LMFDB - Embedded newform 1050.3.c.c.449.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(449,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1050.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.c (of order $2$, degree $1$, not 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.4
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.c.449.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-2.88800 + 0.812085i) q^{3} +2.00000 q^{4} +(4.08424 - 1.14846i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(7.68104 - 4.69059i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-2.88800 + 0.812085i) q^{3} +2.00000 q^{4} +(4.08424 - 1.14846i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(7.68104 - 4.69059i) q^{9} +19.7741i q^{11} +(-5.77599 + 1.62417i) q^{12} -18.5947i q^{13} +3.74166i q^{14} +4.00000 q^{16} -13.2896 q^{17} +(-10.8626 + 6.63350i) q^{18} +5.47422 q^{19} +(2.14857 + 7.64092i) q^{21} -27.9648i q^{22} +34.8062 q^{23} +(8.16849 - 2.29692i) q^{24} +26.2969i q^{26} +(-18.3736 + 19.7841i) q^{27} -5.29150i q^{28} +6.83287i q^{29} -31.4842 q^{31} -5.65685 q^{32} +(-16.0583 - 57.1076i) q^{33} +18.7944 q^{34} +(15.3621 - 9.38119i) q^{36} -10.1809i q^{37} -7.74172 q^{38} +(15.1005 + 53.7014i) q^{39} -28.9124i q^{41} +(-3.03854 - 10.8059i) q^{42} +19.1117i q^{43} +39.5483i q^{44} -49.2233 q^{46} -45.1245 q^{47} +(-11.5520 + 3.24834i) q^{48} -7.00000 q^{49} +(38.3804 - 10.7923i) q^{51} -37.1894i q^{52} -74.1324 q^{53} +(25.9843 - 27.9789i) q^{54} +7.48331i q^{56} +(-15.8095 + 4.44553i) q^{57} -9.66313i q^{58} -32.5630i q^{59} +71.7631 q^{61} +44.5254 q^{62} +(-12.4101 - 20.3221i) q^{63} +8.00000 q^{64} +(22.7098 + 80.7624i) q^{66} +66.6261i q^{67} -26.5793 q^{68} +(-100.520 + 28.2655i) q^{69} -101.245i q^{71} +(-21.7253 + 13.2670i) q^{72} -45.9939i q^{73} +14.3979i q^{74} +10.9484 q^{76} +52.3174 q^{77} +(-21.3553 - 75.9452i) q^{78} +140.809 q^{79} +(36.9967 - 72.0572i) q^{81} +40.8883i q^{82} +100.622 q^{83} +(4.29715 + 15.2818i) q^{84} -27.0280i q^{86} +(-5.54887 - 19.7333i) q^{87} -55.9297i q^{88} -11.2035i q^{89} -49.1969 q^{91} +69.6123 q^{92} +(90.9263 - 25.5678i) q^{93} +63.8157 q^{94} +(16.3370 - 4.59384i) q^{96} +102.496i q^{97} +9.89949 q^{98} +(92.7524 + 151.886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−2.88800	+	0.812085i	−0.962665	+	0.270695i
$3$	−2.88800	+	0.812085i	−0.962665	+	0.270695i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	4.08424	−	1.14846i	0.680707	−	0.191410i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−2.82843			−0.353553
$9$	7.68104	−	4.69059i	0.853449	−	0.521177i
$10$		0			0
$11$			19.7741i			1.79765i	0.438309	+	0.898824i	$0.355577\pi$
$11$			19.7741i			1.79765i	−0.438309	+	0.898824i	$0.644423\pi$
$12$	−5.77599	+	1.62417i	−0.481333	+	0.135347i
$13$		−	18.5947i		−	1.43036i	−0.698940	−	0.715181i	$-0.746344\pi$
$13$		−	18.5947i		−	1.43036i	0.698940	−	0.715181i	$-0.253656\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	−13.2896			−0.781743			−0.390872	−	0.920445i	$-0.627826\pi$
$17$	−13.2896			−0.781743			−0.390872	+	0.920445i	$0.627826\pi$
$18$	−10.8626	+	6.63350i	−0.603479	+	0.368528i
$19$	5.47422			0.288117			0.144058	−	0.989569i	$-0.453985\pi$
$19$	5.47422			0.288117			0.144058	+	0.989569i	$0.453985\pi$
$20$		0			0
$21$	2.14857	+	7.64092i	0.102313	+	0.363853i
$22$		−	27.9648i		−	1.27113i
$23$	34.8062			1.51331			0.756656	−	0.653814i	$-0.226832\pi$
$23$	34.8062			1.51331			0.756656	+	0.653814i	$0.226832\pi$
$24$	8.16849	−	2.29692i	0.340354	−	0.0957051i
$25$		0			0
$26$			26.2969i			1.01142i
$27$	−18.3736	+	19.7841i	−0.680505	+	0.732743i
$28$		−	5.29150i		−	0.188982i
$29$			6.83287i			0.235616i	0.993036	+	0.117808i	$0.0375867\pi$
$29$			6.83287i			0.235616i	−0.993036	+	0.117808i	$0.962413\pi$
$30$		0			0
$31$	−31.4842			−1.01562			−0.507810	−	0.861469i	$-0.669545\pi$
$31$	−31.4842			−1.01562			−0.507810	+	0.861469i	$0.669545\pi$
$32$	−5.65685			−0.176777
$33$	−16.0583	−	57.1076i	−0.486614	−	1.73053i
$34$	18.7944			0.552776
$35$		0			0
$36$	15.3621	−	9.38119i	0.426724	−	0.260589i
$37$		−	10.1809i		−	0.275159i	−0.990491	−	0.137580i	$-0.956068\pi$
$37$		−	10.1809i		−	0.275159i	0.990491	−	0.137580i	$-0.0439323\pi$
$38$	−7.74172			−0.203729
$39$	15.1005	+	53.7014i	0.387191	+	1.37696i
$40$		0			0
$41$		−	28.9124i		−	0.705180i	−0.935778	−	0.352590i	$-0.885301\pi$
$41$		−	28.9124i		−	0.705180i	0.935778	−	0.352590i	$-0.114699\pi$
$42$	−3.03854	−	10.8059i	−0.0723462	−	0.257283i
$43$			19.1117i			0.444458i	0.974995	+	0.222229i	$0.0713332\pi$
$43$			19.1117i			0.444458i	−0.974995	+	0.222229i	$0.928667\pi$
$44$			39.5483i			0.898824i
$45$		0			0
$46$	−49.2233			−1.07007
$47$	−45.1245			−0.960096			−0.480048	−	0.877242i	$-0.659381\pi$
$47$	−45.1245			−0.960096			−0.480048	+	0.877242i	$0.659381\pi$
$48$	−11.5520	+	3.24834i	−0.240666	+	0.0676737i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	38.3804	−	10.7923i	0.752557	−	0.211614i
$52$		−	37.1894i		−	0.715181i
$53$	−74.1324			−1.39872			−0.699362	−	0.714767i	$-0.746533\pi$
$53$	−74.1324			−1.39872			−0.699362	+	0.714767i	$0.746533\pi$
$54$	25.9843	−	27.9789i	0.481190	−	0.518128i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	−15.8095	+	4.44553i	−0.277360	+	0.0779918i
$58$		−	9.66313i		−	0.166606i
$59$		−	32.5630i		−	0.551916i	−0.961170	−	0.275958i	$-0.911005\pi$
$59$		−	32.5630i		−	0.551916i	0.961170	−	0.275958i	$-0.0889950\pi$
$60$		0			0
$61$	71.7631			1.17644			0.588222	−	0.808700i	$-0.299828\pi$
$61$	71.7631			1.17644			0.588222	+	0.808700i	$0.299828\pi$
$62$	44.5254			0.718152
$63$	−12.4101	−	20.3221i	−0.196986	−	0.322573i
$64$	8.00000			0.125000
$65$		0			0
$66$	22.7098	+	80.7624i	0.344088	+	1.22367i
$67$			66.6261i			0.994419i	0.867631	+	0.497210i	$0.165642\pi$
$67$			66.6261i			0.994419i	−0.867631	+	0.497210i	$0.834358\pi$
$68$	−26.5793			−0.390872
$69$	−100.520	+	28.2655i	−1.45681	+	0.409646i
$70$		0			0
$71$		−	101.245i		−	1.42599i	−0.701170	−	0.712994i	$-0.747339\pi$
$71$		−	101.245i		−	1.42599i	0.701170	−	0.712994i	$-0.252661\pi$
$72$	−21.7253	+	13.2670i	−0.301740	+	0.184264i
$73$		−	45.9939i		−	0.630053i	−0.949083	−	0.315026i	$-0.897987\pi$
$73$		−	45.9939i		−	0.630053i	0.949083	−	0.315026i	$-0.102013\pi$
$74$			14.3979i			0.194567i
$75$		0			0
$76$	10.9484			0.144058
$77$	52.3174			0.679447
$78$	−21.3553	−	75.9452i	−0.273786	−	0.973657i
$79$	140.809			1.78239			0.891195	−	0.453620i	$-0.149868\pi$
$79$	140.809			1.78239			0.891195	+	0.453620i	$0.149868\pi$
$80$		0			0
$81$	36.9967	−	72.0572i	0.456749	−	0.889596i
