LMFDB - Embedded newform 201.3.c.a.68.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(68,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("201.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			68.2
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.83909i q^{2} +(-0.0207392 - 2.99993i) q^{3} -10.7386 q^{4} -4.79169i q^{5} +(-11.5170 + 0.0796199i) q^{6} +5.67115 q^{7} +25.8703i q^{8} +(-8.99914 + 0.124433i) q^{9} +O(q^{10})$	\(q-3.83909i q^{2} +(-0.0207392 - 2.99993i) q^{3} -10.7386 q^{4} -4.79169i q^{5} +(-11.5170 + 0.0796199i) q^{6} +5.67115 q^{7} +25.8703i q^{8} +(-8.99914 + 0.124433i) q^{9} -18.3957 q^{10} -12.6800i q^{11} +(0.222711 + 32.2152i) q^{12} +1.63359 q^{13} -21.7721i q^{14} +(-14.3747 + 0.0993759i) q^{15} +56.3638 q^{16} +19.9043i q^{17} +(0.477708 + 34.5485i) q^{18} +26.4601 q^{19} +51.4562i q^{20} +(-0.117615 - 17.0130i) q^{21} -48.6797 q^{22} -26.2740i q^{23} +(77.6090 - 0.536530i) q^{24} +2.03975 q^{25} -6.27152i q^{26} +(0.559924 + 26.9942i) q^{27} -60.9004 q^{28} -34.8296i q^{29} +(0.381514 + 55.1859i) q^{30} -32.9555 q^{31} -112.905i q^{32} +(-38.0391 + 0.262974i) q^{33} +76.4144 q^{34} -27.1744i q^{35} +(96.6385 - 1.33624i) q^{36} -11.9430 q^{37} -101.583i q^{38} +(-0.0338795 - 4.90067i) q^{39} +123.962 q^{40} +76.6892i q^{41} +(-65.3147 + 0.451536i) q^{42} -3.69489 q^{43} +136.166i q^{44} +(0.596241 + 43.1210i) q^{45} -100.868 q^{46} +48.3835i q^{47} +(-1.16894 - 169.088i) q^{48} -16.8381 q^{49} -7.83079i q^{50} +(59.7114 - 0.412800i) q^{51} -17.5426 q^{52} -26.7856i q^{53} +(103.633 - 2.14960i) q^{54} -60.7585 q^{55} +146.714i q^{56} +(-0.548762 - 79.3784i) q^{57} -133.714 q^{58} -110.116i q^{59} +(154.365 - 1.06716i) q^{60} -24.2545 q^{61} +126.519i q^{62} +(-51.0355 + 0.705675i) q^{63} -207.997 q^{64} -7.82767i q^{65} +(1.00958 + 146.036i) q^{66} +8.18535 q^{67} -213.745i q^{68} +(-78.8201 + 0.544903i) q^{69} -104.325 q^{70} +66.3018i q^{71} +(-3.21910 - 232.810i) q^{72} +73.3478 q^{73} +45.8504i q^{74} +(-0.0423029 - 6.11910i) q^{75} -284.145 q^{76} -71.9101i q^{77} +(-18.8141 + 0.130067i) q^{78} -26.2741 q^{79} -270.078i q^{80} +(80.9690 - 2.23957i) q^{81} +294.417 q^{82} +19.9376i q^{83} +(1.26303 + 182.697i) q^{84} +95.3750 q^{85} +14.1850i q^{86} +(-104.486 + 0.722340i) q^{87} +328.035 q^{88} -85.9865i q^{89} +(165.546 - 2.28903i) q^{90} +9.26436 q^{91} +282.147i q^{92} +(0.683472 + 98.8640i) q^{93} +185.749 q^{94} -126.788i q^{95} +(-338.707 + 2.34156i) q^{96} -101.667 q^{97} +64.6429i q^{98} +(1.57780 + 114.109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	3.83909i		−	1.91955i	−0.280776	−	0.959773i	$-0.590592\pi$
$2$		−	3.83909i		−	1.91955i	0.280776	−	0.959773i	$-0.409408\pi$
$3$	−0.0207392	−	2.99993i	−0.00691308	−	0.999976i
$3$	−0.0207392	−	2.99993i	−0.00691308	−	0.999976i
$4$	−10.7386			−2.68466
$5$		−	4.79169i		−	0.958337i	−0.877723	−	0.479169i	$-0.840938\pi$
$5$		−	4.79169i		−	0.958337i	0.877723	−	0.479169i	$-0.159062\pi$
$6$	−11.5170	+	0.0796199i	−1.91950	+	0.0132700i
$7$	5.67115			0.810164			0.405082	−	0.914280i	$-0.367243\pi$
$7$	5.67115			0.810164			0.405082	+	0.914280i	$0.367243\pi$
$8$			25.8703i			3.23378i
$9$	−8.99914	+	0.124433i	−0.999904	+	0.0138258i
$10$	−18.3957			−1.83957
$11$		−	12.6800i		−	1.15273i	−0.817194	−	0.576363i	$-0.804471\pi$
$11$		−	12.6800i		−	1.15273i	0.817194	−	0.576363i	$-0.195529\pi$
$12$	0.222711	+	32.2152i	0.0185593	+	2.68460i
$13$	1.63359			0.125661			0.0628306	−	0.998024i	$-0.479987\pi$
$13$	1.63359			0.125661			0.0628306	+	0.998024i	$0.479987\pi$
$14$		−	21.7721i		−	1.55515i
$15$	−14.3747	+	0.0993759i	−0.958314	+	0.00662506i
$16$	56.3638			3.52274
$17$			19.9043i			1.17084i	0.810730	+	0.585420i	$0.199070\pi$
$17$			19.9043i			1.17084i	−0.810730	+	0.585420i	$0.800930\pi$
$18$	0.477708	+	34.5485i	0.0265393	+	1.91936i
$19$	26.4601			1.39264			0.696318	−	0.717733i	$-0.254820\pi$
$19$	26.4601			1.39264			0.696318	+	0.717733i	$0.254820\pi$
$20$			51.4562i			2.57281i
$21$	−0.117615	−	17.0130i	−0.00560073	−	0.810145i
$22$	−48.6797			−2.21271
$23$		−	26.2740i		−	1.14235i	−0.820829	−	0.571174i	$-0.806488\pi$
$23$		−	26.2740i		−	1.14235i	0.820829	−	0.571174i	$-0.193512\pi$
$24$	77.6090	−	0.536530i	3.23371	−	0.0223554i
$25$	2.03975			0.0815900
$26$		−	6.27152i		−	0.241212i
$27$	0.559924	+	26.9942i	0.0207379	+	0.999785i
$28$	−60.9004			−2.17502
$29$		−	34.8296i		−	1.20102i	−0.799617	−	0.600510i	$-0.794964\pi$
$29$		−	34.8296i		−	1.20102i	0.799617	−	0.600510i	$-0.205036\pi$
$30$	0.381514	+	55.1859i	0.0127171	+	1.83953i
$31$	−32.9555			−1.06308			−0.531540	−	0.847033i	$-0.678386\pi$
$31$	−32.9555			−1.06308			−0.531540	+	0.847033i	$0.678386\pi$
$32$		−	112.905i		−	3.52828i
$33$	−38.0391	+	0.262974i	−1.15270	+	0.00796889i
$34$	76.4144			2.24748
$35$		−	27.1744i		−	0.776410i
$36$	96.6385	−	1.33624i	2.68440	−	0.0371177i
$37$	−11.9430			−0.322784			−0.161392	−	0.986890i	$-0.551598\pi$
$37$	−11.9430			−0.322784			−0.161392	+	0.986890i	$0.551598\pi$
$38$		−	101.583i		−	2.67323i
$39$	−0.0338795	−	4.90067i	−0.000868706	−	0.125658i
$40$	123.962			3.09906
$41$			76.6892i			1.87047i	0.354029	+	0.935235i	$0.384811\pi$
$41$			76.6892i			1.87047i	−0.354029	+	0.935235i	$0.615189\pi$
$42$	−65.3147	+	0.451536i	−1.55511	+	0.0107509i
$43$	−3.69489			−0.0859276			−0.0429638	−	0.999077i	$-0.513680\pi$
$43$	−3.69489			−0.0859276			−0.0429638	+	0.999077i	$0.513680\pi$
$44$			136.166i			3.09468i
$45$	0.596241	+	43.1210i	0.0132498	+	0.958246i
$46$	−100.868			−2.19279
$47$			48.3835i			1.02944i	0.857360	+	0.514718i	$0.172103\pi$
$47$			48.3835i			1.02944i	−0.857360	+	0.514718i	$0.827897\pi$
$48$	−1.16894	−	169.088i	−0.0243530	−	3.52266i
$49$	−16.8381			−0.343634
$50$		−	7.83079i		−	0.156616i
$51$	59.7114	−	0.412800i	1.17081	−	0.00809411i
$52$	−17.5426			−0.337357
$53$		−	26.7856i		−	0.505388i	−0.967546	−	0.252694i	$-0.918683\pi$
$53$		−	26.7856i		−	0.505388i	0.967546	−	0.252694i	$-0.0813166\pi$
$54$	103.633	−	2.14960i	1.91913	−	0.0398074i
$55$	−60.7585			−1.10470
$56$			146.714i			2.61990i
$57$	−0.548762	−	79.3784i	−0.00962741	−	1.39260i
$58$	−133.714			−2.30542
$59$		−	110.116i		−	1.86637i	−0.359393	−	0.933186i	$-0.617016\pi$
$59$		−	110.116i		−	1.86637i	0.359393	−	0.933186i	$-0.382984\pi$
$60$	154.365	−	1.06716i	2.57275	−	0.0177860i
$61$	−24.2545			−0.397615			−0.198808	−	0.980039i	$-0.563707\pi$
$61$	−24.2545			−0.397615			−0.198808	+	0.980039i	$0.563707\pi$
$62$			126.519i			2.04063i
$63$	−51.0355	+	0.705675i	−0.810087	+	0.0112012i
$64$	−207.997			−3.24996
$65$		−	7.82767i		−	0.120426i
$66$	1.00958	+	146.036i	0.0152967	+	2.21266i
$67$	8.18535			0.122169
$67$	8.18535			0.122169
$68$		−	213.745i		−	3.14331i
$69$	−78.8201	+	0.544903i	−1.14232	+	0.00789714i
$70$	−104.325			−1.49036
$71$			66.3018i			0.933828i	0.884303	+	0.466914i	$0.154634\pi$
$71$			66.3018i			0.933828i	−0.884303	+	0.466914i	$0.845366\pi$
$72$	−3.21910	−	232.810i	−0.0447098	−	3.23348i
$73$	73.3478			1.00476			0.502382	−	0.864646i	$-0.332457\pi$
$73$	73.3478			1.00476			0.502382	+	0.864646i	$0.332457\pi$
$74$			45.8504i			0.619600i
$75$	−0.0423029	−	6.11910i	−0.000564038	−	0.0815880i
