LMFDB - Embedded newform 845.2.e.e.146.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			146.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	845.146
Dual form			845.2.e.e.191.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.50000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.36603 - 4.09808i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})$	\(q+(0.866025 + 1.50000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.36603 - 4.09808i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +(-0.866025 - 1.50000i) q^{10} +(2.36603 + 4.09808i) q^{11} +2.73205 q^{12} -3.46410 q^{14} +(1.36603 + 2.36603i) q^{15} +(2.50000 + 4.33013i) q^{16} +(1.73205 - 3.00000i) q^{17} -7.73205 q^{18} +(3.09808 - 5.36603i) q^{19} +(0.500000 - 0.866025i) q^{20} +5.46410 q^{21} +(-4.09808 + 7.09808i) q^{22} +(-0.633975 - 1.09808i) q^{23} +(-2.36603 - 4.09808i) q^{24} +1.00000 q^{25} +4.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(1.26795 + 2.19615i) q^{29} +(-2.36603 + 4.09808i) q^{30} +10.1962 q^{31} +(-2.59808 + 4.50000i) q^{32} +(6.46410 - 11.1962i) q^{33} +6.00000 q^{34} +(1.00000 - 1.73205i) q^{35} +(-2.23205 - 3.86603i) q^{36} +(2.00000 + 3.46410i) q^{37} +10.7321 q^{38} -1.73205 q^{40} +(-1.73205 - 3.00000i) q^{41} +(4.73205 + 8.19615i) q^{42} +(0.0980762 - 0.169873i) q^{43} -4.73205 q^{44} +(2.23205 - 3.86603i) q^{45} +(1.09808 - 1.90192i) q^{46} +6.00000 q^{47} +(6.83013 - 11.8301i) q^{48} +(1.50000 + 2.59808i) q^{49} +(0.866025 + 1.50000i) q^{50} -9.46410 q^{51} +10.3923 q^{53} +(3.46410 + 6.00000i) q^{54} +(-2.36603 - 4.09808i) q^{55} +(-1.73205 + 3.00000i) q^{56} -16.9282 q^{57} +(-2.19615 + 3.80385i) q^{58} +(-4.56218 + 7.90192i) q^{59} -2.73205 q^{60} +(4.19615 - 7.26795i) q^{61} +(8.83013 + 15.2942i) q^{62} +(-4.46410 - 7.73205i) q^{63} +1.00000 q^{64} +22.3923 q^{66} +(-3.19615 - 5.53590i) q^{67} +(1.73205 + 3.00000i) q^{68} +(-1.73205 + 3.00000i) q^{69} +3.46410 q^{70} +(-2.36603 + 4.09808i) q^{71} +(-3.86603 + 6.69615i) q^{72} -4.00000 q^{73} +(-3.46410 + 6.00000i) q^{74} +(-1.36603 - 2.36603i) q^{75} +(3.09808 + 5.36603i) q^{76} -9.46410 q^{77} -8.39230 q^{79} +(-2.50000 - 4.33013i) q^{80} +(1.23205 + 2.13397i) q^{81} +(3.00000 - 5.19615i) q^{82} -6.00000 q^{83} +(-2.73205 + 4.73205i) q^{84} +(-1.73205 + 3.00000i) q^{85} +0.339746 q^{86} +(3.46410 - 6.00000i) q^{87} +(4.09808 + 7.09808i) q^{88} +(6.46410 + 11.1962i) q^{89} +7.73205 q^{90} +1.26795 q^{92} +(-13.9282 - 24.1244i) q^{93} +(5.19615 + 9.00000i) q^{94} +(-3.09808 + 5.36603i) q^{95} +14.1962 q^{96} +(-1.00000 + 1.73205i) q^{97} +(-2.59808 + 4.50000i) q^{98} -21.1244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 - 4 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} - 4 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{12} + 2 q^{15} + 10 q^{16} - 24 q^{18} + 2 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 6 q^{23} - 6 q^{24} + 4 q^{25} + 16 q^{27} - 4 q^{28} + 12 q^{29} - 6 q^{30} + 20 q^{31} + 12 q^{33} + 24 q^{34} + 4 q^{35} - 2 q^{36} + 8 q^{37} + 36 q^{38} + 12 q^{42} - 10 q^{43} - 12 q^{44} + 2 q^{45} - 6 q^{46} + 24 q^{47} + 10 q^{48} + 6 q^{49} - 24 q^{51} - 6 q^{55} - 40 q^{57} + 12 q^{58} + 6 q^{59} - 4 q^{60} - 4 q^{61} + 18 q^{62} - 4 q^{63} + 4 q^{64} + 48 q^{66} + 8 q^{67} - 6 q^{71} - 12 q^{72} - 16 q^{73} - 2 q^{75} + 2 q^{76} - 24 q^{77} + 8 q^{79} - 10 q^{80} - 2 q^{81} + 12 q^{82} - 24 q^{83} - 4 q^{84} + 36 q^{86} + 6 q^{88} + 12 q^{89} + 24 q^{90} + 12 q^{92} - 28 q^{93} - 2 q^{95} + 36 q^{96} - 4 q^{97} - 36 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 - 4 * q^7 - 2 * q^9 + 6 * q^11 + 4 * q^12 + 2 * q^15 + 10 * q^16 - 24 * q^18 + 2 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 6 * q^23 - 6 * q^24 + 4 * q^25 + 16 * q^27 - 4 * q^28 + 12 * q^29 - 6 * q^30 + 20 * q^31 + 12 * q^33 + 24 * q^34 + 4 * q^35 - 2 * q^36 + 8 * q^37 + 36 * q^38 + 12 * q^42 - 10 * q^43 - 12 * q^44 + 2 * q^45 - 6 * q^46 + 24 * q^47 + 10 * q^48 + 6 * q^49 - 24 * q^51 - 6 * q^55 - 40 * q^57 + 12 * q^58 + 6 * q^59 - 4 * q^60 - 4 * q^61 + 18 * q^62 - 4 * q^63 + 4 * q^64 + 48 * q^66 + 8 * q^67 - 6 * q^71 - 12 * q^72 - 16 * q^73 - 2 * q^75 + 2 * q^76 - 24 * q^77 + 8 * q^79 - 10 * q^80 - 2 * q^81 + 12 * q^82 - 24 * q^83 - 4 * q^84 + 36 * q^86 + 6 * q^88 + 12 * q^89 + 24 * q^90 + 12 * q^92 - 28 * q^93 - 2 * q^95 + 36 * q^96 - 4 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	0.990839	+	0.135045i	$0.0431180\pi$
$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	−0.378467	+	0.925615i	$0.623549\pi$
$3$	−1.36603	−	2.36603i	−0.788675	−	1.36603i	−0.926779	−	0.375608i	$-0.877434\pi$
$3$	−1.36603	−	2.36603i	−0.788675	−	1.36603i	0.138104	−	0.990418i	$-0.455899\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	2.36603	−	4.09808i	0.965926	−	1.67303i
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$	1.73205			0.612372
$9$	−2.23205	+	3.86603i	−0.744017	+	1.28868i
$10$	−0.866025	−	1.50000i	−0.273861	−	0.474342i
$11$	2.36603	+	4.09808i	0.713384	+	1.23562i	0.963580	+	0.267421i	$0.0861715\pi$
$11$	2.36603	+	4.09808i	0.713384	+	1.23562i	−0.250196	+	0.968195i	$0.580495\pi$
$12$	2.73205			0.788675
$13$		0			0
$13$		0			0
$14$	−3.46410			−0.925820
$15$	1.36603	+	2.36603i	0.352706	+	0.610905i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	1.73205	−	3.00000i	0.420084	−	0.727607i	−0.575863	−	0.817546i	$-0.695334\pi$
$17$	1.73205	−	3.00000i	0.420084	−	0.727607i	0.995947	+	0.0899392i	$0.0286673\pi$
$18$	−7.73205			−1.82246
$19$	3.09808	−	5.36603i	0.710747	−	1.23105i	−0.253830	−	0.967249i	$-0.581690\pi$
$19$	3.09808	−	5.36603i	0.710747	−	1.23105i	0.964577	−	0.263802i	$-0.0849764\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	5.46410			1.19236
$22$	−4.09808	+	7.09808i	−0.873713	+	1.51331i
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	0.792329	−	0.610094i	$-0.208868\pi$
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	−0.924522	+	0.381130i	$0.875535\pi$
$24$	−2.36603	−	4.09808i	−0.482963	−	0.836516i
$25$	1.00000			0.200000
$26$		0			0
$27$	4.00000			0.769800
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$	1.26795	+	2.19615i	0.235452	+	0.407815i	0.959404	−	0.282035i	$-0.0910095\pi$
$29$	1.26795	+	2.19615i	0.235452	+	0.407815i	−0.723952	+	0.689851i	$0.757676\pi$
$30$	−2.36603	+	4.09808i	−0.431975	+	0.748203i
$31$	10.1962			1.83128			0.915642	−	0.401996i	$-0.131683\pi$
$31$	10.1962			1.83128			0.915642	+	0.401996i	$0.131683\pi$
$32$	−2.59808	+	4.50000i	−0.459279	+	0.795495i
$33$	6.46410	−	11.1962i	1.12526	−	1.94900i
$34$	6.00000			1.02899
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$	−2.23205	−	3.86603i	−0.372008	−	0.644338i
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	10.7321			1.74097
$39$		0			0
$40$	−1.73205			−0.273861
$41$	−1.73205	−	3.00000i	−0.270501	−	0.468521i	0.698489	−	0.715621i	$-0.253856\pi$
$41$	−1.73205	−	3.00000i	−0.270501	−	0.468521i	−0.968990	+	0.247099i	$0.920523\pi$
$42$	4.73205	+	8.19615i	0.730171	+	1.26469i
$43$	0.0980762	−	0.169873i	0.0149565	−	0.0259054i	−0.858450	−	0.512897i	$-0.828572\pi$
$43$	0.0980762	−	0.169873i	0.0149565	−	0.0259054i	0.873407	+	0.486991i	$0.161906\pi$
$44$	−4.73205			−0.713384
$45$	2.23205	−	3.86603i	0.332734	−	0.576313i
$46$	1.09808	−	1.90192i	0.161903	−	0.280423i
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$	6.83013	−	11.8301i	0.985844	−	1.70753i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	0.866025	+	1.50000i	0.122474	+	0.212132i
$51$	−9.46410			−1.32524
$52$		0			0
$53$	10.3923			1.42749			0.713746	−	0.700404i	$-0.246997\pi$
$53$	10.3923			1.42749			0.713746	+	0.700404i	$0.246997\pi$
$54$	3.46410	+	6.00000i	0.471405	+	0.816497i
$55$	−2.36603	−	4.09808i	−0.319035	−	0.552584i
$56$	−1.73205	+	3.00000i	−0.231455	+	0.400892i
$57$	−16.9282			−2.24220
$58$	−2.19615	+	3.80385i	−0.288369	+	0.499470i
$59$	−4.56218	+	7.90192i	−0.593945	+	1.02874i	0.399750	+	0.916624i	$0.369097\pi$
$59$	−4.56218	+	7.90192i	−0.593945	+	1.02874i	−0.993695	+	0.112119i	$0.964236\pi$
$60$	−2.73205			−0.352706
$61$	4.19615	−	7.26795i	0.537262	−	0.930566i	−0.461788	−	0.886990i	$-0.652792\pi$
$61$	4.19615	−	7.26795i	0.537262	−	0.930566i	0.999050	−	0.0435752i	$-0.0138748\pi$
$62$	8.83013	+	15.2942i	1.12143	+	1.94237i
