LMFDB - Embedded newform 845.2.k.a.577.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(268,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("845.268");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$845 = 5 \cdot 13^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	845.k (of order $4$ , degree $2$ , 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:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} + 1$ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	845.577
Dual form			845.2.k.a.268.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.00000 - 1.00000i) q^{3} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +(-1.00000 + 1.00000i) q^{6} +2.00000i q^{7} +3.00000 q^{8} +1.00000i q^{9} +(-1.00000 + 2.00000i) q^{10} +(1.00000 + 1.00000i) q^{11} +(-1.00000 + 1.00000i) q^{12} -2.00000i q^{14} +(-1.00000 - 3.00000i) q^{15} -1.00000 q^{16} +(1.00000 - 1.00000i) q^{17} -1.00000i q^{18} +(5.00000 + 5.00000i) q^{19} +(-1.00000 + 2.00000i) q^{20} +(2.00000 + 2.00000i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(3.00000 + 3.00000i) q^{23} +(3.00000 - 3.00000i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} -2.00000i q^{28} +(1.00000 + 3.00000i) q^{30} +(-5.00000 + 5.00000i) q^{31} -5.00000 q^{32} +2.00000 q^{33} +(-1.00000 + 1.00000i) q^{34} +(4.00000 + 2.00000i) q^{35} -1.00000i q^{36} +(-5.00000 - 5.00000i) q^{38} +(3.00000 - 6.00000i) q^{40} +(7.00000 - 7.00000i) q^{41} +(-2.00000 - 2.00000i) q^{42} +(-1.00000 - 1.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(2.00000 + 1.00000i) q^{45} +(-3.00000 - 3.00000i) q^{46} -6.00000i q^{47} +(-1.00000 + 1.00000i) q^{48} +3.00000 q^{49} +(3.00000 + 4.00000i) q^{50} -2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(-4.00000 - 4.00000i) q^{54} +(3.00000 - 1.00000i) q^{55} +6.00000i q^{56} +10.0000 q^{57} +(7.00000 - 7.00000i) q^{59} +(1.00000 + 3.00000i) q^{60} -14.0000 q^{61} +(5.00000 - 5.00000i) q^{62} -2.00000 q^{63} +7.00000 q^{64} -2.00000 q^{66} +4.00000 q^{67} +(-1.00000 + 1.00000i) q^{68} +6.00000 q^{69} +(-4.00000 - 2.00000i) q^{70} +(-1.00000 + 1.00000i) q^{71} +3.00000i q^{72} +10.0000 q^{73} +(-7.00000 - 1.00000i) q^{75} +(-5.00000 - 5.00000i) q^{76} +(-2.00000 + 2.00000i) q^{77} -2.00000i q^{79} +(-1.00000 + 2.00000i) q^{80} +5.00000 q^{81} +(-7.00000 + 7.00000i) q^{82} +6.00000i q^{83} +(-2.00000 - 2.00000i) q^{84} +(-1.00000 - 3.00000i) q^{85} +(1.00000 + 1.00000i) q^{86} +(3.00000 + 3.00000i) q^{88} +(-5.00000 + 5.00000i) q^{89} +(-2.00000 - 1.00000i) q^{90} +(-3.00000 - 3.00000i) q^{92} +10.0000i q^{93} +6.00000i q^{94} +(15.0000 - 5.00000i) q^{95} +(-5.00000 + 5.00000i) q^{96} -2.00000 q^{97} -3.00000 q^{98} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} + 6 q^{8} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{15} - 2 q^{16} + 2 q^{17} + 10 q^{19} - 2 q^{20} + 4 q^{21} - 2 q^{22} + 6 q^{23} + 6 q^{24} - 6 q^{25}+ \cdots - 2 q^{99}+O(q^{100})$ 2 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 + 6 * q^8 - 2 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^15 - 2 * q^16 + 2 * q^17 + 10 * q^19 - 2 * q^20 + 4 * q^21 - 2 * q^22 + 6 * q^23 + 6 * q^24 - 6 * q^25 + 8 * q^27 + 2 * q^30 - 10 * q^31 - 10 * q^32 + 4 * q^33 - 2 * q^34 + 8 * q^35 - 10 * q^38 + 6 * q^40 + 14 * q^41 - 4 * q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 - 6 * q^46 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 10 * q^53 - 8 * q^54 + 6 * q^55 + 20 * q^57 + 14 * q^59 + 2 * q^60 - 28 * q^61 + 10 * q^62 - 4 * q^63 + 14 * q^64 - 4 * q^66 + 8 * q^67 - 2 * q^68 + 12 * q^69 - 8 * q^70 - 2 * q^71 + 20 * q^73 - 14 * q^75 - 10 * q^76 - 4 * q^77 - 2 * q^80 + 10 * q^81 - 14 * q^82 - 4 * q^84 - 2 * q^85 + 2 * q^86 + 6 * q^88 - 10 * q^89 - 4 * q^90 - 6 * q^92 + 30 * q^95 - 10 * q^96 - 4 * q^97 - 6 * q^98 - 2 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.00000			−0.707107			−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000			−0.707107			−0.353553	+	0.935414i	$0.615027\pi$
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	−0.356822	−	0.934172i	$-0.616140\pi$
$3$	1.00000	−	1.00000i	0.577350	−	0.577350i	0.934172	+	0.356822i	$0.116140\pi$
$4$	−1.00000			−0.500000
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$	−1.00000	+	1.00000i	−0.408248	+	0.408248i
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$	3.00000			1.06066
$9$			1.00000i			0.333333i
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	0.841605	−	0.540094i	$-0.181611\pi$
$11$	1.00000	+	1.00000i	0.301511	+	0.301511i	−0.540094	+	0.841605i	$0.681611\pi$
$12$	−1.00000	+	1.00000i	−0.288675	+	0.288675i
$13$		0			0
$13$		0			0
$14$		−	2.00000i		−	0.534522i
$15$	−1.00000	−	3.00000i	−0.258199	−	0.774597i
$16$	−1.00000			−0.250000
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	0.817898	+	0.575363i	$0.195139\pi$
$18$		−	1.00000i		−	0.235702i
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.987124	+	0.159954i	$0.0511347\pi$
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.159954	+	0.987124i	$0.448865\pi$
$20$	−1.00000	+	2.00000i	−0.223607	+	0.447214i
$21$	2.00000	+	2.00000i	0.436436	+	0.436436i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	3.00000	+	3.00000i	0.625543	+	0.625543i	0.946943	−	0.321400i	$-0.104153\pi$
$23$	3.00000	+	3.00000i	0.625543	+	0.625543i	−0.321400	+	0.946943i	$0.604153\pi$
$24$	3.00000	−	3.00000i	0.612372	−	0.612372i
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		0			0
$27$	4.00000	+	4.00000i	0.769800	+	0.769800i
$28$		−	2.00000i		−	0.377964i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	1.00000	+	3.00000i	0.182574	+	0.547723i
$31$	−5.00000	+	5.00000i	−0.898027	+	0.898027i	−0.995261	−	0.0972349i	$-0.969000\pi$
$31$	−5.00000	+	5.00000i	−0.898027	+	0.898027i	0.0972349	+	0.995261i	$0.469000\pi$
$32$	−5.00000			−0.883883
$33$	2.00000			0.348155
$34$	−1.00000	+	1.00000i	−0.171499	+	0.171499i
$35$	4.00000	+	2.00000i	0.676123	+	0.338062i
$36$		−	1.00000i		−	0.166667i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−5.00000	−	5.00000i	−0.811107	−	0.811107i
$39$		0			0
$40$	3.00000	−	6.00000i	0.474342	−	0.948683i
$41$	7.00000	−	7.00000i	1.09322	−	1.09322i	0.0980332	−	0.995183i	$-0.468745\pi$
$41$	7.00000	−	7.00000i	1.09322	−	1.09322i	0.995183	−	0.0980332i	$-0.0312551\pi$
$42$	−2.00000	−	2.00000i	−0.308607	−	0.308607i
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	0.626734	−	0.779233i	$-0.284391\pi$
$43$	−1.00000	−	1.00000i	−0.152499	−	0.152499i	−0.779233	+	0.626734i	$0.784391\pi$
$44$	−1.00000	−	1.00000i	−0.150756	−	0.150756i
$45$	2.00000	+	1.00000i	0.298142	+	0.149071i
$46$	−3.00000	−	3.00000i	−0.442326	−	0.442326i
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$	−1.00000	+	1.00000i	−0.144338	+	0.144338i
$49$	3.00000			0.428571
$50$	3.00000	+	4.00000i	0.424264	+	0.565685i
$51$		−	2.00000i		−	0.280056i
$52$		0			0
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	0.961524	+	0.274721i	$0.0885855\pi$
$54$	−4.00000	−	4.00000i	−0.544331	−	0.544331i
$55$	3.00000	−	1.00000i	0.404520	−	0.134840i
$56$			6.00000i			0.801784i
$57$	10.0000			1.32453
$58$		0			0
$59$	7.00000	−	7.00000i	0.911322	−	0.911322i	−0.0850540	−	0.996376i	$-0.527106\pi$
$59$	7.00000	−	7.00000i	0.911322	−	0.911322i	0.996376	+	0.0850540i	$0.0271063\pi$
$60$	1.00000	+	3.00000i	0.129099	+	0.387298i
