LMFDB - Embedded newform 804.2.ba.b.353.18

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			353.18
Character	$\chi$	$=$	804.353
Dual form			804.2.ba.b.41.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.44123 + 0.960654i) q^{3} +(0.412679 + 2.87025i) q^{5} +(-0.273979 + 2.86924i) q^{7} +(1.15429 + 2.76905i) q^{9} +O(q^{10})$	\(q+(1.44123 + 0.960654i) q^{3} +(0.412679 + 2.87025i) q^{5} +(-0.273979 + 2.86924i) q^{7} +(1.15429 + 2.76905i) q^{9} +(-4.55535 - 1.82369i) q^{11} +(1.25875 - 1.32014i) q^{13} +(-2.16255 + 4.53313i) q^{15} +(1.49442 + 0.517223i) q^{17} +(3.17757 - 0.303421i) q^{19} +(-3.15121 + 3.87203i) q^{21} +(-5.20992 - 0.248179i) q^{23} +(-3.27055 + 0.960320i) q^{25} +(-0.996499 + 5.09970i) q^{27} +(0.761179 + 0.439467i) q^{29} +(-2.73430 - 2.86765i) q^{31} +(-4.81338 - 7.00447i) q^{33} +(-8.34848 + 0.397687i) q^{35} +(-2.86589 - 4.96387i) q^{37} +(3.08236 - 0.693403i) q^{39} +(6.58885 - 1.26990i) q^{41} +(6.45298 - 5.59154i) q^{43} +(-7.47150 + 4.45582i) q^{45} +(4.64743 + 9.01475i) q^{47} +(-1.28395 - 0.247462i) q^{49} +(1.65693 + 2.18106i) q^{51} +(-4.94001 + 5.70108i) q^{53} +(3.35454 - 13.8276i) q^{55} +(4.87109 + 2.61524i) q^{57} +(0.523482 - 1.78282i) q^{59} +(4.12990 + 10.3160i) q^{61} +(-8.26130 + 2.55327i) q^{63} +(4.30860 + 3.06814i) q^{65} +(3.34986 + 7.46850i) q^{67} +(-7.27028 - 5.36261i) q^{69} +(-4.94506 + 1.71150i) q^{71} +(6.17224 - 2.47099i) q^{73} +(-5.63615 - 1.75782i) q^{75} +(6.48066 - 12.5707i) q^{77} +(11.3480 + 2.75300i) q^{79} +(-6.33524 + 6.39256i) q^{81} +(0.0980278 + 0.124653i) q^{83} +(-0.867843 + 4.50280i) q^{85} +(0.674859 + 1.36460i) q^{87} +(1.62244 + 2.52457i) q^{89} +(3.44293 + 3.97335i) q^{91} +(-1.18594 - 6.75966i) q^{93} +(2.18221 + 8.99519i) q^{95} +(6.23550 - 3.60007i) q^{97} +(-0.208315 - 14.7191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.44123	+	0.960654i	0.832095	+	0.554634i
$3$	1.44123	+	0.960654i	0.832095	+	0.554634i
$4$		0			0
$5$	0.412679	+	2.87025i	0.184556	+	1.28361i	0.845823	+	0.533463i	$0.179110\pi$
$5$	0.412679	+	2.87025i	0.184556	+	1.28361i	−0.661267	+	0.750150i	$0.729981\pi$
$6$		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
$9$	1.15429	+	2.76905i	0.384763	+	0.923015i
$10$		0			0
$11$	−4.55535	−	1.82369i	−1.37349	−	0.549863i	−0.436654	−	0.899629i	$-0.643837\pi$
$11$	−4.55535	−	1.82369i	−1.37349	−	0.549863i	−0.936837	+	0.349767i	$0.886261\pi$
$12$		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
$15$	−2.16255	+	4.53313i	−0.558367	+	1.17045i
$16$		0			0
$17$	1.49442	+	0.517223i	0.362450	+	0.125445i	0.502222	−	0.864739i	$-0.332516\pi$
$17$	1.49442	+	0.517223i	0.362450	+	0.125445i	−0.139773	+	0.990184i	$0.544637\pi$
$18$		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
$21$	−3.15121	+	3.87203i	−0.687650	+	0.844946i
$22$		0			0
$23$	−5.20992	−	0.248179i	−1.08634	−	0.0517489i	−0.503240	−	0.864147i	$-0.667859\pi$
$23$	−5.20992	−	0.248179i	−1.08634	−	0.0517489i	−0.583103	+	0.812398i	$0.698162\pi$
$24$		0			0
$25$	−3.27055	+	0.960320i	−0.654110	+	0.192064i
$26$		0			0
$27$	−0.996499	+	5.09970i	−0.191776	+	0.981439i
$28$		0			0
$29$	0.761179	+	0.439467i	0.141347	+	0.0816070i	0.569006	−	0.822333i	$-0.307328\pi$
$29$	0.761179	+	0.439467i	0.141347	+	0.0816070i	−0.427659	+	0.903940i	$0.640661\pi$
$30$		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
$33$	−4.81338	−	7.00447i	−0.837902	−	1.21932i
$34$		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
$39$	3.08236	−	0.693403i	0.493572	−	0.111033i
$40$		0			0
$41$	6.58885	−	1.26990i	1.02900	−	0.198324i	0.353310	−	0.935506i	$-0.385056\pi$
$41$	6.58885	−	1.26990i	1.02900	−	0.198324i	0.675695	+	0.737182i	$0.263844\pi$
$42$		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
$45$	−7.47150	+	4.45582i	−1.11378	+	0.664235i
$46$		0			0
$47$	4.64743	+	9.01475i	0.677897	+	1.31494i	0.937082	+	0.349109i	$0.113516\pi$
$47$	4.64743	+	9.01475i	0.677897	+	1.31494i	−0.259185	+	0.965828i	$0.583454\pi$
$48$		0			0
$49$	−1.28395	−	0.247462i	−0.183422	−	0.0353517i
$50$		0			0
$51$	1.65693	+	2.18106i	0.232016	+	0.305409i
$52$		0			0
$53$	−4.94001	+	5.70108i	−0.678563	+	0.783103i	−0.985691	−	0.168565i	$-0.946087\pi$
$53$	−4.94001	+	5.70108i	−0.678563	+	0.783103i	0.307128	+	0.951668i	$0.400632\pi$
$54$		0			0
$55$	3.35454	−	13.8276i	0.452326	−	1.86451i
$56$		0			0
$57$	4.87109	+	2.61524i	0.645192	+	0.346398i
$58$		0			0
$59$	0.523482	−	1.78282i	0.0681516	−	0.232103i	−0.918373	−	0.395716i	$-0.870497\pi$
$59$	0.523482	−	1.78282i	0.0681516	−	0.232103i	0.986525	+	0.163613i	$0.0523148\pi$
$60$		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
$63$	−8.26130	+	2.55327i	−1.04083	+	0.321681i
$64$		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
