LMFDB - Embedded newform 819.2.ge.a.275.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(137,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 8, 11]))

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

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

chi := DirichletCharacter("819.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.ge (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$108$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			275.20
Character	$\chi$	$=$	819.275
Dual form			819.2.ge.a.137.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.534230 + 1.99377i) q^{2} +(-0.858370 - 1.50439i) q^{3} +(-1.95768 - 1.13027i) q^{4} +(0.00724515 - 0.0270393i) q^{5} +(3.45799 - 0.907703i) q^{6} +(2.08941 + 1.62307i) q^{7} +(0.380256 - 0.380256i) q^{8} +(-1.52640 + 2.58265i) q^{9} +O(q^{10})$	\(q+(-0.534230 + 1.99377i) q^{2} +(-0.858370 - 1.50439i) q^{3} +(-1.95768 - 1.13027i) q^{4} +(0.00724515 - 0.0270393i) q^{5} +(3.45799 - 0.907703i) q^{6} +(2.08941 + 1.62307i) q^{7} +(0.380256 - 0.380256i) q^{8} +(-1.52640 + 2.58265i) q^{9} +(0.0500396 + 0.0288904i) q^{10} +(3.08127 - 3.08127i) q^{11} +(-0.0199527 + 3.91530i) q^{12} +(-3.51566 + 0.800100i) q^{13} +(-4.35226 + 3.29872i) q^{14} +(-0.0468967 + 0.0123101i) q^{15} +(-1.70553 - 2.95407i) q^{16} +4.58353 q^{17} +(-4.33377 - 4.42303i) q^{18} +(-0.978884 - 0.262291i) q^{19} +(-0.0447452 + 0.0447452i) q^{20} +(0.648252 - 4.53649i) q^{21} +(4.49725 + 7.78947i) q^{22} +(0.348171 - 0.603051i) q^{23} +(-0.898456 - 0.245655i) q^{24} +(4.32945 + 2.49961i) q^{25} +(0.282951 - 7.43686i) q^{26} +(5.19555 + 0.0794361i) q^{27} +(-2.25589 - 5.53904i) q^{28} +(4.86476 + 2.80867i) q^{29} +(0.000510003 - 0.100078i) q^{30} +(-5.51345 + 5.51345i) q^{31} +(7.83976 - 2.10066i) q^{32} +(-7.28032 - 1.99058i) q^{33} +(-2.44866 + 9.13851i) q^{34} +(0.0590248 - 0.0447367i) q^{35} +(5.90729 - 3.33076i) q^{36} +(-1.19724 - 1.19724i) q^{37} +(1.04590 - 1.81155i) q^{38} +(4.22140 + 4.60215i) q^{39} +(-0.00752684 - 0.0130369i) q^{40} +(7.38795 + 7.38795i) q^{41} +(8.69842 + 3.71600i) q^{42} -3.29833i q^{43} +(-9.51480 + 2.54948i) q^{44} +(0.0587740 + 0.0599845i) q^{45} +(1.01634 + 1.01634i) q^{46} +(-6.82773 + 6.82773i) q^{47} +(-2.98010 + 5.10147i) q^{48} +(1.73127 + 6.78253i) q^{49} +(-7.29657 + 7.29657i) q^{50} +(-3.93436 - 6.89543i) q^{51} +(7.78685 + 2.40729i) q^{52} +(9.51169 - 5.49158i) q^{53} +(-2.93399 + 10.3163i) q^{54} +(-0.0609911 - 0.105640i) q^{55} +(1.41169 - 0.177328i) q^{56} +(0.445655 + 1.69777i) q^{57} +(-8.19875 + 8.19875i) q^{58} +(3.80295 + 14.1928i) q^{59} +(0.105722 + 0.0289065i) q^{60} +(-6.31704 + 10.9414i) q^{61} +(-8.04712 - 13.9380i) q^{62} +(-7.38111 + 2.91876i) q^{63} +9.93081i q^{64} +(-0.00383735 + 0.100858i) q^{65} +(7.85812 - 13.4519i) q^{66} +(-7.85197 - 2.10393i) q^{67} +(-8.97307 - 5.18060i) q^{68} +(-1.20609 - 0.00614629i) q^{69} +(0.0576621 + 0.141582i) q^{70} +(8.08749 - 2.16704i) q^{71} +(0.401646 + 1.56249i) q^{72} +(-2.19670 + 8.19820i) q^{73} +(3.02662 - 1.74742i) q^{74} +(0.0441258 - 8.65878i) q^{75} +(1.61988 + 1.61988i) q^{76} +(11.4392 - 1.43692i) q^{77} +(-11.4308 + 5.95791i) q^{78} +4.15411 q^{79} +(-0.0922326 + 0.0247136i) q^{80} +(-4.34020 - 7.88433i) q^{81} +(-18.6768 + 10.7830i) q^{82} +(3.89830 - 14.5487i) q^{83} +(-6.39651 + 8.14829i) q^{84} +(0.0332083 - 0.123935i) q^{85} +(6.57613 + 1.76207i) q^{86} +(0.0495817 - 9.72940i) q^{87} -2.34335i q^{88} +(-1.72018 + 1.72018i) q^{89} +(-0.150994 + 0.0851366i) q^{90} +(-8.64427 - 4.03443i) q^{91} +(-1.36321 + 0.787052i) q^{92} +(13.0270 + 3.56182i) q^{93} +(-9.96536 - 17.2605i) q^{94} +(-0.0141843 + 0.0245680i) q^{95} +(-9.88963 - 9.99095i) q^{96} +(2.06369 - 2.06369i) q^{97} +(-14.4477 - 0.171665i) q^{98} +(3.25460 + 12.6611i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 2 q^{3} - 6 q^{4} - 6 q^{5} - 4 q^{6} + 2 q^{7} + 12 q^{8} + 2 q^{9}+O(q^{10}) $ 432 * q + 2 * q^3 - 6 * q^4 - 6 * q^5 - 4 * q^6 + 2 * q^7 + 12 * q^8 + 2 * q^9	$ 432 q + 2 q^{3} - 6 q^{4} - 6 q^{5} - 4 q^{6} + 2 q^{7} + 12 q^{8} + 2 q^{9} - 12 q^{10} - 6 q^{11} - 4 q^{13} - 12 q^{14} - 24 q^{15} + 190 q^{16} - 26 q^{18} - 8 q^{19} - 12 q^{20} - 24 q^{21} + 4 q^{22} - 6 q^{23} - 46 q^{24} - 4 q^{27} - 12 q^{28} - 12 q^{29} - 6 q^{30} - 12 q^{31} - 24 q^{32} - 4 q^{33} - 66 q^{35} - 12 q^{36} - 6 q^{37} - 32 q^{39} - 12 q^{40} - 12 q^{41} - 16 q^{42} - 48 q^{44} - 2 q^{45} + 12 q^{46} + 36 q^{47} + 80 q^{48} + 42 q^{50} - 36 q^{51} - 38 q^{52} - 24 q^{53} + 14 q^{54} - 8 q^{55} - 12 q^{56} + 10 q^{57} - 14 q^{58} + 56 q^{60} - 2 q^{61} + 98 q^{63} - 42 q^{65} - 34 q^{66} + 10 q^{67} - 102 q^{68} + 30 q^{69} - 16 q^{70} + 48 q^{71} - 62 q^{72} - 32 q^{73} - 90 q^{74} - 36 q^{75} - 12 q^{76} - 72 q^{77} - 32 q^{78} - 32 q^{79} + 114 q^{80} + 6 q^{81} - 12 q^{82} - 12 q^{83} + 34 q^{84} - 12 q^{85} + 42 q^{86} + 88 q^{87} + 30 q^{89} + 228 q^{90} + 8 q^{91} - 12 q^{92} + 52 q^{93} - 2 q^{94} + 6 q^{95} - 90 q^{96} - 6 q^{97} - 64 q^{99}+O(q^{100}) $ 432 * q + 2 * q^3 - 6 * q^4 - 6 * q^5 - 4 * q^6 + 2 * q^7 + 12 * q^8 + 2 * q^9 - 12 * q^10 - 6 * q^11 - 4 * q^13 - 12 * q^14 - 24 * q^15 + 190 * q^16 - 26 * q^18 - 8 * q^19 - 12 * q^20 - 24 * q^21 + 4 * q^22 - 6 * q^23 - 46 * q^24 - 4 * q^27 - 12 * q^28 - 12 * q^29 - 6 * q^30 - 12 * q^31 - 24 * q^32 - 4 * q^33 - 66 * q^35 - 12 * q^36 - 6 * q^37 - 32 * q^39 - 12 * q^40 - 12 * q^41 - 16 * q^42 - 48 * q^44 - 2 * q^45 + 12 * q^46 + 36 * q^47 + 80 * q^48 + 42 * q^50 - 36 * q^51 - 38 * q^52 - 24 * q^53 + 14 * q^54 - 8 * q^55 - 12 * q^56 + 10 * q^57 - 14 * q^58 + 56 * q^60 - 2 * q^61 + 98 * q^63 - 42 * q^65 - 34 * q^66 + 10 * q^67 - 102 * q^68 + 30 * q^69 - 16 * q^70 + 48 * q^71 - 62 * q^72 - 32 * q^73 - 90 * q^74 - 36 * q^75 - 12 * q^76 - 72 * q^77 - 32 * q^78 - 32 * q^79 + 114 * q^80 + 6 * q^81 - 12 * q^82 - 12 * q^83 + 34 * q^84 - 12 * q^85 + 42 * q^86 + 88 * q^87 + 30 * q^89 + 228 * q^90 + 8 * q^91 - 12 * q^92 + 52 * q^93 - 2 * q^94 + 6 * q^95 - 90 * q^96 - 6 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.534230	+	1.99377i	−0.377758	+	1.40981i	0.471516	+	0.881857i	$0.343707\pi$
$2$	−0.534230	+	1.99377i	−0.377758	+	1.40981i	−0.849274	+	0.527953i	$0.822960\pi$
$3$	−0.858370	−	1.50439i	−0.495580	−	0.868562i
$3$	−0.858370	−	1.50439i	−0.495580	−	0.868562i
$4$	−1.95768	−	1.13027i	−0.978839	−	0.565133i
$5$	0.00724515	−	0.0270393i	0.00324013	−	0.0120923i	−0.964287	−	0.264860i	$-0.914674\pi$
$5$	0.00724515	−	0.0270393i	0.00324013	−	0.0120923i	0.967527	+	0.252768i	$0.0813409\pi$
$6$	3.45799	−	0.907703i	1.41172	−	0.370568i
$7$	2.08941	+	1.62307i	0.789723	+	0.613464i
$7$	2.08941	+	1.62307i	0.789723	+	0.613464i
$8$	0.380256	−	0.380256i	0.134441	−	0.134441i
$9$	−1.52640	+	2.58265i	−0.508800	+	0.860884i
$10$	0.0500396	+	0.0288904i	0.0158239	+	0.00913593i
$11$	3.08127	−	3.08127i	0.929039	−	0.929039i	−0.0686049	−	0.997644i	$-0.521855\pi$
$11$	3.08127	−	3.08127i	0.929039	−	0.929039i	0.997644	+	0.0686049i	$0.0218548\pi$
$12$	−0.0199527	+	3.91530i	−0.00575984	+	1.13025i
$13$	−3.51566	+	0.800100i	−0.975068	+	0.221908i
$13$	−3.51566	+	0.800100i	−0.975068	+	0.221908i
$14$	−4.35226	+	3.29872i	−1.16319	+	0.881619i
$15$	−0.0468967	+	0.0123101i	−0.0121087	+	0.00317846i
$16$	−1.70553	−	2.95407i	−0.426383	−	0.738516i
$17$	4.58353			1.11167			0.555835	−	0.831293i	$-0.312399\pi$
$17$	4.58353			1.11167			0.555835	+	0.831293i	$0.312399\pi$
$18$	−4.33377	−	4.42303i	−1.02148	−	1.04252i
$19$	−0.978884	−	0.262291i	−0.224571	−	0.0601737i	0.144779	−	0.989464i	$-0.453753\pi$
$19$	−0.978884	−	0.262291i	−0.224571	−	0.0601737i	−0.369350	+	0.929290i	$0.620420\pi$
$20$	−0.0447452	+	0.0447452i	−0.0100053	+	0.0100053i
$21$	0.648252	−	4.53649i	0.141460	−	0.989944i
$22$	4.49725	+	7.78947i	0.958817	+	1.66072i
$23$	0.348171	−	0.603051i	0.0725988	−	0.125745i	−0.827441	−	0.561553i	$-0.810204\pi$
$23$	0.348171	−	0.603051i	0.0725988	−	0.125745i	0.900040	+	0.435808i	$0.143537\pi$
$24$	−0.898456	−	0.245655i	−0.183397	−	0.0501440i
$25$	4.32945	+	2.49961i	0.865890	+	0.499922i
$26$	0.282951	−	7.43686i	0.0554913	−	1.45849i
$27$	5.19555	+	0.0794361i	0.999883	+	0.0152875i
$28$	−2.25589	−	5.53904i	−0.426323	−	1.04678i
$29$	4.86476	+	2.80867i	0.903364	+	0.521557i	0.878290	−	0.478128i	$-0.158685\pi$
$29$	4.86476	+	2.80867i	0.903364	+	0.521557i	0.0250737	+	0.999686i	$0.492018\pi$
$30$	0.000510003	−	0.100078i	9.31135e−5	−	0.0182716i
$31$	−5.51345	+	5.51345i	−0.990245	+	0.990245i	−0.999953	−	0.00970778i	$-0.996910\pi$
$31$	−5.51345	+	5.51345i	−0.990245	+	0.990245i	0.00970778	+	0.999953i	$0.496910\pi$
$32$	7.83976	−	2.10066i	1.38589	−	0.371347i
$33$	−7.28032	−	1.99058i	−1.26734	−	0.346515i
$34$	−2.44866	+	9.13851i	−0.419941	+	1.56724i
$35$	0.0590248	−	0.0447367i	0.00997701	−	0.00756189i
$36$	5.90729	−	3.33076i	0.984548	−	0.555127i
$37$	−1.19724	−	1.19724i	−0.196825	−	0.196825i	0.601813	−	0.798637i	$-0.294445\pi$
$37$	−1.19724	−	1.19724i	−0.196825	−	0.196825i	−0.798637	+	0.601813i	$0.794445\pi$
$38$	1.04590	−	1.81155i	0.169667	−	0.293872i
$39$	4.22140	+	4.60215i	0.675965	+	0.736934i
$40$	−0.00752684	−	0.0130369i	−0.00119010	−	0.00206131i
$41$	7.38795	+	7.38795i	1.15380	+	1.15380i	0.985783	+	0.168021i	$0.0537376\pi$
$41$	7.38795	+	7.38795i	1.15380	+	1.15380i	0.168021	+	0.985783i	$0.446262\pi$
$42$	8.69842	+	3.71600i	1.34220	+	0.573391i
$43$		−	3.29833i		−	0.502991i	−0.967858	−	0.251496i	$-0.919078\pi$
$43$		−	3.29833i		−	0.502991i	0.967858	−	0.251496i	$-0.0809224\pi$
$44$	−9.51480	+	2.54948i	−1.43441	+	0.384349i
$45$	0.0587740	+	0.0599845i	0.00876152	+	0.00894196i
$46$	1.01634	+	1.01634i	0.149851	+	0.149851i
$47$	−6.82773	+	6.82773i	−0.995927	+	0.995927i	−0.999992	−	0.00406508i	$-0.998706\pi$
$47$	−6.82773	+	6.82773i	−0.995927	+	0.995927i	0.00406508	+	0.999992i	$0.498706\pi$
$48$	−2.98010	+	5.10147i	−0.430141	+	0.736334i
