LMFDB - Embedded newform 201.3.c.a.68.5

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			68.5
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.36787i q^{2} +(-2.80521 - 1.06340i) q^{3} -7.34253 q^{4} +7.21139i q^{5} +(-3.58138 + 9.44756i) q^{6} -0.105037 q^{7} +11.2572i q^{8} +(6.73838 + 5.96610i) q^{9} +O(q^{10})$	\(q-3.36787i q^{2} +(-2.80521 - 1.06340i) q^{3} -7.34253 q^{4} +7.21139i q^{5} +(-3.58138 + 9.44756i) q^{6} -0.105037 q^{7} +11.2572i q^{8} +(6.73838 + 5.96610i) q^{9} +24.2870 q^{10} -4.33578i q^{11} +(20.5973 + 7.80802i) q^{12} +6.10862 q^{13} +0.353752i q^{14} +(7.66856 - 20.2294i) q^{15} +8.54259 q^{16} +25.4084i q^{17} +(20.0930 - 22.6940i) q^{18} -1.67338 q^{19} -52.9498i q^{20} +(0.294651 + 0.111696i) q^{21} -14.6023 q^{22} +29.4161i q^{23} +(11.9709 - 31.5787i) q^{24} -27.0041 q^{25} -20.5730i q^{26} +(-12.5582 - 23.9017i) q^{27} +0.771239 q^{28} +8.15188i q^{29} +(-68.1300 - 25.8267i) q^{30} +45.3772 q^{31} +16.2584i q^{32} +(-4.61066 + 12.1628i) q^{33} +85.5720 q^{34} -0.757464i q^{35} +(-49.4767 - 43.8062i) q^{36} +19.4902 q^{37} +5.63573i q^{38} +(-17.1360 - 6.49589i) q^{39} -81.1799 q^{40} +52.9294i q^{41} +(0.376178 - 0.992346i) q^{42} -21.1076 q^{43} +31.8356i q^{44} +(-43.0238 + 48.5930i) q^{45} +99.0696 q^{46} -67.4214i q^{47} +(-23.9637 - 9.08416i) q^{48} -48.9890 q^{49} +90.9461i q^{50} +(27.0192 - 71.2757i) q^{51} -44.8527 q^{52} +38.7119i q^{53} +(-80.4977 + 42.2944i) q^{54} +31.2670 q^{55} -1.18242i q^{56} +(4.69419 + 1.77947i) q^{57} +27.4545 q^{58} +58.1832i q^{59} +(-56.3066 + 148.535i) q^{60} +88.8138 q^{61} -152.824i q^{62} +(-0.707781 - 0.626662i) q^{63} +88.9266 q^{64} +44.0516i q^{65} +(40.9626 + 15.5281i) q^{66} -8.18535 q^{67} -186.562i q^{68} +(31.2810 - 82.5184i) q^{69} -2.55104 q^{70} +123.773i q^{71} +(-67.1614 + 75.8551i) q^{72} -114.997 q^{73} -65.6402i q^{74} +(75.7520 + 28.7160i) q^{75} +12.2869 q^{76} +0.455419i q^{77} +(-21.8773 + 57.7116i) q^{78} -137.331 q^{79} +61.6039i q^{80} +(9.81140 + 80.4036i) q^{81} +178.259 q^{82} -1.25951i q^{83} +(-2.16348 - 0.820133i) q^{84} -183.230 q^{85} +71.0876i q^{86} +(8.66869 - 22.8677i) q^{87} +48.8087 q^{88} -64.0739i q^{89} +(163.655 + 144.898i) q^{90} -0.641633 q^{91} -215.989i q^{92} +(-127.292 - 48.2539i) q^{93} -227.066 q^{94} -12.0674i q^{95} +(17.2892 - 45.6083i) q^{96} -104.454 q^{97} +164.988i q^{98} +(25.8677 - 29.2161i) 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 $

$2$		−	3.36787i		−	1.68393i	−0.539530	−	0.841967i	$-0.681398\pi$
$2$		−	3.36787i		−	1.68393i	0.539530	−	0.841967i	$-0.318602\pi$
$3$	−2.80521	−	1.06340i	−0.935069	−	0.354466i
$3$	−2.80521	−	1.06340i	−0.935069	−	0.354466i
$4$	−7.34253			−1.83563
$5$			7.21139i			1.44228i	0.692791	+	0.721139i	$0.256381\pi$
$5$			7.21139i			1.44228i	−0.692791	+	0.721139i	$0.743619\pi$
$6$	−3.58138	+	9.44756i	−0.596896	+	1.57459i
$7$	−0.105037			−0.0150053			−0.00750266	−	0.999972i	$-0.502388\pi$
$7$	−0.105037			−0.0150053			−0.00750266	+	0.999972i	$0.502388\pi$
$8$			11.2572i			1.40715i
$9$	6.73838	+	5.96610i	0.748708	+	0.662900i
$10$	24.2870			2.42870
$11$		−	4.33578i		−	0.394162i	−0.980387	−	0.197081i	$-0.936854\pi$
$11$		−	4.33578i		−	0.394162i	0.980387	−	0.197081i	$-0.0631462\pi$
$12$	20.5973	+	7.80802i	1.71644	+	0.650668i
$13$	6.10862			0.469894			0.234947	−	0.972008i	$-0.424508\pi$
$13$	6.10862			0.469894			0.234947	+	0.972008i	$0.424508\pi$
$14$			0.353752i			0.0252680i
$15$	7.66856	−	20.2294i	0.511238	−	1.34863i
$16$	8.54259			0.533912
$17$			25.4084i			1.49461i	0.664481	+	0.747305i	$0.268653\pi$
$17$			25.4084i			1.49461i	−0.664481	+	0.747305i	$0.731347\pi$
$18$	20.0930	−	22.6940i	1.11628	−	1.26078i
$19$	−1.67338			−0.0880729			−0.0440364	−	0.999030i	$-0.514022\pi$
$19$	−1.67338			−0.0880729			−0.0440364	+	0.999030i	$0.514022\pi$
$20$		−	52.9498i		−	2.64749i
$21$	0.294651	+	0.111696i	0.0140310	+	0.00531887i
$22$	−14.6023			−0.663743
$23$			29.4161i			1.27896i	0.768807	+	0.639481i	$0.220851\pi$
$23$			29.4161i			1.27896i	−0.768807	+	0.639481i	$0.779149\pi$
$24$	11.9709	−	31.5787i	0.498785	−	1.31578i
$25$	−27.0041			−1.08016
$26$		−	20.5730i		−	0.791270i
$27$	−12.5582	−	23.9017i	−0.465119	−	0.885248i
$28$	0.771239			0.0275442
$29$			8.15188i			0.281099i	0.990074	+	0.140550i	$0.0448870\pi$
$29$			8.15188i			0.281099i	−0.990074	+	0.140550i	$0.955113\pi$
$30$	−68.1300	−	25.8267i	−2.27100	−	0.860890i
$31$	45.3772			1.46378			0.731890	−	0.681423i	$-0.238639\pi$
$31$	45.3772			1.46378			0.731890	+	0.681423i	$0.238639\pi$
$32$			16.2584i			0.508076i
$33$	−4.61066	+	12.1628i	−0.139717	+	0.368569i
$34$	85.5720			2.51682
$35$		−	0.757464i		−	0.0216418i
$36$	−49.4767	−	43.8062i	−1.37435	−	1.21684i
$37$	19.4902			0.526761			0.263380	−	0.964692i	$-0.415163\pi$
$37$	19.4902			0.526761			0.263380	+	0.964692i	$0.415163\pi$
$38$			5.63573i			0.148309i
$39$	−17.1360	−	6.49589i	−0.439384	−	0.166561i
$40$	−81.1799			−2.02950
$41$			52.9294i			1.29096i	0.763777	+	0.645481i	$0.223343\pi$
$41$			52.9294i			1.29096i	−0.763777	+	0.645481i	$0.776657\pi$
$42$	0.376178	−	0.992346i	0.00895662	−	0.0236273i
$43$	−21.1076			−0.490874			−0.245437	−	0.969412i	$-0.578932\pi$
$43$	−21.1076			−0.490874			−0.245437	+	0.969412i	$0.578932\pi$
$44$			31.8356i			0.723537i
$45$	−43.0238	+	48.5930i	−0.956085	+	1.07984i
$46$	99.0696			2.15369
$47$		−	67.4214i		−	1.43450i	−0.696817	−	0.717249i	$-0.745401\pi$
$47$		−	67.4214i		−	1.43450i	0.696817	−	0.717249i	$-0.254599\pi$
$48$	−23.9637	−	9.08416i	−0.499244	−	0.189253i
$49$	−48.9890			−0.999775
$50$			90.9461i			1.81892i
$51$	27.0192	−	71.2757i	0.529788	−	1.39756i
$52$	−44.8527			−0.862553
$53$			38.7119i			0.730413i	0.930927	+	0.365207i	$0.119002\pi$
$53$			38.7119i			0.730413i	−0.930927	+	0.365207i	$0.880998\pi$
$54$	−80.4977	+	42.2944i	−1.49070	+	0.783229i
$55$	31.2670			0.568491
$56$		−	1.18242i		−	0.0211147i
$57$	4.69419	+	1.77947i	0.0823542	+	0.0312188i
$58$	27.4545			0.473353
$59$			58.1832i			0.986156i	0.869985	+	0.493078i	$0.164128\pi$
$59$			58.1832i			0.986156i	−0.869985	+	0.493078i	$0.835872\pi$
$60$	−56.3066	+	148.535i	−0.938444	+	2.47559i
$61$	88.8138			1.45596			0.727982	−	0.685596i	$-0.240458\pi$
$61$	88.8138			1.45596			0.727982	+	0.685596i	$0.240458\pi$
$62$		−	152.824i		−	2.46491i
$63$	−0.707781	−	0.626662i	−0.0112346	−	0.00994702i
$64$	88.9266			1.38948
$65$			44.0516i			0.677718i
$66$	40.9626	+	15.5281i	0.620645	+	0.235274i
$67$	−8.18535			−0.122169
$67$	−8.18535			−0.122169
$68$		−	186.562i		−	2.74355i
$69$	31.2810	−	82.5184i	0.453348	−	1.19592i
$70$	−2.55104			−0.0364434
$71$			123.773i			1.74328i	0.490150	+	0.871638i	$0.336942\pi$
$71$			123.773i			1.74328i	−0.490150	+	0.871638i	$0.663058\pi$
$72$	−67.1614	+	75.8551i	−0.932798	+	1.05354i
$73$	−114.997			−1.57530			−0.787650	−	0.616123i	$-0.788702\pi$
$73$	−114.997			−1.57530			−0.787650	+	0.616123i	$0.788702\pi$
$74$		−	65.6402i		−	0.887030i
$75$	75.7520	+	28.7160i	1.01003	+	0.382881i
$76$	12.2869			0.161669
$77$			0.455419i			0.00591453i
$78$	−21.8773	+	57.7116i	−0.280478	+	0.739893i
$79$	−137.331			−1.73837			−0.869185	−	0.494487i	$-0.835356\pi$
