LMFDB - Embedded newform 867.2.e.j.829.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(616,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("867.616");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.e (of order $4$, degree $2$, not 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.722204136308736.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{8} + 69x^{4} + 1 $ x^12 + 18x^8 + 69x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.5
Root			$1.32893 + 1.32893i$ of defining polynomial
Character	$\chi$	$=$	867.829
Dual form			867.2.e.j.616.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.53209i q^{2} +(-0.707107 - 0.707107i) q^{3} -4.41147 q^{4} +(0.621819 + 0.621819i) q^{5} +(1.79046 - 1.79046i) q^{6} +(-3.11938 + 3.11938i) q^{7} -6.10607i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+2.53209i q^{2} +(-0.707107 - 0.707107i) q^{3} -4.41147 q^{4} +(0.621819 + 0.621819i) q^{5} +(1.79046 - 1.79046i) q^{6} +(-3.11938 + 3.11938i) q^{7} -6.10607i q^{8} +1.00000i q^{9} +(-1.57450 + 1.57450i) q^{10} +(-2.62823 + 2.62823i) q^{11} +(3.11938 + 3.11938i) q^{12} +3.12061 q^{13} +(-7.89856 - 7.89856i) q^{14} -0.879385i q^{15} +6.63816 q^{16} -2.53209 q^{18} +2.04189i q^{19} +(-2.74314 - 2.74314i) q^{20} +4.41147 q^{21} +(-6.65492 - 6.65492i) q^{22} +(-0.114908 + 0.114908i) q^{23} +(-4.31764 + 4.31764i) q^{24} -4.22668i q^{25} +7.90167i q^{26} +(0.707107 - 0.707107i) q^{27} +(13.7611 - 13.7611i) q^{28} +(-5.89214 - 5.89214i) q^{29} +2.22668 q^{30} +(1.25393 + 1.25393i) q^{31} +4.59627i q^{32} +3.71688 q^{33} -3.87939 q^{35} -4.41147i q^{36} +(-1.93498 - 1.93498i) q^{37} -5.17024 q^{38} +(-2.20661 - 2.20661i) q^{39} +(3.79687 - 3.79687i) q^{40} +(1.83036 - 1.83036i) q^{41} +11.1702i q^{42} -11.7588i q^{43} +(11.5944 - 11.5944i) q^{44} +(-0.621819 + 0.621819i) q^{45} +(-0.290956 - 0.290956i) q^{46} -3.26857 q^{47} +(-4.69388 - 4.69388i) q^{48} -12.4611i q^{49} +10.7023 q^{50} -13.7665 q^{52} +6.46791i q^{53} +(1.79046 + 1.79046i) q^{54} -3.26857 q^{55} +(19.0472 + 19.0472i) q^{56} +(1.44383 - 1.44383i) q^{57} +(14.9194 - 14.9194i) q^{58} +7.23442i q^{59} +3.87939i q^{60} +(-1.77470 + 1.77470i) q^{61} +(-3.17505 + 3.17505i) q^{62} +(-3.11938 - 3.11938i) q^{63} +1.63816 q^{64} +(1.94046 + 1.94046i) q^{65} +9.41147i q^{66} -4.61081 q^{67} +0.162504 q^{69} -9.82295i q^{70} +(-0.797868 - 0.797868i) q^{71} +6.10607 q^{72} +(1.96103 + 1.96103i) q^{73} +(4.89955 - 4.89955i) q^{74} +(-2.98872 + 2.98872i) q^{75} -9.00774i q^{76} -16.3969i q^{77} +(5.58733 - 5.58733i) q^{78} +(-2.44190 + 2.44190i) q^{79} +(4.12773 + 4.12773i) q^{80} -1.00000 q^{81} +(4.63464 + 4.63464i) q^{82} +14.8307i q^{83} -19.4611 q^{84} +29.7743 q^{86} +8.33275i q^{87} +(16.0482 + 16.0482i) q^{88} +11.4192 q^{89} +(-1.57450 - 1.57450i) q^{90} +(-9.73439 + 9.73439i) q^{91} +(0.506912 - 0.506912i) q^{92} -1.77332i q^{93} -8.27631i q^{94} +(-1.26969 + 1.26969i) q^{95} +(3.25005 - 3.25005i) q^{96} +(-3.04438 - 3.04438i) q^{97} +31.5526 q^{98} +(-2.62823 - 2.62823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4}+O(q^{10}) $ 12 * q - 12 * q^4	$ 12 q - 12 q^{4} + 60 q^{13} + 12 q^{16} - 12 q^{18} + 12 q^{21} + 12 q^{33} - 24 q^{35} + 24 q^{38} + 24 q^{50} - 24 q^{52} - 48 q^{64} - 72 q^{67} + 12 q^{69} + 24 q^{72} - 12 q^{81} - 84 q^{84} + 120 q^{86} + 108 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 + 60 * q^13 + 12 * q^16 - 12 * q^18 + 12 * q^21 + 12 * q^33 - 24 * q^35 + 24 * q^38 + 24 * q^50 - 24 * q^52 - 48 * q^64 - 72 * q^67 + 12 * q^69 + 24 * q^72 - 12 * q^81 - 84 * q^84 + 120 * q^86 + 108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			2.53209i			1.79046i	0.445607	+	0.895229i	$0.352988\pi$
$2$			2.53209i			1.79046i	−0.445607	+	0.895229i	$0.647012\pi$
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−4.41147			−2.20574
$5$	0.621819	+	0.621819i	0.278086	+	0.278086i	0.832345	−	0.554259i	$-0.186998\pi$
$5$	0.621819	+	0.621819i	0.278086	+	0.278086i	−0.554259	+	0.832345i	$0.686998\pi$
$6$	1.79046	−	1.79046i	0.730951	−	0.730951i
$7$	−3.11938	+	3.11938i	−1.17902	+	1.17902i	−0.199021	+	0.979995i	$0.563776\pi$
$7$	−3.11938	+	3.11938i	−1.17902	+	1.17902i	−0.979995	+	0.199021i	$0.936224\pi$
$8$		−	6.10607i		−	2.15882i
$9$			1.00000i			0.333333i
$10$	−1.57450	+	1.57450i	−0.497901	+	0.497901i
$11$	−2.62823	+	2.62823i	−0.792442	+	0.792442i	−0.981891	−	0.189449i	$-0.939330\pi$
$11$	−2.62823	+	2.62823i	−0.792442	+	0.792442i	0.189449	+	0.981891i	$0.439330\pi$
$12$	3.11938	+	3.11938i	0.900488	+	0.900488i
$13$	3.12061			0.865503			0.432751	−	0.901513i	$-0.357543\pi$
$13$	3.12061			0.865503			0.432751	+	0.901513i	$0.357543\pi$
$14$	−7.89856	−	7.89856i	−2.11098	−	2.11098i
$15$		−	0.879385i		−	0.227056i
$16$	6.63816			1.65954
$17$		0			0
$17$		0			0
$18$	−2.53209			−0.596819
$19$			2.04189i			0.468441i	0.972183	+	0.234221i	$0.0752538\pi$
$19$			2.04189i			0.468441i	−0.972183	+	0.234221i	$0.924746\pi$
$20$	−2.74314	−	2.74314i	−0.613385	−	0.613385i
$21$	4.41147			0.962663
$22$	−6.65492	−	6.65492i	−1.41883	−	1.41883i
$23$	−0.114908	+	0.114908i	−0.0239599	+	0.0239599i	−0.718985	−	0.695025i	$-0.755393\pi$
$23$	−0.114908	+	0.114908i	−0.0239599	+	0.0239599i	0.695025	+	0.718985i	$0.255393\pi$
$24$	−4.31764	+	4.31764i	−0.881335	+	0.881335i
$25$		−	4.22668i		−	0.845336i
$26$			7.90167i			1.54965i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	13.7611	−	13.7611i	2.60060	−	2.60060i
$29$	−5.89214	−	5.89214i	−1.09414	−	1.09414i	−0.995081	−	0.0990622i	$-0.968416\pi$
$29$	−5.89214	−	5.89214i	−1.09414	−	1.09414i	−0.0990622	−	0.995081i	$-0.531584\pi$
$30$	2.22668			0.406535
$31$	1.25393	+	1.25393i	0.225212	+	0.225212i	0.810689	−	0.585477i	$-0.199093\pi$
$31$	1.25393	+	1.25393i	0.225212	+	0.225212i	−0.585477	+	0.810689i	$0.699093\pi$
$32$			4.59627i			0.812513i
$33$	3.71688			0.647026
$34$		0			0
$35$	−3.87939			−0.655736
$36$		−	4.41147i		−	0.735246i
$37$	−1.93498	−	1.93498i	−0.318110	−	0.318110i	0.529931	−	0.848041i	$-0.322218\pi$
$37$	−1.93498	−	1.93498i	−0.318110	−	0.318110i	−0.848041	+	0.529931i	$0.822218\pi$
$38$	−5.17024			−0.838724
$39$	−2.20661	−	2.20661i	−0.353340	−	0.353340i
$40$	3.79687	−	3.79687i	0.600338	−	0.600338i
$41$	1.83036	−	1.83036i	0.285855	−	0.285855i	−0.549584	−	0.835439i	$-0.685214\pi$
$41$	1.83036	−	1.83036i	0.285855	−	0.285855i	0.835439	+	0.549584i	$0.185214\pi$
$42$			11.1702i			1.72361i
$43$		−	11.7588i		−	1.79320i	−0.442846	−	0.896598i	$-0.646031\pi$
$43$		−	11.7588i		−	1.79320i	0.442846	−	0.896598i	$-0.353969\pi$
$44$	11.5944	−	11.5944i	1.74792	−	1.74792i
$45$	−0.621819	+	0.621819i	−0.0926953	+	0.0926953i
$46$	−0.290956	−	0.290956i	−0.0428991	−	0.0428991i
$47$	−3.26857			−0.476770			−0.238385	−	0.971171i	$-0.576618\pi$
$47$	−3.26857			−0.476770			−0.238385	+	0.971171i	$0.576618\pi$
$48$	−4.69388	−	4.69388i	−0.677504	−	0.677504i
$49$		−	12.4611i		−	1.78016i
$50$	10.7023			1.51354
$51$		0			0
$52$	−13.7665			−1.90907
$53$			6.46791i			0.888436i	0.895919	+	0.444218i	$0.146518\pi$
$53$			6.46791i			0.888436i	−0.895919	+	0.444218i	$0.853482\pi$
$54$	1.79046	+	1.79046i	0.243650	+	0.243650i
$55$	−3.26857			−0.440734
$56$	19.0472	+	19.0472i	2.54528	+	2.54528i
$57$	1.44383	−	1.44383i	0.191240	−	0.191240i
$58$	14.9194	−	14.9194i	1.95902	−	1.95902i
$59$			7.23442i			0.941842i	0.882176	+	0.470921i	$0.156078\pi$
$59$			7.23442i			0.941842i	−0.882176	+	0.470921i	$0.843922\pi$
$60$			3.87939i			0.500826i
$61$	−1.77470	+	1.77470i	−0.227227	+	0.227227i	−0.811533	−	0.584306i	$-0.801367\pi$
$61$	−1.77470	+	1.77470i	−0.227227	+	0.227227i	0.584306	+	0.811533i	$0.301367\pi$
$62$	−3.17505	+	3.17505i	−0.403232	+	0.403232i
$63$	−3.11938	−	3.11938i	−0.393005	−	0.393005i
$64$	1.63816			0.204769
$65$	1.94046	+	1.94046i	0.240684	+	0.240684i
$66$			9.41147i			1.15847i
$67$	−4.61081			−0.563301			−0.281650	−	0.959517i	$-0.590882\pi$
