LMFDB - Embedded newform 867.2.e.h.829.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(616,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [8,0,0,0,0,0,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.1
Root			$-0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	867.829
Dual form			867.2.e.h.616.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.84776i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.41421 q^{4} +(-2.55487 - 2.55487i) q^{5} +(-1.30656 + 1.30656i) q^{6} +(-2.72078 + 2.72078i) q^{7} -1.08239i q^{8} +1.00000i q^{9} +(-4.72078 + 4.72078i) q^{10} +(-0.140652 + 0.140652i) q^{11} +(1.00000 + 1.00000i) q^{12} +0.883480 q^{13} +(5.02734 + 5.02734i) q^{14} +3.61313i q^{15} -4.82843 q^{16} +1.84776 q^{18} +2.24943i q^{19} +(3.61313 + 3.61313i) q^{20} +3.84776 q^{21} +(0.259892 + 0.259892i) q^{22} +(1.80430 - 1.80430i) q^{23} +(-0.765367 + 0.765367i) q^{24} +8.05468i q^{25} -1.63246i q^{26} +(0.707107 - 0.707107i) q^{27} +(3.84776 - 3.84776i) q^{28} +(1.58579 + 1.58579i) q^{29} +6.67619 q^{30} +(-3.35115 - 3.35115i) q^{31} +6.75699i q^{32} +0.198912 q^{33} +13.9024 q^{35} -1.41421i q^{36} +(4.93608 + 4.93608i) q^{37} +4.15640 q^{38} +(-0.624715 - 0.624715i) q^{39} +(-2.76537 + 2.76537i) q^{40} +(-0.438346 + 0.438346i) q^{41} -7.10973i q^{42} -7.17120i q^{43} +(0.198912 - 0.198912i) q^{44} +(2.55487 - 2.55487i) q^{45} +(-3.33390 - 3.33390i) q^{46} -5.49207 q^{47} +(3.41421 + 3.41421i) q^{48} -7.80525i q^{49} +14.8831 q^{50} -1.24943 q^{52} +5.18759i q^{53} +(-1.30656 - 1.30656i) q^{54} +0.718695 q^{55} +(2.94495 + 2.94495i) q^{56} +(1.59059 - 1.59059i) q^{57} +(2.93015 - 2.93015i) q^{58} +5.01933i q^{59} -5.10973i q^{60} +(-10.6316 + 10.6316i) q^{61} +(-6.19212 + 6.19212i) q^{62} +(-2.72078 - 2.72078i) q^{63} +2.82843 q^{64} +(-2.25717 - 2.25717i) q^{65} -0.367542i q^{66} -0.281305 q^{67} -2.55166 q^{69} -25.6884i q^{70} +(-9.85577 - 9.85577i) q^{71} +1.08239 q^{72} +(11.0592 + 11.0592i) q^{73} +(9.12068 - 9.12068i) q^{74} +(5.69552 - 5.69552i) q^{75} -3.18117i q^{76} -0.765367i q^{77} +(-1.15432 + 1.15432i) q^{78} +(3.62359 - 3.62359i) q^{79} +(12.3360 + 12.3360i) q^{80} -1.00000 q^{81} +(0.809957 + 0.809957i) q^{82} +9.51716i q^{83} -5.44155 q^{84} -13.2506 q^{86} -2.24264i q^{87} +(0.152241 + 0.152241i) q^{88} -4.33476 q^{89} +(-4.72078 - 4.72078i) q^{90} +(-2.40375 + 2.40375i) q^{91} +(-2.55166 + 2.55166i) q^{92} +4.73925i q^{93} +10.1480i q^{94} +(5.74699 - 5.74699i) q^{95} +(4.77791 - 4.77791i) q^{96} +(4.20692 + 4.20692i) q^{97} -14.4222 q^{98} +(-0.140652 - 0.140652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{10} + 8 q^{11} + 8 q^{12} + 8 q^{13} + 8 q^{14} - 16 q^{16} + 8 q^{20} + 16 q^{21} + 16 q^{22} + 16 q^{28} + 24 q^{29} + 16 q^{30} - 32 q^{31} - 8 q^{33} + 32 q^{35} + 16 q^{37} - 32 q^{38}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q - 16 * q^10 + 8 * q^11 + 8 * q^12 + 8 * q^13 + 8 * q^14 - 16 * q^16 + 8 * q^20 + 16 * q^21 + 16 * q^22 + 16 * q^28 + 24 * q^29 + 16 * q^30 - 32 * q^31 - 8 * q^33 + 32 * q^35 + 16 * q^37 - 32 * q^38 - 8 * q^39 - 16 * q^40 + 16 * q^41 - 8 * q^44 + 16 * q^46 - 16 * q^47 + 16 * q^48 + 32 * q^50 - 16 * q^52 + 24 * q^55 + 8 * q^57 - 32 * q^61 - 8 * q^65 + 16 * q^67 - 24 * q^69 - 24 * q^71 + 32 * q^73 - 8 * q^74 + 16 * q^75 + 16 * q^78 + 16 * q^79 + 16 * q^80 - 8 * q^81 + 16 * q^82 - 32 * q^86 + 16 * q^88 - 32 * q^89 - 16 * q^90 - 24 * q^92 - 24 * q^95 - 16 * q^97 - 64 * q^98 + 8 * q^99

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 $

$2$		−	1.84776i		−	1.30656i	−0.757115	−	0.653281i	$-0.773392\pi$
$2$		−	1.84776i		−	1.30656i	0.757115	−	0.653281i	$-0.226608\pi$
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.41421			−0.707107
$5$	−2.55487	−	2.55487i	−1.14257	−	1.14257i	−0.987978	−	0.154592i	$-0.950594\pi$
$5$	−2.55487	−	2.55487i	−1.14257	−	1.14257i	−0.154592	−	0.987978i	$-0.549406\pi$
$6$	−1.30656	+	1.30656i	−0.533402	+	0.533402i
$7$	−2.72078	+	2.72078i	−1.02836	+	1.02836i	−0.0287708	+	0.999586i	$0.509159\pi$
$7$	−2.72078	+	2.72078i	−1.02836	+	1.02836i	−0.999586	+	0.0287708i	$0.990841\pi$
$8$		−	1.08239i		−	0.382683i
$9$			1.00000i			0.333333i
$10$	−4.72078	+	4.72078i	−1.49284	+	1.49284i
$11$	−0.140652	+	0.140652i	−0.0424083	+	0.0424083i	−0.727993	−	0.685585i	$-0.759547\pi$
$11$	−0.140652	+	0.140652i	−0.0424083	+	0.0424083i	0.685585	+	0.727993i	$0.259547\pi$
$12$	1.00000	+	1.00000i	0.288675	+	0.288675i
$13$	0.883480			0.245033			0.122517	−	0.992466i	$-0.460904\pi$
$13$	0.883480			0.245033			0.122517	+	0.992466i	$0.460904\pi$
$14$	5.02734	+	5.02734i	1.34361	+	1.34361i
$15$			3.61313i			0.932905i
$16$	−4.82843			−1.20711
$17$		0			0
$17$		0			0
$18$	1.84776			0.435521
$19$			2.24943i			0.516054i	0.966138	+	0.258027i	$0.0830724\pi$
$19$			2.24943i			0.516054i	−0.966138	+	0.258027i	$0.916928\pi$
$20$	3.61313	+	3.61313i	0.807920	+	0.807920i
$21$	3.84776			0.839650
$22$	0.259892	+	0.259892i	0.0554091	+	0.0554091i
$23$	1.80430	−	1.80430i	0.376222	−	0.376222i	−0.493515	−	0.869737i	$-0.664288\pi$
$23$	1.80430	−	1.80430i	0.376222	−	0.376222i	0.869737	+	0.493515i	$0.164288\pi$
$24$	−0.765367	+	0.765367i	−0.156230	+	0.156230i
$25$			8.05468i			1.61094i
$26$		−	1.63246i		−	0.320151i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	3.84776	−	3.84776i	0.727158	−	0.727158i
$29$	1.58579	+	1.58579i	0.294473	+	0.294473i	0.838844	−	0.544371i	$-0.183232\pi$
$29$	1.58579	+	1.58579i	0.294473	+	0.294473i	−0.544371	+	0.838844i	$0.683232\pi$
$30$	6.67619			1.21890
$31$	−3.35115	−	3.35115i	−0.601885	−	0.601885i	0.338928	−	0.940812i	$-0.389936\pi$
$31$	−3.35115	−	3.35115i	−0.601885	−	0.601885i	−0.940812	+	0.338928i	$0.889936\pi$
$32$			6.75699i			1.19448i
$33$	0.198912			0.0346262
$34$		0			0
$35$	13.9024			2.34994
$36$		−	1.41421i		−	0.235702i
$37$	4.93608	+	4.93608i	0.811486	+	0.811486i	0.984857	−	0.173370i	$-0.0554658\pi$
$37$	4.93608	+	4.93608i	0.811486	+	0.811486i	−0.173370	+	0.984857i	$0.555466\pi$
$38$	4.15640			0.674258
$39$	−0.624715	−	0.624715i	−0.100034	−	0.100034i
$40$	−2.76537	+	2.76537i	−0.437243	+	0.437243i
$41$	−0.438346	+	0.438346i	−0.0684581	+	0.0684581i	−0.740507	−	0.672049i	$-0.765415\pi$
$41$	−0.438346	+	0.438346i	−0.0684581	+	0.0684581i	0.672049	+	0.740507i	$0.265415\pi$
$42$		−	7.10973i		−	1.09706i
$43$		−	7.17120i		−	1.09360i	−0.837264	−	0.546799i	$-0.815846\pi$
$43$		−	7.17120i		−	1.09360i	0.837264	−	0.546799i	$-0.184154\pi$
$44$	0.198912	−	0.198912i	0.0299872	−	0.0299872i
$45$	2.55487	−	2.55487i	0.380857	−	0.380857i
$46$	−3.33390	−	3.33390i	−0.491557	−	0.491557i
$47$	−5.49207			−0.801101			−0.400550	−	0.916275i	$-0.631181\pi$
$47$	−5.49207			−0.801101			−0.400550	+	0.916275i	$0.631181\pi$
$48$	3.41421	+	3.41421i	0.492799	+	0.492799i
$49$		−	7.80525i		−	1.11504i
$50$	14.8831			2.10479
$51$		0			0
$52$	−1.24943			−0.173265
$53$			5.18759i			0.712570i	0.934377	+	0.356285i	$0.115957\pi$
$53$			5.18759i			0.712570i	−0.934377	+	0.356285i	$0.884043\pi$
$54$	−1.30656	−	1.30656i	−0.177801	−	0.177801i
$55$	0.718695			0.0969089
$56$	2.94495	+	2.94495i	0.393535	+	0.393535i
$57$	1.59059	−	1.59059i	0.210678	−	0.210678i
$58$	2.93015	−	2.93015i	0.384748	−	0.384748i
$59$			5.01933i			0.653461i	0.945117	+	0.326731i	$0.105947\pi$
$59$			5.01933i			0.653461i	−0.945117	+	0.326731i	$0.894053\pi$
$60$		−	5.10973i		−	0.659664i
$61$	−10.6316	+	10.6316i	−1.36124	+	1.36124i	−0.488892	+	0.872344i	$0.662599\pi$
$61$	−10.6316	+	10.6316i	−1.36124	+	1.36124i	−0.872344	+	0.488892i	$0.837401\pi$
$62$	−6.19212	+	6.19212i	−0.786401	+	0.786401i
$63$	−2.72078	−	2.72078i	−0.342786	−	0.342786i
$64$	2.82843			0.353553
$65$	−2.25717	−	2.25717i	−0.279968	−	0.279968i
$66$		−	0.367542i		−	0.0452413i
$67$	−0.281305			−0.0343668			−0.0171834	−	0.999852i	$-0.505470\pi$
$67$	−0.281305			−0.0343668			−0.0171834	+	0.999852i	$0.505470\pi$
$68$		0			0
$69$	−2.55166			−0.307184
$70$		−	25.6884i		−	3.07035i
$71$	−9.85577	−	9.85577i	−1.16966	−	1.16966i	−0.982288	−	0.187376i	$-0.940002\pi$
