LMFDB - Embedded newform 1155.2.c.f.694.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.c (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + \cdots + 4 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15210x^12 + 40640x^10 + 63865x^8 + 55281x^6 + 22984x^4 + 3428*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.20
Root			$2.74150i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.f.694.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.74150i q^{2} -1.00000i q^{3} -5.51584 q^{4} +(-0.739422 + 2.11027i) q^{5} +2.74150 q^{6} -1.00000i q^{7} -9.63869i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.74150i q^{2} -1.00000i q^{3} -5.51584 q^{4} +(-0.739422 + 2.11027i) q^{5} +2.74150 q^{6} -1.00000i q^{7} -9.63869i q^{8} -1.00000 q^{9} +(-5.78532 - 2.02713i) q^{10} +1.00000 q^{11} +5.51584i q^{12} -3.27608i q^{13} +2.74150 q^{14} +(2.11027 + 0.739422i) q^{15} +15.3928 q^{16} +0.321181i q^{17} -2.74150i q^{18} +3.74693 q^{19} +(4.07853 - 11.6399i) q^{20} -1.00000 q^{21} +2.74150i q^{22} -8.57010i q^{23} -9.63869 q^{24} +(-3.90651 - 3.12077i) q^{25} +8.98137 q^{26} +1.00000i q^{27} +5.51584i q^{28} +8.80350 q^{29} +(-2.02713 + 5.78532i) q^{30} -7.81044 q^{31} +22.9221i q^{32} -1.00000i q^{33} -0.880519 q^{34} +(2.11027 + 0.739422i) q^{35} +5.51584 q^{36} +4.37031i q^{37} +10.2722i q^{38} -3.27608 q^{39} +(20.3403 + 7.12706i) q^{40} +2.60535 q^{41} -2.74150i q^{42} +7.99122i q^{43} -5.51584 q^{44} +(0.739422 - 2.11027i) q^{45} +23.4949 q^{46} -0.447607i q^{47} -15.3928i q^{48} -1.00000 q^{49} +(8.55559 - 10.7097i) q^{50} +0.321181 q^{51} +18.0703i q^{52} -11.0777i q^{53} -2.74150 q^{54} +(-0.739422 + 2.11027i) q^{55} -9.63869 q^{56} -3.74693i q^{57} +24.1348i q^{58} +13.8981 q^{59} +(-11.6399 - 4.07853i) q^{60} +11.9795 q^{61} -21.4124i q^{62} +1.00000i q^{63} -32.0553 q^{64} +(6.91342 + 2.42240i) q^{65} +2.74150 q^{66} +6.38193i q^{67} -1.77158i q^{68} -8.57010 q^{69} +(-2.02713 + 5.78532i) q^{70} -7.35463 q^{71} +9.63869i q^{72} -5.14730i q^{73} -11.9812 q^{74} +(-3.12077 + 3.90651i) q^{75} -20.6675 q^{76} -1.00000i q^{77} -8.98137i q^{78} -4.71606 q^{79} +(-11.3818 + 32.4830i) q^{80} +1.00000 q^{81} +7.14257i q^{82} +5.27773i q^{83} +5.51584 q^{84} +(-0.677780 - 0.237488i) q^{85} -21.9080 q^{86} -8.80350i q^{87} -9.63869i q^{88} +8.21445 q^{89} +(5.78532 + 2.02713i) q^{90} -3.27608 q^{91} +47.2713i q^{92} +7.81044i q^{93} +1.22712 q^{94} +(-2.77056 + 7.90705i) q^{95} +22.9221 q^{96} -16.8348i q^{97} -2.74150i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			2.74150i			1.93854i	0.246008	+	0.969268i	$0.420881\pi$
$2$			2.74150i			1.93854i	−0.246008	+	0.969268i	$0.579119\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−5.51584			−2.75792
$5$	−0.739422	+	2.11027i	−0.330680	+	0.943743i
$5$	−0.739422	+	2.11027i	−0.330680	+	0.943743i
$6$	2.74150			1.11921
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	9.63869i		−	3.40779i
$9$	−1.00000			−0.333333
$10$	−5.78532	−	2.02713i	−1.82948	−	0.641034i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			5.51584i			1.59229i
$13$		−	3.27608i		−	0.908620i	−0.890844	−	0.454310i	$-0.849886\pi$
$13$		−	3.27608i		−	0.908620i	0.890844	−	0.454310i	$-0.150114\pi$
$14$	2.74150			0.732698
$15$	2.11027	+	0.739422i	0.544870	+	0.190918i
$16$	15.3928			3.84820
$17$			0.321181i			0.0778979i	0.999241	+	0.0389489i	$0.0124010\pi$
$17$			0.321181i			0.0778979i	−0.999241	+	0.0389489i	$0.987599\pi$
$18$		−	2.74150i		−	0.646179i
$19$	3.74693			0.859605			0.429803	−	0.902923i	$-0.358583\pi$
$19$	3.74693			0.859605			0.429803	+	0.902923i	$0.358583\pi$
$20$	4.07853	−	11.6399i	0.911988	−	2.60277i
$21$	−1.00000			−0.218218
$22$			2.74150i			0.584490i
$23$		−	8.57010i		−	1.78699i	−0.449075	−	0.893494i	$-0.648246\pi$
$23$		−	8.57010i		−	1.78699i	0.449075	−	0.893494i	$-0.351754\pi$
$24$	−9.63869			−1.96749
$25$	−3.90651	−	3.12077i	−0.781302	−	0.624153i
$26$	8.98137			1.76139
$27$			1.00000i			0.192450i
$28$			5.51584i			1.04240i
$29$	8.80350			1.63477			0.817384	−	0.576093i	$-0.195423\pi$
$29$	8.80350			1.63477			0.817384	+	0.576093i	$0.195423\pi$
$30$	−2.02713	+	5.78532i	−0.370101	+	1.05625i
$31$	−7.81044			−1.40280			−0.701399	−	0.712769i	$-0.747441\pi$
$31$	−7.81044			−1.40280			−0.701399	+	0.712769i	$0.747441\pi$
$32$			22.9221i			4.05209i
$33$		−	1.00000i		−	0.174078i
$34$	−0.880519			−0.151008
$35$	2.11027	+	0.739422i	0.356701	+	0.124985i
$36$	5.51584			0.919307
$37$			4.37031i			0.718474i	0.933246	+	0.359237i	$0.116963\pi$
$37$			4.37031i			0.718474i	−0.933246	+	0.359237i	$0.883037\pi$
$38$			10.2722i			1.66638i
$39$	−3.27608			−0.524592
$40$	20.3403	+	7.12706i	3.21608	+	1.12689i
$41$	2.60535			0.406887			0.203443	−	0.979087i	$-0.434787\pi$
$41$	2.60535			0.406887			0.203443	+	0.979087i	$0.434787\pi$
$42$		−	2.74150i		−	0.423023i
$43$			7.99122i			1.21865i	0.792921	+	0.609325i	$0.208560\pi$
$43$			7.99122i			1.21865i	−0.792921	+	0.609325i	$0.791440\pi$
$44$	−5.51584			−0.831544
$45$	0.739422	−	2.11027i	0.110227	−	0.314581i
$46$	23.4949			3.46414
$47$		−	0.447607i		−	0.0652902i	−0.999467	−	0.0326451i	$-0.989607\pi$
$47$		−	0.447607i		−	0.0652902i	0.999467	−	0.0326451i	$-0.0103931\pi$
$48$		−	15.3928i		−	2.22176i
$49$	−1.00000			−0.142857
$50$	8.55559	−	10.7097i	1.20994	−	1.51458i
$51$	0.321181			0.0449744
$52$			18.0703i			2.50590i
$53$		−	11.0777i		−	1.52164i	−0.648964	−	0.760819i	$-0.724798\pi$
$53$		−	11.0777i		−	1.52164i	0.648964	−	0.760819i	$-0.275202\pi$
$54$	−2.74150			−0.373071
$55$	−0.739422	+	2.11027i	−0.0997036	+	0.284549i
$56$	−9.63869			−1.28802
$57$		−	3.74693i		−	0.496293i
$58$			24.1348i			3.16906i
$59$	13.8981			1.80938			0.904689	−	0.426073i	$-0.140103\pi$
$59$	13.8981			1.80938			0.904689	+	0.426073i	$0.140103\pi$
$60$	−11.6399	−	4.07853i	−1.50271	−	0.526536i
$61$	11.9795			1.53382			0.766910	−	0.641755i	$-0.221793\pi$
$61$	11.9795			1.53382			0.766910	+	0.641755i	$0.221793\pi$
$62$		−	21.4124i		−	2.71937i
$63$			1.00000i			0.125988i
$64$	−32.0553			−4.00691
$65$	6.91342	+	2.42240i	0.857504	+	0.300462i
$66$	2.74150			0.337456
$67$			6.38193i			0.779677i	0.920883	+	0.389839i	$0.127469\pi$
$67$			6.38193i			0.779677i	−0.920883	+	0.389839i	$0.872531\pi$
$68$		−	1.77158i		−	0.214836i
$69$	−8.57010			−1.03172
$70$	−2.02713	+	5.78532i	−0.242288	+	0.691478i
$71$	−7.35463			−0.872834			−0.436417	−	0.899745i	$-0.643753\pi$
$71$	−7.35463			−0.872834			−0.436417	+	0.899745i	$0.643753\pi$
$72$			9.63869i			1.13593i
$73$		−	5.14730i		−	0.602446i	−0.953554	−	0.301223i	$-0.902605\pi$
$73$		−	5.14730i		−	0.602446i	0.953554	−	0.301223i	$-0.0973948\pi$
$74$	−11.9812			−1.39279
$75$	−3.12077	+	3.90651i	−0.360355	+	0.451085i
$76$	−20.6675			−2.37072
$77$		−	1.00000i		−	0.113961i
$78$		−	8.98137i		−	1.01694i
