LMFDB - Embedded newform 197.4.d.a.36.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(36,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("197.36");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.d (of order $7$, degree $6$, 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:	$11.6233762711$
Analytic rank:	$0$
Dimension:	$294$
Relative dimension:	$49$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			36.13
Character	$\chi$	$=$	197.36
Dual form			197.4.d.a.104.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.71290 + 1.30647i) q^{2} +(-8.46100 - 4.07460i) q^{3} +(0.665075 - 0.833977i) q^{4} +(-2.95496 - 3.70540i) q^{5} +28.2772 q^{6} +(-5.24170 - 2.52427i) q^{7} +(4.64553 - 20.3534i) q^{8} +(38.1519 + 47.8410i) q^{9} +(12.8575 + 6.19185i) q^{10} +(55.5583 - 26.7555i) q^{11} +(-9.02533 + 4.34637i) q^{12} +(-3.15417 - 13.8193i) q^{13} +17.5181 q^{14} +(9.90388 + 43.3917i) q^{15} +(15.8870 + 69.6057i) q^{16} +(-20.7646 - 26.0380i) q^{17} +(-166.005 - 79.9439i) q^{18} -19.2315 q^{19} -5.05549 q^{20} +(34.0647 + 42.7157i) q^{21} +(-115.769 + 145.170i) q^{22} +(153.249 - 73.8006i) q^{23} +(-122.238 + 153.282i) q^{24} +(22.8169 - 99.9673i) q^{25} +(26.6115 + 33.3697i) q^{26} +(-71.4487 - 313.037i) q^{27} +(-5.59131 + 2.69263i) q^{28} +(-258.206 + 124.345i) q^{29} +(-83.5581 - 104.779i) q^{30} +(-123.867 + 59.6514i) q^{31} +(-29.9055 - 37.5003i) q^{32} -579.097 q^{33} +(90.3502 + 43.5104i) q^{34} +(6.13559 + 26.8818i) q^{35} +65.2722 q^{36} +(76.7001 - 336.045i) q^{37} +(52.1731 - 25.1252i) q^{38} +(-29.6209 + 129.778i) q^{39} +(-89.1450 + 42.9300i) q^{40} +(-11.4163 - 14.3155i) q^{41} +(-148.221 - 71.3794i) q^{42} +(159.399 - 76.7625i) q^{43} +(14.6370 - 64.1288i) q^{44} +(64.5328 - 282.737i) q^{45} +(-319.331 + 400.428i) q^{46} +(-85.6912 + 375.438i) q^{47} +(149.195 - 653.667i) q^{48} +(-192.753 - 241.705i) q^{49} +(68.7038 + 301.011i) q^{50} +(69.5950 + 304.916i) q^{51} +(-13.6228 - 6.56038i) q^{52} +(178.114 - 223.348i) q^{53} +(602.806 + 755.895i) q^{54} +(-263.313 - 126.805i) q^{55} +(-75.7281 + 94.9600i) q^{56} +(162.717 + 78.3606i) q^{57} +(538.034 - 674.674i) q^{58} +(-303.535 + 146.175i) q^{59} +(42.7745 + 20.5991i) q^{60} +(771.509 - 371.539i) q^{61} +(258.108 - 323.657i) q^{62} +(-79.2175 - 347.074i) q^{63} +(-384.479 - 185.155i) q^{64} +(-41.8858 + 52.5231i) q^{65} +(1571.03 - 756.571i) q^{66} +(-49.6239 + 217.416i) q^{67} -35.5252 q^{68} -1597.34 q^{69} +(-51.7653 - 64.9117i) q^{70} +(322.159 + 403.975i) q^{71} +(1150.96 - 554.275i) q^{72} +(-210.118 + 920.588i) q^{73} +(230.951 + 1011.86i) q^{74} +(-600.381 + 752.854i) q^{75} +(-12.7904 + 16.0386i) q^{76} -358.758 q^{77} +(-89.1913 - 390.772i) q^{78} +(-425.820 + 533.962i) q^{79} +(210.972 - 264.550i) q^{80} +(-303.336 + 1329.00i) q^{81} +(49.6740 + 23.9217i) q^{82} -632.187 q^{83} +58.2795 q^{84} +(-35.1227 + 153.883i) q^{85} +(-332.146 + 416.498i) q^{86} +2691.34 q^{87} +(-286.467 - 1255.10i) q^{88} +(-174.272 - 83.9250i) q^{89} +(194.314 + 851.347i) q^{90} +(-18.3505 + 80.3989i) q^{91} +(40.3737 - 176.889i) q^{92} +1291.10 q^{93} +(-258.024 - 1130.48i) q^{94} +(56.8282 + 71.2603i) q^{95} +(100.232 + 439.143i) q^{96} +(-548.172 - 687.386i) q^{97} +(838.701 + 403.897i) q^{98} +(3399.67 + 1637.19i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 294 q - 5 q^{2} - 5 q^{3} - 161 q^{4} - 5 q^{5} + 58 q^{6} + 15 q^{7} + 115 q^{8} - 446 q^{9} - 211 q^{10} + 93 q^{11} - 47 q^{12} + 23 q^{13} + 656 q^{14} + 343 q^{15} - 1505 q^{16} - 17 q^{17} + 132 q^{18}+ \cdots + 4526 q^{99}+O(q^{100}) $ 294 * q - 5 * q^2 - 5 * q^3 - 161 * q^4 - 5 * q^5 + 58 * q^6 + 15 * q^7 + 115 * q^8 - 446 * q^9 - 211 * q^10 + 93 * q^11 - 47 * q^12 + 23 * q^13 + 656 * q^14 + 343 * q^15 - 1505 * q^16 - 17 * q^17 + 132 * q^18 + 512 * q^19 + 148 * q^20 - 47 * q^21 - 845 * q^22 - 143 * q^23 + 775 * q^24 - 952 * q^25 + 39 * q^26 + 1159 * q^27 - 130 * q^28 - 169 * q^29 + 1048 * q^30 - 269 * q^31 - 39 * q^32 + 234 * q^33 + 761 * q^34 + 949 * q^35 + 15930 * q^36 + 715 * q^37 - 987 * q^38 - 417 * q^39 - 3303 * q^40 + 65 * q^41 - 2334 * q^42 + 581 * q^43 - 1751 * q^44 - 2497 * q^45 + 13 * q^46 - 361 * q^47 - 3995 * q^48 - 3728 * q^49 + 3671 * q^50 + 213 * q^51 + 4036 * q^52 - 47 * q^53 + 1358 * q^54 - 4339 * q^55 + 680 * q^56 - 2470 * q^57 + 1483 * q^58 - 3375 * q^59 + 1549 * q^60 + 805 * q^61 - 1149 * q^62 - 4839 * q^63 - 7061 * q^64 + 457 * q^65 + 1224 * q^66 + 2261 * q^67 + 1216 * q^68 - 4378 * q^69 + 1360 * q^70 - 1687 * q^71 + 936 * q^72 + 3075 * q^73 - 601 * q^74 + 3549 * q^75 - 5960 * q^76 - 4318 * q^77 - 11681 * q^78 + 2973 * q^79 - 1671 * q^80 - 4288 * q^81 + 2197 * q^82 + 9380 * q^83 - 7416 * q^84 - 5171 * q^85 - 3868 * q^86 + 1826 * q^87 - 3252 * q^88 - 79 * q^89 + 19791 * q^90 + 8303 * q^91 + 8077 * q^92 + 2118 * q^93 + 6319 * q^94 - 3280 * q^95 - 13752 * q^96 - 17 * q^97 - 4434 * q^98 + 4526 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	−2.71290	+	1.30647i	−0.959156	+	0.461905i	−0.846887	−	0.531773i	$-0.821526\pi$
$2$	−2.71290	+	1.30647i	−0.959156	+	0.461905i	−0.112269	+	0.993678i	$0.535812\pi$
$3$	−8.46100	−	4.07460i	−1.62832	−	0.784158i	−0.999981	−	0.00621921i	$-0.998020\pi$
$3$	−8.46100	−	4.07460i	−1.62832	−	0.784158i	−0.628340	−	0.777939i	$-0.716265\pi$
$4$	0.665075	−	0.833977i	0.0831343	−	0.104247i
$5$	−2.95496	−	3.70540i	−0.264300	−	0.331421i	0.631918	−	0.775035i	$-0.282268\pi$
$5$	−2.95496	−	3.70540i	−0.264300	−	0.331421i	−0.896218	+	0.443613i	$0.853696\pi$
$6$	28.2772			1.92402
$7$	−5.24170	−	2.52427i	−0.283025	−	0.136298i	0.286986	−	0.957935i	$-0.407347\pi$
$7$	−5.24170	−	2.52427i	−0.283025	−	0.136298i	−0.570011	+	0.821637i	$0.693061\pi$
$8$	4.64553	−	20.3534i	0.205306	−	0.899502i
$9$	38.1519	+	47.8410i	1.41304	+	1.77189i
$10$	12.8575	+	6.19185i	0.406590	+	0.195803i
$11$	55.5583	−	26.7555i	1.52286	−	0.733371i	0.529489	−	0.848317i	$-0.322384\pi$
$11$	55.5583	−	26.7555i	1.52286	−	0.733371i	0.993372	+	0.114946i	$0.0366694\pi$
$12$	−9.02533	+	4.34637i	−0.217116	+	0.104557i
$13$	−3.15417	−	13.8193i	−0.0672931	−	0.294830i	0.930072	−	0.367378i	$-0.119744\pi$
$13$	−3.15417	−	13.8193i	−0.0672931	−	0.294830i	−0.997365	+	0.0725472i	$0.976887\pi$
$14$	17.5181			0.334422
$15$	9.90388	+	43.3917i	0.170478	+	0.746913i
$16$	15.8870	+	69.6057i	0.248235	+	1.08759i
$17$	−20.7646	−	26.0380i	−0.296245	−	0.371479i	0.611326	−	0.791379i	$-0.290637\pi$
$17$	−20.7646	−	26.0380i	−0.296245	−	0.371479i	−0.907570	+	0.419900i	$0.862065\pi$
$18$	−166.005	−	79.9439i	−2.17377	−	1.04683i
$19$	−19.2315			−0.232211			−0.116105	−	0.993237i	$-0.537041\pi$
$19$	−19.2315			−0.232211			−0.116105	+	0.993237i	$0.537041\pi$
$20$	−5.05549			−0.0565221
$21$	34.0647	+	42.7157i	0.353977	+	0.443873i
$22$	−115.769	+	145.170i	−1.12191	+	1.40683i
$23$	153.249	−	73.8006i	1.38933	−	0.669065i	0.418361	−	0.908281i	$-0.362605\pi$
$23$	153.249	−	73.8006i	1.38933	−	0.669065i	0.970966	+	0.239216i	$0.0768905\pi$
$24$	−122.238	+	153.282i	−1.03966	+	1.30369i
$25$	22.8169	−	99.9673i	0.182535	−	0.799739i
$26$	26.6115	+	33.3697i	0.200728	+	0.251705i
$27$	−71.4487	−	313.037i	−0.509271	−	2.23126i
$28$	−5.59131	+	2.69263i	−0.0377378	+	0.0181736i
$29$	−258.206	+	124.345i	−1.65337	+	0.796219i	−0.654160	+	0.756356i	$0.726978\pi$
$29$	−258.206	+	124.345i	−1.65337	+	0.796219i	−0.999205	+	0.0398624i	$0.987308\pi$
$30$	−83.5581	−	104.779i	−0.508518	−	0.637662i
$31$	−123.867	+	59.6514i	−0.717653	+	0.345603i	−0.756815	−	0.653630i	$-0.773245\pi$
$31$	−123.867	+	59.6514i	−0.717653	+	0.345603i	0.0391620	+	0.999233i	$0.487531\pi$
$32$	−29.9055	−	37.5003i	−0.165206	−	0.207162i
$33$	−579.097			−3.05478
$34$	90.3502	+	43.5104i	0.455733	+	0.219470i
$35$	6.13559	+	26.8818i	0.0296315	+	0.129824i
$36$	65.2722			0.302186
$37$	76.7001	−	336.045i	0.340795	−	1.49312i	−0.456605	−	0.889670i	$-0.650935\pi$
$37$	76.7001	−	336.045i	0.340795	−	1.49312i	0.797400	−	0.603451i	$-0.206208\pi$
$38$	52.1731	−	25.1252i	0.222726	−	0.107259i
$39$	−29.6209	+	129.778i	−0.121619	+	0.532847i
$40$	−89.1450	+	42.9300i	−0.352377	+	0.169696i
$41$	−11.4163	−	14.3155i	−0.0434859	−	0.0545295i	0.759613	−	0.650375i	$-0.225388\pi$
$41$	−11.4163	−	14.3155i	−0.0434859	−	0.0545295i	−0.803099	+	0.595846i	$0.796817\pi$
$42$	−148.221	−	71.3794i	−0.544547	−	0.262240i
$43$	159.399	−	76.7625i	0.565305	−	0.272236i	−0.129327	−	0.991602i	$-0.541282\pi$
$43$	159.399	−	76.7625i	0.565305	−	0.272236i	0.694632	+	0.719366i	$0.255567\pi$
$44$	14.6370	−	64.1288i	0.0501502	−	0.219722i
$45$	64.5328	−	282.737i	0.213777	−	0.936620i
$46$	−319.331	+	400.428i	−1.02354	+	1.28348i
$47$	−85.6912	+	375.438i	−0.265944	+	1.16518i	0.648742	+	0.761009i	$0.275296\pi$
$47$	−85.6912	+	375.438i	−0.265944	+	1.16518i	−0.914685	+	0.404167i	$0.867562\pi$
$48$	149.195	−	653.667i	0.448635	−	1.96560i
$49$	−192.753	−	241.705i	−0.561964	−	0.704680i
$50$	68.7038	+	301.011i	0.194324	+	0.851388i
$51$	69.5950	+	304.916i	0.191083	+	0.837190i
$52$	−13.6228	−	6.56038i	−0.0363296	−	0.0174954i
$53$	178.114	−	223.348i	0.461620	−	0.578853i	−0.495477	−	0.868621i	$-0.665007\pi$
$53$	178.114	−	223.348i	0.461620	−	0.578853i	0.957097	+	0.289768i	$0.0935782\pi$
$54$	602.806	+	755.895i	1.51910	+	1.90489i
$55$	−263.313	−	126.805i	−0.645547	−	0.310879i
