LMFDB - Embedded newform 770.2.m.a.197.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(43,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 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("770.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.m (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	770.197
Dual form			770.2.m.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +(-2.12132 + 0.707107i) q^{10} +(-3.00000 + 1.41421i) q^{11} +(-1.41421 - 1.41421i) q^{13} +1.00000i q^{14} -1.00000 q^{16} +(2.12132 + 2.12132i) q^{18} -4.24264 q^{19} +(-1.00000 + 2.00000i) q^{20} +(-1.12132 + 3.12132i) q^{22} +(-2.00000 + 2.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} -2.00000 q^{26} +(0.707107 + 0.707107i) q^{28} -7.07107 q^{29} +(-0.707107 + 0.707107i) q^{32} +(2.12132 - 0.707107i) q^{35} +3.00000 q^{36} +(6.00000 + 6.00000i) q^{37} +(-3.00000 + 3.00000i) q^{38} +(0.707107 + 2.12132i) q^{40} -1.41421i q^{41} +(-5.65685 - 5.65685i) q^{43} +(1.41421 + 3.00000i) q^{44} +(3.00000 - 6.00000i) q^{45} +2.82843i q^{46} +(7.00000 + 7.00000i) q^{47} -1.00000i q^{49} +(4.94975 + 0.707107i) q^{50} +(-1.41421 + 1.41421i) q^{52} +(-4.00000 + 4.00000i) q^{53} +(7.41421 + 0.171573i) q^{55} +1.00000 q^{56} +(-5.00000 + 5.00000i) q^{58} -4.00000i q^{59} -2.82843i q^{61} +(-2.12132 - 2.12132i) q^{63} +1.00000i q^{64} +(1.41421 + 4.24264i) q^{65} +(-3.00000 - 3.00000i) q^{67} +(1.00000 - 2.00000i) q^{70} -8.00000 q^{71} +(2.12132 - 2.12132i) q^{72} +(-4.24264 - 4.24264i) q^{73} +8.48528 q^{74} +4.24264i q^{76} +(1.12132 - 3.12132i) q^{77} +4.24264 q^{79} +(2.00000 + 1.00000i) q^{80} -9.00000 q^{81} +(-1.00000 - 1.00000i) q^{82} +(-8.48528 - 8.48528i) q^{83} -8.00000 q^{86} +(3.12132 + 1.12132i) q^{88} -14.0000i q^{89} +(-2.12132 - 6.36396i) q^{90} +2.00000 q^{91} +(2.00000 + 2.00000i) q^{92} +9.89949 q^{94} +(8.48528 + 4.24264i) q^{95} +(6.00000 + 6.00000i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-4.24264 - 9.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{5}+O(q^{10}) $ 4 * q - 8 * q^5	$ 4 q - 8 q^{5} - 12 q^{11} - 4 q^{16} - 4 q^{20} + 4 q^{22} - 8 q^{23} + 12 q^{25} - 8 q^{26} + 12 q^{36} + 24 q^{37} - 12 q^{38} + 12 q^{45} + 28 q^{47} - 16 q^{53} + 24 q^{55} + 4 q^{56} - 20 q^{58} - 12 q^{67} + 4 q^{70} - 32 q^{71} - 4 q^{77} + 8 q^{80} - 36 q^{81} - 4 q^{82} - 32 q^{86} + 4 q^{88} + 8 q^{91} + 8 q^{92} + 24 q^{97}+O(q^{100}) $ 4 * q - 8 * q^5 - 12 * q^11 - 4 * q^16 - 4 * q^20 + 4 * q^22 - 8 * q^23 + 12 * q^25 - 8 * q^26 + 12 * q^36 + 24 * q^37 - 12 * q^38 + 12 * q^45 + 28 * q^47 - 16 * q^53 + 24 * q^55 + 4 * q^56 - 20 * q^58 - 12 * q^67 + 4 * q^70 - 32 * q^71 - 4 * q^77 + 8 * q^80 - 36 * q^81 - 4 * q^82 - 32 * q^86 + 4 * q^88 + 8 * q^91 + 8 * q^92 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$3$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			3.00000i			1.00000i
$10$	−2.12132	+	0.707107i	−0.670820	+	0.223607i
$11$	−3.00000	+	1.41421i	−0.904534	+	0.426401i
$11$	−3.00000	+	1.41421i	−0.904534	+	0.426401i
$12$		0			0
$13$	−1.41421	−	1.41421i	−0.392232	−	0.392232i	0.483250	−	0.875482i	$-0.339456\pi$
$13$	−1.41421	−	1.41421i	−0.392232	−	0.392232i	−0.875482	+	0.483250i	$0.839456\pi$
$14$			1.00000i			0.267261i
$15$		0			0
$16$	−1.00000			−0.250000
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$	2.12132	+	2.12132i	0.500000	+	0.500000i
$19$	−4.24264			−0.973329			−0.486664	−	0.873589i	$-0.661786\pi$
$19$	−4.24264			−0.973329			−0.486664	+	0.873589i	$0.661786\pi$
$20$	−1.00000	+	2.00000i	−0.223607	+	0.447214i
$21$		0			0
$22$	−1.12132	+	3.12132i	−0.239066	+	0.665468i
$23$	−2.00000	+	2.00000i	−0.417029	+	0.417029i	−0.884178	−	0.467150i	$-0.845281\pi$
$23$	−2.00000	+	2.00000i	−0.417029	+	0.417029i	0.467150	+	0.884178i	$0.345281\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	−2.00000			−0.392232
$27$		0			0
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$	−7.07107			−1.31306			−0.656532	−	0.754298i	$-0.727977\pi$
$29$	−7.07107			−1.31306			−0.656532	+	0.754298i	$0.727977\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		0			0
$35$	2.12132	−	0.707107i	0.358569	−	0.119523i
$36$	3.00000			0.500000
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	0.999909	−	0.0135147i	$-0.00430201\pi$
$37$	6.00000	+	6.00000i	0.986394	+	0.986394i	−0.0135147	+	0.999909i	$0.504302\pi$
$38$	−3.00000	+	3.00000i	−0.486664	+	0.486664i
$39$		0			0
$40$	0.707107	+	2.12132i	0.111803	+	0.335410i
$41$		−	1.41421i		−	0.220863i	−0.993884	−	0.110432i	$-0.964777\pi$
$41$		−	1.41421i		−	0.220863i	0.993884	−	0.110432i	$-0.0352233\pi$
$42$		0			0
$43$	−5.65685	−	5.65685i	−0.862662	−	0.862662i	0.128984	−	0.991647i	$-0.458828\pi$
$43$	−5.65685	−	5.65685i	−0.862662	−	0.862662i	−0.991647	+	0.128984i	$0.958828\pi$
$44$	1.41421	+	3.00000i	0.213201	+	0.452267i
$45$	3.00000	−	6.00000i	0.447214	−	0.894427i
$46$			2.82843i			0.417029i
$47$	7.00000	+	7.00000i	1.02105	+	1.02105i	0.999774	+	0.0212814i	$0.00677460\pi$
$47$	7.00000	+	7.00000i	1.02105	+	1.02105i	0.0212814	+	0.999774i	$0.493225\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	4.94975	+	0.707107i	0.700000	+	0.100000i
$51$		0			0
$52$	−1.41421	+	1.41421i	−0.196116	+	0.196116i
$53$	−4.00000	+	4.00000i	−0.549442	+	0.549442i	−0.926279	−	0.376837i	$-0.877012\pi$
$53$	−4.00000	+	4.00000i	−0.549442	+	0.549442i	0.376837	+	0.926279i	$0.377012\pi$
$54$		0			0
$55$	7.41421	+	0.171573i	0.999732	+	0.0231349i
$56$	1.00000			0.133631
$57$		0			0
$58$	−5.00000	+	5.00000i	−0.656532	+	0.656532i
$59$		−	4.00000i		−	0.520756i	−0.965507	−	0.260378i	$-0.916153\pi$
$59$		−	4.00000i		−	0.520756i	0.965507	−	0.260378i	$-0.0838471\pi$
$60$		0			0
$61$		−	2.82843i		−	0.362143i	−0.983470	−	0.181071i	$-0.942043\pi$
$61$		−	2.82843i		−	0.362143i	0.983470	−	0.181071i	$-0.0579565\pi$
$62$		0			0
$63$	−2.12132	−	2.12132i	−0.267261	−	0.267261i
$64$			1.00000i			0.125000i
$65$	1.41421	+	4.24264i	0.175412	+	0.526235i
$66$		0			0
$67$	−3.00000	−	3.00000i	−0.366508	−	0.366508i	0.499694	−	0.866202i	$-0.333446\pi$
$67$	−3.00000	−	3.00000i	−0.366508	−	0.366508i	−0.866202	+	0.499694i	$0.833446\pi$
$68$		0			0
$69$		0			0
$70$	1.00000	−	2.00000i	0.119523	−	0.239046i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	2.12132	−	2.12132i	0.250000	−	0.250000i
$73$	−4.24264	−	4.24264i	−0.496564	−	0.496564i	0.413803	−	0.910366i	$-0.364200\pi$
$73$	−4.24264	−	4.24264i	−0.496564	−	0.496564i	−0.910366	+	0.413803i	$0.864200\pi$
$74$	8.48528			0.986394
$75$		0			0
$76$			4.24264i			0.486664i
$77$	1.12132	−	3.12132i	0.127786	−	0.355707i
$78$		0			0
$79$	4.24264			0.477334			0.238667	−	0.971101i	$-0.423290\pi$
$79$	4.24264			0.477334			0.238667	+	0.971101i	$0.423290\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	−9.00000			−1.00000
$82$	−1.00000	−	1.00000i	−0.110432	−	0.110432i
