LMFDB - Embedded newform 250.3.f.b.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,3,Mod(7,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([17]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("250.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	250.f (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.81200660901$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			157.1
Root			$3.40366i$ of defining polynomial
Character	$\chi$	$=$	250.157
Dual form			250.3.f.b.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39680 + 0.221232i) q^{2} +(-0.252608 - 0.495771i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-0.243163 - 0.748380i) q^{6} +(-7.20385 - 7.20385i) q^{7} +(2.52015 + 1.28408i) q^{8} +(5.10809 - 7.03068i) q^{9} +O(q^{10})$	\(q+(1.39680 + 0.221232i) q^{2} +(-0.252608 - 0.495771i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-0.243163 - 0.748380i) q^{6} +(-7.20385 - 7.20385i) q^{7} +(2.52015 + 1.28408i) q^{8} +(5.10809 - 7.03068i) q^{9} +(4.56901 - 3.31958i) q^{11} +(-0.174086 - 1.09913i) q^{12} +(22.6344 - 3.58493i) q^{13} +(-8.46863 - 11.6561i) q^{14} +(3.23607 + 2.35114i) q^{16} +(8.10888 - 15.9146i) q^{17} +(8.69040 - 8.69040i) q^{18} +(-13.6027 + 4.41978i) q^{19} +(-1.75171 + 5.39121i) q^{21} +(7.11641 - 3.62599i) q^{22} +(-4.05981 + 25.6327i) q^{23} -1.57379i q^{24} +32.4088 q^{26} +(-9.72206 - 1.53982i) q^{27} +(-9.25031 - 18.1548i) q^{28} +(-14.8092 - 4.81180i) q^{29} +(10.7392 + 33.0518i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-2.79992 - 1.42663i) q^{33} +(14.8473 - 20.4356i) q^{34} +(14.0614 - 10.2162i) q^{36} +(-2.42751 - 15.3267i) q^{37} +(-19.9781 + 3.16422i) q^{38} +(-7.49493 - 10.3159i) q^{39} +(-37.3476 - 27.1346i) q^{41} +(-3.63950 + 7.14292i) q^{42} +(31.8617 - 31.8617i) q^{43} +(10.7424 - 3.49042i) q^{44} +(-11.3415 + 34.9056i) q^{46} +(-8.16953 + 4.16259i) q^{47} +(0.348171 - 2.19827i) q^{48} +54.7908i q^{49} -9.93836 q^{51} +(45.2687 + 7.16986i) q^{52} +(12.8896 + 25.2972i) q^{53} +(-13.2391 - 4.30166i) q^{54} +(-8.90444 - 27.4051i) q^{56} +(5.62735 + 5.62735i) q^{57} +(-19.6210 - 9.99739i) q^{58} +(-23.3065 + 32.0786i) q^{59} +(11.5211 - 8.37057i) q^{61} +(7.68840 + 48.5426i) q^{62} +(-87.4458 + 13.8501i) q^{63} +(4.70228 + 6.47214i) q^{64} +(-3.59532 - 2.61216i) q^{66} +(-24.8631 + 48.7966i) q^{67} +(25.2597 - 25.2597i) q^{68} +(13.7335 - 4.46228i) q^{69} +(-23.8910 + 73.5289i) q^{71} +(21.9011 - 11.1592i) q^{72} +(-15.4792 + 97.7321i) q^{73} -21.9454i q^{74} -28.6054 q^{76} +(-56.8282 - 9.00071i) q^{77} +(-8.18674 - 16.0674i) q^{78} +(110.397 + 35.8702i) q^{79} +(-22.4769 - 69.1767i) q^{81} +(-46.1642 - 46.1642i) q^{82} +(13.6584 + 6.95931i) q^{83} +(-6.66390 + 9.17208i) q^{84} +(51.5533 - 37.4556i) q^{86} +(1.35537 + 8.55747i) q^{87} +(15.7772 - 2.49886i) q^{88} +(43.0149 + 59.2049i) q^{89} +(-188.880 - 137.229i) q^{91} +(-23.5641 + 46.2471i) q^{92} +(13.6733 - 13.6733i) q^{93} +(-12.3321 + 4.00695i) q^{94} +(0.972653 - 2.99352i) q^{96} +(-67.9854 + 34.6403i) q^{97} +(-12.1215 + 76.5319i) q^{98} -49.0800i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} - 40 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 - 40 * q^9	$ 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} - 40 q^{9} + 32 q^{11} - 4 q^{12} + 8 q^{13} - 30 q^{14} + 16 q^{16} + 62 q^{17} + 16 q^{18} + 30 q^{19} - 68 q^{21} + 48 q^{22} + 18 q^{23} - 56 q^{26} + 40 q^{27} - 44 q^{28} + 100 q^{29} + 132 q^{31} + 64 q^{32} + 36 q^{33} + 100 q^{34} + 48 q^{36} - 138 q^{37} - 20 q^{38} - 320 q^{39} - 88 q^{41} + 8 q^{42} + 78 q^{43} + 40 q^{44} - 26 q^{46} + 22 q^{47} + 8 q^{48} - 168 q^{51} + 16 q^{52} - 182 q^{53} + 80 q^{54} + 48 q^{56} - 280 q^{57} + 120 q^{58} - 350 q^{59} + 372 q^{61} + 158 q^{62} - 22 q^{63} - 202 q^{66} + 112 q^{67} + 196 q^{68} - 30 q^{69} + 122 q^{71} + 132 q^{72} + 248 q^{73} + 40 q^{76} - 16 q^{77} - 438 q^{78} + 760 q^{79} - 144 q^{81} - 352 q^{82} - 132 q^{83} - 20 q^{84} + 264 q^{86} - 770 q^{87} - 116 q^{88} + 550 q^{89} - 798 q^{91} - 384 q^{92} - 54 q^{93} + 190 q^{94} - 16 q^{96} + 292 q^{97} + 24 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 - 40 * q^9 + 32 * q^11 - 4 * q^12 + 8 * q^13 - 30 * q^14 + 16 * q^16 + 62 * q^17 + 16 * q^18 + 30 * q^19 - 68 * q^21 + 48 * q^22 + 18 * q^23 - 56 * q^26 + 40 * q^27 - 44 * q^28 + 100 * q^29 + 132 * q^31 + 64 * q^32 + 36 * q^33 + 100 * q^34 + 48 * q^36 - 138 * q^37 - 20 * q^38 - 320 * q^39 - 88 * q^41 + 8 * q^42 + 78 * q^43 + 40 * q^44 - 26 * q^46 + 22 * q^47 + 8 * q^48 - 168 * q^51 + 16 * q^52 - 182 * q^53 + 80 * q^54 + 48 * q^56 - 280 * q^57 + 120 * q^58 - 350 * q^59 + 372 * q^61 + 158 * q^62 - 22 * q^63 - 202 * q^66 + 112 * q^67 + 196 * q^68 - 30 * q^69 + 122 * q^71 + 132 * q^72 + 248 * q^73 + 40 * q^76 - 16 * q^77 - 438 * q^78 + 760 * q^79 - 144 * q^81 - 352 * q^82 - 132 * q^83 - 20 * q^84 + 264 * q^86 - 770 * q^87 - 116 * q^88 + 550 * q^89 - 798 * q^91 - 384 * q^92 - 54 * q^93 + 190 * q^94 - 16 * q^96 + 292 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{1}{20}\right)$

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 $

$2$	1.39680	+	0.221232i	0.698401	+	0.110616i
$2$	1.39680	+	0.221232i	0.698401	+	0.110616i
$3$	−0.252608	−	0.495771i	−0.0842027	−	0.165257i	0.845066	−	0.534663i	$-0.179561\pi$
$3$	−0.252608	−	0.495771i	−0.0842027	−	0.165257i	−0.929268	+	0.369406i	$0.879561\pi$
$4$	1.90211	+	0.618034i	0.475528	+	0.154508i
$5$		0			0
$5$		0			0
$6$	−0.243163	−	0.748380i	−0.0405272	−	0.124730i
$7$	−7.20385	−	7.20385i	−1.02912	−	1.02912i	−0.999563	−	0.0295578i	$-0.990590\pi$
$7$	−7.20385	−	7.20385i	−1.02912	−	1.02912i	−0.0295578	−	0.999563i	$-0.509410\pi$
$8$	2.52015	+	1.28408i	0.315018	+	0.160510i
$9$	5.10809	−	7.03068i	0.567565	−	0.781187i
$10$		0			0
$11$	4.56901	−	3.31958i	0.415365	−	0.301780i	−0.360405	−	0.932796i	$-0.617362\pi$
$11$	4.56901	−	3.31958i	0.415365	−	0.301780i	0.775770	+	0.631016i	$0.217362\pi$
$12$	−0.174086	−	1.09913i	−0.0145071	−	0.0915945i
$13$	22.6344	−	3.58493i	1.74111	−	0.275764i	0.796659	−	0.604429i	$-0.206599\pi$
$13$	22.6344	−	3.58493i	1.74111	−	0.275764i	0.944446	+	0.328666i	$0.106599\pi$
$14$	−8.46863	−	11.6561i	−0.604902	−	0.832576i
$15$		0			0
$16$	3.23607	+	2.35114i	0.202254	+	0.146946i
$17$	8.10888	−	15.9146i	0.476993	−	0.936151i	−0.519658	−	0.854374i	$-0.673941\pi$
$17$	8.10888	−	15.9146i	0.476993	−	0.936151i	0.996651	−	0.0817767i	$-0.0260594\pi$
$18$	8.69040	−	8.69040i	0.482800	−	0.482800i
$19$	−13.6027	+	4.41978i	−0.715931	+	0.232620i	−0.644258	−	0.764808i	$-0.722834\pi$
$19$	−13.6027	+	4.41978i	−0.715931	+	0.232620i	−0.0716731	+	0.997428i	$0.522834\pi$
$20$		0			0
$21$	−1.75171	+	5.39121i	−0.0834148	+	0.256724i
$22$	7.11641	−	3.62599i	0.323473	−	0.164818i
$23$	−4.05981	+	25.6327i	−0.176514	+	1.11446i	0.727232	+	0.686392i	$0.240807\pi$
$23$	−4.05981	+	25.6327i	−0.176514	+	1.11446i	−0.903745	+	0.428071i	$0.859193\pi$
$24$		−	1.57379i		−	0.0655744i
$25$		0			0
$26$	32.4088			1.24649
$27$	−9.72206	−	1.53982i	−0.360076	−	0.0570305i
$28$	−9.25031	−	18.1548i	−0.330368	−	0.648384i
$29$	−14.8092	−	4.81180i	−0.510662	−	0.165924i	0.0423415	−	0.999103i	$-0.486518\pi$
$29$	−14.8092	−	4.81180i	−0.510662	−	0.165924i	−0.553003	+	0.833179i	$0.686518\pi$
$30$		0			0
$31$	10.7392	+	33.0518i	0.346425	+	1.06619i	0.960817	+	0.277185i	$0.0894015\pi$
$31$	10.7392	+	33.0518i	0.346425	+	1.06619i	−0.614392	+	0.789001i	$0.710598\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−2.79992	−	1.42663i	−0.0848462	−	0.0432313i
$34$	14.8473	−	20.4356i	0.436686	−	0.601046i
$35$		0			0
$36$	14.0614	−	10.2162i	0.390593	−	0.283783i
$37$	−2.42751	−	15.3267i	−0.0656084	−	0.414235i	−0.998532	−	0.0541612i	$-0.982752\pi$
$37$	−2.42751	−	15.3267i	−0.0656084	−	0.414235i	0.932924	−	0.360074i	$-0.117248\pi$
$38$	−19.9781	+	3.16422i	−0.525739	+	0.0832688i
$39$	−7.49493	−	10.3159i	−0.192178	−	0.264510i
$40$		0			0
$41$	−37.3476	−	27.1346i	−0.910917	−	0.661820i	0.0303297	−	0.999540i	$-0.490344\pi$
$41$	−37.3476	−	27.1346i	−0.910917	−	0.661820i	−0.941247	+	0.337720i	$0.890344\pi$
$42$	−3.63950	+	7.14292i	−0.0866548	+	0.170070i
$43$	31.8617	−	31.8617i	0.740969	−	0.740969i	−0.231796	−	0.972765i	$-0.574460\pi$
$43$	31.8617	−	31.8617i	0.740969	−	0.740969i	0.972765	+	0.231796i	$0.0744600\pi$
$44$	10.7424	−	3.49042i	0.244145	−	0.0793276i
$45$		0			0
$46$	−11.3415	+	34.9056i	−0.246555	+	0.758817i
$47$	−8.16953	+	4.16259i	−0.173820	+	0.0885657i	−0.538736	−	0.842475i	$-0.681098\pi$
$47$	−8.16953	+	4.16259i	−0.173820	+	0.0885657i	0.364916	+	0.931041i	$0.381098\pi$
$48$	0.348171	−	2.19827i	0.00725357	−	0.0457972i
$49$			54.7908i			1.11818i
$50$		0			0
$51$	−9.93836			−0.194870
$52$	45.2687	+	7.16986i	0.870553	+	0.137882i