$56$	−75.7281	+	94.9600i	−0.180707	+	0.226599i
$57$	162.717	+	78.3606i	0.378113	+	0.182090i
$58$	538.034	−	674.674i	1.21806	−	1.52740i
$59$	−303.535	+	146.175i	−0.669779	+	0.322548i	−0.737687	−	0.675143i	$-0.764082\pi$
$59$	−303.535	+	146.175i	−0.669779	+	0.322548i	0.0679080	+	0.997692i	$0.478368\pi$
$60$	42.7745	+	20.5991i	0.0920361	+	0.0443223i
$61$	771.509	−	371.539i	1.61937	−	0.779848i	0.619385	−	0.785087i	$-0.287382\pi$
$61$	771.509	−	371.539i	1.61937	−	0.779848i	0.999986	+	0.00523912i	$0.00166767\pi$
$62$	258.108	−	323.657i	0.528705	−	0.662975i
$63$	−79.2175	−	347.074i	−0.158420	−	0.694084i
$64$	−384.479	−	185.155i	−0.750936	−	0.361632i
$65$	−41.8858	+	52.5231i	−0.0799276	+	0.100226i
$66$	1571.03	−	756.571i	2.93002	−	1.41102i
$67$	−49.6239	+	217.416i	−0.0904854	+	0.396443i	−0.999807	−	0.0196518i	$-0.993744\pi$
$67$	−49.6239	+	217.416i	−0.0904854	+	0.396443i	0.909321	+	0.416094i	$0.136601\pi$
$68$	−35.5252			−0.0633538
$69$	−1597.34			−2.78692
$70$	−51.7653	−	64.9117i	−0.0883877	−	0.110835i
$71$	322.159	+	403.975i	0.538496	+	0.675253i	0.974421	−	0.224730i	$-0.0721501\pi$
$71$	322.159	+	403.975i	0.538496	+	0.675253i	−0.435925	+	0.899983i	$0.643579\pi$
$72$	1150.96	−	554.275i	1.88392	−	0.907249i
$73$	−210.118	+	920.588i	−0.336883	+	1.47598i	0.468625	+	0.883397i	$0.344749\pi$
$73$	−210.118	+	920.588i	−0.336883	+	1.47598i	−0.805509	+	0.592584i	$0.798108\pi$
$74$	230.951	+	1011.86i	0.362805	+	1.58955i
$75$	−600.381	+	752.854i	−0.924347	+	1.15909i
$76$	−12.7904	+	16.0386i	−0.0193047	+	0.0242073i
$77$	−358.758			−0.530965
$78$	−89.1913	−	390.772i	−0.129473	−	0.567260i
$79$	−425.820	+	533.962i	−0.606437	+	0.760448i	−0.986366	−	0.164568i	$-0.947377\pi$
$79$	−425.820	+	533.962i	−0.606437	+	0.760448i	0.379929	+	0.925016i	$0.375948\pi$
$80$	210.972	−	264.550i	0.294842	−	0.369720i
$81$	−303.336	+	1329.00i	−0.416098	+	1.82305i
$82$	49.6740	+	23.9217i	0.0668972	+	0.0322160i
$83$	−632.187			−0.836042			−0.418021	−	0.908437i	$-0.637276\pi$
$83$	−632.187			−0.836042			−0.418021	+	0.908437i	$0.637276\pi$
$84$	58.2795			0.0757002
$85$	−35.1227	+	153.883i	−0.0448188	+	0.196364i
$86$	−332.146	+	416.498i	−0.416468	+	0.522235i
$87$	2691.34			3.31657
$88$	−286.467	−	1255.10i	−0.347017	−	1.52038i
$89$	−174.272	−	83.9250i	−0.207560	−	0.0999554i	0.327216	−	0.944950i	$-0.393890\pi$
$89$	−174.272	−	83.9250i	−0.207560	−	0.0999554i	−0.534776	+	0.844994i	$0.679604\pi$
$90$	194.314	+	851.347i	0.227584	+	0.997110i
$91$	−18.3505	+	80.3989i	−0.0211391	+	0.0926164i
$92$	40.3737	−	176.889i	0.0457527	−	0.200456i
$93$	1291.10			1.43958
$94$	−258.024	−	1130.48i	−0.283119	−	1.24043i
$95$	56.8282	+	71.2603i	0.0613732	+	0.0769595i
$96$	100.232	+	439.143i	0.106561	+	0.466873i
$97$	−548.172	−	687.386i	−0.573798	−	0.719520i	0.407243	−	0.913320i	$-0.366490\pi$
$97$	−548.172	−	687.386i	−0.573798	−	0.719520i	−0.981041	+	0.193800i	$0.937919\pi$
$98$	838.701	+	403.897i	0.864506	+	0.416324i
$99$	3399.67	+	1637.19i	3.45131	+	1.66206i
$100$	−68.1955	−	85.5145i	−0.0681955	−	0.0855145i
$101$	30.3627	+	133.028i	0.0299129	+	0.131057i	0.987680	−	0.156489i	$-0.0500176\pi$
$101$	30.3627	+	133.028i	0.0299129	+	0.131057i	−0.957767	+	0.287546i	$0.907161\pi$
$102$	−587.166	−	736.283i	−0.569981	−	0.714734i
$103$	−147.632	−	646.818i	−0.141229	−	0.618765i	−0.995151	−	0.0983634i	$-0.968639\pi$
$103$	−147.632	−	646.818i	−0.141229	−	0.618765i	0.853921	−	0.520402i	$-0.174218\pi$
$104$	−295.924			−0.279016
$105$	57.6193	−	252.447i	0.0535530	−	0.234631i
$106$	−191.410	+	838.622i	−0.175390	+	0.768435i
$107$	−4.39108	−	19.2386i	−0.00396731	−	0.0173819i	0.972906	−	0.231203i	$-0.0742662\pi$
$107$	−4.39108	−	19.2386i	−0.00396731	−	0.0173819i	−0.976873	+	0.213821i	$0.931409\pi$
$108$	−308.585	−	148.607i	−0.274940	−	0.132404i
$109$	−285.083	−	1249.03i	−0.250514	−	1.09757i	−0.931059	−	0.364868i	$-0.881114\pi$
$109$	−285.083	−	1249.03i	−0.250514	−	1.09757i	0.680545	−	0.732706i	$-0.261743\pi$
$110$	880.008			0.762777
$111$	−2018.21	+	2530.76i	−1.72577	+	2.16404i
$112$	92.4285	−	404.956i	0.0779792	−	0.341649i
$113$	−2027.48			−1.68787			−0.843936	−	0.536444i	$-0.819767\pi$
$113$	−2027.48			−1.68787			−0.843936	+	0.536444i	$0.819767\pi$
$114$	−543.812			−0.446778
$115$	−726.305	−	349.770i	−0.588941	−	0.283619i
$116$	−68.0249	+	298.037i	−0.0544479	+	0.238552i
$117$	540.794	−	678.134i	0.427320	−	0.535842i
$118$	632.490	−	793.117i	0.493436	−	0.618749i
$119$	43.1150	+	188.899i	0.0332130	+	0.145516i
$120$	929.179			0.706850
$121$	1541.01	−	1932.36i	1.15778	−	1.45181i
$122$	−1607.63	+	2015.90i	−1.19301	+	1.49599i
$123$	38.2629	+	167.641i	0.0280492	+	0.122891i
$124$	−32.6331	+	142.975i	−0.0236334	+	0.103545i
$125$	−971.598	+	467.897i	−0.695219	+	0.334800i
$126$	668.350	+	838.084i	0.472550	+	0.592560i
$127$	−1453.48	−	1822.60i	−1.01555	−	1.27346i	−0.961465	−	0.274928i	$-0.911346\pi$
$127$	−1453.48	−	1822.60i	−1.01555	−	1.27346i	−0.0540885	−	0.998536i	$-0.517225\pi$
$128$	1668.67			1.15227
$129$	−1661.45			−1.13397
$130$	45.0125	−	197.212i	0.0303681	−	0.133051i
$131$	230.488	−	110.997i	0.153724	−	0.0740296i	−0.355440	−	0.934699i	$-0.615669\pi$
$131$	230.488	−	110.997i	0.153724	−	0.0740296i	0.509164	+	0.860670i	$0.329955\pi$
$132$	−385.143	+	482.954i	−0.253957	+	0.318453i
$133$	100.806	+	48.5454i	0.0657215	+	0.0316498i
$134$	−149.422	−	654.662i	−0.0963292	−	0.422046i
$135$	−948.801	+	1189.76i	−0.604888	+	0.758505i
$136$	−626.426	+	301.671i	−0.394967	+	0.190206i
$137$	−405.089	−	195.081i	−0.252621	−	0.121656i	0.303288	−	0.952899i	$-0.401916\pi$
$137$	−405.089	−	195.081i	−0.252621	−	0.121656i	−0.555909	+	0.831243i	$0.687630\pi$
$138$	4333.44	−	2086.88i	2.67309	−	1.28729i
$139$	−421.654	+	528.737i	−0.257296	+	0.322639i	−0.893656	−	0.448753i	$-0.851868\pi$
$139$	−421.654	+	528.737i	−0.257296	+	0.322639i	0.636359	+	0.771393i	$0.280440\pi$
$140$	26.4994	+	12.7614i	0.0159972	+	0.00770384i
$141$	2254.79	−	2827.42i	1.34672	−	1.68874i
$142$	−1401.76	−	675.054i	−0.828405	−	0.398939i
$143$	−544.984	−	683.388i	−0.318698	−	0.399635i
$144$	−2723.89	+	3415.65i	−1.57632	+	1.97665i
$145$	1223.74	+	589.321i	0.700868	+	0.337520i
$146$	−632.686	−	2771.98i	−0.358640	−	1.57130i
$147$	646.035	+	2830.46i	0.362476	+	1.58811i
$148$	−229.243	−	287.461i	−0.127322	−	0.159657i
$149$	−72.1370	+	316.053i	−0.0396624	+	0.173772i	−0.990880	−	0.134749i	$-0.956977\pi$
$149$	−72.1370	+	316.053i	−0.0396624	+	0.173772i	0.951217	+	0.308522i	$0.0998342\pi$
$150$	645.198	−	2826.80i	0.351201	−	1.53871i
$151$	−383.435	+	480.812i	−0.206646	+	0.259125i	−0.874344	−	0.485306i	$-0.838708\pi$
$151$	−383.435	+	480.812i	−0.206646	+	0.259125i	0.667699	+	0.744432i	$0.267279\pi$
$152$	−89.3404	+	391.426i	−0.0476741	+	0.208874i
$153$	453.475	−	1986.80i	0.239616	−	1.04983i
$154$	973.277	−	468.706i	0.509279	−	0.245256i
$155$	587.056	+	282.711i	0.304216	+	0.146503i
$156$	88.5314	+	111.015i	0.0454371	+	0.0569763i
$157$	−1561.05	+	751.762i	−0.793537	+	0.382147i	−0.786314	−	0.617827i	$-0.788013\pi$
$157$	−1561.05	+	751.762i	−0.793537	+	0.382147i	−0.00722249	+	0.999974i	$0.502299\pi$
$158$	457.607	−	2004.91i	0.230413	−	1.00950i
$159$	−2417.08	+	1164.00i	−1.20558	+	0.580575i
$160$	−50.5842	+	221.624i	−0.0249939	+	0.109506i
$161$	−989.576			−0.484407
$162$	−913.373	−	4001.75i	−0.442971	−	1.94078i
$163$	−275.412	−	132.632i	−0.132343	−	0.0637332i	0.366540	−	0.930402i	$-0.380542\pi$
$163$	−275.412	−	132.632i	−0.132343	−	0.0637332i	−0.498884	+	0.866669i	$0.666256\pi$
$164$	−19.5315			−0.00929972
$165$	1711.21	+	2145.79i	0.807379	+	1.01242i
$166$	1715.06	−	825.930i	0.801895	−	0.386172i
$167$	−347.091	−	435.238i	−0.160830	−	0.201675i	0.694886	−	0.719120i	$-0.255455\pi$
$167$	−347.091	−	435.238i	−0.160830	−	0.201675i	−0.855717	+	0.517445i	$0.826883\pi$
$168$	1027.66	−	494.895i	0.471939	−	0.227274i
$169$	1798.40	−	866.065i	0.818572	−	0.394204i
$170$	−105.758	−	463.356i	−0.0477133	−	0.209046i
$171$	−733.718	−	920.053i	−0.328122	−	0.411451i
$172$	41.9940	−	183.988i	0.0186164	−	0.0815636i
$173$	−228.215	+	286.173i	−0.100294	+	0.125765i	−0.829446	−	0.558587i	$-0.811344\pi$
$173$	−228.215	+	286.173i	−0.100294	+	0.125765i	0.729151	+	0.684352i	$0.239915\pi$
$174$	−7301.34	+	3516.14i	−3.18111	+	1.53194i
$175$	−371.944	+	466.403i	−0.160665	+	0.201467i
$176$	2744.99	+	3442.11i	1.17563	+	1.47420i
$177$	3163.82			1.34354
$178$	582.428			0.245252
$179$	3979.10	+	1916.23i	1.66152	+	0.800145i	0.998679	+	0.0513840i	$0.0163632\pi$
$179$	3979.10	+	1916.23i	1.66152	+	0.800145i	0.662840	+	0.748761i	$0.269351\pi$
$180$	−192.877	−	241.860i	−0.0798677	−	0.100151i
$181$	−251.056	−	1099.95i	−0.103099	−	0.451705i	−0.999956	−	0.00938468i	$-0.997013\pi$
$181$	−251.056	−	1099.95i	−0.103099	−	0.451705i	0.896857	−	0.442320i	$-0.145844\pi$
$182$	−55.2552	−	242.089i	−0.0225043	−	0.0985979i
$183$	−8041.62			−3.24838
$184$	−790.173	−	3461.97i	−0.316589	−	1.38707i
$185$	−1471.83	+	708.795i	−0.584924	+	0.281685i
$186$	−3502.62	+	1686.77i	−1.38078	+	0.664948i
$187$	−1850.31	−	891.062i	−0.723572	−	0.348454i
$188$	256.116	+	321.159i	0.0993571	+	0.124590i
$189$	−415.678	+	1821.20i	−0.159980	+	0.700916i
$190$	−247.269	−	119.078i	−0.0944145	−	0.0454676i
$191$	−1934.28			−0.732774			−0.366387	−	0.930462i	$-0.619405\pi$
$191$	−1934.28			−0.732774			−0.366387	+	0.930462i	$0.619405\pi$
