LMFDB - Embedded newform 804.2.ba.b.353.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(41,804)]

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, 33, 53]))

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

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

chi := DirichletCharacter("804.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.ba (of order $66$, 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:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			353.4
Character	$\chi$	$=$	804.353
Dual form			804.2.ba.b.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47255 - 0.911919i) q^{3} +(-0.412679 - 2.87025i) q^{5} +(-0.273979 + 2.86924i) q^{7} +(1.33681 + 2.68569i) q^{9} +O(q^{10})$	\(q+(-1.47255 - 0.911919i) q^{3} +(-0.412679 - 2.87025i) q^{5} +(-0.273979 + 2.86924i) q^{7} +(1.33681 + 2.68569i) q^{9} +(4.55535 + 1.82369i) q^{11} +(1.25875 - 1.32014i) q^{13} +(-2.00974 + 4.60291i) q^{15} +(-1.49442 - 0.517223i) q^{17} +(3.17757 - 0.303421i) q^{19} +(3.01996 - 3.97525i) q^{21} +(5.20992 + 0.248179i) q^{23} +(-3.27055 + 0.960320i) q^{25} +(0.480619 - 5.17388i) q^{27} +(-0.761179 - 0.439467i) q^{29} +(-2.73430 - 2.86765i) q^{31} +(-5.04493 - 6.83959i) q^{33} +(8.34848 - 0.397687i) q^{35} +(-2.86589 - 4.96387i) q^{37} +(-3.05744 + 0.796095i) q^{39} +(-6.58885 + 1.26990i) q^{41} +(6.45298 - 5.59154i) q^{43} +(7.15693 - 4.94530i) q^{45} +(-4.64743 - 9.01475i) q^{47} +(-1.28395 - 0.247462i) q^{49} +(1.72894 + 2.12442i) q^{51} +(4.94001 - 5.70108i) q^{53} +(3.35454 - 13.8276i) q^{55} +(-4.95583 - 2.45088i) q^{57} +(-0.523482 + 1.78282i) q^{59} +(4.12990 + 10.3160i) q^{61} +(-8.07214 + 3.09979i) q^{63} +(-4.30860 - 3.06814i) q^{65} +(3.34986 + 7.46850i) q^{67} +(-7.44555 - 5.11648i) q^{69} +(4.94506 - 1.71150i) q^{71} +(6.17224 - 2.47099i) q^{73} +(5.69178 + 1.56836i) q^{75} +(-6.48066 + 12.5707i) q^{77} +(11.3480 + 2.75300i) q^{79} +(-5.42589 + 7.18051i) q^{81} +(-0.0980278 - 0.124653i) q^{83} +(-0.867843 + 4.50280i) q^{85} +(0.720116 + 1.34127i) q^{87} +(-1.62244 - 2.52457i) q^{89} +(3.44293 + 3.97335i) q^{91} +(1.41133 + 6.71622i) q^{93} +(-2.18221 - 8.99519i) q^{95} +(6.23550 - 3.60007i) q^{97} +(1.19176 + 14.6722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) $ 440 * q - 12 * q^7 + 4 * q^9	$ 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) $ 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{13}{66}\right)$	$1$

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
$3$	−1.47255	−	0.911919i	−0.850177	−	0.526497i
$3$	−1.47255	−	0.911919i	−0.850177	−	0.526497i
$4$		0			0
$5$	−0.412679	−	2.87025i	−0.184556	−	1.28361i	−0.845823	−	0.533463i	$-0.820890\pi$
$5$	−0.412679	−	2.87025i	−0.184556	−	1.28361i	0.661267	−	0.750150i	$-0.270019\pi$
$6$		0			0
$7$	−0.273979	+	2.86924i	−0.103554	+	1.08447i	0.783056	+	0.621952i	$0.213660\pi$
$7$	−0.273979	+	2.86924i	−0.103554	+	1.08447i	−0.886610	+	0.462518i	$0.846946\pi$
$8$		0			0
$9$	1.33681	+	2.68569i	0.445602	+	0.895231i
$10$		0			0
$11$	4.55535	+	1.82369i	1.37349	+	0.549863i	0.936837	−	0.349767i	$-0.113739\pi$
$11$	4.55535	+	1.82369i	1.37349	+	0.549863i	0.436654	+	0.899629i	$0.356163\pi$
$12$		0			0
$13$	1.25875	−	1.32014i	0.349116	−	0.366142i	−0.525639	−	0.850708i	$-0.676174\pi$
$13$	1.25875	−	1.32014i	0.349116	−	0.366142i	0.874755	+	0.484566i	$0.161022\pi$
$14$		0			0
$15$	−2.00974	+	4.60291i	−0.518913	+	1.18847i
$16$		0			0
$17$	−1.49442	−	0.517223i	−0.362450	−	0.125445i	0.139773	−	0.990184i	$-0.455363\pi$
$17$	−1.49442	−	0.517223i	−0.362450	−	0.125445i	−0.502222	+	0.864739i	$0.667484\pi$
$18$		0			0
$19$	3.17757	−	0.303421i	0.728984	−	0.0696096i	0.276037	−	0.961147i	$-0.410979\pi$
$19$	3.17757	−	0.303421i	0.728984	−	0.0696096i	0.452947	+	0.891537i	$0.350373\pi$
$20$		0			0
$21$	3.01996	−	3.97525i	0.659009	−	0.867470i
$22$		0			0
$23$	5.20992	+	0.248179i	1.08634	+	0.0517489i	0.583103	−	0.812398i	$-0.301838\pi$
$23$	5.20992	+	0.248179i	1.08634	+	0.0517489i	0.503240	+	0.864147i	$0.332141\pi$
$24$		0			0
$25$	−3.27055	+	0.960320i	−0.654110	+	0.192064i
$26$		0			0
$27$	0.480619	−	5.17388i	0.0924951	−	0.995713i
$28$		0			0
$29$	−0.761179	−	0.439467i	−0.141347	−	0.0816070i	0.427659	−	0.903940i	$-0.359339\pi$
$29$	−0.761179	−	0.439467i	−0.141347	−	0.0816070i	−0.569006	+	0.822333i	$0.692672\pi$
$30$		0			0
$31$	−2.73430	−	2.86765i	−0.491095	−	0.515045i	0.430820	−	0.902438i	$-0.358224\pi$
$31$	−2.73430	−	2.86765i	−0.491095	−	0.515045i	−0.921915	+	0.387392i	$0.873376\pi$
$32$		0			0
$33$	−5.04493	−	6.83959i	−0.878210	−	1.19062i
$34$		0			0
$35$	8.34848	−	0.397687i	1.41115	−	0.0672214i
$36$		0			0
$37$	−2.86589	−	4.96387i	−0.471150	−	0.816055i	0.528306	−	0.849054i	$-0.322828\pi$
$37$	−2.86589	−	4.96387i	−0.471150	−	0.816055i	−0.999455	+	0.0329989i	$0.989494\pi$
$38$		0			0
$39$	−3.05744	+	0.796095i	−0.489583	+	0.127477i
$40$		0			0
$41$	−6.58885	+	1.26990i	−1.02900	+	0.198324i	−0.675695	−	0.737182i	$-0.736156\pi$
$41$	−6.58885	+	1.26990i	−1.02900	+	0.198324i	−0.353310	+	0.935506i	$0.614944\pi$
$42$		0			0
$43$	6.45298	−	5.59154i	0.984070	−	0.852702i	−0.00502389	−	0.999987i	$-0.501599\pi$
$43$	6.45298	−	5.59154i	0.984070	−	0.852702i	0.989094	+	0.147286i	$0.0470537\pi$
$44$		0			0
$45$	7.15693	−	4.94530i	1.06689	−	0.737201i
$46$		0			0
$47$	−4.64743	−	9.01475i	−0.677897	−	1.31494i	−0.937082	−	0.349109i	$-0.886484\pi$
$47$	−4.64743	−	9.01475i	−0.677897	−	1.31494i	0.259185	−	0.965828i	$-0.416546\pi$
$48$		0			0
$49$	−1.28395	−	0.247462i	−0.183422	−	0.0353517i
$50$		0			0
$51$	1.72894	+	2.12442i	0.242100	+	0.297479i
$52$		0			0
$53$	4.94001	−	5.70108i	0.678563	−	0.783103i	−0.307128	−	0.951668i	$-0.599368\pi$
$53$	4.94001	−	5.70108i	0.678563	−	0.783103i	0.985691	+	0.168565i	$0.0539133\pi$
$54$		0			0
$55$	3.35454	−	13.8276i	0.452326	−	1.86451i
$56$		0			0
$57$	−4.95583	−	2.45088i	−0.656415	−	0.324627i
$58$		0			0
$59$	−0.523482	+	1.78282i	−0.0681516	+	0.232103i	−0.986525	−	0.163613i	$-0.947685\pi$
$59$	−0.523482	+	1.78282i	−0.0681516	+	0.232103i	0.918373	+	0.395716i	$0.129503\pi$
$60$		0			0
$61$	4.12990	+	10.3160i	0.528780	+	1.32083i	0.916862	+	0.399204i	$0.130713\pi$
$61$	4.12990	+	10.3160i	0.528780	+	1.32083i	−0.388082	+	0.921625i	$0.626862\pi$
$62$		0			0
$63$	−8.07214	+	3.09979i	−1.01699	+	0.390537i
$64$		0			0
$65$	−4.30860	−	3.06814i	−0.534416	−	0.380556i
$66$		0			0
$67$	3.34986	+	7.46850i	0.409251	+	0.912422i
$67$	3.34986	+	7.46850i	0.409251	+	0.912422i
$68$		0			0
$69$	−7.44555	−	5.11648i	−0.896339	−	0.615952i
$70$		0			0
$71$	4.94506	−	1.71150i	0.586871	−	0.203118i	−0.0174653	−	0.999847i	$-0.505560\pi$
$71$	4.94506	−	1.71150i	0.586871	−	0.203118i	0.604336	+	0.796730i	$0.293438\pi$
$72$		0			0
$73$	6.17224	−	2.47099i	0.722406	−	0.289208i	0.0188251	−	0.999823i	$-0.494007\pi$
$73$	6.17224	−	2.47099i	0.722406	−	0.289208i	0.703581	+	0.710615i	$0.251583\pi$
$74$		0			0
