LMFDB - Embedded newform 25.4.e.a.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(4,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("25.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.e (of order $10$, degree $4$, 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:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	25.4
Dual form			25.4.e.a.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.47870 + 1.13030i) q^{2} +(1.22604 - 1.68750i) q^{3} +(4.35165 + 3.16166i) q^{4} +(-11.1800 - 0.0808329i) q^{5} +(6.17240 - 4.48451i) q^{6} +8.69522i q^{7} +(-5.63517 - 7.75614i) q^{8} +(6.99898 + 21.5406i) q^{9} +O(q^{10})$	\(q+(3.47870 + 1.13030i) q^{2} +(1.22604 - 1.68750i) q^{3} +(4.35165 + 3.16166i) q^{4} +(-11.1800 - 0.0808329i) q^{5} +(6.17240 - 4.48451i) q^{6} +8.69522i q^{7} +(-5.63517 - 7.75614i) q^{8} +(6.99898 + 21.5406i) q^{9} +(-38.8007 - 12.9180i) q^{10} +(11.2241 - 34.5441i) q^{11} +(10.6706 - 3.46709i) q^{12} +(9.00127 - 2.92469i) q^{13} +(-9.82820 + 30.2481i) q^{14} +(-13.8436 + 18.7672i) q^{15} +(-24.1338 - 74.2761i) q^{16} +(14.7697 + 20.3288i) q^{17} +82.8444i q^{18} +(-43.5581 + 31.6468i) q^{19} +(-48.3961 - 35.6993i) q^{20} +(14.6732 + 10.6607i) q^{21} +(78.0902 - 107.482i) q^{22} +(186.484 + 60.5924i) q^{23} -19.9974 q^{24} +(124.987 + 1.80743i) q^{25} +34.6185 q^{26} +(98.4927 + 32.0022i) q^{27} +(-27.4913 + 37.8386i) q^{28} +(-153.365 - 111.426i) q^{29} +(-69.3703 + 49.6381i) q^{30} +(-201.106 + 146.112i) q^{31} -208.966i q^{32} +(-44.5320 - 61.2930i) q^{33} +(28.4018 + 87.4119i) q^{34} +(0.702860 - 97.2130i) q^{35} +(-37.6471 + 115.866i) q^{36} +(-192.559 + 62.5662i) q^{37} +(-187.296 + 60.8561i) q^{38} +(6.10050 - 18.7754i) q^{39} +(62.3745 + 87.1696i) q^{40} +(-148.823 - 458.030i) q^{41} +(38.9938 + 53.6704i) q^{42} +13.0607i q^{43} +(158.060 - 114.837i) q^{44} +(-76.5077 - 241.391i) q^{45} +(580.235 + 421.565i) q^{46} +(-223.319 + 307.372i) q^{47} +(-154.930 - 50.3398i) q^{48} +267.393 q^{49} +(432.749 + 147.560i) q^{50} +52.4130 q^{51} +(48.4172 + 15.7317i) q^{52} +(354.304 - 487.658i) q^{53} +(306.455 + 222.652i) q^{54} +(-128.278 + 385.297i) q^{55} +(67.4414 - 48.9990i) q^{56} +112.304i q^{57} +(-407.567 - 560.968i) q^{58} +(-121.448 - 373.777i) q^{59} +(-119.578 + 37.8997i) q^{60} +(-127.180 + 391.419i) q^{61} +(-864.740 + 280.971i) q^{62} +(-187.301 + 60.8577i) q^{63} +(43.1236 - 132.721i) q^{64} +(-100.871 + 31.9706i) q^{65} +(-85.6340 - 263.554i) q^{66} +(244.453 + 336.460i) q^{67} +135.161i q^{68} +(330.886 - 240.403i) q^{69} +(112.325 - 337.380i) q^{70} +(259.104 + 188.250i) q^{71} +(127.632 - 175.670i) q^{72} +(-141.434 - 45.9548i) q^{73} -740.574 q^{74} +(156.289 - 208.699i) q^{75} -289.606 q^{76} +(300.368 + 97.5956i) q^{77} +(42.4436 - 58.4187i) q^{78} +(-29.9592 - 21.7667i) q^{79} +(263.813 + 832.361i) q^{80} +(-319.977 + 232.477i) q^{81} -1761.56i q^{82} +(629.297 + 866.153i) q^{83} +(30.1471 + 92.7832i) q^{84} +(-163.483 - 228.470i) q^{85} +(-14.7625 + 45.4342i) q^{86} +(-376.064 + 122.191i) q^{87} +(-331.178 + 107.606i) q^{88} +(-4.60562 + 14.1746i) q^{89} +(6.69655 - 926.204i) q^{90} +(25.4308 + 78.2680i) q^{91} +(619.941 + 853.276i) q^{92} +518.506i q^{93} +(-1124.28 + 816.840i) q^{94} +(489.539 - 350.292i) q^{95} +(-352.630 - 256.200i) q^{96} +(709.473 - 976.506i) q^{97} +(930.181 + 302.234i) q^{98} +822.659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) $ 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	3.47870	+	1.13030i	1.22991	+	0.399621i	0.850680	−	0.525683i	$-0.176190\pi$
$2$	3.47870	+	1.13030i	1.22991	+	0.399621i	0.379226	+	0.925304i	$0.376190\pi$
$3$	1.22604	−	1.68750i	0.235951	−	0.324759i	−0.674578	−	0.738204i	$-0.735674\pi$
$3$	1.22604	−	1.68750i	0.235951	−	0.324759i	0.910529	+	0.413444i	$0.135674\pi$
$4$	4.35165	+	3.16166i	0.543956	+	0.395208i
$5$	−11.1800	−	0.0808329i	−0.999974	−	0.00722991i
$5$	−11.1800	−	0.0808329i	−0.999974	−	0.00722991i
$6$	6.17240	−	4.48451i	0.419979	−	0.305133i
$7$			8.69522i			0.469498i	0.972056	+	0.234749i	$0.0754268\pi$
$7$			8.69522i			0.469498i	−0.972056	+	0.234749i	$0.924573\pi$
$8$	−5.63517	−	7.75614i	−0.249042	−	0.342776i
$9$	6.99898	+	21.5406i	0.259221	+	0.797802i
$10$	−38.8007	−	12.9180i	−1.22699	−	0.408503i
$11$	11.2241	−	34.5441i	0.307653	−	0.946857i	−0.671021	−	0.741438i	$-0.734144\pi$
$11$	11.2241	−	34.5441i	0.307653	−	0.946857i	0.978674	−	0.205419i	$-0.0658558\pi$
$12$	10.6706	−	3.46709i	0.256695	−	0.0834051i
$13$	9.00127	−	2.92469i	0.192039	−	0.0623971i	−0.211419	−	0.977396i	$-0.567808\pi$
$13$	9.00127	−	2.92469i	0.192039	−	0.0623971i	0.403457	+	0.914998i	$0.367808\pi$
$14$	−9.82820	+	30.2481i	−0.187621	+	0.577438i
$15$	−13.8436	+	18.7672i	−0.238293	+	0.323045i
$16$	−24.1338	−	74.2761i	−0.377090	−	1.16056i
$17$	14.7697	+	20.3288i	0.210717	+	0.290026i	0.901273	−	0.433252i	$-0.142634\pi$
$17$	14.7697	+	20.3288i	0.210717	+	0.290026i	−0.690556	+	0.723279i	$0.742634\pi$
$18$			82.8444i			1.08481i
$19$	−43.5581	+	31.6468i	−0.525943	+	0.382120i	−0.818838	−	0.574025i	$-0.805381\pi$
$19$	−43.5581	+	31.6468i	−0.525943	+	0.382120i	0.292895	+	0.956145i	$0.405381\pi$
$20$	−48.3961	−	35.6993i	−0.541085	−	0.399130i
$21$	14.6732	+	10.6607i	0.152474	+	0.110779i
$22$	78.0902	−	107.482i	0.756768	−	1.04160i
$23$	186.484	+	60.5924i	1.69064	+	0.549321i	0.986927	−	0.161168i	$-0.0515261\pi$
$23$	186.484	+	60.5924i	1.69064	+	0.549321i	0.703709	+	0.710489i	$0.251526\pi$
$24$	−19.9974			−0.170082
$25$	124.987	+	1.80743i	0.999895	+	0.0144594i
$26$	34.6185			0.261125
$27$	98.4927	+	32.0022i	0.702035	+	0.228105i
$28$	−27.4913	+	37.8386i	−0.185549	+	0.255386i
$29$	−153.365	−	111.426i	−0.982043	−	0.713496i	−0.0238786	−	0.999715i	$-0.507602\pi$
$29$	−153.365	−	111.426i	−0.982043	−	0.713496i	−0.958164	+	0.286219i	$0.907602\pi$
$30$	−69.3703	+	49.6381i	−0.422174	+	0.302088i
$31$	−201.106	+	146.112i	−1.16515	+	0.846534i	−0.990421	−	0.138082i	$-0.955906\pi$
$31$	−201.106	+	146.112i	−1.16515	+	0.846534i	−0.174733	+	0.984616i	$0.555906\pi$
$32$		−	208.966i		−	1.15438i
$33$	−44.5320	−	61.2930i	−0.234910	−	0.323325i
$34$	28.4018	+	87.4119i	0.143261	+	0.440912i
$35$	0.702860	−	97.2130i	0.00339443	−	0.469486i
$36$	−37.6471	+	115.866i	−0.174292	+	0.536416i
$37$	−192.559	+	62.5662i	−0.855581	+	0.277995i	−0.703782	−	0.710416i	$-0.748507\pi$
$37$	−192.559	+	62.5662i	−0.855581	+	0.277995i	−0.151799	+	0.988411i	$0.548507\pi$
$38$	−187.296	+	60.8561i	−0.799563	+	0.259794i
$39$	6.10050	−	18.7754i	0.0250477	−	0.0770890i
$40$	62.3745	+	87.1696i	0.246557	+	0.344568i
$41$	−148.823	−	458.030i	−0.566884	−	1.74469i	−0.662287	−	0.749251i	$-0.730414\pi$
$41$	−148.823	−	458.030i	−0.566884	−	1.74469i	0.0954027	−	0.995439i	$-0.469586\pi$
$42$	38.9938	+	53.6704i	0.143259	+	0.197179i
$43$			13.0607i			0.0463194i	0.999732	+	0.0231597i	$0.00737263\pi$
$43$			13.0607i			0.0463194i	−0.999732	+	0.0231597i	$0.992627\pi$
$44$	158.060	−	114.837i	0.541555	−	0.393463i
$45$	−76.5077	−	241.391i	−0.253447	−	0.799655i
$46$	580.235	+	421.565i	1.85980	+	1.35123i
$47$	−223.319	+	307.372i	−0.693073	+	0.953934i	0.306924	+	0.951734i	$0.400700\pi$
$47$	−223.319	+	307.372i	−0.693073	+	0.953934i	−0.999998	+	0.00219976i	$0.999300\pi$
$48$	−154.930	−	50.3398i	−0.465879	−	0.151373i
$49$	267.393			0.779572
$50$	432.749	+	147.560i	1.22400	+	0.417363i
$51$	52.4130			0.143908
$52$	48.4172	+	15.7317i	0.129120	+	0.0419538i
$53$	354.304	−	487.658i	0.918253	−	1.26387i	−0.0460155	−	0.998941i	$-0.514652\pi$
$53$	354.304	−	487.658i	0.918253	−	1.26387i	0.964269	−	0.264926i	$-0.0853476\pi$
$54$	306.455	+	222.652i	0.772282	+	0.561095i
$55$	−128.278	+	385.297i	−0.314490	+	0.944608i
$56$	67.4414	−	48.9990i	0.160933	−	0.116924i
$57$			112.304i			0.260966i
$58$	−407.567	−	560.968i	−0.922693	−	1.26998i
$59$	−121.448	−	373.777i	−0.267985	−	0.824774i	−0.990991	−	0.133931i	$-0.957240\pi$
$59$	−121.448	−	373.777i	−0.267985	−	0.824774i	0.723005	−	0.690842i	$-0.242760\pi$
$60$	−119.578	+	37.8997i	−0.257291	+	0.0815471i
$61$	−127.180	+	391.419i	−0.266946	+	0.821575i	0.724293	+	0.689492i	$0.242166\pi$
$61$	−127.180	+	391.419i	−0.266946	+	0.821575i	−0.991239	+	0.132082i	$0.957834\pi$
$62$	−864.740	+	280.971i	−1.77132	+	0.575538i
$63$	−187.301	+	60.8577i	−0.374566	+	0.121704i
$64$	43.1236	−	132.721i	0.0842258	−	0.259220i
$65$	−100.871	+	31.9706i	−0.192485	+	0.0610071i
$66$	−85.6340	−	263.554i	−0.159709	−	0.491535i
$67$	244.453	+	336.460i	0.445741	+	0.613510i	0.971476	−	0.237139i	$-0.0762096\pi$
$67$	244.453	+	336.460i	0.445741	+	0.613510i	−0.525735	+	0.850648i	$0.676210\pi$
$68$			135.161i			0.241039i
$69$	330.886	−	240.403i	0.577305	−	0.419437i
$70$	112.325	−	337.380i	0.191791	−	0.576067i
$71$	259.104	+	188.250i	0.433099	+	0.314665i	0.782887	−	0.622164i	$-0.213746\pi$
$71$	259.104	+	188.250i	0.433099	+	0.314665i	−0.349788	+	0.936829i	$0.613746\pi$
$72$	127.632	−	175.670i	0.208911	−	0.287541i
$73$	−141.434	−	45.9548i	−0.226762	−	0.0736795i	0.193432	−	0.981114i	$-0.438038\pi$
