LMFDB - Embedded newform 65.4.e.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,4,Mod(16,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("65.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	65.e (of order $3$, 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:	$3.83512415037$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 45 x^{12} - 52 x^{11} + 1311 x^{10} - 1336 x^{9} + 20343 x^{8} - 11166 x^{7} + \cdots + 1157776 $ x^14 - 2x^13 + 45x^12 - 52x^11 + 1311x^10 - 1336x^9 + 20343x^8 - 11166x^7 + 216447x^6 - 107836x^5 + 1201133x^4 + 4392x^3 + 3890980x^2 - 1936800*x + 1157776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Root			$1.92689 + 3.33746i$ of defining polynomial
Character	$\chi$	$=$	65.16
Dual form			65.4.e.a.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92689 - 3.33746i) q^{2} +(4.40164 + 7.62386i) q^{3} +(-3.42577 + 5.93361i) q^{4} -5.00000 q^{5} +(16.9629 - 29.3806i) q^{6} +(-17.9862 + 31.1531i) q^{7} -4.42588 q^{8} +(-25.2488 + 43.7322i) q^{9} +O(q^{10})$	\(q+(-1.92689 - 3.33746i) q^{2} +(4.40164 + 7.62386i) q^{3} +(-3.42577 + 5.93361i) q^{4} -5.00000 q^{5} +(16.9629 - 29.3806i) q^{6} +(-17.9862 + 31.1531i) q^{7} -4.42588 q^{8} +(-25.2488 + 43.7322i) q^{9} +(9.63443 + 16.6873i) q^{10} +(-7.21470 - 12.4962i) q^{11} -60.3160 q^{12} +(46.7719 + 3.06350i) q^{13} +138.630 q^{14} +(-22.0082 - 38.1193i) q^{15} +(35.9343 + 62.2401i) q^{16} +(22.4610 - 38.9036i) q^{17} +194.606 q^{18} +(0.473270 - 0.819727i) q^{19} +(17.1289 - 29.6681i) q^{20} -316.675 q^{21} +(-27.8038 + 48.1576i) q^{22} +(78.8366 + 136.549i) q^{23} +(-19.4811 - 33.7423i) q^{24} +25.0000 q^{25} +(-79.8999 - 162.003i) q^{26} -206.856 q^{27} +(-123.234 - 213.447i) q^{28} +(-49.5872 - 85.8875i) q^{29} +(-84.8145 + 146.903i) q^{30} +36.0806 q^{31} +(120.779 - 209.196i) q^{32} +(63.5130 - 110.008i) q^{33} -173.119 q^{34} +(89.9312 - 155.765i) q^{35} +(-172.993 - 299.633i) q^{36} +(-52.1235 - 90.2806i) q^{37} -3.64774 q^{38} +(182.517 + 370.067i) q^{39} +22.1294 q^{40} +(-18.6860 - 32.3651i) q^{41} +(610.197 + 1056.89i) q^{42} +(-222.121 + 384.725i) q^{43} +98.8637 q^{44} +(126.244 - 218.661i) q^{45} +(303.818 - 526.229i) q^{46} +329.017 q^{47} +(-316.340 + 547.917i) q^{48} +(-475.509 - 823.606i) q^{49} +(-48.1721 - 83.4366i) q^{50} +395.461 q^{51} +(-178.408 + 267.032i) q^{52} +493.163 q^{53} +(398.587 + 690.374i) q^{54} +(36.0735 + 62.4812i) q^{55} +(79.6049 - 137.880i) q^{56} +8.33264 q^{57} +(-191.098 + 330.991i) q^{58} +(-17.6071 + 30.4964i) q^{59} +301.580 q^{60} +(-251.498 + 435.608i) q^{61} +(-69.5232 - 120.418i) q^{62} +(-908.262 - 1573.16i) q^{63} -355.961 q^{64} +(-233.860 - 15.3175i) q^{65} -489.529 q^{66} +(227.248 + 393.606i) q^{67} +(153.893 + 266.550i) q^{68} +(-694.020 + 1202.08i) q^{69} -693.148 q^{70} +(-31.0873 + 53.8448i) q^{71} +(111.748 - 193.553i) q^{72} -78.1722 q^{73} +(-200.872 + 347.921i) q^{74} +(110.041 + 190.596i) q^{75} +(3.24263 + 5.61640i) q^{76} +519.061 q^{77} +(883.395 - 1322.22i) q^{78} +925.117 q^{79} +(-179.672 - 311.201i) q^{80} +(-228.787 - 396.270i) q^{81} +(-72.0116 + 124.728i) q^{82} -323.640 q^{83} +(1084.86 - 1879.03i) q^{84} +(-112.305 + 194.518i) q^{85} +1712.01 q^{86} +(436.529 - 756.091i) q^{87} +(31.9314 + 55.3068i) q^{88} +(432.322 + 748.804i) q^{89} -973.031 q^{90} +(-936.689 + 1401.99i) q^{91} -1080.31 q^{92} +(158.814 + 275.073i) q^{93} +(-633.977 - 1098.08i) q^{94} +(-2.36635 + 4.09863i) q^{95} +2126.50 q^{96} +(45.1884 - 78.2686i) q^{97} +(-1832.50 + 3173.99i) q^{98} +728.650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18} - 245 q^{19} + 150 q^{20} - 76 q^{21} - 338 q^{22} + 74 q^{23} - 334 q^{24} + 350 q^{25} + 243 q^{26} - 884 q^{27} - 230 q^{28} + 88 q^{29} + 115 q^{30} + 1000 q^{31} - 80 q^{32} + 194 q^{33} + 854 q^{34} + 35 q^{35} - 425 q^{36} - 633 q^{37} - 596 q^{38} + 970 q^{39} - 210 q^{40} - 162 q^{41} + 1439 q^{42} + 280 q^{43} + 440 q^{44} + 435 q^{45} + 11 q^{46} + 950 q^{47} - 2281 q^{48} - 1694 q^{49} - 50 q^{50} - 860 q^{51} - 956 q^{52} - 1206 q^{53} - 51 q^{54} + 435 q^{55} + 1277 q^{56} + 916 q^{57} + 1213 q^{58} - 1410 q^{59} + 790 q^{60} - 412 q^{61} + 56 q^{62} - 1241 q^{63} - 2358 q^{64} - 615 q^{65} + 4346 q^{66} - 1398 q^{67} + 493 q^{68} - 1080 q^{69} - 660 q^{70} + 584 q^{71} - 1545 q^{72} + 5076 q^{73} - 3840 q^{74} + 100 q^{75} - 3292 q^{76} - 5506 q^{77} + 1179 q^{78} + 928 q^{79} - 670 q^{80} + 473 q^{81} + 1583 q^{82} + 932 q^{83} + 3081 q^{84} - 570 q^{85} + 9858 q^{86} + 282 q^{87} - 3389 q^{88} - 443 q^{89} - 2070 q^{90} + 487 q^{91} + 6182 q^{92} + 2116 q^{93} - 2017 q^{94} + 1225 q^{95} + 954 q^{96} + 1870 q^{97} - 1364 q^{98} + 11378 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9 + 10 * q^10 - 87 * q^11 - 158 * q^12 + 123 * q^13 + 132 * q^14 - 20 * q^15 + 134 * q^16 + 114 * q^17 + 414 * q^18 - 245 * q^19 + 150 * q^20 - 76 * q^21 - 338 * q^22 + 74 * q^23 - 334 * q^24 + 350 * q^25 + 243 * q^26 - 884 * q^27 - 230 * q^28 + 88 * q^29 + 115 * q^30 + 1000 * q^31 - 80 * q^32 + 194 * q^33 + 854 * q^34 + 35 * q^35 - 425 * q^36 - 633 * q^37 - 596 * q^38 + 970 * q^39 - 210 * q^40 - 162 * q^41 + 1439 * q^42 + 280 * q^43 + 440 * q^44 + 435 * q^45 + 11 * q^46 + 950 * q^47 - 2281 * q^48 - 1694 * q^49 - 50 * q^50 - 860 * q^51 - 956 * q^52 - 1206 * q^53 - 51 * q^54 + 435 * q^55 + 1277 * q^56 + 916 * q^57 + 1213 * q^58 - 1410 * q^59 + 790 * q^60 - 412 * q^61 + 56 * q^62 - 1241 * q^63 - 2358 * q^64 - 615 * q^65 + 4346 * q^66 - 1398 * q^67 + 493 * q^68 - 1080 * q^69 - 660 * q^70 + 584 * q^71 - 1545 * q^72 + 5076 * q^73 - 3840 * q^74 + 100 * q^75 - 3292 * q^76 - 5506 * q^77 + 1179 * q^78 + 928 * q^79 - 670 * q^80 + 473 * q^81 + 1583 * q^82 + 932 * q^83 + 3081 * q^84 - 570 * q^85 + 9858 * q^86 + 282 * q^87 - 3389 * q^88 - 443 * q^89 - 2070 * q^90 + 487 * q^91 + 6182 * q^92 + 2116 * q^93 - 2017 * q^94 + 1225 * q^95 + 954 * q^96 + 1870 * q^97 - 1364 * q^98 + 11378 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.92689	−	3.33746i	−0.681257	−	1.17997i	−0.974598	−	0.223963i	$-0.928100\pi$
$2$	−1.92689	−	3.33746i	−0.681257	−	1.17997i	0.293341	−	0.956008i	$-0.405233\pi$
$3$	4.40164	+	7.62386i	0.847095	+	1.46721i	0.883789	+	0.467886i	$0.154984\pi$
$3$	4.40164	+	7.62386i	0.847095	+	1.46721i	−0.0366938	+	0.999327i	$0.511683\pi$
$4$	−3.42577	+	5.93361i	−0.428222	+	0.741702i
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	16.9629	−	29.3806i	1.15418	−	1.99910i
$7$	−17.9862	+	31.1531i	−0.971165	+	1.68211i	−0.279117	+	0.960257i	$0.590042\pi$
$7$	−17.9862	+	31.1531i	−0.971165	+	1.68211i	−0.692049	+	0.721851i	$0.743292\pi$
$8$	−4.42588			−0.195598
$9$	−25.2488	+	43.7322i	−0.935141	+	1.61971i
$10$	9.63443	+	16.6873i	0.304667	+	0.527699i
$11$	−7.21470	−	12.4962i	−0.197756	−	0.342523i	0.750045	−	0.661387i	$-0.230032\pi$
$11$	−7.21470	−	12.4962i	−0.197756	−	0.342523i	−0.947800	+	0.318864i	$0.896699\pi$
$12$	−60.3160			−1.45098
$13$	46.7719	+	3.06350i	0.997862	+	0.0653586i
$13$	46.7719	+	3.06350i	0.997862	+	0.0653586i
$14$	138.630			2.64645
$15$	−22.0082	−	38.1193i	−0.378833	−	0.656157i
$16$	35.9343	+	62.2401i	0.561474	+	0.972502i
$17$	22.4610	−	38.9036i	0.320447	−	0.555030i	−0.660133	−	0.751148i	$-0.729500\pi$
$17$	22.4610	−	38.9036i	0.320447	−	0.555030i	0.980580	+	0.196118i	$0.0628336\pi$
$18$	194.606			2.54828
$19$	0.473270	−	0.819727i	0.00571450	−	0.00989780i	−0.863154	−	0.504941i	$-0.831514\pi$
$19$	0.473270	−	0.819727i	0.00571450	−	0.00989780i	0.868869	+	0.495043i	$0.164848\pi$
$20$	17.1289	−	29.6681i	0.191507	−	0.331699i
$21$	−316.675			−3.29068
$22$	−27.8038	+	48.1576i	−0.269445	+	0.466693i
$23$	78.8366	+	136.549i	0.714721	+	1.23793i	0.963067	+	0.269261i	$0.0867794\pi$
$23$	78.8366	+	136.549i	0.714721	+	1.23793i	−0.248347	+	0.968671i	$0.579887\pi$
$24$	−19.4811	−	33.7423i	−0.165690	−	0.286984i
$25$	25.0000			0.200000
$26$	−79.8999	−	162.003i	−0.602679	−	1.22197i
$27$	−206.856			−1.47442
$28$	−123.234	−	213.447i	−0.831748	−	1.44063i
$29$	−49.5872	−	85.8875i	−0.317521	−	0.549962i	0.662449	−	0.749107i	$-0.269517\pi$
$29$	−49.5872	−	85.8875i	−0.317521	−	0.549962i	−0.979970	+	0.199144i	$0.936184\pi$
$30$	−84.8145	+	146.903i	−0.516164	+	0.894023i
$31$	36.0806			0.209041			0.104520	−	0.994523i	$-0.466669\pi$
$31$	36.0806			0.209041			0.104520	+	0.994523i	$0.466669\pi$
$32$	120.779	−	209.196i	0.667217	−	1.15565i
$33$	63.5130	−	110.008i	0.335036	−	0.580300i
$34$	−173.119			−0.873226
$35$	89.9312	−	155.765i	0.434318	−	0.752262i
$36$	−172.993	−	299.633i	−0.800895	−	1.38719i
$37$	−52.1235	−	90.2806i	−0.231596	−	0.401136i	0.726682	−	0.686974i	$-0.241061\pi$
$37$	−52.1235	−	90.2806i	−0.231596	−	0.401136i	−0.958278	+	0.285838i	$0.907728\pi$
$38$	−3.64774			−0.0155722
$39$	182.517	+	370.067i	0.749389	+	1.51944i
$40$	22.1294			0.0874741
$41$	−18.6860	−	32.3651i	−0.0711772	−	0.123282i	0.828240	−	0.560373i	$-0.189342\pi$
$41$	−18.6860	−	32.3651i	−0.0711772	−	0.123282i	−0.899417	+	0.437091i	$0.856009\pi$
