LMFDB - Embedded newform 804.2.y.b.505.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, 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:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			505.3
Character	$\chi$	$=$	804.505
Dual form			804.2.y.b.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(-1.40224 - 0.901162i) q^{5} +(-1.99913 + 0.800331i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(-1.40224 - 0.901162i) q^{5} +(-1.99913 + 0.800331i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-0.208373 + 4.37429i) q^{11} +(-0.464734 - 0.0443767i) q^{13} +(-0.237216 - 1.64987i) q^{15} +(0.912776 - 3.76251i) q^{17} +(-6.15541 - 2.46425i) q^{19} +(-1.91400 - 0.986737i) q^{21} +(-4.51419 + 0.870038i) q^{23} +(-0.922904 - 2.02088i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(2.53756 + 4.39519i) q^{29} +(-5.39342 + 0.515009i) q^{31} +(-3.44232 + 2.70707i) q^{33} +(3.52448 + 0.679288i) q^{35} +(-5.22914 + 9.05714i) q^{37} +(-0.270798 - 0.380283i) q^{39} +(-4.28708 - 4.08773i) q^{41} +(-2.06844 + 0.607347i) q^{43} +(1.09155 - 1.25971i) q^{45} +(-3.61162 + 10.4351i) q^{47} +(-1.71014 + 1.63062i) q^{49} +(3.44126 - 1.77409i) q^{51} +(10.1057 + 2.96731i) q^{53} +(4.23413 - 5.94601i) q^{55} +(-2.16858 - 6.26569i) q^{57} +(1.79019 - 3.91998i) q^{59} +(-0.277619 - 5.82794i) q^{61} +(-0.507679 - 2.09268i) q^{63} +(0.611676 + 0.481027i) q^{65} +(1.49050 - 8.04850i) q^{67} +(-3.61370 - 2.84184i) q^{69} +(2.29558 + 9.46250i) q^{71} +(-0.234379 - 4.92022i) q^{73} +(0.922904 - 2.02088i) q^{75} +(-3.08432 - 8.91155i) q^{77} +(-5.30590 + 7.45109i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(7.34299 - 3.78558i) q^{83} +(-4.67056 + 4.45337i) q^{85} +(-1.65991 + 4.79600i) q^{87} +(2.01751 - 2.32833i) q^{89} +(0.964580 - 0.283226i) q^{91} +(-3.92116 - 3.73881i) q^{93} +(6.41064 + 9.00249i) q^{95} +(5.10144 - 8.83595i) q^{97} +(-4.30011 - 0.828779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{7}{33}\right)$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$		0			0
$5$	−1.40224	−	0.901162i	−0.627099	−	0.403012i	0.188136	−	0.982143i	$-0.439756\pi$
$5$	−1.40224	−	0.901162i	−0.627099	−	0.403012i	−0.815234	+	0.579131i	$0.803392\pi$
$6$		0			0
$7$	−1.99913	+	0.800331i	−0.755600	+	0.302497i	−0.717295	−	0.696769i	$-0.754620\pi$
$7$	−1.99913	+	0.800331i	−0.755600	+	0.302497i	−0.0383051	+	0.999266i	$0.512196\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−0.208373	+	4.37429i	−0.0628269	+	1.31890i	0.718828	+	0.695188i	$0.244679\pi$
$11$	−0.208373	+	4.37429i	−0.0628269	+	1.31890i	−0.781655	+	0.623711i	$0.785624\pi$
$12$		0			0
$13$	−0.464734	−	0.0443767i	−0.128894	−	0.0123079i	0.0304096	−	0.999538i	$-0.490319\pi$
$13$	−0.464734	−	0.0443767i	−0.128894	−	0.0123079i	−0.159304	+	0.987230i	$0.550925\pi$
$14$		0			0
$15$	−0.237216	−	1.64987i	−0.0612489	−	0.425996i
$16$		0			0
$17$	0.912776	−	3.76251i	0.221381	−	0.912544i	−0.747350	−	0.664430i	$-0.768674\pi$
$17$	0.912776	−	3.76251i	0.221381	−	0.912544i	0.968731	−	0.248113i	$-0.0798106\pi$
$18$		0			0
$19$	−6.15541	−	2.46425i	−1.41215	−	0.565339i	−0.464763	−	0.885435i	$-0.653861\pi$
$19$	−6.15541	−	2.46425i	−1.41215	−	0.565339i	−0.947385	+	0.320096i	$0.896285\pi$
$20$		0			0
$21$	−1.91400	−	0.986737i	−0.417670	−	0.215324i
$22$		0			0
$23$	−4.51419	+	0.870038i	−0.941273	+	0.181416i	−0.636733	−	0.771084i	$-0.719715\pi$
$23$	−4.51419	+	0.870038i	−0.941273	+	0.181416i	−0.304540	+	0.952500i	$0.598503\pi$
$24$		0			0
$25$	−0.922904	−	2.02088i	−0.184581	−	0.404176i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	2.53756	+	4.39519i	0.471214	+	0.816166i	0.999458	−	0.0329265i	$-0.0104827\pi$
$29$	2.53756	+	4.39519i	0.471214	+	0.816166i	−0.528244	+	0.849093i	$0.677149\pi$
$30$		0			0
$31$	−5.39342	+	0.515009i	−0.968686	+	0.0924983i	−0.567389	−	0.823450i	$-0.692047\pi$
$31$	−5.39342	+	0.515009i	−0.968686	+	0.0924983i	−0.401297	+	0.915948i	$0.631440\pi$
$32$		0			0
$33$	−3.44232	+	2.70707i	−0.599232	+	0.471241i
$34$		0			0
$35$	3.52448	+	0.679288i	0.595746	+	0.114821i
$36$		0			0
$37$	−5.22914	+	9.05714i	−0.859666	+	1.48898i	0.0125824	+	0.999921i	$0.495995\pi$
$37$	−5.22914	+	9.05714i	−0.859666	+	1.48898i	−0.872248	+	0.489064i	$0.837339\pi$
$38$		0			0
$39$	−0.270798	−	0.380283i	−0.0433625	−	0.0608940i
$40$		0			0
$41$	−4.28708	−	4.08773i	−0.669530	−	0.638396i	0.277053	−	0.960855i	$-0.410642\pi$
$41$	−4.28708	−	4.08773i	−0.669530	−	0.638396i	−0.946583	+	0.322459i	$0.895491\pi$
$42$		0			0
$43$	−2.06844	+	0.607347i	−0.315433	+	0.0926196i	−0.435617	−	0.900132i	$-0.643470\pi$
$43$	−2.06844	+	0.607347i	−0.315433	+	0.0926196i	0.120184	+	0.992752i	$0.461652\pi$
$44$		0			0
$45$	1.09155	−	1.25971i	0.162718	−	0.187787i
$46$		0			0
$47$	−3.61162	+	10.4351i	−0.526809	+	1.52211i	0.296790	+	0.954943i	$0.404084\pi$
$47$	−3.61162	+	10.4351i	−0.526809	+	1.52211i	−0.823599	+	0.567172i	$0.808037\pi$
$48$		0			0
$49$	−1.71014	+	1.63062i	−0.244306	+	0.232946i
$50$		0			0
$51$	3.44126	−	1.77409i	0.481873	−	0.248423i
$52$		0			0
$53$	10.1057	+	2.96731i	1.38813	+	0.407591i	0.888590	−	0.458702i	$-0.151685\pi$
$53$	10.1057	+	2.96731i	1.38813	+	0.407591i	0.499536	+	0.866293i	$0.333504\pi$
$54$		0			0
$55$	4.23413	−	5.94601i	0.570930	−	0.801759i
$56$		0			0
$57$	−2.16858	−	6.26569i	−0.287235	−	0.829911i
$58$		0			0
$59$	1.79019	−	3.91998i	0.233063	−	0.510338i	−0.756577	−	0.653904i	$-0.773130\pi$
$59$	1.79019	−	3.91998i	0.233063	−	0.510338i	0.989641	+	0.143567i	$0.0458572\pi$
$60$		0			0
$61$	−0.277619	−	5.82794i	−0.0355455	−	0.746191i	−0.944345	−	0.328957i	$-0.893303\pi$
$61$	−0.277619	−	5.82794i	−0.0355455	−	0.746191i	0.908799	−	0.417234i	$-0.137000\pi$
$62$		0			0
$63$	−0.507679	−	2.09268i	−0.0639615	−	0.263653i
$64$		0			0
$65$	0.611676	+	0.481027i	0.0758691	+	0.0596641i
$66$		0			0
$67$	1.49050	−	8.04850i	0.182093	−	0.983281i
$67$	1.49050	−	8.04850i	0.182093	−	0.983281i
$68$		0			0
$69$	−3.61370	−	2.84184i	−0.435038	−	0.342118i
$70$		0			0
$71$	2.29558	+	9.46250i	0.272435	+	1.12299i	0.929401	+	0.369072i	$0.120324\pi$
$71$	2.29558	+	9.46250i	0.272435	+	1.12299i	−0.656966	+	0.753920i	$0.728160\pi$
$72$		0			0
$73$	−0.234379	−	4.92022i	−0.0274320	−	0.575868i	−0.970183	−	0.242372i	$-0.922075\pi$
$73$	−0.234379	−	4.92022i	−0.0274320	−	0.575868i	0.942751	−	0.333496i	$-0.108228\pi$
$74$		0			0
$75$	0.922904	−	2.02088i	0.106568	−	0.233351i
$76$		0			0
$77$	−3.08432	−	8.91155i	−0.351491	−	1.01557i
$78$		0			0
$79$	−5.30590	+	7.45109i	−0.596960	+	0.838313i	−0.996937	−	0.0782124i	$-0.975079\pi$
$79$	−5.30590	+	7.45109i	−0.596960	+	0.838313i	0.399977	+	0.916525i	$0.369018\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	7.34299	−	3.78558i	0.805998	−	0.415521i	−0.00542115	−	0.999985i	$-0.501726\pi$