$69$	−7.27028	−	5.36261i	−0.875239	−	0.645583i
$70$		0			0
$71$	−4.94506	+	1.71150i	−0.586871	+	0.203118i	−0.604336	−	0.796730i	$-0.706562\pi$
$71$	−4.94506	+	1.71150i	−0.586871	+	0.203118i	0.0174653	+	0.999847i	$0.494440\pi$
$72$		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
$75$	−5.63615	−	1.75782i	−0.650806	−	0.202976i
$76$		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
$81$	−6.33524	+	6.39256i	−0.703915	+	0.710284i
$82$		0			0
$83$	0.0980278	+	0.124653i	0.0107600	+	0.0136824i	0.791403	−	0.611294i	$-0.209351\pi$
$83$	0.0980278	+	0.124653i	0.0107600	+	0.0136824i	−0.780643	+	0.624977i	$0.785108\pi$
$84$		0			0
$85$	−0.867843	+	4.50280i	−0.0941308	+	0.488397i
$86$		0			0
$87$	0.674859	+	1.36460i	0.0723524	+	0.146301i
$88$		0			0
$89$	1.62244	+	2.52457i	0.171978	+	0.267603i	0.916534	−	0.399957i	$-0.130975\pi$
$89$	1.62244	+	2.52457i	0.171978	+	0.267603i	−0.744556	+	0.667560i	$0.767339\pi$
$90$		0			0
$91$	3.44293	+	3.97335i	0.360917	+	0.416521i
$92$		0			0
$93$	−1.18594	−	6.75966i	−0.122976	−	0.700944i
$94$		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
$99$	−0.208315	−	14.7191i	−0.0209364	−	1.47932i
$100$		0			0
$101$	3.85442	+	5.41278i	0.383530	+	0.538592i	0.960539	−	0.278146i	$-0.0897198\pi$
$101$	3.85442	+	5.41278i	0.383530	+	0.538592i	−0.577009	+	0.816738i	$0.695780\pi$
$102$		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
$105$	−12.4141	−	7.44684i	−1.21149	−	0.726737i
$106$		0			0
$107$	−15.9522	−	2.29358i	−1.54215	−	0.221728i	−0.681843	−	0.731498i	$-0.738821\pi$
$107$	−15.9522	−	2.29358i	−1.54215	−	0.221728i	−0.860311	+	0.509770i	$0.829730\pi$
$108$		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
$111$	0.638151	−	9.90721i	0.0605706	−	0.940351i
$112$		0			0
$113$	−9.32118	−	7.33026i	−0.876863	−	0.689572i	0.0746407	−	0.997210i	$-0.476219\pi$
$113$	−9.32118	−	7.33026i	−0.876863	−	0.689572i	−0.951503	+	0.307638i	$0.900461\pi$
$114$		0			0
$115$	−1.43769	−	15.0562i	−0.134065	−	1.40400i
$116$		0			0
$117$	5.10850	+	1.96172i	0.472281	+	0.181361i
$118$		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
$123$	10.7160	+	4.49939i	0.966227	+	0.405696i
$124$		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
$129$	14.6718	−	1.85961i	1.29178	−	0.163730i
$130$		0			0
$131$	7.68105	−	11.9519i	0.671096	−	1.04425i	−0.324069	−	0.946033i	$-0.605051\pi$
$131$	7.68105	−	11.9519i	0.671096	−	1.04425i	0.995165	−	0.0982128i	$-0.0313126\pi$
$132$		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	0.934899	−	0.354915i	$-0.115490\pi$
$137$	11.7097	+	7.52537i	1.00043	+	0.642936i	0.0655291	+	0.997851i	$0.479126\pi$
$138$		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
$141$	−1.96204	+	17.4569i	−0.165234	+	1.47014i
$142$		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
$147$	−1.61275	−	1.59008i	−0.133017	−	0.131148i
$148$		0			0
$149$	15.7275	+	7.18251i	1.28845	+	0.588414i	0.937502	−	0.347981i	$-0.113133\pi$
$149$	15.7275	+	7.18251i	1.28845	+	0.588414i	0.350946	+	0.936396i	$0.385860\pi$
$150$		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
$153$	0.292775	+	4.73514i	0.0236694	+	0.382813i
$154$		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
$159$	−12.5965	+	3.47092i	−0.998964	+	0.275262i
$160$		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
$165$	18.1182	−	16.7062i	1.41050	−	1.30058i
$166$		0			0
$167$	8.27884	−	5.89534i	0.640636	−	0.456195i	−0.213009	−	0.977050i	$-0.568326\pi$
$167$	8.27884	−	5.89534i	0.640636	−	0.456195i	0.853645	+	0.520855i	$0.174387\pi$
$168$		0			0
$169$	0.460248	+	9.66180i	0.0354037	+	0.743216i
$170$		0			0
$171$	4.50802	+	8.44860i	0.344737	+	0.646081i
$172$		0			0
$173$	13.3638	−	3.24203i	1.01603	−	0.246487i	0.307036	−	0.951698i	$-0.400663\pi$
$173$	13.3638	−	3.24203i	1.01603	−	0.246487i	0.708997	+	0.705211i	$0.249148\pi$
$174$		0			0
$175$	−1.85932	−	9.64709i	−0.140552	−	0.729251i
$176$		0			0
$177$	2.46713	−	2.06656i	0.185441	−	0.155332i
$178$		0			0
$179$	−2.93658	+	1.88723i	−0.219490	+	0.141058i	−0.645766	−	0.763535i	$-0.723462\pi$
$179$	−2.93658	+	1.88723i	−0.219490	+	0.141058i	0.426275	+	0.904593i	$0.359825\pi$
$180$		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
$183$	−3.95796	+	18.8351i	−0.292581	+	1.39233i
$184$		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
$189$	−14.3592	−	4.25640i	−1.04448	−	0.309608i
$190$		0			0
$191$	−19.9911	−	10.3061i	−1.44650	−	0.745725i	−0.456897	−	0.889520i	$-0.651039\pi$
$191$	−19.9911	−	10.3061i	−1.44650	−	0.745725i	−0.989608	+	0.143795i	$0.954070\pi$
$192$		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
$195$	3.26226	+	8.56097i	0.233616	+	0.613064i
$196$		0			0
$197$	−7.60523	−	21.9739i	−0.541850	−	1.56557i	−0.800332	−	0.599557i	$-0.795343\pi$
