LMFDB - Embedded newform 279.2.i.c.190.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [279,2,Mod(64,279)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(279, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("279.64"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	279.i (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.22782621639$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 13 x^{14} - 28 x^{13} + 90 x^{12} - 119 x^{11} + 382 x^{10} - 356 x^{9} + 1869 x^{8} + \cdots + 81 $ x^16 - 3x^15 + 13x^14 - 28x^13 + 90x^12 - 119x^11 + 382x^10 - 356x^9 + 1869x^8 - 2812x^7 + 5846x^6 - 4987x^5 + 4006x^4 - 1014x^3 + 2493x^2 + 729*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 93)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.3
Root			$0.516428 + 1.58940i$ of defining polynomial
Character	$\chi$	$=$	279.190
Dual form			279.2.i.c.163.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.516428 + 1.58940i) q^{2} +(-0.641469 + 0.466054i) q^{4} -3.89560 q^{5} +(-3.65161 + 2.65305i) q^{7} +(1.63203 + 1.18574i) q^{8} +(-2.01180 - 6.19168i) q^{10} +(0.271099 - 0.196965i) q^{11} +(-0.539553 + 1.66057i) q^{13} +(-6.10256 - 4.43377i) q^{14} +(-1.53183 + 4.71449i) q^{16} +(-2.80760 - 2.03984i) q^{17} +(0.0654667 + 0.201486i) q^{19} +(2.49891 - 1.81556i) q^{20} +(0.453060 + 0.329167i) q^{22} +(2.21890 + 1.61213i) q^{23} +10.1757 q^{25} -2.91796 q^{26} +(1.10593 - 3.40369i) q^{28} +(2.23666 + 6.88374i) q^{29} +(5.52424 + 0.694857i) q^{31} -4.24970 q^{32} +(1.79221 - 5.51585i) q^{34} +(14.2252 - 10.3352i) q^{35} -7.41580 q^{37} +(-0.286433 + 0.208106i) q^{38} +(-6.35775 - 4.61918i) q^{40} +(-2.01180 - 6.19168i) q^{41} +(0.944828 + 2.90788i) q^{43} +(-0.0821051 + 0.252694i) q^{44} +(-1.41641 + 4.35927i) q^{46} +(-1.03045 + 3.17140i) q^{47} +(4.13246 - 12.7184i) q^{49} +(5.25503 + 16.1733i) q^{50} +(-0.427811 - 1.31667i) q^{52} +(9.81866 + 7.13368i) q^{53} +(-1.05609 + 0.767297i) q^{55} -9.10537 q^{56} +(-9.78596 + 7.10992i) q^{58} +(0.423851 - 1.30448i) q^{59} +3.58978 q^{61} +(1.74846 + 9.13908i) q^{62} +(0.868998 + 2.67450i) q^{64} +(2.10188 - 6.46893i) q^{65} -1.37225 q^{67} +2.75167 q^{68} +(23.7731 + 17.2722i) q^{70} +(-1.40560 - 1.02123i) q^{71} +(-10.5313 + 7.65141i) q^{73} +(-3.82973 - 11.7867i) q^{74} +(-0.135898 - 0.0987358i) q^{76} +(-0.467390 + 1.43848i) q^{77} +(-6.88408 - 5.00157i) q^{79} +(5.96740 - 18.3658i) q^{80} +(8.80212 - 6.39512i) q^{82} +(2.45898 + 7.56796i) q^{83} +(10.9373 + 7.94642i) q^{85} +(-4.13386 + 3.00343i) q^{86} +0.675992 q^{88} +(-6.51582 + 4.73402i) q^{89} +(-2.43534 - 7.49522i) q^{91} -2.17469 q^{92} -5.57278 q^{94} +(-0.255032 - 0.784909i) q^{95} +(2.78687 - 2.02478i) q^{97} +22.3488 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 9 q^{4} - 6 q^{5} - 7 q^{7} + 2 q^{8} - 3 q^{10} - 10 q^{11} - 3 q^{13} + 4 q^{14} - 17 q^{16} + q^{17} - 4 q^{19} - 7 q^{20} + 10 q^{22} - 7 q^{23} + 30 q^{25} + 16 q^{26} + 9 q^{28}+ \cdots + 82 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 9 * q^4 - 6 * q^5 - 7 * q^7 + 2 * q^8 - 3 * q^10 - 10 * q^11 - 3 * q^13 + 4 * q^14 - 17 * q^16 + q^17 - 4 * q^19 - 7 * q^20 + 10 * q^22 - 7 * q^23 + 30 * q^25 + 16 * q^26 + 9 * q^28 + 2 * q^29 - 13 * q^31 - 108 * q^32 - 4 * q^34 + 33 * q^35 - 28 * q^37 + 62 * q^38 - 27 * q^40 - 3 * q^41 - 13 * q^43 + 64 * q^44 - q^46 + 20 * q^47 + q^49 + 44 * q^50 + 88 * q^52 + 4 * q^53 - 8 * q^55 - 104 * q^56 - 31 * q^58 - 49 * q^59 + 13 * q^62 - 26 * q^64 + q^65 + 60 * q^67 + 30 * q^68 + 85 * q^70 - 23 * q^71 - 17 * q^73 - 70 * q^74 + 7 * q^76 - 2 * q^77 - 13 * q^79 + 94 * q^80 - 9 * q^82 + 49 * q^83 - 4 * q^85 - 24 * q^86 - 32 * q^88 - 3 * q^89 - 2 * q^91 + 70 * q^92 + 74 * q^94 + 10 * q^95 + 3 * q^97 + 82 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.516428	+	1.58940i	0.365170	+	1.12388i	0.949875	+	0.312631i	$0.101210\pi$
$2$	0.516428	+	1.58940i	0.365170	+	1.12388i	−0.584705	+	0.811246i	$0.698790\pi$
$3$		0			0
$3$		0			0
$4$	−0.641469	+	0.466054i	−0.320734	+	0.233027i
$5$	−3.89560			−1.74217			−0.871083	−	0.491136i	$-0.836582\pi$
$5$	−3.89560			−1.74217			−0.871083	+	0.491136i	$0.836582\pi$
$6$		0			0
$7$	−3.65161	+	2.65305i	−1.38018	+	1.00276i	−0.383315	+	0.923618i	$0.625217\pi$
$7$	−3.65161	+	2.65305i	−1.38018	+	1.00276i	−0.996863	+	0.0791402i	$0.974783\pi$
$8$	1.63203	+	1.18574i	0.577011	+	0.419223i
$9$		0			0
$10$	−2.01180	−	6.19168i	−0.636187	−	1.95798i
$11$	0.271099	−	0.196965i	0.0817394	−	0.0593872i	−0.546165	−	0.837678i	$-0.683913\pi$
$11$	0.271099	−	0.196965i	0.0817394	−	0.0593872i	0.627904	+	0.778290i	$0.283913\pi$
$12$		0			0
$13$	−0.539553	+	1.66057i	−0.149645	+	0.460560i	−0.997579	−	0.0695418i	$-0.977846\pi$
$13$	−0.539553	+	1.66057i	−0.149645	+	0.460560i	0.847934	+	0.530102i	$0.177846\pi$
$14$	−6.10256	−	4.43377i	−1.63098	−	1.18497i
$15$		0			0
$16$	−1.53183	+	4.71449i	−0.382958	+	1.17862i
$17$	−2.80760	−	2.03984i	−0.680944	−	0.494735i	0.192727	−	0.981252i	$-0.438267\pi$
$17$	−2.80760	−	2.03984i	−0.680944	−	0.494735i	−0.873671	+	0.486518i	$0.838267\pi$
$18$		0			0
$19$	0.0654667	+	0.201486i	0.0150191	+	0.0462240i	0.958285	−	0.285814i	$-0.0922639\pi$
$19$	0.0654667	+	0.201486i	0.0150191	+	0.0462240i	−0.943266	+	0.332038i	$0.892264\pi$
$20$	2.49891	−	1.81556i	0.558772	−	0.405972i
$21$		0			0
$22$	0.453060	+	0.329167i	0.0965927	+	0.0701787i
$23$	2.21890	+	1.61213i	0.462673	+	0.336151i	0.794579	−	0.607161i	$-0.207692\pi$
$23$	2.21890	+	1.61213i	0.462673	+	0.336151i	−0.331906	+	0.943312i	$0.607692\pi$
$24$		0			0
$25$	10.1757			2.03514
$26$	−2.91796			−0.572259
$27$		0			0
$28$	1.10593	−	3.40369i	0.209001	−	0.643238i
$29$	2.23666	+	6.88374i	0.415338	+	1.27828i	0.911948	+	0.410305i	$0.134578\pi$
$29$	2.23666	+	6.88374i	0.415338	+	1.27828i	−0.496610	+	0.867974i	$0.665422\pi$
$30$		0			0
$31$	5.52424	+	0.694857i	0.992182	+	0.124800i
$31$	5.52424	+	0.694857i	0.992182	+	0.124800i
$32$	−4.24970			−0.751247
$33$		0			0
$34$	1.79221	−	5.51585i	0.307361	−	0.945960i
$35$	14.2252	−	10.3352i	2.40450	−	1.74697i
$36$		0			0
$37$	−7.41580			−1.21915			−0.609575	−	0.792729i	$-0.708660\pi$
$37$	−7.41580			−1.21915			−0.609575	+	0.792729i	$0.708660\pi$
$38$	−0.286433	+	0.208106i	−0.0464656	+	0.0337593i
$39$		0			0
$40$	−6.35775	−	4.61918i	−1.00525	−	0.730356i
$41$	−2.01180	−	6.19168i	−0.314190	−	0.966978i	−0.976086	−	0.217383i	$-0.930248\pi$
$41$	−2.01180	−	6.19168i	−0.314190	−	0.966978i	0.661896	−	0.749595i	$-0.269752\pi$
$42$		0			0
$43$	0.944828	+	2.90788i	0.144085	+	0.443448i	0.996892	−	0.0787779i	$-0.0251018\pi$
$43$	0.944828	+	2.90788i	0.144085	+	0.443448i	−0.852807	+	0.522226i	$0.825102\pi$
$44$	−0.0821051	+	0.252694i	−0.0123778	+	0.0380950i
$45$		0			0
$46$	−1.41641	+	4.35927i	−0.208839	+	0.642740i
$47$	−1.03045	+	3.17140i	−0.150307	+	0.462596i	−0.997655	−	0.0684411i	$-0.978197\pi$
$47$	−1.03045	+	3.17140i	−0.150307	+	0.462596i	0.847349	+	0.531037i	$0.178197\pi$
$48$		0			0
$49$	4.13246	−	12.7184i	0.590351	−	1.81691i
$50$	5.25503	+	16.1733i	0.743173	+	2.28725i
$51$		0			0
$52$	−0.427811	−	1.31667i	−0.0593267	−	0.182589i
$53$	9.81866	+	7.13368i	1.34870	+	0.979886i	0.999075	+	0.0429949i	$0.0136899\pi$
$53$	9.81866	+	7.13368i	1.34870	+	0.979886i	0.349622	+	0.936891i	$0.386310\pi$
$54$		0			0
$55$	−1.05609	+	0.767297i	−0.142404	+	0.103462i
$56$	−9.10537			−1.21676
$57$		0			0
$58$	−9.78596	+	7.10992i	−1.28496	+	0.933578i
$59$	0.423851	−	1.30448i	0.0551807	−	0.169829i	−0.919668	−	0.392697i	$-0.871542\pi$
$59$	0.423851	−	1.30448i	0.0551807	−	0.169829i	0.974849	+	0.222868i	$0.0715421\pi$
