LMFDB - Embedded newform 387.2.bc.a.233.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(26,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 17]))

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

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

chi := DirichletCharacter("387.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.bc (of order $42$, degree $12$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			233.10
Character	$\chi$	$=$	387.233
Dual form			387.2.bc.a.98.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02203 + 0.492186i) q^{2} +(-0.444673 - 0.557602i) q^{4} +(1.37798 - 1.27858i) q^{5} +(-4.27152 - 2.46616i) q^{7} +(-0.684870 - 3.00061i) q^{8} +O(q^{10})$	\(q+(1.02203 + 0.492186i) q^{2} +(-0.444673 - 0.557602i) q^{4} +(1.37798 - 1.27858i) q^{5} +(-4.27152 - 2.46616i) q^{7} +(-0.684870 - 3.00061i) q^{8} +(2.03765 - 0.628531i) q^{10} +(-3.53920 - 2.82242i) q^{11} +(3.67077 + 1.13228i) q^{13} +(-3.15183 - 4.62288i) q^{14} +(0.459494 - 2.01317i) q^{16} +(-1.69083 + 1.82228i) q^{17} +(4.88737 + 1.91815i) q^{19} +(-1.32569 - 0.199816i) q^{20} +(-2.22803 - 4.62655i) q^{22} +(-0.00325860 + 0.0216194i) q^{23} +(-0.109583 + 1.46228i) q^{25} +(3.19436 + 2.96393i) q^{26} +(0.524291 + 3.47844i) q^{28} +(8.02273 - 5.46981i) q^{29} +(0.356203 + 4.75320i) q^{31} +(-2.37745 + 2.98123i) q^{32} +(-2.62499 + 1.03023i) q^{34} +(-9.03928 + 2.06316i) q^{35} +(7.35131 - 4.24428i) q^{37} +(4.05097 + 4.36591i) q^{38} +(-4.78027 - 3.25913i) q^{40} +(1.56203 - 3.24359i) q^{41} +(1.72534 - 6.32639i) q^{43} +3.22852i q^{44} +(-0.0139712 + 0.0204919i) q^{46} +(0.778515 - 0.620845i) q^{47} +(8.66391 + 15.0063i) q^{49} +(-0.831713 + 1.44057i) q^{50} +(-1.00093 - 2.55032i) q^{52} +(-4.05396 - 13.1426i) q^{53} +(-8.48567 + 0.635913i) q^{55} +(-4.47456 + 14.5062i) q^{56} +(10.8917 - 1.64165i) q^{58} +(-1.57143 - 0.358669i) q^{59} +(-2.44101 - 0.182928i) q^{61} +(-1.97541 + 5.03325i) q^{62} +(-7.61806 + 3.66867i) q^{64} +(6.50598 - 3.13311i) q^{65} +(1.54923 - 3.94738i) q^{67} +(1.76797 + 0.132491i) q^{68} +(-10.2539 - 2.34039i) q^{70} +(3.10917 - 0.468632i) q^{71} +(-3.96842 + 12.8653i) q^{73} +(9.60226 - 0.719590i) q^{74} +(-1.10372 - 3.57816i) q^{76} +(8.15722 + 20.7843i) q^{77} +(-3.10732 + 5.38204i) q^{79} +(-1.94083 - 3.36162i) q^{80} +(3.19290 - 2.54625i) q^{82} +(-6.75189 + 9.90321i) q^{83} +4.67294i q^{85} +(4.87711 - 5.61660i) q^{86} +(-6.04509 + 12.5528i) q^{88} +(-0.659819 - 0.449857i) q^{89} +(-12.8874 - 13.8893i) q^{91} +(0.0135040 - 0.00779655i) q^{92} +(1.10124 - 0.251351i) q^{94} +(9.18723 - 3.60572i) q^{95} +(3.70561 - 4.64669i) q^{97} +(1.46891 + 19.6012i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 24 q^{4} - 6 q^{7}+O(q^{10}) $ 168 * q - 24 * q^4 - 6 * q^7	$ 168 q - 24 q^{4} - 6 q^{7} + 8 q^{10} + 26 q^{13} - 8 q^{16} + 24 q^{19} + 14 q^{25} + 32 q^{31} - 48 q^{34} - 78 q^{37} - 244 q^{40} - 32 q^{43} - 92 q^{46} + 54 q^{49} + 76 q^{52} - 96 q^{55} - 20 q^{58} - 96 q^{64} - 18 q^{67} + 140 q^{70} + 10 q^{73} - 16 q^{76} - 168 q^{88} - 38 q^{91} - 112 q^{94} - 40 q^{97}+O(q^{100}) $ 168 * q - 24 * q^4 - 6 * q^7 + 8 * q^10 + 26 * q^13 - 8 * q^16 + 24 * q^19 + 14 * q^25 + 32 * q^31 - 48 * q^34 - 78 * q^37 - 244 * q^40 - 32 * q^43 - 92 * q^46 + 54 * q^49 + 76 * q^52 - 96 * q^55 - 20 * q^58 - 96 * q^64 - 18 * q^67 + 140 * q^70 + 10 * q^73 - 16 * q^76 - 168 * q^88 - 38 * q^91 - 112 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$-1$

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 $

$2$	1.02203	+	0.492186i	0.722687	+	0.348028i	0.758803	−	0.651320i	$-0.225784\pi$
$2$	1.02203	+	0.492186i	0.722687	+	0.348028i	−0.0361162	+	0.999348i	$0.511499\pi$
$3$		0			0
$3$		0			0
$4$	−0.444673	−	0.557602i	−0.222336	−	0.278801i
$5$	1.37798	−	1.27858i	0.616253	−	0.571800i	−0.309041	−	0.951049i	$-0.600008\pi$
$5$	1.37798	−	1.27858i	0.616253	−	0.571800i	0.925295	+	0.379249i	$0.123818\pi$
$6$		0			0
$7$	−4.27152	−	2.46616i	−1.61448	−	0.932122i	−0.988314	−	0.152434i	$-0.951289\pi$
$7$	−4.27152	−	2.46616i	−1.61448	−	0.932122i	−0.626168	−	0.779688i	$-0.715378\pi$
$8$	−0.684870	−	3.00061i	−0.242138	−	1.06088i
$9$		0			0
$10$	2.03765	−	0.628531i	0.644361	−	0.198759i
$11$	−3.53920	−	2.82242i	−1.06711	−	0.850992i	−0.0778216	−	0.996967i	$-0.524796\pi$
$11$	−3.53920	−	2.82242i	−1.06711	−	0.850992i	−0.989288	+	0.145976i	$0.953368\pi$
$12$		0			0
$13$	3.67077	+	1.13228i	1.01809	+	0.314039i	0.758494	−	0.651679i	$-0.225935\pi$
$13$	3.67077	+	1.13228i	1.01809	+	0.314039i	0.259593	+	0.965718i	$0.416411\pi$
$14$	−3.15183	−	4.62288i	−0.842361	−	1.23552i
$15$		0			0
$16$	0.459494	−	2.01317i	0.114873	−	0.503293i
$17$	−1.69083	+	1.82228i	−0.410086	+	0.441968i	−0.903993	−	0.427547i	$-0.859378\pi$
$17$	−1.69083	+	1.82228i	−0.410086	+	0.441968i	0.493907	+	0.869515i	$0.335568\pi$
$18$		0			0
$19$	4.88737	+	1.91815i	1.12124	+	0.440054i	0.852274	−	0.523096i	$-0.175223\pi$
$19$	4.88737	+	1.91815i	1.12124	+	0.440054i	0.268965	+	0.963150i	$0.413318\pi$
$20$	−1.32569	−	0.199816i	−0.296434	−	0.0446802i
$21$		0			0
$22$	−2.22803	−	4.62655i	−0.475018	−	0.986385i
$23$	−0.00325860	+	0.0216194i	−0.000679465	+	0.00450795i	−0.989168	−	0.146788i	$-0.953107\pi$
$23$	−0.00325860	+	0.0216194i	−0.000679465	+	0.00450795i	0.988489	+	0.151296i	$0.0483446\pi$
$24$		0			0
$25$	−0.109583	+	1.46228i	−0.0219166	+	0.292457i
$26$	3.19436	+	2.96393i	0.626465	+	0.581275i
$27$		0			0
$28$	0.524291	+	3.47844i	0.0990817	+	0.657364i
$29$	8.02273	−	5.46981i	1.48978	−	1.01572i	0.501153	−	0.865359i	$-0.332909\pi$
$29$	8.02273	−	5.46981i	1.48978	−	1.01572i	0.988631	−	0.150359i	$-0.0480429\pi$
$30$		0			0
$31$	0.356203	+	4.75320i	0.0639760	+	0.853700i	0.933217	+	0.359312i	$0.116989\pi$
$31$	0.356203	+	4.75320i	0.0639760	+	0.853700i	−0.869241	+	0.494388i	$0.835392\pi$
$32$	−2.37745	+	2.98123i	−0.420278	+	0.527012i
$33$		0			0
$34$	−2.62499	+	1.03023i	−0.450181	+	0.176683i
$35$	−9.03928	+	2.06316i	−1.52792	+	0.348737i
$36$		0			0
$37$	7.35131	−	4.24428i	1.20855	−	0.697755i	0.246106	−	0.969243i	$-0.420849\pi$
$37$	7.35131	−	4.24428i	1.20855	−	0.697755i	0.962442	+	0.271488i	$0.0875156\pi$
$38$	4.05097	+	4.36591i	0.657154	+	0.708244i
$39$		0			0
$40$	−4.78027	−	3.25913i	−0.755827	−	0.515314i
$41$	1.56203	−	3.24359i	0.243948	−	0.506564i	−0.742661	−	0.669668i	$-0.766436\pi$
$41$	1.56203	−	3.24359i	0.243948	−	0.506564i	0.986609	+	0.163104i	$0.0521507\pi$
$42$		0			0
$43$	1.72534	−	6.32639i	0.263112	−	0.964765i
$43$	1.72534	−	6.32639i	0.263112	−	0.964765i
$44$			3.22852i			0.486718i
$45$		0			0
$46$	−0.0139712	+	0.0204919i	−0.00205993	+	0.00302137i
$47$	0.778515	−	0.620845i	0.113558	−	0.0905596i	−0.565064	−	0.825047i	$-0.691149\pi$
$47$	0.778515	−	0.620845i	0.113558	−	0.0905596i	0.678623	+	0.734487i	$0.262577\pi$
$48$		0			0
$49$	8.66391	+	15.0063i	1.23770	+	2.14376i
$50$	−0.831713	+	1.44057i	−0.117622	+	0.203727i
$51$		0			0
$52$	−1.00093	−	2.55032i	−0.138804	−	0.353666i
$53$	−4.05396	−	13.1426i	−0.556855	−	1.80528i	−0.592054	−	0.805898i	$-0.701683\pi$
$53$	−4.05396	−	13.1426i	−0.556855	−	1.80528i	0.0351999	−	0.999380i	$-0.488793\pi$
$54$		0			0
$55$	−8.48567	+	0.635913i	−1.14421	+	0.0857464i
$56$	−4.47456	+	14.5062i	−0.597938	+	1.93847i
$57$		0			0
$58$	10.8917	−	1.64165i	1.43015	−	0.215560i
$59$	−1.57143	−	0.358669i	−0.204583	−	0.0466947i	0.119001	−	0.992894i	$-0.462031\pi$
$59$	−1.57143	−	0.358669i	−0.204583	−	0.0466947i	−0.323584	+	0.946199i	$0.604888\pi$
$60$		0			0
$61$	−2.44101	−	0.182928i	−0.312539	−	0.0234215i	−0.0824626	−	0.996594i	$-0.526278\pi$
$61$	−2.44101	−	0.182928i	−0.312539	−	0.0234215i	−0.230076	+	0.973173i	$0.573898\pi$
$62$	−1.97541	+	5.03325i	−0.250877	+	0.639224i
$63$		0			0
$64$	−7.61806	+	3.66867i	−0.952258	+	0.458583i
$65$	6.50598	−	3.13311i	0.806967	−	0.388615i
$66$		0			0
$67$	1.54923	−	3.94738i	0.189269	−	0.482250i	−0.804468	−	0.593996i	$-0.797549\pi$
