LMFDB - Embedded newform 805.2.d.b.804.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(804,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("805.804");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.d (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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			804.6
Root			$-1.14412 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	805.804
Dual form			805.2.d.b.804.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.618034i q^{2} -1.00000 q^{3} +1.61803 q^{4} +(2.12132 - 0.707107i) q^{5} -0.618034i q^{6} +(1.58114 - 2.12132i) q^{7} +2.23607i q^{8} -2.00000 q^{9} +O(q^{10})$	\(q+0.618034i q^{2} -1.00000 q^{3} +1.61803 q^{4} +(2.12132 - 0.707107i) q^{5} -0.618034i q^{6} +(1.58114 - 2.12132i) q^{7} +2.23607i q^{8} -2.00000 q^{9} +(0.437016 + 1.31105i) q^{10} +5.99070i q^{11} -1.61803 q^{12} -0.236068 q^{13} +(1.31105 + 0.977198i) q^{14} +(-2.12132 + 0.707107i) q^{15} +1.85410 q^{16} +4.57649i q^{17} -1.23607i q^{18} +4.57649 q^{19} +(3.43237 - 1.14412i) q^{20} +(-1.58114 + 2.12132i) q^{21} -3.70246 q^{22} +(-4.24264 - 2.23607i) q^{23} -2.23607i q^{24} +(4.00000 - 3.00000i) q^{25} -0.145898i q^{26} +5.00000 q^{27} +(2.55834 - 3.43237i) q^{28} +3.00000 q^{29} +(-0.437016 - 1.31105i) q^{30} -3.00000i q^{31} +5.61803i q^{32} -5.99070i q^{33} -2.82843 q^{34} +(1.85410 - 5.61803i) q^{35} -3.23607 q^{36} +3.49613 q^{37} +2.82843i q^{38} +0.236068 q^{39} +(1.58114 + 4.74342i) q^{40} -5.76393i q^{41} +(-1.31105 - 0.977198i) q^{42} +4.91034 q^{43} +9.69316i q^{44} +(-4.24264 + 1.41421i) q^{45} +(1.38197 - 2.62210i) q^{46} -3.00000 q^{47} -1.85410 q^{48} +(-2.00000 - 6.70820i) q^{49} +(1.85410 + 2.47214i) q^{50} -4.57649i q^{51} -0.381966 q^{52} +4.24264 q^{53} +3.09017i q^{54} +(4.23607 + 12.7082i) q^{55} +(4.74342 + 3.53553i) q^{56} -4.57649 q^{57} +1.85410i q^{58} -0.472136i q^{59} +(-3.43237 + 1.14412i) q^{60} -7.73877 q^{61} +1.85410 q^{62} +(-3.16228 + 4.24264i) q^{63} +0.236068 q^{64} +(-0.500776 + 0.166925i) q^{65} +3.70246 q^{66} +11.9814 q^{67} +7.40492i q^{68} +(4.24264 + 2.23607i) q^{69} +(3.47214 + 1.14590i) q^{70} -6.70820 q^{71} -4.47214i q^{72} -15.1803 q^{73} +2.16073i q^{74} +(-4.00000 + 3.00000i) q^{75} +7.40492 q^{76} +(12.7082 + 9.47214i) q^{77} +0.145898i q^{78} +5.24419i q^{79} +(3.93314 - 1.31105i) q^{80} +1.00000 q^{81} +3.56231 q^{82} +6.73722i q^{83} +(-2.55834 + 3.43237i) q^{84} +(3.23607 + 9.70820i) q^{85} +3.03476i q^{86} -3.00000 q^{87} -13.3956 q^{88} -4.24264 q^{89} +(-0.874032 - 2.62210i) q^{90} +(-0.373256 + 0.500776i) q^{91} +(-6.86474 - 3.61803i) q^{92} +3.00000i q^{93} -1.85410i q^{94} +(9.70820 - 3.23607i) q^{95} -5.61803i q^{96} +(4.14590 - 1.23607i) q^{98} -11.9814i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{3} + 4 q^{4} - 16 q^{9}+O(q^{10}) $ 8 * q - 8 * q^3 + 4 * q^4 - 16 * q^9	$ 8 q - 8 q^{3} + 4 q^{4} - 16 q^{9} - 4 q^{12} + 16 q^{13} - 12 q^{16} + 32 q^{25} + 40 q^{27} + 24 q^{29} - 12 q^{35} - 8 q^{36} - 16 q^{39} + 20 q^{46} - 24 q^{47} + 12 q^{48} - 16 q^{49} - 12 q^{50} - 12 q^{52} + 16 q^{55} - 12 q^{62} - 16 q^{64} - 8 q^{70} - 32 q^{73} - 32 q^{75} + 48 q^{77} + 8 q^{81} - 52 q^{82} + 8 q^{85} - 24 q^{87} + 24 q^{95} + 60 q^{98}+O(q^{100}) $ 8 * q - 8 * q^3 + 4 * q^4 - 16 * q^9 - 4 * q^12 + 16 * q^13 - 12 * q^16 + 32 * q^25 + 40 * q^27 + 24 * q^29 - 12 * q^35 - 8 * q^36 - 16 * q^39 + 20 * q^46 - 24 * q^47 + 12 * q^48 - 16 * q^49 - 12 * q^50 - 12 * q^52 + 16 * q^55 - 12 * q^62 - 16 * q^64 - 8 * q^70 - 32 * q^73 - 32 * q^75 + 48 * q^77 + 8 * q^81 - 52 * q^82 + 8 * q^85 - 24 * q^87 + 24 * q^95 + 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$			0.618034i			0.437016i	0.975835	+	0.218508i	$0.0701190\pi$
$2$			0.618034i			0.437016i	−0.975835	+	0.218508i	$0.929881\pi$
$3$	−1.00000			−0.577350			−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000			−0.577350			−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.61803			0.809017
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$6$		−	0.618034i		−	0.252311i
$7$	1.58114	−	2.12132i	0.597614	−	0.801784i
$7$	1.58114	−	2.12132i	0.597614	−	0.801784i
$8$			2.23607i			0.790569i
$9$	−2.00000			−0.666667
$10$	0.437016	+	1.31105i	0.138197	+	0.414590i
$11$			5.99070i			1.80627i	0.429361	+	0.903133i	$0.358739\pi$
$11$			5.99070i			1.80627i	−0.429361	+	0.903133i	$0.641261\pi$
$12$	−1.61803			−0.467086
$13$	−0.236068			−0.0654735			−0.0327367	−	0.999464i	$-0.510422\pi$
$13$	−0.236068			−0.0654735			−0.0327367	+	0.999464i	$0.510422\pi$
$14$	1.31105	+	0.977198i	0.350392	+	0.261167i
$15$	−2.12132	+	0.707107i	−0.547723	+	0.182574i
$16$	1.85410			0.463525
$17$			4.57649i			1.10996i	0.831863	+	0.554981i	$0.187275\pi$
$17$			4.57649i			1.10996i	−0.831863	+	0.554981i	$0.812725\pi$
$18$		−	1.23607i		−	0.291344i
$19$	4.57649			1.04992			0.524960	−	0.851127i	$-0.324080\pi$
$19$	4.57649			1.04992			0.524960	+	0.851127i	$0.324080\pi$
$20$	3.43237	−	1.14412i	0.767501	−	0.255834i
$21$	−1.58114	+	2.12132i	−0.345033	+	0.462910i
$22$	−3.70246			−0.789367
$23$	−4.24264	−	2.23607i	−0.884652	−	0.466252i
$23$	−4.24264	−	2.23607i	−0.884652	−	0.466252i
$24$		−	2.23607i		−	0.456435i
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$		−	0.145898i		−	0.0286130i
$27$	5.00000			0.962250
$28$	2.55834	−	3.43237i	0.483480	−	0.648657i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	−0.437016	−	1.31105i	−0.0797878	−	0.239364i
$31$		−	3.00000i		−	0.538816i	−0.963026	−	0.269408i	$-0.913172\pi$
$31$		−	3.00000i		−	0.538816i	0.963026	−	0.269408i	$-0.0868280\pi$
$32$			5.61803i			0.993137i
$33$		−	5.99070i		−	1.04285i
$34$	−2.82843			−0.485071
$35$	1.85410	−	5.61803i	0.313400	−	0.949621i
$36$	−3.23607			−0.539345
$37$	3.49613			0.574760			0.287380	−	0.957817i	$-0.407216\pi$
$37$	3.49613			0.574760			0.287380	+	0.957817i	$0.407216\pi$
$38$			2.82843i			0.458831i
$39$	0.236068			0.0378011
$40$	1.58114	+	4.74342i	0.250000	+	0.750000i
$41$		−	5.76393i		−	0.900175i	−0.892984	−	0.450087i	$-0.851393\pi$
$41$		−	5.76393i		−	0.900175i	0.892984	−	0.450087i	$-0.148607\pi$
$42$	−1.31105	−	0.977198i	−0.202299	−	0.150785i
$43$	4.91034			0.748820			0.374410	−	0.927263i	$-0.377845\pi$
$43$	4.91034			0.748820			0.374410	+	0.927263i	$0.377845\pi$
$44$			9.69316i			1.46130i
$45$	−4.24264	+	1.41421i	−0.632456	+	0.210819i
$46$	1.38197	−	2.62210i	0.203760	−	0.386607i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	−1.85410			−0.267617
$49$	−2.00000	−	6.70820i	−0.285714	−	0.958315i
$50$	1.85410	+	2.47214i	0.262210	+	0.349613i
$51$		−	4.57649i		−	0.640837i
$52$	−0.381966			−0.0529692
$53$	4.24264			0.582772			0.291386	−	0.956606i	$-0.405884\pi$
$53$	4.24264			0.582772			0.291386	+	0.956606i	$0.405884\pi$
$54$			3.09017i			0.420519i
$55$	4.23607	+	12.7082i	0.571191	+	1.71357i
$56$	4.74342	+	3.53553i	0.633866	+	0.472456i
$57$	−4.57649			−0.606171
$58$			1.85410i			0.243456i
$59$		−	0.472136i		−	0.0614669i	−0.999528	−	0.0307334i	$-0.990216\pi$
$59$		−	0.472136i		−	0.0614669i	0.999528	−	0.0307334i	$-0.00978430\pi$
$60$	−3.43237	+	1.14412i	−0.443117	+	0.147706i
$61$	−7.73877			−0.990848			−0.495424	−	0.868651i	$-0.664987\pi$
$61$	−7.73877			−0.990848			−0.495424	+	0.868651i	$0.664987\pi$
$62$	1.85410			0.235471
$63$	−3.16228	+	4.24264i	−0.398410	+	0.534522i
$64$	0.236068			0.0295085
$65$	−0.500776	+	0.166925i	−0.0621136	+	0.0207045i
$66$	3.70246			0.455741
