LMFDB - Embedded newform 931.2.f.o.324.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [931,2,Mod(324,931)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("931.324"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(931, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.2672476416.4
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} - 4x^{5} + 24x^{4} - 10x^{3} + 9x^{2} + 2x + 1 $ x^8 + 5x^6 - 4x^5 + 24x^4 - 10x^3 + 9x^2 + 2x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			324.3
Root			$0.375512 - 0.650406i$ of defining polynomial
Character	$\chi$	$=$	931.324
Dual form			931.2.f.o.704.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.375512 - 0.650406i) q^{2} +(1.16576 + 2.01915i) q^{3} +(0.717981 + 1.24358i) q^{4} +(2.13271 - 3.69397i) q^{5} +1.75102 q^{6} +2.58049 q^{8} +(-1.21798 + 2.10961i) q^{9} +(-1.60172 - 2.77426i) q^{10} +(-2.04950 - 3.54983i) q^{11} +(-1.67398 + 2.89943i) q^{12} +2.18699 q^{13} +9.94491 q^{15} +(-0.466957 + 0.808794i) q^{16} +(0.295021 + 0.510992i) q^{17} +(0.914733 + 1.58436i) q^{18} +(-0.500000 + 0.866025i) q^{19} +6.12500 q^{20} -3.07844 q^{22} +(2.18494 - 3.78442i) q^{23} +(3.00823 + 5.21040i) q^{24} +(-6.59694 - 11.4262i) q^{25} +(0.821240 - 1.42243i) q^{26} +1.31506 q^{27} -7.36442 q^{29} +(3.73444 - 6.46823i) q^{30} +(2.25925 + 3.91314i) q^{31} +(2.93119 + 5.07697i) q^{32} +(4.77843 - 8.27649i) q^{33} +0.443136 q^{34} -3.49795 q^{36} +(-4.47723 + 7.75479i) q^{37} +(0.375512 + 0.650406i) q^{38} +(2.54950 + 4.41586i) q^{39} +(5.50345 - 9.53226i) q^{40} +2.17744 q^{41} -8.69594 q^{43} +(2.94300 - 5.09743i) q^{44} +(5.19521 + 8.99837i) q^{45} +(-1.64094 - 2.84219i) q^{46} +(-5.91665 + 10.2479i) q^{47} -2.17744 q^{48} -9.90893 q^{50} +(-0.687846 + 1.19138i) q^{51} +(1.57022 + 2.71969i) q^{52} +(-2.20498 - 3.81914i) q^{53} +(0.493821 - 0.855324i) q^{54} -17.4840 q^{55} -2.33152 q^{57} +(-2.76543 + 4.78986i) q^{58} +(5.35892 + 9.28193i) q^{59} +(7.14026 + 12.3673i) q^{60} +(-1.21525 + 2.10488i) q^{61} +3.39350 q^{62} +2.53496 q^{64} +(4.66422 - 8.07866i) q^{65} +(-3.58872 - 6.21584i) q^{66} +(2.82674 + 4.89606i) q^{67} +(-0.423639 + 0.733765i) q^{68} +10.1884 q^{69} +8.32434 q^{71} +(-3.14299 + 5.44382i) q^{72} +(-5.33974 - 9.24870i) q^{73} +(3.36251 + 5.82404i) q^{74} +(15.3809 - 26.6405i) q^{75} -1.43596 q^{76} +3.82947 q^{78} +(-4.28188 + 7.41644i) q^{79} +(1.99177 + 3.44985i) q^{80} +(5.18699 + 8.98412i) q^{81} +(0.817653 - 1.41622i) q^{82} +4.25826 q^{83} +2.51678 q^{85} +(-3.26543 + 5.65589i) q^{86} +(-8.58513 - 14.8699i) q^{87} +(-5.28871 - 9.16031i) q^{88} +(1.89555 - 3.28319i) q^{89} +7.80346 q^{90} +6.27498 q^{92} +(-5.26748 + 9.12354i) q^{93} +(4.44354 + 7.69644i) q^{94} +(2.13271 + 3.69397i) q^{95} +(-6.83411 + 11.8370i) q^{96} -2.11026 q^{97} +9.98499 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 2 q^{4} + 8 q^{5} + 8 q^{6} + 12 q^{8} - 2 q^{9} + 10 q^{10} + 6 q^{11} + 6 q^{12} - 4 q^{13} + 8 q^{15} - 2 q^{16} + 8 q^{17} + 6 q^{18} - 4 q^{19} - 28 q^{22} + 8 q^{23} + 12 q^{24} - 20 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 2 * q^4 + 8 * q^5 + 8 * q^6 + 12 * q^8 - 2 * q^9 + 10 * q^10 + 6 * q^11 + 6 * q^12 - 4 * q^13 + 8 * q^15 - 2 * q^16 + 8 * q^17 + 6 * q^18 - 4 * q^19 - 28 * q^22 + 8 * q^23 + 12 * q^24 - 20 * q^25 + 16 * q^26 + 20 * q^27 + 4 * q^29 - 2 * q^30 - 2 * q^32 + 18 * q^33 + 44 * q^34 - 40 * q^36 - 10 * q^37 - 2 * q^39 + 22 * q^40 - 24 * q^41 + 8 * q^43 + 14 * q^44 + 8 * q^45 + 8 * q^46 + 16 * q^47 + 24 * q^48 + 24 * q^50 + 10 * q^51 + 28 * q^52 - 12 * q^53 + 4 * q^54 + 16 * q^55 - 4 * q^57 - 4 * q^58 + 14 * q^59 + 2 * q^60 + 20 * q^61 + 40 * q^62 - 40 * q^64 - 10 * q^65 - 8 * q^66 - 2 * q^67 - 24 * q^68 - 28 * q^69 - 4 * q^71 + 8 * q^72 - 16 * q^73 + 26 * q^74 + 36 * q^75 + 4 * q^76 + 28 * q^78 + 8 * q^79 + 28 * q^80 + 20 * q^81 - 12 * q^82 - 40 * q^83 - 28 * q^85 - 8 * q^86 - 20 * q^87 + 2 * q^88 + 16 * q^89 + 64 * q^90 + 52 * q^92 - 12 * q^93 + 10 * q^94 + 8 * q^95 - 12 * q^96 - 4 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.375512	−	0.650406i	0.265527	−	0.459906i	−0.702174	−	0.712005i	$-0.747787\pi$
$2$	0.375512	−	0.650406i	0.265527	−	0.459906i	0.967702	+	0.252098i	$0.0811207\pi$
$3$	1.16576	+	2.01915i	0.673050	+	1.16576i	0.977035	+	0.213080i	$0.0683497\pi$
$3$	1.16576	+	2.01915i	0.673050	+	1.16576i	−0.303984	+	0.952677i	$0.598317\pi$
$4$	0.717981	+	1.24358i	0.358991	+	0.621790i
$5$	2.13271	−	3.69397i	0.953779	−	1.65199i	0.216641	−	0.976251i	$-0.430490\pi$
$5$	2.13271	−	3.69397i	0.953779	−	1.65199i	0.737138	−	0.675742i	$-0.236177\pi$
$6$	1.75102			0.714853
$7$		0			0
$7$		0			0
$8$	2.58049			0.912341
$9$	−1.21798	+	2.10961i	−0.405994	+	0.703202i
$10$	−1.60172	−	2.77426i	−0.506508	−	0.877298i
$11$	−2.04950	−	3.54983i	−0.617946	−	1.07031i	−0.989860	−	0.142047i	$-0.954632\pi$
$11$	−2.04950	−	3.54983i	−0.617946	−	1.07031i	0.371913	−	0.928267i	$-0.378702\pi$
$12$	−1.67398	+	2.89943i	−0.483238	+	0.836992i
$13$	2.18699			0.606561			0.303281	−	0.952901i	$-0.401918\pi$
$13$	2.18699			0.606561			0.303281	+	0.952901i	$0.401918\pi$
$14$		0			0
$15$	9.94491			2.56777
$16$	−0.466957	+	0.808794i	−0.116739	+	0.202198i
$17$	0.295021	+	0.510992i	0.0715531	+	0.123934i	0.899582	−	0.436752i	$-0.143871\pi$
$17$	0.295021	+	0.510992i	0.0715531	+	0.123934i	−0.828029	+	0.560685i	$0.810538\pi$
$18$	0.914733	+	1.58436i	0.215605	+	0.373438i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$	6.12500			1.36959
$21$		0			0
$22$	−3.07844			−0.656326
$23$	2.18494	−	3.78442i	0.455591	−	0.789107i	−0.543131	−	0.839648i	$-0.682761\pi$
$23$	2.18494	−	3.78442i	0.455591	−	0.789107i	0.998722	+	0.0505410i	$0.0160946\pi$
$24$	3.00823	+	5.21040i	0.614052	+	1.06357i
$25$	−6.59694	−	11.4262i	−1.31939	−	2.28525i
$26$	0.821240	−	1.42243i	0.161058	−	0.278961i
$27$	1.31506			0.253084
$28$		0			0
$29$	−7.36442			−1.36754			−0.683769	−	0.729698i	$-0.739661\pi$
$29$	−7.36442			−1.36754			−0.683769	+	0.729698i	$0.739661\pi$
$30$	3.73444	−	6.46823i	0.681811	−	1.18093i
$31$	2.25925	+	3.91314i	0.405773	+	0.702820i	0.994411	−	0.105577i	$-0.0336689\pi$
$31$	2.25925	+	3.91314i	0.405773	+	0.702820i	−0.588638	+	0.808397i	$0.700336\pi$
$32$	2.93119	+	5.07697i	0.518166	+	0.897489i
$33$	4.77843	−	8.27649i	0.831818	−	1.44075i
$34$	0.443136			0.0759972
$35$		0			0
$36$	−3.49795			−0.582992
$37$	−4.47723	+	7.75479i	−0.736052	+	1.27488i	0.218208	+	0.975902i	$0.429979\pi$
$37$	−4.47723	+	7.75479i	−0.736052	+	1.27488i	−0.954260	+	0.298978i	$0.903354\pi$
$38$	0.375512	+	0.650406i	0.0609161	+	0.105510i
$39$	2.54950	+	4.41586i	0.408246	+	0.707103i
$40$	5.50345	−	9.53226i	0.870172	−	1.50718i
$41$	2.17744			0.340058			0.170029	−	0.985439i	$-0.445614\pi$
$41$	2.17744			0.340058			0.170029	+	0.985439i	$0.445614\pi$
$42$		0			0
$43$	−8.69594			−1.32612			−0.663059	−	0.748567i	$-0.730742\pi$
$43$	−8.69594			−1.32612			−0.663059	+	0.748567i	$0.730742\pi$
$44$	2.94300	−	5.09743i	0.443674	−	0.768466i
$45$	5.19521	+	8.99837i	0.774457	+	1.34140i
$46$	−1.64094	−	2.84219i	−0.241944	−	0.419059i
$47$	−5.91665	+	10.2479i	−0.863032	+	1.49481i	0.00595694	+	0.999982i	$0.498104\pi$
$47$	−5.91665	+	10.2479i	−0.863032	+	1.49481i	−0.868989	+	0.494832i	$0.835229\pi$
$48$	−2.17744			−0.314286
$49$		0			0
$50$	−9.90893			−1.40133
$51$	−0.687846	+	1.19138i	−0.0963177	+	0.166827i
$52$	1.57022	+	2.71969i	0.217750	+	0.377154i
$53$	−2.20498	−	3.81914i	−0.302877	−	0.524599i	0.673909	−	0.738814i	$-0.264614\pi$
$53$	−2.20498	−	3.81914i	−0.302877	−	0.524599i	−0.976786	+	0.214216i	$0.931281\pi$
$54$	0.493821	−	0.855324i	0.0672006	−	0.116395i
$55$	−17.4840			−2.35754
$56$		0			0
$57$	−2.33152			−0.308817
$58$	−2.76543	+	4.78986i	−0.363119	+	0.628940i
$59$	5.35892	+	9.28193i	0.697672	+	1.20840i	0.969271	+	0.245993i	$0.0791142\pi$
$59$	5.35892	+	9.28193i	0.697672	+	1.20840i	−0.271599	+	0.962410i	$0.587552\pi$
$60$	7.14026	+	12.3673i	0.921804	+	1.59661i
$61$	−1.21525	+	2.10488i	−0.155597	+	0.269502i	−0.933276	−	0.359159i	$-0.883064\pi$