$67$	−4.61081			−0.563301			−0.281650	+	0.959517i	$0.590882\pi$
$68$		0			0
$69$	0.162504			0.0195632
$70$		−	9.82295i		−	1.17407i
$71$	−0.797868	−	0.797868i	−0.0946895	−	0.0946895i	0.658175	−	0.752865i	$-0.271329\pi$
$71$	−0.797868	−	0.797868i	−0.0946895	−	0.0946895i	−0.752865	+	0.658175i	$0.771329\pi$
$72$	6.10607			0.719607
$73$	1.96103	+	1.96103i	0.229521	+	0.229521i	0.812493	−	0.582971i	$-0.198110\pi$
$73$	1.96103	+	1.96103i	0.229521	+	0.229521i	−0.582971	+	0.812493i	$0.698110\pi$
$74$	4.89955	−	4.89955i	0.569562	−	0.569562i
$75$	−2.98872	+	2.98872i	−0.345107	+	0.345107i
$76$		−	9.00774i		−	1.03326i
$77$		−	16.3969i		−	1.86860i
$78$	5.58733	−	5.58733i	0.632640	−	0.632640i
$79$	−2.44190	+	2.44190i	−0.274735	+	0.274735i	−0.831003	−	0.556268i	$-0.812233\pi$
$79$	−2.44190	+	2.44190i	−0.274735	+	0.274735i	0.556268	+	0.831003i	$0.312233\pi$
$80$	4.12773	+	4.12773i	0.461495	+	0.461495i
$81$	−1.00000			−0.111111
$82$	4.63464	+	4.63464i	0.511811	+	0.511811i
$83$			14.8307i			1.62788i	0.580949	+	0.813940i	$0.302681\pi$
$83$			14.8307i			1.62788i	−0.580949	+	0.813940i	$0.697319\pi$
$84$	−19.4611			−2.12338
$85$		0			0
$86$	29.7743			3.21064
$87$			8.33275i			0.893364i
$88$	16.0482	+	16.0482i	1.71074	+	1.71074i
$89$	11.4192			1.21043			0.605217	−	0.796060i	$-0.293086\pi$
$89$	11.4192			1.21043			0.605217	+	0.796060i	$0.293086\pi$
$90$	−1.57450	−	1.57450i	−0.165967	−	0.165967i
$91$	−9.73439	+	9.73439i	−1.02044	+	1.02044i
$92$	0.506912	−	0.506912i	0.0528492	−	0.0528492i
$93$		−	1.77332i		−	0.183885i
$94$		−	8.27631i		−	0.853636i
$95$	−1.26969	+	1.26969i	−0.130267	+	0.130267i
$96$	3.25005	−	3.25005i	0.331707	−	0.331707i
$97$	−3.04438	−	3.04438i	−0.309110	−	0.309110i	0.535454	−	0.844564i	$-0.320140\pi$
$97$	−3.04438	−	3.04438i	−0.309110	−	0.309110i	−0.844564	+	0.535454i	$0.820140\pi$
$98$	31.5526			3.18730
$99$	−2.62823	−	2.62823i	−0.264147	−	0.264147i
$100$			18.6459i			1.86459i
$101$	−9.08647			−0.904137			−0.452069	−	0.891983i	$-0.649314\pi$
$101$	−9.08647			−0.904137			−0.452069	+	0.891983i	$0.649314\pi$
$102$		0			0
$103$	−15.5253			−1.52975			−0.764876	−	0.644178i	$-0.777200\pi$
$103$	−15.5253			−1.52975			−0.764876	+	0.644178i	$0.777200\pi$
$104$		−	19.0547i		−	1.86847i
$105$	2.74314	+	2.74314i	0.267703	+	0.267703i
$106$	−16.3773			−1.59071
$107$	−7.23683	−	7.23683i	−0.699611	−	0.699611i	0.264716	−	0.964326i	$-0.414722\pi$
$107$	−7.23683	−	7.23683i	−0.699611	−	0.699611i	−0.964326	+	0.264716i	$0.914722\pi$
$108$	−3.11938	+	3.11938i	−0.300163	+	0.300163i
$109$	−4.69388	+	4.69388i	−0.449593	+	0.449593i	−0.895219	−	0.445626i	$-0.852981\pi$
$109$	−4.69388	+	4.69388i	−0.449593	+	0.449593i	0.445626	+	0.895219i	$0.352981\pi$
$110$		−	8.27631i		−	0.789115i
$111$			2.73648i			0.259735i
$112$	−20.7070	+	20.7070i	−1.95662	+	1.95662i
$113$	−8.89115	+	8.89115i	−0.836409	+	0.836409i	−0.988384	−	0.151976i	$-0.951436\pi$
$113$	−8.89115	+	8.89115i	−0.836409	+	0.836409i	0.151976	+	0.988384i	$0.451436\pi$
$114$	3.65592	+	3.65592i	0.342408	+	0.342408i
$115$	−0.142903			−0.0133258
$116$	25.9930	+	25.9930i	2.41339	+	2.41339i
$117$			3.12061i			0.288501i
$118$	−18.3182			−1.68633
$119$		0			0
$120$	−5.36959			−0.490174
$121$		−	2.81521i		−	0.255928i
$122$	−4.49369	−	4.49369i	−0.406840	−	0.406840i
$123$	−2.58853			−0.233400
$124$	−5.53166	−	5.53166i	−0.496758	−	0.496758i
$125$	5.73733	−	5.73733i	0.513162	−	0.513162i
$126$	7.89856	−	7.89856i	0.703659	−	0.703659i
$127$			12.5594i			1.11447i	0.830355	+	0.557235i	$0.188138\pi$
$127$			12.5594i			1.11447i	−0.830355	+	0.557235i	$0.811862\pi$
$128$			13.3405i			1.17914i
$129$	−8.31471	+	8.31471i	−0.732069	+	0.732069i
$130$	−4.91341	+	4.91341i	−0.430935	+	0.430935i
$131$	14.1216	+	14.1216i	1.23381	+	1.23381i	0.962490	+	0.271316i	$0.0874590\pi$
$131$	14.1216	+	14.1216i	1.23381	+	1.23381i	0.271316	+	0.962490i	$0.412541\pi$
$132$	−16.3969			−1.42717
$133$	−6.36943	−	6.36943i	−0.552300	−	0.552300i
$134$		−	11.6750i		−	1.00857i
$135$	0.879385			0.0756854
$136$		0			0
$137$	−17.2267			−1.47177			−0.735887	−	0.677104i	$-0.763235\pi$
$137$	−17.2267			−1.47177			−0.735887	+	0.677104i	$0.763235\pi$
$138$			0.411474i			0.0350270i
$139$	−2.38813	−	2.38813i	−0.202559	−	0.202559i	0.598537	−	0.801095i	$-0.295749\pi$
$139$	−2.38813	−	2.38813i	−0.202559	−	0.202559i	−0.801095	+	0.598537i	$0.795749\pi$
$140$	17.1138			1.44638
$141$	2.31123	+	2.31123i	0.194641	+	0.194641i
$142$	2.02027	−	2.02027i	0.169537	−	0.169537i
$143$	−8.20170	+	8.20170i	−0.685861	+	0.685861i
$144$			6.63816i			0.553180i
$145$		−	7.32770i		−	0.608532i
$146$	−4.96551	+	4.96551i	−0.410948	+	0.410948i
$147$	−8.81133	+	8.81133i	−0.726746	+	0.726746i
$148$	8.53614	+	8.53614i	0.701666	+	0.701666i
$149$	1.38413			0.113393			0.0566963	−	0.998391i	$-0.481943\pi$
$149$	1.38413			0.113393			0.0566963	+	0.998391i	$0.481943\pi$
$150$	−7.56769	−	7.56769i	−0.617900	−	0.617900i
$151$		−	6.12836i		−	0.498719i	−0.968411	−	0.249359i	$-0.919780\pi$
$151$		−	6.12836i		−	0.498719i	0.968411	−	0.249359i	$-0.0802200\pi$
$152$	12.4679			1.01128
$153$		0			0
$154$	41.5185			3.34565
$155$			1.55943i			0.125256i
$156$	9.73439	+	9.73439i	0.779375	+	0.779375i
$157$	13.0496			1.04147			0.520737	−	0.853717i	$-0.325657\pi$
$157$	13.0496			1.04147			0.520737	+	0.853717i	$0.325657\pi$
$158$	−6.18310	−	6.18310i	−0.491901	−	0.491901i
$159$	4.57350	−	4.57350i	0.362702	−	0.362702i
$160$	−2.85805	+	2.85805i	−0.225948	+	0.225948i
$161$		−	0.716881i		−	0.0564982i
$162$		−	2.53209i		−	0.198940i
$163$	14.7591	−	14.7591i	1.15603	−	1.15603i	0.170703	−	0.985323i	$-0.445396\pi$
$163$	14.7591	−	14.7591i	1.15603	−	1.15603i	0.985323	−	0.170703i	$-0.0546037\pi$
$164$	−8.07460	+	8.07460i	−0.630521	+	0.630521i
$165$	2.31123	+	2.31123i	0.179929	+	0.179929i
$166$	−37.5526			−2.91465
$167$	8.27837	+	8.27837i	0.640600	+	0.640600i	0.950703	−	0.310103i	$-0.100364\pi$
$167$	8.27837	+	8.27837i	0.640600	+	0.640600i	−0.310103	+	0.950703i	$0.600364\pi$
$168$		−	26.9368i		−	2.07822i
$169$	−3.26176			−0.250905
$170$		0			0
$171$	−2.04189			−0.156147
$172$			51.8735i			3.95532i
$173$	−11.7965	−	11.7965i	−0.896869	−	0.896869i	0.0982887	−	0.995158i	$-0.468663\pi$
$173$	−11.7965	−	11.7965i	−0.896869	−	0.896869i	−0.995158	+	0.0982887i	$0.968663\pi$
$174$	−21.0993			−1.59953
$175$	13.1846	+	13.1846i	0.996665	+	0.996665i
$176$	−17.4466	+	17.4466i	−1.31509	+	1.31509i
$177$	5.11551	−	5.11551i	0.384505	−	0.384505i
$178$			28.9145i			2.16723i
$179$			4.29767i			0.321223i	0.987018	+	0.160611i	$0.0513466\pi$
$179$			4.29767i			0.321223i	−0.987018	+	0.160611i	$0.948653\pi$
$180$	2.74314	−	2.74314i	0.204462	−	0.204462i
$181$	15.7414	−	15.7414i	1.17005	−	1.17005i	0.187856	−	0.982197i	$-0.439846\pi$
$181$	15.7414	−	15.7414i	1.17005	−	1.17005i	0.982197	−	0.187856i	$-0.0601537\pi$
$182$	−24.6483	−	24.6483i	−1.82706	−	1.82706i
$183$	2.50980			0.185530
$184$	0.701633	+	0.701633i	0.0517251	+	0.0517251i
$185$		−	2.40642i		−	0.176924i
$186$	4.49020			0.329237
$187$		0			0
$188$	14.4192			1.05163
$189$			4.41147i			0.320888i
$190$	−3.21496	−	3.21496i	−0.233238	−	0.233238i
$191$	−11.2567			−0.814507			−0.407254	−	0.913315i	$-0.633513\pi$
$191$	−11.2567			−0.814507			−0.407254	+	0.913315i	$0.633513\pi$
$192$	−1.15835	−	1.15835i	−0.0835968	−	0.0835968i
$193$	−4.72541	+	4.72541i	−0.340142	+	0.340142i	−0.856421	−	0.516279i	$-0.827317\pi$
$193$	−4.72541	+	4.72541i	−0.340142	+	0.340142i	0.516279	+	0.856421i	$0.327317\pi$
$194$	7.70865	−	7.70865i	0.553449	−	0.553449i
$195$		−	2.74422i		−	0.196518i
$196$			54.9718i			3.92656i
$197$	−8.98738	+	8.98738i	−0.640324	+	0.640324i	−0.950635	−	0.310311i	$-0.899567\pi$
$197$	−8.98738	+	8.98738i	−0.640324	+	0.640324i	0.310311	+	0.950635i	$0.399567\pi$
$198$	6.65492	−	6.65492i	0.472944	−	0.472944i
$199$	−19.2335	−	19.2335i	−1.36343	−	1.36343i	−0.869508	−	0.493918i	$-0.835564\pi$
$199$	−19.2335	−	19.2335i	−1.36343	−	1.36343i	−0.493918	−	0.869508i	$-0.664436\pi$
