LMFDB - Embedded newform 475.2.e.e.26.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(26,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.2
Root			$-1.02359 - 1.77290i$ of defining polynomial
Character	$\chi$	$=$	475.26
Dual form			475.2.e.e.201.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.595455 - 1.03136i) q^{2} +(1.52359 + 2.63893i) q^{3} +(0.290867 - 0.503797i) q^{4} +(1.81445 - 3.14272i) q^{6} +0.609175 q^{7} -3.07461 q^{8} +(-3.14263 + 5.44319i) q^{9} +4.48517 q^{11} +1.77264 q^{12} +(2.21900 - 3.84342i) q^{13} +(-0.362736 - 0.628278i) q^{14} +(1.24906 + 2.16343i) q^{16} +(1.45172 + 2.51445i) q^{17} +7.48517 q^{18} +(3.60532 + 2.44983i) q^{19} +(0.928131 + 1.60757i) q^{21} +(-2.67071 - 4.62581i) q^{22} +(-1.42363 + 2.46580i) q^{23} +(-4.68443 - 8.11368i) q^{24} -5.28525 q^{26} -10.0107 q^{27} +(0.177189 - 0.306901i) q^{28} +(-0.558149 + 0.966742i) q^{29} -6.22908 q^{31} +(-1.58710 + 2.74893i) q^{32} +(6.83354 + 11.8360i) q^{33} +(1.72886 - 2.99448i) q^{34} +(1.82817 + 3.16649i) q^{36} +3.77264 q^{37} +(0.379847 - 5.17714i) q^{38} +13.5233 q^{39} +(4.15184 + 7.19120i) q^{41} +(1.10532 - 1.91447i) q^{42} +(-4.99438 - 8.65053i) q^{43} +(1.30459 - 2.25961i) q^{44} +3.39082 q^{46} +(-2.94250 + 5.09656i) q^{47} +(-3.80609 + 6.59235i) q^{48} -6.62891 q^{49} +(-4.42363 + 7.66195i) q^{51} +(-1.29087 - 2.23585i) q^{52} +(4.22436 - 7.31681i) q^{53} +(5.96093 + 10.3246i) q^{54} -1.87298 q^{56} +(-0.971912 + 13.2467i) q^{57} +1.32941 q^{58} +(-5.11793 - 8.86451i) q^{59} +(2.49099 - 4.31453i) q^{61} +(3.70913 + 6.42441i) q^{62} +(-1.91441 + 3.31586i) q^{63} +8.77641 q^{64} +(8.13812 - 14.0956i) q^{66} +(4.23808 - 7.34057i) q^{67} +1.68903 q^{68} -8.67608 q^{69} +(-5.80995 - 10.0631i) q^{71} +(9.66236 - 16.7357i) q^{72} +(1.86162 + 3.22443i) q^{73} +(-2.24644 - 3.89095i) q^{74} +(2.28289 - 1.10377i) q^{76} +2.73225 q^{77} +(-8.05253 - 13.9474i) q^{78} +(-4.51908 - 7.82728i) q^{79} +(-5.82432 - 10.0880i) q^{81} +(4.94447 - 8.56407i) q^{82} +2.12178 q^{83} +1.07985 q^{84} +(-5.94786 + 10.3020i) q^{86} -3.40155 q^{87} -13.7901 q^{88} +(-3.96608 + 6.86946i) q^{89} +(1.35176 - 2.34131i) q^{91} +(0.828173 + 1.43444i) q^{92} +(-9.49053 - 16.4381i) q^{93} +7.00850 q^{94} -9.67231 q^{96} +(-4.83628 - 8.37668i) q^{97} +(3.94721 + 6.83677i) q^{98} +(-14.0952 + 24.4136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9} - 4 q^{11} - 12 q^{12} + 7 q^{13} + q^{14} - 7 q^{16} - q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} - 23 q^{24}+ \cdots - 38 q^{99}+O(q^{100}) $ 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9 - 4 * q^11 - 12 * q^12 + 7 * q^13 + q^14 - 7 * q^16 - q^17 + 20 * q^18 + 5 * q^19 + 4 * q^21 + 2 * q^22 + 2 * q^23 - 23 * q^24 + 6 * q^26 - 24 * q^27 - 19 * q^28 + q^29 + 30 * q^32 + 19 * q^33 - 15 * q^34 + 7 * q^36 + 4 * q^37 - 13 * q^38 + 30 * q^39 + 8 * q^41 - 15 * q^42 + q^43 + 12 * q^44 + 24 * q^46 - 12 * q^47 + 23 * q^48 - 20 * q^49 - 22 * q^51 - 3 * q^52 - 5 * q^53 + 34 * q^54 - 82 * q^56 - 7 * q^57 + 54 * q^58 + 5 * q^59 + 37 * q^62 - 3 * q^63 + 112 * q^64 + 31 * q^66 + 4 * q^67 - 32 * q^68 - 18 * q^69 - 20 * q^71 + 17 * q^72 - 20 * q^73 - 25 * q^74 + 63 * q^76 - 28 * q^77 - 18 * q^78 - 17 * q^79 - 12 * q^81 + 21 * q^82 - 2 * q^83 - 40 * q^84 - 8 * q^86 + 32 * q^87 + 14 * q^88 - 11 * q^89 - 6 * q^91 - q^92 - 8 * q^93 - 62 * q^94 + 42 * q^96 + q^97 + 9 * q^98 - 38 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.595455	−	1.03136i	−0.421050	−	0.729280i	0.574992	−	0.818159i	$-0.305005\pi$
$2$	−0.595455	−	1.03136i	−0.421050	−	0.729280i	−0.996042	+	0.0888786i	$0.971672\pi$
$3$	1.52359	+	2.63893i	0.879643	+	1.52359i	0.851734	+	0.523975i	$0.175552\pi$
$3$	1.52359	+	2.63893i	0.879643	+	1.52359i	0.0279089	+	0.999610i	$0.491115\pi$
$4$	0.290867	−	0.503797i	0.145434	−	0.251898i
$5$		0			0
$5$		0			0
$6$	1.81445	−	3.14272i	0.740747	−	1.28301i
$7$	0.609175			0.230247			0.115123	−	0.993351i	$-0.463274\pi$
$7$	0.609175			0.230247			0.115123	+	0.993351i	$0.463274\pi$
$8$	−3.07461			−1.08704
$9$	−3.14263	+	5.44319i	−1.04754	+	1.81440i
$10$		0			0
$11$	4.48517			1.35233			0.676164	−	0.736751i	$-0.263641\pi$
$11$	4.48517			1.35233			0.676164	+	0.736751i	$0.263641\pi$
$12$	1.77264			0.511718
$13$	2.21900	−	3.84342i	0.615439	−	1.06597i	−0.374868	−	0.927078i	$-0.622312\pi$
$13$	2.21900	−	3.84342i	0.615439	−	1.06597i	0.990307	−	0.138894i	$-0.0443547\pi$
$14$	−0.362736	−	0.628278i	−0.0969454	−	0.167914i
$15$		0			0
$16$	1.24906	+	2.16343i	0.312265	+	0.540858i
$17$	1.45172	+	2.51445i	0.352093	+	0.609843i	0.986616	−	0.163061i	$-0.0521368\pi$
$17$	1.45172	+	2.51445i	0.352093	+	0.609843i	−0.634523	+	0.772904i	$0.718803\pi$
$18$	7.48517			1.76427
$19$	3.60532	+	2.44983i	0.827117	+	0.562030i
$19$	3.60532	+	2.44983i	0.827117	+	0.562030i
$20$		0			0
$21$	0.928131	+	1.60757i	0.202535	+	0.350800i
$22$	−2.67071	−	4.62581i	−0.569398	−	0.986227i
$23$	−1.42363	+	2.46580i	−0.296847	+	0.514154i	−0.975413	−	0.220386i	$-0.929268\pi$
$23$	−1.42363	+	2.46580i	−0.296847	+	0.514154i	0.678566	+	0.734540i	$0.262602\pi$
$24$	−4.68443	−	8.11368i	−0.956206	−	1.65620i
$25$		0			0
$26$	−5.28525			−1.03652
$27$	−10.0107			−1.92656
$28$	0.177189	−	0.306901i	0.0334856	−	0.0579987i
$29$	−0.558149	+	0.966742i	−0.103646	+	0.179519i	−0.913184	−	0.407547i	$-0.866384\pi$
$29$	−0.558149	+	0.966742i	−0.103646	+	0.179519i	0.809538	+	0.587067i	$0.199717\pi$
$30$		0			0
$31$	−6.22908			−1.11877			−0.559387	−	0.828906i	$-0.688964\pi$
$31$	−6.22908			−1.11877			−0.559387	+	0.828906i	$0.688964\pi$
$32$	−1.58710	+	2.74893i	−0.280562	+	0.485947i
$33$	6.83354	+	11.8360i	1.18957	+	2.06039i
$34$	1.72886	−	2.99448i	0.296498	−	0.513549i
$35$		0			0
$36$	1.82817	+	3.16649i	0.304696	+	0.527748i
$37$	3.77264			0.620219			0.310109	−	0.950701i	$-0.399634\pi$
$37$	3.77264			0.620219			0.310109	+	0.950701i	$0.399634\pi$
$38$	0.379847	−	5.17714i	0.0616193	−	0.839843i
$39$	13.5233			2.16547
$40$		0			0
$41$	4.15184	+	7.19120i	0.648409	+	1.12308i	0.983503	+	0.180893i	$0.0578987\pi$
$41$	4.15184	+	7.19120i	0.648409	+	1.12308i	−0.335094	+	0.942185i	$0.608768\pi$
$42$	1.10532	−	1.91447i	0.170555	−	0.295409i
$43$	−4.99438	−	8.65053i	−0.761637	−	1.31919i	−0.942007	−	0.335594i	$-0.891063\pi$
$43$	−4.99438	−	8.65053i	−0.761637	−	1.31919i	0.180370	−	0.983599i	$-0.442270\pi$
$44$	1.30459	−	2.25961i	0.196674	−	0.340649i
$45$		0			0
$46$	3.39082			0.499950
$47$	−2.94250	+	5.09656i	−0.429208	+	0.743409i	−0.996803	−	0.0798983i	$-0.974540\pi$
$47$	−2.94250	+	5.09656i	−0.429208	+	0.743409i	0.567595	+	0.823308i	$0.307874\pi$
$48$	−3.80609	+	6.59235i	−0.549362	+	0.951524i
$49$	−6.62891			−0.946986
$50$		0			0
$51$	−4.42363	+	7.66195i	−0.619432	+	1.07289i
$52$	−1.29087	−	2.23585i	−0.179011	−	0.310056i
$53$	4.22436	−	7.31681i	0.580261	−	1.00504i	−0.415188	−	0.909736i	$-0.636284\pi$
$53$	4.22436	−	7.31681i	0.580261	−	1.00504i	0.995448	−	0.0953049i	$-0.0303826\pi$
$54$	5.96093	+	10.3246i	0.811180	+	1.40501i
$55$		0			0
$56$	−1.87298			−0.250287
$57$	−0.971912	+	13.2467i	−0.128733	+	1.75457i
$58$	1.32941			0.174560
$59$	−5.11793	−	8.86451i	−0.666297	−	1.15406i	−0.978932	−	0.204187i	$-0.934545\pi$
$59$	−5.11793	−	8.86451i	−0.666297	−	1.15406i	0.312634	−	0.949874i	$-0.398789\pi$
$60$		0			0
$61$	2.49099	−	4.31453i	0.318939	−	0.552419i	−0.661328	−	0.750097i	$-0.730007\pi$
$61$	2.49099	−	4.31453i	0.318939	−	0.552419i	0.980267	+	0.197678i	$0.0633401\pi$
$62$	3.70913	+	6.42441i	0.471060	+	0.815900i
$63$	−1.91441	+	3.31586i	−0.241193	+	0.417759i
$64$	8.77641			1.09705
$65$		0			0
$66$	8.13812	−	14.0956i	1.00173	−	1.73505i
$67$	4.23808	−	7.34057i	0.517764	−	0.896794i	−0.482023	−	0.876159i	$-0.660098\pi$
$67$	4.23808	−	7.34057i	0.517764	−	0.896794i	0.999787	−	0.0206350i	$-0.00656879\pi$