$60$		0			0
$61$	3.58978			0.459624			0.229812	−	0.973235i	$-0.426189\pi$
$61$	3.58978			0.459624			0.229812	+	0.973235i	$0.426189\pi$
$62$	1.74846	+	9.13908i	0.222055	+	1.16066i
$63$		0			0
$64$	0.868998	+	2.67450i	0.108625	+	0.334313i
$65$	2.10188	−	6.46893i	0.260706	−	0.802372i
$66$		0			0
$67$	−1.37225			−0.167647			−0.0838233	−	0.996481i	$-0.526713\pi$
$67$	−1.37225			−0.167647			−0.0838233	+	0.996481i	$0.526713\pi$
$68$	2.75167			0.333689
$69$		0			0
$70$	23.7731	+	17.2722i	2.84143	+	2.06442i
$71$	−1.40560	−	1.02123i	−0.166814	−	0.121198i	0.501246	−	0.865305i	$-0.332875\pi$
$71$	−1.40560	−	1.02123i	−0.166814	−	0.121198i	−0.668060	+	0.744107i	$0.732875\pi$
$72$		0			0
$73$	−10.5313	+	7.65141i	−1.23259	+	0.895530i	−0.997082	−	0.0763415i	$-0.975676\pi$
$73$	−10.5313	+	7.65141i	−1.23259	+	0.895530i	−0.235510	+	0.971872i	$0.575676\pi$
$74$	−3.82973	−	11.7867i	−0.445197	−	1.37017i
$75$		0			0
$76$	−0.135898	−	0.0987358i	−0.0155886	−	0.0113258i
$77$	−0.467390	+	1.43848i	−0.0532640	+	0.163930i
$78$		0			0
$79$	−6.88408	−	5.00157i	−0.774519	−	0.562721i	0.128810	−	0.991669i	$-0.458884\pi$
$79$	−6.88408	−	5.00157i	−0.774519	−	0.562721i	−0.903329	+	0.428948i	$0.858884\pi$
$80$	5.96740	−	18.3658i	0.667176	−	2.05336i
$81$		0			0
$82$	8.80212	−	6.39512i	0.972032	−	0.706222i
$83$	2.45898	+	7.56796i	0.269908	+	0.830691i	0.990522	+	0.137355i	$0.0438600\pi$
$83$	2.45898	+	7.56796i	0.269908	+	0.830691i	−0.720614	+	0.693336i	$0.756140\pi$
$84$		0			0
$85$	10.9373	+	7.94642i	1.18632	+	0.861910i
$86$	−4.13386	+	3.00343i	−0.445766	+	0.323868i
$87$		0			0
$88$	0.675992			0.0720610
$89$	−6.51582	+	4.73402i	−0.690676	+	0.501805i	−0.876882	−	0.480705i	$-0.840381\pi$
$89$	−6.51582	+	4.73402i	−0.690676	+	0.501805i	0.186206	+	0.982511i	$0.440381\pi$
$90$		0			0
$91$	−2.43534	−	7.49522i	−0.255294	−	0.785713i
$92$	−2.17469			−0.226727
$93$		0			0
$94$	−5.57278			−0.574788
$95$	−0.255032	−	0.784909i	−0.0261658	−	0.0805300i
$96$		0			0
$97$	2.78687	−	2.02478i	0.282964	−	0.205585i	−0.437245	−	0.899342i	$-0.644046\pi$
$97$	2.78687	−	2.02478i	0.282964	−	0.205585i	0.720209	+	0.693757i	$0.244046\pi$
$98$	22.3488			2.25757
$99$		0			0
$100$	−6.52740	+	4.74243i	−0.652740	+	0.474243i
$101$	−0.511553	−	0.371665i	−0.0509014	−	0.0369820i	0.562044	−	0.827108i	$-0.310015\pi$
$101$	−0.511553	−	0.371665i	−0.0509014	−	0.0369820i	−0.612945	+	0.790126i	$0.710015\pi$
$102$		0			0
$103$	0.336189	+	1.03468i	0.0331257	+	0.101950i	0.966252	−	0.257598i	$-0.0829309\pi$
$103$	0.336189	+	1.03468i	0.0331257	+	0.101950i	−0.933127	+	0.359548i	$0.882931\pi$
$104$	−2.84958	+	2.07034i	−0.279424	+	0.203013i
$105$		0			0
$106$	−6.26765	+	19.2898i	−0.608768	+	1.87359i
$107$	−6.45400	−	4.68911i	−0.623932	−	0.453313i	0.230361	−	0.973105i	$-0.426009\pi$
$107$	−6.45400	−	4.68911i	−0.623932	−	0.453313i	−0.854293	+	0.519792i	$0.826009\pi$
$108$		0			0
$109$	0.0678149	−	0.208713i	0.00649549	−	0.0199911i	−0.947756	−	0.318995i	$-0.896655\pi$
$109$	0.0678149	−	0.208713i	0.00649549	−	0.0199911i	0.954252	+	0.299004i	$0.0966545\pi$
$110$	−1.76494	−	1.28230i	−0.168280	−	0.122263i
$111$		0			0
$112$	−6.91413	−	21.2795i	−0.653324	−	2.01072i
$113$	−9.64771	+	7.00947i	−0.907580	+	0.659396i	−0.940402	−	0.340065i	$-0.889551\pi$
$113$	−9.64771	+	7.00947i	−0.907580	+	0.659396i	0.0328213	+	0.999461i	$0.489551\pi$
$114$		0			0
$115$	−8.64395	−	6.28020i	−0.806052	−	0.585631i
$116$	−4.64295	−	3.37330i	−0.431087	−	0.313203i
$117$		0			0
$118$	2.29223			0.211017
$119$	15.6641			1.43592
$120$		0			0
$121$	−3.36449	+	10.3548i	−0.305862	+	0.941348i
$122$	1.85386	+	5.70560i	0.167841	+	0.516561i
$123$		0			0
$124$	−3.86746	+	2.12886i	−0.347309	+	0.191178i
$125$	−20.1625			−1.80339
$126$		0			0
$127$	4.00707	−	12.3325i	0.355570	−	1.09433i	−0.600108	−	0.799919i	$-0.704876\pi$
$127$	4.00707	−	12.3325i	0.355570	−	1.09433i	0.955678	−	0.294413i	$-0.0951242\pi$
$128$	−10.6782	+	7.75820i	−0.943832	+	0.685734i
$129$		0			0
$130$	11.3672			0.996970
$131$	10.7332	−	7.79810i	0.937761	−	0.681323i	−0.0101198	−	0.999949i	$-0.503221\pi$
$131$	10.7332	−	7.79810i	0.937761	−	0.681323i	0.947881	+	0.318626i	$0.103221\pi$
$132$		0			0
$133$	−0.773611	−	0.562061i	−0.0670806	−	0.0487369i
$134$	−0.708667	−	2.18105i	−0.0612195	−	0.188414i
$135$		0			0
$136$	−2.16338	−	6.65818i	−0.185508	−	0.570935i
$137$	3.24841	−	9.99759i	0.277531	−	0.854152i	−0.711008	−	0.703184i	$-0.751761\pi$
$137$	3.24841	−	9.99759i	0.277531	−	0.854152i	0.988539	−	0.150968i	$-0.0482390\pi$
$138$		0			0
$139$	7.25902	−	22.3410i	0.615702	−	1.89494i	0.225316	−	0.974286i	$-0.427659\pi$
$139$	7.25902	−	22.3410i	0.615702	−	1.89494i	0.390387	−	0.920651i	$-0.372341\pi$
$140$	−4.30825	+	13.2594i	−0.364114	+	1.12063i
$141$		0			0
$142$	0.897253	−	2.76146i	0.0752958	−	0.231737i
$143$	0.180802	+	0.556453i	0.0151195	+	0.0465329i
$144$		0			0
$145$	−8.71315	−	26.8163i	−0.723588	−	2.22697i
$146$	−17.5998	−	12.7870i	−1.45657	−	1.05826i
$147$		0			0
$148$	4.75700	−	3.45616i	0.391023	−	0.284095i
$149$	10.6943			0.876113			0.438056	−	0.898948i	$-0.355667\pi$
$149$	10.6943			0.876113			0.438056	+	0.898948i	$0.355667\pi$
$150$		0			0
$151$	−2.27730	+	1.65456i	−0.185324	+	0.134646i	−0.676579	−	0.736370i	$-0.736538\pi$
$151$	−2.27730	+	1.65456i	−0.185324	+	0.134646i	0.491255	+	0.871016i	$0.336538\pi$
$152$	−0.132066	+	0.406458i	−0.0107120	+	0.0329681i
$153$		0			0
$154$	−2.52769			−0.203687
$155$	−21.5202	−	2.70689i	−1.72855	−	0.217422i
$156$		0			0
$157$	4.51797	+	13.9049i	0.360573	+	1.10973i	0.952707	+	0.303890i	$0.0982857\pi$
$157$	4.51797	+	13.9049i	0.360573	+	1.10973i	−0.592134	+	0.805840i	$0.701714\pi$
$158$	4.39438	−	13.5245i	0.349598	−	1.07595i
$159$		0			0
$160$	16.5551			1.30880
$161$	−12.3796			−0.975649
$162$		0			0
$163$	13.9517	+	10.1365i	1.09278	+	0.793950i	0.979866	−	0.199655i	$-0.0639823\pi$
$163$	13.9517	+	10.1365i	1.09278	+	0.793950i	0.112912	+	0.993605i	$0.463982\pi$
$164$	4.17616	+	3.03416i	0.326104	+	0.236928i
$165$		0			0
$166$	−10.7586	+	7.81661i	−0.835033	+	0.606687i
$167$	0.126112	+	0.388134i	0.00975887	+	0.0300347i	0.955817	−	0.293961i	$-0.0949736\pi$
$167$	0.126112	+	0.388134i	0.00975887	+	0.0300347i	−0.946059	+	0.323996i	$0.894974\pi$
$168$		0			0
$169$	8.05084	+	5.84927i	0.619295	+	0.449944i
$170$	−6.98172	+	21.4875i	−0.535474	+	1.64802i
$171$		0			0
$172$	−1.96131	−	1.42497i	−0.149548	−	0.108653i
$173$	−1.15687	+	3.56047i	−0.0879549	+	0.270697i	−0.985354	−	0.170523i	$-0.945454\pi$
$173$	−1.15687	+	3.56047i	−0.0879549	+	0.270697i	0.897399	+	0.441220i	$0.145454\pi$
$174$		0			0
$175$	−37.1577	+	26.9967i	−2.80886	+	2.04076i
$176$	0.513312	+	1.57981i	0.0386923	+	0.119083i
$177$		0			0
$178$	−10.8892	−	7.91148i	−0.816182	−	0.592991i
$179$	1.48194	−	1.07669i	0.110765	−	0.0804757i	−0.531024	−	0.847357i	$-0.678192\pi$
$179$	1.48194	−	1.07669i	0.110765	−	0.0804757i	0.641789	+	0.766881i	$0.278192\pi$
$180$		0			0
$181$	−11.5508			−0.858565			−0.429283	−	0.903170i	$-0.641234\pi$
$181$	−11.5508			−0.858565			−0.429283	+	0.903170i	$0.641234\pi$
$182$	10.6552	−	7.74149i	0.789819	−	0.573837i
$183$		0			0
$184$	1.70975	+	5.26208i	0.126045	+	0.387926i
$185$	28.8890			2.12396
$186$		0			0
$187$	−1.16292			−0.0850409
$188$	−0.817042	−	2.51460i	−0.0595889	−	0.183396i
$189$		0			0
$190$	1.11583	−	0.810698i	0.0809508	−	0.0588142i
$191$	8.89041			0.643287			0.321644	−	0.946861i	$-0.395765\pi$
$191$	8.89041			0.643287			0.321644	+	0.946861i	$0.395765\pi$
$192$		0			0
$193$	9.16501	−	6.65877i	0.659712	−	0.479309i	−0.206854	−	0.978372i	$-0.566322\pi$
