LMFDB - Embedded newform 25.4.d.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(6,25)]

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([4]))

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

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

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, 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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	25.11
Dual form			25.4.d.a.16.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92104 - 1.39571i) q^{2} +(1.98691 - 6.11509i) q^{3} +(-0.729774 + 2.24601i) q^{4} +(-10.2730 + 4.41186i) q^{5} +(-4.71799 - 14.5205i) q^{6} +25.3460 q^{7} +(7.60304 + 23.3997i) q^{8} +(-11.6030 - 8.43010i) q^{9} +O(q^{10})$	\(q+(1.92104 - 1.39571i) q^{2} +(1.98691 - 6.11509i) q^{3} +(-0.729774 + 2.24601i) q^{4} +(-10.2730 + 4.41186i) q^{5} +(-4.71799 - 14.5205i) q^{6} +25.3460 q^{7} +(7.60304 + 23.3997i) q^{8} +(-11.6030 - 8.43010i) q^{9} +(-13.5772 + 22.8136i) q^{10} +(-19.6447 + 14.2727i) q^{11} +(12.2846 + 8.92527i) q^{12} +(-67.4574 - 49.0107i) q^{13} +(48.6907 - 35.3759i) q^{14} +(6.56725 + 71.5866i) q^{15} +(31.9805 + 23.2352i) q^{16} +(12.7778 + 39.3260i) q^{17} -34.0559 q^{18} +(-19.0191 - 58.5348i) q^{19} +(-2.41209 - 26.2931i) q^{20} +(50.3604 - 154.993i) q^{21} +(-17.8175 + 54.8368i) q^{22} +(-36.6257 + 26.6101i) q^{23} +158.198 q^{24} +(86.0710 - 90.6465i) q^{25} -197.993 q^{26} +(65.8438 - 47.8383i) q^{27} +(-18.4969 + 56.9276i) q^{28} +(2.63248 - 8.10193i) q^{29} +(112.530 + 128.354i) q^{30} +(-22.6770 - 69.7925i) q^{31} -102.966 q^{32} +(48.2466 + 148.488i) q^{33} +(79.4345 + 57.7125i) q^{34} +(-260.381 + 111.823i) q^{35} +(27.4017 - 19.9085i) q^{36} +(120.606 + 87.6257i) q^{37} +(-118.234 - 85.9022i) q^{38} +(-433.737 + 315.128i) q^{39} +(-181.343 - 206.843i) q^{40} +(133.631 + 97.0885i) q^{41} +(-119.582 - 368.037i) q^{42} +356.818 q^{43} +(-17.7205 - 54.5381i) q^{44} +(156.391 + 35.4119i) q^{45} +(-33.2192 + 102.238i) q^{46} +(-62.2446 + 191.569i) q^{47} +(205.628 - 149.397i) q^{48} +299.422 q^{49} +(38.8290 - 294.266i) q^{50} +265.870 q^{51} +(159.307 - 115.744i) q^{52} +(47.0610 - 144.839i) q^{53} +(59.7197 - 183.798i) q^{54} +(138.842 - 233.294i) q^{55} +(192.707 + 593.091i) q^{56} -395.735 q^{57} +(-6.25090 - 19.2383i) q^{58} +(-659.788 - 479.364i) q^{59} +(-165.577 - 37.4919i) q^{60} +(-381.688 + 277.312i) q^{61} +(-140.974 - 102.423i) q^{62} +(-294.091 - 213.670i) q^{63} +(-453.646 + 329.593i) q^{64} +(909.222 + 205.877i) q^{65} +(299.930 + 217.912i) q^{66} +(65.2717 + 200.886i) q^{67} -97.6516 q^{68} +(89.9513 + 276.841i) q^{69} +(-344.129 + 578.234i) q^{70} +(-31.0543 + 95.5752i) q^{71} +(109.044 - 335.602i) q^{72} +(944.803 - 686.440i) q^{73} +353.990 q^{74} +(-383.295 - 706.439i) q^{75} +145.350 q^{76} +(-497.915 + 361.757i) q^{77} +(-393.395 + 1210.75i) q^{78} +(-225.748 + 694.782i) q^{79} +(-431.048 - 97.6028i) q^{80} +(-281.373 - 865.976i) q^{81} +392.218 q^{82} +(255.127 + 785.200i) q^{83} +(311.365 + 226.220i) q^{84} +(-304.768 - 347.624i) q^{85} +(685.460 - 498.016i) q^{86} +(-44.3135 - 32.1956i) q^{87} +(-483.337 - 351.165i) q^{88} +(870.591 - 632.521i) q^{89} +(349.857 - 150.250i) q^{90} +(-1709.78 - 1242.23i) q^{91} +(-33.0382 - 101.681i) q^{92} -471.844 q^{93} +(147.802 + 454.887i) q^{94} +(453.631 + 517.421i) q^{95} +(-204.585 + 629.647i) q^{96} +(58.4685 - 179.948i) q^{97} +(575.201 - 417.908i) q^{98} +348.258 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) $ 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	1.92104	−	1.39571i	0.679189	−	0.493460i	−0.193900	−	0.981021i	$-0.562114\pi$
$2$	1.92104	−	1.39571i	0.679189	−	0.493460i	0.873089	+	0.487562i	$0.162114\pi$
$3$	1.98691	−	6.11509i	0.382382	−	1.17685i	−0.555980	−	0.831195i	$-0.687657\pi$
$3$	1.98691	−	6.11509i	0.382382	−	1.17685i	0.938362	−	0.345654i	$-0.112343\pi$
$4$	−0.729774	+	2.24601i	−0.0912218	+	0.280752i
$5$	−10.2730	+	4.41186i	−0.918849	+	0.394609i
$5$	−10.2730	+	4.41186i	−0.918849	+	0.394609i
$6$	−4.71799	−	14.5205i	−0.321018	−	0.987993i
$7$	25.3460			1.36856			0.684279	−	0.729220i	$-0.260117\pi$
$7$	25.3460			1.36856			0.684279	+	0.729220i	$0.260117\pi$
$8$	7.60304	+	23.3997i	0.336010	+	1.03413i
$9$	−11.6030	−	8.43010i	−0.429742	−	0.312226i
$10$	−13.5772	+	22.8136i	−0.429349	+	0.721429i
$11$	−19.6447	+	14.2727i	−0.538463	+	0.391216i	−0.823514	−	0.567296i	$-0.807990\pi$
$11$	−19.6447	+	14.2727i	−0.538463	+	0.391216i	0.285051	+	0.958512i	$0.407990\pi$
$12$	12.2846	+	8.92527i	0.295521	+	0.214709i
$13$	−67.4574	−	49.0107i	−1.43918	−	1.04562i	−0.988213	−	0.153084i	$-0.951080\pi$
$13$	−67.4574	−	49.0107i	−1.43918	−	1.04562i	−0.450966	−	0.892541i	$-0.648920\pi$
$14$	48.6907	−	35.3759i	0.929510	−	0.675328i
$15$	6.56725	+	71.5866i	0.113044	+	1.23224i
$16$	31.9805	+	23.2352i	0.499695	+	0.363050i
$17$	12.7778	+	39.3260i	0.182298	+	0.561056i	0.999891	−	0.0147401i	$-0.00469209\pi$
$17$	12.7778	+	39.3260i	0.182298	+	0.561056i	−0.817593	+	0.575796i	$0.804692\pi$
$18$	−34.0559			−0.445947
$19$	−19.0191	−	58.5348i	−0.229646	−	0.706779i	−0.997787	−	0.0664973i	$-0.978818\pi$
$19$	−19.0191	−	58.5348i	−0.229646	−	0.706779i	0.768140	−	0.640282i	$-0.221182\pi$
$20$	−2.41209	−	26.2931i	−0.0269680	−	0.293965i
$21$	50.3604	−	154.993i	0.523311	−	1.61059i
$22$	−17.8175	+	54.8368i	−0.172669	+	0.531420i
$23$	−36.6257	+	26.6101i	−0.332043	+	0.241243i	−0.741297	−	0.671177i	$-0.765789\pi$
$23$	−36.6257	+	26.6101i	−0.332043	+	0.241243i	0.409254	+	0.912420i	$0.365789\pi$
$24$	158.198			1.34550
$25$	86.0710	−	90.6465i	0.688568	−	0.725172i
$26$	−197.993			−1.49345
$27$	65.8438	−	47.8383i	0.469320	−	0.340981i
$28$	−18.4969	+	56.9276i	−0.124842	+	0.384225i
$29$	2.63248	−	8.10193i	0.0168565	−	0.0518790i	−0.942274	−	0.334842i	$-0.891317\pi$
$29$	2.63248	−	8.10193i	0.0168565	−	0.0518790i	0.959131	+	0.282963i	$0.0913172\pi$
$30$	112.530	+	128.354i	0.684838	+	0.781140i
$31$	−22.6770	−	69.7925i	−0.131384	−	0.404358i	0.863626	−	0.504133i	$-0.168188\pi$
$31$	−22.6770	−	69.7925i	−0.131384	−	0.404358i	−0.995010	+	0.0997747i	$0.968188\pi$
$32$	−102.966			−0.568813
$33$	48.2466	+	148.488i	0.254504	+	0.783284i
$34$	79.4345	+	57.7125i	0.400674	+	0.291106i
$35$	−260.381	+	111.823i	−1.25750	+	0.540045i
$36$	27.4017	−	19.9085i	0.126860	−	0.0921690i
$37$	120.606	+	87.6257i	0.535880	+	0.389340i	0.822553	−	0.568689i	$-0.192549\pi$
$37$	120.606	+	87.6257i	0.535880	+	0.389340i	−0.286673	+	0.958029i	$0.592549\pi$
$38$	−118.234	−	85.9022i	−0.504740	−	0.366715i
$39$	−433.737	+	315.128i	−1.78086	+	1.29387i
$40$	−181.343	−	206.843i	−0.716820	−	0.817619i
$41$	133.631	+	97.0885i	0.509016	+	0.369821i	0.812450	−	0.583031i	$-0.198133\pi$
$41$	133.631	+	97.0885i	0.509016	+	0.369821i	−0.303434	+	0.952852i	$0.598133\pi$
$42$	−119.582	−	368.037i	−0.439332	−	1.35213i
$43$	356.818			1.26545			0.632723	−	0.774378i	$-0.281937\pi$
$43$	356.818			1.26545			0.632723	+	0.774378i	$0.281937\pi$
$44$	−17.7205	−	54.5381i	−0.0607151	−	0.186862i
$45$	156.391	+	35.4119i	0.518075	+	0.117309i
$46$	−33.2192	+	102.238i	−0.106476	+	0.327700i
$47$	−62.2446	+	191.569i	−0.193177	+	0.594536i	0.806816	+	0.590802i	$0.201189\pi$
$47$	−62.2446	+	191.569i	−0.193177	+	0.594536i	−0.999993	+	0.00373425i	$0.998811\pi$
$48$	205.628	−	149.397i	0.618329	−	0.449242i
$49$	299.422			0.872951
$50$	38.8290	−	294.266i	0.109825	−	0.832309i
$51$	265.870			0.729986
$52$	159.307	−	115.744i	0.424845	−	0.308668i
$53$	47.0610	−	144.839i	0.121968	−	0.375380i	−0.871368	−	0.490630i	$-0.836767\pi$
$53$	47.0610	−	144.839i	0.121968	−	0.375380i	0.993337	+	0.115249i	$0.0367667\pi$
$54$	59.7197	−	183.798i	0.150497	−	0.463181i
$55$	138.842	−	233.294i	0.340389	−	0.571951i
$56$	192.707	+	593.091i	0.459849	+	1.41527i
$57$	−395.735			−0.919585
$58$	−6.25090	−	19.2383i	−0.0141514	−	0.0435536i
$59$	−659.788	−	479.364i	−1.45588	−	1.05776i	−0.984412	−	0.175879i	$-0.943723\pi$
$59$	−659.788	−	479.364i	−1.45588	−	1.05776i	−0.471470	−	0.881882i	$-0.656277\pi$
$60$	−165.577	−	37.4919i	−0.356265	−	0.0806697i
$61$	−381.688	+	277.312i	−0.801150	+	0.582069i	−0.911251	−	0.411851i	$-0.864882\pi$
$61$	−381.688	+	277.312i	−0.801150	+	0.582069i	0.110102	+	0.993920i	$0.464882\pi$
$62$	−140.974	−	102.423i	−0.288769	−	0.209803i
$63$	−294.091	−	213.670i	−0.588127	−	0.427299i
$64$	−453.646	+	329.593i	−0.886027	+	0.643736i
$65$	909.222	+	205.877i	1.73500	+	0.392859i
$66$	299.930	+	217.912i	0.559376	+	0.406410i
$67$	65.2717	+	200.886i	0.119018	+	0.366300i	0.992764	−	0.120083i	$-0.0383160\pi$
$67$	65.2717	+	200.886i	0.119018	+	0.366300i	−0.873746	+	0.486383i	$0.838316\pi$
$68$	−97.6516			−0.174147
$69$	89.9513	+	276.841i	0.156940	+	0.483012i
$70$	−344.129	+	578.234i	−0.587589	+	0.987317i
$71$	−31.0543	+	95.5752i	−0.0519079	+	0.159756i	−0.973650	−	0.228047i	$-0.926766\pi$
$71$	−31.0543	+	95.5752i	−0.0519079	+	0.159756i	0.921742	+	0.387803i	$0.126766\pi$
$72$	109.044	−	335.602i	0.178485	−	0.549321i
