LMFDB - Embedded newform 322.2.c.d.321.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(321,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("322.321");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.2312.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x + 4 $ x^4 - x^3 - 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			321.2
Root			$1.28078 - 0.599676i$ of defining polynomial
Character	$\chi$	$=$	322.321
Dual form			322.2.c.d.321.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.936426i q^{3} +1.00000 q^{4} +2.00000 q^{5} -0.936426i q^{6} +(-1.56155 + 2.13578i) q^{7} +1.00000 q^{8} +2.12311 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.936426i q^{3} +1.00000 q^{4} +2.00000 q^{5} -0.936426i q^{6} +(-1.56155 + 2.13578i) q^{7} +1.00000 q^{8} +2.12311 q^{9} +2.00000 q^{10} +0.936426i q^{11} -0.936426i q^{12} -3.33513i q^{13} +(-1.56155 + 2.13578i) q^{14} -1.87285i q^{15} +1.00000 q^{16} +1.12311 q^{17} +2.12311 q^{18} -4.00000 q^{19} +2.00000 q^{20} +(2.00000 + 1.46228i) q^{21} +0.936426i q^{22} +(-1.56155 - 4.53448i) q^{23} -0.936426i q^{24} -1.00000 q^{25} -3.33513i q^{26} -4.79741i q^{27} +(-1.56155 + 2.13578i) q^{28} -2.00000 q^{29} -1.87285i q^{30} +9.06897i q^{31} +1.00000 q^{32} +0.876894 q^{33} +1.12311 q^{34} +(-3.12311 + 4.27156i) q^{35} +2.12311 q^{36} -3.33513i q^{37} -4.00000 q^{38} -3.12311 q^{39} +2.00000 q^{40} +6.67026i q^{41} +(2.00000 + 1.46228i) q^{42} +0.936426i q^{43} +0.936426i q^{44} +4.24621 q^{45} +(-1.56155 - 4.53448i) q^{46} +6.14441i q^{47} -0.936426i q^{48} +(-2.12311 - 6.67026i) q^{49} -1.00000 q^{50} -1.05171i q^{51} -3.33513i q^{52} -0.410574i q^{53} -4.79741i q^{54} +1.87285i q^{55} +(-1.56155 + 2.13578i) q^{56} +3.74571i q^{57} -2.00000 q^{58} +2.80928i q^{59} -1.87285i q^{60} -12.2462 q^{61} +9.06897i q^{62} +(-3.31534 + 4.53448i) q^{63} +1.00000 q^{64} -6.67026i q^{65} +0.876894 q^{66} +7.60669i q^{67} +1.12311 q^{68} +(-4.24621 + 1.46228i) q^{69} +(-3.12311 + 4.27156i) q^{70} -9.36932 q^{71} +2.12311 q^{72} -3.74571i q^{73} -3.33513i q^{74} +0.936426i q^{75} -4.00000 q^{76} +(-2.00000 - 1.46228i) q^{77} -3.12311 q^{78} -12.8147i q^{79} +2.00000 q^{80} +1.87689 q^{81} +6.67026i q^{82} -4.00000 q^{83} +(2.00000 + 1.46228i) q^{84} +2.24621 q^{85} +0.936426i q^{86} +1.87285i q^{87} +0.936426i q^{88} -2.00000 q^{89} +4.24621 q^{90} +(7.12311 + 5.20798i) q^{91} +(-1.56155 - 4.53448i) q^{92} +8.49242 q^{93} +6.14441i q^{94} -8.00000 q^{95} -0.936426i q^{96} +12.2462 q^{97} +(-2.12311 - 6.67026i) q^{98} +1.98813i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 8 q^{5} + 2 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 8 * q^5 + 2 * q^7 + 4 * q^8 - 8 * q^9	$ 4 q + 4 q^{2} + 4 q^{4} + 8 q^{5} + 2 q^{7} + 4 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{14} + 4 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{19} + 8 q^{20} + 8 q^{21} + 2 q^{23} - 4 q^{25} + 2 q^{28} - 8 q^{29} + 4 q^{32} + 20 q^{33} - 12 q^{34} + 4 q^{35} - 8 q^{36} - 16 q^{38} + 4 q^{39} + 8 q^{40} + 8 q^{42} - 16 q^{45} + 2 q^{46} + 8 q^{49} - 4 q^{50} + 2 q^{56} - 8 q^{58} - 16 q^{61} - 38 q^{63} + 4 q^{64} + 20 q^{66} - 12 q^{68} + 16 q^{69} + 4 q^{70} + 12 q^{71} - 8 q^{72} - 16 q^{76} - 8 q^{77} + 4 q^{78} + 8 q^{80} + 24 q^{81} - 16 q^{83} + 8 q^{84} - 24 q^{85} - 8 q^{89} - 16 q^{90} + 12 q^{91} + 2 q^{92} - 32 q^{93} - 32 q^{95} + 16 q^{97} + 8 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 8 * q^5 + 2 * q^7 + 4 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^14 + 4 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^19 + 8 * q^20 + 8 * q^21 + 2 * q^23 - 4 * q^25 + 2 * q^28 - 8 * q^29 + 4 * q^32 + 20 * q^33 - 12 * q^34 + 4 * q^35 - 8 * q^36 - 16 * q^38 + 4 * q^39 + 8 * q^40 + 8 * q^42 - 16 * q^45 + 2 * q^46 + 8 * q^49 - 4 * q^50 + 2 * q^56 - 8 * q^58 - 16 * q^61 - 38 * q^63 + 4 * q^64 + 20 * q^66 - 12 * q^68 + 16 * q^69 + 4 * q^70 + 12 * q^71 - 8 * q^72 - 16 * q^76 - 8 * q^77 + 4 * q^78 + 8 * q^80 + 24 * q^81 - 16 * q^83 + 8 * q^84 - 24 * q^85 - 8 * q^89 - 16 * q^90 + 12 * q^91 + 2 * q^92 - 32 * q^93 - 32 * q^95 + 16 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	0.936426i		−	0.540646i	−0.962770	−	0.270323i	$-0.912870\pi$