$83$	−8.48528	−	8.48528i	−0.931381	−	0.931381i	0.0664117	−	0.997792i	$-0.478845\pi$
$83$	−8.48528	−	8.48528i	−0.931381	−	0.931381i	−0.997792	+	0.0664117i	$0.978845\pi$
$84$		0			0
$85$		0			0
$86$	−8.00000			−0.862662
$87$		0			0
$88$	3.12132	+	1.12132i	0.332734	+	0.119533i
$89$		−	14.0000i		−	1.48400i	−0.670402	−	0.741999i	$-0.733878\pi$
$89$		−	14.0000i		−	1.48400i	0.670402	−	0.741999i	$-0.266122\pi$
$90$	−2.12132	−	6.36396i	−0.223607	−	0.670820i
$91$	2.00000			0.209657
$92$	2.00000	+	2.00000i	0.208514	+	0.208514i
$93$		0			0
$94$	9.89949			1.02105
$95$	8.48528	+	4.24264i	0.870572	+	0.435286i
$96$		0			0
$97$	6.00000	+	6.00000i	0.609208	+	0.609208i	0.942739	−	0.333531i	$-0.108240\pi$
$97$	6.00000	+	6.00000i	0.609208	+	0.609208i	−0.333531	+	0.942739i	$0.608240\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	−4.24264	−	9.00000i	−0.426401	−	0.904534i
$100$	4.00000	−	3.00000i	0.400000	−	0.300000i
$101$		−	5.65685i		−	0.562878i	−0.959579	−	0.281439i	$-0.909188\pi$
$101$		−	5.65685i		−	0.562878i	0.959579	−	0.281439i	$-0.0908117\pi$
$102$		0			0
$103$	3.00000	−	3.00000i	0.295599	−	0.295599i	−0.543688	−	0.839287i	$-0.682973\pi$
$103$	3.00000	−	3.00000i	0.295599	−	0.295599i	0.839287	+	0.543688i	$0.182973\pi$
$104$			2.00000i			0.196116i
$105$		0			0
$106$			5.65685i			0.549442i
$107$	−8.48528	+	8.48528i	−0.820303	+	0.820303i	−0.986151	−	0.165848i	$-0.946964\pi$
$107$	−8.48528	+	8.48528i	−0.820303	+	0.820303i	0.165848	+	0.986151i	$0.446964\pi$
$108$		0			0
$109$	12.7279			1.21911			0.609557	−	0.792742i	$-0.291347\pi$
$109$	12.7279			1.21911			0.609557	+	0.792742i	$0.291347\pi$
$110$	5.36396	−	5.12132i	0.511434	−	0.488299i
$111$		0			0
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	−9.00000	+	9.00000i	−0.846649	+	0.846649i	−0.989713	−	0.143065i	$-0.954304\pi$
$113$	−9.00000	+	9.00000i	−0.846649	+	0.846649i	0.143065	+	0.989713i	$0.454304\pi$
$114$		0			0
$115$	6.00000	−	2.00000i	0.559503	−	0.186501i
$116$			7.07107i			0.656532i
$117$	4.24264	−	4.24264i	0.392232	−	0.392232i
$118$	−2.82843	−	2.82843i	−0.260378	−	0.260378i
$119$		0			0
$120$		0			0
$121$	7.00000	−	8.48528i	0.636364	−	0.771389i
$122$	−2.00000	−	2.00000i	−0.181071	−	0.181071i
$123$		0			0
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	−3.00000			−0.267261
$127$	9.89949	−	9.89949i	0.878438	−	0.878438i	−0.114935	−	0.993373i	$-0.536666\pi$
$127$	9.89949	−	9.89949i	0.878438	−	0.878438i	0.993373	+	0.114935i	$0.0366659\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	4.00000	+	2.00000i	0.350823	+	0.175412i
$131$			1.41421i			0.123560i	0.998090	+	0.0617802i	$0.0196778\pi$
$131$			1.41421i			0.123560i	−0.998090	+	0.0617802i	$0.980322\pi$
$132$		0			0
$133$	3.00000	−	3.00000i	0.260133	−	0.260133i
$134$	−4.24264			−0.366508
$135$		0			0
$136$		0			0
$137$	5.00000	+	5.00000i	0.427179	+	0.427179i	0.887666	−	0.460487i	$-0.152325\pi$
$137$	5.00000	+	5.00000i	0.427179	+	0.427179i	−0.460487	+	0.887666i	$0.652325\pi$
$138$		0			0
$139$	−18.3848			−1.55938			−0.779688	−	0.626168i	$-0.784622\pi$
$139$	−18.3848			−1.55938			−0.779688	+	0.626168i	$0.784622\pi$
$140$	−0.707107	−	2.12132i	−0.0597614	−	0.179284i
$141$		0			0
$142$	−5.65685	+	5.65685i	−0.474713	+	0.474713i
$143$	6.24264	+	2.24264i	0.522036	+	0.187539i
$144$		−	3.00000i		−	0.250000i
$145$	14.1421	+	7.07107i	1.17444	+	0.587220i
$146$	−6.00000			−0.496564
$147$		0			0
$148$	6.00000	−	6.00000i	0.493197	−	0.493197i
$149$	−9.89949			−0.810998			−0.405499	−	0.914095i	$-0.632902\pi$
$149$	−9.89949			−0.810998			−0.405499	+	0.914095i	$0.632902\pi$
$150$		0			0
$151$			18.3848i			1.49613i	0.663624	+	0.748066i	$0.269017\pi$
$151$			18.3848i			1.49613i	−0.663624	+	0.748066i	$0.730983\pi$
$152$	3.00000	+	3.00000i	0.243332	+	0.243332i
$153$		0			0
$154$	−1.41421	−	3.00000i	−0.113961	−	0.241747i
$155$		0			0
$156$		0			0
$157$	7.00000	+	7.00000i	0.558661	+	0.558661i	0.928926	−	0.370265i	$-0.120733\pi$
$157$	7.00000	+	7.00000i	0.558661	+	0.558661i	−0.370265	+	0.928926i	$0.620733\pi$
$158$	3.00000	−	3.00000i	0.238667	−	0.238667i
$159$		0			0
$160$	2.12132	−	0.707107i	0.167705	−	0.0559017i
$161$		−	2.82843i		−	0.222911i
$162$	−6.36396	+	6.36396i	−0.500000	+	0.500000i
$163$	1.00000	−	1.00000i	0.0783260	−	0.0783260i	−0.666858	−	0.745184i	$-0.732361\pi$
$163$	1.00000	−	1.00000i	0.0783260	−	0.0783260i	0.745184	+	0.666858i	$0.232361\pi$
$164$	−1.41421			−0.110432
$165$		0			0
$166$	−12.0000			−0.931381
$167$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$167$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$168$		0			0
$169$		−	9.00000i		−	0.692308i
$170$		0			0
$171$		−	12.7279i		−	0.973329i
$172$	−5.65685	+	5.65685i	−0.431331	+	0.431331i
$173$	12.7279	+	12.7279i	0.967686	+	0.967686i	0.999494	−	0.0318080i	$-0.0101265\pi$
$173$	12.7279	+	12.7279i	0.967686	+	0.967686i	−0.0318080	+	0.999494i	$0.510127\pi$
$174$		0			0
$175$	−4.94975	−	0.707107i	−0.374166	−	0.0534522i
$176$	3.00000	−	1.41421i	0.226134	−	0.106600i
$177$		0			0
$178$	−9.89949	−	9.89949i	−0.741999	−	0.741999i
$179$			2.00000i			0.149487i	0.997203	+	0.0747435i	$0.0238138\pi$
$179$			2.00000i			0.149487i	−0.997203	+	0.0747435i	$0.976186\pi$
$180$	−6.00000	−	3.00000i	−0.447214	−	0.223607i
$181$	4.00000			0.297318			0.148659	−	0.988889i	$-0.452504\pi$
$181$	4.00000			0.297318			0.148659	+	0.988889i	$0.452504\pi$
$182$	1.41421	−	1.41421i	0.104828	−	0.104828i
$183$		0			0
$184$	2.82843			0.208514
$185$	−6.00000	−	18.0000i	−0.441129	−	1.32339i
$186$		0			0
$187$		0			0
$188$	7.00000	−	7.00000i	0.510527	−	0.510527i
$189$		0			0
$190$	9.00000	−	3.00000i	0.652929	−	0.217643i
$191$	−16.0000			−1.15772			−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000			−1.15772			−0.578860	+	0.815427i	$0.696502\pi$
$192$		0			0
$193$	7.07107	+	7.07107i	0.508987	+	0.508987i	0.914215	−	0.405229i	$-0.132808\pi$
$193$	7.07107	+	7.07107i	0.508987	+	0.508987i	−0.405229	+	0.914215i	$0.632808\pi$
$194$	8.48528			0.609208
$195$		0			0
$196$	−1.00000			−0.0714286
$197$	8.48528	−	8.48528i	0.604551	−	0.604551i	−0.336966	−	0.941517i	$-0.609401\pi$
$197$	8.48528	−	8.48528i	0.604551	−	0.604551i	0.941517	+	0.336966i	$0.109401\pi$
$198$	−9.36396	−	3.36396i	−0.665468	−	0.239066i
$199$		−	22.0000i		−	1.55954i	−0.626067	−	0.779769i	$-0.715336\pi$
$199$		−	22.0000i		−	1.55954i	0.626067	−	0.779769i	$-0.284664\pi$
$200$	0.707107	−	4.94975i	0.0500000	−	0.350000i
$201$		0			0
$202$	−4.00000	−	4.00000i	−0.281439	−	0.281439i
$203$	5.00000	−	5.00000i	0.350931	−	0.350931i
$204$		0			0
$205$	−1.41421	+	2.82843i	−0.0987730	+	0.197546i
$206$		−	4.24264i		−	0.295599i
$207$	−6.00000	−	6.00000i	−0.417029	−	0.417029i
$208$	1.41421	+	1.41421i	0.0980581	+	0.0980581i
$209$	12.7279	−	6.00000i	0.880409	−	0.415029i
$210$		0			0