$197$	−7.60523	−	21.9739i	−0.541850	−	1.56557i	0.258482	−	0.966016i	$-0.416778\pi$
$198$		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
$201$	−2.34671	+	13.9819i	−0.165524	+	0.986206i
$202$		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
$207$	−5.32653	−	14.7130i	−0.370220	−	1.02262i
$208$		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
$213$	−8.77113	−	2.28382i	−0.600988	−	0.156485i
$214$		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
$219$	11.2694	+	2.36812i	0.761515	+	0.160023i
$220$		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
$225$	−6.43433	−	7.94782i	−0.428955	−	0.529854i
$226$		0			0
$227$	−3.70345	−	19.2153i	−0.245806	−	1.27536i	−0.869593	−	0.493769i	$-0.835619\pi$
$227$	−3.70345	−	19.2153i	−0.245806	−	1.27536i	0.623787	−	0.781595i	$-0.285593\pi$
$228$		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
$231$	21.4163	−	11.8916i	1.40909	−	0.782413i
$232$		0			0
$233$	0.0573869	+	1.20470i	0.00375954	+	0.0789225i	0.999967	−	0.00808354i	$-0.00257310\pi$
$233$	0.0573869	+	1.20470i	0.00375954	+	0.0789225i	−0.996208	+	0.0870060i	$0.972270\pi$
$234$		0			0
$235$	−23.9567	+	17.0595i	−1.56276	+	1.11284i
$236$		0			0
$237$	13.7104	+	14.8692i	0.890587	+	0.965859i
$238$		0			0
$239$	5.73202	−	9.92816i	0.370774	−	0.642199i	−0.618911	−	0.785461i	$-0.712426\pi$
$239$	5.73202	−	9.92816i	0.370774	−	0.642199i	0.989685	+	0.143262i	$0.0457592\pi$
$240$		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
$243$	−15.2716	+	3.12718i	−0.979671	+	0.200609i
$244$		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
$249$	0.0215327	+	0.273824i	0.00136458	+	0.0173529i
$250$		0			0
$251$	8.82263	−	25.4913i	0.556880	−	1.60900i	−0.217350	−	0.976094i	$-0.569741\pi$
$251$	8.82263	−	25.4913i	0.556880	−	1.60900i	0.774230	−	0.632904i	$-0.218137\pi$
$252$		0			0
$253$	23.2804	+	10.6318i	1.46363	+	0.668416i
$254$		0			0
$255$	−5.57639	+	5.65587i	−0.349207	+	0.354184i
$256$		0			0
$257$	0.387194	−	0.967163i	0.0241525	−	0.0603299i	−0.915802	−	0.401631i	$-0.868443\pi$
$257$	0.387194	−	0.967163i	0.0241525	−	0.0603299i	0.939954	+	0.341301i	$0.110868\pi$
$258$		0			0
$259$	15.0277	−	6.86293i	0.933777	−	0.426442i
$260$		0			0
$261$	−0.338284	+	2.61501i	−0.0209393	+	0.161865i
$262$		0			0
$263$	−16.2766	+	2.34022i	−1.00366	+	0.144304i	−0.624498	−	0.781026i	$-0.714697\pi$
$263$	−16.2766	+	2.34022i	−1.00366	+	0.144304i	−0.379161	+	0.925331i	$0.623787\pi$
$264$		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	$0.00751021\pi$
$269$			0.773869i			0.0471836i	−0.999722	+	0.0235918i	$0.992490\pi$
$270$		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
$273$	1.14504	+	9.03398i	0.0693009	+	0.546762i
$274$		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
$279$	4.78449	−	10.8815i	0.286440	−	0.651458i
$280$		0			0
$281$	1.48895	+	1.41971i	0.0888232	+	0.0846927i	0.733190	−	0.680024i	$-0.238031\pi$
$281$	1.48895	+	1.41971i	0.0888232	+	0.0846927i	−0.644367	+	0.764716i	$0.722879\pi$
$282$		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
$285$	−5.49620	+	15.0605i	−0.325567	+	0.892107i
$286$		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
$291$	12.4452	+	0.801631i	0.729551	+	0.0469924i
$292$		0			0
$293$	3.34108	+	11.3787i	0.195188	+	0.664749i	0.997679	+	0.0680855i	$0.0216891\pi$
$293$	3.34108	+	11.3787i	0.195188	+	0.664749i	−0.802492	+	0.596663i	$0.796493\pi$
$294$		0			0
$295$	5.33315	+	0.766792i	0.310508	+	0.0446443i
$296$		0			0
$297$	13.8397	−	21.4137i	0.803060	−	1.24255i
$298$		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
$303$	0.355303	+	11.5038i	0.0204116	+	0.660878i
$304$		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
$309$	10.6974	−	1.87678i	0.608553	−	0.106766i
$310$		0			0
$311$	−9.56540	−	11.0391i	−0.542404	−	0.625968i	0.416692	−	0.909048i	$-0.363189\pi$
$311$	−9.56540	−	11.0391i	−0.542404	−	0.625968i	−0.959096	+	0.283080i	$0.908644\pi$
$312$		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
$315$	−10.7378	−	22.6583i	−0.605005	−	1.27665i
$316$		0			0
$317$	−2.53662	+	13.1612i	−0.142471	+	0.739208i	0.838477	+	0.544937i	$0.183446\pi$
$317$	−2.53662	+	13.1612i	−0.142471	+	0.739208i	−0.980948	+	0.194271i	$0.937766\pi$
$318$		0			0
$319$	−2.66599	−	3.39008i	−0.149267	−	0.189808i
$320$		0			0
$321$	−20.7874	−	18.6301i	−1.16024	−	1.03983i
$322$		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
$327$	0.116013	−	0.371977i	0.00641556	−	0.0205703i
$328$		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
$333$	10.4371	−	13.6655i	0.571951	−	0.748866i
$334$		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
$339$	−6.39213	−	19.5190i	−0.347173	−	1.06013i
$340$		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