$3$		−	0.936426i		−	0.540646i	0.962770	−	0.270323i	$-0.0871305\pi$
$4$	1.00000			0.500000
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$		−	0.936426i		−	0.382294i
$7$	−1.56155	+	2.13578i	−0.590211	+	0.807249i
$7$	−1.56155	+	2.13578i	−0.590211	+	0.807249i
$8$	1.00000			0.353553
$9$	2.12311			0.707702
$10$	2.00000			0.632456
$11$			0.936426i			0.282343i	0.989985	+	0.141172i	$0.0450869\pi$
$11$			0.936426i			0.282343i	−0.989985	+	0.141172i	$0.954913\pi$
$12$		−	0.936426i		−	0.270323i
$13$		−	3.33513i		−	0.924999i	−0.886619	−	0.462500i	$-0.846953\pi$
$13$		−	3.33513i		−	0.924999i	0.886619	−	0.462500i	$-0.153047\pi$
$14$	−1.56155	+	2.13578i	−0.417343	+	0.570811i
$15$		−	1.87285i		−	0.483569i
$16$	1.00000			0.250000
$17$	1.12311			0.272393			0.136197	−	0.990682i	$-0.456512\pi$
$17$	1.12311			0.272393			0.136197	+	0.990682i	$0.456512\pi$
$18$	2.12311			0.500421
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	2.00000			0.447214
$21$	2.00000	+	1.46228i	0.436436	+	0.319095i
$22$			0.936426i			0.199647i
$23$	−1.56155	−	4.53448i	−0.325606	−	0.945505i
$23$	−1.56155	−	4.53448i	−0.325606	−	0.945505i
$24$		−	0.936426i		−	0.191147i
$25$	−1.00000			−0.200000
$26$		−	3.33513i		−	0.654073i
$27$		−	4.79741i		−	0.923262i
$28$	−1.56155	+	2.13578i	−0.295106	+	0.403624i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		−	1.87285i		−	0.341935i
$31$			9.06897i			1.62884i	0.580279	+	0.814418i	$0.302943\pi$
$31$			9.06897i			1.62884i	−0.580279	+	0.814418i	$0.697057\pi$
$32$	1.00000			0.176777
$33$	0.876894			0.152648
$34$	1.12311			0.192611
$35$	−3.12311	+	4.27156i	−0.527901	+	0.722025i
$36$	2.12311			0.353851
$37$		−	3.33513i		−	0.548292i	−0.961688	−	0.274146i	$-0.911605\pi$
$37$		−	3.33513i		−	0.548292i	0.961688	−	0.274146i	$-0.0883952\pi$
$38$	−4.00000			−0.648886
$39$	−3.12311			−0.500097
$40$	2.00000			0.316228
$41$			6.67026i			1.04172i	0.853642	+	0.520860i	$0.174389\pi$
$41$			6.67026i			1.04172i	−0.853642	+	0.520860i	$0.825611\pi$
$42$	2.00000	+	1.46228i	0.308607	+	0.225635i
$43$			0.936426i			0.142804i	0.997448	+	0.0714018i	$0.0227473\pi$
$43$			0.936426i			0.142804i	−0.997448	+	0.0714018i	$0.977253\pi$
$44$			0.936426i			0.141172i
$45$	4.24621			0.632988
$46$	−1.56155	−	4.53448i	−0.230238	−	0.668573i
$47$			6.14441i			0.896254i	0.893970	+	0.448127i	$0.147909\pi$
$47$			6.14441i			0.896254i	−0.893970	+	0.448127i	$0.852091\pi$
$48$		−	0.936426i		−	0.135162i
$49$	−2.12311	−	6.67026i	−0.303301	−	0.952895i
$50$	−1.00000			−0.141421
$51$		−	1.05171i		−	0.147268i
$52$		−	3.33513i		−	0.462500i
$53$		−	0.410574i		−	0.0563966i	−0.999602	−	0.0281983i	$-0.991023\pi$
$53$		−	0.410574i		−	0.0563966i	0.999602	−	0.0281983i	$-0.00897699\pi$
$54$		−	4.79741i		−	0.652845i
$55$			1.87285i			0.252535i
$56$	−1.56155	+	2.13578i	−0.208671	+	0.285406i
$57$			3.74571i			0.496131i
$58$	−2.00000			−0.262613
$59$			2.80928i			0.365737i	0.983137	+	0.182868i	$0.0585383\pi$
$59$			2.80928i			0.365737i	−0.983137	+	0.182868i	$0.941462\pi$
$60$		−	1.87285i		−	0.241784i
$61$	−12.2462			−1.56797			−0.783983	−	0.620782i	$-0.786815\pi$
$61$	−12.2462			−1.56797			−0.783983	+	0.620782i	$0.786815\pi$
$62$			9.06897i			1.15176i
$63$	−3.31534	+	4.53448i	−0.417694	+	0.571291i
$64$	1.00000			0.125000
$65$		−	6.67026i		−	0.827344i
$66$	0.876894			0.107938
$67$			7.60669i			0.929305i	0.885493	+	0.464653i	$0.153821\pi$
$67$			7.60669i			0.929305i	−0.885493	+	0.464653i	$0.846179\pi$
$68$	1.12311			0.136197
$69$	−4.24621	+	1.46228i	−0.511184	+	0.176038i
$70$	−3.12311	+	4.27156i	−0.373283	+	0.510549i
$71$	−9.36932			−1.11193			−0.555967	−	0.831205i	$-0.687652\pi$
$71$	−9.36932			−1.11193			−0.555967	+	0.831205i	$0.687652\pi$
$72$	2.12311			0.250210
$73$		−	3.74571i		−	0.438402i	−0.975680	−	0.219201i	$-0.929655\pi$