$49$	1.73127	+	6.78253i	0.247325	+	0.968933i
$50$	−7.29657	+	7.29657i	−1.03189	+	1.03189i
$51$	−3.93436	−	6.89543i	−0.550921	−	0.965554i
$52$	7.78685	+	2.40729i	1.07984	+	0.333831i
$53$	9.51169	−	5.49158i	1.30653	−	0.754326i	0.325016	−	0.945709i	$-0.394630\pi$
$53$	9.51169	−	5.49158i	1.30653	−	0.754326i	0.981516	+	0.191382i	$0.0612971\pi$
$54$	−2.93399	+	10.3163i	−0.399266	+	1.40387i
$55$	−0.0609911	−	0.105640i	−0.00822404	−	0.0142444i
$56$	1.41169	−	0.177328i	0.188646	−	0.0236965i
$57$	0.445655	+	1.69777i	0.0590285	+	0.224875i
$58$	−8.19875	+	8.19875i	−1.07655	+	1.07655i
$59$	3.80295	+	14.1928i	0.495102	+	1.84775i	0.529456	+	0.848338i	$0.322396\pi$
$59$	3.80295	+	14.1928i	0.495102	+	1.84775i	−0.0343532	+	0.999410i	$0.510937\pi$
$60$	0.105722	+	0.0289065i	0.0136487	+	0.00373181i
$61$	−6.31704	+	10.9414i	−0.808814	+	1.40091i	0.104871	+	0.994486i	$0.466557\pi$
$61$	−6.31704	+	10.9414i	−0.808814	+	1.40091i	−0.913686	+	0.406422i	$0.866776\pi$
$62$	−8.04712	−	13.9380i	−1.02199	−	1.77013i
$63$	−7.38111	+	2.91876i	−0.929933	+	0.367730i
$64$			9.93081i			1.24135i
$65$	−0.00383735	+	0.100858i	−0.000475964	+	0.0125098i
$66$	7.85812	−	13.4519i	0.967268	−	1.65581i
$67$	−7.85197	−	2.10393i	−0.959270	−	0.257036i	−0.254979	−	0.966947i	$-0.582069\pi$
$67$	−7.85197	−	2.10393i	−0.959270	−	0.257036i	−0.704292	+	0.709911i	$0.748735\pi$
$68$	−8.97307	−	5.18060i	−1.08814	−	0.628241i
$69$	−1.20609	−	0.00614629i	−0.145196	−	0.000739927i
$70$	0.0576621	+	0.141582i	0.00689193	+	0.0169222i
$71$	8.08749	−	2.16704i	0.959808	−	0.257180i	0.255289	−	0.966865i	$-0.417829\pi$
$71$	8.08749	−	2.16704i	0.959808	−	0.257180i	0.704519	+	0.709685i	$0.251163\pi$
$72$	0.401646	+	1.56249i	0.0473345	+	0.184142i
$73$	−2.19670	+	8.19820i	−0.257105	+	0.959527i	0.709803	+	0.704400i	$0.248784\pi$
$73$	−2.19670	+	8.19820i	−0.257105	+	0.959527i	−0.966908	+	0.255127i	$0.917883\pi$
$74$	3.02662	−	1.74742i	0.351837	−	0.203133i
$75$	0.0441258	−	8.65878i	0.00509520	−	0.999830i
$76$	1.61988	+	1.61988i	0.185813	+	0.185813i
$77$	11.4392	−	1.43692i	1.30362	−	0.163752i
$78$	−11.4308	+	5.95791i	−1.29429	+	0.674600i
$79$	4.15411			0.467373			0.233687	−	0.972312i	$-0.424921\pi$
$79$	4.15411			0.467373			0.233687	+	0.972312i	$0.424921\pi$
$80$	−0.0922326	+	0.0247136i	−0.0103119	+	0.00276307i
$81$	−4.34020	−	7.88433i	−0.482244	−	0.876037i
$82$	−18.6768	+	10.7830i	−2.06250	+	1.19079i
$83$	3.89830	−	14.5487i	0.427894	−	1.59692i	−0.329625	−	0.944112i	$-0.606922\pi$
$83$	3.89830	−	14.5487i	0.427894	−	1.59692i	0.757520	−	0.652812i	$-0.226411\pi$
$84$	−6.39651	+	8.14829i	−0.697917	+	0.889052i
$85$	0.0332083	−	0.123935i	0.00360195	−	0.0134427i
$86$	6.57613	+	1.76207i	0.709122	+	0.190009i
$87$	0.0495817	−	9.72940i	0.00531571	−	1.04310i
$88$		−	2.34335i		−	0.249802i
$89$	−1.72018	+	1.72018i	−0.182338	+	0.182338i	−0.792374	−	0.610036i	$-0.791155\pi$
$89$	−1.72018	+	1.72018i	−0.182338	+	0.182338i	0.610036	+	0.792374i	$0.291155\pi$
$90$	−0.150994	+	0.0851366i	−0.0159162	+	0.00897418i
$91$	−8.64427	−	4.03443i	−0.906166	−	0.422923i
$92$	−1.36321	+	0.787052i	−0.142125	+	0.0820559i
$93$	13.0270	+	3.56182i	1.35084	+	0.369344i
$94$	−9.96536	−	17.2605i	−1.02785	−	1.78029i
$95$	−0.0141843	+	0.0245680i	−0.00145528	+	0.00252062i
$96$	−9.88963	−	9.99095i	−1.00936	−	1.01970i
$97$	2.06369	−	2.06369i	0.209536	−	0.209536i	−0.594534	−	0.804070i	$-0.702664\pi$
$97$	2.06369	−	2.06369i	0.209536	−	0.209536i	0.804070	+	0.594534i	$0.202664\pi$
$98$	−14.4477	−	0.171665i	−1.45944	−	0.0173408i
$99$	3.25460	+	12.6611i	0.327100	+	1.27249i
$100$	−5.65044	−	9.78685i	−0.565044	−	0.978685i
$101$	2.72123			0.270773			0.135386	−	0.990793i	$-0.456772\pi$
$101$	2.72123			0.270773			0.135386	+	0.990793i	$0.456772\pi$
$102$	15.8498	−	4.16048i	1.56936	−	0.411949i
$103$	8.98163	−	5.18555i	0.884986	−	0.510947i	0.0126871	−	0.999920i	$-0.495961\pi$
$103$	8.98163	−	5.18555i	0.884986	−	0.510947i	0.872299	+	0.488972i	$0.162628\pi$
$104$	−1.03261	+	1.64109i	−0.101255	+	0.160922i
$105$	−0.117967	−	0.0503958i	−0.0115124	−	0.00491813i
$106$	5.86753	+	21.8979i	0.569905	+	2.12691i
$107$			2.65126i			0.256307i	0.991754	+	0.128153i	$0.0409050\pi$
$107$			2.65126i			0.256307i	−0.991754	+	0.128153i	$0.959095\pi$
$108$	−10.0814	−	6.02786i	−0.970085	−	0.580031i
$109$	18.3433	+	4.91508i	1.75697	+	0.470779i	0.986092	−	0.166202i	$-0.0531504\pi$
$109$	18.3433	+	4.91508i	1.75697	+	0.470779i	0.770879	+	0.636981i	$0.219817\pi$
$110$	0.243205	−	0.0651665i	0.0231887	−	0.00621338i
$111$	−0.773444	+	2.82879i	−0.0734121	+	0.268497i
$112$	1.23111	−	8.94046i	0.116329	−	0.844794i
$113$	−12.4657	+	7.19708i	−1.17267	+	0.677044i	−0.954309	−	0.298823i	$-0.903406\pi$
$113$	−12.4657	+	7.19708i	−1.17267	+	0.677044i	−0.218366	+	0.975867i	$0.570073\pi$
$114$	−3.62305	−	0.0184633i	−0.339330	−	0.00172925i
$115$	−0.0137835	−	0.0137835i	−0.00128532	−	0.00128532i
$116$	−6.34909	−	10.9969i	−0.589498	−	1.02104i
$117$	3.29992	−	10.3010i	0.305078	−	0.952327i
$118$	−30.3289			−2.79200
$119$	9.57687	+	7.43940i	0.877911	+	0.681969i
$120$	−0.0131518	+	0.0225138i	−0.00120059	+	0.00205522i
$121$		−	7.98849i		−	0.726227i
$122$	−18.4400	−	18.4400i	−1.66948	−	1.66948i
$123$	4.77279	−	17.4560i	0.430348	−	1.57395i
$124$	17.0252	−	4.56189i	1.52891	−	0.409670i
$125$	0.197926	−	0.197926i	0.0177030	−	0.0177030i
$126$	−1.87614	−	16.2756i	−0.167140	−	1.44994i
$127$	8.14166	−	4.70059i	0.722455	−	0.417110i	−0.0932003	−	0.995647i	$-0.529710\pi$
$127$	8.14166	−	4.70059i	0.722455	−	0.417110i	0.815656	+	0.578538i	$0.196376\pi$
$128$	−4.12026	−	1.10402i	−0.364183	−	0.0975825i
$129$	−4.96199	+	2.83119i	−0.436879	+	0.249272i
$130$	−0.199037	−	0.0615319i	−0.0174567	−	0.00539671i
$131$	6.86617	−	3.96419i	0.599900	−	0.346353i	−0.169102	−	0.985599i	$-0.554087\pi$
$131$	6.86617	−	3.96419i	0.599900	−	0.346353i	0.769002	+	0.639246i	$0.220753\pi$
$132$	12.0026	+	12.1256i	1.04470	+	1.05540i
$133$	−1.61957	−	2.13683i	−0.140435	−	0.185287i
$134$	8.38951	−	14.5311i	0.724743	−	1.25529i
$135$	0.0397904	−	0.139908i	0.00342461	−	0.0120414i
$136$	1.74292	−	1.74292i	0.149454	−	0.149454i
$137$	−20.9669	−	5.61805i	−1.79132	−	0.479983i	−0.798750	−	0.601663i	$-0.794505\pi$
$137$	−20.9669	−	5.61805i	−1.79132	−	0.479983i	−0.992569	+	0.121681i	$0.961172\pi$
$138$	0.656581	−	2.40138i	0.0558919	−	0.204419i
$139$	−10.4056	−	18.0230i	−0.882591	−	1.52869i	−0.848450	−	0.529275i	$-0.822464\pi$
$139$	−10.4056	−	18.0230i	−0.882591	−	1.52869i	−0.0341408	−	0.999417i	$-0.510869\pi$
$140$	−0.166116	+	0.0208664i	−0.0140393	+	0.00176353i
$141$	16.1323	+	4.41087i	1.35859	+	0.371463i
$142$			17.2823i			1.45030i
$143$	−8.36737	+	13.2980i	−0.699715	+	1.11204i
$144$	10.2327	+	0.104295i	0.852721	+	0.00869128i
$145$	0.111190	−	0.111190i	0.00923386	−	0.00923386i
$146$	−15.1718	−	8.75945i	−1.25563	−	0.724937i
$147$	8.71752	−	8.42644i	0.719009	−	0.695001i
$148$	0.990609	+	3.69700i	0.0814275	+	0.303892i
$149$	−15.4335	−	15.4335i	−1.26436	−	1.26436i	−0.948957	−	0.315405i	$-0.897860\pi$
$149$	−15.4335	−	15.4335i	−1.26436	−	1.26436i	−0.315405	−	0.948957i	$-0.602140\pi$
$150$	17.2401	+	4.71376i	1.40765	+	0.384877i
$151$	3.21394	−	0.861172i	0.261547	−	0.0700812i	−0.125663	−	0.992073i	$-0.540106\pi$
$151$	3.21394	−	0.861172i	0.261547	−	0.0700812i	0.387209	+	0.921992i	$0.373439\pi$
$152$	−0.471964	+	0.272489i	−0.0382814	+	0.0221018i
$153$	−6.99630	+	11.8377i	−0.565618	+	0.957019i
$154$	−3.24627	+	23.5748i	−0.261592	+	1.89971i
$155$	0.109134	+	0.189025i	0.00876584	+	0.0151829i
$156$	−3.06249	−	13.7808i	−0.245195	−	1.10335i
$157$	−1.71198			−0.136631			−0.0683155	−	0.997664i	$-0.521762\pi$
$157$	−1.71198			−0.136631			−0.0683155	+	0.997664i	$0.521762\pi$
$158$	−2.21925	+	8.28234i	−0.176554	+	0.658908i
$159$	−16.4260	−	9.59552i	−1.30267	−	0.760974i
$160$		−	0.227201i		−	0.0179618i
$161$	1.70627	−	0.694913i	0.134473	−	0.0547668i
$162$	18.0382	−	4.44132i	1.41722	−	0.348943i
$163$	−4.22168	+	15.7555i	−0.330668	+	1.23407i	0.577822	+	0.816163i	$0.303903\pi$
$163$	−4.22168	+	15.7555i	−0.330668	+	1.23407i	−0.908490	+	0.417906i	$0.862764\pi$
$164$	−6.11288	−	22.8136i	−0.477336	−	1.78144i
$165$	−0.106571	+	0.182433i	−0.00829652	+	0.0142024i
$166$	26.9242	+	15.5447i	2.08972	+	1.20650i
$167$	1.57731	−	1.57731i	0.122056	−	0.122056i	−0.643440	−	0.765496i	$-0.722494\pi$
$167$	1.57731	−	1.57731i	0.122056	−	0.122056i	0.765496	+	0.643440i	$0.222494\pi$
$168$	−1.47853	−	1.97153i	−0.114071	−	0.152107i
$169$	11.7197	−	5.62575i	0.901514	−	0.432750i
$170$	0.229358	+	0.132420i	0.0175909	+	0.0101561i
$171$	2.17158	−	2.12776i	0.166065	−	0.162714i
$172$	−3.72799	+	6.45707i	−0.284257	+	0.492347i
$173$	−5.90944	+	10.2355i	−0.449287	+	0.778187i	−0.998340	−	0.0576003i	$-0.981655\pi$
$173$	−5.90944	+	10.2355i	−0.449287	+	0.778187i	0.549053	+	0.835787i	$0.314988\pi$
$174$	19.3717	+	5.29659i	1.46857	+	0.401533i
$175$	4.98895	+	12.2497i	0.377129	+	0.925991i
$176$	−14.3575	−	3.84708i	−1.08224	−	0.289984i
$177$	18.0872	−	17.9038i	1.35952	−	1.34573i
$178$	−2.51067	−	4.34861i	−0.188183	−	0.325942i
$179$	4.79989	−	8.31366i	0.358761	−	0.621392i	−0.628993	−	0.777411i	$-0.716533\pi$
$179$	4.79989	−	8.31366i	0.358761	−	0.621392i	0.987754	+	0.156019i	$0.0498660\pi$
$180$	−0.0472622	−	0.183861i	−0.00352272	−	0.0137042i
$181$		−	4.87226i		−	0.362152i	−0.983469	−	0.181076i	$-0.942042\pi$
$181$		−	4.87226i		−	0.362152i	0.983469	−	0.181076i	$-0.0579580\pi$
$182$	12.6618	−	15.0794i	0.938552	−	1.11776i
$183$	21.8826	+	0.111515i	1.61761	+	0.00824344i
$184$	−0.0969194	−	0.361708i	−0.00714499	−	0.0266655i
$185$	−0.0410466	+	0.0236983i	−0.00301781	+	0.00174233i
$186$	−14.0609	+	24.0700i	−1.03099	+	1.76490i
$187$	14.1231	−	14.1231i	1.03278	−	1.03278i
$188$	21.0836	−	5.64934i	1.53768	−	0.412021i
$189$	10.7267	+	8.59872i	0.780252	+	0.625465i
$190$	−0.0414052	−	0.0414052i	−0.00300385	−	0.00300385i
$191$	3.39796	+	1.96181i	0.245868	+	0.141952i	0.617871	−	0.786280i	$-0.287995\pi$