$71$	−9.85577	−	9.85577i	−1.16966	−	1.16966i	−0.187376	−	0.982288i	$-0.559998\pi$
$72$	1.08239			0.127561
$73$	11.0592	+	11.0592i	1.29438	+	1.29438i	0.932048	+	0.362335i	$0.118021\pi$
$73$	11.0592	+	11.0592i	1.29438	+	1.29438i	0.362335	+	0.932048i	$0.381979\pi$
$74$	9.12068	−	9.12068i	1.06026	−	1.06026i
$75$	5.69552	−	5.69552i	0.657662	−	0.657662i
$76$		−	3.18117i		−	0.364906i
$77$		−	0.765367i		−	0.0872216i
$78$	−1.15432	+	1.15432i	−0.130701	+	0.130701i
$79$	3.62359	−	3.62359i	0.407686	−	0.407686i	−0.473245	−	0.880931i	$-0.656918\pi$
$79$	3.62359	−	3.62359i	0.407686	−	0.407686i	0.880931	+	0.473245i	$0.156918\pi$
$80$	12.3360	+	12.3360i	1.37920	+	1.37920i
$81$	−1.00000			−0.111111
$82$	0.809957	+	0.809957i	0.0894448	+	0.0894448i
$83$			9.51716i			1.04464i	0.852748	+	0.522322i	$0.174934\pi$
$83$			9.51716i			1.04464i	−0.852748	+	0.522322i	$0.825066\pi$
$84$	−5.44155			−0.593722
$85$		0			0
$86$	−13.2506			−1.42885
$87$		−	2.24264i		−	0.240436i
$88$	0.152241	+	0.152241i	0.0162289	+	0.0162289i
$89$	−4.33476			−0.459484			−0.229742	−	0.973252i	$-0.573788\pi$
$89$	−4.33476			−0.459484			−0.229742	+	0.973252i	$0.573788\pi$
$90$	−4.72078	−	4.72078i	−0.497614	−	0.497614i
$91$	−2.40375	+	2.40375i	−0.251982	+	0.251982i
$92$	−2.55166	+	2.55166i	−0.266029	+	0.266029i
$93$			4.73925i			0.491437i
$94$			10.1480i			1.04669i
$95$	5.74699	−	5.74699i	0.589629	−	0.589629i
$96$	4.77791	−	4.77791i	0.487643	−	0.487643i
$97$	4.20692	+	4.20692i	0.427148	+	0.427148i	0.887656	−	0.460508i	$-0.152333\pi$
$97$	4.20692	+	4.20692i	0.427148	+	0.427148i	−0.460508	+	0.887656i	$0.652333\pi$
$98$	−14.4222			−1.45686
$99$	−0.140652	−	0.140652i	−0.0141361	−	0.0141361i
$100$		−	11.3910i		−	1.13910i
$101$	−3.48022			−0.346295			−0.173147	−	0.984896i	$-0.555394\pi$
$101$	−3.48022			−0.346295			−0.173147	+	0.984896i	$0.555394\pi$
$102$		0			0
$103$	−10.2649			−1.01143			−0.505716	−	0.862700i	$-0.668772\pi$
$103$	−10.2649			−1.01143			−0.505716	+	0.862700i	$0.668772\pi$
$104$		−	0.956272i		−	0.0937702i
$105$	−9.83051	−	9.83051i	−0.959359	−	0.959359i
$106$	9.58541			0.931018
$107$	1.98682	+	1.98682i	0.192073	+	0.192073i	0.796591	−	0.604518i	$-0.206634\pi$
$107$	1.98682	+	1.98682i	0.192073	+	0.192073i	−0.604518	+	0.796591i	$0.706634\pi$
$108$	−1.00000	+	1.00000i	−0.0962250	+	0.0962250i
$109$	−6.06306	+	6.06306i	−0.580736	+	0.580736i	−0.935105	−	0.354370i	$-0.884695\pi$
$109$	−6.06306	+	6.06306i	−0.580736	+	0.580736i	0.354370	+	0.935105i	$0.384695\pi$
$110$		−	1.32798i		−	0.126618i
$111$		−	6.98067i		−	0.662576i
$112$	13.1371	−	13.1371i	1.24134	−	1.24134i
$113$	2.71511	−	2.71511i	0.255416	−	0.255416i	−0.567770	−	0.823187i	$-0.692194\pi$
$113$	2.71511	−	2.71511i	0.255416	−	0.255416i	0.823187	+	0.567770i	$0.192194\pi$
$114$	−2.93902	−	2.93902i	−0.275265	−	0.275265i
$115$	−9.21946			−0.859719
$116$	−2.24264	−	2.24264i	−0.208224	−	0.208224i
$117$			0.883480i			0.0816777i
$118$	9.27452			0.853788
$119$		0			0
$120$	3.91082			0.357007
$121$			10.9604i			0.996403i
$122$	19.6446	+	19.6446i	1.77854	+	1.77854i
$123$	0.619914			0.0558958
$124$	4.73925	+	4.73925i	0.425597	+	0.425597i
$125$	7.80430	−	7.80430i	0.698037	−	0.698037i
$126$	−5.02734	+	5.02734i	−0.447871	+	0.447871i
$127$		−	18.3041i		−	1.62423i	−0.583500	−	0.812113i	$-0.698317\pi$
$127$		−	18.3041i		−	1.62423i	0.583500	−	0.812113i	$-0.301683\pi$
$128$			8.28772i			0.732538i
$129$	−5.07080	+	5.07080i	−0.446459	+	0.446459i
$130$	−4.17071	+	4.17071i	−0.365796	+	0.365796i
$131$	−8.02413	−	8.02413i	−0.701072	−	0.701072i	0.263569	−	0.964641i	$-0.415100\pi$
$131$	−8.02413	−	8.02413i	−0.701072	−	0.701072i	−0.964641	+	0.263569i	$0.915100\pi$
$132$	−0.281305			−0.0244844
$133$	−6.12019	−	6.12019i	−0.530688	−	0.530688i
$134$			0.519783i			0.0449024i
$135$	−3.61313			−0.310968
$136$		0			0
$137$	−7.14961			−0.610833			−0.305416	−	0.952219i	$-0.598796\pi$
$137$	−7.14961			−0.610833			−0.305416	+	0.952219i	$0.598796\pi$
$138$			4.71485i			0.401355i
$139$	−7.76745	−	7.76745i	−0.658826	−	0.658826i	0.296276	−	0.955102i	$-0.404255\pi$
$139$	−7.76745	−	7.76745i	−0.658826	−	0.658826i	−0.955102	+	0.296276i	$0.904255\pi$
$140$	−19.6610			−1.66166
$141$	3.88348	+	3.88348i	0.327048	+	0.327048i
$142$	−18.2111	+	18.2111i	−1.52824	+	1.52824i
$143$	−0.124263	+	0.124263i	−0.0103914	+	0.0103914i
$144$		−	4.82843i		−	0.402369i
$145$		−	8.10294i		−	0.672913i
$146$	20.4348	−	20.4348i	1.69119	−	1.69119i
$147$	−5.51915	+	5.51915i	−0.455211	+	0.455211i
$148$	−6.98067	−	6.98067i	−0.573807	−	0.573807i
$149$	−5.99480			−0.491114			−0.245557	−	0.969382i	$-0.578971\pi$
$149$	−5.99480			−0.491114			−0.245557	+	0.969382i	$0.578971\pi$
$150$	−10.5239	−	10.5239i	−0.859277	−	0.859277i
$151$			11.4780i			0.934063i	0.884241	+	0.467032i	$0.154677\pi$
$151$			11.4780i			0.934063i	−0.884241	+	0.467032i	$0.845323\pi$
$152$	2.43476			0.197485
$153$		0			0
$154$	−1.41421			−0.113961
$155$			17.1235i			1.37539i
$156$	0.883480	+	0.883480i	0.0707350	+	0.0707350i
$157$	−5.81166			−0.463821			−0.231911	−	0.972737i	$-0.574498\pi$
$157$	−5.81166			−0.463821			−0.231911	+	0.972737i	$0.574498\pi$
$158$	−6.69552	−	6.69552i	−0.532667	−	0.532667i
$159$	3.66818	−	3.66818i	0.290905	−	0.290905i
$160$	17.2632	−	17.2632i	1.36478	−	1.36478i
$161$			9.81817i			0.773780i
$162$			1.84776i			0.145174i
$163$	−3.82458	+	3.82458i	−0.299564	+	0.299564i	−0.840843	−	0.541279i	$-0.817940\pi$
$163$	−3.82458	+	3.82458i	−0.299564	+	0.299564i	0.541279	+	0.840843i	$0.317940\pi$
$164$	0.619914	−	0.619914i	0.0484072	−	0.0484072i
$165$	−0.508194	−	0.508194i	−0.0395629	−	0.0395629i
$166$	17.5854			1.36489
$167$	2.30544	+	2.30544i	0.178400	+	0.178400i	0.790658	−	0.612258i	$-0.209739\pi$
$167$	2.30544	+	2.30544i	0.178400	+	0.178400i	−0.612258	+	0.790658i	$0.709739\pi$
$168$		−	4.16478i		−	0.321320i
$169$	−12.2195			−0.939959
$170$		0			0
$171$	−2.24943			−0.172018
$172$			10.1416i			0.773290i
$173$	11.9072	+	11.9072i	0.905291	+	0.905291i	0.995888	−	0.0905971i	$-0.0288775\pi$
$173$	11.9072	+	11.9072i	0.905291	+	0.905291i	−0.0905971	+	0.995888i	$0.528878\pi$
$174$	−4.14386			−0.314145
$175$	−21.9150	−	21.9150i	−1.65662	−	1.65662i
$176$	0.679129	−	0.679129i	0.0511913	−	0.0511913i
$177$	3.54920	−	3.54920i	0.266774	−	0.266774i
$178$			8.00960i			0.600345i
$179$			1.10332i			0.0824658i	0.999150	+	0.0412329i	$0.0131286\pi$
$179$			1.10332i			0.0824658i	−0.999150	+	0.0412329i	$0.986871\pi$
$180$	−3.61313	+	3.61313i	−0.269307	+	0.269307i
$181$	−10.9390	+	10.9390i	−0.813091	+	0.813091i	−0.985096	−	0.172005i	$-0.944975\pi$
$181$	−10.9390	+	10.9390i	−0.813091	+	0.813091i	0.172005	+	0.985096i	$0.444975\pi$
$182$	4.44155	+	4.44155i	0.329230	+	0.329230i
$183$	15.0353			1.11144
$184$	−1.95295	−	1.95295i	−0.143974	−	0.143974i
$185$		−	25.2220i		−	1.85436i
$186$	8.75699			0.642093
$187$		0			0
$188$	7.76696			0.566464
$189$			3.84776i			0.279883i
$190$	−10.6191	−	10.6191i	−0.770387	−	0.770387i
$191$	5.97069			0.432024			0.216012	−	0.976391i	$-0.430695\pi$
$191$	5.97069			0.432024			0.216012	+	0.976391i	$0.430695\pi$
$192$	−2.00000	−	2.00000i	−0.144338	−	0.144338i
$193$	7.81204	−	7.81204i	0.562323	−	0.562323i	−0.367644	−	0.929967i	$-0.619835\pi$
$193$	7.81204	−	7.81204i	0.562323	−	0.562323i	0.929967	+	0.367644i	$0.119835\pi$
$194$	7.77337	−	7.77337i	0.558096	−	0.558096i
$195$			3.19212i			0.228593i
$196$			11.0383i			0.788449i
$197$	−1.26903	+	1.26903i	−0.0904143	+	0.0904143i	−0.750867	−	0.660453i	$-0.770364\pi$
$197$	−1.26903	+	1.26903i	−0.0904143	+	0.0904143i	0.660453	+	0.750867i	$0.270364\pi$
$198$	−0.259892	+	0.259892i	−0.0184697	+	0.0184697i
$199$	−0.334764	−	0.334764i	−0.0237308	−	0.0237308i	0.695142	−	0.718873i	$-0.255342\pi$
$199$	−0.334764	−	0.334764i	−0.0237308	−	0.0237308i	−0.718873	+	0.695142i	$0.755342\pi$
$200$	8.71832			0.616478
$201$	0.198912	+	0.198912i	0.0140302	+	0.0140302i
$202$			6.43060i			0.452456i
$203$	−8.62914			−0.605647
$204$		0			0
$205$	2.23983			0.156436