$200$	−25.8084			−1.82493
$201$	3.26034	+	3.26034i	0.229967	+	0.229967i
$202$		−	23.0077i		−	1.61882i
$203$	36.7597			2.58003
$204$		0			0
$205$	2.27631			0.158984
$206$		−	39.3114i		−	2.73895i
$207$	−0.114908	−	0.114908i	−0.00798663	−	0.00798663i
$208$	20.7151			1.43634
$209$	−5.36656	−	5.36656i	−0.371213	−	0.371213i
$210$	−6.94587	+	6.94587i	−0.479311	+	0.479311i
$211$	−3.27420	+	3.27420i	−0.225405	+	0.225405i	−0.810770	−	0.585365i	$-0.800951\pi$
$211$	−3.27420	+	3.27420i	−0.225405	+	0.225405i	0.585365	+	0.810770i	$0.300951\pi$
$212$		−	28.5330i		−	1.95966i
$213$			1.12836i			0.0773136i
$214$	18.3243	−	18.3243i	1.25262	−	1.25262i
$215$	7.31183	−	7.31183i	0.498663	−	0.498663i
$216$	−4.31764	−	4.31764i	−0.293778	−	0.293778i
$217$	−7.82295			−0.531056
$218$	−11.8853	−	11.8853i	−0.804976	−	0.804976i
$219$		−	2.77332i		−	0.187403i
$220$	14.4192			0.972143
$221$		0			0
$222$	−6.92902			−0.465045
$223$		−	18.2344i		−	1.22107i	−0.791990	−	0.610534i	$-0.790955\pi$
$223$		−	18.2344i		−	1.22107i	0.791990	−	0.610534i	$-0.209045\pi$
$224$	−14.3375	−	14.3375i	−0.957966	−	0.957966i
$225$	4.22668			0.281779
$226$	−22.5132	−	22.5132i	−1.49755	−	1.49755i
$227$	−18.1695	+	18.1695i	−1.20595	+	1.20595i	−0.233624	+	0.972327i	$0.575058\pi$
$227$	−18.1695	+	18.1695i	−1.20595	+	1.20595i	−0.972327	+	0.233624i	$0.924942\pi$
$228$	−6.36943	+	6.36943i	−0.421826	+	0.421826i
$229$		−	17.5790i		−	1.16166i	−0.814027	−	0.580828i	$-0.802729\pi$
$229$		−	17.5790i		−	1.16166i	0.814027	−	0.580828i	$-0.197271\pi$
$230$		−	0.361844i		−	0.0238593i
$231$	−11.5944	+	11.5944i	−0.762854	+	0.762854i
$232$	−35.9778	+	35.9778i	−2.36206	+	2.36206i
$233$	3.00805	+	3.00805i	0.197064	+	0.197064i	0.798740	−	0.601676i	$-0.205500\pi$
$233$	3.00805	+	3.00805i	0.197064	+	0.197064i	−0.601676	+	0.798740i	$0.705500\pi$
$234$	−7.90167			−0.516549
$235$	−2.03246	−	2.03246i	−0.132583	−	0.132583i
$236$		−	31.9145i		−	2.07745i
$237$	3.45336			0.224320
$238$		0			0
$239$	5.87433			0.379979			0.189990	−	0.981786i	$-0.439155\pi$
$239$	5.87433			0.379979			0.189990	+	0.981786i	$0.439155\pi$
$240$		−	5.83750i		−	0.376809i
$241$	−9.67873	−	9.67873i	−0.623462	−	0.623462i	0.322953	−	0.946415i	$-0.395324\pi$
$241$	−9.67873	−	9.67873i	−0.623462	−	0.623462i	−0.946415	+	0.322953i	$0.895324\pi$
$242$	7.12836			0.458228
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	7.82903	−	7.82903i	0.501202	−	0.501202i
$245$	7.74855	−	7.74855i	0.495037	−	0.495037i
$246$		−	6.55438i		−	0.417892i
$247$			6.37195i			0.405437i
$248$	7.65655	−	7.65655i	0.486192	−	0.486192i
$249$	10.4869	−	10.4869i	0.664579	−	0.664579i
$250$	14.5274	+	14.5274i	0.918795	+	0.918795i
$251$	−15.2986			−0.965639			−0.482820	−	0.875720i	$-0.660387\pi$
$251$	−15.2986			−0.965639			−0.482820	+	0.875720i	$0.660387\pi$
$252$	13.7611	+	13.7611i	0.866866	+	0.866866i
$253$		−	0.604007i		−	0.0379736i
$254$	−31.8016			−1.99541
$255$		0			0
$256$	−30.5030			−1.90644
$257$			26.2199i			1.63555i	0.575537	+	0.817775i	$0.304793\pi$
$257$			26.2199i			1.63555i	−0.575537	+	0.817775i	$0.695207\pi$
$258$	−21.0536	−	21.0536i	−1.31074	−	1.31074i
$259$	12.0719			0.750113
$260$	−8.56028	−	8.56028i	−0.530886	−	0.530886i
$261$	5.89214	−	5.89214i	0.364714	−	0.364714i
$262$	−35.7570	+	35.7570i	−2.20908	+	2.20908i
$263$		−	20.5449i		−	1.26685i	−0.773803	−	0.633426i	$-0.781648\pi$
$263$		−	20.5449i		−	1.26685i	0.773803	−	0.633426i	$-0.218352\pi$
$264$		−	22.6955i		−	1.39681i
$265$	−4.02187	+	4.02187i	−0.247062	+	0.247062i
$266$	16.1280	−	16.1280i	0.988870	−	0.988870i
$267$	−8.07460	−	8.07460i	−0.494158	−	0.494158i
$268$	20.3405			1.24249
$269$	0.242003	+	0.242003i	0.0147552	+	0.0147552i	0.714446	−	0.699691i	$-0.246679\pi$
$269$	0.242003	+	0.242003i	0.0147552	+	0.0147552i	−0.699691	+	0.714446i	$0.746679\pi$
$270$			2.22668i			0.135512i
$271$	−7.73648			−0.469958			−0.234979	−	0.972000i	$-0.575502\pi$
$271$	−7.73648			−0.469958			−0.234979	+	0.972000i	$0.575502\pi$
$272$		0			0
$273$	13.7665			0.833187
$274$		−	43.6195i		−	2.63515i
$275$	11.1087	+	11.1087i	0.669880	+	0.669880i
$276$	−0.716881			−0.0431512
$277$	20.1045	+	20.1045i	1.20796	+	1.20796i	0.971687	+	0.236274i	$0.0759262\pi$
$277$	20.1045	+	20.1045i	1.20796	+	1.20796i	0.236274	+	0.971687i	$0.424074\pi$
$278$	6.04696	−	6.04696i	0.362672	−	0.362672i
$279$	−1.25393	+	1.25393i	−0.0750706	+	0.0750706i
$280$			23.6878i			1.41562i
$281$			15.7297i			0.938354i	0.883104	+	0.469177i	$0.155449\pi$
$281$			15.7297i			0.938354i	−0.883104	+	0.469177i	$0.844551\pi$
$282$	−5.85224	+	5.85224i	−0.348496	+	0.348496i
$283$	−5.74404	+	5.74404i	−0.341448	+	0.341448i	−0.856911	−	0.515464i	$-0.827620\pi$
$283$	−5.74404	+	5.74404i	−0.341448	+	0.341448i	0.515464	+	0.856911i	$0.327620\pi$
$284$	3.51977	+	3.51977i	0.208860	+	0.208860i
$285$	1.79561			0.106363
$286$	−20.7674	−	20.7674i	−1.22800	−	1.22800i
$287$			11.4192i			0.674055i
$288$	−4.59627			−0.270838
$289$		0			0
$290$	18.5544			1.08955
$291$			4.30541i			0.252387i
$292$	−8.65104	−	8.65104i	−0.506264	−	0.506264i
$293$	−21.0797			−1.23149			−0.615743	−	0.787947i	$-0.711144\pi$
$293$	−21.0797			−1.23149			−0.615743	+	0.787947i	$0.711144\pi$
$294$	−22.3111	−	22.3111i	−1.30121	−	1.30121i
$295$	−4.49850	+	4.49850i	−0.261913	+	0.261913i
$296$	−11.8151	+	11.8151i	−0.686741	+	0.686741i
$297$			3.71688i			0.215675i
$298$			3.50475i			0.203025i
$299$	−0.358582	+	0.358582i	−0.0207373	+	0.0207373i
$300$	13.1846	−	13.1846i	0.761216	−	0.761216i
$301$	36.6801	+	36.6801i	2.11421	+	2.11421i
$302$	15.5175			0.892934
$303$	6.42510	+	6.42510i	0.369112	+	0.369112i
$304$			13.5544i			0.777397i
$305$	−2.20708			−0.126377
$306$		0			0
$307$	15.0915			0.861318			0.430659	−	0.902515i	$-0.358281\pi$
$307$	15.0915			0.861318			0.430659	+	0.902515i	$0.358281\pi$
$308$			72.3346i			4.12165i
$309$	10.9780	+	10.9780i	0.624518	+	0.624518i
$310$	−3.94862			−0.224266
$311$	19.0472	+	19.0472i	1.08007	+	1.08007i	0.996502	+	0.0835630i	$0.0266300\pi$
$311$	19.0472	+	19.0472i	1.08007	+	1.08007i	0.0835630	+	0.996502i	$0.473370\pi$
$312$	−13.4737	+	13.4737i	−0.762798	+	0.762798i
$313$	−2.82361	+	2.82361i	−0.159600	+	0.159600i	−0.782390	−	0.622789i	$-0.785999\pi$
$313$	−2.82361	+	2.82361i	−0.159600	+	0.159600i	0.622789	+	0.782390i	$0.285999\pi$
$314$			33.0428i			1.86471i
$315$		−	3.87939i		−	0.218579i
$316$	10.7724	−	10.7724i	0.605993	−	0.605993i
$317$	−1.50855	+	1.50855i	−0.0847285	+	0.0847285i	−0.748201	−	0.663472i	$-0.769082\pi$
$317$	−1.50855	+	1.50855i	−0.0847285	+	0.0847285i	0.663472	+	0.748201i	$0.269082\pi$
$318$	11.5805	+	11.5805i	0.649403	+	0.649403i
$319$	30.9718			1.73409
$320$	1.01864	+	1.01864i	0.0569435	+	0.0569435i
$321$			10.2344i			0.571230i
$322$	1.81521			0.101158
$323$		0			0
$324$	4.41147			0.245082
$325$		−	13.1898i		−	0.731641i
$326$	37.3715	+	37.3715i	2.06981	+	2.06981i
$327$	6.63816			0.367091
$328$	−11.1763	−	11.1763i	−0.617109	−	0.617109i
$329$	10.1959	−	10.1959i	0.562120	−	0.562120i
$330$	−5.85224	+	5.85224i	−0.322155	+	0.322155i
$331$			7.76382i			0.426738i	0.976972	+	0.213369i	$0.0684437\pi$
$331$			7.76382i			0.426738i	−0.976972	+	0.213369i	$0.931556\pi$
$332$		−	65.4252i		−	3.59067i
$333$	1.93498	−	1.93498i	0.106037	−	0.106037i
$334$	−20.9616	+	20.9616i	−1.14697	+	1.14697i
$335$	−2.86709	−	2.86709i	−0.156646	−	0.156646i
$336$	29.2841			1.59758
$337$	−10.5352	−	10.5352i	−0.573887	−	0.573887i	0.359325	−	0.933212i	$-0.383007\pi$
$337$	−10.5352	−	10.5352i	−0.573887	−	0.573887i	−0.933212	+	0.359325i	$0.883007\pi$
$338$		−	8.25908i		−	0.449234i
$339$	12.5740			0.682925
$340$		0			0
$341$	−6.59121			−0.356934
$342$		−	5.17024i		−	0.279575i
$343$	17.0353	+	17.0353i	0.919818	+	0.919818i
$344$	−71.7998			−3.87119
$345$	0.101048	+	0.101048i	0.00544024	+	0.00544024i
$346$	29.8697	−	29.8697i	1.60581	−	1.60581i
$347$	−4.34369	+	4.34369i	−0.233181	+	0.233181i	−0.814019	−	0.580838i	$-0.802725\pi$
