LMFDB - Embedded newform 1470.2.i.v.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(361,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1470.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1470.961
Dual form			1470.2.i.v.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.292893 - 0.507306i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.707107 + 1.22474i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.41421 + 2.44949i) q^{19} -1.00000 q^{20} +0.585786 q^{22} +(-2.41421 + 4.18154i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +8.24264 q^{29} +(-0.500000 + 0.866025i) q^{30} +(2.53553 + 4.39167i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.292893 - 0.507306i) q^{33} -1.41421 q^{34} +1.00000 q^{36} +(0.707107 - 1.22474i) q^{37} +(-1.41421 - 2.44949i) q^{38} +(0.500000 - 0.866025i) q^{40} +8.82843 q^{41} +4.58579 q^{43} +(-0.292893 + 0.507306i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-2.41421 - 4.18154i) q^{46} +(-4.53553 + 7.85578i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(-0.707107 + 1.22474i) q^{51} +(4.65685 + 8.06591i) q^{53} +(0.500000 - 0.866025i) q^{54} -0.585786 q^{55} -2.82843 q^{57} +(-4.12132 + 7.13834i) q^{58} +(1.24264 + 2.15232i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-5.82843 + 10.0951i) q^{61} -5.07107 q^{62} +1.00000 q^{64} +(0.292893 + 0.507306i) q^{66} +(-3.94975 - 6.84116i) q^{67} +(0.707107 - 1.22474i) q^{68} -4.82843 q^{69} +10.8284 q^{71} +(-0.500000 + 0.866025i) q^{72} +(3.82843 + 6.63103i) q^{73} +(0.707107 + 1.22474i) q^{74} +(0.500000 - 0.866025i) q^{75} +2.82843 q^{76} +(5.65685 - 9.79796i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.41421 + 7.64564i) q^{82} +5.17157 q^{83} +1.41421 q^{85} +(-2.29289 + 3.97141i) q^{86} +(4.12132 + 7.13834i) q^{87} +(-0.292893 - 0.507306i) q^{88} +(-3.24264 + 5.61642i) q^{89} -1.00000 q^{90} +4.82843 q^{92} +(-2.53553 + 4.39167i) q^{93} +(-4.53553 - 7.85578i) q^{94} +(1.41421 + 2.44949i) q^{95} +(0.500000 - 0.866025i) q^{96} -8.82843 q^{97} +0.585786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 - 2 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} + 4 q^{15} - 2 q^{16} - 2 q^{18} - 4 q^{20} + 8 q^{22} - 4 q^{23} + 2 q^{24} - 2 q^{25} - 4 q^{27} + 16 q^{29} - 2 q^{30} - 4 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{36} + 2 q^{40} + 24 q^{41} + 24 q^{43} - 4 q^{44} + 2 q^{45} - 4 q^{46} - 4 q^{47} - 4 q^{48} + 4 q^{50} - 4 q^{53} + 2 q^{54} - 8 q^{55} - 8 q^{58} - 12 q^{59} - 2 q^{60} - 12 q^{61} + 8 q^{62} + 4 q^{64} + 4 q^{66} + 4 q^{67} - 8 q^{69} + 32 q^{71} - 2 q^{72} + 4 q^{73} + 2 q^{75} + 2 q^{80} - 2 q^{81} - 12 q^{82} + 32 q^{83} - 12 q^{86} + 8 q^{87} - 4 q^{88} + 4 q^{89} - 4 q^{90} + 8 q^{92} + 4 q^{93} - 4 q^{94} + 2 q^{96} - 24 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 + 4 * q^15 - 2 * q^16 - 2 * q^18 - 4 * q^20 + 8 * q^22 - 4 * q^23 + 2 * q^24 - 2 * q^25 - 4 * q^27 + 16 * q^29 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^36 + 2 * q^40 + 24 * q^41 + 24 * q^43 - 4 * q^44 + 2 * q^45 - 4 * q^46 - 4 * q^47 - 4 * q^48 + 4 * q^50 - 4 * q^53 + 2 * q^54 - 8 * q^55 - 8 * q^58 - 12 * q^59 - 2 * q^60 - 12 * q^61 + 8 * q^62 + 4 * q^64 + 4 * q^66 + 4 * q^67 - 8 * q^69 + 32 * q^71 - 2 * q^72 + 4 * q^73 + 2 * q^75 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 32 * q^83 - 12 * q^86 + 8 * q^87 - 4 * q^88 + 4 * q^89 - 4 * q^90 + 8 * q^92 + 4 * q^93 - 4 * q^94 + 2 * q^96 - 24 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−0.292893	−	0.507306i	−0.0883106	−	0.152958i	0.818487	−	0.574526i	$-0.194813\pi$
$11$	−0.292893	−	0.507306i	−0.0883106	−	0.152958i	−0.906797	+	0.421567i	$0.861480\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.707107	+	1.22474i	0.171499	+	0.297044i	0.938944	−	0.344070i	$-0.111806\pi$
$17$	0.707107	+	1.22474i	0.171499	+	0.297044i	−0.767445	+	0.641114i	$0.778472\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	−0.981399	−	0.191977i	$-0.938510\pi$
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	0.656957	+	0.753928i	$0.271843\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	0.585786			0.124890
$23$	−2.41421	+	4.18154i	−0.503398	+	0.871911i	0.496594	+	0.867983i	$0.334584\pi$
$23$	−2.41421	+	4.18154i	−0.503398	+	0.871911i	−0.999992	+	0.00392850i	$0.998750\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	8.24264			1.53062			0.765310	−	0.643662i	$-0.222586\pi$
$29$	8.24264			1.53062			0.765310	+	0.643662i	$0.222586\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	2.53553	+	4.39167i	0.455395	+	0.788768i	0.998711	−	0.0507607i	$-0.0161646\pi$
$31$	2.53553	+	4.39167i	0.455395	+	0.788768i	−0.543316	+	0.839529i	$0.682831\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.292893	−	0.507306i	0.0509862	−	0.0883106i
$34$	−1.41421			−0.242536
$35$		0			0
$36$	1.00000			0.166667
$37$	0.707107	−	1.22474i	0.116248	−	0.201347i	−0.802030	−	0.597284i	$-0.796247\pi$
$37$	0.707107	−	1.22474i	0.116248	−	0.201347i	0.918278	+	0.395937i	$0.129580\pi$
$38$	−1.41421	−	2.44949i	−0.229416	−	0.397360i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	8.82843			1.37877			0.689384	−	0.724396i	$-0.257881\pi$
$41$	8.82843			1.37877			0.689384	+	0.724396i	$0.257881\pi$
$42$		0			0
$43$	4.58579			0.699326			0.349663	−	0.936876i	$-0.386296\pi$
$43$	4.58579			0.699326			0.349663	+	0.936876i	$0.386296\pi$
$44$	−0.292893	+	0.507306i	−0.0441553	+	0.0764792i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	−2.41421	−	4.18154i	−0.355956	−	0.616535i
$47$	−4.53553	+	7.85578i	−0.661576	+	1.14588i	0.318626	+	0.947881i	$0.396779\pi$
$47$	−4.53553	+	7.85578i	−0.661576	+	1.14588i	−0.980202	+	0.198002i	$0.936555\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	1.00000			0.141421
$51$	−0.707107	+	1.22474i	−0.0990148	+	0.171499i
$52$		0			0
$53$	4.65685	+	8.06591i	0.639668	+	1.10794i	0.985506	+	0.169643i	$0.0542615\pi$
$53$	4.65685	+	8.06591i	0.639668	+	1.10794i	−0.345837	+	0.938294i	$0.612405\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−0.585786			−0.0789874
$56$		0			0
$57$	−2.82843			−0.374634
$58$	−4.12132	+	7.13834i	−0.541156	+	0.937309i
$59$	1.24264	+	2.15232i	0.161778	+	0.280208i	0.935506	−	0.353310i	$-0.114944\pi$
$59$	1.24264	+	2.15232i	0.161778	+	0.280208i	−0.773728	+	0.633517i	$0.781610\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	−5.82843	+	10.0951i	−0.746254	+	1.29255i	0.203353	+	0.979105i	$0.434816\pi$
$61$	−5.82843	+	10.0951i	−0.746254	+	1.29255i	−0.949607	+	0.313444i	$0.898517\pi$
$62$	−5.07107			−0.644026
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	0.292893	+	0.507306i	0.0360527	+	0.0624450i
$67$	−3.94975	−	6.84116i	−0.482538	−	0.835781i	0.517261	−	0.855828i	$-0.326952\pi$
$67$	−3.94975	−	6.84116i	−0.482538	−	0.835781i	−0.999799	+	0.0200468i	$0.993618\pi$
$68$	0.707107	−	1.22474i	0.0857493	−	0.148522i
$69$	−4.82843			−0.581274
$70$		0			0
$71$	10.8284			1.28510			0.642549	−	0.766245i	$-0.277877\pi$
$71$	10.8284			1.28510			0.642549	+	0.766245i	$0.277877\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	3.82843	+	6.63103i	0.448084	+	0.776103i	0.998261	−	0.0589442i	$-0.0187734\pi$
$73$	3.82843	+	6.63103i	0.448084	+	0.776103i	−0.550178	+	0.835048i	$0.685440\pi$
$74$	0.707107	+	1.22474i	0.0821995	+	0.142374i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	2.82843			0.324443
$77$		0			0
$78$		0			0
$79$	5.65685	−	9.79796i	0.636446	−	1.10236i	−0.349761	−	0.936839i	$-0.613737\pi$
$79$	5.65685	−	9.79796i	0.636446	−	1.10236i	0.986207	−	0.165518i	$-0.0529295\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.41421	+	7.64564i	−0.487468	+	0.844320i