$61$	−1.21525	+	2.10488i	−0.155597	+	0.269502i	0.777679	+	0.628662i	$0.216397\pi$
$62$	3.39350			0.430975
$63$		0			0
$64$	2.53496			0.316869
$65$	4.66422	−	8.07866i	0.578525	−	1.00204i
$66$	−3.58872	−	6.21584i	−0.441741	−	0.765117i
$67$	2.82674	+	4.89606i	0.345341	+	0.598148i	0.985416	−	0.170164i	$-0.0544299\pi$
$67$	2.82674	+	4.89606i	0.345341	+	0.598148i	−0.640075	+	0.768313i	$0.721097\pi$
$68$	−0.423639	+	0.733765i	−0.0513738	+	0.0889821i
$69$	10.1884			1.22654
$70$		0			0
$71$	8.32434			0.987918			0.493959	−	0.869485i	$-0.335549\pi$
$71$	8.32434			0.987918			0.493959	+	0.869485i	$0.335549\pi$
$72$	−3.14299	+	5.44382i	−0.370405	+	0.641560i
$73$	−5.33974	−	9.24870i	−0.624970	−	1.08248i	−0.988547	−	0.150915i	$-0.951778\pi$
$73$	−5.33974	−	9.24870i	−0.624970	−	1.08248i	0.363577	−	0.931564i	$-0.381555\pi$
$74$	3.36251	+	5.82404i	0.390884	+	0.677031i
$75$	15.3809	−	26.6405i	1.77603	−	3.07618i
$76$	−1.43596			−0.164716
$77$		0			0
$78$	3.82947			0.433602
$79$	−4.28188	+	7.41644i	−0.481750	+	0.834415i	−0.999781	−	0.0209472i	$-0.993332\pi$
$79$	−4.28188	+	7.41644i	−0.481750	+	0.834415i	0.518031	+	0.855362i	$0.326665\pi$
$80$	1.99177	+	3.44985i	0.222687	+	0.385705i
$81$	5.18699	+	8.98412i	0.576332	+	0.998236i
$82$	0.817653	−	1.41622i	0.0902947	−	0.156395i
$83$	4.25826			0.467404			0.233702	−	0.972308i	$-0.424916\pi$
$83$	4.25826			0.467404			0.233702	+	0.972308i	$0.424916\pi$
$84$		0			0
$85$	2.51678			0.272983
$86$	−3.26543	+	5.65589i	−0.352120	+	0.609890i
$87$	−8.58513	−	14.8699i	−0.920423	−	1.59422i
$88$	−5.28871	−	9.16031i	−0.563778	−	0.976492i
$89$	1.89555	−	3.28319i	0.200928	−	0.348018i	−0.747900	−	0.663812i	$-0.768938\pi$
$89$	1.89555	−	3.28319i	0.200928	−	0.348018i	0.948828	+	0.315794i	$0.102271\pi$
$90$	7.80346			0.822557
$91$		0			0
$92$	6.27498			0.654212
$93$	−5.26748	+	9.12354i	−0.546212	+	0.946067i
$94$	4.44354	+	7.69644i	0.458317	+	0.793828i
$95$	2.13271	+	3.69397i	0.218812	+	0.378993i
$96$	−6.83411	+	11.8370i	−0.697503	+	1.20811i
$97$	−2.11026			−0.214265			−0.107132	−	0.994245i	$-0.534167\pi$
$97$	−2.11026			−0.214265			−0.107132	+	0.994245i	$0.534167\pi$
$98$		0			0
$99$	9.98499			1.00353
$100$	9.47297	−	16.4077i	0.947297	−	1.64077i
$101$	7.53032	+	13.0429i	0.749294	+	1.29782i	0.948161	+	0.317789i	$0.102941\pi$
$101$	7.53032	+	13.0429i	0.749294	+	1.29782i	−0.198867	+	0.980027i	$0.563726\pi$
$102$	0.516589	+	0.894759i	0.0511499	+	0.0885943i
$103$	2.44692	−	4.23818i	0.241102	−	0.417601i	−0.719927	−	0.694050i	$-0.755825\pi$
$103$	2.44692	−	4.23818i	0.241102	−	0.417601i	0.961028	+	0.276450i	$0.0891579\pi$
$104$	5.64350			0.553391
$105$		0			0
$106$	−3.31198			−0.321688
$107$	−0.444325	+	0.769593i	−0.0429545	+	0.0743994i	−0.886703	−	0.462339i	$-0.847010\pi$
$107$	−0.444325	+	0.769593i	−0.0429545	+	0.0743994i	0.843749	+	0.536738i	$0.180344\pi$
$108$	0.944190	+	1.63538i	0.0908547	+	0.157365i
$109$	0.555675	+	0.962457i	0.0532240	+	0.0921867i	0.891410	−	0.453198i	$-0.149717\pi$
$109$	0.555675	+	0.962457i	0.0532240	+	0.0921867i	−0.838186	+	0.545385i	$0.816384\pi$
$110$	−6.56544	+	11.3717i	−0.625990	+	1.08425i
$111$	−20.8775			−1.98160
$112$		0			0
$113$	−12.9161			−1.21504			−0.607522	−	0.794303i	$-0.707836\pi$
$113$	−12.9161			−1.21504			−0.607522	+	0.794303i	$0.707836\pi$
$114$	−0.875512	+	1.51643i	−0.0819992	+	0.142027i
$115$	−9.31970	−	16.1422i	−0.869067	−	1.50527i
$116$	−5.28752	−	9.15825i	−0.490934	−	0.850322i
$117$	−2.66371	+	4.61368i	−0.246260	+	0.426535i
$118$	8.04936			0.741004
$119$		0			0
$120$	25.6628			2.34268
$121$	−2.90087	+	5.02446i	−0.263716	+	0.456769i
$122$	0.912685	+	1.58082i	0.0826306	+	0.143120i
$123$	2.53836	+	4.39657i	0.228876	+	0.396426i
$124$	−3.24420	+	5.61912i	−0.291338	+	0.504612i
$125$	−34.9505			−3.12606
$126$		0			0
$127$	−3.11373			−0.276299			−0.138149	−	0.990411i	$-0.544115\pi$
$127$	−3.11373			−0.276299			−0.138149	+	0.990411i	$0.544115\pi$
$128$	−4.91047	+	8.50518i	−0.434028	+	0.751759i
$129$	−10.1374	−	17.5584i	−0.892544	−	1.54593i
$130$	−3.50294	−	6.06727i	−0.307228	−	0.532135i
$131$	1.85360	−	3.21054i	0.161950	−	0.280506i	−0.773618	−	0.633652i	$-0.781555\pi$
$131$	1.85360	−	3.21054i	0.161950	−	0.280506i	0.935568	+	0.353147i	$0.114888\pi$
$132$	13.7233			1.19446
$133$		0			0
$134$	4.24590			0.366790
$135$	2.80465	−	4.85780i	0.241386	−	0.418093i
$136$	0.761299	+	1.31861i	0.0652809	+	0.113070i
$137$	−0.580491	−	1.00544i	−0.0495947	−	0.0859005i	0.840162	−	0.542335i	$-0.182460\pi$
$137$	−0.580491	−	1.00544i	−0.0495947	−	0.0859005i	−0.889757	+	0.456434i	$0.849126\pi$
$138$	3.82588	−	6.62662i	0.325681	−	0.564095i
$139$	4.24633			0.360169			0.180084	−	0.983651i	$-0.442363\pi$
$139$	4.24633			0.360169			0.180084	+	0.983651i	$0.442363\pi$
$140$		0			0
$141$	−27.5895			−2.32346
$142$	3.12589	−	5.41420i	0.262319	−	0.454350i
$143$	−4.48222	−	7.76344i	−0.374822	−	0.649211i
$144$	−1.13749	−	1.97019i	−0.0947909	−	0.164183i
$145$	−15.7062	+	27.2040i	−1.30433	+	2.25917i
$146$	−8.02055			−0.663785
$147$		0			0
$148$	−12.8583			−1.05694
$149$	11.9966	−	20.7787i	0.982799	−	1.70226i	0.331465	−	0.943468i	$-0.392457\pi$
$149$	11.9966	−	20.7787i	0.982799	−	1.70226i	0.651335	−	0.758791i	$-0.274209\pi$
$150$	−11.5514	−	20.0076i	−0.943169	−	1.63362i
$151$	−4.25035	−	7.36181i	−0.345888	−	0.599096i	0.639627	−	0.768686i	$-0.279089\pi$
$151$	−4.25035	−	7.36181i	−0.345888	−	0.599096i	−0.985515	+	0.169590i	$0.945756\pi$
$152$	−1.29025	+	2.23477i	−0.104653	+	0.181264i
$153$	−1.43732			−0.116201
$154$		0			0
$155$	19.2734			1.54807
$156$	−3.66098	+	6.34101i	−0.293113	+	0.507687i
$157$	2.21938	+	3.84409i	0.177126	+	0.306791i	0.940895	−	0.338698i	$-0.109987\pi$
$157$	2.21938	+	3.84409i	0.177126	+	0.306791i	−0.763769	+	0.645490i	$0.776653\pi$
$158$	3.21580	+	5.56993i	0.255835	+	0.443119i
$159$	5.14094	−	8.90437i	0.407703	−	0.706163i
$160$	25.0055			1.97686
$161$		0			0
$162$	7.79110			0.612127
$163$	0.0734531	−	0.127225i	0.00575329	−	0.00996500i	−0.863134	−	0.504974i	$-0.831502\pi$
$163$	0.0734531	−	0.127225i	0.00575329	−	0.00996500i	0.868888	+	0.495009i	$0.164835\pi$
$164$	1.56336	+	2.70782i	0.122078	+	0.211445i
$165$	−20.3821	−	35.3028i	−1.58674	−	2.74832i
$166$	1.59903	−	2.76960i	0.124109	−	0.214962i
$167$	−0.885641			−0.0685329			−0.0342665	−	0.999413i	$-0.510909\pi$
$167$	−0.885641			−0.0685329			−0.0342665	+	0.999413i	$0.510909\pi$
$168$		0			0
$169$	−8.21709			−0.632084
$170$	0.945083	−	1.63693i	0.0724845	−	0.125547i
$171$	−1.21798	−	2.10961i	−0.0931414	−	0.161326i
$172$	−6.24352	−	10.8141i	−0.476064	−	0.824567i
$173$	12.1319	−	21.0131i	0.922371	−	1.59759i	0.126636	−	0.991949i	$-0.459582\pi$
$173$	12.1319	−	21.0131i	0.922371	−	1.59759i	0.795735	−	0.605645i	$-0.207085\pi$
$174$	−12.8953			−0.977589
$175$		0			0
$176$	3.82811			0.288555
$177$	−12.4944	+	21.6410i	−0.939137	+	1.62663i
$178$	−1.42361	−	2.46576i	−0.106704	−	0.184816i
$179$	6.47332	+	11.2121i	0.483838	+	0.838033i	0.999828	−	0.0185624i	$-0.00590893\pi$
$179$	6.47332	+	11.2121i	0.483838	+	0.838033i	−0.515989	+	0.856595i	$0.672576\pi$
$180$	−7.46013	+	12.9213i	−0.556046	+	0.963099i
$181$	−18.6034			−1.38278			−0.691391	−	0.722481i	$-0.743002\pi$
$181$	−18.6034			−1.38278			−0.691391	+	0.722481i	$0.743002\pi$
$182$		0			0
$183$	−5.66677			−0.418899
$184$	5.63821	−	9.76567i	0.415655	−	0.719935i
$185$	19.0973	+	33.0775i	1.40406	+	2.43191i
$186$	3.95600	+	6.85200i	0.290068	+	0.502413i
$187$	1.20929	−	2.09455i	0.0884320	−	0.153169i
$188$	−16.9922			−1.23928
$189$		0			0
$190$	3.20344			0.232402
$191$	11.6444	−	20.1687i	0.842559	−	1.45935i	−0.0451659	−	0.998980i	$-0.514382\pi$
$191$	11.6444	−	20.1687i	0.842559	−	1.45935i	0.887725	−	0.460375i	$-0.152285\pi$
$192$	2.95514	+	5.11846i	0.213269	+	0.369393i
$193$	−1.59422	−	2.76127i	−0.114754	−	0.198760i	0.802927	−	0.596077i	$-0.203275\pi$
$193$	−1.59422	−	2.76127i	−0.114754	−	0.198760i	−0.917681	+	0.397317i	$0.869941\pi$
$194$	−0.792429	+	1.37253i	−0.0568931	+	0.0985417i
$195$	21.7494			1.55751
