LMFDB - Embedded newform 201.3.h.b.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(97,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("201.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.h (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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			97.2
Character	$\chi$	$=$	201.97
Dual form			201.3.h.b.172.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.01185 + 1.73889i) q^{2} +1.73205i q^{3} +(4.04748 - 7.01044i) q^{4} -4.44467i q^{5} +(-3.01185 - 5.21667i) q^{6} +(8.21480 + 4.74282i) q^{7} +14.2414i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-3.01185 + 1.73889i) q^{2} +1.73205i q^{3} +(4.04748 - 7.01044i) q^{4} -4.44467i q^{5} +(-3.01185 - 5.21667i) q^{6} +(8.21480 + 4.74282i) q^{7} +14.2414i q^{8} -3.00000 q^{9} +(7.72880 + 13.3867i) q^{10} +(-17.4916 - 10.0988i) q^{11} +(12.1424 + 7.01044i) q^{12} +(-22.3013 + 12.8757i) q^{13} -32.9889 q^{14} +7.69840 q^{15} +(-8.57425 - 14.8510i) q^{16} +(-4.68686 - 8.11788i) q^{17} +(9.03554 - 5.21667i) q^{18} +(-5.14112 - 8.90468i) q^{19} +(-31.1591 - 17.9897i) q^{20} +(-8.21480 + 14.2284i) q^{21} +70.2428 q^{22} +(8.64550 + 14.9744i) q^{23} -24.6668 q^{24} +5.24488 q^{25} +(44.7787 - 77.5591i) q^{26} -5.19615i q^{27} +(66.4984 - 38.3929i) q^{28} +(-13.1108 + 22.7086i) q^{29} +(-23.1864 + 13.3867i) q^{30} +(-49.1062 - 28.3515i) q^{31} +(2.31510 + 1.33663i) q^{32} +(17.4916 - 30.2964i) q^{33} +(28.2322 + 16.2999i) q^{34} +(21.0803 - 36.5121i) q^{35} +(-12.1424 + 21.0313i) q^{36} +(-13.4113 - 23.2290i) q^{37} +(30.9685 + 17.8797i) q^{38} +(-22.3013 - 38.6270i) q^{39} +63.2982 q^{40} +(-1.17666 - 0.679346i) q^{41} -57.1385i q^{42} -52.9835i q^{43} +(-141.594 + 81.7493i) q^{44} +13.3340i q^{45} +(-52.0778 - 30.0671i) q^{46} +(-39.5502 + 68.5029i) q^{47} +(25.7227 - 14.8510i) q^{48} +(20.4886 + 35.4873i) q^{49} +(-15.7968 + 9.12026i) q^{50} +(14.0606 - 8.11788i) q^{51} +208.456i q^{52} -46.7126i q^{53} +(9.03554 + 15.6500i) q^{54} +(-44.8858 + 77.7446i) q^{55} +(-67.5441 + 116.990i) q^{56} +(15.4234 - 8.90468i) q^{57} -91.1932i q^{58} -12.2725 q^{59} +(31.1591 - 53.9692i) q^{60} +(14.7664 - 8.52539i) q^{61} +197.200 q^{62} +(-24.6444 - 14.2284i) q^{63} +59.2970 q^{64} +(57.2281 + 99.1220i) q^{65} +121.664i q^{66} +(-24.1112 - 62.5112i) q^{67} -75.8798 q^{68} +(-25.9365 + 14.9744i) q^{69} +146.625i q^{70} +(8.31629 - 14.4042i) q^{71} -42.7241i q^{72} +(51.9567 + 89.9916i) q^{73} +(80.7854 + 46.6415i) q^{74} +9.08439i q^{75} -83.2343 q^{76} +(-95.7934 - 165.919i) q^{77} +(134.336 + 77.5591i) q^{78} +(-45.6242 - 26.3411i) q^{79} +(-66.0080 + 38.1097i) q^{80} +9.00000 q^{81} +4.72523 q^{82} +(31.3558 + 54.3099i) q^{83} +(66.4984 + 115.179i) q^{84} +(-36.0813 + 20.8316i) q^{85} +(92.1325 + 159.578i) q^{86} +(-39.3325 - 22.7086i) q^{87} +(143.821 - 249.104i) q^{88} -54.3000 q^{89} +(-23.1864 - 40.1600i) q^{90} -244.268 q^{91} +139.970 q^{92} +(49.1062 - 85.0544i) q^{93} -275.094i q^{94} +(-39.5784 + 22.8506i) q^{95} +(-2.31510 + 4.00988i) q^{96} +(-39.1432 + 22.5994i) q^{97} +(-123.417 - 71.2549i) q^{98} +(52.4749 + 30.2964i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9}+O(q^{10}) $ 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9	$ 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9} + 30 q^{10} + 12 q^{11} + 102 q^{12} + 30 q^{13} + 6 q^{14} - 6 q^{15} - 98 q^{16} + 4 q^{17} + 39 q^{19} + 108 q^{20} - 21 q^{21} - 82 q^{22} - 13 q^{23} - 36 q^{24} - 222 q^{25} + 29 q^{26} + 189 q^{28} - 90 q^{30} - 93 q^{31} - 33 q^{32} - 12 q^{33} + 72 q^{34} - 93 q^{35} - 102 q^{36} - 33 q^{37} - 210 q^{38} + 30 q^{39} + 274 q^{40} - 15 q^{41} - 9 q^{44} - 228 q^{46} - 131 q^{47} + 294 q^{48} + 295 q^{49} - 423 q^{50} - 12 q^{51} - 56 q^{55} + 349 q^{56} - 117 q^{57} - 116 q^{59} - 108 q^{60} + 120 q^{61} + 282 q^{62} - 63 q^{63} - 276 q^{64} + 136 q^{65} - 25 q^{67} + 10 q^{68} + 39 q^{69} + 169 q^{71} + 187 q^{73} + 849 q^{74} + 386 q^{76} - 348 q^{77} + 87 q^{78} + 51 q^{80} + 216 q^{81} - 14 q^{82} + 104 q^{83} + 189 q^{84} - 243 q^{85} + 641 q^{86} - 766 q^{88} + 152 q^{89} - 90 q^{90} + 32 q^{91} - 216 q^{92} + 93 q^{93} + 762 q^{95} + 33 q^{96} - 84 q^{97} - 1086 q^{98} - 36 q^{99}+O(q^{100}) $ 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9 + 30 * q^10 + 12 * q^11 + 102 * q^12 + 30 * q^13 + 6 * q^14 - 6 * q^15 - 98 * q^16 + 4 * q^17 + 39 * q^19 + 108 * q^20 - 21 * q^21 - 82 * q^22 - 13 * q^23 - 36 * q^24 - 222 * q^25 + 29 * q^26 + 189 * q^28 - 90 * q^30 - 93 * q^31 - 33 * q^32 - 12 * q^33 + 72 * q^34 - 93 * q^35 - 102 * q^36 - 33 * q^37 - 210 * q^38 + 30 * q^39 + 274 * q^40 - 15 * q^41 - 9 * q^44 - 228 * q^46 - 131 * q^47 + 294 * q^48 + 295 * q^49 - 423 * q^50 - 12 * q^51 - 56 * q^55 + 349 * q^56 - 117 * q^57 - 116 * q^59 - 108 * q^60 + 120 * q^61 + 282 * q^62 - 63 * q^63 - 276 * q^64 + 136 * q^65 - 25 * q^67 + 10 * q^68 + 39 * q^69 + 169 * q^71 + 187 * q^73 + 849 * q^74 + 386 * q^76 - 348 * q^77 + 87 * q^78 + 51 * q^80 + 216 * q^81 - 14 * q^82 + 104 * q^83 + 189 * q^84 - 243 * q^85 + 641 * q^86 - 766 * q^88 + 152 * q^89 - 90 * q^90 + 32 * q^91 - 216 * q^92 + 93 * q^93 + 762 * q^95 + 33 * q^96 - 84 * q^97 - 1086 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−3.01185	+	1.73889i	−1.50592	+	0.869445i	−0.505947	+	0.862565i	$0.668857\pi$
$2$	−3.01185	+	1.73889i	−1.50592	+	0.869445i	−0.999976	+	0.00688036i	$0.997810\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	4.04748	−	7.01044i	1.01187	−	1.75261i
$5$		−	4.44467i		−	0.888935i	−0.895795	−	0.444467i	$-0.853393\pi$
$5$		−	4.44467i		−	0.888935i	0.895795	−	0.444467i	$-0.146607\pi$
$6$	−3.01185	−	5.21667i	−0.501974	−	0.869445i
$7$	8.21480	+	4.74282i	1.17354	+	0.677545i	0.954512	−	0.298173i	$-0.0963771\pi$
$7$	8.21480	+	4.74282i	1.17354	+	0.677545i	0.219031	+	0.975718i	$0.429710\pi$
$8$			14.2414i			1.78017i
$9$	−3.00000			−0.333333
$10$	7.72880	+	13.3867i	0.772880	+	1.33867i
$11$	−17.4916	−	10.0988i	−1.59015	−	0.918072i	−0.993280	−	0.115732i	$-0.963079\pi$
$11$	−17.4916	−	10.0988i	−1.59015	−	0.918072i	−0.596867	−	0.802340i	$-0.703588\pi$
$12$	12.1424	+	7.01044i	1.01187	+	0.584203i
$13$	−22.3013	+	12.8757i	−1.71549	+	0.990436i	−0.788756	+	0.614707i	$0.789274\pi$
$13$	−22.3013	+	12.8757i	−1.71549	+	0.990436i	−0.926730	+	0.375729i	$0.877392\pi$
$14$	−32.9889			−2.35635
$15$	7.69840			0.513227
$16$	−8.57425	−	14.8510i	−0.535890	−	0.928189i
$17$	−4.68686	−	8.11788i	−0.275698	−	0.477522i	0.694613	−	0.719383i	$-0.255576\pi$
$17$	−4.68686	−	8.11788i	−0.275698	−	0.477522i	−0.970311	+	0.241861i	$0.922242\pi$
$18$	9.03554	−	5.21667i	0.501974	−	0.289815i
$19$	−5.14112	−	8.90468i	−0.270585	−	0.468667i	0.698427	−	0.715682i	$-0.253884\pi$
$19$	−5.14112	−	8.90468i	−0.270585	−	0.468667i	−0.969012	+	0.247014i	$0.920551\pi$
$20$	−31.1591	−	17.9897i	−1.55796	−	0.899486i
$21$	−8.21480	+	14.2284i	−0.391181	+	0.677545i
$22$	70.2428			3.19285
$23$	8.64550	+	14.9744i	0.375891	+	0.651063i	0.990460	−	0.137801i	$-0.0440033\pi$
$23$	8.64550	+	14.9744i	0.375891	+	0.651063i	−0.614569	+	0.788863i	$0.710670\pi$
$24$	−24.6668			−1.02778
$25$	5.24488			0.209795
$26$	44.7787	−	77.5591i	1.72226	−	2.98304i
$27$		−	5.19615i		−	0.192450i
$28$	66.4984	−	38.3929i	2.37494	−	1.37117i
$29$	−13.1108	+	22.7086i	−0.452098	+	0.783056i	−0.998516	−	0.0544561i	$-0.982658\pi$
$29$	−13.1108	+	22.7086i	−0.452098	+	0.783056i	0.546418	+	0.837512i	$0.315991\pi$
$30$	−23.1864	+	13.3867i	−0.772880	+	0.446222i
$31$	−49.1062	−	28.3515i	−1.58407	−	0.914564i	−0.994256	−	0.107025i	$-0.965867\pi$
$31$	−49.1062	−	28.3515i	−1.58407	−	0.914564i	−0.589815	−	0.807539i	$-0.700799\pi$
$32$	2.31510	+	1.33663i	0.0723470	+	0.0417695i
$33$	17.4916	−	30.2964i	0.530049	−	0.918072i
$34$	28.2322	+	16.2999i	0.830359	+	0.479408i
$35$	21.0803	−	36.5121i	0.602293	−	1.04320i
$36$	−12.1424	+	21.0313i	−0.337290	+	0.584203i
$37$	−13.4113	−	23.2290i	−0.362467	−	0.627811i	0.625899	−	0.779904i	$-0.284732\pi$
$37$	−13.4113	−	23.2290i	−0.362467	−	0.627811i	−0.988366	+	0.152093i	$0.951399\pi$
$38$	30.9685	+	17.8797i	0.814961	+	0.470518i
$39$	−22.3013	−	38.6270i	−0.571828	−	0.990436i
$40$	63.2982			1.58245
$41$	−1.17666	−	0.679346i	−0.0286990	−	0.0165694i	0.485582	−	0.874191i	$-0.338608\pi$
$41$	−1.17666	−	0.679346i	−0.0286990	−	0.0165694i	−0.514281	+	0.857622i	$0.671941\pi$
$42$		−	57.1385i		−	1.36044i
$43$		−	52.9835i		−	1.23217i	−0.787678	−	0.616087i	$-0.788717\pi$
$43$		−	52.9835i		−	1.23217i	0.787678	−	0.616087i	$-0.211283\pi$
$44$	−141.594	+	81.7493i	−3.21804	+	1.85794i
$45$			13.3340i			0.296312i
$46$	−52.0778	−	30.0671i	−1.13213	−	0.653633i
$47$	−39.5502	+	68.5029i	−0.841493	+	1.45751i	0.0471392	+	0.998888i	$0.484990\pi$
$47$	−39.5502	+	68.5029i	−0.841493	+	1.45751i	−0.888632	+	0.458620i	$0.848344\pi$
$48$	25.7227	−	14.8510i	0.535890	−	0.309396i