$83$	5.17157			0.567654			0.283827	−	0.958876i	$-0.408396\pi$
$83$	5.17157			0.567654			0.283827	+	0.958876i	$0.408396\pi$
$84$		0			0
$85$	1.41421			0.153393
$86$	−2.29289	+	3.97141i	−0.247249	+	0.428248i
$87$	4.12132	+	7.13834i	0.441852	+	0.765310i
$88$	−0.292893	−	0.507306i	−0.0312225	−	0.0540790i
$89$	−3.24264	+	5.61642i	−0.343719	+	0.595339i	−0.985120	−	0.171867i	$-0.945020\pi$
$89$	−3.24264	+	5.61642i	−0.343719	+	0.595339i	0.641401	+	0.767206i	$0.278354\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	4.82843			0.503398
$93$	−2.53553	+	4.39167i	−0.262923	+	0.455395i
$94$	−4.53553	−	7.85578i	−0.467805	−	0.810261i
$95$	1.41421	+	2.44949i	0.145095	+	0.251312i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−8.82843			−0.896391			−0.448195	−	0.893936i	$-0.647933\pi$
$97$	−8.82843			−0.896391			−0.448195	+	0.893936i	$0.647933\pi$
$98$		0			0
$99$	0.585786			0.0588738
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−3.17157	−	5.49333i	−0.315583	−	0.546606i	0.663978	−	0.747752i	$-0.268867\pi$
$101$	−3.17157	−	5.49333i	−0.315583	−	0.546606i	−0.979561	+	0.201146i	$0.935534\pi$
$102$	−0.707107	−	1.22474i	−0.0700140	−	0.121268i
$103$	−5.07107	+	8.78335i	−0.499667	+	0.865449i	−1.00000		0.000384289i	$-0.999878\pi$
$103$	−5.07107	+	8.78335i	−0.499667	+	0.865449i	0.500333	+	0.865833i	$0.333211\pi$
$104$		0			0
$105$		0			0
$106$	−9.31371			−0.904627
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	−0.753010	−	0.658009i	$-0.771399\pi$
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	0.946357	+	0.323122i	$0.104732\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−2.65685	−	4.60181i	−0.254480	−	0.440773i	0.710274	−	0.703926i	$-0.248571\pi$
$109$	−2.65685	−	4.60181i	−0.254480	−	0.440773i	−0.964754	+	0.263152i	$0.915238\pi$
$110$	0.292893	−	0.507306i	0.0279263	−	0.0483697i
$111$	1.41421			0.134231
$112$		0			0
$113$	9.31371			0.876160			0.438080	−	0.898936i	$-0.355659\pi$
$113$	9.31371			0.876160			0.438080	+	0.898936i	$0.355659\pi$
$114$	1.41421	−	2.44949i	0.132453	−	0.229416i
$115$	2.41421	+	4.18154i	0.225127	+	0.389931i
$116$	−4.12132	−	7.13834i	−0.382655	−	0.662778i
$117$		0			0
$118$	−2.48528			−0.228789
$119$		0			0
$120$	1.00000			0.0912871
$121$	5.32843	−	9.22911i	0.484402	−	0.839010i
$122$	−5.82843	−	10.0951i	−0.527681	−	0.913970i
$123$	4.41421	+	7.64564i	0.398016	+	0.689384i
$124$	2.53553	−	4.39167i	0.227698	−	0.394384i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−14.1421			−1.25491			−0.627456	−	0.778652i	$-0.715904\pi$
$127$	−14.1421			−1.25491			−0.627456	+	0.778652i	$0.715904\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.29289	+	3.97141i	0.201878	+	0.349663i
$130$		0			0
$131$	−8.41421	+	14.5738i	−0.735153	+	1.27332i	0.219503	+	0.975612i	$0.429556\pi$
$131$	−8.41421	+	14.5738i	−0.735153	+	1.27332i	−0.954656	+	0.297711i	$0.903777\pi$
$132$	−0.585786			−0.0509862
$133$		0			0
$134$	7.89949			0.682412
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	0.707107	+	1.22474i	0.0606339	+	0.105021i
$137$	8.00000	+	13.8564i	0.683486	+	1.18383i	0.973910	+	0.226935i	$0.0728704\pi$
$137$	8.00000	+	13.8564i	0.683486	+	1.18383i	−0.290424	+	0.956898i	$0.593796\pi$
$138$	2.41421	−	4.18154i	0.205512	−	0.355956i
$139$	−17.6569			−1.49763			−0.748817	−	0.662776i	$-0.769378\pi$
$139$	−17.6569			−1.49763			−0.748817	+	0.662776i	$0.769378\pi$
$140$		0			0
$141$	−9.07107			−0.763922
$142$	−5.41421	+	9.37769i	−0.454351	+	0.786959i
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.12132	−	7.13834i	0.342257	−	0.592807i
$146$	−7.65685			−0.633686
$147$		0			0
$148$	−1.41421			−0.116248
$149$	6.94975	−	12.0373i	0.569345	−	0.986135i	−0.427285	−	0.904117i	$-0.640530\pi$
$149$	6.94975	−	12.0373i	0.569345	−	0.986135i	0.996631	−	0.0820185i	$-0.0261367\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−8.89949	−	15.4144i	−0.724231	−	1.25440i	−0.959290	−	0.282423i	$-0.908862\pi$
$151$	−8.89949	−	15.4144i	−0.724231	−	1.25440i	0.235059	−	0.971981i	$-0.424472\pi$
$152$	−1.41421	+	2.44949i	−0.114708	+	0.198680i
$153$	−1.41421			−0.114332
$154$		0			0
$155$	5.07107			0.407318
$156$		0			0
$157$	0.171573	+	0.297173i	0.0136930	+	0.0237170i	0.872791	−	0.488095i	$-0.162308\pi$
$157$	0.171573	+	0.297173i	0.0136930	+	0.0237170i	−0.859098	+	0.511812i	$0.828975\pi$
$158$	5.65685	+	9.79796i	0.450035	+	0.779484i
$159$	−4.65685	+	8.06591i	−0.369313	+	0.639668i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	1.00000			0.0785674
$163$	−7.36396	+	12.7548i	−0.576790	+	0.999029i	0.419055	+	0.907961i	$0.362362\pi$
$163$	−7.36396	+	12.7548i	−0.576790	+	0.999029i	−0.995845	+	0.0910685i	$0.970972\pi$
$164$	−4.41421	−	7.64564i	−0.344692	−	0.597024i
$165$	−0.292893	−	0.507306i	−0.0228017	−	0.0394937i
$166$	−2.58579	+	4.47871i	−0.200696	+	0.347616i
$167$	−1.07107			−0.0828817			−0.0414409	−	0.999141i	$-0.513195\pi$
$167$	−1.07107			−0.0828817			−0.0414409	+	0.999141i	$0.513195\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	−0.707107	+	1.22474i	−0.0542326	+	0.0939336i
$171$	−1.41421	−	2.44949i	−0.108148	−	0.187317i
$172$	−2.29289	−	3.97141i	−0.174831	−	0.302817i
$173$	9.24264	−	16.0087i	0.702705	−	1.21712i	−0.264808	−	0.964301i	$-0.585309\pi$
$173$	9.24264	−	16.0087i	0.702705	−	1.21712i	0.967513	−	0.252820i	$-0.0813579\pi$
$174$	−8.24264			−0.624873
$175$		0			0
$176$	0.585786			0.0441553
$177$	−1.24264	+	2.15232i	−0.0934026	+	0.161778i
$178$	−3.24264	−	5.61642i	−0.243046	−	0.420968i
$179$	−0.292893	−	0.507306i	−0.0218919	−	0.0379178i	0.854872	−	0.518839i	$-0.173636\pi$
$179$	−0.292893	−	0.507306i	−0.0218919	−	0.0379178i	−0.876764	+	0.480921i	$0.840302\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	8.82843			0.656212			0.328106	−	0.944641i	$-0.393590\pi$
$181$	8.82843			0.656212			0.328106	+	0.944641i	$0.393590\pi$
$182$		0			0
$183$	−11.6569			−0.861699
$184$	−2.41421	+	4.18154i	−0.177978	+	0.308267i
$185$	−0.707107	−	1.22474i	−0.0519875	−	0.0900450i
$186$	−2.53553	−	4.39167i	−0.185914	−	0.322013i
$187$	0.414214	−	0.717439i	0.0302903	−	0.0524643i
$188$	9.07107			0.661576
$189$		0			0
$190$	−2.82843			−0.205196
$191$	5.65685	−	9.79796i	0.409316	−	0.708955i	−0.585498	−	0.810674i	$-0.699101\pi$
$191$	5.65685	−	9.79796i	0.409316	−	0.708955i	0.994813	+	0.101719i	$0.0324342\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	10.8995	+	18.8785i	0.784563	+	1.35890i	0.929260	+	0.369427i	$0.120446\pi$
$193$	10.8995	+	18.8785i	0.784563	+	1.35890i	−0.144697	+	0.989476i	$0.546221\pi$
$194$	4.41421	−	7.64564i	0.316922	−	0.548925i
$195$		0			0
$196$		0			0
$197$	−20.8284			−1.48396			−0.741982	−	0.670420i	$-0.766114\pi$
$197$	−20.8284			−1.48396			−0.741982	+	0.670420i	$0.766114\pi$
$198$	−0.292893	+	0.507306i	−0.0208150	+	0.0360527i
$199$	1.46447	+	2.53653i	0.103813	+	0.179810i	0.913253	−	0.407393i	$-0.133562\pi$
$199$	1.46447	+	2.53653i	0.103813	+	0.179810i	−0.809439	+	0.587203i	$0.800229\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	3.94975	−	6.84116i	0.278594	−	0.482538i
$202$	6.34315			0.446302
$203$		0			0
$204$	1.41421			0.0990148
$205$	4.41421	−	7.64564i	0.308302	−	0.533995i
$206$	−5.07107	−	8.78335i	−0.353318	−	0.611965i
$207$	−2.41421	−	4.18154i	−0.167799	−	0.290637i
$208$		0			0
$209$	1.65685			0.114607
$210$		0			0
$211$	−1.65685			−0.114063			−0.0570313	−	0.998372i	$-0.518163\pi$
$211$	−1.65685			−0.114063			−0.0570313	+	0.998372i	$0.518163\pi$
$212$	4.65685	−	8.06591i	0.319834	−	0.553969i
$213$	5.41421	+	9.37769i	0.370976	+	0.642549i