$53$	12.8896	+	25.2972i	0.243199	+	0.477305i	0.980050	−	0.198750i	$-0.0636881\pi$
$53$	12.8896	+	25.2972i	0.243199	+	0.477305i	−0.736851	+	0.676055i	$0.763688\pi$
$54$	−13.2391	−	4.30166i	−0.245169	−	0.0796603i
$55$		0			0
$56$	−8.90444	−	27.4051i	−0.159008	−	0.489376i
$57$	5.62735	+	5.62735i	0.0987255	+	0.0987255i
$58$	−19.6210	−	9.99739i	−0.338293	−	0.172369i
$59$	−23.3065	+	32.0786i	−0.395025	+	0.543706i	−0.959487	−	0.281754i	$-0.909084\pi$
$59$	−23.3065	+	32.0786i	−0.395025	+	0.543706i	0.564461	+	0.825459i	$0.309084\pi$
$60$		0			0
$61$	11.5211	−	8.37057i	0.188871	−	0.137223i	−0.489332	−	0.872098i	$-0.662759\pi$
$61$	11.5211	−	8.37057i	0.188871	−	0.137223i	0.678202	+	0.734875i	$0.262759\pi$
$62$	7.68840	+	48.5426i	0.124006	+	0.782946i
$63$	−87.4458	+	13.8501i	−1.38803	+	0.219842i
$64$	4.70228	+	6.47214i	0.0734732	+	0.101127i
$65$		0			0
$66$	−3.59532	−	2.61216i	−0.0544746	−	0.0395781i
$67$	−24.8631	+	48.7966i	−0.371091	+	0.728308i	−0.998740	−	0.0501893i	$-0.984018\pi$
$67$	−24.8631	+	48.7966i	−0.371091	+	0.728308i	0.627648	+	0.778497i	$0.284018\pi$
$68$	25.2597	−	25.2597i	0.371467	−	0.371467i
$69$	13.7335	−	4.46228i	0.199036	−	0.0646707i
$70$		0			0
$71$	−23.8910	+	73.5289i	−0.336493	+	1.03562i	0.629489	+	0.777009i	$0.283264\pi$
$71$	−23.8910	+	73.5289i	−0.336493	+	1.03562i	−0.965982	+	0.258609i	$0.916736\pi$
$72$	21.9011	−	11.1592i	0.304182	−	0.154988i
$73$	−15.4792	+	97.7321i	−0.212044	+	1.33880i	0.620225	+	0.784424i	$0.287041\pi$
$73$	−15.4792	+	97.7321i	−0.212044	+	1.33880i	−0.832269	+	0.554371i	$0.812959\pi$
$74$		−	21.9454i		−	0.296559i
$75$		0			0
$76$	−28.6054			−0.376387
$77$	−56.8282	−	9.00071i	−0.738029	−	0.116892i
$78$	−8.18674	−	16.0674i	−0.104958	−	0.205992i
$79$	110.397	+	35.8702i	1.39743	+	0.454053i	0.908360	−	0.418189i	$-0.137335\pi$
$79$	110.397	+	35.8702i	1.39743	+	0.454053i	0.489073	+	0.872243i	$0.337335\pi$
$80$		0			0
$81$	−22.4769	−	69.1767i	−0.277492	−	0.854033i
$82$	−46.1642	−	46.1642i	−0.562978	−	0.562978i
$83$	13.6584	+	6.95931i	0.164559	+	0.0838471i	0.534330	−	0.845276i	$-0.320564\pi$
$83$	13.6584	+	6.95931i	0.164559	+	0.0838471i	−0.369771	+	0.929123i	$0.620564\pi$
$84$	−6.66390	+	9.17208i	−0.0793322	+	0.109191i
$85$		0			0
$86$	51.5533	−	37.4556i	0.599456	−	0.435531i
$87$	1.35537	+	8.55747i	0.0155790	+	0.0983617i
$88$	15.7772	−	2.49886i	0.179286	−	0.0283962i
$89$	43.0149	+	59.2049i	0.483314	+	0.665224i	0.979137	−	0.203199i	$-0.0651339\pi$
$89$	43.0149	+	59.2049i	0.483314	+	0.665224i	−0.495824	+	0.868423i	$0.665134\pi$
$90$		0			0
$91$	−188.880	−	137.229i	−2.07560	−	1.50801i
$92$	−23.5641	+	46.2471i	−0.256131	+	0.502686i
$93$	13.6733	−	13.6733i	0.147025	−	0.147025i
$94$	−12.3321	+	4.00695i	−0.131193	+	0.0426271i
$95$		0			0
$96$	0.972653	−	2.99352i	0.0101318	−	0.0311825i
$97$	−67.9854	+	34.6403i	−0.700880	+	0.357116i	−0.767842	−	0.640639i	$-0.778669\pi$
$97$	−67.9854	+	34.6403i	−0.700880	+	0.357116i	0.0669620	+	0.997756i	$0.478669\pi$
$98$	−12.1215	+	76.5319i	−0.123688	+	0.780938i
$99$		−	49.0800i		−	0.495758i
$100$		0			0
$101$	156.192			1.54646			0.773228	−	0.634128i	$-0.218641\pi$
$101$	156.192			1.54646			0.773228	+	0.634128i	$0.218641\pi$
$102$	−13.8819	−	2.19868i	−0.136097	−	0.0215557i
$103$	−73.4520	−	144.158i	−0.713127	−	1.39959i	−0.908088	−	0.418779i	$-0.862458\pi$
$103$	−73.4520	−	144.158i	−0.713127	−	1.39959i	0.194962	−	0.980811i	$-0.437542\pi$
$104$	61.6453	+	20.0298i	0.592743	+	0.192594i
$105$		0			0
$106$	12.4076	+	38.1868i	0.117053	+	0.360252i
$107$	125.552	+	125.552i	1.17338	+	1.17338i	0.981399	+	0.191981i	$0.0614913\pi$
$107$	125.552	+	125.552i	1.17338	+	1.17338i	0.191981	+	0.981399i	$0.438509\pi$
$108$	−17.5408	−	8.93748i	−0.162415	−	0.0827544i
$109$	52.2004	−	71.8476i	0.478902	−	0.659153i	−0.499391	−	0.866377i	$-0.666443\pi$
$109$	52.2004	−	71.8476i	0.478902	−	0.659153i	0.978294	+	0.207224i	$0.0664429\pi$
$110$		0			0
$111$	−6.98533	+	5.07514i	−0.0629309	+	0.0457220i
$112$	−6.37488	−	40.2494i	−0.0569186	−	0.359370i
$113$	−23.7002	+	3.75375i	−0.209736	+	0.0332190i	−0.260418	−	0.965496i	$-0.583861\pi$
$113$	−23.7002	+	3.75375i	−0.209736	+	0.0332190i	0.0506820	+	0.998715i	$0.483861\pi$
$114$	6.61535	+	9.10525i	0.0580294	+	0.0798706i
$115$		0			0
$116$	−25.1949	−	18.3052i	−0.217197	−	0.157803i
$117$	90.4138	−	177.447i	0.772768	−	1.51664i
$118$	−39.6514	+	39.6514i	−0.336029	+	0.336029i
$119$	−173.061	+	56.2310i	−1.45430	+	0.472529i
$120$		0			0
$121$	−27.5348	+	84.7434i	−0.227560	+	0.700359i
$122$	17.9445	−	9.14320i	0.147086	−	0.0749443i
$123$	−4.01826	+	25.3703i	−0.0326688	+	0.206263i
$124$			69.5054i			0.560527i
$125$		0			0
$126$	−125.209			−0.993719
$127$	30.8349	+	4.88376i	0.242794	+	0.0384548i	0.276645	−	0.960972i	$-0.410777\pi$
$127$	30.8349	+	4.88376i	0.242794	+	0.0384548i	−0.0338513	+	0.999427i	$0.510777\pi$
$128$	5.13632	+	10.0806i	0.0401275	+	0.0787546i
$129$	−23.8446	−	7.74759i	−0.184842	−	0.0600588i
$130$		0			0
$131$	39.8145	+	122.536i	0.303928	+	0.935393i	0.980075	+	0.198627i	$0.0636481\pi$
$131$	39.8145	+	122.536i	0.303928	+	0.935393i	−0.676148	+	0.736766i	$0.736352\pi$
$132$	−4.44407	−	4.44407i	−0.0336672	−	0.0336672i
$133$	129.831	+	66.1523i	0.976174	+	0.497386i
$134$	−45.5242	+	62.6587i	−0.339733	+	0.467602i
$135$		0			0
$136$	40.8711	−	29.6946i	0.300523	−	0.218343i
$137$	4.80456	+	30.3348i	0.0350698	+	0.221422i	0.998999	−	0.0447377i	$-0.0142452\pi$
$137$	4.80456	+	30.3348i	0.0350698	+	0.221422i	−0.963929	+	0.266159i	$0.914245\pi$
$138$	20.1702	−	3.19464i	0.146161	−	0.0231496i
$139$	−100.363	−	138.137i	−0.722034	−	0.993794i	−0.999454	−	0.0330456i	$-0.989479\pi$
$139$	−100.363	−	138.137i	−0.722034	−	0.993794i	0.277420	−	0.960749i	$-0.410521\pi$
$140$		0			0
$141$	4.12738	+	2.99872i	0.0292722	+	0.0212675i
$142$	−49.6379	+	97.4199i	−0.349563	+	0.686056i
$143$	91.5163	−	91.5163i	0.639974	−	0.639974i
$144$	33.0602	−	10.7419i	0.229585	−	0.0745967i
$145$		0			0
$146$	−43.2429	+	133.088i	−0.296184	+	0.911561i
$147$	27.1637	−	13.8406i	0.184787	−	0.0941538i
$148$	4.85502	−	30.6534i	0.0328042	−	0.207117i
$149$		−	23.7099i		−	0.159127i	−0.996830	−	0.0795635i	$-0.974647\pi$
$149$		−	23.7099i		−	0.159127i	0.996830	−	0.0795635i	$-0.0253527\pi$
$150$		0			0
$151$	207.294			1.37281			0.686403	−	0.727222i	$-0.259189\pi$
$151$	207.294			1.37281			0.686403	+	0.727222i	$0.259189\pi$
$152$	−39.9561	−	6.32843i	−0.262869	−	0.0416344i
$153$	−70.4694	−	138.304i	−0.460584	−	0.903948i
$154$	−77.3866	−	25.1444i	−0.502510	−	0.163275i
$155$		0			0
$156$	−7.88064	−	24.2541i	−0.0505169	−	0.155475i
$157$	−25.6746	−	25.6746i	−0.163533	−	0.163533i	0.620597	−	0.784130i	$-0.286890\pi$
$157$	−25.6746	−	25.6746i	−0.163533	−	0.163533i	−0.784130	+	0.620597i	$0.786890\pi$
$158$	146.267	+	74.5270i	0.925743	+	0.471690i
$159$	9.28562	−	12.7806i	0.0584001	−	0.0803808i
$160$		0			0
$161$	213.900	−	155.407i	1.32857	−	0.965263i
$162$	−16.0917	−	101.599i	−0.0993312	−	0.627153i
$163$	−81.5666	+	12.9189i	−0.500408	+	0.0792569i	−0.401536	−	0.915843i	$-0.631524\pi$
$163$	−81.5666	+	12.9189i	−0.500408	+	0.0792569i	−0.0988723	+	0.995100i	$0.531524\pi$
$164$	−54.2692	−	74.6952i	−0.330910	−	0.455458i
$165$		0			0
$166$	17.5385	+	12.7424i	0.105653	+	0.0767617i
$167$	−23.8290	+	46.7671i	−0.142689	+	0.280043i	−0.951280	−	0.308328i	$-0.900230\pi$
$167$	−23.8290	+	46.7671i	−0.142689	+	0.280043i	0.808591	+	0.588371i	$0.200230\pi$
$168$	−11.3373	+	11.3373i	−0.0674840	+	0.0674840i
$169$	338.734	−	110.061i	2.00434	−	0.651251i
$170$		0			0
$171$	−38.4097	+	118.213i	−0.224618	+	0.691303i
$172$	80.2961	−	40.9129i	0.466838	−	0.237866i
$173$	6.98501	−	44.1016i	0.0403758	−	0.254923i	−0.959241	−	0.282588i	$-0.908807\pi$
$173$	6.98501	−	44.1016i	0.0403758	−	0.254923i	0.999617	+	0.0276651i	$0.00880720\pi$
$174$			12.2529i			0.0704192i
$175$		0			0
$176$	22.5904			0.128355
$177$	21.7911	+	3.45137i	0.123113	+	0.0194993i
$178$	46.9853	+	92.2138i	0.263962	+	0.518055i
$179$	−310.306	−	100.824i	−1.73355	−	0.563265i	−0.739596	−	0.673051i	$-0.764983\pi$
$179$	−310.306	−	100.824i	−1.73355	−	0.563265i	−0.993955	+	0.109787i	$0.964983\pi$
$180$		0			0
$181$	25.5973	+	78.7805i	0.141422	+	0.435251i	0.996534	−	0.0831923i	$-0.0265116\pi$
$181$	25.5973	+	78.7805i	0.141422	+	0.435251i	−0.855112	+	0.518444i	$0.826512\pi$
$182$	−233.468	−	233.468i	−1.28279	−	1.28279i
$183$	−7.06022	−	3.59736i	−0.0385804	−	0.0196577i
$184$	−43.1457	+	59.3849i	−0.234487	+	0.322744i
$185$		0			0
$186$	22.1239	−	16.0740i	0.118946	−	0.0864191i
$187$	−15.7802	−	99.6320i	−0.0843859	−	0.532791i
$188$	−18.1120	+	2.86866i	−0.0963404	+	0.0152588i
$189$	58.9436	+	81.1289i	0.311871	+	0.429253i
$190$		0			0
$191$	112.018	+	81.3859i	0.586482	+	0.426104i	0.841055	−	0.540950i	$-0.181935\pi$