$42$	610.197	+	1056.89i	2.24180	+	3.88291i
$43$	−222.121	+	384.725i	−0.787748	+	1.36442i	0.139596	+	0.990209i	$0.455420\pi$
$43$	−222.121	+	384.725i	−0.787748	+	1.36442i	−0.927344	+	0.374211i	$0.877914\pi$
$44$	98.8637			0.338733
$45$	126.244	−	218.661i	0.418208	−	0.724357i
$46$	303.818	−	526.229i	0.973816	−	1.68670i
$47$	329.017			1.02111			0.510553	−	0.859846i	$-0.329441\pi$
$47$	329.017			1.02111			0.510553	+	0.859846i	$0.329441\pi$
$48$	−316.340	+	547.917i	−0.951244	+	1.64760i
$49$	−475.509	−	823.606i	−1.38632	−	2.40118i
$50$	−48.1721	−	83.4366i	−0.136251	−	0.235994i
$51$	395.461			1.08580
$52$	−178.408	+	267.032i	−0.475783	+	0.712128i
$53$	493.163			1.27814			0.639068	−	0.769151i	$-0.279320\pi$
$53$	493.163			1.27814			0.639068	+	0.769151i	$0.279320\pi$
$54$	398.587	+	690.374i	1.00446	+	1.73978i
$55$	36.0735	+	62.4812i	0.0884391	+	0.153181i
$56$	79.6049	−	137.880i	0.189958	−	0.329017i
$57$	8.33264			0.0193629
$58$	−191.098	+	330.991i	−0.432627	+	0.749331i
$59$	−17.6071	+	30.4964i	−0.0388517	+	0.0672931i	−0.884797	−	0.465976i	$-0.845703\pi$
$59$	−17.6071	+	30.4964i	−0.0388517	+	0.0672931i	0.845946	+	0.533269i	$0.179037\pi$
$60$	301.580			0.648897
$61$	−251.498	+	435.608i	−0.527886	+	0.914326i	0.471585	+	0.881820i	$0.343682\pi$
$61$	−251.498	+	435.608i	−0.527886	+	0.914326i	−0.999472	+	0.0325053i	$0.989651\pi$
$62$	−69.5232	−	120.418i	−0.142411	−	0.246662i
$63$	−908.262	−	1573.16i	−1.81635	−	3.14602i
$64$	−355.961			−0.695236
$65$	−233.860	−	15.3175i	−0.446257	−	0.0292293i
$66$	−489.529			−0.912983
$67$	227.248	+	393.606i	0.414370	+	0.717710i	0.995362	−	0.0961992i	$-0.0306686\pi$
$67$	227.248	+	393.606i	0.414370	+	0.717710i	−0.580992	+	0.813909i	$0.697335\pi$
$68$	153.893	+	266.550i	0.274445	+	0.475352i
$69$	−694.020	+	1202.08i	−1.21087	+	2.09729i
$70$	−693.148			−1.18353
$71$	−31.0873	+	53.8448i	−0.0519632	+	0.0900029i	−0.890837	−	0.454323i	$-0.849881\pi$
$71$	−31.0873	+	53.8448i	−0.0519632	+	0.0900029i	0.838874	+	0.544326i	$0.183215\pi$
$72$	111.748	−	193.553i	0.182912	−	0.316812i
$73$	−78.1722			−0.125334			−0.0626668	−	0.998035i	$-0.519961\pi$
$73$	−78.1722			−0.125334			−0.0626668	+	0.998035i	$0.519961\pi$
$74$	−200.872	+	347.921i	−0.315553	+	0.546554i
$75$	110.041	+	190.596i	0.169419	+	0.293442i
$76$	3.24263	+	5.61640i	0.00489414	+	0.00847691i
$77$	519.061			0.768215
$78$	883.395	−	1322.22i	1.28237	−	1.91939i
$79$	925.117			1.31752			0.658758	−	0.752355i	$-0.271082\pi$
$79$	925.117			1.31752			0.658758	+	0.752355i	$0.271082\pi$
$80$	−179.672	−	311.201i	−0.251099	−	0.434916i
$81$	−228.787	−	396.270i	−0.313836	−	0.543580i
$82$	−72.0116	+	124.728i	−0.0969798	+	0.167974i
$83$	−323.640			−0.428001			−0.214000	−	0.976834i	$-0.568649\pi$
$83$	−323.640			−0.428001			−0.214000	+	0.976834i	$0.568649\pi$
$84$	1084.86	−	1879.03i	1.40914	−	2.44070i
$85$	−112.305	+	194.518i	−0.143308	+	0.248217i
$86$	1712.01			2.14663
$87$	436.529	−	756.091i	0.537941	−	0.931741i
$88$	31.9314	+	55.3068i	0.0386807	+	0.0669969i
$89$	432.322	+	748.804i	0.514899	+	0.891832i	0.999851	+	0.0172907i	$0.00550409\pi$
$89$	432.322	+	748.804i	0.514899	+	0.891832i	−0.484951	+	0.874541i	$0.661163\pi$
$90$	−973.031			−1.13963
$91$	−936.689	+	1401.99i	−1.07903	+	1.61504i
$92$	−1080.31			−1.22424
$93$	158.814	+	275.073i	0.177078	+	0.306707i
$94$	−633.977	−	1098.08i	−0.695636	−	1.20488i
$95$	−2.36635	+	4.09863i	−0.00255560	+	0.00442643i
$96$	2126.50			2.26079
$97$	45.1884	−	78.2686i	0.0473009	−	0.0819275i	−0.841406	−	0.540404i	$-0.818271\pi$
$97$	45.1884	−	78.2686i	0.0473009	−	0.0819275i	0.888706	+	0.458477i	$0.151605\pi$
$98$	−1832.50	+	3173.99i	−1.88889	+	3.27165i
$99$	728.650			0.739718
$100$	−85.6443	+	148.340i	−0.0856443	+	0.148340i
$101$	−467.792	−	810.240i	−0.460862	−	0.798237i	0.538142	−	0.842854i	$-0.319126\pi$
$101$	−467.792	−	810.240i	−0.460862	−	0.798237i	−0.999004	+	0.0446174i	$0.985793\pi$
$102$	−762.008	−	1319.84i	−0.739706	−	1.28121i
$103$	−80.5284			−0.0770359			−0.0385180	−	0.999258i	$-0.512264\pi$
$103$	−80.5284			−0.0770359			−0.0385180	+	0.999258i	$0.512264\pi$
$104$	−207.007	−	13.5587i	−0.195180	−	0.0127840i
$105$	1583.38			1.47164
$106$	−950.269	−	1645.91i	−0.870738	−	1.50816i
$107$	−475.818	−	824.141i	−0.429898	−	0.744605i	0.566966	−	0.823741i	$-0.308117\pi$
$107$	−475.818	−	824.141i	−0.429898	−	0.744605i	−0.996864	+	0.0791363i	$0.974784\pi$
$108$	708.641	−	1227.40i	0.631380	−	1.09358i
$109$	967.642			0.850306			0.425153	−	0.905122i	$-0.360220\pi$
$109$	967.642			0.850306			0.425153	+	0.905122i	$0.360220\pi$
$110$	139.019	−	240.788i	0.120500	−	0.208711i
$111$	458.858	−	794.765i	0.392368	−	0.679601i
$112$	−2585.29			−2.18114
$113$	53.8752	−	93.3147i	0.0448509	−	0.0776841i	−0.842728	−	0.538339i	$-0.819052\pi$
$113$	53.8752	−	93.3147i	0.0448509	−	0.0776841i	0.887579	+	0.460655i	$0.152385\pi$
$114$	−16.0560	−	27.8099i	−0.0131911	−	0.0228477i
$115$	−394.183	−	682.745i	−0.319633	−	0.553620i
$116$	679.498			0.543877
$117$	−1314.91	+	1968.09i	−1.03900	+	1.55513i
$118$	135.707			0.105872
$119$	807.978	+	1399.46i	0.622414	+	1.07805i
$120$	97.4055	+	168.711i	0.0740989	+	0.128343i
$121$	561.396	−	972.367i	0.421785	−	0.730553i
$122$	1938.43			1.43850
$123$	164.498	−	284.919i	0.120588	−	0.208864i
$124$	−123.604	+	214.088i	−0.0895158	+	0.155046i
$125$	−125.000			−0.0894427
$126$	−3500.23	+	6062.58i	−2.47481	+	4.28649i
$127$	119.853	+	207.592i	0.0837421	+	0.145046i	0.904855	−	0.425721i	$-0.139979\pi$
$127$	119.853	+	207.592i	0.0837421	+	0.145046i	−0.821112	+	0.570767i	$0.806646\pi$
$128$	−280.338	−	485.559i	−0.193583	−	0.335295i
$129$	−3910.79			−2.66919
$130$	399.499	+	810.013i	0.269526	+	0.546484i
$131$	−451.643			−0.301223			−0.150611	−	0.988593i	$-0.548124\pi$
$131$	−451.643			−0.301223			−0.150611	+	0.988593i	$0.548124\pi$
$132$	435.162	+	753.723i	0.286939	+	0.496994i
$133$	17.0247	+	29.4876i	0.0110994	+	0.0192248i
$134$	875.763	−	1516.87i	0.564585	−	0.977890i
$135$	1034.28			0.659382
$136$	−99.4097	+	172.183i	−0.0626788	+	0.108563i
$137$	−869.567	+	1506.13i	−0.542278	+	0.939253i	0.456495	+	0.889726i	$0.349105\pi$
$137$	−869.567	+	1506.13i	−0.542278	+	0.939253i	−0.998773	+	0.0495272i	$0.984229\pi$
$138$	5349.19			3.29966
$139$	1164.70	−	2017.32i	0.710709	−	1.23098i	−0.253882	−	0.967235i	$-0.581707\pi$
$139$	1164.70	−	2017.32i	0.710709	−	1.23098i	0.964591	−	0.263750i	$-0.0849593\pi$
$140$	616.168	+	1067.23i	0.371969	+	0.644269i
$141$	1448.21	+	2508.38i	0.864974	+	1.49818i
$142$	239.607			0.141601
$143$	−299.163	−	606.575i	−0.174946	−	0.354716i
$144$	−3629.20			−2.10023
$145$	247.936	+	429.437i	0.142000	+	0.245951i
$146$	150.629	+	260.897i	0.0853844	+	0.147890i
$147$	4186.04	−	7250.43i	2.34870	−	4.06806i
$148$	714.254			0.396698
$149$	−620.360	+	1074.50i	−0.341086	+	0.590779i	−0.984635	−	0.174626i	$-0.944128\pi$
$149$	−620.360	+	1074.50i	−0.341086	+	0.590779i	0.643548	+	0.765406i	$0.277462\pi$
$150$	424.072	−	734.515i	0.230836	−	0.399819i
$151$	2264.68			1.22051			0.610255	−	0.792205i	$-0.291067\pi$
$151$	2264.68			1.22051			0.610255	+	0.792205i	$0.291067\pi$
$152$	−2.09463	+	3.62801i	−0.00111774	+	0.00193599i
$153$	1134.23	+	1964.54i	0.599326	+	1.03806i
$154$	−1000.17	−	1732.35i	−0.523351	−	0.906471i
$155$	−180.403			−0.0934859
$156$	−2821.10	−	184.778i	−1.44788	−	0.0948339i
$157$	635.607			0.323102			0.161551	−	0.986864i	$-0.448350\pi$
$157$	635.607			0.323102			0.161551	+	0.986864i	$0.448350\pi$
$158$	−1782.59	−	3087.54i	−0.897567	−	1.55463i
$159$	2170.72	+	3759.81i	1.08270	+	1.87530i
$160$	−603.896	+	1045.98i	−0.298389	+	0.516824i
$161$	−5671.90			−2.77645
$162$	−881.691	+	1527.13i	−0.427606	+	0.740635i
$163$	−1342.04	+	2324.49i	−0.644889	+	1.11698i	0.339438	+	0.940628i	$0.389763\pi$
$163$	−1342.04	+	2324.49i	−0.644889	+	1.11698i	−0.984327	+	0.176352i	$0.943570\pi$
$164$	256.056			0.121918
$165$	−317.565	+	550.039i	−0.149833	+	0.259518i
$166$	623.617	+	1080.14i	0.291579	+	0.505029i
$167$	−209.158	−	362.272i	−0.0969168	−	0.167865i	0.813490	−	0.581579i	$-0.197565\pi$
$167$	−209.158	−	362.272i	−0.0969168	−	0.167865i	−0.910407	+	0.413714i	$0.864231\pi$
$168$	1401.57			0.643650
$169$	2178.23	+	286.572i	0.991457	+	0.130438i
$170$	865.596			0.390519
$171$	23.8990	+	41.3942i	0.0106877	+	0.0185117i
$172$	−1521.87	−	2635.96i	−0.674661	−	1.16855i
$173$	−1276.97	+	2211.77i	−0.561192	+	0.972012i	0.436201	+	0.899849i	$0.356324\pi$
$173$	−1276.97	+	2211.77i	−0.561192	+	0.972012i	−0.997393	+	0.0721632i	$0.977010\pi$
$174$	−3364.57			−1.46590
$175$	−449.656	+	778.827i	−0.194233	+	0.336422i
$176$	518.511	−	898.088i	0.222070	−	0.384636i
$177$	−310.000			−0.131644
$178$	1666.07	−	2885.72i	0.701558	−	1.21513i
$179$	−1775.43	−	3075.14i	−0.741352	−	1.28406i	−0.951880	−	0.306472i	$-0.900851\pi$
$179$	−1775.43	−	3075.14i	−0.741352	−	1.28406i	0.210527	−	0.977588i	$-0.432482\pi$
$180$	864.967	+	1498.17i	0.358171	+	0.620371i
$181$	2666.39			1.09498			0.547489	−	0.836813i	$-0.315584\pi$
$181$	2666.39			1.09498			0.547489	+	0.836813i	$0.315584\pi$