$73$	944.803	−	686.440i	1.51481	−	1.10057i	0.550818	−	0.834625i	$-0.314316\pi$
$73$	944.803	−	686.440i	1.51481	−	1.10057i	0.963988	−	0.265946i	$-0.0856843\pi$
$74$	353.990			0.556087
$75$	−383.295	−	706.439i	−0.590122	−	1.08763i
$76$	145.350			0.219378
$77$	−497.915	+	361.757i	−0.736918	+	0.535402i
$78$	−393.395	+	1210.75i	−0.571067	+	1.75756i
$79$	−225.748	+	694.782i	−0.321502	+	0.989481i	0.651493	+	0.758655i	$0.274143\pi$
$79$	−225.748	+	694.782i	−0.321502	+	0.989481i	−0.972995	+	0.230827i	$0.925857\pi$
$80$	−431.048	−	97.6028i	−0.602407	−	0.136404i
$81$	−281.373	−	865.976i	−0.385971	−	1.18790i
$82$	392.218			0.528210
$83$	255.127	+	785.200i	0.337395	+	1.03840i	0.965530	+	0.260292i	$0.0838187\pi$
$83$	255.127	+	785.200i	0.337395	+	1.03840i	−0.628135	+	0.778105i	$0.716181\pi$
$84$	311.365	+	226.220i	0.404438	+	0.293841i
$85$	−304.768	−	347.624i	−0.388902	−	0.443590i
$86$	685.460	−	498.016i	0.859477	−	0.624447i
$87$	−44.3135	−	32.1956i	−0.0546081	−	0.0396751i
$88$	−483.337	−	351.165i	−0.585499	−	0.425390i
$89$	870.591	−	632.521i	1.03688	−	0.753338i	0.0672070	−	0.997739i	$-0.478591\pi$
$89$	870.591	−	632.521i	1.03688	−	0.753338i	0.969674	+	0.244401i	$0.0785912\pi$
$90$	349.857	−	150.250i	0.409758	−	0.175974i
$91$	−1709.78	−	1242.23i	−1.96960	−	1.43100i
$92$	−33.0382	−	101.681i	−0.0374399	−	0.115228i
$93$	−471.844			−0.526107
$94$	147.802	+	454.887i	0.162176	+	0.499128i
$95$	453.631	+	517.421i	0.489912	+	0.558803i
$96$	−204.585	+	629.647i	−0.217504	+	0.669407i
$97$	58.4685	−	179.948i	0.0612018	−	0.188360i	−0.915781	−	0.401678i	$-0.868427\pi$
$97$	58.4685	−	179.948i	0.0612018	−	0.188360i	0.976983	+	0.213318i	$0.0684271\pi$
$98$	575.201	−	417.908i	0.592899	−	0.430766i
$99$	348.258			0.353548
$100$	140.781	+	259.468i	0.140781	+	0.259468i
$101$	487.054			0.479839			0.239919	−	0.970793i	$-0.422879\pi$
$101$	487.054			0.479839			0.239919	+	0.970793i	$0.422879\pi$
$102$	510.747	−	371.079i	0.495799	−	0.360219i
$103$	−270.267	+	831.795i	−0.258545	+	0.795721i	0.734565	+	0.678538i	$0.237386\pi$
$103$	−270.267	+	831.795i	−0.258545	+	0.795721i	−0.993110	+	0.117183i	$0.962614\pi$
$104$	633.956	−	1951.12i	0.597736	−	1.83964i
$105$	166.454	+	1814.44i	0.154707	+	1.68639i
$106$	−111.748	−	343.925i	−0.102395	−	0.315141i
$107$	463.991			0.419212			0.209606	−	0.977786i	$-0.432782\pi$
$107$	463.991			0.419212			0.209606	+	0.977786i	$0.432782\pi$
$108$	59.3944	+	182.797i	0.0529188	+	0.162867i
$109$	−751.336	−	545.877i	−0.660228	−	0.479684i	0.206512	−	0.978444i	$-0.433789\pi$
$109$	−751.336	−	545.877i	−0.660228	−	0.479684i	−0.866740	+	0.498760i	$0.833789\pi$
$110$	−58.8915	−	641.949i	−0.0510462	−	0.556431i
$111$	775.473	−	563.414i	0.663105	−	0.481774i
$112$	810.579	+	588.920i	0.683862	+	0.496855i
$113$	−1412.17	−	1026.01i	−1.17563	−	0.854145i	−0.183958	−	0.982934i	$-0.558891\pi$
$113$	−1412.17	−	1026.01i	−1.17563	−	0.854145i	−0.991672	+	0.128789i	$0.958891\pi$
$114$	−760.221	+	552.333i	−0.624572	+	0.453778i
$115$	258.858	−	434.955i	0.209901	−	0.352693i
$116$	16.2759	+	11.8252i	0.0130274	+	0.00946498i
$117$	369.546	+	1137.35i	0.292005	+	0.898698i
$118$	−1936.53			−1.51078
$119$	323.867	+	996.759i	0.249486	+	0.767838i
$120$	−1625.18	+	697.947i	−1.23631	+	0.530947i
$121$	−229.098	+	705.091i	−0.172125	+	0.529745i
$122$	−346.187	+	1065.45i	−0.256904	+	0.790670i
$123$	859.218	−	624.258i	0.629862	−	0.457622i
$124$	173.304			0.125509
$125$	−484.292	+	1310.95i	−0.346531	+	0.938038i
$126$	−863.181			−0.610304
$127$	−379.875	+	275.996i	−0.265421	+	0.192840i	−0.712534	−	0.701638i	$-0.752452\pi$
$127$	−379.875	+	275.996i	−0.265421	+	0.192840i	0.447112	+	0.894478i	$0.352452\pi$
$128$	−156.906	+	482.907i	−0.108349	+	0.333464i
$129$	708.965	−	2181.97i	0.483883	−	1.48924i
$130$	2033.99	−	873.518i	1.37225	−	0.589328i
$131$	477.036	+	1468.17i	0.318159	+	0.979193i	0.974435	+	0.224672i	$0.0721309\pi$
$131$	477.036	+	1468.17i	0.318159	+	0.979193i	−0.656275	+	0.754521i	$0.727869\pi$
$132$	−368.714			−0.243125
$133$	−482.059	−	1483.63i	−0.314284	−	0.967268i
$134$	405.768	+	294.808i	0.261590	+	0.190056i
$135$	−465.360	+	781.938i	−0.296680	+	0.498508i
$136$	−823.068	+	597.994i	−0.518952	+	0.377041i
$137$	−702.035	−	510.058i	−0.437802	−	0.318082i	0.346959	−	0.937880i	$-0.387214\pi$
$137$	−702.035	−	510.058i	−0.437802	−	0.318082i	−0.784761	+	0.619798i	$0.787214\pi$
$138$	559.191	+	406.276i	0.344939	+	0.250613i
$139$	−217.912	+	158.322i	−0.132972	+	0.0966096i	−0.652283	−	0.757976i	$-0.726189\pi$
$139$	−217.912	+	158.322i	−0.132972	+	0.0966096i	0.519311	+	0.854585i	$0.326189\pi$
$140$	−61.1369	−	666.425i	−0.0369072	−	0.402309i
$141$	1047.79	+	761.262i	0.625813	+	0.454680i
$142$	73.7393	+	226.946i	0.0435779	+	0.134119i
$143$	2024.70			1.18401
$144$	−175.196	−	539.197i	−0.101386	−	0.312035i
$145$	8.70100	+	94.8456i	0.00498330	+	0.0543207i
$146$	856.928	−	2637.35i	0.485752	−	1.49499i
$147$	594.926	−	1830.99i	0.333800	−	1.02733i
$148$	−284.824	+	206.937i	−0.158192	+	0.114933i
$149$	−1570.53			−0.863509			−0.431754	−	0.901991i	$-0.642105\pi$
$149$	−1570.53			−0.863509			−0.431754	+	0.901991i	$0.642105\pi$
$150$	−1722.31	−	822.123i	−0.937508	−	0.447507i
$151$	225.890			0.121739			0.0608697	−	0.998146i	$-0.480613\pi$
$151$	225.890			0.121739			0.0608697	+	0.998146i	$0.480613\pi$
$152$	1225.10	−	890.084i	0.653740	−	0.474970i
$153$	183.261	−	564.019i	0.0968350	−	0.298028i
$154$	−451.604	+	1389.90i	−0.236307	+	0.727279i
$155$	540.876	+	616.934i	0.280285	+	0.319699i
$156$	−391.252	−	1204.15i	−0.200803	−	0.618008i
$157$	3464.54			1.76115			0.880575	−	0.473907i	$-0.157157\pi$
$157$	3464.54			1.76115			0.880575	+	0.473907i	$0.157157\pi$
$158$	536.046	+	1649.78i	0.269909	+	0.830693i
$159$	−792.197	−	575.565i	−0.395128	−	0.287077i
$160$	1057.78	−	454.272i	0.522653	−	0.224458i
$161$	−928.317	+	674.462i	−0.454420	+	0.330156i
$162$	−1749.18	−	1270.86i	−0.848326	−	0.616345i
$163$	−7.00035	−	5.08605i	−0.00336386	−	0.00244399i	0.586102	−	0.810237i	$-0.300662\pi$
$163$	−7.00035	−	5.08605i	−0.00336386	−	0.00244399i	−0.589466	+	0.807793i	$0.700662\pi$
$164$	−315.582	+	229.284i	−0.150261	+	0.109171i
$165$	−1150.75	−	1312.56i	−0.542942	−	0.619290i
$166$	1586.02	+	1152.31i	0.741562	+	0.538776i
$167$	−839.722	−	2584.40i	−0.389100	−	1.19753i	−0.933462	−	0.358676i	$-0.883228\pi$
$167$	−839.722	−	2584.40i	−0.389100	−	1.19753i	0.544362	−	0.838850i	$-0.316772\pi$
$168$	4009.70			1.84140
$169$	1469.55	+	4522.80i	0.668888	+	2.05863i
$170$	−1070.65	−	242.430i	−0.483032	−	0.109374i
$171$	−272.775	+	839.514i	−0.121986	+	0.375434i
$172$	−260.396	+	801.417i	−0.115436	+	0.355276i
$173$	−2341.32	+	1701.07i	−1.02894	+	0.747570i	−0.968097	−	0.250577i	$-0.919380\pi$
$173$	−2341.32	+	1701.07i	−1.02894	+	0.747570i	−0.0608452	+	0.998147i	$0.519380\pi$
$174$	−130.064			−0.0566673
$175$	2181.56	−	2297.53i	0.942346	−	0.992439i
$176$	−959.876			−0.411099
$177$	−4242.29	+	3082.21i	−1.80153	+	1.30889i
$178$	789.618	−	2430.19i	0.332496	−	1.02332i
$179$	−559.451	+	1721.81i	−0.233605	+	0.718962i	0.763698	+	0.645573i	$0.223381\pi$
$179$	−559.451	+	1721.81i	−0.233605	+	0.718962i	−0.997303	+	0.0733891i	$0.976619\pi$
$180$	−193.665	+	325.413i	−0.0801943	+	0.134749i
$181$	−194.516	−	598.659i	−0.0798800	−	0.245845i	0.903139	−	0.429348i	$-0.141256\pi$
$181$	−194.516	−	598.659i	−0.0798800	−	0.245845i	−0.983019	+	0.183502i	$0.941256\pi$
$182$	−5018.35			−2.04387
$183$	937.410	+	2885.05i	0.378663	+	1.16541i
$184$	−901.137	−	654.714i	−0.361047	−	0.262316i
$185$	−1625.59	−	368.084i	−0.646030	−	0.146282i
$186$	−906.430	+	658.560i	−0.357326	+	0.259613i
$187$	−812.304	−	590.173i	−0.317655	−	0.230790i
$188$	−384.842	−	279.604i	−0.149295	−	0.108469i
$189$	1668.88	−	1212.51i	0.642291	−	0.466652i
$190$	1593.61	+	360.845i	0.608489	+	0.137781i
$191$	1081.05	+	785.432i	0.409541	+	0.297549i	0.773416	−	0.633899i	$-0.218546\pi$
$191$	1081.05	+	785.432i	0.409541	+	0.297549i	−0.363875	+	0.931448i	$0.618546\pi$
$192$	1114.14	+	3428.96i	0.418780	+	1.28887i
$193$	−926.251			−0.345456			−0.172728	−	0.984970i	$-0.555258\pi$
$193$	−926.251			−0.345456			−0.172728	+	0.984970i	$0.555258\pi$
$194$	−138.835	−	427.291i	−0.0513804	−	0.158133i
$195$	3065.50	−	5150.91i	1.12577	−	1.89161i
$196$	−218.511	+	672.506i	−0.0796321	+	0.245082i
$197$	367.189	−	1130.09i	0.132798	−	0.408709i	−0.862443	−	0.506154i	$-0.831067\pi$
$197$	367.189	−	1130.09i	0.132798	−	0.408709i	0.995241	+	0.0974446i	$0.0310669\pi$
$198$	669.017	−	486.069i	0.240126	−	0.174462i
$199$	−932.642			−0.332227			−0.166114	−	0.986107i	$-0.553122\pi$
$199$	−932.642			−0.332227			−0.166114	+	0.986107i	$0.553122\pi$
$200$	2775.50	+	1324.85i	0.981289	+	0.468406i
$201$	1358.12			0.476590
$202$	935.649	−	679.789i	0.325901	−	0.236781i
$203$	66.7229	−	205.352i	0.0230691	−	0.0709994i
$204$	−194.025	+	597.148i	−0.0665906	+	0.204945i
$205$	−1801.14	−	407.835i	−0.613643	−	0.138948i
$206$	641.757	+	1975.12i	0.217055	+	0.668027i
$207$	649.295			0.218015