$73$	−141.434	−	45.9548i	−0.226762	−	0.0736795i	−0.420194	+	0.907434i	$0.638038\pi$
$74$	−740.574			−1.16338
$75$	156.289	−	208.699i	0.240623	−	0.321314i
$76$	−289.606			−0.437106
$77$	300.368	+	97.5956i	0.444547	+	0.144442i
$78$	42.4436	−	58.4187i	0.0616128	−	0.0848027i
$79$	−29.9592	−	21.7667i	−0.0426668	−	0.0309993i	0.566247	−	0.824235i	$-0.308395\pi$
$79$	−29.9592	−	21.7667i	−0.0426668	−	0.0309993i	−0.608914	+	0.793236i	$0.708395\pi$
$80$	263.813	+	832.361i	0.368690	+	1.16326i
$81$	−319.977	+	232.477i	−0.438925	+	0.318898i
$82$		−	1761.56i		−	2.37234i
$83$	629.297	+	866.153i	0.832221	+	1.14545i	0.987506	+	0.157584i	$0.0503705\pi$
$83$	629.297	+	866.153i	0.832221	+	1.14545i	−0.155285	+	0.987870i	$0.549629\pi$
$84$	30.1471	+	92.7832i	0.0391585	+	0.120518i
$85$	−163.483	−	228.470i	−0.208614	−	0.291542i
$86$	−14.7625	+	45.4342i	−0.0185102	+	0.0569686i
$87$	−376.064	+	122.191i	−0.463429	+	0.150577i
$88$	−331.178	+	107.606i	−0.401179	+	0.130351i
$89$	−4.60562	+	14.1746i	−0.00548534	+	0.0168821i	−0.953762	−	0.300564i	$-0.902825\pi$
$89$	−4.60562	+	14.1746i	−0.00548534	+	0.0168821i	0.948276	+	0.317446i	$0.102825\pi$
$90$	6.69655	−	926.204i	0.00784309	−	1.08478i
$91$	25.4308	+	78.2680i	0.0292953	+	0.0901617i
$92$	619.941	+	853.276i	0.702536	+	0.966958i
$93$			518.506i			0.578136i
$94$	−1124.28	+	816.840i	−1.23363	+	0.896283i
$95$	489.539	−	350.292i	0.528691	−	0.378307i
$96$	−352.630	−	256.200i	−0.374897	−	0.272379i
$97$	709.473	−	976.506i	0.742640	−	1.02216i	−0.255822	−	0.966724i	$-0.582346\pi$
$97$	709.473	−	976.506i	0.742640	−	1.02216i	0.998462	−	0.0554324i	$-0.0176537\pi$
$98$	930.181	+	302.234i	0.958801	+	0.311533i
$99$	822.659			0.835155
$100$	538.185	+	403.032i	0.538185	+	0.403032i
$101$	−1075.02			−1.05910			−0.529548	−	0.848280i	$-0.677638\pi$
$101$	−1075.02			−1.05910			−0.529548	+	0.848280i	$0.677638\pi$
$102$	182.329	+	59.2424i	0.176993	+	0.0575085i
$103$	−456.961	+	628.952i	−0.437142	+	0.601675i	−0.969574	−	0.244798i	$-0.921278\pi$
$103$	−456.961	+	628.952i	−0.437142	+	0.601675i	0.532432	+	0.846473i	$0.321278\pi$
$104$	−73.4079	−	53.3340i	−0.0692139	−	0.0502868i
$105$	−163.185	−	120.373i	−0.151669	−	0.111878i
$106$	1783.72	−	1295.95i	1.63443	−	1.18749i
$107$		−	226.806i		−	0.204918i	−0.994737	−	0.102459i	$-0.967329\pi$
$107$		−	226.806i		−	0.204918i	0.994737	−	0.102459i	$-0.0326710\pi$
$108$	327.426	+	450.663i	0.291728	+	0.401529i
$109$	5.93962	+	18.2803i	0.00521938	+	0.0160636i	0.953632	−	0.300974i	$-0.0973118\pi$
$109$	5.93962	+	18.2803i	0.00521938	+	0.0160636i	−0.948413	+	0.317038i	$0.897312\pi$
$110$	−881.741	+	1195.34i	−0.764279	+	1.03610i
$111$	−130.505	+	401.652i	−0.111594	+	0.343451i
$112$	645.847	−	209.848i	0.544882	−	0.177043i
$113$	1261.87	−	410.008i	1.05050	−	0.341330i	0.267638	−	0.963519i	$-0.413757\pi$
$113$	1261.87	−	410.008i	1.05050	−	0.341330i	0.782867	+	0.622190i	$0.213757\pi$
$114$	−126.938	+	390.674i	−0.104288	+	0.320964i
$115$	−2080.00	−	692.499i	−1.68662	−	0.561530i
$116$	−315.100	−	969.779i	−0.252210	−	0.776221i
$117$	125.999	+	173.423i	0.0995611	+	0.137034i
$118$		−	1437.53i		−	1.12149i
$119$	−176.763	+	128.426i	−0.136167	+	0.0989310i
$120$	223.572	+	1.61645i	0.170077	+	0.00122967i
$121$	9.48771	+	6.89323i	0.00712826	+	0.00517898i
$122$	−884.841	+	1217.88i	−0.656637	+	0.903783i
$123$	−955.388	−	310.424i	−0.700361	−	0.227561i
$124$	−1337.10			−0.968350
$125$	−1397.21	−	30.3102i	−0.999765	−	0.0216882i
$126$	−720.350			−0.509317
$127$	1082.29	+	351.656i	0.756199	+	0.245704i	0.661647	−	0.749816i	$-0.269858\pi$
$127$	1082.29	+	351.656i	0.756199	+	0.245704i	0.0945527	+	0.995520i	$0.469858\pi$
$128$	−682.588	+	939.502i	−0.471350	+	0.648758i
$129$	22.0399	+	16.0129i	0.0150427	+	0.0109291i
$130$	−387.036	−	2.79831i	−0.261118	−	0.00188791i
$131$	1873.65	−	1361.29i	1.24963	−	0.907909i	0.251429	−	0.967876i	$-0.419099\pi$
$131$	1873.65	−	1361.29i	1.24963	−	0.907909i	0.998200	+	0.0599666i	$0.0190994\pi$
$132$		−	407.521i		−	0.268713i
$133$	−275.176	−	378.747i	−0.179404	−	0.246929i
$134$	470.077	+	1446.75i	0.303048	+	0.932687i
$135$	−1098.57	−	365.748i	−0.700367	−	0.233175i
$136$	74.4430	−	229.112i	0.0469370	−	0.144457i
$137$	−2004.05	+	651.155i	−1.24976	+	0.406072i	−0.857836	−	0.513924i	$-0.828191\pi$
$137$	−2004.05	+	651.155i	−1.24976	+	0.406072i	−0.391927	+	0.919996i	$0.628191\pi$
$138$	1422.78	−	462.290i	0.877647	−	0.285165i
$139$	−186.326	+	573.452i	−0.113698	+	0.349925i	−0.991673	−	0.128780i	$-0.958894\pi$
$139$	−186.326	+	573.452i	−0.113698	+	0.349925i	0.877976	+	0.478705i	$0.158894\pi$
$140$	310.413	−	420.815i	0.187391	−	0.254038i
$141$	244.893	+	753.702i	0.146267	+	0.450164i
$142$	688.567	+	947.732i	0.406925	+	0.560084i
$143$		−	343.767i		−	0.201030i
$144$	1431.04	−	1039.71i	0.828150	−	0.601686i
$145$	1705.63	+	1258.15i	0.976859	+	0.720577i
$146$	−440.065	−	319.726i	−0.249453	−	0.181238i
$147$	327.835	−	451.226i	0.183941	−	0.253173i
$148$	−1035.76	−	336.540i	−0.575265	−	0.186915i
$149$	2592.46			1.42538			0.712692	−	0.701477i	$-0.247476\pi$
$149$	2592.46			1.42538			0.712692	+	0.701477i	$0.247476\pi$
$150$	779.575	−	549.349i	0.424347	−	0.299028i
$151$	499.104			0.268983			0.134492	−	0.990915i	$-0.457060\pi$
$151$	499.104			0.268983			0.134492	+	0.990915i	$0.457060\pi$
$152$	490.914	+	159.508i	0.261963	+	0.0851170i
$153$	−334.522	+	460.430i	−0.176761	+	0.243291i
$154$	934.580	+	679.012i	0.489030	+	0.355301i
$155$	2260.19	−	1617.29i	1.17124	−	0.838088i
$156$	85.9087	−	62.4163i	0.0440910	−	0.0320340i
$157$		−	699.545i		−	0.355604i	−0.984066	−	0.177802i	$-0.943101\pi$
$157$		−	699.545i		−	0.355604i	0.984066	−	0.177802i	$-0.0568986\pi$
$158$	−79.6164	−	109.583i	−0.0400882	−	0.0551767i
$159$	−388.531	−	1195.78i	−0.193789	−	0.596423i
$160$	−16.8913	+	2336.25i	−0.00834610	+	1.15435i
$161$	−526.864	+	1621.52i	−0.257905	+	0.793750i
$162$	−1375.87	+	447.048i	−0.667275	+	0.216811i
$163$	−212.655	+	69.0957i	−0.102187	+	0.0332024i	−0.359664	−	0.933082i	$-0.617109\pi$
$163$	−212.655	+	69.0957i	−0.102187	+	0.0332024i	0.257477	+	0.966284i	$0.417109\pi$
$164$	800.509	−	2463.71i	0.381154	−	1.17307i
$165$	492.915	+	688.858i	0.232566	+	0.325015i
$166$	1210.13	+	3724.38i	0.565807	+	1.74137i
$167$	−1211.89	−	1668.03i	−0.561552	−	0.772910i	0.429971	−	0.902843i	$-0.358524\pi$
$167$	−1211.89	−	1668.03i	−0.561552	−	0.772910i	−0.991523	+	0.129933i	$0.958524\pi$
$168$		−	173.882i		−	0.0798529i
$169$	−1704.94	+	1238.71i	−0.776032	+	0.563820i
$170$	−310.468	−	979.565i	−0.140070	−	0.441936i
$171$	−986.554	−	716.774i	−0.441191	−	0.320544i
$172$	−41.2934	+	56.8355i	−0.0183058	+	0.0251958i
$173$	−1382.80	−	449.299i	−0.607701	−	0.197454i	−0.0110290	−	0.999939i	$-0.503511\pi$
$173$	−1382.80	−	449.299i	−0.607701	−	0.197454i	−0.596672	+	0.802485i	$0.703511\pi$
$174$	−1446.33			−0.630148
$175$	−15.7160	+	1086.79i	−0.00678868	+	0.469449i
$176$	−2836.68			−1.21490
$177$	−779.648	−	253.323i	−0.331085	−	0.107576i
$178$	−32.0432	+	44.1036i	−0.0134929	+	0.0185714i
$179$	−3005.52	−	2183.64i	−1.25499	−	0.911803i	−0.256489	−	0.966547i	$-0.582566\pi$
$179$	−3005.52	−	2183.64i	−1.25499	−	0.911803i	−0.998500	+	0.0547437i	$0.982566\pi$
$180$	430.262	−	1292.34i	0.178166	−	0.535142i
$181$	−441.170	+	320.528i	−0.181171	+	0.131628i	−0.674674	−	0.738116i	$-0.735716\pi$
$181$	−441.170	+	320.528i	−0.181171	+	0.131628i	0.493504	+	0.869744i	$0.335716\pi$
$182$			301.015i			0.122597i
$183$	504.592	+	694.511i	0.203828	+	0.280545i
$184$	−580.906	−	1787.85i	−0.232744	−	0.716314i
$185$	2157.88	−	683.928i	0.857569	−	0.271802i
$186$	−586.067	+	1803.73i	−0.231035	+	0.711053i
$187$	868.014	−	282.035i	0.339441	−	0.110291i
$188$	−1943.61	+	631.519i	−0.754004	+	0.244991i
$189$	−278.266	+	856.416i	−0.107095	+	0.329604i
$190$	2098.90	−	665.235i	0.801421	−	0.254006i
$191$	280.909	+	864.550i	0.106418	+	0.327522i	0.990061	−	0.140641i	$-0.0449162\pi$
$191$	280.909	+	864.550i	0.106418	+	0.327522i	−0.883642	+	0.468162i	$0.844916\pi$
$192$	−171.095	−	235.492i	−0.0643110	−	0.0885165i
$193$		−	1243.23i		−	0.463676i	−0.972754	−	0.231838i	$-0.925526\pi$
$193$		−	1243.23i		−	0.463676i	0.972754	−	0.231838i	$-0.0744739\pi$
$194$	3571.79	−	2595.06i	1.32185	−	0.960382i
$195$	−69.7216	+	209.417i	−0.0256044	+	0.0769059i
$196$	1163.60	+	845.406i	0.424053	+	0.308093i
$197$	377.998	−	520.270i	0.136707	−	0.188161i	−0.735175	−	0.677878i	$-0.762900\pi$
$197$	377.998	−	520.270i	0.136707	−	0.188161i	0.871882	+	0.489717i	$0.162900\pi$
$198$	2861.78	+	929.850i	1.02716	+	0.333745i
$199$	−1167.73			−0.415969			−0.207985	−	0.978132i	$-0.566690\pi$
$199$	−1167.73			−0.415969			−0.207985	+	0.978132i	$0.566690\pi$
$200$	−690.304	−	979.602i	−0.244059	−	0.346342i
$201$	867.485			0.304416
$202$	−3739.68	−	1215.10i	−1.30259	−	0.423237i
$203$	968.878	−	1333.55i	0.334985	−	0.461067i
$204$	228.083	+	165.712i	0.0782795	+	0.0568734i
$205$	1626.82	+	5132.83i	0.554255	+	1.74874i
$206$	−2300.53	+	1671.44i	−0.778086	+	0.565313i
$207$			4441.07i			1.49119i
$208$	−434.469	−	597.995i	−0.144832	−	0.199344i