$191$	112.018	+	81.3859i	0.586482	+	0.426104i	−0.254573	+	0.967053i	$0.581935\pi$
$192$	2.02087	−	3.96617i	0.0105253	−	0.0206571i
$193$	14.7833	−	14.7833i	0.0765975	−	0.0765975i	−0.667770	−	0.744368i	$-0.732751\pi$
$193$	14.7833	−	14.7833i	0.0765975	−	0.0765975i	0.744368	+	0.667770i	$0.232751\pi$
$194$	−102.626	+	33.3451i	−0.528998	+	0.171882i
$195$		0			0
$196$	−33.8626	+	104.218i	−0.172768	+	0.531726i
$197$	5.58697	−	2.84670i	0.0283602	−	0.0144503i	−0.439753	−	0.898119i	$-0.644934\pi$
$197$	5.58697	−	2.84670i	0.0283602	−	0.0144503i	0.468113	+	0.883669i	$0.344934\pi$
$198$	10.8581	−	68.5551i	0.0548387	−	0.346238i
$199$		−	244.037i		−	1.22632i	−0.789961	−	0.613158i	$-0.789899\pi$
$199$		−	244.037i		−	1.22632i	0.789961	−	0.613158i	$-0.210101\pi$
$200$		0			0
$201$	30.4726			0.151605
$202$	218.169	+	34.5546i	1.08005	+	0.171063i
$203$	72.0197	+	141.347i	0.354777	+	0.696288i
$204$	−18.9039	−	6.14224i	−0.0926661	−	0.0301090i
$205$		0			0
$206$	−70.7057	−	217.610i	−0.343232	−	1.05636i
$207$	159.477	+	159.477i	0.770421	+	0.770421i
$208$	81.6750	+	41.6155i	0.392668	+	0.200075i
$209$	−47.4791	+	65.3493i	−0.227173	+	0.312676i
$210$		0			0
$211$	−128.663	+	93.4793i	−0.609778	+	0.443030i	−0.849336	−	0.527852i	$-0.822998\pi$
$211$	−128.663	+	93.4793i	−0.609778	+	0.443030i	0.239558	+	0.970882i	$0.422998\pi$
$212$	8.88288	+	56.0843i	0.0419004	+	0.264549i
$213$	42.4886	−	6.72953i	0.199477	−	0.0315940i
$214$	147.595	+	203.147i	0.689695	+	0.949284i
$215$		0			0
$216$	−22.5238	−	16.3645i	−0.104277	−	0.0757614i
$217$	160.737	−	315.463i	0.740721	−	1.45375i
$218$	88.8086	−	88.8086i	0.407379	−	0.407379i
$219$	52.3629	−	17.0138i	0.239100	−	0.0776884i
$220$		0			0
$221$	126.487	−	389.286i	0.572338	−	1.76147i
$222$	−10.8799	+	5.54359i	−0.0490086	+	0.0249711i
$223$	59.4523	−	375.367i	0.266602	−	1.68326i	−0.383601	−	0.923499i	$-0.625316\pi$
$223$	59.4523	−	375.367i	0.266602	−	1.68326i	0.650203	−	0.759761i	$-0.274684\pi$
$224$		−	57.6308i		−	0.257280i
$225$		0			0
$226$	−33.9350			−0.150155
$227$	−178.162	−	28.2180i	−0.784853	−	0.124309i	−0.248870	−	0.968537i	$-0.580059\pi$
$227$	−178.162	−	28.2180i	−0.784853	−	0.124309i	−0.535983	+	0.844228i	$0.680059\pi$
$228$	7.22597	+	14.1818i	0.0316928	+	0.0622007i
$229$	24.3355	+	7.90707i	0.106268	+	0.0345287i	0.361669	−	0.932307i	$-0.382207\pi$
$229$	24.3355	+	7.90707i	0.106268	+	0.0345287i	−0.255400	+	0.966835i	$0.582207\pi$
$230$		0			0
$231$	9.89298	+	30.4475i	0.0428268	+	0.131807i
$232$	−31.1426	−	31.1426i	−0.134235	−	0.134235i
$233$	244.770	+	124.717i	1.05052	+	0.535265i	0.891974	−	0.452088i	$-0.149321\pi$
$233$	244.770	+	124.717i	1.05052	+	0.535265i	0.158542	+	0.987352i	$0.449321\pi$
$234$	165.547	−	227.856i	0.707467	−	0.973744i
$235$		0			0
$236$	−64.1573	+	46.6130i	−0.271853	+	0.197513i
$237$	−10.1038	−	63.7929i	−0.0426321	−	0.269168i
$238$	−254.172	+	40.2570i	−1.06795	+	0.169147i
$239$	63.7205	+	87.7038i	0.266613	+	0.366962i	0.921243	−	0.388988i	$-0.127175\pi$
$239$	63.7205	+	87.7038i	0.266613	+	0.366962i	−0.654630	+	0.755950i	$0.727175\pi$
$240$		0			0
$241$	−299.048	−	217.271i	−1.24086	−	0.901541i	−0.243209	−	0.969974i	$-0.578200\pi$
$241$	−299.048	−	217.271i	−1.24086	−	0.901541i	−0.997656	+	0.0684333i	$0.978200\pi$
$242$	−57.2086	+	112.278i	−0.236399	+	0.463959i
$243$	−91.2600	+	91.2600i	−0.375556	+	0.375556i
$244$	27.0877	−	8.80134i	0.111015	−	0.0360711i
$245$		0			0
$246$	−11.2254	+	34.5483i	−0.0456318	+	0.140440i
$247$	−292.044	+	148.804i	−1.18236	+	0.602444i
$248$	−15.3768	+	97.0853i	−0.0620032	+	0.391473i
$249$		−	8.52943i		−	0.0342547i
$250$		0			0
$251$	−20.6897			−0.0824293			−0.0412146	−	0.999150i	$-0.513123\pi$
$251$	−20.6897			−0.0824293			−0.0412146	+	0.999150i	$0.513123\pi$
$252$	−174.892	−	27.7001i	−0.694015	−	0.109921i
$253$	66.5404	+	130.593i	0.263005	+	0.516177i
$254$	41.9898	+	13.6433i	0.165314	+	0.0537138i
$255$		0			0
$256$	4.94427	+	15.2169i	0.0193136	+	0.0594410i
$257$	57.5934	+	57.5934i	0.224099	+	0.224099i	0.810222	−	0.586123i	$-0.199347\pi$
$257$	57.5934	+	57.5934i	0.224099	+	0.224099i	−0.586123	+	0.810222i	$0.699347\pi$
$258$	−31.5922	−	16.0970i	−0.122450	−	0.0623916i
$259$	−92.9237	+	127.899i	−0.358779	+	0.493817i
$260$		0			0
$261$	−109.477	+	79.5396i	−0.419452	+	0.304749i
$262$	28.5040	+	179.967i	0.108794	+	0.686898i
$263$	−86.6150	+	13.7185i	−0.329335	+	0.0521615i	−0.318912	−	0.947784i	$-0.603318\pi$
$263$	−86.6150	+	13.7185i	−0.329335	+	0.0521615i	−0.0104222	+	0.999946i	$0.503318\pi$
$264$	−5.22431	−	7.19065i	−0.0197891	−	0.0272373i
$265$		0			0
$266$	166.713	+	121.124i	0.626742	+	0.455355i
$267$	18.4862	−	36.2812i	0.0692367	−	0.135885i
$268$	−77.4504	+	77.4504i	−0.288994	+	0.288994i
$269$	−79.3898	+	25.7953i	−0.295129	+	0.0958934i	−0.452839	−	0.891592i	$-0.649589\pi$
$269$	−79.3898	+	25.7953i	−0.295129	+	0.0958934i	0.157710	+	0.987485i	$0.449589\pi$
$270$		0			0
$271$	33.5180	−	103.158i	0.123683	−	0.380656i	−0.869976	−	0.493094i	$-0.835866\pi$
$271$	33.5180	−	103.158i	0.123683	−	0.380656i	0.993659	+	0.112438i	$0.0358658\pi$
$272$	63.6583	−	32.4355i	0.234038	−	0.119248i
$273$	−20.3217	+	128.306i	−0.0744386	+	0.469987i
$274$			43.4346i			0.158520i
$275$		0			0
$276$	28.8805			0.104639
$277$	55.6330	+	8.81141i	0.200841	+	0.0318101i	0.256044	−	0.966665i	$-0.417581\pi$
$277$	55.6330	+	8.81141i	0.200841	+	0.0318101i	−0.0552032	+	0.998475i	$0.517581\pi$
$278$	−109.626	−	215.154i	−0.394340	−	0.773935i
$279$	287.233	+	93.3277i	1.02951	+	0.334508i
$280$		0			0
$281$	98.2119	+	302.265i	0.349509	+	1.07568i	0.959126	+	0.282981i	$0.0913233\pi$
$281$	98.2119	+	302.265i	0.349509	+	1.07568i	−0.609617	+	0.792696i	$0.708677\pi$
$282$	5.10172	+	5.10172i	0.0180912	+	0.0180912i
$283$	−426.824	−	217.478i	−1.50821	−	0.768472i	−0.512300	−	0.858807i	$-0.671206\pi$
$283$	−426.824	−	217.478i	−1.50821	−	0.768472i	−0.995911	+	0.0903348i	$0.971206\pi$
$284$	−90.8867	+	125.095i	−0.320024	+	0.440475i
$285$		0			0
$286$	148.076	−	107.584i	0.517750	−	0.376167i
$287$	73.5727	+	464.520i	0.256351	+	1.61854i
$288$	48.5551	−	7.69037i	0.168594	−	0.0267027i
$289$	−17.6497	−	24.2927i	−0.0610716	−	0.0840579i
$290$		0			0
$291$	34.3473	+	24.9548i	0.118032	+	0.0857553i
$292$	−89.8450	+	176.331i	−0.307688	+	0.603872i
$293$	−385.350	+	385.350i	−1.31519	+	1.31519i	−0.397652	+	0.917536i	$0.630175\pi$
$293$	−385.350	+	385.350i	−1.31519	+	1.31519i	−0.917536	+	0.397652i	$0.869825\pi$
$294$	41.0043	−	13.3231i	0.139470	−	0.0453167i
$295$		0			0
$296$	13.5630	−	41.7426i	0.0458210	−	0.141022i
$297$	−49.5318	+	25.2377i	−0.166774	+	0.0849754i
$298$	5.24539	−	33.1181i	0.0176020	−	0.111135i
$299$			594.733i			1.98907i
$300$		0			0
$301$	−459.053			−1.52509
$302$	289.548	+	45.8599i	0.958769	+	0.151854i
$303$	−39.4554	−	77.4356i	−0.130216	−	0.255563i
$304$	−54.4108	−	17.6791i	−0.178983	−	0.0581550i
$305$		0			0
$306$	−67.8346	−	208.773i	−0.221682	−	0.682266i
$307$	−40.8331	−	40.8331i	−0.133007	−	0.133007i	0.637469	−	0.770476i	$-0.279981\pi$
$307$	−40.8331	−	40.8331i	−0.133007	−	0.133007i	−0.770476	+	0.637469i	$0.779981\pi$
$308$	−102.531	−	52.2422i	−0.332893	−	0.169617i
$309$	−52.9147	+	72.8308i	−0.171245	+	0.235699i
$310$		0			0
$311$	−419.194	+	304.562i	−1.34789	+	0.979299i	−0.348776	+	0.937206i	$0.613403\pi$
$311$	−419.194	+	304.562i	−1.34789	+	0.979299i	−0.999114	+	0.0420933i	$0.986597\pi$
$312$	−5.64191	−	35.6216i	−0.0180831	−	0.114172i
$313$	199.049	−	31.5263i	0.635940	−	0.100723i	0.169864	−	0.985468i	$-0.445667\pi$
$313$	199.049	−	31.5263i	0.635940	−	0.100723i	0.466076	+	0.884745i	$0.345667\pi$
$314$	−30.1823	−	41.5424i	−0.0961221	−	0.132301i
$315$		0			0
$316$	187.819	+	136.458i	0.594364	+	0.431831i
$317$	−215.645	+	423.227i	−0.680268	+	1.33510i	0.250009	+	0.968243i	$0.419566\pi$
$317$	−215.645	+	423.227i	−0.680268	+	1.33510i	−0.930277	+	0.366857i	$0.880434\pi$
$318$	15.7976	−	15.7976i	0.0496781	−	0.0496781i
$319$	−83.6366	+	27.1752i	−0.262184	+	0.0851886i
$320$		0			0
$321$	30.5295	−	93.9603i	0.0951076	−	0.292711i
$322$	333.157	−	169.752i	1.03465	−	0.527180i
$323$	−39.9636	+	252.321i	−0.123726	+	0.781178i
$324$		−	145.473i		−	0.448992i
$325$		0			0
$326$	−116.790			−0.358253
$327$	−48.8062	−	7.73015i	−0.149255	−	0.0236396i
$328$	−59.2784	−	116.340i	−0.180727	−	0.354697i
$329$	88.8387	+	28.8654i	0.270026	+	0.0877369i
$330$		0			0
$331$	−128.800	−	396.407i	−0.389125	−	1.19760i	−0.933443	−	0.358725i	$-0.883211\pi$
$331$	−128.800	−	396.407i	−0.389125	−	1.19760i	0.544318	−	0.838879i	$-0.316789\pi$
$332$	21.6787	+	21.6787i	0.0652974	+	0.0652974i
$333$	−120.157	−	61.2231i	−0.360832	−	0.183853i
$334$	−43.6308	+	60.0527i	−0.130631	+	0.179798i
$335$		0			0
$336$	−18.3442	+	13.3278i	−0.0545957	+	0.0396661i
$337$	−33.4503	−	211.197i	−0.0992591	−	0.626697i	−0.986294	−	0.164996i	$-0.947239\pi$