$83$	7.34299	−	3.78558i	0.805998	−	0.415521i	0.811419	+	0.584464i	$0.198695\pi$
$84$		0			0
$85$	−4.67056	+	4.45337i	−0.506593	+	0.483036i
$86$		0			0
$87$	−1.65991	+	4.79600i	−0.177961	+	0.514185i
$88$		0			0
$89$	2.01751	−	2.32833i	0.213855	−	0.246802i	−0.638679	−	0.769473i	$-0.720519\pi$
$89$	2.01751	−	2.32833i	0.213855	−	0.246802i	0.852535	+	0.522671i	$0.175064\pi$
$90$		0			0
$91$	0.964580	−	0.283226i	0.101115	−	0.0296902i
$92$		0			0
$93$	−3.92116	−	3.73881i	−0.406605	−	0.387697i
$94$		0			0
$95$	6.41064	+	9.00249i	0.657718	+	0.923636i
$96$		0			0
$97$	5.10144	−	8.83595i	0.517973	−	0.897155i	−0.481809	−	0.876276i	$-0.660020\pi$
$97$	5.10144	−	8.83595i	0.517973	−	0.897155i	0.999782	−	0.0208788i	$-0.00664642\pi$
$98$		0			0
$99$	−4.30011	−	0.828779i	−0.432178	−	0.0832954i
$100$		0			0
$101$	1.05593	−	0.830391i	0.105069	−	0.0826270i	−0.564243	−	0.825609i	$-0.690832\pi$
$101$	1.05593	−	0.830391i	0.105069	−	0.0826270i	0.669311	+	0.742982i	$0.266589\pi$
$102$		0			0
$103$	6.76119	−	0.645615i	0.666199	−	0.0636143i	0.243523	−	0.969895i	$-0.421697\pi$
$103$	6.76119	−	0.645615i	0.666199	−	0.0636143i	0.422676	+	0.906281i	$0.361091\pi$
$104$		0			0
$105$	1.79467	+	3.10846i	0.175142	+	0.303355i
$106$		0			0
$107$	−6.31699	+	4.05969i	−0.610687	+	0.392465i	−0.809115	−	0.587651i	$-0.800053\pi$
$107$	−6.31699	+	4.05969i	−0.610687	+	0.392465i	0.198428	+	0.980116i	$0.436416\pi$
$108$		0			0
$109$	1.81460	+	3.97343i	0.173808	+	0.380585i	0.976409	−	0.215931i	$-0.0692785\pi$
$109$	1.81460	+	3.97343i	0.173808	+	0.380585i	−0.802601	+	0.596516i	$0.796551\pi$
$110$		0			0
$111$	−10.2693	+	1.97924i	−0.974718	+	0.187861i
$112$		0			0
$113$	10.3027	+	5.31141i	0.969197	+	0.499656i	0.868731	−	0.495285i	$-0.164936\pi$
$113$	10.3027	+	5.31141i	0.969197	+	0.499656i	0.100466	+	0.994940i	$0.467967\pi$
$114$		0			0
$115$	7.11400	+	2.84802i	0.663384	+	0.265579i
$116$		0			0
$117$	0.110064	−	0.453688i	0.0101754	−	0.0419435i
$118$		0			0
$119$	1.18650	+	8.25228i	0.108766	+	0.756485i
$120$		0			0
$121$	−8.14081	−	0.777353i	−0.740074	−	0.0706685i
$122$		0			0
$123$	0.281855	−	5.91685i	0.0254140	−	0.533505i
$124$		0			0
$125$	−1.71309	+	11.9148i	−0.153223	+	1.06569i
$126$		0			0
$127$	12.5019	−	5.00501i	1.10937	−	0.444123i	0.256653	−	0.966504i	$-0.417380\pi$
$127$	12.5019	−	5.00501i	1.10937	−	0.444123i	0.852713	+	0.522380i	$0.174956\pi$
$128$		0			0
$129$	−1.81354	−	1.16549i	−0.159673	−	0.102616i
$130$		0			0
$131$	7.14097	+	8.24112i	0.623910	+	0.720030i	0.976445	−	0.215769i	$-0.0692257\pi$
$131$	7.14097	+	8.24112i	0.623910	+	0.720030i	−0.352535	+	0.935799i	$0.614680\pi$
$132$		0			0
$133$	14.2777			1.23803
$134$		0			0
$135$	1.66684			0.143459
$136$		0			0
$137$	−4.29690	−	4.95889i	−0.367109	−	0.423667i	0.541900	−	0.840443i	$-0.317705\pi$
$137$	−4.29690	−	4.95889i	−0.367109	−	0.423667i	−0.909009	+	0.416777i	$0.863160\pi$
$138$		0			0
$139$	−9.56530	−	6.14725i	−0.811318	−	0.521403i	0.0679728	−	0.997687i	$-0.478347\pi$
$139$	−9.56530	−	6.14725i	−0.811318	−	0.521403i	−0.879291	+	0.476284i	$0.841983\pi$
$140$		0			0
$141$	−10.2514	+	4.10405i	−0.863326	+	0.345624i
$142$		0			0
$143$	0.290955	−	2.02364i	0.0243309	−	0.169225i
$144$		0			0
$145$	0.402516	−	8.44984i	0.0334271	−	0.701721i
$146$		0			0
$147$	−2.35225	−	0.224612i	−0.194010	−	0.0185257i
$148$		0			0
$149$	−1.35469	−	9.42205i	−0.110980	−	0.771884i	−0.966970	−	0.254891i	$-0.917960\pi$
$149$	−1.35469	−	9.42205i	−0.110980	−	0.771884i	0.855990	−	0.516993i	$-0.172949\pi$
$150$		0			0
$151$	3.28306	−	13.5329i	0.267171	−	1.10129i	−0.667167	−	0.744908i	$-0.732493\pi$
$151$	3.28306	−	13.5329i	0.267171	−	1.10129i	0.934338	−	0.356387i	$-0.115991\pi$
$152$		0			0
$153$	3.59432	+	1.43895i	0.290583	+	0.116332i
$154$		0			0
$155$	8.02695	+	4.13818i	0.644740	+	0.332387i
$156$		0			0
$157$	−20.3787	+	3.92767i	−1.62640	+	0.313462i	−0.919271	−	0.393625i	$-0.871221\pi$
$157$	−20.3787	+	3.92767i	−1.62640	+	0.313462i	−0.707126	+	0.707088i	$0.750009\pi$
$158$		0			0
$159$	4.37530	+	9.58056i	0.346984	+	0.759788i
$160$		0			0
$161$	8.32813	−	5.35217i	0.656349	−	0.421810i
$162$		0			0
$163$	10.9953	+	19.0444i	0.861219	+	1.49167i	0.870754	+	0.491720i	$0.163632\pi$
$163$	10.9953	+	19.0444i	0.861219	+	1.49167i	−0.00953503	+	0.999955i	$0.503035\pi$
$164$		0			0
$165$	7.26646	−	0.693863i	0.565693	−	0.0540171i
$166$		0			0
$167$	−10.3502	+	8.13949i	−0.800923	+	0.629853i	−0.932384	−	0.361468i	$-0.882276\pi$
$167$	−10.3502	+	8.13949i	−0.800923	+	0.629853i	0.131461	+	0.991321i	$0.458033\pi$
$168$		0			0
$169$	−12.5511	−	2.41902i	−0.965467	−	0.186078i
$170$		0			0
$171$	3.31518	−	5.74206i	0.253518	−	0.439106i
$172$		0			0
$173$	8.67550	+	12.1830i	0.659586	+	0.926259i	0.999901	−	0.0140527i	$-0.00447326\pi$
$173$	8.67550	+	12.1830i	0.659586	+	0.926259i	−0.340315	+	0.940311i	$0.610534\pi$
$174$		0			0
$175$	3.46238	+	3.30137i	0.261731	+	0.249560i
$176$		0			0
$177$	4.13485	−	1.21410i	0.310794	−	0.0912574i
$178$		0			0
$179$	10.7078	−	12.3575i	0.800339	−	0.923640i	−0.198061	−	0.980190i	$-0.563464\pi$
$179$	10.7078	−	12.3575i	0.800339	−	0.923640i	0.998400	+	0.0565493i	$0.0180098\pi$
$180$		0			0
$181$	5.22962	−	15.1100i	0.388715	−	1.12312i	−0.565694	−	0.824615i	$-0.691392\pi$
$181$	5.22962	−	15.1100i	0.388715	−	1.12312i	0.954409	−	0.298503i	$-0.0964872\pi$
$182$		0			0
$183$	4.22266	−	4.02630i	0.312148	−	0.297633i
$184$		0			0
$185$	15.4944	−	7.98794i	1.13917	−	0.587285i
$186$		0			0
$187$	16.2681	+	4.77675i	1.18964	+	0.349311i
$188$		0			0
$189$	1.24908	−	1.75409i	0.0908575	−	0.127592i
$190$		0			0
$191$	7.61105	+	21.9907i	0.550716	+	1.59119i	0.785314	+	0.619098i	$0.212502\pi$
$191$	7.61105	+	21.9907i	0.550716	+	1.59119i	−0.234598	+	0.972093i	$0.575377\pi$
$192$		0			0
$193$	−7.83873	+	17.1644i	−0.564244	+	1.23552i	0.385562	+	0.922682i	$0.374008\pi$
$193$	−7.83873	+	17.1644i	−0.564244	+	1.23552i	−0.949806	+	0.312840i	$0.898720\pi$
$194$		0			0
$195$	0.0370264	+	0.777280i	0.00265152	+	0.0556622i
$196$		0			0
$197$	−6.08682	−	25.0902i	−0.433668	−	1.78760i	−0.598326	−	0.801253i	$-0.704167\pi$
$197$	−6.08682	−	25.0902i	−0.433668	−	1.78760i	0.164658	−	0.986351i	$-0.447348\pi$
$198$		0			0
$199$	−4.97296	−	3.91078i	−0.352524	−	0.277228i	0.426155	−	0.904650i	$-0.359868\pi$
$199$	−4.97296	−	3.91078i	−0.352524	−	0.277228i	−0.778679	+	0.627422i	$0.784110\pi$
$200$		0			0
$201$	7.05872	−	4.14421i	0.497884	−	0.292310i
$202$		0			0
$203$	−8.59053	−	6.75567i	−0.602937	−	0.474155i
$204$		0			0
$205$	2.32780	+	9.59531i	0.162580	+	0.670166i
$206$		0			0
$207$	−0.218747	−	4.59206i	−0.0152040	−	0.319170i
$208$		0			0
$209$	12.0620	−	26.4121i	0.834345	−	1.82696i
$210$		0			0
$211$	7.91698	+	22.8746i	0.545028	+	1.57475i	0.795069	+	0.606519i	$0.207434\pi$
$211$	7.91698	+	22.8746i	0.545028	+	1.57475i	−0.250042	+	0.968235i	$0.580444\pi$
