LMFDB - Embedded newform 325.2.e.e.276.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(126,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("325.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 8x^{10} + 54x^{8} + 78x^{6} + 92x^{4} + 10x^{2} + 1 $ x^12 + 8x^10 + 54x^8 + 78x^6 + 92x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			276.4
Root			$0.165418 - 0.286513i$ of defining polynomial
Character	$\chi$	$=$	325.276
Dual form			325.2.e.e.126.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.165418 + 0.286513i) q^{2} +(-1.34590 - 2.33117i) q^{3} +(0.945274 - 1.63726i) q^{4} +(0.445274 - 0.771236i) q^{6} +(1.67674 - 2.90420i) q^{7} +1.28714 q^{8} +(-2.12291 + 3.67698i) q^{9} +O(q^{10})$	\(q+(0.165418 + 0.286513i) q^{2} +(-1.34590 - 2.33117i) q^{3} +(0.945274 - 1.63726i) q^{4} +(0.445274 - 0.771236i) q^{6} +(1.67674 - 2.90420i) q^{7} +1.28714 q^{8} +(-2.12291 + 3.67698i) q^{9} +(1.62291 + 2.81095i) q^{11} -5.08898 q^{12} +(-3.39414 - 1.21648i) q^{13} +1.10945 q^{14} +(-1.67763 - 2.90574i) q^{16} +(-0.974404 + 1.68772i) q^{17} -1.40467 q^{18} +(0.622905 - 1.07890i) q^{19} -9.02690 q^{21} +(-0.536916 + 0.929966i) q^{22} +(1.34590 + 2.33117i) q^{23} +(-1.73236 - 3.00053i) q^{24} +(-0.212916 - 1.17369i) q^{26} +3.35348 q^{27} +(-3.16995 - 5.49052i) q^{28} +(-1.50000 - 2.59808i) q^{29} +3.78109 q^{31} +(1.84216 - 3.19071i) q^{32} +(4.36854 - 7.56654i) q^{33} -0.644737 q^{34} +(4.01345 + 6.95150i) q^{36} +(0.974404 + 1.68772i) q^{37} +0.412160 q^{38} +(1.73236 + 9.54958i) q^{39} +(-1.39055 - 2.40850i) q^{41} +(-1.49321 - 2.58632i) q^{42} +(-4.36854 + 7.56654i) q^{43} +6.13636 q^{44} +(-0.445274 + 0.771236i) q^{46} +6.86960 q^{47} +(-4.51586 + 7.82169i) q^{48} +(-2.12291 - 3.67698i) q^{49} +5.24581 q^{51} +(-5.20008 + 4.40719i) q^{52} +12.8336 q^{53} +(0.554726 + 0.960814i) q^{54} +(2.15819 - 3.73809i) q^{56} -3.35348 q^{57} +(0.496255 - 0.859539i) q^{58} +(1.26764 - 2.19562i) q^{59} +(3.74581 - 6.48793i) q^{61} +(0.625462 + 1.08333i) q^{62} +(7.11911 + 12.3307i) q^{63} -5.49162 q^{64} +2.89055 q^{66} +(-2.00758 - 3.47722i) q^{67} +(1.84216 + 3.19071i) q^{68} +(3.62291 - 6.27506i) q^{69} +(-2.62291 + 4.54300i) q^{71} +(-2.73247 + 4.73277i) q^{72} +5.46493 q^{73} +(-0.322368 + 0.558359i) q^{74} +(-1.17763 - 2.03972i) q^{76} +10.8848 q^{77} +(-2.44951 + 2.07602i) q^{78} +13.7811 q^{79} +(1.85526 + 3.21341i) q^{81} +(0.460044 - 0.796819i) q^{82} -8.61955 q^{83} +(-8.53289 + 14.7794i) q^{84} -2.89055 q^{86} +(-4.03771 + 6.99351i) q^{87} +(2.08890 + 3.61808i) q^{88} +(-5.15819 - 8.93425i) q^{89} +(-9.22398 + 7.81753i) q^{91} +5.08898 q^{92} +(-5.08898 - 8.81438i) q^{93} +(1.13636 + 1.96823i) q^{94} -9.91745 q^{96} +(-2.63304 + 4.56055i) q^{97} +(0.702335 - 1.21648i) q^{98} -13.7811 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9	$ 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + 44 q^{14} - 16 q^{16} - 12 q^{19} - 8 q^{21} - 32 q^{24} + 24 q^{26} - 18 q^{29} - 16 q^{31} - 16 q^{34} - 2 q^{36} + 32 q^{39} + 14 q^{41} + 4 q^{44} + 10 q^{46} - 6 q^{49} + 24 q^{51} + 22 q^{54} - 16 q^{56} + 4 q^{59} + 6 q^{61} + 12 q^{64} + 4 q^{66} + 24 q^{69} - 12 q^{71} - 8 q^{74} - 10 q^{76} + 104 q^{79} + 14 q^{81} - 90 q^{84} - 4 q^{86} - 20 q^{89} - 44 q^{91} - 56 q^{94} + 12 q^{96} - 104 q^{99}+O(q^{100}) $ 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9 + 44 * q^14 - 16 * q^16 - 12 * q^19 - 8 * q^21 - 32 * q^24 + 24 * q^26 - 18 * q^29 - 16 * q^31 - 16 * q^34 - 2 * q^36 + 32 * q^39 + 14 * q^41 + 4 * q^44 + 10 * q^46 - 6 * q^49 + 24 * q^51 + 22 * q^54 - 16 * q^56 + 4 * q^59 + 6 * q^61 + 12 * q^64 + 4 * q^66 + 24 * q^69 - 12 * q^71 - 8 * q^74 - 10 * q^76 + 104 * q^79 + 14 * q^81 - 90 * q^84 - 4 * q^86 - 20 * q^89 - 44 * q^91 - 56 * q^94 + 12 * q^96 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.165418	+	0.286513i	0.116968	+	0.202595i	0.918565	−	0.395270i	$-0.129349\pi$
$2$	0.165418	+	0.286513i	0.116968	+	0.202595i	−0.801597	+	0.597865i	$0.796016\pi$
$3$	−1.34590	−	2.33117i	−0.777057	−	1.34590i	−0.933631	−	0.358236i	$-0.883378\pi$
$3$	−1.34590	−	2.33117i	−0.777057	−	1.34590i	0.156574	−	0.987666i	$-0.449955\pi$
$4$	0.945274	−	1.63726i	0.472637	−	0.818631i
$5$		0			0
$5$		0			0
$6$	0.445274	−	0.771236i	0.181782	−	0.314856i
$7$	1.67674	−	2.90420i	0.633748	−	1.09768i	−0.353031	−	0.935611i	$-0.614849\pi$
$7$	1.67674	−	2.90420i	0.633748	−	1.09768i	0.986779	−	0.162072i	$-0.0518176\pi$
$8$	1.28714			0.455071
$9$	−2.12291	+	3.67698i	−0.707635	+	1.22566i
$10$		0			0
$11$	1.62291	+	2.81095i	0.489324	+	0.847535i	0.999925	−	0.0122837i	$-0.00391011\pi$
$11$	1.62291	+	2.81095i	0.489324	+	0.847535i	−0.510600	+	0.859818i	$0.670577\pi$
$12$	−5.08898			−1.46906
$13$	−3.39414	−	1.21648i	−0.941365	−	0.337391i
$13$	−3.39414	−	1.21648i	−0.941365	−	0.337391i
$14$	1.10945			0.296514
$15$		0			0
$16$	−1.67763	−	2.90574i	−0.419408	−	0.726436i
$17$	−0.974404	+	1.68772i	−0.236328	+	0.409332i	−0.959658	−	0.281171i	$-0.909277\pi$
$17$	−0.974404	+	1.68772i	−0.236328	+	0.409332i	0.723330	+	0.690503i	$0.242611\pi$
$18$	−1.40467			−0.331084
$19$	0.622905	−	1.07890i	0.142904	−	0.247517i	−0.785685	−	0.618627i	$-0.787689\pi$
$19$	0.622905	−	1.07890i	0.142904	−	0.247517i	0.928589	+	0.371110i	$0.121023\pi$
$20$		0			0
$21$	−9.02690			−1.96983
$22$	−0.536916	+	0.929966i	−0.114471	+	0.198269i
$23$	1.34590	+	2.33117i	0.280640	+	0.486083i	0.971543	−	0.236865i	$-0.0761200\pi$
$23$	1.34590	+	2.33117i	0.280640	+	0.486083i	−0.690903	+	0.722948i	$0.742787\pi$
$24$	−1.73236	−	3.00053i	−0.353616	−	0.612481i
$25$		0			0
$26$	−0.212916	−	1.17369i	−0.0417562	−	0.230180i
$27$	3.35348			0.645377
$28$	−3.16995	−	5.49052i	−0.599065	−	1.03761i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	3.78109			0.679105			0.339552	−	0.940587i	$-0.389724\pi$
$31$	3.78109			0.679105			0.339552	+	0.940587i	$0.389724\pi$
$32$	1.84216	−	3.19071i	0.325650	−	0.564043i
$33$	4.36854	−	7.56654i	0.760466	−	1.31717i
$34$	−0.644737			−0.110571
$35$		0			0
$36$	4.01345	+	6.95150i	0.668909	+	1.15858i
$37$	0.974404	+	1.68772i	0.160191	+	0.277459i	0.934937	−	0.354813i	$-0.115456\pi$
$37$	0.974404	+	1.68772i	0.160191	+	0.277459i	−0.774746	+	0.632273i	$0.782122\pi$
$38$	0.412160			0.0668611
$39$	1.73236	+	9.54958i	0.277399	+	1.52916i
$40$		0			0
$41$	−1.39055	−	2.40850i	−0.217167	−	0.376144i	0.736774	−	0.676139i	$-0.236348\pi$
$41$	−1.39055	−	2.40850i	−0.217167	−	0.376144i	−0.953941	+	0.299995i	$0.903015\pi$
$42$	−1.49321	−	2.58632i	−0.230408	−	0.399078i
$43$	−4.36854	+	7.56654i	−0.666197	+	1.15389i	0.312763	+	0.949831i	$0.398745\pi$
$43$	−4.36854	+	7.56654i	−0.666197	+	1.15389i	−0.978959	+	0.204055i	$0.934588\pi$
$44$	6.13636			0.925091
$45$		0			0
$46$	−0.445274	+	0.771236i	−0.0656520	+	0.113713i
$47$	6.86960			1.00203			0.501017	−	0.865437i	$-0.332959\pi$
$47$	6.86960			1.00203			0.501017	+	0.865437i	$0.332959\pi$
$48$	−4.51586	+	7.82169i	−0.651808	+	1.12896i
$49$	−2.12291	−	3.67698i	−0.303272	−	0.525283i
$50$		0			0
$51$	5.24581			0.734560
$52$	−5.20008	+	4.40719i	−0.721122	+	0.611167i
$53$	12.8336			1.76282			0.881412	−	0.472347i	$-0.156593\pi$
$53$	12.8336			1.76282			0.881412	+	0.472347i	$0.156593\pi$
$54$	0.554726	+	0.960814i	0.0754887	+	0.130750i
$55$		0			0
$56$	2.15819	−	3.73809i	0.288400	−	0.499524i
$57$	−3.35348			−0.444179
$58$	0.496255	−	0.859539i	0.0651614	−	0.112863i
$59$	1.26764	−	2.19562i	0.165033	−	0.285845i	−0.771634	−	0.636067i	$-0.780560\pi$
$59$	1.26764	−	2.19562i	0.165033	−	0.285845i	0.936667	+	0.350221i	$0.113894\pi$
$60$		0			0
$61$	3.74581	−	6.48793i	0.479602	−	0.830695i	−0.520124	−	0.854090i	$-0.674114\pi$
$61$	3.74581	−	6.48793i	0.479602	−	0.830695i	0.999726	+	0.0233957i	$0.00744777\pi$
$62$	0.625462	+	1.08333i	0.0794338	+	0.137583i
$63$	7.11911	+	12.3307i	0.896924	+	1.55352i
$64$	−5.49162			−0.686453
$65$		0			0
$66$	2.89055			0.355802
$67$	−2.00758	−	3.47722i	−0.245264	−	0.424810i	0.716942	−	0.697133i	$-0.245541\pi$
$67$	−2.00758	−	3.47722i	−0.245264	−	0.424810i	−0.962206	+	0.272323i	$0.912208\pi$
$68$	1.84216	+	3.19071i	0.223394	+	0.386930i