$337$	−33.4503	−	211.197i	−0.0992591	−	0.626697i	0.887035	−	0.461702i	$-0.152761\pi$
$338$	497.494	−	78.7953i	1.47188	−	0.233122i
$339$	7.84787	+	10.8017i	0.0231501	+	0.0318633i
$340$		0			0
$341$	158.786	+	115.364i	0.465647	+	0.338312i
$342$	−79.8032	+	156.623i	−0.233343	+	0.457961i
$343$	41.7160	−	41.7160i	0.121621	−	0.121621i
$344$	121.209	−	39.3832i	0.352352	−	0.114486i
$345$		0			0
$346$	19.5133	−	60.0559i	0.0563970	−	0.173572i
$347$	113.136	−	57.6455i	0.326039	−	0.166125i	−0.283307	−	0.959029i	$-0.591432\pi$
$347$	113.136	−	57.6455i	0.326039	−	0.166125i	0.609347	+	0.792904i	$0.291432\pi$
$348$	−2.71074	+	17.1149i	−0.00778949	+	0.0491809i
$349$			117.679i			0.337189i	0.985686	+	0.168594i	$0.0539228\pi$
$349$			117.679i			0.337189i	−0.985686	+	0.168594i	$0.946077\pi$
$350$		0			0
$351$	−225.573			−0.642657
$352$	31.5544	+	4.99772i	0.0896432	+	0.0141981i
$353$	24.8731	+	48.8161i	0.0704619	+	0.138289i	0.923551	−	0.383477i	$-0.125273\pi$
$353$	24.8731	+	48.8161i	0.0704619	+	0.138289i	−0.853089	+	0.521766i	$0.825273\pi$
$354$	29.6743	+	9.64176i	0.0838256	+	0.0272366i
$355$		0			0
$356$	45.2285	+	139.199i	0.127046	+	0.391009i
$357$	71.5944	+	71.5944i	0.200545	+	0.200545i
$358$	−411.130	−	209.481i	−1.14841	−	0.585143i
$359$	269.868	−	371.442i	0.751723	−	1.03466i	−0.246135	−	0.969236i	$-0.579161\pi$
$359$	269.868	−	371.442i	0.751723	−	1.03466i	0.997858	−	0.0654220i	$-0.0208394\pi$
$360$		0			0
$361$	−126.556	+	91.9485i	−0.350571	+	0.254705i
$362$	18.3257	+	115.704i	0.0506234	+	0.319624i
$363$	48.9689	−	7.75591i	0.134900	−	0.0213661i
$364$	−274.458	−	377.760i	−0.754007	−	1.03780i
$365$		0			0
$366$	−9.06588	−	6.58674i	−0.0247702	−	0.0179966i
$367$	254.971	−	500.410i	0.694745	−	1.36351i	−0.226300	−	0.974058i	$-0.572663\pi$
$367$	254.971	−	500.410i	0.694745	−	1.36351i	0.921045	−	0.389456i	$-0.127337\pi$
$368$	−73.4038	+	73.4038i	−0.199467	+	0.199467i
$369$	−381.550	+	123.973i	−1.03401	+	0.335970i
$370$		0			0
$371$	89.3826	−	275.091i	0.240924	−	0.741486i
$372$	34.4588	−	17.5576i	0.0926311	−	0.0471979i
$373$	29.4686	−	186.058i	0.0790044	−	0.498814i	−0.916178	−	0.400772i	$-0.868742\pi$
$373$	29.4686	−	186.058i	0.0790044	−	0.498814i	0.995182	−	0.0980422i	$-0.0312580\pi$
$374$		−	142.657i		−	0.381437i
$375$		0			0
$376$	−25.9335			−0.0689721
$377$	−352.447	−	55.8220i	−0.934871	−	0.148069i
$378$	64.3842	+	126.361i	0.170329	+	0.334289i
$379$	−22.7930	−	7.40589i	−0.0601398	−	0.0195406i	0.278793	−	0.960351i	$-0.410066\pi$
$379$	−22.7930	−	7.40589i	−0.0601398	−	0.0195406i	−0.338932	+	0.940811i	$0.610066\pi$
$380$		0			0
$381$	−5.36791	−	16.5207i	−0.0140890	−	0.0433615i
$382$	138.462	+	138.462i	0.362466	+	0.362466i
$383$	14.2210	+	7.24595i	0.0371305	+	0.0189189i	0.472457	−	0.881354i	$-0.343367\pi$
$383$	14.2210	+	7.24595i	0.0371305	+	0.0189189i	−0.435327	+	0.900273i	$0.643367\pi$
$384$	3.70019	−	5.09288i	0.00963592	−	0.0132627i
$385$		0			0
$386$	23.9199	−	17.3788i	0.0619687	−	0.0450229i
$387$	−61.2570	−	386.761i	−0.158287	−	0.999383i
$388$	−150.725	+	23.8724i	−0.388466	+	0.0615269i
$389$	143.389	+	197.358i	0.368610	+	0.507348i	0.952522	−	0.304469i	$-0.0984789\pi$
$389$	143.389	+	197.358i	0.368610	+	0.507348i	−0.583913	+	0.811817i	$0.698479\pi$
$390$		0			0
$391$	375.012	+	272.462i	0.959110	+	0.696834i
$392$	−70.3557	+	138.081i	−0.179479	+	0.352247i
$393$	50.6926	−	50.6926i	0.128989	−	0.128989i
$394$	8.43367	−	2.74026i	0.0214052	−	0.00695499i
$395$		0			0
$396$	30.3331	−	93.3557i	0.0765988	−	0.235747i
$397$	−191.548	+	97.5985i	−0.482488	+	0.245840i	−0.678277	−	0.734806i	$-0.737273\pi$
$397$	−191.548	+	97.5985i	−0.482488	+	0.245840i	0.195789	+	0.980646i	$0.437273\pi$
$398$	53.9887	−	340.871i	0.135650	−	0.856460i
$399$		−	81.0772i		−	0.203201i
$400$		0			0
$401$	517.832			1.29135			0.645676	−	0.763612i	$-0.276576\pi$
$401$	517.832			1.29135			0.645676	+	0.763612i	$0.276576\pi$
$402$	42.5642	+	6.74150i	0.105881	+	0.0167699i
$403$	361.563	+	709.607i	0.897178	+	1.76081i
$404$	297.095	+	96.5320i	0.735384	+	0.238941i
$405$		0			0
$406$	69.3269	+	213.366i	0.170756	+	0.525533i
$407$	−61.9696	−	61.9696i	−0.152259	−	0.152259i
$408$	−25.0461	−	12.7616i	−0.0613876	−	0.0312785i
$409$	−111.733	+	153.787i	−0.273186	+	0.376008i	−0.923462	−	0.383690i	$-0.874653\pi$
$409$	−111.733	+	153.787i	−0.273186	+	0.376008i	0.650276	+	0.759698i	$0.274653\pi$
$410$		0			0
$411$	13.8254	−	10.0448i	0.0336386	−	0.0244398i
$412$	−50.6197	−	319.600i	−0.122863	−	0.775729i
$413$	398.986	−	63.1932i	0.966068	−	0.153010i
$414$	187.477	+	258.039i	0.452842	+	0.623284i
$415$		0			0
$416$	104.877	+	76.1977i	0.252109	+	0.183168i
$417$	−43.1321	+	84.6516i	−0.103434	+	0.203001i
$418$	−80.7762	+	80.7762i	−0.193245	+	0.193245i
$419$	−101.900	+	33.1094i	−0.243199	+	0.0790200i	−0.428080	−	0.903741i	$-0.640810\pi$
$419$	−101.900	+	33.1094i	−0.243199	+	0.0790200i	0.184882	+	0.982761i	$0.440810\pi$
$420$		0			0
$421$	113.217	−	348.447i	0.268925	−	0.827666i	−0.721838	−	0.692062i	$-0.756703\pi$
$421$	113.217	−	348.447i	0.268925	−	0.827666i	0.990763	−	0.135604i	$-0.0432975\pi$
$422$	−200.398	+	102.108i	−0.474876	+	0.241961i
$423$	−12.4649	+	78.7002i	−0.0294678	+	0.186053i
$424$			80.3039i			0.189396i
$425$		0			0
$426$	60.8369			0.142810
$427$	−143.297	−	22.6960i	−0.335589	−	0.0531521i
$428$	161.218	+	316.409i	0.376678	+	0.739272i
$429$	−68.4889	−	22.2534i	−0.159648	−	0.0518727i
$430$		0			0
$431$	28.4314	+	87.5029i	0.0659662	+	0.203023i	0.978607	−	0.205740i	$-0.0659602\pi$
$431$	28.4314	+	87.5029i	0.0659662	+	0.203023i	−0.912640	+	0.408763i	$0.865960\pi$
$432$	−27.8409	−	27.8409i	−0.0644465	−	0.0644465i
$433$	38.7505	+	19.7444i	0.0894932	+	0.0455990i	0.498164	−	0.867083i	$-0.334008\pi$
$433$	38.7505	+	19.7444i	0.0894932	+	0.0455990i	−0.408671	+	0.912682i	$0.634008\pi$
$434$	294.308	−	405.080i	0.678128	−	0.933363i
$435$		0			0
$436$	143.695	−	104.401i	0.329576	−	0.239451i
$437$	−58.0664	−	366.617i	−0.132875	−	0.838940i
$438$	76.9047	−	12.1805i	0.175581	−	0.0278094i
$439$	−452.403	−	622.679i	−1.03053	−	1.41840i	−0.904548	−	0.426371i	$-0.859792\pi$
$439$	−452.403	−	622.679i	−1.03053	−	1.41840i	−0.125982	−	0.992033i	$-0.540208\pi$
$440$		0			0
$441$	385.217	+	279.876i	0.873507	+	0.634640i
$442$	262.799	−	515.773i	0.594569	−	1.16691i
$443$	479.183	−	479.183i	1.08168	−	1.08168i	0.0853248	−	0.996353i	$-0.472807\pi$
$443$	479.183	−	479.183i	1.08168	−	1.08168i	0.996353	−	0.0853248i	$-0.0271928\pi$
$444$	−16.4235	+	5.33632i	−0.0369898	+	0.0120187i
$445$		0			0
$446$	166.086	−	511.161i	0.372390	−	1.14610i
$447$	−11.7547	+	5.98932i	−0.0262969	+	0.0133989i
$448$	12.7498	−	80.4988i	0.0284593	−	0.179685i
$449$		−	889.585i		−	1.98126i	−0.136578	−	0.990629i	$-0.543610\pi$
$449$		−	889.585i		−	1.98126i	0.136578	−	0.990629i	$-0.456390\pi$
$450$		0			0
$451$	−260.717			−0.578087
$452$	−47.4004	−	7.50749i	−0.104868	−	0.0166095i
$453$	−52.3641	−	102.770i	−0.115594	−	0.226866i
$454$	−242.614	−	78.8300i	−0.534392	−	0.173634i
$455$		0			0
$456$	6.95579	+	21.4077i	0.0152539	+	0.0469468i
$457$	−46.1201	−	46.1201i	−0.100919	−	0.100919i	0.654844	−	0.755764i	$-0.272734\pi$
$457$	−46.1201	−	46.1201i	−0.100919	−	0.100919i	−0.755764	+	0.654844i	$0.772734\pi$
$458$	32.2425	+	16.4284i	0.0703985	+	0.0358698i
$459$	−103.341	+	142.236i	−0.225143	+	0.309883i
$460$		0			0
$461$	−625.212	+	454.243i	−1.35621	+	0.985343i	−0.357532	+	0.933901i	$0.616382\pi$
$461$	−625.212	+	454.243i	−1.35621	+	0.985343i	−0.998676	+	0.0514415i	$0.983618\pi$
$462$	7.08259	+	44.7177i	0.0153303	+	0.0967916i
$463$	449.918	−	71.2599i	0.971744	−	0.153909i	0.349675	−	0.936871i	$-0.386292\pi$
$463$	449.918	−	71.2599i	0.971744	−	0.153909i	0.622069	+	0.782962i	$0.286292\pi$
$464$	−36.6103	−	50.3898i	−0.0789016	−	0.108599i
$465$		0			0
$466$	314.304	+	228.355i	0.674473	+	0.490033i
$467$	158.701	−	311.468i	0.339830	−	0.666955i	−0.656333	−	0.754472i	$-0.727893\pi$
$467$	158.701	−	311.468i	0.339830	−	0.666955i	0.996163	+	0.0875169i	$0.0278932\pi$
$468$	281.646	−	281.646i	0.601807	−	0.601807i
$469$	530.633	−	172.413i	1.13141	−	0.367619i
$470$		0			0
$471$	−6.24313	+	19.2144i	−0.0132551	+	0.0407949i
$472$	−99.9273	+	50.9155i	−0.211710	+	0.107872i
$473$	39.8090	−	251.344i	0.0841627	−	0.531382i
$474$		−	91.3413i		−	0.192703i
$475$		0			0
$476$	−363.935			−0.764569
$477$	243.698	+	38.5979i	0.510896	+	0.0809180i
$478$	69.6021	+	136.602i	0.145611	+	0.285778i
$479$	49.6354	+	16.1275i	0.103623	+	0.0336692i	0.360370	−	0.932810i	$-0.382651\pi$
$479$	49.6354	+	16.1275i	0.103623	+	0.0336692i	−0.256747	+	0.966479i	$0.582651\pi$
$480$		0			0
$481$	−109.890	−	338.207i	−0.228462	−	0.703134i
$482$	−369.644	−	369.644i	−0.766896	−	0.766896i
$483$	−131.079	−	66.7883i	−0.271386	−	0.138278i