$212$		0			0
$213$	−5.64800	+	7.93150i	−0.386994	+	0.543458i
$214$		0			0
$215$	3.44775	+	1.01235i	0.235135	+	0.0690418i
$216$		0			0
$217$	10.3700	−	5.34609i	0.703959	−	0.362916i
$218$		0			0
$219$	3.56497	−	3.39919i	0.240898	−	0.229696i
$220$		0			0
$221$	−0.591166	+	1.70806i	−0.0397661	+	0.114897i
$222$		0			0
$223$	−16.6812	+	19.2511i	−1.11706	+	1.28915i	−0.163966	+	0.986466i	$0.552429\pi$
$223$	−16.6812	+	19.2511i	−1.11706	+	1.28915i	−0.953090	+	0.302686i	$0.902117\pi$
$224$		0			0
$225$	2.13165	−	0.625909i	0.142110	−	0.0417273i
$226$		0			0
$227$	2.39743	+	2.28595i	0.159123	+	0.151724i	0.765458	−	0.643486i	$-0.222512\pi$
$227$	2.39743	+	2.28595i	0.159123	+	0.151724i	−0.606335	+	0.795209i	$0.707361\pi$
$228$		0			0
$229$	−6.69342	−	9.39959i	−0.442314	−	0.621143i	0.531890	−	0.846813i	$-0.321482\pi$
$229$	−6.69342	−	9.39959i	−0.442314	−	0.621143i	−0.974204	+	0.225671i	$0.927543\pi$
$230$		0			0
$231$	4.71510	−	8.16679i	0.310231	−	0.537336i
$232$		0			0
$233$	−7.14497	−	1.37708i	−0.468083	−	0.0902155i	−0.0502443	−	0.998737i	$-0.516000\pi$
$233$	−7.14497	−	1.37708i	−0.468083	−	0.0902155i	−0.417838	+	0.908521i	$0.637212\pi$
$234$		0			0
$235$	14.4681	−	11.3778i	0.943792	−	0.742206i
$236$		0			0
$237$	−9.10578	+	0.869496i	−0.591484	+	0.0564799i
$238$		0			0
$239$	2.43080	+	4.21027i	0.157236	+	0.272340i	0.933871	−	0.357611i	$-0.116408\pi$
$239$	2.43080	+	4.21027i	0.157236	+	0.272340i	−0.776635	+	0.629951i	$0.783075\pi$
$240$		0			0
$241$	1.44414	−	0.928095i	0.0930255	−	0.0597838i	−0.493301	−	0.869859i	$-0.664210\pi$
$241$	1.44414	−	0.928095i	0.0930255	−	0.0597838i	0.586327	+	0.810075i	$0.300574\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	3.86748	−	0.745395i	0.247084	−	0.0476215i
$246$		0			0
$247$	2.75127	+	1.41838i	0.175059	+	0.0902494i
$248$		0			0
$249$	7.66959	+	3.07044i	0.486040	+	0.194581i
$250$		0			0
$251$	2.20886	−	9.10506i	0.139422	−	0.574706i	−0.858645	−	0.512570i	$-0.828694\pi$
$251$	2.20886	−	9.10506i	0.139422	−	0.574706i	0.998068	−	0.0621363i	$-0.0197913\pi$
$252$		0			0
$253$	−2.86517	−	19.9277i	−0.180131	−	1.25284i
$254$		0			0
$255$	−6.42420	−	0.613437i	−0.402299	−	0.0384149i
$256$		0			0
$257$	−1.12339	+	23.5828i	−0.0700750	+	1.47106i	0.640784	+	0.767721i	$0.278609\pi$
$257$	−1.12339	+	23.5828i	−0.0700750	+	1.47106i	−0.710859	+	0.703334i	$0.751694\pi$
$258$		0			0
$259$	3.20503	−	22.2915i	0.199151	−	1.38512i
$260$		0			0
$261$	−4.71159	+	1.88623i	−0.291640	+	0.116755i
$262$		0			0
$263$	0.455108	+	0.292480i	0.0280632	+	0.0180351i	0.554597	−	0.832119i	$-0.312872\pi$
$263$	0.455108	+	0.292480i	0.0280632	+	0.0180351i	−0.526534	+	0.850154i	$0.676509\pi$
$264$		0			0
$265$	−11.4966	−	13.2677i	−0.706228	−	0.815031i
$266$		0			0
$267$	3.08082			0.188543
$268$		0			0
$269$	−3.36580			−0.205216			−0.102608	−	0.994722i	$-0.532719\pi$
$269$	−3.36580			−0.205216			−0.102608	+	0.994722i	$0.532719\pi$
$270$		0			0
$271$	−9.20589	−	10.6242i	−0.559218	−	0.645372i	0.403788	−	0.914853i	$-0.367693\pi$
$271$	−9.20589	−	10.6242i	−0.559218	−	0.645372i	−0.963006	+	0.269481i	$0.913148\pi$
$272$		0			0
$273$	0.845714	+	0.543507i	0.0511849	+	0.0328946i
$274$		0			0
$275$	9.03222	−	3.61595i	0.544663	−	0.218050i
$276$		0			0
$277$	0.504782	−	3.51084i	0.0303294	−	0.210946i	−0.969021	−	0.246978i	$-0.920563\pi$
$277$	0.504782	−	3.51084i	0.0303294	−	0.210946i	0.999351	+	0.0360316i	$0.0114717\pi$
$278$		0			0
$279$	0.257796	−	5.41181i	0.0154339	−	0.323997i
$280$		0			0
$281$	−13.1280	−	1.25357i	−0.783150	−	0.0747818i	−0.304182	−	0.952614i	$-0.598383\pi$
$281$	−13.1280	−	1.25357i	−0.783150	−	0.0747818i	−0.478968	+	0.877832i	$0.658989\pi$
$282$		0			0
$283$	2.14555	+	14.9227i	0.127540	+	0.887060i	0.948659	+	0.316302i	$0.102441\pi$
$283$	2.14555	+	14.9227i	0.127540	+	0.887060i	−0.821119	+	0.570758i	$0.806650\pi$
$284$		0			0
$285$	−2.60555	+	10.7402i	−0.154339	+	0.636195i
$286$		0			0
$287$	11.8420	+	4.74081i	0.699010	+	0.279841i
$288$		0			0
$289$	1.78685	+	0.921187i	0.105109	+	0.0541874i
$290$		0			0
$291$	10.0185	−	1.93091i	0.587295	−	0.113192i
$292$		0			0
$293$	0.650445	+	1.42428i	0.0379994	+	0.0832071i	0.927680	−	0.373377i	$-0.121800\pi$
$293$	0.650445	+	1.42428i	0.0379994	+	0.0832071i	−0.889680	+	0.456584i	$0.849073\pi$
$294$		0			0
$295$	−6.04281	+	3.88348i	−0.351826	+	0.226105i
$296$		0			0
$297$	−2.18963	−	3.79254i	−0.127055	−	0.220066i
$298$		0			0
$299$	2.13651	−	0.204012i	0.123557	−	0.0117983i
$300$		0			0
$301$	3.64899	−	2.86960i	0.210325	−	0.165401i
$302$		0			0
$303$	1.31905	+	0.254227i	0.0757776	+	0.0146049i
$304$		0			0
$305$	−4.86263	+	8.42232i	−0.278433	+	0.482261i
$306$		0			0
$307$	−4.91933	−	6.90823i	−0.280761	−	0.394273i	0.649981	−	0.759951i	$-0.274777\pi$
$307$	−4.91933	−	6.90823i	−0.280761	−	0.394273i	−0.930742	+	0.365677i	$0.880837\pi$
$308$		0			0
$309$	4.91556	+	4.68698i	0.279636	+	0.266633i
$310$		0			0
$311$	10.2291	−	3.00354i	0.580040	−	0.170315i	0.0214655	−	0.999770i	$-0.493167\pi$
$311$	10.2291	−	3.00354i	0.580040	−	0.170315i	0.558574	+	0.829455i	$0.311349\pi$
$312$		0			0
$313$	−11.6831	+	13.4830i	−0.660367	+	0.762104i	−0.982837	−	0.184475i	$-0.940941\pi$
$313$	−11.6831	+	13.4830i	−0.660367	+	0.762104i	0.322470	+	0.946580i	$0.395487\pi$
$314$		0			0
$315$	−1.17396	+	3.39193i	−0.0661451	+	0.191114i
$316$		0			0
$317$	6.90071	−	6.57981i	0.387582	−	0.369559i	−0.471089	−	0.882086i	$-0.656139\pi$
$317$	6.90071	−	6.57981i	0.387582	−	0.369559i	0.858671	+	0.512527i	$0.171290\pi$
$318$		0			0
$319$	−19.7546	+	10.1842i	−1.10605	+	0.570206i
$320$		0			0
$321$	−7.20486	−	2.11554i	−0.402136	−	0.118078i
$322$		0			0
$323$	−14.8903	+	20.9105i	−0.828519	+	1.16349i
$324$		0			0
$325$	0.339225	+	0.980126i	0.0188168	+	0.0543676i
$326$		0			0
$327$	−1.81460	+	3.97343i	−0.100348	+	0.219731i
$328$		0			0
$329$	−1.13143	−	23.7516i	−0.0623777	−	1.30947i
$330$		0			0
$331$	−3.82407	−	15.7630i	−0.210190	−	0.866413i	−0.975008	−	0.222168i	$-0.928687\pi$
$331$	−3.82407	−	15.7630i	−0.210190	−	0.866413i	0.764819	−	0.644245i	$-0.222828\pi$
$332$		0			0
$333$	−8.22077	−	6.46488i	−0.450495	−	0.354273i
$334$		0			0
$335$	−9.34303	+	9.94272i	−0.510464	+	0.543229i
$336$		0			0
$337$	9.58393	+	7.53688i	0.522070	+	0.410560i	0.844113	−	0.536165i	$-0.180127\pi$
$337$	9.58393	+	7.53688i	0.522070	+	0.410560i	−0.322044	+	0.946725i	$0.604370\pi$
$338$		0			0
$339$	2.73274	+	11.2645i	0.148422	+	0.611804i
$340$		0			0
$341$	−1.12896	−	23.6997i	−0.0611364	−	1.28341i
$342$		0			0
$343$	8.37560	−	18.3400i	0.452240	−	0.990267i
$344$		0			0
$345$	2.50629	+	7.24146i	0.134934	+	0.389867i
$346$		0			0
$347$	−8.95448	+	12.5748i	−0.480701	+	0.675051i	−0.981708	−	0.190393i	$-0.939024\pi$
$347$	−8.95448	+	12.5748i	−0.480701	+	0.675051i	0.501007	+	0.865444i	$0.332963\pi$