$79$	−4.71606			−0.530598			−0.265299	−	0.964166i	$-0.585471\pi$
$79$	−4.71606			−0.530598			−0.265299	+	0.964166i	$0.585471\pi$
$80$	−11.3818	+	32.4830i	−1.27252	+	3.63171i
$81$	1.00000			0.111111
$82$			7.14257i			0.788765i
$83$			5.27773i			0.579306i	0.957132	+	0.289653i	$0.0935398\pi$
$83$			5.27773i			0.579306i	−0.957132	+	0.289653i	$0.906460\pi$
$84$	5.51584			0.601827
$85$	−0.677780	−	0.237488i	−0.0735156	−	0.0257592i
$86$	−21.9080			−2.36240
$87$		−	8.80350i		−	0.943834i
$88$		−	9.63869i		−	1.02749i
$89$	8.21445			0.870730			0.435365	−	0.900254i	$-0.356619\pi$
$89$	8.21445			0.870730			0.435365	+	0.900254i	$0.356619\pi$
$90$	5.78532	+	2.02713i	0.609827	+	0.213678i
$91$	−3.27608			−0.343426
$92$			47.2713i			4.92837i
$93$			7.81044i			0.809905i
$94$	1.22712			0.126567
$95$	−2.77056	+	7.90705i	−0.284254	+	0.811247i
$96$	22.9221			2.33947
$97$		−	16.8348i		−	1.70932i	−0.519190	−	0.854659i	$-0.673766\pi$
$97$		−	16.8348i		−	1.70932i	0.519190	−	0.854659i	$-0.326234\pi$
$98$		−	2.74150i		−	0.276934i
$99$	−1.00000			−0.100504
$100$	21.5477	+	17.2136i	2.15477	+	1.72136i
$101$	13.5082			1.34412			0.672061	−	0.740496i	$-0.265409\pi$
$101$	13.5082			1.34412			0.672061	+	0.740496i	$0.265409\pi$
$102$			0.880519i			0.0871844i
$103$			1.45288i			0.143156i	0.997435	+	0.0715780i	$0.0228035\pi$
$103$			1.45288i			0.143156i	−0.997435	+	0.0715780i	$0.977197\pi$
$104$	−31.5771			−3.09639
$105$	0.739422	−	2.11027i	0.0721602	−	0.205942i
$106$	30.3695			2.94975
$107$		−	18.1900i		−	1.75850i	−0.476363	−	0.879249i	$-0.658045\pi$
$107$		−	18.1900i		−	1.75850i	0.476363	−	0.879249i	$-0.341955\pi$
$108$		−	5.51584i		−	0.530762i
$109$	−5.88949			−0.564111			−0.282055	−	0.959398i	$-0.591016\pi$
$109$	−5.88949			−0.564111			−0.282055	+	0.959398i	$0.591016\pi$
$110$	−5.78532	−	2.02713i	−0.551609	−	0.193279i
$111$	4.37031			0.414811
$112$		−	15.3928i		−	1.45448i
$113$			2.16034i			0.203227i	0.994824	+	0.101614i	$0.0324006\pi$
$113$			2.16034i			0.203227i	−0.994824	+	0.101614i	$0.967599\pi$
$114$	10.2722			0.962082
$115$	18.0852	+	6.33692i	1.68646	+	0.590921i
$116$	−48.5587			−4.50856
$117$			3.27608i			0.302873i
$118$			38.1017i			3.50754i
$119$	0.321181			0.0294426
$120$	7.12706	−	20.3403i	0.650608	−	1.85680i
$121$	1.00000			0.0909091
$122$			32.8419i			2.97336i
$123$		−	2.60535i		−	0.234916i
$124$	43.0812			3.86880
$125$	9.47423	−	5.93624i	0.847401	−	0.530954i
$126$	−2.74150			−0.244233
$127$		−	11.0274i		−	0.978520i	−0.872138	−	0.489260i	$-0.837267\pi$
$127$		−	11.0274i		−	0.978520i	0.872138	−	0.489260i	$-0.162733\pi$
$128$		−	42.0356i		−	3.71546i
$129$	7.99122			0.703588
$130$	−6.64103	+	18.9532i	−0.582457	+	1.66230i
$131$	−1.50033			−0.131084			−0.0655420	−	0.997850i	$-0.520878\pi$
$131$	−1.50033			−0.131084			−0.0655420	+	0.997850i	$0.520878\pi$
$132$			5.51584i			0.480092i
$133$		−	3.74693i		−	0.324900i
$134$	−17.4961			−1.51143
$135$	−2.11027	−	0.739422i	−0.181623	−	0.0636393i
$136$	3.09577			0.265460
$137$		−	10.3848i		−	0.887232i	−0.896217	−	0.443616i	$-0.853695\pi$
$137$		−	10.3848i		−	0.887232i	0.896217	−	0.443616i	$-0.146305\pi$
$138$		−	23.4949i		−	2.00002i
$139$	−3.77347			−0.320061			−0.160031	−	0.987112i	$-0.551159\pi$
$139$	−3.77347			−0.320061			−0.160031	+	0.987112i	$0.551159\pi$
$140$	−11.6399	−	4.07853i	−0.983754	−	0.344699i
$141$	−0.447607			−0.0376953
$142$		−	20.1627i		−	1.69202i
$143$		−	3.27608i		−	0.273959i
$144$	−15.3928			−1.28273
$145$	−6.50950	+	18.5778i	−0.540585	+	1.54280i
$146$	14.1113			1.16786
$147$			1.00000i			0.0824786i
$148$		−	24.1059i		−	1.98149i
$149$	−15.3610			−1.25842			−0.629211	−	0.777234i	$-0.716622\pi$
$149$	−15.3610			−1.25842			−0.629211	+	0.777234i	$0.716622\pi$
$150$	−10.7097	−	8.55559i	−0.874444	−	0.698561i
$151$	12.6253			1.02743			0.513716	−	0.857960i	$-0.328268\pi$
$151$	12.6253			1.02743			0.513716	+	0.857960i	$0.328268\pi$
$152$		−	36.1155i		−	2.92935i
$153$		−	0.321181i		−	0.0259660i
$154$	2.74150			0.220917
$155$	5.77521	−	16.4822i	0.463876	−	1.32388i
$156$	18.0703			1.44678
$157$		−	10.5565i		−	0.842499i	−0.906945	−	0.421249i	$-0.861592\pi$
$157$		−	10.5565i		−	0.842499i	0.906945	−	0.421249i	$-0.138408\pi$
$158$		−	12.9291i		−	1.02858i
$159$	−11.0777			−0.878518
$160$	−48.3718	−	16.9491i	−3.82413	−	1.33994i
$161$	−8.57010			−0.675418
$162$			2.74150i			0.215393i
$163$			8.89662i			0.696837i	0.937339	+	0.348418i	$0.113281\pi$
$163$			8.89662i			0.696837i	−0.937339	+	0.348418i	$0.886719\pi$
$164$	−14.3707			−1.12216
$165$	2.11027	+	0.739422i	0.164285	+	0.0575639i
$166$	−14.4689			−1.12300
$167$		−	3.15342i		−	0.244019i	−0.992529	−	0.122009i	$-0.961066\pi$
$167$		−	3.15342i		−	0.244019i	0.992529	−	0.122009i	$-0.0389338\pi$
$168$			9.63869i			0.743641i
$169$	2.26732			0.174409
$170$	0.651075	−	1.85814i	0.0499352	−	0.142513i
$171$	−3.74693			−0.286535
$172$		−	44.0783i		−	3.36094i
$173$		−	0.296556i		−	0.0225467i	−0.999936	−	0.0112734i	$-0.996412\pi$
$173$		−	0.296556i		−	0.0225467i	0.999936	−	0.0112734i	$-0.00358850\pi$
$174$	24.1348			1.82966
$175$	−3.12077	+	3.90651i	−0.235908	+	0.295304i
$176$	15.3928			1.16028
$177$		−	13.8981i		−	1.04464i
$178$			22.5199i			1.68794i
$179$	−5.89846			−0.440871			−0.220436	−	0.975402i	$-0.570748\pi$
$179$	−5.89846			−0.440871			−0.220436	+	0.975402i	$0.570748\pi$
$180$	−4.07853	+	11.6399i	−0.303996	+	0.867589i
$181$	14.9730			1.11293			0.556466	−	0.830870i	$-0.312157\pi$
$181$	14.9730			1.11293			0.556466	+	0.830870i	$0.312157\pi$
$182$		−	8.98137i		−	0.665744i
$183$		−	11.9795i		−	0.885551i
$184$	−82.6045			−6.08968
$185$	−9.22255	−	3.23150i	−0.678055	−	0.237585i
$186$	−21.4124			−1.57003
$187$			0.321181i			0.0234871i
$188$			2.46893i			0.180065i
$189$	1.00000			0.0727393
$190$	−21.6772	−	7.59551i	−1.57263	−	0.551036i
$191$	−1.33774			−0.0967954			−0.0483977	−	0.998828i	$-0.515411\pi$
$191$	−1.33774			−0.0967954			−0.0483977	+	0.998828i	$0.515411\pi$
$192$			32.0553i			2.31339i
$193$		−	20.0099i		−	1.44034i	−0.693795	−	0.720172i	$-0.744063\pi$
$193$		−	20.0099i		−	1.44034i	0.693795	−	0.720172i	$-0.255937\pi$
$194$	46.1527			3.31357
$195$	2.42240	−	6.91342i	0.173472	−	0.495080i
$196$	5.51584			0.393989
$197$			3.43437i			0.244688i	0.992488	+	0.122344i	$0.0390412\pi$
$197$			3.43437i			0.244688i	−0.992488	+	0.122344i	$0.960959\pi$
$198$		−	2.74150i		−	0.194830i
$199$	−3.31715			−0.235147			−0.117573	−	0.993064i	$-0.537512\pi$
$199$	−3.31715			−0.235147			−0.117573	+	0.993064i	$0.537512\pi$
$200$	−30.0801	+	37.6536i	−2.12698	+	2.66251i
$201$	6.38193			0.450147
$202$			37.0329i			2.60563i
$203$		−	8.80350i		−	0.617885i
$204$	−1.77158			−0.124036
$205$	−1.92645	+	5.49799i	−0.134549	+	0.383997i
$206$	−3.98306			−0.277513
$207$			8.57010i			0.595663i
$208$		−	50.4280i		−	3.49655i
