LMFDB - Embedded newform 784.2.m.i.589.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(197,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.197"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,-8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 109x^{16} + 3858x^{12} + 44914x^{8} + 37101x^{4} + 2209 $ x^20 + 109x^16 + 3858x^12 + 44914x^8 + 37101x^4 + 2209
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			589.6
Root			$1.83808 - 1.83808i$ of defining polynomial
Character	$\chi$	$=$	784.589
Dual form			784.2.m.i.197.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.246440 - 1.39258i) q^{2} +(0.905952 + 0.905952i) q^{3} +(-1.87853 + 0.686372i) q^{4} +(2.32368 - 2.32368i) q^{5} +(1.03834 - 1.48487i) q^{6} +(1.41877 + 2.44685i) q^{8} -1.35850i q^{9} +(-3.80855 - 2.66326i) q^{10} +(0.300717 - 0.300717i) q^{11} +(-2.32368 - 1.08004i) q^{12} +(-3.70160 - 3.70160i) q^{13} +4.21029 q^{15} +(3.05779 - 2.57875i) q^{16} -2.70495 q^{17} +(-1.89182 + 0.334789i) q^{18} +(2.49777 + 2.49777i) q^{19} +(-2.77021 + 5.96003i) q^{20} +(-0.492880 - 0.344662i) q^{22} -5.03510i q^{23} +(-0.931392 + 3.50207i) q^{24} -5.79899i q^{25} +(-4.24254 + 6.06698i) q^{26} +(3.94859 - 3.94859i) q^{27} +(0.464798 + 0.464798i) q^{29} +(-1.03758 - 5.86314i) q^{30} +7.75138 q^{31} +(-4.34466 - 3.62269i) q^{32} +0.544870 q^{33} +(0.666608 + 3.76685i) q^{34} +(0.932439 + 2.55200i) q^{36} +(-3.83754 + 3.83754i) q^{37} +(2.86279 - 4.09389i) q^{38} -6.70694i q^{39} +(8.98248 + 2.38894i) q^{40} +10.5868i q^{41} +(8.35006 - 8.35006i) q^{43} +(-0.358503 + 0.771311i) q^{44} +(-3.15673 - 3.15673i) q^{45} +(-7.01176 + 1.24085i) q^{46} -10.2387 q^{47} +(5.10643 + 0.433986i) q^{48} +(-8.07554 + 1.42910i) q^{50} +(-2.45056 - 2.45056i) q^{51} +(9.49426 + 4.41291i) q^{52} +(9.02352 - 9.02352i) q^{53} +(-6.47181 - 4.52562i) q^{54} -1.39754i q^{55} +4.52572i q^{57} +(0.532721 - 0.761811i) q^{58} +(-7.19602 + 7.19602i) q^{59} +(-7.90917 + 2.88982i) q^{60} +(-5.02863 - 5.02863i) q^{61} +(-1.91025 - 10.7944i) q^{62} +(-3.97418 + 6.94305i) q^{64} -17.2027 q^{65} +(-0.134278 - 0.758772i) q^{66} +(0.178322 + 0.178322i) q^{67} +(5.08135 - 1.85660i) q^{68} +(4.56156 - 4.56156i) q^{69} -6.38433i q^{71} +(3.32406 - 1.92741i) q^{72} -1.41284i q^{73} +(6.28979 + 4.39835i) q^{74} +(5.25361 - 5.25361i) q^{75} +(-6.40655 - 2.97775i) q^{76} +(-9.33992 + 1.65286i) q^{78} +8.28731 q^{79} +(1.11313 - 13.0975i) q^{80} +3.07896 q^{81} +(14.7430 - 2.60902i) q^{82} +(2.84836 + 2.84836i) q^{83} +(-6.28545 + 6.28545i) q^{85} +(-13.6859 - 9.57030i) q^{86} +0.842168i q^{87} +(1.16246 + 0.309162i) q^{88} +0.544870i q^{89} +(-3.61804 + 5.17393i) q^{90} +(3.45595 + 9.45861i) q^{92} +(7.02237 + 7.02237i) q^{93} +(2.52321 + 14.2581i) q^{94} +11.6081 q^{95} +(-0.654069 - 7.21804i) q^{96} +3.67469 q^{97} +(-0.408525 - 0.408525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 8 q^{4} + 4 q^{11} - 16 q^{15} + 16 q^{18} - 4 q^{29} + 8 q^{30} - 40 q^{32} + 40 q^{36} - 20 q^{37} + 60 q^{43} + 56 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{51} + 28 q^{53} - 72 q^{58} - 24 q^{60}+ \cdots - 108 q^{99}+O(q^{100}) $ 20 * q - 8 * q^4 + 4 * q^11 - 16 * q^15 + 16 * q^18 - 4 * q^29 + 8 * q^30 - 40 * q^32 + 40 * q^36 - 20 * q^37 + 60 * q^43 + 56 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^51 + 28 * q^53 - 72 * q^58 - 24 * q^60 - 32 * q^64 + 16 * q^65 + 12 * q^67 + 16 * q^72 - 16 * q^74 - 88 * q^78 - 72 * q^79 + 12 * q^81 + 32 * q^85 - 40 * q^86 + 80 * q^88 - 24 * q^92 + 48 * q^93 + 64 * q^95 - 108 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.246440	−	1.39258i	−0.174259	−	0.984700i
$2$	−0.246440	−	1.39258i	−0.174259	−	0.984700i
$3$	0.905952	+	0.905952i	0.523051	+	0.523051i	0.918492	−	0.395440i	$-0.129408\pi$
$3$	0.905952	+	0.905952i	0.523051	+	0.523051i	−0.395440	+	0.918492i	$0.629408\pi$
$4$	−1.87853	+	0.686372i	−0.939267	+	0.343186i
$5$	2.32368	−	2.32368i	1.03918	−	1.03918i	0.0399816	−	0.999200i	$-0.487270\pi$
$5$	2.32368	−	2.32368i	1.03918	−	1.03918i	0.999200	−	0.0399816i	$-0.0127299\pi$
$6$	1.03834	−	1.48487i	0.423902	−	0.606195i
$7$		0			0
$7$		0			0
$8$	1.41877	+	2.44685i	0.501611	+	0.865093i
$9$		−	1.35850i		−	0.452834i
$10$	−3.80855	−	2.66326i	−1.20437	−	0.842195i
$11$	0.300717	−	0.300717i	0.0906695	−	0.0906695i	−0.660317	−	0.750987i	$-0.729578\pi$
$11$	0.300717	−	0.300717i	0.0906695	−	0.0906695i	0.750987	+	0.660317i	$0.229578\pi$
$12$	−2.32368	−	1.08004i	−0.670789	−	0.311781i
$13$	−3.70160	−	3.70160i	−1.02664	−	1.02664i	−0.999635	−	0.0270035i	$-0.991403\pi$
$13$	−3.70160	−	3.70160i	−1.02664	−	1.02664i	−0.0270035	−	0.999635i	$-0.508597\pi$
$14$		0			0
$15$	4.21029			1.08709
$16$	3.05779	−	2.57875i	0.764447	−	0.644687i
$17$	−2.70495			−0.656048			−0.328024	−	0.944669i	$-0.606383\pi$
$17$	−2.70495			−0.656048			−0.328024	+	0.944669i	$0.606383\pi$
$18$	−1.89182	+	0.334789i	−0.445906	+	0.0789106i
$19$	2.49777	+	2.49777i	0.573028	+	0.573028i	0.932973	−	0.359945i	$-0.117205\pi$
$19$	2.49777	+	2.49777i	0.573028	+	0.573028i	−0.359945	+	0.932973i	$0.617205\pi$
$20$	−2.77021	+	5.96003i	−0.619437	+	1.33270i
$21$		0			0
$22$	−0.492880	−	0.344662i	−0.105082	−	0.0734823i
$23$		−	5.03510i		−	1.04989i	−0.851136	−	0.524946i	$-0.824086\pi$
$23$		−	5.03510i		−	1.04989i	0.851136	−	0.524946i	$-0.175914\pi$
$24$	−0.931392	+	3.50207i	−0.190120	+	0.714857i
$25$		−	5.79899i		−	1.15980i
$26$	−4.24254	+	6.06698i	−0.832030	+	1.18983i
$27$	3.94859	−	3.94859i	0.759907	−	0.759907i
$28$		0			0
$29$	0.464798	+	0.464798i	0.0863108	+	0.0863108i	0.748944	−	0.662633i	$-0.230561\pi$
$29$	0.464798	+	0.464798i	0.0863108	+	0.0863108i	−0.662633	+	0.748944i	$0.730561\pi$
$30$	−1.03758	−	5.86314i	−0.189436	−	1.07046i
$31$	7.75138			1.39219			0.696094	−	0.717950i	$-0.254920\pi$
$31$	7.75138			1.39219			0.696094	+	0.717950i	$0.254920\pi$
$32$	−4.34466	−	3.62269i	−0.768035	−	0.640408i
$33$	0.544870			0.0948497
$34$	0.666608	+	3.76685i	0.114322	+	0.646010i
$35$		0			0
$36$	0.932439	+	2.55200i	0.155406	+	0.425333i
$37$	−3.83754	+	3.83754i	−0.630888	+	0.630888i	−0.948291	−	0.317403i	$-0.897189\pi$
$37$	−3.83754	+	3.83754i	−0.630888	+	0.630888i	0.317403	+	0.948291i	$0.397189\pi$
$38$	2.86279	−	4.09389i	0.464405	−	0.664116i
$39$		−	6.70694i		−	1.07397i
$40$	8.98248	+	2.38894i	1.42025	+	0.377724i
$41$			10.5868i			1.65339i	0.562653	+	0.826693i	$0.309781\pi$
$41$			10.5868i			1.65339i	−0.562653	+	0.826693i	$0.690219\pi$
$42$		0			0
$43$	8.35006	−	8.35006i	1.27337	−	1.27337i	0.329065	−	0.944307i	$-0.393267\pi$
$43$	8.35006	−	8.35006i	1.27337	−	1.27337i	0.944307	−	0.329065i	$-0.106733\pi$
$44$	−0.358503	+	0.771311i	−0.0540464	+	0.116279i
$45$	−3.15673	−	3.15673i	−0.470577	−	0.470577i
$46$	−7.01176	+	1.24085i	−1.03383	+	0.182953i
$47$	−10.2387			−1.49346			−0.746731	−	0.665126i	$-0.768378\pi$
$47$	−10.2387			−1.49346			−0.746731	+	0.665126i	$0.768378\pi$
$48$	5.10643	+	0.433986i	0.737049	+	0.0626404i
$49$		0			0
$50$	−8.07554	+	1.42910i	−1.14205	+	0.202106i
$51$	−2.45056	−	2.45056i	−0.343147	−	0.343147i
$52$	9.49426	+	4.41291i	1.31662	+	0.611960i
$53$	9.02352	−	9.02352i	1.23948	−	1.23948i	0.279260	−	0.960215i	$-0.409911\pi$
$53$	9.02352	−	9.02352i	1.23948	−	1.23948i	0.960215	−	0.279260i	$-0.0900892\pi$
$54$	−6.47181	−	4.52562i	−0.880701	−	0.615860i
$55$		−	1.39754i		−	0.188444i
$56$		0			0
$57$			4.52572i			0.599446i
$58$	0.532721	−	0.761811i	0.0699497	−	0.100031i
$59$	−7.19602	+	7.19602i	−0.936842	+	0.936842i	−0.998121	−	0.0612791i	$-0.980482\pi$
$59$	−7.19602	+	7.19602i	−0.936842	+	0.936842i	0.0612791	+	0.998121i	$0.480482\pi$
$60$	−7.90917	+	2.88982i	−1.02107	+	0.373075i
$61$	−5.02863	−	5.02863i	−0.643851	−	0.643851i	0.307649	−	0.951500i	$-0.400458\pi$
$61$	−5.02863	−	5.02863i	−0.643851	−	0.643851i	−0.951500	+	0.307649i	$0.900458\pi$
$62$	−1.91025	−	10.7944i	−0.242602	−	1.37089i
$63$		0			0
$64$	−3.97418	+	6.94305i	−0.496772	+	0.867881i
$65$	−17.2027			−2.13373
$66$	−0.134278	−	0.758772i	−0.0165284	−	0.0933984i
$67$	0.178322	+	0.178322i	0.0217855	+	0.0217855i	0.717916	−	0.696130i	$-0.245096\pi$
$67$	0.178322	+	0.178322i	0.0217855	+	0.0217855i	−0.696130	+	0.717916i	$0.745096\pi$