$347$	−4.34369	+	4.34369i	−0.233181	+	0.233181i	0.580838	+	0.814019i	$0.302725\pi$
$348$		−	36.7597i		−	1.97053i
$349$			1.79830i			0.0962605i	0.998841	+	0.0481303i	$0.0153263\pi$
$349$			1.79830i			0.0962605i	−0.998841	+	0.0481303i	$0.984674\pi$
$350$	−33.3847	+	33.3847i	−1.78449	+	1.78449i
$351$	2.20661	−	2.20661i	0.117780	−	0.117780i
$352$	−12.0801	−	12.0801i	−0.643869	−	0.643869i
$353$	−35.2199			−1.87456			−0.937282	−	0.348571i	$-0.886667\pi$
$353$	−35.2199			−1.87456			−0.937282	+	0.348571i	$0.886667\pi$
$354$	12.9529	+	12.9529i	0.688440	+	0.688440i
$355$		−	0.992259i		−	0.0526637i
$356$	−50.3756			−2.66990
$357$		0			0
$358$	−10.8821			−0.575135
$359$		−	16.7888i		−	0.886079i	−0.896502	−	0.443039i	$-0.853900\pi$
$359$		−	16.7888i		−	0.886079i	0.896502	−	0.443039i	$-0.146100\pi$
$360$	3.79687	+	3.79687i	0.200113	+	0.200113i
$361$	14.8307			0.780563
$362$	39.8587	+	39.8587i	2.09493	+	2.09493i
$363$	−1.99065	+	1.99065i	−0.104482	+	0.104482i
$364$	42.9430	−	42.9430i	2.25083	−	2.25083i
$365$			2.43882i			0.127653i
$366$			6.35504i			0.332183i
$367$	−13.6111	+	13.6111i	−0.710492	+	0.710492i	−0.966638	−	0.256146i	$-0.917547\pi$
$367$	−13.6111	+	13.6111i	−0.710492	+	0.710492i	0.256146	+	0.966638i	$0.417547\pi$
$368$	−0.762774	+	0.762774i	−0.0397624	+	0.0397624i
$369$	1.83036	+	1.83036i	0.0952850	+	0.0952850i
$370$	6.09327			0.316774
$371$	−20.1759	−	20.1759i	−1.04748	−	1.04748i
$372$			7.82295i			0.405601i
$373$	−33.4953			−1.73432			−0.867159	−	0.498031i	$-0.834057\pi$
$373$	−33.4953			−1.73432			−0.867159	+	0.498031i	$0.834057\pi$
$374$		0			0
$375$	−8.11381			−0.418995
$376$			19.9581i			1.02926i
$377$	−18.3871	−	18.3871i	−0.946984	−	0.946984i
$378$	−11.1702			−0.574535
$379$	10.6804	+	10.6804i	0.548613	+	0.548613i	0.926040	−	0.377426i	$-0.123191\pi$
$379$	10.6804	+	10.6804i	0.548613	+	0.548613i	−0.377426	+	0.926040i	$0.623191\pi$
$380$	5.60119	−	5.60119i	0.287335	−	0.287335i
$381$	8.88086	−	8.88086i	0.454980	−	0.454980i
$382$		−	28.5030i		−	1.45834i
$383$			23.7811i			1.21516i	0.794260	+	0.607578i	$0.207859\pi$
$383$			23.7811i			1.21516i	−0.794260	+	0.607578i	$0.792141\pi$
$384$	9.43315	−	9.43315i	0.481383	−	0.481383i
$385$	10.1959	−	10.1959i	0.519632	−	0.519632i
$386$	−11.9651	−	11.9651i	−0.609010	−	0.609010i
$387$	11.7588			0.597732
$388$	13.4302	+	13.4302i	0.681816	+	0.681816i
$389$			24.3378i			1.23398i	0.786973	+	0.616988i	$0.211647\pi$
$389$			24.3378i			1.23398i	−0.786973	+	0.616988i	$0.788353\pi$
$390$	6.94862			0.351857
$391$		0			0
$392$	−76.0883			−3.84304
$393$		−	19.9709i		−	1.00740i
$394$	−22.7568	−	22.7568i	−1.14647	−	1.14647i
$395$	−3.03684			−0.152800
$396$	11.5944	+	11.5944i	0.582639	+	0.582639i
$397$	0.777294	−	0.777294i	0.0390113	−	0.0390113i	−0.687332	−	0.726343i	$-0.741218\pi$
$397$	0.777294	−	0.777294i	0.0390113	−	0.0390113i	0.726343	+	0.687332i	$0.241218\pi$
$398$	48.7009	−	48.7009i	2.44116	−	2.44116i
$399$			9.00774i			0.450951i
$400$		−	28.0574i		−	1.40287i
$401$	16.4923	−	16.4923i	0.823584	−	0.823584i	−0.163036	−	0.986620i	$-0.552129\pi$
$401$	16.4923	−	16.4923i	0.823584	−	0.823584i	0.986620	+	0.163036i	$0.0521287\pi$
$402$	−8.25547	+	8.25547i	−0.411745	+	0.411745i
$403$	3.91302	+	3.91302i	0.194921	+	0.194921i
$404$	40.0847			1.99429
$405$	−0.621819	−	0.621819i	−0.0308984	−	0.0308984i
$406$			93.0788i			4.61943i
$407$	10.1712			0.504167
$408$		0			0
$409$	20.1233			0.995033			0.497517	−	0.867454i	$-0.334245\pi$
$409$	20.1233			0.995033			0.497517	+	0.867454i	$0.334245\pi$
$410$			5.76382i			0.284655i
$411$	12.1811	+	12.1811i	0.600850	+	0.600850i
$412$	68.4894			3.37423
$413$	−22.5669	−	22.5669i	−1.11045	−	1.11045i
$414$	0.290956	−	0.290956i	0.0142997	−	0.0142997i
$415$	−9.22201	+	9.22201i	−0.452691	+	0.452691i
$416$			14.3432i			0.703232i
$417$			3.37733i			0.165388i
$418$	13.5886	−	13.5886i	0.664640	−	0.664640i
$419$	0.863822	−	0.863822i	0.0422005	−	0.0422005i	−0.685692	−	0.727892i	$-0.740500\pi$
$419$	0.863822	−	0.863822i	0.0422005	−	0.0422005i	0.727892	+	0.685692i	$0.240500\pi$
$420$	−12.1013	−	12.1013i	−0.590482	−	0.590482i
$421$	−9.21482			−0.449103			−0.224551	−	0.974462i	$-0.572092\pi$
$421$	−9.21482			−0.449103			−0.224551	+	0.974462i	$0.572092\pi$
$422$	−8.29056	−	8.29056i	−0.403578	−	0.403578i
$423$		−	3.26857i		−	0.158923i
$424$	39.4935			1.91797
$425$		0			0
$426$	−2.85710			−0.138427
$427$		−	11.0719i		−	0.535808i
$428$	31.9251	+	31.9251i	1.54316	+	1.54316i
$429$	11.5990			0.560003
$430$	18.5142	+	18.5142i	0.892834	+	0.892834i
$431$	−3.86450	+	3.86450i	−0.186146	+	0.186146i	−0.794028	−	0.607882i	$-0.792020\pi$
$431$	−3.86450	+	3.86450i	−0.186146	+	0.186146i	0.607882	+	0.794028i	$0.292020\pi$
$432$	4.69388	−	4.69388i	0.225835	−	0.225835i
$433$			13.5125i			0.649369i	0.945822	+	0.324684i	$0.105258\pi$
$433$			13.5125i			0.649369i	−0.945822	+	0.324684i	$0.894742\pi$
$434$		−	19.8084i		−	0.950834i
$435$	−5.18146	+	5.18146i	−0.248432	+	0.248432i
$436$	20.7070	−	20.7070i	0.991683	−	0.991683i
$437$	−0.234628	−	0.234628i	−0.0112238	−	0.0112238i
$438$	7.02229			0.335538
$439$	9.96902	+	9.96902i	0.475795	+	0.475795i	0.903784	−	0.427989i	$-0.140778\pi$
$439$	9.96902	+	9.96902i	0.475795	+	0.475795i	−0.427989	+	0.903784i	$0.640778\pi$
$440$			19.9581i			0.951466i
$441$	12.4611			0.593386
$442$		0			0
$443$	7.18716			0.341472			0.170736	−	0.985317i	$-0.445385\pi$
$443$	7.18716			0.341472			0.170736	+	0.985317i	$0.445385\pi$
$444$		−	12.0719i		−	0.572908i
$445$	7.10069	+	7.10069i	0.336605	+	0.336605i
$446$	46.1712			2.18627
$447$	−0.978730	−	0.978730i	−0.0462923	−	0.0462923i
$448$	−5.11004	+	5.11004i	−0.241426	+	0.241426i
$449$	9.71025	−	9.71025i	0.458255	−	0.458255i	−0.439827	−	0.898082i	$-0.644960\pi$
$449$	9.71025	−	9.71025i	0.458255	−	0.458255i	0.898082	+	0.439827i	$0.144960\pi$
$450$			10.7023i			0.504513i
$451$			9.62124i			0.453047i
$452$	39.2231	−	39.2231i	1.84490	−	1.84490i
$453$	−4.33340	+	4.33340i	−0.203601	+	0.203601i
$454$	−46.0067	−	46.0067i	−2.15920	−	2.15920i
$455$	−12.1061			−0.567541
$456$	−8.81614	−	8.81614i	−0.412854	−	0.412854i
$457$			15.8479i			0.741335i	0.928766	+	0.370667i	$0.120871\pi$
$457$			15.8479i			0.741335i	−0.928766	+	0.370667i	$0.879129\pi$
$458$	44.5117			2.07989
$459$		0			0
$460$	0.630415			0.0293932
$461$		−	7.69553i		−	0.358416i	−0.983811	−	0.179208i	$-0.942646\pi$
$461$		−	7.69553i		−	0.358416i	0.983811	−	0.179208i	$-0.0573536\pi$
$462$	−29.3580	−	29.3580i	−1.36586	−	1.36586i
$463$	−32.7597			−1.52247			−0.761236	−	0.648475i	$-0.775407\pi$
$463$	−32.7597			−1.52247			−0.761236	+	0.648475i	$0.775407\pi$
$464$	−39.1130	−	39.1130i	−1.81577	−	1.81577i
$465$	1.10268	−	1.10268i	0.0511357	−	0.0511357i
$466$	−7.61665	+	7.61665i	−0.352834	+	0.352834i
$467$			17.1726i			0.794654i	0.917677	+	0.397327i	$0.130062\pi$
$467$			17.1726i			0.794654i	−0.917677	+	0.397327i	$0.869938\pi$
$468$		−	13.7665i		−	0.636357i
$469$	14.3829	−	14.3829i	0.664141	−	0.664141i
$470$	5.14637	−	5.14637i	0.237384	−	0.237384i
$471$	−9.22748	−	9.22748i	−0.425180	−	0.425180i
$472$	44.1739			2.03327
$473$	30.9048	+	30.9048i	1.42100	+	1.42100i
$474$			8.74422i			0.401635i
$475$	8.63041			0.395991
$476$		0			0
$477$	−6.46791			−0.296145
$478$			14.8743i			0.680336i
$479$	15.6513	+	15.6513i	0.715128	+	0.715128i	0.967603	−	0.252475i	$-0.0812446\pi$
$479$	15.6513	+	15.6513i	0.715128	+	0.715128i	−0.252475	+	0.967603i	$0.581245\pi$
$480$	4.04189			0.184486
$481$	−6.03834	−	6.03834i	−0.275325	−	0.275325i
$482$	24.5074	−	24.5074i	1.11628	−	1.11628i
$483$	−0.506912	+	0.506912i	−0.0230653	+	0.0230653i
$484$			12.4192i			0.564510i
$485$		−	3.78611i		−	0.171918i
$486$	−1.79046	+	1.79046i	−0.0812168	+	0.0812168i
$487$	22.1943	−	22.1943i	1.00572	−	1.00572i	0.00573460	−	0.999984i	$-0.498175\pi$
$487$	22.1943	−	22.1943i	1.00572	−	1.00572i	0.999984	−	0.00573460i	$-0.00182539\pi$
$488$	10.8364	+	10.8364i	0.490542	+	0.490542i