$192$	2498.64	+	3133.20i	0.939188	+	1.17770i
$193$	−1678.50	+	2104.78i	−0.626017	+	0.785001i	−0.989177	−	0.146726i	$-0.953126\pi$
$193$	−1678.50	+	2104.78i	−0.626017	+	0.785001i	0.363160	+	0.931727i	$0.381698\pi$
$194$	2385.18	+	1148.64i	0.882712	+	0.425092i
$195$	568.407	−	273.730i	0.208741	−	0.100524i
$196$	−329.772			−0.120179
$197$	−2762.78	−	111.427i	−0.999188	−	0.0402986i
$197$	−2762.78	−	111.427i	−0.999188	−	0.0402986i
$198$	−11361.9			−4.07806
$199$	−4493.91	+	2164.15i	−1.60083	+	0.770918i	−0.999603	−	0.0281619i	$-0.991035\pi$
$199$	−4493.91	+	2164.15i	−1.60083	+	0.770918i	−0.601225	+	0.799080i	$0.705320\pi$
$200$	−1928.68	−	928.803i	−0.681891	−	0.328382i
$201$	1305.75	−	1637.36i	0.458213	−	0.574581i
$202$	−256.167	−	321.224i	−0.0892271	−	0.111887i
$203$	1667.32			0.576467
$204$	300.578	+	144.751i	0.103160	+	0.0496794i
$205$	−19.3102	+	84.6037i	−0.00657896	+	0.0288243i
$206$	1245.56	+	1561.88i	0.421272	+	0.528258i
$207$	9377.43	+	4515.93i	3.14868	+	1.51632i
$208$	911.794	−	439.097i	0.303950	−	0.146375i
$209$	−1068.47	+	514.547i	−0.353624	+	0.170296i
$210$	173.497	+	760.141i	0.0570117	+	0.249784i
$211$	−658.083			−0.214712			−0.107356	−	0.994221i	$-0.534239\pi$
$211$	−658.083			−0.214712			−0.107356	+	0.994221i	$0.534239\pi$
$212$	−67.8080	−	297.086i	−0.0219673	−	0.0962451i
$213$	−1079.75	−	4730.70i	−0.347340	−	1.52179i
$214$	37.0471	+	46.4556i	0.0118341	+	0.0148395i
$215$	−755.454	−	363.807i	−0.239635	−	0.115402i
$216$	−6703.29			−2.11158
$217$	799.852			0.250219
$218$	2405.22	+	3016.05i	0.747257	+	0.937031i
$219$	5528.84	−	6932.95i	1.70596	−	2.13920i
$220$	−280.875	+	135.262i	−0.0860753	+	0.0414517i
$221$	−294.333	+	369.082i	−0.0895882	+	0.112340i
$222$	2168.86	−	9502.42i	0.655697	−	2.87280i
$223$	−1433.13	−	1797.08i	−0.430356	−	0.539649i	0.518617	−	0.855006i	$-0.326447\pi$
$223$	−1433.13	−	1797.08i	−0.430356	−	0.539649i	−0.948973	+	0.315358i	$0.897876\pi$
$224$	62.0948	+	272.055i	0.0185218	+	0.0811493i
$225$	5653.05	−	2722.36i	1.67498	−	0.806627i
$226$	5500.36	−	2648.84i	1.61893	−	0.779637i
$227$	3203.40	+	4016.94i	0.936641	+	1.17451i	0.984452	+	0.175654i	$0.0562039\pi$
$227$	3203.40	+	4016.94i	0.936641	+	1.17451i	−0.0478114	+	0.998856i	$0.515225\pi$
$228$	173.570	−	83.5870i	0.0504165	−	0.0242793i
$229$	−2180.66	−	2734.46i	−0.629267	−	0.789075i	0.360349	−	0.932818i	$-0.382658\pi$
$229$	−2180.66	−	2734.46i	−0.629267	−	0.789075i	−0.989615	+	0.143742i	$0.954086\pi$
$230$	2427.36			0.695892
$231$	3035.46	+	1461.80i	0.864582	+	0.416361i
$232$	1331.35	+	5833.02i	0.376756	+	1.65067i
$233$	−3108.34			−0.873967			−0.436984	−	0.899469i	$-0.643953\pi$
$233$	−3108.34			−0.873967			−0.436984	+	0.899469i	$0.643953\pi$
$234$	−581.163	+	2546.24i	−0.162358	+	0.711337i
$235$	1644.36	−	791.884i	0.456453	−	0.219816i
$236$	−79.9671	+	350.359i	−0.0220569	+	0.0966374i
$237$	5778.55	−	2782.80i	1.58378	−	0.762711i
$238$	−363.757	−	456.137i	−0.0990709	−	0.124231i
$239$	5324.53	+	2564.16i	1.44107	+	0.693982i	0.981019	−	0.193911i	$-0.0621173\pi$
$239$	5324.53	+	2564.16i	1.44107	+	0.693982i	0.460050	+	0.887893i	$0.347832\pi$
$240$	−2862.97	+	1378.73i	−0.770016	+	0.370820i
$241$	−1347.38	+	5903.24i	−0.360133	+	1.57785i	0.392720	+	0.919658i	$0.371534\pi$
$241$	−1347.38	+	5903.24i	−0.360133	+	1.57785i	−0.752853	+	0.658188i	$0.771323\pi$
$242$	−1656.04	+	7255.59i	−0.439894	+	1.92730i
$243$	2576.42	−	3230.73i	0.680153	−	0.852885i
$244$	203.256	−	890.523i	0.0533284	−	0.233647i
$245$	−326.036	+	1428.46i	−0.0850192	+	0.372493i
$246$	−322.820	−	404.803i	−0.0836677	−	0.104916i
$247$	60.6594	+	265.766i	0.0156262	+	0.0684627i
$248$	638.679	+	2798.24i	0.163533	+	0.716484i
$249$	5348.93	+	2575.91i	1.36135	+	0.655589i
$250$	2024.56	−	2538.72i	0.512178	−	0.642250i
$251$	677.021	+	848.958i	0.170252	+	0.213489i	0.859636	−	0.510907i	$-0.170690\pi$
$251$	677.021	+	848.958i	0.170252	+	0.213489i	−0.689384	+	0.724396i	$0.742119\pi$
$252$	−342.138	−	164.765i	−0.0855264	−	0.0411873i
$253$	6539.66	−	8200.48i	1.62508	−	2.03778i
$254$	6324.31	+	3045.63i	1.56229	+	0.752361i
$255$	924.185	−	1158.89i	0.226960	−	0.284598i
$256$	−1451.11	+	698.818i	−0.354275	+	0.170610i
$257$	2341.57	+	1127.64i	0.568339	+	0.273698i	0.695907	−	0.718132i	$-0.255003\pi$
$257$	2341.57	+	1127.64i	0.568339	+	0.273698i	−0.127568	+	0.991830i	$0.540717\pi$
$258$	4507.36	−	2170.63i	1.08766	−	0.523789i
$259$	−1250.31	+	1567.84i	−0.299963	+	0.376142i
$260$	15.9459	+	69.8636i	0.00380355	+	0.0166644i
$261$	−15799.9	−	7608.81i	−3.74707	−	1.80450i
$262$	−480.278	+	602.250i	−0.113251	+	0.142012i
$263$	3214.89	−	1548.21i	0.753759	−	0.362991i	−0.0172198	−	0.999852i	$-0.505482\pi$
$263$	3214.89	−	1548.21i	0.753759	−	0.362991i	0.770979	+	0.636860i	$0.219767\pi$
$264$	−2690.22	+	11786.6i	−0.627164	+	2.74779i
$265$	−1353.91			−0.313850
$266$	−336.899			−0.0776564
$267$	1132.56	+	1420.18i	0.259593	+	0.325519i
$268$	148.317	+	185.983i	0.0338056	+	0.0423908i
$269$	−737.113	+	354.975i	−0.167073	+	0.0804580i	−0.515551	−	0.856859i	$-0.672413\pi$
$269$	−737.113	+	354.975i	−0.167073	+	0.0804580i	0.348478	+	0.937317i	$0.386698\pi$
$270$	1019.63	−	4467.28i	0.229824	−	1.00693i
$271$	641.978	+	2812.69i	0.143902	+	0.630475i	0.994507	+	0.104670i	$0.0333786\pi$
$271$	641.978	+	2812.69i	0.143902	+	0.630475i	−0.850605	+	0.525805i	$0.823764\pi$
$272$	1482.51	−	1859.00i	0.330478	−	0.414407i
$273$	482.858	−	605.484i	0.107047	−	0.134233i
$274$	1353.83			0.298496
$275$	−1407.01	−	6164.50i	−0.308530	−	1.35176i
$276$	−1062.35	+	1332.15i	−0.231689	+	0.290529i
$277$	−393.026	+	492.839i	−0.0852514	+	0.106902i	−0.822628	−	0.568580i	$-0.807493\pi$
$277$	−393.026	+	492.839i	−0.0852514	+	0.106902i	0.737377	+	0.675482i	$0.236064\pi$
$278$	453.129	−	1985.29i	0.0977585	−	0.428308i
$279$	−7579.56	−	3650.13i	−1.62644	−	0.783252i
$280$	575.639			0.122861
$281$	−1202.35			−0.255253			−0.127626	−	0.991822i	$-0.540736\pi$
$281$	−1202.35			−0.255253			−0.127626	+	0.991822i	$0.540736\pi$
$282$	−2423.11	+	10616.3i	−0.511681	+	2.24182i
$283$	4451.97	−	5582.59i	0.935131	−	1.17262i	−0.0496413	−	0.998767i	$-0.515808\pi$
$283$	4451.97	−	5582.59i	0.935131	−	1.17262i	0.984772	−	0.173850i	$-0.0556208\pi$
$284$	551.165			0.115161
$285$	−190.466	−	834.486i	−0.0395868	−	0.173441i
$286$	2371.31	+	1141.96i	0.490275	+	0.236104i
$287$	23.7044	+	103.856i	0.00487534	+	0.0213603i
$288$	653.100	−	2861.42i	0.133626	−	0.585454i
$289$	846.436	−	3708.48i	0.172285	−	0.754830i
$290$	−4089.81			−0.828144
$291$	1837.26	+	8049.56i	0.370110	+	1.62156i
$292$	628.005	+	787.493i	0.125860	+	0.157824i
$293$	168.411	+	737.857i	0.0335791	+	0.147120i	0.988938	−	0.148327i	$-0.0473887\pi$
$293$	168.411	+	737.857i	0.0335791	+	0.147120i	−0.955359	+	0.295446i	$0.904532\pi$
$294$	−5450.53	−	6834.75i	−1.08123	−	1.35582i
$295$	1438.57	+	692.780i	0.283922	+	0.136730i
$296$	−6483.35	−	3122.22i	−1.27310	−	0.613092i
$297$	−12345.0	−	15480.2i	−2.41189	−	3.02442i
$298$	−217.212	−	951.666i	−0.0422239	−	0.184995i
$299$	−1503.25	−	1885.01i	−0.290753	−	0.364593i
$300$	228.565	+	1001.41i	0.0439873	+	0.192721i
$301$	−1029.29			−0.197101
$302$	412.057	−	1805.34i	0.0785140	−	0.343992i
$303$	285.136	−	1249.26i	0.0540616	−	0.236859i
$304$	−305.531	−	1338.62i	−0.0576428	−	0.252550i
$305$	−3656.48	−	1760.87i	−0.686458	−	0.330581i
$306$	1365.46	+	5982.45i	0.255091	+	1.11763i
$307$	5898.50			1.09656			0.548282	−	0.836293i	$-0.315282\pi$
$307$	5898.50			1.09656			0.548282	+	0.836293i	$0.315282\pi$
$308$	−238.601	+	299.196i	−0.0441414	+	0.0553516i
$309$	−1386.41	+	6074.27i	−0.255243	+	1.11829i
$310$	−1961.98			−0.359461
$311$	5522.89			1.00699			0.503496	−	0.863998i	$-0.332047\pi$
$311$	5522.89			1.00699			0.503496	+	0.863998i	$0.332047\pi$
$312$	2503.81	+	1205.77i	0.454328	+	0.218793i
$313$	−1466.52	+	6425.22i	−0.264832	+	1.16030i	0.651107	+	0.758986i	$0.274305\pi$
$313$	−1466.52	+	6425.22i	−0.264832	+	1.16030i	−0.915939	+	0.401318i	$0.868552\pi$
$314$	3252.82	−	4078.91i	0.584610	−	0.733078i
$315$	−1051.97	+	1319.12i	−0.188164	+	0.235950i
$316$	162.110	+	710.249i	0.0288588	+	0.126439i
$317$	5099.55			0.903531			0.451765	−	0.892137i	$-0.350794\pi$
$317$	5099.55			0.903531			0.451765	+	0.892137i	$0.350794\pi$
$318$	5036.57	−	6315.66i	0.888166	−	1.11373i
$319$	−11018.6	+	13816.8i	−1.93392	+	2.42506i
$320$	450.045	+	1971.78i	0.0786197	+	0.344455i
$321$	−41.2367	+	180.670i	−0.00717012	+	0.0314143i
$322$	2684.62	−	1292.85i	0.464622	−	0.223750i
$323$	399.334	+	500.749i	0.0687912	+	0.0862614i
$324$	906.616	+	1136.86i	0.155455	+	0.194935i
$325$	−1453.45			−0.248071
$326$	920.446			0.156377
$327$	−2677.22	+	11729.7i	−0.452754	+	1.98364i
$328$	−344.405	+	165.857i	−0.0579773	+	0.0279204i
$329$	1396.88	−	1751.63i	0.234080	−	0.293527i
$330$	−7445.75	−	3585.68i	−1.24205	−	0.598137i
$331$	−164.614	−	721.222i	−0.0273354	−	0.119764i	0.959419	−	0.281983i	$-0.0909921\pi$
$331$	−164.614	−	721.222i	−0.0273354	−	0.119764i	−0.986755	+	0.162219i	$0.948135\pi$
$332$	−420.451	+	527.229i	−0.0695038	+	0.0871550i
$333$	19003.0	−	9151.36i	3.12720	−	1.50598i
$334$	1510.25	+	727.296i	0.247416	+	0.119149i
$335$	952.253	−	458.581i	0.155305	−	0.0747909i
$336$	−2432.07	+	3049.72i	−0.394882	+	0.495167i
$337$	−5868.34	−	2826.04i	−0.948572	−	0.456808i	−0.105387	−	0.994431i	$-0.533608\pi$