$182$	6483.98	+	424.692i	2.64079	+	0.172968i
$183$	−4428.02			−1.78868
$184$	−348.921	−	604.350i	−0.139798	−	0.242137i
$185$	260.618	+	451.403i	0.103573	+	0.179394i
$186$	612.031	−	1060.07i	0.241271	−	0.417893i
$187$	−648.198			−0.253481
$188$	−1127.14	+	1952.26i	−0.437260	+	0.757356i
$189$	3720.56	−	6444.20i	1.43191	−	2.48014i
$190$	18.2387			0.00696408
$191$	1682.32	−	2913.87i	0.637322	−	1.10387i	−0.348696	−	0.937236i	$-0.613375\pi$
$191$	1682.32	−	2913.87i	0.637322	−	1.10387i	0.986018	−	0.166638i	$-0.0532912\pi$
$192$	−1566.81	−	2713.80i	−0.588931	−	1.02006i
$193$	−1718.46	−	2976.45i	−0.640918	−	1.11010i	−0.985228	−	0.171247i	$-0.945221\pi$
$193$	−1718.46	−	2976.45i	−0.640918	−	1.11010i	0.344310	−	0.938856i	$-0.388113\pi$
$194$	−348.291			−0.128896
$195$	−912.587	−	1850.34i	−0.335137	−	0.679514i
$196$	6515.95			2.37462
$197$	373.955	+	647.709i	0.135245	+	0.234251i	0.925691	−	0.378281i	$-0.123485\pi$
$197$	373.955	+	647.709i	0.135245	+	0.234251i	−0.790446	+	0.612531i	$0.790151\pi$
$198$	−1404.03	−	2431.84i	−0.503938	−	0.872847i
$199$	−1413.44	+	2448.15i	−0.503498	+	0.872084i	0.496494	+	0.868040i	$0.334620\pi$
$199$	−1413.44	+	2448.15i	−0.503498	+	0.872084i	−0.999992	+	0.00404361i	$0.998713\pi$
$200$	−110.647			−0.0391196
$201$	−2000.53	+	3465.02i	−0.702022	+	1.21594i
$202$	−1802.76	+	3122.48i	−0.627931	+	1.08761i
$203$	3567.55			1.23346
$204$	−1354.76	+	2346.51i	−0.464961	+	0.805337i
$205$	93.4300	+	161.826i	0.0318314	+	0.0551336i
$206$	155.169	+	268.761i	0.0524813	+	0.0909002i
$207$	−7962.12			−2.67346
$208$	1490.05	+	3021.18i	0.496712	+	1.00712i
$209$	−13.6580			−0.00452030
$210$	−3050.99	−	5284.46i	−1.00256	−	1.73649i
$211$	−2376.93	−	4116.96i	−0.775518	−	1.34324i	−0.934503	−	0.355956i	$-0.884155\pi$
$211$	−2376.93	−	4116.96i	−0.775518	−	1.34324i	0.158985	−	0.987281i	$-0.449178\pi$
$212$	−1689.46	+	2926.24i	−0.547325	+	0.947995i
$213$	−547.340			−0.176071
$214$	−1833.69	+	3176.05i	−0.585742	+	1.01453i
$215$	1110.61	−	1923.63i	0.352292	−	0.610187i
$216$	915.519			0.288394
$217$	−648.954	+	1124.02i	−0.203013	+	0.351629i
$218$	−1864.54	−	3229.47i	−0.579277	−	1.00334i
$219$	−344.085	−	595.973i	−0.106170	−	0.183891i
$220$	−494.319			−0.151486
$221$	1169.73	−	1750.79i	0.356038	−	0.532899i
$222$	−3536.66			−1.06921
$223$	1799.06	+	3116.06i	0.540242	+	0.935727i	0.998890	+	0.0471085i	$0.0150006\pi$
$223$	1799.06	+	3116.06i	0.540242	+	0.935727i	−0.458648	+	0.888618i	$0.651666\pi$
$224$	4344.73	+	7525.29i	1.29596	+	2.24466i
$225$	−631.220	+	1093.31i	−0.187028	+	0.323942i
$226$	−415.246			−0.122220
$227$	3255.47	−	5638.64i	0.951864	−	1.64868i	0.210476	−	0.977599i	$-0.432499\pi$
$227$	3255.47	−	5638.64i	0.951864	−	1.64868i	0.741388	−	0.671077i	$-0.234168\pi$
$228$	−28.5457	+	49.4427i	−0.00829161	+	0.0143615i
$229$	2720.12			0.784938			0.392469	−	0.919765i	$-0.371621\pi$
$229$	2720.12			0.784938			0.392469	+	0.919765i	$0.371621\pi$
$230$	−1519.09	+	2631.14i	−0.435504	+	0.754315i
$231$	2284.72	+	3957.25i	0.650751	+	1.12713i
$232$	219.467	+	380.128i	0.0621065	+	0.107572i
$233$	−5348.65			−1.50387			−0.751935	−	0.659237i	$-0.770879\pi$
$233$	−5348.65			−1.50387			−0.751935	+	0.659237i	$0.770879\pi$
$234$	9102.11	+	596.176i	2.54284	+	0.166552i
$235$	−1645.08			−0.456653
$236$	−120.636	−	208.947i	−0.0332743	−	0.0576327i
$237$	4072.03	+	7052.96i	1.11606	+	1.93308i
$238$	3113.76	−	5393.19i	0.848047	−	1.46886i
$239$	55.0617			0.0149023			0.00745114	−	0.999972i	$-0.497628\pi$
$239$	55.0617			0.0149023			0.00745114	+	0.999972i	$0.497628\pi$
$240$	1581.70	−	2739.58i	0.425409	−	0.736831i
$241$	746.589	−	1293.13i	0.199552	−	0.345634i	−0.748831	−	0.662761i	$-0.769385\pi$
$241$	746.589	−	1293.13i	0.199552	−	0.345634i	0.948383	+	0.317127i	$0.102718\pi$
$242$	−4326.98			−1.14938
$243$	−778.484	+	1348.37i	−0.205513	+	0.355960i
$244$	−1723.15	−	2984.59i	−0.452105	−	0.783068i
$245$	2377.55	+	4118.03i	0.619983	+	1.07384i
$246$	−1267.87			−0.328605
$247$	24.6470	−	36.8904i	0.00634919	−	0.00950315i
$248$	−159.688			−0.0408880
$249$	−1424.54	−	2467.38i	−0.362558	−	0.627968i
$250$	240.861	+	417.183i	0.0609335	+	0.105540i
$251$	−819.028	+	1418.60i	−0.205963	+	0.356738i	−0.950439	−	0.310911i	$-0.899366\pi$
$251$	−819.028	+	1418.60i	−0.205963	+	0.356738i	0.744476	+	0.667649i	$0.232699\pi$
$252$	12446.0			3.11121
$253$	1137.57	−	1970.32i	0.282680	−	0.489617i
$254$	461.887	−	800.011i	0.114100	−	0.197627i
$255$	−1977.30			−0.485583
$256$	−2504.20	+	4337.40i	−0.611377	+	1.05894i
$257$	−489.020	−	847.007i	−0.118693	−	0.205583i	0.800557	−	0.599257i	$-0.204537\pi$
$257$	−489.020	−	847.007i	−0.118693	−	0.205583i	−0.919250	+	0.393674i	$0.871204\pi$
$258$	7535.64	+	13052.1i	1.81840	+	3.14957i
$259$	3750.03			0.899673
$260$	892.038	−	1335.16i	0.212776	−	0.318473i
$261$	5008.07			1.18771
$262$	870.264	+	1507.34i	0.205210	+	0.355435i
$263$	−1073.47	−	1859.31i	−0.251685	−	0.435930i	0.712305	−	0.701870i	$-0.247651\pi$
$263$	−1073.47	−	1859.31i	−0.251685	−	0.435930i	−0.963990	+	0.265939i	$0.914318\pi$
$264$	−281.101	+	486.881i	−0.0655324	+	0.113505i
$265$	−2465.82			−0.571599
$266$	65.6092	−	113.638i	0.0151231	−	0.0261941i
$267$	−3805.85	+	6591.92i	−0.872338	+	1.51093i
$268$	−3114.00			−0.709769
$269$	2777.88	−	4811.42i	0.629629	−	1.09055i	−0.357998	−	0.933722i	$-0.616540\pi$
$269$	2777.88	−	4811.42i	0.629629	−	1.09055i	0.987626	−	0.156826i	$-0.0501262\pi$
$270$	−1992.94	−	3451.87i	−0.449209	−	0.778052i
$271$	182.636	+	316.335i	0.0409386	+	0.0709077i	0.885769	−	0.464127i	$-0.153632\pi$
$271$	182.636	+	316.335i	0.0409386	+	0.0709077i	−0.844830	+	0.535035i	$0.820299\pi$
$272$	3228.49			0.719690
$273$	−14811.5	−	970.135i	−3.28364	−	0.215074i
$274$	6702.22			1.47772
$275$	−180.368	−	312.406i	−0.0395512	−	0.0685046i
$276$	−4755.11	−	8236.10i	−1.03704	−	1.79621i
$277$	−2784.63	+	4823.13i	−0.604016	+	1.04619i	0.388190	+	0.921579i	$0.373100\pi$
$277$	−2784.63	+	4823.13i	−0.604016	+	1.04619i	−0.992206	+	0.124607i	$0.960233\pi$
$278$	−8976.98			−1.93670
$279$	−910.992	+	1577.88i	−0.195483	+	0.338586i
$280$	−398.025	+	689.399i	−0.0849518	+	0.147141i
$281$	−666.014			−0.141392			−0.0706958	−	0.997498i	$-0.522522\pi$
$281$	−666.014			−0.141392			−0.0706958	+	0.997498i	$0.522522\pi$
$282$	5581.07	−	9666.70i	1.17854	−	2.04129i
$283$	1301.73	+	2254.67i	0.273428	+	0.473591i	0.969737	−	0.244151i	$-0.0785092\pi$
$283$	1301.73	+	2254.67i	0.273428	+	0.473591i	−0.696309	+	0.717742i	$0.745176\pi$
$284$	−212.996	−	368.920i	−0.0445035	−	0.0770823i
$285$	−41.6632			−0.00865935
$286$	−1447.97	+	2167.25i	−0.299371	+	0.448084i
$287$	1344.36			0.276499
$288$	6099.06	+	10563.9i	1.24788	+	2.16140i
$289$	1447.51	+	2507.15i	0.294628	+	0.510310i
$290$	955.488	−	1654.95i	0.193476	−	0.335111i
$291$	795.611			0.160273
$292$	267.800	−	463.843i	0.0536706	−	0.0929602i
$293$	4414.91	−	7646.86i	0.880280	−	1.52469i	0.0292506	−	0.999572i	$-0.490688\pi$
$293$	4414.91	−	7646.86i	0.880280	−	1.52469i	0.851030	−	0.525118i	$-0.175979\pi$
$294$	−32264.1			−6.40027
$295$	88.0355	−	152.482i	0.0173750	−	0.0300944i
$296$	230.692	+	399.571i	0.0452998	+	0.0784615i
$297$	1492.40	+	2584.92i	0.291576	+	0.505024i
$298$	4781.45			0.929470
$299$	3269.02	+	6628.18i	0.632283	+	1.28200i
$300$	−1507.90			−0.290196
$301$	−7990.25	−	13839.5i	−1.53007	−	2.65015i
$302$	−4363.78	−	7558.28i	−0.831480	−	1.44017i
$303$	4118.10	−	7132.77i	0.780789	−	1.35237i
$304$	68.0265			0.0128342
$305$	1257.49	−	2178.04i	0.236078	−	0.408899i
$306$	4371.05	−	7570.88i	0.816590	−	1.41437i
$307$	271.114			0.0504016			0.0252008	−	0.999682i	$-0.491977\pi$
$307$	271.114			0.0504016			0.0252008	+	0.999682i	$0.491977\pi$
$308$	−1778.19	+	3079.91i	−0.328966	+	0.569786i
$309$	−354.457	−	613.937i	−0.0652568	−	0.113028i
$310$	347.616	+	602.088i	0.0636879	+	0.110311i
$311$	−7015.73			−1.27918			−0.639591	−	0.768716i	$-0.720896\pi$
$311$	−7015.73			−1.27918			−0.639591	+	0.768716i	$0.720896\pi$
$312$	−807.800	−	1637.87i	−0.146579	−	0.297200i
$313$	−7678.66			−1.38666			−0.693328	−	0.720622i	$-0.743856\pi$
$313$	−7678.66			−1.38666			−0.693328	+	0.720622i	$0.743856\pi$
$314$	−1224.74	−	2121.31i	−0.220115	−	0.381251i
$315$	4541.31	+	7865.78i	0.812298	+	1.40694i
$316$	−3169.24	+	5489.29i	−0.564189	+	0.977204i
$317$	−8354.12			−1.48017			−0.740085	−	0.672513i	$-0.765215\pi$
$317$	−8354.12			−1.48017			−0.740085	+	0.672513i	$0.765215\pi$
$318$	8365.47	−	14489.4i	1.47520	−	2.55512i
$319$	−715.513	+	1239.31i	−0.125583	+	0.217517i
$320$	1779.81			0.310919
$321$	4188.76	−	7255.14i	0.728329	−	1.26150i
$322$	10929.1	+	18929.7i	1.89147	+	3.27613i
$323$	−21.2602	−	36.8238i	−0.00366239	−	0.00634344i
$324$	3135.08			0.537566
$325$	1169.30	+	76.5875i	0.199572	+	0.0130717i
$326$	10343.9			1.75734
$327$	4259.21	+	7377.17i	0.720290	+	1.24758i
$328$	82.7020	+	143.244i	0.0139221	+	0.0241138i
$329$	−5917.77	+	10249.9i	−0.991663	+	1.71761i
$330$	2447.64			0.408298
$331$	−1557.36	+	2697.42i	−0.258611	+	0.447927i	−0.965870	−	0.259027i	$-0.916598\pi$