$67$	1.54923	−	3.94738i	0.189269	−	0.482250i	0.993737	+	0.111747i	$0.0356446\pi$
$68$	1.76797	+	0.132491i	0.214398	+	0.0160669i
$69$		0			0
$70$	−10.2539	−	2.34039i	−1.22558	−	0.279730i
$71$	3.10917	−	0.468632i	0.368991	−	0.0556164i	0.0380702	−	0.999275i	$-0.487879\pi$
$71$	3.10917	−	0.468632i	0.368991	−	0.0556164i	0.330920	+	0.943659i	$0.392641\pi$
$72$		0			0
$73$	−3.96842	+	12.8653i	−0.464469	+	1.50577i	0.356224	+	0.934401i	$0.384064\pi$
$73$	−3.96842	+	12.8653i	−0.464469	+	1.50577i	−0.820693	+	0.571370i	$0.806412\pi$
$74$	9.60226	−	0.719590i	1.11624	−	0.0836506i
$75$		0			0
$76$	−1.10372	−	3.57816i	−0.126605	−	0.410443i
$77$	8.15722	+	20.7843i	0.929602	+	2.36859i
$78$		0			0
$79$	−3.10732	+	5.38204i	−0.349601	+	0.605527i	−0.986179	−	0.165686i	$-0.947016\pi$
$79$	−3.10732	+	5.38204i	−0.349601	+	0.605527i	0.636578	+	0.771213i	$0.280349\pi$
$80$	−1.94083	−	3.36162i	−0.216992	−	0.375841i
$81$		0			0
$82$	3.19290	−	2.54625i	0.352597	−	0.281186i
$83$	−6.75189	+	9.90321i	−0.741116	+	1.08702i	0.251751	+	0.967792i	$0.418994\pi$
$83$	−6.75189	+	9.90321i	−0.741116	+	1.08702i	−0.992867	+	0.119226i	$0.961959\pi$
$84$		0			0
$85$			4.67294i			0.506852i
$86$	4.87711	−	5.61660i	0.525913	−	0.605653i
$87$		0			0
$88$	−6.04509	+	12.5528i	−0.644409	+	1.33813i
$89$	−0.659819	−	0.449857i	−0.0699406	−	0.0476847i	0.527845	−	0.849341i	$-0.323000\pi$
$89$	−0.659819	−	0.449857i	−0.0699406	−	0.0476847i	−0.597786	+	0.801656i	$0.703953\pi$
$90$		0			0
$91$	−12.8874	−	13.8893i	−1.35096	−	1.45599i
$92$	0.0135040	−	0.00779655i	0.00140789	−	0.000812847i
$93$		0			0
$94$	1.10124	−	0.251351i	0.113584	−	0.0259249i
$95$	9.18723	−	3.60572i	0.942590	−	0.369939i
$96$		0			0
$97$	3.70561	−	4.64669i	0.376248	−	0.471800i	−0.557270	−	0.830332i	$-0.688151\pi$
$97$	3.70561	−	4.64669i	0.376248	−	0.471800i	0.933518	+	0.358532i	$0.116722\pi$
$98$	1.46891	+	19.6012i	0.148382	+	1.98002i
$99$		0			0
$100$	0.864101	−	0.589134i	0.0864101	−	0.0589134i
$101$	−0.541574	−	3.59311i	−0.0538886	−	0.357528i	−0.999482	−	0.0321773i	$-0.989756\pi$
$101$	−0.541574	−	3.59311i	−0.0538886	−	0.357528i	0.945594	−	0.325350i	$-0.105482\pi$
$102$		0			0
$103$	−4.07279	−	3.77900i	−0.401304	−	0.372356i	0.453544	−	0.891234i	$-0.350159\pi$
$103$	−4.07279	−	3.77900i	−0.401304	−	0.372356i	−0.854848	+	0.518878i	$0.826350\pi$
$104$	0.883540	−	11.7900i	0.0866382	−	1.15611i
$105$		0			0
$106$	2.32532	−	15.4275i	0.225855	−	1.49845i
$107$	−5.49252	−	11.4053i	−0.530982	−	1.10260i	−0.978103	−	0.208122i	$-0.933265\pi$
$107$	−5.49252	−	11.4053i	−0.530982	−	1.10260i	0.447121	−	0.894474i	$-0.352449\pi$
$108$		0			0
$109$	−7.60093	−	1.14566i	−0.728037	−	0.109734i	−0.225443	−	0.974256i	$-0.572383\pi$
$109$	−7.60093	−	1.14566i	−0.728037	−	0.109734i	−0.502594	+	0.864523i	$0.667621\pi$
$110$	−8.98563	−	3.52660i	−0.856746	−	0.336248i
$111$		0			0
$112$	−6.92755	+	7.46612i	−0.654592	+	0.705482i
$113$	−0.484148	+	2.12119i	−0.0455448	+	0.199545i	−0.992582	−	0.121580i	$-0.961204\pi$
$113$	−0.484148	+	2.12119i	−0.0455448	+	0.199545i	0.947037	+	0.321125i	$0.104061\pi$
$114$		0			0
$115$	0.0231519	+	0.0339576i	0.00215892	+	0.00316656i
$116$	−6.61747	−	2.04122i	−0.614416	−	0.189522i
$117$		0			0
$118$	−1.42952	−	1.14001i	−0.131598	−	0.104946i
$119$	11.7165	−	3.61405i	1.07405	−	0.331299i
$120$		0			0
$121$	2.11217	+	9.25403i	0.192016	+	0.841275i
$122$	−2.40476	−	1.38839i	−0.217716	−	0.125699i
$123$		0			0
$124$	2.49200	−	2.31224i	0.223788	−	0.207645i
$125$	7.57880	+	9.50352i	0.677869	+	0.850020i
$126$		0			0
$127$	8.18380	+	3.94111i	0.726195	+	0.349717i	0.760186	−	0.649705i	$-0.225108\pi$
$127$	8.18380	+	3.94111i	0.726195	+	0.349717i	−0.0339914	+	0.999422i	$0.510822\pi$
$128$	−1.96530			−0.173710
$129$		0			0
$130$	8.19140			0.718434
$131$	9.23805	+	4.44881i	0.807132	+	0.388694i	0.791489	−	0.611183i	$-0.209306\pi$
$131$	9.23805	+	4.44881i	0.807132	+	0.388694i	0.0156429	+	0.999878i	$0.495021\pi$
$132$		0			0
$133$	−16.1460	−	20.2465i	−1.40004	−	1.75559i
$134$	3.52621	−	3.27185i	0.304619	−	0.282645i
$135$		0			0
$136$	6.62596	+	3.82550i	0.568171	+	0.328034i
$137$	1.02583	+	4.49446i	0.0876427	+	0.383988i	0.999658	−	0.0261696i	$-0.00833099\pi$
$137$	1.02583	+	4.49446i	0.0876427	+	0.383988i	−0.912015	+	0.410157i	$0.865474\pi$
$138$		0			0
$139$	14.2636	−	4.39975i	1.20983	−	0.373182i	0.376737	−	0.926320i	$-0.377046\pi$
$139$	14.2636	−	4.39975i	1.20983	−	0.373182i	0.833089	+	0.553138i	$0.186570\pi$
$140$	5.16994	+	4.12289i	0.436940	+	0.348448i
$141$		0			0
$142$	3.40833	+	1.05133i	0.286021	+	0.0882257i
$143$	−9.79582	−	14.3678i	−0.819167	−	1.20150i
$144$		0			0
$145$	4.06160	−	17.7950i	0.337298	−	1.47780i
$146$	−10.3880	+	11.1956i	−0.859715	+	0.926553i
$147$		0			0
$148$	−5.63555	−	2.21179i	−0.463239	−	0.181808i
$149$	−12.8502	−	1.93685i	−1.05273	−	0.158673i	−0.400191	−	0.916432i	$-0.631056\pi$
$149$	−12.8502	−	1.93685i	−1.05273	−	0.158673i	−0.652535	+	0.757759i	$0.726294\pi$
$150$		0			0
$151$	2.12067	+	4.40361i	0.172577	+	0.358361i	0.969261	−	0.246037i	$-0.0791283\pi$
$151$	2.12067	+	4.40361i	0.172577	+	0.358361i	−0.796683	+	0.604397i	$0.793414\pi$
$152$	2.40841	−	15.9788i	0.195348	−	1.29605i
$153$		0			0
$154$	−1.89276	+	25.2571i	−0.152523	+	2.03527i
$155$	6.56820	+	6.09440i	0.527571	+	0.489514i
$156$		0			0
$157$	2.44467	+	16.2193i	0.195106	+	1.29444i	0.845143	+	0.534540i	$0.179515\pi$
$157$	2.44467	+	16.2193i	0.195106	+	1.29444i	−0.650037	+	0.759902i	$0.725247\pi$
$158$	−5.82475	+	3.97125i	−0.463392	+	0.315935i
$159$		0			0
$160$	0.535658	+	7.14786i	0.0423475	+	0.565088i
$161$	0.0672361	−	0.0843114i	0.00529895	−	0.00664467i
$162$		0			0
$163$	9.41590	−	3.69547i	0.737510	−	0.289451i	0.0333023	−	0.999445i	$-0.489398\pi$
$163$	9.41590	−	3.69547i	0.737510	−	0.289451i	0.704208	+	0.709994i	$0.251302\pi$
$164$	−2.50323	+	0.571345i	−0.195469	+	0.0446146i
$165$		0			0
$166$	−11.7749	+	6.79823i	−0.913908	+	0.527645i
$167$	12.7287	+	13.7183i	0.984978	+	1.06155i	0.998098	+	0.0616394i	$0.0196329\pi$
$167$	12.7287	+	13.7183i	0.984978	+	1.06155i	−0.0131209	+	0.999914i	$0.504177\pi$
$168$		0			0
$169$	1.45137	+	0.989529i	0.111644	+	0.0761176i
$170$	−2.29995	+	4.77590i	−0.176398	+	0.366295i
$171$		0			0
$172$	−4.29482	+	1.85112i	−0.327477	+	0.141147i
$173$		−	14.5276i		−	1.10451i	−0.833674	−	0.552257i	$-0.813767\pi$
$173$		−	14.5276i		−	1.10451i	0.833674	−	0.552257i	$-0.186233\pi$
$174$		0			0
$175$	4.07432	−	5.97592i	0.307989	−	0.451737i
$176$	−7.30826	+	5.82815i	−0.550881	+	0.439313i
$177$		0			0
$178$	−0.452944	−	0.784522i	−0.0339496	−	0.0588024i
$179$	−1.95069	+	3.37870i	−0.145801	+	0.252536i	−0.929672	−	0.368389i	$-0.879909\pi$
$179$	−1.95069	+	3.37870i	−0.145801	+	0.252536i	0.783870	+	0.620925i	$0.213243\pi$
$180$		0			0
$181$	6.09090	+	15.5194i	0.452733	+	1.15355i	0.957023	+	0.290011i	$0.0936589\pi$
$181$	6.09090	+	15.5194i	0.452733	+	1.15355i	−0.504290	+	0.863534i	$0.668246\pi$
$182$	−6.33522	−	20.5383i	−0.469598	−	1.52240i
$183$		0			0
$184$	0.0671031	−	0.00502868i	0.00494691	−	0.000370719i
$185$	4.70333	−	15.2478i	0.345795	−	1.12104i
$186$		0			0
$187$	11.1274	−	1.67719i	0.813718	−	0.122648i
$188$	−0.692369	−	0.158029i	−0.0504962	−	0.0115254i
$189$		0			0
$190$	11.1644	+	0.836652i	0.809947	+	0.0606971i
$191$	−2.06486	+	5.26116i	−0.149408	+	0.380685i	−0.985909	−	0.167280i	$-0.946502\pi$
$191$	−2.06486	+	5.26116i	−0.149408	+	0.380685i	0.836502	+	0.547964i	$0.184597\pi$
$192$		0			0
$193$	−8.53199	+	4.10879i	−0.614146	+	0.295757i	−0.714979	−	0.699146i	$-0.753564\pi$
$193$	−8.53199	+	4.10879i	−0.614146	+	0.295757i	0.100832	+	0.994903i	$0.467849\pi$
$194$	6.07430	−	2.92523i	0.436109	−	0.210019i
$195$		0			0
$196$	4.51496	−	11.5039i	0.322497	−	0.821709i
$197$	7.55677	+	0.566301i	0.538397	+	0.0403473i	0.341154	−	0.940007i	$-0.389182\pi$
$197$	7.55677	+	0.566301i	0.538397	+	0.0403473i	0.197243	+	0.980355i	$0.436801\pi$