$193$	9.16501	−	6.65877i	0.659712	−	0.479309i	0.866566	+	0.499063i	$0.166322\pi$
$194$	4.65741	+	3.38381i	0.334383	+	0.242943i
$195$		0			0
$196$	3.27662	+	10.0844i	0.234044	+	0.720314i
$197$	−11.2708	+	8.18873i	−0.803013	+	0.583423i	−0.911796	−	0.410642i	$-0.865304\pi$
$197$	−11.2708	+	8.18873i	−0.803013	+	0.583423i	0.108784	+	0.994065i	$0.465304\pi$
$198$		0			0
$199$	0.138045	−	0.424858i	0.00978573	−	0.0301174i	−0.946044	−	0.324037i	$-0.894960\pi$
$199$	0.138045	−	0.424858i	0.00978573	−	0.0301174i	0.955830	+	0.293920i	$0.0949598\pi$
$200$	16.6071	+	12.0658i	1.17430	+	0.853178i
$201$		0			0
$202$	0.326545	−	1.00500i	0.0229756	−	0.0707116i
$203$	−26.4303	−	19.2028i	−1.85504	−	1.34777i
$204$		0			0
$205$	7.83717	+	24.1203i	0.547371	+	1.68464i
$206$	−1.47091	+	1.06868i	−0.102483	+	0.0744585i
$207$		0			0
$208$	−7.00225	−	5.08743i	−0.485519	−	0.352750i
$209$	0.0574336	+	0.0417280i	0.00397277	+	0.00288638i
$210$		0			0
$211$	20.4011			1.40447			0.702234	−	0.711946i	$-0.252186\pi$
$211$	20.4011			1.40447			0.702234	+	0.711946i	$0.252186\pi$
$212$	−9.62304			−0.660913
$213$		0			0
$214$	4.11985	−	12.6796i	0.281627	−	0.866760i
$215$	−3.68068	−	11.3280i	−0.251020	−	0.772560i
$216$		0			0
$217$	−22.0158	+	12.1187i	−1.49453	+	0.822672i
$218$	0.366750			0.0248394
$219$		0			0
$220$	0.319849	−	0.984394i	0.0215642	−	0.0663678i
$221$	4.90216	−	3.56163i	0.329755	−	0.239581i
$222$		0			0
$223$	20.4372			1.36857			0.684287	−	0.729213i	$-0.260114\pi$
$223$	20.4372			1.36857			0.684287	+	0.729213i	$0.260114\pi$
$224$	15.5182	−	11.2747i	1.03686	−	0.753319i
$225$		0			0
$226$	−16.1232	−	11.7142i	−1.07250	−	0.779218i
$227$	3.74782	+	11.5346i	0.248751	+	0.765578i	0.994997	+	0.0999069i	$0.0318545\pi$
$227$	3.74782	+	11.5346i	0.248751	+	0.765578i	−0.746246	+	0.665671i	$0.768146\pi$
$228$		0			0
$229$	7.28484	+	22.4204i	0.481396	+	1.48158i	0.837134	+	0.546998i	$0.184230\pi$
$229$	7.28484	+	22.4204i	0.481396	+	1.48158i	−0.355738	+	0.934586i	$0.615770\pi$
$230$	5.51778	−	16.9820i	0.363832	−	1.11976i
$231$		0			0
$232$	−4.51203	+	13.8866i	−0.296229	+	0.911700i
$233$	−2.37619	+	7.31317i	−0.155670	+	0.479102i	−0.998228	−	0.0595030i	$-0.981048\pi$
$233$	−2.37619	+	7.31317i	−0.155670	+	0.479102i	0.842559	+	0.538605i	$0.181048\pi$
$234$		0			0
$235$	4.01422	−	12.3545i	0.261859	−	0.805919i
$236$	0.336071	+	1.03432i	0.0218764	+	0.0673285i
$237$		0			0
$238$	8.08937	+	24.8965i	0.524356	+	1.61380i
$239$	−18.0850	−	13.1395i	−1.16982	−	0.849926i	−0.178835	−	0.983879i	$-0.557233\pi$
$239$	−18.0850	−	13.1395i	−1.16982	−	0.849926i	−0.990988	+	0.133954i	$0.957233\pi$
$240$		0			0
$241$	−7.10875	+	5.16481i	−0.457915	+	0.332695i	−0.792713	−	0.609595i	$-0.791332\pi$
$241$	−7.10875	+	5.16481i	−0.457915	+	0.332695i	0.334798	+	0.942290i	$0.391332\pi$
$242$	−18.1955			−1.16965
$243$		0			0
$244$	−2.30273	+	1.67303i	−0.147417	+	0.107105i
$245$	−16.0984	+	49.5458i	−1.02849	+	3.16536i
$246$		0			0
$247$	−0.369905			−0.0235365
$248$	8.19181	+	7.68434i	0.520181	+	0.487956i
$249$		0			0
$250$	−10.4125	−	32.0464i	−0.658544	−	2.02679i
$251$	−2.86536	+	8.81867i	−0.180860	+	0.556630i	−0.999853	−	0.0171745i	$-0.994533\pi$
$251$	−2.86536	+	8.81867i	−0.180860	+	0.556630i	0.818993	+	0.573804i	$0.194533\pi$
$252$		0			0
$253$	0.919074			0.0577817
$254$	21.6707			1.35974
$255$		0			0
$256$	−13.2953	−	9.65961i	−0.830957	−	0.603725i
$257$	−1.64643	−	1.19620i	−0.102701	−	0.0746168i	0.535249	−	0.844694i	$-0.320218\pi$
$257$	−1.64643	−	1.19620i	−0.102701	−	0.0746168i	−0.637951	+	0.770077i	$0.720218\pi$
$258$		0			0
$259$	27.0796	−	19.6745i	1.68264	−	1.22251i
$260$	1.66658	+	5.12921i	0.103357	+	0.318100i
$261$		0			0
$262$	17.9372	+	13.0322i	1.10817	+	0.805129i
$263$	9.14903	−	28.1578i	0.564153	−	1.73629i	−0.106300	−	0.994334i	$-0.533900\pi$
$263$	9.14903	−	28.1578i	0.564153	−	1.73629i	0.670454	−	0.741952i	$-0.266100\pi$
$264$		0			0
$265$	−38.2496	−	27.7900i	−2.34965	−	1.70712i
$266$	0.493827	−	1.51984i	0.0302785	−	0.0931876i
$267$		0			0
$268$	0.880254	−	0.639542i	0.0537700	−	0.0390662i
$269$	6.37967	+	19.6346i	0.388976	+	1.19714i	0.933555	+	0.358434i	$0.116689\pi$
$269$	6.37967	+	19.6346i	0.388976	+	1.19714i	−0.544579	+	0.838709i	$0.683311\pi$
$270$		0			0
$271$	−5.22865	−	3.79884i	−0.317618	−	0.230763i	0.417540	−	0.908658i	$-0.362892\pi$
$271$	−5.22865	−	3.79884i	−0.317618	−	0.230763i	−0.735158	+	0.677895i	$0.762892\pi$
$272$	13.9176	−	10.1117i	0.843878	−	0.613114i
$273$		0			0
$274$	17.5678			1.06131
$275$	2.75863	−	2.00426i	0.166351	−	0.120861i
$276$		0			0
$277$	2.92114	+	8.99034i	0.175514	+	0.540177i	0.999657	−	0.0262054i	$-0.00834238\pi$
$277$	2.92114	+	8.99034i	0.175514	+	0.540177i	−0.824142	+	0.566383i	$0.808342\pi$
$278$	39.2576			2.35451
$279$		0			0
$280$	35.4709			2.11979
$281$	0.701977	+	2.16046i	0.0418765	+	0.128883i	0.969809	−	0.243866i	$-0.0784156\pi$
$281$	0.701977	+	2.16046i	0.0418765	+	0.128883i	−0.927933	+	0.372748i	$0.878416\pi$
$282$		0			0
$283$	21.9439	−	15.9432i	1.30443	−	0.947725i	0.304443	−	0.952531i	$-0.401530\pi$
$283$	21.9439	−	15.9432i	1.30443	−	0.947725i	0.999988	+	0.00480608i	$0.00152983\pi$
$284$	1.37760			0.0817454
$285$		0			0
$286$	−0.791056	+	0.574736i	−0.0467761	+	0.0339848i
$287$	23.7731	+	17.2722i	1.40328	+	1.01954i
$288$		0			0
$289$	−1.53161	−	4.71382i	−0.0900948	−	0.277283i
$290$	38.1222	−	27.6974i	2.23861	−	1.62645i
$291$		0			0
$292$	3.18950	−	9.81628i	0.186652	−	0.574455i
$293$	7.42124	+	5.39185i	0.433554	+	0.314995i	0.783068	−	0.621936i	$-0.213653\pi$
$293$	7.42124	+	5.39185i	0.433554	+	0.314995i	−0.349515	+	0.936931i	$0.613653\pi$
$294$		0			0
$295$	−1.65115	+	5.08173i	−0.0961339	+	0.295870i
$296$	−12.1028	−	8.79322i	−0.703463	−	0.511095i
$297$		0			0
$298$	5.52285	+	16.9976i	0.319930	+	0.984643i
$299$	−3.87426	+	2.81482i	−0.224055	+	0.162785i
$300$		0			0
$301$	−11.1649	−	8.11177i	−0.643534	−	0.467555i
$302$	−3.80582	−	2.76509i	−0.219000	−	0.159113i
$303$		0			0
$304$	−1.05019			−0.0602324
$305$	−13.9843			−0.800741
$306$		0			0
$307$	−2.80255	+	8.62537i	−0.159950	+	0.492276i	−0.998629	−	0.0523508i	$-0.983329\pi$
$307$	−2.80255	+	8.62537i	−0.159950	+	0.492276i	0.838679	+	0.544627i	$0.183329\pi$
$308$	−0.370593	−	1.14057i	−0.0211165	−	0.0649898i
$309$		0			0
$310$	−6.81132	−	35.6022i	−0.386857	−	2.02207i
$311$	11.8965			0.674587			0.337293	−	0.941400i	$-0.390489\pi$
$311$	11.8965			0.674587			0.337293	+	0.941400i	$0.390489\pi$
$312$		0			0
$313$	−4.84664	+	14.9164i	−0.273948	+	0.843127i	0.715547	+	0.698564i	$0.246177\pi$
$313$	−4.84664	+	14.9164i	−0.273948	+	0.843127i	−0.989496	+	0.144562i	$0.953823\pi$
$314$	−19.7672	+	14.3617i	−1.11553	+	0.810480i
$315$		0			0
$316$	6.74692			0.379544
$317$	−12.1599	+	8.83468i	−0.682967	+	0.496205i	−0.874341	−	0.485313i	$-0.838706\pi$
$317$	−12.1599	+	8.83468i	−0.682967	+	0.496205i	0.191373	+	0.981517i	$0.438706\pi$
$318$		0			0
$319$	1.96221	+	1.42563i	0.109863	+	0.0798200i
$320$	−3.38527	−	10.4188i	−0.189242	−	0.582428i
$321$		0			0
$322$	−6.39317	−	19.6762i	−0.356278	−	1.09651i
$323$	0.227195	−	0.699235i	0.0126415	−	0.0389065i
$324$		0			0
$325$	−5.49033	+	16.8975i	−0.304549	+	0.937305i
$326$	−8.90590	+	27.4096i	−0.493252	+	1.51807i
$327$		0			0
$328$	4.05841	−	12.4905i	0.224088	−	0.689672i
$329$	−4.65107	−	14.3145i	−0.256422	−	0.789186i
$330$		0			0
$331$	4.20147	+	12.9308i	0.230934	+	0.710741i	0.997635	+	0.0687370i	$0.0218969\pi$
$331$	4.20147	+	12.9308i	0.230934	+	0.710741i	−0.766701	+	0.642004i	$0.778103\pi$
$332$	−5.10444	−	3.70859i	−0.280142	−	0.203535i
$333$		0			0
