LMFDB - Embedded newform 169.4.c.l.22.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(22,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.c (of order $3$, degree $2$, not 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} + 62 x^{16} - 106 x^{15} + 2016 x^{14} - 2731 x^{13} + 39895 x^{12} - 21896 x^{11} + \cdots + 16777216 $ x^18 - 4x^17 + 62x^16 - 106x^15 + 2016x^14 - 2731x^13 + 39895x^12 - 21896x^11 + 490851x^10 - 318018x^9 + 3391249x^8 - 990441x^7 + 13815033x^6 - 7349264x^5 + 28218112x^4 - 9093120x^3 + 32440320x^2 - 14680064*x + 16777216
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.3
Root			$1.36382 + 2.36220i$ of defining polynomial
Character	$\chi$	$=$	169.22
Dual form			169.4.c.l.146.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.863817 + 1.49617i) q^{2} +(-3.44796 + 5.97204i) q^{3} +(2.50764 + 4.34336i) q^{4} -20.8281 q^{5} +(-5.95681 - 10.3175i) q^{6} +(3.78283 + 6.55206i) q^{7} -22.4856 q^{8} +(-10.2768 - 17.8000i) q^{9} +O(q^{10})$	\(q+(-0.863817 + 1.49617i) q^{2} +(-3.44796 + 5.97204i) q^{3} +(2.50764 + 4.34336i) q^{4} -20.8281 q^{5} +(-5.95681 - 10.3175i) q^{6} +(3.78283 + 6.55206i) q^{7} -22.4856 q^{8} +(-10.2768 - 17.8000i) q^{9} +(17.9916 - 31.1624i) q^{10} +(-2.20147 + 3.81307i) q^{11} -34.5850 q^{12} -13.0707 q^{14} +(71.8143 - 124.386i) q^{15} +(-0.637664 + 1.10447i) q^{16} +(36.5043 + 63.2274i) q^{17} +35.5091 q^{18} +(27.9712 + 48.4475i) q^{19} +(-52.2293 - 90.4639i) q^{20} -52.1722 q^{21} +(-3.80334 - 6.58758i) q^{22} +(16.8122 - 29.1196i) q^{23} +(77.5295 - 134.285i) q^{24} +308.809 q^{25} -44.4536 q^{27} +(-18.9720 + 32.8604i) q^{28} +(-60.7146 + 105.161i) q^{29} +(124.069 + 214.893i) q^{30} +84.1320 q^{31} +(-91.0442 - 157.693i) q^{32} +(-15.1812 - 26.2946i) q^{33} -126.132 q^{34} +(-78.7891 - 136.467i) q^{35} +(51.5411 - 89.2719i) q^{36} +(85.8578 - 148.710i) q^{37} -96.6479 q^{38} +468.332 q^{40} +(46.7857 - 81.0352i) q^{41} +(45.0672 - 78.0586i) q^{42} +(-220.888 - 382.589i) q^{43} -22.0820 q^{44} +(214.046 + 370.739i) q^{45} +(29.0453 + 50.3080i) q^{46} -272.528 q^{47} +(-4.39727 - 7.61630i) q^{48} +(142.880 - 247.476i) q^{49} +(-266.754 + 462.032i) q^{50} -503.461 q^{51} -480.202 q^{53} +(38.3998 - 66.5103i) q^{54} +(45.8525 - 79.4188i) q^{55} +(-85.0594 - 147.327i) q^{56} -385.774 q^{57} +(-104.893 - 181.679i) q^{58} +(175.267 + 303.572i) q^{59} +720.338 q^{60} +(242.233 + 419.560i) q^{61} +(-72.6746 + 125.876i) q^{62} +(77.7509 - 134.669i) q^{63} +304.379 q^{64} +52.4550 q^{66} +(-483.776 + 837.925i) q^{67} +(-183.080 + 317.103i) q^{68} +(115.936 + 200.806i) q^{69} +272.237 q^{70} +(-201.375 - 348.791i) q^{71} +(231.081 + 400.244i) q^{72} +351.621 q^{73} +(148.331 + 256.916i) q^{74} +(-1064.76 + 1844.22i) q^{75} +(-140.283 + 242.978i) q^{76} -33.3112 q^{77} -820.078 q^{79} +(13.2813 - 23.0039i) q^{80} +(430.748 - 746.078i) q^{81} +(80.8285 + 139.999i) q^{82} -192.314 q^{83} +(-130.829 - 226.603i) q^{84} +(-760.315 - 1316.90i) q^{85} +763.226 q^{86} +(-418.683 - 725.180i) q^{87} +(49.5016 - 85.7392i) q^{88} +(-406.786 + 704.573i) q^{89} -739.587 q^{90} +168.636 q^{92} +(-290.083 + 502.439i) q^{93} +(235.414 - 407.750i) q^{94} +(-582.586 - 1009.07i) q^{95} +1255.67 q^{96} +(394.146 + 682.682i) q^{97} +(246.845 + 427.548i) q^{98} +90.4966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9	\( 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9} + 147 q^{10} + 181 q^{11} + 78 q^{12} - 294 q^{14} + 218 q^{15} - 269 q^{16} + 55 q^{17} - 158 q^{18} + 161 q^{19} + 370 q^{20} - 376 q^{21} - 340 q^{22} + 204 q^{23} + 798 q^{24} + 614 q^{25} - 1336 q^{27} + 344 q^{28} - 280 q^{29} - 521 q^{30} - 1412 q^{31} + 680 q^{32} + 500 q^{33} - 432 q^{34} - 20 q^{35} + 909 q^{36} + 298 q^{37} - 1478 q^{38} + 26 q^{40} + 1201 q^{41} + 4 q^{42} + 533 q^{43} - 710 q^{44} - 90 q^{45} - 840 q^{46} - 1912 q^{47} + 132 q^{48} - 403 q^{49} - 1156 q^{50} + 940 q^{51} - 556 q^{53} - 2555 q^{54} + 250 q^{55} - 250 q^{56} + 1620 q^{57} - 2877 q^{58} + 1377 q^{59} + 6314 q^{60} + 136 q^{61} - 2035 q^{62} - 944 q^{63} + 568 q^{64} + 6558 q^{66} - 931 q^{67} + 1536 q^{68} + 2050 q^{69} + 9708 q^{70} + 2046 q^{71} - 4342 q^{72} + 90 q^{73} + 1990 q^{74} - 2393 q^{75} - 3608 q^{76} - 1436 q^{77} + 824 q^{79} - 787 q^{80} + 835 q^{81} - 2757 q^{82} - 7418 q^{83} - 1539 q^{84} - 2106 q^{85} - 250 q^{86} + 786 q^{87} + 636 q^{88} + 1663 q^{89} - 2560 q^{90} + 8020 q^{92} - 1186 q^{93} + 2531 q^{94} + 1614 q^{95} + 6168 q^{96} - 1087 q^{97} - 282 q^{98} - 2714 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9 + 147 * q^10 + 181 * q^11 + 78 * q^12 - 294 * q^14 + 218 * q^15 - 269 * q^16 + 55 * q^17 - 158 * q^18 + 161 * q^19 + 370 * q^20 - 376 * q^21 - 340 * q^22 + 204 * q^23 + 798 * q^24 + 614 * q^25 - 1336 * q^27 + 344 * q^28 - 280 * q^29 - 521 * q^30 - 1412 * q^31 + 680 * q^32 + 500 * q^33 - 432 * q^34 - 20 * q^35 + 909 * q^36 + 298 * q^37 - 1478 * q^38 + 26 * q^40 + 1201 * q^41 + 4 * q^42 + 533 * q^43 - 710 * q^44 - 90 * q^45 - 840 * q^46 - 1912 * q^47 + 132 * q^48 - 403 * q^49 - 1156 * q^50 + 940 * q^51 - 556 * q^53 - 2555 * q^54 + 250 * q^55 - 250 * q^56 + 1620 * q^57 - 2877 * q^58 + 1377 * q^59 + 6314 * q^60 + 136 * q^61 - 2035 * q^62 - 944 * q^63 + 568 * q^64 + 6558 * q^66 - 931 * q^67 + 1536 * q^68 + 2050 * q^69 + 9708 * q^70 + 2046 * q^71 - 4342 * q^72 + 90 * q^73 + 1990 * q^74 - 2393 * q^75 - 3608 * q^76 - 1436 * q^77 + 824 * q^79 - 787 * q^80 + 835 * q^81 - 2757 * q^82 - 7418 * q^83 - 1539 * q^84 - 2106 * q^85 - 250 * q^86 + 786 * q^87 + 636 * q^88 + 1663 * q^89 - 2560 * q^90 + 8020 * q^92 - 1186 * q^93 + 2531 * q^94 + 1614 * q^95 + 6168 * q^96 - 1087 * q^97 - 282 * q^98 - 2714 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.863817	+	1.49617i	−0.305405	+	0.528978i	−0.977351	−	0.211622i	$-0.932125\pi$
$2$	−0.863817	+	1.49617i	−0.305405	+	0.528978i	0.671946	+	0.740600i	$0.265459\pi$
$3$	−3.44796	+	5.97204i	−0.663560	+	1.14932i	0.316114	+	0.948721i	$0.397622\pi$
$3$	−3.44796	+	5.97204i	−0.663560	+	1.14932i	−0.979674	+	0.200598i	$0.935712\pi$
$4$	2.50764	+	4.34336i	0.313455	+	0.542920i
$5$	−20.8281			−1.86292			−0.931460	−	0.363844i	$-0.881464\pi$
$5$	−20.8281			−1.86292			−0.931460	+	0.363844i	$0.881464\pi$
$6$	−5.95681	−	10.3175i	−0.405309	−	0.702016i
$7$	3.78283	+	6.55206i	0.204254	+	0.353778i	0.949895	−	0.312570i	$-0.101190\pi$
$7$	3.78283	+	6.55206i	0.204254	+	0.353778i	−0.745641	+	0.666348i	$0.767857\pi$
$8$	−22.4856			−0.993734
$9$	−10.2768	−	17.8000i	−0.380623	−	0.659258i
$10$	17.9916	−	31.1624i	0.568946	−	0.985443i
$11$	−2.20147	+	3.81307i	−0.0603427	+	0.104517i	−0.894619	−	0.446831i	$-0.852553\pi$
$11$	−2.20147	+	3.81307i	−0.0603427	+	0.104517i	0.834276	+	0.551347i	$0.185886\pi$
$12$	−34.5850			−0.831985
$13$		0			0
$13$		0			0
$14$	−13.0707			−0.249521
$15$	71.8143	−	124.386i	1.23616	−	2.14109i
$16$	−0.637664	+	1.10447i	−0.00996349	+	0.0172573i
$17$	36.5043	+	63.2274i	0.520800	+	0.902052i	0.999707	+	0.0241867i	$0.00769963\pi$
$17$	36.5043	+	63.2274i	0.520800	+	0.902052i	−0.478907	+	0.877865i	$0.658967\pi$
$18$	35.5091			0.464977
$19$	27.9712	+	48.4475i	0.337738	+	0.584980i	0.984007	−	0.178130i	$-0.0570047\pi$
$19$	27.9712	+	48.4475i	0.337738	+	0.584980i	−0.646269	+	0.763110i	$0.723671\pi$
$20$	−52.2293	−	90.4639i	−0.583942	−	1.01142i
$21$	−52.1722			−0.542138
$22$	−3.80334	−	6.58758i	−0.0368580	−	0.0638398i
$23$	16.8122	−	29.1196i	0.152417	−	0.263994i	−0.779699	−	0.626155i	$-0.784628\pi$
$23$	16.8122	−	29.1196i	0.152417	−	0.263994i	0.932115	+	0.362161i	$0.117961\pi$
$24$	77.5295	−	134.285i	0.659402	−	1.14212i
$25$	308.809			2.47047
$26$		0			0
$27$	−44.4536			−0.316855
$28$	−18.9720	+	32.8604i	−0.128049	+	0.221787i
$29$	−60.7146	+	105.161i	−0.388773	+	0.673375i	−0.992285	−	0.123979i	$-0.960434\pi$
$29$	−60.7146	+	105.161i	−0.388773	+	0.673375i	0.603512	+	0.797354i	$0.293768\pi$
$30$	124.069	+	214.893i	0.755059	+	1.30780i
$31$	84.1320			0.487437			0.243719	−	0.969846i	$-0.421633\pi$
$31$	84.1320			0.487437			0.243719	+	0.969846i	$0.421633\pi$
$32$	−91.0442	−	157.693i	−0.502953	−	0.871140i
$33$	−15.1812	−	26.2946i	−0.0800819	−	0.138706i
$34$	−126.132			−0.636220
$35$	−78.7891	−	136.467i	−0.380508	−	0.659059i
$36$	51.5411	−	89.2719i	0.238616	−	0.413296i
$37$	85.8578	−	148.710i	0.381485	−	0.660751i	−0.609790	−	0.792563i	$-0.708746\pi$
$37$	85.8578	−	148.710i	0.381485	−	0.660751i	0.991275	+	0.131812i	$0.0420796\pi$
$38$	−96.6479			−0.412588
$39$		0			0
$40$	468.332			1.85125
$41$	46.7857	−	81.0352i	0.178212	−	0.308673i	−0.763056	−	0.646332i	$-0.776302\pi$
$41$	46.7857	−	81.0352i	0.178212	−	0.308673i	0.941268	+	0.337660i	$0.109635\pi$
$42$	45.0672	−	78.0586i	0.165572	−	0.286779i