$198$		0			0
$199$	14.8519	+	3.38985i	1.05282	+	0.240300i	0.713707	−	0.700444i	$-0.247015\pi$
$199$	14.8519	+	3.38985i	1.05282	+	0.240300i	0.339117	+	0.940744i	$0.389872\pi$
$200$	4.46280	−	0.672658i	0.315567	−	0.0475641i
$201$		0			0
$202$	1.21497	−	3.93883i	0.0854849	−	0.277135i
$203$	−47.7587	+	3.57902i	−3.35200	+	0.251198i
$204$		0			0
$205$	−1.99475	−	6.46681i	−0.139319	−	0.451661i
$206$	−2.30256	−	5.86683i	−0.160427	−	0.408762i
$207$		0			0
$208$	3.96618	−	6.86962i	0.275005	−	0.476322i
$209$	−11.8836	−	20.5829i	−0.822003	−	1.42375i
$210$		0			0
$211$	10.7103	−	8.54121i	0.737330	−	0.588001i	−0.181156	−	0.983454i	$-0.557984\pi$
$211$	10.7103	−	8.54121i	0.737330	−	0.588001i	0.918486	+	0.395453i	$0.129412\pi$
$212$	−5.52567	+	8.10467i	−0.379504	+	0.556631i
$213$		0			0
$214$		−	14.3600i		−	0.981629i
$215$	−5.71132	−	10.9237i	−0.389509	−	0.744987i
$216$		0			0
$217$	10.2006	−	21.1818i	0.692464	−	1.43792i
$218$	−7.20453	−	4.91197i	−0.487952	−	0.332680i
$219$		0			0
$220$	4.12793	+	4.44885i	0.278305	+	0.299942i
$221$	−8.26998	+	4.77467i	−0.556299	+	0.321179i
$222$		0			0
$223$	−11.4298	+	2.60877i	−0.765393	+	0.174696i	−0.587357	−	0.809328i	$-0.699832\pi$
$223$	−11.4298	+	2.60877i	−0.765393	+	0.174696i	−0.178036	+	0.984024i	$0.556974\pi$
$224$	17.5075	−	6.87120i	1.16977	−	0.459102i
$225$		0			0
$226$	−1.53883	+	1.92964i	−0.102362	+	0.128358i
$227$	−1.58478	−	21.1474i	−0.105185	−	1.40360i	−0.761035	−	0.648711i	$-0.775308\pi$
$227$	−1.58478	−	21.1474i	−0.105185	−	1.40360i	0.655849	−	0.754892i	$-0.272311\pi$
$228$		0			0
$229$	11.1597	−	7.60856i	0.737454	−	0.502788i	−0.135386	−	0.990793i	$-0.543228\pi$
$229$	11.1597	−	7.60856i	0.737454	−	0.502788i	0.872841	+	0.488005i	$0.162275\pi$
$230$	0.00694858	+	0.0461008i	0.000458176	+	0.00303980i
$231$		0			0
$232$	−21.9073	−	20.3270i	−1.43828	−	1.33453i
$233$	−0.557120	+	7.43425i	−0.0364982	+	0.487034i	0.948764	+	0.315985i	$0.102335\pi$
$233$	−0.557120	+	7.43425i	−0.0364982	+	0.487034i	−0.985262	+	0.171049i	$0.945284\pi$
$234$		0			0
$235$	0.278980	−	1.85091i	0.0181986	−	0.120740i
$236$	0.498778	+	1.03572i	0.0324677	+	0.0674199i
$237$		0			0
$238$	13.7534	+	2.07299i	0.891500	+	0.134372i
$239$	5.47967	+	2.15061i	0.354451	+	0.139112i	0.535884	−	0.844292i	$-0.319978\pi$
$239$	5.47967	+	2.15061i	0.354451	+	0.139112i	−0.181433	+	0.983403i	$0.558074\pi$
$240$		0			0
$241$	−3.78849	+	4.08302i	−0.244038	+	0.263011i	−0.843179	−	0.537633i	$-0.819319\pi$
$241$	−3.78849	+	4.08302i	−0.244038	+	0.263011i	0.599141	+	0.800644i	$0.295509\pi$
$242$	−2.39599	+	10.4975i	−0.154020	+	0.674806i
$243$		0			0
$244$	0.983448	+	1.44245i	0.0629588	+	0.0923436i
$245$	31.1256	+	9.60097i	1.98854	+	0.613384i
$246$		0			0
$247$	15.7685	+	12.5750i	1.00333	+	0.800126i
$248$	14.0186	−	4.32415i	0.890179	−	0.274584i
$249$		0			0
$250$	3.06830	+	13.4431i	0.194056	+	0.850216i
$251$	2.87983	+	1.66267i	0.181774	+	0.104947i	0.588126	−	0.808770i	$-0.299866\pi$
$251$	2.87983	+	1.66267i	0.181774	+	0.104947i	−0.406352	+	0.913717i	$0.633199\pi$
$252$		0			0
$253$	0.0725518	−	0.0673183i	0.00456129	−	0.00423226i
$254$	6.42436	+	8.05590i	0.403101	+	0.505472i
$255$		0			0
$256$	13.2275	+	6.37004i	0.826720	+	0.398127i
$257$	−1.37522			−0.0857837			−0.0428918	−	0.999080i	$-0.513657\pi$
$257$	−1.37522			−0.0857837			−0.0428918	+	0.999080i	$0.513657\pi$
$258$		0			0
$259$	−41.8683			−2.60157
$260$	−4.64006	−	2.23454i	−0.287764	−	0.138580i
$261$		0			0
$262$	7.25196	+	9.09367i	0.448027	+	0.561809i
$263$	−19.1270	+	17.7472i	−1.17942	+	1.09434i	−0.185682	+	0.982610i	$0.559449\pi$
$263$	−19.1270	+	17.7472i	−1.17942	+	1.09434i	−0.993738	+	0.111732i	$0.964360\pi$
$264$		0			0
$265$	−22.3902	−	12.9270i	−1.37542	−	0.794100i
$266$	−6.53676	−	28.6394i	−0.400794	−	1.75599i
$267$		0			0
$268$	−2.88997	+	0.891438i	−0.176533	+	0.0544533i
$269$	21.1275	+	16.8486i	1.28817	+	1.02728i	0.997515	+	0.0704492i	$0.0224433\pi$
$269$	21.1275	+	16.8486i	1.28817	+	1.02728i	0.290651	+	0.956829i	$0.406128\pi$
$270$		0			0
$271$	−10.5326	−	3.24888i	−0.639810	−	0.197355i	−0.0421583	−	0.999111i	$-0.513423\pi$
$271$	−10.5326	−	3.24888i	−0.639810	−	0.197355i	−0.597652	+	0.801756i	$0.703900\pi$
$272$	2.89164	+	4.24126i	0.175332	+	0.257164i
$273$		0			0
$274$	−1.16367	+	5.09839i	−0.0703001	+	0.308005i
$275$	4.51502	−	4.86603i	0.272266	−	0.293433i
$276$		0			0
$277$	2.95199	+	1.15857i	0.177368	+	0.0696119i	0.452363	−	0.891834i	$-0.350581\pi$
$277$	2.95199	+	1.15857i	0.177368	+	0.0696119i	−0.274995	+	0.961446i	$0.588676\pi$
$278$	16.7434	+	2.52366i	1.00420	+	0.151359i
$279$		0			0
$280$	12.3815	+	25.7104i	0.739934	+	1.53649i
$281$	−1.26043	+	8.36240i	−0.0751909	+	0.498859i	0.919260	+	0.393652i	$0.128789\pi$
$281$	−1.26043	+	8.36240i	−0.0751909	+	0.498859i	−0.994450	+	0.105207i	$0.966450\pi$
$282$		0			0
$283$	0.511506	−	6.82558i	0.0304059	−	0.405738i	−0.961147	−	0.276037i	$-0.910979\pi$
$283$	0.511506	−	6.82558i	0.0304059	−	0.405738i	0.991553	−	0.129702i	$-0.0414020\pi$
$284$	−1.64387	−	1.52529i	−0.0975459	−	0.0905094i
$285$		0			0
$286$	−2.94002	−	19.5058i	−0.173847	−	1.15340i
$287$	−14.6715	+	10.0028i	−0.866029	+	0.590449i
$288$		0			0
$289$	0.808609	+	10.7901i	0.0475652	+	0.634714i
$290$	12.9096	−	16.1881i	0.758075	−	0.950596i
$291$		0			0
$292$	8.93837	−	3.50805i	0.523079	−	0.205293i
$293$	10.7905	−	2.46286i	0.630388	−	0.143882i	0.104623	−	0.994512i	$-0.466636\pi$
$293$	10.7905	−	2.46286i	0.630388	−	0.143882i	0.525765	+	0.850630i	$0.323779\pi$
$294$		0			0
$295$	−2.62400	+	1.51497i	−0.152775	+	0.0882047i
$296$	−17.7701	−	19.1516i	−1.03287	−	1.11317i
$297$		0			0
$298$	−12.1800	−	8.30419i	−0.705569	−	0.481049i
$299$	−0.0364408	+	0.0756701i	−0.00210743	+	0.00437612i
$300$		0			0
$301$	−22.9717	+	22.7683i	−1.32407	+	1.31234i
$302$			5.54440i			0.319044i
$303$		0			0
$304$	6.10729	−	8.95774i	0.350277	−	0.513762i
$305$	−3.59756	+	2.86896i	−0.205996	+	0.164276i
$306$		0			0
$307$	−7.97067	−	13.8056i	−0.454910	−	0.787928i	0.543773	−	0.839233i	$-0.316995\pi$
$307$	−7.97067	−	13.8056i	−0.454910	−	0.787928i	−0.998683	+	0.0513047i	$0.983662\pi$
$308$	7.96206	−	13.7907i	0.453680	−	0.785797i
$309$		0			0
$310$	3.71335	+	9.46146i	0.210904	+	0.537375i
$311$	−5.62006	−	18.2198i	−0.318684	−	1.03315i	−0.963251	−	0.268602i	$-0.913438\pi$
$311$	−5.62006	−	18.2198i	−0.318684	−	1.03315i	0.644567	−	0.764548i	$-0.277038\pi$
$312$		0			0
$313$	−10.3524	+	0.775806i	−0.585153	+	0.0438511i	−0.364018	−	0.931392i	$-0.618595\pi$
$313$	−10.3524	+	0.775806i	−0.585153	+	0.0438511i	−0.221135	+	0.975243i	$0.570976\pi$
$314$	−5.48438	+	17.7799i	−0.309502	+	1.00338i
$315$		0			0
$316$	4.38278	−	0.660597i	0.246550	−	0.0371615i
$317$	23.1318	+	5.27969i	1.29921	+	0.296537i	0.815534	−	0.578709i	$-0.196443\pi$
$317$	23.1318	+	5.27969i	1.29921	+	0.296537i	0.483679	+	0.875246i	$0.339300\pi$
$318$		0			0
$319$	−43.8322	−	3.28477i	−2.45413	−	0.183912i
$320$	−5.80688	+	14.7957i	−0.324614	+	0.827104i
$321$		0			0
$322$	0.110214	−	0.0530765i	0.00614201	−	0.00295784i
$323$	−11.7591	+	5.66289i	−0.654295	+	0.315092i
$324$		0			0
$325$	−2.05797	+	5.24363i	−0.114156	+	0.290864i
$326$	11.4422	+	0.857476i	0.633726	+	0.0474912i
$327$		0			0
$328$	−10.8025	−	2.46561i	−0.596471	−	0.136141i
$329$	−4.85655	+	0.732007i	−0.267750	+	0.0403568i
$330$		0			0
$331$	−7.52285	+	24.3885i	−0.413493	+	1.34051i	0.474338	+	0.880343i	$0.342688\pi$
$331$	−7.52285	+	24.3885i	−0.413493	+	1.34051i	−0.887831	+	0.460170i	$0.847789\pi$
$332$	8.52443	−	0.638818i	0.467839	−	0.0350597i
$333$		0			0
$334$	6.25723	+	20.2855i	0.342381	+	1.10997i
$335$	−2.91224	−	7.42026i	−0.159112	−	0.405412i
$336$		0			0
$337$	2.94940	−	5.10851i	0.160664	−	0.278278i	−0.774443	−	0.632644i	$-0.781970\pi$
$337$	2.94940	−	5.10851i	0.160664	−	0.278278i	0.935107	+	0.354365i	$0.115303\pi$
$338$	0.996320	+	1.72568i	0.0541927	+	0.0938645i