$73$		−	3.74571i		−	0.438402i	0.975680	−	0.219201i	$-0.0703450\pi$
$74$		−	3.33513i		−	0.387701i
$75$			0.936426i			0.108129i
$76$	−4.00000			−0.458831
$77$	−2.00000	−	1.46228i	−0.227921	−	0.166642i
$78$	−3.12311			−0.353622
$79$		−	12.8147i		−	1.44176i	−0.693058	−	0.720882i	$-0.743737\pi$
$79$		−	12.8147i		−	1.44176i	0.693058	−	0.720882i	$-0.256263\pi$
$80$	2.00000			0.223607
$81$	1.87689			0.208544
$82$			6.67026i			0.736607i
$83$	−4.00000			−0.439057			−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$	2.00000	+	1.46228i	0.218218	+	0.159548i
$85$	2.24621			0.243636
$86$			0.936426i			0.100977i
$87$			1.87285i			0.200791i
$88$			0.936426i			0.0998234i
$89$	−2.00000			−0.212000			−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000			−0.212000			−0.106000	+	0.994366i	$0.533804\pi$
$90$	4.24621			0.447590
$91$	7.12311	+	5.20798i	0.746704	+	0.545945i
$92$	−1.56155	−	4.53448i	−0.162803	−	0.472753i
$93$	8.49242			0.880623
$94$			6.14441i			0.633748i
$95$	−8.00000			−0.820783
$96$		−	0.936426i		−	0.0955736i
$97$	12.2462			1.24341			0.621707	−	0.783250i	$-0.286439\pi$
$97$	12.2462			1.24341			0.621707	+	0.783250i	$0.286439\pi$
$98$	−2.12311	−	6.67026i	−0.214466	−	0.673798i
$99$			1.98813i			0.199815i
$100$	−1.00000			−0.100000
$101$		−	10.0054i		−	0.995574i	−0.867299	−	0.497787i	$-0.834146\pi$
$101$		−	10.0054i		−	0.995574i	0.867299	−	0.497787i	$-0.165854\pi$
$102$		−	1.05171i		−	0.104134i
$103$	19.1231			1.88426			0.942128	−	0.335254i	$-0.108822\pi$
$103$	19.1231			1.88426			0.942128	+	0.335254i	$0.108822\pi$
$104$		−	3.33513i		−	0.327037i
$105$	4.00000	+	2.92456i	0.390360	+	0.285408i
$106$		−	0.410574i		−	0.0398784i
$107$		−	19.8955i		−	1.92337i	−0.274154	−	0.961686i	$-0.588398\pi$
$107$		−	19.8955i		−	1.92337i	0.274154	−	0.961686i	$-0.411602\pi$
$108$		−	4.79741i		−	0.461631i
$109$			6.25969i			0.599570i	0.954007	+	0.299785i	$0.0969149\pi$
$109$			6.25969i			0.599570i	−0.954007	+	0.299785i	$0.903085\pi$
$110$			1.87285i			0.178570i
$111$	−3.12311			−0.296432
$112$	−1.56155	+	2.13578i	−0.147553	+	0.201812i
$113$			13.3405i			1.25497i	0.778628	+	0.627486i	$0.215916\pi$
$113$			13.3405i			1.25497i	−0.778628	+	0.627486i	$0.784084\pi$
$114$			3.74571i			0.350817i
$115$	−3.12311	−	9.06897i	−0.291231	−	0.845686i
$116$	−2.00000			−0.185695
$117$		−	7.08084i		−	0.654624i
$118$			2.80928i			0.258615i
$119$	−1.75379	+	2.39871i	−0.160770	+	0.219889i
$120$		−	1.87285i		−	0.170967i
$121$	10.1231			0.920282
$122$	−12.2462			−1.10872
$123$	6.24621			0.563202
$124$			9.06897i			0.814418i
$125$	−12.0000			−1.07331
$126$	−3.31534	+	4.53448i	−0.295354	+	0.403964i
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	1.00000			0.0883883
$129$	0.876894			0.0772062
$130$		−	6.67026i		−	0.585021i
$131$		−	0.936426i		−	0.0818160i	−0.999163	−	0.0409080i	$-0.986975\pi$
$131$		−	0.936426i		−	0.0818160i	0.999163	−	0.0409080i	$-0.0130250\pi$
$132$	0.876894			0.0763239
$133$	6.24621	−	8.54312i	0.541615	−	0.740782i
$134$			7.60669i			0.657118i
$135$		−	9.59482i		−	0.825791i
$136$	1.12311			0.0963055
$137$			14.1617i			1.20991i	0.796258	+	0.604957i	$0.206810\pi$
$137$			14.1617i			1.20991i	−0.796258	+	0.604957i	$0.793190\pi$
$138$	−4.24621	+	1.46228i	−0.361462	+	0.124477i
$139$		−	4.68213i		−	0.397133i	−0.980087	−	0.198567i	$-0.936371\pi$
$139$		−	4.68213i		−	0.397133i	0.980087	−	0.198567i	$-0.0636286\pi$
$140$	−3.12311	+	4.27156i	−0.263951	+	0.361013i
$141$	5.75379			0.484556
$142$	−9.36932			−0.786256
$143$	3.12311			0.261167
$144$	2.12311			0.176925
$145$	−4.00000			−0.332182
$146$		−	3.74571i		−	0.309997i
$147$	−6.24621	+	1.98813i	−0.515179	+	0.163978i
$148$		−	3.33513i		−	0.274146i
$149$		−	6.25969i		−	0.512814i	−0.966569	−	0.256407i	$-0.917461\pi$
$149$		−	6.25969i		−	0.512814i	0.966569	−	0.256407i	$-0.0825387\pi$
$150$			0.936426i			0.0764589i
$151$	−3.12311			−0.254155			−0.127077	−	0.991893i	$-0.540560\pi$
$151$	−3.12311			−0.254155			−0.127077	+	0.991893i	$0.540560\pi$
$152$	−4.00000			−0.324443
$153$	2.38447			0.192773