$63$	−4.46410	−	7.73205i	−0.562424	−	0.974147i
$64$	1.00000			0.125000
$65$		0			0
$66$	22.3923			2.75630
$67$	−3.19615	−	5.53590i	−0.390472	−	0.676318i	0.602040	−	0.798466i	$-0.294355\pi$
$67$	−3.19615	−	5.53590i	−0.390472	−	0.676318i	−0.992512	+	0.122149i	$0.961022\pi$
$68$	1.73205	+	3.00000i	0.210042	+	0.363803i
$69$	−1.73205	+	3.00000i	−0.208514	+	0.361158i
$70$	3.46410			0.414039
$71$	−2.36603	+	4.09808i	−0.280796	+	0.486352i	−0.971581	−	0.236708i	$-0.923932\pi$
$71$	−2.36603	+	4.09808i	−0.280796	+	0.486352i	0.690785	+	0.723060i	$0.257265\pi$
$72$	−3.86603	+	6.69615i	−0.455615	+	0.789149i
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	−3.46410	+	6.00000i	−0.402694	+	0.697486i
$75$	−1.36603	−	2.36603i	−0.157735	−	0.273205i
$76$	3.09808	+	5.36603i	0.355374	+	0.615525i
$77$	−9.46410			−1.07853
$78$		0			0
$79$	−8.39230			−0.944208			−0.472104	−	0.881543i	$-0.656505\pi$
$79$	−8.39230			−0.944208			−0.472104	+	0.881543i	$0.656505\pi$
$80$	−2.50000	−	4.33013i	−0.279508	−	0.484123i
$81$	1.23205	+	2.13397i	0.136895	+	0.237108i
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−2.73205	+	4.73205i	−0.298091	+	0.516309i
$85$	−1.73205	+	3.00000i	−0.187867	+	0.325396i
$86$	0.339746			0.0366357
$87$	3.46410	−	6.00000i	0.371391	−	0.643268i
$88$	4.09808	+	7.09808i	0.436856	+	0.756657i
$89$	6.46410	+	11.1962i	0.685193	+	1.18679i	0.973376	+	0.229214i	$0.0736157\pi$
$89$	6.46410	+	11.1962i	0.685193	+	1.18679i	−0.288183	+	0.957575i	$0.593051\pi$
$90$	7.73205			0.815030
$91$		0			0
$92$	1.26795			0.132193
$93$	−13.9282	−	24.1244i	−1.44429	−	2.50158i
$94$	5.19615	+	9.00000i	0.535942	+	0.928279i
$95$	−3.09808	+	5.36603i	−0.317856	+	0.550543i
$96$	14.1962			1.44889
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	−2.59808	+	4.50000i	−0.262445	+	0.454569i
$99$	−21.1244			−2.12308
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	0.464102	+	0.803848i	0.0461798	+	0.0799858i	0.888191	−	0.459474i	$-0.151962\pi$
$101$	0.464102	+	0.803848i	0.0461798	+	0.0799858i	−0.842012	+	0.539459i	$0.818629\pi$
$102$	−8.19615	−	14.1962i	−0.811540	−	1.40563i
$103$	−0.196152			−0.0193275			−0.00966374	−	0.999953i	$-0.503076\pi$
$103$	−0.196152			−0.0193275			−0.00966374	+	0.999953i	$0.503076\pi$
$104$		0			0
$105$	−5.46410			−0.533242
$106$	9.00000	+	15.5885i	0.874157	+	1.51408i
$107$	−8.83013	−	15.2942i	−0.853641	−	1.47855i	−0.877900	−	0.478843i	$-0.841056\pi$
$107$	−8.83013	−	15.2942i	−0.853641	−	1.47855i	0.0242598	−	0.999706i	$-0.492277\pi$
$108$	−2.00000	+	3.46410i	−0.192450	+	0.333333i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	4.09808	−	7.09808i	0.390736	−	0.676775i
$111$	5.46410	−	9.46410i	0.518630	−	0.898293i
$112$	−10.0000			−0.944911
$113$	−4.26795	+	7.39230i	−0.401495	+	0.695410i	−0.993907	−	0.110226i	$-0.964843\pi$
$113$	−4.26795	+	7.39230i	−0.401495	+	0.695410i	0.592412	+	0.805635i	$0.298176\pi$
$114$	−14.6603	−	25.3923i	−1.37306	−	2.37821i
$115$	0.633975	+	1.09808i	0.0591184	+	0.102396i
$116$	−2.53590			−0.235452
$117$		0			0
$118$	−15.8038			−1.45486
$119$	3.46410	+	6.00000i	0.317554	+	0.550019i
$120$	2.36603	+	4.09808i	0.215988	+	0.374101i
$121$	−5.69615	+	9.86603i	−0.517832	+	0.896911i
$122$	14.5359			1.31602
$123$	−4.73205	+	8.19615i	−0.426675	+	0.739022i
$124$	−5.09808	+	8.83013i	−0.457821	+	0.792969i
$125$	−1.00000			−0.0894427
$126$	7.73205	−	13.3923i	0.688826	−	1.19308i
$127$	−8.09808	−	14.0263i	−0.718588	−	1.24463i	−0.961559	−	0.274598i	$-0.911455\pi$
$127$	−8.09808	−	14.0263i	−0.718588	−	1.24463i	0.242971	−	0.970034i	$-0.421878\pi$
$128$	6.06218	+	10.5000i	0.535826	+	0.928078i
$129$	−0.535898			−0.0471832
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	6.46410	+	11.1962i	0.562628	+	0.974500i
$133$	6.19615	+	10.7321i	0.537275	+	0.930587i
$134$	5.53590	−	9.58846i	0.478229	−	0.828317i
$135$	−4.00000			−0.344265
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	−0.464102	+	0.803848i	−0.0396509	+	0.0686773i	−0.885170	−	0.465268i	$-0.845958\pi$
$137$	−0.464102	+	0.803848i	−0.0396509	+	0.0686773i	0.845519	+	0.533945i	$0.179291\pi$
$138$	−6.00000			−0.510754
$139$	−6.19615	+	10.7321i	−0.525551	+	0.910281i	0.474006	+	0.880521i	$0.342807\pi$
$139$	−6.19615	+	10.7321i	−0.525551	+	0.910281i	−0.999557	+	0.0297592i	$0.990526\pi$
$140$	1.00000	+	1.73205i	0.0845154	+	0.146385i
$141$	−8.19615	−	14.1962i	−0.690241	−	1.19553i
$142$	−8.19615			−0.687806
$143$		0			0
$144$	−22.3205			−1.86004
$145$	−1.26795	−	2.19615i	−0.105297	−	0.182381i
$146$	−3.46410	−	6.00000i	−0.286691	−	0.496564i
$147$	4.09808	−	7.09808i	0.338004	−	0.585439i
$148$	−4.00000			−0.328798
$149$	3.92820	−	6.80385i	0.321811	−	0.557393i	−0.659051	−	0.752098i	$-0.729042\pi$
$149$	3.92820	−	6.80385i	0.321811	−	0.557393i	0.980862	+	0.194706i	$0.0623751\pi$
$150$	2.36603	−	4.09808i	0.193185	−	0.334607i
$151$	−1.80385			−0.146795			−0.0733975	−	0.997303i	$-0.523384\pi$
$151$	−1.80385			−0.146795			−0.0733975	+	0.997303i	$0.523384\pi$
$152$	5.36603	−	9.29423i	0.435242	−	0.753861i
$153$	7.73205	+	13.3923i	0.625099	+	1.08270i
$154$	−8.19615	−	14.1962i	−0.660465	−	1.14396i
$155$	−10.1962			−0.818975
$156$		0			0
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$	−7.26795	−	12.5885i	−0.578207	−	1.00148i
$159$	−14.1962	−	24.5885i	−1.12583	−	1.94999i
$160$	2.59808	−	4.50000i	0.205396	−	0.355756i
$161$	2.53590			0.199857
$162$	−2.13397	+	3.69615i	−0.167661	+	0.290397i
$163$	7.19615	−	12.4641i	0.563646	−	0.976264i	−0.433528	−	0.901140i	$-0.642731\pi$
$163$	7.19615	−	12.4641i	0.563646	−	0.976264i	0.997174	−	0.0751237i	$-0.0239352\pi$
$164$	3.46410			0.270501
$165$	−6.46410	+	11.1962i	−0.503230	+	0.871619i
$166$	−5.19615	−	9.00000i	−0.403300	−	0.698535i
$167$	0.464102	+	0.803848i	0.0359133	+	0.0622036i	0.883423	−	0.468576i	$-0.155233\pi$
$167$	0.464102	+	0.803848i	0.0359133	+	0.0622036i	−0.847510	+	0.530779i	$0.821899\pi$
$168$	9.46410			0.730171
$169$		0			0
$170$	−6.00000			−0.460179
$171$	13.8301	+	23.9545i	1.05762	+	1.83185i
$172$	0.0980762	+	0.169873i	0.00747824	+	0.0129527i
$173$	−4.26795	+	7.39230i	−0.324486	+	0.562027i	−0.981408	−	0.191932i	$-0.938525\pi$
$173$	−4.26795	+	7.39230i	−0.324486	+	0.562027i	0.656922	+	0.753958i	$0.271858\pi$
$174$	12.0000			0.909718
$175$	−1.00000	+	1.73205i	−0.0755929	+	0.130931i
$176$	−11.8301	+	20.4904i	−0.891729	+	1.54452i
$177$	24.9282			1.87372
$178$	−11.1962	+	19.3923i	−0.839187	+	1.45351i
$179$	9.46410	+	16.3923i	0.707380	+	1.22522i	0.965826	+	0.259193i	$0.0834564\pi$
$179$	9.46410	+	16.3923i	0.707380	+	1.22522i	−0.258446	+	0.966026i	$0.583210\pi$
$180$	2.23205	+	3.86603i	0.166367	+	0.288157i
$181$	0.392305			0.0291598			0.0145799	−	0.999894i	$-0.495359\pi$
$181$	0.392305			0.0291598			0.0145799	+	0.999894i	$0.495359\pi$
$182$		0			0
$183$	−22.9282			−1.69490
$184$	−1.09808	−	1.90192i	−0.0809513	−	0.140212i
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$	24.1244	−	41.7846i	1.76888	−	3.06380i
$187$	16.3923			1.19872
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$	−4.00000	+	6.92820i	−0.290957	+	0.503953i
$190$	−10.7321			−0.778585
$191$	2.53590	−	4.39230i	0.183491	−	0.317816i	−0.759576	−	0.650419i	$-0.774593\pi$
$191$	2.53590	−	4.39230i	0.183491	−	0.317816i	0.943067	+	0.332603i	$0.107927\pi$
$192$	−1.36603	−	2.36603i	−0.0985844	−	0.170753i
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$	−3.46410			−0.248708
$195$		0			0
$196$	−3.00000			−0.214286
$197$	6.46410	+	11.1962i	0.460548	+	0.797693i	0.998988	−	0.0449709i	$-0.0143195\pi$
$197$	6.46410	+	11.1962i	0.460548	+	0.797693i	−0.538440	+	0.842664i	$0.680986\pi$
$198$	−18.2942	−	31.6865i	−1.30011	−	2.25186i
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	0.256391	+	0.966573i	$0.417466\pi$
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	−0.965272	+	0.261245i	$0.915867\pi$
$200$	1.73205			0.122474
$201$	−8.73205	+	15.1244i	−0.615911	+	1.06679i
$202$	−0.803848	+	1.39230i	−0.0565585	+	0.0979622i
$203$	−5.07180			−0.355970
$204$	4.73205	−	8.19615i	0.331310	−	0.573845i
$205$	1.73205	+	3.00000i	0.120972	+	0.209529i
$206$	−0.169873	−	0.294229i	−0.0118356	−	0.0204999i
$207$	5.66025			0.393415
$208$		0			0
$209$	29.3205			2.02814
$210$	−4.73205	−	8.19615i	−0.326543	−	0.565588i