$209$	604.311	+	1859.88i	0.200005	+	0.615553i
$210$	−431.615	−	603.190i	−0.141830	−	0.198210i
$211$	1238.89	−	3812.92i	0.404213	−	1.24404i	−0.517337	−	0.855782i	$-0.673077\pi$
$211$	1238.89	−	3812.92i	0.404213	−	1.24404i	0.921550	−	0.388259i	$-0.126923\pi$
$212$	3083.62	−	1001.93i	0.998980	−	0.324588i
$213$	635.344	−	206.436i	0.204381	−	0.0664073i
$214$	256.359	−	788.991i	0.0818893	−	0.252029i
$215$	1.05573	−	146.019i	0.000334885	−	0.0463182i
$216$	−306.809	−	944.262i	−0.0966469	−	0.297449i
$217$	−1270.48	−	1748.66i	−0.397446	−	0.547037i
$218$			70.3052i			0.0218425i
$219$	−250.953	+	182.328i	−0.0774330	+	0.0562584i
$220$	−1776.40	+	1271.11i	−0.544385	+	0.389537i
$221$	192.401	+	139.788i	0.0585625	+	0.0425482i
$222$	−907.973	+	1249.72i	−0.274501	+	0.377818i
$223$	−2746.94	−	892.534i	−0.824881	−	0.268020i	−0.133993	−	0.990982i	$-0.542780\pi$
$223$	−2746.94	−	892.534i	−0.824881	−	0.268020i	−0.690888	+	0.722962i	$0.742780\pi$
$224$	1817.00			0.541981
$225$	835.848	+	2704.95i	0.247659	+	0.801466i
$226$	4853.11			1.42843
$227$	2792.61	+	907.375i	0.816530	+	0.265307i	0.687361	−	0.726316i	$-0.258769\pi$
$227$	2792.61	+	907.375i	0.816530	+	0.265307i	0.129169	+	0.991623i	$0.458769\pi$
$228$	−355.068	+	488.710i	−0.103136	+	0.141954i
$229$	1909.76	+	1387.52i	0.551094	+	0.400393i	0.828189	−	0.560449i	$-0.189372\pi$
$229$	1909.76	+	1387.52i	0.551094	+	0.400393i	−0.277094	+	0.960843i	$0.589372\pi$
$230$	−6452.98	−	4760.02i	−1.84999	−	1.36464i
$231$	532.956	−	387.215i	0.151801	−	0.110290i
$232$			1817.43i			0.514311i
$233$	−49.2757	−	67.8222i	−0.0138548	−	0.0190694i	0.802033	−	0.597279i	$-0.203752\pi$
$233$	−49.2757	−	67.8222i	−0.0138548	−	0.0190694i	−0.815888	+	0.578210i	$0.803752\pi$
$234$	242.294	+	745.704i	0.0676891	+	0.208326i
$235$	2521.56	−	3418.39i	0.699952	−	0.948898i
$236$	653.259	−	2010.52i	0.180185	−	0.554551i
$237$	−73.4624	+	23.8694i	−0.0201346	+	0.00654213i
$238$	−760.066	+	246.960i	−0.207007	+	0.0672608i
$239$	−1729.88	+	5324.03i	−0.468188	+	1.44093i	0.386741	+	0.922188i	$0.373601\pi$
$239$	−1729.88	+	5324.03i	−0.468188	+	1.44093i	−0.854929	+	0.518745i	$0.826399\pi$
$240$	1728.05	+	575.324i	0.464772	+	0.154738i
$241$	−1328.96	−	4090.13i	−0.355212	−	1.09323i	−0.955886	−	0.293737i	$-0.905101\pi$
$241$	−1328.96	−	4090.13i	−0.355212	−	1.09323i	0.600674	−	0.799494i	$-0.294899\pi$
$242$	25.2135	+	34.7034i	0.00669746	+	0.00921827i
$243$			3621.14i			0.955952i
$244$	−1790.98	+	1301.22i	−0.469899	+	0.341402i
$245$	−2989.47	−	21.6142i	−0.779551	−	0.00563624i
$246$	−2972.64	−	2159.75i	−0.770441	−	0.559758i
$247$	−299.521	+	412.255i	−0.0771581	+	0.106199i
$248$	2266.54	+	736.442i	0.580344	+	0.188565i
$249$	2233.18			0.568361
$250$	−4826.23	−	1684.71i	−1.22095	−	0.426201i
$251$	4182.69			1.05183			0.525914	−	0.850538i	$-0.323723\pi$
$251$	4182.69			1.05183			0.525914	+	0.850538i	$0.323723\pi$
$252$	−1007.48	−	327.350i	−0.251846	−	0.0818297i
$253$	4186.21	−	5761.83i	1.04026	−	1.43179i
$254$	3367.47	+	2446.61i	0.831866	+	0.604386i
$255$	−585.980	−	4.23670i	−0.143904	−	0.00104044i
$256$	−4339.63	+	3152.93i	−1.05948	+	0.769757i
$257$			257.733i			0.0625562i	0.999511	+	0.0312781i	$0.00995775\pi$
$257$			257.733i			0.0625562i	−0.999511	+	0.0312781i	$0.990042\pi$
$258$	58.5708	+	80.6158i	0.0141336	+	0.0194532i
$259$	−544.027	−	1674.34i	−0.130518	−	0.401694i
$260$	−540.035	−	179.795i	−0.128814	−	0.0428862i
$261$	1326.80	−	4083.46i	0.314662	−	0.968429i
$262$	8056.52	−	2617.72i	1.89975	−	0.617265i
$263$	−4280.88	+	1390.94i	−1.00369	+	0.326119i	−0.764339	−	0.644814i	$-0.776935\pi$
$263$	−4280.88	+	1390.94i	−1.00369	+	0.326119i	−0.239351	+	0.970933i	$0.576935\pi$
$264$	−224.452	+	690.793i	−0.0523260	+	0.161043i
$265$	−4000.56	+	5423.40i	−0.927367	+	1.25720i
$266$	−529.157	−	1628.58i	−0.121973	−	0.375393i
$267$	18.2730	+	25.1507i	0.00418836	+	0.00576478i
$268$			2237.03i			0.509883i
$269$	−2210.72	+	1606.19i	−0.501079	+	0.364055i	−0.809429	−	0.587218i	$-0.800223\pi$
$269$	−2210.72	+	1606.19i	−0.501079	+	0.364055i	0.308350	+	0.951273i	$0.400223\pi$
$270$	−3408.18	−	2514.04i	−0.768205	−	0.566664i
$271$	1654.98	+	1202.42i	0.370971	+	0.269526i	0.757613	−	0.652704i	$-0.226365\pi$
$271$	1654.98	+	1202.42i	0.370971	+	0.269526i	−0.386642	+	0.922230i	$0.626365\pi$
$272$	1153.49	−	1587.65i	0.257135	−	0.353916i
$273$	163.256	+	53.0452i	0.0361931	+	0.0117599i
$274$	−7707.49			−1.69937
$275$	1465.30	−	4297.27i	0.321311	−	0.942310i
$276$	2199.98			0.479793
$277$	−3569.18	−	1159.70i	−0.774191	−	0.251550i	−0.104833	−	0.994490i	$-0.533431\pi$
$277$	−3569.18	−	1159.70i	−0.774191	−	0.251550i	−0.669358	+	0.742940i	$0.733431\pi$
$278$	−1296.34	+	1784.26i	−0.279675	+	0.384939i
$279$	−4554.89	−	3309.32i	−0.977399	−	0.710122i
$280$	−757.959	+	542.360i	−0.161774	+	0.115758i
$281$	−6179.77	+	4489.87i	−1.31194	+	0.953178i	−0.311942	+	0.950101i	$0.600980\pi$
$281$	−6179.77	+	4489.87i	−1.31194	+	0.953178i	−0.999995	+	0.00307736i	$0.999020\pi$
$282$			2898.71i			0.612111i
$283$	−483.661	−	665.703i	−0.101593	−	0.139830i	0.755194	−	0.655501i	$-0.227543\pi$
$283$	−483.661	−	665.703i	−0.101593	−	0.139830i	−0.856787	+	0.515671i	$0.827543\pi$
$284$	532.348	+	1638.40i	0.111229	+	0.342328i
$285$	9.07789	−	1255.57i	0.00188676	−	0.260960i
$286$	388.560	−	1195.86i	0.0803357	−	0.247248i
$287$	3982.67	−	1294.05i	0.819128	−	0.266151i
$288$	4501.26	−	1462.55i	0.920969	−	0.299241i
$289$	1323.09	−	4072.04i	0.269303	−	0.828830i
$290$	4511.28	+	6304.60i	0.913487	+	1.27662i
$291$	−778.011	−	2394.47i	−0.156728	−	0.482359i
$292$	−470.180	−	647.147i	−0.0942301	−	0.129697i
$293$			5029.58i			1.00284i	0.865205	+	0.501418i	$0.167188\pi$
$293$			5029.58i			1.00284i	−0.865205	+	0.501418i	$0.832812\pi$
$294$	1650.46	−	1199.13i	0.327404	−	0.237873i
$295$	1327.58	+	4188.66i	0.262015	+	0.826690i
$296$	1570.38	+	1140.94i	0.308366	+	0.224041i
$297$	2210.98	−	3043.15i	0.431966	−	0.594550i
$298$	9018.38	+	2930.25i	1.75309	+	0.569613i
$299$	1855.81			0.358943
$300$	1339.95	−	414.054i	0.257874	−	0.0796848i
$301$	−113.566			−0.0217469
$302$	1736.23	+	564.137i	0.330825	+	0.107491i
$303$	−1318.02	+	1814.10i	−0.249895	+	0.343951i
$304$	3401.82	+	2471.57i	0.641802	+	0.466297i
$305$	1453.52	−	4365.80i	0.272879	−	0.819623i
$306$	−1684.12	+	1223.59i	−0.314624	+	0.228588i
$307$		−	1878.17i		−	0.349161i	−0.984643	−	0.174581i	$-0.944143\pi$
$307$		−	1878.17i		−	0.349161i	0.984643	−	0.174581i	$-0.0558570\pi$
$308$	998.534	+	1374.36i	0.184730	+	0.254259i
$309$	501.104	+	1542.24i	0.0922551	+	0.283932i
$310$	9690.54	−	3071.37i	1.77544	−	0.562716i
$311$	−543.357	+	1672.28i	−0.0990705	+	0.304908i	−0.988293	−	0.152567i	$-0.951246\pi$
$311$	−543.357	+	1672.28i	−0.0990705	+	0.304908i	0.889223	+	0.457475i	$0.151246\pi$
$312$	−180.002	+	58.4862i	−0.0326622	+	0.0106126i
$313$	673.763	−	218.919i	0.121672	−	0.0395336i	−0.247548	−	0.968876i	$-0.579625\pi$
$313$	673.763	−	218.919i	0.121672	−	0.0395336i	0.369220	+	0.929342i	$0.379625\pi$
$314$	790.695	−	2433.51i	0.142107	−	0.437359i
$315$	2098.95	−	665.252i	0.375436	−	0.118993i
$316$	−61.5534	−	189.442i	−0.0109578	−	0.0337245i
$317$	−5384.50	−	7411.13i	−0.954018	−	1.31309i	−0.949719	−	0.313103i	$-0.898632\pi$
$317$	−5384.50	−	7411.13i	−0.954018	−	1.31309i	−0.00429902	−	0.999991i	$-0.501368\pi$
$318$		−	4598.90i		−	0.810986i
$319$	−5570.51	+	4047.21i	−0.977707	+	0.710346i
$320$	−492.852	+	1480.34i	−0.0860977	+	0.258604i
$321$	−382.735	−	278.073i	−0.0665489	−	0.0483506i
$322$	−3665.60	+	5045.27i	−0.634398	+	0.873174i
$323$	−1286.68	−	418.068i	−0.221650	−	0.0720183i
$324$	−2127.44			−0.364787
$325$	1130.33	−	349.279i	0.192921	−	0.0596138i
$326$	−817.861			−0.138948
$327$	38.1302	+	12.3892i	0.00644833	+	0.00209519i
$328$	−2713.90	+	3735.37i	−0.456861	+	0.628815i
$329$	−2672.67	−	1941.81i	−0.447870	−	0.325396i
$330$	936.089	+	2953.47i	0.156151	+	0.492677i
$331$	13.5425	−	9.83923i	0.00224884	−	0.00163388i	−0.586660	−	0.809833i	$-0.699558\pi$
$331$	13.5425	−	9.83923i	0.00224884	−	0.00163388i	0.588909	+	0.808199i	$0.299558\pi$
$332$			5758.82i			0.951977i
$333$	−2695.43	−	3709.95i	−0.443570	−	0.610522i
$334$	−2330.45	−	7172.38i	−0.381786	−	1.17502i
$335$	−2705.79	−	3781.40i	−0.441294	−	0.616716i
$336$	437.715	−	1347.15i	0.0710694	−	0.218729i
$337$	1778.38	−	577.831i	0.287461	−	0.0934019i	−0.161737	−	0.986834i	$-0.551710\pi$
$337$	1778.38	−	577.831i	0.287461	−	0.0934019i	0.449198	+	0.893432i	$0.351710\pi$
$338$	−7331.10	+	2382.02i	−1.17976	+	0.383327i
$339$	855.220	−	2632.10i	0.137018	−	0.421699i
$340$	10.9254	−	1511.10i	0.00174269	−	0.241032i
$341$	2790.09	+	8587.01i	0.443084	+	1.36367i
$342$	−2621.76	−	3608.54i	−0.414528	−	0.570549i
$343$			5307.50i			0.835505i
$344$	101.301	−	73.5991i	0.0158772	−	0.0115355i
$345$	−3718.76	+	2660.97i	−0.580322	+	0.415252i
$346$	−4302.50	−	3125.95i	−0.668509	−	0.485700i
$347$	−2763.80	+	3804.05i	−0.427576	+	0.588507i	−0.967395	−	0.253274i	$-0.918493\pi$
$347$	−2763.80	+	3804.05i	−0.427576	+	0.588507i	0.539819	+	0.841781i	$0.318493\pi$