$209$	3.74693			0.259181
$210$	5.78532	+	2.02713i	0.399225	+	0.139885i
$211$	−4.70341			−0.323796			−0.161898	−	0.986807i	$-0.551762\pi$
$211$	−4.70341			−0.323796			−0.161898	+	0.986807i	$0.551762\pi$
$212$			61.1028i			4.19655i
$213$			7.35463i			0.503931i
$214$	49.8680			3.40891
$215$	−16.8637	−	5.90889i	−1.15009	−	0.402983i
$216$	9.63869			0.655830
$217$			7.81044i			0.530208i
$218$		−	16.1461i		−	1.09355i
$219$	−5.14730			−0.347822
$220$	4.07853	−	11.6399i	0.274975	−	0.784764i
$221$	1.05221			0.0707796
$222$			11.9812i			0.804127i
$223$		−	1.75202i		−	0.117324i	−0.998278	−	0.0586621i	$-0.981317\pi$
$223$		−	1.75202i		−	0.117324i	0.998278	−	0.0586621i	$-0.0186834\pi$
$224$	22.9221			1.53155
$225$	3.90651	+	3.12077i	0.260434	+	0.208051i
$226$	−5.92257			−0.393964
$227$		−	3.18872i		−	0.211643i	−0.994385	−	0.105821i	$-0.966253\pi$
$227$		−	3.18872i		−	0.211643i	0.994385	−	0.105821i	$-0.0337472\pi$
$228$			20.6675i			1.36874i
$229$	10.9328			0.722459			0.361229	−	0.932477i	$-0.382357\pi$
$229$	10.9328			0.722459			0.361229	+	0.932477i	$0.382357\pi$
$230$	−17.3727	+	49.5808i	−1.14552	+	3.26926i
$231$	−1.00000			−0.0657952
$232$		−	84.8542i		−	5.57095i
$233$			3.05148i			0.199909i	0.994992	+	0.0999545i	$0.0318697\pi$
$233$			3.05148i			0.199909i	−0.994992	+	0.0999545i	$0.968130\pi$
$234$	−8.98137			−0.587131
$235$	0.944573	+	0.330970i	0.0616171	+	0.0215901i
$236$	−76.6597			−4.99012
$237$			4.71606i			0.306341i
$238$			0.880519i			0.0570756i
$239$	9.56750			0.618870			0.309435	−	0.950921i	$-0.399860\pi$
$239$	9.56750			0.618870			0.309435	+	0.950921i	$0.399860\pi$
$240$	32.4830	+	11.3818i	2.09677	+	0.734691i
$241$	−15.7022			−1.01147			−0.505734	−	0.862689i	$-0.668778\pi$
$241$	−15.7022			−1.01147			−0.505734	+	0.862689i	$0.668778\pi$
$242$			2.74150i			0.176231i
$243$		−	1.00000i		−	0.0641500i
$244$	−66.0771			−4.23015
$245$	0.739422	−	2.11027i	0.0472399	−	0.134820i
$246$	7.14257			0.455393
$247$		−	12.2752i		−	0.781055i
$248$			75.2824i			4.78044i
$249$	5.27773			0.334462
$250$	16.2742	+	25.9736i	1.02927	+	1.64272i
$251$	0.633759			0.0400025			0.0200012	−	0.999800i	$-0.493633\pi$
$251$	0.633759			0.0400025			0.0200012	+	0.999800i	$0.493633\pi$
$252$		−	5.51584i		−	0.347465i
$253$		−	8.57010i		−	0.538797i
$254$	30.2315			1.89689
$255$	−0.237488	+	0.677780i	−0.0148721	+	0.0424443i
$256$	51.1301			3.19563
$257$		−	4.61027i		−	0.287581i	−0.989608	−	0.143790i	$-0.954071\pi$
$257$		−	4.61027i		−	0.287581i	0.989608	−	0.143790i	$-0.0459291\pi$
$258$			21.9080i			1.36393i
$259$	4.37031			0.271558
$260$	−38.1333	−	13.3616i	−2.36493	−	0.828651i
$261$	−8.80350			−0.544923
$262$		−	4.11315i		−	0.254111i
$263$		−	10.6779i		−	0.658430i	−0.944255	−	0.329215i	$-0.893216\pi$
$263$		−	10.6779i		−	0.658430i	0.944255	−	0.329215i	$-0.106784\pi$
$264$	−9.63869			−0.593220
$265$	23.3770	+	8.19109i	1.43603	+	0.503174i
$266$	10.2722			0.629831
$267$		−	8.21445i		−	0.502716i
$268$		−	35.2017i		−	2.15029i
$269$	25.1720			1.53476			0.767382	−	0.641191i	$-0.221559\pi$
$269$	25.1720			1.53476			0.767382	+	0.641191i	$0.221559\pi$
$270$	2.02713	−	5.78532i	0.123367	−	0.352083i
$271$	−14.9292			−0.906881			−0.453441	−	0.891286i	$-0.649804\pi$
$271$	−14.9292			−0.906881			−0.453441	+	0.891286i	$0.649804\pi$
$272$			4.94388i			0.299767i
$273$			3.27608i			0.198277i
$274$	28.4699			1.71993
$275$	−3.90651	−	3.12077i	−0.235571	−	0.188189i
$276$	47.2713			2.84540
$277$		−	1.51698i		−	0.0911462i	−0.998961	−	0.0455731i	$-0.985489\pi$
$277$		−	1.51698i		−	0.0911462i	0.998961	−	0.0455731i	$-0.0145114\pi$
$278$		−	10.3450i		−	0.620450i
$279$	7.81044			0.467599
$280$	7.12706	−	20.3403i	0.425923	−	1.21556i
$281$	19.1124			1.14015			0.570076	−	0.821592i	$-0.306914\pi$
$281$	19.1124			1.14015			0.570076	+	0.821592i	$0.306914\pi$
$282$		−	1.22712i		−	0.0730737i
$283$		−	8.88861i		−	0.528373i	−0.964472	−	0.264187i	$-0.914897\pi$
$283$		−	8.88861i		−	0.528373i	0.964472	−	0.264187i	$-0.0851035\pi$
$284$	40.5670			2.40721
$285$	7.90705	+	2.77056i	0.468373	+	0.164114i
$286$	8.98137			0.531080
$287$		−	2.60535i		−	0.153789i
$288$		−	22.9221i		−	1.35070i
$289$	16.8968			0.993932
$290$	−50.9311	−	17.8458i	−2.99078	−	1.04794i
$291$	−16.8348			−0.986875
$292$			28.3917i			1.66150i
$293$			16.5232i			0.965297i	0.875814	+	0.482649i	$0.160325\pi$
$293$			16.5232i			0.965297i	−0.875814	+	0.482649i	$0.839675\pi$
$294$	−2.74150			−0.159888
$295$	−10.2766	+	29.3288i	−0.598324	+	1.70759i
$296$	42.1240			2.44841
$297$			1.00000i			0.0580259i
$298$		−	42.1123i		−	2.43950i
$299$	−28.0763			−1.62369
$300$	17.2136	−	21.5477i	0.993830	−	1.24406i
$301$	7.99122			0.460606
$302$			34.6123i			1.99171i
$303$		−	13.5082i		−	0.776029i
$304$	57.6758			3.30794
$305$	−8.85791	+	25.2800i	−0.507203	+	1.44753i
$306$	0.880519			0.0503359
$307$			1.59660i			0.0911227i	0.998962	+	0.0455613i	$0.0145076\pi$
$307$			1.59660i			0.0911227i	−0.998962	+	0.0455613i	$0.985492\pi$
$308$			5.51584i			0.314294i
$309$	1.45288			0.0826512
$310$	45.1859	+	15.8328i	2.56639	+	0.899241i
$311$	23.8652			1.35327			0.676635	−	0.736318i	$-0.263437\pi$
$311$	23.8652			1.35327			0.676635	+	0.736318i	$0.263437\pi$
$312$			31.5771i			1.78770i
$313$			30.4151i			1.71916i	0.511001	+	0.859580i	$0.329275\pi$
$313$			30.4151i			1.71916i	−0.511001	+	0.859580i	$0.670725\pi$
$314$	28.9406			1.63321
$315$	−2.11027	−	0.739422i	−0.118900	−	0.0416617i
$316$	26.0130			1.46335
$317$			1.94712i			0.109361i	0.998504	+	0.0546805i	$0.0174140\pi$
$317$			1.94712i			0.109361i	−0.998504	+	0.0546805i	$0.982586\pi$
$318$		−	30.3695i		−	1.70304i
$319$	8.80350			0.492901
$320$	23.7024	−	67.6455i	1.32500	−	3.78150i
$321$	−18.1900			−1.01527
$322$		−	23.4949i		−	1.30932i
$323$			1.20344i			0.0669614i
$324$	−5.51584			−0.306436
$325$	−10.2239	+	12.7980i	−0.567118	+	0.709907i
$326$	−24.3901			−1.35084
$327$			5.88949i			0.325690i
$328$		−	25.1121i		−	1.38659i
$329$	−0.447607			−0.0246774
$330$	−2.02713	+	5.78532i	−0.111590	+	0.318472i
$331$	−32.8178			−1.80383			−0.901915	−	0.431913i	$-0.857839\pi$
$331$	−32.8178			−1.80383			−0.901915	+	0.431913i	$0.857839\pi$
$332$		−	29.1111i		−	1.59768i
$333$		−	4.37031i		−	0.239491i
$334$	8.64511			0.473039
$335$	−13.4676	−	4.71894i	−0.735815	−	0.257823i
$336$	−15.3928			−0.839747
$337$			18.8929i			1.02916i	0.857442	+	0.514581i	$0.172053\pi$
$337$			18.8929i			1.02916i	−0.857442	+	0.514581i	$0.827947\pi$
$338$			6.21587i			0.338099i
$339$	2.16034			0.117333
$340$	3.73853	+	1.30995i	0.202750	+	0.0710419i
$341$	−7.81044			−0.422959
$342$		−	10.2722i		−	0.555458i
$343$			1.00000i			0.0539949i
$344$	77.0249			4.15290
$345$	6.33692	−	18.0852i	0.341168	−	0.973677i
$346$	0.813009			0.0437076
$347$		−	6.81793i		−	0.366005i	−0.983112	−	0.183003i	$-0.941418\pi$
