LMFDB - Embedded newform 819.2.em.a.158.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(158,819)]

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([10, 8, 1]))

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

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

chi := DirichletCharacter("819.158");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.em (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			158.20
Character	$\chi$	$=$	819.158
Dual form			819.2.em.a.254.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45954 - 1.45954i) q^{2} +(-0.873658 + 1.49557i) q^{3} +2.26053i q^{4} +(0.0197941 + 0.0197941i) q^{5} +(3.45799 - 0.907703i) q^{6} +(1.62307 + 2.08941i) q^{7} +(0.380256 - 0.380256i) q^{8} +(-1.47344 - 2.61323i) q^{9} +O(q^{10})$	\(q+(-1.45954 - 1.45954i) q^{2} +(-0.873658 + 1.49557i) q^{3} +2.26053i q^{4} +(0.0197941 + 0.0197941i) q^{5} +(3.45799 - 0.907703i) q^{6} +(1.62307 + 2.08941i) q^{7} +(0.380256 - 0.380256i) q^{8} +(-1.47344 - 2.61323i) q^{9} -0.0577807i q^{10} +(-4.20910 - 1.12782i) q^{11} +(-3.38078 - 1.97493i) q^{12} +(-3.51566 + 0.800100i) q^{13} +(0.680641 - 5.41853i) q^{14} +(-0.0468967 + 0.0123101i) q^{15} +3.41106 q^{16} +(-2.29176 - 3.96945i) q^{17} +(-1.66357 + 5.96467i) q^{18} +(0.716593 - 0.716593i) q^{19} +(-0.0447452 + 0.0447452i) q^{20} +(-4.54286 + 0.601983i) q^{21} +(4.49725 + 7.78947i) q^{22} +(0.348171 + 0.603051i) q^{23} +(0.236485 + 0.900913i) q^{24} -4.99922i q^{25} +(6.29903 + 3.96347i) q^{26} +(5.19555 + 0.0794361i) q^{27} +(-4.72318 + 3.66901i) q^{28} +(4.86476 + 2.80867i) q^{29} +(0.0864149 + 0.0504806i) q^{30} +(7.53151 + 2.01806i) q^{31} +(-5.73910 - 5.73910i) q^{32} +(5.36405 - 5.30966i) q^{33} +(-2.44866 + 9.13851i) q^{34} +(-0.00923075 + 0.0734853i) q^{35} +(5.90729 - 3.33076i) q^{36} +(1.63546 - 0.438219i) q^{37} -2.09180 q^{38} +(1.87488 - 5.95691i) q^{39} +0.0150537 q^{40} +(7.38795 + 7.38795i) q^{41} +(7.50913 + 5.75188i) q^{42} -3.29833i q^{43} +(2.54948 - 9.51480i) q^{44} +(0.0225611 - 0.0808920i) q^{45} +(0.372007 - 1.38835i) q^{46} +(-2.49912 - 9.32685i) q^{47} +(-2.98010 + 5.10147i) q^{48} +(-1.73127 + 6.78253i) q^{49} +(-7.29657 + 7.29657i) q^{50} +(7.93880 + 0.0404567i) q^{51} +(-1.80865 - 7.94725i) q^{52} +(-9.51169 - 5.49158i) q^{53} +(-7.46718 - 7.69906i) q^{54} +(-0.0609911 - 0.105640i) q^{55} +(1.41169 + 0.177328i) q^{56} +(0.445655 + 1.69777i) q^{57} +(-3.00095 - 11.1997i) q^{58} +(10.3899 - 10.3899i) q^{59} +(-0.0278275 - 0.106011i) q^{60} +(-6.31704 - 10.9414i) q^{61} +(-8.04712 - 13.9380i) q^{62} +(3.06860 - 7.32009i) q^{63} +9.93081i q^{64} +(-0.0854266 - 0.0537520i) q^{65} +(-15.5787 - 0.0793903i) q^{66} +(2.10393 + 7.85197i) q^{67} +(8.97307 - 5.18060i) q^{68} +(-1.20609 - 0.00614629i) q^{69} +(0.120728 - 0.0937823i) q^{70} +(8.08749 - 2.16704i) q^{71} +(-1.55398 - 0.433411i) q^{72} +(8.19820 - 2.19670i) q^{73} +(-3.02662 - 1.74742i) q^{74} +(7.47666 + 4.36761i) q^{75} +(1.61988 + 1.61988i) q^{76} +(-4.47518 - 10.6251i) q^{77} +(-11.4308 + 5.95791i) q^{78} +(-2.07705 + 3.59756i) q^{79} +(0.0675189 + 0.0675189i) q^{80} +(-4.65793 + 7.70089i) q^{81} -21.5661i q^{82} +(3.89830 - 14.5487i) q^{83} +(-1.36080 - 10.2693i) q^{84} +(0.0332083 - 0.123935i) q^{85} +(-4.81406 + 4.81406i) q^{86} +(-8.45070 + 4.82176i) q^{87} +(-2.02940 + 1.17167i) q^{88} +(-0.629629 - 2.34981i) q^{89} +(-0.150994 + 0.0851366i) q^{90} +(-7.37790 - 6.04703i) q^{91} +(-1.36321 + 0.787052i) q^{92} +(-9.59812 + 9.50079i) q^{93} +(-9.96536 + 17.2605i) q^{94} +0.0283686 q^{95} +(13.5972 - 3.56920i) q^{96} +(2.06369 - 2.06369i) q^{97} +(12.4263 - 7.37253i) q^{98} +(3.25460 + 12.6611i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q - 6 q^{2} - 4 q^{3} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 432 * q - 6 * q^2 - 4 * q^3 - 4 * q^6 + 2 * q^7 + 12 * q^8 - 4 * q^9	$ 432 q - 6 q^{2} - 4 q^{3} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9} - 12 q^{11} + 36 q^{12} - 4 q^{13} - 12 q^{14} - 24 q^{15} - 380 q^{16} - 26 q^{18} - 8 q^{19} - 12 q^{20} - 6 q^{21} + 4 q^{22} - 6 q^{23} + 20 q^{24} - 4 q^{27} - 12 q^{28} - 12 q^{29} - 24 q^{30} + 18 q^{31} + 18 q^{32} - 16 q^{33} - 36 q^{35} - 12 q^{36} + 40 q^{39} + 24 q^{40} - 12 q^{41} - 34 q^{42} + 108 q^{44} - 2 q^{45} - 12 q^{46} - 6 q^{47} + 80 q^{48} + 42 q^{50} + 36 q^{51} + 4 q^{52} + 24 q^{53} - 34 q^{54} - 8 q^{55} - 12 q^{56} + 10 q^{57} + 4 q^{58} - 6 q^{59} - 34 q^{60} - 2 q^{61} - 16 q^{63} + 36 q^{65} + 8 q^{66} - 26 q^{67} + 102 q^{68} + 30 q^{69} + 56 q^{70} + 48 q^{71} + 10 q^{72} + 52 q^{73} + 90 q^{74} + 30 q^{75} - 12 q^{76} - 72 q^{77} - 32 q^{78} + 16 q^{79} - 198 q^{80} - 12 q^{81} - 12 q^{83} - 104 q^{84} - 12 q^{85} + 60 q^{86} - 38 q^{87} - 6 q^{88} + 228 q^{90} - 16 q^{91} - 12 q^{92} - 26 q^{93} - 2 q^{94} - 12 q^{95} - 78 q^{96} - 6 q^{97} + 36 q^{98} - 64 q^{99}+O(q^{100}) $ 432 * q - 6 * q^2 - 4 * q^3 - 4 * q^6 + 2 * q^7 + 12 * q^8 - 4 * q^9 - 12 * q^11 + 36 * q^12 - 4 * q^13 - 12 * q^14 - 24 * q^15 - 380 * q^16 - 26 * q^18 - 8 * q^19 - 12 * q^20 - 6 * q^21 + 4 * q^22 - 6 * q^23 + 20 * q^24 - 4 * q^27 - 12 * q^28 - 12 * q^29 - 24 * q^30 + 18 * q^31 + 18 * q^32 - 16 * q^33 - 36 * q^35 - 12 * q^36 + 40 * q^39 + 24 * q^40 - 12 * q^41 - 34 * q^42 + 108 * q^44 - 2 * q^45 - 12 * q^46 - 6 * q^47 + 80 * q^48 + 42 * q^50 + 36 * q^51 + 4 * q^52 + 24 * q^53 - 34 * q^54 - 8 * q^55 - 12 * q^56 + 10 * q^57 + 4 * q^58 - 6 * q^59 - 34 * q^60 - 2 * q^61 - 16 * q^63 + 36 * q^65 + 8 * q^66 - 26 * q^67 + 102 * q^68 + 30 * q^69 + 56 * q^70 + 48 * q^71 + 10 * q^72 + 52 * q^73 + 90 * q^74 + 30 * q^75 - 12 * q^76 - 72 * q^77 - 32 * q^78 + 16 * q^79 - 198 * q^80 - 12 * q^81 - 12 * q^83 - 104 * q^84 - 12 * q^85 + 60 * q^86 - 38 * q^87 - 6 * q^88 + 228 * q^90 - 16 * q^91 - 12 * q^92 - 26 * q^93 - 2 * q^94 - 12 * q^95 - 78 * q^96 - 6 * q^97 + 36 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.45954	−	1.45954i	−1.03205	−	1.03205i	−0.999469	−	0.0325837i	$-0.989626\pi$
$2$	−1.45954	−	1.45954i	−1.03205	−	1.03205i	−0.0325837	−	0.999469i	$-0.510374\pi$
$3$	−0.873658	+	1.49557i	−0.504407	+	0.863466i
$3$	−0.873658	+	1.49557i	−0.504407	+	0.863466i
$4$			2.26053i			1.13027i
$5$	0.0197941	+	0.0197941i	0.00885220	+	0.00885220i	0.711519	−	0.702667i	$-0.248008\pi$
$5$	0.0197941	+	0.0197941i	0.00885220	+	0.00885220i	−0.702667	+	0.711519i	$0.748008\pi$
$6$	3.45799	−	0.907703i	1.41172	−	0.370568i
$7$	1.62307	+	2.08941i	0.613464	+	0.789723i
$7$	1.62307	+	2.08941i	0.613464	+	0.789723i
$8$	0.380256	−	0.380256i	0.134441	−	0.134441i
$9$	−1.47344	−	2.61323i	−0.491148	−	0.871076i
$10$		−	0.0577807i		−	0.0182719i
$11$	−4.20910	−	1.12782i	−1.26909	−	0.340052i	−0.439408	−	0.898287i	$-0.644812\pi$
$11$	−4.20910	−	1.12782i	−1.26909	−	0.340052i	−0.829682	+	0.558236i	$0.811479\pi$
$12$	−3.38078	−	1.97493i	−0.975946	−	0.570114i
$13$	−3.51566	+	0.800100i	−0.975068	+	0.221908i
$13$	−3.51566	+	0.800100i	−0.975068	+	0.221908i
$14$	0.680641	−	5.41853i	0.181909	−	1.44816i
$15$	−0.0468967	+	0.0123101i	−0.0121087	+	0.00317846i
$16$	3.41106			0.852765
$17$	−2.29176	−	3.96945i	−0.555835	−	0.962734i	−0.997838	−	0.0657203i	$-0.979065\pi$
$17$	−2.29176	−	3.96945i	−0.555835	−	0.962734i	0.442004	−	0.897013i	$-0.354268\pi$
$18$	−1.66357	+	5.96467i	−0.392106	+	1.40589i
$19$	0.716593	−	0.716593i	0.164398	−	0.164398i	−0.620114	−	0.784512i	$-0.712914\pi$
$19$	0.716593	−	0.716593i	0.164398	−	0.164398i	0.784512	+	0.620114i	$0.212914\pi$
$20$	−0.0447452	+	0.0447452i	−0.0100053	+	0.0100053i
$21$	−4.54286	+	0.601983i	−0.991334	+	0.131364i
$22$	4.49725	+	7.78947i	0.958817	+	1.66072i
$23$	0.348171	+	0.603051i	0.0725988	+	0.125745i	0.900040	−	0.435808i	$-0.143537\pi$
$23$	0.348171	+	0.603051i	0.0725988	+	0.125745i	−0.827441	+	0.561553i	$0.810204\pi$
$24$	0.236485	+	0.900913i	0.0482723	+	0.183898i
$25$		−	4.99922i		−	0.999843i
$26$	6.29903	+	3.96347i	1.23534	+	0.777301i
$27$	5.19555	+	0.0794361i	0.999883	+	0.0152875i
$28$	−4.72318	+	3.66901i	−0.892597	+	0.693377i
$29$	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	$0.492018\pi$
$30$	0.0864149	+	0.0504806i	0.0157771	+	0.00921645i
$31$	7.53151	+	2.01806i	1.35270	+	0.362455i	0.861131	−	0.508384i	$-0.169757\pi$
$31$	7.53151	+	2.01806i	1.35270	+	0.362455i	0.491569	+	0.870838i	$0.336423\pi$
$32$	−5.73910	−	5.73910i	−1.01454	−	1.01454i
$33$	5.36405	−	5.30966i	0.933761	−	0.924293i
$34$	−2.44866	+	9.13851i	−0.419941	+	1.56724i
$35$	−0.00923075	+	0.0734853i	−0.00156028	+	0.0124213i
$36$	5.90729	−	3.33076i	0.984548	−	0.555127i
$37$	1.63546	−	0.438219i	0.268868	−	0.0720428i	−0.121866	−	0.992547i	$-0.538888\pi$
$37$	1.63546	−	0.438219i	0.268868	−	0.0720428i	0.390734	+	0.920504i	$0.372221\pi$
$38$	−2.09180			−0.339334
$39$	1.87488	−	5.95691i	0.300221	−	0.953870i
$40$	0.0150537			0.00238019
$41$	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	$0.446262\pi$
$42$	7.50913	+	5.75188i	1.15868	+	0.887535i
$43$		−	3.29833i		−	0.502991i	−0.967858	−	0.251496i	$-0.919078\pi$
$43$		−	3.29833i		−	0.502991i	0.967858	−	0.251496i	$-0.0809224\pi$