$208$	−1018.55	−	3134.77i	−0.339537	−	1.04499i
$209$	1209.07	+	878.444i	0.400160	+	0.290733i
$210$	2852.20	+	3253.28i	0.937241	+	1.06904i
$211$	16.5873	−	12.0514i	0.00541192	−	0.00393199i	−0.585076	−	0.810978i	$-0.698935\pi$
$211$	16.5873	−	12.0514i	0.00541192	−	0.00393199i	0.590488	+	0.807046i	$0.298935\pi$
$212$	290.966	+	211.399i	0.0942625	+	0.0684857i
$213$	522.749	+	379.799i	0.168160	+	0.122176i
$214$	891.343	−	647.599i	0.284724	−	0.206864i
$215$	−3665.60	+	1574.23i	−1.16275	+	0.499356i
$216$	1620.02	+	1177.01i	0.510315	+	0.370766i
$217$	−574.771	−	1768.96i	−0.179806	−	0.553387i
$218$	−2205.23			−0.685125
$219$	−2320.40	−	7141.45i	−0.715973	−	2.20354i
$220$	422.658	+	482.092i	0.129525	+	0.147739i
$221$	1065.44	−	3279.08i	0.324295	−	0.998076i
$222$	703.347	−	2164.68i	0.212638	−	0.654431i
$223$	−52.3492	+	38.0339i	−0.0157200	+	0.0114213i	−0.595618	−	0.803268i	$-0.703093\pi$
$223$	−52.3492	+	38.0339i	−0.0157200	+	0.0114213i	0.579898	+	0.814689i	$0.303093\pi$
$224$	−2609.79			−0.778454
$225$	−1762.84	+	326.187i	−0.522324	+	0.0966479i
$226$	−4144.85			−1.21996
$227$	2989.40	−	2171.93i	0.874068	−	0.635048i	−0.0576071	−	0.998339i	$-0.518347\pi$
$227$	2989.40	−	2171.93i	0.874068	−	0.635048i	0.931676	+	0.363291i	$0.118347\pi$
$228$	288.797	−	888.826i	0.0838862	−	0.258175i
$229$	−428.443	+	1318.61i	−0.123635	+	0.380508i	−0.993650	−	0.112517i	$-0.964109\pi$
$229$	−428.443	+	1318.61i	−0.123635	+	0.380508i	0.870015	+	0.493025i	$0.164109\pi$
$230$	−109.798	−	1196.86i	−0.0314776	−	0.343123i
$231$	1222.86	+	3763.57i	0.348304	+	1.07197i
$232$	209.598			0.0593137
$233$	453.755	+	1396.51i	0.127581	+	0.392655i	0.994363	−	0.106033i	$-0.0338150\pi$
$233$	453.755	+	1396.51i	0.127581	+	0.392655i	−0.866781	+	0.498689i	$0.833815\pi$
$234$	2297.32	+	1669.10i	0.641797	+	0.466293i
$235$	−205.734	−	2242.61i	−0.0571090	−	0.622519i
$236$	1558.15	−	1132.06i	0.429776	−	0.312251i
$237$	3800.11	+	2760.94i	1.04153	+	0.756719i
$238$	2013.35	+	1462.78i	0.548345	+	0.398396i
$239$	350.099	−	254.362i	0.0947533	−	0.0688423i	−0.539400	−	0.842050i	$-0.681349\pi$
$239$	350.099	−	254.362i	0.0947533	−	0.0688423i	0.634153	+	0.773207i	$0.281349\pi$
$240$	−1453.30	+	2441.97i	−0.390876	+	0.656784i
$241$	−4207.37	−	3056.83i	−1.12457	−	0.817045i	−0.139671	−	0.990198i	$-0.544604\pi$
$241$	−4207.37	−	3056.83i	−1.12457	−	0.817045i	−0.984895	+	0.173153i	$0.944604\pi$
$242$	544.000	+	1674.26i	0.144503	+	0.444734i
$243$	−3657.12			−0.965451
$244$	−344.302	−	1059.65i	−0.0903347	−	0.278021i
$245$	−3075.98	+	1321.01i	−0.802110	+	0.344474i
$246$	779.302	−	2398.45i	0.201978	−	0.621623i
$247$	−1585.85	+	4880.75i	−0.408523	+	1.25731i
$248$	1460.71	−	1061.27i	0.374013	−	0.271737i
$249$	5308.48			1.35105
$250$	899.367	+	3194.31i	0.227524	+	0.808105i
$251$	2594.35			0.652406			0.326203	−	0.945300i	$-0.394231\pi$
$251$	2594.35			0.652406			0.326203	+	0.945300i	$0.394231\pi$
$252$	694.525	−	504.602i	0.173615	−	0.126139i
$253$	339.702	−	1045.50i	0.0844146	−	0.259801i
$254$	−344.543	+	1060.40i	−0.0851125	+	0.261949i
$255$	−2731.30	+	1172.98i	−0.670747	+	0.288059i
$256$	−1013.64	−	3119.66i	−0.247471	−	0.761636i
$257$	1171.38			0.284314			0.142157	−	0.989844i	$-0.454596\pi$
$257$	1171.38			0.284314			0.142157	+	0.989844i	$0.454596\pi$
$258$	−1683.46	−	5181.16i	−0.406231	−	1.25025i
$259$	3056.89	+	2220.96i	0.733383	+	0.532834i
$260$	−1125.93	+	1891.88i	−0.268566	+	0.451267i
$261$	−98.8447	+	71.8149i	−0.0234419	+	0.0170315i
$262$	2965.55	+	2154.59i	0.699282	+	0.508058i
$263$	4765.01	+	3461.98i	1.11720	+	0.811691i	0.983782	−	0.179369i	$-0.0574056\pi$
$263$	4765.01	+	3461.98i	1.11720	+	0.811691i	0.133415	+	0.991060i	$0.457406\pi$
$264$	−3107.75	+	2257.91i	−0.724503	+	0.526383i
$265$	155.549	+	1695.56i	0.0360576	+	0.393048i
$266$	−2996.77	−	2177.28i	−0.690766	−	0.501871i
$267$	−2138.14	−	6580.50i	−0.490082	−	1.50832i
$268$	−498.826			−0.113696
$269$	−1449.81	−	4462.06i	−0.328611	−	1.01136i	−0.969784	−	0.243965i	$-0.921552\pi$
$269$	−1449.81	−	4462.06i	−0.328611	−	1.01136i	0.641173	−	0.767397i	$-0.278448\pi$
$270$	197.389	+	2151.64i	0.0444914	+	0.484981i
$271$	−2216.00	+	6820.16i	−0.496726	+	1.52876i	0.317524	+	0.948250i	$0.397148\pi$
$271$	−2216.00	+	6820.16i	−0.496726	+	1.52876i	−0.814250	+	0.580514i	$0.802852\pi$
$272$	−505.107	+	1554.56i	−0.112598	+	0.346541i
$273$	−10993.5	+	7987.26i	−2.43721	+	1.77074i
$274$	−2060.53			−0.454311
$275$	−397.069	+	3009.19i	−0.0870696	+	0.659857i
$276$	−687.434			−0.149923
$277$	1989.61	−	1445.54i	0.431568	−	0.313552i	−0.350708	−	0.936485i	$-0.614059\pi$
$277$	1989.61	−	1445.54i	0.431568	−	0.313552i	0.782276	+	0.622933i	$0.214059\pi$
$278$	−197.644	+	608.287i	−0.0426400	+	0.131232i
$279$	−325.236	+	1000.97i	−0.0697898	+	0.214791i
$280$	−4596.32	−	5242.66i	−0.981010	−	1.11896i
$281$	−2543.77	−	7828.92i	−0.540031	−	1.66204i	−0.732521	−	0.680745i	$-0.761656\pi$
$281$	−2543.77	−	7828.92i	−0.540031	−	1.66204i	0.192490	−	0.981299i	$-0.438344\pi$
$282$	3075.34			0.649411
$283$	−1598.25	−	4918.91i	−0.335711	−	1.03321i	−0.966371	−	0.257152i	$-0.917216\pi$
$283$	−1598.25	−	4918.91i	−0.335711	−	1.03321i	0.630660	−	0.776059i	$-0.282784\pi$
$284$	−192.001	−	139.497i	−0.0401167	−	0.0291465i
$285$	4065.40	−	1745.93i	0.844960	−	0.362876i
$286$	3889.51	−	2825.90i	0.804167	−	0.584262i
$287$	3387.02	+	2460.81i	0.696617	+	0.506122i
$288$	1194.72	+	868.015i	0.244443	+	0.177598i
$289$	2591.44	−	1882.79i	0.527465	−	0.383226i
$290$	149.092	+	170.058i	0.0301897	+	0.0344350i
$291$	−984.223	−	715.080i	−0.198269	−	0.144051i
$292$	852.260	+	2622.99i	0.170804	+	0.525680i
$293$	3175.13			0.633082			0.316541	−	0.948579i	$-0.397479\pi$
$293$	3175.13			0.633082			0.316541	+	0.948579i	$0.397479\pi$
$294$	−1412.67	−	4347.75i	−0.280233	−	0.862470i
$295$	8892.92	+	2013.64i	1.75514	+	0.397419i
$296$	−1133.44	+	3488.38i	−0.222568	+	0.684993i
$297$	−610.698	+	1879.54i	−0.119314	+	0.367211i
$298$	−3017.05	+	2192.01i	−0.586486	+	0.426107i
$299$	3774.86			0.730119
$300$	1866.39	−	345.346i	0.359187	−	0.0664619i
$301$	9043.92			1.73184
$302$	433.943	−	315.278i	0.0826841	−	0.0600735i
$303$	967.734	−	2978.38i	0.183481	−	0.564698i
$304$	751.827	−	2313.88i	0.141843	−	0.436547i
$305$	2697.63	−	4532.80i	0.506446	−	0.850974i
$306$	−435.159	−	1339.28i	−0.0812953	−	0.250201i
$307$	−8843.99			−1.64415			−0.822073	−	0.569382i	$-0.807183\pi$
$307$	−8843.99			−1.64415			−0.822073	+	0.569382i	$0.807183\pi$
$308$	−449.145	−	1382.32i	−0.0830922	−	0.255731i
$309$	4549.51	+	3305.41i	0.837581	+	0.608538i
$310$	1900.11	+	430.244i	0.348125	+	0.0788266i
$311$	−6340.83	+	4606.88i	−1.15613	+	0.839976i	−0.989283	−	0.146008i	$-0.953358\pi$
$311$	−6340.83	+	4606.88i	−1.15613	+	0.839976i	−0.166844	+	0.985983i	$0.553358\pi$
$312$	−10671.6	−	7753.40i	−1.93642	−	1.40689i
$313$	270.368	+	196.434i	0.0488246	+	0.0354731i	0.611930	−	0.790912i	$-0.290393\pi$
$313$	270.368	+	196.434i	0.0488246	+	0.0354731i	−0.563105	+	0.826385i	$0.690393\pi$
$314$	6655.51	−	4835.51i	1.19615	−	0.869056i
$315$	3963.89	+	897.551i	0.709016	+	0.160544i
$316$	−1395.74	−	1014.07i	−0.248471	−	0.180524i
$317$	716.973	+	2206.62i	0.127032	+	0.390965i	0.994266	−	0.106936i	$-0.0341041\pi$
$317$	716.973	+	2206.62i	0.127032	+	0.390965i	−0.867234	+	0.497901i	$0.834104\pi$
$318$	−2325.16			−0.410027
$319$	63.9222	+	196.732i	0.0112193	+	0.0345295i
$320$	3206.21	−	5387.34i	0.560101	−	0.941130i
$321$	921.909	−	2837.35i	0.160299	−	0.493349i
$322$	−841.975	+	2591.33i	−0.145719	+	0.448476i
$323$	2058.92	−	1495.89i	0.354679	−	0.257689i
$324$	2150.33			0.368713
$325$	−10248.8	+	1896.38i	−1.74923	+	0.323668i
$326$	−20.5466			−0.00349071
$327$	−4830.93	+	3509.87i	−0.816975	+	0.593567i
$328$	−1255.85	+	3865.10i	−0.211410	+	0.650653i
$329$	−1577.65	+	4855.52i	−0.264373	+	0.813658i
$330$	−4042.59	−	915.370i	−0.674355	−	0.152695i
$331$	2571.26	+	7913.54i	0.426977	+	1.31410i	0.901088	+	0.433636i	$0.142770\pi$
$331$	2571.26	+	7913.54i	0.426977	+	1.31410i	−0.474111	+	0.880465i	$0.657230\pi$
$332$	−1949.75			−0.322309
$333$	−660.707	−	2033.45i	−0.108728	−	0.334631i
$334$	−5220.22	−	3792.71i	−0.855203	−	0.621341i
$335$	−1556.82	−	1775.74i	−0.253905	−	0.289609i
$336$	5211.85	−	3786.63i	0.846219	−	0.614814i
$337$	3750.60	+	2724.97i	0.606255	+	0.440470i	0.848094	−	0.529846i	$-0.177750\pi$
$337$	3750.60	+	2724.97i	0.606255	+	0.440470i	−0.241839	+	0.970317i	$0.577750\pi$
$338$	9135.60	+	6637.40i	1.47015	+	1.06813i
$339$	−9079.98	+	6596.99i	−1.45474	+	1.05693i
$340$	1003.18	−	430.825i	0.160015	−	0.0687199i
$341$	1441.61	+	1047.39i	0.228937	+	0.166332i
$342$	647.712	+	1993.45i	0.102410	+	0.315186i
$343$	−1104.52			−0.173874
$344$	2712.90	+	8349.44i	0.425202	+	1.30864i
$345$	−2145.46	−	2447.15i	−0.334805	−	0.381885i
$346$	−2123.55	+	6535.62i	−0.329950	+	1.01548i
$347$	3305.59	−	10173.6i	0.511393	−	1.57391i	−0.278358	−	0.960477i	$-0.589790\pi$
$347$	3305.59	−	10173.6i	0.511393	−	1.57391i	0.789751	−	0.613428i	$-0.210210\pi$