$79$	−137.331			−1.73837			−0.869185	+	0.494487i	$0.835356\pi$
$80$			61.6039i			0.770049i
$81$	9.81140	+	80.4036i	0.121128	+	0.992637i
$82$	178.259			2.17389
$83$		−	1.25951i		−	0.0151748i	−0.999971	−	0.00758739i	$-0.997585\pi$
$83$		−	1.25951i		−	0.0151748i	0.999971	−	0.00758739i	$-0.00241517\pi$
$84$	−2.16348	−	0.820133i	−0.0257558	−	0.00976349i
$85$	−183.230			−2.15564
$86$			71.0876i			0.826600i
$87$	8.66869	−	22.8677i	0.0996401	−	0.262847i
$88$	48.8087			0.554645
$89$		−	64.0739i		−	0.719931i	−0.932966	−	0.359966i	$-0.882788\pi$
$89$		−	64.0739i		−	0.719931i	0.932966	−	0.359966i	$-0.117212\pi$
$90$	163.655	+	144.898i	1.81839	+	1.60998i
$91$	−0.641633			−0.00705091
$92$		−	215.989i		−	2.34770i
$93$	−127.292	−	48.2539i	−1.36873	−	0.518859i
$94$	−227.066			−2.41560
$95$		−	12.0674i		−	0.127025i
$96$	17.2892	−	45.6083i	0.180095	−	0.475086i
$97$	−104.454			−1.07684			−0.538422	−	0.842675i	$-0.680979\pi$
$97$	−104.454			−1.07684			−0.538422	+	0.842675i	$0.680979\pi$
$98$			164.988i			1.68355i
$99$	25.8677	−	29.2161i	0.261290	−	0.295113i
$100$	198.278			1.98278
$101$			40.1956i			0.397976i	0.980002	+	0.198988i	$0.0637655\pi$
$101$			40.1956i			0.397976i	−0.980002	+	0.198988i	$0.936235\pi$
$102$	−240.047	−	90.9970i	−2.35340	−	0.892127i
$103$	63.4888			0.616396			0.308198	−	0.951322i	$-0.400274\pi$
$103$	63.4888			0.616396			0.308198	+	0.951322i	$0.400274\pi$
$104$			68.7659i			0.661211i
$105$	−0.805485	+	2.12484i	−0.00767128	+	0.0202366i
$106$	130.376			1.22997
$107$		−	21.8947i		−	0.204623i	−0.994752	−	0.102312i	$-0.967376\pi$
$107$		−	21.8947i		−	0.204623i	0.994752	−	0.102312i	$-0.0326239\pi$
$108$	92.2090	+	175.499i	0.853787	+	1.62499i
$109$	52.9342			0.485635			0.242817	−	0.970072i	$-0.421928\pi$
$109$	52.9342			0.485635			0.242817	+	0.970072i	$0.421928\pi$
$110$		−	105.303i		−	0.957301i
$111$	−54.6739	−	20.7258i	−0.492558	−	0.186719i
$112$	−0.897290			−0.00801152
$113$		−	35.3840i		−	0.313133i	−0.987667	−	0.156566i	$-0.949958\pi$
$113$		−	35.3840i		−	0.313133i	0.987667	−	0.156566i	$-0.0500425\pi$
$114$	5.99302	−	15.8094i	0.0525704	−	0.138679i
$115$	−212.131			−1.84462
$116$		−	59.8554i		−	0.515995i
$117$	41.1622	+	36.4446i	0.351814	+	0.311493i
$118$	195.953			1.66062
$119$		−	2.66883i		−	0.0224271i
$120$	227.726	+	86.3264i	1.89772	+	0.719387i
$121$	102.201			0.844636
$122$		−	299.113i		−	2.45175i
$123$	56.2850	−	148.478i	0.457601	−	1.20714i
$124$	−333.183			−2.68696
$125$		−	14.4522i		−	0.115618i
$126$	−2.11052	+	2.38371i	−0.0167501	+	0.0189183i
$127$	−157.112			−1.23710			−0.618550	−	0.785745i	$-0.712280\pi$
$127$	−157.112			−1.23710			−0.618550	+	0.785745i	$0.712280\pi$
$128$		−	234.459i		−	1.83171i
$129$	59.2112	+	22.4458i	0.459002	+	0.173998i
$130$	148.360			1.14123
$131$		−	239.075i		−	1.82500i	−0.409075	−	0.912501i	$-0.634149\pi$
$131$		−	239.075i		−	1.82500i	0.409075	−	0.912501i	$-0.365851\pi$
$132$	33.8539	−	89.3055i	0.256469	−	0.676557i
$133$	0.175768			0.00132156
$134$			27.5672i			0.205725i
$135$	172.364	−	90.5621i	1.27677	−	0.670830i
$136$	−286.027			−2.10314
$137$		−	202.041i		−	1.47475i	−0.675481	−	0.737377i	$-0.736064\pi$
$137$		−	202.041i		−	1.47475i	0.675481	−	0.737377i	$-0.263936\pi$
$138$	−277.911	−	105.350i	−2.01385	−	0.763408i
$139$	233.035			1.67651			0.838256	−	0.545276i	$-0.183575\pi$
$139$	233.035			1.67651			0.838256	+	0.545276i	$0.183575\pi$
$140$			5.56170i			0.0397264i
$141$	−71.6957	+	189.131i	−0.508480	+	1.34135i
$142$	416.850			2.93556
$143$		−	26.4857i		−	0.185215i
$144$	57.5632	+	50.9659i	0.399744	+	0.353930i
$145$	−58.7864			−0.405423
$146$			387.294i			2.65270i
$147$	137.424	+	52.0947i	0.934859	+	0.354386i
$148$	−143.107			−0.966939
$149$			136.690i			0.917382i	0.888596	+	0.458691i	$0.151682\pi$
$149$			136.690i			0.917382i	−0.888596	+	0.458691i	$0.848318\pi$
$150$	96.7118	−	255.123i	0.644745	−	1.70082i
$151$	173.273			1.14750			0.573751	−	0.819030i	$-0.305488\pi$
$151$	173.273			1.14750			0.573751	+	0.819030i	$0.305488\pi$
$152$		−	18.8376i		−	0.123932i
$153$	−151.589	+	171.211i	−0.990776	+	1.11903i
$154$	1.53379			0.00995968
$155$			327.232i			2.11118i
$156$	125.821	+	47.6962i	0.806546	+	0.305745i
$157$	−5.19910			−0.0331153			−0.0165576	−	0.999863i	$-0.505271\pi$
$157$	−5.19910			−0.0331153			−0.0165576	+	0.999863i	$0.505271\pi$
$158$			462.513i			2.92730i
$159$	41.1661	−	108.595i	0.258906	−	0.682987i
$160$	−117.246			−0.732787
$161$		−	3.08979i		−	0.0191912i
$162$	270.789	−	33.0435i	1.67153	−	0.203972i
$163$	101.856			0.624885			0.312442	−	0.949937i	$-0.398853\pi$
$163$	101.856			0.624885			0.312442	+	0.949937i	$0.398853\pi$
$164$		−	388.636i		−	2.36973i
$165$	−87.7104	−	33.2492i	−0.531578	−	0.201511i
$166$	−4.24185			−0.0255533
$167$		−	46.8689i		−	0.280652i	−0.990105	−	0.140326i	$-0.955185\pi$
$167$		−	46.8689i		−	0.280652i	0.990105	−	0.140326i	$-0.0448151\pi$
$168$	−1.25739	+	3.31694i	−0.00748444	+	0.0197437i
$169$	−131.685			−0.779199
$170$			617.093i			3.62996i
$171$	−11.2759	−	9.98357i	−0.0659409	−	0.0583835i
$172$	154.983			0.901065
$173$		−	320.838i		−	1.85455i	−0.374378	−	0.927276i	$-0.622144\pi$
$173$		−	320.838i		−	1.85455i	0.374378	−	0.927276i	$-0.377856\pi$
$174$	−77.0154	−	29.1950i	−0.442617	−	0.167787i
$175$	2.83643			0.0162082
$176$		−	37.0388i		−	0.210448i
$177$	61.8718	−	163.216i	0.349558	−	0.922124i
$178$	−215.792			−1.21232
$179$			201.513i			1.12577i	0.826534	+	0.562887i	$0.190309\pi$
$179$			201.513i			1.12577i	−0.826534	+	0.562887i	$0.809691\pi$
$180$	315.904	−	356.796i	1.75502	−	1.98220i
$181$	268.204			1.48179			0.740894	−	0.671622i	$-0.234402\pi$
$181$	268.204			1.48179			0.740894	+	0.671622i	$0.234402\pi$
$182$			2.16093i			0.0118733i
$183$	−249.141	−	94.4443i	−1.36143	−	0.516089i
$184$	−331.143			−1.79969
$185$			140.551i			0.759735i
$186$	−162.513	+	428.704i	−0.873724	+	2.30486i
$187$	110.165			0.589119
$188$			495.043i			2.63321i
$189$	1.31908	+	2.51057i	0.00697926	+	0.0132834i
$190$	−40.6415			−0.213902
$191$		−	194.435i		−	1.01798i	−0.860771	−	0.508992i	$-0.830018\pi$
$191$		−	194.435i		−	1.01798i	0.860771	−	0.508992i	$-0.169982\pi$
$192$	−249.458	−	94.5642i	−1.29926	−	0.492522i
$193$	−115.134			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$193$	−115.134			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$194$			351.787i			1.81333i
$195$	46.8444	−	123.574i	0.240228	−	0.633713i
$196$	359.703			1.83522
$197$			81.7851i			0.415153i	0.978219	+	0.207576i	$0.0665575\pi$
$197$			81.7851i			0.415153i	−0.978219	+	0.207576i	$0.933442\pi$
$198$	−98.3961	−	87.1190i	−0.496950	−	0.439995i
$199$	176.713			0.888005			0.444002	−	0.896026i	$-0.353558\pi$
$199$	176.713			0.888005			0.444002	+	0.896026i	$0.353558\pi$
$200$		−	303.990i		−	1.51995i
$201$	22.9616	+	8.70428i	0.114237	+	0.0433049i
$202$	135.373			0.670165
$203$		−	0.856252i		−	0.00421799i
$204$	−198.389	+	523.344i	−0.972495	+	2.56541i
$205$	−381.694			−1.86192
$206$		−	213.822i		−	1.03797i
$207$	−175.499	+	198.217i	−0.847824	+	0.957570i
$208$	52.1835			0.250882
$209$			7.25543i			0.0347150i
$210$	7.15619	+	2.71277i	0.0340771	+	0.0129179i