$75$	5.69178	+	1.56836i	0.657230	+	0.181098i
$76$		0			0
$77$	−6.48066	+	12.5707i	−0.738540	+	1.43257i
$78$		0			0
$79$	11.3480	+	2.75300i	1.27675	+	0.309736i	0.816134	−	0.577863i	$-0.196113\pi$
$79$	11.3480	+	2.75300i	1.27675	+	0.309736i	0.460617	+	0.887599i	$0.347628\pi$
$80$		0			0
$81$	−5.42589	+	7.18051i	−0.602877	+	0.797834i
$82$		0			0
$83$	−0.0980278	−	0.124653i	−0.0107600	−	0.0136824i	0.780643	−	0.624977i	$-0.214892\pi$
$83$	−0.0980278	−	0.124653i	−0.0107600	−	0.0136824i	−0.791403	+	0.611294i	$0.790649\pi$
$84$		0			0
$85$	−0.867843	+	4.50280i	−0.0941308	+	0.488397i
$86$		0			0
$87$	0.720116	+	1.34127i	0.0772045	+	0.143799i
$88$		0			0
$89$	−1.62244	−	2.52457i	−0.171978	−	0.267603i	0.744556	−	0.667560i	$-0.232661\pi$
$89$	−1.62244	−	2.52457i	−0.171978	−	0.267603i	−0.916534	+	0.399957i	$0.869025\pi$
$90$		0			0
$91$	3.44293	+	3.97335i	0.360917	+	0.416521i
$92$		0			0
$93$	1.41133	+	6.71622i	0.146348	+	0.696440i
$94$		0			0
$95$	−2.18221	−	8.99519i	−0.223890	−	0.922887i
$96$		0			0
$97$	6.23550	−	3.60007i	0.633119	−	0.365532i	−0.148840	−	0.988861i	$-0.547554\pi$
$97$	6.23550	−	3.60007i	0.633119	−	0.365532i	0.781959	+	0.623330i	$0.214221\pi$
$98$		0			0
$99$	1.19176	+	14.6722i	0.119777	+	1.47461i
$100$		0			0
$101$	−3.85442	−	5.41278i	−0.383530	−	0.538592i	0.577009	−	0.816738i	$-0.304220\pi$
$101$	−3.85442	−	5.41278i	−0.383530	−	0.538592i	−0.960539	+	0.278146i	$0.910280\pi$
$102$		0			0
$103$	4.53815	−	4.32712i	0.447157	−	0.426364i	−0.432746	−	0.901516i	$-0.642455\pi$
$103$	4.53815	−	4.32712i	0.447157	−	0.426364i	0.879904	+	0.475152i	$0.157607\pi$
$104$		0			0
$105$	−12.6562	−	7.02753i	−1.23512	−	0.685816i
$106$		0			0
$107$	15.9522	+	2.29358i	1.54215	+	0.221728i	0.860311	−	0.509770i	$-0.170270\pi$
$107$	15.9522	+	2.29358i	1.54215	+	0.221728i	0.681843	+	0.731498i	$0.261179\pi$
$108$		0			0
$109$	−0.0633795	−	0.215851i	−0.00607066	−	0.0206748i	0.956402	−	0.292054i	$-0.0943386\pi$
$109$	−0.0633795	−	0.215851i	−0.00607066	−	0.0206748i	−0.962473	+	0.271379i	$0.912520\pi$
$110$		0			0
$111$	−0.306479	+	9.92301i	−0.0290897	+	0.941851i
$112$		0			0
$113$	9.32118	+	7.33026i	0.876863	+	0.689572i	0.951503	−	0.307638i	$-0.0995386\pi$
$113$	9.32118	+	7.33026i	0.876863	+	0.689572i	−0.0746407	+	0.997210i	$0.523781\pi$
$114$		0			0
$115$	−1.43769	−	15.0562i	−0.134065	−	1.40400i
$116$		0			0
$117$	5.22821	+	1.61585i	0.483348	+	0.149385i
$118$		0			0
$119$	1.89347	−	4.14613i	0.173574	−	0.380075i
$120$		0			0
$121$	9.46434	+	9.02423i	0.860394	+	0.820384i
$122$		0			0
$123$	10.8604	+	4.13851i	0.979254	+	0.373157i
$124$		0			0
$125$	−1.91698	−	4.19760i	−0.171460	−	0.375445i
$126$		0			0
$127$	−11.0452	−	1.05469i	−0.980103	−	0.0935885i	−0.407311	−	0.913289i	$-0.633534\pi$
$127$	−11.0452	−	1.05469i	−0.980103	−	0.0935885i	−0.572792	+	0.819701i	$0.694140\pi$
$128$		0			0
$129$	−14.6014	+	2.34923i	−1.28558	+	0.206838i
$130$		0			0
$131$	−7.68105	+	11.9519i	−0.671096	+	1.04425i	0.324069	+	0.946033i	$0.394949\pi$
$131$	−7.68105	+	11.9519i	−0.671096	+	1.04425i	−0.995165	+	0.0982128i	$0.968687\pi$
$132$		0			0
$133$			9.20033i			0.797770i
$134$		0			0
$135$	−15.0486	+	0.755657i	−1.29518	+	0.0650366i
$136$		0			0
$137$	−11.7097	−	7.52537i	−1.00043	−	0.642936i	−0.0655291	−	0.997851i	$-0.520874\pi$
$137$	−11.7097	−	7.52537i	−1.00043	−	0.642936i	−0.934899	+	0.354915i	$0.884510\pi$
$138$		0			0
$139$	−14.8993	+	2.14219i	−1.26374	+	0.181698i	−0.741414	−	0.671048i	$-0.765844\pi$
$139$	−14.8993	+	2.14219i	−1.26374	+	0.181698i	−0.522325	+	0.852746i	$0.674935\pi$
$140$		0			0
$141$	−1.37715	+	17.5128i	−0.115977	+	1.47484i
$142$		0			0
$143$	8.14160	−	3.71814i	0.680835	−	0.310927i
$144$		0			0
$145$	−0.947256	+	2.36613i	−0.0786653	+	0.196496i
$146$		0			0
$147$	1.66502	+	1.53526i	0.137328	+	0.126626i
$148$		0			0
$149$	−15.7275	−	7.18251i	−1.28845	−	0.588414i	−0.350946	−	0.936396i	$-0.614140\pi$
$149$	−15.7275	−	7.18251i	−1.28845	−	0.588414i	−0.937502	+	0.347981i	$0.886867\pi$
$150$		0			0
$151$	−5.00929	+	14.4734i	−0.407650	+	1.17783i	0.535233	+	0.844704i	$0.320224\pi$
$151$	−5.00929	+	14.4734i	−0.407650	+	1.17783i	−0.942883	+	0.333123i	$0.891897\pi$
$152$		0			0
$153$	−0.608647	−	4.70497i	−0.0492062	−	0.380375i
$154$		0			0
$155$	−7.10248	+	9.03154i	−0.570485	+	0.725430i
$156$		0			0
$157$	0.742429	−	15.5855i	0.0592522	−	1.24386i	−0.752001	−	0.659162i	$-0.770911\pi$
$157$	0.742429	−	15.5855i	0.0592522	−	1.24386i	0.811253	−	0.584695i	$-0.198786\pi$
$158$		0			0
$159$	−12.4733	+	3.89023i	−0.989200	+	0.308516i
$160$		0			0
$161$	−2.13949	+	14.8805i	−0.168616	+	1.17275i
$162$		0			0
$163$	8.90024	−	15.4157i	0.697121	−	1.20745i	−0.272340	−	0.962201i	$-0.587797\pi$
$163$	8.90024	−	15.4157i	0.697121	−	1.20745i	0.969460	−	0.245248i	$-0.0788693\pi$
$164$		0			0
$165$	−17.5494	+	17.3028i	−1.36622	+	1.34702i
$166$		0			0
$167$	−8.27884	+	5.89534i	−0.640636	+	0.456195i	−0.853645	−	0.520855i	$-0.825613\pi$
$167$	−8.27884	+	5.89534i	−0.640636	+	0.456195i	0.213009	+	0.977050i	$0.431674\pi$
$168$		0			0
$169$	0.460248	+	9.66180i	0.0354037	+	0.743216i
$170$		0			0
$171$	5.06269	+	8.12836i	0.387154	+	0.621591i
$172$		0			0
$173$	−13.3638	+	3.24203i	−1.01603	+	0.246487i	−0.708997	−	0.705211i	$-0.750852\pi$
$173$	−13.3638	+	3.24203i	−1.01603	+	0.246487i	−0.307036	+	0.951698i	$0.599337\pi$
$174$		0			0
$175$	−1.85932	−	9.64709i	−0.140552	−	0.729251i
$176$		0			0
$177$	2.39664	−	2.14791i	0.180142	−	0.161447i
$178$		0			0
$179$	2.93658	−	1.88723i	0.219490	−	0.141058i	−0.426275	−	0.904593i	$-0.640175\pi$
$179$	2.93658	−	1.88723i	0.219490	−	0.141058i	0.645766	+	0.763535i	$0.276538\pi$
$180$		0			0
$181$	13.6951	−	7.06029i	1.01795	−	0.524787i	0.133312	−	0.991074i	$-0.457439\pi$
$181$	13.6951	−	7.06029i	1.01795	−	0.524787i	0.884634	+	0.466287i	$0.154409\pi$
$182$		0			0
$183$	3.32587	−	18.9570i	0.245855	−	1.40134i
$184$		0			0
$185$	−13.0648	+	10.2743i	−0.960546	+	0.755382i
$186$		0			0
$187$	−5.86435	−	5.08149i	−0.428844	−	0.371595i
$188$		0			0
$189$	14.7134	+	2.79654i	1.07024	+	0.203418i
$190$		0			0
$191$	19.9911	+	10.3061i	1.44650	+	0.745725i	0.989608	−	0.143795i	$-0.0459304\pi$
$191$	19.9911	+	10.3061i	1.44650	+	0.745725i	0.456897	+	0.889520i	$0.348961\pi$
$192$		0			0
$193$	−18.7628	−	5.50926i	−1.35058	−	0.396565i	−0.475145	−	0.879907i	$-0.657604\pi$
$193$	−18.7628	−	5.50926i	−1.35058	−	0.396565i	−0.875431	+	0.483342i	$0.839423\pi$
$194$		0			0
$195$	3.54673	+	8.44708i	0.253987	+	0.604908i
$196$		0			0
$197$	7.60523	+	21.9739i	0.541850	+	1.56557i	0.800332	+	0.599557i	$0.204657\pi$
$197$	7.60523	+	21.9739i	0.541850	+	1.56557i	−0.258482	+	0.966016i	$0.583222\pi$
$198$		0			0
$199$	11.7674	−	16.5251i	0.834172	−	1.17143i	−0.149016	−	0.988835i	$-0.547611\pi$
$199$	11.7674	−	16.5251i	0.834172	−	1.17143i	0.983188	−	0.182596i	$-0.0584499\pi$
$200$		0			0
$201$	1.87782	−	14.0525i	0.132451	−	0.991190i
$202$		0			0
$203$	1.46948	−	2.06360i	0.103137	−	0.144836i