$68$	1.68903			0.204825
$69$	−8.67608			−1.04448
$70$		0			0
$71$	−5.80995	−	10.0631i	−0.689514	−	1.19427i	−0.971995	−	0.235001i	$-0.924491\pi$
$71$	−5.80995	−	10.0631i	−0.689514	−	1.19427i	0.282481	−	0.959273i	$-0.408843\pi$
$72$	9.66236	−	16.7357i	1.13872	−	1.97232i
$73$	1.86162	+	3.22443i	0.217887	+	0.377391i	0.954162	−	0.299292i	$-0.0967504\pi$
$73$	1.86162	+	3.22443i	0.217887	+	0.377391i	−0.736275	+	0.676682i	$0.763417\pi$
$74$	−2.24644	−	3.89095i	−0.261143	−	0.452313i
$75$		0			0
$76$	2.28289	−	1.10377i	0.261865	−	0.126611i
$77$	2.73225			0.311369
$78$	−8.05253	−	13.9474i	−0.911770	−	1.57923i
$79$	−4.51908	−	7.82728i	−0.508437	−	0.880638i	−0.999952	−	0.00976923i	$-0.996890\pi$
$79$	−4.51908	−	7.82728i	−0.508437	−	0.880638i	0.491516	−	0.870869i	$-0.336443\pi$
$80$		0			0
$81$	−5.82432	−	10.0880i	−0.647146	−	1.12089i
$82$	4.94447	−	8.56407i	0.546025	−	0.945744i
$83$	2.12178			0.232896			0.116448	−	0.993197i	$-0.462849\pi$
$83$	2.12178			0.232896			0.116448	+	0.993197i	$0.462849\pi$
$84$	1.07985			0.117821
$85$		0			0
$86$	−5.94786	+	10.3020i	−0.641374	+	1.11089i
$87$	−3.40155			−0.364684
$88$	−13.7901			−1.47003
$89$	−3.96608	+	6.86946i	−0.420404	+	0.728161i	−0.995979	−	0.0895879i	$-0.971445\pi$
$89$	−3.96608	+	6.86946i	−0.420404	+	0.728161i	0.575575	+	0.817749i	$0.304778\pi$
$90$		0			0
$91$	1.35176	−	2.34131i	0.141703	−	0.245436i
$92$	0.828173	+	1.43444i	0.0863430	+	0.149551i
$93$	−9.49053	−	16.4381i	−0.984122	−	1.70455i
$94$	7.00850			0.722872
$95$		0			0
$96$	−9.67231			−0.987176
$97$	−4.83628	−	8.37668i	−0.491050	−	0.850523i	0.508897	−	0.860827i	$-0.330053\pi$
$97$	−4.83628	−	8.37668i	−0.491050	−	0.850523i	−0.999947	+	0.0103043i	$0.996720\pi$
$98$	3.94721	+	6.83677i	0.398729	+	0.690619i
$99$	−14.0952	+	24.4136i	−1.41662	+	2.45366i
$100$		0			0
$101$	0.485632	−	0.841140i	0.0483222	−	0.0836965i	−0.840853	−	0.541264i	$-0.817946\pi$
$101$	0.485632	−	0.841140i	0.0483222	−	0.0836965i	0.889175	+	0.457568i	$0.151279\pi$
$102$	10.5363			1.04325
$103$	3.34143			0.329241			0.164620	−	0.986357i	$-0.447360\pi$
$103$	3.34143			0.329241			0.164620	+	0.986357i	$0.447360\pi$
$104$	−6.82256	+	11.8170i	−0.669007	+	1.15875i
$105$		0			0
$106$	−10.0617			−0.977275
$107$	−9.51655			−0.920000			−0.460000	−	0.887919i	$-0.652151\pi$
$107$	−9.51655			−0.920000			−0.460000	+	0.887919i	$0.652151\pi$
$108$	−2.91179	+	5.04337i	−0.280187	+	0.485298i
$109$	−2.77178	−	4.80087i	−0.265489	−	0.459840i	0.702203	−	0.711977i	$-0.252200\pi$
$109$	−2.77178	−	4.80087i	−0.265489	−	0.459840i	−0.967692	+	0.252137i	$0.918867\pi$
$110$		0			0
$111$	5.74795	+	9.95573i	0.545571	+	0.944956i
$112$	0.760896	+	1.31791i	0.0718979	+	0.124531i
$113$	−1.54134			−0.144997			−0.0724987	−	0.997369i	$-0.523097\pi$
$113$	−1.54134			−0.144997			−0.0724987	+	0.997369i	$0.523097\pi$
$114$	14.2408	−	6.88542i	1.33378	−	0.644879i
$115$		0			0
$116$	0.324694	+	0.562387i	0.0301471	+	0.0522163i
$117$	13.9470	+	24.1568i	1.28940	+	2.23330i
$118$	−6.09499	+	10.5568i	−0.561089	+	0.971835i
$119$	0.884350	+	1.53174i	0.0810682	+	0.140414i
$120$		0			0
$121$	9.11672			0.828793
$122$	−5.93310			−0.537158
$123$	−12.6514	+	21.9128i	−1.14074	+	1.97581i
$124$	−1.81183	+	3.13819i	−0.162707	+	0.281818i
$125$		0			0
$126$	4.55978			0.406217
$127$	1.15274	−	1.99661i	0.102289	−	0.177171i	−0.810338	−	0.585963i	$-0.800717\pi$
$127$	1.15274	−	1.99661i	0.102289	−	0.177171i	0.912628	+	0.408792i	$0.134050\pi$
$128$	−2.05176	−	3.55376i	−0.181352	−	0.314111i
$129$	15.2187	−	26.3596i	1.33994	−	2.32084i
$130$		0			0
$131$	6.45905	+	11.1874i	0.564330	+	0.977448i	0.997112	+	0.0759493i	$0.0241987\pi$
$131$	6.45905	+	11.1874i	0.564330	+	0.977448i	−0.432782	+	0.901499i	$0.642468\pi$
$132$	7.95060			0.692011
$133$	2.19627	+	1.49238i	0.190441	+	0.129405i
$134$	−10.0943			−0.872018
$135$		0			0
$136$	−4.46346	−	7.73095i	−0.382739	−	0.662923i
$137$	−6.36677	+	11.0276i	−0.543950	+	0.942149i	0.454722	+	0.890633i	$0.349739\pi$
$137$	−6.36677	+	11.0276i	−0.543950	+	0.942149i	−0.998672	+	0.0515159i	$0.983595\pi$
$138$	5.16621	+	8.94814i	0.439777	+	0.761716i
$139$	−5.30433	+	9.18738i	−0.449908	+	0.779263i	−0.998380	−	0.0569059i	$-0.981876\pi$
$139$	−5.30433	+	9.18738i	−0.449908	+	0.779263i	0.548472	+	0.836169i	$0.315210\pi$
$140$		0			0
$141$	−17.9326			−1.51020
$142$	−6.91913	+	11.9843i	−0.580640	+	1.00570i
$143$	9.95258	−	17.2384i	0.832276	−	1.44154i
$144$	−15.7013			−1.30844
$145$		0			0
$146$	2.21703	−	3.84000i	0.183482	−	0.317801i
$147$	−10.0997	−	17.4932i	−0.833010	−	1.44281i
$148$	1.09734	−	1.90065i	0.0902006	−	0.156232i
$149$	−1.88653	−	3.26757i	−0.154551	−	0.267690i	0.778344	−	0.627837i	$-0.216060\pi$
$149$	−1.88653	−	3.26757i	−0.154551	−	0.267690i	−0.932895	+	0.360147i	$0.882726\pi$
$150$		0			0
$151$	−9.51562			−0.774370			−0.387185	−	0.922002i	$-0.626553\pi$
$151$	−9.51562			−0.774370			−0.387185	+	0.922002i	$0.626553\pi$
$152$	−11.0850	−	7.53228i	−0.899109	−	0.610948i
$153$	−18.2488			−1.47533
$154$	−1.62693	−	2.81793i	−0.131102	−	0.227075i
$155$		0			0
$156$	3.93349	−	6.81301i	0.314931	−	0.545477i
$157$	−1.72822	−	2.99336i	−0.137927	−	0.238896i	0.788785	−	0.614669i	$-0.210710\pi$
$157$	−1.72822	−	2.99336i	−0.137927	−	0.238896i	−0.926712	+	0.375773i	$0.877377\pi$
$158$	−5.38182	+	9.32158i	−0.428155	+	0.741585i
$159$	25.7447			2.04169
$160$		0			0
$161$	−0.867239	+	1.50210i	−0.0683480	+	0.118382i
$162$	−6.93624	+	12.0139i	−0.544962	+	0.943902i
$163$	−6.65283			−0.521090			−0.260545	−	0.965462i	$-0.583902\pi$
$163$	−6.65283			−0.521090			−0.260545	+	0.965462i	$0.583902\pi$
$164$	4.83054			0.377202
$165$		0			0
$166$	−1.26343	−	2.18832i	−0.0980609	−	0.169846i
$167$	−8.22775	+	14.2509i	−0.636682	+	1.10277i	0.349474	+	0.936946i	$0.386360\pi$
$167$	−8.22775	+	14.2509i	−0.636682	+	1.10277i	−0.986156	+	0.165820i	$0.946973\pi$
$168$	−2.85364	−	4.94265i	−0.220163	−	0.381334i
$169$	−3.34790	−	5.79874i	−0.257531	−	0.446057i
$170$		0			0
$171$	−24.6651	+	11.9255i	−1.88618	+	0.911968i
$172$	−5.81081			−0.443070
$173$	−11.3912	−	19.7302i	−0.866058	−	1.50006i	−0.865992	−	0.500057i	$-0.833312\pi$
$173$	−11.3912	−	19.7302i	−0.866058	−	1.50006i	−6.58713e−5	−	1.00000i	$-0.500021\pi$
$174$	2.02547	+	3.50822i	0.153550	+	0.265957i
$175$		0			0
$176$	5.60224	+	9.70336i	0.422284	+	0.731418i
$177$	15.5952	−	27.0117i	1.17221	−	2.03032i
$178$	9.44650			0.708045
$179$	−2.32916			−0.174090			−0.0870449	−	0.996204i	$-0.527742\pi$
$179$	−2.32916			−0.174090			−0.0870449	+	0.996204i	$0.527742\pi$
$180$		0			0
$181$	11.1696	−	19.3463i	0.830230	−	1.43800i	−0.0676258	−	0.997711i	$-0.521542\pi$
$181$	11.1696	−	19.3463i	0.830230	−	1.43800i	0.897856	−	0.440290i	$-0.145124\pi$
$182$	−3.21965			−0.238656
$183$	15.1810			1.12221
$184$	4.37710	−	7.58137i	0.322684	−	0.558906i
$185$		0			0
$186$	−11.3024	+	19.5763i	−0.828729	+	1.43540i
$187$	6.51119	+	11.2777i	0.476145	+	0.824708i
$188$	1.71175	+	2.96484i	0.124842	+	0.216233i
$189$	−6.09829			−0.443585
$190$		0			0
$191$	2.23766			0.161911			0.0809556	−	0.996718i	$-0.474203\pi$
$191$	2.23766			0.161911			0.0809556	+	0.996718i	$0.474203\pi$
$192$	13.3716	+	23.1603i	0.965013	+	1.67145i
$193$	−2.27153	−	3.93441i	−0.163508	−	0.283205i	0.772616	−	0.634873i	$-0.218948\pi$
$193$	−2.27153	−	3.93441i	−0.163508	−	0.283205i	−0.936125	+	0.351669i	$0.885614\pi$
$194$	−5.75957	+	9.97587i	−0.413513	+	0.716226i
$195$		0			0
$196$	−1.92813	+	3.33962i	−0.137724	+	0.238544i
$197$	19.2236			1.36962			0.684812	−	0.728720i	$-0.259884\pi$
$197$	19.2236			1.36962			0.684812	+	0.728720i	$0.259884\pi$
$198$	33.5722			2.38587
$199$	3.07547	−	5.32687i	0.218014	−	0.377612i	−0.736186	−	0.676779i	$-0.763375\pi$
$199$	3.07547	−	5.32687i	0.218014	−	0.377612i	0.954201	+	0.299167i	$0.0967087\pi$
$200$		0			0
$201$	25.8283			1.82179
