LMFDB - Embedded newform 250.3.f.b.207.2

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			207.2
Root			$0.0495271i$ of defining polynomial
Character	$\chi$	$=$	250.207
Dual form			250.3.f.b.93.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.221232 + 1.39680i) q^{2} +(2.40328 + 1.22453i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-1.17875 + 3.62781i) q^{6} +(3.03568 + 3.03568i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(-1.01379 - 1.39536i) q^{9} +O(q^{10})$	\(q+(0.221232 + 1.39680i) q^{2} +(2.40328 + 1.22453i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-1.17875 + 3.62781i) q^{6} +(3.03568 + 3.03568i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(-1.01379 - 1.39536i) q^{9} +(15.9782 + 11.6089i) q^{11} +(-5.32811 - 0.843890i) q^{12} +(-2.40210 + 15.1663i) q^{13} +(-3.56865 + 4.91183i) q^{14} +(3.23607 - 2.35114i) q^{16} +(-18.6060 + 9.48022i) q^{17} +(1.72476 - 1.72476i) q^{18} +(-3.15850 - 1.02626i) q^{19} +(3.57830 + 11.0129i) q^{21} +(-12.6804 + 24.8867i) q^{22} +(16.3014 - 2.58189i) q^{23} -7.62902i q^{24} -21.7157 q^{26} +(-4.52526 - 28.5714i) q^{27} +(-7.65035 - 3.89805i) q^{28} +(-6.49731 + 2.11110i) q^{29} +(7.69031 - 23.6683i) q^{31} +(4.00000 + 4.00000i) q^{32} +(24.1848 + 47.4652i) q^{33} +(-17.3582 - 23.8916i) q^{34} +(2.79072 + 2.02758i) q^{36} +(16.6649 + 2.63946i) q^{37} +(0.734721 - 4.63885i) q^{38} +(-24.3445 + 33.5073i) q^{39} +(29.2279 - 21.2353i) q^{41} +(-14.5912 + 7.43457i) q^{42} +(-19.9893 + 19.9893i) q^{43} +(-37.5671 - 12.2063i) q^{44} +(7.21279 + 22.1987i) q^{46} +(12.1343 - 23.8149i) q^{47} +(10.6562 - 1.68778i) q^{48} -30.5693i q^{49} -56.3243 q^{51} +(-4.80420 - 30.3325i) q^{52} +(-86.7430 - 44.1977i) q^{53} +(38.9074 - 12.6418i) q^{54} +(3.75230 - 11.5484i) q^{56} +(-6.33408 - 6.33408i) q^{57} +(-4.38621 - 8.60842i) q^{58} +(63.0774 + 86.8186i) q^{59} +(65.0278 + 47.2455i) q^{61} +(34.7613 + 5.50566i) q^{62} +(1.15833 - 7.31340i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-60.9491 + 44.2821i) q^{66} +(55.4435 - 28.2499i) q^{67} +(29.5316 - 29.5316i) q^{68} +(42.3386 + 13.7566i) q^{69} +(-30.4221 - 93.6296i) q^{71} +(-2.21473 + 4.34665i) q^{72} +(50.7302 - 8.03488i) q^{73} +23.8615i q^{74} +6.64209 q^{76} +(13.2640 + 83.7456i) q^{77} +(-52.1889 - 26.5916i) q^{78} +(35.6183 - 11.5731i) q^{79} +(19.3143 - 59.4433i) q^{81} +(36.1276 + 36.1276i) q^{82} +(1.11819 + 2.19457i) q^{83} +(-13.6127 - 18.7362i) q^{84} +(-32.3434 - 23.4989i) q^{86} +(-18.2000 - 2.88259i) q^{87} +(8.73874 - 55.1742i) q^{88} +(73.7197 - 101.466i) q^{89} +(-53.3319 + 38.7479i) q^{91} +(-29.4115 + 14.9859i) q^{92} +(47.4646 - 47.4646i) q^{93} +(35.9492 + 11.6806i) q^{94} +(4.71499 + 14.5113i) q^{96} +(47.3640 - 92.9571i) q^{97} +(42.6993 - 6.76290i) q^{98} -34.0643i 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 $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{9}{20}\right)$

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 $

$2$	0.221232	+	1.39680i	0.110616	+	0.698401i
$2$	0.221232	+	1.39680i	0.110616	+	0.698401i
$3$	2.40328	+	1.22453i	0.801094	+	0.408178i	0.806078	−	0.591810i	$-0.201586\pi$
$3$	2.40328	+	1.22453i	0.801094	+	0.408178i	−0.00498387	+	0.999988i	$0.501586\pi$
$4$	−1.90211	+	0.618034i	−0.475528	+	0.154508i
$5$		0			0
$5$		0			0
$6$	−1.17875	+	3.62781i	−0.196458	+	0.604636i
$7$	3.03568	+	3.03568i	0.433668	+	0.433668i	0.889874	−	0.456206i	$-0.150792\pi$
$7$	3.03568	+	3.03568i	0.433668	+	0.433668i	−0.456206	+	0.889874i	$0.650792\pi$
$8$	−1.28408	−	2.52015i	−0.160510	−	0.315018i
$9$	−1.01379	−	1.39536i	−0.112643	−	0.155040i
$10$		0			0
$11$	15.9782	+	11.6089i	1.45257	+	1.05535i	0.985223	+	0.171276i	$0.0547890\pi$
$11$	15.9782	+	11.6089i	1.45257	+	1.05535i	0.467344	+	0.884076i	$0.345211\pi$
$12$	−5.32811	−	0.843890i	−0.444010	−	0.0703242i
$13$	−2.40210	+	15.1663i	−0.184777	+	1.16664i	0.704649	+	0.709556i	$0.251104\pi$
$13$	−2.40210	+	15.1663i	−0.184777	+	1.16664i	−0.889426	+	0.457079i	$0.848896\pi$
$14$	−3.56865	+	4.91183i	−0.254904	+	0.350845i
$15$		0			0
$16$	3.23607	−	2.35114i	0.202254	−	0.146946i
$17$	−18.6060	+	9.48022i	−1.09447	+	0.557660i	−0.905510	−	0.424325i	$-0.860512\pi$
$17$	−18.6060	+	9.48022i	−1.09447	+	0.557660i	−0.188960	+	0.981985i	$0.560512\pi$
$18$	1.72476	−	1.72476i	0.0958200	−	0.0958200i
$19$	−3.15850	−	1.02626i	−0.166237	−	0.0540137i	0.224716	−	0.974424i	$-0.427855\pi$
$19$	−3.15850	−	1.02626i	−0.166237	−	0.0540137i	−0.390953	+	0.920411i	$0.627855\pi$
$20$		0			0
$21$	3.57830	+	11.0129i	0.170395	+	0.524423i
$22$	−12.6804	+	24.8867i	−0.576382	+	1.13121i
$23$	16.3014	−	2.58189i	0.708758	−	0.112256i	0.208361	−	0.978052i	$-0.433187\pi$
$23$	16.3014	−	2.58189i	0.708758	−	0.112256i	0.500398	+	0.865796i	$0.333187\pi$
$24$		−	7.62902i		−	0.317876i
$25$		0			0
$26$	−21.7157			−0.835219
$27$	−4.52526	−	28.5714i	−0.167602	−	1.05820i
$28$	−7.65035	−	3.89805i	−0.273227	−	0.139216i
$29$	−6.49731	+	2.11110i	−0.224045	+	0.0727967i	−0.418888	−	0.908038i	$-0.637580\pi$
$29$	−6.49731	+	2.11110i	−0.224045	+	0.0727967i	0.194843	+	0.980834i	$0.437580\pi$
$30$		0			0
$31$	7.69031	−	23.6683i	0.248075	−	0.763495i	−0.747041	−	0.664778i	$-0.768526\pi$
$31$	7.69031	−	23.6683i	0.248075	−	0.763495i	0.995116	−	0.0987170i	$-0.0314739\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	24.1848	+	47.4652i	0.732871	+	1.43834i
$34$	−17.3582	−	23.8916i	−0.510536	−	0.702693i
$35$		0			0
$36$	2.79072	+	2.02758i	0.0775200	+	0.0563216i
$37$	16.6649	+	2.63946i	0.450402	+	0.0713367i	0.377515	−	0.926003i	$-0.376779\pi$
$37$	16.6649	+	2.63946i	0.450402	+	0.0713367i	0.0728873	+	0.997340i	$0.476779\pi$
$38$	0.734721	−	4.63885i	0.0193348	−	0.122075i
$39$	−24.3445	+	33.5073i	−0.624218	+	0.859162i
$40$		0			0
$41$	29.2279	−	21.2353i	0.712875	−	0.517934i	−0.171225	−	0.985232i	$-0.554773\pi$
$41$	29.2279	−	21.2353i	0.712875	−	0.517934i	0.884100	+	0.467298i	$0.154773\pi$
$42$	−14.5912	+	7.43457i	−0.347409	+	0.177014i
$43$	−19.9893	+	19.9893i	−0.464868	+	0.464868i	−0.900247	−	0.435379i	$-0.856614\pi$
$43$	−19.9893	+	19.9893i	−0.464868	+	0.464868i	0.435379	+	0.900247i	$0.356614\pi$
$44$	−37.5671	−	12.2063i	−0.853797	−	0.277416i
$45$		0			0
$46$	7.21279	+	22.1987i	0.156800	+	0.482580i
$47$	12.1343	−	23.8149i	0.258177	−	0.506700i	−0.725140	−	0.688601i	$-0.758225\pi$
$47$	12.1343	−	23.8149i	0.258177	−	0.506700i	0.983317	+	0.181901i	$0.0582250\pi$
$48$	10.6562	−	1.68778i	0.222005	−	0.0351621i
$49$		−	30.5693i		−	0.623864i
$50$		0			0
$51$	−56.3243			−1.10440
$52$	−4.80420	−	30.3325i	−0.0923884	−	0.583318i
$53$	−86.7430	−	44.1977i	−1.63666	−	0.833920i	−0.997918	−	0.0644987i	$-0.979455\pi$
$53$	−86.7430	−	44.1977i	−1.63666	−	0.833920i	−0.638742	−	0.769421i	$-0.720545\pi$
$54$	38.9074	−	12.6418i	0.720508	−	0.234107i
$55$		0			0
$56$	3.75230	−	11.5484i	0.0670054	−	0.206221i
$57$	−6.33408	−	6.33408i	−0.111124	−	0.111124i
$58$	−4.38621	−	8.60842i	−0.0756243	−	0.148421i
$59$	63.0774	+	86.8186i	1.06911	+	1.47150i	0.870975	+	0.491327i	$0.163488\pi$
$59$	63.0774	+	86.8186i	1.06911	+	1.47150i	0.198134	+	0.980175i	$0.436512\pi$
$60$		0			0
$61$	65.0278	+	47.2455i	1.06603	+	0.774516i	0.975194	−	0.221350i	$-0.0710464\pi$
$61$	65.0278	+	47.2455i	1.06603	+	0.774516i	0.0908350	+	0.995866i	$0.471046\pi$
$62$	34.7613	+	5.50566i	0.560667	+	0.0888009i
$63$	1.15833	−	7.31340i	0.0183862	−	0.116086i
$64$	−4.70228	+	6.47214i	−0.0734732	+	0.101127i
$65$		0			0
$66$	−60.9491	+	44.2821i	−0.923472	+	0.670941i
$67$	55.4435	−	28.2499i	0.827515	−	0.421640i	0.0116849	−	0.999932i	$-0.496280\pi$
$67$	55.4435	−	28.2499i	0.827515	−	0.421640i	0.815830	+	0.578292i	$0.196280\pi$
$68$	29.5316	−	29.5316i	0.434288	−	0.434288i
$69$	42.3386	+	13.7566i	0.613602	+	0.199371i
$70$		0			0
$71$	−30.4221	−	93.6296i	−0.428480	−	1.31873i	−0.899622	−	0.436669i	$-0.856158\pi$
$71$	−30.4221	−	93.6296i	−0.428480	−	1.31873i	0.471142	−	0.882057i	$-0.343842\pi$
$72$	−2.21473	+	4.34665i	−0.0307601	+	0.0603701i
$73$	50.7302	−	8.03488i	0.694934	−	0.110067i	0.201033	−	0.979585i	$-0.435570\pi$
$73$	50.7302	−	8.03488i	0.694934	−	0.110067i	0.493902	+	0.869518i	$0.335570\pi$
$74$			23.8615i			0.322453i
$75$		0			0
$76$	6.64209			0.0873960
$77$	13.2640	+	83.7456i	0.172260	+	1.08760i