$331$	−1557.36	+	2697.42i	−0.258611	+	0.447927i	0.707259	+	0.706954i	$0.249931\pi$
$332$	1108.72	−	1920.35i	0.183279	−	0.317449i
$333$	5264.23			0.866300
$334$	−806.046	+	1396.11i	−0.132050	+	0.228718i
$335$	−1136.24	−	1968.03i	−0.185312	−	0.320970i
$336$	−11379.5	−	19709.9i	−1.84763	−	3.20019i
$337$	3747.75			0.605796			0.302898	−	0.953023i	$-0.402046\pi$
$337$	3747.75			0.605796			0.302898	+	0.953023i	$0.402046\pi$
$338$	−3240.78	−	7821.95i	−0.521524	−	1.25875i
$339$	948.557			0.151972
$340$	−769.463	−	1332.75i	−0.122735	−	0.212584i
$341$	−260.311	−	450.872i	−0.0413391	−	0.0716014i
$342$	92.1012	−	159.524i	0.0145622	−	0.0252224i
$343$	21871.9			3.44307
$344$	983.081	−	1702.75i	0.154082	−	0.266878i
$345$	3470.10	−	6010.39i	0.541519	−	0.937938i
$346$	9842.29			1.52926
$347$	2971.20	−	5146.26i	0.459660	−	0.796155i	−0.539282	−	0.842125i	$-0.681304\pi$
$347$	2971.20	−	5146.26i	0.459660	−	0.796155i	0.998943	+	0.0459699i	$0.0146378\pi$
$348$	2990.90	+	5180.39i	0.460716	+	0.797983i
$349$	−2416.61	−	4185.69i	−0.370653	−	0.641991i	0.619013	−	0.785381i	$-0.287533\pi$
$349$	−2416.61	−	4185.69i	−0.370653	−	0.641991i	−0.989666	+	0.143390i	$0.954200\pi$
$350$	3465.74			0.529290
$351$	−9675.05	−	633.703i	−1.47127	−	0.0963663i
$352$	−3485.54			−0.527784
$353$	3042.51	+	5269.79i	0.458744	+	0.794568i	0.998895	−	0.0470002i	$-0.0149661\pi$
$353$	3042.51	+	5269.79i	0.458744	+	0.794568i	−0.540151	+	0.841568i	$0.681633\pi$
$354$	597.335	+	1034.61i	0.0896836	+	0.155337i
$355$	155.437	−	269.224i	0.0232386	−	0.0402505i
$356$	−5924.15			−0.881964
$357$	−7112.85	+	12319.8i	−1.05449	+	1.82643i
$358$	−6842.11	+	11850.9i	−1.01010	+	1.74955i
$359$	10674.8			1.56935			0.784675	−	0.619908i	$-0.212830\pi$
$359$	10674.8			1.56935			0.784675	+	0.619908i	$0.212830\pi$
$360$	−558.741	+	967.767i	−0.0818006	+	0.141683i
$361$	3429.05	+	5939.29i	0.499935	+	0.865912i
$362$	−5137.82	−	8898.97i	−0.745961	−	1.29204i
$363$	9884.25			1.42917
$364$	−5109.98	−	10360.8i	−0.735812	−	1.49191i
$365$	390.861			0.0560509
$366$	8532.28	+	14778.3i	1.21855	+	2.11059i
$367$	1741.04	+	3015.58i	0.247634	+	0.428915i	0.962869	−	0.269969i	$-0.0870136\pi$
$367$	1741.04	+	3015.58i	0.247634	+	0.428915i	−0.715235	+	0.698884i	$0.753680\pi$
$368$	−5665.88	+	9813.60i	−0.802594	+	1.39013i
$369$	1887.20			0.266243
$370$	1004.36	−	1739.60i	0.141120	−	0.244426i
$371$	−8870.15	+	15363.5i	−1.24128	+	2.14996i
$372$	−2176.24			−0.303314
$373$	6999.92	−	12124.2i	0.971694	−	1.68302i	0.281256	−	0.959633i	$-0.409249\pi$
$373$	6999.92	−	12124.2i	0.971694	−	1.68302i	0.690438	−	0.723391i	$-0.257418\pi$
$374$	1249.00	+	2163.34i	0.172686	+	0.299100i
$375$	−550.205	−	952.982i	−0.0757665	−	0.131231i
$376$	−1456.19			−0.199726
$377$	−2056.17	−	4169.04i	−0.280897	−	0.569539i
$378$	−28676.4			−3.90199
$379$	−4182.48	−	7244.26i	−0.566859	−	0.981828i	−0.996874	−	0.0790066i	$-0.974825\pi$
$379$	−4182.48	−	7244.26i	−0.566859	−	0.981828i	0.430015	−	0.902822i	$-0.358508\pi$
$380$	−16.2131	−	28.0820i	−0.00218873	−	0.00379099i
$381$	−1055.10	+	1827.49i	−0.141875	+	0.245735i
$382$	−12966.6			−1.73672
$383$	−4807.30	+	8326.49i	−0.641362	+	1.11087i	0.343767	+	0.939055i	$0.388297\pi$
$383$	−4807.30	+	8326.49i	−0.641362	+	1.11087i	−0.985129	+	0.171816i	$0.945036\pi$
$384$	2467.89	−	4274.51i	0.327966	−	0.568053i
$385$	−2595.31			−0.343556
$386$	−6622.53	+	11470.6i	−0.873259	+	1.51253i
$387$	−11216.6	−	19427.7i	−1.47331	−	2.55185i
$388$	309.610	+	536.261i	0.0405105	+	0.0701663i
$389$	5496.77			0.716445			0.358223	−	0.933636i	$-0.383383\pi$
$389$	5496.77			0.716445			0.358223	+	0.933636i	$0.383383\pi$
$390$	−4416.98	+	6611.11i	−0.573493	+	0.858376i
$391$	7083.00			0.916120
$392$	2104.55	+	3645.18i	0.271162	+	0.469667i
$393$	−1987.97	−	3443.26i	−0.255165	−	0.441958i
$394$	1441.14	−	2496.12i	0.184273	−	0.319170i
$395$	−4625.59			−0.589211
$396$	−2496.19	+	4323.53i	−0.316763	+	0.548650i
$397$	3983.93	−	6900.37i	0.503647	−	0.872341i	−0.496345	−	0.868126i	$-0.665325\pi$
$397$	3983.93	−	6900.37i	0.503647	−	0.872341i	0.999991	−	0.00421578i	$-0.00134193\pi$
$398$	10894.1			1.37205
$399$	−149.873	+	259.587i	−0.0188046	+	0.0325705i
$400$	898.359	+	1556.00i	0.112295	+	0.194500i
$401$	−794.863	−	1376.74i	−0.0989865	−	0.171450i	0.812279	−	0.583269i	$-0.198227\pi$
$401$	−794.863	−	1376.74i	−0.0989865	−	0.171450i	−0.911265	+	0.411820i	$0.864893\pi$
$402$	15419.2			1.91303
$403$	1687.56	+	110.533i	0.208594	+	0.0136626i
$404$	6410.20			0.789405
$405$	1143.93	+	1981.35i	0.140352	+	0.243096i
$406$	−6874.25	−	11906.6i	−0.840304	−	1.45545i
$407$	−752.112	+	1302.70i	−0.0915990	+	0.158654i
$408$	−1750.26			−0.212380
$409$	3706.03	−	6419.03i	0.448047	−	0.776041i	−0.550212	−	0.835025i	$-0.685453\pi$
$409$	3706.03	−	6419.03i	0.448047	−	0.776041i	0.998259	+	0.0589847i	$0.0187863\pi$
$410$	360.058	−	623.638i	0.0433707	−	0.0751203i
$411$	−15310.1			−1.83745
$412$	275.872	−	477.824i	0.0329885	−	0.0571377i
$413$	−633.371	−	1097.03i	−0.0754628	−	0.130705i
$414$	15342.1	+	26573.3i	1.82131	+	3.15460i
$415$	1618.20			0.191408
$416$	6289.95	−	9414.48i	0.741322	−	1.10957i
$417$	20506.4			2.40815
$418$	26.3174	+	45.5831i	0.00307949	+	0.00533383i
$419$	353.667	+	612.568i	0.0412357	+	0.0714223i	0.885907	−	0.463864i	$-0.153537\pi$
$419$	353.667	+	612.568i	0.0412357	+	0.0714223i	−0.844671	+	0.535286i	$0.820204\pi$
$420$	−5424.29	+	9395.15i	−0.630186	+	1.09151i
$421$	8451.82			0.978424			0.489212	−	0.872165i	$-0.337284\pi$
$421$	8451.82			0.978424			0.489212	+	0.872165i	$0.337284\pi$
$422$	−9160.13	+	15865.8i	−1.05665	+	1.83018i
$423$	−8307.28	+	14388.6i	−0.954878	+	1.65390i
$424$	−2182.68			−0.250001
$425$	561.525	−	972.590i	0.0640894	−	0.111006i
$426$	1054.66	+	1826.73i	0.119950	+	0.207759i
$427$	−9047.02	−	15669.9i	−1.02533	−	1.77592i
$428$	6520.18			0.736366
$429$	3307.64	−	4950.70i	0.372247	−	0.557161i
$430$	−8560.04			−0.960004
$431$	7538.05	+	13056.3i	0.842447	+	1.45916i	0.887820	+	0.460192i	$0.152219\pi$
$431$	7538.05	+	13056.3i	0.842447	+	1.45916i	−0.0453721	+	0.998970i	$0.514447\pi$
$432$	−7433.23	−	12874.7i	−0.827851	−	1.43388i
$433$	4041.85	−	7000.69i	0.448588	−	0.776978i	−0.549706	−	0.835358i	$-0.685260\pi$
$433$	4041.85	−	7000.69i	0.448588	−	0.776978i	0.998294	+	0.0583802i	$0.0185936\pi$
$434$	5001.84			0.553217
$435$	−2182.65	+	3780.46i	−0.240575	+	0.416687i
$436$	−3314.92	+	5741.62i	−0.364119	+	0.630673i
$437$	149.244			0.0163371
$438$	−1326.03	+	2296.74i	−0.144657	+	0.250554i
$439$	−811.752	−	1406.00i	−0.0882524	−	0.152858i	0.818520	−	0.574478i	$-0.194795\pi$
$439$	−811.752	−	1406.00i	−0.0882524	−	0.152858i	−0.906773	+	0.421620i	$0.861462\pi$
$440$	−159.657	−	276.534i	−0.0172985	−	0.0299619i
$441$	48024.2			5.18564
$442$	−8097.12	−	530.351i	−0.871359	−	0.0570729i
$443$	−5424.17			−0.581738			−0.290869	−	0.956763i	$-0.593944\pi$
$443$	−5424.17			−0.581738			−0.290869	+	0.956763i	$0.593944\pi$
$444$	3143.88	+	5445.37i	0.336041	+	0.582040i
$445$	−2161.61	−	3744.02i	−0.230270	−	0.398839i
$446$	6933.16	−	12008.6i	0.736087	−	1.27494i
$447$	−10922.4			−1.15573
$448$	6402.40	−	11089.3i	0.675190	−	1.16946i
$449$	1688.72	−	2924.95i	0.177496	−	0.307432i	−0.763526	−	0.645777i	$-0.776534\pi$
$449$	1688.72	−	2924.95i	0.177496	−	0.307432i	0.941022	+	0.338345i	$0.109867\pi$
$450$	4865.15			0.509657
$451$	−269.628	+	467.009i	−0.0281514	+	0.0487597i
$452$	369.129	+	639.350i	0.0384123	+	0.0665320i
$453$	9968.29	+	17265.6i	1.03389	+	1.79075i
$454$	−25091.7			−2.59385
$455$	4683.44	−	7009.95i	0.482557	−	0.722267i
$456$	−36.8793			−0.00378735
$457$	940.205	+	1628.48i	0.0962384	+	0.166690i	0.910125	−	0.414334i	$-0.135986\pi$
$457$	940.205	+	1628.48i	0.0962384	+	0.166690i	−0.813886	+	0.581024i	$0.802652\pi$
$458$	−5241.37	−	9078.31i	−0.534745	−	0.926205i
$459$	−4646.19	+	8047.44i	−0.472474	+	0.818349i
$460$	5401.53			0.547495
$461$	−8368.98	+	14495.5i	−0.845515	+	1.46447i	0.0396589	+	0.999213i	$0.487373\pi$
$461$	−8368.98	+	14495.5i	−0.845515	+	1.46447i	−0.885174	+	0.465261i	$0.845960\pi$
$462$	8804.78	−	15250.3i	0.886657	−	1.53574i
$463$	−5307.74			−0.532768			−0.266384	−	0.963867i	$-0.585829\pi$
$463$	−5307.74			−0.532768			−0.266384	+	0.963867i	$0.585829\pi$
$464$	3563.76	−	6172.62i	0.356560	−	0.617579i
$465$	−794.068	−	1375.37i	−0.0791915	−	0.137164i
$466$	10306.2	+	17850.9i	1.02452	+	1.77452i
$467$	6648.02			0.658745			0.329372	−	0.944200i	$-0.393163\pi$
$467$	6648.02			0.658745			0.329372	+	0.944200i	$0.393163\pi$
$468$	−7173.31	−	14544.4i	−0.708518	−	1.43657i
$469$	−16349.4			−1.60969
$470$	3169.89	+	5490.40i	0.311098	+	0.538837i
$471$	2797.71	+	4845.78i	0.273698	+	0.474059i
$472$	77.9269	−	134.973i	0.00759931	−	0.0131624i
$473$	6410.15			0.623127
$474$	15692.7	−	27180.5i	1.52065	−	2.63384i
$475$	11.8317	−	20.4932i	0.00114290	−	0.00197956i
$476$	−11071.8			−1.06612
$477$	−12451.8	+	21567.1i	−1.19524	+	2.07021i
$478$	−106.098	−	183.766i	−0.0101523	−	0.0175843i
$479$	−6611.23	−	11451.0i	−0.630636	−	1.09229i	−0.987422	−	0.158107i	$-0.949461\pi$