$44$	2.54948	−	9.51480i	0.384349	−	1.43441i
$45$	0.0225611	−	0.0808920i	0.00336320	−	0.0120587i
$46$	0.372007	−	1.38835i	0.0548495	−	0.204701i
$47$	−2.49912	−	9.32685i	−0.364534	−	1.36046i	−0.868051	−	0.496475i	$-0.834627\pi$
$47$	−2.49912	−	9.32685i	−0.364534	−	1.36046i	0.503516	−	0.863986i	$-0.332039\pi$
$48$	−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
$51$	7.93880	+	0.0404567i	1.11165	+	0.00566507i
$52$	−1.80865	−	7.94725i	−0.250815	−	1.10209i
$53$	−9.51169	−	5.49158i	−1.30653	−	0.754326i	−0.325016	−	0.945709i	$-0.605370\pi$
$53$	−9.51169	−	5.49158i	−1.30653	−	0.754326i	−0.981516	+	0.191382i	$0.938703\pi$
$54$	−7.46718	−	7.69906i	−1.01615	−	1.04771i
$55$	−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
$58$	−3.00095	−	11.1997i	−0.394044	−	1.47059i
$59$	10.3899	−	10.3899i	1.35264	−	1.35264i	0.469954	−	0.882691i	$-0.344270\pi$
$59$	10.3899	−	10.3899i	1.35264	−	1.35264i	0.882691	−	0.469954i	$-0.155730\pi$
$60$	−0.0278275	−	0.106011i	−0.00359251	−	0.0136860i
$61$	−6.31704	−	10.9414i	−0.808814	−	1.40091i	−0.913686	−	0.406422i	$-0.866776\pi$
$61$	−6.31704	−	10.9414i	−0.808814	−	1.40091i	0.104871	−	0.994486i	$-0.466557\pi$
$62$	−8.04712	−	13.9380i	−1.02199	−	1.77013i
$63$	3.06860	−	7.32009i	0.386608	−	0.922244i
$64$			9.93081i			1.24135i
$65$	−0.0854266	−	0.0537520i	−0.0105959	−	0.00666712i
$66$	−15.5787	−	0.0793903i	−1.91761	−	0.00977227i
$67$	2.10393	+	7.85197i	0.257036	+	0.959270i	0.966947	+	0.254979i	$0.0820685\pi$
$67$	2.10393	+	7.85197i	0.257036	+	0.959270i	−0.709911	+	0.704292i	$0.751265\pi$
$68$	8.97307	−	5.18060i	1.08814	−	0.628241i
$69$	−1.20609	−	0.00614629i	−0.145196	−	0.000739927i
$70$	0.120728	−	0.0937823i	0.0144297	−	0.0112091i
$71$	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	$0.251163\pi$
$72$	−1.55398	−	0.433411i	−0.183139	−	0.0510780i
$73$	8.19820	−	2.19670i	0.959527	−	0.257105i	0.255127	−	0.966908i	$-0.417883\pi$
$73$	8.19820	−	2.19670i	0.959527	−	0.257105i	0.704400	+	0.709803i	$0.251216\pi$
$74$	−3.02662	−	1.74742i	−0.351837	−	0.203133i
$75$	7.47666	+	4.36761i	0.863331	+	0.504328i
$76$	1.61988	+	1.61988i	0.185813	+	0.185813i
$77$	−4.47518	−	10.6251i	−0.509994	−	1.21084i
$78$	−11.4308	+	5.95791i	−1.29429	+	0.674600i
$79$	−2.07705	+	3.59756i	−0.233687	+	0.404757i	−0.958890	−	0.283777i	$-0.908412\pi$
$79$	−2.07705	+	3.59756i	−0.233687	+	0.404757i	0.725203	+	0.688535i	$0.241746\pi$
$80$	0.0675189	+	0.0675189i	0.00754885	+	0.00754885i
$81$	−4.65793	+	7.70089i	−0.517548	+	0.855654i
$82$		−	21.5661i		−	2.38157i
$83$	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	$-0.226411\pi$
$84$	−1.36080	−	10.2693i	−0.148476	−	1.12047i
$85$	0.0332083	−	0.123935i	0.00360195	−	0.0134427i
$86$	−4.81406	+	4.81406i	−0.519113	+	0.519113i
$87$	−8.45070	+	4.82176i	−0.906010	+	0.516947i
$88$	−2.02940	+	1.17167i	−0.216335	+	0.124901i
$89$	−0.629629	−	2.34981i	−0.0667405	−	0.249079i	0.924493	−	0.381198i	$-0.124488\pi$
$89$	−0.629629	−	2.34981i	−0.0667405	−	0.249079i	−0.991234	+	0.132119i	$0.957822\pi$
$90$	−0.150994	+	0.0851366i	−0.0159162	+	0.00897418i
$91$	−7.37790	−	6.04703i	−0.773414	−	0.633901i
$92$	−1.36321	+	0.787052i	−0.142125	+	0.0820559i
$93$	−9.59812	+	9.50079i	−0.995279	+	0.985186i
$94$	−9.96536	+	17.2605i	−1.02785	+	1.78029i
$95$	0.0283686			0.00291056
$96$	13.5972	−	3.56920i	1.38776	−	0.364280i
$97$	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	$0.202664\pi$
$98$	12.4263	−	7.37253i	1.25524	−	0.744738i
$99$	3.25460	+	12.6611i	0.327100	+	1.27249i
$100$	11.3009			1.13009
$101$	−1.36062	−	2.35666i	−0.135386	−	0.234496i	0.790359	−	0.612645i	$-0.209894\pi$
$101$	−1.36062	−	2.35666i	−0.135386	−	0.234496i	−0.925745	+	0.378148i	$0.876561\pi$
$102$	−11.5280	−	11.6461i	−1.14144	−	1.15313i
$103$			10.3711i			1.02189i	0.859612	+	0.510947i	$0.170705\pi$
$103$			10.3711i			1.02189i	−0.859612	+	0.510947i	$0.829295\pi$
$104$	−1.03261	+	1.64109i	−0.101255	+	0.160922i
$105$	−0.101838	−	0.0780062i	−0.00993834	−	0.00761263i
$106$	5.86753	+	21.8979i	0.569905	+	2.12691i
$107$	−2.29606	−	1.32563i	−0.221968	−	0.128153i	0.384893	−	0.922961i	$-0.374238\pi$
$107$	−2.29606	−	1.32563i	−0.221968	−	0.128153i	−0.606861	+	0.794808i	$0.707572\pi$
$108$	−0.179568	+	11.7447i	−0.0172789	+	1.13013i
$109$	−4.91508	−	18.3433i	−0.470779	−	1.75697i	−0.636981	−	0.770879i	$-0.719817\pi$
$109$	−4.91508	−	18.3433i	−0.470779	−	1.75697i	0.166202	−	0.986092i	$-0.446850\pi$
$110$	−0.0651665	+	0.243205i	−0.00621338	+	0.0231887i
$111$	−0.773444	+	2.82879i	−0.0734121	+	0.268497i
$112$	5.53640	+	7.12711i	0.523141	+	0.673448i
$113$	−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	$0.570073\pi$
$114$	1.82751	−	3.12842i	0.171162	−	0.293003i
$115$	−0.00504511	+	0.0188286i	−0.000470459	+	0.00175578i
$116$	−6.34909	+	10.9969i	−0.589498	+	1.02104i
$117$	7.27096	+	8.00831i	0.672201	+	0.740369i
$118$	−30.3289			−2.79200
$119$	4.57412	−	11.2311i	0.419309	−	1.02956i
$120$	−0.0131518	+	0.0225138i	−0.00120059	+	0.00205522i
$121$	6.91824	+	3.99425i	0.628931	+	0.363113i
$122$	−6.74951	+	25.1895i	−0.611071	+	2.28055i
$123$	−17.5037	+	4.59463i	−1.57826	+	0.414284i
$124$	−4.56189	+	17.0252i	−0.409670	+	1.52891i
$125$	0.197926	−	0.197926i	0.0177030	−	0.0177030i
$126$	−15.1627	+	6.20522i	−1.35080	+	0.552805i
$127$	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	$0.196376\pi$
$128$	3.01624	−	3.01624i	0.266600	−	0.266600i
$129$	4.93288	+	2.88162i	0.434316	+	0.253712i
$130$	0.0462303	+	0.203137i	0.00405467	+	0.0178163i
$131$			7.92837i			0.692705i	0.938104	+	0.346353i	$0.112580\pi$
$131$			7.92837i			0.692705i	−0.938104	+	0.346353i	$0.887420\pi$
$132$	12.0026	+	12.1256i	1.04470	+	1.05540i
$133$	2.66034	+	0.334174i	0.230681	+	0.0289766i
$134$	8.38951	−	14.5311i	0.724743	−	1.25529i
$135$	0.101269	+	0.104414i	0.00871583	+	0.00898649i
$136$	−2.38087	−	0.637951i	−0.204158	−	0.0547039i
$137$	5.61805	+	20.9669i	0.479983	+	1.79132i	0.601663	+	0.798750i	$0.294505\pi$
$137$	5.61805	+	20.9669i	0.479983	+	1.79132i	−0.121681	+	0.992569i	$0.538828\pi$
$138$	1.75136	+	1.76930i	0.149086	+	0.150613i
$139$	−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
$142$	−14.9669	−	8.64116i	−1.25600	−	0.725150i
$143$	15.7001	+	0.597345i	1.31291	+	0.0499525i
$144$	−5.02600	−	8.91388i	−0.418834	−	0.742824i
$145$	0.0406985	+	0.151889i	0.00337983	+	0.0126137i
$146$	−15.1718	−	8.75945i	−1.25563	−	0.724937i
$147$	−8.63119	−	8.51485i	−0.711888	−	0.702293i
$148$	0.990609	+	3.69700i	0.0814275	+	0.303892i
$149$	21.0826	−	5.64905i	1.72715	−	0.462789i	0.747627	−	0.664119i	$-0.231193\pi$
$149$	21.0826	−	5.64905i	1.72715	−	0.462789i	0.979523	+	0.201330i	$0.0645264\pi$
$150$	−4.53780	−	17.2872i	−0.370510	−	1.41150i
$151$	−2.35277	−	2.35277i	−0.191465	−	0.191465i	0.604864	−	0.796329i	$-0.293228\pi$
$151$	−2.35277	−	2.35277i	−0.191465	−	0.191465i	−0.796329	+	0.604864i	$0.793228\pi$
$152$		−	0.544978i		−	0.0442035i
$153$	−6.99630	+	11.8377i	−0.565618	+	0.957019i
$154$	−8.97603	+	22.0395i	−0.723309	+	1.77599i
$155$	0.109134	+	0.189025i	0.00876584	+	0.0151829i
$156$	13.4658	+	4.23822i	1.07813	+	0.339329i
$157$	0.855991	+	1.48262i	0.0683155	+	0.118326i	0.898160	−	0.439669i	$-0.144904\pi$
$157$	0.855991	+	1.48262i	0.0683155	+	0.118326i	−0.829844	+	0.557995i	$0.811571\pi$
$158$	8.28234	−	2.21925i	0.658908	−	0.176554i
$159$	16.5230	−	9.42761i	1.31036	−	0.747658i
$160$		−	0.227201i		−	0.0179618i
$161$	−0.694913	+	1.70627i	−0.0547668	+	0.134473i
$162$	18.0382	−	4.44132i	1.41722	−	0.348943i
$163$	−11.5339	−	11.5339i	−0.903401	−	0.903401i	0.0923276	−	0.995729i	$-0.470569\pi$
$163$	−11.5339	−	11.5339i	−0.903401	−	0.903401i	−0.995729	+	0.0923276i	$0.970569\pi$
$164$	−16.7007	+	16.7007i	−1.30411	+	1.30411i
$165$	0.211277	+	0.00107668i	0.0164479	+	8.38194e-5i
$166$	−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	$0.222494\pi$
$168$	−1.49854	+	1.95636i	−0.115615	+	0.150936i
$169$	11.7197	−	5.62575i	0.901514	−	0.432750i
$170$	−0.229358	+	0.132420i	−0.0175909	+	0.0101561i
$171$	−2.92848	−	0.816762i	−0.223946	−	0.0624594i
$172$	7.45598			0.568513
$173$	−5.90944	−	10.2355i	−0.449287	−	0.778187i	0.549053	−	0.835787i	$-0.314988\pi$
$173$	−5.90944	−	10.2355i	−0.449287	−	0.778187i	−0.998340	+	0.0576003i	$0.981655\pi$
$174$	19.3717	+	5.29659i	1.46857	+	0.401533i
$175$	10.4454	−	8.11409i	0.789599	−	0.613368i
$176$	−14.3575	−	3.84708i	−1.08224	−	0.289984i
$177$	6.46155	+	24.6159i	0.485680	+	1.85025i
$178$	−2.51067	+	4.34861i	−0.188183	+	0.325942i
$179$	−9.59979			−0.717522			−0.358761	−	0.933430i	$-0.616801\pi$
$179$	−9.59979			−0.717522			−0.358761	+	0.933430i	$0.616801\pi$
$180$	0.182859	+	0.0510000i	0.0136295	+	0.00380131i
$181$		−	4.87226i		−	0.362152i	−0.983469	−	0.181076i	$-0.942042\pi$
$181$		−	4.87226i		−	0.362152i	0.983469	−	0.181076i	$-0.0579580\pi$
$182$	1.94246	+	19.5943i	0.143985	+	1.45242i
$183$	21.8826	+	0.111515i	1.61761	+	0.00824344i
$184$	0.361708	+	0.0969194i	0.0266655	+	0.00714499i
$185$	0.0410466	+	0.0236983i	0.00301781	+	0.00174233i
$186$	27.8757	+	0.142056i	2.04394	+	0.0104161i