$43$	−220.888	−	382.589i	−0.783374	−	1.35684i	−0.929966	−	0.367646i	$-0.880164\pi$
$43$	−220.888	−	382.589i	−0.783374	−	1.35684i	0.146592	−	0.989197i	$-0.453170\pi$
$44$	−22.0820			−0.0756589
$45$	214.046	+	370.739i	0.709070	+	1.22814i
$46$	29.0453	+	50.3080i	0.0930978	+	0.161250i
$47$	−272.528			−0.845794			−0.422897	−	0.906178i	$-0.638987\pi$
$47$	−272.528			−0.845794			−0.422897	+	0.906178i	$0.638987\pi$
$48$	−4.39727	−	7.61630i	−0.0132227	−	0.0229025i
$49$	142.880	−	247.476i	0.416561	−	0.721505i
$50$	−266.754	+	462.032i	−0.754494	+	1.30682i
$51$	−503.461			−1.38233
$52$		0			0
$53$	−480.202			−1.24454			−0.622272	−	0.782801i	$-0.713790\pi$
$53$	−480.202			−1.24454			−0.622272	+	0.782801i	$0.713790\pi$
$54$	38.3998	−	66.5103i	0.0967694	−	0.167609i
$55$	45.8525	−	79.4188i	0.112414	−	0.194706i
$56$	−85.0594	−	147.327i	−0.202974	−	0.351561i
$57$	−385.774			−0.896438
$58$	−104.893	−	181.679i	−0.237467	−	0.411305i
$59$	175.267	+	303.572i	0.386743	+	0.669859i	0.992009	−	0.126164i	$-0.0402666\pi$
$59$	175.267	+	303.572i	0.386743	+	0.669859i	−0.605266	+	0.796023i	$0.706933\pi$
$60$	720.338			1.54992
$61$	242.233	+	419.560i	0.508439	+	0.880643i	0.999952	+	0.00977232i	$0.00311068\pi$
$61$	242.233	+	419.560i	0.508439	+	0.880643i	−0.491513	+	0.870870i	$0.663556\pi$
$62$	−72.6746	+	125.876i	−0.148866	+	0.257843i
$63$	77.7509	−	134.669i	0.155487	−	0.269312i
$64$	304.379			0.594491
$65$		0			0
$66$	52.4550			0.0978298
$67$	−483.776	+	837.925i	−0.882129	+	1.52789i	−0.0331598	+	0.999450i	$0.510557\pi$
$67$	−483.776	+	837.925i	−0.882129	+	1.52789i	−0.848969	+	0.528442i	$0.822776\pi$
$68$	−183.080	+	317.103i	−0.326495	+	0.565506i
$69$	115.936	+	200.806i	0.202275	+	0.350351i
$70$	272.237			0.464837
$71$	−201.375	−	348.791i	−0.336603	−	0.583013i	0.647189	−	0.762330i	$-0.275945\pi$
$71$	−201.375	−	348.791i	−0.336603	−	0.583013i	−0.983791	+	0.179317i	$0.942611\pi$
$72$	231.081	+	400.244i	0.378238	+	0.655127i
$73$	351.621			0.563754			0.281877	−	0.959450i	$-0.409043\pi$
$73$	351.621			0.563754			0.281877	+	0.959450i	$0.409043\pi$
$74$	148.331	+	256.916i	0.233015	+	0.403594i
$75$	−1064.76	+	1844.22i	−1.63930	+	2.83936i
$76$	−140.283	+	242.978i	−0.211732	+	0.366730i
$77$	−33.3112			−0.0493009
$78$		0			0
$79$	−820.078			−1.16792			−0.583962	−	0.811781i	$-0.698498\pi$
$79$	−820.078			−1.16792			−0.583962	+	0.811781i	$0.698498\pi$
$80$	13.2813	−	23.0039i	0.0185612	−	0.0321489i
$81$	430.748	−	746.078i	0.590875	−	1.02343i
$82$	80.8285	+	139.999i	0.108854	+	0.188540i
$83$	−192.314			−0.254328			−0.127164	−	0.991882i	$-0.540587\pi$
$83$	−192.314			−0.254328			−0.127164	+	0.991882i	$0.540587\pi$
$84$	−130.829	−	226.603i	−0.169936	−	0.294338i
$85$	−760.315	−	1316.90i	−0.970209	−	1.68045i
$86$	763.226			0.956986
$87$	−418.683	−	725.180i	−0.515948	−	0.893649i
$88$	49.5016	−	85.7392i	0.0599646	−	0.103862i
$89$	−406.786	+	704.573i	−0.484485	+	0.839153i	−0.999841	−	0.0178232i	$-0.994326\pi$
$89$	−406.786	+	704.573i	−0.484485	+	0.839153i	0.515356	+	0.856976i	$0.327660\pi$
$90$	−739.587			−0.866215
$91$		0			0
$92$	168.636			0.191103
$93$	−290.083	+	502.439i	−0.323444	+	0.560221i
$94$	235.414	−	407.750i	0.258310	−	0.447406i
$95$	−582.586	−	1009.07i	−0.629180	−	1.08977i
$96$	1255.67			1.33496
$97$	394.146	+	682.682i	0.412572	+	0.714596i	0.995170	−	0.0981645i	$-0.0312971\pi$
$97$	394.146	+	682.682i	0.412572	+	0.714596i	−0.582598	+	0.812760i	$0.697964\pi$
$98$	246.845	+	427.548i	0.254440	+	0.440703i
$99$	90.4966			0.0918712
$100$	774.381	+	1341.27i	0.774381	+	1.34127i
$101$	796.530	−	1379.63i	0.784730	−	1.35919i	−0.144430	−	0.989515i	$-0.546135\pi$
$101$	796.530	−	1379.63i	0.784730	−	1.35919i	0.929160	−	0.369677i	$-0.120532\pi$
$102$	434.898	−	753.266i	0.422170	−	0.731220i
$103$	−134.659			−0.128819			−0.0644094	−	0.997924i	$-0.520516\pi$
$103$	−134.659			−0.128819			−0.0644094	+	0.997924i	$0.520516\pi$
$104$		0			0
$105$	1086.65			1.00996
$106$	414.806	−	718.466i	0.380090	−	0.658335i
$107$	389.609	−	674.823i	0.352009	−	0.609697i	−0.634592	−	0.772847i	$-0.718832\pi$
$107$	389.609	−	674.823i	0.352009	−	0.609697i	0.986601	+	0.163150i	$0.0521653\pi$
$108$	−111.474	−	193.078i	−0.0993200	−	0.172027i
$109$	−1341.63			−1.17894			−0.589472	−	0.807789i	$-0.700664\pi$
$109$	−1341.63			−1.17894			−0.589472	+	0.807789i	$0.700664\pi$
$110$	79.2163	+	137.207i	0.0686634	+	0.118928i
$111$	592.068	+	1025.49i	0.506276	+	0.876895i
$112$	−9.64870			−0.00814032
$113$	−611.069	−	1058.40i	−0.508712	−	0.881116i	−0.999949	−	0.0100896i	$-0.996788\pi$
$113$	−611.069	−	1058.40i	−0.508712	−	0.881116i	0.491237	−	0.871026i	$-0.336545\pi$
$114$	333.238	−	577.185i	0.273777	−	0.474196i
$115$	−350.166	+	606.505i	−0.283940	+	0.491799i
$116$	−609.002			−0.487452
$117$		0			0
$118$	−605.595			−0.472454
$119$	−276.179	+	478.357i	−0.212751	+	0.368495i
$120$	−1614.79	+	2796.90i	−1.22841	+	2.12767i
$121$	655.807	+	1135.89i	0.492718	+	0.853412i
$122$	−836.981			−0.621120
$123$	322.630	+	558.812i	0.236509	+	0.409645i
$124$	210.973	+	365.416i	0.152790	+	0.264639i
$125$	−3828.38			−2.73937
$126$	134.325	+	232.658i	0.0949733	+	0.164498i
$127$	−224.443	+	388.747i	−0.156820	+	0.271620i	−0.933720	−	0.358004i	$-0.883458\pi$
$127$	−224.443	+	388.747i	−0.156820	+	0.271620i	0.776900	+	0.629624i	$0.216791\pi$
$128$	465.426	−	806.141i	0.321392	−	0.556668i
$129$	3046.45			2.07926
$130$		0			0
$131$	1787.67			1.19229			0.596144	−	0.802877i	$-0.296699\pi$
$131$	1787.67			1.19229			0.596144	+	0.802877i	$0.296699\pi$
$132$	76.1379	−	131.875i	0.0502042	−	0.0869562i
$133$	−211.621	+	366.538i	−0.137969	+	0.238969i
$134$	−835.788	−	1447.63i	−0.538814	−	0.933253i
$135$	925.883			0.590276
$136$	−820.823	−	1421.71i	−0.517537	−	0.896400i
$137$	415.017	+	718.830i	0.258812	+	0.448276i	0.965924	−	0.258826i	$-0.0833356\pi$
$137$	415.017	+	718.830i	0.258812	+	0.448276i	−0.707112	+	0.707102i	$0.750002\pi$
$138$	−400.588			−0.247104
$139$	−494.673	−	856.799i	−0.301854	−	0.522826i	0.674702	−	0.738090i	$-0.264272\pi$
$139$	−494.673	−	856.799i	−0.301854	−	0.522826i	−0.976556	+	0.215264i	$0.930939\pi$
$140$	395.150	−	684.419i	0.238545	−	0.413171i
$141$	939.666	−	1627.55i	0.561235	−	0.972088i
$142$	695.803			0.411201
$143$		0			0
$144$	26.2126			0.0151693
$145$	1264.57	−	2190.30i	0.724253	−	1.25444i
$146$	−303.736	+	526.086i	−0.172174	+	0.298213i
$147$	985.291	+	1706.57i	0.552826	+	0.957523i
$148$	861.202			0.478313
$149$	−234.787	−	406.663i	−0.129091	−	0.223592i	0.794234	−	0.607612i	$-0.207873\pi$
$149$	−234.787	−	406.663i	−0.129091	−	0.223592i	−0.923325	+	0.384021i	$0.874539\pi$
$150$	−1839.51	−	3186.13i	−1.00130	−	1.73431i
$151$	1936.82			1.04382			0.521908	−	0.853002i	$-0.325220\pi$
$151$	1936.82			1.04382			0.521908	+	0.853002i	$0.325220\pi$
$152$	−628.950	−	1089.37i	−0.335622	−	0.581315i
$153$	750.297	−	1299.55i	0.396457	−	0.686683i
$154$	28.7748	−	49.8394i	0.0150567	−	0.0260790i
$155$	−1752.31			−0.908056
$156$		0			0
$157$	−2891.58			−1.46989			−0.734946	−	0.678125i	$-0.762793\pi$
$157$	−2891.58			−1.46989			−0.734946	+	0.678125i	$0.762793\pi$
$158$	708.397	−	1226.98i	0.356690	−	0.617806i
$159$	1655.72	−	2867.78i	0.825829	−	1.43038i
$160$	1896.28	+	3284.45i	0.936961	+	1.62286i
$161$	254.391			0.124527
$162$	744.175	+	1288.95i	0.360913	+	0.625120i
$163$	−1146.99	−	1986.64i	−0.551160	−	0.954638i	−0.998191	−	0.0601193i	$-0.980852\pi$
$163$	−1146.99	−	1986.64i	−0.551160	−	0.954638i	0.447031	−	0.894519i	$-0.352481\pi$
$164$	469.287			0.223446
$165$	316.195	+	547.665i	0.149186	+	0.258398i
$166$	166.124	−	287.736i	0.0776732	−	0.134534i
$167$	563.322	−	975.703i	0.261025	−	0.452109i	−0.705490	−	0.708720i	$-0.749273\pi$
$167$	563.322	−	975.703i	0.261025	−	0.452109i	0.966515	+	0.256612i	$0.0826062\pi$
$168$	1173.12			0.538741
$169$		0			0
$170$	2627.09			1.18523
$171$	574.910	−	995.773i	0.257102	−	0.445314i
$172$	1107.81	−	1918.79i	0.491105	−	0.850619i
$173$	255.950	+	443.318i	0.112483	+	0.194826i	0.916771	−	0.399414i	$-0.130786\pi$
$173$	255.950	+	443.318i	0.112483	+	0.194826i	−0.804288	+	0.594240i	$0.797453\pi$
$174$	1446.66			0.630293
$175$	1168.17	+	2023.33i	0.504602	+	0.873997i
$176$	−2.80760	−	4.86291i	−0.00120245	−	0.00208270i
$177$	−2417.26			−1.02651
$178$	−702.776	−	1217.24i	−0.295929	−	0.512564i
$179$	−181.695	+	314.706i	−0.0758690	+	0.131409i	−0.901464	−	0.432854i	$-0.857506\pi$
$179$	−181.695	+	314.706i	−0.0758690	+	0.131409i	0.825595	+	0.564263i	$0.190840\pi$
$180$	−1073.50	+	1859.36i	−0.444523	+	0.769937i
$181$	780.933			0.320698			0.160349	−	0.987060i	$-0.448738\pi$
$181$	780.933			0.320698			0.160349	+	0.987060i	$0.448738\pi$
$182$		0			0
$183$	−3340.84			−1.34952
$184$	−378.033	+	654.773i	−0.151462	+	0.262340i