$67$	11.9814			1.46376			0.731881	−	0.681432i	$-0.238643\pi$
$67$	11.9814			1.46376			0.731881	+	0.681432i	$0.238643\pi$
$68$			7.40492i			0.897978i
$69$	4.24264	+	2.23607i	0.510754	+	0.269191i
$70$	3.47214	+	1.14590i	0.415000	+	0.136961i
$71$	−6.70820			−0.796117			−0.398059	−	0.917360i	$-0.630316\pi$
$71$	−6.70820			−0.796117			−0.398059	+	0.917360i	$0.630316\pi$
$72$		−	4.47214i		−	0.527046i
$73$	−15.1803			−1.77672			−0.888362	−	0.459143i	$-0.848156\pi$
$73$	−15.1803			−1.77672			−0.888362	+	0.459143i	$0.848156\pi$
$74$			2.16073i			0.251179i
$75$	−4.00000	+	3.00000i	−0.461880	+	0.346410i
$76$	7.40492			0.849402
$77$	12.7082	+	9.47214i	1.44823	+	1.07945i
$78$			0.145898i			0.0165197i
$79$			5.24419i			0.590018i	0.955495	+	0.295009i	$0.0953226\pi$
$79$			5.24419i			0.590018i	−0.955495	+	0.295009i	$0.904677\pi$
$80$	3.93314	−	1.31105i	0.439739	−	0.146580i
$81$	1.00000			0.111111
$82$	3.56231			0.393391
$83$			6.73722i			0.739506i	0.929130	+	0.369753i	$0.120558\pi$
$83$			6.73722i			0.739506i	−0.929130	+	0.369753i	$0.879442\pi$
$84$	−2.55834	+	3.43237i	−0.279137	+	0.374502i
$85$	3.23607	+	9.70820i	0.351001	+	1.05300i
$86$			3.03476i			0.327246i
$87$	−3.00000			−0.321634
$88$	−13.3956			−1.42798
$89$	−4.24264			−0.449719			−0.224860	−	0.974391i	$-0.572192\pi$
$89$	−4.24264			−0.449719			−0.224860	+	0.974391i	$0.572192\pi$
$90$	−0.874032	−	2.62210i	−0.0921311	−	0.276393i
$91$	−0.373256	+	0.500776i	−0.0391279	+	0.0524956i
$92$	−6.86474	−	3.61803i	−0.715698	−	0.377206i
$93$			3.00000i			0.311086i
$94$		−	1.85410i		−	0.191236i
$95$	9.70820	−	3.23607i	0.996041	−	0.332014i
$96$		−	5.61803i		−	0.573388i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	4.14590	−	1.23607i	0.418799	−	0.124862i
$99$		−	11.9814i		−	1.20418i
$100$	6.47214	−	4.85410i	0.647214	−	0.485410i
$101$		−	8.47214i		−	0.843009i	−0.906826	−	0.421505i	$-0.861502\pi$
$101$		−	8.47214i		−	0.843009i	0.906826	−	0.421505i	$-0.138498\pi$
$102$	2.82843			0.280056
$103$			9.48683i			0.934765i	0.884055	+	0.467383i	$0.154803\pi$
$103$			9.48683i			0.934765i	−0.884055	+	0.467383i	$0.845197\pi$
$104$		−	0.527864i		−	0.0517613i
$105$	−1.85410	+	5.61803i	−0.180942	+	0.548264i
$106$			2.62210i			0.254680i
$107$	−13.7295			−1.32728			−0.663639	−	0.748053i	$-0.730989\pi$
$107$	−13.7295			−1.32728			−0.663639	+	0.748053i	$0.730989\pi$
$108$	8.09017			0.778477
$109$		−	17.9721i		−	1.72142i	−0.509099	−	0.860708i	$-0.670021\pi$
$109$		−	17.9721i		−	1.72142i	0.509099	−	0.860708i	$-0.329979\pi$
$110$	−7.85410	+	2.61803i	−0.748859	+	0.249620i
$111$	−3.49613			−0.331838
$112$	2.93159	−	3.93314i	0.277009	−	0.371647i
$113$	4.24264			0.399114			0.199557	−	0.979886i	$-0.436050\pi$
$113$	4.24264			0.399114			0.199557	+	0.979886i	$0.436050\pi$
$114$		−	2.82843i		−	0.264906i
$115$	−10.5811	−	1.74342i	−0.986696	−	0.162574i
$116$	4.85410			0.450692
$117$	0.472136			0.0436490
$118$	0.291796			0.0268620
$119$	9.70820	+	7.23607i	0.889950	+	0.663329i
$120$	−1.58114	−	4.74342i	−0.144338	−	0.433013i
$121$	−24.8885			−2.26259
$122$		−	4.78282i		−	0.433016i
$123$			5.76393i			0.519716i
$124$		−	4.85410i		−	0.435911i
$125$	6.36396	−	9.19239i	0.569210	−	0.822192i
$126$	−2.62210	−	1.95440i	−0.233595	−	0.174111i
$127$		−	12.7082i		−	1.12767i	−0.825887	−	0.563835i	$-0.809325\pi$
$127$		−	12.7082i		−	1.12767i	0.825887	−	0.563835i	$-0.190675\pi$
$128$			11.3820i			1.00603i
$129$	−4.91034			−0.432331
$130$	−0.103165	−	0.309496i	−0.00904821	−	0.0271446i
$131$		−	11.4721i		−	1.00233i	−0.865353	−	0.501163i	$-0.832906\pi$
$131$		−	11.4721i		−	1.00233i	0.865353	−	0.501163i	$-0.167094\pi$
$132$		−	9.69316i		−	0.843682i
$133$	7.23607	−	9.70820i	0.627447	−	0.841808i
$134$			7.40492i			0.639688i
$135$	10.6066	−	3.53553i	0.912871	−	0.304290i
$136$	−10.2333			−0.877502
$137$	4.24264			0.362473			0.181237	−	0.983440i	$-0.441990\pi$
$137$	4.24264			0.362473			0.181237	+	0.983440i	$0.441990\pi$
$138$	−1.38197	+	2.62210i	−0.117641	+	0.223208i
$139$			22.4164i			1.90133i	0.310212	+	0.950667i	$0.399600\pi$
$139$			22.4164i			1.90133i	−0.310212	+	0.950667i	$0.600400\pi$
$140$	3.00000	−	9.09017i	0.253546	−	0.768260i
$141$	3.00000			0.252646
$142$		−	4.14590i		−	0.347916i
$143$		−	1.41421i		−	0.118262i
$144$	−3.70820			−0.309017
$145$	6.36396	−	2.12132i	0.528498	−	0.176166i
$146$		−	9.38197i		−	0.776457i
$147$	2.00000	+	6.70820i	0.164957	+	0.553283i
$148$	5.65685			0.464991
$149$		−	3.57494i		−	0.292870i	−0.989220	−	0.146435i	$-0.953220\pi$
$149$		−	3.57494i		−	0.292870i	0.989220	−	0.146435i	$-0.0467800\pi$
$150$	−1.85410	−	2.47214i	−0.151387	−	0.201849i
$151$	−17.6525			−1.43654			−0.718269	−	0.695765i	$-0.755065\pi$
$151$	−17.6525			−1.43654			−0.718269	+	0.695765i	$0.755065\pi$
$152$			10.2333i			0.830034i
$153$		−	9.15298i		−	0.739975i
$154$	−5.85410	+	7.85410i	−0.471737	+	0.632902i
$155$	−2.12132	−	6.36396i	−0.170389	−	0.511166i
$156$	0.381966			0.0305818
$157$		−	12.7279i		−	1.01580i	−0.861416	−	0.507899i	$-0.830422\pi$
$157$		−	12.7279i		−	1.01580i	0.861416	−	0.507899i	$-0.169578\pi$
$158$	−3.24109			−0.257847
$159$	−4.24264			−0.336463
$160$	3.97255	+	11.9176i	0.314058	+	0.942173i
$161$	−11.4516	+	5.46447i	−0.902514	+	0.430660i
$162$			0.618034i			0.0485573i
$163$			0.708204i			0.0554708i	0.999615	+	0.0277354i	$0.00882959\pi$
$163$			0.708204i			0.0554708i	−0.999615	+	0.0277354i	$0.991170\pi$
$164$		−	9.32624i		−	0.728257i
$165$	−4.23607	−	12.7082i	−0.329777	−	0.989332i
$166$	−4.16383			−0.323176
$167$	−1.41641			−0.109605			−0.0548025	−	0.998497i	$-0.517453\pi$
$167$	−1.41641			−0.109605			−0.0548025	+	0.998497i	$0.517453\pi$
$168$	−4.74342	−	3.53553i	−0.365963	−	0.272772i
$169$	−12.9443			−0.995713
$170$	−6.00000	+	2.00000i	−0.460179	+	0.153393i
$171$	−9.15298			−0.699946
$172$	7.94510			0.605808
$173$	−19.4164			−1.47620			−0.738101	−	0.674690i	$-0.764277\pi$
$173$	−19.4164			−1.47620			−0.738101	+	0.674690i	$0.764277\pi$
$174$		−	1.85410i		−	0.140559i
$175$	−0.0394057	−	13.2287i	−0.00297879	−	0.999996i
$176$			11.1074i			0.837250i
$177$			0.472136i			0.0354879i
$178$		−	2.62210i		−	0.196534i
$179$	6.70820			0.501395			0.250697	−	0.968066i	$-0.419340\pi$
$179$	6.70820			0.501395			0.250697	+	0.968066i	$0.419340\pi$
$180$	−6.86474	+	2.28825i	−0.511667	+	0.170556i
$181$	−18.6398			−1.38549			−0.692743	−	0.721184i	$-0.743598\pi$
$181$	−18.6398			−1.38549			−0.692743	+	0.721184i	$0.743598\pi$
$182$	−0.309496	−	0.230685i	−0.0229414	−	0.0170995i
$183$	7.73877			0.572066
$184$	5.00000	−	9.48683i	0.368605	−	0.699379i
$185$	7.41641	−	2.47214i	0.545265	−	0.181755i
$186$	−1.85410			−0.135949
$187$	−27.4164			−2.00489
$188$	−4.85410			−0.354022
$189$	7.90569	−	10.6066i	0.575055	−	0.771517i
$190$	2.00000	+	6.00000i	0.145095	+	0.435286i
$191$		−	5.57804i		−	0.403613i	−0.979425	−	0.201807i	$-0.935319\pi$
$191$		−	5.57804i		−	0.403613i	0.979425	−	0.201807i	$-0.0646812\pi$
$192$	−0.236068			−0.0170367
$193$			10.4164i			0.749789i	0.927067	+	0.374895i	$0.122321\pi$
$193$			10.4164i			0.749789i	−0.927067	+	0.374895i	$0.877679\pi$
$194$		0			0
$195$	0.500776	−	0.166925i	0.0358613	−	0.0119538i
$196$	−3.23607	−	10.8541i	−0.231148	−	0.775293i
$197$		−	8.88854i		−	0.633283i	−0.948545	−	0.316641i	$-0.897445\pi$
$197$		−	8.88854i		−	0.633283i	0.948545	−	0.316641i	$-0.102555\pi$
$198$	7.40492			0.526245
$199$	19.0525			1.35059			0.675297	−	0.737546i	$-0.264015\pi$
$199$	19.0525			1.35059			0.675297	+	0.737546i	$0.264015\pi$
