LMFDB - Embedded newform 804.2.c.a.671.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.4
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	804.671
Dual form			804.2.c.a.671.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(1.41421 + 1.00000i) q^{3} -2.00000 q^{4} -1.41421i q^{5} +(-1.41421 + 2.00000i) q^{6} -2.00000i q^{7} -2.82843i q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(1.41421 + 1.00000i) q^{3} -2.00000 q^{4} -1.41421i q^{5} +(-1.41421 + 2.00000i) q^{6} -2.00000i q^{7} -2.82843i q^{8} +(1.00000 + 2.82843i) q^{9} +2.00000 q^{10} +5.65685 q^{11} +(-2.82843 - 2.00000i) q^{12} +2.00000 q^{13} +2.82843 q^{14} +(1.41421 - 2.00000i) q^{15} +4.00000 q^{16} -5.65685i q^{17} +(-4.00000 + 1.41421i) q^{18} -4.00000i q^{19} +2.82843i q^{20} +(2.00000 - 2.82843i) q^{21} +8.00000i q^{22} -7.07107 q^{23} +(2.82843 - 4.00000i) q^{24} +3.00000 q^{25} +2.82843i q^{26} +(-1.41421 + 5.00000i) q^{27} +4.00000i q^{28} +5.65685i q^{29} +(2.82843 + 2.00000i) q^{30} +5.65685i q^{32} +(8.00000 + 5.65685i) q^{33} +8.00000 q^{34} -2.82843 q^{35} +(-2.00000 - 5.65685i) q^{36} +8.00000 q^{37} +5.65685 q^{38} +(2.82843 + 2.00000i) q^{39} -4.00000 q^{40} +1.41421i q^{41} +(4.00000 + 2.82843i) q^{42} +4.00000i q^{43} -11.3137 q^{44} +(4.00000 - 1.41421i) q^{45} -10.0000i q^{46} -7.07107 q^{47} +(5.65685 + 4.00000i) q^{48} +3.00000 q^{49} +4.24264i q^{50} +(5.65685 - 8.00000i) q^{51} -4.00000 q^{52} +12.7279i q^{53} +(-7.07107 - 2.00000i) q^{54} -8.00000i q^{55} -5.65685 q^{56} +(4.00000 - 5.65685i) q^{57} -8.00000 q^{58} -1.41421 q^{59} +(-2.82843 + 4.00000i) q^{60} -6.00000 q^{61} +(5.65685 - 2.00000i) q^{63} -8.00000 q^{64} -2.82843i q^{65} +(-8.00000 + 11.3137i) q^{66} -1.00000i q^{67} +11.3137i q^{68} +(-10.0000 - 7.07107i) q^{69} -4.00000i q^{70} -15.5563 q^{71} +(8.00000 - 2.82843i) q^{72} +10.0000 q^{73} +11.3137i q^{74} +(4.24264 + 3.00000i) q^{75} +8.00000i q^{76} -11.3137i q^{77} +(-2.82843 + 4.00000i) q^{78} -8.00000i q^{79} -5.65685i q^{80} +(-7.00000 + 5.65685i) q^{81} -2.00000 q^{82} +15.5563 q^{83} +(-4.00000 + 5.65685i) q^{84} -8.00000 q^{85} -5.65685 q^{86} +(-5.65685 + 8.00000i) q^{87} -16.0000i q^{88} -16.9706i q^{89} +(2.00000 + 5.65685i) q^{90} -4.00000i q^{91} +14.1421 q^{92} -10.0000i q^{94} -5.65685 q^{95} +(-5.65685 + 8.00000i) q^{96} -6.00000 q^{97} +4.24264i q^{98} +(5.65685 + 16.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} + 4 q^{9}+O(q^{10}) $ 4 * q - 8 * q^4 + 4 * q^9	$ 4 q - 8 q^{4} + 4 q^{9} + 8 q^{10} + 8 q^{13} + 16 q^{16} - 16 q^{18} + 8 q^{21} + 12 q^{25} + 32 q^{33} + 32 q^{34} - 8 q^{36} + 32 q^{37} - 16 q^{40} + 16 q^{42} + 16 q^{45} + 12 q^{49} - 16 q^{52} + 16 q^{57} - 32 q^{58} - 24 q^{61} - 32 q^{64} - 32 q^{66} - 40 q^{69} + 32 q^{72} + 40 q^{73} - 28 q^{81} - 8 q^{82} - 16 q^{84} - 32 q^{85} + 8 q^{90} - 24 q^{97}+O(q^{100}) $ 4 * q - 8 * q^4 + 4 * q^9 + 8 * q^10 + 8 * q^13 + 16 * q^16 - 16 * q^18 + 8 * q^21 + 12 * q^25 + 32 * q^33 + 32 * q^34 - 8 * q^36 + 32 * q^37 - 16 * q^40 + 16 * q^42 + 16 * q^45 + 12 * q^49 - 16 * q^52 + 16 * q^57 - 32 * q^58 - 24 * q^61 - 32 * q^64 - 32 * q^66 - 40 * q^69 + 32 * q^72 + 40 * q^73 - 28 * q^81 - 8 * q^82 - 16 * q^84 - 32 * q^85 + 8 * q^90 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			1.41421i			1.00000i
$2$			1.41421i			1.00000i
$3$	1.41421	+	1.00000i	0.816497	+	0.577350i
$3$	1.41421	+	1.00000i	0.816497	+	0.577350i
$4$	−2.00000			−1.00000
$5$		−	1.41421i		−	0.632456i	−0.948683	−	0.316228i	$-0.897584\pi$
$5$		−	1.41421i		−	0.632456i	0.948683	−	0.316228i	$-0.102416\pi$
$6$	−1.41421	+	2.00000i	−0.577350	+	0.816497i
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$		−	2.82843i		−	1.00000i
$9$	1.00000	+	2.82843i	0.333333	+	0.942809i
$10$	2.00000			0.632456
$11$	5.65685			1.70561			0.852803	−	0.522233i	$-0.174901\pi$
$11$	5.65685			1.70561			0.852803	+	0.522233i	$0.174901\pi$
$12$	−2.82843	−	2.00000i	−0.816497	−	0.577350i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$	2.82843			0.755929
$15$	1.41421	−	2.00000i	0.365148	−	0.516398i
$16$	4.00000			1.00000
$17$		−	5.65685i		−	1.37199i	−0.727607	−	0.685994i	$-0.759367\pi$
$17$		−	5.65685i		−	1.37199i	0.727607	−	0.685994i	$-0.240633\pi$
$18$	−4.00000	+	1.41421i	−0.942809	+	0.333333i
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$			2.82843i			0.632456i
$21$	2.00000	−	2.82843i	0.436436	−	0.617213i
$22$			8.00000i			1.70561i
$23$	−7.07107			−1.47442			−0.737210	−	0.675664i	$-0.763857\pi$
$23$	−7.07107			−1.47442			−0.737210	+	0.675664i	$0.763857\pi$
$24$	2.82843	−	4.00000i	0.577350	−	0.816497i
$25$	3.00000			0.600000
$26$			2.82843i			0.554700i
$27$	−1.41421	+	5.00000i	−0.272166	+	0.962250i
$28$			4.00000i			0.755929i
$29$			5.65685i			1.05045i	0.850963	+	0.525226i	$0.176019\pi$
$29$			5.65685i			1.05045i	−0.850963	+	0.525226i	$0.823981\pi$
$30$	2.82843	+	2.00000i	0.516398	+	0.365148i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$			5.65685i			1.00000i
$33$	8.00000	+	5.65685i	1.39262	+	0.984732i
$34$	8.00000			1.37199
$35$	−2.82843			−0.478091
$36$	−2.00000	−	5.65685i	−0.333333	−	0.942809i
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	5.65685			0.917663
$39$	2.82843	+	2.00000i	0.452911	+	0.320256i
$40$	−4.00000			−0.632456
$41$			1.41421i			0.220863i	0.993884	+	0.110432i	$0.0352233\pi$
$41$			1.41421i			0.220863i	−0.993884	+	0.110432i	$0.964777\pi$
$42$	4.00000	+	2.82843i	0.617213	+	0.436436i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	−11.3137			−1.70561
$45$	4.00000	−	1.41421i	0.596285	−	0.210819i
$46$		−	10.0000i		−	1.47442i
$47$	−7.07107			−1.03142			−0.515711	−	0.856763i	$-0.672472\pi$
$47$	−7.07107			−1.03142			−0.515711	+	0.856763i	$0.672472\pi$
$48$	5.65685	+	4.00000i	0.816497	+	0.577350i
$49$	3.00000			0.428571
$50$			4.24264i			0.600000i
$51$	5.65685	−	8.00000i	0.792118	−	1.12022i
$52$	−4.00000			−0.554700
$53$			12.7279i			1.74831i	0.485643	+	0.874157i	$0.338586\pi$
$53$			12.7279i			1.74831i	−0.485643	+	0.874157i	$0.661414\pi$
$54$	−7.07107	−	2.00000i	−0.962250	−	0.272166i
$55$		−	8.00000i		−	1.07872i
$56$	−5.65685			−0.755929
$57$	4.00000	−	5.65685i	0.529813	−	0.749269i
$58$	−8.00000			−1.05045
$59$	−1.41421			−0.184115			−0.0920575	−	0.995754i	$-0.529344\pi$
$59$	−1.41421			−0.184115			−0.0920575	+	0.995754i	$0.529344\pi$
$60$	−2.82843	+	4.00000i	−0.365148	+	0.516398i
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$		0			0
$63$	5.65685	−	2.00000i	0.712697	−	0.251976i
$64$	−8.00000			−1.00000
$65$		−	2.82843i		−	0.350823i
$66$	−8.00000	+	11.3137i	−0.984732	+	1.39262i
$67$		−	1.00000i		−	0.122169i
$67$		−	1.00000i		−	0.122169i
$68$			11.3137i			1.37199i
$69$	−10.0000	−	7.07107i	−1.20386	−	0.851257i
$70$		−	4.00000i		−	0.478091i
$71$	−15.5563			−1.84620			−0.923099	−	0.384561i	$-0.874353\pi$
$71$	−15.5563			−1.84620			−0.923099	+	0.384561i	$0.874353\pi$
$72$	8.00000	−	2.82843i	0.942809	−	0.333333i
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$			11.3137i			1.31519i