$484$	−104.749	+	144.174i	−0.216423	+	0.297880i
$485$		0			0
$486$	−147.662	+	107.283i	−0.303831	+	0.220746i
$487$	93.1133	+	587.894i	0.191198	+	1.20718i	0.877398	+	0.479763i	$0.159277\pi$
$487$	93.1133	+	587.894i	0.191198	+	1.20718i	−0.686200	+	0.727413i	$0.740723\pi$
$488$	39.7834	−	6.30106i	0.0815233	−	0.0129120i
$489$	27.0092	+	37.1750i	0.0552335	+	0.0760224i
$490$		0			0
$491$	−109.988	−	79.9113i	−0.224009	−	0.162752i	0.470120	−	0.882602i	$-0.344210\pi$
$491$	−109.988	−	79.9113i	−0.224009	−	0.162752i	−0.694129	+	0.719850i	$0.744210\pi$
$492$	−23.3229	+	45.7737i	−0.0474042	+	0.0930361i
$493$	−196.664	+	196.664i	−0.398912	+	0.398912i
$494$	−440.847	+	143.240i	−0.892404	+	0.289960i
$495$		0			0
$496$	−42.9567	+	132.207i	−0.0866062	+	0.266547i
$497$	701.798	−	357.584i	1.41207	−	0.719485i
$498$	1.88698	−	11.9139i	0.00378912	−	0.0239235i
$499$			483.808i			0.969555i	0.874637	+	0.484778i	$0.161099\pi$
$499$			483.808i			0.969555i	−0.874637	+	0.484778i	$0.838901\pi$
$500$		0			0
$501$	29.2052			0.0582938
$502$	−28.8995	−	4.57723i	−0.0575687	−	0.00911799i
$503$	141.234	+	277.188i	0.280784	+	0.551070i	0.987725	−	0.156203i	$-0.0499253\pi$
$503$	141.234	+	277.188i	0.280784	+	0.551070i	−0.706941	+	0.707273i	$0.749925\pi$
$504$	−238.161	−	77.3832i	−0.472542	−	0.153538i
$505$		0			0
$506$	64.0525	+	197.133i	0.126586	+	0.389591i
$507$	−140.132	−	140.132i	−0.276395	−	0.276395i
$508$	55.6331	+	28.3465i	0.109514	+	0.0558001i
$509$	−177.828	+	244.759i	−0.349367	+	0.480862i	−0.947148	−	0.320797i	$-0.896049\pi$
$509$	−177.828	+	244.759i	−0.349367	+	0.480862i	0.597781	+	0.801659i	$0.296049\pi$
$510$		0			0
$511$	815.557	−	592.537i	1.59600	−	1.15956i
$512$	3.53971	+	22.3488i	0.00691349	+	0.0436501i
$513$	139.052	−	22.0237i	0.271056	−	0.0429311i
$514$	67.7051	+	93.1881i	0.131722	+	0.181300i
$515$		0			0
$516$	−40.5669	−	29.4736i	−0.0786180	−	0.0571193i
$517$	−23.5087	+	46.1384i	−0.0454713	+	0.0892425i
$518$	−158.091	+	158.091i	−0.305196	+	0.305196i
$519$	−23.6288	+	7.67746i	−0.0455275	+	0.0147928i
$520$		0			0
$521$	−114.065	+	351.056i	−0.218935	+	0.673813i	0.779916	+	0.625885i	$0.215262\pi$
$521$	−114.065	+	351.056i	−0.218935	+	0.673813i	−0.998851	+	0.0479282i	$0.984738\pi$
$522$	−170.514	+	86.8813i	−0.326656	+	0.166439i
$523$	−47.6107	+	300.602i	−0.0910338	+	0.574765i	0.899438	+	0.437049i	$0.143976\pi$
$523$	−47.6107	+	300.602i	−0.0910338	+	0.574765i	−0.990472	+	0.137716i	$0.956024\pi$
$524$			257.685i			0.491765i
$525$		0			0
$526$	−124.019			−0.235777
$527$	613.087	+	97.1035i	1.16335	+	0.184257i
$528$	−5.70653	−	11.1997i	−0.0108078	−	0.0212116i
$529$	−137.442	−	44.6576i	−0.259815	−	0.0844189i
$530$		0			0
$531$	106.483	+	327.721i	0.200533	+	0.617177i
$532$	206.069	+	206.069i	0.387348	+	0.387348i
$533$	−942.615	−	480.286i	−1.76851	−	0.901100i
$534$	33.8481	−	46.5879i	0.0633860	−	0.0872433i
$535$		0			0
$536$	−125.317	+	91.0484i	−0.233801	+	0.169866i
$537$	28.3999	+	179.310i	0.0528862	+	0.333910i
$538$	−116.599	+	18.4674i	−0.216726	+	0.0343260i
$539$	181.883	+	250.340i	0.337445	+	0.464453i
$540$		0			0
$541$	724.924	+	526.688i	1.33997	+	0.973545i	0.999445	+	0.0333098i	$0.0106048\pi$
$541$	724.924	+	526.688i	1.33997	+	0.973545i	0.340525	+	0.940235i	$0.389395\pi$
$542$	69.6399	−	136.676i	0.128487	−	0.252170i
$543$	32.5910	−	32.5910i	0.0600203	−	0.0600203i
$544$	96.0938	−	31.2228i	0.176643	−	0.0573948i
$545$		0			0
$546$	−56.7709	+	174.723i	−0.103976	+	0.320005i
$547$	−524.755	+	267.376i	−0.959333	+	0.488804i	−0.862256	−	0.506473i	$-0.830949\pi$
$547$	−524.755	+	267.376i	−0.959333	+	0.488804i	−0.0970765	+	0.995277i	$0.530949\pi$
$548$	−9.60912	+	60.6696i	−0.0175349	+	0.110711i
$549$		−	123.759i		−	0.225426i
$550$		0			0
$551$	222.712			0.404196
$552$	40.3403	+	6.38928i	0.0730803	+	0.0115748i
$553$	−536.881	−	1053.69i	−0.970852	−	1.90540i
$554$	75.7590	+	24.6156i	0.136749	+	0.0444325i
$555$		0			0
$556$	−105.528	−	324.781i	−0.189798	−	0.584138i
$557$	136.133	+	136.133i	0.244404	+	0.244404i	0.818669	−	0.574265i	$-0.194712\pi$
$557$	136.133	+	136.133i	0.244404	+	0.244404i	−0.574265	+	0.818669i	$0.694712\pi$
$558$	380.561	+	193.905i	0.682009	+	0.347501i
$559$	606.947	−	835.390i	1.08577	−	1.49444i
$560$		0			0
$561$	−45.4085	+	32.9912i	−0.0809421	+	0.0588079i
$562$	70.3120	+	443.932i	0.125110	+	0.789915i
$563$	−931.083	+	147.469i	−1.65379	+	0.261934i	−0.912448	−	0.409194i	$-0.865810\pi$
$563$	−931.083	+	147.469i	−1.65379	+	0.261934i	−0.741341	+	0.671128i	$0.765810\pi$
$564$	5.99744	+	8.25476i	0.0106338	+	0.0146361i
$565$		0			0
$566$	−548.075	−	398.200i	−0.968331	−	0.703534i
$567$	−336.418	+	660.258i	−0.593330	+	1.16448i
$568$	−154.626	+	154.626i	−0.272228	+	0.272228i
$569$	−333.782	+	108.452i	−0.586611	+	0.190602i	−0.587260	−	0.809398i	$-0.699793\pi$
$569$	−333.782	+	108.452i	−0.586611	+	0.190602i	0.000648813		1.00000i	$0.499793\pi$
$570$		0			0
$571$	136.304	−	419.502i	0.238712	−	0.734679i	−0.757896	−	0.652376i	$-0.773772\pi$
$571$	136.304	−	419.502i	0.238712	−	0.734679i	0.996607	−	0.0823034i	$-0.0262277\pi$
$572$	230.634	−	117.514i	0.403207	−	0.205444i
$573$	12.0521	−	76.0941i	0.0210334	−	0.132799i
$574$			665.119i			1.15874i
$575$		0			0
$576$	69.5232			0.120700
$577$	−86.6592	−	13.7255i	−0.150189	−	0.0237876i	0.0808870	−	0.996723i	$-0.474225\pi$
$577$	−86.6592	−	13.7255i	−0.150189	−	0.0237876i	−0.231076	+	0.972936i	$0.574225\pi$
$578$	−19.2788	−	37.8368i	−0.0333544	−	0.0654616i
$579$	−11.0635	−	3.59476i	−0.0191080	−	0.00620857i
$580$		0			0
$581$	−48.2593	−	148.527i	−0.0830625	−	0.255640i
$582$	42.4556	+	42.4556i	0.0729478	+	0.0729478i
$583$	142.869	+	72.7953i	0.245058	+	0.124863i
$584$	−164.506	+	226.423i	−0.281688	+	0.387710i
$585$		0			0
$586$	−623.510	+	453.006i	−1.06401	+	0.773048i
$587$	−106.732	−	673.879i	−0.181826	−	1.14801i	−0.894685	−	0.446698i	$-0.852600\pi$
$587$	−106.732	−	673.879i	−0.181826	−	1.14801i	0.712859	−	0.701308i	$-0.247400\pi$
$588$	60.2224	−	9.53829i	0.102419	−	0.0162216i
$589$	−292.163	−	402.128i	−0.496033	−	0.682731i
$590$		0			0
$591$	−2.82263	−	2.05076i	−0.00477602	−	0.00346998i
$592$	28.1796	−	55.3056i	0.0476007	−	0.0934217i
$593$	−526.775	+	526.775i	−0.888322	+	0.888322i	−0.994362	−	0.106039i	$-0.966183\pi$
$593$	−526.775	+	526.775i	−0.888322	+	0.888322i	0.106039	+	0.994362i	$0.466183\pi$
$594$	−74.7695	+	24.2941i	−0.125875	+	0.0408991i
$595$		0			0
$596$	14.6535	−	45.0990i	0.0245865	−	0.0756694i
$597$	−120.986	+	61.6457i	−0.202657	+	0.103259i
$598$	−131.574	+	830.724i	−0.220023	+	1.38917i
$599$			586.777i			0.979594i	0.871836	+	0.489797i	$0.162929\pi$
$599$			586.777i			0.979594i	−0.871836	+	0.489797i	$0.837071\pi$
$600$		0			0
$601$	−664.202			−1.10516			−0.552581	−	0.833459i	$-0.686357\pi$
$601$	−664.202			−1.10516			−0.552581	+	0.833459i	$0.686357\pi$
$602$	−641.206	−	101.557i	−1.06513	−	0.168700i
$603$	216.070	+	424.062i	0.358326	+	0.703254i
$604$	394.296	+	128.114i	0.652808	+	0.212110i
$605$		0			0
$606$	−37.9802	−	116.891i	−0.0626736	−	0.192889i
$607$	90.2350	+	90.2350i	0.148657	+	0.148657i	0.777518	−	0.628861i	$-0.216478\pi$
$607$	90.2350	+	90.2350i	0.148657	+	0.148657i	−0.628861	+	0.777518i	$0.716478\pi$
$608$	−72.0899	−	36.7316i	−0.118569	−	0.0604139i
$609$	51.8828	−	71.4106i	0.0851935	−	0.117259i
$610$		0			0
$611$	−169.990	+	123.505i	−0.278215	+	0.202135i
$612$	−48.5642	−	306.622i	−0.0793533	−	0.501017i
$613$	773.095	−	122.446i	1.26117	−	0.199749i	0.510180	−	0.860067i	$-0.329579\pi$
$613$	773.095	−	122.446i	1.26117	−	0.199749i	0.750986	+	0.660318i	$0.229579\pi$
$614$	−48.0021	−	66.0693i	−0.0781794	−	0.107605i
$615$		0			0
$616$	−131.658	−	95.6551i	−0.213730	−	0.155284i
$617$	−305.103	+	598.799i	−0.494495	+	0.970500i	0.500031	+	0.866008i	$0.333322\pi$
$617$	−305.103	+	598.799i	−0.494495	+	0.970500i	−0.994526	+	0.104493i	$0.966678\pi$
$618$	−90.0239	+	90.0239i	−0.145670	+	0.145670i
$619$	318.118	−	103.363i	0.513922	−	0.166983i	−0.0405633	−	0.999177i	$-0.512915\pi$
$619$	318.118	−	103.363i	0.513922	−	0.166983i	0.554485	+	0.832194i	$0.312915\pi$
$620$		0			0
$621$	78.9395	−	242.951i	0.127117	−	0.391225i
$622$	−652.910	+	332.674i	−1.04969	+	0.534846i
$623$	116.630	−	736.376i	0.187208	−	1.18198i
$624$		−	51.0046i		−	0.0817381i
$625$		0			0
$626$	285.007			0.455283
$627$	44.3919	+	7.03099i	0.0708005	+	0.0112137i
$628$	−32.9683	−	64.7039i	−0.0524972	−	0.103032i
$629$	−263.602	−	85.6495i	−0.419081	−	0.136168i
$630$		0			0
$631$	27.3879	+	84.2913i	0.0434040	+	0.133584i	0.970410	−	0.241462i	$-0.0776270\pi$
$631$	27.3879	+	84.2913i	0.0434040	+	0.133584i	−0.927006	+	0.375046i	$0.877627\pi$
$632$	232.157	+	232.157i	0.367337	+	0.367337i
$633$	78.8458	+	40.1739i	0.124559	+	0.0634659i
$634$	−394.845	+	543.457i	−0.622783	+	0.857188i
$635$		0			0