$200$	6.70820	+	8.94427i	0.474342	+	0.632456i
$201$	−11.9814			−0.845103
$202$	5.23607			0.368408
$203$	4.74342	−	6.36396i	0.332923	−	0.446663i
$204$		−	7.40492i		−	0.518448i
$205$	−4.07572	−	12.2271i	−0.284660	−	0.853981i
$206$	−5.86319			−0.408507
$207$	8.48528	+	4.47214i	0.589768	+	0.310835i
$208$	−0.437694			−0.0303486
$209$			27.4164i			1.89643i
$210$	−3.47214	−	1.14590i	−0.239600	−	0.0790745i
$211$	8.47214			0.583246			0.291623	−	0.956533i	$-0.405805\pi$
$211$	8.47214			0.583246			0.291623	+	0.956533i	$0.405805\pi$
$212$	6.86474			0.471472
$213$	6.70820			0.459639
$214$		−	8.48528i		−	0.580042i
$215$	10.4164	−	3.47214i	0.710393	−	0.236798i
$216$			11.1803i			0.760726i
$217$	−6.36396	−	4.74342i	−0.432014	−	0.322004i
$218$	11.1074			0.752287
$219$	15.1803			1.02579
$220$	6.85410	+	20.5623i	0.462103	+	1.38631i
$221$		−	1.08036i		−	0.0726731i
$222$		−	2.16073i		−	0.145018i
$223$	24.4721			1.63878			0.819388	−	0.573240i	$-0.194314\pi$
$223$	24.4721			1.63878			0.819388	+	0.573240i	$0.194314\pi$
$224$	11.9176	+	8.88289i	0.796281	+	0.593513i
$225$	−8.00000	+	6.00000i	−0.533333	+	0.400000i
$226$			2.62210i			0.174419i
$227$			22.5486i			1.49660i	0.663358	+	0.748302i	$0.269130\pi$
$227$			22.5486i			1.49660i	−0.663358	+	0.748302i	$0.730870\pi$
$228$	−7.40492			−0.490403
$229$	−14.3972			−0.951392			−0.475696	−	0.879610i	$-0.657804\pi$
$229$	−14.3972			−0.951392			−0.475696	+	0.879610i	$0.657804\pi$
$230$	1.07749	−	6.53950i	0.0710476	−	0.431202i
$231$	−12.7082	−	9.47214i	−0.836138	−	0.623221i
$232$			6.70820i			0.440415i
$233$		−	21.9443i		−	1.43762i	−0.695208	−	0.718809i	$-0.744688\pi$
$233$		−	21.9443i		−	1.43762i	0.695208	−	0.718809i	$-0.255312\pi$
$234$			0.291796i			0.0190753i
$235$	−6.36396	+	2.12132i	−0.415139	+	0.138380i
$236$		−	0.763932i		−	0.0497277i
$237$		−	5.24419i		−	0.340647i
$238$	−4.47214	+	6.00000i	−0.289886	+	0.388922i
$239$	20.1246			1.30175			0.650876	−	0.759184i	$-0.274402\pi$
$239$	20.1246			1.30175			0.650876	+	0.759184i	$0.274402\pi$
$240$	−3.93314	+	1.31105i	−0.253883	+	0.0846278i
$241$	−17.2256			−1.10960			−0.554799	−	0.831984i	$-0.687205\pi$
$241$	−17.2256			−1.10960			−0.554799	+	0.831984i	$0.687205\pi$
$242$		−	15.3820i		−	0.988790i
$243$	−16.0000			−1.02640
$244$	−12.5216			−0.801613
$245$	−8.98606	−	12.8160i	−0.574098	−	0.818786i
$246$	−3.56231			−0.227124
$247$	−1.08036			−0.0687419
$248$	6.70820			0.425971
$249$		−	6.73722i		−	0.426954i
$250$	5.68121	+	3.93314i	0.359311	+	0.248754i
$251$	17.9721			1.13439			0.567195	−	0.823584i	$-0.308029\pi$
$251$	17.9721			1.13439			0.567195	+	0.823584i	$0.308029\pi$
$252$	−5.11667	+	6.86474i	−0.322320	+	0.432438i
$253$	13.3956	−	25.4164i	0.842176	−	1.59792i
$254$	7.85410			0.492810
$255$	−3.23607	−	9.70820i	−0.202650	−	0.607951i
$256$	−6.56231			−0.410144
$257$	−6.70820			−0.418446			−0.209223	−	0.977868i	$-0.567093\pi$
$257$	−6.70820			−0.418446			−0.209223	+	0.977868i	$0.567093\pi$
$258$		−	3.03476i		−	0.188936i
$259$	5.52786	−	7.41641i	0.343485	−	0.460833i
$260$	−0.810272	+	0.270091i	−0.0502510	+	0.0167503i
$261$	−6.00000			−0.371391
$262$	7.09017			0.438032
$263$	−23.2163			−1.43158			−0.715789	−	0.698316i	$-0.753933\pi$
$263$	−23.2163			−1.43158			−0.715789	+	0.698316i	$0.753933\pi$
$264$	13.3956			0.824444
$265$	9.00000	−	3.00000i	0.552866	−	0.184289i
$266$	6.00000	+	4.47214i	0.367884	+	0.274204i
$267$	4.24264			0.259645
$268$	19.3863			1.18421
$269$			25.6525i			1.56406i	0.623241	+	0.782030i	$0.285815\pi$
$269$			25.6525i			1.56406i	−0.623241	+	0.782030i	$0.714185\pi$
$270$	2.18508	+	6.55524i	0.132980	+	0.398939i
$271$		−	18.0000i		−	1.09342i	−0.837321	−	0.546711i	$-0.815880\pi$
$271$		−	18.0000i		−	1.09342i	0.837321	−	0.546711i	$-0.184120\pi$
$272$			8.48528i			0.514496i
$273$	0.373256	−	0.500776i	0.0225905	−	0.0303083i
$274$			2.62210i			0.158407i
$275$	17.9721	+	23.9628i	1.08376	+	1.44501i
$276$	6.86474	+	3.61803i	0.413209	+	0.217780i
$277$			1.58359i			0.0951488i	0.998868	+	0.0475744i	$0.0151491\pi$
$277$			1.58359i			0.0951488i	−0.998868	+	0.0475744i	$0.984851\pi$
$278$	−13.8541			−0.830914
$279$			6.00000i			0.359211i
$280$	12.5623	+	4.14590i	0.750741	+	0.247765i
$281$			6.99226i			0.417123i	0.978009	+	0.208562i	$0.0668782\pi$
$281$			6.99226i			0.417123i	−0.978009	+	0.208562i	$0.933122\pi$
$282$			1.85410i			0.110410i
$283$			5.24419i			0.311735i	0.987778	+	0.155867i	$0.0498173\pi$
$283$			5.24419i			0.311735i	−0.987778	+	0.155867i	$0.950183\pi$
$284$	−10.8541			−0.644072
$285$	−9.70820	+	3.23607i	−0.575064	+	0.191688i
$286$	0.874032			0.0516826
$287$	−12.2271	−	9.11358i	−0.721746	−	0.537957i
$288$		−	11.2361i		−	0.662092i
$289$	−3.94427			−0.232016
$290$	1.31105	+	3.93314i	0.0769874	+	0.230962i
$291$		0			0
$292$	−24.5623			−1.43740
$293$		−	24.9644i		−	1.45843i	−0.684282	−	0.729217i	$-0.739884\pi$
$293$		−	24.9644i		−	1.45843i	0.684282	−	0.729217i	$-0.260116\pi$
$294$	−4.14590	+	1.23607i	−0.241794	+	0.0720889i
$295$	−0.333851	−	1.00155i	−0.0194375	−	0.0583126i
$296$			7.81758i			0.454388i
$297$			29.9535i			1.73808i
$298$	2.20943			0.127989
$299$	1.00155	+	0.527864i	0.0579212	+	0.0305272i
$300$	−6.47214	+	4.85410i	−0.373669	+	0.280252i
$301$	7.76393	−	10.4164i	0.447506	−	0.600392i
$302$		−	10.9098i		−	0.627790i
$303$			8.47214i			0.486711i
$304$	8.48528			0.486664
$305$	−16.4164	+	5.47214i	−0.940001	+	0.313334i
$306$	5.65685			0.323381
$307$	22.9443			1.30950			0.654749	−	0.755846i	$-0.272774\pi$
$307$	22.9443			1.30950			0.654749	+	0.755846i	$0.272774\pi$
$308$	20.5623	+	15.3262i	1.17165	+	0.873293i
$309$		−	9.48683i		−	0.539687i
$310$	3.93314	−	1.31105i	0.223388	−	0.0744625i
$311$		−	22.5279i		−	1.27744i	−0.769440	−	0.638719i	$-0.779465\pi$
$311$		−	22.5279i		−	1.27744i	0.769440	−	0.638719i	$-0.220535\pi$
$312$			0.527864i			0.0298844i
$313$		−	1.00155i		−	0.0566110i	−0.999599	−	0.0283055i	$-0.990989\pi$
$313$		−	1.00155i		−	0.0566110i	0.999599	−	0.0283055i	$-0.00901113\pi$
$314$	7.86629			0.443920
$315$	−3.70820	+	11.2361i	−0.208934	+	0.633081i
$316$			8.48528i			0.477334i
$317$			26.4721i			1.48682i	0.668834	+	0.743412i	$0.266794\pi$
$317$			26.4721i			1.48682i	−0.668834	+	0.743412i	$0.733206\pi$
$318$		−	2.62210i		−	0.147040i
$319$			17.9721i			1.00625i
$320$	0.500776	−	0.166925i	0.0279942	−	0.00933141i
$321$	13.7295			0.766304
$322$	−3.37723	−	7.07749i	−0.188205	−	0.394413i
$323$			20.9443i			1.16537i
$324$	1.61803			0.0898908
$325$	−0.944272	+	0.708204i	−0.0523788	+	0.0392841i
$326$	−0.437694			−0.0242416
$327$			17.9721i			0.993860i
$328$	12.8885			0.711651
$329$	−4.74342	+	6.36396i	−0.261513	+	0.350857i
$330$	7.85410	−	2.61803i	0.432354	−	0.144118i
$331$	−4.34752			−0.238962			−0.119481	−	0.992837i	$-0.538123\pi$
$331$	−4.34752			−0.238962			−0.119481	+	0.992837i	$0.538123\pi$
$332$			10.9010i			0.598273i
$333$	−6.99226			−0.383173
$334$		−	0.875388i		−	0.0478991i
$335$	25.4164	−	8.47214i	1.38865	−	0.462882i
$336$	−2.93159	+	3.93314i	−0.159931	+	0.214571i
$337$	15.2225			0.829222			0.414611	−	0.909999i	$-0.363918\pi$
$337$	15.2225			0.829222			0.414611	+	0.909999i	$0.363918\pi$
$338$		−	8.00000i		−	0.435143i
$339$	−4.24264			−0.230429
$340$	5.23607	+	15.7082i	0.283966	+	0.851897i
$341$	17.9721			0.973245
$342$		−	5.65685i		−	0.305888i
$343$	−17.3925	−	6.36396i	−0.939108	−	0.343622i
$344$			10.9799i			0.591994i
$345$	10.5811	+	1.74342i	0.569669	+	0.0938624i
$346$		−	12.0000i		−	0.645124i
