LMFDB - Embedded newform 588.2.b.d.391.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(391,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.391"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,4,12] 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.15911316233388032.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 10 x^{10} - 20 x^{9} + 35 x^{8} - 56 x^{7} + 84 x^{6} - 112 x^{5} + 140 x^{4} + \cdots + 64 $ x^12 - 4x^11 + 10x^10 - 20x^9 + 35x^8 - 56x^7 + 84x^6 - 112x^5 + 140x^4 - 160x^3 + 160x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.11
Root			$1.34902 - 0.424442i$ of defining polynomial
Character	$\chi$	$=$	588.391
Dual form			588.2.b.d.391.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34902 - 0.424442i) q^{2} +1.00000 q^{3} +(1.63970 - 1.14516i) q^{4} -0.127929i q^{5} +(1.34902 - 0.424442i) q^{6} +(1.72593 - 2.24080i) q^{8} +1.00000 q^{9} +(-0.0542984 - 0.172579i) q^{10} -3.99455i q^{11} +(1.63970 - 1.14516i) q^{12} -0.891655i q^{13} -0.127929i q^{15} +(1.37722 - 3.75543i) q^{16} +5.82842i q^{17} +(1.34902 - 0.424442i) q^{18} -6.31490 q^{19} +(-0.146499 - 0.209765i) q^{20} +(-1.69545 - 5.38872i) q^{22} +6.60535i q^{23} +(1.72593 - 2.24080i) q^{24} +4.98363 q^{25} +(-0.378456 - 1.20286i) q^{26} +1.00000 q^{27} +2.82968 q^{29} +(-0.0542984 - 0.172579i) q^{30} +8.45337 q^{31} +(0.263934 - 5.65069i) q^{32} -3.99455i q^{33} +(2.47383 + 7.86264i) q^{34} +(1.63970 - 1.14516i) q^{36} -8.67912 q^{37} +(-8.51891 + 2.68031i) q^{38} -0.891655i q^{39} +(-0.286663 - 0.220796i) q^{40} +3.24650i q^{41} +0.881836i q^{43} +(-4.57439 - 6.54985i) q^{44} -0.127929i q^{45} +(2.80359 + 8.91074i) q^{46} -10.0136 q^{47} +(1.37722 - 3.75543i) q^{48} +(6.72301 - 2.11526i) q^{50} +5.82842i q^{51} +(-1.02109 - 1.46204i) q^{52} -7.53454 q^{53} +(1.34902 - 0.424442i) q^{54} -0.511019 q^{55} -6.31490 q^{57} +(3.81729 - 1.20104i) q^{58} -0.588819 q^{59} +(-0.146499 - 0.209765i) q^{60} -1.68795i q^{61} +(11.4037 - 3.58796i) q^{62} +(-2.04234 - 7.73491i) q^{64} -0.114069 q^{65} +(-1.69545 - 5.38872i) q^{66} +6.35238i q^{67} +(6.67447 + 9.55685i) q^{68} +6.60535i q^{69} +11.3856i q^{71} +(1.72593 - 2.24080i) q^{72} -15.5139i q^{73} +(-11.7083 + 3.68378i) q^{74} +4.98363 q^{75} +(-10.3545 + 7.23156i) q^{76} +(-0.378456 - 1.20286i) q^{78} +9.82324i q^{79} +(-0.480429 - 0.176187i) q^{80} +1.00000 q^{81} +(1.37795 + 4.37958i) q^{82} -1.48021 q^{83} +0.745624 q^{85} +(0.374288 + 1.18961i) q^{86} +2.82968 q^{87} +(-8.95097 - 6.89430i) q^{88} +0.449983i q^{89} +(-0.0542984 - 0.172579i) q^{90} +(7.56418 + 10.8308i) q^{92} +8.45337 q^{93} +(-13.5085 + 4.25018i) q^{94} +0.807859i q^{95} +(0.263934 - 5.65069i) q^{96} -16.2042i q^{97} -3.99455i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 12 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{8} + 12 q^{9} - 4 q^{12} - 4 q^{16} + 4 q^{18} - 24 q^{20} + 4 q^{24} - 12 q^{25} + 24 q^{26} + 12 q^{27} + 32 q^{29} + 16 q^{31} + 4 q^{32} + 32 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) $ 12 * q + 4 * q^2 + 12 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^8 + 12 * q^9 - 4 * q^12 - 4 * q^16 + 4 * q^18 - 24 * q^20 + 4 * q^24 - 12 * q^25 + 24 * q^26 + 12 * q^27 + 32 * q^29 + 16 * q^31 + 4 * q^32 + 32 * q^34 - 4 * q^36 + 32 * q^37 - 24 * q^38 - 32 * q^40 - 24 * q^44 + 24 * q^46 - 4 * q^48 - 28 * q^50 + 32 * q^52 - 32 * q^53 + 4 * q^54 + 16 * q^55 + 16 * q^58 - 16 * q^59 - 24 * q^60 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 4 * q^72 - 32 * q^74 - 12 * q^75 - 32 * q^76 + 24 * q^78 - 16 * q^80 + 12 * q^81 + 32 * q^82 - 16 * q^83 + 16 * q^85 - 24 * q^86 + 32 * q^87 + 24 * q^88 + 16 * q^93 + 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.34902	−	0.424442i	0.953900	−	0.300126i
$2$	1.34902	−	0.424442i	0.953900	−	0.300126i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.63970	−	1.14516i	0.819849	−	0.572580i
$5$		−	0.127929i		−	0.0572116i	−0.999591	−	0.0286058i	$-0.990893\pi$
$5$		−	0.127929i		−	0.0572116i	0.999591	−	0.0286058i	$-0.00910675\pi$
$6$	1.34902	−	0.424442i	0.550734	−	0.173278i
$7$		0			0
$7$		0			0
$8$	1.72593	−	2.24080i	0.610208	−	0.792241i
$9$	1.00000			0.333333
$10$	−0.0542984	−	0.172579i	−0.0171707	−	0.0545741i
$11$		−	3.99455i		−	1.20440i	−0.798345	−	0.602201i	$-0.794291\pi$
$11$		−	3.99455i		−	1.20440i	0.798345	−	0.602201i	$-0.205709\pi$
$12$	1.63970	−	1.14516i	0.473340	−	0.330579i
$13$		−	0.891655i		−	0.247301i	−0.992326	−	0.123650i	$-0.960540\pi$
$13$		−	0.891655i		−	0.247301i	0.992326	−	0.123650i	$-0.0394601\pi$
$14$		0			0
$15$		−	0.127929i		−	0.0330311i
$16$	1.37722	−	3.75543i	0.344305	−	0.938858i
$17$			5.82842i			1.41360i	0.707414	+	0.706800i	$0.249862\pi$
$17$			5.82842i			1.41360i	−0.707414	+	0.706800i	$0.750138\pi$
$18$	1.34902	−	0.424442i	0.317967	−	0.100042i
$19$	−6.31490			−1.44874			−0.724368	−	0.689413i	$-0.757868\pi$
$19$	−6.31490			−1.44874			−0.724368	+	0.689413i	$0.757868\pi$
$20$	−0.146499	−	0.209765i	−0.0327582	−	0.0469049i
$21$		0			0
$22$	−1.69545	−	5.38872i	−0.361472	−	1.14888i
$23$			6.60535i			1.37731i	0.725089	+	0.688656i	$0.241799\pi$
$23$			6.60535i			1.37731i	−0.725089	+	0.688656i	$0.758201\pi$
$24$	1.72593	−	2.24080i	0.352304	−	0.457401i
$25$	4.98363			0.996727
$26$	−0.378456	−	1.20286i	−0.0742212	−	0.235900i
$27$	1.00000			0.192450
$28$		0			0
$29$	2.82968			0.525459			0.262729	−	0.964870i	$-0.415377\pi$
$29$	2.82968			0.525459			0.262729	+	0.964870i	$0.415377\pi$
$30$	−0.0542984	−	0.172579i	−0.00991349	−	0.0315084i
$31$	8.45337			1.51827			0.759135	−	0.650934i	$-0.225622\pi$
$31$	8.45337			1.51827			0.759135	+	0.650934i	$0.225622\pi$
$32$	0.263934	−	5.65069i	0.0466573	−	0.998911i
$33$		−	3.99455i		−	0.695361i
$34$	2.47383	+	7.86264i	0.424258	+	1.34843i
$35$		0			0
$36$	1.63970	−	1.14516i	0.273283	−	0.190860i
$37$	−8.67912			−1.42684			−0.713419	−	0.700737i	$-0.752854\pi$
$37$	−8.67912			−1.42684			−0.713419	+	0.700737i	$0.752854\pi$
$38$	−8.51891	+	2.68031i	−1.38195	+	0.434803i
$39$		−	0.891655i		−	0.142779i
$40$	−0.286663	−	0.220796i	−0.0453254	−	0.0349110i
$41$			3.24650i			0.507018i	0.967333	+	0.253509i	$0.0815847\pi$
$41$			3.24650i			0.507018i	−0.967333	+	0.253509i	$0.918415\pi$
$42$		0			0
$43$			0.881836i			0.134479i	0.997737	+	0.0672394i	$0.0214191\pi$
$43$			0.881836i			0.134479i	−0.997737	+	0.0672394i	$0.978581\pi$
$44$	−4.57439	−	6.54985i	−0.689616	−	0.987427i
$45$		−	0.127929i		−	0.0190705i
$46$	2.80359	+	8.91074i	0.413366	+	1.31382i
$47$	−10.0136			−1.46063			−0.730314	−	0.683111i	$-0.760626\pi$
$47$	−10.0136			−1.46063			−0.730314	+	0.683111i	$0.760626\pi$
$48$	1.37722	−	3.75543i	0.198785	−	0.542050i
$49$		0			0
$50$	6.72301	−	2.11526i	0.950777	−	0.299143i
$51$			5.82842i			0.816142i
$52$	−1.02109	−	1.46204i	−0.141599	−	0.202749i
$53$	−7.53454			−1.03495			−0.517474	−	0.855699i	$-0.673128\pi$
$53$	−7.53454			−1.03495			−0.517474	+	0.855699i	$0.673128\pi$
$54$	1.34902	−	0.424442i	0.183578	−	0.0577592i
$55$	−0.511019			−0.0689057
$56$		0			0
$57$	−6.31490			−0.836428
$58$	3.81729	−	1.20104i	0.501235	−	0.157704i
$59$	−0.588819			−0.0766577			−0.0383288	−	0.999265i	$-0.512203\pi$
$59$	−0.588819			−0.0766577			−0.0383288	+	0.999265i	$0.512203\pi$
$60$	−0.146499	−	0.209765i	−0.0189130	−	0.0270805i
$61$		−	1.68795i		−	0.216120i	−0.994144	−	0.108060i	$-0.965536\pi$
$61$		−	1.68795i		−	0.216120i	0.994144	−	0.108060i	$-0.0344638\pi$
$62$	11.4037	−	3.58796i	1.44828	−	0.455672i
$63$		0			0
$64$	−2.04234	−	7.73491i	−0.255292	−	0.966864i