$479$	−6611.23	−	11451.0i	−0.630636	−	1.09229i	0.356786	−	0.934186i	$-0.383873\pi$
$480$	−10632.5			−1.01105
$481$	−2161.34	−	4382.28i	−0.204883	−	0.415415i
$482$	−5754.36			−0.543784
$483$	−24965.6	−	43241.7i	−2.35192	−	4.07364i
$484$	3846.43	+	6662.21i	0.361235	+	0.625678i
$485$	−225.942	+	391.343i	−0.0211536	+	0.0366391i
$486$	6000.20			0.560030
$487$	2364.82	−	4095.99i	0.220042	−	0.381124i	−0.734779	−	0.678307i	$-0.762714\pi$
$487$	2364.82	−	4095.99i	0.220042	−	0.381124i	0.954820	+	0.297183i	$0.0960473\pi$
$488$	1113.10	−	1927.95i	0.103254	−	0.178840i
$489$	−23628.7			−2.18513
$490$	9162.52	−	15869.9i	0.844736	−	1.46312i
$491$	−3813.17	−	6604.60i	−0.350480	−	0.607050i	0.635853	−	0.771810i	$-0.280648\pi$
$491$	−3813.17	−	6604.60i	−0.350480	−	0.607050i	−0.986334	+	0.164760i	$0.947315\pi$
$492$	1127.07	+	1952.13i	0.103276	+	0.178880i
$493$	−4455.11			−0.406994
$494$	−170.612	−	11.1749i	−0.0155389	−	0.00101778i
$495$	−3643.25			−0.330812
$496$	1296.53	+	2245.66i	0.117371	+	0.203293i
$497$	−1118.29	−	1936.93i	−0.100930	−	0.174815i
$498$	−5489.87	+	9508.73i	−0.493990	+	0.855615i
$499$	7607.19			0.682454			0.341227	−	0.939981i	$-0.389158\pi$
$499$	7607.19			0.682454			0.341227	+	0.939981i	$0.389158\pi$
$500$	428.222	−	741.702i	0.0383013	−	0.0663398i
$501$	1841.27	−	3189.18i	0.164196	−	0.284395i
$502$	6312.69			0.561254
$503$	−5374.38	+	9308.70i	−0.476405	+	0.825158i	−0.999635	−	0.0270338i	$-0.991394\pi$
$503$	−5374.38	+	9308.70i	−0.476405	+	0.825158i	0.523229	+	0.852192i	$0.324727\pi$
$504$	4019.86	+	6962.60i	0.355275	+	0.615355i
$505$	2338.96	+	4051.20i	0.206104	+	0.356982i
$506$	−8767.83			−0.770312
$507$	7402.99	+	17867.9i	0.648478	+	1.56517i
$508$	−1642.36			−0.143441
$509$	3576.87	+	6195.32i	0.311477	+	0.539494i	0.978682	−	0.205380i	$-0.0658429\pi$
$509$	3576.87	+	6195.32i	0.311477	+	0.539494i	−0.667205	+	0.744874i	$0.732510\pi$
$510$	3810.04	+	6599.18i	0.330807	+	0.572974i
$511$	1406.02	−	2435.30i	0.121720	−	0.210825i
$512$	14815.8			1.27885
$513$	−97.8986	+	169.565i	−0.00842559	+	0.0145935i
$514$	−1884.57	+	3264.17i	−0.161721	+	0.280110i
$515$	402.642			0.0344515
$516$	13397.5	−	23205.1i	1.14300	−	1.97974i
$517$	−2373.76	−	4111.47i	−0.201930	−	0.349753i
$518$	−7225.87	−	12515.6i	−0.612908	−	1.06159i
$519$	−22483.0			−1.90153
$520$	1035.03	+	67.7934i	0.0872871	+	0.00571719i
$521$	−9197.98			−0.773456			−0.386728	−	0.922194i	$-0.626395\pi$
$521$	−9197.98			−0.773456			−0.386728	+	0.922194i	$0.626395\pi$
$522$	−9649.97	−	16714.2i	−0.809134	−	1.40146i
$523$	9407.37	+	16294.0i	0.786531	+	1.36231i	0.928080	+	0.372380i	$0.121458\pi$
$523$	9407.37	+	16294.0i	0.786531	+	1.36231i	−0.141549	+	0.989931i	$0.545208\pi$
$524$	1547.23	−	2679.87i	0.128990	−	0.223418i
$525$	−7916.89			−0.658136
$526$	−4136.91	+	7165.34i	−0.342924	+	0.593961i
$527$	810.407	−	1403.67i	0.0669865	−	0.116024i
$528$	9129.19			0.752457
$529$	−6346.93	+	10993.2i	−0.521651	+	0.903526i
$530$	4751.34	+	8229.57i	0.389406	+	0.674471i
$531$	−889.116	−	1539.99i	−0.0726636	−	0.125857i
$532$	−233.291			−0.0190121
$533$	−774.830	−	1571.02i	−0.0629674	−	0.127671i
$534$	29333.7			2.37714
$535$	2379.09	+	4120.71i	0.192256	+	0.332997i
$536$	−1005.77	−	1742.05i	−0.0810500	−	0.140383i
$537$	15629.6	−	27071.3i	1.25599	−	2.17544i
$538$	−21410.6			−1.71575
$539$	−6861.32	+	11884.2i	−0.548308	+	0.949697i
$540$	−3543.21	+	6137.01i	−0.282362	+	0.489065i
$541$	−20708.1			−1.64567			−0.822837	−	0.568278i	$-0.807610\pi$
$541$	−20708.1			−1.64567			−0.822837	+	0.568278i	$0.807610\pi$
$542$	703.838	−	1219.08i	0.0557794	−	0.0966128i
$543$	11736.5	+	20328.2i	0.927550	+	1.60656i
$544$	−5425.65	−	9397.49i	−0.427615	−	0.740651i
$545$	−4838.21			−0.380268
$546$	25302.3	+	51302.3i	1.98322	+	4.02113i
$547$	15641.6			1.22264			0.611322	−	0.791382i	$-0.290638\pi$
$547$	15641.6			1.22264			0.611322	+	0.791382i	$0.290638\pi$
$548$	−5957.88	−	10319.3i	−0.464430	−	0.804417i
$549$	−12700.1	−	21997.2i	−0.987296	−	1.71005i
$550$	−695.095	+	1203.94i	−0.0538890	+	0.0933385i
$551$	−93.8724			−0.00725789
$552$	3071.65	−	5320.25i	0.236844	−	0.410226i
$553$	−16639.4	+	28820.2i	−1.27953	+	2.21621i
$554$	21462.7			1.64596
$555$	−2294.29	+	3973.82i	−0.175472	+	0.303927i
$556$	7980.00	+	13821.8i	0.608682	+	1.05427i
$557$	9576.31	+	16586.7i	0.728477	+	1.26176i	0.957527	+	0.288344i	$0.0931046\pi$
$557$	9576.31	+	16586.7i	0.728477	+	1.26176i	−0.229050	+	0.973415i	$0.573562\pi$
$558$	7021.51			0.532696
$559$	−11567.6	+	17313.9i	−0.875240	+	1.31002i
$560$	12926.5			0.975434
$561$	−2853.13	−	4941.77i	−0.214723	−	0.371910i
$562$	1283.33	+	2222.80i	0.0963240	+	0.166838i
$563$	6542.78	−	11332.4i	0.489779	−	0.848321i	−0.510152	−	0.860084i	$-0.670411\pi$
$563$	6542.78	−	11332.4i	0.489779	−	0.848321i	0.999931	+	0.0117627i	$0.00374427\pi$
$564$	−19845.0			−1.48160
$565$	−269.376	+	466.573i	−0.0200580	+	0.0347414i
$566$	5016.59	−	8688.98i	0.372549	−	0.645274i
$567$	16460.0			1.21915
$568$	137.589	−	238.311i	0.0101639	−	0.0176044i
$569$	−1922.92	−	3330.59i	−0.141675	−	0.245388i	0.786453	−	0.617651i	$-0.211915\pi$
$569$	−1922.92	−	3330.59i	−0.141675	−	0.245388i	−0.928127	+	0.372263i	$0.878582\pi$
$570$	80.2802	+	139.049i	0.00589924	+	0.0102178i
$571$	−10271.7			−0.752815			−0.376407	−	0.926454i	$-0.622841\pi$
$571$	−10271.7			−0.752815			−0.376407	+	0.926454i	$0.622841\pi$
$572$	4624.05	+	302.869i	0.338009	+	0.0221391i
$573$	29619.9			2.15949
$574$	−2590.43	−	4486.76i	−0.188367	−	0.326261i
$575$	1970.92	+	3413.73i	0.142944	+	0.247586i
$576$	8987.59	−	15567.0i	0.650144	−	1.12608i
$577$	2867.62			0.206899			0.103449	−	0.994635i	$-0.467012\pi$
$577$	2867.62			0.206899			0.103449	+	0.994635i	$0.467012\pi$
$578$	5578.35	−	9661.99i	0.401434	−	0.695304i
$579$	15128.0	−	26202.5i	1.08584	−	1.88073i
$580$	−3397.49			−0.243229
$581$	5821.06	−	10082.4i	0.415660	−	0.719944i
$582$	−1533.05	−	2655.32i	−0.109187	−	0.189118i
$583$	−3558.03	−	6162.68i	−0.252759	−	0.437791i
$584$	345.980			0.0245150
$585$	6574.55	−	9840.45i	0.464657	−	0.695475i
$586$	−34028.1			−2.39879
$587$	1320.89	+	2287.85i	0.0928775	+	0.160869i	0.908721	−	0.417404i	$-0.137060\pi$
$587$	1320.89	+	2287.85i	0.0928775	+	0.160869i	−0.815843	+	0.578273i	$0.803727\pi$
$588$	28680.8	+	49676.7i	2.01153	+	3.48407i
$589$	17.0758	−	29.5762i	0.00119456	−	0.00206905i
$590$	−678.537			−0.0473473
$591$	−3292.03	+	5701.96i	−0.229130	+	0.396865i
$592$	3746.05	−	6488.35i	0.260070	−	0.450455i
$593$	−411.602			−0.0285033			−0.0142517	−	0.999898i	$-0.504537\pi$
$593$	−411.602			−0.0285033			−0.0142517	+	0.999898i	$0.504537\pi$
$594$	5751.38	−	9961.68i	0.397276	−	0.688102i
$595$	−4039.89	−	6997.30i	−0.278352	−	0.482120i
$596$	−4250.43	−	7361.95i	−0.292121	−	0.505969i
$597$	−24885.8			−1.70604
$598$	15822.3	−	23682.0i	1.08197	−	1.61945i
$599$	21406.1			1.46015			0.730075	−	0.683367i	$-0.239485\pi$
$599$	21406.1			1.46015			0.730075	+	0.683367i	$0.239485\pi$
$600$	−487.028	−	843.557i	−0.0331380	−	0.0573968i
$601$	3539.35	+	6130.33i	0.240221	+	0.416075i	0.960777	−	0.277321i	$-0.0894467\pi$
$601$	3539.35	+	6130.33i	0.240221	+	0.416075i	−0.720556	+	0.693397i	$0.756113\pi$
$602$	−30792.6	+	53334.3i	−2.08474	+	3.61087i
$603$	−22951.0			−1.54998
$604$	−7758.28	+	13437.7i	−0.522649	+	0.905254i
$605$	−2806.98	+	4861.83i	−0.188628	+	0.326713i
$606$	−31740.5			−2.12767
$607$	4281.25	−	7415.35i	0.286278	−	0.495848i	−0.686640	−	0.726997i	$-0.740915\pi$
$607$	4281.25	−	7415.35i	0.286278	−	0.495848i	0.972918	+	0.231149i	$0.0742486\pi$
$608$	−114.322	−	198.012i	−0.00762562	−	0.0132080i
$609$	15703.0	+	27198.5i	1.04486	+	1.80975i
$610$	−9692.17			−0.643319
$611$	15388.7	+	1007.94i	1.01892	+	0.0667381i
$612$	−15542.4			−1.02658
$613$	5405.25	+	9362.16i	0.356143	+	0.616858i	0.987313	−	0.158787i	$-0.0507582\pi$
$613$	5405.25	+	9362.16i	0.356143	+	0.616858i	−0.631170	+	0.775645i	$0.717425\pi$
$614$	−522.406	−	904.833i	−0.0343364	−	0.0594724i
$615$	−822.490	+	1424.59i	−0.0539284	+	0.0934068i
$616$	−2297.30			−0.150261
$617$	−2874.76	+	4979.22i	−0.187574	+	0.324888i	−0.944441	−	0.328681i	$-0.893396\pi$
$617$	−2874.76	+	4979.22i	−0.187574	+	0.324888i	0.756867	+	0.653569i	$0.226729\pi$
$618$	−1366.00	+	2365.97i	−0.0889132	+	0.154002i
$619$	5996.39			0.389362			0.194681	−	0.980867i	$-0.437633\pi$
$619$	5996.39			0.389362			0.194681	+	0.980867i	$0.437633\pi$
$620$	618.020	−	1070.44i	0.0400327	−	0.0693387i
$621$	−16307.8	−	28246.0i	−1.05380	−	1.82524i
$622$	13518.5	+	23414.7i	0.871451	+	1.50940i
$623$	−31103.4			−2.00021
$624$	−16474.4	+	24658.0i	−1.05690	+	1.58191i
$625$	625.000			0.0400000
$626$	14795.9	+	25627.2i	0.944669	+	1.63622i
$627$	−60.1175	−	104.127i	−0.00382913	−	0.00663224i
$628$	−2177.44	+	3771.45i	−0.138359	+	0.239645i
$629$	−4682.99			−0.296857
$630$	17501.2	−	30312.9i	1.10677	−	1.91698i
$631$	10555.0	−	18281.7i	0.665906	−	1.15338i	−0.313133	−	0.949709i	$-0.601379\pi$
$631$	10555.0	−	18281.7i	0.665906	−	1.15338i	0.979039	−	0.203674i	$-0.0652882\pi$
$632$	−4094.46			−0.257704