$347$		−	10.9443i		−	0.587519i	−0.955879	−	0.293760i	$-0.905093\pi$
$347$		−	10.9443i		−	0.587519i	0.955879	−	0.293760i	$-0.0949065\pi$
$348$	−4.85410			−0.260207
$349$		−	32.1246i		−	1.71959i	−0.510638	−	0.859796i	$-0.670591\pi$
$349$		−	32.1246i		−	1.71959i	0.510638	−	0.859796i	$-0.329409\pi$
$350$	8.17578	−	0.0243541i	0.437014	−	0.00130178i
$351$	−1.18034			−0.0630019
$352$	−33.6560			−1.79387
$353$	−17.2918			−0.920349			−0.460175	−	0.887828i	$-0.652213\pi$
$353$	−17.2918			−0.920349			−0.460175	+	0.887828i	$0.652213\pi$
$354$	−0.291796			−0.0155088
$355$	−14.2302	+	4.74342i	−0.755263	+	0.251754i
$356$	−6.86474			−0.363830
$357$	−9.70820	−	7.23607i	−0.513813	−	0.382973i
$358$			4.14590i			0.219118i
$359$			12.3941i			0.654134i	0.945001	+	0.327067i	$0.106060\pi$
$359$			12.3941i			0.654134i	−0.945001	+	0.327067i	$0.893940\pi$
$360$	−3.16228	−	9.48683i	−0.166667	−	0.500000i
$361$	1.94427			0.102330
$362$		−	11.5200i		−	0.605480i
$363$	24.8885			1.30631
$364$	−0.603941	+	0.810272i	−0.0316551	+	0.0424698i
$365$	−32.2024	+	10.7341i	−1.68555	+	0.561850i
$366$			4.78282i			0.250002i
$367$		−	32.7031i		−	1.70709i	−0.521019	−	0.853545i	$-0.674448\pi$
$367$		−	32.7031i		−	1.70709i	0.521019	−	0.853545i	$-0.325552\pi$
$368$	−7.86629	−	4.14590i	−0.410059	−	0.216120i
$369$			11.5279i			0.600117i
$370$	1.52786	+	4.58359i	0.0794299	+	0.238290i
$371$	6.70820	−	9.00000i	0.348273	−	0.467257i
$372$			4.85410i			0.251673i
$373$	−28.5393			−1.47771			−0.738855	−	0.673865i	$-0.764633\pi$
$373$	−28.5393			−1.47771			−0.738855	+	0.673865i	$0.764633\pi$
$374$		−	16.9443i		−	0.876167i
$375$	−6.36396	+	9.19239i	−0.328634	+	0.474693i
$376$		−	6.70820i		−	0.345949i
$377$	−0.708204			−0.0364744
$378$	6.55524	+	4.88599i	0.337165	+	0.251308i
$379$			7.48373i			0.384413i	0.981354	+	0.192207i	$0.0615644\pi$
$379$			7.48373i			0.384413i	−0.981354	+	0.192207i	$0.938436\pi$
$380$	15.7082	−	5.23607i	0.805814	−	0.268605i
$381$			12.7082i			0.651061i
$382$	3.44742			0.176385
$383$			23.5502i			1.20336i	0.798738	+	0.601678i	$0.205501\pi$
$383$			23.5502i			1.20336i	−0.798738	+	0.601678i	$0.794499\pi$
$384$		−	11.3820i		−	0.580834i
$385$	33.6560	+	11.1074i	1.71527	+	0.566084i
$386$	−6.43769			−0.327670
$387$	−9.82068			−0.499213
$388$		0			0
$389$		−	9.82068i		−	0.497928i	−0.968513	−	0.248964i	$-0.919910\pi$
$389$		−	9.82068i		−	0.497928i	0.968513	−	0.248964i	$-0.0800902\pi$
$390$	0.103165	+	0.309496i	0.00522399	+	0.0156720i
$391$	10.2333	−	19.4164i	0.517523	−	0.981930i
$392$	15.0000	−	4.47214i	0.757614	−	0.225877i
$393$			11.4721i			0.578693i
$394$	5.49342			0.276755
$395$	3.70820	+	11.1246i	0.186580	+	0.559740i
$396$		−	19.3863i		−	0.974200i
$397$	4.23607			0.212602			0.106301	−	0.994334i	$-0.466099\pi$
$397$	4.23607			0.212602			0.106301	+	0.994334i	$0.466099\pi$
$398$			11.7751i			0.590231i
$399$	−7.23607	+	9.70820i	−0.362257	+	0.486018i
$400$	7.41641	−	5.56231i	0.370820	−	0.278115i
$401$		−	27.0463i		−	1.35063i	−0.737531	−	0.675314i	$-0.764008\pi$
$401$		−	27.0463i		−	1.35063i	0.737531	−	0.675314i	$-0.235992\pi$
$402$		−	7.40492i		−	0.369324i
$403$			0.708204i			0.0352782i
$404$		−	13.7082i		−	0.682009i
$405$	2.12132	−	0.707107i	0.105409	−	0.0351364i
$406$	3.93314	+	2.93159i	0.195199	+	0.145492i
$407$			20.9443i			1.03817i
$408$	10.2333			0.506626
$409$			8.12461i			0.401736i	0.979618	+	0.200868i	$0.0643763\pi$
$409$			8.12461i			0.401736i	−0.979618	+	0.200868i	$0.935624\pi$
$410$	7.55679	−	2.51893i	0.373203	−	0.124401i
$411$	−4.24264			−0.209274
$412$			15.3500i			0.756241i
$413$	−1.00155	−	0.746512i	−0.0492831	−	0.0367335i
$414$	−2.76393	+	5.24419i	−0.135840	+	0.257738i
$415$	4.76393	+	14.2918i	0.233852	+	0.701557i
$416$		−	1.32624i		−	0.0650242i
$417$		−	22.4164i		−	1.09774i
$418$	−16.9443			−0.828771
$419$	−15.9690			−0.780137			−0.390069	−	0.920786i	$-0.627549\pi$
$419$	−15.9690			−0.780137			−0.390069	+	0.920786i	$0.627549\pi$
$420$	−3.00000	+	9.09017i	−0.146385	+	0.443555i
$421$			14.7310i			0.717946i	0.933348	+	0.358973i	$0.116873\pi$
$421$			14.7310i			0.717946i	−0.933348	+	0.358973i	$0.883127\pi$
$422$			5.23607i			0.254888i
$423$	6.00000			0.291730
$424$			9.48683i			0.460721i
$425$	13.7295	+	18.3060i	0.665977	+	0.887970i
$426$			4.14590i			0.200869i
$427$	−12.2361	+	16.4164i	−0.592145	+	0.794446i
$428$	−22.2148			−1.07379
$429$			1.41421i			0.0682789i
$430$	2.14590	+	6.43769i	0.103484	+	0.310453i
$431$			29.3646i			1.41444i	0.706991	+	0.707222i	$0.250052\pi$
$431$			29.3646i			1.41444i	−0.706991	+	0.707222i	$0.749948\pi$
$432$	9.27051			0.446028
$433$		−	22.2148i		−	1.06757i	−0.845619	−	0.533786i	$-0.820769\pi$
$433$		−	22.2148i		−	1.06757i	0.845619	−	0.533786i	$-0.179231\pi$
$434$	2.93159	−	3.93314i	0.140721	−	0.188797i
$435$	−6.36396	+	2.12132i	−0.305129	+	0.101710i
$436$		−	29.0795i		−	1.39266i
$437$	−19.4164	−	10.2333i	−0.928813	−	0.489527i
$438$			9.38197i			0.448288i
$439$			16.4164i			0.783512i	0.920069	+	0.391756i	$0.128132\pi$
$439$			16.4164i			0.783512i	−0.920069	+	0.391756i	$0.871868\pi$
$440$	−28.4164	+	9.47214i	−1.35470	+	0.451566i
$441$	4.00000	+	13.4164i	0.190476	+	0.638877i
$442$	0.667701			0.0317593
$443$		−	29.1803i		−	1.38640i	−0.720745	−	0.693200i	$-0.756200\pi$
$443$		−	29.1803i		−	1.38640i	0.720745	−	0.693200i	$-0.243800\pi$
$444$	−5.65685			−0.268462
$445$	−9.00000	+	3.00000i	−0.426641	+	0.142214i
$446$			15.1246i			0.716171i
$447$			3.57494i			0.169089i
$448$	0.373256	−	0.500776i	0.0176347	−	0.0236594i
$449$	−4.58359			−0.216313			−0.108157	−	0.994134i	$-0.534495\pi$
$449$	−4.58359			−0.216313			−0.108157	+	0.994134i	$0.534495\pi$
$450$	−3.70820	−	4.94427i	−0.174806	−	0.233075i
$451$	34.5300			1.62595
$452$	6.86474			0.322890
$453$	17.6525			0.829386
$454$	−13.9358			−0.654040
$455$	−0.437694	+	1.32624i	−0.0205194	+	0.0621750i
$456$		−	10.2333i		−	0.479220i
$457$	−9.56564			−0.447462			−0.223731	−	0.974651i	$-0.571824\pi$
$457$	−9.56564			−0.447462			−0.223731	+	0.974651i	$0.571824\pi$
$458$		−	8.89794i		−	0.415774i
$459$			22.8825i			1.06806i
$460$	−17.1206	−	2.82091i	−0.798254	−	0.131525i
$461$			34.2361i			1.59453i	0.603628	+	0.797266i	$0.293721\pi$
$461$			34.2361i			1.59453i	−0.603628	+	0.797266i	$0.706279\pi$
$462$	5.85410	−	7.85410i	0.272357	−	0.365406i
$463$		−	30.0000i		−	1.39422i	−0.716965	−	0.697109i	$-0.754469\pi$
$463$		−	30.0000i		−	1.39422i	0.716965	−	0.697109i	$-0.245531\pi$
$464$	5.56231			0.258224
$465$	2.12132	+	6.36396i	0.0983739	+	0.295122i
$466$	13.5623			0.628262
$467$			9.97831i			0.461741i	0.972984	+	0.230870i	$0.0741574\pi$
$467$			9.97831i			0.461741i	−0.972984	+	0.230870i	$0.925843\pi$
$468$	0.763932			0.0353128
$469$	18.9443	−	25.4164i	0.874765	−	1.17362i
$470$	−1.31105	−	3.93314i	−0.0604741	−	0.181422i
$471$			12.7279i			0.586472i
$472$	1.05573			0.0485938
$473$			29.4164i			1.35257i
$474$	3.24109			0.148868
$475$	18.3060	−	13.7295i	0.839935	−	0.629951i
$476$	15.7082	+	11.7082i	0.719984	+	0.536645i
$477$	−8.48528			−0.388514
$478$			12.4377i			0.568887i
$479$	28.4605			1.30039			0.650197	−	0.759766i	$-0.274686\pi$
$479$	28.4605			1.30039			0.650197	+	0.759766i	$0.274686\pi$
$480$	−3.97255	−	11.9176i	−0.181321	−	0.543964i
$481$	−0.825324			−0.0376315
$482$		−	10.6460i		−	0.484912i
$483$	11.4516	−	5.46447i	0.521067	−	0.248642i
$484$	−40.2705			−1.83048
$485$		0			0
$486$		−	9.88854i		−	0.448553i
$487$		−	30.7082i		−	1.39152i	−0.718274	−	0.695761i	$-0.755067\pi$