$65$	−0.114069			−0.0141485
$66$	−1.69545	−	5.38872i	−0.208696	−	0.663305i
$67$			6.35238i			0.776067i	0.921645	+	0.388033i	$0.126846\pi$
$67$			6.35238i			0.776067i	−0.921645	+	0.388033i	$0.873154\pi$
$68$	6.67447	+	9.55685i	0.809398	+	1.15894i
$69$			6.60535i			0.795191i
$70$		0			0
$71$			11.3856i			1.35122i	0.737259	+	0.675610i	$0.236120\pi$
$71$			11.3856i			1.35122i	−0.737259	+	0.675610i	$0.763880\pi$
$72$	1.72593	−	2.24080i	0.203403	−	0.264080i
$73$		−	15.5139i		−	1.81577i	−0.419223	−	0.907883i	$-0.637697\pi$
$73$		−	15.5139i		−	1.81577i	0.419223	−	0.907883i	$-0.362303\pi$
$74$	−11.7083	+	3.68378i	−1.36106	+	0.428231i
$75$	4.98363			0.575461
$76$	−10.3545	+	7.23156i	−1.18775	+	0.829517i
$77$		0			0
$78$	−0.378456	−	1.20286i	−0.0428517	−	0.136197i
$79$			9.82324i			1.10520i	0.833446	+	0.552601i	$0.186364\pi$
$79$			9.82324i			1.10520i	−0.833446	+	0.552601i	$0.813636\pi$
$80$	−0.480429	−	0.176187i	−0.0537136	−	0.0196983i
$81$	1.00000			0.111111
$82$	1.37795	+	4.37958i	0.152169	+	0.483644i
$83$	−1.48021			−0.162474			−0.0812371	−	0.996695i	$-0.525887\pi$
$83$	−1.48021			−0.162474			−0.0812371	+	0.996695i	$0.525887\pi$
$84$		0			0
$85$	0.745624			0.0808743
$86$	0.374288	+	1.18961i	0.0403605	+	0.128279i
$87$	2.82968			0.303374
$88$	−8.95097	−	6.89430i	−0.954177	−	0.734935i
$89$			0.449983i			0.0476981i	0.999716	+	0.0238490i	$0.00759210\pi$
$89$			0.449983i			0.0476981i	−0.999716	+	0.0238490i	$0.992408\pi$
$90$	−0.0542984	−	0.172579i	−0.00572356	−	0.0181914i
$91$		0			0
$92$	7.56418	+	10.8308i	0.788620	+	1.12919i
$93$	8.45337			0.876573
$94$	−13.5085	+	4.25018i	−1.39329	+	0.438372i
$95$			0.807859i			0.0828845i
$96$	0.263934	−	5.65069i	0.0269376	−	0.576722i
$97$		−	16.2042i		−	1.64529i	−0.568555	−	0.822645i	$-0.692497\pi$
$97$		−	16.2042i		−	1.64529i	0.568555	−	0.822645i	$-0.307503\pi$
$98$		0			0
$99$		−	3.99455i		−	0.401467i
$100$	8.17166	−	5.70705i	0.817166	−	0.570705i
$101$			12.0661i			1.20062i	0.799767	+	0.600310i	$0.204956\pi$
$101$			12.0661i			1.20062i	−0.799767	+	0.600310i	$0.795044\pi$
$102$	2.47383	+	7.86264i	0.244945	+	0.778518i
$103$	3.28431			0.323612			0.161806	−	0.986823i	$-0.448268\pi$
$103$	3.28431			0.323612			0.161806	+	0.986823i	$0.448268\pi$
$104$	−1.99802	−	1.53893i	−0.195922	−	0.150905i
$105$		0			0
$106$	−10.1642	+	3.19797i	−0.987237	+	0.310615i
$107$		−	3.33543i		−	0.322449i	−0.986918	−	0.161224i	$-0.948456\pi$
$107$		−	3.33543i		−	0.322449i	0.986918	−	0.161224i	$-0.0515443\pi$
$108$	1.63970	−	1.14516i	0.157780	−	0.110193i
$109$	4.46096			0.427283			0.213641	−	0.976912i	$-0.431468\pi$
$109$	4.46096			0.427283			0.213641	+	0.976912i	$0.431468\pi$
$110$	−0.689373	+	0.216898i	−0.0657292	+	0.0206804i
$111$	−8.67912			−0.823786
$112$		0			0
$113$	−9.16272			−0.861956			−0.430978	−	0.902362i	$-0.641831\pi$
$113$	−9.16272			−0.861956			−0.430978	+	0.902362i	$0.641831\pi$
$114$	−8.51891	+	2.68031i	−0.797869	+	0.251034i
$115$	0.845016			0.0787982
$116$	4.63983	−	3.24044i	0.430797	−	0.300867i
$117$		−	0.891655i		−	0.0824335i
$118$	−0.794327	+	0.249919i	−0.0731237	+	0.0230069i
$119$		0			0
$120$	−0.286663	−	0.220796i	−0.0261686	−	0.0201559i
$121$	−4.95641			−0.450583
$122$	−0.716436	−	2.27707i	−0.0648631	−	0.206157i
$123$			3.24650i			0.292727i
$124$	13.8610	−	9.68045i	1.24475	−	0.869330i
$125$		−	1.27720i		−	0.114236i
$126$		0			0
$127$			14.0775i			1.24917i	0.780955	+	0.624587i	$0.214733\pi$
$127$			14.0775i			1.24917i	−0.780955	+	0.624587i	$0.785267\pi$
$128$	−6.03817	−	9.56768i	−0.533704	−	0.845671i
$129$			0.881836i			0.0776414i
$130$	−0.153880	+	0.0484155i	−0.0134962	+	0.00424632i
$131$	9.76967			0.853580			0.426790	−	0.904351i	$-0.359644\pi$
$131$	9.76967			0.853580			0.426790	+	0.904351i	$0.359644\pi$
$132$	−4.57439	−	6.54985i	−0.398150	−	0.570092i
$133$		0			0
$134$	2.69622	+	8.56948i	0.232918	+	0.740290i
$135$		−	0.127929i		−	0.0110104i
$136$	13.0603	+	10.0594i	1.11991	+	0.862590i
$137$	−3.96852			−0.339054			−0.169527	−	0.985526i	$-0.554224\pi$
$137$	−3.96852			−0.339054			−0.169527	+	0.985526i	$0.554224\pi$
$138$	2.80359	+	8.91074i	0.238657	+	0.758532i
$139$	0.262023			0.0222245			0.0111122	−	0.999938i	$-0.496463\pi$
$139$	0.262023			0.0222245			0.0111122	+	0.999938i	$0.496463\pi$
$140$		0			0
$141$	−10.0136			−0.843294
$142$	4.83252	+	15.3594i	0.405536	+	1.28893i
$143$	−3.56176			−0.297849
$144$	1.37722	−	3.75543i	0.114768	−	0.312953i
$145$		−	0.361999i		−	0.0300623i
$146$	−6.58476	−	20.9286i	−0.544958	−	1.73206i
$147$		0			0
$148$	−14.2311	+	9.93897i	−1.16979	+	0.816979i
$149$	2.69549			0.220823			0.110411	−	0.993886i	$-0.464783\pi$
$149$	2.69549			0.220823			0.110411	+	0.993886i	$0.464783\pi$
$150$	6.72301	−	2.11526i	0.548932	−	0.172710i
$151$		−	4.31664i		−	0.351284i	−0.984454	−	0.175642i	$-0.943800\pi$
$151$		−	4.31664i		−	0.351284i	0.984454	−	0.175642i	$-0.0562000\pi$
$152$	−10.8991	+	14.1504i	−0.884031	+	1.14775i
$153$			5.82842i			0.471200i
$154$		0			0
$155$		−	1.08143i		−	0.0868626i
$156$	−1.02109	−	1.46204i	−0.0817524	−	0.117057i
$157$		−	3.20616i		−	0.255879i	−0.991782	−	0.127940i	$-0.959164\pi$
$157$		−	3.20616i		−	0.255879i	0.991782	−	0.127940i	$-0.0408364\pi$
$158$	4.16940	+	13.2517i	0.331699	+	1.05425i
$159$	−7.53454			−0.597528
$160$	−0.722888	−	0.0337648i	−0.0571493	−	0.00266934i
$161$		0			0
$162$	1.34902	−	0.424442i	0.105989	−	0.0333473i
$163$		−	23.2619i		−	1.82201i	−0.412393	−	0.911006i	$-0.635307\pi$
$163$		−	23.2619i		−	1.82201i	0.412393	−	0.911006i	$-0.364693\pi$
$164$	3.71776	+	5.32328i	0.290308	+	0.415678i
$165$	−0.511019			−0.0397827
$166$	−1.99683	+	0.628263i	−0.154984	+	0.0487627i
$167$	−9.66864			−0.748182			−0.374091	−	0.927392i	$-0.622045\pi$
$167$	−9.66864			−0.748182			−0.374091	+	0.927392i	$0.622045\pi$
$168$		0			0
$169$	12.2050			0.938842
$170$	1.00586	−	0.316474i	0.0771460	−	0.0242725i
$171$	−6.31490			−0.482912
$172$	1.00984	+	1.44595i	0.0769998	+	0.110252i
$173$			20.7065i			1.57429i	0.616768	+	0.787145i	$0.288441\pi$
$173$			20.7065i			1.57429i	−0.616768	+	0.787145i	$0.711559\pi$
$174$	3.81729	−	1.20104i	0.289388	−	0.0910503i
$175$		0			0
$176$	−15.0012	−	5.50137i	−1.13076	−	0.414682i
$177$	−0.588819			−0.0442583
$178$	0.190991	+	0.607035i	0.0143154	+	0.0454992i
$179$		−	1.46793i		−	0.109718i	−0.998494	−	0.0548589i	$-0.982529\pi$
$179$		−	1.46793i		−	0.109718i	0.998494	−	0.0548589i	$-0.0174709\pi$
$180$	−0.146499	−	0.209765i	−0.0109194	−	0.0156350i
$181$		−	23.5472i		−	1.75025i	−0.483898	−	0.875124i	$-0.660779\pi$
$181$		−	23.5472i		−	1.75025i	0.483898	−	0.875124i	$-0.339221\pi$
$182$		0			0
$183$		−	1.68795i		−	0.124777i
$184$	14.8013	+	11.4004i	1.09116	+	0.840446i
$185$			1.11031i			0.0816317i
$186$	11.4037	−	3.58796i	0.836163	−	0.263082i
$187$	23.2819			1.70254
$188$	−16.4192	+	11.4671i	−1.19749	+	0.836326i
$189$		0			0
$190$	0.342889	+	1.08982i	0.0248758	+	0.0790635i
$191$		−	3.69128i		−	0.267092i	−0.991043	−	0.133546i	$-0.957364\pi$
$191$		−	3.69128i		−	0.267092i	0.991043	−	0.133546i	$-0.0426364\pi$
$192$	−2.04234	−	7.73491i	−0.147393	−	0.558219i
$193$	−2.71674			−0.195555			−0.0977777	−	0.995208i	$-0.531173\pi$
$193$	−2.71674			−0.195555			−0.0977777	+	0.995208i	$0.531173\pi$
$194$	−6.87775	−	21.8598i	−0.493794	−	1.56944i
$195$	−0.114069			−0.00816862
$196$		0			0
$197$	4.09843			0.292001			0.146001	−	0.989284i	$-0.453360\pi$
$197$	4.09843			0.292001			0.146001	+	0.989284i	$0.453360\pi$
$198$	−1.69545	−	5.38872i	−0.120491	−	0.382959i