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$	−5.19615	+	9.00000i	−0.356873	+	0.618123i
$213$	12.9282			0.885826
$214$	15.2942	−	26.4904i	1.04549	−	1.81085i
$215$	−0.0980762	+	0.169873i	−0.00668874	+	0.0115852i
$216$	6.92820			0.471405
$217$	−10.1962	+	17.6603i	−0.692160	+	1.19886i
$218$	1.73205	+	3.00000i	0.117309	+	0.203186i
$219$	5.46410	+	9.46410i	0.369230	+	0.639525i
$220$	4.73205			0.319035
$221$		0			0
$222$	18.9282			1.27038
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	0.830599	−	0.556871i	$-0.187998\pi$
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	−0.897564	+	0.440884i	$0.854665\pi$
$224$	−5.19615	−	9.00000i	−0.347183	−	0.601338i
$225$	−2.23205	+	3.86603i	−0.148803	+	0.257735i
$226$	−14.7846			−0.983458
$227$	1.73205	−	3.00000i	0.114960	−	0.199117i	−0.802804	−	0.596244i	$-0.796659\pi$
$227$	1.73205	−	3.00000i	0.114960	−	0.199117i	0.917764	+	0.397127i	$0.129993\pi$
$228$	8.46410	−	14.6603i	0.560549	−	0.970899i
$229$	6.39230			0.422415			0.211208	−	0.977441i	$-0.432260\pi$
$229$	6.39230			0.422415			0.211208	+	0.977441i	$0.432260\pi$
$230$	−1.09808	+	1.90192i	−0.0724050	+	0.125409i
$231$	12.9282	+	22.3923i	0.850613	+	1.47331i
$232$	2.19615	+	3.80385i	0.144184	+	0.249735i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	−6.00000			−0.391397
$236$	−4.56218	−	7.90192i	−0.296972	−	0.514371i
$237$	11.4641	+	19.8564i	0.744673	+	1.28981i
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$	−14.1962			−0.918273			−0.459136	−	0.888366i	$-0.651841\pi$
$239$	−14.1962			−0.918273			−0.459136	+	0.888366i	$0.651841\pi$
$240$	−6.83013	+	11.8301i	−0.440883	+	0.763631i
$241$	1.19615	−	2.07180i	0.0770510	−	0.133456i	−0.824925	−	0.565242i	$-0.808783\pi$
$241$	1.19615	−	2.07180i	0.0770510	−	0.133456i	0.901976	+	0.431785i	$0.142116\pi$
$242$	−19.7321			−1.26842
$243$	9.36603	−	16.2224i	0.600831	−	1.04067i
$244$	4.19615	+	7.26795i	0.268631	+	0.465283i
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$	−16.3923			−1.04514
$247$		0			0
$248$	17.6603			1.12143
$249$	8.19615	+	14.1962i	0.519410	+	0.899645i
$250$	−0.866025	−	1.50000i	−0.0547723	−	0.0948683i
$251$	10.7321	−	18.5885i	0.677401	−	1.17329i	−0.298360	−	0.954453i	$-0.596440\pi$
$251$	10.7321	−	18.5885i	0.677401	−	1.17329i	0.975761	−	0.218840i	$-0.0702271\pi$
$252$	8.92820			0.562424
$253$	3.00000	−	5.19615i	0.188608	−	0.326679i
$254$	14.0263	−	24.2942i	0.880087	−	1.52436i
$255$	9.46410			0.592665
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−9.92820	−	17.1962i	−0.619304	−	1.07267i	−0.989613	−	0.143758i	$-0.954081\pi$
$257$	−9.92820	−	17.1962i	−0.619304	−	1.07267i	0.370309	−	0.928909i	$-0.379252\pi$
$258$	−0.464102	−	0.803848i	−0.0288937	−	0.0500454i
$259$	−8.00000			−0.497096
$260$		0			0
$261$	−11.3205			−0.700722
$262$		0			0
$263$	−0.633975	−	1.09808i	−0.0390925	−	0.0677103i	0.845817	−	0.533473i	$-0.179113\pi$
$263$	−0.633975	−	1.09808i	−0.0390925	−	0.0677103i	−0.884910	+	0.465763i	$0.845780\pi$
$264$	11.1962	−	19.3923i	0.689076	−	1.19351i
$265$	−10.3923			−0.638394
$266$	−10.7321	+	18.5885i	−0.658024	+	1.13973i
$267$	17.6603	−	30.5885i	1.08079	−	1.87198i
$268$	6.39230			0.390472
$269$	9.92820	−	17.1962i	0.605333	−	1.04847i	−0.386665	−	0.922220i	$-0.626373\pi$
$269$	9.92820	−	17.1962i	0.605333	−	1.04847i	0.991999	−	0.126248i	$-0.0402935\pi$
$270$	−3.46410	−	6.00000i	−0.210819	−	0.365148i
$271$	−15.4904	−	26.8301i	−0.940974	−	1.62981i	−0.763619	−	0.645667i	$-0.776579\pi$
$271$	−15.4904	−	26.8301i	−0.940974	−	1.62981i	−0.177355	−	0.984147i	$-0.556754\pi$
$272$	17.3205			1.05021
$273$		0			0
$274$	−1.60770			−0.0971244
$275$	2.36603	+	4.09808i	0.142677	+	0.247123i
$276$	−1.73205	−	3.00000i	−0.104257	−	0.180579i
$277$	13.1962	−	22.8564i	0.792880	−	1.37331i	−0.131297	−	0.991343i	$-0.541914\pi$
$277$	13.1962	−	22.8564i	0.792880	−	1.37331i	0.924177	−	0.381965i	$-0.124753\pi$
$278$	−21.4641			−1.28733
$279$	−22.7583	+	39.4186i	−1.36251	+	2.35993i
$280$	1.73205	−	3.00000i	0.103510	−	0.179284i
$281$	22.3923			1.33581			0.667906	−	0.744245i	$-0.267191\pi$
$281$	22.3923			1.33581			0.667906	+	0.744245i	$0.267191\pi$
$282$	14.1962	−	24.5885i	0.845369	−	1.46422i
$283$	−16.2942	−	28.2224i	−0.968591	−	1.67765i	−0.699640	−	0.714496i	$-0.746656\pi$
$283$	−16.2942	−	28.2224i	−0.968591	−	1.67765i	−0.268952	−	0.963154i	$-0.586677\pi$
$284$	−2.36603	−	4.09808i	−0.140398	−	0.243176i
$285$	16.9282			1.00274
$286$		0			0
$287$	6.92820			0.408959
$288$	−11.5981	−	20.0885i	−0.683423	−	1.18372i
$289$	2.50000	+	4.33013i	0.147059	+	0.254713i
$290$	2.19615	−	3.80385i	0.128963	−	0.223370i
$291$	5.46410			0.320311
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$	2.53590	−	4.39230i	0.148149	−	0.256601i	−0.782395	−	0.622783i	$-0.786002\pi$
$293$	2.53590	−	4.39230i	0.148149	−	0.256601i	0.930543	+	0.366182i	$0.119335\pi$
$294$	14.1962			0.827936
$295$	4.56218	−	7.90192i	0.265620	−	0.460068i
$296$	3.46410	+	6.00000i	0.201347	+	0.348743i
$297$	9.46410	+	16.3923i	0.549163	+	0.951178i
$298$	13.6077			0.788273
$299$		0			0
$300$	2.73205			0.157735
$301$	0.196152	+	0.339746i	0.0113060	+	0.0195826i
$302$	−1.56218	−	2.70577i	−0.0898932	−	0.155700i
$303$	1.26795	−	2.19615i	0.0728418	−	0.126166i
$304$	30.9808			1.77687
$305$	−4.19615	+	7.26795i	−0.240271	+	0.416162i
$306$	−13.3923	+	23.1962i	−0.765587	+	1.32604i
$307$	−18.7846			−1.07209			−0.536047	−	0.844188i	$-0.680083\pi$
$307$	−18.7846			−1.07209			−0.536047	+	0.844188i	$0.680083\pi$
$308$	4.73205	−	8.19615i	0.269634	−	0.467019i
$309$	0.267949	+	0.464102i	0.0152431	+	0.0264018i
$310$	−8.83013	−	15.2942i	−0.501518	−	0.868654i
$311$	−16.3923			−0.929522			−0.464761	−	0.885436i	$-0.653860\pi$
$311$	−16.3923			−0.929522			−0.464761	+	0.885436i	$0.653860\pi$
$312$		0			0
$313$	−14.3923			−0.813501			−0.406751	−	0.913539i	$-0.633338\pi$
$313$	−14.3923			−0.813501			−0.406751	+	0.913539i	$0.633338\pi$
$314$	−8.66025	−	15.0000i	−0.488726	−	0.846499i
$315$	4.46410	+	7.73205i	0.251524	+	0.435652i
$316$	4.19615	−	7.26795i	0.236052	−	0.408854i
$317$	24.0000			1.34797			0.673987	−	0.738743i	$-0.264580\pi$
$317$	24.0000			1.34797			0.673987	+	0.738743i	$0.264580\pi$
$318$	24.5885	−	42.5885i	1.37885	−	2.38824i
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$	−1.00000			−0.0559017
$321$	−24.1244	+	41.7846i	−1.34649	+	2.33219i
$322$	2.19615	+	3.80385i	0.122387	+	0.211980i
$323$	−10.7321	−	18.5885i	−0.597147	−	1.03429i
$324$	−2.46410			−0.136895
$325$		0			0
$326$	24.9282			1.38065
$327$	−2.73205	−	4.73205i	−0.151083	−	0.261683i
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$	−22.3923			−1.23266
$331$	−1.29423	+	2.24167i	−0.0711372	+	0.123213i	−0.899400	−	0.437127i	$-0.855996\pi$
$331$	−1.29423	+	2.24167i	−0.0711372	+	0.123213i	0.828263	+	0.560340i	$0.189329\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	−17.8564			−0.978525
$334$	−0.803848	+	1.39230i	−0.0439846	+	0.0761835i
$335$	3.19615	+	5.53590i	0.174624	+	0.302458i
$336$	13.6603	+	23.6603i	0.745228	+	1.29077i
$337$	−26.3923			−1.43768			−0.718840	−	0.695175i	$-0.755327\pi$
$337$	−26.3923			−1.43768			−0.718840	+	0.695175i	$0.755327\pi$
$338$		0			0
$339$	23.3205			1.26660
$340$	−1.73205	−	3.00000i	−0.0939336	−	0.162698i
$341$	24.1244	+	41.7846i	1.30641	+	2.26276i
$342$	−23.9545	+	41.4904i	−1.29531	+	2.24354i
$343$	−20.0000			−1.07990
$344$	0.169873	−	0.294229i	0.00915894	−	0.0158637i
$345$	1.73205	−	3.00000i	0.0932505	−	0.161515i
$346$	−14.7846			−0.794826
$347$	2.83013	−	4.90192i	0.151929	−	0.263149i	−0.780007	−	0.625770i	$-0.784785\pi$
$347$	2.83013	−	4.90192i	0.151929	−	0.263149i	0.931937	+	0.362621i	$0.118118\pi$
$348$	3.46410	+	6.00000i	0.185695	+	0.321634i
$349$	7.19615	+	12.4641i	0.385201	+	0.667188i	0.991797	−	0.127822i	$-0.0407987\pi$
$349$	7.19615	+	12.4641i	0.385201	+	0.667188i	−0.606596	+	0.795010i	$0.707465\pi$
$350$	−3.46410			−0.185164
$351$		0			0
$352$	−24.5885			−1.31057
$353$	13.8564	+	24.0000i	0.737502	+	1.27739i	0.953617	+	0.301023i	$0.0973281\pi$
$353$	13.8564	+	24.0000i	0.737502	+	1.27739i	−0.216115	+	0.976368i	$0.569339\pi$
$354$	21.5885	+	37.3923i	1.14741	+	1.98738i
$355$	2.36603	−	4.09808i	0.125576	−	0.217503i
$356$	−12.9282			−0.685193
$357$	9.46410	−	16.3923i	0.500893	−	0.867573i