$636$	25.5611	−	18.5712i	0.0401904	−	0.0292000i
$637$	196.421	+	1240.15i	0.308354	+	1.94687i
$638$	−122.836	+	19.4553i	−0.192533	+	0.0304942i
$639$	394.921	+	543.562i	0.618030	+	0.850645i
$640$		0			0
$641$	−763.194	−	554.493i	−1.19063	−	0.865044i	−0.197300	−	0.980343i	$-0.563217\pi$
$641$	−763.194	−	554.493i	−1.19063	−	0.865044i	−0.993331	+	0.115299i	$0.963217\pi$
$642$	63.4307	−	124.490i	0.0988018	−	0.193909i
$643$	−81.8654	+	81.8654i	−0.127318	+	0.127318i	−0.767894	−	0.640576i	$-0.778695\pi$
$643$	−81.8654	+	81.8654i	−0.127318	+	0.127318i	0.640576	+	0.767894i	$0.278695\pi$
$644$	502.909	−	163.405i	0.780915	−	0.253735i
$645$		0			0
$646$	−111.643	+	343.601i	−0.172821	+	0.531890i
$647$	989.616	−	504.234i	1.52955	−	0.779342i	0.531827	−	0.846853i	$-0.321506\pi$
$647$	989.616	−	504.234i	1.52955	−	0.779342i	0.997719	+	0.0675110i	$0.0215058\pi$
$648$	32.1833	−	203.197i	0.0496656	−	0.313576i
$649$			223.936i			0.345047i
$650$		0			0
$651$	−197.001			−0.302613
$652$	−163.133	−	25.8377i	−0.250204	−	0.0396284i
$653$	−278.161	−	545.922i	−0.425975	−	0.836022i	−0.999854	−	0.0170824i	$-0.994562\pi$
$653$	−278.161	−	545.922i	−0.425975	−	0.836022i	0.573880	−	0.818940i	$-0.305438\pi$
$654$	−66.4625	−	21.5950i	−0.101625	−	0.0330199i
$655$		0			0
$656$	−57.0620	−	175.619i	−0.0869848	−	0.267712i
$657$	608.054	+	608.054i	0.925500	+	0.925500i
$658$	117.704	+	59.9733i	0.178882	+	0.0911448i
$659$	306.794	−	422.266i	0.465545	−	0.640768i	−0.510102	−	0.860114i	$-0.670392\pi$
$659$	306.794	−	422.266i	0.465545	−	0.640768i	0.975647	+	0.219346i	$0.0703924\pi$
$660$		0			0
$661$	119.230	−	86.6259i	0.180379	−	0.131053i	−0.493932	−	0.869501i	$-0.664441\pi$
$661$	119.230	−	86.6259i	0.180379	−	0.131053i	0.674311	+	0.738448i	$0.264441\pi$
$662$	−92.2109	−	582.197i	−0.139291	−	0.879452i
$663$	−224.948	+	35.6283i	−0.339289	+	0.0537381i
$664$	25.4849	+	35.0769i	0.0383809	+	0.0528267i
$665$		0			0
$666$	−154.291	−	112.099i	−0.231668	−	0.168317i
$667$	183.462	−	360.064i	0.275055	−	0.539826i
$668$	−74.2292	+	74.2292i	−0.111122	+	0.111122i
$669$	−201.114	+	65.3460i	−0.300619	+	0.0976771i
$670$		0			0
$671$	24.8533	−	76.4905i	0.0370392	−	0.113995i
$672$	−28.5717	+	14.5580i	−0.0425174	+	0.0216637i
$673$	−38.7807	+	244.852i	−0.0576236	+	0.363821i	0.941980	+	0.335669i	$0.108962\pi$
$673$	−38.7807	+	244.852i	−0.0576236	+	0.363821i	−0.999604	+	0.0281522i	$0.991038\pi$
$674$		−	302.401i		−	0.448666i
$675$		0			0
$676$	712.332			1.05375
$677$	301.786	+	47.7981i	0.445769	+	0.0706029i	0.375284	−	0.926910i	$-0.377545\pi$
$677$	301.786	+	47.7981i	0.445769	+	0.0706029i	0.0704851	+	0.997513i	$0.477545\pi$
$678$	8.57225	+	16.8240i	0.0126434	+	0.0248141i
$679$	739.299	+	240.213i	1.08881	+	0.353774i
$680$		0			0
$681$	31.0154	+	95.4556i	0.0455439	+	0.140170i
$682$	196.270	+	196.270i	0.287786	+	0.287786i
$683$	241.102	+	122.848i	0.353005	+	0.179865i	0.621496	−	0.783417i	$-0.286525\pi$
$683$	241.102	+	122.848i	0.353005	+	0.179865i	−0.268491	+	0.963282i	$0.586525\pi$
$684$	−146.119	+	201.116i	−0.213624	+	0.294029i
$685$		0			0
$686$	67.4979	−	49.0401i	0.0983935	−	0.0714870i
$687$	−2.22724	−	14.0622i	−0.00324197	−	0.0204690i
$688$	178.018	−	28.1952i	0.258747	−	0.0409815i
$689$	382.436	+	526.378i	0.555059	+	0.763973i
$690$		0			0
$691$	−432.755	−	314.415i	−0.626274	−	0.455014i	0.228834	−	0.973466i	$-0.426509\pi$
$691$	−432.755	−	314.415i	−0.626274	−	0.455014i	−0.855107	+	0.518451i	$0.826509\pi$
$692$	40.5426	−	79.5693i	0.0585875	−	0.114984i
$693$	−353.565	+	353.565i	−0.510195	+	0.510195i
$694$	170.781	−	55.4902i	0.246082	−	0.0799570i
$695$		0			0
$696$	−7.57274	+	23.3065i	−0.0108804	+	0.0334863i
$697$	−734.683	+	374.340i	−1.05406	+	0.537073i
$698$	−26.0343	+	164.374i	−0.0372984	+	0.235493i
$699$		−	152.855i		−	0.218676i
$700$		0			0
$701$	−617.860			−0.881397			−0.440699	−	0.897655i	$-0.645269\pi$
$701$	−617.860			−0.881397			−0.440699	+	0.897655i	$0.645269\pi$
$702$	−315.081	−	49.9039i	−0.448833	−	0.0710881i
$703$	100.761	+	197.755i	0.143330	+	0.281302i
$704$	42.9696	+	13.9617i	0.0610363	+	0.0198319i
$705$		0			0
$706$	23.9431	+	73.6892i	0.0339137	+	0.104376i
$707$	−1125.18	−	1125.18i	−1.59149	−	1.59149i
$708$	39.3160	+	20.0325i	0.0555311	+	0.0282945i
$709$	−718.310	+	988.668i	−1.01313	+	1.39445i	−0.0962207	+	0.995360i	$0.530675\pi$
$709$	−718.310	+	988.668i	−1.01313	+	1.39445i	−0.916910	+	0.399095i	$0.869325\pi$
$710$		0			0
$711$	816.111	−	592.939i	1.14784	−	0.833951i
$712$	32.3801	+	204.440i	0.0454776	+	0.287134i
$713$	−890.804	+	141.089i	−1.24937	+	0.197881i
$714$	84.1643	+	115.842i	0.117877	+	0.162244i
$715$		0			0
$716$	−527.923	−	383.559i	−0.737323	−	0.535697i
$717$	27.3847	−	53.7455i	0.0381935	−	0.0749589i
$718$	459.128	−	459.128i	0.639454	−	0.639454i
$719$	552.407	−	179.488i	0.768299	−	0.249635i	0.101462	−	0.994839i	$-0.467648\pi$
$719$	552.407	−	179.488i	0.768299	−	0.249635i	0.666837	+	0.745204i	$0.267648\pi$
$720$		0			0
$721$	−509.353	+	1567.63i	−0.706454	+	2.17424i
$722$	−197.116	+	100.436i	−0.273014	+	0.139108i
$723$	−32.1749	+	203.144i	−0.0445019	+	0.280974i
$724$			165.669i			0.228825i
$725$		0			0
$726$	70.1157			0.0965781
$727$	353.383	+	55.9703i	0.486083	+	0.0769880i	0.394666	−	0.918825i	$-0.370860\pi$
$727$	353.383	+	55.9703i	0.486083	+	0.0769880i	0.0914173	+	0.995813i	$0.470860\pi$
$728$	−299.792	−	588.374i	−0.411802	−	0.808206i
$729$	−554.293	−	180.101i	−0.760347	−	0.247052i
$730$		0			0
$731$	−248.702	−	765.427i	−0.340222	−	1.04710i
$732$	−11.2060	−	11.2060i	−0.0153088	−	0.0153088i
$733$	1280.53	+	652.460i	1.74697	+	0.890123i	0.963079	+	0.269219i	$0.0867656\pi$
$733$	1280.53	+	652.460i	1.74697	+	0.890123i	0.783886	+	0.620904i	$0.213234\pi$
$734$	466.851	−	642.566i	0.636037	−	0.875430i
$735$		0			0
$736$	−118.770	+	86.2914i	−0.161372	+	0.117244i
$737$	48.3845	+	305.488i	0.0656506	+	0.414501i
$738$	−560.376	+	88.7549i	−0.759317	+	0.120264i
$739$	−125.167	−	172.278i	−0.169373	−	0.233123i	0.715889	−	0.698214i	$-0.246022\pi$
$739$	−125.167	−	172.278i	−0.169373	−	0.233123i	−0.885263	+	0.465091i	$0.846022\pi$
$740$		0			0
$741$	147.545	+	107.198i	0.199116	+	0.144667i
$742$	185.709	−	364.474i	0.250281	−	0.491205i
$743$	775.885	−	775.885i	1.04426	−	1.04426i	0.0452854	−	0.998974i	$-0.485580\pi$
$743$	775.885	−	775.885i	1.04426	−	1.04426i	0.998974	−	0.0452854i	$-0.0144197\pi$
$744$	52.0164	−	16.9012i	0.0699145	−	0.0227166i
$745$		0			0
$746$	82.3237	−	253.366i	0.110354	−	0.339633i
$747$	118.697	−	60.4792i	0.158898	−	0.0809627i
$748$	31.5603	−	199.264i	0.0421929	−	0.266396i
$749$		−	1808.91i		−	2.41510i
$750$		0			0
$751$	738.937			0.983938			0.491969	−	0.870613i	$-0.336277\pi$
$751$	738.937			0.983938			0.491969	+	0.870613i	$0.336277\pi$
$752$	−36.2240	−	5.73732i	−0.0481702	−	0.00762941i
$753$	5.22640	+	10.2574i	0.00694077	+	0.0136220i
$754$	−479.949	−	155.945i	−0.636537	−	0.206823i
$755$		0			0
$756$	61.9769	+	190.745i	0.0819801	+	0.252309i
$757$	−821.816	−	821.816i	−1.08562	−	1.08562i	−0.995973	−	0.0896488i	$-0.971426\pi$
$757$	−821.816	−	821.816i	−1.08562	−	1.08562i	−0.0896488	−	0.995973i	$-0.528574\pi$
$758$	−30.1989	−	15.3871i	−0.0398402	−	0.0202996i
$759$	47.9356	−	65.9776i	0.0631562	−	0.0869271i
$760$		0			0
$761$	972.054	−	706.239i	1.27734	−	0.928040i	0.277869	−	0.960619i	$-0.410372\pi$
$761$	972.054	−	706.239i	1.27734	−	0.928040i	0.999469	+	0.0325787i	$0.0103719\pi$
$762$	−3.84300	−	24.2637i	−0.00504330	−	0.0318422i
$763$	−893.623	+	141.536i	−1.17120	+	0.185499i
$764$	162.772	+	224.036i	0.213052	+	0.293241i
$765$		0			0
$766$	18.2609	+	13.2673i	0.0238392	+	0.0173202i
$767$	−412.528	+	809.632i	−0.537846	+	1.05558i
$768$	6.29514	−	6.29514i	0.00819680	−	0.00819680i
$769$	596.588	−	193.843i	0.775797	−	0.252072i	0.105753	−	0.994392i	$-0.466275\pi$
$769$	596.588	−	193.843i	0.775797	−	0.252072i	0.670045	+	0.742321i	$0.266275\pi$
$770$		0			0
$771$	14.0046	−	43.1017i	0.0181642	−	0.0559037i
$772$	37.2561	−	18.9829i	0.0482592	−	0.0245893i
$773$	119.204	−	752.625i	0.154210	−	0.973641i	−0.782275	−	0.622933i	$-0.785941\pi$
$773$	119.204	−	752.625i	0.154210	−	0.973641i	0.936485	−	0.350708i	$-0.114059\pi$
$774$		−	553.781i		−	0.715480i
$775$		0			0
$776$	−215.814			−0.278111
$777$	86.8817	+	13.7607i	0.111817	+	0.0177101i
$778$	156.624	+	307.393i	0.201317	+	0.395106i
$779$	627.957	+	204.036i	0.806107	+	0.261920i
$780$		0			0
$781$	134.927	+	415.263i	0.172762	+	0.531706i
$782$	463.540	+	463.540i	0.592763	+	0.592763i
$783$	136.566	+	69.5841i	0.174414	+	0.0888686i
$784$	−128.821	+	177.307i	−0.164312	+	0.226157i
$785$		0			0
$786$	82.0223	−	59.5927i	0.104354	−	0.0758177i
$787$	−172.436	−	1088.72i	−0.219105	−	1.38338i	−0.814603	−	0.580019i	$-0.803045\pi$
$787$	−172.436	−	1088.72i	−0.219105	−	1.38338i	0.595497	−	0.803357i	$-0.296955\pi$