$49$	20.4886	+	35.4873i	0.418135	+	0.724231i
$50$	−15.7968	+	9.12026i	−0.315935	+	0.182405i
$51$	14.0606	−	8.11788i	0.275698	−	0.159174i
$52$			208.456i			4.00877i
$53$		−	46.7126i		−	0.881370i	−0.897662	−	0.440685i	$-0.854736\pi$
$53$		−	46.7126i		−	0.881370i	0.897662	−	0.440685i	$-0.145264\pi$
$54$	9.03554	+	15.6500i	0.167325	+	0.289815i
$55$	−44.8858	+	77.7446i	−0.816106	+	1.41354i
$56$	−67.5441	+	116.990i	−1.20615	+	2.08911i
$57$	15.4234	−	8.90468i	0.270585	−	0.156222i
$58$		−	91.1932i		−	1.57230i
$59$	−12.2725			−0.208008			−0.104004	−	0.994577i	$-0.533165\pi$
$59$	−12.2725			−0.208008			−0.104004	+	0.994577i	$0.533165\pi$
$60$	31.1591	−	53.9692i	0.519318	−	0.899486i
$61$	14.7664	−	8.52539i	0.242072	−	0.139761i	−0.374056	−	0.927406i	$-0.622033\pi$
$61$	14.7664	−	8.52539i	0.242072	−	0.139761i	0.616129	+	0.787645i	$0.288700\pi$
$62$	197.200			3.18065
$63$	−24.6444	−	14.2284i	−0.391181	−	0.225848i
$64$	59.2970			0.926515
$65$	57.2281	+	99.1220i	0.880433	+	1.52495i
$66$			121.664i			1.84339i
$67$	−24.1112	−	62.5112i	−0.359868	−	0.933003i
$67$	−24.1112	−	62.5112i	−0.359868	−	0.933003i
$68$	−75.8798			−1.11588
$69$	−25.9365	+	14.9744i	−0.375891	+	0.217021i
$70$			146.625i			2.09464i
$71$	8.31629	−	14.4042i	0.117131	−	0.202877i	−0.801499	−	0.597997i	$-0.795964\pi$
$71$	8.31629	−	14.4042i	0.117131	−	0.202877i	0.918630	+	0.395120i	$0.129297\pi$
$72$		−	42.7241i		−	0.593390i
$73$	51.9567	+	89.9916i	0.711735	+	1.23276i	0.964205	+	0.265157i	$0.0854238\pi$
$73$	51.9567	+	89.9916i	0.711735	+	1.23276i	−0.252470	+	0.967605i	$0.581243\pi$
$74$	80.7854	+	46.6415i	1.09169	+	0.630290i
$75$			9.08439i			0.121125i
$76$	−83.2343			−1.09519
$77$	−95.7934	−	165.919i	−1.24407	−	2.15479i
$78$	134.336	+	77.5591i	1.72226	+	0.994347i
$79$	−45.6242	−	26.3411i	−0.577521	−	0.333432i	0.182626	−	0.983182i	$-0.441540\pi$
$79$	−45.6242	−	26.3411i	−0.577521	−	0.333432i	−0.760148	+	0.649750i	$0.774873\pi$
$80$	−66.0080	+	38.1097i	−0.825100	+	0.476372i
$81$	9.00000			0.111111
$82$	4.72523			0.0576247
$83$	31.3558	+	54.3099i	0.377781	+	0.654336i	0.990739	−	0.135779i	$-0.0433538\pi$
$83$	31.3558	+	54.3099i	0.377781	+	0.654336i	−0.612958	+	0.790116i	$0.710020\pi$
$84$	66.4984	+	115.179i	0.791648	+	1.37117i
$85$	−36.0813	+	20.8316i	−0.424486	+	0.245077i
$86$	92.1325	+	159.578i	1.07131	+	1.85556i
$87$	−39.3325	−	22.7086i	−0.452098	−	0.261019i
$88$	143.821	−	249.104i	1.63432	−	2.83073i
$89$	−54.3000			−0.610112			−0.305056	−	0.952334i	$-0.598675\pi$
$89$	−54.3000			−0.610112			−0.305056	+	0.952334i	$0.598675\pi$
$90$	−23.1864	−	40.1600i	−0.257627	−	0.446222i
$91$	−244.268			−2.68426
$92$	139.970			1.52141
$93$	49.1062	−	85.0544i	0.528024	−	0.914564i
$94$		−	275.094i		−	2.92653i
$95$	−39.5784	+	22.8506i	−0.416615	+	0.240533i
$96$	−2.31510	+	4.00988i	−0.0241157	+	0.0417695i
$97$	−39.1432	+	22.5994i	−0.403538	+	0.232983i	−0.688010	−	0.725702i	$-0.741515\pi$
$97$	−39.1432	+	22.5994i	−0.403538	+	0.232983i	0.284471	+	0.958685i	$0.408182\pi$
$98$	−123.417	−	71.2549i	−1.25936	−	0.727091i
$99$	52.4749	+	30.2964i	0.530049	+	0.306024i
$100$	21.2285	−	36.7689i	0.212285	−	0.367689i
$101$	103.865	+	59.9666i	1.02837	+	0.593728i	0.916517	−	0.399997i	$-0.130989\pi$
$101$	103.865	+	59.9666i	1.02837	+	0.593728i	0.111851	+	0.993725i	$0.464322\pi$
$102$	−28.2322	+	48.8996i	−0.276786	+	0.479408i
$103$	−22.7737	+	39.4452i	−0.221104	+	0.382963i	−0.955143	−	0.296144i	$-0.904299\pi$
$103$	−22.7737	+	39.4452i	−0.221104	+	0.382963i	0.734040	+	0.679107i	$0.237633\pi$
$104$	−183.367	−	317.601i	−1.76314	−	3.05385i
$105$	63.2408	+	36.5121i	0.602293	+	0.347734i
$106$	81.2281	+	140.691i	0.766303	+	1.32728i
$107$	−1.00311			−0.00937481			−0.00468741	−	0.999989i	$-0.501492\pi$
$107$	−1.00311			−0.00937481			−0.00468741	+	0.999989i	$0.501492\pi$
$108$	−36.4273	−	21.0313i	−0.337290	−	0.194734i
$109$			11.4639i			0.105173i	0.998616	+	0.0525865i	$0.0167465\pi$
$109$			11.4639i			0.105173i	−0.998616	+	0.0525865i	$0.983253\pi$
$110$		−	312.206i		−	2.83824i
$111$	40.2338	−	23.2290i	0.362467	−	0.209270i
$112$		−	162.664i		−	1.45236i
$113$	22.0208	+	12.7137i	0.194874	+	0.112511i	0.594262	−	0.804271i	$-0.297444\pi$
$113$	22.0208	+	12.7137i	0.194874	+	0.112511i	−0.399388	+	0.916782i	$0.630777\pi$
$114$	−30.9685	+	53.6391i	−0.271654	+	0.470518i
$115$	66.5565	−	38.4264i	0.578752	−	0.334143i
$116$	106.132	+	183.825i	0.914928	+	1.58470i
$117$	66.9039	−	38.6270i	0.571828	−	0.330145i
$118$	36.9628	−	21.3405i	0.313244	−	0.180852i
$119$		−	88.9157i		−	0.747190i
$120$			109.636i			0.913631i
$121$	143.471	+	248.499i	1.18571	+	2.05371i
$122$	−29.6494	+	51.3544i	−0.243028	+	0.420937i
$123$	1.17666	−	2.03804i	0.00956635	−	0.0165694i
$124$	−397.513	+	229.504i	−3.20575	+	1.85084i
$125$		−	134.429i		−	1.07543i
$126$	98.9668			0.785451
$127$	−42.2383	+	73.1589i	−0.332585	+	0.576054i	−0.983018	−	0.183510i	$-0.941254\pi$
$127$	−42.2383	+	73.1589i	−0.332585	+	0.576054i	0.650433	+	0.759564i	$0.274587\pi$
$128$	−187.854	+	108.457i	−1.46761	+	0.847324i
$129$	91.7701			0.711396
$130$	−344.725	−	199.027i	−2.65173	−	1.53098i
$131$	−43.9434			−0.335446			−0.167723	−	0.985834i	$-0.553641\pi$
$131$	−43.9434			−0.335446			−0.167723	+	0.985834i	$0.553641\pi$
$132$	−141.594	−	245.248i	−1.07268	−	1.85794i
$133$		−	97.5336i		−	0.733335i
$134$	181.319	+	146.347i	1.35313	+	1.09215i
$135$	−23.0952			−0.171076
$136$	115.610	−	66.7472i	0.850071	−	0.490789i
$137$		−	153.174i		−	1.11806i	−0.829148	−	0.559029i	$-0.811174\pi$
$137$		−	153.174i		−	1.11806i	0.829148	−	0.559029i	$-0.188826\pi$
$138$	52.0778	−	90.2014i	0.377375	−	0.653633i
$139$		−	111.824i		−	0.804487i	−0.915533	−	0.402243i	$-0.868231\pi$
$139$		−	111.824i		−	0.804487i	0.915533	−	0.402243i	$-0.131769\pi$
$140$	−170.644	−	295.564i	−1.21888	−	2.11117i
$141$	−118.651	−	68.5029i	−0.841493	−	0.485836i
$142$			57.8445i			0.407355i
$143$	520.115			3.63717
$144$	25.7227	+	44.5531i	0.178630	+	0.309396i
$145$	100.932	+	58.2734i	0.696086	+	0.401885i
$146$	−312.971	−	180.694i	−2.14364	−	1.23763i
$147$	−61.4659	+	35.4873i	−0.418135	+	0.241410i
$148$	−217.127			−1.46708
$149$	−70.5062			−0.473196			−0.236598	−	0.971608i	$-0.576032\pi$
$149$	−70.5062			−0.473196			−0.236598	+	0.971608i	$0.576032\pi$
$150$	−15.7968	−	27.3608i	−0.105312	−	0.182405i
$151$	113.788	+	197.086i	0.753560	+	1.30520i	0.946087	+	0.323913i	$0.104998\pi$
$151$	113.788	+	197.086i	0.753560	+	1.30520i	−0.192527	+	0.981292i	$0.561668\pi$
$152$	126.815	−	73.2165i	0.834308	−	0.481688i
$153$	14.0606	+	24.3536i	0.0918992	+	0.159174i
$154$	577.030	+	333.149i	3.74695	+	2.16330i
$155$	−126.013	+	218.261i	−0.812988	+	1.40814i
$156$	−361.056			−2.31446
$157$	−51.2071	−	88.6933i	−0.326160	−	0.564926i	0.655586	−	0.755120i	$-0.272421\pi$
$157$	−51.2071	−	88.6933i	−0.326160	−	0.564926i	−0.981746	+	0.190194i	$0.939088\pi$
$158$	183.217			1.15960
$159$	80.9086			0.508859
$160$	5.94086	−	10.2899i	0.0371304	−	0.0643117i
$161$			164.016i			1.01873i
$162$	−27.1066	+	15.6500i	−0.167325	+	0.0966050i
$163$	20.4535	−	35.4264i	0.125481	−	0.217340i	−0.796440	−	0.604718i	$-0.793286\pi$
$163$	20.4535	−	35.4264i	0.125481	−	0.217340i	0.921921	+	0.387378i	$0.126619\pi$
$164$	−9.52502	+	5.49927i	−0.0580794	+	0.0335321i
$165$	−134.658	−	77.7446i	−0.816106	−	0.471179i
$166$	−188.878	−	109.049i	−1.13782	−	0.656920i
$167$	−55.9885	+	96.9750i	−0.335261	+	0.580689i	−0.983535	−	0.180718i	$-0.942158\pi$
$167$	−55.9885	+	96.9750i	−0.335261	+	0.580689i	0.648274	+	0.761407i	$0.275491\pi$
$168$	−202.632	−	116.990i	−1.20615	−	0.696368i
$169$	247.066	−	427.930i	1.46193	−	2.53213i
$170$	72.4476	−	125.483i	0.426162	−	0.738135i
$171$	15.4234	+	26.7140i	0.0901951	+	0.156222i
$172$	−371.438	−	214.450i	−2.15952	−	1.24680i
$173$	−35.9804	−	62.3198i	−0.207979	−	0.360230i	0.743099	−	0.669182i	$-0.233355\pi$
$173$	−35.9804	−	62.3198i	−0.207979	−	0.360230i	−0.951078	+	0.308951i	$0.900022\pi$
$174$	157.951			0.907766
$175$	43.0856	+	24.8755i	0.246203	+	0.142146i
$176$			346.358i			1.96794i
$177$		−	21.2565i		−	0.120093i
$178$	163.543	−	94.4217i	0.918782	−	0.530459i
$179$			114.644i			0.640470i	0.947338	+	0.320235i	$0.103762\pi$
$179$			114.644i			0.640470i	−0.947338	+	0.320235i	$0.896238\pi$
$180$	93.4773	+	53.9692i	0.519318	+	0.299829i
$181$	−82.8610	+	143.519i	−0.457795	+	0.792925i	−0.998844	−	0.0480664i	$-0.984694\pi$
$181$	−82.8610	+	143.519i	−0.457795	+	0.792925i	0.541049	+	0.840991i	$0.318027\pi$
$182$	735.697	−	424.755i	4.04229	−	2.33382i
$183$	14.7664	+	25.5762i	0.0806908	+	0.139761i
$184$	−213.256	+	123.124i	−1.15900	+	0.669150i
$185$	−103.245	+	59.6088i	−0.558083	+	0.322210i
$186$			341.561i			1.83635i
$187$			189.326i			1.01244i
$188$	320.157	+	554.528i	1.70296	+	2.94962i
$189$	24.6444	−	42.6853i	0.130394	−	0.225848i
$190$	79.4694	−	137.645i	0.418260	−	0.724447i