$348$	−2022.83	−	657.256i	−0.311594	−	0.101243i
$349$	10178.2			1.56111			0.780553	−	0.625090i	$-0.214938\pi$
$349$	10178.2			1.56111			0.780553	+	0.625090i	$0.214938\pi$
$350$	−1283.07	+	3762.85i	−0.195951	+	0.574665i
$351$	980.156			0.149051
$352$	−7218.53	−	2345.44i	−1.09304	−	0.355149i
$353$	4417.38	−	6080.00i	0.666043	−	0.916730i	−0.333619	−	0.942708i	$-0.608270\pi$
$353$	4417.38	−	6080.00i	0.666043	−	0.916730i	0.999663	+	0.0259780i	$0.00826999\pi$
$354$	−2425.83	−	1762.47i	−0.364213	−	0.264617i
$355$	−2881.58	−	2125.59i	−0.430813	−	0.317788i
$356$	−64.8575	+	47.1217i	−0.00965573	+	0.00701530i
$357$			455.743i			0.0675643i
$358$	−7987.14	−	10993.4i	−1.17914	−	1.62295i
$359$	1524.63	+	4692.33i	0.224142	+	0.689837i	0.998378	+	0.0569401i	$0.0181344\pi$
$359$	1524.63	+	4692.33i	0.224142	+	0.689837i	−0.774236	+	0.632897i	$0.781866\pi$
$360$	−1441.13	+	1953.68i	−0.210984	+	0.286023i
$361$	−1223.76	+	3766.35i	−0.178417	+	0.549111i
$362$	−1896.99	+	616.369i	−0.275424	+	0.0894908i
$363$	23.2646	−	7.55914i	0.00336385	−	0.00109298i
$364$	−136.791	+	420.999i	−0.0196972	+	0.0606218i
$365$	1577.53	+	525.210i	0.226224	+	0.0753171i
$366$	970.319	+	2986.34i	0.138578	+	0.426498i
$367$	6821.76	+	9389.35i	0.970281	+	1.33548i	0.941905	+	0.335879i	$0.109033\pi$
$367$	6821.76	+	9389.35i	0.970281	+	1.33548i	0.0283755	+	0.999597i	$0.490967\pi$
$368$		−	15313.6i		−	2.16923i
$369$	8824.65	−	6411.48i	1.24497	−	0.904522i
$370$	8279.65	+	59.8627i	1.16335	+	0.00841112i
$371$	4240.29	+	3080.75i	0.593383	+	0.431118i
$372$	−1639.34	+	2256.36i	−0.228484	+	0.314481i
$373$	−4307.75	−	1399.67i	−0.597981	−	0.194296i	−0.00564124	−	0.999984i	$-0.501796\pi$
$373$	−4307.75	−	1399.67i	−0.597981	−	0.194296i	−0.592340	+	0.805688i	$0.701796\pi$
$374$	3338.35			0.461556
$375$	−1764.19	+	2320.64i	−0.242939	+	0.319566i
$376$	3642.47			0.499590
$377$	−1706.37	−	554.433i	−0.233110	−	0.0757421i
$378$	−1936.01	+	2664.69i	−0.263433	+	0.362585i
$379$	5924.25	+	4304.22i	0.802925	+	0.583359i	0.911771	−	0.410700i	$-0.134716\pi$
$379$	5924.25	+	4304.22i	0.802925	+	0.583359i	−0.108846	+	0.994059i	$0.534716\pi$
$380$	3237.81	+	23.4097i	0.437095	+	0.00316024i
$381$	1920.34	−	1395.21i	0.258221	−	0.187609i
$382$			3325.02i			0.445348i
$383$	4966.16	+	6835.33i	0.662556	+	0.911930i	0.999563	−	0.0295722i	$-0.00941450\pi$
$383$	4966.16	+	6835.33i	0.662556	+	0.911930i	−0.337007	+	0.941502i	$0.609414\pi$
$384$	748.528	+	2303.73i	0.0994744	+	0.306151i
$385$	−3350.24	−	1115.40i	−0.443492	−	0.147652i
$386$	1405.22	−	4324.82i	0.185295	−	0.570278i
$387$	−281.336	+	91.4115i	−0.0369537	+	0.0120070i
$388$	6174.76	−	2006.30i	0.807928	−	0.262512i
$389$	1501.14	−	4620.03i	0.195657	−	0.602172i	−0.804311	−	0.594209i	$-0.797465\pi$
$389$	1501.14	−	4620.03i	0.195657	−	0.602172i	0.999968	−	0.00796284i	$-0.00253468\pi$
$390$	−479.244	+	649.693i	−0.0622243	+	0.0843550i
$391$	1522.55	+	4685.92i	0.196927	+	0.606080i
$392$	−1506.81	−	2073.94i	−0.194146	−	0.267219i
$393$		−	4830.77i		−	0.620051i
$394$	1903.00	−	1382.61i	0.243330	−	0.176789i
$395$	333.186	+	245.774i	0.0424416	+	0.0313069i
$396$	3579.92	+	2600.97i	0.454288	+	0.330059i
$397$	−911.614	+	1254.73i	−0.115246	+	0.158622i	−0.862743	−	0.505643i	$-0.831255\pi$
$397$	−911.614	+	1254.73i	−0.115246	+	0.158622i	0.747497	+	0.664265i	$0.231255\pi$
$398$	−4062.17	−	1319.88i	−0.511603	−	0.166230i
$399$	−976.512			−0.122523
$400$	−2882.16	−	9327.16i	−0.360270	−	1.16590i
$401$	−3906.52			−0.486490			−0.243245	−	0.969965i	$-0.578212\pi$
$401$	−3906.52			−0.486490			−0.243245	+	0.969965i	$0.578212\pi$
$402$	3017.72	+	980.517i	0.374404	+	0.121651i
$403$	−1382.88	+	1903.37i	−0.170933	+	0.235269i
$404$	−4678.12	−	3398.85i	−0.576102	−	0.418563i
$405$	3596.14	−	2573.23i	0.441219	−	0.315716i
$406$	4877.74	−	3543.89i	0.596252	−	0.433202i
$407$			7354.02i			0.895640i
$408$	−295.356	−	406.523i	−0.0358390	−	0.0493282i
$409$	59.0808	+	181.832i	0.00714268	+	0.0219829i	0.954564	−	0.298005i	$-0.0963212\pi$
$409$	59.0808	+	181.832i	0.00714268	+	0.0219829i	−0.947422	+	0.319988i	$0.896321\pi$
$410$	−142.392	+	19694.4i	−0.0171518	+	2.37228i
$411$	−1358.22	+	4180.17i	−0.163007	+	0.501685i
$412$	−3977.07	+	1292.23i	−0.475573	+	0.154523i
$413$	3250.08	−	1056.01i	0.387230	−	0.125818i
$414$	−5019.74	+	15449.2i	−0.595910	+	1.83402i
$415$	−6965.56	−	9734.50i	−0.823918	−	1.15144i
$416$	−611.160	−	1880.96i	−0.0720302	−	0.221686i
$417$	739.257	+	1017.50i	0.0868143	+	0.119490i
$418$			7153.01i			0.836999i
$419$	−81.1750	+	58.9771i	−0.00946458	+	0.00687642i	−0.592507	−	0.805565i	$-0.701862\pi$
$419$	−81.1750	+	58.9771i	−0.00946458	+	0.00687642i	0.583043	+	0.812441i	$0.301862\pi$
$420$	−329.546	−	1039.76i	−0.0382862	−	0.120798i
$421$	−11703.6	−	8503.14i	−1.35486	−	0.984365i	−0.998753	−	0.0499211i	$-0.984103\pi$
$421$	−11703.6	−	8503.14i	−1.35486	−	0.984365i	−0.356109	−	0.934444i	$-0.615897\pi$
$422$	8619.49	−	11863.7i	0.994289	−	1.36852i
$423$	−8184.01	−	2659.15i	−0.940709	−	0.305655i
$424$	−5778.91			−0.661907
$425$	1809.28	+	2567.53i	0.206501	+	0.293043i
$426$	2443.51			0.277907
$427$	−3403.47	−	1105.86i	−0.385728	−	0.125330i
$428$	717.084	−	986.981i	0.0809849	−	0.111466i
$429$	−580.107	−	421.472i	−0.0652863	−	0.0474333i
$430$	168.718	−	506.763i	0.0189216	−	0.0568333i
$431$	9275.27	−	6738.88i	1.03660	−	0.753133i	0.0669798	−	0.997754i	$-0.478664\pi$
$431$	9275.27	−	6738.88i	1.03660	−	0.753133i	0.969619	+	0.244621i	$0.0786637\pi$
$432$		−	8087.99i		−	0.900773i
$433$	10231.9	+	14083.1i	1.13560	+	1.56302i	0.776963	+	0.629547i	$0.216759\pi$
$433$	10231.9	+	14083.1i	1.13560	+	1.56302i	0.358640	+	0.933476i	$0.383241\pi$
$434$	−2443.10	−	7519.10i	−0.270214	−	0.831632i
$435$	4214.29	−	1335.70i	0.464505	−	0.147223i
$436$	−31.9489	+	98.3285i	−0.00350934	+	0.0108006i
$437$	−10040.4	+	3262.34i	−1.09908	+	0.357114i
$438$	−1079.08	+	350.613i	−0.117717	+	0.0382487i
$439$	3604.95	−	11094.9i	0.391924	−	1.20622i	−0.539407	−	0.842045i	$-0.681351\pi$
$439$	3604.95	−	11094.9i	0.391924	−	1.20622i	0.931331	−	0.364174i	$-0.118649\pi$
$440$	3711.29	−	1176.27i	0.402111	−	0.127447i
$441$	1871.48	+	5759.82i	0.202082	+	0.621944i
$442$	511.305	+	703.751i	0.0550233	+	0.0757331i
$443$			4438.86i			0.476064i	0.971257	+	0.238032i	$0.0765024\pi$
$443$			4438.86i			0.476064i	−0.971257	+	0.238032i	$0.923498\pi$
$444$	−1837.80	+	1335.24i	−0.196437	+	0.142720i
$445$	52.6368	−	158.101i	0.00560725	−	0.0168420i
$446$	−8546.94	−	6209.72i	−0.907420	−	0.659279i
$447$	3178.45	−	4374.77i	0.336321	−	0.462907i
$448$	1154.04	+	374.969i	0.121703	+	0.0395438i
$449$	−11518.2			−1.21064			−0.605321	−	0.795981i	$-0.706955\pi$
$449$	−11518.2			−1.21064			−0.605321	+	0.795981i	$0.706955\pi$
$450$	−149.736	+	10354.5i	−0.0156858	+	1.08470i
$451$	−17492.6			−1.82638
$452$	6787.54	+	2205.40i	0.706325	+	0.229499i
$453$	611.921	−	842.237i	0.0634670	−	0.0873549i
$454$	8689.06	+	6312.97i	0.898233	+	0.652605i
$455$	−277.991	−	877.096i	−0.0286427	−	0.0903711i
$456$	871.049	−	632.854i	0.0894531	−	0.0649915i
$457$		−	13131.0i		−	1.34407i	−0.740517	−	0.672037i	$-0.765419\pi$
$457$		−	13131.0i		−	1.34407i	0.740517	−	0.672037i	$-0.234581\pi$
$458$	5075.17	+	6985.38i	0.517789	+	0.712675i
$459$	804.144	+	2474.90i	0.0817739	+	0.251674i
$460$	−6862.00	−	9589.78i	−0.695527	−	0.972012i
$461$	474.673	−	1460.89i	0.0479560	−	0.147593i	−0.924211	−	0.381882i	$-0.875276\pi$
$461$	474.673	−	1460.89i	0.0479560	−	0.147593i	0.972167	+	0.234289i	$0.0752761\pi$
$462$	2291.66	−	744.607i	0.230775	−	0.0749832i
$463$	9049.91	−	2940.50i	0.908391	−	0.295154i	0.182695	−	0.983170i	$-0.441518\pi$
$463$	9049.91	−	2940.50i	0.908391	−	0.295154i	0.725696	+	0.688015i	$0.241518\pi$
$464$	−4575.04	+	14080.5i	−0.457739	+	1.40878i
$465$	41.9124	−	5796.93i	0.00417987	−	0.578120i
$466$	−94.7561	−	291.629i	−0.00941951	−	0.0289903i
$467$	1963.43	+	2702.42i	0.194554	+	0.267780i	0.895138	−	0.445790i	$-0.147077\pi$
$467$	1963.43	+	2702.42i	0.194554	+	0.267780i	−0.700584	+	0.713570i	$0.747077\pi$
$468$			1153.04i			0.113888i
$469$	−2925.60	+	2125.57i	−0.288041	+	0.209274i
$470$	12635.6	−	9041.43i	1.24008	−	0.887340i
$471$	−1180.48	−	857.670i	−0.115486	−	0.0839052i
$472$	−2214.69	+	3048.26i	−0.215974	+	0.297262i
$473$	451.169	+	146.594i	0.0438579	+	0.0142503i
$474$	−282.533			−0.0273780
$475$	−5501.39	+	3876.71i	−0.531413	+	0.374475i
$476$	−1175.25			−0.113167
$477$	12984.2	+	4218.83i	1.24635	+	0.404962i
$478$	−12035.5	+	16565.4i	−1.15165	+	1.58512i
$479$	−16918.2	−	12291.8i	−1.61380	−	1.17250i	−0.849385	−	0.527774i	$-0.823027\pi$
$479$	−16918.2	−	12291.8i	−1.61380	−	1.17250i	−0.764417	−	0.644722i	$-0.776973\pi$
$480$	3921.71	+	2892.84i	0.372918	+	0.275082i
$481$	−1550.29	+	1126.35i	−0.146959	+	0.106772i
$482$		−	15730.5i		−	1.48652i
$483$	2090.36	+	2877.13i	0.196925	+	0.271043i
$484$	19.4932	+	59.9939i	0.00183069	+	0.00563428i
$485$	−8010.88	+	10860.0i	−0.750011	+	1.01676i
$486$	−4092.97	+	12596.9i	−0.382019	+	1.17573i
$487$	10542.0	−	3425.32i	0.980915	−	0.318719i	0.225701	−	0.974197i	$-0.427533\pi$