$199$	0.208229			0.0147610			0.00738048	−	0.999973i	$-0.497651\pi$
$199$	0.208229			0.0147610			0.00738048	+	0.999973i	$0.497651\pi$
$200$	8.60140	−	11.1673i	0.608211	−	0.789648i
$201$			6.35238i			0.448062i
$202$	5.12135	+	16.2774i	0.360337	+	1.14527i
$203$		0			0
$204$	6.67447	+	9.55685i	0.467306	+	0.669114i
$205$	0.415321			0.0290073
$206$	4.43059	−	1.39400i	0.308694	−	0.0971243i
$207$			6.60535i			0.459104i
$208$	−3.34855	−	1.22801i	−0.232180	−	0.0851469i
$209$			25.2252i			1.74486i
$210$		0			0
$211$		−	16.5850i		−	1.14176i	−0.821034	−	0.570880i	$-0.806602\pi$
$211$		−	16.5850i		−	1.14176i	0.821034	−	0.570880i	$-0.193398\pi$
$212$	−12.3544	+	8.62825i	−0.848502	+	0.592591i
$213$			11.3856i			0.780127i
$214$	−1.41570	−	4.49956i	−0.0967751	−	0.307584i
$215$	0.112812			0.00769375
$216$	1.72593	−	2.24080i	0.117435	−	0.152467i
$217$		0			0
$218$	6.01792	−	1.89342i	0.407585	−	0.128238i
$219$		−	15.5139i		−	1.04833i
$220$	−0.837916	+	0.585198i	−0.0564923	+	0.0394540i
$221$	5.19694			0.349584
$222$	−11.7083	+	3.68378i	−0.785809	+	0.247239i
$223$	21.3432			1.42925			0.714624	−	0.699509i	$-0.246598\pi$
$223$	21.3432			1.42925			0.714624	+	0.699509i	$0.246598\pi$
$224$		0			0
$225$	4.98363			0.332242
$226$	−12.3607	+	3.88904i	−0.822220	+	0.258695i
$227$	−26.9972			−1.79187			−0.895935	−	0.444185i	$-0.853493\pi$
$227$	−26.9972			−1.79187			−0.895935	+	0.444185i	$0.853493\pi$
$228$	−10.3545	+	7.23156i	−0.685745	+	0.478922i
$229$			2.91694i			0.192757i	0.995345	+	0.0963783i	$0.0307259\pi$
$229$			2.91694i			0.192757i	−0.995345	+	0.0963783i	$0.969274\pi$
$230$	1.13994	−	0.358660i	0.0751656	−	0.0236494i
$231$		0			0
$232$	4.88383	−	6.34074i	0.320639	−	0.416290i
$233$	20.3989			1.33638			0.668189	−	0.743991i	$-0.267070\pi$
$233$	20.3989			1.33638			0.668189	+	0.743991i	$0.267070\pi$
$234$	−0.378456	−	1.20286i	−0.0247404	−	0.0786333i
$235$			1.28103i			0.0835649i
$236$	−0.965485	+	0.674291i	−0.0628477	+	0.0438926i
$237$			9.82324i			0.638088i
$238$		0			0
$239$		−	25.2554i		−	1.63364i	−0.576895	−	0.816818i	$-0.695736\pi$
$239$		−	25.2554i		−	1.63364i	0.576895	−	0.816818i	$-0.304264\pi$
$240$	−0.480429	−	0.176187i	−0.0310115	−	0.0113728i
$241$		−	8.20938i		−	0.528813i	−0.964411	−	0.264406i	$-0.914824\pi$
$241$		−	8.20938i		−	0.528813i	0.964411	−	0.264406i	$-0.0851760\pi$
$242$	−6.68629	+	2.10371i	−0.429811	+	0.135231i
$243$	1.00000			0.0641500
$244$	−1.93297	−	2.76773i	−0.123746	−	0.177186i
$245$		0			0
$246$	1.37795	+	4.37958i	0.0878548	+	0.279232i
$247$			5.63071i			0.358273i
$248$	14.5899	−	18.9423i	0.926460	−	1.20284i
$249$	−1.48021			−0.0938045
$250$	−0.542096	−	1.72296i	−0.0342851	−	0.108970i
$251$	6.55180			0.413546			0.206773	−	0.978389i	$-0.433704\pi$
$251$	6.55180			0.413546			0.206773	+	0.978389i	$0.433704\pi$
$252$		0			0
$253$	26.3854			1.65884
$254$	5.97507	+	18.9908i	0.374909	+	1.19159i
$255$	0.745624			0.0466928
$256$	−12.2065	−	10.3441i	−0.762908	−	0.646507i
$257$		−	18.7522i		−	1.16973i	−0.811130	−	0.584866i	$-0.801147\pi$
$257$		−	18.7522i		−	1.16973i	0.811130	−	0.584866i	$-0.198853\pi$
$258$	0.374288	+	1.18961i	0.0233022	+	0.0740621i
$259$		0			0
$260$	−0.187038	+	0.130627i	−0.0115996	+	0.00810112i
$261$	2.82968			0.175153
$262$	13.1795	−	4.14666i	0.814229	−	0.256181i
$263$			2.10526i			0.129816i	0.997891	+	0.0649079i	$0.0206754\pi$
$263$			2.10526i			0.129816i	−0.997891	+	0.0649079i	$0.979325\pi$
$264$	−8.95097	−	6.89430i	−0.550894	−	0.424315i
$265$			0.963886i			0.0592111i
$266$		0			0
$267$			0.449983i			0.0275385i
$268$	7.27449	+	10.4160i	0.444360	+	0.636258i
$269$		−	11.8021i		−	0.719586i	−0.933032	−	0.359793i	$-0.882847\pi$
$269$		−	11.8021i		−	0.719586i	0.933032	−	0.359793i	$-0.117153\pi$
$270$	−0.0542984	−	0.172579i	−0.00330450	−	0.0105028i
$271$	−11.3243			−0.687900			−0.343950	−	0.938988i	$-0.611765\pi$
$271$	−11.3243			−0.687900			−0.343950	+	0.938988i	$0.611765\pi$
$272$	21.8882	+	8.02702i	1.32717	+	0.486710i
$273$		0			0
$274$	−5.35361	+	1.68441i	−0.323423	+	0.101759i
$275$		−	19.9074i		−	1.20046i
$276$	7.56418	+	10.8308i	0.455310	+	0.651937i
$277$	−11.7638			−0.706821			−0.353410	−	0.935468i	$-0.614978\pi$
$277$	−11.7638			−0.706821			−0.353410	+	0.935468i	$0.614978\pi$
$278$	0.353473	−	0.111213i	0.0211999	−	0.00667014i
$279$	8.45337			0.506090
$280$		0			0
$281$	−9.80481			−0.584906			−0.292453	−	0.956280i	$-0.594471\pi$
$281$	−9.80481			−0.584906			−0.292453	+	0.956280i	$0.594471\pi$
$282$	−13.5085	+	4.25018i	−0.804418	+	0.253094i
$283$	−24.6465			−1.46508			−0.732542	−	0.680722i	$-0.761666\pi$
$283$	−24.6465			−1.46508			−0.732542	+	0.680722i	$0.761666\pi$
$284$	13.0383	+	18.6689i	0.773681	+	1.10780i
$285$			0.807859i			0.0478534i
$286$	−4.80487	+	1.51176i	−0.284118	+	0.0893922i
$287$		0			0
$288$	0.263934	−	5.65069i	0.0155524	−	0.332970i
$289$	−16.9705			−0.998264
$290$	−0.153647	−	0.488343i	−0.00902248	−	0.0286765i
$291$		−	16.2042i		−	0.949909i
$292$	−17.7659	−	25.4381i	−1.03967	−	1.48865i
$293$		−	2.41042i		−	0.140818i	−0.997518	−	0.0704091i	$-0.977570\pi$
$293$		−	2.41042i		−	0.140818i	0.997518	−	0.0704091i	$-0.0224305\pi$
$294$		0			0
$295$			0.0753270i			0.00438571i
$296$	−14.9795	+	19.4481i	−0.870668	+	1.13040i
$297$		−	3.99455i		−	0.231787i
$298$	3.63626	−	1.14408i	0.210643	−	0.0662746i
$299$	5.88969			0.340610
$300$	8.17166	−	5.70705i	0.471791	−	0.329497i
$301$		0			0
$302$	−1.83216	−	5.82323i	−0.105429	−	0.335089i
$303$			12.0661i			0.693178i
$304$	−8.69701	+	23.7152i	−0.498808	+	1.36016i
$305$	−0.215938			−0.0123646
$306$	2.47383	+	7.86264i	0.141419	+	0.449477i
$307$	24.4054			1.39289			0.696446	−	0.717609i	$-0.254764\pi$
$307$	24.4054			1.39289			0.696446	+	0.717609i	$0.254764\pi$
$308$		0			0
$309$	3.28431			0.186838
$310$	−0.459004	−	1.45887i	−0.0260697	−	0.0828582i
$311$	31.1866			1.76843			0.884215	−	0.467079i	$-0.154694\pi$
$311$	31.1866			1.76843			0.884215	+	0.467079i	$0.154694\pi$
$312$	−1.99802	−	1.53893i	−0.113115	−	0.0871249i
$313$		−	2.53807i		−	0.143460i	−0.997424	−	0.0717302i	$-0.977148\pi$
$313$		−	2.53807i		−	0.143460i	0.997424	−	0.0717302i	$-0.0228521\pi$
$314$	−1.36083	−	4.32516i	−0.0767959	−	0.244083i
$315$		0			0
$316$	11.2492	+	16.1072i	0.632816	+	0.906098i
$317$	−18.2520			−1.02514			−0.512568	−	0.858646i	$-0.671306\pi$
$317$	−18.2520			−1.02514			−0.512568	+	0.858646i	$0.671306\pi$
$318$	−10.1642	+	3.19797i	−0.569982	+	0.179333i
$319$		−	11.3033i		−	0.632864i
$320$	−0.989520	+	0.261274i	−0.0553158	+	0.0146057i
$321$		−	3.33543i		−	0.186166i
$322$		0			0
$323$		−	36.8059i		−	2.04793i
$324$	1.63970	−	1.14516i	0.0910943	−	0.0636200i
$325$		−	4.44368i		−	0.246491i
$326$	−9.87332	−	31.3807i	−0.546832	−	1.73802i
$327$	4.46096			0.246692
$328$	7.27474	+	5.60322i	0.401680	+	0.309386i
$329$		0			0
$330$	−0.689373	+	0.216898i	−0.0379487	+	0.0119398i
$331$		−	20.7274i		−	1.13928i	−0.821895	−	0.569639i	$-0.807083\pi$
$331$		−	20.7274i		−	1.13928i	0.821895	−	0.569639i	$-0.192917\pi$
$332$	−2.42710	+	1.69508i	−0.133204	+	0.0930294i
$333$	−8.67912			−0.475613
$334$	−13.0432	+	4.10378i	−0.713690	+	0.224549i
$335$	0.812654			0.0444000
$336$		0			0
$337$	−0.330532			−0.0180052			−0.00900261	−	0.999959i	$-0.502866\pi$
$337$	−0.330532			−0.0180052			−0.00900261	+	0.999959i	$0.502866\pi$
$338$	16.4647	−	5.18029i	0.895561	−	0.281771i
$339$	−9.16272			−0.497651
$340$	1.22260	−	0.853858i	0.0663047	−	0.0463070i
$341$		−	33.7674i		−	1.82861i
$342$	−8.51891	+	2.68031i	−0.460650	+	0.144934i
$343$		0			0
$344$	1.97602	+	1.52199i	0.106540	+	0.0820600i