$211$	47.6290			0.225730			0.112865	−	0.993610i	$-0.463997\pi$
$211$	47.6290			0.225730			0.112865	+	0.993610i	$0.463997\pi$
$212$		−	284.243i		−	1.34077i
$213$	131.619	−	347.208i	0.617931	−	1.63008i
$214$	−73.7384			−0.344572
$215$		−	152.215i		−	0.707977i
$216$	269.066	−	141.370i	1.24568	−	0.654491i
$217$	−4.76629			−0.0219645
$218$		−	178.275i		−	0.817776i
$219$	322.590	+	122.287i	1.47301	+	0.558389i
$220$	−229.579			−1.04354
$221$			155.210i			0.702308i
$222$	−69.8016	+	184.134i	−0.314422	+	0.829435i
$223$	−354.572			−1.59001			−0.795005	−	0.606602i	$-0.792532\pi$
$223$	−354.572			−1.59001			−0.795005	+	0.606602i	$0.792532\pi$
$224$		−	1.70774i		−	0.00762385i
$225$	−181.964	−	161.109i	−0.808727	−	0.716040i
$226$	−119.169			−0.527294
$227$			154.580i			0.680967i	0.940250	+	0.340484i	$0.110591\pi$
$227$			154.580i			0.680967i	−0.940250	+	0.340484i	$0.889409\pi$
$228$	−34.4672	−	13.0658i	−0.151172	−	0.0573062i
$229$	−59.1868			−0.258458			−0.129229	−	0.991615i	$-0.541250\pi$
$229$	−59.1868			−0.258458			−0.129229	+	0.991615i	$0.541250\pi$
$230$			714.429i			3.10621i
$231$	0.484291	−	1.27754i	0.00209650	−	0.00553050i
$232$	−91.7672			−0.395548
$233$			40.9331i			0.175679i	0.996135	+	0.0878393i	$0.0279962\pi$
$233$			40.9331i			0.175679i	−0.996135	+	0.0878393i	$0.972004\pi$
$234$	122.741	−	138.629i	0.524533	−	0.592431i
$235$	486.202			2.06894
$236$		−	427.212i		−	1.81022i
$237$	385.243	+	146.038i	1.62550	+	0.616192i
$238$	−8.98825			−0.0377658
$239$		−	51.5108i		−	0.215526i	−0.994177	−	0.107763i	$-0.965631\pi$
$239$		−	51.5108i		−	0.215526i	0.994177	−	0.107763i	$-0.0343688\pi$
$240$	65.5094	−	172.812i	0.272956	−	0.720049i
$241$	93.9977			0.390032			0.195016	−	0.980800i	$-0.437524\pi$
$241$	93.9977			0.390032			0.195016	+	0.980800i	$0.437524\pi$
$242$		−	344.199i		−	1.42231i
$243$	57.9779	−	235.982i	0.238592	−	0.971120i
$244$	−652.118			−2.67261
$245$		−	353.278i		−	1.44195i
$246$	−500.054	−	189.560i	−2.03274	−	0.770570i
$247$	−10.2221			−0.0413849
$248$			510.819i			2.05975i
$249$	−1.33936	+	3.53318i	−0.00537894	+	0.0141895i
$250$	−48.6731			−0.194692
$251$			194.732i			0.775825i	0.921696	+	0.387913i	$0.126804\pi$
$251$			194.732i			0.775825i	−0.921696	+	0.387913i	$0.873196\pi$
$252$	5.19690	+	4.60128i	0.0206226	+	0.0182591i
$253$	127.542			0.504119
$254$			529.131i			2.08319i
$255$	513.997	+	194.846i	2.01567	+	0.764101i
$256$	−433.921			−1.69500
$257$		−	92.3523i		−	0.359348i	−0.983726	−	0.179674i	$-0.942496\pi$
$257$		−	92.3523i		−	0.359348i	0.983726	−	0.179674i	$-0.0575042\pi$
$258$	75.5943	−	199.415i	0.293001	−	0.772928i
$259$	−2.04719			−0.00790422
$260$		−	323.450i		−	1.24404i
$261$	−48.6349	+	54.9305i	−0.186341	+	0.210461i
$262$	−805.173			−3.07318
$263$		−	82.7406i		−	0.314603i	−0.987551	−	0.157302i	$-0.949721\pi$
$263$		−	82.7406i		−	0.314603i	0.987551	−	0.157302i	$-0.0502794\pi$
$264$	−136.919	−	51.9030i	−0.518631	−	0.196602i
$265$	−279.166			−1.05346
$266$		−	0.591962i		−	0.00222542i
$267$	−68.1360	+	179.741i	−0.255191	+	0.673186i
$268$	60.1012			0.224258
$269$		−	130.182i		−	0.483948i	−0.970283	−	0.241974i	$-0.922205\pi$
$269$		−	130.182i		−	0.483948i	0.970283	−	0.241974i	$-0.0777948\pi$
$270$	−305.001	−	580.500i	−1.12963	−	2.15000i
$271$	28.8716			0.106537			0.0532686	−	0.998580i	$-0.483036\pi$
$271$	28.8716			0.106537			0.0532686	+	0.998580i	$0.483036\pi$
$272$			217.053i			0.797990i
$273$	1.79991	+	0.682311i	0.00659309	+	0.00249931i
$274$	−680.449			−2.48339
$275$			117.084i			0.425760i
$276$	−229.682	+	605.893i	−0.832180	+	2.19527i
$277$	−312.860			−1.12946			−0.564730	−	0.825276i	$-0.691020\pi$
$277$	−312.860			−1.12946			−0.564730	+	0.825276i	$0.691020\pi$
$278$		−	784.832i		−	2.82314i
$279$	305.768	+	270.724i	1.09594	+	0.970338i
$280$	8.52691			0.0304533
$281$			229.526i			0.816819i	0.912799	+	0.408409i	$0.133916\pi$
$281$			229.526i			0.816819i	−0.912799	+	0.408409i	$0.866084\pi$
$282$	636.968	+	241.461i	2.25875	+	0.856246i
$283$	68.0698			0.240529			0.120265	−	0.992742i	$-0.461626\pi$
$283$	68.0698			0.240529			0.120265	+	0.992742i	$0.461626\pi$
$284$		−	908.804i		−	3.20001i
$285$	−12.8325	+	33.8516i	−0.0450261	+	0.118778i
$286$	−89.2002			−0.311889
$287$		−	5.55956i		−	0.0193713i
$288$	−96.9994	+	109.555i	−0.336803	+	0.380401i
$289$	−356.585			−1.23386
$290$			197.985i			0.682706i
$291$	293.015	+	111.076i	1.00692	+	0.381704i
$292$	844.367			2.89167
$293$		−	208.294i		−	0.710901i	−0.934695	−	0.355451i	$-0.884327\pi$
$293$		−	208.294i		−	0.710901i	0.934695	−	0.355451i	$-0.115673\pi$
$294$	175.448	−	462.826i	0.596762	−	1.57424i
$295$	−419.582			−1.42231
$296$			219.404i			0.741231i
$297$	−103.633	+	54.4497i	−0.348931	+	0.183332i
$298$	460.353			1.54481
$299$			179.692i			0.600977i
$300$	−556.211	−	210.848i	−1.85404	−	0.702828i
$301$	2.21708			0.00736573
$302$		−	583.560i		−	1.93232i
$303$	42.7438	−	112.757i	0.141069	−	0.372135i
$304$	−14.2950			−0.0470231
$305$			640.471i			2.09990i
$306$	576.616	+	510.531i	1.88437	+	1.66840i
$307$	33.8579			0.110286			0.0551432	−	0.998478i	$-0.482438\pi$
$307$	33.8579			0.110286			0.0551432	+	0.998478i	$0.482438\pi$
$308$		−	3.34393i		−	0.0108569i
$309$	−178.099	−	67.5137i	−0.576373	−	0.218491i
$310$	1102.07			3.55508
$311$		−	12.3579i		−	0.0397361i	−0.999803	−	0.0198680i	$-0.993675\pi$
$311$		−	12.3579i		−	0.0397361i	0.999803	−	0.0198680i	$-0.00632461\pi$
$312$	73.1254	−	192.903i	0.234376	−	0.618278i
$313$	422.855			1.35097			0.675487	−	0.737371i	$-0.263933\pi$
$313$	422.855			1.35097			0.675487	+	0.737371i	$0.263933\pi$
$314$			17.5099i			0.0557639i
$315$	4.51910	−	5.10408i	0.0143464	−	0.0162034i
$316$	1008.36			3.19101
$317$			376.308i			1.18709i	0.804800	+	0.593546i	$0.202273\pi$
$317$			376.308i			1.18709i	−0.804800	+	0.593546i	$0.797727\pi$
$318$	−365.733	−	138.642i	−1.15010	−	0.435981i
$319$	35.3448			0.110799
$320$			641.284i			2.00401i
$321$	−23.2827	+	61.4191i	−0.0725319	+	0.191337i
$322$	−10.4060			−0.0323168
$323$		−	42.5180i		−	0.131635i
$324$	−72.0405	−	590.365i	−0.222347	−	1.82212i
$325$	−164.958			−0.507562
$326$		−	343.038i		−	1.05226i
$327$	−148.491	−	56.2900i	−0.454102	−	0.172141i
$328$	−595.836			−1.81657
$329$			7.08176i			0.0215251i
$330$	−111.979	+	295.397i	−0.339330	+	0.895143i
$331$	587.652			1.77538			0.887692	−	0.460437i	$-0.152307\pi$
$331$	587.652			1.77538			0.887692	+	0.460437i	$0.152307\pi$
$332$			9.24797i			0.0278553i
$333$	131.332	+	116.280i	0.394390	+	0.349190i
$334$	−157.848			−0.472599
$335$		−	59.0277i		−	0.176202i
$336$	2.51708	+	0.954175i	0.00749132	+	0.00283981i
$337$	637.154			1.89066			0.945332	−	0.326109i	$-0.105738\pi$
$337$	637.154			1.89066			0.945332	+	0.326109i	$0.105738\pi$
$338$			443.497i			1.31212i
$339$	−37.6272	+	99.2594i	−0.110995	+	0.292801i
$340$	1345.37			3.95696
$341$		−	196.746i		−	0.576966i
$342$	−33.6233	+	37.9757i	−0.0983138	+	0.111040i
$343$	10.2925			0.0300073
$344$		−	237.612i		−	0.690733i
$345$	595.072	+	225.579i	1.72485	+	0.653854i
$346$	−1080.54			−3.12294
$347$			535.757i			1.54397i	0.635642	+	0.771984i	$0.280736\pi$
$347$			535.757i			1.54397i	−0.635642	+	0.771984i	$0.719264\pi$