$154$	−2.00000	−	1.46228i	−0.161165	−	0.117834i
$155$			18.1379i			1.45687i
$156$	−3.12311			−0.250049
$157$	10.0000			0.798087			0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000			0.798087			0.399043	+	0.916932i	$0.369342\pi$
$158$		−	12.8147i		−	1.01948i
$159$	−0.384472			−0.0304906
$160$	2.00000			0.158114
$161$	12.1231	+	3.74571i	0.955435	+	0.295203i
$162$	1.87689			0.147463
$163$	16.4924			1.29179			0.645893	−	0.763428i	$-0.276485\pi$
$163$	16.4924			1.29179			0.645893	+	0.763428i	$0.276485\pi$
$164$			6.67026i			0.520860i
$165$	1.75379			0.136532
$166$	−4.00000			−0.310460
$167$			9.89012i			0.765320i	0.923889	+	0.382660i	$0.124992\pi$
$167$			9.89012i			0.765320i	−0.923889	+	0.382660i	$0.875008\pi$
$168$	2.00000	+	1.46228i	0.154303	+	0.112817i
$169$	1.87689			0.144376
$170$	2.24621			0.172277
$171$	−8.49242			−0.649432
$172$			0.936426i			0.0714018i
$173$		−	13.7511i		−	1.04548i	−0.852493	−	0.522738i	$-0.824910\pi$
$173$		−	13.7511i		−	1.04548i	0.852493	−	0.522738i	$-0.175090\pi$
$174$			1.87285i			0.141981i
$175$	1.56155	−	2.13578i	0.118042	−	0.161450i
$176$			0.936426i			0.0705858i
$177$	2.63068			0.197734
$178$	−2.00000			−0.149906
$179$	−2.24621			−0.167890			−0.0839449	−	0.996470i	$-0.526752\pi$
$179$	−2.24621			−0.167890			−0.0839449	+	0.996470i	$0.526752\pi$
$180$	4.24621			0.316494
$181$	8.24621			0.612936			0.306468	−	0.951881i	$-0.400853\pi$
$181$	8.24621			0.612936			0.306468	+	0.951881i	$0.400853\pi$
$182$	7.12311	+	5.20798i	0.528000	+	0.386042i
$183$			11.4677i			0.847715i
$184$	−1.56155	−	4.53448i	−0.115119	−	0.334287i
$185$		−	6.67026i		−	0.490408i
$186$	8.49242			0.622695
$187$			1.05171i			0.0769083i
$188$			6.14441i			0.448127i
$189$	10.2462	+	7.49141i	0.745302	+	0.544920i
$190$	−8.00000			−0.580381
$191$		−	5.32326i		−	0.385178i	−0.981280	−	0.192589i	$-0.938312\pi$
$191$		−	5.32326i		−	0.385178i	0.981280	−	0.192589i	$-0.0616884\pi$
$192$		−	0.936426i		−	0.0675808i
$193$	19.3693			1.39423			0.697117	−	0.716957i	$-0.254466\pi$
$193$	19.3693			1.39423			0.697117	+	0.716957i	$0.254466\pi$
$194$	12.2462			0.879227
$195$	−6.24621			−0.447300
$196$	−2.12311	−	6.67026i	−0.151650	−	0.476447i
$197$	−3.75379			−0.267446			−0.133723	−	0.991019i	$-0.542693\pi$
$197$	−3.75379			−0.267446			−0.133723	+	0.991019i	$0.542693\pi$
$198$			1.98813i			0.141290i
$199$	−20.4924			−1.45267			−0.726335	−	0.687341i	$-0.758778\pi$
$199$	−20.4924			−1.45267			−0.726335	+	0.687341i	$0.758778\pi$
$200$	−1.00000			−0.0707107
$201$	7.12311			0.502425
$202$		−	10.0054i		−	0.703977i
$203$	3.12311	−	4.27156i	0.219199	−	0.299805i
$204$		−	1.05171i		−	0.0736341i
$205$			13.3405i			0.931743i
$206$	19.1231			1.33237
$207$	−3.31534	−	9.62719i	−0.230432	−	0.669136i
$208$		−	3.33513i		−	0.231250i
$209$		−	3.74571i		−	0.259096i
$210$	4.00000	+	2.92456i	0.276026	+	0.201814i
$211$	10.2462			0.705378			0.352689	−	0.935741i	$-0.385267\pi$
$211$	10.2462			0.705378			0.352689	+	0.935741i	$0.385267\pi$
$212$		−	0.410574i		−	0.0281983i
$213$			8.77368i			0.601162i
$214$		−	19.8955i		−	1.36003i
$215$			1.87285i			0.127727i
$216$		−	4.79741i		−	0.326422i
$217$	−19.3693	−	14.1617i	−1.31487	−	0.961357i
$218$			6.25969i			0.423960i
$219$	−3.50758			−0.237020
$220$			1.87285i			0.126268i
$221$		−	3.74571i		−	0.251963i
$222$	−3.12311			−0.209609
$223$		−	28.0281i		−	1.87690i	−0.345419	−	0.938449i	$-0.612263\pi$
$223$		−	28.0281i		−	1.87690i	0.345419	−	0.938449i	$-0.387737\pi$
$224$	−1.56155	+	2.13578i	−0.104336	+	0.142703i
$225$	−2.12311			−0.141540
$226$			13.3405i			0.887399i
$227$	−10.2462			−0.680065			−0.340032	−	0.940414i	$-0.610438\pi$
$227$	−10.2462			−0.680065			−0.340032	+	0.940414i	$0.610438\pi$
$228$			3.74571i			0.248065i
$229$	24.2462			1.60223			0.801117	−	0.598507i	$-0.204239\pi$
$229$	24.2462			1.60223			0.801117	+	0.598507i	$0.204239\pi$
$230$	−3.12311	−	9.06897i	−0.205931	−	0.597990i
$231$	−1.36932	+	1.87285i	−0.0900944	+	0.123225i
$232$	−2.00000			−0.131306
$233$	0.246211			0.0161298			0.00806492	−	0.999967i	$-0.497433\pi$