$487$	10542.0	−	3425.32i	0.980915	−	0.318719i	0.755214	+	0.655478i	$0.227533\pi$
$488$	3752.58	−	1219.29i	0.348097	−	0.113104i
$489$	−144.124	+	443.569i	−0.0133283	+	0.0410202i
$490$	−10375.0	−	3454.18i	−0.956523	−	0.318457i
$491$	−2886.41	−	8883.44i	−0.265299	−	0.816505i	−0.991624	−	0.129155i	$-0.958774\pi$
$491$	−2886.41	−	8883.44i	−0.265299	−	0.816505i	0.726326	−	0.687351i	$-0.241226\pi$
$492$	−3176.06	−	4371.47i	−0.291032	−	0.400571i
$493$		−	4763.47i		−	0.435164i
$494$	−1507.91	+	1095.56i	−0.137337	+	0.0997809i
$495$	−9197.36	−	66.4979i	−0.835133	−	0.00603809i
$496$	15706.1	+	11411.2i	1.42183	+	1.03302i
$497$	−1636.88	+	2252.97i	−0.147734	+	0.203339i
$498$	7768.55	+	2524.16i	0.699030	+	0.227129i
$499$	1309.24			0.117454			0.0587271	−	0.998274i	$-0.481296\pi$
$499$	1309.24			0.117454			0.0587271	+	0.998274i	$0.481296\pi$
$500$	−5984.36	−	4549.41i	−0.535257	−	0.406912i
$501$	−4300.63			−0.383509
$502$	14550.3	+	4727.69i	1.29365	+	0.420333i
$503$	9525.50	−	13110.7i	0.844376	−	1.16218i	−0.140698	−	0.990053i	$-0.544935\pi$
$503$	9525.50	−	13110.7i	0.844376	−	1.16218i	0.985074	−	0.172132i	$-0.0550654\pi$
$504$	1527.49	+	1109.79i	0.135000	+	0.0980831i
$505$	12018.8	+	86.8971i	1.05907	+	0.00765717i
$506$	21075.2	−	15312.0i	1.85159	−	1.34526i
$507$			4395.80i			0.385058i
$508$	3597.91	+	4952.10i	0.314235	+	0.432508i
$509$	2844.93	+	8755.79i	0.247739	+	0.762463i	0.995174	+	0.0981274i	$0.0312853\pi$
$509$	2844.93	+	8755.79i	0.247739	+	0.762463i	−0.747435	+	0.664335i	$0.768715\pi$
$510$	−2033.66	−	677.071i	−0.176573	−	0.0587867i
$511$	399.587	−	1229.80i	0.0345924	−	0.106464i
$512$	−9824.42	+	3192.15i	−0.848012	+	0.275536i
$513$	−5302.92	+	1723.02i	−0.456393	+	0.148291i
$514$	−291.315	+	896.576i	−0.0249988	+	0.0769383i
$515$	5159.68	−	6994.78i	0.441481	−	0.598499i
$516$	45.2825	+	139.365i	0.00386328	+	0.0118900i
$517$	8111.35	+	11164.3i	0.690013	+	0.949722i
$518$		−	6439.45i		−	0.546203i
$519$	−2453.56	+	1782.61i	−0.207513	+	0.150767i
$520$	816.393	+	602.210i	0.0688485	+	0.0507859i
$521$	−1059.37	−	769.675i	−0.0890819	−	0.0647218i	0.542353	−	0.840151i	$-0.317534\pi$
$521$	−1059.37	−	769.675i	−0.0890819	−	0.0647218i	−0.631435	+	0.775429i	$0.717534\pi$
$522$	9231.06	−	12705.5i	0.774009	−	1.06533i
$523$	3843.99	+	1248.99i	0.321388	+	0.104425i	0.465268	−	0.885170i	$-0.345958\pi$
$523$	3843.99	+	1248.99i	0.321388	+	0.104425i	−0.143880	+	0.989595i	$0.545958\pi$
$524$	12457.4			1.03856
$525$	1814.69	+	1358.97i	0.150856	+	0.112972i
$526$	−16464.1			−1.36477
$527$	−5940.57	−	1930.21i	−0.491034	−	0.159547i
$528$	−3477.88	+	4786.89i	−0.286658	+	0.394551i
$529$	21261.6	+	15447.4i	1.74748	+	1.26962i
$530$	−20046.8	+	14344.6i	−1.64298	+	1.17564i
$531$	7201.39	−	5232.12i	0.588538	−	0.427598i
$532$		−	2518.19i		−	0.205220i
$533$	−2679.19	−	3687.59i	−0.217727	−	0.299676i
$534$	35.1386	+	108.146i	0.00284756	+	0.00876389i
$535$	−18.3334	+	2535.70i	−0.00148154	+	0.204912i
$536$	1232.10	−	3792.02i	0.0992886	−	0.305579i
$537$	−7369.78	+	2394.59i	−0.592233	+	0.192428i
$538$	−9505.92	+	3088.66i	−0.761765	+	0.247512i
$539$	3001.23	−	9236.85i	0.239837	−	0.738143i
$540$	−3624.21	−	5064.90i	−0.288817	−	0.403627i
$541$	−3338.01	−	10273.3i	−0.265272	−	0.816424i	−0.991631	−	0.129108i	$-0.958789\pi$
$541$	−3338.01	−	10273.3i	−0.265272	−	0.816424i	0.726358	−	0.687316i	$-0.241211\pi$
$542$	4398.11	+	6053.47i	0.348551	+	0.479740i
$543$			1137.45i			0.0898947i
$544$	4248.02	−	3086.37i	0.334802	−	0.243248i
$545$	−64.9276	−	204.855i	−0.00510311	−	0.0161009i
$546$	507.963	+	369.057i	0.0398147	+	0.0289271i
$547$	−13706.3	+	18865.1i	−1.07137	+	1.47461i	−0.202687	+	0.979244i	$0.564967\pi$
$547$	−13706.3	+	18865.1i	−1.07137	+	1.47461i	−0.868682	+	0.495369i	$0.835033\pi$
$548$	−10779.7	−	3502.52i	−0.840299	−	0.273030i
$549$	−9321.55			−0.724652
$550$	9954.53	−	13292.7i	0.771750	−	1.03055i
$551$	10206.6			0.789139
$552$	−3729.20	−	1211.69i	−0.287546	−	0.0934293i
$553$	189.266	−	260.502i	0.0145541	−	0.0200320i
$554$	−11105.3	−	8068.47i	−0.851658	−	0.618766i
$555$	1491.51	−	4479.94i	0.114074	−	0.342636i
$556$	−2623.89	+	1906.36i	−0.200140	+	0.145410i
$557$			4549.20i			0.346061i	0.984916	+	0.173030i	$0.0553559\pi$
$557$			4549.20i			0.346061i	−0.984916	+	0.173030i	$0.944644\pi$
$558$	−12104.6	−	16660.5i	−0.918330	−	1.26397i
$559$	38.1984	+	117.563i	0.00289020	+	0.00889512i
$560$	−7237.57	+	2293.91i	−0.546148	+	0.173099i
$561$	588.286	−	1810.56i	0.0442736	−	0.136260i
$562$	−26572.5	+	8633.92i	−1.99447	+	0.648043i
$563$	−3108.93	+	1010.15i	−0.232728	+	0.0756180i	−0.423059	−	0.906102i	$-0.639044\pi$
$563$	−3108.93	+	1010.15i	−0.232728	+	0.0756180i	0.190331	+	0.981720i	$0.439044\pi$
$564$	−1317.26	+	4054.11i	−0.0983453	+	0.302676i
$565$	−14140.9	+	4481.90i	−1.05295	+	0.333726i
$566$	−930.070	−	2862.46i	−0.0690703	−	0.212576i
$567$	−2021.44	−	2782.27i	−0.149722	−	0.206074i
$568$		−	3070.47i		−	0.226821i
$569$	−8636.74	+	6274.96i	−0.636329	+	0.462320i	−0.858587	−	0.512668i	$-0.828657\pi$
$569$	−8636.74	+	6274.96i	−0.636329	+	0.462320i	0.222258	+	0.974988i	$0.428657\pi$
$570$	1450.75	−	4357.49i	0.106605	−	0.320202i
$571$	2708.93	+	1968.15i	0.198538	+	0.144246i	0.682613	−	0.730781i	$-0.260844\pi$
$571$	2708.93	+	1968.15i	0.198538	+	0.144246i	−0.484075	+	0.875027i	$0.660844\pi$
$572$	1086.88	−	1495.96i	0.0794485	−	0.109351i
$573$	1803.33	+	585.939i	0.131475	+	0.0427189i
$574$	15317.2			1.11381
$575$	23198.6	+	7910.31i	1.68252	+	0.573709i
$576$	3160.71			0.228639
$577$	−6493.51	−	2109.87i	−0.468507	−	0.152227i	0.0652432	−	0.997869i	$-0.479218\pi$
$577$	−6493.51	−	2109.87i	−0.468507	−	0.152227i	−0.533750	+	0.845642i	$0.679218\pi$
$578$	9205.24	−	12669.9i	0.662435	−	0.911764i
$579$	−2097.94	−	1524.25i	−0.150583	−	0.109405i
$580$	3444.44	+	10867.6i	0.246591	+	0.778025i
$581$	−7531.39	+	5471.88i	−0.537788	+	0.390726i
$582$		−	9209.03i		−	0.655888i
$583$	−12869.0	−	17712.6i	−0.914199	−	1.25829i
$584$	440.574	+	1355.95i	0.0312176	+	0.0960780i
$585$	−1394.66	−	1949.06i	−0.0985677	−	0.137750i
$586$	−5684.93	+	17496.4i	−0.400755	+	1.23340i
$587$	−3384.37	+	1099.65i	−0.237969	+	0.0773208i	−0.425574	−	0.904924i	$-0.639928\pi$
$587$	−3384.37	+	1099.65i	−0.237969	+	0.0773208i	0.187605	+	0.982245i	$0.439928\pi$
$588$	2853.24	−	927.075i	0.200112	−	0.0650203i
$589$	4135.82	−	12728.7i	0.289327	−	0.890456i
$590$	−116.200	+	16071.7i	−0.00810826	+	1.12146i
$591$	−414.514	−	1275.74i	−0.0288508	−	0.0887937i
$592$	9294.35	+	12792.6i	0.645263	+	0.888128i
$593$			5074.20i			0.351387i	0.984445	+	0.175694i	$0.0562168\pi$
$593$			5074.20i			0.351387i	−0.984445	+	0.175694i	$0.943783\pi$
$594$	11131.0	−	8087.13i	0.768872	−	0.558618i
$595$	1986.60	−	1421.52i	0.136878	−	0.0979439i
$596$	11281.5	+	8196.46i	0.775347	+	0.563323i
$597$	−1431.68	+	1970.54i	−0.0981486	+	0.135090i
$598$	6455.80	+	2097.62i	0.441467	+	0.143441i
$599$	728.482			0.0496911			0.0248455	−	0.999691i	$-0.492091\pi$
$599$	728.482			0.0496911			0.0248455	+	0.999691i	$0.492091\pi$
$600$	−2499.42	−	36.1440i	−0.170064	−	0.00245929i
$601$	7319.10			0.496759			0.248380	−	0.968663i	$-0.420102\pi$
$601$	7319.10			0.496759			0.248380	+	0.968663i	$0.420102\pi$
$602$	−395.061	−	128.363i	−0.0267466	−	0.00869050i
$603$	−5536.65	+	7620.54i	−0.373913	+	0.514648i
$604$	2171.93	+	1578.00i	0.146315	+	0.106304i
$605$	−105.516	−	77.8335i	−0.00709063	−	0.00523039i
$606$	−6635.47	+	4820.95i	−0.444798	+	0.323165i
$607$		−	26884.7i		−	1.79772i	−0.438233	−	0.898861i	$-0.644396\pi$
$607$		−	26884.7i		−	1.79772i	0.438233	−	0.898861i	$-0.355604\pi$
$608$	6613.10	+	9102.15i	0.441113	+	0.607140i
$609$	−1062.47	−	3269.96i	−0.0706956	−	0.217579i
$610$	9991.00	−	13544.4i	0.663154	−	0.899012i
$611$	−1111.19	+	3419.88i	−0.0735741	+	0.226438i
$612$	−2911.44	+	945.986i	−0.192301	+	0.0624824i
$613$	19017.8	−	6179.25i	1.25305	−	0.407141i	0.394038	−	0.919094i	$-0.371078\pi$
$613$	19017.8	−	6179.25i	1.25305	−	0.407141i	0.859013	+	0.511953i	$0.171078\pi$
$614$	2122.89	−	6533.58i	0.139532	−	0.429436i
$615$	10656.2	+	3547.79i	0.698698	+	0.232619i
$616$	−935.661	−	2879.67i	−0.0611994	−	0.188352i
$617$	11777.8	+	16210.8i	0.768487	+	1.05773i	0.996460	+	0.0840644i	$0.0267901\pi$
$617$	11777.8	+	16210.8i	0.768487	+	1.05773i	−0.227973	+	0.973667i	$0.573210\pi$
$618$			5931.39i			0.386077i
$619$	6376.94	−	4633.12i	0.414073	−	0.300841i	−0.361176	−	0.932498i	$-0.617625\pi$
$619$	6376.94	−	4633.12i	0.414073	−	0.300841i	0.775248	+	0.631656i	$0.217625\pi$
$620$	14948.9	+	108.082i	0.968324	+	0.00700108i
$621$	16428.2	+	11935.8i	1.06158	+	0.771285i
$622$	−3780.35	+	5203.21i	−0.243695	+	0.335417i
$623$	−123.252	−	40.0469i	−0.00792612	−	0.00257535i
$624$	−1541.79			−0.0989120
$625$	15618.5	+	451.810i	0.999582	+	0.0289159i
$626$	2591.26			0.165444
$627$	3879.45	+	1260.51i	0.247098	+	0.0802870i
$628$	2211.72	−	3044.18i	0.140537	−	0.193433i
$629$	−4115.94	−	2990.40i	−0.260911	−	0.189563i
$630$	8053.55	+	58.2280i	0.509303	+	0.00368232i