$69$	3.62291	−	6.27506i	0.436147	−	0.755428i
$70$		0			0
$71$	−2.62291	+	4.54300i	−0.311282	+	0.539155i	−0.978640	−	0.205581i	$-0.934092\pi$
$71$	−2.62291	+	4.54300i	−0.311282	+	0.539155i	0.667359	+	0.744737i	$0.267425\pi$
$72$	−2.73247	+	4.73277i	−0.322024	+	0.557762i
$73$	5.46493			0.639622			0.319811	−	0.947481i	$-0.396381\pi$
$73$	5.46493			0.639622			0.319811	+	0.947481i	$0.396381\pi$
$74$	−0.322368	+	0.558359i	−0.0374746	+	0.0649079i
$75$		0			0
$76$	−1.17763	−	2.03972i	−0.135084	−	0.233972i
$77$	10.8848			1.24043
$78$	−2.44951	+	2.07602i	−0.277353	+	0.235063i
$79$	13.7811			1.55049			0.775247	−	0.631658i	$-0.217625\pi$
$79$	13.7811			1.55049			0.775247	+	0.631658i	$0.217625\pi$
$80$		0			0
$81$	1.85526	+	3.21341i	0.206140	+	0.357046i
$82$	0.460044	−	0.796819i	0.0508033	−	0.0879940i
$83$	−8.61955			−0.946119			−0.473059	−	0.881031i	$-0.656850\pi$
$83$	−8.61955			−0.946119			−0.473059	+	0.881031i	$0.656850\pi$
$84$	−8.53289	+	14.7794i	−0.931015	+	1.61257i
$85$		0			0
$86$	−2.89055			−0.311696
$87$	−4.03771	+	6.99351i	−0.432888	+	0.749783i
$88$	2.08890	+	3.61808i	0.222677	+	0.385688i
$89$	−5.15819	−	8.93425i	−0.546767	−	0.947028i	−0.998493	−	0.0548717i	$-0.982525\pi$
$89$	−5.15819	−	8.93425i	−0.546767	−	0.947028i	0.451726	−	0.892156i	$-0.350808\pi$
$90$		0			0
$91$	−9.22398	+	7.81753i	−0.966936	+	0.819500i
$92$	5.08898			0.530563
$93$	−5.08898	−	8.81438i	−0.527703	−	0.914008i
$94$	1.13636	+	1.96823i	0.117206	+	0.203007i
$95$		0			0
$96$	−9.91745			−1.01220
$97$	−2.63304	+	4.56055i	−0.267344	+	0.463054i	−0.968175	−	0.250273i	$-0.919479\pi$
$97$	−2.63304	+	4.56055i	−0.267344	+	0.463054i	0.700831	+	0.713328i	$0.252813\pi$
$98$	0.702335	−	1.21648i	0.0709465	−	0.122883i
$99$	−13.7811			−1.38505
$100$		0			0
$101$	−2.85526	−	4.94546i	−0.284109	−	0.492092i	0.688283	−	0.725442i	$-0.258365\pi$
$101$	−2.85526	−	4.94546i	−0.284109	−	0.492092i	−0.972393	+	0.233350i	$0.925031\pi$
$102$	0.867753	+	1.50299i	0.0859203	+	0.148818i
$103$	7.36863			0.726052			0.363026	−	0.931779i	$-0.381744\pi$
$103$	7.36863			0.726052			0.363026	+	0.931779i	$0.381744\pi$
$104$	−4.36872	−	1.56577i	−0.428388	−	0.153537i
$105$		0			0
$106$	2.12291	+	3.67698i	0.206195	+	0.357140i
$107$	4.28722	+	7.42568i	0.414461	+	0.717868i	0.995372	−	0.0960996i	$-0.0306367\pi$
$107$	4.28722	+	7.42568i	0.414461	+	0.717868i	−0.580911	+	0.813967i	$0.697303\pi$
$108$	3.16995	−	5.49052i	0.305029	−	0.528326i
$109$	−8.49162			−0.813350			−0.406675	−	0.913573i	$-0.633312\pi$
$109$	−8.49162			−0.813350			−0.406675	+	0.913573i	$0.633312\pi$
$110$		0			0
$111$	2.62291	−	4.54300i	0.248955	−	0.431203i
$112$	−11.2518			−1.06320
$113$	−3.66621	+	6.35006i	−0.344888	+	0.597363i	−0.985333	−	0.170640i	$-0.945416\pi$
$113$	−3.66621	+	6.35006i	−0.344888	+	0.597363i	0.640446	+	0.768004i	$0.278750\pi$
$114$	−0.554726	−	0.960814i	−0.0519549	−	0.0899885i
$115$		0			0
$116$	−5.67164			−0.526599
$117$	11.6784	−	9.89771i	1.07967	−	0.915044i
$118$	0.838765			0.0772145
$119$	3.26764	+	5.65972i	0.299544	+	0.518826i
$120$		0			0
$121$	0.232358	−	0.402456i	0.0211234	−	0.0365869i
$122$	2.47850			0.224393
$123$	−3.74308	+	6.48321i	−0.337502	+	0.584571i
$124$	3.57417	−	6.19064i	0.320970	−	0.555936i
$125$		0			0
$126$	−2.35526	+	4.07944i	−0.209824	+	0.363425i
$127$	−4.58185	−	7.93599i	−0.406573	−	0.704205i	0.587930	−	0.808912i	$-0.299943\pi$
$127$	−4.58185	−	7.93599i	−0.406573	−	0.704205i	−0.994503	+	0.104707i	$0.966610\pi$
$128$	−4.59273	−	7.95484i	−0.405944	−	0.703115i
$129$	23.5185			2.07069
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	−8.25894	−	14.3049i	−0.718848	−	1.24508i
$133$	−2.08890	−	3.61808i	−0.181130	−	0.313727i
$134$	0.664179	−	1.15039i	0.0573763	−	0.0993787i
$135$		0			0
$136$	−1.25419	+	2.17232i	−0.107546	+	0.186275i
$137$	8.42435	−	14.5914i	0.719741	−	1.24663i	−0.241361	−	0.970435i	$-0.577594\pi$
$137$	8.42435	−	14.5914i	0.719741	−	1.24663i	0.961102	−	0.276193i	$-0.0890729\pi$
$138$	2.39718			0.204061
$139$	0.513452	−	0.889325i	0.0435505	−	0.0754316i	−0.843429	−	0.537241i	$-0.819466\pi$
$139$	0.513452	−	0.889325i	0.0435505	−	0.0754316i	0.886979	+	0.461810i	$0.152800\pi$
$140$		0			0
$141$	−9.24581	−	16.0142i	−0.778638	−	1.34864i
$142$	−1.73551			−0.145640
$143$	−2.08890	−	11.5150i	−0.174682	−	0.962933i
$144$	14.2458			1.18715
$145$		0			0
$146$	0.904000	+	1.56577i	0.0748155	+	0.129584i
$147$	−5.71445	+	9.89771i	−0.471319	+	0.816349i
$148$	3.68431			0.302849
$149$	−7.92583	+	13.7279i	−0.649309	+	1.12464i	0.333979	+	0.942581i	$0.391609\pi$
$149$	−7.92583	+	13.7279i	−0.649309	+	1.12464i	−0.983288	+	0.182056i	$0.941725\pi$
$150$		0			0
$151$	14.5454			1.18369			0.591845	−	0.806052i	$-0.298400\pi$
$151$	14.5454			1.18369			0.591845	+	0.806052i	$0.298400\pi$
$152$	0.801763	−	1.38869i	0.0650316	−	0.112638i
$153$	−4.13713	−	7.16573i	−0.334468	−	0.579315i
$154$	1.80054	+	3.11862i	0.145091	+	0.251306i
$155$		0			0
$156$	17.2727	+	6.19064i	1.38292	+	0.495648i
$157$	−10.9210			−0.871588			−0.435794	−	0.900047i	$-0.643532\pi$
$157$	−10.9210			−0.871588			−0.435794	+	0.900047i	$0.643532\pi$
$158$	2.27964	+	3.94846i	0.181359	+	0.314123i
$159$	−17.2727	−	29.9172i	−1.36982	−	2.37259i
$160$		0			0
$161$	9.02690			0.711420
$162$	−0.613789	+	1.06311i	−0.0482238	+	0.0835261i
$163$	−2.08890	+	3.61808i	−0.163615	+	0.283390i	−0.936163	−	0.351567i	$-0.885649\pi$
$163$	−2.08890	+	3.61808i	−0.163615	+	0.283390i	0.772547	+	0.634957i	$0.218982\pi$
$164$	−5.25779			−0.410564
$165$		0			0
$166$	−1.42583	−	2.46961i	−0.110666	−	0.191679i
$167$	−1.67674	−	2.90420i	−0.129750	−	0.224733i	0.793830	−	0.608140i	$-0.208084\pi$
$167$	−1.67674	−	2.90420i	−0.129750	−	0.224733i	−0.923580	+	0.383407i	$0.874751\pi$
$168$	−11.6188			−0.896413
$169$	10.0404	+	8.25780i	0.772335	+	0.635215i
$170$		0			0
$171$	2.64474	+	4.58082i	0.202248	+	0.350304i
$172$	8.25894	+	14.3049i	0.629738	+	1.09074i
$173$	4.36854	−	7.56654i	0.332134	−	0.575273i	−0.650796	−	0.759253i	$-0.725565\pi$
$173$	4.36854	−	7.56654i	0.332134	−	0.575273i	0.982930	+	0.183979i	$0.0588980\pi$
$174$	−2.67164			−0.202537
$175$		0			0
$176$	5.44527	−	9.43149i	0.410453	−	0.710925i
$177$	−6.82449			−0.512960
$178$	1.70652	−	2.95577i	0.127909	−	0.221545i
$179$	9.00507	+	15.5972i	0.673071	+	1.16579i	0.977029	+	0.213107i	$0.0683584\pi$
$179$	9.00507	+	15.5972i	0.673071	+	1.16579i	−0.303958	+	0.952685i	$0.598308\pi$
$180$		0			0
$181$	1.04366			0.0775749			0.0387875	−	0.999247i	$-0.487650\pi$
$181$	1.04366			0.0775749			0.0387875	+	0.999247i	$0.487650\pi$
$182$	−3.76564	−	1.34963i	−0.279128	−	0.100041i
$183$	−20.1660			−1.49071
$184$	1.73236	+	3.00053i	0.127711	+	0.221202i
$185$		0			0
$186$	1.68362	−	2.91612i	0.123449	−	0.213820i
$187$	−6.32546			−0.462564
$188$	6.49365	−	11.2473i	0.473598	−	0.820296i
$189$	5.62291	−	9.73916i	0.409006	−	0.708419i
$190$		0			0
$191$	−12.7593	+	22.0997i	−0.923228	+	1.59908i	−0.128841	+	0.991665i	$0.541126\pi$
$191$	−12.7593	+	22.0997i	−0.923228	+	1.59908i	−0.794387	+	0.607412i	$0.792208\pi$
$192$	7.39118	+	12.8019i	0.533413	+	0.923898i
$193$	−9.91035	−	17.1652i	−0.713362	−	1.23558i	−0.963588	−	0.267392i	$-0.913838\pi$
$193$	−9.91035	−	17.1652i	−0.713362	−	1.23558i	0.250225	−	0.968188i	$-0.419495\pi$
$194$	−1.74221			−0.125083
$195$		0			0
$196$	−8.02690			−0.573350
$197$	10.8260	+	18.7512i	0.771319	+	1.33596i	0.936840	+	0.349758i	$0.113736\pi$
$197$	10.8260	+	18.7512i	0.771319	+	1.33596i	−0.165521	+	0.986206i	$0.552930\pi$
$198$	−2.27964	−	3.94846i	−0.162007	−	0.280605i
$199$	−9.11453	+	15.7868i	−0.646112	+	1.11910i	0.337932	+	0.941171i	$0.390273\pi$
$199$	−9.11453	+	15.7868i	−0.646112	+	1.11910i	−0.984044	+	0.177928i	$0.943061\pi$
$200$		0			0
$201$	−5.40400	+	9.36000i	−0.381169	+	0.660204i
$202$	0.944625	−	1.63614i	0.0664636	−	0.115118i
$203$	−10.0604			−0.706104
$204$	4.95873	−	8.58877i	0.347180	−	0.601334i
$205$		0			0
$206$	1.21891	+	2.11121i	0.0849252	+	0.147095i
$207$	−11.4289			−0.794363
$208$	2.15934	+	11.9033i	0.149723	+	0.825345i
$209$	4.04366			0.279706
$210$		0			0