$345$	12.3917	−	23.0805i	0.667148	−	1.24261i
$346$		0			0
$347$	2.68001	−	11.0472i	0.143870	−	0.593042i	−0.853534	−	0.521037i	$-0.825545\pi$
$347$	2.68001	−	11.0472i	0.143870	−	0.593042i	0.997404	−	0.0720047i	$-0.0229397\pi$
$348$		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
$351$	5.47799	+	7.73480i	0.292394	+	0.412853i
$352$		0			0
$353$	−6.92313	−	1.33432i	−0.368481	−	0.0710189i	0.00164965	−	0.999999i	$-0.499475\pi$
$353$	−6.92313	−	1.33432i	−0.368481	−	0.0710189i	−0.370130	+	0.928980i	$0.620687\pi$
$354$		0			0
$355$	−6.95316	−	13.4872i	−0.369035	−	0.715829i
$356$		0			0
$357$	−6.71193	+	4.15655i	−0.355233	+	0.219988i
$358$		0			0
$359$	8.77136	−	7.60043i	0.462935	−	0.401135i	−0.391923	−	0.919998i	$-0.628190\pi$
$359$	8.77136	−	7.60043i	0.462935	−	0.401135i	0.854857	+	0.518863i	$0.173644\pi$
$360$		0			0
$361$	−8.65176	+	1.66749i	−0.455356	+	0.0877627i
$362$		0			0
$363$	4.97113	+	22.0979i	0.260917	+	1.15984i
$364$		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
$369$	11.1218	+	16.7790i	0.578979	+	0.873479i
$370$		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
$375$	−1.26963	+	7.89127i	−0.0655635	+	0.407503i
$376$		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
$381$	−14.9055	−	12.1307i	−0.763631	−	0.621473i
$382$		0			0
$383$	13.7852	−	1.31633i	0.704392	−	0.0672613i	0.263288	−	0.964717i	$-0.415193\pi$
$383$	13.7852	−	1.31633i	0.704392	−	0.0672613i	0.441104	+	0.897456i	$0.354587\pi$
$384$		0			0
$385$	38.7556	+	13.4134i	1.97517	+	0.683612i
$386$		0			0
$387$	22.9318	+	11.4143i	1.16569	+	0.580224i
$388$		0			0
$389$	0.683887	−	0.717241i	0.0346745	−	0.0363655i	−0.706168	−	0.708044i	$-0.749578\pi$
$389$	0.683887	−	0.717241i	0.0346745	−	0.0363655i	0.740843	+	0.671678i	$0.234426\pi$
$390$		0			0
$391$	−7.65743	−	3.06557i	−0.387253	−	0.155033i
$392$		0			0
$393$	22.5518	−	9.84667i	1.13759	−	0.496699i
$394$		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
$399$	−8.83833	+	13.2598i	−0.442470	+	0.663820i
$400$		0			0
$401$	17.7271			0.885249			0.442624	−	0.896707i	$-0.354048\pi$
$401$	17.7271			0.885249			0.442624	+	0.896707i	$0.354048\pi$
$402$		0			0
$403$	−7.22752			−0.360029
$404$		0			0
$405$	−20.9626	−	15.5456i	−1.04164	−	0.772468i
$406$		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
$411$	9.64711	+	22.0948i	0.475857	+	1.08985i
$412$		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
$417$	−23.5312	−	11.2256i	−1.15233	−	0.549722i
$418$		0			0
$419$	−6.59427	−	2.28230i	−0.322151	−	0.111498i	0.161206	−	0.986921i	$-0.448462\pi$
$419$	−6.59427	−	2.28230i	−0.322151	−	0.111498i	−0.483357	+	0.875423i	$0.660583\pi$
$420$		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
$423$	−19.5978	+	23.2746i	−0.952877	+	1.13165i
$424$		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
$429$	−15.3058	−	2.46256i	−0.738970	−	0.118893i
$430$		0			0
$431$	24.2306	+	13.9896i	1.16715	+	0.673853i	0.953007	−	0.302950i	$-0.0979714\pi$
$431$	24.2306	+	13.9896i	1.16715	+	0.673853i	0.214141	+	0.976803i	$0.431305\pi$
$432$		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
$435$	−3.63825	+	2.50015i	−0.174441	+	0.119873i
$436$		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
$441$	−0.796819	−	3.84097i	−0.0379438	−	0.182903i
$442$		0			0
$443$	28.3444	−	5.46294i	1.34668	−	0.259552i	0.535595	−	0.844475i	$-0.320088\pi$
$443$	28.3444	−	5.46294i	1.34668	−	0.259552i	0.811089	+	0.584923i	$0.198875\pi$
$444$		0			0
$445$	−6.57658	+	5.69864i	−0.311760	+	0.270141i
$446$		0			0
$447$	15.7671	+	25.4603i	0.745756	+	1.20423i
$448$		0			0
$449$	1.16700	+	2.26366i	0.0550741	+	0.106829i	0.914766	−	0.403984i	$-0.132375\pi$
$449$	1.16700	+	2.26366i	0.0550741	+	0.106829i	−0.859692	+	0.510813i	$0.829345\pi$
$450$		0			0
$451$	−32.3304	−	6.23118i	−1.52238	−	0.293415i
$452$		0			0
$453$	−21.1235	+	16.0473i	−0.992466	+	0.753968i
$454$		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
$459$	−4.12687	+	7.10568i	−0.192626	+	0.331665i
$460$		0			0
$461$	1.46906	−	5.00315i	0.0684208	−	0.233020i	−0.918182	−	0.396158i	$-0.870343\pi$
$461$	1.46906	−	5.00315i	0.0684208	−	0.233020i	0.986603	+	0.163138i	$0.0521615\pi$
$462$		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
$465$	18.9125	−	6.19350i	0.877046	−	0.287217i
$466$		0			0
$467$	−30.8962	−	22.0011i	−1.42971	−	1.01809i	−0.992953	−	0.118509i	$-0.962189\pi$
$467$	−30.8962	−	22.0011i	−1.42971	−	1.01809i	−0.436754	−	0.899581i	$-0.643872\pi$
$468$		0			0
$469$	−22.3467	+	7.56534i	−1.03187	+	0.349335i
$470$		0			0
$471$	16.0423	−	21.7491i	0.739189	−	1.00214i
$472$		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
$477$	−21.4888	−	7.09844i	−0.983902	−	0.325015i
$478$		0			0