$191$	−195.874	+	113.088i	−1.02552	+	0.592083i	−0.915698	−	0.401868i	$-0.868361\pi$
$191$	−195.874	+	113.088i	−1.02552	+	0.592083i	−0.109821	+	0.993951i	$0.535028\pi$
$192$			102.705i			0.534924i
$193$	−117.879			−0.610772			−0.305386	−	0.952229i	$-0.598785\pi$
$193$	−117.879			−0.610772			−0.305386	+	0.952229i	$0.598785\pi$
$194$	78.5956	−	136.132i	0.405132	−	0.701709i
$195$	−171.684	+	99.1220i	−0.880433	+	0.508318i
$196$	331.709			1.69239
$197$	227.126	+	131.131i	1.15292	+	0.665639i	0.949597	−	0.313472i	$-0.101492\pi$
$197$	227.126	+	131.131i	1.15292	+	0.665639i	0.203324	+	0.979112i	$0.434826\pi$
$198$	−210.728			−1.06428
$199$	−0.395138	−	0.684398i	−0.00198562	−	0.00343919i	0.865031	−	0.501719i	$-0.167299\pi$
$199$	−0.395138	−	0.684398i	−0.00198562	−	0.00343919i	−0.867017	+	0.498279i	$0.833965\pi$
$200$			74.6942i			0.373471i
$201$	108.273	−	41.7618i	0.538670	−	0.207770i
$202$	−417.101			−2.06486
$203$	−215.406	+	124.365i	−1.06111	+	0.612633i
$204$		−	131.428i		−	0.644254i
$205$	−3.01947	+	5.22987i	−0.0147291	+	0.0255116i
$206$		−	158.404i		−	0.768950i
$207$	−25.9365	−	44.9233i	−0.125297	−	0.217021i
$208$	382.434	+	220.798i	1.83862	+	1.06153i
$209$			207.676i			0.993667i
$210$	−253.962			−1.20934
$211$	143.778	+	249.031i	0.681412	+	1.18024i	0.974550	+	0.224170i	$0.0719672\pi$
$211$	143.778	+	249.031i	0.681412	+	1.18024i	−0.293138	+	0.956070i	$0.594699\pi$
$212$	−327.476	−	189.068i	−1.54470	−	0.891831i
$213$	24.9489	+	14.4042i	0.117131	+	0.0676255i
$214$	3.02120	−	1.74429i	0.0141177	−	0.00815089i
$215$	−235.494			−1.09532
$216$	74.0003			0.342594
$217$	−268.932	−	465.803i	−1.23932	−	2.14656i
$218$	−19.9344	−	34.5274i	−0.0914421	−	0.158382i
$219$	−155.870	+	89.9916i	−0.711735	+	0.410921i
$220$	363.349	+	629.339i	1.65159	+	2.86063i
$221$	209.046	+	120.693i	0.945910	+	0.546122i
$222$	−80.7854	+	139.924i	−0.363898	+	0.630290i
$223$	−97.9045			−0.439034			−0.219517	−	0.975609i	$-0.570448\pi$
$223$	−97.9045			−0.439034			−0.219517	+	0.975609i	$0.570448\pi$
$224$	12.6787	+	21.9602i	0.0566015	+	0.0980367i
$225$	−15.7346			−0.0699317
$226$	−88.4309			−0.391287
$227$	88.7391	−	153.701i	0.390921	−	0.677096i	−0.601650	−	0.798760i	$-0.705490\pi$
$227$	88.7391	−	153.701i	0.390921	−	0.677096i	0.992571	+	0.121664i	$0.0388231\pi$
$228$		−	144.166i		−	0.632307i
$229$	−93.9879	+	54.2639i	−0.410428	+	0.236960i	−0.690973	−	0.722880i	$-0.742818\pi$
$229$	−93.9879	+	54.2639i	−0.410428	+	0.236960i	0.280546	+	0.959841i	$0.409485\pi$
$230$	−133.639	+	231.469i	−0.581038	+	1.00639i
$231$	287.380	−	165.919i	1.24407	−	0.718265i
$232$	−323.402	−	186.716i	−1.39397	−	0.804811i
$233$	−81.4990	−	47.0535i	−0.349781	−	0.201946i	0.314808	−	0.949155i	$-0.398060\pi$
$233$	−81.4990	−	47.0535i	−0.349781	−	0.201946i	−0.664589	+	0.747209i	$0.731393\pi$
$234$	−134.336	+	232.677i	−0.574086	+	0.994347i
$235$	304.473	+	175.788i	1.29563	+	0.748032i
$236$	−49.6726	+	86.0354i	−0.210477	+	0.364557i
$237$	45.6242	−	79.0234i	0.192507	−	0.333432i
$238$	154.615	+	267.800i	0.649641	+	1.12521i
$239$	−59.6313	−	34.4281i	−0.249503	−	0.144051i	0.370034	−	0.929018i	$-0.379346\pi$
$239$	−59.6313	−	34.4281i	−0.249503	−	0.144051i	−0.619537	+	0.784968i	$0.712680\pi$
$240$	−66.0080	−	114.329i	−0.275033	−	0.476372i
$241$	114.724			0.476032			0.238016	−	0.971261i	$-0.423503\pi$
$241$	114.724			0.476032			0.238016	+	0.971261i	$0.423503\pi$
$242$	−864.227	−	498.961i	−3.57118	−	2.06182i
$243$			15.5885i			0.0641500i
$244$		−	138.025i		−	0.565678i
$245$	157.730	−	91.0652i	0.643794	−	0.371695i
$246$			8.18434i			0.0332697i
$247$	229.307	+	132.391i	0.928370	+	0.535995i
$248$	403.764	−	699.339i	1.62808	−	2.81992i
$249$	−94.0675	+	54.3099i	−0.377781	+	0.218112i
$250$	233.757	+	404.878i	0.935026	+	1.61951i
$251$	15.1636	−	8.75469i	0.0604126	−	0.0348792i	−0.469489	−	0.882938i	$-0.655562\pi$
$251$	15.1636	−	8.75469i	0.0604126	−	0.0348792i	0.529902	+	0.848059i	$0.322229\pi$
$252$	−199.495	+	115.179i	−0.791648	+	0.457058i
$253$		−	349.236i		−	1.38038i
$254$		−	293.791i		−	1.15666i
$255$	−36.0813	−	62.4947i	−0.141495	−	0.245077i
$256$	258.597	−	447.903i	1.01015	−	1.74962i
$257$	83.1354	−	143.995i	0.323484	−	0.560291i	−0.657720	−	0.753262i	$-0.728479\pi$
$257$	83.1354	−	143.995i	0.323484	−	0.560291i	0.981204	+	0.192972i	$0.0618125\pi$
$258$	−276.397	+	159.578i	−1.07131	+	0.618520i
$259$		−	254.429i		−	0.982351i
$260$	926.518			3.56353
$261$	39.3325	−	68.1259i	0.150699	−	0.261019i
$262$	132.351	−	76.4127i	0.505156	−	0.291652i
$263$	8.40919			0.0319741			0.0159871	−	0.999872i	$-0.494911\pi$
$263$	8.40919			0.0319741			0.0159871	+	0.999872i	$0.494911\pi$
$264$	431.462	+	249.104i	1.63432	+	0.943578i
$265$	−207.622			−0.783480
$266$	169.600	+	293.756i	0.637594	+	1.10435i
$267$		−	94.0503i		−	0.352248i
$268$	−535.820	−	83.9829i	−1.99933	−	0.313369i
$269$	7.49104			0.0278477			0.0139239	−	0.999903i	$-0.495568\pi$
$269$	7.49104			0.0278477			0.0139239	+	0.999903i	$0.495568\pi$
$270$	69.5592	−	40.1600i	0.257627	−	0.148741i
$271$		−	63.1817i		−	0.233143i	−0.993182	−	0.116571i	$-0.962810\pi$
$271$		−	63.1817i		−	0.233143i	0.993182	−	0.116571i	$-0.0371904\pi$
$272$	−80.3726	+	139.209i	−0.295487	+	0.511799i
$273$		−	423.084i		−	1.54976i
$274$	266.353	+	461.336i	0.972090	+	1.68371i
$275$	−91.7414	−	52.9669i	−0.333605	−	0.192607i
$276$			242.435i			0.878387i
$277$	126.139			0.455374			0.227687	−	0.973734i	$-0.426884\pi$
$277$	126.139			0.455374			0.227687	+	0.973734i	$0.426884\pi$
$278$	194.449	+	336.796i	0.699457	+	1.21150i
$279$	147.319	+	85.0544i	0.528024	+	0.304855i
$280$	519.982	+	300.212i	1.85708	+	1.07218i
$281$	−25.5706	+	14.7632i	−0.0909987	+	0.0525381i	−0.544809	−	0.838560i	$-0.683398\pi$
$281$	−25.5706	+	14.7632i	−0.0909987	+	0.0525381i	0.453810	+	0.891098i	$0.350064\pi$
$282$	476.476			1.68963
$283$	−14.4901			−0.0512018			−0.0256009	−	0.999672i	$-0.508150\pi$
$283$	−14.4901			−0.0512018			−0.0256009	+	0.999672i	$0.508150\pi$
$284$	−67.3200	−	116.602i	−0.237042	−	0.410569i
$285$	−39.5784	−	68.5518i	−0.138872	−	0.240533i
$286$	−1566.51	+	904.422i	−5.47729	+	3.16232i
$287$	−6.44402	−	11.1614i	−0.0224530	−	0.0388898i
$288$	−6.94531	−	4.00988i	−0.0241157	−	0.0139232i
$289$	100.567	−	174.187i	0.347982	−	0.602722i
$290$	−405.324			−1.39767
$291$	−39.1432	−	67.7981i	−0.134513	−	0.232983i
$292$	841.174			2.88073
$293$	468.877			1.60026			0.800131	−	0.599825i	$-0.204763\pi$
$293$	468.877			1.60026			0.800131	+	0.599825i	$0.204763\pi$
$294$	123.417	−	213.765i	0.419786	−	0.727091i
$295$			54.5471i			0.184906i
$296$	330.813	−	190.995i	1.11761	−	0.645253i
$297$	−52.4749	+	90.8891i	−0.176683	+	0.306024i
$298$	212.354	−	122.603i	0.712597	−	0.411418i
$299$	−385.612	−	222.633i	−1.28967	−	0.744592i
$300$	63.6856	+	36.7689i	0.212285	+	0.122563i
$301$	251.291	−	435.249i	0.834854	−	1.44601i
$302$	−685.421	−	395.728i	−2.26961	−	1.31036i
$303$	−103.865	+	179.900i	−0.342789	+	0.593728i
$304$	−88.1624	+	152.702i	−0.290008	+	0.502309i
$305$	−37.8926	−	65.6319i	−0.124238	−	0.215187i
$306$	−84.6966	−	48.8996i	−0.276786	−	0.159803i
$307$	−105.804	−	183.258i	−0.344639	−	0.596932i	0.640649	−	0.767834i	$-0.278665\pi$
$307$	−105.804	−	183.258i	−0.344639	−	0.596932i	−0.985288	+	0.170902i	$0.945332\pi$
$308$	−1550.89			−5.03535
$309$	−68.3211	−	39.4452i	−0.221104	−	0.127654i
$310$		−	876.492i		−	2.82739i
$311$		−	151.217i		−	0.486230i	−0.969998	−	0.243115i	$-0.921831\pi$
$311$		−	151.217i		−	0.486230i	0.969998	−	0.243115i	$-0.0781692\pi$
$312$	550.101	−	317.601i	1.76314	−	1.01795i
$313$			475.534i			1.51928i	0.650346	+	0.759638i	$0.274624\pi$
$313$			475.534i			1.51928i	−0.650346	+	0.759638i	$0.725376\pi$
$314$	308.456	+	178.087i	0.982344	+	0.567156i
$315$	−63.2408	+	109.536i	−0.200764	+	0.347734i
$316$	−369.326	+	213.230i	−1.16875	+	0.674780i
$317$	76.7771	+	132.982i	0.242199	+	0.419501i	0.961340	−	0.275363i	$-0.0887979\pi$
$317$	76.7771	+	132.982i	0.242199	+	0.419501i	−0.719141	+	0.694864i	$0.755465\pi$
$318$	−243.684	+	140.691i	−0.766303	+	0.442425i
$319$	458.660	−	264.807i	1.43780	−	0.830117i
$320$		−	263.556i		−	0.823612i
$321$		−	1.73743i		−	0.00541255i
$322$	−285.206	−	493.991i	−0.885732	−	1.53413i
$323$	−48.1914	+	83.4700i	−0.149199	+	0.258421i
$324$	36.4273	−	63.0939i	0.112430	−	0.194734i
$325$	−116.968	+	67.5313i	−0.359900	+	0.207789i
$326$			142.265i			0.436397i
$327$	−19.8560			−0.0607216
$328$	9.67480	−	16.7573i	0.0294964	−	0.0510892i
$329$	−649.793	+	375.158i	−1.97506	+	1.14030i
$330$	540.757			1.63866
$331$	−432.115	−	249.482i	−1.30548	−	0.753722i	−0.324145	−	0.946007i	$-0.605077\pi$
$331$	−432.115	−	249.482i	−1.30548	−	0.753722i	−0.981339	+	0.192285i	$0.938410\pi$
$332$	507.648			1.52906
$333$	40.2338	+	69.6871i	0.120822	+	0.209270i
$334$		−	389.432i		−	1.16596i
$335$	−277.842	+	107.166i	−0.829379	+	0.319899i
$336$	281.743			0.838520
$337$	−134.968	+	77.9238i	−0.400498	+	0.231228i	−0.686699	−	0.726942i	$-0.740941\pi$