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$	5.00000	−	5.00000i	0.635001	−	0.635001i
$63$	−2.00000			−0.251976
$64$	7.00000			0.875000
$65$		0			0
$66$	−2.00000			−0.246183
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	−1.00000	+	1.00000i	−0.121268	+	0.121268i
$69$	6.00000			0.722315
$70$	−4.00000	−	2.00000i	−0.478091	−	0.239046i
$71$	−1.00000	+	1.00000i	−0.118678	+	0.118678i	−0.763952	−	0.645273i	$-0.776743\pi$
$71$	−1.00000	+	1.00000i	−0.118678	+	0.118678i	0.645273	+	0.763952i	$0.276743\pi$
$72$			3.00000i			0.353553i
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$		0			0
$75$	−7.00000	−	1.00000i	−0.808290	−	0.115470i
$76$	−5.00000	−	5.00000i	−0.573539	−	0.573539i
$77$	−2.00000	+	2.00000i	−0.227921	+	0.227921i
$78$		0			0
$79$		−	2.00000i		−	0.225018i	−0.993651	−	0.112509i	$-0.964111\pi$
$79$		−	2.00000i		−	0.225018i	0.993651	−	0.112509i	$-0.0358886\pi$
$80$	−1.00000	+	2.00000i	−0.111803	+	0.223607i
$81$	5.00000			0.555556
$82$	−7.00000	+	7.00000i	−0.773021	+	0.773021i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	−2.00000	−	2.00000i	−0.218218	−	0.218218i
$85$	−1.00000	−	3.00000i	−0.108465	−	0.325396i
$86$	1.00000	+	1.00000i	0.107833	+	0.107833i
$87$		0			0
$88$	3.00000	+	3.00000i	0.319801	+	0.319801i
$89$	−5.00000	+	5.00000i	−0.529999	+	0.529999i	−0.920572	−	0.390573i	$-0.872277\pi$
$89$	−5.00000	+	5.00000i	−0.529999	+	0.529999i	0.390573	+	0.920572i	$0.372277\pi$
$90$	−2.00000	−	1.00000i	−0.210819	−	0.105409i
$91$		0			0
$92$	−3.00000	−	3.00000i	−0.312772	−	0.312772i
$93$			10.0000i			1.03695i
$94$			6.00000i			0.618853i
$95$	15.0000	−	5.00000i	1.53897	−	0.512989i
$96$	−5.00000	+	5.00000i	−0.510310	+	0.510310i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	−3.00000			−0.303046
$99$	−1.00000	+	1.00000i	−0.100504	+	0.100504i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$			12.0000i			1.19404i	0.802225	+	0.597022i	$0.203650\pi$
$101$			12.0000i			1.19404i	−0.802225	+	0.597022i	$0.796350\pi$
$102$			2.00000i			0.198030i
$103$	7.00000	+	7.00000i	0.689730	+	0.689730i	0.962172	−	0.272442i	$-0.0878312\pi$
$103$	7.00000	+	7.00000i	0.689730	+	0.689730i	−0.272442	+	0.962172i	$0.587831\pi$
$104$		0			0
$105$	6.00000	−	2.00000i	0.585540	−	0.195180i
$106$	−5.00000	+	5.00000i	−0.485643	+	0.485643i
$107$	7.00000	+	7.00000i	0.676716	+	0.676716i	0.959256	−	0.282540i	$-0.0911770\pi$
$107$	7.00000	+	7.00000i	0.676716	+	0.676716i	−0.282540	+	0.959256i	$0.591177\pi$
$108$	−4.00000	−	4.00000i	−0.384900	−	0.384900i
$109$	−9.00000	−	9.00000i	−0.862044	−	0.862044i	0.129532	−	0.991575i	$-0.458653\pi$
$109$	−9.00000	−	9.00000i	−0.862044	−	0.862044i	−0.991575	+	0.129532i	$0.958653\pi$
$110$	−3.00000	+	1.00000i	−0.286039	+	0.0953463i
$111$		0			0
$112$		−	2.00000i		−	0.188982i
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	−0.431671	−	0.902031i	$-0.642076\pi$
$113$	5.00000	−	5.00000i	0.470360	−	0.470360i	0.902031	+	0.431671i	$0.142076\pi$
$114$	−10.0000			−0.936586
$115$	9.00000	−	3.00000i	0.839254	−	0.279751i
$116$		0			0
$117$		0			0
$118$	−7.00000	+	7.00000i	−0.644402	+	0.644402i
$119$	2.00000	+	2.00000i	0.183340	+	0.183340i
$120$	−3.00000	−	9.00000i	−0.273861	−	0.821584i
$121$		−	9.00000i		−	0.818182i
$122$	14.0000			1.26750
$123$		−	14.0000i		−	1.26234i
$124$	5.00000	−	5.00000i	0.449013	−	0.449013i
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	2.00000			0.178174
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	−0.184257	−	0.982878i	$-0.558988\pi$
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	0.982878	+	0.184257i	$0.0589879\pi$
$128$	3.00000			0.265165
$129$	−2.00000			−0.176090
$130$		0			0
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$	−2.00000			−0.174078
$133$	−10.0000	+	10.0000i	−0.867110	+	0.867110i
$134$	−4.00000			−0.345547
$135$	12.0000	−	4.00000i	1.03280	−	0.344265i
$136$	3.00000	−	3.00000i	0.257248	−	0.257248i
$137$			16.0000i			1.36697i	0.729964	+	0.683486i	$0.239537\pi$
$137$			16.0000i			1.36697i	−0.729964	+	0.683486i	$0.760463\pi$
$138$	−6.00000			−0.510754
$139$		−	14.0000i		−	1.18746i	−0.804663	−	0.593732i	$-0.797654\pi$
$139$		−	14.0000i		−	1.18746i	0.804663	−	0.593732i	$-0.202346\pi$
$140$	−4.00000	−	2.00000i	−0.338062	−	0.169031i
$141$	−6.00000	−	6.00000i	−0.505291	−	0.505291i
$142$	1.00000	−	1.00000i	0.0839181	−	0.0839181i
$143$		0			0
$144$		−	1.00000i		−	0.0833333i
$145$		0			0
$146$	−10.0000			−0.827606
$147$	3.00000	−	3.00000i	0.247436	−	0.247436i
$148$		0			0
$149$	3.00000	+	3.00000i	0.245770	+	0.245770i	0.819232	−	0.573462i	$-0.194400\pi$
$149$	3.00000	+	3.00000i	0.245770	+	0.245770i	−0.573462	+	0.819232i	$0.694400\pi$
$150$	7.00000	+	1.00000i	0.571548	+	0.0816497i
$151$	−7.00000	−	7.00000i	−0.569652	−	0.569652i	0.362379	−	0.932031i	$-0.381965\pi$
$151$	−7.00000	−	7.00000i	−0.569652	−	0.569652i	−0.932031	+	0.362379i	$0.881965\pi$
$152$	15.0000	+	15.0000i	1.21666	+	1.21666i
$153$	1.00000	+	1.00000i	0.0808452	+	0.0808452i
$154$	2.00000	−	2.00000i	0.161165	−	0.161165i
$155$	5.00000	+	15.0000i	0.401610	+	1.20483i
$156$		0			0
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.999268	+	0.0382445i	$0.0121766\pi$
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.0382445	+	0.999268i	$0.487823\pi$
$158$			2.00000i			0.159111i
$159$		−	10.0000i		−	0.793052i
$160$	−5.00000	+	10.0000i	−0.395285	+	0.790569i
$161$	−6.00000	+	6.00000i	−0.472866	+	0.472866i
$162$	−5.00000			−0.392837
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	−7.00000	+	7.00000i	−0.546608	+	0.546608i
$165$	2.00000	−	4.00000i	0.155700	−	0.311400i
$166$		−	6.00000i		−	0.465690i
$167$			18.0000i			1.39288i	0.717614	+	0.696441i	$0.245234\pi$
$167$			18.0000i			1.39288i	−0.717614	+	0.696441i	$0.754766\pi$
$168$	6.00000	+	6.00000i	0.462910	+	0.462910i
$169$		0			0
$170$	1.00000	+	3.00000i	0.0766965	+	0.230089i
$171$	−5.00000	+	5.00000i	−0.382360	+	0.382360i
$172$	1.00000	+	1.00000i	0.0762493	+	0.0762493i
$173$	−11.0000	−	11.0000i	−0.836315	−	0.836315i	0.152057	−	0.988372i	$-0.451410\pi$
$173$	−11.0000	−	11.0000i	−0.836315	−	0.836315i	−0.988372	+	0.152057i	$0.951410\pi$
$174$		0			0
$175$	8.00000	−	6.00000i	0.604743	−	0.453557i
$176$	−1.00000	−	1.00000i	−0.0753778	−	0.0753778i
$177$		−	14.0000i		−	1.05230i
$178$	5.00000	−	5.00000i	0.374766	−	0.374766i
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$	−2.00000	−	1.00000i	−0.149071	−	0.0745356i
$181$		−	8.00000i		−	0.594635i	−0.954779	−	0.297318i	$-0.903908\pi$
$181$		−	8.00000i		−	0.594635i	0.954779	−	0.297318i	$-0.0960920\pi$
$182$		0			0
$183$	−14.0000	+	14.0000i	−1.03491	+	1.03491i
$184$	9.00000	+	9.00000i	0.663489	+	0.663489i
$185$		0			0
$186$		−	10.0000i		−	0.733236i
$187$	2.00000			0.146254
$188$			6.00000i			0.437595i
$189$	−8.00000	+	8.00000i	−0.581914	+	0.581914i
$190$	−15.0000	+	5.00000i	−1.08821	+	0.362738i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$	7.00000	−	7.00000i	0.505181	−	0.505181i
$193$	−18.0000			−1.29567			−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−18.0000			−1.29567			−0.647834	+	0.761781i	$0.724325\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	1.00000	−	1.00000i	0.0710669	−	0.0710669i
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$	−9.00000	−	12.0000i	−0.636396	−	0.848528i
$201$	4.00000	−	4.00000i	0.282138	−	0.282138i