$75$	4.24264	+	3.00000i	0.489898	+	0.346410i
$76$			8.00000i			0.917663i
$77$		−	11.3137i		−	1.28932i
$78$	−2.82843	+	4.00000i	−0.320256	+	0.452911i
$79$		−	8.00000i		−	0.900070i	−0.893011	−	0.450035i	$-0.851411\pi$
$79$		−	8.00000i		−	0.900070i	0.893011	−	0.450035i	$-0.148589\pi$
$80$		−	5.65685i		−	0.632456i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	−2.00000			−0.220863
$83$	15.5563			1.70753			0.853766	−	0.520658i	$-0.174313\pi$
$83$	15.5563			1.70753			0.853766	+	0.520658i	$0.174313\pi$
$84$	−4.00000	+	5.65685i	−0.436436	+	0.617213i
$85$	−8.00000			−0.867722
$86$	−5.65685			−0.609994
$87$	−5.65685	+	8.00000i	−0.606478	+	0.857690i
$88$		−	16.0000i		−	1.70561i
$89$		−	16.9706i		−	1.79888i	−0.437048	−	0.899438i	$-0.643976\pi$
$89$		−	16.9706i		−	1.79888i	0.437048	−	0.899438i	$-0.356024\pi$
$90$	2.00000	+	5.65685i	0.210819	+	0.596285i
$91$		−	4.00000i		−	0.419314i
$92$	14.1421			1.47442
$93$		0			0
$94$		−	10.0000i		−	1.03142i
$95$	−5.65685			−0.580381
$96$	−5.65685	+	8.00000i	−0.577350	+	0.816497i
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$			4.24264i			0.428571i
$99$	5.65685	+	16.0000i	0.568535	+	1.60806i
$100$	−6.00000			−0.600000
$101$		−	7.07107i		−	0.703598i	−0.936076	−	0.351799i	$-0.885570\pi$
$101$		−	7.07107i		−	0.703598i	0.936076	−	0.351799i	$-0.114430\pi$
$102$	11.3137	+	8.00000i	1.12022	+	0.792118i
$103$		−	4.00000i		−	0.394132i	−0.980390	−	0.197066i	$-0.936859\pi$
$103$		−	4.00000i		−	0.394132i	0.980390	−	0.197066i	$-0.0631413\pi$
$104$		−	5.65685i		−	0.554700i
$105$	−4.00000	−	2.82843i	−0.390360	−	0.276026i
$106$	−18.0000			−1.74831
$107$	−12.7279			−1.23045			−0.615227	−	0.788350i	$-0.710936\pi$
$107$	−12.7279			−1.23045			−0.615227	+	0.788350i	$0.710936\pi$
$108$	2.82843	−	10.0000i	0.272166	−	0.962250i
$109$	6.00000			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$110$	11.3137			1.07872
$111$	11.3137	+	8.00000i	1.07385	+	0.759326i
$112$		−	8.00000i		−	0.755929i
$113$			12.7279i			1.19734i	0.800995	+	0.598671i	$0.204304\pi$
$113$			12.7279i			1.19734i	−0.800995	+	0.598671i	$0.795696\pi$
$114$	8.00000	+	5.65685i	0.749269	+	0.529813i
$115$			10.0000i			0.932505i
$116$		−	11.3137i		−	1.05045i
$117$	2.00000	+	5.65685i	0.184900	+	0.522976i
$118$		−	2.00000i		−	0.184115i
$119$	−11.3137			−1.03713
$120$	−5.65685	−	4.00000i	−0.516398	−	0.365148i
$121$	21.0000			1.90909
$122$		−	8.48528i		−	0.768221i
$123$	−1.41421	+	2.00000i	−0.127515	+	0.180334i
$124$		0			0
$125$		−	11.3137i		−	1.01193i
$126$	2.82843	+	8.00000i	0.251976	+	0.712697i
$127$			16.0000i			1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$		−	11.3137i		−	1.00000i
$129$	−4.00000	+	5.65685i	−0.352180	+	0.498058i
$130$	4.00000			0.350823
$131$	7.07107			0.617802			0.308901	−	0.951094i	$-0.400039\pi$
$131$	7.07107			0.617802			0.308901	+	0.951094i	$0.400039\pi$
$132$	−16.0000	−	11.3137i	−1.39262	−	0.984732i
$133$	−8.00000			−0.693688
$134$	1.41421			0.122169
$135$	7.07107	+	2.00000i	0.608581	+	0.172133i
$136$	−16.0000			−1.37199
$137$		−	7.07107i		−	0.604122i	−0.953289	−	0.302061i	$-0.902325\pi$
$137$		−	7.07107i		−	0.604122i	0.953289	−	0.302061i	$-0.0976746\pi$
$138$	10.0000	−	14.1421i	0.851257	−	1.20386i
$139$			2.00000i			0.169638i	0.996396	+	0.0848189i	$0.0270312\pi$
$139$			2.00000i			0.169638i	−0.996396	+	0.0848189i	$0.972969\pi$
$140$	5.65685			0.478091
$141$	−10.0000	−	7.07107i	−0.842152	−	0.595491i
$142$		−	22.0000i		−	1.84620i
$143$	11.3137			0.946100
$144$	4.00000	+	11.3137i	0.333333	+	0.942809i
$145$	8.00000			0.664364
$146$			14.1421i			1.17041i
$147$	4.24264	+	3.00000i	0.349927	+	0.247436i
$148$	−16.0000			−1.31519
$149$			2.82843i			0.231714i	0.993266	+	0.115857i	$0.0369614\pi$
$149$			2.82843i			0.231714i	−0.993266	+	0.115857i	$0.963039\pi$
$150$	−4.24264	+	6.00000i	−0.346410	+	0.489898i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$	−11.3137			−0.917663
$153$	16.0000	−	5.65685i	1.29352	−	0.457330i
$154$	16.0000			1.28932
$155$		0			0
$156$	−5.65685	−	4.00000i	−0.452911	−	0.320256i
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$	11.3137			0.900070
$159$	−12.7279	+	18.0000i	−1.00939	+	1.42749i
$160$	8.00000			0.632456
$161$			14.1421i			1.11456i
$162$	−8.00000	−	9.89949i	−0.628539	−	0.777778i
$163$		−	8.00000i		−	0.626608i	−0.949653	−	0.313304i	$-0.898564\pi$
$163$		−	8.00000i		−	0.626608i	0.949653	−	0.313304i	$-0.101436\pi$
$164$		−	2.82843i		−	0.220863i
$165$	8.00000	−	11.3137i	0.622799	−	0.880771i
$166$			22.0000i			1.70753i
$167$	−4.24264			−0.328305			−0.164153	−	0.986435i	$-0.552489\pi$
$167$	−4.24264			−0.328305			−0.164153	+	0.986435i	$0.552489\pi$
$168$	−8.00000	−	5.65685i	−0.617213	−	0.436436i
$169$	−9.00000			−0.692308
$170$		−	11.3137i		−	0.867722i
$171$	11.3137	−	4.00000i	0.865181	−	0.305888i
$172$		−	8.00000i		−	0.609994i
$173$			22.6274i			1.72033i	0.510015	+	0.860165i	$0.329640\pi$
$173$			22.6274i			1.72033i	−0.510015	+	0.860165i	$0.670360\pi$
$174$	−11.3137	−	8.00000i	−0.857690	−	0.606478i
$175$		−	6.00000i		−	0.453557i
$176$	22.6274			1.70561
$177$	−2.00000	−	1.41421i	−0.150329	−	0.106299i
$178$	24.0000			1.79888
$179$	−25.4558			−1.90266			−0.951330	−	0.308175i	$-0.900282\pi$
$179$	−25.4558			−1.90266			−0.951330	+	0.308175i	$0.900282\pi$
$180$	−8.00000	+	2.82843i	−0.596285	+	0.210819i
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	5.65685			0.419314
$183$	−8.48528	−	6.00000i	−0.627250	−	0.443533i
$184$			20.0000i			1.47442i
$185$		−	11.3137i		−	0.831800i
$186$		0			0
$187$		−	32.0000i		−	2.34007i
$188$	14.1421			1.03142
$189$	10.0000	+	2.82843i	0.727393	+	0.205738i
$190$		−	8.00000i		−	0.580381i
$191$	8.48528			0.613973			0.306987	−	0.951714i	$-0.400679\pi$
$191$	8.48528			0.613973			0.306987	+	0.951714i	$0.400679\pi$
$192$	−11.3137	−	8.00000i	−0.816497	−	0.577350i
$193$	−2.00000			−0.143963			−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000			−0.143963			−0.0719816	+	0.997406i	$0.522932\pi$
$194$		−	8.48528i		−	0.609208i
$195$	2.82843	−	4.00000i	0.202548	−	0.286446i
$196$	−6.00000			−0.428571
$197$			7.07107i			0.503793i	0.967754	+	0.251896i	$0.0810542\pi$
$197$			7.07107i			0.503793i	−0.967754	+	0.251896i	$0.918946\pi$
$198$	−22.6274	+	8.00000i	−1.60806	+	0.568535i
$199$			4.00000i			0.283552i	0.989899	+	0.141776i	$0.0452813\pi$
$199$			4.00000i			0.283552i	−0.989899	+	0.141776i	$0.954719\pi$
$200$		−	8.48528i		−	0.600000i
$201$	1.00000	−	1.41421i	0.0705346	−	0.0997509i
$202$	10.0000			0.703598
$203$	11.3137			0.794067
$204$	−11.3137	+	16.0000i	−0.792118	+	1.12022i
$205$	2.00000			0.139686
$206$	5.65685			0.394132
$207$	−7.07107	−	20.0000i	−0.491473	−	1.39010i
$208$	8.00000			0.554700
$209$		−	22.6274i		−	1.56517i
$210$	4.00000	−	5.65685i	0.276026	−	0.390360i
$211$			4.00000i			0.275371i	0.990476	+	0.137686i	$0.0439664\pi$
$211$			4.00000i			0.275371i	−0.990476	+	0.137686i	$0.956034\pi$
$212$		−	25.4558i		−	1.74831i
$213$	−22.0000	−	15.5563i	−1.50742	−	1.06590i