$76$	−284.145			−3.73876
$77$		−	71.9101i		−	0.933898i
$78$	−18.8141	+	0.130067i	−0.241207	+	0.00166752i
$79$	−26.2741			−0.332583			−0.166292	−	0.986077i	$-0.553179\pi$
$79$	−26.2741			−0.332583			−0.166292	+	0.986077i	$0.553179\pi$
$80$		−	270.078i		−	3.37597i
$81$	80.9690	−	2.23957i	0.999618	−	0.0276490i
$82$	294.417			3.59045
$83$			19.9376i			0.240213i	0.992761	+	0.120106i	$0.0383235\pi$
$83$			19.9376i			0.240213i	−0.992761	+	0.120106i	$0.961676\pi$
$84$	1.26303	+	182.697i	0.0150361	+	2.17496i
$85$	95.3750			1.12206
$86$			14.1850i			0.164942i
$87$	−104.486	+	0.722340i	−1.20099	+	0.00830275i
$88$	328.035			3.72767
$89$		−	85.9865i		−	0.966141i	−0.875582	−	0.483070i	$-0.839522\pi$
$89$		−	85.9865i		−	0.966141i	0.875582	−	0.483070i	$-0.160478\pi$
$90$	165.546	−	2.28903i	1.83940	−	0.0254336i
$91$	9.26436			0.101806
$92$			282.147i			3.06682i
$93$	0.683472	+	98.8640i	0.00734916	+	1.06305i
$94$	185.749			1.97605
$95$		−	126.788i		−	1.33462i
$96$	−338.707	+	2.34156i	−3.52820	+	0.0243913i
$97$	−101.667			−1.04811			−0.524057	−	0.851683i	$-0.675582\pi$
$97$	−101.667			−1.04811			−0.524057	+	0.851683i	$0.675582\pi$
$98$			64.6429i			0.659622i
$99$	1.57780	+	114.109i	0.0159374	+	1.15262i
$100$	−21.9041			−0.219041
$101$		−	128.142i		−	1.26873i	−0.773034	−	0.634365i	$-0.781262\pi$
$101$		−	128.142i		−	1.26873i	0.773034	−	0.634365i	$-0.218738\pi$
$102$	−1.58478	−	229.238i	−0.0155370	−	2.24743i
$103$	126.274			1.22596			0.612981	−	0.790098i	$-0.289970\pi$
$103$	126.274			1.22596			0.612981	+	0.790098i	$0.289970\pi$
$104$			42.2616i			0.406361i
$105$	−81.5211	+	0.563576i	−0.776392	+	0.00536739i
$106$	−102.832			−0.970116
$107$		−	126.151i		−	1.17898i	−0.807775	−	0.589491i	$-0.799328\pi$
$107$		−	126.151i		−	1.17898i	0.807775	−	0.589491i	$-0.200672\pi$
$108$	−6.01282	−	289.881i	−0.0556743	−	2.68408i
$109$	113.017			1.03686			0.518428	−	0.855121i	$-0.326517\pi$
$109$	113.017			1.03686			0.518428	+	0.855121i	$0.326517\pi$
$110$			233.258i			2.12052i
$111$	0.247689	+	35.8282i	0.00223144	+	0.322777i
$112$	319.648			2.85400
$113$		−	78.0544i		−	0.690747i	−0.938465	−	0.345373i	$-0.887752\pi$
$113$		−	78.0544i		−	0.690747i	0.938465	−	0.345373i	$-0.112248\pi$
$114$	−304.741	+	2.10675i	−2.67317	+	0.0184803i
$115$	−125.897			−1.09475
$116$			374.023i			3.22433i
$117$	−14.7009	+	0.203272i	−0.125649	+	0.00173737i
$118$	−422.746			−3.58259
$119$			112.880i			0.948572i
$120$	−2.57088	−	371.878i	−0.0214240	−	3.09898i
$121$	−39.7822			−0.328779
$122$			93.1155i			0.763242i
$123$	230.062	−	1.59048i	1.87042	−	0.0129307i
$124$	353.897			2.85401
$125$		−	129.566i		−	1.03653i
$126$	2.70915	+	195.930i	0.0215012	+	1.55500i
$127$	152.006			1.19689			0.598447	−	0.801162i	$-0.295785\pi$
$127$	152.006			1.19689			0.598447	+	0.801162i	$0.295785\pi$
$128$			346.902i			2.71017i
$129$	0.0766292	+	11.0844i	0.000594025	+	0.0859256i
$130$	−30.0512			−0.231163
$131$			186.787i			1.42586i	0.701236	+	0.712929i	$0.252632\pi$
$131$			186.787i			1.42586i	−0.701236	+	0.712929i	$0.747368\pi$
$132$	408.488	−	2.82398i	3.09461	−	0.0213938i
$133$	150.059			1.12826
$134$		−	31.4243i		−	0.234510i
$135$	129.348	−	2.68298i	0.958131	−	0.0198739i
$136$	−514.929			−3.78624
$137$			16.0500i			0.117153i	0.998283	+	0.0585767i	$0.0186562\pi$
$137$			16.0500i			0.117153i	−0.998283	+	0.0585767i	$0.981344\pi$
$138$	2.09193	+	302.598i	0.0151589	+	2.19274i
$139$	244.052			1.75577			0.877885	−	0.478871i	$-0.158954\pi$
$139$	244.052			1.75577			0.877885	+	0.478871i	$0.158954\pi$
$140$			291.816i			2.08440i
$141$	145.147	−	1.00344i	1.02941	−	0.00711657i
$142$	254.539			1.79253
$143$		−	20.7140i		−	0.144853i
$144$	−507.226	+	7.01349i	−3.52240	+	0.0487048i
$145$	−166.892			−1.15098
$146$		−	281.589i		−	1.92869i
$147$	0.349209	+	50.5130i	0.00237557	+	0.343626i
$148$	128.252			0.866567
$149$		−	38.5772i		−	0.258907i	−0.991585	−	0.129454i	$-0.958678\pi$
$149$		−	38.5772i		−	0.258907i	0.991585	−	0.129454i	$-0.0413223\pi$
$150$	−23.4918	+	0.162405i	−0.156612	+	0.00108270i
$151$	191.919			1.27099			0.635494	−	0.772105i	$-0.280796\pi$
$151$	191.919			1.27099			0.635494	+	0.772105i	$0.280796\pi$
$152$			684.530i			4.50349i
$153$	−2.47674	−	179.121i	−0.0161878	−	1.17073i
$154$	−276.070			−1.79266
$155$			157.912i			1.01879i
$156$	0.363820	+	52.6265i	0.00233218	+	0.337349i
$157$	−72.2129			−0.459955			−0.229977	−	0.973196i	$-0.573865\pi$
$157$	−72.2129			−0.459955			−0.229977	+	0.973196i	$0.573865\pi$
$158$			100.869i			0.638410i
$159$	−80.3548	+	0.555513i	−0.505376	+	0.00349379i
$160$	−541.005			−3.38128
$161$		−	149.004i		−	0.925489i
$162$	−8.59792	−	310.848i	−0.0530736	−	1.91881i
$163$	−54.6578			−0.335324			−0.167662	−	0.985845i	$-0.553622\pi$
$163$	−54.6578			−0.335324			−0.167662	+	0.985845i	$0.553622\pi$
$164$		−	823.538i		−	5.02157i
$165$	1.26009	+	182.271i	0.00763689	+	1.10467i
$166$	76.5425			0.461099
$167$			58.6583i			0.351247i	0.984457	+	0.175624i	$0.0561942\pi$
$167$			58.6583i			0.351247i	−0.984457	+	0.175624i	$0.943806\pi$
$168$	440.132	−	3.04274i	2.61983	−	0.0181116i
$169$	−166.331			−0.984209
$170$		−	366.154i		−	2.15384i
$171$	−238.118	+	3.29250i	−1.39250	+	0.0192544i
$172$	39.6781			0.230686
$173$		−	58.2061i		−	0.336452i	−0.985748	−	0.168226i	$-0.946196\pi$
$173$		−	58.2061i		−	0.336452i	0.985748	−	0.168226i	$-0.0538038\pi$
$174$	2.77313	+	401.133i	0.0159375	+	2.30536i
$175$	11.5677			0.0661013
$176$		−	714.693i		−	4.06076i
$177$	−330.340	+	2.28372i	−1.86633	+	0.0129024i
$178$	−330.110			−1.85455
$179$			145.157i			0.810930i	0.914111	+	0.405465i	$0.132890\pi$
$179$			145.157i			0.810930i	−0.914111	+	0.405465i	$0.867110\pi$
$180$	−6.40282	−	463.061i	−0.0355712	−	2.57256i
$181$	13.1087			0.0724237			0.0362118	−	0.999344i	$-0.488471\pi$
$181$	13.1087			0.0724237			0.0362118	+	0.999344i	$0.488471\pi$
$182$		−	35.5667i		−	0.195422i
$183$	0.503021	+	72.7619i	0.00274875	+	0.397606i
$184$	679.716			3.69411
$185$			57.2272i			0.309336i
$186$	379.548	−	2.62391i	2.04058	−	0.0141071i
$187$	252.386			1.34966
$188$		−	519.573i		−	2.76368i
$189$	3.17541	+	153.088i	0.0168011	+	0.809990i
$190$	−486.753			−2.56186
$191$			294.023i			1.53939i	0.638415	+	0.769693i	$0.279591\pi$
$191$			294.023i			1.53939i	−0.638415	+	0.769693i	$0.720409\pi$
$192$	4.31371	+	623.978i	0.0224672	+	3.24988i
$193$	94.7184			0.490769			0.245384	−	0.969426i	$-0.421086\pi$
$193$	94.7184			0.490769			0.245384	+	0.969426i	$0.421086\pi$
$194$			390.309i			2.01190i
$195$	−23.4825	+	0.162340i	−0.120423	+	0.000832513i
$196$	180.818			0.922541
$197$		−	104.252i		−	0.529199i	−0.964358	−	0.264600i	$-0.914760\pi$
$197$		−	104.252i		−	0.529199i	0.964358	−	0.264600i	$-0.0852398\pi$
$198$	438.075	−	6.05733i	2.21250	−	0.0305926i
$199$	−139.014			−0.698562			−0.349281	−	0.937018i	$-0.613574\pi$
$199$	−139.014			−0.698562			−0.349281	+	0.937018i	$0.613574\pi$
$200$			52.7689i			0.263844i
$201$	−0.169758	−	24.5555i	−0.000844567	−	0.122167i
$202$	−491.948			−2.43539
$203$		−	197.524i		−	0.973024i
$204$	−641.219	+	4.43291i	−3.14323	+	0.0217299i
$205$	367.471			1.79254
$206$		−	484.778i		−	2.35329i
$207$	3.26934	+	236.443i	0.0157939	+	1.14224i