$489$	−20.8726			−0.943891
$490$	19.6200	+	19.6200i	0.886343	+	0.886343i
$491$			0.206148i			0.00930331i	0.999989	+	0.00465166i	$0.00148067\pi$
$491$			0.206148i			0.00930331i	−0.999989	+	0.00465166i	$0.998519\pi$
$492$	11.4192			0.514818
$493$		0			0
$494$	−16.1343			−0.725918
$495$		−	3.26857i		−	0.146911i
$496$	8.32375	+	8.32375i	0.373748	+	0.373748i
$497$	4.97771			0.223281
$498$	26.5537	+	26.5537i	1.18990	+	1.18990i
$499$	3.88953	−	3.88953i	0.174119	−	0.174119i	−0.614667	−	0.788787i	$-0.710710\pi$
$499$	3.88953	−	3.88953i	0.174119	−	0.174119i	0.788787	+	0.614667i	$0.210710\pi$
$500$	−25.3101	+	25.3101i	−1.13190	+	1.13190i
$501$		−	11.7074i		−	0.523047i
$502$		−	38.7374i		−	1.72894i
$503$	−3.98196	+	3.98196i	−0.177547	+	0.177547i	−0.790286	−	0.612739i	$-0.790068\pi$
$503$	−3.98196	+	3.98196i	−0.177547	+	0.177547i	0.612739	+	0.790286i	$0.290068\pi$
$504$	−19.0472	+	19.0472i	−0.848428	+	0.848428i
$505$	−5.65014	−	5.65014i	−0.251428	−	0.251428i
$506$	1.52940			0.0679901
$507$	2.30642	+	2.30642i	0.102431	+	0.102431i
$508$		−	55.4056i		−	2.45823i
$509$	−15.8530			−0.702671			−0.351335	−	0.936250i	$-0.614272\pi$
$509$	−15.8530			−0.702671			−0.351335	+	0.936250i	$0.614272\pi$
$510$		0			0
$511$	−12.2344			−0.541219
$512$		−	50.5553i		−	2.23425i
$513$	1.44383	+	1.44383i	0.0637468	+	0.0637468i
$514$	−66.3911			−2.92838
$515$	−9.65392	−	9.65392i	−0.425403	−	0.425403i
$516$	36.6801	−	36.6801i	1.61475	−	1.61475i
$517$	8.59056	−	8.59056i	0.377812	−	0.377812i
$518$			30.5672i			1.34304i
$519$			16.6827i			0.732291i
$520$	11.8486	−	11.8486i	0.519594	−	0.519594i
$521$	25.1553	−	25.1553i	1.10207	−	1.10207i	0.107911	−	0.994161i	$-0.465584\pi$
$521$	25.1553	−	25.1553i	1.10207	−	1.10207i	0.994161	−	0.107911i	$-0.0344163\pi$
$522$	14.9194	+	14.9194i	0.653006	+	0.653006i
$523$	−6.32770			−0.276691			−0.138345	−	0.990384i	$-0.544178\pi$
$523$	−6.32770			−0.276691			−0.138345	+	0.990384i	$0.544178\pi$
$524$	−62.2969	−	62.2969i	−2.72145	−	2.72145i
$525$		−	18.6459i		−	0.813774i
$526$	52.0215			2.26824
$527$		0			0
$528$	24.6732			1.07376
$529$			22.9736i			0.998852i
$530$	−10.1837	−	10.1837i	−0.442353	−	0.442353i
$531$	−7.23442			−0.313947
$532$	28.0986	+	28.0986i	1.21823	+	1.21823i
$533$	5.71186	−	5.71186i	0.247408	−	0.247408i
$534$	20.4456	−	20.4456i	0.884768	−	0.884768i
$535$		−	9.00000i		−	0.389104i
$536$			28.1539i			1.21607i
$537$	3.03891	−	3.03891i	0.131139	−	0.131139i
$538$	−0.612773	+	0.612773i	−0.0264185	+	0.0264185i
$539$	32.7507	+	32.7507i	1.41067	+	1.41067i
$540$	−3.87939			−0.166942
$541$	6.72635	+	6.72635i	0.289188	+	0.289188i	0.836759	−	0.547571i	$-0.184447\pi$
$541$	6.72635	+	6.72635i	0.289188	+	0.289188i	−0.547571	+	0.836759i	$0.684447\pi$
$542$		−	19.5895i		−	0.841439i
$543$	−22.2618			−0.955344
$544$		0			0
$545$	−5.83750			−0.250051
$546$			34.8580i			1.49179i
$547$	18.3510	+	18.3510i	0.784632	+	0.784632i	0.980609	−	0.195976i	$-0.0627876\pi$
$547$	18.3510	+	18.3510i	0.784632	+	0.784632i	−0.195976	+	0.980609i	$0.562788\pi$
$548$	75.9951			3.24635
$549$	−1.77470	−	1.77470i	−0.0757422	−	0.0757422i
$550$	−28.1282	+	28.1282i	−1.19939	+	1.19939i
$551$	12.0311	−	12.0311i	0.512542	−	0.512542i
$552$		−	0.992259i		−	0.0422334i
$553$		−	15.2344i		−	0.647834i
$554$	−50.9063	+	50.9063i	−2.16280	+	2.16280i
$555$	−1.70160	+	1.70160i	−0.0722288	+	0.0722288i
$556$	10.5352	+	10.5352i	0.446791	+	0.446791i
$557$	3.03684			0.128675			0.0643374	−	0.997928i	$-0.479507\pi$
$557$	3.03684			0.128675			0.0643374	+	0.997928i	$0.479507\pi$
$558$	−3.17505	−	3.17505i	−0.134411	−	0.134411i
$559$		−	36.6946i		−	1.55202i
$560$	−25.7520			−1.08822
$561$		0			0
$562$	−39.8289			−1.68008
$563$		−	32.7050i		−	1.37835i	−0.724594	−	0.689176i	$-0.757973\pi$
$563$		−	32.7050i		−	1.37835i	0.724594	−	0.689176i	$-0.242027\pi$
$564$	−10.1959	−	10.1959i	−0.429326	−	0.429326i
$565$	−11.0574			−0.465187
$566$	−14.5444	−	14.5444i	−0.611348	−	0.611348i
$567$	3.11938	−	3.11938i	0.131002	−	0.131002i
$568$	−4.87183	+	4.87183i	−0.204418	+	0.204418i
$569$		−	10.7980i		−	0.452675i	−0.974049	−	0.226337i	$-0.927325\pi$
$569$		−	10.7980i		−	0.452675i	0.974049	−	0.226337i	$-0.0726751\pi$
$570$			4.54664i			0.190438i
$571$	−2.99062	+	2.99062i	−0.125153	+	0.125153i	−0.766909	−	0.641756i	$-0.778206\pi$
$571$	−2.99062	+	2.99062i	−0.125153	+	0.125153i	0.641756	+	0.766909i	$0.278206\pi$
$572$	36.1816	−	36.1816i	1.51283	−	1.51283i
$573$	7.95970	+	7.95970i	0.332521	+	0.332521i
$574$	−28.9145			−1.20687
$575$	0.485678	+	0.485678i	0.0202542	+	0.0202542i
$576$			1.63816i			0.0682565i
$577$	11.4311			0.475882			0.237941	−	0.971280i	$-0.423528\pi$
$577$	11.4311			0.475882			0.237941	+	0.971280i	$0.423528\pi$
$578$		0			0
$579$	6.68273			0.277725
$580$			32.3259i			1.34226i
$581$	−46.2626	−	46.2626i	−1.91930	−	1.91930i
$582$	−10.9017			−0.451889
$583$	−16.9992	−	16.9992i	−0.704034	−	0.704034i
$584$	11.9742	−	11.9742i	0.495496	−	0.495496i
$585$	−1.94046	+	1.94046i	−0.0802281	+	0.0802281i
$586$		−	53.3756i		−	2.20492i
$587$		−	19.8256i		−	0.818292i	−0.912469	−	0.409146i	$-0.865827\pi$
$587$		−	19.8256i		−	0.818292i	0.912469	−	0.409146i	$-0.134173\pi$
$588$	38.8710	−	38.8710i	1.60301	−	1.60301i
$589$	−2.56038	+	2.56038i	−0.105498	+	0.105498i
$590$	−11.3906	−	11.3906i	−0.468944	−	0.468944i
$591$	12.7101			0.522823
$592$	−12.8447	−	12.8447i	−0.527915	−	0.527915i
$593$			15.0933i			0.619806i	0.950768	+	0.309903i	$0.100297\pi$
$593$			15.0933i			0.619806i	−0.950768	+	0.309903i	$0.899703\pi$
$594$	−9.41147			−0.386157
$595$		0			0
$596$	−6.10607			−0.250114
$597$			27.2003i			1.11323i
$598$	−0.907962	−	0.907962i	−0.0371293	−	0.0371293i
$599$	−37.8776			−1.54764			−0.773819	−	0.633407i	$-0.781656\pi$
$599$	−37.8776			−1.54764			−0.773819	+	0.633407i	$0.781656\pi$
$600$	18.2493	+	18.2493i	0.745024	+	0.745024i
$601$	24.0017	−	24.0017i	0.979051	−	0.979051i	−0.0207343	−	0.999785i	$-0.506600\pi$
$601$	24.0017	−	24.0017i	0.979051	−	0.979051i	0.999785	+	0.0207343i	$0.00660040\pi$
$602$	−92.8773	+	92.8773i	−3.78540	+	3.78540i
$603$		−	4.61081i		−	0.187767i
$604$			27.0351i			1.10004i
$605$	1.75055	−	1.75055i	0.0711700	−	0.0711700i
$606$	−16.2689	+	16.2689i	−0.660880	+	0.660880i
$607$	−13.2802	−	13.2802i	−0.539027	−	0.539027i	0.384216	−	0.923243i	$-0.374472\pi$
$607$	−13.2802	−	13.2802i	−0.539027	−	0.539027i	−0.923243	+	0.384216i	$0.874472\pi$
$608$	−9.38507			−0.380615
$609$	−25.9930	−	25.9930i	−1.05329	−	1.05329i
$610$		−	5.58853i		−	0.226273i
$611$	−10.1999			−0.412646
$612$		0			0
$613$	17.9590			0.725359			0.362679	−	0.931914i	$-0.381862\pi$
$613$	17.9590			0.725359			0.362679	+	0.931914i	$0.381862\pi$
$614$			38.2131i			1.54215i
$615$	−1.60960	−	1.60960i	−0.0649051	−	0.0649051i
$616$	−100.121			−4.03398
$617$	1.50688	+	1.50688i	0.0606645	+	0.0606645i	0.736788	−	0.676124i	$-0.236341\pi$
$617$	1.50688	+	1.50688i	0.0606645	+	0.0606645i	−0.676124	+	0.736788i	$0.736341\pi$
$618$	−27.7974	+	27.7974i	−1.11817	+	1.11817i
$619$	2.08075	−	2.08075i	0.0836325	−	0.0836325i	−0.664053	−	0.747686i	$-0.731165\pi$
$619$	2.08075	−	2.08075i	0.0836325	−	0.0836325i	0.747686	+	0.664053i	$0.231165\pi$
$620$		−	6.87939i		−	0.276283i
$621$			0.162504i			0.00652105i
$622$	−48.2291	+	48.2291i	−1.93381	+	1.93381i
$623$	−35.6209	+	35.6209i	−1.42712	+	1.42712i
$624$	−14.6478	−	14.6478i	−0.586382	−	0.586382i
$625$	−13.9982			−0.559930
$626$	−7.14964	−	7.14964i	−0.285757	−	0.285757i
$627$			7.58946i			0.303094i
$628$	−57.5681			−2.29722
$629$		0			0
$630$	9.82295			0.391356
$631$		−	9.05913i		−	0.360638i	−0.983608	−	0.180319i	$-0.942287\pi$
$631$		−	9.05913i		−	0.360638i	0.983608	−	0.180319i	$-0.0577130\pi$
$632$	14.9104	+	14.9104i	0.593103	+	0.593103i
$633$	4.63041			0.184042
$634$	−3.81978	−	3.81978i	−0.151703	−	0.151703i
$635$	−7.80970	+	7.80970i	−0.309918	+	0.309918i
$636$	−20.1759	+	20.1759i	−0.800026	+	0.800026i
$637$		−	38.8863i		−	1.54073i