$211$	−9.64981	−	16.7140i	−0.664320	−	1.15064i	−0.979469	−	0.201594i	$-0.935388\pi$
$211$	−9.64981	−	16.7140i	−0.664320	−	1.15064i	0.315149	−	0.949042i	$-0.397946\pi$
$212$	12.1312	−	21.0119i	0.833176	−	1.44310i
$213$	14.1207			0.967534
$214$	−1.41837	+	2.45669i	−0.0969577	+	0.167936i
$215$		0			0
$216$	4.31638			0.293692
$217$	6.33991	−	10.9810i	0.430381	−	0.745442i
$218$	−1.40467	−	2.43296i	−0.0951362	−	0.164781i
$219$	−7.35526	−	12.7397i	−0.497023	−	0.860868i
$220$		0			0
$221$	5.36034	−	4.54300i	0.360575	−	0.305596i
$222$	1.73551			0.116480
$223$	6.18537	+	10.7134i	0.414203	+	0.717421i	0.995344	−	0.0963818i	$-0.0307270\pi$
$223$	6.18537	+	10.7134i	0.414203	+	0.717421i	−0.581141	+	0.813803i	$0.697394\pi$
$224$	−6.17763	−	10.7000i	−0.412760	−	0.714922i
$225$		0			0
$226$	−2.42583			−0.161364
$227$	−3.08141	+	5.33715i	−0.204520	+	0.354239i	−0.949980	−	0.312311i	$-0.898897\pi$
$227$	−3.08141	+	5.33715i	−0.204520	+	0.354239i	0.745460	+	0.666551i	$0.232230\pi$
$228$	−3.16995	+	5.49052i	−0.209935	+	0.363619i
$229$	−26.9832			−1.78310			−0.891551	−	0.452920i	$-0.850382\pi$
$229$	−26.9832			−1.78310			−0.891551	+	0.452920i	$0.850382\pi$
$230$		0			0
$231$	−14.6498	−	25.3742i	−0.963887	−	1.66950i
$232$	−1.93070	−	3.34408i	−0.126757	−	0.219549i
$233$	−0.824319			−0.0540029			−0.0270015	−	0.999635i	$-0.508596\pi$
$233$	−0.824319			−0.0540029			−0.0270015	+	0.999635i	$0.508596\pi$
$234$	4.76764	+	1.70875i	0.311671	+	0.111705i
$235$		0			0
$236$	−2.39654	−	4.15092i	−0.156001	−	0.270202i
$237$	−18.5480	−	32.1261i	−1.20482	−	2.08681i
$238$	−1.08106	+	1.87244i	−0.0700744	+	0.121372i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	−11.3469	+	19.6534i	−0.730917	+	1.26599i	0.225575	+	0.974226i	$0.427574\pi$
$241$	−11.3469	+	19.6534i	−0.730917	+	1.26599i	−0.956492	+	0.291760i	$0.905759\pi$
$242$	0.153745			0.00988310
$243$	10.0242	−	17.3625i	0.643054	−	1.11380i
$244$	−7.08163	−	12.2657i	−0.453355	−	0.785234i
$245$		0			0
$246$	−2.47670			−0.157908
$247$	−3.42669	+	2.90420i	−0.218035	+	0.184790i
$248$	4.86678			0.309041
$249$	11.6011	+	20.0936i	0.735188	+	1.27338i
$250$		0			0
$251$	−9.51345	+	16.4778i	−0.600484	+	1.04007i	0.392264	+	0.919853i	$0.371692\pi$
$251$	−9.51345	+	16.4778i	−0.600484	+	1.04007i	−0.992748	+	0.120216i	$0.961641\pi$
$252$	26.9180			1.69568
$253$	−4.36854	+	7.56654i	−0.274648	+	0.475704i
$254$	1.51584	−	2.62552i	0.0951124	−	0.164739i
$255$		0			0
$256$	−3.97218	+	6.88001i	−0.248261	+	0.430001i
$257$	−1.05573	−	1.82857i	−0.0658544	−	0.114063i	0.831218	−	0.555946i	$-0.187644\pi$
$257$	−1.05573	−	1.82857i	−0.0658544	−	0.114063i	−0.897073	+	0.441883i	$0.854311\pi$
$258$	3.89039	+	6.73836i	0.242205	+	0.419512i
$259$	6.53528			0.406083
$260$		0			0
$261$	12.7374			0.788427
$262$	1.65418	+	2.86513i	0.102196	+	0.177008i
$263$	14.9587	+	25.9092i	0.922391	+	1.59763i	0.795704	+	0.605685i	$0.207101\pi$
$263$	14.9587	+	25.9092i	0.922391	+	1.59763i	0.126687	+	0.991943i	$0.459566\pi$
$264$	5.62291	−	9.73916i	0.346066	−	0.599404i
$265$		0			0
$266$	0.691084	−	1.19699i	0.0423731	−	0.0733923i
$267$	−13.8848	+	24.0492i	−0.849738	+	1.47179i
$268$	−7.59083			−0.463684
$269$	−9.29455	+	16.0986i	−0.566699	+	0.981551i	0.430191	+	0.902738i	$0.358446\pi$
$269$	−9.29455	+	16.0986i	−0.566699	+	0.981551i	−0.996889	+	0.0788127i	$0.974887\pi$
$270$		0			0
$271$	−2.91238	−	5.04439i	−0.176914	−	0.306425i	0.763908	−	0.645326i	$-0.223278\pi$
$271$	−2.91238	−	5.04439i	−0.176914	−	0.306425i	−0.940822	+	0.338901i	$0.889945\pi$
$272$	6.53876			0.396471
$273$	30.6386	+	10.9810i	1.85433	+	0.664603i
$274$	5.57417			0.336748
$275$		0			0
$276$	−6.84927	−	11.8633i	−0.412278	−	0.714086i
$277$	−6.77017	+	11.7263i	−0.406780	+	0.704564i	−0.994527	−	0.104481i	$-0.966682\pi$
$277$	−6.77017	+	11.7263i	−0.406780	+	0.704564i	0.587747	+	0.809045i	$0.300015\pi$
$278$	0.339738			0.0203761
$279$	−8.02690	+	13.9030i	−0.480558	+	0.832351i
$280$		0			0
$281$	−0.464716			−0.0277226			−0.0138613	−	0.999904i	$-0.504412\pi$
$281$	−0.464716			−0.0277226			−0.0138613	+	0.999904i	$0.504412\pi$
$282$	3.05885	−	5.29809i	0.182152	−	0.315496i
$283$	−5.03022	−	8.71259i	−0.299015	−	0.517910i	0.676896	−	0.736079i	$-0.263325\pi$
$283$	−5.03022	−	8.71259i	−0.299015	−	0.517910i	−0.975911	+	0.218169i	$0.929991\pi$
$284$	4.95873	+	8.58877i	0.294246	+	0.509649i
$285$		0			0
$286$	2.95365	−	2.50329i	0.174653	−	0.148022i
$287$	−9.32634			−0.550516
$288$	7.82145	+	13.5471i	0.460883	+	0.798273i
$289$	6.60107	+	11.4334i	0.388298	+	0.672553i
$290$		0			0
$291$	14.1752			0.830967
$292$	5.16586	−	8.94752i	0.302309	−	0.523614i
$293$	−6.72506	+	11.6481i	−0.392882	+	0.680492i	−0.992828	−	0.119548i	$-0.961855\pi$
$293$	−6.72506	+	11.6481i	−0.392882	+	0.680492i	0.599946	+	0.800040i	$0.295189\pi$
$294$	−3.78109			−0.220518
$295$		0			0
$296$	1.25419	+	2.17232i	0.0728983	+	0.126264i
$297$	5.44238	+	9.42647i	0.315799	+	0.546979i
$298$	−5.24431			−0.303795
$299$	−1.73236	−	9.54958i	−0.100185	−	0.552266i
$300$		0			0
$301$	14.6498	+	25.3742i	0.844401	+	1.46255i
$302$	2.40608	+	4.16745i	0.138454	+	0.239810i
$303$	−7.68581	+	13.3122i	−0.441538	+	0.764767i
$304$	−4.18002			−0.239741
$305$		0			0
$306$	1.36872	−	2.37068i	0.0782442	−	0.135523i
$307$	24.6077			1.40444			0.702219	−	0.711961i	$-0.252193\pi$
$307$	24.6077			1.40444			0.702219	+	0.711961i	$0.252193\pi$
$308$	10.2891	−	17.8212i	0.586274	−	1.01546i
$309$	−9.91745	−	17.1775i	−0.564184	−	0.977196i
$310$		0			0
$311$	2.43781			0.138236			0.0691178	−	0.997609i	$-0.477982\pi$
$311$	2.43781			0.138236			0.0691178	+	0.997609i	$0.477982\pi$
$312$	2.22978	+	12.2916i	0.126236	+	0.695875i
$313$	−19.2965			−1.09071			−0.545353	−	0.838207i	$-0.683604\pi$
$313$	−19.2965			−1.09071			−0.545353	+	0.838207i	$0.683604\pi$
$314$	−1.80653	−	3.12900i	−0.101948	−	0.176579i
$315$		0			0
$316$	13.0269	−	22.5633i	0.732821	−	1.26928i
$317$	−28.8217			−1.61879			−0.809395	−	0.587265i	$-0.800205\pi$
$317$	−28.8217			−1.61879			−0.809395	+	0.587265i	$0.800205\pi$
$318$	5.71445	−	9.89771i	0.320450	−	0.555036i
$319$	4.86872	−	8.43286i	0.272596	−	0.472150i
$320$		0			0
$321$	11.5404	−	19.9885i	0.644120	−	1.11565i
$322$	1.49321	+	2.58632i	0.0832136	+	0.144130i
$323$	1.21392	+	2.10258i	0.0675445	+	0.116990i
$324$	7.01492			0.389718
$325$		0			0
$326$	−1.38217			−0.0765512
$327$	11.4289	+	19.7954i	0.632019	+	1.09469i
$328$	−1.78982	−	3.10006i	−0.0988264	−	0.171172i
$329$	11.5185	−	19.9507i	0.635037	−	1.09992i
$330$		0			0
$331$	1.48655	−	2.57478i	0.0817081	−	0.141522i	−0.822276	−	0.569089i	$-0.807296\pi$
$331$	1.48655	−	2.57478i	0.0817081	−	0.141522i	0.903984	+	0.427567i	$0.140629\pi$
$332$	−8.14783	+	14.1125i	−0.447171	+	0.774522i
$333$	−8.27427			−0.453427
$334$	0.554726	−	0.960814i	0.0303533	−	0.0525734i
$335$		0			0
$336$	15.1438	+	26.2299i	0.826163	+	1.43096i
$337$	1.90370			0.103701			0.0518505	−	0.998655i	$-0.483488\pi$
$337$	1.90370			0.103701			0.0518505	+	0.998655i	$0.483488\pi$
$338$	−0.705107	+	4.24268i	−0.0383528	+	0.230771i
$339$	19.7374			1.07199
$340$		0			0
$341$	6.13636	+	10.6285i	0.332302	+	0.575565i
$342$	−0.874976	+	1.51550i	−0.0473133	+	0.0819490i
$343$	9.23611			0.498703
$344$	−5.62291	+	9.73916i	−0.303167	+	0.525100i
$345$		0			0
$346$	2.89055			0.155397
$347$	6.31735	−	10.9420i	0.339133	−	0.587396i	−0.645137	−	0.764067i	$-0.723200\pi$
$347$	6.31735	−	10.9420i	0.339133	−	0.587396i	0.984270	+	0.176671i	$0.0565329\pi$
$348$	7.63347	+	13.2216i	0.409197	+	0.708750i
$349$	−4.48655	−	7.77093i	−0.240159	−	0.415968i	0.720600	−	0.693351i	$-0.243866\pi$
$349$	−4.48655	−	7.77093i	−0.240159	−	0.415968i	−0.960760	+	0.277383i	$0.910533\pi$
$350$		0			0
$351$	−11.3822	−	4.07944i	−0.607535	−	0.217744i
$352$	11.9586			0.637395
$353$	17.1252	+	29.6618i	0.911484	+	1.57874i	0.811969	+	0.583701i	$0.198396\pi$
$353$	17.1252	+	29.6618i	0.911484	+	1.57874i	0.0995150	+	0.995036i	$0.468271\pi$
$354$	−1.12890	−	1.95530i	−0.0600001	−	0.103923i
$355$		0			0
$356$	−19.5036			−1.03369
$357$	8.79585	−	15.2349i	0.465526	−	0.806315i
$358$	−2.97921	+	5.16014i	−0.157456	+	0.272722i