$345$	0.845016			0.0454941
$346$	8.78872	+	27.9335i	0.472485	+	1.50171i
$347$			21.9951i			1.18076i	0.807127	+	0.590378i	$0.201021\pi$
$347$			21.9951i			1.18076i	−0.807127	+	0.590378i	$0.798979\pi$
$348$	4.63983	−	3.24044i	0.248721	−	0.173706i
$349$			26.6709i			1.42766i	0.700318	+	0.713831i	$0.253041\pi$
$349$			26.6709i			1.42766i	−0.700318	+	0.713831i	$0.746959\pi$
$350$		0			0
$351$		−	0.891655i		−	0.0475930i
$352$	−22.5720	−	1.05430i	−1.20309	−	0.0561941i
$353$		−	7.77165i		−	0.413643i	−0.978379	−	0.206822i	$-0.933688\pi$
$353$		−	7.77165i		−	0.413643i	0.978379	−	0.206822i	$-0.0663120\pi$
$354$	−0.794327	+	0.249919i	−0.0422180	+	0.0132831i
$355$	1.45655			0.0773055
$356$	0.515302	+	0.737836i	0.0273109	+	0.0391052i
$357$		0			0
$358$	−0.623049	−	1.98026i	−0.0329292	−	0.104660i
$359$			16.7870i			0.885984i	0.896526	+	0.442992i	$0.146083\pi$
$359$			16.7870i			0.885984i	−0.896526	+	0.442992i	$0.853917\pi$
$360$	−0.286663	−	0.220796i	−0.0151085	−	0.0116370i
$361$	20.8779			1.09884
$362$	−9.99441	−	31.7656i	−0.525295	−	1.66956i
$363$	−4.95641			−0.260144
$364$		0			0
$365$	−1.98468			−0.103883
$366$	−0.716436	−	2.27707i	−0.0374487	−	0.119025i
$367$	4.03640			0.210698			0.105349	−	0.994435i	$-0.466404\pi$
$367$	4.03640			0.210698			0.105349	+	0.994435i	$0.466404\pi$
$368$	24.8059	+	9.09703i	1.29310	+	0.474215i
$369$			3.24650i			0.169006i
$370$	0.471263	+	1.49783i	0.0244998	+	0.0778685i
$371$		0			0
$372$	13.8610	−	9.68045i	0.718658	−	0.501908i
$373$	20.7790			1.07590			0.537948	−	0.842978i	$-0.319200\pi$
$373$	20.7790			1.07590			0.537948	+	0.842978i	$0.319200\pi$
$374$	31.4077	−	9.88181i	1.62405	−	0.510976i
$375$		−	1.27720i		−	0.0659541i
$376$	−17.2827	+	22.4384i	−0.891287	+	1.15717i
$377$		−	2.52310i		−	0.129946i
$378$		0			0
$379$		−	10.7800i		−	0.553732i	−0.960909	−	0.276866i	$-0.910704\pi$
$379$		−	10.7800i		−	0.553732i	0.960909	−	0.276866i	$-0.0892958\pi$
$380$	0.925127	+	1.32464i	0.0474580	+	0.0679528i
$381$			14.0775i			0.721211i
$382$	−1.56673	−	4.97960i	−0.0801611	−	0.254779i
$383$	6.52981			0.333658			0.166829	−	0.985986i	$-0.446647\pi$
$383$	6.52981			0.333658			0.166829	+	0.985986i	$0.446647\pi$
$384$	−6.03817	−	9.56768i	−0.308134	−	0.488249i
$385$		0			0
$386$	−3.66493	+	1.15310i	−0.186540	+	0.0586912i
$387$			0.881836i			0.0448263i
$388$	−18.5564	−	26.5701i	−0.942060	−	1.34889i
$389$	31.8697			1.61586			0.807928	−	0.589281i	$-0.200589\pi$
$389$	31.8697			1.61586			0.807928	+	0.589281i	$0.200589\pi$
$390$	−0.153880	+	0.0484155i	−0.00779204	+	0.00245161i
$391$	−38.4988			−1.94697
$392$		0			0
$393$	9.76967			0.492814
$394$	5.52886	−	1.73955i	0.278540	−	0.0876371i
$395$	1.25668			0.0632303
$396$	−4.57439	−	6.54985i	−0.229872	−	0.329142i
$397$			15.4218i			0.773997i	0.922080	+	0.386999i	$0.126488\pi$
$397$			15.4218i			0.773997i	−0.922080	+	0.386999i	$0.873512\pi$
$398$	0.280905	−	0.0883811i	0.0140805	−	0.00443015i
$399$		0			0
$400$	6.86357	−	18.7157i	0.343178	−	0.935785i
$401$	27.6959			1.38307			0.691533	−	0.722345i	$-0.256936\pi$
$401$	27.6959			1.38307			0.691533	+	0.722345i	$0.256936\pi$
$402$	2.69622	+	8.56948i	0.134475	+	0.427407i
$403$		−	7.53748i		−	0.375469i
$404$	13.8176	+	19.7847i	0.687450	+	0.984327i
$405$		−	0.127929i		−	0.00635684i
$406$		0			0
$407$			34.6692i			1.71849i
$408$	13.0603	+	10.0594i	0.646582	+	0.498017i
$409$			24.8476i			1.22864i	0.789058	+	0.614319i	$0.210569\pi$
$409$			24.8476i			1.22864i	−0.789058	+	0.614319i	$0.789431\pi$
$410$	0.560276	−	0.176280i	0.0276700	−	0.00870583i
$411$	−3.96852			−0.195753
$412$	5.38527	−	3.76105i	0.265313	−	0.185294i
$413$		0			0
$414$	2.80359	+	8.91074i	0.137789	+	0.437939i
$415$			0.189362i			0.00929541i
$416$	−5.03847	−	0.235338i	−0.247031	−	0.0115384i
$417$	0.262023			0.0128313
$418$	10.7066	+	34.0292i	0.523677	+	1.66442i
$419$	21.9087			1.07031			0.535155	−	0.844754i	$-0.320253\pi$
$419$	21.9087			1.07031			0.535155	+	0.844754i	$0.320253\pi$
$420$		0			0
$421$	−18.8226			−0.917357			−0.458679	−	0.888602i	$-0.651677\pi$
$421$	−18.8226			−0.917357			−0.458679	+	0.888602i	$0.651677\pi$
$422$	−7.03938	−	22.3735i	−0.342671	−	1.08912i
$423$	−10.0136			−0.486876
$424$	−13.0041	+	16.8834i	−0.631534	+	0.819929i
$425$			29.0467i			1.40897i
$426$	4.83252	+	15.3594i	0.234136	+	0.744163i
$427$		0			0
$428$	−3.81960	−	5.46911i	−0.184628	−	0.264359i
$429$	−3.56176			−0.171963
$430$	0.152186	−	0.0478823i	0.00733906	−	0.00230909i
$431$		−	21.8458i		−	1.05227i	−0.850400	−	0.526137i	$-0.823640\pi$
$431$		−	21.8458i		−	1.05227i	0.850400	−	0.526137i	$-0.176360\pi$
$432$	1.37722	−	3.75543i	0.0662616	−	0.180683i
$433$		−	23.7440i		−	1.14107i	−0.821275	−	0.570533i	$-0.806737\pi$
$433$		−	23.7440i		−	1.14107i	0.821275	−	0.570533i	$-0.193263\pi$
$434$		0			0
$435$		−	0.361999i		−	0.0173565i
$436$	7.31463	−	5.10851i	0.350307	−	0.244653i
$437$		−	41.7121i		−	1.99536i
$438$	−6.58476	−	20.9286i	−0.314632	−	1.00000i
$439$	−31.8858			−1.52183			−0.760914	−	0.648852i	$-0.775249\pi$
$439$	−31.8858			−1.52183			−0.760914	+	0.648852i	$0.775249\pi$
$440$	−0.881982	+	1.14509i	−0.0420468	+	0.0545900i
$441$		0			0
$442$	7.01076	−	2.20580i	0.333468	−	0.104919i
$443$		−	15.6824i		−	0.745095i	−0.928013	−	0.372548i	$-0.878484\pi$
$443$		−	15.6824i		−	0.745095i	0.928013	−	0.372548i	$-0.121516\pi$
$444$	−14.2311	+	9.93897i	−0.675380	+	0.471683i
$445$	0.0575658			0.00272888
$446$	28.7924	−	9.05895i	1.36336	−	0.428954i
$447$	2.69549			0.127492
$448$		0			0
$449$	−9.72484			−0.458943			−0.229472	−	0.973315i	$-0.573700\pi$
$449$	−9.72484			−0.458943			−0.229472	+	0.973315i	$0.573700\pi$
$450$	6.72301	−	2.11526i	0.316926	−	0.0997144i
$451$	12.9683			0.610653
$452$	−15.0241	+	10.4928i	−0.706674	+	0.493539i
$453$		−	4.31664i		−	0.202814i
$454$	−36.4198	+	11.4588i	−1.70926	+	0.537786i
$455$		0			0
$456$	−10.8991	+	14.1504i	−0.510395	+	0.662653i
$457$	−11.4077			−0.533628			−0.266814	−	0.963748i	$-0.585971\pi$
$457$	−11.4077			−0.533628			−0.266814	+	0.963748i	$0.585971\pi$
$458$	1.23807	+	3.93500i	0.0578512	+	0.183870i
$459$			5.82842i			0.272047i
$460$	1.38557	−	0.967678i	0.0646026	−	0.0451182i
$461$		−	19.6446i		−	0.914940i	−0.889225	−	0.457470i	$-0.848756\pi$
$461$		−	19.6446i		−	0.914940i	0.889225	−	0.457470i	$-0.151244\pi$
$462$		0			0
$463$			6.73057i			0.312796i	0.987694	+	0.156398i	$0.0499883\pi$
$463$			6.73057i			0.312796i	−0.987694	+	0.156398i	$0.950012\pi$
$464$	3.89710	−	10.6267i	0.180918	−	0.493331i
$465$		−	1.08143i		−	0.0501502i
$466$	27.5185	−	8.65816i	1.27477	−	0.401082i
$467$	22.1216			1.02367			0.511833	−	0.859085i	$-0.328966\pi$
$467$	22.1216			1.02367			0.511833	+	0.859085i	$0.328966\pi$
$468$	−1.02109	−	1.46204i	−0.0471997	−	0.0675830i
$469$		0			0
$470$	0.543721	+	1.72813i	0.0250800	+	0.0797125i
$471$		−	3.20616i		−	0.147732i
$472$	−1.01626	+	1.31942i	−0.0467771	+	0.0607314i
$473$	3.52254			0.161966
$474$	4.16940	+	13.2517i	0.191507	+	0.608672i
$475$	−31.4711			−1.44399
$476$		0			0
$477$	−7.53454			−0.344983
$478$	−10.7194	−	34.0700i	−0.490296	−	1.55832i
$479$	21.2649			0.971618			0.485809	−	0.874065i	$-0.338525\pi$
$479$	21.2649			0.971618			0.485809	+	0.874065i	$0.338525\pi$
$480$	−0.722888	−	0.0337648i	−0.0329952	−	0.00154114i
$481$			7.73878i			0.352858i
$482$	−3.48441	−	11.0746i	−0.158710	−	0.504434i
$483$		0			0
$484$	−8.12702	+	5.67588i	−0.369410	+	0.257995i
$485$	−2.07299			−0.0941297
$486$	1.34902	−	0.424442i	0.0611927	−	0.0192531i
$487$			35.4341i			1.60567i	0.596200	+	0.802836i	$0.296677\pi$