$638$			78.4234i			3.10481i
$639$	0.797868	−	0.797868i	0.0315632	−	0.0315632i
$640$	−8.29537	+	8.29537i	−0.327903	+	0.327903i
$641$	−2.32990	−	2.32990i	−0.0920256	−	0.0920256i	0.659595	−	0.751621i	$-0.270728\pi$
$641$	−2.32990	−	2.32990i	−0.0920256	−	0.0920256i	−0.751621	+	0.659595i	$0.770728\pi$
$642$	−25.9145			−1.02276
$643$	−14.4161	−	14.4161i	−0.568515	−	0.568515i	0.363197	−	0.931712i	$-0.381685\pi$
$643$	−14.4161	−	14.4161i	−0.568515	−	0.568515i	−0.931712	+	0.363197i	$0.881685\pi$
$644$			3.16250i			0.124620i
$645$	−10.3405			−0.407156
$646$		0			0
$647$	−6.14290			−0.241502			−0.120751	−	0.992683i	$-0.538530\pi$
$647$	−6.14290			−0.241502			−0.120751	+	0.992683i	$0.538530\pi$
$648$			6.10607i			0.239869i
$649$	−19.0137	−	19.0137i	−0.746355	−	0.746355i
$650$	33.3979			1.30997
$651$	5.53166	+	5.53166i	0.216803	+	0.216803i
$652$	−65.1096	+	65.1096i	−2.54989	+	2.54989i
$653$	−24.2351	+	24.2351i	−0.948393	+	0.948393i	−0.998732	−	0.0503390i	$-0.983970\pi$
$653$	−24.2351	+	24.2351i	−0.948393	+	0.948393i	0.0503390	+	0.998732i	$0.483970\pi$
$654$			16.8084i			0.657260i
$655$			17.5621i			0.686209i
$656$	12.1502	−	12.1502i	0.474387	−	0.474387i
$657$	−1.96103	+	1.96103i	−0.0765072	+	0.0765072i
$658$	25.8170	+	25.8170i	1.00645	+	1.00645i
$659$	32.3884			1.26167			0.630836	−	0.775916i	$-0.282712\pi$
$659$	32.3884			1.26167			0.630836	+	0.775916i	$0.282712\pi$
$660$	−10.1959	−	10.1959i	−0.396876	−	0.396876i
$661$		−	4.49970i		−	0.175018i	−0.996164	−	0.0875089i	$-0.972109\pi$
$661$		−	4.49970i		−	0.175018i	0.996164	−	0.0875089i	$-0.0278906\pi$
$662$	−19.6587			−0.764057
$663$		0			0
$664$	90.5572			3.51430
$665$		−	7.92127i		−	0.307174i
$666$	4.89955	+	4.89955i	0.189854	+	0.189854i
$667$	1.35410			0.0524311
$668$	−36.5198	−	36.5198i	−1.41299	−	1.41299i
$669$	−12.8937	+	12.8937i	−0.498499	+	0.498499i
$670$	7.25974	−	7.25974i	0.280468	−	0.280468i
$671$		−	9.32863i		−	0.360128i
$672$			20.2763i			0.782176i
$673$	8.32923	−	8.32923i	0.321068	−	0.321068i	−0.528109	−	0.849177i	$-0.677099\pi$
$673$	8.32923	−	8.32923i	0.321068	−	0.321068i	0.849177	+	0.528109i	$0.177099\pi$
$674$	26.6760	−	26.6760i	1.02752	−	1.02752i
$675$	−2.98872	−	2.98872i	−0.115036	−	0.115036i
$676$	14.3892			0.553430
$677$	−10.4071	−	10.4071i	−0.399976	−	0.399976i	0.478248	−	0.878225i	$-0.341272\pi$
$677$	−10.4071	−	10.4071i	−0.399976	−	0.399976i	−0.878225	+	0.478248i	$0.841272\pi$
$678$			31.8384i			1.22275i
$679$	18.9932			0.728892
$680$		0			0
$681$	25.6955			0.984655
$682$		−	16.6895i		−	0.639076i
$683$	29.5569	+	29.5569i	1.13097	+	1.13097i	0.990017	+	0.140948i	$0.0450151\pi$
$683$	29.5569	+	29.5569i	1.13097	+	1.13097i	0.140948	+	0.990017i	$0.454985\pi$
$684$	9.00774			0.344420
$685$	−10.7119	−	10.7119i	−0.409280	−	0.409280i
$686$	−43.1348	+	43.1348i	−1.64690	+	1.64690i
$687$	−12.4303	+	12.4303i	−0.474244	+	0.474244i
$688$		−	78.0565i		−	2.97588i
$689$			20.1839i			0.768944i
$690$	−0.255863	+	0.255863i	−0.00974052	+	0.00974052i
$691$	−23.5028	+	23.5028i	−0.894090	+	0.894090i	−0.994905	−	0.100815i	$-0.967855\pi$
$691$	−23.5028	+	23.5028i	−0.894090	+	0.894090i	0.100815	+	0.994905i	$0.467855\pi$
$692$	52.0398	+	52.0398i	1.97826	+	1.97826i
$693$	16.3969			0.622868
$694$	−10.9986	−	10.9986i	−0.417501	−	0.417501i
$695$		−	2.96997i		−	0.112657i
$696$	50.8803			1.92861
$697$		0			0
$698$	−4.55344			−0.172350
$699$		−	4.25402i		−	0.160902i
$700$	−58.1637	−	58.1637i	−2.19838	−	2.19838i
$701$	9.91859			0.374620			0.187310	−	0.982301i	$-0.440023\pi$
$701$	9.91859			0.374620			0.187310	+	0.982301i	$0.440023\pi$
$702$	5.58733	+	5.58733i	0.210880	+	0.210880i
$703$	3.95102	−	3.95102i	0.149016	−	0.149016i
$704$	−4.30545	+	4.30545i	−0.162268	+	0.162268i
$705$			2.87433i			0.108254i
$706$		−	89.1799i		−	3.35633i
$707$	28.3442	−	28.3442i	1.06599	−	1.06599i
$708$	−22.5669	+	22.5669i	−0.848117	+	0.848117i
$709$	−13.4823	−	13.4823i	−0.506339	−	0.506339i	0.407062	−	0.913401i	$-0.366553\pi$
$709$	−13.4823	−	13.4823i	−0.506339	−	0.506339i	−0.913401	+	0.407062i	$0.866553\pi$
$710$	2.51249			0.0942920
$711$	−2.44190	−	2.44190i	−0.0915783	−	0.0915783i
$712$		−	69.7265i		−	2.61311i
$713$	−0.288171			−0.0107921
$714$		0			0
$715$	−10.1999			−0.381456
$716$		−	18.9590i		−	0.708533i
$717$	−4.15378	−	4.15378i	−0.155126	−	0.155126i
$718$	42.5107			1.58649
$719$	−30.0687	−	30.0687i	−1.12137	−	1.12137i	−0.991535	−	0.129837i	$-0.958555\pi$
$719$	−30.0687	−	30.0687i	−1.12137	−	1.12137i	−0.129837	−	0.991535i	$-0.541445\pi$
$720$	−4.12773	+	4.12773i	−0.153832	+	0.153832i
$721$	48.4293	−	48.4293i	1.80360	−	1.80360i
$722$			37.5526i			1.39756i
$723$			13.6878i			0.509054i
$724$	−69.4430	+	69.4430i	−2.58083	+	2.58083i
$725$	−24.9042	+	24.9042i	−0.924919	+	0.924919i
$726$	−5.04051	−	5.04051i	−0.187071	−	0.187071i
$727$	−8.13610			−0.301751			−0.150876	−	0.988553i	$-0.548209\pi$
$727$	−8.13610			−0.301751			−0.150876	+	0.988553i	$0.548209\pi$
$728$	59.4389	+	59.4389i	2.20295	+	2.20295i
$729$		−	1.00000i		−	0.0370370i
$730$	−6.17530			−0.228558
$731$		0			0
$732$	−11.0719			−0.409230
$733$			19.7965i			0.731202i	0.930772	+	0.365601i	$0.119137\pi$
$733$			19.7965i			0.731202i	−0.930772	+	0.365601i	$0.880863\pi$
$734$	−34.4645	−	34.4645i	−1.27211	−	1.27211i
$735$	−10.9581			−0.404196
$736$	−0.528146	−	0.528146i	−0.0194677	−	0.0194677i
$737$	12.1183	−	12.1183i	0.446383	−	0.446383i
$738$	−4.63464	+	4.63464i	−0.170604	+	0.170604i
$739$			6.52940i			0.240188i	0.992763	+	0.120094i	$0.0383196\pi$
$739$			6.52940i			0.240188i	−0.992763	+	0.120094i	$0.961680\pi$
$740$			10.6159i			0.390247i
$741$	4.50565	−	4.50565i	0.165519	−	0.165519i
$742$	51.0872	−	51.0872i	1.87547	−	1.87547i
$743$	−10.9556	−	10.9556i	−0.401920	−	0.401920i	0.476989	−	0.878909i	$-0.341728\pi$
$743$	−10.9556	−	10.9556i	−0.401920	−	0.401920i	−0.878909	+	0.476989i	$0.841728\pi$
$744$	−10.8280			−0.396974
$745$	0.860681	+	0.860681i	0.0315329	+	0.0315329i
$746$		−	84.8130i		−	3.10522i
$747$	−14.8307			−0.542627
$748$		0			0
$749$	45.1489			1.64970
$750$		−	20.5449i		−	0.750193i
$751$	−19.6709	−	19.6709i	−0.717801	−	0.717801i	0.250354	−	0.968154i	$-0.419453\pi$
$751$	−19.6709	−	19.6709i	−0.717801	−	0.717801i	−0.968154	+	0.250354i	$0.919453\pi$
$752$	−21.6973			−0.791218
$753$	10.8177	+	10.8177i	0.394221	+	0.394221i
$754$	46.5578	−	46.5578i	1.69553	−	1.69553i
$755$	3.81073	−	3.81073i	0.138687	−	0.138687i
$756$		−	19.4611i		−	0.707794i
$757$			9.35328i			0.339951i	0.985448	+	0.169975i	$0.0543688\pi$
$757$			9.35328i			0.339951i	−0.985448	+	0.169975i	$0.945631\pi$
$758$	−27.0436	+	27.0436i	−0.982269	+	0.982269i
$759$	−0.427098	+	0.427098i	−0.0155027	+	0.0155027i
$760$	7.75279	+	7.75279i	0.281223	+	0.281223i
$761$	37.5458			1.36103			0.680517	−	0.732732i	$-0.261755\pi$
$761$	37.5458			1.36103			0.680517	+	0.732732i	$0.261755\pi$
$762$	22.4871	+	22.4871i	0.814622	+	0.814622i
$763$		−	29.2841i		−	1.06015i
$764$	49.6587			1.79659
$765$		0			0
$766$	−60.2158			−2.17568
$767$			22.5758i			0.815167i
$768$	21.5689	+	21.5689i	0.778300	+	0.778300i
$769$	26.2253			0.945707			0.472853	−	0.881141i	$-0.343224\pi$
$769$	26.2253			0.945707			0.472853	+	0.881141i	$0.343224\pi$
$770$	25.8170	+	25.8170i	0.930380	+	0.930380i
$771$	18.5403	−	18.5403i	0.667711	−	0.667711i
$772$	20.8460	−	20.8460i	0.750264	−	0.750264i
$773$			33.4567i			1.20335i	0.798740	+	0.601676i	$0.205500\pi$
$773$			33.4567i			1.20335i	−0.798740	+	0.601676i	$0.794500\pi$
$774$			29.7743i			1.07021i
$775$	5.29994	−	5.29994i	0.190380	−	0.190380i
$776$	−18.5892	+	18.5892i	−0.667314	+	0.667314i
$777$	−8.53614	−	8.53614i	−0.306232	−	0.306232i
$778$	−61.6255			−2.20938
$779$	3.73740	+	3.73740i	0.133906	+	0.133906i
$780$			12.1061i			0.433467i
$781$	4.19396			0.150072
$782$		0			0
$783$	−8.33275			−0.297788
$784$		−	82.7187i		−	2.95424i
$785$	8.11451	+	8.11451i	0.289619	+	0.289619i
$786$	50.5681			1.80370