$68$	5.08135	−	1.85660i	0.616204	−	0.225146i
$69$	4.56156	−	4.56156i	0.549147	−	0.549147i
$70$		0			0
$71$		−	6.38433i		−	0.757680i	−0.925462	−	0.378840i	$-0.876323\pi$
$71$		−	6.38433i		−	0.757680i	0.925462	−	0.378840i	$-0.123677\pi$
$72$	3.32406	−	1.92741i	0.391744	−	0.227147i
$73$		−	1.41284i		−	0.165361i	−0.996576	−	0.0826803i	$-0.973652\pi$
$73$		−	1.41284i		−	0.165361i	0.996576	−	0.0826803i	$-0.0263480\pi$
$74$	6.28979	+	4.39835i	0.731173	+	0.511297i
$75$	5.25361	−	5.25361i	0.606634	−	0.606634i
$76$	−6.40655	−	2.97775i	−0.734882	−	0.341571i
$77$		0			0
$78$	−9.33992	+	1.65286i	−1.05754	+	0.187149i
$79$	8.28731			0.932395			0.466198	−	0.884681i	$-0.345624\pi$
$79$	8.28731			0.932395			0.466198	+	0.884681i	$0.345624\pi$
$80$	1.11313	−	13.0975i	0.124452	−	1.46435i
$81$	3.07896			0.342106
$82$	14.7430	−	2.60902i	1.62809	−	0.288118i
$83$	2.84836	+	2.84836i	0.312648	+	0.312648i	0.845935	−	0.533286i	$-0.179043\pi$
$83$	2.84836	+	2.84836i	0.312648	+	0.312648i	−0.533286	+	0.845935i	$0.679043\pi$
$84$		0			0
$85$	−6.28545	+	6.28545i	−0.681753	+	0.681753i
$86$	−13.6859	−	9.57030i	−1.47579	−	1.03199i
$87$			0.842168i			0.0902899i
$88$	1.16246	+	0.309162i	0.123918	+	0.0329567i
$89$			0.544870i			0.0577561i	0.999583	+	0.0288780i	$0.00919344\pi$
$89$			0.544870i			0.0577561i	−0.999583	+	0.0288780i	$0.990807\pi$
$90$	−3.61804	+	5.17393i	−0.381375	+	0.545380i
$91$		0			0
$92$	3.45595	+	9.45861i	0.360308	+	0.986129i
$93$	7.02237	+	7.02237i	0.728186	+	0.728186i
$94$	2.52321	+	14.2581i	0.260250	+	1.47061i
$95$	11.6081			1.19096
$96$	−0.654069	−	7.21804i	−0.0667556	−	0.736688i
$97$	3.67469			0.373108			0.186554	−	0.982445i	$-0.440268\pi$
$97$	3.67469			0.373108			0.186554	+	0.982445i	$0.440268\pi$
$98$		0			0
$99$	−0.408525	−	0.408525i	−0.0410583	−	0.0410583i
$100$	3.98027	+	10.8936i	0.398027	+	1.08936i
$101$	2.78275	−	2.78275i	0.276894	−	0.276894i	−0.554974	−	0.831868i	$-0.687272\pi$
$101$	2.78275	−	2.78275i	0.276894	−	0.276894i	0.831868	+	0.554974i	$0.187272\pi$
$102$	−2.80867	+	4.01650i	−0.278100	+	0.397693i
$103$			13.8625i			1.36591i	0.730461	+	0.682955i	$0.239305\pi$
$103$			13.8625i			1.36591i	−0.730461	+	0.682955i	$0.760695\pi$
$104$	3.80555	−	14.3090i	0.373165	−	1.40311i
$105$		0			0
$106$	−14.7897	−	10.3422i	−1.43650	−	1.00452i
$107$	−6.91294	+	6.91294i	−0.668299	+	0.668299i	−0.957322	−	0.289023i	$-0.906670\pi$
$107$	−6.91294	+	6.91294i	−0.668299	+	0.668299i	0.289023	+	0.957322i	$0.406670\pi$
$108$	−4.70737	+	10.1278i	−0.452966	+	0.974546i
$109$	10.5377	+	10.5377i	1.00932	+	1.00932i	0.999956	+	0.00936859i	$0.00298216\pi$
$109$	10.5377	+	10.5377i	1.00932	+	1.00932i	0.00936859	+	0.999956i	$0.497018\pi$
$110$	−1.94618	+	0.344410i	−0.185561	+	0.0328382i
$111$	−6.95325			−0.659974
$112$		0			0
$113$	0.0535041			0.00503324			0.00251662	−	0.999997i	$-0.499199\pi$
$113$	0.0535041			0.00503324			0.00251662	+	0.999997i	$0.499199\pi$
$114$	6.30241	−	1.11532i	0.590275	−	0.104459i
$115$	−11.7000	−	11.7000i	−1.09103	−	1.09103i
$116$	−1.19216	−	0.554114i	−0.110690	−	0.0514482i
$117$	−5.02863	+	5.02863i	−0.464897	+	0.464897i
$118$	11.7944	+	8.24761i	1.08576	+	0.759254i
$119$		0			0
$120$	5.97343	+	10.3020i	0.545297	+	0.940435i
$121$			10.8191i			0.983558i
$122$	−5.76350	+	8.24201i	−0.521803	+	0.746197i
$123$	−9.59116	+	9.59116i	−0.864806	+	0.864806i
$124$	−14.5612	+	5.32033i	−1.30764	+	0.477780i
$125$	−1.85660	−	1.85660i	−0.166060	−	0.166060i
$126$		0			0
$127$	5.69350			0.505216			0.252608	−	0.967569i	$-0.418712\pi$
$127$	5.69350			0.505216			0.252608	+	0.967569i	$0.418712\pi$
$128$	10.6481	+	3.82330i	0.941169	+	0.337935i
$129$	15.1295			1.33208
$130$	4.23942	+	23.9560i	0.371822	+	2.10108i
$131$	1.84988	+	1.84988i	0.161625	+	0.161625i	0.783286	−	0.621661i	$-0.213542\pi$
$131$	1.84988	+	1.84988i	0.161625	+	0.161625i	−0.621661	+	0.783286i	$0.713542\pi$
$132$	−1.02356	+	0.373983i	−0.0890892	+	0.0325511i
$133$		0			0
$134$	0.204381	−	0.292272i	0.0176558	−	0.0252485i
$135$		−	18.3505i		−	1.57936i
$136$	−3.83771	−	6.61862i	−0.329081	−	0.567542i
$137$		−	13.6297i		−	1.16446i	−0.813022	−	0.582232i	$-0.802179\pi$
$137$		−	13.6297i		−	1.16446i	0.813022	−	0.582232i	$-0.197821\pi$
$138$	−7.47646	−	5.22817i	−0.636439	−	0.445051i
$139$	−14.5483	+	14.5483i	−1.23397	+	1.23397i	−0.271549	+	0.962425i	$0.587536\pi$
$139$	−14.5483	+	14.5483i	−1.23397	+	1.23397i	−0.962425	+	0.271549i	$0.912464\pi$
$140$		0			0
$141$	−9.27573	−	9.27573i	−0.781157	−	0.781157i
$142$	−8.89066	+	1.57335i	−0.746087	+	0.132033i
$143$	−2.22627			−0.186170
$144$	−3.50324	−	4.15401i	−0.291936	−	0.346168i
$145$	2.16008			0.179385
$146$	−1.96749	+	0.348180i	−0.162831	+	0.0288156i
$147$		0			0
$148$	4.57497	−	9.84294i	0.376061	−	0.809085i
$149$	−4.87681	+	4.87681i	−0.399523	+	0.399523i	−0.878065	−	0.478541i	$-0.841166\pi$
$149$	−4.87681	+	4.87681i	−0.399523	+	0.399523i	0.478541	+	0.878065i	$0.341166\pi$
$150$	−8.61074	−	6.02135i	−0.703064	−	0.491641i
$151$		−	0.133987i		−	0.0109037i	−0.999985	−	0.00545187i	$-0.998265\pi$
$151$		−	0.133987i		−	0.0109037i	0.999985	−	0.00545187i	$-0.00173539\pi$
$152$	−2.56791	+	9.65545i	−0.208285	+	0.783160i
$153$			3.67469i			0.297081i
$154$		0			0
$155$	18.0117	−	18.0117i	1.44674	−	1.44674i
$156$	4.60346	+	12.5992i	0.368571	+	1.00874i
$157$	2.62716	+	2.62716i	0.209670	+	0.209670i	0.804127	−	0.594457i	$-0.202633\pi$
$157$	2.62716	+	2.62716i	0.209670	+	0.209670i	−0.594457	+	0.804127i	$0.702633\pi$
$158$	−2.04232	−	11.5407i	−0.162478	−	0.918129i
$159$	16.3497			1.29662
$160$	−18.5136	+	1.67763i	−1.46363	+	0.132628i
$161$		0			0
$162$	−0.758778	−	4.28768i	−0.0596152	−	0.336872i
$163$	13.3620	+	13.3620i	1.04659	+	1.04659i	0.998860	+	0.0477322i	$0.0151994\pi$
$163$	13.3620	+	13.3620i	1.04659	+	1.04659i	0.0477322	+	0.998860i	$0.484801\pi$
$164$	−7.26651	−	19.8877i	−0.567419	−	1.55297i
$165$	1.26610	−	1.26610i	0.0985661	−	0.0985661i
$166$	3.26461	−	4.66851i	0.253383	−	0.362347i
$167$			4.72699i			0.365785i	0.983133	+	0.182893i	$0.0585461\pi$
$167$			4.72699i			0.365785i	−0.983133	+	0.182893i	$0.941454\pi$
$168$		0			0
$169$			14.4037i			1.10797i
$170$	10.3020	+	7.20398i	0.790124	+	0.552520i
$171$	3.39323	−	3.39323i	0.259487	−	0.259487i
$172$	−9.95463	+	21.4171i	−0.759033	+	1.63304i
$173$	10.5090	+	10.5090i	0.798988	+	0.798988i	0.982936	−	0.183948i	$-0.0588878\pi$
$173$	10.5090	+	10.5090i	0.798988	+	0.798988i	−0.183948	+	0.982936i	$0.558888\pi$
$174$	1.17278	−	0.207544i	0.0889085	−	0.0157339i
$175$		0			0
$176$	0.144055	−	1.69500i	0.0108586	−	0.127765i
$177$	−13.0385			−0.980033
$178$	0.758772	−	0.134278i	0.0568724	−	0.0100645i
$179$	7.92036	+	7.92036i	0.591996	+	0.591996i	0.938170	−	0.346174i	$-0.112519\pi$
$179$	7.92036	+	7.92036i	0.591996	+	0.591996i	−0.346174	+	0.938170i	$0.612519\pi$
$180$	8.09672	+	3.76334i	0.603494	+	0.280502i
$181$	1.84499	−	1.84499i	0.137137	−	0.137137i	−0.635206	−	0.772343i	$-0.719085\pi$
$181$	1.84499	−	1.84499i	0.137137	−	0.137137i	0.772343	+	0.635206i	$0.219085\pi$
$182$		0			0
$183$		−	9.11140i		−	0.673534i
$184$	12.3202	−	7.14366i	0.908254	−	0.526637i
$185$			17.8345i			1.31121i
$186$	8.04860	−	11.5098i	0.590152	−	0.843938i
$187$	−0.813425	+	0.813425i	−0.0594835	+	0.0594835i
$188$	19.2337	−	7.02753i	1.40276	−	0.512535i
$189$		0			0
$190$	−2.86069	−	16.1651i	−0.207536	−	1.17274i
$191$	21.4688			1.55343			0.776713	−	0.629855i	$-0.216886\pi$
$191$	21.4688			1.55343			0.776713	+	0.629855i	$0.216886\pi$
$192$	−9.89048	+	2.68965i	−0.713784	+	0.194109i
$193$	−12.7305			−0.916358			−0.458179	−	0.888860i	$-0.651498\pi$
$193$	−12.7305			−0.916358			−0.458179	+	0.888860i	$0.651498\pi$
$194$	−0.905589	−	5.11728i	−0.0650175	−	0.367399i
$195$	−15.5848	−	15.5848i	−1.11605	−	1.11605i
$196$		0			0
$197$	−4.30651	+	4.30651i	−0.306826	+	0.306826i	−0.843677	−	0.536851i	$-0.819614\pi$
$197$	−4.30651	+	4.30651i	−0.306826	+	0.306826i	0.536851	+	0.843677i	$0.319614\pi$
$198$	−0.468225	+	0.669579i	−0.0332753	+	0.0475849i
$199$		−	5.86352i		−	0.415654i	−0.978166	−	0.207827i	$-0.933361\pi$
$199$		−	5.86352i		−	0.415654i	0.978166	−	0.207827i	$-0.0666390\pi$