$202$	−1.15669			−0.0813843
$203$	−0.340010	+	0.588915i	−0.0238641	+	0.0413338i
$204$	2.57338	+	4.45722i	0.180172	+	0.312068i
$205$		0			0
$206$	−1.98967	−	3.44621i	−0.138627	−	0.240109i
$207$	−8.94786	−	15.4981i	−0.621919	−	1.07720i
$208$	11.0866			0.768720
$209$	16.1705	+	10.9879i	1.11853	+	0.760049i
$210$		0			0
$211$	−6.34661	−	10.9926i	−0.436919	−	0.756765i	0.560531	−	0.828133i	$-0.310597\pi$
$211$	−6.34661	−	10.9926i	−0.436919	−	0.756765i	−0.997450	+	0.0713679i	$0.977264\pi$
$212$	−2.45746	−	4.25644i	−0.168779	−	0.292333i
$213$	17.7039	−	30.6641i	1.21305	−	2.10107i
$214$	5.66668	+	9.81497i	0.387366	+	0.670938i
$215$		0			0
$216$	30.7791			2.09425
$217$	−3.79460			−0.257594
$218$	−3.30094	+	5.71740i	−0.223568	+	0.387231i
$219$	−5.67269	+	9.82538i	−0.383325	+	0.663938i
$220$		0			0
$221$	12.8854			0.866767
$222$	6.84528	−	11.8564i	0.459425	−	0.795748i
$223$	11.2688	+	19.5181i	0.754614	+	1.30703i	0.945566	+	0.325430i	$0.105509\pi$
$223$	11.2688	+	19.5181i	0.754614	+	1.30703i	−0.190952	+	0.981599i	$0.561158\pi$
$224$	−0.966820	+	1.67458i	−0.0645984	+	0.111888i
$225$		0			0
$226$	0.917800	+	1.58968i	0.0610512	+	0.105744i
$227$	−18.1124			−1.20216			−0.601080	−	0.799189i	$-0.705263\pi$
$227$	−18.1124			−1.20216			−0.601080	+	0.799189i	$0.705263\pi$
$228$	6.39095	+	4.34268i	0.423251	+	0.287601i
$229$	−9.41604			−0.622229			−0.311115	−	0.950372i	$-0.600702\pi$
$229$	−9.41604			−0.622229			−0.311115	+	0.950372i	$0.600702\pi$
$230$		0			0
$231$	4.16282	+	7.21022i	0.273894	+	0.474398i
$232$	1.71609	−	2.97236i	0.112667	−	0.195145i
$233$	7.85000	+	13.5966i	0.514271	+	0.890743i	0.999863	+	0.0165573i	$0.00527061\pi$
$233$	7.85000	+	13.5966i	0.514271	+	0.890743i	−0.485592	+	0.874185i	$0.661396\pi$
$234$	16.6096	−	28.7686i	1.08580	−	1.88066i
$235$		0			0
$236$	−5.95455			−0.387608
$237$	13.7704	−	23.8511i	0.894485	−	1.54929i
$238$	1.05318	−	1.82416i	0.0682676	−	0.118243i
$239$	−23.4610			−1.51757			−0.758783	−	0.651344i	$-0.774205\pi$
$239$	−23.4610			−1.51757			−0.758783	+	0.651344i	$0.774205\pi$
$240$		0			0
$241$	−6.58469	+	11.4050i	−0.424157	+	0.734662i	−0.996341	−	0.0854634i	$-0.972763\pi$
$241$	−6.58469	+	11.4050i	−0.424157	+	0.734662i	0.572184	+	0.820125i	$0.306096\pi$
$242$	−5.42860	−	9.40260i	−0.348963	−	0.604422i
$243$	2.73161	−	4.73128i	0.175233	−	0.303512i
$244$	−1.44910	−	2.50991i	−0.0927689	−	0.160680i
$245$		0			0
$246$	30.1333			1.92123
$247$	17.4159	−	8.42058i	1.10815	−	0.535789i
$248$	19.1520			1.21615
$249$	3.23272	+	5.59923i	0.204865	+	0.354837i
$250$		0			0
$251$	8.66257	−	15.0040i	0.546776	−	0.947045i	−0.451716	−	0.892162i	$-0.649188\pi$
$251$	8.66257	−	15.0040i	0.546776	−	0.947045i	0.998493	−	0.0548830i	$-0.0174786\pi$
$252$	1.11368	+	1.92895i	0.0701551	+	0.121512i
$253$	−6.38521	+	11.0595i	−0.401435	+	0.695305i
$254$	−2.74563			−0.172276
$255$		0			0
$256$	6.33295	−	10.9690i	0.395809	−	0.685562i
$257$	−2.83980	+	4.91867i	−0.177142	+	0.306818i	−0.940900	−	0.338683i	$-0.890018\pi$
$257$	−2.83980	+	4.91867i	−0.177142	+	0.306818i	0.763759	+	0.645502i	$0.223352\pi$
$258$	−36.2483			−2.25672
$259$	2.29820			0.142803
$260$		0			0
$261$	−3.50811	−	6.07622i	−0.217146	−	0.376108i
$262$	7.69215	−	13.3232i	0.475222	−	0.823109i
$263$	2.82882	+	4.89966i	0.174433	+	0.302126i	0.939965	−	0.341272i	$-0.110858\pi$
$263$	2.82882	+	4.89966i	0.174433	+	0.302126i	−0.765532	+	0.643398i	$0.777524\pi$
$264$	−21.0105	−	36.3912i	−1.29311	−	2.23972i
$265$		0			0
$266$	0.231393	−	3.15379i	0.0141876	−	0.193371i
$267$	−24.1707			−1.47922
$268$	−2.46544	−	4.27026i	−0.150601	−	0.260848i
$269$	11.9959	+	20.7775i	0.731402	+	1.26683i	0.956284	+	0.292440i	$0.0944672\pi$
$269$	11.9959	+	20.7775i	0.731402	+	1.26683i	−0.224881	+	0.974386i	$0.572199\pi$
$270$		0			0
$271$	10.6497	+	18.4459i	0.646926	+	1.12051i	0.983853	+	0.178978i	$0.0572791\pi$
$271$	10.6497	+	18.4459i	0.646926	+	1.12051i	−0.336927	+	0.941531i	$0.609388\pi$
$272$	−3.62656	+	6.28138i	−0.219892	+	0.380865i
$273$	8.23808			0.498591
$274$	15.1645			0.916121
$275$		0			0
$276$	−2.52359	+	4.37098i	−0.151902	+	0.263102i
$277$	0.821109			0.0493357			0.0246678	−	0.999696i	$-0.492147\pi$
$277$	0.821109			0.0493357			0.0246678	+	0.999696i	$0.492147\pi$
$278$	12.6340			0.757735
$279$	19.5757	−	33.9060i	1.17196	−	2.02990i
$280$		0			0
$281$	0.293739	−	0.508772i	0.0175230	−	0.0303508i	−0.857131	−	0.515099i	$-0.827755\pi$
$281$	0.293739	−	0.508772i	0.0175230	−	0.0303508i	0.874654	+	0.484748i	$0.161089\pi$
$282$	10.6780	+	18.4949i	0.635869	+	1.10136i
$283$	15.4712	+	26.7969i	0.919667	+	1.59291i	0.799921	+	0.600105i	$0.204875\pi$
$283$	15.4712	+	26.7969i	0.919667	+	1.59291i	0.119746	+	0.992805i	$0.461792\pi$
$284$	−6.75969			−0.401114
$285$		0			0
$286$	−23.7052			−1.40172
$287$	2.52920	+	4.38070i	0.149294	+	0.258585i
$288$	−9.97530	−	17.2777i	−0.587800	−	1.01810i
$289$	4.28504	−	7.42191i	0.252061	−	0.436583i
$290$		0			0
$291$	14.7370	−	25.5252i	0.863896	−	1.49631i
$292$	2.16594			0.126752
$293$	−3.76271			−0.219820			−0.109910	−	0.993942i	$-0.535056\pi$
$293$	−3.76271			−0.219820			−0.109910	+	0.993942i	$0.535056\pi$
$294$	−12.0278	+	20.8328i	−0.701478	+	1.21499i
$295$		0			0
$296$	−11.5994			−0.674202
$297$	−44.8998			−2.60535
$298$	−2.24669	+	3.89138i	−0.130147	+	0.225422i
$299$	6.31806	+	10.9432i	0.365383	+	0.632861i
$300$		0			0
$301$	−3.04246	−	5.26969i	−0.175364	−	0.303740i
$302$	5.66612	+	9.81401i	0.326049	+	0.564733i
$303$	2.95961			0.170025
$304$	−0.796788	+	10.8598i	−0.0456989	+	0.622855i
$305$		0			0
$306$	10.8663	+	18.8211i	0.621187	+	1.07593i
$307$	10.1709	+	17.6166i	0.580485	+	1.00543i	0.995422	+	0.0955798i	$0.0304705\pi$
$307$	10.1709	+	17.6166i	0.580485	+	1.00543i	−0.414936	+	0.909850i	$0.636196\pi$
$308$	0.794723	−	1.37650i	0.0452835	−	0.0784334i
$309$	5.09095	+	8.81779i	0.289614	+	0.501626i
$310$		0			0
$311$	−7.67830			−0.435397			−0.217698	−	0.976016i	$-0.569855\pi$
$311$	−7.67830			−0.435397			−0.217698	+	0.976016i	$0.569855\pi$
$312$	−41.5790			−2.35395
$313$	11.9964	−	20.7783i	0.678074	−	1.17446i	−0.297486	−	0.954726i	$-0.596148\pi$
$313$	11.9964	−	20.7783i	0.678074	−	1.17446i	0.975560	−	0.219733i	$-0.0705185\pi$
$314$	−2.05815	+	3.56482i	−0.116148	+	0.201174i
$315$		0			0
$316$	−5.25781			−0.295775
$317$	0.519518	−	0.899831i	0.0291790	−	0.0505395i	−0.851067	−	0.525057i	$-0.824044\pi$
$317$	0.519518	−	0.899831i	0.0291790	−	0.0505395i	0.880246	+	0.474517i	$0.157377\pi$
$318$	−15.3298	−	26.5520i	−0.859653	−	1.48896i
$319$	−2.50339	+	4.33600i	−0.140163	+	0.242769i
$320$		0			0
$321$	−14.4993	−	25.1135i	−0.809271	−	1.40170i
$322$	2.06561			0.115112
$323$	−0.926066	+	12.6218i	−0.0515277	+	0.702298i
$324$	−6.77641			−0.376467
$325$		0			0
$326$	3.96146	+	6.86145i	0.219405	+	0.380020i
$327$	8.44610	−	14.6291i	0.467070	−	0.808990i
$328$	−12.7653	−	22.1102i	−0.704846	−	1.22083i
$329$	−1.79250	+	3.10470i	−0.0988236	+	0.171167i
$330$		0			0
$331$	30.8316			1.69466			0.847328	−	0.531069i	$-0.178210\pi$
$331$	30.8316			1.69466			0.847328	+	0.531069i	$0.178210\pi$
$332$	0.617157	−	1.06895i	0.0338709	−	0.0586661i
$333$	−11.8560	+	20.5352i	−0.649705	+	1.12532i
$334$	19.5970			1.07230
$335$		0			0
$336$	−2.31858	+	4.01590i	−0.126489	+	0.219085i
$337$	10.3576	+	17.9400i	0.564217	+	0.977252i	0.997122	+	0.0758124i	$0.0241550\pi$
$337$	10.3576	+	17.9400i	0.564217	+	0.977252i	−0.432906	+	0.901439i	$0.642512\pi$
$338$	−3.98705	+	6.90577i	−0.216867	+	0.375625i
$339$	−2.34837	−	4.06749i	−0.127546	−	0.220916i
$340$		0			0
$341$	−27.9384			−1.51295
$342$	26.9864	+	18.3374i	1.45926	+	0.991572i
$343$	−8.30239			−0.448287
$344$	15.3558	+	26.5970i	0.827929	+	1.43402i
$345$		0			0
$346$	−13.5659	+	23.4968i	−0.729308	+	1.26320i
$347$	4.11068	+	7.11991i	0.220673	+	0.382217i	0.955013	−	0.296566i	$-0.0958413\pi$