$347$		−	6.81793i		−	0.366005i	0.983112	−	0.183003i	$-0.0585817\pi$
$348$			48.5587i			2.60302i
$349$	−14.8345			−0.794075			−0.397037	−	0.917802i	$-0.629962\pi$
$349$	−14.8345			−0.794075			−0.397037	+	0.917802i	$0.629962\pi$
$350$	−10.7097	−	8.55559i	−0.572458	−	0.457315i
$351$	3.27608			0.174864
$352$			22.9221i			1.22175i
$353$			24.7729i			1.31853i	0.751910	+	0.659265i	$0.229133\pi$
$353$			24.7729i			1.31853i	−0.751910	+	0.659265i	$0.770867\pi$
$354$	38.1017			2.02508
$355$	5.43817	−	15.5203i	0.288628	−	0.823731i
$356$	−45.3096			−2.40140
$357$		−	0.321181i		−	0.0169987i
$358$		−	16.1706i		−	0.854645i
$359$	−19.8773			−1.04908			−0.524542	−	0.851384i	$-0.675764\pi$
$359$	−19.8773			−1.04908			−0.524542	+	0.851384i	$0.675764\pi$
$360$	−20.3403	−	7.12706i	−1.07203	−	0.375629i
$361$	−4.96050			−0.261079
$362$			41.0485i			2.15746i
$363$		−	1.00000i		−	0.0524864i
$364$	18.0703			0.947142
$365$	10.8622	+	3.80603i	0.568554	+	0.199217i
$366$	32.8419			1.71667
$367$		−	6.28879i		−	0.328272i	−0.986438	−	0.164136i	$-0.947516\pi$
$367$		−	6.28879i		−	0.328272i	0.986438	−	0.164136i	$-0.0524836\pi$
$368$		−	131.918i		−	6.87669i
$369$	−2.60535			−0.135629
$370$	8.85918	−	25.2836i	0.460567	−	1.31443i
$371$	−11.0777			−0.575125
$372$		−	43.0812i		−	2.23365i
$373$		−	25.3240i		−	1.31123i	−0.755096	−	0.655614i	$-0.772410\pi$
$373$		−	25.3240i		−	1.31123i	0.755096	−	0.655614i	$-0.227590\pi$
$374$	−0.880519			−0.0455306
$375$	−5.93624	−	9.47423i	−0.306546	−	0.489247i
$376$	−4.31434			−0.222495
$377$		−	28.8409i		−	1.48538i
$378$			2.74150i			0.141008i
$379$	−17.5271			−0.900306			−0.450153	−	0.892951i	$-0.648631\pi$
$379$	−17.5271			−0.900306			−0.450153	+	0.892951i	$0.648631\pi$
$380$	15.2820	−	43.6140i	0.783950	−	2.23735i
$381$	−11.0274			−0.564949
$382$		−	3.66742i		−	0.187641i
$383$			23.1078i			1.18075i	0.807128	+	0.590376i	$0.201020\pi$
$383$			23.1078i			1.18075i	−0.807128	+	0.590376i	$0.798980\pi$
$384$	−42.0356			−2.14512
$385$	2.11027	+	0.739422i	0.107550	+	0.0376844i
$386$	54.8572			2.79216
$387$		−	7.99122i		−	0.406217i
$388$			92.8582i			4.71416i
$389$	33.6469			1.70597			0.852984	−	0.521938i	$-0.174791\pi$
$389$	33.6469			1.70597			0.852984	+	0.521938i	$0.174791\pi$
$390$	18.9532	+	6.64103i	0.959730	+	0.336281i
$391$	2.75255			0.139203
$392$			9.63869i			0.486827i
$393$			1.50033i			0.0756814i
$394$	−9.41532			−0.474337
$395$	3.48716	−	9.95217i	0.175458	−	0.500748i
$396$	5.51584			0.277181
$397$		−	0.681518i		−	0.0342044i	−0.999854	−	0.0171022i	$-0.994556\pi$
$397$		−	0.681518i		−	0.0342044i	0.999854	−	0.0171022i	$-0.00544407\pi$
$398$		−	9.09399i		−	0.455840i
$399$	−3.74693			−0.187581
$400$	−60.1322	−	48.0374i	−3.00661	−	2.40187i
$401$	23.0539			1.15126			0.575629	−	0.817711i	$-0.304757\pi$
$401$	23.0539			1.15126			0.575629	+	0.817711i	$0.304757\pi$
$402$			17.4961i			0.872626i
$403$			25.5876i			1.27461i
$404$	−74.5093			−3.70698
$405$	−0.739422	+	2.11027i	−0.0367422	+	0.104860i
$406$	24.1348			1.19779
$407$			4.37031i			0.216628i
$408$		−	3.09577i		−	0.153263i
$409$	−15.4408			−0.763498			−0.381749	−	0.924266i	$-0.624678\pi$
$409$	−15.4408			−0.763498			−0.381749	+	0.924266i	$0.624678\pi$
$410$	−15.0728	−	5.28137i	−0.744391	−	0.260828i
$411$	−10.3848			−0.512243
$412$		−	8.01383i		−	0.394813i
$413$		−	13.8981i		−	0.683880i
$414$	−23.4949			−1.15471
$415$	−11.1374	−	3.90247i	−0.546716	−	0.191565i
$416$	75.0945			3.68181
$417$			3.77347i			0.184788i
$418$			10.2722i			0.502431i
$419$	−34.1328			−1.66750			−0.833749	−	0.552144i	$-0.813810\pi$
$419$	−34.1328			−1.66750			−0.833749	+	0.552144i	$0.813810\pi$
$420$	−4.07853	+	11.6399i	−0.199012	+	0.567971i
$421$	−33.0179			−1.60920			−0.804598	−	0.593820i	$-0.797619\pi$
$421$	−33.0179			−1.60920			−0.804598	+	0.593820i	$0.797619\pi$
$422$		−	12.8944i		−	0.627691i
$423$			0.447607i			0.0217634i
$424$	−106.774			−5.18542
$425$	1.00233	−	1.25470i	0.0486202	−	0.0608618i
$426$	−20.1627			−0.976888
$427$		−	11.9795i		−	0.579729i
$428$			100.333i			4.84979i
$429$	−3.27608			−0.158170
$430$	16.1992	−	46.2318i	0.781196	−	2.22950i
$431$	−19.5640			−0.942367			−0.471183	−	0.882035i	$-0.656173\pi$
$431$	−19.5640			−0.942367			−0.471183	+	0.882035i	$0.656173\pi$
$432$			15.3928i			0.740587i
$433$			38.7699i			1.86316i	0.363536	+	0.931580i	$0.381569\pi$
$433$			38.7699i			1.86316i	−0.363536	+	0.931580i	$0.618431\pi$
$434$	−21.4124			−1.02783
$435$	18.5778	+	6.50950i	0.890737	+	0.312107i
$436$	32.4855			1.55577
$437$		−	32.1116i		−	1.53610i
$438$		−	14.1113i		−	0.674266i
$439$	20.0104			0.955042			0.477521	−	0.878620i	$-0.341535\pi$
$439$	20.0104			0.955042			0.477521	+	0.878620i	$0.341535\pi$
$440$	20.3403	+	7.12706i	0.969684	+	0.339769i
$441$	1.00000			0.0476190
$442$			2.88465i			0.137209i
$443$		−	14.4987i		−	0.688853i	−0.938813	−	0.344426i	$-0.888073\pi$
$443$		−	14.4987i		−	0.688853i	0.938813	−	0.344426i	$-0.111927\pi$
$444$	−24.1059			−1.14402
$445$	−6.07394	+	17.3347i	−0.287933	+	0.821745i
$446$	4.80318			0.227437
$447$			15.3610i			0.726551i
$448$			32.0553i			1.51447i
$449$	−39.4324			−1.86093			−0.930465	−	0.366381i	$-0.880597\pi$
$449$	−39.4324			−1.86093			−0.930465	+	0.366381i	$0.880597\pi$
$450$	−8.55559	+	10.7097i	−0.403314	+	0.504861i
$451$	2.60535			0.122681
$452$		−	11.9161i		−	0.560485i
$453$		−	12.6253i		−	0.593188i
$454$	8.74189			0.410277
$455$	2.42240	−	6.91342i	0.113564	−	0.324106i
$456$	−36.1155			−1.69126
$457$			21.2123i			0.992272i	0.868245	+	0.496136i	$0.165248\pi$
$457$			21.2123i			0.992272i	−0.868245	+	0.496136i	$0.834752\pi$
$458$			29.9723i			1.40051i
$459$	−0.321181			−0.0149915
$460$	−99.7553	−	34.9534i	−4.65112	−	1.62971i
$461$	−20.9292			−0.974768			−0.487384	−	0.873188i	$-0.662049\pi$
$461$	−20.9292			−0.974768			−0.487384	+	0.873188i	$0.662049\pi$
$462$		−	2.74150i		−	0.127546i
$463$			32.1340i			1.49340i	0.665163	+	0.746698i	$0.268362\pi$
$463$			32.1340i			1.49340i	−0.665163	+	0.746698i	$0.731638\pi$
$464$	135.511			6.29092
$465$	−16.4822	−	5.77521i	−0.764343	−	0.267819i
$466$	−8.36564			−0.387531
$467$			42.3025i			1.95752i	0.205000	+	0.978762i	$0.434281\pi$
$467$			42.3025i			1.95752i	−0.205000	+	0.978762i	$0.565719\pi$
$468$		−	18.0703i		−	0.835301i
$469$	6.38193			0.294690
$470$	−0.907356	+	2.58955i	−0.0418532	+	0.119447i
$471$	−10.5565			−0.486417
$472$		−	133.959i		−	6.16598i
$473$			7.99122i			0.367437i
$474$	−12.9291			−0.593852
$475$	−14.6374	−	11.6933i	−0.671611	−	0.536525i
$476$	−1.77158			−0.0812004
$477$			11.0777i			0.507213i
$478$			26.2293i			1.19970i
$479$	−0.321113			−0.0146720			−0.00733601	−	0.999973i	$-0.502335\pi$
$479$	−0.321113			−0.0146720			−0.00733601	+	0.999973i	$0.502335\pi$
$480$	−16.9491	+	48.3718i	−0.773616	+	2.20786i