$787$	−6.21943	−	6.21943i	−0.221699	−	0.221699i	0.587515	−	0.809214i	$-0.300106\pi$
$787$	−6.21943	−	6.21943i	−0.221699	−	0.221699i	−0.809214	+	0.587515i	$0.800106\pi$
$788$	39.6476	−	39.6476i	1.41239	−	1.41239i
$789$	−14.5274	+	14.5274i	−0.517190	+	0.517190i
$790$		−	7.68954i		−	0.273582i
$791$		−	55.4698i		−	1.97228i
$792$	−16.0482	+	16.0482i	−0.570247	+	0.570247i
$793$	−5.53814	+	5.53814i	−0.196665	+	0.196665i
$794$	1.96818	+	1.96818i	0.0698480	+	0.0698480i
$795$	5.68779			0.201725
$796$	84.8481	+	84.8481i	3.00736	+	3.00736i
$797$			13.8972i			0.492265i	0.969236	+	0.246133i	$0.0791599\pi$
$797$			13.8972i			0.492265i	−0.969236	+	0.246133i	$0.920840\pi$
$798$	−22.8084			−0.807409
$799$		0			0
$800$	19.4270			0.686847
$801$			11.4192i			0.403478i
$802$	41.7599	+	41.7599i	1.47459	+	1.47459i
$803$	−10.3081			−0.363765
$804$	−14.3829	−	14.3829i	−0.507246	−	0.507246i
$805$	0.445771	−	0.445771i	0.0157114	−	0.0157114i
$806$	−9.90811	+	9.90811i	−0.348998	+	0.348998i
$807$		−	0.342244i		−	0.0120476i
$808$			55.4826i			1.95187i
$809$	25.5872	−	25.5872i	0.899597	−	0.899597i	−0.0958032	−	0.995400i	$-0.530542\pi$
$809$	25.5872	−	25.5872i	0.899597	−	0.899597i	0.995400	+	0.0958032i	$0.0305420\pi$
$810$	1.57450	−	1.57450i	0.0553223	−	0.0553223i
$811$	−20.5994	−	20.5994i	−0.723343	−	0.723343i	0.245941	−	0.969285i	$-0.420903\pi$
$811$	−20.5994	−	20.5994i	−0.723343	−	0.723343i	−0.969285	+	0.245941i	$0.920903\pi$
$812$	−162.164			−5.69086
$813$	5.47052	+	5.47052i	0.191859	+	0.191859i
$814$			25.7543i			0.902689i
$815$	18.3550			0.642949
$816$		0			0
$817$	24.0101			0.840007
$818$			50.9540i			1.78156i
$819$	−9.73439	−	9.73439i	−0.340147	−	0.340147i
$820$	−10.0419			−0.350678
$821$	29.3554	+	29.3554i	1.02451	+	1.02451i	0.999692	+	0.0248198i	$0.00790119\pi$
$821$	29.3554	+	29.3554i	1.02451	+	1.02451i	0.0248198	+	0.999692i	$0.492099\pi$
$822$	−30.8436	+	30.8436i	−1.07580	+	1.07580i
$823$	−11.6967	+	11.6967i	−0.407720	+	0.407720i	−0.880943	−	0.473223i	$-0.843091\pi$
$823$	−11.6967	+	11.6967i	−0.407720	+	0.407720i	0.473223	+	0.880943i	$0.343091\pi$
$824$			94.7984i			3.30246i
$825$		−	15.7101i		−	0.546955i
$826$	57.1415	−	57.1415i	1.98821	−	1.98821i
$827$	−13.8184	+	13.8184i	−0.480513	+	0.480513i	−0.905296	−	0.424782i	$-0.860351\pi$
$827$	−13.8184	+	13.8184i	−0.480513	+	0.480513i	0.424782	+	0.905296i	$0.360351\pi$
$828$	0.506912	+	0.506912i	0.0176164	+	0.0176164i
$829$	40.3519			1.40148			0.700739	−	0.713418i	$-0.252854\pi$
$829$	40.3519			1.40148			0.700739	+	0.713418i	$0.252854\pi$
$830$	−23.3509	−	23.3509i	−0.810523	−	0.810523i
$831$		−	28.4320i		−	0.986295i
$832$	5.11205			0.177229
$833$		0			0
$834$	−8.55169			−0.296121
$835$			10.2953i			0.356284i
$836$	23.6744	+	23.6744i	0.818797	+	0.818797i
$837$	1.77332			0.0612949
$838$	2.18727	+	2.18727i	0.0755582	+	0.0755582i
$839$	−18.5711	+	18.5711i	−0.641146	+	0.641146i	−0.950837	−	0.309691i	$-0.899774\pi$
$839$	−18.5711	+	18.5711i	−0.641146	+	0.641146i	0.309691	+	0.950837i	$0.399774\pi$
$840$	16.7498	−	16.7498i	0.577923	−	0.577923i
$841$			40.4347i			1.39430i
$842$		−	23.3327i		−	0.804100i
$843$	11.1226	−	11.1226i	0.383081	−	0.383081i
$844$	14.4440	−	14.4440i	0.497184	−	0.497184i
$845$	−2.02823	−	2.02823i	−0.0697731	−	0.0697731i
$846$	8.27631			0.284545
$847$	8.78171	+	8.78171i	0.301743	+	0.301743i
$848$			42.9350i			1.47439i
$849$	8.12330			0.278791
$850$		0			0
$851$	0.444689			0.0152437
$852$		−	4.97771i		−	0.170534i
$853$	32.1833	+	32.1833i	1.10193	+	1.10193i	0.994177	+	0.107757i	$0.0343669\pi$
$853$	32.1833	+	32.1833i	1.10193	+	1.10193i	0.107757	+	0.994177i	$0.465633\pi$
$854$	28.0351			0.959341
$855$	−1.26969	−	1.26969i	−0.0434223	−	0.0434223i
$856$	−44.1886	+	44.1886i	−1.51033	+	1.51033i
$857$	21.8163	−	21.8163i	0.745232	−	0.745232i	−0.228347	−	0.973580i	$-0.573332\pi$
$857$	21.8163	−	21.8163i	0.745232	−	0.745232i	0.973580	+	0.228347i	$0.0733322\pi$
$858$			29.3696i			1.00266i
$859$			25.4284i			0.867605i	0.901008	+	0.433803i	$0.142829\pi$
$859$			25.4284i			0.867605i	−0.901008	+	0.433803i	$0.857171\pi$
$860$	−32.2559	+	32.2559i	−1.09992	+	1.09992i
$861$	8.07460	−	8.07460i	0.275182	−	0.275182i
$862$	−9.78525	−	9.78525i	−0.333287	−	0.333287i
$863$	0.238541			0.00812004			0.00406002	−	0.999992i	$-0.498708\pi$
$863$	0.238541			0.00812004			0.00406002	+	0.999992i	$0.498708\pi$
$864$	3.25005	+	3.25005i	0.110569	+	0.110569i
$865$		−	14.6705i		−	0.498814i
$866$	−34.2148			−1.16267
$867$		0			0
$868$	34.5107			1.17137
$869$		−	12.8357i		−	0.435423i
$870$	−13.1199	−	13.1199i	−0.444807	−	0.444807i
$871$	−14.3886			−0.487538
$872$	28.6612	+	28.6612i	0.970590	+	0.970590i
$873$	3.04438	−	3.04438i	0.103037	−	0.103037i
$874$	0.594100	−	0.594100i	0.0200957	−	0.0200957i
$875$			35.7939i			1.21005i
$876$			12.2344i			0.413363i
$877$	−29.1198	+	29.1198i	−0.983306	+	0.983306i	−0.999863	−	0.0165573i	$-0.994729\pi$
$877$	−29.1198	+	29.1198i	−0.983306	+	0.983306i	0.0165573	+	0.999863i	$0.494729\pi$
$878$	−25.2424	+	25.2424i	−0.851891	+	0.851891i
$879$	14.9056	+	14.9056i	0.502752	+	0.502752i
$880$	−21.6973			−0.731415
$881$	9.95225	+	9.95225i	0.335300	+	0.335300i	0.854595	−	0.519295i	$-0.173805\pi$
$881$	9.95225	+	9.95225i	0.335300	+	0.335300i	−0.519295	+	0.854595i	$0.673805\pi$
$882$			31.5526i			1.06243i
$883$	32.0496			1.07856			0.539278	−	0.842128i	$-0.318697\pi$
$883$	32.0496			1.07856			0.539278	+	0.842128i	$0.318697\pi$
$884$		0			0
$885$	6.36184			0.213851
$886$			18.1985i			0.611391i
$887$	−10.6278	−	10.6278i	−0.356848	−	0.356848i	0.505802	−	0.862650i	$-0.331197\pi$
$887$	−10.6278	−	10.6278i	−0.356848	−	0.356848i	−0.862650	+	0.505802i	$0.831197\pi$
$888$	16.7091			0.560722
$889$	−39.1777	−	39.1777i	−1.31398	−	1.31398i
$890$	−17.9796	+	17.9796i	−0.602677	+	0.602677i
$891$	2.62823	−	2.62823i	0.0880491	−	0.0880491i
$892$			80.4407i			2.69335i
$893$		−	6.67406i		−	0.223339i
$894$	2.47823	−	2.47823i	0.0828844	−	0.0828844i
$895$	−2.67237	+	2.67237i	−0.0893275	+	0.0893275i
$896$	−41.6141	−	41.6141i	−1.39023	−	1.39023i
$897$	0.507112			0.0169320
$898$	24.5872	+	24.5872i	0.820486	+	0.820486i
$899$		−	14.7766i		−	0.492828i
$900$	−18.6459			−0.621530
$901$		0			0
$902$	−24.3618			−0.811161
$903$		−	51.8735i		−	1.72624i
$904$	54.2899	+	54.2899i	1.80566	+	1.80566i
$905$	19.5767			0.650750
$906$	−10.9726	−	10.9726i	−0.364539	−	0.364539i
$907$	−1.77594	+	1.77594i	−0.0589690	+	0.0589690i	−0.735976	−	0.677007i	$-0.763277\pi$
$907$	−1.77594	+	1.77594i	−0.0589690	+	0.0589690i	0.677007	+	0.735976i	$0.263277\pi$
$908$	80.1542	−	80.1542i	2.66001	−	2.66001i
$909$		−	9.08647i		−	0.301379i
$910$		−	30.6536i		−	1.01616i
$911$	14.8461	−	14.8461i	0.491873	−	0.491873i	−0.417023	−	0.908896i	$-0.636926\pi$
$911$	14.8461	−	14.8461i	0.491873	−	0.491873i	0.908896	+	0.417023i	$0.136926\pi$
$912$	9.58439	−	9.58439i	0.317371	−	0.317371i
$913$	−38.9785	−	38.9785i	−1.29000	−	1.29000i
$914$	−40.1284			−1.32733
$915$	1.56064	+	1.56064i	0.0515932	+	0.0515932i
$916$			77.5494i			2.56231i
$917$	−88.1011			−2.90936
$918$		0			0
$919$	−43.9050			−1.44829			−0.724146	−	0.689647i	$-0.757766\pi$
$919$	−43.9050			−1.44829			−0.724146	+	0.689647i	$0.757766\pi$
$920$			0.872578i			0.0287680i
$921$	−10.6713	−	10.6713i	−0.351632	−	0.351632i
$922$	19.4858			0.641729
$923$	−2.48984	−	2.48984i	−0.0819540	−	0.0819540i
$924$	51.1483	−	51.1483i	1.68266	−	1.68266i
$925$	−8.17856	+	8.17856i	−0.268910	+	0.268910i
$926$		−	82.9505i		−	2.72592i
$927$		−	15.5253i		−	0.509917i
$928$	27.0819	−	27.0819i	0.889006	−	0.889006i
$929$	33.8964	−	33.8964i	1.11210	−	1.11210i	0.119239	−	0.992866i	$-0.461954\pi$
$929$	33.8964	−	33.8964i	1.11210	−	1.11210i	0.992866	−	0.119239i	$-0.0380456\pi$
$930$	2.79209	+	2.79209i	0.0915563	+	0.0915563i
$931$	25.4442			0.833900
$932$	−13.2699	−	13.2699i	−0.434671	−	0.434671i
$933$		−	26.9368i		−	0.881870i
$934$	−43.4826			−1.42279
$935$		0			0
$936$	19.0547			0.622822