$206$			18.9671i			1.32150i
$207$	1.80430	+	1.80430i	0.125407	+	0.125407i
$208$	−4.26582			−0.295781
$209$	−0.316387	−	0.316387i	−0.0218850	−	0.0218850i
$210$	−18.1644	+	18.1644i	−1.25346	+	1.25346i
$211$	−0.729646	+	0.729646i	−0.0502309	+	0.0502309i	−0.731776	−	0.681545i	$-0.761308\pi$
$211$	−0.729646	+	0.729646i	−0.0502309	+	0.0502309i	0.681545	+	0.731776i	$0.261308\pi$
$212$		−	7.33636i		−	0.503863i
$213$			13.9382i			0.955027i
$214$	3.67116	−	3.67116i	0.250955	−	0.250955i
$215$	−18.3215	+	18.3215i	−1.24951	+	1.24951i
$216$	−0.765367	−	0.765367i	−0.0520766	−	0.0520766i
$217$	18.2355			1.23790
$218$	11.2031	+	11.2031i	0.758768	+	0.758768i
$219$		−	15.6401i		−	1.05686i
$220$	−1.01639			−0.0685249
$221$		0			0
$222$	−12.8986			−0.865697
$223$			11.9018i			0.797002i	0.917168	+	0.398501i	$0.130469\pi$
$223$			11.9018i			0.797002i	−0.917168	+	0.398501i	$0.869531\pi$
$224$	−18.3842	−	18.3842i	−1.22835	−	1.22835i
$225$	−8.05468			−0.536979
$226$	−5.01688	−	5.01688i	−0.333718	−	0.333718i
$227$	−14.1107	+	14.1107i	−0.936559	+	0.936559i	−0.998104	−	0.0615451i	$-0.980397\pi$
$227$	−14.1107	+	14.1107i	−0.936559	+	0.936559i	0.0615451	+	0.998104i	$0.480397\pi$
$228$	−2.24943	+	2.24943i	−0.148972	+	0.148972i
$229$			0.0263629i			0.00174211i	1.00000		0.000871055i	$0.000277265\pi$
$229$			0.0263629i			0.00174211i	−1.00000		0.000871055i	$0.999723\pi$
$230$			17.0353i			1.12328i
$231$	−0.541196	+	0.541196i	−0.0356081	+	0.0356081i
$232$	1.71644	−	1.71644i	0.112690	−	0.112690i
$233$	−16.0305	−	16.0305i	−1.05020	−	1.05020i	−0.998672	−	0.0515243i	$-0.983592\pi$
$233$	−16.0305	−	16.0305i	−1.05020	−	1.05020i	−0.0515243	−	0.998672i	$-0.516408\pi$
$234$	1.63246			0.106717
$235$	14.0315	+	14.0315i	0.915314	+	0.915314i
$236$		−	7.09841i		−	0.462067i
$237$	−5.12453			−0.332874
$238$		0			0
$239$	10.3205			0.667577			0.333789	−	0.942648i	$-0.391673\pi$
$239$	10.3205			0.667577			0.333789	+	0.942648i	$0.391673\pi$
$240$		−	17.4457i		−	1.12612i
$241$	3.50388	+	3.50388i	0.225705	+	0.225705i	0.810896	−	0.585191i	$-0.198980\pi$
$241$	3.50388	+	3.50388i	0.225705	+	0.225705i	−0.585191	+	0.810896i	$0.698980\pi$
$242$	20.2522			1.30186
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	15.0353	−	15.0353i	0.962539	−	0.962539i
$245$	−19.9414	+	19.9414i	−1.27401	+	1.27401i
$246$		−	1.14545i		−	0.0730314i
$247$			1.98733i			0.126450i
$248$	−3.62726	+	3.62726i	−0.230331	+	0.230331i
$249$	6.72965	−	6.72965i	0.426474	−	0.426474i
$250$	−14.4205	−	14.4205i	−0.912030	−	0.912030i
$251$	−27.6021			−1.74223			−0.871115	−	0.491079i	$-0.836603\pi$
$251$	−27.6021			−1.74223			−0.871115	+	0.491079i	$0.836603\pi$
$252$	3.84776	+	3.84776i	0.242386	+	0.242386i
$253$			0.507556i			0.0319098i
$254$	−33.8216			−2.12215
$255$		0			0
$256$	20.9706			1.31066
$257$		−	24.6239i		−	1.53600i	−0.640450	−	0.768000i	$-0.721252\pi$
$257$		−	24.6239i		−	1.53600i	0.640450	−	0.768000i	$-0.278748\pi$
$258$	9.36962	+	9.36962i	0.583327	+	0.583327i
$259$	−26.8599			−1.66899
$260$	3.19212	+	3.19212i	0.197967	+	0.197967i
$261$	−1.58579	+	1.58579i	−0.0981577	+	0.0981577i
$262$	−14.8267	+	14.8267i	−0.915994	+	0.915994i
$263$			18.9015i			1.16552i	0.812645	+	0.582759i	$0.198027\pi$
$263$			18.9015i			1.16552i	−0.812645	+	0.582759i	$0.801973\pi$
$264$		−	0.215301i		−	0.0132509i
$265$	13.2536	−	13.2536i	0.814162	−	0.814162i
$266$	−11.3086	+	11.3086i	−0.693377	+	0.693377i
$267$	3.06514	+	3.06514i	0.187584	+	0.187584i
$268$	0.397825			0.0243010
$269$	−10.0447	−	10.0447i	−0.612435	−	0.612435i	0.331145	−	0.943580i	$-0.392565\pi$
$269$	−10.0447	−	10.0447i	−0.612435	−	0.612435i	−0.943580	+	0.331145i	$0.892565\pi$
$270$			6.67619i			0.406300i
$271$	−19.9314			−1.21074			−0.605372	−	0.795942i	$-0.706976\pi$
$271$	−19.9314			−1.21074			−0.605372	+	0.795942i	$0.706976\pi$
$272$		0			0
$273$	3.39942			0.205742
$274$			13.2108i			0.798092i
$275$	−1.13291	−	1.13291i	−0.0683170	−	0.0683170i
$276$	3.60859			0.217212
$277$	−15.1341	−	15.1341i	−0.909322	−	0.909322i	0.0868958	−	0.996217i	$-0.472305\pi$
$277$	−15.1341	−	15.1341i	−0.909322	−	0.909322i	−0.996217	+	0.0868958i	$0.972305\pi$
$278$	−14.3524	+	14.3524i	−0.860798	+	0.860798i
$279$	3.35115	−	3.35115i	0.200628	−	0.200628i
$280$		−	15.0479i		−	0.899283i
$281$			21.4669i			1.28061i	0.768121	+	0.640305i	$0.221192\pi$
$281$			21.4669i			1.28061i	−0.768121	+	0.640305i	$0.778808\pi$
$282$	7.17574	−	7.17574i	0.427309	−	0.427309i
$283$	14.0165	−	14.0165i	0.833195	−	0.833195i	−0.154758	−	0.987952i	$-0.549460\pi$
$283$	14.0165	−	14.0165i	0.833195	−	0.833195i	0.987952	+	0.154758i	$0.0494597\pi$
$284$	13.9382	+	13.9382i	0.827078	+	0.827078i
$285$	−8.12747			−0.481430
$286$	0.229609	+	0.229609i	0.0135771	+	0.0135771i
$287$		−	2.38528i		−	0.140799i
$288$	−6.75699			−0.398159
$289$		0			0
$290$	−14.9723			−0.879203
$291$		−	5.94948i		−	0.348765i
$292$	−15.6401	−	15.6401i	−0.915267	−	0.915267i
$293$	−20.3717			−1.19013			−0.595064	−	0.803678i	$-0.702873\pi$
$293$	−20.3717			−1.19013			−0.595064	+	0.803678i	$0.702873\pi$
$294$	10.1981	+	10.1981i	0.594762	+	0.594762i
$295$	12.8237	−	12.8237i	0.746626	−	0.746626i
$296$	5.34277	−	5.34277i	0.310542	−	0.310542i
$297$			0.198912i			0.0115421i
$298$			11.0770i			0.641671i
$299$	1.59406	−	1.59406i	0.0921868	−	0.0921868i
$300$	−8.05468	+	8.05468i	−0.465037	+	0.465037i
$301$	19.5112	+	19.5112i	1.12461	+	1.12461i
$302$	21.2085			1.22041
$303$	2.46088	+	2.46088i	0.141374	+	0.141374i
$304$		−	10.8612i		−	0.622933i
$305$	54.3246			3.11062
$306$		0			0
$307$	−13.6278			−0.777779			−0.388890	−	0.921284i	$-0.627141\pi$
$307$	−13.6278			−0.777779			−0.388890	+	0.921284i	$0.627141\pi$
$308$			1.08239i			0.0616750i
$309$	7.25839	+	7.25839i	0.412915	+	0.412915i
$310$	31.6401			1.79704
$311$	1.82843	+	1.82843i	0.103681	+	0.103681i	0.757044	−	0.653364i	$-0.226643\pi$
$311$	1.82843	+	1.82843i	0.103681	+	0.103681i	−0.653364	+	0.757044i	$0.726643\pi$
$312$	−0.676186	+	0.676186i	−0.0382815	+	0.0382815i
$313$	2.79565	−	2.79565i	0.158019	−	0.158019i	−0.623669	−	0.781689i	$-0.714359\pi$
$313$	2.79565	−	2.79565i	0.158019	−	0.158019i	0.781689	+	0.623669i	$0.214359\pi$
$314$			10.7386i			0.606012i
$315$			13.9024i			0.783314i
$316$	−5.12453	+	5.12453i	−0.288277	+	0.288277i
$317$	23.6983	−	23.6983i	1.33103	−	1.33103i	0.426582	−	0.904449i	$-0.359718\pi$
$317$	23.6983	−	23.6983i	1.33103	−	1.33103i	0.904449	−	0.426582i	$-0.140282\pi$
$318$	−6.77791	−	6.77791i	−0.380086	−	0.380086i
$319$	−0.446089			−0.0249762
$320$	−7.22625	−	7.22625i	−0.403960	−	0.403960i
$321$		−	2.80979i		−	0.156827i
$322$	18.1416			1.01099
$323$		0			0
$324$	1.41421			0.0785674
$325$			7.11615i			0.394733i
$326$	7.06691	+	7.06691i	0.391400	+	0.391400i
$327$	8.57446			0.474169
$328$	0.474462	+	0.474462i	0.0261978	+	0.0261978i
$329$	14.9427	−	14.9427i	0.823817	−	0.823817i
$330$	−0.939021	+	0.939021i	−0.0516914	+	0.0516914i
$331$			19.3037i			1.06103i	0.847676	+	0.530515i	$0.178001\pi$
$331$			19.3037i			1.06103i	−0.847676	+	0.530515i	$0.821999\pi$
$332$		−	13.4593i		−	0.738675i
$333$	−4.93608	+	4.93608i	−0.270495	+	0.270495i
$334$	4.25989	−	4.25989i	0.233091	−	0.233091i
$335$	0.718695	+	0.718695i	0.0392665	+	0.0392665i
$336$	−18.5786			−1.01355
$337$	12.3123	+	12.3123i	0.670695	+	0.670695i	0.957876	−	0.287181i	$-0.0927183\pi$
$337$	12.3123	+	12.3123i	0.670695	+	0.670695i	−0.287181	+	0.957876i	$0.592718\pi$
$338$			22.5786i			1.22812i
$339$	−3.83975			−0.208547
$340$		0			0
$341$	0.942695			0.0510498
$342$			4.15640i			0.224753i
$343$	2.19090	+	2.19090i	0.118298	+	0.118298i
$344$	−7.76205			−0.418502
$345$	6.51915	+	6.51915i	0.350979	+	0.350979i
$346$	22.0017	−	22.0017i	1.18282	−	1.18282i
$347$	21.9974	−	21.9974i	1.18088	−	1.18088i	0.201365	−	0.979516i	$-0.435462\pi$
$347$	21.9974	−	21.9974i	1.18088	−	1.18088i	0.979516	−	0.201365i	$-0.0645376\pi$
$348$			3.17157i			0.170014i
$349$		−	30.0407i		−	1.60804i	−0.594600	−	0.804022i	$-0.702690\pi$
$349$		−	30.0407i		−	1.60804i	0.594600	−	0.804022i	$-0.297310\pi$