$348$		0			0
$349$	18.1578	+	5.33160i	0.971963	+	0.285394i	0.728903	−	0.684617i	$-0.240031\pi$
$349$	18.1578	+	5.33160i	0.971963	+	0.285394i	0.243060	+	0.970011i	$0.421849\pi$
$350$		0			0
$351$	0.414951	−	0.213922i	0.0221485	−	0.0114183i
$352$		0			0
$353$	−24.3642	+	23.2312i	−1.29678	+	1.23647i	−0.341805	+	0.939771i	$0.611038\pi$
$353$	−24.3642	+	23.2312i	−1.29678	+	1.23647i	−0.954970	+	0.296702i	$0.904113\pi$
$354$		0			0
$355$	5.30831	−	15.3373i	0.281736	−	0.814022i
$356$		0			0
$357$	−5.45967	+	6.30079i	−0.288956	+	0.333473i
$358$		0			0
$359$	−27.4354	+	8.05575i	−1.44798	+	0.425166i	−0.908874	−	0.417070i	$-0.863057\pi$
$359$	−27.4354	+	8.05575i	−1.44798	+	0.425166i	−0.539109	+	0.842236i	$0.681239\pi$
$360$		0			0
$361$	18.0656	+	17.2255i	0.950820	+	0.906605i
$362$		0			0
$363$	−4.74361	−	6.66147i	−0.248975	−	0.349637i
$364$		0			0
$365$	−4.10526	+	7.11052i	−0.214879	+	0.372182i
$366$		0			0
$367$	−9.65430	−	1.86071i	−0.503950	−	0.0971285i	−0.0690612	−	0.997612i	$-0.522000\pi$
$367$	−9.65430	−	1.86071i	−0.503950	−	0.0971285i	−0.434889	+	0.900484i	$0.643212\pi$
$368$		0			0
$369$	4.65624	−	3.66170i	0.242394	−	0.190621i
$370$		0			0
$371$	−22.5775	+	2.15589i	−1.17216	+	0.111928i
$372$		0			0
$373$	14.2631	+	24.7045i	0.738518	+	1.27915i	0.953163	+	0.302458i	$0.0978073\pi$
$373$	14.2631	+	24.7045i	0.738518	+	1.27915i	−0.214645	+	0.976692i	$0.568859\pi$
$374$		0			0
$375$	−10.1264	+	6.50787i	−0.522927	+	0.336065i
$376$		0			0
$377$	−0.984248	−	2.15520i	−0.0506914	−	0.110999i
$378$		0			0
$379$	−14.1586	+	2.72884i	−0.727277	+	0.140171i	−0.539434	−	0.842028i	$-0.681362\pi$
$379$	−14.1586	+	2.72884i	−0.727277	+	0.140171i	−0.187843	+	0.982199i	$0.560150\pi$
$380$		0			0
$381$	11.9696	+	6.17073i	0.613219	+	0.316136i
$382$		0			0
$383$	3.78344	+	1.51466i	0.193325	+	0.0773956i	0.466305	−	0.884624i	$-0.345585\pi$
$383$	3.78344	+	1.51466i	0.193325	+	0.0773956i	−0.272980	+	0.962020i	$0.588009\pi$
$384$		0			0
$385$	−3.70581	+	15.2756i	−0.188866	+	0.778514i
$386$		0			0
$387$	−0.306796	−	2.13382i	−0.0155953	−	0.108468i
$388$		0			0
$389$	−7.49919	−	0.716086i	−0.380224	−	0.0363070i	−0.0968055	−	0.995303i	$-0.530862\pi$
$389$	−7.49919	−	0.716086i	−0.380224	−	0.0363070i	−0.283418	+	0.958996i	$0.591469\pi$
$390$		0			0
$391$	−0.846911	+	17.7788i	−0.0428301	+	0.899115i
$392$		0			0
$393$	−1.55188	+	10.7936i	−0.0782821	+	0.544464i
$394$		0			0
$395$	14.1547	−	5.66671i	0.712203	−	0.285123i
$396$		0			0
$397$	−6.62823	−	4.25971i	−0.332661	−	0.213789i	0.363637	−	0.931541i	$-0.381535\pi$
$397$	−6.62823	−	4.25971i	−0.332661	−	0.213789i	−0.696299	+	0.717752i	$0.745171\pi$
$398$		0			0
$399$	9.34990	+	10.7904i	0.468080	+	0.540194i
$400$		0			0
$401$	−26.3539			−1.31605			−0.658026	−	0.752995i	$-0.728608\pi$
$401$	−26.3539			−1.31605			−0.658026	+	0.752995i	$0.728608\pi$
$402$		0			0
$403$	2.52936			0.125996
$404$		0			0
$405$	1.09155	+	1.25971i	0.0542395	+	0.0625957i
$406$		0			0
$407$	−38.5290	−	24.7611i	−1.90981	−	1.22736i
$408$		0			0
$409$	−23.1960	+	9.28630i	−1.14697	+	0.459178i	−0.865756	−	0.500467i	$-0.833162\pi$
$409$	−23.1960	+	9.28630i	−1.14697	+	0.459178i	−0.281215	+	0.959645i	$0.590737\pi$
$410$		0			0
$411$	0.933806	−	6.49476i	0.0460613	−	0.320363i
$412$		0			0
$413$	−0.441551	+	9.26929i	−0.0217273	+	0.456112i
$414$		0			0
$415$	−13.7080	−	1.30896i	−0.672900	−	0.0642542i
$416$		0			0
$417$	−1.61816	−	11.2546i	−0.0792417	−	0.551138i
$418$		0			0
$419$	0.678308	−	2.79602i	0.0331375	−	0.136595i	−0.952840	−	0.303473i	$-0.901854\pi$
$419$	0.678308	−	2.79602i	0.0331375	−	0.136595i	0.985977	+	0.166879i	$0.0533688\pi$
$420$		0			0
$421$	−12.3820	−	4.95701i	−0.603463	−	0.241590i	0.0497534	−	0.998762i	$-0.484156\pi$
$421$	−12.3820	−	4.95701i	−0.603463	−	0.241590i	−0.653216	+	0.757172i	$0.726581\pi$
$422$		0			0
$423$	−9.81489	−	5.05993i	−0.477216	−	0.246022i
$424$		0			0
$425$	−8.44599	+	1.62783i	−0.409691	+	0.0789614i
$426$		0			0
$427$	5.21928	+	11.4286i	0.252579	+	0.553070i
$428$		0			0
$429$	1.71990	−	1.10531i	0.0830374	−	0.0533649i
$430$		0			0
$431$	−18.9487	−	32.8201i	−0.912727	−	1.58089i	−0.810195	−	0.586160i	$-0.800639\pi$
$431$	−18.9487	−	32.8201i	−0.912727	−	1.58089i	−0.102532	−	0.994730i	$-0.532694\pi$
$432$		0			0
$433$	26.2086	−	2.50261i	1.25950	−	0.120268i	0.556134	−	0.831093i	$-0.312284\pi$
$433$	26.2086	−	2.50261i	1.25950	−	0.120268i	0.703369	+	0.710825i	$0.251678\pi$
$434$		0			0
$435$	6.64956	−	5.22927i	0.318822	−	0.250724i
$436$		0			0
$437$	29.9307	+	5.76867i	1.43178	+	0.275953i
$438$		0			0
$439$	−11.0246	+	19.0952i	−0.526177	+	0.911365i	0.473358	+	0.880870i	$0.343042\pi$
$439$	−11.0246	+	19.0952i	−0.526177	+	0.911365i	−0.999535	+	0.0304946i	$0.990292\pi$
$440$		0			0
$441$	−1.37064	−	1.92480i	−0.0652687	−	0.0916571i
$442$		0			0
$443$	−10.0086	−	9.54317i	−0.475522	−	0.453410i	0.414016	−	0.910269i	$-0.364126\pi$
$443$	−10.0086	−	9.54317i	−0.475522	−	0.453410i	−0.889539	+	0.456860i	$0.848974\pi$
$444$		0			0
$445$	−4.92722	+	1.44676i	−0.233573	+	0.0685831i
$446$		0			0
$447$	6.23358	−	7.19393i	0.294838	−	0.340261i
$448$		0			0
$449$	2.29173	−	6.62151i	0.108153	−	0.312488i	−0.877918	−	0.478811i	$-0.841068\pi$
$449$	2.29173	−	6.62151i	0.108153	−	0.312488i	0.986071	+	0.166322i	$0.0531893\pi$
$450$		0			0
$451$	18.7742	−	17.9012i	0.884044	−	0.842934i
$452$		0			0
$453$	12.3775	−	6.38102i	0.581544	−	0.299807i
$454$		0			0
$455$	−1.60780	−	0.472093i	−0.0753749	−	0.0221321i
$456$		0			0
$457$	−11.4709	+	16.1086i	−0.536585	+	0.753528i	−0.990499	−	0.137517i	$-0.956088\pi$
$457$	−11.4709	+	16.1086i	−0.536585	+	0.753528i	0.453914	+	0.891045i	$0.350027\pi$
$458$		0			0
$459$	1.26629	+	3.65871i	0.0591055	+	0.170774i
$460$		0			0
$461$	5.77843	−	12.6530i	0.269128	−	0.589309i	−0.726022	−	0.687671i	$-0.758633\pi$
$461$	5.77843	−	12.6530i	0.269128	−	0.589309i	0.995151	+	0.0983621i	$0.0313603\pi$
$462$		0			0
$463$	−1.20309	−	25.2560i	−0.0559124	−	1.17374i	−0.836236	−	0.548369i	$-0.815249\pi$
$463$	−1.20309	−	25.2560i	−0.0559124	−	1.17374i	0.780324	−	0.625376i	$-0.215054\pi$
$464$		0			0
$465$	2.12911	+	8.77629i	0.0987349	+	0.406991i
$466$		0			0
$467$	−16.6830	−	13.1197i	−0.771998	−	0.607106i	0.152496	−	0.988304i	$-0.451269\pi$
$467$	−16.6830	−	13.1197i	−0.771998	−	0.607106i	−0.924493	+	0.381199i	$0.875511\pi$
$468$		0			0
$469$	3.46177	+	17.2829i	0.159850	+	0.798050i
$470$		0			0
$471$	−16.3135	−	12.8291i	−0.751688	−	0.591134i
$472$		0			0
$473$	−2.22571	−	9.17449i	−0.102338	−	0.421844i
$474$		0			0
$475$	0.700896	+	14.7136i	0.0321593	+	0.675107i
$476$		0			0
$477$	−4.37530	+	9.58056i	−0.200331	+	0.438664i
$478$		0			0
$479$	3.76807	+	10.8871i	0.172168	+	0.497445i	0.997765	−	0.0668134i	$-0.0212832\pi$