$481$	14.3175			0.652820
$482$		−	43.0477i		−	1.96077i
$483$			8.57010i			0.389953i
$484$	−5.51584			−0.250720
$485$	35.5261	+	12.4480i	1.61316	+	0.565236i
$486$	2.74150			0.124357
$487$		−	3.24284i		−	0.146947i	−0.997297	−	0.0734737i	$-0.976592\pi$
$487$		−	3.24284i		−	0.146947i	0.997297	−	0.0734737i	$-0.0234085\pi$
$488$		−	115.467i		−	5.22693i
$489$	8.89662			0.402319
$490$	5.78532	+	2.02713i	0.261354	+	0.0915763i
$491$	6.07037			0.273952			0.136976	−	0.990574i	$-0.456262\pi$
$491$	6.07037			0.273952			0.136976	+	0.990574i	$0.456262\pi$
$492$			14.3707i			0.647880i
$493$			2.82752i			0.127345i
$494$	33.6526			1.51410
$495$	0.739422	−	2.11027i	0.0332345	−	0.0948497i
$496$	−120.225			−5.39825
$497$			7.35463i			0.329900i
$498$			14.4689i			0.648367i
$499$	26.7444			1.19724			0.598622	−	0.801031i	$-0.295715\pi$
$499$	26.7444			1.19724			0.598622	+	0.801031i	$0.295715\pi$
$500$	−52.2583	+	32.7434i	−2.33706	+	1.46433i
$501$	−3.15342			−0.140884
$502$			1.73745i			0.0775462i
$503$		−	41.4428i		−	1.84784i	−0.382584	−	0.923921i	$-0.624966\pi$
$503$		−	41.4428i		−	1.84784i	0.382584	−	0.923921i	$-0.375034\pi$
$504$	9.63869			0.429341
$505$	−9.98830	+	28.5061i	−0.444473	+	1.26850i
$506$	23.4949			1.04448
$507$		−	2.26732i		−	0.100695i
$508$			60.8251i			2.69868i
$509$	8.60888			0.381582			0.190791	−	0.981631i	$-0.438895\pi$
$509$	8.60888			0.381582			0.190791	+	0.981631i	$0.438895\pi$
$510$	−1.85814	−	0.651075i	−0.0822797	−	0.0288301i
$511$	−5.14730			−0.227703
$512$			56.1021i			2.47939i
$513$			3.74693i			0.165431i
$514$	12.6391			0.557485
$515$	−3.06596	−	1.07429i	−0.135103	−	0.0473388i
$516$	−44.0783			−1.94044
$517$		−	0.447607i		−	0.0196857i
$518$			11.9812i			0.526424i
$519$	−0.296556			−0.0130174
$520$	23.3488	−	66.6363i	1.02391	−	2.92219i
$521$	23.4019			1.02525			0.512627	−	0.858611i	$-0.328672\pi$
$521$	23.4019			1.02525			0.512627	+	0.858611i	$0.328672\pi$
$522$		−	24.1348i		−	1.05635i
$523$			9.25116i			0.404525i	0.979331	+	0.202262i	$0.0648294\pi$
$523$			9.25116i			0.404525i	−0.979331	+	0.202262i	$0.935171\pi$
$524$	8.27556			0.361519
$525$	3.90651	+	3.12077i	0.170494	+	0.136201i
$526$	29.2736			1.27639
$527$		−	2.50857i		−	0.109275i
$528$		−	15.3928i		−	0.669886i
$529$	−50.4465			−2.19333
$530$	−22.4559	+	64.0880i	−0.975422	+	2.78380i
$531$	−13.8981			−0.603126
$532$			20.6675i			0.896049i
$533$		−	8.53532i		−	0.369706i
$534$	22.5199			0.974533
$535$	38.3860	+	13.4501i	1.65957	+	0.581499i
$536$	61.5135			2.65698
$537$			5.89846i			0.254537i
$538$			69.0091i			2.97519i
$539$	−1.00000			−0.0430730
$540$	11.6399	+	4.07853i	0.500903	+	0.175512i
$541$	−32.5619			−1.39995			−0.699973	−	0.714169i	$-0.746805\pi$
$541$	−32.5619			−1.39995			−0.699973	+	0.714169i	$0.746805\pi$
$542$		−	40.9283i		−	1.75802i
$543$		−	14.9730i		−	0.642552i
$544$	−7.36214			−0.315649
$545$	4.35482	−	12.4284i	0.186540	−	0.532376i
$546$	−8.98137			−0.384367
$547$		−	1.78967i		−	0.0765206i	−0.999268	−	0.0382603i	$-0.987818\pi$
$547$		−	1.78967i		−	0.0765206i	0.999268	−	0.0382603i	$-0.0121816\pi$
$548$			57.2808i			2.44691i
$549$	−11.9795			−0.511273
$550$	8.55559	−	10.7097i	0.364812	−	0.456664i
$551$	32.9861			1.40526
$552$			82.6045i			3.51588i
$553$			4.71606i			0.200547i
$554$	4.15879			0.176690
$555$	−3.23150	+	9.22255i	−0.137170	+	0.391475i
$556$	20.8138			0.882704
$557$		−	34.5753i		−	1.46500i	−0.680765	−	0.732502i	$-0.738353\pi$
$557$		−	34.5753i		−	1.46500i	0.680765	−	0.732502i	$-0.261647\pi$
$558$			21.4124i			0.906457i
$559$	26.1799			1.10729
$560$	32.4830	+	11.3818i	1.37266	+	0.480968i
$561$	0.321181			0.0135603
$562$			52.3968i			2.21023i
$563$			20.7870i			0.876068i	0.898958	+	0.438034i	$0.144325\pi$
$563$			20.7870i			0.876068i	−0.898958	+	0.438034i	$0.855675\pi$
$564$	2.46893			0.103961
$565$	−4.55890	−	1.59740i	−0.191795	−	0.0672032i
$566$	24.3682			1.02427
$567$		−	1.00000i		−	0.0419961i
$568$			70.8890i			2.97443i
$569$	−11.9893			−0.502616			−0.251308	−	0.967907i	$-0.580861\pi$
$569$	−11.9893			−0.502616			−0.251308	+	0.967907i	$0.580861\pi$
$570$	−7.59551	+	21.6772i	−0.318141	+	0.907958i
$571$	6.17943			0.258601			0.129300	−	0.991605i	$-0.458727\pi$
$571$	6.17943			0.258601			0.129300	+	0.991605i	$0.458727\pi$
$572$			18.0703i			0.755558i
$573$			1.33774i			0.0558849i
$574$	7.14257			0.298125
$575$	−26.7453	+	33.4792i	−1.11535	+	1.39618i
$576$	32.0553			1.33564
$577$		−	1.88391i		−	0.0784282i	−0.999231	−	0.0392141i	$-0.987515\pi$
$577$		−	1.88391i		−	0.0784282i	0.999231	−	0.0392141i	$-0.0124854\pi$
$578$			46.3227i			1.92677i
$579$	−20.0099			−0.831583
$580$	35.9054	−	102.472i	1.49089	−	4.25492i
$581$	5.27773			0.218957
$582$		−	46.1527i		−	1.91309i
$583$		−	11.0777i		−	0.458791i
$584$	−49.6132			−2.05301
$585$	−6.91342	−	2.42240i	−0.285835	−	0.100154i
$586$	−45.2985			−1.87126
$587$			1.05073i			0.0433681i	0.999765	+	0.0216840i	$0.00690279\pi$
$587$			1.05073i			0.0433681i	−0.999765	+	0.0216840i	$0.993097\pi$
$588$		−	5.51584i		−	0.227469i
$589$	−29.2652			−1.20585
$590$	−80.4049	−	28.1732i	−3.31022	−	1.15987i
$591$	3.43437			0.141271
$592$			67.2713i			2.76484i
$593$		−	20.1947i		−	0.829297i	−0.909982	−	0.414648i	$-0.863905\pi$
$593$		−	20.1947i		−	0.829297i	0.909982	−	0.414648i	$-0.136095\pi$
$594$	−2.74150			−0.112485
$595$	−0.237488	+	0.677780i	−0.00973608	+	0.0277863i
$596$	84.7289			3.47063
$597$			3.31715i			0.135762i
$598$		−	76.9712i		−	3.14759i
$599$	−11.1597			−0.455972			−0.227986	−	0.973664i	$-0.573214\pi$
$599$	−11.1597			−0.455972			−0.227986	+	0.973664i	$0.573214\pi$
$600$	37.6536	+	30.0801i	1.53720	+	1.22801i
$601$	27.4198			1.11848			0.559239	−	0.829007i	$-0.311093\pi$
$601$	27.4198			1.11848			0.559239	+	0.829007i	$0.311093\pi$
$602$			21.9080i			0.892902i
$603$		−	6.38193i		−	0.259892i
$604$	−69.6391			−2.83358
$605$	−0.739422	+	2.11027i	−0.0300618	+	0.0857948i
$606$	37.0329			1.50436
$607$		−	9.41818i		−	0.382272i	−0.981564	−	0.191136i	$-0.938783\pi$
$607$		−	9.41818i		−	0.382272i	0.981564	−	0.191136i	$-0.0612172\pi$
$608$			85.8874i			3.48320i
$609$	−8.80350			−0.356736
$610$	−69.3053	−	24.2840i	−2.80609	−	0.983230i
$611$	−1.46639			−0.0593240
$612$			1.77158i			0.0716121i
$613$		−	29.3064i		−	1.18368i	−0.806057	−	0.591838i	$-0.798403\pi$
$613$		−	29.3064i		−	1.18368i	0.806057	−	0.591838i	$-0.201597\pi$
$614$	−4.37708			−0.176645
$615$	5.49799	+	1.92645i	0.221701	+	0.0776820i
$616$	−9.63869			−0.388354
$617$			1.10478i			0.0444767i	0.999753	+	0.0222384i	$0.00707928\pi$
$617$			1.10478i			0.0444767i	−0.999753	+	0.0222384i	$0.992921\pi$
$618$			3.98306i			0.160222i
$619$	20.4181			0.820672			0.410336	−	0.911934i	$-0.365411\pi$
$619$	20.4181			0.820672			0.410336	+	0.911934i	$0.365411\pi$
$620$	−31.8552	+	90.9130i	−1.27933	+	3.65116i