$348$	104.651	−	76.0332i	0.0161203	−	0.0117121i
$349$	−9482.77			−1.45444			−0.727222	−	0.686402i	$-0.759189\pi$
$349$	−9482.77			−1.45444			−0.727222	+	0.686402i	$0.759189\pi$
$350$	984.162	−	7458.47i	0.150302	−	1.13906i
$351$	−6786.24			−1.03197
$352$	2022.74	−	1469.61i	0.306285	−	0.222529i
$353$	2145.00	−	6601.64i	0.323419	−	0.995381i	−0.648730	−	0.761019i	$-0.724700\pi$
$353$	2145.00	−	6601.64i	0.323419	−	0.995381i	0.972149	−	0.234363i	$-0.0753004\pi$
$354$	−3847.72	+	11842.1i	−0.577695	+	1.77796i
$355$	−102.642	−	1118.86i	−0.0153456	−	0.167275i
$356$	785.317	+	2416.96i	0.116915	+	0.359827i
$357$	6738.76			0.999029
$358$	1328.43	+	4088.50i	0.196117	+	0.603586i
$359$	−5372.08	−	3903.05i	−0.789771	−	0.573802i	0.118125	−	0.992999i	$-0.462312\pi$
$359$	−5372.08	−	3903.05i	−0.789771	−	0.573802i	−0.907895	+	0.419197i	$0.862312\pi$
$360$	360.417	+	3928.74i	0.0527657	+	0.575175i
$361$	2484.45	−	1805.06i	0.362218	−	0.263167i
$362$	−1209.23	−	878.557i	−0.175568	−	0.127558i
$363$	3856.50	+	2801.91i	0.557613	+	0.405130i
$364$	4037.81	−	2933.64i	0.581426	−	0.422430i
$365$	−6677.53	+	11220.2i	−0.957584	+	1.60901i
$366$	5827.51	+	4233.93i	0.832264	+	0.604675i
$367$	−3255.00	−	10017.9i	−0.462969	−	1.42487i	−0.861519	−	0.507725i	$-0.830486\pi$
$367$	−3255.00	−	10017.9i	−0.462969	−	1.42487i	0.398550	−	0.917147i	$-0.369514\pi$
$368$	−1789.60			−0.253504
$369$	−732.058	−	2253.04i	−0.103278	−	0.317856i
$370$	−3636.55	+	1561.75i	−0.510960	+	0.219437i
$371$	1192.81	−	3671.09i	0.166921	−	0.513730i
$372$	344.340	−	1059.77i	0.0479924	−	0.147706i
$373$	9685.26	−	7036.76i	1.34446	−	0.976808i	0.345194	−	0.938531i	$-0.387813\pi$
$373$	9685.26	−	7036.76i	1.34446	−	0.976808i	0.999267	−	0.0382767i	$-0.0121868\pi$
$374$	−2384.18			−0.329634
$375$	7054.32	+	5566.23i	0.971423	+	0.766504i
$376$	−4955.91			−0.679739
$377$	−574.661	+	417.516i	−0.0785055	+	0.0570376i
$378$	1513.66	−	4658.56i	0.205963	−	0.633890i
$379$	1704.97	−	5247.34i	0.231077	−	0.711182i	−0.766541	−	0.642196i	$-0.778024\pi$
$379$	1704.97	−	5247.34i	0.231077	−	0.711182i	0.997618	−	0.0689861i	$-0.0219764\pi$
$380$	−1493.18	+	641.262i	−0.201575	+	0.0865685i
$381$	932.959	+	2871.35i	0.125451	+	0.386099i
$382$	3172.98			0.424984
$383$	−1287.09	−	3961.26i	−0.171716	−	0.528488i	0.827752	−	0.561094i	$-0.189619\pi$
$383$	−1287.09	−	3961.26i	−0.171716	−	0.528488i	−0.999468	+	0.0326057i	$0.989619\pi$
$384$	2641.26	+	1918.99i	0.351006	+	0.255021i
$385$	3519.09	−	5913.07i	0.465842	−	0.782748i
$386$	−1779.36	+	1292.78i	−0.234630	+	0.170469i
$387$	−4140.17	−	3008.01i	−0.543815	−	0.395105i
$388$	361.496	+	262.642i	0.0472994	+	0.0343650i
$389$	893.320	−	649.035i	0.116435	−	0.0845948i	−0.528044	−	0.849217i	$-0.677074\pi$
$389$	893.320	−	649.035i	0.116435	−	0.0845948i	0.644479	+	0.764622i	$0.277074\pi$
$390$	−1300.27	−	14173.7i	−0.168825	−	1.84028i
$391$	−1514.47	−	1100.32i	−0.195882	−	0.142317i
$392$	2276.52	+	7006.40i	0.293320	+	0.902747i
$393$	9925.80			1.27402
$394$	−871.902	−	2683.44i	−0.111487	−	0.343121i
$395$	−746.155	−	8133.49i	−0.0950459	−	1.03605i
$396$	−254.150	+	782.192i	−0.0322513	+	0.0992592i
$397$	−1096.55	+	3374.83i	−0.138625	+	0.426645i	−0.996136	−	0.0878208i	$-0.972010\pi$
$397$	−1096.55	+	3374.83i	−0.138625	+	0.426645i	0.857511	+	0.514466i	$0.172010\pi$
$398$	−1791.64	+	1301.70i	−0.225645	+	0.163941i
$399$	−10030.3			−1.25851
$400$	4858.78	−	899.042i	0.607348	−	0.112380i
$401$	5742.86			0.715174			0.357587	−	0.933880i	$-0.383599\pi$
$401$	5742.86			0.715174			0.357587	+	0.933880i	$0.383599\pi$
$402$	2609.00	−	1895.55i	0.323695	−	0.235178i
$403$	−1890.85	+	5819.44i	−0.233722	+	0.719322i
$404$	−355.439	+	1093.93i	−0.0437717	+	0.134715i
$405$	6711.12	+	7654.83i	0.823403	+	0.939190i
$406$	−158.436	−	487.615i	−0.0193671	−	0.0596057i
$407$	−3619.93			−0.440868
$408$	2021.42	+	6221.30i	0.245283	+	0.754902i
$409$	8612.96	+	6257.68i	1.04128	+	0.756534i	0.970535	−	0.240960i	$-0.0774624\pi$
$409$	8612.96	+	6257.68i	1.04128	+	0.756534i	0.0707449	+	0.997494i	$0.477462\pi$
$410$	−4029.27	+	1730.41i	−0.485345	+	0.208436i
$411$	−4513.93	+	3279.57i	−0.541742	+	0.393599i
$412$	−1670.99	−	1214.05i	−0.199815	−	0.145174i
$413$	−16723.0	−	12150.0i	−1.99246	−	1.44761i
$414$	1247.32	−	906.231i	0.148073	−	0.107582i
$415$	−6085.12	−	6940.81i	−0.719776	−	0.820991i
$416$	6945.83	+	5046.44i	0.818624	+	0.594765i
$417$	535.183	+	1647.13i	0.0628490	+	0.193429i
$418$	3548.73			0.415249
$419$	1030.84	+	3172.59i	0.120190	+	0.369907i	0.992994	−	0.118164i	$-0.0377008\pi$
$419$	1030.84	+	3172.59i	0.120190	+	0.369907i	−0.872804	+	0.488071i	$0.837701\pi$
$420$	−4196.72	−	950.271i	−0.487569	−	0.110401i
$421$	1995.28	−	6140.84i	0.230983	−	0.710894i	−0.766646	−	0.642071i	$-0.778076\pi$
$421$	1995.28	−	6140.84i	0.230983	−	0.710894i	0.997629	−	0.0688231i	$-0.0219244\pi$
$422$	15.0445	−	46.3022i	0.00173544	−	0.00534113i
$423$	2337.17	−	1698.05i	0.268646	−	0.195183i
$424$	3747.00			0.429176
$425$	4664.56	+	2226.57i	0.532387	+	0.254128i
$426$	1534.31			0.174501
$427$	−9674.28	+	7028.78i	−1.09642	+	0.796596i
$428$	−338.608	+	1042.13i	−0.0382413	+	0.117694i
$429$	4022.89	−	12381.2i	0.452744	−	1.39340i
$430$	−4844.59	+	8140.29i	−0.543318	+	0.912929i
$431$	1200.22	+	3693.89i	0.134136	+	0.412827i	0.995455	−	0.0952377i	$-0.0303611\pi$
$431$	1200.22	+	3693.89i	0.134136	+	0.412827i	−0.861319	+	0.508065i	$0.830361\pi$
$432$	3217.25			0.358310
$433$	2533.22	+	7796.46i	0.281152	+	0.865298i	0.987526	+	0.157458i	$0.0503300\pi$
$433$	2533.22	+	7796.46i	0.281152	+	0.865298i	−0.706373	+	0.707839i	$0.749670\pi$
$434$	−3573.13	−	2596.03i	−0.395197	−	0.287127i
$435$	597.277	+	135.243i	0.0658328	+	0.0149066i
$436$	1774.35	−	1289.14i	0.194899	−	0.141603i
$437$	2254.21	+	1637.78i	0.246758	+	0.179280i
$438$	−14425.0	−	10480.4i	−1.57364	−	1.14331i
$439$	−139.778	+	101.554i	−0.0151964	+	0.0110408i	−0.595358	−	0.803461i	$-0.702990\pi$
$439$	−139.778	+	101.554i	−0.0151964	+	0.0110408i	0.580161	+	0.814502i	$0.302990\pi$
$440$	6514.63	+	1475.12i	0.705847	+	0.159826i
$441$	−3474.21	−	2524.16i	−0.375144	−	0.272558i
$442$	−2529.92	−	7786.28i	−0.272253	−	0.837909i
$443$	−6880.56			−0.737935			−0.368967	−	0.929442i	$-0.620289\pi$
$443$	−6880.56			−0.737935			−0.368967	+	0.929442i	$0.620289\pi$
$444$	699.516	+	2152.89i	0.0747692	+	0.230116i
$445$	−6153.03	+	10338.8i	−0.655464	+	1.10137i
$446$	−47.4802	+	146.129i	−0.00504093	+	0.0155144i
$447$	−3120.51	+	9603.93i	−0.330190	+	1.01622i
$448$	−11498.1	+	8353.88i	−1.21258	+	0.880990i
$449$	−186.617			−0.0196147			−0.00980736	−	0.999952i	$-0.503122\pi$
$449$	−186.617			−0.0196147			−0.00980736	+	0.999952i	$0.503122\pi$
$450$	−2931.22	+	3087.04i	−0.307065	+	0.323388i
$451$	−4010.85			−0.418766
$452$	3334.99	−	2423.01i	0.347046	−	0.252144i
$453$	448.824	−	1381.34i	0.0465509	−	0.143269i
$454$	2711.36	−	8344.70i	0.280287	−	0.862635i
$455$	23045.2	+	5218.16i	2.37445	+	0.537651i
$456$	−3008.79	−	9260.09i	−0.308990	−	0.950973i
$457$	−1840.33			−0.188374			−0.0941870	−	0.995555i	$-0.530025\pi$
$457$	−1840.33			−0.188374			−0.0941870	+	0.995555i	$0.530025\pi$
$458$	1017.35	+	3131.09i	0.103794	+	0.319446i
$459$	2722.63	+	1978.10i	0.276866	+	0.201155i
$460$	788.006	+	898.816i	0.0798717	+	0.0911033i
$461$	−11998.7	+	8717.55i	−1.21222	+	0.880731i	−0.995431	−	0.0954872i	$-0.969559\pi$
$461$	−11998.7	+	8717.55i	−1.21222	+	0.880731i	−0.216791	+	0.976218i	$0.569559\pi$
$462$	7602.03	+	5523.20i	0.765538	+	0.556196i
$463$	12947.9	+	9407.22i	1.29966	+	0.944256i	0.999952	−	0.00977536i	$-0.00311164\pi$
$463$	12947.9	+	9407.22i	1.29966	+	0.944256i	0.299705	+	0.954032i	$0.403112\pi$
$464$	272.438	−	197.938i	0.0272578	−	0.0198039i
$465$	4847.28	−	2081.71i	0.483413	−	0.207606i
$466$	2820.82	+	2049.44i	0.280412	+	0.203731i
$467$	5127.34	+	15780.3i	0.508062	+	1.56365i	0.795562	+	0.605873i	$0.207176\pi$
$467$	5127.34	+	15780.3i	0.508062	+	1.56365i	−0.287500	+	0.957781i	$0.592824\pi$
$468$	−2824.18			−0.278948
$469$	1654.38	+	5091.66i	0.162883	+	0.501303i
$470$	−3525.27	−	4020.99i	−0.345976	−	0.394627i
$471$	6883.74	−	21186.0i	0.673431	−	2.07261i
$472$	6200.60	−	19083.5i	0.604673	−	1.86099i
$473$	−7009.57	+	5092.75i	−0.681396	+	0.495063i
$474$	11153.6			1.08081
$475$	−6942.96	−	3314.13i	−0.670663	−	0.320132i
$476$	−2475.08			−0.238330
$477$	−1767.06	+	1283.84i	−0.169618	+	0.123235i
$478$	317.537	−	977.278i	0.0303845	−	0.0935139i
$479$	2286.85	−	7038.19i	0.218139	−	0.671364i	−0.780777	−	0.624810i	$-0.785176\pi$
$479$	2286.85	−	7038.19i	0.218139	−	0.671364i	0.998916	−	0.0465532i	$-0.0148237\pi$
$480$	−676.205	−	7370.99i	−0.0643008	−	0.700913i
$481$	−3841.20	−	11822.0i	−0.364124	−	1.12066i
$482$	−12349.0			−1.16697
$483$	2279.91	+	7016.84i	0.214781	+	0.661029i
$484$	−1416.45	−	1029.11i	−0.133025	−	0.0966486i
$485$	193.253	+	2106.56i	0.0180931	+	0.197225i
$486$	−7025.47	+	5104.30i	−0.655724	+	0.476411i
$487$	2312.03	+	1679.79i	0.215130	+	0.156301i	0.690132	−	0.723684i	$-0.257553\pi$