$350$	−40.4936	+	40.4936i	−2.16447	+	2.16447i
$351$	0.624715	−	0.624715i	0.0333448	−	0.0333448i
$352$	−0.950385	−	0.950385i	−0.0506557	−	0.0506557i
$353$	17.2848			0.919977			0.459989	−	0.887925i	$-0.347853\pi$
$353$	17.2848			0.919977			0.459989	+	0.887925i	$0.347853\pi$
$354$	−6.55807	−	6.55807i	−0.348558	−	0.348558i
$355$			50.3603i			2.67285i
$356$	6.13028			0.324904
$357$		0			0
$358$	2.03866			0.107747
$359$		−	29.3555i		−	1.54932i	−0.632375	−	0.774662i	$-0.717920\pi$
$359$		−	29.3555i		−	1.54932i	0.632375	−	0.774662i	$-0.282080\pi$
$360$	−2.76537	−	2.76537i	−0.145748	−	0.145748i
$361$	13.9401			0.733688
$362$	20.2127	+	20.2127i	1.06235	+	1.06235i
$363$	7.75020	−	7.75020i	0.406780	−	0.406780i
$364$	3.39942	−	3.39942i	0.178178	−	0.178178i
$365$		−	56.5096i		−	2.95785i
$366$		−	27.7817i		−	1.45217i
$367$	8.79638	−	8.79638i	0.459167	−	0.459167i	−0.439215	−	0.898382i	$-0.644743\pi$
$367$	8.79638	−	8.79638i	0.459167	−	0.459167i	0.898382	+	0.439215i	$0.144743\pi$
$368$	−8.71191	+	8.71191i	−0.454140	+	0.454140i
$369$	−0.438346	−	0.438346i	−0.0228194	−	0.0228194i
$370$	−46.6042			−2.42284
$371$	−14.1143	−	14.1143i	−0.732776	−	0.732776i
$372$		−	6.70231i		−	0.347498i
$373$	18.2837			0.946696			0.473348	−	0.880875i	$-0.343045\pi$
$373$	18.2837			0.946696			0.473348	+	0.880875i	$0.343045\pi$
$374$		0			0
$375$	−11.0369			−0.569945
$376$			5.94457i			0.306568i
$377$	1.40101	+	1.40101i	0.0721557	+	0.0721557i
$378$	7.10973			0.365685
$379$	2.49190	+	2.49190i	0.128000	+	0.128000i	0.768205	−	0.640204i	$-0.221150\pi$
$379$	2.49190	+	2.49190i	0.128000	+	0.128000i	−0.640204	+	0.768205i	$0.721150\pi$
$380$	−8.12747	+	8.12747i	−0.416930	+	0.416930i
$381$	−12.9430	+	12.9430i	−0.663088	+	0.663088i
$382$		−	11.0324i		−	0.564467i
$383$		−	33.2583i		−	1.69942i	−0.527251	−	0.849709i	$-0.676777\pi$
$383$		−	33.2583i		−	1.69942i	0.527251	−	0.849709i	$-0.323223\pi$
$384$	5.86030	−	5.86030i	0.299057	−	0.299057i
$385$	−1.95541	+	1.95541i	−0.0996569	+	0.0996569i
$386$	−14.4348	−	14.4348i	−0.734710	−	0.734710i
$387$	7.17120			0.364533
$388$	−5.94948	−	5.94948i	−0.302039	−	0.302039i
$389$		−	10.0157i		−	0.507818i	−0.967228	−	0.253909i	$-0.918284\pi$
$389$		−	10.0157i		−	0.507818i	0.967228	−	0.253909i	$-0.0817163\pi$
$390$	5.89828			0.298671
$391$		0			0
$392$	−8.44834			−0.426706
$393$			11.3478i			0.572423i
$394$	2.34485	+	2.34485i	0.118132	+	0.118132i
$395$	−18.5156			−0.931619
$396$	0.198912	+	0.198912i	0.00999572	+	0.00999572i
$397$	−22.2111	+	22.2111i	−1.11474	+	1.11474i	−0.122242	+	0.992500i	$0.539008\pi$
$397$	−22.2111	+	22.2111i	−1.11474	+	1.11474i	−0.992500	+	0.122242i	$0.960992\pi$
$398$	−0.618564	+	0.618564i	−0.0310058	+	0.0310058i
$399$			8.65526i			0.433305i
$400$		−	38.8914i		−	1.94457i
$401$	0.515673	−	0.515673i	0.0257515	−	0.0257515i	−0.694114	−	0.719865i	$-0.744204\pi$
$401$	0.515673	−	0.515673i	0.0257515	−	0.0257515i	0.719865	+	0.694114i	$0.244204\pi$
$402$	0.367542	−	0.367542i	0.0183313	−	0.0183313i
$403$	−2.96068	−	2.96068i	−0.147482	−	0.147482i
$404$	4.92177			0.244867
$405$	2.55487	+	2.55487i	0.126952	+	0.126952i
$406$			15.9446i			0.791316i
$407$	−1.38854			−0.0688274
$408$		0			0
$409$	25.9074			1.28104			0.640520	−	0.767941i	$-0.278719\pi$
$409$	25.9074			1.28104			0.640520	+	0.767941i	$0.278719\pi$
$410$		−	4.13866i		−	0.204394i
$411$	5.05554	+	5.05554i	0.249371	+	0.249371i
$412$	14.5168			0.715191
$413$	−13.6565	−	13.6565i	−0.671991	−	0.671991i
$414$	3.33390	−	3.33390i	0.163852	−	0.163852i
$415$	24.3151	−	24.3151i	1.19358	−	1.19358i
$416$			5.96966i			0.292687i
$417$			10.9848i			0.537929i
$418$	−0.584608	+	0.584608i	−0.0285941	+	0.0285941i
$419$	23.2076	−	23.2076i	1.13377	−	1.13377i	0.144220	−	0.989546i	$-0.453933\pi$
$419$	23.2076	−	23.2076i	1.13377	−	1.13377i	0.989546	−	0.144220i	$-0.0460674\pi$
$420$	13.9024	+	13.9024i	0.678370	+	0.678370i
$421$	6.36144			0.310038			0.155019	−	0.987912i	$-0.450456\pi$
$421$	6.36144			0.310038			0.155019	+	0.987912i	$0.450456\pi$
$422$	1.34821	+	1.34821i	0.0656298	+	0.0656298i
$423$		−	5.49207i		−	0.267034i
$424$	5.61500			0.272689
$425$		0			0
$426$	25.7544			1.24780
$427$		−	57.8524i		−	2.79967i
$428$	−2.80979	−	2.80979i	−0.135816	−	0.135816i
$429$	0.175735			0.00848457
$430$	33.8536	+	33.8536i	1.63257	+	1.63257i
$431$	−6.39329	+	6.39329i	−0.307954	+	0.307954i	−0.844115	−	0.536162i	$-0.819874\pi$
$431$	−6.39329	+	6.39329i	−0.307954	+	0.307954i	0.536162	+	0.844115i	$0.319874\pi$
$432$	−3.41421	+	3.41421i	−0.164266	+	0.164266i
$433$			6.09106i			0.292718i	0.989232	+	0.146359i	$0.0467554\pi$
$433$			6.09106i			0.292718i	−0.989232	+	0.146359i	$0.953245\pi$
$434$		−	33.6948i		−	1.61740i
$435$	−5.72965	+	5.72965i	−0.274716	+	0.274716i
$436$	8.57446	−	8.57446i	0.410642	−	0.410642i
$437$	4.05863	+	4.05863i	0.194151	+	0.194151i
$438$	−28.8991			−1.38085
$439$	−22.0923	−	22.0923i	−1.05441	−	1.05441i	−0.998432	−	0.0559763i	$-0.982173\pi$
$439$	−22.0923	−	22.0923i	−1.05441	−	1.05441i	−0.0559763	−	0.998432i	$-0.517827\pi$
$440$		−	0.777910i		−	0.0370854i
$441$	7.80525			0.371679
$442$		0			0
$443$	−8.90575			−0.423125			−0.211563	−	0.977364i	$-0.567855\pi$
$443$	−8.90575			−0.423125			−0.211563	+	0.977364i	$0.567855\pi$
$444$			9.87216i			0.468512i
$445$	11.0747	+	11.0747i	0.524993	+	0.524993i
$446$	21.9916			1.04133
$447$	4.23897	+	4.23897i	0.200496	+	0.200496i
$448$	−7.69552	+	7.69552i	−0.363579	+	0.363579i
$449$	−12.2710	+	12.2710i	−0.579102	+	0.579102i	−0.934656	−	0.355554i	$-0.884292\pi$
$449$	−12.2710	+	12.2710i	−0.579102	+	0.579102i	0.355554	+	0.934656i	$0.384292\pi$
$450$			14.8831i			0.701596i
$451$		−	0.123309i		−	0.00580638i
$452$	−3.83975	+	3.83975i	−0.180607	+	0.180607i
$453$	8.11615	−	8.11615i	0.381330	−	0.381330i
$454$	26.0731	+	26.0731i	1.22367	+	1.22367i
$455$	12.2825			0.575814
$456$	−1.72164	−	1.72164i	−0.0806231	−	0.0806231i
$457$		−	24.8622i		−	1.16301i	−0.813545	−	0.581503i	$-0.802465\pi$
$457$		−	24.8622i		−	1.16301i	0.813545	−	0.581503i	$-0.197535\pi$
$458$	0.0487123			0.00227618
$459$		0			0
$460$	13.0383			0.607913
$461$		−	11.3886i		−	0.530421i	−0.964191	−	0.265210i	$-0.914559\pi$
$461$		−	11.3886i		−	0.530421i	0.964191	−	0.265210i	$-0.0854414\pi$
$462$	1.00000	+	1.00000i	0.0465242	+	0.0465242i
$463$	24.9668			1.16031			0.580154	−	0.814507i	$-0.302992\pi$
$463$	24.9668			1.16031			0.580154	+	0.814507i	$0.302992\pi$
$464$	−7.65685	−	7.65685i	−0.355461	−	0.355461i
$465$	12.1081	−	12.1081i	0.561501	−	0.561501i
$466$	−29.6206	+	29.6206i	−1.37215	+	1.37215i
$467$			3.32307i			0.153773i	0.997040	+	0.0768866i	$0.0244979\pi$
$467$			3.32307i			0.153773i	−0.997040	+	0.0768866i	$0.975502\pi$
$468$		−	1.24943i		−	0.0577549i
$469$	0.765367	−	0.765367i	0.0353414	−	0.0353414i
$470$	25.9268	−	25.9268i	1.19592	−	1.19592i
$471$	4.10947	+	4.10947i	0.189354	+	0.189354i
$472$	5.43289			0.250069
$473$	1.00865	+	1.00865i	0.0463776	+	0.0463776i
$474$			9.46889i			0.434921i
$475$	−18.1184			−0.831331
$476$		0			0
$477$	−5.18759			−0.237523
$478$		−	19.0698i		−	0.872232i
$479$	−0.218509	−	0.218509i	−0.00998391	−	0.00998391i	0.702097	−	0.712081i	$-0.252247\pi$
$479$	−0.218509	−	0.218509i	−0.00998391	−	0.00998391i	−0.712081	+	0.702097i	$0.752247\pi$
$480$	−24.4138			−1.11433
$481$	4.36093	+	4.36093i	0.198841	+	0.198841i
$482$	6.47433	−	6.47433i	0.294898	−	0.294898i
$483$	6.94249	−	6.94249i	0.315894	−	0.315894i
$484$		−	15.5004i		−	0.704563i
$485$		−	21.4962i		−	0.976094i
$486$	1.30656	−	1.30656i	0.0592669	−	0.0592669i
$487$	−23.0853	+	23.0853i	−1.04610	+	1.04610i	−0.0472107	+	0.998885i	$0.515033\pi$
$487$	−23.0853	+	23.0853i	−1.04610	+	1.04610i	−0.998885	+	0.0472107i	$0.984967\pi$
$488$	11.5076	+	11.5076i	0.520923	+	0.520923i
$489$	5.40878			0.244593
$490$	36.8468	+	36.8468i	1.66457	+	1.66457i
$491$		−	21.7074i		−	0.979640i	−0.871824	−	0.489820i	$-0.837063\pi$
$491$		−	21.7074i		−	0.979640i	0.871824	−	0.489820i	$-0.162937\pi$
$492$	−0.876691			−0.0395243
$493$		0			0
