LMFDB - Embedded newform 211.3.e.a.15.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [211,3,Mod(15,211)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(211, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("211.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 211 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	211.e (of order $6$, degree $2$, 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:	$5.74933357800$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			15.3
Character	$\chi$	$=$	211.15
Dual form			211.3.e.a.197.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.96716 + 1.71309i) q^{2} +(-2.59992 + 1.50106i) q^{3} +(3.86935 - 6.70190i) q^{4} +5.80352 q^{5} +(5.14291 - 8.90778i) q^{6} +(-3.19116 + 1.84241i) q^{7} +12.8094i q^{8} +(0.00637874 - 0.0110483i) q^{9} +O(q^{10})$	\(q+(-2.96716 + 1.71309i) q^{2} +(-2.59992 + 1.50106i) q^{3} +(3.86935 - 6.70190i) q^{4} +5.80352 q^{5} +(5.14291 - 8.90778i) q^{6} +(-3.19116 + 1.84241i) q^{7} +12.8094i q^{8} +(0.00637874 - 0.0110483i) q^{9} +(-17.2200 + 9.94195i) q^{10} +3.36905 q^{11} +23.2325i q^{12} -16.3775 q^{13} +(6.31244 - 10.9335i) q^{14} +(-15.0887 + 8.71145i) q^{15} +(-6.46629 - 11.2000i) q^{16} +(-18.3899 + 10.6174i) q^{17} +0.0437094i q^{18} +(7.78756 + 13.4885i) q^{19} +(22.4558 - 38.8947i) q^{20} +(5.53116 - 9.58025i) q^{21} +(-9.99651 + 5.77149i) q^{22} -27.9752i q^{23} +(-19.2277 - 33.3034i) q^{24} +8.68090 q^{25} +(48.5947 - 28.0562i) q^{26} -26.9808i q^{27} +28.5158i q^{28} +(-15.0581 - 8.69377i) q^{29} +(29.8470 - 51.6965i) q^{30} +(32.6640 - 18.8586i) q^{31} +(-6.00013 - 3.46417i) q^{32} +(-8.75926 + 5.05716i) q^{33} +(36.3771 - 63.0070i) q^{34} +(-18.5200 + 10.6925i) q^{35} +(-0.0493631 - 0.0854995i) q^{36} +(-1.44396 - 2.50101i) q^{37} +(-46.2138 - 26.6816i) q^{38} +(42.5803 - 24.5837i) q^{39} +74.3398i q^{40} +(-47.6543 - 27.5132i) q^{41} +37.9015i q^{42} +(-25.6148 + 44.3662i) q^{43} +(13.0360 - 22.5791i) q^{44} +(0.0370192 - 0.0641191i) q^{45} +(47.9240 + 83.0068i) q^{46} +(-3.93527 - 6.81609i) q^{47} +(33.6237 + 19.4126i) q^{48} +(-17.7110 + 30.6764i) q^{49} +(-25.7576 + 14.8712i) q^{50} +(31.8748 - 55.2087i) q^{51} +(-63.3704 + 109.761i) q^{52} +(-16.3678 - 28.3498i) q^{53} +(46.2206 + 80.0564i) q^{54} +19.5524 q^{55} +(-23.6003 - 40.8769i) q^{56} +(-40.4940 - 23.3792i) q^{57} +59.5728 q^{58} +(-20.7864 - 36.0031i) q^{59} +134.831i q^{60} +(-60.0543 - 34.6723i) q^{61} +(-64.6128 + 111.913i) q^{62} +0.0470092i q^{63} +75.4681 q^{64} -95.0475 q^{65} +(17.3267 - 30.0108i) q^{66} -69.7008i q^{67} +164.330i q^{68} +(41.9925 + 72.7332i) q^{69} +(36.6344 - 63.4526i) q^{70} +31.7552 q^{71} +(0.141522 + 0.0817080i) q^{72} +(-22.6393 + 39.2124i) q^{73} +(8.56890 + 4.94726i) q^{74} +(-22.5696 + 13.0306i) q^{75} +120.531 q^{76} +(-10.7512 + 6.20719i) q^{77} +(-84.2282 + 145.888i) q^{78} -13.3548 q^{79} +(-37.5273 - 64.9992i) q^{80} +(40.5573 + 70.2474i) q^{81} +188.530 q^{82} +(-53.6861 - 92.9871i) q^{83} +(-42.8039 - 74.1386i) q^{84} +(-106.726 + 61.6184i) q^{85} -175.522i q^{86} +52.1996 q^{87} +43.1556i q^{88} -34.3851i q^{89} +0.253669i q^{90} +(52.2633 - 30.1742i) q^{91} +(-187.487 - 108.246i) q^{92} +(-56.6158 + 98.0614i) q^{93} +(23.3531 + 13.4829i) q^{94} +(45.1953 + 78.2806i) q^{95} +20.7998 q^{96} +86.7468i q^{97} -121.362i q^{98} +(0.0214903 - 0.0372223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} + 55 q^{4} - 4 q^{5} - q^{6} - 24 q^{7} + 82 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 + 55 * q^4 - 4 * q^5 - q^6 - 24 * q^7 + 82 * q^9	$ 68 q - 3 q^{2} + 55 q^{4} - 4 q^{5} - q^{6} - 24 q^{7} + 82 q^{9} + 4 q^{11} + 32 q^{13} + 12 q^{14} - 73 q^{16} + 51 q^{17} - 8 q^{19} - 46 q^{20} - 32 q^{21} - 33 q^{22} + 32 q^{24} + 252 q^{25} + 42 q^{26} - 60 q^{29} + 32 q^{30} + 126 q^{31} - 78 q^{32} - 117 q^{33} - 50 q^{34} - 45 q^{35} - 12 q^{36} + 113 q^{37} + 33 q^{38} - 162 q^{39} - 75 q^{41} + 13 q^{43} + 15 q^{44} + 83 q^{45} + 79 q^{46} - 117 q^{47} + 3 q^{48} + 130 q^{49} - 90 q^{50} - 181 q^{51} - 22 q^{52} - 140 q^{53} + 125 q^{54} - 50 q^{55} - 75 q^{56} - 234 q^{57} - 70 q^{58} - 84 q^{59} - 366 q^{61} - 75 q^{62} + 142 q^{64} + 72 q^{65} + 144 q^{66} + 130 q^{69} - 466 q^{70} + 402 q^{71} + 450 q^{72} - 54 q^{73} - 330 q^{74} - 402 q^{75} + 10 q^{76} + 69 q^{77} + 316 q^{78} - 370 q^{79} - 13 q^{80} - 206 q^{81} + 88 q^{82} - 105 q^{83} + 216 q^{84} - 168 q^{85} - 346 q^{87} + 264 q^{91} + 534 q^{92} + 310 q^{93} - 537 q^{94} + 265 q^{95} + 80 q^{96} - 50 q^{99}+O(q^{100}) $ 68 * q - 3 * q^2 + 55 * q^4 - 4 * q^5 - q^6 - 24 * q^7 + 82 * q^9 + 4 * q^11 + 32 * q^13 + 12 * q^14 - 73 * q^16 + 51 * q^17 - 8 * q^19 - 46 * q^20 - 32 * q^21 - 33 * q^22 + 32 * q^24 + 252 * q^25 + 42 * q^26 - 60 * q^29 + 32 * q^30 + 126 * q^31 - 78 * q^32 - 117 * q^33 - 50 * q^34 - 45 * q^35 - 12 * q^36 + 113 * q^37 + 33 * q^38 - 162 * q^39 - 75 * q^41 + 13 * q^43 + 15 * q^44 + 83 * q^45 + 79 * q^46 - 117 * q^47 + 3 * q^48 + 130 * q^49 - 90 * q^50 - 181 * q^51 - 22 * q^52 - 140 * q^53 + 125 * q^54 - 50 * q^55 - 75 * q^56 - 234 * q^57 - 70 * q^58 - 84 * q^59 - 366 * q^61 - 75 * q^62 + 142 * q^64 + 72 * q^65 + 144 * q^66 + 130 * q^69 - 466 * q^70 + 402 * q^71 + 450 * q^72 - 54 * q^73 - 330 * q^74 - 402 * q^75 + 10 * q^76 + 69 * q^77 + 316 * q^78 - 370 * q^79 - 13 * q^80 - 206 * q^81 + 88 * q^82 - 105 * q^83 + 216 * q^84 - 168 * q^85 - 346 * q^87 + 264 * q^91 + 534 * q^92 + 310 * q^93 - 537 * q^94 + 265 * q^95 + 80 * q^96 - 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/211\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.96716	+	1.71309i	−1.48358	+	0.856544i	−0.999826	−	0.0186605i	$-0.994060\pi$
$2$	−2.96716	+	1.71309i	−1.48358	+	0.856544i	−0.483752	+	0.875205i	$0.660727\pi$
$3$	−2.59992	+	1.50106i	−0.866639	+	0.500354i	−0.866230	−	0.499646i	$-0.833464\pi$
$3$	−2.59992	+	1.50106i	−0.866639	+	0.500354i	−0.000409100		1.00000i	$0.500130\pi$
$4$	3.86935	−	6.70190i	0.967337	−	1.67548i
$5$	5.80352			1.16070			0.580352	−	0.814365i	$-0.302915\pi$
$5$	5.80352			1.16070			0.580352	+	0.814365i	$0.302915\pi$
$6$	5.14291	−	8.90778i	0.857151	−	1.48463i
$7$	−3.19116	+	1.84241i	−0.455879	+	0.263202i	−0.710310	−	0.703889i	$-0.751445\pi$
$7$	−3.19116	+	1.84241i	−0.455879	+	0.263202i	0.254431	+	0.967091i	$0.418112\pi$
$8$			12.8094i			1.60118i
$9$	0.00637874	−	0.0110483i	0.000708749	−	0.00122759i
$10$	−17.2200	+	9.94195i	−1.72200	+	0.994195i
$11$	3.36905			0.306277			0.153139	−	0.988205i	$-0.451062\pi$
$11$	3.36905			0.306277			0.153139	+	0.988205i	$0.451062\pi$
$12$			23.2325i			1.93604i
$13$	−16.3775			−1.25981			−0.629906	−	0.776672i	$-0.716906\pi$
$13$	−16.3775			−1.25981			−0.629906	+	0.776672i	$0.716906\pi$
$14$	6.31244	−	10.9335i	0.450889	−	0.780962i
$15$	−15.0887	+	8.71145i	−1.00591	+	0.580764i
$16$	−6.46629	−	11.2000i	−0.404143	−	0.699997i
$17$	−18.3899	+	10.6174i	−1.08176	+	0.624553i	−0.931370	−	0.364074i	$-0.881386\pi$
$17$	−18.3899	+	10.6174i	−1.08176	+	0.624553i	−0.150388	+	0.988627i	$0.548052\pi$
$18$			0.0437094i			0.00242830i
$19$	7.78756	+	13.4885i	0.409872	+	0.709918i	0.994875	−	0.101112i	$-0.0322402\pi$
$19$	7.78756	+	13.4885i	0.409872	+	0.709918i	−0.585003	+	0.811031i	$0.698907\pi$
$20$	22.4558	−	38.8947i	1.12279	−	1.94473i
$21$	5.53116	−	9.58025i	0.263389	−	0.456202i
$22$	−9.99651	+	5.77149i	−0.454387	+	0.262340i
$23$		−	27.9752i		−	1.21631i	−0.793817	−	0.608157i	$-0.791909\pi$
$23$		−	27.9752i		−	1.21631i	0.793817	−	0.608157i	$-0.208091\pi$
$24$	−19.2277	−	33.3034i	−0.801156	−	1.38764i
$25$	8.68090			0.347236
$26$	48.5947	−	28.0562i	1.86903	−	1.07908i
$27$		−	26.9808i		−	0.999290i
$28$			28.5158i			1.01842i
$29$	−15.0581	−	8.69377i	−0.519243	−	0.299785i	0.217382	−	0.976087i	$-0.430248\pi$
$29$	−15.0581	−	8.69377i	−0.519243	−	0.299785i	−0.736625	+	0.676301i	$0.763582\pi$
$30$	29.8470	−	51.6965i	0.994900	−	1.72322i
$31$	32.6640	−	18.8586i	1.05368	−	0.608341i	0.130000	−	0.991514i	$-0.458502\pi$
$31$	32.6640	−	18.8586i	1.05368	−	0.608341i	0.923676	+	0.383173i	$0.125169\pi$
$32$	−6.00013	−	3.46417i	−0.187504	−	0.108255i
$33$	−8.75926	+	5.05716i	−0.265432	+	0.153247i
$34$	36.3771	−	63.0070i	1.06992	−	1.85315i
$35$	−18.5200	+	10.6925i	−0.529141	+	0.305500i
$36$	−0.0493631	−	0.0854995i	−0.00137120	−	0.00237499i
$37$	−1.44396	−	2.50101i	−0.0390259	−	0.0675949i	0.845853	−	0.533417i	$-0.179092\pi$
$37$	−1.44396	−	2.50101i	−0.0390259	−	0.0675949i	−0.884879	+	0.465822i	$0.845759\pi$
$38$	−46.2138	−	26.6816i	−1.21615	−	0.702146i
$39$	42.5803	−	24.5837i	1.09180	−	0.630352i
$40$			74.3398i			1.85850i
$41$	−47.6543	−	27.5132i	−1.16230	−	0.671055i	−0.210446	−	0.977605i	$-0.567492\pi$
$41$	−47.6543	−	27.5132i	−1.16230	−	0.671055i	−0.951854	+	0.306551i	$0.900825\pi$
$42$			37.9015i			0.902416i
$43$	−25.6148	+	44.3662i	−0.595694	+	1.03177i	0.397754	+	0.917492i	$0.369790\pi$
$43$	−25.6148	+	44.3662i	−0.595694	+	1.03177i	−0.993449	+	0.114281i	$0.963544\pi$