$187$	5.16942	+	19.2925i	0.378025	+	1.41081i
$188$	21.0836	−	5.64934i	1.53768	−	0.412021i
$189$	8.26677	+	10.9846i	0.601319	+	0.799009i
$190$	−0.0414052	−	0.0414052i	−0.00300385	−	0.00300385i
$191$	−3.39796	+	1.96181i	−0.245868	+	0.141952i	−0.617871	−	0.786280i	$-0.712005\pi$
$191$	−3.39796	+	1.96181i	−0.245868	+	0.141952i	0.372003	+	0.928232i	$0.378671\pi$
$192$	−14.8522	−	8.67613i	−1.07186	−	0.626146i
$193$	−7.86945	+	2.10861i	−0.566455	+	0.151781i	−0.530670	−	0.847578i	$-0.678060\pi$
$193$	−7.86945	+	2.10861i	−0.566455	+	0.151781i	−0.0357848	+	0.999360i	$0.511393\pi$
$194$	−6.02409			−0.432505
$195$	0.155023	−	0.0808003i	0.0111015	−	0.00578623i
$196$	−15.3321	−	3.91360i	−1.09515	−	0.279543i
$197$	−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	$0.147561\pi$
$198$	13.7292	−	23.2297i	0.975693	−	1.65086i
$199$	11.7204	−	6.76680i	0.830840	−	0.479686i	−0.0232999	−	0.999729i	$-0.507417\pi$
$199$	11.7204	−	6.76680i	0.830840	−	0.479686i	0.854140	+	0.520043i	$0.174084\pi$
$200$	−1.90098	−	1.90098i	−0.134420	−	0.134420i
$201$	−13.5813	−	3.71337i	−0.957948	−	0.261921i
$202$	−1.45376	+	5.42552i	−0.102287	+	0.381738i
$203$	2.02739	+	14.7232i	0.142295	+	1.03336i
$204$	−0.0914536	+	17.9459i	−0.00640303	+	1.25646i
$205$			0.292476i			0.0204274i
$206$	15.1371	−	15.1371i	1.05465	−	1.05465i
$207$	1.06290	−	1.79841i	0.0738766	−	0.124998i
$208$	−11.9921	+	2.72919i	−0.831504	+	0.189235i
$209$	−3.82440	+	2.20802i	−0.264539	+	0.152732i
$210$	0.0347830	+	0.262490i	0.00240026	+	0.0181135i
$211$	13.9971			0.963601			0.481800	−	0.876281i	$-0.339983\pi$
$211$	13.9971			0.963601			0.481800	+	0.876281i	$0.339983\pi$
$212$	12.4139	−	21.5015i	0.852589	−	1.47673i
$213$	−3.82475	+	13.9886i	−0.262068	+	0.958485i
$214$	1.41638	+	5.28601i	0.0968218	+	0.361344i
$215$	0.0652876	−	0.0652876i	0.00445258	−	0.00445258i
$216$	2.00584	−	1.94543i	0.136480	−	0.132370i
$217$	8.00763	+	19.0119i	0.543593	+	1.29061i
$218$	−19.5991	+	33.9466i	−1.32742	+	2.29916i
$219$	−3.87711	+	14.1801i	−0.261991	+	0.958205i
$220$	0.238802	−	0.137872i	0.0161000	−	0.00929534i
$221$	11.2330	+	12.1216i	0.755614	+	0.815386i
$222$	5.25762	−	2.99987i	0.352868	−	0.201338i
$223$	−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	$-0.243358\pi$
$224$	2.67636	−	21.3063i	0.178822	−	1.42359i
$225$	−13.0641	+	7.36606i	−0.870940	+	0.491071i
$226$	28.6987	+	7.68979i	1.90901	+	0.511517i
$227$	−3.91747	+	1.04968i	−0.260012	+	0.0696700i	−0.386470	−	0.922302i	$-0.626306\pi$
$227$	−3.91747	+	1.04968i	−0.260012	+	0.0696700i	0.126458	+	0.991972i	$0.459639\pi$
$228$	−3.83786	+	1.00742i	−0.254169	+	0.0667179i
$229$	−2.26392	−	2.26392i	−0.149604	−	0.149604i	0.628337	−	0.777941i	$-0.283736\pi$
$229$	−2.26392	−	2.26392i	−0.149604	−	0.149604i	−0.777941	+	0.628337i	$0.783736\pi$
$230$	0.0348447	−	0.0201176i	0.00229759	−	0.00132651i
$231$	19.8003	+	2.58975i	1.30276	+	0.170393i
$232$	2.91787	−	0.781841i	0.191568	−	0.0513304i
$233$	1.66608	+	2.88573i	0.109148	+	0.189050i	0.915425	−	0.402488i	$-0.131854\pi$
$233$	1.66608	+	2.88573i	0.109148	+	0.189050i	−0.806277	+	0.591538i	$0.798521\pi$
$234$	1.07620	−	22.3008i	0.0703532	−	1.45785i
$235$	0.135149	−	0.234085i	0.00881614	−	0.0152700i
$236$	23.4866	+	23.4866i	1.52885	+	1.52885i
$237$	−3.56576	−	6.24941i	−0.231621	−	0.405943i
$238$	−23.0685	+	9.71622i	−1.49531	+	0.629809i
$239$	−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	$0.478533\pi$
$240$	−0.159968	+	0.0419906i	−0.0103259	+	0.00271048i
$241$	−13.7794	+	3.69217i	−0.887607	+	0.237834i	−0.673686	−	0.739017i	$-0.735290\pi$
$241$	−13.7794	+	3.69217i	−0.887607	+	0.237834i	−0.213921	+	0.976851i	$0.568623\pi$
$242$	−4.26769	−	15.9272i	−0.274338	−	1.02384i
$243$	−7.44775	−	13.6942i	−0.477774	−	0.878483i
$244$	24.7335	−	14.2799i	1.58340	−	0.914175i
$245$	−0.168523	+	0.0999851i	−0.0107665	+	0.00638782i
$246$	32.2535	+	18.8414i	2.05641	+	1.20128i
$247$	−1.94595	+	3.09264i	−0.123818	+	0.196780i
$248$	3.63129	−	2.09652i	0.230587	−	0.133129i
$249$	18.3527	+	18.5407i	1.16306	+	1.17497i
$250$	−0.577762			−0.0365409
$251$	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	$-0.0380688\pi$
$252$	16.5473	+	6.93667i	1.04238	+	0.436969i
$253$	−0.785353	−	2.93098i	−0.0493747	−	0.184269i
$254$	−18.7438	−	5.02239i	−1.17609	−	0.315133i
$255$	0.156341	+	0.157942i	0.00979044	+	0.00989073i
$256$	11.0570			0.691060
$257$	5.82305	+	10.0858i	0.363232	+	0.629136i	0.988491	−	0.151282i	$-0.0483400\pi$
$257$	5.82305	+	10.0858i	0.363232	+	0.629136i	−0.625259	+	0.780417i	$0.715007\pi$
$258$	−2.99391	−	11.4056i	−0.186393	−	0.710081i
$259$	3.57009	+	2.70588i	0.221834	+	0.168135i
$260$	0.121508	−	0.193109i	0.00753562	−	0.0119761i
$261$	0.171754	−	16.8512i	0.0106313	−	1.04306i
$262$	11.5718	−	11.5718i	0.714908	−	0.714908i
$263$	−5.41734	+	3.12770i	−0.334047	+	0.192862i	−0.657637	−	0.753335i	$-0.728444\pi$
$263$	−5.41734	+	3.12770i	−0.334047	+	0.192862i	0.323589	+	0.946198i	$0.395110\pi$
$264$	0.0206836	−	4.05874i	0.00127299	−	0.249798i
$265$	−0.0795746	−	0.296976i	−0.00488823	−	0.0182431i
$266$	−3.39513	−	4.37062i	−0.208169	−	0.267980i
$267$	4.06437	+	1.11128i	0.248736	+	0.0680090i
$268$	−17.7496	+	4.75599i	−1.08423	+	0.290519i
$269$	−21.8350	+	12.6064i	−1.33130	+	0.768629i	−0.985500	−	0.169678i	$-0.945727\pi$
$269$	−21.8350	+	12.6064i	−1.33130	+	0.768629i	−0.345804	+	0.938307i	$0.612394\pi$
$270$	0.00458987	−	0.300202i	0.000279331	−	0.0182697i
$271$	14.6738	−	3.93185i	0.891373	−	0.238843i	0.216065	−	0.976379i	$-0.430678\pi$
$271$	14.6738	−	3.93185i	0.891373	−	0.238843i	0.675308	+	0.737536i	$0.264011\pi$
$272$	−7.81735	−	13.5400i	−0.473996	−	0.820986i
$273$	15.4895	−	5.75111i	0.937467	−	0.348073i
$274$	22.4022	−	38.8018i	1.35337	−	2.34410i
$275$	−5.63824	+	21.0422i	−0.339999	+	1.26889i
$276$	0.0138939	−	2.72639i	0.000836314	−	0.164110i
$277$	5.48879	+	3.16895i	0.329789	+	0.190404i	0.655748	−	0.754980i	$-0.272354\pi$
$277$	5.48879	+	3.16895i	0.329789	+	0.190404i	−0.325958	+	0.945384i	$0.605687\pi$
$278$	−11.1180	+	41.4928i	−0.666811	+	2.48857i
$279$	−5.82359	−	22.6551i	−0.348649	−	1.35632i
$280$	0.0244332	+	0.0314533i	0.00146016	+	0.00187969i
$281$	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	$0.487047\pi$
$282$	−17.1079	−	29.9837i	−1.01876	−	1.78550i
$283$	−6.13068	−	3.53955i	−0.364431	−	0.210404i	0.306592	−	0.951841i	$-0.400811\pi$
$283$	−6.13068	−	3.53955i	−0.364431	−	0.210404i	−0.671023	+	0.741437i	$0.734145\pi$
$284$	4.89865	+	18.2820i	0.290682	+	1.08484i
$285$	−0.0247845	+	0.0424272i	−0.00146811	+	0.00251317i
$286$	−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
$289$	−2.00437	+	3.47167i	−0.117904	+	0.204216i
$290$	0.162287	−	0.281089i	0.00952983	−	0.0165061i
$291$	1.28343	+	4.88935i	0.0752359	+	0.286619i
$292$	4.96571	+	18.5323i	0.290596	+	1.08452i
$293$	−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	$0.593152\pi$
$294$	0.169806	+	25.0254i	0.00990327	+	1.45951i
$295$	0.411316			0.0239478
$296$	0.455257	−	0.788529i	0.0264613	−	0.0458323i
$297$	−21.7790	−	6.19402i	−1.26374	−	0.359413i
$298$	−39.0159	−	22.5259i	−2.26013	−	1.30489i
$299$	−1.70655	−	1.84155i	−0.0986924	−	0.106499i
$300$	−9.87311	+	16.9012i	−0.570024	+	0.975793i
$301$	6.89157	−	5.35343i	0.397224	−	0.308567i
$302$			6.86793i			0.395205i
$303$	4.71326	+	0.0240191i	0.270769	+	0.00137986i
$304$	2.44434	−	2.44434i	0.140193	−	0.140193i
$305$	0.0915358	−	0.341616i	0.00524133	−	0.0195609i
$306$	27.4890	−	7.06618i	1.57144	−	0.403946i
$307$	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
$310$	0.116605	−	0.435176i	0.00662273	−	0.0247164i
$311$	−3.91428	−	6.77973i	−0.221958	−	0.384443i	0.733444	−	0.679750i	$-0.237912\pi$
$311$	−3.91428	−	6.77973i	−0.221958	−	0.384443i	−0.955403	+	0.295306i	$0.904578\pi$
$312$	−1.55222	−	2.97809i	−0.0878771	−	0.168601i
$313$	5.95736	−	10.3184i	0.336730	−	0.583233i	−0.647086	−	0.762417i	$-0.724012\pi$
$313$	5.95736	−	10.3184i	0.336730	−	0.583233i	0.983816	+	0.179184i	$0.0573458\pi$
$314$	0.914591	−	3.41330i	0.0516134	−	0.192624i
$315$	0.205635	−	0.0841543i	0.0115862	−	0.00474156i
$316$	−8.13240	−	4.69524i	−0.457483	−	0.264128i
$317$	−5.47895	+	1.46808i	−0.307729	+	0.0824557i	−0.409379	−	0.912365i	$-0.634255\pi$
$317$	−5.47895	+	1.46808i	−0.307729	+	0.0824557i	0.101650	+	0.994820i	$0.467588\pi$
$318$	−37.8760	−	10.3560i	−2.12398	−	0.580736i
$319$	−17.3086	−	17.3086i	−0.969094	−	0.969094i
$320$	−0.196572	+	0.196572i	−0.0109887	+	0.0109887i
$321$	3.98854	−	2.27576i	0.222618	−	0.127021i
$322$	3.50463	−	1.47612i	0.195305	−	0.0822607i
$323$	−4.48674	−	1.20222i	−0.249649	−	0.0668932i
$324$	−17.4081	−	10.5294i	−0.967116	−	0.584967i
$325$	3.99987	+	17.5755i	0.221873	+	0.974915i
$326$			33.6683i			1.86472i
$327$	31.7278	+	8.67496i	1.75455	+	0.479726i
$328$	5.61863			0.310237
$329$	15.4314	−	20.3598i	0.850759	−	1.12247i
$330$	−0.306796	−	0.309939i	−0.0168885	−	0.0170616i
$331$	13.7558	+	3.68586i	0.756088	+	0.202593i	0.616217	−	0.787577i	$-0.288665\pi$
$331$	13.7558	+	3.68586i	0.756088	+	0.202593i	0.139871	+	0.990170i	$0.455331\pi$
$332$	32.8877	+	8.81224i	1.80495	+	0.483634i