$494$	3.67210			0.165216
$495$			0.718695i			0.0323030i
$496$	16.1808	+	16.1808i	0.726539	+	0.726539i
$497$	53.6307			2.40566
$498$	−12.4348	−	12.4348i	−0.557215	−	0.557215i
$499$	−1.58322	+	1.58322i	−0.0708745	+	0.0708745i	−0.741656	−	0.670781i	$-0.765959\pi$
$499$	−1.58322	+	1.58322i	−0.0708745	+	0.0708745i	0.670781	+	0.741656i	$0.265959\pi$
$500$	−11.0369	+	11.0369i	−0.493587	+	0.493587i
$501$		−	3.26038i		−	0.145663i
$502$			51.0021i			2.27633i
$503$	−10.2049	+	10.2049i	−0.455015	+	0.455015i	−0.897015	−	0.442000i	$-0.854269\pi$
$503$	−10.2049	+	10.2049i	−0.455015	+	0.455015i	0.442000	+	0.897015i	$0.354269\pi$
$504$	−2.94495	+	2.94495i	−0.131178	+	0.131178i
$505$	8.89149	+	8.89149i	0.395666	+	0.395666i
$506$	0.937842			0.0416922
$507$	8.64047	+	8.64047i	0.383737	+	0.383737i
$508$			25.8859i			1.14850i
$509$	−35.4472			−1.57117			−0.785584	−	0.618755i	$-0.787637\pi$
$509$	−35.4472			−1.57117			−0.785584	+	0.618755i	$0.787637\pi$
$510$		0			0
$511$	−60.1793			−2.66218
$512$		−	22.1731i		−	0.979922i
$513$	1.59059	+	1.59059i	0.0702261	+	0.0702261i
$514$	−45.4991			−2.00688
$515$	26.2255	+	26.2255i	1.15563	+	1.15563i
$516$	7.17120	−	7.17120i	0.315694	−	0.315694i
$517$	0.772472	−	0.772472i	0.0339733	−	0.0339733i
$518$			49.6307i			2.18065i
$519$		−	16.8394i		−	0.739167i
$520$	−2.44315	+	2.44315i	−0.107139	+	0.107139i
$521$	−10.1110	+	10.1110i	−0.442972	+	0.442972i	−0.893010	−	0.450037i	$-0.851411\pi$
$521$	−10.1110	+	10.1110i	−0.442972	+	0.442972i	0.450037	+	0.893010i	$0.351411\pi$
$522$	2.93015	+	2.93015i	0.128249	+	0.128249i
$523$	−6.23946			−0.272832			−0.136416	−	0.990652i	$-0.543558\pi$
$523$	−6.23946			−0.272832			−0.136416	+	0.990652i	$0.543558\pi$
$524$	11.3478	+	11.3478i	0.495733	+	0.495733i
$525$			30.9925i			1.35262i
$526$	34.9255			1.52282
$527$		0			0
$528$	−0.960434			−0.0417975
$529$			16.4890i			0.716915i
$530$	−24.4894	−	24.4894i	−1.06375	−	1.06375i
$531$	−5.01933			−0.217820
$532$	8.65526	+	8.65526i	0.375253	+	0.375253i
$533$	−0.387270	+	0.387270i	−0.0167745	+	0.0167745i
$534$	5.66364	−	5.66364i	0.245090	−	0.245090i
$535$		−	10.1521i		−	0.438914i
$536$			0.304482i			0.0131516i
$537$	0.780163	−	0.780163i	0.0336665	−	0.0336665i
$538$	−18.5602	+	18.5602i	−0.800185	+	0.800185i
$539$	1.09783	+	1.09783i	0.0472867	+	0.0472867i
$540$	5.10973			0.219888
$541$	16.9908	+	16.9908i	0.730490	+	0.730490i	0.970717	−	0.240227i	$-0.0772219\pi$
$541$	16.9908	+	16.9908i	0.730490	+	0.730490i	−0.240227	+	0.970717i	$0.577222\pi$
$542$			36.8284i			1.58191i
$543$	15.4701			0.663886
$544$		0			0
$545$	30.9806			1.32706
$546$		−	6.28130i		−	0.268815i
$547$	22.3661	+	22.3661i	0.956304	+	0.956304i	0.999084	−	0.0427807i	$-0.0136217\pi$
$547$	22.3661	+	22.3661i	0.956304	+	0.956304i	−0.0427807	+	0.999084i	$0.513622\pi$
$548$	10.1111			0.431924
$549$	−10.6316	−	10.6316i	−0.453745	−	0.453745i
$550$	−2.09334	+	2.09334i	−0.0892604	+	0.0892604i
$551$	−3.56711	+	3.56711i	−0.151964	+	0.151964i
$552$			2.76190i			0.117554i
$553$			19.7179i			0.838492i
$554$	−27.9642	+	27.9642i	−1.18809	+	1.18809i
$555$	−17.8347	+	17.8347i	−0.757040	+	0.757040i
$556$	10.9848	+	10.9848i	0.465861	+	0.465861i
$557$	14.7772			0.626131			0.313065	−	0.949732i	$-0.398644\pi$
$557$	14.7772			0.626131			0.313065	+	0.949732i	$0.398644\pi$
$558$	−6.19212	−	6.19212i	−0.262134	−	0.262134i
$559$		−	6.33561i		−	0.267968i
$560$	−67.1269			−2.83663
$561$		0			0
$562$	39.6657			1.67320
$563$			9.39006i			0.395744i	0.980228	+	0.197872i	$0.0634030\pi$
$563$			9.39006i			0.395744i	−0.980228	+	0.197872i	$0.936597\pi$
$564$	−5.49207	−	5.49207i	−0.231258	−	0.231258i
$565$	−13.8735			−0.583663
$566$	−25.8991	−	25.8991i	−1.08862	−	1.08862i
$567$	2.72078	−	2.72078i	0.114262	−	0.114262i
$568$	−10.6678	+	10.6678i	−0.447611	+	0.447611i
$569$		−	23.3520i		−	0.978968i	−0.872012	−	0.489484i	$-0.837185\pi$
$569$		−	23.3520i		−	0.978968i	0.872012	−	0.489484i	$-0.162815\pi$
$570$			15.0176i			0.629018i
$571$	−23.5046	+	23.5046i	−0.983637	+	0.983637i	−0.999868	−	0.0162308i	$-0.994833\pi$
$571$	−23.5046	+	23.5046i	−0.983637	+	0.983637i	0.0162308	+	0.999868i	$0.494833\pi$
$572$	0.175735	−	0.175735i	0.00734785	−	0.00734785i
$573$	−4.22192	−	4.22192i	−0.176373	−	0.176373i
$574$	−4.40743			−0.183962
$575$	14.5330	+	14.5330i	0.606069	+	0.606069i
$576$			2.82843i			0.117851i
$577$	33.8072			1.40741			0.703705	−	0.710492i	$-0.251528\pi$
$577$	33.8072			1.40741			0.703705	+	0.710492i	$0.251528\pi$
$578$		0			0
$579$	−11.0479			−0.459135
$580$			11.4593i			0.475821i
$581$	−25.8941	−	25.8941i	−1.07427	−	1.07427i
$582$	−10.9932			−0.455683
$583$	−0.729646	−	0.729646i	−0.0302189	−	0.0302189i
$584$	11.9704	−	11.9704i	0.495339	−	0.495339i
$585$	2.25717	−	2.25717i	0.0933226	−	0.0933226i
$586$			37.6420i			1.55498i
$587$			29.2440i			1.20703i	0.797352	+	0.603514i	$0.206233\pi$
$587$			29.2440i			1.20703i	−0.797352	+	0.603514i	$0.793767\pi$
$588$	7.80525	−	7.80525i	0.321883	−	0.321883i
$589$	7.53818	−	7.53818i	0.310605	−	0.310605i
$590$	−23.6951	−	23.6951i	−0.975514	−	0.975514i
$591$	1.79467			0.0738230
$592$	−23.8335	−	23.8335i	−0.979550	−	0.979550i
$593$		−	0.632327i		−	0.0259665i	−0.999916	−	0.0129833i	$-0.995867\pi$
$593$		−	0.632327i		−	0.0259665i	0.999916	−	0.0129833i	$-0.00413282\pi$
$594$	0.367542			0.0150804
$595$		0			0
$596$	8.47793			0.347270
$597$			0.473428i			0.0193761i
$598$	−2.94544	−	2.94544i	−0.120448	−	0.120448i
$599$	−8.12959			−0.332166			−0.166083	−	0.986112i	$-0.553112\pi$
$599$	−8.12959			−0.332166			−0.166083	+	0.986112i	$0.553112\pi$
$600$	−6.16478	−	6.16478i	−0.251676	−	0.251676i
$601$	−3.13482	+	3.13482i	−0.127872	+	0.127872i	−0.768146	−	0.640274i	$-0.778821\pi$
$601$	−3.13482	+	3.13482i	−0.127872	+	0.127872i	0.640274	+	0.768146i	$0.278821\pi$
$602$	36.0521	−	36.0521i	1.46937	−	1.46937i
$603$		−	0.281305i		−	0.0114556i
$604$		−	16.2323i		−	0.660483i
$605$	28.0024	−	28.0024i	1.13846	−	1.13846i
$606$	4.54712	−	4.54712i	0.184714	−	0.184714i
$607$	−17.0613	−	17.0613i	−0.692495	−	0.692495i	0.270285	−	0.962780i	$-0.412882\pi$
$607$	−17.0613	−	17.0613i	−0.692495	−	0.692495i	−0.962780	+	0.270285i	$0.912882\pi$
$608$	−15.1994			−0.616415
$609$	6.10172	+	6.10172i	0.247254	+	0.247254i
$610$		−	100.379i		−	4.06422i
$611$	−4.85213			−0.196296
$612$		0			0
$613$	−0.549449			−0.0221921			−0.0110960	−	0.999938i	$-0.503532\pi$
$613$	−0.549449			−0.0221921			−0.0110960	+	0.999938i	$0.503532\pi$
$614$			25.1809i			1.01622i
$615$	−1.58380	−	1.58380i	−0.0638649	−	0.0638649i
$616$	−0.828427			−0.0333783
$617$	0.0254607	+	0.0254607i	0.00102501	+	0.00102501i	0.707619	−	0.706594i	$-0.249769\pi$
$617$	0.0254607	+	0.0254607i	0.00102501	+	0.00102501i	−0.706594	+	0.707619i	$0.749769\pi$
$618$	13.4118	−	13.4118i	0.539500	−	0.539500i
$619$	−7.92038	+	7.92038i	−0.318347	+	0.318347i	−0.848132	−	0.529785i	$-0.822273\pi$
$619$	−7.92038	+	7.92038i	−0.318347	+	0.318347i	0.529785	+	0.848132i	$0.322273\pi$
$620$		−	24.2163i		−	0.972549i
$621$		−	2.55166i		−	0.102395i
$622$	3.37849	−	3.37849i	0.135465	−	0.135465i
$623$	11.7939	−	11.7939i	0.472514	−	0.472514i
$624$	3.01639	+	3.01639i	0.120752	+	0.120752i
$625$	0.395541			0.0158217
$626$	−5.16569	−	5.16569i	−0.206462	−	0.206462i
$627$			0.447439i			0.0178690i
$628$	8.21893			0.327971
$629$		0			0
$630$	25.6884			1.02345
$631$		−	9.12882i		−	0.363413i	−0.983353	−	0.181706i	$-0.941838\pi$
$631$		−	9.12882i		−	0.363413i	0.983353	−	0.181706i	$-0.0581620\pi$
$632$	−3.92214	−	3.92214i	−0.156015	−	0.156015i
$633$	1.03188			0.0410134
$634$	−43.7888	−	43.7888i	−1.73908	−	1.73908i
$635$	−46.7645	+	46.7645i	−1.85579	+	1.85579i
$636$	−5.18759	+	5.18759i	−0.205701	+	0.205701i
$637$		−	6.89578i		−	0.273221i
$638$			0.824265i			0.0326330i
$639$	9.85577	−	9.85577i	0.389888	−	0.389888i
$640$	21.1740	−	21.1740i	0.836976	−	0.836976i
$641$	−24.5491	−	24.5491i	−0.969629	−	0.969629i	0.0299229	−	0.999552i	$-0.490474\pi$
$641$	−24.5491	−	24.5491i	−0.969629	−	0.969629i	−0.999552	+	0.0299229i	$0.990474\pi$