$185$	−1788.25	+	3097.34i	−0.710675	+	1.23093i
$186$	−501.158	−	868.031i	−0.197563	−	0.342189i
$187$	−321.453			−0.125706
$188$	−683.403	−	1183.69i	−0.265119	−	0.459199i
$189$	−168.160	−	291.262i	−0.0647189	−	0.112096i
$190$	2012.99			0.768619
$191$	2004.87	+	3472.54i	0.759515	+	1.31552i	0.943098	+	0.332514i	$0.107897\pi$
$191$	2004.87	+	3472.54i	0.759515	+	1.31552i	−0.183584	+	0.983004i	$0.558770\pi$
$192$	−1049.49	+	1817.76i	−0.394480	+	0.683260i
$193$	−82.6579	+	143.168i	−0.0308282	+	0.0533960i	−0.881028	−	0.473064i	$-0.843148\pi$
$193$	−82.6579	+	143.168i	−0.0308282	+	0.0533960i	0.850200	+	0.526460i	$0.176481\pi$
$194$	−1361.88			−0.504007
$195$		0			0
$196$	1433.17			0.522293
$197$	410.638	−	711.246i	0.148511	−	0.257229i	−0.782166	−	0.623070i	$-0.785885\pi$
$197$	410.638	−	711.246i	0.148511	−	0.257229i	0.930677	+	0.365841i	$0.119219\pi$
$198$	−78.1725	+	135.399i	−0.0280580	+	0.0485978i
$199$	19.2851	+	33.4028i	0.00686978	+	0.0118988i	0.869440	−	0.494039i	$-0.164480\pi$
$199$	19.2851	+	33.4028i	0.00686978	+	0.0118988i	−0.862570	+	0.505938i	$0.831147\pi$
$200$	−6943.76			−2.45499
$201$	−3336.08	−	5778.26i	−1.17069	−	2.02770i
$202$	1376.11	+	2383.50i	0.479322	+	0.830209i
$203$	−918.693			−0.317633
$204$	−1262.50	−	2186.72i	−0.433298	−	0.750494i
$205$	−974.456	+	1687.81i	−0.331995	+	0.575032i
$206$	116.321	−	201.473i	0.0393419	−	0.0681423i
$207$	−691.104			−0.232053
$208$		0			0
$209$	−246.311			−0.0815202
$210$	−938.663	+	1625.81i	−0.308447	+	0.534246i
$211$	−2522.00	+	4368.24i	−0.822853	+	1.42522i	0.0806966	+	0.996739i	$0.474286\pi$
$211$	−2522.00	+	4368.24i	−0.822853	+	1.42522i	−0.903549	+	0.428484i	$0.859048\pi$
$212$	−1204.17	−	2085.69i	−0.390108	−	0.675688i
$213$	2777.33			0.893423
$214$	673.102	+	1165.85i	0.215011	+	0.372410i
$215$	4600.67	+	7968.59i	1.45936	+	2.52769i
$216$	999.567			0.314870
$217$	318.257	+	551.237i	0.0995608	+	0.172444i
$218$	1158.92	−	2007.31i	0.360056	−	0.623635i
$219$	−1212.37	+	2099.89i	−0.374085	+	0.647934i
$220$	459.926			0.140946
$221$		0			0
$222$	−2045.75			−0.618477
$223$	−3063.89	+	5306.81i	−0.920059	+	1.59359i	−0.120738	+	0.992684i	$0.538526\pi$
$223$	−3063.89	+	5306.81i	−0.920059	+	1.59359i	−0.799321	+	0.600905i	$0.794807\pi$
$224$	688.810	−	1193.05i	0.205460	−	0.355867i
$225$	−3173.57	−	5496.78i	−0.940317	−	1.62868i
$226$	2111.41			0.621454
$227$	3171.46	+	5493.13i	0.927300	+	1.60613i	0.787819	+	0.615907i	$0.211210\pi$
$227$	3171.46	+	5493.13i	0.927300	+	1.60613i	0.139481	+	0.990225i	$0.455457\pi$
$228$	−967.382	−	1675.56i	−0.280993	−	0.486695i
$229$	1334.67			0.385141			0.192571	−	0.981283i	$-0.438318\pi$
$229$	1334.67			0.385141			0.192571	+	0.981283i	$0.438318\pi$
$230$	−604.958	−	1047.82i	−0.173434	−	0.300396i
$231$	114.856	−	198.936i	0.0327141	−	0.0566624i
$232$	1365.21	−	2364.61i	0.386337	−	0.669156i
$233$	−5392.39			−1.51617			−0.758084	−	0.652157i	$-0.773864\pi$
$233$	−5392.39			−1.51617			−0.758084	+	0.652157i	$0.773864\pi$
$234$		0			0
$235$	5676.24			1.57565
$236$	−879.015	+	1522.50i	−0.242453	+	0.419941i
$237$	2827.59	−	4897.54i	0.774987	−	1.34232i
$238$	−477.137	−	826.425i	−0.129950	−	0.225081i
$239$	−3748.70			−1.01458			−0.507288	−	0.861777i	$-0.669352\pi$
$239$	−3748.70			−1.01458			−0.507288	+	0.861777i	$0.669352\pi$
$240$	91.5867	+	158.633i	0.0246329	+	0.0426655i
$241$	−1914.74	−	3316.42i	−0.511780	−	0.886429i	−0.999907	−	0.0136563i	$-0.995653\pi$
$241$	−1914.74	−	3316.42i	−0.511780	−	0.886429i	0.488127	−	0.872773i	$-0.337680\pi$
$242$	−2265.99			−0.601914
$243$	2370.28	+	4105.44i	0.625734	+	1.08380i
$244$	−1214.87	+	2104.21i	−0.318746	+	0.552084i
$245$	−2975.92	+	5154.45i	−0.776019	+	1.34410i
$246$	−1114.77			−0.288924
$247$		0			0
$248$	−1891.76			−0.484383
$249$	663.091	−	1148.51i	0.168762	−	0.292304i
$250$	3307.02	−	5727.92i	0.836617	−	1.44906i
$251$	238.289	+	412.728i	0.0599229	+	0.103790i	0.894431	−	0.447207i	$-0.147581\pi$
$251$	238.289	+	412.728i	0.0599229	+	0.103790i	−0.834508	+	0.550996i	$0.814248\pi$
$252$	779.886			0.194953
$253$	74.0233	+	128.212i	0.0183945	+	0.0318602i
$254$	−387.756	−	671.612i	−0.0957872	−	0.165908i
$255$	10486.1			2.57517
$256$	2021.60	+	3501.52i	0.493555	+	0.854863i
$257$	−127.338	+	220.556i	−0.0309071	+	0.0535327i	−0.881065	−	0.472995i	$-0.843173\pi$
$257$	−127.338	+	220.556i	−0.0309071	+	0.0535327i	0.850158	+	0.526527i	$0.176506\pi$
$258$	−2631.57	+	4558.01i	−0.635017	+	1.09988i
$259$	1299.14			0.311679
$260$		0			0
$261$	2495.81			0.591904
$262$	−1544.22	+	2674.67i	−0.364131	+	0.630694i
$263$	−1122.48	+	1944.20i	−0.263176	+	0.455834i	−0.967084	−	0.254457i	$-0.918103\pi$
$263$	−1122.48	+	1944.20i	−0.263176	+	0.455834i	0.703908	+	0.710291i	$0.251437\pi$
$264$	341.358	+	591.250i	0.0795802	+	0.137837i
$265$	10001.7			2.31848
$266$	−365.603	−	633.243i	−0.0842727	−	0.145965i
$267$	−2805.16	−	4858.68i	−0.642970	−	1.11366i
$268$	−4852.55			−1.10603
$269$	−2292.66	−	3971.00i	−0.519650	−	0.900060i	−0.999739	−	0.0228404i	$-0.992729\pi$
$269$	−2292.66	−	3971.00i	−0.519650	−	0.900060i	0.480089	−	0.877220i	$-0.340604\pi$
$270$	−799.793	+	1385.28i	−0.180274	+	0.312243i
$271$	3986.40	−	6904.64i	0.893566	−	1.54770i	0.0579969	−	0.998317i	$-0.481529\pi$
$271$	3986.40	−	6904.64i	0.893566	−	1.54770i	0.835569	−	0.549385i	$-0.185138\pi$
$272$	−93.1099			−0.0207560
$273$		0			0
$274$	−1433.99			−0.316171
$275$	−679.834	+	1177.51i	−0.149075	+	0.258205i
$276$	−581.450	+	1007.10i	−0.126809	+	0.219639i
$277$	−2654.40	−	4597.55i	−0.575766	−	0.997256i	−0.995958	−	0.0898206i	$-0.971371\pi$
$277$	−2654.40	−	4597.55i	−0.575766	−	0.997256i	0.420192	−	0.907435i	$-0.361963\pi$
$278$	1709.23			0.368751
$279$	−864.609	−	1497.55i	−0.185530	−	0.321347i
$280$	1771.62	+	3068.54i	0.378124	+	0.654930i
$281$	6534.86			1.38732			0.693661	−	0.720302i	$-0.255997\pi$
$281$	6534.86			1.38732			0.693661	+	0.720302i	$0.255997\pi$
$282$	1623.40	+	2811.81i	0.342808	+	0.593761i
$283$	−2096.30	+	3630.90i	−0.440326	+	0.762667i	−0.997713	−	0.0675855i	$-0.978470\pi$
$283$	−2096.30	+	3630.90i	−0.440326	+	0.762667i	0.557388	+	0.830252i	$0.311804\pi$
$284$	1009.95	−	1749.29i	0.211020	−	0.365497i
$285$	8034.93			1.66999
$286$		0			0
$287$	707.930			0.145602
$288$	−1871.29	+	3241.17i	−0.382871	+	0.663152i
$289$	−208.633	+	361.362i	−0.0424654	+	0.0735523i
$290$	2184.71	+	3784.03i	0.442381	+	0.766227i
$291$	−5436.00			−1.09506
$292$	881.738	+	1527.22i	0.176712	+	0.306074i
$293$	1196.95	+	2073.17i	0.238656	+	0.413365i	0.960329	−	0.278870i	$-0.0899597\pi$
$293$	1196.95	+	2073.17i	0.238656	+	0.413365i	−0.721673	+	0.692235i	$0.756626\pi$
$294$	−3404.44			−0.675344
$295$	−3650.48	−	6322.81i	−0.720471	−	1.24789i
$296$	−1930.57	+	3343.84i	−0.379094	+	0.656611i
$297$	97.8635	−	169.504i	0.0191199	−	0.0331167i
$298$	811.253			0.157700
$299$		0			0
$300$	−10680.1			−2.05539
$301$	1671.16	−	2894.54i	0.320014	−	0.554280i
$302$	−1673.06	+	2897.82i	−0.318787	+	0.552156i
$303$	5492.81	+	9513.82i	1.04143	+	1.80381i
$304$	−71.3448			−0.0134602
$305$	−5045.25	−	8738.63i	−0.947181	−	1.64057i
$306$	1296.24	+	2245.15i	0.242160	+	0.419433i
$307$	−821.783			−0.152774			−0.0763870	−	0.997078i	$-0.524338\pi$
$307$	−821.783			−0.152774			−0.0763870	+	0.997078i	$0.524338\pi$
$308$	−83.5326	−	144.683i	−0.0154536	−	0.0267664i
$309$	464.298	−	804.188i	0.0854790	−	0.148054i
$310$	1513.67	−	2621.76i	0.277325	−	0.480341i
$311$	−5490.98			−1.00117			−0.500587	−	0.865686i	$-0.666882\pi$
$311$	−5490.98			−1.00117			−0.500587	+	0.865686i	$0.666882\pi$
$312$		0			0
$313$	−315.481			−0.0569714			−0.0284857	−	0.999594i	$-0.509069\pi$
$313$	−315.481			−0.0569714			−0.0284857	+	0.999594i	$0.509069\pi$
$314$	2497.79	−	4326.31i	0.448913	−	0.777540i
$315$	−1619.40	+	2804.89i	−0.289660	+	0.501706i
$316$	−2056.46	−	3561.90i	−0.366092	−	0.634090i
$317$	−8295.72			−1.46982			−0.734912	−	0.678163i	$-0.762777\pi$
$317$	−8295.72			−1.46982			−0.734912	+	0.678163i	$0.762777\pi$
$318$	2860.47	+	4954.48i	0.504425	+	0.873690i
$319$	−267.323	−	463.018i	−0.0469192	−	0.0812665i
$320$	−6339.64			−1.10749
$321$	2686.71	+	4653.52i	0.467158	+	0.809141i
$322$	−219.747	+	380.613i	−0.0380311	+	0.0658719i
$323$	−2042.14	+	3537.09i	−0.351788	+	0.609315i
$324$	4320.65			0.740852
$325$		0			0
$326$	3963.15			0.673309
$327$	4625.88	−	8012.27i	0.782300	−	1.35498i
$328$	−1052.01	+	1822.13i	−0.177096	+	0.306738i
$329$	−1030.93	−	1785.62i	−0.172757	−	0.299223i
$330$	−1092.54			−0.182249
$331$	−427.534	−	740.510i	−0.0709951	−	0.122967i	0.828343	−	0.560222i	$-0.189284\pi$
$331$	−427.534	−	740.510i	−0.0709951	−	0.122967i	−0.899338	+	0.437255i	$0.855951\pi$
$332$	−482.255	−	835.291i	−0.0797205	−	0.138080i
$333$	−3529.38			−0.580807
$334$	973.214	+	1685.66i	0.159437	+	0.276153i