$337$	−5868.34	−	2826.04i	−0.948572	−	0.456808i	−0.843185	+	0.537623i	$0.819322\pi$
$338$	−3747.41	+	4699.10i	−0.603054	+	0.756206i
$339$	17154.5	+	8261.19i	2.74840	+	1.32356i
$340$	104.975	+	131.635i	0.0167444	+	0.0209968i
$341$	−5285.86	+	6628.26i	−0.839430	+	1.05261i
$342$	3192.52	+	1537.44i	0.504771	+	0.243085i
$343$	844.273	+	3699.00i	0.132905	+	0.582295i
$344$	−821.885	−	3600.91i	−0.128817	−	0.564385i
$345$	4720.09	+	5918.81i	0.736583	+	0.923646i
$346$	245.251	−	1074.52i	0.0381063	−	0.166955i
$347$	−451.005	+	1975.98i	−0.0697729	+	0.305695i	−0.997758	−	0.0669216i	$-0.978682\pi$
$347$	−451.005	+	1975.98i	−0.0697729	+	0.305695i	0.927985	+	0.372617i	$0.121539\pi$
$348$	1789.94	−	2244.51i	0.275721	−	0.345743i
$349$	1408.36	−	6170.44i	0.216011	−	0.946407i	−0.744381	−	0.667755i	$-0.767255\pi$
$349$	1408.36	−	6170.44i	0.216011	−	0.946407i	0.960392	−	0.278652i	$-0.0898876\pi$
$350$	399.709	−	1751.24i	0.0610438	−	0.267450i
$351$	−4100.61	+	1974.75i	−0.623573	+	0.300297i
$352$	−2664.84	−	1283.32i	−0.403512	−	0.194321i
$353$	−5550.76	−	6960.44i	−0.836933	−	1.04948i	−0.998042	−	0.0625441i	$-0.980079\pi$
$353$	−5550.76	−	6960.44i	−0.836933	−	1.04948i	0.161109	−	0.986937i	$-0.448493\pi$
$354$	−8583.14	+	4133.42i	−1.28867	+	0.620590i
$355$	544.922	−	2387.46i	0.0814689	−	0.356938i
$356$	−185.895	+	89.5225i	−0.0276754	+	0.0133278i
$357$	404.893	−	1773.95i	0.0600258	−	0.262990i
$358$	−13298.4			−1.96325
$359$	−938.836	−	4113.31i	−0.138022	−	0.604714i	−0.995868	−	0.0908077i	$-0.971055\pi$
$359$	−938.836	−	4113.31i	−0.138022	−	0.604714i	0.857846	−	0.513906i	$-0.171802\pi$
$360$	−5454.87	−	2626.93i	−0.798602	−	0.384587i
$361$	−6489.15			−0.946078
$362$	2118.14	+	2656.06i	0.307532	+	0.385633i
$363$	−20912.1	+	10070.7i	−3.02369	+	1.45613i
$364$	54.8464	+	68.7752i	0.00789761	+	0.00990329i
$365$	4032.04	−	1941.73i	0.578210	−	0.278451i
$366$	21816.1	−	10506.1i	3.11570	−	1.50044i
$367$	−2389.98	−	10471.2i	−0.339934	−	1.48935i	−0.799209	−	0.601054i	$-0.794748\pi$
$367$	−2389.98	−	10471.2i	−0.339934	−	1.48935i	0.459275	−	0.888294i	$-0.348109\pi$
$368$	7571.61	+	9494.50i	1.07255	+	1.34493i
$369$	249.317	−	1092.33i	0.0351733	−	0.154104i
$370$	3066.91	−	3845.79i	0.430922	−	0.540359i
$371$	−1497.41	+	721.116i	−0.209547	+	0.100912i
$372$	858.676	−	1076.75i	0.119678	−	0.150072i
$373$	4054.16	+	5083.76i	0.562779	+	0.705703i	0.979069	−	0.203529i	$-0.0652412\pi$
$373$	4054.16	+	5083.76i	0.562779	+	0.705703i	−0.416290	+	0.909232i	$0.636670\pi$
$374$	6183.85			0.854971
$375$	10127.2			1.39458
$376$	7243.36	+	3488.22i	0.993478	+	0.478434i
$377$	2532.80	+	3176.03i	0.346010	+	0.433882i
$378$	−1251.65	−	5483.82i	−0.170311	−	0.746183i
$379$	−1771.89	−	7763.17i	−0.240148	−	1.05216i	−0.940882	−	0.338734i	$-0.890001\pi$
$379$	−1771.89	−	7763.17i	−0.240148	−	1.05216i	0.700734	−	0.713422i	$-0.252856\pi$
$380$	97.2245			0.0131250
$381$	4871.49	+	21343.4i	0.655050	+	2.86996i
$382$	5247.53	−	2527.08i	0.702845	−	0.338472i
$383$	−7556.68	+	3639.10i	−1.00817	+	0.485508i	−0.863702	−	0.504002i	$-0.831860\pi$
$383$	−7556.68	+	3639.10i	−1.00817	+	0.485508i	−0.144465	+	0.989510i	$0.546146\pi$
$384$	−14118.6	−	6799.18i	−1.87627	−	0.903565i
$385$	1060.12	+	1329.35i	0.140334	+	0.175973i
$386$	1803.80	−	7902.96i	0.237852	−	1.04210i
$387$	9753.78	+	4697.17i	1.28117	+	0.616978i
$388$	−937.839			−0.122710
$389$	6375.90	+	7995.13i	0.831031	+	1.04208i	0.998420	+	0.0561891i	$0.0178950\pi$
$389$	6375.90	+	7995.13i	0.831031	+	1.04208i	−0.167389	+	0.985891i	$0.553534\pi$
$390$	−1184.41	+	1485.21i	−0.153782	+	0.192837i
$391$	−5103.77	−	2457.85i	−0.660125	−	0.317899i
$392$	−5814.97	+	2800.34i	−0.749235	+	0.360813i
$393$	−2402.43			−0.308363
$394$	7640.73	−	3307.19i	0.976991	−	0.422877i
$395$	3236.83			0.412310
$396$	3626.42	−	1746.39i	0.460187	−	0.221615i
$397$	−10127.0	−	4876.91i	−1.28025	−	0.616536i	−0.334797	−	0.942290i	$-0.608668\pi$
$397$	−10127.0	−	4876.91i	−1.28025	−	0.616536i	−0.945455	+	0.325754i	$0.894382\pi$
$398$	9364.15	−	11742.3i	1.17935	−	1.47886i
$399$	−655.113	−	821.486i	−0.0821972	−	0.103072i
$400$	7320.79			0.915099
$401$	−9269.78	−	4464.09i	−1.15439	−	0.555925i	−0.244041	−	0.969765i	$-0.578473\pi$
$401$	−9269.78	−	4464.09i	−1.15439	−	0.555925i	−0.910350	+	0.413840i	$0.864187\pi$
$402$	−1403.23	+	6147.93i	−0.174096	+	0.762764i
$403$	1215.04	+	1523.61i	0.150187	+	0.188329i
$404$	131.136	+	63.1516i	0.0161491	+	0.00777700i
$405$	5820.83	−	2803.16i	0.714171	−	0.343927i
$406$	−4523.28	+	2178.29i	−0.552922	+	0.266273i
$407$	−4729.72	−	20722.3i	−0.576028	−	2.52374i
$408$	6529.38			0.792285
$409$	481.645	+	2110.23i	0.0582294	+	0.255120i	0.995662	−	0.0930482i	$-0.0296611\pi$
$409$	481.645	+	2110.23i	0.0582294	+	0.255120i	−0.937432	+	0.348168i	$0.886804\pi$
$410$	−58.1450	−	254.750i	−0.00700384	−	0.0306858i
$411$	2632.58	+	3301.15i	0.315951	+	0.396190i
$412$	−637.617	−	307.060i	−0.0762455	−	0.0367179i
$413$	1960.03			0.233527
$414$	−31340.0			−3.72047
$415$	1868.09	+	2342.51i	0.220966	+	0.277082i
$416$	−423.902	+	531.557i	−0.0499604	+	0.0626483i
$417$	5722.01	−	2755.57i	0.671961	−	0.323599i
$418$	2226.41	−	2791.83i	0.260520	−	0.326682i
$419$	−3573.29	+	15655.6i	−0.416627	+	1.82536i	0.134469	+	0.990918i	$0.457067\pi$
$419$	−3573.29	+	15655.6i	−0.416627	+	1.82536i	−0.551096	+	0.834442i	$0.685790\pi$
$420$	−172.214	−	215.949i	−0.0200075	−	0.0250887i
$421$	−2662.94	−	11667.1i	−0.308275	−	1.35064i	−0.857292	−	0.514830i	$-0.827855\pi$
$421$	−2662.94	−	11667.1i	−0.308275	−	1.35064i	0.549017	−	0.835811i	$-0.315002\pi$
$422$	1785.32	−	859.763i	0.205943	−	0.0991768i
$423$	−21230.6	+	10224.1i	−2.44035	+	1.17521i
$424$	−3718.46	−	4662.80i	−0.425906	−	0.534070i
$425$	−3076.74	+	1481.68i	−0.351162	+	0.169110i
$426$	9109.76	+	11423.3i	1.03608	+	1.29920i
$427$	−4981.89			−0.564615
$428$	−18.9649	−	9.13304i	−0.00214183	−	0.00103145i
$429$	1826.57	+	8002.74i	0.205566	+	0.900643i
$430$	2524.77			0.283152
$431$	3259.33	−	14280.1i	0.364261	−	1.59593i	−0.377991	−	0.925809i	$-0.623385\pi$
$431$	3259.33	−	14280.1i	0.364261	−	1.59593i	0.742252	−	0.670121i	$-0.233758\pi$
$432$	20654.1	−	9946.47i	2.30028	−	1.10775i
$433$	−2957.18	+	12956.3i	−0.328206	+	1.43796i	0.494343	+	0.869267i	$0.335409\pi$
$433$	−2957.18	+	12956.3i	−0.328206	+	1.43796i	−0.822548	+	0.568695i	$0.807448\pi$
$434$	−2169.92	+	1044.98i	−0.239999	+	0.115577i
$435$	−7952.80	−	9972.49i	−0.876569	−	1.09918i
$436$	−1231.27	−	592.946i	−0.135245	−	0.0651307i
$437$	−2947.19	+	1419.29i	−0.322616	+	0.155364i
$438$	−5941.55	+	26031.7i	−0.648170	+	2.83982i
$439$	−2032.29	+	8904.04i	−0.220947	+	0.968033i	0.735820	+	0.677178i	$0.236797\pi$
$439$	−2032.29	+	8904.04i	−0.220947	+	0.968033i	−0.956767	+	0.290856i	$0.906060\pi$
$440$	−3804.14	+	4770.23i	−0.412171	+	0.516845i
$441$	4209.51	−	18443.0i	0.454541	−	1.99147i
$442$	316.304	−	1385.82i	0.0340386	−	0.149133i
$443$	−5455.04	−	6840.40i	−0.585049	−	0.733628i	0.397916	−	0.917422i	$-0.369734\pi$
$443$	−5455.04	−	6840.40i	−0.585049	−	0.733628i	−0.982965	+	0.183794i	$0.941162\pi$
$444$	768.332	+	3366.28i	0.0821248	+	0.359812i
$445$	203.991	+	893.743i	0.0217306	+	0.0952079i
$446$	6235.76	+	3002.99i	0.662045	+	0.318824i
$447$	1898.14	−	2380.20i	0.200848	−	0.251855i
$448$	1547.94	+	1941.06i	0.163244	+	0.204702i
$449$	−946.728	−	455.920i	−0.0995075	−	0.0479203i	0.383468	−	0.923554i	$-0.374730\pi$
$449$	−946.728	−	455.920i	−0.0995075	−	0.0479203i	−0.482975	+	0.875634i	$0.660444\pi$
$450$	−11779.5	+	14771.0i	−1.23398	+	1.54736i
$451$	−1017.29	−	489.900i	−0.106213	−	0.0511496i
$452$	−1348.43	+	1690.87i	−0.140320	+	0.175956i
$453$	5203.36	−	2505.81i	0.539680	−	0.259896i
$454$	−13938.5	−	6712.44i	−1.44090	−	0.693899i
$455$	352.136	−	169.580i	0.0362821	−	0.0174726i
$456$	2350.81	−	2947.83i	0.241419	−	0.302730i
$457$	−2963.73	−	12984.9i	−0.303364	−	1.32912i	−0.865014	−	0.501748i	$-0.832690\pi$
$457$	−2963.73	−	12984.9i	−0.303364	−	1.32912i	0.561650	−	0.827375i	$-0.310167\pi$
$458$	9488.40	+	4569.37i	0.968043	+	0.466185i
$459$	−6667.27	+	8360.49i	−0.677999	+	0.850183i
$460$	−774.747	+	373.098i	−0.0785277	+	0.0378170i
$461$	2414.97	−	10580.7i	0.243984	−	1.06896i	−0.693370	−	0.720582i	$-0.743875\pi$
$461$	2414.97	−	10580.7i	0.243984	−	1.06896i	0.937353	−	0.348380i	$-0.113268\pi$
$462$	−10144.7			−1.02159
$463$	7631.80			0.766048			0.383024	−	0.923738i	$-0.374883\pi$
$463$	7631.80			0.766048			0.383024	+	0.923738i	$0.374883\pi$
$464$	−12757.3	−	15997.1i	−1.27638	−	1.60053i
$465$	−3815.14	−	4784.04i	−0.380480	−	0.477106i
$466$	8432.64	−	4060.94i	0.838271	−	0.403690i
$467$	413.718	−	1812.62i	0.0409949	−	0.179610i	−0.950285	−	0.311380i	$-0.899209\pi$
$467$	413.718	−	1812.62i	0.0409949	−	0.179610i	0.991280	+	0.131770i	$0.0420660\pi$
$468$	−205.880	−	902.019i	−0.0203351	−	0.0890937i
$469$	808.932	−	1014.37i	0.0796439	−	0.0998704i
$470$	−3426.43	+	4296.61i	−0.336275	+	0.421676i
$471$	16271.2			1.59180
$472$	1565.08	+	6857.04i	0.152624	+	0.668689i
$473$	6802.12	−	8529.59i	0.661230	−	0.829156i
$474$	−12041.0	+	15098.9i	−1.16680	+	1.46312i
$475$	−438.802	+	1922.52i	−0.0423866	+	0.185708i
$476$	186.212	+	89.6751i	0.0179307	+	0.00863499i
$477$	17480.6			1.67795
$478$	−17794.9			−1.70276
$479$	784.762	−	3438.27i	0.0748574	−	0.327972i	−0.923609	−	0.383336i	$-0.874775\pi$