$191$	3.39796	+	1.96181i	0.245868	+	0.141952i	−0.372003	+	0.928232i	$0.621329\pi$
$192$	14.9399	−	8.52431i	1.07819	−	0.615189i
$193$	2.10861	−	7.86945i	0.151781	−	0.566455i	−0.847578	−	0.530670i	$-0.821940\pi$
$193$	2.10861	−	7.86945i	0.151781	−	0.566455i	0.999360	−	0.0357848i	$-0.0113931\pi$
$194$	3.01205	+	5.21702i	0.216252	+	0.374560i
$195$	0.155023	−	0.0808003i	0.0111015	−	0.00578623i
$196$	4.27679	−	15.2348i	0.305485	−	1.08820i
$197$	−1.45607	+	5.43411i	−0.103740	+	0.387165i	−0.998199	−	0.0599858i	$-0.980894\pi$
$197$	−1.45607	+	5.43411i	−0.103740	+	0.387165i	0.894459	+	0.447150i	$0.147561\pi$
$198$	−26.9821	−	0.275012i	−1.91753	−	0.0195443i
$199$			13.5336i			0.959372i	0.877440	+	0.479686i	$0.159249\pi$
$199$			13.5336i			0.959372i	−0.877440	+	0.479686i	$0.840751\pi$
$200$	2.59679	−	0.695808i	0.183621	−	0.0492011i
$201$	3.57476	+	13.6184i	0.252144	+	0.960568i
$202$	−1.45376	+	5.42552i	−0.102287	+	0.381738i
$203$	5.60581	+	13.7643i	0.393451	+	0.966067i
$204$	−0.0914536	+	17.9459i	−0.00640303	+	1.25646i
$205$	0.253292	−	0.146238i	0.0176907	−	0.0102137i
$206$	5.54055	+	20.6776i	0.386028	+	1.44068i
$207$	1.02602	+	1.81970i	0.0713134	+	0.126478i
$208$	8.35961	+	9.02089i	0.579634	+	0.625486i
$209$	−3.82440	+	2.20802i	−0.264539	+	0.152732i
$210$	0.163499	−	0.208276i	0.0112825	−	0.0143724i
$211$	13.9971			0.963601			0.481800	−	0.876281i	$-0.339983\pi$
$211$	13.9971			0.963601			0.481800	+	0.876281i	$0.339983\pi$
$212$	−24.8278			−1.70518
$213$	−10.2021	−	10.3067i	−0.699039	−	0.706200i
$214$	−5.28601	−	1.41638i	−0.361344	−	0.0968218i
$215$	−0.0891845	−	0.0238969i	−0.00608233	−	0.00162976i
$216$	2.00584	−	1.94543i	0.136480	−	0.132370i
$217$	−20.4686	+	2.57113i	−1.38950	+	0.174540i
$218$	−19.5991	+	33.9466i	−1.32742	+	2.29916i
$219$	14.2189	−	3.73239i	0.960825	−	0.252211i
$220$			0.275744i			0.0185907i
$221$	−16.1141	+	3.66728i	−1.08395	+	0.246688i
$222$	−5.22677	−	3.05330i	−0.350798	−	0.204924i
$223$	−3.72448	−	13.9000i	−0.249410	−	0.930810i	−0.971115	−	0.238610i	$-0.923308\pi$
$223$	−3.72448	−	13.9000i	−0.249410	−	0.930810i	0.721706	−	0.692200i	$-0.243358\pi$
$224$	19.7900	+	8.33536i	1.32227	+	0.556930i
$225$	−13.0641	+	7.36606i	−0.870940	+	0.491071i
$226$	−7.68979	−	28.6987i	−0.511517	−	1.90901i
$227$	1.04968	−	3.91747i	0.0696700	−	0.260012i	−0.922302	−	0.386470i	$-0.873694\pi$
$227$	1.04968	−	3.91747i	0.0696700	−	0.260012i	0.991972	+	0.126458i	$0.0403610\pi$
$228$	1.04648	−	3.82739i	0.0693049	−	0.253475i
$229$	−0.828653	+	3.09257i	−0.0547589	+	0.204363i	−0.987885	−	0.155185i	$-0.950403\pi$
$229$	−0.828653	+	3.09257i	−0.0547589	+	0.204363i	0.933126	+	0.359548i	$0.117069\pi$
$230$	0.0348447	−	0.0201176i	0.00229759	−	0.00132651i
$231$	−11.9807	−	15.9756i	−0.788274	−	1.05112i
$232$	2.91787	−	0.781841i	0.191568	−	0.0513304i
$233$	1.66608	−	2.88573i	0.109148	−	0.189050i	−0.806277	−	0.591538i	$-0.798521\pi$
$233$	1.66608	−	2.88573i	0.109148	−	0.189050i	0.915425	+	0.402488i	$0.131854\pi$
$234$	18.7749	+	12.0824i	1.22736	+	0.789851i
$235$	0.135149	+	0.234085i	0.00881614	+	0.0152700i
$236$	8.59670	−	32.0833i	0.559597	−	2.08845i
$237$	−3.56576	−	6.24941i	−0.231621	−	0.405943i
$238$	−19.9487	+	15.1198i	−1.29308	+	0.980068i
$239$	−5.76821	+	1.54559i	−0.373115	+	0.0999758i	−0.440503	−	0.897751i	$-0.645200\pi$
$239$	−5.76821	+	1.54559i	−0.373115	+	0.0999758i	0.0673886	+	0.997727i	$0.478533\pi$
$240$	0.116349	+	0.117541i	0.00751028	+	0.00758722i
$241$	3.69217	−	13.7794i	0.237834	−	0.887607i	−0.739017	−	0.673686i	$-0.764710\pi$
$241$	3.69217	−	13.7794i	0.237834	−	0.887607i	0.976851	−	0.213921i	$-0.0686234\pi$
$242$	15.9272	+	4.26769i	1.02384	+	0.274338i
$243$	−8.13564	+	13.2970i	−0.521902	+	0.853006i
$244$	24.7335	−	14.2799i	1.58340	−	0.914175i
$245$	0.195938	+	0.00232810i	0.0125180	+	0.000148737i
$246$	32.2535	+	18.8414i	2.05641	+	1.20128i
$247$	3.65128	+	0.138921i	0.232325	+	0.00883932i
$248$			4.19305i			0.266259i
$249$	−25.2331	+	6.62356i	−1.59908	+	0.419751i
$250$	0.288881	+	0.500356i	0.0182704	+	0.0316453i
$251$	9.50191	−	16.4578i	0.599755	−	1.03881i	−0.393101	−	0.919495i	$-0.628598\pi$
$251$	9.50191	−	16.4578i	0.599755	−	1.03881i	0.992857	−	0.119312i	$-0.0380688\pi$
$252$	17.7488	+	2.62862i	1.11807	+	0.165587i
$253$	−0.785353	−	2.93098i	−0.0493747	−	0.184269i
$254$	5.02239	+	18.7438i	0.315133	+	1.17609i
$255$	−0.214952	+	0.0564239i	−0.0134608	+	0.00353340i
$256$	−5.52848	+	9.57561i	−0.345530	+	0.598476i
$257$	5.82305	−	10.0858i	0.363232	−	0.629136i	−0.625259	−	0.780417i	$-0.715007\pi$
$257$	5.82305	−	10.0858i	0.363232	−	0.629136i	0.988491	+	0.151282i	$0.0483400\pi$
$258$	−2.99391	−	11.4056i	−0.186393	−	0.710081i
$259$	−0.558318	−	4.44473i	−0.0346922	−	0.276182i
$260$	0.121508	−	0.193109i	0.00753562	−	0.0119761i
$261$	−14.6794	+	8.27684i	−0.908632	+	0.512323i
$262$	4.23557	+	15.8074i	0.261675	+	0.976583i
$263$		−	6.25540i		−	0.385725i	−0.981226	−	0.192862i	$-0.938223\pi$
$263$		−	6.25540i		−	0.385725i	0.981226	−	0.192862i	$-0.0617771\pi$
$264$	−3.52532	+	2.01146i	−0.216968	+	0.123797i
$265$	−0.0795746	−	0.296976i	−0.00488823	−	0.0182431i
$266$	5.12558	−	2.08750i	0.314270	−	0.127993i
$267$	4.06437	+	1.11128i	0.248736	+	0.0680090i
$268$	12.9936	+	12.9936i	0.793712	+	0.793712i
$269$		−	25.2129i		−	1.53726i	−0.639695	−	0.768629i	$-0.720939\pi$
$269$		−	25.2129i		−	1.53726i	0.639695	−	0.768629i	$-0.279061\pi$
$270$	0.257688	+	0.154076i	0.0156824	+	0.00937677i
$271$	−10.7420	−	10.7420i	−0.652530	−	0.652530i	0.301071	−	0.953602i	$-0.402656\pi$
$271$	−10.7420	−	10.7420i	−0.652530	−	0.652530i	−0.953602	+	0.301071i	$0.902656\pi$
$272$	−7.81735	−	13.5400i	−0.473996	−	0.820986i
$273$	1.35061	+	16.4674i	0.0817429	+	0.996653i
$274$	22.4022	−	38.8018i	1.35337	−	2.34410i
$275$	21.0422	−	5.63824i	1.26889	−	0.339999i
$276$	2.35418	+	1.37523i	0.141705	+	0.0827791i
$277$	−5.48879	+	3.16895i	−0.329789	+	0.190404i	−0.655748	−	0.754980i	$-0.727646\pi$
$277$	−5.48879	+	3.16895i	−0.329789	+	0.190404i	0.325958	+	0.945384i	$0.394313\pi$
$278$	41.4928	−	11.1180i	2.48857	−	0.666811i
$279$	−5.82359	−	22.6551i	−0.348649	−	1.35632i
$280$	0.00543312	−	0.0394560i	0.000324691	−	0.00235794i
$281$	9.64710	+	2.58493i	0.575498	+	0.154204i	0.534817	−	0.844968i	$-0.320381\pi$
$281$	9.64710	+	2.58493i	0.575498	+	0.154204i	0.0406810	+	0.999172i	$0.487047\pi$
$282$	−17.4126	+	29.8077i	−1.03691	+	1.77503i
$283$	6.13068	−	3.53955i	0.364431	−	0.210404i	−0.306592	−	0.951841i	$-0.599189\pi$
$283$	6.13068	−	3.53955i	0.364431	−	0.210404i	0.671023	+	0.741437i	$0.265855\pi$
$284$	−18.2820	−	4.89865i	−1.08484	−	0.290682i
$285$	0.0491353		0.000250397i	0.00291052		1.48322e-5i
$286$	−22.0431	−	23.7868i	−1.30344	−	1.40655i
$287$	3.44528	+	27.4276i	0.203369	+	1.61900i
$288$	−6.54135	+	23.4538i	−0.385453	+	1.38203i
$289$	4.00874			0.235808
$290$	0.162287	+	0.281089i	0.00952983	+	0.0165061i
$291$	−4.87602	−	1.33319i	−0.285837	−	0.0781532i
$292$	13.5666	−	13.5666i	0.793924	−	0.793924i
$293$	−1.01983	−	0.273262i	−0.0595790	−	0.0159641i	0.228906	−	0.973448i	$-0.426485\pi$
$293$	−1.01983	−	0.273262i	−0.0595790	−	0.0159641i	−0.288485	+	0.957484i	$0.593152\pi$
$294$	12.1432	+	21.8824i	0.708208	+	1.27621i
$295$	0.411316			0.0239478
$296$	−0.910514			−0.0529226
$297$	16.2537	−	15.7641i	0.943133	−	0.914728i
$298$	39.0159	−	22.5259i	2.26013	−	1.30489i
$299$	−0.741551	+	2.39869i	−0.0428850	+	0.138720i
$300$	−9.87311	+	16.9012i	−0.570024	+	0.975793i
$301$	5.35343	−	6.89157i	0.308567	−	0.397224i
$302$			6.86793i			0.395205i
$303$	−2.33583	−	4.09381i	−0.134190	−	0.235183i
$304$	0.894691	+	3.33903i	0.0513140	+	0.191507i
$305$	0.250081	+	0.250081i	0.0143196	+	0.0143196i
$306$	−19.8640	−	20.2731i	−1.13555	−	1.15893i
$307$	8.37484	+	8.37484i	0.477977	+	0.477977i	0.904484	−	0.426507i	$-0.140256\pi$
$307$	8.37484	+	8.37484i	0.477977	+	0.477977i	−0.426507	+	0.904484i	$0.640256\pi$
$308$	−24.0183	−	10.1163i	−1.36857	−	0.576429i
$309$	−15.5107	−	9.06079i	−0.882371	−	0.515450i
$310$	−0.435176	+	0.116605i	−0.0247164	+	0.00662273i
$311$	7.82856			0.443917			0.221958	−	0.975056i	$-0.428755\pi$
$311$	7.82856			0.443917			0.221958	+	0.975056i	$0.428755\pi$
$312$	3.35521	+	0.144783i	0.189951	+	0.00819671i
$313$	−11.9147			−0.673459			−0.336730	−	0.941601i	$-0.609321\pi$
$313$	−11.9147			−0.673459			−0.336730	+	0.941601i	$0.609321\pi$
$314$	0.914591	−	3.41330i	0.0516134	−	0.192624i
$315$	0.0254440	+	0.220727i	0.00143360	+	0.0124365i
$316$	−8.13240	−	4.69524i	−0.457483	−	0.264128i
$317$	4.01087	+	4.01087i	0.225273	+	0.225273i	0.810715	−	0.585442i	$-0.199079\pi$
$317$	4.01087	+	4.01087i	0.225273	+	0.225273i	−0.585442	+	0.810715i	$0.699079\pi$
$318$	27.9066	−	27.6236i	1.56492	−	1.54905i
$319$	23.6440	−	6.33538i	1.32381	−	0.354713i
$320$	0.268522	+	0.0719502i	0.0150108	+	0.00402214i
$321$	3.98854	−	2.27576i	0.222618	−	0.127021i
$322$	0.473959	+	3.77315i	0.0264127	+	0.210270i
$323$	−4.48674	−	1.20222i	−0.249649	−	0.0668932i
$324$	−0.414681	+	20.3406i	−0.0230378	+	1.13003i
$325$	−17.2208	−	5.32377i	−0.955238	−	0.295310i
$326$	−29.1576	−	16.8342i	−1.61489	−	0.932358i
$327$	−8.35114	−	31.8145i	−0.461819	−	1.75935i
$328$	5.61863			0.310237
$329$	−25.3478	+	3.18403i	−1.39747	+	0.175541i
$330$	−0.306796	−	0.309939i	−0.0168885	−	0.0170616i
$331$	−3.68586	−	13.7558i	−0.202593	−	0.756088i	−0.990170	−	0.139871i	$-0.955331\pi$
$331$	−3.68586	−	13.7558i	−0.202593	−	0.756088i	0.787577	−	0.616217i	$-0.211335\pi$
$332$	−24.0755	+	24.0755i	−1.32131	+	1.32131i
$333$	4.91952	−	1.26459i	0.269588	−	0.0692988i
$334$	2.30215	+	3.98744i	0.125968	+	0.218183i
$335$	−0.113777	+	0.197068i	−0.00621632	+	0.0107670i
$336$	−14.5067	+	5.82215i	−0.791406	+	0.317624i
$337$	−23.0684	−	13.3186i	−1.25662	−	0.725508i	−0.284202	−	0.958765i	$-0.591729\pi$
$337$	−23.0684	−	13.3186i	−1.25662	−	0.725508i	−0.972415	+	0.233256i	$0.925062\pi$
$338$	4.95547	+	26.3718i	0.269542	+	1.43444i