$347$	4.11068	+	7.11991i	0.220673	+	0.382217i	−0.734340	+	0.678782i	$0.762508\pi$
$348$	−0.989399	+	1.71369i	−0.0530373	+	0.0918634i
$349$	11.9216			0.638150			0.319075	−	0.947730i	$-0.396628\pi$
$349$	11.9216			0.638150			0.319075	+	0.947730i	$0.396628\pi$
$350$		0			0
$351$	−22.2138	+	38.4754i	−1.18568	+	2.05366i
$352$	−7.11839	+	12.3294i	−0.379412	+	0.657160i
$353$	11.7983			0.627959			0.313980	−	0.949430i	$-0.398338\pi$
$353$	11.7983			0.627959			0.313980	+	0.949430i	$0.398338\pi$
$354$	−37.1450			−1.97423
$355$		0			0
$356$	2.30721	+	3.99620i	0.122282	+	0.211798i
$357$	−2.69477	+	4.66747i	−0.142622	+	0.247029i
$358$	1.38691	+	2.40220i	0.0733005	+	0.126960i
$359$	−0.0554058	−	0.0959656i	−0.00292420	−	0.00506487i	0.864560	−	0.502530i	$-0.167597\pi$
$359$	−0.0554058	−	0.0959656i	−0.00292420	−	0.00506487i	−0.867484	+	0.497465i	$0.834264\pi$
$360$		0			0
$361$	6.99666	+	17.6648i	0.368245	+	0.929729i
$362$	−26.6040			−1.39827
$363$	13.8901	+	24.0584i	0.729042	+	1.26274i
$364$	−0.786364	−	1.36202i	−0.0412167	−	0.0713894i
$365$		0			0
$366$	−9.03958	−	15.6570i	−0.472507	−	0.818405i
$367$	5.86986	−	10.1669i	0.306404	−	0.530708i	−0.671169	−	0.741305i	$-0.734207\pi$
$367$	5.86986	−	10.1669i	0.306404	−	0.530708i	0.977573	+	0.210597i	$0.0675408\pi$
$368$	−7.11278			−0.370779
$369$	−52.1908			−2.71694
$370$		0			0
$371$	2.57338	−	4.45722i	0.133603	−	0.231407i
$372$	−11.0419			−0.572498
$373$	−14.5190			−0.751763			−0.375882	−	0.926668i	$-0.622660\pi$
$373$	−14.5190			−0.751763			−0.375882	+	0.926668i	$0.622660\pi$
$374$	7.75424	−	13.4307i	0.400962	−	0.694487i
$375$		0			0
$376$	9.04704	−	15.6699i	0.466566	−	0.808115i
$377$	2.47706	+	4.29040i	0.127575	+	0.220967i
$378$	3.63125	+	6.28952i	0.186772	+	0.323498i
$379$	−6.59023			−0.338518			−0.169259	−	0.985572i	$-0.554137\pi$
$379$	−6.59023			−0.338518			−0.169259	+	0.985572i	$0.554137\pi$
$380$		0			0
$381$	7.02522			0.359913
$382$	−1.33242	−	2.30782i	−0.0681727	−	0.118079i
$383$	−1.43461	−	2.48481i	−0.0733049	−	0.126968i	0.827043	−	0.562139i	$-0.190021\pi$
$383$	−1.43461	−	2.48481i	−0.0733049	−	0.126968i	−0.900348	+	0.435171i	$0.856688\pi$
$384$	6.25207	−	10.8289i	0.319050	−	0.552610i
$385$		0			0
$386$	−2.70519	+	4.68552i	−0.137690	+	0.238487i
$387$	62.7819			3.19138
$388$	−5.62686			−0.285660
$389$	3.16575	−	5.48323i	0.160510	−	0.278011i	−0.774542	−	0.632523i	$-0.782020\pi$
$389$	3.16575	−	5.48323i	0.160510	−	0.278011i	0.935052	+	0.354512i	$0.115353\pi$
$390$		0			0
$391$	−8.26682			−0.418071
$392$	20.3813			1.02941
$393$	−19.6818	+	34.0899i	−0.992817	+	1.71961i
$394$	−11.4468	−	19.8264i	−0.576680	−	0.998840i
$395$		0			0
$396$	8.19966	+	14.2022i	0.412049	+	0.713689i
$397$	−15.2749	−	26.4569i	−0.766626	−	1.32784i	−0.939382	−	0.342871i	$-0.888601\pi$
$397$	−15.2749	−	26.4569i	−0.766626	−	1.32784i	0.172756	−	0.984965i	$-0.444733\pi$
$398$	−7.32522			−0.367180
$399$	−0.592065	+	8.06957i	−0.0296403	+	0.403984i
$400$		0			0
$401$	−15.1711	−	26.2771i	−0.757609	−	1.31222i	−0.944067	−	0.329754i	$-0.893034\pi$
$401$	−15.1711	−	26.2771i	−0.757609	−	1.31222i	0.186458	−	0.982463i	$-0.440299\pi$
$402$	−15.3796	−	26.6382i	−0.767064	−	1.32859i
$403$	−13.8223	+	23.9409i	−0.688538	+	1.19258i
$404$	−0.282509	−	0.489320i	−0.0140553	−	0.0243446i
$405$		0			0
$406$	0.809843			0.0401919
$407$	16.9209			0.838740
$408$	13.6009	−	23.5575i	0.673347	−	1.16627i
$409$	7.48628	−	12.9666i	0.370173	−	0.641158i	−0.619419	−	0.785060i	$-0.712632\pi$
$409$	7.48628	−	12.9666i	0.370173	−	0.641158i	0.989592	+	0.143903i	$0.0459652\pi$
$410$		0			0
$411$	−38.8013			−1.91393
$412$	0.971912	−	1.68340i	0.0478827	−	0.0829352i
$413$	−3.11772	−	5.40004i	−0.153413	−	0.265719i
$414$	−10.6561	+	18.4569i	−0.523718	+	0.907107i
$415$		0			0
$416$	7.04353	+	12.1997i	0.345337	+	0.598142i
$417$	−32.3264			−1.58303
$418$	1.70368	−	23.2203i	0.0833296	−	1.13574i
$419$	−6.17419			−0.301629			−0.150815	−	0.988562i	$-0.548190\pi$
$419$	−6.17419			−0.301629			−0.150815	+	0.988562i	$0.548190\pi$
$420$		0			0
$421$	13.7714	+	23.8528i	0.671177	+	1.16251i	0.977571	+	0.210608i	$0.0675443\pi$
$421$	13.7714	+	23.8528i	0.671177	+	1.16251i	−0.306394	+	0.951905i	$0.599122\pi$
$422$	−7.55824	+	13.0913i	−0.367929	+	0.637272i
$423$	−18.4943	−	32.0331i	−0.899226	−	1.55750i
$424$	−12.9883	+	22.4963i	−0.630766	+	1.09252i
$425$		0			0
$426$	−42.1675			−2.04302
$427$	1.51745	−	2.62830i	0.0734347	−	0.127193i
$428$	−2.76805	+	4.79441i	−0.133799	+	0.231746i
$429$	60.6544			2.92842
$430$		0			0
$431$	7.52941	−	13.0413i	0.362679	−	0.628179i	−0.625722	−	0.780046i	$-0.715195\pi$
$431$	7.52941	−	13.0413i	0.362679	−	0.628179i	0.988401	+	0.151868i	$0.0485288\pi$
$432$	−12.5040	−	21.6575i	−0.601598	−	1.04200i
$433$	−0.485420	+	0.840772i	−0.0233278	+	0.0404049i	−0.877454	−	0.479661i	$-0.840759\pi$
$433$	−0.485420	+	0.840772i	−0.0233278	+	0.0404049i	0.854126	+	0.520066i	$0.174093\pi$
$434$	2.25951	+	3.91359i	0.108460	+	0.187858i
$435$		0			0
$436$	−3.22488			−0.154444
$437$	−11.1734	+	5.40234i	−0.534497	+	0.258429i
$438$	13.5113			0.645596
$439$	13.7187	+	23.7616i	0.654760	+	1.13408i	0.981954	+	0.189120i	$0.0605636\pi$
$439$	13.7187	+	23.7616i	0.654760	+	1.13408i	−0.327194	+	0.944957i	$0.606103\pi$
$440$		0			0
$441$	20.8322	−	36.0824i	0.992008	−	1.71821i
$442$	−7.67269	−	13.2895i	−0.364952	−	0.632116i
$443$	−4.38272	+	7.59109i	−0.208229	+	0.360664i	−0.951157	−	0.308708i	$-0.900103\pi$
$443$	−4.38272	+	7.59109i	−0.208229	+	0.360664i	0.742928	+	0.669372i	$0.233437\pi$
$444$	6.68755			0.317377
$445$		0			0
$446$	13.4201	−	23.2443i	0.635461	−	1.10065i
$447$	5.74859	−	9.95686i	0.271899	−	0.470943i
$448$	5.34637			0.252592
$449$	−9.63397			−0.454655			−0.227327	−	0.973818i	$-0.572999\pi$
$449$	−9.63397			−0.454655			−0.227327	+	0.973818i	$0.572999\pi$
$450$		0			0
$451$	18.6217	+	32.2538i	0.876862	+	1.51877i
$452$	−0.448326	+	0.776524i	−0.0210875	+	0.0365246i
$453$	−14.4979	−	25.1110i	−0.681169	−	1.17982i
$454$	10.7851	+	18.6803i	0.506169	+	0.876711i
$455$		0			0
$456$	2.98825	−	40.7285i	0.139938	−	1.90729i
$457$	10.6708			0.499161			0.249580	−	0.968354i	$-0.419707\pi$
$457$	10.6708			0.499161			0.249580	+	0.968354i	$0.419707\pi$
$458$	5.60683	+	9.71131i	0.261990	+	0.453780i
$459$	−14.5327	−	25.1714i	−0.678330	−	1.17490i
$460$		0			0
$461$	−2.84340	−	4.92491i	−0.132430	−	0.229376i	0.792183	−	0.610284i	$-0.208945\pi$
$461$	−2.84340	−	4.92491i	−0.132430	−	0.229376i	−0.924613	+	0.380908i	$0.875611\pi$
$462$	4.95754	−	8.58672i	0.230646	−	0.399490i
$463$	−35.3550			−1.64309			−0.821543	−	0.570147i	$-0.806886\pi$
$463$	−35.3550			−1.64309			−0.821543	+	0.570147i	$0.806886\pi$
$464$	−2.78864			−0.129459
$465$		0			0
$466$	9.34864	−	16.1923i	0.433067	−	0.750095i
$467$	32.9071			1.52276			0.761380	−	0.648306i	$-0.224522\pi$
$467$	32.9071			1.52276			0.761380	+	0.648306i	$0.224522\pi$
$468$	16.2269			0.750086
$469$	2.58173	−	4.47169i	0.119213	−	0.206484i
$470$		0			0
$471$	5.26617	−	9.12127i	0.242652	−	0.420286i
$472$	15.7356	+	27.2549i	0.724292	+	1.25451i
$473$	−22.4006	−	38.7991i	−1.02998	−	1.78398i
$474$	−32.7986			−1.50649
$475$		0			0
$476$	1.02891			0.0471602
$477$	26.5512	+	45.9880i	1.21569	+	2.10564i
$478$	13.9700	+	24.1967i	0.638971	+	1.10673i
$479$	4.52861	−	7.84378i	0.206917	−	0.358391i	−0.743825	−	0.668375i	$-0.766990\pi$
$479$	4.52861	−	7.84378i	0.206917	−	0.358391i	0.950742	+	0.309984i	$0.100324\pi$
$480$		0			0
$481$	8.37149	−	14.4998i	0.381707	−	0.661136i
$482$	15.6835			0.714366
$483$	−5.28525			−0.240487
$484$	2.65175	−	4.59297i	0.120534	−	0.208772i
$485$		0			0
$486$	−6.50619			−0.295127
$487$	16.5206			0.748620			0.374310	−	0.927304i	$-0.377880\pi$
$487$	16.5206			0.748620			0.374310	+	0.927304i	$0.377880\pi$
$488$	−7.65884	+	13.2655i	−0.346700	+	0.600501i