$359$	22.4043			1.18245			0.591227	−	0.806505i	$-0.298644\pi$
$359$	22.4043			1.18245			0.591227	+	0.806505i	$0.298644\pi$
$360$		0			0
$361$	8.72398	+	15.1104i	0.459157	+	0.795283i
$362$	0.172641	+	0.299023i	0.00907381	+	0.0157163i
$363$	−1.25092			−0.0656565
$364$	4.08016	+	22.4918i	0.213858	+	1.17889i
$365$		0			0
$366$	−3.33582	−	5.77781i	−0.174366	−	0.302011i
$367$	6.59753	+	11.4273i	0.344388	+	0.596498i	0.985242	−	0.171165i	$-0.0547530\pi$
$367$	6.59753	+	11.4273i	0.344388	+	0.596498i	−0.640854	+	0.767663i	$0.721420\pi$
$368$	4.51586	−	7.82169i	0.235405	−	0.407734i
$369$	11.8080			0.614700
$370$		0			0
$371$	21.5185	−	37.2712i	1.11719	−	1.93502i
$372$	−19.2419			−0.997647
$373$	7.63070	−	13.2168i	0.395103	−	0.684338i	−0.598012	−	0.801488i	$-0.704042\pi$
$373$	7.63070	−	13.2168i	0.395103	−	0.684338i	0.993114	+	0.117149i	$0.0373756\pi$
$374$	−1.04635	−	1.81233i	−0.0541053	−	0.0937131i
$375$		0			0
$376$	8.84210			0.455997
$377$	1.93070	+	10.6430i	0.0994362	+	0.548140i
$378$	3.72052			0.191363
$379$	−9.11453	−	15.7868i	−0.468182	−	0.810915i	0.531157	−	0.847273i	$-0.321757\pi$
$379$	−9.11453	−	15.7868i	−0.468182	−	0.810915i	−0.999339	+	0.0363588i	$0.988424\pi$
$380$		0			0
$381$	−12.3334	+	21.3621i	−0.631861	+	1.09442i
$382$	−8.44246			−0.431954
$383$	−0.720440	+	1.24784i	−0.0368128	+	0.0637616i	−0.883845	−	0.467780i	$-0.845054\pi$
$383$	−0.720440	+	1.24784i	−0.0368128	+	0.0637616i	0.847032	+	0.531542i	$0.178387\pi$
$384$	−12.3627	+	21.4129i	−0.630883	+	1.09272i
$385$		0			0
$386$	3.27870	−	5.67888i	0.166882	−	0.289048i
$387$	−18.5480	−	32.1261i	−0.942848	−	1.63306i
$388$	4.97788	+	8.62194i	0.252714	+	0.437713i
$389$	−18.7912			−0.952754			−0.476377	−	0.879241i	$-0.658050\pi$
$389$	−18.7912			−0.952754			−0.476377	+	0.879241i	$0.658050\pi$
$390$		0			0
$391$	−5.24581			−0.265292
$392$	−2.73247	−	4.73277i	−0.138010	−	0.239041i
$393$	−13.4590	−	23.3117i	−0.678918	−	1.17592i
$394$	−3.58163	+	6.20357i	−0.180440	+	0.312531i
$395$		0			0
$396$	−13.0269	+	22.5633i	−0.654627	+	1.13385i
$397$	8.54634	−	14.8027i	0.428928	−	0.742926i	−0.567850	−	0.823132i	$-0.692225\pi$
$397$	8.54634	−	14.8027i	0.428928	−	0.742926i	0.996778	+	0.0802063i	$0.0255579\pi$
$398$	−6.03084			−0.302298
$399$	−5.62291	+	9.73916i	−0.281497	+	0.487568i
$400$		0			0
$401$	−11.1011	−	19.2276i	−0.554361	−	0.960182i	−0.997953	−	0.0639527i	$-0.979629\pi$
$401$	−11.1011	−	19.2276i	−0.554361	−	0.960182i	0.443592	−	0.896229i	$-0.353704\pi$
$402$	−3.57568			−0.178339
$403$	−12.8336	−	4.59962i	−0.639285	−	0.229124i
$404$	−10.7960			−0.537122
$405$		0			0
$406$	−1.66418	−	2.88244i	−0.0825918	−	0.143053i
$407$	−3.16273	+	5.47801i	−0.156771	+	0.271535i
$408$	6.75207			0.334277
$409$	4.81638	−	8.34221i	0.238155	−	0.412496i	−0.722030	−	0.691862i	$-0.756791\pi$
$409$	4.81638	−	8.34221i	0.238155	−	0.412496i	0.960185	+	0.279366i	$0.0901242\pi$
$410$		0			0
$411$	−45.3534			−2.23712
$412$	6.96537	−	12.0644i	0.343159	−	0.594369i
$413$	−4.25101	−	7.36296i	−0.209178	−	0.362308i
$414$	−1.89055	−	3.27452i	−0.0929153	−	0.160934i
$415$		0			0
$416$	−10.1340	+	8.58877i	−0.496859	+	0.421099i
$417$	−2.76423			−0.135365
$418$	0.668896	+	1.15856i	0.0327168	+	0.0566671i
$419$	0.978168	+	1.69424i	0.0477866	+	0.0827689i	0.888929	−	0.458044i	$-0.151450\pi$
$419$	0.978168	+	1.69424i	0.0477866	+	0.0827689i	−0.841143	+	0.540813i	$0.818117\pi$
$420$		0			0
$421$	−12.0807			−0.588778			−0.294389	−	0.955686i	$-0.595116\pi$
$421$	−12.0807			−0.588778			−0.294389	+	0.955686i	$0.595116\pi$
$422$	3.19251	−	5.52959i	0.155409	−	0.269176i
$423$	−14.5835	+	25.2594i	−0.709075	+	1.22815i
$424$	16.5185			0.802210
$425$		0			0
$426$	2.33582	+	4.04576i	0.113171	+	0.196018i
$427$	−12.5615	−	21.7571i	−0.607893	−	1.05290i
$428$	16.2104			0.783558
$429$	−24.0320	+	20.3676i	−1.16027	+	0.983359i
$430$		0			0
$431$	−12.2945	−	21.2948i	−0.592207	−	1.02573i	−0.993934	−	0.109974i	$-0.964923\pi$
$431$	−12.2945	−	21.2948i	−0.592207	−	1.02573i	0.401727	−	0.915759i	$-0.368410\pi$
$432$	−5.62590	−	9.74434i	−0.270676	−	0.468825i
$433$	18.0364	−	31.2400i	0.866775	−	1.50130i	0.00150085	−	0.999999i	$-0.499522\pi$
$433$	18.0364	−	31.2400i	0.866775	−	1.50130i	0.865274	−	0.501299i	$-0.167144\pi$
$434$	4.19495			0.201364
$435$		0			0
$436$	−8.02690	+	13.9030i	−0.384419	+	0.665833i
$437$	3.35348			0.160419
$438$	2.43339	−	4.21475i	0.116272	−	0.201389i
$439$	−1.26764	−	2.19562i	−0.0605013	−	0.104791i	0.834188	−	0.551480i	$-0.185937\pi$
$439$	−1.26764	−	2.19562i	−0.0605013	−	0.104791i	−0.894690	+	0.446688i	$0.852603\pi$
$440$		0			0
$441$	18.0269			0.858424
$442$	2.18833	+	0.784309i	0.104088	+	0.0373058i
$443$	−19.3579			−0.919721			−0.459860	−	0.887991i	$-0.652101\pi$
$443$	−19.3579			−0.919721			−0.459860	+	0.887991i	$0.652101\pi$
$444$	−4.95873	−	8.58877i	−0.235331	−	0.407605i
$445$		0			0
$446$	−2.04635	+	3.54438i	−0.0968973	+	0.167831i
$447$	42.6696			2.01820
$448$	−9.20801	+	15.9487i	−0.435038	+	0.753507i
$449$	12.4040	−	21.4844i	0.585381	−	1.01391i	−0.409447	−	0.912334i	$-0.634278\pi$
$449$	12.4040	−	21.4844i	0.585381	−	1.01391i	0.994828	−	0.101576i	$-0.0323884\pi$
$450$		0			0
$451$	4.51345	−	7.81753i	0.212530	−	0.368113i
$452$	6.93114	+	12.0051i	0.326013	+	0.564672i
$453$	−19.5767	−	33.9079i	−0.919795	−	1.59313i
$454$	−2.03888			−0.0956896
$455$		0			0
$456$	−4.31638			−0.202133
$457$	−3.78374	−	6.55363i	−0.176996	−	0.306566i	0.763854	−	0.645389i	$-0.223305\pi$
$457$	−3.78374	−	6.55363i	−0.176996	−	0.306566i	−0.940850	+	0.338823i	$0.889971\pi$
$458$	−4.46352	−	7.73105i	−0.208567	−	0.361248i
$459$	−3.26764	+	5.65972i	−0.152520	+	0.264173i
$460$		0			0
$461$	6.17164	−	10.6896i	0.287442	−	0.497864i	−0.685756	−	0.727831i	$-0.740528\pi$
$461$	6.17164	−	10.6896i	0.287442	−	0.497864i	0.973198	+	0.229967i	$0.0738618\pi$
$462$	4.84669	−	8.39472i	0.225489	−	0.390558i
$463$	22.8578			1.06229			0.531146	−	0.847281i	$-0.321762\pi$
$463$	22.8578			1.06229			0.531146	+	0.847281i	$0.321762\pi$
$464$	−5.03289	+	8.71723i	−0.233646	+	0.404687i
$465$		0			0
$466$	−0.136357	−	0.236178i	−0.00631664	−	0.0109407i
$467$	−15.2976			−0.707889			−0.353945	−	0.935266i	$-0.615160\pi$
$467$	−15.2976			−0.707889			−0.353945	+	0.935266i	$0.615160\pi$
$468$	−5.16586	−	28.4766i	−0.238792	−	1.31633i
$469$	−13.4647			−0.621743
$470$		0			0
$471$	14.6985	+	25.4586i	0.677273	+	1.17307i
$472$	1.63163	−	2.82606i	0.0751017	−	0.130080i
$473$	−28.3589			−1.30394
$474$	6.13636	−	10.6285i	0.281852	−	0.488182i
$475$		0			0
$476$	12.3553			0.566303
$477$	−27.2444	+	47.1887i	−1.24744	+	2.16062i
$478$	0.661673	+	1.14605i	0.0302642	+	0.0524192i
$479$	−12.1414	−	21.0296i	−0.554756	−	0.960866i	−0.997922	−	0.0644264i	$-0.979478\pi$
$479$	−12.1414	−	21.0296i	−0.554756	−	0.960866i	0.443166	−	0.896439i	$-0.353855\pi$
$480$		0			0
$481$	−1.25419	−	6.91369i	−0.0571861	−	0.315237i
$482$	−7.50793			−0.341977
$483$	−12.1493	−	21.0433i	−0.552814	−	0.957501i
$484$	−0.439284	−	0.760862i	−0.0199674	−	0.0345846i
$485$		0			0
$486$	6.63276			0.300868
$487$	−18.4441	+	31.9462i	−0.835783	+	1.44762i	0.0576081	+	0.998339i	$0.481653\pi$
$487$	−18.4441	+	31.9462i	−0.835783	+	1.44762i	−0.893391	+	0.449280i	$0.851681\pi$
$488$	4.82136	−	8.35085i	0.218253	−	0.378025i
$489$	11.2458			0.508553
$490$		0			0
$491$	17.6767	+	30.6170i	0.797739	+	1.38172i	0.921085	+	0.389361i	$0.127304\pi$
$491$	17.6767	+	30.6170i	0.797739	+	1.38172i	−0.123346	+	0.992364i	$0.539363\pi$
$492$	7.07647	+	12.2568i	0.319032	+	0.552580i
$493$	5.84642			0.263310
$494$	−1.39893	−	0.501383i	−0.0629407	−	0.0225583i
$495$		0			0
$496$	−6.34328	−	10.9869i	−0.284822	−	0.493326i
$497$	8.79585	+	15.2349i	0.394548	+	0.683377i
$498$	−3.83806	+	6.64771i	−0.171988	+	0.297891i
$499$	16.2189			0.726058			0.363029	−	0.931778i	$-0.381743\pi$
$499$	16.2189			0.726058			0.363029	+	0.931778i	$0.381743\pi$
$500$		0			0
$501$	−4.51345	+	7.81753i	−0.201646	+	0.349261i
$502$	−6.29480			−0.280950
$503$	−10.1192	+	17.5270i	−0.451193	+	0.781489i	−0.998460	−	0.0554688i	$-0.982335\pi$
$503$	−10.1192	+	17.5270i	−0.451193	+	0.781489i	0.547268	+	0.836958i	$0.315668\pi$