$479$	784.762	−	3438.27i	0.0748574	−	0.327972i	0.998466	+	0.0553646i	$0.0176321\pi$
$480$	1331.02	−	1669.05i	0.126568	−	0.158711i
$481$	−4885.85			−0.463151
$482$	−4057.08	−	17775.2i	−0.383392	−	1.67975i
$483$	8372.81	+	4032.13i	0.788770	+	0.379852i
$484$	−586.661	−	2570.33i	−0.0550959	−	0.241391i
$485$	−927.216	+	4062.40i	−0.0868097	+	0.380338i
$486$	−2768.74	+	12130.6i	−0.258421	+	1.13222i
$487$	3222.04			0.299804			0.149902	−	0.988701i	$-0.452104\pi$
$487$	3222.04			0.299804			0.149902	+	0.988701i	$0.452104\pi$
$488$	−3978.02	−	17428.8i	−0.369009	−	1.61674i
$489$	1789.84	+	2244.39i	0.165521	+	0.207556i
$490$	−981.727	−	4301.23i	−0.0905100	−	0.396550i
$491$	−2183.98	−	2738.63i	−0.200737	−	0.251716i	0.671266	−	0.741216i	$-0.265751\pi$
$491$	−2183.98	−	2738.63i	−0.200737	−	0.251716i	−0.872003	+	0.489500i	$0.837179\pi$
$492$	165.256	+	79.5831i	0.0151429	+	0.00729245i
$493$	8599.25	+	4141.18i	0.785580	+	0.378315i
$494$	−511.777	−	641.748i	−0.0466112	−	0.0584486i
$495$	−3979.42	−	17435.0i	−0.361337	−	1.58312i
$496$	−6119.96	−	7674.19i	−0.554021	−	0.694720i
$497$	−668.920	−	2930.73i	−0.0603726	−	0.264510i
$498$	−17876.5			−1.60856
$499$	−2607.18	+	11422.8i	−0.233895	+	1.02476i	0.712481	+	0.701691i	$0.247571\pi$
$499$	−2607.18	+	11422.8i	−0.233895	+	1.02476i	−0.946376	+	0.323068i	$0.895286\pi$
$500$	−255.970	+	1121.48i	−0.0228946	+	0.100308i
$501$	1163.31	+	5096.81i	0.103738	+	0.454508i
$502$	−2945.83	−	1418.64i	−0.261910	−	0.126129i
$503$	−2892.24	−	12671.7i	−0.256379	−	1.12327i	−0.925090	−	0.379747i	$-0.876011\pi$
$503$	−2892.24	−	12671.7i	−0.256379	−	1.12327i	0.668712	−	0.743522i	$-0.266846\pi$
$504$	−7432.16			−0.656854
$505$	403.201	−	505.598i	0.0355291	−	0.0445521i
$506$	−7027.83	+	30790.9i	−0.617441	+	2.70519i
$507$	−18745.2			−1.64202
$508$	−2486.68			−0.217182
$509$	−5089.36	−	2450.91i	−0.443187	−	0.213427i	0.198963	−	0.980007i	$-0.436243\pi$
$509$	−5089.36	−	2450.91i	−0.443187	−	0.213427i	−0.642149	+	0.766580i	$0.721957\pi$
$510$	−993.173	+	4351.37i	−0.0862322	+	0.377808i
$511$	3425.19	−	4295.05i	0.296520	−	0.371824i
$512$	−5299.45	+	6645.31i	−0.457432	+	0.573601i
$513$	1374.06	+	6020.16i	0.118258	+	0.518122i
$514$	−7825.67			−0.671548
$515$	−1960.47	+	2458.36i	−0.167745	+	0.210346i
$516$	−1104.99	+	1385.61i	−0.0942722	+	0.118214i
$517$	5284.16	+	23151.4i	0.449511	+	1.96943i
$518$	1343.64	−	5886.88i	0.113969	−	0.499333i
$519$	3096.97	−	1491.42i	0.261931	−	0.126139i
$520$	874.443	+	1096.52i	0.0737439	+	0.0924720i
$521$	11827.7	+	14831.4i	0.994585	+	1.24717i	0.968888	+	0.247501i	$0.0796093\pi$
$521$	11827.7	+	14831.4i	0.994585	+	1.24717i	0.0256976	+	0.999670i	$0.491819\pi$
$522$	52804.1			4.42754
$523$	−7756.09			−0.648471			−0.324235	−	0.945976i	$-0.605107\pi$
$523$	−7756.09			−0.648471			−0.324235	+	0.945976i	$0.605107\pi$
$524$	60.7227	−	266.043i	0.00506237	−	0.0221797i
$525$	5047.43	−	2430.71i	0.419596	−	0.202067i
$526$	−6699.01	+	8400.29i	−0.555305	+	0.696331i
$527$	4125.26	+	1986.62i	0.340985	+	0.164210i
$528$	−9200.14	−	40308.5i	−0.758305	−	3.32235i
$529$	10452.6	−	13107.1i	0.859093	−	1.07727i
$530$	3673.04	−	1768.84i	0.301031	−	0.144969i
$531$	−18573.6	−	8944.59i	−1.51794	−	0.731002i
$532$	107.529	−	51.7833i	0.00876311	−	0.00422009i
$533$	−161.822	+	202.919i	−0.0131507	+	0.0164904i
$534$	−4927.93	−	2373.16i	−0.399349	−	0.192316i
$535$	−58.3113	+	73.1200i	−0.00471218	+	0.00590889i
$536$	4194.64	+	2020.03i	0.338024	+	0.162784i
$537$	−25859.3	−	32426.5i	−2.07805	−	2.60579i
$538$	1535.95	−	1926.03i	0.123085	−	0.154344i
$539$	−17176.0	−	8271.53i	−1.37258	−	0.661002i
$540$	361.208	+	1582.56i	0.0287851	+	0.126116i
$541$	4217.17	+	18476.6i	0.335139	+	1.46834i	0.809036	+	0.587760i	$0.199990\pi$
$541$	4217.17	+	18476.6i	0.335139	+	1.46834i	−0.473897	+	0.880581i	$0.657153\pi$
$542$	−5416.30	−	6791.83i	−0.429244	−	0.538255i
$543$	−2357.67	+	10329.6i	−0.186330	+	0.816366i
$544$	−355.457	+	1557.36i	−0.0280149	+	0.122741i
$545$	−3785.76	+	4747.19i	−0.297549	+	0.373114i
$546$	−518.902	+	2273.46i	−0.0406721	+	0.178196i
$547$	264.899	−	1160.60i	0.0207062	−	0.0907196i	−0.963519	−	0.267640i	$-0.913756\pi$
$547$	264.899	−	1160.60i	0.0207062	−	0.0907196i	0.984225	+	0.176920i	$0.0566134\pi$
$548$	−432.107	+	208.092i	−0.0336838	+	0.0162212i
$549$	47209.4	+	22734.9i	3.67003	+	1.76740i
$550$	11870.8	+	14885.5i	0.920312	+	1.15403i
$551$	4965.67	−	2391.34i	0.383929	−	0.184890i
$552$	−7420.52	+	32511.4i	−0.572171	+	2.50684i
$553$	3579.89	−	1723.98i	0.275284	−	0.132570i
$554$	422.364	−	1850.50i	0.0323909	−	0.141914i
$555$	15341.2			1.17333
$556$	160.523	+	703.299i	0.0122441	+	0.0536448i
$557$	−2635.17	−	1269.03i	−0.200459	−	0.0965359i	0.330961	−	0.943644i	$-0.392627\pi$
$557$	−2635.17	−	1269.03i	−0.200459	−	0.0965359i	−0.531420	+	0.847108i	$0.678341\pi$
$558$	25331.4			1.92180
$559$	−1563.58	−	1960.67i	−0.118305	−	0.148349i
$560$	−1773.65	+	854.143i	−0.133840	+	0.0644538i
$561$	12024.7	+	15078.6i	0.904964	+	1.13479i
$562$	3261.85	−	1570.83i	0.244827	−	0.117903i
$563$	−7517.35	+	3620.16i	−0.562733	+	0.270998i	−0.693550	−	0.720409i	$-0.743954\pi$
$563$	−7517.35	+	3620.16i	−0.562733	+	0.270998i	0.130817	+	0.991407i	$0.458240\pi$
$564$	−858.400	−	3760.89i	−0.0640871	−	0.280784i
$565$	5991.13	+	7512.64i	0.446104	+	0.559397i
$566$	−4784.30	+	20961.4i	−0.355299	+	1.55666i
$567$	4944.76	−	6200.53i	0.366244	−	0.459255i
$568$	9718.86	−	4680.36i	0.717948	−	0.345745i
$569$	−5080.76	+	6371.07i	−0.374335	+	0.469401i	−0.932939	−	0.360033i	$-0.882765\pi$
$569$	−5080.76	+	6371.07i	−0.374335	+	0.469401i	0.558605	+	0.829434i	$0.311337\pi$
$570$	1606.94	+	2015.04i	0.118083	+	0.148072i
$571$	25316.4			1.85544			0.927721	−	0.373275i	$-0.121765\pi$
$571$	25316.4			1.85544			0.927721	+	0.373275i	$0.121765\pi$
$572$	−932.385			−0.0681556
$573$	16366.0	+	7881.44i	1.19319	+	0.574611i
$574$	−199.991	−	250.781i	−0.0145426	−	0.0182359i
$575$	−3880.99	−	17003.7i	−0.281476	−	1.23323i
$576$	−5810.60	−	25457.9i	−0.420327	−	1.84157i
$577$	−9844.68			−0.710293			−0.355147	−	0.934811i	$-0.615569\pi$
$577$	−9844.68			−0.710293			−0.355147	+	0.934811i	$0.615569\pi$
$578$	2548.70	+	11166.6i	0.183412	+	0.803579i
$579$	22778.0	−	10969.3i	1.63492	−	0.787337i
$580$	1305.36	−	628.627i	0.0934517	−	0.0450040i
$581$	3313.74	+	1595.81i	0.236621	+	0.113951i
$582$	−15500.8	−	19437.4i	−1.10400	−	1.38437i
$583$	3919.94	−	17174.4i	0.278469	−	1.22005i
$584$	17761.0	+	8553.24i	1.25848	+	0.606054i
$585$	−4110.78			−0.290530
$586$	−1420.87	−	1781.71i	−0.100163	−	0.125600i
$587$	13306.2	−	16685.4i	0.935612	−	1.17322i	−0.0490589	−	0.998796i	$-0.515622\pi$
$587$	13306.2	−	16685.4i	0.935612	−	1.17322i	0.984671	−	0.174424i	$-0.0558064\pi$
$588$	2790.20	+	1343.69i	0.195691	+	0.0942396i
$589$	2382.15	−	1147.18i	0.166646	−	0.0802527i
$590$	−4807.80			−0.335482
$591$	22921.9	+	12200.0i	1.59540	+	0.849140i
$592$	24609.2			1.70850
$593$	8025.41	−	3864.83i	0.555757	−	0.267639i	−0.134853	−	0.990866i	$-0.543056\pi$
$593$	8025.41	−	3864.83i	0.555757	−	0.267639i	0.690610	+	0.723227i	$0.257342\pi$
$594$	53715.2	+	25867.9i	3.71037	+	1.78682i
$595$	572.545	−	717.949i	0.0394488	−	0.0494673i
$596$	215.604	+	270.359i	0.0148180	+	0.0185811i
$597$	46841.0			3.21118
$598$	6540.87	+	3149.92i	0.447285	+	0.215401i
$599$	−6134.27	+	26876.0i	−0.418430	+	1.83326i	0.122858	+	0.992424i	$0.460794\pi$
$599$	−6134.27	+	26876.0i	−0.418430	+	1.83326i	−0.541288	+	0.840837i	$0.682063\pi$
$600$	12534.1	+	15717.2i	0.852835	+	1.06942i
$601$	−5231.86	−	2519.53i	−0.355095	−	0.171005i	0.247828	−	0.968804i	$-0.420283\pi$
$601$	−5231.86	−	2519.53i	−0.355095	−	0.171005i	−0.602923	+	0.797799i	$0.705997\pi$
$602$	2792.37	−	1344.73i	0.189051	−	0.0910420i
$603$	−12294.7	+	5920.80i	−0.830312	+	0.399857i
$604$	145.973	+	639.552i	0.00983374	+	0.0430844i
$605$	−11713.8			−0.787163
$606$	858.573	+	3761.66i	0.0575531	+	0.252156i
$607$	−4870.83	−	21340.5i	−0.325701	−	1.42699i	−0.827236	−	0.561854i	$-0.810088\pi$
$607$	−4870.83	−	21340.5i	−0.325701	−	1.42699i	0.501535	−	0.865137i	$-0.332769\pi$
$608$	575.126	+	721.185i	0.0383626	+	0.0481051i
$609$	−14107.2	−	6793.67i	−0.938674	−	0.452041i
$610$	12220.2			0.811117
$611$	5458.59			0.361425
$612$	−1355.35	−	1699.56i	−0.0895211	−	0.112256i
$613$	−5069.75	+	6357.27i	−0.334038	+	0.418871i	−0.920277	−	0.391268i	$-0.872037\pi$
$613$	−5069.75	+	6357.27i	−0.334038	+	0.418871i	0.586239	+	0.810138i	$0.300608\pi$
$614$	−16002.1	+	7706.19i	−1.05178	+	0.506509i
$615$	508.111	−	637.151i	0.0333154	−	0.0417762i
$616$	−1666.62	+	7301.96i	−0.109010	+	0.477604i
$617$	4408.49	+	5528.07i	0.287648	+	0.360700i	0.904570	−	0.426325i	$-0.140192\pi$
$617$	4408.49	+	5528.07i	0.287648	+	0.360700i	−0.616922	+	0.787024i	$0.711621\pi$
$618$	−4174.62	−	18290.2i	−0.271728	−	1.19052i
$619$	11662.5	−	5616.36i	0.757278	−	0.364686i	−0.0150695	−	0.999886i	$-0.504797\pi$
$619$	11662.5	−	5616.36i	0.757278	−	0.364686i	0.772347	+	0.635201i	$0.219083\pi$
$620$	626.210	−	301.567i	0.0405633	−	0.0195342i
$621$	−34051.7	−	42699.5i	−2.20040	−	2.75922i
$622$	−14983.1	+	7215.47i	−0.965862	+	0.465135i
$623$	701.633	+	879.820i	0.0451209	+	0.0565798i
$624$	−9503.84			−0.609709
$625$	−6943.18	−	3343.66i	−0.444364	−	0.213994i
$626$	−4415.82	−	19347.0i	−0.281935	−	1.23524i
$627$	11136.9			0.709353