$335$	10076.1	−	17452.4i	1.64334	−	2.84634i
$336$	33.2683	−	57.6224i	0.00540159	−	0.00935583i
$337$	−3400.09			−0.549598			−0.274799	−	0.961502i	$-0.588611\pi$
$337$	−3400.09			−0.549598			−0.274799	+	0.961502i	$0.588611\pi$
$338$		0			0
$339$	8427.75			1.35024
$340$	3813.19	−	6604.65i	0.608234	−	1.05349i
$341$	−185.214	+	320.801i	−0.0294133	+	0.0509453i
$342$	993.233	+	1720.33i	0.157041	+	0.272002i
$343$	4756.99			0.748844
$344$	4966.80	+	8602.75i	0.778465	+	1.34834i
$345$	−2414.71	−	4182.41i	−0.376823	−	0.652676i
$346$	−884.375			−0.137411
$347$	−1772.16	−	3069.48i	−0.274164	−	0.474865i	0.695760	−	0.718274i	$-0.255068\pi$
$347$	−1772.16	−	3069.48i	−0.274164	−	0.474865i	−0.969924	+	0.243409i	$0.921734\pi$
$348$	2099.81	−	3636.98i	0.323453	−	0.560238i
$349$	−4169.60	+	7221.96i	−0.639523	+	1.10769i	0.346014	+	0.938229i	$0.387535\pi$
$349$	−4169.60	+	7221.96i	−0.639523	+	1.10769i	−0.985537	+	0.169458i	$0.945798\pi$
$350$	−4036.34			−0.616433
$351$		0			0
$352$	801.726			0.121398
$353$	−2160.97	+	3742.92i	−0.325827	+	0.564349i	−0.981679	−	0.190540i	$-0.938976\pi$
$353$	−2160.97	+	3742.92i	−0.325827	+	0.564349i	0.655852	+	0.754889i	$0.272309\pi$
$354$	2088.07	−	3616.64i	0.313501	−	0.543000i
$355$	4194.25	+	7264.65i	0.627063	+	1.08611i
$356$	−4080.29			−0.607458
$357$	−1904.51	−	3298.71i	−0.282346	−	0.489037i
$358$	−313.903	−	543.696i	−0.0463416	−	0.0802660i
$359$	−4535.87			−0.666836			−0.333418	−	0.942779i	$-0.608202\pi$
$359$	−4535.87			−0.666836			−0.333418	+	0.942779i	$0.608202\pi$
$360$	−4812.97	−	8336.30i	−0.704627	−	1.22045i
$361$	1864.73	−	3229.80i	0.271865	−	0.470885i
$362$	−674.583	+	1168.41i	−0.0979428	+	0.169642i
$363$	−9044.78			−1.30779
$364$		0			0
$365$	−7323.58			−1.05023
$366$	2885.87	−	4998.48i	0.412150	−	0.713865i
$367$	−112.681	+	195.170i	−0.0160270	+	0.0277596i	−0.873928	−	0.486056i	$-0.838435\pi$
$367$	−112.681	+	195.170i	−0.0160270	+	0.0277596i	0.857901	+	0.513816i	$0.171768\pi$
$368$	21.4411	+	37.1370i	0.00303721	+	0.00526060i
$369$	−1923.23			−0.271326
$370$	−3089.44	−	5351.07i	−0.434088	−	0.751862i
$371$	−1816.52	−	3146.31i	−0.254203	−	0.440292i
$372$	−2909.70			−0.405540
$373$	−1464.63	−	2536.81i	−0.203313	−	0.352148i	0.746281	−	0.665631i	$-0.231837\pi$
$373$	−1464.63	−	2536.81i	−0.203313	−	0.352148i	−0.949594	+	0.313483i	$0.898504\pi$
$374$	277.677	−	480.950i	0.0383912	−	0.0664956i
$375$	13200.1	−	22863.2i	1.81773	−	3.14840i
$376$	6127.97			0.840495
$377$		0			0
$378$	581.039			0.0790620
$379$	3905.38	−	6764.32i	0.529303	−	0.916780i	−0.470113	−	0.882606i	$-0.655787\pi$
$379$	3905.38	−	6764.32i	0.529303	−	0.916780i	0.999416	−	0.0341735i	$-0.0108799\pi$
$380$	2921.83	−	5060.76i	0.394439	−	0.683189i
$381$	−1547.74	−	2680.77i	−0.208119	−	0.360472i
$382$	−6927.36			−0.927839
$383$	2788.07	+	4829.08i	0.371968	+	0.644268i	0.989868	−	0.141989i	$-0.0453496\pi$
$383$	2788.07	+	4829.08i	0.371968	+	0.644268i	−0.617900	+	0.786257i	$0.712016\pi$
$384$	3209.54	+	5559.08i	0.426526	+	0.738764i
$385$	693.809			0.0918435
$386$	−142.802	−	247.341i	−0.0188302	−	0.0326149i
$387$	−4540.05	+	7863.59i	−0.596340	+	1.03289i
$388$	−1976.76	+	3423.84i	−0.258646	+	0.447988i
$389$	12425.7			1.61956			0.809778	−	0.586737i	$-0.199588\pi$
$389$	12425.7			1.61956			0.809778	+	0.586737i	$0.199588\pi$
$390$		0			0
$391$	2454.87			0.317515
$392$	−3212.76	+	5564.66i	−0.413951	+	0.716984i
$393$	−6163.82	+	10676.1i	−0.791154	+	1.37032i
$394$	709.432	+	1228.77i	0.0907123	+	0.157118i
$395$	17080.6			2.17575
$396$	226.933	+	393.060i	0.0287975	+	0.0498787i
$397$	−3209.41	−	5558.86i	−0.405732	−	0.702748i	0.588674	−	0.808370i	$-0.299650\pi$
$397$	−3209.41	−	5558.86i	−0.405732	−	0.702748i	−0.994406	+	0.105622i	$0.966317\pi$
$398$	−66.6353			−0.00839227
$399$	−1459.32	−	2527.61i	−0.183101	−	0.317140i
$400$	−196.916	+	341.069i	−0.0246145	+	0.0426336i
$401$	776.687	−	1345.26i	0.0967230	−	0.167529i	−0.813603	−	0.581420i	$-0.802497\pi$
$401$	776.687	−	1345.26i	0.0967230	−	0.167529i	0.910326	+	0.413891i	$0.135831\pi$
$402$	11527.0			1.43014
$403$		0			0
$404$	7989.65			0.983911
$405$	−8971.65	+	15539.4i	−1.10075	+	1.90656i
$406$	793.582	−	1374.52i	0.0970069	−	0.168021i
$407$	378.027	+	654.763i	0.0460396	+	0.0797430i
$408$	11320.7			1.37367
$409$	−4380.77	−	7587.72i	−0.529622	−	0.917331i	−0.999403	−	0.0345486i	$-0.989001\pi$
$409$	−4380.77	−	7587.72i	−0.529622	−	0.917331i	0.469782	−	0.882783i	$-0.344333\pi$
$410$	−1683.50	−	2915.91i	−0.202786	−	0.351236i
$411$	−5723.84			−0.686949
$412$	−337.676	−	584.872i	−0.0403789	−	0.0699383i
$413$	−1326.01	+	2296.72i	−0.157987	+	0.273642i
$414$	596.987	−	1034.01i	0.0708703	−	0.122751i
$415$	4005.54			0.473793
$416$		0			0
$417$	6822.45			0.801191
$418$	212.768	−	368.525i	0.0248967	−	0.0431223i
$419$	−4130.85	+	7154.85i	−0.481636	+	0.834218i	−0.999778	−	0.0210768i	$-0.993291\pi$
$419$	−4130.85	+	7154.85i	−0.481636	+	0.834218i	0.518142	+	0.855295i	$0.326624\pi$
$420$	2724.92	+	4719.70i	0.316577	+	0.548328i
$421$	−4431.95			−0.513064			−0.256532	−	0.966536i	$-0.582580\pi$
$421$	−4431.95			−0.513064			−0.256532	+	0.966536i	$0.582580\pi$
$422$	−4357.10	−	7546.72i	−0.502607	−	0.870541i
$423$	2800.72	+	4851.00i	0.321929	+	0.557597i
$424$	10797.6			1.23674
$425$	11272.9	+	19525.2i	1.28662	+	2.22849i
$426$	−2399.10	+	4155.36i	−0.272856	+	0.472601i
$427$	−1832.66	+	3174.25i	−0.207701	+	0.359749i
$428$	3908.00			0.441356
$429$		0			0
$430$	−15896.5			−1.78279
$431$	5038.01	−	8726.09i	0.563045	−	0.975223i	−0.434183	−	0.900825i	$-0.642963\pi$
$431$	5038.01	−	8726.09i	0.563045	−	0.975223i	0.997229	−	0.0743985i	$-0.0237037\pi$
$432$	28.3464	−	49.0975i	0.00315699	−	0.00546806i
$433$	−49.8380	−	86.3220i	−0.00553132	−	0.00958053i	0.863246	−	0.504783i	$-0.168427\pi$
$433$	−49.8380	−	86.3220i	−0.00553132	−	0.00958053i	−0.868778	+	0.495202i	$0.835094\pi$
$434$	−1099.66			−0.121626
$435$	8720.36	+	15104.1i	0.961170	+	1.66480i
$436$	−3364.33	−	5827.19i	−0.369546	−	0.640073i
$437$	1881.03			0.205908
$438$	−2094.54	−	3627.84i	−0.228495	−	0.395765i
$439$	−5714.38	+	9897.60i	−0.621258	+	1.07605i	0.367993	+	0.929828i	$0.380045\pi$
$439$	−5714.38	+	9897.60i	−0.621258	+	1.07605i	−0.989252	+	0.146223i	$0.953288\pi$
$440$	−1031.02	+	1785.78i	−0.111709	+	0.193486i
$441$	−5873.42			−0.634210
$442$		0			0
$443$	−4786.94			−0.513396			−0.256698	−	0.966492i	$-0.582635\pi$
$443$	−4786.94			−0.513396			−0.256698	+	0.966492i	$0.582635\pi$
$444$	−2969.39	+	5143.13i	−0.317389	+	0.549735i
$445$	8472.56	−	14674.9i	0.902557	−	1.56327i
$446$	−5293.28	−	9168.22i	−0.561982	−	0.973381i
$447$	3238.15			0.342638
$448$	1151.42	+	1994.31i	0.121427	+	0.210318i
$449$	3238.18	+	5608.69i	0.340355	+	0.589511i	0.984499	−	0.175393i	$-0.0561196\pi$
$449$	3238.18	+	5608.69i	0.340355	+	0.589511i	−0.644144	+	0.764904i	$0.722786\pi$
$450$	10965.5			1.14871
$451$	205.995	+	356.794i	0.0215076	+	0.0372523i
$452$	3064.68	−	5308.19i	0.318917	−	0.552381i
$453$	−6678.08	+	11566.8i	−0.692635	+	1.19968i
$454$	−10958.2			−1.13281
$455$		0			0
$456$	8674.37			0.890822
$457$	464.181	−	803.985i	0.0475131	−	0.0822950i	−0.841291	−	0.540583i	$-0.818204\pi$
$457$	464.181	−	803.985i	0.0475131	−	0.0822950i	0.888804	+	0.458288i	$0.151537\pi$
$458$	−1152.91	+	1996.90i	−0.117624	+	0.203731i
$459$	−1622.75	−	2810.68i	−0.165018	−	0.285820i
$460$	−3512.36			−0.356010
$461$	5269.60	+	9127.22i	0.532386	+	0.922119i	0.999285	+	0.0378085i	$0.0120377\pi$
$461$	5269.60	+	9127.22i	0.532386	+	0.922119i	−0.466899	+	0.884310i	$0.654629\pi$
$462$	198.428	+	343.688i	0.0199821	+	0.0346100i
$463$	−4928.72			−0.494724			−0.247362	−	0.968923i	$-0.579564\pi$
$463$	−4928.72			−0.494724			−0.247362	+	0.968923i	$0.579564\pi$
$464$	−77.4310	−	134.114i	−0.00774708	−	0.0134183i
$465$	6041.88	−	10464.8i	0.602549	−	1.04365i
$466$	4658.04	−	8067.96i	0.463046	−	0.802019i
$467$	326.459			0.0323484			0.0161742	−	0.999869i	$-0.494851\pi$
$467$	326.459			0.0323484			0.0161742	+	0.999869i	$0.494851\pi$
$468$		0			0
$469$	−7320.17			−0.720712
$470$	−4903.23	+	8492.64i	−0.481211	+	0.833482i
$471$	9970.04	−	17268.6i	0.975361	−	1.68938i
$472$	−3941.00	−	6826.00i	−0.384320	−	0.665662i
$473$	1945.12			0.189083
$474$	4885.05	+	8461.15i	0.473371	+	0.819902i
$475$	8637.74	+	14961.0i	0.834372	+	1.44518i
$476$	−2770.24			−0.266751
$477$	4934.95	+	8547.58i	0.473702	+	0.820475i
$478$	3238.19	−	5608.71i	0.309857	−	0.536687i
$479$	−931.754	+	1613.85i	−0.0888787	+	0.153943i	−0.907037	−	0.421050i	$-0.861662\pi$
$479$	−931.754	+	1613.85i	−0.0888787	+	0.153943i	0.818159	+	0.574992i	$0.194995\pi$
$480$	−26153.1			−2.48692
$481$		0			0
$482$	6615.92			0.625201
$483$	−877.129	+	1519.23i	−0.0826310	+	0.143121i
$484$	−3289.06	+	5696.82i	−0.308890	+	0.535013i