$358$	−16.3923	+	28.3923i	−0.866360	+	1.50058i
$359$	−2.19615			−0.115908			−0.0579542	−	0.998319i	$-0.518458\pi$
$359$	−2.19615			−0.115908			−0.0579542	+	0.998319i	$0.518458\pi$
$360$	3.86603	−	6.69615i	0.203757	−	0.352918i
$361$	−9.69615	−	16.7942i	−0.510324	−	0.883907i
$362$	0.339746	+	0.588457i	0.0178567	+	0.0309286i
$363$	31.1244			1.63361
$364$		0			0
$365$	4.00000			0.209370
$366$	−19.8564	−	34.3923i	−1.03791	−	1.79771i
$367$	−5.90192	−	10.2224i	−0.308078	−	0.533607i	0.669864	−	0.742484i	$-0.266352\pi$
$367$	−5.90192	−	10.2224i	−0.308078	−	0.533607i	−0.977942	+	0.208877i	$0.933019\pi$
$368$	3.16987	−	5.49038i	0.165241	−	0.286206i
$369$	15.4641			0.805029
$370$	3.46410	−	6.00000i	0.180090	−	0.311925i
$371$	−10.3923	+	18.0000i	−0.539542	+	0.934513i
$372$	27.8564			1.44429
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	14.1962	+	24.5885i	0.734066	+	1.27144i
$375$	1.36603	+	2.36603i	0.0705412	+	0.122181i
$376$	10.3923			0.535942
$377$		0			0
$378$	−13.8564			−0.712697
$379$	−9.49038	−	16.4378i	−0.487488	−	0.844354i	0.512408	−	0.858742i	$-0.328753\pi$
$379$	−9.49038	−	16.4378i	−0.487488	−	0.844354i	−0.999896	+	0.0143877i	$0.995420\pi$
$380$	−3.09808	−	5.36603i	−0.158928	−	0.275271i
$381$	−22.1244	+	38.3205i	−1.13347	+	1.96322i
$382$	8.78461			0.449460
$383$	−6.46410	+	11.1962i	−0.330300	+	0.572097i	−0.982571	−	0.185890i	$-0.940483\pi$
$383$	−6.46410	+	11.1962i	−0.330300	+	0.572097i	0.652270	+	0.757986i	$0.273817\pi$
$384$	16.5622	−	28.6865i	0.845185	−	1.46390i
$385$	9.46410			0.482335
$386$	−8.66025	+	15.0000i	−0.440795	+	0.763480i
$387$	0.437822	+	0.758330i	0.0222558	+	0.0385481i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$		0			0
$391$	−4.39230			−0.222128
$392$	2.59808	+	4.50000i	0.131223	+	0.227284i
$393$		0			0
$394$	−11.1962	+	19.3923i	−0.564054	+	0.976970i
$395$	8.39230			0.422263
$396$	10.5622	−	18.2942i	0.530769	−	0.919320i
$397$	−14.3923	+	24.9282i	−0.722329	+	1.25111i	0.237735	+	0.971330i	$0.423595\pi$
$397$	−14.3923	+	24.9282i	−0.722329	+	1.25111i	−0.960064	+	0.279781i	$0.909738\pi$
$398$	−34.6410			−1.73640
$399$	16.9282	−	29.3205i	0.847470	−	1.46786i
$400$	2.50000	+	4.33013i	0.125000	+	0.216506i
$401$	18.4641	+	31.9808i	0.922053	+	1.59704i	0.796233	+	0.604990i	$0.206823\pi$
$401$	18.4641	+	31.9808i	0.922053	+	1.59704i	0.125820	+	0.992053i	$0.459844\pi$
$402$	−30.2487			−1.50867
$403$		0			0
$404$	−0.928203			−0.0461798
$405$	−1.23205	−	2.13397i	−0.0612211	−	0.106038i
$406$	−4.39230	−	7.60770i	−0.217986	−	0.377564i
$407$	−9.46410	+	16.3923i	−0.469118	+	0.812536i
$408$	−16.3923			−0.811540
$409$	8.80385	−	15.2487i	0.435322	−	0.754000i	−0.562000	−	0.827137i	$-0.689968\pi$
$409$	8.80385	−	15.2487i	0.435322	−	0.754000i	0.997322	+	0.0731372i	$0.0233011\pi$
$410$	−3.00000	+	5.19615i	−0.148159	+	0.256620i
$411$	2.53590			0.125087
$412$	0.0980762	−	0.169873i	0.00483187	−	0.00836904i
$413$	−9.12436	−	15.8038i	−0.448980	−	0.777657i
$414$	4.90192	+	8.49038i	0.240916	+	0.417279i
$415$	6.00000			0.294528
$416$		0			0
$417$	33.8564			1.65796
$418$	25.3923	+	43.9808i	1.24198	+	2.15117i
$419$	1.26795	+	2.19615i	0.0619434	+	0.107289i	0.895334	−	0.445395i	$-0.146937\pi$
$419$	1.26795	+	2.19615i	0.0619434	+	0.107289i	−0.833391	+	0.552684i	$0.813604\pi$
$420$	2.73205	−	4.73205i	0.133310	−	0.230900i
$421$	−30.7846			−1.50035			−0.750175	−	0.661239i	$-0.770031\pi$
$421$	−30.7846			−1.50035			−0.750175	+	0.661239i	$0.770031\pi$
$422$	6.92820	−	12.0000i	0.337260	−	0.584151i
$423$	−13.3923	+	23.1962i	−0.651156	+	1.12784i
$424$	18.0000			0.874157
$425$	1.73205	−	3.00000i	0.0840168	−	0.145521i
$426$	11.1962	+	19.3923i	0.542455	+	0.939560i
$427$	8.39230	+	14.5359i	0.406132	+	0.703441i
$428$	17.6603			0.853641
$429$		0			0
$430$	−0.339746			−0.0163840
$431$	12.7583	+	22.0981i	0.614547	+	1.06443i	0.990464	+	0.137773i	$0.0439946\pi$
$431$	12.7583	+	22.0981i	0.614547	+	1.06443i	−0.375917	+	0.926653i	$0.622672\pi$
$432$	10.0000	+	17.3205i	0.481125	+	0.833333i
$433$	−17.3923	+	30.1244i	−0.835821	+	1.44768i	0.0575395	+	0.998343i	$0.481674\pi$
$433$	−17.3923	+	30.1244i	−0.835821	+	1.44768i	−0.893360	+	0.449341i	$0.851659\pi$
$434$	−35.3205			−1.69544
$435$	−3.46410	+	6.00000i	−0.166091	+	0.287678i
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	−7.85641			−0.375823
$438$	−9.46410	+	16.3923i	−0.452212	+	0.783255i
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	−0.940963	−	0.338508i	$-0.890078\pi$
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	0.177325	−	0.984152i	$-0.443256\pi$
$440$	−4.09808	−	7.09808i	−0.195368	−	0.338388i
$441$	−13.3923			−0.637729
$442$		0			0
$443$	−16.9808			−0.806780			−0.403390	−	0.915028i	$-0.632168\pi$
$443$	−16.9808			−0.806780			−0.403390	+	0.915028i	$0.632168\pi$
$444$	5.46410	+	9.46410i	0.259315	+	0.449146i
$445$	−6.46410	−	11.1962i	−0.306428	−	0.530749i
$446$	1.73205	−	3.00000i	0.0820150	−	0.142054i
$447$	−21.4641			−1.01522
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	−10.2679	+	17.7846i	−0.484574	+	0.839308i	−0.999843	−	0.0177212i	$-0.994359\pi$
$449$	−10.2679	+	17.7846i	−0.484574	+	0.839308i	0.515268	+	0.857029i	$0.327692\pi$
$450$	−7.73205			−0.364492
$451$	8.19615	−	14.1962i	0.385942	−	0.668471i
$452$	−4.26795	−	7.39230i	−0.200747	−	0.347705i
$453$	2.46410	+	4.26795i	0.115774	+	0.200526i
$454$	6.00000			0.281594
$455$		0			0
$456$	−29.3205			−1.37306
$457$	−5.39230	−	9.33975i	−0.252241	−	0.436895i	0.711901	−	0.702280i	$-0.247834\pi$
$457$	−5.39230	−	9.33975i	−0.252241	−	0.436895i	−0.964143	+	0.265385i	$0.914501\pi$
$458$	5.53590	+	9.58846i	0.258676	+	0.448039i
$459$	6.92820	−	12.0000i	0.323381	−	0.560112i
$460$	−1.26795			−0.0591184
$461$	1.73205	−	3.00000i	0.0806696	−	0.139724i	−0.822868	−	0.568232i	$-0.807627\pi$
$461$	1.73205	−	3.00000i	0.0806696	−	0.139724i	0.903538	+	0.428508i	$0.140961\pi$
$462$	−22.3923	+	38.7846i	−1.04178	+	1.80442i
$463$	−2.39230			−0.111180			−0.0555899	−	0.998454i	$-0.517704\pi$
$463$	−2.39230			−0.111180			−0.0555899	+	0.998454i	$0.517704\pi$
$464$	−6.33975	+	10.9808i	−0.294315	+	0.509769i
$465$	13.9282	+	24.1244i	0.645905	+	1.11874i
$466$	−5.19615	−	9.00000i	−0.240707	−	0.416917i
$467$	27.8038			1.28661			0.643304	−	0.765611i	$-0.277563\pi$
$467$	27.8038			1.28661			0.643304	+	0.765611i	$0.277563\pi$
$468$		0			0
$469$	12.7846			0.590338
$470$	−5.19615	−	9.00000i	−0.239681	−	0.415139i
$471$	13.6603	+	23.6603i	0.629431	+	1.09021i
$472$	−7.90192	+	13.6865i	−0.363716	+	0.629974i
$473$	0.928203			0.0426788
$474$	−19.8564	+	34.3923i	−0.912035	+	1.57969i
$475$	3.09808	−	5.36603i	0.142149	−	0.246210i
$476$	−6.92820			−0.317554
$477$	−23.1962	+	40.1769i	−1.06208	+	1.83957i
$478$	−12.2942	−	21.2942i	−0.562325	−	0.973975i
$479$	−17.8301	−	30.8827i	−0.814679	−	1.41107i	−0.909558	−	0.415577i	$-0.863580\pi$
$479$	−17.8301	−	30.8827i	−0.814679	−	1.41107i	0.0948787	−	0.995489i	$-0.469754\pi$
$480$	−14.1962			−0.647963
$481$		0			0
$482$	4.14359			0.188736
$483$	−3.46410	−	6.00000i	−0.157622	−	0.273009i
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$	32.4449			1.47173
$487$	13.1962	−	22.8564i	0.597975	−	1.03572i	−0.395145	−	0.918619i	$-0.629306\pi$
$487$	13.1962	−	22.8564i	0.597975	−	1.03572i	0.993120	−	0.117104i	$-0.0373610\pi$
$488$	7.26795	−	12.5885i	0.329005	−	0.569853i
$489$	−39.3205			−1.77813
$490$	2.59808	−	4.50000i	0.117369	−	0.203289i
$491$	1.26795	+	2.19615i	0.0572217	+	0.0991110i	0.893217	−	0.449625i	$-0.148442\pi$
$491$	1.26795	+	2.19615i	0.0572217	+	0.0991110i	−0.835996	+	0.548736i	$0.815109\pi$
$492$	−4.73205	−	8.19615i	−0.213337	−	0.369511i
$493$	8.78461			0.395639
$494$		0			0
$495$	21.1244			0.949469
$496$	25.4904	+	44.1506i	1.14455	+	1.98242i
$497$	−4.73205	−	8.19615i	−0.212261	−	0.367648i
$498$	−14.1962	+	24.5885i	−0.636145	+	1.10184i
$499$	−38.9808			−1.74502			−0.872509	−	0.488598i	$-0.837509\pi$
$499$	−38.9808			−1.74502			−0.872509	+	0.488598i	$0.837509\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	1.26795	−	2.19615i	0.0566478	−	0.0981169i
$502$	37.1769			1.65929
$503$	−9.75833	+	16.9019i	−0.435102	+	0.753620i	−0.997304	−	0.0733807i	$-0.976621\pi$
$503$	−9.75833	+	16.9019i	−0.435102	+	0.753620i	0.562202	+	0.827000i	$0.309955\pi$
$504$	−7.73205	−	13.3923i	−0.344413	−	0.596541i