$489$	−10.1362	−	17.5563i	−0.458373	−	0.793925i
$490$		0			0
$491$	0.695625	+	1.20486i	0.0313931	+	0.0543745i	0.881295	−	0.472566i	$-0.156672\pi$
$491$	0.695625	+	1.20486i	0.0313931	+	0.0543745i	−0.849902	+	0.526941i	$0.823339\pi$
$492$	7.35974	+	12.7474i	0.331803	+	0.574699i
$493$	−3.24109			−0.145972
$494$	−19.0550	−	12.9480i	−0.857326	−	0.582557i
$495$		0			0
$496$	−7.78048	−	13.4762i	−0.349354	−	0.605099i
$497$	−3.53928	−	6.13021i	−0.158758	−	0.274977i
$498$	3.84988	−	6.66818i	0.172517	−	0.298808i
$499$	8.33255	+	14.4324i	0.373016	+	0.646083i	0.990028	−	0.140871i	$-0.0449902\pi$
$499$	8.33255	+	14.4324i	0.373016	+	0.646083i	−0.617012	+	0.786954i	$0.711657\pi$
$500$		0			0
$501$	−50.1427			−2.24021
$502$	−20.6327			−0.920881
$503$	7.81956	−	13.5439i	0.348657	−	0.603892i	−0.637354	−	0.770571i	$-0.719971\pi$
$503$	7.81956	−	13.5439i	0.348657	−	0.603892i	0.986011	+	0.166679i	$0.0533045\pi$
$504$	5.88607	−	10.1950i	0.262186	−	0.454120i
$505$		0			0
$506$	15.2084			0.676096
$507$	10.2016	−	17.6697i	0.453070	−	0.784741i
$508$	−0.670591	−	1.16150i	−0.0297526	−	0.0515331i
$509$	9.57702	−	16.5879i	0.424494	−	0.735245i	−0.571879	−	0.820338i	$-0.693785\pi$
$509$	9.57702	−	16.5879i	0.424494	−	0.735245i	0.996373	+	0.0850929i	$0.0271187\pi$
$510$		0			0
$511$	1.13406	+	1.96424i	0.0501677	+	0.0868929i
$512$	−23.2910			−1.02933
$513$	−36.0919	−	24.5246i	−1.59349	−	1.08279i
$514$	6.76389			0.298342
$515$		0			0
$516$	−8.85327	−	15.3343i	−0.389743	−	0.675055i
$517$	−13.1976	+	22.8589i	−0.580430	+	1.00533i
$518$	−1.36848	−	2.37027i	−0.0601273	−	0.104144i
$519$	34.7110	−	60.1212i	1.52364	−	2.63903i
$520$		0			0
$521$	−19.2394			−0.842892			−0.421446	−	0.906853i	$-0.638477\pi$
$521$	−19.2394			−0.842892			−0.421446	+	0.906853i	$0.638477\pi$
$522$	−4.17784	+	7.23622i	−0.182859	+	0.316721i
$523$	3.31973	−	5.74993i	0.145161	−	0.251427i	−0.784272	−	0.620418i	$-0.786963\pi$
$523$	3.31973	−	5.74993i	0.145161	−	0.251427i	0.929433	+	0.368990i	$0.120296\pi$
$524$	7.51490			0.328290
$525$		0			0
$526$	3.36887	−	5.83505i	0.146890	−	0.254420i
$527$	−9.04285	−	15.6627i	−0.393913	−	0.682277i
$528$	−17.0710	+	29.5678i	−0.742919	+	1.28677i
$529$	7.44657	+	12.8978i	0.323764	+	0.560775i
$530$		0			0
$531$	64.3349			2.79190
$532$	1.39068	−	0.672391i	0.0602935	−	0.0291519i
$533$	36.8517			1.59623
$534$	14.3925	+	24.9286i	0.622826	+	1.07877i
$535$		0			0
$536$	−13.0305	+	22.5694i	−0.562830	+	0.974850i
$537$	−3.54868	−	6.14649i	−0.153137	−	0.265241i
$538$	14.2860	−	24.7441i	0.615914	−	1.06679i
$539$	−29.7317			−1.28064
$540$		0			0
$541$	−20.8756	+	36.1575i	−0.897510	+	1.55453i	−0.0668435	+	0.997763i	$0.521293\pi$
$541$	−20.8756	+	36.1575i	−0.897510	+	1.55453i	−0.830667	+	0.556770i	$0.812040\pi$
$542$	12.6829	−	21.9674i	0.544777	−	0.943581i
$543$	68.0714			2.92122
$544$	−9.21606			−0.395135
$545$		0			0
$546$	−4.90540	−	8.49641i	−0.209932	−	0.363613i
$547$	6.10258	−	10.5700i	0.260927	−	0.451939i	−0.705561	−	0.708649i	$-0.749305\pi$
$547$	6.10258	−	10.5700i	0.260927	−	0.451939i	0.966489	+	0.256710i	$0.0826384\pi$
$548$	3.70377	+	6.41512i	0.158217	+	0.274040i
$549$	15.6565	+	27.1179i	0.668204	+	1.15736i
$550$		0			0
$551$	−4.38066	+	2.11804i	−0.186622	+	0.0902317i
$552$	26.6756			1.13539
$553$	−2.75291	−	4.76819i	−0.117066	−	0.202764i
$554$	−0.488934	−	0.846858i	−0.0207728	−	0.0359795i
$555$		0			0
$556$	3.08571	+	5.34461i	0.130863	+	0.226662i
$557$	17.5774	−	30.4450i	0.744779	−	1.28999i	−0.205519	−	0.978653i	$-0.565888\pi$
$557$	17.5774	−	30.4450i	0.744779	−	1.28999i	0.950298	−	0.311342i	$-0.100778\pi$
$558$	−46.6257			−1.97382
$559$	−44.3301			−1.87496
$560$		0			0
$561$	−19.8407	+	34.3651i	−0.837675	+	1.45090i
$562$	−0.699634			−0.0295123
$563$	−17.8406			−0.751891			−0.375945	−	0.926642i	$-0.622682\pi$
$563$	−17.8406			−0.751891			−0.375945	+	0.926642i	$0.622682\pi$
$564$	−5.21600	+	9.03438i	−0.219633	+	0.380416i
$565$		0			0
$566$	18.4248	−	31.9127i	0.774452	−	1.34139i
$567$	−3.54803	−	6.14537i	−0.149003	−	0.258081i
$568$	17.8633	+	30.9402i	0.749529	+	1.29822i
$569$	31.6042			1.32492			0.662459	−	0.749098i	$-0.269513\pi$
$569$	31.6042			1.32492			0.662459	+	0.749098i	$0.269513\pi$
$570$		0			0
$571$	−4.73053			−0.197967			−0.0989833	−	0.995089i	$-0.531559\pi$
$571$	−4.73053			−0.197967			−0.0989833	+	0.995089i	$0.531559\pi$
$572$	−5.78975	−	10.0281i	−0.242082	−	0.419298i
$573$	3.40926	+	5.90501i	0.142424	+	0.246685i
$574$	3.01205	−	5.21702i	0.125721	−	0.217754i
$575$		0			0
$576$	−27.5810	+	47.7717i	−1.14921	+	1.99049i
$577$	−24.4074			−1.01609			−0.508047	−	0.861330i	$-0.669632\pi$
$577$	−24.4074			−1.01609			−0.508047	+	0.861330i	$0.669632\pi$
$578$	−10.2062			−0.424522
$579$	6.92174	−	11.9888i	0.287658	−	0.498238i
$580$		0			0
$581$	1.29254			0.0536235
$582$	−35.1008			−1.45497
$583$	18.9470	−	32.8171i	0.784703	−	1.35915i
$584$	−5.72377	−	9.91386i	−0.236851	−	0.410239i
$585$		0			0
$586$	2.24052	+	3.88070i	0.0925551	+	0.160310i
$587$	−14.3077	−	24.7817i	−0.590543	−	1.02285i	−0.994159	−	0.107922i	$-0.965580\pi$
$587$	−14.3077	−	24.7817i	−0.590543	−	1.02285i	0.403616	−	0.914928i	$-0.367753\pi$
$588$	−11.7507			−0.484590
$589$	−22.4578	−	15.2602i	−0.925358	−	0.628785i
$590$		0			0
$591$	29.2888	+	50.7297i	1.20478	+	2.08674i
$592$	4.71225	+	8.16186i	0.193672	+	0.335450i
$593$	1.85756	−	3.21738i	0.0762807	−	0.132122i	−0.825362	−	0.564604i	$-0.809029\pi$
$593$	1.85756	−	3.21738i	0.0762807	−	0.132122i	0.901642	+	0.432482i	$0.142362\pi$
$594$	26.7358	+	46.3077i	1.09698	+	1.90003i
$595$		0			0
$596$	−2.19492			−0.0899076
$597$	18.7430			0.767099
$598$	7.52423	−	13.0324i	0.307689	−	0.532933i
$599$	−3.54970	+	6.14826i	−0.145037	+	0.251211i	−0.929387	−	0.369108i	$-0.879663\pi$
$599$	−3.54970	+	6.14826i	−0.145037	+	0.251211i	0.784350	+	0.620319i	$0.212997\pi$
$600$		0			0
$601$	−11.0596			−0.451131			−0.225566	−	0.974228i	$-0.572423\pi$
$601$	−11.0596			−0.451131			−0.225566	+	0.974228i	$0.572423\pi$
$602$	−3.62329	+	6.27572i	−0.147674	+	0.255779i
$603$	26.6374	+	46.1373i	1.08476	+	1.87886i
$604$	−2.76778	+	4.79394i	−0.112619	+	0.195063i
$605$		0			0
$606$	−1.76231	−	3.05242i	−0.0715891	−	0.123996i
$607$	−27.1193			−1.10074			−0.550369	−	0.834921i	$-0.685513\pi$
$607$	−27.1193			−1.10074			−0.550369	+	0.834921i	$0.685513\pi$
$608$	−12.4564	+	6.02266i	−0.505174	+	0.244251i
$609$	−2.07214			−0.0839673
$610$		0			0
$611$	13.0588	+	22.6185i	0.528302	+	0.915046i
$612$	−5.30798	+	9.19369i	−0.214562	+	0.371633i
$613$	20.9156	+	36.2268i	0.844772	+	1.46319i	0.885819	+	0.464031i	$0.153597\pi$
$613$	20.9156	+	36.2268i	0.844772	+	1.46319i	−0.0410468	+	0.999157i	$0.513069\pi$
$614$	12.1127	−	20.9797i	0.488827	−	0.846673i
$615$		0			0
$616$	−8.40062			−0.338471
$617$	−8.85262	+	15.3332i	−0.356393	+	0.617291i	−0.987355	−	0.158523i	$-0.949327\pi$
$617$	−8.85262	+	15.3332i	−0.356393	+	0.617291i	0.630962	+	0.775813i	$0.282660\pi$
$618$	6.06286	−	10.5012i	0.243884	−	0.422420i
$619$	−39.8064			−1.59995			−0.799976	−	0.600032i	$-0.795155\pi$
$619$	−39.8064			−1.59995			−0.799976	+	0.600032i	$0.795155\pi$
$620$		0			0
$621$	14.2515	−	24.6844i	0.571895	−	0.990551i
$622$	4.57208	+	7.91908i	0.183324	+	0.317526i
$623$	−2.41604	+	4.18471i	−0.0967966	+	0.167657i
$624$	16.8914	+	29.2568i	0.676198	+	1.17121i
$625$		0			0
$626$	−28.5732			−1.14201
$627$	−4.35919	+	59.4137i	−0.174089	+	2.37275i
$628$	−2.01072			−0.0802366
$629$	5.47681	+	9.48611i	0.218375	+	0.378236i
$630$		0			0
$631$	−23.0990	+	40.0087i	−0.919557	+	1.59272i	−0.119469	+	0.992838i	$0.538119\pi$
$631$	−23.0990	+	40.0087i	−0.919557	+	1.59272i	−0.800088	+	0.599882i	$0.795214\pi$
$632$	13.8944	+	24.0659i	0.552691	+	0.957288i
$633$	19.3392	−	33.4965i	0.768664	−	1.33137i
$634$	−1.23740			−0.0491433
$635$		0			0
$636$	7.48829	−	12.9701i	0.296930	−	0.514298i