$204$		0			0
$205$	6.36399	+	18.3876i	0.444481	+	1.28424i
$206$		0			0
$207$	6.29813	+	14.3240i	0.437750	+	0.995588i
$208$		0			0
$209$	15.0283	+	4.41271i	1.03953	+	0.305233i
$210$		0			0
$211$	7.21754	+	3.72090i	0.496876	+	0.256157i	0.688401	−	0.725330i	$-0.258313\pi$
$211$	7.21754	+	3.72090i	0.496876	+	0.256157i	−0.191525	+	0.981488i	$0.561343\pi$
$212$		0			0
$213$	−8.84260	−	1.98922i	−0.605885	−	0.136299i
$214$		0			0
$215$	−18.7121	−	16.2141i	−1.27616	−	1.10579i
$216$		0			0
$217$	8.97711	−	7.05968i	0.609406	−	0.479242i
$218$		0			0
$219$	−11.3423	−	1.98992i	−0.766440	−	0.134467i
$220$		0			0
$221$	−2.56391	+	1.32179i	−0.172467	+	0.0889132i
$222$		0			0
$223$	−17.6132	+	11.3193i	−1.17946	+	0.757995i	−0.975288	−	0.220939i	$-0.929088\pi$
$223$	−17.6132	+	11.3193i	−1.17946	+	0.757995i	−0.204176	+	0.978934i	$0.565452\pi$
$224$		0			0
$225$	−6.95122	−	7.49993i	−0.463415	−	0.499995i
$226$		0			0
$227$	3.70345	+	19.2153i	0.245806	+	1.27536i	0.869593	+	0.493769i	$0.164381\pi$
$227$	3.70345	+	19.2153i	0.245806	+	1.27536i	−0.623787	+	0.781595i	$0.714407\pi$
$228$		0			0
$229$	25.8908	−	6.28104i	1.71091	−	0.415063i	0.743594	−	0.668631i	$-0.233120\pi$
$229$	25.8908	−	6.28104i	1.71091	−	0.415063i	0.967317	+	0.253569i	$0.0816044\pi$
$230$		0			0
$231$	21.0066	−	12.6012i	1.38213	−	0.829098i
$232$		0			0
$233$	−0.0573869	−	1.20470i	−0.00375954	−	0.0789225i	0.996208	−	0.0870060i	$-0.0277299\pi$
$233$	−0.0573869	−	1.20470i	−0.00375954	−	0.0789225i	−0.999967	+	0.00808354i	$0.997427\pi$
$234$		0			0
$235$	−23.9567	+	17.0595i	−1.56276	+	1.11284i
$236$		0			0
$237$	−14.2000	−	14.4024i	−0.922389	−	0.935536i
$238$		0			0
$239$	−5.73202	+	9.92816i	−0.370774	+	0.642199i	−0.989685	−	0.143262i	$-0.954241\pi$
$239$	−5.73202	+	9.92816i	−0.370774	+	0.642199i	0.618911	+	0.785461i	$0.287574\pi$
$240$		0			0
$241$	4.19075	−	29.1473i	0.269950	−	1.87754i	−0.178802	−	0.983885i	$-0.557222\pi$
$241$	4.19075	−	29.1473i	0.269950	−	1.87754i	0.448752	−	0.893656i	$-0.351869\pi$
$242$		0			0
$243$	14.5379	−	5.62568i	0.932609	−	0.360888i
$244$		0			0
$245$	−0.180415	+	3.78738i	−0.0115263	+	0.241967i
$246$		0			0
$247$	3.59922	−	4.57678i	0.229013	−	0.291214i
$248$		0			0
$249$	0.0306779	+	0.272951i	0.00194413	+	0.0172975i
$250$		0			0
$251$	−8.82263	+	25.4913i	−0.556880	+	1.60900i	0.217350	+	0.976094i	$0.430259\pi$
$251$	−8.82263	+	25.4913i	−0.556880	+	1.60900i	−0.774230	+	0.632904i	$0.781863\pi$
$252$		0			0
$253$	23.2804	+	10.6318i	1.46363	+	0.668416i
$254$		0			0
$255$	5.38413	−	5.83919i	0.337167	−	0.365664i
$256$		0			0
$257$	−0.387194	+	0.967163i	−0.0241525	+	0.0603299i	−0.939954	−	0.341301i	$-0.889132\pi$
$257$	−0.387194	+	0.967163i	−0.0241525	+	0.0603299i	0.915802	+	0.401631i	$0.131557\pi$
$258$		0			0
$259$	15.0277	−	6.86293i	0.933777	−	0.426442i
$260$		0			0
$261$	0.162723	−	2.63178i	0.0100723	−	0.162903i
$262$		0			0
$263$	16.2766	−	2.34022i	1.00366	−	0.144304i	0.379161	−	0.925331i	$-0.376213\pi$
$263$	16.2766	−	2.34022i	1.00366	−	0.144304i	0.624498	+	0.781026i	$0.285303\pi$
$264$		0			0
$265$	−18.4021	−	11.8263i	−1.13043	−	0.726486i
$266$		0			0
$267$	0.0869244	+	5.19708i	0.00531968	+	0.318056i
$268$		0			0
$269$		−	0.773869i		−	0.0471836i	−0.999722	−	0.0235918i	$-0.992490\pi$
$269$		−	0.773869i		−	0.0471836i	0.999722	−	0.0235918i	$-0.00751021\pi$
$270$		0			0
$271$	−14.5273	+	22.6050i	−0.882472	+	1.37315i	0.0448918	+	0.998992i	$0.485706\pi$
$271$	−14.5273	+	22.6050i	−0.882472	+	1.37315i	−0.927364	+	0.374161i	$0.877931\pi$
$272$		0			0
$273$	−1.44651	−	8.99064i	−0.0875468	−	0.544138i
$274$		0			0
$275$	−16.6498	−	1.58987i	−1.00402	−	0.0958725i
$276$		0			0
$277$	−2.01847	−	4.41983i	−0.121278	−	0.265562i	0.839250	−	0.543746i	$-0.182995\pi$
$277$	−2.01847	−	4.41983i	−0.121278	−	0.265562i	−0.960528	+	0.278184i	$0.910267\pi$
$278$		0			0
$279$	4.04640	−	11.1770i	0.242252	−	0.669149i
$280$		0			0
$281$	−1.48895	−	1.41971i	−0.0888232	−	0.0846927i	0.644367	−	0.764716i	$-0.277121\pi$
$281$	−1.48895	−	1.41971i	−0.0888232	−	0.0846927i	−0.733190	+	0.680024i	$0.761969\pi$
$282$		0			0
$283$	−6.63031	+	14.5184i	−0.394131	+	0.863027i	0.603701	+	0.797211i	$0.293692\pi$
$283$	−6.63031	+	14.5184i	−0.394131	+	0.863027i	−0.997832	+	0.0658158i	$0.979035\pi$
$284$		0			0
$285$	−4.98947	+	15.2359i	−0.295551	+	0.902495i
$286$		0			0
$287$	−1.83843	−	19.2529i	−0.108519	−	1.13646i
$288$		0			0
$289$	−11.3971	−	8.96281i	−0.670420	−	0.527224i
$290$		0			0
$291$	−12.4651	−	0.384991i	−0.730715	−	0.0225686i
$292$		0			0
$293$	−3.34108	−	11.3787i	−0.195188	−	0.664749i	−0.997679	−	0.0680855i	$-0.978311\pi$
$293$	−3.34108	−	11.3787i	−0.195188	−	0.664749i	0.802492	−	0.596663i	$-0.203507\pi$
$294$		0			0
$295$	5.33315	+	0.766792i	0.310508	+	0.0446443i
$296$		0			0
$297$	11.6249	−	22.6923i	0.674547	−	1.31674i
$298$		0			0
$299$	6.88564	−	6.56544i	0.398207	−	0.379689i
$300$		0			0
$301$	14.2755	+	20.0471i	0.822824	+	1.15549i
$302$		0			0
$303$	0.739814	+	11.4855i	0.0425012	+	0.659826i
$304$		0			0
$305$	27.9051	−	16.1110i	1.59784	−	0.922516i
$306$		0			0
$307$	−3.62873	−	14.9578i	−0.207102	−	0.853688i	−0.976604	−	0.215044i	$-0.931011\pi$
$307$	−3.62873	−	14.9578i	−0.207102	−	0.853688i	0.769502	−	0.638644i	$-0.220505\pi$
$308$		0			0
$309$	−10.6286	+	2.23347i	−0.604642	+	0.127058i
$310$		0			0
$311$	9.56540	+	11.0391i	0.542404	+	0.625968i	0.959096	−	0.283080i	$-0.0913561\pi$
$311$	9.56540	+	11.0391i	0.542404	+	0.625968i	−0.416692	+	0.909048i	$0.636811\pi$
$312$		0			0
$313$	10.2057	+	15.8803i	0.576858	+	0.897609i	0.999964	−	0.00847122i	$-0.00269650\pi$
$313$	10.2057	+	15.8803i	0.576858	+	0.897609i	−0.423106	+	0.906080i	$0.639060\pi$
$314$		0			0
$315$	12.2284	+	21.8898i	0.688991	+	1.23335i
$316$		0			0
$317$	2.53662	−	13.1612i	0.142471	−	0.739208i	−0.838477	−	0.544937i	$-0.816554\pi$
$317$	2.53662	−	13.1612i	0.142471	−	0.739208i	0.980948	−	0.194271i	$-0.0622342\pi$
$318$		0			0
$319$	−2.66599	−	3.39008i	−0.149267	−	0.189808i
$320$		0			0
$321$	−21.3988	−	17.9245i	−1.19436	−	1.00045i
$322$		0			0
$323$	−4.90555	−	1.19007i	−0.272952	−	0.0662175i
$324$		0			0
$325$	−2.84906	+	5.52640i	−0.158037	+	0.306550i
$326$		0			0
$327$	−0.103509	+	0.375648i	−0.00572406	+	0.0207734i
$328$		0			0
$329$	27.1388	−	10.8647i	1.49621	−	0.598991i
$330$		0			0
$331$	−2.04960	+	0.709374i	−0.112656	+	0.0389907i	−0.382815	−	0.923825i	$-0.625045\pi$
$331$	−2.04960	+	0.709374i	−0.112656	+	0.0389907i	0.270158	+	0.962816i	$0.412924\pi$
$332$		0			0
$333$	9.50029	−	14.3326i	0.520613	−	0.785424i
$334$		0			0
$335$	20.0540	−	12.6970i	1.09567	−	0.693713i
$336$		0			0
$337$	−18.1955	−	12.9570i	−0.991172	−	0.705810i	−0.0352341	−	0.999379i	$-0.511218\pi$
$337$	−18.1955	−	12.9570i	−0.991172	−	0.705810i	−0.955938	+	0.293569i	$0.905157\pi$
$338$		0			0
$339$	−7.04130	−	19.2943i	−0.382431	−	1.04792i
$340$		0			0
$341$	−7.22600	−	18.0497i	−0.391310	−	0.977445i