$337$	−134.968	+	77.9238i	−0.400498	+	0.231228i	0.286201	+	0.958170i	$0.407608\pi$
$338$			1718.48i			5.08426i
$339$	−22.0208	+	38.1411i	−0.0649580	+	0.112511i
$340$			337.261i			0.991945i
$341$	572.631	+	991.827i	1.67927	+	2.90858i
$342$	−92.9056	−	53.6391i	−0.271654	−	0.156839i
$343$		−	76.1010i		−	0.221869i
$344$	754.557			2.19348
$345$	66.5565	+	115.279i	0.192917	+	0.334143i
$346$	216.735	+	125.132i	0.626401	+	0.361653i
$347$	321.160	+	185.422i	0.925532	+	0.534356i	0.885396	−	0.464838i	$-0.153887\pi$
$347$	321.160	+	185.422i	0.925532	+	0.534356i	0.0401362	+	0.999194i	$0.487221\pi$
$348$	−318.395	+	183.825i	−0.914928	+	0.528234i
$349$	−588.621			−1.68659			−0.843296	−	0.537449i	$-0.819388\pi$
$349$	−588.621			−1.68659			−0.843296	+	0.537449i	$0.819388\pi$
$350$	−173.023			−0.494351
$351$	66.9039	+	115.881i	0.190609	+	0.330145i
$352$	−26.9966	−	46.7595i	−0.0766949	−	0.132839i
$353$	507.457	−	292.980i	1.43755	−	0.829972i	0.439875	−	0.898059i	$-0.355023\pi$
$353$	507.457	−	292.980i	1.43755	−	0.829972i	0.997679	+	0.0680869i	$0.0216895\pi$
$354$	36.9628	+	64.0214i	0.104415	+	0.180852i
$355$	−64.0221	−	36.9632i	−0.180344	−	0.104122i
$356$	−219.778	+	380.667i	−0.617354	+	1.06929i
$357$	154.006			0.431391
$358$	−199.354	−	345.290i	−0.556853	−	0.964498i
$359$	−59.4744			−0.165667			−0.0828335	−	0.996563i	$-0.526397\pi$
$359$	−59.4744			−0.165667			−0.0828335	+	0.996563i	$0.526397\pi$
$360$	−189.895			−0.527485
$361$	127.638	−	221.075i	0.353567	−	0.612396i
$362$		−	576.344i		−	1.59211i
$363$	−430.414	+	248.499i	−1.18571	+	0.684572i
$364$	−988.668	+	1712.42i	−2.71612	+	4.70446i
$365$	399.983	−	230.930i	1.09584	−	0.632686i
$366$	−88.9483	−	51.3544i	−0.243028	−	0.140312i
$367$	148.424	+	85.6929i	0.404426	+	0.233496i	0.688392	−	0.725339i	$-0.258317\pi$
$367$	148.424	+	85.6929i	0.404426	+	0.233496i	−0.283966	+	0.958834i	$0.591650\pi$
$368$	148.257	−	256.789i	0.402873	−	0.697796i
$369$	3.52998	+	2.03804i	0.00956635	+	0.00552313i
$370$	207.306	−	359.065i	0.560287	−	0.970446i
$371$	221.549	−	383.735i	0.597168	−	1.03433i
$372$	−397.513	−	688.512i	−1.06858	−	1.85084i
$373$	60.1491	+	34.7271i	0.161258	+	0.0931022i	0.578457	−	0.815713i	$-0.303655\pi$
$373$	60.1491	+	34.7271i	0.161258	+	0.0931022i	−0.417199	+	0.908815i	$0.636988\pi$
$374$	−329.218	−	570.222i	−0.880262	−	1.52466i
$375$	232.837			0.620899
$376$	−975.574	−	563.248i	−2.59461	−	1.49800i
$377$		−	675.243i		−	1.79110i
$378$			171.416i			0.453480i
$379$	−481.637	+	278.073i	−1.27081	+	0.733703i	−0.975140	−	0.221588i	$-0.928876\pi$
$379$	−481.637	+	278.073i	−1.27081	+	0.733703i	−0.295670	+	0.955290i	$0.595543\pi$
$380$			369.949i			0.973551i
$381$	−126.715	−	73.1589i	−0.332585	−	0.192018i
$382$	393.295	−	681.207i	1.02957	−	1.78326i
$383$	−377.941	+	218.204i	−0.986790	+	0.569724i	−0.904313	−	0.426869i	$-0.859616\pi$
$383$	−377.941	+	218.204i	−0.986790	+	0.569724i	−0.0824770	+	0.996593i	$0.526283\pi$
$384$	−187.854	−	325.372i	−0.489203	−	0.847324i
$385$	−737.456	+	425.771i	−1.91547	+	1.10590i
$386$	355.033	−	204.979i	0.919775	−	0.531032i
$387$			158.950i			0.410725i
$388$			365.881i			0.942994i
$389$	118.908	+	205.955i	0.305676	+	0.529447i	0.977412	−	0.211344i	$-0.0677841\pi$
$389$	118.908	+	205.955i	0.305676	+	0.529447i	−0.671735	+	0.740791i	$0.734451\pi$
$390$	344.725	−	597.081i	0.883909	−	1.53098i
$391$	81.0405	−	140.366i	0.207265	−	0.358993i
$392$	−505.388	+	291.786i	−1.28925	+	0.744351i
$393$		−	76.1122i		−	0.193670i
$394$	−912.089			−2.31495
$395$	−117.078	+	202.785i	−0.296399	+	0.513379i
$396$	424.782	−	245.248i	1.07268	−	0.619313i
$397$	143.863			0.362375			0.181187	−	0.983449i	$-0.442006\pi$
$397$	143.863			0.362375			0.181187	+	0.983449i	$0.442006\pi$
$398$	2.38019	+	1.37420i	0.00598037	+	0.00345277i
$399$	168.933			0.423391
$400$	−44.9709	−	77.8918i	−0.112427	−	0.194729i
$401$		−	458.609i		−	1.14366i	−0.820371	−	0.571832i	$-0.806233\pi$
$401$		−	458.609i		−	1.14366i	0.820371	−	0.571832i	$-0.193767\pi$
$402$	−253.481	+	314.054i	−0.630550	+	0.781229i
$403$	1460.18			3.62327
$404$	840.784	−	485.427i	2.08115	−	1.20155i
$405$		−	40.0021i		−	0.0987705i
$406$	432.513	−	749.134i	1.06530	−	1.84516i
$407$			541.751i			1.33108i
$408$	115.610	+	200.242i	0.283357	+	0.490789i
$409$	117.461	+	67.8160i	0.287190	+	0.165809i	0.636674	−	0.771133i	$-0.280310\pi$
$409$	117.461	+	67.8160i	0.287190	+	0.165809i	−0.349484	+	0.936942i	$0.613643\pi$
$410$		−	21.0021i		−	0.0512246i
$411$	265.305			0.645511
$412$	184.352	+	319.307i	0.447456	+	0.775017i
$413$	−100.816	−	58.2061i	−0.244106	−	0.140935i
$414$	156.233	+	90.2014i	0.377375	+	0.217878i
$415$	241.390	−	139.367i	0.581662	−	0.335823i
$416$	−68.8398			−0.165480
$417$	193.684			0.464471
$418$	−361.126	−	625.489i	−0.863939	−	1.49639i
$419$	−298.071	−	516.275i	−0.711387	−	1.23216i	−0.964336	−	0.264679i	$-0.914734\pi$
$419$	−298.071	−	516.275i	−0.711387	−	1.23216i	0.252949	−	0.967480i	$-0.418599\pi$
$420$	511.932	−	295.564i	1.21888	−	0.703723i
$421$	−354.660	−	614.289i	−0.842423	−	1.45912i	−0.887841	−	0.460151i	$-0.847795\pi$
$421$	−354.660	−	614.289i	−0.842423	−	1.45912i	0.0454181	−	0.998968i	$-0.485538\pi$
$422$	−866.074	−	500.028i	−2.05231	−	1.18490i
$423$	118.651	−	205.509i	0.280498	−	0.485836i
$424$	665.251			1.56899
$425$	−24.5820	−	42.5773i	−0.0578400	−	0.100182i
$426$	−100.190			−0.235187
$427$	161.738			0.378776
$428$	−4.06005	+	7.03221i	−0.00948609	+	0.0164304i
$429$			900.865i			2.09992i
$430$	709.273	−	409.499i	1.64947	−	0.952323i
$431$	7.46743	−	12.9340i	0.0173258	−	0.0300092i	−0.857232	−	0.514930i	$-0.827818\pi$
$431$	7.46743	−	12.9340i	0.0173258	−	0.0300092i	0.874558	+	0.484920i	$0.161151\pi$
$432$	−77.1682	+	44.5531i	−0.178630	+	0.103132i
$433$	425.282	+	245.537i	0.982177	+	0.567060i	0.902927	−	0.429795i	$-0.141414\pi$
$433$	425.282	+	245.537i	0.982177	+	0.567060i	0.0792500	+	0.996855i	$0.474747\pi$
$434$	1619.96	+	935.285i	3.73263	+	2.15504i
$435$	−100.932	+	174.820i	−0.232029	+	0.401885i
$436$	80.3666	+	46.3997i	0.184327	+	0.106421i
$437$	88.8951	−	153.971i	0.203421	−	0.352336i
$438$	312.971	−	542.082i	0.714546	−	1.23763i
$439$	−389.397	−	674.456i	−0.887009	−	1.53635i	−0.843393	−	0.537297i	$-0.819445\pi$
$439$	−389.397	−	674.456i	−0.887009	−	1.53635i	−0.0436165	−	0.999048i	$-0.513888\pi$
$440$	−1107.19	−	639.235i	−2.51634	−	1.45281i
$441$	−61.4659	−	106.462i	−0.139378	−	0.241410i
$442$	−839.487			−1.89929
$443$	−592.619	−	342.149i	−1.33774	−	0.772344i	−0.351268	−	0.936275i	$-0.614249\pi$
$443$	−592.619	−	342.149i	−1.33774	−	0.772344i	−0.986472	+	0.163931i	$0.947583\pi$
$444$		−	376.076i		−	0.847018i
$445$			241.346i			0.542350i
$446$	294.873	−	170.245i	0.661151	−	0.381716i
$447$		−	122.120i		−	0.273200i
$448$	487.113	+	281.235i	1.08731	+	0.627756i
$449$	−173.595	+	300.676i	−0.386627	+	0.669657i	−0.991993	−	0.126290i	$-0.959693\pi$
$449$	−173.595	+	300.676i	−0.386627	+	0.669657i	0.605367	+	0.795947i	$0.293026\pi$
$450$	47.3903	−	27.3608i	0.105312	−	0.0608018i
$451$	13.7211	+	23.7657i	0.0304238	+	0.0526956i
$452$	178.257	−	102.917i	0.394374	−	0.227692i
$453$	−341.363	+	197.086i	−0.753560	+	0.435068i
$454$			617.230i			1.35954i
$455$			1085.69i			2.38613i
$456$	126.815	+	219.650i	0.278103	+	0.481688i
$457$	151.498	−	262.402i	0.331506	−	0.574185i	−0.651302	−	0.758819i	$-0.725777\pi$
$457$	151.498	−	262.402i	0.331506	−	0.574185i	0.982807	+	0.184634i	$0.0591100\pi$
$458$	188.718	−	326.869i	0.412048	−	0.713688i
$459$	−42.1817	+	24.3536i	−0.0918992	+	0.0530580i
$460$		−	622.120i		−	1.35244i
$461$	128.738			0.279259			0.139629	−	0.990204i	$-0.455409\pi$
$461$	128.738			0.279259			0.139629	+	0.990204i	$0.455409\pi$
$462$	−577.030	+	999.446i	−1.24898	+	2.16330i
$463$	−550.481	+	317.820i	−1.18894	+	0.686437i	−0.958066	−	0.286546i	$-0.907493\pi$
$463$	−550.481	+	317.820i	−1.18894	+	0.686437i	−0.230877	+	0.972983i	$0.574159\pi$
$464$	449.662			0.969099
$465$	−378.039	−	218.261i	−0.812988	−	0.469379i
$466$	327.283			0.702325
$467$	311.578	+	539.668i	0.667190	+	1.15561i	0.978687	+	0.205359i	$0.0658363\pi$
$467$	311.578	+	539.668i	0.667190	+	1.15561i	−0.311497	+	0.950247i	$0.600830\pi$
$468$		−	625.368i		−	1.33626i
$469$	98.4108	−	627.872i	0.209831	−	1.33875i
$470$	−1222.70			−2.60149
$471$	153.621	−	88.6933i	0.326160	−	0.188309i
$472$		−	174.777i		−	0.370290i
$473$	−535.069	+	926.767i	−1.13122	+	1.95934i
$474$			317.342i			0.669497i
$475$	−26.9645	−	46.7039i	−0.0567674	−	0.0983241i
$476$	−623.338	−	359.884i	−1.30953	−	0.756059i
$477$			140.138i			0.293790i
$478$	239.467			0.500977
$479$	−419.014	−	725.753i	−0.874767	−	1.51514i	−0.857010	−	0.515299i	$-0.827681\pi$
$479$	−419.014	−	725.753i	−0.874767	−	1.51514i	−0.0177568	−	0.999842i	$-0.505652\pi$
$480$	17.8226	+	10.2899i	0.0371304	+	0.0214372i
$481$	598.178	+	345.358i	1.24361	+	0.718001i