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	2.29289	−	3.97141i	0.156374	−	0.270848i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	5.31371			0.359890
$219$	−3.82843	+	6.63103i	−0.258701	+	0.448084i
$220$	0.292893	+	0.507306i	0.0197469	+	0.0342026i
$221$		0			0
$222$	−0.707107	+	1.22474i	−0.0474579	+	0.0821995i
$223$	−17.6569			−1.18239			−0.591195	−	0.806529i	$-0.701344\pi$
$223$	−17.6569			−1.18239			−0.591195	+	0.806529i	$0.701344\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	−4.65685	+	8.06591i	−0.309769	+	0.536536i
$227$	−6.82843	−	11.8272i	−0.453219	−	0.784998i	0.545365	−	0.838199i	$-0.316391\pi$
$227$	−6.82843	−	11.8272i	−0.453219	−	0.784998i	−0.998584	+	0.0532009i	$0.983058\pi$
$228$	1.41421	+	2.44949i	0.0936586	+	0.162221i
$229$	12.8995	−	22.3426i	0.852423	−	1.47644i	−0.0265930	−	0.999646i	$-0.508466\pi$
$229$	12.8995	−	22.3426i	0.852423	−	1.47644i	0.879016	−	0.476793i	$-0.158201\pi$
$230$	−4.82843			−0.318377
$231$		0			0
$232$	8.24264			0.541156
$233$	−3.48528	+	6.03668i	−0.228328	+	0.395476i	−0.957313	−	0.289054i	$-0.906659\pi$
$233$	−3.48528	+	6.03668i	−0.228328	+	0.395476i	0.728984	+	0.684530i	$0.239993\pi$
$234$		0			0
$235$	4.53553	+	7.85578i	0.295866	+	0.512454i
$236$	1.24264	−	2.15232i	0.0808890	−	0.140104i
$237$	11.3137			0.734904
$238$		0			0
$239$	23.3137			1.50804			0.754019	−	0.656852i	$-0.228113\pi$
$239$	23.3137			1.50804			0.754019	+	0.656852i	$0.228113\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−8.12132	−	14.0665i	−0.523140	−	0.906105i	−0.999637	−	0.0269294i	$-0.991427\pi$
$241$	−8.12132	−	14.0665i	−0.523140	−	0.906105i	0.476497	−	0.879176i	$-0.341906\pi$
$242$	5.32843	+	9.22911i	0.342524	+	0.593269i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	11.6569			0.746254
$245$		0			0
$246$	−8.82843			−0.562880
$247$		0			0
$248$	2.53553	+	4.39167i	0.161007	+	0.278872i
$249$	2.58579	+	4.47871i	0.163868	+	0.283827i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	17.6569			1.11449			0.557245	−	0.830348i	$-0.311858\pi$
$251$	17.6569			1.11449			0.557245	+	0.830348i	$0.311858\pi$
$252$		0			0
$253$	2.82843			0.177822
$254$	7.07107	−	12.2474i	0.443678	−	0.768473i
$255$	0.707107	+	1.22474i	0.0442807	+	0.0766965i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.949747	−	1.64501i	0.0592436	−	0.102613i	−0.834882	−	0.550428i	$-0.814464\pi$
$257$	0.949747	−	1.64501i	0.0592436	−	0.102613i	0.894126	+	0.447815i	$0.147798\pi$
$258$	−4.58579			−0.285499
$259$		0			0
$260$		0			0
$261$	−4.12132	+	7.13834i	−0.255103	+	0.441852i
$262$	−8.41421	−	14.5738i	−0.519832	−	0.900375i
$263$	10.8995	+	18.8785i	0.672092	+	1.16410i	0.977310	+	0.211814i	$0.0679373\pi$
$263$	10.8995	+	18.8785i	0.672092	+	1.16410i	−0.305218	+	0.952282i	$0.598729\pi$
$264$	0.292893	−	0.507306i	0.0180263	−	0.0312225i
$265$	9.31371			0.572137
$266$		0			0
$267$	−6.48528			−0.396893
$268$	−3.94975	+	6.84116i	−0.241269	+	0.417891i
$269$	3.82843	+	6.63103i	0.233423	+	0.404301i	0.958813	−	0.284037i	$-0.0916739\pi$
$269$	3.82843	+	6.63103i	0.233423	+	0.404301i	−0.725390	+	0.688338i	$0.758341\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	−7.12132	+	12.3345i	−0.432589	+	0.749267i	−0.997095	−	0.0761621i	$-0.975733\pi$
$271$	−7.12132	+	12.3345i	−0.432589	+	0.749267i	0.564506	+	0.825429i	$0.309067\pi$
$272$	−1.41421			−0.0857493
$273$		0			0
$274$	−16.0000			−0.966595
$275$	−0.292893	+	0.507306i	−0.0176621	+	0.0305917i
$276$	2.41421	+	4.18154i	0.145319	+	0.251699i
$277$	−10.9497	−	18.9655i	−0.657907	−	1.13953i	−0.981157	−	0.193214i	$-0.938109\pi$
$277$	−10.9497	−	18.9655i	−0.657907	−	1.13953i	0.323250	−	0.946314i	$-0.395225\pi$
$278$	8.82843	−	15.2913i	0.529494	−	0.917110i
$279$	−5.07107			−0.303597
$280$		0			0
$281$	−13.5147			−0.806221			−0.403110	−	0.915151i	$-0.632071\pi$
$281$	−13.5147			−0.806221			−0.403110	+	0.915151i	$0.632071\pi$
$282$	4.53553	−	7.85578i	0.270087	−	0.467805i
$283$	15.2426	+	26.4010i	0.906081	+	1.56938i	0.819460	+	0.573137i	$0.194274\pi$
$283$	15.2426	+	26.4010i	0.906081	+	1.56938i	0.0866213	+	0.996241i	$0.472393\pi$
$284$	−5.41421	−	9.37769i	−0.321274	−	0.556464i
$285$	−1.41421	+	2.44949i	−0.0837708	+	0.145095i
$286$		0			0
$287$		0			0
$288$	1.00000			0.0589256
$289$	7.50000	−	12.9904i	0.441176	−	0.764140i
$290$	4.12132	+	7.13834i	0.242012	+	0.419178i
$291$	−4.41421	−	7.64564i	−0.258766	−	0.448195i
$292$	3.82843	−	6.63103i	0.224042	−	0.388052i
$293$	28.6274			1.67243			0.836216	−	0.548401i	$-0.184763\pi$
$293$	28.6274			1.67243			0.836216	+	0.548401i	$0.184763\pi$
$294$		0			0
$295$	2.48528			0.144699
$296$	0.707107	−	1.22474i	0.0410997	−	0.0711868i
$297$	0.292893	+	0.507306i	0.0169954	+	0.0294369i
$298$	6.94975	+	12.0373i	0.402588	+	0.697303i
$299$		0			0
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	17.7990			1.02422
$303$	3.17157	−	5.49333i	0.182202	−	0.315583i
$304$	−1.41421	−	2.44949i	−0.0811107	−	0.140488i
$305$	5.82843	+	10.0951i	0.333735	+	0.578046i
$306$	0.707107	−	1.22474i	0.0404226	−	0.0700140i
$307$	7.31371			0.417415			0.208708	−	0.977978i	$-0.433074\pi$
$307$	7.31371			0.417415			0.208708	+	0.977978i	$0.433074\pi$
$308$		0			0
$309$	−10.1421			−0.576966
$310$	−2.53553	+	4.39167i	−0.144009	+	0.249430i
$311$	−14.5858	−	25.2633i	−0.827084	−	1.43255i	−0.900316	−	0.435237i	$-0.856665\pi$
$311$	−14.5858	−	25.2633i	−0.827084	−	1.43255i	0.0732320	−	0.997315i	$-0.476669\pi$
$312$		0			0
$313$	14.4142	−	24.9662i	0.814740	−	1.41117i	−0.0947753	−	0.995499i	$-0.530213\pi$
$313$	14.4142	−	24.9662i	0.814740	−	1.41117i	0.909515	−	0.415672i	$-0.136453\pi$
$314$	−0.343146			−0.0193648
$315$		0			0
$316$	−11.3137			−0.636446
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$	−4.65685	−	8.06591i	−0.261143	−	0.452314i
$319$	−2.41421	−	4.18154i	−0.135170	−	0.234121i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	4.00000			0.223258
$322$		0			0
$323$	−4.00000			−0.222566
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−7.36396	−	12.7548i	−0.407852	−	0.706421i
$327$	2.65685	−	4.60181i	0.146924	−	0.254480i
$328$	8.82843			0.487468
$329$		0			0
$330$	0.585786			0.0322465
$331$	9.31371	−	16.1318i	0.511928	−	0.886685i	−0.487977	−	0.872857i	$-0.662265\pi$
$331$	9.31371	−	16.1318i	0.511928	−	0.886685i	0.999904	−	0.0138281i	$-0.00440178\pi$
$332$	−2.58579	−	4.47871i	−0.141913	−	0.245801i
$333$	0.707107	+	1.22474i	0.0387492	+	0.0671156i
$334$	0.535534	−	0.927572i	0.0293031	−	0.0507545i
$335$	−7.89949			−0.431596
$336$		0			0
$337$	−3.17157			−0.172767			−0.0863833	−	0.996262i	$-0.527531\pi$
$337$	−3.17157			−0.172767			−0.0863833	+	0.996262i	$0.527531\pi$
$338$	6.50000	−	11.2583i	0.353553	−	0.612372i
$339$	4.65685	+	8.06591i	0.252926	+	0.438080i
$340$	−0.707107	−	1.22474i	−0.0383482	−	0.0664211i
$341$	1.48528	−	2.57258i	0.0804325	−	0.139313i
$342$	2.82843			0.152944
$343$		0			0
$344$	4.58579			0.247249
$345$	−2.41421	+	4.18154i	−0.129977	+	0.225127i
$346$	9.24264	+	16.0087i	0.496887	+	0.860634i
$347$	−0.828427	−	1.43488i	−0.0444723	−	0.0770283i	0.842932	−	0.538019i	$-0.180827\pi$
$347$	−0.828427	−	1.43488i	−0.0444723	−	0.0770283i	−0.887405	+	0.460991i	$0.847494\pi$
$348$	4.12132	−	7.13834i	0.220926	−	0.382655i
$349$	5.79899			0.310413			0.155206	−	0.987882i	$-0.450396\pi$
$349$	5.79899			0.310413			0.155206	+	0.987882i	$0.450396\pi$
$350$		0			0
$351$		0			0
$352$	−0.292893	+	0.507306i	−0.0156113	+	0.0270395i
$353$	−0.363961	−	0.630399i	−0.0193717	−	0.0335528i	0.856177	−	0.516683i	$-0.172833\pi$
$353$	−0.363961	−	0.630399i	−0.0193717	−	0.0335528i	−0.875549	+	0.483130i	$0.839500\pi$