$342$		0			0
$343$	−4.62244	+	15.7426i	−0.249588	+	0.850019i
$344$		0			0
$345$	−11.6129	+	23.4820i	−0.625220	+	1.26423i
$346$		0			0
$347$	−2.68001	+	11.0472i	−0.143870	+	0.593042i	0.853534	+	0.521037i	$0.174455\pi$
$347$	−2.68001	+	11.0472i	−0.143870	+	0.593042i	−0.997404	+	0.0720047i	$0.977060\pi$
$348$		0			0
$349$	−8.47039	+	9.77535i	−0.453409	+	0.523262i	−0.935723	−	0.352736i	$-0.885251\pi$
$349$	−8.47039	+	9.77535i	−0.453409	+	0.523262i	0.482313	+	0.875999i	$0.339797\pi$
$350$		0			0
$351$	−6.22528	−	7.14713i	−0.332281	−	0.381485i
$352$		0			0
$353$	6.92313	+	1.33432i	0.368481	+	0.0710189i	0.370130	−	0.928980i	$-0.379313\pi$
$353$	6.92313	+	1.33432i	0.368481	+	0.0710189i	−0.00164965	+	0.999999i	$0.500525\pi$
$354$		0			0
$355$	−6.95316	−	13.4872i	−0.369035	−	0.715829i
$356$		0			0
$357$	−6.56917	+	4.37869i	−0.347677	+	0.231745i
$358$		0			0
$359$	−8.77136	+	7.60043i	−0.462935	+	0.401135i	−0.854857	−	0.518863i	$-0.826356\pi$
$359$	−8.77136	+	7.60043i	−0.462935	+	0.401135i	0.391923	+	0.919998i	$0.371810\pi$
$360$		0			0
$361$	−8.65176	+	1.66749i	−0.455356	+	0.0877627i
$362$		0			0
$363$	−5.70735	−	21.9193i	−0.299558	−	1.15047i
$364$		0			0
$365$	−9.63951	−	16.6961i	−0.504555	−	0.873915i
$366$		0			0
$367$	−5.33054	+	0.253925i	−0.278252	+	0.0132548i	−0.186244	−	0.982504i	$-0.559631\pi$
$367$	−5.33054	+	0.253925i	−0.278252	+	0.0132548i	−0.0920077	+	0.995758i	$0.529328\pi$
$368$		0			0
$369$	−12.2186	−	15.9980i	−0.636073	−	0.832823i
$370$		0			0
$371$	15.0043	+	15.7360i	0.778984	+	0.816975i
$372$		0			0
$373$	−21.4669	−	12.3939i	−1.11151	−	0.641733i	−0.172293	−	0.985046i	$-0.555117\pi$
$373$	−21.4669	−	12.3939i	−1.11151	−	0.641733i	−0.939221	+	0.343313i	$0.888451\pi$
$374$		0			0
$375$	−1.00502	+	7.92931i	−0.0518992	+	0.409468i
$376$		0			0
$377$	−1.53830	+	0.451685i	−0.0792263	+	0.0232629i
$378$		0			0
$379$	0.240410	+	0.0114521i	0.0123490	+	0.000588257i	0.0537555	−	0.998554i	$-0.482881\pi$
$379$	0.240410	+	0.0114521i	0.0123490	+	0.000588257i	−0.0414065	+	0.999142i	$0.513184\pi$
$380$		0			0
$381$	15.3028	+	11.6254i	0.783987	+	0.595588i
$382$		0			0
$383$	−13.7852	+	1.31633i	−0.704392	+	0.0672613i	−0.441104	−	0.897456i	$-0.645413\pi$
$383$	−13.7852	+	1.31633i	−0.704392	+	0.0672613i	−0.263288	+	0.964717i	$0.584807\pi$
$384$		0			0
$385$	38.7556	+	13.4134i	1.97517	+	0.683612i
$386$		0			0
$387$	23.6435	+	9.85591i	1.20187	+	0.501004i
$388$		0			0
$389$	−0.683887	+	0.717241i	−0.0346745	+	0.0363655i	−0.740843	−	0.671678i	$-0.765574\pi$
$389$	−0.683887	+	0.717241i	−0.0346745	+	0.0363655i	0.706168	+	0.708044i	$0.250422\pi$
$390$		0			0
$391$	−7.65743	−	3.06557i	−0.387253	−	0.155033i
$392$		0			0
$393$	22.2099	−	10.5953i	1.12034	−	0.534464i
$394$		0			0
$395$	3.21869	−	33.7077i	0.161950	−	1.69602i
$396$		0			0
$397$	−0.0894249	−	0.621964i	−0.00448810	−	0.0312155i	0.987454	−	0.157905i	$-0.0504739\pi$
$397$	−0.0894249	−	0.621964i	−0.00448810	−	0.0312155i	−0.991942	+	0.126689i	$0.959565\pi$
$398$		0			0
$399$	8.38996	−	13.5479i	0.420023	−	0.678246i
$400$		0			0
$401$	−17.7271			−0.885249			−0.442624	−	0.896707i	$-0.645952\pi$
$401$	−17.7271			−0.885249			−0.442624	+	0.896707i	$0.645952\pi$
$402$		0			0
$403$	−7.22752			−0.360029
$404$		0			0
$405$	22.8490	+	12.6104i	1.13538	+	0.626616i
$406$		0			0
$407$	−4.00260	−	27.8387i	−0.198401	−	1.37991i
$408$		0			0
$409$	−1.27676	+	13.3708i	−0.0631315	+	0.661143i	0.907416	+	0.420234i	$0.138052\pi$
$409$	−1.27676	+	13.3708i	−0.0631315	+	0.661143i	−0.970548	+	0.240910i	$0.922554\pi$
$410$		0			0
$411$	10.3806	+	21.7598i	0.512037	+	1.07333i
$412$		0			0
$413$	−4.97190	−	1.99045i	−0.244651	−	0.0979436i
$414$		0			0
$415$	−0.317329	+	0.332806i	−0.0155771	+	0.0163368i
$416$		0			0
$417$	23.8934	+	10.4324i	1.17007	+	0.510879i
$418$		0			0
$419$	6.59427	+	2.28230i	0.322151	+	0.111498i	0.483357	−	0.875423i	$-0.339417\pi$
$419$	6.59427	+	2.28230i	0.322151	+	0.111498i	−0.161206	+	0.986921i	$0.551538\pi$
$420$		0			0
$421$	25.9279	−	2.47581i	1.26365	−	0.120664i	0.558368	−	0.829593i	$-0.311428\pi$
$421$	25.9279	−	2.47581i	1.26365	−	0.120664i	0.705279	+	0.708930i	$0.250822\pi$
$422$		0			0
$423$	17.9981	−	24.5326i	0.875100	−	1.19281i
$424$		0			0
$425$	5.38427	+	0.256484i	0.261175	+	0.0124413i
$426$		0			0
$427$	−30.7306	+	9.02330i	−1.48716	+	0.436668i
$428$		0			0
$429$	−15.3796	−	1.94933i	−0.742532	−	0.0941144i
$430$		0			0
$431$	−24.2306	−	13.9896i	−1.16715	−	0.673853i	−0.214141	−	0.976803i	$-0.568695\pi$
$431$	−24.2306	−	13.9896i	−1.16715	−	0.673853i	−0.953007	+	0.302950i	$0.902029\pi$
$432$		0			0
$433$	16.5700	+	17.3781i	0.796301	+	0.835137i	0.989275	−	0.146067i	$-0.0466617\pi$
$433$	16.5700	+	17.3781i	0.796301	+	0.835137i	−0.192974	+	0.981204i	$0.561813\pi$
$434$		0			0
$435$	3.55260	−	2.62043i	0.170334	−	0.125640i
$436$		0			0
$437$	16.6302	−	0.792193i	0.795530	−	0.0378957i
$438$		0			0
$439$	6.66863	+	11.5504i	0.318276	+	0.551270i	0.980128	−	0.198364i	$-0.0635627\pi$
$439$	6.66863	+	11.5504i	0.318276	+	0.551270i	−0.661852	+	0.749634i	$0.730229\pi$
$440$		0			0
$441$	−1.05179	−	3.77911i	−0.0500853	−	0.179958i
$442$		0			0
$443$	−28.3444	+	5.46294i	−1.34668	+	0.259552i	−0.811089	−	0.584923i	$-0.801125\pi$
$443$	−28.3444	+	5.46294i	−1.34668	+	0.259552i	−0.535595	+	0.844475i	$0.679912\pi$
$444$		0			0
$445$	−6.57658	+	5.69864i	−0.311760	+	0.270141i
$446$		0			0
$447$	16.6097	+	24.9188i	0.785611	+	1.17862i
$448$		0			0
$449$	−1.16700	−	2.26366i	−0.0550741	−	0.106829i	0.859692	−	0.510813i	$-0.170655\pi$
$449$	−1.16700	−	2.26366i	−0.0550741	−	0.106829i	−0.914766	+	0.403984i	$0.867625\pi$
$450$		0			0
$451$	−32.3304	−	6.23118i	−1.52238	−	0.293415i
$452$		0			0
$453$	20.5750	−	16.7447i	0.966697	−	0.786736i
$454$		0			0
$455$	9.98368	−	11.5218i	0.468042	−	0.540150i
$456$		0			0
$457$	−8.37612	+	34.5268i	−0.391818	+	1.61510i	0.344723	+	0.938705i	$0.387973\pi$
$457$	−8.37612	+	34.5268i	−0.391818	+	1.61510i	−0.736541	+	0.676393i	$0.763542\pi$
$458$		0			0
$459$	−3.39429	+	7.48335i	−0.158432	+	0.349293i
$460$		0			0
$461$	−1.46906	+	5.00315i	−0.0684208	+	0.233020i	−0.986603	−	0.163138i	$-0.947838\pi$
$461$	−1.46906	+	5.00315i	−0.0684208	+	0.233020i	0.918182	+	0.396158i	$0.129657\pi$
$462$		0			0
$463$	13.5553	+	33.8596i	0.629970	+	1.57359i	0.807754	+	0.589519i	$0.200683\pi$
$463$	13.5553	+	33.8596i	0.629970	+	1.57359i	−0.177785	+	0.984069i	$0.556893\pi$
$464$		0			0
$465$	18.6948	−	6.82250i	0.866950	−	0.316386i
$466$		0			0
$467$	30.8962	+	22.0011i	1.42971	+	1.01809i	0.992953	+	0.118509i	$0.0378115\pi$
$467$	30.8962	+	22.0011i	1.42971	+	1.01809i	0.436754	+	0.899581i	$0.356128\pi$
$468$		0			0
$469$	−22.3467	+	7.56534i	−1.03187	+	0.349335i
$470$		0			0
$471$	−15.3060	+	22.2734i	−0.705262	+	1.02630i
$472$		0			0
$473$	39.5928	−	13.7032i	1.82048	−	0.630074i
$474$		0			0
$475$	−10.1010	+	4.04384i	−0.463466	+	0.185544i
$476$		0			0