$348$	−63.6501	+	167.907i	−0.182902	+	0.482491i
$349$	270.624			0.775426			0.387713	−	0.921780i	$-0.373265\pi$
$349$	270.624			0.775426			0.387713	+	0.921780i	$0.373265\pi$
$350$		−	9.55273i		−	0.0272935i
$351$	−76.7134	−	146.007i	−0.218557	−	0.415973i
$352$	70.4931			0.200264
$353$			548.993i			1.55522i	0.628746	+	0.777611i	$0.283569\pi$
$353$			548.993i			1.55522i	−0.628746	+	0.777611i	$0.716431\pi$
$354$	−549.690	−	208.376i	−1.55280	−	0.588633i
$355$	−892.572			−2.51429
$356$			470.464i			1.32153i
$357$	−2.83802	+	7.48661i	−0.00794964	+	0.0209709i
$358$	678.670			1.89573
$359$		−	224.629i		−	0.625707i	−0.949801	−	0.312853i	$-0.898715\pi$
$359$		−	224.629i		−	0.625707i	0.949801	−	0.312853i	$-0.101285\pi$
$360$	−547.021	−	484.327i	−1.51950	−	1.34535i
$361$	−358.200			−0.992243
$362$		−	903.274i		−	2.49523i
$363$	−286.695	−	108.680i	−0.789793	−	0.299394i
$364$	4.71121			0.0129429
$365$		−	829.287i		−	2.27202i
$366$	−318.076	+	839.074i	−0.869060	+	2.29255i
$367$	477.396			1.30081			0.650403	−	0.759589i	$-0.274600\pi$
$367$	477.396			1.30081			0.650403	+	0.759589i	$0.274600\pi$
$368$			251.290i			0.682853i
$369$	−315.782	+	356.658i	−0.855778	+	0.966554i
$370$	473.357			1.27934
$371$		−	4.06619i		−	0.0109601i
$372$	934.647	+	354.306i	2.51249	+	0.952434i
$373$	612.746			1.64275			0.821375	−	0.570388i	$-0.193207\pi$
$373$	612.746			1.64275			0.821375	+	0.570388i	$0.193207\pi$
$374$		−	371.022i		−	0.992037i
$375$	−15.3684	+	40.5414i	−0.0409824	+	0.108110i
$376$	758.975			2.01855
$377$			49.7968i			0.132087i
$378$	8.45526	−	4.44249i	0.0223684	−	0.0117526i
$379$	−236.802			−0.624808			−0.312404	−	0.949949i	$-0.601134\pi$
$379$	−236.802			−0.624808			−0.312404	+	0.949949i	$0.601134\pi$
$380$			88.6053i			0.233172i
$381$	440.731	+	167.072i	1.15677	+	0.438509i
$382$	−654.831			−1.71422
$383$		−	123.820i		−	0.323291i	−0.986849	−	0.161645i	$-0.948320\pi$
$383$		−	123.820i		−	0.323291i	0.986849	−	0.161645i	$-0.0516801\pi$
$384$	−249.323	+	657.707i	−0.649279	+	1.71278i
$385$	−3.28420			−0.00853039
$386$			387.756i			1.00455i
$387$	−142.231	−	125.930i	−0.367522	−	0.325400i
$388$	766.956			1.97669
$389$		−	242.285i		−	0.622840i	−0.950272	−	0.311420i	$-0.899195\pi$
$389$		−	242.285i		−	0.622840i	0.950272	−	0.311420i	$-0.100805\pi$
$390$	−416.181	−	157.766i	−1.06713	−	0.404527i
$391$	−747.416			−1.91155
$392$		−	551.478i		−	1.40683i
$393$	−254.232	+	670.655i	−0.646900	+	1.70650i
$394$	275.441			0.699089
$395$		−	990.349i		−	2.50721i
$396$	−189.934	+	214.520i	−0.479632	+	0.541718i
$397$	76.0437			0.191546			0.0957730	−	0.995403i	$-0.469468\pi$
$397$	76.0437			0.191546			0.0957730	+	0.995403i	$0.469468\pi$
$398$		−	595.146i		−	1.49534i
$399$	−0.493065	−	0.186911i	−0.00123575	−	0.000468448i
$400$	−230.685			−0.576712
$401$		−	287.846i		−	0.717821i	−0.933372	−	0.358911i	$-0.883148\pi$
$401$		−	287.846i		−	0.717821i	0.933372	−	0.358911i	$-0.116852\pi$
$402$	29.3148	−	77.3316i	0.0729225	−	0.192367i
$403$	277.192			0.687821
$404$		−	295.137i		−	0.730537i
$405$	−579.821	+	70.7538i	−1.43166	+	0.174701i
$406$	−2.88374			−0.00710281
$407$		−	84.5051i		−	0.207629i
$408$	802.364	+	304.160i	1.96658	+	0.745490i
$409$	−122.320			−0.299070			−0.149535	−	0.988756i	$-0.547778\pi$
$409$	−122.320			−0.299070			−0.149535	+	0.988756i	$0.547778\pi$
$410$			1285.50i			3.13536i
$411$	−214.850	+	566.768i	−0.522750	+	1.37900i
$412$	−466.168			−1.13148
$413$		−	6.11141i		−	0.0147976i
$414$	667.568	+	591.059i	1.61248	+	1.42768i
$415$	9.08279			0.0218862
$416$			99.3167i			0.238742i
$417$	−653.712	−	247.809i	−1.56766	−	0.594266i
$418$	24.4353			0.0584577
$419$		−	341.256i		−	0.814453i	−0.913327	−	0.407227i	$-0.866496\pi$
$419$		−	341.256i		−	0.814453i	0.913327	−	0.407227i	$-0.133504\pi$
$420$	5.91429	−	15.6017i	0.0140817	−	0.0371470i
$421$	184.129			0.437361			0.218681	−	0.975796i	$-0.429825\pi$
$421$	184.129			0.437361			0.218681	+	0.975796i	$0.429825\pi$
$422$		−	160.408i		−	0.380114i
$423$	402.242	−	454.311i	0.950928	−	1.07402i
$424$	−435.787			−1.02780
$425$		−	686.130i		−	1.61442i
$426$	−1169.35	−	443.277i	−2.74495	−	1.04056i
$427$	−9.32876			−0.0218472
$428$			160.762i			0.375613i
$429$	−28.1648	+	74.2978i	−0.0656522	+	0.173188i
$430$	−512.640			−1.19219
$431$		−	564.785i		−	1.31041i	−0.755453	−	0.655203i	$-0.772583\pi$
$431$		−	564.785i		−	1.31041i	0.755453	−	0.655203i	$-0.227417\pi$
$432$	−107.280	−	204.182i	−0.248333	−	0.472644i
$433$	−628.507			−1.45152			−0.725759	−	0.687949i	$-0.758511\pi$
$433$	−628.507			−1.45152			−0.725759	+	0.687949i	$0.758511\pi$
$434$			16.0522i			0.0369867i
$435$	164.908	+	62.5132i	0.379099	+	0.143709i
$436$	−388.671			−0.891446
$437$		−	49.2245i		−	0.112642i
$438$	411.847	−	1086.44i	0.940290	−	2.48046i
$439$	−173.290			−0.394738			−0.197369	−	0.980329i	$-0.563240\pi$
$439$	−173.290			−0.394738			−0.197369	+	0.980329i	$0.563240\pi$
$440$			351.978i			0.799951i
$441$	−330.106	−	292.273i	−0.748540	−	0.662750i
$442$	522.727			1.18264
$443$			252.126i			0.569133i	0.958656	+	0.284566i	$0.0918496\pi$
$443$			252.126i			0.569133i	−0.958656	+	0.284566i	$0.908150\pi$
$444$	401.445	+	152.179i	0.904155	+	0.342747i
$445$	462.062			1.03834
$446$			1194.15i			2.67747i
$447$	145.356	−	383.444i	0.325180	−	0.857816i
$448$	−9.34061			−0.0208496
$449$		−	174.807i		−	0.389325i	−0.980870	−	0.194663i	$-0.937639\pi$
$449$		−	174.807i		−	0.389325i	0.980870	−	0.194663i	$-0.0623612\pi$
$450$	−542.593	+	612.829i	−1.20576	+	1.36184i
$451$	229.491			0.508848
$452$			259.808i			0.574796i
$453$	−486.066	−	184.258i	−1.07299	−	0.406750i
$454$	520.603			1.14670
$455$		−	4.62706i		−	0.0101694i
$456$	−20.0318	+	52.8434i	−0.0439295	+	0.115885i
$457$	748.733			1.63836			0.819182	−	0.573533i	$-0.194428\pi$
$457$	748.733			1.63836			0.819182	+	0.573533i	$0.194428\pi$
$458$			199.333i			0.435225i
$459$	607.303	−	319.084i	1.32310	−	0.695171i
$460$	1557.58			3.38604
$461$			72.5362i			0.157345i	0.996901	+	0.0786726i	$0.0250682\pi$
$461$			72.5362i			0.157345i	−0.996901	+	0.0786726i	$0.974932\pi$
$462$	−4.30260	−	1.63103i	−0.00931299	−	0.00353036i
$463$	−439.643			−0.949553			−0.474777	−	0.880106i	$-0.657471\pi$
$463$	−439.643			−0.949553			−0.474777	+	0.880106i	$0.657471\pi$
$464$			69.6382i			0.150082i
$465$	347.978	−	917.954i	0.748339	−	1.97409i
$466$	137.857			0.295831
$467$		−	356.668i		−	0.763744i	−0.924215	−	0.381872i	$-0.875280\pi$
$467$		−	356.668i		−	0.763744i	0.924215	−	0.381872i	$-0.124720\pi$
$468$	−302.235	−	267.596i	−0.645800	−	0.571786i
$469$	0.859767			0.00183319
$470$		−	1637.46i		−	3.48396i
$471$	14.5845	+	5.52870i	0.0309651	+	0.0117382i
$472$	−654.979			−1.38767
$473$			91.5180i			0.193484i
$474$	491.835	−	1297.45i	1.03763	−	2.73723i
$475$	45.1882			0.0951331
$476$			19.5959i			0.0411679i
$477$	−230.959	+	260.855i	−0.484190	+	0.546866i
$478$	−173.482			−0.362932
$479$		−	125.239i		−	0.261459i	−0.991418	−	0.130729i	$-0.958268\pi$
$479$		−	125.239i		−	0.261459i	0.991418	−	0.130729i	$-0.0417319\pi$
$480$	328.899	+	124.679i	0.685206	+	0.259748i
$481$	119.058			0.247522
$482$		−	316.572i		−	0.656788i
