	−14480.6			−1.68836			−0.844179	−	0.536061i	$-0.819912\pi$
$419$	−14480.6			−1.68836			−0.844179	+	0.536061i	$0.819912\pi$
$420$		0			0
$421$	14248.8			1.64951			0.824753	−	0.565494i	$-0.191314\pi$
$421$	14248.8			1.64951			0.824753	+	0.565494i	$0.191314\pi$
$422$		−	2047.30i		−	0.236164i
$423$	1271.30	+	1763.42i	0.146129	+	0.202697i
$424$	2389.74			0.273717
$425$	−12169.5			−1.38896
$426$	−222.446	+	434.593i	−0.0252994	+	0.0494275i
$427$		0			0
$428$		−	731.660i		−	0.0826311i
$429$	−327.928	+	640.674i	−0.0369056	+	0.0721026i
$430$		−	3512.85i		−	0.393964i
$431$			5573.15i			0.622851i	0.950270	+	0.311426i	$0.100807\pi$
$431$			5573.15i			0.622851i	−0.950270	+	0.311426i	$0.899193\pi$
$432$	2219.01	−	338.893i	0.247134	−	0.0377431i
$433$		−	2939.93i		−	0.326291i	−0.986602	−	0.163146i	$-0.947836\pi$
$433$		−	2939.93i		−	0.326291i	0.986602	−	0.163146i	$-0.0521640\pi$
$434$		0			0
$435$	−4316.44	−	2209.37i	−0.475765	−	0.243520i
$436$	2331.77			0.256127
$437$	1152.66			0.126177
$438$	1247.60	−	2437.45i	0.136102	−	0.265904i
$439$			9573.31i			1.04080i	0.853924	+	0.520398i	$0.174216\pi$
$439$			9573.31i			1.04080i	−0.853924	+	0.520398i	$0.825784\pi$
$440$	841.424			0.0911666
$441$		0			0
$442$	1373.00			0.147753
$443$			7156.17i			0.767494i	0.923438	+	0.383747i	$0.125366\pi$
$443$			7156.17i			0.767494i	−0.923438	+	0.383747i	$0.874634\pi$
$444$	2837.96	−	5544.53i	0.303342	−	0.592639i
$445$	3985.61			0.424575
$446$	3042.65			0.323035
$447$	12507.3	+	6401.86i	1.32344	+	0.677400i
$448$		0			0
$449$		−	14839.2i		−	1.55970i	−0.625964	−	0.779852i	$-0.715294\pi$
$449$		−	14839.2i		−	1.55970i	0.625964	−	0.779852i	$-0.284706\pi$
$450$	4592.10	−	3310.57i	0.481052	−	0.346804i
$451$		−	11907.0i		−	1.24319i
$452$			9135.77i			0.950687i
$453$	−3647.66	+	7126.45i	−0.378327	+	0.739139i
$454$		−	2918.30i		−	0.301680i
$455$		0			0
$456$	−175.516	+	342.907i	−0.0180248	+	0.0352151i
$457$	−7574.83			−0.775352			−0.387676	−	0.921796i	$-0.626722\pi$
$457$	−7574.83			−0.775352			−0.387676	+	0.921796i	$0.626722\pi$
$458$	−9589.03			−0.978310
$459$	16099.4	−	2458.75i	1.63716	−	0.250032i
$460$		−	2234.30i		−	0.226467i
$461$	−14850.5			−1.50034			−0.750170	−	0.661245i	$-0.770029\pi$
$461$	−14850.5			−1.50034			−0.750170	+	0.661245i	$0.770029\pi$
$462$		0			0
$463$	3361.43			0.337406			0.168703	−	0.985667i	$-0.446042\pi$
$463$	3361.43			0.337406			0.168703	+	0.985667i	$0.446042\pi$
$464$			3324.91i			0.332662i
$465$	−2944.47	−	1507.12i	−0.293648	−	0.150304i
$466$	3338.83			0.331906
$467$	−230.845			−0.0228741			−0.0114371	−	0.999935i	$-0.503641\pi$
$467$	−230.845			−0.0228741			−0.0114371	+	0.999935i	$0.503641\pi$
$468$	−518.095	+	373.509i	−0.0511730	+	0.0368920i
$469$		0			0
$470$			723.134i			0.0709696i
$471$	−2550.32	−	1305.38i	−0.249496	−	0.127704i
$472$			1636.42i			0.159581i
$473$		−	9160.74i		−	0.890510i
$474$	−9873.19	−	5053.58i	−0.956731	−	0.489702i
$475$			971.480i			0.0938411i
$476$		0			0
$477$	−6542.45	+	4716.63i	−0.628005	+	0.452745i
$478$	7058.50			0.675415
$479$	−4400.86			−0.419792			−0.209896	−	0.977724i	$-0.567313\pi$
$479$	−4400.86			−0.419792			−0.209896	+	0.977724i	$0.567313\pi$
$480$	664.685	+	340.218i	0.0632054	+	0.0323516i
$481$			1772.23i			0.167998i
$482$	−9859.18			−0.931688
$483$		0			0
$484$	−3129.75			−0.293928
$485$			985.992i			0.0923125i
$486$	−5406.16	+	5307.45i	−0.504585	+	0.495372i
$487$	−11944.6			−1.11142			−0.555711	−	0.831376i	$-0.687554\pi$
$487$	−11944.6			−1.11142			−0.555711	+	0.831376i	$0.687554\pi$
$488$	−5023.02			−0.465945
$489$	5472.87	−	10692.4i	0.506118	−	0.988804i
$490$		0			0
$491$			19916.7i			1.83060i	0.402768	+	0.915302i	$0.368048\pi$
$491$			19916.7i			1.83060i	−0.402768	+	0.915302i	$0.631952\pi$
$492$	4814.41	−	9405.93i	0.441160	−	0.861894i
$493$			24123.0i			2.20374i
$494$		−	109.605i		−	0.00998255i
$495$	−2303.59	+	1660.72i	−0.209169	+	0.150795i
$496$			2268.09i			0.205324i