$196$		0			0
$197$	−8.25178			−0.587915			−0.293958	−	0.955818i	$-0.594972\pi$
$197$	−8.25178			−0.587915			−0.293958	+	0.955818i	$0.594972\pi$
$198$	3.74949	−	6.49430i	0.266464	−	0.461530i
$199$	−9.80120	−	16.9762i	−0.694789	−	1.20341i	−0.970252	−	0.242098i	$-0.922165\pi$
$199$	−9.80120	−	16.9762i	−0.694789	−	1.20341i	0.275463	−	0.961312i	$-0.411169\pi$
$200$	−17.0234	−	29.4853i	−1.20373	−	2.08493i
$201$	−6.59059	+	11.4152i	−0.464864	+	0.805168i
$202$	11.3109			0.795832
$203$		0			0
$204$	−1.97544			−0.138309
$205$	4.64385	−	8.04338i	0.324340	−	0.561774i
$206$	−1.83769	−	3.18298i	−0.128038	−	0.221769i
$207$	5.32243	+	9.21872i	0.369934	+	0.640745i
$208$	−1.02123	+	1.76882i	−0.0708095	+	0.122646i
$209$	4.09899			0.283533
$210$		0			0
$211$	9.49078			0.653372			0.326686	−	0.945133i	$-0.394068\pi$
$211$	9.49078			0.653372			0.326686	+	0.945133i	$0.394068\pi$
$212$	3.16627	−	5.48414i	0.217460	−	0.376652i
$213$	9.70416	+	16.8081i	0.664918	+	1.15167i
$214$	0.333699	+	0.577983i	0.0228112	+	0.0395101i
$215$	−18.5460	+	32.1225i	−1.26482	+	2.19074i
$216$	3.39350			0.230899
$217$		0			0
$218$	0.834651			0.0565297
$219$	12.4497	−	21.5635i	0.841272	−	1.45713i
$220$	−12.5532	−	21.7427i	−0.846334	−	1.46589i
$221$	0.645207	+	1.11753i	0.0434013	+	0.0751733i
$222$	−7.83974	+	13.5788i	−0.526169	+	0.911351i
$223$	18.8829			1.26449			0.632247	−	0.774767i	$-0.282133\pi$
$223$	18.8829			1.26449			0.632247	+	0.774767i	$0.282133\pi$
$224$		0			0
$225$	32.1398			2.14265
$226$	−4.85015	+	8.40071i	−0.322627	+	0.558807i
$227$	−10.2703	−	17.7886i	−0.681660	−	1.18067i	−0.974474	−	0.224501i	$-0.927925\pi$
$227$	−10.2703	−	17.7886i	−0.681660	−	1.18067i	0.292813	−	0.956170i	$-0.405409\pi$
$228$	−1.67398	−	2.89943i	−0.110862	−	0.192019i
$229$	−3.49250	+	6.04918i	−0.230791	+	0.399741i	−0.958041	−	0.286631i	$-0.907465\pi$
$229$	−3.49250	+	6.04918i	−0.230791	+	0.399741i	0.727250	+	0.686372i	$0.240798\pi$
$230$	−13.9986			−0.923043
$231$		0			0
$232$	−19.0038			−1.24766
$233$	−9.76325	+	16.9104i	−0.639612	+	1.10784i	0.345907	+	0.938269i	$0.387571\pi$
$233$	−9.76325	+	16.9104i	−0.639612	+	1.10784i	−0.985518	+	0.169571i	$0.945762\pi$
$234$	2.00051	+	3.46498i	0.130777	+	0.226513i
$235$	25.2370	+	43.7118i	1.64628	+	2.85145i
$236$	−7.69521	+	13.3285i	−0.500916	+	0.867612i
$237$	−19.9666			−1.29697
$238$		0			0
$239$	−17.8056			−1.15175			−0.575873	−	0.817539i	$-0.695338\pi$
$239$	−17.8056			−1.15175			−0.575873	+	0.817539i	$0.695338\pi$
$240$	−4.64385	+	8.04338i	−0.299759	+	0.519198i
$241$	−7.61340	−	13.1868i	−0.490422	−	0.849436i	0.509517	−	0.860461i	$-0.329824\pi$
$241$	−7.61340	−	13.1868i	−0.490422	−	0.849436i	−0.999939	+	0.0110245i	$0.996491\pi$
$242$	2.17862	+	3.77349i	0.140047	+	0.242569i
$243$	−10.1209	+	17.5300i	−0.649259	+	1.12455i
$244$	−3.49012			−0.223432
$245$		0			0
$246$	3.81274			0.243092
$247$	−1.09349	+	1.89399i	−0.0695773	+	0.120511i
$248$	5.82998	+	10.0978i	0.370204	+	0.641212i
$249$	4.96409	+	8.59806i	0.314587	+	0.544880i
$250$	−13.1243	+	22.7320i	−0.830055	+	1.43770i
$251$	6.70311			0.423097			0.211548	−	0.977368i	$-0.432149\pi$
$251$	6.70311			0.423097			0.211548	+	0.977368i	$0.432149\pi$
$252$		0			0
$253$	−17.9121			−1.12612
$254$	−1.16924	+	2.02519i	−0.0733648	+	0.127072i
$255$	2.93396	+	5.08177i	0.183732	+	0.318233i
$256$	6.22284	+	10.7783i	0.388927	+	0.673642i
$257$	−4.12568	+	7.14588i	−0.257353	+	0.445748i	−0.965532	−	0.260285i	$-0.916184\pi$
$257$	−4.12568	+	7.14588i	−0.257353	+	0.445748i	0.708179	+	0.706033i	$0.249517\pi$
$258$	−15.2268			−0.947979
$259$		0			0
$260$	13.3953			0.830741
$261$	8.96973	−	15.5360i	0.555212	−	0.961656i
$262$	−1.39210	−	2.41119i	−0.0860043	−	0.148964i
$263$	0.350152	+	0.606482i	0.0215913	+	0.0373973i	0.876619	−	0.481185i	$-0.159793\pi$
$263$	0.350152	+	0.606482i	0.0215913	+	0.0373973i	−0.855028	+	0.518582i	$0.826460\pi$
$264$	12.3307	−	21.3574i	0.758902	−	1.31446i
$265$	−18.8104			−1.15551
$266$		0			0
$267$	8.83902			0.540939
$268$	−4.05909	+	7.03055i	−0.247949	+	0.429459i
$269$	−6.98260	−	12.0942i	−0.425736	−	0.737397i	0.570752	−	0.821122i	$-0.306652\pi$
$269$	−6.98260	−	12.0942i	−0.425736	−	0.737397i	−0.996489	+	0.0837251i	$0.973318\pi$
$270$	−2.10636	−	3.64832i	−0.128189	−	0.222030i
$271$	4.16285	−	7.21027i	0.252875	−	0.437993i	−0.711441	−	0.702746i	$-0.751957\pi$
$271$	4.16285	−	7.21027i	0.252875	−	0.437993i	0.964316	+	0.264753i	$0.0852905\pi$
$272$	−0.551049			−0.0334122
$273$		0			0
$274$	−0.871925			−0.0526749
$275$	−27.0408	+	46.8361i	−1.63062	+	2.82432i
$276$	7.31511	+	12.6701i	0.440318	+	0.762653i
$277$	7.57504	+	13.1203i	0.455140	+	0.788325i	0.998696	−	0.0510473i	$-0.0162559\pi$
$277$	7.57504	+	13.1203i	0.455140	+	0.788325i	−0.543556	+	0.839373i	$0.682923\pi$
$278$	1.59455	−	2.76184i	0.0956346	−	0.165644i
$279$	−11.0069			−0.658966
$280$		0			0
$281$	−10.2038			−0.608708			−0.304354	−	0.952559i	$-0.598441\pi$
$281$	−10.2038			−0.608708			−0.304354	+	0.952559i	$0.598441\pi$
$282$	−10.3602	+	17.9444i	−0.616940	+	1.06857i
$283$	3.14558	+	5.44831i	0.186985	+	0.323868i	0.944244	−	0.329247i	$-0.106795\pi$
$283$	3.14558	+	5.44831i	0.186985	+	0.323868i	−0.757258	+	0.653115i	$0.773462\pi$
$284$	5.97672	+	10.3520i	0.354653	+	0.614277i
$285$	−4.97246	+	8.61255i	−0.294543	+	0.510163i
$286$	−6.73251			−0.398102
$287$		0			0
$288$	−14.2805			−0.841488
$289$	8.32593	−	14.4209i	0.489760	−	0.848290i
$290$	11.7957	+	20.4308i	0.692670	+	1.19974i
$291$	−2.46005	−	4.26094i	−0.144211	−	0.249781i
$292$	7.66767	−	13.2808i	0.448716	−	0.777200i
$293$	−1.48286			−0.0866294			−0.0433147	−	0.999061i	$-0.513792\pi$
$293$	−1.48286			−0.0866294			−0.0433147	+	0.999061i	$0.513792\pi$
$294$		0			0
$295$	45.7162			2.66170
$296$	−11.5535	+	20.0112i	−0.671531	+	1.16313i
$297$	−2.69521	−	4.66825i	−0.156392	−	0.270879i
$298$	−9.00973	−	15.6053i	−0.521920	−	0.903991i
$299$	4.77843	−	8.27649i	0.276344	−	0.478642i
$300$	44.1727			2.55031
$301$		0			0
$302$	−6.38422			−0.367371
$303$	−17.5570	+	30.4097i	−1.00863	+	1.74699i
$304$	−0.466957	−	0.808794i	−0.0267818	−	0.0463875i
$305$	5.18358	+	8.97822i	0.296811	+	0.514092i
$306$	−0.539731	+	0.934842i	−0.0308544	+	0.0534414i
$307$	29.9624			1.71004			0.855022	−	0.518592i	$-0.173544\pi$
$307$	29.9624			1.71004			0.855022	+	0.518592i	$0.173544\pi$
$308$		0			0
$309$	11.4100			0.649095
$310$	7.23738	−	12.5355i	0.411055	−	0.711969i
$311$	2.19057	+	3.79418i	0.124216	+	0.215148i	0.921426	−	0.388553i	$-0.127025\pi$
$311$	2.19057	+	3.79418i	0.124216	+	0.215148i	−0.797210	+	0.603702i	$0.793692\pi$
$312$	6.57895	+	11.3951i	0.372460	+	0.645119i
$313$	10.2268	−	17.7133i	0.578053	−	1.00122i	−0.417650	−	0.908608i	$-0.637146\pi$
$313$	10.2268	−	17.7133i	0.578053	−	1.00122i	0.995703	−	0.0926086i	$-0.0295205\pi$
$314$	3.33362			0.188127
$315$		0			0
$316$	−12.2972			−0.691774
$317$	4.40824	−	7.63529i	0.247591	−	0.428841i	−0.715266	−	0.698853i	$-0.753694\pi$
$317$	4.40824	−	7.63529i	0.247591	−	0.428841i	0.962857	+	0.270012i	$0.0870276\pi$
$318$	−3.86097	−	6.68740i	−0.216513	−	0.375011i
$319$	15.0934	+	26.1425i	0.845066	+	1.46370i
$320$	5.40634	−	9.36405i	0.302223	−	0.523466i
$321$	−2.07190			−0.115642
$322$		0			0
$323$	−0.590042			−0.0328308
$324$	−7.44832	+	12.9009i	−0.413796	+	0.716715i
$325$	−14.4274	−	24.9890i	−0.800290	−	1.38614i
$326$	−0.0551651	−	0.0955487i	−0.00305531	−	0.00529195i
$327$	−1.29556	+	2.24398i	−0.0716449	+	0.124093i
$328$	5.61885			0.310249
$329$		0			0
$330$	−30.6148			−1.68529
$331$	−6.02899	+	10.4425i	−0.331383	+	0.573973i	−0.982783	−	0.184762i	$-0.940849\pi$
$331$	−6.02899	+	10.4425i	−0.331383	+	0.573973i	0.651400	+	0.758734i	$0.274182\pi$
$332$	3.05735	+	5.29548i	0.167794	+	0.290627i
$333$	−10.9064	−	18.8904i	−0.597665	−	1.03519i
$334$	−0.332569	+	0.576026i	−0.0181974	+	0.0315187i
$335$	24.1145			1.31752
$336$		0			0
$337$	27.5871			1.50277			0.751383	−	0.659866i	$-0.229387\pi$
$337$	27.5871			1.50277			0.751383	+	0.659866i	$0.229387\pi$
$338$	−3.08562	+	5.34444i	−0.167835	+	0.290699i