$339$	21.5274	+	12.5756i	1.16921	+	0.683011i
$340$	−0.205091	+	0.205091i	−0.0111226	+	0.0111226i
$341$			33.9769i			1.83995i
$342$	3.08214	+	5.46634i	0.166663	+	0.295586i
$343$	−7.39120	+	16.9815i	−0.399087	+	0.916913i
$344$	−1.25421	−	1.25421i	−0.0676226	−	0.0676226i
$345$	−0.00890446	+	0.0325671i	−0.000479400	+	0.00175336i
$346$	−17.2502	−	17.2502i	−0.927375	−	0.927375i
$347$	−21.4944	−	12.4098i	−1.15388	−	0.666192i	−0.204049	−	0.978961i	$-0.565410\pi$
$347$	−21.4944	−	12.4098i	−1.15388	−	0.666192i	−0.949829	+	0.312768i	$0.898744\pi$
$348$	−11.0939	+	18.9910i	−0.594694	+	1.01802i
$349$	−31.5685	+	8.45874i	−1.68982	+	0.452786i	−0.970344	−	0.241730i	$-0.922285\pi$
$349$	−31.5685	+	8.45874i	−1.68982	+	0.452786i	−0.719477	+	0.694516i	$0.755619\pi$
$350$	−27.0884	+	3.40267i	−1.44794	+	0.181880i
$351$	−18.3293	+	3.87768i	−0.978346	+	0.206975i
$352$	17.6837	−	30.6291i	0.942547	−	1.63254i
$353$	−3.75528	−	3.75528i	−0.199873	−	0.199873i	0.600072	−	0.799946i	$-0.295138\pi$
$353$	−3.75528	−	3.75528i	−0.199873	−	0.199873i	−0.799946	+	0.600072i	$0.795138\pi$
$354$	26.0334	+	45.6266i	1.38366	+	2.42503i
$355$		−	0.234380i		−	0.0124396i
$356$	5.31181	−	1.42330i	0.281525	−	0.0754345i
$357$	2.97128	−	20.7931i	0.157257	−	1.10049i
$358$	14.0113	+	14.0113i	0.740520	+	0.740520i
$359$	4.22453	+	15.7661i	0.222962	+	0.832105i	0.983211	+	0.182473i	$0.0584104\pi$
$359$	4.22453	+	15.7661i	0.222962	+	0.832105i	−0.760249	+	0.649632i	$0.774923\pi$
$360$	0.0451587		0.000460275i	0.00238007		2.42586e-5i
$361$	−15.5651	−	8.98650i	−0.819214	−	0.472973i
$362$	9.71417	+	2.60290i	0.510566	+	0.136806i
$363$	−12.0178	+	6.85709i	−0.630773	+	0.359904i
$364$	12.3627	+	17.6684i	0.647982	+	0.926077i
$365$	0.205758	+	0.118794i	0.0107699	+	0.00621798i
$366$	−11.9127	+	43.5693i	−0.622685	+	2.27741i
$367$	14.3288			0.747959			0.373980	−	0.927437i	$-0.377993\pi$
$367$	14.3288			0.747959			0.373980	+	0.927437i	$0.377993\pi$
$368$	−2.37527			−0.123819
$369$	−30.3575	+	7.80354i	−1.58035	+	0.406236i
$370$	−0.0253206	−	0.0944979i	−0.00131636	−	0.00491271i
$371$	28.7871	+	3.96400i	1.49455	+	0.205801i
$372$	−21.4768	−	21.6968i	−1.11352	−	1.12493i
$373$	−13.7473			−0.711807			−0.355903	−	0.934523i	$-0.615827\pi$
$373$	−13.7473			−0.711807			−0.355903	+	0.934523i	$0.615827\pi$
$374$	20.6133	+	35.7032i	1.06589	+	1.84617i
$375$	−0.467652	−	0.127865i	−0.0241494	−	0.00660290i
$376$			5.19257i			0.267787i
$377$	−19.3501	−	5.98203i	−0.996578	−	0.308090i
$378$	−22.8744	+	16.7929i	−1.17653	+	0.863734i
$379$	8.69371	+	2.32947i	0.446566	+	0.119657i	0.475092	−	0.879936i	$-0.342415\pi$
$379$	8.69371	+	2.32947i	0.446566	+	0.119657i	−0.0285263	+	0.999593i	$0.509081\pi$
$380$	0.0555366	−	0.0320641i	0.00284897	−	0.00164485i
$381$	−14.0601	−	8.21342i	−0.720321	−	0.420786i
$382$	−5.72671	+	5.72671i	−0.293004	+	0.293004i
$383$	−1.42909	−	1.42909i	−0.0730231	−	0.0730231i	0.669652	−	0.742675i	$-0.266443\pi$
$383$	−1.42909	−	1.42909i	−0.0730231	−	0.0730231i	−0.742675	+	0.669652i	$0.766443\pi$
$384$	1.87583	+	7.14615i	0.0957254	+	0.364676i
$385$	0.0440254	−	0.319718i	0.00224374	−	0.0162943i
$386$	14.5634	+	8.40819i	0.741258	+	0.427965i
$387$	8.51845	+	5.03458i	0.433017	+	0.255922i
$388$	−6.37256	+	1.70752i	−0.323518	+	0.0866864i
$389$	−0.777419	+	1.34653i	−0.0394167	+	0.0682717i	−0.885061	−	0.465476i	$-0.845883\pi$
$389$	−0.777419	+	1.34653i	−0.0394167	+	0.0682717i	0.845644	+	0.533747i	$0.179217\pi$
$390$	0.0782793	+	0.352247i	0.00396382	+	0.0178367i
$391$	1.59585	−	2.76410i	0.0807058	−	0.139787i
$392$	3.23743	+	1.92077i	0.163515	+	0.0970136i
$393$	−11.8574	−	6.92669i	−0.598127	−	0.349405i
$394$	−10.0565	−	5.80613i	−0.506640	−	0.292509i
$395$	0.0300971	−	0.112324i	0.00151435	−	0.00565163i
$396$	7.93897	−	28.4650i	0.398948	−	1.43042i
$397$	−6.61507	+	24.6878i	−0.332001	+	1.23904i	0.575083	+	0.818095i	$0.304970\pi$
$397$	−6.61507	+	24.6878i	−0.332001	+	1.23904i	−0.907084	+	0.420949i	$0.861697\pi$
$398$	−26.9829	−	7.23006i	−1.35253	−	0.362410i
$399$	−1.82445	+	4.27067i	−0.0913365	+	0.213801i
$400$		−	17.0526i		−	0.852632i
$401$	2.13442	+	7.96576i	0.106588	+	0.397791i	0.998520	−	0.0543771i	$-0.0173173\pi$
$401$	2.13442	+	7.96576i	0.106588	+	0.397791i	−0.891933	+	0.452168i	$0.850651\pi$
$402$	−29.0617	−	0.148101i	−1.44947	−	0.00738659i
$403$	14.9721	−	23.7947i	0.745813	−	1.18530i
$404$	−5.32730	−	3.07572i	−0.265043	−	0.153023i
$405$	−0.244632	+	0.0602326i	−0.0121559	+	0.00299298i
$406$	−30.4377	+	3.82339i	−1.51060	+	0.189752i
$407$	−7.37804			−0.365716
$408$	−4.11810	−	1.12596i	−0.203876	−	0.0557436i
$409$	0.0773258	+	0.288584i	0.00382352	+	0.0142696i	0.967811	−	0.251677i	$-0.0809821\pi$
$409$	0.0773258	+	0.288584i	0.00382352	+	0.0142696i	−0.963988	+	0.265947i	$0.914315\pi$
$410$	0.156249	+	0.583130i	0.00771661	+	0.0287988i
$411$	9.54556	+	36.3648i	0.470848	+	1.79374i
$412$	−23.4442			−1.15501
$413$	−15.0900	+	35.8271i	−0.742532	+	1.76294i
$414$	−4.17621	+	1.07351i	−0.205249	+	0.0527603i
$415$	−0.365141	−	0.210815i	−0.0179241	−	0.0103485i
$416$	−25.8812	+	13.6578i	−1.26893	+	0.669628i
$417$	−18.1819	+	31.1245i	−0.890370	+	1.52417i
$418$	−2.35918	−	8.80457i	−0.115391	−	0.430646i
$419$		−	5.52463i		−	0.269896i	−0.990853	−	0.134948i	$-0.956913\pi$
$419$		−	5.52463i		−	0.269896i	0.990853	−	0.134948i	$-0.0430867\pi$
$420$	0.173980	+	0.231993i	0.00848936	+	0.0113201i
$421$	14.2007	+	3.80507i	0.692101	+	0.185448i	0.587690	−	0.809086i	$-0.300038\pi$
$421$	14.2007	+	3.80507i	0.692101	+	0.185448i	0.104411	+	0.994534i	$0.466704\pi$
$422$	−7.47767	+	27.9071i	−0.364007	+	1.35849i
$423$	−7.21180	−	28.0555i	−0.350650	−	1.36411i
$424$	1.52867	−	5.70509i	0.0742389	−	0.277063i
$425$	19.8442	+	11.4570i	0.962583	+	0.555747i
$426$	25.9994	−	14.8346i	1.25968	−	0.718740i
$427$	−30.9576	+	12.6081i	−1.49815	+	0.610151i
$428$	2.99663	−	5.19031i	0.144847	−	0.250883i
$429$	27.1878	+	1.17320i	1.31264	+	0.0566424i
$430$	0.0952900	−	0.165047i	0.00459529	−	0.00795928i
$431$	34.6537	−	9.28542i	1.66921	−	0.447263i	0.704311	−	0.709892i	$-0.251256\pi$
$431$	34.6537	−	9.28542i	1.66921	−	0.447263i	0.964897	+	0.262629i	$0.0845895\pi$
$432$	−8.62650	−	15.4835i	−0.415043	−	0.744948i
$433$	2.24779	+	1.29776i	0.108022	+	0.0623665i	0.553038	−	0.833156i	$-0.313469\pi$
$433$	2.24779	+	1.29776i	0.108022	+	0.0623665i	−0.445016	+	0.895523i	$0.646802\pi$
$434$	5.80868	−	42.1833i	0.278825	−	2.02486i
$435$	−0.262717	−	0.0718316i	−0.0125963	−	0.00344406i
$436$	−30.3550	−	30.3550i	−1.45374	−	1.45374i
$437$	−0.498994	+	0.498994i	−0.0238701	+	0.0238701i
$438$	−0.154631	+	30.3432i	−0.00738856	+	1.44986i
$439$	−22.1932	+	12.8133i	−1.05923	+	0.611544i	−0.925218	−	0.379436i	$-0.876118\pi$
$439$	−22.1932	+	12.8133i	−1.05923	+	0.611544i	−0.134007	+	0.990980i	$0.542785\pi$
$440$	−0.0633624	−	0.0169779i	−0.00302068	−	0.000809390i
$441$	−20.1595	−	5.88158i	−0.959978	−	0.280075i
$442$	1.29692	−	34.0870i	0.0616880	−	1.62136i
$443$		−	20.4507i		−	0.971641i	−0.874059	−	0.485820i	$-0.838521\pi$
$443$		−	20.4507i		−	0.971641i	0.874059	−	0.485820i	$-0.161479\pi$
$444$	4.71144	−	4.66366i	0.223595	−	0.221328i
$445$	0.0340494	+	0.0589753i	0.00161410	+	0.00279570i
$446$	29.7031			1.40648
$447$	−9.97041	+	36.4657i	−0.471584	+	1.72477i
$448$	−16.1184	+	20.7495i	−0.761524	+	0.980324i
$449$	5.91107	+	22.0604i	0.278961	+	1.04110i	0.953140	+	0.302528i	$0.0978306\pi$
$449$	5.91107	+	22.0604i	0.278961	+	1.04110i	−0.674180	+	0.738567i	$0.735503\pi$
$450$	−7.70702	−	29.9820i	−0.363312	−	1.41337i
$451$	45.5286			2.14386
$452$	32.5384			1.53048
$453$	−4.05429	−	4.09582i	−0.190487	−	0.192439i
$454$	7.24978	+	4.18566i	0.340249	+	0.196443i
$455$	−0.171717	+	0.204505i	−0.00805022	+	0.00958732i
$456$	0.815051	+	0.476124i	0.0381682	+	0.0222966i
$457$	−6.56859	−	1.76005i	−0.307266	−	0.0823316i	0.101891	−	0.994796i	$-0.467511\pi$
$457$	−6.56859	−	1.76005i	−0.307266	−	0.0823316i	−0.409157	+	0.912464i	$0.634177\pi$
$458$	−5.72320	−	3.30429i	−0.267428	−	0.154399i
$459$	23.8139	+	0.364097i	1.11154	+	0.0169946i
$460$	0.0114046	+	0.0425626i	0.000531743	+	0.00198449i
$461$	21.0912	+	21.0912i	0.982316	+	0.982316i	0.999846	−	0.0175307i	$-0.00558048\pi$
$461$	21.0912	+	21.0912i	0.982316	+	0.982316i	−0.0175307	+	0.999846i	$0.505580\pi$
$462$	38.2522	−	15.3522i	1.77965	−	0.714249i
$463$	3.07411	−	0.823704i	0.142866	−	0.0382808i	−0.186677	−	0.982421i	$-0.559772\pi$
$463$	3.07411	−	0.823704i	0.142866	−	0.0382808i	0.329543	+	0.944140i	$0.393105\pi$
$464$		−	19.1611i		−	0.889532i
$465$	0.190691	−	0.326434i	0.00884310	−	0.0151380i
$466$	4.86342	+	4.86342i	0.225293	+	0.225293i
$467$	10.9273	−	18.9267i	0.505657	−	0.875824i	−0.494321	−	0.869279i	$-0.664583\pi$
$467$	10.9273	−	18.9267i	0.505657	−	0.875824i	0.999979	−	0.00654466i	$-0.00208324\pi$
$468$	−18.1030	+	16.4362i	−0.836813	+	0.759765i
$469$	−12.9912	−	17.1403i	−0.599876	−	0.791465i
$470$	−0.538912	+	0.144401i	−0.0248582	+	0.00666072i
$471$	1.46951	+	2.57549i	0.0677116	+	0.118673i
$472$	6.84300	+	3.95081i	0.314975	+	0.181851i
$473$	−10.1631	−	10.1631i	−0.467298	−	0.467298i
$474$	14.3648	−	3.77070i	0.659799	−	0.173194i
$475$	−3.58240	−	3.58240i	−0.164372	−	0.164372i
$476$	−10.3399	−	25.3884i	−0.473930	−	1.16367i
$477$	−0.335817	+	32.9478i	−0.0153760	+	1.50857i
$478$		−	12.3262i		−	0.563787i
$479$	−1.94266	+	1.94266i	−0.0887625	+	0.0887625i	−0.750094	−	0.661331i	$-0.769992\pi$
$479$	−1.94266	+	1.94266i	−0.0887625	+	0.0887625i	0.661331	+	0.750094i	$0.269992\pi$
$480$	−0.341800	+	0.195022i	−0.0156009	+	0.00890152i
$481$	5.16699	+	3.25117i	0.235594	+	0.148240i
$482$	25.5005	+	14.7227i	1.16151	+	0.670600i
$483$	−2.51003	−	1.97041i	−0.114210	−	0.0896566i
$484$	−9.02912	+	15.6389i	−0.410415	+	0.710859i
$485$	−0.0408490	−	0.0707525i	−0.00185486	−	0.00321270i
$486$	−22.1650	−	23.3243i	−1.00542	−	1.05801i
$487$	−24.8645	+	24.8645i	−1.12672	+	1.12672i	−0.136013	+	0.990707i	$0.543429\pi$