$497$		0			0
$498$	2501.78	+	1280.53i	0.225115	+	0.115225i
$499$	1331.14			0.119419			0.0597093	−	0.998216i	$-0.480983\pi$
$499$	1331.14			0.119419			0.0597093	+	0.998216i	$0.480983\pi$
$500$	4128.44			0.369259
$501$	−6110.28	+	11937.7i	−0.544885	+	1.06454i
$502$		−	2589.97i		−	0.230271i
$503$	10393.2			0.921288			0.460644	−	0.887585i	$-0.347618\pi$
$503$	10393.2			0.921288			0.460644	+	0.887585i	$0.347618\pi$
$504$		0			0
$505$	4423.62			0.389799
$506$		−	5826.57i		−	0.511903i
$507$	−5118.66	+	10000.3i	−0.448378	+	0.875998i
$508$	6217.94			0.543064
$509$	10264.0			0.893802			0.446901	−	0.894583i	$-0.352528\pi$
$509$	10264.0			0.893802			0.446901	+	0.894583i	$0.352528\pi$
$510$	4822.44	+	2468.36i	0.418708	+	0.214315i
$511$		0			0
$512$		−	512.000i		−	0.0441942i
$513$	−196.280	−	1285.20i	−0.0168927	−	0.110610i
$514$			2912.16i			0.249902i
$515$			5770.66i			0.493759i
$516$	3704.02	−	7236.55i	0.316009	−	0.617387i
$517$			1885.78i			0.160418i
$518$		0			0
$519$	2372.50	−	4635.17i	0.200658	−	0.392026i
$520$	−212.457			−0.0179170
$521$	3099.94			0.260673			0.130337	−	0.991470i	$-0.458394\pi$
$521$	3099.94			0.260673			0.130337	+	0.991470i	$0.458394\pi$
$522$	−6562.38	−	9102.69i	−0.550244	−	0.763245i
$523$			9544.68i			0.798011i	0.916949	+	0.399005i	$0.130645\pi$
$523$			9544.68i			0.798011i	−0.916949	+	0.399005i	$0.869355\pi$
$524$	8379.70			0.698605
$525$		0			0
$526$	−4273.10			−0.354213
$527$			16455.5i			1.36018i
$528$	1733.35	+	887.215i	0.142868	+	0.0731270i
$529$	−3304.78			−0.271619
$530$	−2682.89			−0.219881
$531$	−3229.80	−	4480.06i	−0.263957	−	0.366136i
$532$		0			0
$533$			3006.47i			0.244324i
$534$	8210.46	+	4202.51i	0.665358	+	0.340563i
$535$			821.412i			0.0663790i
$536$		−	822.231i		−	0.0662593i
$537$	13877.9	+	7103.37i	1.11522	+	0.570825i
$538$			5774.91i			0.462777i
$539$		0			0
$540$	−2491.21	+	380.465i	−0.198527	+	0.0303196i
$541$	−6807.65			−0.541005			−0.270503	−	0.962719i	$-0.587190\pi$
$541$	−6807.65			−0.541005			−0.270503	+	0.962719i	$0.587190\pi$
$542$	11715.4			0.928450
$543$	−4476.74	−	2291.41i	−0.353804	−	0.181094i
$544$		−	3714.68i		−	0.292767i
$545$	−2617.80			−0.205751
$546$		0			0
$547$	−14906.9			−1.16521			−0.582606	−	0.812754i	$-0.697967\pi$
$547$	−14906.9			−1.16521			−0.582606	+	0.812754i	$0.697967\pi$
$548$			2443.36i			0.190465i
$549$	13751.6	−	9913.93i	1.06904	−	0.770703i
$550$	4910.71			0.380715
$551$	1925.72			0.148890
$552$	2355.89	−	4602.72i	0.181655	−	0.354900i
$553$		0			0
$554$			5606.06i			0.429925i
$555$	−3186.09	+	6224.68i	−0.243679	+	0.476077i
$556$		−	7226.45i		−	0.551204i
$557$			12311.3i			0.936532i	0.883588	+	0.468266i	$0.155121\pi$
$557$			12311.3i			0.936532i	−0.883588	+	0.468266i	$0.844879\pi$
$558$	−4476.54	−	6209.42i	−0.339618	−	0.471085i
$559$			2313.06i			0.175013i
$560$		0			0
$561$	12575.9	+	6436.95i	0.946442	+	0.484435i
$562$	9331.05			0.700368
$563$	−835.850			−0.0625699			−0.0312850	−	0.999511i	$-0.509960\pi$
$563$	−835.850			−0.0625699			−0.0312850	+	0.999511i	$0.509960\pi$
$564$	−762.488	+	1489.67i	−0.0569265	+	0.111217i
$565$		−	10256.4i		−	0.763703i
$566$	10749.2			0.798271
$567$		0			0
$568$	−375.828			−0.0277630
$569$		−	6109.57i		−	0.450134i	−0.974343	−	0.225067i	$-0.927740\pi$
$569$		−	6109.57i		−	0.450134i	0.974343	−	0.225067i	$-0.0722602\pi$
$570$	197.047	−	384.971i	0.0144796	−	0.0282889i
$571$	−12639.4			−0.926342			−0.463171	−	0.886269i	$-0.653288\pi$
$571$	−12639.4			−0.926342			−0.463171	+	0.886269i	$0.653288\pi$
$572$	−554.042			−0.0404994
$573$	−1902.54	−	973.814i	−0.138708	−	0.0709977i
$574$		0			0
$575$		−	13039.8i		−	0.945736i
$576$	1010.53	+	1401.71i	0.0731000	+	0.101397i
$577$		−	17707.0i		−	1.27756i	−0.769389	−	0.638781i	$-0.779439\pi$
$577$		−	17707.0i		−	1.27756i	0.769389	−	0.638781i	$-0.220561\pi$
$578$		−	17124.8i		−	1.23235i
$579$	−1932.91	+	3776.33i	−0.138737	+	0.271051i
$580$		−	3732.78i		−	0.267233i