$211$			5.65685i			0.389434i	0.980859	+	0.194717i	$0.0623788\pi$
$211$			5.65685i			0.389434i	−0.980859	+	0.194717i	$0.937621\pi$
$212$	4.00000	+	4.00000i	0.274721	+	0.274721i
$213$		0			0
$214$			12.0000i			0.820303i
$215$	5.65685	+	16.9706i	0.385794	+	1.15738i
$216$		0			0
$217$		0			0
$218$	9.00000	−	9.00000i	0.609557	−	0.609557i
$219$		0			0
$220$	0.171573	−	7.41421i	0.0115674	−	0.499866i
$221$		0			0
$222$		0			0
$223$	−7.00000	+	7.00000i	−0.468755	+	0.468755i	−0.901511	−	0.432756i	$-0.857541\pi$
$223$	−7.00000	+	7.00000i	−0.468755	+	0.468755i	0.432756	+	0.901511i	$0.357541\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−12.0000	+	9.00000i	−0.800000	+	0.600000i
$226$			12.7279i			0.846649i
$227$	−15.5563	+	15.5563i	−1.03251	+	1.03251i	−0.0330577	+	0.999453i	$0.510525\pi$
$227$	−15.5563	+	15.5563i	−1.03251	+	1.03251i	−0.999453	+	0.0330577i	$0.989475\pi$
$228$		0			0
$229$			2.00000i			0.132164i	0.997814	+	0.0660819i	$0.0210498\pi$
$229$			2.00000i			0.132164i	−0.997814	+	0.0660819i	$0.978950\pi$
$230$	2.82843	−	5.65685i	0.186501	−	0.373002i
$231$		0			0
$232$	5.00000	+	5.00000i	0.328266	+	0.328266i
$233$	18.3848	+	18.3848i	1.20443	+	1.20443i	0.972806	+	0.231621i	$0.0744028\pi$
$233$	18.3848	+	18.3848i	1.20443	+	1.20443i	0.231621	+	0.972806i	$0.425597\pi$
$234$		−	6.00000i		−	0.392232i
$235$	−7.00000	−	21.0000i	−0.456630	−	1.36989i
$236$	−4.00000			−0.260378
$237$		0			0
$238$		0			0
$239$	−12.7279			−0.823301			−0.411650	−	0.911342i	$-0.635048\pi$
$239$	−12.7279			−0.823301			−0.411650	+	0.911342i	$0.635048\pi$
$240$		0			0
$241$		−	21.2132i		−	1.36646i	−0.730202	−	0.683231i	$-0.760574\pi$
$241$		−	21.2132i		−	1.36646i	0.730202	−	0.683231i	$-0.239426\pi$
$242$	−1.05025	−	10.9497i	−0.0675128	−	0.703876i
$243$		0			0
$244$	−2.82843			−0.181071
$245$	−1.00000	+	2.00000i	−0.0638877	+	0.127775i
$246$		0			0
$247$	6.00000	+	6.00000i	0.381771	+	0.381771i
$248$		0			0
$249$		0			0
$250$	−9.19239	−	6.36396i	−0.581378	−	0.402492i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	−2.12132	+	2.12132i	−0.133631	+	0.133631i
$253$	3.17157	−	8.82843i	0.199395	−	0.555038i
$254$		−	14.0000i		−	0.878438i
$255$		0			0
$256$	1.00000			0.0625000
$257$	8.00000	+	8.00000i	0.499026	+	0.499026i	0.911135	−	0.412108i	$-0.135208\pi$
$257$	8.00000	+	8.00000i	0.499026	+	0.499026i	−0.412108	+	0.911135i	$0.635208\pi$
$258$		0			0
$259$	−8.48528			−0.527250
$260$	4.24264	−	1.41421i	0.263117	−	0.0877058i
$261$		−	21.2132i		−	1.31306i
$262$	1.00000	+	1.00000i	0.0617802	+	0.0617802i
$263$	9.89949	+	9.89949i	0.610429	+	0.610429i	0.943058	−	0.332629i	$-0.107936\pi$
$263$	9.89949	+	9.89949i	0.610429	+	0.610429i	−0.332629	+	0.943058i	$0.607936\pi$
$264$		0			0
$265$	12.0000	−	4.00000i	0.737154	−	0.245718i
$266$		−	4.24264i		−	0.260133i
$267$		0			0
$268$	−3.00000	+	3.00000i	−0.183254	+	0.183254i
$269$			18.0000i			1.09748i	0.835993	+	0.548740i	$0.184892\pi$
$269$			18.0000i			1.09748i	−0.835993	+	0.548740i	$0.815108\pi$
$270$		0			0
$271$			31.1127i			1.88996i	0.327125	+	0.944981i	$0.393920\pi$
$271$			31.1127i			1.88996i	−0.327125	+	0.944981i	$0.606080\pi$
$272$		0			0
$273$		0			0
$274$	7.07107			0.427179
$275$	−14.6569	−	7.75736i	−0.883842	−	0.467786i
$276$		0			0
$277$	−5.65685	+	5.65685i	−0.339887	+	0.339887i	−0.856325	−	0.516437i	$-0.827258\pi$
$277$	−5.65685	+	5.65685i	−0.339887	+	0.339887i	0.516437	+	0.856325i	$0.327258\pi$
$278$	−13.0000	+	13.0000i	−0.779688	+	0.779688i
$279$		0			0
$280$	−2.00000	−	1.00000i	−0.119523	−	0.0597614i
$281$		−	28.2843i		−	1.68730i	−0.536895	−	0.843649i	$-0.680403\pi$
$281$		−	28.2843i		−	1.68730i	0.536895	−	0.843649i	$-0.319597\pi$
$282$		0			0
$283$	−4.24264	−	4.24264i	−0.252199	−	0.252199i	0.569673	−	0.821872i	$-0.307070\pi$
$283$	−4.24264	−	4.24264i	−0.252199	−	0.252199i	−0.821872	+	0.569673i	$0.807070\pi$
$284$			8.00000i			0.474713i
$285$		0			0
$286$	6.00000	−	2.82843i	0.354787	−	0.167248i
$287$	1.00000	+	1.00000i	0.0590281	+	0.0590281i
$288$	−2.12132	−	2.12132i	−0.125000	−	0.125000i
$289$			17.0000i			1.00000i
$290$	15.0000	−	5.00000i	0.880830	−	0.293610i
$291$		0			0
$292$	−4.24264	+	4.24264i	−0.248282	+	0.248282i
$293$	−21.2132	−	21.2132i	−1.23929	−	1.23929i	−0.960292	−	0.278996i	$-0.909998\pi$
$293$	−21.2132	−	21.2132i	−1.23929	−	1.23929i	−0.278996	−	0.960292i	$-0.590002\pi$
$294$		0			0
$295$	−4.00000	+	8.00000i	−0.232889	+	0.465778i
$296$		−	8.48528i		−	0.493197i
$297$		0			0
$298$	−7.00000	+	7.00000i	−0.405499	+	0.405499i
$299$	5.65685			0.327144
$300$		0			0
$301$	8.00000			0.461112
$302$	13.0000	+	13.0000i	0.748066	+	0.748066i
$303$		0			0
$304$	4.24264			0.243332
$305$	−2.82843	+	5.65685i	−0.161955	+	0.323911i
$306$		0			0
$307$	−18.3848	+	18.3848i	−1.04927	+	1.04927i	−0.0505532	+	0.998721i	$0.516098\pi$
$307$	−18.3848	+	18.3848i	−1.04927	+	1.04927i	−0.998721	+	0.0505532i	$0.983902\pi$
$308$	−3.12132	−	1.12132i	−0.177854	−	0.0638932i
$309$		0			0
$310$		0			0
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$		0			0
$313$	−12.0000	+	12.0000i	−0.678280	+	0.678280i	−0.959611	−	0.281331i	$-0.909224\pi$
$313$	−12.0000	+	12.0000i	−0.678280	+	0.678280i	0.281331	+	0.959611i	$0.409224\pi$
$314$	9.89949			0.558661
$315$	2.12132	+	6.36396i	0.119523	+	0.358569i
$316$		−	4.24264i		−	0.238667i
$317$	8.00000	+	8.00000i	0.449325	+	0.449325i	0.895130	−	0.445805i	$-0.147083\pi$
$317$	8.00000	+	8.00000i	0.449325	+	0.449325i	−0.445805	+	0.895130i	$0.647083\pi$
$318$		0			0
$319$	21.2132	−	10.0000i	1.18771	−	0.559893i
$320$	1.00000	−	2.00000i	0.0559017	−	0.111803i
$321$		0			0
$322$	−2.00000	−	2.00000i	−0.111456	−	0.111456i
$323$		0			0
$324$			9.00000i			0.500000i
$325$	1.41421	−	9.89949i	0.0784465	−	0.549125i
$326$		−	1.41421i		−	0.0783260i
$327$		0			0
$328$	−1.00000	+	1.00000i	−0.0552158	+	0.0552158i
$329$	−9.89949			−0.545777
$330$		0			0
$331$	4.00000			0.219860			0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000			0.219860			0.109930	+	0.993939i	$0.464937\pi$
$332$	−8.48528	+	8.48528i	−0.465690	+	0.465690i
$333$	−18.0000	+	18.0000i	−0.986394	+	0.986394i
$334$		0			0
$335$	3.00000	+	9.00000i	0.163908	+	0.491723i
$336$		0			0
$337$	15.5563	−	15.5563i	0.847408	−	0.847408i	−0.142401	−	0.989809i	$-0.545482\pi$
$337$	15.5563	−	15.5563i	0.847408	−	0.847408i	0.989809	+	0.142401i	$0.0454822\pi$
$338$	−6.36396	−	6.36396i	−0.346154	−	0.346154i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−9.00000	−	9.00000i	−0.486664	−	0.486664i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$			8.00000i			0.431331i
$345$		0			0
$346$	18.0000			0.967686
$347$	2.82843	−	2.82843i	0.151838	−	0.151838i	−0.627100	−	0.778938i	$-0.715758\pi$
$347$	2.82843	−	2.82843i	0.151838	−	0.151838i	0.778938	+	0.627100i	$0.215758\pi$
$348$		0			0
$349$	33.9411			1.81683			0.908413	−	0.418073i	$-0.137294\pi$