$477$	21.9152	+	5.64611i	1.00343	+	0.258518i
$478$		0			0
$479$	15.8205	−	30.6876i	0.722859	−	1.40215i	−0.184941	−	0.982750i	$-0.559210\pi$
$479$	15.8205	−	30.6876i	0.722859	−	1.40215i	0.907801	−	0.419402i	$-0.137760\pi$
$480$		0			0
$481$	−10.1605	−	2.46490i	−0.463278	−	0.112390i
$482$		0			0
$483$	16.7203	−	19.9612i	0.760801	−	0.908267i
$484$		0			0
$485$	−12.9063	−	16.4118i	−0.586047	−	0.745219i
$486$		0			0
$487$	7.59904	−	39.4276i	0.344346	−	1.78663i	−0.235465	−	0.971883i	$-0.575661\pi$
$487$	7.59904	−	39.4276i	0.344346	−	1.78663i	0.579810	−	0.814752i	$-0.303127\pi$
$488$		0			0
$489$	−27.1639	+	14.5841i	−1.22839	+	0.659514i
$490$		0			0
$491$	11.4876	+	17.8750i	0.518427	+	0.806688i	0.997469	−	0.0711041i	$-0.0226522\pi$
$491$	11.4876	+	17.8750i	0.518427	+	0.806688i	−0.479042	+	0.877792i	$0.659016\pi$
$492$		0			0
$493$	0.910217	+	1.05045i	0.0409941	+	0.0473097i
$494$		0			0
$495$	41.6210	−	9.47557i	1.87073	−	0.425895i
$496$		0			0
$497$	3.55586	+	14.6575i	0.159502	+	0.657477i
$498$		0			0
$499$	27.2460	−	15.7305i	1.21970	−	0.704194i	0.254846	−	0.966982i	$-0.417975\pi$
$499$	27.2460	−	15.7305i	1.21970	−	0.704194i	0.964854	+	0.262788i	$0.0846419\pi$
$500$		0			0
$501$	17.5671	−	1.13155i	0.784839	−	0.0505537i
$502$		0			0
$503$	−24.3950	−	34.2579i	−1.08772	−	1.52749i	−0.827109	−	0.562042i	$-0.810016\pi$
$503$	−24.3950	−	34.2579i	−1.08772	−	1.52749i	−0.260609	−	0.965444i	$-0.583923\pi$
$504$		0			0
$505$	−13.9454	+	13.2969i	−0.620561	+	0.591704i
$506$		0			0
$507$	8.13304	−	14.6472i	0.361201	−	0.650505i
$508$		0			0
$509$	22.8411	+	3.28406i	1.01242	+	0.145563i	0.628504	−	0.777806i	$-0.283668\pi$
$509$	22.8411	+	3.28406i	1.01242	+	0.145563i	0.383912	+	0.923370i	$0.374577\pi$
$510$		0			0
$511$	5.39880	+	18.3866i	0.238829	+	0.813376i
$512$		0			0
$513$	−0.0426641	−	16.5862i	−0.00188367	−	0.732298i
$514$		0			0
$515$	−14.2927	−	11.2399i	−0.629811	−	0.495289i
$516$		0			0
$517$	−4.73058	−	49.5409i	−0.208051	−	2.17880i
$518$		0			0
$519$	22.6354	+	7.41268i	0.993583	+	0.325381i
$520$		0			0
$521$	−10.1543	+	22.2347i	−0.444866	+	0.974121i	0.545813	+	0.837907i	$0.316221\pi$
$521$	−10.1543	+	22.2347i	−0.444866	+	0.974121i	−0.990679	+	0.136214i	$0.956507\pi$
$522$		0			0
$523$	−19.2841	−	18.3873i	−0.843234	−	0.804022i	0.139272	−	0.990254i	$-0.455524\pi$
$523$	−19.2841	−	18.3873i	−0.843234	−	0.804022i	−0.982506	+	0.186232i	$0.940372\pi$
$524$		0			0
$525$	−6.05941	+	15.9014i	−0.264455	+	0.693993i
$526$		0			0
$527$	2.60297	+	5.69971i	0.113387	+	0.248283i
$528$		0			0
$529$	4.18581	+	0.399697i	0.181992	+	0.0173781i
$530$		0			0
$531$	−5.48789	+	0.977370i	−0.238154	+	0.0424142i
$532$		0			0
$533$	−6.61729	+	10.2967i	−0.286627	+	0.446000i
$534$		0			0
$535$		−	46.7332i		−	2.02045i
$536$		0			0
$537$	−6.04526	+	0.101111i	−0.260872	+	0.00436325i
$538$		0			0
$539$	−5.39757	−	3.46881i	−0.232490	−	0.149412i
$540$		0			0
$541$	−14.4964	+	2.08427i	−0.623249	+	0.0896097i	−0.446702	−	0.894683i	$-0.647402\pi$
$541$	−14.4964	+	2.08427i	−0.623249	+	0.0896097i	−0.176547	+	0.984292i	$0.556493\pi$
$542$		0			0
$543$	−26.6051	−	2.09215i	−1.14173	−	0.0897827i
$544$		0			0
$545$	−0.593390	+	0.270992i	−0.0254180	+	0.0116080i
$546$		0			0
$547$	−13.2130	+	33.0045i	−0.564948	+	1.41117i	0.320863	+	0.947126i	$0.396027\pi$
$547$	−13.2130	+	33.0045i	−0.564948	+	1.41117i	−0.885811	+	0.464046i	$0.846397\pi$
$548$		0			0
$549$	−22.1847	+	24.8822i	−0.946821	+	1.06194i
$550$		0			0
$551$	−2.55204	−	1.16548i	−0.108721	−	0.0496511i
$552$		0			0
$553$	−11.0081	+	31.8058i	−0.468112	+	1.35252i
$554$		0			0
$555$	28.6080	−	3.21535i	1.21434	−	0.136484i
$556$		0			0
$557$	−6.36471	+	8.09338i	−0.269681	+	0.342928i	−0.901965	−	0.431809i	$-0.857875\pi$
$557$	−6.36471	+	8.09338i	−0.269681	+	0.342928i	0.632284	+	0.774737i	$0.282118\pi$
$558$		0			0
$559$	0.741082	−	15.5572i	0.0313444	−	0.658001i
$560$		0			0
$561$	4.00164	+	12.8306i	0.168949	+	0.541706i
$562$		0			0
$563$	1.76420	−	12.2703i	0.0743520	−	0.517130i	−0.918277	−	0.395938i	$-0.870419\pi$
$563$	1.76420	−	12.2703i	0.0743520	−	0.517130i	0.992629	−	0.121191i	$-0.0386715\pi$
$564$		0			0
$565$	17.1930	−	29.7791i	0.723314	−	1.25282i
$566$		0			0
$567$	−19.1160	−	17.5355i	−0.802796	−	0.736421i
$568$		0			0
$569$	−14.4597	+	10.2967i	−0.606180	+	0.431659i	−0.841499	−	0.540259i	$-0.818326\pi$
$569$	−14.4597	+	10.2967i	−0.606180	+	0.431659i	0.235318	+	0.971918i	$0.424387\pi$
$570$		0			0
$571$	−0.852971	−	17.9061i	−0.0356957	−	0.749345i	−0.943783	−	0.330565i	$-0.892761\pi$
$571$	−0.852971	−	17.9061i	−0.0356957	−	0.749345i	0.908088	−	0.418780i	$-0.137542\pi$
$572$		0			0
$573$	−20.0395	−	33.4065i	−0.837164	−	1.39558i
$574$		0			0
$575$	−17.2776	+	4.19151i	−0.720527	+	0.174798i
$576$		0			0
$577$	4.51436	+	23.4227i	0.187935	+	0.975100i	0.946305	+	0.323276i	$0.104784\pi$
$577$	4.51436	+	23.4227i	0.187935	+	0.975100i	−0.758370	+	0.651825i	$0.774004\pi$
$578$		0			0
$579$	22.6052	+	25.2228i	0.939439	+	1.04822i
$580$		0			0
$581$	0.384515	−	0.247113i	0.0159524	−	0.0102520i
$582$		0			0
$583$	32.9005	−	16.9614i	1.36260	−	0.702469i
$584$		0			0
$585$	2.48031	−	15.6731i	0.102548	−	0.648002i
$586$		0			0
$587$	−21.0887	+	16.5843i	−0.870423	+	0.684508i	−0.949976	−	0.312323i	$-0.898893\pi$
$587$	−21.0887	+	16.5843i	−0.870423	+	0.684508i	0.0795534	+	0.996831i	$0.474651\pi$
$588$		0			0
$589$	−9.55853	−	8.28252i	−0.393853	−	0.341275i
$590$		0			0
$591$	8.83931	−	39.2930i	0.363600	−	1.61630i
$592$		0			0
$593$	10.4172	+	5.37044i	0.427783	+	0.220538i	0.658653	−	0.752447i	$-0.271127\pi$
$593$	10.4172	+	5.37044i	0.427783	+	0.220538i	−0.230869	+	0.972985i	$0.574157\pi$
$594$		0			0
$595$	−12.6818	−	3.72372i	−0.519904	−	0.152658i
$596$		0			0
$597$	−32.3977	+	13.6030i	−1.32595	+	0.556735i
$598$		0			0
$599$	−7.04181	−	20.3460i	−0.287721	−	0.831315i	−0.992539	−	0.121927i	$-0.961093\pi$
$599$	−7.04181	−	20.3460i	−0.287721	−	0.831315i	0.704818	−	0.709388i	$-0.251028\pi$
$600$		0			0
$601$	−14.3803	+	20.1943i	−0.586584	+	0.823743i	−0.996070	−	0.0885743i	$-0.971769\pi$
$601$	−14.3803	+	20.1943i	−0.586584	+	0.823743i	0.409485	+	0.912317i	$0.365708\pi$
$602$		0			0
$603$	−15.5800	+	18.9806i	−0.634465	+	0.772951i
$604$		0			0
$605$	21.9960	−	30.8891i	0.894266	−	1.25582i
$606$		0			0
$607$	−11.2024	−	32.3671i	−0.454690	−	1.31374i	−0.906718	−	0.421738i	$-0.861420\pi$
$607$	−11.2024	−	32.3671i	−0.454690	−	1.31374i	0.452027	−	0.892004i	$-0.350701\pi$
$608$		0			0
$609$	−4.04572	+	1.69870i	−0.163941	+	0.0688349i
$610$		0			0
$611$	−17.7507	−	5.21209i	−0.718118	−	0.210858i
$612$		0			0
$613$	−23.0170	−	11.8661i	−0.929647	−	0.479266i	−0.0742502	−	0.997240i	$-0.523656\pi$
$613$	−23.0170	−	11.8661i	−0.929647	−	0.479266i	−0.855397	+	0.517973i	$0.826687\pi$
$614$		0			0
$615$	7.39666	−	32.8800i	0.298262	−	1.32585i
$616$		0			0
$617$	11.7828	+	10.2099i	0.474358	+	0.411034i	0.858955	−	0.512051i	$-0.171114\pi$