$214$		−	18.0000i		−	1.23045i
$215$	5.65685			0.385794
$216$	14.1421	+	4.00000i	0.962250	+	0.272166i
$217$		0			0
$218$			8.48528i			0.574696i
$219$	14.1421	+	10.0000i	0.955637	+	0.675737i
$220$			16.0000i			1.07872i
$221$		−	11.3137i		−	0.761042i
$222$	−11.3137	+	16.0000i	−0.759326	+	1.07385i
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$	11.3137			0.755929
$225$	3.00000	+	8.48528i	0.200000	+	0.565685i
$226$	−18.0000			−1.19734
$227$	−7.07107			−0.469323			−0.234662	−	0.972077i	$-0.575398\pi$
$227$	−7.07107			−0.469323			−0.234662	+	0.972077i	$0.575398\pi$
$228$	−8.00000	+	11.3137i	−0.529813	+	0.749269i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	−14.1421			−0.932505
$231$	11.3137	−	16.0000i	0.744387	−	1.05272i
$232$	16.0000			1.05045
$233$			18.3848i			1.20443i	0.798335	+	0.602213i	$0.205714\pi$
$233$			18.3848i			1.20443i	−0.798335	+	0.602213i	$0.794286\pi$
$234$	−8.00000	+	2.82843i	−0.522976	+	0.184900i
$235$			10.0000i			0.652328i
$236$	2.82843			0.184115
$237$	8.00000	−	11.3137i	0.519656	−	0.734904i
$238$		−	16.0000i		−	1.03713i
$239$	−8.48528			−0.548867			−0.274434	−	0.961606i	$-0.588490\pi$
$239$	−8.48528			−0.548867			−0.274434	+	0.961606i	$0.588490\pi$
$240$	5.65685	−	8.00000i	0.365148	−	0.516398i
$241$	−16.0000			−1.03065			−0.515325	−	0.856995i	$-0.672329\pi$
$241$	−16.0000			−1.03065			−0.515325	+	0.856995i	$0.672329\pi$
$242$			29.6985i			1.90909i
$243$	−15.5563	+	1.00000i	−0.997940	+	0.0641500i
$244$	12.0000			0.768221
$245$		−	4.24264i		−	0.271052i
$246$	−2.82843	−	2.00000i	−0.180334	−	0.127515i
$247$		−	8.00000i		−	0.509028i
$248$		0			0
$249$	22.0000	+	15.5563i	1.39419	+	0.985844i
$250$	16.0000			1.01193
$251$	2.82843			0.178529			0.0892644	−	0.996008i	$-0.471548\pi$
$251$	2.82843			0.178529			0.0892644	+	0.996008i	$0.471548\pi$
$252$	−11.3137	+	4.00000i	−0.712697	+	0.251976i
$253$	−40.0000			−2.51478
$254$	−22.6274			−1.41977
$255$	−11.3137	−	8.00000i	−0.708492	−	0.500979i
$256$	16.0000			1.00000
$257$			16.9706i			1.05859i	0.848436	+	0.529297i	$0.177544\pi$
$257$			16.9706i			1.05859i	−0.848436	+	0.529297i	$0.822456\pi$
$258$	−8.00000	−	5.65685i	−0.498058	−	0.352180i
$259$		−	16.0000i		−	0.994192i
$260$			5.65685i			0.350823i
$261$	−16.0000	+	5.65685i	−0.990375	+	0.350150i
$262$			10.0000i			0.617802i
$263$	1.41421			0.0872041			0.0436021	−	0.999049i	$-0.486117\pi$
$263$	1.41421			0.0872041			0.0436021	+	0.999049i	$0.486117\pi$
$264$	16.0000	−	22.6274i	0.984732	−	1.39262i
$265$	18.0000			1.10573
$266$		−	11.3137i		−	0.693688i
$267$	16.9706	−	24.0000i	1.03858	−	1.46878i
$268$			2.00000i			0.122169i
$269$		−	19.7990i		−	1.20717i	−0.797300	−	0.603583i	$-0.793739\pi$
$269$		−	19.7990i		−	1.20717i	0.797300	−	0.603583i	$-0.206261\pi$
$270$	−2.82843	+	10.0000i	−0.172133	+	0.608581i
$271$			2.00000i			0.121491i	0.998153	+	0.0607457i	$0.0193479\pi$
$271$			2.00000i			0.121491i	−0.998153	+	0.0607457i	$0.980652\pi$
$272$		−	22.6274i		−	1.37199i
$273$	4.00000	−	5.65685i	0.242091	−	0.342368i
$274$	10.0000			0.604122
$275$	16.9706			1.02336
$276$	20.0000	+	14.1421i	1.20386	+	0.851257i
$277$	−22.0000			−1.32185			−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000			−1.32185			−0.660926	+	0.750451i	$0.729836\pi$
$278$	−2.82843			−0.169638
$279$		0			0
$280$			8.00000i			0.478091i
$281$		−	4.24264i		−	0.253095i	−0.991961	−	0.126547i	$-0.959610\pi$
$281$		−	4.24264i		−	0.253095i	0.991961	−	0.126547i	$-0.0403896\pi$
$282$	10.0000	−	14.1421i	0.595491	−	0.842152i
$283$			28.0000i			1.66443i	0.554455	+	0.832214i	$0.312927\pi$
$283$			28.0000i			1.66443i	−0.554455	+	0.832214i	$0.687073\pi$
$284$	31.1127			1.84620
$285$	−8.00000	−	5.65685i	−0.473879	−	0.335083i
$286$			16.0000i			0.946100i
$287$	2.82843			0.166957
$288$	−16.0000	+	5.65685i	−0.942809	+	0.333333i
$289$	−15.0000			−0.882353
$290$			11.3137i			0.664364i
$291$	−8.48528	−	6.00000i	−0.497416	−	0.351726i
$292$	−20.0000			−1.17041
$293$			5.65685i			0.330477i	0.986254	+	0.165238i	$0.0528394\pi$
$293$			5.65685i			0.330477i	−0.986254	+	0.165238i	$0.947161\pi$
$294$	−4.24264	+	6.00000i	−0.247436	+	0.349927i
$295$			2.00000i			0.116445i
$296$		−	22.6274i		−	1.31519i
$297$	−8.00000	+	28.2843i	−0.464207	+	1.64122i
$298$	−4.00000			−0.231714
$299$	−14.1421			−0.817861
$300$	−8.48528	−	6.00000i	−0.489898	−	0.346410i
$301$	8.00000			0.461112
$302$		0			0
$303$	7.07107	−	10.0000i	0.406222	−	0.574485i
$304$		−	16.0000i		−	0.917663i
$305$			8.48528i			0.485866i
$306$	8.00000	+	22.6274i	0.457330	+	1.29352i
$307$		−	8.00000i		−	0.456584i	−0.973593	−	0.228292i	$-0.926686\pi$
$307$		−	8.00000i		−	0.456584i	0.973593	−	0.228292i	$-0.0733141\pi$
$308$			22.6274i			1.28932i
$309$	4.00000	−	5.65685i	0.227552	−	0.321807i
$310$		0			0
$311$	−19.7990			−1.12270			−0.561349	−	0.827579i	$-0.689717\pi$
$311$	−19.7990			−1.12270			−0.561349	+	0.827579i	$0.689717\pi$
$312$	5.65685	−	8.00000i	0.320256	−	0.452911i
$313$	−26.0000			−1.46961			−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000			−1.46961			−0.734803	+	0.678280i	$0.762726\pi$
$314$		−	19.7990i		−	1.11732i
$315$	−2.82843	−	8.00000i	−0.159364	−	0.450749i
$316$			16.0000i			0.900070i
$317$		−	25.4558i		−	1.42974i	−0.699256	−	0.714871i	$-0.746485\pi$
$317$		−	25.4558i		−	1.42974i	0.699256	−	0.714871i	$-0.253515\pi$
$318$	−25.4558	−	18.0000i	−1.42749	−	1.00939i
$319$			32.0000i			1.79166i
$320$			11.3137i			0.632456i
$321$	−18.0000	−	12.7279i	−1.00466	−	0.710403i
$322$	−20.0000			−1.11456
$323$	−22.6274			−1.25902
$324$	14.0000	−	11.3137i	0.777778	−	0.628539i
$325$	6.00000			0.332820
$326$	11.3137			0.626608
$327$	8.48528	+	6.00000i	0.469237	+	0.331801i
$328$	4.00000			0.220863
$329$			14.1421i			0.779681i
$330$	16.0000	+	11.3137i	0.880771	+	0.622799i
$331$			4.00000i			0.219860i	0.993939	+	0.109930i	$0.0350627\pi$
$331$			4.00000i			0.219860i	−0.993939	+	0.109930i	$0.964937\pi$
$332$	−31.1127			−1.70753
$333$	8.00000	+	22.6274i	0.438397	+	1.23997i
$334$		−	6.00000i		−	0.328305i
$335$	−1.41421			−0.0772667
$336$	8.00000	−	11.3137i	0.436436	−	0.617213i
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$		−	12.7279i		−	0.692308i
$339$	−12.7279	+	18.0000i	−0.691286	+	0.977626i
$340$	16.0000			0.867722
$341$		0			0
$342$	5.65685	+	16.0000i	0.305888	+	0.865181i
$343$		−	20.0000i		−	1.07990i
$344$	11.3137			0.609994
$345$	−10.0000	+	14.1421i	−0.538382	+	0.761387i
$346$	−32.0000			−1.72033
$347$	−11.3137			−0.607352			−0.303676	−	0.952775i	$-0.598214\pi$
$347$	−11.3137			−0.607352			−0.303676	+	0.952775i	$0.598214\pi$
$348$	11.3137	−	16.0000i	0.606478	−	0.857690i
$349$	20.0000			1.07058			0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000			1.07058			0.535288	+	0.844670i	$0.320203\pi$
$350$	8.48528			0.453557
$351$	−2.82843	+	10.0000i	−0.150970	+	0.533761i
$352$			32.0000i			1.70561i
$353$			21.2132i			1.12906i	0.825411	+	0.564532i	$0.190943\pi$
$353$			21.2132i			1.12906i	−0.825411	+	0.564532i	$0.809057\pi$