$788$	12.3864	−	1.96181i	0.0157188	−	0.00248961i
$789$	28.6809	+	39.4758i	0.0363509	+	0.0500327i
$790$		0			0
$791$	197.774	+	143.691i	0.250031	+	0.181658i
$792$	63.0226	−	123.689i	0.0795740	−	0.156173i
$793$	230.765	−	230.765i	0.291003	−	0.291003i
$794$	−289.146	+	93.9493i	−0.364164	+	0.118324i
$795$		0			0
$796$	150.823	−	464.185i	0.189476	−	0.583148i
$797$	932.407	−	475.085i	1.16990	−	0.596091i	0.242492	−	0.970154i	$-0.422035\pi$
$797$	932.407	−	475.085i	1.16990	−	0.596091i	0.927404	+	0.374062i	$0.122035\pi$
$798$	17.9368	−	113.249i	0.0224773	−	0.141916i
$799$			163.769i			0.204967i
$800$		0			0
$801$	635.975			0.793976
$802$	723.309	+	114.561i	0.901881	+	0.142844i
$803$	253.705	+	497.924i	0.315946	+	0.620079i
$804$	57.9623	+	18.8331i	0.0720924	+	0.0234242i
$805$		0			0
$806$	348.044	+	1071.17i	0.431816	+	1.32899i
$807$	32.8431	+	32.8431i	0.0406978	+	0.0406978i
$808$	393.627	+	200.563i	0.487162	+	0.248222i
$809$	−476.312	+	655.588i	−0.588767	+	0.810368i	−0.994622	−	0.103569i	$-0.966974\pi$
$809$	−476.312	+	655.588i	−0.588767	+	0.810368i	0.405855	+	0.913937i	$0.366974\pi$
$810$		0			0
$811$	−288.711	+	209.761i	−0.355994	+	0.258644i	−0.751379	−	0.659871i	$-0.770611\pi$
$811$	−288.711	+	209.761i	−0.355994	+	0.258644i	0.395385	+	0.918515i	$0.370611\pi$
$812$	49.6326	+	313.368i	0.0611239	+	0.385921i
$813$	−59.6097	+	9.44124i	−0.0733206	+	0.0116128i
$814$	−72.8496	−	100.269i	−0.0894958	−	0.123180i
$815$		0			0
$816$	−32.1612	−	23.3665i	−0.0394132	−	0.0286354i
$817$	−292.583	+	574.226i	−0.358119	+	0.702847i
$818$	−190.091	+	190.091i	−0.232386	+	0.232386i
$819$	−1929.63	+	626.975i	−2.35608	+	0.765537i
$820$		0			0
$821$	−456.889	+	1406.16i	−0.556503	+	1.71274i	0.135438	+	0.990786i	$0.456756\pi$
$821$	−456.889	+	1406.16i	−0.556503	+	1.71274i	−0.691941	+	0.721954i	$0.743244\pi$
$822$	21.5336	−	10.9719i	0.0261966	−	0.0133479i
$823$	32.3733	−	204.397i	0.0393357	−	0.248356i	−0.960183	−	0.279371i	$-0.909874\pi$
$823$	32.3733	−	204.397i	0.0393357	−	0.248356i	0.999519	+	0.0310153i	$0.00987405\pi$
$824$		−	457.617i		−	0.555360i
$825$		0			0
$826$	571.285			0.691628
$827$	−415.905	−	65.8728i	−0.502908	−	0.0796528i	−0.100174	−	0.994970i	$-0.531940\pi$
$827$	−415.905	−	65.8728i	−0.502908	−	0.0796528i	−0.402734	+	0.915317i	$0.631940\pi$
$828$	204.781	+	401.906i	0.247320	+	0.485393i
$829$	−1383.10	−	449.395i	−1.66839	−	0.542093i	−0.685787	−	0.727802i	$-0.740542\pi$
$829$	−1383.10	−	449.395i	−1.66839	−	0.542093i	−0.982605	+	0.185709i	$0.940542\pi$
$830$		0			0
$831$	−9.68491	−	29.8071i	−0.0116545	−	0.0358690i
$832$	129.635	+	129.635i	0.155812	+	0.155812i
$833$	871.972	+	444.292i	1.04679	+	0.533364i
$834$	−78.9747	+	108.699i	−0.0946939	+	0.130335i
$835$		0			0
$836$	−130.699	+	94.9581i	−0.156338	+	0.113586i
$837$	−53.5130	−	337.868i	−0.0639343	−	0.403665i
$838$	−149.659	+	23.7037i	−0.178591	+	0.0282860i
$839$	−342.847	−	471.888i	−0.408638	−	0.562441i	0.554248	−	0.832352i	$-0.313006\pi$
$839$	−342.847	−	471.888i	−0.408638	−	0.562441i	−0.962885	+	0.269910i	$0.913006\pi$
$840$		0			0
$841$	−484.225	−	351.810i	−0.575772	−	0.418323i
$842$	235.230	−	461.665i	0.279370	−	0.548295i
$843$	125.045	−	125.045i	0.148334	−	0.148334i
$844$	−302.505	+	98.2900i	−0.358419	+	0.116457i
$845$		0			0
$846$	−34.8220	+	107.171i	−0.0411607	+	0.126680i
$847$	808.835	−	412.122i	0.954941	−	0.486567i
$848$	−17.7658	+	112.169i	−0.0209502	+	0.132274i
$849$			266.544i			0.313950i
$850$		0			0
$851$	402.719			0.473230
$852$	84.9772	+	13.4591i	0.0997385	+	0.0157970i
$853$	−335.123	−	657.717i	−0.392876	−	0.771063i	0.606842	−	0.794823i	$-0.292436\pi$
$853$	−335.123	−	657.717i	−0.392876	−	0.771063i	−0.999718	+	0.0237600i	$0.992436\pi$
$854$	−195.136	−	63.4035i	−0.228496	−	0.0742430i
$855$		0			0
$856$	155.190	+	477.627i	0.181297	+	0.557975i
$857$	−189.288	−	189.288i	−0.220873	−	0.220873i	0.587993	−	0.808866i	$-0.299918\pi$
$857$	−189.288	−	189.288i	−0.220873	−	0.220873i	−0.808866	+	0.587993i	$0.799918\pi$
$858$	−90.7423	−	46.2355i	−0.105760	−	0.0538875i
$859$	−689.325	+	948.775i	−0.802474	+	1.10451i	0.189967	+	0.981790i	$0.439162\pi$
$859$	−689.325	+	948.775i	−0.802474	+	1.10451i	−0.992441	+	0.122720i	$0.960838\pi$
$860$		0			0
$861$	211.711	−	153.817i	0.245889	−	0.178649i
$862$	20.3547	+	128.514i	0.0236133	+	0.149088i
$863$	−238.733	+	37.8116i	−0.276631	+	0.0438141i	−0.293209	−	0.956048i	$-0.594723\pi$
$863$	−238.733	+	37.8116i	−0.276631	+	0.0438141i	0.0165773	+	0.999863i	$0.494723\pi$
$864$	−32.7289	−	45.0475i	−0.0378807	−	0.0521383i
$865$		0			0
$866$	49.7588	+	36.1519i	0.0574582	+	0.0417458i
$867$	−7.58518	+	14.8868i	−0.00874877	+	0.0171704i
$868$	500.706	−	500.706i	0.576850	−	0.576850i
$869$	623.481	−	202.581i	0.717469	−	0.233120i
$870$		0			0
$871$	−387.828	+	1193.61i	−0.445268	+	1.37039i
$872$	223.811	−	114.037i	0.256664	−	0.130777i
$873$	−103.731	+	654.929i	−0.118821	+	0.750205i
$874$		−	524.937i		−	0.600615i
$875$		0			0
$876$	110.115			0.125702
$877$	−338.646	−	53.6362i	−0.386141	−	0.0611587i	−0.0396540	−	0.999213i	$-0.512626\pi$
$877$	−338.646	−	53.6362i	−0.386141	−	0.0611587i	−0.346487	+	0.938055i	$0.612626\pi$
$878$	−494.161	−	969.845i	−0.562826	−	1.10461i
$879$	288.388	+	93.7030i	0.328087	+	0.106602i
$880$		0			0
$881$	66.8030	+	205.598i	0.0758263	+	0.233369i	0.981785	−	0.189998i	$-0.0608481\pi$
$881$	66.8030	+	205.598i	0.0758263	+	0.233369i	−0.905958	+	0.423367i	$0.860848\pi$
$882$	476.154	+	476.154i	0.539857	+	0.539857i
$883$	305.211	+	155.513i	0.345653	+	0.176119i	0.618195	−	0.786025i	$-0.287864\pi$
$883$	305.211	+	155.513i	0.345653	+	0.176119i	−0.272542	+	0.962144i	$0.587864\pi$
$884$	481.184	−	662.293i	0.544326	−	0.749200i
$885$		0			0
$886$	775.335	−	563.314i	0.875096	−	0.635794i
$887$	−18.6058	−	117.473i	−0.0209761	−	0.132438i	0.974978	−	0.222302i	$-0.0713569\pi$
$887$	−18.6058	−	117.473i	−0.0209761	−	0.132438i	−0.995954	+	0.0898635i	$0.971357\pi$
$888$	−24.1209	+	3.82038i	−0.0271632	+	0.00430223i
$889$	−186.948	−	257.311i	−0.210290	−	0.289439i
$890$		0			0
$891$	−332.335	−	241.455i	−0.372991	−	0.270994i
$892$	345.074	−	677.247i	0.386855	−	0.759245i
$893$	92.7300	−	92.7300i	0.103841	−	0.103841i
$894$	−17.7440	+	5.76539i	−0.0198479	+	0.00644898i
$895$		0			0
$896$	35.6178	−	109.620i	0.0397520	−	0.122344i
$897$	294.852	−	150.234i	0.328709	−	0.167485i
$898$	196.804	−	1242.57i	0.219159	−	1.38371i
$899$		−	541.145i		−	0.601941i
$900$		0			0
$901$	507.114			0.562834
$902$	−364.171	−	57.6789i	−0.403737	−	0.0639456i
$903$	115.961	+	227.585i	0.128417	+	0.252033i
$904$	−64.5481	−	20.9730i	−0.0714028	−	0.0232002i
$905$		0			0
$906$	−50.4062	−	155.134i	−0.0556360	−	0.171230i
$907$	102.765	+	102.765i	0.113302	+	0.113302i	0.761485	−	0.648183i	$-0.224471\pi$
$907$	102.765	+	102.765i	0.113302	+	0.113302i	−0.648183	+	0.761485i	$0.724471\pi$
$908$	−321.444	−	163.784i	−0.354013	−	0.180379i
$909$	797.843	−	1098.14i	0.877715	−	1.20807i
$910$		0			0
$911$	−107.266	+	77.9334i	−0.117745	+	0.0855471i	−0.645100	−	0.764099i	$-0.723184\pi$
$911$	−107.266	+	77.9334i	−0.117745	+	0.0855471i	0.527354	+	0.849646i	$0.323184\pi$
$912$	4.97980	+	31.4412i	0.00546030	+	0.0344750i
$913$	85.5075	−	13.5431i	0.0936555	−	0.0148336i
$914$	−54.2175	−	74.6239i	−0.0593189	−	0.0816454i
$915$		0			0
$916$	41.4020	+	30.0803i	0.0451986	+	0.0328387i
$917$	595.916	−	1169.55i	0.649854	−	1.27541i
$918$	−175.814	+	175.814i	−0.191518	+	0.191518i
$919$	1104.79	−	358.968i	1.20217	−	0.390607i	0.361609	−	0.932330i	$-0.382228\pi$
$919$	1104.79	−	358.968i	1.20217	−	0.390607i	0.840557	+	0.541723i	$0.182228\pi$
$920$		0			0
$921$	−9.92910	+	30.5586i	−0.0107808	+	0.0331798i
$922$	−973.790	+	496.171i	−1.05617	+	0.538146i
$923$	−277.161	+	1749.93i	−0.300283	+	1.89591i
$924$			64.0287i			0.0692952i
$925$		0			0
$926$	644.211			0.695692
$927$	−1388.73	−	219.953i	−1.49809	−	0.237274i
$928$	−39.9896	−	78.4839i	−0.0430922	−	0.0845732i
$929$	68.6295	+	22.2991i	0.0738746	+	0.0240033i	0.345721	−	0.938337i	$-0.387634\pi$
$929$	68.6295	+	22.2991i	0.0738746	+	0.0240033i	−0.271847	+	0.962341i	$0.587634\pi$
$930$		0			0
$931$	−242.163	−	745.303i	−0.260111	−	0.800540i
$932$	388.501	+	388.501i	0.416847	+	0.416847i
$933$	256.885	+	130.889i	0.275332	+	0.140289i
$934$	290.580	−	399.949i	0.311114	−	0.428211i
$935$		0			0
$936$	455.712	−	331.094i	0.486872	−	0.353733i
$937$	−1.09335	−	6.90314i	−0.00116686	−	0.00736728i	0.987098	−	0.160117i	$-0.0511872\pi$
$937$	−1.09335	−	6.90314i	−0.00116686	−	0.00736728i	−0.988265	+	0.152750i	$0.951187\pi$
$938$	779.333	−	123.434i	0.830845	−	0.131593i
$939$	−65.9113	−	90.7191i	−0.0701931	−	0.0966125i
$940$		0			0
$941$	−895.131	−	650.351i	−0.951255	−	0.691127i	−0.000151406	−	1.00000i	$-0.500048\pi$