$339$	−15.0570	−	26.0796i	−0.817786	−	1.41645i
$340$	1.80700	+	3.12982i	0.0979985	+	0.169738i
$341$	9.26065	−	16.0399i	0.501493	−	0.868611i
$342$	−1.82947			−0.0989262
$343$		0			0
$344$	−22.4398			−1.20987
$345$	21.7290	−	37.6358i	1.16985	−	2.02624i
$346$	−9.11135	−	15.7813i	−0.489829	−	0.848409i
$347$	−0.495768	−	0.858695i	−0.0266142	−	0.0460972i	0.852412	−	0.522871i	$-0.175139\pi$
$347$	−0.495768	−	0.858695i	−0.0266142	−	0.0460972i	−0.879026	+	0.476774i	$0.841806\pi$
$348$	12.3279	−	21.3526i	0.660846	−	1.14462i
$349$	−31.6583			−1.69463			−0.847316	−	0.531090i	$-0.821783\pi$
$349$	−31.6583			−1.69463			−0.847316	+	0.531090i	$0.821783\pi$
$350$		0			0
$351$	2.87602			0.153511
$352$	12.0149	−	20.8104i	0.640397	−	1.10920i
$353$	4.45191	+	7.71093i	0.236951	+	0.410411i	0.959838	−	0.280555i	$-0.0905186\pi$
$353$	4.45191	+	7.71093i	0.236951	+	0.410411i	−0.722887	+	0.690966i	$0.757185\pi$
$354$	9.38360	+	16.2529i	0.498733	+	0.863831i
$355$	17.7534	−	30.7499i	0.942255	−	1.63203i
$356$	5.44389			0.288525
$357$		0			0
$358$	9.72323			0.513889
$359$	10.8499	−	18.7925i	0.572635	−	0.991833i	−0.423659	−	0.905822i	$-0.639255\pi$
$359$	10.8499	−	18.7925i	0.572635	−	0.991833i	0.996294	−	0.0860111i	$-0.0274120\pi$
$360$	13.4062	+	23.2202i	0.706569	+	1.22381i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	−6.98581	+	12.0998i	−0.367166	+	0.635950i
$363$	−13.5269			−0.709976
$364$		0			0
$365$	−45.5526			−2.38433
$366$	−2.12794	+	3.68570i	−0.111229	+	0.192655i
$367$	6.38859	+	11.0654i	0.333482	+	0.577608i	0.983192	−	0.182575i	$-0.0584431\pi$
$367$	6.38859	+	11.0654i	0.333482	+	0.577608i	−0.649710	+	0.760182i	$0.725110\pi$
$368$	2.04055	+	3.53433i	0.106371	+	0.184240i
$369$	−2.65208	+	4.59353i	−0.138062	+	0.239130i
$370$	28.6851			1.49127
$371$		0			0
$372$	−15.1278			−0.784340
$373$	6.60912	−	11.4473i	0.342207	−	0.592721i	−0.642635	−	0.766172i	$-0.722159\pi$
$373$	6.60912	−	11.4473i	0.342207	−	0.592721i	0.984842	+	0.173452i	$0.0554921\pi$
$374$	−0.908206	−	1.57306i	−0.0469622	−	0.0813409i
$375$	−40.7438	−	70.5703i	−2.10400	−	3.64423i
$376$	−15.2679	+	26.4447i	−0.787379	+	1.36378i
$377$	−16.1059			−0.829496
$378$		0			0
$379$	−1.72767			−0.0887443			−0.0443722	−	0.999015i	$-0.514129\pi$
$379$	−1.72767			−0.0887443			−0.0443722	+	0.999015i	$0.514129\pi$
$380$	−3.06250	+	5.30440i	−0.157103	+	0.272110i
$381$	−3.62985	−	6.28709i	−0.185963	−	0.322097i
$382$	−8.74522	−	15.1472i	−0.447444	−	0.774996i
$383$	−2.42781	+	4.20510i	−0.124056	+	0.214870i	−0.921363	−	0.388702i	$-0.872923\pi$
$383$	−2.42781	+	4.20510i	−0.124056	+	0.214870i	0.797308	+	0.603573i	$0.206257\pi$
$384$	−22.8977			−1.16849
$385$		0			0
$386$	−2.39459			−0.121881
$387$	10.5915	−	18.3450i	0.538396	−	0.932529i
$388$	−1.51513	−	2.62428i	−0.0769190	−	0.133228i
$389$	−5.31493	−	9.20572i	−0.269477	−	0.466749i	0.699250	−	0.714878i	$-0.253518\pi$
$389$	−5.31493	−	9.20572i	−0.269477	−	0.466749i	−0.968727	+	0.248129i	$0.920184\pi$
$390$	8.16716	−	14.1459i	0.413560	−	0.716307i
$391$	2.57841			0.130396
$392$		0			0
$393$	8.64341			0.436002
$394$	−3.09864	+	5.36701i	−0.156107	+	0.270386i
$395$	18.2641	+	31.6343i	0.918965	+	1.59169i
$396$	7.16904	+	12.4171i	0.360258	+	0.623985i
$397$	6.37569	−	11.0430i	0.319987	−	0.554233i	−0.660498	−	0.750828i	$-0.729655\pi$
$397$	6.37569	−	11.0430i	0.319987	−	0.554233i	0.980485	+	0.196594i	$0.0629882\pi$
$398$	−14.7219			−0.737941
$399$		0			0
$400$	12.3220			0.616098
$401$	−9.62568	+	16.6722i	−0.480683	+	0.832568i	−0.999754	−	0.0221631i	$-0.992945\pi$
$401$	−9.62568	+	16.6722i	−0.480683	+	0.832568i	0.519071	+	0.854731i	$0.326278\pi$
$402$	4.94969	+	8.57311i	0.246868	+	0.427588i
$403$	4.94095	+	8.55798i	0.246126	+	0.426303i
$404$	−10.8133	+	18.7291i	−0.537979	+	0.931808i
$405$	44.2495			2.19877
$406$		0			0
$407$	36.7043			1.81936
$408$	−1.77498	+	3.07436i	−0.0878746	+	0.152203i
$409$	1.56990	+	2.71915i	0.0776266	+	0.134453i	0.902225	−	0.431265i	$-0.141932\pi$
$409$	1.56990	+	2.71915i	0.0776266	+	0.134453i	−0.824599	+	0.565718i	$0.808599\pi$
$410$	−3.48764	−	6.04077i	−0.172242	−	0.298333i
$411$	1.35342	−	2.34420i	0.0667595	−	0.115631i
$412$	7.02736			0.346213
$413$		0			0
$414$	7.99455			0.392910
$415$	9.08165	−	15.7299i	0.445800	−	0.772149i
$416$	6.41047	+	11.1033i	0.314299	+	0.544382i
$417$	4.95019	+	8.57398i	0.242412	+	0.419869i
$418$	1.53922	−	2.66601i	0.0752858	−	0.130399i
$419$	−12.4881			−0.610085			−0.305043	−	0.952339i	$-0.598671\pi$
$419$	−12.4881			−0.610085			−0.305043	+	0.952339i	$0.598671\pi$
$420$		0			0
$421$	−14.5141			−0.707376			−0.353688	−	0.935364i	$-0.615072\pi$
$421$	−14.5141			−0.707376			−0.353688	+	0.935364i	$0.615072\pi$
$422$	3.56390	−	6.17286i	0.173488	−	0.300490i
$423$	−14.4127	−	24.9636i	−0.700771	−	1.21377i
$424$	−5.68993	−	9.85524i	−0.276327	−	0.478613i
$425$	3.89248	−	6.74197i	0.188813	−	0.327033i
$426$	14.5761			0.706215
$427$		0			0
$428$	−1.27607			−0.0616811
$429$	10.4504	−	18.1006i	0.504549	−	0.873904i
$430$	13.9285	+	24.1248i	0.671690	+	1.16340i
$431$	−11.8336	−	20.4963i	−0.570003	−	0.987274i	−0.996565	−	0.0828154i	$-0.973609\pi$
$431$	−11.8336	−	20.4963i	−0.570003	−	0.987274i	0.426562	−	0.904458i	$-0.359725\pi$
$432$	−0.614077	+	1.06361i	−0.0295448	+	0.0511731i
$433$	−4.61912			−0.221981			−0.110990	−	0.993821i	$-0.535402\pi$
$433$	−4.61912			−0.221981			−0.110990	+	0.993821i	$0.535402\pi$
$434$		0			0
$435$	−73.2385			−3.51152
$436$	−0.797929	+	1.38205i	−0.0382139	+	0.0661883i
$437$	2.18494	+	3.78442i	0.104520	+	0.181034i
$438$	−9.35002	−	16.1947i	−0.446761	−	0.773813i
$439$	9.48014	−	16.4201i	0.452462	−	0.783688i	−0.546076	−	0.837736i	$-0.683879\pi$
$439$	9.48014	−	16.4201i	0.452462	−	0.783688i	0.998538	+	0.0540478i	$0.0172123\pi$
$440$	−45.1172			−2.15088
$441$		0			0
$442$	0.969132			0.0460969
$443$	11.2344	−	19.4586i	0.533764	−	0.924507i	−0.465458	−	0.885070i	$-0.654110\pi$
$443$	11.2344	−	19.4586i	0.533764	−	0.924507i	0.999222	−	0.0394366i	$-0.0125563\pi$
$444$	−14.9896	−	25.9628i	−0.711377	−	1.23214i
$445$	−8.08535	−	14.0042i	−0.383282	−	0.663864i
$446$	7.09077	−	12.2816i	0.335758	−	0.581549i
$447$	55.9405			2.64589
$448$		0			0
$449$	15.7360			0.742629			0.371314	−	0.928507i	$-0.378907\pi$
$449$	15.7360			0.742629			0.371314	+	0.928507i	$0.378907\pi$
$450$	12.0689	−	20.9039i	0.568933	−	0.985421i
$451$	−4.46265	−	7.72953i	−0.210138	−	0.363969i
$452$	−9.27352	−	16.0622i	−0.436190	−	0.755503i
$453$	9.90974	−	17.1642i	0.465600	−	0.806444i
$454$	−15.4264			−0.723997
$455$		0			0
$456$	−6.01645			−0.281746
$457$	−11.4283	+	19.7944i	−0.534594	+	0.925945i	0.464588	+	0.885527i	$0.346202\pi$
$457$	−11.4283	+	19.7944i	−0.534594	+	0.925945i	−0.999183	+	0.0404180i	$0.987131\pi$
$458$	2.62295	+	4.54308i	0.122562	+	0.212284i
$459$	0.387971	+	0.671985i	0.0181089	+	0.0313656i
$460$	13.3827	−	23.1796i	0.623974	−	1.08075i
$461$	−26.0021			−1.21104			−0.605519	−	0.795831i	$-0.707035\pi$
$461$	−26.0021			−1.21104			−0.605519	+	0.795831i	$0.707035\pi$
$462$		0			0
$463$	20.3481			0.945654			0.472827	−	0.881155i	$-0.343233\pi$
$463$	20.3481			0.945654			0.472827	+	0.881155i	$0.343233\pi$
$464$	3.43887	−	5.95630i	0.159646	−	0.276514i
$465$	22.4681	+	38.9158i	1.04193	+	1.80468i
$466$	7.33243	+	12.7001i	0.339668	+	0.588323i
$467$	7.56509	−	13.1031i	0.350071	−	0.606340i	−0.636191	−	0.771532i	$-0.719491\pi$
$467$	7.56509	−	13.1031i	0.350071	−	0.606340i	0.986262	+	0.165192i	$0.0528242\pi$
$468$	−7.64997			−0.353620
$469$		0			0
$470$	37.9073			1.74853
$471$	−5.17453	+	8.96255i	−0.238430	+	0.412972i
$472$	13.8287	+	23.9519i	0.636515	+	1.10248i
$473$	17.8223	+	30.8691i	0.819470	+	1.41936i
$474$	−7.49768	+	12.9864i	−0.344380	+	0.596483i
$475$	13.1939			0.605377
$476$		0			0
$477$	10.7425			0.491865
$478$	−6.68621	+	11.5808i	−0.305820	+	0.529696i
$479$	13.9632	+	24.1850i	0.637997	+	1.10504i	0.985872	+	0.167502i	$0.0535699\pi$
$479$	13.9632	+	24.1850i	0.637997	+	1.10504i	−0.347875	+	0.937541i	$0.613097\pi$
$480$	29.1504	+	50.4900i	1.33053	+	2.30454i