$483$	−3.28567	+	8.66750i	−0.00680264	+	0.0179451i
$484$	−750.413			−1.55044
$485$		−	753.257i		−	1.55311i
$486$	−794.756	−	195.262i	−1.63530	−	0.401773i
$487$	−893.464			−1.83463			−0.917314	−	0.398164i	$-0.869648\pi$
$487$	−893.464			−1.83463			−0.917314	+	0.398164i	$0.869648\pi$
$488$			999.794i			2.04876i
$489$	−285.728	−	108.314i	−0.584310	−	0.221500i
$490$	−1189.79			−2.42815
$491$		−	182.524i		−	0.371739i	−0.982574	−	0.185869i	$-0.940490\pi$
$491$		−	182.524i		−	0.371739i	0.982574	−	0.185869i	$-0.0595101\pi$
$492$	−413.274	+	1090.20i	−0.839987	+	2.21586i
$493$	−207.126			−0.420134
$494$			34.4266i			0.0696894i
$495$	210.689	+	186.542i	0.425634	+	0.376852i
$496$	387.638			0.781529
$497$		−	13.0007i		−	0.0261584i
$498$	11.8993	+	4.51077i	0.0238941	+	0.00905778i
$499$	405.427			0.812480			0.406240	−	0.913766i	$-0.366840\pi$
$499$	405.427			0.812480			0.406240	+	0.913766i	$0.366840\pi$
$500$			106.116i			0.212231i
$501$	−49.8402	+	131.477i	−0.0994815	+	0.262429i
$502$	655.832			1.30644
$503$			582.261i			1.15758i	0.815478	+	0.578788i	$0.196474\pi$
$503$			582.261i			1.15758i	−0.815478	+	0.578788i	$0.803526\pi$
$504$	7.05445	−	7.96761i	0.0139969	−	0.0158088i
$505$	−289.866			−0.573992
$506$		−	429.545i		−	0.848902i
$507$	369.403	+	140.033i	0.728605	+	0.276199i
$508$	1153.60			2.27086
$509$			452.060i			0.888134i	0.895994	+	0.444067i	$0.146465\pi$
$509$			452.060i			0.888134i	−0.895994	+	0.444067i	$0.853535\pi$
$510$	656.214	−	1731.07i	1.28669	−	3.39426i
$511$	12.0790			0.0236379
$512$			523.551i			1.02256i
$513$	21.0147	+	39.9967i	0.0409644	+	0.0779663i
$514$	−311.030			−0.605117
$515$			457.842i			0.889013i
$516$	−434.760	−	164.809i	−0.842558	−	0.319396i
$517$	−292.325			−0.565425
$518$			6.89467i			0.0133102i
$519$	−341.178	+	900.016i	−0.657375	+	1.73413i
$520$	−495.897			−0.953649
$521$			683.044i			1.31103i	0.755184	+	0.655513i	$0.227547\pi$
$521$			683.044i			1.31103i	−0.755184	+	0.655513i	$0.772453\pi$
$522$	184.998	+	163.796i	0.354403	+	0.313785i
$523$	−158.421			−0.302909			−0.151455	−	0.988464i	$-0.548396\pi$
$523$	−158.421			−0.302909			−0.151455	+	0.988464i	$0.548396\pi$
$524$			1755.42i			3.35003i
$525$	−7.95679	−	3.01626i	−0.0151558	−	0.00574525i
$526$	−278.659			−0.529771
$527$			1152.96i			2.18778i
$528$	−39.3870	+	103.902i	−0.0745965	+	0.196783i
$529$	−336.309			−0.635745
$530$			940.195i			1.77395i
$531$	−347.127	+	392.060i	−0.653722	+	0.738343i
$532$	−1.29058			−0.00242590
$533$			323.326i			0.606615i
$534$	605.342	+	229.473i	1.13360	+	0.429724i
$535$	157.891			0.295123
$536$		−	92.1440i		−	0.171910i
$537$	214.289	−	565.287i	0.399048	−	1.05268i
$538$	−438.436			−0.814936
$539$			212.406i			0.394073i
$540$	−1265.59	+	664.955i	−2.34369	+	1.23140i
$541$	−82.9855			−0.153393			−0.0766964	−	0.997054i	$-0.524437\pi$
$541$	−82.9855			−0.153393			−0.0766964	+	0.997054i	$0.524437\pi$
$542$		−	97.2356i		−	0.179402i
$543$	−752.367	−	285.207i	−1.38557	−	0.525243i
$544$	−413.100			−0.759376
$545$			381.729i			0.700420i
$546$	2.29793	−	6.06187i	0.00420866	−	0.0111023i
$547$	72.1231			0.131852			0.0659261	−	0.997825i	$-0.479000\pi$
$547$	72.1231			0.131852			0.0659261	+	0.997825i	$0.479000\pi$
$548$			1483.49i			2.70711i
$549$	598.461	+	529.872i	1.09009	+	0.965158i
$550$	394.323			0.716951
$551$		−	13.6412i		−	0.0247572i
$552$	928.924	+	352.136i	1.68283	+	0.637928i
$553$	14.4249			0.0260848
$554$			1053.67i			1.90193i
$555$	149.461	−	394.275i	0.269300	−	0.710405i
$556$	−1711.07			−3.07746
$557$			28.7215i			0.0515647i	0.999668	+	0.0257823i	$0.00820769\pi$
$557$			28.7215i			0.0515647i	−0.999668	+	0.0257823i	$0.991792\pi$
$558$	911.764	−	1029.79i	1.63399	−	1.84550i
$559$	−128.938			−0.230659
$560$		−	6.47070i		−	0.0115548i
$561$	−309.036	−	117.149i	−0.550867	−	0.208822i
$562$	773.013			1.37547
$563$		−	1078.00i		−	1.91475i	−0.288847	−	0.957375i	$-0.593272\pi$
$563$		−	1078.00i		−	1.91475i	0.288847	−	0.957375i	$-0.406728\pi$
$564$	526.427	−	1388.70i	0.933382	−	2.46223i
$565$	255.167			0.451624
$566$		−	229.250i		−	0.405035i
$567$	−1.03056	−	8.44537i	−0.00181757	−	0.0148948i
$568$	−1393.33			−2.45305
$569$			413.657i			0.726989i	0.931596	+	0.363494i	$0.118416\pi$
$569$			413.657i			0.726989i	−0.931596	+	0.363494i	$0.881584\pi$
$570$	114.008	+	43.2180i	0.200014	+	0.0758210i
$571$	41.1521			0.0720702			0.0360351	−	0.999351i	$-0.488527\pi$
$571$	41.1521			0.0720702			0.0360351	+	0.999351i	$0.488527\pi$
$572$			194.472i			0.339986i
$573$	−206.761	+	545.430i	−0.360840	+	0.951885i
$574$	−18.7239			−0.0326200
$575$		−	794.356i		−	1.38149i
$576$	599.221	+	530.545i	1.04031	+	0.921084i
$577$	−36.8708			−0.0639009			−0.0319504	−	0.999489i	$-0.510172\pi$
$577$	−36.8708			−0.0639009			−0.0319504	+	0.999489i	$0.510172\pi$
$578$			1200.93i			2.07774i
$579$	322.975	+	122.433i	0.557815	+	0.211456i
$580$	431.641			0.744208
$581$			0.132295i			0.000227703i
$582$	374.089	−	986.835i	0.642764	−	1.69559i
$583$	167.846			0.287901
$584$		−	1294.54i		−	2.21668i
$585$	−262.816	+	296.837i	−0.449259	+	0.507413i
$586$	−701.507			−1.19711
$587$		−	888.196i		−	1.51311i	−0.653929	−	0.756556i	$-0.726881\pi$
$587$		−	888.196i		−	1.51311i	0.653929	−	0.756556i	$-0.273119\pi$
$588$	−1009.04	−	382.507i	−1.71606	−	0.650522i
$589$	−75.9334			−0.128919
$590$			1413.09i			2.39508i
$591$	86.9700	−	229.424i	0.147157	−	0.388196i
$592$	166.496			0.281244
$593$		−	186.421i		−	0.314369i	−0.987569	−	0.157185i	$-0.949758\pi$
$593$		−	186.421i		−	0.314369i	0.987569	−	0.157185i	$-0.0502417\pi$
$594$	183.379	+	349.021i	0.308719	+	0.587577i
$595$	19.2459			0.0323461
$596$		−	1003.65i		−	1.68398i
$597$	−495.716	−	187.916i	−0.830346	−	0.314767i
$598$	605.179			1.01201
$599$			883.167i			1.47440i	0.675673	+	0.737201i	$0.263853\pi$
$599$			883.167i			1.47440i	−0.675673	+	0.737201i	$0.736147\pi$
$600$	−323.262	+	852.755i	−0.538770	+	1.42126i
$601$	709.460			1.18047			0.590233	−	0.807233i	$-0.299036\pi$
$601$	709.460			1.18047			0.590233	+	0.807233i	$0.299036\pi$
$602$		−	7.46685i		−	0.0124034i
$603$	−55.1560	−	48.8346i	−0.0914693	−	0.0809861i
$604$	−1272.26			−2.10639
$605$			737.011i			1.21820i
$606$	−379.750	−	143.956i	−0.626651	−	0.237550i
$607$	158.653			0.261372			0.130686	−	0.991424i	$-0.458282\pi$
$607$	158.653			0.261372			0.130686	+	0.991424i	$0.458282\pi$
$608$		−	27.2066i		−	0.0447477i
$609$	−0.910535	+	2.40196i	−0.00149513	+	0.00394411i
$610$	2157.02			3.53610
$611$		−	411.852i		−	0.674062i
$612$	1113.04	−	1257.12i	1.81870	−	2.05412i
$613$	−894.314			−1.45891			−0.729457	−	0.684027i	$-0.760227\pi$
$613$	−894.314			−1.45891			−0.729457	+	0.684027i	$0.760227\pi$
$614$		−	114.029i		−	0.185715i
$615$	1070.73	+	405.893i	1.74103	+	0.659988i
$616$	−5.12673			−0.00832262
$617$			500.137i			0.810594i	0.914185	+	0.405297i	$0.132832\pi$
$617$			500.137i			0.810594i	−0.914185	+	0.405297i	$0.867168\pi$
$618$	−227.377	+	599.814i	−0.367924	+	0.970573i
$619$	−1136.19			−1.83552			−0.917760	−	0.397135i	$-0.870005\pi$
$619$	−1136.19			−1.83552			−0.917760	+	0.397135i	$0.870005\pi$
$620$		−	2402.71i		−	3.87534i
$621$	703.096	−	369.414i	1.13220	−	0.594870i