$78$	−52.1889	−	26.5916i	−0.669088	−	0.340918i
$79$	35.6183	−	11.5731i	0.450864	−	0.146495i	−0.0747784	−	0.997200i	$-0.523825\pi$
$79$	35.6183	−	11.5731i	0.450864	−	0.146495i	0.525643	+	0.850706i	$0.323825\pi$
$80$		0			0
$81$	19.3143	−	59.4433i	0.238448	−	0.733868i
$82$	36.1276	+	36.1276i	0.440581	+	0.440581i
$83$	1.11819	+	2.19457i	0.0134721	+	0.0264406i	0.897645	−	0.440720i	$-0.145277\pi$
$83$	1.11819	+	2.19457i	0.0134721	+	0.0264406i	−0.884172	+	0.467161i	$0.845277\pi$
$84$	−13.6127	−	18.7362i	−0.162055	−	0.223050i
$85$		0			0
$86$	−32.3434	−	23.4989i	−0.376086	−	0.273242i
$87$	−18.2000	−	2.88259i	−0.209195	−	0.0331333i
$88$	8.73874	−	55.1742i	0.0993038	−	0.626980i
$89$	73.7197	−	101.466i	0.828311	−	1.14007i	−0.159924	−	0.987129i	$-0.551125\pi$
$89$	73.7197	−	101.466i	0.828311	−	1.14007i	0.988235	−	0.152943i	$-0.0488750\pi$
$90$		0			0
$91$	−53.3319	+	38.7479i	−0.586064	+	0.425801i
$92$	−29.4115	+	14.9859i	−0.319690	+	0.162890i
$93$	47.4646	−	47.4646i	0.510373	−	0.510373i
$94$	35.9492	+	11.6806i	0.382439	+	0.124262i
$95$		0			0
$96$	4.71499	+	14.5113i	0.0491145	+	0.151159i
$97$	47.3640	−	92.9571i	0.488289	−	0.958320i	−0.507054	−	0.861915i	$-0.669265\pi$
$97$	47.3640	−	92.9571i	0.488289	−	0.958320i	0.995342	−	0.0964057i	$-0.0307346\pi$
$98$	42.6993	−	6.76290i	0.435707	−	0.0690092i
$99$		−	34.0643i		−	0.344084i
$100$		0			0
$101$	−153.672			−1.52150			−0.760751	−	0.649044i	$-0.775169\pi$
$101$	−153.672			−1.52150			−0.760751	+	0.649044i	$0.775169\pi$
$102$	−12.4607	−	78.6739i	−0.122164	−	0.771312i
$103$	−23.5663	−	12.0076i	−0.228799	−	0.116579i	0.335834	−	0.941921i	$-0.390982\pi$
$103$	−23.5663	−	12.0076i	−0.228799	−	0.116579i	−0.564632	+	0.825343i	$0.690982\pi$
$104$	41.3057	−	13.4210i	0.397170	−	0.129048i
$105$		0			0
$106$	42.5452	−	130.941i	0.401370	−	1.23529i
$107$	−43.3886	−	43.3886i	−0.405501	−	0.405501i	0.474666	−	0.880166i	$-0.342569\pi$
$107$	−43.3886	−	43.3886i	−0.405501	−	0.405501i	−0.880166	+	0.474666i	$0.842569\pi$
$108$	26.2656	+	51.5492i	0.243200	+	0.477308i
$109$	4.51121	+	6.20915i	0.0413873	+	0.0569647i	0.829209	−	0.558939i	$-0.188791\pi$
$109$	4.51121	+	6.20915i	0.0413873	+	0.0569647i	−0.787822	+	0.615903i	$0.788791\pi$
$110$		0			0
$111$	36.8183	+	26.7501i	0.331696	+	0.240992i
$112$	16.9610	+	2.68635i	0.151437	+	0.0239853i
$113$	21.3215	−	134.618i	0.188685	−	1.19131i	−0.693516	−	0.720441i	$-0.743939\pi$
$113$	21.3215	−	134.618i	0.188685	−	1.19131i	0.882202	−	0.470872i	$-0.156061\pi$
$114$	7.44616	−	10.2488i	0.0653172	−	0.0899014i
$115$		0			0
$116$	11.0539	−	8.03112i	0.0952921	−	0.0692338i
$117$	23.5976	−	12.0236i	0.201689	−	0.102766i
$118$	−107.314	+	107.314i	−0.909438	+	0.909438i
$119$	−85.2607	−	27.7029i	−0.716476	−	0.232797i
$120$		0			0
$121$	83.1472	+	255.901i	0.687167	+	2.11488i
$122$	−51.6064	+	101.283i	−0.423003	+	0.830190i
$123$	96.2461	−	15.2439i	0.782488	−	0.123934i
$124$			49.7727i			0.401393i
$125$		0			0
$126$	10.4716			0.0831082
$127$	19.5250	+	123.276i	0.153740	+	0.970677i	0.937088	+	0.349093i	$0.113510\pi$
$127$	19.5250	+	123.276i	0.153740	+	0.970677i	−0.783348	+	0.621583i	$0.786490\pi$
$128$	−10.0806	−	5.13632i	−0.0787546	−	0.0401275i
$129$	−72.5175	+	23.5624i	−0.562151	+	0.182654i
$130$		0			0
$131$	52.6853	−	162.149i	0.402178	−	1.23778i	−0.521050	−	0.853526i	$-0.674460\pi$
$131$	52.6853	−	162.149i	0.402178	−	1.23778i	0.923229	−	0.384251i	$-0.125540\pi$
$132$	−75.3373	−	75.3373i	−0.570737	−	0.570737i
$133$	−6.47280	−	12.7036i	−0.0486677	−	0.0955157i
$134$	51.7253	+	71.1938i	0.386010	+	0.531297i
$135$		0			0
$136$	47.7831	+	34.7165i	0.351346	+	0.255268i
$137$	−116.319	−	18.4231i	−0.849041	−	0.134475i	−0.283273	−	0.959039i	$-0.591420\pi$
$137$	−116.319	−	18.4231i	−0.849041	−	0.134475i	−0.565768	+	0.824564i	$0.691420\pi$
$138$	−9.84866	+	62.1820i	−0.0713671	+	0.450594i
$139$	−64.0359	+	88.1378i	−0.460690	+	0.634085i	−0.974652	−	0.223728i	$-0.928177\pi$
$139$	−64.0359	+	88.1378i	−0.460690	+	0.634085i	0.513962	+	0.857813i	$0.328177\pi$
$140$		0			0
$141$	58.3243	−	42.3751i	0.413648	−	0.300533i
$142$	124.052	−	63.2075i	0.873603	−	0.445123i
$143$	−214.444	+	214.444i	−1.49961	+	1.49961i
$144$	−6.56138	−	2.13192i	−0.0455651	−	0.0148050i
$145$		0			0
$146$	22.4463	+	69.0825i	0.153742	+	0.473168i
$147$	37.4331	−	73.4667i	0.254647	−	0.499773i
$148$	−33.3298	+	5.27892i	−0.225201	+	0.0356684i
$149$			61.4078i			0.412133i	0.978538	+	0.206066i	$0.0660663\pi$
$149$			61.4078i			0.412133i	−0.978538	+	0.206066i	$0.933934\pi$
$150$		0			0
$151$	−168.345			−1.11487			−0.557433	−	0.830222i	$-0.688214\pi$
$151$	−168.345			−1.11487			−0.557433	+	0.830222i	$0.688214\pi$
$152$	1.46944	+	9.27769i	0.00966738	+	0.0610374i
$153$	32.0909	+	16.3511i	0.209744	+	0.106870i
$154$	−114.042	+	37.0543i	−0.740530	+	0.240613i
$155$		0			0
$156$	25.5973	−	78.7805i	0.164085	−	0.505003i
$157$	84.0849	+	84.0849i	0.535572	+	0.535572i	0.922225	−	0.386653i	$-0.126369\pi$
$157$	84.0849	+	84.0849i	0.535572	+	0.535572i	−0.386653	+	0.922225i	$0.626369\pi$
$158$	24.0452	+	47.1913i	0.152185	+	0.298679i
$159$	−154.346	−	212.439i	−0.970730	−	1.33610i
$160$		0			0
$161$	57.3237	+	41.6481i	0.356048	+	0.258684i
$162$	87.3034	+	13.8275i	0.538910	+	0.0853550i
$163$	−5.28541	+	33.3708i	−0.0324258	+	0.204729i	−0.998582	−	0.0532277i	$-0.983049\pi$
$163$	−5.28541	+	33.3708i	−0.0324258	+	0.204729i	0.966157	+	0.257956i	$0.0830491\pi$
$164$	−42.4706	+	58.4557i	−0.258967	+	0.356437i
$165$		0			0
$166$	−2.81800	+	2.04740i	−0.0169759	+	0.0123337i
$167$	−119.421	+	60.8479i	−0.715095	+	0.364359i	−0.773381	−	0.633941i	$-0.781436\pi$
$167$	−119.421	+	60.8479i	−0.715095	+	0.364359i	0.0582868	+	0.998300i	$0.481436\pi$
$168$	23.1592	−	23.1592i	0.137853	−	0.137853i
$169$	−63.5167	−	20.6378i	−0.375839	−	0.122117i
$170$		0			0
$171$	1.77005	+	5.44766i	0.0103512	+	0.0318577i
$172$	25.6679	−	50.3760i	0.149232	−	0.292884i
$173$	−130.283	+	20.6348i	−0.753082	+	0.119276i	−0.521161	−	0.853458i	$-0.674501\pi$
$173$	−130.283	+	20.6348i	−0.753082	+	0.119276i	−0.231921	+	0.972735i	$0.574501\pi$
$174$		−	26.0595i		−	0.149767i
$175$		0			0
$176$	79.0007			0.448868
$177$	45.2805	+	285.890i	0.255822	+	1.61520i
$178$	158.038	+	80.5242i	0.887852	+	0.452383i
$179$	−215.065	+	69.8787i	−1.20148	+	0.390384i	−0.840304	−	0.542115i	$-0.817624\pi$
$179$	−215.065	+	69.8787i	−1.20148	+	0.390384i	−0.361173	+	0.932499i	$0.617624\pi$
$180$		0			0
$181$	−18.7263	+	57.6336i	−0.103460	+	0.318418i	−0.989366	−	0.145447i	$-0.953538\pi$
$181$	−18.7263	+	57.6336i	−0.103460	+	0.318418i	0.885906	+	0.463865i	$0.153538\pi$
$182$	−65.9218	−	65.9218i	−0.362208	−	0.362208i
$183$	98.4264	+	193.173i	0.537849	+	1.05559i
$184$	−27.4391	−	37.7667i	−0.149125	−	0.205254i
$185$		0			0
$186$	76.7994	+	55.7980i	0.412900	+	0.299989i
$187$	−407.346	−	64.5172i	−2.17832	−	0.345012i
$188$	−8.36240	+	52.7981i	−0.0444808	+	0.280841i
$189$	72.9963	−	100.471i	0.386224	−	0.531591i
$190$		0			0
$191$	−144.737	+	105.158i	−0.757787	+	0.550565i	−0.898231	−	0.439524i	$-0.855147\pi$
$191$	−144.737	+	105.158i	−0.757787	+	0.550565i	0.140444	+	0.990089i	$0.455147\pi$
$192$	−19.2262	+	9.79626i	−0.100137	+	0.0510222i
$193$	125.750	−	125.750i	0.651554	−	0.651554i	−0.301813	−	0.953367i	$-0.597592\pi$
$193$	125.750	−	125.750i	0.651554	−	0.651554i	0.953367	+	0.301813i	$0.0975918\pi$
$194$	140.321	+	45.5931i	0.723304	+	0.235016i
$195$		0			0
$196$	18.8929	+	58.1463i	0.0963922	+	0.296665i
$197$	−129.093	+	253.359i	−0.655294	+	1.28609i	0.289108	+	0.957296i	$0.406641\pi$
$197$	−129.093	+	253.359i	−0.655294	+	1.28609i	−0.944403	+	0.328791i	$0.893359\pi$
$198$	47.5811	−	7.53611i	0.240309	−	0.0380612i
$199$		−	6.73587i		−	0.0338486i	−0.999857	−	0.0169243i	$-0.994613\pi$
$199$		−	6.73587i		−	0.0338486i	0.999857	−	0.0169243i	$-0.00538743\pi$
$200$		0			0
$201$	167.839			0.835021
$202$	−33.9971	−	214.649i	−0.168302	−	1.06262i
$203$	−26.1324	−	13.3151i	−0.128731	−	0.0655917i
$204$	107.135	−	34.8103i	0.525172	−	0.170639i
$205$		0			0
$206$	11.5587	−	35.5739i	0.0561100	−	0.172689i
$207$	−20.1289	−	20.1289i	−0.0972410	−	0.0972410i
$208$	27.8847	+	54.7267i	0.134061	+	0.263109i
$209$	−38.5536	−	53.0645i	−0.184467	−	0.253897i
$210$		0			0