$633$	20924.7	−	36242.7i	1.31388	−	2.27570i
$634$	16097.4	+	27881.6i	1.00838	+	1.74656i
$635$	−599.266	−	1037.96i	−0.0374506	−	0.0648664i
$636$	−29745.6			−1.85455
$637$	−19717.4	−	39978.4i	−1.22642	−	2.48666i
$638$	5514.85			0.342218
$639$	−1569.84	−	2719.03i	−0.0971858	−	0.168331i
$640$	1401.69	+	2427.79i	0.0865728	+	0.149948i
$641$	8557.16	−	14821.4i	0.527281	−	0.913278i	−0.472213	−	0.881484i	$-0.656545\pi$
$641$	8557.16	−	14821.4i	0.527281	−	0.913278i	0.999494	−	0.0317937i	$-0.0101219\pi$
$642$	−32285.0			−1.98472
$643$	−1891.46	+	3276.11i	−0.116006	+	0.200929i	−0.918182	−	0.396160i	$-0.870343\pi$
$643$	−1891.46	+	3276.11i	−0.116006	+	0.200929i	0.802175	+	0.597089i	$0.203676\pi$
$644$	19430.6	−	33654.8i	1.18893	−	2.05930i
$645$	19553.9			1.19370
$646$	−81.9320	+	141.910i	−0.00499005	+	0.00864302i
$647$	3.97962	+	6.89290i	0.000241816	+	0.000418837i	0.866146	−	0.499791i	$-0.166590\pi$
$647$	3.97962	+	6.89290i	0.000241816	+	0.000418837i	−0.865904	+	0.500209i	$0.833256\pi$
$648$	1012.58	+	1753.84i	0.0613857	+	0.106323i
$649$	508.120			0.0307326
$650$	−1997.50	−	4050.07i	−0.120536	−	0.244395i
$651$	−11425.8			−0.687886
$652$	−9195.07	−	15926.3i	−0.552311	−	0.956631i
$653$	4947.82	+	8569.88i	0.296513	+	0.513576i	0.975336	−	0.220726i	$-0.0708427\pi$
$653$	4947.82	+	8569.88i	0.296513	+	0.513576i	−0.678822	+	0.734302i	$0.737509\pi$
$654$	16414.0	−	28429.9i	0.981405	−	1.69984i
$655$	2258.21			0.134711
$656$	1342.94	−	2326.04i	0.0799283	−	0.138440i
$657$	1973.75	−	3418.64i	0.117205	−	0.203004i
$658$	45611.5			2.70231
$659$	−2327.51	+	4031.37i	−0.137583	+	0.238300i	−0.926581	−	0.376095i	$-0.877267\pi$
$659$	−2327.51	+	4031.37i	−0.137583	+	0.238300i	0.788998	+	0.614395i	$0.210600\pi$
$660$	−2175.81	−	3768.62i	−0.128323	−	0.222262i
$661$	−10457.1	−	18112.3i	−0.615334	−	1.06579i	−0.990326	−	0.138762i	$-0.955688\pi$
$661$	−10457.1	−	18112.3i	−0.615334	−	1.06579i	0.374992	−	0.927028i	$-0.377646\pi$
$662$	12003.4			0.704722
$663$	18496.5	+	1211.49i	1.08347	+	0.0709661i
$664$	1432.39			0.0837162
$665$	−85.1234	−	147.438i	−0.00496382	−	0.00859759i
$666$	−10143.6	−	17569.2i	−0.590173	−	1.02221i
$667$	7818.57	−	13542.2i	0.453877	−	0.786139i
$668$	2866.11			0.166007
$669$	−15837.6	+	27431.6i	−0.915273	+	1.58530i
$670$	−4378.81	+	7584.33i	−0.252490	+	0.437326i
$671$	7257.94			0.417570
$672$	−38247.8	+	66247.1i	−2.19560	+	3.80289i
$673$	5960.45	+	10323.8i	0.341394	+	0.591312i	0.984692	−	0.174304i	$-0.0557675\pi$
$673$	5960.45	+	10323.8i	0.341394	+	0.591312i	−0.643298	+	0.765616i	$0.722434\pi$
$674$	−7221.49	−	12508.0i	−0.412702	−	0.714822i
$675$	−5171.40			−0.294885
$676$	−9162.53	+	11943.0i	−0.521309	+	0.679509i
$677$	−26933.7			−1.52902			−0.764510	−	0.644612i	$-0.777019\pi$
$677$	−26933.7			−1.52902			−0.764510	+	0.644612i	$0.777019\pi$
$678$	−1827.76	−	3165.77i	−0.103532	−	0.179323i
$679$	1625.54	+	2815.51i	0.0918740	+	0.159130i
$680$	497.049	−	860.913i	0.0280308	−	0.0485508i
$681$	57317.5			3.22528
$682$	−1003.18	+	1737.56i	−0.0563250	+	0.0975578i
$683$	12564.9	−	21763.0i	0.703927	−	1.21924i	−0.263151	−	0.964755i	$-0.584762\pi$
$683$	12564.9	−	21763.0i	0.703927	−	1.21924i	0.967078	−	0.254482i	$-0.0819049\pi$
$684$	−327.490			−0.0183069
$685$	4347.83	−	7530.67i	0.242514	−	0.420047i
$686$	−42144.7	−	72996.8i	−2.34562	−	4.06273i
$687$	11973.0	+	20737.8i	0.664918	+	1.15167i
$688$	−31927.1			−1.76920
$689$	23066.2	+	1510.81i	1.27540	+	0.0835372i
$690$	−26745.9			−1.47565
$691$	658.391	+	1140.37i	0.0362466	+	0.0627809i	0.883580	−	0.468281i	$-0.155126\pi$
$691$	658.391	+	1140.37i	0.0362466	+	0.0627809i	−0.847333	+	0.531062i	$0.821793\pi$
$692$	−8749.21	−	15154.1i	−0.480629	−	0.832473i
$693$	−13105.7	+	22699.7i	−0.718389	+	1.24429i
$694$	−22900.6			−1.25259
$695$	−5823.50	+	10086.6i	−0.317839	+	0.550513i
$696$	−1932.03	+	3346.37i	−0.105220	+	0.182247i
$697$	−1678.83			−0.0912340
$698$	−9313.05	+	16130.7i	−0.505020	+	0.874721i
$699$	−23542.8	−	40777.3i	−1.27392	−	2.20650i
$700$	−3080.84	−	5336.17i	−0.166350	−	0.288126i
$701$	8861.36			0.477445			0.238723	−	0.971088i	$-0.423271\pi$
$701$	8861.36			0.477445			0.238723	+	0.971088i	$0.423271\pi$
$702$	16527.8	+	33511.2i	0.888604	+	1.80171i
$703$	−98.6739			−0.00529382
$704$	2568.15	+	4448.17i	0.137487	+	0.238135i
$705$	−7241.06	−	12541.9i	−0.386828	−	0.670006i
$706$	11725.1	−	20308.6i	0.625045	−	1.08261i
$707$	33655.3			1.79029
$708$	1061.99	−	1839.42i	0.0563729	−	0.0976408i
$709$	−17746.5	+	30737.9i	−0.940035	+	1.62819i	−0.174634	+	0.984633i	$0.555874\pi$
$709$	−17746.5	+	30737.9i	−0.940035	+	1.62819i	−0.765401	+	0.643554i	$0.777459\pi$
$710$	−1198.03			−0.0633259
$711$	−23358.1	+	40457.4i	−1.23206	+	2.13400i
$712$	−1913.41	−	3314.12i	−0.100713	−	0.174441i
$713$	2844.47	+	4926.77i	0.149406	+	0.258778i
$714$	54822.6			2.87351
$715$	1495.82	+	3032.88i	0.0782383	+	0.158634i
$716$	24328.9			1.26985
$717$	242.361	+	419.782i	0.0126236	+	0.0218648i
$718$	−20569.2	−	35626.9i	−1.06913	−	1.85179i
$719$	−17742.0	+	30730.0i	−0.920255	+	1.59393i	−0.121235	+	0.992624i	$0.538686\pi$
$719$	−17742.0	+	30730.0i	−0.920255	+	1.59393i	−0.799020	+	0.601305i	$0.794648\pi$
$720$	18146.0			0.939251
$721$	1448.40	−	2508.71i	0.0748146	−	0.129583i
$722$	13214.8	−	22888.7i	0.681168	−	1.17982i
$723$	13144.9			0.676158
$724$	−9134.44	+	15821.3i	−0.468893	+	0.812147i
$725$	−1239.68	−	2147.19i	−0.0635042	−	0.109992i
$726$	−19045.8	−	32988.3i	−0.973631	−	1.68638i
$727$	−5310.74			−0.270928			−0.135464	−	0.990782i	$-0.543252\pi$
$727$	−5310.74			−0.270928			−0.135464	+	0.990782i	$0.543252\pi$
$728$	4145.67	−	6205.03i	0.211056	−	0.315898i
$729$	−26060.9			−1.32403
$730$	−753.144	−	1304.48i	−0.0381851	−	0.0661385i
$731$	9978.13	+	17282.6i	0.504863	+	0.874448i
$732$	15169.4	−	26274.1i	0.765951	−	1.32667i
$733$	23033.8			1.16067			0.580336	−	0.814377i	$-0.302921\pi$
$733$	23033.8			1.16067			0.580336	+	0.814377i	$0.302921\pi$
$734$	6709.58	−	11621.3i	0.337405	−	0.584402i
$735$	−20930.2	+	36252.2i	−1.05037	+	1.81929i
$736$	38087.3			1.90749
$737$	3279.06	−	5679.49i	0.163888	−	0.283863i
$738$	−3636.41	−	6298.45i	−0.181380	−	0.314159i
$739$	−7292.26	−	12630.6i	−0.362990	−	0.628718i	0.625461	−	0.780255i	$-0.284911\pi$
$739$	−7292.26	−	12630.6i	−0.362990	−	0.628718i	−0.988452	+	0.151537i	$0.951578\pi$
$740$	−3571.27			−0.177409
$741$	389.734	+	25.5270i	0.0193215	+	0.00126553i
$742$	68367.0			3.38252
$743$	−9240.01	−	16004.2i	−0.456236	−	0.790223i	0.542523	−	0.840041i	$-0.317469\pi$
$743$	−9240.01	−	16004.2i	−0.456236	−	0.790223i	−0.998758	+	0.0498179i	$0.984136\pi$
$744$	−702.890	−	1217.44i	−0.0346360	−	0.0599914i
$745$	3101.80	−	5372.48i	0.152539	−	0.264204i
$746$	−53952.1			−2.64789
$747$	8171.52	−	14153.5i	0.400241	−	0.693238i
$748$	2220.58	−	3846.16i	0.108546	−	0.188007i
$749$	34232.7			1.67001
$750$	−2120.36	+	3672.57i	−0.103233	+	0.178805i
$751$	10513.4	+	18209.7i	0.510838	+	0.884797i	0.999921	+	0.0125598i	$0.00399803\pi$
$751$	10513.4	+	18209.7i	0.510838	+	0.884797i	−0.489083	+	0.872237i	$0.662669\pi$
$752$	11823.0	+	20478.0i	0.573325	+	0.993028i
$753$	−14420.3			−0.697880
$754$	−9952.00	+	14895.7i	−0.480677	+	0.719453i
$755$	−11323.4			−0.545829
$756$	25491.6	+	44152.7i	1.22635	+	2.12410i
$757$	−19496.7	−	33769.2i	−0.936087	−	1.62135i	−0.772684	−	0.634791i	$-0.781086\pi$
$757$	−19496.7	−	33769.2i	−0.936087	−	1.62135i	−0.163403	−	0.986559i	$-0.552247\pi$
$758$	−16118.3	+	27917.7i	−0.772353	+	1.33775i
$759$	20028.6			0.957829
$760$	10.4732	−	18.1401i	0.000499871	−	0.000865801i
$761$	−3134.85	+	5429.72i	−0.149328	+	0.258643i	−0.930979	−	0.365072i	$-0.881044\pi$
$761$	−3134.85	+	5429.72i	−0.149328	+	0.258643i	0.781652	+	0.623715i	$0.214378\pi$
$762$	8132.23			0.386614
$763$	−17404.2	+	30145.0i	−0.825788	+	1.43031i
$764$	11526.5	+	19964.5i	0.545830	+	0.945406i
$765$	−5671.14	−	9822.70i	−0.268027	−	0.464236i
$766$	37052.5			1.74773
$767$	−916.944	+	1372.44i	−0.0431668	+	0.0646099i
$768$	−44090.3			−2.07158
$769$	7963.81	+	13793.7i	0.373449	+	0.646833i	0.990094	−	0.140409i	$-0.0448418\pi$
$769$	7963.81	+	13793.7i	0.373449	+	0.646833i	−0.616645	+	0.787242i	$0.711508\pi$
$770$	5000.86	+	8661.74i	0.234050	+	0.405386i
$771$	4304.98	−	7456.44i	0.201089	−	0.348297i
$772$	23548.2			1.09782
$773$	13186.1	−	22839.1i	0.613548	−	1.06270i	−0.377090	−	0.926177i	$-0.623075\pi$
$773$	13186.1	−	22839.1i	0.613548	−	1.06270i	0.990637	−	0.136519i	$-0.0435915\pi$
$774$	−43226.2	+	74869.9i	−2.00741	+	3.47693i
$775$	902.015			0.0418082
$776$	−199.998	+	346.407i	−0.00925196	+	0.0160249i
$777$	16506.2	+	28589.7i	0.762109	+	1.32001i
$778$	−10591.6	−	18345.3i	−0.488083	−	0.845385i
$779$	−35.3741			−0.00162697
$780$	14105.5	+	923.891i	0.647510	+	0.0424110i
$781$	897.143			0.0411041
$782$	−13648.1	−	23639.3i	−0.624113	−	1.08099i
$783$	10257.4	+	17766.3i	0.468160	+	0.810877i
$784$	34174.2	−	59191.5i	1.55677	−	2.69641i
$785$	−3178.03			−0.144495
$786$	−7661.17	+	13269.5i	−0.347665	+	0.602174i
$787$	−15925.9	+	27584.5i	−0.721344	+	1.24940i	0.239117	+	0.970991i	$0.423142\pi$