$628$	−411.262	+	1801.86i	−0.0261324	+	0.114493i
$629$	−10342.6	+	4980.73i	−0.655622	+	0.315731i
$630$	1130.49	−	4953.01i	0.0714919	−	0.313227i
$631$	−1672.33	+	805.352i	−0.105506	+	0.0508091i	−0.485892	−	0.874019i	$-0.661505\pi$
$631$	−1672.33	+	805.352i	−0.105506	+	0.0508091i	0.380386	+	0.924828i	$0.375791\pi$
$632$	8889.78	+	11147.4i	0.559520	+	0.701615i
$633$	5568.04	+	2681.43i	0.349621	+	0.168368i
$634$	−13834.6	+	6662.38i	−0.866627	+	0.417346i
$635$	−2458.51	+	10771.4i	−0.153643	+	0.673152i
$636$	−636.785	+	2789.94i	−0.0397015	+	0.173944i
$637$	−2732.23	+	3426.11i	−0.169945	+	0.213104i
$638$	11841.1	−	51879.1i	0.734784	−	3.21930i
$639$	−7035.57	+	30824.8i	−0.435560	+	1.90831i
$640$	−4930.86	−	6183.10i	−0.304546	−	0.381888i
$641$	−5510.97	−	24145.1i	−0.339579	−	1.48779i	−0.799951	−	0.600066i	$-0.795141\pi$
$641$	−5510.97	−	24145.1i	−0.339579	−	1.48779i	0.460372	−	0.887726i	$-0.347716\pi$
$642$	−124.168	−	544.014i	−0.00763318	−	0.0334432i
$643$	−2616.16	−	1259.88i	−0.160453	−	0.0772701i	0.351934	−	0.936025i	$-0.385524\pi$
$643$	−2616.16	−	1259.88i	−0.160453	−	0.0772701i	−0.512387	+	0.858755i	$0.671239\pi$
$644$	−658.142	+	825.284i	−0.0402709	+	0.0504981i
$645$	4909.53	+	6156.35i	0.299709	+	0.375823i
$646$	−1737.57	−	836.768i	−0.105826	−	0.0509632i
$647$	−16479.8	+	20665.0i	−1.00137	+	1.25568i	−0.0347725	+	0.999395i	$0.511071\pi$
$647$	−16479.8	+	20665.0i	−1.00137	+	1.25568i	−0.966601	+	0.256287i	$0.917501\pi$
$648$	25640.5	+	12347.8i	1.55441	+	0.748563i
$649$	−12952.9	+	16242.5i	−0.783432	+	0.982393i
$650$	3943.07	−	1898.88i	0.237939	−	0.114585i
$651$	−6767.55	−	3259.08i	−0.407437	−	0.196211i
$652$	−293.782	+	141.478i	−0.0176463	+	0.00849800i
$653$	−2907.95	+	3646.45i	−0.174268	+	0.218525i	−0.861293	−	0.508109i	$-0.830345\pi$
$653$	−2907.95	+	3646.45i	−0.174268	+	0.218525i	0.687025	+	0.726634i	$0.258916\pi$
$654$	−8061.36	−	35319.1i	−0.481994	−	2.11175i
$655$	−1092.37	−	526.059i	−0.0651642	−	0.0313814i
$656$	815.072	−	1022.07i	0.0485110	−	0.0608309i
$657$	−52058.3	+	25069.9i	−3.09130	+	1.48869i
$658$	−1501.15	+	6576.96i	−0.0889375	+	0.389661i
$659$	−5911.70			−0.349449			−0.174725	−	0.984617i	$-0.555904\pi$
$659$	−5911.70			−0.349449			−0.174725	+	0.984617i	$0.555904\pi$
$660$	2927.62			0.172663
$661$	−1293.25	−	1621.68i	−0.0760990	−	0.0954251i	0.742325	−	0.670040i	$-0.233723\pi$
$661$	−1293.25	−	1621.68i	−0.0760990	−	0.0954251i	−0.818424	+	0.574615i	$0.805152\pi$
$662$	1388.83	+	1741.54i	0.0815386	+	0.102246i
$663$	3994.22	−	1923.51i	0.233971	−	0.112674i
$664$	−2936.85	+	12867.2i	−0.171644	+	0.752022i
$665$	−117.996	−	516.976i	−0.00688075	−	0.0301465i
$666$	−39597.4	+	49653.5i	−2.30385	+	2.88894i
$667$	−30392.9	+	38111.5i	−1.76434	+	2.21242i
$668$	−593.820			−0.0343946
$669$	4803.28	+	21044.6i	0.277587	+	1.21619i
$670$	−1984.25	+	2488.17i	−0.114415	+	0.143472i
$671$	32923.1	−	41284.2i	1.89416	−	2.37520i
$672$	583.132	−	2554.87i	0.0334744	−	0.146661i
$673$	−3465.47	−	1668.88i	−0.198490	−	0.0955878i	0.331998	−	0.943280i	$-0.392277\pi$
$673$	−3465.47	−	1668.88i	−0.198490	−	0.0955878i	−0.530488	+	0.847692i	$0.677991\pi$
$674$	19612.4			1.12083
$675$	−32923.7			−1.87739
$676$	473.794	−	2075.83i	0.0269568	−	0.118106i
$677$	9776.67	−	12259.6i	0.555019	−	0.695972i	−0.422609	−	0.906312i	$-0.638886\pi$
$677$	9776.67	−	12259.6i	0.555019	−	0.695972i	0.977628	+	0.210340i	$0.0674571\pi$
$678$	−57331.6			−3.24750
$679$	1138.21	+	4986.81i	0.0643304	+	0.281850i
$680$	2968.87	+	1429.73i	0.167428	+	0.0806292i
$681$	−10736.6	−	47040.0i	−0.604150	−	2.64695i
$682$	5680.44	−	24887.6i	0.318937	−	1.39736i
$683$	−7742.75	+	33923.2i	−0.433775	+	1.90049i	0.00109818	+	0.999999i	$0.499650\pi$
$683$	−7742.75	+	33923.2i	−0.433775	+	1.90049i	−0.434873	+	0.900492i	$0.643207\pi$
$684$	−1255.28			−0.0701708
$685$	474.170	+	2077.47i	0.0264483	+	0.115878i
$686$	−7123.05	−	8932.02i	−0.396442	−	0.497123i
$687$	7308.72	+	32021.6i	0.405888	+	1.77831i
$688$	7875.48	+	9875.54i	0.436410	+	0.547241i
$689$	−3648.33	−	1756.94i	−0.201727	−	0.0971468i
$690$	−20537.9	−	9890.52i	−1.13314	−	0.545689i
$691$	2421.92	+	3037.00i	0.133335	+	0.167196i	0.844017	−	0.536317i	$-0.180185\pi$
$691$	2421.92	+	3037.00i	0.133335	+	0.167196i	−0.710682	+	0.703514i	$0.751613\pi$
$692$	86.8815	+	380.653i	0.00477275	+	0.0209108i
$693$	−13687.3	−	17163.4i	−0.750272	−	0.940812i
$694$	−1358.02	−	5949.87i	−0.0742791	−	0.325438i
$695$	3205.15			0.174933
$696$	12502.7	−	54777.9i	0.680910	−	2.98326i
$697$	−135.694	+	594.514i	−0.00737414	+	0.0323082i
$698$	4240.71	+	18579.8i	0.229962	+	1.00753i
$699$	26299.7	+	12665.3i	1.42310	+	0.685328i
$700$	141.599	+	620.386i	0.00764563	+	0.0334977i
$701$	9002.00			0.485023			0.242511	−	0.970149i	$-0.422029\pi$
$701$	9002.00			0.485023			0.242511	+	0.970149i	$0.422029\pi$
$702$	8544.61	−	10714.6i	0.459395	−	0.576064i
$703$	−1475.05	+	6462.64i	−0.0791362	+	0.346718i
$704$	−26314.9			−1.40878
$705$	−17139.6			−0.915622
$706$	24152.3	+	11631.1i	1.28751	+	0.620032i
$707$	176.646	−	773.936i	0.00939668	−	0.0411695i
$708$	2104.18	−	2638.55i	0.111695	−	0.140061i
$709$	4399.62	−	5516.95i	0.233048	−	0.292233i	−0.651532	−	0.758621i	$-0.725873\pi$
$709$	4399.62	−	5516.95i	0.233048	−	0.292233i	0.884580	+	0.466388i	$0.154445\pi$
$710$	1640.81	+	7188.87i	0.0867304	+	0.379991i
$711$	−41791.1			−2.20435
$712$	−2517.75	+	3157.15i	−0.132523	+	0.166179i
$713$	−14580.2	+	18283.0i	−0.765823	+	0.960312i
$714$	1219.17	+	5341.54i	0.0639025	+	0.279975i
$715$	−921.823	+	4038.77i	−0.0482157	+	0.211247i
$716$	4244.49	−	2044.04i	0.221542	−	0.106689i
$717$	−34603.0	−	43390.7i	−1.80233	−	2.26005i
$718$	7920.87	+	9932.46i	0.411705	+	0.516262i
$719$	−5908.21			−0.306452			−0.153226	−	0.988191i	$-0.548966\pi$
$719$	−5908.21			−0.306452			−0.153226	+	0.988191i	$0.548966\pi$
$720$	20705.3			1.07172
$721$	−858.901	+	3763.09i	−0.0443650	+	0.194376i
$722$	17604.4	−	8477.85i	0.907437	−	0.436999i
$723$	35453.5	−	44457.3i	1.82369	−	2.28684i
$724$	−1084.30	−	522.173i	−0.0556600	−	0.0268044i
$725$	6539.02	+	28649.3i	0.334970	+	1.46760i
$726$	43575.4	−	54641.8i	2.22760	−	2.79332i
$727$	16978.4	−	8176.34i	0.866152	−	0.417117i	0.0526044	−	0.998615i	$-0.483248\pi$
$727$	16978.4	−	8176.34i	0.866152	−	0.417117i	0.813547	+	0.581499i	$0.197533\pi$
$728$	1551.14	+	746.992i	0.0789687	+	0.0380293i
$729$	−1802.10	+	867.848i	−0.0915564	+	0.0440912i
$730$	−8401.73	+	10535.4i	−0.425976	+	0.534156i
$731$	−5308.60	−	2556.49i	−0.268599	−	0.129350i
$732$	−5348.28	+	6706.53i	−0.270052	+	0.338634i
$733$	−26621.1	−	12820.1i	−1.34144	−	0.646002i	−0.381020	−	0.924567i	$-0.624427\pi$
$733$	−26621.1	−	12820.1i	−1.34144	−	0.646002i	−0.960417	+	0.278565i	$0.910141\pi$
$734$	20164.0	+	25284.9i	1.01399	+	1.27150i
$735$	8579.00	−	10757.7i	0.430532	−	0.539870i
$736$	−7350.51	−	3539.82i	−0.368130	−	0.177282i
$737$	3060.06	+	13407.0i	0.152943	+	0.670086i
$738$	750.719	+	3289.11i	0.0374449	+	0.164057i
$739$	21673.5	+	27177.7i	1.07885	+	1.35284i	0.931495	+	0.363753i	$0.118505\pi$
$739$	21673.5	+	27177.7i	1.07885	+	1.35284i	0.147356	+	0.989084i	$0.452924\pi$
$740$	−387.757	+	1698.87i	−0.0192625	+	0.0843944i
$741$	569.653	−	2495.81i	0.0282412	−	0.123733i
$742$	3120.22	−	3912.64i	0.154376	−	0.193581i
$743$	−3620.25	+	15861.3i	−0.178754	+	0.783171i	0.803453	+	0.595368i	$0.202994\pi$
$743$	−3620.25	+	15861.3i	−0.178754	+	0.783171i	−0.982207	+	0.187803i	$0.939863\pi$
$744$	5997.84	−	26278.2i	0.295553	−	1.29490i
$745$	1384.27	−	666.627i	0.0680746	−	0.0327830i
$746$	−17640.3	−	8495.13i	−0.865761	−	0.416929i
$747$	−24119.2	−	30244.5i	−1.18136	−	1.48138i
$748$	−1973.72	+	950.493i	−0.0964790	+	0.0464618i
$749$	−25.5467	+	111.927i	−0.00124627	+	0.00546026i
$750$	−27474.1	+	13230.8i	−1.33762	+	0.644162i
$751$	6944.06	−	30423.9i	0.337407	−	1.47828i	−0.467032	−	0.884240i	$-0.654677\pi$
$751$	6944.06	−	30423.9i	0.337407	−	1.47828i	0.804439	−	0.594035i	$-0.202466\pi$
$752$	−27494.0			−1.33325
$753$	−2269.11	−	9941.63i	−0.109815	−	0.481133i
$754$	−11020.6	−	5307.24i	−0.532290	−	0.256337i
$755$	2914.64			0.140496
$756$	1242.39	+	1557.90i	0.0597687	+	0.0749476i
$757$	5574.50	−	2684.54i	0.267647	−	0.128892i	−0.295248	−	0.955421i	$-0.595402\pi$
$757$	5574.50	−	2684.54i	0.267647	−	0.128892i	0.562894	+	0.826529i	$0.309688\pi$
$758$	14949.3	+	18745.8i	0.716336	+	0.898257i
$759$	−88745.8	+	42737.7i	−4.24410	+	2.04385i
$760$	1714.39	−	825.606i	0.0818255	−	0.0394051i
$761$	−1109.04	−	4859.02i	−0.0528287	−	0.231458i	0.941620	−	0.336676i	$-0.109303\pi$
$761$	−1109.04	−	4859.02i	−0.0528287	−	0.231458i	−0.994449	+	0.105219i	$0.966446\pi$
$762$	−41100.3	−	51538.1i	−1.95395	−	2.45017i
$763$	−1658.57	+	7266.68i	−0.0786951	+	0.344786i
$764$	−1286.44	+	1613.15i	−0.0609187	+	0.0763897i
$765$	−8701.91	+	4190.62i	−0.411266	+	0.198055i
$766$	15746.2	−	19745.1i	0.742731	−	0.931356i
$767$	2977.45	+	3733.60i	0.140169	+	0.175766i
$768$	15125.3			0.710659
$769$	41291.1			1.93627			0.968136	−	0.250423i	$-0.0805697\pi$
$769$	41291.1			1.93627			0.968136	+	0.250423i	$0.0805697\pi$
$770$	−4612.74	−	2221.38i	−0.215885	−	0.103965i
$771$	−15217.3	−	19081.9i	−0.710816	−	0.891335i
$772$	639.006	+	2799.67i	0.0297906	+	0.130521i
$773$	934.940	+	4096.24i	0.0435025	+	0.190597i	0.992010	−	0.126157i	$-0.0402642\pi$