$354$	−1.24264	−	2.15232i	−0.0660456	−	0.114394i
$355$	5.41421	−	9.37769i	0.287357	−	0.497716i
$356$	6.48528			0.343719
$357$		0			0
$358$	0.585786			0.0309598
$359$	−9.41421	+	16.3059i	−0.496863	+	0.860592i	−0.999993	−	0.00361830i	$-0.998848\pi$
$359$	−9.41421	+	16.3059i	−0.496863	+	0.860592i	0.503130	+	0.864211i	$0.332182\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	−4.41421	+	7.64564i	−0.232006	+	0.401846i
$363$	10.6569			0.559340
$364$		0			0
$365$	7.65685			0.400778
$366$	5.82843	−	10.0951i	0.304657	−	0.527681i
$367$	8.24264	+	14.2767i	0.430262	+	0.745236i	0.996896	−	0.0787338i	$-0.0250877\pi$
$367$	8.24264	+	14.2767i	0.430262	+	0.745236i	−0.566633	+	0.823970i	$0.691754\pi$
$368$	−2.41421	−	4.18154i	−0.125850	−	0.217978i
$369$	−4.41421	+	7.64564i	−0.229795	+	0.398016i
$370$	1.41421			0.0735215
$371$		0			0
$372$	5.07107			0.262923
$373$	−5.53553	+	9.58783i	−0.286619	+	0.496439i	−0.973001	−	0.230803i	$-0.925865\pi$
$373$	−5.53553	+	9.58783i	−0.286619	+	0.496439i	0.686381	+	0.727242i	$0.259198\pi$
$374$	0.414214	+	0.717439i	0.0214185	+	0.0370979i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	−4.53553	+	7.85578i	−0.233902	+	0.405131i
$377$		0			0
$378$		0			0
$379$	−24.4853			−1.25772			−0.628862	−	0.777517i	$-0.716479\pi$
$379$	−24.4853			−1.25772			−0.628862	+	0.777517i	$0.716479\pi$
$380$	1.41421	−	2.44949i	0.0725476	−	0.125656i
$381$	−7.07107	−	12.2474i	−0.362262	−	0.627456i
$382$	5.65685	+	9.79796i	0.289430	+	0.501307i
$383$	7.94975	−	13.7694i	0.406213	−	0.703582i	−0.588249	−	0.808680i	$-0.700182\pi$
$383$	7.94975	−	13.7694i	0.406213	−	0.703582i	0.994462	+	0.105098i	$0.0335157\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−21.7990			−1.10954
$387$	−2.29289	+	3.97141i	−0.116554	+	0.201878i
$388$	4.41421	+	7.64564i	0.224098	+	0.388149i
$389$	−13.5355	−	23.4442i	−0.686279	−	1.18867i	−0.973033	−	0.230666i	$-0.925910\pi$
$389$	−13.5355	−	23.4442i	−0.686279	−	1.18867i	0.286754	−	0.958004i	$-0.407424\pi$
$390$		0			0
$391$	−6.82843			−0.345328
$392$		0			0
$393$	−16.8284			−0.848882
$394$	10.4142	−	18.0379i	0.524660	−	0.908739i
$395$	−5.65685	−	9.79796i	−0.284627	−	0.492989i
$396$	−0.292893	−	0.507306i	−0.0147184	−	0.0254931i
$397$	10.3137	−	17.8639i	0.517630	−	0.896562i	−0.482160	−	0.876083i	$-0.660148\pi$
$397$	10.3137	−	17.8639i	0.517630	−	0.896562i	0.999790	−	0.0204787i	$-0.00651902\pi$
$398$	−2.92893			−0.146814
$399$		0			0
$400$	1.00000			0.0500000
$401$	12.6569	−	21.9223i	0.632053	−	1.09475i	−0.355078	−	0.934837i	$-0.615546\pi$
$401$	12.6569	−	21.9223i	0.632053	−	1.09475i	0.987131	−	0.159912i	$-0.0511209\pi$
$402$	3.94975	+	6.84116i	0.196995	+	0.341206i
$403$		0			0
$404$	−3.17157	+	5.49333i	−0.157792	+	0.273303i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−0.828427			−0.0410636
$408$	−0.707107	+	1.22474i	−0.0350070	+	0.0606339i
$409$	−9.19239	−	15.9217i	−0.454534	−	0.787277i	0.544127	−	0.839003i	$-0.316861\pi$
$409$	−9.19239	−	15.9217i	−0.454534	−	0.787277i	−0.998661	+	0.0517263i	$0.983528\pi$
$410$	4.41421	+	7.64564i	0.218002	+	0.377591i
$411$	−8.00000	+	13.8564i	−0.394611	+	0.683486i
$412$	10.1421			0.499667
$413$		0			0
$414$	4.82843			0.237304
$415$	2.58579	−	4.47871i	0.126931	−	0.219851i
$416$		0			0
$417$	−8.82843	−	15.2913i	−0.432330	−	0.748817i
$418$	−0.828427	+	1.43488i	−0.0405197	+	0.0701822i
$419$	17.6569			0.862594			0.431297	−	0.902210i	$-0.358056\pi$
$419$	17.6569			0.862594			0.431297	+	0.902210i	$0.358056\pi$
$420$		0			0
$421$	16.6274			0.810371			0.405185	−	0.914235i	$-0.367207\pi$
$421$	16.6274			0.810371			0.405185	+	0.914235i	$0.367207\pi$
$422$	0.828427	−	1.43488i	0.0403272	−	0.0698488i
$423$	−4.53553	−	7.85578i	−0.220525	−	0.381961i
$424$	4.65685	+	8.06591i	0.226157	+	0.391715i
$425$	0.707107	−	1.22474i	0.0342997	−	0.0594089i
$426$	−10.8284			−0.524639
$427$		0			0
$428$	−4.00000			−0.193347
$429$		0			0
$430$	2.29289	+	3.97141i	0.110573	+	0.191518i
$431$	−7.07107	−	12.2474i	−0.340601	−	0.589939i	0.643943	−	0.765073i	$-0.277297\pi$
$431$	−7.07107	−	12.2474i	−0.340601	−	0.589939i	−0.984545	+	0.175134i	$0.943964\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−8.82843			−0.424267			−0.212134	−	0.977241i	$-0.568041\pi$
$433$	−8.82843			−0.424267			−0.212134	+	0.977241i	$0.568041\pi$
$434$		0			0
$435$	8.24264			0.395204
$436$	−2.65685	+	4.60181i	−0.127240	+	0.220387i
$437$	−6.82843	−	11.8272i	−0.326648	−	0.565771i
$438$	−3.82843	−	6.63103i	−0.182929	−	0.316843i
$439$	16.7782	−	29.0607i	0.800779	−	1.38699i	−0.118326	−	0.992975i	$-0.537753\pi$
$439$	16.7782	−	29.0607i	0.800779	−	1.38699i	0.919104	−	0.394014i	$-0.128914\pi$
$440$	−0.585786			−0.0279263
$441$		0			0
$442$		0			0
$443$	−6.82843	+	11.8272i	−0.324428	+	0.561926i	−0.981397	−	0.191992i	$-0.938505\pi$
$443$	−6.82843	+	11.8272i	−0.324428	+	0.561926i	0.656968	+	0.753918i	$0.271839\pi$
$444$	−0.707107	−	1.22474i	−0.0335578	−	0.0581238i
$445$	3.24264	+	5.61642i	0.153716	+	0.266244i
$446$	8.82843	−	15.2913i	0.418038	−	0.724063i
$447$	13.8995			0.657424
$448$		0			0
$449$	−25.1127			−1.18514			−0.592571	−	0.805518i	$-0.701887\pi$
$449$	−25.1127			−1.18514			−0.592571	+	0.805518i	$0.701887\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	−2.58579	−	4.47871i	−0.121760	−	0.210894i
$452$	−4.65685	−	8.06591i	−0.219040	−	0.379388i
$453$	8.89949	−	15.4144i	0.418135	−	0.724231i
$454$	13.6569			0.640948
$455$		0			0
$456$	−2.82843			−0.132453
$457$	4.89949	−	8.48617i	0.229189	−	0.396966i	−0.728379	−	0.685174i	$-0.759726\pi$
$457$	4.89949	−	8.48617i	0.229189	−	0.396966i	0.957568	+	0.288208i	$0.0930594\pi$
$458$	12.8995	+	22.3426i	0.602754	+	1.04400i
$459$	−0.707107	−	1.22474i	−0.0330049	−	0.0571662i
$460$	2.41421	−	4.18154i	0.112563	−	0.194965i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$	33.6569			1.56417			0.782083	−	0.623174i	$-0.214157\pi$
$463$	33.6569			1.56417			0.782083	+	0.623174i	$0.214157\pi$
$464$	−4.12132	+	7.13834i	−0.191327	+	0.331389i
$465$	2.53553	+	4.39167i	0.117583	+	0.203659i
$466$	−3.48528	−	6.03668i	−0.161453	−	0.279644i
$467$	−10.2426	+	17.7408i	−0.473973	+	0.820945i	−0.999556	−	0.0297972i	$-0.990514\pi$
$467$	−10.2426	+	17.7408i	−0.473973	+	0.820945i	0.525583	+	0.850742i	$0.323847\pi$
$468$		0			0
$469$		0			0
$470$	−9.07107			−0.418417
$471$	−0.171573	+	0.297173i	−0.00790566	+	0.0136930i
$472$	1.24264	+	2.15232i	0.0571972	+	0.0990684i
$473$	−1.34315	−	2.32640i	−0.0617579	−	0.106968i
$474$	−5.65685	+	9.79796i	−0.259828	+	0.450035i
$475$	2.82843			0.129777
$476$		0			0
$477$	−9.31371			−0.426445
$478$	−11.6569	+	20.1903i	−0.533172	+	0.923481i
$479$	8.24264	+	14.2767i	0.376616	+	0.652318i	0.990567	−	0.137026i	$-0.0437543\pi$
$479$	8.24264	+	14.2767i	0.376616	+	0.652318i	−0.613952	+	0.789344i	$0.710421\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$		0			0
$482$	16.2426			0.739832
$483$		0			0
$484$	−10.6569			−0.484402
$485$	−4.41421	+	7.64564i	−0.200439	+	0.347171i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−12.2426	−	21.2049i	−0.554767	−	0.960885i	−0.997922	−	0.0644394i	$-0.979474\pi$
$487$	−12.2426	−	21.2049i	−0.554767	−	0.960885i	0.443155	−	0.896445i	$-0.353859\pi$
$488$	−5.82843	+	10.0951i	−0.263840	+	0.456985i
$489$	−14.7279			−0.666020
$490$		0			0
$491$	11.8995			0.537017			0.268508	−	0.963277i	$-0.413469\pi$
$491$	11.8995			0.537017			0.268508	+	0.963277i	$0.413469\pi$
$492$	4.41421	−	7.64564i	0.199008	−	0.344692i
$493$	5.82843	+	10.0951i	0.262499	+	0.454662i
$494$		0			0
$495$	0.292893	−	0.507306i	0.0131646	−	0.0228017i