$487$	−24.8645	+	24.8645i	−1.12672	+	1.12672i	−0.990707	+	0.136013i	$0.956571\pi$
$488$	1.75846	+	6.56265i	0.0796015	+	0.297077i
$489$	27.3263	−	7.17301i	1.23574	−	0.324375i
$490$	−0.109318	+	0.389412i	−0.00493846	+	0.0175918i
$491$	−23.6585			−1.06769			−0.533847	−	0.845581i	$-0.679254\pi$
$491$	−23.6585			−1.06769			−0.533847	+	0.845581i	$0.679254\pi$
$492$	−29.0735	+	28.7787i	−1.31073	+	1.29744i
$493$	22.2978	+	12.8736i	1.00424	+	0.579799i
$494$	−2.22760	+	7.20560i	−0.100224	+	0.324195i
$495$	0.365927	+	0.00372968i	0.0164472	+	0.000167637i
$496$	25.6905	+	6.88374i	1.15354	+	0.309089i
$497$	20.4153	+	8.59875i	0.915753	+	0.385707i
$498$	0.274411	−	53.8476i	0.0122967	−	2.41297i
$499$	−4.53212	−	1.21438i	−0.202885	−	0.0543630i	0.155945	−	0.987766i	$-0.450158\pi$
$499$	−4.53212	−	1.21438i	−0.202885	−	0.0543630i	−0.358830	+	0.933403i	$0.616824\pi$
$500$	−0.611183	+	0.163766i	−0.0273329	+	0.00732384i
$501$	−3.72681	−	1.01898i	−0.166502	−	0.0455247i
$502$	27.7369	+	27.7369i	1.23796	+	1.23796i
$503$	−9.28013	−	5.35789i	−0.413781	−	0.238896i	0.278632	−	0.960398i	$-0.410119\pi$
$503$	−9.28013	−	5.35789i	−0.413781	−	0.238896i	−0.692413	+	0.721502i	$0.743452\pi$
$504$	−1.69684	+	3.91659i	−0.0755831	+	0.174459i
$505$	0.0197157	−	0.0735802i	0.000877339	−	0.00327427i
$506$	6.26326			0.278436
$507$	−18.5232	−	12.8020i	−0.822643	−	0.568558i
$508$	−21.2517			−0.942890
$509$	13.6296	−	3.65204i	0.604121	−	0.161874i	0.0562220	−	0.998418i	$-0.482095\pi$
$509$	13.6296	−	3.65204i	0.604121	−	0.161874i	0.547899	+	0.836545i	$0.315428\pi$
$510$	0.00233762	−	0.458710i	0.000103511	−	0.0203120i
$511$	−17.8961	+	13.5640i	−0.791676	+	0.600036i
$512$	−22.1706	−	22.1706i	−0.979811	−	0.979811i
$513$	−5.06500	−	1.44050i	−0.223625	−	0.0635998i
$514$	16.9980	+	16.9980i	0.749748	+	0.749748i
$515$	−0.0751401	−	0.280427i	−0.00331107	−	0.0123571i
$516$	12.9140	+	0.0658105i	0.568506	+	0.00289715i
$517$			42.0762i			1.85051i
$518$	9.16004	+	1.26135i	0.402469	+	0.0554204i
$519$	20.4706	+	0.104320i	0.898561	+	0.00457913i
$520$	0.0368926	+	0.0398109i	0.00161785	+	0.00174582i
$521$	−22.0638	+	12.7386i	−0.966635	+	0.558087i	−0.898209	−	0.439569i	$-0.855131\pi$
$521$	−22.0638	+	12.7386i	−0.966635	+	0.558087i	−0.0684261	+	0.997656i	$0.521798\pi$
$522$	−8.65995	−	33.6891i	−0.379036	−	1.47453i
$523$	19.1997			0.839542			0.419771	−	0.907630i	$-0.362110\pi$
$523$	19.1997			0.839542			0.419771	+	0.907630i	$0.362110\pi$
$524$	−17.9223			−0.782941
$525$	14.1460	−	18.0201i	0.617383	−	0.786463i
$526$	12.4719	+	3.34182i	0.543799	+	0.145710i
$527$	−25.2711	+	25.2711i	−1.10082	+	1.10082i
$528$	6.53652	+	24.9015i	0.284466	+	1.08370i
$529$	11.2576	+	19.4987i	0.489459	+	0.847768i
$530$	0.634615			0.0275659
$531$	−42.4600	−	11.8422i	−1.84261	−	0.513909i
$532$	0.755412	+	6.01378i	0.0327513	+	0.260730i
$533$	−31.8846	−	20.0624i	−1.38108	−	0.868999i
$534$	−4.38694	+	7.50976i	−0.189841	+	0.324979i
$535$	0.0716881	+	0.0192088i	0.00309935	+	0.000830467i
$536$	−3.78579	+	2.18573i	−0.163521	+	0.0944091i
$537$	−16.6271	−	0.0847328i	−0.717512	−	0.00365649i
$538$	50.2688	+	13.4695i	2.16724	+	0.580710i
$539$	26.2334	+	15.5643i	1.12995	+	0.670402i
$540$	−0.236030	+	0.228921i	−0.0101571	+	0.00985121i
$541$	42.1301	−	11.2887i	1.81132	−	0.485340i	0.815666	−	0.578523i	$-0.196371\pi$
$541$	42.1301	−	11.2887i	1.81132	−	0.485340i	0.995649	+	0.0931822i	$0.0297039\pi$
$542$	27.1558	−	15.6784i	1.16644	−	0.673446i
$543$	−7.32979	+	4.18220i	−0.314551	+	0.179475i
$544$	35.9338	−	9.62842i	1.54065	−	0.412815i
$545$	0.265800	−	0.460379i	0.0113856	−	0.0197205i
$546$	−33.5538	−	6.10457i	−1.43597	−	0.261251i
$547$	−11.4904	−	19.9020i	−0.491295	−	0.850948i	0.508655	−	0.860971i	$-0.330143\pi$
$547$	−11.4904	−	19.9020i	−0.491295	−	0.850948i	−0.999950	+	0.0100226i	$0.996810\pi$
$548$	34.6964	+	34.6964i	1.48216	+	1.48216i
$549$	−18.6156	−	33.0158i	−0.794495	−	1.40908i
$550$			44.9655i			1.91733i
$551$	−4.02535	−	4.02535i	−0.171486	−	0.171486i
$552$	−0.460959	+	0.456284i	−0.0196197	+	0.0194208i
$553$	8.67963	+	6.74242i	0.369096	+	0.286717i
$554$	−3.38590	−	12.6363i	−0.143853	−	0.536867i
$555$	0.0708847	+	0.0414084i	0.00300889	+	0.00175769i
$556$			47.0443i			1.99512i
$557$	4.79149	+	17.8821i	0.203022	+	0.757688i	0.990043	+	0.140762i	$0.0449553\pi$
$557$	4.79149	+	17.8821i	0.203022	+	0.757688i	−0.787022	+	0.616925i	$0.788378\pi$
$558$	48.2802	+	0.492091i	2.04386	+	0.0208319i
$559$	2.63900	+	11.5958i	0.111618	+	0.490450i
$560$	−0.232824	−	0.0980632i	−0.00983860	−	0.00414393i
$561$	−33.3696	−	9.12386i	−1.40886	−	0.385210i
$562$	−10.3075	+	17.8532i	−0.434797	+	0.753091i
$563$	−7.09029	+	12.2807i	−0.298820	+	0.517571i	−0.975866	−	0.218369i	$-0.929926\pi$
$563$	−7.09029	+	12.2807i	−0.298820	+	0.517571i	0.677046	+	0.735940i	$0.263260\pi$
$564$	−26.5964	−	26.8689i	−1.11991	−	1.13138i
$565$	0.104288	+	0.389207i	0.00438742	+	0.0163741i
$566$	3.78187	+	14.1141i	0.158964	+	0.593261i
$567$	3.72839	−	23.5181i	0.156577	−	0.987666i
$568$	2.25129	−	3.89935i	0.0944620	−	0.163613i
$569$	2.98775	+	5.17494i	0.125253	+	0.216945i	0.921832	−	0.387590i	$-0.126692\pi$
$569$	2.98775	+	5.17494i	0.125253	+	0.216945i	−0.796579	+	0.604535i	$0.793359\pi$
$570$	−0.0267488	+	0.0978308i	−0.00112038	+	0.00409768i
$571$		−	21.4127i		−	0.896094i	−0.894010	−	0.448047i	$-0.852120\pi$
$571$		−	21.4127i		−	0.896094i	0.894010	−	0.448047i	$-0.147880\pi$
$572$	31.4109	−	16.5759i	1.31336	−	0.693073i
$573$	0.0346321	−	6.79584i	0.00144677	−	0.283900i
$574$	−56.5251	−	7.78355i	−2.35931	−	0.324879i
$575$	3.01478	−	1.74058i	0.125725	−	0.0725874i
$576$	−25.6478	−	15.1584i	−1.06866	−	0.631600i
$577$	−1.40353	−	0.376075i	−0.0584297	−	0.0156562i	0.229486	−	0.973312i	$-0.426296\pi$
$577$	−1.40353	−	0.376075i	−0.0584297	−	0.0156562i	−0.287915	+	0.957656i	$0.592962\pi$
$578$	−2.14159	+	7.99251i	−0.0890783	+	0.332445i
$579$	−13.6487	+	3.58272i	−0.567221	+	0.148893i
$580$	−0.343349	+	0.0920002i	−0.0142568	+	0.00382010i
$581$	31.7587	−	24.0709i	1.31757	−	0.998630i
$582$	5.26300	−	9.00944i	0.218158	−	0.373453i
$583$	12.3871	−	46.2292i	0.513020	−	1.91462i
$584$	2.28211	+	3.95273i	0.0944343	+	0.163565i
$585$	−0.254623	−	0.163860i	−0.0105274	−	0.00677477i
$586$	1.08965	−	1.88732i	0.0450128	−	0.0779645i
$587$	36.2856	−	9.72268i	1.49766	−	0.401298i	0.585348	−	0.810782i	$-0.300958\pi$
$587$	36.2856	−	9.72268i	1.49766	−	0.401298i	0.912317	+	0.409484i	$0.134291\pi$
$588$	−26.5902	+	6.64313i	−1.09656	+	0.273958i
$589$	6.84316	−	3.95090i	0.281967	−	0.162794i
$590$	−0.219737	+	0.820071i	−0.00904645	+	0.0337618i
$591$	9.42489	−	2.47398i	0.387688	−	0.101766i
$592$	−1.49479	+	5.57865i	−0.0614356	+	0.229281i
$593$	−1.62436	−	6.06221i	−0.0667046	−	0.248945i	0.924520	−	0.381134i	$-0.124466\pi$
$593$	−1.62436	−	6.06221i	−0.0667046	−	0.248945i	−0.991225	+	0.132189i	$0.957800\pi$
$594$	22.7469	+	40.8278i	0.933317	+	1.67518i
$595$	0.270542	−	0.205052i	0.0110911	−	0.00840631i
$596$	12.7699	+	47.6578i	0.523074	+	1.95214i
$597$	20.3599	−	11.6168i	0.833274	−	0.475446i
$598$	−4.38629	−	2.75994i	−0.179369	−	0.112862i
$599$			32.3033i			1.31988i	0.751320	+	0.659938i	$0.229417\pi$
$599$			32.3033i			1.31988i	−0.751320	+	0.659938i	$0.770583\pi$
$600$	−3.27578	−	3.30934i	−0.133733	−	0.135103i
$601$	17.4914	−	30.2959i	0.713487	−	1.23580i	−0.250053	−	0.968232i	$-0.580448\pi$
$601$	17.4914	−	30.2959i	0.713487	−	1.23580i	0.963540	−	0.267564i	$-0.0862187\pi$
$602$	10.8803	+	14.3552i	0.443446	+	0.585075i
$603$	17.4190	−	17.0675i	0.709355	−	0.695041i
$604$	−7.26521	−	1.94671i	−0.295617	−	0.0792104i
$605$	−0.216003	−	0.0578778i	−0.00878177	−	0.00235307i
$606$	9.40999	−	2.47007i	0.382255	−	0.100340i
$607$	−22.7667			−0.924071			−0.462036	−	0.886861i	$-0.652881\pi$
$607$	−22.7667			−0.924071			−0.462036	+	0.886861i	$0.652881\pi$
$608$	−8.22520			−0.333576
$609$	15.8951	−	20.2482i	0.644103	−	0.820500i
$610$	−0.632204	+	0.365003i	−0.0255972	+	0.0147786i
$611$	18.5411	−	29.4668i	0.750092	−	1.19210i
$612$	27.0762	−	15.2666i	1.09449	−	0.617118i
$613$	−8.62173	−	32.1767i	−0.348228	−	1.29961i	−0.888795	−	0.458305i	$-0.848457\pi$
$613$	−8.62173	−	32.1767i	−0.348228	−	1.29961i	0.540567	−	0.841301i	$-0.318210\pi$
$614$	−21.1716	+	12.2234i	−0.854416	+	0.493298i
$615$	−0.437417	−	0.255524i	−0.0176384	−	0.0103037i
$616$	3.80342	−	4.89621i	0.153244	−	0.197274i
$617$	4.06410	−	15.1674i	0.163615	−	0.610618i	−0.834598	−	0.550859i	$-0.814300\pi$
$617$	4.06410	−	15.1674i	0.163615	−	0.610618i	0.998213	−	0.0597587i	$-0.0190331\pi$
$618$	26.3514	−	26.0842i	1.06001	−	1.04926i
$619$	−12.2602	+	3.28510i	−0.492778	+	0.132039i	−0.496646	−	0.867953i	$-0.665435\pi$
$619$	−12.2602	+	3.28510i	−0.492778	+	0.132039i	0.00386838	+	0.999993i	$0.498769\pi$
$620$		−	0.493401i		−	0.0198155i
$621$	1.85684	−	3.10552i	0.0745126	−	0.124620i
$622$	−4.18225	+	15.6084i	−0.167693	+	0.625838i
$623$	−6.38613	+	0.802184i	−0.255855	+	0.0321388i
$624$	6.39533	−	20.3194i	0.256018	−	0.813427i
$625$	12.4941	+	21.6405i	0.499765	+	0.865618i
$626$	6.36520	−	23.7552i	0.254404	−	0.949450i
$627$	6.60448	+	3.85811i	0.263757	+	0.154078i
$628$	3.35151	+	1.93499i	0.133740	+	0.0772146i
$629$	−5.48757	−	5.48757i	−0.218804	−	0.218804i
$630$	−0.453672	−	0.0671893i	−0.0180747	−	0.00267689i
$631$	−9.93089	+	2.66097i	−0.395342	+	0.105932i	−0.451013	−	0.892518i	$-0.648937\pi$
$631$	−9.93089	+	2.66097i	−0.395342	+	0.105932i	0.0556703	+	0.998449i	$0.482270\pi$
$632$	1.57962	−	1.57962i	0.0628341	−	0.0628341i
$633$	−12.0147	−	21.0572i	−0.477541	−	0.836947i
$634$	−10.1395	+	5.85404i	−0.402691	+	0.232494i
$635$	−0.0681129	−	0.254201i	−0.00270298	−	0.0100877i
$636$	21.3114	+	37.3507i	0.845052	+	1.48105i
$637$	−11.5133	−	22.4599i	−0.456172	−	0.889892i
$638$			50.5252i			2.00031i
$639$	−6.74805	+	24.1950i	−0.266949	+	0.957137i
$640$	−0.0597038	+	0.103410i	−0.00236000	+	0.00408764i
$641$	13.7805	+	23.8685i	0.544297	+	0.942750i	0.998651	+	0.0519285i	$0.0165368\pi$