$581$		0			0
$582$	−1039.65	+	2031.17i	−0.0740462	+	0.144664i
$583$	−6996.39			−0.497017
$584$	2107.86			0.149356
$585$	581.649	−	419.327i	0.0411081	−	0.0296359i
$586$			2604.27i			0.183586i
$587$	11725.2			0.824446			0.412223	−	0.911083i	$-0.364752\pi$
$587$	11725.2			0.824446			0.412223	+	0.911083i	$0.364752\pi$
$588$		0			0
$589$	1313.63			0.0918968
$590$		−	1837.16i		−	0.128194i
$591$	2929.44	+	1499.43i	0.203894	+	0.104363i
$592$	4794.80			0.332880
$593$	15047.5			1.04204			0.521018	−	0.853545i	$-0.325552\pi$
$593$	15047.5			1.04204			0.521018	+	0.853545i	$0.325552\pi$
$594$	−6496.54	+	992.170i	−0.448748	+	0.0685340i
$595$		0			0
$596$			10816.1i			0.743363i
$597$	15833.3	+	8104.25i	1.08545	+	0.555586i
$598$			1471.19i			0.100605i
$599$		−	6111.49i		−	0.416876i	−0.978036	−	0.208438i	$-0.933162\pi$
$599$		−	6111.49i		−	0.416876i	0.978036	−	0.208438i	$-0.0668379\pi$
$600$	3879.23	+	1985.58i	0.263948	+	0.135102i
$601$		−	7494.08i		−	0.508636i	−0.967121	−	0.254318i	$-0.918149\pi$
$601$		−	7494.08i		−	0.508636i	0.967121	−	0.254318i	$-0.0818509\pi$
$602$		0			0
$603$	1622.84	+	2251.04i	0.109597	+	0.152022i
$604$	−6162.81			−0.415168
$605$	3513.67			0.236118
$606$	9112.76	+	4664.35i	0.610859	+	0.312667i
$607$		−	20688.9i		−	1.38342i	−0.722174	−	0.691711i	$-0.756857\pi$
$607$		−	20688.9i		−	1.38342i	0.722174	−	0.691711i	$-0.243143\pi$
$608$	−296.539			−0.0197800
$609$		0			0
$610$	5639.19			0.374302
$611$		−	476.153i		−	0.0315272i
$612$	7331.66	+	10169.8i	0.484256	+	0.671713i
$613$	−23291.0			−1.53461			−0.767305	−	0.641282i	$-0.778403\pi$
$613$	−23291.0			−1.53461			−0.767305	+	0.641282i	$0.778403\pi$
$614$	−1289.79			−0.0847746
$615$	−5404.99	+	10559.7i	−0.354391	+	0.692374i
$616$		0			0
$617$			11640.9i			0.759554i	0.925078	+	0.379777i	$0.123999\pi$
$617$			11640.9i			0.759554i	−0.925078	+	0.379777i	$0.876001\pi$
$618$	−6084.70	+	11887.7i	−0.396056	+	0.773776i
$619$		−	16140.9i		−	1.04807i	−0.851696	−	0.524036i	$-0.824426\pi$
$619$		−	16140.9i		−	1.04807i	0.851696	−	0.524036i	$-0.175574\pi$
$620$		−	2546.32i		−	0.164940i
$621$	2634.59	+	17250.8i	0.170246	+	1.11474i
$622$		−	2673.68i		−	0.172355i
$623$		0			0
$624$	−437.667	−	224.019i	−0.0280781	−	0.0143717i
$625$	8469.36			0.542039
$626$	3370.96			0.215224
$627$	513.855	−	1003.92i	0.0327295	−	0.0639437i
$628$		−	2205.47i		−	0.140140i
$629$	34787.4			2.20519
$630$		0			0
$631$	9424.67			0.594596			0.297298	−	0.954785i	$-0.403914\pi$
$631$	9424.67			0.594596			0.297298	+	0.954785i	$0.403914\pi$
$632$		−	8538.14i		−	0.537388i
$633$	−2423.53	+	4734.85i	−0.152175	+	0.297304i
$634$	6027.42			0.377570
$635$	−6980.69			−0.436252
$636$	−5526.81	−	2828.89i	−0.344579	−	0.176372i
$637$		0			0
$638$		−	9734.27i		−	0.604049i
$639$	1028.91	−	741.771i	0.0636982	−	0.0459218i
$640$			574.807i			0.0355019i
$641$		−	1685.33i		−	0.103848i	−0.998651	−	0.0519241i	$-0.983465\pi$
$641$		−	1685.33i		−	0.103848i	0.998651	−	0.0519241i	$-0.0165354\pi$
$642$	−866.114	+	1692.13i	−0.0532442	+	0.104023i
$643$		−	10186.5i		−	0.624752i	−0.949958	−	0.312376i	$-0.898875\pi$
$643$		−	10186.5i		−	0.624752i	0.949958	−	0.312376i	$-0.101125\pi$
$644$		0			0
$645$	−4158.39	+	8124.26i	−0.253855	+	0.495957i
$646$	−2151.46			−0.131034
$647$	−327.586			−0.0199053			−0.00995266	−	0.999950i	$-0.503168\pi$
$647$	−327.586			−0.0199053			−0.00995266	+	0.999950i	$0.503168\pi$
$648$	−5533.13	−	1843.02i	−0.335435	−	0.111729i
$649$		−	4790.90i		−	0.289768i
$650$	−1239.94			−0.0748223
$651$		0			0
$652$	9246.55			0.555403
$653$		−	2043.73i		−	0.122477i	−0.998123	−	0.0612384i	$-0.980495\pi$
$653$		−	2043.73i		−	0.122477i	0.998123	−	0.0612384i	$-0.0195050\pi$
$654$	−5392.74	−	2760.27i	−0.322436	−	0.165038i
$655$	−9407.63			−0.561201
$656$	8134.07			0.484119
$657$	−5770.73	+	4160.28i	−0.342675	+	0.247044i
$658$		0			0
$659$			27567.4i			1.62955i	0.579778	+	0.814774i	$0.303139\pi$