$482$	−345.530	+	199.492i	−0.716868	+	0.413884i
$483$	−284.084			−0.588166
$484$	2322.79			4.79915
$485$	100.447	+	173.979i	0.207107	+	0.358719i
$486$	−27.1066	−	46.9500i	−0.0557749	−	0.0966050i
$487$	−390.823	+	225.642i	−0.802512	+	0.463330i	−0.844349	−	0.535794i	$-0.820012\pi$
$487$	−390.823	+	225.642i	−0.802512	+	0.463330i	0.0418370	+	0.999124i	$0.486679\pi$
$488$	121.413	+	210.294i	0.248798	+	0.430930i
$489$	61.3604	+	35.4264i	0.125481	+	0.0724467i
$490$	−316.705	+	548.549i	−0.646336	+	1.11949i
$491$	−638.489			−1.30038			−0.650192	−	0.759770i	$-0.725312\pi$
$491$	−638.489			−1.30038			−0.650192	+	0.759770i	$0.725312\pi$
$492$	−9.52502	−	16.4978i	−0.0193598	−	0.0335321i
$493$	245.795			0.498569
$494$	−920.851			−1.86407
$495$	134.658	−	233.234i	0.272035	−	0.471179i
$496$			972.370i			1.96042i
$497$	136.633	−	78.8853i	0.274916	−	0.158723i
$498$	188.878	−	327.146i	0.379273	−	0.656920i
$499$	−12.3728	+	7.14341i	−0.0247951	+	0.0143155i	−0.512346	−	0.858779i	$-0.671224\pi$
$499$	−12.3728	+	7.14341i	−0.0247951	+	0.0143155i	0.487551	+	0.873094i	$0.337890\pi$
$500$	−942.403	−	544.097i	−1.88481	−	1.08819i
$501$	−167.966	−	96.9750i	−0.335261	−	0.193563i
$502$	−30.4469	+	52.7356i	−0.0606512	+	0.105051i
$503$	444.757	+	256.780i	0.884208	+	0.510498i	0.872044	−	0.489428i	$-0.162794\pi$
$503$	444.757	+	256.780i	0.884208	+	0.510498i	0.0121647	+	0.999926i	$0.496128\pi$
$504$	202.632	−	350.970i	0.402049	−	0.696368i
$505$	266.532	−	461.647i	0.527786	−	0.914152i
$506$	607.284	+	1051.85i	1.20017	+	2.07875i
$507$	741.197	+	427.930i	1.46193	+	0.844044i
$508$	341.917	+	592.218i	0.673065	+	1.16578i
$509$	−893.098			−1.75461			−0.877307	−	0.479930i	$-0.840662\pi$
$509$	−893.098			−1.75461			−0.877307	+	0.479930i	$0.840662\pi$
$510$	217.343	+	125.483i	0.426162	+	0.246045i
$511$			985.684i			1.92893i
$512$			931.029i			1.81842i
$513$	−46.2701	+	26.7140i	−0.0901951	+	0.0520742i
$514$			578.253i			1.12501i
$515$	175.321	+	101.222i	0.340429	+	0.196547i
$516$	371.438	−	643.349i	0.719840	−	1.24680i
$517$	1383.59	−	798.818i	2.67620	−	1.54510i
$518$	442.424	+	766.301i	0.854100	+	1.47935i
$519$	107.941	−	62.3198i	0.207979	−	0.120077i
$520$	−1411.63	+	815.006i	−2.71468	+	1.56732i
$521$		−	73.4418i		−	0.140963i	−0.997513	−	0.0704816i	$-0.977546\pi$
$521$		−	73.4418i		−	0.140963i	0.997513	−	0.0704816i	$-0.0224536\pi$
$522$			273.580i			0.524099i
$523$	329.915	+	571.429i	0.630812	+	1.09260i	0.987386	+	0.158332i	$0.0506115\pi$
$523$	329.915	+	571.429i	0.630812	+	1.09260i	−0.356574	+	0.934267i	$0.616055\pi$
$524$	−177.860	+	308.062i	−0.339427	+	0.587905i
$525$	−43.0856	+	74.6265i	−0.0820678	+	0.142146i
$526$	−25.3272	+	14.6227i	−0.0481506	+	0.0277997i
$527$			531.518i			1.00857i
$528$	−599.910			−1.13619
$529$	115.011	−	199.204i	0.217412	−	0.376568i
$530$	625.326	−	361.032i	1.17986	−	0.681193i
$531$	36.8174			0.0693360
$532$	−683.753	−	394.765i	−1.28525	−	0.742039i
$533$	34.9881			0.0656437
$534$	163.543	+	283.265i	0.306261	+	0.530459i
$535$			4.45847i			0.00833360i
$536$	890.245	−	343.376i	1.66090	−	0.640626i
$537$	−198.569			−0.369775
$538$	−22.5619	+	13.0261i	−0.0419365	+	0.0242121i
$539$		−	827.641i		−	1.53551i
$540$	−93.4773	+	161.907i	−0.173106	+	0.299829i
$541$			367.834i			0.679914i	0.940441	+	0.339957i	$0.110413\pi$
$541$			367.834i			0.679914i	−0.940441	+	0.339957i	$0.889587\pi$
$542$	109.866	+	190.294i	0.202705	+	0.351095i
$543$	−248.583	−	143.519i	−0.457795	−	0.264308i
$544$		−	25.0583i		−	0.0460630i
$545$	50.9531			0.0934919
$546$	735.697	+	1274.26i	1.34743	+	2.33382i
$547$	−547.689	−	316.208i	−1.00126	−	0.578078i	−0.0926390	−	0.995700i	$-0.529530\pi$
$547$	−547.689	−	316.208i	−1.00126	−	0.578078i	−0.908621	+	0.417622i	$0.862864\pi$
$548$	−1073.82	−	619.968i	−1.95952	−	1.13133i
$549$	−44.2992	+	25.5762i	−0.0806908	+	0.0465869i
$550$	368.415			0.669845
$551$	269.617			0.489324
$552$	−213.256	−	369.371i	−0.386334	−	0.669150i
$553$	−249.862	−	432.774i	−0.451831	−	0.782594i
$554$	−379.910	+	219.341i	−0.685758	+	0.395923i
$555$	−103.245	−	178.826i	−0.186028	−	0.322210i
$556$	−783.933	−	452.604i	−1.40995	−	0.814036i
$557$	519.943	−	900.568i	0.933470	−	1.61682i	0.156131	−	0.987736i	$-0.450098\pi$
$557$	519.943	−	900.568i	0.933470	−	1.61682i	0.777339	−	0.629082i	$-0.216569\pi$
$558$	−591.601			−1.06022
$559$	682.198	+	1181.60i	1.22039	+	2.11378i
$560$	−722.990			−1.29105
$561$	−327.923			−0.584533
$562$	51.3432	−	88.9291i	0.0913580	−	0.158237i
$563$		−	280.968i		−	0.499056i	−0.968368	−	0.249528i	$-0.919725\pi$
$563$		−	280.968i		−	0.499056i	0.968368	−	0.249528i	$-0.0802754\pi$
$564$	−960.471	+	554.528i	−1.70296	+	0.983206i
$565$	56.5082	−	97.8752i	0.100015	−	0.173230i
$566$	43.6420	−	25.1967i	0.0771059	−	0.0445171i
$567$	73.9332	+	42.6853i	0.130394	+	0.0752828i
$568$	205.136	+	118.435i	0.361155	+	0.208513i
$569$	534.824	−	926.342i	0.939937	−	1.62802i	0.174352	−	0.984683i	$-0.444217\pi$
$569$	534.824	−	926.342i	0.939937	−	1.62802i	0.765585	−	0.643335i	$-0.222450\pi$
$570$	238.408	+	137.645i	0.418260	+	0.241482i
$571$	−348.422	+	603.485i	−0.610197	+	1.05689i	0.381010	+	0.924571i	$0.375576\pi$
$571$	−348.422	+	603.485i	−0.610197	+	1.05689i	−0.991207	+	0.132321i	$0.957757\pi$
$572$	2105.15	−	3646.23i	3.68034	−	6.37453i
$573$	−195.874	−	339.264i	−0.341839	−	0.592083i
$574$	38.8168	+	22.4109i	0.0676251	+	0.0390434i
$575$	45.3446	+	78.5391i	0.0788601	+	0.136590i
$576$	−177.891			−0.308838
$577$	−47.5131	−	27.4317i	−0.0823451	−	0.0475420i	0.458262	−	0.888817i	$-0.348472\pi$
$577$	−47.5131	−	27.4317i	−0.0823451	−	0.0475420i	−0.540607	+	0.841275i	$0.681805\pi$
$578$			699.498i			1.21020i
$579$		−	204.172i		−	0.352629i
$580$	817.044	−	471.720i	1.40870	−	0.813311i
$581$			594.860i			1.02386i
$582$	235.787	+	136.132i	0.405132	+	0.233903i
$583$	−471.741	+	817.079i	−0.809161	+	1.40151i
$584$	−1281.60	+	739.934i	−2.19453	+	1.26701i
$585$	−171.684	−	297.366i	−0.293478	−	0.508318i
$586$	−1412.19	+	815.326i	−2.40987	+	1.39134i
$587$	−757.309	+	437.232i	−1.29013	+	0.744859i	−0.978678	−	0.205401i	$-0.934150\pi$
$587$	−757.309	+	437.232i	−1.29013	+	0.744859i	−0.311456	+	0.950261i	$0.600817\pi$
$588$			574.537i			0.977103i
$589$			583.033i			0.989870i
$590$	−94.8515	−	164.288i	−0.160765	−	0.278454i
$591$	−227.126	+	393.393i	−0.384307	+	0.665639i
$592$	−229.983	+	398.343i	−0.388485	+	0.672876i
$593$	−760.379	+	439.005i	−1.28226	+	0.740312i	−0.977261	−	0.212041i	$-0.931989\pi$
$593$	−760.379	+	439.005i	−1.28226	+	0.740312i	−0.304998	+	0.952353i	$0.598656\pi$
$594$		−	364.992i		−	0.614465i
$595$	−395.201			−0.664203
$596$	−285.372	+	494.279i	−0.478812	+	0.829328i
$597$	1.18541	−	0.684398i	0.00198562	−	0.00114640i
$598$	1548.54			2.58953
$599$	−51.7503	−	29.8781i	−0.0863945	−	0.0498799i	0.456180	−	0.889887i	$-0.349217\pi$
$599$	−51.7503	−	29.8781i	−0.0863945	−	0.0498799i	−0.542575	+	0.840007i	$0.682551\pi$
$600$	−129.374			−0.215623
$601$	−281.045	−	486.783i	−0.467628	−	0.809956i	0.531688	−	0.846941i	$-0.321558\pi$
$601$	−281.045	−	486.783i	−0.467628	−	0.809956i	−0.999316	+	0.0369847i	$0.988225\pi$
$602$			1747.87i			2.90344i
$603$	72.3335	+	187.534i	0.119956	+	0.311001i
$604$	1842.21			3.05002
$605$	1104.50	−	637.683i	1.82562	−	1.05402i
$606$		−	722.440i		−	1.19215i
$607$	261.982	−	453.765i	0.431601	−	0.747554i	−0.565411	−	0.824809i	$-0.691282\pi$
$607$	261.982	−	453.765i	0.431601	−	0.747554i	0.997011	+	0.0772554i	$0.0246157\pi$
$608$		−	27.4870i		−	0.0452089i
$609$	−215.406	−	373.094i	−0.353704	−	0.612633i
$610$	228.253	+	131.782i	0.374186	+	0.216036i
$611$		−	2036.94i		−	3.33378i
$612$	227.640			0.371960
$613$	253.622	+	439.285i	0.413738	+	0.716616i	0.995295	−	0.0968901i	$-0.0308895\pi$
$613$	253.622	+	439.285i	0.413738	+	0.716616i	−0.581557	+	0.813506i	$0.697556\pi$
$614$	637.331	+	367.963i	1.03800	+	0.599289i
$615$	−9.05841	−	5.22987i	−0.0147291	−	0.00850386i
$616$	2362.91	−	1364.23i	3.83590	−	2.21466i
$617$	603.737			0.978503			0.489252	−	0.872143i	$-0.337270\pi$
$617$	603.737			0.978503			0.489252	+	0.872143i	$0.337270\pi$
$618$	274.363			0.443954
$619$	−252.213	−	436.845i	−0.407452	−	0.705727i	0.587152	−	0.809477i	$-0.300249\pi$
$619$	−252.213	−	436.845i	−0.407452	−	0.705727i	−0.994603	+	0.103750i	$0.966916\pi$
$620$	1020.07	+	1766.81i	1.64527	+	2.84970i
$621$	77.8095	−	44.9233i	0.125297	−	0.0723403i
$622$	262.951	+	455.444i	0.422750	+	0.732225i
$623$	−446.064	−	257.535i	−0.715993	−	0.413379i
$624$	−382.434	+	662.395i	−0.612875	+	1.06153i
$625$	−466.369			−0.746191
$626$	−826.901	−	1432.23i	−1.32093	−	2.28791i
$627$	−359.706			−0.573694
$628$	−829.039			−1.32013
$629$	−125.714	+	217.742i	−0.199863	+	0.346172i
$630$		−	439.875i		−	0.698215i
$631$	376.670	−	217.471i	0.596942	−	0.344645i	−0.170896	−	0.985289i	$-0.554666\pi$
$631$	376.670	−	217.471i	0.596942	−	0.344645i	0.767838	+	0.640645i	$0.221333\pi$