$202$		−	12.0000i		−	0.844317i
$203$		0			0
$204$			2.00000i			0.140028i
$205$	−7.00000	−	21.0000i	−0.488901	−	1.46670i
$206$	−7.00000	−	7.00000i	−0.487713	−	0.487713i
$207$	−3.00000	+	3.00000i	−0.208514	+	0.208514i
$208$		0			0
$209$			10.0000i			0.691714i
$210$	−6.00000	+	2.00000i	−0.414039	+	0.138013i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−5.00000	+	5.00000i	−0.343401	+	0.343401i
$213$			2.00000i			0.137038i
$214$	−7.00000	−	7.00000i	−0.478510	−	0.478510i
$215$	−3.00000	+	1.00000i	−0.204598	+	0.0681994i
$216$	12.0000	+	12.0000i	0.816497	+	0.816497i
$217$	−10.0000	−	10.0000i	−0.678844	−	0.678844i
$218$	9.00000	+	9.00000i	0.609557	+	0.609557i
$219$	10.0000	−	10.0000i	0.675737	−	0.675737i
$220$	−3.00000	+	1.00000i	−0.202260	+	0.0674200i
$221$		0			0
$222$		0			0
$223$			2.00000i			0.133930i	0.997755	+	0.0669650i	$0.0213316\pi$
$223$			2.00000i			0.133930i	−0.997755	+	0.0669650i	$0.978668\pi$
$224$		−	10.0000i		−	0.668153i
$225$	4.00000	−	3.00000i	0.266667	−	0.200000i
$226$	−5.00000	+	5.00000i	−0.332595	+	0.332595i
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$	−10.0000			−0.662266
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	−0.601002	−	0.799248i	$-0.705232\pi$
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	0.799248	+	0.601002i	$0.205232\pi$
$230$	−9.00000	+	3.00000i	−0.593442	+	0.197814i
$231$			4.00000i			0.263181i
$232$		0			0
$233$	1.00000	+	1.00000i	0.0655122	+	0.0655122i	0.739104	−	0.673592i	$-0.235249\pi$
$233$	1.00000	+	1.00000i	0.0655122	+	0.0655122i	−0.673592	+	0.739104i	$0.735249\pi$
$234$		0			0
$235$	−12.0000	−	6.00000i	−0.782794	−	0.391397i
$236$	−7.00000	+	7.00000i	−0.455661	+	0.455661i
$237$	−2.00000	−	2.00000i	−0.129914	−	0.129914i
$238$	−2.00000	−	2.00000i	−0.129641	−	0.129641i
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	0.603391	−	0.797445i	$-0.293816\pi$
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	−0.797445	+	0.603391i	$0.793816\pi$
$240$	1.00000	+	3.00000i	0.0645497	+	0.193649i
$241$	−17.0000	−	17.0000i	−1.09507	−	1.09507i	−0.994979	−	0.100088i	$-0.968088\pi$
$241$	−17.0000	−	17.0000i	−1.09507	−	1.09507i	−0.100088	−	0.994979i	$-0.531912\pi$
$242$			9.00000i			0.578542i
$243$	−7.00000	+	7.00000i	−0.449050	+	0.449050i
$244$	14.0000			0.896258
$245$	3.00000	−	6.00000i	0.191663	−	0.383326i
$246$			14.0000i			0.892607i
$247$		0			0
$248$	−15.0000	+	15.0000i	−0.952501	+	0.952501i
$249$	6.00000	+	6.00000i	0.380235	+	0.380235i
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$			2.00000i			0.126239i	0.998006	+	0.0631194i	$0.0201049\pi$
$251$			2.00000i			0.126239i	−0.998006	+	0.0631194i	$0.979895\pi$
$252$	2.00000			0.125988
$253$			6.00000i			0.377217i
$254$	−9.00000	+	9.00000i	−0.564710	+	0.564710i
$255$	−4.00000	−	2.00000i	−0.250490	−	0.125245i
$256$	−17.0000			−1.06250
$257$	−11.0000	+	11.0000i	−0.686161	+	0.686161i	−0.961381	−	0.275220i	$-0.911249\pi$
$257$	−11.0000	+	11.0000i	−0.686161	+	0.686161i	0.275220	+	0.961381i	$0.411249\pi$
$258$	2.00000			0.124515
$259$		0			0
$260$		0			0
$261$		0			0
$262$	20.0000			1.23560
$263$	1.00000	−	1.00000i	0.0616626	−	0.0616626i	−0.675603	−	0.737266i	$-0.736117\pi$
$263$	1.00000	−	1.00000i	0.0616626	−	0.0616626i	0.737266	+	0.675603i	$0.236117\pi$
$264$	6.00000			0.369274
$265$	−5.00000	−	15.0000i	−0.307148	−	0.921443i
$266$	10.0000	−	10.0000i	0.613139	−	0.613139i
$267$			10.0000i			0.611990i
$268$	−4.00000			−0.244339
$269$			12.0000i			0.731653i	0.930683	+	0.365826i	$0.119214\pi$
$269$			12.0000i			0.731653i	−0.930683	+	0.365826i	$0.880786\pi$
$270$	−12.0000	+	4.00000i	−0.730297	+	0.243432i
$271$	9.00000	+	9.00000i	0.546711	+	0.546711i	0.925488	−	0.378777i	$-0.123655\pi$
$271$	9.00000	+	9.00000i	0.546711	+	0.546711i	−0.378777	+	0.925488i	$0.623655\pi$
$272$	−1.00000	+	1.00000i	−0.0606339	+	0.0606339i
$273$		0			0
$274$		−	16.0000i		−	0.966595i
$275$	1.00000	−	7.00000i	0.0603023	−	0.422116i
$276$	−6.00000			−0.361158
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	−0.995545	−	0.0942828i	$-0.969944\pi$
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	0.0942828	+	0.995545i	$0.469944\pi$
$278$			14.0000i			0.839664i
$279$	−5.00000	−	5.00000i	−0.299342	−	0.299342i
$280$	12.0000	+	6.00000i	0.717137	+	0.358569i
$281$	−1.00000	−	1.00000i	−0.0596550	−	0.0596550i	0.676650	−	0.736305i	$-0.263431\pi$
$281$	−1.00000	−	1.00000i	−0.0596550	−	0.0596550i	−0.736305	+	0.676650i	$0.763431\pi$
$282$	6.00000	+	6.00000i	0.357295	+	0.357295i
$283$	−9.00000	−	9.00000i	−0.534994	−	0.534994i	0.387060	−	0.922055i	$-0.373491\pi$
$283$	−9.00000	−	9.00000i	−0.534994	−	0.534994i	−0.922055	+	0.387060i	$0.873491\pi$
$284$	1.00000	−	1.00000i	0.0593391	−	0.0593391i
$285$	10.0000	−	20.0000i	0.592349	−	1.18470i
$286$		0			0
$287$	14.0000	+	14.0000i	0.826394	+	0.826394i
$288$		−	5.00000i		−	0.294628i
$289$			15.0000i			0.882353i
$290$		0			0
$291$	−2.00000	+	2.00000i	−0.117242	+	0.117242i
$292$	−10.0000			−0.585206
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$	−3.00000	+	3.00000i	−0.174964	+	0.174964i
$295$	−7.00000	−	21.0000i	−0.407556	−	1.22267i
$296$		0			0
$297$			8.00000i			0.464207i
$298$	−3.00000	−	3.00000i	−0.173785	−	0.173785i
$299$		0			0
$300$	7.00000	+	1.00000i	0.404145	+	0.0577350i
$301$	2.00000	−	2.00000i	0.115278	−	0.115278i
$302$	7.00000	+	7.00000i	0.402805	+	0.402805i
$303$	12.0000	+	12.0000i	0.689382	+	0.689382i
$304$	−5.00000	−	5.00000i	−0.286770	−	0.286770i
$305$	−14.0000	+	28.0000i	−0.801638	+	1.60328i
$306$	−1.00000	−	1.00000i	−0.0571662	−	0.0571662i
$307$		−	18.0000i		−	1.02731i	−0.857996	−	0.513657i	$-0.828290\pi$
$307$		−	18.0000i		−	1.02731i	0.857996	−	0.513657i	$-0.171710\pi$
$308$	2.00000	−	2.00000i	0.113961	−	0.113961i
$309$	14.0000			0.796432
$310$	−5.00000	−	15.0000i	−0.283981	−	0.851943i
$311$			6.00000i			0.340229i	0.985424	+	0.170114i	$0.0544137\pi$
$311$			6.00000i			0.340229i	−0.985424	+	0.170114i	$0.945586\pi$
$312$		0			0
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$	−13.0000	−	13.0000i	−0.733632	−	0.733632i
$315$	−2.00000	+	4.00000i	−0.112687	+	0.225374i
$316$			2.00000i			0.112509i
$317$	14.0000			0.786318			0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000			0.786318			0.393159	+	0.919470i	$0.371382\pi$
$318$			10.0000i			0.560772i
$319$		0			0
$320$	7.00000	−	14.0000i	0.391312	−	0.782624i
$321$	14.0000			0.781404
$322$	6.00000	−	6.00000i	0.334367	−	0.334367i
$323$	10.0000			0.556415
$324$	−5.00000			−0.277778
$325$		0			0
$326$	4.00000			0.221540
$327$	−18.0000			−0.995402
$328$	21.0000	−	21.0000i	1.15953	−	1.15953i
$329$	12.0000			0.661581
$330$	−2.00000	+	4.00000i	−0.110096	+	0.220193i
$331$	3.00000	−	3.00000i	0.164895	−	0.164895i	−0.619836	−	0.784731i	$-0.712801\pi$
$331$	3.00000	−	3.00000i	0.164895	−	0.164895i	0.784731	+	0.619836i	$0.212801\pi$
$332$		−	6.00000i		−	0.329293i
$333$		0			0
$334$		−	18.0000i		−	0.984916i
$335$	4.00000	−	8.00000i	0.218543	−	0.437087i
$336$	−2.00000	−	2.00000i	−0.109109	−	0.109109i
$337$	13.0000	−	13.0000i	0.708155	−	0.708155i	−0.257992	−	0.966147i	$-0.583061\pi$
$337$	13.0000	−	13.0000i	0.708155	−	0.708155i	0.966147	+	0.257992i	$0.0830608\pi$
$338$		0			0
$339$		−	10.0000i		−	0.543125i
$340$	1.00000	+	3.00000i	0.0542326	+	0.162698i
$341$	−10.0000			−0.541530
$342$	5.00000	−	5.00000i	0.270369	−	0.270369i