$208$	92.0757			0.442672
$209$		−	335.514i		−	1.60533i
$210$	2.16362	+	312.967i	0.0103030	+	1.49032i
$211$	−106.853			−0.506412			−0.253206	−	0.967412i	$-0.581485\pi$
$211$	−106.853			−0.506412			−0.253206	+	0.967412i	$0.581485\pi$
$212$			287.641i			1.35680i
$213$	198.901	−	1.37505i	0.933805	−	0.00645563i
$214$	−484.306			−2.26311
$215$			17.7047i			0.0823476i
$216$	−698.347	+	14.4854i	−3.23309	+	0.0670620i
$217$	−186.895			−0.861269
$218$		−	433.884i		−	1.99029i
$219$	−1.52118	−	220.038i	−0.00694602	−	1.00474i
$220$	652.464			2.96575
$221$			32.5155i			0.147129i
$222$	137.548	−	0.950903i	0.619585	−	0.00428335i
$223$	−99.4660			−0.446036			−0.223018	−	0.974814i	$-0.571591\pi$
$223$	−99.4660			−0.446036			−0.223018	+	0.974814i	$0.571591\pi$
$224$		−	640.301i		−	2.85849i
$225$	−18.3560	+	0.253811i	−0.0815822	+	0.00112805i
$226$	−299.658			−1.32592
$227$			394.623i			1.73843i	0.494436	+	0.869214i	$0.335375\pi$
$227$			394.623i			1.73843i	−0.494436	+	0.869214i	$0.664625\pi$
$228$	5.89296	+	852.416i	0.0258463	+	3.73867i
$229$	−126.476			−0.552298			−0.276149	−	0.961115i	$-0.589058\pi$
$229$	−126.476			−0.552298			−0.276149	+	0.961115i	$0.589058\pi$
$230$			483.329i			2.10143i
$231$	−215.725	+	1.49136i	−0.933875	+	0.00645611i
$232$	901.051			3.88384
$233$		−	145.322i		−	0.623700i	−0.950131	−	0.311850i	$-0.899051\pi$
$233$		−	145.322i		−	0.623700i	0.950131	−	0.311850i	$-0.100949\pi$
$234$	0.780381	+	56.4383i	0.00333496	+	0.241189i
$235$	231.838			0.986546
$236$			1182.50i			5.01058i
$237$	0.544905	+	78.8204i	0.00229918	+	0.332576i
$238$	433.357			1.82083
$239$			103.766i			0.434166i	0.976153	+	0.217083i	$0.0696543\pi$
$239$			103.766i			0.434166i	−0.976153	+	0.217083i	$0.930346\pi$
$240$	−810.214	+	5.60121i	−3.37589	+	0.0233384i
$241$	159.392			0.661378			0.330689	−	0.943740i	$-0.392719\pi$
$241$	159.392			0.661378			0.330689	+	0.943740i	$0.392719\pi$
$242$			152.728i			0.631106i
$243$	−8.39779	−	242.855i	−0.0345588	−	0.999403i
$244$	260.461			1.06746
$245$			80.6828i			0.329317i
$246$	−6.10599	−	883.230i	−0.0248211	−	3.59037i
$247$	43.2251			0.175000
$248$		−	852.567i		−	3.43777i
$249$	59.8115	−	0.413492i	0.240207	−	0.00166061i
$250$	−497.416			−1.98966
$251$			74.1101i			0.295260i	0.989043	+	0.147630i	$0.0471644\pi$
$251$			74.1101i			0.295260i	−0.989043	+	0.147630i	$0.952836\pi$
$252$	548.051	−	7.57799i	2.17481	−	0.0300714i
$253$	−333.154			−1.31681
$254$		−	583.564i		−	2.29750i
$255$	−1.97801	−	286.118i	−0.00775689	−	1.12203i
$256$	499.799			1.95234
$257$			25.5622i			0.0994639i	0.998763	+	0.0497319i	$0.0158367\pi$
$257$			25.5622i			0.0994639i	−0.998763	+	0.0497319i	$0.984163\pi$
$258$	42.5540	−	0.294187i	0.164938	−	0.00114026i
$259$	−67.7307			−0.261508
$260$			84.0586i			0.323302i
$261$	4.33393	+	313.436i	0.0166051	+	1.20091i
$262$	717.094			2.73700
$263$		−	425.344i		−	1.61728i	−0.588306	−	0.808638i	$-0.700205\pi$
$263$		−	425.344i		−	1.61728i	0.588306	−	0.808638i	$-0.299795\pi$
$264$	−6.80320	−	984.081i	−0.0257697	−	3.72758i
$265$	−128.348			−0.484332
$266$		−	576.091i		−	2.16576i
$267$	−257.953	+	1.78330i	−0.966118	+	0.00667901i
$268$	−87.8996			−0.327983
$269$			268.192i			0.996995i	0.866891	+	0.498497i	$0.166115\pi$
$269$			268.192i			0.996995i	−0.866891	+	0.498497i	$0.833885\pi$
$270$	−10.3002	−	496.578i	−0.0381489	−	1.83918i
$271$	300.580			1.10915			0.554576	−	0.832133i	$-0.312881\pi$
$271$	300.580			1.10915			0.554576	+	0.832133i	$0.312881\pi$
$272$			1121.88i			4.12456i
$273$	−0.192136	−	27.7924i	−0.000703794	−	0.101804i
$274$	61.6175			0.224882
$275$		−	25.8640i		−	0.0940509i
$276$	846.421	−	5.85152i	3.06674	−	0.0212012i
$277$	−189.584			−0.684419			−0.342210	−	0.939624i	$-0.611175\pi$
$277$	−189.584			−0.684419			−0.342210	+	0.939624i	$0.611175\pi$
$278$		−	936.939i		−	3.37028i
$279$	296.571	−	4.10073i	1.06298	−	0.0146980i
$280$	703.008			2.51074
$281$		−	106.252i		−	0.378120i	−0.981966	−	0.189060i	$-0.939456\pi$
$281$		−	106.252i		−	0.378120i	0.981966	−	0.189060i	$-0.0605440\pi$
$282$	−3.85229	−	557.233i	−0.0136606	−	1.97600i
$283$	167.010			0.590142			0.295071	−	0.955475i	$-0.404657\pi$
$283$	167.010			0.590142			0.295071	+	0.955475i	$0.404657\pi$
$284$		−	711.991i		−	2.50701i
$285$	−380.356	+	2.62950i	−1.33458	+	0.00922631i
$286$	−79.5229			−0.278052
$287$			434.916i			1.51539i
$288$	14.0491	+	1016.05i	0.0487814	+	3.52794i
$289$	−107.180			−0.370865
$290$			640.716i			2.20936i
$291$	2.10850	+	304.994i	0.00724570	+	1.04809i
$292$	−787.656			−2.69745
$293$			267.240i			0.912083i	0.889959	+	0.456041i	$0.150733\pi$
$293$			267.240i			0.912083i	−0.889959	+	0.456041i	$0.849267\pi$
$294$	193.924	−	1.34065i	0.659606	−	0.00456002i
$295$	−527.641			−1.78861
$296$		−	308.969i		−	1.04382i
$297$	342.286	−	7.09983i	1.15248	−	0.0239052i
$298$	−148.101			−0.496984
$299$		−	42.9211i		−	0.143549i
$300$	0.454275	+	65.7108i	0.00151425	+	0.219036i
$301$	−20.9543			−0.0696155
$302$		−	736.796i		−	2.43972i
$303$	−384.416	+	2.65756i	−1.26870	+	0.00877083i
$304$	1491.39			4.90590
$305$			116.220i			0.381050i
$306$	−687.664	+	9.50843i	−2.24727	+	0.0310733i
$307$	200.908			0.654424			0.327212	−	0.944951i	$-0.393891\pi$
$307$	200.908			0.654424			0.327212	+	0.944951i	$0.393891\pi$
$308$			772.217i			2.50720i
$309$	−2.61883	−	378.813i	−0.00847518	−	1.22593i
$310$	606.240			1.95561
$311$		−	143.936i		−	0.462818i	−0.972857	−	0.231409i	$-0.925666\pi$
$311$		−	143.936i		−	0.462818i	0.972857	−	0.231409i	$-0.0743335\pi$
$312$	126.782	−	0.876473i	0.406351	−	0.00280921i
$313$	130.402			0.416619			0.208310	−	0.978063i	$-0.433204\pi$
$313$	130.402			0.416619			0.208310	+	0.978063i	$0.433204\pi$
$314$			277.232i			0.882905i
$315$	3.38137	+	244.546i	0.0107345	+	0.776336i
$316$	282.148			0.892874
$317$		−	325.451i		−	1.02666i	−0.858191	−	0.513330i	$-0.828412\pi$
$317$		−	325.451i		−	1.02666i	0.858191	−	0.513330i	$-0.171588\pi$
$318$	2.13267	+	308.490i	0.00670650	+	0.970093i
$319$	−441.639			−1.38445
$320$			996.659i			3.11456i
$321$	−378.444	+	2.61628i	−1.17895	+	0.00815040i
$322$	−572.039			−1.77652
$323$			526.669i			1.63055i
$324$	−869.497	+	24.0499i	−2.68363	+	0.0742282i
$325$	3.33212			0.0102527
$326$			209.836i			0.643669i
$327$	−2.34389	−	339.044i	−0.00716787	−	1.03683i
$328$	−1983.97			−6.04869
$329$			274.390i			0.834012i
$330$	699.756	−	4.83759i	2.12047	−	0.0146594i
$331$	−500.666			−1.51259			−0.756293	−	0.654233i	$-0.772992\pi$
$331$	−500.666			−1.51259			−0.756293	+	0.654233i	$0.772992\pi$
$332$		−	214.103i		−	0.644889i
$333$	107.477	−	1.48610i	0.322754	−	0.00446276i
$334$	225.195			0.674235
$335$		−	39.2216i		−	0.117080i
$336$	−6.62925	−	958.920i	−0.0197299	−	2.85393i
$337$	116.975			0.347106			0.173553	−	0.984825i	$-0.444475\pi$
$337$	116.975			0.347106			0.173553	+	0.984825i	$0.444475\pi$
$338$			638.562i			1.88924i
$339$	−234.158	+	1.61879i	−0.690730	+	0.00477519i
$340$	−1024.20			−3.01235
$341$			417.875i			1.22544i
$342$	12.6402	+	914.158i	0.0369597	+	2.67298i
$343$	−373.377			−1.08856
$344$		−	95.5878i		−	0.277871i
$345$	2.61100	+	377.681i	0.00756813	+	1.09473i
$346$	−223.459			−0.645834