$632$	375.134	−	649.750i	0.593566	−	1.02809i
$633$	−431.334	+	249.031i	−0.681412	+	0.393414i
$634$	−462.482	−	267.014i	−0.729467	−	0.421158i
$635$	325.167	+	187.735i	0.512075	+	0.295646i
$636$	327.476	−	567.205i	0.514899	−	0.891831i
$637$	−913.846	−	527.609i	−1.43461	−	0.828272i
$638$	−920.941	+	1595.12i	−1.44348	+	2.50018i
$639$	−24.9489	+	43.2127i	−0.0390436	+	0.0676255i
$640$	482.058	+	834.949i	0.753216	+	1.30461i
$641$	−518.313	−	299.248i	−0.808600	−	0.466845i	0.0378694	−	0.999283i	$-0.487943\pi$
$641$	−518.313	−	299.248i	−0.808600	−	0.466845i	−0.846469	+	0.532437i	$0.821276\pi$
$642$	3.02120	+	5.23287i	0.00470592	+	0.00815089i
$643$	−1080.98			−1.68114			−0.840572	−	0.541700i	$-0.817781\pi$
$643$	−1080.98			−1.68114			−0.840572	+	0.541700i	$0.817781\pi$
$644$	1149.82	+	663.851i	1.78544	+	1.03082i
$645$		−	407.888i		−	0.632385i
$646$		−	335.198i		−	0.518883i
$647$	−489.101	+	282.382i	−0.755951	+	0.436449i	−0.827840	−	0.560964i	$-0.810431\pi$
$647$	−489.101	+	282.382i	−0.755951	+	0.436449i	0.0718888	+	0.997413i	$0.477097\pi$
$648$			128.172i			0.197797i
$649$	214.665	+	123.937i	0.330763	+	0.190966i
$650$	234.859	−	406.788i	0.361321	−	0.625827i
$651$	806.795	−	465.803i	1.23932	−	0.715520i
$652$	−165.570	−	286.776i	−0.253942	−	0.439840i
$653$	10.5400	−	6.08527i	0.0161409	−	0.00931894i	−0.491908	−	0.870647i	$-0.663700\pi$
$653$	10.5400	−	6.08527i	0.0161409	−	0.00931894i	0.508049	+	0.861328i	$0.330367\pi$
$654$	59.8031	−	34.5274i	0.0914421	−	0.0527941i
$655$			195.314i			0.298189i
$656$			23.2995i			0.0355175i
$657$	−155.870	−	269.975i	−0.237245	−	0.410921i
$658$	1304.72	−	2259.84i	1.98286	−	3.43441i
$659$	333.590	−	577.795i	0.506206	−	0.876775i	−0.493768	−	0.869594i	$-0.664381\pi$
$659$	333.590	−	577.795i	0.506206	−	0.876775i	0.999974	−	0.00718133i	$-0.00228591\pi$
$660$	−1090.05	+	629.339i	−1.65159	+	0.953544i
$661$			643.969i			0.974234i	0.873337	+	0.487117i	$0.161952\pi$
$661$			643.969i			0.974234i	−0.873337	+	0.487117i	$0.838048\pi$
$662$	1735.29			2.62128
$663$	−209.046	+	362.079i	−0.315303	+	0.546122i
$664$	−773.447	+	446.550i	−1.16483	+	0.672515i
$665$	−433.505			−0.651887
$666$	−242.356	−	139.924i	−0.363898	−	0.210097i
$667$	−453.399			−0.679758
$668$	453.225	+	785.008i	0.678480	+	1.17516i
$669$		−	169.576i		−	0.253476i
$670$	650.467	−	805.905i	0.970846	−	1.20284i
$671$	−344.385			−0.513241
$672$	−38.0362	+	21.9602i	−0.0566015	+	0.0326789i
$673$			831.451i			1.23544i	0.786398	+	0.617720i	$0.211943\pi$
$673$			831.451i			1.23544i	−0.786398	+	0.617720i	$0.788057\pi$
$674$	271.002	−	469.389i	0.402080	−	0.696422i
$675$		−	27.2532i		−	0.0403751i
$676$	−1999.98	−	3464.08i	−2.95856	−	5.12437i
$677$	461.020	+	266.170i	0.680975	+	0.393161i	0.800222	−	0.599703i	$-0.204715\pi$
$677$	461.020	+	266.170i	0.680975	+	0.393161i	−0.119247	+	0.992865i	$0.538048\pi$
$678$		−	153.167i		−	0.225910i
$679$	−428.738			−0.631426
$680$	−296.670	−	513.847i	−0.436279	−	0.755657i
$681$	266.217	+	153.701i	0.390921	+	0.225699i
$682$	−3449.36	−	1991.49i	−5.05771	−	2.92007i
$683$	878.186	−	507.021i	1.28578	−	0.742344i	0.307879	−	0.951426i	$-0.400381\pi$
$683$	878.186	−	507.021i	1.28578	−	0.742344i	0.977898	+	0.209082i	$0.0670475\pi$
$684$	249.703			0.365063
$685$	−680.808			−0.993880
$686$	132.331	+	229.204i	0.192903	+	0.334117i
$687$	−93.9879	−	162.792i	−0.136809	−	0.236960i
$688$	−786.859	+	454.294i	−1.14369	+	0.660310i
$689$	601.456	+	1041.75i	0.872940	+	1.51198i
$690$	−400.916	−	231.469i	−0.581038	−	0.335462i
$691$	422.582	−	731.933i	0.611551	−	1.05924i	−0.379428	−	0.925221i	$-0.623879\pi$
$691$	422.582	−	731.933i	0.611551	−	1.05924i	0.990979	−	0.134016i	$-0.0427874\pi$
$692$	−582.519			−0.841791
$693$	287.380	+	497.757i	0.414690	+	0.718265i
$694$	−1289.71			−1.85837
$695$	−497.020			−0.715136
$696$	323.402	−	560.148i	0.464658	−	0.804811i
$697$			12.7360i			0.0182726i
$698$	1772.83	−	1023.55i	2.53988	−	1.46640i
$699$	81.4990	−	141.160i	0.116594	−	0.201946i
$700$	348.776	−	201.366i	0.498252	−	0.287666i
$701$	51.2046	+	29.5630i	0.0730451	+	0.0421726i	0.536078	−	0.844169i	$-0.319905\pi$
$701$	51.2046	+	29.5630i	0.0730451	+	0.0421726i	−0.463033	+	0.886341i	$0.653239\pi$
$702$	−403.009	−	232.677i	−0.574086	−	0.331449i
$703$	−137.898	+	238.846i	−0.196156	+	0.339753i
$704$	−1037.20	−	598.828i	−1.47330	−	0.850608i
$705$	−304.473	+	527.363i	−0.431877	+	0.748032i
$706$	−1018.92	+	1764.82i	−1.44323	+	2.49975i
$707$	568.821	+	985.226i	0.804556	+	1.39353i
$708$	−149.018	−	86.0354i	−0.210477	−	0.121519i
$709$	−279.076	−	483.373i	−0.393619	−	0.681767i	0.599305	−	0.800521i	$-0.295444\pi$
$709$	−279.076	−	483.373i	−0.393619	−	0.681767i	−0.992924	+	0.118753i	$0.962110\pi$
$710$	257.100			0.362112
$711$	136.873	+	79.0234i	0.192507	+	0.111144i
$712$		−	773.306i		−	1.08610i
$713$		−	980.451i		−	1.37511i
$714$	−463.844	+	267.800i	−0.649641	+	0.375070i
$715$		−	2311.74i		−	3.23320i
$716$	803.705	+	464.020i	1.12249	+	0.648072i
$717$	59.6313	−	103.284i	0.0831677	−	0.144051i
$718$	179.128	−	103.420i	0.249482	−	0.144038i
$719$	165.639	+	286.895i	0.230374	+	0.399019i	0.957918	−	0.287042i	$-0.0926718\pi$
$719$	165.639	+	286.895i	0.230374	+	0.399019i	−0.727544	+	0.686061i	$0.759338\pi$
$720$	198.024	−	114.329i	0.275033	−	0.158791i
$721$	−374.163	+	216.023i	−0.518949	+	0.299616i
$722$			887.792i			1.22963i
$723$			198.707i			0.274837i
$724$	670.756	+	1161.78i	0.926458	+	1.60467i
$725$	−68.7647	+	119.104i	−0.0948479	+	0.164281i
$726$	864.227	−	1496.88i	1.19039	−	2.06182i
$727$	913.740	−	527.548i	1.25686	−	0.725651i	0.284401	−	0.958705i	$-0.408205\pi$
$727$	913.740	−	527.548i	1.25686	−	0.725651i	0.972464	+	0.233054i	$0.0748720\pi$
$728$		−	3478.70i		−	4.77844i
$729$	−27.0000			−0.0370370
$730$	−803.125	+	1391.05i	−1.10017	+	1.90555i
$731$	−430.114	+	248.326i	−0.588391	+	0.339708i
$732$	239.067			0.326594
$733$	446.716	+	257.911i	0.609435	+	0.351857i	0.772744	−	0.634718i	$-0.218884\pi$
$733$	446.716	+	257.911i	0.609435	+	0.351857i	−0.163309	+	0.986575i	$0.552217\pi$
$734$	−596.042			−0.812046
$735$	157.730	+	273.196i	0.214598	+	0.371695i
$736$			46.2232i			0.0628032i
$737$	−209.544	+	1336.92i	−0.284321	+	1.81400i
$738$	−14.1757			−0.0192082
$739$	554.438	−	320.105i	0.750254	−	0.433159i	−0.0755318	−	0.997143i	$-0.524065\pi$
$739$	554.438	−	320.105i	0.750254	−	0.433159i	0.825786	+	0.563984i	$0.190732\pi$
$740$			965.061i			1.30414i
$741$	−229.307	+	397.172i	−0.309457	+	0.535995i
$742$			1541.00i			2.07682i
$743$	−661.468	−	1145.70i	−0.890267	−	1.54199i	−0.839556	−	0.543274i	$-0.817185\pi$
$743$	−661.468	−	1145.70i	−0.890267	−	1.54199i	−0.0507111	−	0.998713i	$-0.516149\pi$
$744$	1211.29	+	699.339i	1.62808	+	0.939972i
$745$			313.377i			0.420640i
$746$	−241.547			−0.323789
$747$	−94.0675	−	162.930i	−0.125927	−	0.218112i
$748$	1327.26	+	766.295i	1.77441	+	1.02446i
$749$	−8.24031	−	4.75754i	−0.0110017	−	0.00635186i
$750$	−701.270	+	404.878i	−0.935026	+	0.539838i
$751$	−830.069			−1.10528			−0.552642	−	0.833419i	$-0.686380\pi$
$751$	−830.069			−1.10528			−0.552642	+	0.833419i	$0.686380\pi$
$752$	1356.45			1.80379
$753$	15.1636	+	26.2641i	0.0201375	+	0.0348792i
$754$	1174.17	+	2033.73i	1.55726	+	2.69725i
$755$	875.982	−	505.749i	1.16024	−	0.669866i
$756$	−199.495	−	345.536i	−0.263883	−	0.457058i
$757$	−672.085	−	388.028i	−0.887827	−	0.512587i	−0.0145959	−	0.999893i	$-0.504646\pi$
$757$	−672.085	−	388.028i	−0.887827	−	0.512587i	−0.873231	+	0.487306i	$0.837980\pi$
$758$	967.078	−	1675.03i	1.27583	−	2.20980i
$759$	604.895			0.796963
$760$	−325.424	−	563.650i	−0.428189	−	0.741645i
$761$	201.405			0.264659			0.132329	−	0.991206i	$-0.457754\pi$
$761$	201.405			0.264659			0.132329	+	0.991206i	$0.457754\pi$
$762$	508.861			0.667797
$763$	−54.3710	+	94.1733i	−0.0712594	+	0.123425i
$764$			1830.88i			2.39644i
$765$	108.244	−	62.4947i	0.141495	−	0.0816924i
$766$	758.866	−	1314.39i	0.990687	−	1.71592i
$767$	273.692	−	158.016i	0.356835	−	0.206019i
$768$	775.792	+	447.903i	1.01015	+	0.583208i
$769$	−241.533	−	139.449i	−0.314088	−	0.181339i	0.334667	−	0.942337i	$-0.391376\pi$
$769$	−241.533	−	139.449i	−0.314088	−	0.181339i	−0.648754	+	0.760998i	$0.724710\pi$
$770$	1480.74	−	2564.71i	1.92303	−	3.33079i
$771$	249.406	+	143.995i	0.323484	+	0.186764i
$772$	−477.112	+	826.383i	−0.618021	+	1.07044i
$773$	−479.342	+	830.244i	−0.620106	+	1.07405i	0.369360	+	0.929286i	$0.379577\pi$
$773$	−479.342	+	830.244i	−0.620106	+	1.07405i	−0.989466	+	0.144768i	$0.953756\pi$
$774$	−276.397	−	478.734i	−0.357103	−	0.618520i
$775$	−257.556	−	148.700i	−0.332330	−	0.191871i
$776$	−321.845	−	557.453i	−0.414749	−	0.718367i
$777$	440.684			0.567161
$778$	−716.266	−	413.536i	−0.920650	−	0.531538i
$779$			13.9704i			0.0179337i
$780$			1604.78i			2.05741i
$781$	−290.931	+	167.969i	−0.372511	+	0.215069i
$782$			563.682i			0.720821i