$659$			27567.4i			1.62955i	−0.579778	+	0.814774i	$0.696861\pi$
$660$	−1945.98	−	996.048i	−0.114769	−	0.0587441i
$661$			21266.1i			1.25137i	0.780077	+	0.625684i	$0.215180\pi$
$661$			21266.1i			1.25137i	−0.780077	+	0.625684i	$0.784820\pi$
$662$			1577.84i			0.0926352i
$663$	−3175.37	−	1625.31i	−0.186005	−	0.0952064i
$664$			2163.49i			0.126445i
$665$		0			0
$666$	−13126.9	+	9463.50i	−0.763747	+	0.550606i
$667$	−25848.2			−1.50052
$668$	−10323.5			−0.597944
$669$	−7036.81	−	3601.78i	−0.406665	−	0.208151i
$670$			923.093i			0.0532272i
$671$	14705.8			0.846065
$672$		0			0
$673$	−9377.40			−0.537106			−0.268553	−	0.963265i	$-0.586545\pi$
$673$	−9377.40			−0.537106			−0.268553	+	0.963265i	$0.586545\pi$
$674$		−	3812.31i		−	0.217871i
$675$	−14539.2	+	2220.47i	−0.829058	+	0.126616i
$676$	−8648.11			−0.492041
$677$	−10684.6			−0.606563			−0.303282	−	0.952901i	$-0.598082\pi$
$677$	−10684.6			−0.606563			−0.303282	+	0.952901i	$0.598082\pi$
$678$	10814.6	−	21128.5i	0.612585	−	1.19681i
$679$		0			0
$680$			4170.35i			0.235185i
$681$	−3454.58	+	6749.23i	−0.194391	+	0.379781i
$682$		−	6640.25i		−	0.372827i
$683$		−	28851.3i		−	1.61634i	−0.588947	−	0.808172i	$-0.700457\pi$
$683$		−	28851.3i		−	1.61634i	0.588947	−	0.808172i	$-0.299543\pi$
$684$	811.843	−	585.279i	0.0453824	−	0.0327174i
$685$		−	2743.08i		−	0.153004i
$686$		0			0
$687$	22176.8	+	11351.2i	1.23158	+	0.630384i
$688$	6258.03			0.346781
$689$	1766.57			0.0976791
$690$	−2644.89	+	5167.33i	−0.145926	+	0.285097i
$691$			1316.34i			0.0724689i	0.999343	+	0.0362344i	$0.0115363\pi$
$691$			1316.34i			0.0724689i	−0.999343	+	0.0362344i	$0.988464\pi$
$692$	4008.40			0.220197
$693$		0			0
$694$	10482.3			0.573348
$695$			8112.91i			0.442792i
$696$	3935.92	−	7689.61i	0.214354	−	0.418784i
$697$	59014.5			3.20708
$698$	−9005.07			−0.488320
$699$	−7721.80	−	3952.39i	−0.417833	−	0.213867i
$700$		0			0
$701$		−	12811.2i		−	0.690259i	−0.938555	−	0.345129i	$-0.887835\pi$
$701$		−	12811.2i		−	0.690259i	0.938555	−	0.345129i	$-0.112165\pi$
$702$	1640.36	−	250.520i	0.0881928	−	0.0134691i
$703$		−	2777.05i		−	0.148988i
$704$			1498.97i			0.0802480i
$705$	856.021	−	1672.41i	0.0457300	−	0.0893428i
$706$			19198.8i			1.02345i
$707$		0			0
$708$	1937.13	−	3784.58i	0.102828	−	0.200895i
$709$	32965.8			1.74620			0.873101	−	0.487539i	$-0.162105\pi$
$709$	32965.8			1.74620			0.873101	+	0.487539i	$0.162105\pi$
$710$	421.930			0.0223025
$711$	16851.7	+	23375.1i	0.888874	+	1.23296i
$712$			7100.24i			0.373726i
$713$	−17632.4			−0.926141
$714$		0			0
$715$	622.006			0.0325339
$716$			12001.3i			0.626411i
$717$	−16324.4	−	8355.61i	−0.850272	−	0.435210i
$718$	−20331.8			−1.05679
$719$	−8614.96			−0.446848			−0.223424	−	0.974721i	$-0.571723\pi$
$719$	−8614.96			−0.446848			−0.223424	+	0.974721i	$0.571723\pi$
$720$	−1134.50	−	1573.66i	−0.0587224	−	0.0814541i
$721$		0			0
$722$		−	13546.3i		−	0.698254i
$723$	22801.6	+	11671.0i	1.17289	+	0.600342i
$724$		−	3871.40i		−	0.198729i
$725$		−	21785.2i		−	1.11598i
$726$	7238.25	+	3704.89i	0.370023	+	0.189396i
$727$		−	26635.3i		−	1.35880i	−0.733768	−	0.679400i	$-0.762240\pi$
$727$		−	26635.3i		−	1.35880i	0.733768	−	0.679400i	$-0.237760\pi$
$728$		0			0
$729$	18785.7	−	5875.05i	0.954415	−	0.298484i
$730$	−2366.43			−0.119980
$731$	45403.4			2.29727
$732$	11616.9	+	5946.07i	0.586573	+	0.300237i
$733$			6152.65i			0.310032i	0.987912	+	0.155016i	$0.0495429\pi$
$733$			6152.65i			0.310032i	−0.987912	+	0.155016i	$0.950457\pi$
$734$	767.978			0.0386193
$735$		0			0
$736$	3980.34			0.199344
$737$			2407.23i			0.120314i
$738$	−22268.8	+	16054.2i	−1.11074	+	0.800763i
$739$	14728.6			0.733153			0.366577	−	0.930388i	$-0.380530\pi$
$739$	14728.6			0.733153			0.366577	+	0.930388i	$0.380530\pi$
$740$	−5382.98			−0.267408
$741$	−129.747	+	253.487i	−0.00643236	+	0.0125669i
$742$		0			0
$743$		−	27255.1i		−	1.34575i	−0.739755	−	0.672876i	$-0.765059\pi$