$641$	13.7805	+	23.8685i	0.544297	+	0.942750i	−0.454354	+	0.890821i	$0.650130\pi$
$642$	2.40656	+	9.16801i	0.0949792	+	0.361833i
$643$	−28.2307	−	7.56440i	−1.11331	−	0.298311i	−0.345138	−	0.938552i	$-0.612168\pi$
$643$	−28.2307	−	7.56440i	−1.11331	−	0.298311i	−0.768174	+	0.640241i	$0.778834\pi$
$644$	−4.12576	−	0.568121i	−0.162578	−	0.0223871i
$645$	0.0406029	+	0.154681i	0.00159874	+	0.00609056i
$646$	4.79390	−	8.30328i	0.188614	−	0.326688i
$647$	8.36380	−	14.4865i	0.328815	−	0.569524i	−0.653462	−	0.756959i	$-0.726684\pi$
$647$	8.36380	−	14.4865i	0.328815	−	0.569524i	0.982277	+	0.187435i	$0.0600174\pi$
$648$	−4.64845	−	1.34768i	−0.182609	−	0.0529418i
$649$	55.4499	+	32.0140i	2.17660	+	1.25666i
$650$	19.8143	−	31.4902i	0.777179	−	1.23515i
$651$	21.4376	+	28.5858i	0.840207	+	1.12037i
$652$	26.0726	−	26.0726i	1.02108	−	1.02108i
$653$	−2.34269	−	1.35256i	−0.0916767	−	0.0529296i	0.453461	−	0.891276i	$-0.350189\pi$
$653$	−2.34269	−	1.35256i	−0.0916767	−	0.0529296i	−0.545137	+	0.838347i	$0.683523\pi$
$654$	67.8924	+	0.345984i	2.65480	+	0.0135290i
$655$	−0.0574422	−	0.214377i	−0.00224445	−	0.00837642i
$656$	9.22412	−	34.4249i	0.360141	−	1.34407i
$657$	−17.8201	−	18.1871i	−0.695227	−	0.709545i
$658$	7.19333	−	52.2388i	0.280425	−	2.03648i
$659$		−	1.73029i		−	0.0674024i	−0.999432	−	0.0337012i	$-0.989271\pi$
$659$		−	1.73029i		−	0.0674024i	0.999432	−	0.0337012i	$-0.0107295\pi$
$660$	0.414828	−	0.236691i	0.0161472	−	0.00921318i
$661$	−3.97384	+	14.8306i	−0.154565	+	0.576843i	0.844578	+	0.535433i	$0.179852\pi$
$661$	−3.97384	+	14.8306i	−0.154565	+	0.576843i	−0.999142	+	0.0414098i	$0.986815\pi$
$662$	29.3951			1.14247
$663$	19.3489	+	21.0941i	0.751449	+	0.819226i
$664$	−4.04987	−	7.01458i	−0.157165	−	0.272218i
$665$	−0.0695124	+	0.0283104i	−0.00269558	+	0.00109783i
$666$	−0.106857	+	10.4840i	−0.00414062	+	0.406246i
$667$	3.38754	−	1.95580i	0.131166	−	0.0757288i
$668$	−4.87064	+	1.30508i	−0.188451	+	0.0504953i
$669$	−17.7140	+	17.5344i	−0.684864	+	0.677919i
$670$	−0.332126	−	0.332126i	−0.0128311	−	0.0128311i
$671$	14.2490	+	53.1781i	0.550078	+	2.05292i
$672$	−4.44748	−	36.9268i	−0.171565	−	1.42448i
$673$	25.0785	+	14.4791i	0.966707	+	0.558128i	0.898231	−	0.439524i	$-0.144853\pi$
$673$	25.0785	+	14.4791i	0.966707	+	0.558128i	0.0684760	+	0.997653i	$0.478186\pi$
$674$	38.8780	−	38.8780i	1.49753	−	1.49753i
$675$	22.2953	+	13.3307i	0.858146	+	0.513100i
$676$	−29.3019	−	2.23295i	−1.12700	−	0.0858825i
$677$			7.45855i			0.286655i	0.989675	+	0.143328i	$0.0457803\pi$
$677$			7.45855i			0.286655i	−0.989675	+	0.143328i	$0.954220\pi$
$678$	−36.5734	+	36.2026i	−1.40459	+	1.39035i
$679$	7.66142	−	0.962378i	0.294018	−	0.0369327i
$680$	−0.0344995	−	0.0597548i	−0.00132299	−	0.00229149i
$681$	−6.79444	+	1.78350i	−0.260363	+	0.0683440i
$682$	−67.7422	−	18.1515i	−2.59398	−	0.695056i
$683$	−8.44591	+	8.44591i	−0.323174	+	0.323174i	−0.849983	−	0.526810i	$-0.823388\pi$
$683$	−8.44591	+	8.44591i	−0.323174	+	0.323174i	0.526810	+	0.849983i	$0.323388\pi$
$684$	−6.65617	+	1.71100i	−0.254505	+	0.0654218i
$685$	−0.303816	+	0.526225i	−0.0116082	+	0.0201060i
$686$	−29.9086	−	23.8084i	−1.14192	−	0.909008i
$687$	5.36374	−	1.40795i	0.204639	−	0.0537168i
$688$	−9.74349	+	5.62541i	−0.371467	+	0.214467i
$689$	−29.0460	+	26.9168i	−1.10657	+	1.02545i
$690$	−0.0601744	−	0.0351518i	−0.00229080	−	0.00133821i
$691$	−36.2491	−	9.71292i	−1.37898	−	0.369497i	−0.508230	−	0.861221i	$-0.669700\pi$
$691$	−36.2491	−	9.71292i	−1.37898	−	0.369497i	−0.870751	+	0.491725i	$0.836367\pi$
$692$	23.1376	−	13.3585i	0.879558	−	0.507813i
$693$	−13.7497	+	31.7367i	−0.522309	+	1.20558i
$694$	36.2252	−	36.2252i	1.37509	−	1.37509i
$695$	−0.562719	+	0.150780i	−0.0213452	+	0.00571942i
$696$	−3.68081	−	3.71852i	−0.139521	−	0.140950i
$697$	33.8629	+	33.8629i	1.28265	+	1.28265i
$698$		−	67.4592i		−	2.55337i
$699$	−5.77138	−	0.0294113i	−0.218294	−	0.00111244i
$700$	4.07868	−	29.6198i	0.154159	−	1.11952i
$701$	−43.6670			−1.64928			−0.824640	−	0.565658i	$-0.808622\pi$
$701$	−43.6670			−1.64928			−0.824640	+	0.565658i	$0.808622\pi$
$702$	2.06084	−	38.6161i	0.0777815	−	1.45747i
$703$	0.857932	+	1.48598i	0.0323575	+	0.0560449i
$704$	30.5995	+	30.5995i	1.15326	+	1.15326i
$705$	0.236148	−	0.404248i	0.00889384	−	0.0152249i
$706$	9.49336	−	5.48099i	0.357287	−	0.206280i
$707$	5.68578	+	4.41676i	0.213836	+	0.166109i
$708$	−55.6451	+	14.6065i	−2.09127	+	0.548947i
$709$	12.4707	−	3.34152i	0.468348	−	0.125493i	−0.0169240	−	0.999857i	$-0.505387\pi$
$709$	12.4707	−	3.34152i	0.468348	−	0.125493i	0.485272	+	0.874363i	$0.338721\pi$
$710$	0.467301	+	0.125213i	0.0175375	+	0.00469916i
$711$	−6.34083	+	10.7286i	−0.237800	+	0.402355i
$712$			1.30822i			0.0490275i
$713$	1.40526	+	5.24452i	0.0526276	+	0.196409i
$714$	39.8695	+	17.0324i	1.49208	+	0.637421i
$715$	0.298946	+	0.322594i	0.0111799	+	0.0120643i
$716$	−18.7933	+	10.8503i	−0.702338	+	0.405495i
$717$	7.27643	+	7.35098i	0.271743	+	0.274527i
$718$	−33.6910			−1.25734
$719$	−6.85282	−	11.8694i	−0.255567	−	0.442655i	0.709482	−	0.704723i	$-0.248929\pi$
$719$	−6.85282	−	11.8694i	−0.255567	−	0.442655i	−0.965049	+	0.262068i	$0.915596\pi$
$720$	0.0769572	−	0.275928i	0.00286802	−	0.0102832i
$721$	27.1828	+	3.74310i	1.01234	+	0.139400i
$722$	26.2324	−	26.2324i	0.976267	−	0.976267i
$723$	−23.8988	+	6.27332i	−0.888807	+	0.233307i
$724$	−5.50694	+	9.53831i	−0.204664	+	0.354488i
$725$	14.0412	+	24.3200i	0.521476	+	0.903222i
$726$	−7.25118	−	27.6241i	−0.269117	−	1.02523i
$727$	18.0700	−	10.4327i	0.670178	−	0.386928i	−0.125966	−	0.992035i	$-0.540203\pi$
$727$	18.0700	−	10.4327i	0.670178	−	0.386928i	0.796144	+	0.605107i	$0.206870\pi$
$728$	−4.82115	+	1.75292i	−0.178684	+	0.0649676i
$729$	26.9874	+	0.825427i	0.999533	+	0.0305714i
$730$	−0.346771	+	0.346771i	−0.0128346	+	0.0128346i
$731$		−	15.1180i		−	0.559160i
$732$	−42.7130	−	24.9515i	−1.57872	−	0.922232i
$733$	−42.5983	−	11.4142i	−1.57340	−	0.421592i	−0.636527	−	0.771254i	$-0.719630\pi$
$733$	−42.5983	−	11.4142i	−1.57340	−	0.421592i	−0.936876	+	0.349662i	$0.886296\pi$
$734$	−7.65489	+	28.5684i	−0.282547	+	1.05448i
$735$	−0.164685	−	0.296766i	−0.00607449	−	0.0109464i
$736$	1.46278	−	5.45916i	0.0539187	−	0.201227i
$737$	−30.6768	+	17.7113i	−1.13000	+	0.652403i
$738$	0.659396	−	64.6948i	0.0242727	−	2.38145i
$739$	−16.2981	+	4.36706i	−0.599536	+	0.160645i	−0.545808	−	0.837911i	$-0.683777\pi$
$739$	−16.2981	+	4.36706i	−0.599536	+	0.160645i	−0.0537280	+	0.998556i	$0.517110\pi$
$740$	0.107141			0.00393859
$741$	−2.92516	−	5.61220i	−0.107458	−	0.206170i
$742$	−23.2822	+	55.2772i	−0.854717	+	2.02929i
$743$	−7.90104	−	7.90104i	−0.289861	−	0.289861i	0.547164	−	0.837025i	$-0.315707\pi$
$743$	−7.90104	−	7.90104i	−0.289861	−	0.289861i	−0.837025	+	0.547164i	$0.815707\pi$
$744$	6.30800	−	3.59919i	0.231262	−	0.131953i
$745$	−0.529129	+	0.305493i	−0.0193858	+	0.0111924i
$746$	7.34420	−	27.4089i	0.268890	−	1.00351i
$747$	31.6238	+	32.2751i	1.15705	+	1.18088i
$748$	−43.6113	+	11.6856i	−1.59459	+	0.427269i
$749$	−4.30318	+	5.53957i	−0.157235	+	0.202411i
$750$	0.504766	−	0.864082i	0.0184315	−	0.0315518i
$751$	16.0279	+	9.25372i	0.584867	+	0.337673i	0.763065	−	0.646322i	$-0.223694\pi$
$751$	16.0279	+	9.25372i	0.584867	+	0.337673i	−0.178198	+	0.983995i	$0.557027\pi$
$752$	31.8145	+	8.52466i	1.16015	+	0.310862i
$753$	−32.9152	−	0.167738i	−1.19950	−	0.00611271i
$754$	22.2642	−	35.3838i	0.810814	−	1.28860i
$755$		−	0.0931418i		−	0.00338978i
$756$	−11.2806	−	28.9575i	−0.410270	−	1.05318i
$757$	−2.92499	−	5.06623i	−0.106311	−	0.184135i	0.807962	−	0.589234i	$-0.200570\pi$
$757$	−2.92499	−	5.06623i	−0.106311	−	0.184135i	−0.914273	+	0.405099i	$0.867237\pi$
$758$	−9.28887	+	16.0888i	−0.337387	+	0.584372i
$759$	−3.73522	+	3.69734i	−0.135580	+	0.134205i
$760$	0.00394844	+	0.0147358i	0.000143225	+	0.000534523i
$761$	12.1394	−	12.1394i	0.440054	−	0.440054i	−0.451976	−	0.892030i	$-0.649281\pi$
$761$	12.1394	−	12.1394i	0.440054	−	0.440054i	0.892030	+	0.451976i	$0.149281\pi$
$762$	23.8870	−	23.6448i	0.865335	−	0.856560i
$763$	30.3492	+	40.0421i	1.09871	+	1.44962i
$764$	−4.43474	−	7.68120i	−0.160443	−	0.277896i
$765$	0.269393	+	0.274941i	0.00973991	+	0.00994050i
$766$	3.61275	−	2.08582i	0.130534	−	0.0753637i
$767$	−24.7255	−	46.8543i	−0.892788	−	1.69181i
$768$	19.1510	+	0.0975946i	0.691051	+	0.00352164i
$769$	−6.30925	+	6.30925i	−0.227517	+	0.227517i	−0.811655	−	0.584137i	$-0.801433\pi$
$769$	−6.30925	+	6.30925i	−0.227517	+	0.227517i	0.584137	+	0.811655i	$0.301433\pi$
$770$	0.613924	+	0.258579i	0.0221243	+	0.00931855i
$771$	−20.1714	−	0.102795i	−0.726454	−	0.00370206i
$772$	−13.0225	+	13.0225i	−0.468692	+	0.468692i
$773$	35.3138	+	35.3138i	1.27015	+	1.27015i	0.946010	+	0.324138i	$0.105074\pi$
$773$	35.3138	+	35.3138i	1.27015	+	1.27015i	0.324138	+	0.946010i	$0.394926\pi$
$774$	−14.5886	+	14.2942i	−0.524377	+	0.513796i
$775$	−37.6517	+	10.0887i	−1.35249	+	0.362398i
$776$		−	1.56946i		−	0.0563405i
$777$	−6.20737	+	4.65515i	−0.222688	+	0.167003i
$778$	−2.26935	−	2.26935i	−0.0813602	−	0.0813602i
$779$	−5.29415	−	9.16974i	−0.189683	−	0.328540i
$780$	−0.394812	−	0.0170368i	−0.0141365	−	0.000610014i
$781$	18.2425	−	31.5970i	0.652769	−	1.13063i
$782$	4.65843	+	4.65843i	0.166585	+	0.166585i
$783$	25.0520	+	14.9790i	0.895285	+	0.535306i
$784$	17.0833	−	16.6821i	0.610118	−	0.595789i
$785$	−0.0124036	+	0.0462907i	−0.000442702	+	0.00165219i
$786$	20.1448	−	19.9405i	0.718542	−	0.711256i
$787$	30.2276	−	8.09946i	1.07750	−	0.288715i	0.323927	−	0.946082i	$-0.394997\pi$
$787$	30.2276	−	8.09946i	1.07750	−	0.288715i	0.753570	+	0.657367i	$0.228330\pi$
$788$	8.99250	−	8.99250i	0.320345	−	0.320345i
$789$	−9.41059	+	5.36945i	−0.335026	+	0.191158i
$790$	0.207870	+	0.120014i	0.00739567	+	0.00426989i
$791$	−37.7274	−	5.19509i	−1.34143	−	0.184716i
$792$	6.05205	+	3.57689i	0.215050	+	0.127099i