$631$	−16963.8	+	12324.9i	−1.07023	+	0.777570i	−0.975954	−	0.217976i	$-0.930055\pi$
$631$	−16963.8	+	12324.9i	−1.07023	+	0.777570i	−0.0942793	+	0.995546i	$0.530055\pi$
$632$			355.027i			0.0223453i
$633$	−4915.37	−	6765.43i	−0.308639	−	0.424805i
$634$	−10354.3	−	31867.2i	−0.648614	−	1.99623i
$635$	−12071.6	−	4019.01i	−0.754403	−	0.251165i
$636$	2089.88	−	6432.00i	0.130298	−	0.401015i
$637$	2406.88	−	782.042i	0.149708	−	0.0486430i
$638$	−23952.7	+	7782.70i	−1.48636	+	0.482947i
$639$	−2241.57	+	6898.83i	−0.138772	+	0.427095i
$640$	7707.31	−	10448.5i	0.476028	−	0.645333i
$641$	2348.68	+	7228.51i	0.144723	+	0.445412i	0.996975	−	0.0777194i	$-0.0247638\pi$
$641$	2348.68	+	7228.51i	0.144723	+	0.445412i	−0.852252	+	0.523131i	$0.824764\pi$
$642$	−1017.12	−	1399.94i	−0.0625270	−	0.0860610i
$643$			14619.2i			0.896616i	0.893879	+	0.448308i	$0.147973\pi$
$643$			14619.2i			0.896616i	−0.893879	+	0.448308i	$0.852027\pi$
$644$	−7419.42	+	5390.53i	−0.453985	+	0.329839i
$645$	−245.113	−	180.807i	−0.0149633	−	0.0110376i
$646$	−4003.44	−	2908.67i	−0.243828	−	0.177152i
$647$	9416.76	−	12961.1i	0.572196	−	0.787561i	−0.420616	−	0.907239i	$-0.638186\pi$
$647$	9416.76	−	12961.1i	0.572196	−	0.787561i	0.992813	+	0.119678i	$0.0381862\pi$
$648$	3606.24	+	1171.74i	0.218621	+	0.0710344i
$649$	−14274.9			−0.863390
$650$	4326.86	+	62.5705i	0.261097	+	0.00377572i
$651$	−4508.53			−0.271433
$652$	−1143.86	−	371.661i	−0.0687069	−	0.0223242i
$653$	−5353.52	+	7368.49i	−0.320826	+	0.441579i	−0.938719	−	0.344683i	$-0.887986\pi$
$653$	−5353.52	+	7368.49i	−0.320826	+	0.441579i	0.617893	+	0.786262i	$0.287986\pi$
$654$	118.640	+	86.1969i	0.00709356	+	0.00515377i
$655$	−21057.5	+	15067.8i	−1.25616	+	0.898851i
$656$	−30429.0	+	22108.0i	−1.81106	+	1.31581i
$657$		−	3368.22i		−	0.200011i
$658$	−7102.60	−	9775.89i	−0.420803	−	0.579185i
$659$	5049.09	+	15539.5i	0.298459	+	0.918563i	0.982038	+	0.188686i	$0.0604227\pi$
$659$	5049.09	+	15539.5i	0.298459	+	0.918563i	−0.683578	+	0.729877i	$0.739577\pi$
$660$	−32.9411	+	4556.10i	−0.00194277	+	0.268706i
$661$	−1787.15	+	5500.28i	−0.105162	+	0.323655i	−0.989768	−	0.142683i	$-0.954427\pi$
$661$	−1787.15	+	5500.28i	−0.105162	+	0.323655i	0.884606	+	0.466338i	$0.154427\pi$
$662$	58.2317	−	18.9206i	0.00341879	−	0.00111083i
$663$	471.784	−	153.292i	0.0276358	−	0.00897943i
$664$	3171.81	−	9761.84i	0.185377	−	0.570531i
$665$	3045.86	+	4256.65i	0.177614	+	0.248219i
$666$	−5183.26	−	15952.4i	−0.301573	−	0.928145i
$667$	−21848.6	−	30072.0i	−1.26834	−	1.74572i
$668$		−	11090.3i		−	0.642359i
$669$	−4874.00	+	3541.17i	−0.281674	+	0.204648i
$670$	−5138.54	−	16212.7i	−0.296297	−	0.934854i
$671$	12093.7	+	8786.61i	0.695788	+	0.505519i
$672$	2227.72	−	3066.19i	0.127881	−	0.176013i
$673$	−7876.10	−	2559.10i	−0.451116	−	0.146577i	0.0746423	−	0.997210i	$-0.476218\pi$
$673$	−7876.10	−	2559.10i	−0.451116	−	0.146577i	−0.525759	+	0.850634i	$0.676218\pi$
$674$	6839.57			0.390876
$675$	12252.5	+	4177.88i	0.698663	+	0.238232i
$676$	−11335.7			−0.644953
$677$	−10271.6	−	3337.44i	−0.583116	−	0.189466i	0.00257998	−	0.999997i	$-0.499179\pi$
$677$	−10271.6	−	3337.44i	−0.583116	−	0.189466i	−0.585696	+	0.810531i	$0.699179\pi$
$678$	5950.11	−	8189.62i	0.337039	−	0.463895i
$679$	8490.93	+	6169.03i	0.479900	+	0.348668i
$680$	−850.796	+	2555.47i	−0.0479802	+	0.144114i
$681$	4955.05	−	3600.05i	0.278822	−	0.202576i
$682$			33025.3i			1.85426i
$683$	7306.97	+	10057.2i	0.409361	+	0.563437i	0.963062	−	0.269278i	$-0.0867852\pi$
$683$	7306.97	+	10057.2i	0.409361	+	0.563437i	−0.553702	+	0.832715i	$0.686785\pi$
$684$	−2026.95	−	6238.30i	−0.113307	−	0.348724i
$685$	22458.0	−	7117.95i	1.25267	−	0.397026i
$686$	−5999.06	+	18463.2i	−0.333885	+	1.02759i
$687$	4682.89	−	1521.56i	0.260063	−	0.0844996i
$688$	970.097	−	315.204i	0.0537567	−	0.0174666i
$689$	1762.94	−	5425.77i	0.0974784	−	0.300008i
$690$	−15944.1	+	5053.42i	−0.879686	+	0.278812i
$691$	−8687.68	−	26737.9i	−0.478285	−	1.47201i	−0.841475	−	0.540295i	$-0.818313\pi$
$691$	−8687.68	−	26737.9i	−0.478285	−	1.47201i	0.363190	−	0.931715i	$-0.381687\pi$
$692$	−4596.93	−	6327.13i	−0.252528	−	0.347574i
$693$			7153.20i			0.392103i
$694$	−13914.2	+	10109.2i	−0.761058	+	0.552941i
$695$	2129.49	−	6396.16i	0.116224	−	0.349094i
$696$	3066.91	+	2228.24i	0.167027	+	0.121352i
$697$	7113.11	−	9790.36i	0.386554	−	0.532046i
$698$	35406.9	+	11504.4i	1.92001	+	0.623850i
$699$	−174.864			−0.00946202
$700$	−3504.45	+	4679.64i	−0.189222	+	0.252677i
$701$	23069.6			1.24298			0.621488	−	0.783423i	$-0.286528\pi$
$701$	23069.6			1.24298			0.621488	+	0.783423i	$0.286528\pi$
$702$	3409.67	+	1107.87i	0.183319	+	0.0595638i
$703$	6407.48	−	8819.14i	0.343759	−	0.473144i
$704$	−4100.69	−	2979.33i	−0.219532	−	0.159500i
$705$	−2676.99	−	8446.22i	−0.143009	−	0.451210i
$706$	22238.9	−	16157.5i	1.18552	−	0.861327i
$707$		−	9347.56i		−	0.497243i
$708$	−2591.84	−	3567.36i	−0.137581	−	0.189364i
$709$	4051.16	+	12468.2i	0.214590	+	0.660441i	0.999182	+	0.0404290i	$0.0128725\pi$
$709$	4051.16	+	12468.2i	0.214590	+	0.660441i	−0.784592	+	0.620012i	$0.787128\pi$
$710$	−7621.61	−	10651.3i	−0.402865	−	0.563011i
$711$	259.184	−	797.686i	0.0136711	−	0.0420753i
$712$	135.894	−	44.1546i	0.00715287	−	0.00232411i
$713$	−46356.4	+	15062.1i	−2.43487	+	0.791137i
$714$	−515.125	+	1585.39i	−0.0270001	+	0.0830978i
$715$	−27.7877	+	3843.33i	−0.00145343	+	0.201025i
$716$	−6175.06	−	19004.9i	−0.322308	−	0.991963i
$717$	6863.39	+	9446.65i	0.357487	+	0.492039i
$718$			18046.5i			0.938007i
$719$	13375.0	−	9717.48i	0.693744	−	0.504035i	−0.184145	−	0.982899i	$-0.558952\pi$
$719$	13375.0	−	9717.48i	0.693744	−	0.504035i	0.877889	+	0.478865i	$0.158952\pi$
$720$	−16083.2	+	11508.4i	−0.832479	+	0.595683i
$721$	−5468.88	−	3973.37i	−0.282485	−	0.205237i
$722$	−8514.20	+	11718.8i	−0.438872	+	0.604056i
$723$	−8531.46	−	2772.04i	−0.438850	−	0.142591i
$724$	−2933.22			−0.150569
$725$	−18967.3	−	14204.1i	−0.971623	−	0.727621i
$726$	89.4748			0.00457400
$727$	4673.55	+	1518.53i	0.238421	+	0.0774678i	0.425790	−	0.904822i	$-0.359996\pi$
$727$	4673.55	+	1518.53i	0.238421	+	0.0774678i	−0.187369	+	0.982290i	$0.559996\pi$
$728$	463.751	−	638.298i	0.0236095	−	0.0324958i
$729$	−2528.69	−	1837.20i	−0.128471	−	0.0933395i
$730$	4894.11	+	3610.13i	0.248136	+	0.183037i
$731$	−265.508	+	192.903i	−0.0134339	+	0.00976027i
$732$			4617.62i			0.233159i
$733$	4433.98	+	6102.85i	0.223428	+	0.307523i	0.905985	−	0.423310i	$-0.139132\pi$
$733$	4433.98	+	6102.85i	0.223428	+	0.307523i	−0.682557	+	0.730833i	$0.739132\pi$
$734$	13118.1	+	40373.4i	0.659670	+	2.03026i
$735$	−3701.68	+	5018.22i	−0.185767	+	0.251837i
$736$	12661.7	−	38968.8i	0.634127	−	1.95164i
$737$	14366.5	−	4667.94i	0.718040	−	0.233305i
$738$	37945.2	−	12329.1i	1.89266	−	0.614962i
$739$	−9160.93	+	28194.5i	−0.456009	+	1.40345i	0.413938	+	0.910305i	$0.364153\pi$
$739$	−9160.93	+	28194.5i	−0.456009	+	1.40345i	−0.869947	+	0.493145i	$0.835847\pi$
$740$	11552.7	+	3846.25i	0.573898	+	0.191069i
$741$	328.455	+	1010.88i	0.0162836	+	0.0501156i
$742$	11268.5	+	15509.8i	0.557522	+	0.767363i
$743$		−	27303.1i		−	1.34812i	−0.738675	−	0.674061i	$-0.764548\pi$
$743$		−	27303.1i		−	1.34812i	0.738675	−	0.674061i	$-0.235452\pi$
$744$	4021.61	−	2921.87i	0.198171	−	0.143980i
$745$	−28983.8	−	209.556i	−1.42535	−	0.0103054i
$746$	−13403.3	−	9738.09i	−0.657816	−	0.477931i
$747$	−14253.1	+	19617.7i	−0.698115	+	0.960873i
$748$	4669.00	+	1517.05i	0.228229	+	0.0741561i
$749$	1972.13			0.0962083
$750$	−8760.09	+	6078.74i	−0.426498	+	0.295952i
$751$	20268.4			0.984825			0.492412	−	0.870362i	$-0.336115\pi$
$751$	20268.4			0.984825			0.492412	+	0.870362i	$0.336115\pi$
$752$	28220.0	+	9169.22i	1.36845	+	0.444637i
$753$	5128.14	−	7058.28i	0.248180	−	0.341591i
$754$	−5309.28	−	3857.42i	−0.256436	−	0.186311i
$755$	−5580.01	−	40.3440i	−0.268976	−	0.00194473i
$756$	−3918.62	+	2847.04i	−0.188517	+	0.136965i
$757$		−	7255.23i		−	0.348343i	−0.984715	−	0.174172i	$-0.944275\pi$
$757$		−	7255.23i		−	0.348343i	0.984715	−	0.174172i	$-0.0557247\pi$
$758$	15743.6	+	21669.3i	0.754400	+	1.03834i
$759$	−4590.62	−	14128.5i	−0.219537	−	0.675666i
$760$	−5475.55	−	1822.99i	−0.261341	−	0.0870087i
$761$	6945.76	−	21376.9i	0.330859	−	1.01828i	−0.637867	−	0.770147i	$-0.720183\pi$
$761$	6945.76	−	21376.9i	0.330859	−	1.01828i	0.968726	−	0.248133i	$-0.0798169\pi$
$762$	8257.31	−	2682.96i	0.392560	−	0.127550i
$763$	−158.951	+	51.6463i	−0.00754183	+	0.00245049i
$764$	−1510.99	+	4650.36i	−0.0715522	+	0.220215i
$765$	3777.19	−	5120.59i	0.178516	−	0.242007i
$766$	9549.82	+	29391.3i	0.450456	+	1.38636i
$767$	−2186.36	−	3009.27i	−0.102927	−	0.141667i
$768$			11188.7i			0.525701i
$769$	−122.347	+	88.8907i	−0.00573727	+	0.00416837i	−0.590650	−	0.806928i	$-0.701129\pi$
$769$	−122.347	+	88.8907i	−0.00573727	+	0.00416837i	0.584913	+	0.811096i	$0.301129\pi$
$770$	−10393.8	−	7666.93i	−0.486448	−	0.358827i
$771$	434.924	+	315.991i	0.0203157	+	0.0147602i
$772$	3930.66	−	5410.09i	0.183248	−	0.252220i