$82$			40.8883i			0.498637i
$83$	100.622			1.21231			0.606154	−	0.795347i	$-0.292712\pi$
$83$	100.622			1.21231			0.606154	+	0.795347i	$0.292712\pi$
$84$	4.29715	+	15.2818i	0.0511565	+	0.181927i
$85$		0			0
$86$		−	27.0280i		−	0.314279i
$87$	−5.54887	−	19.7333i	−0.0637801	−	0.226819i
$88$		−	55.9297i		−	0.635565i
$89$		−	11.2035i		−	0.125882i	−0.998017	−	0.0629410i	$-0.979952\pi$
$89$		−	11.2035i		−	0.125882i	0.998017	−	0.0629410i	$-0.0200480\pi$
$90$		0			0
$91$	−49.1969			−0.540626
$92$	69.6123			0.756656
$93$	90.9263	−	25.5678i	0.977702	−	0.274923i
$94$	63.8157			0.678890
$95$		0			0
$96$	16.3370	−	4.59384i	0.170177	−	0.0478525i
$97$			102.496i			1.05666i	0.849038	+	0.528332i	$0.177182\pi$
$97$			102.496i			1.05666i	−0.849038	+	0.528332i	$0.822818\pi$
$98$	9.89949			0.101015
$99$	92.7524	+	151.886i	0.936893	+	1.53420i
$100$		0			0
$101$			141.006i			1.39610i	0.716050	+	0.698049i	$0.245948\pi$
$101$			141.006i			1.39610i	−0.716050	+	0.698049i	$0.754052\pi$
$102$	−54.2781	+	15.2626i	−0.532138	+	0.149634i
$103$		−	59.0361i		−	0.573166i	−0.958055	−	0.286583i	$-0.907481\pi$
$103$		−	59.0361i		−	0.573166i	0.958055	−	0.286583i	$-0.0925194\pi$
$104$			52.5937i			0.505709i
$105$		0			0
$106$	104.839			0.989048
$107$	90.2764			0.843705			0.421852	−	0.906664i	$-0.361380\pi$
$107$	90.2764			0.843705			0.421852	+	0.906664i	$0.361380\pi$
$108$	−36.7473	+	39.5681i	−0.340253	+	0.366372i
$109$	92.1672			0.845570			0.422785	−	0.906230i	$-0.361052\pi$
$109$	92.1672			0.845570			0.422785	+	0.906230i	$0.361052\pi$
$110$		0			0
$111$	8.26774	+	29.4024i	0.0744842	+	0.264886i
$112$		−	10.5830i		−	0.0944911i
$113$	148.929			1.31795			0.658977	−	0.752163i	$-0.270989\pi$
$113$	148.929			1.31795			0.658977	+	0.752163i	$0.270989\pi$
$114$	22.3580	−	6.28693i	0.196123	−	0.0551485i
$115$		0			0
$116$			13.6657i			0.117808i
$117$	−87.2202	−	142.827i	−0.745471	−	1.22074i
$118$			46.0511i			0.390263i
$119$			35.1611i			0.295471i
$120$		0			0
$121$	−270.016			−2.23154
$122$	−101.488			−0.831871
$123$	23.4793	+	83.4988i	0.190889	+	0.678852i
$124$	−62.9684			−0.507810
$125$		0			0
$126$	17.5506	+	28.7398i	0.139290	+	0.228094i
$127$			77.7817i			0.612455i	0.951958	+	0.306227i	$0.0990668\pi$
$127$			77.7817i			0.612455i	−0.951958	+	0.306227i	$0.900933\pi$
$128$	−11.3137			−0.0883883
$129$	−15.5203	−	55.1944i	−0.120312	−	0.427864i
$130$		0			0
$131$		−	229.780i		−	1.75405i	−0.480447	−	0.877024i	$-0.659526\pi$
$131$		−	229.780i		−	1.75405i	0.480447	−	0.877024i	$-0.340474\pi$
$132$	−32.1165	−	114.215i	−0.243307	−	0.865267i
$133$		−	14.4834i		−	0.108898i
$134$		−	94.2235i		−	0.703160i
$135$		0			0
$136$	37.5888			0.276388
$137$	143.560			1.04788			0.523941	−	0.851754i	$-0.324461\pi$
$137$	143.560			1.04788			0.523941	+	0.851754i	$0.324461\pi$
$138$	142.157	−	39.9735i	1.03012	−	0.289663i
$139$	257.958			1.85581			0.927906	−	0.372815i	$-0.121607\pi$
$139$	257.958			1.85581			0.927906	+	0.372815i	$0.121607\pi$
$140$		0			0
$141$	130.319	−	36.6449i	0.924251	−	0.259893i
$142$			143.182i			1.00833i
$143$	367.694			2.57129
$144$	30.7241	−	18.7624i	0.213362	−	0.130294i
$145$		0			0
$146$			65.0451i			0.445515i
$147$	20.2160	−	5.68459i	0.137524	−	0.0386707i
$148$		−	20.3618i		−	0.137580i
$149$		−	117.530i		−	0.788791i	−0.918941	−	0.394396i	$-0.870954\pi$
$149$		−	117.530i		−	0.788791i	0.918941	−	0.394396i	$-0.129046\pi$
$150$		0			0
$151$	251.056			1.66262			0.831311	−	0.555808i	$-0.187591\pi$
$151$	251.056			1.66262			0.831311	+	0.555808i	$0.187591\pi$
$152$	−15.4834			−0.101865
$153$	−102.078	+	62.3363i	−0.667178	+	0.407427i
$154$	−73.9880			−0.480442
$155$		0			0
$156$	30.2009	+	107.403i	0.193596	+	0.688479i
$157$			18.6419i			0.118738i	0.998236	+	0.0593690i	$0.0189089\pi$
$157$			18.6419i			0.118738i	−0.998236	+	0.0593690i	$0.981091\pi$
$158$	−199.134			−1.26034
$159$	214.094	−	60.2018i	1.34650	−	0.378628i
$160$		0			0
$161$		−	92.0884i		−	0.571978i
$162$	−52.3212	+	101.904i	−0.322970	+	0.629039i
$163$			14.1896i			0.0870529i	0.999052	+	0.0435265i	$0.0138593\pi$
$163$			14.1896i			0.0870529i	−0.999052	+	0.0435265i	$0.986141\pi$
$164$		−	57.8247i		−	0.352590i
$165$		0			0
$166$	−142.300			−0.857231
$167$	173.839			1.04095			0.520476	−	0.853877i	$-0.325755\pi$
$167$	173.839			1.04095			0.520476	+	0.853877i	$0.325755\pi$
$168$	−6.07708	−	21.6118i	−0.0361731	−	0.128642i
$169$	−176.763			−1.04593
$170$		0			0
$171$	42.0477	−	25.6773i	0.245893	−	0.150160i
$172$			38.2233i			0.222229i
$173$	164.076			0.948415			0.474207	−	0.880413i	$-0.342735\pi$
$173$	164.076			0.948415			0.474207	+	0.880413i	$0.342735\pi$
$174$	7.84728	+	27.9071i	0.0450993	+	0.160386i
$175$		0			0
$176$			79.0965i			0.449412i
$177$	26.4439	+	94.0419i	0.149401	+	0.531310i
$178$			15.8441i			0.0890120i
$179$		−	267.494i		−	1.49438i	−0.664611	−	0.747189i	$-0.731403\pi$
$179$		−	267.494i		−	1.49438i	0.664611	−	0.747189i	$-0.268597\pi$
$180$		0			0
$181$	188.355			1.04063			0.520317	−	0.853973i	$-0.325814\pi$
$181$	188.355			1.04063			0.520317	+	0.853973i	$0.325814\pi$
$182$	69.5750			0.382280
$183$	−207.251	+	58.2777i	−1.13252	+	0.318457i
$184$	−98.4467			−0.535036
$185$		0			0
$186$	−128.589	+	36.1584i	−0.691340	+	0.194400i
$187$		−	262.791i		−	1.40530i
$188$	−90.2490			−0.480048
$189$	52.3437	+	48.6121i	0.276951	+	0.257207i
$190$		0			0
$191$			300.383i			1.57268i	0.617791	+	0.786342i	$0.288028\pi$
$191$			300.383i			1.57268i	−0.617791	+	0.786342i	$0.711972\pi$
$192$	−23.1040	+	6.49668i	−0.120333	+	0.0338369i
$193$		−	209.232i		−	1.08410i	−0.840345	−	0.542051i	$-0.817648\pi$
$193$		−	209.232i		−	1.08410i	0.840345	−	0.542051i	$-0.182352\pi$
$194$		−	144.952i		−	0.747175i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−97.0683			−0.492733			−0.246366	−	0.969177i	$-0.579237\pi$
$197$	−97.0683			−0.492733			−0.246366	+	0.969177i	$0.579237\pi$
$198$	−131.172	−	214.799i	−0.662483	−	1.08484i
$199$	−292.070			−1.46769			−0.733845	−	0.679317i	$-0.762276\pi$
$199$	−292.070			−1.46769			−0.733845	+	0.679317i	$0.762276\pi$
$200$		0			0
$201$	−54.1060	−	192.416i	−0.269184	−	0.957293i
$202$		−	199.413i		−	0.987191i
$203$	18.0781			0.0890545
$204$	76.7608	−	21.5846i	0.376279	−	0.105807i
$205$		0			0
$206$			83.4897i			0.405290i
$207$	267.347	−	163.262i	1.29153	−	0.788703i
$208$		−	74.3788i		−	0.357590i
$209$			108.248i			0.517933i
$210$		0			0
$211$	−88.4332			−0.419115			−0.209557	−	0.977796i	$-0.567202\pi$
$211$	−88.4332			−0.419115			−0.209557	+	0.977796i	$0.567202\pi$
$212$	−148.265			−0.699362
$213$	82.2196	+	292.396i	0.386008	+	1.37275i