$44$	13.0360	−	22.5791i	0.296273	−	0.513161i
$45$	0.0370192	−	0.0641191i	0.000822649	−	0.00142487i
$46$	47.9240	+	83.0068i	1.04183	+	1.80450i
$47$	−3.93527	−	6.81609i	−0.0837292	−	0.145023i	0.821120	−	0.570756i	$-0.193350\pi$
$47$	−3.93527	−	6.81609i	−0.0837292	−	0.145023i	−0.904849	+	0.425733i	$0.860016\pi$
$48$	33.6237	+	19.4126i	0.700493	+	0.404430i
$49$	−17.7110	+	30.6764i	−0.361449	+	0.626049i
$50$	−25.7576	+	14.8712i	−0.515152	+	0.297423i
$51$	31.8748	−	55.2087i	0.624996	−	1.08252i
$52$	−63.3704	+	109.761i	−1.21866	+	2.11078i
$53$	−16.3678	−	28.3498i	−0.308826	−	0.534902i	0.669280	−	0.743010i	$-0.266603\pi$
$53$	−16.3678	−	28.3498i	−0.308826	−	0.534902i	−0.978106	+	0.208108i	$0.933269\pi$
$54$	46.2206	+	80.0564i	0.855936	+	1.48253i
$55$	19.5524			0.355498
$56$	−23.6003	−	40.8769i	−0.421433	−	0.729944i
$57$	−40.4940	−	23.3792i	−0.710421	−	0.410162i
$58$	59.5728			1.02712
$59$	−20.7864	−	36.0031i	−0.352312	−	0.610222i	0.634342	−	0.773052i	$-0.281271\pi$
$59$	−20.7864	−	36.0031i	−0.352312	−	0.610222i	−0.986654	+	0.162831i	$0.947938\pi$
$60$			134.831i			2.24718i
$61$	−60.0543	−	34.6723i	−0.984496	−	0.568399i	−0.0808716	−	0.996725i	$-0.525770\pi$
$61$	−60.0543	−	34.6723i	−0.984496	−	0.568399i	−0.903625	+	0.428325i	$0.859104\pi$
$62$	−64.6128	+	111.913i	−1.04214	+	1.80504i
$63$			0.0470092i			0.000746177i
$64$	75.4681			1.17919
$65$	−95.0475			−1.46227
$66$	17.3267	−	30.0108i	0.262526	−	0.454709i
$67$		−	69.7008i		−	1.04031i	−0.854072	−	0.520156i	$-0.825874\pi$
$67$		−	69.7008i		−	1.04031i	0.854072	−	0.520156i	$-0.174126\pi$
$68$			164.330i			2.41661i
$69$	41.9925	+	72.7332i	0.608588	+	1.05410i
$70$	36.6344	−	63.4526i	0.523349	−	0.906466i
$71$	31.7552			0.447257			0.223628	−	0.974675i	$-0.428210\pi$
$71$	31.7552			0.447257			0.223628	+	0.974675i	$0.428210\pi$
$72$	0.141522	+	0.0817080i	0.00196559	+	0.00113483i
$73$	−22.6393	+	39.2124i	−0.310127	+	0.537156i	−0.978390	−	0.206769i	$-0.933705\pi$
$73$	−22.6393	+	39.2124i	−0.310127	+	0.537156i	0.668262	+	0.743926i	$0.267038\pi$
$74$	8.56890	+	4.94726i	0.115796	+	0.0668548i
$75$	−22.5696	+	13.0306i	−0.300928	+	0.173741i
$76$	120.531			1.58594
$77$	−10.7512	+	6.20719i	−0.139626	+	0.0806129i
$78$	−84.2282	+	145.888i	−1.07985	+	1.87035i
$79$	−13.3548			−0.169048			−0.0845242	−	0.996421i	$-0.526937\pi$
$79$	−13.3548			−0.169048			−0.0845242	+	0.996421i	$0.526937\pi$
$80$	−37.5273	−	64.9992i	−0.469091	−	0.812490i
$81$	40.5573	+	70.2474i	0.500708	+	0.867251i
$82$	188.530			2.29915
$83$	−53.6861	−	92.9871i	−0.646821	−	1.12033i	−0.983878	−	0.178842i	$-0.942765\pi$
$83$	−53.6861	−	92.9871i	−0.646821	−	1.12033i	0.337057	−	0.941484i	$-0.390569\pi$
$84$	−42.8039	−	74.1386i	−0.509571	−	0.882602i
$85$	−106.726	+	61.6184i	−1.25560	+	0.724922i
$86$		−	175.522i		−	2.04095i
$87$	52.1996			0.599995
$88$			43.1556i			0.490405i
$89$		−	34.3851i		−	0.386350i	−0.981164	−	0.193175i	$-0.938122\pi$
$89$		−	34.3851i		−	0.386350i	0.981164	−	0.193175i	$-0.0618784\pi$
$90$			0.253669i			0.00281854i
$91$	52.2633	−	30.1742i	0.574322	−	0.331585i
$92$	−187.487	−	108.246i	−2.03790	−	1.17658i
$93$	−56.6158	+	98.0614i	−0.608772	+	1.05442i
$94$	23.3531	+	13.4829i	0.248438	+	0.143436i
$95$	45.1953	+	78.2806i	0.475740	+	0.824006i
$96$	20.7998			0.216664
$97$			86.7468i			0.894297i	0.894460	+	0.447149i	$0.147560\pi$
$97$			86.7468i			0.894297i	−0.894460	+	0.447149i	$0.852440\pi$
$98$		−	121.362i		−	1.23839i
$99$	0.0214903	−	0.0372223i	0.000217074	−	0.000375983i
$100$	33.5894	−	58.1786i	0.335894	−	0.581786i
$101$	2.94836	+	5.10672i	0.0291917	+	0.0505615i	0.880252	−	0.474506i	$-0.157373\pi$
$101$	2.94836	+	5.10672i	0.0291917	+	0.0505615i	−0.851060	+	0.525068i	$0.824040\pi$
$102$			218.417i			2.14135i
$103$	−54.6122	+	94.5911i	−0.530215	+	0.918360i	0.469163	+	0.883111i	$0.344556\pi$
$103$	−54.6122	+	94.5911i	−0.530215	+	0.918360i	−0.999379	+	0.0352484i	$0.988778\pi$
$104$		−	209.787i		−	2.01718i
$105$	32.1002	−	55.5992i	0.305716	−	0.529516i
$106$	97.1314	+	56.0789i	0.916334	+	0.529046i
$107$	201.727			1.88530			0.942650	−	0.333782i	$-0.108325\pi$
$107$	201.727			1.88530			0.942650	+	0.333782i	$0.108325\pi$
$108$	−180.823	−	104.398i	−1.67429	−	0.966650i
$109$	107.580			0.986973			0.493486	−	0.869754i	$-0.335722\pi$
$109$	107.580			0.986973			0.493486	+	0.869754i	$0.335722\pi$
$110$	−58.0150	+	33.4950i	−0.527409	+	0.304500i
$111$	7.50835	+	4.33495i	0.0676427	+	0.0390536i
$112$	41.2699	+	23.8272i	0.368481	+	0.212743i
$113$	4.83787			0.0428130			0.0214065	−	0.999771i	$-0.493186\pi$
$113$	4.83787			0.0428130			0.0214065	+	0.999771i	$0.493186\pi$
$114$	160.203			1.40529
$115$		−	162.355i		−	1.41178i
$116$	−116.530	+	67.2784i	−1.00457	+	0.579986i
$117$	−0.104468	+	0.180944i	−0.000892890	+	0.00154653i
$118$	123.353	+	71.2178i	1.04536	+	0.603541i
$119$	39.1233	−	67.7636i	0.328767	−	0.569442i
$120$	−111.589	−	193.277i	−0.929906	−	1.61064i
$121$	−109.649			−0.906194
$122$	237.587			1.94744
$123$	165.196			1.34306
$124$		−	291.881i		−	2.35388i
$125$	−94.7083			−0.757666
$126$	−0.0805309	−	0.139484i	−0.000639134	−	0.00110701i
$127$	−136.224	+	78.6492i	−1.07263	+	0.619285i	−0.928900	−	0.370332i	$-0.879244\pi$
$127$	−136.224	+	78.6492i	−1.07263	+	0.619285i	−0.143733	+	0.989616i	$0.545911\pi$
$128$	−199.925	+	115.427i	−1.56192	+	0.901772i
$129$		−	153.798i		−	1.19223i
$130$	282.021	−	162.825i	2.16939	−	1.25250i
$131$	−54.4545	+	31.4393i	−0.415683	+	0.239995i	−0.693229	−	0.720718i	$-0.743812\pi$
$131$	−54.4545	+	31.4393i	−0.415683	+	0.239995i	0.277546	+	0.960712i	$0.410479\pi$
$132$			78.2716i			0.592967i
$133$	−49.7026	−	28.6958i	−0.373704	−	0.215758i
$134$	119.404	+	206.813i	0.891073	+	1.54338i
$135$		−	156.584i		−	1.15988i
$136$	−136.003	−	235.564i	−1.00002	−	1.73209i
$137$	−109.669	+	189.953i	−0.800507	+	1.38652i	0.118776	+	0.992921i	$0.462103\pi$
$137$	−109.669	+	189.953i	−0.800507	+	1.38652i	−0.919283	+	0.393598i	$0.871230\pi$
$138$	−249.197	−	143.874i	−1.80577	−	1.04256i
$139$	−124.060	+	214.878i	−0.892516	+	1.54588i	−0.0556659	+	0.998449i	$0.517728\pi$
$139$	−124.060	+	214.878i	−0.892516	+	1.54588i	−0.836850	+	0.547433i	$0.815605\pi$
$140$			165.492i			1.18209i
$141$	20.4628	+	11.8142i	0.145126	+	0.0837885i
$142$	−94.2227	+	54.3995i	−0.663540	+	0.383095i
$143$	−55.1768			−0.385852
$144$	−0.164987			−0.00114575
$145$	−87.3898	−	50.4545i	−0.602688	−	0.347962i
$146$		−	155.132i		−	1.06255i
$147$		−	106.341i		−	0.723411i
$148$	−22.3487			−0.151005
$149$	−100.290	−	57.9025i	−0.673088	−	0.388608i	0.124158	−	0.992263i	$-0.460377\pi$
$149$	−100.290	−	57.9025i	−0.673088	−	0.388608i	−0.797246	+	0.603655i	$0.793711\pi$
$150$	44.6451	−	77.3275i	0.297634	−	0.515517i
$151$	−39.7723			−0.263393			−0.131696	−	0.991290i	$-0.542042\pi$
$151$	−39.7723			−0.263393			−0.131696	+	0.991290i	$0.542042\pi$
$152$	−172.779	+	99.7542i	−1.13671	+	0.656277i
$153$			0.270903i			0.00177061i
$154$	21.2669	−	36.8354i	0.138097	−	0.239191i
$155$	189.566	−	109.446i	1.22301	−	0.706104i
$156$		−	380.492i		−	2.43905i
$157$	145.086	−	83.7657i	0.924117	−	0.533539i	0.0391709	−	0.999233i	$-0.487528\pi$
$157$	145.086	−	83.7657i	0.924117	−	0.533539i	0.884946	+	0.465693i	$0.154195\pi$
$158$	39.6258	−	22.8780i	0.250796	−	0.144797i
$159$	85.1097	+	49.1381i	0.535281	+	0.309045i
$160$	−34.8219	−	20.1044i	−0.217637	−	0.125653i
$161$	51.5419	+	89.2732i	0.320136	+	0.554492i
$162$	−240.680	−	138.957i	−1.48568	−	0.857757i
$163$	−17.2640	+	29.9022i	−0.105914	+	0.183449i	−0.914111	−	0.405463i	$-0.867110\pi$
$163$	−17.2640	+	29.9022i	−0.105914	+	0.183449i	0.808197	+	0.588912i	$0.200444\pi$
$164$	−368.782	+	212.916i	−2.24867	+	1.29827i
$165$	−50.8346	+	29.3493i	−0.308088	+	0.177875i
$166$	318.590	+	183.938i	1.91922	+	1.10806i
$167$	165.816	+	95.7340i	0.992911	+	0.573258i	0.906143	−	0.422971i	$-0.139013\pi$
$167$	165.816	+	95.7340i	0.992911	+	0.573258i	0.0867680	+	0.996229i	$0.472346\pi$
$168$	122.717	+	70.8510i	0.730461	+	0.421732i
$169$	99.2239			0.587124
$170$	211.116	−	365.663i	1.24186	−	2.15096i
$171$	0.198699			0.00116199
$172$	198.225	+	343.337i	1.15247	+	1.99614i
$173$	86.9870	−	150.666i	0.502815	−	0.870901i	−0.497180	−	0.867648i	$-0.665631\pi$
$173$	86.9870	−	150.666i	0.502815	−	0.870901i	0.999995	−	0.00325353i	$-0.00103563\pi$
$174$	−154.884	+	89.4225i	−0.890140	+	0.513923i
$175$	−27.7021	+	15.9938i	−0.158298	+	0.0913932i
$176$	−21.7853	−	37.7332i	−0.123780	−	0.214393i
$177$	108.086	+	62.4033i	0.610654	+	0.352561i
$178$	58.9048	+	102.026i	0.330926	+	0.573180i
$179$	−159.040	+	275.466i	−0.888493	+	1.53891i	−0.0468350	+	0.998903i	$0.514914\pi$
$179$	−159.040	+	275.466i	−0.888493	+	1.53891i	−0.841658	+	0.540012i	$0.818420\pi$
$180$	−0.286480	−	0.496198i	−0.00159156	−	0.00275666i
$181$	−129.378	−	74.6965i	−0.714796	−	0.412688i	0.0980380	−	0.995183i	$-0.468743\pi$
$181$	−129.378	−	74.6965i	−0.714796	−	0.412688i	−0.812834	+	0.582495i	$0.802077\pi$
$182$	−103.382	+	179.063i	−0.568034	+	0.983864i