$487$	2312.03	+	1679.79i	0.215130	+	0.156301i	−0.475002	+	0.879985i	$0.657553\pi$
$488$	−9391.03	−	6822.98i	−0.871131	−	0.632914i
$489$	−45.0107	+	32.7022i	−0.00416249	+	0.00302422i
$490$	−4065.32	+	6830.89i	−0.374801	+	0.629772i
$491$	−7425.15	−	5394.69i	−0.682469	−	0.495843i	0.191707	−	0.981452i	$-0.438598\pi$
$491$	−7425.15	−	5394.69i	−0.682469	−	0.495843i	−0.874176	+	0.485609i	$0.838598\pi$
$492$	775.058	+	2385.38i	0.0710209	+	0.218580i
$493$	352.254			0.0321799
$494$	3765.65	+	11589.5i	0.342965	+	1.05554i
$495$	−3577.67	+	1536.47i	−0.324857	+	0.139513i
$496$	896.421	−	2758.90i	0.0811502	−	0.249755i
$497$	−787.103	+	2422.45i	−0.0710390	+	0.218636i
$498$	10197.8	−	7409.13i	0.917618	−	0.666689i
$499$	4648.40			0.417016			0.208508	−	0.978021i	$-0.433139\pi$
$499$	4648.40			0.417016			0.208508	+	0.978021i	$0.433139\pi$
$500$	−2590.98	−	2044.42i	−0.231745	−	0.182859i
$501$	−17472.3			−1.55809
$502$	4983.84	−	3620.97i	0.443107	−	0.321936i
$503$	−2840.32	+	8741.60i	−0.251776	+	0.774888i	0.742671	+	0.669656i	$0.233558\pi$
$503$	−2840.32	+	8741.60i	−0.251776	+	0.774888i	−0.994448	+	0.105232i	$0.966442\pi$
$504$	2763.83	−	8506.19i	0.244267	−	0.751778i
$505$	−5003.53	+	2148.81i	−0.440899	+	0.189348i
$506$	−806.633	−	2482.56i	−0.0708680	−	0.218109i
$507$	30577.2			2.67846
$508$	−342.667	−	1054.62i	−0.0299279	−	0.0921086i
$509$	−7828.83	−	5687.97i	−0.681742	−	0.495314i	0.192193	−	0.981357i	$-0.438440\pi$
$509$	−7828.83	−	5687.97i	−0.681742	−	0.495314i	−0.873935	+	0.486043i	$0.838440\pi$
$510$	−3609.78	+	6065.46i	−0.313419	+	0.526633i
$511$	23947.0	−	17398.5i	2.07310	−	1.50620i
$512$	−9587.68	−	6965.86i	−0.827577	−	0.601270i
$513$	−4052.49	−	2944.31i	−0.348776	−	0.253400i
$514$	2250.26	−	1634.91i	0.193103	−	0.140297i
$515$	−893.300	−	9737.45i	−0.0764340	−	0.833172i
$516$	4383.35	+	3184.69i	0.373966	+	0.271702i
$517$	−1511.43	−	4651.71i	−0.128574	−	0.395710i
$518$	8972.24			0.761038
$519$	5750.18	+	17697.2i	0.486329	+	1.49677i
$520$	2095.39	+	22840.8i	0.176709	+	1.92623i
$521$	2178.75	−	6705.51i	0.183211	−	0.563865i	−0.816702	−	0.577059i	$-0.804200\pi$
$521$	2178.75	−	6705.51i	0.183211	−	0.563865i	0.999913	+	0.0131946i	$0.00420008\pi$
$522$	−89.6512	+	275.918i	−0.00751710	+	0.0231353i
$523$	15824.3	−	11497.0i	1.32304	−	0.961242i	0.323147	−	0.946349i	$-0.395259\pi$
$523$	15824.3	−	11497.0i	1.32304	−	0.961242i	0.999889	−	0.0148933i	$-0.00474087\pi$
$524$	−3645.65			−0.303933
$525$	−9715.03	−	17905.4i	−0.807616	−	1.48849i
$526$	13985.7			1.15932
$527$	2454.90	−	1783.59i	0.202917	−	0.147428i
$528$	−1907.19	+	5869.73i	−0.157197	+	0.483801i
$529$	−3126.47	+	9622.27i	−0.256963	+	0.790850i
$530$	2665.34	+	3040.14i	0.218443	+	0.249161i
$531$	3614.45	+	11124.1i	0.295394	+	0.909128i
$532$	3684.04			0.300232
$533$	−4256.02	−	13098.7i	−0.345870	−	1.06448i
$534$	−13291.9	−	9657.16i	−1.07715	−	0.782596i
$535$	−4766.60	+	2047.06i	−0.385193	+	0.165425i
$536$	−4204.41	+	3054.68i	−0.338811	+	0.246161i
$537$	9417.45	+	6842.18i	0.756784	+	0.549836i
$538$	−9012.90	−	6548.25i	−0.722256	−	0.524749i
$539$	−5882.06	+	4273.56i	−0.470052	+	0.341513i
$540$	−1416.64	−	1615.84i	−0.112893	−	0.128768i
$541$	6906.11	+	5017.58i	0.548830	+	0.398748i	0.827354	−	0.561681i	$-0.189845\pi$
$541$	6906.11	+	5017.58i	0.548830	+	0.398748i	−0.278524	+	0.960429i	$0.589845\pi$
$542$	5261.97	+	16194.7i	0.417013	+	1.28343i
$543$	−4047.34			−0.319868
$544$	−1315.68	−	4049.25i	−0.103694	−	0.319136i
$545$	10126.8	+	2293.04i	0.795938	+	0.180226i
$546$	−9971.01	+	30687.6i	−0.781539	+	2.40533i
$547$	1619.69	−	4984.91i	0.126605	−	0.389651i	−0.867585	−	0.497289i	$-0.834329\pi$
$547$	1619.69	−	4984.91i	0.126605	−	0.389651i	0.994190	+	0.107638i	$0.0343288\pi$
$548$	1657.92	−	1204.55i	0.129239	−	0.0938977i
$549$	6766.51			0.526025
$550$	3437.18	+	6334.95i	0.266476	+	0.491133i
$551$	−524.312			−0.0405380
$552$	−5794.12	+	4209.67i	−0.446764	+	0.324593i
$553$	−5721.83	+	17610.0i	−0.439994	+	1.35416i
$554$	1804.56	−	5553.87i	0.138391	−	0.425923i
$555$	−5480.77	+	9209.26i	−0.419181	+	0.704344i
$556$	−196.568	−	604.973i	−0.0149934	−	0.0461449i
$557$	−13344.1			−1.01509			−0.507547	−	0.861624i	$-0.669448\pi$
$557$	−13344.1			−1.01509			−0.507547	+	0.861624i	$0.669448\pi$
$558$	772.283	+	2376.84i	0.0585902	+	0.180322i
$559$	−24070.0	−	17487.9i	−1.82120	−	1.32318i
$560$	−10925.4	−	2473.85i	−0.824429	−	0.186677i
$561$	−5222.94	+	3794.69i	−0.393071	+	0.285583i
$562$	−15813.6	−	11489.3i	−1.18693	−	0.862358i
$563$	−2950.31	−	2143.53i	−0.220854	−	0.160460i	0.471857	−	0.881675i	$-0.343584\pi$
$563$	−2950.31	−	2143.53i	−0.220854	−	0.160460i	−0.692711	+	0.721215i	$0.743584\pi$
$564$	−2474.45	+	1797.79i	−0.184740	+	0.134221i
$565$	19033.9	+	4309.88i	1.41728	+	0.320917i
$566$	−9935.69	−	7218.70i	−0.737859	−	0.536086i
$567$	−7131.68	−	21949.1i	−0.528223	−	1.62570i
$568$	−2472.54			−0.182651
$569$	−5792.42	−	17827.2i	−0.426768	−	1.31346i	−0.901291	−	0.433214i	$-0.857380\pi$
$569$	−5792.42	−	17827.2i	−0.426768	−	1.31346i	0.474523	−	0.880243i	$-0.342620\pi$
$570$	5372.97	−	9028.13i	0.394823	−	0.663415i
$571$	−8067.28	+	24828.5i	−0.591252	+	1.81969i	−0.0186911	+	0.999825i	$0.505950\pi$
$571$	−8067.28	+	24828.5i	−0.591252	+	1.81969i	−0.572561	+	0.819862i	$0.694050\pi$
$572$	−1477.57	+	4547.49i	−0.108008	+	0.332413i
$573$	6950.95	−	5050.16i	0.506771	−	0.368191i
$574$	9941.17			0.722886
$575$	−740.298	+	5610.35i	−0.0536914	+	0.406901i
$576$	8042.17			0.581754
$577$	−16335.4	+	11868.4i	−1.17860	+	0.856302i	−0.992013	−	0.126137i	$-0.959742\pi$
$577$	−16335.4	+	11868.4i	−1.17860	+	0.856302i	−0.186585	+	0.982439i	$0.559742\pi$
$578$	2350.41	−	7233.82i	0.169142	−	0.520566i
$579$	−1840.38	+	5664.11i	−0.132096	+	0.406550i
$580$	−219.374	−	49.6733i	−0.0157052	−	0.00355616i
$581$	6466.46	+	19901.7i	0.461745	+	1.42111i
$582$	−2888.78			−0.205745
$583$	1142.74	+	3517.00i	0.0811794	+	0.249845i
$584$	23245.9	+	16889.1i	1.64713	+	1.19671i
$585$	−8814.17	−	10053.6i	−0.622942	−	0.710540i
$586$	6099.54	−	4431.57i	0.429982	−	0.312400i
$587$	7195.79	+	5228.05i	0.505966	+	0.367606i	0.811291	−	0.584642i	$-0.198765\pi$
$587$	7195.79	+	5228.05i	0.505966	+	0.367606i	−0.305325	+	0.952248i	$0.598765\pi$
$588$	3678.27	+	2672.42i	0.257975	+	0.187430i
$589$	−3653.99	+	2654.78i	−0.255620	+	0.185719i
$590$	19894.1	−	8543.70i	1.38818	−	0.596167i
$591$	−6181.04	−	4490.79i	−0.430210	−	0.312566i
$592$	1821.05	+	5604.62i	0.126427	+	0.389102i
$593$	−6531.27			−0.452288			−0.226144	−	0.974094i	$-0.572612\pi$
$593$	−6531.27			−0.452288			−0.226144	+	0.974094i	$0.572612\pi$
$594$	1450.12	+	4463.02i	0.100167	+	0.308283i
$595$	−7724.65	−	8810.90i	−0.532235	−	0.607078i
$596$	1146.13	−	3527.43i	0.0787708	−	0.242432i
$597$	−1853.08	+	5703.19i	−0.127038	+	0.390981i
$598$	7251.64	−	5268.63i	0.495889	−	0.360285i
$599$	2394.54			0.163336			0.0816681	−	0.996660i	$-0.473975\pi$
$599$	2394.54			0.163336			0.0816681	+	0.996660i	$0.473975\pi$
$600$	13616.3	−	14340.1i	0.926470	−	0.975720i
$601$	22481.5			1.52586			0.762928	−	0.646484i	$-0.223761\pi$
$601$	22481.5			1.52586			0.762928	+	0.646484i	$0.223761\pi$
$602$	17373.7	−	12622.7i	1.17624	−	0.854591i
$603$	936.136	−	2881.13i	0.0632212	−	0.194575i
$604$	−164.849	+	507.352i	−0.0111053	+	0.0341786i
$605$	−757.227	−	8254.18i	−0.0508854	−	0.554678i
$606$	−2297.92	−	7072.26i	−0.154037	−	0.474077i
$607$	−1223.57			−0.0818173			−0.0409086	−	0.999163i	$-0.513025\pi$
$607$	−1223.57			−0.0818173			−0.0409086	+	0.999163i	$0.513025\pi$
$608$	1958.32	+	6027.10i	0.130626	+	0.402025i
$609$	−1123.17	−	816.033i	−0.0747344	−	0.0542977i
$610$	−1144.24	−	12472.8i	−0.0759489	−	0.827883i
$611$	13587.8	−	9872.11i	0.899678	−	0.653654i
$612$	1133.05	+	823.213i	0.0748383	+	0.0543732i
$613$	8004.11	+	5815.33i	0.527378	+	0.383163i	0.819376	−	0.573256i	$-0.194320\pi$
$613$	8004.11	+	5815.33i	0.527378	+	0.383163i	−0.291998	+	0.956419i	$0.594320\pi$
$614$	−16989.6	+	12343.7i	−1.11669	+	0.811320i
$615$	−6072.65	+	10203.8i	−0.398167	+	0.669035i
$616$	−12250.7	−	8900.64i	−0.801289	−	0.582170i
$617$	−5134.77	−	15803.2i	−0.335037	−	1.03114i	−0.966704	−	0.255899i	$-0.917629\pi$
$617$	−5134.77	−	15803.2i	−0.335037	−	1.03114i	0.631666	−	0.775240i	$-0.282371\pi$
$618$	13353.2			0.869164
$619$	358.137	+	1102.23i	0.0232548	+	0.0715710i	0.962010	−	0.273013i	$-0.0880201\pi$
$619$	358.137	+	1102.23i	0.0232548	+	0.0715710i	−0.938756	+	0.344584i	$0.888020\pi$
$620$	−1780.36	+	764.592i	−0.115324	+	0.0495270i
$621$	−1138.59	+	3504.22i	−0.0735750	+	0.226441i
$622$	−5751.07	+	17700.0i	−0.370735	+	1.14100i
$623$	22066.0	−	16031.9i	1.41903	−	1.03099i
$624$	−21193.2			−1.35963
$625$	−808.558	−	15604.1i	−0.0517477	−	0.998660i
$626$	793.552			0.0506657
$627$	7774.09	−	5648.20i	0.495163	−	0.359757i
$628$	−2528.33	+	7781.41i	−0.160655	+	0.494446i
$629$	−1904.88	+	5862.63i	−0.120751	+	0.371635i
$630$	8867.50	−	3808.23i	0.560777	−	0.240831i
$631$	307.908	+	947.644i	0.0194257	+	0.0597862i	0.960299	−	0.278971i	$-0.0899934\pi$