$214$	−127.670			−0.596590
$215$		0			0
$216$	51.9685	−	55.9578i	0.240595	−	0.259064i
$217$			83.2994i			0.383868i
$218$	−130.344			−0.597909
$219$	37.3509	+	132.830i	0.170552	+	0.606530i
$220$		0			0
$221$			247.117i			1.11818i
$222$	−11.6924	−	41.5812i	−0.0526683	−	0.187303i
$223$		−	330.233i		−	1.48087i	−0.672130	−	0.740433i	$-0.734620\pi$
$223$		−	330.233i		−	1.48087i	0.672130	−	0.740433i	$-0.265380\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	−210.617			−0.931935
$227$	283.024			1.24680			0.623402	−	0.781902i	$-0.285750\pi$
$227$	283.024			1.24680			0.623402	+	0.781902i	$0.285750\pi$
$228$	−31.6191	+	8.89106i	−0.138680	+	0.0389959i
$229$	17.0978			0.0746629			0.0373314	−	0.999303i	$-0.488114\pi$
$229$	17.0978			0.0746629			0.0373314	+	0.999303i	$0.488114\pi$
$230$		0			0
$231$	−151.093	+	42.4862i	−0.654080	+	0.183923i
$232$		−	19.3263i		−	0.0833029i
$233$	−223.943			−0.961129			−0.480564	−	0.876960i	$-0.659568\pi$
$233$	−223.943			−0.961129			−0.480564	+	0.876960i	$0.659568\pi$
$234$	123.348	+	201.987i	0.527128	+	0.863193i
$235$		0			0
$236$		−	65.1261i		−	0.275958i
$237$	−406.655	+	114.349i	−1.71584	+	0.482484i
$238$		−	49.7253i		−	0.208930i
$239$			10.9304i			0.0457340i	0.999739	+	0.0228670i	$0.00727942\pi$
$239$			10.9304i			0.0457340i	−0.999739	+	0.0228670i	$0.992721\pi$
$240$		0			0
$241$	177.306			0.735710			0.367855	−	0.929883i	$-0.380092\pi$
$241$	177.306			0.735710			0.367855	+	0.929883i	$0.380092\pi$
$242$	381.861			1.57794
$243$	−48.3296	+	238.145i	−0.198887	+	0.980022i
$244$	143.526			0.588222
$245$		0			0
$246$	−33.2047	−	118.085i	−0.134979	−	0.480021i
$247$		−	101.791i		−	0.412111i
$248$	89.0508			0.359076
$249$	−290.595	+	81.7132i	−1.16705	+	0.328166i
$250$		0			0
$251$		−	182.001i		−	0.725103i	−0.931964	−	0.362551i	$-0.881906\pi$
$251$		−	182.001i		−	0.725103i	0.931964	−	0.362551i	$-0.118094\pi$
$252$	−24.8203	−	40.6442i	−0.0984932	−	0.161287i
$253$			688.262i			2.72040i
$254$		−	110.000i		−	0.433071i
$255$		0			0
$256$	16.0000			0.0625000
$257$	155.204			0.603906			0.301953	−	0.953323i	$-0.402361\pi$
$257$	155.204			0.603906			0.301953	+	0.953323i	$0.402361\pi$
$258$	21.9490	+	78.0567i	0.0850737	+	0.302545i
$259$	−26.9361			−0.104000
$260$		0			0
$261$	32.0502	+	52.4835i	0.122798	+	0.201086i
$262$			324.958i			1.24030i
$263$	−159.605			−0.606861			−0.303431	−	0.952854i	$-0.598132\pi$
$263$	−159.605			−0.606861			−0.303431	+	0.952854i	$0.598132\pi$
$264$	45.4196	+	161.525i	0.172044	+	0.611836i
$265$		0			0
$266$			20.4827i			0.0770025i
$267$	9.09818	+	32.3556i	0.0340756	+	0.121182i
$268$			133.252i			0.497210i
$269$			198.340i			0.737323i	0.929564	+	0.368661i	$0.120184\pi$
$269$			198.340i			0.737323i	−0.929564	+	0.368661i	$0.879816\pi$
$270$		0			0
$271$	46.2341			0.170606			0.0853028	−	0.996355i	$-0.472814\pi$
$271$	46.2341			0.170606			0.0853028	+	0.996355i	$0.472814\pi$
$272$	−53.1586			−0.195436
$273$	142.081	−	39.9521i	0.520442	−	0.146345i
$274$	−203.024			−0.740965
$275$		0			0
$276$	−201.040	+	56.5311i	−0.728406	+	0.204823i
$277$			387.786i			1.39995i	0.714168	+	0.699974i	$0.246805\pi$
$277$			387.786i			1.39995i	−0.714168	+	0.699974i	$0.753195\pi$
$278$	−364.807			−1.31226
$279$	−241.831	+	147.680i	−0.866779	+	0.529318i
$280$		0			0
$281$		−	46.9368i		−	0.167035i	−0.996506	−	0.0835174i	$-0.973385\pi$
$281$		−	46.9368i		−	0.167035i	0.996506	−	0.0835174i	$-0.0266154\pi$
$282$	−184.299	+	51.8237i	−0.653544	+	0.183772i
$283$			32.3428i			0.114286i	0.998366	+	0.0571428i	$0.0181990\pi$
$283$			32.3428i			0.114286i	−0.998366	+	0.0571428i	$0.981801\pi$
$284$		−	202.490i		−	0.712994i
$285$		0			0
$286$	−519.998			−1.81817
$287$	−76.4949			−0.266533
$288$	−43.4505	+	26.5340i	−0.150870	+	0.0921320i
$289$	−112.386			−0.388877
$290$		0			0
$291$	−83.2358	−	296.009i	−0.286034	−	1.01721i
$292$		−	91.9877i		−	0.315026i
$293$	−36.5402			−0.124711			−0.0623553	−	0.998054i	$-0.519861\pi$
$293$	−36.5402			−0.124711			−0.0623553	+	0.998054i	$0.519861\pi$
$294$	−28.5897	+	8.03923i	−0.0972439	+	0.0273443i
$295$		0			0
$296$			28.7959i			0.0972834i
$297$	−391.213	−	363.323i	−1.31721	−	1.22331i
$298$			166.212i			0.557760i
$299$		−	647.210i		−	2.16458i
$300$		0			0
$301$	50.5647			0.167989
$302$	−355.047			−1.17565
$303$	−114.509	−	407.225i	−0.377917	−	1.34398i
$304$	21.8969			0.0720292
$305$		0			0
$306$	144.360	−	88.1568i	0.471766	−	0.288094i
$307$		−	57.4988i		−	0.187292i	−0.995606	−	0.0936462i	$-0.970148\pi$
$307$		−	57.4988i		−	0.187292i	0.995606	−	0.0936462i	$-0.0298523\pi$
$308$	104.635			0.339724
$309$	47.9423	+	170.496i	0.155153	+	0.551767i
$310$		0			0
$311$			230.523i			0.741231i	0.928786	+	0.370615i	$0.120853\pi$
$311$			230.523i			0.741231i	−0.928786	+	0.370615i	$0.879147\pi$
$312$	−42.7106	−	151.890i	−0.136893	−	0.486828i
$313$		−	449.686i		−	1.43670i	−0.695684	−	0.718348i	$-0.744899\pi$
$313$		−	449.686i		−	1.43670i	0.695684	−	0.718348i	$-0.255101\pi$
$314$		−	26.3636i		−	0.0839605i
$315$		0			0
$316$	281.618			0.891195
$317$	370.113			1.16755			0.583775	−	0.811916i	$-0.301575\pi$
$317$	370.113			1.16755			0.583775	+	0.811916i	$0.301575\pi$
$318$	−302.775	+	85.1382i	−0.952122	+	0.267730i
$319$	−135.114			−0.423555
$320$		0			0
$321$	−260.718	+	73.3121i	−0.812205	+	0.228387i
$322$			130.233i			0.404449i
$323$	−72.7504			−0.225233
$324$	73.9933	−	144.114i	0.228374	−	0.444798i
$325$		0			0
$326$		−	20.0672i		−	0.0615557i
$327$	−266.178	+	74.8475i	−0.814001	+	0.228892i
$328$			81.7765i			0.249319i
$329$			119.388i			0.362882i
$330$		0			0
$331$	−125.253			−0.378409			−0.189204	−	0.981938i	$-0.560591\pi$
$331$	−125.253			−0.378409			−0.189204	+	0.981938i	$0.560591\pi$
$332$	201.243			0.606154
$333$	−47.7544	−	78.1998i	−0.143407	−	0.234834i
$334$	−245.845			−0.736064
$335$		0			0
$336$	8.59430	+	30.5637i	0.0255783	+	0.0909633i
$337$			5.34562i			0.0158624i	0.999969	+	0.00793119i	$0.00252460\pi$
$337$			5.34562i			0.0158624i	−0.999969	+	0.00793119i	$0.997475\pi$
$338$	249.980			0.739586
$339$	−430.106	+	120.943i	−1.26875	+	0.356764i
$340$		0			0
$341$		−	622.573i		−	1.82573i
$342$	−59.4644	+	36.3133i	−0.173873	+	0.106179i
$343$			18.5203i			0.0539949i
$344$		−	54.0560i		−	0.157139i
$345$		0			0
$346$	−232.038			−0.670630
$347$	−277.074			−0.798485			−0.399242	−	0.916845i	$-0.630727\pi$
$347$	−277.074			−0.798485			−0.399242	+	0.916845i	$0.630727\pi$
$348$	−11.0977	−	39.4666i	−0.0318900	−	0.113410i
$349$	−371.020			−1.06309			−0.531547	−	0.847029i	$-0.678389\pi$
$349$	−371.020			−1.06309			−0.531547	+	0.847029i	$0.678389\pi$