$505$	−0.464102	−	0.803848i	−0.0206523	−	0.0357707i
$506$	10.3923			0.461994
$507$		0			0
$508$	16.1962			0.718588
$509$	−19.7321	−	34.1769i	−0.874608	−	1.51487i	−0.857180	−	0.515017i	$-0.827786\pi$
$509$	−19.7321	−	34.1769i	−0.874608	−	1.51487i	−0.0174278	−	0.999848i	$-0.505548\pi$
$510$	8.19615	+	14.1962i	0.362932	+	0.628616i
$511$	4.00000	−	6.92820i	0.176950	−	0.306486i
$512$	−8.66025			−0.382733
$513$	12.3923	−	21.4641i	0.547134	−	0.947663i
$514$	17.1962	−	29.7846i	0.758490	−	1.31374i
$515$	0.196152			0.00864351
$516$	0.267949	−	0.464102i	0.0117958	−	0.0204309i
$517$	14.1962	+	24.5885i	0.624346	+	1.08140i
$518$	−6.92820	−	12.0000i	−0.304408	−	0.527250i
$519$	23.3205			1.02366
$520$		0			0
$521$	−28.3923			−1.24389			−0.621945	−	0.783061i	$-0.713657\pi$
$521$	−28.3923			−1.24389			−0.621945	+	0.783061i	$0.713657\pi$
$522$	−9.80385	−	16.9808i	−0.429103	−	0.743228i
$523$	12.0981	+	20.9545i	0.529012	+	0.916276i	0.999428	+	0.0338306i	$0.0107707\pi$
$523$	12.0981	+	20.9545i	0.529012	+	0.916276i	−0.470416	+	0.882445i	$0.655896\pi$
$524$		0			0
$525$	5.46410			0.238473
$526$	1.09808	−	1.90192i	0.0478784	−	0.0829278i
$527$	17.6603	−	30.5885i	0.769293	−	1.33245i
$528$	64.6410			2.81314
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$	−9.00000	−	15.5885i	−0.390935	−	0.677119i
$531$	−20.3660	−	35.2750i	−0.883810	−	1.53080i
$532$	−12.3923			−0.537275
$533$		0			0
$534$	61.1769			2.64738
$535$	8.83013	+	15.2942i	0.381760	+	0.661227i
$536$	−5.53590	−	9.58846i	−0.239114	−	0.414158i
$537$	25.8564	−	44.7846i	1.11579	−	1.93260i
$538$	34.3923			1.48276
$539$	−7.09808	+	12.2942i	−0.305736	+	0.529550i
$540$	2.00000	−	3.46410i	0.0860663	−	0.149071i
$541$	−26.3923			−1.13469			−0.567347	−	0.823479i	$-0.692030\pi$
$541$	−26.3923			−1.13469			−0.567347	+	0.823479i	$0.692030\pi$
$542$	26.8301	−	46.4711i	1.15245	−	1.99611i
$543$	−0.535898	−	0.928203i	−0.0229976	−	0.0398330i
$544$	9.00000	+	15.5885i	0.385872	+	0.668350i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−12.1962			−0.521470			−0.260735	−	0.965410i	$-0.583965\pi$
$547$	−12.1962			−0.521470			−0.260735	+	0.965410i	$0.583965\pi$
$548$	−0.464102	−	0.803848i	−0.0198254	−	0.0343387i
$549$	18.7321	+	32.4449i	0.799464	+	1.38471i
$550$	−4.09808	+	7.09808i	−0.174743	+	0.302663i
$551$	15.7128			0.669388
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	8.39230	−	14.5359i	0.356877	−	0.618129i
$554$	45.7128			1.94215
$555$	−5.46410	+	9.46410i	−0.231938	+	0.401729i
$556$	−6.19615	−	10.7321i	−0.262775	−	0.455140i
$557$	−0.928203	−	1.60770i	−0.0393292	−	0.0681202i	0.845691	−	0.533673i	$-0.179189\pi$
$557$	−0.928203	−	1.60770i	−0.0393292	−	0.0681202i	−0.885020	+	0.465553i	$0.845855\pi$
$558$	−78.8372			−3.33744
$559$		0			0
$560$	10.0000			0.422577
$561$	−22.3923	−	38.7846i	−0.945404	−	1.63749i
$562$	19.3923	+	33.5885i	0.818015	+	1.41684i
$563$	11.0263	−	19.0981i	0.464702	−	0.804888i	−0.534486	−	0.845177i	$-0.679495\pi$
$563$	11.0263	−	19.0981i	0.464702	−	0.804888i	0.999188	+	0.0402895i	$0.0128280\pi$
$564$	16.3923			0.690241
$565$	4.26795	−	7.39230i	0.179554	−	0.310997i
$566$	28.2224	−	48.8827i	1.18628	−	2.05469i
$567$	−4.92820			−0.206965
$568$	−4.09808	+	7.09808i	−0.171951	+	0.297829i
$569$	1.26795	+	2.19615i	0.0531552	+	0.0920675i	0.891379	−	0.453259i	$-0.149739\pi$
$569$	1.26795	+	2.19615i	0.0531552	+	0.0920675i	−0.838223	+	0.545327i	$0.816406\pi$
$570$	14.6603	+	25.3923i	0.614050	+	1.06357i
$571$	36.3923			1.52297			0.761485	−	0.648182i	$-0.224470\pi$
$571$	36.3923			1.52297			0.761485	+	0.648182i	$0.224470\pi$
$572$		0			0
$573$	−13.8564			−0.578860
$574$	6.00000	+	10.3923i	0.250435	+	0.433766i
$575$	−0.633975	−	1.09808i	−0.0264386	−	0.0457929i
$576$	−2.23205	+	3.86603i	−0.0930021	+	0.161084i
$577$	−4.00000			−0.166522			−0.0832611	−	0.996528i	$-0.526534\pi$
$577$	−4.00000			−0.166522			−0.0832611	+	0.996528i	$0.526534\pi$
$578$	−4.33013	+	7.50000i	−0.180110	+	0.311959i
$579$	13.6603	−	23.6603i	0.567701	−	0.983287i
$580$	2.53590			0.105297
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	4.73205	+	8.19615i	0.196150	+	0.339741i
$583$	24.5885	+	42.5885i	1.01835	+	1.76383i
$584$	−6.92820			−0.286691
$585$		0			0
$586$	8.78461			0.362889
$587$	4.26795	+	7.39230i	0.176157	+	0.305113i	0.940561	−	0.339624i	$-0.110300\pi$
$587$	4.26795	+	7.39230i	0.176157	+	0.305113i	−0.764404	+	0.644738i	$0.776967\pi$
$588$	4.09808	+	7.09808i	0.169002	+	0.292720i
$589$	31.5885	−	54.7128i	1.30158	−	2.25440i
$590$	15.8038			0.650634
$591$	17.6603	−	30.5885i	0.726446	−	1.25824i
$592$	−10.0000	+	17.3205i	−0.410997	+	0.711868i
$593$	26.7846			1.09991			0.549956	−	0.835194i	$-0.314644\pi$
$593$	26.7846			1.09991			0.549956	+	0.835194i	$0.314644\pi$
$594$	−16.3923	+	28.3923i	−0.672584	+	1.16495i
$595$	−3.46410	−	6.00000i	−0.142014	−	0.245976i
$596$	3.92820	+	6.80385i	0.160905	+	0.278696i
$597$	54.6410			2.23631
$598$		0			0
$599$	−7.60770			−0.310842			−0.155421	−	0.987848i	$-0.549673\pi$
$599$	−7.60770			−0.310842			−0.155421	+	0.987848i	$0.549673\pi$
$600$	−2.36603	−	4.09808i	−0.0965926	−	0.167303i
$601$	−21.7846	−	37.7321i	−0.888613	−	1.53912i	−0.841516	−	0.540232i	$-0.818336\pi$
$601$	−21.7846	−	37.7321i	−0.888613	−	1.53912i	−0.0470967	−	0.998890i	$-0.514997\pi$
$602$	−0.339746	+	0.588457i	−0.0138470	+	0.0239837i
$603$	28.5359			1.16207
$604$	0.901924	−	1.56218i	0.0366988	−	0.0635641i
$605$	5.69615	−	9.86603i	0.231582	−	0.401111i
$606$	4.39230			0.178425
$607$	−12.4904	+	21.6340i	−0.506969	+	0.878096i	0.492999	+	0.870030i	$0.335901\pi$
$607$	−12.4904	+	21.6340i	−0.506969	+	0.878096i	−0.999967	+	0.00806581i	$0.997433\pi$
$608$	16.0981	+	27.8827i	0.652863	+	1.13079i
$609$	6.92820	+	12.0000i	0.280745	+	0.486265i
$610$	−14.5359			−0.588541
$611$		0			0
$612$	−15.4641			−0.625099
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	−0.999574	−	0.0291886i	$-0.990708\pi$
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	0.474509	−	0.880251i	$-0.342626\pi$
$614$	−16.2679	−	28.1769i	−0.656521	−	1.13713i
$615$	4.73205	−	8.19615i	0.190815	−	0.330501i
$616$	−16.3923			−0.660465
$617$	−16.8564	+	29.1962i	−0.678613	+	1.17539i	0.296785	+	0.954944i	$0.404085\pi$
$617$	−16.8564	+	29.1962i	−0.678613	+	1.17539i	−0.975399	+	0.220449i	$0.929248\pi$
$618$	−0.464102	+	0.803848i	−0.0186689	+	0.0323355i
$619$	6.98076			0.280581			0.140290	−	0.990110i	$-0.455196\pi$
$619$	6.98076			0.280581			0.140290	+	0.990110i	$0.455196\pi$
$620$	5.09808	−	8.83013i	0.204744	−	0.354626i
$621$	−2.53590	−	4.39230i	−0.101762	−	0.176257i
$622$	−14.1962	−	24.5885i	−0.569214	−	0.985907i
$623$	−25.8564			−1.03592
$624$		0			0
$625$	1.00000			0.0400000
$626$	−12.4641	−	21.5885i	−0.498166	−	0.862848i
$627$	−40.0526	−	69.3731i	−1.59955	−	2.77049i
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$	13.8564			0.552491
$630$	−7.73205	+	13.3923i	−0.308052	+	0.533562i
$631$	−2.90192	+	5.02628i	−0.115524	+	0.200093i	−0.917989	−	0.396606i	$-0.870188\pi$
$631$	−2.90192	+	5.02628i	−0.115524	+	0.200093i	0.802465	+	0.596699i	$0.203521\pi$
$632$	−14.5359			−0.578207
$633$	−10.9282	+	18.9282i	−0.434357	+	0.752329i
$634$	20.7846	+	36.0000i	0.825462	+	1.42974i
$635$	8.09808	+	14.0263i	0.321362	+	0.556616i
$636$	28.3923			1.12583
$637$		0			0
$638$	−20.7846			−0.822871
$639$	−10.5622	−	18.2942i	−0.417833	−	0.723708i
$640$	−6.06218	−	10.5000i	−0.239629	−	0.415049i
$641$	−6.46410	+	11.1962i	−0.255317	+	0.442221i	−0.964981	−	0.262318i	$-0.915513\pi$
$641$	−6.46410	+	11.1962i	−0.255317	+	0.442221i	0.709665	+	0.704539i	$0.248846\pi$
$642$	−83.5692			−3.29821
$643$	3.39230	−	5.87564i	0.133779	−	0.231713i	−0.791351	−	0.611362i	$-0.790622\pi$
$643$	3.39230	−	5.87564i	0.133779	−	0.231713i	0.925131	+	0.379649i	$0.123955\pi$
$644$	−1.26795	+	2.19615i	−0.0499642	+	0.0865405i
$645$	0.535898			0.0211010
$646$	18.5885	−	32.1962i	0.731353	−	1.26674i
$647$	−11.0263	−	19.0981i	−0.433488	−	0.750823i	0.563683	−	0.825991i	$-0.309384\pi$
$647$	−11.0263	−	19.0981i	−0.433488	−	0.750823i	−0.997171	+	0.0751683i	$0.976051\pi$
$648$	2.13397	+	3.69615i	0.0838304	+	0.145199i
$649$	−43.1769			−1.69484
$650$		0			0
$651$	55.7128			2.18356
$652$	7.19615	+	12.4641i	0.281823	+	0.488132i
$653$	−3.92820	−	6.80385i	−0.153722	−	0.266255i	0.778871	−	0.627185i	$-0.215793\pi$