$200$	14.1893	−	8.22744i	1.00333	−	0.581768i
$201$			0.323102i			0.0227898i
$202$	−4.56096	−	3.18941i	−0.320908	−	0.224406i
$203$		0			0
$204$	6.28545	+	2.92146i	0.440070	+	0.204543i
$205$	24.6004	+	24.6004i	1.71817	+	1.71817i
$206$	19.3045	−	3.41626i	1.34501	−	0.238022i
$207$	−6.84020			−0.475427
$208$	−20.8642	−	1.77321i	−1.44667	−	0.122950i
$209$	1.50224			0.103912
$210$		0			0
$211$	−1.72014	−	1.72014i	−0.118420	−	0.118420i	0.645414	−	0.763833i	$-0.276685\pi$
$211$	−1.72014	−	1.72014i	−0.118420	−	0.118420i	−0.763833	+	0.645414i	$0.776685\pi$
$212$	−10.7575	+	23.1445i	−0.738828	+	1.58957i
$213$	5.78389	−	5.78389i	0.396306	−	0.396306i
$214$	11.3304	+	7.92317i	0.774532	+	0.541617i
$215$		−	38.8058i		−	2.64653i
$216$	15.2638	+	4.05948i	1.03857	+	0.276212i
$217$		0			0
$218$	12.0776	−	17.2714i	0.817998	−	1.16977i
$219$	1.27997	−	1.27997i	0.0864921	−	0.0864921i
$220$	0.959233	+	2.62533i	0.0646715	+	0.177000i
$221$	10.0127	+	10.0127i	0.673524	+	0.673524i
$222$	1.71356	+	9.68293i	0.115007	+	0.649876i
$223$	27.1830			1.82031			0.910154	−	0.414270i	$-0.135963\pi$
$223$	27.1830			1.82031			0.910154	+	0.414270i	$0.135963\pi$
$224$		0			0
$225$	−7.87795			−0.525197
$226$	−0.0131855	−	0.0745085i	−0.000877089	−	0.00495623i
$227$	15.0932	+	15.0932i	1.00177	+	1.00177i	0.999998	+	0.00177264i	$0.000564249\pi$
$227$	15.0932	+	15.0932i	1.00177	+	1.00177i	0.00177264	+	0.999998i	$0.499436\pi$
$228$	−3.10633	−	8.50172i	−0.205722	−	0.563040i
$229$	−2.02020	+	2.02020i	−0.133499	+	0.133499i	−0.770699	−	0.637200i	$-0.780093\pi$
$229$	−2.02020	+	2.02020i	−0.133499	+	0.133499i	0.637200	+	0.770699i	$0.280093\pi$
$230$	−13.4098	+	19.1764i	−0.884213	+	1.26446i
$231$		0			0
$232$	−0.477850	+	1.79673i	−0.0313724	+	0.117961i
$233$		−	16.6200i		−	1.08881i	−0.838822	−	0.544406i	$-0.816755\pi$
$233$		−	16.6200i		−	1.08881i	0.838822	−	0.544406i	$-0.183245\pi$
$234$	8.24201	+	5.76350i	0.538797	+	0.376772i
$235$	−23.7914	+	23.7914i	−1.55198	+	1.55198i
$236$	8.57882	−	18.4571i	0.558434	−	1.20146i
$237$	7.50790	+	7.50790i	0.487691	+	0.487691i
$238$		0			0
$239$	−2.17404			−0.140627			−0.0703135	−	0.997525i	$-0.522400\pi$
$239$	−2.17404			−0.140627			−0.0703135	+	0.997525i	$0.522400\pi$
$240$	12.8742	−	10.8573i	0.831023	−	0.700834i
$241$	−13.8374			−0.891344			−0.445672	−	0.895196i	$-0.647035\pi$
$241$	−13.8374			−0.891344			−0.445672	+	0.895196i	$0.647035\pi$
$242$	15.0665	−	2.66627i	0.968509	−	0.171394i
$243$	−9.05639	−	9.05639i	−0.580968	−	0.580968i
$244$	12.8980	+	5.99495i	0.825709	+	0.383787i
$245$		0			0
$246$	15.7201	+	10.9928i	1.00227	+	0.700874i
$247$		−	18.4915i		−	1.17659i
$248$	10.9974	+	18.9665i	0.698338	+	1.20437i
$249$			5.16096i			0.327062i
$250$	−2.12792	+	3.04300i	−0.134582	+	0.192456i
$251$	9.65581	−	9.65581i	0.609469	−	0.609469i	−0.333338	−	0.942807i	$-0.608175\pi$
$251$	9.65581	−	9.65581i	0.609469	−	0.609469i	0.942807	+	0.333338i	$0.108175\pi$
$252$		0			0
$253$	−1.51414	−	1.51414i	−0.0951931	−	0.0951931i
$254$	−1.40310	−	7.92863i	−0.0880386	−	0.497486i
$255$	−11.3886			−0.713184
$256$	2.70012	−	15.7705i	0.168757	−	0.985658i
$257$	−16.7641			−1.04572			−0.522858	−	0.852420i	$-0.675134\pi$
$257$	−16.7641			−1.04572			−0.522858	+	0.852420i	$0.675134\pi$
$258$	−3.72851	−	21.0690i	−0.232127	−	1.31170i
$259$		0			0
$260$	32.3158	−	11.8074i	2.00414	−	0.732266i
$261$	0.631429	−	0.631429i	0.0390845	−	0.0390845i
$262$	2.12022	−	3.03199i	0.130988	−	0.187317i
$263$		−	10.4830i		−	0.646410i	−0.946329	−	0.323205i	$-0.895240\pi$
$263$		−	10.4830i		−	0.646410i	0.946329	−	0.323205i	$-0.104760\pi$
$264$	0.773045	+	1.33322i	0.0475777	+	0.0820538i
$265$		−	41.9356i		−	2.57608i
$266$		0			0
$267$	−0.493626	+	0.493626i	−0.0302094	+	0.0302094i
$268$	−0.457379	−	0.212589i	−0.0279388	−	0.0129859i
$269$	−4.63575	−	4.63575i	−0.282647	−	0.282647i	0.551517	−	0.834164i	$-0.314049\pi$
$269$	−4.63575	−	4.63575i	−0.282647	−	0.282647i	−0.834164	+	0.551517i	$0.814049\pi$
$270$	−25.5545	+	4.52230i	−1.55520	+	0.275219i
$271$	−8.64515			−0.525156			−0.262578	−	0.964911i	$-0.584573\pi$
$271$	−8.64515			−0.525156			−0.262578	+	0.964911i	$0.584573\pi$
$272$	−8.27117	+	6.97539i	−0.501513	+	0.422945i
$273$		0			0
$274$	−18.9804	+	3.35890i	−1.14665	+	0.202919i
$275$	−1.74385	−	1.74385i	−0.105158	−	0.105158i
$276$	−5.43812	+	11.7000i	−0.327336	+	0.704256i
$277$	−7.94721	+	7.94721i	−0.477502	+	0.477502i	−0.904332	−	0.426830i	$-0.859630\pi$
$277$	−7.94721	+	7.94721i	−0.477502	+	0.477502i	0.426830	+	0.904332i	$0.359630\pi$
$278$	23.8449	+	16.6744i	1.43012	+	1.00006i
$279$		−	10.5303i		−	0.630431i
$280$		0			0
$281$			9.46552i			0.564666i	0.959317	+	0.282333i	$0.0911083\pi$
$281$			9.46552i			0.564666i	−0.959317	+	0.282333i	$0.908892\pi$
$282$	−10.6312	+	15.2031i	−0.633082	+	0.905329i
$283$	6.84543	−	6.84543i	0.406918	−	0.406918i	−0.473744	−	0.880663i	$-0.657098\pi$
$283$	6.84543	−	6.84543i	0.406918	−	0.406918i	0.880663	+	0.473744i	$0.157098\pi$
$284$	4.38202	+	11.9932i	0.260025	+	0.711664i
$285$	10.5163	+	10.5163i	0.622934	+	0.622934i
$286$	0.548641	+	3.10024i	0.0324418	+	0.183321i
$287$		0			0
$288$	−4.92144	+	5.90224i	−0.289999	+	0.347793i
$289$	−9.68323			−0.569602
$290$	−0.532330	−	3.00808i	−0.0312595	−	0.176641i
$291$	3.32909	+	3.32909i	0.195155	+	0.195155i
$292$	0.969735	+	2.65407i	0.0567494	+	0.155318i
$293$	−20.0723	+	20.0723i	−1.17264	+	1.17264i	−0.191059	+	0.981578i	$0.561192\pi$
$293$	−20.0723	+	20.0723i	−1.17264	+	1.17264i	−0.981578	+	0.191059i	$0.938808\pi$
$294$		0			0
$295$			33.4425i			1.94710i
$296$	−14.8345	−	3.94531i	−0.862237	−	0.229316i
$297$		−	2.37482i		−	0.137801i
$298$	7.99316	+	5.58948i	0.463031	+	0.323790i
$299$	−18.6379	+	18.6379i	−1.07786	+	1.07786i
$300$	−6.26315	+	13.4750i	−0.361603	+	0.777980i
$301$		0			0
$302$	−0.186588	+	0.0330198i	−0.0107369	+	0.00190008i
$303$	5.04207			0.289659
$304$	14.0788	+	1.19653i	0.807473	+	0.0686256i
$305$	−23.3699			−1.33816
$306$	5.11728	−	0.905589i	0.292536	−	0.0517691i
$307$	18.4969	+	18.4969i	1.05568	+	1.05568i	0.998356	+	0.0573195i	$0.0182554\pi$
$307$	18.4969	+	18.4969i	1.05568	+	1.05568i	0.0573195	+	0.998356i	$0.481745\pi$
$308$		0			0
$309$	−12.5587	+	12.5587i	−0.714441	+	0.714441i
$310$	−29.5215	−	20.6439i	−1.67671	−	1.17249i
$311$		−	4.96974i		−	0.281808i	−0.990023	−	0.140904i	$-0.954999\pi$
$311$		−	4.96974i		−	0.281808i	0.990023	−	0.140904i	$-0.0450009\pi$
$312$	16.4109	−	9.51561i	0.929084	−	0.538715i
$313$		−	18.9242i		−	1.06966i	−0.844960	−	0.534829i	$-0.820376\pi$
$313$		−	18.9242i		−	1.06966i	0.844960	−	0.534829i	$-0.179624\pi$
$314$	3.01108	−	4.30596i	0.169925	−	0.242999i
$315$		0			0
$316$	−15.5680	+	5.68818i	−0.875768	+	0.319985i
$317$	−2.32340	−	2.32340i	−0.130495	−	0.130495i	0.638842	−	0.769338i	$-0.279414\pi$
$317$	−2.32340	−	2.32340i	−0.130495	−	0.130495i	−0.769338	+	0.638842i	$0.779414\pi$
$318$	−4.02923	−	22.7683i	−0.225948	−	1.27678i
$319$	0.279545			0.0156515
$320$	6.89871	+	25.3682i	0.385649	+	1.41812i
$321$	−12.5256			−0.699110
$322$		0			0
$323$	−6.75636	−	6.75636i	−0.375934	−	0.375934i
$324$	−5.78393	+	2.11331i	−0.321329	+	0.117406i
$325$	−21.4655	+	21.4655i	−1.19069	+	1.19069i
$326$	15.3147	−	21.9005i	0.848201	−	1.21296i
$327$			19.0932i			1.05586i
$328$	−25.9044	+	15.0203i	−1.43033	+	0.829357i
$329$		0			0
$330$	−2.07516	−	1.45113i	−0.114234	−	0.0798819i
$331$	−19.5108	+	19.5108i	−1.07241	+	1.07241i	−0.0752455	+	0.997165i	$0.523974\pi$
$331$	−19.5108	+	19.5108i	−1.07241	+	1.07241i	−0.997165	+	0.0752455i	$0.976026\pi$
$332$	−7.30578	−	3.39571i	−0.400957	−	0.186364i
$333$	5.21331	+	5.21331i	0.285688	+	0.285688i
$334$	6.58269	−	1.16492i	0.360189	−	0.0637415i
$335$	0.828726			0.0452781
$336$		0			0
$337$	4.93980			0.269088			0.134544	−	0.990908i	$-0.457043\pi$
$337$	4.93980			0.269088			0.134544	+	0.990908i	$0.457043\pi$
$338$	20.0582	−	3.54964i	1.09102	−	0.193075i
$339$	0.0484721	+	0.0484721i	0.00263264	+	0.00263264i
$340$	7.49328	−	16.1216i	0.406380	−	0.874316i
$341$	2.33097	−	2.33097i	0.126229	−	0.126229i
$342$	−5.56156	−	3.88910i	−0.300735	−	0.210299i
$343$		0			0
$344$	32.2782	+	8.58454i	1.74032	+	0.462848i
$345$		−	21.1992i		−	1.14133i