$642$	−5.19181			−0.204904
$643$	−10.3257	−	10.3257i	−0.407206	−	0.407206i	0.473557	−	0.880763i	$-0.342970\pi$
$643$	−10.3257	−	10.3257i	−0.407206	−	0.407206i	−0.880763	+	0.473557i	$0.842970\pi$
$644$		−	13.8850i		−	0.547145i
$645$	25.9104			1.02022
$646$		0			0
$647$	39.5994			1.55681			0.778407	−	0.627760i	$-0.216028\pi$
$647$	39.5994			1.55681			0.778407	+	0.627760i	$0.216028\pi$
$648$			1.08239i			0.0425204i
$649$	−0.705981	−	0.705981i	−0.0277122	−	0.0277122i
$650$	13.1489			0.515743
$651$	−12.8944	−	12.8944i	−0.505373	−	0.505373i
$652$	5.40878	−	5.40878i	0.211824	−	0.211824i
$653$	−28.1303	+	28.1303i	−1.10082	+	1.10082i	−0.106513	+	0.994311i	$0.533968\pi$
$653$	−28.1303	+	28.1303i	−1.10082	+	1.10082i	−0.994311	+	0.106513i	$0.966032\pi$
$654$		−	15.8435i		−	0.619531i
$655$			41.0012i			1.60205i
$656$	2.11652	−	2.11652i	0.0826362	−	0.0826362i
$657$	−11.0592	+	11.0592i	−0.431461	+	0.431461i
$658$	−27.6105	−	27.6105i	−1.07637	−	1.07637i
$659$	16.4351			0.640219			0.320109	−	0.947381i	$-0.396280\pi$
$659$	16.4351			0.640219			0.320109	+	0.947381i	$0.396280\pi$
$660$	0.718695	+	0.718695i	0.0279752	+	0.0279752i
$661$			34.4462i			1.33980i	0.742450	+	0.669902i	$0.233664\pi$
$661$			34.4462i			1.33980i	−0.742450	+	0.669902i	$0.766336\pi$
$662$	35.6687			1.38630
$663$		0			0
$664$	10.3013			0.399768
$665$			31.2725i			1.21270i
$666$	9.12068	+	9.12068i	0.353419	+	0.353419i
$667$	5.72245			0.221574
$668$	−3.26038	−	3.26038i	−0.126148	−	0.126148i
$669$	8.41583	−	8.41583i	0.325375	−	0.325375i
$670$	1.32798	−	1.32798i	0.0513042	−	0.0513042i
$671$		−	2.99072i		−	0.115455i
$672$			25.9993i			1.00294i
$673$	−23.8869	+	23.8869i	−0.920772	+	0.920772i	−0.997084	−	0.0763119i	$-0.975686\pi$
$673$	−23.8869	+	23.8869i	−0.920772	+	0.920772i	0.0763119	+	0.997084i	$0.475686\pi$
$674$	22.7502	−	22.7502i	0.876305	−	0.876305i
$675$	5.69552	+	5.69552i	0.219221	+	0.219221i
$676$	17.2809			0.664651
$677$	9.42514	+	9.42514i	0.362238	+	0.362238i	0.864636	−	0.502399i	$-0.167549\pi$
$677$	9.42514	+	9.42514i	0.362238	+	0.362238i	−0.502399	+	0.864636i	$0.667549\pi$
$678$			7.09494i			0.272479i
$679$	−22.8922			−0.878521
$680$		0			0
$681$	19.9555			0.764697
$682$		−	1.74187i		−	0.0666998i
$683$	18.2176	+	18.2176i	0.697077	+	0.697077i	0.963779	−	0.266702i	$-0.0859339\pi$
$683$	18.2176	+	18.2176i	0.697077	+	0.697077i	−0.266702	+	0.963779i	$0.585934\pi$
$684$	3.18117			0.121635
$685$	18.2663	+	18.2663i	0.697920	+	0.697920i
$686$	4.04826	−	4.04826i	0.154563	−	0.154563i
$687$	0.0186414	−	0.0186414i	0.000711213	−	0.000711213i
$688$			34.6256i			1.32009i
$689$			4.58313i			0.174603i
$690$	12.0458	−	12.0458i	0.458576	−	0.458576i
$691$	−4.32569	+	4.32569i	−0.164557	+	0.164557i	−0.784582	−	0.620025i	$-0.787122\pi$
$691$	−4.32569	+	4.32569i	−0.164557	+	0.164557i	0.620025	+	0.784582i	$0.287122\pi$
$692$	−16.8394	−	16.8394i	−0.640137	−	0.640137i
$693$	0.765367			0.0290739
$694$	−40.6458	−	40.6458i	−1.54290	−	1.54290i
$695$			39.6896i			1.50551i
$696$	−2.42742			−0.0920110
$697$		0			0
$698$	−55.5080			−2.10101
$699$			22.6706i			0.857481i
$700$	30.9925	+	30.9925i	1.17141	+	1.17141i
$701$	−18.4012			−0.695005			−0.347503	−	0.937679i	$-0.612970\pi$
$701$	−18.4012			−0.695005			−0.347503	+	0.937679i	$0.612970\pi$
$702$	−1.15432	−	1.15432i	−0.0435671	−	0.0435671i
$703$	−11.1034	+	11.1034i	−0.418771	+	0.418771i
$704$	−0.397825	+	0.397825i	−0.0149936	+	0.0149936i
$705$		−	19.8435i		−	0.747351i
$706$		−	31.9382i		−	1.20201i
$707$	9.46889	−	9.46889i	0.356114	−	0.356114i
$708$	−5.01933	+	5.01933i	−0.188638	+	0.188638i
$709$	−10.0817	−	10.0817i	−0.378627	−	0.378627i	0.491979	−	0.870607i	$-0.336274\pi$
$709$	−10.0817	−	10.0817i	−0.378627	−	0.378627i	−0.870607	+	0.491979i	$0.836274\pi$
$710$	93.0537			3.49224
$711$	3.62359	+	3.62359i	0.135895	+	0.135895i
$712$			4.69192i			0.175837i
$713$	−12.0929			−0.452884
$714$		0			0
$715$	0.634953			0.0237459
$716$		−	1.56033i		−	0.0583121i
$717$	−7.29769	−	7.29769i	−0.272537	−	0.272537i
$718$	−54.2419			−2.02429
$719$	−21.5498	−	21.5498i	−0.803672	−	0.803672i	0.179995	−	0.983667i	$-0.442392\pi$
$719$	−21.5498	−	21.5498i	−0.803672	−	0.803672i	−0.983667	+	0.179995i	$0.942392\pi$
$720$	−12.3360	+	12.3360i	−0.459735	+	0.459735i
$721$	27.9285	−	27.9285i	1.04011	−	1.04011i
$722$		−	25.7579i		−	0.958609i
$723$		−	4.95524i		−	0.184287i
$724$	15.4701	−	15.4701i	0.574942	−	0.574942i
$725$	−12.7730	+	12.7730i	−0.474377	+	0.474377i
$726$	−14.3205	−	14.3205i	−0.531483	−	0.531483i
$727$	−46.6448			−1.72996			−0.864980	−	0.501806i	$-0.832669\pi$
$727$	−46.6448			−1.72996			−0.864980	+	0.501806i	$0.832669\pi$
$728$	2.60180	+	2.60180i	0.0964292	+	0.0964292i
$729$		−	1.00000i		−	0.0370370i
$730$	−104.416			−3.86462
$731$		0			0
$732$	−21.2632			−0.785910
$733$			40.8084i			1.50729i	0.657279	+	0.753647i	$0.271707\pi$
$733$			40.8084i			1.50729i	−0.657279	+	0.753647i	$0.728293\pi$
$734$	−16.2536	−	16.2536i	−0.599931	−	0.599931i
$735$	28.2014			1.04022
$736$	12.1916	+	12.1916i	0.449388	+	0.449388i
$737$	0.0395661	−	0.0395661i	0.00145744	−	0.00145744i
$738$	−0.809957	+	0.809957i	−0.0298149	+	0.0298149i
$739$			37.9474i			1.39592i	0.716138	+	0.697959i	$0.245908\pi$
$739$			37.9474i			1.39592i	−0.716138	+	0.697959i	$0.754092\pi$
$740$			35.6693i			1.31123i
$741$	1.40525	−	1.40525i	0.0516232	−	0.0516232i
$742$	−26.0798	+	26.0798i	−0.957418	+	0.957418i
$743$	1.31959	+	1.31959i	0.0484112	+	0.0484112i	0.730898	−	0.682487i	$-0.239102\pi$
$743$	1.31959	+	1.31959i	0.0484112	+	0.0484112i	−0.682487	+	0.730898i	$0.739102\pi$
$744$	5.12972			0.188065
$745$	15.3159	+	15.3159i	0.561132	+	0.561132i
$746$		−	33.7840i		−	1.23692i
$747$	−9.51716			−0.348215
$748$		0			0
$749$	−10.8114			−0.395039
$750$			20.3936i			0.744669i
$751$	−27.7029	−	27.7029i	−1.01089	−	1.01089i	−0.999940	−	0.0109535i	$-0.996513\pi$
$751$	−27.7029	−	27.7029i	−1.01089	−	1.01089i	−0.0109535	−	0.999940i	$-0.503487\pi$
$752$	26.5181			0.967014
$753$	19.5176	+	19.5176i	0.711263	+	0.711263i
$754$	2.58873	−	2.58873i	0.0942760	−	0.0942760i
$755$	29.3247	−	29.3247i	1.06723	−	1.06723i
$756$		−	5.44155i		−	0.197907i
$757$			24.3356i			0.884493i	0.896894	+	0.442246i	$0.145818\pi$
$757$			24.3356i			0.884493i	−0.896894	+	0.442246i	$0.854182\pi$
$758$	4.60443	−	4.60443i	0.167240	−	0.167240i
$759$	0.358897	−	0.358897i	0.0130271	−	0.0130271i
$760$	−6.22050	−	6.22050i	−0.225641	−	0.225641i
$761$	25.3506			0.918957			0.459479	−	0.888189i	$-0.348036\pi$
$761$	25.3506			0.918957			0.459479	+	0.888189i	$0.348036\pi$
$762$	23.9155	+	23.9155i	0.866366	+	0.866366i
$763$		−	32.9925i		−	1.19441i
$764$	−8.44384			−0.305487
$765$		0			0
$766$	−61.4533			−2.22040
$767$			4.43448i			0.160120i
$768$	−14.8284	−	14.8284i	−0.535075	−	0.535075i
$769$	−10.7211			−0.386614			−0.193307	−	0.981138i	$-0.561921\pi$
$769$	−10.7211			−0.386614			−0.193307	+	0.981138i	$0.561921\pi$
$770$	3.61313	+	3.61313i	0.130208	+	0.130208i
$771$	−17.4118	+	17.4118i	−0.627069	+	0.627069i
$772$	−11.0479	+	11.0479i	−0.397622	+	0.397622i
$773$		−	51.2753i		−	1.84424i	−0.386900	−	0.922122i	$-0.626454\pi$
$773$		−	51.2753i		−	1.84424i	0.386900	−	0.922122i	$-0.373546\pi$
$774$		−	13.2506i		−	0.476285i
$775$	26.9925	−	26.9925i	0.969598	−	0.969598i
$776$	4.55354	−	4.55354i	0.163462	−	0.163462i
$777$	18.9928	+	18.9928i	0.681364	+	0.681364i
$778$	−18.5067			−0.663496
$779$	−0.986028	−	0.986028i	−0.0353281	−	0.0353281i
$780$		−	4.51434i		−	0.161639i
$781$	2.77247			0.0992069
$782$		0			0
$783$	2.24264			0.0801454
$784$			37.6871i			1.34597i
$785$	14.8480	+	14.8480i	0.529949	+	0.529949i
$786$	20.9681			0.747906
$787$	15.7537	+	15.7537i	0.561558	+	0.561558i	0.929750	−	0.368192i	$-0.120023\pi$
$787$	15.7537	+	15.7537i	0.561558	+	0.561558i	−0.368192	+	0.929750i	$0.620023\pi$
$788$	1.79467	−	1.79467i	0.0639326	−	0.0639326i
$789$	13.3654	−	13.3654i	0.475821	−	0.475821i
$790$			34.2123i			1.21722i
$791$			14.7744i			0.525319i
$792$	−0.152241	+	0.152241i	−0.00540965	+	0.00540965i