$481$	−9.79165	+	16.9596i	−0.446461	+	0.773293i
$482$	−11.4357			−0.520881
$483$		0			0
$484$	−8.33109			−0.378686
$485$	−4.50059	+	7.79525i	−0.204361	+	0.353964i
$486$	7.60107	+	13.1654i	0.344792	+	0.597197i
$487$	−0.330326	−	0.572142i	−0.0149685	−	0.0259262i	0.858444	−	0.512907i	$-0.171431\pi$
$487$	−0.330326	−	0.572142i	−0.0149685	−	0.0259262i	−0.873413	+	0.486981i	$0.838098\pi$
$488$	−3.13595	+	5.43163i	−0.141958	+	0.245878i
$489$	0.342514			0.0154890
$490$		0			0
$491$	−5.09463			−0.229917			−0.114959	−	0.993370i	$-0.536674\pi$
$491$	−5.09463			−0.229917			−0.114959	+	0.993370i	$0.536674\pi$
$492$	−3.64499	+	6.31331i	−0.164329	+	0.284626i
$493$	−2.17266	−	3.76316i	−0.0978517	−	0.169484i
$494$	0.821240	+	1.42243i	0.0369493	+	0.0639981i
$495$	21.2951	−	36.8843i	0.957146	−	1.65782i
$496$	−4.21989			−0.189479
$497$		0			0
$498$	7.45631			0.334125
$499$	6.39951	−	11.0843i	0.286482	−	0.496201i	−0.686486	−	0.727143i	$-0.740848\pi$
$499$	6.39951	−	11.0843i	0.286482	−	0.496201i	0.972967	+	0.230943i	$0.0741809\pi$
$500$	−25.0938	−	43.4637i	−1.12223	−	1.94376i
$501$	−1.03244	−	1.78824i	−0.0461261	−	0.0798928i
$502$	2.51710	−	4.35974i	0.112344	−	0.194585i
$503$	−32.1398			−1.43304			−0.716522	−	0.697565i	$-0.754267\pi$
$503$	−32.1398			−1.43304			−0.716522	+	0.697565i	$0.754267\pi$
$504$		0			0
$505$	64.2401			2.85865
$506$	−6.72621	+	11.6501i	−0.299016	+	0.517912i
$507$	−9.57913	−	16.5915i	−0.425424	−	0.736856i
$508$	−2.23560	−	3.87217i	−0.0991887	−	0.171800i
$509$	18.2323	−	31.5792i	0.808130	−	1.39972i	−0.106027	−	0.994363i	$-0.533813\pi$
$509$	18.2323	−	31.5792i	0.808130	−	1.39972i	0.914157	−	0.405360i	$-0.132854\pi$
$510$	4.40695			0.195143
$511$		0			0
$512$	−10.2949			−0.454973
$513$	−0.657531	+	1.13888i	−0.0290307	+	0.0502826i
$514$	3.09848	+	5.36673i	0.136668	+	0.236716i
$515$	−10.4372	−	18.0777i	−0.459916	−	0.796598i
$516$	14.5569	−	25.2132i	0.640830	−	1.10995i
$517$	48.5046			2.13323
$518$		0			0
$519$	56.5714			2.48321
$520$	12.0360	−	20.8469i	0.527812	−	0.914198i
$521$	17.7606	+	30.7623i	0.778107	+	1.34772i	0.933032	+	0.359794i	$0.117153\pi$
$521$	17.7606	+	30.7623i	0.778107	+	1.34772i	−0.154925	+	0.987926i	$0.549513\pi$
$522$	−6.73648	−	11.6679i	−0.294848	−	0.510691i
$523$	7.08114	−	12.2649i	0.309636	−	0.536306i	−0.668646	−	0.743581i	$-0.733126\pi$
$523$	7.08114	−	12.2649i	0.309636	−	0.536306i	0.978283	+	0.207274i	$0.0664593\pi$
$524$	5.32341			0.232554
$525$		0			0
$526$	0.525946			0.0229323
$527$	−1.33305	+	2.30892i	−0.0580687	+	0.100578i
$528$	4.46265	+	7.72953i	0.194212	+	0.336385i
$529$	1.95209	+	3.38111i	0.0848733	+	0.147005i
$530$	−7.06352	+	12.2344i	−0.306820	+	0.531427i
$531$	−26.1083			−1.13300
$532$		0			0
$533$	4.76202			0.206266
$534$	3.31916	−	5.74895i	0.143634	−	0.248781i
$535$	1.89524	+	3.28265i	0.0819382	+	0.141921i
$536$	7.29438	+	12.6342i	0.315069	+	0.545716i
$537$	−15.0926	+	26.1412i	−0.651295	+	1.12808i
$538$	−10.4882			−0.452178
$539$		0			0
$540$	8.05475			0.346621
$541$	8.37268	−	14.5019i	0.359970	−	0.623486i	−0.627986	−	0.778225i	$-0.716120\pi$
$541$	8.37268	−	14.5019i	0.359970	−	0.623486i	0.987955	+	0.154739i	$0.0494537\pi$
$542$	−3.12640	−	5.41509i	−0.134290	−	0.232598i
$543$	−21.6871	−	37.5631i	−0.930682	−	1.61199i
$544$	−1.72952	+	2.99562i	−0.0741527	+	0.128436i
$545$	4.74039			0.203056
$546$		0			0
$547$	−41.3888			−1.76966			−0.884829	−	0.465917i	$-0.845725\pi$
$547$	−41.3888			−1.76966			−0.884829	+	0.465917i	$0.845725\pi$
$548$	0.833563	−	1.44377i	0.0356081	−	0.0616750i
$549$	−2.96031	−	5.12741i	−0.126343	−	0.218833i
$550$	20.3083	+	35.1750i	0.865950	+	1.49987i
$551$	3.68221	−	6.37778i	0.156867	−	0.271702i
$552$	26.2912			1.11903
$553$		0			0
$554$	11.3781			0.483408
$555$	−44.5257	+	77.1208i	−1.89001	+	3.27359i
$556$	3.04878	+	5.28065i	0.129297	+	0.223949i
$557$	−18.8375	−	32.6275i	−0.798172	−	1.38247i	−0.920806	−	0.390022i	$-0.872468\pi$
$557$	−18.8375	−	32.6275i	−0.798172	−	1.38247i	0.122634	−	0.992452i	$-0.460866\pi$
$558$	−4.13322	+	7.15896i	−0.174973	+	0.303063i
$559$	−19.0179			−0.804372
$560$		0			0
$561$	5.63895			0.238077
$562$	−3.83165	+	6.63661i	−0.161628	+	0.279949i
$563$	−1.72907	−	2.99484i	−0.0728717	−	0.126217i	0.827287	−	0.561779i	$-0.189883\pi$
$563$	−1.72907	−	2.99484i	−0.0728717	−	0.126217i	−0.900159	+	0.435562i	$0.856550\pi$
$564$	−19.8087	−	34.3098i	−0.834099	−	1.44470i
$565$	−27.5464	+	47.7117i	−1.15888	+	2.00725i
$566$	4.72482			0.198599
$567$		0			0
$568$	21.4809			0.901318
$569$	−3.84602	+	6.66151i	−0.161234	+	0.279265i	−0.935311	−	0.353826i	$-0.884881\pi$
$569$	−3.84602	+	6.66151i	−0.161234	+	0.279265i	0.774078	+	0.633091i	$0.218214\pi$
$570$	3.73444	+	6.46823i	0.156418	+	0.270924i
$571$	0.208566	+	0.361246i	0.00872819	+	0.0151177i	0.870357	−	0.492422i	$-0.163888\pi$
$571$	0.208566	+	0.361246i	0.00872819	+	0.0151177i	−0.861628	+	0.507540i	$0.830555\pi$
$572$	6.43630	−	11.1480i	0.269115	−	0.466122i
$573$	54.2982			2.26834
$574$		0			0
$575$	−57.6557			−2.40441
$576$	−3.08753	+	5.34776i	−0.128647	+	0.222823i
$577$	11.6453	+	20.1702i	0.484798	+	0.839695i	0.999847	−	0.0174655i	$-0.00555972\pi$
$577$	11.6453	+	20.1702i	0.484798	+	0.839695i	−0.515049	+	0.857161i	$0.672226\pi$
$578$	−6.25297	−	10.8305i	−0.260089	−	0.450488i
$579$	3.71694	−	6.43793i	0.154471	−	0.267551i
$580$	−45.1071			−1.87297
$581$		0			0
$582$	−3.69512			−0.153168
$583$	−9.03819	+	15.6546i	−0.374324	+	0.648348i
$584$	−13.7792	−	23.8662i	−0.570186	−	0.987590i
$585$	11.3619	+	19.6793i	0.469755	+	0.813640i
$586$	−0.556830	+	0.964458i	−0.0230025	+	0.0398414i
$587$	30.5061			1.25912			0.629562	−	0.776951i	$-0.283234\pi$
$587$	30.5061			1.25912			0.629562	+	0.776951i	$0.283234\pi$
$588$		0			0
$589$	−4.51850			−0.186182
$590$	17.1670	−	29.7341i	0.706754	−	1.22413i
$591$	−9.61958	−	16.6616i	−0.395697	−	0.685366i
$592$	−4.18135	−	7.24231i	−0.171853	−	0.297657i
$593$	−16.3431	+	28.3070i	−0.671129	+	1.16243i	0.306455	+	0.951885i	$0.400857\pi$
$593$	−16.3431	+	28.3070i	−0.671129	+	1.16243i	−0.977584	+	0.210544i	$0.932476\pi$
$594$	−4.04834			−0.166105
$595$		0			0
$596$	34.4533			1.41126
$597$	22.8516	−	39.5802i	0.935256	−	1.61991i
$598$	−3.58872	−	6.21584i	−0.146754	−	0.254185i
$599$	10.1869	+	17.6442i	0.416225	+	0.720923i	0.995556	−	0.0941691i	$-0.0300194\pi$
$599$	10.1869	+	17.6442i	0.416225	+	0.720923i	−0.579331	+	0.815092i	$0.696686\pi$
$600$	39.6902	−	68.7455i	1.62035	−	2.80652i
$601$	−12.3891			−0.505363			−0.252682	−	0.967549i	$-0.581313\pi$
$601$	−12.3891			−0.505363			−0.252682	+	0.967549i	$0.581313\pi$
$602$		0			0
$603$	−13.7717			−0.560826
$604$	6.10334	−	10.5713i	0.248341	−	0.430140i
$605$	12.3735	+	21.4315i	0.503053	+	0.871313i
$606$	13.1858	+	22.8384i	0.535635	+	0.927747i
$607$	−16.6740	+	28.8802i	−0.676776	+	1.17221i	0.299170	+	0.954200i	$0.403290\pi$
$607$	−16.6740	+	28.8802i	−0.676776	+	1.17221i	−0.975946	+	0.218011i	$0.930043\pi$
$608$	−5.86237			−0.237751
$609$		0			0
$610$	7.78599			0.315245
$611$	−12.9396	+	22.4121i	−0.523481	+	0.906696i
$612$	−1.03197	−	1.78742i	−0.0417149	−	0.0722523i
$613$	19.3992	+	33.6005i	0.783528	+	1.35711i	0.929874	+	0.367877i	$0.119915\pi$
$613$	19.3992	+	33.6005i	0.783528	+	1.35711i	−0.146346	+	0.989233i	$0.546751\pi$
$614$	11.2512	−	19.4877i	0.454063	−	0.786460i
$615$	21.6544			0.873190
$616$		0			0
$617$	1.98936			0.0800887			0.0400443	−	0.999198i	$-0.487250\pi$
$617$	1.98936			0.0800887			0.0400443	+	0.999198i	$0.487250\pi$
$618$	4.28461	−	7.42116i	0.172352	−	0.298523i
$619$	6.50072	+	11.2596i	0.261286	+	0.452561i	0.966584	−	0.256350i	$-0.0825200\pi$
$619$	6.50072	+	11.2596i	0.261286	+	0.452561i	−0.705298	+	0.708911i	$0.749187\pi$
$620$	13.8379	+	23.9680i	0.555744	+	0.962576i
$621$	2.87333	−	4.97675i	0.115303	−	0.199710i
$622$	3.29035			0.131931
$623$		0			0
$624$	−4.76202			−0.190633
$625$	−41.5546	+	71.9747i	−1.66219	+	2.87899i
$626$	−7.68057	−	13.3031i	−0.306977	−	0.531700i
$627$	4.77843	+	8.27649i	0.190832	+	0.330531i