$637$	−14.7095	+	25.4776i	−0.582813	+	1.00946i
$638$	5.96262			0.236062
$639$	73.0340			2.88918
$640$		0			0
$641$	−3.30674	−	5.72744i	−0.130608	−	0.226220i	0.793303	−	0.608827i	$-0.208360\pi$
$641$	−3.30674	−	5.72744i	−0.130608	−	0.226220i	−0.923911	+	0.382607i	$0.875026\pi$
$642$	−17.2673	+	29.9079i	−0.681487	+	1.18037i
$643$	−15.3076	−	26.5135i	−0.603673	−	1.04559i	−0.992260	−	0.124180i	$-0.960370\pi$
$643$	−15.3076	−	26.5135i	−0.603673	−	1.04559i	0.388587	−	0.921412i	$-0.372963\pi$
$644$	0.504503	+	0.873824i	0.0198802	+	0.0344335i
$645$		0			0
$646$	13.5691	−	6.56063i	0.533868	−	0.258125i
$647$	11.8979			0.467753			0.233877	−	0.972266i	$-0.424859\pi$
$647$	11.8979			0.467753			0.233877	+	0.972266i	$0.424859\pi$
$648$	17.9075	+	31.0167i	0.703474	+	1.21845i
$649$	−22.9548	−	39.7588i	−0.901053	−	1.56067i
$650$		0			0
$651$	−5.78140	−	10.0137i	−0.226591	−	0.392467i
$652$	−1.93509	+	3.35167i	−0.0757839	+	0.131262i
$653$	1.42899			0.0559207			0.0279604	−	0.999609i	$-0.491099\pi$
$653$	1.42899			0.0559207			0.0279604	+	0.999609i	$0.491099\pi$
$654$	−20.1171			−0.786640
$655$		0			0
$656$	−10.3718	+	17.9645i	−0.404950	+	0.701395i
$657$	−23.4015			−0.912981
$658$	4.26941			0.166439
$659$	12.2485	−	21.2150i	0.477134	−	0.826420i	−0.522523	−	0.852625i	$-0.675009\pi$
$659$	12.2485	−	21.2150i	0.477134	−	0.826420i	0.999657	+	0.0262051i	$0.00834231\pi$
$660$		0			0
$661$	1.61303	−	2.79385i	0.0627396	−	0.108668i	−0.832949	−	0.553349i	$-0.813350\pi$
$661$	1.61303	−	2.79385i	0.0627396	−	0.108668i	0.895689	+	0.444681i	$0.146683\pi$
$662$	−18.3588	−	31.7984i	−0.713535	−	1.23588i
$663$	19.6320	+	34.0037i	0.762445	+	1.32059i
$664$	−6.52366			−0.253167
$665$		0			0
$666$	28.2389			1.09423
$667$	−1.58919	−	2.75256i	−0.0615338	−	0.106580i
$668$	4.78636	+	8.29023i	0.185190	+	0.320758i
$669$	−34.3379	+	59.4750i	−1.32758	+	2.29944i
$670$		0			0
$671$	11.1725	−	19.3514i	0.431311	−	0.747052i
$672$	−5.89213			−0.227294
$673$	−37.1424			−1.43173			−0.715866	−	0.698237i	$-0.753968\pi$
$673$	−37.1424			−1.43173			−0.715866	+	0.698237i	$0.753968\pi$
$674$	12.3350	−	21.3649i	0.475127	−	0.822944i
$675$		0			0
$676$	−3.89518			−0.149815
$677$	24.7550			0.951412			0.475706	−	0.879604i	$-0.342193\pi$
$677$	24.7550			0.951412			0.475706	+	0.879604i	$0.342193\pi$
$678$	−2.79669	+	4.84402i	−0.107406	+	0.186033i
$679$	−2.94614	−	5.10287i	−0.113063	−	0.195830i
$680$		0			0
$681$	−27.5957	−	47.7972i	−1.05747	−	1.83159i
$682$	16.6361	+	28.8145i	0.637028	+	1.10337i
$683$	−40.1153			−1.53497			−0.767484	−	0.641068i	$-0.778492\pi$
$683$	−40.1153			−1.53497			−0.767484	+	0.641068i	$0.778492\pi$
$684$	−1.16621	+	15.8949i	−0.0445912	+	0.607757i
$685$		0			0
$686$	4.94370	+	8.56274i	0.188751	+	0.326927i
$687$	−14.3461	−	24.8482i	−0.547340	−	0.948020i
$688$	12.4766	−	21.6100i	0.475664	−	0.823875i
$689$	−18.7477	−	32.4720i	−0.714230	−	1.23708i
$690$		0			0
$691$	39.4963			1.50251			0.751254	−	0.660013i	$-0.229449\pi$
$691$	39.4963			1.50251			0.751254	+	0.660013i	$0.229449\pi$
$692$	−13.2533			−0.503816
$693$	−8.58645	+	14.8722i	−0.326172	+	0.564947i
$694$	4.89545	−	8.47917i	0.185829	−	0.321865i
$695$		0			0
$696$	10.4584			0.396426
$697$	−12.0546	+	20.8792i	−0.456600	+	0.790855i
$698$	−7.09879	−	12.2955i	−0.268693	−	0.465390i
$699$	−23.9203	+	41.4312i	−0.904748	+	1.56707i
$700$		0			0
$701$	−0.0109776	−	0.0190137i	−0.000414618	−	0.000718139i	0.865818	−	0.500359i	$-0.166799\pi$
$701$	−0.0109776	−	0.0190137i	−0.000414618	−	0.000718139i	−0.866233	+	0.499641i	$0.833465\pi$
$702$	52.9092			1.99693
$703$	13.6016	+	9.24234i	0.512994	+	0.348581i
$704$	39.3637			1.48357
$705$		0			0
$706$	−7.02535	−	12.1683i	−0.264402	−	0.457958i
$707$	0.295835	−	0.512402i	0.0111260	−	0.0192708i
$708$	−9.07226	−	15.7136i	−0.340957	−	0.590554i
$709$	8.90087	−	15.4168i	0.334279	−	0.578989i	−0.649067	−	0.760731i	$-0.724840\pi$
$709$	8.90087	−	15.4168i	0.334279	−	0.578989i	0.983346	+	0.181743i	$0.0581738\pi$
$710$		0			0
$711$	56.8071			2.13043
$712$	12.1942	−	21.1209i	0.456996	−	0.791540i
$713$	8.86789	−	15.3596i	0.332105	−	0.575223i
$714$	6.41844			0.240204
$715$		0			0
$716$	−0.677477	+	1.17342i	−0.0253185	+	0.0438529i
$717$	−35.7448	−	61.9118i	−1.33491	−	2.31214i
$718$	−0.0659833	+	0.114286i	−0.00246247	+	0.00426513i
$719$	−9.40515	−	16.2902i	−0.350753	−	0.607522i	0.635629	−	0.771995i	$-0.280741\pi$
$719$	−9.40515	−	16.2902i	−0.350753	−	0.607522i	−0.986382	+	0.164473i	$0.947408\pi$
$720$		0			0
$721$	2.03552			0.0758066
$722$	14.0526	−	17.7347i	0.522983	−	0.660016i
$723$	−40.1294			−1.49243
$724$	−6.49774	−	11.2544i	−0.241487	−	0.418267i
$725$		0			0
$726$	16.5419	−	28.6513i	0.613926	−	1.06335i
$727$	2.50151	+	4.33274i	0.0927758	+	0.160692i	0.908678	−	0.417497i	$-0.137093\pi$
$727$	2.50151	+	4.33274i	0.0927758	+	0.160692i	−0.815902	+	0.578190i	$0.803759\pi$
$728$	−4.15613	+	7.19864i	−0.154037	+	0.266799i
$729$	−18.2986			−0.677725
$730$		0			0
$731$	14.5009	−	25.1162i	0.536334	−	0.928957i
$732$	4.41565	−	7.64812i	0.163207	−	0.282683i
$733$	23.5259			0.868950			0.434475	−	0.900684i	$-0.356934\pi$
$733$	23.5259			0.868950			0.434475	+	0.900684i	$0.356934\pi$
$734$	−13.9809			−0.516046
$735$		0			0
$736$	−4.51887	−	7.82691i	−0.166568	−	0.288504i
$737$	19.0085	−	32.9237i	0.700187	−	1.21276i
$738$	31.0772	+	53.8274i	1.14397	+	1.98141i
$739$	18.6918	+	32.3752i	0.687590	+	1.19094i	0.972615	+	0.232421i	$0.0746646\pi$
$739$	18.6918	+	32.3752i	0.687590	+	1.19094i	−0.285026	+	0.958520i	$0.592002\pi$
$740$		0			0
$741$	48.7559	+	33.1299i	1.79109	+	1.21706i
$742$	−6.12932			−0.225014
$743$	5.19430	+	8.99679i	0.190560	+	0.330060i	0.945436	−	0.325808i	$-0.105636\pi$
$743$	5.19430	+	8.99679i	0.190560	+	0.330060i	−0.754876	+	0.655868i	$0.772303\pi$
$744$	29.1797	+	50.5407i	1.06978	+	1.85291i
$745$		0			0
$746$	8.64539	+	14.9742i	0.316530	+	0.548246i
$747$	−6.66797	+	11.5493i	−0.243968	+	0.422566i
$748$	7.57556			0.276990
$749$	−5.79725			−0.211827
$750$		0			0
$751$	15.6413	−	27.0915i	0.570758	−	0.988581i	−0.425731	−	0.904850i	$-0.639983\pi$
$751$	15.6413	−	27.0915i	0.570758	−	0.988581i	0.996488	−	0.0837314i	$-0.0266838\pi$
$752$	−14.7014			−0.536105
$753$	52.7927			1.92387
$754$	2.94996	−	5.10947i	0.107431	−	0.186076i
$755$		0			0
$756$	−1.77379	+	3.07230i	−0.0645122	+	0.111738i
$757$	−6.31205	−	10.9328i	−0.229415	−	0.397359i	0.728220	−	0.685344i	$-0.240348\pi$
$757$	−6.31205	−	10.9328i	−0.229415	−	0.397359i	−0.957635	+	0.287985i	$0.907015\pi$
$758$	3.92419	+	6.79689i	0.142533	+	0.246874i
$759$	−38.9137			−1.41248
$760$		0			0
$761$	11.5495			0.418668			0.209334	−	0.977844i	$-0.432870\pi$
$761$	11.5495			0.418668			0.209334	+	0.977844i	$0.432870\pi$
$762$	−4.18320	−	7.24551i	−0.151541	−	0.262477i
$763$	−1.68850	−	2.92457i	−0.0611279	−	0.105877i
$764$	0.650861	−	1.12732i	0.0235473	−	0.0407851i
$765$		0			0
$766$	−1.70849	+	2.95918i	−0.0617301	+	0.106920i
$767$	−45.4267			−1.64026
$768$	38.5951			1.39268
$769$	13.4603	−	23.3140i	0.485392	−	0.840724i	−0.514467	−	0.857510i	$-0.672010\pi$
$769$	13.4603	−	23.3140i	0.485392	−	0.840724i	0.999859	+	0.0167864i	$0.00534353\pi$
$770$		0			0
$771$	−17.3067			−0.623286
$772$	−2.64286			−0.0951184
$773$	10.6666	−	18.4750i	0.383649	−	0.664500i	−0.607932	−	0.793989i	$-0.708001\pi$
$773$	10.6666	−	18.4750i	0.383649	−	0.664500i	0.991581	+	0.129489i	$0.0413338\pi$
$774$	−37.3838	−	64.7506i	−1.34373	−	2.32741i
$775$		0			0
$776$	14.8697	+	25.7550i	0.533790	+	0.924552i
$777$	3.50151	+	6.06479i	0.125616	+	0.217573i
$778$	−7.54024			−0.270331
$779$	−2.64851	+	36.0979i	−0.0948926	+	1.29334i
$780$		0			0
$781$	−26.0586	−	45.1348i	−0.932450	−	1.61505i
$782$	4.92252	+	8.52605i	0.176029	+	0.304891i
$783$	5.58747	−	9.67779i	0.199680	−	0.345856i
$784$	−8.27989	−	14.3412i	−0.295710	−	0.512185i