$346$	12.0448	−	17.2245i	0.647532	−	0.925994i
$347$	−5.31266	+	5.31266i	−0.285198	+	0.285198i	−0.835178	−	0.549980i	$-0.814635\pi$
$347$	−5.31266	+	5.31266i	−0.285198	+	0.285198i	0.549980	+	0.835178i	$0.314635\pi$
$348$	−0.578041	−	1.58204i	−0.0309862	−	0.0848064i
$349$	10.1009	+	10.1009i	0.540687	+	0.540687i	0.923730	−	0.383043i	$-0.125124\pi$
$349$	10.1009	+	10.1009i	0.540687	+	0.540687i	−0.383043	+	0.923730i	$0.625124\pi$
$350$		0			0
$351$	−29.2322			−1.56030
$352$	−2.39592	+	0.217108i	−0.127703	+	0.0115719i
$353$	−24.1905			−1.28753			−0.643766	−	0.765223i	$-0.722629\pi$
$353$	−24.1905			−1.28753			−0.643766	+	0.765223i	$0.722629\pi$
$354$	3.21320	+	18.1571i	0.170780	+	0.965038i
$355$	−14.8351	−	14.8351i	−0.787367	−	0.787367i
$356$	−0.373983	−	1.02356i	−0.0198211	−	0.0542484i
$357$		0			0
$358$	9.07781	−	12.9816i	0.479777	−	0.686099i
$359$		−	20.1894i		−	1.06555i	−0.846256	−	0.532777i	$-0.821149\pi$
$359$		−	20.1894i		−	1.06555i	0.846256	−	0.532777i	$-0.178851\pi$
$360$	3.24538	−	12.2027i	0.171046	−	0.643140i
$361$		−	6.52227i		−	0.343277i
$362$	−3.02397	−	2.11461i	−0.158937	−	0.111142i
$363$	−9.80162	+	9.80162i	−0.514451	+	0.514451i
$364$		0			0
$365$	−3.28299	−	3.28299i	−0.171840	−	0.171840i
$366$	−12.6883	+	2.24541i	−0.663229	+	0.117370i
$367$	6.44949			0.336661			0.168330	−	0.985731i	$-0.446162\pi$
$367$	6.44949			0.336661			0.168330	+	0.985731i	$0.446162\pi$
$368$	−12.9843	−	15.3963i	−0.676851	−	0.802586i
$369$	14.3823			0.748710
$370$	24.8358	−	4.39512i	1.29115	−	0.228491i
$371$		0			0
$372$	−18.0117	−	8.37181i	−0.933865	−	0.434058i
$373$	17.2319	−	17.2319i	0.892232	−	0.892232i	−0.102500	−	0.994733i	$-0.532684\pi$
$373$	17.2319	−	17.2319i	0.892232	−	0.892232i	0.994733	+	0.102500i	$0.0326843\pi$
$374$	1.33322	+	0.932296i	0.0689390	+	0.0482079i
$375$		−	3.36399i		−	0.173716i
$376$	−14.5263	−	25.0525i	−0.749137	−	1.29198i
$377$		−	3.44099i		−	0.177220i
$378$		0			0
$379$	−17.7287	+	17.7287i	−0.910663	+	0.910663i	−0.996324	−	0.0856617i	$-0.972700\pi$
$379$	−17.7287	+	17.7287i	−0.910663	+	0.910663i	0.0856617	+	0.996324i	$0.472700\pi$
$380$	−21.8061	+	7.96744i	−1.11863	+	0.408721i
$381$	5.15803	+	5.15803i	0.264254	+	0.264254i
$382$	−5.29076	−	29.8969i	−0.270699	−	1.52966i
$383$	21.6273			1.10510			0.552551	−	0.833479i	$-0.313654\pi$
$383$	21.6273			1.10510			0.552551	+	0.833479i	$0.313654\pi$
$384$	6.18295	+	13.1104i	0.315522	+	0.669037i
$385$		0			0
$386$	3.13729	+	17.7281i	0.159684	+	0.902338i
$387$	−11.3436	−	11.3436i	−0.576627	−	0.576627i
$388$	−6.90303	+	2.52220i	−0.350448	+	0.128045i
$389$	3.57958	−	3.57958i	0.181492	−	0.181492i	−0.610514	−	0.792006i	$-0.709037\pi$
$389$	3.57958	−	3.57958i	0.181492	−	0.181492i	0.792006	+	0.610514i	$0.209037\pi$
$390$	−17.8623	+	25.5437i	−0.904492	+	1.29346i
$391$			13.6197i			0.688778i
$392$		0			0
$393$			3.35181i			0.169076i
$394$	7.05844	+	4.93585i	0.355599	+	0.248665i
$395$	19.2571	−	19.2571i	0.968928	−	0.968928i
$396$	1.04783	+	0.487028i	0.0526553	+	0.0244741i
$397$	−11.4468	−	11.4468i	−0.574498	−	0.574498i	0.358884	−	0.933382i	$-0.383157\pi$
$397$	−11.4468	−	11.4468i	−0.574498	−	0.574498i	−0.933382	+	0.358884i	$0.883157\pi$
$398$	−8.16539	+	1.44500i	−0.409294	+	0.0724315i
$399$		0			0
$400$	−14.9541	−	17.7321i	−0.747707	−	0.886604i
$401$	−21.7819			−1.08774			−0.543868	−	0.839171i	$-0.683041\pi$
$401$	−21.7819			−1.08774			−0.543868	+	0.839171i	$0.683041\pi$
$402$	0.449944	−	0.0796251i	0.0224412	−	0.00397134i
$403$	−28.6925	−	28.6925i	−1.42928	−	1.42928i
$404$	−3.31749	+	7.13748i	−0.165051	+	0.355103i
$405$	7.15452	−	7.15452i	0.355511	−	0.355511i
$406$		0			0
$407$			2.30803i			0.114405i
$408$	2.51937	−	9.47293i	0.124728	−	0.468980i
$409$		−	11.7660i		−	0.581790i	−0.956755	−	0.290895i	$-0.906047\pi$
$409$		−	11.7660i		−	0.581790i	0.956755	−	0.290895i	$-0.0939531\pi$
$410$	28.1955	−	40.3205i	1.39247	−	1.99129i
$411$	12.3479	−	12.3479i	0.609075	−	0.609075i
$412$	−9.51481	−	26.0411i	−0.468761	−	1.28295i
$413$		0			0
$414$	1.68570	+	9.52550i	0.0828475	+	0.468153i
$415$	13.2374			0.649797
$416$	2.67244	+	29.4920i	0.131027	+	1.44596i
$417$	−26.3602			−1.29086
$418$	−0.370213	−	2.09199i	−0.0181077	−	0.102323i
$419$	−9.80162	−	9.80162i	−0.478840	−	0.478840i	0.425920	−	0.904761i	$-0.359950\pi$
$419$	−9.80162	−	9.80162i	−0.478840	−	0.478840i	−0.904761	+	0.425920i	$0.859950\pi$
$420$		0			0
$421$	−15.0848	+	15.0848i	−0.735188	+	0.735188i	−0.971642	−	0.236455i	$-0.924014\pi$
$421$	−15.0848	+	15.0848i	−0.735188	+	0.735188i	0.236455	+	0.971642i	$0.424014\pi$
$422$	−1.97152	+	2.81934i	−0.0959720	+	0.137243i
$423$			13.9093i			0.676291i
$424$	34.8815	+	9.27692i	1.69400	+	0.450527i
$425$			15.6860i			0.760883i
$426$	−9.47989	−	6.62912i	−0.459302	−	0.321182i
$427$		0			0
$428$	8.24135	−	17.7311i	0.398361	−	0.857063i
$429$	−2.01689	−	2.01689i	−0.0973763	−	0.0973763i
$430$	−54.0400	+	9.56328i	−2.60604	+	0.461182i
$431$	4.48903			0.216229			0.108115	−	0.994138i	$-0.465519\pi$
$431$	4.48903			0.216229			0.108115	+	0.994138i	$0.465519\pi$
$432$	1.89153	−	22.2564i	0.0910062	−	1.07081i
$433$	−24.0001			−1.15337			−0.576685	−	0.816966i	$-0.695654\pi$
$433$	−24.0001			−1.15337			−0.576685	+	0.816966i	$0.695654\pi$
$434$		0			0
$435$	1.95693	+	1.95693i	0.0938277	+	0.0938277i
$436$	−27.0281	−	12.5626i	−1.29441	−	0.601640i
$437$	12.5765	−	12.5765i	0.601617	−	0.601617i
$438$	−2.09788	−	1.46701i	−0.100241	−	0.0700967i
$439$			14.4436i			0.689356i	0.938721	+	0.344678i	$0.112012\pi$
$439$			14.4436i			0.689356i	−0.938721	+	0.344678i	$0.887988\pi$
$440$	3.41958	−	1.98279i	0.163022	−	0.0945258i
$441$		0			0
$442$	11.4759	−	16.4109i	0.545851	−	0.780587i
$443$	−5.23960	+	5.23960i	−0.248941	+	0.248941i	−0.820536	−	0.571595i	$-0.806325\pi$
$443$	−5.23960	+	5.23960i	−0.248941	+	0.248941i	0.571595	+	0.820536i	$0.306325\pi$
$444$	13.0619	−	4.77252i	0.619892	−	0.226494i
$445$	1.26610	+	1.26610i	0.0600191	+	0.0600191i
$446$	−6.69897	−	37.8544i	−0.317206	−	1.79246i
$447$	−8.83630			−0.417943
$448$		0			0
$449$	19.7284			0.931041			0.465520	−	0.885037i	$-0.345867\pi$
$449$	19.7284			0.931041			0.465520	+	0.885037i	$0.345867\pi$
$450$	1.94144	+	10.9706i	0.0915204	+	0.517161i
$451$	3.18364	+	3.18364i	0.149912	+	0.149912i
$452$	−0.100509	+	0.0367237i	−0.00472756	+	0.00172734i
$453$	0.121386	−	0.121386i	0.00570322	−	0.00570322i
$454$	17.2989	−	24.7380i	0.811876	−	1.16101i
$455$		0			0
$456$	−11.0738	+	6.42096i	−0.518577	+	0.300689i
$457$		−	1.27953i		−	0.0598541i	−0.999552	−	0.0299270i	$-0.990473\pi$
$457$		−	1.27953i		−	0.0598541i	0.999552	−	0.0299270i	$-0.00952749\pi$
$458$	3.31114	+	2.31543i	0.154720	+	0.108193i
$459$	−10.6808	+	10.6808i	−0.498535	+	0.498535i
$460$	30.0093	+	13.9483i	1.39919	+	0.650341i
$461$	−6.44148	−	6.44148i	−0.300009	−	0.300009i	0.541008	−	0.841017i	$-0.318043\pi$
$461$	−6.44148	−	6.44148i	−0.300009	−	0.300009i	−0.841017	+	0.541008i	$0.818043\pi$
$462$		0			0
$463$	12.5243			0.582055			0.291028	−	0.956715i	$-0.406003\pi$
$463$	12.5243			0.582055			0.291028	+	0.956715i	$0.406003\pi$
$464$	2.61985	+	0.222656i	0.121623	+	0.0103365i
$465$	32.6355			1.51344
$466$	−23.1446	+	4.09583i	−1.07215	+	0.189736i
$467$	26.0540	+	26.0540i	1.20564	+	1.20564i	0.972426	+	0.233210i	$0.0749230\pi$
$467$	26.0540	+	26.0540i	1.20564	+	1.20564i	0.233210	+	0.972426i	$0.425077\pi$
$468$	5.99495	−	12.8980i	0.277117	−	0.596209i
$469$		0			0
$470$	38.9944	+	27.2682i	1.79868	+	1.25779i
$471$			4.76016i			0.219337i
$472$	−27.8171	−	7.39809i	−1.28039	−	0.340525i
$473$		−	5.02201i		−	0.230912i
$474$	8.60508	−	12.3056i	0.395244	−	0.565213i
$475$	14.4846	−	14.4846i	0.664597	−	0.664597i
$476$		0			0
$477$	−12.2585	−	12.2585i	−0.561277	−	0.561277i
$478$	0.535770	+	3.02751i	0.0245055	+	0.138475i
$479$	−16.8401			−0.769442			−0.384721	−	0.923033i	$-0.625702\pi$
$479$	−16.8401			−0.769442			−0.384721	+	0.923033i	$0.625702\pi$
$480$	−18.2923	−	15.2526i	−0.834924	−	0.696182i
$481$	28.4101			1.29539
$482$	3.41008	+	19.2696i	0.155325	+	0.877707i
$483$		0			0
$484$	−7.42596	−	20.3241i	−0.337543	−	0.923824i
$485$	8.53881	−	8.53881i	0.387727	−	0.387727i
$486$	−10.3799	+	14.8436i	−0.470840	+	0.673318i