$743$		−	27255.1i		−	1.34575i	0.739755	−	0.672876i	$-0.234941\pi$
$744$	2684.89	−	5245.48i	0.132302	−	0.258479i
$745$		−	12142.9i		−	0.597156i
$746$			5927.17i			0.290897i
$747$	−4270.08	−	5923.04i	−0.209149	−	0.290111i
$748$			10875.4i			0.531608i
$749$		0			0
$750$	−9547.94	−	4887.10i	−0.464855	−	0.237936i
$751$	−6151.38			−0.298891			−0.149445	−	0.988770i	$-0.547749\pi$
$751$	−6151.38			−0.298891			−0.149445	+	0.988770i	$0.547749\pi$
$752$	−1288.24			−0.0624698
$753$	−3065.92	+	5989.89i	−0.148378	+	0.289886i
$754$			2457.88i			0.118714i
$755$	6918.80			0.333511
$756$		0			0
$757$	−21107.3			−1.01342			−0.506710	−	0.862117i	$-0.669139\pi$
$757$	−21107.3			−1.01342			−0.506710	+	0.862117i	$0.669139\pi$
$758$			26390.7i			1.26458i
$759$	−6897.30	+	13475.3i	−0.329850	+	0.644428i
$760$	332.915			0.0158896
$761$	−15061.9			−0.717470			−0.358735	−	0.933439i	$-0.616792\pi$
$761$	−15061.9			−0.717470			−0.358735	+	0.933439i	$0.616792\pi$
$762$	−14380.4	−	7360.58i	−0.683657	−	0.349929i
$763$		0			0
$764$		−	1645.28i		−	0.0779113i
$765$	−8231.02	−	11417.3i	−0.389011	−	0.539598i
$766$		−	17903.8i		−	0.844505i
$767$			1209.69i			0.0569483i
$768$	−606.088	+	1184.12i	−0.0284770	+	0.0556355i
$769$			26099.2i			1.22387i	0.790906	+	0.611937i	$0.209610\pi$
$769$			26099.2i			1.22387i	−0.790906	+	0.611937i	$0.790390\pi$
$770$		0			0
$771$	3447.31	−	6735.03i	0.161027	−	0.314599i
$772$	−3265.69			−0.152247
$773$	17.6908			0.000823150			0.000411575	−	1.00000i	$-0.499869\pi$
$773$	17.6908			0.000823150			0.000411575		1.00000i	$0.499869\pi$
$774$	−17132.8	+	12351.5i	−0.795639	+	0.573598i
$775$		−	14860.8i		−	0.688795i
$776$	−1756.51			−0.0812566
$777$		0			0
$778$	17539.3			0.808244
$779$		−	4711.07i		−	0.216677i
$780$	491.355	+	251.500i	0.0225556	+	0.0115450i
$781$	1100.30			0.0504122
$782$	28878.3			1.32057
$783$	4401.53	+	28820.4i	0.200891	+	1.31540i
$784$		0			0
$785$			2476.01i			0.112577i
$786$	−19379.9	−	9919.60i	−0.879465	−	0.450153i
$787$			2385.86i			0.108064i	0.998539	+	0.0540322i	$0.0172074\pi$
$787$			2385.86i			0.108064i	−0.998539	+	0.0540322i	$0.982793\pi$
$788$			2533.32i			0.114525i
$789$	9882.50	+	5058.34i	0.445914	+	0.228241i
$790$			9585.51i			0.431693i
$791$		0			0
$792$	−2958.52	−	4103.77i	−0.132735	−	0.184117i
$793$	−3713.17			−0.166278
$794$	2741.96			0.122555
$795$	6204.78	+	3175.91i	0.276806	+	0.141683i
$796$			13692.3i			0.609688i
$797$	−13183.5			−0.585927			−0.292964	−	0.956124i	$-0.594641\pi$
$797$	−13183.5			−0.585927			−0.292964	+	0.956124i	$0.594641\pi$
$798$		0			0
$799$	−9346.49			−0.413836
$800$			3354.68i			0.148257i
$801$	−14013.7	−	19438.5i	−0.618166	−	0.857461i
$802$	−5524.41			−0.243234
$803$	−6171.12			−0.271201
$804$	−973.329	+	1901.59i	−0.0426948	+	0.0834130i
$805$		0			0
$806$			1676.64i			0.0732721i
$807$	6836.14	−	13355.8i	0.298195	−	0.582584i
$808$			7880.53i			0.343114i
$809$		−	30768.0i		−	1.33714i	−0.743649	−	0.668570i	$-0.766907\pi$
$809$		−	30768.0i		−	1.33714i	0.743649	−	0.668570i	$-0.233093\pi$
$810$	6211.87	+	2069.10i	0.269460	+	0.0897540i
$811$		−	42776.4i		−	1.85214i	−0.377357	−	0.926068i	$-0.623167\pi$
$811$		−	42776.4i		−	1.85214i	0.377357	−	0.926068i	$-0.376833\pi$
$812$		0			0
$813$	−27094.5	−	13868.3i	−1.16881	−	0.598256i
$814$	−14037.6			−0.604446
$815$	−10380.8			−0.446164
$816$	−4397.31	+	8591.03i	−0.188648	+	0.368562i
$817$		−	3624.52i		−	0.155209i
$818$	5334.75			0.228026
$819$		0			0
$820$	−9131.86			−0.388901
$821$		−	41732.6i		−	1.77403i	−0.461742	−	0.887014i	$-0.652776\pi$
$821$		−	41732.6i		−	1.77403i	0.461742	−	0.887014i	$-0.347224\pi$
$822$	2892.36	−	5650.81i	0.122728	−	0.239775i
$823$	−15644.7			−0.662624			−0.331312	−	0.943521i	$-0.607491\pi$
$823$	−15644.7			−0.662624			−0.331312	+	0.943521i	$0.607491\pi$
$824$	−10280.3			−0.434623
$825$	−11357.1	−	5813.13i	−0.479278	−	0.245318i
$826$		0			0
$827$		−	24395.1i		−	1.02576i	−0.858461	−	0.512879i	$-0.828579\pi$