$783$	117.998	+	68.1259i	0.150699	+	0.0870062i
$784$	351.349	−	608.554i	0.448149	−	0.776217i
$785$	−394.213	+	227.599i	−0.502182	+	0.289935i
$786$	132.351	+	229.238i	0.168385	+	0.291652i
$787$	−1037.71	+	599.119i	−1.31856	+	0.761270i	−0.983497	−	0.180926i	$-0.942090\pi$
$787$	−1037.71	+	599.119i	−1.31856	+	0.761270i	−0.335061	+	0.942196i	$0.608757\pi$
$788$	1838.57	−	1061.50i	2.33321	−	1.34708i
$789$			14.5652i			0.0184603i
$790$		−	814.341i		−	1.03081i
$791$	120.597	+	208.881i	0.152462	+	0.264072i
$792$	−431.462	+	747.313i	−0.544775	+	0.943578i
$793$	−219.540	+	380.255i	−0.276848	+	0.479514i
$794$	−433.292	+	250.162i	−0.545708	+	0.315065i
$795$		−	359.612i		−	0.452343i
$796$	−6.39724			−0.00803674
$797$	−312.747	+	541.694i	−0.392406	+	0.679667i	−0.992766	−	0.120063i	$-0.961690\pi$
$797$	−312.747	+	541.694i	−0.392406	+	0.679667i	0.600361	+	0.799729i	$0.295024\pi$
$798$	−508.800	+	293.756i	−0.637594	+	0.368115i
$799$	741.464			0.927991
$800$	12.1424	+	7.01043i	0.0151780	+	0.00876304i
$801$	162.900			0.203371
$802$	797.471	+	1381.26i	0.994353	+	1.72227i
$803$		−	2098.80i		−	2.61370i
$804$	145.463	−	928.068i	0.180924	−	1.15431i
$805$	728.998			0.905587
$806$	−4397.83	+	2539.09i	−5.45636	+	3.15023i
$807$			12.9749i			0.0160779i
$808$	−854.005	+	1479.18i	−1.05694	+	1.83067i
$809$		−	228.765i		−	0.282775i	−0.989954	−	0.141387i	$-0.954844\pi$
$809$		−	228.765i		−	0.282775i	0.989954	−	0.141387i	$-0.0451563\pi$
$810$	69.5592	+	120.480i	0.0858755	+	0.148741i
$811$	276.492	+	159.633i	0.340928	+	0.196835i	0.660682	−	0.750666i	$-0.270267\pi$
$811$	276.492	+	159.633i	0.340928	+	0.196835i	−0.319754	+	0.947500i	$0.603600\pi$
$812$			2013.45i			2.47962i
$813$	109.434			0.134605
$814$	−942.045	−	1631.67i	−1.15730	−	2.00451i
$815$	−157.459	−	90.9090i	−0.193201	−	0.111545i
$816$	−241.118	−	139.209i	−0.295487	−	0.170600i
$817$	−471.801	+	272.395i	−0.577480	+	0.333408i
$818$	−471.698			−0.576648
$819$	732.803			0.894753
$820$	24.4425	+	42.3356i	0.0298079	+	0.0516288i
$821$	−18.6356	−	32.2779i	−0.0226987	−	0.0393153i	0.854453	−	0.519529i	$-0.173893\pi$
$821$	−18.6356	−	32.2779i	−0.0226987	−	0.0393153i	−0.877152	+	0.480214i	$0.840559\pi$
$822$	−799.058	+	461.336i	−0.972090	+	0.561236i
$823$	−574.045	−	994.275i	−0.697503	−	1.20811i	−0.969330	−	0.245764i	$-0.920961\pi$
$823$	−574.045	−	994.275i	−0.697503	−	1.20811i	0.271827	−	0.962346i	$-0.412372\pi$
$824$	−561.753	−	324.328i	−0.681739	−	0.393602i
$825$	91.7414	−	158.901i	0.111202	−	0.192607i
$826$	404.856			0.490140
$827$	−503.292	−	871.728i	−0.608576	−	1.05408i	−0.991475	−	0.130294i	$-0.958408\pi$
$827$	−503.292	−	871.728i	−0.608576	−	1.05408i	0.382899	−	0.923790i	$-0.374926\pi$
$828$	−419.910			−0.507137
$829$	−202.628			−0.244425			−0.122213	−	0.992504i	$-0.538999\pi$
$829$	−202.628			−0.244425			−0.122213	+	0.992504i	$0.538999\pi$
$830$	−484.686	+	839.501i	−0.583959	+	1.01145i
$831$			218.479i			0.262910i
$832$	−1322.40	+	763.488i	−1.58942	+	0.917654i
$833$	192.055	−	332.648i	0.230558	−	0.399338i
$834$	−583.347	+	336.796i	−0.699457	+	0.403832i
$835$	431.022	+	248.851i	0.516194	+	0.298025i
$836$	1455.90	+	840.566i	1.74151	+	1.00546i
$837$	−147.319	+	255.163i	−0.176008	+	0.304855i
$838$	1795.49	+	1036.63i	2.14259	+	1.23702i
$839$	214.198	−	371.002i	0.255301	−	0.442195i	−0.709676	−	0.704528i	$-0.751159\pi$
$839$	214.198	−	371.002i	0.255301	−	0.442195i	0.964977	+	0.262333i	$0.0844920\pi$
$840$	−519.982	+	900.635i	−0.619026	+	1.07218i
$841$	76.7121	+	132.869i	0.0912153	+	0.157990i
$842$	2136.36	+	1233.43i	2.53725	+	1.46488i
$843$	−25.5706	−	44.2896i	−0.0303329	−	0.0525381i
$844$	2327.75			2.75800
$845$	−1902.01	−	1098.13i	−2.25090	−	1.29956i
$846$			825.281i			0.975509i
$847$			2721.83i			3.21350i
$848$	−693.730	+	400.525i	−0.818078	+	0.472318i
$849$		−	25.0976i		−	0.0295614i
$850$	148.074	+	85.4908i	0.174205	+	0.100577i
$851$	231.894	−	401.653i	0.272496	−	0.471978i
$852$	201.960	−	116.602i	0.237042	−	0.136856i
$853$	711.830	+	1232.93i	0.834502	+	1.44540i	0.894435	+	0.447198i	$0.147578\pi$
$853$	711.830	+	1232.93i	0.834502	+	1.44540i	−0.0599330	+	0.998202i	$0.519089\pi$
$854$	−487.129	+	281.244i	−0.570408	+	0.329325i
$855$	118.735	−	68.5518i	0.138872	−	0.0801775i
$856$		−	14.2856i		−	0.0166888i
$857$		−	561.014i		−	0.654626i	−0.944916	−	0.327313i	$-0.893857\pi$
$857$		−	561.014i		−	0.654626i	0.944916	−	0.327313i	$-0.106143\pi$
$858$	−1566.51	−	2713.27i	−1.82576	−	3.16232i
$859$	−591.409	+	1024.35i	−0.688485	+	1.19249i	0.283843	+	0.958871i	$0.408391\pi$
$859$	−591.409	+	1024.35i	−0.688485	+	1.19249i	−0.972328	+	0.233620i	$0.924943\pi$
$860$	−953.158	+	1650.92i	−1.10832	+	1.91967i
$861$	19.3321	−	11.1614i	0.0224530	−	0.0129633i
$862$			51.9402i			0.0602554i
$863$	−162.090			−0.187821			−0.0939107	−	0.995581i	$-0.529937\pi$
$863$	−162.090			−0.187821			−0.0939107	+	0.995581i	$0.529937\pi$
$864$	6.94531	−	12.0296i	0.00803855	−	0.0139232i
$865$	−276.991	+	159.921i	−0.320221	+	0.184880i
$866$	−1707.85			−1.97211
$867$	301.700	+	174.187i	0.347982	+	0.200907i
$868$	−4353.98			−5.01611
$869$	532.027	+	921.498i	0.612229	+	1.06041i
$870$		−	702.042i		−	0.806945i
$871$	1342.58	+	1083.63i	1.54143	+	1.24413i
$872$	−163.261			−0.187226
$873$	117.430	−	67.7981i	0.134513	−	0.0776610i
$874$			618.315i			0.707454i
$875$	637.570	−	1104.30i	0.728652	−	1.26206i
$876$			1456.96i			1.66319i
$877$	−32.3813	−	56.0860i	−0.0369228	−	0.0639522i	0.846973	−	0.531635i	$-0.178422\pi$
$877$	−32.3813	−	56.0860i	−0.0369228	−	0.0639522i	−0.883896	+	0.467683i	$0.845089\pi$
$878$	2345.61	+	1354.24i	2.67154	+	1.54241i
$879$			812.119i			0.923912i
$880$	1539.45			1.74937
$881$	20.3233	+	35.2011i	0.0230685	+	0.0399558i	0.877329	−	0.479889i	$-0.159323\pi$
$881$	20.3233	+	35.2011i	0.0230685	+	0.0399558i	−0.854261	+	0.519845i	$0.825990\pi$
$882$	370.251	+	213.765i	0.419786	+	0.242364i
$883$	498.313	+	287.701i	0.564341	+	0.325823i	0.754886	−	0.655856i	$-0.227692\pi$
$883$	498.313	+	287.701i	0.564341	+	0.325823i	−0.190545	+	0.981679i	$0.561025\pi$
$884$	1692.22	−	977.004i	1.91428	−	1.10521i
$885$	−94.4784			−0.106755
$886$	2379.83			2.68604
$887$	−433.940	−	751.607i	−0.489223	−	0.847358i	0.510701	−	0.859759i	$-0.329386\pi$
$887$	−433.940	−	751.607i	−0.489223	−	0.847358i	−0.999923	+	0.0124003i	$0.996053\pi$
$888$	330.813	+	572.985i	0.372537	+	0.645253i
$889$	−693.958	+	400.657i	−0.780605	+	0.450683i
$890$	−419.674	−	726.896i	−0.471544	−	0.816737i
$891$	−157.425	−	90.8891i	−0.176683	−	0.102008i
$892$	−396.266	+	686.353i	−0.444245	+	0.769455i
$893$	813.329			0.910782
$894$	212.354	+	367.808i	0.237532	+	0.411418i
$895$	509.556			0.569336
$896$	−2057.58			−2.29640
$897$	385.612	−	667.899i	0.429891	−	0.744592i
$898$		−	1207.45i		−	1.34460i
$899$	1287.65	−	743.423i	1.43231	−	0.826944i
$900$	−63.6856	+	110.307i	−0.0707617	+	0.122563i
$901$	−379.207	+	218.935i	−0.420874	+	0.242992i
$902$	−82.6519	−	47.7191i	−0.0916318	−	0.0529037i
$903$	753.873	+	435.249i	0.834854	+	0.482003i
$904$	−181.060	+	313.606i	−0.200288	+	0.346909i
$905$	637.897	+	368.290i	0.704858	+	0.406950i
$906$	685.421	−	1187.18i	0.756536	−	1.31036i
$907$	101.146	−	175.190i	0.111517	−	0.193153i	−0.804865	−	0.593458i	$-0.797762\pi$
$907$	101.146	−	175.190i	0.111517	−	0.193153i	0.916382	+	0.400305i	$0.131096\pi$
$908$	−718.339	−	1244.20i	−0.791123	−	1.37026i
$909$	−311.595	−	179.900i	−0.342789	−	0.197909i
$910$	−1887.90	−	3269.93i	−2.07461	−	3.59333i
$911$	1772.81			1.94600			0.973002	−	0.230798i	$-0.0741336\pi$
$911$	1772.81			1.94600			0.973002	+	0.230798i	$0.0741336\pi$
$912$	−264.487	−	152.702i	−0.290008	−	0.167436i
$913$		−	1266.62i		−	1.38732i
$914$			1053.75i			1.15290i
$915$	113.678	−	65.6319i	0.124238	−	0.0717289i
$916$			878.528i			0.959092i
$917$	−360.986	−	208.415i	−0.393660	−	0.227280i
$918$	84.6966	−	146.699i	0.0922621	−	0.159803i
$919$	−309.363	+	178.611i	−0.336630	+	0.194354i	−0.658781	−	0.752335i	$-0.728928\pi$
$919$	−309.363	+	178.611i	−0.336630	+	0.194354i	0.322151	+	0.946688i	$0.395594\pi$
$920$	547.244	+	947.855i	0.594831	+	1.03028i
$921$	317.412	−	183.258i	0.344639	−	0.198977i
$922$	−387.740	+	223.862i	−0.420542	+	0.242800i
$923$			428.311i			0.464042i
$924$		−	2686.22i		−	2.90716i
$925$	−70.3405	−	121.833i	−0.0760438	−	0.131712i
$926$	1105.31	−	1914.45i	1.19364	−	2.06744i
$927$	68.3211	−	118.336i	0.0737012	−	0.127654i
$928$	−60.7059	+	35.0485i	−0.0654158	+	0.0377678i
$929$			506.296i			0.544990i	0.962157	+	0.272495i	$0.0878489\pi$
$929$			506.296i			0.544990i	−0.962157	+	0.272495i	$0.912151\pi$
$930$	1518.13			1.63240
$931$	210.669	−	364.889i	0.226282	−	0.391933i
$932$	−659.731	+	380.896i	−0.707866	+	0.408687i
$933$	261.916			0.280725
$934$	−1876.85	−	1083.60i	−2.00947	−	1.16017i
$935$	841.494			0.899994
$936$	550.101	+	952.803i	0.587715	+	1.01795i
$937$			686.990i			0.733181i	0.930382	+	0.366590i	$0.119475\pi$