$354$	2.00000	−	2.82843i	0.106299	−	0.150329i
$355$			22.0000i			1.16764i
$356$			33.9411i			1.79888i
$357$	−16.0000	−	11.3137i	−0.846810	−	0.598785i
$358$		−	36.0000i		−	1.90266i
$359$	21.2132			1.11959			0.559795	−	0.828631i	$-0.310880\pi$
$359$	21.2132			1.11959			0.559795	+	0.828631i	$0.310880\pi$
$360$	−4.00000	−	11.3137i	−0.210819	−	0.596285i
$361$	3.00000			0.157895
$362$			11.3137i			0.594635i
$363$	29.6985	+	21.0000i	1.55877	+	1.10221i
$364$			8.00000i			0.419314i
$365$		−	14.1421i		−	0.740233i
$366$	8.48528	−	12.0000i	0.443533	−	0.627250i
$367$		−	8.00000i		−	0.417597i	−0.977959	−	0.208798i	$-0.933045\pi$
$367$		−	8.00000i		−	0.417597i	0.977959	−	0.208798i	$-0.0669552\pi$
$368$	−28.2843			−1.47442
$369$	−4.00000	+	1.41421i	−0.208232	+	0.0736210i
$370$	16.0000			0.831800
$371$	25.4558			1.32160
$372$		0			0
$373$	18.0000			0.932005			0.466002	−	0.884783i	$-0.345694\pi$
$373$	18.0000			0.932005			0.466002	+	0.884783i	$0.345694\pi$
$374$	45.2548			2.34007
$375$	11.3137	−	16.0000i	0.584237	−	0.826236i
$376$			20.0000i			1.03142i
$377$			11.3137i			0.582686i
$378$	−4.00000	+	14.1421i	−0.205738	+	0.727393i
$379$		−	34.0000i		−	1.74646i	−0.487306	−	0.873231i	$-0.662020\pi$
$379$		−	34.0000i		−	1.74646i	0.487306	−	0.873231i	$-0.337980\pi$
$380$	11.3137			0.580381
$381$	−16.0000	+	22.6274i	−0.819705	+	1.15924i
$382$			12.0000i			0.613973i
$383$	−5.65685			−0.289052			−0.144526	−	0.989501i	$-0.546166\pi$
$383$	−5.65685			−0.289052			−0.144526	+	0.989501i	$0.546166\pi$
$384$	11.3137	−	16.0000i	0.577350	−	0.816497i
$385$	−16.0000			−0.815436
$386$		−	2.82843i		−	0.143963i
$387$	−11.3137	+	4.00000i	−0.575108	+	0.203331i
$388$	12.0000			0.609208
$389$			25.4558i			1.29066i	0.763903	+	0.645331i	$0.223281\pi$
$389$			25.4558i			1.29066i	−0.763903	+	0.645331i	$0.776719\pi$
$390$	5.65685	+	4.00000i	0.286446	+	0.202548i
$391$			40.0000i			2.02289i
$392$		−	8.48528i		−	0.428571i
$393$	10.0000	+	7.07107i	0.504433	+	0.356688i
$394$	−10.0000			−0.503793
$395$	−11.3137			−0.569254
$396$	−11.3137	−	32.0000i	−0.568535	−	1.60806i
$397$	12.0000			0.602263			0.301131	−	0.953583i	$-0.402636\pi$
$397$	12.0000			0.602263			0.301131	+	0.953583i	$0.402636\pi$
$398$	−5.65685			−0.283552
$399$	−11.3137	−	8.00000i	−0.566394	−	0.400501i
$400$	12.0000			0.600000
$401$			26.8701i			1.34183i	0.741536	+	0.670913i	$0.234098\pi$
$401$			26.8701i			1.34183i	−0.741536	+	0.670913i	$0.765902\pi$
$402$	2.00000	+	1.41421i	0.0997509	+	0.0705346i
$403$		0			0
$404$			14.1421i			0.703598i
$405$	8.00000	+	9.89949i	0.397523	+	0.491910i
$406$			16.0000i			0.794067i
$407$	45.2548			2.24320
$408$	−22.6274	−	16.0000i	−1.12022	−	0.792118i
$409$	−18.0000			−0.890043			−0.445021	−	0.895520i	$-0.646804\pi$
$409$	−18.0000			−0.890043			−0.445021	+	0.895520i	$0.646804\pi$
$410$			2.82843i			0.139686i
$411$	7.07107	−	10.0000i	0.348790	−	0.493264i
$412$			8.00000i			0.394132i
$413$			2.82843i			0.139178i
$414$	28.2843	−	10.0000i	1.39010	−	0.491473i
$415$		−	22.0000i		−	1.07994i
$416$			11.3137i			0.554700i
$417$	−2.00000	+	2.82843i	−0.0979404	+	0.138509i
$418$	32.0000			1.56517
$419$	26.8701			1.31269			0.656344	−	0.754462i	$-0.272102\pi$
$419$	26.8701			1.31269			0.656344	+	0.754462i	$0.272102\pi$
$420$	8.00000	+	5.65685i	0.390360	+	0.276026i
$421$	30.0000			1.46211			0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000			1.46211			0.731055	+	0.682318i	$0.239028\pi$
$422$	−5.65685			−0.275371
$423$	−7.07107	−	20.0000i	−0.343807	−	0.972433i
$424$	36.0000			1.74831
$425$		−	16.9706i		−	0.823193i
$426$	22.0000	−	31.1127i	1.06590	−	1.50742i
$427$			12.0000i			0.580721i
$428$	25.4558			1.23045
$429$	16.0000	+	11.3137i	0.772487	+	0.546231i
$430$			8.00000i			0.385794i
$431$	15.5563			0.749323			0.374661	−	0.927162i	$-0.377759\pi$
$431$	15.5563			0.749323			0.374661	+	0.927162i	$0.377759\pi$
$432$	−5.65685	+	20.0000i	−0.272166	+	0.962250i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$	11.3137	+	8.00000i	0.542451	+	0.383571i
$436$	−12.0000			−0.574696
$437$			28.2843i			1.35302i
$438$	−14.1421	+	20.0000i	−0.675737	+	0.955637i
$439$		−	8.00000i		−	0.381819i	−0.981608	−	0.190910i	$-0.938856\pi$
$439$		−	8.00000i		−	0.381819i	0.981608	−	0.190910i	$-0.0611437\pi$
$440$	−22.6274			−1.07872
$441$	3.00000	+	8.48528i	0.142857	+	0.404061i
$442$	16.0000			0.761042
$443$	−11.3137			−0.537531			−0.268765	−	0.963206i	$-0.586616\pi$
$443$	−11.3137			−0.537531			−0.268765	+	0.963206i	$0.586616\pi$
$444$	−22.6274	−	16.0000i	−1.07385	−	0.759326i
$445$	−24.0000			−1.13771
$446$	−11.3137			−0.535720
$447$	−2.82843	+	4.00000i	−0.133780	+	0.189194i
$448$			16.0000i			0.755929i
$449$			22.6274i			1.06785i	0.845531	+	0.533927i	$0.179284\pi$
$449$			22.6274i			1.06785i	−0.845531	+	0.533927i	$0.820716\pi$
$450$	−12.0000	+	4.24264i	−0.565685	+	0.200000i
$451$			8.00000i			0.376705i
$452$		−	25.4558i		−	1.19734i
$453$		0			0
$454$		−	10.0000i		−	0.469323i
$455$	−5.65685			−0.265197
$456$	−16.0000	−	11.3137i	−0.749269	−	0.529813i
$457$	8.00000			0.374224			0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000			0.374224			0.187112	+	0.982339i	$0.440087\pi$
$458$			14.1421i			0.660819i
$459$	28.2843	+	8.00000i	1.32020	+	0.373408i
$460$		−	20.0000i		−	0.932505i
$461$		−	31.1127i		−	1.44906i	−0.689242	−	0.724531i	$-0.742056\pi$
$461$		−	31.1127i		−	1.44906i	0.689242	−	0.724531i	$-0.257944\pi$
$462$	22.6274	+	16.0000i	1.05272	+	0.744387i
$463$			2.00000i			0.0929479i	0.998920	+	0.0464739i	$0.0147984\pi$
$463$			2.00000i			0.0929479i	−0.998920	+	0.0464739i	$0.985202\pi$
$464$			22.6274i			1.05045i
$465$		0			0
$466$	−26.0000			−1.20443
$467$	−41.0122			−1.89782			−0.948909	−	0.315550i	$-0.897811\pi$
$467$	−41.0122			−1.89782			−0.948909	+	0.315550i	$0.897811\pi$
$468$	−4.00000	−	11.3137i	−0.184900	−	0.522976i
$469$	−2.00000			−0.0923514
$470$	−14.1421			−0.652328
$471$	−19.7990	−	14.0000i	−0.912289	−	0.645086i
$472$			4.00000i			0.184115i
$473$			22.6274i			1.04041i
$474$	16.0000	+	11.3137i	0.734904	+	0.519656i
$475$		−	12.0000i		−	0.550598i
$476$	22.6274			1.03713
$477$	−36.0000	+	12.7279i	−1.64833	+	0.582772i
$478$		−	12.0000i		−	0.548867i
$479$	−9.89949			−0.452319			−0.226160	−	0.974090i	$-0.572617\pi$
$479$	−9.89949			−0.452319			−0.226160	+	0.974090i	$0.572617\pi$
$480$	11.3137	+	8.00000i	0.516398	+	0.365148i
$481$	16.0000			0.729537
$482$		−	22.6274i		−	1.03065i
$483$	−14.1421	+	20.0000i	−0.643489	+	0.910032i
$484$	−42.0000			−1.90909
$485$			8.48528i			0.385297i
$486$	−1.41421	−	22.0000i	−0.0641500	−	0.997940i
$487$			8.00000i			0.362515i	0.983436	+	0.181257i	$0.0580167\pi$
$487$			8.00000i			0.362515i	−0.983436	+	0.181257i	$0.941983\pi$
$488$			16.9706i			0.768221i
$489$	8.00000	−	11.3137i	0.361773	−	0.511624i
$490$	6.00000			0.271052
$491$	−18.3848			−0.829693			−0.414847	−	0.909891i	$-0.636165\pi$
$491$	−18.3848			−0.829693			−0.414847	+	0.909891i	$0.636165\pi$
$492$	2.82843	−	4.00000i	0.127515	−	0.180334i
$493$	32.0000			1.44121