$653$	−3.92820	−	6.80385i	−0.153722	−	0.266255i	−0.932593	+	0.360929i	$0.882460\pi$
$654$	4.73205	−	8.19615i	0.185038	−	0.320495i
$655$		0			0
$656$	8.66025	−	15.0000i	0.338126	−	0.585652i
$657$	8.92820	−	15.4641i	0.348322	−	0.603312i
$658$	−20.7846			−0.810268
$659$	10.7321	−	18.5885i	0.418061	−	0.724103i	−0.577683	−	0.816261i	$-0.696043\pi$
$659$	10.7321	−	18.5885i	0.418061	−	0.724103i	0.995744	+	0.0921577i	$0.0293764\pi$
$660$	−6.46410	−	11.1962i	−0.251615	−	0.435810i
$661$	−5.39230	−	9.33975i	−0.209736	−	0.363274i	0.741895	−	0.670516i	$-0.233927\pi$
$661$	−5.39230	−	9.33975i	−0.209736	−	0.363274i	−0.951631	+	0.307242i	$0.900594\pi$
$662$	−4.48334			−0.174250
$663$		0			0
$664$	−10.3923			−0.403300
$665$	−6.19615	−	10.7321i	−0.240276	−	0.416171i
$666$	−15.4641	−	26.7846i	−0.599222	−	1.03788i
$667$	1.60770	−	2.78461i	0.0622502	−	0.107821i
$668$	−0.928203			−0.0359133
$669$	−2.73205	+	4.73205i	−0.105627	+	0.182952i
$670$	−5.53590	+	9.58846i	−0.213870	+	0.370434i
$671$	39.7128			1.53310
$672$	−14.1962	+	24.5885i	−0.547628	+	0.948520i
$673$	7.19615	+	12.4641i	0.277391	+	0.480456i	0.970736	−	0.240151i	$-0.0771968\pi$
$673$	7.19615	+	12.4641i	0.277391	+	0.480456i	−0.693344	+	0.720606i	$0.743863\pi$
$674$	−22.8564	−	39.5885i	−0.880396	−	1.52489i
$675$	4.00000			0.153960
$676$		0			0
$677$	10.3923			0.399409			0.199704	−	0.979856i	$-0.436002\pi$
$677$	10.3923			0.399409			0.199704	+	0.979856i	$0.436002\pi$
$678$	20.1962	+	34.9808i	0.775629	+	1.34343i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$	−3.00000	+	5.19615i	−0.115045	+	0.199263i
$681$	−9.46410			−0.362665
$682$	−41.7846	+	72.3731i	−1.60002	+	2.77131i
$683$	−16.2679	+	28.1769i	−0.622476	+	1.07816i	0.366547	+	0.930399i	$0.380540\pi$
$683$	−16.2679	+	28.1769i	−0.622476	+	1.07816i	−0.989023	+	0.147760i	$0.952794\pi$
$684$	−27.6603			−1.05762
$685$	0.464102	−	0.803848i	0.0177324	−	0.0307134i
$686$	−17.3205	−	30.0000i	−0.661300	−	1.14541i
$687$	−8.73205	−	15.1244i	−0.333149	−	0.577030i
$688$	0.980762			0.0373912
$689$		0			0
$690$	6.00000			0.228416
$691$	23.8827	+	41.3660i	0.908540	+	1.57364i	0.816093	+	0.577920i	$0.196135\pi$
$691$	23.8827	+	41.3660i	0.908540	+	1.57364i	0.0924469	+	0.995718i	$0.470531\pi$
$692$	−4.26795	−	7.39230i	−0.162243	−	0.281013i
$693$	21.1244	−	36.5885i	0.802448	−	1.38988i
$694$	9.80385			0.372149
$695$	6.19615	−	10.7321i	0.235033	−	0.407090i
$696$	6.00000	−	10.3923i	0.227429	−	0.393919i
$697$	−12.0000			−0.454532
$698$	−12.4641	+	21.5885i	−0.471773	+	0.817135i
$699$	8.19615	+	14.1962i	0.310007	+	0.536948i
$700$	−1.00000	−	1.73205i	−0.0377964	−	0.0654654i
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$	24.7846			0.934769
$704$	2.36603	+	4.09808i	0.0891729	+	0.154452i
$705$	8.19615	+	14.1962i	0.308685	+	0.534658i
$706$	−24.0000	+	41.5692i	−0.903252	+	1.56448i
$707$	−1.85641			−0.0698174
$708$	−12.4641	+	21.5885i	−0.468430	+	0.811344i
$709$	−15.1962	+	26.3205i	−0.570703	+	0.988487i	0.425790	+	0.904822i	$0.359996\pi$
$709$	−15.1962	+	26.3205i	−0.570703	+	0.988487i	−0.996494	+	0.0836656i	$0.973337\pi$
$710$	8.19615			0.307596
$711$	18.7321	−	32.4449i	0.702507	−	1.21678i
$712$	11.1962	+	19.3923i	0.419594	+	0.726757i
$713$	−6.46410	−	11.1962i	−0.242083	−	0.419299i
$714$	32.7846			1.22693
$715$		0			0
$716$	−18.9282			−0.707380
$717$	19.3923	+	33.5885i	0.724219	+	1.25438i
$718$	−1.90192	−	3.29423i	−0.0709792	−	0.122940i
$719$	12.9282	−	22.3923i	0.482141	−	0.835092i	−0.517649	−	0.855593i	$-0.673193\pi$
$719$	12.9282	−	22.3923i	0.482141	−	0.835092i	0.999790	+	0.0205009i	$0.00652609\pi$
$720$	22.3205			0.831836
$721$	0.196152	−	0.339746i	0.00730510	−	0.0126528i
$722$	16.7942	−	29.0885i	0.625016	−	1.08256i
$723$	−6.53590			−0.243073
$724$	−0.196152	+	0.339746i	−0.00728995	+	0.0126266i
$725$	1.26795	+	2.19615i	0.0470905	+	0.0815631i
$726$	26.9545	+	46.6865i	1.00037	+	1.73270i
$727$	44.5885			1.65369			0.826847	−	0.562427i	$-0.190132\pi$
$727$	44.5885			1.65369			0.826847	+	0.562427i	$0.190132\pi$
$728$		0			0
$729$	−43.7846			−1.62165
$730$	3.46410	+	6.00000i	0.128212	+	0.222070i
$731$	−0.339746	−	0.588457i	−0.0125660	−	0.0217649i
$732$	11.4641	−	19.8564i	0.423725	−	0.733914i
$733$	38.0000			1.40356			0.701781	−	0.712393i	$-0.252388\pi$
$733$	38.0000			1.40356			0.701781	+	0.712393i	$0.252388\pi$
$734$	10.2224	−	17.7058i	0.377317	−	0.653532i
$735$	−4.09808	+	7.09808i	−0.151160	+	0.261816i
$736$	6.58846			0.242854
$737$	15.1244	−	26.1962i	0.557113	−	0.964948i
$738$	13.3923	+	23.1962i	0.492978	+	0.853862i
$739$	9.09808	+	15.7583i	0.334678	+	0.579680i	0.983423	−	0.181326i	$-0.0580391\pi$
$739$	9.09808	+	15.7583i	0.334678	+	0.579680i	−0.648745	+	0.761006i	$0.724706\pi$
$740$	4.00000			0.147043
$741$		0			0
$742$	−36.0000			−1.32160
$743$	8.07180	+	13.9808i	0.296126	+	0.512904i	0.975246	−	0.221122i	$-0.0709720\pi$
$743$	8.07180	+	13.9808i	0.296126	+	0.512904i	−0.679121	+	0.734027i	$0.737639\pi$
$744$	−24.1244	−	41.7846i	−0.884442	−	1.53190i
$745$	−3.92820	+	6.80385i	−0.143918	+	0.249274i
$746$	17.3205			0.634149
$747$	13.3923	−	23.1962i	0.489999	−	0.848703i
$748$	−8.19615	+	14.1962i	−0.299681	+	0.519063i
$749$	35.3205			1.29058
$750$	−2.36603	+	4.09808i	−0.0863950	+	0.149641i
$751$	−18.1962	−	31.5167i	−0.663987	−	1.15006i	−0.979559	−	0.201158i	$-0.935530\pi$
$751$	−18.1962	−	31.5167i	−0.663987	−	1.15006i	0.315572	−	0.948902i	$-0.397804\pi$
$752$	15.0000	+	25.9808i	0.546994	+	0.947421i
$753$	−58.6410			−2.13700
$754$		0			0
$755$	1.80385			0.0656487
$756$	−4.00000	−	6.92820i	−0.145479	−	0.251976i
$757$	1.19615	+	2.07180i	0.0434749	+	0.0753007i	0.886944	−	0.461877i	$-0.152824\pi$
$757$	1.19615	+	2.07180i	0.0434749	+	0.0753007i	−0.843469	+	0.537178i	$0.819490\pi$
$758$	16.4378	−	28.4711i	0.597049	−	1.03412i
$759$	−16.3923			−0.595003
$760$	−5.36603	+	9.29423i	−0.194646	+	0.337137i
$761$	9.92820	−	17.1962i	0.359897	−	0.623360i	−0.628046	−	0.778176i	$-0.716145\pi$
$761$	9.92820	−	17.1962i	0.359897	−	0.623360i	0.987943	+	0.154816i	$0.0494785\pi$
$762$	−76.6410			−2.77641
$763$	−2.00000	+	3.46410i	−0.0724049	+	0.125409i
$764$	2.53590	+	4.39230i	0.0917456	+	0.158908i
$765$	−7.73205	−	13.3923i	−0.279553	−	0.484200i
$766$	−22.3923			−0.809067
$767$		0			0
$768$	51.9090			1.87310
$769$	−17.3923	−	30.1244i	−0.627183	−	1.08631i	−0.988114	−	0.153720i	$-0.950875\pi$
$769$	−17.3923	−	30.1244i	−0.627183	−	1.08631i	0.360932	−	0.932592i	$-0.382459\pi$
$770$	8.19615	+	14.1962i	0.295369	+	0.511594i
$771$	−27.1244	+	46.9808i	−0.976860	+	1.69197i
$772$	−10.0000			−0.359908
$773$	−3.46410	+	6.00000i	−0.124595	+	0.215805i	−0.921575	−	0.388201i	$-0.873097\pi$
$773$	−3.46410	+	6.00000i	−0.124595	+	0.215805i	0.796980	+	0.604006i	$0.206430\pi$
$774$	−0.758330	+	1.31347i	−0.0272576	+	0.0472116i
$775$	10.1962			0.366257
$776$	−1.73205	+	3.00000i	−0.0621770	+	0.107694i
$777$	10.9282	+	18.9282i	0.392047	+	0.679046i
$778$	5.19615	+	9.00000i	0.186291	+	0.322666i
$779$	−21.4641			−0.769031
$780$		0			0
$781$	−22.3923			−0.801260
$782$	−3.80385	−	6.58846i	−0.136025	−	0.235603i
$783$	5.07180	+	8.78461i	0.181251	+	0.313936i
$784$	−7.50000	+	12.9904i	−0.267857	+	0.463942i
$785$	10.0000			0.356915
$786$		0			0
$787$	−15.7846	+	27.3397i	−0.562661	+	0.974557i	0.434603	+	0.900622i	$0.356889\pi$
$787$	−15.7846	+	27.3397i	−0.562661	+	0.974557i	−0.997263	+	0.0739343i	$0.976444\pi$
$788$	−12.9282			−0.460548
$789$	−1.73205	+	3.00000i	−0.0616626	+	0.106803i
$790$	7.26795	+	12.5885i	0.258582	+	0.447877i
$791$	−8.53590	−	14.7846i	−0.303502	−	0.525680i
$792$	−36.5885			−1.30011
$793$		0			0
$794$	−49.8564			−1.76934
$795$	14.1962	+	24.5885i	0.503486	+	0.872063i
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	20.3205	−	35.1962i	0.719789	−	1.24671i	−0.241294	−	0.970452i	$-0.577572\pi$
$797$	20.3205	−	35.1962i	0.719789	−	1.24671i	0.961083	−	0.276260i	$-0.0890949\pi$
$798$	58.6410			2.07587
$799$	10.3923	−	18.0000i	0.367653	−	0.636794i
$800$	−2.59808	+	4.50000i	−0.0918559	+	0.159099i
$801$	−57.7128			−2.03918
$802$	−31.9808	+	55.3923i	−1.12928	+	1.95597i
$803$	−9.46410	−	16.3923i	−0.333981	−	0.578472i
$804$	−8.73205	−	15.1244i	−0.307956	−	0.533395i
$805$	−2.53590			−0.0893787
$806$		0			0
$807$	−54.2487			−1.90965
$808$	0.803848	+	1.39230i	0.0282793	+	0.0489811i