$350$		0			0
$351$	367.879	+	341.652i	1.04809	+	0.973368i
$352$		−	111.859i		−	0.317782i
$353$	−200.070			−0.566770			−0.283385	−	0.959006i	$-0.591457\pi$
$353$	−200.070			−0.566770			−0.283385	+	0.959006i	$0.591457\pi$
$354$	−37.3974	−	132.995i	−0.105642	−	0.375693i
$355$		0			0
$356$		−	22.4070i		−	0.0629410i
$357$	−28.5538	−	101.545i	−0.0799825	−	0.284440i
$358$			378.293i			1.05669i
$359$		−	13.1711i		−	0.0366884i	−0.999832	−	0.0183442i	$-0.994161\pi$
$359$		−	13.1711i		−	0.0366884i	0.999832	−	0.0183442i	$-0.00583947\pi$
$360$		0			0
$361$	−331.033			−0.916989
$362$	−266.374			−0.735839
$363$	779.806	−	219.276i	2.14823	−	0.604066i
$364$	−98.3939			−0.270313
$365$		0			0
$366$	293.098	−	82.4171i	0.800814	−	0.225183i
$367$			347.808i			0.947706i	0.880604	+	0.473853i	$0.157137\pi$
$367$			347.808i			0.947706i	−0.880604	+	0.473853i	$0.842863\pi$
$368$	139.225			0.378328
$369$	−135.616	−	222.077i	−0.367523	−	0.601835i
$370$		0			0
$371$			196.136i			0.528668i
$372$	181.853	−	51.1357i	0.488851	−	0.137462i
$373$			558.926i			1.49846i	0.662310	+	0.749230i	$0.269576\pi$
$373$			558.926i			1.49846i	−0.662310	+	0.749230i	$0.730424\pi$
$374$			371.643i			0.993697i
$375$		0			0
$376$	127.631			0.339445
$377$	127.055			0.337016
$378$	−74.0252	−	68.7479i	−0.195834	−	0.181873i
$379$	585.239			1.54417			0.772083	−	0.635522i	$-0.219215\pi$
$379$	585.239			1.54417			0.772083	+	0.635522i	$0.219215\pi$
$380$		0			0
$381$	−63.1654	−	224.633i	−0.165788	−	0.589589i
$382$		−	424.805i		−	1.11206i
$383$	391.278			1.02161			0.510807	−	0.859696i	$-0.329347\pi$
$383$	391.278			1.02161			0.510807	+	0.859696i	$0.329347\pi$
$384$	32.6739	−	9.18769i	0.0850884	−	0.0239263i
$385$		0			0
$386$			295.899i			0.766577i
$387$	89.6451	+	146.797i	0.231641	+	0.379322i
$388$			204.993i			0.528332i
$389$		−	412.091i		−	1.05936i	−0.848197	−	0.529680i	$-0.822312\pi$
$389$		−	412.091i		−	1.05936i	0.848197	−	0.529680i	$-0.177688\pi$
$390$		0			0
$391$	−462.561			−1.18302
$392$	19.7990			0.0505076
$393$	186.601	+	663.604i	0.474812	+	1.68856i
$394$	137.275			0.348415
$395$		0			0
$396$	185.505	+	303.772i	0.468447	+	0.767100i
$397$		−	620.931i		−	1.56406i	−0.623243	−	0.782028i	$-0.714185\pi$
$397$		−	620.931i		−	1.56406i	0.623243	−	0.782028i	$-0.285815\pi$
$398$	413.050			1.03781
$399$	11.7618	+	41.8281i	0.0294781	+	0.104832i
$400$		0			0
$401$		−	517.392i		−	1.29025i	−0.764075	−	0.645127i	$-0.776804\pi$
$401$		−	517.392i		−	1.29025i	0.764075	−	0.645127i	$-0.223196\pi$
$402$	76.5175	+	272.117i	0.190342	+	0.676908i
$403$			585.439i			1.45270i
$404$			282.012i			0.698049i
$405$		0			0
$406$	−25.5662			−0.0629710
$407$	201.318			0.494639
$408$	−108.556	+	30.5253i	−0.266069	+	0.0748168i
$409$	46.7243			0.114240			0.0571202	−	0.998367i	$-0.481808\pi$
$409$	46.7243			0.114240			0.0571202	+	0.998367i	$0.481808\pi$
$410$		0			0
$411$	−414.600	+	116.583i	−1.00876	+	0.283656i
$412$		−	118.072i		−	0.286583i
$413$	−86.1537			−0.208605
$414$	−378.086	+	230.887i	−0.913252	+	0.557697i
$415$		0			0
$416$			105.187i			0.252855i
$417$	−744.981	+	209.484i	−1.78652	+	0.502359i
$418$		−	153.086i		−	0.366234i
$419$			165.753i			0.395591i	0.980243	+	0.197796i	$0.0633783\pi$
$419$			165.753i			0.395591i	−0.980243	+	0.197796i	$0.936622\pi$
$420$		0			0
$421$	660.766			1.56952			0.784758	−	0.619802i	$-0.212787\pi$
$421$	660.766			1.56952			0.784758	+	0.619802i	$0.212787\pi$
$422$	125.063			0.296359
$423$	−346.603	+	211.661i	−0.819392	+	0.500380i
$424$	209.678			0.494524
$425$		0			0
$426$	−116.276	−	413.510i	−0.272949	−	0.970680i
$427$		−	189.867i		−	0.444654i
$428$	180.553			0.421852
$429$	−1061.90	+	298.599i	−2.47529	+	0.696034i
$430$		0			0
$431$		−	182.301i		−	0.422972i	−0.977381	−	0.211486i	$-0.932170\pi$
$431$		−	182.301i		−	0.422972i	0.977381	−	0.211486i	$-0.0678303\pi$
$432$	−73.4946	+	79.1363i	−0.170126	+	0.183186i
$433$		−	116.523i		−	0.269106i	−0.990906	−	0.134553i	$-0.957040\pi$
$433$		−	116.523i		−	0.269106i	0.990906	−	0.134553i	$-0.0429598\pi$
$434$		−	117.803i		−	0.271436i
$435$		0			0
$436$	184.334			0.422785
$437$	190.537			0.436010
$438$	−52.8222	−	187.850i	−0.120599	−	0.428881i
$439$	−377.751			−0.860481			−0.430240	−	0.902714i	$-0.641571\pi$
$439$	−377.751			−0.860481			−0.430240	+	0.902714i	$0.641571\pi$
$440$		0			0
$441$	−53.7673	+	32.8342i	−0.121921	+	0.0744539i
$442$		−	349.476i		−	0.790669i
$443$	152.788			0.344893			0.172447	−	0.985019i	$-0.444833\pi$
$443$	152.788			0.344893			0.172447	+	0.985019i	$0.444833\pi$
$444$	16.5355	+	58.8047i	0.0372421	+	0.132443i
$445$		0			0
$446$			467.020i			1.04713i
$447$	95.4442	+	339.426i	0.213522	+	0.759342i
$448$		−	21.1660i		−	0.0472456i
$449$		−	201.173i		−	0.448047i	−0.974584	−	0.224023i	$-0.928081\pi$
$449$		−	201.173i		−	0.448047i	0.974584	−	0.224023i	$-0.0719192\pi$
$450$		0			0
$451$	571.717			1.26767
$452$	297.858			0.658977
$453$	−725.048	+	203.879i	−1.60055	+	0.450063i
$454$	−400.257			−0.881623
$455$		0			0
$456$	44.7161	−	12.5739i	0.0980616	−	0.0275743i
$457$		−	718.056i		−	1.57124i	−0.618710	−	0.785620i	$-0.712344\pi$
$457$		−	718.056i		−	1.57124i	0.618710	−	0.785620i	$-0.287656\pi$
$458$	−24.1799			−0.0527946
$459$	244.179	−	262.923i	0.531981	−	0.572817i
$460$		0			0
$461$			344.884i			0.748121i	0.927404	+	0.374061i	$0.122035\pi$
$461$			344.884i			0.748121i	−0.927404	+	0.374061i	$0.877965\pi$
$462$	213.677	−	60.0845i	0.462505	−	0.130053i
$463$			561.331i			1.21238i	0.795321	+	0.606189i	$0.207303\pi$
$463$			561.331i			1.21238i	−0.795321	+	0.606189i	$0.792697\pi$
$464$			27.3315i			0.0589040i
$465$		0			0
$466$	316.703			0.679621
$467$	146.016			0.312668			0.156334	−	0.987704i	$-0.450032\pi$
$467$	146.016			0.312668			0.156334	+	0.987704i	$0.450032\pi$
$468$	−174.440	−	285.653i	−0.372736	−	0.610370i
$469$	176.276			0.375855
$470$		0			0
$471$	−15.1388	−	53.8377i	−0.0321418	−	0.114305i
$472$			92.1022i			0.195132i
$473$	−377.917			−0.798978
$474$	575.097	−	161.713i	1.21329	−	0.341168i
$475$		0			0
$476$			70.3222i			0.147736i
$477$	−569.414	+	347.725i	−1.19374	+	0.728983i
$478$		−	15.4579i		−	0.0323388i
$479$		−	48.7573i		−	0.101790i	−0.998704	−	0.0508949i	$-0.983793\pi$
$479$		−	48.7573i		−	0.101790i	0.998704	−	0.0508949i	$-0.0162074\pi$
$480$		0			0
$481$	−189.310			−0.393577
$482$	−250.749			−0.520226
$483$	74.7836	+	265.951i	0.154831	+	0.550623i
$484$	−540.033			−1.11577
$485$		0			0
$486$	68.3484	−	336.788i	0.140635	−	0.692980i
$487$			562.319i			1.15466i	0.816511	+	0.577329i	$0.195905\pi$