$787$	−15925.9	+	27584.5i	−0.721344	+	1.24940i	−0.960461	+	0.278414i	$0.910191\pi$
$788$	−5124.34			−0.231659
$789$	9450.05	−	16368.0i	0.426402	−	0.738549i
$790$	8912.97	+	15437.7i	0.401404	+	0.695253i
$791$	1938.03	+	3356.76i	0.0871154	+	0.150888i
$792$	−3224.92			−0.144688
$793$	−13097.6	+	19603.8i	−0.586517	+	0.877869i
$794$	−30706.3			−1.37245
$795$	−10853.6	−	18799.0i	−0.484199	−	0.838658i
$796$	−9684.24	−	16773.6i	−0.431217	−	0.746890i
$797$	−17095.8	+	29610.7i	−0.759803	+	1.31602i	0.183148	+	0.983085i	$0.441371\pi$
$797$	−17095.8	+	29610.7i	−0.759803	+	1.31602i	−0.942951	+	0.332932i	$0.891962\pi$
$798$	1155.15			0.0512430
$799$	7390.05	−	12799.9i	0.327210	−	0.566745i
$800$	3019.48	−	5229.89i	0.133443	−	0.231131i
$801$	−43662.5			−1.92601
$802$	−3063.22	+	5305.65i	−0.134870	+	0.233602i
$803$	563.989	+	976.857i	0.0247855	+	0.0429297i
$804$	−13706.7	−	23740.7i	−0.601242	−	1.04138i
$805$	28359.5			1.24167
$806$	−2882.83	−	5845.15i	−0.125985	−	0.255443i
$807$	48908.8			2.13342
$808$	2070.39	+	3586.03i	0.0901438	+	0.156134i
$809$	3285.89	+	5691.33i	0.142801	+	0.247338i	0.928550	−	0.371207i	$-0.121056\pi$
$809$	3285.89	+	5691.33i	0.142801	+	0.247338i	−0.785749	+	0.618545i	$0.787723\pi$
$810$	4408.45	−	7635.67i	0.191231	−	0.331222i
$811$	22734.2			0.984347			0.492173	−	0.870497i	$-0.336203\pi$
$811$	22734.2			0.984347			0.492173	+	0.870497i	$0.336203\pi$
$812$	−12221.6	+	21168.4i	−0.528195	+	0.914860i
$813$	−1607.80	+	2784.79i	−0.0693578	+	0.120131i
$814$	5796.93			0.249610
$815$	6710.22	−	11622.4i	0.288403	−	0.499529i
$816$	14210.6	+	24613.5i	0.609646	+	1.05594i
$817$	210.246	+	364.157i	0.00900317	+	0.0155939i
$818$	−28564.4			−1.22094
$819$	−37661.8	−	76362.0i	−1.60685	−	3.25800i
$820$	−1280.28			−0.0545236
$821$	−1456.61	−	2522.92i	−0.0619197	−	0.107248i	0.833404	−	0.552665i	$-0.186389\pi$
$821$	−1456.61	−	2522.92i	−0.0619197	−	0.107248i	−0.895323	+	0.445417i	$0.853056\pi$
$822$	29500.7	+	51096.8i	1.25177	+	2.16813i
$823$	−5828.90	+	10096.0i	−0.246881	+	0.427610i	−0.962659	−	0.270718i	$-0.912739\pi$
$823$	−5828.90	+	10096.0i	−0.246881	+	0.427610i	0.715778	+	0.698328i	$0.246072\pi$
$824$	356.409			0.0150681
$825$	1587.82	−	2750.19i	0.0670072	−	0.116060i
$826$	−2440.87	+	4227.70i	−0.102819	+	0.178088i
$827$	−5441.17			−0.228788			−0.114394	−	0.993435i	$-0.536493\pi$
$827$	−5441.17			−0.228788			−0.114394	+	0.993435i	$0.536493\pi$
$828$	27276.4	−	47244.1i	1.14483	−	1.98291i
$829$	−4028.65	−	6977.82i	−0.168783	−	0.292340i	0.769210	−	0.638997i	$-0.220650\pi$
$829$	−4028.65	−	6977.82i	−0.168783	−	0.292340i	−0.937992	+	0.346657i	$0.887317\pi$
$830$	−3118.08	−	5400.68i	−0.130398	−	0.225856i
$831$	−49027.8			−2.04664
$832$	−16649.0	−	1090.49i	−0.693750	−	0.0454397i
$833$	−42721.7			−1.77697
$834$	−39513.4	−	68439.2i	−1.64057	−	2.84155i
$835$	1045.79	+	1811.36i	0.0433425	+	0.0750714i
$836$	46.7892	−	81.0413i	0.00193569	−	0.00335272i
$837$	−7463.48			−0.308215
$838$	1362.95	−	2360.70i	0.0561841	−	0.0973138i
$839$	−2318.44	+	4015.66i	−0.0954011	+	0.165240i	−0.909776	−	0.415100i	$-0.863747\pi$
$839$	−2318.44	+	4015.66i	−0.0954011	+	0.165240i	0.814375	+	0.580339i	$0.197080\pi$
$840$	−7007.84			−0.287849
$841$	7276.72	−	12603.7i	0.298361	−	0.516776i
$842$	−16285.7	−	28207.6i	−0.666558	−	1.15451i
$843$	−2931.55	−	5077.59i	−0.119772	−	0.207452i
$844$	32571.2			1.32837
$845$	−10891.1	−	1432.86i	−0.443393	−	0.0583335i
$846$	64028.7			2.60207
$847$	20194.8	+	34978.4i	0.819246	+	1.41898i
$848$	17721.5	+	30694.5i	0.717640	+	1.24299i
$849$	−11459.5	+	19848.5i	−0.463239	+	0.802353i
$850$	−4327.98			−0.174645
$851$	8218.49	−	14234.8i	0.331053	−	0.573401i
$852$	1875.06	−	3247.70i	0.0753974	−	0.130592i
$853$	−29776.8			−1.19524			−0.597620	−	0.801780i	$-0.703887\pi$
$853$	−29776.8			−1.19524			−0.597620	+	0.801780i	$0.703887\pi$
$854$	−34865.1	+	60388.2i	−1.39703	+	2.41972i
$855$	−119.495	−	206.971i	−0.00477969	−	0.00827867i
$856$	2105.91	+	3647.55i	0.0840872	+	0.145643i
$857$	6356.84			0.253379			0.126689	−	0.991942i	$-0.459565\pi$
$857$	6356.84			0.253379			0.126689	+	0.991942i	$0.459565\pi$
$858$	−22896.2	−	1499.67i	−0.911031	−	0.0596713i
$859$	22742.5			0.903335			0.451668	−	0.892186i	$-0.350829\pi$
$859$	22742.5			0.903335			0.451668	+	0.892186i	$0.350829\pi$
$860$	7609.37	+	13179.8i	0.301718	+	0.522590i
$861$	5917.40	+	10249.2i	0.234221	+	0.405683i
$862$	29049.9	−	50315.9i	1.14785	−	1.98813i
$863$	13616.7			0.537102			0.268551	−	0.963265i	$-0.413455\pi$
$863$	13616.7			0.537102			0.268551	+	0.963265i	$0.413455\pi$
$864$	−24983.9	+	43273.4i	−0.983760	+	1.70392i
$865$	6384.84	−	11058.9i	0.250972	−	0.434697i
$866$	−31152.7			−1.22242
$867$	−12742.8	+	22071.2i	−0.499155	+	0.864563i
$868$	−4446.34	−	7701.29i	−0.173869	−	0.301151i
$869$	−6674.45	−	11560.5i	−0.260547	−	0.451280i
$870$	16822.8			0.655572
$871$	9423.03	+	19105.9i	0.366576	+	0.743258i
$872$	−4282.67			−0.166318
$873$	2281.91	+	3952.38i	0.0884660	+	0.153228i
$874$	−287.576	−	498.096i	−0.0111297	−	0.0192773i
$875$	2248.28	−	3894.13i	0.0868637	−	0.150452i
$876$	4715.03			0.181856
$877$	−3470.13	+	6010.44i	−0.133612	+	0.231423i	−0.925067	−	0.379805i	$-0.875991\pi$
$877$	−3470.13	+	6010.44i	−0.133612	+	0.231423i	0.791454	+	0.611229i	$0.209324\pi$
$878$	−3128.31	+	5418.39i	−0.120245	+	0.208271i
$879$	77731.4			2.98272
$880$	−2592.56	+	4490.44i	−0.0993126	+	0.172014i
$881$	18289.9	+	31679.1i	0.699437	+	1.21146i	0.968662	+	0.248382i	$0.0798990\pi$
$881$	18289.9	+	31679.1i	0.699437	+	1.21146i	−0.269225	+	0.963077i	$0.586768\pi$
$882$	−92537.1	−	160279.i	−3.53275	−	6.11890i
$883$	41508.3			1.58195			0.790976	−	0.611847i	$-0.209573\pi$
$883$	41508.3			1.58195			0.790976	+	0.611847i	$0.209573\pi$
$884$	6381.28	+	12938.5i	0.242789	+	0.492273i
$885$	1550.00			0.0588731
$886$	10451.8	+	18103.0i	0.396313	+	0.686435i
$887$	−10884.7	−	18852.8i	−0.412031	−	0.713658i	0.583081	−	0.812414i	$-0.301847\pi$
$887$	−10884.7	−	18852.8i	−0.412031	−	0.713658i	−0.995112	+	0.0987561i	$0.968514\pi$
$888$	−2030.85	+	3517.53i	−0.0767464	+	0.132929i
$889$	−8622.83			−0.325310
$890$	−8330.35	+	14428.6i	−0.313746	+	0.543424i
$891$	−3301.25	+	5717.94i	−0.124126	+	0.214992i
$892$	−24652.7			−0.925373
$893$	155.714	−	269.704i	0.00583511	−	0.0101067i
$894$	21046.2	+	36453.1i	0.787350	+	1.36373i
$895$	8877.16	+	15375.7i	0.331543	+	0.574249i
$896$	20168.9			0.752003
$897$	−36143.2	+	54097.4i	−1.34536	+	2.01367i
$898$	−13015.9			−0.483681
$899$	−1789.13	−	3098.87i	−0.0663748	−	0.114965i
$900$	−4324.83	−	7490.83i	−0.160179	−	0.277438i
$901$	11076.9	−	19185.8i	0.409574	−	0.709404i
$902$	2078.17			0.0767133
$903$	70340.3	−	121833.i	2.59223	−	4.48987i
$904$	−238.445	+	412.999i	−0.00877276	+	0.0151949i
$905$	−13331.9			−0.489689
$906$	38415.5	−	66537.6i	1.40869	−	2.43992i
$907$	10399.1	+	18011.8i	0.380703	+	0.659397i	0.991163	−	0.132650i	$-0.0423488\pi$
$907$	10399.1	+	18011.8i	0.380703	+	0.659397i	−0.610460	+	0.792047i	$0.709015\pi$
$908$	22305.0	+	38633.4i	0.815217	+	1.41200i
$909$	47244.8			1.72388
$910$	−32419.9	−	2123.46i	−1.18100	−	0.0773539i
$911$	18274.3			0.664604			0.332302	−	0.943173i	$-0.392175\pi$
$911$	18274.3			0.664604			0.332302	+	0.943173i	$0.392175\pi$
$912$	299.428	+	518.624i	0.0108718	+	0.0188305i
$913$	2334.96	+	4044.28i	0.0846397	+	0.146600i
$914$	3623.34	−	6275.80i	0.131126	−	0.227117i
$915$	22140.1			0.799922
$916$	−9318.53	+	16140.2i	−0.336128	+	0.582190i
$917$	8123.35	−	14070.1i	0.292537	−	0.506690i
$918$	35810.7			1.28751
$919$	−12689.8	+	21979.3i	−0.455491	+	0.788934i	−0.998716	−	0.0506531i	$-0.983870\pi$
$919$	−12689.8	+	21979.3i	−0.455491	+	0.788934i	0.543225	+	0.839587i	$0.317203\pi$
$920$	1744.61	+	3021.75i	0.0625195	+	0.108287i
$921$	1193.35	+	2066.93i	0.0426950	+	0.0739498i
$922$	64504.3			2.30405
$923$	−1618.97	+	2423.19i	−0.0577345	+	0.0864142i
$924$	−31307.7			−1.11466
$925$	−1303.09	−	2257.02i	−0.0463192	−	0.0802273i
$926$	10227.4	+	17714.4i	0.362952	+	0.628651i
$927$	2033.25	−	3521.69i	0.0720395	−	0.124776i
$928$	−23956.4			−0.847421
$929$	12141.9	−	21030.4i	0.428808	−	0.742717i	−0.567960	−	0.823056i	$-0.692267\pi$
$929$	12141.9	−	21030.4i	0.428808	−	0.742717i	0.996768	+	0.0803392i	$0.0256003\pi$
$930$	−3060.16	+	5300.35i	−0.107899	+	0.186887i
$931$	−900.176			−0.0316886
$932$	18323.3	−	31736.8i	0.643990	−	1.11542i
$933$	−30880.7	−	53486.9i	−1.08359	−	1.87683i
$934$	−12810.0	−	22187.5i	−0.448774	−	0.777300i
$935$	3240.99			0.113360
$936$	5819.63	−	8710.53i	0.203227	−	0.304180i
$937$	−13213.9			−0.460703			−0.230351	−	0.973108i	$-0.573988\pi$
$937$	−13213.9			−0.460703			−0.230351	+	0.973108i	$0.573988\pi$
$938$	31503.3	+	54565.4i	1.09661	+	1.89939i
$939$	−33798.7	−	58541.0i	−1.17463	−	2.03452i
$940$	5635.68	−	9761.29i	0.195549	−	0.338700i
$941$	−30546.3			−1.05822			−0.529108	−	0.848554i	$-0.677474\pi$
$941$	−30546.3			−1.05822			−0.529108	+	0.848554i	$0.677474\pi$
$942$	10781.7	−	18674.5i	0.372917	−	0.645911i
$943$	2946.28	−	5103.11i	0.101744	−	0.176225i