$334$	−0.551773	+	0.400887i	−0.0301917	+	0.0219355i
$335$	5.34573			0.292068
$336$		0			0
$337$	8.37831	−	6.08720i	0.456396	−	0.331591i	−0.335720	−	0.941962i	$-0.608980\pi$
$337$	8.37831	−	6.08720i	0.456396	−	0.331591i	0.792116	+	0.610371i	$0.208980\pi$
$338$	−5.13917	+	15.8168i	−0.279534	+	0.860318i
$339$		0			0
$340$	−10.7194			−0.581341
$341$	1.63448	−	0.899706i	0.0885119	−	0.0487218i
$342$		0			0
$343$	8.88887	+	27.3571i	0.479954	+	1.47715i
$344$	−1.90601	+	5.86608i	−0.102765	+	0.316278i
$345$		0			0
$346$	−6.25645			−0.336349
$347$	2.52600			0.135603			0.0678013	−	0.997699i	$-0.478402\pi$
$347$	2.52600			0.135603			0.0678013	+	0.997699i	$0.478402\pi$
$348$		0			0
$349$	−28.2338	−	20.5130i	−1.51132	−	1.09804i	−0.965588	−	0.260076i	$-0.916252\pi$
$349$	−28.2338	−	20.5130i	−1.51132	−	1.09804i	−0.545730	−	0.837961i	$-0.683748\pi$
$350$	−62.0979	−	45.1167i	−3.31927	−	2.41159i
$351$		0			0
$352$	−1.15209	+	0.837041i	−0.0614065	+	0.0446145i
$353$	−2.82453	−	8.69302i	−0.150335	−	0.462683i	0.847324	−	0.531077i	$-0.178213\pi$
$353$	−2.82453	−	8.69302i	−0.150335	−	0.462683i	−0.997658	+	0.0683940i	$0.978213\pi$
$354$		0			0
$355$	5.47567	+	3.97831i	0.290618	+	0.211147i
$356$	1.97338	−	6.07345i	0.104589	−	0.321892i
$357$		0			0
$358$	2.47661	+	1.79936i	0.130893	+	0.0950993i
$359$	1.45727	−	4.48500i	0.0769115	−	0.236709i	−0.905208	−	0.424970i	$-0.860285\pi$
$359$	1.45727	−	4.48500i	0.0769115	−	0.236709i	0.982119	+	0.188260i	$0.0602848\pi$
$360$		0			0
$361$	15.3350	−	11.1415i	0.807106	−	0.586397i
$362$	−5.96517	−	18.3589i	−0.313522	−	0.964922i
$363$		0			0
$364$	5.05538	+	3.67295i	0.264974	+	0.192515i
$365$	41.0256	−	29.8069i	2.14738	−	1.56016i
$366$		0			0
$367$	−24.4353			−1.27551			−0.637756	−	0.770238i	$-0.720137\pi$
$367$	−24.4353			−1.27551			−0.637756	+	0.770238i	$0.720137\pi$
$368$	−10.9993	+	7.99148i	−0.573380	+	0.416585i
$369$		0			0
$370$	14.9191	+	45.9162i	0.775607	+	2.38707i
$371$	−54.7799			−2.84403
$372$		0			0
$373$	−3.54248			−0.183422			−0.0917112	−	0.995786i	$-0.529234\pi$
$373$	−3.54248			−0.183422			−0.0917112	+	0.995786i	$0.529234\pi$
$374$	−0.600563	−	1.84834i	−0.0310544	−	0.0955755i
$375$		0			0
$376$	−5.44218	+	3.95398i	−0.280659	+	0.203911i
$377$	−12.6378			−0.650877
$378$		0			0
$379$	−19.5473	+	14.2019i	−1.00408	+	0.729503i	−0.962958	−	0.269651i	$-0.913092\pi$
$379$	−19.5473	+	14.2019i	−1.00408	+	0.729503i	−0.0411172	+	0.999154i	$0.513092\pi$
$380$	0.529405	+	0.384636i	0.0271579	+	0.0197314i
$381$		0			0
$382$	4.59126	+	14.1304i	0.234909	+	0.722976i
$383$	0.960947	−	0.698169i	0.0491021	−	0.0356747i	−0.562963	−	0.826482i	$-0.690339\pi$
$383$	0.960947	−	0.698169i	0.0491021	−	0.0356747i	0.612066	+	0.790807i	$0.290339\pi$
$384$		0			0
$385$	1.82076	−	5.60374i	0.0927947	−	0.285593i
$386$	15.3165	+	11.1281i	0.779592	+	0.566406i
$387$		0			0
$388$	−0.844034	+	2.59767i	−0.0428493	+	0.131877i
$389$	14.7772	+	10.7362i	0.749232	+	0.544349i	0.895589	−	0.444883i	$-0.146755\pi$
$389$	14.7772	+	10.7362i	0.749232	+	0.544349i	−0.146356	+	0.989232i	$0.546755\pi$
$390$		0			0
$391$	−2.94131	−	9.05242i	−0.148748	−	0.457800i
$392$	21.8250	−	15.8568i	1.10233	−	0.800890i
$393$		0			0
$394$	−18.8358	−	13.6850i	−0.948932	−	0.689440i
$395$	26.8176	+	19.4841i	1.34934	+	0.980354i
$396$		0			0
$397$	−2.65218			−0.133109			−0.0665546	−	0.997783i	$-0.521201\pi$
$397$	−2.65218			−0.133109			−0.0665546	+	0.997783i	$0.521201\pi$
$398$	0.746560			0.0374217
$399$		0			0
$400$	−15.5875	+	47.9733i	−0.779374	+	2.39867i
$401$	5.13071	+	15.7907i	0.256216	+	0.788551i	0.993588	+	0.113064i	$0.0360665\pi$
$401$	5.13071	+	15.7907i	0.256216	+	0.788551i	−0.737372	+	0.675487i	$0.763934\pi$
$402$		0			0
$403$	−4.13448	+	8.79848i	−0.205953	+	0.438284i
$404$	0.501361			0.0249436
$405$		0			0
$406$	16.8715	−	51.9253i	0.837321	−	2.57701i
$407$	−2.01042	+	1.46065i	−0.0996526	+	0.0724018i
$408$		0			0
$409$	25.6723			1.26942			0.634708	−	0.772752i	$-0.281120\pi$
$409$	25.6723			1.26942			0.634708	+	0.772752i	$0.281120\pi$
$410$	−34.2896	+	24.9128i	−1.69344	+	1.23036i
$411$		0			0
$412$	−0.697874	−	0.507035i	−0.0343818	−	0.0249798i
$413$	1.91311	+	5.88794i	0.0941379	+	0.289727i
$414$		0			0
$415$	−9.57920	−	29.4817i	−0.470224	−	1.44720i
$416$	2.29294	−	7.05693i	0.112420	−	0.345995i
$417$		0			0
$418$	−0.0366622	+	0.112835i	−0.00179321	+	0.00551892i
$419$	−9.62824	+	29.6327i	−0.470370	+	1.44765i	0.381731	+	0.924273i	$0.375328\pi$
$419$	−9.62824	+	29.6327i	−0.470370	+	1.44765i	−0.852101	+	0.523377i	$0.824672\pi$
$420$		0			0
$421$	−9.44103	+	29.0565i	−0.460128	+	1.41613i	0.404881	+	0.914370i	$0.367313\pi$
$421$	−9.44103	+	29.0565i	−0.460128	+	1.41613i	−0.865008	+	0.501758i	$0.832687\pi$
$422$	10.5357	+	32.4255i	0.512869	+	1.57845i
$423$		0			0
$424$	7.56569	+	23.2848i	0.367422	+	1.13081i
$425$	−28.5694	−	20.7569i	−1.38582	−	1.00686i
$426$		0			0
$427$	−13.1085	+	9.52385i	−0.634363	+	0.460891i
$428$	6.32542			0.305751
$429$		0			0
$430$	16.1039	−	11.7001i	0.776598	−	0.564231i
$431$	11.3322	−	34.8768i	0.545851	−	1.67996i	−0.173106	−	0.984903i	$-0.555380\pi$
$431$	11.3322	−	34.8768i	0.545851	−	1.67996i	0.718957	−	0.695054i	$-0.244620\pi$
$432$		0			0
$433$	−13.7562			−0.661083			−0.330541	−	0.943791i	$-0.607231\pi$
$433$	−13.7562			−0.661083			−0.330541	+	0.943791i	$0.607231\pi$
$434$	−30.6311	−	28.7336i	−1.47034	−	1.37926i
$435$		0			0
$436$	0.0537703	+	0.165488i	0.00257513	+	0.00792544i
$437$	−0.179556	+	0.552618i	−0.00858935	+	0.0264353i
$438$		0			0
$439$	−5.74749			−0.274313			−0.137156	−	0.990549i	$-0.543796\pi$
$439$	−5.74749			−0.274313			−0.137156	+	0.990549i	$0.543796\pi$
$440$	−2.63340			−0.125542
$441$		0			0
$442$	8.19247	+	5.95218i	0.389676	+	0.283116i
$443$	25.9488	+	18.8529i	1.23286	+	0.895728i	0.997102	−	0.0760822i	$-0.0242412\pi$
$443$	25.9488	+	18.8529i	1.23286	+	0.895728i	0.235763	+	0.971811i	$0.424241\pi$
$444$		0			0
$445$	25.3830	−	18.4419i	1.20327	−	0.874228i
$446$	10.5543	+	32.4829i	0.499762	+	1.53811i
$447$		0			0
$448$	−10.2688	−	7.46074i	−0.485156	−	0.352487i
$449$	6.97569	−	21.4690i	0.329203	−	1.01318i	−0.640304	−	0.768121i	$-0.721192\pi$
$449$	6.97569	−	21.4690i	0.329203	−	1.01318i	0.969507	−	0.245062i	$-0.0788083\pi$
$450$		0			0
$451$	−1.76494	−	1.28230i	−0.0831078	−	0.0603814i
$452$	2.92191	−	8.99271i	0.137435	−	0.422982i
$453$		0			0
$454$	−16.3976	+	11.9136i	−0.769579	+	0.559132i
$455$	9.48713	+	29.1984i	0.444764	+	1.36884i
$456$		0			0
$457$	−6.70189	−	4.86921i	−0.313501	−	0.227772i	0.419896	−	0.907572i	$-0.362066\pi$
$457$	−6.70189	−	4.86921i	−0.313501	−	0.227772i	−0.733397	+	0.679800i	$0.762066\pi$
$458$	−31.8730	+	23.1571i	−1.48933	+	1.08206i
$459$		0			0
$460$	8.47173			0.394997
$461$	−12.7815	+	9.28628i	−0.595292	+	0.432505i	−0.844205	−	0.536021i	$-0.819927\pi$
$461$	−12.7815	+	9.28628i	−0.595292	+	0.432505i	0.248913	+	0.968526i	$0.419927\pi$
$462$		0			0
$463$	−4.39852	−	13.5373i	−0.204417	−	0.629130i	−0.999737	−	0.0229403i	$-0.992697\pi$
$463$	−4.39852	−	13.5373i	−0.204417	−	0.629130i	0.795320	−	0.606190i	$-0.207303\pi$
$464$	−35.8795			−1.66567
$465$		0			0
$466$	−12.8507			−0.595298
$467$	−8.10983	−	24.9595i	−0.375278	−	1.15499i	−0.943291	−	0.331968i	$-0.892287\pi$
$467$	−8.10983	−	24.9595i	−0.375278	−	1.15499i	0.568012	−	0.823020i	$-0.307713\pi$
$468$		0			0
$469$	5.01091	−	3.64064i	0.231382	−	0.168109i
$470$	21.7093			1.00138
$471$		0			0
$472$	2.23851	−	1.62638i	0.103036	−	0.0748600i
$473$	0.828893	+	0.602226i	0.0381125	+	0.0276904i
$474$		0			0
$475$	0.666171	+	2.05026i	0.0305660	+	0.0940725i