$494$	11.3137			0.509028
$495$	22.6274	−	8.00000i	1.01703	−	0.359573i
$496$		0			0
$497$			31.1127i			1.39560i
$498$	−22.0000	+	31.1127i	−0.985844	+	1.39419i
$499$		−	4.00000i		−	0.179065i	−0.995984	−	0.0895323i	$-0.971463\pi$
$499$		−	4.00000i		−	0.179065i	0.995984	−	0.0895323i	$-0.0285372\pi$
$500$			22.6274i			1.01193i
$501$	−6.00000	−	4.24264i	−0.268060	−	0.189547i
$502$			4.00000i			0.178529i
$503$	−22.6274			−1.00891			−0.504453	−	0.863439i	$-0.668306\pi$
$503$	−22.6274			−1.00891			−0.504453	+	0.863439i	$0.668306\pi$
$504$	−5.65685	−	16.0000i	−0.251976	−	0.712697i
$505$	−10.0000			−0.444994
$506$		−	56.5685i		−	2.51478i
$507$	−12.7279	−	9.00000i	−0.565267	−	0.399704i
$508$		−	32.0000i		−	1.41977i
$509$		−	2.82843i		−	0.125368i	−0.998033	−	0.0626839i	$-0.980034\pi$
$509$		−	2.82843i		−	0.125368i	0.998033	−	0.0626839i	$-0.0199660\pi$
$510$	11.3137	−	16.0000i	0.500979	−	0.708492i
$511$		−	20.0000i		−	0.884748i
$512$			22.6274i			1.00000i
$513$	20.0000	+	5.65685i	0.883022	+	0.249756i
$514$	−24.0000			−1.05859
$515$	−5.65685			−0.249271
$516$	8.00000	−	11.3137i	0.352180	−	0.498058i
$517$	−40.0000			−1.75920
$518$	22.6274			0.994192
$519$	−22.6274	+	32.0000i	−0.993233	+	1.40464i
$520$	−8.00000			−0.350823
$521$			4.24264i			0.185873i	0.995672	+	0.0929367i	$0.0296254\pi$
$521$			4.24264i			0.185873i	−0.995672	+	0.0929367i	$0.970375\pi$
$522$	−8.00000	−	22.6274i	−0.350150	−	0.990375i
$523$			32.0000i			1.39926i	0.714504	+	0.699631i	$0.246652\pi$
$523$			32.0000i			1.39926i	−0.714504	+	0.699631i	$0.753348\pi$
$524$	−14.1421			−0.617802
$525$	6.00000	−	8.48528i	0.261861	−	0.370328i
$526$			2.00000i			0.0872041i
$527$		0			0
$528$	32.0000	+	22.6274i	1.39262	+	0.984732i
$529$	27.0000			1.17391
$530$			25.4558i			1.10573i
$531$	−1.41421	−	4.00000i	−0.0613716	−	0.173585i
$532$	16.0000			0.693688
$533$			2.82843i			0.122513i
$534$	33.9411	+	24.0000i	1.46878	+	1.03858i
$535$			18.0000i			0.778208i
$536$	−2.82843			−0.122169
$537$	−36.0000	−	25.4558i	−1.55351	−	1.09850i
$538$	28.0000			1.20717
$539$	16.9706			0.730974
$540$	−14.1421	−	4.00000i	−0.608581	−	0.172133i
$541$	−30.0000			−1.28980			−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000			−1.28980			−0.644900	+	0.764267i	$0.723101\pi$
$542$	−2.82843			−0.121491
$543$	11.3137	+	8.00000i	0.485518	+	0.343313i
$544$	32.0000			1.37199
$545$		−	8.48528i		−	0.363470i
$546$	8.00000	+	5.65685i	0.342368	+	0.242091i
$547$			2.00000i			0.0855138i	0.999086	+	0.0427569i	$0.0136141\pi$
$547$			2.00000i			0.0855138i	−0.999086	+	0.0427569i	$0.986386\pi$
$548$			14.1421i			0.604122i
$549$	−6.00000	−	16.9706i	−0.256074	−	0.724286i
$550$			24.0000i			1.02336i
$551$	22.6274			0.963960
$552$	−20.0000	+	28.2843i	−0.851257	+	1.20386i
$553$	−16.0000			−0.680389
$554$		−	31.1127i		−	1.32185i
$555$	11.3137	−	16.0000i	0.480240	−	0.679162i
$556$		−	4.00000i		−	0.169638i
$557$			2.82843i			0.119844i	0.998203	+	0.0599222i	$0.0190852\pi$
$557$			2.82843i			0.119844i	−0.998203	+	0.0599222i	$0.980915\pi$
$558$		0			0
$559$			8.00000i			0.338364i
$560$	−11.3137			−0.478091
$561$	32.0000	−	45.2548i	1.35104	−	1.91066i
$562$	6.00000			0.253095
$563$	−36.7696			−1.54965			−0.774826	−	0.632175i	$-0.782163\pi$
$563$	−36.7696			−1.54965			−0.774826	+	0.632175i	$0.782163\pi$
$564$	20.0000	+	14.1421i	0.842152	+	0.595491i
$565$	18.0000			0.757266
$566$	−39.5980			−1.66443
$567$	11.3137	+	14.0000i	0.475131	+	0.587945i
$568$			44.0000i			1.84620i
$569$		−	14.1421i		−	0.592869i	−0.955053	−	0.296435i	$-0.904202\pi$
$569$		−	14.1421i		−	0.592869i	0.955053	−	0.296435i	$-0.0957977\pi$
$570$	8.00000	−	11.3137i	0.335083	−	0.473879i
$571$			12.0000i			0.502184i	0.967963	+	0.251092i	$0.0807897\pi$
$571$			12.0000i			0.502184i	−0.967963	+	0.251092i	$0.919210\pi$
$572$	−22.6274			−0.946100
$573$	12.0000	+	8.48528i	0.501307	+	0.354478i
$574$			4.00000i			0.166957i
$575$	−21.2132			−0.884652
$576$	−8.00000	−	22.6274i	−0.333333	−	0.942809i
$577$	22.0000			0.915872			0.457936	−	0.888985i	$-0.348589\pi$
$577$	22.0000			0.915872			0.457936	+	0.888985i	$0.348589\pi$
$578$		−	21.2132i		−	0.882353i
$579$	−2.82843	−	2.00000i	−0.117545	−	0.0831172i
$580$	−16.0000			−0.664364
$581$		−	31.1127i		−	1.29077i
$582$	8.48528	−	12.0000i	0.351726	−	0.497416i
$583$			72.0000i			2.98194i
$584$		−	28.2843i		−	1.17041i
$585$	8.00000	−	2.82843i	0.330759	−	0.116941i
$586$	−8.00000			−0.330477
$587$	−33.9411			−1.40090			−0.700450	−	0.713701i	$-0.747017\pi$
$587$	−33.9411			−1.40090			−0.700450	+	0.713701i	$0.747017\pi$
$588$	−8.48528	−	6.00000i	−0.349927	−	0.247436i
$589$		0			0
$590$	−2.82843			−0.116445
$591$	−7.07107	+	10.0000i	−0.290865	+	0.411345i
$592$	32.0000			1.31519
$593$		−	9.89949i		−	0.406524i	−0.979124	−	0.203262i	$-0.934846\pi$
$593$		−	9.89949i		−	0.406524i	0.979124	−	0.203262i	$-0.0651542\pi$
$594$	−40.0000	−	11.3137i	−1.64122	−	0.464207i
$595$			16.0000i			0.655936i
$596$		−	5.65685i		−	0.231714i
$597$	−4.00000	+	5.65685i	−0.163709	+	0.231520i
$598$		−	20.0000i		−	0.817861i
$599$	−16.9706			−0.693398			−0.346699	−	0.937976i	$-0.612698\pi$
$599$	−16.9706			−0.693398			−0.346699	+	0.937976i	$0.612698\pi$
$600$	8.48528	−	12.0000i	0.346410	−	0.489898i
$601$	28.0000			1.14214			0.571072	−	0.820900i	$-0.306528\pi$
$601$	28.0000			1.14214			0.571072	+	0.820900i	$0.306528\pi$
$602$			11.3137i			0.461112i
$603$	2.82843	−	1.00000i	0.115182	−	0.0407231i
$604$		0			0
$605$		−	29.6985i		−	1.20742i
$606$	14.1421	+	10.0000i	0.574485	+	0.406222i
$607$		−	36.0000i		−	1.46119i	−0.682808	−	0.730597i	$-0.739242\pi$
$607$		−	36.0000i		−	1.46119i	0.682808	−	0.730597i	$-0.260758\pi$
$608$	22.6274			0.917663
$609$	16.0000	+	11.3137i	0.648353	+	0.458455i
$610$	−12.0000			−0.485866
$611$	−14.1421			−0.572130
$612$	−32.0000	+	11.3137i	−1.29352	+	0.457330i
$613$	−26.0000			−1.05013			−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000			−1.05013			−0.525065	+	0.851062i	$0.675959\pi$
$614$	11.3137			0.456584
$615$	2.82843	+	2.00000i	0.114053	+	0.0806478i
$616$	−32.0000			−1.28932
$617$			5.65685i			0.227736i	0.993496	+	0.113868i	$0.0363242\pi$
$617$			5.65685i			0.227736i	−0.993496	+	0.113868i	$0.963676\pi$
$618$	8.00000	+	5.65685i	0.321807	+	0.227552i
$619$		−	48.0000i		−	1.92928i	−0.263566	−	0.964641i	$-0.584899\pi$
$619$		−	48.0000i		−	1.92928i	0.263566	−	0.964641i	$-0.415101\pi$
$620$		0			0
$621$	10.0000	−	35.3553i	0.401286	−	1.41876i
$622$		−	28.0000i		−	1.12270i
$623$	−33.9411			−1.35982
$624$	11.3137	+	8.00000i	0.452911	+	0.320256i
$625$	−1.00000			−0.0400000
$626$		−	36.7696i		−	1.46961i
$627$	22.6274	−	32.0000i	0.903652	−	1.27796i
$628$	28.0000			1.11732
$629$		−	45.2548i		−	1.80443i
$630$	11.3137	−	4.00000i	0.450749	−	0.159364i
$631$			10.0000i			0.398094i	0.979990	+	0.199047i	$0.0637846\pi$
$631$			10.0000i			0.398094i	−0.979990	+	0.199047i	$0.936215\pi$
$632$	−22.6274			−0.900070
$633$	−4.00000	+	5.65685i	−0.158986	+	0.224840i
$634$	36.0000			1.42974