$233$	0.246211			0.0161298			0.00806492	+	0.999967i	$0.497433\pi$
$234$		−	7.08084i		−	0.462889i
$235$			12.2888i			0.801634i
$236$			2.80928i			0.182868i
$237$	−12.0000			−0.779484
$238$	−1.75379	+	2.39871i	−0.113681	+	0.155485i
$239$	−23.6155			−1.52756			−0.763781	−	0.645476i	$-0.776659\pi$
$239$	−23.6155			−1.52756			−0.763781	+	0.645476i	$0.776659\pi$
$240$		−	1.87285i		−	0.120892i
$241$	−3.75379			−0.241803			−0.120901	−	0.992665i	$-0.538578\pi$
$241$	−3.75379			−0.241803			−0.120901	+	0.992665i	$0.538578\pi$
$242$	10.1231			0.650738
$243$		−	16.1498i		−	1.03601i
$244$	−12.2462			−0.783983
$245$	−4.24621	−	13.3405i	−0.271280	−	0.852295i
$246$	6.24621			0.398244
$247$			13.3405i			0.848837i
$248$			9.06897i			0.575880i
$249$			3.74571i			0.237374i
$250$	−12.0000			−0.758947
$251$	22.7386			1.43525			0.717625	−	0.696430i	$-0.245229\pi$
$251$	22.7386			1.43525			0.717625	+	0.696430i	$0.245229\pi$
$252$	−3.31534	+	4.53448i	−0.208847	+	0.285646i
$253$	4.24621	−	1.46228i	0.266957	−	0.0919327i
$254$		0			0
$255$		−	2.10341i		−	0.131721i
$256$	1.00000			0.0625000
$257$			20.8319i			1.29946i	0.760165	+	0.649730i	$0.225118\pi$
$257$			20.8319i			1.29946i	−0.760165	+	0.649730i	$0.774882\pi$
$258$	0.876894			0.0545931
$259$	7.12311	+	5.20798i	0.442608	+	0.323608i
$260$		−	6.67026i		−	0.413672i
$261$	−4.24621			−0.262834
$262$		−	0.936426i		−	0.0578526i
$263$		−	6.14441i		−	0.378881i	−0.981892	−	0.189440i	$-0.939333\pi$
$263$		−	6.14441i		−	0.378881i	0.981892	−	0.189440i	$-0.0606674\pi$
$264$	0.876894			0.0539691
$265$		−	0.821147i		−	0.0504427i
$266$	6.24621	−	8.54312i	0.382980	−	0.523812i
$267$			1.87285i			0.114617i
$268$			7.60669i			0.464653i
$269$			17.4968i			1.06680i	0.845863	+	0.533400i	$0.179086\pi$
$269$			17.4968i			1.06680i	−0.845863	+	0.533400i	$0.820914\pi$
$270$		−	9.59482i		−	0.583922i
$271$		−	4.27156i		−	0.259479i	−0.991548	−	0.129739i	$-0.958586\pi$
$271$		−	4.27156i		−	0.259479i	0.991548	−	0.129739i	$-0.0414141\pi$
$272$	1.12311			0.0680983
$273$	4.87689	−	6.67026i	0.295163	−	0.403703i
$274$			14.1617i			0.855538i
$275$		−	0.936426i		−	0.0564686i
$276$	−4.24621	+	1.46228i	−0.255592	+	0.0880189i
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$		−	4.68213i		−	0.280816i
$279$			19.2544i			1.15273i
$280$	−3.12311	+	4.27156i	−0.186641	+	0.255274i
$281$			17.0862i			1.01928i	0.860388	+	0.509640i	$0.170221\pi$
$281$			17.0862i			1.01928i	−0.860388	+	0.509640i	$0.829779\pi$
$282$	5.75379			0.342633
$283$	20.0000			1.18888			0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000			1.18888			0.594438	+	0.804141i	$0.297374\pi$
$284$	−9.36932			−0.555967
$285$			7.49141i			0.443753i
$286$	3.12311			0.184673
$287$	−14.2462	−	10.4160i	−0.840927	−	0.614835i
$288$	2.12311			0.125105
$289$	−15.7386			−0.925802
$290$	−4.00000			−0.234888
$291$		−	11.4677i		−	0.672247i
$292$		−	3.74571i		−	0.219201i
$293$	14.4924			0.846656			0.423328	−	0.905976i	$-0.360862\pi$
$293$	14.4924			0.846656			0.423328	+	0.905976i	$0.360862\pi$
$294$	−6.24621	+	1.98813i	−0.364286	+	0.115950i
$295$			5.61856i			0.327125i
$296$		−	3.33513i		−	0.193851i
$297$	4.49242			0.260677
$298$		−	6.25969i		−	0.362614i
$299$	−15.1231	+	5.20798i	−0.874592	+	0.301186i
$300$			0.936426i			0.0540646i
$301$	−2.00000	−	1.46228i	−0.115278	−	0.0842844i
$302$	−3.12311			−0.179715
$303$	−9.36932			−0.538253
$304$	−4.00000			−0.229416
$305$	−24.4924			−1.40243
$306$	2.38447			0.136311
$307$			1.98813i			0.113469i	0.998389	+	0.0567343i	$0.0180688\pi$
$307$			1.98813i			0.113469i	−0.998389	+	0.0567343i	$0.981931\pi$
$308$	−2.00000	−	1.46228i	−0.113961	−	0.0833211i
$309$		−	17.9074i		−	1.01872i
$310$			18.1379i			1.03017i
$311$			23.2306i			1.31729i	0.752454	+	0.658645i	$0.228870\pi$
$311$			23.2306i			1.31729i	−0.752454	+	0.658645i	$0.771130\pi$
$312$	−3.12311			−0.176811
$313$	−14.4924			−0.819160			−0.409580	−	0.912274i	$-0.634325\pi$
$313$	−14.4924			−0.819160			−0.409580	+	0.912274i	$0.634325\pi$
$314$	10.0000			0.564333