$937$			686.990i			0.733181i	−0.930382	+	0.366590i	$0.880525\pi$
$938$	795.402	+	2062.18i	0.847977	+	2.19849i
$939$	−823.648			−0.877155
$940$	2464.70	−	1422.99i	2.62202	−	1.51382i
$941$		−	828.003i		−	0.879918i	−0.898018	−	0.439959i	$-0.854993\pi$
$941$		−	828.003i		−	0.879918i	0.898018	−	0.439959i	$-0.145007\pi$
$942$	−308.456	+	534.261i	−0.327448	+	0.567156i
$943$		−	23.4931i		−	0.0249132i
$944$	105.227	+	182.259i	0.111469	+	0.193071i
$945$	−189.722	−	109.536i	−0.200764	−	0.115911i
$946$		−	3721.71i		−	3.93415i
$947$	−1352.73			−1.42844			−0.714220	−	0.699921i	$-0.753218\pi$
$947$	−1352.73			−1.42844			−0.714220	+	0.699921i	$0.753218\pi$
$948$	−369.326	−	639.691i	−0.389584	−	0.674780i
$949$	−2317.40	−	1337.95i	−2.44194	−	1.40986i
$950$	162.426	+	93.7767i	0.170975	+	0.0987123i
$951$	−230.331	+	132.982i	−0.242199	+	0.139834i
$952$	1266.28			1.33013
$953$	−402.515			−0.422366			−0.211183	−	0.977447i	$-0.567732\pi$
$953$	−402.515			−0.422366			−0.211183	+	0.977447i	$0.567732\pi$
$954$	−243.684	−	422.074i	−0.255434	−	0.442425i
$955$	502.639	+	870.596i	0.526323	+	0.911619i
$956$	−482.713	+	278.694i	−0.504929	+	0.291521i
$957$	458.660	+	794.422i	0.479268	+	0.830117i
$958$	2524.01	+	1457.24i	2.63466	+	1.52112i
$959$	726.476	−	1258.29i	0.757535	−	1.31209i
$960$	456.492			0.475512
$961$	1127.11	+	1952.22i	1.17285	+	2.03144i
$962$	−2402.16			−2.49705
$963$	3.00932			0.00312494
$964$	464.342	−	804.264i	0.481683	−	0.834299i
$965$			523.933i			0.542936i
$966$	855.618	−	493.991i	0.885732	−	0.511378i
$967$	519.776	−	900.279i	0.537514	−	0.931002i	−0.461523	−	0.887128i	$-0.652697\pi$
$967$	519.776	−	900.279i	0.537514	−	0.931002i	0.999037	−	0.0438738i	$-0.0139699\pi$
$968$	−3538.97	+	2043.23i	−3.65596	+	2.11077i
$969$	−144.574	−	83.4700i	−0.149199	−	0.0861403i
$970$	−605.060	−	349.332i	−0.623773	−	0.360136i
$971$	−382.500	+	662.509i	−0.393924	+	0.682296i	−0.992963	−	0.118424i	$-0.962216\pi$
$971$	−382.500	+	662.509i	−0.393924	+	0.682296i	0.599040	+	0.800719i	$0.295549\pi$
$972$	109.282	+	63.0939i	0.112430	+	0.0649115i
$973$	530.359	−	918.609i	0.545076	−	0.944100i
$974$	784.733	−	1359.20i	0.805681	−	1.39548i
$975$	−116.968	−	202.594i	−0.119967	−	0.207789i
$976$	−253.222	−	146.198i	−0.259449	−	0.149793i
$977$	−23.5702	−	40.8247i	−0.0241250	−	0.0417858i	0.853711	−	0.520747i	$-0.174347\pi$
$977$	−23.5702	−	40.8247i	−0.0241250	−	0.0417858i	−0.877836	+	0.478962i	$0.841013\pi$
$978$	−246.411			−0.251954
$979$	949.795	+	548.364i	0.970168	+	0.560127i
$980$		−	1474.34i		−	1.50443i
$981$		−	34.3916i		−	0.0350577i
$982$	1923.03	−	1110.26i	1.95828	−	1.13061i
$983$		−	157.380i		−	0.160102i	−0.996791	−	0.0800510i	$-0.974492\pi$
$983$		−	157.380i		−	0.160102i	0.996791	−	0.0800510i	$-0.0255083\pi$
$984$	29.0244	+	16.7573i	0.0294964	+	0.0170297i
$985$	582.834	−	1009.50i	0.591710	−	1.02487i
$986$	−740.295	+	427.410i	−0.750807	+	0.433478i
$987$	−649.793	−	1125.48i	−0.658352	−	1.14030i
$988$	1856.23	−	1071.70i	1.87878	−	1.08471i
$989$	793.398	−	458.069i	0.802223	−	0.463163i
$990$			936.619i			0.946079i
$991$			264.352i			0.266753i	0.991065	+	0.133376i	$0.0425819\pi$
$991$			264.352i			0.266753i	−0.991065	+	0.133376i	$0.957418\pi$
$992$	−75.7906	−	131.273i	−0.0764018	−	0.132332i
$993$	432.115	−	748.446i	0.435161	−	0.753722i
$994$	−274.346	+	475.181i	−0.276002	+	0.478049i
$995$	−3.04193	+	1.75626i	−0.00305721	+	0.00176508i
$996$			879.273i			0.882804i
$997$	−1523.15			−1.52773			−0.763866	−	0.645374i	$-0.776701\pi$
$997$	−1523.15			−1.52773			−0.763866	+	0.645374i	$0.776701\pi$
$998$	24.8432	−	43.0297i	0.0248930	−	0.0431159i
$999$	−120.702	+	69.6871i	−0.120822	+	0.0697568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.b.97.2	✓	24
67.38	odd	6	inner	201.3.h.b.172.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.b.97.2	✓	24	1.1	even	1	trivial
201.3.h.b.172.2	yes	24	67.38	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.01185 + 1.73889i) q^{2} +1.73205i q^{3} +(4.04748 - 7.01044i) q^{4} -4.44467i q^{5} +(-3.01185 - 5.21667i) q^{6} +(8.21480 + 4.74282i) q^{7} +14.2414i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-3.01185 + 1.73889i) q^{2} +1.73205i q^{3} +(4.04748 - 7.01044i) q^{4} -4.44467i q^{5} +(-3.01185 - 5.21667i) q^{6} +(8.21480 + 4.74282i) q^{7} +14.2414i q^{8} -3.00000 q^{9} +(7.72880 + 13.3867i) q^{10} +(-17.4916 - 10.0988i) q^{11} +(12.1424 + 7.01044i) q^{12} +(-22.3013 + 12.8757i) q^{13} -32.9889 q^{14} +7.69840 q^{15} +(-8.57425 - 14.8510i) q^{16} +(-4.68686 - 8.11788i) q^{17} +(9.03554 - 5.21667i) q^{18} +(-5.14112 - 8.90468i) q^{19} +(-31.1591 - 17.9897i) q^{20} +(-8.21480 + 14.2284i) q^{21} +70.2428 q^{22} +(8.64550 + 14.9744i) q^{23} -24.6668 q^{24} +5.24488 q^{25} +(44.7787 - 77.5591i) q^{26} -5.19615i q^{27} +(66.4984 - 38.3929i) q^{28} +(-13.1108 + 22.7086i) q^{29} +(-23.1864 + 13.3867i) q^{30} +(-49.1062 - 28.3515i) q^{31} +(2.31510 + 1.33663i) q^{32} +(17.4916 - 30.2964i) q^{33} +(28.2322 + 16.2999i) q^{34} +(21.0803 - 36.5121i) q^{35} +(-12.1424 + 21.0313i) q^{36} +(-13.4113 - 23.2290i) q^{37} +(30.9685 + 17.8797i) q^{38} +(-22.3013 - 38.6270i) q^{39} +63.2982 q^{40} +(-1.17666 - 0.679346i) q^{41} -57.1385i q^{42} -52.9835i q^{43} +(-141.594 + 81.7493i) q^{44} +13.3340i q^{45} +(-52.0778 - 30.0671i) q^{46} +(-39.5502 + 68.5029i) q^{47} +(25.7227 - 14.8510i) q^{48} +(20.4886 + 35.4873i) q^{49} +(-15.7968 + 9.12026i) q^{50} +(14.0606 - 8.11788i) q^{51} +208.456i q^{52} -46.7126i q^{53} +(9.03554 + 15.6500i) q^{54} +(-44.8858 + 77.7446i) q^{55} +(-67.5441 + 116.990i) q^{56} +(15.4234 - 8.90468i) q^{57} -91.1932i q^{58} -12.2725 q^{59} +(31.1591 - 53.9692i) q^{60} +(14.7664 - 8.52539i) q^{61} +197.200 q^{62} +(-24.6444 - 14.2284i) q^{63} +59.2970 q^{64} +(57.2281 + 99.1220i) q^{65} +121.664i q^{66} +(-24.1112 - 62.5112i) q^{67} -75.8798 q^{68} +(-25.9365 + 14.9744i) q^{69} +146.625i q^{70} +(8.31629 - 14.4042i) q^{71} -42.7241i q^{72} +(51.9567 + 89.9916i) q^{73} +(80.7854 + 46.6415i) q^{74} +9.08439i q^{75} -83.2343 q^{76} +(-95.7934 - 165.919i) q^{77} +(134.336 + 77.5591i) q^{78} +(-45.6242 - 26.3411i) q^{79} +(-66.0080 + 38.1097i) q^{80} +9.00000 q^{81} +4.72523 q^{82} +(31.3558 + 54.3099i) q^{83} +(66.4984 + 115.179i) q^{84} +(-36.0813 + 20.8316i) q^{85} +(92.1325 + 159.578i) q^{86} +(-39.3325 - 22.7086i) q^{87} +(143.821 - 249.104i) q^{88} -54.3000 q^{89} +(-23.1864 - 40.1600i) q^{90} -244.268 q^{91} +139.970 q^{92} +(49.1062 - 85.0544i) q^{93} -275.094i q^{94} +(-39.5784 + 22.8506i) q^{95} +(-2.31510 + 4.00988i) q^{96} +(-39.1432 + 22.5994i) q^{97} +(-123.417 - 71.2549i) q^{98} +(52.4749 + 30.2964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9}+O(q^{10}) \) 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9	\( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9} + 30 q^{10} + 12 q^{11} + 102 q^{12} + 30 q^{13} + 6 q^{14} - 6 q^{15} - 98 q^{16} + 4 q^{17} + 39 q^{19} + 108 q^{20} - 21 q^{21} - 82 q^{22} - 13 q^{23} - 36 q^{24} - 222 q^{25} + 29 q^{26} + 189 q^{28} - 90 q^{30} - 93 q^{31} - 33 q^{32} - 12 q^{33} + 72 q^{34} - 93 q^{35} - 102 q^{36} - 33 q^{37} - 210 q^{38} + 30 q^{39} + 274 q^{40} - 15 q^{41} - 9 q^{44} - 228 q^{46} - 131 q^{47} + 294 q^{48} + 295 q^{49} - 423 q^{50} - 12 q^{51} - 56 q^{55} + 349 q^{56} - 117 q^{57} - 116 q^{59} - 108 q^{60} + 120 q^{61} + 282 q^{62} - 63 q^{63} - 276 q^{64} + 136 q^{65} - 25 q^{67} + 10 q^{68} + 39 q^{69} + 169 q^{71} + 187 q^{73} + 849 q^{74} + 386 q^{76} - 348 q^{77} + 87 q^{78} + 51 q^{80} + 216 q^{81} - 14 q^{82} + 104 q^{83} + 189 q^{84} - 243 q^{85} + 641 q^{86} - 766 q^{88} + 152 q^{89} - 90 q^{90} + 32 q^{91} - 216 q^{92} + 93 q^{93} + 762 q^{95} + 33 q^{96} - 84 q^{97} - 1086 q^{98} - 36 q^{99}+O(q^{100}) \) 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9 + 30 * q^10 + 12 * q^11 + 102 * q^12 + 30 * q^13 + 6 * q^14 - 6 * q^15 - 98 * q^16 + 4 * q^17 + 39 * q^19 + 108 * q^20 - 21 * q^21 - 82 * q^22 - 13 * q^23 - 36 * q^24 - 222 * q^25 + 29 * q^26 + 189 * q^28 - 90 * q^30 - 93 * q^31 - 33 * q^32 - 12 * q^33 + 72 * q^34 - 93 * q^35 - 102 * q^36 - 33 * q^37 - 210 * q^38 + 30 * q^39 + 274 * q^40 - 15 * q^41 - 9 * q^44 - 228 * q^46 - 131 * q^47 + 294 * q^48 + 295 * q^49 - 423 * q^50 - 12 * q^51 - 56 * q^55 + 349 * q^56 - 117 * q^57 - 116 * q^59 - 108 * q^60 + 120 * q^61 + 282 * q^62 - 63 * q^63 - 276 * q^64 + 136 * q^65 - 25 * q^67 + 10 * q^68 + 39 * q^69 + 169 * q^71 + 187 * q^73 + 849 * q^74 + 386 * q^76 - 348 * q^77 + 87 * q^78 + 51 * q^80 + 216 * q^81 - 14 * q^82 + 104 * q^83 + 189 * q^84 - 243 * q^85 + 641 * q^86 - 766 * q^88 + 152 * q^89 - 90 * q^90 + 32 * q^91 - 216 * q^92 + 93 * q^93 + 762 * q^95 + 33 * q^96 - 84 * q^97 - 1086 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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