$339$		0			0
$340$	2.60564	−	2.07793i	0.141311	−	0.112692i
$341$	12.1549	−	17.8279i	0.658222	−	0.965435i
$342$		0			0
$343$		−	50.9402i		−	2.75051i
$344$	−20.1647	−	0.844314i	−1.08721	−	0.0455224i
$345$		0			0
$346$	7.15029	−	14.8477i	0.384402	−	0.798218i
$347$	−2.00135	−	1.36450i	−0.107438	−	0.0732502i	0.508409	−	0.861116i	$-0.330234\pi$
$347$	−2.00135	−	1.36450i	−0.107438	−	0.0732502i	−0.615847	+	0.787865i	$0.711186\pi$
$348$		0			0
$349$	10.8413	+	11.6841i	0.580321	+	0.625437i	0.953163	−	0.302458i	$-0.0978072\pi$
$349$	10.8413	+	11.6841i	0.580321	+	0.625437i	−0.372842	+	0.927895i	$0.621617\pi$
$350$	7.10535	−	4.10228i	0.379797	−	0.219276i
$351$		0			0
$352$	16.8286	−	3.84101i	0.896966	−	0.204727i
$353$	−29.1379	+	11.4358i	−1.55085	+	0.608664i	−0.977554	−	0.210683i	$-0.932431\pi$
$353$	−29.1379	+	11.4358i	−1.55085	+	0.608664i	−0.573297	+	0.819347i	$0.694336\pi$
$354$		0			0
$355$	3.68520	−	4.62110i	0.195590	−	0.245262i
$356$	0.0425624	+	0.567955i	0.00225580	+	0.0301016i
$357$		0			0
$358$	−3.65662	+	2.49304i	−0.193258	+	0.131761i
$359$	4.08755	+	27.1191i	0.215732	+	1.43129i	0.790243	+	0.612794i	$0.209954\pi$
$359$	4.08755	+	27.1191i	0.215732	+	1.43129i	−0.574511	+	0.818497i	$0.694808\pi$
$360$		0			0
$361$	6.27909	+	5.82614i	0.330478	+	0.306639i
$362$	−1.41330	+	18.8592i	−0.0742814	+	0.991216i
$363$		0			0
$364$	−2.01403	+	13.3622i	−0.105564	+	0.700370i
$365$	10.9809	+	22.8021i	0.574768	+	1.19352i
$366$		0			0
$367$	10.1333	+	1.52735i	0.528956	+	0.0797272i	0.408090	−	0.912942i	$-0.366195\pi$
$367$	10.1333	+	1.52735i	0.528956	+	0.0797272i	0.120865	+	0.992669i	$0.461433\pi$
$368$	0.0420263	+	0.0164941i	0.00219077	+	0.000859814i
$369$		0			0
$370$	12.3117	−	13.2689i	0.640056	−	0.689816i
$371$	−15.0953	+	66.1367i	−0.783707	+	3.43365i
$372$		0			0
$373$	−10.5651	−	15.4961i	−0.547038	−	0.802358i	0.448787	−	0.893639i	$-0.351856\pi$
$373$	−10.5651	−	15.4961i	−0.547038	−	0.802358i	−0.995825	+	0.0912809i	$0.970904\pi$
$374$	12.1981	+	3.76262i	0.630749	+	0.194560i
$375$		0			0
$376$	−2.39610	−	1.91082i	−0.123569	−	0.0985432i
$377$	35.6430	−	10.9944i	1.83571	−	0.566240i
$378$		0			0
$379$	3.30228	+	14.4682i	0.169627	+	0.743183i	0.986148	+	0.165868i	$0.0530424\pi$
$379$	3.30228	+	14.4682i	0.169627	+	0.743183i	−0.816521	+	0.577315i	$0.804100\pi$
$380$	−6.09587	−	3.51945i	−0.312712	−	0.180544i
$381$		0			0
$382$	−4.69982	+	4.36080i	−0.240464	+	0.223118i
$383$	17.2126	+	21.5839i	0.879522	+	1.10289i	0.993991	+	0.109459i	$0.0349118\pi$
$383$	17.2126	+	21.5839i	0.879522	+	1.10289i	−0.114469	+	0.993427i	$0.536517\pi$
$384$		0			0
$385$	37.8149	+	18.2107i	1.92723	+	0.928104i
$386$	−10.7423			−0.546767
$387$		0			0
$388$	−4.23879			−0.215192
$389$	−19.5548	−	9.41708i	−0.991466	−	0.477465i	−0.133432	−	0.991058i	$-0.542600\pi$
$389$	−19.5548	−	9.41708i	−0.991466	−	0.477465i	−0.858034	+	0.513593i	$0.828314\pi$
$390$		0			0
$391$	−0.0338869	−	0.0424928i	−0.00171373	−	0.00214895i
$392$	39.0945	−	36.2744i	1.97457	−	1.83214i
$393$		0			0
$394$	7.44455	+	4.29811i	0.375051	+	0.216536i
$395$	2.59954	+	11.3893i	0.130797	+	0.573059i
$396$		0			0
$397$	−17.1407	+	5.28720i	−0.860266	+	0.265357i	−0.693338	−	0.720612i	$-0.743861\pi$
$397$	−17.1407	+	5.28720i	−0.860266	+	0.265357i	−0.166928	+	0.985969i	$0.553385\pi$
$398$	13.5107	+	10.7744i	0.677232	+	0.540074i
$399$		0			0
$400$	2.89348	+	0.892520i	0.144674	+	0.0446260i
$401$	−5.76485	−	8.45549i	−0.287883	−	0.422247i	0.654868	−	0.755743i	$-0.272724\pi$
$401$	−5.76485	−	8.45549i	−0.287883	−	0.422247i	−0.942752	+	0.333496i	$0.891772\pi$
$402$		0			0
$403$	−4.07443	+	17.8512i	−0.202962	+	0.889233i
$404$	−1.76270	+	1.89974i	−0.0876977	+	0.0945156i
$405$		0			0
$406$	−50.5725	−	19.8483i	−2.50987	−	0.985053i
$407$	−37.9969	−	5.72711i	−1.88344	−	0.283883i
$408$		0			0
$409$	8.85252	+	18.3824i	0.437729	+	0.908953i	0.996808	+	0.0798389i	$0.0254406\pi$
$409$	8.85252	+	18.3824i	0.437729	+	0.908953i	−0.559079	+	0.829114i	$0.688845\pi$
$410$	1.14417	−	7.59108i	0.0565066	−	0.374897i
$411$		0			0
$412$	−0.296118	+	3.95142i	−0.0145887	+	0.194672i
$413$	5.82786	+	5.40747i	0.286770	+	0.266084i
$414$		0			0
$415$	3.35807	+	22.2793i	0.164841	+	1.09365i
$416$	−12.1027	+	8.25146i	−0.593383	+	0.404561i
$417$		0			0
$418$	−2.01478	−	26.8854i	−0.0985461	−	1.31501i
$419$	13.1939	−	16.5446i	0.644564	−	0.808258i	−0.347001	−	0.937865i	$-0.612800\pi$
$419$	13.1939	−	16.5446i	0.644564	−	0.808258i	0.991566	+	0.129607i	$0.0413714\pi$
$420$		0			0
$421$	4.06670	−	1.59606i	0.198199	−	0.0777872i	−0.264166	−	0.964477i	$-0.585097\pi$
$421$	4.06670	−	1.59606i	0.198199	−	0.0777872i	0.462364	+	0.886690i	$0.347001\pi$
$422$	15.1502	−	3.45793i	0.737500	−	0.168330i
$423$		0			0
$424$	−36.6595	+	21.1654i	−1.78034	+	1.02788i
$425$	−2.47941	−	2.67216i	−0.120269	−	0.129619i
$426$		0			0
$427$	9.97567	+	6.80130i	0.482757	+	0.329138i
$428$	−3.91727	+	8.13429i	−0.189348	+	0.393186i
$429$		0			0
$430$	−0.460702	−	13.9754i	−0.0222170	−	0.673953i
$431$			38.5080i			1.85487i	0.373988	+	0.927433i	$0.377990\pi$
$431$			38.5080i			1.85487i	−0.373988	+	0.927433i	$0.622010\pi$
$432$		0			0
$433$	−0.227907	+	0.334279i	−0.0109525	+	0.0160644i	−0.831676	−	0.555261i	$-0.812618\pi$
$433$	−0.227907	+	0.334279i	−0.0109525	+	0.0160644i	0.820723	+	0.571326i	$0.193571\pi$
$434$	20.8508	−	16.6280i	1.00087	−	0.798167i
$435$		0			0
$436$	2.74111	+	4.74773i	0.131275	+	0.227375i
$437$	−0.0573952	+	0.0994114i	−0.00274559	+	0.00475549i
$438$		0			0
$439$	−0.0545136	−	0.138898i	−0.00260179	−	0.00662926i	0.929567	−	0.368653i	$-0.120181\pi$
$439$	−0.0545136	−	0.138898i	−0.00260179	−	0.00662926i	−0.932169	+	0.362024i	$0.882086\pi$
$440$	7.71971	+	25.0267i	0.368023	+	1.19310i
$441$		0			0
$442$	−10.8022	+	0.809515i	−0.513810	+	0.0385047i
$443$	8.43602	−	27.3489i	0.400807	−	1.29939i	−0.500324	−	0.865839i	$-0.666786\pi$
$443$	8.43602	−	27.3489i	0.400807	−	1.29939i	0.901131	−	0.433547i	$-0.142738\pi$
$444$		0			0
$445$	−1.48440	+	0.223737i	−0.0703673	+	0.0106062i
$446$	−12.9656	−	2.95931i	−0.613939	−	0.140128i
$447$		0			0
$448$	41.5882	+	3.11661i	1.96486	+	0.147246i
$449$	2.46858	−	6.28983i	0.116499	−	0.296835i	−0.860716	−	0.509085i	$-0.829984\pi$
$449$	2.46858	−	6.28983i	0.116499	−	0.296835i	0.977215	+	0.212250i	$0.0680791\pi$
$450$		0			0
$451$	−14.6831	+	7.07102i	−0.691401	+	0.332961i
$452$	1.39807	−	0.673274i	0.0657596	−	0.0316681i
$453$		0			0
$454$	8.78875	−	22.3934i	0.412477	−	1.05097i
$455$	−35.5172	−	2.66164i	−1.66507	−	0.124780i
$456$		0			0
$457$	−18.7735	−	4.28492i	−0.878186	−	0.200440i	−0.240419	−	0.970669i	$-0.577285\pi$
$457$	−18.7735	−	4.28492i	−0.878186	−	0.200440i	−0.637767	+	0.770229i	$0.720142\pi$
$458$	15.1504	−	2.28356i	0.707933	−	0.106704i
$459$		0			0
$460$	0.00863980	−	0.0280095i	0.000402833	−	0.00130595i
$461$	−20.9095	+	1.56695i	−0.973851	+	0.0729801i	−0.552141	−	0.833751i	$-0.686189\pi$
$461$	−20.9095	+	1.56695i	−0.973851	+	0.0729801i	−0.421710	+	0.906731i	$0.638570\pi$
$462$		0			0
$463$	1.90308	+	6.16962i	0.0884434	+	0.286727i	0.988979	−	0.148056i	$-0.0473015\pi$
$463$	1.90308	+	6.16962i	0.0884434	+	0.286727i	−0.900536	+	0.434782i	$0.856825\pi$
$464$	−7.32528	−	18.6645i	−0.340067	−	0.866478i
$465$		0			0
$466$	−4.22843	+	7.32385i	−0.195878	+	0.339271i
$467$	0.658686	+	1.14088i	0.0304803	+	0.0527935i	0.880863	−	0.473371i	$-0.156963\pi$
$467$	0.658686	+	1.14088i	0.0304803	+	0.0527935i	−0.850383	+	0.526164i	$0.823630\pi$
$468$		0			0
$469$	−16.3525	+	13.0407i	−0.755087	+	0.602162i
$470$	1.19612	−	1.75438i	0.0551729	−	0.0809237i
$471$		0			0
$472$			4.96090i			0.228344i
$473$	−23.9621	+	17.5207i	−1.10178	+	0.805605i
$474$		0			0
$475$	−3.34045	+	6.93652i	−0.153271	+	0.318270i
$476$	−7.22519	−	4.92605i	−0.331166	−	0.225785i
$477$		0			0
$478$	4.54191	+	4.89502i	0.207742	+	0.223893i
$479$	10.1672	−	5.87005i	0.464553	−	0.268210i	−0.249404	−	0.968400i	$-0.580235\pi$