$333$	−3.55492	−	3.62813i	−0.194808	−	0.198820i
$334$	−4.60430			−0.251936
$335$	−0.113777	+	0.197068i	−0.00621632	+	0.0107670i
$336$	−15.4960	+	2.05340i	−0.845376	+	0.112022i
$337$	−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	$0.925062\pi$
$338$	−25.3164	−	8.89435i	−1.37703	−	0.483789i
$339$	0.127051	−	24.9311i	0.00690044	−	1.35407i
$340$	0.280159	+	0.0750685i	0.0151938	+	0.00407116i
$341$	−29.4249	−	16.9885i	−1.59345	−	0.919976i
$342$	3.08214	+	5.46634i	0.166663	+	0.295586i
$343$	−16.9815	+	7.39120i	−0.916913	+	0.399087i
$344$	−1.25421	−	1.25421i	−0.0676226	−	0.0676226i
$345$	−0.0237517	−	0.0239951i	−0.00127875	−	0.00129185i
$346$	−6.31400	+	23.5642i	−0.339443	+	1.26682i
$347$			24.8196i			1.33238i	0.745780	+	0.666192i	$0.232077\pi$
$347$			24.8196i			1.33238i	−0.745780	+	0.666192i	$0.767923\pi$
$348$	−10.8997	−	19.1031i	−0.584287	−	1.02403i
$349$	−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
$353$	−1.37453	+	5.12981i	−0.0731588	+	0.273032i	−0.992810	−	0.119705i	$-0.961805\pi$
$353$	−1.37453	+	5.12981i	−0.0731588	+	0.273032i	0.919651	+	0.392737i	$0.128472\pi$
$354$	26.4971	−	45.3589i	1.40830	−	2.41080i
$355$	0.202979	+	0.117190i	0.0107730	+	0.00621981i
$356$	5.31181	−	1.42330i	0.281525	−	0.0754345i
$357$	12.8007	+	16.6531i	0.677486	+	0.881374i
$358$	14.0113	+	14.0113i	0.740520	+	0.740520i
$359$	−15.7661	−	4.22453i	−0.832105	−	0.222962i	−0.182473	−	0.983211i	$-0.558410\pi$
$359$	−15.7661	−	4.22453i	−0.832105	−	0.222962i	−0.649632	+	0.760249i	$0.725077\pi$
$360$	−0.0221807	−	0.0393387i	−0.00116903	−	0.00207333i
$361$			17.9730i			0.945947i
$362$	−7.11127	+	7.11127i	−0.373760	+	0.373760i
$363$	−12.0178	+	6.85709i	−0.630773	+	0.359904i
$364$	13.6695	−	16.6780i	0.716476	−	0.874163i
$365$	0.205758	+	0.118794i	0.0107699	+	0.00621798i
$366$	−31.7758	−	32.1013i	−1.66095	−	1.67796i
$367$	−7.16442	−	12.4091i	−0.373980	−	0.647752i	0.616194	−	0.787594i	$-0.288674\pi$
$367$	−7.16442	−	12.4091i	−0.373980	−	0.647752i	−0.990174	+	0.139843i	$0.955340\pi$
$368$	1.18763	+	2.05704i	0.0619097	+	0.107231i
$369$	8.42069	−	30.1921i	0.438363	−	1.57174i
$370$	−0.0253206	−	0.0944979i	−0.00131636	−	0.00491271i
$371$	−3.96400	−	28.7871i	−0.205801	−	1.49455i
$372$	−21.4768	−	21.6968i	−1.11352	−	1.12493i
$373$	6.87364	−	11.9055i	0.355903	−	0.616443i	−0.631369	−	0.775483i	$-0.717507\pi$
$373$	6.87364	−	11.9055i	0.355903	−	0.616443i	0.987272	+	0.159040i	$0.0508399\pi$
$374$	20.6133	−	35.7032i	1.06589	−	1.84617i
$375$	0.123092	+	0.468930i	0.00635643	+	0.0242155i
$376$	−4.49690	−	2.59629i	−0.231910	−	0.133893i
$377$	−19.3501	−	5.98203i	−0.996578	−	0.308090i
$378$	3.96673	−	28.0981i	0.204026	−	1.44521i
$379$	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	$0.509081\pi$
$380$			0.0641282i			0.00328971i
$381$	−0.0829798	+	16.2831i	−0.00425119	+	0.834209i
$382$	7.82283	+	2.09612i	0.400251	+	0.107247i
$383$	1.95217	−	0.523084i	0.0997515	−	0.0267283i	−0.208598	−	0.978001i	$-0.566890\pi$
$383$	1.95217	−	0.523084i	0.0997515	−	0.0267283i	0.308350	+	0.951273i	$0.400223\pi$
$384$	1.87583	+	7.14615i	0.0957254	+	0.364676i
$385$	0.121732	−	0.298896i	0.00620402	−	0.0152332i
$386$	14.5634	+	8.40819i	0.741258	+	0.427965i
$387$	−8.61930	+	4.85991i	−0.438144	+	0.247043i
$388$	4.66504	+	4.66504i	0.236832	+	0.236832i
$389$	1.55484			0.0788334			0.0394167	−	0.999223i	$-0.487450\pi$
$389$	1.55484			0.0788334			0.0394167	+	0.999223i	$0.487450\pi$
$390$	−0.344195	−	0.108332i	−0.0174290	−	0.00548560i
$391$	1.59585	−	2.76410i	0.0807058	−	0.139787i
$392$	1.92077	+	3.23743i	0.0970136	+	0.163515i
$393$	−11.8574	−	6.92669i	−0.598127	−	0.349405i
$394$	10.0565	−	5.80613i	0.506640	−	0.292509i
$395$	−0.112324	+	0.0300971i	−0.00565163	+	0.00151435i
$396$	−28.6209	+	7.35713i	−1.43825	+	0.369710i
$397$	−18.0727	−	18.0727i	−0.907043	−	0.907043i	0.0889893	−	0.996033i	$-0.471636\pi$
$397$	−18.0727	−	18.0727i	−0.907043	−	0.907043i	−0.996033	+	0.0889893i	$0.971636\pi$
$398$	−26.9829	−	7.23006i	−1.35253	−	0.362410i
$399$	−2.82401	+	3.68676i	−0.141377	+	0.184569i
$400$		−	17.0526i		−	0.852632i
$401$	−7.96576	−	2.13442i	−0.397791	−	0.106588i	0.0543771	−	0.998520i	$-0.482683\pi$
$401$	−7.96576	−	2.13442i	−0.397791	−	0.106588i	−0.452168	+	0.891933i	$0.649349\pi$
$402$	14.4026	+	25.2423i	0.718337	+	1.25897i
$403$	−28.0929	−	1.06885i	−1.39941	−	0.0532434i
$404$	5.32730	−	3.07572i	0.265043	−	0.153023i
$405$	−0.244632	+	0.0602326i	−0.0121559	+	0.00299298i
$406$	18.5300	−	24.4482i	0.919630	−	1.21334i
$407$	−7.37804			−0.365716
$408$	3.03416	−	3.00340i	0.150213	−	0.148690i
$409$	0.211258	−	0.211258i	0.0104460	−	0.0104460i	−0.701864	−	0.712311i	$-0.747649\pi$
$409$	0.211258	−	0.211258i	0.0104460	−	0.0104460i	0.712311	+	0.701864i	$0.247649\pi$
$410$	0.426881	−	0.426881i	0.0210822	−	0.0210822i
$411$	−36.2656	−	9.91569i	−1.78885	−	0.489105i
$412$	−23.4442			−1.15501
$413$	38.5722	+	4.84519i	1.89801	+	0.238416i
$414$	−4.17621	+	1.07351i	−0.205249	+	0.0527603i
$415$	0.365141	−	0.210815i	0.0179241	−	0.0103485i
$416$	24.7686	+	15.5849i	1.21438	+	0.764111i
$417$	36.0456	+	0.183691i	1.76516	+	0.00899537i
$418$	8.80457	+	2.35918i	0.430646	+	0.115391i
$419$		−	5.52463i		−	0.269896i	−0.990853	−	0.134948i	$-0.956913\pi$
$419$		−	5.52463i		−	0.269896i	0.990853	−	0.134948i	$-0.0430867\pi$
$420$	0.176336	−	0.230207i	0.00860429	−	0.0112330i
$421$	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	$0.466704\pi$
$422$	−20.4294	−	20.4294i	−0.994487	−	0.994487i
$423$	−20.6909	+	20.2734i	−1.00603	+	0.985725i
$424$	−5.70509	+	1.52867i	−0.277063	+	0.0742389i
$425$	−19.8442	+	11.4570i	−0.962583	+	0.555747i
$426$	25.9994	−	14.8346i	1.25968	−	0.718740i
$427$	12.6081	−	30.9576i	0.610151	−	1.49815i
$428$	2.99663	−	5.19031i	0.144847	−	0.250883i
$429$	−14.6099	+	22.9587i	−0.705373	+	1.10846i
$430$	−0.190580			−0.00919059
$431$	−25.3682	−	25.3682i	−1.22194	−	1.22194i	−0.966940	−	0.255005i	$-0.917923\pi$
$431$	−25.3682	−	25.3682i	−1.22194	−	1.22194i	−0.255005	−	0.966940i	$-0.582077\pi$
$432$	17.7223	+	0.270961i	0.852666	+	0.0130366i
$433$	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	$0.646802\pi$
$434$	16.0612	−	39.4361i	0.770962	−	1.89300i
$435$	−0.262717	−	0.0718316i	−0.0125963	−	0.00344406i
$436$	41.4656	−	11.1107i	1.98584	−	0.532105i
$437$	0.681639	+	0.182645i	0.0326072	+	0.00873707i
$438$	26.3553	−	15.0377i	1.25931	−	0.718529i
$439$		−	25.6265i		−	1.22309i	−0.791210	−	0.611544i	$-0.790549\pi$
$439$		−	25.6265i		−	1.22309i	0.791210	−	0.611544i	$-0.209451\pi$
$440$	−0.0633624	−	0.0169779i	−0.00302068	−	0.000809390i
$441$	20.2752	−	5.46946i	0.965487	−	0.260450i
$442$	1.29692	−	34.0870i	0.0616880	−	1.62136i
$443$	17.7108	+	10.2253i	0.841465	+	0.485820i	0.857762	−	0.514047i	$-0.171854\pi$
$443$	17.7108	+	10.2253i	0.841465	+	0.485820i	−0.0162966	+	0.999867i	$0.505188\pi$
$444$	−6.39457	−	1.74839i	−0.303473	−	0.0829751i
$445$	0.0340494	−	0.0589753i	0.00161410	−	0.00279570i
$446$	−14.8515	+	25.7236i	−0.703241	+	1.21805i
$447$	−9.97041	+	36.4657i	−0.471584	+	1.72477i
$448$	−20.7495	+	16.1184i	−0.980324	+	0.761524i
$449$	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	$0.735503\pi$
$450$	29.8187	+	8.31653i	1.40567	+	0.392045i
$451$	−22.7643	−	39.4289i	−1.07193	−	1.85664i
$452$	−16.2692	−	28.1791i	−0.765240	−	1.32543i
$453$	5.57423	−	1.46321i	0.261900	−	0.0687474i
$454$	7.24978	+	4.18566i	0.340249	+	0.196443i
$455$	−0.0263434	−	0.265735i	−0.00123500	−	0.0124578i
$456$	0.815051	+	0.476124i	0.0381682	+	0.0222966i
$457$	4.80854	−	4.80854i	0.224934	−	0.224934i	−0.585638	−	0.810572i	$-0.699156\pi$
$457$	4.80854	−	4.80854i	0.224934	−	0.224934i	0.810572	+	0.585638i	$0.199156\pi$
$458$			6.60858i			0.308799i
$459$	−11.5916	−	20.8055i	−0.541052	−	0.971118i
$460$	−0.0425626	−	0.0114046i	−0.00198449	−	0.000531743i
$461$	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	$0.505580\pi$
$462$	−25.1195	−	32.6792i	−1.16867	−	1.52038i
$463$	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	$0.393105\pi$
$464$	16.5940	+	9.58055i	0.770357	+	0.444766i
$465$	−0.378046	−	0.00192655i	−0.0175315	−	8.93415e-5i
$466$	1.78013	−	6.64355i	0.0824631	−	0.307757i
$467$	10.9273	+	18.9267i	0.505657	+	0.875824i	0.999979	+	0.00654466i	$0.00208324\pi$
$467$	10.9273	+	18.9267i	0.505657	+	0.875824i	−0.494321	+	0.869279i	$0.664583\pi$
$468$	−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
$471$	−2.96520	−	0.0151109i	−0.136629	−	0.000696272i
$472$		−	7.90162i		−	0.363702i
$473$	−3.71994	+	13.8830i	−0.171043	+	0.638341i
$474$	−3.91690	+	14.3257i	−0.179909	+	0.658000i
$475$	−3.58240	−	3.58240i	−0.164372	−	0.164372i
$476$	25.3884	+	10.3399i	1.16367	+	0.473930i
$477$	−0.335817	+	32.9478i	−0.0153760	+	1.50857i
$478$	10.6748	+	6.16310i	0.488254	+	0.281894i
$479$	2.65373	+	0.711063i	0.121252	+	0.0324893i	0.318935	−	0.947777i	$-0.396675\pi$
$479$	2.65373	+	0.711063i	0.121252	+	0.0324893i	−0.197683	+	0.980266i	$0.563342\pi$
$480$	0.339794	+	0.198496i	0.0155094	+	0.00906006i
$481$	−5.39909	+	2.84916i	−0.246177	+	0.129910i
$482$	25.5005	+	14.7227i	1.16151	+	0.670600i