$487$			562.319i			1.15466i	−0.816511	+	0.577329i	$0.804095\pi$
$488$	−202.977			−0.415936
$489$	−11.5232	−	40.9796i	−0.0235648	−	0.0838028i
$490$		0			0
$491$			124.234i			0.253022i	0.991965	+	0.126511i	$0.0403778\pi$
$491$			124.234i			0.253022i	−0.991965	+	0.126511i	$0.959622\pi$
$492$	46.9586	+	166.998i	0.0954443	+	0.339426i
$493$		−	90.8063i		−	0.184191i
$494$			143.955i			0.291407i
$495$		0			0
$496$	−125.937			−0.253905
$497$	−267.870			−0.538973
$498$	410.963	−	115.560i	0.825227	−	0.232048i
$499$	751.671			1.50635			0.753177	−	0.657817i	$-0.228520\pi$
$499$	751.671			1.50635			0.753177	+	0.657817i	$0.228520\pi$
$500$		0			0
$501$	−502.046	+	141.172i	−1.00209	+	0.281780i
$502$			257.388i			0.512725i
$503$	725.516			1.44238			0.721189	−	0.692739i	$-0.243596\pi$
$503$	725.516			1.44238			0.721189	+	0.692739i	$0.243596\pi$
$504$	35.1012	+	57.4796i	0.0696452	+	0.114047i
$505$		0			0
$506$		−	973.349i		−	1.92361i
$507$	510.490	−	143.546i	1.00688	−	0.283129i
$508$			155.563i			0.306227i
$509$			495.288i			0.973062i	0.873663	+	0.486531i	$0.161738\pi$
$509$			495.288i			0.973062i	−0.873663	+	0.486531i	$0.838262\pi$
$510$		0			0
$511$	−121.688			−0.238138
$512$	−22.6274			−0.0441942
$513$	−100.581	+	108.302i	−0.196065	+	0.211116i
$514$	−219.492			−0.427026
$515$		0			0
$516$	−31.0406	−	110.389i	−0.0601562	−	0.213932i
$517$		−	892.298i		−	1.72591i
$518$	38.0934			0.0735394
$519$	−473.850	+	133.243i	−0.913006	+	0.256731i
$520$		0			0
$521$		−	496.127i		−	0.952260i	−0.879375	−	0.476130i	$-0.842039\pi$
$521$		−	496.127i		−	0.952260i	0.879375	−	0.476130i	$-0.157961\pi$
$522$	−45.3258	−	74.2229i	−0.0868311	−	0.142189i
$523$		−	863.914i		−	1.65184i	−0.563785	−	0.825922i	$-0.690655\pi$
$523$		−	863.914i		−	1.65184i	0.563785	−	0.825922i	$-0.309345\pi$
$524$		−	459.560i		−	0.877024i
$525$		0			0
$526$	225.715			0.429116
$527$	418.414			0.793954
$528$	−64.2331	−	228.430i	−0.121654	−	0.432633i
$529$	682.468			1.29011
$530$		0			0
$531$	−152.740	−	250.118i	−0.287646	−	0.471032i
$532$		−	28.9669i		−	0.0544490i
$533$	−537.617			−1.00866
$534$	−12.8668	−	45.7578i	−0.0240951	−	0.0856887i
$535$		0			0
$536$		−	188.447i		−	0.351580i
$537$	217.228	+	772.521i	0.404521	+	1.43859i
$538$		−	280.495i		−	0.521366i
$539$		−	138.419i		−	0.256807i
$540$		0			0
$541$	−606.291			−1.12069			−0.560343	−	0.828261i	$-0.689331\pi$
$541$	−606.291			−1.12069			−0.560343	+	0.828261i	$0.689331\pi$
$542$	−65.3849			−0.120636
$543$	−543.968	+	152.960i	−1.00178	+	0.281694i
$544$	75.1775			0.138194
$545$		0			0
$546$	−200.932	+	56.5008i	−0.368008	+	0.103481i
$547$			940.119i			1.71868i	0.511404	+	0.859341i	$0.329126\pi$
$547$			940.119i			1.71868i	−0.511404	+	0.859341i	$0.670874\pi$
$548$	287.120			0.523941
$549$	551.215	−	336.611i	1.00403	−	0.613135i
$550$		0			0
$551$			37.4046i			0.0678850i
$552$	284.314	−	79.9470i	0.515061	−	0.144832i
$553$		−	372.545i		−	0.673680i
$554$		−	548.412i		−	0.989913i
$555$		0			0
$556$	515.916			0.927906
$557$	−302.696			−0.543439			−0.271720	−	0.962376i	$-0.587592\pi$
$557$	−302.696			−0.543439			−0.271720	+	0.962376i	$0.587592\pi$
$558$	342.001	−	208.851i	0.612905	−	0.374284i
$559$	355.376			0.635735
$560$		0			0
$561$	213.409	+	758.939i	0.380407	+	1.35283i
$562$			66.3786i			0.118111i
$563$	−705.188			−1.25255			−0.626277	−	0.779601i	$-0.715422\pi$
$563$	−705.188			−1.25255			−0.626277	+	0.779601i	$0.715422\pi$
$564$	260.639	−	73.2898i	0.462125	−	0.129946i
$565$		0			0
$566$		−	45.7396i		−	0.0808121i
$567$	−190.646	−	97.8840i	−0.336236	−	0.172635i
$568$			286.365i			0.504163i
$569$			428.736i			0.753491i	0.926317	+	0.376746i	$0.122957\pi$
$569$			428.736i			0.753491i	−0.926317	+	0.376746i	$0.877043\pi$
$570$		0			0
$571$	222.414			0.389517			0.194758	−	0.980851i	$-0.437608\pi$
$571$	222.414			0.389517			0.194758	+	0.980851i	$0.437608\pi$
$572$	735.388			1.28564
$573$	−243.936	−	867.504i	−0.425718	−	1.51397i
$574$	108.180			0.188467
$575$		0			0
$576$	61.4483	−	37.5247i	0.106681	−	0.0651471i
$577$		−	677.458i		−	1.17410i	−0.809549	−	0.587052i	$-0.800288\pi$
$577$		−	677.458i		−	1.17410i	0.809549	−	0.587052i	$-0.199712\pi$
$578$	158.937			0.274978
$579$	169.914	+	604.261i	0.293461	+	1.04363i
$580$		0			0
$581$		−	266.220i		−	0.458209i
$582$	117.713	+	418.620i	0.202256	+	0.719279i
$583$		−	1465.90i		−	2.51441i
$584$			130.090i			0.222757i
$585$		0			0
$586$	51.6757			0.0881837
$587$	681.642			1.16123			0.580615	−	0.814178i	$-0.302812\pi$
$587$	681.642			1.16123			0.580615	+	0.814178i	$0.302812\pi$
$588$	40.4319	−	11.3692i	0.0687618	−	0.0193353i
$589$	−172.352			−0.292617
$590$		0			0
$591$	280.333	−	78.8277i	0.474337	−	0.133380i
$592$		−	40.7235i		−	0.0687898i
$593$	39.3230			0.0663120			0.0331560	−	0.999450i	$-0.489444\pi$
$593$	39.3230			0.0663120			0.0331560	+	0.999450i	$0.489444\pi$
$594$	553.258	+	513.816i	0.931411	+	0.865010i
$595$		0			0
$596$		−	235.060i		−	0.394396i
$597$	843.498	−	237.186i	1.41289	−	0.397296i
$598$			915.293i			1.53059i
$599$		−	564.730i		−	0.942788i	−0.881923	−	0.471394i	$-0.843751\pi$
$599$		−	564.730i		−	0.942788i	0.881923	−	0.471394i	$-0.156249\pi$
$600$		0			0
$601$	−223.287			−0.371527			−0.185763	−	0.982595i	$-0.559476\pi$
$601$	−223.287			−0.371527			−0.185763	+	0.982595i	$0.559476\pi$
$602$	−71.5093			−0.118786
$603$	312.516	+	511.757i	0.518268	+	0.848686i
$604$	502.112			0.831311
$605$		0			0
$606$	161.940	+	575.903i	0.267228	+	0.950334i
$607$			343.966i			0.566665i	0.959022	+	0.283332i	$0.0914400\pi$
$607$			343.966i			0.566665i	−0.959022	+	0.283332i	$0.908560\pi$
$608$	−30.9669			−0.0509324
$609$	−52.2094	+	14.6809i	−0.0857297	+	0.0241066i
$610$		0			0
$611$			839.076i			1.37328i
$612$	−204.156	+	124.673i	−0.333589	+	0.203713i
$613$		−	532.494i		−	0.868668i	−0.900752	−	0.434334i	$-0.856984\pi$
$613$		−	532.494i		−	0.868668i	0.900752	−	0.434334i	$-0.143016\pi$
$614$			81.3156i			0.132436i
$615$		0			0
$616$	−147.976			−0.240221
$617$	−553.837			−0.897630			−0.448815	−	0.893625i	$-0.648154\pi$
$617$	−553.837			−0.897630			−0.448815	+	0.893625i	$0.648154\pi$
$618$	−67.8007	−	241.118i	−0.109710	−	0.390158i
$619$	−467.768			−0.755684			−0.377842	−	0.925870i	$-0.623334\pi$
$619$	−467.768			−0.755684			−0.377842	+	0.925870i	$0.623334\pi$
$620$		0			0
$621$	−639.516	+	688.607i	−1.02982	+	1.10887i
$622$		−	326.008i		−	0.524129i
$623$	−29.6416			−0.0475789
$624$	60.4019	+	214.806i	0.0967979	+	0.344240i
$625$		0			0
$626$			635.952i			1.01590i
$627$	−87.9065	−	312.620i	−0.140202	−	0.498596i
$628$			37.2838i			0.0593690i
$629$			135.300i			0.215104i