$479$	3.76807	+	10.8871i	0.172168	+	0.497445i	−0.825598	+	0.564259i	$0.809162\pi$
$480$		0			0
$481$	2.83209	−	3.97711i	0.129132	−	0.181341i
$482$		0			0
$483$	9.49867	+	2.78906i	0.432204	+	0.126907i
$484$		0			0
$485$	−15.1160	+	7.79286i	−0.686384	+	0.353856i
$486$		0			0
$487$	−6.96417	+	6.64032i	−0.315577	+	0.300902i	−0.831267	−	0.555873i	$-0.812384\pi$
$487$	−6.96417	+	6.64032i	−0.315577	+	0.300902i	0.515690	+	0.856775i	$0.327535\pi$
$488$		0			0
$489$	−7.19242	+	20.7811i	−0.325253	+	0.939756i
$490$		0			0
$491$	6.67958	−	7.70864i	0.301445	−	0.347886i	−0.584737	−	0.811223i	$-0.698802\pi$
$491$	6.67958	−	7.70864i	0.301445	−	0.347886i	0.886182	+	0.463336i	$0.153348\pi$
$492$		0			0
$493$	18.8532	−	5.53579i	0.849105	−	0.249320i
$494$		0			0
$495$	5.28291	+	5.03724i	0.237449	+	0.226407i
$496$		0			0
$497$	−12.1623	−	17.0796i	−0.545554	−	0.766123i
$498$		0			0
$499$	−13.2742	+	22.9915i	−0.594233	+	1.02924i	0.399422	+	0.916767i	$0.369211\pi$
$499$	−13.2742	+	22.9915i	−0.594233	+	1.02924i	−0.993655	+	0.112474i	$0.964122\pi$
$500$		0			0
$501$	−12.9294	−	2.49193i	−0.577641	−	0.111331i
$502$		0			0
$503$	−3.54014	+	2.78400i	−0.157847	+	0.124132i	−0.693959	−	0.720015i	$-0.744135\pi$
$503$	−3.54014	+	2.78400i	−0.157847	+	0.124132i	0.536112	+	0.844147i	$0.319893\pi$
$504$		0			0
$505$	−2.22898	+	0.212841i	−0.0991881	+	0.00947132i
$506$		0			0
$507$	−6.39103	−	11.0696i	−0.283835	−	0.491617i
$508$		0			0
$509$	8.78303	−	5.64451i	0.389301	−	0.250189i	−0.331319	−	0.943519i	$-0.607494\pi$
$509$	8.78303	−	5.64451i	0.389301	−	0.250189i	0.720620	+	0.693330i	$0.243857\pi$
$510$		0			0
$511$	4.40636	+	9.64858i	0.194926	+	0.426828i
$512$		0			0
$513$	6.51054	−	1.25480i	0.287447	−	0.0554009i
$514$		0			0
$515$	−10.0626	−	5.18762i	−0.443410	−	0.228594i
$516$		0			0
$517$	−44.8936	−	17.9727i	−1.97442	−	0.790437i
$518$		0			0
$519$	−3.52608	+	14.5347i	−0.154778	+	0.638002i
$520$		0			0
$521$	−1.56980	−	10.9182i	−0.0687740	−	0.478334i	−0.994879	−	0.101069i	$-0.967774\pi$
$521$	−1.56980	−	10.9182i	−0.0687740	−	0.478334i	0.926105	−	0.377265i	$-0.123135\pi$
$522$		0			0
$523$	19.8278	+	1.89332i	0.867008	+	0.0827893i	0.519074	−	0.854730i	$-0.326277\pi$
$523$	19.8278	+	1.89332i	0.867008	+	0.0827893i	0.347935	+	0.937519i	$0.386883\pi$
$524$		0			0
$525$	−0.227634	+	4.77863i	−0.00993477	+	0.208556i
$526$		0			0
$527$	−2.98525	+	20.7629i	−0.130040	+	0.904446i
$528$		0			0
$529$	−1.73153	+	0.693202i	−0.0752841	+	0.0301392i
$530$		0			0
$531$	3.62531	+	2.32984i	0.157325	+	0.101107i
$532$		0			0
$533$	1.81095	+	2.08995i	0.0784412	+	0.0905259i
$534$		0			0
$535$	12.5163			0.541129
$536$		0			0
$537$	16.3513			0.705609
$538$		0			0
$539$	−6.77646	−	7.82045i	−0.291883	−	0.336851i
$540$		0			0
$541$	29.8403	+	19.1772i	1.28293	+	0.824491i	0.991247	−	0.132023i	$-0.0421473\pi$
$541$	29.8403	+	19.1772i	1.28293	+	0.824491i	0.291686	+	0.956514i	$0.405784\pi$
$542$		0			0
$543$	14.8441	−	5.94266i	0.637019	−	0.255024i
$544$		0			0
$545$	1.03620	−	7.20693i	0.0443859	−	0.308711i
$546$		0			0
$547$	1.77333	−	37.2267i	0.0758220	−	1.59170i	−0.565710	−	0.824604i	$-0.691398\pi$
$547$	1.77333	−	37.2267i	0.0758220	−	1.59170i	0.641532	−	0.767096i	$-0.278299\pi$
$548$		0			0
$549$	5.80813	+	0.554609i	0.247885	+	0.0236701i
$550$		0			0
$551$	−4.78888	−	33.3074i	−0.204013	−	1.41894i
$552$		0			0
$553$	4.64384	−	19.1422i	0.197476	−	0.814008i
$554$		0			0
$555$	16.1836	+	6.47893i	0.686955	+	0.275015i
$556$		0			0
$557$	9.81758	+	5.06132i	0.415984	+	0.214455i	0.653496	−	0.756930i	$-0.273302\pi$
$557$	9.81758	+	5.06132i	0.415984	+	0.214455i	−0.237512	+	0.971385i	$0.576332\pi$
$558$		0			0
$559$	0.988225	−	0.190465i	0.0417974	−	0.00805580i
$560$		0			0
$561$	7.04333	+	15.4227i	0.297370	+	0.651149i
$562$		0			0
$563$	−19.9716	+	12.8350i	−0.841703	+	0.540930i	−0.888977	−	0.457952i	$-0.848583\pi$
$563$	−19.9716	+	12.8350i	−0.841703	+	0.540930i	0.0472736	+	0.998882i	$0.484947\pi$
$564$		0			0
$565$	−9.66037	−	16.7323i	−0.406415	−	0.703931i
$566$		0			0
$567$	2.14363	−	0.204692i	0.0900241	−	0.00859625i
$568$		0			0
$569$	21.0675	−	16.5677i	0.883195	−	0.694552i	−0.0697928	−	0.997562i	$-0.522234\pi$
$569$	21.0675	−	16.5677i	0.883195	−	0.694552i	0.952988	+	0.303009i	$0.0979914\pi$
$570$		0			0
$571$	35.9896	+	6.93643i	1.50612	+	0.290280i	0.874510	−	0.485007i	$-0.161183\pi$
$571$	35.9896	+	6.93643i	1.50612	+	0.290280i	0.631608	+	0.775288i	$0.282395\pi$
$572$		0			0
$573$	−11.6353	+	20.1529i	−0.486071	+	0.841899i
$574$		0			0
$575$	5.92440	+	8.31966i	0.247065	+	0.346954i
$576$		0			0
$577$	7.23841	+	6.90181i	0.301339	+	0.287326i	0.825629	−	0.564214i	$-0.190821\pi$
$577$	7.23841	+	6.90181i	0.301339	+	0.287326i	−0.524290	+	0.851540i	$0.675669\pi$
$578$		0			0
$579$	−18.1053	+	5.31619i	−0.752429	+	0.220933i
$580$		0			0
$581$	−11.6499	+	13.4447i	−0.483319	+	0.557780i
$582$		0			0
$583$	−15.0856	+	43.5870i	−0.624782	+	1.80519i
$584$		0			0
$585$	−0.563182	+	0.536993i	−0.0232847	+	0.0222019i
$586$		0			0
$587$	−6.85925	+	3.53619i	−0.283111	+	0.145954i	−0.593934	−	0.804514i	$-0.702426\pi$
$587$	−6.85925	+	3.53619i	−0.283111	+	0.145954i	0.310822	+	0.950468i	$0.399396\pi$
$588$		0			0
$589$	34.4678	+	10.1207i	1.42022	+	0.417015i
$590$		0			0
$591$	14.9759	−	21.0307i	0.616026	−	0.865088i
$592$		0			0
$593$	6.56263	+	18.9615i	0.269495	+	0.778654i	0.995823	+	0.0913059i	$0.0291041\pi$
$593$	6.56263	+	18.9615i	0.269495	+	0.778654i	−0.726328	+	0.687348i	$0.758775\pi$
$594$		0			0
$595$	5.77289	−	12.6409i	0.236665	−	0.518225i
$596$		0			0
$597$	−0.301027	−	6.31933i	−0.0123202	−	0.258633i
$598$		0			0
$599$	−8.59216	−	35.4174i	−0.351066	−	1.44711i	−0.824288	−	0.566171i	$-0.808424\pi$
$599$	−8.59216	−	35.4174i	−0.351066	−	1.44711i	0.473222	−	0.880943i	$-0.343091\pi$
$600$		0			0
$601$	−14.1426	−	11.1219i	−0.576890	−	0.453671i	0.286591	−	0.958053i	$-0.407478\pi$
$601$	−14.1426	−	11.1219i	−0.576890	−	0.453671i	−0.863481	+	0.504382i	$0.831720\pi$
$602$		0			0
$603$	7.75446	+	2.62075i	0.315786	+	0.106725i
$604$		0			0
$605$	10.7148	+	8.42622i	0.435619	+	0.342575i
$606$		0			0
$607$	−1.98390	−	8.17773i	−0.0805238	−	0.331924i	0.917274	−	0.398257i	$-0.130385\pi$
$607$	−1.98390	−	8.17773i	−0.0805238	−	0.331924i	−0.997797	+	0.0663337i	$0.978870\pi$
$608$		0			0
$609$	−0.520008	−	10.9163i	−0.0210718	−	0.442351i
$610$		0			0
$611$	2.14152	−	4.68927i	0.0866366	−	0.189708i
$612$		0			0
$613$	3.29936	+	9.53287i	0.133260	+	0.385029i	0.991814	−	0.127695i	$-0.0407578\pi$
$613$	3.29936	+	9.53287i	0.133260	+	0.385029i	−0.858554	+	0.512724i	$0.828637\pi$
$614$		0			0
$615$	−5.72727	+	8.04283i	−0.230946	+	0.324318i
$616$		0			0
$617$	−36.7903	−	10.8026i	−1.48112	−	0.434896i	−0.561425	−	0.827528i	$-0.689747\pi$
$617$	−36.7903	−	10.8026i	−1.48112	−	0.434896i	−0.919696	+	0.392631i	$0.871565\pi$