$617$	11.7828	+	10.2099i	0.474358	+	0.411034i	−0.384597	+	0.923085i	$0.625659\pi$
$618$		0			0
$619$	13.0161	−	10.2360i	0.523160	−	0.411418i	−0.321347	−	0.946961i	$-0.604136\pi$
$619$	13.0161	−	10.2360i	0.523160	−	0.411418i	0.844508	+	0.535544i	$0.179893\pi$
$620$		0			0
$621$	3.78803	−	26.8362i	0.152009	−	1.07690i
$622$		0			0
$623$	7.68809	−	3.96348i	0.308017	−	0.158794i
$624$		0			0
$625$	−25.5946	+	16.4487i	−1.02379	+	0.657947i
$626$		0			0
$627$	−18.1059	−	20.2025i	−0.723080	−	0.806811i
$628$		0			0
$629$	1.71541	+	8.90040i	0.0683980	+	0.354882i
$630$		0			0
$631$	−12.6793	+	3.07597i	−0.504756	+	0.122452i	−0.480048	−	0.877242i	$-0.659381\pi$
$631$	−12.6793	+	3.07597i	−0.504756	+	0.122452i	−0.0247079	+	0.999695i	$0.507866\pi$
$632$		0			0
$633$	−7.23503	−	12.0610i	−0.287567	−	0.479383i
$634$		0			0
$635$	1.53091	+	32.1377i	0.0607522	+	1.27535i
$636$		0			0
$637$	−1.94287	+	1.38351i	−0.0769791	+	0.0548166i
$638$		0			0
$639$	11.2072	+	10.9930i	0.443348	+	0.434875i
$640$		0			0
$641$	18.7729	−	32.5157i	0.741487	−	1.28429i	−0.210332	−	0.977630i	$-0.567454\pi$
$641$	18.7729	−	32.5157i	0.741487	−	1.28429i	0.951818	−	0.306663i	$-0.0992123\pi$
$642$		0			0
$643$	−0.929880	+	6.46746i	−0.0366709	+	0.255052i	−0.999907	−	0.0136029i	$-0.995670\pi$
$643$	−0.929880	+	6.46746i	−0.0366709	+	0.255052i	0.963237	+	0.268655i	$0.0865790\pi$
$644$		0			0
$645$	12.7685	+	40.9400i	0.502761	+	1.61201i
$646$		0			0
$647$	−1.31497	+	27.6046i	−0.0516969	+	1.08525i	0.812778	+	0.582574i	$0.197954\pi$
$647$	−1.31497	+	27.6046i	−0.0516969	+	1.08525i	−0.864475	+	0.502677i	$0.832349\pi$
$648$		0			0
$649$	−5.63595	+	7.16669i	−0.221230	+	0.281317i
$650$		0			0
$651$	−19.6571	+	2.20933i	−0.770422	+	0.0865905i
$652$		0			0
$653$	−0.0497588	+	0.143769i	−0.00194721	+	0.00562611i	−0.945970	−	0.324253i	$-0.894887\pi$
$653$	−0.0497588	+	0.143769i	−0.00194721	+	0.00562611i	0.944023	+	0.329880i	$0.107008\pi$
$654$		0			0
$655$	37.4748	+	17.1142i	1.46426	+	0.668707i
$656$		0			0
$657$	14.8874	+	13.2735i	0.580814	+	0.517849i
$658$		0			0
$659$	−14.5115	+	36.2480i	−0.565289	+	1.41202i	0.320195	+	0.947352i	$0.396252\pi$
$659$	−14.5115	+	36.2480i	−0.565289	+	1.41202i	−0.885483	+	0.464671i	$0.846173\pi$
$660$		0			0
$661$	−28.9799	+	13.2347i	−1.12719	+	0.514769i	−0.889665	−	0.456613i	$-0.849062\pi$
$661$	−28.9799	+	13.2347i	−1.12719	+	0.514769i	−0.237521	+	0.971382i	$0.576335\pi$
$662$		0			0
$663$	4.98086	+	0.391681i	0.193440	+	0.0152116i
$664$		0			0
$665$	26.4072	−	3.79678i	1.02403	−	0.147233i
$666$		0			0
$667$	−3.85662	−	2.47850i	−0.149329	−	0.0959678i
$668$		0			0
$669$	36.2585	−	0.606446i	1.40184	−	0.0234466i
$670$		0			0
$671$			54.5247i			2.10490i
$672$		0			0
$673$	11.2718	−	17.5392i	0.434495	−	0.676087i	−0.553099	−	0.833115i	$-0.686555\pi$
$673$	11.2718	−	17.5392i	0.434495	−	0.676087i	0.987594	+	0.157028i	$0.0501914\pi$
$674$		0			0
$675$	3.39669	+	17.3830i	0.130739	+	0.669071i
$676$		0			0
$677$	−7.29459	−	0.696549i	−0.280354	−	0.0267706i	−0.0460681	−	0.998938i	$-0.514669\pi$
$677$	−7.29459	−	0.696549i	−0.280354	−	0.0267706i	−0.234286	+	0.972168i	$0.575275\pi$
$678$		0			0
$679$	8.62105	+	18.8775i	0.330846	+	0.724451i
$680$		0			0
$681$	12.0693	−	31.6727i	0.462496	−	1.21370i
$682$		0			0
$683$	−19.8958	−	18.9706i	−0.761292	−	0.725891i	0.206278	−	0.978493i	$-0.433865\pi$
$683$	−19.8958	−	18.9706i	−0.761292	−	0.725891i	−0.967570	+	0.252603i	$0.918713\pi$
$684$		0			0
$685$	−16.7673	+	36.7153i	−0.640646	+	1.40282i
$686$		0			0
$687$	−43.8533	−	14.3612i	−1.67311	−	0.547912i
$688$		0			0
$689$	−1.30798	−	13.6978i	−0.0498301	−	0.521844i
$690$		0			0
$691$	5.01612	+	3.94472i	0.190822	+	0.150064i	0.708999	−	0.705209i	$-0.249147\pi$
$691$	5.01612	+	3.94472i	0.190822	+	0.150064i	−0.518177	+	0.855273i	$0.673389\pi$
$692$		0			0
$693$	−42.4245	−	0.600423i	−1.61157	−	0.0228082i
$694$		0			0
$695$	12.2972	+	41.8805i	0.466461	+	1.58862i
$696$		0			0
$697$	10.5033	+	1.51015i	0.397841	+	0.0572009i
$698$		0			0
$699$	−1.01408	+	1.82631i	−0.0383561	+	0.0690775i
$700$		0			0
$701$	−10.2133	+	9.73839i	−0.385752	+	0.367814i	−0.857998	−	0.513653i	$-0.828292\pi$
$701$	−10.2133	+	9.73839i	−0.385752	+	0.367814i	0.472246	+	0.881467i	$0.343443\pi$
$702$		0			0
$703$	−10.6127	−	14.9035i	−0.400266	−	0.562095i
$704$		0			0
$705$	50.8342	−	3.27438i	1.91453	−	0.123320i
$706$		0			0
$707$	16.5866	−	9.57627i	0.623803	−	0.360153i
$708$		0			0
$709$	−7.75370	−	31.9612i	−0.291196	−	1.20033i	−0.909942	−	0.414736i	$-0.863874\pi$
$709$	−7.75370	−	31.9612i	−0.291196	−	1.20033i	0.618745	−	0.785592i	$-0.287641\pi$
$710$		0			0
$711$	7.77639	+	34.1575i	0.291638	+	1.28101i
$712$		0			0
$713$	−13.5338	−	15.6188i	−0.506844	−	0.584930i
$714$		0			0
$715$	−14.0319	−	21.8340i	−0.524762	−	0.816546i
$716$		0			0
$717$	17.4944	−	9.39257i	0.653339	−	0.350772i
$718$		0			0
$719$	−2.79908	+	14.5230i	−0.104388	+	0.541617i	0.891653	+	0.452720i	$0.149546\pi$
$719$	−2.79908	+	14.5230i	−0.104388	+	0.541617i	−0.996041	+	0.0888971i	$0.971666\pi$
$720$		0			0
$721$	11.1722	+	14.2066i	0.416073	+	0.529080i
$722$		0			0
$723$	−32.7510	+	39.0992i	−1.21802	+	1.45412i
$724$		0			0
$725$	2.91150	+	0.706323i	0.108130	+	0.0262322i
$726$		0			0
$727$	−6.31770	+	12.2546i	−0.234310	+	0.454499i	−0.976449	−	0.215747i	$-0.930781\pi$
$727$	−6.31770	+	12.2546i	−0.234310	+	0.454499i	0.742139	+	0.670246i	$0.233812\pi$
$728$		0			0
$729$	−26.5380	−	4.97332i	−0.982889	−	0.184197i
$730$		0			0
$731$	−12.5355	+	5.01847i	−0.463643	+	0.185615i
$732$		0			0
$733$	−4.69450	+	1.62478i	−0.173395	+	0.0600127i	−0.412386	−	0.911009i	$-0.635305\pi$
$733$	−4.69450	+	1.62478i	−0.173395	+	0.0600127i	0.238991	+	0.971022i	$0.423183\pi$
$734$		0			0
$735$	3.71946	−	5.41259i	0.137194	−	0.199646i
$736$		0			0
$737$	1.63960	+	40.1307i	0.0603955	+	1.47824i
$738$		0			0
$739$	7.24093	+	5.15624i	0.266362	+	0.189675i	0.705432	−	0.708777i	$-0.250753\pi$
$739$	7.24093	+	5.15624i	0.266362	+	0.189675i	−0.439071	+	0.898453i	$0.644692\pi$
$740$		0			0
$741$	−9.47368	+	3.45734i	−0.348024	+	0.127009i
$742$		0			0
$743$	−14.1770	−	35.4125i	−0.520104	−	1.29916i	−0.923313	−	0.384049i	$-0.874529\pi$
$743$	−14.1770	−	35.4125i	−0.520104	−	1.29916i	0.403209	−	0.915108i	$-0.367895\pi$
$744$		0			0
$745$	−14.1252	+	48.1059i	−0.517506	+	1.76246i
$746$		0			0
$747$	0.203734	−	0.429909i	0.00745424	−	0.0157295i
$748$		0			0
$749$	−10.9514	+	45.1421i	−0.400154	+	1.64946i
$750$		0			0
$751$	8.03102	−	9.26829i	0.293056	−	0.338205i	−0.590060	−	0.807359i	$-0.700896\pi$
$751$	8.03102	−	9.26829i	0.293056	−	0.338205i	0.883116	+	0.469155i	$0.155441\pi$
$752$		0			0
$753$	36.2378	−	29.4917i	1.32058	−	1.07474i
$754$		0			0
$755$	43.6094	+	8.40503i	1.58711	+	0.305890i
$756$		0			0
$757$	3.74952	+	7.27305i	0.136279	+	0.264343i	0.947093	−	0.320960i	$-0.104006\pi$
$757$	3.74952	+	7.27305i	0.136279	+	0.264343i	−0.810814	+	0.585304i	$0.800975\pi$
$758$		0			0