$487$		−	23.6166i		−	1.07017i	−0.844798	−	0.535086i	$-0.820279\pi$
$487$		−	23.6166i		−	1.07017i	0.844798	−	0.535086i	$-0.179721\pi$
$488$	5.16985	−	19.4388i	0.234028	−	0.879954i
$489$			24.2106i			1.09484i
$490$		0			0
$491$	−3.03082	+	3.03082i	−0.136779	+	0.136779i	−0.772181	−	0.635402i	$-0.780834\pi$
$491$	−3.03082	+	3.03082i	−0.136779	+	0.136779i	0.635402	+	0.772181i	$0.280834\pi$
$492$	11.4342	−	24.6004i	0.515495	−	1.10907i
$493$	−1.25726	−	1.25726i	−0.0566240	−	0.0566240i
$494$	−25.7508	+	4.55704i	−1.15858	+	0.205031i
$495$	−1.89856			−0.0853341
$496$	23.7021	−	19.9889i	1.06425	−	0.897526i
$497$		0			0
$498$	7.18702	−	1.27186i	0.322058	−	0.0569936i
$499$	−6.99004	−	6.99004i	−0.312917	−	0.312917i	0.533121	−	0.846039i	$-0.321019\pi$
$499$	−6.99004	−	6.99004i	−0.312917	−	0.312917i	−0.846039	+	0.533121i	$0.821019\pi$
$500$	4.76202	+	2.21337i	0.212964	+	0.0989851i
$501$	−4.28242	+	4.28242i	−0.191325	+	0.191325i
$502$	−15.8260	−	11.0669i	−0.706350	−	0.493939i
$503$		−	23.6060i		−	1.05254i	−0.850318	−	0.526269i	$-0.823590\pi$
$503$		−	23.6060i		−	1.05254i	0.850318	−	0.526269i	$-0.176410\pi$
$504$		0			0
$505$		−	12.9324i		−	0.575486i
$506$	−1.73541	+	2.48170i	−0.0771484	+	0.110325i
$507$	−13.0490	+	13.0490i	−0.579528	+	0.579528i
$508$	−10.6954	+	3.90786i	−0.474533	+	0.173383i
$509$	−11.6259	−	11.6259i	−0.515311	−	0.515311i	0.400838	−	0.916149i	$-0.368719\pi$
$509$	−11.6259	−	11.6259i	−0.515311	−	0.515311i	−0.916149	+	0.400838i	$0.868719\pi$
$510$	2.80661	+	15.8595i	0.124279	+	0.702272i
$511$		0			0
$512$	−22.6271	+	0.126366i	−0.999984	+	0.00558463i
$513$	19.7254			0.870896
$514$	4.13134	+	23.3453i	0.182226	+	1.02972i
$515$	32.2120	+	32.2120i	1.41943	+	1.41943i
$516$	−28.4213	+	10.3845i	−1.25118	+	0.457151i
$517$	−3.07894	+	3.07894i	−0.135411	+	0.135411i
$518$		0			0
$519$			19.0414i			0.835824i
$520$	−24.4067	−	42.0924i	−1.07030	−	1.84587i
$521$		−	44.6289i		−	1.95523i	−0.210408	−	0.977614i	$-0.567479\pi$
$521$		−	44.6289i		−	1.95523i	0.210408	−	0.977614i	$-0.432521\pi$
$522$	−1.03492	−	0.723704i	−0.0452973	−	0.0316757i
$523$	−10.5513	+	10.5513i	−0.461375	+	0.461375i	−0.899106	−	0.437731i	$-0.855782\pi$
$523$	−10.5513	+	10.5513i	−0.461375	+	0.461375i	0.437731	+	0.899106i	$0.355782\pi$
$524$	−4.74478	−	2.20536i	−0.207277	−	0.0963417i
$525$		0			0
$526$	−14.5984	+	2.58343i	−0.636520	+	0.112643i
$527$	−20.9671			−0.913342
$528$	1.66610	−	1.40508i	0.0725075	−	0.0611483i
$529$	−2.35224			−0.102271
$530$	−58.3985	+	10.3346i	−2.53667	+	0.448906i
$531$	9.77581	+	9.77581i	0.424234	+	0.424234i
$532$		0			0
$533$	39.1882	−	39.1882i	1.69743	−	1.69743i
$534$	0.809060	+	0.565762i	0.0350115	+	0.0244829i
$535$			32.1270i			1.38897i
$536$	−0.183329	+	0.689325i	−0.00791862	+	0.0297743i
$537$			14.3509i			0.619288i
$538$	−5.31320	+	7.59807i	−0.229068	+	0.327576i
$539$		0			0
$540$	12.5953	+	34.4721i	0.542016	+	1.48344i
$541$	22.3446	+	22.3446i	0.960670	+	0.960670i	0.999255	−	0.0385851i	$-0.0122851\pi$
$541$	22.3446	+	22.3446i	0.960670	+	0.960670i	−0.0385851	+	0.999255i	$0.512285\pi$
$542$	2.13051	+	12.0390i	0.0915132	+	0.517121i
$543$	3.34295			0.143460
$544$	11.7521	+	9.79922i	0.503867	+	0.420138i
$545$	48.9723			2.09774
$546$		0			0
$547$	13.2104	+	13.2104i	0.564836	+	0.564836i	0.930677	−	0.365841i	$-0.119219\pi$
$547$	13.2104	+	13.2104i	0.564836	+	0.564836i	−0.365841	+	0.930677i	$0.619219\pi$
$548$	9.35506	+	25.6039i	0.399628	+	1.09374i
$549$	−6.83142	+	6.83142i	−0.291558	+	0.291558i
$550$	−1.99869	+	2.85820i	−0.0852246	+	0.121874i
$551$			2.32192i			0.0989170i
$552$	17.6333	+	4.68966i	0.750522	+	0.199605i
$553$		0			0
$554$	13.0256	+	9.10858i	0.553405	+	0.386987i
$555$	−16.1571	+	16.1571i	−0.685833	+	0.685833i
$556$	17.3440	−	37.3151i	0.735549	−	1.58251i
$557$	−9.24770	−	9.24770i	−0.391838	−	0.391838i	0.483504	−	0.875342i	$-0.339364\pi$
$557$	−9.24770	−	9.24770i	−0.391838	−	0.391838i	−0.875342	+	0.483504i	$0.839364\pi$
$558$	−14.6642	+	2.59508i	−0.620785	+	0.109858i
$559$	−61.8171			−2.61459
$560$		0			0
$561$	−1.47385			−0.0622259
$562$	13.1815	−	2.33268i	0.556026	−	0.0983982i
$563$	4.69823	+	4.69823i	0.198007	+	0.198007i	0.799145	−	0.601138i	$-0.205286\pi$
$563$	4.69823	+	4.69823i	0.198007	+	0.198007i	−0.601138	+	0.799145i	$0.705286\pi$
$564$	23.7914	+	11.0582i	1.00180	+	0.465633i
$565$	0.124326	−	0.124326i	0.00523045	−	0.00523045i
$566$	−11.2198	−	7.84579i	−0.471602	−	0.329783i
$567$		0			0
$568$	15.6215	−	9.05790i	0.655464	−	0.380061i
$569$		−	43.0920i		−	1.80651i	−0.429103	−	0.903256i	$-0.641170\pi$
$569$		−	43.0920i		−	1.80651i	0.429103	−	0.903256i	$-0.358830\pi$
$570$	12.0531	−	17.2364i	0.504851	−	0.721955i
$571$	16.6719	−	16.6719i	0.697699	−	0.697699i	−0.266215	−	0.963914i	$-0.585773\pi$
$571$	16.6719	−	16.6719i	0.697699	−	0.697699i	0.963914	+	0.266215i	$0.0857730\pi$
$572$	4.18212	−	1.52805i	0.174863	−	0.0638909i
$573$	19.4497	+	19.4497i	0.812521	+	0.812521i
$574$		0			0
$575$	−29.1985			−1.21766
$576$	9.43215	+	5.39893i	0.393006	+	0.224956i
$577$	33.3064			1.38657			0.693283	−	0.720666i	$-0.256164\pi$
$577$	33.3064			1.38657			0.693283	+	0.720666i	$0.256164\pi$
$578$	2.38633	+	13.4846i	0.0992583	+	0.560887i
$579$	−11.5332	−	11.5332i	−0.479303	−	0.479303i
$580$	−4.05779	+	1.48262i	−0.168491	+	0.0615625i
$581$		0			0
$582$	3.81559	−	5.45643i	0.158161	−	0.226176i
$583$		−	5.42705i		−	0.224765i
$584$	3.45701	−	2.00450i	0.143052	−	0.0829467i
$585$			23.3699i			0.966226i
$586$	32.8989	+	23.0056i	1.35904	+	0.950353i
$587$	9.82134	−	9.82134i	0.405370	−	0.405370i	−0.474750	−	0.880121i	$-0.657462\pi$
$587$	9.82134	−	9.82134i	0.405370	−	0.405370i	0.880121	+	0.474750i	$0.157462\pi$
$588$		0			0
$589$	19.3612	+	19.3612i	0.797763	+	0.797763i
$590$	46.5712	−	8.24156i	1.91731	−	0.339300i
$591$	−7.80298			−0.320972
$592$	−1.83833	+	21.6304i	−0.0755549	+	0.889006i
$593$	−28.4089			−1.16661			−0.583307	−	0.812251i	$-0.698242\pi$
$593$	−28.4089			−1.16661			−0.583307	+	0.812251i	$0.698242\pi$
$594$	−3.30711	+	0.585249i	−0.135692	+	0.0240131i
$595$		0			0
$596$	5.81395	−	12.5086i	0.238148	−	0.512370i
$597$	5.31206	−	5.31206i	0.217408	−	0.217408i
$598$	30.5479	+	21.3616i	1.24919	+	0.873541i
$599$			2.21791i			0.0906213i	0.998973	+	0.0453106i	$0.0144278\pi$
$599$			2.21791i			0.0906213i	−0.998973	+	0.0453106i	$0.985572\pi$
$600$	20.3085	+	5.40114i	0.829090	+	0.220501i
$601$			41.6237i			1.69787i	0.528501	+	0.848933i	$0.322754\pi$
$601$			41.6237i			1.69787i	−0.528501	+	0.848933i	$0.677246\pi$
$602$		0			0
$603$	0.242251	−	0.242251i	0.00986521	−	0.00986521i
$604$	0.0919653	+	0.251700i	0.00374201	+	0.0102415i
$605$	25.1402	+	25.1402i	1.02210	+	1.02210i
$606$	−1.24257	−	7.02146i	−0.0504758	−	0.285227i
$607$	−7.17022			−0.291030			−0.145515	−	0.989356i	$-0.546484\pi$
$607$	−7.17022			−0.291030			−0.145515	+	0.989356i	$0.546484\pi$
$608$	−1.80331	−	19.9006i	−0.0731340	−	0.807077i
$609$		0			0
$610$	5.75927	+	32.5443i	0.233186	+	1.31768i
$611$	37.8994	+	37.8994i	1.53325	+	1.53325i
$612$	−2.52220	−	6.90303i	−0.101954	−	0.279038i
$613$	−18.0645	+	18.0645i	−0.729616	+	0.729616i	−0.970543	−	0.240927i	$-0.922549\pi$
$613$	−18.0645	+	18.0645i	−0.729616	+	0.729616i	0.240927	+	0.970543i	$0.422549\pi$
$614$	21.2000	−	30.3168i	0.855562	−	1.22348i
$615$			44.5736i			1.79738i
$616$		0			0
$617$		−	17.1272i		−	0.689513i	−0.938692	−	0.344757i	$-0.887961\pi$
$617$		−	17.1272i		−	0.689513i	0.938692	−	0.344757i	$-0.112039\pi$
$618$	20.5839	+	14.3940i	0.828008	+	0.579012i
$619$	−6.69394	+	6.69394i	−0.269052	+	0.269052i	−0.828718	−	0.559666i	$-0.810929\pi$
$619$	−6.69394	+	6.69394i	−0.269052	+	0.269052i	0.559666	+	0.828718i	$0.310929\pi$
$620$	−21.4729	+	46.1984i	−0.862373	+	1.85537i
$621$	−19.8816	−	19.8816i	−0.797820	−	0.797820i
$622$	−6.92074	+	1.22474i	−0.277496	+	0.0491077i
$623$		0			0
$624$	−17.2955	−	20.5084i	−0.692374	−	0.820993i
$625$	20.3666			0.814666
$626$	−26.3534	+	4.66367i	−1.05329	+	0.186398i
$627$	1.36096	+	1.36096i	0.0543515	+	0.0543515i
$628$	−6.73842	−	3.13200i	−0.268892	−	0.124981i
$629$	10.3804	−	10.3804i	0.413893	−	0.413893i
$630$		0			0
$631$			18.0767i			0.719622i	0.933025	+	0.359811i	$0.117159\pi$