$631$	307.908	+	947.644i	0.0194257	+	0.0597862i	−0.940874	+	0.338757i	$0.889993\pi$
$632$	−17974.1			−1.13128
$633$	−40.7377	−	125.378i	−0.00255794	−	0.00787253i
$634$	4457.14	+	3238.30i	0.279204	+	0.202854i
$635$	2684.82	−	4511.27i	0.167786	−	0.281928i
$636$	1870.85	−	1359.25i	0.116642	−	0.0847451i
$637$	−20198.3	−	14674.9i	−1.25633	−	0.912779i
$638$	397.379	+	288.713i	0.0246589	+	0.0179158i
$639$	1166.03	−	847.171i	0.0721870	−	0.0524469i
$640$	−518.614	−	5653.17i	−0.0320313	−	0.349158i
$641$	7930.49	+	5761.84i	0.488667	+	0.355037i	0.804671	−	0.593720i	$-0.202341\pi$
$641$	7930.49	+	5761.84i	0.488667	+	0.355037i	−0.316004	+	0.948758i	$0.602341\pi$
$642$	−2189.10	−	6737.37i	−0.134575	−	0.414179i
$643$	−17768.7			−1.08978			−0.544890	−	0.838507i	$-0.683429\pi$
$643$	−17768.7			−1.08978			−0.544890	+	0.838507i	$0.683429\pi$
$644$	−837.389	−	2577.22i	−0.0512387	−	0.157697i
$645$	2343.31	+	25543.3i	0.143051	+	1.55933i
$646$	1867.42	−	5747.32i	0.113735	−	0.350039i
$647$	4881.63	−	15024.1i	0.296625	−	0.912919i	−0.686045	−	0.727559i	$-0.740655\pi$
$647$	4881.63	−	15024.1i	0.296625	−	0.912919i	0.982671	−	0.185360i	$-0.0593451\pi$
$648$	18124.3	−	13168.1i	1.09875	−	0.798289i
$649$	19803.1			1.19775
$650$	−17041.5	+	17947.4i	−1.02834	+	1.08301i
$651$	−11959.4			−0.720008
$652$	16.5320	−	12.0112i	0.000993011	−	0.000721465i
$653$	−3404.43	+	10477.8i	−0.204021	+	0.627912i	0.795731	+	0.605650i	$0.207087\pi$
$653$	−3404.43	+	10477.8i	−0.204021	+	0.627912i	−0.999752	+	0.0222618i	$0.992913\pi$
$654$	−4381.60	+	13485.2i	−0.261979	+	0.806289i
$655$	−11378.0	−	12977.9i	−0.678738	−	0.774183i
$656$	2017.71	+	6209.88i	0.120089	+	0.369596i
$657$	−16749.3			−0.994602
$658$	3746.19	+	11529.6i	0.221948	+	0.683085i
$659$	16120.2	+	11712.0i	0.952891	+	0.692316i	0.951489	−	0.307683i	$-0.0995536\pi$
$659$	16120.2	+	11712.0i	0.952891	+	0.692316i	0.00140247	+	0.999999i	$0.499554\pi$
$660$	3787.82	−	1626.71i	0.223395	−	0.0959391i
$661$	−17878.2	+	12989.2i	−1.05201	+	0.764331i	−0.972594	−	0.232510i	$-0.925306\pi$
$661$	−17878.2	+	12989.2i	−1.05201	+	0.764331i	−0.0794179	+	0.996841i	$0.525306\pi$
$662$	15984.5	+	11613.4i	0.938454	+	0.681827i
$663$	−17934.9	−	13030.5i	−1.05058	−	0.763292i
$664$	−16433.7	+	11939.8i	−0.960471	+	0.697823i
$665$	11497.8	+	13114.6i	0.670472	+	0.764754i
$666$	−4107.35	−	2984.17i	−0.238974	−	0.173625i
$667$	119.177	+	366.789i	0.00691837	+	0.0212926i
$668$	6417.40			0.371702
$669$	128.568	+	395.690i	0.00743006	+	0.0228674i
$670$	−5469.13	−	1238.38i	−0.315360	−	0.0714074i
$671$	3540.14	−	10895.4i	0.203675	−	0.626846i
$672$	−5185.42	+	15959.1i	−0.297666	+	0.916123i
$673$	−5374.68	+	3904.94i	−0.307844	+	0.223662i	−0.730971	−	0.682409i	$-0.760932\pi$
$673$	−5374.68	+	3904.94i	−0.307844	+	0.223662i	0.423127	+	0.906070i	$0.360932\pi$
$674$	11008.3			0.629116
$675$	1330.87	−	10086.0i	0.0758891	−	0.575126i
$676$	−11230.7			−0.638980
$677$	18346.6	−	13329.6i	1.04153	−	0.756716i	0.0709471	−	0.997480i	$-0.477398\pi$
$677$	18346.6	−	13329.6i	1.04153	−	0.756716i	0.970584	+	0.240764i	$0.0773979\pi$
$678$	−8235.46	+	25346.1i	−0.466491	+	1.43571i
$679$	1481.95	−	4560.96i	0.0837582	−	0.257781i
$680$	5817.16	−	9774.48i	0.328055	−	0.551227i
$681$	−7341.85	−	22595.9i	−0.413128	−	1.27148i
$682$	4231.24			0.237570
$683$	7114.67	+	21896.7i	0.398587	+	1.22673i	0.926132	+	0.377199i	$0.123113\pi$
$683$	7114.67	+	21896.7i	0.398587	+	1.22673i	−0.527545	+	0.849527i	$0.676887\pi$
$684$	−1686.50	−	1225.31i	−0.0942760	−	0.0684955i
$685$	9462.34	+	2142.57i	0.527792	+	0.119509i
$686$	−2121.83	+	1541.60i	−0.118093	+	0.0857997i
$687$	7212.16	+	5239.94i	0.400525	+	0.290999i
$688$	11411.2	+	8290.72i	0.632337	+	0.459420i
$689$	−10273.3	+	7463.97i	−0.568042	+	0.412706i
$690$	−7537.03	−	1706.62i	−0.415841	−	0.0941595i
$691$	11092.1	+	8058.89i	0.610657	+	0.443668i	0.849646	−	0.527354i	$-0.176816\pi$
$691$	11092.1	+	8058.89i	0.610657	+	0.443668i	−0.238989	+	0.971022i	$0.576816\pi$
$692$	−2111.98	−	6500.02i	−0.116020	−	0.357072i
$693$	8826.97			0.483851
$694$	−7849.23	−	24157.4i	−0.429326	−	1.32133i
$695$	1540.13	−	2587.85i	0.0840580	−	0.141241i
$696$	416.453	−	1281.71i	0.0226805	−	0.0698033i
$697$	−2110.60	+	6495.75i	−0.114698	+	0.353004i
$698$	−18216.8	+	13235.2i	−0.987843	+	0.717710i
$699$	9441.38			0.510881
$700$	3568.24	+	6576.49i	0.192667	+	0.355097i
$701$	−5528.50			−0.297872			−0.148936	−	0.988847i	$-0.547585\pi$
$701$	−5528.50			−0.297872			−0.148936	+	0.988847i	$0.547585\pi$
$702$	−13036.6	+	9471.66i	−0.700905	+	0.509237i
$703$	2835.32	−	8726.23i	0.152114	−	0.468159i
$704$	4207.55	−	12949.5i	0.225253	−	0.693257i
$705$	−14122.5	−	3197.79i	−0.754448	−	0.170831i
$706$	−5093.37	−	15675.8i	−0.271518	−	0.835646i
$707$	12344.9			0.656687
$708$	−3826.76	−	11777.6i	−0.203134	−	0.625181i
$709$	−496.907	−	361.024i	−0.0263212	−	0.0191235i	0.574547	−	0.818472i	$-0.305178\pi$
$709$	−496.907	−	361.024i	−0.0263212	−	0.0191235i	−0.600868	+	0.799348i	$0.705178\pi$
$710$	−1758.78	−	2006.10i	−0.0929661	−	0.106039i
$711$	8476.44	−	6158.49i	0.447104	−	0.324840i
$712$	21420.0	+	15562.5i	1.12745	+	0.819143i
$713$	2687.75	+	1952.76i	0.141174	+	0.102569i
$714$	12945.4	−	9405.39i	0.678529	−	0.492980i
$715$	−20799.8	+	8932.67i	−1.08793	+	0.467221i
$716$	−3458.94	−	2513.07i	−0.180540	−	0.131170i
$717$	−859.830	−	2646.28i	−0.0447851	−	0.137834i
$718$	−15767.5			−0.819552
$719$	1234.35	+	3798.93i	0.0640242	+	0.197046i	0.977952	−	0.208831i	$-0.0669659\pi$
$719$	1234.35	+	3798.93i	0.0640242	+	0.197046i	−0.913927	+	0.405878i	$0.866966\pi$
$720$	4178.66	+	4766.26i	0.216291	+	0.246706i
$721$	−6850.19	+	21082.7i	−0.353834	+	1.08899i
$722$	2253.37	−	6935.17i	0.116152	−	0.357480i
$723$	−27052.5	+	19654.8i	−1.39155	+	1.01102i
$724$	1486.55			0.0763083
$725$	−507.831	−	935.966i	−0.0260143	−	0.0479461i
$726$	11319.1			0.578640
$727$	−10749.4	+	7809.89i	−0.548381	+	0.398422i	−0.827188	−	0.561925i	$-0.810061\pi$
$727$	−10749.4	+	7809.89i	−0.548381	+	0.398422i	0.278807	+	0.960347i	$0.410061\pi$
$728$	16068.3	−	49453.1i	0.818036	−	2.51766i
$729$	330.675	−	1017.71i	0.0168000	−	0.0517052i
$730$	2832.36	+	30874.3i	0.143603	+	1.56535i
$731$	4559.34	+	14032.2i	0.230689	+	0.709986i
$732$	−7163.96			−0.361732
$733$	−10595.1	−	32608.5i	−0.533889	−	1.64314i	−0.746038	−	0.665903i	$-0.768046\pi$
$733$	−10595.1	−	32608.5i	−0.533889	−	1.64314i	0.212150	−	0.977237i	$-0.431954\pi$
$734$	−20235.0	−	14701.6i	−1.01756	−	0.739301i
$735$	1966.38	+	21434.6i	0.0986817	+	1.07568i
$736$	3771.21	−	2739.94i	0.188870	−	0.137222i
$737$	−4149.42	−	3014.73i	−0.207389	−	0.150677i
$738$	−4550.91	−	3306.43i	−0.226994	−	0.164921i
$739$	20288.0	−	14740.1i	1.00989	−	0.733727i	0.0457025	−	0.998955i	$-0.485447\pi$
$739$	20288.0	−	14740.1i	1.00989	−	0.733727i	0.964186	+	0.265228i	$0.0854474\pi$
$740$	2013.03	−	3382.47i	0.100001	−	0.168030i
$741$	26695.3	+	19395.2i	1.32345	+	0.961541i
$742$	−2832.37	−	8717.13i	−0.140134	−	0.431288i
$743$	8670.63			0.428122			0.214061	−	0.976820i	$-0.431331\pi$
$743$	8670.63			0.428122			0.214061	+	0.976820i	$0.431331\pi$
$744$	−3587.45	−	11041.0i	−0.176777	−	0.544065i
$745$	16134.1	−	6928.96i	0.793435	−	0.340748i
$746$	8784.44	−	27035.7i	0.431128	−	1.32687i
$747$	3659.07	−	11261.4i	0.179221	−	0.551586i
$748$	1918.34	−	1393.75i	0.0937718	−	0.0681292i
$749$	11760.3			0.573716
$750$	21320.5	+	847.118i	1.03802	+	0.0412431i
$751$	6944.56			0.337431			0.168715	−	0.985665i	$-0.446038\pi$
$751$	6944.56			0.337431			0.168715	+	0.985665i	$0.446038\pi$
$752$	−6441.75	+	4680.21i	−0.312376	+	0.226954i
$753$	5154.75	−	15864.7i	0.249468	−	0.767784i
$754$	−521.212	+	1604.13i	−0.0251743	+	0.0774786i
$755$	−2320.58	+	996.594i	−0.111860	+	0.0480394i
$756$	1505.41	+	4633.18i	0.0724224	+	0.222893i
$757$	37367.3			1.79410			0.897052	−	0.441925i	$-0.145704\pi$
$757$	37367.3			1.79410			0.897052	+	0.441925i	$0.145704\pi$
$758$	−4048.49	−	12460.0i	−0.193995	−	0.597054i
$759$	−5718.34	−	4154.62i	−0.273468	−	0.198686i
$760$	−8658.54	+	14548.8i	−0.413261	+	0.694397i
$761$	−28169.5	+	20466.3i	−1.34184	+	0.974906i	−0.342468	+	0.939529i	$0.611263\pi$
$761$	−28169.5	+	20466.3i	−1.34184	+	0.974906i	−0.999374	+	0.0353764i	$0.988737\pi$
$762$	5799.84	+	4213.83i	0.275729	+	0.200329i
$763$	−19043.4	−	13835.8i	−0.903561	−	0.656475i
$764$	−2553.02	+	1854.88i	−0.120896	+	0.0878364i
$765$	605.724	+	6602.71i	0.0286274	+	0.312054i
$766$	−8001.34	−	5813.32i	−0.377416	−	0.274208i
$767$	21013.6	+	64673.3i	0.989255	+	3.04461i
$768$	−21091.0			−0.990959
$769$	−2846.58	−	8760.87i	−0.133485	−	0.410826i	0.861866	−	0.507136i	$-0.169296\pi$
$769$	−2846.58	−	8760.87i	−0.133485	−	0.410826i	−0.995351	+	0.0963104i	$0.969296\pi$
$770$	−1492.67	−	16270.9i	−0.0698597	−	0.761509i
$771$	2327.43	−	7163.09i	0.108716	−	0.334595i
$772$	675.954	−	2080.37i	0.0315131	−	0.0969873i
$773$	−29472.7	+	21413.1i	−1.37136	+	0.996348i	−0.373726	+	0.927539i	$0.621920\pi$