$621$	8.57010			0.343906
$622$			65.4265i			2.62336i
$623$		−	8.21445i		−	0.329105i
$624$	−50.4280			−2.01874
$625$	5.52164	+	24.3826i	0.220866	+	0.975304i
$626$	−83.3830			−3.33265
$627$		−	3.74693i		−	0.149638i
$628$			58.2278i			2.32354i
$629$	−1.40366			−0.0559676
$630$	2.02713	−	5.78532i	0.0807627	−	0.230493i
$631$	−13.7236			−0.546327			−0.273164	−	0.961968i	$-0.588070\pi$
$631$	−13.7236			−0.546327			−0.273164	+	0.961968i	$0.588070\pi$
$632$			45.4566i			1.80817i
$633$			4.70341i			0.186944i
$634$	−5.33803			−0.212000
$635$	23.2707	+	8.15387i	0.923471	+	0.323576i
$636$	61.1028			2.42288
$637$			3.27608i			0.129803i
$638$			24.1348i			0.955507i
$639$	7.35463			0.290945
$640$	88.7066	+	31.0820i	3.50644	+	1.22863i
$641$	−0.376867			−0.0148854			−0.00744268	−	0.999972i	$-0.502369\pi$
$641$	−0.376867			−0.0148854			−0.00744268	+	0.999972i	$0.502369\pi$
$642$		−	49.8680i		−	1.96813i
$643$		−	33.5125i		−	1.32160i	−0.750561	−	0.660802i	$-0.770217\pi$
$643$		−	33.5125i		−	1.32160i	0.750561	−	0.660802i	$-0.229783\pi$
$644$	47.2713			1.86275
$645$	−5.90889	+	16.8637i	−0.232662	+	0.664006i
$646$	−3.29925			−0.129807
$647$		−	17.3294i		−	0.681290i	−0.940192	−	0.340645i	$-0.889355\pi$
$647$		−	17.3294i		−	0.681290i	0.940192	−	0.340645i	$-0.110645\pi$
$648$		−	9.63869i		−	0.378643i
$649$	13.8981			0.545548
$650$	−35.0858	−	28.0288i	−1.37618	−	1.09938i
$651$	7.81044			0.306115
$652$		−	49.0723i		−	1.92182i
$653$		−	13.0222i		−	0.509600i	−0.966994	−	0.254800i	$-0.917990\pi$
$653$		−	13.0222i		−	0.509600i	0.966994	−	0.254800i	$-0.0820096\pi$
$654$	−16.1461			−0.631361
$655$	1.10937	−	3.16610i	0.0433468	−	0.123710i
$656$	40.1036			1.56578
$657$			5.14730i			0.200815i
$658$		−	1.22712i		−	0.0478379i
$659$	−25.3363			−0.986961			−0.493480	−	0.869757i	$-0.664276\pi$
$659$	−25.3363			−0.986961			−0.493480	+	0.869757i	$0.664276\pi$
$660$	−11.6399	−	4.07853i	−0.453084	−	0.158757i
$661$	18.9816			0.738298			0.369149	−	0.929370i	$-0.379649\pi$
$661$	18.9816			0.738298			0.369149	+	0.929370i	$0.379649\pi$
$662$		−	89.9702i		−	3.49679i
$663$		−	1.05221i		−	0.0408646i
$664$	50.8703			1.97415
$665$	7.90705	+	2.77056i	0.306622	+	0.107438i
$666$	11.9812			0.464263
$667$		−	75.4468i		−	2.92131i
$668$			17.3938i			0.672985i
$669$	−1.75202			−0.0677371
$670$	12.9370	−	36.9215i	0.499800	−	1.42640i
$671$	11.9795			0.462464
$672$		−	22.9221i		−	0.884238i
$673$			36.9323i			1.42364i	0.702364	+	0.711818i	$0.252128\pi$
$673$			36.9323i			1.42364i	−0.702364	+	0.711818i	$0.747872\pi$
$674$	−51.7950			−1.99507
$675$	3.12077	−	3.90651i	0.120118	−	0.150362i
$676$	−12.5062			−0.481007
$677$			26.8111i			1.03044i	0.857059	+	0.515218i	$0.172289\pi$
$677$			26.8111i			1.03044i	−0.857059	+	0.515218i	$0.827711\pi$
$678$			5.92257i			0.227455i
$679$	−16.8348			−0.646061
$680$	−2.28908	+	6.53291i	−0.0877821	+	0.250526i
$681$	−3.18872			−0.122192
$682$		−	21.4124i		−	0.819922i
$683$			2.06237i			0.0789144i	0.999221	+	0.0394572i	$0.0125629\pi$
$683$			2.06237i			0.0789144i	−0.999221	+	0.0394572i	$0.987437\pi$
$684$	20.6675			0.790241
$685$	21.9147	+	7.67874i	0.837319	+	0.293389i
$686$	−2.74150			−0.104671
$687$		−	10.9328i		−	0.417112i
$688$			123.007i			4.68961i
$689$	−36.2914			−1.38259
$690$	49.5808	+	17.3727i	1.88751	+	0.661367i
$691$	−24.8568			−0.945599			−0.472799	−	0.881170i	$-0.656756\pi$
$691$	−24.8568			−0.945599			−0.472799	+	0.881170i	$0.656756\pi$
$692$			1.63575i			0.0621821i
$693$			1.00000i			0.0379869i
$694$	18.6914			0.709514
$695$	2.79019	−	7.96305i	0.105838	−	0.302056i
$696$	−84.8542			−3.21639
$697$			0.836789i			0.0316956i
$698$		−	40.6689i		−	1.53934i
$699$	3.05148			0.115417
$700$	17.2136	−	21.5477i	0.650615	−	0.814426i
$701$	−18.6532			−0.704523			−0.352262	−	0.935902i	$-0.614587\pi$
$701$	−18.6532			−0.704523			−0.352262	+	0.935902i	$0.614587\pi$
$702$			8.98137i			0.338980i
$703$			16.3753i			0.617604i
$704$	−32.0553			−1.20813
$705$	0.330970	−	0.944573i	0.0124651	−	0.0355747i
$706$	−67.9151			−2.55602
$707$		−	13.5082i		−	0.508030i
$708$			76.6597i			2.88105i
$709$	−48.8055			−1.83293			−0.916464	−	0.400118i	$-0.868969\pi$
$709$	−48.8055			−1.83293			−0.916464	+	0.400118i	$0.868969\pi$
$710$	42.5489	+	14.9088i	1.59683	+	0.559516i
$711$	4.71606			0.176866
$712$		−	79.1765i		−	2.96726i
$713$			66.9363i			2.50678i
$714$	0.880519			0.0329526
$715$	6.91342	+	2.42240i	0.258547	+	0.0905927i
$716$	32.5349			1.21589
$717$		−	9.56750i		−	0.357305i
$718$		−	54.4937i		−	2.03369i
$719$	25.3396			0.945008			0.472504	−	0.881329i	$-0.343350\pi$
$719$	25.3396			0.945008			0.472504	+	0.881329i	$0.343350\pi$
$720$	11.3818	−	32.4830i	0.424174	−	1.21057i
$721$	1.45288			0.0541079
$722$		−	13.5992i		−	0.506110i
$723$			15.7022i			0.583972i
$724$	−82.5886			−3.06938
$725$	−34.3910	−	27.4737i	−1.27725	−	1.02035i
$726$	2.74150			0.101747
$727$		−	7.41951i		−	0.275174i	−0.990490	−	0.137587i	$-0.956065\pi$
$727$		−	7.41951i		−	0.275174i	0.990490	−	0.137587i	$-0.0439347\pi$
$728$			31.5771i			1.17032i
$729$	−1.00000			−0.0370370
$730$	−10.4342	+	29.7788i	−0.386188	+	1.10216i
$731$	−2.56663			−0.0949303
$732$			66.0771i			2.44228i
$733$			34.1167i			1.26013i	0.776543	+	0.630065i	$0.216972\pi$
$733$			34.1167i			1.26013i	−0.776543	+	0.630065i	$0.783028\pi$
$734$	17.2407			0.636367
$735$	−2.11027	−	0.739422i	−0.0778386	−	0.0272740i
$736$	196.444			7.24103
$737$			6.38193i			0.235082i
$738$		−	7.14257i		−	0.262922i
$739$	−29.4973			−1.08507			−0.542537	−	0.840032i	$-0.682536\pi$
$739$	−29.4973			−1.08507			−0.542537	+	0.840032i	$0.682536\pi$
$740$	50.8701	+	17.8245i	1.87002	+	0.655240i
$741$	−12.2752			−0.450942
$742$		−	30.3695i		−	1.11490i
$743$		−	1.70796i		−	0.0626589i	−0.999509	−	0.0313295i	$-0.990026\pi$
$743$		−	1.70796i		−	0.0626589i	0.999509	−	0.0313295i	$-0.00997411\pi$
$744$	75.2824			2.75999
$745$	11.3583	−	32.4159i	0.416135	−	1.18763i
$746$	69.4259			2.54186
$747$		−	5.27773i		−	0.193102i
$748$		−	1.77158i		−	0.0647755i
$749$	−18.1900			−0.664649
$750$	25.9736	−	16.2742i	0.948423	−	0.594251i
$751$	−22.7214			−0.829116			−0.414558	−	0.910023i	$-0.636064\pi$
$751$	−22.7214			−0.829116			−0.414558	+	0.910023i	$0.636064\pi$
$752$		−	6.88993i		−	0.251250i
$753$		−	0.633759i		−	0.0230954i
$754$	79.0675			2.87947
$755$	−9.33542	+	26.6428i	−0.339751	+	0.969632i
$756$	−5.51584			−0.200609
$757$			3.35702i			0.122013i	0.998137	+	0.0610066i	$0.0194311\pi$
$757$			3.35702i			0.122013i	−0.998137	+	0.0610066i	$0.980569\pi$
$758$		−	48.0506i		−	1.74528i
$759$	−8.57010			−0.311075
$760$	76.2136	+	26.7046i	2.76456	+	0.968678i
$761$	12.3406			0.447345			0.223672	−	0.974664i	$-0.428195\pi$
$761$	12.3406			0.447345			0.223672	+	0.974664i	$0.428195\pi$
$762$		−	30.2315i		−	1.09517i
$763$			5.88949i			0.213214i