$315$	−6.63068	+	9.06897i	−0.373597	+	0.510979i
$316$		−	12.8147i		−	0.720882i
$317$	−24.2462			−1.36180			−0.680901	−	0.732375i	$-0.738412\pi$
$317$	−24.2462			−1.36180			−0.680901	+	0.732375i	$0.738412\pi$
$318$	−0.384472			−0.0215601
$319$		−	1.87285i		−	0.104860i
$320$	2.00000			0.111803
$321$	−18.6307			−1.03986
$322$	12.1231	+	3.74571i	0.675594	+	0.208740i
$323$	−4.49242			−0.249965
$324$	1.87689			0.104272
$325$			3.33513i			0.185000i
$326$	16.4924			0.913431
$327$	5.86174			0.324155
$328$			6.67026i			0.368304i
$329$	−13.1231	−	9.59482i	−0.723500	−	0.528980i
$330$	1.75379			0.0965429
$331$	2.24621			0.123463			0.0617315	−	0.998093i	$-0.480338\pi$
$331$	2.24621			0.123463			0.0617315	+	0.998093i	$0.480338\pi$
$332$	−4.00000			−0.219529
$333$		−	7.08084i		−	0.388028i
$334$			9.89012i			0.541163i
$335$			15.2134i			0.831196i
$336$	2.00000	+	1.46228i	0.109109	+	0.0797739i
$337$		−	34.1725i		−	1.86149i	−0.365665	−	0.930746i	$-0.619158\pi$
$337$		−	34.1725i		−	1.86149i	0.365665	−	0.930746i	$-0.380842\pi$
$338$	1.87689			0.102090
$339$	12.4924			0.678495
$340$	2.24621			0.121818
$341$	−8.49242			−0.459890
$342$	−8.49242			−0.459218
$343$	17.5616	+	5.88148i	0.948235	+	0.317570i
$344$			0.936426i			0.0504887i
$345$	−8.49242	+	2.92456i	−0.457217	+	0.157453i
$346$		−	13.7511i		−	0.739264i
$347$	−16.4924			−0.885360			−0.442680	−	0.896680i	$-0.645972\pi$
$347$	−16.4924			−0.885360			−0.442680	+	0.896680i	$0.645972\pi$
$348$			1.87285i			0.100395i
$349$			30.8373i			1.65068i	0.564633	+	0.825342i	$0.309018\pi$
$349$			30.8373i			1.65068i	−0.564633	+	0.825342i	$0.690982\pi$
$350$	1.56155	−	2.13578i	0.0834685	−	0.114162i
$351$	−16.0000			−0.854017
$352$			0.936426i			0.0499117i
$353$		−	26.6811i		−	1.42009i	−0.704157	−	0.710045i	$-0.748675\pi$
$353$		−	26.6811i		−	1.42009i	0.704157	−	0.710045i	$-0.251325\pi$
$354$	2.63068			0.139819
$355$	−18.7386			−0.994543
$356$	−2.00000			−0.106000
$357$	2.24621	+	1.64229i	0.118882	+	0.0869194i
$358$	−2.24621			−0.118716
$359$		−	11.9935i		−	0.632994i	−0.948593	−	0.316497i	$-0.897493\pi$
$359$		−	11.9935i		−	0.632994i	0.948593	−	0.316497i	$-0.102507\pi$
$360$	4.24621			0.223795
$361$	−3.00000			−0.157895
$362$	8.24621			0.433411
$363$		−	9.47954i		−	0.497547i
$364$	7.12311	+	5.20798i	0.373352	+	0.272973i
$365$		−	7.49141i		−	0.392118i
$366$			11.4677i			0.599425i
$367$	−11.1231			−0.580621			−0.290311	−	0.956932i	$-0.593759\pi$
$367$	−11.1231			−0.580621			−0.290311	+	0.956932i	$0.593759\pi$
$368$	−1.56155	−	4.53448i	−0.0814016	−	0.236376i
$369$			14.1617i			0.737227i
$370$		−	6.67026i		−	0.346771i
$371$	0.876894	+	0.641132i	0.0455261	+	0.0332859i
$372$	8.49242			0.440312
$373$			36.6865i			1.89955i	0.312930	+	0.949776i	$0.398690\pi$
$373$			36.6865i			1.89955i	−0.312930	+	0.949776i	$0.601310\pi$
$374$			1.05171i			0.0543824i
$375$			11.2371i			0.580282i
$376$			6.14441i			0.316874i
$377$			6.67026i			0.343536i
$378$	10.2462	+	7.49141i	0.527008	+	0.385317i
$379$		−	1.98813i		−	0.102123i	−0.998695	−	0.0510617i	$-0.983739\pi$
$379$		−	1.98813i		−	0.102123i	0.998695	−	0.0510617i	$-0.0162605\pi$
$380$	−8.00000			−0.410391
$381$		0			0
$382$		−	5.32326i		−	0.272362i
$383$	−27.1231			−1.38593			−0.692963	−	0.720973i	$-0.743695\pi$
$383$	−27.1231			−1.38593			−0.692963	+	0.720973i	$0.743695\pi$
$384$		−	0.936426i		−	0.0477868i
$385$	−4.00000	−	2.92456i	−0.203859	−	0.149049i
$386$	19.3693			0.985872
$387$			1.98813i			0.101062i
$388$	12.2462			0.621707
$389$			23.3459i			1.18369i	0.806054	+	0.591843i	$0.201599\pi$
$389$			23.3459i			1.18369i	−0.806054	+	0.591843i	$0.798401\pi$
$390$	−6.24621			−0.316289
$391$	−1.75379	−	5.09271i	−0.0886929	−	0.257549i
$392$	−2.12311	−	6.67026i	−0.107233	−	0.336899i
$393$	−0.876894			−0.0442335
$394$	−3.75379			−0.189113
$395$		−	25.6294i		−	1.28955i
$396$			1.98813i			0.0999074i
$397$		−	19.6002i		−	0.983707i	−0.870678	−	0.491853i	$-0.836320\pi$
$397$		−	19.6002i		−	0.983707i	0.870678	−	0.491853i	$-0.163680\pi$
$398$	−20.4924			−1.02719