$793$	13.4543	−	43.5206i	0.477777	−	1.54546i
$794$	−45.6879	−	26.3779i	−1.62140	−	0.936116i
$795$	−0.378465	+	0.374627i	−0.0134228	+	0.0132867i
$796$	15.2966	−	26.4944i	0.542173	−	0.939070i
$797$	−1.32499	−	2.29495i	−0.0469335	−	0.0812912i	0.841604	−	0.540095i	$-0.181612\pi$
$797$	−1.32499	−	2.29495i	−0.0469335	−	0.0812912i	−0.888538	+	0.458803i	$0.848278\pi$
$798$	−7.54007	−	5.91905i	−0.266916	−	0.209532i
$799$	−31.2951	+	31.2951i	−1.10714	+	1.10714i
$800$	39.1927	+	10.5016i	1.38567	+	0.371289i
$801$	−1.81694	−	7.06830i	−0.0641985	−	0.249746i
$802$	−17.0222			−0.601074
$803$	18.4923	+	32.0296i	0.652578	+	1.13030i
$804$	8.39419	−	30.7009i	0.296040	−	1.08274i
$805$	−0.00642777	−	0.0511710i	−0.000226549	−	0.00180354i
$806$	39.4427	+	42.5628i	1.38931	+	1.49921i
$807$	−37.9301	+	21.6420i	−1.33520	+	0.761834i
$808$	1.03477	−	1.03477i	0.0364030	−	0.0364030i
$809$	−13.4428	−	7.76120i	−0.472624	−	0.272869i	0.244714	−	0.969595i	$-0.421306\pi$
$809$	−13.4428	−	7.76120i	−0.472624	−	0.272869i	−0.717337	+	0.696726i	$0.754639\pi$
$810$	0.0105995	−	0.519918i	0.000372430	−	0.0182681i
$811$	−0.0406233	+	0.0406233i	−0.00142648	+	0.00142648i	−0.707820	−	0.706393i	$-0.750321\pi$
$811$	−0.0406233	+	0.0406233i	−0.00142648	+	0.00142648i	0.706393	+	0.707820i	$0.250321\pi$
$812$	4.58298	−	33.2822i	0.160831	−	1.16798i
$813$	−6.93959	+	25.3808i	−0.243382	+	0.890144i
$814$	3.94157	−	14.7101i	0.138152	−	0.515590i
$815$	0.395431	+	0.228302i	0.0138514	+	0.00799708i
$816$	−13.6594	+	23.3827i	−0.478174	+	0.818560i
$817$	−0.865123	+	3.22868i	−0.0302668	+	0.112957i
$818$	−0.616681			−0.0215617
$819$	23.6142	−	16.1670i	0.825145	−	0.564921i
$820$	−0.661151			−0.0230884
$821$	−8.81773	+	32.9082i	−0.307741	+	1.14850i	0.622819	+	0.782366i	$0.285987\pi$
$821$	−8.81773	+	32.9082i	−0.307741	+	1.14850i	−0.930560	+	0.366139i	$0.880679\pi$
$822$	−77.6026	−	0.395468i	−2.70670	−	0.0137935i
$823$	−8.03299	−	4.63785i	−0.280013	−	0.161665i	0.353417	−	0.935466i	$-0.385020\pi$
$823$	−8.03299	−	4.63785i	−0.280013	−	0.161665i	−0.633429	+	0.773801i	$0.718353\pi$
$824$	1.44348	−	5.38716i	0.0502862	−	0.187671i
$825$	−26.5441	−	26.8160i	−0.924148	−	0.933615i
$826$	−63.3695	−	49.2260i	−2.20491	−	1.71279i
$827$	35.6880	−	35.6880i	1.24099	−	1.24099i	0.281406	−	0.959589i	$-0.409199\pi$
$827$	35.6880	−	35.6880i	1.24099	−	1.24099i	0.959589	−	0.281406i	$-0.0908008\pi$
$828$	0.0481292	−	4.72207i	0.00167261	−	0.164103i
$829$	−7.23565	−	4.17750i	−0.251305	−	0.145091i	0.369057	−	0.929407i	$-0.379681\pi$
$829$	−7.23565	−	4.17750i	−0.251305	−	0.145091i	−0.620361	+	0.784316i	$0.713014\pi$
$830$	0.615386	−	0.615386i	0.0213604	−	0.0213604i
$831$	9.47876	+	5.53716i	0.328815	+	0.192082i
$832$	−7.94564	−	34.9133i	−0.275465	−	1.21040i
$833$	7.93534	+	31.0879i	0.274943	+	1.07713i
$834$	−52.3419	−	52.8782i	−1.81245	−	1.83102i
$835$	−0.0312215	−	0.0540771i	−0.00108046	−	0.00187142i
$836$	9.98259			0.345255
$837$	−29.0834	+	28.2074i	−1.00527	+	0.974991i
$838$	11.0148	+	2.95142i	0.380502	+	0.101955i
$839$	5.97400	−	5.97400i	0.206246	−	0.206246i	−0.596424	−	0.802670i	$-0.703412\pi$
$839$	5.97400	−	5.97400i	0.206246	−	0.206246i	0.802670	+	0.596424i	$0.203412\pi$
$840$	−0.0640209	+	0.0256943i	−0.00220893	+	0.000886536i
$841$	1.27728	+	2.21231i	0.0440440	+	0.0762865i
$842$	−15.1729	+	26.2802i	−0.522892	+	0.905676i
$843$	−4.39203	−	16.7319i	−0.151269	−	0.576276i
$844$	−27.4018	−	15.8205i	−0.943210	−	0.544562i
$845$	−0.0672053	−	0.357651i	−0.00231193	−	0.0123036i
$846$	59.7891	+	0.609394i	2.05559	+	0.0209514i
$847$	12.9659	−	16.6912i	0.445514	−	0.573518i
$848$	−32.4450	−	18.7321i	−1.11416	−	0.643263i
$849$	−10.5873	−	6.18472i	−0.363354	−	0.212259i
$850$	−33.4440	+	33.4440i	−1.14712	+	1.14712i
$851$	−1.13884	+	0.305151i	−0.0390389	+	0.0104604i
$852$	8.32324	+	31.7082i	0.285149	+	1.08631i
$853$	−5.62942	+	21.0093i	−0.192748	+	0.719345i	0.800091	+	0.599879i	$0.204785\pi$
$853$	−5.62942	+	21.0093i	−0.192748	+	0.719345i	−0.992838	+	0.119465i	$0.961882\pi$
$854$	−8.59927	−	68.4581i	−0.294261	−	2.34259i
$855$	−0.0417996	−	0.0741337i	−0.00142951	−	0.00253532i
$856$	1.00816	+	1.00816i	0.0344581	+	0.0344581i
$857$	−0.358868	+	0.621578i	−0.0122587	+	0.0212327i	−0.872090	−	0.489346i	$-0.837235\pi$
$857$	−0.358868	+	0.621578i	−0.0122587	+	0.0212327i	0.859831	+	0.510579i	$0.170569\pi$
$858$	−16.8636	+	53.5795i	−0.575714	+	1.82917i
$859$	−0.202393	−	0.350555i	−0.00690557	−	0.0119608i	0.862552	−	0.505968i	$-0.168865\pi$
$859$	−0.202393	−	0.350555i	−0.00690557	−	0.0119608i	−0.869458	+	0.494008i	$0.835531\pi$
$860$	0.147585	+	0.147585i	0.00503259	+	0.00503259i
$861$	38.3046	−	28.7261i	1.30542	−	0.978984i
$862$			74.0521i			2.52222i
$863$	10.4136	−	2.79030i	0.354481	−	0.0949830i	−0.0771838	−	0.997017i	$-0.524593\pi$
$863$	10.4136	−	2.79030i	0.354481	−	0.0949830i	0.431665	+	0.902034i	$0.357926\pi$
$864$	40.8987	−	10.2913i	1.39140	−	0.350117i
$865$	0.233944	+	0.233944i	0.00795435	+	0.00795435i
$866$	−3.78828	+	3.78828i	−0.128731	+	0.128731i
$867$	−3.44098	−	6.03072i	−0.116862	−	0.204814i
$868$	42.9770	+	18.1015i	1.45873	+	0.614405i
$869$	12.7999	−	12.7999i	0.434208	−	0.434208i
$870$	0.283567	−	0.485422i	0.00961382	−	0.0164574i
$871$	29.2882	+	1.11433i	0.992392	+	0.0377577i
$872$	8.84415	−	5.10617i	0.299501	−	0.172917i
$873$	2.17978	+	8.47982i	0.0737744	+	0.286999i
$874$	−0.728303	−	1.26146i	−0.0246352	−	0.0426695i
$875$	0.734795	−	0.0923003i	0.0248406	−	0.00312032i
$876$	−32.0546	−	8.76433i	−1.08303	−	0.296119i
$877$	−32.0386	+	32.0386i	−1.08187	+	1.08187i	−0.0855316	+	0.996335i	$0.527259\pi$
$877$	−32.0386	+	32.0386i	−1.08187	+	1.08187i	−0.996335	+	0.0855316i	$0.972741\pi$
$878$	−13.6905	−	51.0935i	−0.462031	−	1.72432i
$879$	0.464296	+	1.76878i	0.0156603	+	0.0596596i
$880$	−0.208044	+	0.360343i	−0.00701317	+	0.0121472i
$881$	−15.3340	−	26.5593i	−0.516615	−	0.894804i	−0.999814	−	0.0192934i	$-0.993858\pi$
$881$	−15.3340	−	26.5593i	−0.516615	−	0.894804i	0.483198	−	0.875511i	$-0.339475\pi$
$882$	22.4964	−	37.0514i	0.757492	−	1.24759i
$883$		−	8.00661i		−	0.269444i	−0.990883	−	0.134722i	$-0.956986\pi$
$883$		−	8.00661i		−	0.269444i	0.990883	−	0.134722i	$-0.0430141\pi$
$884$	35.6912	+	11.0339i	1.20043	+	0.371109i
$885$	−0.353062	−	0.618782i	−0.0118680	−	0.0208001i
$886$	40.7740	+	10.9254i	1.36983	+	0.367045i
$887$	23.6921	+	13.6787i	0.795504	+	0.459284i	0.841897	−	0.539639i	$-0.181439\pi$
$887$	23.6921	+	13.6787i	0.795504	+	0.459284i	−0.0463928	+	0.998923i	$0.514773\pi$
$888$	0.781558	+	1.36977i	0.0262274	+	0.0459665i
$889$	24.6407	+	3.39304i	0.826421	+	0.113799i
$890$	−0.135773	+	0.0363804i	−0.00455114	+	0.00121947i
$891$	−37.6671	−	10.9204i	−1.26190	−	0.365849i
$892$	−8.41931	+	31.4213i	−0.281899	+	1.05206i
$893$	8.47441	−	4.89270i	0.283585	−	0.163728i
$894$	−67.3779	−	39.3598i	−2.25345	−	1.31639i
$895$	−0.190019	−	0.190019i	−0.00635164	−	0.00635164i
$896$	−6.81701	−	8.99423i	−0.227740	−	0.300476i
$897$	4.24510	−	0.943380i	0.141740	−	0.0314986i
$898$	−47.1413			−1.57313
$899$	−42.3071	+	11.3362i	−1.41102	+	0.378082i
$900$	33.9009	+	0.345531i	1.13003	+	0.0115177i
$901$	43.5971	−	25.1708i	1.45243	−	0.838561i
$902$	−24.3227	+	90.7737i	−0.809859	+	3.02243i
$903$	−14.9629	−	2.13815i	−0.497933	−	0.0711532i
$904$	−2.00343	+	7.47690i	−0.0666330	+	0.248678i
$905$	−0.131742	−	0.0353002i	−0.00437926	−	0.00117342i
$906$	10.3321	−	5.89522i	0.343260	−	0.195856i
$907$		−	17.8337i		−	0.592157i	−0.955164	−	0.296079i	$-0.904321\pi$
$907$		−	17.8337i		−	0.592157i	0.955164	−	0.296079i	$-0.0956790\pi$
$908$	−6.48273	+	6.48273i	−0.215137	+	0.215137i
$909$	−4.15370	+	7.02801i	−0.137769	+	0.233104i
$910$	−0.315999	−	0.451617i	−0.0104753	−	0.0149710i
$911$	44.1029	−	25.4628i	1.46119	−	0.843621i	0.462128	−	0.886813i	$-0.347086\pi$
$911$	44.1029	−	25.4628i	1.46119	−	0.843621i	0.999067	+	0.0431923i	$0.0137528\pi$
$912$	4.25524	−	4.21209i	0.140905	−	0.139476i
$913$	−32.8167	−	56.8402i	−1.08607	−	1.88114i
$914$	7.01827	−	12.1560i	0.232144	−	0.402085i
$915$	0.161558	−	0.590881i	0.00534094	−	0.0195339i
$916$	5.11766	−	5.11766i	0.169092	−	0.169092i
$917$	20.7804	+	2.86148i	0.686230	+	0.0944944i
$918$	−13.4480	+	47.2851i	−0.443851	+	1.56064i
$919$	−2.89944	−	5.02197i	−0.0956436	−	0.165660i	0.814233	−	0.580538i	$-0.197158\pi$
$919$	−2.89944	−	5.02197i	−0.0956436	−	0.165660i	−0.909877	+	0.414878i	$0.863824\pi$
$920$	−0.0104825			−0.000345598
$921$	5.41034	−	19.7878i	0.178277	−	0.652029i
$922$	−53.3186	+	30.7835i	−1.75596	+	1.01380i
$923$	−26.6990	+	14.0894i	−0.878808	+	0.463757i
$924$	5.39772	+	44.8165i	0.177572	+	1.47436i
$925$	−2.19075	−	8.17601i	−0.0720315	−	0.268825i
$926$			6.56912i			0.215875i
$927$	−0.317103	+	31.1117i	−0.0104150	+	1.02184i
$928$	44.0386	+	11.8001i	1.44564	+	0.387358i
$929$	−7.70441	+	2.06439i	−0.252773	+	0.0677304i	−0.382981	−	0.923756i	$-0.625102\pi$
$929$	−7.70441	+	2.06439i	−0.252773	+	0.0677304i	0.130207	+	0.991487i	$0.458436\pi$
$930$	0.548962	+	0.554586i	0.0180012	+	0.0181856i
$931$	0.0842826	−	7.09340i	0.00276225	−	0.232477i
$932$	−6.52328	+	3.76621i	−0.213677	+	0.123366i
$933$	−6.71980	−	11.7772i	−0.219996	−	0.385569i
$934$	31.8979	+	31.8979i	1.04373	+	1.04373i
$935$	−0.279554	−	0.484202i	−0.00914241	−	0.0158351i
$936$	−2.66220	−	5.17183i	−0.0870168	−	0.169047i
$937$	−9.59395			−0.313421			−0.156710	−	0.987645i	$-0.550089\pi$
$937$	−9.59395			−0.313421			−0.156710	+	0.987645i	$0.550089\pi$
$938$	41.1141	−	16.7446i	1.34242	−	0.546729i
$939$	10.2272	+	17.9244i	0.333753	+	0.584941i
$940$		−	0.611016i		−	0.0199292i
$941$	10.2733	+	10.2733i	0.334900	+	0.334900i	0.854444	−	0.519544i	$-0.173898\pi$
$941$	10.2733	+	10.2733i	0.334900	+	0.334900i	−0.519544	+	0.854444i	$0.673898\pi$
$942$	−5.92001	+	1.55397i	−0.192884	+	0.0506311i
$943$	7.02758	−	1.88304i	0.228850	−	0.0613201i
$944$	35.4405	−	35.4405i	1.15349	−	1.15349i
$945$	0.310220	−	0.227743i	0.0100914	−	0.00740848i