$483$	−1.94472	−	2.52998i	−0.0884879	−	0.115118i
$484$	−9.02912	+	15.6389i	−0.410415	+	0.710859i
$485$	0.0816979			0.00370971
$486$	−9.11695	+	30.8576i	−0.413553	+	1.39973i
$487$	33.9656	+	9.10105i	1.53913	+	0.412408i	0.925984	−	0.377563i	$-0.123238\pi$
$487$	33.9656	+	9.10105i	1.53913	+	0.412408i	0.613144	+	0.789971i	$0.289904\pi$
$488$	−6.56265	−	1.75846i	−0.297077	−	0.0796015i
$489$	27.3263	−	7.17301i	1.23574	−	0.324375i
$490$	0.391899	+	0.100034i	0.0177042	+	0.00451908i
$491$	−23.6585			−1.06769			−0.533847	−	0.845581i	$-0.679254\pi$
$491$	−23.6585			−1.06769			−0.533847	+	0.845581i	$0.679254\pi$
$492$	−10.3863	−	39.5677i	−0.468251	−	1.78385i
$493$		−	25.7473i		−	1.15960i
$494$	7.35403	−	1.67364i	0.330874	−	0.0753008i
$495$	−0.186194	+	0.315038i	−0.00836879	+	0.0141599i
$496$	25.6905	+	6.88374i	1.15354	+	0.309089i
$497$	17.6544	+	13.3808i	0.791909	+	0.600212i
$498$	0.274411	−	53.8476i	0.0122967	−	2.41297i
$499$	3.31774	−	3.31774i	0.148522	−	0.148522i	−0.628935	−	0.777458i	$-0.716509\pi$
$499$	3.31774	−	3.31774i	0.148522	−	0.148522i	0.777458	+	0.628935i	$0.216509\pi$
$500$	0.447417	+	0.447417i	0.0200091	+	0.0200091i
$501$	0.980943	+	3.73700i	0.0438253	+	0.166957i
$502$	−37.8893	+	10.1524i	−1.69108	+	0.453124i
$503$	−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	$0.743452\pi$
$504$	−1.61665	−	3.95036i	−0.0720114	−	0.175963i
$505$	0.0197157	−	0.0735802i	0.000877339	−	0.00327427i
$506$	−3.13163	+	5.42414i	−0.139218	+	0.241132i
$507$	−1.82531	+	22.4426i	−0.0810646	+	0.996709i
$508$	10.6258	+	18.4045i	0.471445	+	0.816567i
$509$	−3.65204	+	13.6296i	−0.161874	+	0.604121i	0.836545	+	0.547899i	$0.184572\pi$
$509$	−3.65204	+	13.6296i	−0.161874	+	0.604121i	−0.998418	+	0.0562220i	$0.982095\pi$
$510$	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
$513$	3.78001	−	3.66617i	0.166892	−	0.161865i
$514$	6.22169	−	23.2197i	0.274427	−	1.02418i
$515$	−0.205287	+	0.205287i	−0.00904601	+	0.00904601i
$516$	−6.51398	+	11.1509i	−0.286762	+	0.490892i
$517$			42.0762i			1.85051i
$518$	−1.26135	−	9.16004i	−0.0554204	−	0.402469i
$519$	20.4706	+	0.104320i	0.898561	+	0.00457913i
$520$	−0.0529235	+	0.0120444i	−0.00232085	+	0.000528184i
$521$	22.0638	+	12.7386i	0.966635	+	0.558087i	0.898209	−	0.439569i	$-0.144869\pi$
$521$	22.0638	+	12.7386i	0.966635	+	0.558087i	0.0684261	+	0.997656i	$0.478202\pi$
$522$	−24.8457	+	24.3443i	−1.08747	+	1.06552i
$523$	−9.59983	+	16.6274i	−0.419771	+	0.727065i	−0.995916	−	0.0902826i	$-0.971223\pi$
$523$	−9.59983	+	16.6274i	−0.419771	+	0.727065i	0.576145	+	0.817347i	$0.304556\pi$
$524$	−17.9223			−0.782941
$525$	3.00944	+	22.7108i	0.131343	+	0.991179i
$526$	12.4719	+	3.34182i	0.543799	+	0.145710i
$527$	−9.24985	−	34.5209i	−0.402930	−	1.50375i
$528$	18.2971	−	18.1116i	0.796279	−	0.788205i
$529$	11.2576	−	19.4987i	0.489459	−	0.847768i
$530$	−0.317307	+	0.549592i	−0.0137829	+	0.0238728i
$531$	−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
$534$	−4.31017	−	7.55408i	−0.186519	−	0.326897i
$535$	−0.0192088	−	0.0716881i	−0.000830467	−	0.00309935i
$536$	3.78579	+	2.18573i	0.163521	+	0.0944091i
$537$	8.38693	−	14.3571i	0.361923	−	0.619556i
$538$	50.2688	+	13.4695i	2.16724	+	0.580710i
$539$	14.9366	−	26.5958i	0.643365	−	1.14556i
$540$	−0.236030	+	0.228921i	−0.0101571	+	0.00985121i
$541$	−11.2887	+	42.1301i	−0.485340	+	1.81132i	0.0931822	+	0.995649i	$0.470296\pi$
$541$	−11.2887	+	42.1301i	−0.485340	+	1.81132i	−0.578523	+	0.815666i	$0.696371\pi$
$542$	−27.1558	−	15.6784i	−1.16644	−	0.673446i
$543$	7.28679	+	4.25669i	0.312706	+	0.182672i
$544$	−9.62842	+	35.9338i	−0.412815	+	1.54065i
$545$	0.265800	−	0.460379i	0.0113856	−	0.0197205i
$546$	−31.0016	−	14.2136i	−1.32675	−	0.608286i
$547$	−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	$0.996810\pi$
$548$	−47.3962	+	12.6998i	−2.02467	+	0.542508i
$549$	−19.2847	+	32.6295i	−0.823050	+	1.39259i
$550$	38.9412	−	22.4827i	1.66046	−	0.958667i
$551$	5.49873	−	1.47338i	0.234254	−	0.0627681i
$552$	−0.460959	+	0.456284i	−0.0196197	+	0.0194208i
$553$	−10.8880	+	1.49929i	−0.463004	+	0.0637561i
$554$	−3.38590	−	12.6363i	−0.143853	−	0.536867i
$555$	−0.0713030	+	0.0406838i	−0.00302665	+	0.00172693i
$556$	40.7416	−	23.5222i	1.72783	−	0.997562i
$557$	13.0906	−	13.0906i	0.554666	−	0.554666i	−0.373118	−	0.927784i	$-0.621711\pi$
$557$	13.0906	−	13.0906i	0.554666	−	0.554666i	0.927784	+	0.373118i	$0.121711\pi$
$558$	−24.5663	+	41.5658i	−1.03997	+	1.75962i
$559$	2.63900	+	11.5958i	0.111618	+	0.490450i
$560$	−0.0314867	+	0.250663i	−0.00133055	+	0.0105924i
$561$	−33.3696	−	9.12386i	−1.40886	−	0.385210i
$562$	−10.3075	−	17.8532i	−0.434797	−	0.753091i
$563$	14.1806			0.597640			0.298820	−	0.954310i	$-0.403407\pi$
$563$	14.1806			0.597640			0.298820	+	0.954310i	$0.403407\pi$
$564$	−9.97092	+	36.4676i	−0.419851	+	1.53556i
$565$	−0.389207	−	0.104288i	−0.0163741	−	0.00438742i
$566$	3.78187	+	14.1141i	0.158964	+	0.593261i
$567$	−23.6505	+	2.76676i	−0.993227	+	0.116193i
$568$	2.25129	−	3.89935i	0.0944620	−	0.163613i
$569$	−5.97551			−0.250506			−0.125253	−	0.992125i	$-0.539974\pi$
$569$	−5.97551			−0.250506			−0.125253	+	0.992125i	$0.539974\pi$
$570$	0.0980983	−	0.0257503i	0.00410889	−	0.00107856i
$571$	−18.5439	+	10.7064i	−0.776040	+	0.448047i	−0.835025	−	0.550212i	$-0.814547\pi$
$571$	−18.5439	+	10.7064i	−0.776040	+	0.448047i	0.0589850	+	0.998259i	$0.481214\pi$
$572$	−1.35032	+	35.4906i	−0.0564596	+	1.48394i
$573$	0.0346321	−	6.79584i	0.00144677	−	0.283900i
$574$	45.0604	−	35.0033i	1.88078	−	1.46101i
$575$	3.01478	−	1.74058i	0.125725	−	0.0725874i
$576$	25.9515	−	14.6325i	1.08131	−	0.609687i
$577$	0.376075	+	1.40353i	0.0156562	+	0.0584297i	0.973312	−	0.229486i	$-0.0737044\pi$
$577$	0.376075	+	1.40353i	0.0156562	+	0.0584297i	−0.957656	+	0.287915i	$0.907038\pi$
$578$	7.99251	−	2.14159i	0.332445	−	0.0890783i
$579$	3.72164	−	13.6115i	0.154666	−	0.565674i
$580$	−0.343349	+	0.0920002i	−0.0142568	+	0.00382010i
$581$	36.7254	−	15.4684i	1.52363	−	0.641737i
$582$	5.26300	−	9.00944i	0.218158	−	0.373453i
$583$	33.8421	+	33.8421i	1.40160	+	1.40160i
$584$	2.28211	−	3.95273i	0.0944343	−	0.163565i
$585$	−0.0145952	+	0.302440i	−0.000603438	+	0.0125043i
$586$	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	$0.134291\pi$
$588$	19.2481	−	19.5111i	0.793777	−	0.804623i
$589$	6.84316	−	3.95090i	0.281967	−	0.162794i
$590$	−0.600334	−	0.600334i	−0.0247153	−	0.0247153i
$591$	−6.85498	−	6.92520i	−0.281976	−	0.284865i
$592$	5.57865	−	1.49479i	0.229281	−	0.0614356i
$593$	6.06221	+	1.62436i	0.248945	+	0.0667046i	0.381134	−	0.924520i	$-0.375534\pi$
$593$	6.06221	+	1.62436i	0.248945	+	0.0667046i	−0.132189	+	0.991225i	$0.542200\pi$
$594$	22.7469	+	40.8278i	0.933317	+	1.67518i
$595$	0.312851	−	0.131770i	0.0128256	−	0.00540204i
$596$	12.7699	+	47.6578i	0.523074	+	1.95214i
$597$	−0.119455	+	23.4406i	−0.00488896	+	0.959359i
$598$	−0.197031	+	5.17860i	−0.00805721	+	0.211769i
$599$	27.9754	−	16.1516i	1.14305	−	0.659938i	0.195863	−	0.980631i	$-0.437249\pi$
$599$	27.9754	−	16.1516i	1.14305	−	0.659938i	0.947183	+	0.320693i	$0.103916\pi$
$600$	4.50386	−	1.18224i	0.183869	−	0.0482647i
$601$	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	$-0.0862187\pi$
$602$	−17.8721	−	2.24498i	−0.728413	−	0.0914985i
$603$	17.4190	−	17.0675i	0.709355	−	0.695041i
$604$	5.31850	−	5.31850i	0.216407	−	0.216407i
$605$	0.0578778	+	0.216003i	0.00235307	+	0.00878177i
$606$	−6.84414	−	6.91426i	−0.278024	−	0.280872i
$607$	11.3833	−	19.7165i	0.462036	−	0.800269i	−0.537027	−	0.843565i	$-0.680453\pi$
$607$	11.3833	−	19.7165i	0.462036	−	0.800269i	0.999062	+	0.0432960i	$0.0137859\pi$
$608$	−8.22520			−0.333576
$609$	−23.7907	−	9.83091i	−0.964049	−	0.398369i
$610$	−0.632204	+	0.365003i	−0.0255972	+	0.0147786i
$611$	16.2485	+	30.7905i	0.657343	+	1.24565i
$612$	−26.7594	−	15.8154i	−1.08169	−	0.639298i
$613$	−23.5550	+	23.5550i	−0.951377	+	0.951377i	−0.998872	−	0.0474942i	$-0.984876\pi$
$613$	−23.5550	+	23.5550i	−0.951377	+	0.951377i	0.0474942	+	0.998872i	$0.484876\pi$
$614$		−	24.4469i		−	0.986595i
$615$	−0.437417	−	0.255524i	−0.0176384	−	0.0103037i
$616$	−5.74197	−	2.33853i	−0.231350	−	0.0942223i
$617$	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	$-0.0190331\pi$
$618$	9.41387	+	35.8631i	0.378682	+	1.44263i
$619$	8.97507	+	8.97507i	0.360738	+	0.360738i	0.864085	−	0.503346i	$-0.167898\pi$
$619$	8.97507	+	8.97507i	0.360738	+	0.360738i	−0.503346	+	0.864085i	$0.667898\pi$
$620$	−0.427298	+	0.246701i	−0.0171607	+	0.00990773i
$621$	1.76104	+	3.16083i	0.0706680	+	0.126840i
$622$	−4.18225	+	15.6084i	−0.167693	+	0.625838i
$623$	3.88778	−	5.12946i	0.155761	−	0.205507i
$624$	6.39533	−	20.3194i	0.256018	−	0.813427i
$625$	−24.9882			−0.999530
$626$	−23.7552	+	6.36520i	−0.949450	+	0.254404i
$627$	0.0389783	−	7.64870i	0.00155664	−	0.305460i
$628$	−3.35151	+	1.93499i	−0.133740	+	0.0772146i
$629$	−5.48757	−	5.48757i	−0.218804	−	0.218804i
$630$	−0.422960	−	0.177306i	−0.0168511	−	0.00706405i
$631$	−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	$0.482270\pi$