$476$	−10.0480	+	7.30031i	−0.460550	+	0.334609i
$477$		0			0
$478$	11.5444	−	35.5300i	0.528028	−	1.62510i
$479$	−33.7797	−	24.5424i	−1.54343	−	1.12137i	−0.948136	−	0.317866i	$-0.897034\pi$
$479$	−33.7797	−	24.5424i	−1.54343	−	1.12137i	−0.595299	−	0.803505i	$-0.702966\pi$
$480$		0			0
$481$	4.00121	−	12.3145i	0.182440	−	0.561492i
$482$	−11.8801	−	8.63141i	−0.541125	−	0.393150i
$483$		0			0
$484$	−2.66770	−	8.21033i	−0.121259	−	0.373197i
$485$	−10.8565	+	7.88774i	−0.492970	+	0.358164i
$486$		0			0
$487$	27.9442	+	20.3026i	1.26627	+	0.919999i	0.999048	−	0.0436354i	$-0.0138940\pi$
$487$	27.9442	+	20.3026i	1.26627	+	0.919999i	0.267223	+	0.963635i	$0.413894\pi$
$488$	5.85863	+	4.25655i	0.265208	+	0.192685i
$489$		0			0
$490$	−87.0619			−3.93305
$491$	−13.4986			−0.609183			−0.304592	−	0.952483i	$-0.598520\pi$
$491$	−13.4986			−0.609183			−0.304592	+	0.952483i	$0.598520\pi$
$492$		0			0
$493$	7.76209	−	23.8893i	0.349587	−	1.07592i
$494$	−0.191029	−	0.587928i	−0.00859481	−	0.0264521i
$495$		0			0
$496$	−11.7381	+	24.9796i	−0.527056	+	1.12162i
$497$	7.84208			0.351766
$498$		0			0
$499$	−11.6754	+	35.9332i	−0.522663	+	1.60859i	0.246227	+	0.969212i	$0.420809\pi$
$499$	−11.6754	+	35.9332i	−0.522663	+	1.60859i	−0.768891	+	0.639380i	$0.779191\pi$
$500$	12.9336	−	9.39683i	0.578409	−	0.420239i
$501$		0			0
$502$	−15.4962			−0.691628
$503$	4.35146	−	3.16152i	0.194022	−	0.140965i	−0.486533	−	0.873662i	$-0.661739\pi$
$503$	4.35146	−	3.16152i	0.194022	−	0.140965i	0.680555	+	0.732697i	$0.261739\pi$
$504$		0			0
$505$	1.99280	+	1.44786i	0.0886787	+	0.0644288i
$506$	0.474636	+	1.46078i	0.0211001	+	0.0649395i
$507$		0			0
$508$	3.17720	+	9.77842i	0.140966	+	0.433847i
$509$	5.70619	−	17.5619i	0.252923	−	0.778416i	−0.741309	−	0.671164i	$-0.765795\pi$
$509$	5.70619	−	17.5619i	0.252923	−	0.778416i	0.994232	−	0.107252i	$-0.0342052\pi$
$510$		0			0
$511$	18.1565	−	55.8799i	0.803196	−	2.47198i
$512$	0.329482	−	1.01404i	0.0145612	−	0.0448147i
$513$		0			0
$514$	1.05098	−	3.23458i	0.0463568	−	0.142671i
$515$	−1.30966	−	4.03072i	−0.0577105	−	0.177615i
$516$		0			0
$517$	0.345300	+	1.06273i	0.0151863	+	0.0467386i
$518$	45.2553	+	32.8799i	1.98840	+	1.44466i
$519$		0			0
$520$	11.1008	−	8.06522i	0.486803	−	0.353683i
$521$	20.3286			0.890610			0.445305	−	0.895379i	$-0.353095\pi$
$521$	20.3286			0.890610			0.445305	+	0.895379i	$0.353095\pi$
$522$		0			0
$523$	4.34617	−	3.15768i	0.190045	−	0.138076i	−0.488694	−	0.872455i	$-0.662527\pi$
$523$	4.34617	−	3.15768i	0.190045	−	0.138076i	0.678739	+	0.734379i	$0.262527\pi$
$524$	−3.25065	+	10.0045i	−0.142005	+	0.437047i
$525$		0			0
$526$	49.4789			2.15738
$527$	−14.0925	−	13.2195i	−0.613877	−	0.575849i
$528$		0			0
$529$	−4.78282	−	14.7200i	−0.207949	−	0.640001i
$530$	24.4163	−	75.1455i	1.06057	−	3.26411i
$531$		0			0
$532$	0.758198			0.0328721
$533$	11.3672			0.492368
$534$		0			0
$535$	25.1422	+	18.2669i	1.08699	+	0.789747i
$536$	−2.23955	−	1.62713i	−0.0967340	−	0.0702813i
$537$		0			0
$538$	−27.9127	+	20.2797i	−1.20340	+	0.874322i
$539$	−1.38477	−	4.26189i	−0.0596464	−	0.183573i
$540$		0			0
$541$	−23.7833	−	17.2796i	−1.02252	−	0.742907i	−0.0557247	−	0.998446i	$-0.517747\pi$
$541$	−23.7833	−	17.2796i	−1.02252	−	0.742907i	−0.966799	+	0.255540i	$0.917747\pi$
$542$	3.33766	−	10.2723i	0.143365	−	0.441232i
$543$		0			0
$544$	11.9315	+	8.66872i	0.511557	+	0.371668i
$545$	−0.264180	+	0.813062i	−0.0113162	+	0.0348277i
$546$		0			0
$547$	30.5120	−	22.1683i	1.30460	−	0.947848i	0.304612	−	0.952477i	$-0.401473\pi$
$547$	30.5120	−	22.1683i	1.30460	−	0.947848i	0.999989	+	0.00462851i	$0.00147330\pi$
$548$	2.57566	+	7.92708i	0.110027	+	0.338628i
$549$		0			0
$550$	4.61021	+	3.34951i	0.196580	+	0.142824i
$551$	−1.24055	+	0.901312i	−0.0528492	+	0.0383972i
$552$		0			0
$553$	38.4074			1.63325
$554$	−12.7807	+	9.28573i	−0.543001	+	0.394513i
$555$		0			0
$556$	5.75567	+	17.7141i	0.244095	+	0.751247i
$557$	−2.12741			−0.0901411			−0.0450706	−	0.998984i	$-0.514351\pi$
$557$	−2.12741			−0.0901411			−0.0450706	+	0.998984i	$0.514351\pi$
$558$		0			0
$559$	−5.33854			−0.225796
$560$	26.9347	+	82.8964i	1.13820	+	3.50301i
$561$		0			0
$562$	−3.07133	+	2.23145i	−0.129556	+	0.0941280i
$563$	15.4591			0.651523			0.325761	−	0.945452i	$-0.394379\pi$
$563$	15.4591			0.651523			0.325761	+	0.945452i	$0.394379\pi$
$564$		0			0
$565$	37.5836	−	27.3061i	1.58116	−	1.14878i
$566$	36.6726	+	26.6442i	1.54147	+	1.11994i
$567$		0			0
$568$	−1.08308	−	3.33336i	−0.0454448	−	0.139865i
$569$	35.1864	−	25.5644i	1.47509	−	1.07172i	0.495992	−	0.868327i	$-0.334804\pi$
$569$	35.1864	−	25.5644i	1.47509	−	1.07172i	0.979098	−	0.203389i	$-0.0651955\pi$
$570$		0			0
$571$	2.96846	−	9.13599i	0.124226	−	0.382329i	−0.869533	−	0.493875i	$-0.835580\pi$
$571$	2.96846	−	9.13599i	0.124226	−	0.382329i	0.993759	+	0.111545i	$0.0355801\pi$
$572$	−0.375316	−	0.272683i	−0.0156928	−	0.0114015i
$573$		0			0
$574$	−15.1753	+	46.7049i	−0.633407	+	1.94943i
$575$	22.5789	+	16.4045i	0.941605	+	0.684116i
$576$		0			0
$577$	14.1659	+	43.5981i	0.589734	+	1.81501i	0.579365	+	0.815068i	$0.303301\pi$
$577$	14.1659	+	43.5981i	0.589734	+	1.81501i	0.0103692	+	0.999946i	$0.496699\pi$
$578$	6.70118	−	4.86869i	0.278732	−	0.202511i
$579$		0			0
$580$	18.0871	+	13.1410i	0.751025	+	0.545651i
$581$	−29.0574	−	21.1114i	−1.20550	−	0.875849i
$582$		0			0
$583$	4.06691			0.168434
$584$	−26.2600			−1.08665
$585$		0			0
$586$	−4.73728	+	14.5798i	−0.195695	+	0.602288i
$587$	0.0941267	+	0.289692i	0.00388502	+	0.0119569i	0.952980	−	0.303032i	$-0.0979991\pi$
$587$	0.0941267	+	0.289692i	0.00388502	+	0.0119569i	−0.949095	+	0.314989i	$0.897999\pi$
$588$		0			0
$589$	0.221650	+	1.15855i	0.00913292	+	0.0477370i
$590$	−8.92962			−0.367627
$591$		0			0
$592$	11.3597	−	34.9617i	0.466883	−	1.43692i
$593$	26.6318	−	19.3492i	1.09364	−	0.794575i	0.113629	−	0.993523i	$-0.463753\pi$
$593$	26.6318	−	19.3492i	1.09364	−	0.794575i	0.980010	+	0.198948i	$0.0637526\pi$
$594$		0			0
$595$	−61.0210			−2.50162
$596$	−6.86007	+	4.98413i	−0.280999	+	0.204158i
$597$		0			0
$598$	−6.47466	−	4.70412i	−0.264768	−	0.192366i
$599$	−0.143565	−	0.441848i	−0.00586591	−	0.0180534i	0.948081	−	0.318030i	$-0.103021\pi$
$599$	−0.143565	−	0.441848i	−0.00586591	−	0.0180534i	−0.953947	+	0.299976i	$0.903021\pi$
$600$		0			0
$601$	1.30809	+	4.02587i	0.0533579	+	0.164219i	0.974184	−	0.225754i	$-0.0724845\pi$
$601$	1.30809	+	4.02587i	0.0533579	+	0.164219i	−0.920826	+	0.389973i	$0.872484\pi$
$602$	7.12700	−	21.9347i	0.290475	−	0.893990i
$603$		0			0
$604$	0.689705	−	2.12269i	0.0280637	−	0.0863711i
$605$	13.1067	−	40.3383i	0.532863	−	1.63998i
$606$		0			0
$607$	−5.04332	+	15.5217i	−0.204702	+	0.630008i	0.795023	+	0.606579i	$0.207459\pi$
$607$	−5.04332	+	15.5217i	−0.204702	+	0.630008i	−0.999725	+	0.0234296i	$0.992541\pi$
$608$	−0.278214	−	0.856254i	−0.0112831	−	0.0347257i
$609$		0			0
$610$	−7.22191	−	22.2267i	−0.292406	−	0.899934i
$611$	−4.71035	−	3.42227i	−0.190561	−	0.138450i
$612$		0			0
$613$	15.7794	−	11.4644i	0.637322	−	0.463042i	−0.221607	−	0.975136i	$-0.571130\pi$
$613$	15.7794	−	11.4644i	0.637322	−	0.463042i	0.858929	+	0.512094i	$0.171130\pi$
$614$	−15.1565			−0.611666
$615$		0			0
$616$	−2.46846	+	1.79344i	−0.0994570	+	0.0722597i
$617$	1.04989	−	3.23124i	0.0422672	−	0.130085i	−0.927696	−	0.373336i	$-0.878214\pi$
$617$	1.04989	−	3.23124i	0.0422672	−	0.130085i	0.969963	+	0.243251i	$0.0782139\pi$
$618$		0			0
$619$	−26.4142			−1.06168			−0.530839	−	0.847473i	$-0.678123\pi$
$619$	−26.4142			−1.06168			−0.530839	+	0.847473i	$0.678123\pi$