$487$			35.4341i			1.60567i	−0.596200	+	0.802836i	$0.703323\pi$
$488$	−3.78235	−	2.91328i	−0.171219	−	0.131878i
$489$		−	23.2619i		−	1.05194i
$490$		0			0
$491$			15.1925i			0.685628i	0.939403	+	0.342814i	$0.111380\pi$
$491$			15.1925i			0.685628i	−0.939403	+	0.342814i	$0.888620\pi$
$492$	3.71776	+	5.32328i	0.167609	+	0.239992i
$493$			16.4926i			0.742789i
$494$	2.38991	+	7.59592i	0.107527	+	0.341757i
$495$	−0.511019			−0.0229686
$496$	11.6422	−	31.7460i	0.522748	−	1.42544i
$497$		0			0
$498$	−1.99683	+	0.628263i	−0.0894801	+	0.0281532i
$499$			11.0894i			0.496431i	0.968705	+	0.248216i	$0.0798442\pi$
$499$			11.0894i			0.496431i	−0.968705	+	0.248216i	$0.920156\pi$
$500$	−1.46259	−	2.09422i	−0.0654092	−	0.0936562i
$501$	−9.66864			−0.431963
$502$	8.83849	−	2.78086i	0.394481	−	0.124116i
$503$	−5.67396			−0.252989			−0.126495	−	0.991967i	$-0.540373\pi$
$503$	−5.67396			−0.252989			−0.126495	+	0.991967i	$0.540373\pi$
$504$		0			0
$505$	1.54360			0.0686894
$506$	35.5944	−	11.1991i	1.58236	−	0.497859i
$507$	12.2050			0.542041
$508$	16.1210	+	23.0828i	0.715252	+	1.02413i
$509$		−	12.7986i		−	0.567288i	−0.958930	−	0.283644i	$-0.908457\pi$
$509$		−	12.7986i		−	0.567288i	0.958930	−	0.283644i	$-0.0915435\pi$
$510$	1.00586	−	0.316474i	0.0445402	−	0.0140137i
$511$		0			0
$512$	−20.8573	−	8.77344i	−0.921771	−	0.387735i
$513$	−6.31490			−0.278809
$514$	−7.95924	−	25.2971i	−0.351067	−	1.11581i
$515$		−	0.420158i		−	0.0185144i
$516$	1.00984	+	1.44595i	0.0444559	+	0.0636542i
$517$			39.9997i			1.75918i
$518$		0			0
$519$			20.7065i			0.908916i
$520$	−0.196874	+	0.255604i	−0.00863350	+	0.0112090i
$521$			28.2632i			1.23823i	0.785299	+	0.619117i	$0.212509\pi$
$521$			28.2632i			1.23823i	−0.785299	+	0.619117i	$0.787491\pi$
$522$	3.81729	−	1.20104i	0.167078	−	0.0525679i
$523$	10.7622			0.470599			0.235300	−	0.971923i	$-0.424393\pi$
$523$	10.7622			0.470599			0.235300	+	0.971923i	$0.424393\pi$
$524$	16.0193	−	11.1878i	0.699807	−	0.488742i
$525$		0			0
$526$	0.893560	+	2.84003i	0.0389611	+	0.123831i
$527$			49.2698i			2.14623i
$528$	−15.0012	−	5.50137i	−0.652846	−	0.239417i
$529$	−20.6307			−0.896986
$530$	0.409114	+	1.30030i	0.0177708	+	0.0564814i
$531$	−0.588819			−0.0255526
$532$		0			0
$533$	2.89475			0.125386
$534$	0.190991	+	0.607035i	0.00826501	+	0.0262690i
$535$	−0.426699			−0.0184478
$536$	14.2344	+	10.9638i	0.614832	+	0.473562i
$537$		−	1.46793i		−	0.0633457i
$538$	−5.00930	−	15.9212i	−0.215966	−	0.686413i
$539$		0			0
$540$	−0.146499	−	0.209765i	−0.00630432	−	0.00902685i
$541$	−5.32590			−0.228978			−0.114489	−	0.993424i	$-0.536523\pi$
$541$	−5.32590			−0.228978			−0.114489	+	0.993424i	$0.536523\pi$
$542$	−15.2766	+	4.80649i	−0.656187	+	0.206456i
$543$		−	23.5472i		−	1.01051i
$544$	32.9346	+	1.53832i	1.41206	+	0.0659548i
$545$		−	0.570686i		−	0.0244455i
$546$		0			0
$547$			18.5001i			0.791007i	0.918465	+	0.395503i	$0.129430\pi$
$547$			18.5001i			0.791007i	−0.918465	+	0.395503i	$0.870570\pi$
$548$	−6.50718	+	4.54459i	−0.277973	+	0.194135i
$549$		−	1.68795i		−	0.0720399i
$550$	−8.44952	−	26.8554i	−0.360289	−	1.14512i
$551$	−17.8692			−0.761252
$552$	14.8013	+	11.4004i	0.629983	+	0.485232i
$553$		0			0
$554$	−15.8696	+	4.99307i	−0.674236	+	0.212135i
$555$			1.11031i			0.0471301i
$556$	0.429638	−	0.300058i	0.0182207	−	0.0127253i
$557$	−29.9362			−1.26844			−0.634219	−	0.773153i	$-0.718678\pi$
$557$	−29.9362			−1.26844			−0.634219	+	0.773153i	$0.718678\pi$
$558$	11.4037	−	3.58796i	0.482759	−	0.151891i
$559$	0.786294			0.0332567
$560$		0			0
$561$	23.2819			0.982963
$562$	−13.2269	+	4.16157i	−0.557941	+	0.175545i
$563$	12.3772			0.521635			0.260818	−	0.965388i	$-0.416008\pi$
$563$	12.3772			0.521635			0.260818	+	0.965388i	$0.416008\pi$
$564$	−16.4192	+	11.4671i	−0.691374	+	0.482853i
$565$			1.17218i			0.0493139i
$566$	−33.2486	+	10.4610i	−1.39754	+	0.439709i
$567$		0			0
$568$	25.5128	+	19.6507i	1.07049	+	0.824525i
$569$	−36.7233			−1.53952			−0.769761	−	0.638332i	$-0.779625\pi$
$569$	−36.7233			−1.53952			−0.769761	+	0.638332i	$0.779625\pi$
$570$	0.342889	+	1.08982i	0.0143620	+	0.0456474i
$571$		−	6.32118i		−	0.264533i	−0.991214	−	0.132267i	$-0.957775\pi$
$571$		−	6.32118i		−	0.264533i	0.991214	−	0.132267i	$-0.0422255\pi$
$572$	−5.84021	+	4.07878i	−0.244191	+	0.170542i
$573$		−	3.69128i		−	0.154206i
$574$		0			0
$575$			32.9187i			1.37280i
$576$	−2.04234	−	7.73491i	−0.0850975	−	0.322288i
$577$			5.08565i			0.211718i	0.994381	+	0.105859i	$0.0337593\pi$
$577$			5.08565i			0.211718i	−0.994381	+	0.105859i	$0.966241\pi$
$578$	−22.8935	+	7.20299i	−0.952244	+	0.299605i
$579$	−2.71674			−0.112904
$580$	−0.414546	−	0.593569i	−0.0172131	−	0.0246466i
$581$		0			0
$582$	−6.87775	−	21.8598i	−0.285092	−	0.906118i
$583$			30.0971i			1.24649i
$584$	−34.7635	−	26.7759i	−1.43853	−	1.10800i
$585$	−0.114069			−0.00471615
$586$	−1.02308	−	3.25170i	−0.0422631	−	0.134326i
$587$	−30.0719			−1.24120			−0.620601	−	0.784127i	$-0.713111\pi$
$587$	−30.0719			−1.24120			−0.620601	+	0.784127i	$0.713111\pi$
$588$		0			0
$589$	−53.3821			−2.19957
$590$	0.0319719	+	0.101617i	0.00131626	+	0.00418353i
$591$	4.09843			0.168587
$592$	−11.9531	+	32.5938i	−0.491268	+	1.33960i
$593$		−	21.5543i		−	0.885130i	−0.896736	−	0.442565i	$-0.854069\pi$
$593$		−	21.5543i		−	0.885130i	0.896736	−	0.442565i	$-0.145931\pi$
$594$	−1.69545	−	5.38872i	−0.0695653	−	0.221102i
$595$		0			0
$596$	4.41978	−	3.08676i	0.181041	−	0.126439i
$597$	0.208229			0.00852225
$598$	7.94530	−	2.49983i	0.324908	−	0.102226i
$599$			18.3543i			0.749936i	0.927038	+	0.374968i	$0.122346\pi$
$599$			18.3543i			0.749936i	−0.927038	+	0.374968i	$0.877654\pi$
$600$	8.60140	−	11.1673i	0.351151	−	0.455904i
$601$			12.2204i			0.498482i	0.968441	+	0.249241i	$0.0801812\pi$
$601$			12.2204i			0.498482i	−0.968441	+	0.249241i	$0.919819\pi$
$602$		0			0
$603$			6.35238i			0.258689i
$604$	−4.94325	−	7.07799i	−0.201138	−	0.288000i
$605$			0.634069i			0.0257786i
$606$	5.12135	+	16.2774i	0.208041	+	0.661222i
$607$	−26.5749			−1.07864			−0.539322	−	0.842100i	$-0.681319\pi$
$607$	−26.5749			−1.07864			−0.539322	+	0.842100i	$0.681319\pi$
$608$	−1.66671	+	35.6835i	−0.0675942	+	1.44716i
$609$		0			0
$610$	−0.291304	+	0.0916530i	−0.0117945	+	0.00371092i
$611$			8.92864i			0.361214i
$612$	6.67447	+	9.55685i	0.269799	+	0.386313i
$613$	−19.1590			−0.773824			−0.386912	−	0.922117i	$-0.626458\pi$
$613$	−19.1590			−0.773824			−0.386912	+	0.922117i	$0.626458\pi$
$614$	32.9234	−	10.3587i	1.32868	−	0.418043i
$615$	0.415321			0.0167474
$616$		0			0
$617$	−14.7860			−0.595263			−0.297632	−	0.954681i	$-0.596197\pi$
$617$	−14.7860			−0.595263			−0.297632	+	0.954681i	$0.596197\pi$
$618$	4.43059	−	1.39400i	0.178224	−	0.0560748i
$619$	−25.3494			−1.01888			−0.509439	−	0.860507i	$-0.670147\pi$
$619$	−25.3494			−1.01888			−0.509439	+	0.860507i	$0.670147\pi$
$620$	−1.23841	−	1.77322i	−0.0497358	−	0.0712142i
$621$			6.60535i			0.265064i
$622$	42.0713	−	13.2369i	1.68691	−	0.530751i
$623$		0			0
$624$	−3.34855	−	1.22801i	−0.134049	−	0.0491596i
$625$	24.7548			0.990191
$626$	−1.07726	−	3.42391i	−0.0430561	−	0.136847i
$627$			25.2252i			1.00740i
$628$	−3.67156	−	5.25713i	−0.146511	−	0.209782i
$629$		−	50.5856i		−	2.01698i
$630$		0			0
$631$			36.7075i			1.46130i	0.682752	+	0.730650i	$0.260783\pi$
$631$			36.7075i			1.46130i	−0.682752	+	0.730650i	$0.739217\pi$
$632$	22.0119	+	16.9542i	0.875586	+	0.674403i
$633$		−	16.5850i		−	0.659195i
$634$	−24.6223	+	7.74693i	−0.977878	+	0.307670i