$347$			406.232i			1.17070i	0.810782	+	0.585348i	$0.199042\pi$
$347$			406.232i			1.17070i	−0.810782	+	0.585348i	$0.800958\pi$
$348$	1122.04	−	7.75694i	3.22425	−	0.0222901i
$349$	226.754			0.649725			0.324862	−	0.945761i	$-0.394682\pi$
$349$	226.754			0.649725			0.324862	+	0.945761i	$0.394682\pi$
$350$		−	44.4096i		−	0.126884i
$351$	0.914689	+	44.0976i	0.00260595	+	0.125634i
$352$	−1431.63			−4.06714
$353$			230.128i			0.651922i	0.945383	+	0.325961i	$0.105688\pi$
$353$			230.128i			0.651922i	−0.945383	+	0.325961i	$0.894312\pi$
$354$	8.76742	+	1268.21i	0.0247667	+	3.58250i
$355$	317.697			0.894922
$356$			923.378i			2.59376i
$357$	338.632	−	2.34105i	0.948549	−	0.00655756i
$358$	557.269			1.55662
$359$			235.311i			0.655463i	0.944771	+	0.327731i	$0.106284\pi$
$359$			235.311i			0.655463i	−0.944771	+	0.327731i	$0.893716\pi$
$360$	−1115.55	+	15.4249i	−3.09876	+	0.0428470i
$361$	339.137			0.939437
$362$		−	50.3255i		−	0.139021i
$363$	0.825053	+	119.344i	0.00227287	+	0.328771i
$364$	−99.4866			−0.273315
$365$		−	351.460i		−	0.962903i
$366$	279.340	−	1.93114i	0.763223	−	0.00527635i
$367$	−146.389			−0.398880			−0.199440	−	0.979910i	$-0.563912\pi$
$367$	−146.389			−0.398880			−0.199440	+	0.979910i	$0.563912\pi$
$368$		−	1480.90i		−	4.02420i
$369$	−9.54263	−	690.137i	−0.0258608	−	1.87029i
$370$	219.701			0.593786
$371$		−	151.905i		−	0.409447i
$372$	−7.33956	−	1061.67i	−0.0197300	−	2.85394i
$373$	422.079			1.13158			0.565790	−	0.824550i	$-0.308571\pi$
$373$	422.079			1.13158			0.565790	+	0.824550i	$0.308571\pi$
$374$		−	968.934i		−	2.59073i
$375$	−388.689	+	2.68710i	−1.03650	+	0.00716560i
$376$	−1251.69			−3.32897
$377$		−	56.8974i		−	0.150922i
$378$	587.720	−	12.1907i	1.55481	−	0.0322505i
$379$	−308.784			−0.814732			−0.407366	−	0.913265i	$-0.633553\pi$
$379$	−308.784			−0.814732			−0.407366	+	0.913265i	$0.633553\pi$
$380$			1361.54i			3.58299i
$381$	−3.15248	−	456.006i	−0.00827423	−	1.19687i
$382$	1128.78			2.95492
$383$		−	224.435i		−	0.585993i	−0.956113	−	0.292997i	$-0.905348\pi$
$383$		−	224.435i		−	0.585993i	0.956113	−	0.292997i	$-0.0946525\pi$
$384$	1040.68	−	7.19448i	2.71011	−	0.0187356i
$385$	−344.571			−0.894989
$386$		−	363.633i		−	0.942054i
$387$	33.2508	−	0.459764i	0.0859194	−	0.00118802i
$388$	1091.77			2.81383
$389$			478.018i			1.22884i	0.788980	+	0.614419i	$0.210610\pi$
$389$			478.018i			1.22884i	−0.788980	+	0.614419i	$0.789390\pi$
$390$	0.623239	+	90.1514i	0.00159805	+	0.231157i
$391$	522.965			1.33751
$392$		−	435.606i		−	1.11124i
$393$	560.349	−	3.87383i	1.42582	−	0.00985707i
$394$	−400.234			−1.01582
$395$			125.897i			0.318727i
$396$	−16.9435	−	1225.38i	−0.0427865	−	3.09438i
$397$	637.519			1.60584			0.802921	−	0.596085i	$-0.203278\pi$
$397$	637.519			1.60584			0.802921	+	0.596085i	$0.203278\pi$
$398$			533.687i			1.34092i
$399$	−3.11211	−	450.167i	−0.00779978	−	1.12824i
$400$	114.968			0.287420
$401$		−	369.176i		−	0.920639i	−0.887753	−	0.460319i	$-0.847735\pi$
$401$		−	369.176i		−	0.920639i	0.887753	−	0.460319i	$-0.152265\pi$
$402$	−94.2708	+	0.651717i	−0.234504	+	0.00162119i
$403$	−53.8359			−0.133588
$404$			1376.07i			3.40611i
$405$	−10.7313	−	387.978i	−0.0264971	−	0.957971i
$406$	−758.312			−1.86776
$407$			151.437i			0.372082i
$408$	10.6792	+	1544.75i	0.0261746	+	3.78615i
$409$	94.3701			0.230734			0.115367	−	0.993323i	$-0.463196\pi$
$409$	94.3701			0.230734			0.115367	+	0.993323i	$0.463196\pi$
$410$		−	1410.75i		−	3.44086i
$411$	48.1489	−	0.332865i	0.117151	−	0.000809891i
$412$	−1356.01			−3.29129
$413$		−	624.484i		−	1.51207i
$414$	907.728	−	12.5513i	2.19258	−	0.0303172i
$415$	95.5349			0.230205
$416$		−	184.441i		−	0.443368i
$417$	−5.06146	−	732.139i	−0.0121378	−	1.75573i
$418$	−1288.07			−3.08150
$419$			591.925i			1.41271i	0.707858	+	0.706355i	$0.249662\pi$
$419$			591.925i			1.41271i	−0.707858	+	0.706355i	$0.750338\pi$
$420$	875.426	−	6.05204i	2.08435	−	0.0144096i
$421$	−489.190			−1.16197			−0.580986	−	0.813914i	$-0.697333\pi$
$421$	−489.190			−1.16197			−0.580986	+	0.813914i	$0.697333\pi$
$422$			410.218i			0.972081i
$423$	−6.02048	−	435.410i	−0.0142328	−	1.02934i
$424$	692.950			1.63432
$425$			40.5997i			0.0955288i
$426$	−5.27894	−	763.598i	−0.0123919	−	1.79248i
$427$	−137.551			−0.322134
$428$			1354.69i			3.16517i
$429$	−62.1404	+	0.429592i	−0.144849	+	0.00100138i
$430$	67.9702			0.158070
$431$			788.376i			1.82918i	0.404384	+	0.914589i	$0.367486\pi$
$431$			788.376i			1.82918i	−0.404384	+	0.914589i	$0.632514\pi$
$432$	31.5595	+	1521.50i	0.0730543	+	3.52198i
$433$	−64.7792			−0.149606			−0.0748028	−	0.997198i	$-0.523833\pi$
$433$	−64.7792			−0.149606			−0.0748028	+	0.997198i	$0.523833\pi$
$434$			717.509i			1.65325i
$435$	3.46122	+	500.665i	0.00795684	+	1.15095i
$436$	−1213.65			−2.78361
$437$		−	695.213i		−	1.59088i
$438$	−844.747	+	5.83995i	−1.92865	+	0.0133332i
$439$	555.788			1.26603			0.633016	−	0.774139i	$-0.281817\pi$
$439$	555.788			1.26603			0.633016	+	0.774139i	$0.281817\pi$
$440$		−	1571.84i		−	3.57236i
$441$	151.528	−	2.09520i	0.343601	−	0.00475103i
$442$	124.830			0.282421
$443$		−	40.4244i		−	0.0912515i	−0.998959	−	0.0456258i	$-0.985472\pi$
$443$		−	40.4244i		−	0.0912515i	0.998959	−	0.0456258i	$-0.0145282\pi$
$444$	−2.65985	−	384.746i	−0.00599065	−	0.866546i
$445$	−412.020			−0.925889
$446$			381.859i			0.856187i
$447$	−115.729	+	0.800061i	−0.258901	+	0.00178985i
$448$	−1179.58			−2.63300
$449$			342.734i			0.763328i	0.924301	+	0.381664i	$0.124649\pi$
$449$			342.734i			0.763328i	−0.924301	+	0.381664i	$0.875351\pi$
$450$	0.974405	+	70.4704i	0.00216534	+	0.156601i
$451$	972.419			2.15614
$452$			838.198i			1.85442i
$453$	−3.98026	−	575.744i	−0.00878645	−	1.27096i
$454$	1515.00			3.33699
$455$		−	44.3919i		−	0.0975646i
$456$	2053.54	−	14.1966i	4.50338	−	0.0311330i
$457$	554.462			1.21326			0.606632	−	0.794983i	$-0.292520\pi$
$457$	554.462			1.21326			0.606632	+	0.794983i	$0.292520\pi$
$458$			485.554i			1.06016i
$459$	−537.300	+	11.1449i	−1.17059	+	0.0242808i
$460$	1351.96			2.93904
$461$		−	256.090i		−	0.555509i	−0.960652	−	0.277755i	$-0.910410\pi$
$461$		−	256.090i		−	0.555509i	0.960652	−	0.277755i	$-0.0895902\pi$
$462$	5.72548	+	828.189i	0.0123928	+	1.79262i
$463$	−407.247			−0.879582			−0.439791	−	0.898100i	$-0.644948\pi$
$463$	−407.247			−0.879582			−0.439791	+	0.898100i	$0.644948\pi$
$464$		−	1963.13i		−	4.23088i
$465$	473.725	−	3.27498i	1.01876	−	0.00704297i
$466$	−557.905			−1.19722
$467$		−	3.62045i		−	0.00775257i	−0.999992	−	0.00387629i	$-0.998766\pi$
$467$		−	3.62045i		−	0.00775257i	0.999992	−	0.00387629i	$-0.00123386\pi$
$468$	157.868	−	2.18287i	0.337325	−	0.00466425i
$469$	46.4204			0.0989773
$470$		−	890.049i		−	1.89372i
$471$	1.49764	+	216.634i	0.00317971	+	0.459944i
$472$	2848.73			6.03545
$473$			46.8511i			0.0990510i
$474$	302.599	−	2.09194i	0.638394	−	0.00441338i
$475$	53.9720			0.113625
$476$		−	1212.18i		−	2.54659i
$477$	3.33300	+	241.047i	0.00698741	+	0.505340i
$478$	398.366			0.833402
$479$		−	687.936i		−	1.43619i	−0.695945	−	0.718096i	$-0.745014\pi$
$479$		−	687.936i		−	1.43619i	0.695945	−	0.718096i	$-0.254986\pi$
$480$	11.2200	+	1622.98i	0.0233751	+	3.38120i