$620$	15.0661	−	8.29321i	0.605069	−	0.333063i
$621$		0			0
$622$	6.14367	+	18.9083i	0.246339	+	0.758153i
$623$	11.2336	−	34.5736i	0.450066	−	1.38516i
$624$		0			0
$625$	27.6666			1.10666
$626$	−26.2112			−1.04761
$627$		0			0
$628$	−9.37856	−	6.81392i	−0.374245	−	0.271905i
$629$	20.8206	+	15.1271i	0.830173	+	0.603156i
$630$		0			0
$631$	22.2666	−	16.1776i	0.886418	−	0.644020i	−0.0485238	−	0.998822i	$-0.515452\pi$
$631$	22.2666	−	16.1776i	0.886418	−	0.644020i	0.934942	+	0.354802i	$0.115452\pi$
$632$	−5.30447	−	16.3255i	−0.211000	−	0.649392i
$633$		0			0
$634$	−20.3216	−	14.7645i	−0.807072	−	0.586372i
$635$	−15.6100	+	48.0425i	−0.619462	+	1.90651i
$636$		0			0
$637$	18.8901	+	13.7245i	0.748454	+	0.543784i
$638$	−1.25256	+	3.85498i	−0.0495893	+	0.152620i
$639$		0			0
$640$	41.5982	−	30.2228i	1.64431	−	1.19466i
$641$	2.75540	+	8.48026i	0.108832	+	0.334950i	0.990611	−	0.136713i	$-0.0436539\pi$
$641$	2.75540	+	8.48026i	0.108832	+	0.334950i	−0.881779	+	0.471663i	$0.843654\pi$
$642$		0			0
$643$	10.2409	+	7.44043i	0.403861	+	0.293422i	0.771112	−	0.636700i	$-0.219701\pi$
$643$	10.2409	+	7.44043i	0.403861	+	0.293422i	−0.367251	+	0.930122i	$0.619701\pi$
$644$	7.94112	−	5.76956i	0.312924	−	0.227353i
$645$		0			0
$646$	1.22870			0.0483424
$647$	−23.4822	+	17.0608i	−0.923179	+	0.670729i	−0.944313	−	0.329048i	$-0.893272\pi$
$647$	−23.4822	+	17.0608i	−0.923179	+	0.670729i	0.0211340	+	0.999777i	$0.493272\pi$
$648$		0			0
$649$	−0.142031	−	0.437127i	−0.00557521	−	0.0171587i
$650$	−29.6923			−1.16463
$651$		0			0
$652$	−13.6737			−0.535503
$653$	−10.0340	−	30.8814i	−0.392660	−	1.20848i	−0.930769	−	0.365608i	$-0.880861\pi$
$653$	−10.0340	−	30.8814i	−0.392660	−	1.20848i	0.538109	−	0.842875i	$-0.319139\pi$
$654$		0			0
$655$	−41.8121	+	30.3783i	−1.63373	+	1.18698i
$656$	32.2724			1.26002
$657$		0			0
$658$	20.3496	−	14.7849i	0.793310	−	0.576374i
$659$	7.47182	+	5.42860i	0.291061	+	0.211468i	0.723728	−	0.690086i	$-0.242427\pi$
$659$	7.47182	+	5.42860i	0.291061	+	0.211468i	−0.432667	+	0.901554i	$0.642427\pi$
$660$		0			0
$661$	−6.52827	−	20.0920i	−0.253920	−	0.781487i	−0.994040	−	0.109012i	$-0.965231\pi$
$661$	−6.52827	−	20.0920i	−0.253920	−	0.781487i	0.740120	−	0.672475i	$-0.234769\pi$
$662$	−18.3825	+	13.3557i	−0.714456	+	0.519083i
$663$		0			0
$664$	−4.96051	+	15.2669i	−0.192505	+	0.592469i
$665$	3.01368	+	2.18957i	0.116865	+	0.0849077i
$666$		0			0
$667$	−6.13452	+	18.8801i	−0.237530	+	0.731041i
$668$	−0.261789	−	0.190201i	−0.0101289	−	0.00735908i
$669$		0			0
$670$	2.76069	+	8.49652i	0.106655	+	0.328249i
$671$	0.973185	−	0.707060i	0.0375694	−	0.0272957i
$672$		0			0
$673$	−32.7484	−	23.7931i	−1.26236	−	0.917158i	−0.263489	−	0.964662i	$-0.584873\pi$
$673$	−32.7484	−	23.7931i	−1.26236	−	0.917158i	−0.998871	+	0.0475044i	$0.984873\pi$
$674$	14.0018	+	10.1729i	0.539330	+	0.391846i
$675$		0			0
$676$	−7.89044			−0.303478
$677$	−16.5546			−0.636245			−0.318123	−	0.948050i	$-0.603052\pi$
$677$	−16.5546			−0.636245			−0.318123	+	0.948050i	$0.603052\pi$
$678$		0			0
$679$	−4.80472	+	14.7874i	−0.184388	+	0.567489i
$680$	8.42765	+	25.9376i	0.323186	+	0.994663i
$681$		0			0
$682$	2.27408	+	2.13321i	0.0870792	+	0.0816848i
$683$	15.8493			0.606455			0.303228	−	0.952918i	$-0.401936\pi$
$683$	15.8493			0.606455			0.303228	+	0.952918i	$0.401936\pi$
$684$		0			0
$685$	−12.6545	+	38.9466i	−0.483505	+	1.48807i
$686$	−38.8910	+	28.2560i	−1.48487	+	1.07882i
$687$		0			0
$688$	−15.1565			−0.577836
$689$	−17.1437	+	12.4556i	−0.653122	+	0.474521i
$690$		0			0
$691$	−0.221090	−	0.160631i	−0.00841065	−	0.00611069i	0.583572	−	0.812061i	$-0.301655\pi$
$691$	−0.221090	−	0.160631i	−0.00841065	−	0.00611069i	−0.591983	+	0.805951i	$0.701655\pi$
$692$	−0.917278	−	2.82309i	−0.0348697	−	0.107318i
$693$		0			0
$694$	1.30450	+	4.01483i	0.0495180	+	0.152401i
$695$	−28.2783	+	87.0315i	−1.07266	+	3.30129i
$696$		0			0
$697$	−6.98172	+	21.4875i	−0.264452	+	0.813899i
$698$	18.0227	−	55.4683i	0.682171	−	2.09951i
$699$		0			0
$700$	11.2536	−	34.6350i	0.425346	−	1.30908i
$701$	6.92750	+	21.3207i	0.261648	+	0.805270i	0.992447	+	0.122677i	$0.0391479\pi$
$701$	6.92750	+	21.3207i	0.261648	+	0.805270i	−0.730798	+	0.682593i	$0.760852\pi$
$702$		0			0
$703$	−0.485488	−	1.49418i	−0.0183105	−	0.0563540i
$704$	0.762368	+	0.553892i	0.0287328	+	0.0208756i
$705$		0			0
$706$	12.3580	−	8.97865i	0.465101	−	0.337916i
$707$	2.85403			0.107337
$708$		0			0
$709$	−11.9791	+	8.70336i	−0.449886	+	0.326861i	−0.789551	−	0.613685i	$-0.789686\pi$
$709$	−11.9791	+	8.70336i	−0.449886	+	0.326861i	0.339665	+	0.940547i	$0.389686\pi$
$710$	−3.49534	+	10.7576i	−0.131178	+	0.403724i
$711$		0			0
$712$	−16.2474			−0.608896
$713$	11.1375	+	10.4476i	0.417104	+	0.391265i
$714$		0			0
$715$	−0.704334	−	2.16772i	−0.0263406	−	0.0810680i
$716$	−0.448821	+	1.38133i	−0.0167732	+	0.0516227i
$717$		0			0
$718$	7.88105			0.294118
$719$	25.1086			0.936392			0.468196	−	0.883625i	$-0.344904\pi$
$719$	25.1086			0.936392			0.468196	+	0.883625i	$0.344904\pi$
$720$		0			0
$721$	−3.97270	−	2.88633i	−0.147951	−	0.107493i
$722$	25.6278	+	18.6197i	0.953769	+	0.692954i
$723$		0			0
$724$	7.40949	−	5.38331i	0.275371	−	0.200069i
$725$	22.7596	+	70.0470i	0.845272	+	2.60148i
$726$		0			0
$727$	−1.07036	−	0.777660i	−0.0396973	−	0.0288418i	0.567760	−	0.823194i	$-0.307810\pi$
$727$	−1.07036	−	0.777660i	−0.0396973	−	0.0288418i	−0.607457	+	0.794353i	$0.707810\pi$
$728$	4.91283	−	15.1201i	0.182082	−	0.560390i
$729$		0			0
$730$	68.5619	+	49.8131i	2.53759	+	1.84367i
$731$	3.27892	−	10.0915i	0.121275	−	0.373247i
$732$		0			0
$733$	−17.2687	+	12.5465i	−0.637835	+	0.463414i	−0.859106	−	0.511798i	$-0.828980\pi$
$733$	−17.2687	+	12.5465i	−0.637835	+	0.463414i	0.221271	+	0.975212i	$0.428980\pi$
$734$	−12.6191	−	38.8375i	−0.465779	−	1.43352i
$735$		0			0
$736$	−9.42965	−	6.85104i	−0.347582	−	0.252533i
$737$	−0.372015	+	0.270285i	−0.0137033	+	0.00995606i
$738$		0			0
$739$	−22.1603			−0.815178			−0.407589	−	0.913165i	$-0.633630\pi$
$739$	−22.1603			−0.815178			−0.407589	+	0.913165i	$0.633630\pi$
$740$	−18.5314	+	13.4638i	−0.681227	+	0.494941i
$741$		0			0
$742$	−28.2899	−	87.0673i	−1.03855	−	3.19634i
$743$	29.6842			1.08901			0.544503	−	0.838759i	$-0.316718\pi$
$743$	29.6842			1.08901			0.544503	+	0.838759i	$0.316718\pi$
$744$		0			0
$745$	−41.6608			−1.52633
$746$	−1.82943	−	5.63042i	−0.0669804	−	0.206144i
$747$		0			0
$748$	0.745974	−	0.541982i	0.0272755	−	0.0198168i
$749$	36.0079			1.31570
$750$		0			0
$751$	−12.6150	+	9.16532i	−0.460327	+	0.334447i	−0.793660	−	0.608362i	$-0.791827\pi$
$751$	−12.6150	+	9.16532i	−0.460327	+	0.334447i	0.333333	+	0.942809i	$0.391827\pi$
$752$	−13.3730	−	9.71609i	−0.487665	−	0.354309i
$753$		0			0
$754$	−6.52649	−	20.0865i	−0.237681	−	0.731506i
$755$	8.87146	−	6.44549i	0.322866	−	0.234576i
$756$		0			0
$757$	6.55255	−	20.1667i	0.238157	−	0.732970i	−0.758530	−	0.651638i	$-0.774082\pi$
$757$	6.55255	−	20.1667i	0.238157	−	0.732970i	0.996687	−	0.0813329i	$-0.0259177\pi$
$758$	−32.6673	−	23.7342i	−1.18653	−	0.862065i
$759$		0			0
$760$	0.514478	−	1.58340i	0.0186621	−	0.0574359i
$761$	−19.7619	−	14.3579i	−0.716369	−	0.520473i	0.168853	−	0.985641i	$-0.445994\pi$
$761$	−19.7619	−	14.3579i	−0.716369	−	0.520473i	−0.885222	+	0.465169i	$0.845994\pi$
$762$		0			0
$763$	0.306092	+	0.942053i	0.0110813	+	0.0341046i
$764$	−5.70292	+	4.14341i	−0.206324	+	0.149903i
$765$		0			0
$766$	1.60593	+	1.16678i	0.0580246	+	0.0421574i
$767$	1.93749	+	1.40767i	0.0699588	+	0.0508280i
$768$		0			0
$769$	23.9568			0.863903			0.431952	−	0.901897i	$-0.357825\pi$