$941$	−895.131	−	650.351i	−0.951255	−	0.691127i	−0.951103	+	0.308873i	$0.900048\pi$
$942$	−12.9712	+	25.4575i	−0.0137699	+	0.0270250i
$943$	847.156	−	847.156i	0.898363	−	0.898363i
$944$	−150.843	+	49.0118i	−0.159791	+	0.0519193i
$945$		0			0
$946$	111.210	−	342.271i	0.117559	−	0.361808i
$947$	−553.987	+	282.271i	−0.584992	+	0.298068i	−0.721327	−	0.692595i	$-0.756468\pi$
$947$	−553.987	+	282.271i	−0.584992	+	0.298068i	0.136335	+	0.990663i	$0.456468\pi$
$948$	20.2076	−	127.586i	0.0213160	−	0.134584i
$949$			2267.60i			2.38946i
$950$		0			0
$951$	264.298			0.277915
$952$	−508.345	−	80.5139i	−0.533976	−	0.0845734i
$953$	−757.601	−	1486.88i	−0.794965	−	1.56021i	−0.827984	−	0.560751i	$-0.810512\pi$
$953$	−757.601	−	1486.88i	−0.794965	−	1.56021i	0.0330196	−	0.999455i	$-0.489488\pi$
$954$	331.858	+	107.827i	0.347860	+	0.113026i
$955$		0			0
$956$	66.9997	+	206.204i	0.0700834	+	0.215695i
$957$	34.5999	+	34.5999i	0.0361546	+	0.0361546i
$958$	65.7630	+	33.5079i	0.0686461	+	0.0349769i
$959$	183.916	−	253.138i	0.191779	−	0.263961i
$960$		0			0
$961$	−199.625	+	145.036i	−0.207726	+	0.150922i
$962$	−78.6727	−	496.720i	−0.0817804	−	0.516341i
$963$	1524.04	−	241.385i	1.58260	−	0.250659i
$964$	−434.543	−	598.097i	−0.450770	−	0.620432i
$965$		0			0
$966$	−168.316	−	122.289i	−0.174241	−	0.126593i
$967$	−289.998	+	569.153i	−0.299894	+	0.588576i	−0.990951	−	0.134225i	$-0.957146\pi$
$967$	−289.998	+	569.153i	−0.299894	+	0.588576i	0.691057	+	0.722801i	$0.257146\pi$
$968$	−178.209	+	178.209i	−0.184100	+	0.184100i
$969$	135.188	−	43.9254i	0.139513	−	0.0453306i
$970$		0			0
$971$	−108.279	+	333.249i	−0.111513	+	0.343201i	−0.991204	−	0.132345i	$-0.957749\pi$
$971$	−108.279	+	333.249i	−0.111513	+	0.343201i	0.879691	+	0.475546i	$0.157749\pi$
$972$	−229.989	+	117.185i	−0.236614	+	0.120561i
$973$	−272.123	+	1718.12i	−0.279674	+	1.76579i
$974$			841.772i			0.864242i
$975$		0			0
$976$	56.9635			0.0583642
$977$	960.639	+	152.150i	0.983253	+	0.155732i	0.627305	−	0.778774i	$-0.284158\pi$
$977$	960.639	+	152.150i	0.983253	+	0.155732i	0.355948	+	0.934506i	$0.384158\pi$
$978$	29.5022	+	57.9013i	0.0301659	+	0.0592038i
$979$	393.071	+	127.717i	0.401503	+	0.130456i
$980$		0			0
$981$	−238.494	−	734.008i	−0.243113	−	0.748225i
$982$	−135.953	−	135.953i	−0.138445	−	0.138445i
$983$	−731.267	−	372.599i	−0.743913	−	0.379043i	0.0405830	−	0.999176i	$-0.487078\pi$
$983$	−731.267	−	372.599i	−0.743913	−	0.379043i	−0.784496	+	0.620133i	$0.787078\pi$
$984$	−42.7041	+	58.7771i	−0.0433984	+	0.0597328i
$985$		0			0
$986$	−318.208	+	231.192i	−0.322727	+	0.234475i
$987$	−8.13072	−	51.3353i	−0.00823781	−	0.0520115i
$988$	−647.466	+	102.549i	−0.655330	+	0.103794i
$989$	687.347	+	946.051i	0.694991	+	0.956574i
$990$		0			0
$991$	280.178	+	203.561i	0.282722	+	0.205410i	0.720104	−	0.693866i	$-0.244094\pi$
$991$	280.178	+	203.561i	0.282722	+	0.205410i	−0.437382	+	0.899276i	$0.644094\pi$
$992$	−89.2504	+	175.164i	−0.0899702	+	0.176576i
$993$	−163.991	+	163.991i	−0.165147	+	0.165147i
$994$	1059.38	−	344.214i	1.06578	−	0.346292i
$995$		0			0
$996$	5.27148	−	16.2239i	0.00529265	−	0.0162891i
$997$	−1161.91	+	592.022i	−1.16540	+	0.593803i	−0.926151	−	0.377154i	$-0.876903\pi$
$997$	−1161.91	+	592.022i	−1.16540	+	0.593803i	−0.239254	+	0.970957i	$0.576903\pi$
$998$	−107.034	+	675.784i	−0.107248	+	0.677138i
$999$			152.745i			0.152898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.3.f.b.157.1		16
5.2	odd	4		250.3.f.a.93.1		16
5.3	odd	4		250.3.f.c.93.2		16
5.4	even	2		50.3.f.a.27.2	yes	16
20.19	odd	2		400.3.bg.a.177.1		16
25.9	even	10		250.3.f.a.207.1		16
25.12	odd	20		50.3.f.a.13.2	✓	16
25.13	odd	20	inner	250.3.f.b.43.1		16
25.16	even	5		250.3.f.c.207.2		16
100.87	even	20		400.3.bg.a.113.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.13.2	✓	16	25.12	odd	20
50.3.f.a.27.2	yes	16	5.4	even	2
250.3.f.a.93.1		16	5.2	odd	4
250.3.f.a.207.1		16	25.9	even	10
250.3.f.b.43.1		16	25.13	odd	20	inner
250.3.f.b.157.1		16	1.1	even	1	trivial
250.3.f.c.93.2		16	5.3	odd	4
250.3.f.c.207.2		16	25.16	even	5
400.3.bg.a.113.1		16	100.87	even	20
400.3.bg.a.177.1		16	20.19	odd	2

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	250.f (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.39680 + 0.221232i) q^{2} +(-0.252608 - 0.495771i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-0.243163 - 0.748380i) q^{6} +(-7.20385 - 7.20385i) q^{7} +(2.52015 + 1.28408i) q^{8} +(5.10809 - 7.03068i) q^{9} +O(q^{10})\)	\(q+(1.39680 + 0.221232i) q^{2} +(-0.252608 - 0.495771i) q^{3} +(1.90211 + 0.618034i) q^{4} +(-0.243163 - 0.748380i) q^{6} +(-7.20385 - 7.20385i) q^{7} +(2.52015 + 1.28408i) q^{8} +(5.10809 - 7.03068i) q^{9} +(4.56901 - 3.31958i) q^{11} +(-0.174086 - 1.09913i) q^{12} +(22.6344 - 3.58493i) q^{13} +(-8.46863 - 11.6561i) q^{14} +(3.23607 + 2.35114i) q^{16} +(8.10888 - 15.9146i) q^{17} +(8.69040 - 8.69040i) q^{18} +(-13.6027 + 4.41978i) q^{19} +(-1.75171 + 5.39121i) q^{21} +(7.11641 - 3.62599i) q^{22} +(-4.05981 + 25.6327i) q^{23} -1.57379i q^{24} +32.4088 q^{26} +(-9.72206 - 1.53982i) q^{27} +(-9.25031 - 18.1548i) q^{28} +(-14.8092 - 4.81180i) q^{29} +(10.7392 + 33.0518i) q^{31} +(4.00000 + 4.00000i) q^{32} +(-2.79992 - 1.42663i) q^{33} +(14.8473 - 20.4356i) q^{34} +(14.0614 - 10.2162i) q^{36} +(-2.42751 - 15.3267i) q^{37} +(-19.9781 + 3.16422i) q^{38} +(-7.49493 - 10.3159i) q^{39} +(-37.3476 - 27.1346i) q^{41} +(-3.63950 + 7.14292i) q^{42} +(31.8617 - 31.8617i) q^{43} +(10.7424 - 3.49042i) q^{44} +(-11.3415 + 34.9056i) q^{46} +(-8.16953 + 4.16259i) q^{47} +(0.348171 - 2.19827i) q^{48} +54.7908i q^{49} -9.93836 q^{51} +(45.2687 + 7.16986i) q^{52} +(12.8896 + 25.2972i) q^{53} +(-13.2391 - 4.30166i) q^{54} +(-8.90444 - 27.4051i) q^{56} +(5.62735 + 5.62735i) q^{57} +(-19.6210 - 9.99739i) q^{58} +(-23.3065 + 32.0786i) q^{59} +(11.5211 - 8.37057i) q^{61} +(7.68840 + 48.5426i) q^{62} +(-87.4458 + 13.8501i) q^{63} +(4.70228 + 6.47214i) q^{64} +(-3.59532 - 2.61216i) q^{66} +(-24.8631 + 48.7966i) q^{67} +(25.2597 - 25.2597i) q^{68} +(13.7335 - 4.46228i) q^{69} +(-23.8910 + 73.5289i) q^{71} +(21.9011 - 11.1592i) q^{72} +(-15.4792 + 97.7321i) q^{73} -21.9454i q^{74} -28.6054 q^{76} +(-56.8282 - 9.00071i) q^{77} +(-8.18674 - 16.0674i) q^{78} +(110.397 + 35.8702i) q^{79} +(-22.4769 - 69.1767i) q^{81} +(-46.1642 - 46.1642i) q^{82} +(13.6584 + 6.95931i) q^{83} +(-6.66390 + 9.17208i) q^{84} +(51.5533 - 37.4556i) q^{86} +(1.35537 + 8.55747i) q^{87} +(15.7772 - 2.49886i) q^{88} +(43.0149 + 59.2049i) q^{89} +(-188.880 - 137.229i) q^{91} +(-23.5641 + 46.2471i) q^{92} +(13.6733 - 13.6733i) q^{93} +(-12.3321 + 4.00695i) q^{94} +(0.972653 - 2.99352i) q^{96} +(-67.9854 + 34.6403i) q^{97} +(-12.1215 + 76.5319i) q^{98} -49.0800i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} - 40 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 - 40 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} - 40 q^{9} + 32 q^{11} - 4 q^{12} + 8 q^{13} - 30 q^{14} + 16 q^{16} + 62 q^{17} + 16 q^{18} + 30 q^{19} - 68 q^{21} + 48 q^{22} + 18 q^{23} - 56 q^{26} + 40 q^{27} - 44 q^{28} + 100 q^{29} + 132 q^{31} + 64 q^{32} + 36 q^{33} + 100 q^{34} + 48 q^{36} - 138 q^{37} - 20 q^{38} - 320 q^{39} - 88 q^{41} + 8 q^{42} + 78 q^{43} + 40 q^{44} - 26 q^{46} + 22 q^{47} + 8 q^{48} - 168 q^{51} + 16 q^{52} - 182 q^{53} + 80 q^{54} + 48 q^{56} - 280 q^{57} + 120 q^{58} - 350 q^{59} + 372 q^{61} + 158 q^{62} - 22 q^{63} - 202 q^{66} + 112 q^{67} + 196 q^{68} - 30 q^{69} + 122 q^{71} + 132 q^{72} + 248 q^{73} + 40 q^{76} - 16 q^{77} - 438 q^{78} + 760 q^{79} - 144 q^{81} - 352 q^{82} - 132 q^{83} - 20 q^{84} + 264 q^{86} - 770 q^{87} - 116 q^{88} + 550 q^{89} - 798 q^{91} - 384 q^{92} - 54 q^{93} + 190 q^{94} - 16 q^{96} + 292 q^{97} + 24 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 - 40 * q^9 + 32 * q^11 - 4 * q^12 + 8 * q^13 - 30 * q^14 + 16 * q^16 + 62 * q^17 + 16 * q^18 + 30 * q^19 - 68 * q^21 + 48 * q^22 + 18 * q^23 - 56 * q^26 + 40 * q^27 - 44 * q^28 + 100 * q^29 + 132 * q^31 + 64 * q^32 + 36 * q^33 + 100 * q^34 + 48 * q^36 - 138 * q^37 - 20 * q^38 - 320 * q^39 - 88 * q^41 + 8 * q^42 + 78 * q^43 + 40 * q^44 - 26 * q^46 + 22 * q^47 + 8 * q^48 - 168 * q^51 + 16 * q^52 - 182 * q^53 + 80 * q^54 + 48 * q^56 - 280 * q^57 + 120 * q^58 - 350 * q^59 + 372 * q^61 + 158 * q^62 - 22 * q^63 - 202 * q^66 + 112 * q^67 + 196 * q^68 - 30 * q^69 + 122 * q^71 + 132 * q^72 + 248 * q^73 + 40 * q^76 - 16 * q^77 - 438 * q^78 + 760 * q^79 - 144 * q^81 - 352 * q^82 - 132 * q^83 - 20 * q^84 + 264 * q^86 - 770 * q^87 - 116 * q^88 + 550 * q^89 - 798 * q^91 - 384 * q^92 - 54 * q^93 + 190 * q^94 - 16 * q^96 + 292 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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