$349$	33.9411			1.81683			0.908413	+	0.418073i	$0.137294\pi$
$350$	−4.00000	+	3.00000i	−0.213809	+	0.160357i
$351$		0			0
$352$	1.12132	−	3.12132i	0.0597666	−	0.166367i
$353$	−4.00000	+	4.00000i	−0.212899	+	0.212899i	−0.805498	−	0.592599i	$-0.798102\pi$
$353$	−4.00000	+	4.00000i	−0.212899	+	0.212899i	0.592599	+	0.805498i	$0.298102\pi$
$354$		0			0
$355$	16.0000	+	8.00000i	0.849192	+	0.424596i
$356$	−14.0000			−0.741999
$357$		0			0
$358$	1.41421	+	1.41421i	0.0747435	+	0.0747435i
$359$	−9.89949			−0.522475			−0.261238	−	0.965275i	$-0.584131\pi$
$359$	−9.89949			−0.522475			−0.261238	+	0.965275i	$0.584131\pi$
$360$	−6.36396	+	2.12132i	−0.335410	+	0.111803i
$361$	−1.00000			−0.0526316
$362$	2.82843	−	2.82843i	0.148659	−	0.148659i
$363$		0			0
$364$		−	2.00000i		−	0.104828i
$365$	4.24264	+	12.7279i	0.222070	+	0.666210i
$366$		0			0
$367$	25.0000	+	25.0000i	1.30499	+	1.30499i	0.924984	+	0.380005i	$0.124078\pi$
$367$	25.0000	+	25.0000i	1.30499	+	1.30499i	0.380005	+	0.924984i	$0.375922\pi$
$368$	2.00000	−	2.00000i	0.104257	−	0.104257i
$369$	4.24264			0.220863
$370$	−16.9706	−	8.48528i	−0.882258	−	0.441129i
$371$		−	5.65685i		−	0.293689i
$372$		0			0
$373$	14.1421	+	14.1421i	0.732252	+	0.732252i	0.971065	−	0.238813i	$-0.0767584\pi$
$373$	14.1421	+	14.1421i	0.732252	+	0.732252i	−0.238813	+	0.971065i	$0.576758\pi$
$374$		0			0
$375$		0			0
$376$		−	9.89949i		−	0.510527i
$377$	10.0000	+	10.0000i	0.515026	+	0.515026i
$378$		0			0
$379$			30.0000i			1.54100i	0.637442	+	0.770498i	$0.279993\pi$
$379$			30.0000i			1.54100i	−0.637442	+	0.770498i	$0.720007\pi$
$380$	4.24264	−	8.48528i	0.217643	−	0.435286i
$381$		0			0
$382$	−11.3137	+	11.3137i	−0.578860	+	0.578860i
$383$	−9.00000	+	9.00000i	−0.459879	+	0.459879i	−0.898616	−	0.438737i	$-0.855426\pi$
$383$	−9.00000	+	9.00000i	−0.459879	+	0.459879i	0.438737	+	0.898616i	$0.355426\pi$
$384$		0			0
$385$	−5.36396	+	5.12132i	−0.273373	+	0.261007i
$386$	10.0000			0.508987
$387$	16.9706	−	16.9706i	0.862662	−	0.862662i
$388$	6.00000	−	6.00000i	0.304604	−	0.304604i
$389$			30.0000i			1.52106i	0.649303	+	0.760530i	$0.275061\pi$
$389$			30.0000i			1.52106i	−0.649303	+	0.760530i	$0.724939\pi$
$390$		0			0
$391$		0			0
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$		0			0
$394$		−	12.0000i		−	0.604551i
$395$	−8.48528	−	4.24264i	−0.426941	−	0.213470i
$396$	−9.00000	+	4.24264i	−0.452267	+	0.213201i
$397$	−9.00000	−	9.00000i	−0.451697	−	0.451697i	0.444220	−	0.895918i	$-0.353481\pi$
$397$	−9.00000	−	9.00000i	−0.451697	−	0.451697i	−0.895918	+	0.444220i	$0.853481\pi$
$398$	−15.5563	−	15.5563i	−0.779769	−	0.779769i
$399$		0			0
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	22.0000			1.09863			0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000			1.09863			0.549314	+	0.835616i	$0.314889\pi$
$402$		0			0
$403$		0			0
$404$	−5.65685			−0.281439
$405$	18.0000	+	9.00000i	0.894427	+	0.447214i
$406$		−	7.07107i		−	0.350931i
$407$	−26.4853	−	9.51472i	−1.31283	−	0.471627i
$408$		0			0
$409$	−9.89949			−0.489499			−0.244749	−	0.969586i	$-0.578706\pi$
$409$	−9.89949			−0.489499			−0.244749	+	0.969586i	$0.578706\pi$
$410$	1.00000	+	3.00000i	0.0493865	+	0.148159i
$411$		0			0
$412$	−3.00000	−	3.00000i	−0.147799	−	0.147799i
$413$	2.82843	+	2.82843i	0.139178	+	0.139178i
$414$	−8.48528			−0.417029
$415$	8.48528	+	25.4558i	0.416526	+	1.24958i
$416$	2.00000			0.0980581
$417$		0			0
$418$	4.75736	−	13.2426i	0.232690	−	0.647719i
$419$		−	8.00000i		−	0.390826i	−0.980721	−	0.195413i	$-0.937395\pi$
$419$		−	8.00000i		−	0.390826i	0.980721	−	0.195413i	$-0.0626047\pi$
$420$		0			0
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$	4.00000	+	4.00000i	0.194717	+	0.194717i
$423$	−21.0000	+	21.0000i	−1.02105	+	1.02105i
$424$	5.65685			0.274721
$425$		0			0
$426$		0			0
$427$	2.00000	+	2.00000i	0.0967868	+	0.0967868i
$428$	8.48528	+	8.48528i	0.410152	+	0.410152i
$429$		0			0
$430$	16.0000	+	8.00000i	0.771589	+	0.385794i
$431$			9.89949i			0.476842i	0.971162	+	0.238421i	$0.0766298\pi$
$431$			9.89949i			0.476842i	−0.971162	+	0.238421i	$0.923370\pi$
$432$		0			0
$433$	20.0000	−	20.0000i	0.961139	−	0.961139i	−0.0381340	−	0.999273i	$-0.512141\pi$
$433$	20.0000	−	20.0000i	0.961139	−	0.961139i	0.999273	+	0.0381340i	$0.0121414\pi$
$434$		0			0
$435$		0			0
$436$		−	12.7279i		−	0.609557i
$437$	8.48528	−	8.48528i	0.405906	−	0.405906i
$438$		0			0
$439$	−31.1127			−1.48493			−0.742464	−	0.669886i	$-0.766343\pi$
$439$	−31.1127			−1.48493			−0.742464	+	0.669886i	$0.766343\pi$
$440$	−5.12132	−	5.36396i	−0.244149	−	0.255717i
$441$	3.00000			0.142857
$442$		0			0
$443$	−15.0000	+	15.0000i	−0.712672	+	0.712672i	−0.967093	−	0.254422i	$-0.918115\pi$
$443$	−15.0000	+	15.0000i	−0.712672	+	0.712672i	0.254422	+	0.967093i	$0.418115\pi$
$444$		0			0
$445$	−14.0000	+	28.0000i	−0.663664	+	1.32733i
$446$			9.89949i			0.468755i
$447$		0			0
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$		−	24.0000i		−	1.13263i	−0.824189	−	0.566315i	$-0.808369\pi$
$449$		−	24.0000i		−	1.13263i	0.824189	−	0.566315i	$-0.191631\pi$
$450$	−2.12132	+	14.8492i	−0.100000	+	0.700000i
$451$	2.00000	+	4.24264i	0.0941763	+	0.199778i
$452$	9.00000	+	9.00000i	0.423324	+	0.423324i
$453$		0			0
$454$			22.0000i			1.03251i
$455$	−4.00000	−	2.00000i	−0.187523	−	0.0937614i
$456$		0			0
$457$	−1.41421	+	1.41421i	−0.0661541	+	0.0661541i	−0.739410	−	0.673256i	$-0.764895\pi$
$457$	−1.41421	+	1.41421i	−0.0661541	+	0.0661541i	0.673256	+	0.739410i	$0.264895\pi$
$458$	1.41421	+	1.41421i	0.0660819	+	0.0660819i
$459$		0			0
$460$	−2.00000	−	6.00000i	−0.0932505	−	0.279751i
$461$			2.82843i			0.131733i	0.997828	+	0.0658665i	$0.0209811\pi$
$461$			2.82843i			0.131733i	−0.997828	+	0.0658665i	$0.979019\pi$
$462$		0			0
$463$	−10.0000	+	10.0000i	−0.464739	+	0.464739i	−0.900205	−	0.435466i	$-0.856584\pi$
$463$	−10.0000	+	10.0000i	−0.464739	+	0.464739i	0.435466	+	0.900205i	$0.356584\pi$
$464$	7.07107			0.328266
$465$		0			0
$466$	26.0000			1.20443
$467$	−2.00000	−	2.00000i	−0.0925490	−	0.0925490i	0.659317	−	0.751865i	$-0.270846\pi$
$467$	−2.00000	−	2.00000i	−0.0925490	−	0.0925490i	−0.751865	+	0.659317i	$0.770846\pi$
$468$	−4.24264	−	4.24264i	−0.196116	−	0.196116i
$469$	4.24264			0.195907
$470$	−19.7990	−	9.89949i	−0.913259	−	0.456630i
$471$		0			0
$472$	−2.82843	+	2.82843i	−0.130189	+	0.130189i
$473$	24.9706	+	8.97056i	1.14815	+	0.412467i
$474$		0			0
$475$	−12.7279	−	16.9706i	−0.583997	−	0.778663i
$476$		0			0
$477$	−12.0000	−	12.0000i	−0.549442	−	0.549442i
$478$	−9.00000	+	9.00000i	−0.411650	+	0.411650i
$479$	−8.48528			−0.387702			−0.193851	−	0.981031i	$-0.562098\pi$
$479$	−8.48528			−0.387702			−0.193851	+	0.981031i	$0.562098\pi$
$480$		0			0
$481$		−	16.9706i		−	0.773791i
$482$	−15.0000	−	15.0000i	−0.683231	−	0.683231i
$483$		0			0