$769$	23.9568			0.863903			0.431952	+	0.901897i	$0.357825\pi$
$770$	9.84689			0.354857
$771$		0			0
$772$	−2.77572	+	8.54279i	−0.0999003	+	0.307462i
$773$	−13.9669	−	42.9856i	−0.502353	−	1.54608i	−0.805175	−	0.593037i	$-0.797929\pi$
$773$	−13.9669	−	42.9856i	−0.502353	−	1.54608i	0.302822	−	0.953047i	$-0.402071\pi$
$774$		0			0
$775$	56.2130	+	7.07067i	2.01923	+	0.253986i
$776$	6.94914			0.249459
$777$		0			0
$778$	−9.43287	+	29.0314i	−0.338185	+	1.04083i
$779$	1.11583	−	0.810698i	0.0399788	−	0.0290463i
$780$		0			0
$781$	−0.582204			−0.0208329
$782$	12.8690	−	9.34985i	0.460193	−	0.334350i
$783$		0			0
$784$	53.6305	+	38.9648i	1.91538	+	1.39160i
$785$	−17.6002	−	54.1679i	−0.628178	−	1.93333i
$786$		0			0
$787$	−6.14933	−	18.9257i	−0.219200	−	0.674628i	−0.998829	−	0.0483860i	$-0.984592\pi$
$787$	−6.14933	−	18.9257i	−0.219200	−	0.674628i	0.779629	−	0.626242i	$-0.215408\pi$
$788$	3.41349	−	10.5056i	0.121600	−	0.374248i
$789$		0			0
$790$	−17.1188	+	52.6862i	−0.609058	+	1.87449i
$791$	16.6332	−	51.1917i	0.591408	−	1.82017i
$792$		0			0
$793$	−1.93687	+	5.96108i	−0.0687804	+	0.211684i
$794$	−1.36966	−	4.21538i	−0.0486075	−	0.149598i
$795$		0			0
$796$	0.109455	+	0.336869i	0.00387955	+	0.0119400i
$797$	−33.3028	−	24.1959i	−1.17964	−	0.857062i	−0.187513	−	0.982262i	$-0.560043\pi$
$797$	−33.3028	−	24.1959i	−1.17964	−	0.857062i	−0.992131	+	0.125200i	$0.960043\pi$
$798$		0			0
$799$	9.36225	−	6.80207i	0.331213	−	0.240640i
$800$	−43.2437			−1.52890
$801$		0			0
$802$	−22.4482	+	16.3095i	−0.792672	+	0.575910i
$803$	−1.34796	+	4.14858i	−0.0475683	+	0.146400i
$804$		0			0
$805$	48.2260			1.69974
$806$	−16.1195	−	2.02756i	−0.567785	−	0.0714179i
$807$		0			0
$808$	−0.394172	−	1.21314i	−0.0138669	−	0.0426780i
$809$	−13.6189	+	41.9145i	−0.478813	+	1.47364i	0.361932	+	0.932205i	$0.382117\pi$
$809$	−13.6189	+	41.9145i	−0.478813	+	1.47364i	−0.840745	+	0.541431i	$0.817883\pi$
$810$		0			0
$811$	24.0093			0.843079			0.421539	−	0.906810i	$-0.361490\pi$
$811$	24.0093			0.843079			0.421539	+	0.906810i	$0.361490\pi$
$812$	25.9037			0.909043
$813$		0			0
$814$	−3.35980	−	2.44104i	−0.117761	−	0.0855583i
$815$	−54.3501	−	39.4877i	−1.90380	−	1.38319i
$816$		0			0
$817$	−0.524043	+	0.380739i	−0.0183339	+	0.0133204i
$818$	13.2579	+	40.8037i	0.463552	+	1.42667i
$819$		0			0
$820$	−16.2687	−	11.8199i	−0.568127	−	0.412768i
$821$	−12.9352	+	39.8104i	−0.451441	+	1.38939i	0.423822	+	0.905745i	$0.360688\pi$
$821$	−12.9352	+	39.8104i	−0.451441	+	1.38939i	−0.875263	+	0.483647i	$0.839312\pi$
$822$		0			0
$823$	−33.7649	−	24.5316i	−1.17697	−	0.855118i	−0.185143	−	0.982712i	$-0.559275\pi$
$823$	−33.7649	−	24.5316i	−1.17697	−	0.855118i	−0.991827	+	0.127593i	$0.959275\pi$
$824$	−0.678196	+	2.08727i	−0.0236261	+	0.0727135i
$825$		0			0
$826$	−8.37033	+	6.08140i	−0.291241	+	0.211599i
$827$	−5.57224	−	17.1496i	−0.193766	−	0.596350i	−0.999989	−	0.00473793i	$-0.998492\pi$
$827$	−5.57224	−	17.1496i	−0.193766	−	0.596350i	0.806223	−	0.591612i	$-0.201508\pi$
$828$		0			0
$829$	−10.2529	−	7.44918i	−0.356098	−	0.258721i	0.395325	−	0.918542i	$-0.370632\pi$
$829$	−10.2529	−	7.44918i	−0.356098	−	0.258721i	−0.751423	+	0.659821i	$0.770632\pi$
$830$	41.9114	−	30.4504i	1.45477	−	1.05695i
$831$		0			0
$832$	−4.91007			−0.170226
$833$	−37.5458	+	27.2786i	−1.30089	+	0.945149i
$834$		0			0
$835$	−0.491284	−	1.51202i	−0.0170016	−	0.0523254i
$836$	−0.0562894			−0.00194681
$837$		0			0
$838$	−52.0705			−1.79875
$839$	13.3184	+	40.9897i	0.459801	+	1.41512i	0.865405	+	0.501073i	$0.167061\pi$
$839$	13.3184	+	40.9897i	0.459801	+	1.41512i	−0.405604	+	0.914049i	$0.632939\pi$
$840$		0			0
$841$	−18.9218	+	13.7475i	−0.652474	+	0.474050i
$842$	−51.0581			−1.75958
$843$		0			0
$844$	−13.0866	+	9.50800i	−0.450461	+	0.327279i
$845$	−31.3629	−	22.7864i	−1.07891	−	0.783878i
$846$		0			0
$847$	−15.1861	−	46.7379i	−0.521800	−	1.60593i
$848$	−48.6722	+	35.3624i	−1.67141	+	1.21435i
$849$		0			0
$850$	18.2370	−	56.1277i	0.625523	−	1.92516i
$851$	−16.4549	−	11.9552i	−0.564067	−	0.409819i
$852$		0			0
$853$	13.8701	−	42.6879i	0.474904	−	1.46160i	−0.371183	−	0.928560i	$-0.621048\pi$
$853$	13.8701	−	42.6879i	0.474904	−	1.46160i	0.846087	−	0.533045i	$-0.178952\pi$
$854$	−21.9068	−	15.9162i	−0.749636	−	0.544642i
$855$		0			0
$856$	−4.97308	−	15.3056i	−0.169976	−	0.523133i
$857$	11.5054	−	8.35916i	0.393017	−	0.285544i	−0.373674	−	0.927560i	$-0.621902\pi$
$857$	11.5054	−	8.35916i	0.393017	−	0.285544i	0.766691	+	0.642017i	$0.221902\pi$
$858$		0			0
$859$	19.0567	+	13.8455i	0.650205	+	0.472402i	0.863341	−	0.504621i	$-0.168368\pi$
$859$	19.0567	+	13.8455i	0.650205	+	0.472402i	−0.213136	+	0.977023i	$0.568368\pi$
$860$	7.64048	+	5.55113i	0.260538	+	0.189292i
$861$		0			0
$862$	61.2856			2.08739
$863$	−33.9831			−1.15680			−0.578400	−	0.815754i	$-0.696323\pi$
$863$	−33.9831			−1.15680			−0.578400	+	0.815754i	$0.696323\pi$
$864$		0			0
$865$	4.50669	−	13.8702i	0.153232	−	0.471600i
$866$	−7.10411	−	21.8642i	−0.241408	−	0.742976i
$867$		0			0
$868$	8.47448	−	18.0343i	0.287643	−	0.612126i
$869$	−2.85140			−0.0967272
$870$		0			0
$871$	0.740400	−	2.27872i	0.0250875	−	0.0772114i
$872$	0.358155	−	0.260215i	0.0121287	−	0.00881200i
$873$		0			0
$874$	−0.971060			−0.0328466
$875$	73.6256	−	53.4921i	2.48900	−	1.80836i
$876$		0			0
$877$	34.2692	+	24.8980i	1.15719	+	0.840747i	0.989420	−	0.145080i	$-0.0463439\pi$
$877$	34.2692	+	24.8980i	1.15719	+	0.840747i	0.167769	+	0.985826i	$0.446344\pi$
$878$	−2.96817	−	9.13508i	−0.100171	−	0.308294i
$879$		0			0
$880$	−1.99966	−	6.15431i	−0.0674084	−	0.207462i
$881$	10.3273	−	31.7841i	0.347934	−	1.07083i	−0.612060	−	0.790812i	$-0.709659\pi$
$881$	10.3273	−	31.7841i	0.347934	−	1.07083i	0.959994	−	0.280020i	$-0.0903412\pi$
$882$		0			0
$883$	−5.00096	+	15.3914i	−0.168296	+	0.517961i	−0.999264	−	0.0383588i	$-0.987787\pi$
$883$	−5.00096	+	15.3914i	−0.168296	+	0.517961i	0.830968	+	0.556320i	$0.187787\pi$
$884$	−1.48467	+	4.56934i	−0.0499349	+	0.153684i
$885$		0			0
$886$	−16.5642	+	50.9793i	−0.556484	+	1.71268i
$887$	13.2941	+	40.9151i	0.446373	+	1.37379i	0.880971	+	0.473170i	$0.156891\pi$
$887$	13.2941	+	40.9151i	0.446373	+	1.37379i	−0.434598	+	0.900625i	$0.643109\pi$
$888$		0			0
$889$	18.0865	+	55.6644i	0.606600	+	1.86692i
$890$	42.4201	+	30.8200i	1.42192	+	1.03309i
$891$		0			0
$892$	−13.1098	+	9.52483i	−0.438949	+	0.318915i
$893$	−0.706452			−0.0236405
$894$		0			0
$895$	−5.77304	+	4.19436i	−0.192972	+	0.140202i
$896$	18.4099	−	56.6598i	0.615031	−	1.89287i
$897$		0			0
$898$	37.7253			1.25891
$899$	7.57264	+	39.5816i	0.252562	+	1.32012i
$900$		0			0
$901$	−13.0153	−	40.0571i	−0.433604	−	1.33449i
$902$	1.12663	−	3.46742i	0.0375128	−	0.115452i
$903$		0			0
$904$	−24.0568			−0.800117
$905$	44.9974			1.49576
$906$		0			0
$907$	−14.9442	−	10.8576i	−0.496214	−	0.360521i	0.311355	−	0.950294i	$-0.399217\pi$
$907$	−14.9442	−	10.8576i	−0.496214	−	0.360521i	−0.807569	+	0.589773i	$0.799217\pi$
$908$	−7.77985	−	5.65239i	−0.258183	−	0.187581i
$909$		0			0
$910$	−41.5086	+	30.1577i	−1.37600	+	0.999720i
$911$	−6.45301	−	19.8603i	−0.213798	−	0.658002i	−0.999237	−	0.0390629i	$-0.987563\pi$
$911$	−6.45301	−	19.8603i	−0.213798	−	0.658002i	0.785439	−	0.618939i	$-0.212437\pi$
$912$		0			0
$913$	2.15725	+	1.56733i	0.0713945	+	0.0518711i
$914$	4.27808	−	13.1666i	0.141506	−	0.435512i
$915$		0			0
$916$	−15.1221	−	10.9869i	−0.499649	−	0.363016i
$917$	−18.5046	+	56.9512i	−0.611075	+	1.88069i
$918$		0			0
$919$	12.0720	−	8.77082i	0.398218	−	0.289323i	−0.370597	−	0.928794i	$-0.620847\pi$