$343$			20.0000i			1.07990i
$344$	−3.00000	−	3.00000i	−0.161749	−	0.161749i
$345$	6.00000	−	12.0000i	0.323029	−	0.646058i
$346$	11.0000	+	11.0000i	0.591364	+	0.591364i
$347$	3.00000	+	3.00000i	0.161048	+	0.161048i	0.783031	−	0.621983i	$-0.213673\pi$
$347$	3.00000	+	3.00000i	0.161048	+	0.161048i	−0.621983	+	0.783031i	$0.713673\pi$
$348$		0			0
$349$	−9.00000	+	9.00000i	−0.481759	+	0.481759i	−0.905693	−	0.423934i	$-0.860649\pi$
$349$	−9.00000	+	9.00000i	−0.481759	+	0.481759i	0.423934	+	0.905693i	$0.360649\pi$
$350$	−8.00000	+	6.00000i	−0.427618	+	0.320713i
$351$		0			0
$352$	−5.00000	−	5.00000i	−0.266501	−	0.266501i
$353$		−	12.0000i		−	0.638696i	−0.947638	−	0.319348i	$-0.896536\pi$
$353$		−	12.0000i		−	0.638696i	0.947638	−	0.319348i	$-0.103464\pi$
$354$			14.0000i			0.744092i
$355$	1.00000	+	3.00000i	0.0530745	+	0.159223i
$356$	5.00000	−	5.00000i	0.264999	−	0.264999i
$357$	4.00000			0.211702
$358$	20.0000			1.05703
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	−0.733003	−	0.680225i	$-0.761882\pi$
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	0.680225	+	0.733003i	$0.261882\pi$
$360$	6.00000	+	3.00000i	0.316228	+	0.158114i
$361$			31.0000i			1.63158i
$362$			8.00000i			0.420471i
$363$	−9.00000	−	9.00000i	−0.472377	−	0.472377i
$364$		0			0
$365$	10.0000	−	20.0000i	0.523424	−	1.04685i
$366$	14.0000	−	14.0000i	0.731792	−	0.731792i
$367$	−1.00000	−	1.00000i	−0.0521996	−	0.0521996i	0.680525	−	0.732725i	$-0.261752\pi$
$367$	−1.00000	−	1.00000i	−0.0521996	−	0.0521996i	−0.732725	+	0.680525i	$0.761752\pi$
$368$	−3.00000	−	3.00000i	−0.156386	−	0.156386i
$369$	7.00000	+	7.00000i	0.364405	+	0.364405i
$370$		0			0
$371$	10.0000	+	10.0000i	0.519174	+	0.519174i
$372$		−	10.0000i		−	0.518476i
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	−0.979263	−	0.202593i	$-0.935063\pi$
$373$	−15.0000	+	15.0000i	−0.776671	+	0.776671i	0.202593	+	0.979263i	$0.435063\pi$
$374$	−2.00000			−0.103418
$375$	−9.00000	+	13.0000i	−0.464758	+	0.671317i
$376$		−	18.0000i		−	0.928279i
$377$		0			0
$378$	8.00000	−	8.00000i	0.411476	−	0.411476i
$379$	1.00000	+	1.00000i	0.0513665	+	0.0513665i	0.732323	−	0.680957i	$-0.238436\pi$
$379$	1.00000	+	1.00000i	0.0513665	+	0.0513665i	−0.680957	+	0.732323i	$0.738436\pi$
$380$	−15.0000	+	5.00000i	−0.769484	+	0.256495i
$381$		−	18.0000i		−	0.922168i
$382$	−8.00000			−0.409316
$383$		−	30.0000i		−	1.53293i	−0.642287	−	0.766464i	$-0.722014\pi$
$383$		−	30.0000i		−	1.53293i	0.642287	−	0.766464i	$-0.277986\pi$
$384$	3.00000	−	3.00000i	0.153093	−	0.153093i
$385$	2.00000	+	6.00000i	0.101929	+	0.305788i
$386$	18.0000			0.916176
$387$	1.00000	−	1.00000i	0.0508329	−	0.0508329i
$388$	2.00000			0.101535
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$	9.00000			0.454569
$393$	−20.0000	+	20.0000i	−1.00887	+	1.00887i
$394$	6.00000			0.302276
$395$	−4.00000	−	2.00000i	−0.201262	−	0.100631i
$396$	1.00000	−	1.00000i	0.0502519	−	0.0502519i
$397$		−	16.0000i		−	0.803017i	−0.915855	−	0.401508i	$-0.868486\pi$
$397$		−	16.0000i		−	0.803017i	0.915855	−	0.401508i	$-0.131514\pi$
$398$	8.00000			0.401004
$399$			20.0000i			1.00125i
$400$	3.00000	+	4.00000i	0.150000	+	0.200000i
$401$	11.0000	+	11.0000i	0.549314	+	0.549314i	0.926242	−	0.376929i	$-0.123020\pi$
$401$	11.0000	+	11.0000i	0.549314	+	0.549314i	−0.376929	+	0.926242i	$0.623020\pi$
$402$	−4.00000	+	4.00000i	−0.199502	+	0.199502i
$403$		0			0
$404$		−	12.0000i		−	0.597022i
$405$	5.00000	−	10.0000i	0.248452	−	0.496904i
$406$		0			0
$407$		0			0
$408$		−	6.00000i		−	0.297044i
$409$	7.00000	+	7.00000i	0.346128	+	0.346128i	0.858665	−	0.512537i	$-0.171294\pi$
$409$	7.00000	+	7.00000i	0.346128	+	0.346128i	−0.512537	+	0.858665i	$0.671294\pi$
$410$	7.00000	+	21.0000i	0.345705	+	1.03712i
$411$	16.0000	+	16.0000i	0.789222	+	0.789222i
$412$	−7.00000	−	7.00000i	−0.344865	−	0.344865i
$413$	14.0000	+	14.0000i	0.688895	+	0.688895i
$414$	3.00000	−	3.00000i	0.147442	−	0.147442i
$415$	12.0000	+	6.00000i	0.589057	+	0.294528i
$416$		0			0
$417$	−14.0000	−	14.0000i	−0.685583	−	0.685583i
$418$		−	10.0000i		−	0.489116i
$419$		−	38.0000i		−	1.85642i	−0.372055	−	0.928211i	$-0.621347\pi$
$419$		−	38.0000i		−	1.85642i	0.372055	−	0.928211i	$-0.378653\pi$
$420$	−6.00000	+	2.00000i	−0.292770	+	0.0975900i
$421$	11.0000	−	11.0000i	0.536107	−	0.536107i	−0.386276	−	0.922383i	$-0.626239\pi$
$421$	11.0000	−	11.0000i	0.536107	−	0.536107i	0.922383	+	0.386276i	$0.126239\pi$
$422$	−4.00000			−0.194717
$423$	6.00000			0.291730
$424$	15.0000	−	15.0000i	0.728464	−	0.728464i
$425$	−7.00000	−	1.00000i	−0.339550	−	0.0485071i
$426$		−	2.00000i		−	0.0969003i
$427$		−	28.0000i		−	1.35501i
$428$	−7.00000	−	7.00000i	−0.338358	−	0.338358i
$429$		0			0
$430$	3.00000	−	1.00000i	0.144673	−	0.0482243i
$431$	−13.0000	+	13.0000i	−0.626188	+	0.626188i	−0.947107	−	0.320919i	$-0.896008\pi$
$431$	−13.0000	+	13.0000i	−0.626188	+	0.626188i	0.320919	+	0.947107i	$0.396008\pi$
$432$	−4.00000	−	4.00000i	−0.192450	−	0.192450i
$433$	17.0000	+	17.0000i	0.816968	+	0.816968i	0.985668	−	0.168700i	$-0.0539568\pi$
$433$	17.0000	+	17.0000i	0.816968	+	0.816968i	−0.168700	+	0.985668i	$0.553957\pi$
$434$	10.0000	+	10.0000i	0.480015	+	0.480015i
$435$		0			0
$436$	9.00000	+	9.00000i	0.431022	+	0.431022i
$437$			30.0000i			1.43509i
$438$	−10.0000	+	10.0000i	−0.477818	+	0.477818i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$	9.00000	−	3.00000i	0.429058	−	0.143019i
$441$			3.00000i			0.142857i
$442$		0			0
$443$	25.0000	−	25.0000i	1.18779	−	1.18779i	0.210108	−	0.977678i	$-0.432619\pi$
$443$	25.0000	−	25.0000i	1.18779	−	1.18779i	0.977678	−	0.210108i	$-0.0673814\pi$
$444$		0			0
$445$	5.00000	+	15.0000i	0.237023	+	0.711068i
$446$		−	2.00000i		−	0.0947027i
$447$	6.00000			0.283790
$448$			14.0000i			0.661438i
$449$	3.00000	−	3.00000i	0.141579	−	0.141579i	−0.632765	−	0.774344i	$-0.718080\pi$
$449$	3.00000	−	3.00000i	0.141579	−	0.141579i	0.774344	+	0.632765i	$0.218080\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	14.0000			0.659234
$452$	−5.00000	+	5.00000i	−0.235180	+	0.235180i
$453$	−14.0000			−0.657777
$454$	−12.0000			−0.563188
$455$		0			0
$456$	30.0000			1.40488
$457$	−2.00000			−0.0935561			−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000			−0.0935561			−0.0467780	+	0.998905i	$0.514895\pi$
$458$	−3.00000	+	3.00000i	−0.140181	+	0.140181i
$459$	8.00000			0.373408
$460$	−9.00000	+	3.00000i	−0.419627	+	0.139876i
$461$	−17.0000	+	17.0000i	−0.791769	+	0.791769i	−0.981782	−	0.190013i	$-0.939147\pi$
$461$	−17.0000	+	17.0000i	−0.791769	+	0.791769i	0.190013	+	0.981782i	$0.439147\pi$
$462$		−	4.00000i		−	0.186097i
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$		0			0
$465$	20.0000	+	10.0000i	0.927478	+	0.463739i
$466$	−1.00000	−	1.00000i	−0.0463241	−	0.0463241i
$467$	9.00000	−	9.00000i	0.416470	−	0.416470i	−0.467515	−	0.883985i	$-0.654851\pi$
$467$	9.00000	−	9.00000i	0.416470	−	0.416470i	0.883985	+	0.467515i	$0.154851\pi$
$468$		0			0
$469$			8.00000i			0.369406i
$470$	12.0000	+	6.00000i	0.553519	+	0.276759i
$471$	26.0000			1.19802
$472$	21.0000	−	21.0000i	0.966603	−	0.966603i
$473$		−	2.00000i		−	0.0919601i
$474$	2.00000	+	2.00000i	0.0918630	+	0.0918630i
$475$	5.00000	−	35.0000i	0.229416	−	1.60591i
$476$	−2.00000	−	2.00000i	−0.0916698	−	0.0916698i