$504$	9.16326	+	15.8712i	0.408164	+	0.706961i
$505$		0			0
$506$	−2.89055			−0.128500
$507$	5.73700	−	34.5200i	0.254789	−	1.53309i
$508$	−17.3244			−0.768646
$509$	10.0185	+	17.3526i	0.444063	+	0.769140i	0.997986	−	0.0634276i	$-0.0202032\pi$
$509$	10.0185	+	17.3526i	0.444063	+	0.769140i	−0.553923	+	0.832568i	$0.686870\pi$
$510$		0			0
$511$	9.16326	−	15.8712i	0.405359	−	0.702102i
$512$	−20.9992			−0.928042
$513$	2.08890	−	3.61808i	0.0922271	−	0.159742i
$514$	0.349273	−	0.604959i	0.0154058	−	0.0266836i
$515$		0			0
$516$	22.2314	−	38.5060i	0.978685	−	1.69513i
$517$	11.1487	+	19.3101i	0.490320	+	0.849259i
$518$	1.08106	+	1.87244i	0.0474988	+	0.0822704i
$519$	−23.5185			−1.03235
$520$		0			0
$521$	16.0269			0.702151			0.351076	−	0.936347i	$-0.385816\pi$
$521$	16.0269			0.702151			0.351076	+	0.936347i	$0.385816\pi$
$522$	2.10700	+	3.64944i	0.0922210	+	0.159732i
$523$	5.86898	+	10.1654i	0.256633	+	0.444501i	0.965338	−	0.261004i	$-0.0840536\pi$
$523$	5.86898	+	10.1654i	0.256633	+	0.444501i	−0.708705	+	0.705505i	$0.750720\pi$
$524$	9.45274	−	16.3726i	0.412945	−	0.715241i
$525$		0			0
$526$	−4.94887	+	8.57170i	−0.215781	+	0.373744i
$527$	−3.68431	+	6.38142i	−0.160491	+	0.277979i
$528$	−29.3152			−1.27578
$529$	7.87709	−	13.6435i	0.342482	−	0.593197i
$530$		0			0
$531$	5.38217	+	9.32219i	0.233566	+	0.404548i
$532$	−7.89832			−0.342436
$533$	1.78982	+	9.86635i	0.0775258	+	0.427359i
$534$	−9.18722			−0.397570
$535$		0			0
$536$	−2.58402	−	4.47565i	−0.111613	−	0.193319i
$537$	24.2399	−	41.9847i	1.04603	−	1.81177i
$538$	−6.14995			−0.265143
$539$	6.89055	−	11.9348i	0.296797	−	0.514067i
$540$		0			0
$541$	−21.8080			−0.937599			−0.468800	−	0.883305i	$-0.655313\pi$
$541$	−21.8080			−0.937599			−0.468800	+	0.883305i	$0.655313\pi$
$542$	0.963521	−	1.66887i	0.0413868	−	0.0716840i
$543$	−1.40467	−	2.43296i	−0.0602801	−	0.104408i
$544$	3.59001	+	6.21808i	0.153920	+	0.266598i
$545$		0			0
$546$	1.92197	+	10.5948i	0.0822527	+	0.453416i
$547$	−6.30924			−0.269764			−0.134882	−	0.990862i	$-0.543065\pi$
$547$	−6.30924			−0.269764			−0.134882	+	0.990862i	$0.543065\pi$
$548$	−15.9266	−	27.5858i	−0.680352	−	1.17840i
$549$	15.9040	+	27.5465i	0.678766	+	1.17566i
$550$		0			0
$551$	−3.73743			−0.159220
$552$	4.66317	−	8.07684i	0.198478	−	0.343773i
$553$	23.1073	−	40.0230i	0.982622	−	1.70195i
$554$	−4.47964			−0.190322
$555$		0			0
$556$	−0.970706	−	1.68131i	−0.0411671	−	0.0713035i
$557$	−17.9189	−	31.0364i	−0.759247	−	1.31506i	−0.943235	−	0.332126i	$-0.892234\pi$
$557$	−17.9189	−	31.0364i	−0.759247	−	1.31506i	0.183987	−	0.982929i	$-0.441099\pi$
$558$	−5.31119			−0.224840
$559$	24.0320	−	20.3676i	1.01644	−	0.861459i
$560$		0			0
$561$	8.51345	+	14.7457i	0.359438	+	0.622565i
$562$	−0.0768725	−	0.133147i	−0.00324267	−	0.00561647i
$563$	−2.50106	+	4.33196i	−0.105407	+	0.182570i	−0.913904	−	0.405929i	$-0.866948\pi$
$563$	−2.50106	+	4.33196i	−0.105407	+	0.182570i	0.808497	+	0.588500i	$0.200281\pi$
$564$	−34.9593			−1.47205
$565$		0			0
$566$	1.66418	−	2.88244i	0.0699507	−	0.121158i
$567$	12.4432			0.522564
$568$	−3.37603	+	5.84746i	−0.141655	+	0.245354i
$569$	6.58402	+	11.4039i	0.276017	+	0.478075i	0.970391	−	0.241539i	$-0.0776522\pi$
$569$	6.58402	+	11.4039i	0.276017	+	0.478075i	−0.694375	+	0.719614i	$0.744319\pi$
$570$		0			0
$571$	19.8349			0.830065			0.415032	−	0.909807i	$-0.363770\pi$
$571$	19.8349			0.830065			0.415032	+	0.909807i	$0.363770\pi$
$572$	−20.8276	−	7.46475i	−0.870848	−	0.312117i
$573$	68.6909			2.86960
$574$	−1.54275	−	2.67212i	−0.0643930	−	0.111532i
$575$		0			0
$576$	11.6582	−	20.1926i	0.485758	−	0.841357i
$577$	10.9210			0.454646			0.227323	−	0.973819i	$-0.427003\pi$
$577$	10.9210			0.454646			0.227323	+	0.973819i	$0.427003\pi$
$578$	−2.18388	+	3.78258i	−0.0908373	+	0.157335i
$579$	−26.6767	+	46.2054i	−1.10865	+	1.92023i
$580$		0			0
$581$	−14.4527	+	25.0329i	−0.599601	+	1.03854i
$582$	2.34484	+	4.06139i	0.0971969	+	0.168350i
$583$	20.8276	+	36.0745i	0.862593	+	1.49406i
$584$	7.03411			0.291073
$585$		0			0
$586$	−4.44979			−0.183819
$587$	−20.2247	−	35.0303i	−0.834764	−	1.44585i	−0.894222	−	0.447624i	$-0.852270\pi$
$587$	−20.2247	−	35.0303i	−0.834764	−	1.44585i	0.0594576	−	0.998231i	$-0.481063\pi$
$588$	10.8034	+	18.7121i	0.445526	+	0.771673i
$589$	2.35526	−	4.07944i	0.0970469	−	0.168090i
$590$		0			0
$591$	29.1414	−	50.4744i	1.19872	−	2.07624i
$592$	3.26938	−	5.66274i	0.134371	−	0.232737i
$593$	1.47709			0.0606569			0.0303284	−	0.999540i	$-0.490345\pi$
$593$	1.47709			0.0606569			0.0303284	+	0.999540i	$0.490345\pi$
$594$	−1.80054	+	3.11862i	−0.0738769	+	0.127959i
$595$		0			0
$596$	14.9842	+	25.9533i	0.613775	+	1.06309i
$597$	49.0690			2.00826
$598$	2.44951	−	2.07602i	0.100168	−	0.0848947i
$599$	2.27271			0.0928606			0.0464303	−	0.998922i	$-0.485215\pi$
$599$	2.27271			0.0928606			0.0464303	+	0.998922i	$0.485215\pi$
$600$		0			0
$601$	−3.70215	−	6.41231i	−0.151014	−	0.261563i	0.780587	−	0.625048i	$-0.214920\pi$
$601$	−3.70215	−	6.41231i	−0.151014	−	0.261563i	−0.931600	+	0.363484i	$0.881587\pi$
$602$	−4.84669	+	8.39472i	−0.197536	+	0.342143i
$603$	17.0476			0.694231
$604$	13.7494	−	23.8147i	0.559456	−	0.969005i
$605$		0			0
$606$	−5.08549			−0.206584
$607$	5.34661	−	9.26059i	0.217012	−	0.375876i	−0.736881	−	0.676022i	$-0.763702\pi$
$607$	5.34661	−	9.26059i	0.217012	−	0.375876i	0.953893	+	0.300146i	$0.0970356\pi$
$608$	−2.29498	−	3.97502i	−0.0930736	−	0.161208i
$609$	13.5404	+	23.4526i	0.548683	+	0.950347i
$610$		0			0
$611$	−23.3164	−	8.35673i	−0.943280	−	0.338077i
$612$	−15.6429			−0.632327
$613$	−3.04075	−	5.26673i	−0.122815	−	0.212721i	0.798062	−	0.602575i	$-0.205859\pi$
$613$	−3.04075	−	5.26673i	−0.122815	−	0.212721i	−0.920877	+	0.389854i	$0.872525\pi$
$614$	4.07057	+	7.05043i	0.164275	+	0.284532i
$615$		0			0
$616$	14.0101			0.564485
$617$	−15.9194	+	27.5732i	−0.640892	+	1.11006i	0.344342	+	0.938844i	$0.388102\pi$
$617$	−15.9194	+	27.5732i	−0.640892	+	1.11006i	−0.985234	+	0.171213i	$0.945231\pi$
$618$	3.28106	−	5.68295i	0.131983	−	0.228602i
$619$	−26.4043			−1.06128			−0.530639	−	0.847598i	$-0.678048\pi$
$619$	−26.4043			−1.06128			−0.530639	+	0.847598i	$0.678048\pi$
$620$		0			0
$621$	4.51345	+	7.81753i	0.181119	+	0.313707i
$622$	0.403259	+	0.698464i	0.0161692	+	0.0280059i
$623$	−34.5957			−1.38605
$624$	24.8424	−	21.0545i	0.994491	−	0.842853i
$625$		0			0
$626$	−3.19200	−	5.52871i	−0.127578	−	0.220972i
$627$	−5.44238	−	9.42647i	−0.217348	−	0.376457i
$628$	−10.3233	+	17.8805i	−0.411944	+	0.713509i
$629$	−3.79785			−0.151430
$630$		0			0
$631$	−17.5840	+	30.4564i	−0.700009	+	1.21245i	0.268454	+	0.963293i	$0.413487\pi$
$631$	−17.5840	+	30.4564i	−0.700009	+	1.21245i	−0.968463	+	0.249158i	$0.919846\pi$
$632$	17.7381			0.705585
$633$	−25.9754	+	44.9907i	−1.03243	+	1.78822i
$634$	−4.76764	−	8.25780i	−0.189347	−	0.327959i
$635$		0			0
$636$	−65.3098			−2.58970
$637$	2.73247	+	15.0626i	0.108264	+	0.596804i
$638$	3.22150			0.127540
$639$	−11.1364	−	19.2887i	−0.440547	−	0.763051i
$640$		0			0
$641$	−2.76257	+	4.78491i	−0.109115	+	0.188993i	−0.915412	−	0.402518i	$-0.868135\pi$
$641$	−2.76257	+	4.78491i	−0.109115	+	0.188993i	0.806297	+	0.591511i	$0.201468\pi$
$642$	7.63594			0.301367
$643$	16.0776	−	27.8472i	0.634039	−	1.09819i	−0.352679	−	0.935744i	$-0.614729\pi$
$643$	16.0776	−	27.8472i	0.634039	−	1.09819i	0.986718	−	0.162444i	$-0.0519375\pi$
$644$	8.53289	−	14.7794i	0.336243	−	0.582390i
$645$		0			0
$646$	−0.401610	+	0.695609i	−0.0158011	+	0.0273684i
$647$	6.89216	+	11.9376i	0.270959	+	0.469314i	0.969108	−	0.246638i	$-0.0793260\pi$
$647$	6.89216	+	11.9376i	0.270959	+	0.469314i	−0.698149	+	0.715953i	$0.745993\pi$
$648$	2.38797	+	4.13609i	0.0938085	+	0.162481i
$649$	8.22905			0.323019
$650$		0			0
$651$	−34.1316			−1.33772
$652$	3.94916	+	6.84015i	0.154661	+	0.267881i
$653$	−4.25101	−	7.36296i	−0.166355	−	0.288135i	0.770781	−	0.637100i	$-0.219866\pi$
$653$	−4.25101	−	7.36296i	−0.166355	−	0.288135i	−0.937136	+	0.348965i	$0.886533\pi$
$654$	−3.78109	+	6.54905i	−0.147852	+	0.256088i
$655$		0			0