$635$	1.80092			0.0714673
$636$	−12.3544	+	8.62825i	−0.489883	+	0.342132i
$637$		0			0
$638$	−4.79760	−	15.2484i	−0.189939	−	0.603688i
$639$			11.3856i			0.450407i
$640$	−1.22398	+	0.772457i	−0.0483822	+	0.0305341i
$641$	−7.29371			−0.288084			−0.144042	−	0.989572i	$-0.546010\pi$
$641$	−7.29371			−0.288084			−0.144042	+	0.989572i	$0.546010\pi$
$642$	−1.41570	−	4.49956i	−0.0558731	−	0.177584i
$643$	20.6956			0.816155			0.408077	−	0.912947i	$-0.366199\pi$
$643$	20.6956			0.816155			0.408077	+	0.912947i	$0.366199\pi$
$644$		0			0
$645$	0.112812			0.00444199
$646$	−15.6220	−	49.6518i	−0.614638	−	1.95352i
$647$	−15.8548			−0.623315			−0.311658	−	0.950194i	$-0.600884\pi$
$647$	−15.8548			−0.623315			−0.311658	+	0.950194i	$0.600884\pi$
$648$	1.72593	−	2.24080i	0.0678009	−	0.0880268i
$649$			2.35206i			0.0923266i
$650$	−1.88608	−	5.99461i	−0.0739783	−	0.235128i
$651$		0			0
$652$	−26.6386	−	38.1425i	−1.04325	−	1.49377i
$653$	−28.8161			−1.12766			−0.563831	−	0.825890i	$-0.690673\pi$
$653$	−28.8161			−1.12766			−0.563831	+	0.825890i	$0.690673\pi$
$654$	6.01792	−	1.89342i	0.235319	−	0.0740385i
$655$		−	1.24982i		−	0.0488347i
$656$	12.1920	+	4.47114i	0.476017	+	0.174569i
$657$		−	15.5139i		−	0.605256i
$658$		0			0
$659$		−	20.6316i		−	0.803693i	−0.915707	−	0.401846i	$-0.868369\pi$
$659$		−	20.6316i		−	0.803693i	0.915707	−	0.401846i	$-0.131631\pi$
$660$	−0.837916	+	0.585198i	−0.0326158	+	0.0227788i
$661$			23.9517i			0.931611i	0.884887	+	0.465806i	$0.154235\pi$
$661$			23.9517i			0.931611i	−0.884887	+	0.465806i	$0.845765\pi$
$662$	−8.79756	−	27.9616i	−0.341927	−	1.08676i
$663$	5.19694			0.201832
$664$	−2.55474	+	3.31685i	−0.0991431	+	0.128719i
$665$		0			0
$666$	−11.7083	+	3.68378i	−0.453687	+	0.142744i
$667$			18.6911i			0.723721i
$668$	−15.8537	+	11.0721i	−0.613396	+	0.428394i
$669$	21.3432			0.825176
$670$	1.09628	−	0.344924i	0.0423532	−	0.0133256i
$671$	−6.74259			−0.260295
$672$		0			0
$673$	3.43936			0.132577			0.0662887	−	0.997800i	$-0.478884\pi$
$673$	3.43936			0.132577			0.0662887	+	0.997800i	$0.478884\pi$
$674$	−0.445894	+	0.140292i	−0.0171752	+	0.00540383i
$675$	4.98363			0.191820
$676$	20.0124	−	13.9766i	0.769709	−	0.537562i
$677$			33.1949i			1.27579i	0.770125	+	0.637893i	$0.220194\pi$
$677$			33.1949i			1.27579i	−0.770125	+	0.637893i	$0.779806\pi$
$678$	−12.3607	+	3.88904i	−0.474709	+	0.149358i
$679$		0			0
$680$	1.28689	−	1.67079i	0.0493501	−	0.0640720i
$681$	−26.9972			−1.03454
$682$	−14.3323	−	45.5528i	−0.548812	−	1.74431i
$683$			8.54104i			0.326814i	0.986559	+	0.163407i	$0.0522483\pi$
$683$			8.54104i			0.326814i	−0.986559	+	0.163407i	$0.947752\pi$
$684$	−10.3545	+	7.23156i	−0.395915	+	0.276506i
$685$			0.507689i			0.0193978i
$686$		0			0
$687$			2.91694i			0.111288i
$688$	3.31168	+	1.21448i	0.126256	+	0.0463017i
$689$			6.71821i			0.255943i
$690$	1.13994	−	0.358660i	0.0433969	−	0.0136540i
$691$	2.45848			0.0935249			0.0467625	−	0.998906i	$-0.485110\pi$
$691$	2.45848			0.0935249			0.0467625	+	0.998906i	$0.485110\pi$
$692$	23.7123	+	33.9525i	0.901406	+	1.29068i
$693$		0			0
$694$	9.33563	+	29.6717i	0.354375	+	1.12632i
$695$		−	0.0335203i		−	0.00127150i
$696$	4.88383	−	6.34074i	0.185121	−	0.240345i
$697$	−18.9220			−0.716720
$698$	11.3203	+	35.9795i	0.428478	+	1.36185i
$699$	20.3989			0.771559
$700$		0			0
$701$	43.1693			1.63048			0.815241	−	0.579123i	$-0.196605\pi$
$701$	43.1693			1.63048			0.815241	+	0.579123i	$0.196605\pi$
$702$	−0.378456	−	1.20286i	−0.0142839	−	0.0453990i
$703$	54.8077			2.06711
$704$	−30.8975	+	8.15822i	−1.16449	+	0.307475i
$705$			1.28103i			0.0482462i
$706$	−3.29861	−	10.4841i	−0.124145	−	0.394574i
$707$		0			0
$708$	−0.965485	+	0.674291i	−0.0362852	+	0.0253414i
$709$	26.0798			0.979447			0.489723	−	0.871878i	$-0.337098\pi$
$709$	26.0798			0.979447			0.489723	+	0.871878i	$0.337098\pi$
$710$	1.96491	−	0.618219i	0.0737417	−	0.0232014i
$711$			9.82324i			0.368400i
$712$	1.00832	+	0.776638i	0.0377884	+	0.0291057i
$713$			55.8375i			2.09113i
$714$		0			0
$715$			0.455652i			0.0170404i
$716$	−1.68101	−	2.40695i	−0.0628222	−	0.0899521i
$717$		−	25.2554i		−	0.943180i
$718$	7.12511	+	22.6460i	0.265907	+	0.845140i
$719$	−38.1219			−1.42171			−0.710854	−	0.703340i	$-0.751691\pi$
$719$	−38.1219			−1.42171			−0.710854	+	0.703340i	$0.751691\pi$
$720$	−0.480429	−	0.176187i	−0.0179045	−	0.00656608i
$721$		0			0
$722$	28.1647	−	8.86146i	1.04818	−	0.329789i
$723$		−	8.20938i		−	0.305310i
$724$	−26.9653	−	38.6103i	−1.00216	−	1.43494i
$725$	14.1021			0.523739
$726$	−6.68629	+	2.10371i	−0.248151	+	0.0780759i
$727$	−30.8059			−1.14253			−0.571264	−	0.820766i	$-0.693547\pi$
$727$	−30.8059			−1.14253			−0.571264	+	0.820766i	$0.693547\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−2.67737	+	0.842381i	−0.0990939	+	0.0311779i
$731$	−5.13971			−0.190099
$732$	−1.93297	−	2.76773i	−0.0714446	−	0.102298i
$733$		−	41.1095i		−	1.51841i	−0.650849	−	0.759207i	$-0.725587\pi$
$733$		−	41.1095i		−	1.51841i	0.650849	−	0.759207i	$-0.274413\pi$
$734$	5.44517	−	1.71322i	0.200985	−	0.0632360i
$735$		0			0
$736$	37.3248	+	1.74337i	1.37581	+	0.0642617i
$737$	25.3749			0.934696
$738$	1.37795	+	4.37958i	0.0507230	+	0.161215i
$739$		−	28.8483i		−	1.06120i	−0.847622	−	0.530600i	$-0.821967\pi$
$739$		−	28.8483i		−	1.06120i	0.847622	−	0.530600i	$-0.178033\pi$
$740$	1.27148	+	1.82058i	0.0467407	+	0.0669257i
$741$			5.63071i			0.206849i
$742$		0			0
$743$		−	0.365822i		−	0.0134207i	−0.999977	−	0.00671036i	$-0.997864\pi$
$743$		−	0.365822i		−	0.0134207i	0.999977	−	0.00671036i	$-0.00213599\pi$
$744$	14.5899	−	18.9423i	0.534892	−	0.694457i
$745$		−	0.344831i		−	0.0126336i
$746$	28.0312	−	8.81948i	1.02630	−	0.322904i
$747$	−1.48021			−0.0541581
$748$	38.1753	−	26.6615i	1.39583	−	0.974841i
$749$		0			0
$750$	−0.542096	−	1.72296i	−0.0197945	−	0.0629136i
$751$			19.9623i			0.728434i	0.931314	+	0.364217i	$0.118663\pi$
$751$			19.9623i			0.728434i	−0.931314	+	0.364217i	$0.881337\pi$
$752$	−13.7909	+	37.6052i	−0.502902	+	1.37132i
$753$	6.55180			0.238761
$754$	−1.07091	−	3.40371i	−0.0390002	−	0.123956i
$755$	−0.552224			−0.0200975
$756$		0			0
$757$	−3.04476			−0.110664			−0.0553319	−	0.998468i	$-0.517622\pi$
$757$	−3.04476			−0.110664			−0.0553319	+	0.998468i	$0.517622\pi$
$758$	−4.57549	−	14.5424i	−0.166189	−	0.528205i
$759$	26.3854			0.957729
$760$	1.81025	+	1.39431i	0.0656646	+	0.0505768i
$761$			7.52068i			0.272624i	0.990666	+	0.136312i	$0.0435250\pi$
$761$			7.52068i			0.272624i	−0.990666	+	0.136312i	$0.956475\pi$
$762$	5.97507	+	18.9908i	0.216454	+	0.687963i
$763$		0			0
$764$	−4.22711	−	6.05259i	−0.152931	−	0.218975i
$765$	0.745624			0.0269581
$766$	8.80884	−	2.77153i	0.318276	−	0.100139i
$767$			0.525023i			0.0189575i
$768$	−12.2065	−	10.3441i	−0.440465	−	0.373261i
$769$			42.4363i			1.53029i	0.643857	+	0.765146i	$0.277333\pi$
$769$			42.4363i			1.53029i	−0.643857	+	0.765146i	$0.722667\pi$
$770$		0			0
$771$		−	18.7522i		−	0.675346i
$772$	−4.45464	+	3.11110i	−0.160326	+	0.111971i
$773$		−	23.7646i		−	0.854752i	−0.904074	−	0.427376i	$-0.859438\pi$
$773$		−	23.7646i		−	0.854752i	0.904074	−	0.427376i	$-0.140562\pi$
$774$	0.374288	+	1.18961i	0.0134535	+	0.0427598i
$775$	42.1285			1.51330
$776$	−36.3104	−	27.9673i	−1.30347	−	1.00397i
$777$		0			0
$778$	42.9928	−	13.5268i	1.54137	−	0.484960i
$779$		−	20.5013i		−	0.734535i
$780$	−0.187038	+	0.130627i	−0.00669703	+	0.00467718i
$781$	45.4803			1.62741
$782$	−51.9355	+	16.3405i	−1.85721	+	0.584335i
$783$	2.82968			0.101125