$809$	1.26795	+	2.19615i	0.0445787	+	0.0772126i	0.887454	−	0.460897i	$-0.152472\pi$
$809$	1.26795	+	2.19615i	0.0445787	+	0.0772126i	−0.842875	+	0.538109i	$0.819139\pi$
$810$	2.13397	−	3.69615i	0.0749802	−	0.129870i
$811$	17.8038			0.625178			0.312589	−	0.949889i	$-0.398804\pi$
$811$	17.8038			0.625178			0.312589	+	0.949889i	$0.398804\pi$
$812$	2.53590	−	4.39230i	0.0889926	−	0.154140i
$813$	−42.3205	+	73.3013i	−1.48425	+	2.57079i
$814$	−32.7846			−1.14910
$815$	−7.19615	+	12.4641i	−0.252070	+	0.436598i
$816$	−23.6603	−	40.9808i	−0.828275	−	1.43461i
$817$	−0.607695	−	1.05256i	−0.0212606	−	0.0368244i
$818$	30.4974			1.06632
$819$		0			0
$820$	−3.46410			−0.120972
$821$	−14.3205	−	24.8038i	−0.499789	−	0.865660i	0.500211	−	0.865904i	$-0.333256\pi$
$821$	−14.3205	−	24.8038i	−0.499789	−	0.865660i	−1.00000		0.000243419i	$0.999923\pi$
$822$	2.19615	+	3.80385i	0.0765996	+	0.132674i
$823$	7.70577	−	13.3468i	0.268606	−	0.465240i	−0.699896	−	0.714245i	$-0.746770\pi$
$823$	7.70577	−	13.3468i	0.268606	−	0.465240i	0.968502	+	0.249005i	$0.0801036\pi$
$824$	−0.339746			−0.0118356
$825$	6.46410	−	11.1962i	0.225051	−	0.389800i
$826$	15.8038	−	27.3731i	0.549886	−	0.952431i
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$	−2.83013	+	4.90192i	−0.0983537	+	0.170354i
$829$	−0.196152	−	0.339746i	−0.00681266	−	0.0117999i	0.862599	−	0.505888i	$-0.168835\pi$
$829$	−0.196152	−	0.339746i	−0.00681266	−	0.0117999i	−0.869412	+	0.494088i	$0.835502\pi$
$830$	5.19615	+	9.00000i	0.180361	+	0.312395i
$831$	−72.1051			−2.50130
$832$		0			0
$833$	10.3923			0.360072
$834$	29.3205	+	50.7846i	1.01529	+	1.75853i
$835$	−0.464102	−	0.803848i	−0.0160609	−	0.0278183i
$836$	−14.6603	+	25.3923i	−0.507035	+	0.878211i
$837$	40.7846			1.40972
$838$	−2.19615	+	3.80385i	−0.0758648	+	0.131402i
$839$	−0.169873	+	0.294229i	−0.00586467	+	0.0101579i	−0.868943	−	0.494912i	$-0.835200\pi$
$839$	−0.169873	+	0.294229i	−0.00586467	+	0.0101579i	0.863078	+	0.505070i	$0.168533\pi$
$840$	−9.46410			−0.326543
$841$	11.2846	−	19.5455i	0.389124	−	0.673983i
$842$	−26.6603	−	46.1769i	−0.918773	−	1.59136i
$843$	−30.5885	−	52.9808i	−1.05352	−	1.82475i
$844$	8.00000			0.275371
$845$		0			0
$846$	−46.3923			−1.59500
$847$	−11.3923	−	19.7321i	−0.391444	−	0.678001i
$848$	25.9808	+	45.0000i	0.892183	+	1.54531i
$849$	−44.5167	+	77.1051i	−1.52781	+	2.64624i
$850$	6.00000			0.205798
$851$	2.53590	−	4.39230i	0.0869295	−	0.150566i
$852$	−6.46410	+	11.1962i	−0.221456	+	0.383574i
$853$	8.00000			0.273915			0.136957	−	0.990577i	$-0.456268\pi$
$853$	8.00000			0.273915			0.136957	+	0.990577i	$0.456268\pi$
$854$	−14.5359	+	25.1769i	−0.497408	+	0.861536i
$855$	−13.8301	−	23.9545i	−0.472980	−	0.819226i
$856$	−15.2942	−	26.4904i	−0.522746	−	0.905423i
$857$	−35.5692			−1.21502			−0.607511	−	0.794311i	$-0.707832\pi$
$857$	−35.5692			−1.21502			−0.607511	+	0.794311i	$0.707832\pi$
$858$		0			0
$859$	−17.1769			−0.586069			−0.293034	−	0.956102i	$-0.594665\pi$
$859$	−17.1769			−0.586069			−0.293034	+	0.956102i	$0.594665\pi$
$860$	−0.0980762	−	0.169873i	−0.00334437	−	0.00579262i
$861$	−9.46410	−	16.3923i	−0.322536	−	0.558648i
$862$	−22.0981	+	38.2750i	−0.752663	+	1.30365i
$863$	−38.7846			−1.32024			−0.660122	−	0.751159i	$-0.729495\pi$
$863$	−38.7846			−1.32024			−0.660122	+	0.751159i	$0.729495\pi$
$864$	−10.3923	+	18.0000i	−0.353553	+	0.612372i
$865$	4.26795	−	7.39230i	0.145115	−	0.251346i
$866$	−60.2487			−2.04733
$867$	6.83013	−	11.8301i	0.231963	−	0.401772i
$868$	−10.1962	−	17.6603i	−0.346080	−	0.599428i
$869$	−19.8564	−	34.3923i	−0.673582	−	1.16668i
$870$	−12.0000			−0.406838
$871$		0			0
$872$	3.46410			0.117309
$873$	−4.46410	−	7.73205i	−0.151087	−	0.261690i
$874$	−6.80385	−	11.7846i	−0.230144	−	0.398620i
$875$	1.00000	−	1.73205i	0.0338062	−	0.0585540i
$876$	−10.9282			−0.369230
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	−0.882415	−	0.470471i	$-0.844084\pi$
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	0.848648	+	0.528958i	$0.177417\pi$
$878$	27.7128	−	48.0000i	0.935262	−	1.61992i
$879$	−13.8564			−0.467365
$880$	11.8301	−	20.4904i	0.398794	−	0.690731i
$881$	23.6603	+	40.9808i	0.797134	+	1.38068i	0.921475	+	0.388437i	$0.126985\pi$
$881$	23.6603	+	40.9808i	0.797134	+	1.38068i	−0.124341	+	0.992240i	$0.539682\pi$
$882$	−11.5981	−	20.0885i	−0.390528	−	0.676414i
$883$	23.8038			0.801063			0.400532	−	0.916283i	$-0.368825\pi$
$883$	23.8038			0.801063			0.400532	+	0.916283i	$0.368825\pi$
$884$		0			0
$885$	−24.9282			−0.837952
$886$	−14.7058	−	25.4711i	−0.494050	−	0.855720i
$887$	23.9545	+	41.4904i	0.804313	+	1.39311i	0.916754	+	0.399452i	$0.130800\pi$
$887$	23.9545	+	41.4904i	0.804313	+	1.39311i	−0.112441	+	0.993658i	$0.535867\pi$
$888$	9.46410	−	16.3923i	0.317594	−	0.550090i
$889$	32.3923			1.08640
$890$	11.1962	−	19.3923i	0.375296	−	0.650032i
$891$	−5.83013	+	10.0981i	−0.195317	+	0.338298i
$892$	2.00000			0.0669650
$893$	18.5885	−	32.1962i	0.622039	−	1.07740i
$894$	−18.5885	−	32.1962i	−0.621691	−	1.07680i
$895$	−9.46410	−	16.3923i	−0.316350	−	0.547934i
$896$	−24.2487			−0.810093
$897$		0			0
$898$	−35.5692			−1.18696
$899$	12.9282	+	22.3923i	0.431180	+	0.746825i
$900$	−2.23205	−	3.86603i	−0.0744017	−	0.128868i
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$	28.3923			0.945360
$903$	0.535898	−	0.928203i	0.0178336	−	0.0308887i
$904$	−7.39230	+	12.8038i	−0.245864	+	0.425850i
$905$	−0.392305			−0.0130407
$906$	−4.26795	+	7.39230i	−0.141793	+	0.245593i
$907$	26.8827	+	46.5622i	0.892625	+	1.54607i	0.836717	+	0.547636i	$0.184472\pi$
$907$	26.8827	+	46.5622i	0.892625	+	1.54607i	0.0559081	+	0.998436i	$0.482195\pi$
$908$	1.73205	+	3.00000i	0.0574801	+	0.0995585i
$909$	−4.14359			−0.137434
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	−42.3205	−	73.3013i	−1.40137	−	2.42725i
$913$	−14.1962	−	24.5885i	−0.469824	−	0.813759i
$914$	9.33975	−	16.1769i	0.308931	−	0.535085i
$915$	22.9282			0.757983
$916$	−3.19615	+	5.53590i	−0.105604	+	0.182911i
$917$		0			0
$918$	24.0000			0.792118
$919$	−4.58846	+	7.94744i	−0.151359	+	0.262162i	−0.931727	−	0.363158i	$-0.881698\pi$
$919$	−4.58846	+	7.94744i	−0.151359	+	0.262162i	0.780368	+	0.625320i	$0.215032\pi$
$920$	1.09808	+	1.90192i	0.0362025	+	0.0627046i
$921$	25.6603	+	44.4449i	0.845534	+	1.46451i
$922$	6.00000			0.197599
$923$		0			0
$924$	−25.8564			−0.850613
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$	−2.07180	−	3.58846i	−0.0680835	−	0.117924i
$927$	0.437822	−	0.758330i	0.0143800	−	0.0249068i
$928$	−13.1769			−0.432553
$929$	−22.2679	+	38.5692i	−0.730588	+	1.26542i	0.226045	+	0.974117i	$0.427420\pi$
$929$	−22.2679	+	38.5692i	−0.730588	+	1.26542i	−0.956632	+	0.291298i	$0.905913\pi$
$930$	−24.1244	+	41.7846i	−0.791069	+	1.37017i
$931$	18.5885			0.609212
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$	22.3923	+	38.7846i	0.733091	+	1.26975i
$934$	24.0788	+	41.7058i	0.787884	+	1.36465i
$935$	−16.3923			−0.536086
$936$		0			0
$937$	34.7846			1.13636			0.568182	−	0.822903i	$-0.307647\pi$
$937$	34.7846			1.13636			0.568182	+	0.822903i	$0.307647\pi$
$938$	11.0718	+	19.1769i	0.361507	+	0.626148i
$939$	19.6603	+	34.0526i	0.641588	+	1.11126i
$940$	3.00000	−	5.19615i	0.0978492	−	0.169480i
$941$	31.1769			1.01634			0.508169	−	0.861257i	$-0.330322\pi$
$941$	31.1769			1.01634			0.508169	+	0.861257i	$0.330322\pi$
$942$	−23.6603	+	40.9808i	−0.770893	+	1.33523i
$943$	−2.19615	+	3.80385i	−0.0715166	+	0.123870i
$944$	−45.6218			−1.48486
$945$	4.00000	−	6.92820i	0.130120	−	0.225374i
$946$	0.803848	+	1.39230i	0.0261353	+	0.0452677i
$947$	−20.3205	−	35.1962i	−0.660328	−	1.14372i	−0.980529	−	0.196372i	$-0.937084\pi$
$947$	−20.3205	−	35.1962i	−0.660328	−	1.14372i	0.320202	−	0.947349i	$-0.396249\pi$
$948$	−22.9282			−0.744673
$949$		0			0
$950$	10.7321			0.348194
$951$	−32.7846	−	56.7846i	−1.06311	−	1.84137i
$952$	6.00000	+	10.3923i	0.194461	+	0.336817i
$953$	−0.464102	+	0.803848i	−0.0150337	+	0.0260392i	−0.873444	−	0.486924i	$-0.838119\pi$
$953$	−0.464102	+	0.803848i	−0.0150337	+	0.0260392i	0.858411	+	0.512963i	$0.171452\pi$
$954$	−80.3538			−2.60155
$955$	−2.53590	+	4.39230i	−0.0820597	+	0.142132i
$956$	7.09808	−	12.2942i	0.229568	−	0.397624i
$957$	32.7846			1.05978
$958$	30.8827	−	53.4904i	0.997774	−	1.72820i