$628$	−3.18695	+	5.51996i	−0.127173	+	0.220271i
$629$	−5.28351			−0.210667
$630$		0			0
$631$	−14.9918			−0.596814			−0.298407	−	0.954439i	$-0.596455\pi$
$631$	−14.9918			−0.596814			−0.298407	+	0.954439i	$0.596455\pi$
$632$	−11.0494	+	19.1381i	−0.439520	+	0.761271i
$633$	11.0639	+	19.1633i	0.439752	+	0.761674i
$634$	−3.31069	−	5.73429i	−0.131484	−	0.227738i
$635$	−6.64069	+	11.5020i	−0.263528	+	0.456444i
$636$	14.7644			0.585447
$637$		0			0
$638$	22.6710			0.897552
$639$	−10.1389	+	17.5611i	−0.401088	+	0.694706i
$640$	20.9453	+	36.2782i	0.827934	+	1.43402i
$641$	−12.0274	−	20.8320i	−0.475053	−	0.822815i	0.524539	−	0.851386i	$-0.324238\pi$
$641$	−12.0274	−	20.8320i	−0.475053	−	0.822815i	−0.999592	+	0.0285709i	$0.990904\pi$
$642$	−0.778024	+	1.34758i	−0.0307061	+	0.0531846i
$643$	24.3676			0.960964			0.480482	−	0.877005i	$-0.340462\pi$
$643$	24.3676			0.960964			0.480482	+	0.877005i	$0.340462\pi$
$644$		0			0
$645$	−86.4803			−3.40516
$646$	−0.221568	+	0.383767i	−0.00871748	+	0.0150991i
$647$	19.1201	+	33.1170i	0.751688	+	1.30196i	0.947004	+	0.321222i	$0.104093\pi$
$647$	19.1201	+	33.1170i	0.751688	+	1.30196i	−0.195316	+	0.980740i	$0.562573\pi$
$648$	13.3850	+	23.1835i	0.525811	+	0.910732i
$649$	21.9662	−	38.0466i	0.862248	−	1.49346i
$650$	−21.6707			−0.849995
$651$		0			0
$652$	0.210952			0.00826151
$653$	−10.5812	+	18.3271i	−0.414074	+	0.717197i	−0.995331	−	0.0965234i	$-0.969228\pi$
$653$	−10.5812	+	18.3271i	−0.414074	+	0.717197i	0.581257	+	0.813720i	$0.302561\pi$
$654$	0.973000	+	1.68529i	0.0380473	+	0.0658999i
$655$	−7.90642	−	13.6943i	−0.308929	−	0.535081i
$656$	−1.01677	+	1.76110i	−0.0396982	+	0.0687593i
$657$	26.0148			1.01493
$658$		0			0
$659$	24.6069			0.958548			0.479274	−	0.877665i	$-0.340900\pi$
$659$	24.6069			0.958548			0.479274	+	0.877665i	$0.340900\pi$
$660$	29.2679	−	50.6935i	1.13925	−	1.97324i
$661$	19.0976	+	33.0781i	0.742812	+	1.28659i	0.951210	+	0.308544i	$0.0998417\pi$
$661$	19.0976	+	33.0781i	0.742812	+	1.28659i	−0.208398	+	0.978044i	$0.566825\pi$
$662$	4.52792	+	7.84258i	0.175983	+	0.304811i
$663$	−1.50431	+	2.60554i	−0.0584226	+	0.101191i
$664$	10.9884			0.426432
$665$		0			0
$666$	−16.3819			−0.634786
$667$	−16.0908	+	27.8701i	−0.623039	+	1.07913i
$668$	−0.635874	−	1.10137i	−0.0246027	−	0.0426131i
$669$	22.0129	+	38.1275i	0.851068	+	1.47409i
$670$	9.05529	−	15.6842i	0.349836	−	0.605935i
$671$	9.96264			0.384603
$672$		0			0
$673$	−28.0333			−1.08060			−0.540302	−	0.841471i	$-0.681690\pi$
$673$	−28.0333			−1.08060			−0.540302	+	0.841471i	$0.681690\pi$
$674$	10.3593	−	17.9428i	0.399025	−	0.691132i
$675$	−8.67539	−	15.0262i	−0.333916	−	0.578359i
$676$	−5.89972	−	10.2186i	−0.226912	−	0.393023i
$677$	2.61817	−	4.53481i	0.100625	−	0.174287i	−0.811318	−	0.584606i	$-0.801249\pi$
$677$	2.61817	−	4.53481i	0.100625	−	0.174287i	0.911942	+	0.410319i	$0.134583\pi$
$678$	−22.6164			−0.868578
$679$		0			0
$680$	6.49454			0.249054
$681$	23.9452	−	41.4744i	0.917584	−	1.58930i
$682$	−6.95497	−	12.0464i	−0.266320	−	0.461279i
$683$	0.625857	+	1.08402i	0.0239478	+	0.0414787i	0.877751	−	0.479117i	$-0.159043\pi$
$683$	0.625857	+	1.08402i	0.0239478	+	0.0414787i	−0.853803	+	0.520596i	$0.825710\pi$
$684$	1.74898	−	3.02932i	0.0668738	−	0.115829i
$685$	−4.95209			−0.189210
$686$		0			0
$687$	−16.2856			−0.621335
$688$	4.06063	−	7.03322i	0.154810	−	0.268139i
$689$	−4.82226	−	8.35240i	−0.183713	−	0.318201i
$690$	−16.3190	−	28.2654i	−0.621255	−	1.07604i
$691$	−25.4025	+	43.9984i	−0.966357	+	1.67378i	−0.260434	+	0.965492i	$0.583865\pi$
$691$	−25.4025	+	43.9984i	−0.966357	+	1.67378i	−0.705924	+	0.708288i	$0.749468\pi$
$692$	34.8419			1.32449
$693$		0			0
$694$	−0.744668			−0.0282672
$695$	9.05620	−	15.6858i	0.343521	−	0.594997i
$696$	−22.1539	−	38.3716i	−0.839740	−	1.45447i
$697$	0.642389	+	1.11265i	0.0243322	+	0.0421447i
$698$	−11.8881	+	20.5908i	−0.449971	+	0.779372i
$699$	−45.5263			−1.72196
$700$		0			0
$701$	0.998799			0.0377241			0.0188621	−	0.999822i	$-0.493996\pi$
$701$	0.998799			0.0377241			0.0188621	+	0.999822i	$0.493996\pi$
$702$	1.07998	−	1.87058i	0.0407613	−	0.0706006i
$703$	−4.47723	−	7.75479i	−0.168862	−	0.292478i
$704$	−5.19538	−	8.99867i	−0.195808	−	0.339150i
$705$	−58.8405	+	101.915i	−2.21606	+	3.83833i
$706$	6.68698			0.251668
$707$		0			0
$708$	−35.8830			−1.34857
$709$	6.98123	−	12.0918i	0.262185	−	0.454119i	−0.704637	−	0.709568i	$-0.748890\pi$
$709$	6.98123	−	12.0918i	0.262185	−	0.454119i	0.966822	+	0.255449i	$0.0822234\pi$
$710$	−13.3333	−	23.0939i	−0.500389	−	0.866698i
$711$	−10.4305	−	18.0662i	−0.391175	−	0.677534i
$712$	4.89146	−	8.47225i	0.183315	−	0.317511i
$713$	19.7453			0.739467
$714$		0			0
$715$	−38.2372			−1.42999
$716$	−9.29544	+	16.1002i	−0.347387	+	0.601692i
$717$	−20.7570	−	35.9521i	−0.775184	−	1.34266i
$718$	−8.14852	−	14.1137i	−0.304100	−	0.526717i
$719$	9.28469	−	16.0816i	0.346260	−	0.599741i	−0.639321	−	0.768940i	$-0.720785\pi$
$719$	9.28469	−	16.0816i	0.346260	−	0.599741i	0.985582	+	0.169199i	$0.0541180\pi$
$720$	−9.70377			−0.361638
$721$		0			0
$722$	−0.751024			−0.0279502
$723$	17.7508	−	30.7452i	0.660158	−	1.14343i
$724$	−13.3569	−	23.1348i	−0.496406	−	0.859800i
$725$	48.5827	+	84.1477i	1.80432	+	3.12517i
$726$	−5.07950	+	8.79795i	−0.188518	+	0.326522i
$727$	32.1991			1.19420			0.597099	−	0.802168i	$-0.296320\pi$
$727$	32.1991			1.19420			0.597099	+	0.802168i	$0.296320\pi$
$728$		0			0
$729$	−16.0724			−0.595272
$730$	−17.1055	+	29.6277i	−0.633105	+	1.09657i
$731$	−2.56549	−	4.44355i	−0.0948879	−	0.164351i
$732$	−4.06863	−	7.04708i	−0.150381	−	0.260468i
$733$	4.77812	−	8.27594i	0.176484	−	0.305679i	−0.764190	−	0.644991i	$-0.776861\pi$
$733$	4.77812	−	8.27594i	0.176484	−	0.305679i	0.940674	+	0.339312i	$0.110194\pi$
$734$	9.59598			0.354194
$735$		0			0
$736$	25.6179			0.944287
$737$	11.5868	−	20.0689i	0.426805	−	0.739247i
$738$	1.99177	+	3.44985i	0.0733182	+	0.126991i
$739$	10.1425	+	17.5673i	0.373097	+	0.646223i	0.990040	−	0.140785i	$-0.0449625\pi$
$739$	10.1425	+	17.5673i	0.373097	+	0.646223i	−0.616943	+	0.787008i	$0.711629\pi$
$740$	−27.4230	+	47.4981i	−1.00809	+	1.74606i
$741$	−5.09899			−0.187316
$742$		0			0
$743$	0.965374			0.0354161			0.0177081	−	0.999843i	$-0.494363\pi$
$743$	0.965374			0.0354161			0.0177081	+	0.999843i	$0.494363\pi$
$744$	−13.5927	+	23.5432i	−0.498332	+	0.863136i
$745$	−51.1706	−	88.6301i	−1.87475	−	3.24716i
$746$	−4.96361	−	8.59722i	−0.181731	−	0.314767i
$747$	−5.18648	+	8.98324i	−0.189763	+	0.328680i
$748$	3.47299			0.126985
$749$		0			0
$750$	−61.1991			−2.23468
$751$	0.328889	−	0.569653i	0.0120013	−	0.0207869i	−0.859962	−	0.510357i	$-0.829513\pi$
$751$	0.328889	−	0.569653i	0.0120013	−	0.0207869i	0.871964	+	0.489571i	$0.162846\pi$
$752$	−5.52564	−	9.57069i	−0.201499	−	0.349007i
$753$	7.81420	+	13.5346i	0.284765	+	0.493228i
$754$	−6.04796	+	10.4754i	−0.220254	+	0.381491i
$755$	−36.2591			−1.31960
$756$		0			0
$757$	−1.47679			−0.0536749			−0.0268375	−	0.999640i	$-0.508544\pi$
$757$	−1.47679			−0.0536749			−0.0268375	+	0.999640i	$0.508544\pi$
$758$	−0.648760	+	1.12369i	−0.0235640	+	0.0408141i
$759$	−20.8812	−	36.1672i	−0.757938	−	1.31279i
$760$	5.50345	+	9.53226i	0.199631	+	0.345771i
$761$	9.24235	−	16.0082i	0.335035	−	0.580297i	−0.648457	−	0.761252i	$-0.724585\pi$
$761$	9.24235	−	16.0082i	0.335035	−	0.580297i	0.983492	+	0.180954i	$0.0579186\pi$
$762$	−5.45221			−0.197513
$763$		0			0
$764$	33.4418			1.20988
$765$	−3.06540	+	5.30942i	−0.110830	+	0.191963i
$766$	1.82335	+	3.15813i	0.0658802	+	0.114108i
$767$	11.7199	+	20.2995i	0.423181	+	0.732971i
$768$	−14.5086	+	25.1297i	−0.523535	+	0.906790i
$769$	4.34052			0.156523			0.0782617	−	0.996933i	$-0.475063\pi$
$769$	4.34052			0.156523			0.0782617	+	0.996933i	$0.475063\pi$
$770$		0			0
$771$	−19.2382			−0.692845
$772$	2.28924	−	3.96507i	0.0823914	−	0.142706i
$773$	16.7757	+	29.0563i	0.603379	+	1.04508i	0.992305	+	0.123814i	$0.0395127\pi$
$773$	16.7757	+	29.0563i	0.603379	+	1.04508i	−0.388926	+	0.921269i	$0.627154\pi$