$773$	−17286.8	−	5616.83i	−0.804351	−	0.261349i	−0.122148	−	0.992512i	$-0.538978\pi$
$773$	−17286.8	−	5616.83i	−0.804351	−	0.261349i	−0.682203	+	0.731162i	$0.738978\pi$
$774$	−1082.00			−0.0502479
$775$	−25399.8	+	17898.6i	−1.17727	+	0.829598i
$776$	−11571.9			−0.535319
$777$	−3492.45	−	1134.77i	−0.161250	−	0.0523932i
$778$	10444.0	−	14375.0i	0.481281	−	0.662426i
$779$	20977.6	+	15241.1i	0.964828	+	0.700989i
$780$	−965.509	+	690.873i	−0.0443215	+	0.0317144i
$781$	9411.13	−	6837.59i	0.431187	−	0.313275i
$782$			18021.9i			0.824118i
$783$	−11539.5	−	15882.7i	−0.526676	−	0.724908i
$784$	−6453.21	−	19860.9i	−0.293969	−	0.904743i
$785$	−56.5462	+	7820.95i	−0.00257098	+	0.355594i
$786$	5460.21	−	16804.8i	0.247785	−	0.762605i
$787$	11893.1	−	3864.31i	0.538683	−	0.175029i	−0.0270244	−	0.999635i	$-0.508603\pi$
$787$	11893.1	−	3864.31i	0.538683	−	0.175029i	0.565707	+	0.824606i	$0.308603\pi$
$788$	3289.83	−	1068.93i	0.148725	−	0.0483238i
$789$	−2901.32	+	8929.34i	−0.130912	+	0.402906i
$790$	881.258	+	1231.57i	0.0396883	+	0.0554651i
$791$	3565.11	+	10972.3i	0.160254	+	0.493210i
$792$	−4635.82	−	6380.66i	−0.207988	−	0.286271i
$793$			3895.23i			0.174431i
$794$	−4589.45	+	3334.43i	−0.205131	+	0.149036i
$795$	4247.14	+	13400.2i	0.189472	+	0.597808i
$796$	−5081.54	−	3691.95i	−0.226269	−	0.164394i
$797$	21825.3	−	30040.0i	0.970003	−	1.33509i	0.0279569	−	0.999609i	$-0.491100\pi$
$797$	21825.3	−	30040.0i	0.970003	−	1.33509i	0.942046	−	0.335485i	$-0.108900\pi$
$798$	−3396.99	−	1103.75i	−0.150692	−	0.0489628i
$799$	−9546.86			−0.422708
$800$	377.691	−	26118.0i	0.0166918	−	1.15426i
$801$	−337.566			−0.0148905
$802$	−13589.6	−	4415.53i	−0.598337	−	0.194411i
$803$	−3174.93	+	4369.92i	−0.139528	+	0.192044i
$804$	3774.99	+	2742.69i	0.165589	+	0.120308i
$805$	6021.44	−	18086.1i	0.263637	−	0.791864i
$806$	−6962.00	+	5058.19i	−0.304251	+	0.221051i
$807$			5699.84i			0.248629i
$808$	6057.93	+	8338.03i	0.263759	+	0.363033i
$809$	−3432.02	−	10562.7i	−0.149151	−	0.459040i	0.848370	−	0.529404i	$-0.177584\pi$
$809$	−3432.02	−	10562.7i	−0.149151	−	0.459040i	−0.997521	+	0.0703630i	$0.977584\pi$
$810$	15418.4	−	4886.80i	0.668825	−	0.211981i
$811$	−5574.58	+	17156.8i	−0.241369	+	0.742856i	0.754844	+	0.655904i	$0.227713\pi$
$811$	−5574.58	+	17156.8i	−0.241369	+	0.742856i	−0.996213	+	0.0869518i	$0.972287\pi$
$812$	8432.44	−	2739.87i	0.364434	−	0.118412i
$813$	4058.15	−	1318.57i	0.175062	−	0.0568812i
$814$	−8312.24	+	25582.4i	−0.357916	+	1.10155i
$815$	2383.07	−	755.304i	0.102424	−	0.0324627i
$816$	−1264.92	−	3893.04i	−0.0542662	−	0.167014i
$817$	−413.329	−	568.898i	−0.0176996	−	0.0243614i
$818$			699.318i			0.0298913i
$819$	−1507.95	+	1095.59i	−0.0643372	+	0.0467437i
$820$	−9148.88	+	27479.7i	−0.389625	+	1.17029i
$821$	−16590.6	−	12053.7i	−0.705255	−	0.512398i	0.176384	−	0.984321i	$-0.443560\pi$
$821$	−16590.6	−	12053.7i	−0.705255	−	0.512398i	−0.881640	+	0.471923i	$0.843560\pi$
$822$	−9449.68	+	13006.4i	−0.400968	+	0.551885i
$823$	19780.8	+	6427.18i	0.837808	+	0.272220i	0.696331	−	0.717721i	$-0.254815\pi$
$823$	19780.8	+	6427.18i	0.837808	+	0.272220i	0.141477	+	0.989942i	$0.454815\pi$
$824$	7453.29			0.315107
$825$	−5455.13	−	7741.31i	−0.230210	−	0.326688i
$826$	12499.7			0.526536
$827$	−14926.8	−	4850.01i	−0.627637	−	0.203932i	−0.0221087	−	0.999756i	$-0.507038\pi$
$827$	−14926.8	−	4850.01i	−0.627637	−	0.203932i	−0.605528	+	0.795824i	$0.707038\pi$
$828$	−14041.2	+	19326.0i	−0.589329	+	0.811141i
$829$	−22986.9	−	16701.0i	−0.963050	−	0.699697i	−0.00919265	−	0.999958i	$-0.502926\pi$
$829$	−22986.9	−	16701.0i	−0.963050	−	0.699697i	−0.953857	+	0.300261i	$0.902926\pi$
$830$	−13228.2	−	41736.6i	−0.553202	−	1.74542i
$831$	−6332.94	+	4601.15i	−0.264365	+	0.192072i
$832$		−	1320.78i		−	0.0550357i
$833$	3949.32	+	5435.77i	0.164269	+	0.226096i
$834$	1421.58	+	4375.16i	0.0590229	+	0.181654i
$835$	13414.2	+	18746.6i	0.555949	+	0.776950i
$836$	−3250.55	+	10004.2i	−0.134477	+	0.413877i
$837$	−24483.4	+	7955.15i	−1.01108	+	0.328519i
$838$	−349.045	+	113.412i	−0.0143885	+	0.00467511i
$839$	4628.06	−	14243.7i	0.190439	−	0.586111i	−0.809561	−	0.587036i	$-0.800295\pi$
$839$	4628.06	−	14243.7i	0.190439	−	0.586111i	1.00000		0.000925439i	$0.000294577\pi$
$840$	−14.0554	+	1944.01i	−0.000577330	+	0.0798508i
$841$	3568.47	+	10982.6i	0.146315	+	0.450310i
$842$	−31102.1	−	42808.4i	−1.27298	−	1.75211i
$843$			15933.1i			0.650968i
$844$	17446.4	−	12675.6i	0.711528	−	0.516956i
$845$	19161.5	−	13711.0i	0.780088	−	0.558195i
$846$	−25464.1	−	18500.7i	−1.03484	−	0.751854i
$847$	−59.9381	+	82.4978i	−0.00243152	+	0.00334670i
$848$	−44772.0	−	14547.3i	−1.81306	−	0.589100i
$849$	−1716.36			−0.0693820
$850$	3391.87	+	10976.7i	0.136871	+	0.442938i
$851$	−39700.2			−1.59918
$852$	3417.48	+	1110.41i	0.137419	+	0.0446501i
$853$	−25863.4	+	35597.9i	−1.03815	+	1.42890i	−0.139509	+	0.990221i	$0.544552\pi$
$853$	−25863.4	+	35597.9i	−1.03815	+	1.42890i	−0.898645	+	0.438676i	$0.855448\pi$
$854$	−10589.7	−	7693.88i	−0.424324	−	0.308290i
$855$	10971.8	+	8093.31i	0.438862	+	0.323726i
$856$	−1759.14	+	1278.09i	−0.0702409	+	0.0510330i
$857$			11649.7i			0.464347i	0.972674	+	0.232174i	$0.0745838\pi$
$857$			11649.7i			0.464347i	−0.972674	+	0.232174i	$0.925416\pi$
$858$	−1541.63	−	2121.87i	−0.0613407	−	0.0844283i
$859$	4444.79	+	13679.7i	0.176548	+	0.543357i	0.999701	−	0.0244618i	$-0.00778722\pi$
$859$	4444.79	+	13679.7i	0.176548	+	0.543357i	−0.823153	+	0.567819i	$0.807787\pi$
$860$	466.257	−	632.086i	0.0184875	−	0.0250627i
$861$	2699.21	−	8307.31i	0.106839	−	0.328818i
$862$	39882.8	−	12958.7i	1.57589	−	0.512037i
$863$	2550.07	−	828.568i	0.100586	−	0.0326823i	−0.258292	−	0.966067i	$-0.583160\pi$
$863$	2550.07	−	828.568i	0.100586	−	0.0326823i	0.358877	+	0.933385i	$0.383160\pi$
$864$	6687.37	−	20581.6i	0.263321	−	0.810418i
$865$	15423.4	+	5134.96i	0.606258	+	0.201843i
$866$	19675.8	+	60555.9i	0.772068	+	2.37618i
$867$	−5249.41	−	7225.19i	−0.205628	−	0.283022i
$868$		−	11626.4i		−	0.454638i
$869$	−1088.17	+	790.604i	−0.0424784	+	0.0308624i
$870$	16170.0	+	116.911i	0.630132	+	0.00455591i
$871$	3184.42	+	2313.62i	0.123881	+	0.0900046i
$872$	108.314	−	149.081i	0.00420638	−	0.00578959i
$873$	26000.2	+	8447.96i	1.00799	+	0.327515i
$874$	−38615.1			−1.49448
$875$	263.554	−	12149.1i	0.0101826	−	0.469387i
$876$	−1668.52			−0.0643539
$877$	5950.39	+	1933.40i	0.229111	+	0.0744427i	0.421323	−	0.906911i	$-0.361566\pi$
$877$	5950.39	+	1933.40i	0.229111	+	0.0744427i	−0.192212	+	0.981354i	$0.561566\pi$
$878$	25081.1	−	34521.1i	0.964061	−	1.32692i
$879$	8487.41	+	6166.47i	0.325681	+	0.236621i
$880$	31714.2	+	229.297i	1.21487	+	0.00878363i
$881$	22671.6	−	16471.9i	0.866998	−	0.629911i	−0.0627817	−	0.998027i	$-0.519997\pi$
$881$	22671.6	−	16471.9i	0.866998	−	0.629911i	0.929780	+	0.368116i	$0.119997\pi$
$882$			22152.0i			0.845689i
$883$	11482.2	+	15803.8i	0.437606	+	0.602312i	0.969678	−	0.244386i	$-0.0785866\pi$
$883$	11482.2	+	15803.8i	0.437606	+	0.602312i	−0.532072	+	0.846699i	$0.678587\pi$
$884$	395.302	+	1216.62i	0.0150401	+	0.0462887i
$885$	8696.03	+	2895.19i	0.330298	+	0.109967i
$886$	−5017.23	+	15441.5i	−0.190245	+	0.585515i
$887$	47458.4	−	15420.2i	1.79650	−	0.583719i	0.796716	−	0.604354i	$-0.206569\pi$
$887$	47458.4	−	15420.2i	1.79650	−	0.583719i	0.999787	+	0.0206354i	$0.00656891\pi$
$888$	3850.69	−	1251.16i	0.145519	−	0.0472819i
$889$	−3057.73	+	9410.71i	−0.115358	+	0.355034i
$890$	361.809	−	490.490i	0.0136268	−	0.0184733i
$891$	4439.26	+	13662.6i	0.166914	+	0.513709i
$892$	−9131.82	−	12568.9i	−0.342776	−	0.471790i
$893$		−	20455.9i		−	0.766551i
$894$	16001.7	−	11625.9i	0.598631	−	0.434931i
$895$	33425.4	+	24656.1i	1.24836	+	0.920853i
$896$	−8169.18	−	5935.25i	−0.304590	−	0.221298i
$897$	2275.29	−	3131.67i	0.0846932	−	0.116570i
$898$	−40068.5	−	13019.0i	−1.48898	−	0.483798i
$899$	47123.5			1.74823
$900$	−4914.81	+	14413.7i	−0.182030	+	0.533839i
$901$	15146.5			0.560046
$902$	−60851.6	−	19771.9i	−2.24627	−	0.729858i
$903$	−139.236	+	191.642i	−0.00513121	+	0.00706250i
$904$	−10290.9	−	7476.81i	−0.378619	−	0.275083i
$905$	4958.21	−	3547.86i	0.182117	−	0.130315i
$906$	3080.67	−	2238.24i	0.112967	−	0.0820756i
$907$			49849.8i			1.82496i	0.409126	+	0.912478i	$0.365834\pi$
$907$			49849.8i			1.82496i	−0.409126	+	0.912478i	$0.634166\pi$
$908$	9283.67	+	12777.9i	0.339305	+	0.467014i
$909$	−7524.06	−	23156.7i	−0.274540	−	0.844949i
$910$	24.3319	−	3365.37i	0.000886369	−	0.122594i
$911$	−5822.92	+	17921.1i	−0.211769	+	0.651759i	0.787598	+	0.616190i	$0.211324\pi$
$911$	−5822.92	+	17921.1i	−0.211769	+	0.651759i	−0.999367	+	0.0355694i	$0.988676\pi$
$912$	8341.54	−	2710.33i	0.302868	−	0.0984079i
$913$	36983.7	−	12016.7i	1.34062	−	0.435593i
$914$	14841.9	−	45678.8i	0.537120	−	1.65309i
$915$	−5585.22	−	7805.45i	−0.201794	−	0.282011i
$916$	3923.74	+	12076.0i	0.141533	+	0.435593i
$917$	11836.7	+	16291.8i	0.426261	+	0.586698i
$918$			9518.36i			0.342214i
$919$	−7094.09	+	5154.16i	−0.254638	+	0.185006i	−0.707780	−	0.706433i	$-0.750303\pi$