$477$	5.00000	+	5.00000i	0.228934	+	0.228934i
$478$	3.00000	+	3.00000i	0.137217	+	0.137217i
$479$	7.00000	−	7.00000i	0.319838	−	0.319838i	−0.528867	−	0.848705i	$-0.677383\pi$
$479$	7.00000	−	7.00000i	0.319838	−	0.319838i	0.848705	+	0.528867i	$0.177383\pi$
$480$	5.00000	+	15.0000i	0.228218	+	0.684653i
$481$		0			0
$482$	17.0000	+	17.0000i	0.774329	+	0.774329i
$483$			12.0000i			0.546019i
$484$			9.00000i			0.409091i
$485$	−2.00000	+	4.00000i	−0.0908153	+	0.181631i
$486$	7.00000	−	7.00000i	0.317526	−	0.317526i
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	−42.0000			−1.90125
$489$	−4.00000	+	4.00000i	−0.180886	+	0.180886i
$490$	−3.00000	+	6.00000i	−0.135526	+	0.271052i
$491$		−	22.0000i		−	0.992846i	−0.868081	−	0.496423i	$-0.834646\pi$
$491$		−	22.0000i		−	0.992846i	0.868081	−	0.496423i	$-0.165354\pi$
$492$			14.0000i			0.631169i
$493$		0			0
$494$		0			0
$495$	1.00000	+	3.00000i	0.0449467	+	0.134840i
$496$	5.00000	−	5.00000i	0.224507	−	0.224507i
$497$	−2.00000	−	2.00000i	−0.0897123	−	0.0897123i
$498$	−6.00000	−	6.00000i	−0.268866	−	0.268866i
$499$	−3.00000	−	3.00000i	−0.134298	−	0.134298i	0.636762	−	0.771060i	$-0.280273\pi$
$499$	−3.00000	−	3.00000i	−0.134298	−	0.134298i	−0.771060	+	0.636762i	$0.780273\pi$
$500$	11.0000	−	2.00000i	0.491935	−	0.0894427i
$501$	18.0000	+	18.0000i	0.804181	+	0.804181i
$502$		−	2.00000i		−	0.0892644i
$503$	−3.00000	+	3.00000i	−0.133763	+	0.133763i	−0.770818	−	0.637055i	$-0.780152\pi$
$503$	−3.00000	+	3.00000i	−0.133763	+	0.133763i	0.637055	+	0.770818i	$0.280152\pi$
$504$	−6.00000			−0.267261
$505$	24.0000	+	12.0000i	1.06799	+	0.533993i
$506$		−	6.00000i		−	0.266733i
$507$		0			0
$508$	−9.00000	+	9.00000i	−0.399310	+	0.399310i
$509$	−13.0000	−	13.0000i	−0.576215	−	0.576215i	0.357643	−	0.933858i	$-0.383580\pi$
$509$	−13.0000	−	13.0000i	−0.576215	−	0.576215i	−0.933858	+	0.357643i	$0.883580\pi$
$510$	4.00000	+	2.00000i	0.177123	+	0.0885615i
$511$			20.0000i			0.884748i
$512$	11.0000			0.486136
$513$			40.0000i			1.76604i
$514$	11.0000	−	11.0000i	0.485189	−	0.485189i
$515$	21.0000	−	7.00000i	0.925371	−	0.308457i
$516$	2.00000			0.0880451
$517$	6.00000	−	6.00000i	0.263880	−	0.263880i
$518$		0			0
$519$	−22.0000			−0.965693
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	−0.482405	−	0.875948i	$-0.660237\pi$
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	0.875948	+	0.482405i	$0.160237\pi$
$524$	20.0000			0.873704
$525$	2.00000	−	14.0000i	0.0872872	−	0.611010i
$526$	−1.00000	+	1.00000i	−0.0436021	+	0.0436021i
$527$			10.0000i			0.435607i
$528$	−2.00000			−0.0870388
$529$		−	5.00000i		−	0.217391i
$530$	5.00000	+	15.0000i	0.217186	+	0.651558i
$531$	7.00000	+	7.00000i	0.303774	+	0.303774i
$532$	10.0000	−	10.0000i	0.433555	−	0.433555i
$533$		0			0
$534$		−	10.0000i		−	0.432742i
$535$	21.0000	−	7.00000i	0.907909	−	0.302636i
$536$	12.0000			0.518321
$537$	−20.0000	+	20.0000i	−0.863064	+	0.863064i
$538$		−	12.0000i		−	0.517357i
$539$	3.00000	+	3.00000i	0.129219	+	0.129219i
$540$	−12.0000	+	4.00000i	−0.516398	+	0.172133i
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$	−9.00000	−	9.00000i	−0.386583	−	0.386583i
$543$	−8.00000	−	8.00000i	−0.343313	−	0.343313i
$544$	−5.00000	+	5.00000i	−0.214373	+	0.214373i
$545$	−27.0000	+	9.00000i	−1.15655	+	0.385518i
$546$		0			0
$547$	−9.00000	−	9.00000i	−0.384812	−	0.384812i	0.488020	−	0.872832i	$-0.337719\pi$
$547$	−9.00000	−	9.00000i	−0.384812	−	0.384812i	−0.872832	+	0.488020i	$0.837719\pi$
$548$		−	16.0000i		−	0.683486i
$549$		−	14.0000i		−	0.597505i
$550$	−1.00000	+	7.00000i	−0.0426401	+	0.298481i
$551$		0			0
$552$	18.0000			0.766131
$553$	4.00000			0.170097
$554$	15.0000	−	15.0000i	0.637289	−	0.637289i
$555$		0			0
$556$			14.0000i			0.593732i
$557$		−	24.0000i		−	1.01691i	−0.861088	−	0.508456i	$-0.830216\pi$
$557$		−	24.0000i		−	1.01691i	0.861088	−	0.508456i	$-0.169784\pi$
$558$	5.00000	+	5.00000i	0.211667	+	0.211667i
$559$		0			0
$560$	−4.00000	−	2.00000i	−0.169031	−	0.0845154i
$561$	2.00000	−	2.00000i	0.0844401	−	0.0844401i
$562$	1.00000	+	1.00000i	0.0421825	+	0.0421825i
$563$	15.0000	+	15.0000i	0.632175	+	0.632175i	0.948613	−	0.316438i	$-0.102487\pi$
$563$	15.0000	+	15.0000i	0.632175	+	0.632175i	−0.316438	+	0.948613i	$0.602487\pi$
$564$	6.00000	+	6.00000i	0.252646	+	0.252646i
$565$	−5.00000	−	15.0000i	−0.210352	−	0.631055i
$566$	9.00000	+	9.00000i	0.378298	+	0.378298i
$567$			10.0000i			0.419961i
$568$	−3.00000	+	3.00000i	−0.125877	+	0.125877i
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$	−10.0000	+	20.0000i	−0.418854	+	0.837708i
$571$		−	6.00000i		−	0.251092i	−0.992088	−	0.125546i	$-0.959932\pi$
$571$		−	6.00000i		−	0.251092i	0.992088	−	0.125546i	$-0.0400683\pi$
$572$		0			0
$573$	8.00000	−	8.00000i	0.334205	−	0.334205i
$574$	−14.0000	−	14.0000i	−0.584349	−	0.584349i
$575$	3.00000	−	21.0000i	0.125109	−	0.875761i
$576$			7.00000i			0.291667i
$577$	−46.0000			−1.91501			−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−46.0000			−1.91501			−0.957503	+	0.288425i	$0.906868\pi$
$578$		−	15.0000i		−	0.623918i
$579$	−18.0000	+	18.0000i	−0.748054	+	0.748054i
$580$		0			0
$581$	−12.0000			−0.497844
$582$	2.00000	−	2.00000i	0.0829027	−	0.0829027i
$583$	10.0000			0.414158
$584$	30.0000			1.24141
$585$		0			0
$586$	−6.00000			−0.247858
$587$	4.00000			0.165098			0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000			0.165098			0.0825488	+	0.996587i	$0.473694\pi$
$588$	−3.00000	+	3.00000i	−0.123718	+	0.123718i
$589$	−50.0000			−2.06021
$590$	7.00000	+	21.0000i	0.288185	+	0.864556i
$591$	−6.00000	+	6.00000i	−0.246807	+	0.246807i
$592$		0			0
$593$	−10.0000			−0.410651			−0.205325	−	0.978694i	$-0.565825\pi$
$593$	−10.0000			−0.410651			−0.205325	+	0.978694i	$0.565825\pi$
$594$		−	8.00000i		−	0.328244i
$595$	6.00000	−	2.00000i	0.245976	−	0.0819920i
$596$	−3.00000	−	3.00000i	−0.122885	−	0.122885i
$597$	−8.00000	+	8.00000i	−0.327418	+	0.327418i
$598$		0			0
$599$			30.0000i			1.22577i	0.790173	+	0.612883i	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$	−21.0000	−	3.00000i	−0.857321	−	0.122474i
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$	−2.00000	+	2.00000i	−0.0815139	+	0.0815139i
$603$			4.00000i			0.162893i
$604$	7.00000	+	7.00000i	0.284826	+	0.284826i
$605$	−18.0000	−	9.00000i	−0.731804	−	0.365902i
$606$	−12.0000	−	12.0000i	−0.487467	−	0.487467i
$607$	−13.0000	−	13.0000i	−0.527654	−	0.527654i	0.392218	−	0.919872i	$-0.371708\pi$
$607$	−13.0000	−	13.0000i	−0.527654	−	0.527654i	−0.919872	+	0.392218i	$0.871708\pi$
$608$	−25.0000	−	25.0000i	−1.01388	−	1.01388i
$609$		0			0
$610$	14.0000	−	28.0000i	0.566843	−	1.13369i
$611$		0			0
$612$	−1.00000	−	1.00000i	−0.0404226	−	0.0404226i
$613$		−	20.0000i		−	0.807792i	−0.914805	−	0.403896i	$-0.867656\pi$
$613$		−	20.0000i		−	0.807792i	0.914805	−	0.403896i	$-0.132344\pi$
$614$			18.0000i			0.726421i
$615$	−28.0000	−	14.0000i	−1.12907	−	0.564534i
$616$	−6.00000	+	6.00000i	−0.241747	+	0.241747i
$617$	22.0000			0.885687			0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000			0.885687			0.442843	+	0.896599i	$0.353970\pi$
$618$	−14.0000			−0.563163
$619$	−25.0000	+	25.0000i	−1.00483	+	1.00483i	−0.00484658	+	0.999988i	$0.501543\pi$
$619$	−25.0000	+	25.0000i	−1.00483	+	1.00483i	−0.999988	+	0.00484658i	$0.998457\pi$
$620$	−5.00000	−	15.0000i	−0.200805	−	0.602414i