$632$	0.578183	+	2.15781i	0.0229989	+	0.0858330i
$633$	−12.2287	+	20.9336i	−0.486047	+	0.832037i
$634$	10.1395	+	5.85404i	0.402691	+	0.232494i
$635$	0.254201	+	0.0681129i	0.0100877	+	0.00270298i
$636$	21.3114	+	37.3507i	0.845052	+	1.48105i
$637$	0.659860	−	25.2302i	0.0261446	−	0.999658i
$638$			50.5252i			2.00031i
$639$	−17.5794	−	17.9415i	−0.695431	−	0.709753i
$640$	0.119408			0.00472000
$641$	13.7805	−	23.8685i	0.544297	−	0.942750i	−0.454354	−	0.890821i	$-0.650130\pi$
$641$	13.7805	−	23.8685i	0.544297	−	0.942750i	0.998651	−	0.0519285i	$-0.0165368\pi$
$642$	−9.14301	−	2.49987i	−0.360846	−	0.0986620i
$643$	−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	$0.778834\pi$
$644$	−3.85707	−	1.57087i	−0.151990	−	0.0619010i
$645$	0.0406029	+	0.154681i	0.00159874	+	0.00609056i
$646$	4.79390	+	8.30328i	0.188614	+	0.326688i
$647$	−16.7276			−0.657630			−0.328815	−	0.944394i	$-0.606649\pi$
$647$	−16.7276			−0.657630			−0.328815	+	0.944394i	$0.606649\pi$
$648$	1.15710	+	4.69952i	0.0454553	+	0.184615i
$649$	−55.4499	+	32.0140i	−2.17660	+	1.25666i
$650$	19.8143	−	31.4902i	0.777179	−	1.23515i
$651$	−35.4295	−	4.63394i	−1.38859	−	0.181618i
$652$	26.0726	−	26.0726i	1.02108	−	1.02108i
$653$	2.34269	−	1.35256i	0.0916767	−	0.0529296i	−0.453461	−	0.891276i	$-0.649811\pi$
$653$	2.34269	−	1.35256i	0.0916767	−	0.0529296i	0.545137	+	0.838347i	$0.316477\pi$
$654$	−33.6466	−	58.9695i	−1.31568	−	2.30589i
$655$	−0.156935	+	0.156935i	−0.00613196	+	0.00613196i
$656$	25.2008	+	25.2008i	0.983924	+	0.983924i
$657$	−17.8201	−	18.1871i	−0.695227	−	0.709545i
$658$	−52.2388	+	7.19333i	−2.03648	+	0.280425i
$659$		−	1.73029i		−	0.0674024i	−0.999432	−	0.0337012i	$-0.989271\pi$
$659$		−	1.73029i		−	0.0674024i	0.999432	−	0.0337012i	$-0.0107295\pi$
$660$	−0.00243387	+	0.477597i	−9.47382e−5	+	0.0185904i
$661$	14.8306	−	3.97384i	0.576843	−	0.154565i	0.0414098	−	0.999142i	$-0.486815\pi$
$661$	14.8306	−	3.97384i	0.576843	−	0.154565i	0.535433	+	0.844578i	$0.320148\pi$
$662$	−14.6975	−	25.4569i	−0.571236	−	0.989409i
$663$	−27.9425	+	6.20960i	−1.08520	+	0.241161i
$664$	−4.04987	−	7.01458i	−0.157165	−	0.272218i
$665$	0.0460443	+	0.0592737i	0.00178552	+	0.00229854i
$666$	−0.106857	+	10.4840i	−0.00414062	+	0.406246i
$667$			3.91160i			0.151458i
$668$	3.56556	+	3.56556i	0.137956	+	0.137956i
$669$	24.0423	+	6.57360i	0.929527	+	0.254150i
$670$	0.453692	−	0.121566i	0.0175277	−	0.00469652i
$671$	14.2490	+	53.1781i	0.550078	+	2.05292i
$672$	29.5268	+	22.6171i	1.13902	+	0.872474i
$673$	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	$0.478186\pi$
$674$	14.2303	+	53.1084i	0.548132	+	2.04566i
$675$	0.397118	−	25.9737i	0.0152851	−	0.999726i
$676$	12.7172	+	26.4927i	0.489123	+	1.01895i
$677$	−6.45930	−	3.72928i	−0.248251	−	0.143328i	0.370712	−	0.928748i	$-0.379114\pi$
$677$	−6.45930	−	3.72928i	−0.248251	−	0.143328i	−0.618963	+	0.785420i	$0.712447\pi$
$678$	−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
$681$	1.85266	−	6.77591i	0.0709941	−	0.259653i
$682$	18.1515	+	67.7422i	0.695056	+	2.59398i
$683$	11.5373	+	3.09142i	0.441464	+	0.118290i	0.472702	−	0.881222i	$-0.343279\pi$
$683$	11.5373	+	3.09142i	0.441464	+	0.118290i	−0.0312388	+	0.999512i	$0.509945\pi$
$684$	1.84632	−	6.61992i	0.0705957	−	0.253119i
$685$	−0.303816	+	0.526225i	−0.0116082	+	0.0201060i
$686$	35.5729	+	13.9974i	1.35818	+	0.534424i
$687$	5.36374	−	1.40795i	0.204639	−	0.0537168i
$688$		−	11.2508i		−	0.428933i
$689$	37.8336	+	11.6962i	1.44135	+	0.445590i
$690$	−0.000355137		0.0696885i	−1.35198e−5		0.00265300i
$691$	26.5362	−	26.5362i	1.00948	−	1.00948i	0.00952937	−	0.999955i	$-0.496967\pi$
$691$	26.5362	−	26.5362i	1.00948	−	1.00948i	0.999955	−	0.00952937i	$-0.00303334\pi$
$692$	23.1376	−	13.3585i	0.879558	−	0.507813i
$693$	−21.1718	+	27.3501i	−0.804251	+	1.03895i
$694$	36.2252	−	36.2252i	1.37509	−	1.37509i
$695$	0.150780	−	0.562719i	0.00571942	−	0.0213452i
$696$	−1.37993	+	5.04694i	−0.0523060	+	0.191304i
$697$	12.3947	−	46.2576i	0.469482	−	1.75213i
$698$	58.4214	+	33.7296i	2.21128	+	1.27669i
$699$	−5.77138	−	0.0294113i	−0.218294	−	0.00111244i
$700$	18.3422	+	23.6122i	0.693268	+	0.892457i
$701$	−43.6670			−1.64928			−0.824640	−	0.565658i	$-0.808622\pi$
$701$	−43.6670			−1.64928			−0.824640	+	0.565658i	$0.808622\pi$
$702$	32.4121	+	21.0928i	1.22331	+	0.796095i
$703$	0.857932	−	1.48598i	0.0323575	−	0.0560449i
$704$	11.2002	−	41.7998i	0.422124	−	1.57539i
$705$	0.232015	+	0.406634i	0.00873821	+	0.0153147i
$706$	9.49336	−	5.48099i	0.357287	−	0.206280i
$707$	2.71565	−	6.66792i	0.102132	−	0.250773i
$708$	−55.6451	+	14.6065i	−2.09127	+	0.548947i
$709$	−3.34152	+	12.4707i	−0.125493	+	0.468348i	−0.999857	−	0.0169240i	$-0.994613\pi$
$709$	−3.34152	+	12.4707i	−0.125493	+	0.468348i	0.874363	+	0.485272i	$0.161279\pi$
$710$	−0.125213	−	0.467301i	−0.00469916	−	0.0175375i
$711$	12.4617	+	0.127014i	0.467349	+	0.00476341i
$712$	−1.13295	−	0.654108i	−0.0424591	−	0.0245137i
$713$	1.40526	+	5.24452i	0.0526276	+	0.196409i
$714$	5.62269	−	42.9891i	0.210424	−	1.60883i
$715$	0.298946	+	0.322594i	0.0111799	+	0.0120643i
$716$		−	21.7006i		−	0.810990i
$717$	2.72792	−	9.97707i	0.101876	−	0.372600i
$718$	16.8455	+	29.1772i	0.628668	+	1.08889i
$719$	13.7056			0.511134			0.255567	−	0.966791i	$-0.417738\pi$
$719$	13.7056			0.511134			0.255567	+	0.966791i	$0.417738\pi$
$720$	0.0769572	−	0.275928i	0.00286802	−	0.0102832i
$721$	−21.6695	+	16.8330i	−0.807013	+	0.626895i
$722$	26.2324	−	26.2324i	0.976267	−	0.976267i
$723$	6.51657	−	23.8337i	0.242354	−	0.886383i
$724$	11.0139			0.409328
$725$	14.0412	−	24.3200i	0.521476	−	0.903222i
$726$	27.5488	+	7.53235i	1.02243	+	0.279552i
$727$	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	$0.206870\pi$
$728$	−5.10491	+	0.506072i	−0.189201	+	0.0187563i
$729$	26.9874	+	0.825427i	0.999533	+	0.0305714i
$730$	−0.126927	−	0.473698i	−0.00469778	−	0.0175324i
$731$	−13.0926	+	7.55900i	−0.484246	+	0.279580i
$732$	−0.252084	+	49.4663i	−0.00931728	+	1.82833i
$733$	31.1841	−	31.1841i	1.15181	−	1.15181i	0.165621	−	0.986189i	$-0.447037\pi$
$733$	31.1841	−	31.1841i	1.15181	−	1.15181i	0.986189	−	0.165621i	$-0.0529629\pi$
$734$	−7.65489	+	28.5684i	−0.282547	+	1.05448i
$735$	−0.00230288	−	0.339391i	−8.49431e−5	−	0.0125186i
$736$	1.46278	−	5.45916i	0.0539187	−	0.201227i
$737$		−	35.4226i		−	1.30481i
$738$	−56.3571	+	31.7764i	−2.07453	+	1.16970i
$739$	11.9310	+	11.9310i	0.438891	+	0.438891i	0.891639	−	0.452748i	$-0.149556\pi$
$739$	11.9310	+	11.9310i	0.438891	+	0.438891i	−0.452748	+	0.891639i	$0.649556\pi$
$740$	−0.0535707	+	0.0927871i	−0.00196930	+	0.00341092i
$741$	−2.92516	−	5.61220i	−0.107458	−	0.206170i
$742$	−36.2303	+	47.8016i	−1.33006	+	1.75485i
$743$	−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	$0.815707\pi$
$744$	−0.0370101	+	7.26248i	−0.00135686	+	0.266255i
$745$	0.529129	+	0.305493i	0.0193858	+	0.0111924i
$746$	−27.4089	+	7.34420i	−1.00351	+	0.268890i
$747$	−43.7629	+	11.2495i	−1.60120	+	0.411597i
$748$	−43.6113	+	11.6856i	−1.59459	+	0.427269i
$749$	−0.956883	−	6.94900i	−0.0349638	−	0.253911i
$750$	0.504766	−	0.864082i	0.0184315	−	0.0315518i
$751$	−16.0279	+	9.25372i	−0.584867	+	0.337673i	−0.763065	−	0.646322i	$-0.776306\pi$
$751$	−16.0279	+	9.25372i	−0.584867	+	0.337673i	0.178198	+	0.983995i	$0.442973\pi$
$752$	−8.52466	−	31.8145i	−0.310862	−	1.16015i
$753$	16.3123	+	28.5892i	0.594454	+	1.04185i
$754$	19.5112	+	36.9733i	0.710556	+	1.34649i
$755$		−	0.0931418i		−	0.00338978i
$756$	−24.8309	+	18.6873i	−0.903092	+	0.679650i
$757$	−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
$759$	5.06960	+	1.38612i	0.184015	+	0.0503131i
$760$	0.0107873	−	0.0107873i	0.000391298	−	0.000391298i
$761$	4.44334	+	16.5828i	0.161071	+	0.601125i	0.998509	+	0.0545922i	$0.0173859\pi$
$761$	4.44334	+	16.5828i	0.161071	+	0.601125i	−0.837438	+	0.546533i	$0.815947\pi$
$762$	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
$765$	−0.372802	+	0.0958305i	−0.0134787	+	0.00346476i
$766$	−3.61275	−	2.08582i	−0.130534	−	0.0753637i
$767$	−28.2143	+	44.8401i	−1.01876	+	1.61908i
$768$	−9.66000	+	16.5364i	−0.348575	+	0.596707i
$769$	−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
$772$	−4.76658	−	17.7891i	−0.171553	−	0.640245i
$773$	12.9257	−	48.2395i	0.464906	−	1.73505i	−0.192294	−	0.981337i	$-0.561593\pi$
$773$	12.9257	−	48.2395i	0.464906	−	1.73505i	0.657200	−	0.753716i	$-0.271741\pi$
$774$	19.6735	+	5.48700i	0.707149	+	0.197226i
$775$	10.0887	−	37.6517i	0.362398	−	1.35249i
$776$		−	1.56946i		−	0.0563405i
$777$	−7.16586	+	2.97529i	−0.257074	+	0.106738i
$778$	−2.26935	−	2.26935i	−0.0813602	−	0.0813602i
$779$	10.5883			0.379365
$780$	0.182652	+	0.350435i	0.00653997	+	0.0125476i
$781$	−36.4851			−1.30554
$782$	−6.36354	+	1.70511i	−0.227560	+	0.0609744i
$783$	25.0520	+	14.9790i	0.895285	+	0.535306i
$784$	−5.90548	+	23.1356i	−0.210910	+	0.826272i
$785$	−0.0124036	+	0.0462907i	−0.000442702	+	0.00165219i
$786$	7.19661	+	27.4162i	0.256694	+	0.977904i
$787$	−22.1281	−	22.1281i	−0.788783	−	0.788783i	0.192512	−	0.981295i	$-0.438337\pi$