$399$	−8.00000	−	5.84912i	−0.400501	−	0.292822i
$400$	−1.00000			−0.0500000
$401$			2.92456i			0.146045i	0.997330	+	0.0730227i	$0.0232646\pi$
$401$			2.92456i			0.146045i	−0.997330	+	0.0730227i	$0.976735\pi$
$402$	7.12311			0.355268
$403$	30.2462			1.50667
$404$		−	10.0054i		−	0.497787i
$405$	3.75379			0.186527
$406$	3.12311	−	4.27156i	0.154997	−	0.211994i
$407$	3.12311			0.154807
$408$		−	1.05171i		−	0.0520672i
$409$		−	6.67026i		−	0.329823i	−0.986308	−	0.164912i	$-0.947266\pi$
$409$		−	6.67026i		−	0.329823i	0.986308	−	0.164912i	$-0.0527339\pi$
$410$			13.3405i			0.658842i
$411$	13.2614			0.654135
$412$	19.1231			0.942128
$413$	−6.00000	−	4.38684i	−0.295241	−	0.215862i
$414$	−3.31534	−	9.62719i	−0.162940	−	0.473151i
$415$	−8.00000			−0.392705
$416$		−	3.33513i		−	0.163518i
$417$	−4.38447			−0.214709
$418$		−	3.74571i		−	0.183208i
$419$	24.4924			1.19653			0.598267	−	0.801297i	$-0.295856\pi$
$419$	24.4924			1.19653			0.598267	+	0.801297i	$0.295856\pi$
$420$	4.00000	+	2.92456i	0.195180	+	0.142704i
$421$		−	19.6002i		−	0.955256i	−0.878562	−	0.477628i	$-0.841497\pi$
$421$		−	19.6002i		−	0.955256i	0.878562	−	0.477628i	$-0.158503\pi$
$422$	10.2462			0.498778
$423$			13.0452i			0.634281i
$424$		−	0.410574i		−	0.0199392i
$425$	−1.12311			−0.0544786
$426$			8.77368i			0.425086i
$427$	19.1231	−	26.1552i	0.925432	−	1.26574i
$428$		−	19.8955i		−	0.961686i
$429$		−	2.92456i		−	0.141199i
$430$			1.87285i			0.0903170i
$431$			24.2824i			1.16964i	0.811163	+	0.584820i	$0.198835\pi$
$431$			24.2824i			1.16964i	−0.811163	+	0.584820i	$0.801165\pi$
$432$		−	4.79741i		−	0.230816i
$433$	13.6155			0.654321			0.327160	−	0.944969i	$-0.393908\pi$
$433$	13.6155			0.654321			0.327160	+	0.944969i	$0.393908\pi$
$434$	−19.3693	−	14.1617i	−0.929757	−	0.679782i
$435$			3.74571i			0.179593i
$436$			6.25969i			0.299785i
$437$	6.24621	+	18.1379i	0.298797	+	0.867655i
$438$	−3.50758			−0.167599
$439$			18.6638i			0.890774i	0.895338	+	0.445387i	$0.146934\pi$
$439$			18.6638i			0.890774i	−0.895338	+	0.445387i	$0.853066\pi$
$440$			1.87285i			0.0892848i
$441$	−4.50758	−	14.1617i	−0.214647	−	0.674365i
$442$		−	3.74571i		−	0.178165i
$443$	40.4924			1.92385			0.961927	−	0.273308i	$-0.0881179\pi$
$443$	40.4924			1.92385			0.961927	+	0.273308i	$0.0881179\pi$
$444$	−3.12311			−0.148216
$445$	−4.00000			−0.189618
$446$		−	28.0281i		−	1.32717i
$447$	−5.86174			−0.277251
$448$	−1.56155	+	2.13578i	−0.0737764	+	0.100906i
$449$	6.87689			0.324541			0.162270	−	0.986746i	$-0.448118\pi$
$449$	6.87689			0.324541			0.162270	+	0.986746i	$0.448118\pi$
$450$	−2.12311			−0.100084
$451$	−6.24621			−0.294123
$452$			13.3405i			0.627486i
$453$			2.92456i			0.137408i
$454$	−10.2462			−0.480879
$455$	14.2462	+	10.4160i	0.667873	+	0.488308i
$456$			3.74571i			0.175409i
$457$			25.8599i			1.20968i	0.796349	+	0.604838i	$0.206762\pi$
$457$			25.8599i			1.20968i	−0.796349	+	0.604838i	$0.793238\pi$
$458$	24.2462			1.13295
$459$		−	5.38800i		−	0.251490i
$460$	−3.12311	−	9.06897i	−0.145616	−	0.422843i
$461$		−	24.1671i		−	1.12557i	−0.826602	−	0.562786i	$-0.809729\pi$
$461$		−	24.1671i		−	1.12557i	0.826602	−	0.562786i	$-0.190271\pi$
$462$	−1.36932	+	1.87285i	−0.0637064	+	0.0871330i
$463$	33.3693			1.55080			0.775402	−	0.631468i	$-0.217547\pi$
$463$	33.3693			1.55080			0.775402	+	0.631468i	$0.217547\pi$
$464$	−2.00000			−0.0928477
$465$	16.9848			0.787653
$466$	0.246211			0.0114055
$467$	40.4924			1.87377			0.936883	−	0.349643i	$-0.113697\pi$
$467$	40.4924			1.87377			0.936883	+	0.349643i	$0.113697\pi$
$468$		−	7.08084i		−	0.327312i
$469$	−16.2462	−	11.8782i	−0.750180	−	0.548487i
$470$			12.2888i			0.566841i
$471$		−	9.36426i		−	0.431483i
$472$			2.80928i			0.129308i
$473$	−0.876894			−0.0403196
$474$	−12.0000			−0.551178
$475$	4.00000			0.183533
$476$	−1.75379	+	2.39871i	−0.0803848	+	0.109944i
$477$		−	0.871691i		−	0.0399120i
$478$	−23.6155			−1.08015
$479$	4.87689			0.222831			0.111415	−	0.993774i	$-0.464462\pi$
$479$	4.87689			0.222831			0.111415	+	0.993774i	$0.464462\pi$