$630$		0			0
$631$	822.827			1.30400			0.652002	−	0.758217i	$-0.273929\pi$
$631$	822.827			1.30400			0.652002	+	0.758217i	$0.273929\pi$
$632$	−398.267			−0.630170
$633$	255.395	−	71.8152i	0.403467	−	0.113452i
$634$	−523.419			−0.825582
$635$		0			0
$636$	428.188	−	120.404i	0.673252	−	0.189314i
$637$			130.163i			0.204337i
$638$	191.080			0.299499
$639$	−474.900	−	777.668i	−0.743192	−	1.21701i
$640$		0			0
$641$			64.4367i			0.100525i	0.998736	+	0.0502626i	$0.0160058\pi$
$641$			64.4367i			0.100525i	−0.998736	+	0.0502626i	$0.983994\pi$
$642$	368.711	−	103.679i	0.574316	−	0.161494i
$643$			367.448i			0.571458i	0.958310	+	0.285729i	$0.0922357\pi$
$643$			367.448i			0.571458i	−0.958310	+	0.285729i	$0.907764\pi$
$644$		−	184.177i		−	0.285989i
$645$		0			0
$646$	102.885			0.159264
$647$	−335.963			−0.519262			−0.259631	−	0.965708i	$-0.583601\pi$
$647$	−335.963			−0.519262			−0.259631	+	0.965708i	$0.583601\pi$
$648$	−104.642	+	203.809i	−0.161485	+	0.314520i
$649$	643.906			0.992151
$650$		0			0
$651$	−67.6462	−	240.568i	−0.103911	−	0.369537i
$652$			28.3793i			0.0435265i
$653$	365.159			0.559202			0.279601	−	0.960116i	$-0.409798\pi$
$653$	365.159			0.559202			0.279601	+	0.960116i	$0.409798\pi$
$654$	376.433	−	105.850i	0.575586	−	0.161851i
$655$		0			0
$656$		−	115.649i		−	0.176295i
$657$	−215.739	−	353.281i	−0.328369	−	0.537718i
$658$		−	168.840i		−	0.256596i
$659$		−	895.096i		−	1.35826i	−0.734016	−	0.679132i	$-0.762357\pi$
$659$		−	895.096i		−	1.35826i	0.734016	−	0.679132i	$-0.237643\pi$
$660$		0			0
$661$	511.388			0.773658			0.386829	−	0.922151i	$-0.373570\pi$
$661$	511.388			0.773658			0.386829	+	0.922151i	$0.373570\pi$
$662$	177.135			0.267575
$663$	−200.680	−	713.672i	−0.302684	−	1.07643i
$664$	−284.601			−0.428616
$665$		0			0
$666$	67.5349	+	110.591i	0.101404	+	0.166053i
$667$			237.826i			0.356560i
$668$	347.678			0.520476
$669$	268.177	+	953.712i	0.400863	+	1.42558i
$670$		0			0
$671$			1419.05i			2.11483i
$672$	−12.1542	−	43.2236i	−0.0180866	−	0.0643208i
$673$		−	265.771i		−	0.394904i	−0.980313	−	0.197452i	$-0.936733\pi$
$673$		−	265.771i		−	0.394904i	0.980313	−	0.197452i	$-0.0632667\pi$
$674$		−	7.55985i		−	0.0112164i
$675$		0			0
$676$	−353.525			−0.522967
$677$	−788.674			−1.16495			−0.582477	−	0.812847i	$-0.697917\pi$
$677$	−788.674			−1.16495			−0.582477	+	0.812847i	$0.697917\pi$
$678$	608.262	−	171.039i	0.897141	−	0.252270i
$679$	271.180			0.399382
$680$		0			0
$681$	−817.373	+	229.840i	−1.20025	+	0.337503i
$682$			880.451i			1.29098i
$683$	644.795			0.944062			0.472031	−	0.881582i	$-0.343521\pi$
$683$	644.795			0.944062			0.472031	+	0.881582i	$0.343521\pi$
$684$	84.0954	−	51.3547i	0.122946	−	0.0750800i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	−49.3784	+	13.8849i	−0.0718753	+	0.0202109i
$688$			76.4467i			0.111114i
$689$			1378.47i			2.00068i
$690$		0			0
$691$	−758.839			−1.09818			−0.549088	−	0.835765i	$-0.685025\pi$
$691$	−758.839			−1.09818			−0.549088	+	0.835765i	$0.685025\pi$
$692$	328.151			0.474207
$693$	401.852	−	245.400i	0.579873	−	0.354112i
$694$	391.842			0.564614
$695$		0			0
$696$	15.6946	+	55.8142i	0.0225497	+	0.0801928i
$697$			384.235i			0.551270i
$698$	524.701			0.751721
$699$	646.746	−	181.861i	0.925245	−	0.260173i
$700$		0			0
$701$			633.097i			0.903134i	0.892237	+	0.451567i	$0.149135\pi$
$701$			633.097i			0.903134i	−0.892237	+	0.451567i	$0.850865\pi$
$702$	−520.259	−	483.169i	−0.741110	−	0.688275i
$703$		−	55.7324i		−	0.0792780i
$704$			158.193i			0.224706i
$705$		0			0
$706$	282.942			0.400767
$707$	373.067			0.527676
$708$	52.8879	+	188.084i	0.0747004	+	0.265655i
$709$	906.040			1.27791			0.638956	−	0.769243i	$-0.279366\pi$
$709$	906.040			1.27791			0.638956	+	0.769243i	$0.279366\pi$
$710$		0			0
$711$	1081.56	−	660.477i	1.52118	−	0.928941i
$712$			31.6883i			0.0445060i
$713$	−1095.84			−1.53695
$714$	40.3811	+	143.606i	0.0565562	+	0.201129i
$715$		0			0
$716$		−	534.988i		−	0.747189i
$717$	−8.87642	−	31.5670i	−0.0123799	−	0.0440265i
$718$			18.6268i			0.0259426i
$719$		−	144.683i		−	0.201228i	−0.994926	−	0.100614i	$-0.967919\pi$
$719$		−	144.683i		−	0.201228i	0.994926	−	0.100614i	$-0.0320806\pi$
$720$		0			0
$721$	−156.195			−0.216636
$722$	468.151			0.648409
$723$	−512.059	+	143.988i	−0.708243	+	0.199153i
$724$	376.709			0.520317
$725$		0			0
$726$	−1102.81	+	310.103i	−1.51902	+	0.427139i
$727$		−	194.850i		−	0.268019i	−0.990980	−	0.134009i	$-0.957215\pi$
$727$		−	194.850i		−	0.268019i	0.990980	−	0.134009i	$-0.0427853\pi$
$728$	139.150			0.191140
$729$	−53.8185	−	727.011i	−0.0738251	−	0.997271i
$730$		0			0
$731$		−	253.987i		−	0.347452i
$732$	−414.503	+	116.555i	−0.566261	+	0.159229i
$733$		−	883.063i		−	1.20472i	−0.798223	−	0.602362i	$-0.794226\pi$
$733$		−	883.063i		−	1.20472i	0.798223	−	0.602362i	$-0.205774\pi$
$734$		−	491.875i		−	0.670129i
$735$		0			0
$736$	−196.893			−0.267518
$737$	−1317.47			−1.78762
$738$	191.790	+	314.064i	0.259878	+	0.425561i
$739$	679.219			0.919106			0.459553	−	0.888150i	$-0.348010\pi$
$739$	679.219			0.919106			0.459553	+	0.888150i	$0.348010\pi$
$740$		0			0
$741$	82.6633	+	293.973i	0.111556	+	0.396725i
$742$		−	277.378i		−	0.373825i
$743$	−1349.22			−1.81591			−0.907953	−	0.419073i	$-0.862355\pi$
$743$	−1349.22			−1.81591			−0.907953	+	0.419073i	$0.862355\pi$
$744$	−257.178	+	72.3168i	−0.345670	+	0.0972000i
$745$		0			0
$746$		−	790.440i		−	1.05957i
$747$	772.878	−	471.975i	1.03464	−	0.631827i
$748$		−	525.582i		−	0.702650i
$749$		−	238.849i		−	0.318891i
$750$		0			0
$751$	171.226			0.227997			0.113998	−	0.993481i	$-0.463634\pi$
$751$	171.226			0.227997			0.113998	+	0.993481i	$0.463634\pi$
$752$	−180.498			−0.240024
$753$	147.800	+	525.618i	0.196282	+	0.698031i
$754$	−179.683			−0.238306
$755$		0			0
$756$	104.687	+	97.2242i	0.138475	+	0.128603i
$757$		−	317.899i		−	0.419946i	−0.977707	−	0.209973i	$-0.932662\pi$
$757$		−	317.899i		−	0.419946i	0.977707	−	0.209973i	$-0.0673376\pi$
$758$	−827.653			−1.09189
$759$	−558.927	−	1987.70i	−0.736399	−	2.61884i
$760$		0			0
$761$			423.830i			0.556938i	0.960445	+	0.278469i	$0.0898269\pi$
$761$			423.830i			0.556938i	−0.960445	+	0.278469i	$0.910173\pi$
$762$	89.3293	+	317.680i	0.117230	+	0.416902i
$763$		−	243.851i		−	0.319596i
$764$			600.766i			0.786342i
$765$		0			0
$766$	−553.351			−0.722390
$767$	−605.500			−0.789439
$768$	−46.2079	+	12.9934i	−0.0601666	+	0.0169184i
$769$	−169.095			−0.219889			−0.109945	−	0.993938i	$-0.535067\pi$
$769$	−169.095			−0.219889			−0.109945	+	0.993938i	$0.535067\pi$
$770$		0			0