$211$	150.905	+	109.639i	0.715189	+	0.519615i	0.884844	−	0.465888i	$-0.154265\pi$
$211$	150.905	+	109.639i	0.715189	+	0.519615i	−0.169654	+	0.985504i	$0.554265\pi$
$212$	192.311	+	30.4590i	0.907126	+	0.143675i
$213$	41.5396	−	262.271i	0.195022	−	1.23132i
$214$	51.0063	−	70.2042i	0.238347	−	0.328057i
$215$		0			0
$216$	−66.1933	+	48.0922i	−0.306450	+	0.222649i
$217$	95.1948	−	48.5042i	0.438686	−	0.223521i
$218$	−7.67493	+	7.67493i	−0.0352061	+	0.0352061i
$219$	131.758	+	42.8107i	0.601634	+	0.195483i
$220$		0			0
$221$	−99.0861	−	304.956i	−0.448353	−	1.37989i
$222$	−29.2192	+	57.3459i	−0.131618	+	0.258315i
$223$	108.214	−	17.1394i	0.485265	−	0.0768585i	0.0909918	−	0.995852i	$-0.470996\pi$
$223$	108.214	−	17.1394i	0.485265	−	0.0768585i	0.394273	+	0.918993i	$0.370996\pi$
$224$			24.2854i			0.108417i
$225$		0			0
$226$	192.752			0.852886
$227$	−37.3191	−	235.624i	−0.164401	−	1.03799i	−0.922542	−	0.385898i	$-0.873892\pi$
$227$	−37.3191	−	235.624i	−0.164401	−	1.03799i	0.758140	−	0.652091i	$-0.226108\pi$
$228$	15.9628	+	8.13346i	0.0700123	+	0.0356731i
$229$	337.031	−	109.508i	1.47175	−	0.478201i	0.540115	−	0.841591i	$-0.318381\pi$
$229$	337.031	−	109.508i	1.47175	−	0.478201i	0.931637	+	0.363390i	$0.118381\pi$
$230$		0			0
$231$	−70.6721	+	217.506i	−0.305940	+	0.941586i
$232$	13.6634	+	13.6634i	0.0588938	+	0.0588938i
$233$	−137.042	−	268.960i	−0.588162	−	1.15433i	−0.972882	−	0.231300i	$-0.925702\pi$
$233$	−137.042	−	268.960i	−0.588162	−	1.15433i	0.384720	−	0.923033i	$-0.374298\pi$
$234$	22.0151	+	30.3012i	0.0940817	+	0.129492i
$235$		0			0
$236$	−173.637	−	126.155i	−0.735751	−	0.534555i
$237$	99.7723	+	15.8024i	0.420980	+	0.0666767i
$238$	19.8331	−	125.221i	0.0833322	−	0.526139i
$239$	−147.049	+	202.396i	−0.615269	+	0.846845i	−0.996998	−	0.0774294i	$-0.975329\pi$
$239$	−147.049	+	202.396i	−0.615269	+	0.846845i	0.381729	+	0.924274i	$0.375329\pi$
$240$		0			0
$241$	134.577	−	97.7760i	0.558411	−	0.405709i	−0.272466	−	0.962165i	$-0.587839\pi$
$241$	134.577	−	97.7760i	0.558411	−	0.405709i	0.830877	+	0.556456i	$0.187839\pi$
$242$	−339.048	+	172.753i	−1.40102	+	0.713857i
$243$	−64.8857	+	64.8857i	−0.267019	+	0.267019i
$244$	−152.890	−	49.6768i	−0.626596	−	0.203594i
$245$		0			0
$246$	42.5854	+	131.064i	0.173111	+	0.532782i
$247$	23.1516	−	45.4375i	0.0937310	−	0.183957i
$248$	−69.5227	+	11.0113i	−0.280333	+	0.0444004i
$249$			6.64342i			0.0266804i
$250$		0			0
$251$	−254.134			−1.01248			−0.506242	−	0.862391i	$-0.668966\pi$
$251$	−254.134			−1.01248			−0.506242	+	0.862391i	$0.668966\pi$
$252$	2.31666	+	14.6268i	0.00919309	+	0.0580429i
$253$	290.441	+	147.987i	1.14799	+	0.584929i
$254$	−167.873	+	54.5451i	−0.660915	+	0.214744i
$255$		0			0
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	208.034	+	208.034i	0.809470	+	0.809470i	0.984554	−	0.175083i	$-0.0560194\pi$
$257$	208.034	+	208.034i	0.809470	+	0.809470i	−0.175083	+	0.984554i	$0.556019\pi$
$258$	−48.9551	−	96.0799i	−0.189749	−	0.372403i
$259$	42.5767	+	58.6018i	0.164389	+	0.226262i
$260$		0			0
$261$	9.53265	+	6.92588i	0.0365236	+	0.0265359i
$262$	238.145	+	37.7185i	0.908952	+	0.143964i
$263$	5.12987	−	32.3887i	0.0195052	−	0.123151i	−0.976014	−	0.217706i	$-0.930143\pi$
$263$	5.12987	−	32.3887i	0.0195052	−	0.123151i	0.995520	+	0.0945547i	$0.0301427\pi$
$264$	88.5643	−	121.898i	0.335471	−	0.461736i
$265$		0			0
$266$	16.3124	−	11.8517i	0.0613249	−	0.0445551i
$267$	301.418	−	153.580i	1.12891	−	0.575207i
$268$	−88.0004	+	88.0004i	−0.328360	+	0.328360i
$269$	234.274	+	76.1202i	0.870906	+	0.282975i	0.710176	−	0.704024i	$-0.248615\pi$
$269$	234.274	+	76.1202i	0.870906	+	0.282975i	0.160730	+	0.986998i	$0.448615\pi$
$270$		0			0
$271$	−66.4989	−	204.663i	−0.245383	−	0.755213i	−0.995573	−	0.0939900i	$-0.970038\pi$
$271$	−66.4989	−	204.663i	−0.245383	−	0.755213i	0.750190	−	0.661223i	$-0.229962\pi$
$272$	−37.9209	+	74.4240i	−0.139415	+	0.273617i
$273$	−175.619	+	27.8154i	−0.643295	+	0.101888i
$274$		−	166.550i		−	0.607846i
$275$		0			0
$276$	−89.0348			−0.322590
$277$	−18.3162	−	115.644i	−0.0661234	−	0.417486i	−0.998440	−	0.0558424i	$-0.982216\pi$
$277$	−18.3162	−	115.644i	−0.0661234	−	0.417486i	0.932316	−	0.361644i	$-0.117784\pi$
$278$	−137.278	−	69.9465i	−0.493805	−	0.251606i
$279$	−40.8222	+	13.2639i	−0.146316	+	0.0475410i
$280$		0			0
$281$	−86.1504	+	265.144i	−0.306585	+	0.943571i	0.672496	+	0.740101i	$0.265222\pi$
$281$	−86.1504	+	265.144i	−0.306585	+	0.943571i	−0.979081	+	0.203471i	$0.934778\pi$
$282$	72.0928	+	72.0928i	0.255648	+	0.255648i
$283$	31.0915	+	61.0205i	0.109864	+	0.215620i	0.939392	−	0.342845i	$-0.111390\pi$
$283$	31.0915	+	61.0205i	0.109864	+	0.215620i	−0.829528	+	0.558465i	$0.811390\pi$
$284$	115.732	+	159.292i	0.407509	+	0.560888i
$285$		0			0
$286$	−346.978	−	252.095i	−1.21321	−	0.881449i
$287$	153.190	+	24.2629i	0.533763	+	0.0845397i
$288$	1.52629	−	9.63660i	0.00529961	−	0.0334604i
$289$	86.4382	−	118.972i	0.299094	−	0.411668i
$290$		0			0
$291$	227.658	−	165.403i	0.782330	−	0.568396i
$292$	−91.5288	+	46.6362i	−0.313455	+	0.159713i
$293$	−105.951	+	105.951i	−0.361609	+	0.361609i	−0.864405	−	0.502796i	$-0.832305\pi$
$293$	−105.951	+	105.951i	−0.361609	+	0.361609i	0.502796	+	0.864405i	$0.332305\pi$
$294$	110.900	+	36.0335i	0.377210	+	0.122563i
$295$		0			0
$296$	−14.7472	−	45.3872i	−0.0498217	−	0.153335i
$297$	259.376	−	509.053i	0.873319	−	1.71398i
$298$	−85.7745	+	13.5854i	−0.287834	+	0.0455884i
$299$			253.434i			0.847605i
$300$		0			0
$301$	−121.362			−0.403197
$302$	−37.2432	−	235.144i	−0.123322	−	0.778624i
$303$	−369.316	−	188.176i	−1.21887	−	0.621043i
$304$	−12.6340	+	4.10504i	−0.0415592	+	0.0135034i
$305$		0			0
$306$	−15.7398	+	48.4420i	−0.0514371	+	0.158307i
$307$	−54.2997	−	54.2997i	−0.176872	−	0.176872i	0.613119	−	0.789991i	$-0.289915\pi$
$307$	−54.2997	−	54.2997i	−0.176872	−	0.176872i	−0.789991	+	0.613119i	$0.789915\pi$
$308$	−76.9872	−	151.096i	−0.249958	−	0.490571i
$309$	−41.9327	−	57.7153i	−0.135704	−	0.186781i
$310$		0			0
$311$	−38.3357	−	27.8525i	−0.123266	−	0.0895579i	0.524444	−	0.851445i	$-0.324273\pi$
$311$	−38.3357	−	27.8525i	−0.123266	−	0.0895579i	−0.647710	+	0.761887i	$0.724273\pi$
$312$	115.704	+	18.3257i	0.370845	+	0.0587361i
$313$	−23.0002	+	145.218i	−0.0734832	+	0.463955i	0.923318	+	0.384036i	$0.125466\pi$
$313$	−23.0002	+	145.218i	−0.0734832	+	0.463955i	−0.996801	+	0.0799187i	$0.974534\pi$
$314$	−98.8477	+	136.052i	−0.314802	+	0.433287i
$315$		0			0
$316$	−60.5974	+	44.0266i	−0.191764	+	0.139325i
$317$	60.5119	−	30.8324i	0.190889	−	0.0972630i	−0.355934	−	0.934511i	$-0.615837\pi$
$317$	60.5119	−	30.8324i	0.190889	−	0.0972630i	0.546823	+	0.837248i	$0.315837\pi$
$318$	262.589	−	262.589i	0.825753	−	0.825753i
$319$	−128.323	−	41.6947i	−0.402267	−	0.130704i
$320$		0			0
$321$	−51.1442	−	157.406i	−0.159328	−	0.490360i
$322$	−45.4924	+	89.2838i	−0.141281	+	0.277279i
$323$	68.4962	−	10.8487i	0.212063	−	0.0335874i
$324$			125.005i			0.385817i
$325$		0			0
$326$	−47.7817			−0.146570
$327$	3.23840	+	20.4465i	0.00990336	+	0.0625274i
$328$	−91.0469	−	46.3907i	−0.277582	−	0.141435i
$329$	109.130	−	35.4586i	0.331703	−	0.107777i
$330$		0			0
$331$	−10.7322	+	33.0304i	−0.0324236	+	0.0997897i	−0.965959	−	0.258697i	$-0.916707\pi$
$331$	−10.7322	+	33.0304i	−0.0324236	+	0.0997897i	0.933535	+	0.358486i	$0.116707\pi$
$332$	−3.48324	−	3.48324i	−0.0104917	−	0.0104917i
$333$	−13.2117	−	25.9294i	−0.0396747	−	0.0778660i
$334$	−111.412	−	153.346i	−0.333569	−	0.459119i
$335$		0			0
$336$	37.4724	+	27.2253i	0.111525	+	0.0810277i
$337$	−134.926	−	21.3702i	−0.400374	−	0.0634131i	−0.0469995	−	0.998895i	$-0.514966\pi$
$337$	−134.926	−	21.3702i	−0.400374	−	0.0634131i	−0.353375	+	0.935482i	$0.614966\pi$
$338$	14.7751	−	93.2861i	0.0437132	−	0.275994i
$339$	216.086	−	297.417i	0.637422	−	0.877336i
$340$		0			0
$341$	397.640	−	288.903i	1.16610	−	0.847222i
$342$	−7.21771	+	3.67761i	−0.0211044	+	0.0107532i
$343$	241.547	−	241.547i	0.704218	−	0.704218i
$344$	76.0439	+	24.7082i	0.221058	+	0.0718260i
$345$		0			0
$346$	−57.6455	−	177.415i	−0.166606	−	0.512759i
$347$	140.732	−	276.202i	0.405567	−	0.795970i	−0.594399	−	0.804170i	$-0.702610\pi$
$347$	140.732	−	276.202i	0.405567	−	0.795970i	0.999966	+	0.00819994i	$0.00261015\pi$