$183$	208.181			1.13760
$184$	358.346			1.94753
$185$	−8.38005	−	14.5147i	−0.0452976	−	0.0784577i
$186$		−	387.951i		−	2.08576i
$187$	−61.9565	+	35.7706i	−0.331318	+	0.191287i
$188$	−60.9077			−0.323977
$189$	49.7099	+	86.1000i	0.263015	+	0.455556i
$190$	−268.203	−	154.847i	−1.41160	−	0.814985i
$191$	−67.1172	−	38.7501i	−0.351399	−	0.202880i	0.313902	−	0.949455i	$-0.398364\pi$
$191$	−67.1172	−	38.7501i	−0.351399	−	0.202880i	−0.665301	+	0.746575i	$0.731697\pi$
$192$	−196.211	+	113.282i	−1.02193	+	0.590012i
$193$	320.356			1.65988			0.829938	−	0.557856i	$-0.188376\pi$
$193$	320.356			1.65988			0.829938	+	0.557856i	$0.188376\pi$
$194$	−148.605	−	257.391i	−0.766005	−	1.32676i
$195$	247.116	−	142.672i	1.26726	−	0.731652i
$196$	137.060	+	237.395i	0.699286	+	1.21120i
$197$	295.381	+	170.538i	1.49940	+	0.865676i	1.00000		0.000697422i	$-0.000221996\pi$
$197$	295.381	+	170.538i	1.49940	+	0.865676i	0.499396	+	0.866374i	$0.333555\pi$
$198$			0.147259i			0.000743734i
$199$	55.4179			0.278482			0.139241	−	0.990259i	$-0.455534\pi$
$199$	55.4179			0.278482			0.139241	+	0.990259i	$0.455534\pi$
$200$			111.197i			0.555987i
$201$	104.625	+	181.216i	0.520524	+	0.901574i
$202$	−17.4965	−	10.1016i	−0.0866164	−	0.0500080i
$203$	64.0701			0.315616
$204$	−246.669	−	427.244i	−1.20916	−	2.09433i
$205$	−276.563	−	159.674i	−1.34909	−	0.778896i
$206$		−	374.222i		−	1.81661i
$207$	−0.309079	−	0.178447i	−0.00149313	−	0.000862061i
$208$	105.902	+	183.428i	0.509144	+	0.881864i
$209$	26.2367	+	45.4433i	0.125534	+	0.217432i
$210$			219.962i			1.04744i
$211$	−105.149	+	182.933i	−0.498338	+	0.866983i
$211$	−105.149	+	182.933i	−0.498338	+	0.866983i
$212$	−253.330			−1.19495
$213$	−82.5609	+	47.6666i	−0.387610	+	0.223787i
$214$	−598.556	+	345.576i	−2.79699	+	1.61484i
$215$	−148.656	+	257.480i	−0.691425	+	1.19758i
$216$	345.609			1.60004
$217$	−69.4906	+	120.361i	−0.320233	+	0.554660i
$218$	−319.207	+	184.294i	−1.46425	+	0.845386i
$219$		−	135.932i		−	0.620694i
$220$	75.6549	−	131.038i	0.343886	−	0.595628i
$221$	301.181	−	173.887i	1.36281	−	0.786819i
$222$	−29.7046			−0.133804
$223$		−	15.3935i		−	0.0690292i	−0.999404	−	0.0345146i	$-0.989011\pi$
$223$		−	15.3935i		−	0.0690292i	0.999404	−	0.0345146i	$-0.0109885\pi$
$224$	25.5298			0.113972
$225$	0.0553732	−	0.0959093i	0.000246103	−	0.000426263i
$226$	−14.3547	+	8.28770i	−0.0635164	+	0.0366712i
$227$	27.5983	+	47.8017i	0.121579	+	0.210580i	0.920390	−	0.391001i	$-0.127871\pi$
$227$	27.5983	+	47.8017i	0.121579	+	0.210580i	−0.798812	+	0.601581i	$0.794538\pi$
$228$	−313.371	+	180.925i	−1.37443	+	0.793529i
$229$			402.733i			1.75866i	0.476213	+	0.879330i	$0.342009\pi$
$229$			402.733i			1.75866i	−0.476213	+	0.879330i	$0.657991\pi$
$230$	278.128	+	481.732i	1.20925	+	2.09449i
$231$	18.6348	−	32.2764i	0.0806700	−	0.139725i
$232$	111.362	−	192.885i	0.480009	−	0.831401i
$233$	−233.760	+	134.962i	−1.00326	+	0.579235i	−0.909212	−	0.416333i	$-0.863315\pi$
$233$	−233.760	+	134.962i	−1.00326	+	0.579235i	−0.0940515	+	0.995567i	$0.529982\pi$
$234$		−	0.715853i		−	0.00305920i
$235$	−22.8385	−	39.5574i	−0.0971849	−	0.168329i
$236$	−321.719			−1.36322
$237$	34.7214	−	20.0464i	0.146504	−	0.0845840i
$238$			268.087i			1.12642i
$239$		−	269.552i		−	1.12783i	−0.825831	−	0.563917i	$-0.809294\pi$
$239$		−	269.552i		−	1.12783i	0.825831	−	0.563917i	$-0.190706\pi$
$240$	195.136	+	112.662i	0.813065	+	0.469424i
$241$	50.5390	−	87.5362i	0.209706	−	0.363221i	−0.741916	−	0.670493i	$-0.766083\pi$
$241$	50.5390	−	87.5362i	0.209706	−	0.363221i	0.951622	+	0.307272i	$0.0994161\pi$
$242$	325.347	−	187.839i	1.34441	−	0.776195i
$243$	−0.596608	−	0.344452i	−0.00245518	−	0.00141750i
$244$	−464.742	+	268.319i	−1.90468	+	1.09967i
$245$	−102.786	+	178.031i	−0.419536	+	0.726658i
$246$	−490.164	+	282.996i	−1.99253	+	1.15039i
$247$	−127.541	−	220.908i	−0.516361	−	0.894363i
$248$	241.567	+	418.407i	0.974061	+	1.68712i
$249$	279.159	+	161.173i	1.12112	+	0.647279i
$250$	281.014	−	162.244i	1.12406	−	0.648975i
$251$			342.583i			1.36487i	0.730945	+	0.682437i	$0.239080\pi$
$251$			342.583i			1.36487i	−0.730945	+	0.682437i	$0.760920\pi$
$252$	0.315051	+	0.181895i	0.00125020	+	0.000721805i
$253$		−	94.2499i		−	0.372529i
$254$	269.466	−	466.729i	1.06089	−	1.83751i
$255$	184.986	−	320.405i	0.725436	−	1.25649i
$256$	244.537	−	423.550i	0.955222	−	1.65449i
$257$	−92.5790	−	160.352i	−0.360230	−	0.623936i	0.627769	−	0.778400i	$-0.283968\pi$
$257$	−92.5790	−	160.352i	−0.360230	−	0.623936i	−0.987998	+	0.154464i	$0.950635\pi$
$258$	263.470	+	456.343i	1.02120	+	1.76877i
$259$	9.21579	+	5.32074i	0.0355822	+	0.0205434i
$260$	−367.772	+	636.999i	−1.41451	+	2.45000i
$261$	−0.192103	+	0.110911i	−0.000736027	+	0.000424945i
$262$	107.717	−	186.571i	0.411132	−	0.712102i
$263$	32.8468	−	56.8922i	0.124893	−	0.216320i	−0.796798	−	0.604245i	$-0.793475\pi$
$263$	32.8468	−	56.8922i	0.124893	−	0.216320i	0.921691	+	0.387925i	$0.126808\pi$
$264$	−64.7793	−	112.201i	−0.245376	−	0.425004i
$265$	−94.9907	−	164.529i	−0.358456	−	0.620863i
$266$	196.634			0.739226
$267$	51.6142	+	89.3984i	0.193312	+	0.334826i
$268$	−467.128	−	269.697i	−1.74302	−	1.00633i
$269$	−418.739			−1.55665			−0.778325	−	0.627862i	$-0.783930\pi$
$269$	−418.739			−1.55665			−0.778325	+	0.627862i	$0.783930\pi$
$270$	268.242	+	464.609i	0.993489	+	1.72077i
$271$		−	445.166i		−	1.64268i	−0.570440	−	0.821339i	$-0.693227\pi$
$271$		−	445.166i		−	1.64268i	0.570440	−	0.821339i	$-0.306773\pi$
$272$	237.829	+	137.311i	0.874371	+	0.504818i
$273$	−90.5868	+	156.901i	−0.331820	+	0.574729i
$274$		−	751.494i		−	2.74268i
$275$	29.2464			0.106351
$276$	649.935			2.35484
$277$	−145.387	+	251.818i	−0.524863	+	0.909089i	0.474718	+	0.880138i	$0.342550\pi$
$277$	−145.387	+	251.818i	−0.524863	+	0.909089i	−0.999581	+	0.0289510i	$0.990783\pi$
$278$		−	850.101i		−	3.05792i
$279$		−	0.481176i		−	0.00172464i
$280$	−136.965	−	237.230i	−0.489160	−	0.847250i
$281$	263.107	−	455.715i	0.936325	−	1.62176i	0.164071	−	0.986449i	$-0.447538\pi$
$281$	263.107	−	455.715i	0.936325	−	1.62176i	0.772254	−	0.635314i	$-0.219129\pi$
$282$	−80.9550			−0.287074
$283$	205.505	+	118.648i	0.726167	+	0.419253i	0.817018	−	0.576612i	$-0.195626\pi$
$283$	205.505	+	118.648i	0.726167	+	0.419253i	−0.0908514	+	0.995864i	$0.528959\pi$
$284$	122.872	−	212.820i	0.432648	−	0.749368i
$285$	−235.008	−	135.682i	−0.824590	−	0.476077i
$286$	163.718	−	94.5228i	0.572441	−	0.330499i
$287$	202.763			0.706492
$288$	−0.0765465	+	0.0441942i	−0.000265787	+	0.000153452i
$289$	80.9586	−	140.224i	0.280134	−	0.485206i
$290$	345.732			1.19218
$291$	−130.212	−	225.535i	−0.447465	−	0.775033i
$292$	175.199	+	303.453i	0.599995	+	1.03922i
$293$	422.033			1.44039			0.720193	−	0.693774i	$-0.244053\pi$
$293$	422.033			1.44039			0.720193	+	0.693774i	$0.244053\pi$
$294$	182.172	+	315.532i	0.619633	+	1.07324i
$295$	−120.634	−	208.945i	−0.408930	−	0.708287i
$296$	32.0365	−	18.4963i	0.108231	−	0.0624874i
$297$		−	90.8998i		−	0.306060i
$298$	396.769			1.33144
$299$			458.165i			1.53232i
$300$			201.679i			0.672264i
$301$		−	188.773i		−	0.627152i
$302$	118.011	−	68.1335i	0.390764	−	0.225608i
$303$	−15.3310	−	8.85136i	−0.0505974	−	0.0292124i
$304$	100.713	−	174.441i	0.331294	−	0.573818i
$305$	−348.526	−	201.222i	−1.14271	−	0.659744i
$306$	−0.464081	−	0.803811i	−0.00151660	−	0.00262683i
$307$	−371.752			−1.21092			−0.605460	−	0.795876i	$-0.707011\pi$
$307$	−371.752			−1.21092			−0.605460	+	0.795876i	$0.707011\pi$
$308$			96.0711i			0.311919i
$309$		−	327.905i		−	1.06118i
$310$	−374.982	+	649.487i	−1.20962	+	2.09512i
$311$	208.151	−	360.527i	0.669295	−	1.15925i	−0.308807	−	0.951125i	$-0.599930\pi$
$311$	208.151	−	360.527i	0.669295	−	1.15925i	0.978102	−	0.208128i	$-0.0667369\pi$
$312$	314.903	+	545.428i	1.00931	+	1.74817i
$313$		−	25.4441i		−	0.0812910i	−0.999174	−	0.0406455i	$-0.987059\pi$
$313$		−	25.4441i		−	0.0812910i	0.999174	−	0.0406455i	$-0.0129414\pi$
$314$	−286.996	+	497.092i	−0.914000	+	1.58309i
$315$			0.272819i			0.000866092i
$316$	−51.6744	+	89.5027i	−0.163527	+	0.283236i
$317$	21.9086	+	12.6489i	0.0691121	+	0.0399019i	0.534158	−	0.845385i	$-0.320629\pi$
$317$	21.9086	+	12.6489i	0.0691121	+	0.0399019i	−0.465046	+	0.885287i	$0.653962\pi$
$318$	−336.712			−1.05884
$319$	−50.7314	−	29.2898i	−0.159033	−	0.0918175i
$320$	437.981			1.36869
$321$	−524.474	+	302.805i	−1.63387	+	0.943318i
$322$	−305.866	−	176.592i	−0.949894	−	0.548422i
$323$	−286.425	−	165.367i	−0.886764	−	0.511973i
$324$	627.721			1.93741
$325$	−142.172			−0.437452
$326$		−	118.299i		−	0.362881i
$327$	−279.699	+	161.484i	−0.855349	+	0.493836i
$328$	352.429	−	610.424i	1.07448	−	1.86105i
$329$	25.1161	+	14.5008i	0.0763408	+	0.0440754i
$330$	100.556	−	174.168i	0.304715	−	0.527783i
$331$	39.5615	+	68.5225i	0.119521	+	0.207017i	0.919578	−	0.392908i	$-0.128531\pi$
$331$	39.5615	+	68.5225i	0.119521	+	0.207017i	−0.800057	+	0.599924i	$0.795197\pi$
$332$	−830.921			−2.50277