$784$		0			0
$785$	−0.410160			−0.0146393
$786$	13.1795	−	4.14666i	0.470096	−	0.147906i
$787$	−19.9519			−0.711210			−0.355605	−	0.934636i	$-0.615725\pi$
$787$	−19.9519			−0.711210			−0.355605	+	0.934636i	$0.615725\pi$
$788$	6.72019	−	4.69336i	0.239397	−	0.167194i
$789$			2.10526i			0.0749492i
$790$	1.69528	−	0.533387i	0.0603154	−	0.0189770i
$791$		0			0
$792$	−8.95097	−	6.89430i	−0.318059	−	0.244978i
$793$	−1.50507			−0.0534465
$794$	6.54565	+	20.8043i	0.232296	+	0.738316i
$795$			0.963886i			0.0341855i
$796$	0.341433	−	0.238455i	0.0121018	−	0.00845183i
$797$		−	27.9236i		−	0.989106i	−0.869147	−	0.494553i	$-0.835332\pi$
$797$		−	27.9236i		−	0.989106i	0.869147	−	0.494553i	$-0.164668\pi$
$798$		0			0
$799$		−	58.3633i		−	2.06474i
$800$	1.31535	−	28.1610i	0.0465046	−	0.995641i
$801$			0.449983i			0.0158994i
$802$	37.3622	−	11.7553i	1.31931	−	0.415093i
$803$	−61.9711			−2.18691
$804$	7.27449	+	10.4160i	0.256551	+	0.367344i
$805$		0			0
$806$	−3.19922	−	10.1682i	−0.112688	−	0.358160i
$807$		−	11.8021i		−	0.415453i
$808$	27.0376	+	20.8252i	0.951181	+	0.732628i
$809$	−21.7399			−0.764333			−0.382166	−	0.924094i	$-0.624822\pi$
$809$	−21.7399			−0.764333			−0.382166	+	0.924094i	$0.624822\pi$
$810$	−0.0542984	−	0.172579i	−0.00190785	−	0.00606379i
$811$	21.4122			0.751885			0.375942	−	0.926643i	$-0.377319\pi$
$811$	21.4122			0.751885			0.375942	+	0.926643i	$0.377319\pi$
$812$		0			0
$813$	−11.3243			−0.397159
$814$	14.7150	+	46.7693i	0.515762	+	1.63926i
$815$	−2.97587			−0.104240
$816$	21.8882	+	8.02702i	0.766241	+	0.281002i
$817$		−	5.56870i		−	0.194824i
$818$	10.5464	+	33.5199i	0.368746	+	1.17200i
$819$		0			0
$820$	0.681001	−	0.475609i	0.0237816	−	0.0166090i
$821$	−26.7099			−0.932183			−0.466092	−	0.884736i	$-0.654338\pi$
$821$	−26.7099			−0.932183			−0.466092	+	0.884736i	$0.654338\pi$
$822$	−5.35361	+	1.68441i	−0.186729	+	0.0587505i
$823$		−	24.2476i		−	0.845217i	−0.906312	−	0.422608i	$-0.861115\pi$
$823$		−	24.2476i		−	0.845217i	0.906312	−	0.422608i	$-0.138885\pi$
$824$	5.66848	−	7.35946i	0.197471	−	0.256379i
$825$		−	19.9074i		−	0.693085i
$826$		0			0
$827$			34.2930i			1.19248i	0.802805	+	0.596242i	$0.203340\pi$
$827$			34.2930i			1.19248i	−0.802805	+	0.596242i	$0.796660\pi$
$828$	7.56418	+	10.8308i	0.262873	+	0.376396i
$829$		−	0.807148i		−	0.0280334i	−0.999902	−	0.0140167i	$-0.995538\pi$
$829$		−	0.807148i		−	0.0280334i	0.999902	−	0.0140167i	$-0.00446180\pi$
$830$	0.0803731	+	0.255453i	0.00278979	+	0.00886689i
$831$	−11.7638			−0.408083
$832$	−6.89687	+	1.82106i	−0.239106	+	0.0631340i
$833$		0			0
$834$	0.353473	−	0.111213i	0.0122398	−	0.00385101i
$835$			1.23690i			0.0428047i
$836$	28.8868	+	41.3616i	0.999071	+	1.43052i
$837$	8.45337			0.292191
$838$	29.5552	−	9.29896i	1.02097	−	0.321227i
$839$	27.7282			0.957284			0.478642	−	0.878010i	$-0.341129\pi$
$839$	27.7282			0.957284			0.478642	+	0.878010i	$0.341129\pi$
$840$		0			0
$841$	−20.9929			−0.723893
$842$	−25.3920	+	7.98910i	−0.875067	+	0.275322i
$843$	−9.80481			−0.337696
$844$	−18.9925	−	27.1944i	−0.653748	−	0.936071i
$845$		−	1.56137i		−	0.0537127i
$846$	−13.5085	+	4.25018i	−0.464431	+	0.146124i
$847$		0			0
$848$	−10.3767	+	28.2954i	−0.356338	+	0.971670i
$849$	−24.6465			−0.845866
$850$	12.3286	+	39.1845i	0.422869	+	1.34402i
$851$		−	57.3287i		−	1.96520i
$852$	13.0383	+	18.6689i	0.446685	+	0.639587i
$853$			16.3380i			0.559402i	0.960087	+	0.279701i	$0.0902354\pi$
$853$			16.3380i			0.559402i	−0.960087	+	0.279701i	$0.909765\pi$
$854$		0			0
$855$			0.807859i			0.0276282i
$856$	−7.47403	−	5.75672i	−0.255457	−	0.196761i
$857$			29.5296i			1.00871i	0.863496	+	0.504355i	$0.168270\pi$
$857$			29.5296i			1.00871i	−0.863496	+	0.504355i	$0.831730\pi$
$858$	−4.80487	+	1.51176i	−0.164036	+	0.0516106i
$859$	15.1259			0.516090			0.258045	−	0.966133i	$-0.416922\pi$
$859$	15.1259			0.516090			0.258045	+	0.966133i	$0.416922\pi$
$860$	0.184978	−	0.129188i	0.00630771	−	0.00440528i
$861$		0			0
$862$	−9.27225	−	29.4703i	−0.315814	−	1.00376i
$863$		−	16.1792i		−	0.550748i	−0.961337	−	0.275374i	$-0.911198\pi$
$863$		−	16.1792i		−	0.550748i	0.961337	−	0.275374i	$-0.0888016\pi$
$864$	0.263934	−	5.65069i	0.00897921	−	0.192241i
$865$	2.64897			0.0900676
$866$	−10.0780	−	32.0311i	−0.342463	−	1.08846i
$867$	−16.9705			−0.576348
$868$		0			0
$869$	39.2394			1.33111
$870$	−0.153647	−	0.488343i	−0.00520913	−	0.0165564i
$871$	5.66413			0.191922
$872$	7.69930	−	9.99611i	0.260731	−	0.338511i
$873$		−	16.2042i		−	0.548430i
$874$	−17.7044	−	56.2704i	−0.598859	−	1.90337i
$875$		0			0
$876$	−17.7659	−	25.4381i	−0.600254	−	0.859475i
$877$	39.6822			1.33997			0.669987	−	0.742373i	$-0.266300\pi$
$877$	39.6822			1.33997			0.669987	+	0.742373i	$0.266300\pi$
$878$	−43.0146	+	13.5337i	−1.45167	+	0.456740i
$879$		−	2.41042i		−	0.0813014i
$880$	−0.703786	+	1.91910i	−0.0237246	+	0.0646927i
$881$		−	27.4290i		−	0.924106i	−0.886852	−	0.462053i	$-0.847113\pi$
$881$		−	27.4290i		−	0.924106i	0.886852	−	0.462053i	$-0.152887\pi$
$882$		0			0
$883$		−	37.1425i		−	1.24994i	−0.780647	−	0.624972i	$-0.785110\pi$
$883$		−	37.1425i		−	1.24994i	0.780647	−	0.624972i	$-0.214890\pi$
$884$	8.52141	−	5.95132i	0.286606	−	0.200165i
$885$			0.0753270i			0.00253209i
$886$	−6.65628	−	21.1559i	−0.223622	−	0.710746i
$887$	27.7126			0.930497			0.465248	−	0.885180i	$-0.345965\pi$
$887$	27.7126			0.930497			0.465248	+	0.885180i	$0.345965\pi$
$888$	−14.9795	+	19.4481i	−0.502681	+	0.652637i
$889$		0			0
$890$	0.0776574	−	0.0244334i	0.00260308	−	0.000819008i
$891$		−	3.99455i		−	0.133822i
$892$	34.9964	−	24.4414i	1.17177	−	0.818358i
$893$	63.2346			2.11607
$894$	3.63626	−	1.14408i	0.121615	−	0.0382637i
$895$	−0.187790			−0.00627714
$896$		0			0
$897$	5.88969			0.196651
$898$	−13.1190	+	4.12763i	−0.437786	+	0.137741i
$899$	23.9203			0.797788
$900$	8.17166	−	5.70705i	0.272389	−	0.190235i
$901$		−	43.9145i		−	1.46300i
$902$	17.4944	−	5.50428i	0.582501	−	0.183273i
$903$		0			0
$904$	−15.8142	+	20.5318i	−0.525973	+	0.682877i
$905$	−3.01237			−0.100135
$906$	−1.83216	−	5.82323i	−0.0608696	−	0.193464i
$907$			39.9740i			1.32732i	0.748036	+	0.663658i	$0.230997\pi$
$907$			39.9740i			1.32732i	−0.748036	+	0.663658i	$0.769003\pi$
$908$	−44.2673	+	30.9161i	−1.46906	+	1.02599i
$909$			12.0661i			0.400207i
$910$		0			0
$911$		−	35.0711i		−	1.16196i	−0.813918	−	0.580979i	$-0.802670\pi$
$911$		−	35.0711i		−	1.16196i	0.813918	−	0.580979i	$-0.197330\pi$
$912$	−8.69701	+	23.7152i	−0.287987	+	0.785287i
$913$			5.91277i			0.195684i
$914$	−15.3891	+	4.84189i	−0.509028	+	0.160155i
$915$	−0.215938			−0.00713868
$916$	3.34036	+	4.78290i	0.110369	+	0.158031i
$917$		0			0
$918$	2.47383	+	7.86264i	0.0816484	+	0.259506i
$919$			0.330846i			0.0109136i	0.999985	+	0.00545681i	$0.00173696\pi$
$919$			0.330846i			0.0109136i	−0.999985	+	0.00545681i	$0.998263\pi$
$920$	1.45844	−	1.89351i	0.0480833	−	0.0624272i
$921$	24.4054			0.804187
$922$	−8.33799	−	26.5009i	−0.274597	−	0.872761i
$923$	10.1520			0.334157
$924$		0			0
$925$	−43.2536			−1.42217
$926$	2.85674	+	9.07966i	0.0938782	+	0.298376i
$927$	3.28431			0.107871
$928$	0.746849	−	15.9897i	0.0245165	−	0.524887i
$929$			28.4574i			0.933658i	0.884348	+	0.466829i	$0.154604\pi$
$929$			28.4574i			0.933658i	−0.884348	+	0.466829i	$0.845396\pi$
$930$	−0.459004	−	1.45887i	−0.0150513	−	0.0478382i
$931$		0			0
$932$	33.4481	−	23.3600i	1.09563	−	0.765183i
$933$	31.1866			1.02100
$934$	29.8425	−	9.38934i	0.976476	−	0.307229i
$935$		−	2.97843i		−	0.0974051i