$919$	−7094.09	+	5154.16i	−0.254638	+	0.185006i	0.453142	+	0.891439i	$0.350303\pi$
$920$	6350.04	+	20035.2i	0.227559	+	0.717978i
$921$	−3169.40	−	2302.71i	−0.113393	−	0.0823852i
$922$	3302.49	−	4545.49i	0.117963	−	0.162362i
$923$	2882.84	+	936.691i	0.102806	+	0.0334037i
$924$	3543.48			0.126160
$925$	−24180.4	+	7471.92i	−0.859512	+	0.265595i
$926$	34805.6			1.23519
$927$	−16746.3	−	5441.20i	−0.593334	−	0.192786i
$928$	−23284.3	+	32048.1i	−0.823648	+	1.13365i
$929$	−22997.5	−	16708.7i	−0.812190	−	0.590091i	0.102275	−	0.994756i	$-0.467388\pi$
$929$	−22997.5	−	16708.7i	−0.812190	−	0.590091i	−0.914465	+	0.404666i	$0.867388\pi$
$930$	6698.06	−	20118.4i	0.236170	−	0.709364i
$931$	−11647.1	+	8462.14i	−0.410010	+	0.297890i
$932$		−	450.931i		−	0.0158484i
$933$	2155.79	+	2967.20i	0.0756458	+	0.104117i
$934$	3775.63	+	11620.2i	0.132272	+	0.407092i
$935$	−9727.24	+	3083.00i	−0.340230	+	0.107834i
$936$	635.068	−	1954.54i	0.0221772	−	0.0682544i
$937$	−43257.4	+	14055.2i	−1.50817	+	0.490035i	−0.942389	−	0.334520i	$-0.891426\pi$
$937$	−43257.4	+	14055.2i	−1.50817	+	0.490035i	−0.565783	+	0.824554i	$0.691426\pi$
$938$	−12579.8	+	4087.43i	−0.437895	+	0.142281i
$939$	456.635	−	1405.38i	0.0158698	−	0.0488422i
$940$	21780.8	−	6903.30i	0.755755	−	0.239533i
$941$	4223.88	+	12999.8i	0.146328	+	0.450351i	0.997179	−	0.0750552i	$-0.0239133\pi$
$941$	4223.88	+	12999.8i	0.146328	+	0.450351i	−0.850851	+	0.525406i	$0.823913\pi$
$942$	−3137.12	−	4317.87i	−0.108506	−	0.149346i
$943$		−	94432.8i		−	3.26103i
$944$	−24831.7	+	18041.3i	−0.856149	+	0.622028i
$945$	3180.26	−	9552.28i	0.109475	−	0.328821i
$946$	1403.79	+	1019.91i	0.0482464	+	0.0350531i
$947$	−32358.0	+	44537.0i	−1.11034	+	1.52825i	−0.289431	+	0.957199i	$0.593466\pi$
$947$	−32358.0	+	44537.0i	−1.11034	+	1.52825i	−0.820911	+	0.571056i	$0.806534\pi$
$948$	−395.150	−	128.392i	−0.0135378	−	0.00439871i
$949$	−1407.49			−0.0481445
$950$	−23519.5	+	7267.69i	−0.803236	+	0.248205i
$951$	−19107.9			−0.651541
$952$	1992.18	+	647.298i	0.0678224	+	0.0220368i
$953$	−12776.5	+	17585.3i	−0.434282	+	0.597738i	−0.968929	−	0.247337i	$-0.920444\pi$
$953$	−12776.5	+	17585.3i	−0.434282	+	0.597738i	0.534647	+	0.845075i	$0.320444\pi$
$954$	40399.7	+	29352.1i	1.37106	+	0.996132i
$955$	−3070.70	−	9688.42i	−0.104048	−	0.328283i
$956$	−24360.6	+	17699.0i	−0.824141	+	0.598774i
$957$			14362.3i			0.485126i
$958$	−44959.9	−	61882.0i	−1.51627	−	2.08697i
$959$	−5661.94	−	17425.6i	−0.190650	−	0.586761i
$960$	1893.81	+	2646.64i	0.0636693	+	0.0889791i
$961$	9889.04	−	30435.3i	0.331947	−	1.02163i
$962$	−6666.10	+	2165.95i	−0.223413	+	0.0725914i
$963$	4885.55	−	1587.41i	0.163484	−	0.0531190i
$964$	7148.42	−	22000.6i	0.238833	−	0.735052i
$965$	−100.494	+	13899.3i	−0.00335234	+	0.463664i
$966$	4019.71	+	12371.4i	0.133884	+	0.412053i
$967$	−29162.4	−	40138.5i	−0.969802	−	1.33482i	−0.942147	−	0.335200i	$-0.891196\pi$
$967$	−29162.4	−	40138.5i	−0.969802	−	1.33482i	−0.0276547	−	0.999618i	$-0.508804\pi$
$968$		−	112.433i		−	0.00373318i
$969$	−2283.01	+	1658.70i	−0.0756872	+	0.0549899i
$970$	−40142.5	+	28724.1i	−1.32876	+	0.950800i
$971$	−37633.6	−	27342.4i	−1.24379	−	0.903666i	−0.245945	−	0.969284i	$-0.579098\pi$
$971$	−37633.6	−	27342.4i	−1.24379	−	0.903666i	−0.997845	+	0.0656175i	$0.979098\pi$
$972$	−11448.8	+	15758.0i	−0.377800	+	0.519997i
$973$	−4986.29	−	1620.14i	−0.164289	−	0.0533807i
$974$	40544.2			1.33380
$975$	796.418	−	2335.65i	0.0261598	−	0.0767188i
$976$	32142.4			1.05415
$977$	34596.3	+	11241.0i	1.13289	+	0.368098i	0.814673	−	0.579920i	$-0.196916\pi$
$977$	34596.3	+	11241.0i	1.13289	+	0.368098i	0.318216	+	0.948018i	$0.396916\pi$
$978$	−1002.73	+	1380.14i	−0.0327850	+	0.0451247i
$979$	437.956	+	318.194i	0.0142974	+	0.0103877i
$980$	−12940.8	−	9545.74i	−0.421815	−	0.311150i
$981$	−352.198	+	255.887i	−0.0114626	+	0.00832806i
$982$		−	34165.3i		−	1.11024i
$983$	−3908.33	−	5379.35i	−0.126812	−	0.174542i	0.740890	−	0.671626i	$-0.234404\pi$
$983$	−3908.33	−	5379.35i	−0.126812	−	0.174542i	−0.867702	+	0.497084i	$0.834404\pi$
$984$	2976.08	+	9159.42i	0.0964165	+	0.296739i
$985$	−4268.09	+	5786.09i	−0.138064	+	0.187168i
$986$	5384.14	−	16570.7i	0.173901	−	0.535211i
$987$	−6553.60	+	2129.39i	−0.211351	+	0.0686721i
$988$	−2606.82	+	847.007i	−0.0839413	+	0.0272742i
$989$	−791.378	+	2435.61i	−0.0254442	+	0.0783093i
$990$	−31919.7	−	10627.1i	−1.02472	−	0.341163i
$991$	5457.01	+	16794.9i	0.174922	+	0.538354i	0.999630	−	0.0272046i	$-0.00866058\pi$
$991$	5457.01	+	16794.9i	0.174922	+	0.538354i	−0.824708	+	0.565559i	$0.808661\pi$
$992$	30532.5	+	42024.4i	0.977225	+	1.34504i
$993$		−	34.9163i		−	0.00111585i
$994$	−8240.74	+	5987.25i	−0.262958	+	0.191050i
$995$	13055.2	+	94.3906i	0.415958	+	0.00300742i
$996$	9718.00	+	7060.54i	0.309163	+	0.224620i
$997$	11824.7	−	16275.3i	0.375619	−	0.516995i	−0.578799	−	0.815471i	$-0.696478\pi$
$997$	11824.7	−	16275.3i	0.375619	−	0.516995i	0.954417	+	0.298476i	$0.0964783\pi$
$998$	4554.45	+	1479.83i	0.144458	+	0.0469371i
$999$	−20967.9			−0.664060

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.e.a.4.6	✓	24
3.2	odd	2		225.4.m.a.154.1		24
5.2	odd	4		125.4.d.b.101.2		48
5.3	odd	4		125.4.d.b.101.11		48
5.4	even	2		125.4.e.a.24.1		24
25.6	even	5		125.4.e.a.99.1		24
25.8	odd	20		125.4.d.b.26.11		48
25.12	odd	20		625.4.a.g.1.5		24
25.13	odd	20		625.4.a.g.1.20		24
25.17	odd	20		125.4.d.b.26.2		48
25.19	even	10	inner	25.4.e.a.19.6	yes	24
75.44	odd	10		225.4.m.a.19.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.e.a.4.6	✓	24	1.1	even	1	trivial
25.4.e.a.19.6	yes	24	25.19	even	10	inner
125.4.d.b.26.2		48	25.17	odd	20
125.4.d.b.26.11		48	25.8	odd	20
125.4.d.b.101.2		48	5.2	odd	4
125.4.d.b.101.11		48	5.3	odd	4
125.4.e.a.24.1		24	5.4	even	2
125.4.e.a.99.1		24	25.6	even	5
225.4.m.a.19.1		24	75.44	odd	10
225.4.m.a.154.1		24	3.2	odd	2
625.4.a.g.1.5		24	25.12	odd	20
625.4.a.g.1.20		24	25.13	odd	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.47870 + 1.13030i) q^{2} +(1.22604 - 1.68750i) q^{3} +(4.35165 + 3.16166i) q^{4} +(-11.1800 - 0.0808329i) q^{5} +(6.17240 - 4.48451i) q^{6} +8.69522i q^{7} +(-5.63517 - 7.75614i) q^{8} +(6.99898 + 21.5406i) q^{9} +O(q^{10})\)	\(q+(3.47870 + 1.13030i) q^{2} +(1.22604 - 1.68750i) q^{3} +(4.35165 + 3.16166i) q^{4} +(-11.1800 - 0.0808329i) q^{5} +(6.17240 - 4.48451i) q^{6} +8.69522i q^{7} +(-5.63517 - 7.75614i) q^{8} +(6.99898 + 21.5406i) q^{9} +(-38.8007 - 12.9180i) q^{10} +(11.2241 - 34.5441i) q^{11} +(10.6706 - 3.46709i) q^{12} +(9.00127 - 2.92469i) q^{13} +(-9.82820 + 30.2481i) q^{14} +(-13.8436 + 18.7672i) q^{15} +(-24.1338 - 74.2761i) q^{16} +(14.7697 + 20.3288i) q^{17} +82.8444i q^{18} +(-43.5581 + 31.6468i) q^{19} +(-48.3961 - 35.6993i) q^{20} +(14.6732 + 10.6607i) q^{21} +(78.0902 - 107.482i) q^{22} +(186.484 + 60.5924i) q^{23} -19.9974 q^{24} +(124.987 + 1.80743i) q^{25} +34.6185 q^{26} +(98.4927 + 32.0022i) q^{27} +(-27.4913 + 37.8386i) q^{28} +(-153.365 - 111.426i) q^{29} +(-69.3703 + 49.6381i) q^{30} +(-201.106 + 146.112i) q^{31} -208.966i q^{32} +(-44.5320 - 61.2930i) q^{33} +(28.4018 + 87.4119i) q^{34} +(0.702860 - 97.2130i) q^{35} +(-37.6471 + 115.866i) q^{36} +(-192.559 + 62.5662i) q^{37} +(-187.296 + 60.8561i) q^{38} +(6.10050 - 18.7754i) q^{39} +(62.3745 + 87.1696i) q^{40} +(-148.823 - 458.030i) q^{41} +(38.9938 + 53.6704i) q^{42} +13.0607i q^{43} +(158.060 - 114.837i) q^{44} +(-76.5077 - 241.391i) q^{45} +(580.235 + 421.565i) q^{46} +(-223.319 + 307.372i) q^{47} +(-154.930 - 50.3398i) q^{48} +267.393 q^{49} +(432.749 + 147.560i) q^{50} +52.4130 q^{51} +(48.4172 + 15.7317i) q^{52} +(354.304 - 487.658i) q^{53} +(306.455 + 222.652i) q^{54} +(-128.278 + 385.297i) q^{55} +(67.4414 - 48.9990i) q^{56} +112.304i q^{57} +(-407.567 - 560.968i) q^{58} +(-121.448 - 373.777i) q^{59} +(-119.578 + 37.8997i) q^{60} +(-127.180 + 391.419i) q^{61} +(-864.740 + 280.971i) q^{62} +(-187.301 + 60.8577i) q^{63} +(43.1236 - 132.721i) q^{64} +(-100.871 + 31.9706i) q^{65} +(-85.6340 - 263.554i) q^{66} +(244.453 + 336.460i) q^{67} +135.161i q^{68} +(330.886 - 240.403i) q^{69} +(112.325 - 337.380i) q^{70} +(259.104 + 188.250i) q^{71} +(127.632 - 175.670i) q^{72} +(-141.434 - 45.9548i) q^{73} -740.574 q^{74} +(156.289 - 208.699i) q^{75} -289.606 q^{76} +(300.368 + 97.5956i) q^{77} +(42.4436 - 58.4187i) q^{78} +(-29.9592 - 21.7667i) q^{79} +(263.813 + 832.361i) q^{80} +(-319.977 + 232.477i) q^{81} -1761.56i q^{82} +(629.297 + 866.153i) q^{83} +(30.1471 + 92.7832i) q^{84} +(-163.483 - 228.470i) q^{85} +(-14.7625 + 45.4342i) q^{86} +(-376.064 + 122.191i) q^{87} +(-331.178 + 107.606i) q^{88} +(-4.60562 + 14.1746i) q^{89} +(6.69655 - 926.204i) q^{90} +(25.4308 + 78.2680i) q^{91} +(619.941 + 853.276i) q^{92} +518.506i q^{93} +(-1124.28 + 816.840i) q^{94} +(489.539 - 350.292i) q^{95} +(-352.630 - 256.200i) q^{96} +(709.473 - 976.506i) q^{97} +(930.181 + 302.234i) q^{98} +822.659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

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