$656$	−4.66565	+	8.08115i	−0.182163	+	0.315516i
$657$	−11.6015	+	20.0944i	−0.452619	+	0.783959i
$658$	7.62150			0.297117
$659$	−2.02183	+	3.50192i	−0.0787594	+	0.136415i	−0.902715	−	0.430239i	$-0.858429\pi$
$659$	−2.02183	+	3.50192i	−0.0787594	+	0.136415i	0.823956	+	0.566654i	$0.191763\pi$
$660$		0			0
$661$	−15.6364	−	27.0830i	−0.608184	−	1.05341i	−0.991540	−	0.129805i	$-0.958565\pi$
$661$	−15.6364	−	27.0830i	−0.608184	−	1.05341i	0.383356	−	0.923601i	$-0.374768\pi$
$662$	0.983609			0.0382290
$663$	−17.8050	−	6.38142i	−0.691489	−	0.247834i
$664$	−11.0945			−0.430551
$665$		0			0
$666$	−1.36872	−	2.37068i	−0.0530366	−	0.0918622i
$667$	4.03771	−	6.99351i	0.156341	−	0.270790i
$668$	−6.33991			−0.245298
$669$	16.6498	−	28.8383i	0.643719	−	1.11495i
$670$		0			0
$671$	24.3164			0.938723
$672$	−16.6290	+	28.8022i	−0.641477	+	1.11107i
$673$	16.0370	+	27.7768i	0.618179	+	1.07072i	0.989818	+	0.142340i	$0.0454627\pi$
$673$	16.0370	+	27.7768i	0.618179	+	1.07072i	−0.371639	+	0.928377i	$0.621204\pi$
$674$	0.314906	+	0.545433i	0.0121297	+	0.0210093i
$675$		0			0
$676$	23.0111	−	8.63282i	0.885041	−	0.332031i
$677$	14.2382			0.547220			0.273610	−	0.961841i	$-0.411782\pi$
$677$	14.2382			0.547220			0.273610	+	0.961841i	$0.411782\pi$
$678$	3.26493	+	5.65503i	0.125389	+	0.217180i
$679$	8.82983	+	15.2937i	0.338858	+	0.586919i
$680$		0			0
$681$	16.5891			0.635695
$682$	−2.03013	+	3.51629i	−0.0777377	+	0.134646i
$683$	12.8923	−	22.3302i	0.493311	−	0.854440i	−0.506659	−	0.862146i	$-0.669120\pi$
$683$	12.8923	−	22.3302i	0.493311	−	0.854440i	0.999970	+	0.00770647i	$0.00245307\pi$
$684$	10.0000			0.382360
$685$		0			0
$686$	1.52782	+	2.64626i	0.0583325	+	0.101035i
$687$	36.3168	+	62.9025i	1.38557	+	2.39988i
$688$	29.3152			1.11763
$689$	−43.5589	−	15.6118i	−1.65946	−	0.594761i
$690$		0			0
$691$	0.0218318	+	0.0378138i	0.000830522	+	0.00143851i	0.866440	−	0.499281i	$-0.166402\pi$
$691$	0.0218318	+	0.0378138i	0.000830522	+	0.00143851i	−0.865610	+	0.500719i	$0.833069\pi$
$692$	−8.25894	−	14.3049i	−0.313958	−	0.543791i
$693$	−23.1073	+	40.0230i	−0.877774	+	1.52035i
$694$	4.18002			0.158671
$695$		0			0
$696$	−5.19707	+	9.00160i	−0.196995	+	0.341205i
$697$	5.41982			0.205290
$698$	1.48431	−	2.57091i	0.0561821	−	0.0973103i
$699$	1.10945	+	1.92163i	0.0419634	+	0.0726827i
$700$		0			0
$701$	−14.5454			−0.549373			−0.274687	−	0.961534i	$-0.588574\pi$
$701$	−14.5454			−0.549373			−0.274687	+	0.961534i	$0.588574\pi$
$702$	−0.714008	−	3.93595i	−0.0269485	−	0.148553i
$703$	2.42785			0.0915679
$704$	−8.91238	−	15.4367i	−0.335898	−	0.581792i
$705$		0			0
$706$	−5.66565	+	9.81320i	−0.213230	+	0.369325i
$707$	−19.1501			−0.720214
$708$	−6.45101	+	11.1735i	−0.242444	+	0.419925i
$709$	−9.81638	+	17.0025i	−0.368662	+	0.638541i	−0.989357	−	0.145511i	$-0.953517\pi$
$709$	−9.81638	+	17.0025i	−0.368662	+	0.638541i	0.620695	+	0.784052i	$0.286851\pi$
$710$		0			0
$711$	−29.2560	+	50.6728i	−1.09718	+	1.90038i
$712$	−6.63929	−	11.4996i	−0.248818	−	0.430965i
$713$	5.08898	+	8.81438i	0.190584	+	0.330101i
$714$	5.81998			0.217807
$715$		0			0
$716$	34.0490			1.27247
$717$	−5.38361	−	9.32468i	−0.201055	−	0.348237i
$718$	3.70608	+	6.41912i	0.138310	+	0.239559i
$719$	−23.7156	+	41.0766i	−0.884443	+	1.53190i	−0.0380914	+	0.999274i	$0.512128\pi$
$719$	−23.7156	+	41.0766i	−0.884443	+	1.53190i	−0.846351	+	0.532625i	$0.821206\pi$
$720$		0			0
$721$	12.3553	−	21.3999i	0.460134	−	0.796976i
$722$	−2.88621	+	4.99906i	−0.107414	+	0.186046i
$723$	61.0872			2.27186
$724$	0.986548	−	1.70875i	0.0366648	−	0.0635052i
$725$		0			0
$726$	−0.206926	−	0.358406i	−0.00767973	−	0.0133017i
$727$	34.0951			1.26452			0.632259	−	0.774757i	$-0.282128\pi$
$727$	34.0951			1.26452			0.632259	+	0.774757i	$0.282128\pi$
$728$	−11.8725	+	10.0622i	−0.440024	+	0.372931i
$729$	−42.8349			−1.58648
$730$		0			0
$731$	−8.51345	−	14.7457i	−0.314881	−	0.545391i
$732$	−19.0624	+	33.0170i	−0.704565	+	1.22034i
$733$	−14.3920			−0.531580			−0.265790	−	0.964031i	$-0.585633\pi$
$733$	−14.3920			−0.531580			−0.265790	+	0.964031i	$0.585633\pi$
$734$	−2.18270	+	3.78055i	−0.0805651	+	0.139543i
$735$		0			0
$736$	9.91745			0.365562
$737$	6.51621	−	11.2864i	0.240028	−	0.415740i
$738$	1.95326	+	3.38314i	0.0719004	+	0.124535i
$739$	17.2240	+	29.8328i	0.633594	+	1.09742i	0.986811	+	0.161876i	$0.0517545\pi$
$739$	17.2240	+	29.8328i	0.633594	+	1.09742i	−0.353217	+	0.935541i	$0.614912\pi$
$740$		0			0
$741$	11.3822	+	4.07944i	0.418134	+	0.149862i
$742$	14.2382			0.522702
$743$	−20.3567	−	35.2589i	−0.746816	−	1.29352i	−0.949342	−	0.314246i	$-0.898248\pi$
$743$	−20.3567	−	35.2589i	−0.746816	−	1.29352i	0.202526	−	0.979277i	$-0.435085\pi$
$744$	−6.55021	−	11.3453i	−0.240142	−	0.415939i
$745$		0			0
$746$	5.04903			0.184858
$747$	18.2985	−	31.6939i	0.669507	−	1.15962i
$748$	−5.97929	+	10.3564i	−0.218625	+	0.378669i
$749$	28.7542			1.05066
$750$		0			0
$751$	−16.2509	−	28.1474i	−0.593003	−	1.02711i	−0.993825	−	0.110956i	$-0.964609\pi$
$751$	−16.2509	−	28.1474i	−0.593003	−	1.02711i	0.400822	−	0.916156i	$-0.368725\pi$
$752$	−11.5247	−	19.9613i	−0.420261	−	0.727914i
$753$	51.2167			1.86644
$754$	−2.72997	+	2.31371i	−0.0994196	+	0.0842603i
$755$		0			0
$756$	−10.6304	−	18.4123i	−0.386623	−	0.669650i
$757$	6.51621	+	11.2864i	0.236836	+	0.410211i	0.959805	−	0.280669i	$-0.0905564\pi$
$757$	6.51621	+	11.2864i	0.236836	+	0.410211i	−0.722969	+	0.690881i	$0.757223\pi$
$758$	3.01542	−	5.22286i	0.109525	−	0.189703i
$759$	23.5185			0.853668
$760$		0			0
$761$	1.99493	−	3.45532i	0.0723161	−	0.125255i	−0.827600	−	0.561318i	$-0.810294\pi$
$761$	1.99493	−	3.45532i	0.0723161	−	0.125255i	0.899916	+	0.436063i	$0.143628\pi$
$762$	−8.16070			−0.295631
$763$	−14.2382	+	24.6613i	−0.515458	+	0.892800i
$764$	24.1220	+	41.7805i	0.872703	+	1.51157i
$765$		0			0
$766$	−0.476696			−0.0172237
$767$	−6.97348	+	5.91018i	−0.251798	+	0.213404i
$768$	21.3847			0.771652
$769$	−3.33343	−	5.77367i	−0.120207	−	0.208204i	0.799642	−	0.600476i	$-0.205022\pi$
$769$	−3.33343	−	5.77367i	−0.120207	−	0.208204i	−0.919849	+	0.392272i	$0.871689\pi$
$770$		0			0
$771$	−2.84181	+	4.92216i	−0.102345	+	0.177267i
$772$	−37.4720			−1.34865
$773$	−24.1675	+	41.8593i	−0.869244	+	1.50557i	−0.00647254	+	0.999979i	$0.502060\pi$
$773$	−24.1675	+	41.8593i	−0.869244	+	1.50557i	−0.862771	+	0.505595i	$0.831273\pi$
$774$	6.13636	−	10.6285i	0.220567	−	0.382033i
$775$		0			0
$776$	−3.38907	+	5.87005i	−0.121661	+	0.210723i
$777$	−8.79585	−	15.2349i	−0.315549	−	0.546548i
$778$	−3.10841	−	5.38393i	−0.111442	−	0.193023i
$779$	−3.46472			−0.124136
$780$		0			0
$781$	−17.0269			−0.609271
$782$	−0.867753	−	1.50299i	−0.0310308	−	0.0537469i
$783$	−5.03022	−	8.71259i	−0.179765	−	0.311363i
$784$	−7.12291	+	12.3372i	−0.254389	+	0.440615i
$785$		0			0
$786$	4.45274	−	7.71236i	0.158824	−	0.275091i
$787$	13.9806	−	24.2151i	0.498355	−	0.863176i	−0.501643	−	0.865074i	$-0.667271\pi$
$787$	13.9806	−	24.2151i	0.498355	−	0.863176i	0.999998	+	0.00189876i	$0.000604394\pi$
$788$	40.9341			1.45822
$789$	40.2658	−	69.7424i	1.43350	−	2.48290i
$790$		0			0
$791$	12.2945	+	21.2948i	0.437144	+	0.757155i
$792$	−17.7381			−0.630297
$793$	−20.6062	+	17.4642i	−0.731749	+	0.620174i
$794$	5.65488			0.200684
$795$		0			0
$796$	17.2314	+	29.8457i	0.610752	+	1.05785i
$797$	−18.6212	+	32.2529i	−0.659597	+	1.14246i	0.321123	+	0.947038i	$0.395940\pi$
$797$	−18.6212	+	32.2529i	−0.659597	+	1.14246i	−0.980720	+	0.195418i	$0.937393\pi$
$798$	−3.72052			−0.131705
$799$	−6.69377	+	11.5939i	−0.236808	+	0.410164i
$800$		0			0
$801$	43.8014			1.54765
$802$	3.67264	−	6.36120i	0.129685	−	0.224622i
$803$	8.86907	+	15.3617i	0.312983	+	0.542102i
$804$	10.2165	+	17.6955i	0.360309	+	0.624073i
$805$		0			0
$806$	−0.805054	−	4.43784i	−0.0283568	−	0.156316i
$807$	50.0382			1.76143
$808$	−3.67511	−	6.36548i	−0.129290	−	0.223937i
$809$	−7.26434	−	12.5822i	−0.255400	−	0.442367i	0.709604	−	0.704601i	$-0.248874\pi$
$809$	−7.26434	−	12.5822i	−0.255400	−	0.442367i	−0.965004	+	0.262234i	$0.915541\pi$
$810$		0			0
$811$	44.0538			1.54694			0.773469	−	0.633834i	$-0.218520\pi$