$793$	−9.39280	+	9.39280i	−0.333548	+	0.333548i
$794$	41.0407	+	41.0407i	1.45648	+	1.45648i
$795$	−18.7434			−0.664760
$796$	0.473428	+	0.473428i	0.0167802	+	0.0167802i
$797$			12.5375i			0.444102i	0.975035	+	0.222051i	$0.0712751\pi$
$797$			12.5375i			0.444102i	−0.975035	+	0.222051i	$0.928725\pi$
$798$	15.9928			0.566140
$799$		0			0
$800$	−54.4253			−1.92423
$801$		−	4.33476i		−	0.153161i
$802$	−0.952840	−	0.952840i	−0.0336460	−	0.0336460i
$803$	−3.11101			−0.109785
$804$	−0.281305	−	0.281305i	−0.00992085	−	0.00992085i
$805$	25.0841	−	25.0841i	0.884098	−	0.884098i
$806$	−5.47062	+	5.47062i	−0.192694	+	0.192694i
$807$			14.2053i			0.500051i
$808$			3.76696i			0.132521i
$809$	6.57125	−	6.57125i	0.231033	−	0.231033i	−0.582091	−	0.813124i	$-0.697765\pi$
$809$	6.57125	−	6.57125i	0.231033	−	0.231033i	0.813124	+	0.582091i	$0.197765\pi$
$810$	4.72078	−	4.72078i	0.165871	−	0.165871i
$811$	7.98029	+	7.98029i	0.280226	+	0.280226i	0.833199	−	0.552973i	$-0.186507\pi$
$811$	7.98029	+	7.98029i	0.280226	+	0.280226i	−0.552973	+	0.833199i	$0.686507\pi$
$812$	12.2034			0.428257
$813$	14.0936	+	14.0936i	0.494284	+	0.494284i
$814$			2.56569i			0.0899274i
$815$	19.5426			0.684547
$816$		0			0
$817$	16.1311			0.564356
$818$		−	47.8707i		−	1.67376i
$819$	−2.40375	−	2.40375i	−0.0839939	−	0.0839939i
$820$	−3.16760			−0.110617
$821$	−5.87348	−	5.87348i	−0.204986	−	0.204986i	0.597146	−	0.802132i	$-0.296301\pi$
$821$	−5.87348	−	5.87348i	−0.204986	−	0.204986i	−0.802132	+	0.597146i	$0.796301\pi$
$822$	9.34142	−	9.34142i	0.325819	−	0.325819i
$823$	−13.1698	+	13.1698i	−0.459071	+	0.459071i	−0.898350	−	0.439280i	$-0.855234\pi$
$823$	−13.1698	+	13.1698i	−0.459071	+	0.459071i	0.439280	+	0.898350i	$0.355234\pi$
$824$			11.1107i			0.387058i
$825$			1.60218i			0.0557806i
$826$	−25.2339	+	25.2339i	−0.877999	+	0.877999i
$827$	−19.7042	+	19.7042i	−0.685181	+	0.685181i	−0.961163	−	0.275982i	$-0.910997\pi$
$827$	−19.7042	+	19.7042i	−0.685181	+	0.685181i	0.275982	+	0.961163i	$0.410997\pi$
$828$	−2.55166	−	2.55166i	−0.0886763	−	0.0886763i
$829$	−12.4653			−0.432937			−0.216469	−	0.976290i	$-0.569454\pi$
$829$	−12.4653			−0.432937			−0.216469	+	0.976290i	$0.569454\pi$
$830$	−44.9284	−	44.9284i	−1.55949	−	1.55949i
$831$			21.4029i			0.742458i
$832$	2.49886			0.0866323
$833$		0			0
$834$	20.2973			0.702839
$835$		−	11.7802i		−	0.407669i
$836$	0.447439	+	0.447439i	0.0154750	+	0.0154750i
$837$	−4.73925			−0.163812
$838$	−42.8821	−	42.8821i	−1.48134	−	1.48134i
$839$	−30.5545	+	30.5545i	−1.05486	+	1.05486i	−0.0564530	+	0.998405i	$0.517979\pi$
$839$	−30.5545	+	30.5545i	−1.05486	+	1.05486i	−0.998405	+	0.0564530i	$0.982021\pi$
$840$	−10.6405	+	10.6405i	−0.367131	+	0.367131i
$841$		−	23.9706i		−	0.826571i
$842$		−	11.7544i		−	0.405084i
$843$	15.1794	−	15.1794i	0.522807	−	0.522807i
$844$	1.03188	−	1.03188i	0.0355186	−	0.0355186i
$845$	31.2191	+	31.2191i	1.07397	+	1.07397i
$846$	−10.1480			−0.348896
$847$	−29.8209	−	29.8209i	−1.02466	−	1.02466i
$848$		−	25.0479i		−	0.860148i
$849$	−19.8223			−0.680301
$850$		0			0
$851$	17.8123			0.610597
$852$		−	19.7115i		−	0.675306i
$853$	6.89545	+	6.89545i	0.236096	+	0.236096i	0.815231	−	0.579136i	$-0.196610\pi$
$853$	6.89545	+	6.89545i	0.236096	+	0.236096i	−0.579136	+	0.815231i	$0.696610\pi$
$854$	−106.897			−3.65795
$855$	5.74699	+	5.74699i	0.196543	+	0.196543i
$856$	2.15052	−	2.15052i	0.0735032	−	0.0735032i
$857$	−16.9704	+	16.9704i	−0.579698	+	0.579698i	−0.934820	−	0.355122i	$-0.884439\pi$
$857$	−16.9704	+	16.9704i	−0.579698	+	0.579698i	0.355122	+	0.934820i	$0.384439\pi$
$858$		−	0.324716i		−	0.0110856i
$859$		−	16.5708i		−	0.565389i	−0.959210	−	0.282695i	$-0.908772\pi$
$859$		−	16.5708i		−	0.565389i	0.959210	−	0.282695i	$-0.0912283\pi$
$860$	25.9104	−	25.9104i	0.883539	−	0.883539i
$861$	−1.68665	+	1.68665i	−0.0574808	+	0.0574808i
$862$	11.8133	+	11.8133i	0.402361	+	0.402361i
$863$	−56.5312			−1.92435			−0.962173	−	0.272440i	$-0.912169\pi$
$863$	−56.5312			−1.92435			−0.962173	+	0.272440i	$0.912169\pi$
$864$	4.77791	+	4.77791i	0.162548	+	0.162548i
$865$		−	60.8428i		−	2.06872i
$866$	11.2548			0.382454
$867$		0			0
$868$	−25.7889			−0.875331
$869$			1.01933i			0.0345785i
$870$	10.5870	+	10.5870i	0.358933	+	0.358933i
$871$	−0.248527			−0.00842101
$872$	6.56261	+	6.56261i	0.222238	+	0.222238i
$873$	−4.20692	+	4.20692i	−0.142383	+	0.142383i
$874$	7.49938	−	7.49938i	0.253670	−	0.253670i
$875$			42.4675i			1.43566i
$876$			22.1184i			0.747312i
$877$	28.4067	−	28.4067i	0.959226	−	0.959226i	−0.0399748	−	0.999201i	$-0.512728\pi$
$877$	28.4067	−	28.4067i	0.959226	−	0.959226i	0.999201	+	0.0399748i	$0.0127278\pi$
$878$	−40.8213	+	40.8213i	−1.37765	+	1.37765i
$879$	14.4050	+	14.4050i	0.485868	+	0.485868i
$880$	−3.47017			−0.116979
$881$	−7.89180	−	7.89180i	−0.265882	−	0.265882i	0.561557	−	0.827438i	$-0.310203\pi$
$881$	−7.89180	−	7.89180i	−0.265882	−	0.265882i	−0.827438	+	0.561557i	$0.810203\pi$
$882$		−	14.4222i		−	0.485621i
$883$	39.5682			1.33158			0.665789	−	0.746140i	$-0.268095\pi$
$883$	39.5682			1.33158			0.665789	+	0.746140i	$0.268095\pi$
$884$		0			0
$885$	−18.1355			−0.609617
$886$			16.4557i			0.552840i
$887$	−29.9310	−	29.9310i	−1.00499	−	1.00499i	−0.999988	−	0.00499773i	$-0.998409\pi$
$887$	−29.9310	−	29.9310i	−1.00499	−	1.00499i	−0.00499773	−	0.999988i	$-0.501591\pi$
$888$	−7.55582			−0.253557
$889$	49.8014	+	49.8014i	1.67028	+	1.67028i
$890$	20.4635	−	20.4635i	0.685937	−	0.685937i
$891$	0.140652	−	0.140652i	0.00471203	−	0.00471203i
$892$		−	16.8317i		−	0.563566i
$893$		−	12.3540i		−	0.413412i
$894$	7.83259	−	7.83259i	0.261961	−	0.261961i
$895$	2.81883	−	2.81883i	0.0942230	−	0.0942230i
$896$	−22.5490	−	22.5490i	−0.753310	−	0.753310i
$897$	−2.25434			−0.0752702
$898$	22.6738	+	22.6738i	0.756634	+	0.756634i
$899$		−	10.6284i		−	0.354478i
$900$	11.3910			0.379701
$901$		0			0
$902$	−0.227845			−0.00758640
$903$		−	27.5930i		−	0.918239i
$904$	−2.93882	−	2.93882i	−0.0977437	−	0.0977437i
$905$	55.8955			1.85803
$906$	−14.9967	−	14.9967i	−0.498231	−	0.498231i
$907$	−14.4700	+	14.4700i	−0.480470	+	0.480470i	−0.905282	−	0.424812i	$-0.860340\pi$
$907$	−14.4700	+	14.4700i	−0.480470	+	0.480470i	0.424812	+	0.905282i	$0.360340\pi$
$908$	19.9555	−	19.9555i	0.662247	−	0.662247i
$909$		−	3.48022i		−	0.115432i
$910$		−	22.6951i		−	0.752337i
$911$	1.61082	−	1.61082i	0.0533689	−	0.0533689i	−0.679919	−	0.733288i	$-0.737985\pi$
$911$	1.61082	−	1.61082i	0.0533689	−	0.0533689i	0.733288	+	0.679919i	$0.237985\pi$
$912$	−7.68003	+	7.68003i	−0.254311	+	0.254311i
$913$	−1.33861	−	1.33861i	−0.0443015	−	0.0443015i
$914$	−45.9394			−1.51954
$915$	−38.4133	−	38.4133i	−1.26990	−	1.26990i
$916$		−	0.0372828i		−	0.00123186i
$917$	43.6637			1.44190
$918$		0			0
$919$	36.0659			1.18970			0.594851	−	0.803836i	$-0.297211\pi$
$919$	36.0659			1.18970			0.594851	+	0.803836i	$0.297211\pi$
$920$			9.97908i			0.329000i
$921$	9.63630	+	9.63630i	0.317527	+	0.317527i
$922$	−21.0434			−0.693028
$923$	−8.70737	−	8.70737i	−0.286607	−	0.286607i
$924$	0.765367	−	0.765367i	0.0251787	−	0.0251787i
$925$	−39.7585	+	39.7585i	−1.30725	+	1.30725i
$926$		−	46.1327i		−	1.51602i
$927$		−	10.2649i		−	0.337144i
$928$	−10.7151	+	10.7151i	−0.351742	+	0.351742i
$929$	−39.1824	+	39.1824i	−1.28553	+	1.28553i	−0.348059	+	0.937473i	$0.613159\pi$
$929$	−39.1824	+	39.1824i	−1.28553	+	1.28553i	−0.937473	+	0.348059i	$0.886841\pi$
$930$	−22.3729	−	22.3729i	−0.733637	−	0.733637i
$931$	17.5574			0.575419
$932$	22.6706	+	22.6706i	0.742601	+	0.742601i
$933$		−	2.58579i		−	0.0846548i
$934$	6.14023			0.200914
$935$		0			0
$936$	0.956272			0.0312567
$937$		−	40.8695i		−	1.33515i	−0.744543	−	0.667575i	$-0.767332\pi$
$937$		−	40.8695i		−	1.33515i	0.744543	−	0.667575i	$-0.232668\pi$
$938$	−1.41421	−	1.41421i	−0.0461757	−	0.0461757i
$939$	−3.95365			−0.129022
$940$	−19.8435	−	19.8435i	−0.647225	−	0.647225i
$941$	−10.8567	+	10.8567i	−0.353917	+	0.353917i	−0.861565	−	0.507648i	$-0.830515\pi$