$774$	−7.95446	−	13.7775i	−0.285917	−	0.495223i
$775$	29.8083	−	51.6295i	1.07075	−	1.85459i
$776$	−5.44551			−0.195483
$777$		0			0
$778$	−7.98328			−0.286214
$779$	−1.08872	+	1.88571i	−0.0390074	+	0.0675627i
$780$	15.6157	+	27.0471i	0.559130	+	0.968442i
$781$	−17.0607	−	29.5500i	−0.610480	−	1.05738i
$782$	0.968225	−	1.67701i	0.0346236	−	0.0599699i
$783$	−9.68467			−0.346102
$784$		0			0
$785$	18.9333			0.675757
$786$	3.24570	−	5.62173i	0.115770	−	0.200520i
$787$	−21.0285	−	36.4225i	−0.749587	−	1.29832i	−0.948021	−	0.318208i	$-0.896919\pi$
$787$	−21.0285	−	36.4225i	−0.749587	−	1.29832i	0.198435	−	0.980114i	$-0.436414\pi$
$788$	−5.92463	−	10.2618i	−0.211056	−	0.365560i
$789$	−0.816386	+	1.41402i	−0.0290641	+	0.0503405i
$790$	27.4335			0.976041
$791$		0			0
$792$	25.7662			0.915562
$793$	−2.65774	+	4.60335i	−0.0943793	+	0.163470i
$794$	−4.78830	−	8.29358i	−0.169930	−	0.294328i
$795$	−21.9283	−	37.9810i	−0.777718	−	1.34705i
$796$	14.0742	−	24.3772i	0.498845	−	0.864025i
$797$	−2.71101			−0.0960289			−0.0480145	−	0.998847i	$-0.515289\pi$
$797$	−2.71101			−0.0960289			−0.0480145	+	0.998847i	$0.515289\pi$
$798$		0			0
$799$	−6.98214			−0.247010
$800$	38.6738	−	66.9849i	1.36732	−	2.36827i
$801$	4.61749	+	7.99774i	0.163151	+	0.282586i
$802$	7.22912	+	12.5212i	0.255269	+	0.442139i
$803$	−21.8876	+	37.9104i	−0.772395	+	1.33783i
$804$	−18.9277			−0.667528
$805$		0			0
$806$	7.42155			0.261413
$807$	16.2800	−	28.1978i	0.573084	−	0.992611i
$808$	19.4319	+	33.6571i	0.683612	+	1.18405i
$809$	−6.65791	−	11.5318i	−0.234079	−	0.405438i	0.724925	−	0.688828i	$-0.241874\pi$
$809$	−6.65791	−	11.5318i	−0.234079	−	0.405438i	−0.959005	+	0.283390i	$0.908541\pi$
$810$	16.6162	−	28.7801i	0.583834	−	1.01123i
$811$	15.1310			0.531320			0.265660	−	0.964067i	$-0.414410\pi$
$811$	15.1310			0.531320			0.265660	+	0.964067i	$0.414410\pi$
$812$		0			0
$813$	19.4115			0.680791
$814$	13.7829	−	23.8727i	0.483091	−	0.836737i
$815$	−0.313309	−	0.542667i	−0.0109747	−	0.0190088i
$816$	−0.642389	−	1.11265i	−0.0224881	−	0.0389506i
$817$	4.34797	−	7.53090i	0.152116	−	0.263473i
$818$	2.35807			0.0824478
$819$		0			0
$820$	13.3368			0.465741
$821$	12.1867	−	21.1080i	0.425319	−	0.736675i	−0.571131	−	0.820859i	$-0.693495\pi$
$821$	12.1867	−	21.1080i	0.425319	−	0.736675i	0.996450	+	0.0841843i	$0.0268285\pi$
$822$	−1.01645	−	1.76055i	−0.0354529	−	0.0614062i
$823$	−5.89383	−	10.2084i	−0.205446	−	0.355843i	0.744829	−	0.667256i	$-0.232531\pi$
$823$	−5.89383	−	10.2084i	−0.205446	−	0.355843i	−0.950275	+	0.311413i	$0.899198\pi$
$824$	6.31425	−	10.9366i	0.219967	−	0.380994i
$825$	−126.092			−4.38997
$826$		0			0
$827$	17.5429			0.610028			0.305014	−	0.952348i	$-0.401339\pi$
$827$	17.5429			0.610028			0.305014	+	0.952348i	$0.401339\pi$
$828$	−7.64281	+	13.2377i	−0.265606	+	0.460043i
$829$	25.4864	+	44.1438i	0.885180	+	1.53318i	0.845508	+	0.533963i	$0.179298\pi$
$829$	25.4864	+	44.1438i	0.885180	+	1.53318i	0.0396720	+	0.999213i	$0.487369\pi$
$830$	−6.82054	−	11.8135i	−0.236744	−	0.410053i
$831$	−17.6613	+	30.5903i	−0.612664	+	1.06117i
$832$	5.54391			0.192201
$833$		0			0
$834$	7.43542			0.257468
$835$	−1.88882	+	3.27153i	−0.0653653	+	0.113216i
$836$	2.94300	+	5.09743i	0.101786	+	0.176298i
$837$	2.97105	+	5.14602i	0.102695	+	0.177872i
$838$	−4.68944	+	8.12235i	−0.161994	+	0.280582i
$839$	5.84311			0.201727			0.100863	−	0.994900i	$-0.467840\pi$
$839$	5.84311			0.201727			0.100863	+	0.994900i	$0.467840\pi$
$840$		0			0
$841$	25.2347			0.870163
$842$	−5.45023	+	9.44008i	−0.187827	+	0.325327i
$843$	−11.8952	−	20.6030i	−0.409691	−	0.709606i
$844$	6.81420	+	11.8025i	0.234555	+	0.406260i
$845$	−17.5247	+	30.3537i	−0.602868	+	1.04420i
$846$	−21.6486			−0.744295
$847$		0			0
$848$	4.11852			0.141431
$849$	−7.33397	+	12.7028i	−0.251701	+	0.435959i
$850$	−2.92334	−	5.06338i	−0.100270	−	0.173672i
$851$	19.5650	+	33.8875i	0.670678	+	1.16165i
$852$	−13.9348	+	24.1358i	−0.477399	+	0.826879i
$853$	37.0096			1.26719			0.633593	−	0.773667i	$-0.281579\pi$
$853$	37.0096			1.26719			0.633593	+	0.773667i	$0.281579\pi$
$854$		0			0
$855$	−10.3904			−0.355345
$856$	−1.14658	+	1.98593i	−0.0391892	+	0.0678776i
$857$	20.0635	+	34.7509i	0.685355	+	1.18707i	0.973325	+	0.229430i	$0.0736862\pi$
$857$	20.0635	+	34.7509i	0.685355	+	1.18707i	−0.287970	+	0.957639i	$0.592980\pi$
$858$	−7.84848	−	13.5940i	−0.267943	−	0.464090i
$859$	−7.21938	+	12.5043i	−0.246322	+	0.426643i	−0.962503	−	0.271273i	$-0.912555\pi$
$859$	−7.21938	+	12.5043i	−0.246322	+	0.426643i	0.716180	+	0.697915i	$0.245889\pi$
$860$	−53.2626			−1.81624
$861$		0			0
$862$	−17.7746			−0.605405
$863$	−15.3092	+	26.5162i	−0.521130	+	0.902623i	0.478568	+	0.878050i	$0.341156\pi$
$863$	−15.3092	+	26.5162i	−0.521130	+	0.902623i	−0.999698	+	0.0245728i	$0.992177\pi$
$864$	3.85469	+	6.67652i	0.131139	+	0.227140i
$865$	−51.7478	−	89.6298i	−1.75948	−	3.04750i
$866$	−1.73454	+	3.00431i	−0.0589420	+	0.102090i
$867$	38.8240			1.31853
$868$		0			0
$869$	35.1028			1.19078
$870$	−27.5020	+	47.6348i	−0.932404	+	1.61497i
$871$	6.18204	+	10.7076i	0.209471	+	0.362814i
$872$	1.43391	+	2.48361i	0.0485585	+	0.0841057i
$873$	2.57026	−	4.45182i	0.0869901	−	0.150671i
$874$	3.28188			0.111011
$875$		0			0
$876$	35.7546			1.20804
$877$	8.03427	−	13.9158i	0.271298	−	0.469902i	−0.697897	−	0.716199i	$-0.745880\pi$
$877$	8.03427	−	13.9158i	0.271298	−	0.469902i	0.969194	+	0.246297i	$0.0792138\pi$
$878$	−7.11981	−	12.3319i	−0.240282	−	0.416181i
$879$	−1.72865	−	2.99411i	−0.0583059	−	0.100989i
$880$	8.16426	−	14.1409i	0.275217	−	0.476690i
$881$	40.2468			1.35595			0.677975	−	0.735085i	$-0.262858\pi$
$881$	40.2468			1.35595			0.677975	+	0.735085i	$0.262858\pi$
$882$		0			0
$883$	−0.564426			−0.0189944			−0.00949722	−	0.999955i	$-0.503023\pi$
$883$	−0.564426			−0.0189944			−0.00949722	+	0.999955i	$0.503023\pi$
$884$	−0.926494	+	1.60473i	−0.0311614	+	0.0539730i
$885$	53.2940	+	92.3080i	1.79146	+	3.10290i
$886$	−8.43733	−	14.6139i	−0.283458	−	0.490963i
$887$	−17.7918	+	30.8163i	−0.597390	+	1.03471i	0.395814	+	0.918331i	$0.370462\pi$
$887$	−17.7918	+	30.8163i	−0.597390	+	1.03471i	−0.993205	+	0.116380i	$0.962871\pi$
$888$	−53.8741			−1.80790
$889$		0			0
$890$	−12.1446			−0.407087
$891$	21.2614	−	36.8259i	0.712284	−	1.23371i
$892$	13.5576	+	23.4824i	0.453942	+	0.786250i
$893$	−5.91665	−	10.2479i	−0.197993	−	0.342934i
$894$	21.0063	−	36.3840i	0.702557	−	1.21686i
$895$	55.2229			1.84590
$896$		0			0
$897$	22.2820			0.743973
$898$	5.90906	−	10.2348i	0.197188	−	0.341540i
$899$	−16.6381	−	28.8180i	−0.554911	−	0.961134i
$900$	23.0758	+	39.9684i	0.769193	+	1.33228i
$901$	1.30103	−	2.25345i	0.0433436	−	0.0750733i
$902$	−6.70311			−0.223189
$903$		0			0
$904$	−33.3299			−1.10854
$905$	−39.6758	+	68.7205i	−1.31887	+	2.28435i
$906$	−7.44246	−	12.8907i	−0.247259	−	0.428265i
$907$	−15.1841	−	26.2996i	−0.504179	−	0.873264i	−0.999988	−	0.00483233i	$-0.998462\pi$
$907$	−15.1841	−	26.2996i	−0.504179	−	0.873264i	0.495809	−	0.868431i	$-0.334872\pi$
$908$	14.7477	−	25.5438i	0.489419	−	0.847699i
$909$	−36.6871			−1.21684
$910$		0			0
$911$	17.9947			0.596191			0.298096	−	0.954536i	$-0.403649\pi$
$911$	17.9947			0.596191			0.298096	+	0.954536i	$0.403649\pi$
$912$	1.08872	−	1.88571i	0.0360510	−	0.0624422i
$913$	−8.72728	−	15.1161i	−0.288831	−	0.500270i
$914$	8.58295	+	14.8661i	0.283899	+	0.491727i
$915$	−12.0856	+	20.9329i	−0.399537	+	0.692019i
$916$	−10.0302			−0.331407
$917$		0			0
$918$	0.582751			0.0192336
$919$	−20.9784	+	36.3357i	−0.692014	+	1.19860i	0.279163	+	0.960244i	$0.409943\pi$
$919$	−20.9784	+	36.3357i	−0.692014	+	1.19860i	−0.971177	+	0.238360i	$0.923390\pi$
$920$	−24.0494	−	41.6548i	−0.792885	−	1.37332i
$921$	34.9289	+	60.4986i	1.15095	+	1.99350i
$922$	−9.76411	+	16.9119i	−0.321564	+	0.556965i
$923$	18.2052			0.599232
$924$		0			0
$925$	118.144			3.88456
$926$	7.64094	−	13.2345i	0.251097	−	0.434913i
$927$	5.96060	+	10.3241i	0.195772	+	0.339087i
$928$	−21.5865	−	37.3889i	−0.708612	−	1.22735i