$479$	10.1672	−	5.87005i	0.464553	−	0.268210i	0.713957	+	0.700190i	$0.246901\pi$
$480$		0			0
$481$	31.7907	−	7.25601i	1.44953	−	0.330846i
$482$	−5.88157	+	2.30835i	−0.267898	+	0.105142i
$483$		0			0
$484$	4.22084	−	5.29277i	0.191856	−	0.240580i
$485$	−0.834903	−	11.1410i	−0.0379110	−	0.505887i
$486$		0			0
$487$	30.5471	−	20.8267i	1.38422	−	0.943747i	0.384434	−	0.923152i	$-0.374397\pi$
$487$	30.5471	−	20.8267i	1.38422	−	0.943747i	0.999788	−	0.0205942i	$-0.00655579\pi$
$488$	1.12288	+	7.44979i	0.0508302	+	0.337236i
$489$		0			0
$490$	27.0859	+	25.1321i	1.22362	+	1.13535i
$491$	−1.54177	+	20.5735i	−0.0695791	+	0.928468i	0.847765	+	0.530372i	$0.177948\pi$
$491$	−1.54177	+	20.5735i	−0.0695791	+	0.928468i	−0.917344	+	0.398096i	$0.869671\pi$
$492$		0			0
$493$	−3.59755	+	23.8682i	−0.162026	+	1.07497i
$494$	9.92674	+	20.6131i	0.446625	+	0.927426i
$495$		0			0
$496$	9.73269	+	1.46697i	0.437011	+	0.0658688i
$497$	−14.4366	−	5.66595i	−0.647570	−	0.254152i
$498$		0			0
$499$	10.0358	−	10.8161i	0.449266	−	0.484194i	−0.467287	−	0.884105i	$-0.654769\pi$
$499$	10.0358	−	10.8161i	0.449266	−	0.484194i	0.916554	+	0.399912i	$0.130959\pi$
$500$	1.92909	−	8.45191i	0.0862717	−	0.377981i
$501$		0			0
$502$	2.12494	+	3.11672i	0.0948409	+	0.139106i
$503$	−15.4363	−	4.76146i	−0.688270	−	0.212303i	−0.0691575	−	0.997606i	$-0.522031\pi$
$503$	−15.4363	−	4.76146i	−0.688270	−	0.212303i	−0.619112	+	0.785303i	$0.712507\pi$
$504$		0			0
$505$	−5.34037	−	4.25880i	−0.237643	−	0.189514i
$506$	0.107284	−	0.0330926i	0.00476933	−	0.00147114i
$507$		0			0
$508$	−1.44154	−	6.31581i	−0.0639581	−	0.280219i
$509$	24.8877	+	14.3689i	1.10313	+	0.636891i	0.937041	−	0.349220i	$-0.113553\pi$
$509$	24.8877	+	14.3689i	1.10313	+	0.636891i	0.166087	+	0.986111i	$0.446887\pi$
$510$		0			0
$511$	48.6791	−	45.1676i	2.15344	−	1.99810i
$512$	12.8344	+	16.0939i	0.567207	+	0.711255i
$513$		0			0
$514$	−1.40552	−	0.676862i	−0.0619947	−	0.0298551i
$515$	−10.4440			−0.460218
$516$		0			0
$517$	−4.50761			−0.198244
$518$	−42.7909	−	20.6070i	−1.88012	−	0.905419i
$519$		0			0
$520$	−13.8570	−	17.3761i	−0.607670	−	0.761994i
$521$	24.0798	−	22.3428i	1.05495	−	0.978855i	0.0551474	−	0.998478i	$-0.482437\pi$
$521$	24.0798	−	22.3428i	1.05495	−	0.978855i	0.999807	+	0.0196232i	$0.00624664\pi$
$522$		0			0
$523$	−26.8669	−	15.5116i	−1.17481	−	0.678276i	−0.220000	−	0.975500i	$-0.570606\pi$
$523$	−26.8669	−	15.5116i	−1.17481	−	0.678276i	−0.954808	+	0.297224i	$0.903939\pi$
$524$	−1.62724	−	7.12942i	−0.0710865	−	0.311450i
$525$		0			0
$526$	−28.2834	+	8.72426i	−1.23321	+	0.380396i
$527$	−9.26395	−	7.38775i	−0.403544	−	0.321816i
$528$		0			0
$529$	21.9777	+	6.77923i	0.955553	+	0.294749i
$530$	−16.5211	−	24.2320i	−0.717630	−	1.05257i
$531$		0			0
$532$	−4.10978	+	18.0061i	−0.178181	+	0.780664i
$533$	9.40652	−	10.1378i	0.407441	−	0.439117i
$534$		0			0
$535$	−22.1513	−	8.69374i	−0.957684	−	0.375863i
$536$	−12.9056	−	1.94520i	−0.557437	−	0.0840200i
$537$		0			0
$538$	13.3004	+	27.6185i	0.573420	+	1.19072i
$539$	11.6908	−	77.5637i	0.503560	−	3.34090i
$540$		0			0
$541$	1.46518	−	19.5515i	0.0629932	−	0.840585i	−0.872809	−	0.488061i	$-0.837704\pi$
$541$	1.46518	−	19.5515i	0.0629932	−	0.840585i	0.935803	−	0.352524i	$-0.114677\pi$
$542$	−9.16563	−	8.50446i	−0.393698	−	0.365298i
$543$		0			0
$544$	−1.41277	−	9.37314i	−0.0605722	−	0.401870i
$545$	−11.9388	+	8.13972i	−0.511401	+	0.348667i
$546$		0			0
$547$	−3.09695	−	41.3260i	−0.132416	−	1.76697i	−0.528667	−	0.848829i	$-0.677308\pi$
$547$	−3.09695	−	41.3260i	−0.132416	−	1.76697i	0.396251	−	0.918142i	$-0.370311\pi$
$548$	2.04996	−	2.57057i	0.0875700	−	0.109809i
$549$		0			0
$550$	7.00949	−	2.75102i	0.298886	−	0.117304i
$551$	49.7020	−	11.3442i	2.11738	−	0.483277i
$552$		0			0
$553$	26.5460	−	15.3263i	1.12885	−	0.651741i
$554$	2.44681	+	2.63703i	0.103955	+	0.112037i
$555$		0			0
$556$	−8.79597	−	5.99699i	−0.373032	−	0.254329i
$557$	−2.26484	+	4.70300i	−0.0959645	+	0.199272i	−0.943425	−	0.331586i	$-0.892416\pi$
$557$	−2.26484	+	4.70300i	−0.0959645	+	0.199272i	0.847460	+	0.530859i	$0.178130\pi$
$558$		0			0
$559$	13.4966	−	21.2691i	0.570844	−	0.899589i
$560$			19.1456i			0.809051i
$561$		0			0
$562$	−5.40405	+	7.92629i	−0.227956	+	0.334350i
$563$	4.15988	−	3.31740i	0.175318	−	0.139812i	−0.531899	−	0.846808i	$-0.678522\pi$
$563$	4.15988	−	3.31740i	0.175318	−	0.139812i	0.707218	+	0.706996i	$0.249950\pi$
$564$		0			0
$565$	2.04497	+	3.54199i	0.0860325	+	0.149013i
$566$	3.88223	−	6.72422i	0.163182	−	0.282640i
$567$		0			0
$568$	−3.53556	−	9.00846i	−0.148349	−	0.377987i
$569$	−11.5178	−	37.3397i	−0.482851	−	1.56536i	−0.789630	−	0.613583i	$-0.789728\pi$
$569$	−11.5178	−	37.3397i	−0.482851	−	1.56536i	0.306780	−	0.951780i	$-0.400748\pi$
$570$		0			0
$571$	−20.4033	+	1.52902i	−0.853853	+	0.0639875i	−0.494462	−	0.869199i	$-0.664635\pi$
$571$	−20.4033	+	1.52902i	−0.853853	+	0.0639875i	−0.359392	+	0.933187i	$0.617016\pi$
$572$	−3.65560	+	11.8512i	−0.152848	+	0.495522i
$573$		0			0
$574$	−19.9180	+	3.00215i	−0.831361	+	0.125307i
$575$	−0.0312566	−	0.00713411i	−0.00130349	−	0.000297513i
$576$		0			0
$577$	−40.6348	−	3.04516i	−1.69165	−	0.126771i	−0.806241	−	0.591588i	$-0.798501\pi$
$577$	−40.6348	−	3.04516i	−1.69165	−	0.126771i	−0.885407	+	0.464816i	$0.846120\pi$
$578$	−4.48432	+	11.4259i	−0.186523	+	0.475253i
$579$		0			0
$580$	−11.7286	+	5.64821i	−0.487005	+	0.234529i
$581$	53.2637	−	25.6505i	2.20975	−	1.06416i
$582$		0			0
$583$	−22.7462	+	57.9564i	−0.942052	+	2.40031i
$584$	41.3216	+	3.09663i	1.70990	+	0.128139i
$585$		0			0
$586$	12.2405	+	2.79380i	0.505648	+	0.115411i
$587$	−14.3487	+	2.16271i	−0.592232	+	0.0892647i	−0.438319	−	0.898820i	$-0.644426\pi$
$587$	−14.3487	+	2.16271i	−0.592232	+	0.0892647i	−0.153914	+	0.988084i	$0.549188\pi$
$588$		0			0
$589$	−7.37646	+	23.9139i	−0.303942	+	0.985355i
$590$	−3.42746	+	0.256852i	−0.141106	+	0.0105744i
$591$		0			0
$592$	−5.16659	−	16.7497i	−0.212346	−	0.688408i
$593$	−2.65140	−	6.75565i	−0.108880	−	0.277421i	0.866041	−	0.499973i	$-0.166657\pi$
$593$	−2.65140	−	6.75565i	−0.108880	−	0.277421i	−0.974921	+	0.222552i	$0.928561\pi$
$594$		0			0
$595$	11.5242	−	19.9606i	0.472447	−	0.818303i
$596$	4.63413	+	8.02654i	0.189821	+	0.328780i
$597$		0			0
$598$	−0.0744875	+	0.0594018i	−0.00304602	+	0.00242912i
$599$	−2.63466	+	3.86433i	−0.107649	+	0.157892i	−0.876283	−	0.481797i	$-0.839984\pi$
$599$	−2.63466	+	3.86433i	−0.107649	+	0.157892i	0.768634	+	0.639689i	$0.220937\pi$
$600$		0			0
$601$		−	20.5171i		−	0.836911i	−0.908237	−	0.418456i	$-0.862572\pi$
$601$		−	20.5171i		−	0.836911i	0.908237	−	0.418456i	$-0.137428\pi$
$602$	−34.6841	+	11.9637i	−1.41362	+	0.487602i
$603$		0			0
$604$	1.51246	−	3.14065i	0.0615411	−	0.127791i
$605$	14.7426	+	10.0513i	0.599371	+	0.408644i
$606$		0			0
$607$	−21.4926	−	23.1635i	−0.872357	−	0.940177i	0.126300	−	0.991992i	$-0.459690\pi$
$607$	−21.4926	−	23.1635i	−0.872357	−	0.940177i	−0.998657	+	0.0518151i	$0.983499\pi$
$608$	−17.3379	+	10.0101i	−0.703147	+	0.405962i
$609$		0			0
$610$	−5.08888	+	1.16150i	−0.206043	+	0.0470279i
$611$	3.56072	−	1.39748i	0.144051	−	0.0565360i
$612$		0			0
$613$	9.41719	−	11.8088i	0.380357	−	0.476952i	−0.554395	−	0.832254i	$-0.687050\pi$
$613$	9.41719	−	11.8088i	0.380357	−	0.476952i	0.934752	+	0.355302i	$0.115622\pi$
$614$	−1.35138	−	18.0329i	−0.0545371	−	0.727747i
$615$		0			0
$616$	56.7789	−	38.7112i	2.28769	−	1.55972i
$617$	4.62333	+	30.6738i	0.186128	+	1.23488i	0.865433	+	0.501024i	$0.167043\pi$
$617$	4.62333	+	30.6738i	0.186128	+	1.23488i	−0.679305	+	0.733856i	$0.737719\pi$
$618$		0			0
$619$	24.0178	+	22.2852i	0.965355	+	0.895719i	0.994593	−	0.103854i	$-0.0331174\pi$
$619$	24.0178	+	22.2852i	0.965355	+	0.895719i	−0.0292375	+	0.999572i	$0.509308\pi$
$620$	0.477550	−	6.37246i	0.0191789	−	0.255924i
$621$		0			0
$622$	3.22363	−	21.3874i	0.129256	−	0.857555i