$481$	−19.5101			−0.0405615
$482$		−	611.922i		−	1.26955i
$483$	−447.001	+	3.09023i	−0.925467	+	0.00639798i
$484$	427.207			0.882659
$485$			487.157i			1.00445i
$486$	−932.343	+	32.2399i	−1.91840	+	0.0663372i
$487$	157.402			0.323208			0.161604	−	0.986856i	$-0.448333\pi$
$487$	157.402			0.323208			0.161604	+	0.986856i	$0.448333\pi$
$488$		−	627.472i		−	1.28580i
$489$	1.13356	+	163.969i	0.00231812	+	0.335316i
$490$	309.749			0.632140
$491$		−	658.103i		−	1.34033i	−0.742211	−	0.670166i	$-0.766223\pi$
$491$		−	658.103i		−	1.34033i	0.742211	−	0.670166i	$-0.233777\pi$
$492$	−2470.56	+	17.0796i	−5.02145	+	0.0347146i
$493$	693.258			1.40620
$494$		−	165.945i		−	0.335921i
$495$	546.775	−	7.56034i	1.10460	−	0.0152734i
$496$	−1857.50			−3.74495
$497$			376.007i			0.756554i
$498$	−1.58743	−	229.622i	−0.00318762	−	0.461088i
$499$	370.285			0.742054			0.371027	−	0.928622i	$-0.379006\pi$
$499$	370.285			0.742054			0.371027	+	0.928622i	$0.379006\pi$
$500$			1391.36i			2.78273i
$501$	175.971	−	1.21653i	0.351239	−	0.00242820i
$502$	284.516			0.566765
$503$			254.078i			0.505126i	0.967581	+	0.252563i	$0.0812734\pi$
$503$			254.078i			0.505126i	−0.967581	+	0.252563i	$0.918727\pi$
$504$	−18.2560	−	1320.30i	−0.0362222	−	2.61965i
$505$	−614.015			−1.21587
$506$			1279.01i			2.52769i
$507$	3.44959	+	498.982i	0.00680392	+	0.984186i
$508$	−1632.33			−3.21326
$509$		−	587.707i		−	1.15463i	−0.816522	−	0.577315i	$-0.804101\pi$
$509$		−	587.707i		−	1.15463i	0.816522	−	0.577315i	$-0.195899\pi$
$510$	−1098.43	+	7.59375i	−2.15379	+	0.0148897i
$511$	415.966			0.814024
$512$		−	531.167i		−	1.03744i
$513$	14.8156	+	714.269i	0.0288804	+	1.39234i
$514$	98.1357			0.190926
$515$		−	605.066i		−	1.17489i
$516$	−0.822893	−	119.031i	−0.00159475	−	0.230681i
$517$	613.502			1.18666
$518$			260.024i			0.501978i
$519$	−174.614	+	1.20715i	−0.336443	+	0.00232592i
$520$	202.504			0.389431
$521$			423.930i			0.813685i	0.913498	+	0.406843i	$0.133370\pi$
$521$			423.930i			0.813685i	−0.913498	+	0.406843i	$0.866630\pi$
$522$	1203.31	−	16.6384i	2.30519	−	0.0318743i
$523$	489.850			0.936616			0.468308	−	0.883565i	$-0.344864\pi$
$523$	489.850			0.936616			0.468308	+	0.883565i	$0.344864\pi$
$524$		−	2005.84i		−	3.82794i
$525$	−0.239906	−	34.7023i	−0.000456963	−	0.0660997i
$526$	−1632.93			−3.10444
$527$		−	655.955i		−	1.24470i
$528$	−2144.03	+	14.8222i	−4.06066	+	0.0280723i
$529$	−161.323			−0.304959
$530$			492.740i			0.929699i
$531$	13.7020	+	990.949i	0.0258042	+	1.86619i
$532$	−1611.43			−3.02901
$533$			125.279i			0.235045i
$534$	6.84624	+	990.307i	0.0128207	+	1.85451i
$535$	−604.477			−1.12986
$536$			211.757i			0.395070i
$537$	435.459	−	3.01044i	0.810911	−	0.00560603i
$538$	1029.61			1.91378
$539$			213.507i			0.396116i
$540$	−1389.02	+	28.8116i	−2.57226	+	0.0533547i
$541$	−319.175			−0.589972			−0.294986	−	0.955502i	$-0.595315\pi$
$541$	−319.175			−0.589972			−0.294986	+	0.955502i	$0.595315\pi$
$542$		−	1153.95i		−	2.12907i
$543$	−0.271864	−	39.3251i	−0.000500671	−	0.0724219i
$544$	2247.29			4.13105
$545$		−	541.543i		−	0.993657i
$546$	−106.698	+	0.737628i	−0.195417	+	0.00135097i
$547$	232.053			0.424228			0.212114	−	0.977245i	$-0.431965\pi$
$547$	232.053			0.424228			0.212114	+	0.977245i	$0.431965\pi$
$548$		−	172.355i		−	0.314517i
$549$	218.270	−	3.01805i	0.397577	−	0.00549737i
$550$	−99.2943			−0.180535
$551$		−	921.594i		−	1.67258i
$552$	−14.0968	−	2039.10i	−0.0255377	−	3.69402i
$553$	−149.004			−0.269447
$554$			727.831i			1.31377i
$555$	171.678	−	1.18685i	0.309329	−	0.00213847i
$556$	−2620.79			−4.71365
$557$		−	240.394i		−	0.431586i	−0.976439	−	0.215793i	$-0.930766\pi$
$557$		−	240.394i		−	0.431586i	0.976439	−	0.215793i	$-0.0692337\pi$
$558$	−15.7431	−	1138.56i	−0.0282134	−	2.04044i
$559$	−6.03595			−0.0107978
$560$		−	1531.65i		−	2.73509i
$561$	−5.23430	−	757.140i	−0.00933030	−	1.34963i
$562$	−407.910			−0.725819
$563$			635.607i			1.12896i	0.825445	+	0.564482i	$0.190924\pi$
$563$			635.607i			1.12896i	−0.825445	+	0.564482i	$0.809076\pi$
$564$	−1558.68	+	10.7755i	−2.76362	+	0.0191056i
$565$	−374.012			−0.661968
$566$		−	641.168i		−	1.13281i
$567$	459.187	−	12.7009i	0.809854	−	0.0224002i
$568$	−1715.25			−3.01980
$569$			624.533i			1.09760i	0.835955	+	0.548799i	$0.184915\pi$
$569$			624.533i			1.09760i	−0.835955	+	0.548799i	$0.815085\pi$
$570$	10.0949	+	1460.22i	0.0177103	+	2.56180i
$571$	423.424			0.741549			0.370774	−	0.928723i	$-0.379092\pi$
$571$	423.424			0.741549			0.370774	+	0.928723i	$0.379092\pi$
$572$			222.440i			0.388881i
$573$	882.047	−	6.09781i	1.53935	−	0.0106419i
$574$	1669.68			2.90886
$575$		−	53.5924i		−	0.0932041i
$576$	1871.80	−	25.8816i	3.24965	−	0.0449334i
$577$	−806.459			−1.39768			−0.698838	−	0.715280i	$-0.746299\pi$
$577$	−806.459			−1.39768			−0.698838	+	0.715280i	$0.746299\pi$
$578$			411.474i			0.711893i
$579$	−1.96439	−	284.148i	−0.00339273	−	0.490757i
$580$	1792.20			3.09000
$581$			113.069i			0.194612i
$582$	1170.90	−	8.09472i	2.01186	−	0.0139085i
$583$	−339.641			−0.582575
$584$			1897.53i			3.24919i
$585$	0.974017	+	70.4423i	0.00166499	+	0.120414i
$586$	1025.96			1.75079
$587$			324.424i			0.552682i	0.961060	+	0.276341i	$0.0891219\pi$
$587$			324.424i			0.552682i	−0.961060	+	0.276341i	$0.910878\pi$
$588$	−3.75003	−	542.441i	−0.00637760	−	0.922519i
$589$	−872.005			−1.48048
$590$			2025.66i			3.43333i
$591$	−312.749	+	2.16211i	−0.529186	+	0.00365840i
$592$	−673.155			−1.13709
$593$			688.725i			1.16143i	0.814109	+	0.580713i	$0.197226\pi$
$593$			688.725i			1.16143i	−0.814109	+	0.580713i	$0.802774\pi$
$594$	−27.2569	−	1314.07i	−0.0458871	−	2.21224i
$595$	540.886			0.909052
$596$			414.266i			0.695078i
$597$	2.88304	+	417.032i	0.00482922	+	0.698546i
$598$	−164.778			−0.275549
$599$			234.425i			0.391361i	0.980668	+	0.195680i	$0.0626915\pi$
$599$			234.425i			0.391361i	−0.980668	+	0.195680i	$0.937309\pi$
$600$	158.303	−	1.09439i	0.263838	−	0.00182398i
$601$	143.247			0.238348			0.119174	−	0.992873i	$-0.461975\pi$
$601$	143.247			0.238348			0.119174	+	0.992873i	$0.461975\pi$
$602$			80.4454i			0.133630i
$603$	−73.6611	+	1.01852i	−0.122158	+	0.00168909i
$604$	−2060.95			−3.41217
$605$			190.624i			0.315081i
$606$	10.2026	+	1475.81i	0.0168360	+	2.43533i
$607$	−874.705			−1.44103			−0.720515	−	0.693439i	$-0.756095\pi$
$607$	−874.705			−1.44103			−0.720515	+	0.693439i	$0.756095\pi$
$608$		−	2987.48i		−	4.91361i
$609$	−592.557	+	4.09649i	−0.973000	+	0.00672659i
$610$	446.180			0.731443
$611$			79.0390i			0.129360i
$612$	26.5968	+	1923.52i	0.0434588	+	3.14301i
$613$	681.518			1.11178			0.555888	−	0.831257i	$-0.312378\pi$
$613$	681.518			1.11178			0.555888	+	0.831257i	$0.312378\pi$
$614$		−	771.305i		−	1.25620i
$615$	−7.62106	−	1102.39i	−0.0123920	−	1.79250i
$616$	1860.33			3.02002
$617$		−	636.434i		−	1.03150i	−0.856740	−	0.515749i	$-0.827514\pi$
$617$		−	636.434i		−	1.03150i	0.856740	−	0.515749i	$-0.172486\pi$
$618$	−1454.30	+	10.0539i	−2.35324	+	0.0162685i
$619$	−234.549			−0.378915			−0.189458	−	0.981889i	$-0.560673\pi$
$619$	−234.549			−0.378915			−0.189458	+	0.981889i	$0.560673\pi$
$620$		−	1695.76i		−	2.73510i
$621$	709.245	−	14.7114i	1.14210	−	0.0236899i