$348$	36.4000	−	5.76519i	0.104598	−	0.0165666i
$349$			134.320i			0.384872i	0.981310	+	0.192436i	$0.0616388\pi$
$349$			134.320i			0.384872i	−0.981310	+	0.192436i	$0.938361\pi$
$350$		0			0
$351$	444.191			1.26550
$352$	17.4775	+	110.348i	0.0496519	+	0.313490i
$353$	407.275	+	207.517i	1.15375	+	0.587866i	0.922869	−	0.385115i	$-0.125838\pi$
$353$	407.275	+	207.517i	1.15375	+	0.587866i	0.230884	+	0.972981i	$0.425838\pi$
$354$	−389.314	+	126.496i	−1.09976	+	0.357333i
$355$		0			0
$356$	−77.5134	+	238.562i	−0.217734	+	0.670118i
$357$	−170.982	−	170.982i	−0.478942	−	0.478942i
$358$	−145.186	−	284.943i	−0.405547	−	0.795931i
$359$	160.357	+	220.712i	0.446676	+	0.614797i	0.971679	−	0.236303i	$-0.0759359\pi$
$359$	160.357	+	220.712i	0.446676	+	0.614797i	−0.525003	+	0.851100i	$0.675936\pi$
$360$		0			0
$361$	−283.132	−	205.708i	−0.784300	−	0.569827i
$362$	−84.6457	−	13.4066i	−0.233828	−	0.0370347i
$363$	−113.533	+	716.818i	−0.312762	+	1.97470i
$364$	77.4957	−	106.664i	0.212900	−	0.293032i
$365$		0			0
$366$	−248.049	+	180.218i	−0.677730	+	0.492400i
$367$	−131.060	+	66.7782i	−0.357111	+	0.181957i	−0.623337	−	0.781954i	$-0.714223\pi$
$367$	−131.060	+	66.7782i	−0.357111	+	0.181957i	0.266226	+	0.963911i	$0.414223\pi$
$368$	46.6822	−	46.6822i	0.126854	−	0.126854i
$369$	−59.2618	−	19.2553i	−0.160601	−	0.0521824i
$370$		0			0
$371$	−129.154	−	397.494i	−0.348123	−	1.07141i
$372$	−60.9484	+	119.618i	−0.163840	+	0.321553i
$373$	−280.873	+	44.4859i	−0.753011	+	0.119265i	−0.521128	−	0.853479i	$-0.674489\pi$
$373$	−280.873	+	44.4859i	−0.753011	+	0.119265i	−0.231883	+	0.972744i	$0.574489\pi$
$374$		−	583.254i		−	1.55950i
$375$		0			0
$376$	−75.5985			−0.201060
$377$	−16.4104	−	103.611i	−0.0435288	−	0.274830i
$378$	156.487	+	79.7340i	0.413986	+	0.210937i
$379$	664.737	−	215.986i	1.75392	−	0.569884i	0.757381	−	0.652974i	$-0.226479\pi$
$379$	664.737	−	215.986i	1.75392	−	0.569884i	0.996542	+	0.0830897i	$0.0264788\pi$
$380$		0			0
$381$	−104.031	+	320.176i	−0.273048	+	0.840356i
$382$	−178.905	−	178.905i	−0.468338	−	0.468338i
$383$	−227.760	−	447.004i	−0.594673	−	1.16711i	−0.970653	−	0.240484i	$-0.922694\pi$
$383$	−227.760	−	447.004i	−0.594673	−	1.16711i	0.375980	−	0.926628i	$-0.377306\pi$
$384$	−17.9369	−	24.6880i	−0.0467107	−	0.0642917i
$385$		0			0
$386$	203.468	+	147.828i	0.527119	+	0.382974i
$387$	48.1572	+	7.62736i	0.124437	+	0.0197089i
$388$	−32.6410	+	206.087i	−0.0841264	+	0.531153i
$389$	−252.774	+	347.914i	−0.649805	+	0.894379i	−0.999091	−	0.0426369i	$-0.986424\pi$
$389$	−252.774	+	347.914i	−0.649805	+	0.894379i	0.349286	+	0.937016i	$0.386424\pi$
$390$		0			0
$391$	−278.827	+	202.580i	−0.713114	+	0.518107i
$392$	−77.0392	+	39.2534i	−0.196529	+	0.100136i
$393$	325.174	−	325.174i	0.827415	−	0.827415i
$394$	−382.452	−	124.266i	−0.970691	−	0.315397i
$395$		0			0
$396$	21.0529	+	64.7942i	0.0531639	+	0.163622i
$397$	−258.120	+	506.590i	−0.650177	+	1.27604i	0.296860	+	0.954921i	$0.404060\pi$
$397$	−258.120	+	506.590i	−0.650177	+	1.27604i	−0.947037	+	0.321123i	$0.895940\pi$
$398$	9.40868	−	1.49019i	0.0236399	−	0.00374419i
$399$		−	38.4565i		−	0.0963821i
$400$		0			0
$401$	596.762			1.48818			0.744092	−	0.668077i	$-0.232882\pi$
$401$	596.762			1.48818			0.744092	+	0.668077i	$0.232882\pi$
$402$	37.1314	+	234.438i	0.0923666	+	0.583180i
$403$	340.487	+	173.487i	0.844882	+	0.430489i
$404$	292.301	−	94.9743i	0.723517	−	0.235085i
$405$		0			0
$406$	12.8173	−	39.4475i	0.0315696	−	0.0971613i
$407$	235.634	+	235.634i	0.578954	+	0.578954i
$408$	72.3248	+	141.945i	0.177267	+	0.347905i
$409$	11.2451	+	15.4776i	0.0274942	+	0.0378425i	0.822543	−	0.568703i	$-0.192555\pi$
$409$	11.2451	+	15.4776i	0.0274942	+	0.0378425i	−0.795049	+	0.606546i	$0.792555\pi$
$410$		0			0
$411$	−256.987	−	186.712i	−0.625272	−	0.454287i
$412$	52.2468	+	8.27508i	0.126813	+	0.0200852i
$413$	−72.0706	+	455.036i	−0.174505	+	1.10178i
$414$	23.6629	−	32.5692i	0.0571568	−	0.0786696i
$415$		0			0
$416$	−70.2734	+	51.0566i	−0.168927	+	0.122732i
$417$	−261.824	+	133.406i	−0.627875	+	0.319918i
$418$	65.5913	−	65.5913i	0.156917	−	0.156917i
$419$	−427.833	−	139.011i	−1.02108	−	0.331769i	−0.249822	−	0.968292i	$-0.580372\pi$
$419$	−427.833	−	139.011i	−1.02108	−	0.331769i	−0.771258	+	0.636523i	$0.780372\pi$
$420$		0			0
$421$	222.954	+	686.182i	0.529582	+	1.62989i	0.755072	+	0.655641i	$0.227602\pi$
$421$	222.954	+	686.182i	0.529582	+	1.62989i	−0.225490	+	0.974245i	$0.572398\pi$
$422$	−119.759	+	235.040i	−0.283789	+	0.556967i
$423$	−45.5320	+	7.21156i	−0.107641	+	0.0170486i
$424$			275.358i			0.649430i
$425$		0			0
$426$	375.531			0.881527
$427$	53.9814	+	340.825i	0.126420	+	0.798186i
$428$	109.346	+	55.7143i	0.255480	+	0.130174i
$429$	−777.964	+	252.776i	−1.81344	+	0.589221i
$430$		0			0
$431$	−81.0065	+	249.312i	−0.187950	+	0.578451i	−0.999987	−	0.00515539i	$-0.998359\pi$
$431$	−81.0065	+	249.312i	−0.187950	+	0.578451i	0.812037	+	0.583607i	$0.198359\pi$
$432$	−81.8194	−	81.8194i	−0.189397	−	0.189397i
$433$	148.962	+	292.354i	0.344023	+	0.675183i	0.996587	−	0.0825505i	$-0.0263066\pi$
$433$	148.962	+	292.354i	0.344023	+	0.675183i	−0.652564	+	0.757734i	$0.726307\pi$
$434$	88.8108	+	122.238i	0.204633	+	0.281654i
$435$		0			0
$436$	−12.4183	−	9.02242i	−0.0284823	−	0.0206936i
$437$	−54.1378	−	8.57459i	−0.123885	−	0.0196215i
$438$	−30.6491	+	193.511i	−0.0699751	+	0.441806i
$439$	−235.016	+	323.472i	−0.535344	+	0.736837i	−0.987933	−	0.154882i	$-0.950500\pi$
$439$	−235.016	+	323.472i	−0.535344	+	0.736837i	0.452589	+	0.891719i	$0.350500\pi$
$440$		0			0
$441$	−42.6552	+	30.9908i	−0.0967239	+	0.0702740i
$442$	404.042	−	205.870i	0.914122	−	0.465768i
$443$	123.250	−	123.250i	0.278216	−	0.278216i	−0.554181	−	0.832396i	$-0.686968\pi$
$443$	123.250	−	123.250i	0.278216	−	0.278216i	0.832396	+	0.554181i	$0.186968\pi$
$444$	−86.5650	−	28.1267i	−0.194966	−	0.0633484i
$445$		0			0
$446$	47.8808	+	147.362i	0.107356	+	0.330408i
$447$	−75.1959	+	147.580i	−0.168223	+	0.330157i
$448$	−33.9219	+	5.37271i	−0.0757186	+	0.0119926i
$449$		−	330.000i		−	0.734966i	−0.930030	−	0.367483i	$-0.880220\pi$
$449$		−	330.000i		−	0.734966i	0.930030	−	0.367483i	$-0.119780\pi$
$450$		0			0
$451$	713.527			1.58210
$452$	42.6429	+	269.237i	0.0943427	+	0.595657i
$453$	−404.580	−	206.144i	−0.893112	−	0.455063i
$454$	320.863	−	104.255i	0.706747	−	0.229636i
$455$		0			0
$456$	−7.82935	+	24.0963i	−0.0171696	+	0.0528427i
$457$	−105.636	−	105.636i	−0.231151	−	0.231151i	0.582022	−	0.813173i	$-0.302262\pi$
$457$	−105.636	−	105.636i	−0.231151	−	0.231151i	−0.813173	+	0.582022i	$0.802262\pi$
$458$	227.523	+	446.539i	0.496775	+	0.974977i
$459$	355.060	+	488.698i	0.773551	+	1.06470i
$460$		0			0
$461$	−81.4590	−	59.1834i	−0.176701	−	0.128381i	0.495919	−	0.868369i	$-0.334831\pi$
$461$	−81.4590	−	59.1834i	−0.176701	−	0.128381i	−0.672620	+	0.739988i	$0.734831\pi$
$462$	−319.448	−	50.5956i	−0.691446	−	0.109514i
$463$	0.953017	−	6.01712i	0.00205835	−	0.0129959i	−0.986638	−	0.162929i	$-0.947906\pi$
$463$	0.953017	−	6.01712i	0.00205835	−	0.0129959i	0.988696	+	0.149933i	$0.0479058\pi$
$464$	−16.0622	+	22.1078i	−0.0346169	+	0.0476461i
$465$		0			0
$466$	345.365	−	250.923i	0.741127	−	0.538461i
$467$	−127.516	+	64.9728i	−0.273054	+	0.139128i	−0.585156	−	0.810921i	$-0.698967\pi$
$467$	−127.516	+	64.9728i	−0.273054	+	0.139128i	0.312102	+	0.950049i	$0.398967\pi$
$468$	−37.4544	+	37.4544i	−0.0800307	+	0.0800307i
$469$	254.066	+	82.5511i	0.541719	+	0.176015i
$470$		0			0
$471$	99.1149	+	305.044i	0.210435	+	0.647652i
$472$	137.799	−	270.446i	0.291948	−	0.572980i
$473$	−551.447	+	87.3407i	−1.16585	+	0.184653i
$474$			142.858i			0.301389i
$475$		0			0
$476$	179.297			0.376674
$477$	26.2672	+	165.845i	0.0550676	+	0.347683i
$478$	−315.239	−	160.622i	−0.659496	−	0.336030i
$479$	−189.361	+	61.5271i	−0.395326	+	0.128449i	−0.499932	−	0.866065i	$-0.666642\pi$
$479$	−189.361	+	61.5271i	−0.395326	+	0.128449i	0.104606	+	0.994514i	$0.466642\pi$
$480$		0			0
$481$	−80.0614	+	246.404i	−0.166448	+	0.512274i
$482$	166.346	+	166.346i	0.345117	+	0.345117i
$483$	86.7655	+	170.287i	0.179639	+	0.352561i
$484$	−316.311	−	435.364i	−0.653534	−	0.899513i
$485$		0			0
$486$	−104.987	−	76.2777i	−0.216023	−	0.156950i