$787$	−22.1281	−	22.1281i	−0.788783	−	0.788783i	−0.981295	+	0.192512i	$0.938337\pi$
$788$	−12.2840	−	3.29148i	−0.437599	−	0.117254i
$789$	0.0552135	−	10.8345i	0.00196565	−	0.385720i
$790$	0.207870	+	0.120014i	0.00739567	+	0.00426989i
$791$	−35.2704	−	14.3646i	−1.25407	−	0.510746i
$792$	6.05205	+	3.57689i	0.215050	+	0.127099i
$793$	30.9628	+	33.4121i	1.09952	+	1.18650i
$794$			52.7558i			1.87223i
$795$	0.513669	+	0.140447i	0.0182180	+	0.00498113i
$796$	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	$0.848278\pi$
$798$	9.50274	−	1.25923i	0.336393	−	0.0445761i
$799$	−31.2951	+	31.2951i	−1.10714	+	1.10714i
$800$	−28.6910	+	28.6910i	−1.01438	+	1.01438i
$801$	−5.21286	+	5.10767i	−0.184187	+	0.180471i
$802$	8.51109	+	14.7416i	0.300537	+	0.520546i
$803$	−36.9845			−1.30516
$804$	8.39419	−	30.7009i	0.296040	−	1.08274i
$805$	−0.0475292	+	0.0200189i	−0.00167519	+	0.000705573i
$806$	39.4427	+	42.5628i	1.38931	+	1.49921i
$807$	0.222542	−	43.6694i	0.00783387	−	1.53724i
$808$	−1.41352	−	0.378751i	−0.0497274	−	0.0133244i
$809$			15.5224i			0.545739i	0.962051	+	0.272869i	$0.0879727\pi$
$809$			15.5224i			0.545739i	−0.962051	+	0.272869i	$0.912027\pi$
$810$	0.444963	+	0.269139i	0.0156344	+	0.00945657i
$811$	−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	$0.250321\pi$
$812$	−33.2822	+	4.58298i	−1.16798	+	0.160831i
$813$	−6.93959	+	25.3808i	−0.243382	+	0.890144i
$814$	10.7686	+	10.7686i	0.377438	+	0.377438i
$815$		−	0.456605i		−	0.0159942i
$816$	27.0797	+	0.138000i	0.947981	+	0.00483097i
$817$	−2.36356	−	2.36356i	−0.0826905	−	0.0826905i
$818$	−0.616681			−0.0215617
$819$	−4.93136	+	28.1901i	−0.172316	+	0.985042i
$820$	−0.661151			−0.0230884
$821$	−24.0905	−	24.0905i	−0.840764	−	0.840764i	0.148194	−	0.988958i	$-0.452654\pi$
$821$	−24.0905	−	24.0905i	−0.840764	−	0.840764i	−0.988958	+	0.148194i	$0.952654\pi$
$822$	38.4588	+	67.4036i	1.34141	+	2.35097i
$823$			9.27570i			0.323331i	0.986846	+	0.161665i	$0.0516865\pi$
$823$			9.27570i			0.323331i	−0.986846	+	0.161665i	$0.948313\pi$
$824$	3.94367	+	3.94367i	0.137384	+	0.137384i
$825$	−26.5441	−	26.8160i	−0.924148	−	0.933615i
$826$	−49.2260	−	63.3695i	−1.71279	−	2.20491i
$827$	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	$-0.0908008\pi$
$828$	4.06537	+	2.40272i	0.141281	+	0.0835001i
$829$			8.35501i			0.290181i	0.989418	+	0.145091i	$0.0463474\pi$
$829$			8.35501i			0.290181i	−0.989418	+	0.145091i	$0.953653\pi$
$830$	−0.840633	−	0.225247i	−0.0291788	−	0.00781843i
$831$	−9.53470	+	5.44027i	−0.330755	+	0.188721i
$832$	−7.94564	−	34.9133i	−0.275465	−	1.21040i
$833$	30.8906	−	8.67175i	1.07030	−	0.300458i
$834$	−52.3419	−	52.8782i	−1.81245	−	1.83102i
$835$	0.0624429			0.00216093
$836$	−4.99129	−	8.64517i	−0.172627	−	0.299000i
$837$	38.9700	+	11.0832i	1.34700	+	0.383092i
$838$	−8.06343	+	8.06343i	−0.278547	+	0.278547i
$839$	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	$0.203412\pi$
$840$	−0.0683868	+	0.00906206i	−0.00235957	+	0.000312671i
$841$	1.27728	+	2.21231i	0.0440440	+	0.0762865i
$842$	−15.1729	−	26.2802i	−0.522892	−	0.905676i
$843$	−12.2942	+	12.1695i	−0.423435	+	0.419141i
$844$			31.6409i			1.08912i
$845$	0.343337	+	0.120624i	0.0118112	+	0.00414959i
$846$	59.7891	+	0.609394i	2.05559	+	0.0209514i
$847$	2.88318	+	20.9380i	0.0990673	+	0.719438i
$848$	−32.4450	−	18.7321i	−1.11416	−	0.643263i
$849$	10.6498	−	6.07649i	0.365499	−	0.208545i
$850$	45.6854	+	12.2414i	1.56700	+	0.419876i
$851$	0.833688	+	0.833688i	0.0285785	+	0.0285785i
$852$	−31.6217	−	8.64597i	−1.08334	−	0.296206i
$853$	−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	$0.961882\pi$
$854$	−63.5861	+	26.7819i	−2.17587	+	0.916457i
$855$	−0.0417996	−	0.0741337i	−0.00142951	−	0.00253532i
$856$	−1.37717	+	0.369011i	−0.0470707	+	0.0126125i
$857$	0.717736			0.0245174			0.0122587	−	0.999925i	$-0.496098\pi$
$857$	0.717736			0.0245174			0.0122587	+	0.999925i	$0.496098\pi$
$858$	54.8330	−	12.1854i	1.87197	−	0.416004i
$859$	0.404786			0.0138111			0.00690557	−	0.999976i	$-0.497802\pi$
$859$	0.404786			0.0138111			0.00690557	+	0.999976i	$0.497802\pi$
$860$	0.147585	+	0.147585i	0.00503259	+	0.00503259i
$861$	−38.0099	−	29.1150i	−1.29537	−	0.992238i
$862$			74.0521i			2.52222i
$863$	−2.79030	+	10.4136i	−0.0949830	+	0.354481i	−0.997017	−	0.0771838i	$-0.975407\pi$
$863$	−2.79030	+	10.4136i	−0.0949830	+	0.354481i	0.902034	+	0.431665i	$0.142074\pi$
$864$	−29.3619	−	30.2737i	−0.998911	−	1.02993i
$865$	0.0856296	−	0.319574i	0.00291149	−	0.0108658i
$866$	−1.38661	−	5.17489i	−0.0471189	−	0.175850i
$867$	−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
$870$	0.278605	+	0.488287i	0.00944559	+	0.0165545i
$871$	−13.6790	−	25.9215i	−0.463497	−	0.878315i
$872$	−8.84415	−	5.10617i	−0.299501	−	0.172917i
$873$	−8.43363	−	2.35217i	−0.285435	−	0.0796088i
$874$	−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
$877$	−11.7269	−	43.7656i	−0.395991	−	1.47786i	−0.820086	−	0.572240i	$-0.806074\pi$
$877$	−11.7269	−	43.7656i	−0.395991	−	1.47786i	0.424095	−	0.905618i	$-0.360592\pi$
$878$	−37.4030	+	37.4030i	−1.26229	+	1.26229i
$879$	1.29966	−	1.28648i	0.0438366	−	0.0433920i
$880$	−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	$-0.339475\pi$
$882$	−37.5755	−	21.6097i	−1.26523	−	0.727635i
$883$		−	8.00661i		−	0.269444i	−0.990883	−	0.134722i	$-0.956986\pi$
$883$		−	8.00661i		−	0.269444i	0.990883	−	0.134722i	$-0.0430141\pi$
$884$	−27.4012	+	25.3926i	−0.921603	+	0.854045i
$885$	−0.359350	+	0.615151i	−0.0120794	+	0.0206781i
$886$	−10.9254	−	40.7740i	−0.367045	−	1.36983i
$887$	−23.6921	+	13.6787i	−0.795504	+	0.459284i	−0.841897	−	0.539639i	$-0.818561\pi$
$887$	−23.6921	+	13.6787i	−0.795504	+	0.459284i	0.0463928	+	0.998923i	$0.485227\pi$
$888$	0.781558	+	1.36977i	0.0262274	+	0.0459665i
$889$	23.0360	+	9.38187i	0.772601	+	0.314658i
$890$	−0.135773	+	0.0363804i	−0.00455114	+	0.00121947i
$891$	28.2909	−	27.1605i	0.947782	−	0.909910i
$892$	31.4213	−	8.41931i	1.05206	−	0.281899i
$893$	−8.47441	−	4.89270i	−0.283585	−	0.163728i
$894$	67.7755	−	38.6711i	2.26675	−	1.29335i
$895$	−0.190019	−	0.190019i	−0.00635164	−	0.00635164i
$896$	11.1977	+	1.40659i	0.374090	+	0.0469908i
$897$	4.24510	−	0.943380i	0.141740	−	0.0314986i
$898$	23.5707	−	40.8256i	0.786563	−	1.36237i
$899$	30.9710	+	30.9710i	1.03294	+	1.03294i
$900$	−16.6512	−	29.5318i	−0.555040	−	0.984393i
$901$			50.3416i			1.67712i
$902$	−24.3227	+	90.7737i	−0.809859	+	3.02243i
$903$	1.98554	+	14.9839i	0.0660747	+	0.498632i
$904$	−2.00343	+	7.47690i	−0.0666330	+	0.248678i
$905$	0.0964420	−	0.0964420i	0.00320584	−	0.00320584i
$906$	−10.2714	−	6.00022i	−0.341246	−	0.199344i
$907$	−15.4444	+	8.91683i	−0.512823	+	0.296079i	−0.733993	−	0.679157i	$-0.762346\pi$
$907$	−15.4444	+	8.91683i	−0.512823	+	0.296079i	0.221170	+	0.975235i	$0.429012\pi$
$908$	−2.37284	−	8.85557i	−0.0787455	−	0.293882i
$909$	−4.15370	+	7.02801i	−0.137769	+	0.233104i
$910$	−0.349402	+	0.426300i	−0.0115826	+	0.0141317i
$911$	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	$0.0137528\pi$
$912$	1.52016	+	5.79120i	0.0503375	+	0.191766i
$913$	−32.8167	+	56.8402i	−1.08607	+	1.88114i
$914$	−14.0365			−0.464288
$915$	0.430939	+	0.435354i	0.0142464	+	0.0143924i
$916$	5.11766	−	5.11766i	0.169092	−	0.169092i
$917$	−16.5656	+	12.8683i	−0.547045	+	0.424949i
$918$	−13.4480	+	47.2851i	−0.443851	+	1.56064i
$919$	5.79888			0.191287			0.0956436	−	0.995416i	$-0.469509\pi$
$919$	5.79888			0.191287			0.0956436	+	0.995416i	$0.469509\pi$
$920$	0.00524126	+	0.00907813i	0.000172799	+	0.000299297i
$921$	−19.8419	+	5.20839i	−0.653812	+	0.171622i
$922$		−	61.5671i		−	2.02760i
$923$	−26.6990	+	14.0894i	−0.878808	+	0.463757i
$924$	−5.85420	+	44.7592i	−0.192589	+	1.47247i
$925$	−2.19075	−	8.17601i	−0.0720315	−	0.268825i
$926$	−5.68902	−	3.28456i	−0.186953	−	0.107937i
$927$	27.1020	−	15.2812i	0.890148	−	0.501901i
$928$	−11.8001	−	44.0386i	−0.387358	−	1.44564i
$929$	2.06439	−	7.70441i	0.0677304	−	0.252773i	−0.923756	−	0.382981i	$-0.874898\pi$
$929$	2.06439	−	7.70441i	0.0677304	−	0.252773i	0.991487	+	0.130207i	$0.0415643\pi$
$930$	0.548962	+	0.554586i	0.0180012	+	0.0181856i
$931$	3.61969	+	6.10093i	0.118631	+	0.199950i
$932$	−6.52328	+	3.76621i	−0.213677	+	0.123366i
$933$	13.5593	+	0.0690990i	0.443911	+	0.00226220i
$934$	11.6754	−	43.5733i	0.382032	−	1.42576i
$935$	−0.279554	+	0.484202i	−0.00914241	+	0.0158351i
$936$	5.81004	+	0.280383i	0.189907	+	0.00916459i
$937$	−9.59395			−0.313421			−0.156710	−	0.987645i	$-0.550089\pi$
$937$	−9.59395			−0.313421			−0.156710	+	0.987645i	$0.550089\pi$
$938$	43.9781	−	6.05583i	1.43594	−	0.197730i
$939$	10.2272	+	17.9244i	0.333753	+	0.584941i
$940$	0.529156	+	0.305508i	0.0172592	+	0.00996458i
$941$	3.76029	−	14.0336i	0.122582	−	0.457482i	−0.877160	−	0.480198i	$-0.840565\pi$
$941$	3.76029	−	14.0336i	0.122582	−	0.457482i	0.999742	+	0.0227160i	$0.00723136\pi$
$942$	4.30578	+	4.34989i	0.140290	+	0.141727i
$943$	−1.88304	+	7.02758i	−0.0613201	+	0.228850i
$944$	35.4405	−	35.4405i	1.15349	−	1.15349i
$945$	−0.0537962	+	0.381063i	−0.00174999	+	0.0123960i
$946$	25.6923	−	14.8334i	0.835327	−	0.482276i