$622$	−41.6198			−0.0669129
$623$			6.73015i			0.0108028i
$624$	−146.385	−	55.4917i	−0.234592	−	0.0889290i
$625$	−570.882			−0.913411
$626$		−	1424.12i		−	2.27495i
$627$	7.71540	−	20.3530i	0.0123053	−	0.0324609i
$628$	38.1745			0.0607874
$629$			495.213i			0.787302i
$630$	−17.1899	−	15.2197i	−0.0272855	−	0.0241583i
$631$	−156.930			−0.248701			−0.124351	−	0.992238i	$-0.539685\pi$
$631$	−156.930			−0.248701			−0.124351	+	0.992238i	$0.539685\pi$
$632$		−	1545.96i		−	2.44614i
$633$	−133.609	−	50.6485i	−0.211073	−	0.0800135i
$634$	1267.36			1.99898
$635$		−	1132.99i		−	1.78424i
$636$	−302.263	+	797.361i	−0.475257	+	1.25371i
$637$	−299.255			−0.469788
$638$		−	119.037i		−	0.186578i
$639$	−738.439	+	834.026i	−1.15562	+	1.30521i
$640$	1690.78			2.64184
$641$		−	139.789i		−	0.218080i	−0.994037	−	0.109040i	$-0.965222\pi$
$641$		−	139.789i		−	0.218080i	0.994037	−	0.109040i	$-0.0347776\pi$
$642$	206.851	+	78.4131i	0.322198	+	0.122139i
$643$	−167.720			−0.260839			−0.130420	−	0.991459i	$-0.541632\pi$
$643$	−167.720			−0.260839			−0.130420	+	0.991459i	$0.541632\pi$
$644$			22.6869i			0.0352281i
$645$	−161.865	+	426.995i	−0.250953	+	0.662007i
$646$	−143.195			−0.221664
$647$			251.487i			0.388696i	0.980933	+	0.194348i	$0.0622592\pi$
$647$			251.487i			0.388696i	−0.980933	+	0.194348i	$0.937741\pi$
$648$	−905.118	+	110.449i	−1.39679	+	0.170446i
$649$	252.270			0.388706
$650$			555.556i			0.854701i
$651$	13.3704	+	5.06846i	0.0205383	+	0.00778565i
$652$	−747.882			−1.14706
$653$		−	714.165i		−	1.09367i	−0.837241	−	0.546834i	$-0.815833\pi$
$653$		−	714.165i		−	1.09367i	0.837241	−	0.546834i	$-0.184167\pi$
$654$	−189.577	+	500.099i	−0.289874	+	0.764677i
$655$	1724.06			2.63216
$656$			452.154i			0.689259i
$657$	−774.892	−	686.082i	−1.17944	−	1.04427i
$658$	23.8504			0.0362468
$659$			29.4007i			0.0446142i	0.999751	+	0.0223071i	$0.00710115\pi$
$659$			29.4007i			0.0446142i	−0.999751	+	0.0223071i	$0.992899\pi$
$660$	644.016	+	244.133i	0.975782	+	0.369899i
$661$	905.070			1.36924			0.684622	−	0.728899i	$-0.259967\pi$
$661$	905.070			1.36924			0.684622	+	0.728899i	$0.259967\pi$
$662$		−	1979.14i		−	2.98963i
$663$	165.050	−	435.397i	0.248944	−	0.656707i
$664$	14.1785			0.0213532
$665$			1.26753i			0.00190606i
$666$	391.616	−	442.309i	0.588012	−	0.664127i
$667$	−239.797			−0.359516
$668$			344.136i			0.515174i
$669$	994.649	+	377.051i	1.48677	+	0.563604i
$670$	−198.798			−0.296713
$671$		−	385.078i		−	0.573886i
$672$	−1.81601	+	4.79057i	−0.00270239	+	0.00712882i
$673$	914.894			1.35943			0.679713	−	0.733478i	$-0.262104\pi$
$673$	914.894			1.35943			0.679713	+	0.733478i	$0.262104\pi$
$674$		−	2145.85i		−	3.18375i
$675$	339.123	+	645.443i	0.502404	+	0.956213i
$676$	966.898			1.43032
$677$			723.694i			1.06897i	0.845177	+	0.534486i	$0.179495\pi$
$677$			723.694i			1.06897i	−0.845177	+	0.534486i	$0.820505\pi$
$678$	334.292	+	126.723i	0.493057	+	0.186908i
$679$	10.9716			0.0161584
$680$		−	2062.65i		−	3.03331i
$681$	164.379	−	433.628i	0.241379	−	0.636751i
$682$	−662.613			−0.971573
$683$		−	43.9394i		−	0.0643329i	−0.999483	−	0.0321665i	$-0.989759\pi$
$683$		−	43.9394i		−	0.0643329i	0.999483	−	0.0321665i	$-0.0102407\pi$
$684$	82.7935	+	73.3046i	0.121043	+	0.107171i
$685$	1457.00			2.12701
$686$		−	34.6637i		−	0.0505302i
$687$	166.031	+	62.9390i	0.241676	+	0.0916143i
$688$	−180.314			−0.262084
$689$			236.476i			0.343217i
$690$	759.722	−	2004.12i	1.10105	−	2.90452i
$691$	131.383			0.190135			0.0950673	−	0.995471i	$-0.469693\pi$
$691$	131.383			0.190135			0.0950673	+	0.995471i	$0.469693\pi$
$692$			2355.76i			3.40428i
$693$	−2.71707	+	3.06878i	−0.00392074	+	0.00442826i
$694$	1804.36			2.59994
$695$			1680.51i			2.41800i
$696$	257.426	+	97.5850i	0.369865	+	0.140208i
$697$	−1344.85			−1.92948
$698$		−	911.425i		−	1.30577i
$699$	43.5281	−	114.826i	0.0622720	−	0.164272i
$700$	−20.8266			−0.0297523
$701$		−	429.574i		−	0.612802i	−0.951902	−	0.306401i	$-0.900875\pi$
$701$		−	429.574i		−	0.612802i	0.951902	−	0.306401i	$-0.0991249\pi$
$702$	−491.730	+	258.361i	−0.700471	+	0.368035i
$703$	−32.6145			−0.0463933
$704$		−	385.567i		−	0.547680i
$705$	−1363.90	−	517.025i	−1.93460	−	0.733369i
$706$	1848.94			2.61889
$707$		−	4.22203i		−	0.00597176i
$708$	−454.296	+	1198.42i	−0.641660	+	1.69268i
$709$	−207.589			−0.292791			−0.146395	−	0.989226i	$-0.546767\pi$
$709$	−207.589			−0.292791			−0.146395	+	0.989226i	$0.546767\pi$
$710$			3006.06i			4.23389i
$711$	−925.390	−	819.332i	−1.30153	−	1.15237i
$712$	721.292			1.01305
$713$			1334.82i			1.87212i
$714$	25.2139	+	9.55807i	0.0353136	+	0.0133867i
$715$	190.998			0.267131
$716$		−	1479.62i		−	2.06651i
$717$	−54.7764	+	144.499i	−0.0763967	+	0.201532i
$718$	−756.520			−1.05365
$719$		−	933.878i		−	1.29886i	−0.760423	−	0.649428i	$-0.775008\pi$
$719$		−	933.878i		−	1.29886i	0.760423	−	0.649428i	$-0.224992\pi$
$720$	−367.535	+	415.110i	−0.510465	+	0.576542i
$721$	−6.66869			−0.00924922
$722$			1206.37i			1.67087i
$723$	−263.683	−	99.9569i	−0.364707	−	0.138253i
$724$	−1969.29			−2.72002
$725$		−	220.134i		−	0.303633i
$726$	−366.020	+	965.550i	−0.504160	+	1.32996i
$727$	−422.780			−0.581540			−0.290770	−	0.956793i	$-0.593911\pi$
$727$	−422.780			−0.581540			−0.290770	+	0.956793i	$0.593911\pi$
$728$		−	7.22298i		−	0.00992168i
$729$	−413.583	+	600.325i	−0.567329	+	0.823491i
$730$	−2792.93			−3.82593
$731$		−	536.310i		−	0.733666i
$732$	1829.33	+	693.460i	2.49908	+	0.947350i
$733$	−1176.32			−1.60480			−0.802399	−	0.596787i	$-0.796444\pi$
$733$	−1176.32			−1.60480			−0.802399	+	0.596787i	$0.796444\pi$
$734$		−	1607.81i		−	2.19047i
$735$	−375.675	+	991.019i	−0.511122	+	1.34833i
$736$	−478.260			−0.649810
$737$			35.4899i			0.0481546i
$738$	1201.18	+	1063.51i	1.62761	+	1.44107i
$739$	381.466			0.516192			0.258096	−	0.966119i	$-0.416905\pi$
$739$	381.466			0.516192			0.258096	+	0.966119i	$0.416905\pi$
$740$		−	1032.00i		−	1.39459i
$741$	28.6750	+	10.8701i	0.0386978	+	0.0146695i
$742$	−13.6944			−0.0184561
$743$			27.8340i			0.0374616i	0.999825	+	0.0187308i	$0.00596255\pi$
$743$			27.8340i			0.0374616i	−0.999825	+	0.0187308i	$0.994037\pi$
$744$	543.203	−	1432.95i	0.730112	−	1.92601i
$745$	−985.724			−1.32312
$746$		−	2063.65i		−	2.76628i
$747$	7.51434	−	8.48703i	0.0100594	−	0.0113615i
$748$	−808.891			−1.08140
$749$			2.29976i			0.00307044i
$750$	136.538	+	51.7588i	0.182051	+	0.0690117i
$751$	−1300.01			−1.73104			−0.865521	−	0.500873i	$-0.833012\pi$
$751$	−1300.01			−1.73104			−0.865521	+	0.500873i	$0.833012\pi$
$752$		−	575.953i		−	0.765895i
$753$	207.078	−	546.264i	0.275003	−	0.725450i
$754$	167.709			0.222426
$755$			1249.54i			1.65502i
$756$	−9.68538	−	18.4339i	−0.0128114	−	0.0243835i
$757$	611.673			0.808022			0.404011	−	0.914754i	$-0.367616\pi$
$757$	611.673			0.808022			0.404011	+	0.914754i	$0.367616\pi$
$758$			797.518i			1.05213i
$759$	−357.782	−	135.628i	−0.471386	−	0.178693i
$760$	135.845			0.178744
$761$			279.692i			0.367532i	0.982970	+	0.183766i	$0.0588289\pi$
$761$			279.692i			0.367532i	−0.982970	+	0.183766i	$0.941171\pi$
$762$	562.676	−	1484.32i	0.738421	−	1.94793i