$764$	7.37876			0.266954
$765$	0.677780	+	0.237488i	0.0245052	+	0.00858641i
$766$	−63.3500			−2.28893
$767$		−	45.5312i		−	1.64404i
$768$		−	51.1301i		−	1.84500i
$769$	−37.3271			−1.34605			−0.673025	−	0.739620i	$-0.735005\pi$
$769$	−37.3271			−1.34605			−0.673025	+	0.739620i	$0.735005\pi$
$770$	−2.02713	+	5.78532i	−0.0730526	+	0.208489i
$771$	−4.61027			−0.166035
$772$			110.371i			3.97236i
$773$			31.9729i			1.14998i	0.818159	+	0.574992i	$0.194995\pi$
$773$			31.9729i			1.14998i	−0.818159	+	0.574992i	$0.805005\pi$
$774$	21.9080			0.787465
$775$	30.5116	+	24.3746i	1.09601	+	0.875560i
$776$	−162.266			−5.82500
$777$		−	4.37031i		−	0.156784i
$778$			92.2432i			3.30708i
$779$	9.76206			0.349762
$780$	−13.3616	+	38.1333i	−0.478422	+	1.36539i
$781$	−7.35463			−0.263169
$782$			7.54614i			0.269849i
$783$			8.80350i			0.314611i
$784$	−15.3928			−0.549743
$785$	22.2771	+	7.80569i	0.795102	+	0.278597i
$786$	−4.11315			−0.146711
$787$		−	10.4801i		−	0.373576i	−0.982400	−	0.186788i	$-0.940192\pi$
$787$		−	10.4801i		−	0.373576i	0.982400	−	0.186788i	$-0.0598078\pi$
$788$		−	18.9434i		−	0.674831i
$789$	−10.6779			−0.380145
$790$	27.2839	+	9.56005i	0.970718	+	0.340131i
$791$	2.16034			0.0768128
$792$			9.63869i			0.342496i
$793$		−	39.2458i		−	1.39366i
$794$	1.86838			0.0663065
$795$	8.19109	−	23.3770i	0.290508	−	0.829095i
$796$	18.2969			0.648516
$797$		−	24.7892i		−	0.878078i	−0.898468	−	0.439039i	$-0.855319\pi$
$797$		−	24.7892i		−	0.878078i	0.898468	−	0.439039i	$-0.144681\pi$
$798$		−	10.2722i		−	0.363633i
$799$	0.143763			0.00508597
$800$	71.5344	−	89.5453i	2.52912	−	3.16590i
$801$	−8.21445			−0.290243
$802$			63.2024i			2.23175i
$803$		−	5.14730i		−	0.181644i
$804$	−35.2017			−1.24147
$805$	6.33692	−	18.0852i	0.223347	−	0.637421i
$806$	−70.1485			−2.47088
$807$		−	25.1720i		−	0.886096i
$808$		−	130.202i		−	4.58048i
$809$	22.0085			0.773777			0.386888	−	0.922127i	$-0.373550\pi$
$809$	22.0085			0.773777			0.386888	+	0.922127i	$0.373550\pi$
$810$	−5.78532	−	2.02713i	−0.203276	−	0.0712260i
$811$	11.4766			0.402997			0.201498	−	0.979489i	$-0.435419\pi$
$811$	11.4766			0.402997			0.201498	+	0.979489i	$0.435419\pi$
$812$			48.5587i			1.70408i
$813$			14.9292i			0.523588i
$814$	−11.9812			−0.419941
$815$	−18.7743	−	6.57835i	−0.657635	−	0.230430i
$816$	4.94388			0.173071
$817$			29.9426i			1.04756i
$818$		−	42.3310i		−	1.48007i
$819$	3.27608			0.114475
$820$	10.6260	−	30.3261i	0.371076	−	1.05903i
$821$	2.71106			0.0946167			0.0473084	−	0.998880i	$-0.484936\pi$
$821$	2.71106			0.0946167			0.0473084	+	0.998880i	$0.484936\pi$
$822$		−	28.4699i		−	0.993002i
$823$		−	2.20617i		−	0.0769022i	−0.999260	−	0.0384511i	$-0.987758\pi$
$823$		−	2.20617i		−	0.0769022i	0.999260	−	0.0384511i	$-0.0122424\pi$
$824$	14.0038			0.487846
$825$	−3.12077	+	3.90651i	−0.108651	+	0.136007i
$826$	38.1017			1.32573
$827$		−	0.695867i		−	0.0241977i	−0.999927	−	0.0120988i	$-0.996149\pi$
$827$		−	0.695867i		−	0.0241977i	0.999927	−	0.0120988i	$-0.00385127\pi$
$828$		−	47.2713i		−	1.64279i
$829$	8.13710			0.282613			0.141307	−	0.989966i	$-0.454870\pi$
$829$	8.13710			0.282613			0.141307	+	0.989966i	$0.454870\pi$
$830$	10.6986	−	30.5333i	0.371355	−	1.05983i
$831$	−1.51698			−0.0526233
$832$			105.016i			3.64076i
$833$		−	0.321181i		−	0.0111283i
$834$	−10.3450			−0.358217
$835$	6.65458	+	2.33171i	0.230291	+	0.0806921i
$836$	−20.6675			−0.714800
$837$		−	7.81044i		−	0.269968i
$838$		−	93.5753i		−	3.23250i
$839$	12.1312			0.418817			0.209408	−	0.977828i	$-0.432846\pi$
$839$	12.1312			0.418817			0.209408	+	0.977828i	$0.432846\pi$
$840$	−20.3403	−	7.12706i	−0.701806	−	0.245907i
$841$	48.5016			1.67247
$842$		−	90.5188i		−	3.11948i
$843$		−	19.1124i		−	0.658267i
$844$	25.9433			0.893005
$845$	−1.67651	+	4.78467i	−0.0576736	+	0.164598i
$846$	−1.22712			−0.0421891
$847$		−	1.00000i		−	0.0343604i
$848$		−	170.517i		−	5.85557i
$849$	−8.88861			−0.305056
$850$	3.43976	+	2.74789i	0.117983	+	0.0942520i
$851$	37.4540			1.28391
$852$		−	40.5670i		−	1.38980i
$853$			23.3765i			0.800396i	0.916429	+	0.400198i	$0.131059\pi$
$853$			23.3765i			0.800396i	−0.916429	+	0.400198i	$0.868941\pi$
$854$	32.8419			1.12383
$855$	2.77056	−	7.90705i	0.0947513	−	0.270416i
$856$	−175.328			−5.99259
$857$		−	14.0962i		−	0.481518i	−0.970585	−	0.240759i	$-0.922604\pi$
$857$		−	14.0962i		−	0.481518i	0.970585	−	0.240759i	$-0.0773964\pi$
$858$		−	8.98137i		−	0.306619i
$859$	14.1965			0.484378			0.242189	−	0.970229i	$-0.422135\pi$
$859$	14.1965			0.484378			0.242189	+	0.970229i	$0.422135\pi$
$860$	93.0173	+	32.5925i	3.17186	+	1.11139i
$861$	−2.60535			−0.0887900
$862$		−	53.6349i		−	1.82681i
$863$		−	45.2583i		−	1.54061i	−0.637675	−	0.770305i	$-0.720104\pi$
$863$		−	45.2583i		−	1.54061i	0.637675	−	0.770305i	$-0.279896\pi$
$864$	−22.9221			−0.779825
$865$	0.625814	+	0.219280i	0.0212783	+	0.00745574i
$866$	−106.288			−3.61180
$867$		−	16.8968i		−	0.573847i
$868$		−	43.0812i		−	1.46227i
$869$	−4.71606			−0.159981
$870$	−17.8458	+	50.9311i	−0.605030	+	1.72673i
$871$	20.9077			0.708431
$872$			56.7670i			1.92237i
$873$			16.8348i			0.569772i
$874$	88.0340			2.97779
$875$	−5.93624	−	9.47423i	−0.200682	−	0.320287i
$876$	28.3917			0.959266
$877$		−	0.189912i		−	0.00641287i	−0.999995	−	0.00320643i	$-0.998979\pi$
$877$		−	0.189912i		−	0.00641287i	0.999995	−	0.00320643i	$-0.00102064\pi$
$878$			54.8584i			1.85138i
$879$	16.5232			0.557315
$880$	−11.3818	+	32.4830i	−0.383680	+	1.09500i
$881$	42.2462			1.42331			0.711655	−	0.702529i	$-0.247946\pi$
$881$	42.2462			1.42331			0.711655	+	0.702529i	$0.247946\pi$
$882$			2.74150i			0.0923112i
$883$		−	10.1090i		−	0.340195i	−0.985427	−	0.170098i	$-0.945592\pi$
$883$		−	10.1090i		−	0.340195i	0.985427	−	0.170098i	$-0.0544083\pi$
$884$	−5.80385			−0.195204
$885$	29.3288	+	10.2766i	0.985876	+	0.345443i
$886$	39.7481			1.33537
$887$		−	1.62079i		−	0.0544208i	−0.999630	−	0.0272104i	$-0.991338\pi$
$887$		−	1.62079i		−	0.0544208i	0.999630	−	0.0272104i	$-0.00866241\pi$
$888$		−	42.1240i		−	1.41359i
$889$	−11.0274			−0.369846
$890$	−47.5232	−	16.6517i	−1.59298	−	0.558167i
$891$	1.00000			0.0335013
$892$			9.66388i			0.323571i
$893$		−	1.67715i		−	0.0561238i
$894$	−42.1123			−1.40844
$895$	4.36145	−	12.4474i	0.145787	−	0.416069i
$896$	−42.0356			−1.40431
$897$			28.0763i			0.937440i
$898$		−	108.104i		−	3.60748i
$899$	−68.7592			−2.29325
$900$	−21.5477	−	17.2136i	−0.718256	−	0.573788i
$901$	3.55795			0.118532
$902$			7.14257i			0.237821i
$903$		−	7.99122i		−	0.265931i
$904$	20.8228			0.692557
$905$	−11.0714	+	31.5971i	−0.368024	+	1.05032i
$906$	34.6123			1.14992
$907$			14.7430i			0.489532i	0.969582	+	0.244766i	$0.0787112\pi$
$907$			14.7430i			0.489532i	−0.969582	+	0.244766i	$0.921289\pi$
$908$			17.5885i			0.583694i