$487$		−	30.7082i		−	1.39152i	0.718274	−	0.695761i	$-0.244933\pi$
$488$		−	17.3044i		−	0.783334i
$489$		−	0.708204i		−	0.0320261i
$490$	7.92075	−	5.55369i	0.357823	−	0.250890i
$491$	−8.12461			−0.366659			−0.183329	−	0.983052i	$-0.558687\pi$
$491$	−8.12461			−0.366659			−0.183329	+	0.983052i	$0.558687\pi$
$492$			9.32624i			0.420459i
$493$			13.7295i			0.618344i
$494$		−	0.667701i		−	0.0300413i
$495$	−8.47214	−	25.4164i	−0.380794	−	1.14238i
$496$		−	5.56231i		−	0.249755i
$497$	−10.6066	+	14.2302i	−0.475771	+	0.638314i
$498$	4.16383			0.186586
$499$	−17.7639			−0.795223			−0.397611	−	0.917554i	$-0.630161\pi$
$499$	−17.7639			−0.795223			−0.397611	+	0.917554i	$0.630161\pi$
$500$	10.2971	−	14.8736i	0.460501	−	0.665167i
$501$	1.41641			0.0632804
$502$			11.1074i			0.495747i
$503$			7.07107i			0.315283i	0.987496	+	0.157642i	$0.0503891\pi$
$503$			7.07107i			0.315283i	−0.987496	+	0.157642i	$0.949611\pi$
$504$	−9.48683	−	7.07107i	−0.422577	−	0.314970i
$505$	−5.99070	−	17.9721i	−0.266583	−	0.799749i
$506$	15.7082	+	8.27895i	0.698315	+	0.368044i
$507$	12.9443			0.574875
$508$		−	20.5623i		−	0.912305i
$509$		−	22.5967i		−	1.00158i	−0.865568	−	0.500792i	$-0.833042\pi$
$509$		−	22.5967i		−	1.00158i	0.865568	−	0.500792i	$-0.166958\pi$
$510$	6.00000	−	2.00000i	0.265684	−	0.0885615i
$511$	−24.0022	+	32.2024i	−1.06180	+	1.42455i
$512$			18.7082i			0.826794i
$513$	22.8825			1.01029
$514$		−	4.14590i		−	0.182868i
$515$	6.70820	+	20.1246i	0.295599	+	0.886796i
$516$	−7.94510			−0.349764
$517$		−	17.9721i		−	0.790413i
$518$	4.58359	+	3.41641i	0.201391	+	0.150108i
$519$	19.4164			0.852286
$520$	−0.373256	−	1.11977i	−0.0163684	−	0.0491051i
$521$	−10.4884			−0.459504			−0.229752	−	0.973249i	$-0.573792\pi$
$521$	−10.4884			−0.459504			−0.229752	+	0.973249i	$0.573792\pi$
$522$		−	3.70820i		−	0.162304i
$523$			37.9473i			1.65932i	0.558268	+	0.829660i	$0.311466\pi$
$523$			37.9473i			1.65932i	−0.558268	+	0.829660i	$0.688534\pi$
$524$		−	18.5623i		−	0.810898i
$525$	0.0394057	+	13.2287i	0.00171981	+	0.577348i
$526$		−	14.3485i		−	0.625623i
$527$	13.7295			0.598065
$528$		−	11.1074i		−	0.483387i
$529$	13.0000	+	18.9737i	0.565217	+	0.824942i
$530$	1.85410	+	5.56231i	0.0805370	+	0.241611i
$531$			0.944272i			0.0409779i
$532$	11.7082	−	15.7082i	0.507615	−	0.681037i
$533$			1.36068i			0.0589376i
$534$			2.62210i			0.113469i
$535$	−29.1246	+	9.70820i	−1.25917	+	0.419722i
$536$			26.7912i			1.15721i
$537$	−6.70820			−0.289480
$538$	−15.8541			−0.683519
$539$	40.1869	−	11.9814i	1.73097	−	0.516076i
$540$	17.1618	−	5.72061i	0.738528	−	0.246176i
$541$	24.8885			1.07004			0.535021	−	0.844839i	$-0.320304\pi$
$541$	24.8885			1.07004			0.535021	+	0.844839i	$0.320304\pi$
$542$	11.1246			0.477843
$543$	18.6398			0.799911
$544$	−25.7109			−1.10235
$545$	−12.7082	−	38.1246i	−0.544360	−	1.63308i
$546$	0.309496	+	0.230685i	0.0132452	+	0.00987241i
$547$			38.1246i			1.63009i	0.579397	+	0.815045i	$0.303288\pi$
$547$			38.1246i			1.63009i	−0.579397	+	0.815045i	$0.696712\pi$
$548$	6.86474			0.293247
$549$	15.4775			0.660565
$550$	−14.8098	+	11.1074i	−0.631494	+	0.473620i
$551$	13.7295			0.584895
$552$	−5.00000	+	9.48683i	−0.212814	+	0.403786i
$553$	11.1246	+	8.29180i	0.473067	+	0.352603i
$554$	−0.978714			−0.0415816
$555$	−7.41641	+	2.47214i	−0.314809	+	0.104936i
$556$			36.2705i			1.53821i
$557$	39.1853			1.66034			0.830168	−	0.557514i	$-0.188245\pi$
$557$	39.1853			1.66034			0.830168	+	0.557514i	$0.188245\pi$
$558$	−3.70820			−0.156981
$559$	−1.15917			−0.0490279
$560$	3.43769	−	10.4164i	0.145269	−	0.440174i
$561$	27.4164			1.15752
$562$	−4.32145			−0.182289
$563$		−	1.41421i		−	0.0596020i	−0.999556	−	0.0298010i	$-0.990513\pi$
$563$		−	1.41421i		−	0.0596020i	0.999556	−	0.0298010i	$-0.00948736\pi$
$564$	4.85410			0.204395
$565$	9.00000	−	3.00000i	0.378633	−	0.126211i
$566$	−3.24109			−0.136233
$567$	1.58114	−	2.12132i	0.0664016	−	0.0890871i
$568$		−	15.0000i		−	0.629386i
$569$			7.99381i			0.335118i	0.985862	+	0.167559i	$0.0535884\pi$
$569$			7.99381i			0.335118i	−0.985862	+	0.167559i	$0.946412\pi$
$570$	−2.00000	−	6.00000i	−0.0837708	−	0.251312i
$571$		−	14.7310i		−	0.616474i	−0.951310	−	0.308237i	$-0.900261\pi$
$571$		−	14.7310i		−	0.616474i	0.951310	−	0.308237i	$-0.0997390\pi$
$572$		−	2.28825i		−	0.0956764i
$573$			5.57804i			0.233026i
$574$	5.63250	−	7.55679i	0.235096	−	0.315414i
$575$	−23.6788	+	3.78365i	−0.987473	+	0.157789i
$576$	−0.472136			−0.0196723
$577$	4.23607			0.176350			0.0881749	−	0.996105i	$-0.471897\pi$
$577$	4.23607			0.176350			0.0881749	+	0.996105i	$0.471897\pi$
$578$		−	2.43769i		−	0.101395i
$579$		−	10.4164i		−	0.432891i
$580$	10.2971	−	3.43237i	0.427564	−	0.142521i
$581$	14.2918	+	10.6525i	0.592924	+	0.441939i
$582$		0			0
$583$			25.4164i			1.05264i
$584$		−	33.9443i		−	1.40462i
$585$	1.00155	−	0.333851i	0.0414091	−	0.0138030i
$586$	15.4288			0.637359
$587$	−17.8328			−0.736039			−0.368020	−	0.929818i	$-0.619964\pi$
$587$	−17.8328			−0.736039			−0.368020	+	0.929818i	$0.619964\pi$
$588$	3.23607	+	10.8541i	0.133453	+	0.447616i
$589$		−	13.7295i		−	0.565713i
$590$	0.618993	−	0.206331i	0.0254835	−	0.00849451i
$591$			8.88854i			0.365626i
$592$	6.48218			0.266416
$593$	38.8328			1.59467			0.797336	−	0.603535i	$-0.206242\pi$
$593$	38.8328			1.59467			0.797336	+	0.603535i	$0.206242\pi$
$594$	−18.5123			−0.759569
$595$	25.7109	+	8.48528i	1.05404	+	0.347863i
$596$		−	5.78437i		−	0.236937i
$597$	−19.0525			−0.779766
$598$	−0.326238	+	0.618993i	−0.0133409	+	0.0253125i
$599$	−6.00000			−0.245153			−0.122577	−	0.992459i	$-0.539116\pi$
$599$	−6.00000			−0.245153			−0.122577	+	0.992459i	$0.539116\pi$
$600$	−6.70820	−	8.94427i	−0.273861	−	0.365148i
$601$			24.7082i			1.00787i	0.863742	+	0.503934i	$0.168115\pi$
$601$			24.7082i			1.00787i	−0.863742	+	0.503934i	$0.831885\pi$
$602$	6.43769	+	4.79837i	0.262381	+	0.195567i
$603$	−23.9628			−0.975841
$604$	−28.5623			−1.16218
$605$	−52.7966	+	17.5989i	−2.14649	+	0.715495i
$606$	−5.23607			−0.212701
$607$	13.8885			0.563719			0.281859	−	0.959456i	$-0.409049\pi$
$607$	13.8885			0.563719			0.281859	+	0.959456i	$0.409049\pi$
$608$			25.7109i			1.04271i
$609$	−4.74342	+	6.36396i	−0.192213	+	0.257881i
$610$	−3.38197	−	10.1459i	−0.136932	−	0.410795i
$611$	0.708204			0.0286509
$612$		−	14.8098i		−	0.598652i
$613$	−6.81603			−0.275297			−0.137648	−	0.990481i	$-0.543954\pi$
$613$	−6.81603			−0.275297			−0.137648	+	0.990481i	$0.543954\pi$
$614$			14.1803i			0.572272i
$615$	4.07572	+	12.2271i	0.164349	+	0.493046i
$616$	−21.1803	+	28.4164i	−0.853380	+	1.14493i
$617$	41.1884			1.65818			0.829092	−	0.559113i	$-0.188858\pi$
$617$	41.1884			1.65818			0.829092	+	0.559113i	$0.188858\pi$
$618$	5.86319			0.235852
$619$	−1.25659			−0.0505066			−0.0252533	−	0.999681i	$-0.508039\pi$
$619$	−1.25659			−0.0505066			−0.0252533	+	0.999681i	$0.508039\pi$
$620$	−3.43237	−	10.2971i	−0.137847	−	0.413542i
$621$	−21.2132	−	11.1803i	−0.851257	−	0.448652i
$622$	13.9230			0.558261
$623$	−6.70820	+	9.00000i	−0.268759	+	0.360577i
$624$	0.437694			0.0175218
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$	0.618993			0.0247399
$627$		−	27.4164i		−	1.09491i
$628$		−	20.5942i		−	0.821798i
$629$			16.0000i			0.637962i
$630$	−6.94427	−	2.29180i	−0.276666	−	0.0913073i
$631$			31.7016i			1.26202i	0.775775	+	0.631010i	$0.217359\pi$
$631$			31.7016i			1.26202i	−0.775775	+	0.631010i	$0.782641\pi$