$937$			2.39094i			0.0781086i	0.999237	+	0.0390543i	$0.0124345\pi$
$937$			2.39094i			0.0781086i	−0.999237	+	0.0390543i	$0.987565\pi$
$938$	36.4188	+	36.4188i	1.18912	+	1.18912i
$939$	3.99319			0.130313
$940$	8.96615	+	8.96615i	0.292443	+	0.292443i
$941$	15.5291	−	15.5291i	0.506233	−	0.506233i	−0.407135	−	0.913368i	$-0.633472\pi$
$941$	15.5291	−	15.5291i	0.506233	−	0.506233i	0.913368	+	0.407135i	$0.133472\pi$
$942$	23.3648	−	23.3648i	0.761266	−	0.761266i
$943$			0.420645i			0.0136981i
$944$			48.0232i			1.56302i
$945$	−2.74314	+	2.74314i	−0.0892343	+	0.0892343i
$946$	−78.2536	+	78.2536i	−2.54425	+	2.54425i
$947$	−4.27941	−	4.27941i	−0.139062	−	0.139062i	0.634149	−	0.773211i	$-0.281351\pi$
$947$	−4.27941	−	4.27941i	−0.139062	−	0.139062i	−0.773211	+	0.634149i	$0.781351\pi$
$948$	−15.2344			−0.494791
$949$	6.11963	+	6.11963i	0.198651	+	0.198651i
$950$			21.8530i			0.709004i
$951$	2.13341			0.0691805
$952$		0			0
$953$	−53.8955			−1.74585			−0.872923	−	0.487858i	$-0.837778\pi$
$953$	−53.8955			−1.74585			−0.872923	+	0.487858i	$0.837778\pi$
$954$		−	16.3773i		−	0.530236i
$955$	−6.99964	−	6.99964i	−0.226503	−	0.226503i
$956$	−25.9145			−0.838134
$957$	−21.9004	−	21.9004i	−0.707939	−	0.707939i
$958$	−39.6306	+	39.6306i	−1.28041	+	1.28041i
$959$	53.7366	−	53.7366i	1.73525	−	1.73525i
$960$		−	1.44057i		−	0.0464942i
$961$		−	27.8553i		−	0.898559i
$962$	15.2896	−	15.2896i	0.492957	−	0.492957i
$963$	7.23683	−	7.23683i	0.233204	−	0.233204i
$964$	42.6974	+	42.6974i	1.37519	+	1.37519i
$965$	−5.87670			−0.189178
$966$	−1.28355	−	1.28355i	−0.0412974	−	0.0412974i
$967$			55.4175i			1.78211i	0.453900	+	0.891053i	$0.350032\pi$
$967$			55.4175i			1.78211i	−0.453900	+	0.891053i	$0.649968\pi$
$968$	−17.1898			−0.552503
$969$		0			0
$970$	9.58677			0.307813
$971$			28.4201i			0.912046i	0.889968	+	0.456023i	$0.150727\pi$
$971$			28.4201i			0.912046i	−0.889968	+	0.456023i	$0.849273\pi$
$972$	−3.11938	−	3.11938i	−0.100054	−	0.100054i
$973$	14.8990			0.477640
$974$	56.1979	+	56.1979i	1.80070	+	1.80070i
$975$	−9.32663	+	9.32663i	−0.298691	+	0.298691i
$976$	−11.7807	+	11.7807i	−0.377091	+	0.377091i
$977$		−	56.3492i		−	1.80277i	−0.433019	−	0.901385i	$-0.642552\pi$
$977$		−	56.3492i		−	1.80277i	0.433019	−	0.901385i	$-0.357448\pi$
$978$		−	52.8512i		−	1.69000i
$979$	−30.0123	+	30.0123i	−0.959199	+	0.959199i
$980$	−34.1825	+	34.1825i	−1.09192	+	1.09192i
$981$	−4.69388	−	4.69388i	−0.149864	−	0.149864i
$982$	−0.521984			−0.0166572
$983$	−7.45022	−	7.45022i	−0.237625	−	0.237625i	0.578241	−	0.815866i	$-0.303739\pi$
$983$	−7.45022	−	7.45022i	−0.237625	−	0.237625i	−0.815866	+	0.578241i	$0.803739\pi$
$984$			15.8057i			0.503868i
$985$	−11.1771			−0.356130
$986$		0			0
$987$	−14.4192			−0.458969
$988$		−	28.1097i		−	0.894288i
$989$	1.35117	+	1.35117i	0.0429648	+	0.0429648i
$990$	8.27631			0.263038
$991$	−25.7630	−	25.7630i	−0.818388	−	0.818388i	0.167486	−	0.985874i	$-0.446435\pi$
$991$	−25.7630	−	25.7630i	−0.818388	−	0.818388i	−0.985874	+	0.167486i	$0.946435\pi$
$992$	−5.76338	+	5.76338i	−0.182987	+	0.182987i
$993$	5.48985	−	5.48985i	0.174215	−	0.174215i
$994$			12.6040i			0.399775i
$995$		−	23.9195i		−	0.758300i
$996$	−46.2626	+	46.2626i	−1.46589	+	1.46589i
$997$	−0.608971	+	0.608971i	−0.0192863	+	0.0192863i	−0.716684	−	0.697398i	$-0.754341\pi$
$997$	−0.608971	+	0.608971i	−0.0192863	+	0.0192863i	0.697398	+	0.716684i	$0.254341\pi$
$998$	9.84864	+	9.84864i	0.311753	+	0.311753i
$999$	−2.73648			−0.0865785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.e.j.829.5		12
17.2	even	8		867.2.a.i.1.1	✓	3
17.3	odd	16		867.2.h.l.712.5		24
17.4	even	4	inner	867.2.e.j.616.1		12
17.5	odd	16		867.2.h.l.733.2		24
17.6	odd	16		867.2.h.l.757.1		24
17.7	odd	16		867.2.h.l.688.5		24
17.8	even	8		867.2.d.d.577.6		6
17.9	even	8		867.2.d.d.577.5		6
17.10	odd	16		867.2.h.l.688.6		24
17.11	odd	16		867.2.h.l.757.2		24
17.12	odd	16		867.2.h.l.733.1		24
17.13	even	4	inner	867.2.e.j.616.2		12
17.14	odd	16		867.2.h.l.712.6		24
17.15	even	8		867.2.a.j.1.1	yes	3
17.16	even	2	inner	867.2.e.j.829.6		12
51.2	odd	8		2601.2.a.y.1.3		3
51.32	odd	8		2601.2.a.z.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.i.1.1	✓	3	17.2	even	8
867.2.a.j.1.1	yes	3	17.15	even	8
867.2.d.d.577.5		6	17.9	even	8
867.2.d.d.577.6		6	17.8	even	8
867.2.e.j.616.1		12	17.4	even	4	inner
867.2.e.j.616.2		12	17.13	even	4	inner
867.2.e.j.829.5		12	1.1	even	1	trivial
867.2.e.j.829.6		12	17.16	even	2	inner
867.2.h.l.688.5		24	17.7	odd	16
867.2.h.l.688.6		24	17.10	odd	16
867.2.h.l.712.5		24	17.3	odd	16
867.2.h.l.712.6		24	17.14	odd	16
867.2.h.l.733.1		24	17.12	odd	16
867.2.h.l.733.2		24	17.5	odd	16
867.2.h.l.757.1		24	17.6	odd	16
867.2.h.l.757.2		24	17.11	odd	16
2601.2.a.y.1.3		3	51.2	odd	8
2601.2.a.z.1.3		3	51.32	odd	8

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.53209i q^{2} +(-0.707107 - 0.707107i) q^{3} -4.41147 q^{4} +(0.621819 + 0.621819i) q^{5} +(1.79046 - 1.79046i) q^{6} +(-3.11938 + 3.11938i) q^{7} -6.10607i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+2.53209i q^{2} +(-0.707107 - 0.707107i) q^{3} -4.41147 q^{4} +(0.621819 + 0.621819i) q^{5} +(1.79046 - 1.79046i) q^{6} +(-3.11938 + 3.11938i) q^{7} -6.10607i q^{8} +1.00000i q^{9} +(-1.57450 + 1.57450i) q^{10} +(-2.62823 + 2.62823i) q^{11} +(3.11938 + 3.11938i) q^{12} +3.12061 q^{13} +(-7.89856 - 7.89856i) q^{14} -0.879385i q^{15} +6.63816 q^{16} -2.53209 q^{18} +2.04189i q^{19} +(-2.74314 - 2.74314i) q^{20} +4.41147 q^{21} +(-6.65492 - 6.65492i) q^{22} +(-0.114908 + 0.114908i) q^{23} +(-4.31764 + 4.31764i) q^{24} -4.22668i q^{25} +7.90167i q^{26} +(0.707107 - 0.707107i) q^{27} +(13.7611 - 13.7611i) q^{28} +(-5.89214 - 5.89214i) q^{29} +2.22668 q^{30} +(1.25393 + 1.25393i) q^{31} +4.59627i q^{32} +3.71688 q^{33} -3.87939 q^{35} -4.41147i q^{36} +(-1.93498 - 1.93498i) q^{37} -5.17024 q^{38} +(-2.20661 - 2.20661i) q^{39} +(3.79687 - 3.79687i) q^{40} +(1.83036 - 1.83036i) q^{41} +11.1702i q^{42} -11.7588i q^{43} +(11.5944 - 11.5944i) q^{44} +(-0.621819 + 0.621819i) q^{45} +(-0.290956 - 0.290956i) q^{46} -3.26857 q^{47} +(-4.69388 - 4.69388i) q^{48} -12.4611i q^{49} +10.7023 q^{50} -13.7665 q^{52} +6.46791i q^{53} +(1.79046 + 1.79046i) q^{54} -3.26857 q^{55} +(19.0472 + 19.0472i) q^{56} +(1.44383 - 1.44383i) q^{57} +(14.9194 - 14.9194i) q^{58} +7.23442i q^{59} +3.87939i q^{60} +(-1.77470 + 1.77470i) q^{61} +(-3.17505 + 3.17505i) q^{62} +(-3.11938 - 3.11938i) q^{63} +1.63816 q^{64} +(1.94046 + 1.94046i) q^{65} +9.41147i q^{66} -4.61081 q^{67} +0.162504 q^{69} -9.82295i q^{70} +(-0.797868 - 0.797868i) q^{71} +6.10607 q^{72} +(1.96103 + 1.96103i) q^{73} +(4.89955 - 4.89955i) q^{74} +(-2.98872 + 2.98872i) q^{75} -9.00774i q^{76} -16.3969i q^{77} +(5.58733 - 5.58733i) q^{78} +(-2.44190 + 2.44190i) q^{79} +(4.12773 + 4.12773i) q^{80} -1.00000 q^{81} +(4.63464 + 4.63464i) q^{82} +14.8307i q^{83} -19.4611 q^{84} +29.7743 q^{86} +8.33275i q^{87} +(16.0482 + 16.0482i) q^{88} +11.4192 q^{89} +(-1.57450 - 1.57450i) q^{90} +(-9.73439 + 9.73439i) q^{91} +(0.506912 - 0.506912i) q^{92} -1.77332i q^{93} -8.27631i q^{94} +(-1.26969 + 1.26969i) q^{95} +(3.25005 - 3.25005i) q^{96} +(-3.04438 - 3.04438i) q^{97} +31.5526 q^{98} +(-2.62823 - 2.62823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4}+O(q^{10}) \) 12 * q - 12 * q^4	\( 12 q - 12 q^{4} + 60 q^{13} + 12 q^{16} - 12 q^{18} + 12 q^{21} + 12 q^{33} - 24 q^{35} + 24 q^{38} + 24 q^{50} - 24 q^{52} - 48 q^{64} - 72 q^{67} + 12 q^{69} + 24 q^{72} - 12 q^{81} - 84 q^{84} + 120 q^{86} + 108 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 + 60 * q^13 + 12 * q^16 - 12 * q^18 + 12 * q^21 + 12 * q^33 - 24 * q^35 + 24 * q^38 + 24 * q^50 - 24 * q^52 - 48 * q^64 - 72 * q^67 + 12 * q^69 + 24 * q^72 - 12 * q^81 - 84 * q^84 + 120 * q^86 + 108 * q^98

Introduction

L-functions

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