$941$	−10.8567	+	10.8567i	−0.353917	+	0.353917i	0.507648	+	0.861565i	$0.330515\pi$
$942$	7.59331	−	7.59331i	0.247403	−	0.247403i
$943$			1.58181i			0.0515108i
$944$		−	24.2355i		−	0.788798i
$945$	9.83051	−	9.83051i	0.319786	−	0.319786i
$946$	1.86373	−	1.86373i	0.0605952	−	0.0605952i
$947$	−28.9127	−	28.9127i	−0.939537	−	0.939537i	0.0587361	−	0.998274i	$-0.481293\pi$
$947$	−28.9127	−	28.9127i	−0.939537	−	0.939537i	−0.998274	+	0.0587361i	$0.981293\pi$
$948$	7.24718			0.235377
$949$	9.77059	+	9.77059i	0.317167	+	0.317167i
$950$			33.4785i			1.08619i
$951$	−33.5145			−1.08678
$952$		0			0
$953$	−25.5007			−0.826050			−0.413025	−	0.910720i	$-0.635528\pi$
$953$	−25.5007			−0.826050			−0.413025	+	0.910720i	$0.635528\pi$
$954$			9.58541i			0.310339i
$955$	−15.2543	−	15.2543i	−0.493618	−	0.493618i
$956$	−14.5954			−0.472049
$957$	0.315433	+	0.315433i	0.0101965	+	0.0101965i
$958$	−0.403751	+	0.403751i	−0.0130446	+	0.0130446i
$959$	19.4525	−	19.4525i	0.628154	−	0.628154i
$960$			10.2195i			0.329832i
$961$		−	8.53954i		−	0.275469i
$962$	8.05794	−	8.05794i	0.259798	−	0.259798i
$963$	−1.98682	+	1.98682i	−0.0640243	+	0.0640243i
$964$	−4.95524	−	4.95524i	−0.159597	−	0.159597i
$965$	−39.9174			−1.28499
$966$	−12.8281	−	12.8281i	−0.412736	−	0.412736i
$967$		−	12.0223i		−	0.386610i	−0.981139	−	0.193305i	$-0.938079\pi$
$967$		−	12.0223i		−	0.386610i	0.981139	−	0.193305i	$-0.0619207\pi$
$968$	11.8635			0.381307
$969$		0			0
$970$	−39.7199			−1.27533
$971$		−	48.0362i		−	1.54155i	−0.637105	−	0.770777i	$-0.719868\pi$
$971$		−	48.0362i		−	1.54155i	0.637105	−	0.770777i	$-0.280132\pi$
$972$	−1.00000	−	1.00000i	−0.0320750	−	0.0320750i
$973$	42.2670			1.35502
$974$	42.6561	+	42.6561i	1.36679	+	1.36679i
$975$	5.03188	−	5.03188i	0.161149	−	0.161149i
$976$	51.3339	−	51.3339i	1.64316	−	1.64316i
$977$			29.7041i			0.950319i	0.879900	+	0.475160i	$0.157610\pi$
$977$			29.7041i			0.950319i	−0.879900	+	0.475160i	$0.842390\pi$
$978$		−	9.99411i		−	0.319577i
$979$	0.609695	−	0.609695i	0.0194859	−	0.0194859i
$980$	28.2014	−	28.2014i	0.900859	−	0.900859i
$981$	−6.06306	−	6.06306i	−0.193579	−	0.193579i
$982$	−40.1100			−1.27996
$983$	−2.77733	−	2.77733i	−0.0885830	−	0.0885830i	0.661427	−	0.750010i	$-0.269951\pi$
$983$	−2.77733	−	2.77733i	−0.0885830	−	0.0885830i	−0.750010	+	0.661427i	$0.769951\pi$
$984$		−	0.670991i		−	0.0213904i
$985$	6.48438			0.206609
$986$		0			0
$987$	−21.1322			−0.672644
$988$		−	2.81050i		−	0.0894140i
$989$	−12.9390	−	12.9390i	−0.411435	−	0.411435i
$990$	1.32798			0.0422058
$991$	6.38425	+	6.38425i	0.202802	+	0.202802i	0.801200	−	0.598397i	$-0.204196\pi$
$991$	6.38425	+	6.38425i	0.202802	+	0.202802i	−0.598397	+	0.801200i	$0.704196\pi$
$992$	22.6437	−	22.6437i	0.718938	−	0.718938i
$993$	13.6498	−	13.6498i	0.433163	−	0.433163i
$994$		−	99.0966i		−	3.14315i
$995$			1.71056i			0.0542283i
$996$	−9.51716	+	9.51716i	−0.301563	+	0.301563i
$997$	25.9633	−	25.9633i	0.822266	−	0.822266i	−0.164167	−	0.986433i	$-0.552494\pi$
$997$	25.9633	−	25.9633i	0.822266	−	0.822266i	0.986433	+	0.164167i	$0.0524936\pi$
$998$	2.92540	+	2.92540i	0.0926020	+	0.0926020i
$999$	6.98067			0.220859

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.e.h.829.1		8
17.2	even	8		867.2.a.m.1.4		4
17.3	odd	16		867.2.h.f.712.1		8
17.4	even	4	inner	867.2.e.h.616.4		8
17.5	odd	16		867.2.h.g.733.2		8
17.6	odd	16		51.2.h.a.43.2	yes	8
17.7	odd	16		867.2.h.f.688.1		8
17.8	even	8		867.2.d.e.577.2		8
17.9	even	8		867.2.d.e.577.1		8
17.10	odd	16		867.2.h.b.688.1		8
17.11	odd	16		867.2.h.g.757.2		8
17.12	odd	16		51.2.h.a.19.2	✓	8
17.13	even	4		867.2.e.i.616.4		8
17.14	odd	16		867.2.h.b.712.1		8
17.15	even	8		867.2.a.n.1.4		4
17.16	even	2		867.2.e.i.829.1		8
51.2	odd	8		2601.2.a.bc.1.1		4
51.23	even	16		153.2.l.e.145.1		8
51.29	even	16		153.2.l.e.19.1		8
51.32	odd	8		2601.2.a.bd.1.1		4
68.23	even	16		816.2.bq.a.145.2		8
68.63	even	16		816.2.bq.a.529.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.19.2	✓	8	17.12	odd	16
51.2.h.a.43.2	yes	8	17.6	odd	16
153.2.l.e.19.1		8	51.29	even	16
153.2.l.e.145.1		8	51.23	even	16
816.2.bq.a.145.2		8	68.23	even	16
816.2.bq.a.529.2		8	68.63	even	16
867.2.a.m.1.4		4	17.2	even	8
867.2.a.n.1.4		4	17.15	even	8
867.2.d.e.577.1		8	17.9	even	8
867.2.d.e.577.2		8	17.8	even	8
867.2.e.h.616.4		8	17.4	even	4	inner
867.2.e.h.829.1		8	1.1	even	1	trivial
867.2.e.i.616.4		8	17.13	even	4
867.2.e.i.829.1		8	17.16	even	2
867.2.h.b.688.1		8	17.10	odd	16
867.2.h.b.712.1		8	17.14	odd	16
867.2.h.f.688.1		8	17.7	odd	16
867.2.h.f.712.1		8	17.3	odd	16
867.2.h.g.733.2		8	17.5	odd	16
867.2.h.g.757.2		8	17.11	odd	16
2601.2.a.bc.1.1		4	51.2	odd	8
2601.2.a.bd.1.1		4	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 $\F_{q}$
Belyi maps

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-1.84776i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.41421 q^{4} +(-2.55487 - 2.55487i) q^{5} +(-1.30656 + 1.30656i) q^{6} +(-2.72078 + 2.72078i) q^{7} -1.08239i q^{8} +1.00000i q^{9} +(-4.72078 + 4.72078i) q^{10} +(-0.140652 + 0.140652i) q^{11} +(1.00000 + 1.00000i) q^{12} +0.883480 q^{13} +(5.02734 + 5.02734i) q^{14} +3.61313i q^{15} -4.82843 q^{16} +1.84776 q^{18} +2.24943i q^{19} +(3.61313 + 3.61313i) q^{20} +3.84776 q^{21} +(0.259892 + 0.259892i) q^{22} +(1.80430 - 1.80430i) q^{23} +(-0.765367 + 0.765367i) q^{24} +8.05468i q^{25} -1.63246i q^{26} +(0.707107 - 0.707107i) q^{27} +(3.84776 - 3.84776i) q^{28} +(1.58579 + 1.58579i) q^{29} +6.67619 q^{30} +(-3.35115 - 3.35115i) q^{31} +6.75699i q^{32} +0.198912 q^{33} +13.9024 q^{35} -1.41421i q^{36} +(4.93608 + 4.93608i) q^{37} +4.15640 q^{38} +(-0.624715 - 0.624715i) q^{39} +(-2.76537 + 2.76537i) q^{40} +(-0.438346 + 0.438346i) q^{41} -7.10973i q^{42} -7.17120i q^{43} +(0.198912 - 0.198912i) q^{44} +(2.55487 - 2.55487i) q^{45} +(-3.33390 - 3.33390i) q^{46} -5.49207 q^{47} +(3.41421 + 3.41421i) q^{48} -7.80525i q^{49} +14.8831 q^{50} -1.24943 q^{52} +5.18759i q^{53} +(-1.30656 - 1.30656i) q^{54} +0.718695 q^{55} +(2.94495 + 2.94495i) q^{56} +(1.59059 - 1.59059i) q^{57} +(2.93015 - 2.93015i) q^{58} +5.01933i q^{59} -5.10973i q^{60} +(-10.6316 + 10.6316i) q^{61} +(-6.19212 + 6.19212i) q^{62} +(-2.72078 - 2.72078i) q^{63} +2.82843 q^{64} +(-2.25717 - 2.25717i) q^{65} -0.367542i q^{66} -0.281305 q^{67} -2.55166 q^{69} -25.6884i q^{70} +(-9.85577 - 9.85577i) q^{71} +1.08239 q^{72} +(11.0592 + 11.0592i) q^{73} +(9.12068 - 9.12068i) q^{74} +(5.69552 - 5.69552i) q^{75} -3.18117i q^{76} -0.765367i q^{77} +(-1.15432 + 1.15432i) q^{78} +(3.62359 - 3.62359i) q^{79} +(12.3360 + 12.3360i) q^{80} -1.00000 q^{81} +(0.809957 + 0.809957i) q^{82} +9.51716i q^{83} -5.44155 q^{84} -13.2506 q^{86} -2.24264i q^{87} +(0.152241 + 0.152241i) q^{88} -4.33476 q^{89} +(-4.72078 - 4.72078i) q^{90} +(-2.40375 + 2.40375i) q^{91} +(-2.55166 + 2.55166i) q^{92} +4.73925i q^{93} +10.1480i q^{94} +(5.74699 - 5.74699i) q^{95} +(4.77791 - 4.77791i) q^{96} +(4.20692 + 4.20692i) q^{97} -14.4222 q^{98} +(-0.140652 - 0.140652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{10} + 8 q^{11} + 8 q^{12} + 8 q^{13} + 8 q^{14} - 16 q^{16} + 8 q^{20} + 16 q^{21} + 16 q^{22} + 16 q^{28} + 24 q^{29} + 16 q^{30} - 32 q^{31} - 8 q^{33} + 32 q^{35} + 16 q^{37} - 32 q^{38}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q - 16 * q^10 + 8 * q^11 + 8 * q^12 + 8 * q^13 + 8 * q^14 - 16 * q^16 + 8 * q^20 + 16 * q^21 + 16 * q^22 + 16 * q^28 + 24 * q^29 + 16 * q^30 - 32 * q^31 - 8 * q^33 + 32 * q^35 + 16 * q^37 - 32 * q^38 - 8 * q^39 - 16 * q^40 + 16 * q^41 - 8 * q^44 + 16 * q^46 - 16 * q^47 + 16 * q^48 + 32 * q^50 - 16 * q^52 + 24 * q^55 + 8 * q^57 - 32 * q^61 - 8 * q^65 + 16 * q^67 - 24 * q^69 - 24 * q^71 + 32 * q^73 - 8 * q^74 + 16 * q^75 + 16 * q^78 + 16 * q^79 + 16 * q^80 - 8 * q^81 + 16 * q^82 - 32 * q^86 + 16 * q^88 - 32 * q^89 - 16 * q^90 - 24 * q^92 - 24 * q^95 - 16 * q^97 - 64 * q^98 + 8 * q^99

Introduction

L-functions

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