$485$	−8209.31	−	14218.9i	−0.768589	−	1.33123i
$486$	−8189.94			−0.764410
$487$	−8689.58	−	15050.8i	−0.808548	−	1.40045i	−0.913870	−	0.406007i	$-0.866921\pi$
$487$	−8689.58	−	15050.8i	−0.808548	−	1.40045i	0.105322	−	0.994438i	$-0.466413\pi$
$488$	−5446.77	−	9434.08i	−0.505253	−	0.875125i
$489$	15819.1			1.46291
$490$	−5141.30	−	8905.00i	−0.474001	−	0.820994i
$491$	−9629.10	+	16678.1i	−0.885041	+	1.53294i	−0.0393748	+	0.999225i	$0.512537\pi$
$491$	−9629.10	+	16678.1i	−0.885041	+	1.53294i	−0.845666	+	0.533712i	$0.820797\pi$
$492$	−1618.08	+	2802.60i	−0.148270	+	0.256811i
$493$	−8865.39			−0.809892
$494$		0			0
$495$	−1884.87			−0.171149
$496$	−53.6479	+	92.9209i	−0.00485658	+	0.00841184i
$497$	1523.53	−	2638.84i	0.137505	−	0.238165i
$498$	1145.58	+	1984.20i	0.103082	+	0.178543i
$499$	−13088.2			−1.17416			−0.587082	−	0.809528i	$-0.699723\pi$
$499$	−13088.2			−1.17416			−0.587082	+	0.809528i	$0.699723\pi$
$500$	−9600.20	−	16628.0i	−0.858668	−	1.48726i
$501$	3884.62	+	6728.36i	0.346411	+	0.600002i
$502$	−823.351			−0.0732031
$503$	−9418.49	−	16313.3i	−0.834890	−	1.44607i	−0.894120	−	0.447828i	$-0.852198\pi$
$503$	−9418.49	−	16313.3i	−0.834890	−	1.44607i	0.0592291	−	0.998244i	$-0.481136\pi$
$504$	−1748.28	+	3028.11i	−0.154513	+	0.267624i
$505$	−16590.2	+	28735.1i	−1.46189	+	2.53207i
$506$	−255.770			−0.0224711
$507$		0			0
$508$	−2251.29			−0.196624
$509$	−76.5973	+	132.670i	−0.00667017	+	0.0115531i	−0.869341	−	0.494212i	$-0.835457\pi$
$509$	−76.5973	+	132.670i	−0.00667017	+	0.0115531i	0.862671	+	0.505765i	$0.168790\pi$
$510$	−9058.10	+	15689.1i	−0.786469	+	1.36220i
$511$	1330.12	+	2303.84i	0.115149	+	0.199444i
$512$	461.635			0.0398468
$513$	−1243.42	−	2153.67i	−0.107014	−	0.185354i
$514$	−219.993	−	381.040i	−0.0188784	−	0.0326983i
$515$	2804.69			0.239979
$516$	7639.40	+	13231.8i	0.651755	+	1.12887i
$517$	599.964	−	1039.17i	0.0510375	−	0.0883996i
$518$	−1122.22	+	1943.74i	−0.0951883	+	0.164871i
$519$	−3530.02			−0.298556
$520$		0			0
$521$	−10847.8			−0.912192			−0.456096	−	0.889931i	$-0.650753\pi$
$521$	−10847.8			−0.912192			−0.456096	+	0.889931i	$0.650753\pi$
$522$	−2155.92	+	3734.17i	−0.180771	+	0.313104i
$523$	−9924.94	+	17190.5i	−0.829804	+	1.43726i	0.0683884	+	0.997659i	$0.478214\pi$
$523$	−9924.94	+	17190.5i	−0.829804	+	1.43726i	−0.898192	+	0.439603i	$0.855119\pi$
$524$	4482.84	+	7764.52i	0.373729	+	0.647318i
$525$	−16111.2			−1.33934
$526$	−1939.24	−	3358.86i	−0.160751	−	0.278428i
$527$	3071.18	+	5319.44i	0.253857	+	0.439694i
$528$	38.7219			0.00319158
$529$	5518.20	+	9557.80i	0.453538	+	0.785551i
$530$	−8639.62	+	14964.3i	−0.708077	+	1.22643i
$531$	3602.38	−	6239.50i	0.294407	−	0.509927i
$532$	−2122.67			−0.172988
$533$		0			0
$534$	9692.57			0.785465
$535$	−8114.81	+	14055.3i	−0.655764	+	1.13582i
$536$	10878.0	−	18841.3i	0.876602	−	1.51832i
$537$	−1252.96	−	2170.18i	−0.100687	−	0.174395i
$538$	7921.75			0.634815
$539$	629.095	+	1089.62i	0.0502728	+	0.0870750i
$540$	2321.78	+	4021.44i	0.185025	+	0.320473i
$541$	−15828.2			−1.25787			−0.628936	−	0.777457i	$-0.716509\pi$
$541$	−15828.2			−1.25787			−0.628936	+	0.777457i	$0.716509\pi$
$542$	6887.03	+	11928.7i	0.545800	+	0.945353i
$543$	−2692.62	+	4663.76i	−0.212802	+	0.368584i
$544$	6647.02	−	11513.0i	0.523876	−	0.907379i
$545$	27943.6			2.19628
$546$		0			0
$547$	6963.82			0.544335			0.272168	−	0.962250i	$-0.412259\pi$
$547$	6963.82			0.544335			0.272168	+	0.962250i	$0.412259\pi$
$548$	−2081.43	+	3605.14i	−0.162252	+	0.281029i
$549$	4978.77	−	8623.49i	0.387047	−	0.670385i
$550$	−1174.50	−	2034.30i	−0.0910564	−	0.157714i
$551$	−6793.04			−0.525215
$552$	−2606.88	−	4515.26i	−0.201008	−	0.348156i
$553$	−3102.22	−	5373.20i	−0.238553	−	0.413186i
$554$	9171.64			0.703368
$555$	−12331.6	−	21359.0i	−0.943151	−	1.63359i
$556$	2480.93	−	4297.09i	0.189235	−	0.327765i
$557$	9416.39	−	16309.7i	0.716311	−	1.24069i	−0.246140	−	0.969234i	$-0.579162\pi$
$557$	9416.39	−	16309.7i	0.716311	−	1.24069i	0.962452	−	0.271453i	$-0.0875042\pi$
$558$	2987.45			0.226647
$559$		0			0
$560$	200.964			0.0151648
$561$	1108.36	−	1919.73i	0.0834134	−	0.144476i
$562$	−5644.92	+	9777.30i	−0.423695	+	0.733862i
$563$	9830.77	+	17027.4i	0.735911	+	1.27463i	0.954323	+	0.298778i	$0.0965789\pi$
$563$	9830.77	+	17027.4i	0.735911	+	1.27463i	−0.218412	+	0.975857i	$0.570088\pi$
$564$	9425.38			0.703688
$565$	12727.4	+	22044.5i	0.947690	+	1.64145i
$566$	−3621.64	−	6272.87i	−0.268956	−	0.465845i
$567$	6517.79			0.482754
$568$	4528.04	+	7842.79i	0.334493	+	0.579360i
$569$	−1076.70	+	1864.90i	−0.0793282	+	0.137400i	−0.902960	−	0.429724i	$-0.858611\pi$
$569$	−1076.70	+	1864.90i	−0.0793282	+	0.137400i	0.823632	+	0.567125i	$0.191944\pi$
$570$	−6940.70	+	12021.7i	−0.510025	+	0.883389i
$571$	4437.31			0.325212			0.162606	−	0.986691i	$-0.448010\pi$
$571$	4437.31			0.325212			0.162606	+	0.986691i	$0.448010\pi$
$572$		0			0
$573$	−27650.8			−2.01593
$574$	−611.521	+	1059.19i	−0.0444676	+	0.0770202i
$575$	5191.75	−	8992.38i	0.376541	−	0.652188i
$576$	−3128.05	−	5417.94i	−0.226277	−	0.391923i
$577$	14826.7			1.06975			0.534873	−	0.844933i	$-0.320360\pi$
$577$	14826.7			1.06975			0.534873	+	0.844933i	$0.320360\pi$
$578$	−360.441	−	624.302i	−0.0259383	−	0.0449265i
$579$	−570.002	−	987.272i	−0.0409127	−	0.0708629i
$580$	12684.3			0.908084
$581$	−727.493	−	1260.05i	−0.0519475	−	0.0899756i
$582$	4695.71	−	8133.20i	0.334439	−	0.579265i
$583$	1057.15	−	1831.04i	0.0750991	−	0.130075i
$584$	−7906.41			−0.560222
$585$		0			0
$586$	−4135.77			−0.291548
$587$	8504.84	−	14730.8i	0.598011	−	1.03579i	−0.395104	−	0.918637i	$-0.629291\pi$
$587$	8504.84	−	14730.8i	0.598011	−	1.03579i	0.993114	−	0.117149i	$-0.0373754\pi$
$588$	−4941.51	+	8558.95i	−0.346572	+	0.600281i
$589$	2353.27	+	4075.99i	0.164626	+	0.285141i
$590$	12613.4			0.880143
$591$	2831.72	+	4904.69i	0.197092	+	0.341374i
$592$	109.497	+	189.654i	0.00760184	+	0.0131668i
$593$	9173.23			0.635244			0.317622	−	0.948217i	$-0.397116\pi$
$593$	9173.23			0.635244			0.317622	+	0.948217i	$0.397116\pi$
$594$	169.072	+	292.842i	0.0116786	+	0.0202280i
$595$	5752.29	−	9963.25i	0.396337	−	0.686476i
$596$	1177.52	−	2039.53i	0.0809283	−	0.140172i
$597$	−265.977			−0.0182340
$598$		0			0
$599$	2983.22			0.203491			0.101745	−	0.994810i	$-0.467557\pi$
$599$	2983.22			0.203491			0.101745	+	0.994810i	$0.467557\pi$
$600$	23941.8	−	41468.4i	1.62903	−	2.82157i
$601$	9098.00	−	15758.2i	0.617496	−	1.06953i	−0.372445	−	0.928054i	$-0.621481\pi$
$601$	9098.00	−	15758.2i	0.617496	−	1.06953i	0.989941	−	0.141480i	$-0.0451862\pi$
$602$	2887.16	+	5000.70i	0.195468	+	0.338560i
$603$	19886.7			1.34303
$604$	4856.86	+	8412.32i	0.327190	+	0.566709i
$605$	−13659.2	−	23658.4i	−0.917893	−	1.58984i
$606$	−18979.1			−1.27223
$607$	8336.28	+	14438.9i	0.557428	+	0.965494i	0.997710	+	0.0676345i	$0.0215452\pi$
$607$	8336.28	+	14438.9i	0.557428	+	0.965494i	−0.440282	+	0.897860i	$0.645121\pi$
$608$	5093.23	−	8821.73i	0.339733	−	0.588435i
$609$	3167.61	−	5486.47i	0.210769	−	0.365062i
$610$	17432.7			1.15710
$611$		0			0
$612$	7525.90			0.497086
$613$	−8378.47	+	14511.9i	−0.552044	+	0.956168i	0.446083	+	0.894992i	$0.352819\pi$
$613$	−8378.47	+	14511.9i	−0.552044	+	0.956168i	−0.998127	+	0.0611768i	$0.980515\pi$
$614$	709.870	−	1229.53i	0.0466580	−	0.0808141i
$615$	−6719.76	−	11639.0i	−0.440597	−	0.763136i
$616$	749.024			0.0489920
$617$	−5992.72	−	10379.7i	−0.391017	−	0.677262i	0.601567	−	0.798823i	$-0.294543\pi$
$617$	−5992.72	−	10379.7i	−0.391017	−	0.677262i	−0.992584	+	0.121561i	$0.961210\pi$
$618$	802.137	+	1389.34i	0.0522115	+	0.0904329i
$619$	−22471.2			−1.45912			−0.729560	−	0.683917i	$-0.760275\pi$
$619$	−22471.2			−1.45912			−0.729560	+	0.683917i	$0.760275\pi$
$620$	−4394.16	−	7610.90i	−0.284635	−	0.493002i
$621$	−747.363	+	1294.47i	−0.0482941	+	0.0836479i
$622$	4743.20	−	8215.46i	0.305764	−	0.529598i
$623$	−6155.20			−0.395832
$624$		0			0
$625$	41136.7			2.63275
$626$	272.518	−	472.015i	0.0173994	−	0.0301366i
$627$	849.271	−	1470.98i	0.0540935	−	0.0936927i
$628$	−7251.04	−	12559.2i	−0.460745	−	0.798035i
$629$	12536.7			0.794709
$630$	−2797.73	−	4845.82i	−0.176928	−	0.306447i
$631$	495.783	+	858.721i	0.0312786	+	0.0541762i	0.881241	−	0.472667i	$-0.156709\pi$
$631$	495.783	+	858.721i	0.0312786	+	0.0541762i	−0.849962	+	0.526843i	$0.823375\pi$
$632$	18440.0			1.16061
$633$	−17391.5	−	30123.0i	−1.09202	−	1.89144i
$634$	7165.98	−	12411.8i	0.448892	−	0.777504i
$635$	4674.72	−	8096.85i	0.292143	−	0.506006i
$636$	16607.8			1.03544
$637$		0			0
$638$	923.674			0.0573175
$639$	−4138.98	+	7168.93i	−0.256237	+	0.443816i
$640$	−9693.92	+	16790.4i	−0.598728	+	1.03703i
$641$	4241.88	+	7347.15i	0.261379	+	0.452722i	0.966609	−	0.256257i	$-0.0824893\pi$