$635$	22.6274			0.897942
$636$	25.4558	−	36.0000i	1.00939	−	1.42749i
$637$	6.00000			0.237729
$638$	−45.2548			−1.79166
$639$	−15.5563	−	44.0000i	−0.615400	−	1.74061i
$640$	−16.0000			−0.632456
$641$		−	1.41421i		−	0.0558581i	−0.999610	−	0.0279290i	$-0.991109\pi$
$641$		−	1.41421i		−	0.0558581i	0.999610	−	0.0279290i	$-0.00889125\pi$
$642$	18.0000	−	25.4558i	0.710403	−	1.00466i
$643$			16.0000i			0.630978i	0.948929	+	0.315489i	$0.102169\pi$
$643$			16.0000i			0.630978i	−0.948929	+	0.315489i	$0.897831\pi$
$644$		−	28.2843i		−	1.11456i
$645$	8.00000	+	5.65685i	0.315000	+	0.222738i
$646$		−	32.0000i		−	1.25902i
$647$	48.0833			1.89035			0.945174	−	0.326567i	$-0.105892\pi$
$647$	48.0833			1.89035			0.945174	+	0.326567i	$0.105892\pi$
$648$	16.0000	+	19.7990i	0.628539	+	0.777778i
$649$	−8.00000			−0.314027
$650$			8.48528i			0.332820i
$651$		0			0
$652$			16.0000i			0.626608i
$653$		−	43.8406i		−	1.71562i	−0.513970	−	0.857808i	$-0.671826\pi$
$653$		−	43.8406i		−	1.71562i	0.513970	−	0.857808i	$-0.328174\pi$
$654$	−8.48528	+	12.0000i	−0.331801	+	0.469237i
$655$		−	10.0000i		−	0.390732i
$656$			5.65685i			0.220863i
$657$	10.0000	+	28.2843i	0.390137	+	1.10347i
$658$	−20.0000			−0.779681
$659$	32.5269			1.26707			0.633534	−	0.773715i	$-0.281604\pi$
$659$	32.5269			1.26707			0.633534	+	0.773715i	$0.281604\pi$
$660$	−16.0000	+	22.6274i	−0.622799	+	0.880771i
$661$	26.0000			1.01128			0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000			1.01128			0.505641	+	0.862744i	$0.331256\pi$
$662$	−5.65685			−0.219860
$663$	11.3137	−	16.0000i	0.439388	−	0.621389i
$664$		−	44.0000i		−	1.70753i
$665$			11.3137i			0.438727i
$666$	−32.0000	+	11.3137i	−1.23997	+	0.438397i
$667$		−	40.0000i		−	1.54881i
$668$	8.48528			0.328305
$669$	−8.00000	+	11.3137i	−0.309298	+	0.437413i
$670$		−	2.00000i		−	0.0772667i
$671$	−33.9411			−1.31028
$672$	16.0000	+	11.3137i	0.617213	+	0.436436i
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$		−	14.1421i		−	0.544735i
$675$	−4.24264	+	15.0000i	−0.163299	+	0.577350i
$676$	18.0000			0.692308
$677$		−	24.0416i		−	0.923995i	−0.886881	−	0.461997i	$-0.847133\pi$
$677$		−	24.0416i		−	0.923995i	0.886881	−	0.461997i	$-0.152867\pi$
$678$	−25.4558	−	18.0000i	−0.977626	−	0.691286i
$679$			12.0000i			0.460518i
$680$			22.6274i			0.867722i
$681$	−10.0000	−	7.07107i	−0.383201	−	0.270964i
$682$		0			0
$683$	36.7696			1.40695			0.703474	−	0.710721i	$-0.251631\pi$
$683$	36.7696			1.40695			0.703474	+	0.710721i	$0.251631\pi$
$684$	−22.6274	+	8.00000i	−0.865181	+	0.305888i
$685$	−10.0000			−0.382080
$686$	28.2843			1.07990
$687$	14.1421	+	10.0000i	0.539556	+	0.381524i
$688$			16.0000i			0.609994i
$689$			25.4558i			0.969790i
$690$	−20.0000	−	14.1421i	−0.761387	−	0.538382i
$691$		−	8.00000i		−	0.304334i	−0.988355	−	0.152167i	$-0.951375\pi$
$691$		−	8.00000i		−	0.304334i	0.988355	−	0.152167i	$-0.0486252\pi$
$692$		−	45.2548i		−	1.72033i
$693$	32.0000	−	11.3137i	1.21558	−	0.429772i
$694$		−	16.0000i		−	0.607352i
$695$	2.82843			0.107288
$696$	22.6274	+	16.0000i	0.857690	+	0.606478i
$697$	8.00000			0.303022
$698$			28.2843i			1.07058i
$699$	−18.3848	+	26.0000i	−0.695376	+	0.983410i
$700$			12.0000i			0.453557i
$701$		−	15.5563i		−	0.587555i	−0.955874	−	0.293778i	$-0.905087\pi$
$701$		−	15.5563i		−	0.587555i	0.955874	−	0.293778i	$-0.0949125\pi$
$702$	−14.1421	−	4.00000i	−0.533761	−	0.150970i
$703$		−	32.0000i		−	1.20690i
$704$	−45.2548			−1.70561
$705$	−10.0000	+	14.1421i	−0.376622	+	0.532624i
$706$	−30.0000			−1.12906
$707$	−14.1421			−0.531870
$708$	4.00000	+	2.82843i	0.150329	+	0.106299i
$709$	6.00000			0.225335			0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000			0.225335			0.112667	+	0.993633i	$0.464061\pi$
$710$	−31.1127			−1.16764
$711$	22.6274	−	8.00000i	0.848594	−	0.300023i
$712$	−48.0000			−1.79888
$713$		0			0
$714$	16.0000	−	22.6274i	0.598785	−	0.846810i
$715$		−	16.0000i		−	0.598366i
$716$	50.9117			1.90266
$717$	−12.0000	−	8.48528i	−0.448148	−	0.316889i
$718$			30.0000i			1.11959i
$719$	35.3553			1.31853			0.659266	−	0.751910i	$-0.270867\pi$
$719$	35.3553			1.31853			0.659266	+	0.751910i	$0.270867\pi$
$720$	16.0000	−	5.65685i	0.596285	−	0.210819i
$721$	−8.00000			−0.297936
$722$			4.24264i			0.157895i
$723$	−22.6274	−	16.0000i	−0.841523	−	0.595046i
$724$	−16.0000			−0.594635
$725$			16.9706i			0.630271i
$726$	−29.6985	+	42.0000i	−1.10221	+	1.55877i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	−11.3137			−0.419314
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$	20.0000			0.740233
$731$	22.6274			0.836905
$732$	16.9706	+	12.0000i	0.627250	+	0.443533i
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$	11.3137			0.417597
$735$	4.24264	−	6.00000i	0.156492	−	0.221313i
$736$		−	40.0000i		−	1.47442i
$737$		−	5.65685i		−	0.208373i
$738$	−2.00000	−	5.65685i	−0.0736210	−	0.208232i
$739$			44.0000i			1.61857i	0.587419	+	0.809283i	$0.300144\pi$
$739$			44.0000i			1.61857i	−0.587419	+	0.809283i	$0.699856\pi$
$740$			22.6274i			0.831800i
$741$	8.00000	−	11.3137i	0.293887	−	0.415619i
$742$			36.0000i			1.32160i
$743$	35.3553			1.29706			0.648531	−	0.761188i	$-0.275384\pi$
$743$	35.3553			1.29706			0.648531	+	0.761188i	$0.275384\pi$
$744$		0			0
$745$	4.00000			0.146549
$746$			25.4558i			0.932005i
$747$	15.5563	+	44.0000i	0.569177	+	1.60988i
$748$			64.0000i			2.34007i
$749$			25.4558i			0.930136i
$750$	22.6274	+	16.0000i	0.826236	+	0.584237i
$751$			16.0000i			0.583848i	0.956441	+	0.291924i	$0.0942955\pi$
$751$			16.0000i			0.583848i	−0.956441	+	0.291924i	$0.905705\pi$
$752$	−28.2843			−1.03142
$753$	4.00000	+	2.82843i	0.145768	+	0.103074i
$754$	−16.0000			−0.582686
$755$		0			0
$756$	−20.0000	−	5.65685i	−0.727393	−	0.205738i
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$	48.0833			1.74646
$759$	−56.5685	−	40.0000i	−2.05331	−	1.45191i
$760$			16.0000i			0.580381i
$761$		−	5.65685i		−	0.205061i	−0.994730	−	0.102530i	$-0.967306\pi$
$761$		−	5.65685i		−	0.205061i	0.994730	−	0.102530i	$-0.0326939\pi$
$762$	−32.0000	−	22.6274i	−1.15924	−	0.819705i
$763$		−	12.0000i		−	0.434429i
$764$	−16.9706			−0.613973
$765$	−8.00000	−	22.6274i	−0.289241	−	0.818096i
$766$		−	8.00000i		−	0.289052i
$767$	−2.82843			−0.102129
$768$	22.6274	+	16.0000i	0.816497	+	0.577350i
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		−	22.6274i		−	0.815436i
$771$	−16.9706	+	24.0000i	−0.611180	+	0.864339i
$772$	4.00000			0.143963
$773$			36.7696i			1.32251i	0.750162	+	0.661254i	$0.229976\pi$
$773$			36.7696i			1.32251i	−0.750162	+	0.661254i	$0.770024\pi$
$774$	−5.65685	−	16.0000i	−0.203331	−	0.575108i
$775$		0			0
$776$			16.9706i			0.609208i
$777$	16.0000	−	22.6274i	0.573997	−	0.811754i
$778$	−36.0000			−1.29066
$779$	5.65685			0.202678
$780$	−5.65685	+	8.00000i	−0.202548	+	0.286446i
$781$	−88.0000			−3.14889
$782$	−56.5685			−2.02289
$783$	−28.2843	−	8.00000i	−1.01080	−	0.285897i
$784$	12.0000			0.428571
$785$			19.7990i			0.706656i
$786$	−10.0000	+	14.1421i	−0.356688	+	0.504433i