$623$	1.70901	+	3.54879i	0.0684699	+	0.142179i
$624$		0			0
$625$	15.3445	+	2.31281i	0.613779	+	0.0925123i
$626$	−10.9624	−	4.30241i	−0.438144	−	0.171959i
$627$		0			0
$628$	7.95685	−	8.57545i	0.317513	−	0.342198i
$629$	−4.69554	+	20.5725i	−0.187223	+	0.820280i
$630$		0			0
$631$	10.8802	+	15.9583i	0.433134	+	0.635291i	0.979307	−	0.202381i	$-0.0648681\pi$
$631$	10.8802	+	15.9583i	0.433134	+	0.635291i	−0.546172	+	0.837673i	$0.683916\pi$
$632$	18.2775	+	5.63787i	0.727041	+	0.224262i
$633$		0			0
$634$	21.0429	+	16.7812i	0.835722	+	0.666466i
$635$	16.3162	−	5.03288i	0.647488	−	0.199724i
$636$		0			0
$637$	14.8118	+	64.8948i	0.586865	+	2.57122i
$638$	−43.1813	−	24.9307i	−1.70956	−	0.987016i
$639$		0			0
$640$	−2.70816	+	2.51280i	−0.107049	+	0.0993273i
$641$	−27.0536	−	33.9241i	−1.06855	−	1.33992i	−0.937280	−	0.348577i	$-0.886665\pi$
$641$	−27.0536	−	33.9241i	−1.06855	−	1.33992i	−0.131273	−	0.991346i	$-0.541906\pi$
$642$		0			0
$643$	−27.4191	−	13.2044i	−1.08131	−	0.520729i	−0.193571	−	0.981086i	$-0.562007\pi$
$643$	−27.4191	−	13.2044i	−1.08131	−	0.520729i	−0.887734	+	0.460357i	$0.847721\pi$
$644$	−0.0769103			−0.00303069
$645$		0			0
$646$	−14.8054			−0.582511
$647$	−40.8241	−	19.6599i	−1.60496	−	0.772909i	−0.605229	−	0.796051i	$-0.706919\pi$
$647$	−40.8241	−	19.6599i	−1.60496	−	0.772909i	−0.999732	+	0.0231423i	$0.992633\pi$
$648$		0			0
$649$	4.54930	+	5.70464i	0.178576	+	0.223927i
$650$	−4.68415	+	4.34626i	−0.183728	+	0.170474i
$651$		0			0
$652$	−6.24759	−	3.60705i	−0.244675	−	0.141263i
$653$	−3.05418	−	13.3812i	−0.119519	−	0.523649i	−0.998872	−	0.0474779i	$-0.984882\pi$
$653$	−3.05418	−	13.3812i	−0.119519	−	0.523649i	0.879353	−	0.476171i	$-0.157976\pi$
$654$		0			0
$655$	18.4181	−	5.68122i	0.719653	−	0.221984i
$656$	−5.81217	−	4.63505i	−0.226927	−	0.180968i
$657$		0			0
$658$	−5.32384	−	1.64219i	−0.207545	−	0.0640191i
$659$	14.2642	+	20.9217i	0.555654	+	0.814994i	0.996587	−	0.0825455i	$-0.0263050\pi$
$659$	14.2642	+	20.9217i	0.555654	+	0.814994i	−0.440934	+	0.897540i	$0.645353\pi$
$660$		0			0
$661$	4.93297	−	21.6127i	0.191870	−	0.840638i	−0.783733	−	0.621098i	$-0.786687\pi$
$661$	4.93297	−	21.6127i	0.191870	−	0.840638i	0.975603	−	0.219541i	$-0.0704559\pi$
$662$	−19.6923	+	21.2232i	−0.765362	+	0.824864i
$663$		0			0
$664$	34.3398	+	13.4774i	1.33264	+	0.523024i
$665$	−48.1357	−	7.25530i	−1.86662	−	0.281348i
$666$		0			0
$667$	0.0921110	+	0.191270i	0.00356655	+	0.00740602i
$668$	1.98923	−	13.1977i	0.0769658	−	0.510635i
$669$		0			0
$670$	0.675739	−	9.01712i	0.0261061	−	0.348362i
$671$	8.12291	+	7.53696i	0.313582	+	0.290961i
$672$		0			0
$673$	−5.54673	−	36.8002i	−0.213811	−	1.41854i	−0.795906	−	0.605421i	$-0.793005\pi$
$673$	−5.54673	−	36.8002i	−0.213811	−	1.41854i	0.582095	−	0.813121i	$-0.302233\pi$
$674$	5.52872	−	3.76942i	0.212958	−	0.145193i
$675$		0			0
$676$	−0.0936225	−	1.24931i	−0.00360086	−	0.0480502i
$677$	−2.47522	+	3.10383i	−0.0951306	+	0.119290i	−0.827118	−	0.562028i	$-0.810021\pi$
$677$	−2.47522	+	3.10383i	−0.0951306	+	0.119290i	0.731988	+	0.681318i	$0.238593\pi$
$678$		0			0
$679$	−27.2881	+	10.7098i	−1.04722	+	0.411004i
$680$	14.0217	−	3.20036i	0.537707	−	0.122728i
$681$		0			0
$682$	21.1973	−	12.2383i	0.811687	−	0.468628i
$683$	7.46101	+	8.04106i	0.285488	+	0.307683i	0.859471	−	0.511184i	$-0.170793\pi$
$683$	7.46101	+	8.04106i	0.285488	+	0.307683i	−0.573983	+	0.818867i	$0.694603\pi$
$684$		0			0
$685$	7.16012	+	4.88169i	0.273574	+	0.186520i
$686$	25.0720	−	52.0626i	0.957254	−	1.98776i
$687$		0			0
$688$	−11.9433	−	6.38034i	−0.455336	−	0.243248i
$689$		−	52.8338i		−	2.01281i
$690$		0			0
$691$	−7.48068	+	10.9721i	−0.284579	+	0.417400i	−0.941736	−	0.336353i	$-0.890806\pi$
$691$	−7.48068	+	10.9721i	−0.284579	+	0.417400i	0.657157	+	0.753754i	$0.271759\pi$
$692$	−8.10063	+	6.46004i	−0.307940	+	0.245574i
$693$		0			0
$694$	−1.37386	−	2.37960i	−0.0521512	−	0.0903285i
$695$	14.0296	−	24.3000i	0.532174	−	0.921753i
$696$		0			0
$697$	3.26961	+	8.33082i	0.123845	+	0.315552i
$698$	5.32940	+	17.2775i	0.201721	+	0.653963i
$699$		0			0
$700$	−5.14393	+	0.385484i	−0.194422	+	0.0145699i
$701$	−7.32945	+	23.7615i	−0.276829	+	0.897459i	0.705245	+	0.708964i	$0.250837\pi$
$701$	−7.32945	+	23.7615i	−0.276829	+	0.897459i	−0.982074	+	0.188495i	$0.939639\pi$
$702$		0			0
$703$	44.0697	−	6.64244i	1.66212	−	0.250525i
$704$	37.3164	+	8.51722i	1.40641	+	0.321005i
$705$		0			0
$706$	−35.4084	−	2.65349i	−1.33261	−	0.0998655i
$707$	−6.54785	+	16.6836i	−0.246257	+	0.627453i
$708$		0			0
$709$	21.8424	−	10.5187i	0.820308	−	0.395040i	0.0238367	−	0.999716i	$-0.492412\pi$
$709$	21.8424	−	10.5187i	0.820308	−	0.395040i	0.796471	+	0.604676i	$0.206698\pi$
$710$	6.04084	−	2.90912i	0.226709	−	0.109177i
$711$		0			0
$712$	−0.897955	+	2.28795i	−0.0336523	+	0.0857447i
$713$	−0.103922	−	0.00778788i	−0.00389191	−	0.000291658i
$714$		0			0
$715$	−31.8689	−	7.27388i	−1.19183	−	0.272028i
$716$	2.75139	−	0.414705i	0.102824	−	0.0154983i
$717$		0			0
$718$	−9.17002	+	29.7285i	−0.342222	+	1.10946i
$719$	−12.8556	+	0.963396i	−0.479434	+	0.0359286i	−0.312256	−	0.949998i	$-0.601085\pi$
$719$	−12.8556	+	0.963396i	−0.479434	+	0.0359286i	−0.167178	+	0.985927i	$0.553466\pi$
$720$		0			0
$721$	8.07738	+	26.1862i	0.300817	+	0.975226i
$722$	3.54990	+	9.04499i	0.132113	+	0.336620i
$723$		0			0
$724$	5.94517	−	10.2973i	0.220951	−	0.382698i
$725$	7.11926	+	12.3309i	0.264403	+	0.457959i
$726$		0			0
$727$	−25.7454	+	20.5313i	−0.954844	+	0.761463i	−0.971166	−	0.238404i	$-0.923376\pi$
$727$	−25.7454	+	20.5313i	−0.954844	+	0.761463i	0.0163221	+	0.999867i	$0.494804\pi$
$728$	−32.8502	+	48.1823i	−1.21751	+	1.78576i
$729$		0			0
$730$			28.7092i			1.06258i
$731$	8.61121	+	13.8409i	0.318497	+	0.511924i
$732$		0			0
$733$	2.52045	−	5.23377i	0.0930949	−	0.193314i	−0.849222	−	0.528036i	$-0.822928\pi$
$733$	2.52045	−	5.23377i	0.0930949	−	0.193314i	0.942317	+	0.334723i	$0.108643\pi$
$734$	9.60487	+	6.54849i	0.354522	+	0.241709i
$735$		0			0
$736$	−0.0567053	−	0.0611137i	−0.00209018	−	0.00225268i
$737$	−16.6242	+	9.59800i	−0.612361	+	0.353547i
$738$		0			0
$739$	8.09639	−	1.84795i	0.297831	−	0.0679779i	−0.0709945	−	0.997477i	$-0.522617\pi$
$739$	8.09639	−	1.84795i	0.297831	−	0.0679779i	0.368825	+	0.929499i	$0.379760\pi$
$740$	−10.5937	+	4.15770i	−0.389430	+	0.152840i
$741$		0			0
$742$	−47.9794	+	60.1643i	−1.76138	+	2.20870i
$743$	1.42098	+	18.9616i	0.0521306	+	0.695634i	0.960645	+	0.277780i	$0.0895987\pi$
$743$	1.42098	+	18.9616i	0.0521306	+	0.695634i	−0.908514	+	0.417854i	$0.862782\pi$
$744$		0			0
$745$	−20.1837	+	13.7610i	−0.739475	+	0.504166i
$746$	−3.17090	−	21.0375i	−0.116095	−	0.770238i
$747$		0			0
$748$	−5.88327	−	5.45888i	−0.215114	−	0.199596i
$749$	−4.66601	+	62.2636i	−0.170492	+	2.27506i
$750$		0			0
$751$	−1.86349	+	12.3634i	−0.0679996	+	0.451148i	0.928758	+	0.370686i	$0.120877\pi$
$751$	−1.86349	+	12.3634i	−0.0679996	+	0.451148i	−0.996758	+	0.0804614i	$0.974361\pi$
$752$	−0.892146	−	1.85256i	−0.0325332	−	0.0675559i
$753$		0			0
$754$	41.8396	+	6.30631i	1.52371	+	0.229662i
$755$	8.55262	+	3.35666i	0.311262	+	0.122161i
$756$		0			0
$757$	−1.36390	+	1.46993i	−0.0495717	+	0.0534256i	−0.757351	−	0.653008i	$-0.773507\pi$
$757$	−1.36390	+	1.46993i	−0.0495717	+	0.0534256i	0.707779	+	0.706434i	$0.249697\pi$
$758$	−3.74601	+	16.4123i	−0.136061	+	0.596123i
$759$		0			0
$760$	−17.1114	−	25.0979i	−0.620697	−	0.910396i
$761$	40.2710	+	12.4220i	1.45982	+	0.450296i	0.920146	−	0.391575i	$-0.128070\pi$
$761$	40.2710	+	12.4220i	1.45982	+	0.450296i	0.539678	+	0.841871i	$0.318546\pi$
$762$		0			0
$763$	29.6421	+	23.6388i	1.07312	+	0.855782i
$764$	3.85182	−	1.18813i	0.139354	−	0.0429850i
$765$		0			0
$766$	6.96856	+	30.5313i	0.251784	+	1.10314i
$767$	−5.36225	−	3.09589i	−0.193620	−	0.111786i
$768$		0			0
$769$	2.32722	−	2.15935i	0.0839217	−	0.0778680i	−0.637097	−	0.770784i	$-0.719865\pi$