$622$	−552.585			−0.888401
$623$		−	487.642i		−	0.782733i
$624$	−1.90958	−	276.220i	−0.00306023	−	0.442661i
$625$	−569.846			−0.911753
$626$		−	500.625i		−	0.799721i
$627$	−1006.52	+	6.95830i	−1.60529	+	0.0110978i
$628$	775.468			1.23482
$629$		−	237.717i		−	0.377929i
$630$	938.835	−	12.9814i	1.49021	−	0.0206054i
$631$	1158.73			1.83634			0.918169	−	0.396189i	$-0.129668\pi$
$631$	1158.73			1.83634			0.918169	+	0.396189i	$0.129668\pi$
$632$		−	679.718i		−	1.07550i
$633$	2.21605	+	320.551i	0.00350087	+	0.506400i
$634$	−1249.44			−1.97072
$635$		−	728.363i		−	1.14703i
$636$	862.902	−	5.96545i	1.35676	−	0.00937964i
$637$	−27.5066			−0.0431815
$638$			1695.49i			2.65751i
$639$	−8.25010	−	596.659i	−0.0129109	−	0.933739i
$640$	1662.24			2.59726
$641$		−	62.8230i		−	0.0980078i	−0.998799	−	0.0490039i	$-0.984395\pi$
$641$		−	62.8230i		−	0.0980078i	0.998799	−	0.0490039i	$-0.0156047\pi$
$642$	10.0441	+	1452.88i	0.0156451	+	2.26306i
$643$	760.991			1.18350			0.591751	−	0.806121i	$-0.298437\pi$
$643$	760.991			1.18350			0.591751	+	0.806121i	$0.298437\pi$
$644$			1600.10i			2.48462i
$645$	53.1129	−	0.367183i	0.0823457	−	0.000569276i
$646$	2021.93			3.12992
$647$			81.5812i			0.126091i	0.998011	+	0.0630457i	$0.0200814\pi$
$647$			81.5812i			0.126091i	−0.998011	+	0.0630457i	$0.979919\pi$
$648$	57.9383	+	2094.69i	0.0894110	+	3.23255i
$649$	−1396.27			−2.15142
$650$		−	12.7923i		−	0.0196805i
$651$	3.87607	+	560.673i	0.00595402	+	0.861248i
$652$	586.950			0.900230
$653$		−	1169.20i		−	1.79050i	−0.445559	−	0.895252i	$-0.646995\pi$
$653$		−	1169.20i		−	1.79050i	0.445559	−	0.895252i	$-0.353005\pi$
$654$	−1301.62	+	8.99843i	−1.99025	+	0.0137591i
$655$	895.027			1.36645
$656$			4322.50i			6.58918i
$657$	−660.067	+	9.12685i	−1.00467	+	0.0138917i
$658$	1053.41			1.60092
$659$			540.252i			0.819806i	0.912129	+	0.409903i	$0.134437\pi$
$659$			540.252i			0.819806i	−0.912129	+	0.409903i	$0.865563\pi$
$660$	−13.5316	−	1957.35i	−0.0205024	−	2.96568i
$661$	−654.868			−0.990724			−0.495362	−	0.868687i	$-0.664964\pi$
$661$	−654.868			−0.990724			−0.495362	+	0.868687i	$0.664964\pi$
$662$			1922.10i			2.90348i
$663$	97.5442	−	0.674347i	0.147126	−	0.00101712i
$664$	−515.792			−0.776796
$665$		−	719.036i		−	1.08126i
$666$	−5.70528	−	412.614i	−0.00856649	−	0.619541i
$667$	−915.113			−1.37198
$668$		−	629.910i		−	0.942979i
$669$	2.06285	+	298.391i	0.00308348	+	0.446025i
$670$	−150.576			−0.224740
$671$			307.547i			0.458342i
$672$	−1920.86	+	13.2794i	−2.85842	+	0.0197610i
$673$	−938.797			−1.39494			−0.697472	−	0.716612i	$-0.745692\pi$
$673$	−938.797			−1.39494			−0.697472	+	0.716612i	$0.745692\pi$
$674$		−	449.077i		−	0.666286i
$675$	1.14210	+	55.0614i	0.00169201	+	0.0815724i
$676$	1786.17			2.64227
$677$		−	403.553i		−	0.596091i	−0.954552	−	0.298045i	$-0.903665\pi$
$677$		−	403.553i		−	0.596091i	0.954552	−	0.298045i	$-0.0963347\pi$
$678$	6.21469	+	898.953i	0.00916620	+	1.32589i
$679$	−576.569			−0.849144
$680$			2467.38i			3.62850i
$681$	1183.84	−	8.18419i	1.73839	−	0.0120179i
$682$	1604.26			2.35229
$683$		−	461.008i		−	0.674976i	−0.941330	−	0.337488i	$-0.890423\pi$
$683$		−	461.008i		−	0.674976i	0.941330	−	0.337488i	$-0.109577\pi$
$684$	2557.06	−	35.3569i	3.73840	−	0.0516914i
$685$	76.9067			0.112272
$686$			1433.43i			2.08955i
$687$	2.62302	+	379.420i	0.00381808	+	0.552285i
$688$	−208.258			−0.302701
$689$		−	43.7568i		−	0.0635077i
$690$	1449.95	−	10.0239i	2.10138	−	0.0145274i
$691$	−471.114			−0.681786			−0.340893	−	0.940102i	$-0.610729\pi$
$691$	−471.114			−0.681786			−0.340893	+	0.940102i	$0.610729\pi$
$692$			625.055i			0.903258i
$693$	8.94796	+	647.129i	0.0129119	+	0.933808i
$694$	1559.56			2.24721
$695$		−	1169.42i		−	1.68262i
$696$	−18.6871	−	2703.09i	−0.0268493	−	3.88375i
$697$	−1526.44			−2.19002
$698$		−	870.529i		−	1.24718i
$699$	−435.956	+	3.01387i	−0.623685	+	0.00431169i
$700$	−124.222			−0.177459
$701$			943.997i			1.34664i	0.739350	+	0.673322i	$0.235133\pi$
$701$			943.997i			1.34664i	−0.739350	+	0.673322i	$0.764867\pi$
$702$	169.295	−	3.51158i	0.241161	−	0.00500225i
$703$	−316.014			−0.449521
$704$			2637.41i			3.74632i
$705$	−4.80815	−	695.499i	−0.00682008	−	0.986523i
$706$	883.485			1.25139
$707$		−	726.711i		−	1.02788i
$708$	3547.40	−	24.5241i	5.01046	−	0.0346385i
$709$	−1137.25			−1.60402			−0.802012	−	0.597308i	$-0.796237\pi$
$709$	−1137.25			−1.60402			−0.802012	+	0.597308i	$0.796237\pi$
$710$		−	1219.67i		−	1.71784i
$711$	236.444	−	3.26935i	0.332552	−	0.00459824i
$712$	2224.50			3.12429
$713$			865.872i			1.21441i
$714$	−8.98750	−	1300.04i	−0.0125875	−	1.82079i
$715$	−99.2548			−0.138818
$716$		−	1558.78i		−	2.17707i
$717$	311.290	−	2.15202i	0.434156	−	0.00300143i
$718$	903.382			1.25819
$719$			611.398i			0.850345i	0.905112	+	0.425172i	$0.139787\pi$
$719$			611.398i			0.850345i	−0.905112	+	0.425172i	$0.860213\pi$
$720$	33.6065	+	2430.47i	0.0466756	+	3.37565i
$721$	716.119			0.993231
$722$		−	1301.98i		−	1.80329i
$723$	−3.30567	−	478.165i	−0.00457216	−	0.661363i
$724$	−140.769			−0.194433
$725$		−	71.0436i		−	0.0979912i
$726$	458.172	−	3.16746i	0.631091	−	0.00436289i
$727$	−237.071			−0.326094			−0.163047	−	0.986618i	$-0.552132\pi$
$727$	−237.071			−0.326094			−0.163047	+	0.986618i	$0.552132\pi$
$728$			239.672i			0.329219i
$729$	−728.373	+	30.2294i	−0.999140	+	0.0414669i
$730$	−1349.29			−1.84834
$731$		−	73.5440i		−	0.100607i
$732$	−5.40176	−	781.364i	−0.00737946	−	1.06744i
$733$	−184.330			−0.251474			−0.125737	−	0.992064i	$-0.540129\pi$
$733$	−184.330			−0.251474			−0.125737	+	0.992064i	$0.540129\pi$
$734$			562.002i			0.765670i
$735$	242.042	−	1.67330i	0.329309	−	0.00227660i
$736$	−2966.47			−4.03052
$737$		−	103.790i		−	0.140828i
$738$	−2649.50	+	36.6351i	−3.59011	+	0.0496410i
$739$	−1160.98			−1.57101			−0.785506	−	0.618855i	$-0.787597\pi$
$739$	−1160.98			−1.57101			−0.785506	+	0.618855i	$0.787597\pi$
$740$		−	614.543i		−	0.830463i
$741$	−0.896456	−	129.672i	−0.00120979	−	0.174996i
$742$	−583.178			−0.785954
$743$		−	579.683i		−	0.780192i	−0.920774	−	0.390096i	$-0.872442\pi$
$743$		−	579.683i		−	0.780192i	0.920774	−	0.390096i	$-0.127558\pi$
$744$	−2557.64	+	17.6816i	−3.43769	+	0.0237656i
$745$	−184.850			−0.248120
$746$		−	1620.40i		−	2.17212i
$747$	−2.48089	−	179.422i	−0.00332114	−	0.240190i
$748$	−2710.28			−3.62337
$749$		−	715.422i		−	0.955169i
$750$	10.3160	+	1492.21i	0.0137547	+	1.98962i
$751$	1387.52			1.84757			0.923784	−	0.382914i	$-0.125079\pi$
$751$	1387.52			1.84757			0.923784	+	0.382914i	$0.125079\pi$
$752$			2727.08i			3.62643i
$753$	222.325	−	1.53699i	0.295252	−	0.00204115i
$754$	−218.435			−0.289701
$755$		−	919.617i		−	1.21804i
$756$	−34.0996	−	1643.96i	−0.0451053	−	2.17455i
$757$	−109.543			−0.144707			−0.0723536	−	0.997379i	$-0.523051\pi$
$757$	−109.543			−0.144707			−0.0723536	+	0.997379i	$0.523051\pi$
$758$			1185.45i			1.56392i
$759$	6.90937	+	999.439i	0.00910325	+	1.31678i
$760$	3280.05			4.31586
$761$			1294.31i			1.70080i	0.526137	+	0.850400i	$0.323640\pi$
$761$			1294.31i			1.70080i	−0.526137	+	0.850400i	$0.676360\pi$
$762$	−1750.65	+	12.1027i	−2.29744	+	0.0158828i