$631$			18.0767i			0.719622i	−0.933025	+	0.359811i	$0.882841\pi$
$632$	11.7578	+	20.2778i	0.467700	+	0.806609i
$633$		−	3.11673i		−	0.123879i
$634$	−2.66294	+	3.80809i	−0.105759	+	0.151239i
$635$	13.2299	−	13.2299i	0.525012	−	0.525012i
$636$	−30.7136	+	11.2220i	−1.21787	+	0.444982i
$637$		0			0
$638$	−0.0688910	−	0.389288i	−0.00272742	−	0.0154120i
$639$	−8.67313			−0.343104
$640$	33.6270	−	15.8587i	1.32922	−	0.626870i
$641$	17.0007			0.671487			0.335744	−	0.941953i	$-0.391012\pi$
$641$	17.0007			0.671487			0.335744	+	0.941953i	$0.391012\pi$
$642$	3.08680	+	17.4428i	0.121826	+	0.688413i
$643$	5.91368	+	5.91368i	0.233213	+	0.233213i	0.814032	−	0.580820i	$-0.197268\pi$
$643$	5.91368	+	5.91368i	0.233213	+	0.233213i	−0.580820	+	0.814032i	$0.697268\pi$
$644$		0			0
$645$	35.1561	−	35.1561i	1.38427	−	1.38427i
$646$	−7.74370	+	11.0738i	−0.304672	+	0.435692i
$647$		−	39.1001i		−	1.53718i	−0.639739	−	0.768592i	$-0.720958\pi$
$647$		−	39.1001i		−	1.53718i	0.639739	−	0.768592i	$-0.279042\pi$
$648$	4.36834	+	7.53376i	0.171604	+	0.295954i
$649$			4.32793i			0.169886i
$650$	35.1824	+	24.6024i	1.37997	+	0.964987i
$651$		0			0
$652$	−34.2723	−	15.9297i	−1.34221	−	0.623854i
$653$	−15.1966	−	15.1966i	−0.594691	−	0.594691i	0.344204	−	0.938895i	$-0.388149\pi$
$653$	−15.1966	−	15.1966i	−0.594691	−	0.594691i	−0.938895	+	0.344204i	$0.888149\pi$
$654$	26.5888	−	4.70533i	1.03970	−	0.183993i
$655$	8.59708			0.335916
$656$	27.3008	+	32.3723i	1.06592	+	1.26393i
$657$	−1.91935			−0.0748810
$658$		0			0
$659$	−6.07124	−	6.07124i	−0.236502	−	0.236502i	0.578898	−	0.815400i	$-0.303483\pi$
$659$	−6.07124	−	6.07124i	−0.236502	−	0.236502i	−0.815400	+	0.578898i	$0.803483\pi$
$660$	−1.50940	+	3.24744i	−0.0587534	+	0.126406i
$661$	7.71469	−	7.71469i	0.300067	−	0.300067i	−0.540973	−	0.841040i	$-0.681944\pi$
$661$	7.71469	−	7.71469i	0.300067	−	0.300067i	0.841040	+	0.540973i	$0.181944\pi$
$662$	31.9785	+	22.3620i	1.24288	+	0.869125i
$663$			18.1420i			0.704575i
$664$	−2.92835	+	11.0107i	−0.113642	+	0.427298i
$665$		0			0
$666$	5.97517	−	8.54470i	0.231533	−	0.331100i
$667$	2.34030	−	2.34030i	0.0906169	−	0.0906169i
$668$	−3.24447	−	8.87981i	−0.125532	−	0.343570i
$669$	24.6265	+	24.6265i	0.952115	+	0.952115i
$670$	−0.204231	−	1.15406i	−0.00789013	−	0.0445854i
$671$	−3.02439			−0.116755
$672$		0			0
$673$	36.3104			1.39966			0.699831	−	0.714308i	$-0.253259\pi$
$673$	36.3104			1.39966			0.699831	+	0.714308i	$0.253259\pi$
$674$	−1.21736	−	6.87905i	−0.0468911	−	0.264971i
$675$	−22.8979	−	22.8979i	−0.881339	−	0.881339i
$676$	−9.88628	−	27.0578i	−0.380242	−	1.04068i
$677$	23.9019	−	23.9019i	0.918626	−	0.918626i	−0.0783033	−	0.996930i	$-0.524950\pi$
$677$	23.9019	−	23.9019i	0.918626	−	0.918626i	0.996930	+	0.0783033i	$0.0249502\pi$
$678$	0.0555556	−	0.0794465i	0.00213360	−	0.00305113i
$679$		0			0
$680$	−24.2972	−	6.46196i	−0.931755	−	0.247805i
$681$			27.3474i			1.04796i
$682$	−3.82050	−	2.67161i	−0.146294	−	0.102301i
$683$	9.10864	−	9.10864i	0.348533	−	0.348533i	−0.511030	−	0.859563i	$-0.670736\pi$
$683$	9.10864	−	9.10864i	0.348533	−	0.348533i	0.859563	+	0.511030i	$0.170736\pi$
$684$	−4.04528	+	8.70332i	−0.154675	+	0.332780i
$685$	−31.6711	−	31.6711i	−1.21009	−	1.21009i
$686$		0			0
$687$	−3.66041			−0.139653
$688$	4.00000	−	47.0654i	0.152499	−	1.79435i
$689$	−66.8029			−2.54499
$690$	−29.5215	+	5.22433i	−1.12386	+	0.198887i
$691$	29.0434	+	29.0434i	1.10486	+	1.10486i	0.993815	+	0.111047i	$0.0354205\pi$
$691$	29.0434	+	29.0434i	1.10486	+	1.10486i	0.111047	+	0.993815i	$0.464579\pi$
$692$	−26.9547	−	12.5285i	−1.02466	−	0.476262i
$693$		0			0
$694$	8.70753	+	6.08903i	0.330533	+	0.231136i
$695$			67.6114i			2.56465i
$696$	−2.06066	+	1.19484i	−0.0781092	+	0.0452904i
$697$		−	28.6369i		−	1.08470i
$698$	11.5770	−	16.5555i	0.438195	−	0.626634i
$699$	15.0569	−	15.0569i	0.569505	−	0.569505i
$700$		0			0
$701$	−13.5706	−	13.5706i	−0.512556	−	0.512556i	0.402753	−	0.915309i	$-0.368054\pi$
$701$	−13.5706	−	13.5706i	−0.512556	−	0.512556i	−0.915309	+	0.402753i	$0.868054\pi$
$702$	7.20398	+	40.7081i	0.271897	+	1.53643i
$703$	−19.1706			−0.723033
$704$	0.892789	+	3.28299i	0.0336483	+	0.123732i
$705$	−43.1077			−1.62353
$706$	5.96151	+	33.6871i	0.224364	+	1.26783i
$707$		0			0
$708$	24.4933	−	8.94925i	0.920513	−	0.336334i
$709$	11.5928	−	11.5928i	0.435375	−	0.435375i	−0.455077	−	0.890452i	$-0.650388\pi$
$709$	11.5928	−	11.5928i	0.435375	−	0.435375i	0.890452	+	0.455077i	$0.150388\pi$
$710$	−17.0031	+	24.3150i	−0.638115	+	0.912527i
$711$		−	11.2583i		−	0.422221i
$712$	−1.33322	+	0.773045i	−0.0499644	+	0.0289711i
$713$		−	39.0290i		−	1.46165i
$714$		0			0
$715$	−5.17313	+	5.17313i	−0.193464	+	0.193464i
$716$	−20.3150	−	9.44236i	−0.759207	−	0.352878i
$717$	−1.96957	−	1.96957i	−0.0735551	−	0.0735551i
$718$	−28.1152	+	4.97546i	−1.04925	+	0.185682i
$719$	−40.8361			−1.52293			−0.761464	−	0.648207i	$-0.775519\pi$
$719$	−40.8361			−1.52293			−0.761464	+	0.648207i	$0.775519\pi$
$720$	−17.7930	−	1.51220i	−0.663106	−	0.0563562i
$721$		0			0
$722$	−9.08276	+	1.60735i	−0.338025	+	0.0598193i
$723$	−12.5360	−	12.5360i	−0.466219	−	0.466219i
$724$	−2.19953	+	4.73224i	−0.0817450	+	0.175872i
$725$	2.69536	−	2.69536i	0.100103	−	0.100103i
$726$	16.0650	+	11.2340i	0.596228	+	0.416932i
$727$		−	29.6262i		−	1.09878i	−0.835567	−	0.549388i	$-0.814861\pi$
$727$		−	29.6262i		−	1.09878i	0.835567	−	0.549388i	$-0.185139\pi$
$728$		0			0
$729$		−	25.6462i		−	0.949859i
$730$	−3.76276	+	5.38088i	−0.139266	+	0.199155i
$731$	−22.5865	+	22.5865i	−0.835393	+	0.835393i
$732$	6.25381	+	17.1161i	0.231148	+	0.632629i
$733$	−8.48565	−	8.48565i	−0.313425	−	0.313425i	0.532810	−	0.846235i	$-0.321136\pi$
$733$	−8.48565	−	8.48565i	−0.313425	−	0.313425i	−0.846235	+	0.532810i	$0.821136\pi$
$734$	−1.58941	−	8.98140i	−0.0586662	−	0.331510i
$735$		0			0
$736$	−18.2406	+	21.8758i	−0.672358	+	0.806353i
$737$	0.107249			0.00395056
$738$	−3.54436	−	20.0284i	−0.130470	−	0.737255i
$739$	−21.7402	−	21.7402i	−0.799727	−	0.799727i	0.183325	−	0.983052i	$-0.441314\pi$
$739$	−21.7402	−	21.7402i	−0.799727	−	0.799727i	−0.983052	+	0.183325i	$0.941314\pi$
$740$	−12.2411	−	33.5026i	−0.449991	−	1.23158i
$741$	16.7524	−	16.7524i	0.615415	−	0.615415i
$742$		0			0
$743$		−	33.3740i		−	1.22437i	−0.790714	−	0.612186i	$-0.790290\pi$
$743$		−	33.3740i		−	1.22437i	0.790714	−	0.612186i	$-0.209710\pi$
$744$	−7.21958	+	27.1459i	−0.264682	+	0.995215i
$745$			22.6643i			0.830355i
$746$	−28.2433	−	19.7501i	−1.03406	−	0.723101i
$747$	3.86951	−	3.86951i	0.141578	−	0.141578i
$748$	0.969735	−	2.08636i	0.0354570	−	0.0762849i
$749$		0			0
$750$	−4.68461	+	0.829020i	−0.171058	+	0.0302715i
$751$	−44.8823			−1.63778			−0.818889	−	0.573951i	$-0.805410\pi$
$751$	−44.8823			−1.63778			−0.818889	+	0.573951i	$0.805410\pi$
$752$	−31.3076	+	26.4029i	−1.14167	+	0.962815i
$753$	17.4954			0.637567
$754$	−4.79184	+	0.847997i	−0.174508	+	0.0308822i
$755$	−0.311344	−	0.311344i	−0.0113310	−	0.0113310i
$756$		0			0
$757$	1.21561	−	1.21561i	0.0441819	−	0.0441819i	−0.684671	−	0.728853i	$-0.740054\pi$
$757$	1.21561	−	1.21561i	0.0441819	−	0.0441819i	0.728853	+	0.684671i	$0.240054\pi$
$758$	29.0576	+	20.3195i	1.05542	+	0.738038i
$759$		−	2.74347i		−	0.0995818i
$760$	16.4692	+	28.4032i	0.597400	+	1.03029i
$761$			1.31035i			0.0475003i	0.999718	+	0.0237501i	$0.00756061\pi$
$761$			1.31035i			0.0475003i	−0.999718	+	0.0237501i	$0.992439\pi$
$762$	5.91181	−	8.45410i	0.214162	−	0.306260i
$763$		0			0
$764$	−40.3298	+	14.7356i	−1.45908	+	0.533114i
$765$	8.53881	+	8.53881i	0.308721	+	0.308721i
$766$	−5.32982	−	30.1176i	−0.192574	−	1.08819i
$767$	53.2735			1.92360
$768$	16.7335	−	11.8412i	0.603818	−	0.427281i
$769$	12.6459			0.456022			0.228011	−	0.973659i	$-0.426778\pi$
$769$	12.6459			0.456022			0.228011	+	0.973659i	$0.426778\pi$
$770$		0			0
$771$	−15.1875	−	15.1875i	−0.546963	−	0.546963i
$772$	23.9146	−	8.73783i	0.860706	−	0.314481i
$773$	11.6533	−	11.6533i	0.419139	−	0.419139i	−0.465768	−	0.884907i	$-0.654222\pi$
$773$	11.6533	−	11.6533i	0.419139	−	0.419139i	0.884907	+	0.465768i	$0.154222\pi$