$769$	2.32722	−	2.15935i	0.0839217	−	0.0778680i	0.721018	+	0.692916i	$0.243674\pi$
$770$	29.6851	+	37.2239i	1.06978	+	1.34146i
$771$		0			0
$772$	6.08502	+	2.93039i	0.219005	+	0.105467i
$773$	37.3679			1.34403			0.672015	−	0.740538i	$-0.265429\pi$
$773$	37.3679			1.34403			0.672015	+	0.740538i	$0.265429\pi$
$774$		0			0
$775$	−6.98956			−0.251073
$776$	−16.4808	−	7.93673i	−0.591626	−	0.284912i
$777$		0			0
$778$	−15.3507	−	19.2491i	−0.550348	−	0.690115i
$779$	13.8559	−	12.8564i	0.496440	−	0.460629i
$780$		0			0
$781$	−12.3267	−	7.11680i	−0.441082	−	0.254659i
$782$	−0.0137192	−	0.0601077i	−0.000490597	−	0.00214945i
$783$		0			0
$784$	34.1914	−	10.5466i	1.22112	−	0.376666i
$785$	24.1065	+	19.2243i	0.860397	+	0.686143i
$786$		0			0
$787$	10.1493	+	3.13063i	0.361782	+	0.111595i	0.470317	−	0.882498i	$-0.344140\pi$
$787$	10.1493	+	3.13063i	0.361782	+	0.111595i	−0.108535	+	0.994093i	$0.534616\pi$
$788$	−3.04452	−	4.46549i	−0.108456	−	0.159076i
$789$		0			0
$790$	−2.94885	+	12.9197i	−0.104915	+	0.459664i
$791$	7.29924	−	7.86671i	0.259531	−	0.279708i
$792$		0			0
$793$	−8.75324	−	3.43539i	−0.310837	−	0.121994i
$794$	−20.1206	−	3.03270i	−0.714055	−	0.107626i
$795$		0			0
$796$	−4.71405	−	9.78884i	−0.167085	−	0.346956i
$797$	−1.66009	+	11.0140i	−0.0588035	+	0.390136i	0.939997	+	0.341181i	$0.110827\pi$
$797$	−1.66009	+	11.0140i	−0.0588035	+	0.390136i	−0.998801	+	0.0489546i	$0.984411\pi$
$798$		0			0
$799$	−0.184982	+	2.46842i	−0.00654420	+	0.0873263i
$800$	−4.09888	−	3.80320i	−0.144917	−	0.134464i
$801$		0			0
$802$	−1.73021	−	11.4792i	−0.0610957	−	0.405344i
$803$	50.3563	−	34.3324i	1.77704	−	1.21156i
$804$		0			0
$805$	−0.0151488	−	0.202147i	−0.000533925	−	0.00712473i
$806$	−12.9503	+	16.2392i	−0.456155	+	0.572001i
$807$		0			0
$808$	−10.4106	+	4.08587i	−0.366244	+	0.143740i
$809$	9.30679	−	2.12421i	0.327209	−	0.0746834i	−0.0557606	−	0.998444i	$-0.517758\pi$
$809$	9.30679	−	2.12421i	0.327209	−	0.0746834i	0.382970	+	0.923761i	$0.374901\pi$
$810$		0			0
$811$	−26.3691	+	15.2242i	−0.925943	+	0.534593i	−0.885526	−	0.464589i	$-0.846202\pi$
$811$	−26.3691	+	15.2242i	−0.925943	+	0.534593i	−0.0404169	+	0.999183i	$0.512869\pi$
$812$	23.2327	+	25.0389i	0.815307	+	0.878691i
$813$		0			0
$814$	−36.0153	−	24.5548i	−1.26234	−	0.860647i
$815$	8.25000	−	17.1313i	0.288985	−	0.600083i
$816$		0			0
$817$	20.5673	−	27.6099i	0.719560	−	0.965950i
$818$			23.1446i			0.809231i
$819$		0			0
$820$	−2.71890	+	3.98789i	−0.0949479	+	0.139263i
$821$	−39.6272	+	31.6017i	−1.38300	+	1.10291i	−0.400572	+	0.916265i	$0.631188\pi$
$821$	−39.6272	+	31.6017i	−1.38300	+	1.10291i	−0.982428	+	0.186640i	$0.940240\pi$
$822$		0			0
$823$	8.15712	+	14.1285i	0.284339	+	0.492490i	0.972449	−	0.233117i	$-0.0748925\pi$
$823$	8.15712	+	14.1285i	0.284339	+	0.492490i	−0.688109	+	0.725607i	$0.741559\pi$
$824$	−8.54997	+	14.8090i	−0.297852	+	0.515896i
$825$		0			0
$826$	3.29480	+	8.39501i	0.114641	+	0.292100i
$827$	−11.6283	−	37.6980i	−0.404355	−	1.31089i	−0.897529	−	0.440956i	$-0.854639\pi$
$827$	−11.6283	−	37.6980i	−0.404355	−	1.31089i	0.493174	−	0.869931i	$-0.335837\pi$
$828$		0			0
$829$	18.4782	−	1.38475i	0.641774	−	0.0480943i	0.250132	−	0.968212i	$-0.419526\pi$
$829$	18.4782	−	1.38475i	0.641774	−	0.0480943i	0.391642	+	0.920117i	$0.371907\pi$
$830$	−7.53350	+	24.4230i	−0.261492	+	0.847735i
$831$		0			0
$832$	−32.1181	+	4.84103i	−1.11349	+	0.167832i
$833$	−41.9950	−	9.58508i	−1.45504	−	0.332103i
$834$		0			0
$835$	35.0799	+	2.62888i	1.21399	+	0.0909761i
$836$	−6.19279	+	15.7790i	−0.214182	+	0.545727i
$837$		0			0
$838$	21.6276	−	10.4153i	0.747115	−	0.359791i
$839$	10.4226	−	5.01924i	0.359826	−	0.173283i	−0.245232	−	0.969464i	$-0.578864\pi$
$839$	10.4226	−	5.01924i	0.359826	−	0.173283i	0.605058	+	0.796181i	$0.293150\pi$
$840$		0			0
$841$	23.8506	−	60.7703i	0.822434	−	2.09553i
$842$	4.94186	+	0.370341i	0.170308	+	0.0127628i
$843$		0			0
$844$	−9.52520	−	2.17406i	−0.327871	−	0.0748344i
$845$	3.26516	−	0.492144i	0.112325	−	0.0169303i
$846$		0			0
$847$	13.7998	−	44.7377i	0.474165	−	1.53721i
$848$	−28.3212	+	2.12238i	−0.972552	+	0.0728827i
$849$		0			0
$850$	−1.21884	−	3.95137i	−0.0418057	−	0.135531i
$851$	0.0678038	+	0.172761i	0.00232428	+	0.00592218i
$852$		0			0
$853$	−23.9139	+	41.4201i	−0.818797	+	1.41820i	0.0877725	+	0.996141i	$0.472025\pi$
$853$	−23.9139	+	41.4201i	−0.818797	+	1.41820i	−0.906569	+	0.422057i	$0.861308\pi$
$854$	6.84797	+	11.8610i	0.234333	+	0.405876i
$855$		0			0
$856$	−30.4613	+	24.2921i	−1.04115	+	0.830287i
$857$	10.9205	−	16.0174i	0.373036	−	0.547143i	−0.593116	−	0.805117i	$-0.702103\pi$
$857$	10.9205	−	16.0174i	0.373036	−	0.547143i	0.966152	+	0.257974i	$0.0830549\pi$
$858$		0			0
$859$			23.0010i			0.784784i	0.919798	+	0.392392i	$0.128352\pi$
$859$			23.0010i			0.784784i	−0.919798	+	0.392392i	$0.871648\pi$
$860$	−3.55138	+	8.04210i	−0.121101	+	0.274233i
$861$		0			0
$862$	−18.9531	+	39.3565i	−0.645545	+	1.34049i
$863$	−7.52802	−	5.13252i	−0.256257	−	0.174713i	0.428377	−	0.903600i	$-0.359085\pi$
$863$	−7.52802	−	5.13252i	−0.256257	−	0.174713i	−0.684634	+	0.728887i	$0.740038\pi$
$864$		0			0
$865$	−18.5748	−	20.0188i	−0.631561	−	0.680661i
$866$	−0.397456	+	0.229471i	−0.0135061	+	0.00779776i
$867$		0			0
$868$	−16.3470	+	3.73109i	−0.554853	+	0.126642i
$869$	26.1878	−	10.2780i	0.888361	−	0.348656i
$870$		0			0
$871$	10.1564	−	12.7358i	0.344137	−	0.431535i
$872$	1.76798	+	23.5921i	0.0598714	+	0.798928i
$873$		0			0
$874$	−0.107589	+	0.0733528i	−0.00363924	+	0.00248119i
$875$	−8.93578	−	59.2850i	−0.302084	−	2.00420i
$876$		0			0
$877$	−31.3132	−	29.0544i	−1.05737	−	0.981098i	−0.0575212	−	0.998344i	$-0.518320\pi$
$877$	−31.3132	−	29.0544i	−1.05737	−	0.981098i	−0.999851	+	0.0172460i	$0.994510\pi$
$878$	0.0126490	−	0.168790i	0.000426885	−	0.00569638i
$879$		0			0
$880$	−2.61891	+	17.3753i	−0.0882834	+	0.585722i
$881$	−5.58123	−	11.5895i	−0.188036	−	0.390462i	0.785544	−	0.618806i	$-0.212383\pi$
$881$	−5.58123	−	11.5895i	−0.188036	−	0.390462i	−0.973581	+	0.228344i	$0.926669\pi$
$882$		0			0
$883$	2.27003	+	0.342152i	0.0763926	+	0.0115143i	0.187127	−	0.982336i	$-0.440082\pi$
$883$	2.27003	+	0.342152i	0.0763926	+	0.0115143i	−0.110735	+	0.993850i	$0.535320\pi$
$884$	6.33980	+	2.48819i	0.213231	+	0.0836869i
$885$		0			0
$886$	22.0826	−	23.7994i	0.741881	−	0.799557i
$887$	−0.651256	+	2.85334i	−0.0218671	+	0.0958058i	−0.984684	−	0.174349i	$-0.944218\pi$
$887$	−0.651256	+	2.85334i	−0.0218671	+	0.0958058i	0.962817	+	0.270155i	$0.0870750\pi$
$888$		0			0
$889$	−25.2378	−	37.0171i	−0.846450	−	1.24151i
$890$	−1.62723	−	0.501933i	−0.0545448	−	0.0168248i
$891$		0			0
$892$	6.53716	+	5.21321i	0.218880	+	0.174551i
$893$	4.99577	−	1.54099i	0.167177	−	0.0515673i
$894$		0			0
$895$	1.63192	+	7.14991i	0.0545491	+	0.238995i
$896$	8.39483	+	4.84676i	0.280452	+	0.161919i
$897$		0			0
$898$	5.61873	−	5.21342i	0.187499	−	0.173974i
$899$	28.8568	+	36.1853i	0.962429	+	1.20685i
$900$		0			0
$901$	30.8041	+	14.8345i	1.02623	+	0.494208i
$902$	−18.4869			−0.615547
$903$		0			0
$904$	6.69645			0.222720
$905$	28.2360	+	13.5977i	0.938595	+	0.452003i
$906$		0			0
$907$	3.91450	+	4.90862i	0.129979	+	0.162988i	0.842562	−	0.538599i	$-0.181046\pi$
$907$	3.91450	+	4.90862i	0.129979	+	0.162988i	−0.712583	+	0.701588i	$0.752475\pi$
$908$	−11.0871	+	10.2874i	−0.367939	+	0.341398i
$909$		0			0
$910$	−34.9897	−	20.2013i	−1.15990	−	0.669668i
$911$	6.10012	+	26.7264i	0.202106	+	0.885484i	0.969652	+	0.244490i	$0.0786205\pi$
$911$	6.10012	+	26.7264i	0.202106	+	0.885484i	−0.767546	+	0.640994i	$0.778522\pi$
$912$		0			0
$913$	51.8473	−	15.9928i	1.71590	−	0.529284i
$914$	−17.0781	−	13.6194i	−0.564895	−	0.450489i
$915$		0			0
$916$	−9.20497	−	2.83936i	−0.304141	−	0.0938150i
$917$	−28.4890	−	41.7857i	−0.940790	−	1.37989i
$918$		0			0