$773$	−29472.7	+	21413.1i	−1.37136	+	0.996348i	−0.997630	+	0.0688091i	$0.978080\pi$
$774$	−12151.7			−0.564321
$775$	−8278.27	−	3951.52i	−0.383696	−	0.183152i
$776$	4655.26			0.215353
$777$	19655.2	−	14280.3i	0.907497	−	0.659336i
$778$	810.233	−	2493.64i	0.0373371	−	0.114912i
$779$	3141.52	−	9668.59i	0.144488	−	0.444690i
$780$	9331.90	+	10644.2i	0.428379	+	0.488618i
$781$	−754.065	−	2320.77i	−0.0345487	−	0.106330i
$782$	−4445.08			−0.203268
$783$	−214.250	−	659.394i	−0.00977865	−	0.0300956i
$784$	9575.67	+	6957.13i	0.436209	+	0.316925i
$785$	−35591.4	+	15285.1i	−1.61823	+	0.694965i
$786$	19067.8	−	13853.6i	0.865301	−	0.628678i
$787$	−10648.5	−	7736.57i	−0.482309	−	0.350418i	0.319910	−	0.947448i	$-0.396347\pi$
$787$	−10648.5	−	7736.57i	−0.482309	−	0.350418i	−0.802219	+	0.597030i	$0.796347\pi$
$788$	2270.24	+	1649.42i	0.102632	+	0.0745663i
$789$	30638.0	−	22259.8i	1.38243	−	1.00440i
$790$	−12785.4	−	14583.3i	−0.575804	−	0.656774i
$791$	−35793.1	−	26005.2i	−1.60892	−	1.16895i
$792$	2647.82	+	8149.15i	0.118796	+	0.365615i
$793$	39339.0			1.76162
$794$	2603.79	+	8013.65i	0.116379	+	0.358178i
$795$	10677.6	+	2417.74i	0.476346	+	0.107860i
$796$	680.618	−	2094.73i	0.0303063	−	0.0932734i
$797$	6554.28	−	20172.0i	0.291298	−	0.896523i	−0.693142	−	0.720801i	$-0.743774\pi$
$797$	6554.28	−	20172.0i	0.291298	−	0.896523i	0.984440	−	0.175722i	$-0.0562260\pi$
$798$	−19268.6	+	13999.5i	−0.854763	+	0.621022i
$799$	−8328.99			−0.368784
$800$	−8862.40	+	9333.52i	−0.391667	+	0.412487i
$801$	−15433.7			−0.680803
$802$	11032.3	−	8015.40i	0.485739	−	0.352910i
$803$	−8763.02	+	26969.8i	−0.385106	+	1.18523i
$804$	−991.123	+	3050.36i	−0.0434754	+	0.133803i
$805$	6561.02	−	11024.4i	0.287261	−	0.482681i
$806$	4489.88	+	13818.4i	0.196215	+	0.603888i
$807$	−30166.5			−1.31588
$808$	3703.09	+	11396.9i	0.161231	+	0.496217i
$809$	−382.384	−	277.819i	−0.0166180	−	0.0120736i	0.579445	−	0.815011i	$-0.303269\pi$
$809$	−382.384	−	277.819i	−0.0166180	−	0.0120736i	−0.596063	+	0.802938i	$0.703269\pi$
$810$	23576.3	+	5338.41i	1.02270	+	0.231571i
$811$	−12121.4	+	8806.71i	−0.524833	+	0.381314i	−0.818422	−	0.574618i	$-0.805151\pi$
$811$	−12121.4	+	8806.71i	−0.524833	+	0.381314i	0.293588	+	0.955932i	$0.405151\pi$
$812$	412.530	+	299.721i	0.0178288	+	0.0129534i
$813$	37302.9	+	27102.1i	1.60919	+	1.16914i
$814$	−6954.02	+	5052.39i	−0.299433	+	0.217551i
$815$	94.3538	+	21.3647i	0.00405530	+	0.000918249i
$816$	8502.67	+	6177.55i	0.364771	+	0.265021i
$817$	−6786.35	−	20886.2i	−0.290605	−	0.894391i
$818$	25279.8			1.08054
$819$	9366.53	+	28827.2i	0.399625	+	1.22992i
$820$	2230.43	−	3747.75i	0.0949876	−	0.159606i
$821$	11714.4	−	36053.1i	0.497970	−	1.53260i	−0.314306	−	0.949322i	$-0.601772\pi$
$821$	11714.4	−	36053.1i	0.497970	−	1.53260i	0.812276	−	0.583273i	$-0.198228\pi$
$822$	−4094.10	+	12600.3i	−0.173720	+	0.534656i
$823$	−4281.51	+	3110.70i	−0.181342	+	0.131752i	−0.674753	−	0.738044i	$-0.735750\pi$
$823$	−4281.51	+	3110.70i	−0.181342	+	0.131752i	0.493411	+	0.869796i	$0.335750\pi$
$824$	−21518.6			−0.909754
$825$	17612.5	+	8407.10i	0.743259	+	0.354785i
$826$	−49083.4			−2.06759
$827$	−18995.1	+	13800.7i	−0.798697	+	0.580288i	−0.910532	−	0.413439i	$-0.864327\pi$
$827$	−18995.1	+	13800.7i	−0.798697	+	0.580288i	0.111834	+	0.993727i	$0.464327\pi$
$828$	−473.839	+	1458.33i	−0.0198877	+	0.0612081i
$829$	−10606.5	+	32643.5i	−0.444366	+	1.36762i	0.438812	+	0.898579i	$0.355399\pi$
$829$	−10606.5	+	32643.5i	−0.444366	+	1.36762i	−0.883178	+	0.469038i	$0.844601\pi$
$830$	−21377.1	−	4840.46i	−0.893990	−	0.202428i
$831$	−4886.41	−	15038.8i	−0.203980	−	0.627787i
$832$	46755.4			1.94826
$833$	3825.96	+	11775.1i	0.159137	+	0.489775i
$834$	3327.02	+	2417.22i	0.138136	+	0.100362i
$835$	20028.5	+	22844.9i	0.830078	+	0.946804i
$836$	−2855.35	+	2074.53i	−0.118127	+	0.0858243i
$837$	−4831.89	−	3510.57i	−0.199539	−	0.144974i
$838$	6408.30	+	4655.90i	0.264166	+	0.191928i
$839$	27933.6	−	20294.9i	1.14943	−	0.835112i	0.161027	−	0.986950i	$-0.448519\pi$
$839$	27933.6	−	20294.9i	1.14943	−	0.835112i	0.988405	+	0.151838i	$0.0485193\pi$
$840$	−41191.8	+	17690.2i	−1.69197	+	0.726631i
$841$	19672.4	+	14292.8i	0.806610	+	0.586036i
$842$	−4737.86	−	14581.6i	−0.193916	−	0.596812i
$843$	−52928.8			−2.16247
$844$	14.9626	+	46.0500i	0.000610228	+	0.00187809i
$845$	−35050.7	−	39979.5i	−1.42696	−	1.62762i
$846$	2119.79	−	6524.05i	0.0861465	−	0.265132i
$847$	−5806.73	+	17871.3i	−0.235563	+	0.724987i
$848$	4870.40	−	3538.55i	0.197229	−	0.143295i
$849$	−33255.1			−1.34430
$850$	12068.4	−	2233.08i	0.486993	−	0.0901105i
$851$	−6749.02			−0.271861
$852$	−1234.52	+	896.933i	−0.0496409	+	0.0360662i
$853$	6539.69	−	20127.1i	0.262503	−	0.807901i	−0.729755	−	0.683708i	$-0.760366\pi$
$853$	6539.69	−	20127.1i	0.262503	−	0.807901i	0.992258	−	0.124192i	$-0.0396339\pi$
$854$	−8774.48	+	27005.1i	−0.351588	+	1.08208i
$855$	−901.589	−	9827.81i	−0.0360628	−	0.393104i
$856$	3527.74	+	10857.3i	0.140859	+	0.433521i
$857$	−16183.1			−0.645046			−0.322523	−	0.946562i	$-0.604531\pi$
$857$	−16183.1			−0.645046			−0.322523	+	0.946562i	$0.604531\pi$
$858$	−9552.49	−	29399.5i	−0.380089	−	1.16979i
$859$	29106.1	+	21146.8i	1.15610	+	0.839953i	0.989279	−	0.146035i	$-0.0466511\pi$
$859$	29106.1	+	21146.8i	1.15610	+	0.839953i	0.166817	+	0.985988i	$0.446651\pi$
$860$	−860.676	−	9381.83i	−0.0341265	−	0.371997i
$861$	21777.8	−	15822.5i	0.862003	−	0.626282i
$862$	7461.28	+	5420.94i	0.294817	+	0.214197i
$863$	21700.2	+	15766.1i	0.855948	+	0.621883i	0.926780	−	0.375606i	$-0.122565\pi$
$863$	21700.2	+	15766.1i	0.855948	+	0.621883i	−0.0708315	+	0.997488i	$0.522565\pi$
$864$	−6779.68	+	4925.72i	−0.266955	+	0.193954i
$865$	16547.6	−	27804.7i	0.650445	−	1.09293i
$866$	15748.0	+	11441.6i	0.617945	+	0.448963i
$867$	−6364.47	−	19587.8i	−0.249306	−	0.767286i
$868$	4392.57			0.171767
$869$	−5481.66	−	16870.8i	−0.213984	−	0.658576i
$870$	1336.15	−	573.823i	0.0520687	−	0.0223614i
$871$	5442.49	−	16750.2i	0.211724	−	0.651619i
$872$	7060.96	−	21731.4i	0.274213	−	0.843942i
$873$	−2195.39	+	1595.04i	−0.0851118	+	0.0618373i
$874$	6616.28			0.256063
$875$	−12274.9	+	33227.4i	−0.474248	+	1.28376i
$876$	17733.2			0.683959
$877$	−22554.6	+	16386.8i	−0.868430	+	0.630952i	−0.930165	−	0.367141i	$-0.880337\pi$
$877$	−22554.6	+	16386.8i	−0.868430	+	0.630952i	0.0617350	+	0.998093i	$0.480337\pi$
$878$	−126.777	+	390.179i	−0.00487303	+	0.0149976i
$879$	6308.70	−	19416.2i	0.242079	−	0.745042i
$880$	9860.85	−	4234.84i	0.377738	−	0.162223i
$881$	3889.97	+	11972.1i	0.148759	+	0.457832i	0.997475	−	0.0710161i	$-0.0226242\pi$
$881$	3889.97	+	11972.1i	0.148759	+	0.457832i	−0.848717	+	0.528848i	$0.822624\pi$
$882$	−10197.1			−0.389290
$883$	−753.143	−	2317.94i	−0.0287036	−	0.0883407i	0.935678	−	0.352854i	$-0.114789\pi$
$883$	−753.143	−	2317.94i	−0.0287036	−	0.0883407i	−0.964382	+	0.264513i	$0.914789\pi$
$884$	6587.33	+	4785.98i	0.250629	+	0.182093i
$885$	29983.0	−	50380.1i	1.13883	−	1.91357i
$886$	−13217.8	+	9603.30i	−0.501197	+	0.364141i
$887$	−39882.6	−	28976.4i	−1.50973	−	1.09688i	−0.966298	−	0.257426i	$-0.917126\pi$
$887$	−39882.6	−	28976.4i	−1.50973	−	1.09688i	−0.543429	−	0.839455i	$-0.682874\pi$
$888$	19079.7	+	13862.2i	0.721028	+	0.523857i
$889$	−9628.34	+	6995.40i	−0.363244	+	0.263912i
$890$	2609.89	+	28449.2i	0.0982962	+	1.07148i
$891$	17887.3	+	12995.9i	0.672555	+	0.488640i
$892$	−47.2216	−	145.333i	−0.00177253	−	0.00545529i
$893$	12397.3			0.464568
$894$	7409.74	+	22804.8i	0.277202	+	0.853141i
$895$	−1849.13	−	20156.5i	−0.0690609	−	0.752801i
$896$	−3976.95	+	12239.8i	−0.148282	+	0.456364i
$897$	7500.31	−	23083.6i	0.279184	−	0.859241i
$898$	−358.498	+	260.464i	−0.0133221	+	0.00967907i
$899$	−625.150			−0.0231924
$900$	553.857	−	4197.41i	0.0205132	−	0.155460i
$901$	6297.27			0.232844
$902$	−7704.99	+	5598.01i	−0.284422	+	0.206644i
$903$	17969.5	−	55304.3i	0.662222	−	2.03811i
$904$	13271.4	−	40845.3i	0.488276	−	1.50276i
$905$	4639.47	+	5291.88i	0.170410	+	0.194373i
$906$	−1065.75	−	3280.03i	−0.0390806	−	0.120278i
$907$	−432.170			−0.0158214			−0.00791068	−	0.999969i	$-0.502518\pi$
$907$	−432.170			−0.0158214			−0.00791068	+	0.999969i	$0.502518\pi$
$908$	2696.59	+	8299.25i	0.0985567	+	0.303326i
$909$	−5651.30	−	4105.91i	−0.206207	−	0.149818i
$910$	51553.7	−	22140.2i	1.87801	−	0.806529i
$911$	−2373.17	+	1724.21i	−0.0863080	+	0.0627064i	−0.630102	−	0.776512i	$-0.716987\pi$
$911$	−2373.17	+	1724.21i	−0.0863080	+	0.0627064i	0.543794	+	0.839218i	$0.316987\pi$
$912$	−12655.8	−	9194.97i	−0.459512	−	0.333855i
$913$	−16218.8	−	11783.7i	−0.587913	−	0.427144i
$914$	−3535.34	+	2568.57i	−0.127942	+	0.0929550i
$915$	−22358.5	−	25502.5i	−0.807813	−	0.921408i
$916$	−2648.96	−	1924.58i	−0.0955502	−	0.0694213i
$917$	12091.0	+	37212.2i	0.435419	+	1.34008i
$918$	7991.13			0.287306
$919$	−3268.74	−	10060.2i	−0.117330	−	0.361103i	0.875096	−	0.483949i	$-0.160798\pi$
$919$	−3268.74	−	10060.2i	−0.117330	−	0.361103i	−0.992426	+	0.122846i	$0.960798\pi$