$641$	4241.88	+	7347.15i	0.261379	+	0.452722i	−0.705229	+	0.708979i	$0.749156\pi$
$642$	−9283.31			−0.570690
$643$	11263.8	+	19509.4i	0.690823	+	1.19654i	0.971569	+	0.236758i	$0.0760849\pi$
$643$	11263.8	+	19509.4i	0.690823	+	1.19654i	−0.280746	+	0.959782i	$0.590582\pi$
$644$	637.921	+	1104.91i	0.0390336	+	0.0676081i
$645$	−63451.6			−3.87350
$646$	−3528.07	−	6110.79i	−0.214876	−	0.372176i
$647$	−2743.08	+	4751.16i	−0.166680	+	0.288698i	−0.937251	−	0.348657i	$-0.886638\pi$
$647$	−2743.08	+	4751.16i	−0.166680	+	0.288698i	0.770571	+	0.637354i	$0.219971\pi$
$648$	−9685.65	+	16776.0i	−0.587173	+	1.01701i
$649$	−1543.39			−0.0933485
$650$		0			0
$651$	−4389.35			−0.264258
$652$	5752.48	−	9963.58i	0.345528	−	0.598472i
$653$	−10218.1	+	17698.2i	−0.612348	+	1.06062i	0.378495	+	0.925603i	$0.376442\pi$
$653$	−10218.1	+	17698.2i	−0.612348	+	1.06062i	−0.990844	+	0.135015i	$0.956892\pi$
$654$	7991.83	+	13842.3i	0.477837	+	0.827638i
$655$	−37233.8			−2.22114
$656$	59.6671	+	103.346i	0.00355123	+	0.00615091i
$657$	−3613.54	−	6258.83i	−0.214578	−	0.371660i
$658$	3562.13			0.211043
$659$	4306.56	+	7459.18i	0.254567	+	0.440923i	0.964778	−	0.263066i	$-0.0847336\pi$
$659$	4306.56	+	7459.18i	0.254567	+	0.440923i	−0.710211	+	0.703989i	$0.751400\pi$
$660$	−1585.81	+	2746.70i	−0.0935264	+	0.161992i
$661$	14634.4	−	25347.5i	0.861138	−	1.49153i	−0.00969383	−	0.999953i	$-0.503086\pi$
$661$	14634.4	−	25347.5i	0.861138	−	1.49153i	0.870832	−	0.491581i	$-0.163581\pi$
$662$	1477.24			0.0867291
$663$		0			0
$664$	4324.31			0.252735
$665$	4407.65	−	7634.27i	0.257024	−	0.445179i
$666$	3048.74	−	5280.57i	0.177382	−	0.307234i
$667$	2041.49	+	3535.97i	0.118511	+	0.205267i
$668$	5650.44			0.327279
$669$	−21128.3	−	36595.3i	−1.22103	−	2.11488i
$670$	17407.8	+	30151.3i	1.00377	+	1.73857i
$671$	−2133.08			−0.122722
$672$	4749.97	+	8227.19i	0.272670	+	0.472278i
$673$	11270.3	−	19520.7i	0.645522	−	1.11808i	−0.338658	−	0.940909i	$-0.609973\pi$
$673$	11270.3	−	19520.7i	0.645522	−	1.11808i	0.984181	−	0.177168i	$-0.0566937\pi$
$674$	2937.05	−	5087.12i	0.167850	−	0.290725i
$675$	−13727.7			−0.782782
$676$		0			0
$677$	−18727.0			−1.06313			−0.531563	−	0.847019i	$-0.678395\pi$
$677$	−18727.0			−1.06313			−0.531563	+	0.847019i	$0.678395\pi$
$678$	−7280.03	+	12609.4i	−0.412372	+	0.714249i
$679$	−2981.98	+	5164.94i	−0.168539	+	0.291918i
$680$	17096.2	+	29611.4i	0.964129	+	1.66992i
$681$	−43740.2			−2.46128
$682$	−319.983	−	554.226i	−0.0179659	−	0.0311179i
$683$	−2523.88	−	4371.49i	−0.141396	−	0.244906i	0.786626	−	0.617429i	$-0.211826\pi$
$683$	−2523.88	−	4371.49i	−0.141396	−	0.244906i	−0.928023	+	0.372524i	$0.878493\pi$
$684$	5766.67			0.322360
$685$	−8644.00	−	14971.8i	−0.482146	−	0.835102i
$686$	−4109.17	+	7117.29i	−0.228701	+	0.396121i
$687$	−4601.88	+	7970.69i	−0.255564	+	0.442650i
$688$	563.408			0.0312206
$689$		0			0
$690$	8343.48			0.460335
$691$	−8223.46	+	14243.4i	−0.452728	+	0.784148i	−0.998554	−	0.0537505i	$-0.982882\pi$
$691$	−8223.46	+	14243.4i	−0.452728	+	0.784148i	0.545826	+	0.837898i	$0.316216\pi$
$692$	−1283.66	+	2223.37i	−0.0705166	+	0.122138i
$693$	342.333	+	592.939i	0.0187650	+	0.0325020i
$694$	6123.30			0.334924
$695$	10303.1	+	17845.5i	0.562329	+	0.973982i
$696$	9414.35	+	16306.1i	0.512716	+	0.888049i
$697$	6831.52			0.371252
$698$	−7203.54	−	12476.9i	−0.390628	−	0.676587i
$699$	18592.7	−	32203.6i	1.00607	−	1.74256i
$700$	−5858.71	+	10147.6i	−0.316340	+	0.547918i
$701$	14841.3			0.799639			0.399820	−	0.916594i	$-0.369073\pi$
$701$	14841.3			0.799639			0.399820	+	0.916594i	$0.369073\pi$
$702$		0			0
$703$	9606.18			0.515368
$704$	−670.083	+	1160.62i	−0.0358732	+	0.0621342i
$705$	−19571.4	+	33898.7i	−1.04554	+	1.81092i
$706$	−3733.37	−	6466.39i	−0.199019	−	0.344711i
$707$	12052.6			0.641136
$708$	−6061.61	−	10499.0i	−0.321764	−	0.557312i
$709$	−9664.87	−	16740.0i	−0.511949	−	0.886722i	−0.999904	−	0.0138529i	$-0.995590\pi$
$709$	−9664.87	−	16740.0i	−0.511949	−	0.886722i	0.487955	−	0.872869i	$-0.337743\pi$
$710$	−14492.2			−0.766034
$711$	8427.79	+	14597.4i	0.444539	+	0.769963i
$712$	9146.83	−	15842.8i	0.481450	−	0.833895i
$713$	1414.44	−	2449.89i	0.0742936	−	0.128680i
$714$	6580.59			0.344919
$715$		0			0
$716$	−1822.51			−0.0951261
$717$	12925.4	−	22387.4i	0.673231	−	1.16607i
$718$	3918.16	−	6786.45i	0.203655	−	0.352741i
$719$	−10670.0	−	18481.0i	−0.553443	−	0.958591i	−0.998023	−	0.0628517i	$-0.979980\pi$
$719$	−10670.0	−	18481.0i	−0.553443	−	0.958591i	0.444580	−	0.895739i	$-0.353353\pi$
$720$	−545.958			−0.0282592
$721$	−509.392	−	882.293i	−0.0263117	−	0.0455732i
$722$	3221.56	+	5579.91i	0.166058	+	0.287621i
$723$	26407.7			1.35839
$724$	1958.30	+	3391.88i	0.100524	+	0.174113i
$725$	−18749.2	+	32474.6i	−0.960452	+	1.66355i
$726$	7813.03	−	13532.6i	0.399406	−	0.691791i
$727$	−15092.3			−0.769934			−0.384967	−	0.922930i	$-0.625787\pi$
$727$	−15092.3			−0.769934			−0.384967	+	0.922930i	$0.625787\pi$
$728$		0			0
$729$	−9430.08			−0.479098
$730$	6326.23	−	10957.4i	0.320746	−	0.555548i
$731$	16126.7	−	27932.3i	0.815962	−	1.41329i
$732$	−8377.63	−	14510.5i	−0.423014	−	0.732681i
$733$	9108.56			0.458980			0.229490	−	0.973311i	$-0.426294\pi$
$733$	9108.56			0.458980			0.229490	+	0.973311i	$0.426294\pi$
$734$	−194.672	−	337.181i	−0.00978946	−	0.0169558i
$735$	−20521.7	−	35544.6i	−1.02987	−	1.78379i
$736$	−6122.62			−0.306634
$737$	−2130.04	−	3689.34i	−0.106460	−	0.184394i
$738$	1661.32	−	2877.49i	0.0828645	−	0.143526i
$739$	−9536.37	+	16517.5i	−0.474697	+	0.822200i	−0.999580	−	0.0289748i	$-0.990776\pi$
$739$	−9536.37	+	16517.5i	−0.474697	+	0.822200i	0.524883	+	0.851174i	$0.324109\pi$
$740$	−17937.2			−0.891059
$741$		0			0
$742$	6276.57			0.310539
$743$	6138.27	−	10631.8i	0.303084	−	0.524957i	−0.673749	−	0.738960i	$-0.735317\pi$
$743$	6138.27	−	10631.8i	0.303084	−	0.524957i	0.976833	+	0.214004i	$0.0686504\pi$
$744$	6522.71	−	11297.7i	0.321417	−	0.556710i
$745$	4890.17	+	8470.02i	0.240486	+	0.416533i
$746$	5060.68			0.248371
$747$	1976.38	+	3423.19i	0.0968031	+	0.167668i
$748$	−806.090	−	1396.19i	−0.0394032	−	0.0682483i
$749$	5895.30			0.287596
$750$	22804.9	+	39499.3i	1.11029	+	1.92308i
$751$	−14332.8	+	24825.1i	−0.696417	+	1.20623i	0.273283	+	0.961934i	$0.411890\pi$
$751$	−14332.8	+	24825.1i	−0.696417	+	1.20623i	−0.969701	+	0.244297i	$0.921443\pi$
$752$	173.781	−	300.998i	0.00842707	−	0.0145961i
$753$	−3286.44			−0.159050
$754$		0			0
$755$	−40340.3			−1.94455
$756$	843.372	−	1460.76i	0.0405729	−	0.0702744i
$757$	14308.9	−	24783.7i	0.687008	−	1.18993i	−0.285793	−	0.958291i	$-0.592257\pi$
$757$	14308.9	−	24783.7i	0.687008	−	1.18993i	0.972801	−	0.231642i	$-0.0744096\pi$
$758$	6747.06	+	11686.3i	0.323304	+	0.559979i
$759$	−1020.92			−0.0488233
$760$	13099.8	+	22689.5i	0.625237	+	1.08294i
$761$	13208.6	+	22878.0i	0.629189	+	1.08979i	0.987715	+	0.156268i	$0.0499463\pi$
$761$	13208.6	+	22878.0i	0.629189	+	1.08979i	−0.358525	+	0.933520i	$0.616720\pi$
$762$	5347.86			0.254242
$763$	−5075.16	−	8790.44i	−0.240804	−	0.417084i
$764$	−10055.0	+	17415.8i	−0.476148	+	0.824712i
$765$	−15627.2	+	27067.2i	−0.738567	+	1.27924i
$766$	−9633.54			−0.454404
$767$		0			0
$768$	−27881.6			−1.31001
$769$	15762.1	−	27300.8i	0.739136	−	1.28022i	−0.213748	−	0.976889i	$-0.568567\pi$
$769$	15762.1	−	27300.8i	0.739136	−	1.28022i	0.952885	−	0.303333i	$-0.0980994\pi$
$770$	−599.323	+	1038.06i	−0.0280495	+	0.0485832i
$771$	−878.112	−	1520.93i	−0.0410174	−	0.0710442i
$772$	−829.105			−0.0386530
$773$	10833.3	+	18763.8i	0.504071	+	0.873077i	0.999989	+	0.00470766i	$0.00149850\pi$
$773$	10833.3	+	18763.8i	0.504071	+	0.873077i	−0.495918	+	0.868370i	$0.665168\pi$
$774$	−7843.54	−	13585.4i	−0.364251	−	0.630901i
$775$	25980.7			1.20420
$776$	−8862.63	−	15350.5i	−0.409987	−	0.710118i
$777$	−4479.39	+	7758.52i	−0.206817	+	0.358218i
$778$	−10733.5	+	18591.0i	−0.494621	+	0.856708i
$779$	5234.61			0.240756
$780$		0			0
$781$	1773.28			0.0812460
$782$	−2120.56	+	3672.92i	−0.0969707	+	0.167958i
$783$	2698.98	−	4674.78i	0.123185	−	0.213363i
$784$	182.219	+	315.613i	0.00830080	+	0.0143774i
$785$	60226.0			2.73829
$786$	−10648.8	−	18444.3i	−0.483246	−	0.837006i
$787$	13135.6	+	22751.5i	0.594959	+	1.03050i	0.993553	+	0.113372i	$0.0361652\pi$
$787$	13135.6	+	22751.5i	0.594959	+	1.03050i	−0.398593	+	0.917128i	$0.630501\pi$
$788$	4118.93			0.186207
$789$	−7740.55	−	13407.0i	−0.349266	−	0.604946i
$790$	−14754.5	+	25555.6i	−0.664485	+	1.15092i
$791$	4623.14	−	8007.51i	0.207813	−	0.359942i
$792$	−2034.87			−0.0912956
$793$		0			0
$794$	11089.4			0.495651
$795$	−34485.4	+	59730.4i	−1.53845	+	2.66468i
$796$	−96.7204	+	167.525i	−0.00430674	+	0.00745949i