$947$	−27.5465	+	27.5465i	−0.895142	+	0.895142i	−0.995002	−	0.0998592i	$-0.968161\pi$
$947$	−27.5465	+	27.5465i	−0.895142	+	0.895142i	0.0998592	+	0.995002i	$0.468161\pi$
$948$	14.1270	−	8.06051i	0.458823	−	0.261793i
$949$	−27.0645	+	14.2822i	−0.878550	+	0.463621i
$950$			10.4573i			0.339281i
$951$	2.59112	−	9.47675i	0.0840228	−	0.307305i
$952$	−2.53138	−	6.01005i	−0.0820424	−	0.194787i
$953$	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	$0.151028\pi$
$954$	48.5788	−	47.5985i	1.57280	−	1.54106i
$955$	−0.106092	−	0.0284273i	−0.00343306	−	0.000919885i
$956$	−3.49385	−	13.0392i	−0.112999	−	0.421719i
$957$	41.0079	−	10.7644i	1.32560	−	0.347962i
$958$	−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
$961$	25.8043	+	14.8981i	0.832398	+	0.480585i
$962$	12.0387	+	3.72173i	0.388142	+	0.119993i
$963$	−0.0810639	+	7.95336i	−0.00261225	+	0.256293i
$964$	−8.34626	−	31.1487i	−0.268815	−	1.00323i
$965$	−0.197507	−	0.114031i	−0.00635797	−	0.00367078i
$966$	−0.854215	+	6.53103i	−0.0274839	+	0.210132i
$967$	−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	$0.945327\pi$
$968$	4.14954	−	1.11187i	0.133371	−	0.0357367i
$969$	5.71788	−	5.65990i	0.183685	−	0.181822i
$970$	−0.119242	−	0.119242i	−0.00382862	−	0.00382862i
$971$		−	10.9089i		−	0.350082i	−0.984561	−	0.175041i	$-0.943994\pi$
$971$		−	10.9089i		−	0.350082i	0.984561	−	0.175041i	$-0.0560058\pi$
$972$	30.9562	−	16.8359i	0.992919	−	0.540011i
$973$	20.7684	−	50.9942i	0.665806	−	1.63480i
$974$	−36.2909	−	62.8576i	−1.16283	−	2.01409i
$975$	−29.7799	−	9.37293i	−0.953720	−	0.300174i
$976$	−21.5478	−	37.3219i	−0.689729	−	1.19465i
$977$	−18.6211	+	4.98951i	−0.595742	+	0.159629i	−0.544076	−	0.839036i	$-0.683120\pi$
$977$	−18.6211	+	4.98951i	−0.595742	+	0.159629i	−0.0516661	+	0.998664i	$0.516453\pi$
$978$	−50.3532	−	29.4146i	−1.61012	−	0.940575i
$979$			10.6007i			0.338799i
$980$	−0.226020	−	0.380952i	−0.00721993	−	0.0121691i
$981$	−40.6932	+	39.8720i	−1.29923	+	1.27302i
$982$	34.5306	+	34.5306i	1.10192	+	1.10192i
$983$	−28.8685	+	28.8685i	−0.920761	+	0.920761i	−0.997083	−	0.0763219i	$-0.975682\pi$
$983$	−28.8685	+	28.8685i	−0.920761	+	0.920761i	0.0763219	+	0.997083i	$0.475682\pi$
$984$	−4.90876	+	8.40304i	−0.156486	+	0.267879i
$985$	−0.136385	+	0.0787419i	−0.00434559	+	0.00250893i
$986$	−37.5792	+	37.5792i	−1.19677	+	1.19677i
$987$	16.9678	+	40.8662i	0.540090	+	1.30079i
$988$	−6.99101	−	4.39888i	−0.222414	−	0.139947i
$989$	1.98906	−	1.14839i	0.0632485	−	0.0365165i
$990$	0.731569	−	0.188053i	0.0232508	−	0.00597672i
$991$	2.83903			0.0901848			0.0450924	−	0.998983i	$-0.485642\pi$
$991$	2.83903			0.0901848			0.0450924	+	0.998983i	$0.485642\pi$
$992$	−31.6423	−	54.8060i	−1.00464	−	1.74009i
$993$	−17.5303	+	17.3526i	−0.556308	+	0.550667i
$994$	−6.23747	−	45.2973i	−0.197841	−	1.43674i
$995$	0.365939	+	0.0980530i	0.0116010	+	0.00310849i
$996$	−41.9119	+	41.4869i	−1.32803	+	1.31456i
$997$	−21.7609	+	37.6909i	−0.689173	+	1.19368i	0.282932	+	0.959140i	$0.408693\pi$
$997$	−21.7609	+	37.6909i	−0.689173	+	1.19368i	−0.972106	+	0.234543i	$0.924641\pi$
$998$	−9.68476			−0.306566
$999$	8.53190	−	2.14687i	0.269937	−	0.0679241i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.em.a.158.20	✓	432	1.1	even	1	trivial
819.2.em.a.254.20	yes	432	819.254	even	12	inner
819.2.fe.a.527.89	yes	432	91.72	odd	12
819.2.fe.a.704.89	yes	432	9.2	odd	6
819.2.ge.a.137.20	yes	432	117.20	even	12
819.2.ge.a.275.20	yes	432	7.2	even	3
819.2.gf.a.2.20	yes	432	63.2	odd	6
819.2.gf.a.410.20	yes	432	13.7	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.em (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.45954 - 1.45954i) q^{2} +(-0.873658 + 1.49557i) q^{3} +2.26053i q^{4} +(0.0197941 + 0.0197941i) q^{5} +(3.45799 - 0.907703i) q^{6} +(1.62307 + 2.08941i) q^{7} +(0.380256 - 0.380256i) q^{8} +(-1.47344 - 2.61323i) q^{9} +O(q^{10})\)	\(q+(-1.45954 - 1.45954i) q^{2} +(-0.873658 + 1.49557i) q^{3} +2.26053i q^{4} +(0.0197941 + 0.0197941i) q^{5} +(3.45799 - 0.907703i) q^{6} +(1.62307 + 2.08941i) q^{7} +(0.380256 - 0.380256i) q^{8} +(-1.47344 - 2.61323i) q^{9} -0.0577807i q^{10} +(-4.20910 - 1.12782i) q^{11} +(-3.38078 - 1.97493i) q^{12} +(-3.51566 + 0.800100i) q^{13} +(0.680641 - 5.41853i) q^{14} +(-0.0468967 + 0.0123101i) q^{15} +3.41106 q^{16} +(-2.29176 - 3.96945i) q^{17} +(-1.66357 + 5.96467i) q^{18} +(0.716593 - 0.716593i) q^{19} +(-0.0447452 + 0.0447452i) q^{20} +(-4.54286 + 0.601983i) q^{21} +(4.49725 + 7.78947i) q^{22} +(0.348171 + 0.603051i) q^{23} +(0.236485 + 0.900913i) q^{24} -4.99922i q^{25} +(6.29903 + 3.96347i) q^{26} +(5.19555 + 0.0794361i) q^{27} +(-4.72318 + 3.66901i) q^{28} +(4.86476 + 2.80867i) q^{29} +(0.0864149 + 0.0504806i) q^{30} +(7.53151 + 2.01806i) q^{31} +(-5.73910 - 5.73910i) q^{32} +(5.36405 - 5.30966i) q^{33} +(-2.44866 + 9.13851i) q^{34} +(-0.00923075 + 0.0734853i) q^{35} +(5.90729 - 3.33076i) q^{36} +(1.63546 - 0.438219i) q^{37} -2.09180 q^{38} +(1.87488 - 5.95691i) q^{39} +0.0150537 q^{40} +(7.38795 + 7.38795i) q^{41} +(7.50913 + 5.75188i) q^{42} -3.29833i q^{43} +(2.54948 - 9.51480i) q^{44} +(0.0225611 - 0.0808920i) q^{45} +(0.372007 - 1.38835i) q^{46} +(-2.49912 - 9.32685i) q^{47} +(-2.98010 + 5.10147i) q^{48} +(-1.73127 + 6.78253i) q^{49} +(-7.29657 + 7.29657i) q^{50} +(7.93880 + 0.0404567i) q^{51} +(-1.80865 - 7.94725i) q^{52} +(-9.51169 - 5.49158i) q^{53} +(-7.46718 - 7.69906i) q^{54} +(-0.0609911 - 0.105640i) q^{55} +(1.41169 + 0.177328i) q^{56} +(0.445655 + 1.69777i) q^{57} +(-3.00095 - 11.1997i) q^{58} +(10.3899 - 10.3899i) q^{59} +(-0.0278275 - 0.106011i) q^{60} +(-6.31704 - 10.9414i) q^{61} +(-8.04712 - 13.9380i) q^{62} +(3.06860 - 7.32009i) q^{63} +9.93081i q^{64} +(-0.0854266 - 0.0537520i) q^{65} +(-15.5787 - 0.0793903i) q^{66} +(2.10393 + 7.85197i) q^{67} +(8.97307 - 5.18060i) q^{68} +(-1.20609 - 0.00614629i) q^{69} +(0.120728 - 0.0937823i) q^{70} +(8.08749 - 2.16704i) q^{71} +(-1.55398 - 0.433411i) q^{72} +(8.19820 - 2.19670i) q^{73} +(-3.02662 - 1.74742i) q^{74} +(7.47666 + 4.36761i) q^{75} +(1.61988 + 1.61988i) q^{76} +(-4.47518 - 10.6251i) q^{77} +(-11.4308 + 5.95791i) q^{78} +(-2.07705 + 3.59756i) q^{79} +(0.0675189 + 0.0675189i) q^{80} +(-4.65793 + 7.70089i) q^{81} -21.5661i q^{82} +(3.89830 - 14.5487i) q^{83} +(-1.36080 - 10.2693i) q^{84} +(0.0332083 - 0.123935i) q^{85} +(-4.81406 + 4.81406i) q^{86} +(-8.45070 + 4.82176i) q^{87} +(-2.02940 + 1.17167i) q^{88} +(-0.629629 - 2.34981i) q^{89} +(-0.150994 + 0.0851366i) q^{90} +(-7.37790 - 6.04703i) q^{91} +(-1.36321 + 0.787052i) q^{92} +(-9.59812 + 9.50079i) q^{93} +(-9.96536 + 17.2605i) q^{94} +0.0283686 q^{95} +(13.5972 - 3.56920i) q^{96} +(2.06369 - 2.06369i) q^{97} +(12.4263 - 7.37253i) q^{98} +(3.25460 + 12.6611i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 6 q^{2} - 4 q^{3} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 432 * q - 6 * q^2 - 4 * q^3 - 4 * q^6 + 2 * q^7 + 12 * q^8 - 4 * q^9	\( 432 q - 6 q^{2} - 4 q^{3} - 4 q^{6} + 2 q^{7} + 12 q^{8} - 4 q^{9} - 12 q^{11} + 36 q^{12} - 4 q^{13} - 12 q^{14} - 24 q^{15} - 380 q^{16} - 26 q^{18} - 8 q^{19} - 12 q^{20} - 6 q^{21} + 4 q^{22} - 6 q^{23} + 20 q^{24} - 4 q^{27} - 12 q^{28} - 12 q^{29} - 24 q^{30} + 18 q^{31} + 18 q^{32} - 16 q^{33} - 36 q^{35} - 12 q^{36} + 40 q^{39} + 24 q^{40} - 12 q^{41} - 34 q^{42} + 108 q^{44} - 2 q^{45} - 12 q^{46} - 6 q^{47} + 80 q^{48} + 42 q^{50} + 36 q^{51} + 4 q^{52} + 24 q^{53} - 34 q^{54} - 8 q^{55} - 12 q^{56} + 10 q^{57} + 4 q^{58} - 6 q^{59} - 34 q^{60} - 2 q^{61} - 16 q^{63} + 36 q^{65} + 8 q^{66} - 26 q^{67} + 102 q^{68} + 30 q^{69} + 56 q^{70} + 48 q^{71} + 10 q^{72} + 52 q^{73} + 90 q^{74} + 30 q^{75} - 12 q^{76} - 72 q^{77} - 32 q^{78} + 16 q^{79} - 198 q^{80} - 12 q^{81} - 12 q^{83} - 104 q^{84} - 12 q^{85} + 60 q^{86} - 38 q^{87} - 6 q^{88} + 228 q^{90} - 16 q^{91} - 12 q^{92} - 26 q^{93} - 2 q^{94} - 12 q^{95} - 78 q^{96} - 6 q^{97} + 36 q^{98} - 64 q^{99}+O(q^{100}) \) 432 * q - 6 * q^2 - 4 * q^3 - 4 * q^6 + 2 * q^7 + 12 * q^8 - 4 * q^9 - 12 * q^11 + 36 * q^12 - 4 * q^13 - 12 * q^14 - 24 * q^15 - 380 * q^16 - 26 * q^18 - 8 * q^19 - 12 * q^20 - 6 * q^21 + 4 * q^22 - 6 * q^23 + 20 * q^24 - 4 * q^27 - 12 * q^28 - 12 * q^29 - 24 * q^30 + 18 * q^31 + 18 * q^32 - 16 * q^33 - 36 * q^35 - 12 * q^36 + 40 * q^39 + 24 * q^40 - 12 * q^41 - 34 * q^42 + 108 * q^44 - 2 * q^45 - 12 * q^46 - 6 * q^47 + 80 * q^48 + 42 * q^50 + 36 * q^51 + 4 * q^52 + 24 * q^53 - 34 * q^54 - 8 * q^55 - 12 * q^56 + 10 * q^57 + 4 * q^58 - 6 * q^59 - 34 * q^60 - 2 * q^61 - 16 * q^63 + 36 * q^65 + 8 * q^66 - 26 * q^67 + 102 * q^68 + 30 * q^69 + 56 * q^70 + 48 * q^71 + 10 * q^72 + 52 * q^73 + 90 * q^74 + 30 * q^75 - 12 * q^76 - 72 * q^77 - 32 * q^78 + 16 * q^79 - 198 * q^80 - 12 * q^81 - 12 * q^83 - 104 * q^84 - 12 * q^85 + 60 * q^86 - 38 * q^87 - 6 * q^88 + 228 * q^90 - 16 * q^91 - 12 * q^92 - 26 * q^93 - 2 * q^94 - 12 * q^95 - 78 * q^96 - 6 * q^97 + 36 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

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