$771$	−448.228	+	126.039i	−0.581360	+	0.163474i
$772$		−	418.464i		−	0.542051i
$773$	603.486			0.780706			0.390353	−	0.920665i	$-0.372353\pi$
$773$	603.486			0.780706			0.390353	+	0.920665i	$0.372353\pi$
$774$	−126.777	−	207.603i	−0.163795	−	0.268221i
$775$		0			0
$776$		−	289.904i		−	0.373587i
$777$	77.7913	−	21.8744i	0.100118	−	0.0281524i
$778$			582.785i			0.749081i
$779$		−	158.273i		−	0.203174i
$780$		0			0
$781$	2002.04			2.56343
$782$	654.160			0.836522
$783$	−135.182	−	125.545i	−0.172646	−	0.160338i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	−263.894	−	938.478i	−0.335743	−	1.19399i
$787$			1458.37i			1.85307i	0.376205	+	0.926536i	$0.377229\pi$
$787$			1458.37i			1.85307i	−0.376205	+	0.926536i	$0.622771\pi$
$788$	−194.137			−0.246366
$789$	460.937	−	129.612i	0.584204	−	0.164274i
$790$		0			0
$791$		−	394.029i		−	0.498140i
$792$	−262.343	−	429.598i	−0.331242	−	0.542422i
$793$		−	1334.41i		−	1.68274i
$794$			878.128i			1.10596i
$795$		0			0
$796$	−584.141			−0.733845
$797$	−47.8528			−0.0600412			−0.0300206	−	0.999549i	$-0.509557\pi$
$797$	−47.8528			−0.0600412			−0.0300206	+	0.999549i	$0.509557\pi$
$798$	−16.6337	−	59.1538i	−0.0208442	−	0.0741276i
$799$	599.688			0.750548
$800$		0			0
$801$	−52.5510	−	86.0544i	−0.0656068	−	0.107434i
$802$			731.703i			0.912347i
$803$	909.489			1.13261
$804$	−108.212	−	384.832i	−0.134592	−	0.478646i
$805$		0			0
$806$		−	827.936i		−	1.02722i
$807$	−161.069	−	572.804i	−0.199589	−	0.709795i
$808$		−	398.825i		−	0.493595i
$809$		−	267.783i		−	0.331005i	−0.986209	−	0.165503i	$-0.947075\pi$
$809$		−	267.783i		−	0.331005i	0.986209	−	0.165503i	$-0.0529247\pi$
$810$		0			0
$811$	−658.395			−0.811831			−0.405915	−	0.913911i	$-0.633047\pi$
$811$	−658.395			−0.811831			−0.405915	+	0.913911i	$0.633047\pi$
$812$	36.1561			0.0445273
$813$	−133.524	+	37.5460i	−0.164236	+	0.0461820i
$814$	−284.707			−0.349763
$815$		0			0
$816$	153.522	−	43.1692i	0.188139	−	0.0529035i
$817$			104.622i			0.128056i
$818$	−66.0782			−0.0807802
$819$	−377.884	+	230.763i	−0.461396	+	0.281762i
$820$		0			0
$821$			1104.72i			1.34558i	0.739833	+	0.672791i	$0.234905\pi$
$821$			1104.72i			1.34558i	−0.739833	+	0.672791i	$0.765095\pi$
$822$	586.333	−	164.873i	0.713301	−	0.200575i
$823$			1044.86i			1.26957i	0.772688	+	0.634787i	$0.218912\pi$
$823$			1044.86i			1.26957i	−0.772688	+	0.634787i	$0.781088\pi$
$824$			166.979i			0.202645i
$825$		0			0
$826$	121.840			0.147506
$827$	1417.09			1.71354			0.856768	−	0.515702i	$-0.172469\pi$
$827$	1417.09			1.71354			0.856768	+	0.515702i	$0.172469\pi$
$828$	534.695	−	326.523i	0.645767	−	0.394352i
$829$	1178.56			1.42166			0.710832	−	0.703362i	$-0.248319\pi$
$829$	1178.56			1.42166			0.710832	+	0.703362i	$0.248319\pi$
$830$		0			0
$831$	−314.915	−	1119.92i	−0.378959	−	1.34768i
$832$		−	148.758i		−	0.178795i
$833$	93.0275			0.111678
$834$	1053.56	−	296.254i	1.26326	−	0.355221i
$835$		0			0
$836$			216.496i			0.258966i
$837$	578.480	−	622.886i	0.691135	−	0.744188i
$838$		−	234.410i		−	0.279725i
$839$			631.629i			0.752836i	0.926450	+	0.376418i	$0.122844\pi$
$839$			631.629i			0.752836i	−0.926450	+	0.376418i	$0.877156\pi$
$840$		0			0
$841$	794.312			0.944485
$842$	−934.465			−1.10982
$843$	38.1166	+	135.553i	0.0452155	+	0.160799i
$844$	−176.866			−0.209557
$845$		0			0
$846$	490.171	−	299.333i	0.579398	−	0.353822i
$847$			714.396i			0.843443i
$848$	−296.530			−0.349681
$849$	−26.2651	−	93.4059i	−0.0309365	−	0.110019i
$850$		0			0
$851$		−	354.358i		−	0.416401i
$852$	164.439	+	584.791i	0.193004	+	0.686375i
$853$		−	274.418i		−	0.321710i	−0.986978	−	0.160855i	$-0.948575\pi$
$853$		−	274.418i		−	0.321710i	0.986978	−	0.160855i	$-0.0514251\pi$
$854$			268.513i			0.314418i
$855$		0			0
$856$	−255.340			−0.298295
$857$	−1272.83			−1.48521			−0.742606	−	0.669729i	$-0.766410\pi$
$857$	−1272.83			−1.48521			−0.742606	+	0.669729i	$0.766410\pi$
$858$	1501.75	−	422.282i	1.75029	−	0.492170i
$859$	−1092.97			−1.27237			−0.636185	−	0.771537i	$-0.719488\pi$
$859$	−1092.97			−1.27237			−0.636185	+	0.771537i	$0.719488\pi$
$860$		0			0
$861$	220.917	−	62.1204i	0.256582	−	0.0721491i
$862$			257.813i			0.299086i
$863$	782.875			0.907155			0.453577	−	0.891217i	$-0.350148\pi$
$863$	782.875			0.907155			0.453577	+	0.891217i	$0.350148\pi$
$864$	103.937	−	111.916i	0.120297	−	0.129532i
$865$		0			0
$866$			164.788i			0.190286i
$867$	324.569	−	91.2665i	0.374359	−	0.105267i
$868$			166.599i			0.191934i
$869$			2784.37i			3.20411i
$870$		0			0
$871$	1238.89			1.42238
$872$	−260.688			−0.298954
$873$	480.769	+	787.279i	0.550709	+	0.901809i
$874$	−269.459			−0.308306
$875$		0			0
$876$	74.7018	+	265.660i	0.0852760	+	0.303265i
$877$			240.309i			0.274012i	0.990570	+	0.137006i	$0.0437480\pi$
$877$			240.309i			0.274012i	−0.990570	+	0.137006i	$0.956252\pi$
$878$	534.221			0.608452
$879$	105.528	−	29.6737i	0.120055	−	0.0337585i
$880$		0			0
$881$		−	402.445i		−	0.456805i	−0.973567	−	0.228403i	$-0.926650\pi$
$881$		−	402.445i		−	0.456805i	0.973567	−	0.228403i	$-0.0733502\pi$
$882$	76.0384	−	46.4345i	0.0862113	−	0.0526468i
$883$		−	99.2223i		−	0.112370i	−0.998420	−	0.0561848i	$-0.982106\pi$
$883$		−	99.2223i		−	0.112370i	0.998420	−	0.0561848i	$-0.0178936\pi$
$884$			494.234i			0.559088i
$885$		0			0
$886$	−216.074			−0.243876
$887$	197.974			0.223195			0.111597	−	0.993754i	$-0.464403\pi$
$887$	197.974			0.223195			0.111597	+	0.993754i	$0.464403\pi$
$888$	−23.3847	−	83.1624i	−0.0263341	−	0.0936514i
$889$	205.791			0.231486
$890$		0			0
$891$	1424.87	+	731.577i	1.59918	+	0.821074i
$892$		−	660.466i		−	0.740433i
$893$	−247.021			−0.276620
$894$	−134.979	−	480.021i	−0.150983	−	0.536936i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	525.589	+	1869.14i	0.585941	+	2.08377i
$898$			284.501i			0.316817i
$899$		−	215.127i		−	0.239296i
$900$		0			0
$901$	985.193			1.09344
$902$	−808.530			−0.896375
$903$	−146.031	+	41.0628i	−0.161717	+	0.0454738i
$904$	−421.234			−0.465967
$905$		0			0
$906$	1025.37	−	288.328i	1.13176	−	0.318243i
$907$		−	1429.61i		−	1.57620i	−0.615550	−	0.788098i	$-0.711066\pi$
$907$		−	1429.61i		−	1.57620i	0.615550	−	0.788098i	$-0.288934\pi$
$908$	566.049			0.623402
$909$	661.402	+	1083.07i	0.727615	+	1.19150i
$910$		0			0
$911$			291.143i			0.319587i	0.987150	+	0.159793i	$0.0510828\pi$
$911$			291.143i			0.319587i	−0.987150	+	0.159793i	$0.948917\pi$
$912$	−63.2381	+	17.7821i	−0.0693400	+	0.0194979i
$913$			1989.70i			2.17930i
$914$			1015.49i			1.11103i
$915$		0			0
$916$	34.1956			0.0373314
$917$	−607.941			−0.662968