$763$	640.938			0.840023
$764$		−	3157.40i		−	4.13273i
$765$	−858.293	+	11.8678i	−1.12195	+	0.0155134i
$766$	−861.629			−1.12484
$767$		−	179.885i		−	0.234530i
$768$	−10.3655	−	1499.36i	−0.0134967	−	1.95229i
$769$	341.724			0.444375			0.222188	−	0.975004i	$-0.428680\pi$
$769$	341.724			0.444375			0.222188	+	0.975004i	$0.428680\pi$
$770$			1322.84i			1.71797i
$771$	76.6848	−	0.530141i	0.0994615	−	0.000687602i
$772$	−1017.15			−1.31755
$773$			804.738i			1.04106i	0.853844	+	0.520529i	$0.174265\pi$
$773$			804.738i			1.04106i	−0.853844	+	0.520529i	$0.825735\pi$
$774$	−1.76508	−	127.653i	−0.00228046	−	0.164926i
$775$	−67.2209			−0.0867366
$776$		−	2630.15i		−	3.38937i
$777$	1.40468	+	203.187i	0.00180783	+	0.261502i
$778$	1835.16			2.35881
$779$			2029.20i			2.60488i
$780$	252.170	−	1.74331i	0.323294	−	0.00223501i
$781$	840.706			1.07645
$782$		−	2007.71i		−	2.56741i
$783$	940.197	−	19.5019i	1.20076	−	0.0249067i
$784$	−949.059			−1.21053
$785$			346.022i			0.440792i
$786$	−14.8720	−	2151.23i	−0.0189211	−	2.73694i
$787$	349.911			0.444613			0.222307	−	0.974977i	$-0.428641\pi$
$787$	349.911			0.444613			0.222307	+	0.974977i	$0.428641\pi$
$788$			1119.53i			1.42072i
$789$	−1276.00	+	8.82131i	−1.61724	+	0.0111804i
$790$	483.331			0.611812
$791$		−	442.658i		−	0.559618i
$792$	−2952.03	+	40.8182i	−3.72731	+	0.0515381i
$793$	−39.6221			−0.0499648
$794$		−	2447.50i		−	3.08249i
$795$	2.66184	+	385.035i	0.00334823	+	0.484321i
$796$	1492.82			1.87540
$797$		−	480.973i		−	0.603480i	−0.953390	−	0.301740i	$-0.902433\pi$
$797$		−	480.973i		−	0.603480i	0.953390	−	0.301740i	$-0.0975674\pi$
$798$	−1728.23	+	11.9477i	−2.16570	+	0.0149720i
$799$	−963.038			−1.20530
$800$		−	230.298i		−	0.287872i
$801$	10.6995	+	773.805i	0.0133577	+	0.966048i
$802$	−1417.30			−1.76721
$803$		−	930.050i		−	1.15822i
$804$	1.82297	+	263.692i	0.00226738	+	0.327976i
$805$	−713.979			−0.886931
$806$			206.681i			0.256428i
$807$	804.555	−	5.56209i	0.996971	−	0.00689231i
$808$	3315.06			4.10280
$809$			784.529i			0.969751i	0.874583	+	0.484876i	$0.161135\pi$
$809$			784.529i			0.969751i	−0.874583	+	0.484876i	$0.838865\pi$
$810$	−1489.48	+	41.1985i	−1.83887	+	0.0508624i
$811$	−307.334			−0.378957			−0.189479	−	0.981885i	$-0.560680\pi$
$811$	−307.334			−0.378957			−0.189479	+	0.981885i	$0.560680\pi$
$812$			2121.14i			2.61224i
$813$	−6.23380	−	901.718i	−0.00766765	−	1.10912i
$814$	581.383			0.714229
$815$			261.903i			0.321353i
$816$	3365.56	−	23.2670i	4.12447	−	0.0285134i
$817$	−97.7671			−0.119666
$818$		−	362.296i		−	0.442904i
$819$	−83.3713	+	1.15279i	−0.101796	+	0.00140755i
$820$	−3946.14			−4.81236
$821$			43.9955i			0.0535877i	0.999641	+	0.0267938i	$0.00852976\pi$
$821$			43.9955i			0.0535877i	−0.999641	+	0.0267938i	$0.991470\pi$
$822$	−1.27790	−	184.848i	−0.00155462	−	0.224876i
$823$	848.133			1.03054			0.515269	−	0.857028i	$-0.327692\pi$
$823$	848.133			1.03054			0.515269	+	0.857028i	$0.327692\pi$
$824$			3266.75i			3.96450i
$825$	−77.5902	+	0.536400i	−0.0940487	+	0.000650182i
$826$	−2397.45			−2.90249
$827$			858.514i			1.03811i	0.854742	+	0.519053i	$0.173715\pi$
$827$			858.514i			1.03811i	−0.854742	+	0.519053i	$0.826285\pi$
$828$	−35.1083	−	2539.08i	−0.0424013	−	3.06652i
$829$	1346.76			1.62455			0.812277	−	0.583272i	$-0.198228\pi$
$829$	1346.76			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$830$		−	366.767i		−	0.441889i
$831$	3.93183	+	568.739i	0.00473145	+	0.684403i
$832$	−339.784			−0.408394
$833$		−	335.150i		−	0.402340i
$834$	−2810.75	+	19.4314i	−3.37020	+	0.0232990i
$835$	281.072			0.336613
$836$			3602.96i			4.30976i
$837$	−18.4526	−	889.606i	−0.0220461	−	1.06285i
$838$	2272.46			2.71176
$839$		−	484.627i		−	0.577625i	−0.957386	−	0.288812i	$-0.906740\pi$
$839$		−	484.627i		−	0.577625i	0.957386	−	0.288812i	$-0.0932604\pi$
$840$	−14.5799	−	2108.97i	−0.0173570	−	2.51068i
$841$	−372.101			−0.442450
$842$			1878.05i			2.23046i
$843$	−318.747	+	2.20358i	−0.378111	+	0.00261397i
$844$	1147.45			1.35954
$845$			797.008i			0.943204i
$846$	−1671.58	+	23.1132i	−1.97586	+	0.0273205i
$847$	−225.611			−0.266365
$848$		−	1509.74i		−	1.78035i
$849$	−3.46367	−	501.019i	−0.00407970	−	0.590128i
$850$	155.866			0.183372
$851$			313.791i			0.368732i
$852$	−2135.92	+	14.7662i	−2.50695	+	0.0173312i
$853$	−968.358			−1.13524			−0.567619	−	0.823291i	$-0.692135\pi$
$853$	−968.358			−1.13524			−0.567619	+	0.823291i	$0.692135\pi$
$854$			528.072i			0.618351i
$855$	15.7766	+	1140.99i	0.0184522	+	1.33449i
$856$	3263.56			3.81257
$857$			123.391i			0.143980i	0.997405	+	0.0719900i	$0.0229350\pi$
$857$			123.391i			0.143980i	−0.997405	+	0.0719900i	$0.977065\pi$
$858$	1.64924	+	238.563i	0.00192220	+	0.278045i
$859$	−612.298			−0.712804			−0.356402	−	0.934333i	$-0.615997\pi$
$859$	−612.298			−0.712804			−0.356402	+	0.934333i	$0.615997\pi$
$860$		−	190.125i		−	0.221075i
$861$	1304.72	−	9.01983i	1.51535	−	0.0104760i
$862$	3026.65			3.51119
$863$		−	1471.83i		−	1.70548i	−0.522338	−	0.852739i	$-0.674940\pi$
$863$		−	1471.83i		−	1.70548i	0.522338	−	0.852739i	$-0.325060\pi$
$864$	3047.78	−	63.2182i	3.52752	−	0.0731692i
$865$	−278.905			−0.322434
$866$			248.694i			0.287175i
$867$	2.22283	+	321.532i	0.00256382	+	0.370856i
$868$	2007.00			2.31221
$869$			333.155i			0.383378i
$870$	1922.10	−	13.2880i	2.20931	−	0.0152735i
$871$	13.3716			0.0153520
$872$			2923.79i			3.35297i
$873$	914.916	−	12.6507i	1.04801	−	0.0144910i
$874$	−2668.99			−3.05376
$875$		−	734.788i		−	0.839758i
$876$	16.3354	+	2362.91i	0.0186477	+	2.69739i
$877$	56.4906			0.0644135			0.0322067	−	0.999481i	$-0.489747\pi$
$877$	56.4906			0.0644135			0.0322067	+	0.999481i	$0.489747\pi$
$878$		−	2133.72i		−	2.43021i
$879$	801.701	−	5.54236i	0.912061	−	0.00630530i
$880$	−3424.59			−3.89157
$881$			545.209i			0.618853i	0.950923	+	0.309426i	$0.100137\pi$
$881$			545.209i			0.618853i	−0.950923	+	0.309426i	$0.899863\pi$
$882$	−8.04368	−	581.731i	−0.00911982	−	0.659559i
$883$	−1134.29			−1.28459			−0.642294	−	0.766458i	$-0.722017\pi$
$883$	−1134.29			−1.28459			−0.642294	+	0.766458i	$0.722017\pi$
$884$		−	349.172i		−	0.394991i
$885$	10.9429	+	1582.89i	0.0123648	+	1.78857i
$886$	−155.193			−0.175162
$887$		−	718.778i		−	0.810348i	−0.914240	−	0.405174i	$-0.867211\pi$
$887$		−	718.778i		−	0.810348i	0.914240	−	0.405174i	$-0.132789\pi$
$888$	−926.886	+	6.40779i	−1.04379	+	0.00721598i
$889$	862.047			0.969681
$890$			1581.78i			1.77729i
$891$	−28.3977	−	1026.69i	−0.0318718	−	1.15229i
$892$	1068.13			1.19746
$893$			1280.23i			1.43363i
$894$	3.07151	+	444.293i	0.00343569	+	0.496973i
$895$	695.544			0.777145
$896$			1967.33i			2.19568i
$897$	−128.760	+	0.890151i	−0.143545	+	0.000992364i
$898$	1315.79			1.46524
$899$			1147.83i			1.27678i
$900$	197.118	−	2.72559i	0.219020	−	0.00302843i
$901$	533.147			0.591729
$902$		−	3733.21i		−	4.13881i
$903$	0.434575	+	62.8613i	0.000481257	+	0.0696138i
$904$	2019.29			2.23373
$905$		−	62.8127i		−	0.0694063i
$906$	−2210.34	+	15.2806i	−2.43966	+	0.0168660i
$907$	130.501			0.143881			0.0719407	−	0.997409i	$-0.477081\pi$
$907$	130.501			0.143881			0.0719407	+	0.997409i	$0.477081\pi$
$908$		−	4237.72i		−	4.66709i