$632$	−11.7264			−0.466450
$633$	−8.47214			−0.336737
$634$	−16.3607			−0.649766
$635$	−8.98606	−	26.9582i	−0.356601	−	1.06980i
$636$	−6.86474			−0.272205
$637$	0.472136	+	1.58359i	0.0187067	+	0.0627442i
$638$	−11.1074			−0.439745
$639$	13.4164			0.530745
$640$	8.04827	+	24.1448i	0.318136	+	0.954407i
$641$		−	6.81603i		−	0.269217i	−0.990899	−	0.134608i	$-0.957022\pi$
$641$		−	6.81603i		−	0.269217i	0.990899	−	0.134608i	$-0.0429777\pi$
$642$			8.48528i			0.334887i
$643$			1.00155i			0.0394973i	0.999805	+	0.0197487i	$0.00628661\pi$
$643$			1.00155i			0.0394973i	−0.999805	+	0.0197487i	$0.993713\pi$
$644$	−18.5291	+	8.84169i	−0.730149	+	0.348411i
$645$	−10.4164	+	3.47214i	−0.410146	+	0.136715i
$646$	−12.9443			−0.509286
$647$	−29.8328			−1.17285			−0.586425	−	0.810004i	$-0.699465\pi$
$647$	−29.8328			−1.17285			−0.586425	+	0.810004i	$0.699465\pi$
$648$			2.23607i			0.0878410i
$649$	2.82843			0.111025
$650$	−0.437694	−	0.583592i	−0.0171678	−	0.0228904i
$651$	6.36396	+	4.74342i	0.249423	+	0.185909i
$652$			1.14590i			0.0448768i
$653$		−	37.9443i		−	1.48487i	−0.669916	−	0.742437i	$-0.733670\pi$
$653$		−	37.9443i		−	1.48487i	0.669916	−	0.742437i	$-0.266330\pi$
$654$	−11.1074			−0.434333
$655$	−8.11203	−	24.3361i	−0.316963	−	0.950889i
$656$		−	10.6869i		−	0.417254i
$657$	30.3607			1.18448
$658$	−3.93314	−	2.93159i	−0.153330	−	0.114285i
$659$		−	15.5563i		−	0.605989i	−0.952992	−	0.302995i	$-0.902014\pi$
$659$		−	15.5563i		−	0.605989i	0.952992	−	0.302995i	$-0.0979864\pi$
$660$	−6.85410	−	20.5623i	−0.266796	−	0.800387i
$661$	16.4791			0.640962			0.320481	−	0.947255i	$-0.396155\pi$
$661$	16.4791			0.640962			0.320481	+	0.947255i	$0.396155\pi$
$662$		−	2.68692i		−	0.104430i
$663$			1.08036i			0.0419578i
$664$	−15.0649			−0.584631
$665$	8.48528	−	25.7109i	0.329045	−	0.997025i
$666$		−	4.32145i		−	0.167453i
$667$	−12.7279	−	6.70820i	−0.492827	−	0.259743i
$668$	−2.29180			−0.0886723
$669$	−24.4721			−0.946147
$670$	5.23607	+	15.7082i	0.202287	+	0.606861i
$671$		−	46.3607i		−	1.78973i
$672$	−11.9176	−	8.88289i	−0.459733	−	0.342665i
$673$		−	4.41641i		−	0.170240i	−0.996371	−	0.0851200i	$-0.972873\pi$
$673$		−	4.41641i		−	0.170240i	0.996371	−	0.0851200i	$-0.0271274\pi$
$674$			9.40802i			0.362383i
$675$	20.0000	−	15.0000i	0.769800	−	0.577350i
$676$	−20.9443			−0.805549
$677$		−	27.1251i		−	1.04250i	−0.853403	−	0.521251i	$-0.825466\pi$
$677$		−	27.1251i		−	1.04250i	0.853403	−	0.521251i	$-0.174534\pi$
$678$		−	2.62210i		−	0.100701i
$679$		0			0
$680$	−21.7082	+	7.23607i	−0.832472	+	0.277491i
$681$		−	22.5486i		−	0.864064i
$682$			11.1074i			0.425323i
$683$		−	7.65248i		−	0.292814i	−0.989224	−	0.146407i	$-0.953229\pi$
$683$		−	7.65248i		−	0.292814i	0.989224	−	0.146407i	$-0.0467709\pi$
$684$	−14.8098			−0.566268
$685$	9.00000	−	3.00000i	0.343872	−	0.114624i
$686$	3.93314	−	10.7492i	0.150168	−	0.410405i
$687$	14.3972			0.549286
$688$	9.10427			0.347097
$689$	−1.00155			−0.0381561
$690$	−1.07749	+	6.53950i	−0.0410194	+	0.248955i
$691$			37.4164i			1.42339i	0.702490	+	0.711694i	$0.252072\pi$
$691$			37.4164i			1.42339i	−0.702490	+	0.711694i	$0.747928\pi$
$692$	−31.4164			−1.19427
$693$	−25.4164	−	18.9443i	−0.965489	−	0.719633i
$694$	6.76393			0.256755
$695$	15.8508	+	47.5524i	0.601255	+	1.80376i
$696$		−	6.70820i		−	0.254274i
$697$	26.3786			0.999160
$698$	19.8541			0.751489
$699$			21.9443i			0.830009i
$700$	−0.0637598	−	21.4045i	−0.00240989	−	0.809013i
$701$		−	19.7990i		−	0.747798i	−0.927470	−	0.373899i	$-0.878021\pi$
$701$		−	19.7990i		−	0.747798i	0.927470	−	0.373899i	$-0.121979\pi$
$702$		−	0.729490i		−	0.0275328i
$703$	16.0000			0.603451
$704$			1.41421i			0.0533002i
$705$	6.36396	−	2.12132i	0.239681	−	0.0798935i
$706$		−	10.6869i		−	0.402207i
$707$	−17.9721	−	13.3956i	−0.675911	−	0.503794i
$708$			0.763932i			0.0287103i
$709$		−	12.7279i		−	0.478007i	−0.971019	−	0.239004i	$-0.923179\pi$
$709$		−	12.7279i		−	0.478007i	0.971019	−	0.239004i	$-0.0768208\pi$
$710$	−2.93159	−	8.79478i	−0.110021	−	0.330062i
$711$		−	10.4884i		−	0.393345i
$712$		−	9.48683i		−	0.355534i
$713$	−6.70820	+	12.7279i	−0.251224	+	0.476664i
$714$	4.47214	−	6.00000i	0.167365	−	0.224544i
$715$	−1.00000	−	3.00000i	−0.0373979	−	0.112194i
$716$	10.8541			0.405637
$717$	−20.1246			−0.751567
$718$	−7.65996			−0.285867
$719$		−	27.3050i		−	1.01830i	−0.860677	−	0.509151i	$-0.829959\pi$
$719$		−	27.3050i		−	1.01830i	0.860677	−	0.509151i	$-0.170041\pi$
$720$	−7.86629	+	2.62210i	−0.293159	+	0.0977198i
$721$	20.1246	+	15.0000i	0.749480	+	0.558629i
$722$			1.20163i			0.0447199i
$723$	17.2256			0.640627
$724$	−30.1599			−1.12088
$725$	12.0000	−	9.00000i	0.445669	−	0.334252i
$726$			15.3820i			0.570878i
$727$		−	24.4543i		−	0.906960i	−0.891267	−	0.453480i	$-0.850182\pi$
$727$		−	24.4543i		−	0.906960i	0.891267	−	0.453480i	$-0.149818\pi$
$728$	−1.11977	−	0.834626i	−0.0415014	−	0.0309333i
$729$	13.0000			0.481481
$730$	−6.63405	−	19.9022i	−0.245537	−	0.736612i
$731$			22.4721i			0.831162i
$732$	12.5216			0.462811
$733$		−	22.2148i		−	0.820521i	−0.911968	−	0.410260i	$-0.865438\pi$
$733$		−	22.2148i		−	0.820521i	0.911968	−	0.410260i	$-0.134562\pi$
$734$	20.2117			0.746026
$735$	8.98606	+	12.8160i	0.331456	+	0.472727i
$736$	12.5623	−	23.8353i	0.463053	−	0.878581i
$737$			71.7771i			2.64394i
$738$	−7.12461			−0.262261
$739$	15.1803			0.558418			0.279209	−	0.960230i	$-0.409928\pi$
$739$	15.1803			0.558418			0.279209	+	0.960230i	$0.409928\pi$
$740$	12.0000	−	4.00000i	0.441129	−	0.147043i
$741$	1.08036			0.0396881
$742$	5.56231	+	4.14590i	0.204199	+	0.152201i
$743$	−20.2117			−0.741494			−0.370747	−	0.928734i	$-0.620898\pi$
$743$	−20.2117			−0.741494			−0.370747	+	0.928734i	$0.620898\pi$
$744$	−6.70820			−0.245935
$745$	−2.52786	−	7.58359i	−0.0926138	−	0.277841i
$746$		−	17.6383i		−	0.645783i
$747$		−	13.4744i		−	0.493004i
$748$	−44.3607			−1.62199
$749$	−21.7082	+	29.1246i	−0.793201	+	1.06419i
$750$	−5.68121	−	3.93314i	−0.207448	−	0.143618i
$751$		−	25.2194i		−	0.920269i	−0.887849	−	0.460135i	$-0.847801\pi$
$751$		−	25.2194i		−	0.920269i	0.887849	−	0.460135i	$-0.152199\pi$
$752$	−5.56231			−0.202836
$753$	−17.9721			−0.654940
$754$		−	0.437694i		−	0.0159399i
$755$	−37.4466	+	12.4822i	−1.36282	+	0.454273i
$756$	12.7917	−	17.1618i	0.465229	−	0.624170i
$757$	2.90724			0.105665			0.0528327	−	0.998603i	$-0.483175\pi$
$757$	2.90724			0.105665			0.0528327	+	0.998603i	$0.483175\pi$
$758$	−4.62520			−0.167995
$759$	−13.3956	+	25.4164i	−0.486230	+	0.922557i
$760$	7.23607	+	21.7082i	0.262480	+	0.787439i
$761$			2.34752i			0.0850977i	0.999094	+	0.0425488i	$0.0135478\pi$
$761$			2.34752i			0.0850977i	−0.999094	+	0.0425488i	$0.986452\pi$
$762$	−7.85410			−0.284524
$763$	−38.1246	−	28.4164i	−1.38020	−	1.02874i
$764$		−	9.02546i		−	0.326530i
$765$	−6.47214	−	19.4164i	−0.234001	−	0.702002i
$766$	−14.5548			−0.525886
$767$			0.111456i			0.00402445i
$768$	6.56231			0.236797
$769$	−5.73567			−0.206833			−0.103417	−	0.994638i	$-0.532978\pi$
$769$	−5.73567			−0.206833			−0.103417	+	0.994638i	$0.532978\pi$
$770$	−6.86474	+	20.8005i	−0.247388	+	0.749599i
$771$	6.70820			0.241590
$772$			16.8541i			0.606592i
$773$			38.5176i			1.38538i	0.721234	+	0.692691i	$0.243575\pi$
$773$			38.5176i			1.38538i	−0.721234	+	0.692691i	$0.756425\pi$
$774$		−	6.06952i		−	0.218164i
$775$	−9.00000	−	12.0000i	−0.323290	−	0.431053i
$776$		0			0
$777$	−5.52786	+	7.41641i	−0.198311	+	0.266062i
$778$	6.06952			0.217603