$618$		0			0
$619$	38.0670	−	19.6249i	1.53004	−	0.788792i	0.531733	−	0.846912i	$-0.321541\pi$
$619$	38.0670	−	19.6249i	1.53004	−	0.788792i	0.998310	+	0.0581208i	$0.0185109\pi$
$620$		0			0
$621$	3.32720	−	3.17248i	0.133516	−	0.127307i
$622$		0			0
$623$	−2.16983	+	6.26931i	−0.0869323	+	0.251175i
$624$		0			0
$625$	5.86499	−	6.76855i	0.234599	−	0.270742i
$626$		0			0
$627$	27.8598	−	8.18039i	1.11261	−	0.326693i
$628$		0			0
$629$	29.3046	+	27.9419i	1.16845	+	1.11411i
$630$		0			0
$631$	−9.68347	−	13.5985i	−0.385493	−	0.541349i	0.575543	−	0.817771i	$-0.304791\pi$
$631$	−9.68347	−	13.5985i	−0.385493	−	0.541349i	−0.961036	+	0.276422i	$0.910851\pi$
$632$		0			0
$633$	−12.1030	+	20.9629i	−0.481050	+	0.833202i
$634$		0			0
$635$	−22.0410	−	4.24805i	−0.874669	−	0.168579i
$636$		0			0
$637$	0.867124	−	0.681914i	0.0343567	−	0.0270184i
$638$		0			0
$639$	−9.69288	+	0.925558i	−0.383444	+	0.0366145i
$640$		0			0
$641$	−19.2918	−	33.4144i	−0.761981	−	1.31979i	−0.941828	−	0.336095i	$-0.890894\pi$
$641$	−19.2918	−	33.4144i	−0.761981	−	1.31979i	0.179847	−	0.983695i	$-0.442440\pi$
$642$		0			0
$643$	−13.3501	+	8.57960i	−0.526477	+	0.338346i	−0.776730	−	0.629834i	$-0.783123\pi$
$643$	−13.3501	+	8.57960i	−0.526477	+	0.338346i	0.250252	+	0.968181i	$0.419486\pi$
$644$		0			0
$645$	1.49271	+	3.26859i	0.0587755	+	0.128700i
$646$		0			0
$647$	−3.42780	+	0.660654i	−0.134761	+	0.0259730i	−0.256185	−	0.966628i	$-0.582466\pi$
$647$	−3.42780	+	0.660654i	−0.134761	+	0.0259730i	0.121425	+	0.992601i	$0.461254\pi$
$648$		0			0
$649$	16.7741	+	8.64765i	0.658441	+	0.339450i
$650$		0			0
$651$	10.8312	+	4.33616i	0.424508	+	0.169947i
$652$		0			0
$653$	2.53736	−	10.4591i	0.0992946	−	0.409298i	−0.900372	−	0.435121i	$-0.856706\pi$
$653$	2.53736	−	10.4591i	0.0992946	−	0.409298i	0.999667	+	0.0258232i	$0.00822068\pi$
$654$		0			0
$655$	−2.58674	−	17.9912i	−0.101072	−	0.702973i
$656$		0			0
$657$	4.90350	+	0.468227i	0.191304	+	0.0182673i
$658$		0			0
$659$	0.621064	−	13.0377i	0.0241932	−	0.507878i	−0.953953	−	0.299958i	$-0.903027\pi$
$659$	0.621064	−	13.0377i	0.0241932	−	0.507878i	0.978146	−	0.207920i	$-0.0666695\pi$
$660$		0			0
$661$	−2.76495	+	19.2306i	−0.107544	+	0.747985i	0.862675	+	0.505758i	$0.168787\pi$
$661$	−2.76495	+	19.2306i	−0.107544	+	0.747985i	−0.970220	+	0.242227i	$0.922122\pi$
$662$		0			0
$663$	−1.67800	+	0.671769i	−0.0651681	+	0.0260894i
$664$		0			0
$665$	−20.0207	−	12.8665i	−0.776369	−	0.498942i
$666$		0			0
$667$	−15.2790	−	17.6329i	−0.591606	−	0.682750i
$668$		0			0
$669$	−25.4729			−0.984840
$670$		0			0
$671$	25.5509			0.986383
$672$		0			0
$673$	22.4025	+	25.8539i	0.863554	+	0.996595i	0.999982	+	0.00594457i	$0.00189223\pi$
$673$	22.4025	+	25.8539i	0.863554	+	0.996595i	−0.136428	+	0.990650i	$0.543562\pi$
$674$		0			0
$675$	1.86897	+	1.20111i	0.0719365	+	0.0462308i
$676$		0			0
$677$	−8.69984	+	3.48289i	−0.334362	+	0.133858i	−0.532767	−	0.846262i	$-0.678848\pi$
$677$	−8.69984	+	3.48289i	−0.334362	+	0.133858i	0.198405	+	0.980120i	$0.436424\pi$
$678$		0			0
$679$	−3.12676	+	21.7471i	−0.119994	+	0.834576i
$680$		0			0
$681$	−0.157619	+	3.30884i	−0.00603999	+	0.126795i
$682$		0			0
$683$	25.2393	+	2.41006i	0.965753	+	0.0922182i	0.566001	−	0.824405i	$-0.308490\pi$
$683$	25.2393	+	2.41006i	0.965753	+	0.0922182i	0.399753	+	0.916623i	$0.369096\pi$
$684$		0			0
$685$	1.55651	+	10.8257i	0.0594710	+	0.413630i
$686$		0			0
$687$	2.72048	−	11.2140i	0.103793	−	0.427840i
$688$		0			0
$689$	−4.56479	−	1.82747i	−0.173905	−	0.0696209i
$690$		0			0
$691$	−40.1633	−	20.7056i	−1.52788	−	0.787679i	−0.529716	−	0.848175i	$-0.677702\pi$
$691$	−40.1633	−	20.7056i	−1.52788	−	0.787679i	−0.998168	+	0.0604955i	$0.980732\pi$
$692$		0			0
$693$	9.25979	−	1.78468i	0.351750	−	0.0677943i
$694$		0			0
$695$	7.87314	+	17.2398i	0.298645	+	0.653942i
$696$		0			0
$697$	−19.2933	+	12.3990i	−0.730785	+	0.469647i
$698$		0			0
$699$	−3.63823	−	6.30160i	−0.137611	−	0.238349i
$700$		0			0
$701$	6.68903	−	0.638725i	0.252641	−	0.0241243i	0.0320331	−	0.999487i	$-0.489802\pi$
$701$	6.68903	−	0.638725i	0.252641	−	0.0241243i	0.220608	+	0.975362i	$0.429196\pi$
$702$		0			0
$703$	54.5066	−	42.8645i	2.05576	−	1.61666i
$704$		0			0
$705$	18.0733	+	3.48335i	0.680681	+	0.131190i
$706$		0			0
$707$	−1.44635	+	2.50515i	−0.0543956	+	0.0942159i
$708$		0			0
$709$	8.26091	+	11.6008i	0.310245	+	0.435678i	0.940030	−	0.341091i	$-0.110796\pi$
$709$	8.26091	+	11.6008i	0.310245	+	0.435678i	−0.629785	+	0.776769i	$0.716857\pi$
$710$		0			0
$711$	−6.62014	−	6.31229i	−0.248275	−	0.236729i
$712$		0			0
$713$	23.8988	−	7.01733i	0.895018	−	0.262801i
$714$		0			0
$715$	−2.23161	+	2.57542i	−0.0834575	+	0.0963151i
$716$		0			0
$717$	−1.59008	+	4.59422i	−0.0593825	+	0.171574i
$718$		0			0
$719$	−6.82534	+	6.50795i	−0.254542	+	0.242706i	−0.806596	−	0.591103i	$-0.798693\pi$
$719$	−6.82534	+	6.50795i	−0.254542	+	0.242706i	0.552054	+	0.833808i	$0.313844\pi$
$720$		0			0
$721$	−12.9998	+	6.70186i	−0.484137	+	0.249590i
$722$		0			0
$723$	1.64712	+	0.483638i	0.0612570	+	0.0179867i
$724$		0			0
$725$	6.54021	−	9.18444i	0.242897	−	0.341102i
$726$		0			0
$727$	−3.22228	−	9.31016i	−0.119508	−	0.345295i	0.869342	−	0.494211i	$-0.164543\pi$
$727$	−3.22228	−	9.31016i	−0.119508	−	0.345295i	−0.988850	+	0.148916i	$0.952422\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	0.397135	+	8.33689i	0.0146886	+	0.308351i
$732$		0			0
$733$	−9.24938	−	38.1265i	−0.341634	−	1.40823i	−0.840621	−	0.541624i	$-0.817810\pi$
$733$	−9.24938	−	38.1265i	−0.341634	−	1.40823i	0.498987	−	0.866609i	$-0.333706\pi$
$734$		0			0
$735$	3.09599	+	2.43471i	0.114197	+	0.0898058i
$736$		0			0
$737$	34.8959	+	8.19695i	1.28541	+	0.301939i
$738$		0			0
$739$	−2.94814	−	2.31845i	−0.108449	−	0.0852854i	0.562462	−	0.826823i	$-0.309854\pi$
$739$	−2.94814	−	2.31845i	−0.108449	−	0.0852854i	−0.670911	+	0.741538i	$0.734097\pi$
$740$		0			0
$741$	0.729761	+	3.00812i	0.0268084	+	0.110506i
$742$		0			0
$743$	2.16539	+	45.4571i	0.0794404	+	1.66766i	0.589688	+	0.807631i	$0.299251\pi$
$743$	2.16539	+	45.4571i	0.0794404	+	1.66766i	−0.510248	+	0.860028i	$0.670446\pi$
$744$		0			0
$745$	−6.59120	+	14.4327i	−0.241483	+	0.528774i
$746$		0			0
$747$	2.70203	+	7.80700i	0.0988620	+	0.285643i
$748$		0			0
$749$	9.37940	−	13.1715i	0.342716	−	0.481277i
$750$		0			0
$751$	−4.73690	−	1.39088i	−0.172852	−	0.0507539i	0.194161	−	0.980970i	$-0.437801\pi$
$751$	−4.73690	−	1.39088i	−0.172852	−	0.0507539i	−0.367013	+	0.930216i	$0.619620\pi$
$752$		0			0
$753$	8.32764	−	4.29320i	0.303476	−	0.156453i
$754$		0			0
$755$	−16.7990	+	16.0178i	−0.611378	+	0.582947i
$756$		0			0
$757$	0.0525275	−	0.151768i	0.00190914	−	0.00551611i	−0.944042	−	0.329825i	$-0.893010\pi$