$333$	−0.0368426			−0.000110638
$334$	−656.003			−1.96408
$335$		−	404.511i		−	1.20749i
$336$	−143.064			−0.425787
$337$	141.950	+	245.864i	0.421216	+	0.729568i	0.996059	−	0.0886963i	$-0.0282701\pi$
$337$	141.950	+	245.864i	0.421216	+	0.729568i	−0.574843	+	0.818264i	$0.694937\pi$
$338$	−294.413	+	169.979i	−0.871044	+	0.502898i
$339$	−12.5781	+	7.26194i	−0.0371034	+	0.0214217i
$340$			953.691i			2.80497i
$341$	110.047	−	63.5355i	0.322717	−	0.186321i
$342$	−0.589572	+	0.340390i	−0.00172390	+	0.000995292i
$343$		−	311.081i		−	0.906941i
$344$	−568.306	−	328.111i	−1.65205	−	0.953812i
$345$	243.705	+	422.109i	0.706391	+	1.22350i
$346$			596.066i			1.72273i
$347$	143.412	+	248.397i	0.413291	+	0.715841i	0.995247	−	0.0973789i	$-0.0310459\pi$
$347$	143.412	+	248.397i	0.413291	+	0.715841i	−0.581956	+	0.813220i	$0.697713\pi$
$348$	201.978	−	349.837i	0.580397	−	1.00528i
$349$	−42.4613	−	24.5151i	−0.121666	−	0.0702438i	0.437932	−	0.899008i	$-0.355711\pi$
$349$	−42.4613	−	24.5151i	−0.121666	−	0.0702438i	−0.559598	+	0.828764i	$0.689044\pi$
$350$	54.7977	−	94.9123i	0.156565	−	0.271178i
$351$			441.880i			1.25892i
$352$	−20.2147	−	11.6710i	−0.0574282	−	0.0331562i
$353$	−253.692	+	146.469i	−0.718674	+	0.414927i	−0.814265	−	0.580494i	$-0.802859\pi$
$353$	−253.692	+	146.469i	−0.718674	+	0.414927i	0.0955902	+	0.995421i	$0.469526\pi$
$354$	−427.610			−1.20794
$355$	184.292			0.519133
$356$	−230.446	−	133.048i	−0.647320	−	0.373730i
$357$			234.906i			0.658001i
$358$		−	1089.80i		−	3.04413i
$359$	348.847			0.971718			0.485859	−	0.874037i	$-0.338507\pi$
$359$	348.847			0.971718			0.485859	+	0.874037i	$0.338507\pi$
$360$	0.821329	+	0.474195i	0.00228147	+	0.00131721i
$361$	59.2078	−	102.551i	0.164010	−	0.284075i
$362$	511.847			1.41394
$363$	285.080	−	164.591i	0.785343	−	0.453418i
$364$		−	467.018i		−	1.28302i
$365$	−131.388	+	227.570i	−0.359966	+	0.623480i
$366$	−617.707	+	356.633i	−1.68772	+	0.974408i
$367$			285.767i			0.778657i	0.921099	+	0.389328i	$0.127293\pi$
$367$			285.767i			0.778657i	−0.921099	+	0.389328i	$0.872707\pi$
$368$	−313.321	+	180.896i	−0.851416	+	0.491565i
$369$	−0.607949	+	0.351000i	−0.00164756	+	0.000951219i
$370$	49.7298	+	28.7115i	0.134405	+	0.0775988i
$371$	104.464	+	60.3124i	0.281575	+	0.162567i
$372$	438.132	+	758.867i	1.17777	+	2.03996i
$373$	−600.080	−	346.456i	−1.60879	−	0.928837i	−0.989641	−	0.143565i	$-0.954143\pi$
$373$	−600.080	−	346.456i	−1.60879	−	0.928837i	−0.619152	−	0.785271i	$-0.712523\pi$
$374$	122.556	−	212.274i	0.327691	−	0.567577i
$375$	246.234	−	142.163i	0.656623	−	0.379102i
$376$	87.3102	−	50.4086i	0.232208	−	0.134065i
$377$	246.614	+	142.383i	0.654148	+	0.377673i
$378$	−294.994	−	170.315i	−0.780407	−	0.450568i
$379$	−73.7760	−	42.5946i	−0.194660	−	0.112387i	0.399502	−	0.916732i	$-0.369183\pi$
$379$	−73.7760	−	42.5946i	−0.194660	−	0.112387i	−0.594162	+	0.804345i	$0.702516\pi$
$380$	699.505			1.84080
$381$	236.115	−	408.963i	0.619723	−	1.07339i
$382$	265.530			0.695104
$383$	−359.860	−	623.296i	−0.939582	−	1.62740i	−0.766253	−	0.642539i	$-0.777881\pi$
$383$	−359.860	−	623.296i	−0.939582	−	1.62740i	−0.173329	−	0.984864i	$-0.555452\pi$
$384$	346.526	−	600.201i	0.902411	−	1.56302i
$385$	−62.3947	+	36.0236i	−0.162064	+	0.0935678i
$386$	−950.547	+	548.798i	−2.46256	+	1.42176i
$387$	0.326781	+	0.566002i	0.000844396	+	0.00146254i
$388$	581.369	+	335.653i	1.49837	+	0.865086i
$389$	219.197	+	379.661i	0.563490	+	0.975993i	0.997188	+	0.0749349i	$0.0238749\pi$
$389$	219.197	+	379.661i	0.563490	+	0.975993i	−0.433699	+	0.901058i	$0.642792\pi$
$390$	−488.820	+	846.662i	−1.25339	+	2.17093i
$391$	297.024	+	514.461i	0.759653	+	1.31576i
$392$	−392.947	−	226.868i	−1.00242	−	0.578745i
$393$	94.3847	−	163.479i	0.240165	−	0.415977i
$394$	−1168.59			−2.96596
$395$	−77.5050			−0.196215
$396$	−0.166307	−	0.288052i	−0.000419967	−	0.000727404i
$397$			464.184i			1.16923i	0.811311	+	0.584615i	$0.198754\pi$
$397$			464.184i			1.16923i	−0.811311	+	0.584615i	$0.801246\pi$
$398$	−164.433	+	94.9357i	−0.413149	+	0.238532i
$399$	172.297			0.431822
$400$	−56.1332	−	97.2256i	−0.140333	−	0.243064i
$401$	−377.481	−	217.939i	−0.941349	−	0.543488i	−0.0509658	−	0.998700i	$-0.516230\pi$
$401$	−377.481	−	217.939i	−0.941349	−	0.543488i	−0.890383	+	0.455213i	$0.849563\pi$
$402$	−620.880	−	358.465i	−1.54448	−	0.891704i
$403$	−534.956	+	308.857i	−1.32743	+	0.766394i
$404$	45.6330			0.112953
$405$	235.375	+	407.682i	0.581174	+	1.00662i
$406$	−190.106	+	109.758i	−0.468242	+	0.270339i
$407$	−4.86477	−	8.42603i	−0.0119528	−	0.0207028i
$408$	707.192	+	408.298i	1.73331	+	1.00073i
$409$			653.119i			1.59687i	0.602083	+	0.798434i	$0.294338\pi$
$409$			653.119i			1.59687i	−0.602083	+	0.798434i	$0.705662\pi$
$410$	1094.14			2.66864
$411$		−	658.483i		−	1.60215i
$412$	422.627	+	732.011i	1.02579	+	1.77673i
$413$	132.665	+	76.5943i	0.321223	+	0.185458i
$414$	1.22278			0.00295357
$415$	−311.569	−	539.653i	−0.750768	−	1.30037i
$416$	98.2673	+	56.7347i	0.236220	+	0.136381i
$417$		−	744.885i		−	1.78630i
$418$	−155.697	−	89.8916i	−0.372480	−	0.215052i
$419$	−40.4434	−	70.0500i	−0.0965236	−	0.167184i	0.813720	−	0.581257i	$-0.197439\pi$
$419$	−40.4434	−	70.0500i	−0.0965236	−	0.167184i	−0.910243	+	0.414073i	$0.864106\pi$
$420$	−248.414	−	430.265i	−0.591461	−	1.02444i
$421$		−	233.828i		−	0.555411i	−0.960666	−	0.277705i	$-0.910426\pi$
$421$		−	233.828i		−	0.555411i	0.960666	−	0.277705i	$-0.0895739\pi$
$422$	−1.38670	−	722.922i	−0.00328602	−	1.71309i
$423$	−0.100408			−0.000237372
$424$	363.145	−	209.662i	0.856473	−	0.494485i
$425$	−159.641	+	92.1686i	−0.375625	+	0.216867i
$426$	163.314	−	282.868i	0.383366	−	0.664010i
$427$	255.523			0.598415
$428$	780.552	−	1351.96i	1.82372	−	3.15878i
$429$	143.455	−	82.8238i	0.334394	−	0.193063i
$430$		−	1018.65i		−	2.36895i
$431$	−393.127	+	680.917i	−0.912128	+	1.57985i	−0.101076	+	0.994879i	$0.532229\pi$
$431$	−393.127	+	680.917i	−0.912128	+	1.57985i	−0.811052	+	0.584974i	$0.801105\pi$
$432$	−302.184	+	174.466i	−0.699500	+	0.403856i
$433$	832.259			1.92208			0.961038	−	0.276416i	$-0.0891468\pi$
$433$	832.259			1.92208			0.961038	+	0.276416i	$0.0891468\pi$
$434$		−	476.174i		−	1.09718i
$435$	302.942			0.696417
$436$	416.264	−	720.991i	0.954735	−	1.65365i
$437$	377.342	−	217.859i	0.863483	−	0.498532i
$438$	232.864	+	403.332i	0.531652	+	0.920848i
$439$	503.798	−	290.868i	1.14760	−	0.662569i	0.199302	−	0.979938i	$-0.436133\pi$
$439$	503.798	−	290.868i	1.14760	−	0.662569i	0.948302	+	0.317369i	$0.102799\pi$
$440$			250.455i			0.569215i
$441$	0.225948	+	0.391354i	0.000512354	+	0.000887423i
$442$	−595.768	+	1031.90i	−1.34789	+	2.33462i
$443$	205.940	−	356.699i	0.464877	−	0.805190i	−0.534319	−	0.845283i	$-0.679432\pi$
$443$	205.940	−	356.699i	0.464877	−	0.805190i	0.999196	+	0.0400929i	$0.0127654\pi$
$444$	58.1048	−	33.5468i	0.130867	−	0.0755559i
$445$		−	199.555i		−	0.448438i
$446$	26.3704	+	45.6749i	0.0591265	+	0.102410i
$447$	347.661			0.777766
$448$	−240.830	+	139.044i	−0.537568	+	0.310365i
$449$		−	111.439i		−	0.248195i	−0.992270	−	0.124097i	$-0.960396\pi$
$449$		−	111.439i		−	0.248195i	0.992270	−	0.124097i	$-0.0396035\pi$
$450$			0.379437i			0.000843194i
$451$	−160.550	−	92.6935i	−0.355986	−	0.205529i
$452$	18.7194	−	32.4229i	0.0414146	−	0.0717321i
$453$	103.405	−	59.7007i	0.228266	−	0.131790i
$454$	−163.777	−	94.5568i	−0.360743	−	0.208275i
$455$	303.311	−	175.117i	0.666618	−	0.384872i
$456$	299.475	−	518.705i	0.656742	−	1.13751i
$457$	−696.594	+	402.179i	−1.52428	+	0.880041i	−0.524689	+	0.851294i	$0.675818\pi$
$457$	−696.594	+	402.179i	−1.52428	+	0.880041i	−0.999587	+	0.0287467i	$0.990848\pi$
$458$	−689.917	−	1194.97i	−1.50637	−	2.60911i
$459$	286.466	+	496.174i	0.624110	+	1.08099i
$460$	−1088.09	−	628.207i	−2.36541	−	1.36567i
$461$	−424.362	+	245.006i	−0.920525	+	0.531465i	−0.883802	−	0.467860i	$-0.845025\pi$
$461$	−424.362	+	245.006i	−0.920525	+	0.531465i	−0.0367224	+	0.999326i	$0.511692\pi$
$462$			127.692i			0.276390i
$463$	403.819	+	233.145i	0.872180	+	0.503553i	0.868072	−	0.496438i	$-0.165359\pi$
$463$	403.819	+	233.145i	0.872180	+	0.503553i	0.00410803	+	0.999992i	$0.498692\pi$
$464$			224.866i			0.484625i
$465$	−328.571	+	569.102i	−0.706604	+	1.22387i
$466$	462.403	−	800.905i	0.992280	−	1.71868i
$467$	96.2381	−	166.689i	0.206077	−	0.356937i	−0.744398	−	0.667736i	$-0.767263\pi$
$467$	96.2381	−	166.689i	0.206077	−	0.356937i	0.950475	+	0.310800i	$0.100597\pi$
$468$	0.808447	+	1.40027i	0.00172745	+	0.00299203i
$469$	128.418	+	222.426i	0.273812	+	0.474256i
$470$	135.531	+	78.2486i	0.288363	+	0.166486i
$471$	−251.475	+	435.568i	−0.533917	+	0.924772i
$472$	461.179	−	266.262i	0.977073	−	0.564113i
$473$	−86.2978	+	149.472i	−0.182448	+	0.316009i
$474$	−68.6826	+	118.962i	−0.144900	+	0.250974i
$475$	67.6030	+	117.092i	0.142322	+	0.246509i
$476$	−302.763	−	524.402i	−0.636058	−	1.10168i
$477$	−0.417623			−0.000875520
$478$	461.767	+	799.804i	0.966040	+	1.67323i