$909$	−13.5082			−0.448040
$910$	18.9532	+	6.64103i	0.628291	+	0.220148i
$911$	36.8452			1.22074			0.610368	−	0.792118i	$-0.291022\pi$
$911$	36.8452			1.22074			0.610368	+	0.792118i	$0.291022\pi$
$912$		−	57.6758i		−	1.90984i
$913$			5.27773i			0.174667i
$914$	−58.1537			−1.92355
$915$	25.2800	+	8.85791i	0.835733	+	0.292834i
$916$	−60.3035			−1.99248
$917$			1.50033i			0.0495451i
$918$		−	0.880519i		−	0.0290615i
$919$	52.0581			1.71724			0.858620	−	0.512613i	$-0.171322\pi$
$919$	52.0581			1.71724			0.858620	+	0.512613i	$0.171322\pi$
$920$	61.0796	−	174.318i	2.01373	−	5.74710i
$921$	1.59660			0.0526097
$922$		−	57.3774i		−	1.88962i
$923$			24.0943i			0.793074i
$924$	5.51584			0.181458
$925$	13.6387	−	17.0727i	0.448438	−	0.561346i
$926$	−88.0956			−2.89500
$927$		−	1.45288i		−	0.0477187i
$928$			201.794i			6.62423i
$929$	−2.34020			−0.0767794			−0.0383897	−	0.999263i	$-0.512223\pi$
$929$	−2.34020			−0.0767794			−0.0383897	+	0.999263i	$0.512223\pi$
$930$	15.8328	−	45.1859i	0.519177	−	1.48171i
$931$	−3.74693			−0.122801
$932$		−	16.8315i		−	0.551333i
$933$		−	23.8652i		−	0.781311i
$934$	−115.972			−3.79473
$935$	−0.677780	−	0.237488i	−0.0221658	−	0.00776670i
$936$	31.5771			1.03213
$937$			45.4497i			1.48478i	0.669969	+	0.742389i	$0.266307\pi$
$937$			45.4497i			1.48478i	−0.669969	+	0.742389i	$0.733693\pi$
$938$			17.4961i			0.571268i
$939$	30.4151			0.992558
$940$	−5.21011	−	1.82558i	−0.169935	−	0.0595438i
$941$	52.7015			1.71802			0.859010	−	0.511959i	$-0.171080\pi$
$941$	52.7015			1.71802			0.859010	+	0.511959i	$0.171080\pi$
$942$		−	28.9406i		−	0.942936i
$943$		−	22.3281i		−	0.727102i
$944$	213.931			6.96285
$945$	−0.739422	+	2.11027i	−0.0240534	+	0.0686472i
$946$	−21.9080			−0.712289
$947$			21.7233i			0.705914i	0.935640	+	0.352957i	$0.114824\pi$
$947$			21.7233i			0.705914i	−0.935640	+	0.352957i	$0.885176\pi$
$948$		−	26.0130i		−	0.844863i
$949$	−16.8629			−0.547394
$950$	32.0572	−	40.1286i	1.04007	−	1.30194i
$951$	1.94712			0.0631396
$952$		−	3.09577i		−	0.100334i
$953$		−	10.8408i		−	0.351169i	−0.984464	−	0.175585i	$-0.943818\pi$
$953$		−	10.8408i		−	0.351169i	0.984464	−	0.175585i	$-0.0561816\pi$
$954$	−30.3695			−0.983250
$955$	0.989154	−	2.82300i	0.0320083	−	0.0913500i
$956$	−52.7728			−1.70679
$957$		−	8.80350i		−	0.284577i
$958$		−	0.880332i		−	0.0284422i
$959$	−10.3848			−0.335342
$960$	−67.6455	−	23.7024i	−2.18325	−	0.764992i
$961$	30.0030			0.967840
$962$			39.2514i			1.26552i
$963$			18.1900i			0.586166i
$964$	86.6109			2.78955
$965$	42.2264	+	14.7958i	1.35932	+	0.476293i
$966$	−23.4949			−0.755937
$967$			60.3817i			1.94174i	0.239597	+	0.970872i	$0.422985\pi$
$967$			60.3817i			1.94174i	−0.239597	+	0.970872i	$0.577015\pi$
$968$		−	9.63869i		−	0.309799i
$969$	1.20344			0.0386602
$970$	−34.1263	+	97.3949i	−1.09573	+	3.12716i
$971$	28.9492			0.929025			0.464513	−	0.885567i	$-0.346230\pi$
$971$	28.9492			0.929025			0.464513	+	0.885567i	$0.346230\pi$
$972$			5.51584i			0.176921i
$973$			3.77347i			0.120972i
$974$	8.89027			0.284863
$975$	12.7980	+	10.2239i	0.409865	+	0.327426i
$976$	184.398			5.90245
$977$			53.5760i			1.71405i	0.515276	+	0.857024i	$0.327689\pi$
$977$			53.5760i			1.71405i	−0.515276	+	0.857024i	$0.672311\pi$
$978$			24.3901i			0.779910i
$979$	8.21445			0.262535
$980$	−4.07853	+	11.6399i	−0.130284	+	0.371824i
$981$	5.88949			0.188037
$982$			16.6419i			0.531066i
$983$		−	16.6747i		−	0.531840i	−0.963995	−	0.265920i	$-0.914324\pi$
$983$		−	16.6747i		−	0.531840i	0.963995	−	0.265920i	$-0.0856757\pi$
$984$	−25.1121			−0.800545
$985$	−7.24745	−	2.53945i	−0.230923	−	0.0809135i
$986$	−7.75165			−0.246863
$987$			0.447607i			0.0142475i
$988$			67.7082i			2.15409i
$989$	68.4855			2.17771
$990$	5.78532	+	2.02713i	0.183870	+	0.0644264i
$991$	−12.2629			−0.389545			−0.194772	−	0.980848i	$-0.562397\pi$
$991$	−12.2629			−0.389545			−0.194772	+	0.980848i	$0.562397\pi$
$992$		−	179.032i		−	5.68426i
$993$			32.8178i			1.04144i
$994$	−20.1627			−0.639523
$995$	2.45278	−	7.00010i	0.0777582	−	0.221918i
$996$	−29.1111			−0.922420
$997$			51.4842i			1.63052i	0.579093	+	0.815261i	$0.303407\pi$
$997$			51.4842i			1.63052i	−0.579093	+	0.815261i	$0.696593\pi$
$998$			73.3199i			2.32090i
$999$	−4.37031			−0.138270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.f.694.20	yes	20
5.2	odd	4		5775.2.a.cn.1.1		10
5.3	odd	4		5775.2.a.co.1.10		10
5.4	even	2	inner	1155.2.c.f.694.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.f.694.1	✓	20	5.4	even	2	inner
1155.2.c.f.694.20	yes	20	1.1	even	1	trivial
5775.2.a.cn.1.1		10	5.2	odd	4
5775.2.a.co.1.10		10	5.3	odd	4

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.74150i q^{2} -1.00000i q^{3} -5.51584 q^{4} +(-0.739422 + 2.11027i) q^{5} +2.74150 q^{6} -1.00000i q^{7} -9.63869i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.74150i q^{2} -1.00000i q^{3} -5.51584 q^{4} +(-0.739422 + 2.11027i) q^{5} +2.74150 q^{6} -1.00000i q^{7} -9.63869i q^{8} -1.00000 q^{9} +(-5.78532 - 2.02713i) q^{10} +1.00000 q^{11} +5.51584i q^{12} -3.27608i q^{13} +2.74150 q^{14} +(2.11027 + 0.739422i) q^{15} +15.3928 q^{16} +0.321181i q^{17} -2.74150i q^{18} +3.74693 q^{19} +(4.07853 - 11.6399i) q^{20} -1.00000 q^{21} +2.74150i q^{22} -8.57010i q^{23} -9.63869 q^{24} +(-3.90651 - 3.12077i) q^{25} +8.98137 q^{26} +1.00000i q^{27} +5.51584i q^{28} +8.80350 q^{29} +(-2.02713 + 5.78532i) q^{30} -7.81044 q^{31} +22.9221i q^{32} -1.00000i q^{33} -0.880519 q^{34} +(2.11027 + 0.739422i) q^{35} +5.51584 q^{36} +4.37031i q^{37} +10.2722i q^{38} -3.27608 q^{39} +(20.3403 + 7.12706i) q^{40} +2.60535 q^{41} -2.74150i q^{42} +7.99122i q^{43} -5.51584 q^{44} +(0.739422 - 2.11027i) q^{45} +23.4949 q^{46} -0.447607i q^{47} -15.3928i q^{48} -1.00000 q^{49} +(8.55559 - 10.7097i) q^{50} +0.321181 q^{51} +18.0703i q^{52} -11.0777i q^{53} -2.74150 q^{54} +(-0.739422 + 2.11027i) q^{55} -9.63869 q^{56} -3.74693i q^{57} +24.1348i q^{58} +13.8981 q^{59} +(-11.6399 - 4.07853i) q^{60} +11.9795 q^{61} -21.4124i q^{62} +1.00000i q^{63} -32.0553 q^{64} +(6.91342 + 2.42240i) q^{65} +2.74150 q^{66} +6.38193i q^{67} -1.77158i q^{68} -8.57010 q^{69} +(-2.02713 + 5.78532i) q^{70} -7.35463 q^{71} +9.63869i q^{72} -5.14730i q^{73} -11.9812 q^{74} +(-3.12077 + 3.90651i) q^{75} -20.6675 q^{76} -1.00000i q^{77} -8.98137i q^{78} -4.71606 q^{79} +(-11.3818 + 32.4830i) q^{80} +1.00000 q^{81} +7.14257i q^{82} +5.27773i q^{83} +5.51584 q^{84} +(-0.677780 - 0.237488i) q^{85} -21.9080 q^{86} -8.80350i q^{87} -9.63869i q^{88} +8.21445 q^{89} +(5.78532 + 2.02713i) q^{90} -3.27608 q^{91} +47.2713i q^{92} +7.81044i q^{93} +1.22712 q^{94} +(-2.77056 + 7.90705i) q^{95} +22.9221 q^{96} -16.8348i q^{97} -2.74150i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more