$487$	−371.062	−	58.7704i	−0.761934	−	0.120678i	−0.236638	−	0.971598i	$-0.576045\pi$
$487$	−371.062	−	58.7704i	−0.761934	−	0.120678i	−0.525296	+	0.850919i	$0.676045\pi$
$488$	35.5647	−	224.547i	0.0728784	−	0.460136i
$489$	−53.5659	+	73.7272i	−0.109542	+	0.150771i
$490$		0			0
$491$	263.402	−	191.373i	0.536460	−	0.389761i	−0.286309	−	0.958137i	$-0.592428\pi$
$491$	263.402	−	191.373i	0.536460	−	0.389761i	0.822769	+	0.568376i	$0.192428\pi$
$492$	−173.650	+	88.4789i	−0.352946	+	0.179835i
$493$	100.875	−	100.875i	0.204615	−	0.204615i
$494$	68.5891	+	22.2859i	0.138844	+	0.0451132i
$495$		0			0
$496$	−30.7612	−	94.6734i	−0.0620186	−	0.190874i
$497$	191.877	−	376.581i	0.386071	−	0.757708i
$498$	−9.27954	+	1.46974i	−0.0186336	+	0.00295128i
$499$		−	400.069i		−	0.801742i	−0.916134	−	0.400871i	$-0.868708\pi$
$499$		−	400.069i		−	0.801742i	0.916134	−	0.400871i	$-0.131292\pi$
$500$		0			0
$501$	−361.512			−0.721581
$502$	−56.2224	−	354.974i	−0.111997	−	0.707120i
$503$	−159.768	−	81.4059i	−0.317630	−	0.161841i	0.287905	−	0.957659i	$-0.407041\pi$
$503$	−159.768	−	81.4059i	−0.317630	−	0.161841i	−0.605536	+	0.795818i	$0.707041\pi$
$504$	−19.9182	+	6.47183i	−0.0395203	+	0.0128409i
$505$		0			0
$506$	−142.454	+	438.428i	−0.281530	+	0.866459i
$507$	−127.377	−	127.377i	−0.251236	−	0.251236i
$508$	−113.327	−	222.418i	−0.223086	−	0.437830i
$509$	−274.861	−	378.313i	−0.540002	−	0.743248i	0.448612	−	0.893727i	$-0.351919\pi$
$509$	−274.861	−	378.313i	−0.540002	−	0.743248i	−0.988613	+	0.150478i	$0.951919\pi$
$510$		0			0
$511$	178.392	+	129.609i	0.349103	+	0.253638i
$512$	22.3488	+	3.53971i	0.0436501	+	0.00691349i
$513$	−15.0286	+	94.8869i	−0.0292955	+	0.184965i
$514$	−244.559	+	336.606i	−0.475795	+	0.654875i
$515$		0			0
$516$	123.374	−	89.6366i	0.239097	−	0.173714i
$517$	470.349	−	239.655i	0.909766	−	0.463549i
$518$	−72.4358	+	72.4358i	−0.139837	+	0.139837i
$519$	−338.375	−	109.945i	−0.651975	−	0.211839i
$520$		0			0
$521$	−14.5003	−	44.6274i	−0.0278317	−	0.0856571i	0.936176	−	0.351532i	$-0.114339\pi$
$521$	−14.5003	−	44.6274i	−0.0278317	−	0.0856571i	−0.964008	+	0.265875i	$0.914339\pi$
$522$	−7.56516	+	14.8475i	−0.0144926	+	0.0284434i
$523$	901.048	−	142.712i	1.72285	−	0.272872i	0.784892	−	0.619633i	$-0.212719\pi$
$523$	901.048	−	142.712i	1.72285	−	0.272872i	0.937953	+	0.346761i	$0.112719\pi$
$524$			340.987i			0.650738i
$525$		0			0
$526$	46.3755			0.0881664
$527$	81.2954	+	513.279i	0.154261	+	0.973964i
$528$	189.861	+	96.7390i	0.359585	+	0.183218i
$529$	−244.038	+	79.2928i	−0.461320	+	0.149892i
$530$		0			0
$531$	57.1961	−	176.032i	0.107714	−	0.331509i
$532$	20.1633	+	20.1633i	0.0379009	+	0.0379009i
$533$	251.852	+	494.287i	0.472517	+	0.927367i
$534$	281.204	+	387.045i	0.526600	+	0.724803i
$535$		0			0
$536$	−142.388	−	103.451i	−0.265649	−	0.193005i
$537$	−602.429	−	95.4154i	−1.12184	−	0.177682i
$538$	−54.4960	+	344.074i	−0.101294	+	0.639543i
$539$	354.875	−	488.444i	0.658396	−	0.906204i
$540$		0			0
$541$	−221.533	+	160.953i	−0.409487	+	0.297510i	−0.773394	−	0.633925i	$-0.781443\pi$
$541$	−221.533	+	160.953i	−0.409487	+	0.297510i	0.363907	+	0.931435i	$0.381443\pi$
$542$	271.162	−	138.164i	0.500298	−	0.254915i
$543$	−115.579	+	115.579i	−0.212852	+	0.212852i
$544$	−112.345	−	36.5031i	−0.206516	−	0.0671012i
$545$		0			0
$546$	−77.7052	−	239.152i	−0.142317	−	0.438007i
$547$	−167.934	+	329.590i	−0.307010	+	0.602541i	−0.992033	−	0.125981i	$-0.959792\pi$
$547$	−167.934	+	329.590i	−0.307010	+	0.602541i	0.685023	+	0.728522i	$0.259792\pi$
$548$	232.637	−	36.8461i	0.424521	−	0.0672375i
$549$		−	138.634i		−	0.252521i
$550$		0			0
$551$	22.6883			0.0411766
$552$	−19.6973	−	124.364i	−0.0356835	−	0.225297i
$553$	143.258	+	72.9935i	0.259056	+	0.131995i
$554$	157.479	−	51.1681i	0.284259	−	0.0923613i
$555$		0			0
$556$	67.3313	−	207.224i	0.121099	−	0.372706i
$557$	−348.444	−	348.444i	−0.625572	−	0.625572i	0.321379	−	0.946951i	$-0.395854\pi$
$557$	−348.444	−	348.444i	−0.625572	−	0.625572i	−0.946951	+	0.321379i	$0.895854\pi$
$558$	−27.5583	−	54.0862i	−0.0493876	−	0.0969286i
$559$	−255.147	−	351.179i	−0.456434	−	0.628228i
$560$		0			0
$561$	−899.962	−	653.861i	−1.60421	−	1.16553i
$562$	−389.412	−	61.6768i	−0.692904	−	0.109745i
$563$	2.82791	−	17.8547i	0.00502292	−	0.0317135i	−0.985050	−	0.172271i	$-0.944890\pi$
$563$	2.82791	−	17.8547i	0.00502292	−	0.0317135i	0.990073	+	0.140558i	$0.0448895\pi$
$564$	−84.7502	+	116.649i	−0.150266	+	0.206824i
$565$		0			0
$566$	−78.3552	+	56.9284i	−0.138437	+	0.100580i
$567$	239.083	−	121.819i	0.421662	−	0.214848i
$568$	−196.896	+	196.896i	−0.346648	+	0.346648i
$569$	103.461	+	33.6166i	0.181830	+	0.0590801i	0.398517	−	0.917161i	$-0.369525\pi$
$569$	103.461	+	33.6166i	0.181830	+	0.0590801i	−0.216687	+	0.976241i	$0.569525\pi$
$570$		0			0
$571$	−308.868	−	950.597i	−0.540924	−	1.66479i	−0.730489	−	0.682925i	$-0.760708\pi$
$571$	−308.868	−	950.597i	−0.540924	−	1.66479i	0.189564	−	0.981868i	$-0.439292\pi$
$572$	275.364	−	540.431i	0.481405	−	0.944810i
$573$	−476.614	+	75.4882i	−0.831787	+	0.131742i
$574$			219.344i			0.382132i
$575$		0			0
$576$	13.7981			0.0239550
$577$	−36.5466	−	230.746i	−0.0633389	−	0.399906i	−0.998906	−	0.0467579i	$-0.985111\pi$
$577$	−36.5466	−	230.746i	−0.0633389	−	0.399906i	0.935567	−	0.353148i	$-0.114889\pi$
$578$	185.303	+	94.4167i	0.320594	+	0.163351i
$579$	456.198	−	148.228i	0.787906	−	0.256006i
$580$		0			0
$581$	−3.26754	+	10.0565i	−0.00562399	+	0.0173089i
$582$	281.401	+	281.401i	0.483506	+	0.483506i
$583$	−872.914	−	1713.19i	−1.49728	−	2.93858i
$584$	−85.3907	−	117.530i	−0.146217	−	0.201250i
$585$		0			0
$586$	−171.433	−	124.553i	−0.292547	−	0.212548i
$587$	1054.05	+	166.945i	1.79565	+	0.284403i	0.963021	−	0.269428i	$-0.0868346\pi$
$587$	1054.05	+	166.945i	1.79565	+	0.284403i	0.832629	+	0.553831i	$0.186835\pi$
$588$	−25.7972	+	162.877i	−0.0438727	+	0.277001i
$589$	−48.5797	+	66.8643i	−0.0824783	+	0.113522i
$590$		0			0
$591$	−620.493	+	450.815i	−1.04990	+	0.762800i
$592$	60.1345	−	30.6400i	0.101578	−	0.0517568i
$593$	167.596	−	167.596i	0.282624	−	0.282624i	−0.551531	−	0.834155i	$-0.685956\pi$
$593$	167.596	−	167.596i	0.282624	−	0.282624i	0.834155	+	0.551531i	$0.185956\pi$
$594$	768.429	+	249.678i	1.29365	+	0.420333i
$595$		0			0
$596$	−37.9521	−	116.805i	−0.0636780	−	0.195981i
$597$	8.24830	−	16.1882i	0.0138162	−	0.0271159i
$598$	−353.997	+	56.0676i	−0.591968	+	0.0937585i
$599$		−	982.845i		−	1.64081i	−0.571783	−	0.820405i	$-0.693748\pi$
$599$		−	982.845i		−	1.64081i	0.571783	−	0.820405i	$-0.306252\pi$
$600$		0			0
$601$	−334.454			−0.556495			−0.278248	−	0.960509i	$-0.589754\pi$
$601$	−334.454			−0.556495			−0.278248	+	0.960509i	$0.589754\pi$
$602$	−26.8492	−	169.519i	−0.0446000	−	0.281593i
$603$	−95.6267	−	48.7243i	−0.158585	−	0.0808031i
$604$	320.211	−	104.043i	0.530150	−	0.172256i
$605$		0			0
$606$	181.140	−	557.492i	0.298911	−	0.919954i
$607$	311.482	+	311.482i	0.513151	+	0.513151i	0.915490	−	0.402340i	$-0.131803\pi$
$607$	311.482	+	311.482i	0.513151	+	0.513151i	−0.402340	+	0.915490i	$0.631803\pi$
$608$	−8.52897	−	16.7391i	−0.0140279	−	0.0275313i
$609$	−46.4987	−	63.9999i	−0.0763525	−	0.105090i
$610$		0			0
$611$	332.035	+	241.238i	0.543430	+	0.394825i
$612$	−71.1460	−	11.2684i	−0.116252	−	0.0184125i
$613$	124.870	−	788.398i	0.203703	−	1.28613i	−0.647812	−	0.761800i	$-0.724316\pi$
$613$	124.870	−	788.398i	0.203703	−	1.28613i	0.851515	−	0.524330i	$-0.175684\pi$
$614$	63.8332	−	87.8588i	0.103963	−	0.143093i
$615$		0			0
$616$	194.019	−	140.963i	0.314966	−	0.228836i
$617$	−294.720	+	150.167i	−0.477666	+	0.243383i	−0.676210	−	0.736709i	$-0.736379\pi$
$617$	−294.720	+	150.167i	−0.477666	+	0.243383i	0.198544	+	0.980092i	$0.436379\pi$
$618$	71.3401	−	71.3401i	0.115437	−	0.115437i
$619$	701.808	+	228.031i	1.13378	+	0.368386i	0.815010	−	0.579447i	$-0.196731\pi$
$619$	701.808	+	228.031i	1.13378	+	0.368386i	0.318767	+	0.947833i	$0.396731\pi$
$620$		0			0
$621$	−147.537	−	454.071i	−0.237579	−	0.731193i
$622$	30.4234	−	59.7092i	0.0489122	−	0.0959956i
$623$	531.808	−	84.2302i	0.853625	−	0.135201i
$624$			165.669i			0.265496i
$625$		0			0
$626$	−207.929			−0.332155
$627$	−27.6759	−	174.739i	−0.0441402	−	0.278691i
$628$	−211.906	−	107.972i	−0.337430	−	0.171929i