$773$	934.940	+	4096.24i	0.0435025	+	0.190597i	−0.948508	+	0.316754i	$0.897407\pi$
$774$	−32597.7			−1.51383
$775$	3136.92	+	13743.7i	0.145396	+	0.637019i
$776$	−16537.2	+	7963.89i	−0.765014	+	0.368411i
$777$	16967.2	−	8170.96i	0.783390	−	0.377261i
$778$	−27742.6	−	13360.1i	−1.27843	−	0.615660i
$779$	219.551	+	275.309i	0.0100979	+	0.0126623i
$780$	149.748	−	656.089i	0.00687416	−	0.0301176i
$781$	28707.1	+	13824.6i	1.31527	+	0.633399i
$782$	17057.1			0.780002
$783$	57373.2	+	71943.7i	2.61858	+	3.28360i
$784$	13761.8	−	17256.7i	0.626903	−	0.786112i
$785$	7398.42	+	3562.89i	0.336383	+	0.161994i
$786$	6517.57	−	3138.69i	0.295768	−	0.142434i
$787$	−37098.1			−1.68031			−0.840156	−	0.542345i	$-0.817536\pi$
$787$	−37098.1			−1.68031			−0.840156	+	0.542345i	$0.817536\pi$
$788$	−1930.38	+	2229.99i	−0.0872678	+	0.100812i
$789$	−33509.5			−1.51200
$790$	−8781.19	+	4228.80i	−0.395469	+	0.190448i
$791$	10627.5	+	5117.92i	0.477711	+	0.230053i
$792$	49115.8	−	61589.2i	2.20360	−	2.76323i
$793$	−7567.90	−	9489.85i	−0.338896	−	0.424962i
$794$	33845.1			1.51274
$795$	11455.5	+	5516.67i	0.511049	+	0.246108i
$796$	−1183.93	+	5187.14i	−0.0527177	+	0.230972i
$797$	−21665.2	−	27167.3i	−0.962888	−	1.20742i	−0.978226	−	0.207541i	$-0.933454\pi$
$797$	−21665.2	−	27167.3i	−0.962888	−	1.20742i	0.0153387	−	0.999882i	$-0.495117\pi$
$798$	2850.50	+	1372.73i	0.126449	+	0.0608949i
$799$	11555.0	−	5564.60i	0.511623	−	0.246385i
$800$	−4431.15	+	2133.93i	−0.195831	+	0.0943073i
$801$	−2633.76	−	11539.3i	−0.116179	−	0.509013i
$802$	30980.2			1.36403
$803$	12957.0	+	56768.1i	0.569416	+	2.49477i
$804$	−497.100	−	2177.94i	−0.0218052	−	0.0955348i
$805$	2924.16	+	3666.78i	0.128029	+	0.160543i
$806$	−5286.84	−	2546.01i	−0.231043	−	0.111265i
$807$	7683.10			0.335140
$808$	2848.62			0.124027
$809$	−23711.4	−	29733.1i	−1.03047	−	1.29216i	−0.955504	−	0.294977i	$-0.904688\pi$
$809$	−23711.4	−	29733.1i	−1.03047	−	1.29216i	−0.0749615	−	0.997186i	$-0.523883\pi$
$810$	−12129.1	+	15209.4i	−0.526140	+	0.659759i
$811$	−34874.1	+	16794.5i	−1.50998	+	0.727168i	−0.991764	−	0.128081i	$-0.959118\pi$
$811$	−34874.1	+	16794.5i	−1.50998	+	0.727168i	−0.518217	+	0.855249i	$0.673404\pi$
$812$	1108.89	−	1390.51i	0.0479242	−	0.0600951i
$813$	6028.81	−	26414.0i	0.260073	−	1.13946i
$814$	39904.2	+	50038.3i	1.71823	+	2.15459i
$815$	322.379	+	1412.44i	0.0138558	+	0.0607061i
$816$	−20118.2	+	9688.41i	−0.863085	+	0.415640i
$817$	−3065.47	+	1476.25i	−0.131270	+	0.0632162i
$818$	−4063.59	−	5095.58i	−0.173692	−	0.217803i
$819$	−4546.47	+	2189.47i	−0.193976	+	0.0934141i
$820$	57.7148	+	72.3721i	0.00245791	+	0.00308213i
$821$	25901.0			1.10104			0.550518	−	0.834823i	$-0.314430\pi$
$821$	25901.0			1.10104			0.550518	+	0.834823i	$0.314430\pi$
$822$	−11454.8	−	5516.33i	−0.486048	−	0.234068i
$823$	4658.04	+	20408.2i	0.197289	+	0.864380i	0.972542	+	0.232729i	$0.0747654\pi$
$823$	4658.04	+	20408.2i	0.197289	+	0.864380i	−0.775253	+	0.631651i	$0.782377\pi$
$824$	−13850.8			−0.585576
$825$	−13213.2	+	57890.8i	−0.557606	+	2.44303i
$826$	−5317.37	+	2560.71i	−0.223989	+	0.107867i
$827$	−4945.56	+	21667.9i	−0.207949	+	0.911085i	0.757980	+	0.652278i	$0.226187\pi$
$827$	−4945.56	+	21667.9i	−0.207949	+	0.911085i	−0.965929	+	0.258807i	$0.916671\pi$
$828$	10002.9	−	4817.13i	0.419836	−	0.202182i
$829$	−16408.8	−	20576.0i	−0.687456	−	0.862043i	0.308561	−	0.951205i	$-0.400153\pi$
$829$	−16408.8	−	20576.0i	−0.687456	−	0.862043i	−0.996017	+	0.0891617i	$0.971581\pi$
$830$	−8128.35	−	3914.41i	−0.339927	−	0.163700i
$831$	5333.51	−	2568.49i	0.222644	−	0.107220i
$832$	−1346.01	+	5897.26i	−0.0560872	+	0.245734i
$833$	−2291.07	+	10037.8i	−0.0952952	+	0.417516i
$834$	−11923.2	+	14951.2i	−0.495043	+	0.620765i
$835$	−587.093	+	2572.22i	−0.0243320	+	0.106605i
$836$	−281.490	+	1233.29i	−0.0116454	+	0.0510218i
$837$	27523.3	+	34513.1i	1.13661	+	1.42526i
$838$	−10759.5	−	47140.5i	−0.443534	−	1.94325i
$839$	−4359.15	−	19098.7i	−0.179374	−	0.785889i	−0.981920	−	0.189298i	$-0.939379\pi$
$839$	−4359.15	−	19098.7i	−0.179374	−	0.785889i	0.802546	−	0.596591i	$-0.203478\pi$
$840$	−4870.48	−	2345.50i	−0.200057	−	0.0963422i
$841$	36002.1	−	45145.2i	1.47616	−	1.85105i
$842$	22467.0	+	28172.7i	0.919552	+	1.15308i
$843$	10173.1	+	4899.09i	0.415634	+	0.200159i
$844$	−437.674	+	548.826i	−0.0178500	+	0.0223831i
$845$	−8523.33	−	4104.62i	−0.346996	−	0.167104i
$846$	44239.1	−	55474.1i	1.79784	−	2.25442i
$847$	−12955.3	+	6238.95i	−0.525561	+	0.253097i
$848$	18376.0	+	8849.42i	0.744144	+	0.358361i
$849$	−60415.0	+	29094.3i	−2.44221	+	1.17611i
$850$	6411.13	−	8039.30i	0.258706	−	0.324407i
$851$	−13046.2	−	57158.9i	−0.525519	−	2.30245i
$852$	−4663.41	−	2245.78i	−0.187519	−	0.0903042i
$853$	20700.4	−	25957.5i	0.830914	−	1.04193i	−0.167514	−	0.985870i	$-0.553574\pi$
$853$	20700.4	−	25957.5i	0.830914	−	1.04193i	0.998427	−	0.0560630i	$-0.0178548\pi$
$854$	13515.4	−	6508.67i	0.541554	−	0.260799i
$855$	−1241.06	+	5437.44i	−0.0496414	+	0.217493i
$856$	−411.970			−0.0164496
$857$	40342.8			1.60803			0.804017	−	0.594607i	$-0.202692\pi$
$857$	40342.8			1.60803			0.804017	+	0.594607i	$0.202692\pi$
$858$	−15410.6	−	19324.3i	−0.613182	−	0.768906i
$859$	−19434.0	−	24369.5i	−0.771920	−	0.967957i	0.228064	−	0.973646i	$-0.426761\pi$
$859$	−19434.0	−	24369.5i	−0.771920	−	0.967957i	−0.999984	+	0.00568884i	$0.998189\pi$
$860$	−805.840	+	388.072i	−0.0319522	+	0.0153874i
$861$	222.608	−	975.308i	0.00881121	−	0.0386044i
$862$	9814.15	+	42998.6i	0.387786	+	1.69900i
$863$	14665.5	−	18389.9i	0.578469	−	0.725377i	−0.403382	−	0.915032i	$-0.632165\pi$
$863$	14665.5	−	18389.9i	0.578469	−	0.725377i	0.981851	+	0.189655i	$0.0607368\pi$
$864$	−9602.28	+	12040.9i	−0.378097	+	0.474119i
$865$	1734.75			0.0681889
$866$	−8904.35	−	39012.5i	−0.349402	−	1.53083i
$867$	−22272.3	+	27928.6i	−0.872441	+	1.09401i
$868$	531.961	−	667.059i	0.0208018	−	0.0260846i
$869$	−9371.46	+	41059.0i	−0.365828	+	1.60280i
$870$	34603.9	+	16664.4i	1.34848	+	0.649396i
$871$	3161.07			0.122972
$872$	−26746.4			−1.03870
$873$	11971.4	−	52450.2i	0.464114	−	2.03341i
$874$	6141.19	−	7700.81i	0.237676	−	0.298036i
$875$	6273.93			0.242397
$876$	−2104.83	−	9221.85i	−0.0811821	−	0.355682i
$877$	26885.7	+	12947.5i	1.03519	+	0.498523i	0.872736	−	0.488192i	$-0.162343\pi$
$877$	26885.7	+	12947.5i	1.03519	+	0.498523i	0.162458	+	0.986715i	$0.448058\pi$
$878$	−6119.42	−	26810.9i	−0.235217	−	1.03055i
$879$	1581.55	−	6929.22i	0.0606875	−	0.265889i
$880$	4643.07	−	20342.6i	0.177861	−	0.779260i
$881$	−50194.6			−1.91952			−0.959761	−	0.280817i	$-0.909395\pi$
$881$	−50194.6			−1.91952			−0.959761	+	0.280817i	$0.909395\pi$
$882$	12675.2	+	55533.8i	0.483897	+	2.12009i
$883$	10332.0	+	12955.9i	0.393770	+	0.493772i	0.938712	−	0.344702i	$-0.112020\pi$
$883$	10332.0	+	12955.9i	0.393770	+	0.493772i	−0.544943	+	0.838473i	$0.683449\pi$
$884$	112.053	+	490.934i	0.00426327	+	0.0186786i
$885$	−9348.96	−	11723.2i	−0.355098	−	0.445279i
$886$	23735.7	+	11430.5i	0.900020	+	0.433427i
$887$	3126.00	+	1505.40i	0.118332	+	0.0569858i	0.492113	−	0.870531i	$-0.336225\pi$
$887$	3126.00	+	1505.40i	0.118332	+	0.0569858i	−0.373781	+	0.927517i	$0.621939\pi$
$888$	42133.9	+	52834.2i	1.59225	+	1.99662i
$889$	3017.95	+	13222.5i	0.113857	+	0.498840i
$890$	−1721.05	−	2158.13i	−0.0648200	−	0.0812817i
$891$	18705.2	+	81953.0i	0.703310	+	3.08140i
$892$	−2451.86			−0.0920342
$893$	1647.97	−	7220.22i	0.0617549	−	0.270566i
$894$	−2039.83	+	8937.10i	−0.0763113	+	0.334341i
$895$	−4657.67	−	20406.6i	−0.173954	−	0.762141i
$896$	−8746.68	−	4212.18i	−0.326123	−	0.157053i
$897$	5038.30	+	22074.2i	0.187541	+	0.821670i
$898$	3164.02			0.117578
$899$	24565.9	−	30804.6i	0.911366	−	1.14282i
$900$	1489.31	−	6525.09i	0.0551596	−	0.241670i
$901$	−9514.02			−0.351785
$902$	3399.84			0.125501
$903$	8708.84	+	4193.96i	0.320944	+	0.154558i
$904$	−9418.74	+	41266.2i	−0.346529	+	1.51824i
$905$	−3333.89	+	4180.57i	−0.122456	+	0.153555i
$906$	−10842.5	+	13596.0i	−0.397590	+	0.498562i
$907$	1680.90	+	7364.49i	0.0615361	+	0.269607i	0.996331	−	0.0855798i	$-0.0272742\pi$
$907$	1680.90	+	7364.49i	0.0615361	+	0.269607i	−0.934795	+	0.355187i	$0.884417\pi$
$908$	5480.54			0.200306
$909$	−5205.79	+	6527.85i	−0.189951	+	0.238191i
$910$	−733.760	+	920.106i	−0.0267296	+	0.0335178i
$911$	−887.098	−	3886.63i	−0.0322622	−	0.141350i	0.956232	−	0.292610i	$-0.0945239\pi$
$911$	−887.098	−	3886.63i	−0.0322622	−	0.141350i	−0.988494	+	0.151261i	$0.951667\pi$
$912$	−2869.24	+	12571.0i	−0.104178	+	0.456433i
$913$	−35123.2	+	16914.5i	−1.27318	+	0.613129i
$914$	25004.7	+	31354.9i	0.904902	+	1.13471i
$915$	23762.7	+	29797.4i	0.858546	+	1.07658i
$916$	−3730.78			−0.134573
$917$	−1488.34			−0.0535979
$918$	7164.96	−	31391.7i	0.257602	−	1.12863i
$919$	−5239.23	+	2523.08i	−0.188059	+	0.0905644i	−0.525544	−	0.850767i	$-0.676138\pi$
$919$	−5239.23	+	2523.08i	−0.188059	+	0.0905644i	0.337485	+	0.941331i	$0.390424\pi$
$920$	−10493.1	+	13157.9i	−0.376029	+	0.471525i
$921$	−49907.3	−	24034.1i	−1.78556	−	0.859880i
$922$	7271.71	+	31859.4i	0.259741	+	1.13800i
$923$	4566.52	−	5726.23i	0.162848	−	0.204205i
$924$	3237.91	−	1559.30i	0.115281	−	0.0555163i
$925$	−31843.5	−	15335.0i	−1.13190	−	0.545094i
$926$	−20704.3	+	9970.69i	−0.734759	+	0.353841i
$927$	25312.0	−	31740.2i	0.896822	−	1.12458i