$811$	44.0538			1.54694			0.773469	+	0.633834i	$0.218520\pi$
$812$	−9.50986	+	16.4716i	−0.333731	+	0.578039i
$813$	−7.83955	+	13.5785i	−0.274945	+	0.476219i
$814$	−2.09269			−0.0733489
$815$		0			0
$816$	−8.80054	−	15.2430i	−0.308080	−	0.533611i
$817$	5.44238	+	9.42647i	0.190405	+	0.329790i
$818$	3.18687			0.111426
$819$	−9.16326	−	50.5123i	−0.320190	−	1.76504i
$820$		0			0
$821$	−13.5135	−	23.4060i	−0.471623	−	0.816875i	0.527850	−	0.849337i	$-0.322998\pi$
$821$	−13.5135	−	23.4060i	−0.471623	−	0.816875i	−0.999473	+	0.0324629i	$0.989665\pi$
$822$	−7.50229	−	12.9943i	−0.261672	−	0.453230i
$823$	19.7981	−	34.2914i	0.690120	−	1.19532i	−0.281679	−	0.959509i	$-0.590891\pi$
$823$	19.7981	−	34.2914i	0.690120	−	1.19532i	0.971798	−	0.235814i	$-0.0757755\pi$
$824$	9.48442			0.330405
$825$		0			0
$826$	1.40639	−	2.43594i	0.0489345	−	0.0847571i
$827$	−26.5639			−0.923716			−0.461858	−	0.886954i	$-0.652817\pi$
$827$	−26.5639			−0.923716			−0.461858	+	0.886954i	$0.652817\pi$
$828$	−10.8034	+	18.7121i	−0.375445	+	0.650290i
$829$	−6.99162	−	12.1098i	−0.242829	−	0.420592i	0.718690	−	0.695331i	$-0.244742\pi$
$829$	−6.99162	−	12.1098i	−0.242829	−	0.420592i	−0.961519	+	0.274738i	$0.911409\pi$
$830$		0			0
$831$	36.4480			1.26437
$832$	18.6393	+	6.68044i	0.646202	+	0.231603i
$833$	8.27427			0.286686
$834$	−0.457254	−	0.791986i	−0.0158334	−	0.0274242i
$835$		0			0
$836$	3.82237	−	6.62054i	0.132199	−	0.228976i
$837$	12.6798			0.438278
$838$	−0.323614	+	0.560515i	−0.0111791	+	0.0193627i
$839$	−7.19707	+	12.4657i	−0.248471	+	0.430364i	−0.963102	−	0.269138i	$-0.913261\pi$
$839$	−7.19707	+	12.4657i	−0.248471	+	0.430364i	0.714631	+	0.699502i	$0.246595\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−1.99837	−	3.46128i	−0.0688684	−	0.119284i
$843$	0.625462	+	1.08333i	0.0215421	+	0.0373119i
$844$	−36.4868			−1.25593
$845$		0			0
$846$	−9.64952			−0.331757
$847$	−0.779207	−	1.34963i	−0.0267739	−	0.0463737i
$848$	−21.5300	−	37.2910i	−0.739343	−	1.28058i
$849$	−13.5404	+	23.4526i	−0.464704	+	0.804891i
$850$		0			0
$851$	−2.62291	+	4.54300i	−0.0899120	+	0.155732i
$852$	13.3479	−	23.1193i	0.457292	−	0.792053i
$853$	−27.2633			−0.933478			−0.466739	−	0.884395i	$-0.654571\pi$
$853$	−27.2633			−0.933478			−0.466739	+	0.884395i	$0.654571\pi$
$854$	4.15580	−	7.19806i	0.142209	−	0.246312i
$855$		0			0
$856$	5.51823	+	9.55786i	0.188609	+	0.326681i
$857$	−50.6201			−1.72915			−0.864575	−	0.502503i	$-0.832413\pi$
$857$	−50.6201			−1.72915			−0.864575	+	0.502503i	$0.832413\pi$
$858$	−9.81092	−	3.51629i	−0.334939	−	0.120044i
$859$	1.27992			0.0436702			0.0218351	−	0.999762i	$-0.493049\pi$
$859$	1.27992			0.0436702			0.0218351	+	0.999762i	$0.493049\pi$
$860$		0			0
$861$	12.5523	+	21.7413i	0.427782	+	0.740941i
$862$	4.06749	−	7.04509i	0.138539	−	0.239957i
$863$	8.38448			0.285411			0.142706	−	0.989765i	$-0.454420\pi$
$863$	8.38448			0.285411			0.142706	+	0.989765i	$0.454420\pi$
$864$	6.17763	−	10.7000i	0.210167	−	0.364020i
$865$		0			0
$866$	11.9342			0.405541
$867$	17.7688	−	30.7765i	0.603460	−	1.04522i
$868$	−11.9859	−	20.7602i	−0.406828	−	0.704646i
$869$	22.3654	+	38.7380i	0.758695	+	1.31410i
$870$		0			0
$871$	2.58402	+	14.2443i	0.0875562	+	0.482651i
$872$	−10.9299			−0.370132
$873$	−11.1794	−	19.3632i	−0.378365	−	0.655347i
$874$	0.554726	+	0.960814i	0.0187639	+	0.0325000i
$875$		0			0
$876$	−27.8109			−0.939645
$877$	27.9431	−	48.3989i	0.943572	−	1.63431i	0.184985	−	0.982741i	$-0.440776\pi$
$877$	27.9431	−	48.3989i	0.943572	−	1.63431i	0.758586	−	0.651573i	$-0.225890\pi$
$878$	0.419382	−	0.726391i	0.0141535	−	0.0245145i
$879$	36.2051			1.22117
$880$		0			0
$881$	−12.5975	−	21.8195i	−0.424420	−	0.735116i	0.571946	−	0.820291i	$-0.306189\pi$
$881$	−12.5975	−	21.8195i	−0.424420	−	0.735116i	−0.996366	+	0.0851746i	$0.972855\pi$
$882$	2.98198	+	5.16494i	0.100408	+	0.173913i
$883$	−30.7868			−1.03606			−0.518029	−	0.855363i	$-0.673334\pi$
$883$	−30.7868			−1.03606			−0.518029	+	0.855363i	$0.673334\pi$
$884$	−2.37110	−	13.0707i	−0.0797489	−	0.439614i
$885$		0			0
$886$	−3.20215	−	5.54628i	−0.107578	−	0.186331i
$887$	6.23603	+	10.8011i	0.209385	+	0.362666i	0.951521	−	0.307584i	$-0.0995204\pi$
$887$	6.23603	+	10.8011i	0.209385	+	0.362666i	−0.742136	+	0.670250i	$0.766187\pi$
$888$	3.37603	−	5.84746i	0.113292	−	0.196228i
$889$	−30.7302			−1.03066
$890$		0			0
$891$	−6.02183	+	10.4301i	−0.201739	+	0.349422i
$892$	23.3875			0.783071
$893$	4.27911	−	7.41163i	0.143195	−	0.248021i
$894$	7.05833	+	12.2254i	0.236066	+	0.408878i
$895$		0			0
$896$	−30.8032			−1.02906
$897$	−19.9301	+	16.8912i	−0.665447	+	0.563981i
$898$	8.20739			0.273884
$899$	−5.67164	−	9.82357i	−0.189160	−	0.327634i
$900$		0			0
$901$	−12.5051	+	21.6594i	−0.416604	+	0.721580i
$902$	2.98643			0.0994372
$903$	39.4344	−	68.3024i	1.31230	−	2.27296i
$904$	−4.71891	+	8.17338i	−0.156948	+	0.271843i
$905$		0			0
$906$	6.47670	−	11.2180i	0.215174	−	0.372692i
$907$	19.4455	+	33.6807i	0.645678	+	1.11835i	0.984144	+	0.177369i	$0.0567587\pi$
$907$	19.4455	+	33.6807i	0.645678	+	1.11835i	−0.338466	+	0.940979i	$0.609908\pi$
$908$	5.82555	+	10.0901i	0.193328	+	0.334853i
$909$	24.2458			0.804183
$910$		0			0
$911$	0.165096			0.00546989			0.00273494	−	0.999996i	$-0.499129\pi$
$911$	0.165096			0.00546989			0.00273494	+	0.999996i	$0.499129\pi$
$912$	5.62590	+	9.74434i	0.186292	+	0.322667i
$913$	−13.9887	−	24.2292i	−0.462959	−	0.801868i
$914$	1.25180	−	2.16818i	0.0414059	−	0.0717171i
$915$		0			0
$916$	−25.5065	+	44.1786i	−0.842760	+	1.45970i
$917$	16.7674	−	29.0420i	0.553708	−	0.959050i
$918$	−2.16211			−0.0713603
$919$	−0.447663	+	0.775375i	−0.0147670	+	0.0255773i	−0.873314	−	0.487157i	$-0.838034\pi$
$919$	−0.447663	+	0.775375i	−0.0147670	+	0.0255773i	0.858547	+	0.512734i	$0.171367\pi$
$920$		0			0
$921$	−33.1196	−	57.3648i	−1.09133	−	1.89024i
$922$	4.08361			0.134486
$923$	14.4290	−	12.2289i	0.474935	−	0.402518i
$924$	−55.3923			−1.82227
$925$		0			0
$926$	3.78109	+	6.54905i	0.124254	+	0.215215i
$927$	−15.6429	+	27.0943i	−0.513780	+	0.889893i
$928$	−11.0529			−0.362831
$929$	6.14474	−	10.6430i	0.201602	−	0.349185i	−0.747443	−	0.664326i	$-0.768718\pi$
$929$	6.14474	−	10.6430i	0.201602	−	0.349185i	0.949045	+	0.315141i	$0.102052\pi$
$930$		0			0
$931$	−5.28947			−0.173356
$932$	−0.779207	+	1.34963i	−0.0255238	+	0.0442085i
$933$	−3.28106	−	5.68295i	−0.107417	−	0.186052i
$934$	−2.53051	−	4.38296i	−0.0828007	−	0.143415i
$935$		0			0
$936$	15.0317	−	12.7397i	0.491326	−	0.416410i
$937$	−5.77242			−0.188577			−0.0942884	−	0.995545i	$-0.530058\pi$
$937$	−5.77242			−0.188577			−0.0942884	+	0.995545i	$0.530058\pi$
$938$	−2.22731	−	3.85781i	−0.0727242	−	0.125962i
$939$	25.9713	+	44.9835i	0.847540	+	1.46798i
$940$		0			0
$941$	−55.8887			−1.82192			−0.910960	−	0.412495i	$-0.864658\pi$
$941$	−55.8887			−1.82192			−0.910960	+	0.412495i	$0.864658\pi$
$942$	−4.86282	+	8.42264i	−0.158439	+	0.274425i
$943$	3.74308	−	6.48321i	0.121891	−	0.211122i
$944$	−8.50655			−0.276864
$945$		0			0
$946$	−4.69108	−	8.12520i	−0.152520	−	0.264173i
$947$	0.948188	+	1.64231i	0.0308120	+	0.0533679i	0.881020	−	0.473079i	$-0.156857\pi$
$947$	0.948188	+	1.64231i	0.0308120	+	0.0533679i	−0.850208	+	0.526447i	$0.823524\pi$
$948$	−70.1318			−2.27777
$949$	−18.5487	−	6.64798i	−0.602117	−	0.215802i
$950$		0			0
$951$	38.7912	+	67.1884i	1.25789	+	2.17873i
$952$	4.20590	+	7.28483i	0.136314	+	0.236103i
$953$	−16.8262	+	29.1438i	−0.545053	+	0.944059i	0.453551	+	0.891230i	$0.350157\pi$
$953$	−16.8262	+	29.1438i	−0.545053	+	0.944059i	−0.998604	+	0.0528285i	$0.983176\pi$
$954$	−18.0269			−0.583643
$955$		0			0
$956$	3.78109	−	6.54905i	0.122289	−	0.211811i
$957$	−26.2113			−0.847290
$958$	4.01683	−	6.95735i	0.129778	−	0.224782i
$959$	−28.2509	−	48.9320i	−0.912269	−	1.58010i
$960$		0			0
$961$	−16.7033			−0.538817
$962$	1.77339	−	1.50299i	0.0571765	−	0.0484584i
$963$	−36.4054			−1.17315
$964$	21.4518	+	37.1556i	0.690917	+	1.19670i
$965$		0			0
$966$	4.01944	−	6.96188i	0.129323	−	0.223995i
$967$	−23.0493			−0.741216			−0.370608	−	0.928789i	$-0.620851\pi$