$774$	−13.0013	+	18.5923i	−0.467322	+	0.668287i
$775$		−	44.9502i		−	1.61466i
$776$	5.21354	+	8.99142i	0.187155	+	0.322773i
$777$		0			0
$778$	−5.86699	−	4.10269i	−0.210342	−	0.147088i
$779$	−26.4435	+	26.4435i	−0.947437	+	0.947437i
$780$	39.9735	+	18.5796i	1.43128	+	0.665257i
$781$	−1.91987	−	1.91987i	−0.0686985	−	0.0686985i
$782$	18.9665	−	3.35644i	0.678240	−	0.120026i
$783$	3.67059			0.131176
$784$		0			0
$785$	12.2094			0.435771
$786$	4.66765	−	0.826019i	0.166490	−	0.0294631i
$787$	13.7215	+	13.7215i	0.489117	+	0.489117i	0.908028	−	0.418910i	$-0.137588\pi$
$787$	13.7215	+	13.7215i	0.489117	+	0.489117i	−0.418910	+	0.908028i	$0.637588\pi$
$788$	5.13406	−	11.0458i	0.182893	−	0.393491i
$789$	9.49710	−	9.49710i	0.338106	−	0.338106i
$790$	−31.5626	−	22.0712i	−1.12295	−	0.785259i
$791$		0			0
$792$	0.419997	−	1.57920i	0.0149239	−	0.0561145i
$793$			37.2280i			1.32200i
$794$	−13.1196	+	18.7615i	−0.465597	+	0.665820i
$795$	37.9916	−	37.9916i	1.34742	−	1.34742i
$796$	4.02455	+	11.0148i	0.142647	+	0.390410i
$797$	−13.4205	−	13.4205i	−0.475377	−	0.475377i	0.428272	−	0.903650i	$-0.359122\pi$
$797$	−13.4205	−	13.4205i	−0.475377	−	0.475377i	−0.903650	+	0.428272i	$0.859122\pi$
$798$		0			0
$799$	27.6951			0.979782
$800$	−21.0080	+	25.1947i	−0.742744	+	0.890766i
$801$	0.740207			0.0261539
$802$	5.36793	+	30.3329i	0.189548	+	1.07109i
$803$	−0.424865	−	0.424865i	−0.0149932	−	0.0149932i
$804$	−0.221768	−	0.606958i	−0.00782116	−	0.0214058i
$805$		0			0
$806$	−32.8855	+	47.0274i	−1.15834	+	1.65647i
$807$		−	8.39954i		−	0.295678i
$808$	10.7570	+	2.86089i	0.378432	+	0.100646i
$809$			22.3697i			0.786476i	0.919437	+	0.393238i	$0.128645\pi$
$809$			22.3697i			0.786476i	−0.919437	+	0.393238i	$0.871355\pi$
$810$	−11.7264	−	8.20005i	−0.412023	−	0.288120i
$811$	5.78629	−	5.78629i	0.203184	−	0.203184i	−0.598179	−	0.801363i	$-0.704109\pi$
$811$	5.78629	−	5.78629i	0.203184	−	0.203184i	0.801363	+	0.598179i	$0.204109\pi$
$812$		0			0
$813$	−7.83209	−	7.83209i	−0.274683	−	0.274683i
$814$	3.21410	−	0.568790i	0.112654	−	0.0199361i
$815$	62.0981			2.17520
$816$	−13.8126	−	1.17391i	−0.483539	−	0.0410951i
$817$	41.7131			1.45936
$818$	−16.3850	+	2.89961i	−0.572889	+	0.101382i
$819$		0			0
$820$	−63.0978	−	29.3277i	−2.20347	−	1.02417i
$821$	−20.5635	+	20.5635i	−0.717670	+	0.717670i	−0.968128	−	0.250457i	$-0.919419\pi$
$821$	−20.5635	+	20.5635i	−0.717670	+	0.717670i	0.250457	+	0.968128i	$0.419419\pi$
$822$	−20.2383	−	14.1523i	−0.705893	−	0.493619i
$823$			16.8580i			0.587632i	0.955862	+	0.293816i	$0.0949253\pi$
$823$			16.8580i			0.587632i	−0.955862	+	0.293816i	$0.905075\pi$
$824$	−33.9194	+	19.6677i	−1.18164	+	0.685155i
$825$		−	3.15970i		−	0.110006i
$826$		0			0
$827$	−26.8509	+	26.8509i	−0.933697	+	0.933697i	−0.997935	−	0.0642374i	$-0.979539\pi$
$827$	−26.8509	+	26.8509i	−0.933697	+	0.933697i	0.0642374	+	0.997935i	$0.479539\pi$
$828$	12.8496	−	4.69492i	0.446553	−	0.163160i
$829$	−7.12663	−	7.12663i	−0.247518	−	0.247518i	0.572433	−	0.819951i	$-0.306000\pi$
$829$	−7.12663	−	7.12663i	−0.247518	−	0.247518i	−0.819951	+	0.572433i	$0.806000\pi$
$830$	−3.26221	−	18.4340i	−0.113233	−	0.639855i
$831$	−14.3996			−0.499516
$832$	40.4112	−	10.9896i	1.40101	−	0.380995i
$833$		0			0
$834$	6.49619	+	36.7085i	0.224945	+	1.27111i
$835$	10.9840	+	10.9840i	0.380118	+	0.380118i
$836$	−2.82202	+	1.03110i	−0.0976015	+	0.0356613i
$837$	30.6070	−	30.6070i	1.05793	−	1.05793i
$838$	−11.2340	+	16.0650i	−0.388072	+	0.554956i
$839$			10.3160i			0.356150i	0.984017	+	0.178075i	$0.0569869\pi$
$839$			10.3160i			0.356150i	−0.984017	+	0.178075i	$0.943013\pi$
$840$		0			0
$841$		−	28.5679i		−	0.985101i
$842$	24.7242	+	17.2892i	0.852052	+	0.595826i
$843$	−8.57531	+	8.57531i	−0.295349	+	0.295349i
$844$	4.41201	+	2.05069i	0.151868	+	0.0705877i
$845$	33.4695	+	33.4695i	1.15139	+	1.15139i
$846$	19.3697	−	3.42779i	0.665944	−	0.117850i
$847$		0			0
$848$	4.32261	−	50.8614i	0.148439	−	1.74659i
$849$	12.4033			0.425678
$850$	21.8439	−	3.86566i	0.749241	−	0.132591i
$851$	19.3224	+	19.3224i	0.662364	+	0.662364i
$852$	−6.89534	+	14.8351i	−0.236230	+	0.508244i
$853$	−1.19902	+	1.19902i	−0.0410536	+	0.0410536i	−0.727336	−	0.686282i	$-0.759242\pi$
$853$	−1.19902	+	1.19902i	−0.0410536	+	0.0410536i	0.686282	+	0.727336i	$0.259242\pi$
$854$		0			0
$855$		−	15.7696i		−	0.539308i
$856$	−26.7228	−	7.10707i	−0.913368	−	0.242915i
$857$			23.2444i			0.794012i	0.917816	+	0.397006i	$0.129951\pi$
$857$			23.2444i			0.794012i	−0.917816	+	0.397006i	$0.870049\pi$
$858$	−2.31163	+	3.30571i	−0.0789177	+	0.112855i
$859$	22.0844	−	22.0844i	0.753512	−	0.753512i	−0.221621	−	0.975133i	$-0.571135\pi$
$859$	22.0844	−	22.0844i	0.753512	−	0.753512i	0.975133	+	0.221621i	$0.0711348\pi$
$860$	26.6352	+	72.8980i	0.908252	+	2.48580i
$861$		0			0
$862$	−1.10628	−	6.25132i	−0.0376799	−	0.212921i
$863$	32.6633			1.11187			0.555936	−	0.831225i	$-0.312360\pi$
$863$	32.6633			1.11187			0.555936	+	0.831225i	$0.312360\pi$
$864$	−31.4598	+	2.85076i	−1.07029	+	0.0969849i
$865$	48.8394			1.66059
$866$	5.91458	+	33.4219i	0.200985	+	1.13572i
$867$	−8.77254	−	8.77254i	−0.297931	−	0.297931i
$868$		0			0
$869$	2.49213	−	2.49213i	0.0845398	−	0.0845398i
$870$	2.24291	−	3.20744i	0.0760417	−	0.108742i
$871$		−	1.32015i		−	0.0447316i
$872$	−10.8336	+	40.7346i	−0.366871	+	1.37945i
$873$		−	4.99208i		−	0.168956i
$874$	−20.6131	−	14.4144i	−0.697250	−	0.487575i
$875$		0			0
$876$	−1.52593	+	3.28299i	−0.0515563	+	0.110922i
$877$	−18.7824	−	18.7824i	−0.634238	−	0.634238i	0.314890	−	0.949128i	$-0.398032\pi$
$877$	−18.7824	−	18.7824i	−0.634238	−	0.634238i	−0.949128	+	0.314890i	$0.898032\pi$
$878$	20.1138	−	3.55948i	0.678809	−	0.120127i
$879$	−36.3691			−1.22670
$880$	−3.60390	−	4.27338i	−0.121488	−	0.144056i
$881$	−37.5249			−1.26424			−0.632122	−	0.774869i	$-0.717816\pi$
$881$	−37.5249			−1.26424			−0.632122	+	0.774869i	$0.717816\pi$
$882$		0			0
$883$	20.1752	+	20.1752i	0.678950	+	0.678950i	0.959763	−	0.280812i	$-0.0906039\pi$
$883$	20.1752	+	20.1752i	0.678950	+	0.678950i	−0.280812	+	0.959763i	$0.590604\pi$
$884$	−25.6815	−	11.9367i	−0.863763	−	0.401475i
$885$	−30.2973	+	30.2973i	−1.01843	+	1.01843i
$886$	8.58779	+	6.00530i	0.288512	+	0.201752i
$887$		−	9.35833i		−	0.314222i	−0.987581	−	0.157111i	$-0.949782\pi$
$887$		−	9.35833i		−	0.314222i	0.987581	−	0.157111i	$-0.0502180\pi$
$888$	−9.86508	−	17.0136i	−0.331050	−	0.570939i
$889$		0			0
$890$	1.45113	−	2.07516i	0.0486419	−	0.0695597i
$891$	0.925895	−	0.925895i	0.0310186	−	0.0310186i
$892$	−51.0642	+	18.6577i	−1.70976	+	0.624704i
$893$	−25.5738	−	25.5738i	−0.855796	−	0.855796i
$894$	2.17762	+	12.3052i	0.0728304	+	0.411548i
$895$	36.8088			1.23038
$896$		0			0
$897$	−33.7701			−1.12755
$898$	−4.86186	−	27.4733i	−0.162242	−	0.916795i
$899$	3.60282	+	3.60282i	0.120161	+	0.120161i
$900$	14.7990	−	5.40721i	0.493300	−	0.180240i
$901$	−24.4082	+	24.4082i	−0.813155	+	0.813155i
$902$	3.64888	−	5.21804i	0.121495	−	0.173742i
$903$		0			0
$904$	0.0759100	+	0.130917i	0.00252473	+	0.00435422i
$905$		−	8.57436i		−	0.285021i
$906$	−0.198954	−	0.139125i	−0.00660980	−	0.00462212i
$907$	8.35250	−	8.35250i	0.277340	−	0.277340i	−0.554706	−	0.832046i	$-0.687169\pi$
$907$	8.35250	−	8.35250i	0.277340	−	0.277340i	0.832046	+	0.554706i	$0.187169\pi$
$908$	−38.7127	−	17.9936i	−1.28472	−	0.597137i
$909$	−3.78037	−	3.78037i	−0.125387	−	0.125387i
$910$		0			0
$911$	−29.8691			−0.989608			−0.494804	−	0.869004i	$-0.664760\pi$
$911$	−29.8691			−0.989608			−0.494804	+	0.869004i	$0.664760\pi$
$912$	11.6707	+	13.8387i	0.386455	+	0.458245i
$913$	1.71310			0.0566954
$914$	−1.78185	+	0.315328i	−0.0589383	+	0.0104301i
$915$	−21.1720	−	21.1720i	−0.699924	−	0.699924i
$916$	2.40841	−	5.18163i	0.0795761	−	0.171206i
$917$		0			0
$918$	17.5059	+	12.2416i	0.577782	+	0.404033i
$919$			48.3175i			1.59385i	0.604081	+	0.796923i	$0.293540\pi$
$919$			48.3175i			1.59385i	−0.604081	+	0.796923i	$0.706460\pi$
$920$	12.0285	−	45.2277i	0.396569	−	1.49111i
$921$			33.5146i			1.10434i
$922$	−7.38281	+	10.5577i	−0.243140	+	0.347699i
$923$	−23.6322	+	23.6322i	−0.777864	+	0.777864i
$924$		0			0
$925$	22.2539	+	22.2539i	0.731703	+	0.731703i