$779$		−	26.3786i		−	0.945111i
$780$	0.810272	−	0.270091i	0.0290124	−	0.00967080i
$781$		−	40.1869i		−	1.43800i
$782$	12.0000	+	6.32456i	0.429119	+	0.226166i
$783$	15.0000			0.536056
$784$	−3.70820	−	12.4377i	−0.132436	−	0.444203i
$785$	−9.00000	−	27.0000i	−0.321224	−	0.963671i
$786$	−7.09017			−0.252898
$787$			44.4295i			1.58374i	0.610689	+	0.791870i	$0.290893\pi$
$787$			44.4295i			1.58374i	−0.610689	+	0.791870i	$0.709107\pi$
$788$		−	14.3820i		−	0.512336i
$789$	23.2163			0.826522
$790$	−6.87539	+	2.29180i	−0.244615	+	0.0815384i
$791$	6.70820	−	9.00000i	0.238516	−	0.320003i
$792$	26.7912			0.951985
$793$	1.82688			0.0648743
$794$			2.61803i			0.0929105i
$795$	−9.00000	+	3.00000i	−0.319197	+	0.106399i
$796$	30.8276			1.09265
$797$			15.2225i			0.539209i	0.962971	+	0.269604i	$0.0868929\pi$
$797$			15.2225i			0.539209i	−0.962971	+	0.269604i	$0.913107\pi$
$798$	−6.00000	−	4.47214i	−0.212398	−	0.158312i
$799$		−	13.7295i		−	0.485714i
$800$	16.8541	+	22.4721i	0.595882	+	0.794510i
$801$	8.48528			0.299813
$802$	16.7155			0.590246
$803$		−	90.9409i		−	3.20924i
$804$	−19.3863			−0.683703
$805$	−20.4286	+	19.6894i	−0.720013	+	0.693960i
$806$	−0.437694			−0.0154171
$807$		−	25.6525i		−	0.903010i
$808$	18.9443			0.666457
$809$	36.0000			1.26569			0.632846	−	0.774277i	$-0.281886\pi$
$809$	36.0000			1.26569			0.632846	+	0.774277i	$0.281886\pi$
$810$	0.437016	+	1.31105i	0.0153552	+	0.0460655i
$811$			19.5836i			0.687673i	0.939030	+	0.343836i	$0.111727\pi$
$811$			19.5836i			0.687673i	−0.939030	+	0.343836i	$0.888273\pi$
$812$	7.67501	−	10.2971i	0.269340	−	0.361358i
$813$			18.0000i			0.631288i
$814$	−12.9443			−0.453696
$815$	0.500776	+	1.50233i	0.0175414	+	0.0526242i
$816$		−	8.48528i		−	0.297044i
$817$	22.4721			0.786201
$818$	−5.02129			−0.175565
$819$	0.746512	−	1.00155i	0.0260853	−	0.0349970i
$820$	−6.59465	−	19.7839i	−0.230295	−	0.690885i
$821$	−36.0000			−1.25641			−0.628204	−	0.778048i	$-0.716210\pi$
$821$	−36.0000			−1.25641			−0.628204	+	0.778048i	$0.716210\pi$
$822$		−	2.62210i		−	0.0914561i
$823$			51.5410i			1.79661i	0.439375	+	0.898304i	$0.355200\pi$
$823$			51.5410i			1.79661i	−0.439375	+	0.898304i	$0.644800\pi$
$824$	−21.2132			−0.738997
$825$	−17.9721	−	23.9628i	−0.625709	−	0.834278i
$826$	0.461370	−	0.618993i	0.0160531	−	0.0215375i
$827$	−18.9737			−0.659779			−0.329890	−	0.944020i	$-0.607011\pi$
$827$	−18.9737			−0.659779			−0.329890	+	0.944020i	$0.607011\pi$
$828$	13.7295	+	7.23607i	0.477132	+	0.251471i
$829$		−	13.4164i		−	0.465971i	−0.972480	−	0.232986i	$-0.925151\pi$
$829$		−	13.4164i		−	0.465971i	0.972480	−	0.232986i	$-0.0748495\pi$
$830$	−8.83282	+	2.94427i	−0.306592	+	0.102197i
$831$		−	1.58359i		−	0.0549342i
$832$	−0.0557281			−0.00193202
$833$	30.7000	−	9.15298i	1.06369	−	0.317132i
$834$	13.8541			0.479728
$835$	−3.00465	+	1.00155i	−0.103980	+	0.0346601i
$836$			44.3607i			1.53425i
$837$		−	15.0000i		−	0.518476i
$838$		−	9.86939i		−	0.340932i
$839$	27.4589			0.947988			0.473994	−	0.880528i	$-0.342812\pi$
$839$	27.4589			0.947988			0.473994	+	0.880528i	$0.342812\pi$
$840$	−12.5623	−	4.14590i	−0.433441	−	0.143047i
$841$	−20.0000			−0.689655
$842$	−9.10427			−0.313754
$843$		−	6.99226i		−	0.240826i
$844$	13.7082			0.471856
$845$	−27.4589	+	9.15298i	−0.944617	+	0.314872i
$846$			3.70820i			0.127491i
$847$	−39.3522	+	52.7966i	−1.35216	+	1.81411i
$848$	7.86629			0.270129
$849$		−	5.24419i		−	0.179980i
$850$	−11.3137	+	8.48528i	−0.388057	+	0.291043i
$851$	−14.8328	−	7.81758i	−0.508462	−	0.267983i
$852$	10.8541			0.371855
$853$	−8.00000			−0.273915			−0.136957	−	0.990577i	$-0.543732\pi$
$853$	−8.00000			−0.273915			−0.136957	+	0.990577i	$0.543732\pi$
$854$	−10.1459	−	7.56231i	−0.347185	−	0.258777i
$855$	−19.4164	+	6.47214i	−0.664027	+	0.221342i
$856$		−	30.7000i		−	1.04931i
$857$	−17.2918			−0.590677			−0.295338	−	0.955393i	$-0.595432\pi$
$857$	−17.2918			−0.590677			−0.295338	+	0.955393i	$0.595432\pi$
$858$	−0.874032			−0.0298390
$859$			11.8328i			0.403730i	0.979413	+	0.201865i	$0.0647003\pi$
$859$			11.8328i			0.403730i	−0.979413	+	0.201865i	$0.935300\pi$
$860$	16.8541	−	5.61803i	0.574720	−	0.191573i
$861$	12.2271	+	9.11358i	0.416700	+	0.310590i
$862$	−18.1483			−0.618135
$863$		−	23.6525i		−	0.805140i	−0.915389	−	0.402570i	$-0.868117\pi$
$863$		−	23.6525i		−	0.805140i	0.915389	−	0.402570i	$-0.131883\pi$
$864$			28.0902i			0.955647i
$865$	−41.1884	+	13.7295i	−1.40045	+	0.466816i
$866$	13.7295			0.466547
$867$	3.94427			0.133954
$868$	−10.2971	−	7.67501i	−0.349507	−	0.260507i
$869$	−31.4164			−1.06573
$870$	−1.31105	−	3.93314i	−0.0444487	−	0.133346i
$871$	−2.82843			−0.0958376
$872$	40.1869			1.36090
$873$		0			0
$874$	6.32456	−	12.0000i	0.213931	−	0.405906i
$875$	−9.43769	−	28.0344i	−0.319052	−	0.947737i
$876$	24.5623			0.829883
$877$			34.2492i			1.15651i	0.815855	+	0.578257i	$0.196267\pi$
$877$			34.2492i			1.15651i	−0.815855	+	0.578257i	$0.803733\pi$
$878$	−10.1459			−0.342407
$879$			24.9644i			0.842027i
$880$	7.85410	+	23.5623i	0.264762	+	0.794285i
$881$	6.24574			0.210424			0.105212	−	0.994450i	$-0.466448\pi$
$881$	6.24574			0.210424			0.105212	+	0.994450i	$0.466448\pi$
$882$	−8.29180	+	2.47214i	−0.279199	+	0.0832411i
$883$			22.5836i			0.759998i	0.924987	+	0.379999i	$0.124076\pi$
$883$			22.5836i			0.759998i	−0.924987	+	0.379999i	$0.875924\pi$
$884$		−	1.74806i		−	0.0587938i
$885$	0.333851	+	1.00155i	0.0112223	+	0.0336668i
$886$	18.0344			0.605879
$887$	21.0000			0.705111			0.352555	−	0.935791i	$-0.385313\pi$
$887$	21.0000			0.705111			0.352555	+	0.935791i	$0.385313\pi$
$888$		−	7.81758i		−	0.262341i
$889$	−26.9582	−	20.0934i	−0.904148	−	0.673912i
$890$	−1.85410	−	5.56231i	−0.0621496	−	0.186449i
$891$			5.99070i			0.200696i
$892$	39.5967			1.32580
$893$	−13.7295			−0.459439
$894$	−2.20943			−0.0738945
$895$	14.2302	−	4.74342i	0.475665	−	0.158555i
$896$	24.1448	+	17.9965i	0.806621	+	0.601220i
$897$	−1.00155	−	0.527864i	−0.0334408	−	0.0176249i
$898$		−	2.83282i		−	0.0945323i
$899$		−	9.00000i		−	0.300167i
$900$	−12.9443	+	9.70820i	−0.431476	+	0.323607i
$901$			19.4164i			0.646854i
$902$			21.3407i			0.710568i
$903$	−7.76393	+	10.4164i	−0.258367	+	0.346636i
$904$			9.48683i			0.315527i
$905$	−39.5410	+	13.1803i	−1.31439	+	0.438129i
$906$			10.9098i			0.362455i
$907$	12.3941			0.411538			0.205769	−	0.978601i	$-0.434030\pi$
$907$	12.3941			0.411538			0.205769	+	0.978601i	$0.434030\pi$
$908$			36.4844i			1.21078i
$909$			16.9443i			0.562006i
$910$	−0.819660	−	0.270510i	−0.0271715	−	0.00896731i
$911$			19.7202i			0.653359i	0.945135	+	0.326679i	$0.105930\pi$
$911$			19.7202i			0.653359i	−0.945135	+	0.326679i	$0.894070\pi$
$912$	−8.48528			−0.280976
$913$	−40.3607			−1.33574
$914$		−	5.91189i		−	0.195548i
$915$	16.4164	−	5.47214i	0.542710	−	0.180903i
$916$	−23.2951			−0.769692
$917$	−24.3361	−	18.1390i	−0.803648	−	0.599004i
$918$	−14.1421			−0.466760
$919$			33.9411i			1.11961i	0.828623	+	0.559807i	$0.189125\pi$
$919$			33.9411i			1.11961i	−0.828623	+	0.559807i	$0.810875\pi$
$920$	3.89840	−	23.6601i	0.128526	−	0.780052i
$921$	−22.9443			−0.756039
$922$	−21.1591			−0.696836
$923$	1.58359			0.0521246
$924$	−20.5623	−	15.3262i	−0.676450	−	0.504196i
$925$	13.9845	−	10.4884i	0.459808	−	0.344856i
$926$	18.5410			0.609296
$927$		−	18.9737i		−	0.623177i
$928$			16.8541i			0.553263i
$929$			29.6525i			0.972866i	0.873718	+	0.486433i	$0.161702\pi$
$929$			29.6525i			0.972866i	−0.873718	+	0.486433i	$0.838298\pi$