$797$	168.492	+	291.836i	0.00748843	+	0.0129703i	0.869745	−	0.493501i	$-0.164283\pi$
$797$	168.492	+	291.836i	0.00748843	+	0.0129703i	−0.862257	+	0.506471i	$0.830950\pi$
$798$	5042.33			0.223680
$799$	−9948.46	−	17231.2i	−0.440490	−	0.762951i
$800$	−28115.2	−	48697.0i	−1.24253	−	2.15212i
$801$	16721.8			0.737625
$802$	1341.83	+	2324.12i	0.0590794	+	0.102329i
$803$	−774.084	+	1340.75i	−0.0340185	+	0.0589217i
$804$	16731.4	−	28979.6i	0.733918	−	1.27118i
$805$	−5298.47			−0.231983
$806$		0			0
$807$	31619.9			1.37927
$808$	−17910.5	+	31021.9i	−0.779813	+	1.35068i
$809$	−3239.35	+	5610.72i	−0.140778	+	0.243835i	−0.927790	−	0.373103i	$-0.878294\pi$
$809$	−3239.35	+	5610.72i	−0.140778	+	0.243835i	0.787012	+	0.616938i	$0.211627\pi$
$810$	−15499.7	−	26846.3i	−0.672352	−	1.16455i
$811$	−36823.2			−1.59437			−0.797186	−	0.603734i	$-0.793679\pi$
$811$	−36823.2			−1.59437			−0.797186	+	0.603734i	$0.793679\pi$
$812$	−2303.75	−	3990.21i	−0.0995638	−	0.172450i
$813$	27489.9	+	47613.8i	1.18587	+	2.05399i
$814$	−1306.19			−0.0562430
$815$	23889.6	+	41378.0i	1.02677	+	1.77841i
$816$	321.039	−	556.056i	0.0137728	−	0.0238552i
$817$	12357.0	−	21402.9i	0.529151	−	0.916516i
$818$	15136.7			0.646997
$819$		0			0
$820$	−9774.34			−0.416262
$821$	−4262.27	+	7382.46i	−0.181187	+	0.313824i	−0.942285	−	0.334812i	$-0.891327\pi$
$821$	−4262.27	+	7382.46i	−0.181187	+	0.313824i	0.761098	+	0.648636i	$0.224660\pi$
$822$	4944.35	−	8563.86i	0.209798	−	0.363381i
$823$	6656.54	+	11529.5i	0.281935	+	0.488325i	0.971861	−	0.235554i	$-0.0756905\pi$
$823$	6656.54	+	11529.5i	0.281935	+	0.488325i	−0.689927	+	0.723879i	$0.742357\pi$
$824$	3027.89			0.128012
$825$	−4688.08	−	8119.99i	−0.197840	−	0.342669i
$826$	−2290.86	−	3967.89i	−0.0965004	−	0.167144i
$827$	41849.9			1.75969			0.879845	−	0.475261i	$-0.157646\pi$
$827$	41849.9			1.75969			0.879845	+	0.475261i	$0.157646\pi$
$828$	−1733.04	−	3001.71i	−0.0727383	−	0.125986i
$829$	6508.59	−	11273.2i	0.272681	−	0.472298i	−0.696866	−	0.717201i	$-0.745423\pi$
$829$	6508.59	−	11273.2i	0.272681	−	0.472298i	0.969547	+	0.244903i	$0.0787563\pi$
$830$	−3460.05	+	5992.98i	−0.144699	+	0.250626i
$831$	36609.0			1.52822
$832$		0			0
$833$	20863.0			0.867780
$834$	−5893.35	+	10207.6i	−0.244688	+	0.423812i
$835$	−11732.9	+	20322.0i	−0.486269	+	0.842242i
$836$	−617.661	−	1069.82i	−0.0255529	−	0.0442590i
$837$	−3739.97			−0.154447
$838$	−7136.60	−	12361.0i	−0.294188	−	0.509549i
$839$	10104.7	+	17501.9i	0.415796	+	0.720181i	0.995512	−	0.0946385i	$-0.0301695\pi$
$839$	10104.7	+	17501.9i	0.415796	+	0.720181i	−0.579715	+	0.814819i	$0.696836\pi$
$840$	−24433.9			−1.00363
$841$	4821.97	+	8351.90i	0.197711	+	0.342445i
$842$	3828.39	−	6630.97i	0.156692	−	0.271399i
$843$	−22531.9	+	39026.4i	−0.920570	+	1.59447i
$844$	−25297.1			−1.03171
$845$		0			0
$846$	−9677.25			−0.393275
$847$	−4961.61	+	8593.77i	−0.201279	+	0.348625i
$848$	306.207	−	530.366i	0.0124000	−	0.0214774i
$849$	−14455.9	−	25038.4i	−0.584365	−	1.01215i
$850$	−38950.7			−1.57176
$851$	−2886.92	−	5000.29i	−0.116289	−	0.201419i
$852$	6964.54	+	12062.9i	0.280048	+	0.485058i
$853$	7958.24			0.319443			0.159721	−	0.987162i	$-0.448940\pi$
$853$	7958.24			0.319443			0.159721	+	0.987162i	$0.448940\pi$
$854$	−3166.16	−	5483.94i	−0.126866	−	0.219738i
$855$	−11974.3	+	20740.0i	−0.478960	+	0.829583i
$856$	−8760.61	+	15173.8i	−0.349803	+	0.605877i
$857$	−2144.65			−0.0854840			−0.0427420	−	0.999086i	$-0.513609\pi$
$857$	−2144.65			−0.0854840			−0.0427420	+	0.999086i	$0.513609\pi$
$858$		0			0
$859$	−41723.5			−1.65726			−0.828632	−	0.559794i	$-0.810880\pi$
$859$	−41723.5			−1.65726			−0.828632	+	0.559794i	$0.810880\pi$
$860$	−23073.6	+	39964.7i	−0.914889	+	1.58463i
$861$	−2440.91	+	4227.78i	−0.0966156	+	0.167343i
$862$	8703.84	+	15075.5i	0.343914	+	0.595677i
$863$	−10393.8			−0.409977			−0.204989	−	0.978764i	$-0.565716\pi$
$863$	−10393.8			−0.409977			−0.204989	+	0.978764i	$0.565716\pi$
$864$	4047.24	+	7010.03i	0.159363	+	0.276025i
$865$	−5330.94	−	9233.47i	−0.209546	−	0.362945i
$866$	172.204			0.00675718
$867$	−1438.71	−	2491.92i	−0.0563567	−	0.0976126i
$868$	−1596.15	+	2764.61i	−0.0624157	+	0.108107i
$869$	1805.38	−	3127.01i	0.0704757	−	0.122067i
$870$	−30131.2			−1.17419
$871$		0			0
$872$	30167.4			1.17156
$873$	8101.14	−	14031.6i	0.314069	−	0.543983i
$874$	−1624.86	+	2814.35i	−0.0628854	+	0.108921i
$875$	−14482.1	−	25083.8i	−0.559525	−	0.969127i
$876$	−12160.8			−0.469035
$877$	2502.79	+	4334.97i	0.0963664	+	0.166912i	0.910178	−	0.414217i	$-0.135945\pi$
$877$	2502.79	+	4334.97i	0.0963664	+	0.166912i	−0.813812	+	0.581129i	$0.802611\pi$
$878$	−9872.35	−	17099.4i	−0.379471	−	0.657263i
$879$	−16508.1			−0.633451
$880$	58.4769	+	101.285i	0.00224006	+	0.00387990i
$881$	7298.57	−	12641.5i	0.279109	−	0.483431i	−0.692054	−	0.721845i	$-0.743294\pi$
$881$	7298.57	−	12641.5i	0.279109	−	0.483431i	0.971164	+	0.238414i	$0.0766275\pi$
$882$	5073.56	−	8787.66i	0.193691	−	0.335483i
$883$	−5629.11			−0.214535			−0.107268	−	0.994230i	$-0.534210\pi$
$883$	−5629.11			−0.214535			−0.107268	+	0.994230i	$0.534210\pi$
$884$		0			0
$885$	50346.8			1.91230
$886$	4135.04	−	7162.09i	0.156794	−	0.271575i
$887$	−8507.44	+	14735.3i	−0.322043	+	0.557794i	−0.980909	−	0.194465i	$-0.937703\pi$
$887$	−8507.44	+	14735.3i	−0.322043	+	0.557794i	0.658867	+	0.752260i	$0.271036\pi$
$888$	−13313.0	−	23058.8i	−0.503103	−	0.871401i
$889$	−3396.12			−0.128124
$890$	14637.5	+	25352.9i	0.551291	+	0.954865i
$891$	1896.56	+	3284.94i	0.0713100	+	0.123513i
$892$	−30732.5			−1.15359
$893$	−7622.94	−	13203.3i	−0.285657	−	0.494773i
$894$	−2797.16	+	4844.83i	−0.104643	+	0.181248i
$895$	3784.36	−	6554.71i	0.141338	−	0.244804i
$896$	7042.51			0.262582
$897$		0			0
$898$	−11188.8			−0.415784
$899$	−5108.04	+	8847.39i	−0.189502	+	0.328228i
$900$	15916.3	−	27567.9i	0.589494	−	1.02103i
$901$	−17529.4	−	30361.9i	−0.648158	−	1.12264i
$902$	−711.768			−0.0262741
$903$	11524.2	+	19960.5i	0.424697	+	0.735596i
$904$	13740.3	+	23798.8i	0.505525	+	0.875595i
$905$	−16265.3			−0.597434
$906$	−11537.3	−	19983.1i	−0.423069	−	0.732776i
$907$	9592.67	−	16615.0i	0.351179	−	0.608260i	−0.635277	−	0.772284i	$-0.719114\pi$
$907$	9592.67	−	16615.0i	0.351179	−	0.608260i	0.986456	+	0.164024i	$0.0524476\pi$
$908$	−15905.8	+	27549.6i	−0.581334	+	1.00690i
$909$	−32743.2			−1.19474
$910$		0			0
$911$	30427.5			1.10659			0.553297	−	0.832984i	$-0.313369\pi$
$911$	30427.5			1.10659			0.553297	+	0.832984i	$0.313369\pi$
$912$	245.994	−	426.074i	0.00893166	−	0.0154701i
$913$	423.375	−	733.307i	0.0153468	−	0.0265815i
$914$	801.934	+	1388.99i	0.0290215	+	0.0502667i
$915$	69583.3			2.51405
$916$	3346.87	+	5796.95i	0.120725	+	0.209101i
$917$	6762.47	+	11712.9i	0.243529	+	0.421805i
$918$	5607.03			0.201590
$919$	19875.4	+	34425.2i	0.713415	+	1.23567i	0.963568	+	0.267465i	$0.0861859\pi$
$919$	19875.4	+	34425.2i	0.713415	+	1.23567i	−0.250153	+	0.968206i	$0.580481\pi$
$920$	7873.70	−	13637.7i	0.282161	−	0.488718i
$921$	2833.47	−	4907.72i	0.101375	−	0.175586i
$922$	−18207.9			−0.650374
$923$		0			0
$924$	1152.07			0.0410176
$925$	26513.6	−	45922.9i	0.942446	−	1.63236i
$926$	4257.51	−	7374.23i	0.151091	−	0.261698i
$927$	1383.86	+	2396.92i	0.0490314	+	0.0849248i
$928$	22110.9			0.782138
$929$	3130.44	+	5422.08i	0.110556	+	0.191488i	0.915995	−	0.401191i	$-0.131404\pi$
$929$	3130.44	+	5422.08i	0.110556	+	0.191488i	−0.805439	+	0.592679i	$0.798070\pi$
$930$	10438.2	+	18079.4i	0.368044	+	0.637470i
$931$	15986.1			0.562755
$932$	−13522.2	−	23421.1i	−0.475251	−	0.823159i
$933$	18932.7	−	32792.3i	0.664338	−	1.15067i
$934$	−282.001	+	488.440i	−0.00987939	+	0.0171116i
$935$	6695.26			0.234180
$936$		0			0
$937$	−24497.3			−0.854101			−0.427050	−	0.904228i	$-0.640447\pi$
$937$	−24497.3			−0.854101			−0.427050	+	0.904228i	$0.640447\pi$
$938$	6323.29	−	10952.3i	0.220109	−	0.381241i
$939$	1087.76	−	1884.06i	0.0378039	−	0.0654783i
$940$	14234.0	+	24654.0i	0.493895	+	0.855451i
$941$	−10199.1			−0.353326			−0.176663	−	0.984271i	$-0.556530\pi$
$941$	−10199.1			−0.353326			−0.176663	+	0.984271i	$0.556530\pi$
$942$	17224.6	+	29833.8i	0.595761	+	1.03189i
$943$	−1573.14	−	2724.76i	−0.0543251	−	0.0940938i
$944$	−447.046			−0.0154133
$945$	3502.46	+	6066.44i	0.120566	+	0.208827i
$946$	−1680.22	+	2910.23i	−0.0577471	+	0.100021i
$947$	50.5642	−	87.5797i	0.00173507	−	0.00300523i	−0.865157	−	0.501502i	$-0.832781\pi$
$947$	50.5642	−	87.5797i	0.00173507	−	0.00300523i	0.866892	+	0.498497i	$0.166114\pi$
$948$	28362.4			0.971695
$949$		0			0
$950$	−29845.7			−1.01929
$951$	28603.3	−	49542.4i	0.975316	−	1.68930i
$952$	6210.07	−	10756.2i	0.211418	−	0.366186i
$953$	21098.5	+	36543.7i	0.717155	+	1.24215i	0.962122	+	0.272618i	$0.0878894\pi$