$909$	15.9450	+	1153.17i	0.0175412	+	1.26861i
$910$	−170.425			−0.187280
$911$		−	64.9871i		−	0.0713360i	−0.999364	−	0.0356680i	$-0.988644\pi$
$911$		−	64.9871i		−	0.0713360i	0.999364	−	0.0356680i	$-0.0113559\pi$
$912$	−30.9304	−	4474.07i	−0.0339149	−	4.90578i
$913$	252.809			0.276899
$914$		−	2128.63i		−	2.32892i
$915$	348.652	−	2.41032i	0.381041	−	0.00263423i
$916$	1358.18			1.48273
$917$			1059.30i			1.15518i
$918$	42.7862	+	2062.74i	0.0466081	+	2.24700i
$919$	431.293			0.469307			0.234654	−	0.972079i	$-0.424604\pi$
$919$	431.293			0.469307			0.234654	+	0.972079i	$0.424604\pi$
$920$		−	3256.98i		−	3.54020i
$921$	−4.16668	−	602.710i	−0.00452409	−	0.654408i
$922$	−983.153			−1.06633
$923$			108.310i			0.117346i
$924$	2316.60	−	16.0152i	2.50714	−	0.0173325i
$925$	−24.3608			−0.0263360
$926$			1563.46i			1.68840i
$927$	−1136.36	+	15.7126i	−1.22585	+	0.0169500i
$928$	−3932.44			−4.23754
$929$		−	1569.05i		−	1.68897i	−0.535579	−	0.844485i	$-0.679907\pi$
$929$		−	1569.05i		−	1.68897i	0.535579	−	0.844485i	$-0.320093\pi$
$930$	−12.5730	−	1818.68i	−0.0135193	−	1.95557i
$931$	−445.537			−0.478557
$932$			1560.56i			1.67442i
$933$	−431.799	+	2.98513i	−0.462807	+	0.00319950i
$934$	−13.8993			−0.0148814
$935$		−	1209.35i		−	1.29343i
$936$	−5.25871	−	380.318i	−0.00561828	−	0.406322i
$937$	58.2293			0.0621444			0.0310722	−	0.999517i	$-0.490108\pi$
$937$	58.2293			0.0621444			0.0310722	+	0.999517i	$0.490108\pi$
$938$		−	178.212i		−	0.189992i
$939$	−2.70444	−	391.196i	−0.00288012	−	0.416610i
$940$	−2489.63			−2.64854
$941$			14.5572i			0.0154699i	0.999970	+	0.00773496i	$0.00246214\pi$
$941$			14.5572i			0.0154699i	−0.999970	+	0.00773496i	$0.997538\pi$
$942$	831.676	−	5.74959i	0.882884	−	0.00610359i
$943$	2014.93			2.13673
$944$		−	6206.56i		−	6.57475i
$945$	733.550	−	15.2156i	0.776243	−	0.0161011i
$946$	179.866			0.190133
$947$		−	558.732i		−	0.590002i	−0.955497	−	0.295001i	$-0.904680\pi$
$947$		−	558.732i		−	0.590002i	0.955497	−	0.295001i	$-0.0953200\pi$
$948$	−5.85154	−	846.424i	−0.00617251	−	0.892852i
$949$	119.821			0.126260
$950$		−	207.203i		−	0.218109i
$951$	−976.330	+	6.74961i	−1.02664	+	0.00709738i
$952$	−2920.24			−3.06748
$953$			335.155i			0.351685i	0.984418	+	0.175842i	$0.0562649\pi$
$953$			335.155i			0.351685i	−0.984418	+	0.175842i	$0.943735\pi$
$954$	925.403	−	12.7957i	0.970024	−	0.0134127i
$955$	1408.86			1.47525
$956$		−	1114.30i		−	1.16559i
$957$	9.15926	+	1324.89i	0.00957080	+	1.38442i
$958$	−2641.05			−2.75684
$959$			91.0221i			0.0949135i
$960$	2989.90	−	20.6699i	3.11448	−	0.0215312i
$961$	125.063			0.130138
$962$			74.9010i			0.0778596i
$963$	15.6973	+	1135.25i	0.0163004	+	1.17887i
$964$	−1711.66			−1.77558
$965$		−	453.861i		−	0.470322i
$966$	11.8637	+	1716.08i	0.0122812	+	1.77648i
$967$	533.263			0.551461			0.275730	−	0.961235i	$-0.411080\pi$
$967$	533.263			0.551461			0.275730	+	0.961235i	$0.411080\pi$
$968$		−	1029.18i		−	1.06320i
$969$	1579.97	−	10.9227i	1.63051	−	0.0112722i
$970$	1870.24			1.92808
$971$			621.012i			0.639559i	0.947492	+	0.319779i	$0.103609\pi$
$971$			621.012i			0.639559i	−0.947492	+	0.319779i	$0.896391\pi$
$972$	90.1808	+	2607.93i	0.0927786	+	2.68306i
$973$	1384.06			1.42246
$974$		−	604.282i		−	0.620413i
$975$	−0.0691057	−	9.99613i	−7.08777e−5	−	0.0102524i
$976$	−1367.08			−1.40070
$977$			569.664i			0.583075i	0.956559	+	0.291537i	$0.0941668\pi$
$977$			569.664i			0.583075i	−0.956559	+	0.291537i	$0.905833\pi$
$978$	629.494	−	4.35185i	0.643654	−	0.00444974i
$979$	−1090.31			−1.11370
$980$		−	866.423i		−	0.884105i
$981$	−1017.06	+	14.0630i	−1.03676	+	0.0143354i
$982$	−2526.52			−2.57283
$983$		−	1551.10i		−	1.57793i	−0.614439	−	0.788964i	$-0.710618\pi$
$983$		−	1551.10i		−	1.57793i	0.614439	−	0.788964i	$-0.289382\pi$
$984$	41.1461	+	5951.77i	0.0418151	+	6.04855i
$985$	−499.544			−0.507151
$986$		−	2661.48i		−	2.69927i
$987$	823.150	−	5.69064i	0.833992	−	0.00576559i
$988$	−464.179			−0.469816
$989$			97.0795i			0.0981592i
$990$	−29.0248	−	2099.12i	−0.0293180	−	2.12032i
$991$	−860.116			−0.867927			−0.433963	−	0.900930i	$-0.642885\pi$
$991$	−860.116			−0.867927			−0.433963	+	0.900930i	$0.642885\pi$
$992$			3720.84i			3.75084i
$993$	10.3834	+	1501.96i	0.0104566	+	1.51255i
$994$	1443.53			1.45224
$995$			666.111i			0.669458i
$996$	−642.294	+	4.44034i	−0.644874	+	0.00445817i
$997$	−18.1182			−0.0181727			−0.00908635	−	0.999959i	$-0.502892\pi$
$997$	−18.1182			−0.0181727			−0.00908635	+	0.999959i	$0.502892\pi$
$998$		−	1421.56i		−	1.42441i
$999$	−6.68719	−	322.392i	−0.00669388	−	0.322715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.2	✓	44
3.2	odd	2	inner	201.3.c.a.68.43	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.2	✓	44	1.1	even	1	trivial
201.3.c.a.68.43	yes	44	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.83909i q^{2} +(-0.0207392 - 2.99993i) q^{3} -10.7386 q^{4} -4.79169i q^{5} +(-11.5170 + 0.0796199i) q^{6} +5.67115 q^{7} +25.8703i q^{8} +(-8.99914 + 0.124433i) q^{9} +O(q^{10})\)	\(q-3.83909i q^{2} +(-0.0207392 - 2.99993i) q^{3} -10.7386 q^{4} -4.79169i q^{5} +(-11.5170 + 0.0796199i) q^{6} +5.67115 q^{7} +25.8703i q^{8} +(-8.99914 + 0.124433i) q^{9} -18.3957 q^{10} -12.6800i q^{11} +(0.222711 + 32.2152i) q^{12} +1.63359 q^{13} -21.7721i q^{14} +(-14.3747 + 0.0993759i) q^{15} +56.3638 q^{16} +19.9043i q^{17} +(0.477708 + 34.5485i) q^{18} +26.4601 q^{19} +51.4562i q^{20} +(-0.117615 - 17.0130i) q^{21} -48.6797 q^{22} -26.2740i q^{23} +(77.6090 - 0.536530i) q^{24} +2.03975 q^{25} -6.27152i q^{26} +(0.559924 + 26.9942i) q^{27} -60.9004 q^{28} -34.8296i q^{29} +(0.381514 + 55.1859i) q^{30} -32.9555 q^{31} -112.905i q^{32} +(-38.0391 + 0.262974i) q^{33} +76.4144 q^{34} -27.1744i q^{35} +(96.6385 - 1.33624i) q^{36} -11.9430 q^{37} -101.583i q^{38} +(-0.0338795 - 4.90067i) q^{39} +123.962 q^{40} +76.6892i q^{41} +(-65.3147 + 0.451536i) q^{42} -3.69489 q^{43} +136.166i q^{44} +(0.596241 + 43.1210i) q^{45} -100.868 q^{46} +48.3835i q^{47} +(-1.16894 - 169.088i) q^{48} -16.8381 q^{49} -7.83079i q^{50} +(59.7114 - 0.412800i) q^{51} -17.5426 q^{52} -26.7856i q^{53} +(103.633 - 2.14960i) q^{54} -60.7585 q^{55} +146.714i q^{56} +(-0.548762 - 79.3784i) q^{57} -133.714 q^{58} -110.116i q^{59} +(154.365 - 1.06716i) q^{60} -24.2545 q^{61} +126.519i q^{62} +(-51.0355 + 0.705675i) q^{63} -207.997 q^{64} -7.82767i q^{65} +(1.00958 + 146.036i) q^{66} +8.18535 q^{67} -213.745i q^{68} +(-78.8201 + 0.544903i) q^{69} -104.325 q^{70} +66.3018i q^{71} +(-3.21910 - 232.810i) q^{72} +73.3478 q^{73} +45.8504i q^{74} +(-0.0423029 - 6.11910i) q^{75} -284.145 q^{76} -71.9101i q^{77} +(-18.8141 + 0.130067i) q^{78} -26.2741 q^{79} -270.078i q^{80} +(80.9690 - 2.23957i) q^{81} +294.417 q^{82} +19.9376i q^{83} +(1.26303 + 182.697i) q^{84} +95.3750 q^{85} +14.1850i q^{86} +(-104.486 + 0.722340i) q^{87} +328.035 q^{88} -85.9865i q^{89} +(165.546 - 2.28903i) q^{90} +9.26436 q^{91} +282.147i q^{92} +(0.683472 + 98.8640i) q^{93} +185.749 q^{94} -126.788i q^{95} +(-338.707 + 2.34156i) q^{96} -101.667 q^{97} +64.6429i q^{98} +(1.57780 + 114.109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more