$944$	−2530.80			−0.0872569
$945$	−18602.8	+	32221.0i	−0.640369	+	1.10915i
$946$	−12351.6	−	21393.6i	−0.424510	−	0.735272i
$947$	−13882.0	−	24044.3i	−0.476350	−	0.825062i	0.523283	−	0.852159i	$-0.324707\pi$
$947$	−13882.0	−	24044.3i	−0.476350	−	0.825062i	−0.999633	+	0.0270969i	$0.991374\pi$
$948$	−55799.4			−1.91169
$949$	−3656.26	−	239.480i	−0.125066	−	0.00819164i
$950$	−91.1936			−0.00311443
$951$	−36771.8	−	63690.6i	−1.25385	−	2.17172i
$952$	−3576.01	−	6193.84i	−0.121743	−	0.210865i
$953$	−1741.45	+	3016.28i	−0.0591931	+	0.102525i	−0.894103	−	0.447861i	$-0.852186\pi$
$953$	−1741.45	+	3016.28i	−0.0591931	+	0.102525i	0.834910	+	0.550386i	$0.185519\pi$
$954$	95972.6			3.25705
$955$	−8411.61	+	14569.3i	−0.285019	+	0.493668i
$956$	−188.629	+	326.715i	−0.00638148	+	0.0110530i
$957$	−12597.7			−0.425524
$958$	−25478.1	+	44129.4i	−0.859250	+	1.48826i
$959$	−31280.5	−	54179.4i	−1.05328	−	1.82434i
$960$	7834.05	+	13569.0i	0.263378	+	0.456184i
$961$	−28489.2			−0.956302
$962$	−10461.0	+	15657.6i	−0.350600	+	0.524761i
$963$	48055.4			1.60806
$964$	5115.29	+	8859.94i	0.170905	+	0.296016i
$965$	8592.28	+	14882.3i	0.286627	+	0.496453i
$966$	−96211.8	+	166644.i	−3.20452	+	5.55039i
$967$	−32297.0			−1.07404			−0.537022	−	0.843568i	$-0.680451\pi$
$967$	−32297.0			−1.07404			−0.537022	+	0.843568i	$0.680451\pi$
$968$	−2484.67	+	4303.58i	−0.0825004	+	0.142895i
$969$	187.160	−	324.170i	0.00620478	−	0.0107470i
$970$	1741.46			0.0576441
$971$	−17088.5	+	29598.2i	−0.564776	+	0.978221i	0.432295	+	0.901732i	$0.357704\pi$
$971$	−17088.5	+	29598.2i	−0.564776	+	0.978221i	−0.997070	+	0.0764881i	$0.975629\pi$
$972$	−5333.82	−	9238.44i	−0.176011	−	0.304859i
$973$	41897.2	+	72568.0i	1.38043	+	2.39098i
$974$	−18227.0			−0.599620
$975$	4562.94	+	9251.68i	0.149878	+	0.303888i
$976$	−36149.7			−1.18558
$977$	−28613.9	−	49560.8i	−0.936991	−	1.62292i	−0.771044	−	0.636781i	$-0.780265\pi$
$977$	−28613.9	−	49560.8i	−0.936991	−	1.62292i	−0.165947	−	0.986135i	$-0.553068\pi$
$978$	45529.9	+	78860.1i	1.48863	+	2.57839i
$979$	6238.15	−	10804.8i	0.203649	−	0.352730i
$980$	−32579.7			−1.06196
$981$	−24431.8	+	42317.1i	−0.795156	+	1.37725i
$982$	−14695.1	+	25452.6i	−0.477534	+	0.827113i
$983$	−6396.10			−0.207532			−0.103766	−	0.994602i	$-0.533089\pi$
$983$	−6396.10			−0.207532			−0.103766	+	0.994602i	$0.533089\pi$
$984$	−728.048	+	1261.02i	−0.0235867	+	0.0408534i
$985$	−1869.78	−	3238.55i	−0.0604833	−	0.104760i
$986$	8584.49	+	14868.8i	0.277268	+	0.480242i
$987$	−104191.			−3.36013
$988$	134.458	+	272.624i	0.00432964	+	0.00877865i
$989$	−70045.1			−2.25208
$990$	7020.13	+	12159.2i	0.225368	+	0.390349i
$991$	−12770.5	−	22119.2i	−0.409353	−	0.709020i	0.585464	−	0.810698i	$-0.300912\pi$
$991$	−12770.5	−	22119.2i	−0.409353	−	0.709020i	−0.994817	+	0.101678i	$0.967579\pi$
$992$	4357.79	−	7547.91i	0.139476	−	0.241579i
$993$	−27419.7			−0.876272
$994$	−4309.62	+	7464.49i	−0.137518	+	0.238188i
$995$	7067.20	−	12240.7i	0.225171	−	0.390008i
$996$	19520.7			0.621020
$997$	31048.1	−	53776.9i	0.986261	−	1.70825i	0.350070	−	0.936723i	$-0.386158\pi$
$997$	31048.1	−	53776.9i	0.986261	−	1.70825i	0.636191	−	0.771531i	$-0.280509\pi$
$998$	−14658.2	−	25388.7i	−0.464926	−	0.805276i
$999$	10782.1	+	18675.1i	0.341471	+	0.591445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.4.e.a.16.2	✓	14
13.3	even	3		845.4.a.k.1.6		7
13.9	even	3	inner	65.4.e.a.61.2	yes	14
13.10	even	6		845.4.a.h.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.e.a.16.2	✓	14	1.1	even	1	trivial
65.4.e.a.61.2	yes	14	13.9	even	3	inner
845.4.a.h.1.2		7	13.10	even	6
845.4.a.k.1.6		7	13.3	even	3

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	65.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92689 - 3.33746i) q^{2} +(4.40164 + 7.62386i) q^{3} +(-3.42577 + 5.93361i) q^{4} -5.00000 q^{5} +(16.9629 - 29.3806i) q^{6} +(-17.9862 + 31.1531i) q^{7} -4.42588 q^{8} +(-25.2488 + 43.7322i) q^{9} +O(q^{10})\)	\(q+(-1.92689 - 3.33746i) q^{2} +(4.40164 + 7.62386i) q^{3} +(-3.42577 + 5.93361i) q^{4} -5.00000 q^{5} +(16.9629 - 29.3806i) q^{6} +(-17.9862 + 31.1531i) q^{7} -4.42588 q^{8} +(-25.2488 + 43.7322i) q^{9} +(9.63443 + 16.6873i) q^{10} +(-7.21470 - 12.4962i) q^{11} -60.3160 q^{12} +(46.7719 + 3.06350i) q^{13} +138.630 q^{14} +(-22.0082 - 38.1193i) q^{15} +(35.9343 + 62.2401i) q^{16} +(22.4610 - 38.9036i) q^{17} +194.606 q^{18} +(0.473270 - 0.819727i) q^{19} +(17.1289 - 29.6681i) q^{20} -316.675 q^{21} +(-27.8038 + 48.1576i) q^{22} +(78.8366 + 136.549i) q^{23} +(-19.4811 - 33.7423i) q^{24} +25.0000 q^{25} +(-79.8999 - 162.003i) q^{26} -206.856 q^{27} +(-123.234 - 213.447i) q^{28} +(-49.5872 - 85.8875i) q^{29} +(-84.8145 + 146.903i) q^{30} +36.0806 q^{31} +(120.779 - 209.196i) q^{32} +(63.5130 - 110.008i) q^{33} -173.119 q^{34} +(89.9312 - 155.765i) q^{35} +(-172.993 - 299.633i) q^{36} +(-52.1235 - 90.2806i) q^{37} -3.64774 q^{38} +(182.517 + 370.067i) q^{39} +22.1294 q^{40} +(-18.6860 - 32.3651i) q^{41} +(610.197 + 1056.89i) q^{42} +(-222.121 + 384.725i) q^{43} +98.8637 q^{44} +(126.244 - 218.661i) q^{45} +(303.818 - 526.229i) q^{46} +329.017 q^{47} +(-316.340 + 547.917i) q^{48} +(-475.509 - 823.606i) q^{49} +(-48.1721 - 83.4366i) q^{50} +395.461 q^{51} +(-178.408 + 267.032i) q^{52} +493.163 q^{53} +(398.587 + 690.374i) q^{54} +(36.0735 + 62.4812i) q^{55} +(79.6049 - 137.880i) q^{56} +8.33264 q^{57} +(-191.098 + 330.991i) q^{58} +(-17.6071 + 30.4964i) q^{59} +301.580 q^{60} +(-251.498 + 435.608i) q^{61} +(-69.5232 - 120.418i) q^{62} +(-908.262 - 1573.16i) q^{63} -355.961 q^{64} +(-233.860 - 15.3175i) q^{65} -489.529 q^{66} +(227.248 + 393.606i) q^{67} +(153.893 + 266.550i) q^{68} +(-694.020 + 1202.08i) q^{69} -693.148 q^{70} +(-31.0873 + 53.8448i) q^{71} +(111.748 - 193.553i) q^{72} -78.1722 q^{73} +(-200.872 + 347.921i) q^{74} +(110.041 + 190.596i) q^{75} +(3.24263 + 5.61640i) q^{76} +519.061 q^{77} +(883.395 - 1322.22i) q^{78} +925.117 q^{79} +(-179.672 - 311.201i) q^{80} +(-228.787 - 396.270i) q^{81} +(-72.0116 + 124.728i) q^{82} -323.640 q^{83} +(1084.86 - 1879.03i) q^{84} +(-112.305 + 194.518i) q^{85} +1712.01 q^{86} +(436.529 - 756.091i) q^{87} +(31.9314 + 55.3068i) q^{88} +(432.322 + 748.804i) q^{89} -973.031 q^{90} +(-936.689 + 1401.99i) q^{91} -1080.31 q^{92} +(158.814 + 275.073i) q^{93} +(-633.977 - 1098.08i) q^{94} +(-2.36635 + 4.09863i) q^{95} +2126.50 q^{96} +(45.1884 - 78.2686i) q^{97} +(-1832.50 + 3173.99i) q^{98} +728.650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18} - 245 q^{19} + 150 q^{20} - 76 q^{21} - 338 q^{22} + 74 q^{23} - 334 q^{24} + 350 q^{25} + 243 q^{26} - 884 q^{27} - 230 q^{28} + 88 q^{29} + 115 q^{30} + 1000 q^{31} - 80 q^{32} + 194 q^{33} + 854 q^{34} + 35 q^{35} - 425 q^{36} - 633 q^{37} - 596 q^{38} + 970 q^{39} - 210 q^{40} - 162 q^{41} + 1439 q^{42} + 280 q^{43} + 440 q^{44} + 435 q^{45} + 11 q^{46} + 950 q^{47} - 2281 q^{48} - 1694 q^{49} - 50 q^{50} - 860 q^{51} - 956 q^{52} - 1206 q^{53} - 51 q^{54} + 435 q^{55} + 1277 q^{56} + 916 q^{57} + 1213 q^{58} - 1410 q^{59} + 790 q^{60} - 412 q^{61} + 56 q^{62} - 1241 q^{63} - 2358 q^{64} - 615 q^{65} + 4346 q^{66} - 1398 q^{67} + 493 q^{68} - 1080 q^{69} - 660 q^{70} + 584 q^{71} - 1545 q^{72} + 5076 q^{73} - 3840 q^{74} + 100 q^{75} - 3292 q^{76} - 5506 q^{77} + 1179 q^{78} + 928 q^{79} - 670 q^{80} + 473 q^{81} + 1583 q^{82} + 932 q^{83} + 3081 q^{84} - 570 q^{85} + 9858 q^{86} + 282 q^{87} - 3389 q^{88} - 443 q^{89} - 2070 q^{90} + 487 q^{91} + 6182 q^{92} + 2116 q^{93} - 2017 q^{94} + 1225 q^{95} + 954 q^{96} + 1870 q^{97} - 1364 q^{98} + 11378 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9 + 10 * q^10 - 87 * q^11 - 158 * q^12 + 123 * q^13 + 132 * q^14 - 20 * q^15 + 134 * q^16 + 114 * q^17 + 414 * q^18 - 245 * q^19 + 150 * q^20 - 76 * q^21 - 338 * q^22 + 74 * q^23 - 334 * q^24 + 350 * q^25 + 243 * q^26 - 884 * q^27 - 230 * q^28 + 88 * q^29 + 115 * q^30 + 1000 * q^31 - 80 * q^32 + 194 * q^33 + 854 * q^34 + 35 * q^35 - 425 * q^36 - 633 * q^37 - 596 * q^38 + 970 * q^39 - 210 * q^40 - 162 * q^41 + 1439 * q^42 + 280 * q^43 + 440 * q^44 + 435 * q^45 + 11 * q^46 + 950 * q^47 - 2281 * q^48 - 1694 * q^49 - 50 * q^50 - 860 * q^51 - 956 * q^52 - 1206 * q^53 - 51 * q^54 + 435 * q^55 + 1277 * q^56 + 916 * q^57 + 1213 * q^58 - 1410 * q^59 + 790 * q^60 - 412 * q^61 + 56 * q^62 - 1241 * q^63 - 2358 * q^64 - 615 * q^65 + 4346 * q^66 - 1398 * q^67 + 493 * q^68 - 1080 * q^69 - 660 * q^70 + 584 * q^71 - 1545 * q^72 + 5076 * q^73 - 3840 * q^74 + 100 * q^75 - 3292 * q^76 - 5506 * q^77 + 1179 * q^78 + 928 * q^79 - 670 * q^80 + 473 * q^81 + 1583 * q^82 + 932 * q^83 + 3081 * q^84 - 570 * q^85 + 9858 * q^86 + 282 * q^87 - 3389 * q^88 - 443 * q^89 - 2070 * q^90 + 487 * q^91 + 6182 * q^92 + 2116 * q^93 - 2017 * q^94 + 1225 * q^95 + 954 * q^96 + 1870 * q^97 - 1364 * q^98 + 11378 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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