$621$			24.0000i			0.963087i
$622$		−	6.00000i		−	0.240578i
$623$	−10.0000	−	10.0000i	−0.400642	−	0.400642i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−9.00000	+	9.00000i	−0.359712	+	0.359712i
$627$	10.0000	+	10.0000i	0.399362	+	0.399362i
$628$	−13.0000	−	13.0000i	−0.518756	−	0.518756i
$629$		0			0
$630$	2.00000	−	4.00000i	0.0796819	−	0.159364i
$631$	−11.0000	−	11.0000i	−0.437903	−	0.437903i	0.453403	−	0.891306i	$-0.350210\pi$
$631$	−11.0000	−	11.0000i	−0.437903	−	0.437903i	−0.891306	+	0.453403i	$0.850210\pi$
$632$		−	6.00000i		−	0.238667i
$633$	4.00000	−	4.00000i	0.158986	−	0.158986i
$634$	−14.0000			−0.556011
$635$	−9.00000	−	27.0000i	−0.357154	−	1.07146i
$636$			10.0000i			0.396526i
$637$		0			0
$638$		0			0
$639$	−1.00000	−	1.00000i	−0.0395594	−	0.0395594i
$640$	3.00000	−	6.00000i	0.118585	−	0.237171i
$641$		−	24.0000i		−	0.947943i	−0.880540	−	0.473972i	$-0.842820\pi$
$641$		−	24.0000i		−	0.947943i	0.880540	−	0.473972i	$-0.157180\pi$
$642$	−14.0000			−0.552536
$643$		−	34.0000i		−	1.34083i	−0.741987	−	0.670415i	$-0.766116\pi$
$643$		−	34.0000i		−	1.34083i	0.741987	−	0.670415i	$-0.233884\pi$
$644$	6.00000	−	6.00000i	0.236433	−	0.236433i
$645$	−2.00000	+	4.00000i	−0.0787499	+	0.157500i
$646$	−10.0000			−0.393445
$647$	1.00000	−	1.00000i	0.0393141	−	0.0393141i	−0.687176	−	0.726491i	$-0.741150\pi$
$647$	1.00000	−	1.00000i	0.0393141	−	0.0393141i	0.726491	+	0.687176i	$0.241150\pi$
$648$	15.0000			0.589256
$649$	14.0000			0.549548
$650$		0			0
$651$	−20.0000			−0.783862
$652$	4.00000			0.156652
$653$	13.0000	−	13.0000i	0.508729	−	0.508729i	−0.405407	−	0.914136i	$-0.632870\pi$
$653$	13.0000	−	13.0000i	0.508729	−	0.508729i	0.914136	+	0.405407i	$0.132870\pi$
$654$	18.0000			0.703856
$655$	−20.0000	+	40.0000i	−0.781465	+	1.56293i
$656$	−7.00000	+	7.00000i	−0.273304	+	0.273304i
$657$			10.0000i			0.390137i
$658$	−12.0000			−0.467809
$659$			26.0000i			1.01282i	0.862294	+	0.506408i	$0.169027\pi$
$659$			26.0000i			1.01282i	−0.862294	+	0.506408i	$0.830973\pi$
$660$	−2.00000	+	4.00000i	−0.0778499	+	0.155700i
$661$	−17.0000	−	17.0000i	−0.661223	−	0.661223i	0.294445	−	0.955668i	$-0.404865\pi$
$661$	−17.0000	−	17.0000i	−0.661223	−	0.661223i	−0.955668	+	0.294445i	$0.904865\pi$
$662$	−3.00000	+	3.00000i	−0.116598	+	0.116598i
$663$		0			0
$664$			18.0000i			0.698535i
$665$	10.0000	+	30.0000i	0.387783	+	1.16335i
$666$		0			0
$667$		0			0
$668$		−	18.0000i		−	0.696441i
$669$	2.00000	+	2.00000i	0.0773245	+	0.0773245i
$670$	−4.00000	+	8.00000i	−0.154533	+	0.309067i
$671$	−14.0000	−	14.0000i	−0.540464	−	0.540464i
$672$	−10.0000	−	10.0000i	−0.385758	−	0.385758i
$673$	−15.0000	−	15.0000i	−0.578208	−	0.578208i	0.356202	−	0.934409i	$-0.384072\pi$
$673$	−15.0000	−	15.0000i	−0.578208	−	0.578208i	−0.934409	+	0.356202i	$0.884072\pi$
$674$	−13.0000	+	13.0000i	−0.500741	+	0.500741i
$675$	4.00000	−	28.0000i	0.153960	−	1.07772i
$676$		0			0
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	0.109973	−	0.993935i	$-0.464924\pi$
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	−0.993935	+	0.109973i	$0.964924\pi$
$678$			10.0000i			0.384048i
$679$		−	4.00000i		−	0.153506i
$680$	−3.00000	−	9.00000i	−0.115045	−	0.345134i
$681$	12.0000	−	12.0000i	0.459841	−	0.459841i
$682$	10.0000			0.382920
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	5.00000	−	5.00000i	0.191180	−	0.191180i
$685$	32.0000	+	16.0000i	1.22266	+	0.611329i
$686$		−	20.0000i		−	0.763604i
$687$		−	6.00000i		−	0.228914i
$688$	1.00000	+	1.00000i	0.0381246	+	0.0381246i
$689$		0			0
$690$	−6.00000	+	12.0000i	−0.228416	+	0.456832i
$691$	3.00000	−	3.00000i	0.114125	−	0.114125i	−0.647738	−	0.761863i	$-0.724285\pi$
$691$	3.00000	−	3.00000i	0.114125	−	0.114125i	0.761863	+	0.647738i	$0.224285\pi$
$692$	11.0000	+	11.0000i	0.418157	+	0.418157i
$693$	−2.00000	−	2.00000i	−0.0759737	−	0.0759737i
$694$	−3.00000	−	3.00000i	−0.113878	−	0.113878i
$695$	−28.0000	−	14.0000i	−1.06210	−	0.531050i
$696$		0			0
$697$		−	14.0000i		−	0.530288i
$698$	9.00000	−	9.00000i	0.340655	−	0.340655i
$699$	2.00000			0.0756469
$700$	−8.00000	+	6.00000i	−0.302372	+	0.226779i
$701$			12.0000i			0.453234i	0.973984	+	0.226617i	$0.0727665\pi$
$701$			12.0000i			0.453234i	−0.973984	+	0.226617i	$0.927233\pi$
$702$		0			0
$703$		0			0
$704$	7.00000	+	7.00000i	0.263822	+	0.263822i
$705$	−18.0000	+	6.00000i	−0.677919	+	0.225973i
$706$			12.0000i			0.451626i
$707$	−24.0000			−0.902613
$708$			14.0000i			0.526152i
$709$	−29.0000	+	29.0000i	−1.08912	+	1.08912i	−0.0934984	+	0.995619i	$0.529805\pi$
$709$	−29.0000	+	29.0000i	−1.08912	+	1.08912i	−0.995619	+	0.0934984i	$0.970195\pi$
$710$	−1.00000	−	3.00000i	−0.0375293	−	0.112588i
$711$	2.00000			0.0750059
$712$	−15.0000	+	15.0000i	−0.562149	+	0.562149i
$713$	−30.0000			−1.12351
$714$	−4.00000			−0.149696
$715$		0			0
$716$	20.0000			0.747435
$717$	−6.00000			−0.224074
$718$	1.00000	−	1.00000i	0.0373197	−	0.0373197i
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$	−2.00000	−	1.00000i	−0.0745356	−	0.0372678i
$721$	−14.0000	+	14.0000i	−0.521387	+	0.521387i
$722$		−	31.0000i		−	1.15370i
$723$	−34.0000			−1.26447
$724$			8.00000i			0.297318i
$725$		0			0
$726$	9.00000	+	9.00000i	0.334021	+	0.334021i
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.368418	+	0.929660i	$0.620100\pi$
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.929660	+	0.368418i	$0.879900\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$	−10.0000	+	20.0000i	−0.370117	+	0.740233i
$731$	−2.00000			−0.0739727
$732$	14.0000	−	14.0000i	0.517455	−	0.517455i
$733$		−	4.00000i		−	0.147743i	−0.997268	−	0.0738717i	$-0.976464\pi$
$733$		−	4.00000i		−	0.147743i	0.997268	−	0.0738717i	$-0.0235355\pi$
$734$	1.00000	+	1.00000i	0.0369107	+	0.0369107i
$735$	−3.00000	−	9.00000i	−0.110657	−	0.331970i
$736$	−15.0000	−	15.0000i	−0.552907	−	0.552907i
$737$	4.00000	+	4.00000i	0.147342	+	0.147342i
$738$	−7.00000	−	7.00000i	−0.257674	−	0.257674i
$739$	3.00000	−	3.00000i	0.110357	−	0.110357i	−0.649772	−	0.760129i	$-0.725136\pi$
$739$	3.00000	−	3.00000i	0.110357	−	0.110357i	0.760129	+	0.649772i	$0.225136\pi$
$740$		0			0
$741$		0			0
$742$	−10.0000	−	10.0000i	−0.367112	−	0.367112i
$743$			34.0000i			1.24734i	0.781688	+	0.623670i	$0.214359\pi$
$743$			34.0000i			1.24734i	−0.781688	+	0.623670i	$0.785641\pi$
$744$			30.0000i			1.09985i
$745$	9.00000	−	3.00000i	0.329734	−	0.109911i
$746$	15.0000	−	15.0000i	0.549189	−	0.549189i
$747$	−6.00000			−0.219529
$748$	−2.00000			−0.0731272
$749$	−14.0000	+	14.0000i	−0.511549	+	0.511549i
$750$	9.00000	−	13.0000i	0.328634	−	0.474693i
$751$		−	50.0000i		−	1.82453i	−0.409605	−	0.912263i	$-0.634333\pi$
$751$		−	50.0000i		−	1.82453i	0.409605	−	0.912263i	$-0.365667\pi$
$752$			6.00000i			0.218797i
$753$	2.00000	+	2.00000i	0.0728841	+	0.0728841i
$754$		0			0
$755$	−21.0000	+	7.00000i	−0.764268	+	0.254756i
$756$	8.00000	−	8.00000i	0.290957	−	0.290957i
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.944986	−	0.327111i	$-0.893925\pi$
$757$	−35.0000	−	35.0000i	−1.27210	−	1.27210i	−0.327111	−	0.944986i	$-0.606075\pi$
$758$	−1.00000	−	1.00000i	−0.0363216	−	0.0363216i
$759$	6.00000	+	6.00000i	0.217786	+	0.217786i
$760$	45.0000	−	15.0000i	1.63232	−	0.544107i
$761$	7.00000	+	7.00000i	0.253750	+	0.253750i	0.822506	−	0.568756i	$-0.192575\pi$