$785$		0			0
$786$	46.8786			1.67210
$787$	−3.52489			−0.125649			−0.0628243	−	0.998025i	$-0.520011\pi$
$787$	−3.52489			−0.125649			−0.0628243	+	0.998025i	$0.520011\pi$
$788$	5.59151	−	9.68478i	0.199189	−	0.345006i
$789$	−8.61990	+	14.9301i	−0.306877	+	0.531526i
$790$		0			0
$791$	−0.938948			−0.0333852
$792$	43.3373	−	75.0624i	1.53992	−	2.66723i
$793$	−11.0550	−	19.1479i	−0.392575	−	0.679961i
$794$	−18.1911	+	31.5078i	−0.645576	+	1.11817i
$795$		0			0
$796$	−1.78911	−	3.09882i	−0.0634132	−	0.109835i
$797$	39.0084			1.38175			0.690875	−	0.722974i	$-0.257226\pi$
$797$	39.0084			1.38175			0.690875	+	0.722974i	$0.257226\pi$
$798$	8.67516	−	4.19443i	0.307097	−	0.148481i
$799$	−17.0867			−0.604484
$800$		0			0
$801$	−24.9278	−	43.1763i	−0.880782	−	1.52556i
$802$	−18.0674	+	31.2937i	−0.637983	+	1.10502i
$803$	8.34969	+	14.4621i	0.294654	+	0.510356i
$804$	7.51261	−	13.0122i	0.264949	−	0.458906i
$805$		0			0
$806$	32.9222			1.15964
$807$	−36.5535	+	63.3126i	−1.28675	+	2.22871i
$808$	−1.49313	+	2.58618i	−0.0525282	+	0.0909814i
$809$	50.7196			1.78321			0.891604	−	0.452816i	$-0.149581\pi$
$809$	50.7196			1.78321			0.891604	+	0.452816i	$0.149581\pi$
$810$		0			0
$811$	−14.5188	+	25.1473i	−0.509824	+	0.883041i	0.490111	+	0.871660i	$0.336956\pi$
$811$	−14.5188	+	25.1473i	−0.509824	+	0.883041i	−0.999935	+	0.0113812i	$0.996377\pi$
$812$	0.197796	+	0.342592i	0.00694127	+	0.0120226i
$813$	−32.4516	+	56.2078i	−1.13813	+	1.97129i
$814$	−10.0757	−	17.4515i	−0.353151	−	0.611676i
$815$		0			0
$816$	−22.1015			−0.773706
$817$	3.18597	−	43.4233i	0.111463	−	1.51919i
$818$	−17.8310			−0.623445
$819$	8.49614	+	14.7158i	0.296879	+	0.514210i
$820$		0			0
$821$	−16.4939	+	28.5682i	−0.575640	+	0.997038i	0.420331	+	0.907371i	$0.361914\pi$
$821$	−16.4939	+	28.5682i	−0.575640	+	0.997038i	−0.995972	+	0.0896677i	$0.971420\pi$
$822$	23.1044	+	40.0180i	0.805859	+	1.39579i
$823$	−13.2767	+	22.9959i	−0.462796	+	0.801586i	−0.999099	−	0.0424397i	$-0.986487\pi$
$823$	−13.2767	+	22.9959i	−0.462796	+	0.801586i	0.536303	+	0.844025i	$0.319820\pi$
$824$	−10.2736			−0.357898
$825$		0			0
$826$	−3.71292	+	6.43096i	−0.129189	+	0.223762i
$827$	−16.3833	+	28.3767i	−0.569703	+	0.986754i	0.426892	+	0.904302i	$0.359608\pi$
$827$	−16.3833	+	28.3767i	−0.569703	+	0.986754i	−0.996595	+	0.0824515i	$0.973725\pi$
$828$	−10.4106			−0.361792
$829$	32.4548			1.12720			0.563601	−	0.826047i	$-0.309416\pi$
$829$	32.4548			1.12720			0.563601	+	0.826047i	$0.309416\pi$
$830$		0			0
$831$	1.25103	+	2.16685i	0.0433978	+	0.0751671i
$832$	19.4748	−	33.7314i	0.675168	−	1.16943i
$833$	−9.62329	−	16.6680i	−0.333427	−	0.577513i
$834$	19.2489	+	33.3401i	0.666536	+	1.15447i
$835$		0			0
$836$	10.2391	−	4.95061i	0.354127	−	0.171220i
$837$	62.3576			2.15539
$838$	3.67645	+	6.36780i	0.127001	+	0.219972i
$839$	17.6049	+	30.4926i	0.607788	+	1.05272i	0.991604	+	0.129310i	$0.0412763\pi$
$839$	17.6049	+	30.4926i	0.607788	+	1.05272i	−0.383816	+	0.923410i	$0.625390\pi$
$840$		0			0
$841$	13.8769	+	24.0356i	0.478515	+	0.828813i
$842$	16.4005	−	28.4065i	0.565198	−	0.978952i
$843$	1.79015			0.0616560
$844$	−7.38408			−0.254171
$845$		0			0
$846$	−22.0251	+	38.1486i	−0.757238	+	1.31158i
$847$	5.55368			0.190827
$848$	21.1059			0.724779
$849$	−47.1434	+	81.6547i	−1.61796	+	2.80238i
$850$		0			0
$851$	−5.37084	+	9.30257i	−0.184110	+	0.318888i
$852$	−10.2990	−	17.8383i	−0.352837	−	0.611132i
$853$	−0.894126	−	1.54867i	−0.0306143	−	0.0530255i	0.850312	−	0.526278i	$-0.176413\pi$
$853$	−0.894126	−	1.54867i	−0.0306143	−	0.0530255i	−0.880927	+	0.473253i	$0.843080\pi$
$854$	−3.61430			−0.123679
$855$		0			0
$856$	29.2597			1.00008
$857$	1.80690	+	3.12964i	0.0617224	+	0.106906i	0.895235	−	0.445594i	$-0.147007\pi$
$857$	1.80690	+	3.12964i	0.0617224	+	0.106906i	−0.833513	+	0.552500i	$0.813674\pi$
$858$	−36.1170	−	62.5564i	−1.23301	−	2.13564i
$859$	12.6824	−	21.9666i	0.432719	−	0.749491i	−0.564388	−	0.825510i	$-0.690888\pi$
$859$	12.6824	−	21.9666i	0.432719	−	0.749491i	0.997106	+	0.0760192i	$0.0242210\pi$
$860$		0			0
$861$	−7.70691	+	13.3488i	−0.262651	+	0.454924i
$862$	−17.9337			−0.610824
$863$	29.9878			1.02080			0.510398	−	0.859939i	$-0.329498\pi$
$863$	29.9878			1.02080			0.510398	+	0.859939i	$0.329498\pi$
$864$	15.8880	−	27.5188i	0.540520	−	0.936209i
$865$		0			0
$866$	1.15618			0.0392887
$867$	26.1145			0.886895
$868$	−1.10372	+	1.91171i	−0.0374628	+	0.0648875i
$869$	−20.2688	−	35.1067i	−0.687573	−	1.19091i
$870$		0			0
$871$	−18.8086	−	32.5774i	−0.637305	−	1.10384i
$872$	8.52216	+	14.7608i	0.288597	+	0.499864i
$873$	60.7945			2.05758
$874$	12.2250	+	8.30695i	0.413517	+	0.280987i
$875$		0			0
$876$	3.30000	+	5.71576i	0.111497	+	0.193118i
$877$	5.32389	+	9.22125i	0.179775	+	0.311380i	0.941803	−	0.336164i	$-0.109130\pi$
$877$	5.32389	+	9.22125i	0.179775	+	0.311380i	−0.762028	+	0.647544i	$0.775796\pi$
$878$	16.3378	−	28.2979i	0.551374	−	0.955007i
$879$	−5.73281	−	9.92951i	−0.193363	−	0.334914i
$880$		0			0
$881$	−31.5797			−1.06395			−0.531973	−	0.846761i	$-0.678549\pi$
$881$	−31.5797			−1.06395			−0.531973	+	0.846761i	$0.678549\pi$
$882$	−49.6185			−1.67074
$883$	8.50871	−	14.7375i	0.286341	−	0.495957i	−0.686593	−	0.727042i	$-0.740894\pi$
$883$	8.50871	−	14.7375i	0.286341	−	0.495957i	0.972933	+	0.231085i	$0.0742277\pi$
$884$	3.74795	−	6.49163i	0.126057	−	0.218337i
$885$		0			0
$886$	10.4388			0.350700
$887$	−6.61451	+	11.4567i	−0.222093	+	0.384677i	−0.955443	−	0.295174i	$-0.904622\pi$
$887$	−6.61451	+	11.4567i	−0.222093	+	0.384677i	0.733350	+	0.679851i	$0.237956\pi$
$888$	−17.6727	−	30.6100i	−0.593057	−	1.02721i
$889$	0.702223	−	1.21629i	0.0235518	−	0.0407929i
$890$		0			0
$891$	−26.1230	−	45.2464i	−0.875155	−	1.51581i
$892$	13.1109			0.438985
$893$	−23.0943	+	11.1661i	−0.772823	+	0.373659i
$894$	−13.6921			−0.457933
$895$		0			0
$896$	−1.24988	−	2.16486i	−0.0417557	−	0.0723229i
$897$	−19.2522	+	33.3458i	−0.642812	+	1.11338i
$898$	5.73659	+	9.93607i	0.191433	+	0.331571i
$899$	3.47675	−	6.02191i	0.115956	−	0.200842i
$900$		0			0
$901$	24.5303			0.817222
$902$	22.1768	−	38.4113i	0.738406	−	1.27896i
$903$	9.27088	−	16.0576i	0.308516	−	0.534365i
$904$	4.73903			0.157618
$905$		0			0
$906$	−17.2656	+	29.9050i	−0.573613	+	0.993526i
$907$	−7.44520	−	12.8955i	−0.247214	−	0.428187i	0.715538	−	0.698574i	$-0.246182\pi$
$907$	−7.44520	−	12.8955i	−0.247214	−	0.428187i	−0.962752	+	0.270387i	$0.912848\pi$
$908$	−5.26829	+	9.12494i	−0.174834	+	0.302822i
$909$	3.05232	+	5.28678i	0.101239	+	0.175351i
$910$		0			0
$911$	−49.5480			−1.64160			−0.820800	−	0.571216i	$-0.806472\pi$
$911$	−49.5480			−1.64160			−0.820800	+	0.571216i	$0.806472\pi$
$912$	−29.8723	+	14.4432i	−0.989172	+	0.478263i
$913$	9.51655			0.314952
$914$	−6.35400	−	11.0055i	−0.210172	−	0.364028i
$915$		0			0
$916$	−2.73882	+	4.74377i	−0.0904931	+	0.156739i
$917$	3.93469	+	6.81509i	0.129935	+	0.225054i
$918$	−17.3072	+	29.9769i	−0.571222	+	0.989385i
$919$	27.3835			0.903300			0.451650	−	0.892195i	$-0.350836\pi$
$919$	27.3835			0.903300			0.451650	+	0.892195i	$0.350836\pi$
$920$		0			0
$921$	−30.9926	+	53.6807i	−1.02124	+	1.76884i
$922$	−3.38623	+	5.86513i	−0.111520	+	0.193158i
$923$	−51.5691			−1.69742
$924$	4.84331			0.159333
$925$		0			0
$926$	21.0523	+	36.4637i	0.691821	+	1.19827i
$927$	−10.5009	+	18.1880i	−0.344893	+	0.597373i
$928$	−1.77167	−	3.06863i	−0.0581580	−	0.100733i
$929$	−26.0947	−	45.1973i	−0.856139	−	1.48288i	−0.875584	−	0.483066i	$-0.839523\pi$
$929$	−26.0947	−	45.1973i	−0.856139	−	1.48288i	0.0194449	−	0.999811i	$-0.493810\pi$
$930$		0			0
$931$	−23.8993	−	16.2397i	−0.783269	−	0.532234i
$932$	9.13323			0.299169
$933$	−11.6985	−	20.2625i	−0.382993	−	0.663364i
$934$	−19.5947	−	33.9390i	−0.641158	−	1.11052i
$935$		0			0
$936$	−42.8815	−	74.2729i	−1.40163	−	2.42769i