$928$	12384.7	+	5964.18i	0.438092	+	0.210974i
$929$	−10646.3	+	13350.0i	−0.375988	+	0.471474i	−0.933439	−	0.358736i	$-0.883208\pi$
$929$	−10646.3	+	13350.0i	−0.375988	+	0.471474i	0.557451	+	0.830210i	$0.311779\pi$
$930$	16600.3	+	7994.28i	0.585317	+	0.281874i
$931$	3706.93	+	4648.34i	0.130494	+	0.163634i
$932$	−2067.28	+	2592.29i	−0.0726567	+	0.0911086i
$933$	−46729.2	−	22503.6i	−1.63971	−	0.789641i
$934$	1245.75	+	5457.97i	0.0436424	+	0.191210i
$935$	2165.85	+	9489.19i	0.0757548	+	0.331904i
$936$	−11290.1	−	14157.3i	−0.394260	−	0.494386i
$937$	−3906.31	+	17114.6i	−0.136194	+	0.596703i	0.860058	+	0.510197i	$0.170427\pi$
$937$	−3906.31	+	17114.6i	−0.136194	+	0.596703i	−0.996251	+	0.0865065i	$0.972430\pi$
$938$	−869.317	+	3808.73i	−0.0302603	+	0.132579i
$939$	38588.4	−	48388.4i	1.34109	−	1.68168i
$940$	433.211	−	1898.02i	0.0150317	−	0.0658582i
$941$	−852.556	+	3735.29i	−0.0295351	+	0.129402i	−0.987546	−	0.157330i	$-0.949712\pi$
$941$	−852.556	+	3735.29i	−0.0295351	+	0.129402i	0.958011	+	0.286731i	$0.0925687\pi$
$942$	−44142.1	+	21257.7i	−1.52678	+	0.735259i
$943$	−2806.02	−	1351.31i	−0.0968999	−	0.0466645i
$944$	−14996.9	−	18805.5i	−0.517063	−	0.648376i
$945$	7976.61	−	3841.33i	0.274581	−	0.132231i
$946$	−7309.88	+	32026.7i	−0.251231	+	1.10072i
$947$	−8217.17	+	3957.18i	−0.281966	+	0.135788i	−0.569522	−	0.821976i	$-0.692872\pi$
$947$	−8217.17	+	3957.18i	−0.281966	+	0.135788i	0.287556	+	0.957764i	$0.407157\pi$
$948$	1522.37	−	6669.95i	0.0521565	−	0.228512i
$949$	13384.7			0.457834
$950$	−1321.28	−	5788.89i	−0.0451240	−	0.197701i
$951$	−43147.3	−	20778.6i	−1.47124	−	0.708511i
$952$	4045.04			0.137710
$953$	12807.5	+	16060.1i	0.435336	+	0.545894i	0.950307	−	0.311313i	$-0.100769\pi$
$953$	12807.5	+	16060.1i	0.435336	+	0.545894i	−0.514971	+	0.857207i	$0.672197\pi$
$954$	−47423.2	+	22837.8i	−1.60942	+	0.775053i
$955$	5715.74	+	7167.31i	0.193672	+	0.242857i
$956$	5679.66	−	2735.18i	0.192148	−	0.0925336i
$957$	149526.	−	72008.0i	5.05067	−	2.43228i
$958$	2362.99	+	10353.0i	0.0796920	+	0.349153i
$959$	1630.92	+	2045.11i	0.0549167	+	0.0688634i
$960$	4226.38	−	18517.0i	0.142089	−	0.622534i
$961$	−6789.55	+	8513.83i	−0.227906	+	0.285785i
$962$	13254.8	−	6383.19i	0.444234	−	0.213932i
$963$	752.866	−	944.064i	0.0251929	−	0.0315909i
$964$	4027.06	+	5049.77i	0.134547	+	0.168716i
$965$	12759.0			0.425622
$966$	−27982.5			−0.932009
$967$	−42143.1	−	20295.0i	−1.40148	−	0.674916i	−0.428017	−	0.903770i	$-0.640788\pi$
$967$	−42143.1	−	20295.0i	−1.40148	−	0.674916i	−0.973461	+	0.228854i	$0.926502\pi$
$968$	−32171.4	−	40341.6i	−1.06821	−	1.33949i
$969$	−1338.41	−	5863.97i	−0.0443715	−	0.194404i
$970$	−2791.93	−	12232.3i	−0.0924161	−	0.404901i
$971$	52229.0			1.72617			0.863083	−	0.505062i	$-0.168530\pi$
$971$	52229.0			1.72617			0.863083	+	0.505062i	$0.168530\pi$
$972$	−980.841	−	4297.35i	−0.0323668	−	0.141808i
$973$	3544.86	−	1707.11i	0.116796	−	0.0562462i
$974$	−8741.09	+	4209.49i	−0.287559	+	0.138481i
$975$	12297.7	+	5922.24i	0.403939	+	0.194527i
$976$	38118.3	+	47798.8i	1.25014	+	1.56762i
$977$	1018.29	−	4461.42i	0.0333450	−	0.146094i	−0.955515	−	0.294942i	$-0.904700\pi$
$977$	1018.29	−	4461.42i	0.0333450	−	0.146094i	0.988860	+	0.148849i	$0.0475567\pi$
$978$	−7787.89	−	3750.45i	−0.254631	−	0.122624i
$979$	−11927.7			−0.389389
$980$	974.464	+	1221.94i	0.0317634	+	0.0398300i
$981$	48878.5	−	61291.7i	1.59079	−	1.99479i
$982$	9502.86	+	4576.33i	0.308807	+	0.148714i
$983$	49763.8	−	23965.0i	1.61467	−	0.777583i	0.614731	−	0.788737i	$-0.289265\pi$
$983$	49763.8	−	23965.0i	1.61467	−	0.777583i	0.999938	+	0.0111537i	$0.00355042\pi$
$984$	3589.81			0.116300
$985$	7751.03	+	10566.5i	0.250729	+	0.341803i
$986$	−28739.3			−0.928240
$987$	−18956.1	+	9128.80i	−0.611328	+	0.294400i
$988$	261.986	+	126.166i	0.00843612	+	0.00406262i
$989$	18762.5	−	23527.5i	0.603250	−	0.756451i
$990$	33574.0	+	42100.5i	1.07783	+	1.35156i
$991$	−13704.2			−0.439283			−0.219642	−	0.975581i	$-0.570489\pi$
$991$	−13704.2			−0.439283			−0.219642	+	0.975581i	$0.570489\pi$
$992$	5941.26	+	2861.16i	0.190156	+	0.0915745i
$993$	−1545.89	+	6773.00i	−0.0494033	+	0.216450i
$994$	5643.62	+	7076.87i	0.180085	+	0.225820i
$995$	21298.4	+	10256.8i	0.678597	+	0.326795i
$996$	5705.69	−	2747.72i	0.181518	−	0.0874144i
$997$	−26342.9	+	12686.1i	−0.836798	+	0.402981i	−0.802660	−	0.596437i	$-0.796583\pi$
$997$	−26342.9	+	12686.1i	−0.836798	+	0.402981i	−0.0341375	+	0.999417i	$0.510868\pi$
$998$	−7850.47	−	34395.2i	−0.249000	−	1.09094i
$999$	−110675.			−3.50510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.d.a.36.13	✓	294
197.104	even	7	inner	197.4.d.a.104.13	yes	294

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.d.a.36.13	✓	294	1.1	even	1	trivial
197.4.d.a.104.13	yes	294	197.104	even	7	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.71290 + 1.30647i) q^{2} +(-8.46100 - 4.07460i) q^{3} +(0.665075 - 0.833977i) q^{4} +(-2.95496 - 3.70540i) q^{5} +28.2772 q^{6} +(-5.24170 - 2.52427i) q^{7} +(4.64553 - 20.3534i) q^{8} +(38.1519 + 47.8410i) q^{9} +(12.8575 + 6.19185i) q^{10} +(55.5583 - 26.7555i) q^{11} +(-9.02533 + 4.34637i) q^{12} +(-3.15417 - 13.8193i) q^{13} +17.5181 q^{14} +(9.90388 + 43.3917i) q^{15} +(15.8870 + 69.6057i) q^{16} +(-20.7646 - 26.0380i) q^{17} +(-166.005 - 79.9439i) q^{18} -19.2315 q^{19} -5.05549 q^{20} +(34.0647 + 42.7157i) q^{21} +(-115.769 + 145.170i) q^{22} +(153.249 - 73.8006i) q^{23} +(-122.238 + 153.282i) q^{24} +(22.8169 - 99.9673i) q^{25} +(26.6115 + 33.3697i) q^{26} +(-71.4487 - 313.037i) q^{27} +(-5.59131 + 2.69263i) q^{28} +(-258.206 + 124.345i) q^{29} +(-83.5581 - 104.779i) q^{30} +(-123.867 + 59.6514i) q^{31} +(-29.9055 - 37.5003i) q^{32} -579.097 q^{33} +(90.3502 + 43.5104i) q^{34} +(6.13559 + 26.8818i) q^{35} +65.2722 q^{36} +(76.7001 - 336.045i) q^{37} +(52.1731 - 25.1252i) q^{38} +(-29.6209 + 129.778i) q^{39} +(-89.1450 + 42.9300i) q^{40} +(-11.4163 - 14.3155i) q^{41} +(-148.221 - 71.3794i) q^{42} +(159.399 - 76.7625i) q^{43} +(14.6370 - 64.1288i) q^{44} +(64.5328 - 282.737i) q^{45} +(-319.331 + 400.428i) q^{46} +(-85.6912 + 375.438i) q^{47} +(149.195 - 653.667i) q^{48} +(-192.753 - 241.705i) q^{49} +(68.7038 + 301.011i) q^{50} +(69.5950 + 304.916i) q^{51} +(-13.6228 - 6.56038i) q^{52} +(178.114 - 223.348i) q^{53} +(602.806 + 755.895i) q^{54} +(-263.313 - 126.805i) q^{55} +(-75.7281 + 94.9600i) q^{56} +(162.717 + 78.3606i) q^{57} +(538.034 - 674.674i) q^{58} +(-303.535 + 146.175i) q^{59} +(42.7745 + 20.5991i) q^{60} +(771.509 - 371.539i) q^{61} +(258.108 - 323.657i) q^{62} +(-79.2175 - 347.074i) q^{63} +(-384.479 - 185.155i) q^{64} +(-41.8858 + 52.5231i) q^{65} +(1571.03 - 756.571i) q^{66} +(-49.6239 + 217.416i) q^{67} -35.5252 q^{68} -1597.34 q^{69} +(-51.7653 - 64.9117i) q^{70} +(322.159 + 403.975i) q^{71} +(1150.96 - 554.275i) q^{72} +(-210.118 + 920.588i) q^{73} +(230.951 + 1011.86i) q^{74} +(-600.381 + 752.854i) q^{75} +(-12.7904 + 16.0386i) q^{76} -358.758 q^{77} +(-89.1913 - 390.772i) q^{78} +(-425.820 + 533.962i) q^{79} +(210.972 - 264.550i) q^{80} +(-303.336 + 1329.00i) q^{81} +(49.6740 + 23.9217i) q^{82} -632.187 q^{83} +58.2795 q^{84} +(-35.1227 + 153.883i) q^{85} +(-332.146 + 416.498i) q^{86} +2691.34 q^{87} +(-286.467 - 1255.10i) q^{88} +(-174.272 - 83.9250i) q^{89} +(194.314 + 851.347i) q^{90} +(-18.3505 + 80.3989i) q^{91} +(40.3737 - 176.889i) q^{92} +1291.10 q^{93} +(-258.024 - 1130.48i) q^{94} +(56.8282 + 71.2603i) q^{95} +(100.232 + 439.143i) q^{96} +(-548.172 - 687.386i) q^{97} +(838.701 + 403.897i) q^{98} +(3399.67 + 1637.19i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 294 q - 5 q^{2} - 5 q^{3} - 161 q^{4} - 5 q^{5} + 58 q^{6} + 15 q^{7} + 115 q^{8} - 446 q^{9} - 211 q^{10} + 93 q^{11} - 47 q^{12} + 23 q^{13} + 656 q^{14} + 343 q^{15} - 1505 q^{16} - 17 q^{17} + 132 q^{18}+ \cdots + 4526 q^{99}+O(q^{100}) \) 294 * q - 5 * q^2 - 5 * q^3 - 161 * q^4 - 5 * q^5 + 58 * q^6 + 15 * q^7 + 115 * q^8 - 446 * q^9 - 211 * q^10 + 93 * q^11 - 47 * q^12 + 23 * q^13 + 656 * q^14 + 343 * q^15 - 1505 * q^16 - 17 * q^17 + 132 * q^18 + 512 * q^19 + 148 * q^20 - 47 * q^21 - 845 * q^22 - 143 * q^23 + 775 * q^24 - 952 * q^25 + 39 * q^26 + 1159 * q^27 - 130 * q^28 - 169 * q^29 + 1048 * q^30 - 269 * q^31 - 39 * q^32 + 234 * q^33 + 761 * q^34 + 949 * q^35 + 15930 * q^36 + 715 * q^37 - 987 * q^38 - 417 * q^39 - 3303 * q^40 + 65 * q^41 - 2334 * q^42 + 581 * q^43 - 1751 * q^44 - 2497 * q^45 + 13 * q^46 - 361 * q^47 - 3995 * q^48 - 3728 * q^49 + 3671 * q^50 + 213 * q^51 + 4036 * q^52 - 47 * q^53 + 1358 * q^54 - 4339 * q^55 + 680 * q^56 - 2470 * q^57 + 1483 * q^58 - 3375 * q^59 + 1549 * q^60 + 805 * q^61 - 1149 * q^62 - 4839 * q^63 - 7061 * q^64 + 457 * q^65 + 1224 * q^66 + 2261 * q^67 + 1216 * q^68 - 4378 * q^69 + 1360 * q^70 - 1687 * q^71 + 936 * q^72 + 3075 * q^73 - 601 * q^74 + 3549 * q^75 - 5960 * q^76 - 4318 * q^77 - 11681 * q^78 + 2973 * q^79 - 1671 * q^80 - 4288 * q^81 + 2197 * q^82 + 9380 * q^83 - 7416 * q^84 - 5171 * q^85 - 3868 * q^86 + 1826 * q^87 - 3252 * q^88 - 79 * q^89 + 19791 * q^90 + 8303 * q^91 + 8077 * q^92 + 2118 * q^93 + 6319 * q^94 - 3280 * q^95 - 13752 * q^96 - 17 * q^97 - 4434 * q^98 + 4526 * q^99

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