$629$	−335.089	+	108.877i	−0.532733	+	0.173096i
$630$		0			0
$631$	−86.2411	+	265.423i	−0.136674	+	0.420638i	−0.995847	−	0.0910471i	$-0.970979\pi$
$631$	−86.2411	+	265.423i	−0.136674	+	0.420638i	0.859173	+	0.511685i	$0.170979\pi$
$632$	−74.9025	−	74.9025i	−0.118517	−	0.118517i
$633$	228.411	+	448.281i	0.360838	+	0.708185i
$634$	56.4539	+	77.7021i	0.0890440	+	0.122559i
$635$		0			0
$636$	424.878	+	308.692i	0.668048	+	0.485365i
$637$	463.622	+	73.4305i	0.727821	+	0.115276i
$638$	29.8501	−	188.466i	0.0467870	−	0.295402i
$639$	−99.8054	+	137.370i	−0.156190	+	0.214977i
$640$		0			0
$641$	−258.559	+	187.854i	−0.403369	+	0.293065i	−0.770912	−	0.636942i	$-0.780199\pi$
$641$	−258.559	+	187.854i	−0.403369	+	0.293065i	0.367543	+	0.930007i	$0.380199\pi$
$642$	208.550	−	106.261i	0.324844	−	0.165516i
$643$	−331.237	+	331.237i	−0.515144	+	0.515144i	−0.916098	−	0.400954i	$-0.868679\pi$
$643$	−331.237	+	331.237i	−0.515144	+	0.515144i	0.400954	+	0.916098i	$0.368679\pi$
$644$	−134.776	−	43.7914i	−0.209280	−	0.0679991i
$645$		0			0
$646$	30.3071	+	93.2756i	0.0469150	+	0.144390i
$647$	−52.8755	+	103.774i	−0.0817242	+	0.160393i	−0.928252	−	0.371951i	$-0.878689\pi$
$647$	−52.8755	+	103.774i	−0.0817242	+	0.160393i	0.846528	+	0.532344i	$0.178689\pi$
$648$	−174.607	+	27.6550i	−0.269455	+	0.0426775i
$649$			2119.47i			3.26574i
$650$		0			0
$651$	288.175			0.442665
$652$	−10.5708	−	66.7416i	−0.0162129	−	0.102364i
$653$	143.296	+	73.0129i	0.219442	+	0.111811i	0.560256	−	0.828319i	$-0.310703\pi$
$653$	143.296	+	73.0129i	0.219442	+	0.111811i	−0.340814	+	0.940131i	$0.610703\pi$
$654$	−27.8432	+	9.04681i	−0.0425737	+	0.0138330i
$655$		0			0
$656$	44.6562	−	137.438i	0.0680735	−	0.209509i
$657$	−62.6413	−	62.6413i	−0.0953444	−	0.0953444i
$658$	73.6717	+	144.589i	0.111963	+	0.219740i
$659$	406.460	+	559.444i	0.616783	+	0.848929i	0.997114	−	0.0759218i	$-0.0241899\pi$
$659$	406.460	+	559.444i	0.616783	+	0.848929i	−0.380331	+	0.924850i	$0.624190\pi$
$660$		0			0
$661$	109.891	+	79.8405i	0.166250	+	0.120787i	0.667799	−	0.744341i	$-0.267236\pi$
$661$	109.891	+	79.8405i	0.166250	+	0.120787i	−0.501549	+	0.865129i	$0.667236\pi$
$662$	−48.5112	−	7.68343i	−0.0732798	−	0.0116064i
$663$	135.296	−	854.228i	0.204067	−	1.28843i
$664$	4.09479	−	5.63600i	0.00616685	−	0.00848794i
$665$		0			0
$666$	33.2954	−	24.1905i	0.0499931	−	0.0363221i
$667$	−100.465	+	51.1894i	−0.150622	+	0.0767457i
$668$	189.546	−	189.546i	0.283751	−	0.283751i
$669$	281.057	+	91.3209i	0.420115	+	0.136504i
$670$		0			0
$671$	490.563	+	1509.80i	0.731093	+	2.25007i
$672$	−29.7383	+	58.3647i	−0.0442534	+	0.0868522i
$673$	−808.411	+	128.040i	−1.20120	+	0.190252i	−0.724791	−	0.688969i	$-0.758064\pi$
$673$	−808.411	+	128.040i	−1.20120	+	0.190252i	−0.476414	+	0.879221i	$0.658064\pi$
$674$		−	193.193i		−	0.286636i
$675$		0			0
$676$	133.571			0.197590
$677$	−161.374	−	1018.88i	−0.238367	−	1.50499i	−0.758934	−	0.651168i	$-0.774279\pi$
$677$	−161.374	−	1018.88i	−0.238367	−	1.50499i	0.520567	−	0.853821i	$-0.325721\pi$
$678$	463.238	+	236.031i	0.683242	+	0.348129i
$679$	425.969	−	138.406i	0.627348	−	0.203838i
$680$		0			0
$681$	198.840	−	611.968i	0.291983	−	0.898631i
$682$	491.510	+	491.510i	0.720690	+	0.720690i
$683$	−323.239	−	634.392i	−0.473264	−	0.928832i	−0.997033	−	0.0769723i	$-0.975475\pi$
$683$	−323.239	−	634.392i	−0.473264	−	0.928832i	0.523770	−	0.851860i	$-0.324525\pi$
$684$	−6.73368	−	9.26811i	−0.00984456	−	0.0135499i
$685$		0			0
$686$	390.831	+	283.955i	0.569724	+	0.413929i
$687$	944.077	+	149.527i	1.37420	+	0.217652i
$688$	−17.6891	+	111.684i	−0.0257109	+	0.162332i
$689$	878.680	−	1209.40i	1.27530	−	1.75530i
$690$		0			0
$691$	−43.7044	+	31.7531i	−0.0632481	+	0.0459524i	−0.618960	−	0.785422i	$-0.712446\pi$
$691$	−43.7044	+	31.7531i	−0.0632481	+	0.0459524i	0.555712	+	0.831375i	$0.312446\pi$
$692$	235.060	−	119.769i	0.339682	−	0.173077i
$693$	103.408	−	103.408i	0.149218	−	0.149218i
$694$	416.933	+	135.470i	0.600769	+	0.195202i
$695$		0			0
$696$	16.1057	+	49.5681i	0.0231403	+	0.0712185i
$697$	−342.498	+	672.190i	−0.491389	+	0.964405i
$698$	−187.619	+	29.7159i	−0.268795	+	0.0425729i
$699$		−	814.198i		−	1.16480i
$700$		0			0
$701$	−743.065			−1.06001			−0.530003	−	0.847996i	$-0.677809\pi$
$701$	−743.065			−1.06001			−0.530003	+	0.847996i	$0.677809\pi$
$702$	98.2691	+	620.447i	0.139985	+	0.883828i
$703$	−49.9273	−	25.4392i	−0.0710204	−	0.0361867i
$704$	−150.268	+	48.8251i	−0.213449	+	0.0693539i
$705$		0			0
$706$	−199.758	+	614.792i	−0.282943	+	0.870810i
$707$	−466.498	−	466.498i	−0.659827	−	0.659827i
$708$	−262.818	−	515.810i	−0.371212	−	0.728545i
$709$	−415.044	−	571.258i	−0.585393	−	0.805724i	0.408881	−	0.912588i	$-0.365919\pi$
$709$	−415.044	−	571.258i	−0.585393	−	0.805724i	−0.994274	+	0.106864i	$0.965919\pi$
$710$		0			0
$711$	−52.2580	−	37.9677i	−0.0734993	−	0.0534004i
$712$	−350.372	−	55.4935i	−0.492096	−	0.0779403i
$713$	64.2540	−	405.684i	0.0901178	−	0.568981i
$714$	201.002	−	276.655i	0.281515	−	0.387472i
$715$		0			0
$716$	365.890	−	265.834i	0.511019	−	0.371277i
$717$	−601.241	+	306.348i	−0.838551	+	0.427263i
$718$	−272.815	+	272.815i	−0.379965	+	0.379965i
$719$	−472.434	−	153.503i	−0.657072	−	0.213495i	−0.0385419	−	0.999257i	$-0.512271\pi$
$719$	−472.434	−	153.503i	−0.657072	−	0.213495i	−0.618530	+	0.785762i	$0.712271\pi$
$720$		0			0
$721$	−35.0884	−	107.991i	−0.0486662	−	0.149779i
$722$	224.695	−	440.989i	0.311212	−	0.610788i
$723$	443.156	−	70.1891i	0.612941	−	0.0970803i
$724$		−	121.199i		−	0.167402i
$725$		0			0
$726$	−1026.37			−1.41373
$727$	−4.08595	−	25.7977i	−0.00562029	−	0.0354851i	0.984719	−	0.174152i	$-0.0557183\pi$
$727$	−4.08595	−	25.7977i	−0.00562029	−	0.0354851i	−0.990339	+	0.138667i	$0.955718\pi$
$728$	166.133	+	84.6488i	0.228204	+	0.116276i
$729$	−770.383	+	250.313i	−1.05677	+	0.343364i
$730$		0			0
$731$	182.418	−	561.424i	0.249546	−	0.768022i
$732$	−306.606	−	306.606i	−0.418860	−	0.418860i
$733$	635.542	+	1247.32i	0.867042	+	1.70167i	0.698051	+	0.716048i	$0.254051\pi$
$733$	635.542	+	1247.32i	0.867042	+	1.70167i	0.168991	+	0.985618i	$0.445949\pi$
$734$	−122.271	−	168.291i	−0.166581	−	0.229279i
$735$		0			0
$736$	75.5333	+	54.8782i	0.102627	+	0.0745627i
$737$	1213.84	+	192.253i	1.64700	+	0.260859i
$738$	13.7853	−	87.0368i	0.0186792	−	0.117936i
$739$	−611.917	+	842.232i	−0.828034	+	1.13969i	0.160252	+	0.987076i	$0.448769\pi$
$739$	−611.917	+	842.232i	−0.828034	+	1.13969i	−0.988286	+	0.152615i	$0.951231\pi$
$740$		0			0
$741$	111.279	−	80.8492i	0.150175	−	0.109108i
$742$	526.647	−	268.340i	0.709767	−	0.361645i
$743$	−273.617	+	273.617i	−0.368259	+	0.368259i	−0.866842	−	0.498583i	$-0.833854\pi$
$743$	−273.617	+	273.617i	−0.368259	+	0.368259i	0.498583	+	0.866842i	$0.333854\pi$
$744$	−180.566	−	58.6695i	−0.242697	−	0.0788569i
$745$		0			0
$746$	−124.276	−	382.482i	−0.166590	−	0.512711i
$747$	1.92861	−	3.78510i	0.00258180	−	0.00506707i
$748$	814.691	−	129.034i	1.08916	−	0.172506i
$749$		−	263.427i		−	0.351705i
$750$		0			0
$751$	−1071.26			−1.42645			−0.713225	−	0.700935i	$-0.752766\pi$
$751$	−1071.26			−1.42645			−0.713225	+	0.700935i	$0.752766\pi$
$752$	−16.7248	−	105.596i	−0.0222404	−	0.140420i
$753$	−610.755	−	311.195i	−0.811095	−	0.413274i
$754$	141.094	−	45.8441i	0.187127	−	0.0608012i
$755$		0			0
$756$	−76.7528	+	236.221i	−0.101525	+	0.312461i
$757$	605.160	+	605.160i	0.799418	+	0.799418i	0.983004	−	0.183586i	$-0.0587704\pi$
$757$	605.160	+	605.160i	0.799418	+	0.799418i	−0.183586	+	0.983004i	$0.558770\pi$
$758$	448.751	+	880.723i	0.592019	+	1.16190i
$759$	516.796	+	711.309i	0.680891	+	0.937166i
$760$		0			0
$761$	676.103	+	491.218i	0.888440	+	0.645489i	0.935471	−	0.353404i	$-0.114976\pi$
$761$	676.103	+	491.218i	0.888440	+	0.645489i	−0.0470307	+	0.998893i	$0.514976\pi$
$762$	−470.237	−	74.4782i	−0.617109	−	0.0977405i
$763$	−5.15439	+	32.5436i	−0.00675543	+	0.0426521i
$764$	210.316	−	289.475i	0.275282	−	0.378894i
$765$		0			0
$766$	573.988	−	417.027i	0.749332	−	0.544422i
$767$	−1468.23	+	748.102i	−1.91425	+	0.975361i
$768$	30.5161	−	30.5161i	0.0397345	−	0.0397345i
$769$	−304.763	−	99.0236i	−0.396311	−	0.128769i	0.104080	−	0.994569i	$-0.466810\pi$
$769$	−304.763	−	99.0236i	−0.396311	−	0.128769i	−0.500391	+	0.865800i	$0.666810\pi$