$967$	−23.0493			−0.741216			−0.370608	+	0.928789i	$0.620851\pi$
$968$	0.299076	−	0.518015i	0.00961267	−	0.0166496i
$969$	3.26764	−	5.65972i	0.104972	−	0.181816i
$970$		0			0
$971$	−7.45964	+	12.9205i	−0.239391	+	0.414638i	−0.960540	−	0.278143i	$-0.910281\pi$
$971$	−7.45964	+	12.9205i	−0.239391	+	0.414638i	0.721148	+	0.692781i	$0.243615\pi$
$972$	−18.9513	−	32.8246i	−0.607862	−	1.05285i
$973$	−1.72185	−	2.98233i	−0.0552000	−	0.0956092i
$974$	−12.2040			−0.391041
$975$		0			0
$976$	−25.1364			−0.804595
$977$	11.6821	+	20.2339i	0.373742	+	0.647341i	0.990138	−	0.140096i	$-0.0447411\pi$
$977$	11.6821	+	20.2339i	0.373742	+	0.647341i	−0.616396	+	0.787437i	$0.711408\pi$
$978$	1.86026	+	3.22207i	0.0594846	+	0.103030i
$979$	16.7425	−	28.9989i	0.535093	−	0.926808i
$980$		0			0
$981$	18.0269	−	31.2235i	0.575555	−	0.996890i
$982$	−5.84810	+	10.1292i	−0.186620	+	0.323236i
$983$	5.31119			0.169401			0.0847003	−	0.996406i	$-0.473007\pi$
$983$	5.31119			0.169401			0.0847003	+	0.996406i	$0.473007\pi$
$984$	−4.81785	+	8.34476i	−0.153587	+	0.266021i
$985$		0			0
$986$	0.967105	+	1.67508i	0.0307989	+	0.0533453i
$987$	−62.0112			−1.97384
$988$	1.51577	+	8.35565i	0.0482231	+	0.265829i
$989$	−23.5185			−0.747846
$990$		0			0
$991$	12.0440	+	20.8607i	0.382589	+	0.662663i	0.991432	−	0.130628i	$-0.0416992\pi$
$991$	12.0440	+	20.8607i	0.382589	+	0.662663i	−0.608843	+	0.793291i	$0.708366\pi$
$992$	6.96537	−	12.0644i	0.221151	−	0.383044i
$993$	−8.00299			−0.253967
$994$	−2.90999	+	5.04025i	−0.0922993	+	0.159867i
$995$		0			0
$996$	43.8648			1.38991
$997$	−10.2050	+	17.6755i	−0.323195	+	0.559790i	−0.981145	−	0.193271i	$-0.938090\pi$
$997$	−10.2050	+	17.6755i	−0.323195	+	0.559790i	0.657951	+	0.753061i	$0.271424\pi$
$998$	2.68290	+	4.64692i	0.0849258	+	0.147096i
$999$	3.26764	+	5.65972i	0.103384	+	0.179066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.e.e.276.4		12
5.2	odd	4		65.2.n.a.29.3	yes	12
5.3	odd	4		65.2.n.a.29.4	yes	12
5.4	even	2	inner	325.2.e.e.276.3		12
13.3	even	3		4225.2.a.br.1.3		6
13.9	even	3	inner	325.2.e.e.126.4		12
13.10	even	6		4225.2.a.bq.1.4		6
15.2	even	4		585.2.bs.a.289.4		12
15.8	even	4		585.2.bs.a.289.3		12
20.3	even	4		1040.2.dh.a.289.1		12
20.7	even	4		1040.2.dh.a.289.6		12
65.2	even	12		845.2.d.d.844.5		12
65.3	odd	12		845.2.b.d.339.4		6
65.7	even	12		845.2.l.f.654.6		24
65.8	even	4		845.2.l.f.699.8		24
65.9	even	6	inner	325.2.e.e.126.3		12
65.12	odd	4		845.2.n.e.484.4		12
65.17	odd	12		845.2.n.e.529.3		12
65.18	even	4		845.2.l.f.699.6		24
65.22	odd	12		65.2.n.a.9.4	yes	12
65.23	odd	12		845.2.b.e.339.3		6
65.28	even	12		845.2.d.d.844.8		12
65.29	even	6		4225.2.a.br.1.4		6
65.32	even	12		845.2.l.f.654.8		24
65.33	even	12		845.2.l.f.654.7		24
65.37	even	12		845.2.d.d.844.7		12
65.38	odd	4		845.2.n.e.484.3		12
65.42	odd	12		845.2.b.d.339.3		6
65.43	odd	12		845.2.n.e.529.4		12
65.47	even	4		845.2.l.f.699.5		24
65.48	odd	12		65.2.n.a.9.3	✓	12
65.49	even	6		4225.2.a.bq.1.3		6
65.57	even	4		845.2.l.f.699.7		24
65.58	even	12		845.2.l.f.654.5		24
65.62	odd	12		845.2.b.e.339.4		6
65.63	even	12		845.2.d.d.844.6		12
195.113	even	12		585.2.bs.a.334.4		12
195.152	even	12		585.2.bs.a.334.3		12
260.87	even	12		1040.2.dh.a.529.1		12
260.243	even	12		1040.2.dh.a.529.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.3	✓	12	65.48	odd	12
65.2.n.a.9.4	yes	12	65.22	odd	12
65.2.n.a.29.3	yes	12	5.2	odd	4
65.2.n.a.29.4	yes	12	5.3	odd	4
325.2.e.e.126.3		12	65.9	even	6	inner
325.2.e.e.126.4		12	13.9	even	3	inner
325.2.e.e.276.3		12	5.4	even	2	inner
325.2.e.e.276.4		12	1.1	even	1	trivial
585.2.bs.a.289.3		12	15.8	even	4
585.2.bs.a.289.4		12	15.2	even	4
585.2.bs.a.334.3		12	195.152	even	12
585.2.bs.a.334.4		12	195.113	even	12
845.2.b.d.339.3		6	65.42	odd	12
845.2.b.d.339.4		6	65.3	odd	12
845.2.b.e.339.3		6	65.23	odd	12
845.2.b.e.339.4		6	65.62	odd	12
845.2.d.d.844.5		12	65.2	even	12
845.2.d.d.844.6		12	65.63	even	12
845.2.d.d.844.7		12	65.37	even	12
845.2.d.d.844.8		12	65.28	even	12
845.2.l.f.654.5		24	65.58	even	12
845.2.l.f.654.6		24	65.7	even	12
845.2.l.f.654.7		24	65.33	even	12
845.2.l.f.654.8		24	65.32	even	12
845.2.l.f.699.5		24	65.47	even	4
845.2.l.f.699.6		24	65.18	even	4
845.2.l.f.699.7		24	65.57	even	4
845.2.l.f.699.8		24	65.8	even	4
845.2.n.e.484.3		12	65.38	odd	4
845.2.n.e.484.4		12	65.12	odd	4
845.2.n.e.529.3		12	65.17	odd	12
845.2.n.e.529.4		12	65.43	odd	12
1040.2.dh.a.289.1		12	20.3	even	4
1040.2.dh.a.289.6		12	20.7	even	4
1040.2.dh.a.529.1		12	260.87	even	12
1040.2.dh.a.529.6		12	260.243	even	12
4225.2.a.bq.1.3		6	65.49	even	6
4225.2.a.bq.1.4		6	13.10	even	6
4225.2.a.br.1.3		6	13.3	even	3
4225.2.a.br.1.4		6	65.29	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.165418 + 0.286513i) q^{2} +(-1.34590 - 2.33117i) q^{3} +(0.945274 - 1.63726i) q^{4} +(0.445274 - 0.771236i) q^{6} +(1.67674 - 2.90420i) q^{7} +1.28714 q^{8} +(-2.12291 + 3.67698i) q^{9} +O(q^{10})\)	\(q+(0.165418 + 0.286513i) q^{2} +(-1.34590 - 2.33117i) q^{3} +(0.945274 - 1.63726i) q^{4} +(0.445274 - 0.771236i) q^{6} +(1.67674 - 2.90420i) q^{7} +1.28714 q^{8} +(-2.12291 + 3.67698i) q^{9} +(1.62291 + 2.81095i) q^{11} -5.08898 q^{12} +(-3.39414 - 1.21648i) q^{13} +1.10945 q^{14} +(-1.67763 - 2.90574i) q^{16} +(-0.974404 + 1.68772i) q^{17} -1.40467 q^{18} +(0.622905 - 1.07890i) q^{19} -9.02690 q^{21} +(-0.536916 + 0.929966i) q^{22} +(1.34590 + 2.33117i) q^{23} +(-1.73236 - 3.00053i) q^{24} +(-0.212916 - 1.17369i) q^{26} +3.35348 q^{27} +(-3.16995 - 5.49052i) q^{28} +(-1.50000 - 2.59808i) q^{29} +3.78109 q^{31} +(1.84216 - 3.19071i) q^{32} +(4.36854 - 7.56654i) q^{33} -0.644737 q^{34} +(4.01345 + 6.95150i) q^{36} +(0.974404 + 1.68772i) q^{37} +0.412160 q^{38} +(1.73236 + 9.54958i) q^{39} +(-1.39055 - 2.40850i) q^{41} +(-1.49321 - 2.58632i) q^{42} +(-4.36854 + 7.56654i) q^{43} +6.13636 q^{44} +(-0.445274 + 0.771236i) q^{46} +6.86960 q^{47} +(-4.51586 + 7.82169i) q^{48} +(-2.12291 - 3.67698i) q^{49} +5.24581 q^{51} +(-5.20008 + 4.40719i) q^{52} +12.8336 q^{53} +(0.554726 + 0.960814i) q^{54} +(2.15819 - 3.73809i) q^{56} -3.35348 q^{57} +(0.496255 - 0.859539i) q^{58} +(1.26764 - 2.19562i) q^{59} +(3.74581 - 6.48793i) q^{61} +(0.625462 + 1.08333i) q^{62} +(7.11911 + 12.3307i) q^{63} -5.49162 q^{64} +2.89055 q^{66} +(-2.00758 - 3.47722i) q^{67} +(1.84216 + 3.19071i) q^{68} +(3.62291 - 6.27506i) q^{69} +(-2.62291 + 4.54300i) q^{71} +(-2.73247 + 4.73277i) q^{72} +5.46493 q^{73} +(-0.322368 + 0.558359i) q^{74} +(-1.17763 - 2.03972i) q^{76} +10.8848 q^{77} +(-2.44951 + 2.07602i) q^{78} +13.7811 q^{79} +(1.85526 + 3.21341i) q^{81} +(0.460044 - 0.796819i) q^{82} -8.61955 q^{83} +(-8.53289 + 14.7794i) q^{84} -2.89055 q^{86} +(-4.03771 + 6.99351i) q^{87} +(2.08890 + 3.61808i) q^{88} +(-5.15819 - 8.93425i) q^{89} +(-9.22398 + 7.81753i) q^{91} +5.08898 q^{92} +(-5.08898 - 8.81438i) q^{93} +(1.13636 + 1.96823i) q^{94} -9.91745 q^{96} +(-2.63304 + 4.56055i) q^{97} +(0.702335 - 1.21648i) q^{98} -13.7811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9	\( 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + 44 q^{14} - 16 q^{16} - 12 q^{19} - 8 q^{21} - 32 q^{24} + 24 q^{26} - 18 q^{29} - 16 q^{31} - 16 q^{34} - 2 q^{36} + 32 q^{39} + 14 q^{41} + 4 q^{44} + 10 q^{46} - 6 q^{49} + 24 q^{51} + 22 q^{54} - 16 q^{56} + 4 q^{59} + 6 q^{61} + 12 q^{64} + 4 q^{66} + 24 q^{69} - 12 q^{71} - 8 q^{74} - 10 q^{76} + 104 q^{79} + 14 q^{81} - 90 q^{84} - 4 q^{86} - 20 q^{89} - 44 q^{91} - 56 q^{94} + 12 q^{96} - 104 q^{99}+O(q^{100}) \) 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9 + 44 * q^14 - 16 * q^16 - 12 * q^19 - 8 * q^21 - 32 * q^24 + 24 * q^26 - 18 * q^29 - 16 * q^31 - 16 * q^34 - 2 * q^36 + 32 * q^39 + 14 * q^41 + 4 * q^44 + 10 * q^46 - 6 * q^49 + 24 * q^51 + 22 * q^54 - 16 * q^56 + 4 * q^59 + 6 * q^61 + 12 * q^64 + 4 * q^66 + 24 * q^69 - 12 * q^71 - 8 * q^74 - 10 * q^76 + 104 * q^79 + 14 * q^81 - 90 * q^84 - 4 * q^86 - 20 * q^89 - 44 * q^91 - 56 * q^94 + 12 * q^96 - 104 * q^99

Introduction

L-functions

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