$959$	−0.928203	−	1.60770i	−0.0299732	−	0.0519152i
$960$	1.36603	+	2.36603i	0.0440883	+	0.0763631i
$961$	72.9615			2.35360
$962$		0			0
$963$	78.8372			2.54049
$964$	1.19615	+	2.07180i	0.0385255	+	0.0667281i
$965$	−5.00000	−	8.66025i	−0.160956	−	0.278783i
$966$	6.00000	−	10.3923i	0.193047	−	0.334367i
$967$	−50.3923			−1.62051			−0.810254	−	0.586079i	$-0.800671\pi$
$967$	−50.3923			−1.62051			−0.810254	+	0.586079i	$0.800671\pi$
$968$	−9.86603	+	17.0885i	−0.317106	+	0.549244i
$969$	−29.3205	+	50.7846i	−0.941910	+	1.63144i
$970$	3.46410			0.111226
$971$	−9.46410	+	16.3923i	−0.303717	+	0.526054i	−0.976975	−	0.213354i	$-0.931561\pi$
$971$	−9.46410	+	16.3923i	−0.303717	+	0.526054i	0.673257	+	0.739408i	$0.264895\pi$
$972$	9.36603	+	16.2224i	0.300415	+	0.520335i
$973$	−12.3923	−	21.4641i	−0.397279	−	0.688108i
$974$	45.7128			1.46473
$975$		0			0
$976$	41.9615			1.34316
$977$	7.85641	+	13.6077i	0.251349	+	0.435349i	0.963897	−	0.266274i	$-0.0857926\pi$
$977$	7.85641	+	13.6077i	0.251349	+	0.435349i	−0.712549	+	0.701623i	$0.752459\pi$
$978$	−34.0526	−	58.9808i	−1.08888	−	1.88600i
$979$	−30.5885	+	52.9808i	−0.977611	+	1.69327i
$980$	3.00000			0.0958315
$981$	−4.46410	+	7.73205i	−0.142528	+	0.246865i
$982$	−2.19615	+	3.80385i	−0.0700820	+	0.121386i
$983$	−34.3923			−1.09694			−0.548472	−	0.836169i	$-0.684790\pi$
$983$	−34.3923			−1.09694			−0.548472	+	0.836169i	$0.684790\pi$
$984$	−8.19615	+	14.1962i	−0.261284	+	0.452557i
$985$	−6.46410	−	11.1962i	−0.205963	−	0.356739i
$986$	7.60770	+	13.1769i	0.242278	+	0.419638i
$987$	32.7846			1.04355
$988$		0			0
$989$	−0.248711			−0.00790856
$990$	18.2942	+	31.6865i	0.581429	+	1.00706i
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$	−26.4904	+	45.8827i	−0.841070	+	1.45678i
$993$	7.07180			0.224417
$994$	8.19615	−	14.1962i	0.259966	−	0.450275i
$995$	10.0000	−	17.3205i	0.317021	−	0.549097i
$996$	−16.3923			−0.519410
$997$	−16.8038	+	29.1051i	−0.532183	+	0.921768i	0.467111	+	0.884199i	$0.345295\pi$
$997$	−16.8038	+	29.1051i	−0.532183	+	0.921768i	−0.999294	+	0.0375696i	$0.988038\pi$
$998$	−33.7583	−	58.4711i	−1.06860	−	1.85087i
$999$	8.00000	+	13.8564i	0.253109	+	0.438397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.e.146.2		4
13.2	odd	12		845.2.c.e.506.4		4
13.3	even	3		65.2.a.c.1.1	✓	2
13.4	even	6		845.2.e.f.191.1		4
13.5	odd	4		845.2.m.c.361.1		4
13.6	odd	12		845.2.m.a.316.1		4
13.7	odd	12		845.2.m.c.316.1		4
13.8	odd	4		845.2.m.a.361.1		4
13.9	even	3	inner	845.2.e.e.191.2		4
13.10	even	6		845.2.a.d.1.2		2
13.11	odd	12		845.2.c.e.506.2		4
13.12	even	2		845.2.e.f.146.1		4
39.23	odd	6		7605.2.a.be.1.1		2
39.29	odd	6		585.2.a.k.1.2		2
52.3	odd	6		1040.2.a.h.1.1		2
65.3	odd	12		325.2.b.e.274.4		4
65.29	even	6		325.2.a.g.1.2		2
65.42	odd	12		325.2.b.e.274.1		4
65.49	even	6		4225.2.a.w.1.1		2
91.55	odd	6		3185.2.a.k.1.1		2
104.3	odd	6		4160.2.a.bj.1.2		2
104.29	even	6		4160.2.a.y.1.1		2
143.120	odd	6		7865.2.a.h.1.2		2
156.107	even	6		9360.2.a.cm.1.1		2
195.29	odd	6		2925.2.a.z.1.1		2
195.68	even	12		2925.2.c.v.2224.1		4
195.107	even	12		2925.2.c.v.2224.4		4
260.159	odd	6		5200.2.a.ca.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.a.c.1.1	✓	2	13.3	even	3
325.2.a.g.1.2		2	65.29	even	6
325.2.b.e.274.1		4	65.42	odd	12
325.2.b.e.274.4		4	65.3	odd	12
585.2.a.k.1.2		2	39.29	odd	6
845.2.a.d.1.2		2	13.10	even	6
845.2.c.e.506.2		4	13.11	odd	12
845.2.c.e.506.4		4	13.2	odd	12
845.2.e.e.146.2		4	1.1	even	1	trivial
845.2.e.e.191.2		4	13.9	even	3	inner
845.2.e.f.146.1		4	13.12	even	2
845.2.e.f.191.1		4	13.4	even	6
845.2.m.a.316.1		4	13.6	odd	12
845.2.m.a.361.1		4	13.8	odd	4
845.2.m.c.316.1		4	13.7	odd	12
845.2.m.c.361.1		4	13.5	odd	4
1040.2.a.h.1.1		2	52.3	odd	6
2925.2.a.z.1.1		2	195.29	odd	6
2925.2.c.v.2224.1		4	195.68	even	12
2925.2.c.v.2224.4		4	195.107	even	12
3185.2.a.k.1.1		2	91.55	odd	6
4160.2.a.y.1.1		2	104.29	even	6
4160.2.a.bj.1.2		2	104.3	odd	6
4225.2.a.w.1.1		2	65.49	even	6
5200.2.a.ca.1.2		2	260.159	odd	6
7605.2.a.be.1.1		2	39.23	odd	6
7865.2.a.h.1.2		2	143.120	odd	6
9360.2.a.cm.1.1		2	156.107	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.36603 - 4.09808i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 1.50000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(2.36603 - 4.09808i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +(-0.866025 - 1.50000i) q^{10} +(2.36603 + 4.09808i) q^{11} +2.73205 q^{12} -3.46410 q^{14} +(1.36603 + 2.36603i) q^{15} +(2.50000 + 4.33013i) q^{16} +(1.73205 - 3.00000i) q^{17} -7.73205 q^{18} +(3.09808 - 5.36603i) q^{19} +(0.500000 - 0.866025i) q^{20} +5.46410 q^{21} +(-4.09808 + 7.09808i) q^{22} +(-0.633975 - 1.09808i) q^{23} +(-2.36603 - 4.09808i) q^{24} +1.00000 q^{25} +4.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(1.26795 + 2.19615i) q^{29} +(-2.36603 + 4.09808i) q^{30} +10.1962 q^{31} +(-2.59808 + 4.50000i) q^{32} +(6.46410 - 11.1962i) q^{33} +6.00000 q^{34} +(1.00000 - 1.73205i) q^{35} +(-2.23205 - 3.86603i) q^{36} +(2.00000 + 3.46410i) q^{37} +10.7321 q^{38} -1.73205 q^{40} +(-1.73205 - 3.00000i) q^{41} +(4.73205 + 8.19615i) q^{42} +(0.0980762 - 0.169873i) q^{43} -4.73205 q^{44} +(2.23205 - 3.86603i) q^{45} +(1.09808 - 1.90192i) q^{46} +6.00000 q^{47} +(6.83013 - 11.8301i) q^{48} +(1.50000 + 2.59808i) q^{49} +(0.866025 + 1.50000i) q^{50} -9.46410 q^{51} +10.3923 q^{53} +(3.46410 + 6.00000i) q^{54} +(-2.36603 - 4.09808i) q^{55} +(-1.73205 + 3.00000i) q^{56} -16.9282 q^{57} +(-2.19615 + 3.80385i) q^{58} +(-4.56218 + 7.90192i) q^{59} -2.73205 q^{60} +(4.19615 - 7.26795i) q^{61} +(8.83013 + 15.2942i) q^{62} +(-4.46410 - 7.73205i) q^{63} +1.00000 q^{64} +22.3923 q^{66} +(-3.19615 - 5.53590i) q^{67} +(1.73205 + 3.00000i) q^{68} +(-1.73205 + 3.00000i) q^{69} +3.46410 q^{70} +(-2.36603 + 4.09808i) q^{71} +(-3.86603 + 6.69615i) q^{72} -4.00000 q^{73} +(-3.46410 + 6.00000i) q^{74} +(-1.36603 - 2.36603i) q^{75} +(3.09808 + 5.36603i) q^{76} -9.46410 q^{77} -8.39230 q^{79} +(-2.50000 - 4.33013i) q^{80} +(1.23205 + 2.13397i) q^{81} +(3.00000 - 5.19615i) q^{82} -6.00000 q^{83} +(-2.73205 + 4.73205i) q^{84} +(-1.73205 + 3.00000i) q^{85} +0.339746 q^{86} +(3.46410 - 6.00000i) q^{87} +(4.09808 + 7.09808i) q^{88} +(6.46410 + 11.1962i) q^{89} +7.73205 q^{90} +1.26795 q^{92} +(-13.9282 - 24.1244i) q^{93} +(5.19615 + 9.00000i) q^{94} +(-3.09808 + 5.36603i) q^{95} +14.1962 q^{96} +(-1.00000 + 1.73205i) q^{97} +(-2.59808 + 4.50000i) q^{98} -21.1244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 - 4 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} - 4 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{12} + 2 q^{15} + 10 q^{16} - 24 q^{18} + 2 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 6 q^{23} - 6 q^{24} + 4 q^{25} + 16 q^{27} - 4 q^{28} + 12 q^{29} - 6 q^{30} + 20 q^{31} + 12 q^{33} + 24 q^{34} + 4 q^{35} - 2 q^{36} + 8 q^{37} + 36 q^{38} + 12 q^{42} - 10 q^{43} - 12 q^{44} + 2 q^{45} - 6 q^{46} + 24 q^{47} + 10 q^{48} + 6 q^{49} - 24 q^{51} - 6 q^{55} - 40 q^{57} + 12 q^{58} + 6 q^{59} - 4 q^{60} - 4 q^{61} + 18 q^{62} - 4 q^{63} + 4 q^{64} + 48 q^{66} + 8 q^{67} - 6 q^{71} - 12 q^{72} - 16 q^{73} - 2 q^{75} + 2 q^{76} - 24 q^{77} + 8 q^{79} - 10 q^{80} - 2 q^{81} + 12 q^{82} - 24 q^{83} - 4 q^{84} + 36 q^{86} + 6 q^{88} + 12 q^{89} + 24 q^{90} + 12 q^{92} - 28 q^{93} - 2 q^{95} + 36 q^{96} - 4 q^{97} - 36 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 - 4 * q^7 - 2 * q^9 + 6 * q^11 + 4 * q^12 + 2 * q^15 + 10 * q^16 - 24 * q^18 + 2 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 6 * q^23 - 6 * q^24 + 4 * q^25 + 16 * q^27 - 4 * q^28 + 12 * q^29 - 6 * q^30 + 20 * q^31 + 12 * q^33 + 24 * q^34 + 4 * q^35 - 2 * q^36 + 8 * q^37 + 36 * q^38 + 12 * q^42 - 10 * q^43 - 12 * q^44 + 2 * q^45 - 6 * q^46 + 24 * q^47 + 10 * q^48 + 6 * q^49 - 24 * q^51 - 6 * q^55 - 40 * q^57 + 12 * q^58 + 6 * q^59 - 4 * q^60 - 4 * q^61 + 18 * q^62 - 4 * q^63 + 4 * q^64 + 48 * q^66 + 8 * q^67 - 6 * q^71 - 12 * q^72 - 16 * q^73 - 2 * q^75 + 2 * q^76 - 24 * q^77 + 8 * q^79 - 10 * q^80 - 2 * q^81 + 12 * q^82 - 24 * q^83 - 4 * q^84 + 36 * q^86 + 6 * q^88 + 12 * q^89 + 24 * q^90 + 12 * q^92 - 28 * q^93 - 2 * q^95 + 36 * q^96 - 4 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more