$496$	−5.07107			−0.227698
$497$		0			0
$498$	−5.17157			−0.231744
$499$	−7.89949	+	13.6823i	−0.353630	+	0.612505i	−0.986883	−	0.161440i	$-0.948386\pi$
$499$	−7.89949	+	13.6823i	−0.353630	+	0.612505i	0.633253	+	0.773945i	$0.281719\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−0.535534	−	0.927572i	−0.0239259	−	0.0414409i
$502$	−8.82843	+	15.2913i	−0.394032	+	0.682483i
$503$	−23.8995			−1.06563			−0.532813	−	0.846233i	$-0.678865\pi$
$503$	−23.8995			−1.06563			−0.532813	+	0.846233i	$0.678865\pi$
$504$		0			0
$505$	−6.34315			−0.282266
$506$	−1.41421	+	2.44949i	−0.0628695	+	0.108893i
$507$	−6.50000	−	11.2583i	−0.288675	−	0.500000i
$508$	7.07107	+	12.2474i	0.313728	+	0.543393i
$509$	−9.17157	+	15.8856i	−0.406523	+	0.704118i	−0.994497	−	0.104761i	$-0.966592\pi$
$509$	−9.17157	+	15.8856i	−0.406523	+	0.704118i	0.587975	+	0.808879i	$0.299926\pi$
$510$	−1.41421			−0.0626224
$511$		0			0
$512$	1.00000			0.0441942
$513$	1.41421	−	2.44949i	0.0624391	−	0.108148i
$514$	0.949747	+	1.64501i	0.0418916	+	0.0725583i
$515$	5.07107	+	8.78335i	0.223458	+	0.387041i
$516$	2.29289	−	3.97141i	0.100939	−	0.174831i
$517$	5.31371			0.233697
$518$		0			0
$519$	18.4853			0.811414
$520$		0			0
$521$	−6.07107	−	10.5154i	−0.265978	−	0.460688i	0.701841	−	0.712333i	$-0.252362\pi$
$521$	−6.07107	−	10.5154i	−0.265978	−	0.460688i	−0.967819	+	0.251646i	$0.919028\pi$
$522$	−4.12132	−	7.13834i	−0.180385	−	0.312436i
$523$	−10.5563	+	18.2841i	−0.461597	+	0.799509i	−0.999041	−	0.0437902i	$-0.986057\pi$
$523$	−10.5563	+	18.2841i	−0.461597	+	0.799509i	0.537444	+	0.843300i	$0.319390\pi$
$524$	16.8284			0.735153
$525$		0			0
$526$	−21.7990			−0.950481
$527$	−3.58579	+	6.21076i	−0.156199	+	0.270545i
$528$	0.292893	+	0.507306i	0.0127465	+	0.0220777i
$529$	−0.156854	−	0.271680i	−0.00681975	−	0.0118122i
$530$	−4.65685	+	8.06591i	−0.202281	+	0.350361i
$531$	−2.48528			−0.107852
$532$		0			0
$533$		0			0
$534$	3.24264	−	5.61642i	0.140323	−	0.243046i
$535$	−2.00000	−	3.46410i	−0.0864675	−	0.149766i
$536$	−3.94975	−	6.84116i	−0.170603	−	0.295493i
$537$	0.292893	−	0.507306i	0.0126393	−	0.0218919i
$538$	−7.65685			−0.330110
$539$		0			0
$540$	1.00000			0.0430331
$541$	1.24264	−	2.15232i	0.0534253	−	0.0925353i	−0.838076	−	0.545554i	$-0.816319\pi$
$541$	1.24264	−	2.15232i	0.0534253	−	0.0925353i	0.891501	+	0.453018i	$0.149653\pi$
$542$	−7.12132	−	12.3345i	−0.305887	−	0.529812i
$543$	4.41421	+	7.64564i	0.189432	+	0.328106i
$544$	0.707107	−	1.22474i	0.0303170	−	0.0525105i
$545$	−5.31371			−0.227614
$546$		0			0
$547$	27.4142			1.17215			0.586074	−	0.810258i	$-0.300673\pi$
$547$	27.4142			1.17215			0.586074	+	0.810258i	$0.300673\pi$
$548$	8.00000	−	13.8564i	0.341743	−	0.591916i
$549$	−5.82843	−	10.0951i	−0.248751	−	0.430850i
$550$	−0.292893	−	0.507306i	−0.0124890	−	0.0216316i
$551$	−11.6569	+	20.1903i	−0.496599	+	0.860134i
$552$	−4.82843			−0.205512
$553$		0			0
$554$	21.8995			0.930420
$555$	0.707107	−	1.22474i	0.0300150	−	0.0519875i
$556$	8.82843	+	15.2913i	0.374409	+	0.648495i
$557$	−6.31371	−	10.9357i	−0.267520	−	0.463359i	0.700700	−	0.713456i	$-0.252871\pi$
$557$	−6.31371	−	10.9357i	−0.267520	−	0.463359i	−0.968221	+	0.250097i	$0.919538\pi$
$558$	2.53553	−	4.39167i	0.107338	−	0.185914i
$559$		0			0
$560$		0			0
$561$	0.828427			0.0349762
$562$	6.75736	−	11.7041i	0.285042	−	0.493707i
$563$	−13.0711	−	22.6398i	−0.550880	−	0.954152i	−0.998211	−	0.0597836i	$-0.980959\pi$
$563$	−13.0711	−	22.6398i	−0.550880	−	0.954152i	0.447332	−	0.894368i	$-0.352374\pi$
$564$	4.53553	+	7.85578i	0.190980	+	0.330788i
$565$	4.65685	−	8.06591i	0.195915	−	0.339335i
$566$	−30.4853			−1.28139
$567$		0			0
$568$	10.8284			0.454351
$569$	−17.4853	+	30.2854i	−0.733021	+	1.26963i	0.222565	+	0.974918i	$0.428557\pi$
$569$	−17.4853	+	30.2854i	−0.733021	+	1.26963i	−0.955586	+	0.294712i	$0.904776\pi$
$570$	−1.41421	−	2.44949i	−0.0592349	−	0.102598i
$571$	−2.34315	−	4.05845i	−0.0980576	−	0.169841i	0.812823	−	0.582511i	$-0.197930\pi$
$571$	−2.34315	−	4.05845i	−0.0980576	−	0.169841i	−0.910881	+	0.412670i	$0.864596\pi$
$572$		0			0
$573$	11.3137			0.472637
$574$		0			0
$575$	4.82843			0.201359
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−6.07107	−	10.5154i	−0.252742	−	0.437762i	0.711538	−	0.702648i	$-0.247999\pi$
$577$	−6.07107	−	10.5154i	−0.252742	−	0.437762i	−0.964280	+	0.264886i	$0.914666\pi$
$578$	7.50000	+	12.9904i	0.311959	+	0.540329i
$579$	−10.8995	+	18.8785i	−0.452968	+	0.784563i
$580$	−8.24264			−0.342257
$581$		0			0
$582$	8.82843			0.365950
$583$	2.72792	−	4.72490i	0.112979	−	0.195685i
$584$	3.82843	+	6.63103i	0.158421	+	0.274394i
$585$		0			0
$586$	−14.3137	+	24.7921i	−0.591294	+	1.02415i
$587$	−19.7990			−0.817192			−0.408596	−	0.912715i	$-0.633981\pi$
$587$	−19.7990			−0.817192			−0.408596	+	0.912715i	$0.633981\pi$
$588$		0			0
$589$	−14.3431			−0.590999
$590$	−1.24264	+	2.15232i	−0.0511587	+	0.0886095i
$591$	−10.4142	−	18.0379i	−0.428384	−	0.741982i
$592$	0.707107	+	1.22474i	0.0290619	+	0.0503367i
$593$	18.6066	−	32.2276i	0.764082	−	1.32343i	−0.176649	−	0.984274i	$-0.556526\pi$
$593$	18.6066	−	32.2276i	0.764082	−	1.32343i	0.940731	−	0.339154i	$-0.110141\pi$
$594$	−0.585786			−0.0240351
$595$		0			0
$596$	−13.8995			−0.569345
$597$	−1.46447	+	2.53653i	−0.0599366	+	0.103813i
$598$		0			0
$599$	−2.34315	−	4.05845i	−0.0957383	−	0.165824i	0.814178	−	0.580615i	$-0.197188\pi$
$599$	−2.34315	−	4.05845i	−0.0957383	−	0.165824i	−0.909917	+	0.414791i	$0.863855\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−42.1838			−1.72071			−0.860356	−	0.509694i	$-0.829759\pi$
$601$	−42.1838			−1.72071			−0.860356	+	0.509694i	$0.829759\pi$
$602$		0			0
$603$	7.89949			0.321692
$604$	−8.89949	+	15.4144i	−0.362115	+	0.627202i
$605$	−5.32843	−	9.22911i	−0.216631	−	0.375217i
$606$	3.17157	+	5.49333i	0.128836	+	0.223151i
$607$	−2.48528	+	4.30463i	−0.100874	+	0.174720i	−0.912045	−	0.410090i	$-0.865497\pi$
$607$	−2.48528	+	4.30463i	−0.100874	+	0.174720i	0.811171	+	0.584809i	$0.198831\pi$
$608$	2.82843			0.114708
$609$		0			0
$610$	−11.6569			−0.471972
$611$		0			0
$612$	0.707107	+	1.22474i	0.0285831	+	0.0495074i
$613$	2.60660	+	4.51477i	0.105280	+	0.182350i	0.913852	−	0.406046i	$-0.133093\pi$
$613$	2.60660	+	4.51477i	0.105280	+	0.182350i	−0.808573	+	0.588396i	$0.799760\pi$
$614$	−3.65685	+	6.33386i	−0.147579	+	0.255614i
$615$	8.82843			0.355997
$616$		0			0
$617$	−44.2843			−1.78282			−0.891409	−	0.453200i	$-0.850282\pi$
$617$	−44.2843			−1.78282			−0.891409	+	0.453200i	$0.850282\pi$
$618$	5.07107	−	8.78335i	0.203988	−	0.353318i
$619$	0.928932	+	1.60896i	0.0373369	+	0.0646695i	0.884090	−	0.467317i	$-0.154779\pi$
$619$	0.928932	+	1.60896i	0.0373369	+	0.0646695i	−0.846753	+	0.531986i	$0.821446\pi$
$620$	−2.53553	−	4.39167i	−0.101829	−	0.176374i
$621$	2.41421	−	4.18154i	0.0968791	−	0.167799i
$622$	29.1716			1.16967
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	14.4142	+	24.9662i	0.576108	+	0.997848i
$627$	0.828427	+	1.43488i	0.0330842	+	0.0573035i
$628$	0.171573	−	0.297173i	0.00684650	−	0.0118585i
$629$	2.00000			0.0797452
$630$		0			0
$631$	24.8284			0.988404			0.494202	−	0.869347i	$-0.335460\pi$
$631$	24.8284			0.988404			0.494202	+	0.869347i	$0.335460\pi$
$632$	5.65685	−	9.79796i	0.225018	−	0.389742i
$633$	−0.828427	−	1.43488i	−0.0329270	−	0.0570313i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	−7.07107	+	12.2474i	−0.280607	+	0.486025i
$636$	9.31371			0.369313
$637$		0			0
$638$	4.82843			0.191159
$639$	−5.41421	+	9.37769i	−0.214183	+	0.370976i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$	−2.00000	+	3.46410i	−0.0789337	+	0.136717i