$827$		−	24395.1i		−	1.02576i	0.858461	−	0.512879i	$-0.171421\pi$
$828$	−10897.1	+	7856.00i	−0.457367	+	0.329728i
$829$			37859.0i			1.58612i	0.609140	+	0.793062i	$0.291515\pi$
$829$			37859.0i			1.58612i	−0.609140	+	0.793062i	$0.708485\pi$
$830$		−	2428.88i		−	0.101576i
$831$	6636.26	−	12965.3i	0.277027	−	0.541228i
$832$		−	378.486i		−	0.0157712i
$833$		0			0
$834$	−8554.42	+	16712.8i	−0.355174	+	0.693905i
$835$	11589.8			0.480339
$836$	868.171			0.0359167
$837$	3002.51	+	19659.9i	0.123993	+	0.811880i
$838$			28961.1i			1.19385i
$839$	−40533.9			−1.66792			−0.833960	−	0.551826i	$-0.813931\pi$
$839$	−40533.9			−1.66792			−0.833960	+	0.551826i	$0.813931\pi$
$840$		0			0
$841$	−18794.8			−0.770625
$842$		−	28497.5i		−	1.16638i
$843$	−21580.2	−	11045.8i	−0.881685	−	0.451289i
$844$	−4094.60			−0.166993
$845$	9708.96			0.395264
$846$	3526.85	−	2542.60i	0.143328	−	0.103329i
$847$		0			0
$848$		−	4779.48i		−	0.193547i
$849$	−24859.9	−	12724.5i	−1.00493	−	0.514374i
$850$			24339.0i			0.982142i
$851$			37275.3i			1.50150i
$852$	869.186	+	444.892i	0.0349505	+	0.0178894i
$853$			38466.5i			1.54404i	0.635598	+	0.772021i	$0.280754\pi$
$853$			38466.5i			1.54404i	−0.635598	+	0.772021i	$0.719246\pi$
$854$		0			0
$855$	−911.431	+	657.075i	−0.0364565	+	0.0262824i
$856$	−1463.32			−0.0584290
$857$	26108.2			1.04065			0.520326	−	0.853968i	$-0.325811\pi$
$857$	26108.2			1.04065			0.520326	+	0.853968i	$0.325811\pi$
$858$	1281.35	+	655.856i	0.0509842	+	0.0260962i
$859$		−	24287.2i		−	0.964689i	−0.875982	−	0.482345i	$-0.839785\pi$
$859$		−	24287.2i		−	0.964689i	0.875982	−	0.482345i	$-0.160215\pi$
$860$	−7025.70			−0.278575
$861$		0			0
$862$	11146.3			0.440423
$863$		−	37500.0i		−	1.47916i	−0.673070	−	0.739579i	$-0.735025\pi$
$863$		−	37500.0i		−	1.47916i	0.673070	−	0.739579i	$-0.264975\pi$
$864$	−677.786	−	4438.02i	−0.0266884	−	0.174750i
$865$	−4500.11			−0.176888
$866$	−5879.86			−0.230723
$867$	−20271.8	+	39605.1i	−0.794079	+	1.55139i
$868$		0			0
$869$			24996.9i			0.975791i
$870$	−4418.73	+	8632.89i	−0.172194	+	0.336416i
$871$		−	607.818i		−	0.0236454i
$872$		−	4663.54i		−	0.181109i
$873$	4808.85	−	3466.83i	0.186432	−	0.134404i
$874$		−	2305.33i		−	0.0892206i
$875$		0			0
$876$	−4874.89	−	2495.21i	−0.188022	−	0.0962389i
$877$	−14841.4			−0.571446			−0.285723	−	0.958312i	$-0.592234\pi$
$877$	−14841.4			−0.571446			−0.285723	+	0.958312i	$0.592234\pi$
$878$	19146.6			0.735954
$879$	3082.84	−	6022.96i	0.118295	−	0.231114i
$880$		−	1682.85i		−	0.0644645i
$881$	30469.3			1.16520			0.582598	−	0.812760i	$-0.302036\pi$
$881$	30469.3			1.16520			0.582598	+	0.812760i	$0.302036\pi$
$882$		0			0
$883$	−6758.53			−0.257580			−0.128790	−	0.991672i	$-0.541109\pi$
$883$	−6758.53			−0.257580			−0.128790	+	0.991672i	$0.541109\pi$
$884$		−	2746.00i		−	0.104477i
$885$	−2174.76	+	4248.84i	−0.0826031	+	0.161382i
$886$	14312.3			0.542700
$887$	−35333.1			−1.33751			−0.668754	−	0.743484i	$-0.733172\pi$
$887$	−35333.1			−1.33751			−0.668754	+	0.743484i	$0.733172\pi$
$888$	−11089.1	−	5675.92i	−0.419059	−	0.214495i
$889$		0			0
$890$		−	7971.22i		−	0.300220i
$891$	16199.2	+	5395.76i	0.609084	+	0.202879i
$892$		−	6085.29i		−	0.228420i
$893$			746.121i			0.0279597i
$894$	12803.7	−	25014.7i	0.478994	−	0.935811i
$895$		−	13473.5i		−	0.503207i
$896$		0			0
$897$	1741.55	−	3402.47i	0.0648257	−	0.126650i
$898$	−29678.5			−1.10288
$899$	−29457.9			−1.09285
$900$	−6621.13	−	9184.20i	−0.245227	−	0.340155i
$901$		−	34676.2i		−	1.28217i
$902$	−23813.9			−0.879065
$903$		0			0
$904$	18271.5			0.672237
$905$			4346.30i			0.159642i
$906$	14252.9	+	7295.33i	0.522650	+	0.267518i
$907$	−20962.3			−0.767411			−0.383706	−	0.923455i	$-0.625352\pi$
$907$	−20962.3			−0.767411			−0.383706	+	0.923455i	$0.625352\pi$
$908$	−5836.60			−0.213320
$909$	−15553.8	−	21574.7i	−0.567533	−	0.787226i
$910$		0			0
$911$			5419.65i			0.197103i	0.995132	+	0.0985516i	$0.0314209\pi$