$757$	0.0525275	−	0.151768i	0.00190914	−	0.00551611i	0.945951	+	0.324309i	$0.105132\pi$
$758$		0			0
$759$	13.1840	−	15.2152i	0.478550	−	0.552277i
$760$		0			0
$761$	28.2495	−	8.29479i	1.02404	−	0.300686i	0.273756	−	0.961799i	$-0.411734\pi$
$761$	28.2495	−	8.29479i	1.02404	−	0.300686i	0.750286	+	0.661113i	$0.229916\pi$
$762$		0			0
$763$	−6.80769	−	6.49112i	−0.246455	−	0.234994i
$764$		0			0
$765$	−3.74335	−	5.25680i	−0.135341	−	0.190060i
$766$		0			0
$767$	−1.00592	+	1.74230i	−0.0363217	+	0.0629110i
$768$		0			0
$769$	45.1761	+	8.70698i	1.62909	+	0.313982i	0.920234	−	0.391369i	$-0.127998\pi$
$769$	45.1761	+	8.70698i	1.62909	+	0.313982i	0.708858	+	0.705351i	$0.249211\pi$
$770$		0			0
$771$	−18.5584	+	14.5945i	−0.668363	+	0.525607i
$772$		0			0
$773$	47.1550	−	4.50275i	1.69605	−	0.161953i	0.798239	−	0.602341i	$-0.205765\pi$
$773$	47.1550	−	4.50275i	1.69605	−	0.161953i	0.897808	+	0.440388i	$0.145159\pi$
$774$		0			0
$775$	6.01838	+	10.4241i	0.216187	+	0.374446i
$776$		0			0
$777$	18.9456	−	12.1756i	0.679670	−	0.436797i
$778$		0			0
$779$	16.3156	+	35.7261i	0.584566	+	1.28002i
$780$		0			0
$781$	−41.8701	+	8.06980i	−1.49823	+	0.288760i
$782$		0			0
$783$	−4.51095	−	2.32556i	−0.161208	−	0.0831087i
$784$		0			0
$785$	32.1152	+	12.8570i	1.14624	+	0.458885i
$786$		0			0
$787$	2.66164	−	10.9714i	0.0948770	−	0.391089i	−0.904496	−	0.426481i	$-0.859753\pi$
$787$	2.66164	−	10.9714i	0.0948770	−	0.391089i	0.999373	+	0.0353927i	$0.0112682\pi$
$788$		0			0
$789$	0.0769907	+	0.535482i	0.00274094	+	0.0190637i
$790$		0			0
$791$	−24.8473	−	2.37263i	−0.883470	−	0.0843612i
$792$		0			0
$793$	−0.129606	+	2.72076i	−0.00460244	+	0.0966171i
$794$		0			0
$795$	2.49844	−	17.3770i	0.0886106	−	0.616300i
$796$		0			0
$797$	−19.3762	+	7.75706i	−0.686340	+	0.274769i	−0.688508	−	0.725229i	$-0.741734\pi$
$797$	−19.3762	+	7.75706i	−0.686340	+	0.274769i	0.00216832	+	0.999998i	$0.499310\pi$
$798$		0			0
$799$	35.9656	+	23.1137i	1.27237	+	0.817703i
$800$		0			0
$801$	2.01751	+	2.32833i	0.0712851	+	0.0822674i
$802$		0			0
$803$	21.5713			0.761235
$804$		0			0
$805$	−16.5012			−0.581590
$806$		0			0
$807$	−2.20413	−	2.54370i	−0.0775891	−	0.0895425i
$808$		0			0
$809$	−40.2146	−	25.8444i	−1.41387	−	0.908639i	−0.413872	−	0.910335i	$-0.635824\pi$
$809$	−40.2146	−	25.8444i	−1.41387	−	0.908639i	−0.999999	+	0.00169556i	$0.999460\pi$
$810$		0			0
$811$	−7.48590	+	2.99690i	−0.262866	+	0.105236i	−0.499352	−	0.866399i	$-0.666428\pi$
$811$	−7.48590	+	2.99690i	−0.262866	+	0.105236i	0.236486	+	0.971635i	$0.424004\pi$
$812$		0			0
$813$	2.00063	−	13.9147i	0.0701652	−	0.488010i
$814$		0			0
$815$	1.74411	−	36.6133i	0.0610934	−	1.28251i
$816$		0			0
$817$	14.2287	+	1.35868i	0.497800	+	0.0475342i
$818$		0			0
$819$	0.143069	+	0.995070i	0.00499925	+	0.0347705i
$820$		0			0
$821$	−4.20508	+	17.3336i	−0.146758	+	0.604946i	0.850162	+	0.526522i	$0.176504\pi$
$821$	−4.20508	+	17.3336i	−0.146758	+	0.604946i	−0.996920	+	0.0784243i	$0.975011\pi$
$822$		0			0
$823$	−26.0705	−	10.4370i	−0.908760	−	0.363812i	−0.130276	−	0.991478i	$-0.541586\pi$
$823$	−26.0705	−	10.4370i	−0.908760	−	0.363812i	−0.778483	+	0.627665i	$0.784011\pi$
$824$		0			0
$825$	8.64760	+	4.45815i	0.301071	+	0.155213i
$826$		0			0
$827$	44.2529	−	8.52906i	1.53883	−	0.296584i	0.651831	−	0.758364i	$-0.274001\pi$
$827$	44.2529	−	8.52906i	1.53883	−	0.296584i	0.886995	+	0.461780i	$0.152789\pi$
$828$		0			0
$829$	−3.55655	−	7.78775i	−0.123524	−	0.270480i	0.837760	−	0.546038i	$-0.183865\pi$
$829$	−3.55655	−	7.78775i	−0.123524	−	0.270480i	−0.961284	+	0.275558i	$0.911137\pi$
$830$		0			0
$831$	2.98388	−	1.91762i	0.103510	−	0.0665216i
$832$		0			0
$833$	4.57425	+	7.92283i	0.158488	+	0.274510i
$834$		0			0
$835$	21.8484	−	2.08627i	0.756096	−	0.0721984i
$836$		0			0
$837$	4.25880	−	3.34915i	0.147206	−	0.115764i
$838$		0			0
$839$	24.2294	+	4.66984i	0.836493	+	0.161221i	0.589471	−	0.807789i	$-0.299336\pi$
$839$	24.2294	+	4.66984i	0.836493	+	0.161221i	0.247021	+	0.969010i	$0.420548\pi$
$840$		0			0
$841$	1.62154	−	2.80860i	0.0559153	−	0.0968481i
$842$		0			0
$843$	−7.64962	−	10.7424i	−0.263467	−	0.369988i
$844$		0			0
$845$	15.4196	+	14.7026i	0.530451	+	0.505784i
$846$		0			0
$847$	16.8967	−	4.96132i	0.580577	−	0.170473i
$848$		0			0
$849$	−9.87275	+	11.3938i	−0.338832	+	0.391033i
$850$		0			0
$851$	15.7253	−	45.4352i	0.539055	−	1.55750i
$852$		0			0
$853$	−11.3855	+	10.8560i	−0.389831	+	0.371703i	−0.859497	−	0.511141i	$-0.829223\pi$
$853$	−11.3855	+	10.8560i	−0.389831	+	0.371703i	0.469666	+	0.882844i	$0.344374\pi$
$854$		0			0
$855$	−9.82318	+	5.06420i	−0.335946	+	0.173192i
$856$		0			0
$857$	15.3562	+	4.50900i	0.524559	+	0.154024i	0.533282	−	0.845938i	$-0.320958\pi$
$857$	15.3562	+	4.50900i	0.524559	+	0.154024i	−0.00872301	+	0.999962i	$0.502777\pi$
$858$		0			0
$859$	10.4418	−	14.6634i	0.356269	−	0.500310i	−0.597079	−	0.802182i	$-0.703672\pi$
$859$	10.4418	−	14.6634i	0.356269	−	0.500310i	0.953348	+	0.301872i	$0.0976116\pi$
$860$		0			0
$861$	4.17198	+	12.0541i	0.142181	+	0.410804i
$862$		0			0
$863$	−23.6637	+	51.8162i	−0.805520	+	1.76384i	−0.179950	+	0.983676i	$0.557593\pi$
$863$	−23.6637	+	51.8162i	−0.805520	+	1.76384i	−0.625571	+	0.780168i	$0.715134\pi$
$864$		0			0
$865$	−1.18620	−	24.9015i	−0.0403322	−	0.846676i
$866$		0			0
$867$	0.473953	+	1.95366i	0.0160963	+	0.0663498i
$868$		0			0
$869$	−31.4876	−	24.7621i	−1.06814	−	0.839998i
$870$		0			0
$871$	−1.04985	+	3.67427i	−0.0355728	+	0.124498i
$872$		0			0
$873$	8.02000	+	6.30700i	0.271436	+	0.213460i
$874$		0			0
$875$	−6.11110	−	25.1903i	−0.206593	−	0.851587i
$876$		0			0
$877$	1.17412	+	24.6479i	0.0396473	+	0.832300i	0.927874	+	0.372894i	$0.121635\pi$
$877$	1.17412	+	24.6479i	0.0396473	+	0.832300i	−0.888227	+	0.459406i	$0.848062\pi$
$878$		0			0
$879$	−0.650445	+	1.42428i	−0.0219390	+	0.0480397i
$880$		0			0
$881$	9.78014	+	28.2579i	0.329501	+	0.952031i	0.981106	+	0.193472i	$0.0619750\pi$
$881$	9.78014	+	28.2579i	0.329501	+	0.952031i	−0.651604	+	0.758559i	$0.725904\pi$
$882$		0			0
$883$	4.56309	−	6.40797i	0.153560	−	0.215645i	−0.730628	−	0.682776i	$-0.760773\pi$
$883$	4.56309	−	6.40797i	0.153560	−	0.215645i	0.884189	+	0.467130i	$0.154712\pi$
$884$		0			0
$885$	−6.89213	−	2.02371i	−0.231676	−	0.0680263i
$886$		0			0
$887$	5.48261	−	2.82648i	0.184088	−	0.0949040i	−0.363719	−	0.931509i	$-0.618493\pi$
$887$	5.48261	−	2.82648i	0.184088	−	0.0949040i	0.547807	+	0.836605i	$0.315463\pi$
$888$		0			0
$889$	−20.9873	+	20.0114i	−0.703892	+	0.671159i
$890$		0			0
$891$	1.43231	−	4.13840i	0.0479843	−	0.138641i
$892$		0			0
$893$	47.9457	−	55.3323i	1.60444	−	1.85163i
$894$		0			0
$895$	−26.1509	+	7.67861i	−0.874130	+	0.256668i
$896$		0			0
$897$	1.55330	+	1.48106i	0.0518630	+	0.0494513i
$898$		0			0
$899$	−15.9497	−	22.3982i	−0.531952	−	0.747022i