$484$	−8.48528	−	7.00000i	−0.385695	−	0.318182i
$485$	−6.00000	−	18.0000i	−0.272446	−	0.817338i
$486$		0			0
$487$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$487$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$488$	−2.00000	+	2.00000i	−0.0905357	+	0.0905357i
$489$		0			0
$490$	0.707107	+	2.12132i	0.0319438	+	0.0958315i
$491$		−	2.82843i		−	0.127645i	−0.997961	−	0.0638226i	$-0.979671\pi$
$491$		−	2.82843i		−	0.127645i	0.997961	−	0.0638226i	$-0.0203292\pi$
$492$		0			0
$493$		0			0
$494$	8.48528			0.381771
$495$	−0.514719	+	22.2426i	−0.0231349	+	0.999732i
$496$		0			0
$497$	5.65685	−	5.65685i	0.253745	−	0.253745i
$498$		0			0
$499$		−	44.0000i		−	1.96971i	−0.173379	−	0.984855i	$-0.555468\pi$
$499$		−	44.0000i		−	1.96971i	0.173379	−	0.984855i	$-0.444532\pi$
$500$	−11.0000	+	2.00000i	−0.491935	+	0.0894427i
$501$		0			0
$502$		0			0
$503$	19.7990	+	19.7990i	0.882793	+	0.882793i	0.993818	−	0.111024i	$-0.0354132\pi$
$503$	19.7990	+	19.7990i	0.882793	+	0.882793i	−0.111024	+	0.993818i	$0.535413\pi$
$504$			3.00000i			0.133631i
$505$	−5.65685	+	11.3137i	−0.251727	+	0.503453i
$506$	−4.00000	−	8.48528i	−0.177822	−	0.377217i
$507$		0			0
$508$	−9.89949	−	9.89949i	−0.439219	−	0.439219i
$509$		0			0		1.00000			$0$
$509$		0			0		−1.00000			$\pi$
$510$		0			0
$511$	6.00000			0.265424
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	11.3137			0.499026
$515$	−9.00000	+	3.00000i	−0.396587	+	0.132196i
$516$		0			0
$517$	−30.8995	−	11.1005i	−1.35896	−	0.488200i
$518$	−6.00000	+	6.00000i	−0.263625	+	0.263625i
$519$		0			0
$520$	2.00000	−	4.00000i	0.0877058	−	0.175412i
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$	−15.0000	−	15.0000i	−0.656532	−	0.656532i
$523$	−9.89949	−	9.89949i	−0.432875	−	0.432875i	0.456730	−	0.889605i	$-0.349020\pi$
$523$	−9.89949	−	9.89949i	−0.432875	−	0.432875i	−0.889605	+	0.456730i	$0.849020\pi$
$524$	1.41421			0.0617802
$525$		0			0
$526$	14.0000			0.610429
$527$		0			0
$528$		0			0
$529$			15.0000i			0.652174i
$530$	5.65685	−	11.3137i	0.245718	−	0.491436i
$531$	12.0000			0.520756
$532$	−3.00000	−	3.00000i	−0.130066	−	0.130066i
$533$	−2.00000	+	2.00000i	−0.0866296	+	0.0866296i
$534$		0			0
$535$	25.4558	−	8.48528i	1.10055	−	0.366851i
$536$			4.24264i			0.183254i
$537$		0			0
$538$	12.7279	+	12.7279i	0.548740	+	0.548740i
$539$	1.41421	+	3.00000i	0.0609145	+	0.129219i
$540$		0			0
$541$			41.0122i			1.76325i	0.471949	+	0.881626i	$0.343551\pi$
$541$			41.0122i			1.76325i	−0.471949	+	0.881626i	$0.656449\pi$
$542$	22.0000	+	22.0000i	0.944981	+	0.944981i
$543$		0			0
$544$		0			0
$545$	−25.4558	−	12.7279i	−1.09041	−	0.545204i
$546$		0			0
$547$	2.82843	−	2.82843i	0.120935	−	0.120935i	−0.644049	−	0.764984i	$-0.722747\pi$
$547$	2.82843	−	2.82843i	0.120935	−	0.120935i	0.764984	+	0.644049i	$0.222747\pi$
$548$	5.00000	−	5.00000i	0.213589	−	0.213589i
$549$	8.48528			0.362143
$550$	−15.8492	+	4.87868i	−0.675814	+	0.208028i
$551$	30.0000			1.27804
$552$		0			0
$553$	−3.00000	+	3.00000i	−0.127573	+	0.127573i
$554$			8.00000i			0.339887i
$555$		0			0
$556$			18.3848i			0.779688i
$557$	−1.41421	+	1.41421i	−0.0599222	+	0.0599222i	−0.736433	−	0.676511i	$-0.763491\pi$
$557$	−1.41421	+	1.41421i	−0.0599222	+	0.0599222i	0.676511	+	0.736433i	$0.263491\pi$
$558$		0			0
$559$			16.0000i			0.676728i
$560$	−2.12132	+	0.707107i	−0.0896421	+	0.0298807i
$561$		0			0
$562$	−20.0000	−	20.0000i	−0.843649	−	0.843649i
$563$	−14.1421	−	14.1421i	−0.596020	−	0.596020i	0.343231	−	0.939251i	$-0.388479\pi$
$563$	−14.1421	−	14.1421i	−0.596020	−	0.596020i	−0.939251	+	0.343231i	$0.888479\pi$
$564$		0			0
$565$	27.0000	−	9.00000i	1.13590	−	0.378633i
$566$	−6.00000			−0.252199
$567$	6.36396	−	6.36396i	0.267261	−	0.267261i
$568$	5.65685	+	5.65685i	0.237356	+	0.237356i
$569$	−28.2843			−1.18574			−0.592869	−	0.805299i	$-0.702005\pi$
$569$	−28.2843			−1.18574			−0.592869	+	0.805299i	$0.702005\pi$
$570$		0			0
$571$		−	33.9411i		−	1.42039i	−0.704004	−	0.710196i	$-0.748606\pi$
$571$		−	33.9411i		−	1.42039i	0.704004	−	0.710196i	$-0.251394\pi$
$572$	2.24264	−	6.24264i	0.0937695	−	0.261018i
$573$		0			0
$574$	1.41421			0.0590281
$575$	−14.0000	−	2.00000i	−0.583840	−	0.0834058i
$576$	−3.00000			−0.125000
$577$	2.00000	+	2.00000i	0.0832611	+	0.0832611i	0.747511	−	0.664250i	$-0.231249\pi$
$577$	2.00000	+	2.00000i	0.0832611	+	0.0832611i	−0.664250	+	0.747511i	$0.731249\pi$
$578$	12.0208	+	12.0208i	0.500000	+	0.500000i
$579$		0			0
$580$	7.07107	−	14.1421i	0.293610	−	0.587220i
$581$	12.0000			0.497844
$582$		0			0
$583$	6.34315	−	17.6569i	0.262706	−	0.731272i
$584$			6.00000i			0.248282i
$585$	−12.7279	+	4.24264i	−0.526235	+	0.175412i
$586$	−30.0000			−1.23929
$587$	14.0000	+	14.0000i	0.577842	+	0.577842i	0.934308	−	0.356466i	$-0.116019\pi$
$587$	14.0000	+	14.0000i	0.577842	+	0.577842i	−0.356466	+	0.934308i	$0.616019\pi$
$588$		0			0
$589$		0			0
$590$	2.82843	+	8.48528i	0.116445	+	0.349334i
$591$		0			0
$592$	−6.00000	−	6.00000i	−0.246598	−	0.246598i
$593$	−24.0416	−	24.0416i	−0.987271	−	0.987271i	0.0126486	−	0.999920i	$-0.495974\pi$
$593$	−24.0416	−	24.0416i	−0.987271	−	0.987271i	−0.999920	+	0.0126486i	$0.995974\pi$
$594$		0			0
$595$		0			0
$596$			9.89949i			0.405499i
$597$		0			0
$598$	4.00000	−	4.00000i	0.163572	−	0.163572i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$			29.6985i			1.21143i	0.795683	+	0.605713i	$0.207112\pi$
$601$			29.6985i			1.21143i	−0.795683	+	0.605713i	$0.792888\pi$
$602$	5.65685	−	5.65685i	0.230556	−	0.230556i
$603$	9.00000	−	9.00000i	0.366508	−	0.366508i
$604$	18.3848			0.748066
$605$	−22.4853	+	9.97056i	−0.914157	+	0.405361i
$606$		0			0
$607$	5.65685	−	5.65685i	0.229605	−	0.229605i	−0.582923	−	0.812527i	$-0.698091\pi$
$607$	5.65685	−	5.65685i	0.229605	−	0.229605i	0.812527	+	0.582923i	$0.198091\pi$
$608$	3.00000	−	3.00000i	0.121666	−	0.121666i
$609$		0			0
$610$	2.00000	+	6.00000i	0.0809776	+	0.242933i
$611$		−	19.7990i		−	0.800981i
$612$		0			0
$613$	7.07107	+	7.07107i	0.285598	+	0.285598i	0.835337	−	0.549739i	$-0.185273\pi$
$613$	7.07107	+	7.07107i	0.285598	+	0.285598i	−0.549739	+	0.835337i	$0.685273\pi$
$614$			26.0000i			1.04927i
$615$		0			0
$616$	−3.00000	+	1.41421i	−0.120873	+	0.0569803i
$617$	−17.0000	−	17.0000i	−0.684394	−	0.684394i	0.276593	−	0.960987i	$-0.410795\pi$
$617$	−17.0000	−	17.0000i	−0.684394	−	0.684394i	−0.960987	+	0.276593i	$0.910795\pi$
$618$		0			0
$619$			12.0000i			0.482321i	0.970485	+	0.241160i	$0.0775280\pi$
$619$			12.0000i			0.482321i	−0.970485	+	0.241160i	$0.922472\pi$
$620$		0			0
$621$		0			0
$622$	−21.2132	+	21.2132i	−0.850572	+	0.850572i
$623$	9.89949	+	9.89949i	0.396615	+	0.396615i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$			16.9706i			0.678280i
$627$		0			0
$628$	7.00000	−	7.00000i	0.279330	−	0.279330i
$629$		0			0
$630$	6.00000	+	3.00000i	0.239046	+	0.119523i