$911$			5419.65i			0.197103i	−0.995132	+	0.0985516i	$0.968579\pi$
$912$	685.814	+	351.033i	0.0249008	+	0.0127455i
$913$		−	6334.00i		−	0.229600i
$914$			15149.7i			0.548256i
$915$	−13041.9	−	6675.47i	−0.471204	−	0.241185i
$916$			19178.1i			0.691770i
$917$		0			0
$918$	−4917.50	−	32198.8i	−0.176799	−	1.15765i
$919$	25412.6			0.912168			0.456084	−	0.889937i	$-0.349252\pi$
$919$	25412.6			0.912168			0.456084	+	0.889937i	$0.349252\pi$
$920$	−4468.60			−0.160136
$921$	2982.92	+	1526.81i	0.106722	+	0.0546254i
$922$			29701.0i			1.06090i
$923$	−277.823			−0.00990754
$924$		0			0
$925$	−31416.1			−1.11671
$926$		−	6722.87i		−	0.238582i
$927$	28144.5	−	20290.1i	0.997181	−	0.718895i
$928$	6649.83			0.235228
$929$	553.488			0.0195472			0.00977360	−	0.999952i	$-0.496889\pi$
$929$	553.488			0.0195472			0.00977360	+	0.999952i	$0.496889\pi$
$930$	−3014.25	+	5888.94i	−0.106281	+	0.207641i
$931$		0			0
$932$		−	6677.66i		−	0.234693i
$933$	−3165.01	+	6183.49i	−0.111059	+	0.216976i
$934$			461.689i			0.0161745i
$935$		−	12209.4i		−	0.427050i
$936$	747.017	+	1036.19i	0.0260866	+	0.0361848i
$937$			18956.6i			0.660923i	0.943819	+	0.330462i	$0.107204\pi$
$937$			18956.6i			0.660923i	−0.943819	+	0.330462i	$0.892796\pi$
$938$		0			0
$939$	−7796.09	−	3990.42i	−0.270943	−	0.138682i
$940$	1446.27			0.0501831
$941$	33085.4			1.14618			0.573089	−	0.819493i	$-0.305745\pi$
$941$	33085.4			1.14618			0.573089	+	0.819493i	$0.305745\pi$
$942$	−2610.76	+	5100.64i	−0.0903005	+	0.176420i
$943$			63235.1i			2.18369i
$944$	3272.83			0.112841
$945$		0			0
$946$	−18321.5			−0.629686
$947$		−	13416.8i		−	0.460388i	−0.973145	−	0.230194i	$-0.926064\pi$
$947$		−	13416.8i		−	0.460388i	0.973145	−	0.230194i	$-0.0739360\pi$
$948$	−10107.2	+	19746.4i	−0.346271	+	0.676511i
$949$	1558.19			0.0532993
$950$	1942.96			0.0663557
$951$	−13939.8	−	7135.05i	−0.475319	−	0.243291i
$952$		0			0
$953$		−	36353.5i		−	1.23568i	−0.786303	−	0.617841i	$-0.788007\pi$
$953$		−	36353.5i		−	1.23568i	0.786303	−	0.617841i	$-0.211993\pi$
$954$	9433.26	+	13084.9i	0.320139	+	0.444066i
$955$			1847.11i			0.0625874i
$956$		−	14117.0i		−	0.477590i
$957$	−11523.1	+	22512.7i	−0.389225	+	0.760430i
$958$			8801.72i			0.296838i
$959$		0			0
$960$	680.436	−	1329.37i	0.0228760	−	0.0446929i
$961$	9696.26			0.325476
$962$	3544.46			0.118792
$963$	4006.17	−	2888.15i	0.134057	−	0.0966453i
$964$			19718.4i			0.658803i
$965$	3666.29			0.122303
$966$		0			0
$967$	3453.28			0.114840			0.0574198	−	0.998350i	$-0.481713\pi$
$967$	3453.28			0.114840			0.0574198	+	0.998350i	$0.481713\pi$
$968$			6259.50i			0.207839i
$969$	4975.74	+	2546.82i	0.164957	+	0.0844332i
$970$	1971.98			0.0652748
$971$	50640.0			1.67365			0.836826	−	0.547469i	$-0.184409\pi$
$971$	50640.0			1.67365			0.836826	+	0.547469i	$0.184409\pi$
$972$	10614.9	+	10812.3i	0.350281	+	0.356796i
$973$		0			0
$974$			23889.2i			0.785894i
$975$	2867.64	+	1467.80i	0.0941929	+	0.0482125i
$976$			10046.0i			0.329473i
$977$			31078.3i			1.01769i	0.860859	+	0.508844i	$0.169927\pi$
$977$			31078.3i			1.01769i	−0.860859	+	0.508844i	$0.830073\pi$
$978$	−21384.7	−	10945.7i	−0.699190	−	0.357880i
$979$		−	20787.2i		−	0.678613i
$980$		0			0
$981$	9204.42	+	12767.5i	0.299566	+	0.415529i
$982$	39833.3			1.29443
$983$	−40309.6			−1.30791			−0.653956	−	0.756533i	$-0.726892\pi$
$983$	−40309.6			−1.30791			−0.653956	+	0.756533i	$0.726892\pi$
$984$	−18811.9	−	9628.83i	−0.609451	−	0.311947i
$985$		−	2844.09i		−	0.0920001i
$986$	48246.0			1.55828
$987$		0			0
$988$	−219.211			−0.00705873
$989$			48650.6i			1.56420i
$990$	3321.44	+	4607.17i	0.106628	+	0.147905i
$991$	4014.56			0.128685			0.0643425	−	0.997928i	$-0.479505\pi$
$991$	4014.56			0.128685			0.0643425	+	0.997928i	$0.479505\pi$
$992$	4536.19			0.145186
$993$	1867.79	−	3649.11i	0.0596904	−	0.116617i
$994$		0			0
$995$		−	15372.0i		−	0.489773i
$996$	2561.07	−	5003.56i	0.0814764	−	0.159181i