$643$	−48.4264			−1.90975			−0.954876	−	0.297006i	$-0.904012\pi$
$643$	−48.4264			−1.90975			−0.954876	+	0.297006i	$0.904012\pi$
$644$		0			0
$645$	4.58579			0.180565
$646$	2.00000	−	3.46410i	0.0786889	−	0.136293i
$647$	16.5355	+	28.6404i	0.650079	+	1.12597i	0.983103	+	0.183052i	$0.0585975\pi$
$647$	16.5355	+	28.6404i	0.650079	+	1.12597i	−0.333024	+	0.942918i	$0.608069\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	0.727922	−	1.26080i	0.0285734	−	0.0494907i
$650$		0			0
$651$		0			0
$652$	14.7279			0.576790
$653$	−16.4142	+	28.4303i	−0.642338	+	1.11256i	0.342572	+	0.939492i	$0.388702\pi$
$653$	−16.4142	+	28.4303i	−0.642338	+	1.11256i	−0.984910	+	0.173070i	$0.944631\pi$
$654$	2.65685	+	4.60181i	0.103891	+	0.179945i
$655$	8.41421	+	14.5738i	0.328771	+	0.569447i
$656$	−4.41421	+	7.64564i	−0.172346	+	0.298512i
$657$	−7.65685			−0.298722
$658$		0			0
$659$	20.1005			0.783005			0.391502	−	0.920177i	$-0.371956\pi$
$659$	20.1005			0.783005			0.391502	+	0.920177i	$0.371956\pi$
$660$	−0.292893	+	0.507306i	−0.0114009	+	0.0197469i
$661$	−13.8284	−	23.9515i	−0.537863	−	0.931607i	−0.999019	−	0.0442875i	$-0.985898\pi$
$661$	−13.8284	−	23.9515i	−0.537863	−	0.931607i	0.461155	−	0.887319i	$-0.347435\pi$
$662$	9.31371	+	16.1318i	0.361988	+	0.626981i
$663$		0			0
$664$	5.17157			0.200696
$665$		0			0
$666$	−1.41421			−0.0547997
$667$	−19.8995	+	34.4669i	−0.770512	+	1.33457i
$668$	0.535534	+	0.927572i	0.0207204	+	0.0358888i
$669$	−8.82843	−	15.2913i	−0.341327	−	0.591195i
$670$	3.94975	−	6.84116i	0.152592	−	0.264297i
$671$	6.82843			0.263609
$672$		0			0
$673$	41.5980			1.60348			0.801742	−	0.597670i	$-0.203907\pi$
$673$	41.5980			1.60348			0.801742	+	0.597670i	$0.203907\pi$
$674$	1.58579	−	2.74666i	0.0610822	−	0.105797i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	5.58579	−	9.67487i	0.214679	−	0.371835i	−0.738494	−	0.674260i	$-0.764463\pi$
$677$	5.58579	−	9.67487i	0.214679	−	0.371835i	0.953173	+	0.302425i	$0.0977961\pi$
$678$	−9.31371			−0.357691
$679$		0			0
$680$	1.41421			0.0542326
$681$	6.82843	−	11.8272i	0.261666	−	0.453219i
$682$	1.48528	+	2.57258i	0.0568744	+	0.0985093i
$683$	−15.8995	−	27.5387i	−0.608377	−	1.05374i	−0.991508	−	0.130046i	$-0.958487\pi$
$683$	−15.8995	−	27.5387i	−0.608377	−	1.05374i	0.383131	−	0.923694i	$-0.374846\pi$
$684$	−1.41421	+	2.44949i	−0.0540738	+	0.0936586i
$685$	16.0000			0.611329
$686$		0			0
$687$	25.7990			0.984293
$688$	−2.29289	+	3.97141i	−0.0874157	+	0.151408i
$689$		0			0
$690$	−2.41421	−	4.18154i	−0.0919075	−	0.159189i
$691$	−6.14214	+	10.6385i	−0.233658	+	0.404707i	−0.958882	−	0.283806i	$-0.908403\pi$
$691$	−6.14214	+	10.6385i	−0.233658	+	0.404707i	0.725224	+	0.688513i	$0.241736\pi$
$692$	−18.4853			−0.702705
$693$		0			0
$694$	1.65685			0.0628933
$695$	−8.82843	+	15.2913i	−0.334881	+	0.580031i
$696$	4.12132	+	7.13834i	0.156218	+	0.270578i
$697$	6.24264	+	10.8126i	0.236457	+	0.409555i
$698$	−2.89949	+	5.02207i	−0.109748	+	0.190088i
$699$	−6.97056			−0.263651
$700$		0			0
$701$	−11.5563			−0.436477			−0.218239	−	0.975895i	$-0.570031\pi$
$701$	−11.5563			−0.436477			−0.218239	+	0.975895i	$0.570031\pi$
$702$		0			0
$703$	2.00000	+	3.46410i	0.0754314	+	0.130651i
$704$	−0.292893	−	0.507306i	−0.0110388	−	0.0191198i
$705$	−4.53553	+	7.85578i	−0.170818	+	0.295866i
$706$	0.727922			0.0273957
$707$		0			0
$708$	2.48528			0.0934026
$709$	22.5563	−	39.0687i	0.847121	−	1.46726i	−0.0366445	−	0.999328i	$-0.511667\pi$
$709$	22.5563	−	39.0687i	0.847121	−	1.46726i	0.883766	−	0.467929i	$-0.155000\pi$
$710$	5.41421	+	9.37769i	0.203192	+	0.351939i
$711$	5.65685	+	9.79796i	0.212149	+	0.367452i
$712$	−3.24264	+	5.61642i	−0.121523	+	0.210484i
$713$	−24.4853			−0.916981
$714$		0			0
$715$		0			0
$716$	−0.292893	+	0.507306i	−0.0109459	+	0.0189589i
$717$	11.6569	+	20.1903i	0.435333	+	0.754019i
$718$	−9.41421	−	16.3059i	−0.351335	−	0.608531i
$719$	−6.14214	+	10.6385i	−0.229063	+	0.396749i	−0.957531	−	0.288331i	$-0.906900\pi$
$719$	−6.14214	+	10.6385i	−0.229063	+	0.396749i	0.728468	+	0.685080i	$0.240233\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	−11.0000			−0.409378
$723$	8.12132	−	14.0665i	0.302035	−	0.523140i
$724$	−4.41421	−	7.64564i	−0.164053	−	0.284148i
$725$	−4.12132	−	7.13834i	−0.153062	−	0.265111i
$726$	−5.32843	+	9.22911i	−0.197756	+	0.342524i
$727$	−45.6569			−1.69332			−0.846659	−	0.532135i	$-0.821390\pi$
$727$	−45.6569			−1.69332			−0.846659	+	0.532135i	$0.821390\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−3.82843	+	6.63103i	−0.141696	+	0.245425i
$731$	3.24264	+	5.61642i	0.119933	+	0.207731i
$732$	5.82843	+	10.0951i	0.215425	+	0.373127i
$733$	−7.97056	+	13.8054i	−0.294399	+	0.509915i	−0.974845	−	0.222884i	$-0.928453\pi$
$733$	−7.97056	+	13.8054i	−0.294399	+	0.509915i	0.680446	+	0.732799i	$0.261786\pi$
$734$	−16.4853			−0.608483
$735$		0			0
$736$	4.82843			0.177978
$737$	−2.31371	+	4.00746i	−0.0852265	+	0.147617i
$738$	−4.41421	−	7.64564i	−0.162489	−	0.281440i
$739$	21.5563	+	37.3367i	0.792963	+	1.37345i	0.924125	+	0.382091i	$0.124796\pi$
$739$	21.5563	+	37.3367i	0.792963	+	1.37345i	−0.131161	+	0.991361i	$0.541871\pi$
$740$	−0.707107	+	1.22474i	−0.0259938	+	0.0450225i
$741$		0			0
$742$		0			0
$743$	5.65685			0.207530			0.103765	−	0.994602i	$-0.466911\pi$
$743$	5.65685			0.207530			0.103765	+	0.994602i	$0.466911\pi$
$744$	−2.53553	+	4.39167i	−0.0929572	+	0.161007i
$745$	−6.94975	−	12.0373i	−0.254619	−	0.441013i
$746$	−5.53553	−	9.58783i	−0.202670	−	0.351035i
$747$	−2.58579	+	4.47871i	−0.0946090	+	0.163868i
$748$	−0.828427			−0.0302903
$749$		0			0
$750$	1.00000			0.0365148
$751$	−12.7574	+	22.0964i	−0.465523	+	0.806309i	−0.999225	−	0.0393635i	$-0.987467\pi$
$751$	−12.7574	+	22.0964i	−0.465523	+	0.806309i	0.533702	+	0.845672i	$0.320800\pi$
$752$	−4.53553	−	7.85578i	−0.165394	−	0.286471i
$753$	8.82843	+	15.2913i	0.321726	+	0.557245i
$754$		0			0
$755$	−17.7990			−0.647772
$756$		0			0
$757$	23.7574			0.863476			0.431738	−	0.901999i	$-0.357901\pi$
$757$	23.7574			0.863476			0.431738	+	0.901999i	$0.357901\pi$
$758$	12.2426	−	21.2049i	0.444673	−	0.770196i
$759$	1.41421	+	2.44949i	0.0513327	+	0.0889108i
$760$	1.41421	+	2.44949i	0.0512989	+	0.0888523i
$761$	−9.48528	+	16.4290i	−0.343841	+	0.595550i	−0.985143	−	0.171739i	$-0.945062\pi$
$761$	−9.48528	+	16.4290i	−0.343841	+	0.595550i	0.641301	+	0.767289i	$0.278395\pi$
$762$	14.1421			0.512316
$763$		0			0
$764$	−11.3137			−0.409316
$765$	−0.707107	+	1.22474i	−0.0255655	+	0.0442807i
$766$	7.94975	+	13.7694i	0.287236	+	0.497507i
$767$		0			0
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	30.5858			1.10295			0.551476	−	0.834191i	$-0.314065\pi$
$769$	30.5858			1.10295			0.551476	+	0.834191i	$0.314065\pi$
$770$		0			0
$771$	1.89949			0.0684086
$772$	10.8995	−	18.8785i	0.392281	−	0.679451i
$773$	14.1716	+	24.5459i	0.509716	+	0.882854i	0.999937	+	0.0112557i	$0.00358288\pi$
$773$	14.1716	+	24.5459i	0.509716	+	0.882854i	−0.490221	+	0.871598i	$0.663084\pi$
$774$	−2.29289	−	3.97141i	−0.0824163	−	0.142749i
$775$	2.53553	−	4.39167i	0.0910791	−	0.157754i
$776$	−8.82843			−0.316922
$777$		0			0
$778$	27.0711			0.970545
$779$	−12.4853	+	21.6251i	−0.447332	+	0.774801i
$780$		0			0
$781$	−3.17157	−	5.49333i	−0.113488	−	0.196567i
$782$	3.41421	−	5.91359i	0.122092	−	0.211470i
$783$	−8.24264			−0.294568
$784$		0			0
$785$	0.343146			0.0122474
$786$	8.41421	−	14.5738i	0.300125	−	0.519832i
$787$	14.4853	+	25.0892i	0.516345	+	0.894335i	0.999820	+	0.0189770i	$0.00604093\pi$