$479$	−78.2455	−	45.1751i	−0.163352	−	0.0943112i	0.416096	−	0.909321i	$-0.363398\pi$
$479$	−78.2455	−	45.1751i	−0.163352	−	0.0943112i	−0.579447	+	0.815010i	$0.696732\pi$
$480$	120.712			0.251483
$481$	23.6485	+	40.9604i	0.0491653	+	0.0851567i
$482$			346.311i			0.718488i
$483$	−268.009	−	154.735i	−0.554885	−	0.320363i
$484$	−424.272	+	734.860i	−0.876595	+	1.51831i
$485$			503.437i			1.03802i
$486$	2.36031			0.00485660
$487$	−223.267			−0.458454			−0.229227	−	0.973373i	$-0.573620\pi$
$487$	−223.267			−0.458454			−0.229227	+	0.973373i	$0.573620\pi$
$488$	444.133	−	769.261i	0.910108	−	1.57635i
$489$		−	103.658i		−	0.211979i
$490$		−	704.328i		−	1.43740i
$491$	320.671	+	555.419i	0.653098	+	1.13120i	0.982367	+	0.186963i	$0.0598644\pi$
$491$	320.671	+	555.419i	0.653098	+	1.13120i	−0.329269	+	0.944236i	$0.606802\pi$
$492$	639.202	−	1107.13i	1.29919	−	2.25026i
$493$	369.221			0.748927
$494$	756.869	+	436.979i	1.53212	+	0.884572i
$495$	0.124720	−	0.216021i	0.000251959	−	0.000436406i
$496$	−422.430	−	243.890i	−0.851673	−	0.491714i
$497$	−101.336	+	58.5063i	−0.203895	+	0.117719i
$498$	−1104.41			−2.21769
$499$	240.078	−	138.609i	0.481118	−	0.277773i	−0.239764	−	0.970831i	$-0.577070\pi$
$499$	240.078	−	138.609i	0.481118	−	0.277773i	0.720882	+	0.693058i	$0.243737\pi$
$500$	−366.459	+	634.726i	−0.732918	+	1.26945i
$501$	−574.811			−1.14733
$502$	−586.876	−	1016.50i	−1.16907	−	2.02490i
$503$	−414.843	−	718.530i	−0.824738	−	1.42849i	−0.902119	−	0.431487i	$-0.857989\pi$
$503$	−414.843	−	718.530i	−0.824738	−	1.42849i	0.0773810	−	0.997002i	$-0.475344\pi$
$504$	−0.602160			−0.00119476
$505$	17.1109	+	29.6370i	0.0338830	+	0.0586870i
$506$	161.459	+	279.654i	0.319088	+	0.552677i
$507$	−257.974	+	148.941i	−0.508824	+	0.293770i
$508$			1217.28i			2.39623i
$509$	−266.940			−0.524441			−0.262220	−	0.965008i	$-0.584455\pi$
$509$	−266.940			−0.524441			−0.262220	+	0.965008i	$0.584455\pi$
$510$			1267.59i			2.48547i
$511$		−	166.844i		−	0.326505i
$512$			752.237i			1.46921i
$513$	363.930	−	210.115i	0.709414	−	0.409581i
$514$	549.393	+	317.192i	1.06886	+	0.617105i
$515$	−316.943	+	548.962i	−0.615424	+	1.06594i
$516$	−1030.74	−	595.098i	−1.99756	−	1.15329i
$517$	−13.2581	−	22.9638i	−0.0256444	−	0.0444173i
$518$	−36.4596			−0.0703853
$519$			522.292i			1.00634i
$520$		−	1217.50i		−	2.34135i
$521$	−412.308	+	714.138i	−0.791378	+	1.37071i	0.133736	+	0.991017i	$0.457303\pi$
$521$	−412.308	+	714.138i	−0.791378	+	1.37071i	−0.925114	+	0.379690i	$0.876031\pi$
$522$	0.380000	−	0.658179i	0.000727969	−	0.00126088i
$523$	−428.479	−	742.148i	−0.819272	−	1.41902i	−0.906219	−	0.422808i	$-0.861044\pi$
$523$	−428.479	−	742.148i	−0.819272	−	1.41902i	0.0869471	−	0.996213i	$-0.472289\pi$
$524$			486.598i			0.928622i
$525$	48.0154	−	83.1652i	0.0914580	−	0.158410i
$526$			225.078i			0.427904i
$527$	−400.458	+	693.613i	−0.759882	+	1.31615i
$528$	113.280	+	65.4022i	0.214545	+	0.123868i
$529$	−253.612			−0.479418
$530$	563.705	+	325.455i	1.06359	+	0.614066i
$531$	−0.530364			−0.000998802
$532$	−384.633	+	222.068i	−0.722995	+	0.417421i
$533$	780.461	+	450.599i	1.46428	+	0.845402i
$534$	−306.295	−	176.839i	−0.573586	−	0.331160i
$535$	1170.73			2.18828
$536$	892.828			1.66572
$537$		−	954.917i		−	1.77824i
$538$	1242.46	−	717.336i	2.30941	−	1.33334i
$539$	−59.6693	+	103.350i	−0.110704	+	0.191745i
$540$	−1049.41	−	605.877i	−1.94335	−	1.12200i
$541$	−282.930	+	490.050i	−0.522977	+	0.905822i	0.476666	+	0.879085i	$0.341845\pi$
$541$	−282.930	+	490.050i	−0.522977	+	0.905822i	−0.999642	+	0.0267376i	$0.991488\pi$
$542$	762.608	+	1320.88i	1.40703	+	2.43704i
$543$	448.497			0.825961
$544$	147.122			0.270445
$545$	624.343			1.14558
$546$		−	620.733i		−	1.13687i
$547$	−119.761			−0.218942			−0.109471	−	0.993990i	$-0.534916\pi$
$547$	−119.761			−0.218942			−0.109471	+	0.993990i	$0.534916\pi$
$548$	848.698	+	1469.99i	1.54872	+	2.68246i
$549$	−0.766142	+	0.442332i	−0.00139552	+	0.000805705i
$550$	−86.7787	+	50.1017i	−0.157779	+	0.0910940i
$551$		−	270.813i		−	0.491494i
$552$	−931.670	+	537.900i	−1.68781	+	0.974457i
$553$	42.6173	−	24.6051i	0.0770657	−	0.0444939i
$554$		−	996.243i		−	1.79827i
$555$	43.5749	+	25.1580i	0.0785133	+	0.0453297i
$556$	960.060	+	1662.87i	1.72673	+	2.99078i
$557$			375.208i			0.673623i	0.941572	+	0.336812i	$0.109349\pi$
$557$			375.208i			0.673623i	−0.941572	+	0.336812i	$0.890651\pi$
$558$	0.824297	+	1.42772i	0.00147723	+	0.00255864i
$559$	419.508	−	726.610i	0.750462	−	1.29984i
$560$	239.511	+	138.282i	0.427698	+	0.246932i
$561$	107.388	−	186.001i	0.191422	−	0.331553i
$562$			1802.90i			3.20802i
$563$	−380.845	−	219.881i	−0.676456	−	0.390552i	0.122062	−	0.992522i	$-0.461049\pi$
$563$	−380.845	−	219.881i	−0.676456	−	0.390552i	−0.798519	+	0.601970i	$0.794383\pi$
$564$	158.355	−	91.4263i	0.280771	−	0.162103i
$565$	28.0767			0.0496932
$566$	−813.022			−1.43643
$567$	−258.850	−	149.447i	−0.456525	−	0.263575i
$568$			406.766i			0.716137i
$569$		−	525.657i		−	0.923826i	−0.886925	−	0.461913i	$-0.847163\pi$
$569$		−	525.657i		−	0.923826i	0.886925	−	0.461913i	$-0.152837\pi$
$570$	929.741			1.63112
$571$	369.952	+	213.592i	0.647902	+	0.374066i	0.787652	−	0.616120i	$-0.211297\pi$
$571$	369.952	+	213.592i	0.647902	+	0.374066i	−0.139750	+	0.990187i	$0.544630\pi$
$572$	−213.498	+	369.790i	−0.373248	+	0.646485i
$573$	232.665			0.406048
$574$	−601.630	+	347.351i	−1.04814	+	0.605142i
$575$		−	242.850i		−	0.422348i
$576$	0.481392	−	0.833795i	0.000835750	−	0.00144756i
$577$	100.786	−	58.1889i	0.174673	−	0.100847i	−0.410115	−	0.912034i	$-0.634511\pi$
$577$	100.786	−	58.1889i	0.174673	−	0.100847i	0.584787	+	0.811187i	$0.301178\pi$
$578$			554.757i			0.959788i
$579$	−832.899	+	480.874i	−1.43851	+	0.830526i
$580$	−676.283	+	390.452i	−1.16600	+	0.673193i
$581$	342.642	+	197.824i	0.589745	+	0.340489i
$582$	772.721	+	446.131i	1.32770	+	0.766548i
$583$	−55.1439	−	95.5120i	−0.0945864	−	0.163828i
$584$	−502.288	−	289.996i	−0.860083	−	0.496569i
$585$	−0.606284	+	1.05011i	−0.00103638	+	0.00179507i
$586$	−1252.24	+	722.980i	−2.13693	+	1.23375i
$587$	−727.905	+	420.256i	−1.24004	+	0.715939i	−0.969103	−	0.246657i	$-0.920668\pi$
$587$	−727.905	+	420.256i	−1.24004	+	0.715939i	−0.270940	+	0.962596i	$0.587335\pi$
$588$	−712.690	−	411.472i	−1.21206	−	0.699782i
$589$	508.745	+	293.724i	0.863744	+	0.498683i
$590$	715.882	+	413.314i	1.21336	+	0.700533i
$591$	−1023.95			−1.73258
$592$	−18.6741	+	32.3445i	−0.0315441	+	0.0546360i
$593$	−681.363			−1.14901			−0.574505	−	0.818501i	$-0.694805\pi$
$593$	−681.363			−1.14901			−0.574505	+	0.818501i	$0.694805\pi$
$594$	155.719	+	269.714i	0.262154	+	0.454064i
$595$	227.053	−	393.268i	0.381602	−	0.660954i
$596$	−776.115	+	448.090i	−1.30221	+	0.751829i
$597$	−144.082	+	83.1857i	−0.241343	+	0.139340i
$598$	−784.878	−	1359.45i	−1.31250	−	2.27332i
$599$	621.143	+	358.617i	1.03697	+	0.598693i	0.918973	−	0.394321i	$-0.129020\pi$
$599$	621.143	+	358.617i	1.03697	+	0.598693i	0.117994	+	0.993014i	$0.462354\pi$
$600$	−166.914	−	289.104i	−0.278190	−	0.481840i
$601$	5.95802	−	10.3196i	0.00991351	−	0.0171707i	−0.861026	−	0.508561i	$-0.830178\pi$
$601$	5.95802	−	10.3196i	0.00991351	−	0.0171707i	0.870940	+	0.491390i	$0.163511\pi$
$602$	323.384	+	560.118i	0.537183	+	0.930429i
$603$	−0.770076	−	0.444604i	−0.00127708	−	0.000737320i
$604$	−153.893	+	266.550i	−0.254789	+	0.441308i
$605$	−636.354			−1.05182
$606$	60.6527			0.100087
$607$	−9.14823	−	15.8452i	−0.0150712	−	0.0261041i	0.858391	−	0.512995i	$-0.171464\pi$
$607$	−9.14823	−	15.8452i	−0.0150712	−	0.0261041i	−0.873463	+	0.486891i	$0.838131\pi$
$608$		−	107.910i		−	0.177483i
$609$	−166.577	+	96.1733i	−0.273525	+	0.157920i
$610$	1378.84			2.26040
$611$	64.4501	+	111.631i	0.105483	+	0.182702i
$612$	1.81557	+	1.04822i	0.00296661	+	0.00171277i
$613$	−960.261	−	554.407i	−1.56649	−	0.904416i	−0.996573	−	0.0827166i	$-0.973640\pi$
$613$	−960.261	−	554.407i	−1.56649	−	0.904416i	−0.569921	−	0.821699i	$-0.693026\pi$
$614$	1103.05	−	636.844i	1.79649	−	1.03721i
$615$	958.721			1.55890
$616$	−79.5105	−	137.716i	−0.129076	−	0.223565i
$617$	389.409	−	224.826i	0.631134	−	0.364385i	−0.150057	−	0.988677i	$-0.547946\pi$
$617$	389.409	−	224.826i	0.631134	−	0.364385i	0.781191	+	0.624292i	$0.214612\pi$
$618$	561.731	+	972.946i	0.908949	+	1.57435i
$619$	797.516	+	460.446i	1.28839	+	0.743854i	0.978368	−	0.206874i	$-0.0663289\pi$
$619$	797.516	+	460.446i	1.28839	+	0.743854i	0.310026	+	0.950728i	$0.399662\pi$
$620$		−	1693.94i		−	2.73216i
$621$	−754.794			−1.21545
$622$			1426.32i			2.29312i
$623$	63.3516	+	109.728i	0.101688	+	0.176129i
$624$	−550.673	−	317.931i	−0.882489	−	0.509505i
$625$	−766.664			−1.22666
$626$	43.5880	+	75.4966i	0.0696294	+	0.120602i
$627$	−136.426	−	78.7659i	−0.217586	−	0.125623i
$628$		−	1296.47i		−	2.06445i
$629$	53.1085	+	30.6622i	0.0844332	+	0.0487475i
$630$	−0.467363	−	0.809496i	−0.000741846	−	0.00128491i
$631$	−473.395	−	819.945i	−0.750230	−	1.29944i	−0.947711	−	0.319130i	$-0.896609\pi$