$761$	7.00000	+	7.00000i	0.253750	+	0.253750i	−0.568756	+	0.822506i	$0.692575\pi$
$762$			18.0000i			0.652071i
$763$	18.0000	−	18.0000i	0.651644	−	0.651644i
$764$	−8.00000			−0.289430
$765$	3.00000	−	1.00000i	0.108465	−	0.0361551i
$766$			30.0000i			1.08394i
$767$		0			0
$768$	−17.0000	+	17.0000i	−0.613435	+	0.613435i
$769$	15.0000	+	15.0000i	0.540914	+	0.540914i	0.923797	−	0.382883i	$-0.125069\pi$
$769$	15.0000	+	15.0000i	0.540914	+	0.540914i	−0.382883	+	0.923797i	$0.625069\pi$
$770$	−2.00000	−	6.00000i	−0.0720750	−	0.216225i
$771$			22.0000i			0.792311i
$772$	18.0000			0.647834
$773$		−	32.0000i		−	1.15096i	−0.817816	−	0.575480i	$-0.804815\pi$
$773$		−	32.0000i		−	1.15096i	0.817816	−	0.575480i	$-0.195185\pi$
$774$	−1.00000	+	1.00000i	−0.0359443	+	0.0359443i
$775$	35.0000	+	5.00000i	1.25724	+	0.179605i
$776$	−6.00000			−0.215387
$777$		0			0
$778$	18.0000			0.645331
$779$	70.0000			2.50801
$780$		0			0
$781$	−2.00000			−0.0715656
$782$	−6.00000			−0.214560
$783$		0			0
$784$	−3.00000			−0.107143
$785$	39.0000	−	13.0000i	1.39197	−	0.463990i
$786$	20.0000	−	20.0000i	0.713376	−	0.713376i
$787$			22.0000i			0.784215i	0.919919	+	0.392108i	$0.128254\pi$
$787$			22.0000i			0.784215i	−0.919919	+	0.392108i	$0.871746\pi$
$788$	6.00000			0.213741
$789$		−	2.00000i		−	0.0712019i
$790$	4.00000	+	2.00000i	0.142314	+	0.0711568i
$791$	10.0000	+	10.0000i	0.355559	+	0.355559i
$792$	−3.00000	+	3.00000i	−0.106600	+	0.106600i
$793$		0			0
$794$			16.0000i			0.567819i
$795$	−20.0000	−	10.0000i	−0.709327	−	0.354663i
$796$	8.00000			0.283552
$797$	17.0000	−	17.0000i	0.602171	−	0.602171i	−0.338717	−	0.940888i	$-0.609993\pi$
$797$	17.0000	−	17.0000i	0.602171	−	0.602171i	0.940888	+	0.338717i	$0.109993\pi$
$798$		−	20.0000i		−	0.707992i
$799$	−6.00000	−	6.00000i	−0.212265	−	0.212265i
$800$	15.0000	+	20.0000i	0.530330	+	0.707107i
$801$	−5.00000	−	5.00000i	−0.176666	−	0.176666i
$802$	−11.0000	−	11.0000i	−0.388424	−	0.388424i
$803$	10.0000	+	10.0000i	0.352892	+	0.352892i
$804$	−4.00000	+	4.00000i	−0.141069	+	0.141069i
$805$	6.00000	+	18.0000i	0.211472	+	0.634417i
$806$		0			0
$807$	12.0000	+	12.0000i	0.422420	+	0.422420i
$808$			36.0000i			1.26648i
$809$			28.0000i			0.984428i	0.870474	+	0.492214i	$0.163812\pi$
$809$			28.0000i			0.984428i	−0.870474	+	0.492214i	$0.836188\pi$
$810$	−5.00000	+	10.0000i	−0.175682	+	0.351364i
$811$	27.0000	−	27.0000i	0.948098	−	0.948098i	−0.0506198	−	0.998718i	$-0.516120\pi$
$811$	27.0000	−	27.0000i	0.948098	−	0.948098i	0.998718	+	0.0506198i	$0.0161197\pi$
$812$		0			0
$813$	18.0000			0.631288
$814$		0			0
$815$	−4.00000	+	8.00000i	−0.140114	+	0.280228i
$816$			2.00000i			0.0700140i
$817$		−	10.0000i		−	0.349856i
$818$	−7.00000	−	7.00000i	−0.244749	−	0.244749i
$819$		0			0
$820$	7.00000	+	21.0000i	0.244451	+	0.733352i
$821$	−9.00000	+	9.00000i	−0.314102	+	0.314102i	−0.846496	−	0.532394i	$-0.821292\pi$
$821$	−9.00000	+	9.00000i	−0.314102	+	0.314102i	0.532394	+	0.846496i	$0.321292\pi$
$822$	−16.0000	−	16.0000i	−0.558064	−	0.558064i
$823$	−9.00000	−	9.00000i	−0.313720	−	0.313720i	0.532629	−	0.846349i	$-0.321204\pi$
$823$	−9.00000	−	9.00000i	−0.313720	−	0.313720i	−0.846349	+	0.532629i	$0.821204\pi$
$824$	21.0000	+	21.0000i	0.731570	+	0.731570i
$825$	−6.00000	−	8.00000i	−0.208893	−	0.278524i
$826$	−14.0000	−	14.0000i	−0.487122	−	0.487122i
$827$			46.0000i			1.59958i	0.600282	+	0.799788i	$0.295055\pi$
$827$			46.0000i			1.59958i	−0.600282	+	0.799788i	$0.704945\pi$
$828$	3.00000	−	3.00000i	0.104257	−	0.104257i
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	−12.0000	−	6.00000i	−0.416526	−	0.208263i
$831$			30.0000i			1.04069i
$832$		0			0
$833$	3.00000	−	3.00000i	0.103944	−	0.103944i
$834$	14.0000	+	14.0000i	0.484780	+	0.484780i
$835$	36.0000	+	18.0000i	1.24583	+	0.622916i
$836$		−	10.0000i		−	0.345857i
$837$	−40.0000			−1.38260
$838$			38.0000i			1.31269i
$839$	35.0000	−	35.0000i	1.20833	−	1.20833i	0.236768	−	0.971566i	$-0.423912\pi$
$839$	35.0000	−	35.0000i	1.20833	−	1.20833i	0.971566	−	0.236768i	$-0.0760881\pi$
$840$	18.0000	−	6.00000i	0.621059	−	0.207020i
$841$	29.0000			1.00000
$842$	−11.0000	+	11.0000i	−0.379085	+	0.379085i
$843$	−2.00000			−0.0688837
$844$	−4.00000			−0.137686
$845$		0			0
$846$	−6.00000			−0.206284
$847$	18.0000			0.618487
$848$	−5.00000	+	5.00000i	−0.171701	+	0.171701i
$849$	−18.0000			−0.617758
$850$	7.00000	+	1.00000i	0.240098	+	0.0342997i
$851$		0			0
$852$		−	2.00000i		−	0.0685189i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$			28.0000i			0.958140i
$855$	5.00000	+	15.0000i	0.170996	+	0.512989i
$856$	21.0000	+	21.0000i	0.717765	+	0.717765i
$857$	−3.00000	+	3.00000i	−0.102478	+	0.102478i	−0.756487	−	0.654009i	$-0.773086\pi$
$857$	−3.00000	+	3.00000i	−0.102478	+	0.102478i	0.654009	+	0.756487i	$0.273086\pi$
$858$		0			0
$859$		−	30.0000i		−	1.02359i	−0.859109	−	0.511793i	$-0.828981\pi$
$859$		−	30.0000i		−	1.02359i	0.859109	−	0.511793i	$-0.171019\pi$
$860$	3.00000	−	1.00000i	0.102299	−	0.0340997i
$861$	28.0000			0.954237
$862$	13.0000	−	13.0000i	0.442782	−	0.442782i
$863$		−	30.0000i		−	1.02121i	−0.859815	−	0.510606i	$-0.829421\pi$
$863$		−	30.0000i		−	1.02121i	0.859815	−	0.510606i	$-0.170579\pi$
$864$	−20.0000	−	20.0000i	−0.680414	−	0.680414i
$865$	−33.0000	+	11.0000i	−1.12203	+	0.374011i
$866$	−17.0000	−	17.0000i	−0.577684	−	0.577684i
$867$	15.0000	+	15.0000i	0.509427	+	0.509427i
$868$	10.0000	+	10.0000i	0.339422	+	0.339422i
$869$	2.00000	−	2.00000i	0.0678454	−	0.0678454i
$870$		0			0
$871$		0			0
$872$	−27.0000	−	27.0000i	−0.914335	−	0.914335i
$873$		−	2.00000i		−	0.0676897i
$874$		−	30.0000i		−	1.01477i
$875$	−4.00000	−	22.0000i	−0.135225	−	0.743736i
$876$	−10.0000	+	10.0000i	−0.337869	+	0.337869i
$877$	−38.0000			−1.28317			−0.641584	−	0.767052i	$-0.721723\pi$
$877$	−38.0000			−1.28317			−0.641584	+	0.767052i	$0.721723\pi$
$878$		0			0
$879$	6.00000	−	6.00000i	0.202375	−	0.202375i
$880$	−3.00000	+	1.00000i	−0.101130	+	0.0337100i
$881$		−	52.0000i		−	1.75192i	−0.482380	−	0.875962i	$-0.660227\pi$
$881$		−	52.0000i		−	1.75192i	0.482380	−	0.875962i	$-0.339773\pi$
$882$		−	3.00000i		−	0.101015i
$883$	39.0000	+	39.0000i	1.31245	+	1.31245i	0.919601	+	0.392853i	$0.128512\pi$
$883$	39.0000	+	39.0000i	1.31245	+	1.31245i	0.392853	+	0.919601i	$0.371488\pi$
$884$		0			0
$885$	−28.0000	−	14.0000i	−0.941210	−	0.470605i
$886$	−25.0000	+	25.0000i	−0.839891	+	0.839891i
$887$	−1.00000	−	1.00000i	−0.0335767	−	0.0335767i	0.690119	−	0.723696i	$-0.257558\pi$
$887$	−1.00000	−	1.00000i	−0.0335767	−	0.0335767i	−0.723696	+	0.690119i	$0.757558\pi$
$888$		0			0
$889$	18.0000	+	18.0000i	0.603701	+	0.603701i
$890$	−5.00000	−	15.0000i	−0.167600	−	0.502801i
$891$	5.00000	+	5.00000i	0.167506	+	0.167506i
$892$		−	2.00000i		−	0.0669650i
$893$	30.0000	−	30.0000i	1.00391	−	1.00391i
$894$	−6.00000			−0.200670
$895$	−20.0000	+	40.0000i	−0.668526	+	1.33705i
$896$			6.00000i			0.200446i
$897$		0			0
$898$	−3.00000	+	3.00000i	−0.100111	+	0.100111i
$899$		0			0
$900$	−4.00000	+	3.00000i	−0.133333	+	0.100000i
$901$		−	10.0000i		−	0.333148i
$902$	−14.0000			−0.466149
$903$		−	4.00000i		−	0.133112i
$904$	15.0000	−	15.0000i	0.498893	−	0.498893i
$905$	−16.0000	−	8.00000i	−0.531858	−	0.265929i
$906$	14.0000			0.465119
$907$	−39.0000	+	39.0000i	−1.29497	+	1.29497i	−0.363303	+	0.931671i	$0.618351\pi$