$770$		0			0
$771$	245.220	+	754.708i	0.318054	+	0.978869i
$772$	−161.473	+	316.908i	−0.209162	+	0.410503i
$773$	771.310	−	122.164i	0.997814	−	0.158038i	0.363897	−	0.931439i	$-0.381446\pi$
$773$	771.310	−	122.164i	0.997814	−	0.158038i	0.633917	+	0.773401i	$0.281446\pi$
$774$			68.9536i			0.0890873i
$775$		0			0
$776$	−295.085			−0.380264
$777$	30.5639	+	192.973i	0.0393358	+	0.248357i
$778$	−541.888	−	276.106i	−0.696514	−	0.354892i
$779$	−114.109	+	37.0763i	−0.146482	+	0.0475948i
$780$		0			0
$781$	600.842	−	1849.20i	0.769324	−	2.36774i
$782$	−344.650	−	344.650i	−0.440728	−	0.440728i
$783$	89.7192	+	176.084i	0.114584	+	0.224884i
$784$	−71.8728	−	98.9244i	−0.0916745	−	0.126179i
$785$		0			0
$786$	526.143	+	382.265i	0.669393	+	0.486342i
$787$	−1130.54	−	179.060i	−1.43652	−	0.227523i	−0.610883	−	0.791721i	$-0.709185\pi$
$787$	−1130.54	−	179.060i	−1.43652	−	0.227523i	−0.825639	+	0.564198i	$0.809185\pi$
$788$	88.9648	−	561.702i	0.112900	−	0.712819i
$789$	51.9895	−	71.5575i	0.0658930	−	0.0906939i
$790$		0			0
$791$	473.383	−	343.933i	0.598462	−	0.434808i
$792$	−85.8471	+	43.7413i	−0.108393	+	0.0552289i
$793$	−872.740	+	872.740i	−1.10055	+	1.10055i
$794$	−764.710	−	248.469i	−0.963111	−	0.312934i
$795$		0			0
$796$	4.16300	+	12.8124i	0.00522990	+	0.0160960i
$797$	369.247	−	724.688i	0.463296	−	0.909270i	−0.534641	−	0.845079i	$-0.679553\pi$
$797$	369.247	−	724.688i	0.463296	−	0.909270i	0.997938	−	0.0641912i	$-0.0204468\pi$
$798$	53.7161	−	8.50779i	0.0673134	−	0.0106614i
$799$			558.136i			0.698543i
$800$		0			0
$801$	−216.318			−0.270060
$802$	132.023	+	833.558i	0.164617	+	1.03935i
$803$	903.855	+	460.537i	1.12560	+	0.573521i
$804$	−319.249	+	103.730i	−0.397076	+	0.129018i
$805$		0			0
$806$	−167.000	+	513.974i	−0.207197	+	0.637685i
$807$	469.814	+	469.814i	0.582174	+	0.582174i
$808$	197.327	+	387.275i	0.244216	+	0.479301i
$809$	100.488	+	138.310i	0.124213	+	0.170964i	0.866595	−	0.499013i	$-0.166304\pi$
$809$	100.488	+	138.310i	0.124213	+	0.170964i	−0.742382	+	0.669977i	$0.766304\pi$
$810$		0			0
$811$	285.260	+	207.253i	0.351738	+	0.255553i	0.749598	−	0.661894i	$-0.230247\pi$
$811$	285.260	+	207.253i	0.351738	+	0.255553i	−0.397860	+	0.917446i	$0.630247\pi$
$812$	57.9359	+	9.17615i	0.0713497	+	0.0113007i
$813$	90.8005	−	573.292i	0.111686	−	0.705156i
$814$	−277.005	+	381.264i	−0.340301	+	0.468384i
$815$		0			0
$816$	−182.269	+	132.426i	−0.223369	+	0.162287i
$817$	83.6506	−	42.6221i	0.102387	−	0.0521690i
$818$	−19.1314	+	19.1314i	−0.0233880	+	0.0233880i
$819$	108.134	+	35.1350i	0.132032	+	0.0428999i
$820$		0			0
$821$	−79.5914	−	244.957i	−0.0969445	−	0.298364i	0.890811	−	0.454374i	$-0.150137\pi$
$821$	−79.5914	−	244.957i	−0.0969445	−	0.298364i	−0.987756	+	0.156009i	$0.950137\pi$
$822$	203.946	−	400.266i	0.248109	−	0.486942i
$823$	−707.978	+	112.133i	−0.860240	+	0.136249i	−0.570942	−	0.820990i	$-0.693422\pi$
$823$	−707.978	+	112.133i	−0.860240	+	0.136249i	−0.289298	+	0.957239i	$0.593422\pi$
$824$			74.8092i			0.0907879i
$825$		0			0
$826$	−651.540			−0.788789
$827$	−210.601	−	1329.68i	−0.254656	−	1.60784i	−0.701125	−	0.713038i	$-0.747319\pi$
$827$	−210.601	−	1329.68i	−0.254656	−	1.60784i	0.446469	−	0.894799i	$-0.352681\pi$
$828$	50.7278	+	25.8471i	0.0612654	+	0.0312163i
$829$	360.692	−	117.196i	0.435093	−	0.141370i	−0.0832774	−	0.996526i	$-0.526539\pi$
$829$	360.692	−	117.196i	0.435093	−	0.141370i	0.518371	+	0.855156i	$0.326539\pi$
$830$		0			0
$831$	97.5907	−	300.353i	0.117438	−	0.361436i
$832$	−86.8627	−	86.8627i	−0.104402	−	0.104402i
$833$	289.804	+	568.772i	0.347904	+	0.682800i
$834$	−244.265	−	336.202i	−0.292884	−	0.403120i
$835$		0			0
$836$	106.129	+	77.1072i	0.126948	+	0.0922335i
$837$	−711.038	−	112.617i	−0.849508	−	0.134549i
$838$	99.5211	−	628.351i	0.118760	−	0.749823i
$839$	236.136	−	325.013i	0.281449	−	0.387382i	−0.644764	−	0.764382i	$-0.723044\pi$
$839$	236.136	−	325.013i	0.281449	−	0.387382i	0.926213	+	0.377000i	$0.123044\pi$
$840$		0			0
$841$	−642.625	+	466.894i	−0.764120	+	0.555166i
$842$	−909.137	+	463.228i	−1.07973	+	0.550152i
$843$	−531.720	+	531.720i	−0.630748	+	0.630748i
$844$	−354.799	−	115.281i	−0.420378	−	0.136589i
$845$		0			0
$846$	−20.1463	−	62.0038i	−0.0238135	−	0.0732906i
$847$	−524.424	+	1029.24i	−0.619154	+	1.21516i
$848$	−384.621	+	60.9180i	−0.453563	+	0.0718373i
$849$			184.722i			0.217576i
$850$		0			0
$851$	278.476			0.327234
$852$	83.0793	+	524.542i	0.0975109	+	0.615660i
$853$	163.158	+	83.1331i	0.191275	+	0.0974596i	0.547005	−	0.837129i	$-0.315768\pi$
$853$	163.158	+	83.1331i	0.191275	+	0.0974596i	−0.355730	+	0.934589i	$0.615768\pi$
$854$	−464.123	+	150.803i	−0.543470	+	0.176584i
$855$		0			0
$856$	−53.6312	+	165.060i	−0.0626533	+	0.192827i
$857$	−534.946	−	534.946i	−0.624207	−	0.624207i	0.322397	−	0.946604i	$-0.395511\pi$
$857$	−534.946	−	534.946i	−0.624207	−	0.624207i	−0.946604	+	0.322397i	$0.895511\pi$
$858$	−525.188	−	1030.74i	−0.612108	−	1.20133i
$859$	−844.089	−	1161.79i	−0.982641	−	1.35249i	−0.935394	−	0.353606i	$-0.884955\pi$
$859$	−844.089	−	1161.79i	−0.982641	−	1.35249i	−0.0472468	−	0.998883i	$-0.515045\pi$
$860$		0			0
$861$	338.448	+	245.897i	0.393087	+	0.285594i
$862$	−366.161	−	57.9943i	−0.424781	−	0.0672787i
$863$	−242.561	+	1531.47i	−0.281068	+	1.77459i	0.293327	+	0.956012i	$0.405237\pi$
$863$	−242.561	+	1531.47i	−0.281068	+	1.77459i	−0.574395	+	0.818578i	$0.694763\pi$
$864$	96.1845	−	132.387i	0.111325	−	0.153225i
$865$		0			0
$866$	−375.406	+	272.748i	−0.433494	+	0.314952i
$867$	353.420	−	180.077i	0.407636	−	0.207701i
$868$	−151.094	+	151.094i	−0.174071	+	0.174071i
$869$	703.467	+	228.570i	0.809514	+	0.263027i
$870$		0			0
$871$	295.264	+	908.729i	0.338994	+	1.04332i
$872$	9.85522	−	19.3420i	0.0113019	−	0.0221811i
$873$	−177.726	+	28.1490i	−0.203580	+	0.0322440i
$874$		−	77.5168i		−	0.0886920i
$875$		0			0
$876$	−277.077			−0.316298
$877$	−227.820	−	1438.40i	−0.259772	−	1.64014i	−0.680354	−	0.732884i	$-0.738174\pi$
$877$	−227.820	−	1438.40i	−0.259772	−	1.64014i	0.420582	−	0.907255i	$-0.361826\pi$
$878$	−503.819	−	256.708i	−0.573825	−	0.292379i
$879$	−384.372	+	124.890i	−0.437283	+	0.142082i
$880$		0			0
$881$	−48.9623	+	150.691i	−0.0555759	+	0.171045i	−0.974991	−	0.222243i	$-0.928662\pi$
$881$	−48.9623	+	150.691i	−0.0555759	+	0.171045i	0.919416	+	0.393288i	$0.128662\pi$
$882$	−52.7248	−	52.7248i	−0.0597786	−	0.0597786i
$883$	592.151	+	1162.16i	0.670613	+	1.31615i	0.935997	+	0.352009i	$0.114501\pi$
$883$	592.151	+	1162.16i	0.670613	+	1.31615i	−0.265384	+	0.964143i	$0.585499\pi$
$884$	376.946	+	518.822i	0.426409	+	0.586902i
$885$		0			0
$886$	199.422	+	144.889i	0.225081	+	0.163531i
$887$	1001.95	+	158.693i	1.12959	+	0.178909i	0.693128	−	0.720814i	$-0.256232\pi$
$887$	1001.95	+	158.693i	1.12959	+	0.178909i	0.436460	+	0.899724i	$0.356232\pi$
$888$	20.1365	−	127.137i	0.0226762	−	0.143172i
$889$	−314.954	+	433.498i	−0.354279	+	0.487624i
$890$		0			0
$891$	998.677	−	725.582i	1.12085	−	0.814345i
$892$	−195.243	+	99.4812i	−0.218882	+	0.111526i
$893$	−62.7665	+	62.7665i	−0.0702873	+	0.0702873i
$894$	−222.776	−	72.3843i	−0.249190	−	0.0809668i
$895$		0			0
$896$	−15.0092	−	46.1936i	−0.0167514	−	0.0515554i
$897$	−310.338	+	609.073i	−0.345973	+	0.679011i
$898$	460.945	−	73.0064i	0.513301	−	0.0812989i
$899$			170.016i			0.189116i
$900$		0			0
$901$	2032.94			2.25632
$902$	157.855	+	996.657i	0.175005	+	1.10494i
$903$	−291.668	−	148.612i	−0.322998	−	0.164576i
$904$	−366.637	+	119.127i	−0.405571	+	0.131778i
$905$		0			0
$906$	198.436	−	610.723i	0.219024	−	0.674088i
$907$	−165.144	−	165.144i	−0.182078	−	0.182078i	0.610183	−	0.792261i	$-0.291096\pi$
$907$	−165.144	−	165.144i	−0.182078	−	0.182078i	−0.792261	+	0.610183i	$0.791096\pi$
$908$	216.608	+	425.118i	0.238556	+	0.468192i
$909$	155.791	+	214.427i	0.171387	+	0.235894i
$910$		0			0
$911$	547.636	+	397.881i	0.601137	+	0.436752i	0.846282	−	0.532735i	$-0.178836\pi$
$911$	547.636	+	397.881i	0.601137	+	0.436752i	−0.245145	+	0.969486i	$0.578836\pi$
$912$	−35.3898	−	5.60520i	−0.0388046	−	0.00614605i
$913$	−7.60977	+	48.0462i	−0.00833491	+	0.0526245i
$914$	124.182	−	170.922i	0.135867	−	0.187005i
$915$		0			0
$916$	−573.392	+	416.593i	−0.625974	+	0.454796i