$631$	−473.395	−	819.945i	−0.750230	−	1.29944i	0.197480	−	0.980307i	$-0.436724\pi$
$632$		−	171.068i		−	0.270676i
$633$	−1.21507	−	633.447i	−0.00191955	−	1.00071i
$634$	−86.6748			−0.136711
$635$	−790.581	+	456.442i	−1.24501	+	0.718807i
$636$	658.637	−	380.265i	1.03559	−	0.597900i
$637$	290.063	−	502.404i	0.455358	−	0.788703i
$638$	200.704			0.314583
$639$	0.202558	−	0.350841i	0.000316993	−	0.000549048i
$640$	−1160.27	+	669.883i	−1.81292	+	1.04669i
$641$		−	140.517i		−	0.219215i	−0.993975	−	0.109607i	$-0.965041\pi$
$641$		−	140.517i		−	0.219215i	0.993975	−	0.109607i	$-0.0349593\pi$
$642$	1037.46	−	1796.94i	1.61599	−	2.79897i
$643$	−628.484	+	362.855i	−0.977425	+	0.564316i	−0.901492	−	0.432797i	$-0.857527\pi$
$643$	−628.484	+	362.855i	−0.977425	+	0.564316i	−0.0759330	+	0.997113i	$0.524194\pi$
$644$	797.734			1.23872
$645$		−	892.570i		−	1.38383i
$646$	1133.16			1.75411
$647$	290.654	−	503.427i	0.449233	−	0.778094i	−0.549103	−	0.835754i	$-0.685031\pi$
$647$	290.654	−	503.427i	0.449233	−	0.778094i	0.998336	+	0.0576602i	$0.0183640\pi$
$648$	−899.828	+	519.516i	−1.38862	+	0.801722i
$649$	−70.0304	−	121.296i	−0.107905	−	0.186897i
$650$	421.846	−	243.553i	0.648994	−	0.374697i
$651$		−	417.239i		−	0.640920i
$652$	133.601	+	231.404i	0.204910	+	0.354914i
$653$	87.5586	−	151.656i	0.134087	−	0.232245i	−0.791161	−	0.611607i	$-0.790523\pi$
$653$	87.5586	−	151.656i	0.134087	−	0.232245i	0.925248	+	0.379362i	$0.123857\pi$
$654$	553.274	−	958.299i	0.845985	−	1.46529i
$655$	−316.028	+	182.459i	−0.482485	+	0.278563i
$656$			711.635i			1.08481i
$657$	0.288821	+	0.500252i	0.000439605	+	0.000761418i
$658$	−99.3647			−0.151010
$659$	86.9058	−	50.1751i	0.131875	−	0.0761382i	−0.432611	−	0.901581i	$-0.642408\pi$
$659$	86.9058	−	50.1751i	0.131875	−	0.0761382i	0.564486	+	0.825442i	$0.309074\pi$
$660$			454.251i			0.688259i
$661$		−	435.326i		−	0.658587i	−0.944228	−	0.329294i	$-0.893189\pi$
$661$		−	435.326i		−	0.658587i	0.944228	−	0.329294i	$-0.106811\pi$
$662$	−234.770	−	135.545i	−0.354638	−	0.204750i
$663$	−522.031	+	904.184i	−0.787377	+	1.36378i
$664$	1191.11	−	687.688i	1.79384	−	1.03568i
$665$	−288.451	−	166.537i	−0.433760	−	0.250432i
$666$	0.109318	−	0.0631146i	0.000164141	−	9.47667e-5i
$667$	−243.210	+	421.252i	−0.364633	+	0.631562i
$668$	1283.20	−	740.856i	1.92096	−	1.10907i
$669$	23.1066	+	40.0218i	0.0345390	+	0.0598234i
$670$	692.962	+	1200.25i	1.03427	+	1.79141i
$671$	−202.326	−	116.813i	−0.301529	−	0.174088i
$672$	−66.3753	+	38.3218i	−0.0987728	+	0.0570265i
$673$		−	354.921i		−	0.527371i	−0.964609	−	0.263686i	$-0.915062\pi$
$673$		−	354.921i		−	0.527371i	0.964609	−	0.263686i	$-0.0849381\pi$
$674$	−842.375	−	486.345i	−1.24981	−	0.721581i
$675$		−	234.218i		−	0.346989i
$676$	383.932	−	664.989i	0.567946	−	0.983712i
$677$	−19.3664	+	33.5436i	−0.0286062	+	0.0495474i	−0.879974	−	0.475022i	$-0.842440\pi$
$677$	−19.3664	+	33.5436i	−0.0286062	+	0.0495474i	0.851368	+	0.524569i	$0.175774\pi$
$678$	24.8807	−	43.0946i	0.0366972	−	0.0635614i
$679$	−159.824	−	276.823i	−0.235381	−	0.407692i
$680$	−789.296	−	1367.10i	−1.16073	−	2.01044i
$681$	−143.507	−	82.8537i	−0.210730	−	0.121665i
$682$	−217.684	+	377.039i	−0.319184	+	0.552844i
$683$	918.081	−	530.054i	1.34419	−	0.776068i	0.356770	−	0.934192i	$-0.383878\pi$
$683$	918.081	−	530.054i	1.34419	−	0.776068i	0.987419	+	0.158124i	$0.0505447\pi$
$684$	0.768837	−	1.33166i	0.00112403	−	0.00194688i
$685$	−636.469	+	1102.40i	−0.929153	+	1.60934i
$686$	532.909	+	923.025i	0.776835	+	1.34552i
$687$	−604.528	−	1047.07i	−0.879953	−	1.52412i
$688$	662.533			0.962983
$689$	268.064	+	464.300i	0.389062	+	0.673875i
$690$	−1446.22	−	834.976i	−2.09597	−	1.21011i
$691$	730.475			1.05713			0.528564	−	0.848894i	$-0.322731\pi$
$691$	730.475			1.05713			0.528564	+	0.848894i	$0.322731\pi$
$692$	−673.166	−	1165.96i	−0.972783	−	1.68491i
$693$			0.158376i			0.000228537i
$694$	−851.052	−	491.355i	−1.22630	−	0.708004i
$695$	−719.983	+	1247.05i	−1.03595	+	1.79431i
$696$			668.647i			0.960699i
$697$	1168.48			1.67644
$698$	167.986			0.240668
$699$	405.172	−	701.778i	0.579645	−	1.00397i
$700$			247.542i			0.353632i
$701$			164.711i			0.234965i	0.993075	+	0.117483i	$0.0374825\pi$
$701$			164.711i			0.234965i	−0.993075	+	0.117483i	$0.962518\pi$
$702$	−756.979	−	1311.13i	−1.07832	−	1.86770i
$703$	22.4898	−	38.9535i	0.0319912	−	0.0554104i
$704$	254.256			0.361159
$705$	118.756	+	68.5639i	0.168448	+	0.0972538i
$706$	501.829	−	869.194i	0.710806	−	1.23115i
$707$	−18.8174	−	10.8642i	−0.0266158	−	0.0153666i
$708$	836.442	−	482.920i	1.18142	−	0.682091i
$709$	667.418			0.941352			0.470676	−	0.882306i	$-0.344010\pi$
$709$	667.418			0.941352			0.470676	+	0.882306i	$0.344010\pi$
$710$	−546.824	+	315.709i	−0.770174	+	0.444660i
$711$	−0.0851870	+	0.147548i	−0.000119813	+	0.000207522i
$712$	440.454			0.618614
$713$	−527.572	−	913.782i	−0.739933	−	1.28160i
$714$	−402.415	−	697.004i	−0.563607	−	0.976196i
$715$	−320.220			−0.447860
$716$	1230.76	+	2131.74i	1.71894	+	2.97730i
$717$	404.615	+	700.814i	0.564317	+	0.977425i
$718$	−1035.08	+	597.606i	−1.44162	+	0.832320i
$719$		−	168.586i		−	0.234472i	−0.993104	−	0.117236i	$-0.962597\pi$
$719$		−	168.586i		−	0.234472i	0.993104	−	0.117236i	$-0.0374035\pi$
$720$	−0.957508			−0.00132987
$721$		−	402.473i		−	0.558215i
$722$			405.713i			0.561929i
$723$			303.449i			0.419708i
$724$	−1001.22	+	578.053i	−1.38290	+	0.798416i
$725$	−130.717	−	75.4698i	−0.180300	−	0.104096i
$726$	−563.917	+	976.733i	−0.776745	+	1.34536i
$727$	−99.5337	−	57.4658i	−0.136910	−	0.0790452i	0.429980	−	0.902838i	$-0.358520\pi$
$727$	−99.5337	−	57.4658i	−0.136910	−	0.0790452i	−0.566891	+	0.823793i	$0.691854\pi$
$728$	386.514	+	669.463i	0.530926	+	0.919592i
$729$	−727.964			−0.998578
$730$		−	900.315i		−	1.23331i
$731$		−	1087.85i		−	1.48817i
$732$	805.526	−	1395.21i	1.10045	−	1.90603i
$733$	98.5228	−	170.646i	0.134410	−	0.232806i	−0.790962	−	0.611866i	$-0.790419\pi$
$733$	98.5228	−	170.646i	0.134410	−	0.232806i	0.925372	+	0.379060i	$0.123753\pi$
$734$	−489.544	−	847.916i	−0.666954	−	1.15520i
$735$		−	617.155i		−	0.839666i
$736$	−96.9110	+	167.855i	−0.131673	+	0.228064i
$737$		−	234.826i		−	0.318624i
$738$	1.20259	−	2.08294i	0.00162952	−	0.00282242i
$739$	280.761	+	162.098i	0.379921	+	0.219347i	0.677784	−	0.735261i	$-0.262941\pi$
$739$	280.761	+	162.098i	0.379921	+	0.219347i	−0.297863	+	0.954609i	$0.596274\pi$
$740$	−129.701			−0.175272
$741$	663.193	+	382.894i	0.894997	+	0.516727i
$742$	−413.282			−0.556984
$743$	179.496	−	103.632i	0.241582	−	0.139478i	−0.374321	−	0.927299i	$-0.622124\pi$
$743$	179.496	−	103.632i	0.241582	−	0.139478i	0.615904	+	0.787821i	$0.288791\pi$
$744$	−1256.11	−	725.215i	−1.68832	−	0.974752i
$745$	−582.036	−	336.039i	−0.781257	−	0.451059i
$746$	2374.04			3.18236
$747$	−1.36980			−0.00183374
$748$			553.635i			0.740154i
$749$	−643.743	+	371.665i	−0.859470	+	0.496215i
$750$	−487.076	+	843.640i	−0.649435	+	1.12485i
$751$	−757.974	−	437.616i	−1.00929	−	0.582711i	−0.0983034	−	0.995156i	$-0.531342\pi$
$751$	−757.974	−	437.616i	−1.00929	−	0.582711i	−0.910982	+	0.412445i	$0.864675\pi$
$752$	−50.8933	+	88.1497i	−0.0676772	+	0.117220i
$753$	−514.239	−	890.688i	−0.682920	−	1.18285i
$754$	−975.656			−1.29397
$755$	−230.820			−0.305721
$756$	769.379			1.01770
$757$			134.820i			0.178098i	0.996027	+	0.0890490i	$0.0283828\pi$
$757$			134.820i			0.178098i	−0.996027	+	0.0890490i	$0.971617\pi$
$758$	291.873			0.385057
$759$	141.475	+	245.042i	0.186397	+	0.322848i
$760$	−1002.73	+	578.926i	−1.31938	+	0.761744i
$761$	361.097	−	208.480i	0.474503	−	0.273955i	−0.243620	−	0.969871i	$-0.578335\pi$
$761$	361.097	−	208.480i	0.474503	−	0.273955i	0.718123	+	0.695916i	$0.245001\pi$
$762$			1617.94i			2.12328i
$763$	−343.305	+	198.207i	−0.449941	+	0.259773i
$764$	−519.399	+	299.875i	−0.679842	+	0.392507i
$765$			1.57219i			0.00205515i
$766$	2135.52	+	1232.94i	2.78789	+	1.60959i
$767$	340.430	+	589.642i	0.443846	+	0.768764i
$768$			1468.26i			1.91180i
$769$	−315.418	−	546.320i	−0.410167	−	0.710430i	0.584741	−	0.811220i	$-0.301196\pi$
$769$	−315.418	−	546.320i	−0.410167	−	0.710430i	−0.994908	+	0.100790i	$0.967863\pi$
$770$	123.423	−	213.775i	0.160290	−	0.277630i
$771$	481.396	+	277.934i	0.624378	+	0.360485i
$772$	1239.57	−	2147.00i	1.60566	−	2.78108i
$773$			1260.60i			1.63079i	0.578904	+	0.815396i	$0.303481\pi$
$773$			1260.60i			1.63079i	−0.578904	+	0.815396i	$0.696519\pi$
$774$	−1.93922	−	1.11961i	−0.00250545	−	0.00144652i
$775$	283.553	−	163.709i	0.365874	−	0.211238i
$776$	−1111.18			−1.43193
$777$	−31.9471			−0.0411159
$778$	−1300.79	−	751.010i	−1.67196	−	0.965308i
$779$		−	857.044i		−	1.10018i
$780$		−	2208.19i		−	2.83102i
$781$	106.985			0.136985
$782$	−1762.63	−	1017.66i	−2.25401	−	1.30135i
$783$	−234.565	+	406.279i	−0.299572	+	0.518875i
$784$	458.099			0.584309
$785$	842.012	−	486.136i	1.07263	−	0.619282i
$786$			646.758i			0.822847i