$920$	12145.9	+	2750.22i	0.435260	+	0.0985567i
$921$	−17572.2	+	54081.8i	−0.628691	+	1.93491i
$922$	−10882.7	+	33493.5i	−0.388723	+	1.19637i
$923$	6779.05	−	4925.27i	0.241750	−	0.175641i
$924$	−9345.45			−0.332730
$925$	18323.7	−	3390.51i	0.651328	−	0.120518i
$926$	38003.3			1.34867
$927$	10148.0	−	7372.97i	0.359552	−	0.261230i
$928$	−271.056	+	834.224i	−0.00958820	+	0.0295094i
$929$	−9454.04	+	29096.5i	−0.333882	+	1.02758i	0.633387	+	0.773835i	$0.281664\pi$
$929$	−9454.04	+	29096.5i	−0.333882	+	1.02758i	−0.967270	+	0.253750i	$0.918336\pi$
$930$	6406.33	−	10764.5i	0.225884	−	0.379549i
$931$	−5694.74	−	17526.6i	−0.200470	−	0.616984i
$932$	−3467.73			−0.121877
$933$	15572.8	+	47928.2i	0.546443	+	1.68178i
$934$	31874.6	+	23158.3i	1.11667	+	0.811308i
$935$	10948.6	+	2479.11i	0.382949	+	0.0867118i
$936$	−23803.9	+	17294.6i	−0.831256	+	0.603943i
$937$	17873.9	+	12986.1i	0.623174	+	0.452763i	0.854029	−	0.520226i	$-0.174152\pi$
$937$	17873.9	+	12986.1i	0.623174	+	0.452763i	−0.230855	+	0.972988i	$0.574152\pi$
$938$	10284.6	+	7472.22i	0.358001	+	0.260103i
$939$	1738.41	−	1263.03i	0.0604162	−	0.0438949i
$940$	5187.08	+	1174.52i	0.179983	+	0.0407538i
$941$	−28774.2	−	20905.7i	−0.996825	−	0.724236i	−0.0354197	−	0.999373i	$-0.511277\pi$
$941$	−28774.2	−	20905.7i	−0.996825	−	0.724236i	−0.961405	+	0.275137i	$0.911277\pi$
$942$	−16345.7	−	50306.8i	−0.565361	−	1.74000i
$943$	−7477.87			−0.258232
$944$	−9962.23	−	30660.6i	−0.343478	−	1.05712i
$945$	−11795.0	+	19819.0i	−0.406024	+	0.682237i
$946$	−6357.61	+	19566.7i	−0.218503	+	0.672483i
$947$	−6605.74	+	20330.4i	−0.226671	+	0.697623i	0.771446	+	0.636294i	$0.219534\pi$
$947$	−6605.74	+	20330.4i	−0.226671	+	0.697623i	−0.998118	+	0.0613283i	$0.980466\pi$
$948$	−8974.33	+	6520.23i	−0.307461	+	0.223383i
$949$	−97376.9			−3.33086
$950$	−17963.3	+	3323.82i	−0.613480	+	0.113515i
$951$	14918.2			0.508682
$952$	−20861.5	+	15156.8i	−0.710216	+	0.516002i
$953$	−4024.50	+	12386.2i	−0.136796	+	0.421015i	−0.995865	−	0.0908451i	$-0.971043\pi$
$953$	−4024.50	+	12386.2i	−0.136796	+	0.421015i	0.859069	+	0.511860i	$0.171043\pi$
$954$	−1602.70	+	4932.61i	−0.0543914	+	0.167400i
$955$	−14570.9	−	3299.32i	−0.493722	−	0.111794i
$956$	315.807	+	971.955i	0.0106840	+	0.0328821i
$957$	1330.04			0.0449260
$958$	−5430.19	−	16712.4i	−0.183133	−	0.563626i
$959$	−17793.8	−	12928.0i	−0.599158	−	0.435314i
$960$	−26573.6	−	30310.4i	−0.893396	−	1.01903i
$961$	19744.7	−	14345.3i	0.662773	−	0.481533i
$962$	−23879.2	−	17349.3i	−0.800309	−	0.581459i
$963$	−5383.70	−	3911.49i	−0.180153	−	0.130889i
$964$	9936.11	−	7219.01i	0.331972	−	0.241192i
$965$	9515.42	−	4086.49i	0.317422	−	0.136320i
$966$	14173.3	+	10297.5i	0.472069	+	0.342978i
$967$	10317.6	+	31754.4i	0.343115	+	1.05600i	0.962585	+	0.270979i	$0.0873475\pi$
$967$	10317.6	+	31754.4i	0.343115	+	1.05600i	−0.619470	+	0.785020i	$0.712653\pi$
$968$	−18240.8			−0.605662
$969$	−5056.62	−	15562.7i	−0.167639	−	0.515939i
$970$	3311.41	+	3777.06i	0.109611	+	0.125025i
$971$	−13984.1	+	43038.8i	−0.462176	+	1.42243i	0.400324	+	0.916373i	$0.368897\pi$
$971$	−13984.1	+	43038.8i	−0.462176	+	1.42243i	−0.862500	+	0.506057i	$0.831103\pi$
$972$	2668.87	−	8213.95i	0.0880701	−	0.271052i
$973$	−5523.21	+	4012.85i	−0.181980	+	0.132216i
$974$	6786.01			0.223242
$975$	−8766.92	+	66440.1i	−0.287965	+	2.18235i
$976$	−18650.0			−0.611651
$977$	48483.8	−	35225.6i	1.58765	−	1.15350i	0.680454	−	0.732791i	$-0.261783\pi$
$977$	48483.8	−	35225.6i	1.58765	−	1.15350i	0.907198	−	0.420705i	$-0.138217\pi$
$978$	−40.8243	+	125.644i	−0.00133478	+	0.00410804i
$979$	−8074.70	+	24851.4i	−0.263604	+	0.811290i
$980$	−722.233	−	7872.73i	−0.0235417	−	0.256617i
$981$	4115.97	+	12667.7i	0.133958	+	0.412281i
$982$	−21793.4			−0.708204
$983$	−15019.9	−	46226.4i	−0.487344	−	1.49989i	−0.828557	−	0.559904i	$-0.810838\pi$
$983$	−15019.9	−	46226.4i	−0.487344	−	1.49989i	0.341214	−	0.939986i	$-0.389162\pi$
$984$	21140.2	+	15359.2i	0.684882	+	0.497596i
$985$	1213.65	+	13229.5i	0.0392591	+	0.427945i
$986$	676.692	−	491.646i	0.0218563	−	0.0158795i
$987$	26557.3	+	19295.0i	0.856461	+	0.622255i
$988$	−9804.91	−	7123.69i	−0.315724	−	0.229387i
$989$	−13068.7	+	9494.96i	−0.420182	+	0.305280i
$990$	−4728.37	+	7945.02i	−0.151795	+	0.255060i
$991$	10825.5	+	7865.19i	0.347007	+	0.252115i	0.747612	−	0.664136i	$-0.231200\pi$
$991$	10825.5	+	7865.19i	0.347007	+	0.252115i	−0.400606	+	0.916251i	$0.631200\pi$
$992$	2334.96	+	7186.26i	0.0747329	+	0.230004i
$993$	53500.9			1.70977
$994$	1869.00	+	5752.19i	0.0596389	+	0.183550i
$995$	9581.07	−	4114.68i	0.305267	−	0.131100i
$996$	−3873.99	+	11922.9i	−0.123245	+	0.379310i
$997$	9464.53	−	29128.8i	0.300647	−	0.925295i	−0.680619	−	0.732637i	$-0.738289\pi$
$997$	9464.53	−	29128.8i	0.300647	−	0.925295i	0.981266	−	0.192658i	$-0.0617107\pi$
$998$	8929.75	−	6487.84i	0.283233	−	0.205781i
$999$	12133.0			0.384257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.d.a.11.5	✓	28
3.2	odd	2		225.4.h.b.136.3		28
5.2	odd	4		125.4.e.b.74.10		56
5.3	odd	4		125.4.e.b.74.5		56
5.4	even	2		125.4.d.a.51.3		28
25.4	even	10		625.4.a.d.1.10		14
25.9	even	10		125.4.d.a.76.3		28
25.12	odd	20		125.4.e.b.49.5		56
25.13	odd	20		125.4.e.b.49.10		56
25.16	even	5	inner	25.4.d.a.16.5	yes	28
25.21	even	5		625.4.a.c.1.5		14
75.41	odd	10		225.4.h.b.91.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.5	✓	28	1.1	even	1	trivial
25.4.d.a.16.5	yes	28	25.16	even	5	inner
125.4.d.a.51.3		28	5.4	even	2
125.4.d.a.76.3		28	25.9	even	10
125.4.e.b.49.5		56	25.12	odd	20
125.4.e.b.49.10		56	25.13	odd	20
125.4.e.b.74.5		56	5.3	odd	4
125.4.e.b.74.10		56	5.2	odd	4
225.4.h.b.91.3		28	75.41	odd	10
225.4.h.b.136.3		28	3.2	odd	2
625.4.a.c.1.5		14	25.21	even	5
625.4.a.d.1.10		14	25.4	even	10

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.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.92104 - 1.39571i) q^{2} +(1.98691 - 6.11509i) q^{3} +(-0.729774 + 2.24601i) q^{4} +(-10.2730 + 4.41186i) q^{5} +(-4.71799 - 14.5205i) q^{6} +25.3460 q^{7} +(7.60304 + 23.3997i) q^{8} +(-11.6030 - 8.43010i) q^{9} +O(q^{10})\)	\(q+(1.92104 - 1.39571i) q^{2} +(1.98691 - 6.11509i) q^{3} +(-0.729774 + 2.24601i) q^{4} +(-10.2730 + 4.41186i) q^{5} +(-4.71799 - 14.5205i) q^{6} +25.3460 q^{7} +(7.60304 + 23.3997i) q^{8} +(-11.6030 - 8.43010i) q^{9} +(-13.5772 + 22.8136i) q^{10} +(-19.6447 + 14.2727i) q^{11} +(12.2846 + 8.92527i) q^{12} +(-67.4574 - 49.0107i) q^{13} +(48.6907 - 35.3759i) q^{14} +(6.56725 + 71.5866i) q^{15} +(31.9805 + 23.2352i) q^{16} +(12.7778 + 39.3260i) q^{17} -34.0559 q^{18} +(-19.0191 - 58.5348i) q^{19} +(-2.41209 - 26.2931i) q^{20} +(50.3604 - 154.993i) q^{21} +(-17.8175 + 54.8368i) q^{22} +(-36.6257 + 26.6101i) q^{23} +158.198 q^{24} +(86.0710 - 90.6465i) q^{25} -197.993 q^{26} +(65.8438 - 47.8383i) q^{27} +(-18.4969 + 56.9276i) q^{28} +(2.63248 - 8.10193i) q^{29} +(112.530 + 128.354i) q^{30} +(-22.6770 - 69.7925i) q^{31} -102.966 q^{32} +(48.2466 + 148.488i) q^{33} +(79.4345 + 57.7125i) q^{34} +(-260.381 + 111.823i) q^{35} +(27.4017 - 19.9085i) q^{36} +(120.606 + 87.6257i) q^{37} +(-118.234 - 85.9022i) q^{38} +(-433.737 + 315.128i) q^{39} +(-181.343 - 206.843i) q^{40} +(133.631 + 97.0885i) q^{41} +(-119.582 - 368.037i) q^{42} +356.818 q^{43} +(-17.7205 - 54.5381i) q^{44} +(156.391 + 35.4119i) q^{45} +(-33.2192 + 102.238i) q^{46} +(-62.2446 + 191.569i) q^{47} +(205.628 - 149.397i) q^{48} +299.422 q^{49} +(38.8290 - 294.266i) q^{50} +265.870 q^{51} +(159.307 - 115.744i) q^{52} +(47.0610 - 144.839i) q^{53} +(59.7197 - 183.798i) q^{54} +(138.842 - 233.294i) q^{55} +(192.707 + 593.091i) q^{56} -395.735 q^{57} +(-6.25090 - 19.2383i) q^{58} +(-659.788 - 479.364i) q^{59} +(-165.577 - 37.4919i) q^{60} +(-381.688 + 277.312i) q^{61} +(-140.974 - 102.423i) q^{62} +(-294.091 - 213.670i) q^{63} +(-453.646 + 329.593i) q^{64} +(909.222 + 205.877i) q^{65} +(299.930 + 217.912i) q^{66} +(65.2717 + 200.886i) q^{67} -97.6516 q^{68} +(89.9513 + 276.841i) q^{69} +(-344.129 + 578.234i) q^{70} +(-31.0543 + 95.5752i) q^{71} +(109.044 - 335.602i) q^{72} +(944.803 - 686.440i) q^{73} +353.990 q^{74} +(-383.295 - 706.439i) q^{75} +145.350 q^{76} +(-497.915 + 361.757i) q^{77} +(-393.395 + 1210.75i) q^{78} +(-225.748 + 694.782i) q^{79} +(-431.048 - 97.6028i) q^{80} +(-281.373 - 865.976i) q^{81} +392.218 q^{82} +(255.127 + 785.200i) q^{83} +(311.365 + 226.220i) q^{84} +(-304.768 - 347.624i) q^{85} +(685.460 - 498.016i) q^{86} +(-44.3135 - 32.1956i) q^{87} +(-483.337 - 351.165i) q^{88} +(870.591 - 632.521i) q^{89} +(349.857 - 150.250i) q^{90} +(-1709.78 - 1242.23i) q^{91} +(-33.0382 - 101.681i) q^{92} -471.844 q^{93} +(147.802 + 454.887i) q^{94} +(453.631 + 517.421i) q^{95} +(-204.585 + 629.647i) q^{96} +(58.4685 - 179.948i) q^{97} +(575.201 - 417.908i) q^{98} +348.258 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

Introduction

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