$759$	−24.5862	−	36.8857i	−0.892424	−	1.33887i
$760$		0			0
$761$	19.6756	−	17.0490i	0.713240	−	0.618026i	−0.220748	−	0.975331i	$-0.570850\pi$
$761$	19.6756	−	17.0490i	0.713240	−	0.618026i	0.933988	+	0.357305i	$0.116304\pi$
$762$		0			0
$763$	0.636692	−	0.122712i	0.0230498	−	0.00444248i
$764$		0			0
$765$	−13.2533	+	3.68861i	−0.479173	+	0.133362i
$766$		0			0
$767$	1.69464	+	2.93520i	0.0611898	+	0.105984i
$768$		0			0
$769$	−14.9664	+	0.712936i	−0.539701	+	0.0257091i	−0.315663	−	0.948871i	$-0.602227\pi$
$769$	−14.9664	+	0.712936i	−0.539701	+	0.0257091i	−0.224038	+	0.974580i	$0.571924\pi$
$770$		0			0
$771$	1.45214	−	1.07111i	0.0522974	−	0.0385749i
$772$		0			0
$773$	14.5862	+	15.2976i	0.524630	+	0.550216i	0.931723	−	0.363171i	$-0.118306\pi$
$773$	14.5862	+	15.2976i	0.524630	+	0.550216i	−0.407092	+	0.913387i	$0.633457\pi$
$774$		0			0
$775$	11.6965	+	6.75299i	0.420152	+	0.242575i
$776$		0			0
$777$	−28.3875	−	3.59806i	−1.01840	−	0.129080i
$778$		0			0
$779$	−20.5512	+	6.03438i	−0.736323	+	0.216204i
$780$		0			0
$781$	25.6477	+	1.22175i	0.917749	+	0.0437178i
$782$		0			0
$783$	−2.63959	+	3.72703i	−0.0943311	+	0.133193i
$784$		0			0
$785$	−45.0406	+	4.30086i	−1.60757	+	0.153504i
$786$		0			0
$787$	28.6471	+	9.91487i	1.02116	+	0.353427i	0.785800	−	0.618481i	$-0.212252\pi$
$787$	28.6471	+	9.91487i	1.02116	+	0.353427i	0.235361	+	0.971908i	$0.424373\pi$
$788$		0			0
$789$	−26.1022	−	11.3969i	−0.929264	−	0.405739i
$790$		0			0
$791$	−23.5860	+	24.7363i	−0.838623	+	0.879523i
$792$		0			0
$793$	18.8171	+	7.53324i	0.668216	+	0.267513i
$794$		0			0
$795$	16.3134	+	34.1961i	0.578577	+	1.21281i
$796$		0			0
$797$	−0.489388	+	5.12511i	−0.0173350	+	0.181541i	−0.999992	−	0.00388978i	$-0.998762\pi$
$797$	−0.489388	+	5.12511i	−0.0173350	+	0.181541i	0.982657	+	0.185430i	$0.0593679\pi$
$798$		0			0
$799$	2.28256	+	15.8756i	0.0807512	+	0.561637i
$800$		0			0
$801$	4.61132	−	7.73223i	0.162933	−	0.273205i
$802$		0			0
$803$	32.6231			1.15124
$804$		0			0
$805$	43.5936			1.53647
$806$		0			0
$807$	−0.705706	+	1.13956i	−0.0248420	+	0.0401145i
$808$		0			0
$809$	6.77273	+	47.1054i	0.238116	+	1.65614i	0.661322	+	0.750102i	$0.269996\pi$
$809$	6.77273	+	47.1054i	0.238116	+	1.65614i	−0.423205	+	0.906034i	$0.639095\pi$
$810$		0			0
$811$	−5.29996	+	55.5037i	−0.186107	+	1.94900i	0.110207	+	0.993909i	$0.464849\pi$
$811$	−5.29996	+	55.5037i	−0.186107	+	1.94900i	−0.296314	+	0.955091i	$0.595757\pi$
$812$		0			0
$813$	42.0061	−	20.0392i	1.47322	−	0.702805i
$814$		0			0
$815$	−47.9197	−	19.1842i	−1.67856	−	0.671992i
$816$		0			0
$817$	18.8082	−	19.7255i	0.658016	−	0.690107i
$818$		0			0
$819$	−6.06867	+	14.5583i	−0.212057	+	0.508707i
$820$		0			0
$821$	24.9574	+	8.63785i	0.871021	+	0.301463i	0.725775	−	0.687932i	$-0.241481\pi$
$821$	24.9574	+	8.63785i	0.871021	+	0.301463i	0.145246	+	0.989396i	$0.453603\pi$
$822$		0			0
$823$	−51.3598	+	4.90427i	−1.79029	+	0.170952i	−0.936732	−	0.350046i	$-0.886166\pi$
$823$	−51.3598	+	4.90427i	−1.79029	+	0.170952i	−0.853558	+	0.520998i	$0.825560\pi$
$824$		0			0
$825$	23.0679	+	17.5245i	0.803121	+	0.610123i
$826$		0			0
$827$	−10.2403	−	0.487808i	−0.356092	−	0.0169627i	−0.131226	−	0.991353i	$-0.541891\pi$
$827$	−10.2403	−	0.487808i	−0.356092	−	0.0169627i	−0.224866	+	0.974390i	$0.572194\pi$
$828$		0			0
$829$	21.5744	−	6.33483i	0.749311	−	0.220018i	0.115288	−	0.993332i	$-0.463221\pi$
$829$	21.5744	−	6.33483i	0.749311	−	0.220018i	0.634023	+	0.773314i	$0.281403\pi$
$830$		0			0
$831$	−1.05823	+	8.34910i	−0.0367096	+	0.289627i
$832$		0			0
$833$	1.79077	+	1.03390i	0.0620465	+	0.0358225i
$834$		0			0
$835$	20.3376	+	21.3294i	0.703811	+	0.738136i
$836$		0			0
$837$	−16.1510	+	12.7687i	−0.558261	+	0.441350i
$838$		0			0
$839$	−53.4161	+	2.54452i	−1.84413	+	0.0878467i	−0.940362	−	0.340177i	$-0.889513\pi$
$839$	−53.4161	+	2.54452i	−1.84413	+	0.0878467i	−0.903768	+	0.428023i	$0.859210\pi$
$840$		0			0
$841$	−14.1137	−	24.4457i	−0.486681	−	0.842956i
$842$		0			0
$843$	0.897891	+	3.44839i	0.0309250	+	0.118769i
$844$		0			0
$845$	27.5418	−	5.30825i	0.947468	−	0.182609i
$846$		0			0
$847$	−28.4857	+	24.6830i	−0.978779	+	0.848117i
$848$		0			0
$849$	23.0030	−	15.3327i	0.789462	−	0.526217i
$850$		0			0
$851$	−13.6991	−	26.5726i	−0.469600	−	0.910898i
$852$		0			0
$853$	−3.05824	−	0.589427i	−0.104712	−	0.0201816i	0.136626	−	0.990623i	$-0.456374\pi$
$853$	−3.05824	−	0.589427i	−0.104712	−	0.0201816i	−0.241338	+	0.970441i	$0.577586\pi$
$854$		0			0
$855$	21.2411	−	17.8856i	0.726431	−	0.611674i
$856$		0			0
$857$	−24.6999	+	28.5052i	−0.843732	+	0.973718i	−0.999902	−	0.0140119i	$-0.995540\pi$
$857$	−24.6999	+	28.5052i	−0.843732	+	0.973718i	0.156170	+	0.987730i	$0.450085\pi$
$858$		0			0
$859$	−2.42294	+	9.98747i	−0.0826695	+	0.340768i	−0.998093	−	0.0617230i	$-0.980340\pi$
$859$	−2.42294	+	9.98747i	−0.0826695	+	0.340768i	0.915424	+	0.402491i	$0.131856\pi$
$860$		0			0
$861$	−14.8499	+	30.0273i	−0.506083	+	1.02333i
$862$		0			0
$863$	−0.902901	+	3.07500i	−0.0307351	+	0.104674i	−0.973432	−	0.228976i	$-0.926462\pi$
$863$	−0.902901	+	3.07500i	−0.0307351	+	0.104674i	0.942697	+	0.333650i	$0.108280\pi$
$864$		0			0
$865$	14.8204	+	37.0196i	0.503909	+	1.25870i
$866$		0			0
$867$	8.60950	+	23.5915i	0.292394	+	0.801208i
$868$		0			0
$869$	46.6736	+	33.2361i	1.58329	+	1.12746i
$870$		0			0
$871$	14.0761	+	4.97870i	0.476952	+	0.168697i
$872$		0			0
$873$	18.0043	+	11.9340i	0.609355	+	0.403906i
$874$		0			0
$875$	12.5691	−	4.35022i	0.424914	−	0.147064i
$876$		0			0
$877$	9.62173	−	3.85196i	0.324903	−	0.130071i	−0.203477	−	0.979080i	$-0.565224\pi$
$877$	9.62173	−	3.85196i	0.324903	−	0.130071i	0.528379	+	0.849008i	$0.322800\pi$
$878$		0			0
$879$	−5.45652	+	19.8025i	−0.184044	+	0.667920i
$880$		0			0
$881$	−22.3744	+	43.4003i	−0.753813	+	1.46219i	0.128589	+	0.991698i	$0.458955\pi$
$881$	−22.3744	+	43.4003i	−0.753813	+	1.46219i	−0.882402	+	0.470496i	$0.844075\pi$
$882$		0			0
$883$	−34.8833	−	8.46259i	−1.17392	−	0.284789i	−0.399058	−	0.916926i	$-0.630663\pi$
$883$	−34.8833	−	8.46259i	−1.17392	−	0.284789i	−0.774857	+	0.632137i	$0.782178\pi$
$884$		0			0
$885$	−7.15408	−	5.99254i	−0.240482	−	0.201437i
$886$		0			0
$887$	−28.5878	−	36.3524i	−0.959885	−	1.22059i	−0.975339	−	0.220713i	$-0.929162\pi$
$887$	−28.5878	−	36.3524i	−0.959885	−	1.22059i	0.0154536	−	0.999881i	$-0.495081\pi$
$888$		0			0
$889$	6.05230	−	31.4023i	0.202988	−	1.05320i
$890$		0			0
$891$	−37.8119	+	22.8146i	−1.26675	+	0.764318i
$892$		0			0
$893$	−17.5028	−	27.2349i	−0.585709	−	0.911380i
$894$		0			0
$895$	−6.62867	−	7.64990i	−0.221572	−	0.255708i
$896$		0			0
$897$	−16.1266	+	3.38880i	−0.538452	+	0.113149i
$898$		0			0
$899$	0.821054	+	3.38443i	0.0273837	+	0.112877i
$900$		0			0
$901$	−10.3312	+	5.96471i	−0.344181	+	0.198713i
$902$		0			0
$903$	−2.74002	−	42.5384i	−0.0911821	−	1.41559i
$904$		0			0
$905$	−25.9164	−	36.3946i	−0.861492	−	1.20980i