$787$	−59.6529	+	103.322i	−0.0757978	+	0.131286i	−0.901433	−	0.432919i	$-0.857484\pi$
$787$	−59.6529	+	103.322i	−0.0757978	+	0.131286i	0.825635	+	0.564204i	$0.190817\pi$
$788$	2285.86	−	1319.74i	2.90084	−	1.67480i
$789$			197.220i			0.249962i
$790$	229.970	−	132.773i	0.291101	−	0.168067i
$791$	−15.4384	+	8.91336i	−0.0195176	+	0.0112685i
$792$	0.476797	+	0.275279i	0.000602016	+	0.000347574i
$793$	983.541	+	567.848i	1.24028	+	0.716076i
$794$	−795.189	−	1377.31i	−1.00150	−	1.73464i
$795$	493.936	+	285.174i	0.621303	+	0.358710i
$796$	214.431	−	371.405i	0.269386	−	0.466589i
$797$	−683.727	+	394.750i	−0.857876	+	0.495295i	−0.863301	−	0.504690i	$-0.831607\pi$
$797$	−683.727	+	394.750i	−0.857876	+	0.495295i	0.00542418	+	0.999985i	$0.498273\pi$
$798$	−511.232	+	295.160i	−0.640642	+	0.369875i
$799$	144.738	+	83.5648i	0.181149	+	0.104587i
$800$	−52.0865	−	30.0722i	−0.0651081	−	0.0375902i
$801$	−0.379897	−	0.219334i	−0.000474279	−	0.000273825i
$802$	1493.39			1.86209
$803$	−76.2730	+	132.109i	−0.0949850	+	0.164519i
$804$	1619.33			2.01409
$805$	299.125	+	518.099i	0.371584	+	0.643602i
$806$	1058.20	−	1832.85i	1.31290	−	2.27401i
$807$	1088.69	−	628.553i	1.34905	−	0.778876i
$808$	−65.4141	+	37.7668i	−0.0809580	+	0.0467411i
$809$	−558.105	−	966.667i	−0.689871	−	1.19489i	−0.971879	−	0.235479i	$-0.924334\pi$
$809$	−558.105	−	966.667i	−0.689871	−	1.19489i	0.282009	−	0.959412i	$-0.408999\pi$
$810$	−1396.79	−	806.438i	−1.72443	−	0.995603i
$811$	−248.029	−	429.598i	−0.305831	−	0.529714i	0.671615	−	0.740900i	$-0.265601\pi$
$811$	−248.029	−	429.598i	−0.305831	−	0.529714i	−0.977446	+	0.211186i	$0.932267\pi$
$812$	247.909	−	429.392i	0.305307	−	0.528808i
$813$	668.222	+	1157.39i	0.821921	+	1.42361i
$814$	28.8691	+	16.6676i	0.0354657	+	0.0204761i
$815$	−100.192	+	173.538i	−0.122935	+	0.212930i
$816$	−824.447			−1.01035
$817$	−797.909			−0.976633
$818$	−1118.85	−	1937.91i	−1.36779	−	2.36908i
$819$		−	0.769895i		−	0.000940042i
$820$	−2140.24	+	1235.67i	−2.61004	+	1.50691i
$821$	−115.358			−0.140510			−0.0702548	−	0.997529i	$-0.522381\pi$
$821$	−115.358			−0.140510			−0.0702548	+	0.997529i	$0.522381\pi$
$822$	1128.04	+	1953.82i	1.37231	+	2.37691i
$823$	−165.836	−	95.7452i	−0.201501	−	0.116337i	0.395854	−	0.918313i	$-0.370449\pi$
$823$	−165.836	−	95.7452i	−0.201501	−	0.116337i	−0.597356	+	0.801977i	$0.703782\pi$
$824$	−1211.66	−	699.550i	−1.47046	−	0.848969i
$825$	−76.0382	+	43.9007i	−0.0921675	+	0.0532130i
$826$	−524.851			−0.635413
$827$	153.494	+	265.859i	0.185603	+	0.321474i	0.943780	−	0.330576i	$-0.107243\pi$
$827$	153.494	+	265.859i	0.185603	+	0.321474i	−0.758177	+	0.652049i	$0.773910\pi$
$828$	−2.39187	+	1.38094i	−0.00288873	+	0.00166781i
$829$	545.013	+	943.991i	0.657435	+	1.13871i	0.981278	+	0.192599i	$0.0616917\pi$
$829$	545.013	+	943.991i	0.657435	+	1.13871i	−0.323843	+	0.946111i	$0.604975\pi$
$830$	1848.95	+	1067.49i	2.22765	+	1.28613i
$831$		−	872.940i		−	1.05047i
$832$	−1235.98			−1.48556
$833$		−	752.180i		−	0.902977i
$834$	1276.05	+	2210.19i	1.53004	+	2.65011i
$835$	962.318	+	555.595i	1.15248	+	0.665383i
$836$	406.076			0.485736
$837$	−508.820	−	881.301i	−0.607909	−	1.05293i
$838$	240.004	+	138.566i	0.286401	+	0.165353i
$839$			513.660i			0.612229i	0.951995	+	0.306114i	$0.0990290\pi$
$839$			513.660i			0.612229i	−0.951995	+	0.306114i	$0.900971\pi$
$840$	712.194	+	411.185i	0.847850	+	0.489506i
$841$	−269.337	−	466.505i	−0.320258	−	0.554703i
$842$	400.568	+	693.804i	0.475734	+	0.823995i
$843$			1579.76i			1.87398i
$844$	819.143	+	1412.53i	0.970549	+	1.67362i
$845$	575.848			0.681478
$846$	0.297927	−	0.172008i	0.000352160	−	0.000203320i
$847$	349.909	−	202.020i	0.413115	−	0.238512i
$848$	−211.678	+	366.636i	−0.249620	+	0.432354i
$849$	−712.395			−0.839099
$850$	315.786	−	546.958i	0.371513	−	0.643480i
$851$	−69.9663	+	40.3950i	−0.0822165	+	0.0474677i
$852$			737.754i			0.865908i
$853$	−479.907	+	831.224i	−0.562611	+	0.974471i	0.434656	+	0.900596i	$0.356870\pi$
$853$	−479.907	+	831.224i	−0.562611	+	0.974471i	−0.997268	+	0.0738748i	$0.976463\pi$
$854$	−758.178	+	437.734i	−0.887796	+	0.512569i
$855$	1.15316			0.00134872
$856$			2584.01i			3.01870i
$857$	208.520			0.243314			0.121657	−	0.992572i	$-0.461179\pi$
$857$	208.520			0.243314			0.121657	+	0.992572i	$0.461179\pi$
$858$	−283.769	+	491.503i	−0.330733	+	0.572847i
$859$	−939.132	+	542.208i	−1.09329	+	0.631209i	−0.934449	−	0.356096i	$-0.884108\pi$
$859$	−939.132	+	542.208i	−1.09329	+	0.631209i	−0.158836	+	0.987305i	$0.550774\pi$
$860$	1150.41	+	1992.56i	1.33768	+	2.31693i
$861$	−527.167	+	304.360i	−0.612273	+	0.353496i
$862$		−	2693.85i		−	3.12511i
$863$	−676.938	−	1172.49i	−0.784401	−	1.35862i	−0.929356	−	0.369185i	$-0.879637\pi$
$863$	−676.938	−	1172.49i	−0.784401	−	1.35862i	0.144955	−	0.989438i	$-0.453696\pi$
$864$	−93.4663	+	161.888i	−0.108179	+	0.187371i
$865$	504.831	−	874.393i	0.583620	−	1.01086i
$866$	−2469.44	+	1425.73i	−2.85155	+	1.64634i
$867$			486.096i			0.560664i
$868$	537.766	+	931.438i	0.619546	+	1.07309i
$869$	−44.9931			−0.0517757
$870$	−898.875	+	518.966i	−1.03319	+	0.596512i
$871$			1141.53i			1.31060i
$872$			1378.04i			1.58032i
$873$	0.958406	+	0.553336i	0.00109783	+	0.000633833i
$874$	−746.422	+	1292.84i	−0.854030	+	1.47922i
$875$	302.229	−	174.492i	0.345405	−	0.199419i
$876$	−911.003	−	525.968i	−1.03996	−	0.600420i
$877$	−58.4969	+	33.7732i	−0.0667011	+	0.0385099i	−0.532980	−	0.846128i	$-0.678928\pi$
$877$	−58.4969	+	33.7732i	−0.0667011	+	0.0385099i	0.466279	+	0.884638i	$0.345594\pi$
$878$	−996.565	+	1726.10i	−1.13504	+	1.96595i
$879$	−1097.25	+	633.498i	−1.24829	+	0.720703i
$880$	−126.431	−	218.986i	−0.143672	−	0.248847i
$881$	−668.718	−	1158.25i	−0.759044	−	1.31470i	−0.943338	−	0.331832i	$-0.892333\pi$
$881$	−668.718	−	1158.25i	−0.759044	−	1.31470i	0.184294	−	0.982871i	$-0.441000\pi$
$882$	−1.34085	−	0.774138i	−0.00152023	−	0.000877708i
$883$	1093.41	−	631.278i	1.23829	−	0.714924i	0.269542	−	0.962989i	$-0.413128\pi$
$883$	1093.41	−	631.278i	1.23829	−	0.714924i	0.968744	+	0.248064i	$0.0797944\pi$
$884$		−	2691.32i		−	3.04448i
$885$	627.278	+	362.159i	0.708789	+	0.409219i
$886$			1411.18i			1.59275i
$887$	−74.6803	+	129.350i	−0.0841942	+	0.145829i	−0.905048	−	0.425310i	$-0.860165\pi$
$887$	−74.6803	+	129.350i	−0.0841942	+	0.145829i	0.820853	+	0.571139i	$0.193498\pi$
$888$	−55.5281	+	96.1776i	−0.0625317	+	0.108308i
$889$	289.809	−	501.963i	0.325994	−	0.564638i
$890$	341.855	+	592.111i	0.384107	+	0.665293i
$891$	136.640	+	236.667i	0.153356	+	0.265620i
$892$	−103.166	−	59.5628i	−0.115657	−	0.0667744i
$893$	61.2923	−	106.161i	0.0686364	−	0.118882i
$894$	−1031.57	+	595.575i	−1.15388	+	0.666191i
$895$	−922.994	+	1598.67i	−1.03128	+	1.78623i
$896$	425.328	−	736.690i	0.474697	−	0.822199i
$897$	−687.735	−	1191.19i	−0.766705	−	1.32797i
$898$	190.906	+	330.658i	0.212590	+	0.368216i
$899$	−655.808			−0.729486
$900$	−0.428516	−	0.742212i	−0.000476129	−	0.000824680i
$901$	602.003	+	347.566i	0.668150	+	0.385756i
$902$	635.169			0.704178
$903$	283.360	+	490.793i	0.313798	+	0.543514i
$904$			61.9703i			0.0685512i
$905$	−750.849	−	433.503i	−0.829668	−	0.479009i
$906$	−204.545	+	354.283i	−0.225767	+	0.391041i
$907$		−	261.065i		−	0.287834i	−0.989590	−	0.143917i	$-0.954030\pi$
$907$		−	261.065i		−	0.287834i	0.989590	−	0.143917i	$-0.0459698\pi$
$908$	427.150			0.470430
$909$	0.0752274			8.27585e−5
$910$	−599.981	+	1039.20i	−0.659320	+	1.14198i
$911$			843.571i			0.925984i	0.886362	+	0.462992i	$0.153224\pi$
$911$			843.571i			0.925984i	−0.886362	+	0.462992i	$0.846776\pi$
$912$			604.708i			0.663057i
$913$	−180.871	−	313.278i	−0.198107	−	0.343131i
$914$	1377.94	−	2386.65i	1.50759	−	2.61122i
$915$	1208.19			1.32042
$916$	2699.08	+	1558.31i	2.94659	+	1.70122i
$917$	115.848	−	200.655i	0.126334	−	0.218817i
$918$	−1699.98	−	981.485i	−1.85183	−	1.06916i
$919$	−184.295	+	106.403i	−0.200538	+	0.115781i	−0.596907	−	0.802311i	$-0.703604\pi$
$919$	−184.295	+	106.403i	−0.200538	+	0.115781i	0.396368	+	0.918092i	$0.370270\pi$
$920$	2079.67			2.26051
$921$	966.525	−	558.023i	1.04943	−	0.605889i
$922$	839.432	−	1453.94i	0.910447	−	1.57694i
$923$	−520.072			−0.563459
$924$	−144.209	−	249.777i	−0.156070	−	0.270321i
$925$	−12.5349	−	21.7110i	−0.0135512	−	0.0234714i
$926$	−1597.59			−1.72526
$927$	0.696714	+	1.20674i	0.000751580	+	0.00130177i
$928$	60.2335	+	104.327i	0.0649068	+	0.112422i
$929$	−383.000	+	221.125i	−0.412272	+	0.238025i	−0.691765	−	0.722122i	$-0.743167\pi$
$929$	−383.000	+	221.125i	−0.412272	+	0.238025i	0.279494	+	0.960148i	$0.409833\pi$
$930$		−	2251.48i		−	2.42095i
$931$	−551.702			−0.592591
$932$			2088.85i			2.24126i
$933$			1249.79i			1.33954i
$934$			659.458i			0.706058i
$935$	−359.566	+	207.596i	−0.384563	+	0.222027i
$936$	−2.31779	−	1.33818i	−0.00247627	−	0.00142968i
$937$	763.477	−	1322.38i	0.814810	−	1.41129i	−0.0946539	−	0.995510i	$-0.530174\pi$
$937$	763.477	−	1322.38i	0.814810	−	1.41129i	0.909464	−	0.415782i	$-0.136492\pi$