$479$	−15.8205	+	30.6876i	−0.722859	+	1.40215i	0.184941	+	0.982750i	$0.440790\pi$
$479$	−15.8205	+	30.6876i	−0.722859	+	1.40215i	−0.907801	+	0.419402i	$0.862240\pi$
$480$		0			0
$481$	−10.1605	−	2.46490i	−0.463278	−	0.112390i
$482$		0			0
$483$	17.3785	−	19.3909i	0.790749	−	0.882317i
$484$		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
$489$	27.6364	−	13.6675i	1.24976	−	0.618065i
$490$		0			0
$491$	−11.4876	−	17.8750i	−0.518427	−	0.806688i	0.479042	−	0.877792i	$-0.340984\pi$
$491$	−11.4876	−	17.8750i	−0.518427	−	0.806688i	−0.997469	+	0.0711041i	$0.977348\pi$
$492$		0			0
$493$	0.910217	+	1.05045i	0.0409941	+	0.0473097i
$494$		0			0
$495$	42.1613	−	6.67216i	1.89501	−	0.299891i
$496$		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
$501$	17.5951	−	0.543436i	0.786091	−	0.0242789i
$502$		0			0
$503$	24.3950	+	34.2579i	1.08772	+	1.52749i	0.827109	+	0.562042i	$0.189984\pi$
$503$	24.3950	+	34.2579i	1.08772	+	1.52749i	0.260609	+	0.965444i	$0.416077\pi$
$504$		0			0
$505$	−13.9454	+	13.2969i	−0.620561	+	0.591704i
$506$		0			0
$507$	−8.61832	+	14.3670i	−0.382753	+	0.638062i
$508$		0			0
$509$	−22.8411	−	3.28406i	−1.01242	−	0.145563i	−0.383912	−	0.923370i	$-0.625423\pi$
$509$	−22.8411	−	3.28406i	−1.01242	−	0.145563i	−0.628504	+	0.777806i	$0.716332\pi$
$510$		0			0
$511$	5.39880	+	18.3866i	0.238829	+	0.813376i
$512$		0			0
$513$	−1.61909	+	16.5070i	−0.0714845	+	0.728803i
$514$		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
$519$	22.3748	+	8.16550i	0.982146	+	0.358426i
$520$		0			0
$521$	10.1543	−	22.2347i	0.444866	−	0.974121i	−0.545813	−	0.837907i	$-0.683779\pi$
$521$	10.1543	−	22.2347i	0.444866	−	0.974121i	0.990679	−	0.136214i	$-0.0434934\pi$
$522$		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
$525$	6.58780	−	15.6898i	0.287515	−	0.684761i
$526$		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
$531$	5.54095	−	0.608338i	0.240457	−	0.0263996i
$532$		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
$543$	26.5202	+	2.98070i	1.13809	+	0.127914i
$544$		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
$549$	−23.7984	+	23.3435i	−1.01569	+	0.996278i
$550$		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
$555$	28.6995	−	2.25685i	1.21823	−	0.0957979i
$556$		0			0
$557$	6.36471	−	8.09338i	0.269681	−	0.342928i	−0.632284	−	0.774737i	$-0.717882\pi$
$557$	6.36471	−	8.09338i	0.269681	−	0.342928i	0.901965	+	0.431809i	$0.142125\pi$
$558$		0			0
$559$	0.741082	−	15.5572i	0.0313444	−	0.658001i
$560$		0			0
$561$	−3.57033	−	12.9572i	−0.150739	−	0.547053i
$562$		0			0
$563$	−1.76420	+	12.2703i	−0.0743520	+	0.517130i	0.918277	+	0.395938i	$0.129581\pi$
$563$	−1.76420	+	12.2703i	−0.0743520	+	0.517130i	−0.992629	+	0.121191i	$0.961329\pi$
$564$		0			0
$565$	17.1930	−	29.7791i	0.723314	−	1.25282i
$566$		0			0
$567$	−16.6060	−	19.9287i	−0.697388	−	0.836927i
$568$		0			0
$569$	14.4597	−	10.2967i	0.606180	−	0.431659i	−0.235318	−	0.971918i	$-0.575613\pi$
$569$	14.4597	−	10.2967i	0.606180	−	0.431659i	0.841499	+	0.540259i	$0.181674\pi$
$570$		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
$573$	−18.9111	−	34.0580i	−0.790025	−	1.42279i
$574$		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
$579$	−21.7490	−	25.9647i	−0.903859	−	1.07906i
$580$		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
$585$	−3.52245	+	15.4722i	−0.145636	+	0.639698i
$586$		0			0
$587$	21.0887	−	16.5843i	0.870423	−	0.684508i	−0.0795534	−	0.996831i	$-0.525349\pi$
$587$	21.0887	−	16.5843i	0.870423	−	0.684508i	0.949976	+	0.312323i	$0.101107\pi$
$588$		0			0
$589$	−9.55853	−	8.28252i	−0.393853	−	0.341275i
$590$		0			0
$591$	10.1484	−	38.9754i	0.417449	−	1.60323i
$592$		0			0
$593$	−10.4172	−	5.37044i	−0.427783	−	0.220538i	0.230869	−	0.972985i	$-0.425843\pi$
$593$	−10.4172	−	5.37044i	−0.427783	−	0.220538i	−0.658653	+	0.752447i	$0.728873\pi$
$594$		0			0
$595$	−12.6818	−	3.72372i	−0.519904	−	0.152658i
$596$		0			0
$597$	32.8345	−	12.5120i	1.34382	−	0.512081i
$598$		0			0
$599$	7.04181	+	20.3460i	0.287721	+	0.831315i	0.992539	+	0.121927i	$0.0389073\pi$
$599$	7.04181	+	20.3460i	0.287721	+	0.831315i	−0.704818	+	0.709388i	$0.748972\pi$
$600$		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
$603$	−16.8139	+	17.8967i	−0.684715	+	0.728811i
$604$		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
$609$	−4.10026	+	1.56246i	−0.166151	+	0.0633139i
$610$		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
$615$	−8.49209	+	32.6143i	−0.342434	+	1.31514i
$616$		0			0
$617$	−11.7828	−	10.2099i	−0.474358	−	0.411034i	0.384597	−	0.923085i	$-0.374341\pi$
$617$	−11.7828	−	10.2099i	−0.474358	−	0.411034i	−0.858955	+	0.512051i	$0.828886\pi$
$618$		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