$907$	−39.0000	+	39.0000i	−1.29497	+	1.29497i	−0.931671	+	0.363303i	$0.881649\pi$
$908$	−12.0000			−0.398234
$909$	−12.0000			−0.398015
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$	−10.0000			−0.331133
$913$	−6.00000	+	6.00000i	−0.198571	+	0.198571i
$914$	2.00000			0.0661541
$915$	14.0000	+	42.0000i	0.462826	+	1.38848i
$916$	−3.00000	+	3.00000i	−0.0991228	+	0.0991228i
$917$		−	40.0000i		−	1.32092i
$918$	−8.00000			−0.264039
$919$		−	10.0000i		−	0.329870i	−0.986304	−	0.164935i	$-0.947259\pi$
$919$		−	10.0000i		−	0.329870i	0.986304	−	0.164935i	$-0.0527414\pi$
$920$	27.0000	−	9.00000i	0.890164	−	0.296721i
$921$	−18.0000	−	18.0000i	−0.593120	−	0.593120i
$922$	17.0000	−	17.0000i	0.559865	−	0.559865i
$923$		0			0
$924$		−	4.00000i		−	0.131590i
$925$		0			0
$926$	−24.0000			−0.788689
$927$	−7.00000	+	7.00000i	−0.229910	+	0.229910i
$928$		0			0
$929$	19.0000	+	19.0000i	0.623370	+	0.623370i	0.946392	−	0.323022i	$-0.104699\pi$
$929$	19.0000	+	19.0000i	0.623370	+	0.623370i	−0.323022	+	0.946392i	$0.604699\pi$
$930$	−20.0000	−	10.0000i	−0.655826	−	0.327913i
$931$	15.0000	+	15.0000i	0.491605	+	0.491605i
$932$	−1.00000	−	1.00000i	−0.0327561	−	0.0327561i
$933$	6.00000	+	6.00000i	0.196431	+	0.196431i
$934$	−9.00000	+	9.00000i	−0.294489	+	0.294489i
$935$	2.00000	−	4.00000i	0.0654070	−	0.130814i
$936$		0			0
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	0.583461	−	0.812141i	$-0.301698\pi$
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	−0.812141	+	0.583461i	$0.801698\pi$
$938$		−	8.00000i		−	0.261209i
$939$		−	18.0000i		−	0.587408i
$940$	12.0000	+	6.00000i	0.391397	+	0.195698i
$941$	−21.0000	+	21.0000i	−0.684580	+	0.684580i	−0.961029	−	0.276448i	$-0.910843\pi$
$941$	−21.0000	+	21.0000i	−0.684580	+	0.684580i	0.276448	+	0.961029i	$0.410843\pi$
$942$	−26.0000			−0.847126
$943$	42.0000			1.36771
$944$	−7.00000	+	7.00000i	−0.227831	+	0.227831i
$945$	8.00000	+	24.0000i	0.260240	+	0.780720i
$946$			2.00000i			0.0650256i
$947$		−	18.0000i		−	0.584921i	−0.956278	−	0.292461i	$-0.905526\pi$
$947$		−	18.0000i		−	0.584921i	0.956278	−	0.292461i	$-0.0944741\pi$
$948$	2.00000	+	2.00000i	0.0649570	+	0.0649570i
$949$		0			0
$950$	−5.00000	+	35.0000i	−0.162221	+	1.13555i
$951$	14.0000	−	14.0000i	0.453981	−	0.453981i
$952$	6.00000	+	6.00000i	0.194461	+	0.194461i
$953$	13.0000	+	13.0000i	0.421111	+	0.421111i	0.885586	−	0.464475i	$-0.153757\pi$
$953$	13.0000	+	13.0000i	0.421111	+	0.421111i	−0.464475	+	0.885586i	$0.653757\pi$
$954$	−5.00000	−	5.00000i	−0.161881	−	0.161881i
$955$	8.00000	−	16.0000i	0.258874	−	0.517748i
$956$	3.00000	+	3.00000i	0.0970269	+	0.0970269i
$957$		0			0
$958$	−7.00000	+	7.00000i	−0.226160	+	0.226160i
$959$	−32.0000			−1.03333
$960$	−7.00000	−	21.0000i	−0.225924	−	0.677772i
$961$		−	19.0000i		−	0.612903i
$962$		0			0
$963$	−7.00000	+	7.00000i	−0.225572	+	0.225572i
$964$	17.0000	+	17.0000i	0.547533	+	0.547533i
$965$	−18.0000	+	36.0000i	−0.579441	+	1.15888i
$966$		−	12.0000i		−	0.386094i
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$		−	27.0000i		−	0.867813i
$969$	10.0000	−	10.0000i	0.321246	−	0.321246i
$970$	2.00000	−	4.00000i	0.0642161	−	0.128432i
$971$	−60.0000			−1.92549			−0.962746	−	0.270408i	$-0.912841\pi$
$971$	−60.0000			−1.92549			−0.962746	+	0.270408i	$0.912841\pi$
$972$	7.00000	−	7.00000i	0.224525	−	0.224525i
$973$	28.0000			0.897639
$974$	16.0000			0.512673
$975$		0			0
$976$	14.0000			0.448129
$977$	−62.0000			−1.98356			−0.991778	−	0.127971i	$-0.959153\pi$
$977$	−62.0000			−1.98356			−0.991778	+	0.127971i	$0.959153\pi$
$978$	4.00000	−	4.00000i	0.127906	−	0.127906i
$979$	−10.0000			−0.319601
$980$	−3.00000	+	6.00000i	−0.0958315	+	0.191663i
$981$	9.00000	−	9.00000i	0.287348	−	0.287348i
$982$			22.0000i			0.702048i
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$		−	42.0000i		−	1.33891i
$985$	−6.00000	+	12.0000i	−0.191176	+	0.382352i
$986$		0			0
$987$	12.0000	−	12.0000i	0.381964	−	0.381964i
$988$		0			0
$989$		−	6.00000i		−	0.190789i
$990$	−1.00000	−	3.00000i	−0.0317821	−	0.0953463i
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$	25.0000	−	25.0000i	0.793751	−	0.793751i
$993$		−	6.00000i		−	0.190404i
$994$	2.00000	+	2.00000i	0.0634361	+	0.0634361i
$995$	−8.00000	+	16.0000i	−0.253617	+	0.507234i
$996$	−6.00000	−	6.00000i	−0.190117	−	0.190117i
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	0.835112	−	0.550079i	$-0.185403\pi$
$997$	9.00000	+	9.00000i	0.285033	+	0.285033i	−0.550079	+	0.835112i	$0.685403\pi$
$998$	3.00000	+	3.00000i	0.0949633	+	0.0949633i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.k.a.577.1		2
5.3	odd	4		845.2.f.a.408.1		2
13.2	odd	12		845.2.t.a.657.1		4
13.3	even	3		845.2.o.b.357.1		4
13.4	even	6		845.2.o.a.587.1		4
13.5	odd	4		65.2.f.a.47.1	yes	2
13.6	odd	12		845.2.t.a.427.1		4
13.7	odd	12		845.2.t.b.427.1		4
13.8	odd	4		845.2.f.a.437.1		2
13.9	even	3		845.2.o.b.587.1		4
13.10	even	6		845.2.o.a.357.1		4
13.11	odd	12		845.2.t.b.657.1		4
13.12	even	2		65.2.k.a.57.1	yes	2
39.5	even	4		585.2.n.c.307.1		2
39.38	odd	2		585.2.w.b.577.1		2
52.31	even	4		1040.2.cd.b.177.1		2
52.51	odd	2		1040.2.bg.a.577.1		2
65.3	odd	12		845.2.t.b.188.1		4
65.8	even	4	inner	845.2.k.a.268.1		2
65.12	odd	4		325.2.f.a.18.1		2
65.18	even	4		65.2.k.a.8.1	yes	2
65.23	odd	12		845.2.t.a.188.1		4
65.28	even	12		845.2.o.a.488.1		4
65.33	even	12		845.2.o.b.258.1		4
65.38	odd	4		65.2.f.a.18.1	✓	2
65.43	odd	12		845.2.t.a.418.1		4
65.44	odd	4		325.2.f.a.307.1		2
65.48	odd	12		845.2.t.b.418.1		4
65.57	even	4		325.2.k.a.268.1		2
65.58	even	12		845.2.o.a.258.1		4
65.63	even	12		845.2.o.b.488.1		4
65.64	even	2		325.2.k.a.57.1		2
195.38	even	4		585.2.n.c.343.1		2
195.83	odd	4		585.2.w.b.73.1		2
260.83	odd	4		1040.2.bg.a.593.1		2
260.103	even	4		1040.2.cd.b.993.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.a.18.1	✓	2	65.38	odd	4
65.2.f.a.47.1	yes	2	13.5	odd	4
65.2.k.a.8.1	yes	2	65.18	even	4
65.2.k.a.57.1	yes	2	13.12	even	2
325.2.f.a.18.1		2	65.12	odd	4
325.2.f.a.307.1		2	65.44	odd	4
325.2.k.a.57.1		2	65.64	even	2
325.2.k.a.268.1		2	65.57	even	4
585.2.n.c.307.1		2	39.5	even	4
585.2.n.c.343.1		2	195.38	even	4
585.2.w.b.73.1		2	195.83	odd	4
585.2.w.b.577.1		2	39.38	odd	2
845.2.f.a.408.1		2	5.3	odd	4
845.2.f.a.437.1		2	13.8	odd	4
845.2.k.a.268.1		2	65.8	even	4	inner
845.2.k.a.577.1		2	1.1	even	1	trivial
845.2.o.a.258.1		4	65.58	even	12
845.2.o.a.357.1		4	13.10	even	6
845.2.o.a.488.1		4	65.28	even	12
845.2.o.a.587.1		4	13.4	even	6
845.2.o.b.258.1		4	65.33	even	12
845.2.o.b.357.1		4	13.3	even	3
845.2.o.b.488.1		4	65.63	even	12
845.2.o.b.587.1		4	13.9	even	3
845.2.t.a.188.1		4	65.23	odd	12
845.2.t.a.418.1		4	65.43	odd	12
845.2.t.a.427.1		4	13.6	odd	12
845.2.t.a.657.1		4	13.2	odd	12
845.2.t.b.188.1		4	65.3	odd	12
845.2.t.b.418.1		4	65.48	odd	12
845.2.t.b.427.1		4	13.7	odd	12
845.2.t.b.657.1		4	13.11	odd	12
1040.2.bg.a.577.1		2	52.51	odd	2
1040.2.bg.a.593.1		2	260.83	odd	4
1040.2.cd.b.177.1		2	52.31	even	4
1040.2.cd.b.993.1		2	260.103	even	4

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 $\F_{q}$
Belyi maps

Introduction

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Modular forms

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	845.2.k.a.577.1

Level	$845$
Weight	$2$
Character	845.577
Analytic conductor	$6.747$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$