$997$			41700.6i			1.32465i	0.749218	+	0.662323i	$0.230429\pi$
$997$			41700.6i			1.32465i	−0.749218	+	0.662323i	$0.769571\pi$
$998$		−	2662.28i		−	0.0844418i
$999$	41561.4	−	6347.37i	1.31626	−	0.201023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.d.a.293.3		16
3.2	odd	2	inner	294.4.d.a.293.14		16
7.2	even	3		294.4.f.a.227.2		16
7.3	odd	6		294.4.f.a.215.5		16
7.4	even	3		42.4.f.a.5.8	yes	16
7.5	odd	6		42.4.f.a.17.3	yes	16
7.6	odd	2	inner	294.4.d.a.293.6		16
21.2	odd	6		294.4.f.a.227.5		16
21.5	even	6		42.4.f.a.17.8	yes	16
21.11	odd	6		42.4.f.a.5.3	✓	16
21.17	even	6		294.4.f.a.215.2		16
21.20	even	2	inner	294.4.d.a.293.11		16
28.11	odd	6		336.4.bc.e.257.1		16
28.19	even	6		336.4.bc.e.17.3		16
84.11	even	6		336.4.bc.e.257.3		16
84.47	odd	6		336.4.bc.e.17.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.3	✓	16	21.11	odd	6
42.4.f.a.5.8	yes	16	7.4	even	3
42.4.f.a.17.3	yes	16	7.5	odd	6
42.4.f.a.17.8	yes	16	21.5	even	6
294.4.d.a.293.3		16	1.1	even	1	trivial
294.4.d.a.293.6		16	7.6	odd	2	inner
294.4.d.a.293.11		16	21.20	even	2	inner
294.4.d.a.293.14		16	3.2	odd	2	inner
294.4.f.a.215.2		16	21.17	even	6
294.4.f.a.215.5		16	7.3	odd	6
294.4.f.a.227.2		16	7.2	even	3
294.4.f.a.227.5		16	21.2	odd	6
336.4.bc.e.17.1		16	84.47	odd	6
336.4.bc.e.17.3		16	28.19	even	6
336.4.bc.e.257.1		16	28.11	odd	6
336.4.bc.e.257.3		16	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +(-2.36753 + 4.62545i) q^{3} -4.00000 q^{4} +4.49068 q^{5} +(9.25090 + 4.73506i) q^{6} +8.00000i q^{8} +(-15.7896 - 21.9018i) q^{9} -8.98135i q^{10} -23.4214i q^{11} +(9.47012 - 18.5018i) q^{12} +5.91384i q^{13} +(-10.6318 + 20.7714i) q^{15} +16.0000 q^{16} +116.084 q^{17} +(-43.8036 + 31.5792i) q^{18} -9.26685i q^{19} -17.9627 q^{20} -46.8428 q^{22} +124.386i q^{23} +(-37.0036 - 18.9402i) q^{24} -104.834 q^{25} +11.8277 q^{26} +(138.688 - 21.1808i) q^{27} +207.807i q^{29} +(41.5428 + 21.2636i) q^{30} +141.756i q^{31} -32.0000i q^{32} +(108.335 + 55.4509i) q^{33} -232.167i q^{34} +(63.1584 + 87.6072i) q^{36} +299.675 q^{37} -18.5337 q^{38} +(-27.3542 - 14.0012i) q^{39} +35.9254i q^{40} +508.379 q^{41} +391.127 q^{43} +93.6856i q^{44} +(-70.9060 - 98.3539i) q^{45} +248.771 q^{46} -80.5151 q^{47} +(-37.8805 + 74.0072i) q^{48} +209.668i q^{50} +(-274.832 + 536.939i) q^{51} -23.6554i q^{52} -298.718i q^{53} +(-42.3617 - 277.376i) q^{54} -105.178i q^{55} +(42.8634 + 21.9396i) q^{57} +415.614 q^{58} +204.552 q^{59} +(42.5273 - 83.0856i) q^{60} +627.877i q^{61} +283.512 q^{62} -64.0000 q^{64} +26.5572i q^{65} +(110.902 - 216.669i) q^{66} -102.779 q^{67} -464.335 q^{68} +(-575.340 - 294.487i) q^{69} +46.9785i q^{71} +(175.214 - 126.317i) q^{72} -263.482i q^{73} -599.351i q^{74} +(248.197 - 484.904i) q^{75} +37.0674i q^{76} +(-28.0024 + 54.7084i) q^{78} -1067.27 q^{79} +71.8508 q^{80} +(-230.377 + 691.641i) q^{81} -1016.76i q^{82} +270.436 q^{83} +521.294 q^{85} -782.254i q^{86} +(-961.201 - 491.990i) q^{87} +187.371 q^{88} +887.530 q^{89} +(-196.708 + 141.812i) q^{90} -497.543i q^{92} +(-655.685 - 335.612i) q^{93} +161.030i q^{94} -41.6144i q^{95} +(148.014 + 75.7610i) q^{96} +219.564i q^{97} +(-512.971 + 369.815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 64 q^{4} - 36 q^{9} + 256 q^{16} + 96 q^{18} + 24 q^{22} + 388 q^{25} - 720 q^{30} + 144 q^{36} + 1924 q^{37} - 1188 q^{39} + 1732 q^{43} - 336 q^{46} - 3276 q^{51} - 2664 q^{57} + 1560 q^{58} - 1024 q^{64}+ \cdots - 4284 q^{99}+O(q^{100}) \) 16 * q - 64 * q^4 - 36 * q^9 + 256 * q^16 + 96 * q^18 + 24 * q^22 + 388 * q^25 - 720 * q^30 + 144 * q^36 + 1924 * q^37 - 1188 * q^39 + 1732 * q^43 - 336 * q^46 - 3276 * q^51 - 2664 * q^57 + 1560 * q^58 - 1024 * q^64 + 1412 * q^67 - 384 * q^72 + 2832 * q^78 + 5312 * q^79 - 252 * q^81 + 5232 * q^85 - 96 * q^88 - 4032 * q^93 - 4284 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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