$946$	25.6923	−	14.8334i	0.835327	−	0.482276i
$947$	37.6293	+	10.0827i	1.22279	+	0.327645i	0.811767	−	0.583981i	$-0.198506\pi$
$947$	37.6293	+	10.0827i	1.22279	+	0.327645i	0.411020	+	0.911626i	$0.365173\pi$
$948$	−0.0828855	+	16.2646i	−0.00269199	+	0.528249i
$949$	1.16347	−	30.5797i	0.0377678	−	0.992657i
$950$	9.05632	−	5.22867i	0.293826	−	0.169640i
$951$	2.59112	−	9.47675i	0.0840228	−	0.307305i
$952$	6.47054	−	0.812788i	0.209712	−	0.0263426i
$953$	1.51612	−	2.62599i	0.0491119	−	0.0850642i	−0.840424	−	0.541929i	$-0.817694\pi$
$953$	1.51612	−	2.62599i	0.0491119	−	0.0850642i	0.889536	+	0.456865i	$0.151028\pi$
$954$	−65.5109	−	18.2712i	−2.12099	−	0.591552i
$955$	0.0776648	−	0.0776648i	0.00251317	−	0.00251317i
$956$	13.0392	+	3.49385i	0.421719	+	0.112999i
$957$	−29.8262	−	30.1317i	−0.964143	−	0.974020i
$958$	−2.83540	−	4.91105i	−0.0916076	−	0.158669i
$959$	−34.6899	−	45.7691i	−1.12019	−	1.47796i
$960$	−0.122250	−	0.465722i	−0.00394559	−	0.0150311i
$961$		−	29.7963i		−	0.961171i
$962$	−9.24245	+	8.56493i	−0.297988	+	0.276144i
$963$	−6.84728	−	4.04688i	−0.220651	−	0.130409i
$964$	−22.8024	+	22.8024i	−0.734416	+	0.734416i
$965$	−0.197507	−	0.114031i	−0.00635797	−	0.00367078i
$966$	5.26948	−	3.95178i	0.169543	−	0.127147i
$967$	−1.44740	−	5.40176i	−0.0465452	−	0.173709i	0.938740	−	0.344625i	$-0.111994\pi$
$967$	−1.44740	−	5.40176i	−0.0465452	−	0.173709i	−0.985286	+	0.170916i	$0.945327\pi$
$968$	−3.03768	−	3.03768i	−0.0976346	−	0.0976346i
$969$	2.04267	+	7.78177i	0.0656202	+	0.249987i
$970$	0.162887	−	0.0436455i	0.00522999	−	0.00140137i
$971$	−9.44735	+	5.45443i	−0.303180	+	0.175041i	−0.643871	−	0.765134i	$-0.722672\pi$
$971$	−9.44735	+	5.45443i	−0.303180	+	0.175041i	0.340691	+	0.940175i	$0.389339\pi$
$972$	30.9562	−	16.8359i	0.992919	−	0.540011i
$973$	7.51110	−	54.5465i	0.240795	−	1.74868i
$974$	−36.2909	−	62.8576i	−1.16283	−	2.01409i
$975$	6.77276	+	30.4766i	0.216902	+	0.976033i
$976$	43.0956			1.37946
$977$	4.98951	−	18.6211i	0.159629	−	0.595742i	−0.839036	−	0.544076i	$-0.816880\pi$
$977$	4.98951	−	18.6211i	0.159629	−	0.595742i	0.998664	−	0.0516661i	$-0.0164532\pi$
$978$	−0.297174	+	58.3145i	−0.00950259	+	1.86469i
$979$			10.6007i			0.338799i
$980$	−0.380952	−	0.226020i	−0.0121691	−	0.00721993i
$981$	−40.6932	+	39.8720i	−1.29923	+	1.27302i
$982$	12.6391	−	47.1697i	0.403330	−	1.50525i
$983$	−10.5666	−	39.4351i	−0.337022	−	1.25778i	−0.901660	−	0.432445i	$-0.857651\pi$
$983$	−10.5666	−	39.4351i	−0.337022	−	1.25778i	0.564638	−	0.825338i	$-0.309016\pi$
$984$	−4.82286	−	8.45263i	−0.153747	−	0.269460i
$985$	0.136385	+	0.0787419i	0.00434559	+	0.00250893i
$986$	−37.5792	+	37.5792i	−1.19677	+	1.19677i
$987$	26.5479	+	35.4000i	0.845028	+	1.12680i
$988$	−6.99101	−	4.39888i	−0.222414	−	0.139947i
$989$	−1.98906	−	1.14839i	−0.0632485	−	0.0365165i
$990$	−0.202925	+	0.727584i	−0.00644940	+	0.0231241i
$991$	−1.41951	+	2.45867i	−0.0450924	+	0.0781023i	−0.887691	−	0.460440i	$-0.847692\pi$
$991$	−1.41951	+	2.45867i	−0.0450924	+	0.0781023i	0.842598	+	0.538543i	$0.181025\pi$
$992$	−31.6423	+	54.8060i	−1.00464	+	1.74009i
$993$	−17.5303	+	17.3526i	−0.556308	+	0.550667i
$994$	−28.0504	+	36.1098i	−0.889706	+	1.14533i
$995$	0.365939	+	0.0980530i	0.0116010	+	0.00310849i
$996$	56.8847	+	15.5533i	1.80246	+	0.492826i
$997$	−21.7609	−	37.6909i	−0.689173	−	1.19368i	−0.972106	−	0.234543i	$-0.924641\pi$
$997$	−21.7609	−	37.6909i	−0.689173	−	1.19368i	0.282932	−	0.959140i	$-0.408693\pi$
$998$	4.84238	−	8.38725i	0.153283	−	0.265494i
$999$	−6.12520	−	6.31541i	−0.193793	−	0.199811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.ge.a.275.20	yes	432
7.4	even	3		819.2.em.a.158.20	✓	432
9.2	odd	6		819.2.gf.a.2.20	yes	432
13.7	odd	12		819.2.fe.a.527.89	yes	432
63.11	odd	6		819.2.fe.a.704.89	yes	432
91.46	odd	12		819.2.gf.a.410.20	yes	432
117.20	even	12		819.2.em.a.254.20	yes	432
819.137	even	12	inner	819.2.ge.a.137.20	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.em.a.158.20	✓	432	7.4	even	3
819.2.em.a.254.20	yes	432	117.20	even	12
819.2.fe.a.527.89	yes	432	13.7	odd	12
819.2.fe.a.704.89	yes	432	63.11	odd	6
819.2.ge.a.137.20	yes	432	819.137	even	12	inner
819.2.ge.a.275.20	yes	432	1.1	even	1	trivial
819.2.gf.a.2.20	yes	432	9.2	odd	6
819.2.gf.a.410.20	yes	432	91.46	odd	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.ge (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.534230 + 1.99377i) q^{2} +(-0.858370 - 1.50439i) q^{3} +(-1.95768 - 1.13027i) q^{4} +(0.00724515 - 0.0270393i) q^{5} +(3.45799 - 0.907703i) q^{6} +(2.08941 + 1.62307i) q^{7} +(0.380256 - 0.380256i) q^{8} +(-1.52640 + 2.58265i) q^{9} +O(q^{10})\)	\(q+(-0.534230 + 1.99377i) q^{2} +(-0.858370 - 1.50439i) q^{3} +(-1.95768 - 1.13027i) q^{4} +(0.00724515 - 0.0270393i) q^{5} +(3.45799 - 0.907703i) q^{6} +(2.08941 + 1.62307i) q^{7} +(0.380256 - 0.380256i) q^{8} +(-1.52640 + 2.58265i) q^{9} +(0.0500396 + 0.0288904i) q^{10} +(3.08127 - 3.08127i) q^{11} +(-0.0199527 + 3.91530i) q^{12} +(-3.51566 + 0.800100i) q^{13} +(-4.35226 + 3.29872i) q^{14} +(-0.0468967 + 0.0123101i) q^{15} +(-1.70553 - 2.95407i) q^{16} +4.58353 q^{17} +(-4.33377 - 4.42303i) q^{18} +(-0.978884 - 0.262291i) q^{19} +(-0.0447452 + 0.0447452i) q^{20} +(0.648252 - 4.53649i) q^{21} +(4.49725 + 7.78947i) q^{22} +(0.348171 - 0.603051i) q^{23} +(-0.898456 - 0.245655i) q^{24} +(4.32945 + 2.49961i) q^{25} +(0.282951 - 7.43686i) q^{26} +(5.19555 + 0.0794361i) q^{27} +(-2.25589 - 5.53904i) q^{28} +(4.86476 + 2.80867i) q^{29} +(0.000510003 - 0.100078i) q^{30} +(-5.51345 + 5.51345i) q^{31} +(7.83976 - 2.10066i) q^{32} +(-7.28032 - 1.99058i) q^{33} +(-2.44866 + 9.13851i) q^{34} +(0.0590248 - 0.0447367i) q^{35} +(5.90729 - 3.33076i) q^{36} +(-1.19724 - 1.19724i) q^{37} +(1.04590 - 1.81155i) q^{38} +(4.22140 + 4.60215i) q^{39} +(-0.00752684 - 0.0130369i) q^{40} +(7.38795 + 7.38795i) q^{41} +(8.69842 + 3.71600i) q^{42} -3.29833i q^{43} +(-9.51480 + 2.54948i) q^{44} +(0.0587740 + 0.0599845i) q^{45} +(1.01634 + 1.01634i) q^{46} +(-6.82773 + 6.82773i) q^{47} +(-2.98010 + 5.10147i) q^{48} +(1.73127 + 6.78253i) q^{49} +(-7.29657 + 7.29657i) q^{50} +(-3.93436 - 6.89543i) q^{51} +(7.78685 + 2.40729i) q^{52} +(9.51169 - 5.49158i) q^{53} +(-2.93399 + 10.3163i) q^{54} +(-0.0609911 - 0.105640i) q^{55} +(1.41169 - 0.177328i) q^{56} +(0.445655 + 1.69777i) q^{57} +(-8.19875 + 8.19875i) q^{58} +(3.80295 + 14.1928i) q^{59} +(0.105722 + 0.0289065i) q^{60} +(-6.31704 + 10.9414i) q^{61} +(-8.04712 - 13.9380i) q^{62} +(-7.38111 + 2.91876i) q^{63} +9.93081i q^{64} +(-0.00383735 + 0.100858i) q^{65} +(7.85812 - 13.4519i) q^{66} +(-7.85197 - 2.10393i) q^{67} +(-8.97307 - 5.18060i) q^{68} +(-1.20609 - 0.00614629i) q^{69} +(0.0576621 + 0.141582i) q^{70} +(8.08749 - 2.16704i) q^{71} +(0.401646 + 1.56249i) q^{72} +(-2.19670 + 8.19820i) q^{73} +(3.02662 - 1.74742i) q^{74} +(0.0441258 - 8.65878i) q^{75} +(1.61988 + 1.61988i) q^{76} +(11.4392 - 1.43692i) q^{77} +(-11.4308 + 5.95791i) q^{78} +4.15411 q^{79} +(-0.0922326 + 0.0247136i) q^{80} +(-4.34020 - 7.88433i) q^{81} +(-18.6768 + 10.7830i) q^{82} +(3.89830 - 14.5487i) q^{83} +(-6.39651 + 8.14829i) q^{84} +(0.0332083 - 0.123935i) q^{85} +(6.57613 + 1.76207i) q^{86} +(0.0495817 - 9.72940i) q^{87} -2.34335i q^{88} +(-1.72018 + 1.72018i) q^{89} +(-0.150994 + 0.0851366i) q^{90} +(-8.64427 - 4.03443i) q^{91} +(-1.36321 + 0.787052i) q^{92} +(13.0270 + 3.56182i) q^{93} +(-9.96536 - 17.2605i) q^{94} +(-0.0141843 + 0.0245680i) q^{95} +(-9.88963 - 9.99095i) q^{96} +(2.06369 - 2.06369i) q^{97} +(-14.4477 - 0.171665i) q^{98} +(3.25460 + 12.6611i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 2 q^{3} - 6 q^{4} - 6 q^{5} - 4 q^{6} + 2 q^{7} + 12 q^{8} + 2 q^{9}+O(q^{10}) \) 432 * q + 2 * q^3 - 6 * q^4 - 6 * q^5 - 4 * q^6 + 2 * q^7 + 12 * q^8 + 2 * q^9	\( 432 q + 2 q^{3} - 6 q^{4} - 6 q^{5} - 4 q^{6} + 2 q^{7} + 12 q^{8} + 2 q^{9} - 12 q^{10} - 6 q^{11} - 4 q^{13} - 12 q^{14} - 24 q^{15} + 190 q^{16} - 26 q^{18} - 8 q^{19} - 12 q^{20} - 24 q^{21} + 4 q^{22} - 6 q^{23} - 46 q^{24} - 4 q^{27} - 12 q^{28} - 12 q^{29} - 6 q^{30} - 12 q^{31} - 24 q^{32} - 4 q^{33} - 66 q^{35} - 12 q^{36} - 6 q^{37} - 32 q^{39} - 12 q^{40} - 12 q^{41} - 16 q^{42} - 48 q^{44} - 2 q^{45} + 12 q^{46} + 36 q^{47} + 80 q^{48} + 42 q^{50} - 36 q^{51} - 38 q^{52} - 24 q^{53} + 14 q^{54} - 8 q^{55} - 12 q^{56} + 10 q^{57} - 14 q^{58} + 56 q^{60} - 2 q^{61} + 98 q^{63} - 42 q^{65} - 34 q^{66} + 10 q^{67} - 102 q^{68} + 30 q^{69} - 16 q^{70} + 48 q^{71} - 62 q^{72} - 32 q^{73} - 90 q^{74} - 36 q^{75} - 12 q^{76} - 72 q^{77} - 32 q^{78} - 32 q^{79} + 114 q^{80} + 6 q^{81} - 12 q^{82} - 12 q^{83} + 34 q^{84} - 12 q^{85} + 42 q^{86} + 88 q^{87} + 30 q^{89} + 228 q^{90} + 8 q^{91} - 12 q^{92} + 52 q^{93} - 2 q^{94} + 6 q^{95} - 90 q^{96} - 6 q^{97} - 64 q^{99}+O(q^{100}) \) 432 * q + 2 * q^3 - 6 * q^4 - 6 * q^5 - 4 * q^6 + 2 * q^7 + 12 * q^8 + 2 * q^9 - 12 * q^10 - 6 * q^11 - 4 * q^13 - 12 * q^14 - 24 * q^15 + 190 * q^16 - 26 * q^18 - 8 * q^19 - 12 * q^20 - 24 * q^21 + 4 * q^22 - 6 * q^23 - 46 * q^24 - 4 * q^27 - 12 * q^28 - 12 * q^29 - 6 * q^30 - 12 * q^31 - 24 * q^32 - 4 * q^33 - 66 * q^35 - 12 * q^36 - 6 * q^37 - 32 * q^39 - 12 * q^40 - 12 * q^41 - 16 * q^42 - 48 * q^44 - 2 * q^45 + 12 * q^46 + 36 * q^47 + 80 * q^48 + 42 * q^50 - 36 * q^51 - 38 * q^52 - 24 * q^53 + 14 * q^54 - 8 * q^55 - 12 * q^56 + 10 * q^57 - 14 * q^58 + 56 * q^60 - 2 * q^61 + 98 * q^63 - 42 * q^65 - 34 * q^66 + 10 * q^67 - 102 * q^68 + 30 * q^69 - 16 * q^70 + 48 * q^71 - 62 * q^72 - 32 * q^73 - 90 * q^74 - 36 * q^75 - 12 * q^76 - 72 * q^77 - 32 * q^78 - 32 * q^79 + 114 * q^80 + 6 * q^81 - 12 * q^82 - 12 * q^83 + 34 * q^84 - 12 * q^85 + 42 * q^86 + 88 * q^87 + 30 * q^89 + 228 * q^90 + 8 * q^91 - 12 * q^92 + 52 * q^93 - 2 * q^94 + 6 * q^95 - 90 * q^96 - 6 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more