$929$	−9.55726	+	16.5537i	−0.313563	+	0.543108i	−0.979131	−	0.203230i	$-0.934856\pi$
$929$	−9.55726	+	16.5537i	−0.313563	+	0.543108i	0.665568	+	0.746338i	$0.268190\pi$
$930$	33.7481			1.10664
$931$		0			0
$932$	−28.0393			−0.918458
$933$	−5.10736	+	8.84620i	−0.167207	+	0.289612i
$934$	−5.68157	−	9.84076i	−0.185907	−	0.322000i
$935$	−5.15814	−	8.93416i	−0.168689	−	0.292178i
$936$	−6.87368	+	11.9056i	−0.224673	+	0.389145i
$937$	−44.3779			−1.44976			−0.724881	−	0.688874i	$-0.758105\pi$
$937$	−44.3779			−1.44976			−0.724881	+	0.688874i	$0.758105\pi$
$938$		0			0
$939$	47.6879			1.55623
$940$	−36.2394	+	62.7686i	−1.18200	+	2.04728i
$941$	−18.8086	−	32.5774i	−0.613142	−	1.06199i	−0.990707	−	0.136010i	$-0.956572\pi$
$941$	−18.8086	−	32.5774i	−0.613142	−	1.06199i	0.377565	−	0.925983i	$-0.376761\pi$
$942$	3.88620	+	6.73109i	0.126619	+	0.219311i
$943$	4.75756	−	8.24034i	0.154928	−	0.268342i
$944$	−10.0096			−0.325783
$945$		0			0
$946$	26.7699			0.870366
$947$	−14.5848	+	25.2616i	−0.473942	+	0.820891i	−0.999555	−	0.0298325i	$-0.990503\pi$
$947$	−14.5848	+	25.2616i	−0.473942	+	0.820891i	0.525613	+	0.850724i	$0.323836\pi$
$948$	−14.3356	−	24.8300i	−0.465599	−	0.806441i
$949$	−11.6779	−	20.2268i	−0.379082	−	0.656590i
$950$	4.95446	−	8.58138i	0.160744	−	0.278417i
$951$	20.5558			0.666566
$952$		0			0
$953$	25.0234			0.810586			0.405293	−	0.914187i	$-0.367170\pi$
$953$	25.0234			0.810586			0.405293	+	0.914187i	$0.367170\pi$
$954$	4.03394	−	6.98698i	0.130603	−	0.226212i
$955$	−49.6683	−	86.0281i	−1.60723	−	2.78380i
$956$	−12.7841	−	22.1427i	−0.413466	−	0.716145i
$957$	−35.1904	+	60.9515i	−1.13754	+	1.97028i
$958$	20.9735			0.677622
$959$		0			0
$960$	25.2099			0.813647
$961$	5.29157	−	9.16527i	0.170696	−	0.295654i
$962$	7.35376	+	12.7371i	0.237095	+	0.410660i
$963$	−1.08236	−	1.87470i	−0.0348785	−	0.0604114i
$964$	10.9326	−	18.9357i	0.352114	−	0.609879i
$965$	−13.6000			−0.437801
$966$		0			0
$967$	−28.8469			−0.927655			−0.463828	−	0.885926i	$-0.653524\pi$
$967$	−28.8469			−0.927655			−0.463828	+	0.885926i	$0.653524\pi$
$968$	−7.48567	+	12.9656i	−0.240599	+	0.416729i
$969$	−0.687846	−	1.19138i	−0.0220968	−	0.0382728i
$970$	3.38005	+	5.85442i	0.108527	+	0.187974i
$971$	1.59964	−	2.77065i	0.0513348	−	0.0889145i	−0.839216	−	0.543798i	$-0.816986\pi$
$971$	1.59964	−	2.77065i	0.0513348	−	0.0889145i	0.890551	+	0.454883i	$0.150319\pi$
$972$	−29.0666			−0.932312
$973$		0			0
$974$	−0.496166			−0.0158982
$975$	33.6378	−	58.2623i	1.07727	−	1.86589i
$976$	−1.13494	−	1.96578i	−0.0363286	−	0.0629231i
$977$	27.2484	+	47.1957i	0.871755	+	1.50992i	0.860180	+	0.509990i	$0.170351\pi$
$977$	27.2484	+	47.1957i	0.871755	+	1.50992i	0.0115745	+	0.999933i	$0.496316\pi$
$978$	0.128618	−	0.222773i	0.00411276	−	0.00712350i
$979$	−15.5397			−0.496651
$980$		0			0
$981$	−2.70721			−0.0864345
$982$	−1.91309	+	3.31358i	−0.0610493	+	0.105740i
$983$	−2.72880	−	4.72642i	−0.0870352	−	0.150749i	0.819221	−	0.573477i	$-0.194406\pi$
$983$	−2.72880	−	4.72642i	−0.0870352	−	0.150749i	−0.906257	+	0.422728i	$0.861073\pi$
$984$	6.55022	+	11.3453i	0.208813	+	0.361675i
$985$	−17.5987	+	30.4818i	−0.560741	+	0.971232i
$986$	−3.26344			−0.103929
$987$		0			0
$988$	−3.14043			−0.0999104
$989$	−19.0001	+	32.9091i	−0.604168	+	1.04645i
$990$	−15.9932	−	27.7010i	−0.508296	−	0.880395i
$991$	−17.1455	−	29.6970i	−0.544646	−	0.943355i	−0.998629	−	0.0523446i	$-0.983331\pi$
$991$	−17.1455	−	29.6970i	−0.544646	−	0.943355i	0.453983	−	0.891010i	$-0.350003\pi$
$992$	−13.2446	+	22.9403i	−0.420516	+	0.728355i
$993$	−28.1134			−0.892151
$994$		0			0
$995$	−83.6127			−2.65070
$996$	−7.12825	+	12.3465i	−0.225867	+	0.391214i
$997$	11.6069	+	20.1037i	0.367594	+	0.636691i	0.989189	−	0.146648i	$-0.0468483\pi$
$997$	11.6069	+	20.1037i	0.367594	+	0.636691i	−0.621595	+	0.783339i	$0.713515\pi$
$998$	−4.80619	−	8.32456i	−0.152137	−	0.263509i
$999$	−5.88784	+	10.1980i	−0.186283	+	0.322651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.f.o.324.3		8
7.2	even	3		931.2.a.l.1.2	✓	4
7.3	odd	6		931.2.f.n.704.3		8
7.4	even	3	inner	931.2.f.o.704.3		8
7.5	odd	6		931.2.a.m.1.2	yes	4
7.6	odd	2		931.2.f.n.324.3		8
21.2	odd	6		8379.2.a.bv.1.3		4
21.5	even	6		8379.2.a.bu.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.l.1.2	✓	4	7.2	even	3
931.2.a.m.1.2	yes	4	7.5	odd	6
931.2.f.n.324.3		8	7.6	odd	2
931.2.f.n.704.3		8	7.3	odd	6
931.2.f.o.324.3		8	1.1	even	1	trivial
931.2.f.o.704.3		8	7.4	even	3	inner
8379.2.a.bu.1.3		4	21.5	even	6
8379.2.a.bv.1.3		4	21.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.375512 - 0.650406i) q^{2} +(1.16576 + 2.01915i) q^{3} +(0.717981 + 1.24358i) q^{4} +(2.13271 - 3.69397i) q^{5} +1.75102 q^{6} +2.58049 q^{8} +(-1.21798 + 2.10961i) q^{9} +(-1.60172 - 2.77426i) q^{10} +(-2.04950 - 3.54983i) q^{11} +(-1.67398 + 2.89943i) q^{12} +2.18699 q^{13} +9.94491 q^{15} +(-0.466957 + 0.808794i) q^{16} +(0.295021 + 0.510992i) q^{17} +(0.914733 + 1.58436i) q^{18} +(-0.500000 + 0.866025i) q^{19} +6.12500 q^{20} -3.07844 q^{22} +(2.18494 - 3.78442i) q^{23} +(3.00823 + 5.21040i) q^{24} +(-6.59694 - 11.4262i) q^{25} +(0.821240 - 1.42243i) q^{26} +1.31506 q^{27} -7.36442 q^{29} +(3.73444 - 6.46823i) q^{30} +(2.25925 + 3.91314i) q^{31} +(2.93119 + 5.07697i) q^{32} +(4.77843 - 8.27649i) q^{33} +0.443136 q^{34} -3.49795 q^{36} +(-4.47723 + 7.75479i) q^{37} +(0.375512 + 0.650406i) q^{38} +(2.54950 + 4.41586i) q^{39} +(5.50345 - 9.53226i) q^{40} +2.17744 q^{41} -8.69594 q^{43} +(2.94300 - 5.09743i) q^{44} +(5.19521 + 8.99837i) q^{45} +(-1.64094 - 2.84219i) q^{46} +(-5.91665 + 10.2479i) q^{47} -2.17744 q^{48} -9.90893 q^{50} +(-0.687846 + 1.19138i) q^{51} +(1.57022 + 2.71969i) q^{52} +(-2.20498 - 3.81914i) q^{53} +(0.493821 - 0.855324i) q^{54} -17.4840 q^{55} -2.33152 q^{57} +(-2.76543 + 4.78986i) q^{58} +(5.35892 + 9.28193i) q^{59} +(7.14026 + 12.3673i) q^{60} +(-1.21525 + 2.10488i) q^{61} +3.39350 q^{62} +2.53496 q^{64} +(4.66422 - 8.07866i) q^{65} +(-3.58872 - 6.21584i) q^{66} +(2.82674 + 4.89606i) q^{67} +(-0.423639 + 0.733765i) q^{68} +10.1884 q^{69} +8.32434 q^{71} +(-3.14299 + 5.44382i) q^{72} +(-5.33974 - 9.24870i) q^{73} +(3.36251 + 5.82404i) q^{74} +(15.3809 - 26.6405i) q^{75} -1.43596 q^{76} +3.82947 q^{78} +(-4.28188 + 7.41644i) q^{79} +(1.99177 + 3.44985i) q^{80} +(5.18699 + 8.98412i) q^{81} +(0.817653 - 1.41622i) q^{82} +4.25826 q^{83} +2.51678 q^{85} +(-3.26543 + 5.65589i) q^{86} +(-8.58513 - 14.8699i) q^{87} +(-5.28871 - 9.16031i) q^{88} +(1.89555 - 3.28319i) q^{89} +7.80346 q^{90} +6.27498 q^{92} +(-5.26748 + 9.12354i) q^{93} +(4.44354 + 7.69644i) q^{94} +(2.13271 + 3.69397i) q^{95} +(-6.83411 + 11.8370i) q^{96} -2.11026 q^{97} +9.98499 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 2 q^{4} + 8 q^{5} + 8 q^{6} + 12 q^{8} - 2 q^{9} + 10 q^{10} + 6 q^{11} + 6 q^{12} - 4 q^{13} + 8 q^{15} - 2 q^{16} + 8 q^{17} + 6 q^{18} - 4 q^{19} - 28 q^{22} + 8 q^{23} + 12 q^{24} - 20 q^{25}+ \cdots + 16 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 2 * q^4 + 8 * q^5 + 8 * q^6 + 12 * q^8 - 2 * q^9 + 10 * q^10 + 6 * q^11 + 6 * q^12 - 4 * q^13 + 8 * q^15 - 2 * q^16 + 8 * q^17 + 6 * q^18 - 4 * q^19 - 28 * q^22 + 8 * q^23 + 12 * q^24 - 20 * q^25 + 16 * q^26 + 20 * q^27 + 4 * q^29 - 2 * q^30 - 2 * q^32 + 18 * q^33 + 44 * q^34 - 40 * q^36 - 10 * q^37 - 2 * q^39 + 22 * q^40 - 24 * q^41 + 8 * q^43 + 14 * q^44 + 8 * q^45 + 8 * q^46 + 16 * q^47 + 24 * q^48 + 24 * q^50 + 10 * q^51 + 28 * q^52 - 12 * q^53 + 4 * q^54 + 16 * q^55 - 4 * q^57 - 4 * q^58 + 14 * q^59 + 2 * q^60 + 20 * q^61 + 40 * q^62 - 40 * q^64 - 10 * q^65 - 8 * q^66 - 2 * q^67 - 24 * q^68 - 28 * q^69 - 4 * q^71 + 8 * q^72 - 16 * q^73 + 26 * q^74 + 36 * q^75 + 4 * q^76 + 28 * q^78 + 8 * q^79 + 28 * q^80 + 20 * q^81 - 12 * q^82 - 40 * q^83 - 28 * q^85 - 8 * q^86 - 20 * q^87 + 2 * q^88 + 16 * q^89 + 64 * q^90 + 52 * q^92 - 12 * q^93 + 10 * q^94 + 8 * q^95 - 12 * q^96 - 4 * q^97 + 16 * q^99

Introduction

L-functions

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