$621$	6.45732	−	26.3217i	0.259123	−	1.05626i
$622$		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
$627$	−17.4202	−	20.7967i	−0.695694	−	0.830541i
$628$		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
$633$	6.82764	+	12.2962i	0.271374	+	0.488731i
$634$		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
$639$	−10.4473	−	11.7175i	−0.413287	−	0.463538i
$640$		0			0
$641$	−18.7729	+	32.5157i	−0.741487	+	1.28429i	0.210332	+	0.977630i	$0.432546\pi$
$641$	−18.7729	+	32.5157i	−0.741487	+	1.28429i	−0.951818	+	0.306663i	$0.900788\pi$
$642$		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
$645$	11.3923	+	41.3442i	0.448571	+	1.62792i
$646$		0			0
$647$	1.31497	−	27.6046i	0.0516969	−	1.08525i	−0.812778	−	0.582574i	$-0.802046\pi$
$647$	1.31497	−	27.6046i	0.0516969	−	1.08525i	0.864475	−	0.502677i	$-0.167651\pi$
$648$		0			0
$649$	−5.63595	+	7.16669i	−0.221230	+	0.281317i
$650$		0			0
$651$	19.7200	−	1.55072i	0.772887	−	0.0607777i
$652$		0			0
$653$	0.0497588	−	0.143769i	0.00194721	−	0.00562611i	−0.944023	−	0.329880i	$-0.892992\pi$
$653$	0.0497588	−	0.143769i	0.00194721	−	0.00562611i	0.945970	+	0.324253i	$0.105113\pi$
$654$		0			0
$655$	37.4748	+	17.1142i	1.46426	+	0.668707i
$656$		0			0
$657$	13.9668	+	14.2390i	0.544898	+	0.555516i
$658$		0			0
$659$	14.5115	−	36.2480i	0.565289	−	1.41202i	−0.320195	−	0.947352i	$-0.603748\pi$
$659$	14.5115	−	36.2480i	0.565289	−	1.41202i	0.885483	−	0.464671i	$-0.153827\pi$
$660$		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
$663$	4.96497	+	0.558031i	0.192823	+	0.0216721i
$664$		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
$675$	−1.63825	−	17.6358i	−0.0630562	−	0.678802i
$676$		0			0
$677$	7.29459	+	0.696549i	0.280354	+	0.0267706i	0.234286	−	0.972168i	$-0.424725\pi$
$677$	7.29459	+	0.696549i	0.280354	+	0.0267706i	0.0460681	+	0.998938i	$0.485331\pi$
$678$		0			0
$679$	8.62105	+	18.8775i	0.330846	+	0.724451i
$680$		0			0
$681$	13.1217	−	31.2514i	0.502826	−	1.19756i
$682$		0			0
$683$	19.8958	+	18.9706i	0.761292	+	0.725891i	0.967570	−	0.252603i	$-0.0812866\pi$
$683$	19.8958	+	18.9706i	0.761292	+	0.725891i	−0.206278	+	0.978493i	$0.566135\pi$
$684$		0			0
$685$	−16.7673	+	36.7153i	−0.640646	+	1.40282i
$686$		0			0
$687$	43.3485	+	15.8197i	1.65385	+	0.603558i
$688$		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
$693$	42.2895	+	3.43500i	1.60645	+	0.130485i
$694$		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
$699$	−1.07459	+	1.79138i	−0.0406448	+	0.0677561i
$700$		0			0
$701$	10.2133	−	9.73839i	0.385752	−	0.367814i	−0.472246	−	0.881467i	$-0.656557\pi$
$701$	10.2133	−	9.73839i	0.385752	−	0.367814i	0.857998	+	0.513653i	$0.171708\pi$
$702$		0			0
$703$	−10.6127	−	14.9035i	−0.400266	−	0.562095i
$704$		0			0
$705$	−50.9153	+	1.57255i	−1.91758	+	0.0592258i
$706$		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
$711$	5.47570	+	34.6009i	0.205355	+	1.29764i
$712$		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
$717$	17.7987	−	8.80227i	0.664704	−	0.328727i
$718$		0			0
$719$	2.79908	−	14.5230i	0.104388	−	0.541617i	−0.891653	−	0.452720i	$-0.850454\pi$
$719$	2.79908	−	14.5230i	0.104388	−	0.541617i	0.996041	−	0.0888971i	$-0.0283342\pi$
$720$		0			0
$721$	11.1722	+	14.2066i	0.416073	+	0.529080i
$722$		0			0
$723$	34.0403	−	37.9821i	1.26597	−	1.41257i
$724$		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
$729$	−25.0140	−	10.1637i	−0.926444	−	0.376434i
$730$		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
$735$	3.89838	−	5.28517i	0.143794	−	0.194947i
$736$		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
$741$	9.58400	−	3.13859i	0.352077	−	0.115299i
$742$		0			0
$743$	14.1770	+	35.4125i	0.520104	+	1.29916i	0.923313	+	0.384049i	$0.125471\pi$
$743$	14.1770	+	35.4125i	0.520104	+	1.29916i	−0.403209	+	0.915108i	$0.632105\pi$
$744$		0			0
$745$	−14.1252	+	48.1059i	−0.517506	+	1.76246i
$746$		0			0
$747$	−0.232016	+	0.415329i	−0.00848903	+	0.0151961i
$748$		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
$753$	37.2038	−	28.2634i	1.35578	−	1.02997i
$754$		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
$759$	23.3390	+	37.6873i	0.847151	+	1.36796i
$760$		0			0
$761$	−19.6756	+	17.0490i	−0.713240	+	0.618026i	−0.933988	−	0.357305i	$-0.883696\pi$
$761$	−19.6756	+	17.0490i	−0.713240	+	0.618026i	0.220748	+	0.975331i	$0.429150\pi$
$762$		0			0
$763$	0.636692	−	0.122712i	0.0230498	−	0.00444248i
$764$		0			0
$765$	−13.4702	+	2.79443i	−0.487016	+	0.101033i
$766$		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
$771$	1.48714	−	1.02195i	0.0535582	−	0.0368045i
$772$		0			0
$773$	−14.5862	−	15.2976i	−0.524630	−	0.550216i	0.407092	−	0.913387i	$-0.366543\pi$
$773$	−14.5862	−	15.2976i	−0.524630	−	0.550216i	−0.931723	+	0.363171i	$0.881694\pi$