$918$	−345.321	+	371.829i	−0.376167	+	0.405043i
$919$	−1118.26			−1.21682			−0.608412	−	0.793621i	$-0.708193\pi$
$919$	−1118.26			−1.21682			−0.608412	+	0.793621i	$0.708193\pi$
$920$		0			0
$921$	46.6939	+	166.056i	0.0506991	+	0.180300i
$922$		−	487.740i		−	0.529002i
$923$	−1882.62			−2.03968
$924$	−302.185	+	84.9724i	−0.327040	+	0.0919614i
$925$		0			0
$926$		−	793.842i		−	0.857281i
$927$	−276.914	−	453.459i	−0.298721	−	0.489168i
$928$		−	38.6525i		−	0.0416514i
$929$			1182.23i			1.27258i	0.771449	+	0.636292i	$0.219532\pi$
$929$			1182.23i			1.27258i	−0.771449	+	0.636292i	$0.780468\pi$
$930$		0			0
$931$	−38.3195			−0.0411596
$932$	−447.886			−0.480564
$933$	−187.204	−	665.749i	−0.200647	−	0.713557i
$934$	−206.498			−0.221089
$935$		0			0
$936$	246.696	+	403.974i	0.263564	+	0.431597i
$937$			1442.28i			1.53925i	0.638494	+	0.769627i	$0.279558\pi$
$937$			1442.28i			1.53925i	−0.638494	+	0.769627i	$0.720442\pi$
$938$	−249.292			−0.265770
$939$	365.183	+	1298.69i	0.388906	+	1.38306i
$940$		0			0
$941$		−	617.890i		−	0.656631i	−0.944568	−	0.328315i	$-0.893519\pi$
$941$		−	617.890i		−	0.656631i	0.944568	−	0.328315i	$-0.106481\pi$
$942$	21.4095	+	76.1380i	0.0227277	+	0.0808259i
$943$		−	1006.33i		−	1.06716i
$944$		−	130.252i		−	0.137979i
$945$		0			0
$946$	534.455			0.564963
$947$	850.033			0.897606			0.448803	−	0.893631i	$-0.351851\pi$
$947$	850.033			0.897606			0.448803	+	0.893631i	$0.351851\pi$
$948$	−813.311	+	228.697i	−0.857922	+	0.241242i
$949$	−855.242			−0.901203
$950$		0			0
$951$	−1068.88	+	300.563i	−1.12396	+	0.316050i
$952$		−	99.4505i		−	0.104465i
$953$	−774.098			−0.812275			−0.406138	−	0.913812i	$-0.633125\pi$
$953$	−774.098			−0.812275			−0.406138	+	0.913812i	$0.633125\pi$
$954$	805.273	−	491.757i	0.844101	−	0.515469i
$955$		0			0
$956$			21.8608i			0.0228670i
$957$	390.209	−	109.724i	0.407742	−	0.114654i
$958$			68.9533i			0.0719763i
$959$		−	379.824i		−	0.396062i
$960$		0			0
$961$	30.2557			0.0314835
$962$	267.725			0.278301
$963$	693.417	−	423.450i	0.720059	−	0.439720i
$964$	354.612			0.367855
$965$		0			0
$966$	−105.760	−	376.111i	−0.109482	−	0.389349i
$967$		−	1167.79i		−	1.20764i	−0.797122	−	0.603819i	$-0.793645\pi$
$967$		−	1167.79i		−	1.20764i	0.797122	−	0.603819i	$-0.206355\pi$
$968$	763.721			0.788968
$969$	210.103	−	59.0795i	0.216824	−	0.0609695i
$970$		0			0
$971$			624.999i			0.643665i	0.946797	+	0.321833i	$0.104299\pi$
$971$			624.999i			0.643665i	−0.946797	+	0.321833i	$0.895701\pi$
$972$	−96.6593	+	476.291i	−0.0994437	+	0.490011i
$973$		−	682.492i		−	0.701431i
$974$		−	795.239i		−	0.816467i
$975$		0			0
$976$	287.052			0.294111
$977$	−258.970			−0.265066			−0.132533	−	0.991179i	$-0.542311\pi$
$977$	−258.970			−0.265066			−0.132533	+	0.991179i	$0.542311\pi$
$978$	16.2962	+	57.9539i	0.0166628	+	0.0592575i
$979$	221.539			0.226291
$980$		0			0
$981$	707.939	−	432.319i	0.721651	−	0.440692i
$982$		−	175.693i		−	0.178913i
$983$	1153.22			1.17316			0.586582	−	0.809890i	$-0.300473\pi$
$983$	1153.22			1.17316			0.586582	+	0.809890i	$0.300473\pi$
$984$	−66.4095	−	236.170i	−0.0674893	−	0.240010i
$985$		0			0
$986$			128.420i			0.130243i
$987$	−96.9533	−	344.793i	−0.0982303	−	0.349334i
$988$		−	203.583i		−	0.206056i
$989$			665.204i			0.672603i
$990$		0			0
$991$	−977.180			−0.986054			−0.493027	−	0.870014i	$-0.664110\pi$
$991$	−977.180			−0.986054			−0.493027	+	0.870014i	$0.664110\pi$
$992$	178.102			0.179538
$993$	361.731	−	101.716i	0.364281	−	0.102433i
$994$	378.825			0.381111
$995$		0			0
$996$	−581.189	+	163.426i	−0.583523	+	0.164083i
$997$		−	1274.45i		−	1.27829i	−0.769087	−	0.639144i	$-0.779289\pi$
$997$		−	1274.45i		−	1.27829i	0.769087	−	0.639144i	$-0.220711\pi$
$998$	−1063.02			−1.06515
$999$	201.419	+	187.060i	0.201621	+	0.187247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.c.449.4		32
3.2	odd	2	inner	1050.3.c.c.449.30		32
5.2	odd	4		1050.3.e.d.701.4		16
5.3	odd	4		210.3.e.a.71.13	yes	16
5.4	even	2	inner	1050.3.c.c.449.29		32
15.2	even	4		1050.3.e.d.701.12		16
15.8	even	4		210.3.e.a.71.5	✓	16
15.14	odd	2	inner	1050.3.c.c.449.3		32
20.3	even	4		1680.3.l.c.1121.8		16
60.23	odd	4		1680.3.l.c.1121.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.5	✓	16	15.8	even	4
210.3.e.a.71.13	yes	16	5.3	odd	4
1050.3.c.c.449.3		32	15.14	odd	2	inner
1050.3.c.c.449.4		32	1.1	even	1	trivial
1050.3.c.c.449.29		32	5.4	even	2	inner
1050.3.c.c.449.30		32	3.2	odd	2	inner
1050.3.e.d.701.4		16	5.2	odd	4
1050.3.e.d.701.12		16	15.2	even	4
1680.3.l.c.1121.7		16	60.23	odd	4
1680.3.l.c.1121.8		16	20.3	even	4

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-2.88800 + 0.812085i) q^{3} +2.00000 q^{4} +(4.08424 - 1.14846i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(7.68104 - 4.69059i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-2.88800 + 0.812085i) q^{3} +2.00000 q^{4} +(4.08424 - 1.14846i) q^{6} -2.64575i q^{7} -2.82843 q^{8} +(7.68104 - 4.69059i) q^{9} +19.7741i q^{11} +(-5.77599 + 1.62417i) q^{12} -18.5947i q^{13} +3.74166i q^{14} +4.00000 q^{16} -13.2896 q^{17} +(-10.8626 + 6.63350i) q^{18} +5.47422 q^{19} +(2.14857 + 7.64092i) q^{21} -27.9648i q^{22} +34.8062 q^{23} +(8.16849 - 2.29692i) q^{24} +26.2969i q^{26} +(-18.3736 + 19.7841i) q^{27} -5.29150i q^{28} +6.83287i q^{29} -31.4842 q^{31} -5.65685 q^{32} +(-16.0583 - 57.1076i) q^{33} +18.7944 q^{34} +(15.3621 - 9.38119i) q^{36} -10.1809i q^{37} -7.74172 q^{38} +(15.1005 + 53.7014i) q^{39} -28.9124i q^{41} +(-3.03854 - 10.8059i) q^{42} +19.1117i q^{43} +39.5483i q^{44} -49.2233 q^{46} -45.1245 q^{47} +(-11.5520 + 3.24834i) q^{48} -7.00000 q^{49} +(38.3804 - 10.7923i) q^{51} -37.1894i q^{52} -74.1324 q^{53} +(25.9843 - 27.9789i) q^{54} +7.48331i q^{56} +(-15.8095 + 4.44553i) q^{57} -9.66313i q^{58} -32.5630i q^{59} +71.7631 q^{61} +44.5254 q^{62} +(-12.4101 - 20.3221i) q^{63} +8.00000 q^{64} +(22.7098 + 80.7624i) q^{66} +66.6261i q^{67} -26.5793 q^{68} +(-100.520 + 28.2655i) q^{69} -101.245i q^{71} +(-21.7253 + 13.2670i) q^{72} -45.9939i q^{73} +14.3979i q^{74} +10.9484 q^{76} +52.3174 q^{77} +(-21.3553 - 75.9452i) q^{78} +140.809 q^{79} +(36.9967 - 72.0572i) q^{81} +40.8883i q^{82} +100.622 q^{83} +(4.29715 + 15.2818i) q^{84} -27.0280i q^{86} +(-5.54887 - 19.7333i) q^{87} -55.9297i q^{88} -11.2035i q^{89} -49.1969 q^{91} +69.6123 q^{92} +(90.9263 - 25.5678i) q^{93} +63.8157 q^{94} +(16.3370 - 4.59384i) q^{96} +102.496i q^{97} +9.89949 q^{98} +(92.7524 + 151.886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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