$900$		0			0
$901$	20.3888	−	35.3144i	0.679249	−	1.17649i
$902$		0			0
$903$	4.55828	+	0.878537i	0.151690	+	0.0292359i
$904$		0			0
$905$	−20.9497	+	16.4750i	−0.696392	+	0.547649i
$906$		0			0
$907$	−13.9691	+	1.33388i	−0.463836	+	0.0442909i	−0.324358	−	0.945934i	$-0.605148\pi$
$907$	−13.9691	+	1.33388i	−0.463836	+	0.0442909i	−0.139477	+	0.990225i	$0.544542\pi$
$908$		0			0
$909$	0.671664	+	1.16336i	0.0222777	+	0.0385861i
$910$		0			0
$911$	−31.1448	+	20.0156i	−1.03187	+	0.663146i	−0.942964	−	0.332894i	$-0.891975\pi$
$911$	−31.1448	+	20.0156i	−1.03187	+	0.663146i	−0.0889105	+	0.996040i	$0.528339\pi$
$912$		0			0
$913$	15.0291	+	32.9092i	0.497392	+	1.08914i
$914$		0			0
$915$	−9.54951	+	1.84052i	−0.315697	+	0.0608456i
$916$		0			0
$917$	−20.8714	−	10.7599i	−0.689233	−	0.355324i
$918$		0			0
$919$	−23.4478	−	9.38709i	−0.773472	−	0.309651i	−0.0488573	−	0.998806i	$-0.515558\pi$
$919$	−23.4478	−	9.38709i	−0.773472	−	0.309651i	−0.724615	+	0.689154i	$0.757982\pi$
$920$		0			0
$921$	1.99942	−	8.24171i	0.0658830	−	0.271573i
$922$		0			0
$923$	−0.646919	−	4.49942i	−0.0212936	−	0.148100i
$924$		0			0
$925$	23.1294	+	2.20859i	0.760489	+	0.0726179i
$926$		0			0
$927$	−0.323174	+	6.78425i	−0.0106144	+	0.222824i
$928$		0			0
$929$	−1.37092	+	9.53499i	−0.0449786	+	0.312833i	0.954895	+	0.296943i	$0.0959672\pi$
$929$	−1.37092	+	9.53499i	−0.0449786	+	0.312833i	−0.999874	+	0.0158898i	$0.994942\pi$
$930$		0			0
$931$	14.5449	−	5.82290i	0.476690	−	0.190838i
$932$		0			0
$933$	8.96857	+	5.76375i	0.293618	+	0.188697i
$934$		0			0
$935$	−18.5071	−	21.3584i	−0.605248	−	0.698493i
$936$		0			0
$937$	30.1347			0.984457			0.492229	−	0.870466i	$-0.336182\pi$
$937$	30.1347			0.984457			0.492229	+	0.870466i	$0.336182\pi$
$938$		0			0
$939$	−17.8406			−0.582205
$940$		0			0
$941$	−11.6282	−	13.4197i	−0.379069	−	0.437468i	0.533869	−	0.845567i	$-0.320737\pi$
$941$	−11.6282	−	13.4197i	−0.379069	−	0.437468i	−0.912938	+	0.408099i	$0.866192\pi$
$942$		0			0
$943$	22.9092	+	14.7228i	0.746026	+	0.479442i
$944$		0			0
$945$	−3.33223	+	1.33402i	−0.108398	+	0.0433958i
$946$		0			0
$947$	−4.91945	+	34.2155i	−0.159861	+	1.11185i	0.739027	+	0.673676i	$0.235286\pi$
$947$	−4.91945	+	34.2155i	−0.159861	+	1.11185i	−0.898888	+	0.438179i	$0.855624\pi$
$948$		0			0
$949$	−0.109419	+	2.29700i	−0.00355190	+	0.0745636i
$950$		0			0
$951$	9.49169	+	0.906347i	0.307789	+	0.0293903i
$952$		0			0
$953$	3.60260	+	25.0566i	0.116700	+	0.811664i	0.961149	+	0.276029i	$0.0890187\pi$
$953$	3.60260	+	25.0566i	0.116700	+	0.811664i	−0.844449	+	0.535635i	$0.820072\pi$
$954$		0			0
$955$	9.14468	−	37.6949i	0.295915	−	1.21978i
$956$		0			0
$957$	−20.6332	−	8.26029i	−0.666977	−	0.267017i
$958$		0			0
$959$	12.5588	+	6.47452i	0.405546	+	0.209073i
$960$		0			0
$961$	−1.61607	+	0.311472i	−0.0521313	+	0.0100475i
$962$		0			0
$963$	−3.11936	−	6.83045i	−0.100520	−	0.220108i
$964$		0			0
$965$	26.4597	−	17.0046i	0.851766	−	0.547397i
$966$		0			0
$967$	12.4682	+	21.5955i	0.400949	+	0.694464i	0.993841	−	0.110818i	$-0.0353471\pi$
$967$	12.4682	+	21.5955i	0.400949	+	0.694464i	−0.592892	+	0.805282i	$0.702014\pi$
$968$		0			0
$969$	−25.5542	+	2.44013i	−0.820919	+	0.0783882i
$970$		0			0
$971$	−3.52707	+	2.77372i	−0.113189	+	0.0890129i	−0.673149	−	0.739507i	$-0.735059\pi$
$971$	−3.52707	+	2.77372i	−0.113189	+	0.0890129i	0.559960	+	0.828520i	$0.310816\pi$
$972$		0			0
$973$	24.0421	+	4.63374i	0.770755	+	0.148551i
$974$		0			0
$975$	−0.518585	+	0.898216i	−0.0166080	+	0.0287659i
$976$		0			0
$977$	34.3323	+	48.2130i	1.09839	+	1.54247i	0.811360	+	0.584547i	$0.198728\pi$
$977$	34.3323	+	48.2130i	1.09839	+	1.54247i	0.287028	+	0.957922i	$0.407333\pi$
$978$		0			0
$979$	9.76439	+	9.31033i	0.312071	+	0.297559i
$980$		0			0
$981$	−4.19123	+	1.23066i	−0.133816	+	0.0392918i
$982$		0			0
$983$	−22.4532	+	25.9123i	−0.716145	+	0.826475i	−0.990838	−	0.135057i	$-0.956878\pi$
$983$	−22.4532	+	25.9123i	−0.716145	+	0.826475i	0.274693	+	0.961532i	$0.411424\pi$
$984$		0			0
$985$	−14.0752	+	40.6676i	−0.448473	+	1.29578i
$986$		0			0
$987$	17.2093	−	16.4091i	0.547779	−	0.522307i
$988$		0			0
$989$	8.80889	−	4.54130i	0.280106	−	0.144405i
$990$		0			0
$991$	−22.3712	−	6.56878i	−0.710645	−	0.208664i	−0.0936203	−	0.995608i	$-0.529844\pi$
$991$	−22.3712	−	6.56878i	−0.710645	−	0.208664i	−0.617025	+	0.786944i	$0.711662\pi$
$992$		0			0
$993$	9.40866	−	13.2126i	0.298575	−	0.419290i
$994$		0			0
$995$	3.44902	+	9.96528i	0.109341	+	0.315921i
$996$		0			0
$997$	−0.418807	+	0.917060i	−0.0132638	+	0.0290436i	−0.916148	−	0.400840i	$-0.868718\pi$
$997$	−0.418807	+	0.917060i	−0.0132638	+	0.0290436i	0.902884	+	0.429884i	$0.141446\pi$
$998$		0			0
$999$	−0.497625	−	10.4464i	−0.0157442	−	0.330511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.505.3	yes	120
67.54	even	33	inner	804.2.y.b.121.3	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.121.3	✓	120	67.54	even	33	inner
804.2.y.b.505.3	yes	120	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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(-1.40224 - 0.901162i) q^{5} +(-1.99913 + 0.800331i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(-1.40224 - 0.901162i) q^{5} +(-1.99913 + 0.800331i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-0.208373 + 4.37429i) q^{11} +(-0.464734 - 0.0443767i) q^{13} +(-0.237216 - 1.64987i) q^{15} +(0.912776 - 3.76251i) q^{17} +(-6.15541 - 2.46425i) q^{19} +(-1.91400 - 0.986737i) q^{21} +(-4.51419 + 0.870038i) q^{23} +(-0.922904 - 2.02088i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(2.53756 + 4.39519i) q^{29} +(-5.39342 + 0.515009i) q^{31} +(-3.44232 + 2.70707i) q^{33} +(3.52448 + 0.679288i) q^{35} +(-5.22914 + 9.05714i) q^{37} +(-0.270798 - 0.380283i) q^{39} +(-4.28708 - 4.08773i) q^{41} +(-2.06844 + 0.607347i) q^{43} +(1.09155 - 1.25971i) q^{45} +(-3.61162 + 10.4351i) q^{47} +(-1.71014 + 1.63062i) q^{49} +(3.44126 - 1.77409i) q^{51} +(10.1057 + 2.96731i) q^{53} +(4.23413 - 5.94601i) q^{55} +(-2.16858 - 6.26569i) q^{57} +(1.79019 - 3.91998i) q^{59} +(-0.277619 - 5.82794i) q^{61} +(-0.507679 - 2.09268i) q^{63} +(0.611676 + 0.481027i) q^{65} +(1.49050 - 8.04850i) q^{67} +(-3.61370 - 2.84184i) q^{69} +(2.29558 + 9.46250i) q^{71} +(-0.234379 - 4.92022i) q^{73} +(0.922904 - 2.02088i) q^{75} +(-3.08432 - 8.91155i) q^{77} +(-5.30590 + 7.45109i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(7.34299 - 3.78558i) q^{83} +(-4.67056 + 4.45337i) q^{85} +(-1.65991 + 4.79600i) q^{87} +(2.01751 - 2.32833i) q^{89} +(0.964580 - 0.283226i) q^{91} +(-3.92116 - 3.73881i) q^{93} +(6.41064 + 9.00249i) q^{95} +(5.10144 - 8.83595i) q^{97} +(-4.30011 - 0.828779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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