$774$		0			0
$775$	11.6965	+	6.75299i	0.420152	+	0.242575i
$776$		0			0
$777$	28.2513	+	4.54537i	1.01351	+	0.163064i
$778$		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
$783$	−2.99967	+	3.44386i	−0.107199	+	0.123074i
$784$		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
$789$	−25.7065	−	12.2634i	−0.915176	−	0.436588i
$790$		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
$795$	−15.1607	−	34.7226i	−0.537695	−	1.23148i
$796$		0			0
$797$	0.489388	−	5.12511i	0.0173350	−	0.181541i	−0.982657	−	0.185430i	$-0.940632\pi$
$797$	0.489388	−	5.12511i	0.0173350	−	0.181541i	0.999992	+	0.00388978i	$0.00123816\pi$
$798$		0			0
$799$	2.28256	+	15.8756i	0.0807512	+	0.561637i
$800$		0			0
$801$	−5.11787	+	7.40669i	−0.180831	+	0.261702i
$802$		0			0
$803$	−32.6231			−1.15124
$804$		0			0
$805$	43.5936			1.53647
$806$		0			0
$807$	−0.743421	+	1.11532i	−0.0261696	+	0.0392613i
$808$		0			0
$809$	−6.77273	−	47.1054i	−0.238116	−	1.65614i	−0.661322	−	0.750102i	$-0.730004\pi$
$809$	−6.77273	−	47.1054i	−0.238116	−	1.65614i	0.423205	−	0.906034i	$-0.360905\pi$
$810$		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
$813$	−42.6527	+	18.6232i	−1.49590	+	0.653145i
$814$		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
$819$	−7.02827	+	14.1200i	−0.245588	+	0.493394i
$820$		0			0
$821$	−24.9574	−	8.63785i	−0.871021	−	0.301463i	−0.145246	−	0.989396i	$-0.546397\pi$
$821$	−24.9574	−	8.63785i	−0.871021	−	0.301463i	−0.725775	+	0.687932i	$0.758519\pi$
$822$		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
$825$	22.4689	+	18.2861i	0.782268	+	0.636640i
$826$		0			0
$827$	10.2403	+	0.487808i	0.356092	+	0.0169627i	0.224866	−	0.974390i	$-0.427806\pi$
$827$	10.2403	+	0.487808i	0.356092	+	0.0169627i	0.131226	+	0.991353i	$0.458109\pi$
$828$		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
$831$	1.33685	−	8.30905i	0.0463748	−	0.288238i
$832$		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
$837$	17.3489	−	11.0865i	0.599666	−	0.383206i
$838$		0			0
$839$	53.4161	−	2.54452i	1.84413	−	0.0878467i	0.903768	−	0.428023i	$-0.140790\pi$
$839$	53.4161	−	2.54452i	1.84413	−	0.0878467i	0.940362	+	0.340177i	$0.110487\pi$
$840$		0			0
$841$	−14.1137	−	24.4457i	−0.486681	−	0.842956i
$842$		0			0
$843$	0.782068	+	3.47649i	0.0269358	+	0.119737i
$844$		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
$849$	−23.5029	+	14.5549i	−0.806618	+	0.499522i
$850$		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
$855$	−22.3892	+	16.4257i	−0.765695	+	0.561747i
$856$		0			0
$857$	24.6999	−	28.5052i	0.843732	−	0.973718i	−0.156170	−	0.987730i	$-0.549915\pi$
$857$	24.6999	−	28.5052i	0.843732	−	0.973718i	0.999902	+	0.0140119i	$0.00446026\pi$
$858$		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
$861$	−15.8458	+	29.5139i	−0.540022	+	1.00583i
$862$		0			0
$863$	0.902901	−	3.07500i	0.0307351	−	0.104674i	−0.942697	−	0.333650i	$-0.891720\pi$
$863$	0.902901	−	3.07500i	0.0307351	−	0.104674i	0.973432	+	0.228976i	$0.0735377\pi$
$864$		0			0
$865$	14.8204	+	37.0196i	0.503909	+	1.25870i
$866$		0			0
$867$	−7.81574	−	23.8662i	−0.265437	−	0.810538i
$868$		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
$873$	17.1663	+	13.1109i	0.580992	+	0.443736i
$874$		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
$879$	−6.11570	+	19.6089i	−0.206277	+	0.661392i
$880$		0			0
$881$	22.3744	−	43.4003i	0.753813	−	1.46219i	−0.128589	−	0.991698i	$-0.541045\pi$
$881$	22.3744	−	43.4003i	0.753813	−	1.46219i	0.882402	−	0.470496i	$-0.155925\pi$
$882$		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
$885$	6.94968	+	6.22844i	0.233611	+	0.209367i
$886$		0			0
$887$	28.5878	+	36.3524i	0.959885	+	1.22059i	0.975339	+	0.220713i	$0.0708383\pi$
$887$	28.5878	+	36.3524i	0.959885	+	1.22059i	−0.0154536	+	0.999881i	$0.504919\pi$
$888$		0			0
$889$	6.05230	−	31.4023i	0.202988	−	1.05320i
$890$		0			0
$891$	40.5173	−	17.5669i	1.35738	−	0.588512i
$892$		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
$897$	−16.2309	+	2.84760i	−0.541934	+	0.0950786i
$898$		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
$903$	1.31592	+	42.6062i	0.0437911	+	1.41785i
$904$		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
$909$	−10.5391	+	16.9210i	−0.349561	+	0.561234i
$910$		0			0
$911$	−26.4171	−	3.79821i	−0.875239	−	0.125840i	−0.309969	−	0.950747i	$-0.600319\pi$
$911$	−26.4171	−	3.79821i	−0.875239	−	0.125840i	−0.565270	+	0.824906i	$0.691228\pi$
$912$		0			0
$913$	−0.219224	−	0.746609i	−0.00725526	−	0.0247091i
$914$		0			0
$915$	−55.6949	−	3.58746i	−1.84122	−	0.118598i
$916$		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
$921$	9.13946	−	25.0436i	0.301155	−	0.825215i