$787$		−	44.0000i		−	1.56843i	−0.620489	−	0.784215i	$-0.713066\pi$
$787$		−	44.0000i		−	1.56843i	0.620489	−	0.784215i	$-0.286934\pi$
$788$		−	14.1421i		−	0.503793i
$789$	2.00000	+	1.41421i	0.0712019	+	0.0503473i
$790$		−	16.0000i		−	0.569254i
$791$	25.4558			0.905106
$792$	45.2548	−	16.0000i	1.60806	−	0.568535i
$793$	−12.0000			−0.426132
$794$			16.9706i			0.602263i
$795$	25.4558	+	18.0000i	0.902826	+	0.638394i
$796$		−	8.00000i		−	0.283552i
$797$		−	16.9706i		−	0.601128i	−0.953762	−	0.300564i	$-0.902825\pi$
$797$		−	16.9706i		−	0.601128i	0.953762	−	0.300564i	$-0.0971749\pi$
$798$	11.3137	−	16.0000i	0.400501	−	0.566394i
$799$			40.0000i			1.41510i
$800$			16.9706i			0.600000i
$801$	48.0000	−	16.9706i	1.69600	−	0.599625i
$802$	−38.0000			−1.34183
$803$	56.5685			1.99626
$804$	−2.00000	+	2.82843i	−0.0705346	+	0.0997509i
$805$	20.0000			0.704907
$806$		0			0
$807$	19.7990	−	28.0000i	0.696957	−	0.985647i
$808$	−20.0000			−0.703598
$809$		−	46.6690i		−	1.64080i	−0.571793	−	0.820398i	$-0.693752\pi$
$809$		−	46.6690i		−	1.64080i	0.571793	−	0.820398i	$-0.306248\pi$
$810$	−14.0000	+	11.3137i	−0.491910	+	0.397523i
$811$			28.0000i			0.983213i	0.870817	+	0.491606i	$0.163590\pi$
$811$			28.0000i			0.983213i	−0.870817	+	0.491606i	$0.836410\pi$
$812$	−22.6274			−0.794067
$813$	−2.00000	+	2.82843i	−0.0701431	+	0.0991973i
$814$			64.0000i			2.24320i
$815$	−11.3137			−0.396302
$816$	22.6274	−	32.0000i	0.792118	−	1.12022i
$817$	16.0000			0.559769
$818$		−	25.4558i		−	0.890043i
$819$	11.3137	−	4.00000i	0.395333	−	0.139771i
$820$	−4.00000			−0.139686
$821$		−	16.9706i		−	0.592277i	−0.955145	−	0.296138i	$-0.904301\pi$
$821$		−	16.9706i		−	0.592277i	0.955145	−	0.296138i	$-0.0956990\pi$
$822$	14.1421	+	10.0000i	0.493264	+	0.348790i
$823$			4.00000i			0.139431i	0.997567	+	0.0697156i	$0.0222092\pi$
$823$			4.00000i			0.139431i	−0.997567	+	0.0697156i	$0.977791\pi$
$824$	−11.3137			−0.394132
$825$	24.0000	+	16.9706i	0.835573	+	0.590839i
$826$	−4.00000			−0.139178
$827$	52.3259			1.81955			0.909775	−	0.415102i	$-0.136254\pi$
$827$	52.3259			1.81955			0.909775	+	0.415102i	$0.136254\pi$
$828$	14.1421	+	40.0000i	0.491473	+	1.39010i
$829$	−30.0000			−1.04194			−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000			−1.04194			−0.520972	+	0.853574i	$0.674430\pi$
$830$	31.1127			1.07994
$831$	−31.1127	−	22.0000i	−1.07929	−	0.763172i
$832$	−16.0000			−0.554700
$833$		−	16.9706i		−	0.587995i
$834$	−4.00000	−	2.82843i	−0.138509	−	0.0979404i
$835$			6.00000i			0.207639i
$836$			45.2548i			1.56517i
$837$		0			0
$838$			38.0000i			1.31269i
$839$	26.8701			0.927657			0.463829	−	0.885925i	$-0.346475\pi$
$839$	26.8701			0.927657			0.463829	+	0.885925i	$0.346475\pi$
$840$	−8.00000	+	11.3137i	−0.276026	+	0.390360i
$841$	−3.00000			−0.103448
$842$			42.4264i			1.46211i
$843$	4.24264	−	6.00000i	0.146124	−	0.206651i
$844$		−	8.00000i		−	0.275371i
$845$			12.7279i			0.437854i
$846$	28.2843	−	10.0000i	0.972433	−	0.343807i
$847$		−	42.0000i		−	1.44314i
$848$			50.9117i			1.74831i
$849$	−28.0000	+	39.5980i	−0.960958	+	1.35900i
$850$	24.0000			0.823193
$851$	−56.5685			−1.93914
$852$	44.0000	+	31.1127i	1.50742	+	1.06590i
$853$	−42.0000			−1.43805			−0.719026	−	0.694983i	$-0.755412\pi$
$853$	−42.0000			−1.43805			−0.719026	+	0.694983i	$0.755412\pi$
$854$	−16.9706			−0.580721
$855$	−5.65685	−	16.0000i	−0.193460	−	0.547188i
$856$			36.0000i			1.23045i
$857$			1.41421i			0.0483086i	0.999708	+	0.0241543i	$0.00768930\pi$
$857$			1.41421i			0.0483086i	−0.999708	+	0.0241543i	$0.992311\pi$
$858$	−16.0000	+	22.6274i	−0.546231	+	0.772487i
$859$		−	24.0000i		−	0.818869i	−0.912339	−	0.409435i	$-0.865726\pi$
$859$		−	24.0000i		−	0.818869i	0.912339	−	0.409435i	$-0.134274\pi$
$860$	−11.3137			−0.385794
$861$	4.00000	+	2.82843i	0.136320	+	0.0963925i
$862$			22.0000i			0.749323i
$863$	−4.24264			−0.144421			−0.0722106	−	0.997389i	$-0.523005\pi$
$863$	−4.24264			−0.144421			−0.0722106	+	0.997389i	$0.523005\pi$
$864$	−28.2843	−	8.00000i	−0.962250	−	0.272166i
$865$	32.0000			1.08803
$866$			2.82843i			0.0961139i
$867$	−21.2132	−	15.0000i	−0.720438	−	0.509427i
$868$		0			0
$869$		−	45.2548i		−	1.53517i
$870$	−11.3137	+	16.0000i	−0.383571	+	0.542451i
$871$		−	2.00000i		−	0.0677674i
$872$		−	16.9706i		−	0.574696i
$873$	−6.00000	−	16.9706i	−0.203069	−	0.574367i
$874$	−40.0000			−1.35302
$875$	−22.6274			−0.764946
$876$	−28.2843	−	20.0000i	−0.955637	−	0.675737i
$877$	−52.0000			−1.75592			−0.877958	−	0.478738i	$-0.841094\pi$
$877$	−52.0000			−1.75592			−0.877958	+	0.478738i	$0.841094\pi$
$878$	11.3137			0.381819
$879$	−5.65685	+	8.00000i	−0.190801	+	0.269833i
$880$		−	32.0000i		−	1.07872i
$881$		−	11.3137i		−	0.381169i	−0.981671	−	0.190584i	$-0.938962\pi$
$881$		−	11.3137i		−	0.381169i	0.981671	−	0.190584i	$-0.0610382\pi$
$882$	−12.0000	+	4.24264i	−0.404061	+	0.142857i
$883$		−	28.0000i		−	0.942275i	−0.882060	−	0.471138i	$-0.843844\pi$
$883$		−	28.0000i		−	0.942275i	0.882060	−	0.471138i	$-0.156156\pi$
$884$			22.6274i			0.761042i
$885$	−2.00000	+	2.82843i	−0.0672293	+	0.0950765i
$886$		−	16.0000i		−	0.537531i
$887$	18.3848			0.617300			0.308650	−	0.951176i	$-0.400123\pi$
$887$	18.3848			0.617300			0.308650	+	0.951176i	$0.400123\pi$
$888$	22.6274	−	32.0000i	0.759326	−	1.07385i
$889$	32.0000			1.07325
$890$		−	33.9411i		−	1.13771i
$891$	−39.5980	+	32.0000i	−1.32658	+	1.07204i
$892$		−	16.0000i		−	0.535720i
$893$			28.2843i			0.946497i
$894$	−5.65685	−	4.00000i	−0.189194	−	0.133780i
$895$			36.0000i			1.20335i
$896$	−22.6274			−0.755929
$897$	−20.0000	−	14.1421i	−0.667781	−	0.472192i
$898$	−32.0000			−1.06785
$899$		0			0
$900$	−6.00000	−	16.9706i	−0.200000	−	0.565685i
$901$	72.0000			2.39867
$902$	−11.3137			−0.376705
$903$	11.3137	+	8.00000i	0.376497	+	0.266223i
$904$	36.0000			1.19734
$905$		−	11.3137i		−	0.376080i
$906$		0			0
$907$			32.0000i			1.06254i	0.847202	+	0.531271i	$0.178286\pi$
$907$			32.0000i			1.06254i	−0.847202	+	0.531271i	$0.821714\pi$
$908$	14.1421			0.469323
$909$	20.0000	−	7.07107i	0.663358	−	0.234533i
$910$		−	8.00000i		−	0.265197i
$911$	−18.3848			−0.609115			−0.304557	−	0.952494i	$-0.598509\pi$
$911$	−18.3848			−0.609115			−0.304557	+	0.952494i	$0.598509\pi$
$912$	16.0000	−	22.6274i	0.529813	−	0.749269i
$913$	88.0000			2.91237
$914$			11.3137i			0.374224i
$915$	−8.48528	+	12.0000i	−0.280515	+	0.396708i
$916$	−20.0000			−0.660819
$917$		−	14.1421i		−	0.467014i
$918$	−11.3137	+	40.0000i	−0.373408	+	1.32020i
$919$			56.0000i			1.84727i	0.383274	+	0.923635i	$0.374797\pi$
$919$			56.0000i			1.84727i	−0.383274	+	0.923635i	$0.625203\pi$
$920$	28.2843			0.932505
$921$	8.00000	−	11.3137i	0.263609	−	0.372799i
$922$	44.0000			1.44906
$923$	−31.1127			−1.02409
$924$	−22.6274	+	32.0000i	−0.744387	+	1.05272i
$925$	24.0000			0.789115
$926$	−2.82843			−0.0929479
$927$	11.3137	−	4.00000i	0.371591	−	0.131377i
$928$	−32.0000			−1.05045
$929$			26.8701i			0.881578i	0.897611	+	0.440789i	$0.145301\pi$