$763$	−5.56006			−0.00728710
$764$			1427.64i			1.86864i
$765$	−1234.67	−	1093.16i	−1.61395	−	1.42897i
$766$	−417.010			−0.544400
$767$			355.419i			0.463389i
$768$	1217.24	+	461.430i	1.58495	+	0.600820i
$769$	1333.43			1.73397			0.866987	−	0.498331i	$-0.166053\pi$
$769$	1333.43			1.73397			0.866987	+	0.498331i	$0.166053\pi$
$770$			11.0608i			0.0143646i
$771$	−98.2071	+	259.067i	−0.127376	+	0.336015i
$772$	845.375			1.09505
$773$		−	178.958i		−	0.231511i	−0.993278	−	0.115755i	$-0.963071\pi$
$773$		−	178.958i		−	0.231511i	0.993278	−	0.115755i	$-0.0369289\pi$
$774$	−424.115	+	479.015i	−0.547953	+	0.618882i
$775$	−1225.37			−1.58112
$776$		−	1175.86i		−	1.51528i
$777$	5.74280	+	2.17698i	0.00739099	+	0.00280177i
$778$	−815.982			−1.04882
$779$		−	88.5713i		−	0.113699i
$780$	−343.956	+	907.345i	−0.440969	+	1.16326i
$781$	536.651			0.687134
$782$			2517.20i			3.21892i
$783$	194.844	−	102.373i	0.248843	−	0.130745i
$784$	−418.493			−0.533792
$785$		−	37.4927i		−	0.0477614i
$786$	2258.68	+	856.219i	2.87364	+	1.08934i
$787$	18.3930			0.0233711			0.0116855	−	0.999932i	$-0.496280\pi$
$787$	18.3930			0.0233711			0.0116855	+	0.999932i	$0.496280\pi$
$788$		−	600.509i		−	0.762067i
$789$	−87.9861	+	232.105i	−0.111516	+	0.294176i
$790$	−3335.36			−4.22198
$791$			3.71664i			0.00469865i
$792$	328.891	+	291.197i	0.415267	+	0.367674i
$793$	542.530			0.684149
$794$		−	256.105i		−	0.322551i
$795$	783.120	+	296.865i	0.985056	+	0.373415i
$796$	−1297.52			−1.63005
$797$			284.802i			0.357343i	0.983909	+	0.178672i	$0.0571799\pi$
$797$			284.802i			0.357343i	−0.983909	+	0.178672i	$0.942820\pi$
$798$	−0.629491	+	1.66058i	−0.000788835	+	0.00208092i
$799$	1713.07			2.14401
$800$		−	439.044i		−	0.548805i
$801$	382.271	−	431.754i	0.477242	−	0.539019i
$802$	−969.428			−1.20876
$803$			498.601i			0.620923i
$804$	−168.596	−	63.9114i	−0.209697	−	0.0794918i
$805$	22.2817			0.0276791
$806$		−	933.546i		−	1.15825i
$807$	−138.435	+	365.187i	−0.171543	+	0.452525i
$808$	−452.489			−0.560011
$809$			450.001i			0.556243i	0.960546	+	0.278122i	$0.0897118\pi$
$809$			450.001i			0.556243i	−0.960546	+	0.278122i	$0.910288\pi$
$810$	238.289	+	1952.76i	0.294184	+	2.41082i
$811$	1166.06			1.43780			0.718900	−	0.695114i	$-0.244646\pi$
$811$	1166.06			1.43780			0.718900	+	0.695114i	$0.244646\pi$
$812$			6.28705i			0.00774267i
$813$	−80.9907	−	30.7019i	−0.0996196	−	0.0377638i
$814$	−284.602			−0.349634
$815$			734.524i			0.901257i
$816$	230.814	−	608.879i	0.282860	−	0.746176i
$817$	35.3211			0.0432327
$818$			411.956i			0.503614i
$819$	−4.32357	−	3.82804i	−0.00527908	−	0.00467405i
$820$	2802.60			3.41781
$821$		−	1240.49i		−	1.51095i	−0.655177	−	0.755475i	$-0.727406\pi$
$821$		−	1240.49i		−	1.51095i	0.655177	−	0.755475i	$-0.272594\pi$
$822$	1908.80	+	723.587i	2.32214	+	0.880276i
$823$	−580.249			−0.705041			−0.352520	−	0.935804i	$-0.614675\pi$
$823$	−580.249			−0.705041			−0.352520	+	0.935804i	$0.614675\pi$
$824$			714.705i			0.867360i
$825$	124.507	−	328.445i	0.150917	−	0.398115i
$826$	−20.5824			−0.0249182
$827$		−	303.742i		−	0.367282i	−0.982993	−	0.183641i	$-0.941212\pi$
$827$		−	303.742i		−	0.367282i	0.982993	−	0.183641i	$-0.0587883\pi$
$828$	1288.61	−	1455.41i	1.55629	−	1.75775i
$829$	210.136			0.253481			0.126740	−	0.991936i	$-0.459548\pi$
$829$	210.136			0.253481			0.126740	+	0.991936i	$0.459548\pi$
$830$		−	30.5896i		−	0.0368550i
$831$	877.638	+	332.694i	1.05612	+	0.400354i
$832$	543.219			0.652908
$833$		−	1244.73i		−	1.49427i
$834$	−834.587	+	2201.62i	−1.00070	+	2.63983i
$835$	337.990			0.404778
$836$		−	53.2732i		−	0.0637239i
$837$	−569.856	−	1084.59i	−0.680831	−	1.29581i
$838$	−1149.30			−1.37148
$839$			1303.18i			1.55325i	0.629963	+	0.776625i	$0.283070\pi$
$839$			1303.18i			1.55325i	−0.629963	+	0.776625i	$0.716930\pi$
$840$	−23.9198	−	9.06749i	−0.0284759	−	0.0107946i
$841$	774.547			0.920983
$842$		−	620.122i		−	0.736487i
$843$	244.077	−	643.868i	0.289534	−	0.763782i
$844$	−349.717			−0.414357
$845$		−	949.629i		−	1.12382i
$846$	−1530.06	−	1354.70i	−1.80858	−	1.60130i
$847$	−10.7349			−0.0126740
$848$			330.700i			0.389976i
$849$	−190.950	−	72.3851i	−0.224911	−	0.0852593i
$850$	−2310.79			−2.71858
$851$			573.325i			0.673708i
$852$	−966.419	+	2549.38i	−1.13429	+	2.99223i
$853$	591.411			0.693331			0.346665	−	0.937989i	$-0.387314\pi$
$853$	591.411			0.693331			0.346665	+	0.937989i	$0.387314\pi$
$854$			31.4180i			0.0367893i
$855$	71.9954	−	81.3148i	0.0842051	−	0.0951050i
$856$	246.472			0.287935
$857$			1248.43i			1.45674i	0.685182	+	0.728372i	$0.259723\pi$
$857$			1248.43i			1.45674i	−0.685182	+	0.728372i	$0.740277\pi$
$858$	250.225	+	94.8552i	0.291638	+	0.110554i
$859$	420.291			0.489279			0.244640	−	0.969614i	$-0.421330\pi$
$859$	420.291			0.489279			0.244640	+	0.969614i	$0.421330\pi$
$860$			1117.64i			1.29958i
$861$	−5.91202	+	15.5957i	−0.00686646	+	0.0181135i
$862$	−1902.12			−2.20664
$863$			1190.67i			1.37969i	0.723959	+	0.689843i	$0.242320\pi$
$863$			1190.67i			1.37969i	−0.723959	+	0.689843i	$0.757680\pi$
$864$	388.604	−	204.177i	0.449773	−	0.236316i
$865$	2313.68			2.67478
$866$			2116.73i			2.44426i
$867$	1000.30	+	379.191i	1.15374	+	0.437360i
$868$	34.9966			0.0403187
$869$			595.439i			0.685200i
$870$	210.536	−	555.388i	0.241996	−	0.638377i
$871$	−50.0012			−0.0574067
$872$			595.890i			0.683360i
$873$	−703.850	−	623.182i	−0.806242	−	0.713840i
$874$	−165.782			−0.189681
$875$			1.51802i			0.00173488i
$876$	−2368.63	−	897.897i	−2.70391	−	1.02500i
$877$	994.838			1.13436			0.567182	−	0.823592i	$-0.308033\pi$
$877$	994.838			1.13436			0.567182	+	0.823592i	$0.308033\pi$
$878$			583.618i			0.664712i
$879$	−221.499	+	584.308i	−0.251990	+	0.664742i
$880$	267.101			0.303524
$881$		−	964.002i		−	1.09421i	−0.837063	−	0.547107i	$-0.815729\pi$
$881$		−	964.002i		−	1.09421i	0.837063	−	0.547107i	$-0.184271\pi$
$882$	−984.336	+	1111.75i	−1.11603	+	1.26049i
$883$	−353.754			−0.400627			−0.200314	−	0.979732i	$-0.564196\pi$
$883$	−353.754			−0.400627			−0.200314	+	0.979732i	$0.564196\pi$
$884$		−	1139.63i		−	1.28918i
$885$	1177.01	+	446.182i	1.32996	+	0.504160i
$886$	849.126			0.958382
$887$		−	1509.93i		−	1.70229i	−0.524932	−	0.851144i	$-0.675909\pi$
$887$		−	1509.93i		−	1.70229i	0.524932	−	0.851144i	$-0.324091\pi$
$888$	233.314	−	615.474i	0.262741	−	0.693102i
$889$	16.5026			0.0185631
$890$		−	1556.16i		−	1.74850i
$891$	348.613	−	42.5401i	0.391260	−	0.0477443i
$892$	2603.46			2.91867
$893$			112.822i			0.126340i
$894$	−1291.39	−	489.538i	−1.44450	−	0.547582i
$895$	−1453.19			−1.62368
$896$			24.6270i			0.0274854i
$897$	191.084	−	504.074i	0.213026	−	0.561955i
$898$	−588.727			−0.655598
$899$			369.909i			0.411467i
$900$	1336.07	+	1182.95i	1.48453	+	1.31439i
$901$	−983.606			−1.09168
$902$		−	772.894i		−	0.856866i
$903$	−6.21938	−	2.35764i	−0.00688747	−	0.00261090i
$904$	398.324			0.440624
$905$			1934.12i			2.13715i
$906$	−620.555	+	1637.01i	−0.684940	+	1.80685i
$907$	674.481			0.743640			0.371820	−	0.928305i	$-0.378734\pi$
$907$	674.481			0.743640			0.371820	+	0.928305i	$0.378734\pi$
$908$		−	1135.00i		−	1.25000i