$930$	−3.93314	+	1.31105i	−0.128973	+	0.0429910i
$931$	−9.15298	−	30.7000i	−0.299977	−	1.00615i
$932$		−	35.5066i		−	1.16306i
$933$			22.5279i			0.737529i
$934$	−6.16693			−0.201788
$935$	−58.1590	+	19.3863i	−1.90200	+	0.634001i
$936$			1.05573i			0.0345076i
$937$			6.48218i			0.211764i	0.994379	+	0.105882i	$0.0337665\pi$
$937$			6.48218i			0.211764i	−0.994379	+	0.105882i	$0.966233\pi$
$938$	15.7082	+	11.7082i	0.512891	+	0.382286i
$939$			1.00155i			0.0326844i
$940$	−10.2971	+	3.43237i	−0.335855	+	0.111952i
$941$	38.1838			1.24476			0.622378	−	0.782717i	$-0.286167\pi$
$941$	38.1838			1.24476			0.622378	+	0.782717i	$0.286167\pi$
$942$	−7.86629			−0.256298
$943$	−12.8885	+	24.4543i	−0.419709	+	0.796341i
$944$		−	0.875388i		−	0.0284915i
$945$	9.27051	−	28.0902i	0.301570	−	0.913773i
$946$	−18.1803			−0.591094
$947$		−	31.6525i		−	1.02857i	−0.857620	−	0.514284i	$-0.828058\pi$
$947$		−	31.6525i		−	1.02857i	0.857620	−	0.514284i	$-0.171942\pi$
$948$		−	8.48528i		−	0.275589i
$949$	3.58359			0.116328
$950$	8.48528	+	11.3137i	0.275299	+	0.367065i
$951$		−	26.4721i		−	0.858418i
$952$	−16.1803	+	21.7082i	−0.524408	+	0.703567i
$953$	42.4264			1.37433			0.687163	−	0.726503i	$-0.258856\pi$
$953$	42.4264			1.37433			0.687163	+	0.726503i	$0.258856\pi$
$954$		−	5.24419i		−	0.169787i
$955$	−3.94427	−	11.8328i	−0.127634	−	0.382901i
$956$	32.5623			1.05314
$957$		−	17.9721i		−	0.580956i
$958$			17.5896i			0.568293i
$959$	6.70820	−	9.00000i	0.216619	−	0.290625i
$960$	−0.500776	+	0.166925i	−0.0161625	+	0.00538749i
$961$	22.0000			0.709677
$962$		−	0.510078i		−	0.0164456i
$963$	27.4589			0.884852
$964$	−27.8716			−0.897684
$965$	7.36551	+	22.0965i	0.237104	+	0.711313i
$966$	3.37723	+	7.07749i	0.108660	+	0.227715i
$967$			11.2918i			0.363120i	0.983380	+	0.181560i	$0.0581146\pi$
$967$			11.2918i			0.363120i	−0.983380	+	0.181560i	$0.941885\pi$
$968$		−	55.6525i		−	1.78874i
$969$		−	20.9443i		−	0.672827i
$970$		0			0
$971$	−31.7016			−1.01735			−0.508676	−	0.860958i	$-0.669865\pi$
$971$	−31.7016			−1.01735			−0.508676	+	0.860958i	$0.669865\pi$
$972$	−25.8885			−0.830375
$973$	47.5524	+	35.4435i	1.52446	+	1.13626i
$974$	18.9787			0.608117
$975$	0.944272	−	0.708204i	0.0302409	−	0.0226807i
$976$	−14.3485			−0.459283
$977$	−8.48528			−0.271468			−0.135734	−	0.990745i	$-0.543339\pi$
$977$	−8.48528			−0.271468			−0.135734	+	0.990745i	$0.543339\pi$
$978$	0.437694			0.0139959
$979$		−	25.4164i		−	0.812312i
$980$	−14.5397	−	20.7368i	−0.464455	−	0.662412i
$981$			35.9442i			1.14761i
$982$		−	5.02129i		−	0.160236i
$983$		−	35.3553i		−	1.12766i	−0.825891	−	0.563830i	$-0.809327\pi$
$983$		−	35.3553i		−	1.12766i	0.825891	−	0.563830i	$-0.190673\pi$
$984$	−12.8885			−0.410872
$985$	−6.28515	−	18.8554i	−0.200262	−	0.600785i
$986$	−8.48528			−0.270226
$987$	4.74342	−	6.36396i	0.150985	−	0.202567i
$988$	−1.74806			−0.0556133
$989$	−20.8328	−	10.9799i	−0.662445	−	0.349139i
$990$	15.7082	−	5.23607i	0.499239	−	0.166413i
$991$	53.1935			1.68975			0.844874	−	0.534966i	$-0.179676\pi$
$991$	53.1935			1.68975			0.844874	+	0.534966i	$0.179676\pi$
$992$	16.8541			0.535118
$993$	4.34752			0.137965
$994$	−8.79478	−	6.55524i	−0.278953	−	0.207920i
$995$	40.4164	−	13.4721i	1.28129	−	0.427095i
$996$		−	10.9010i		−	0.345413i
$997$	32.2492			1.02134			0.510672	−	0.859776i	$-0.329397\pi$
$997$	32.2492			1.02134			0.510672	+	0.859776i	$0.329397\pi$
$998$		−	10.9787i		−	0.347525i
$999$	17.4806			0.553063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.d.b.804.6	yes	8
5.4	even	2		805.2.d.c.804.4	yes	8
7.6	odd	2		805.2.d.c.804.5	yes	8
23.22	odd	2	inner	805.2.d.b.804.5	yes	8
35.34	odd	2	inner	805.2.d.b.804.3	✓	8
115.114	odd	2		805.2.d.c.804.3	yes	8
161.160	even	2		805.2.d.c.804.6	yes	8
805.804	even	2	inner	805.2.d.b.804.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.d.b.804.3	✓	8	35.34	odd	2	inner
805.2.d.b.804.4	yes	8	805.804	even	2	inner
805.2.d.b.804.5	yes	8	23.22	odd	2	inner
805.2.d.b.804.6	yes	8	1.1	even	1	trivial
805.2.d.c.804.3	yes	8	115.114	odd	2
805.2.d.c.804.4	yes	8	5.4	even	2
805.2.d.c.804.5	yes	8	7.6	odd	2
805.2.d.c.804.6	yes	8	161.160	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.618034i q^{2} -1.00000 q^{3} +1.61803 q^{4} +(2.12132 - 0.707107i) q^{5} -0.618034i q^{6} +(1.58114 - 2.12132i) q^{7} +2.23607i q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q+0.618034i q^{2} -1.00000 q^{3} +1.61803 q^{4} +(2.12132 - 0.707107i) q^{5} -0.618034i q^{6} +(1.58114 - 2.12132i) q^{7} +2.23607i q^{8} -2.00000 q^{9} +(0.437016 + 1.31105i) q^{10} +5.99070i q^{11} -1.61803 q^{12} -0.236068 q^{13} +(1.31105 + 0.977198i) q^{14} +(-2.12132 + 0.707107i) q^{15} +1.85410 q^{16} +4.57649i q^{17} -1.23607i q^{18} +4.57649 q^{19} +(3.43237 - 1.14412i) q^{20} +(-1.58114 + 2.12132i) q^{21} -3.70246 q^{22} +(-4.24264 - 2.23607i) q^{23} -2.23607i q^{24} +(4.00000 - 3.00000i) q^{25} -0.145898i q^{26} +5.00000 q^{27} +(2.55834 - 3.43237i) q^{28} +3.00000 q^{29} +(-0.437016 - 1.31105i) q^{30} -3.00000i q^{31} +5.61803i q^{32} -5.99070i q^{33} -2.82843 q^{34} +(1.85410 - 5.61803i) q^{35} -3.23607 q^{36} +3.49613 q^{37} +2.82843i q^{38} +0.236068 q^{39} +(1.58114 + 4.74342i) q^{40} -5.76393i q^{41} +(-1.31105 - 0.977198i) q^{42} +4.91034 q^{43} +9.69316i q^{44} +(-4.24264 + 1.41421i) q^{45} +(1.38197 - 2.62210i) q^{46} -3.00000 q^{47} -1.85410 q^{48} +(-2.00000 - 6.70820i) q^{49} +(1.85410 + 2.47214i) q^{50} -4.57649i q^{51} -0.381966 q^{52} +4.24264 q^{53} +3.09017i q^{54} +(4.23607 + 12.7082i) q^{55} +(4.74342 + 3.53553i) q^{56} -4.57649 q^{57} +1.85410i q^{58} -0.472136i q^{59} +(-3.43237 + 1.14412i) q^{60} -7.73877 q^{61} +1.85410 q^{62} +(-3.16228 + 4.24264i) q^{63} +0.236068 q^{64} +(-0.500776 + 0.166925i) q^{65} +3.70246 q^{66} +11.9814 q^{67} +7.40492i q^{68} +(4.24264 + 2.23607i) q^{69} +(3.47214 + 1.14590i) q^{70} -6.70820 q^{71} -4.47214i q^{72} -15.1803 q^{73} +2.16073i q^{74} +(-4.00000 + 3.00000i) q^{75} +7.40492 q^{76} +(12.7082 + 9.47214i) q^{77} +0.145898i q^{78} +5.24419i q^{79} +(3.93314 - 1.31105i) q^{80} +1.00000 q^{81} +3.56231 q^{82} +6.73722i q^{83} +(-2.55834 + 3.43237i) q^{84} +(3.23607 + 9.70820i) q^{85} +3.03476i q^{86} -3.00000 q^{87} -13.3956 q^{88} -4.24264 q^{89} +(-0.874032 - 2.62210i) q^{90} +(-0.373256 + 0.500776i) q^{91} +(-6.86474 - 3.61803i) q^{92} +3.00000i q^{93} -1.85410i q^{94} +(9.70820 - 3.23607i) q^{95} -5.61803i q^{96} +(4.14590 - 1.23607i) q^{98} -11.9814i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{3} + 4 q^{4} - 16 q^{9}+O(q^{10}) \) 8 * q - 8 * q^3 + 4 * q^4 - 16 * q^9	\( 8 q - 8 q^{3} + 4 q^{4} - 16 q^{9} - 4 q^{12} + 16 q^{13} - 12 q^{16} + 32 q^{25} + 40 q^{27} + 24 q^{29} - 12 q^{35} - 8 q^{36} - 16 q^{39} + 20 q^{46} - 24 q^{47} + 12 q^{48} - 16 q^{49} - 12 q^{50} - 12 q^{52} + 16 q^{55} - 12 q^{62} - 16 q^{64} - 8 q^{70} - 32 q^{73} - 32 q^{75} + 48 q^{77} + 8 q^{81} - 52 q^{82} + 8 q^{85} - 24 q^{87} + 24 q^{95} + 60 q^{98}+O(q^{100}) \) 8 * q - 8 * q^3 + 4 * q^4 - 16 * q^9 - 4 * q^12 + 16 * q^13 - 12 * q^16 + 32 * q^25 + 40 * q^27 + 24 * q^29 - 12 * q^35 - 8 * q^36 - 16 * q^39 + 20 * q^46 - 24 * q^47 + 12 * q^48 - 16 * q^49 - 12 * q^50 - 12 * q^52 + 16 * q^55 - 12 * q^62 - 16 * q^64 - 8 * q^70 - 32 * q^73 - 32 * q^75 + 48 * q^77 + 8 * q^81 - 52 * q^82 + 8 * q^85 - 24 * q^87 + 24 * q^95 + 60 * q^98

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