$929$			26.8701i			0.881578i	−0.897611	+	0.440789i	$0.854699\pi$
$930$		0			0
$931$		−	12.0000i		−	0.393284i
$932$		−	36.7696i		−	1.20443i
$933$	−28.0000	−	19.7990i	−0.916679	−	0.648190i
$934$		−	58.0000i		−	1.89782i
$935$	−45.2548			−1.47999
$936$	16.0000	−	5.65685i	0.522976	−	0.184900i
$937$	−6.00000			−0.196011			−0.0980057	−	0.995186i	$-0.531246\pi$
$937$	−6.00000			−0.196011			−0.0980057	+	0.995186i	$0.531246\pi$
$938$		−	2.82843i		−	0.0923514i
$939$	−36.7696	−	26.0000i	−1.19993	−	0.848478i
$940$		−	20.0000i		−	0.652328i
$941$			7.07107i			0.230510i	0.993336	+	0.115255i	$0.0367686\pi$
$941$			7.07107i			0.230510i	−0.993336	+	0.115255i	$0.963231\pi$
$942$	19.7990	−	28.0000i	0.645086	−	0.912289i
$943$		−	10.0000i		−	0.325645i
$944$	−5.65685			−0.184115
$945$	4.00000	−	14.1421i	0.130120	−	0.460044i
$946$	−32.0000			−1.04041
$947$	−9.89949			−0.321690			−0.160845	−	0.986980i	$-0.551422\pi$
$947$	−9.89949			−0.321690			−0.160845	+	0.986980i	$0.551422\pi$
$948$	−16.0000	+	22.6274i	−0.519656	+	0.734904i
$949$	20.0000			0.649227
$950$	16.9706			0.550598
$951$	25.4558	−	36.0000i	0.825462	−	1.16738i
$952$			32.0000i			1.03713i
$953$		−	25.4558i		−	0.824596i	−0.911049	−	0.412298i	$-0.864726\pi$
$953$		−	25.4558i		−	0.824596i	0.911049	−	0.412298i	$-0.135274\pi$
$954$	−18.0000	−	50.9117i	−0.582772	−	1.64833i
$955$		−	12.0000i		−	0.388311i
$956$	16.9706			0.548867
$957$	−32.0000	+	45.2548i	−1.03441	+	1.46288i
$958$		−	14.0000i		−	0.452319i
$959$	−14.1421			−0.456673
$960$	−11.3137	+	16.0000i	−0.365148	+	0.516398i
$961$	31.0000			1.00000
$962$			22.6274i			0.729537i
$963$	−12.7279	−	36.0000i	−0.410152	−	1.16008i
$964$	32.0000			1.03065
$965$			2.82843i			0.0910503i
$966$	−28.2843	−	20.0000i	−0.910032	−	0.643489i
$967$			12.0000i			0.385894i	0.981209	+	0.192947i	$0.0618045\pi$
$967$			12.0000i			0.385894i	−0.981209	+	0.192947i	$0.938195\pi$
$968$		−	59.3970i		−	1.90909i
$969$	−32.0000	−	22.6274i	−1.02799	−	0.726897i
$970$	−12.0000			−0.385297
$971$	15.5563			0.499227			0.249614	−	0.968346i	$-0.419696\pi$
$971$	15.5563			0.499227			0.249614	+	0.968346i	$0.419696\pi$
$972$	31.1127	−	2.00000i	0.997940	−	0.0641500i
$973$	4.00000			0.128234
$974$	−11.3137			−0.362515
$975$	8.48528	+	6.00000i	0.271746	+	0.192154i
$976$	−24.0000			−0.768221
$977$		−	5.65685i		−	0.180979i	−0.995897	−	0.0904894i	$-0.971157\pi$
$977$		−	5.65685i		−	0.180979i	0.995897	−	0.0904894i	$-0.0288431\pi$
$978$	16.0000	+	11.3137i	0.511624	+	0.361773i
$979$		−	96.0000i		−	3.06817i
$980$			8.48528i			0.271052i
$981$	6.00000	+	16.9706i	0.191565	+	0.541828i
$982$		−	26.0000i		−	0.829693i
$983$	31.1127			0.992341			0.496170	−	0.868225i	$-0.334739\pi$
$983$	31.1127			0.992341			0.496170	+	0.868225i	$0.334739\pi$
$984$	5.65685	+	4.00000i	0.180334	+	0.127515i
$985$	10.0000			0.318626
$986$			45.2548i			1.44121i
$987$	−14.1421	+	20.0000i	−0.450149	+	0.636607i
$988$			16.0000i			0.509028i
$989$		−	28.2843i		−	0.899388i
$990$	11.3137	+	32.0000i	0.359573	+	1.01703i
$991$			42.0000i			1.33417i	0.744980	+	0.667087i	$0.232459\pi$
$991$			42.0000i			1.33417i	−0.744980	+	0.667087i	$0.767541\pi$
$992$		0			0
$993$	−4.00000	+	5.65685i	−0.126936	+	0.179515i
$994$	−44.0000			−1.39560
$995$	5.65685			0.179334
$996$	−44.0000	−	31.1127i	−1.39419	−	0.985844i
$997$	28.0000			0.886769			0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000			0.886769			0.443384	+	0.896332i	$0.353778\pi$
$998$	5.65685			0.179065
$999$	−11.3137	+	40.0000i	−0.357950	+	1.26554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.a.671.4	yes	4
3.2	odd	2	inner	804.2.c.a.671.1	✓	4
4.3	odd	2	inner	804.2.c.a.671.3	yes	4
12.11	even	2	inner	804.2.c.a.671.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.a.671.1	✓	4	3.2	odd	2	inner
804.2.c.a.671.2	yes	4	12.11	even	2	inner
804.2.c.a.671.3	yes	4	4.3	odd	2	inner
804.2.c.a.671.4	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(1.41421 + 1.00000i) q^{3} -2.00000 q^{4} -1.41421i q^{5} +(-1.41421 + 2.00000i) q^{6} -2.00000i q^{7} -2.82843i q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(1.41421 + 1.00000i) q^{3} -2.00000 q^{4} -1.41421i q^{5} +(-1.41421 + 2.00000i) q^{6} -2.00000i q^{7} -2.82843i q^{8} +(1.00000 + 2.82843i) q^{9} +2.00000 q^{10} +5.65685 q^{11} +(-2.82843 - 2.00000i) q^{12} +2.00000 q^{13} +2.82843 q^{14} +(1.41421 - 2.00000i) q^{15} +4.00000 q^{16} -5.65685i q^{17} +(-4.00000 + 1.41421i) q^{18} -4.00000i q^{19} +2.82843i q^{20} +(2.00000 - 2.82843i) q^{21} +8.00000i q^{22} -7.07107 q^{23} +(2.82843 - 4.00000i) q^{24} +3.00000 q^{25} +2.82843i q^{26} +(-1.41421 + 5.00000i) q^{27} +4.00000i q^{28} +5.65685i q^{29} +(2.82843 + 2.00000i) q^{30} +5.65685i q^{32} +(8.00000 + 5.65685i) q^{33} +8.00000 q^{34} -2.82843 q^{35} +(-2.00000 - 5.65685i) q^{36} +8.00000 q^{37} +5.65685 q^{38} +(2.82843 + 2.00000i) q^{39} -4.00000 q^{40} +1.41421i q^{41} +(4.00000 + 2.82843i) q^{42} +4.00000i q^{43} -11.3137 q^{44} +(4.00000 - 1.41421i) q^{45} -10.0000i q^{46} -7.07107 q^{47} +(5.65685 + 4.00000i) q^{48} +3.00000 q^{49} +4.24264i q^{50} +(5.65685 - 8.00000i) q^{51} -4.00000 q^{52} +12.7279i q^{53} +(-7.07107 - 2.00000i) q^{54} -8.00000i q^{55} -5.65685 q^{56} +(4.00000 - 5.65685i) q^{57} -8.00000 q^{58} -1.41421 q^{59} +(-2.82843 + 4.00000i) q^{60} -6.00000 q^{61} +(5.65685 - 2.00000i) q^{63} -8.00000 q^{64} -2.82843i q^{65} +(-8.00000 + 11.3137i) q^{66} -1.00000i q^{67} +11.3137i q^{68} +(-10.0000 - 7.07107i) q^{69} -4.00000i q^{70} -15.5563 q^{71} +(8.00000 - 2.82843i) q^{72} +10.0000 q^{73} +11.3137i q^{74} +(4.24264 + 3.00000i) q^{75} +8.00000i q^{76} -11.3137i q^{77} +(-2.82843 + 4.00000i) q^{78} -8.00000i q^{79} -5.65685i q^{80} +(-7.00000 + 5.65685i) q^{81} -2.00000 q^{82} +15.5563 q^{83} +(-4.00000 + 5.65685i) q^{84} -8.00000 q^{85} -5.65685 q^{86} +(-5.65685 + 8.00000i) q^{87} -16.0000i q^{88} -16.9706i q^{89} +(2.00000 + 5.65685i) q^{90} -4.00000i q^{91} +14.1421 q^{92} -10.0000i q^{94} -5.65685 q^{95} +(-5.65685 + 8.00000i) q^{96} -6.00000 q^{97} +4.24264i q^{98} +(5.65685 + 16.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} + 4 q^{9}+O(q^{10}) \) 4 * q - 8 * q^4 + 4 * q^9	\( 4 q - 8 q^{4} + 4 q^{9} + 8 q^{10} + 8 q^{13} + 16 q^{16} - 16 q^{18} + 8 q^{21} + 12 q^{25} + 32 q^{33} + 32 q^{34} - 8 q^{36} + 32 q^{37} - 16 q^{40} + 16 q^{42} + 16 q^{45} + 12 q^{49} - 16 q^{52} + 16 q^{57} - 32 q^{58} - 24 q^{61} - 32 q^{64} - 32 q^{66} - 40 q^{69} + 32 q^{72} + 40 q^{73} - 28 q^{81} - 8 q^{82} - 16 q^{84} - 32 q^{85} + 8 q^{90} - 24 q^{97}+O(q^{100}) \) 4 * q - 8 * q^4 + 4 * q^9 + 8 * q^10 + 8 * q^13 + 16 * q^16 - 16 * q^18 + 8 * q^21 + 12 * q^25 + 32 * q^33 + 32 * q^34 - 8 * q^36 + 32 * q^37 - 16 * q^40 + 16 * q^42 + 16 * q^45 + 12 * q^49 - 16 * q^52 + 16 * q^57 - 32 * q^58 - 24 * q^61 - 32 * q^64 - 32 * q^66 - 40 * q^69 + 32 * q^72 + 40 * q^73 - 28 * q^81 - 8 * q^82 - 16 * q^84 - 32 * q^85 + 8 * q^90 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more