$922$		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
$927$	17.2203	+	7.57161i	0.565590	+	0.248684i
$928$		0			0
$929$	15.3850	+	33.6885i	0.504766	+	1.10528i	0.974891	+	0.222684i	$0.0714818\pi$
$929$	15.3850	+	33.6885i	0.504766	+	1.10528i	−0.470124	+	0.882600i	$0.655791\pi$
$930$		0			0
$931$	−4.15493	−	0.396748i	−0.136172	−	0.0130029i
$932$		0			0
$933$	−3.18123	−	25.0989i	−0.104149	−	0.821700i
$934$		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	0.0290436	−	0.999578i	$-0.490754\pi$
$941$	−26.6308	−	17.1146i	−0.868140	−	0.557919i	−0.897183	+	0.441659i	$0.854390\pi$
$942$		0			0
$943$	−34.6425	+	4.98084i	−1.12812	+	0.162199i
$944$		0			0
$945$	6.29117	−	42.9711i	0.204652	−	1.39785i
$946$		0			0
$947$	12.7776	−	5.83533i	0.415216	−	0.189623i	−0.196843	−	0.980435i	$-0.563069\pi$
$947$	12.7776	−	5.83533i	0.415216	−	0.189623i	0.612059	+	0.790812i	$0.290342\pi$
$948$		0			0
$949$	4.50727	−	11.2586i	0.146312	−	0.365470i
$950$		0			0
$951$	−16.2992	+	16.5315i	−0.528539	+	0.536072i
$952$		0			0
$953$	7.32518	+	3.34530i	0.237286	+	0.108365i	0.530509	−	0.847679i	$-0.322001\pi$
$953$	7.32518	+	3.34530i	0.237286	+	0.108365i	−0.293223	+	0.956044i	$0.594728\pi$
$954$		0			0
$955$	21.3312	−	61.6325i	0.690262	−	1.99438i
$956$		0			0
$957$	−0.585610	−	7.44698i	−0.0189301	−	0.240727i
$958$		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
$963$	−12.0624	−	46.8197i	−0.388705	−	1.50874i
$964$		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
$969$	5.92678	+	6.42771i	0.190396	+	0.206488i
$970$		0			0
$971$	−7.01760	+	4.99721i	−0.225205	+	0.160368i	−0.687091	−	0.726572i	$-0.741113\pi$
$971$	−7.01760	+	4.99721i	−0.225205	+	0.160368i	0.461885	+	0.886940i	$0.347173\pi$
$972$		0			0
$973$	−2.06437	−	43.3364i	−0.0661806	−	1.38930i
$974$		0			0
$975$	−9.41510	+	5.22786i	−0.301525	+	0.167425i
$976$		0			0
$977$	−46.8344	+	11.3619i	−1.49837	+	0.363500i	−0.899347	−	0.437235i	$-0.855958\pi$
$977$	−46.8344	+	11.3619i	−1.49837	+	0.363500i	−0.599019	+	0.800735i	$0.704442\pi$
$978$		0			0
$979$	−2.78677	−	14.4591i	−0.0890654	−	0.462115i
$980$		0			0
$981$	0.524543	−	0.424655i	0.0167474	−	0.0135582i
$982$		0			0
$983$	−32.9135	+	21.1522i	−1.04978	+	0.674652i	−0.947386	−	0.320092i	$-0.896286\pi$
$983$	−32.9135	+	21.1522i	−1.04978	+	0.674652i	−0.102392	+	0.994744i	$0.532650\pi$
$984$		0			0
$985$	59.9319	−	30.8970i	1.90959	−	0.984462i
$986$		0			0
$987$	−49.5504	−	10.4124i	−1.57721	−	0.331430i
$988$		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
$993$	−3.63541	−	0.946587i	−0.115366	−	0.0300390i
$994$		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
$999$	28.1701	−	9.66871i	0.891264	−	0.305904i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.4	✓	440	67.41	odd	66	inner
804.2.ba.b.41.18	yes	440	201.41	even	66	inner
804.2.ba.b.353.4	yes	440	3.2	odd	2	inner
804.2.ba.b.353.18	yes	440	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.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.44123 + 0.960654i) q^{3} +(0.412679 + 2.87025i) q^{5} +(-0.273979 + 2.86924i) q^{7} +(1.15429 + 2.76905i) q^{9} +O(q^{10})\)	\(q+(1.44123 + 0.960654i) q^{3} +(0.412679 + 2.87025i) q^{5} +(-0.273979 + 2.86924i) q^{7} +(1.15429 + 2.76905i) q^{9} +(-4.55535 - 1.82369i) q^{11} +(1.25875 - 1.32014i) q^{13} +(-2.16255 + 4.53313i) q^{15} +(1.49442 + 0.517223i) q^{17} +(3.17757 - 0.303421i) q^{19} +(-3.15121 + 3.87203i) q^{21} +(-5.20992 - 0.248179i) q^{23} +(-3.27055 + 0.960320i) q^{25} +(-0.996499 + 5.09970i) q^{27} +(0.761179 + 0.439467i) q^{29} +(-2.73430 - 2.86765i) q^{31} +(-4.81338 - 7.00447i) q^{33} +(-8.34848 + 0.397687i) q^{35} +(-2.86589 - 4.96387i) q^{37} +(3.08236 - 0.693403i) q^{39} +(6.58885 - 1.26990i) q^{41} +(6.45298 - 5.59154i) q^{43} +(-7.47150 + 4.45582i) q^{45} +(4.64743 + 9.01475i) q^{47} +(-1.28395 - 0.247462i) q^{49} +(1.65693 + 2.18106i) q^{51} +(-4.94001 + 5.70108i) q^{53} +(3.35454 - 13.8276i) q^{55} +(4.87109 + 2.61524i) q^{57} +(0.523482 - 1.78282i) q^{59} +(4.12990 + 10.3160i) q^{61} +(-8.26130 + 2.55327i) q^{63} +(4.30860 + 3.06814i) q^{65} +(3.34986 + 7.46850i) q^{67} +(-7.27028 - 5.36261i) q^{69} +(-4.94506 + 1.71150i) q^{71} +(6.17224 - 2.47099i) q^{73} +(-5.63615 - 1.75782i) q^{75} +(6.48066 - 12.5707i) q^{77} +(11.3480 + 2.75300i) q^{79} +(-6.33524 + 6.39256i) q^{81} +(0.0980278 + 0.124653i) q^{83} +(-0.867843 + 4.50280i) q^{85} +(0.674859 + 1.36460i) q^{87} +(1.62244 + 2.52457i) q^{89} +(3.44293 + 3.97335i) q^{91} +(-1.18594 - 6.75966i) q^{93} +(2.18221 + 8.99519i) q^{95} +(6.23550 - 3.60007i) q^{97} +(-0.208315 - 14.7191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 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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