$787$	14.4853	+	25.0892i	0.516345	+	0.894335i	−0.483475	+	0.875358i	$0.660626\pi$
$788$	10.4142	+	18.0379i	0.370991	+	0.642575i
$789$	−10.8995	+	18.8785i	−0.388032	+	0.672092i
$790$	11.3137			0.402524
$791$		0			0
$792$	0.585786			0.0208150
$793$		0			0
$794$	10.3137	+	17.8639i	0.366020	+	0.633965i
$795$	4.65685	+	8.06591i	0.165162	+	0.286068i
$796$	1.46447	−	2.53653i	0.0519066	−	0.0899049i
$797$	−26.4853			−0.938157			−0.469078	−	0.883157i	$-0.655414\pi$
$797$	−26.4853			−0.938157			−0.469078	+	0.883157i	$0.655414\pi$
$798$		0			0
$799$	−12.8284			−0.453837
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−3.24264	−	5.61642i	−0.114573	−	0.198446i
$802$	12.6569	+	21.9223i	0.446929	+	0.774104i
$803$	2.24264	−	3.88437i	0.0791411	−	0.137076i
$804$	−7.89949			−0.278594
$805$		0			0
$806$		0			0
$807$	−3.82843	+	6.63103i	−0.134767	+	0.233423i
$808$	−3.17157	−	5.49333i	−0.111576	−	0.193255i
$809$	−12.5563	−	21.7482i	−0.441458	−	0.764627i	0.556340	−	0.830955i	$-0.312205\pi$
$809$	−12.5563	−	21.7482i	−0.441458	−	0.764627i	−0.997798	+	0.0663274i	$0.978872\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	3.02944			0.106378			0.0531890	−	0.998584i	$-0.483061\pi$
$811$	3.02944			0.106378			0.0531890	+	0.998584i	$0.483061\pi$
$812$		0			0
$813$	−14.2426			−0.499511
$814$	0.414214	−	0.717439i	0.0145182	−	0.0251462i
$815$	7.36396	+	12.7548i	0.257948	+	0.446780i
$816$	−0.707107	−	1.22474i	−0.0247537	−	0.0428746i
$817$	−6.48528	+	11.2328i	−0.226891	+	0.392987i
$818$	18.3848			0.642809
$819$		0			0
$820$	−8.82843			−0.308302
$821$	2.22183	−	3.84831i	0.0775422	−	0.134307i	−0.824647	−	0.565648i	$-0.808626\pi$
$821$	2.22183	−	3.84831i	0.0775422	−	0.134307i	0.902189	+	0.431341i	$0.141959\pi$
$822$	−8.00000	−	13.8564i	−0.279032	−	0.483298i
$823$	−8.14214	−	14.1026i	−0.283817	−	0.491585i	0.688505	−	0.725232i	$-0.258267\pi$
$823$	−8.14214	−	14.1026i	−0.283817	−	0.491585i	−0.972322	+	0.233646i	$0.924934\pi$
$824$	−5.07107	+	8.78335i	−0.176659	+	0.305982i
$825$	−0.585786			−0.0203945
$826$		0			0
$827$	−11.1127			−0.386426			−0.193213	−	0.981157i	$-0.561891\pi$
$827$	−11.1127			−0.386426			−0.193213	+	0.981157i	$0.561891\pi$
$828$	−2.41421	+	4.18154i	−0.0838997	+	0.145319i
$829$	−22.6569	−	39.2428i	−0.786905	−	1.36296i	−0.927854	−	0.372943i	$-0.878349\pi$
$829$	−22.6569	−	39.2428i	−0.786905	−	1.36296i	0.140949	−	0.990017i	$-0.454985\pi$
$830$	2.58579	+	4.47871i	0.0897540	+	0.155458i
$831$	10.9497	−	18.9655i	0.379843	−	0.657907i
$832$		0			0
$833$		0			0
$834$	17.6569			0.611407
$835$	−0.535534	+	0.927572i	−0.0185329	+	0.0321000i
$836$	−0.828427	−	1.43488i	−0.0286518	−	0.0496263i
$837$	−2.53553	−	4.39167i	−0.0876409	−	0.151798i
$838$	−8.82843	+	15.2913i	−0.304973	+	0.528229i
$839$	−5.17157			−0.178543			−0.0892713	−	0.996007i	$-0.528454\pi$
$839$	−5.17157			−0.178543			−0.0892713	+	0.996007i	$0.528454\pi$
$840$		0			0
$841$	38.9411			1.34280
$842$	−8.31371	+	14.3998i	−0.286509	+	0.496249i
$843$	−6.75736	−	11.7041i	−0.232736	−	0.403110i
$844$	0.828427	+	1.43488i	0.0285156	+	0.0493905i
$845$	−6.50000	+	11.2583i	−0.223607	+	0.387298i
$846$	9.07107			0.311870
$847$		0			0
$848$	−9.31371			−0.319834
$849$	−15.2426	+	26.4010i	−0.523126	+	0.906081i
$850$	0.707107	+	1.22474i	0.0242536	+	0.0420084i
$851$	3.41421	+	5.91359i	0.117038	+	0.202715i
$852$	5.41421	−	9.37769i	0.185488	−	0.321274i
$853$	−6.68629			−0.228934			−0.114467	−	0.993427i	$-0.536516\pi$
$853$	−6.68629			−0.228934			−0.114467	+	0.993427i	$0.536516\pi$
$854$		0			0
$855$	−2.82843			−0.0967302
$856$	2.00000	−	3.46410i	0.0683586	−	0.118401i
$857$	13.6360	+	23.6183i	0.465798	+	0.806786i	0.999237	−	0.0390524i	$-0.0124339\pi$
$857$	13.6360	+	23.6183i	0.465798	+	0.806786i	−0.533439	+	0.845839i	$0.679101\pi$
$858$		0			0
$859$	8.48528	−	14.6969i	0.289514	−	0.501453i	−0.684180	−	0.729313i	$-0.739840\pi$
$859$	8.48528	−	14.6969i	0.289514	−	0.501453i	0.973694	+	0.227860i	$0.0731730\pi$
$860$	−4.58579			−0.156374
$861$		0			0
$862$	14.1421			0.481683
$863$	0.485281	−	0.840532i	0.0165192	−	0.0286120i	−0.857648	−	0.514238i	$-0.828075\pi$
$863$	0.485281	−	0.840532i	0.0165192	−	0.0286120i	0.874167	+	0.485626i	$0.161408\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−9.24264	−	16.0087i	−0.314259	−	0.544313i
$866$	4.41421	−	7.64564i	0.150001	−	0.259809i
$867$	15.0000			0.509427
$868$		0			0
$869$	−6.62742			−0.224820
$870$	−4.12132	+	7.13834i	−0.139726	+	0.242012i
$871$		0			0
$872$	−2.65685	−	4.60181i	−0.0899724	−	0.155837i
$873$	4.41421	−	7.64564i	0.149398	−	0.258766i
$874$	13.6569			0.461950
$875$		0			0
$876$	7.65685			0.258701
$877$	−10.7071	+	18.5453i	−0.361553	+	0.626229i	−0.988217	−	0.153061i	$-0.951087\pi$
$877$	−10.7071	+	18.5453i	−0.361553	+	0.626229i	0.626663	+	0.779290i	$0.284420\pi$
$878$	16.7782	+	29.0607i	0.566236	+	0.980749i
$879$	14.3137	+	24.7921i	0.482789	+	0.836216i
$880$	0.292893	−	0.507306i	0.00987343	−	0.0171013i
$881$	−31.6569			−1.06655			−0.533273	−	0.845943i	$-0.679038\pi$
$881$	−31.6569			−1.06655			−0.533273	+	0.845943i	$0.679038\pi$
$882$		0			0
$883$	−10.0416			−0.337928			−0.168964	−	0.985622i	$-0.554042\pi$
$883$	−10.0416			−0.337928			−0.168964	+	0.985622i	$0.554042\pi$
$884$		0			0
$885$	1.24264	+	2.15232i	0.0417709	+	0.0723493i
$886$	−6.82843	−	11.8272i	−0.229405	−	0.397342i
$887$	−11.8492	+	20.5235i	−0.397859	+	0.689111i	−0.993461	−	0.114168i	$-0.963580\pi$
$887$	−11.8492	+	20.5235i	−0.397859	+	0.689111i	0.595603	+	0.803279i	$0.296913\pi$
$888$	1.41421			0.0474579
$889$		0			0
$890$	−6.48528			−0.217387
$891$	−0.292893	+	0.507306i	−0.00981229	+	0.0169954i
$892$	8.82843	+	15.2913i	0.295598	+	0.511990i
$893$	−12.8284	−	22.2195i	−0.429287	−	0.743547i
$894$	−6.94975	+	12.0373i	−0.232434	+	0.402588i
$895$	−0.585786			−0.0195807
$896$		0			0
$897$		0			0
$898$	12.5563	−	21.7482i	0.419011	−	0.725748i
$899$	20.8995	+	36.1990i	0.697037	+	1.20730i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−6.58579	+	11.4069i	−0.219404	+	0.380019i
$902$	5.17157			0.172195
$903$		0			0
$904$	9.31371			0.309769
$905$	4.41421	−	7.64564i	0.146733	−	0.254150i
$906$	8.89949	+	15.4144i	0.295666	+	0.512108i
$907$	−21.6066	−	37.4237i	−0.717435	−	1.24263i	−0.962013	−	0.273005i	$-0.911983\pi$
$907$	−21.6066	−	37.4237i	−0.717435	−	1.24263i	0.244577	−	0.969630i	$-0.421351\pi$
$908$	−6.82843	+	11.8272i	−0.226609	+	0.392499i
$909$	6.34315			0.210389
$910$		0			0
$911$	5.65685			0.187420			0.0937100	−	0.995600i	$-0.470127\pi$
$911$	5.65685			0.187420			0.0937100	+	0.995600i	$0.470127\pi$
$912$	1.41421	−	2.44949i	0.0468293	−	0.0811107i
$913$	−1.51472	−	2.62357i	−0.0501299	−	0.0868275i
$914$	4.89949	+	8.48617i	0.162061	+	0.280698i
$915$	−5.82843	+	10.0951i	−0.192682	+	0.333735i
$916$	−25.7990			−0.852423
$917$		0			0
$918$	1.41421			0.0466760
$919$	−13.3848	+	23.1831i	−0.441523	+	0.764740i	−0.997803	−	0.0662548i	$-0.978895\pi$
$919$	−13.3848	+	23.1831i	−0.441523	+	0.764740i	0.556280	+	0.830995i	$0.312228\pi$
$920$	2.41421	+	4.18154i	0.0795943	+	0.137861i
$921$	3.65685	+	6.33386i	0.120497	+	0.208708i
$922$	−7.00000	+	12.1244i	−0.230533	+	0.399294i
$923$		0			0
$924$		0			0
$925$	−1.41421			−0.0464991
$926$	−16.8284	+	29.1477i	−0.553016	+	0.957853i
$927$	−5.07107	−	8.78335i	−0.166556	−	0.288483i
$928$	−4.12132	−	7.13834i	−0.135289	−	0.234327i
$929$	−5.82843	+	10.0951i	−0.191224	+	0.331211i	−0.945656	−	0.325168i	$-0.894579\pi$
$929$	−5.82843	+	10.0951i	−0.191224	+	0.331211i	0.754432	+	0.656378i	$0.227913\pi$
$930$	−5.07107			−0.166287
$931$		0			0
$932$	6.97056			0.228328
$933$	14.5858	−	25.2633i	0.477517	−	0.827084i