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	−3.00000	−	3.00000i	−0.119334	−	0.119334i
$633$		0			0
$634$	11.3137			0.449325
$635$	−29.6985	+	9.89949i	−1.17855	+	0.392849i
$636$		0			0
$637$	−1.41421	+	1.41421i	−0.0560332	+	0.0560332i
$638$	7.92893	−	22.0711i	0.313909	−	0.873802i
$639$		−	24.0000i		−	0.949425i
$640$	−0.707107	−	2.12132i	−0.0279508	−	0.0838525i
$641$	8.00000			0.315981			0.157991	−	0.987441i	$-0.449498\pi$
$641$	8.00000			0.315981			0.157991	+	0.987441i	$0.449498\pi$
$642$		0			0
$643$	28.0000	−	28.0000i	1.10421	−	1.10421i	0.110316	−	0.993897i	$-0.464814\pi$
$643$	28.0000	−	28.0000i	1.10421	−	1.10421i	0.993897	−	0.110316i	$-0.0351862\pi$
$644$	−2.82843			−0.111456
$645$		0			0
$646$		0			0
$647$	−19.0000	−	19.0000i	−0.746967	−	0.746967i	0.226941	−	0.973908i	$-0.427127\pi$
$647$	−19.0000	−	19.0000i	−0.746967	−	0.746967i	−0.973908	+	0.226941i	$0.927127\pi$
$648$	6.36396	+	6.36396i	0.250000	+	0.250000i
$649$	5.65685	+	12.0000i	0.222051	+	0.471041i
$650$	−6.00000	−	8.00000i	−0.235339	−	0.313786i
$651$		0			0
$652$	−1.00000	−	1.00000i	−0.0391630	−	0.0391630i
$653$	4.00000	−	4.00000i	0.156532	−	0.156532i	−0.624496	−	0.781028i	$-0.714696\pi$
$653$	4.00000	−	4.00000i	0.156532	−	0.156532i	0.781028	+	0.624496i	$0.214696\pi$
$654$		0			0
$655$	1.41421	−	2.82843i	0.0552579	−	0.110516i
$656$			1.41421i			0.0552158i
$657$	12.7279	−	12.7279i	0.496564	−	0.496564i
$658$	−7.00000	+	7.00000i	−0.272888	+	0.272888i
$659$	−31.1127			−1.21198			−0.605989	−	0.795473i	$-0.707223\pi$
$659$	−31.1127			−1.21198			−0.605989	+	0.795473i	$0.707223\pi$
$660$		0			0
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$	2.82843	−	2.82843i	0.109930	−	0.109930i
$663$		0			0
$664$			12.0000i			0.465690i
$665$	−9.00000	+	3.00000i	−0.349005	+	0.116335i
$666$			25.4558i			0.986394i
$667$	14.1421	−	14.1421i	0.547586	−	0.547586i
$668$		0			0
$669$		0			0
$670$	8.48528	+	4.24264i	0.327815	+	0.163908i
$671$	4.00000	+	8.48528i	0.154418	+	0.327571i
$672$		0			0
$673$	15.5563	+	15.5563i	0.599653	+	0.599653i	0.940220	−	0.340567i	$-0.110619\pi$
$673$	15.5563	+	15.5563i	0.599653	+	0.599653i	−0.340567	+	0.940220i	$0.610619\pi$
$674$		−	22.0000i		−	0.847408i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−18.3848	+	18.3848i	−0.706584	+	0.706584i	−0.965815	−	0.259231i	$-0.916531\pi$
$677$	−18.3848	+	18.3848i	−0.706584	+	0.706584i	0.259231	+	0.965815i	$0.416531\pi$
$678$		0			0
$679$	−8.48528			−0.325635
$680$		0			0
$681$		0			0
$682$		0			0
$683$	33.0000	−	33.0000i	1.26271	−	1.26271i	0.312936	−	0.949774i	$-0.398688\pi$
$683$	33.0000	−	33.0000i	1.26271	−	1.26271i	0.949774	−	0.312936i	$-0.101312\pi$
$684$	−12.7279			−0.486664
$685$	−5.00000	−	15.0000i	−0.191040	−	0.573121i
$686$	1.00000			0.0381802
$687$		0			0
$688$	5.65685	+	5.65685i	0.215666	+	0.215666i
$689$	11.3137			0.431018
$690$		0			0
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$	12.7279	−	12.7279i	0.483843	−	0.483843i
$693$	9.36396	+	3.36396i	0.355707	+	0.127786i
$694$		−	4.00000i		−	0.151838i
$695$	36.7696	+	18.3848i	1.39475	+	0.697374i
$696$		0			0
$697$		0			0
$698$	24.0000	−	24.0000i	0.908413	−	0.908413i
$699$		0			0
$700$	−0.707107	+	4.94975i	−0.0267261	+	0.187083i
$701$		−	38.1838i		−	1.44218i	−0.692841	−	0.721090i	$-0.743641\pi$
$701$		−	38.1838i		−	1.44218i	0.692841	−	0.721090i	$-0.256359\pi$
$702$		0			0
$703$	−25.4558	−	25.4558i	−0.960085	−	0.960085i
$704$	−1.41421	−	3.00000i	−0.0533002	−	0.113067i
$705$		0			0
$706$			5.65685i			0.212899i
$707$	4.00000	+	4.00000i	0.150435	+	0.150435i
$708$		0			0
$709$		−	10.0000i		−	0.375558i	−0.982211	−	0.187779i	$-0.939871\pi$
$709$		−	10.0000i		−	0.375558i	0.982211	−	0.187779i	$-0.0601289\pi$
$710$	16.9706	−	5.65685i	0.636894	−	0.212298i
$711$			12.7279i			0.477334i
$712$	−9.89949	+	9.89949i	−0.370999	+	0.370999i
$713$		0			0
$714$		0			0
$715$	−10.2426	−	10.7279i	−0.383053	−	0.401202i
$716$	2.00000			0.0747435
$717$		0			0
$718$	−7.00000	+	7.00000i	−0.261238	+	0.261238i
$719$		−	24.0000i		−	0.895049i	−0.894272	−	0.447524i	$-0.852306\pi$
$719$		−	24.0000i		−	0.895049i	0.894272	−	0.447524i	$-0.147694\pi$
$720$	−3.00000	+	6.00000i	−0.111803	+	0.223607i
$721$			4.24264i			0.158004i
$722$	−0.707107	+	0.707107i	−0.0263158	+	0.0263158i
$723$		0			0
$724$		−	4.00000i		−	0.148659i
$725$	−21.2132	−	28.2843i	−0.787839	−	1.05045i
$726$		0			0
$727$	−31.0000	−	31.0000i	−1.14973	−	1.14973i	−0.986606	−	0.163120i	$-0.947844\pi$
$727$	−31.0000	−	31.0000i	−1.14973	−	1.14973i	−0.163120	−	0.986606i	$-0.552156\pi$
$728$	−1.41421	−	1.41421i	−0.0524142	−	0.0524142i
$729$		−	27.0000i		−	1.00000i
$730$	12.0000	+	6.00000i	0.444140	+	0.222070i
$731$		0			0
$732$		0			0
$733$	9.89949	+	9.89949i	0.365646	+	0.365646i	0.865887	−	0.500240i	$-0.166755\pi$
$733$	9.89949	+	9.89949i	0.365646	+	0.365646i	−0.500240	+	0.865887i	$0.666755\pi$
$734$	35.3553			1.30499
$735$		0			0
$736$		−	2.82843i		−	0.104257i
$737$	13.2426	+	4.75736i	0.487799	+	0.175240i
$738$	3.00000	−	3.00000i	0.110432	−	0.110432i
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	−18.0000	+	6.00000i	−0.661693	+	0.220564i
$741$		0			0
$742$	−4.00000	−	4.00000i	−0.146845	−	0.146845i
$743$	1.41421	+	1.41421i	0.0518825	+	0.0518825i	0.732572	−	0.680690i	$-0.238320\pi$
$743$	1.41421	+	1.41421i	0.0518825	+	0.0518825i	−0.680690	+	0.732572i	$0.738320\pi$
$744$		0			0
$745$	19.7990	+	9.89949i	0.725379	+	0.362689i
$746$	20.0000			0.732252
$747$	25.4558	−	25.4558i	0.931381	−	0.931381i
$748$		0			0
$749$		−	12.0000i		−	0.438470i
$750$		0			0
$751$	4.00000			0.145962			0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000			0.145962			0.0729810	+	0.997333i	$0.476749\pi$
$752$	−7.00000	−	7.00000i	−0.255264	−	0.255264i
$753$		0			0
$754$	14.1421			0.515026
$755$	18.3848	−	36.7696i	0.669091	−	1.33818i
$756$		0			0
$757$	−14.0000	−	14.0000i	−0.508839	−	0.508839i	0.405331	−	0.914170i	$-0.367156\pi$
$757$	−14.0000	−	14.0000i	−0.508839	−	0.508839i	−0.914170	+	0.405331i	$0.867156\pi$
$758$	21.2132	+	21.2132i	0.770498	+	0.770498i
$759$		0			0
$760$	−3.00000	−	9.00000i	−0.108821	−	0.326464i
$761$		−	9.89949i		−	0.358856i	−0.983771	−	0.179428i	$-0.942575\pi$
$761$		−	9.89949i		−	0.358856i	0.983771	−	0.179428i	$-0.0574248\pi$
$762$		0			0
$763$	−9.00000	+	9.00000i	−0.325822	+	0.325822i
$764$			16.0000i			0.578860i
$765$		0			0
$766$			12.7279i			0.459879i
$767$	−5.65685	+	5.65685i	−0.204257	+	0.204257i
$768$		0			0
$769$	43.8406			1.58093			0.790467	−	0.612505i	$-0.209838\pi$
$769$	43.8406			1.58093			0.790467	+	0.612505i	$0.209838\pi$
$770$	−0.171573	+	7.41421i	−0.00618306	+	0.267190i
$771$		0			0
$772$	7.07107	−	7.07107i	0.254493	−	0.254493i
$773$	15.0000	−	15.0000i	0.539513	−	0.539513i	−0.383873	−	0.923386i	$-0.625410\pi$