$917$	652.167	−	332.296i	0.711196	−	0.362373i
$918$	−604.064	+	604.064i	−0.658022	+	0.658022i
$919$	−1508.64	−	490.188i	−1.64161	−	0.533393i	−0.664716	−	0.747096i	$-0.731448\pi$
$919$	−1508.64	−	490.188i	−1.64161	−	0.533393i	−0.976899	+	0.213703i	$0.931448\pi$
$920$		0			0
$921$	−64.0057	−	196.989i	−0.0694959	−	0.213886i
$922$	64.6462	−	126.875i	0.0701152	−	0.137609i
$923$	1493.09	−	236.482i	1.61765	−	0.256210i
$924$		−	457.399i		−	0.495021i
$925$		0			0
$926$	8.61556			0.00930406
$927$	7.13627	+	45.0566i	0.00769824	+	0.0486048i
$928$	−34.4337	−	17.5448i	−0.0371052	−	0.0189061i
$929$	−1055.34	+	342.899i	−1.13599	+	0.369106i	−0.815850	−	0.578264i	$-0.803730\pi$
$929$	−1055.34	+	342.899i	−1.13599	+	0.369106i	−0.320141	+	0.947370i	$0.603730\pi$
$930$		0			0
$931$	−31.3721	+	96.5533i	−0.0336972	+	0.103709i
$932$	426.895	+	426.895i	0.458042	+	0.458042i
$933$	−58.0251	−	113.881i	−0.0621920	−	0.122059i
$934$	−118.965	−	163.741i	−0.127371	−	0.175312i
$935$		0			0
$936$	−60.6024	−	44.0302i	−0.0647462	−	0.0470408i
$937$	1045.94	+	165.660i	1.11626	+	0.176799i	0.687195	−	0.726473i	$-0.258842\pi$
$937$	1045.94	+	165.660i	1.11626	+	0.176799i	0.429069	+	0.903272i	$0.358842\pi$
$938$	−59.1000	+	373.143i	−0.0630064	+	0.397807i
$939$	−233.100	+	320.835i	−0.248243	+	0.341677i
$940$		0			0
$941$	−1507.67	+	1095.38i	−1.60219	+	1.16406i	−0.719054	+	0.694954i	$0.755425\pi$
$941$	−1507.67	+	1095.38i	−1.60219	+	1.16406i	−0.883141	+	0.469108i	$0.844575\pi$
$942$	−404.159	+	205.929i	−0.429044	+	0.218609i
$943$	421.629	−	421.629i	0.447114	−	0.447114i
$944$	408.246	+	132.647i	0.432464	+	0.140516i
$945$		0			0
$946$	−243.995	−	750.940i	−0.257923	−	0.793806i
$947$	68.9086	−	135.241i	0.0727651	−	0.142810i	−0.851758	−	0.523935i	$-0.824463\pi$
$947$	68.9086	−	135.241i	0.0727651	−	0.142810i	0.924523	+	0.381126i	$0.124463\pi$
$948$	−199.545	+	31.6048i	−0.210490	+	0.0333384i
$949$			788.688i			0.831073i
$950$		0			0
$951$	183.182			0.192621
$952$	39.6661	+	250.442i	0.0416661	+	0.263069i
$953$	391.244	+	199.349i	0.410539	+	0.209180i	0.647048	−	0.762449i	$-0.276003\pi$
$953$	391.244	+	199.349i	0.410539	+	0.209180i	−0.236509	+	0.971629i	$0.576003\pi$
$954$	−225.841	+	73.3803i	−0.236731	+	0.0769186i
$955$		0			0
$956$	154.617	−	475.861i	0.161733	−	0.497763i
$957$	−257.340	−	257.340i	−0.268903	−	0.268903i
$958$	−127.834	−	250.888i	−0.133438	−	0.261887i
$959$	−297.179	−	409.032i	−0.309885	−	0.426520i
$960$		0			0
$961$	276.416	+	200.828i	0.287633	+	0.208978i
$962$	−361.889	−	57.3177i	−0.376184	−	0.0595818i
$963$	−16.5558	+	104.530i	−0.0171920	+	0.108546i
$964$	−195.552	+	269.154i	−0.202855	+	0.279206i
$965$		0			0
$966$	−218.662	+	158.867i	−0.226358	+	0.164459i
$967$	878.028	−	447.377i	0.907991	−	0.462645i	0.0633586	−	0.997991i	$-0.479819\pi$
$967$	878.028	−	447.377i	0.907991	−	0.462645i	0.844633	+	0.535346i	$0.179819\pi$
$968$	538.140	−	538.140i	0.555929	−	0.555929i
$969$	177.900	+	57.8033i	0.183592	+	0.0596526i
$970$		0			0
$971$	98.9422	+	304.513i	0.101897	+	0.313607i	0.988990	−	0.147984i	$-0.0472785\pi$
$971$	98.9422	+	304.513i	0.101897	+	0.313607i	−0.887092	+	0.461592i	$0.847279\pi$
$972$	83.3184	−	163.522i	0.0857185	−	0.168232i
$973$	−461.950	+	73.1657i	−0.474769	+	0.0751960i
$974$		−	531.302i		−	0.545484i
$975$		0			0
$976$	321.515			0.329421
$977$	195.642	+	1235.23i	0.200248	+	1.26431i	0.859009	+	0.511961i	$0.171081\pi$
$977$	195.642	+	1235.23i	0.200248	+	1.26431i	−0.658761	+	0.752352i	$0.728919\pi$
$978$	−114.833	−	58.5102i	−0.117416	−	0.0598264i
$979$	2355.82	−	765.452i	2.40635	−	0.781872i
$980$		0			0
$981$	4.09059	−	12.5895i	0.00416981	−	0.0128334i
$982$	325.583	+	325.583i	0.331551	+	0.331551i
$983$	−173.746	−	340.995i	−0.176750	−	0.346892i	0.785586	−	0.618752i	$-0.212361\pi$
$983$	−173.746	−	340.995i	−0.176750	−	0.346892i	−0.962337	+	0.271860i	$0.912361\pi$
$984$	−162.004	−	222.980i	−0.164639	−	0.226606i
$985$		0			0
$986$	163.219	+	118.586i	0.165537	+	0.120270i
$987$	305.691	+	48.4167i	0.309717	+	0.0490544i
$988$	−15.9550	+	100.736i	−0.0161488	+	0.101959i
$989$	−274.244	+	377.465i	−0.277295	+	0.381663i
$990$		0			0
$991$	−166.968	+	121.309i	−0.168485	+	0.122411i	−0.668832	−	0.743413i	$-0.733206\pi$
$991$	−166.968	+	121.309i	−0.168485	+	0.122411i	0.500348	+	0.865825i	$0.333206\pi$
$992$	125.435	−	63.9121i	0.126446	−	0.0644276i
$993$	−66.2394	+	66.2394i	−0.0667063	+	0.0667063i
$994$	568.458	+	184.703i	0.571890	+	0.185818i
$995$		0			0
$996$	−4.10586	−	12.6365i	−0.00412235	−	0.0126873i
$997$	325.309	−	638.454i	0.326288	−	0.640376i	−0.668344	−	0.743852i	$-0.732997\pi$
$997$	325.309	−	638.454i	0.326288	−	0.640376i	0.994632	+	0.103477i	$0.0329967\pi$
$998$	558.818	−	88.5080i	0.559938	−	0.0886854i
$999$		−	488.083i		−	0.488572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.3.f.b.207.2		16
5.2	odd	4		250.3.f.a.43.2		16
5.3	odd	4		250.3.f.c.43.1		16
5.4	even	2		50.3.f.a.37.1	yes	16
20.19	odd	2		400.3.bg.a.337.2		16
25.2	odd	20		50.3.f.a.23.1	✓	16
25.11	even	5		250.3.f.c.157.1		16
25.14	even	10		250.3.f.a.157.2		16
25.23	odd	20	inner	250.3.f.b.93.2		16
100.27	even	20		400.3.bg.a.273.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.23.1	✓	16	25.2	odd	20
50.3.f.a.37.1	yes	16	5.4	even	2
250.3.f.a.43.2		16	5.2	odd	4
250.3.f.a.157.2		16	25.14	even	10
250.3.f.b.93.2		16	25.23	odd	20	inner
250.3.f.b.207.2		16	1.1	even	1	trivial
250.3.f.c.43.1		16	5.3	odd	4
250.3.f.c.157.1		16	25.11	even	5
400.3.bg.a.273.2		16	100.27	even	20
400.3.bg.a.337.2		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)

\(f(q)\)	\(=\)	\(q+(0.221232 + 1.39680i) q^{2} +(2.40328 + 1.22453i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-1.17875 + 3.62781i) q^{6} +(3.03568 + 3.03568i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(-1.01379 - 1.39536i) q^{9} +O(q^{10})\)	\(q+(0.221232 + 1.39680i) q^{2} +(2.40328 + 1.22453i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-1.17875 + 3.62781i) q^{6} +(3.03568 + 3.03568i) q^{7} +(-1.28408 - 2.52015i) q^{8} +(-1.01379 - 1.39536i) q^{9} +(15.9782 + 11.6089i) q^{11} +(-5.32811 - 0.843890i) q^{12} +(-2.40210 + 15.1663i) q^{13} +(-3.56865 + 4.91183i) q^{14} +(3.23607 - 2.35114i) q^{16} +(-18.6060 + 9.48022i) q^{17} +(1.72476 - 1.72476i) q^{18} +(-3.15850 - 1.02626i) q^{19} +(3.57830 + 11.0129i) q^{21} +(-12.6804 + 24.8867i) q^{22} +(16.3014 - 2.58189i) q^{23} -7.62902i q^{24} -21.7157 q^{26} +(-4.52526 - 28.5714i) q^{27} +(-7.65035 - 3.89805i) q^{28} +(-6.49731 + 2.11110i) q^{29} +(7.69031 - 23.6683i) q^{31} +(4.00000 + 4.00000i) q^{32} +(24.1848 + 47.4652i) q^{33} +(-17.3582 - 23.8916i) q^{34} +(2.79072 + 2.02758i) q^{36} +(16.6649 + 2.63946i) q^{37} +(0.734721 - 4.63885i) q^{38} +(-24.3445 + 33.5073i) q^{39} +(29.2279 - 21.2353i) q^{41} +(-14.5912 + 7.43457i) q^{42} +(-19.9893 + 19.9893i) q^{43} +(-37.5671 - 12.2063i) q^{44} +(7.21279 + 22.1987i) q^{46} +(12.1343 - 23.8149i) q^{47} +(10.6562 - 1.68778i) q^{48} -30.5693i q^{49} -56.3243 q^{51} +(-4.80420 - 30.3325i) q^{52} +(-86.7430 - 44.1977i) q^{53} +(38.9074 - 12.6418i) q^{54} +(3.75230 - 11.5484i) q^{56} +(-6.33408 - 6.33408i) q^{57} +(-4.38621 - 8.60842i) q^{58} +(63.0774 + 86.8186i) q^{59} +(65.0278 + 47.2455i) q^{61} +(34.7613 + 5.50566i) q^{62} +(1.15833 - 7.31340i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-60.9491 + 44.2821i) q^{66} +(55.4435 - 28.2499i) q^{67} +(29.5316 - 29.5316i) q^{68} +(42.3386 + 13.7566i) q^{69} +(-30.4221 - 93.6296i) q^{71} +(-2.21473 + 4.34665i) q^{72} +(50.7302 - 8.03488i) q^{73} +23.8615i q^{74} +6.64209 q^{76} +(13.2640 + 83.7456i) q^{77} +(-52.1889 - 26.5916i) q^{78} +(35.6183 - 11.5731i) q^{79} +(19.3143 - 59.4433i) q^{81} +(36.1276 + 36.1276i) q^{82} +(1.11819 + 2.19457i) q^{83} +(-13.6127 - 18.7362i) q^{84} +(-32.3434 - 23.4989i) q^{86} +(-18.2000 - 2.88259i) q^{87} +(8.73874 - 55.1742i) q^{88} +(73.7197 - 101.466i) q^{89} +(-53.3319 + 38.7479i) q^{91} +(-29.4115 + 14.9859i) q^{92} +(47.4646 - 47.4646i) q^{93} +(35.9492 + 11.6806i) q^{94} +(4.71499 + 14.5113i) q^{96} +(47.3640 - 92.9571i) q^{97} +(42.6993 - 6.76290i) q^{98} -34.0643i 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

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