$919$	9.39014	−	41.1409i	0.309752	−	1.35711i	−0.545157	−	0.838334i	$-0.683530\pi$
$919$	9.39014	−	41.1409i	0.309752	−	1.35711i	0.854909	−	0.518778i	$-0.173613\pi$
$920$	0.0860375	−	0.0927263i	0.00283657	−	0.00305710i
$921$		0			0
$922$	−22.1414	−	8.68987i	−0.729189	−	0.286186i
$923$	11.9437	+	1.80022i	0.393130	+	0.0592549i
$924$		0			0
$925$	5.40076	+	11.2148i	0.177576	+	0.368740i
$926$	−1.09159	+	7.24223i	−0.0358719	+	0.237994i
$927$		0			0
$928$	−2.76691	+	36.9218i	−0.0908283	+	1.21202i
$929$	20.1129	+	18.6620i	0.659882	+	0.612281i	0.937323	−	0.348462i	$-0.113296\pi$
$929$	20.1129	+	18.6620i	0.659882	+	0.612281i	−0.277441	+	0.960743i	$0.589486\pi$
$930$		0			0
$931$	13.5593	+	89.9602i	0.444389	+	2.94833i
$932$	4.39309	−	2.99516i	0.143900	−	0.0981097i
$933$		0			0
$934$	0.111676	+	1.49021i	0.00365415	+	0.0487612i
$935$	13.1890	−	16.5385i	0.431327	−	0.540866i
$936$		0			0
$937$	−28.1148	+	11.0342i	−0.918470	+	0.360473i	−0.777023	−	0.629473i	$-0.783271\pi$
$937$	−28.1148	+	11.0342i	−0.918470	+	0.360473i	−0.141448	+	0.989946i	$0.545176\pi$
$938$	−23.1312	+	5.27955i	−0.755261	+	0.172383i
$939$		0			0
$940$	−1.15613	+	0.667490i	−0.0377087	+	0.0217711i
$941$	−40.9586	−	44.1428i	−1.33521	−	1.43901i	−0.807870	−	0.589361i	$-0.799380\pi$
$941$	−40.9586	−	44.1428i	−1.33521	−	1.43901i	−0.527341	−	0.849654i	$-0.676811\pi$
$942$		0			0
$943$	0.0650344	+	0.0443397i	0.00211781	+	0.00144390i
$944$	−1.44413	+	2.99876i	−0.0470023	+	0.0976013i
$945$		0			0
$946$	−33.1135	+	6.11302i	−1.07661	+	0.198752i
$947$			30.6699i			0.996638i	0.866994	+	0.498319i	$0.166049\pi$
$947$			30.6699i			0.996638i	−0.866994	+	0.498319i	$0.833951\pi$
$948$		0			0
$949$	−29.1343	+	42.7322i	−0.945740	+	1.38715i
$950$	−6.82812	+	5.44524i	−0.221533	+	0.176667i
$951$		0			0
$952$	−18.8686	−	32.6814i	−0.611535	−	1.05921i
$953$	−8.62265	+	14.9349i	−0.279315	+	0.483788i	−0.971215	−	0.238206i	$-0.923441\pi$
$953$	−8.62265	+	14.9349i	−0.279315	+	0.483788i	0.691900	+	0.721994i	$0.256774\pi$
$954$		0			0
$955$	3.88150	+	9.88989i	0.125602	+	0.320029i
$956$	−1.23748	−	4.01180i	−0.0400228	−	0.129751i
$957$		0			0
$958$	13.2804	−	0.995229i	0.429071	−	0.0321544i
$959$	6.70221	−	21.7280i	0.216426	−	0.701635i
$960$		0			0
$961$	8.18771	−	1.23410i	0.264120	−	0.0398096i
$962$	36.0625	+	8.23102i	1.16270	+	0.265379i
$963$		0			0
$964$	3.96134	+	0.296861i	0.127586	+	0.00956126i
$965$	−6.50353	+	16.5707i	−0.209356	+	0.533430i
$966$		0			0
$967$	−33.0812	+	15.9311i	−1.06382	+	0.512309i	−0.882110	−	0.471043i	$-0.843878\pi$
$967$	−33.0812	+	15.9311i	−1.06382	+	0.512309i	−0.181711	+	0.983352i	$0.558163\pi$
$968$	26.3212	−	12.6756i	0.845995	−	0.407410i
$969$		0			0
$970$	4.63014	−	11.7974i	0.148665	−	0.378792i
$971$	45.1022	+	3.37994i	1.44740	+	0.108467i	0.775112	−	0.631824i	$-0.217693\pi$
$971$	45.1022	+	3.37994i	1.44740	+	0.108467i	0.672286	+	0.740292i	$0.265313\pi$
$972$		0			0
$973$	−71.7779	−	16.3828i	−2.30109	−	0.525210i
$974$	41.4708	−	6.25071i	1.32881	−	0.200286i
$975$		0			0
$976$	−1.48989	+	4.83011i	−0.0476903	+	0.154608i
$977$	−32.4022	+	2.42821i	−1.03664	+	0.0776854i	−0.582162	−	0.813073i	$-0.697793\pi$
$977$	−32.4022	+	2.42821i	−1.03664	+	0.0776854i	−0.454477	+	0.890758i	$0.650174\pi$
$978$		0			0
$979$	1.06555	+	3.45442i	0.0340550	+	0.110404i
$980$	−8.48718	−	21.6250i	−0.271113	−	0.690785i
$981$		0			0
$982$	−11.7017	+	20.2680i	−0.373417	+	0.646777i
$983$	−4.12967	−	7.15279i	−0.131716	−	0.228139i	0.792622	−	0.609713i	$-0.208715\pi$
$983$	−4.12967	−	7.15279i	−0.131716	−	0.228139i	−0.924338	+	0.381574i	$0.875382\pi$
$984$		0			0
$985$	11.1372	−	8.88160i	0.354860	−	0.282991i
$986$	−15.4244	+	22.6234i	−0.491213	+	0.720477i
$987$		0			0
$988$		−	14.3843i		−	0.457626i
$989$	0.131150	+	0.0579159i	0.00417034	+	0.00184162i
$990$		0			0
$991$	4.12411	−	8.56380i	0.131007	−	0.272038i	−0.825139	−	0.564930i	$-0.808903\pi$
$991$	4.12411	−	8.56380i	0.131007	−	0.272038i	0.956146	+	0.292892i	$0.0946175\pi$
$992$	−15.0173	−	10.2386i	−0.476798	−	0.325076i
$993$		0			0
$994$	−11.9660	−	12.8963i	−0.379538	−	0.409045i
$995$	24.7999	−	14.3182i	0.786210	−	0.453919i
$996$		0			0
$997$	57.6272	−	13.1530i	1.82507	−	0.416561i	0.834212	−	0.551444i	$-0.185923\pi$
$997$	57.6272	−	13.1530i	1.82507	−	0.416561i	0.990862	+	0.134883i	$0.0430659\pi$
$998$	15.5805	−	6.11489i	0.493192	−	0.193564i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.bc.a.233.10	yes	168
3.2	odd	2	inner	387.2.bc.a.233.5	yes	168
43.12	odd	42	inner	387.2.bc.a.98.5	✓	168
129.98	even	42	inner	387.2.bc.a.98.10	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.bc.a.98.5	✓	168	43.12	odd	42	inner
387.2.bc.a.98.10	yes	168	129.98	even	42	inner
387.2.bc.a.233.5	yes	168	3.2	odd	2	inner
387.2.bc.a.233.10	yes	168	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.bc (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02203 + 0.492186i) q^{2} +(-0.444673 - 0.557602i) q^{4} +(1.37798 - 1.27858i) q^{5} +(-4.27152 - 2.46616i) q^{7} +(-0.684870 - 3.00061i) q^{8} +O(q^{10})\)	\(q+(1.02203 + 0.492186i) q^{2} +(-0.444673 - 0.557602i) q^{4} +(1.37798 - 1.27858i) q^{5} +(-4.27152 - 2.46616i) q^{7} +(-0.684870 - 3.00061i) q^{8} +(2.03765 - 0.628531i) q^{10} +(-3.53920 - 2.82242i) q^{11} +(3.67077 + 1.13228i) q^{13} +(-3.15183 - 4.62288i) q^{14} +(0.459494 - 2.01317i) q^{16} +(-1.69083 + 1.82228i) q^{17} +(4.88737 + 1.91815i) q^{19} +(-1.32569 - 0.199816i) q^{20} +(-2.22803 - 4.62655i) q^{22} +(-0.00325860 + 0.0216194i) q^{23} +(-0.109583 + 1.46228i) q^{25} +(3.19436 + 2.96393i) q^{26} +(0.524291 + 3.47844i) q^{28} +(8.02273 - 5.46981i) q^{29} +(0.356203 + 4.75320i) q^{31} +(-2.37745 + 2.98123i) q^{32} +(-2.62499 + 1.03023i) q^{34} +(-9.03928 + 2.06316i) q^{35} +(7.35131 - 4.24428i) q^{37} +(4.05097 + 4.36591i) q^{38} +(-4.78027 - 3.25913i) q^{40} +(1.56203 - 3.24359i) q^{41} +(1.72534 - 6.32639i) q^{43} +3.22852i q^{44} +(-0.0139712 + 0.0204919i) q^{46} +(0.778515 - 0.620845i) q^{47} +(8.66391 + 15.0063i) q^{49} +(-0.831713 + 1.44057i) q^{50} +(-1.00093 - 2.55032i) q^{52} +(-4.05396 - 13.1426i) q^{53} +(-8.48567 + 0.635913i) q^{55} +(-4.47456 + 14.5062i) q^{56} +(10.8917 - 1.64165i) q^{58} +(-1.57143 - 0.358669i) q^{59} +(-2.44101 - 0.182928i) q^{61} +(-1.97541 + 5.03325i) q^{62} +(-7.61806 + 3.66867i) q^{64} +(6.50598 - 3.13311i) q^{65} +(1.54923 - 3.94738i) q^{67} +(1.76797 + 0.132491i) q^{68} +(-10.2539 - 2.34039i) q^{70} +(3.10917 - 0.468632i) q^{71} +(-3.96842 + 12.8653i) q^{73} +(9.60226 - 0.719590i) q^{74} +(-1.10372 - 3.57816i) q^{76} +(8.15722 + 20.7843i) q^{77} +(-3.10732 + 5.38204i) q^{79} +(-1.94083 - 3.36162i) q^{80} +(3.19290 - 2.54625i) q^{82} +(-6.75189 + 9.90321i) q^{83} +4.67294i q^{85} +(4.87711 - 5.61660i) q^{86} +(-6.04509 + 12.5528i) q^{88} +(-0.659819 - 0.449857i) q^{89} +(-12.8874 - 13.8893i) q^{91} +(0.0135040 - 0.00779655i) q^{92} +(1.10124 - 0.251351i) q^{94} +(9.18723 - 3.60572i) q^{95} +(3.70561 - 4.64669i) q^{97} +(1.46891 + 19.6012i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 24 q^{4} - 6 q^{7}+O(q^{10}) \) 168 * q - 24 * q^4 - 6 * q^7	\( 168 q - 24 q^{4} - 6 q^{7} + 8 q^{10} + 26 q^{13} - 8 q^{16} + 24 q^{19} + 14 q^{25} + 32 q^{31} - 48 q^{34} - 78 q^{37} - 244 q^{40} - 32 q^{43} - 92 q^{46} + 54 q^{49} + 76 q^{52} - 96 q^{55} - 20 q^{58} - 96 q^{64} - 18 q^{67} + 140 q^{70} + 10 q^{73} - 16 q^{76} - 168 q^{88} - 38 q^{91} - 112 q^{94} - 40 q^{97}+O(q^{100}) \) 168 * q - 24 * q^4 - 6 * q^7 + 8 * q^10 + 26 * q^13 - 8 * q^16 + 24 * q^19 + 14 * q^25 + 32 * q^31 - 48 * q^34 - 78 * q^37 - 244 * q^40 - 32 * q^43 - 92 * q^46 + 54 * q^49 + 76 * q^52 - 96 * q^55 - 20 * q^58 - 96 * q^64 - 18 * q^67 + 140 * q^70 + 10 * q^73 - 16 * q^76 - 168 * q^88 - 38 * q^91 - 112 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

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Database

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