$953$	21098.5	+	36543.7i	0.717155	+	1.24215i	−0.244968	+	0.969531i	$0.578777\pi$
$954$	−17051.6			−0.578684
$955$	−41757.6	−	72326.2i	−1.41491	−	2.45070i
$956$	−9400.40	−	16282.0i	−0.318024	−	0.550833i
$957$	3686.88			0.124535
$958$	−1609.73	−	2788.13i	−0.0542881	−	0.0940297i
$959$	−3139.88	+	5438.43i	−0.105727	+	0.183124i
$960$	21858.8	−	37860.5i	0.734885	−	1.27286i
$961$	−22712.8			−0.762405
$962$		0			0
$963$	−16015.8			−0.535931
$964$	9602.94	−	16632.8i	0.320840	−	0.555712i
$965$	1721.60	−	2981.91i	0.0574305	−	0.0994725i
$966$	−1515.36	−	2624.68i	−0.0504719	−	0.0874198i
$967$	1221.07			0.0406069			0.0203035	−	0.999794i	$-0.493537\pi$
$967$	1221.07			0.0406069			0.0203035	+	0.999794i	$0.493537\pi$
$968$	−14746.2	−	25541.2i	−0.489630	−	0.848064i
$969$	−14082.4	−	24391.5i	−0.466865	−	0.808634i
$970$	28365.4			0.938924
$971$	21457.8	+	37166.1i	0.709181	+	1.22834i	0.965161	+	0.261656i	$0.0842684\pi$
$971$	21457.8	+	37166.1i	0.709181	+	1.22834i	−0.255980	+	0.966682i	$0.582398\pi$
$972$	−11887.6	+	20590.0i	−0.392279	+	0.679448i
$973$	3742.53	−	6482.25i	0.123309	−	0.213578i
$974$	30024.8			0.987739
$975$		0			0
$976$	−617.853			−0.0202633
$977$	−15626.8	+	27066.4i	−0.511714	+	0.886315i	0.488193	+	0.872735i	$0.337656\pi$
$977$	−15626.8	+	27066.4i	−0.511714	+	0.886315i	−0.999908	+	0.0135799i	$0.995677\pi$
$978$	−13664.8	+	23668.1i	−0.446781	+	0.773847i
$979$	−1791.06	−	3102.20i	−0.0584703	−	0.101273i
$980$	−29850.2			−0.972989
$981$	13787.7	+	23881.0i	0.448733	+	0.777228i
$982$	−16635.6	−	28813.6i	−0.540593	−	0.936334i
$983$	−41688.2			−1.35264			−0.676320	−	0.736608i	$-0.736426\pi$
$983$	−41688.2			−1.35264			−0.676320	+	0.736608i	$0.736426\pi$
$984$	−7254.54	−	12565.2i	−0.235027	−	0.407078i
$985$	−8552.79	+	14813.9i	−0.276665	+	0.479197i
$986$	7658.07	−	13264.2i	0.247345	−	0.428415i
$987$	14218.4			0.458537
$988$		0			0
$989$	−14854.4			−0.477597
$990$	1628.18	−	2820.09i	0.0522697	−	0.0905338i
$991$	−10186.0	+	17642.6i	−0.326506	+	0.565526i	−0.981816	−	0.189835i	$-0.939205\pi$
$991$	−10186.0	+	17642.6i	−0.326506	+	0.565526i	0.655310	+	0.755360i	$0.272538\pi$
$992$	−7659.73	−	13267.0i	−0.245158	−	0.424626i
$993$	5896.47			0.188438
$994$	2632.11	+	4558.94i	0.0839893	+	0.145474i
$995$	−401.672	−	695.717i	−0.0127979	−	0.0221665i
$996$	6651.18			0.211597
$997$	−9348.27	−	16191.7i	−0.296954	−	0.514339i	0.678484	−	0.734615i	$-0.262637\pi$
$997$	−9348.27	−	16191.7i	−0.296954	−	0.514339i	−0.975437	+	0.220277i	$0.929304\pi$
$998$	11305.8	−	19582.2i	0.358596	−	0.621106i
$999$	−3816.69	+	6610.70i	−0.120876	+	0.209363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.c.l.22.3		18
13.2	odd	12		169.4.e.h.23.7		36
13.3	even	3	inner	169.4.c.l.146.3		18
13.4	even	6		169.4.a.l.1.3	yes	9
13.5	odd	4		169.4.e.h.147.12		36
13.6	odd	12		169.4.b.g.168.7		18
13.7	odd	12		169.4.b.g.168.12		18
13.8	odd	4		169.4.e.h.147.7		36
13.9	even	3		169.4.a.k.1.7	✓	9
13.10	even	6		169.4.c.k.146.7		18
13.11	odd	12		169.4.e.h.23.12		36
13.12	even	2		169.4.c.k.22.7		18
39.17	odd	6		1521.4.a.bg.1.7		9
39.35	odd	6		1521.4.a.bh.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.7	✓	9	13.9	even	3
169.4.a.l.1.3	yes	9	13.4	even	6
169.4.b.g.168.7		18	13.6	odd	12
169.4.b.g.168.12		18	13.7	odd	12
169.4.c.k.22.7		18	13.12	even	2
169.4.c.k.146.7		18	13.10	even	6
169.4.c.l.22.3		18	1.1	even	1	trivial
169.4.c.l.146.3		18	13.3	even	3	inner
169.4.e.h.23.7		36	13.2	odd	12
169.4.e.h.23.12		36	13.11	odd	12
169.4.e.h.147.7		36	13.8	odd	4
169.4.e.h.147.12		36	13.5	odd	4
1521.4.a.bg.1.7		9	39.17	odd	6
1521.4.a.bh.1.3		9	39.35	odd	6

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.863817 + 1.49617i) q^{2} +(-3.44796 + 5.97204i) q^{3} +(2.50764 + 4.34336i) q^{4} -20.8281 q^{5} +(-5.95681 - 10.3175i) q^{6} +(3.78283 + 6.55206i) q^{7} -22.4856 q^{8} +(-10.2768 - 17.8000i) q^{9} +O(q^{10})\)	\(q+(-0.863817 + 1.49617i) q^{2} +(-3.44796 + 5.97204i) q^{3} +(2.50764 + 4.34336i) q^{4} -20.8281 q^{5} +(-5.95681 - 10.3175i) q^{6} +(3.78283 + 6.55206i) q^{7} -22.4856 q^{8} +(-10.2768 - 17.8000i) q^{9} +(17.9916 - 31.1624i) q^{10} +(-2.20147 + 3.81307i) q^{11} -34.5850 q^{12} -13.0707 q^{14} +(71.8143 - 124.386i) q^{15} +(-0.637664 + 1.10447i) q^{16} +(36.5043 + 63.2274i) q^{17} +35.5091 q^{18} +(27.9712 + 48.4475i) q^{19} +(-52.2293 - 90.4639i) q^{20} -52.1722 q^{21} +(-3.80334 - 6.58758i) q^{22} +(16.8122 - 29.1196i) q^{23} +(77.5295 - 134.285i) q^{24} +308.809 q^{25} -44.4536 q^{27} +(-18.9720 + 32.8604i) q^{28} +(-60.7146 + 105.161i) q^{29} +(124.069 + 214.893i) q^{30} +84.1320 q^{31} +(-91.0442 - 157.693i) q^{32} +(-15.1812 - 26.2946i) q^{33} -126.132 q^{34} +(-78.7891 - 136.467i) q^{35} +(51.5411 - 89.2719i) q^{36} +(85.8578 - 148.710i) q^{37} -96.6479 q^{38} +468.332 q^{40} +(46.7857 - 81.0352i) q^{41} +(45.0672 - 78.0586i) q^{42} +(-220.888 - 382.589i) q^{43} -22.0820 q^{44} +(214.046 + 370.739i) q^{45} +(29.0453 + 50.3080i) q^{46} -272.528 q^{47} +(-4.39727 - 7.61630i) q^{48} +(142.880 - 247.476i) q^{49} +(-266.754 + 462.032i) q^{50} -503.461 q^{51} -480.202 q^{53} +(38.3998 - 66.5103i) q^{54} +(45.8525 - 79.4188i) q^{55} +(-85.0594 - 147.327i) q^{56} -385.774 q^{57} +(-104.893 - 181.679i) q^{58} +(175.267 + 303.572i) q^{59} +720.338 q^{60} +(242.233 + 419.560i) q^{61} +(-72.6746 + 125.876i) q^{62} +(77.7509 - 134.669i) q^{63} +304.379 q^{64} +52.4550 q^{66} +(-483.776 + 837.925i) q^{67} +(-183.080 + 317.103i) q^{68} +(115.936 + 200.806i) q^{69} +272.237 q^{70} +(-201.375 - 348.791i) q^{71} +(231.081 + 400.244i) q^{72} +351.621 q^{73} +(148.331 + 256.916i) q^{74} +(-1064.76 + 1844.22i) q^{75} +(-140.283 + 242.978i) q^{76} -33.3112 q^{77} -820.078 q^{79} +(13.2813 - 23.0039i) q^{80} +(430.748 - 746.078i) q^{81} +(80.8285 + 139.999i) q^{82} -192.314 q^{83} +(-130.829 - 226.603i) q^{84} +(-760.315 - 1316.90i) q^{85} +763.226 q^{86} +(-418.683 - 725.180i) q^{87} +(49.5016 - 85.7392i) q^{88} +(-406.786 + 704.573i) q^{89} -739.587 q^{90} +168.636 q^{92} +(-290.083 + 502.439i) q^{93} +(235.414 - 407.750i) q^{94} +(-582.586 - 1009.07i) q^{95} +1255.67 q^{96} +(394.146 + 682.682i) q^{97} +(246.845 + 427.548i) q^{98} +90.4966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9	\( 18 q + 5 q^{2} - q^{3} - 37 q^{4} - 60 q^{5} + 48 q^{6} + 38 q^{7} - 120 q^{8} - 66 q^{9} + 147 q^{10} + 181 q^{11} + 78 q^{12} - 294 q^{14} + 218 q^{15} - 269 q^{16} + 55 q^{17} - 158 q^{18} + 161 q^{19} + 370 q^{20} - 376 q^{21} - 340 q^{22} + 204 q^{23} + 798 q^{24} + 614 q^{25} - 1336 q^{27} + 344 q^{28} - 280 q^{29} - 521 q^{30} - 1412 q^{31} + 680 q^{32} + 500 q^{33} - 432 q^{34} - 20 q^{35} + 909 q^{36} + 298 q^{37} - 1478 q^{38} + 26 q^{40} + 1201 q^{41} + 4 q^{42} + 533 q^{43} - 710 q^{44} - 90 q^{45} - 840 q^{46} - 1912 q^{47} + 132 q^{48} - 403 q^{49} - 1156 q^{50} + 940 q^{51} - 556 q^{53} - 2555 q^{54} + 250 q^{55} - 250 q^{56} + 1620 q^{57} - 2877 q^{58} + 1377 q^{59} + 6314 q^{60} + 136 q^{61} - 2035 q^{62} - 944 q^{63} + 568 q^{64} + 6558 q^{66} - 931 q^{67} + 1536 q^{68} + 2050 q^{69} + 9708 q^{70} + 2046 q^{71} - 4342 q^{72} + 90 q^{73} + 1990 q^{74} - 2393 q^{75} - 3608 q^{76} - 1436 q^{77} + 824 q^{79} - 787 q^{80} + 835 q^{81} - 2757 q^{82} - 7418 q^{83} - 1539 q^{84} - 2106 q^{85} - 250 q^{86} + 786 q^{87} + 636 q^{88} + 1663 q^{89} - 2560 q^{90} + 8020 q^{92} - 1186 q^{93} + 2531 q^{94} + 1614 q^{95} + 6168 q^{96} - 1087 q^{97} - 282 q^{98} - 2714 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 - q^3 - 37 * q^4 - 60 * q^5 + 48 * q^6 + 38 * q^7 - 120 * q^8 - 66 * q^9 + 147 * q^10 + 181 * q^11 + 78 * q^12 - 294 * q^14 + 218 * q^15 - 269 * q^16 + 55 * q^17 - 158 * q^18 + 161 * q^19 + 370 * q^20 - 376 * q^21 - 340 * q^22 + 204 * q^23 + 798 * q^24 + 614 * q^25 - 1336 * q^27 + 344 * q^28 - 280 * q^29 - 521 * q^30 - 1412 * q^31 + 680 * q^32 + 500 * q^33 - 432 * q^34 - 20 * q^35 + 909 * q^36 + 298 * q^37 - 1478 * q^38 + 26 * q^40 + 1201 * q^41 + 4 * q^42 + 533 * q^43 - 710 * q^44 - 90 * q^45 - 840 * q^46 - 1912 * q^47 + 132 * q^48 - 403 * q^49 - 1156 * q^50 + 940 * q^51 - 556 * q^53 - 2555 * q^54 + 250 * q^55 - 250 * q^56 + 1620 * q^57 - 2877 * q^58 + 1377 * q^59 + 6314 * q^60 + 136 * q^61 - 2035 * q^62 - 944 * q^63 + 568 * q^64 + 6558 * q^66 - 931 * q^67 + 1536 * q^68 + 2050 * q^69 + 9708 * q^70 + 2046 * q^71 - 4342 * q^72 + 90 * q^73 + 1990 * q^74 - 2393 * q^75 - 3608 * q^76 - 1436 * q^77 + 824 * q^79 - 787 * q^80 + 835 * q^81 - 2757 * q^82 - 7418 * q^83 - 1539 * q^84 - 2106 * q^85 - 250 * q^86 + 786 * q^87 + 636 * q^88 + 1663 * q^89 - 2560 * q^90 + 8020 * q^92 - 1186 * q^93 + 2531 * q^94 + 1614 * q^95 + 6168 * q^96 - 1087 * q^97 - 282 * q^98 - 2714 * q^99

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