$926$	−3.08649	−	17.4411i	−0.101428	−	0.573150i
$927$	18.8322			0.618531
$928$	−0.335569	−	3.70321i	−0.0110156	−	0.121564i
$929$	43.8732			1.43943			0.719716	−	0.694269i	$-0.244272\pi$
$929$	43.8732			1.43943			0.719716	+	0.694269i	$0.244272\pi$
$930$	−8.04269	−	45.4474i	−0.263730	−	1.49028i
$931$		0			0
$932$	11.4075	+	31.2212i	0.373665	+	1.02269i
$933$	4.50234	−	4.50234i	0.147400	−	0.147400i
$934$	29.8615	−	42.7030i	0.977097	−	1.39728i
$935$			3.78028i			0.123628i
$936$	−19.4388	−	5.16985i	−0.635377	−	0.168982i
$937$			53.2767i			1.74047i	0.492634	+	0.870237i	$0.336034\pi$
$937$			53.2767i			1.74047i	−0.492634	+	0.870237i	$0.663966\pi$
$938$		0			0
$939$	17.1444	−	17.1444i	0.559486	−	0.559486i
$940$	28.3632	−	61.0227i	0.925106	−	1.99034i
$941$	−13.8068	−	13.8068i	−0.450089	−	0.450089i	0.445295	−	0.895384i	$-0.353099\pi$
$941$	−13.8068	−	13.8068i	−0.450089	−	0.450089i	−0.895384	+	0.445295i	$0.853099\pi$
$942$	6.62888	−	1.17309i	0.215981	−	0.0382214i
$943$	53.3058			1.73588
$944$	−3.44717	+	40.5606i	−0.112196	+	1.32013i
$945$		0			0
$946$	−6.99352	+	1.23762i	−0.227379	+	0.0402386i
$947$	−31.2741	−	31.2741i	−1.01627	−	1.01627i	−0.999865	−	0.0164065i	$-0.994777\pi$
$947$	−31.2741	−	31.2741i	−1.01627	−	1.01627i	−0.0164065	−	0.999865i	$-0.505223\pi$
$948$	−19.2571	−	8.95064i	−0.625441	−	0.290703i
$949$	−5.22977	+	5.22977i	−0.169766	+	0.169766i
$950$	−23.7404	−	16.6013i	−0.770241	−	0.538617i
$951$		−	4.20978i		−	0.136511i
$952$		0			0
$953$			10.3382i			0.334886i	0.985882	+	0.167443i	$0.0535511\pi$
$953$			10.3382i			0.334886i	−0.985882	+	0.167443i	$0.946449\pi$
$954$	−14.0499	+	20.0918i	−0.454882	+	0.650497i
$955$	49.8866	−	49.8866i	1.61429	−	1.61429i
$956$	4.08401	−	1.49220i	0.132086	−	0.0482612i
$957$	0.253254	+	0.253254i	0.00818654	+	0.00818654i
$958$	4.15006	+	23.4511i	0.134082	+	0.757670i
$959$		0			0
$960$	−16.7324	+	29.2322i	−0.540037	+	0.943466i
$961$	29.0839			0.938189
$962$	−7.00137	−	39.5632i	−0.225733	−	1.27557i
$963$	9.39126	+	9.39126i	0.302629	+	0.302629i
$964$	25.9940	−	9.49760i	0.837211	−	0.305897i
$965$	−29.5815	+	29.5815i	−0.952263	+	0.952263i
$966$		0			0
$967$			37.2109i			1.19662i	0.801264	+	0.598311i	$0.204161\pi$
$967$			37.2109i			1.19662i	−0.801264	+	0.598311i	$0.795839\pi$
$968$	−26.4728	+	15.3499i	−0.850869	+	0.493364i
$969$		−	12.2419i		−	0.393265i
$970$	−13.9952	−	9.78663i	−0.449360	−	0.314230i
$971$	−23.6322	+	23.6322i	−0.758393	+	0.758393i	−0.976030	−	0.217636i	$-0.930165\pi$
$971$	−23.6322	+	23.6322i	−0.758393	+	0.758393i	0.217636	+	0.976030i	$0.430165\pi$
$972$	23.2288	+	10.7967i	0.745064	+	0.346304i
$973$		0			0
$974$	−32.8879	+	5.82007i	−1.05380	+	0.186487i
$975$	−38.8935			−1.24559
$976$	−28.3441	−	2.40891i	−0.907272	−	0.0771073i
$977$	−37.8525			−1.21101			−0.605505	−	0.795842i	$-0.707029\pi$
$977$	−37.8525			−1.21101			−0.605505	+	0.795842i	$0.707029\pi$
$978$	33.7152	−	5.96647i	1.07809	−	0.190787i
$979$	0.163851	+	0.163851i	0.00523672	+	0.00523672i
$980$		0			0
$981$	14.3154	−	14.3154i	0.457057	−	0.457057i
$982$	4.96756	+	3.47373i	0.158521	+	0.110851i
$983$		−	1.49319i		−	0.0476254i	−0.999716	−	0.0238127i	$-0.992419\pi$
$983$		−	1.49319i		−	0.0476254i	0.999716	−	0.0238127i	$-0.00758053\pi$
$984$	−37.0758	−	9.86050i	−1.18193	−	0.314341i
$985$			20.0139i			0.637697i
$986$	−1.44099	+	2.06066i	−0.0458904	+	0.0656248i
$987$		0			0
$988$	12.6921	+	34.7369i	0.403788	+	1.10513i
$989$	−42.0434	−	42.0434i	−1.33690	−	1.33690i
$990$	0.467881	+	2.64389i	0.0148702	+	0.0840284i
$991$	33.8705			1.07593			0.537966	−	0.842967i	$-0.319193\pi$
$991$	33.8705			1.07593			0.537966	+	0.842967i	$0.319193\pi$
$992$	−33.6771	−	28.0809i	−1.06925	−	0.891568i
$993$	−35.3517			−1.12185
$994$		0			0
$995$	−13.6249	−	13.6249i	−0.431940	−	0.431940i
$996$	−3.54234	−	9.69504i	−0.112243	−	0.307199i
$997$	−0.113441	+	0.113441i	−0.00359271	+	0.00359271i	−0.708901	−	0.705308i	$-0.750809\pi$
$997$	−0.113441	+	0.113441i	−0.00359271	+	0.00359271i	0.705308	+	0.708901i	$0.250809\pi$
$998$	−8.01154	+	11.4568i	−0.253601	+	0.362658i
$999$			30.3058i			0.958833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.i.589.6	yes	20
7.2	even	3		784.2.x.n.557.3		40
7.3	odd	6		784.2.x.n.765.9		40
7.4	even	3		784.2.x.n.765.10		40
7.5	odd	6		784.2.x.n.557.4		40
7.6	odd	2	inner	784.2.m.i.589.5	yes	20
16.5	even	4	inner	784.2.m.i.197.6	yes	20
112.5	odd	12		784.2.x.n.165.9		40
112.37	even	12		784.2.x.n.165.10		40
112.53	even	12		784.2.x.n.373.3		40
112.69	odd	4	inner	784.2.m.i.197.5	✓	20
112.101	odd	12		784.2.x.n.373.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.i.197.5	✓	20	112.69	odd	4	inner
784.2.m.i.197.6	yes	20	16.5	even	4	inner
784.2.m.i.589.5	yes	20	7.6	odd	2	inner
784.2.m.i.589.6	yes	20	1.1	even	1	trivial
784.2.x.n.165.9		40	112.5	odd	12
784.2.x.n.165.10		40	112.37	even	12
784.2.x.n.373.3		40	112.53	even	12
784.2.x.n.373.4		40	112.101	odd	12
784.2.x.n.557.3		40	7.2	even	3
784.2.x.n.557.4		40	7.5	odd	6
784.2.x.n.765.9		40	7.3	odd	6
784.2.x.n.765.10		40	7.4	even	3

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.246440 - 1.39258i) q^{2} +(0.905952 + 0.905952i) q^{3} +(-1.87853 + 0.686372i) q^{4} +(2.32368 - 2.32368i) q^{5} +(1.03834 - 1.48487i) q^{6} +(1.41877 + 2.44685i) q^{8} -1.35850i q^{9} +(-3.80855 - 2.66326i) q^{10} +(0.300717 - 0.300717i) q^{11} +(-2.32368 - 1.08004i) q^{12} +(-3.70160 - 3.70160i) q^{13} +4.21029 q^{15} +(3.05779 - 2.57875i) q^{16} -2.70495 q^{17} +(-1.89182 + 0.334789i) q^{18} +(2.49777 + 2.49777i) q^{19} +(-2.77021 + 5.96003i) q^{20} +(-0.492880 - 0.344662i) q^{22} -5.03510i q^{23} +(-0.931392 + 3.50207i) q^{24} -5.79899i q^{25} +(-4.24254 + 6.06698i) q^{26} +(3.94859 - 3.94859i) q^{27} +(0.464798 + 0.464798i) q^{29} +(-1.03758 - 5.86314i) q^{30} +7.75138 q^{31} +(-4.34466 - 3.62269i) q^{32} +0.544870 q^{33} +(0.666608 + 3.76685i) q^{34} +(0.932439 + 2.55200i) q^{36} +(-3.83754 + 3.83754i) q^{37} +(2.86279 - 4.09389i) q^{38} -6.70694i q^{39} +(8.98248 + 2.38894i) q^{40} +10.5868i q^{41} +(8.35006 - 8.35006i) q^{43} +(-0.358503 + 0.771311i) q^{44} +(-3.15673 - 3.15673i) q^{45} +(-7.01176 + 1.24085i) q^{46} -10.2387 q^{47} +(5.10643 + 0.433986i) q^{48} +(-8.07554 + 1.42910i) q^{50} +(-2.45056 - 2.45056i) q^{51} +(9.49426 + 4.41291i) q^{52} +(9.02352 - 9.02352i) q^{53} +(-6.47181 - 4.52562i) q^{54} -1.39754i q^{55} +4.52572i q^{57} +(0.532721 - 0.761811i) q^{58} +(-7.19602 + 7.19602i) q^{59} +(-7.90917 + 2.88982i) q^{60} +(-5.02863 - 5.02863i) q^{61} +(-1.91025 - 10.7944i) q^{62} +(-3.97418 + 6.94305i) q^{64} -17.2027 q^{65} +(-0.134278 - 0.758772i) q^{66} +(0.178322 + 0.178322i) q^{67} +(5.08135 - 1.85660i) q^{68} +(4.56156 - 4.56156i) q^{69} -6.38433i q^{71} +(3.32406 - 1.92741i) q^{72} -1.41284i q^{73} +(6.28979 + 4.39835i) q^{74} +(5.25361 - 5.25361i) q^{75} +(-6.40655 - 2.97775i) q^{76} +(-9.33992 + 1.65286i) q^{78} +8.28731 q^{79} +(1.11313 - 13.0975i) q^{80} +3.07896 q^{81} +(14.7430 - 2.60902i) q^{82} +(2.84836 + 2.84836i) q^{83} +(-6.28545 + 6.28545i) q^{85} +(-13.6859 - 9.57030i) q^{86} +0.842168i q^{87} +(1.16246 + 0.309162i) q^{88} +0.544870i q^{89} +(-3.61804 + 5.17393i) q^{90} +(3.45595 + 9.45861i) q^{92} +(7.02237 + 7.02237i) q^{93} +(2.52321 + 14.2581i) q^{94} +11.6081 q^{95} +(-0.654069 - 7.21804i) q^{96} +3.67469 q^{97} +(-0.408525 - 0.408525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 8 q^{4} + 4 q^{11} - 16 q^{15} + 16 q^{18} - 4 q^{29} + 8 q^{30} - 40 q^{32} + 40 q^{36} - 20 q^{37} + 60 q^{43} + 56 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{51} + 28 q^{53} - 72 q^{58} - 24 q^{60}+ \cdots - 108 q^{99}+O(q^{100}) \) 20 * q - 8 * q^4 + 4 * q^11 - 16 * q^15 + 16 * q^18 - 4 * q^29 + 8 * q^30 - 40 * q^32 + 40 * q^36 - 20 * q^37 + 60 * q^43 + 56 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^51 + 28 * q^53 - 72 * q^58 - 24 * q^60 - 32 * q^64 + 16 * q^65 + 12 * q^67 + 16 * q^72 - 16 * q^74 - 88 * q^78 - 72 * q^79 + 12 * q^81 + 32 * q^85 - 40 * q^86 + 80 * q^88 - 24 * q^92 + 48 * q^93 + 64 * q^95 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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