$938$	−762.072	−	439.982i	−0.812443	−	0.469064i
$939$	38.1932	+	66.1525i	0.0406743	+	0.0704500i
$940$	−353.479			−0.376042
$941$			573.175i			0.609112i	0.952494	+	0.304556i	$0.0985081\pi$
$941$			573.175i			0.609112i	−0.952494	+	0.304556i	$0.901492\pi$
$942$		−	1723.20i		−	1.82930i
$943$	−769.688	+	1333.14i	−0.816213	+	1.41372i
$944$	−268.822	+	465.613i	−0.284769	+	0.493234i
$945$	288.493	+	499.684i	0.305283	+	0.528766i
$946$		−	591.343i		−	0.625098i
$947$	510.869	−	884.852i	0.539461	−	0.934374i	−0.459472	−	0.888192i	$-0.651961\pi$
$947$	510.869	−	884.852i	0.539461	−	0.934374i	0.998933	−	0.0461814i	$-0.0147052\pi$
$948$		−	310.266i		−	0.327285i
$949$	370.776	−	642.203i	0.390702	−	0.676715i
$950$	−401.178	−	231.620i	−0.422292	−	0.243811i
$951$	−75.9472			−0.0798604
$952$	868.013	+	501.147i	0.911778	+	0.526415i
$953$	−224.135			−0.235189			−0.117595	−	0.993062i	$-0.537518\pi$
$953$	−224.135			−0.235189			−0.117595	+	0.993062i	$0.537518\pi$
$954$	1.23915	−	0.715426i	0.00129890	−	0.000749922i
$955$	−389.516	−	224.887i	−0.407870	−	0.235484i
$956$	−1806.51	−	1042.99i	−1.88966	−	1.09100i
$957$	175.863			0.183765
$958$	309.556			0.323127
$959$		−	808.227i		−	0.842781i
$960$	−1138.71	+	657.437i	−1.18616	+	0.684830i
$961$	230.790	−	399.741i	0.240156	−	0.415963i
$962$	−140.338	−	81.0239i	−0.145881	−	0.0842245i
$963$	1.28677	−	2.22874i	0.00133621	−	0.00231438i
$964$	−391.106	−	677.416i	−0.405712	−	0.702713i
$965$	1859.19			1.92663
$966$	1060.30			1.09762
$967$	1372.61			1.41945			0.709724	−	0.704480i	$-0.248820\pi$
$967$	1372.61			1.41945			0.709724	+	0.704480i	$0.248820\pi$
$968$		−	1404.55i		−	1.45098i
$969$	992.907			1.02467
$970$	−862.433	−	1493.78i	−0.889106	−	1.53998i
$971$	−466.888	+	269.558i	−0.480832	+	0.277609i	−0.720763	−	0.693181i	$-0.756209\pi$
$971$	−466.888	+	269.558i	−0.480832	+	0.277609i	0.239931	+	0.970790i	$0.422875\pi$
$972$	−4.61697	+	2.66561i	−0.00474997	+	0.00274239i
$973$		−	914.277i		−	0.939648i
$974$	662.468	−	382.476i	0.680152	−	0.392686i
$975$	369.635	−	213.409i	0.379113	−	0.218881i
$976$			896.806i			0.918859i
$977$	−179.792	−	103.803i	−0.184024	−	0.106246i	0.405158	−	0.914247i	$-0.367217\pi$
$977$	−179.792	−	103.803i	−0.184024	−	0.106246i	−0.589182	+	0.808000i	$0.700550\pi$
$978$	177.575	+	307.568i	0.181569	+	0.314487i
$979$		−	115.845i		−	0.118330i
$980$	795.432	+	1377.73i	0.811665	+	1.40585i
$981$	0.686225	−	1.18858i	0.000699516	−	0.00121160i
$982$	−1902.96	−	1098.68i	−1.93784	−	1.11881i
$983$	−166.794	+	288.896i	−0.169678	+	0.293892i	−0.938307	−	0.345804i	$-0.887606\pi$
$983$	−166.794	+	288.896i	−0.169678	+	0.293892i	0.768628	+	0.639696i	$0.220940\pi$
$984$			2116.07i			2.15048i
$985$	1714.25	+	989.723i	1.74036	+	1.00479i
$986$	−1095.54	+	632.509i	−1.11109	+	0.641490i
$987$	−87.0665			−0.0882133
$988$	−1974.00			−1.99798
$989$	1241.15	+	716.581i	1.25496	+	0.724551i
$990$			0.854623i			0.000863256i
$991$			18.0230i			0.0181867i	0.999959	+	0.00909333i	$0.00289454\pi$
$991$			18.0230i			0.0181867i	−0.999959	+	0.00909333i	$0.997105\pi$
$992$	−261.317			−0.263425
$993$	−205.713	−	118.769i	−0.207163	−	0.119606i
$994$	200.453	−	347.195i	0.201663	−	0.349290i
$995$	321.619			0.323235
$996$	2160.33	−	1247.26i	2.16900	−	1.25227i
$997$		−	1262.58i		−	1.26638i	−0.773997	−	0.633190i	$-0.781745\pi$
$997$		−	1262.58i		−	1.26638i	0.773997	−	0.633190i	$-0.218255\pi$
$998$	−474.899	+	822.549i	−0.475851	+	0.824197i
$999$	−67.4793	+	38.9592i	−0.0675469	+	0.0389982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	211.3.e.a.15.3	✓	68
211.197	odd	6	inner	211.3.e.a.197.3	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
211.3.e.a.15.3	✓	68	1.1	even	1	trivial
211.3.e.a.197.3	yes	68	211.197	odd	6	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:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	211.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.96716 + 1.71309i) q^{2} +(-2.59992 + 1.50106i) q^{3} +(3.86935 - 6.70190i) q^{4} +5.80352 q^{5} +(5.14291 - 8.90778i) q^{6} +(-3.19116 + 1.84241i) q^{7} +12.8094i q^{8} +(0.00637874 - 0.0110483i) q^{9} +O(q^{10})\)	\(q+(-2.96716 + 1.71309i) q^{2} +(-2.59992 + 1.50106i) q^{3} +(3.86935 - 6.70190i) q^{4} +5.80352 q^{5} +(5.14291 - 8.90778i) q^{6} +(-3.19116 + 1.84241i) q^{7} +12.8094i q^{8} +(0.00637874 - 0.0110483i) q^{9} +(-17.2200 + 9.94195i) q^{10} +3.36905 q^{11} +23.2325i q^{12} -16.3775 q^{13} +(6.31244 - 10.9335i) q^{14} +(-15.0887 + 8.71145i) q^{15} +(-6.46629 - 11.2000i) q^{16} +(-18.3899 + 10.6174i) q^{17} +0.0437094i q^{18} +(7.78756 + 13.4885i) q^{19} +(22.4558 - 38.8947i) q^{20} +(5.53116 - 9.58025i) q^{21} +(-9.99651 + 5.77149i) q^{22} -27.9752i q^{23} +(-19.2277 - 33.3034i) q^{24} +8.68090 q^{25} +(48.5947 - 28.0562i) q^{26} -26.9808i q^{27} +28.5158i q^{28} +(-15.0581 - 8.69377i) q^{29} +(29.8470 - 51.6965i) q^{30} +(32.6640 - 18.8586i) q^{31} +(-6.00013 - 3.46417i) q^{32} +(-8.75926 + 5.05716i) q^{33} +(36.3771 - 63.0070i) q^{34} +(-18.5200 + 10.6925i) q^{35} +(-0.0493631 - 0.0854995i) q^{36} +(-1.44396 - 2.50101i) q^{37} +(-46.2138 - 26.6816i) q^{38} +(42.5803 - 24.5837i) q^{39} +74.3398i q^{40} +(-47.6543 - 27.5132i) q^{41} +37.9015i q^{42} +(-25.6148 + 44.3662i) q^{43} +(13.0360 - 22.5791i) q^{44} +(0.0370192 - 0.0641191i) q^{45} +(47.9240 + 83.0068i) q^{46} +(-3.93527 - 6.81609i) q^{47} +(33.6237 + 19.4126i) q^{48} +(-17.7110 + 30.6764i) q^{49} +(-25.7576 + 14.8712i) q^{50} +(31.8748 - 55.2087i) q^{51} +(-63.3704 + 109.761i) q^{52} +(-16.3678 - 28.3498i) q^{53} +(46.2206 + 80.0564i) q^{54} +19.5524 q^{55} +(-23.6003 - 40.8769i) q^{56} +(-40.4940 - 23.3792i) q^{57} +59.5728 q^{58} +(-20.7864 - 36.0031i) q^{59} +134.831i q^{60} +(-60.0543 - 34.6723i) q^{61} +(-64.6128 + 111.913i) q^{62} +0.0470092i q^{63} +75.4681 q^{64} -95.0475 q^{65} +(17.3267 - 30.0108i) q^{66} -69.7008i q^{67} +164.330i q^{68} +(41.9925 + 72.7332i) q^{69} +(36.6344 - 63.4526i) q^{70} +31.7552 q^{71} +(0.141522 + 0.0817080i) q^{72} +(-22.6393 + 39.2124i) q^{73} +(8.56890 + 4.94726i) q^{74} +(-22.5696 + 13.0306i) q^{75} +120.531 q^{76} +(-10.7512 + 6.20719i) q^{77} +(-84.2282 + 145.888i) q^{78} -13.3548 q^{79} +(-37.5273 - 64.9992i) q^{80} +(40.5573 + 70.2474i) q^{81} +188.530 q^{82} +(-53.6861 - 92.9871i) q^{83} +(-42.8039 - 74.1386i) q^{84} +(-106.726 + 61.6184i) q^{85} -175.522i q^{86} +52.1996 q^{87} +43.1556i q^{88} -34.3851i q^{89} +0.253669i q^{90} +(52.2633 - 30.1742i) q^{91} +(-187.487 - 108.246i) q^{92} +(-56.6158 + 98.0614i) q^{93} +(23.3531 + 13.4829i) q^{94} +(45.1953 + 78.2806i) q^{95} +20.7998 q^{96} +86.7468i q^{97} -121.362i q^{98} +(0.0214903 - 0.0372223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} + 55 q^{4} - 4 q^{5} - q^{6} - 24 q^{7} + 82 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 + 55 * q^4 - 4 * q^5 - q^6 - 24 * q^7 + 82 * q^9	\( 68 q - 3 q^{2} + 55 q^{4} - 4 q^{5} - q^{6} - 24 q^{7} + 82 q^{9} + 4 q^{11} + 32 q^{13} + 12 q^{14} - 73 q^{16} + 51 q^{17} - 8 q^{19} - 46 q^{20} - 32 q^{21} - 33 q^{22} + 32 q^{24} + 252 q^{25} + 42 q^{26} - 60 q^{29} + 32 q^{30} + 126 q^{31} - 78 q^{32} - 117 q^{33} - 50 q^{34} - 45 q^{35} - 12 q^{36} + 113 q^{37} + 33 q^{38} - 162 q^{39} - 75 q^{41} + 13 q^{43} + 15 q^{44} + 83 q^{45} + 79 q^{46} - 117 q^{47} + 3 q^{48} + 130 q^{49} - 90 q^{50} - 181 q^{51} - 22 q^{52} - 140 q^{53} + 125 q^{54} - 50 q^{55} - 75 q^{56} - 234 q^{57} - 70 q^{58} - 84 q^{59} - 366 q^{61} - 75 q^{62} + 142 q^{64} + 72 q^{65} + 144 q^{66} + 130 q^{69} - 466 q^{70} + 402 q^{71} + 450 q^{72} - 54 q^{73} - 330 q^{74} - 402 q^{75} + 10 q^{76} + 69 q^{77} + 316 q^{78} - 370 q^{79} - 13 q^{80} - 206 q^{81} + 88 q^{82} - 105 q^{83} + 216 q^{84} - 168 q^{85} - 346 q^{87} + 264 q^{91} + 534 q^{92} + 310 q^{93} - 537 q^{94} + 265 q^{95} + 80 q^{96} - 50 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 + 55 * q^4 - 4 * q^5 - q^6 - 24 * q^7 + 82 * q^9 + 4 * q^11 + 32 * q^13 + 12 * q^14 - 73 * q^16 + 51 * q^17 - 8 * q^19 - 46 * q^20 - 32 * q^21 - 33 * q^22 + 32 * q^24 + 252 * q^25 + 42 * q^26 - 60 * q^29 + 32 * q^30 + 126 * q^31 - 78 * q^32 - 117 * q^33 - 50 * q^34 - 45 * q^35 - 12 * q^36 + 113 * q^37 + 33 * q^38 - 162 * q^39 - 75 * q^41 + 13 * q^43 + 15 * q^44 + 83 * q^45 + 79 * q^46 - 117 * q^47 + 3 * q^48 + 130 * q^49 - 90 * q^50 - 181 * q^51 - 22 * q^52 - 140 * q^53 + 125 * q^54 - 50 * q^55 - 75 * q^56 - 234 * q^57 - 70 * q^58 - 84 * q^59 - 366 * q^61 - 75 * q^62 + 142 * q^64 + 72 * q^65 + 144 * q^66 + 130 * q^69 - 466 * q^70 + 402 * q^71 + 450 * q^72 - 54 * q^73 - 330 * q^74 - 402 * q^75 + 10 * q^76 + 69 * q^77 + 316 * q^78 - 370 * q^79 - 13 * q^80 - 206 * q^81 + 88 * q^82 - 105 * q^83 + 216 * q^84 - 168 * q^85 - 346 * q^87 + 264 * q^91 + 534 * q^92 + 310 * q^93 - 537 * q^94 + 265 * q^95 + 80 * q^96 - 50 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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