$937$	7.78988	−	13.4925i	0.254484	−	0.440780i	−0.710271	−	0.703928i	$-0.751428\pi$
$937$	7.78988	−	13.4925i	0.254484	−	0.440780i	0.964755	+	0.263149i	$0.0847610\pi$
$938$	−6.14922			−0.200779
$939$	73.1099			2.38585
$940$		0			0
$941$	29.3277	−	50.7970i	0.956055	−	1.65594i	0.224119	−	0.974562i	$-0.428050\pi$
$941$	29.3277	−	50.7970i	0.956055	−	1.65594i	0.731936	−	0.681373i	$-0.238617\pi$
$942$	−12.5431			−0.408675
$943$	−23.6427			−0.769913
$944$	12.7852	−	22.1446i	0.416122	−	0.720745i
$945$		0			0
$946$	−26.6771	+	46.2062i	−0.867349	+	1.50229i
$947$	6.15326	+	10.6578i	0.199954	+	0.346331i	0.948513	−	0.316737i	$-0.102587\pi$
$947$	6.15326	+	10.6578i	0.199954	+	0.346331i	−0.748559	+	0.663068i	$0.769254\pi$
$948$	−8.01072	−	13.8750i	−0.260176	−	0.450638i
$949$	16.5238			0.536384
$950$		0			0
$951$	3.16612			0.102668
$952$	−2.71903	−	4.70950i	−0.0881244	−	0.152636i
$953$	4.13499	+	7.16201i	0.133945	+	0.232000i	0.925194	−	0.379494i	$-0.123902\pi$
$953$	4.13499	+	7.16201i	0.133945	+	0.232000i	−0.791249	+	0.611494i	$0.790569\pi$
$954$	31.6200	−	54.7675i	1.02374	−	1.77316i
$955$		0			0
$956$	−6.82403	+	11.8196i	−0.220705	+	0.382272i
$957$	−15.2565			−0.493173
$958$	−10.7863			−0.348490
$959$	−3.87848	+	6.71773i	−0.125243	+	0.216927i
$960$		0			0
$961$	7.80138			0.251657
$962$	−19.9394			−0.642871
$963$	29.9070	−	51.8004i	0.963738	−	1.66924i
$964$	3.83054	+	6.63469i	0.123373	+	0.213689i
$965$		0			0
$966$	3.14713	+	5.45099i	0.101257	+	0.175383i
$967$	7.11235	+	12.3190i	0.228718	+	0.396151i	0.957428	−	0.288671i	$-0.0932133\pi$
$967$	7.11235	+	12.3190i	0.228718	+	0.396151i	−0.728711	+	0.684822i	$0.759880\pi$
$968$	−28.0304			−0.900931
$969$	−34.7191	+	16.7866i	−1.11534	+	0.539264i
$970$		0			0
$971$	−4.86930	−	8.43388i	−0.156263	−	0.270656i	0.777255	−	0.629186i	$-0.216612\pi$
$971$	−4.86930	−	8.43388i	−0.156263	−	0.270656i	−0.933518	+	0.358530i	$0.883278\pi$
$972$	−1.58907	−	2.75235i	−0.0509694	−	0.0882816i
$973$	−3.23127	+	5.59672i	−0.103590	+	0.179423i
$974$	−9.83727	−	17.0387i	−0.315207	−	0.545954i
$975$		0			0
$976$	12.4456			0.398374
$977$	6.35308			0.203253			0.101627	−	0.994823i	$-0.467595\pi$
$977$	6.35308			0.203253			0.101627	+	0.994823i	$0.467595\pi$
$978$	−12.0712	+	20.9080i	−0.385996	+	0.668564i
$979$	−17.7885	+	30.8107i	−0.568524	+	0.984713i
$980$		0			0
$981$	34.8427			1.11244
$982$	0.828426	−	1.43488i	0.0264361	−	0.0457887i
$983$	4.94043	+	8.55708i	0.157575	+	0.272929i	0.933994	−	0.357289i	$-0.116299\pi$
$983$	4.94043	+	8.55708i	0.157575	+	0.272929i	−0.776418	+	0.630218i	$0.782966\pi$
$984$	38.8981	−	67.3735i	1.24003	−	2.14779i
$985$		0			0
$986$	1.92993	+	3.34273i	0.0614613	+	0.106454i
$987$	−10.9241			−0.347718
$988$	0.823458	−	11.2234i	0.0261977	−	0.357062i
$989$	28.4406			0.904358
$990$		0			0
$991$	−18.6675	−	32.3331i	−0.592993	−	1.02709i	−0.993827	−	0.110943i	$-0.964613\pi$
$991$	−18.6675	−	32.3331i	−0.592993	−	1.02709i	0.400834	−	0.916151i	$-0.368720\pi$
$992$	9.88614	−	17.1233i	0.313885	−	0.543665i
$993$	46.9745	+	81.3623i	1.49069	+	2.58195i
$994$	−4.21496	+	7.30053i	−0.133690	+	0.231559i
$995$		0			0
$996$	3.76117			0.119177
$997$	−21.8474	+	37.8408i	−0.691914	+	1.19843i	0.279296	+	0.960205i	$0.409899\pi$
$997$	−21.8474	+	37.8408i	−0.691914	+	1.19843i	−0.971210	+	0.238225i	$0.923434\pi$
$998$	9.92332	−	17.1877i	0.314117	−	0.544067i
$999$	−37.7669			−1.19489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.e.26.2		8
5.2	odd	4		475.2.j.c.349.6		16
5.3	odd	4		475.2.j.c.349.3		16
5.4	even	2		95.2.e.c.26.3	yes	8
15.14	odd	2		855.2.k.h.406.2		8
19.7	even	3		9025.2.a.bg.1.3		4
19.11	even	3	inner	475.2.e.e.201.2		8
19.12	odd	6		9025.2.a.bp.1.2		4
20.19	odd	2		1520.2.q.o.881.4		8
95.49	even	6		95.2.e.c.11.3	✓	8
95.64	even	6		1805.2.a.o.1.2		4
95.68	odd	12		475.2.j.c.49.6		16
95.69	odd	6		1805.2.a.i.1.3		4
95.87	odd	12		475.2.j.c.49.3		16
285.239	odd	6		855.2.k.h.676.2		8
380.239	odd	6		1520.2.q.o.961.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.3	✓	8	95.49	even	6
95.2.e.c.26.3	yes	8	5.4	even	2
475.2.e.e.26.2		8	1.1	even	1	trivial
475.2.e.e.201.2		8	19.11	even	3	inner
475.2.j.c.49.3		16	95.87	odd	12
475.2.j.c.49.6		16	95.68	odd	12
475.2.j.c.349.3		16	5.3	odd	4
475.2.j.c.349.6		16	5.2	odd	4
855.2.k.h.406.2		8	15.14	odd	2
855.2.k.h.676.2		8	285.239	odd	6
1520.2.q.o.881.4		8	20.19	odd	2
1520.2.q.o.961.4		8	380.239	odd	6
1805.2.a.i.1.3		4	95.69	odd	6
1805.2.a.o.1.2		4	95.64	even	6
9025.2.a.bg.1.3		4	19.7	even	3
9025.2.a.bp.1.2		4	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.595455 - 1.03136i) q^{2} +(1.52359 + 2.63893i) q^{3} +(0.290867 - 0.503797i) q^{4} +(1.81445 - 3.14272i) q^{6} +0.609175 q^{7} -3.07461 q^{8} +(-3.14263 + 5.44319i) q^{9} +4.48517 q^{11} +1.77264 q^{12} +(2.21900 - 3.84342i) q^{13} +(-0.362736 - 0.628278i) q^{14} +(1.24906 + 2.16343i) q^{16} +(1.45172 + 2.51445i) q^{17} +7.48517 q^{18} +(3.60532 + 2.44983i) q^{19} +(0.928131 + 1.60757i) q^{21} +(-2.67071 - 4.62581i) q^{22} +(-1.42363 + 2.46580i) q^{23} +(-4.68443 - 8.11368i) q^{24} -5.28525 q^{26} -10.0107 q^{27} +(0.177189 - 0.306901i) q^{28} +(-0.558149 + 0.966742i) q^{29} -6.22908 q^{31} +(-1.58710 + 2.74893i) q^{32} +(6.83354 + 11.8360i) q^{33} +(1.72886 - 2.99448i) q^{34} +(1.82817 + 3.16649i) q^{36} +3.77264 q^{37} +(0.379847 - 5.17714i) q^{38} +13.5233 q^{39} +(4.15184 + 7.19120i) q^{41} +(1.10532 - 1.91447i) q^{42} +(-4.99438 - 8.65053i) q^{43} +(1.30459 - 2.25961i) q^{44} +3.39082 q^{46} +(-2.94250 + 5.09656i) q^{47} +(-3.80609 + 6.59235i) q^{48} -6.62891 q^{49} +(-4.42363 + 7.66195i) q^{51} +(-1.29087 - 2.23585i) q^{52} +(4.22436 - 7.31681i) q^{53} +(5.96093 + 10.3246i) q^{54} -1.87298 q^{56} +(-0.971912 + 13.2467i) q^{57} +1.32941 q^{58} +(-5.11793 - 8.86451i) q^{59} +(2.49099 - 4.31453i) q^{61} +(3.70913 + 6.42441i) q^{62} +(-1.91441 + 3.31586i) q^{63} +8.77641 q^{64} +(8.13812 - 14.0956i) q^{66} +(4.23808 - 7.34057i) q^{67} +1.68903 q^{68} -8.67608 q^{69} +(-5.80995 - 10.0631i) q^{71} +(9.66236 - 16.7357i) q^{72} +(1.86162 + 3.22443i) q^{73} +(-2.24644 - 3.89095i) q^{74} +(2.28289 - 1.10377i) q^{76} +2.73225 q^{77} +(-8.05253 - 13.9474i) q^{78} +(-4.51908 - 7.82728i) q^{79} +(-5.82432 - 10.0880i) q^{81} +(4.94447 - 8.56407i) q^{82} +2.12178 q^{83} +1.07985 q^{84} +(-5.94786 + 10.3020i) q^{86} -3.40155 q^{87} -13.7901 q^{88} +(-3.96608 + 6.86946i) q^{89} +(1.35176 - 2.34131i) q^{91} +(0.828173 + 1.43444i) q^{92} +(-9.49053 - 16.4381i) q^{93} +7.00850 q^{94} -9.67231 q^{96} +(-4.83628 - 8.37668i) q^{97} +(3.94721 + 6.83677i) q^{98} +(-14.0952 + 24.4136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{3} - 5 q^{4} - 2 q^{6} + 8 q^{7} - 24 q^{8} - q^{9} - 4 q^{11} - 12 q^{12} + 7 q^{13} + q^{14} - 7 q^{16} - q^{17} + 20 q^{18} + 5 q^{19} + 4 q^{21} + 2 q^{22} + 2 q^{23} - 23 q^{24}+ \cdots - 38 q^{99}+O(q^{100}) \) 8 * q + q^2 + 3 * q^3 - 5 * q^4 - 2 * q^6 + 8 * q^7 - 24 * q^8 - q^9 - 4 * q^11 - 12 * q^12 + 7 * q^13 + q^14 - 7 * q^16 - q^17 + 20 * q^18 + 5 * q^19 + 4 * q^21 + 2 * q^22 + 2 * q^23 - 23 * q^24 + 6 * q^26 - 24 * q^27 - 19 * q^28 + q^29 + 30 * q^32 + 19 * q^33 - 15 * q^34 + 7 * q^36 + 4 * q^37 - 13 * q^38 + 30 * q^39 + 8 * q^41 - 15 * q^42 + q^43 + 12 * q^44 + 24 * q^46 - 12 * q^47 + 23 * q^48 - 20 * q^49 - 22 * q^51 - 3 * q^52 - 5 * q^53 + 34 * q^54 - 82 * q^56 - 7 * q^57 + 54 * q^58 + 5 * q^59 + 37 * q^62 - 3 * q^63 + 112 * q^64 + 31 * q^66 + 4 * q^67 - 32 * q^68 - 18 * q^69 - 20 * q^71 + 17 * q^72 - 20 * q^73 - 25 * q^74 + 63 * q^76 - 28 * q^77 - 18 * q^78 - 17 * q^79 - 12 * q^81 + 21 * q^82 - 2 * q^83 - 40 * q^84 - 8 * q^86 + 32 * q^87 + 14 * q^88 - 11 * q^89 - 6 * q^91 - q^92 - 8 * q^93 - 62 * q^94 + 42 * q^96 + q^97 + 9 * q^98 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more