$934$	−10.2426	−	17.7408i	−0.335149	−	0.580496i
$935$	−0.414214	−	0.717439i	−0.0135462	−	0.0234628i
$936$		0			0
$937$	17.0294			0.556327			0.278164	−	0.960534i	$-0.410274\pi$
$937$	17.0294			0.556327			0.278164	+	0.960534i	$0.410274\pi$
$938$		0			0
$939$	28.8284			0.940780
$940$	4.53553	−	7.85578i	0.147933	−	0.256227i
$941$	18.1421	+	31.4231i	0.591417	+	1.02436i	0.994042	+	0.108999i	$0.0347645\pi$
$941$	18.1421	+	31.4231i	0.591417	+	1.02436i	−0.402625	+	0.915365i	$0.631902\pi$
$942$	−0.171573	−	0.297173i	−0.00559015	−	0.00968242i
$943$	−21.3137	+	36.9164i	−0.694070	+	1.20216i
$944$	−2.48528			−0.0808890
$945$		0			0
$946$	2.68629			0.0873389
$947$	−18.2426	+	31.5972i	−0.592806	+	1.02677i	0.401046	+	0.916058i	$0.368647\pi$
$947$	−18.2426	+	31.5972i	−0.592806	+	1.02677i	−0.993852	+	0.110713i	$0.964687\pi$
$948$	−5.65685	−	9.79796i	−0.183726	−	0.318223i
$949$		0			0
$950$	−1.41421	+	2.44949i	−0.0458831	+	0.0794719i
$951$	18.0000			0.583690
$952$		0			0
$953$	−23.5980			−0.764414			−0.382207	−	0.924077i	$-0.624836\pi$
$953$	−23.5980			−0.764414			−0.382207	+	0.924077i	$0.624836\pi$
$954$	4.65685	−	8.06591i	0.150771	−	0.261143i
$955$	−5.65685	−	9.79796i	−0.183052	−	0.317055i
$956$	−11.6569	−	20.1903i	−0.377010	−	0.653000i
$957$	2.41421	−	4.18154i	0.0780404	−	0.135170i
$958$	−16.4853			−0.532615
$959$		0			0
$960$	1.00000			0.0322749
$961$	2.64214	−	4.57631i	0.0852302	−	0.147623i
$962$		0			0
$963$	2.00000	+	3.46410i	0.0644491	+	0.111629i
$964$	−8.12132	+	14.0665i	−0.261570	+	0.453053i
$965$	21.7990			0.701734
$966$		0			0
$967$	−44.2843			−1.42409			−0.712043	−	0.702136i	$-0.752230\pi$
$967$	−44.2843			−1.42409			−0.712043	+	0.702136i	$0.752230\pi$
$968$	5.32843	−	9.22911i	0.171262	−	0.296635i
$969$	−2.00000	−	3.46410i	−0.0642493	−	0.111283i
$970$	−4.41421	−	7.64564i	−0.141732	−	0.245487i
$971$	22.4853	−	38.9456i	0.721587	−	1.24983i	−0.238776	−	0.971075i	$-0.576746\pi$
$971$	22.4853	−	38.9456i	0.721587	−	1.24983i	0.960363	−	0.278751i	$-0.0899204\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	24.4853			0.784559
$975$		0			0
$976$	−5.82843	−	10.0951i	−0.186563	−	0.323137i
$977$	−2.65685	−	4.60181i	−0.0850003	−	0.147225i	0.820391	−	0.571803i	$-0.193756\pi$
$977$	−2.65685	−	4.60181i	−0.0850003	−	0.147225i	−0.905391	+	0.424578i	$0.860422\pi$
$978$	7.36396	−	12.7548i	0.235474	−	0.407852i
$979$	3.79899			0.121416
$980$		0			0
$981$	5.31371			0.169654
$982$	−5.94975	+	10.3053i	−0.189864	+	0.328854i
$983$	−8.43503	−	14.6099i	−0.269036	−	0.465983i	0.699577	−	0.714557i	$-0.253372\pi$
$983$	−8.43503	−	14.6099i	−0.269036	−	0.465983i	−0.968613	+	0.248573i	$0.920038\pi$
$984$	4.41421	+	7.64564i	0.140720	+	0.243734i
$985$	−10.4142	+	18.0379i	−0.331824	+	0.574737i
$986$	−11.6569			−0.371230
$987$		0			0
$988$		0			0
$989$	−11.0711	+	19.1757i	−0.352039	+	0.609750i
$990$	0.292893	+	0.507306i	0.00930876	+	0.0161232i
$991$	−10.4142	−	18.0379i	−0.330818	−	0.572994i	0.651854	−	0.758344i	$-0.273991\pi$
$991$	−10.4142	−	18.0379i	−0.330818	−	0.572994i	−0.982673	+	0.185350i	$0.940658\pi$
$992$	2.53553	−	4.39167i	0.0805033	−	0.139436i
$993$	18.6274			0.591123
$994$		0			0
$995$	2.92893			0.0928534
$996$	2.58579	−	4.47871i	0.0819338	−	0.141913i
$997$	−1.34315	−	2.32640i	−0.0425379	−	0.0736777i	0.843973	−	0.536386i	$-0.180211\pi$
$997$	−1.34315	−	2.32640i	−0.0425379	−	0.0736777i	−0.886510	+	0.462709i	$0.846878\pi$
$998$	−7.89949	−	13.6823i	−0.250054	−	0.433106i
$999$	−0.707107	+	1.22474i	−0.0223719	+	0.0387492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.v.961.2		4
7.2	even	3		1470.2.a.u.1.1	✓	2
7.3	odd	6		1470.2.i.u.361.2		4
7.4	even	3	inner	1470.2.i.v.361.2		4
7.5	odd	6		1470.2.a.v.1.1	yes	2
7.6	odd	2		1470.2.i.u.961.2		4
21.2	odd	6		4410.2.a.br.1.2		2
21.5	even	6		4410.2.a.bn.1.2		2
35.9	even	6		7350.2.a.df.1.1		2
35.19	odd	6		7350.2.a.dd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.a.u.1.1	✓	2	7.2	even	3
1470.2.a.v.1.1	yes	2	7.5	odd	6
1470.2.i.u.361.2		4	7.3	odd	6
1470.2.i.u.961.2		4	7.6	odd	2
1470.2.i.v.361.2		4	7.4	even	3	inner
1470.2.i.v.961.2		4	1.1	even	1	trivial
4410.2.a.bn.1.2		2	21.5	even	6
4410.2.a.br.1.2		2	21.2	odd	6
7350.2.a.dd.1.1		2	35.19	odd	6
7350.2.a.df.1.1		2	35.9	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.292893 - 0.507306i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.707107 + 1.22474i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-1.41421 + 2.44949i) q^{19} -1.00000 q^{20} +0.585786 q^{22} +(-2.41421 + 4.18154i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +8.24264 q^{29} +(-0.500000 + 0.866025i) q^{30} +(2.53553 + 4.39167i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.292893 - 0.507306i) q^{33} -1.41421 q^{34} +1.00000 q^{36} +(0.707107 - 1.22474i) q^{37} +(-1.41421 - 2.44949i) q^{38} +(0.500000 - 0.866025i) q^{40} +8.82843 q^{41} +4.58579 q^{43} +(-0.292893 + 0.507306i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-2.41421 - 4.18154i) q^{46} +(-4.53553 + 7.85578i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(-0.707107 + 1.22474i) q^{51} +(4.65685 + 8.06591i) q^{53} +(0.500000 - 0.866025i) q^{54} -0.585786 q^{55} -2.82843 q^{57} +(-4.12132 + 7.13834i) q^{58} +(1.24264 + 2.15232i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-5.82843 + 10.0951i) q^{61} -5.07107 q^{62} +1.00000 q^{64} +(0.292893 + 0.507306i) q^{66} +(-3.94975 - 6.84116i) q^{67} +(0.707107 - 1.22474i) q^{68} -4.82843 q^{69} +10.8284 q^{71} +(-0.500000 + 0.866025i) q^{72} +(3.82843 + 6.63103i) q^{73} +(0.707107 + 1.22474i) q^{74} +(0.500000 - 0.866025i) q^{75} +2.82843 q^{76} +(5.65685 - 9.79796i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.41421 + 7.64564i) q^{82} +5.17157 q^{83} +1.41421 q^{85} +(-2.29289 + 3.97141i) q^{86} +(4.12132 + 7.13834i) q^{87} +(-0.292893 - 0.507306i) q^{88} +(-3.24264 + 5.61642i) q^{89} -1.00000 q^{90} +4.82843 q^{92} +(-2.53553 + 4.39167i) q^{93} +(-4.53553 - 7.85578i) q^{94} +(1.41421 + 2.44949i) q^{95} +(0.500000 - 0.866025i) q^{96} -8.82843 q^{97} +0.585786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} + 4 q^{15} - 2 q^{16} - 2 q^{18} - 4 q^{20} + 8 q^{22} - 4 q^{23} + 2 q^{24} - 2 q^{25} - 4 q^{27} + 16 q^{29} - 2 q^{30} - 4 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{36} + 2 q^{40} + 24 q^{41} + 24 q^{43} - 4 q^{44} + 2 q^{45} - 4 q^{46} - 4 q^{47} - 4 q^{48} + 4 q^{50} - 4 q^{53} + 2 q^{54} - 8 q^{55} - 8 q^{58} - 12 q^{59} - 2 q^{60} - 12 q^{61} + 8 q^{62} + 4 q^{64} + 4 q^{66} + 4 q^{67} - 8 q^{69} + 32 q^{71} - 2 q^{72} + 4 q^{73} + 2 q^{75} + 2 q^{80} - 2 q^{81} - 12 q^{82} + 32 q^{83} - 12 q^{86} + 8 q^{87} - 4 q^{88} + 4 q^{89} - 4 q^{90} + 8 q^{92} + 4 q^{93} - 4 q^{94} + 2 q^{96} - 24 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 + 4 * q^15 - 2 * q^16 - 2 * q^18 - 4 * q^20 + 8 * q^22 - 4 * q^23 + 2 * q^24 - 2 * q^25 - 4 * q^27 + 16 * q^29 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^36 + 2 * q^40 + 24 * q^41 + 24 * q^43 - 4 * q^44 + 2 * q^45 - 4 * q^46 - 4 * q^47 - 4 * q^48 + 4 * q^50 - 4 * q^53 + 2 * q^54 - 8 * q^55 - 8 * q^58 - 12 * q^59 - 2 * q^60 - 12 * q^61 + 8 * q^62 + 4 * q^64 + 4 * q^66 + 4 * q^67 - 8 * q^69 + 32 * q^71 - 2 * q^72 + 4 * q^73 + 2 * q^75 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 32 * q^83 - 12 * q^86 + 8 * q^87 - 4 * q^88 + 4 * q^89 - 4 * q^90 + 8 * q^92 + 4 * q^93 - 4 * q^94 + 2 * q^96 - 24 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

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Database

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