$773$	15.0000	−	15.0000i	0.539513	−	0.539513i	0.923386	+	0.383873i	$0.125410\pi$
$774$		−	24.0000i		−	0.862662i
$775$		0			0
$776$		−	8.48528i		−	0.304604i
$777$		0			0
$778$	21.2132	+	21.2132i	0.760530	+	0.760530i
$779$			6.00000i			0.214972i
$780$		0			0
$781$	24.0000	−	11.3137i	0.858788	−	0.404836i
$782$		0			0
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	−7.00000	−	21.0000i	−0.249841	−	0.749522i
$786$		0			0
$787$	8.48528	−	8.48528i	0.302468	−	0.302468i	−0.539511	−	0.841979i	$-0.681391\pi$
$787$	8.48528	−	8.48528i	0.302468	−	0.302468i	0.841979	+	0.539511i	$0.181391\pi$
$788$	−8.48528	−	8.48528i	−0.302276	−	0.302276i
$789$		0			0
$790$	−9.00000	+	3.00000i	−0.320206	+	0.106735i
$791$		−	12.7279i		−	0.452553i
$792$	−3.36396	+	9.36396i	−0.119533	+	0.332734i
$793$	−4.00000	+	4.00000i	−0.142044	+	0.142044i
$794$	−12.7279			−0.451697
$795$		0			0
$796$	−22.0000			−0.779769
$797$	−29.0000	−	29.0000i	−1.02723	−	1.02723i	−0.999619	−	0.0276140i	$-0.991209\pi$
$797$	−29.0000	−	29.0000i	−1.02723	−	1.02723i	−0.0276140	−	0.999619i	$-0.508791\pi$
$798$		0			0
$799$		0			0
$800$	−4.94975	−	0.707107i	−0.175000	−	0.0250000i
$801$	42.0000			1.48400
$802$	15.5563	−	15.5563i	0.549314	−	0.549314i
$803$	18.7279	+	6.72792i	0.660894	+	0.237423i
$804$		0			0
$805$	−2.82843	+	5.65685i	−0.0996890	+	0.199378i
$806$		0			0
$807$		0			0
$808$	−4.00000	+	4.00000i	−0.140720	+	0.140720i
$809$	−45.2548			−1.59108			−0.795538	−	0.605904i	$-0.792811\pi$
$809$	−45.2548			−1.59108			−0.795538	+	0.605904i	$0.792811\pi$
$810$	19.0919	−	6.36396i	0.670820	−	0.223607i
$811$			29.6985i			1.04285i	0.853296	+	0.521427i	$0.174600\pi$
$811$			29.6985i			1.04285i	−0.853296	+	0.521427i	$0.825400\pi$
$812$	−5.00000	−	5.00000i	−0.175466	−	0.175466i
$813$		0			0
$814$	−25.4558	+	12.0000i	−0.892227	+	0.420600i
$815$	−3.00000	+	1.00000i	−0.105085	+	0.0350285i
$816$		0			0
$817$	24.0000	+	24.0000i	0.839654	+	0.839654i
$818$	−7.00000	+	7.00000i	−0.244749	+	0.244749i
$819$			6.00000i			0.209657i
$820$	2.82843	+	1.41421i	0.0987730	+	0.0493865i
$821$		−	46.6690i		−	1.62876i	−0.580331	−	0.814380i	$-0.697077\pi$
$821$		−	46.6690i		−	1.62876i	0.580331	−	0.814380i	$-0.302923\pi$
$822$		0			0
$823$	16.0000	−	16.0000i	0.557725	−	0.557725i	−0.370934	−	0.928659i	$-0.620962\pi$
$823$	16.0000	−	16.0000i	0.557725	−	0.557725i	0.928659	+	0.370934i	$0.120962\pi$
$824$	−4.24264			−0.147799
$825$		0			0
$826$	4.00000			0.139178
$827$	16.9706	−	16.9706i	0.590124	−	0.590124i	−0.347541	−	0.937665i	$-0.612983\pi$
$827$	16.9706	−	16.9706i	0.590124	−	0.590124i	0.937665	+	0.347541i	$0.112983\pi$
$828$	−6.00000	+	6.00000i	−0.208514	+	0.208514i
$829$		−	16.0000i		−	0.555703i	−0.960624	−	0.277851i	$-0.910378\pi$
$829$		−	16.0000i		−	0.555703i	0.960624	−	0.277851i	$-0.0896223\pi$
$830$	24.0000	+	12.0000i	0.833052	+	0.416526i
$831$		0			0
$832$	1.41421	−	1.41421i	0.0490290	−	0.0490290i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−6.00000	−	12.7279i	−0.207514	−	0.440204i
$837$		0			0
$838$	−5.65685	−	5.65685i	−0.195413	−	0.195413i
$839$			48.0000i			1.65714i	0.559883	+	0.828572i	$0.310846\pi$
$839$			48.0000i			1.65714i	−0.559883	+	0.828572i	$0.689154\pi$
$840$		0			0
$841$	21.0000			0.724138
$842$	4.24264	−	4.24264i	0.146211	−	0.146211i
$843$		0			0
$844$	5.65685			0.194717
$845$	−9.00000	+	18.0000i	−0.309609	+	0.619219i
$846$			29.6985i			1.02105i
$847$	1.05025	+	10.9497i	0.0360871	+	0.376238i
$848$	4.00000	−	4.00000i	0.137361	−	0.137361i
$849$		0			0
$850$		0			0
$851$	−24.0000			−0.822709
$852$		0			0
$853$	9.89949	+	9.89949i	0.338952	+	0.338952i	0.855973	−	0.517021i	$-0.172959\pi$
$853$	9.89949	+	9.89949i	0.338952	+	0.338952i	−0.517021	+	0.855973i	$0.672959\pi$
$854$	2.82843			0.0967868
$855$	−12.7279	+	25.4558i	−0.435286	+	0.870572i
$856$	12.0000			0.410152
$857$	−26.8701	+	26.8701i	−0.917864	+	0.917864i	−0.996874	−	0.0790101i	$-0.974824\pi$
$857$	−26.8701	+	26.8701i	−0.917864	+	0.917864i	0.0790101	+	0.996874i	$0.474824\pi$
$858$		0			0
$859$		−	20.0000i		−	0.682391i	−0.939992	−	0.341196i	$-0.889168\pi$
$859$		−	20.0000i		−	0.682391i	0.939992	−	0.341196i	$-0.110832\pi$
$860$	16.9706	−	5.65685i	0.578691	−	0.192897i
$861$		0			0
$862$	7.00000	+	7.00000i	0.238421	+	0.238421i
$863$	32.0000	−	32.0000i	1.08929	−	1.08929i	0.0936914	−	0.995601i	$-0.470133\pi$
$863$	32.0000	−	32.0000i	1.08929	−	1.08929i	0.995601	−	0.0936914i	$-0.0298667\pi$
$864$		0			0
$865$	−12.7279	−	38.1838i	−0.432762	−	1.29829i
$866$		−	28.2843i		−	0.961139i
$867$		0			0
$868$		0			0
$869$	−12.7279	+	6.00000i	−0.431765	+	0.203536i
$870$		0			0
$871$			8.48528i			0.287513i
$872$	−9.00000	−	9.00000i	−0.304778	−	0.304778i
$873$	−18.0000	+	18.0000i	−0.609208	+	0.609208i
$874$		−	12.0000i		−	0.405906i
$875$	9.19239	+	6.36396i	0.310759	+	0.215141i
$876$		0			0
$877$	22.6274	−	22.6274i	0.764074	−	0.764074i	−0.212982	−	0.977056i	$-0.568318\pi$
$877$	22.6274	−	22.6274i	0.764074	−	0.764074i	0.977056	+	0.212982i	$0.0683177\pi$
$878$	−22.0000	+	22.0000i	−0.742464	+	0.742464i
$879$		0			0
$880$	−7.41421	−	0.171573i	−0.249933	−	0.00578372i
$881$	22.0000			0.741199			0.370599	−	0.928793i	$-0.379152\pi$
$881$	22.0000			0.741199			0.370599	+	0.928793i	$0.379152\pi$
$882$	2.12132	−	2.12132i	0.0714286	−	0.0714286i
$883$	−3.00000	+	3.00000i	−0.100958	+	0.100958i	−0.755782	−	0.654824i	$-0.772743\pi$
$883$	−3.00000	+	3.00000i	−0.100958	+	0.100958i	0.654824	+	0.755782i	$0.272743\pi$
$884$		0			0
$885$		0			0
$886$			21.2132i			0.712672i
$887$	25.4558	−	25.4558i	0.854724	−	0.854724i	−0.135987	−	0.990711i	$-0.543421\pi$
$887$	25.4558	−	25.4558i	0.854724	−	0.854724i	0.990711	+	0.135987i	$0.0434205\pi$
$888$		0			0
$889$			14.0000i			0.469545i
$890$	9.89949	+	29.6985i	0.331832	+	0.995495i
$891$	27.0000	−	12.7279i	0.904534	−	0.426401i
$892$	7.00000	+	7.00000i	0.234377	+	0.234377i
$893$	−29.6985	−	29.6985i	−0.993822	−	0.993822i
$894$		0			0
$895$	2.00000	−	4.00000i	0.0668526	−	0.133705i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−16.9706	−	16.9706i	−0.566315	−	0.566315i
$899$		0			0
$900$	9.00000	+	12.0000i	0.300000	+	0.400000i
$901$		0			0
$902$	4.41421	+	1.58579i	0.146977	+	0.0528009i
$903$		0			0
$904$	12.7279			0.423324
$905$	−8.00000	−	4.00000i	−0.265929	−	0.132964i
$906$		0			0
$907$	−35.0000	−	35.0000i	−1.16216	−	1.16216i	−0.984003	−	0.178153i	$-0.942988\pi$
$907$	−35.0000	−	35.0000i	−1.16216	−	1.16216i	−0.178153	−	0.984003i	$-0.557012\pi$
$908$	15.5563	+	15.5563i	0.516256	+	0.516256i
$909$	16.9706			0.562878
$910$	−4.24264	+	1.41421i	−0.140642	+	0.0468807i
$911$	−20.0000			−0.662630			−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000			−0.662630			−0.331315	+	0.943520i	$0.607492\pi$
$912$		0			0
$913$	37.4558	+	13.4558i	1.23961	+	0.445323i
$914$			2.00000i			0.0661541i
$915$		0			0
$916$	2.00000			0.0660819