$936$	−1.99802	−	1.53893i	−0.0653072	−	0.0503016i
$937$		−	11.8966i		−	0.388645i	−0.980938	−	0.194323i	$-0.937749\pi$
$937$		−	11.8966i		−	0.388645i	0.980938	−	0.194323i	$-0.0622509\pi$
$938$		0			0
$939$		−	2.53807i		−	0.0828269i
$940$	1.46698	+	2.10050i	0.0478475	+	0.0685106i
$941$			16.7967i			0.547556i	0.961793	+	0.273778i	$0.0882733\pi$
$941$			16.7967i			0.547556i	−0.961793	+	0.273778i	$0.911727\pi$
$942$	−1.36083	−	4.32516i	−0.0443381	−	0.140921i
$943$	−21.4443			−0.698321
$944$	−0.810934	+	2.21127i	−0.0263936	+	0.0719707i
$945$		0			0
$946$	4.75197	−	1.49511i	0.154500	−	0.0486103i
$947$		−	20.6321i		−	0.670455i	−0.942137	−	0.335227i	$-0.891187\pi$
$947$		−	20.6321i		−	0.670455i	0.942137	−	0.335227i	$-0.108813\pi$
$948$	11.2492	+	16.1072i	0.365356	+	0.523136i
$949$	−13.8331			−0.449040
$950$	−42.4551	+	13.3577i	−1.37743	+	0.433380i
$951$	−18.2520			−0.591863
$952$		0			0
$953$	21.9025			0.709492			0.354746	−	0.934963i	$-0.384567\pi$
$953$	21.9025			0.709492			0.354746	+	0.934963i	$0.384567\pi$
$954$	−10.1642	+	3.19797i	−0.329079	+	0.103538i
$955$	−0.472222			−0.0152807
$956$	−28.9215	−	41.4112i	−0.935387	−	1.33934i
$957$		−	11.3033i		−	0.365384i
$958$	28.6867	−	9.02571i	0.926826	−	0.291608i
$959$		0			0
$960$	−0.989520	+	0.261274i	−0.0319366	+	0.00843260i
$961$	40.4594			1.30514
$962$	3.28466	+	10.4398i	0.105902	+	0.336591i
$963$		−	3.33543i		−	0.107483i
$964$	−9.40105	−	13.4609i	−0.302787	−	0.433547i
$965$			0.347550i			0.0111880i
$966$		0			0
$967$			0.651178i			0.0209405i	0.999945	+	0.0104702i	$0.00333284\pi$
$967$			0.651178i			0.0209405i	−0.999945	+	0.0104702i	$0.996667\pi$
$968$	−8.55441	+	11.1063i	−0.274949	+	0.356970i
$969$		−	36.8059i		−	1.18238i
$970$	−2.79650	+	0.879864i	−0.0897903	+	0.0282507i
$971$	59.4641			1.90829			0.954147	−	0.299338i	$-0.0967659\pi$
$971$	59.4641			1.90829			0.954147	+	0.299338i	$0.0967659\pi$
$972$	1.63970	−	1.14516i	0.0525933	−	0.0367310i
$973$		0			0
$974$	15.0397	+	47.8012i	0.481904	+	1.53165i
$975$		−	4.44368i		−	0.142312i
$976$	−6.33898	−	2.32468i	−0.202906	−	0.0744111i
$977$	−22.2437			−0.711639			−0.355819	−	0.934555i	$-0.615798\pi$
$977$	−22.2437			−0.711639			−0.355819	+	0.934555i	$0.615798\pi$
$978$	−9.87332	−	31.3807i	−0.315714	−	1.00344i
$979$	1.79748			0.0574476
$980$		0			0
$981$	4.46096			0.142428
$982$	6.44834	+	20.4950i	0.205775	+	0.654021i
$983$	−19.0956			−0.609055			−0.304527	−	0.952504i	$-0.598498\pi$
$983$	−19.0956			−0.609055			−0.304527	+	0.952504i	$0.598498\pi$
$984$	7.27474	+	5.60322i	0.231910	+	0.178624i
$985$		−	0.524309i		−	0.0167059i
$986$	7.00014	+	22.2488i	0.222930	+	0.708546i
$987$		0			0
$988$	6.44806	+	9.23266i	0.205140	+	0.293730i
$989$	−5.82484			−0.185219
$990$	−0.689373	+	0.216898i	−0.0219097	+	0.00689346i
$991$		−	27.3523i		−	0.868876i	−0.900702	−	0.434438i	$-0.856947\pi$
$991$		−	27.3523i		−	0.868876i	0.900702	−	0.434438i	$-0.143053\pi$
$992$	2.23113	−	47.7674i	0.0708384	−	1.51662i
$993$		−	20.7274i		−	0.657763i
$994$		0			0
$995$		−	0.0266385i		−	0.000844499i
$996$	−2.42710	+	1.69508i	−0.0769056	+	0.0537106i
$997$			32.6936i			1.03542i	0.855557	+	0.517708i	$0.173215\pi$
$997$			32.6936i			1.03542i	−0.855557	+	0.517708i	$0.826785\pi$
$998$	4.70682	+	14.9598i	0.148992	+	0.473546i
$999$	−8.67912			−0.274595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.b.d.391.11	yes	12
3.2	odd	2		1764.2.b.m.1567.2		12
4.3	odd	2		588.2.b.c.391.12	yes	12
7.2	even	3		588.2.o.e.31.4		24
7.3	odd	6		588.2.o.f.19.7		24
7.4	even	3		588.2.o.e.19.7		24
7.5	odd	6		588.2.o.f.31.4		24
7.6	odd	2		588.2.b.c.391.11	✓	12
12.11	even	2		1764.2.b.l.1567.1		12
21.20	even	2		1764.2.b.l.1567.2		12
28.3	even	6		588.2.o.e.19.4		24
28.11	odd	6		588.2.o.f.19.4		24
28.19	even	6		588.2.o.e.31.7		24
28.23	odd	6		588.2.o.f.31.7		24
28.27	even	2	inner	588.2.b.d.391.12	yes	12
84.83	odd	2		1764.2.b.m.1567.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.11	✓	12	7.6	odd	2
588.2.b.c.391.12	yes	12	4.3	odd	2
588.2.b.d.391.11	yes	12	1.1	even	1	trivial
588.2.b.d.391.12	yes	12	28.27	even	2	inner
588.2.o.e.19.4		24	28.3	even	6
588.2.o.e.19.7		24	7.4	even	3
588.2.o.e.31.4		24	7.2	even	3
588.2.o.e.31.7		24	28.19	even	6
588.2.o.f.19.4		24	28.11	odd	6
588.2.o.f.19.7		24	7.3	odd	6
588.2.o.f.31.4		24	7.5	odd	6
588.2.o.f.31.7		24	28.23	odd	6
1764.2.b.l.1567.1		12	12.11	even	2
1764.2.b.l.1567.2		12	21.20	even	2
1764.2.b.m.1567.1		12	84.83	odd	2
1764.2.b.m.1567.2		12	3.2	odd	2

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34902 - 0.424442i) q^{2} +1.00000 q^{3} +(1.63970 - 1.14516i) q^{4} -0.127929i q^{5} +(1.34902 - 0.424442i) q^{6} +(1.72593 - 2.24080i) q^{8} +1.00000 q^{9} +(-0.0542984 - 0.172579i) q^{10} -3.99455i q^{11} +(1.63970 - 1.14516i) q^{12} -0.891655i q^{13} -0.127929i q^{15} +(1.37722 - 3.75543i) q^{16} +5.82842i q^{17} +(1.34902 - 0.424442i) q^{18} -6.31490 q^{19} +(-0.146499 - 0.209765i) q^{20} +(-1.69545 - 5.38872i) q^{22} +6.60535i q^{23} +(1.72593 - 2.24080i) q^{24} +4.98363 q^{25} +(-0.378456 - 1.20286i) q^{26} +1.00000 q^{27} +2.82968 q^{29} +(-0.0542984 - 0.172579i) q^{30} +8.45337 q^{31} +(0.263934 - 5.65069i) q^{32} -3.99455i q^{33} +(2.47383 + 7.86264i) q^{34} +(1.63970 - 1.14516i) q^{36} -8.67912 q^{37} +(-8.51891 + 2.68031i) q^{38} -0.891655i q^{39} +(-0.286663 - 0.220796i) q^{40} +3.24650i q^{41} +0.881836i q^{43} +(-4.57439 - 6.54985i) q^{44} -0.127929i q^{45} +(2.80359 + 8.91074i) q^{46} -10.0136 q^{47} +(1.37722 - 3.75543i) q^{48} +(6.72301 - 2.11526i) q^{50} +5.82842i q^{51} +(-1.02109 - 1.46204i) q^{52} -7.53454 q^{53} +(1.34902 - 0.424442i) q^{54} -0.511019 q^{55} -6.31490 q^{57} +(3.81729 - 1.20104i) q^{58} -0.588819 q^{59} +(-0.146499 - 0.209765i) q^{60} -1.68795i q^{61} +(11.4037 - 3.58796i) q^{62} +(-2.04234 - 7.73491i) q^{64} -0.114069 q^{65} +(-1.69545 - 5.38872i) q^{66} +6.35238i q^{67} +(6.67447 + 9.55685i) q^{68} +6.60535i q^{69} +11.3856i q^{71} +(1.72593 - 2.24080i) q^{72} -15.5139i q^{73} +(-11.7083 + 3.68378i) q^{74} +4.98363 q^{75} +(-10.3545 + 7.23156i) q^{76} +(-0.378456 - 1.20286i) q^{78} +9.82324i q^{79} +(-0.480429 - 0.176187i) q^{80} +1.00000 q^{81} +(1.37795 + 4.37958i) q^{82} -1.48021 q^{83} +0.745624 q^{85} +(0.374288 + 1.18961i) q^{86} +2.82968 q^{87} +(-8.95097 - 6.89430i) q^{88} +0.449983i q^{89} +(-0.0542984 - 0.172579i) q^{90} +(7.56418 + 10.8308i) q^{92} +8.45337 q^{93} +(-13.5085 + 4.25018i) q^{94} +0.807859i q^{95} +(0.263934 - 5.65069i) q^{96} -16.2042i q^{97} -3.99455i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 12 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{8} + 12 q^{9} - 4 q^{12} - 4 q^{16} + 4 q^{18} - 24 q^{20} + 4 q^{24} - 12 q^{25} + 24 q^{26} + 12 q^{27} + 32 q^{29} + 16 q^{31} + 4 q^{32} + 32 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) \) 12 * q + 4 * q^2 + 12 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^8 + 12 * q^9 - 4 * q^12 - 4 * q^16 + 4 * q^18 - 24 * q^20 + 4 * q^24 - 12 * q^25 + 24 * q^26 + 12 * q^27 + 32 * q^29 + 16 * q^31 + 4 * q^32 + 32 * q^34 - 4 * q^36 + 32 * q^37 - 24 * q^38 - 32 * q^40 - 24 * q^44 + 24 * q^46 - 4 * q^48 - 28 * q^50 + 32 * q^52 - 32 * q^53 + 4 * q^54 + 16 * q^55 + 16 * q^58 - 16 * q^59 - 24 * q^60 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 4 * q^72 - 32 * q^74 - 12 * q^75 - 32 * q^76 + 24 * q^78 - 16 * q^80 + 12 * q^81 + 32 * q^82 - 16 * q^83 + 16 * q^85 - 24 * q^86 + 32 * q^87 + 24 * q^88 + 16 * q^93 + 4 * q^96

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