$919$	12.0720	−	8.77082i	0.398218	−	0.289323i	0.768815	+	0.639471i	$0.220847\pi$
$920$	−6.66052	−	20.4990i	−0.219591	−	0.675831i
$921$		0			0
$922$	−21.3603	−	15.5192i	−0.703465	−	0.511098i
$923$	2.45422	−	1.78310i	0.0807818	−	0.0586914i
$924$		0			0
$925$	−75.4610			−2.48114
$926$	19.2446	−	13.9820i	0.632418	−	0.459479i
$927$		0			0
$928$	−9.50514	−	29.2538i	−0.312022	−	0.960304i
$929$	19.8663			0.651793			0.325897	−	0.945405i	$-0.394334\pi$
$929$	19.8663			0.651793			0.325897	+	0.945405i	$0.394334\pi$
$930$		0			0
$931$	2.83312			0.0928516
$932$	−1.88408	−	5.79861i	−0.0617151	−	0.189940i
$933$		0			0
$934$	35.4826	−	25.7796i	1.16102	−	0.843534i
$935$	4.53026			0.148155
$936$		0			0
$937$	−8.17157	+	5.93699i	−0.266954	+	0.193953i	−0.713207	−	0.700954i	$-0.752758\pi$
$937$	−8.17157	+	5.93699i	−0.266954	+	0.193953i	0.446253	+	0.894907i	$0.352758\pi$
$938$	8.37422	+	6.08422i	0.273428	+	0.198657i
$939$		0			0
$940$	3.18287	+	9.79587i	0.103814	+	0.319506i
$941$	−10.2657	+	7.45844i	−0.334651	+	0.243138i	−0.742401	−	0.669955i	$-0.766313\pi$
$941$	−10.2657	+	7.45844i	−0.334651	+	0.243138i	0.407751	+	0.913093i	$0.366313\pi$
$942$		0			0
$943$	5.51778	−	16.9820i	0.179684	−	0.553010i
$944$	5.50069	+	3.99648i	0.179032	+	0.130074i
$945$		0			0
$946$	−0.529116	+	1.62845i	−0.0172030	+	0.0529455i
$947$	13.4397	+	9.76448i	0.436730	+	0.317303i	0.784334	−	0.620338i	$-0.213005\pi$
$947$	13.4397	+	9.76448i	0.436730	+	0.317303i	−0.347604	+	0.937641i	$0.613005\pi$
$948$		0			0
$949$	−7.02356	−	21.6163i	−0.227994	−	0.701694i
$950$	−2.91466	+	2.11763i	−0.0945642	+	0.0687049i
$951$		0			0
$952$	25.5643	+	18.5735i	0.828543	+	0.601972i
$953$	−44.7050	−	32.4801i	−1.44814	−	1.05213i	−0.986262	−	0.165189i	$-0.947177\pi$
$953$	−44.7050	−	32.4801i	−1.44814	−	1.05213i	−0.461875	−	0.886945i	$-0.652823\pi$
$954$		0			0
$955$	−34.6335			−1.12071
$956$	17.7247			0.573258
$957$		0			0
$958$	21.5630	−	66.3639i	0.696667	−	2.14412i
$959$	14.6622	+	45.1255i	0.473466	+	1.45718i
$960$		0			0
$961$	30.0343	+	7.67711i	0.968850	+	0.247649i
$962$	21.6390			0.697669
$963$		0			0
$964$	2.15296	−	6.62613i	0.0693421	−	0.213413i
$965$	−35.7032	+	25.9399i	−1.14933	+	0.835036i
$966$		0			0
$967$	−44.8302			−1.44164			−0.720821	−	0.693121i	$-0.756235\pi$
$967$	−44.8302			−1.44164			−0.720821	+	0.693121i	$0.756235\pi$
$968$	−17.7691	+	12.9100i	−0.571121	+	0.414943i
$969$		0			0
$970$	−18.1434	−	13.1820i	−0.582550	−	0.423248i
$971$	18.8116	+	57.8963i	0.603694	+	1.85798i	0.505530	+	0.862809i	$0.331297\pi$
$971$	18.8116	+	57.8963i	0.603694	+	1.85798i	0.0981642	+	0.995170i	$0.468703\pi$
$972$		0			0
$973$	32.7646	+	100.839i	1.05038	+	3.23275i
$974$	−17.8379	+	54.8994i	−0.571563	+	1.75909i
$975$		0			0
$976$	−5.49893	+	16.9240i	−0.176016	+	0.541723i
$977$	−8.89298	+	27.3698i	−0.284512	+	0.875636i	0.702033	+	0.712144i	$0.252276\pi$
$977$	−8.89298	+	27.3698i	−0.284512	+	0.875636i	−0.986545	+	0.163492i	$0.947724\pi$
$978$		0			0
$979$	−0.833996	+	2.56678i	−0.0266546	+	0.0820346i
$980$	−12.7644	−	39.2848i	−0.407744	−	1.25491i
$981$		0			0
$982$	−6.97106	−	21.4547i	−0.222455	−	0.684647i
$983$	25.6405	+	18.6289i	0.817807	+	0.594171i	0.916083	−	0.400988i	$-0.131333\pi$
$983$	25.6405	+	18.6289i	0.817807	+	0.594171i	−0.0982768	+	0.995159i	$0.531333\pi$
$984$		0			0
$985$	43.9066	−	31.9000i	1.39898	−	1.01642i
$986$	41.9782			1.33686
$987$		0			0
$988$	0.237282	−	0.172396i	0.00754896	−	0.00548464i
$989$	−2.59139	+	7.97548i	−0.0824015	+	0.253606i
$990$		0			0
$991$	−2.33148			−0.0740618			−0.0370309	−	0.999314i	$-0.511790\pi$
$991$	−2.33148			−0.0740618			−0.0370309	+	0.999314i	$0.511790\pi$
$992$	−23.4763	−	2.95293i	−0.745374	−	0.0937557i
$993$		0			0
$994$	4.04987	+	12.4642i	0.128454	+	0.395341i
$995$	−0.537767	+	1.65508i	−0.0170484	+	0.0524695i
$996$		0			0
$997$	22.7279			0.719800			0.359900	−	0.932991i	$-0.382811\pi$
$997$	22.7279			0.719800			0.359900	+	0.932991i	$0.382811\pi$
$998$	−63.1419			−1.99872
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.i.c.190.3		16
3.2	odd	2		93.2.f.b.4.2	✓	16
31.8	even	5	inner	279.2.i.c.163.3		16
31.15	odd	10		8649.2.a.bg.1.6		8
31.16	even	5		8649.2.a.bh.1.6		8
93.8	odd	10		93.2.f.b.70.2	yes	16
93.47	odd	10		2883.2.a.p.1.3		8
93.77	even	10		2883.2.a.o.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.f.b.4.2	✓	16	3.2	odd	2
93.2.f.b.70.2	yes	16	93.8	odd	10
279.2.i.c.163.3		16	31.8	even	5	inner
279.2.i.c.190.3		16	1.1	even	1	trivial
2883.2.a.o.1.3		8	93.77	even	10
2883.2.a.p.1.3		8	93.47	odd	10
8649.2.a.bg.1.6		8	31.15	odd	10
8649.2.a.bh.1.6		8	31.16	even	5

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:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.516428 + 1.58940i) q^{2} +(-0.641469 + 0.466054i) q^{4} -3.89560 q^{5} +(-3.65161 + 2.65305i) q^{7} +(1.63203 + 1.18574i) q^{8} +(-2.01180 - 6.19168i) q^{10} +(0.271099 - 0.196965i) q^{11} +(-0.539553 + 1.66057i) q^{13} +(-6.10256 - 4.43377i) q^{14} +(-1.53183 + 4.71449i) q^{16} +(-2.80760 - 2.03984i) q^{17} +(0.0654667 + 0.201486i) q^{19} +(2.49891 - 1.81556i) q^{20} +(0.453060 + 0.329167i) q^{22} +(2.21890 + 1.61213i) q^{23} +10.1757 q^{25} -2.91796 q^{26} +(1.10593 - 3.40369i) q^{28} +(2.23666 + 6.88374i) q^{29} +(5.52424 + 0.694857i) q^{31} -4.24970 q^{32} +(1.79221 - 5.51585i) q^{34} +(14.2252 - 10.3352i) q^{35} -7.41580 q^{37} +(-0.286433 + 0.208106i) q^{38} +(-6.35775 - 4.61918i) q^{40} +(-2.01180 - 6.19168i) q^{41} +(0.944828 + 2.90788i) q^{43} +(-0.0821051 + 0.252694i) q^{44} +(-1.41641 + 4.35927i) q^{46} +(-1.03045 + 3.17140i) q^{47} +(4.13246 - 12.7184i) q^{49} +(5.25503 + 16.1733i) q^{50} +(-0.427811 - 1.31667i) q^{52} +(9.81866 + 7.13368i) q^{53} +(-1.05609 + 0.767297i) q^{55} -9.10537 q^{56} +(-9.78596 + 7.10992i) q^{58} +(0.423851 - 1.30448i) q^{59} +3.58978 q^{61} +(1.74846 + 9.13908i) q^{62} +(0.868998 + 2.67450i) q^{64} +(2.10188 - 6.46893i) q^{65} -1.37225 q^{67} +2.75167 q^{68} +(23.7731 + 17.2722i) q^{70} +(-1.40560 - 1.02123i) q^{71} +(-10.5313 + 7.65141i) q^{73} +(-3.82973 - 11.7867i) q^{74} +(-0.135898 - 0.0987358i) q^{76} +(-0.467390 + 1.43848i) q^{77} +(-6.88408 - 5.00157i) q^{79} +(5.96740 - 18.3658i) q^{80} +(8.80212 - 6.39512i) q^{82} +(2.45898 + 7.56796i) q^{83} +(10.9373 + 7.94642i) q^{85} +(-4.13386 + 3.00343i) q^{86} +0.675992 q^{88} +(-6.51582 + 4.73402i) q^{89} +(-2.43534 - 7.49522i) q^{91} -2.17469 q^{92} -5.57278 q^{94} +(-0.255032 - 0.784909i) q^{95} +(2.78687 - 2.02478i) q^{97} +22.3488 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 9 q^{4} - 6 q^{5} - 7 q^{7} + 2 q^{8} - 3 q^{10} - 10 q^{11} - 3 q^{13} + 4 q^{14} - 17 q^{16} + q^{17} - 4 q^{19} - 7 q^{20} + 10 q^{22} - 7 q^{23} + 30 q^{25} + 16 q^{26} + 9 q^{28}+ \cdots + 82 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 9 * q^4 - 6 * q^5 - 7 * q^7 + 2 * q^8 - 3 * q^10 - 10 * q^11 - 3 * q^13 + 4 * q^14 - 17 * q^16 + q^17 - 4 * q^19 - 7 * q^20 + 10 * q^22 - 7 * q^23 + 30 * q^25 + 16 * q^26 + 9 * q^28 + 2 * q^29 - 13 * q^31 - 108 * q^32 - 4 * q^34 + 33 * q^35 - 28 * q^37 + 62 * q^38 - 27 * q^40 - 3 * q^41 - 13 * q^43 + 64 * q^44 - q^46 + 20 * q^47 + q^49 + 44 * q^50 + 88 * q^52 + 4 * q^53 - 8 * q^55 - 104 * q^56 - 31 * q^58 - 49 * q^59 + 13 * q^62 - 26 * q^64 + q^65 + 60 * q^67 + 30 * q^68 + 85 * q^70 - 23 * q^71 - 17 * q^73 - 70 * q^74 + 7 * q^76 - 2 * q^77 - 13 * q^79 + 94 * q^80 - 9 * q^82 + 49 * q^83 - 4 * q^85 - 24 * q^86 - 32 * q^88 - 3 * q^89 - 2 * q^91 + 70 * q^92 + 74 * q^94 + 10 * q^95 + 3 * q^97 + 82 * q^98

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