$906$		0			0
$907$	29.9758	−	28.5819i	0.995331	−	0.949046i	−0.00337035	−	0.999994i	$-0.501073\pi$
$907$	29.9758	−	28.5819i	0.995331	−	0.949046i	0.998701	+	0.0509482i	$0.0162243\pi$
$908$		0			0
$909$	9.38445	−	17.5876i	0.311262	−	0.583345i
$910$		0			0
$911$	26.4171	+	3.79821i	0.875239	+	0.125840i	0.565270	−	0.824906i	$-0.308772\pi$
$911$	26.4171	+	3.79821i	0.875239	+	0.125840i	0.309969	+	0.950747i	$0.399681\pi$
$912$		0			0
$913$	−0.219224	−	0.746609i	−0.00725526	−	0.0247091i
$914$		0			0
$915$	−55.7837	−	1.72292i	−1.84415	−	0.0569578i
$916$		0			0
$917$	−32.1885	−	25.3133i	−1.06296	−	0.835920i
$918$		0			0
$919$	−3.20676	−	33.5827i	−0.105781	−	1.10779i	−0.880032	−	0.474914i	$-0.842479\pi$
$919$	−3.20676	−	33.5827i	−0.105781	−	1.10779i	0.774251	−	0.632879i	$-0.218127\pi$
$920$		0			0
$921$	−8.29684	+	25.3352i	−0.273390	+	0.834825i
$922$		0			0
$923$	3.96519	−	8.68255i	0.130516	−	0.285790i
$924$		0			0
$925$	14.1399	+	13.4824i	0.464919	+	0.443299i
$926$		0			0
$927$	17.6879	+	6.40355i	0.580948	+	0.210320i
$928$		0			0
$929$	−15.3850	−	33.6885i	−0.504766	−	1.10528i	−0.974891	−	0.222684i	$-0.928518\pi$
$929$	−15.3850	−	33.6885i	−0.504766	−	1.10528i	0.470124	−	0.882600i	$-0.344209\pi$
$930$		0			0
$931$	−4.15493	−	0.396748i	−0.136172	−	0.0130029i
$932$		0			0
$933$	−4.01880	−	24.9785i	−0.131570	−	0.817758i
$934$		0			0
$935$	−12.1650	+	18.9292i	−0.397839	+	0.619050i
$936$		0			0
$937$			21.7270i			0.709791i	0.934906	+	0.354895i	$0.115484\pi$
$937$			21.7270i			0.709791i	−0.934906	+	0.354895i	$0.884516\pi$
$938$		0			0
$939$	−0.546782	−	32.6913i	−0.0178436	−	1.06684i
$940$		0			0
$941$	26.6308	+	17.1146i	0.868140	+	0.557919i	0.897183	−	0.441659i	$-0.145610\pi$
$941$	26.6308	+	17.1146i	0.868140	+	0.557919i	−0.0290436	+	0.999578i	$0.509246\pi$
$942$		0			0
$943$	−34.6425	+	4.98084i	−1.12812	+	0.162199i
$944$		0			0
$945$	1.95485	−	43.3852i	0.0635913	−	1.41132i
$946$		0			0
$947$	−12.7776	+	5.83533i	−0.415216	+	0.189623i	−0.612059	−	0.790812i	$-0.709658\pi$
$947$	−12.7776	+	5.83533i	−0.415216	+	0.189623i	0.196843	+	0.980435i	$0.436931\pi$
$948$		0			0
$949$	4.50727	−	11.2586i	0.146312	−	0.365470i
$950$		0			0
$951$	−15.7373	+	17.0674i	−0.510316	+	0.553447i
$952$		0			0
$953$	−7.32518	−	3.34530i	−0.237286	−	0.108365i	0.293223	−	0.956044i	$-0.405272\pi$
$953$	−7.32518	−	3.34530i	−0.237286	−	0.108365i	−0.530509	+	0.847679i	$0.677999\pi$
$954$		0			0
$955$	21.3312	−	61.6325i	0.690262	−	1.99438i
$956$		0			0
$957$	0.834323	+	7.42323i	0.0269698	+	0.239959i
$958$		0			0
$959$	24.8003	−	31.5361i	0.800843	−	1.01835i
$960$		0			0
$961$	0.728012	−	15.2829i	0.0234843	−	0.492995i
$962$		0			0
$963$	15.1651	+	45.9087i	0.488690	+	1.47939i
$964$		0			0
$965$	−8.06991	+	56.1275i	−0.259780	+	1.80681i
$966$		0			0
$967$	−20.2335	+	35.0455i	−0.650666	+	1.12699i	0.332295	+	0.943175i	$0.392177\pi$
$967$	−20.2335	+	35.0455i	−0.650666	+	1.12699i	−0.982962	+	0.183812i	$0.941156\pi$
$968$		0			0
$969$	6.13842	+	6.22591i	0.197194	+	0.200005i
$970$		0			0
$971$	7.01760	−	4.99721i	0.225205	−	0.160368i	−0.461885	−	0.886940i	$-0.652827\pi$
$971$	7.01760	−	4.99721i	0.225205	−	0.160368i	0.687091	+	0.726572i	$0.258887\pi$
$972$		0			0
$973$	−2.06437	−	43.3364i	−0.0661806	−	1.38930i
$974$		0			0
$975$	9.23501	−	5.53979i	0.295757	−	0.177415i
$976$		0			0
$977$	46.8344	−	11.3619i	1.49837	−	0.363500i	0.599019	−	0.800735i	$-0.295558\pi$
$977$	46.8344	−	11.3619i	1.49837	−	0.363500i	0.899347	+	0.437235i	$0.144042\pi$
$978$		0			0
$979$	−2.78677	−	14.4591i	−0.0890654	−	0.462115i
$980$		0			0
$981$	0.494983	−	0.458769i	0.0158036	−	0.0146474i
$982$		0			0
$983$	32.9135	−	21.1522i	1.04978	−	0.674652i	0.102392	−	0.994744i	$-0.467350\pi$
$983$	32.9135	−	21.1522i	1.04978	−	0.674652i	0.947386	+	0.320092i	$0.103714\pi$
$984$		0			0
$985$	59.9319	−	30.8970i	1.90959	−	0.984462i
$986$		0			0
$987$	−49.8709	−	8.74950i	−1.58741	−	0.278500i
$988$		0			0
$989$	35.0072	−	27.5300i	1.11316	−	0.875402i
$990$		0			0
$991$	−39.9792	−	34.6421i	−1.26998	−	1.10044i	−0.990093	−	0.140410i	$-0.955158\pi$
$991$	−39.9792	−	34.6421i	−1.26998	−	1.10044i	−0.279886	−	0.960033i	$-0.590297\pi$
$992$		0			0
$993$	3.66503	+	0.824482i	0.116306	+	0.0261642i
$994$		0			0
$995$	−52.2872	−	26.9559i	−1.65762	−	0.854560i
$996$		0			0
$997$	−8.66787	−	2.54512i	−0.274514	−	0.0806047i	0.141578	−	0.989927i	$-0.454782\pi$
$997$	−8.66787	−	2.54512i	−0.274514	−	0.0806047i	−0.416092	+	0.909322i	$0.636601\pi$
$998$		0			0
$999$	−27.0599	+	12.4420i	−0.856136	+	0.393649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.353.4	yes	440
3.2	odd	2	inner	804.2.ba.b.353.18	yes	440
67.41	odd	66	inner	804.2.ba.b.41.18	yes	440
201.41	even	66	inner	804.2.ba.b.41.4	✓	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.4	✓	440	201.41	even	66	inner
804.2.ba.b.41.18	yes	440	67.41	odd	66	inner
804.2.ba.b.353.4	yes	440	1.1	even	1	trivial
804.2.ba.b.353.18	yes	440	3.2	odd	2	inner

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.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.47255 - 0.911919i) q^{3} +(-0.412679 - 2.87025i) q^{5} +(-0.273979 + 2.86924i) q^{7} +(1.33681 + 2.68569i) q^{9} +O(q^{10})\)	\(q+(-1.47255 - 0.911919i) q^{3} +(-0.412679 - 2.87025i) q^{5} +(-0.273979 + 2.86924i) q^{7} +(1.33681 + 2.68569i) q^{9} +(4.55535 + 1.82369i) q^{11} +(1.25875 - 1.32014i) q^{13} +(-2.00974 + 4.60291i) q^{15} +(-1.49442 - 0.517223i) q^{17} +(3.17757 - 0.303421i) q^{19} +(3.01996 - 3.97525i) q^{21} +(5.20992 + 0.248179i) q^{23} +(-3.27055 + 0.960320i) q^{25} +(0.480619 - 5.17388i) q^{27} +(-0.761179 - 0.439467i) q^{29} +(-2.73430 - 2.86765i) q^{31} +(-5.04493 - 6.83959i) q^{33} +(8.34848 - 0.397687i) q^{35} +(-2.86589 - 4.96387i) q^{37} +(-3.05744 + 0.796095i) q^{39} +(-6.58885 + 1.26990i) q^{41} +(6.45298 - 5.59154i) q^{43} +(7.15693 - 4.94530i) q^{45} +(-4.64743 - 9.01475i) q^{47} +(-1.28395 - 0.247462i) q^{49} +(1.72894 + 2.12442i) q^{51} +(4.94001 - 5.70108i) q^{53} +(3.35454 - 13.8276i) q^{55} +(-4.95583 - 2.45088i) q^{57} +(-0.523482 + 1.78282i) q^{59} +(4.12990 + 10.3160i) q^{61} +(-8.07214 + 3.09979i) q^{63} +(-4.30860 - 3.06814i) q^{65} +(3.34986 + 7.46850i) q^{67} +(-7.44555 - 5.11648i) q^{69} +(4.94506 - 1.71150i) q^{71} +(6.17224 - 2.47099i) q^{73} +(5.69178 + 1.56836i) q^{75} +(-6.48066 + 12.5707i) q^{77} +(11.3480 + 2.75300i) q^{79} +(-5.42589 + 7.18051i) q^{81} +(-0.0980278 - 0.124653i) q^{83} +(-0.867843 + 4.50280i) q^{85} +(0.720116 + 1.34127i) q^{87} +(-1.62244 - 2.52457i) q^{89} +(3.44293 + 3.97335i) q^{91} +(1.41133 + 6.71622i) q^{93} +(-2.18221 - 8.99519i) q^{95} +(6.23550 - 3.60007i) q^{97} +(1.19176 + 14.6722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 440 * q - 12 * q^7 + 4 * q^9	\( 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) \) 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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