$909$	−239.811	+	270.853i	−0.263818	+	0.297968i
$910$	−15.5833			−0.0171245
$911$		−	674.294i		−	0.740169i	−0.928998	−	0.370084i	$-0.879329\pi$
$911$		−	674.294i		−	0.740169i	0.928998	−	0.370084i	$-0.120671\pi$
$912$	40.1005	+	15.2013i	0.0439699	+	0.0166681i
$913$	−5.46095			−0.00598133
$914$		−	2521.63i		−	2.75890i
$915$	681.074	−	1796.65i	0.744344	−	1.96356i
$916$	434.581			0.474433
$917$			25.1118i			0.0273847i
$918$	−1074.63	−	2045.32i	−1.17062	−	2.22801i
$919$	−203.147			−0.221052			−0.110526	−	0.993873i	$-0.535254\pi$
$919$	−203.147			−0.221052			−0.110526	+	0.993873i	$0.535254\pi$
$920$		−	2388.00i		−	2.59565i
$921$	−94.9785	−	36.0044i	−0.103125	−	0.0390927i
$922$	244.292			0.264959
$923$			756.080i			0.819155i
$924$	−3.55592	+	9.38040i	−0.00384840	+	0.0101520i
$925$	−526.314			−0.568988
$926$			1480.66i			1.59898i
$927$	427.811	+	378.780i	0.461501	+	0.408608i
$928$	−132.537			−0.142820
$929$			827.074i			0.890284i	0.895460	+	0.445142i	$0.146847\pi$
$929$			827.074i			0.890284i	−0.895460	+	0.445142i	$0.853153\pi$
$930$	−3091.55	−	1171.94i	−3.32424	−	1.26015i
$931$	81.9774			0.0880530
$932$		−	300.552i		−	0.322481i
$933$	−13.1414	+	34.6665i	−0.0140851	+	0.0371560i
$934$	−1201.21			−1.28609
$935$			794.444i			0.849672i
$936$	−410.264	+	463.370i	−0.438316	+	0.495054i
$937$	1701.42			1.81581			0.907906	−	0.419174i	$-0.137680\pi$
$937$	1701.42			1.81581			0.907906	+	0.419174i	$0.137680\pi$
$938$		−	2.89558i		−	0.00308697i
$939$	−1186.20	−	449.663i	−1.26325	−	0.478874i
$940$	−3569.95			−3.79782
$941$		−	1317.04i		−	1.39962i	−0.714331	−	0.699808i	$-0.753269\pi$
$941$		−	1317.04i		−	1.39962i	0.714331	−	0.699808i	$-0.246731\pi$
$942$	18.6199	−	49.1188i	0.0197664	−	0.0521431i
$943$	−1556.98			−1.65109
$944$			497.035i			0.526520i
$945$	−18.1047	+	9.51240i	−0.0191584	+	0.0100660i
$946$	308.220			0.325814
$947$		−	1119.52i		−	1.18218i	−0.806607	−	0.591088i	$-0.798699\pi$
$947$		−	1119.52i		−	1.18218i	0.806607	−	0.591088i	$-0.201301\pi$
$948$	−2828.65	−	1072.29i	−2.98381	−	1.13110i
$949$	−702.472			−0.740224
$950$		−	152.188i		−	0.160198i
$951$	400.165	−	1055.62i	0.420783	−	1.11001i
$952$	30.0435			0.0315583
$953$			913.020i			0.958048i	0.877802	+	0.479024i	$0.159009\pi$
$953$			913.020i			0.958048i	−0.877802	+	0.479024i	$0.840991\pi$
$954$	878.526	+	777.839i	0.920887	+	0.815345i
$955$	1402.15			1.46821
$956$			378.220i			0.395627i
$957$	−99.1495	−	37.5855i	−0.103605	−	0.0392743i
$958$	−421.787			−0.440279
$959$			21.2219i			0.0221292i
$960$	681.939	−	1798.93i	0.710353	−	1.87389i
$961$	1098.09			1.14265
$962$		−	400.972i		−	0.416810i
$963$	130.626	−	147.535i	0.135645	−	0.153203i
$964$	−690.181			−0.715955
$965$		−	830.277i		−	0.860390i
$966$	29.1910	+	11.0657i	0.0302184	+	0.0114552i
$967$	1055.04			1.09105			0.545525	−	0.838095i	$-0.316330\pi$
$967$	1055.04			1.09105			0.545525	+	0.838095i	$0.316330\pi$
$968$			1150.50i			1.18853i
$969$	−45.2135	+	119.272i	−0.0466599	+	0.123087i
$970$	−2536.87			−2.61533
$971$		−	1722.70i		−	1.77415i	−0.461625	−	0.887075i	$-0.652733\pi$
$971$		−	1722.70i		−	1.77415i	0.461625	−	0.887075i	$-0.347267\pi$
$972$	−425.704	+	1732.71i	−0.437967	+	1.78262i
$973$	−24.4774			−0.0251566
$974$			3009.07i			3.08939i
$975$	462.741	+	175.416i	0.474606	+	0.179913i
$976$	758.700			0.777357
$977$		−	474.230i		−	0.485394i	−0.970102	−	0.242697i	$-0.921968\pi$
$977$		−	474.230i		−	0.485394i	0.970102	−	0.242697i	$-0.0780321\pi$
$978$	−364.786	+	962.293i	−0.372991	+	0.983940i
$979$	−277.811			−0.283770
$980$			2593.96i			2.64689i
$981$	356.690	+	315.810i	0.363599	+	0.321927i
$982$	−614.716			−0.625983
$983$		−	1230.01i		−	1.25129i	−0.780110	−	0.625643i	$-0.784837\pi$
$983$		−	1230.01i		−	1.25129i	0.780110	−	0.625643i	$-0.215163\pi$
$984$	1671.44	+	633.610i	1.69862	+	0.643913i
$985$	−589.784			−0.598765
$986$			697.573i			0.707478i
$987$	7.53072	−	19.8658i	0.00762991	−	0.0201275i
$988$	75.0559			0.0759675
$989$		−	620.904i		−	0.627810i
$990$	628.249	−	709.572i	0.634594	−	0.716739i
$991$	−681.272			−0.687459			−0.343730	−	0.939069i	$-0.611690\pi$
$991$	−681.272			−0.687459			−0.343730	+	0.939069i	$0.611690\pi$
$992$			737.761i			0.743711i
$993$	−1648.49	−	624.908i	−1.66011	−	0.629313i
$994$	−43.7847			−0.0440490
$995$			1274.34i			1.28075i
$996$	9.83426	−	25.9425i	0.00987375	−	0.0260466i
$997$	672.795			0.674820			0.337410	−	0.941358i	$-0.390449\pi$
$997$	672.795			0.674820			0.337410	+	0.941358i	$0.390449\pi$
$998$		−	1365.43i		−	1.36816i
$999$	−244.762	−	465.848i	−0.245007	−	0.466314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.5	✓	44
3.2	odd	2	inner	201.3.c.a.68.40	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.5	✓	44	1.1	even	1	trivial
201.3.c.a.68.40	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)

\(f(q)\)	\(=\)	\(q-3.36787i q^{2} +(-2.80521 - 1.06340i) q^{3} -7.34253 q^{4} +7.21139i q^{5} +(-3.58138 + 9.44756i) q^{6} -0.105037 q^{7} +11.2572i q^{8} +(6.73838 + 5.96610i) q^{9} +O(q^{10})\)	\(q-3.36787i q^{2} +(-2.80521 - 1.06340i) q^{3} -7.34253 q^{4} +7.21139i q^{5} +(-3.58138 + 9.44756i) q^{6} -0.105037 q^{7} +11.2572i q^{8} +(6.73838 + 5.96610i) q^{9} +24.2870 q^{10} -4.33578i q^{11} +(20.5973 + 7.80802i) q^{12} +6.10862 q^{13} +0.353752i q^{14} +(7.66856 - 20.2294i) q^{15} +8.54259 q^{16} +25.4084i q^{17} +(20.0930 - 22.6940i) q^{18} -1.67338 q^{19} -52.9498i q^{20} +(0.294651 + 0.111696i) q^{21} -14.6023 q^{22} +29.4161i q^{23} +(11.9709 - 31.5787i) q^{24} -27.0041 q^{25} -20.5730i q^{26} +(-12.5582 - 23.9017i) q^{27} +0.771239 q^{28} +8.15188i q^{29} +(-68.1300 - 25.8267i) q^{30} +45.3772 q^{31} +16.2584i q^{32} +(-4.61066 + 12.1628i) q^{33} +85.5720 q^{34} -0.757464i q^{35} +(-49.4767 - 43.8062i) q^{36} +19.4902 q^{37} +5.63573i q^{38} +(-17.1360 - 6.49589i) q^{39} -81.1799 q^{40} +52.9294i q^{41} +(0.376178 - 0.992346i) q^{42} -21.1076 q^{43} +31.8356i q^{44} +(-43.0238 + 48.5930i) q^{45} +99.0696 q^{46} -67.4214i q^{47} +(-23.9637 - 9.08416i) q^{48} -48.9890 q^{49} +90.9461i q^{50} +(27.0192 - 71.2757i) q^{51} -44.8527 q^{52} +38.7119i q^{53} +(-80.4977 + 42.2944i) q^{54} +31.2670 q^{55} -1.18242i q^{56} +(4.69419 + 1.77947i) q^{57} +27.4545 q^{58} +58.1832i q^{59} +(-56.3066 + 148.535i) q^{60} +88.8138 q^{61} -152.824i q^{62} +(-0.707781 - 0.626662i) q^{63} +88.9266 q^{64} +44.0516i q^{65} +(40.9626 + 15.5281i) q^{66} -8.18535 q^{67} -186.562i q^{68} +(31.2810 - 82.5184i) q^{69} -2.55104 q^{70} +123.773i q^{71} +(-67.1614 + 75.8551i) q^{72} -114.997 q^{73} -65.6402i q^{74} +(75.7520 + 28.7160i) q^{75} +12.2869 q^{76} +0.455419i q^{77} +(-21.8773 + 57.7116i) q^{78} -137.331 q^{79} +61.6039i q^{80} +(9.81140 + 80.4036i) q^{81} +178.259 q^{82} -1.25951i q^{83} +(-2.16348 - 0.820133i) q^{84} -183.230 q^{85} +71.0876i q^{86} +(8.66869 - 22.8677i) q^{87} +48.8087 q^{88} -64.0739i q^{89} +(163.655 + 144.898i) q^{90} -0.641633 q^{91} -215.989i q^{92} +(-127.292 - 48.2539i) q^{93} -227.066 q^{94} -12.0674i q^{95} +(17.2892 - 45.6083i) q^{96} -104.454 q^{97} +164.988i q^{98} +(25.8677 - 29.2161i) 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