$917$	−1.00000	−	1.00000i	−0.0330229	−	0.0330229i
$918$		0			0
$919$	−38.1838			−1.25957			−0.629783	−	0.776771i	$-0.716856\pi$
$919$	−38.1838			−1.25957			−0.629783	+	0.776771i	$0.716856\pi$
$920$	−5.65685	−	2.82843i	−0.186501	−	0.0932505i
$921$		0			0
$922$	2.00000	+	2.00000i	0.0658665	+	0.0658665i
$923$	11.3137	+	11.3137i	0.372395	+	0.372395i
$924$		0			0
$925$	−6.00000	+	42.0000i	−0.197279	+	1.38095i
$926$			14.1421i			0.464739i
$927$	9.00000	+	9.00000i	0.295599	+	0.295599i
$928$	5.00000	−	5.00000i	0.164133	−	0.164133i
$929$		−	6.00000i		−	0.196854i	−0.995144	−	0.0984268i	$-0.968619\pi$
$929$		−	6.00000i		−	0.196854i	0.995144	−	0.0984268i	$-0.0313810\pi$
$930$		0			0
$931$			4.24264i			0.139047i
$932$	18.3848	−	18.3848i	0.602213	−	0.602213i
$933$		0			0
$934$	−2.82843			−0.0925490
$935$		0			0
$936$	−6.00000			−0.196116
$937$	−31.1127	+	31.1127i	−1.01641	+	1.01641i	−0.0165444	+	0.999863i	$0.505266\pi$
$937$	−31.1127	+	31.1127i	−1.01641	+	1.01641i	−0.999863	+	0.0165444i	$0.994734\pi$
$938$	3.00000	−	3.00000i	0.0979535	−	0.0979535i
$939$		0			0
$940$	−21.0000	+	7.00000i	−0.684944	+	0.228315i
$941$			39.5980i			1.29086i	0.763821	+	0.645429i	$0.223321\pi$
$941$			39.5980i			1.29086i	−0.763821	+	0.645429i	$0.776679\pi$
$942$		0			0
$943$	2.82843	+	2.82843i	0.0921063	+	0.0921063i
$944$			4.00000i			0.130189i
$945$		0			0
$946$	24.0000	−	11.3137i	0.780307	−	0.367840i
$947$	39.0000	+	39.0000i	1.26733	+	1.26733i	0.947462	+	0.319867i	$0.103638\pi$
$947$	39.0000	+	39.0000i	1.26733	+	1.26733i	0.319867	+	0.947462i	$0.396362\pi$
$948$		0			0
$949$			12.0000i			0.389536i
$950$	−21.0000	−	3.00000i	−0.681330	−	0.0973329i
$951$		0			0
$952$		0			0
$953$	9.89949	+	9.89949i	0.320676	+	0.320676i	0.849026	−	0.528350i	$-0.177189\pi$
$953$	9.89949	+	9.89949i	0.320676	+	0.320676i	−0.528350	+	0.849026i	$0.677189\pi$
$954$	−16.9706			−0.549442
$955$	32.0000	+	16.0000i	1.03550	+	0.517748i
$956$			12.7279i			0.411650i
$957$		0			0
$958$	−6.00000	+	6.00000i	−0.193851	+	0.193851i
$959$	−7.07107			−0.228337
$960$		0			0
$961$	−31.0000			−1.00000
$962$	−12.0000	−	12.0000i	−0.386896	−	0.386896i
$963$	−25.4558	−	25.4558i	−0.820303	−	0.820303i
$964$	−21.2132			−0.683231
$965$	−7.07107	−	21.2132i	−0.227626	−	0.682877i
$966$		0			0
$967$	12.7279	−	12.7279i	0.409302	−	0.409302i	−0.472193	−	0.881495i	$-0.656537\pi$
$967$	12.7279	−	12.7279i	0.409302	−	0.409302i	0.881495	+	0.472193i	$0.156537\pi$
$968$	−10.9497	+	1.05025i	−0.351938	+	0.0337564i
$969$		0			0
$970$	−16.9706	−	8.48528i	−0.544892	−	0.272446i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$		0			0
$973$	13.0000	−	13.0000i	0.416761	−	0.416761i
$974$		0			0
$975$		0			0
$976$			2.82843i			0.0905357i
$977$	−15.0000	−	15.0000i	−0.479893	−	0.479893i	0.425205	−	0.905097i	$-0.360202\pi$
$977$	−15.0000	−	15.0000i	−0.479893	−	0.479893i	−0.905097	+	0.425205i	$0.860202\pi$
$978$		0			0
$979$	19.7990	+	42.0000i	0.632778	+	1.34233i
$980$	2.00000	+	1.00000i	0.0638877	+	0.0319438i
$981$			38.1838i			1.21911i
$982$	−2.00000	−	2.00000i	−0.0638226	−	0.0638226i
$983$	−23.0000	+	23.0000i	−0.733586	+	0.733586i	−0.971328	−	0.237742i	$-0.923593\pi$
$983$	−23.0000	+	23.0000i	−0.733586	+	0.733586i	0.237742	+	0.971328i	$0.423593\pi$
$984$		0			0
$985$	−25.4558	+	8.48528i	−0.811091	+	0.270364i
$986$		0			0
$987$		0			0
$988$	6.00000	−	6.00000i	0.190885	−	0.190885i
$989$	22.6274			0.719510
$990$	15.3640	+	16.0919i	0.488299	+	0.511434i
$991$	−28.0000			−0.889449			−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000			−0.889449			−0.444725	+	0.895667i	$0.646698\pi$
$992$		0			0
$993$		0			0
$994$		−	8.00000i		−	0.253745i
$995$	−22.0000	+	44.0000i	−0.697447	+	1.39489i
$996$		0			0
$997$	7.07107	−	7.07107i	0.223943	−	0.223943i	−0.586214	−	0.810157i	$-0.699382\pi$
$997$	7.07107	−	7.07107i	0.223943	−	0.223943i	0.810157	+	0.586214i	$0.199382\pi$
$998$	−31.1127	−	31.1127i	−0.984855	−	0.984855i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.a.197.2	yes	4
5.3	odd	4	inner	770.2.m.a.43.1	✓	4
11.10	odd	2	inner	770.2.m.a.197.1	yes	4
55.43	even	4	inner	770.2.m.a.43.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.a.43.1	✓	4	5.3	odd	4	inner
770.2.m.a.43.2	yes	4	55.43	even	4	inner
770.2.m.a.197.1	yes	4	11.10	odd	2	inner
770.2.m.a.197.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.00000 - 1.00000i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +(-2.12132 + 0.707107i) q^{10} +(-3.00000 + 1.41421i) q^{11} +(-1.41421 - 1.41421i) q^{13} +1.00000i q^{14} -1.00000 q^{16} +(2.12132 + 2.12132i) q^{18} -4.24264 q^{19} +(-1.00000 + 2.00000i) q^{20} +(-1.12132 + 3.12132i) q^{22} +(-2.00000 + 2.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} -2.00000 q^{26} +(0.707107 + 0.707107i) q^{28} -7.07107 q^{29} +(-0.707107 + 0.707107i) q^{32} +(2.12132 - 0.707107i) q^{35} +3.00000 q^{36} +(6.00000 + 6.00000i) q^{37} +(-3.00000 + 3.00000i) q^{38} +(0.707107 + 2.12132i) q^{40} -1.41421i q^{41} +(-5.65685 - 5.65685i) q^{43} +(1.41421 + 3.00000i) q^{44} +(3.00000 - 6.00000i) q^{45} +2.82843i q^{46} +(7.00000 + 7.00000i) q^{47} -1.00000i q^{49} +(4.94975 + 0.707107i) q^{50} +(-1.41421 + 1.41421i) q^{52} +(-4.00000 + 4.00000i) q^{53} +(7.41421 + 0.171573i) q^{55} +1.00000 q^{56} +(-5.00000 + 5.00000i) q^{58} -4.00000i q^{59} -2.82843i q^{61} +(-2.12132 - 2.12132i) q^{63} +1.00000i q^{64} +(1.41421 + 4.24264i) q^{65} +(-3.00000 - 3.00000i) q^{67} +(1.00000 - 2.00000i) q^{70} -8.00000 q^{71} +(2.12132 - 2.12132i) q^{72} +(-4.24264 - 4.24264i) q^{73} +8.48528 q^{74} +4.24264i q^{76} +(1.12132 - 3.12132i) q^{77} +4.24264 q^{79} +(2.00000 + 1.00000i) q^{80} -9.00000 q^{81} +(-1.00000 - 1.00000i) q^{82} +(-8.48528 - 8.48528i) q^{83} -8.00000 q^{86} +(3.12132 + 1.12132i) q^{88} -14.0000i q^{89} +(-2.12132 - 6.36396i) q^{90} +2.00000 q^{91} +(2.00000 + 2.00000i) q^{92} +9.89949 q^{94} +(8.48528 + 4.24264i) q^{95} +(6.00000 + 6.00000i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-4.24264 - 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{5}+O(q^{10}) \) 4 * q - 8 * q^5	\( 4 q - 8 q^{5} - 12 q^{11} - 4 q^{16} - 4 q^{20} + 4 q^{22} - 8 q^{23} + 12 q^{25} - 8 q^{26} + 12 q^{36} + 24 q^{37} - 12 q^{38} + 12 q^{45} + 28 q^{47} - 16 q^{53} + 24 q^{55} + 4 q^{56} - 20 q^{58} - 12 q^{67} + 4 q^{70} - 32 q^{71} - 4 q^{77} + 8 q^{80} - 36 q^{81} - 4 q^{82} - 32 q^{86} + 4 q^{88} + 8 q^{91} + 8 q^{92} + 24 q^{97}+O(q^{100}) \) 4 * q - 8 * q^5 - 12 * q^11 - 4 * q^16 - 4 * q^20 + 4 * q^22 - 8 * q^23 + 12 * q^25 - 8 * q^26 + 12 * q^36 + 24 * q^37 - 12 * q^38 + 12 * q^45 + 28 * q^47 - 16 * q^53 + 24 * q^55 + 4 * q^56 - 20 * q^58 - 12 * q^67 + 4 * q^70 - 32 * q^71 - 4 * q^77 + 8 * q^80 - 36 * q^81 - 4 * q^82 - 32 * q^86 + 4 * q^88 + 8 * q^91 + 8 * q^92 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more