$480$		−	1.87285i		−	0.0854836i
$481$	−11.1231			−0.507170
$482$	−3.75379			−0.170980
$483$	3.50758	−	11.3524i	0.159600	−	0.516552i
$484$	10.1231			0.460141
$485$	24.4924			1.11214
$486$		−	16.1498i		−	0.732570i
$487$	−4.49242			−0.203571			−0.101786	−	0.994806i	$-0.532456\pi$
$487$	−4.49242			−0.203571			−0.101786	+	0.994806i	$0.532456\pi$
$488$	−12.2462			−0.554360
$489$		−	15.4439i		−	0.698399i
$490$	−4.24621	−	13.3405i	−0.191824	−	0.602664i
$491$	14.7386			0.665145			0.332573	−	0.943078i	$-0.392083\pi$
$491$	14.7386			0.665145			0.332573	+	0.943078i	$0.392083\pi$
$492$	6.24621			0.281601
$493$	−2.24621			−0.101164
$494$			13.3405i			0.600219i
$495$			3.97626i			0.178720i
$496$			9.06897i			0.407209i
$497$	14.6307	−	20.0108i	0.656276	−	0.897607i
$498$			3.74571i			0.167849i
$499$	7.50758			0.336085			0.168043	−	0.985780i	$-0.446255\pi$
$499$	7.50758			0.336085			0.168043	+	0.985780i	$0.446255\pi$
$500$	−12.0000			−0.536656
$501$	9.26137			0.413767
$502$	22.7386			1.01487
$503$	−31.6155			−1.40967			−0.704833	−	0.709373i	$-0.748978\pi$
$503$	−31.6155			−1.40967			−0.704833	+	0.709373i	$0.748978\pi$
$504$	−3.31534	+	4.53448i	−0.147677	+	0.201982i
$505$		−	20.0108i		−	0.890469i
$506$	4.24621	−	1.46228i	0.188767	−	0.0650062i
$507$		−	1.75757i		−	0.0780566i
$508$		0			0
$509$		−	16.6757i		−	0.739136i	−0.929204	−	0.369568i	$-0.879506\pi$
$509$		−	16.6757i		−	0.739136i	0.929204	−	0.369568i	$-0.120494\pi$
$510$		−	2.10341i		−	0.0931406i
$511$	8.00000	+	5.84912i	0.353899	+	0.258750i
$512$	1.00000			0.0441942
$513$			19.1896i			0.847244i
$514$			20.8319i			0.918857i
$515$	38.2462			1.68533
$516$	0.876894			0.0386031
$517$	−5.75379			−0.253051
$518$	7.12311	+	5.20798i	0.312971	+	0.228826i
$519$	−12.8769			−0.565233
$520$		−	6.67026i		−	0.292510i
$521$	−3.36932			−0.147612			−0.0738062	−	0.997273i	$-0.523515\pi$
$521$	−3.36932			−0.147612			−0.0738062	+	0.997273i	$0.523515\pi$
$522$	−4.24621			−0.185852
$523$	16.4924			0.721163			0.360582	−	0.932728i	$-0.382578\pi$
$523$	16.4924			0.721163			0.360582	+	0.932728i	$0.382578\pi$
$524$		−	0.936426i		−	0.0409080i
$525$	−2.00000	−	1.46228i	−0.0872872	−	0.0638191i
$526$		−	6.14441i		−	0.267909i
$527$			10.1854i			0.443683i
$528$	0.876894			0.0381619
$529$	−18.1231	+	14.1617i	−0.787961	+	0.615725i
$530$		−	0.821147i		−	0.0356683i
$531$			5.96440i			0.258833i
$532$	6.24621	−	8.54312i	0.270808	−	0.370391i
$533$	22.2462			0.963590
$534$			1.87285i			0.0810463i
$535$		−	39.7910i		−	1.72032i
$536$			7.60669i			0.328559i
$537$			2.10341i			0.0907689i
$538$			17.4968i			0.754341i
$539$	6.24621	−	1.98813i	0.269043	−	0.0856349i
$540$		−	9.59482i		−	0.412895i
$541$	−36.7386			−1.57952			−0.789759	−	0.613418i	$-0.789794\pi$
$541$	−36.7386			−1.57952			−0.789759	+	0.613418i	$0.789794\pi$
$542$		−	4.27156i		−	0.183479i
$543$		−	7.72197i		−	0.331381i
$544$	1.12311			0.0481528
$545$			12.5194i			0.536271i
$546$	4.87689	−	6.67026i	0.208712	−	0.285461i
$547$	16.4924			0.705165			0.352583	−	0.935781i	$-0.385304\pi$
$547$	16.4924			0.705165			0.352583	+	0.935781i	$0.385304\pi$
$548$			14.1617i			0.604957i
$549$	−26.0000			−1.10965
$550$		−	0.936426i		−	0.0399294i
$551$	8.00000			0.340811
$552$	−4.24621	+	1.46228i	−0.180731	+	0.0622387i
$553$	27.3693	+	20.0108i	1.16386	+	0.850945i
$554$	−10.0000			−0.424859
$555$	−6.24621			−0.265137
$556$		−	4.68213i		−	0.198567i
$557$			43.3567i			1.83708i	0.395325	+	0.918542i	$0.370632\pi$
$557$			43.3567i			1.83708i	−0.395325	+	0.918542i	$0.629368\pi$
$558$			19.2544i			0.815103i
$559$	3.12311			0.132093
$560$	−3.12311	+	4.27156i	−0.131975	+	0.180506i
$561$	0.984845			0.0415802
$562$			17.0862i			0.720739i
$563$	−6.73863			−0.284000			−0.142000	−	0.989867i	$-0.545353\pi$
$563$	−6.73863			−0.284000			−0.142000	+	0.989867i	$0.545353\pi$
$564$	5.75379			0.242278
$565$			26.6811i			1.12248i
$566$	20.0000			0.840663
$567$	−2.93087	+	4.00863i	−0.123085	+	0.168347i
$568$	−9.36932			−0.393128
$569$			6.67026i			0.279632i	0.990178	+	0.139816i	$0.0446511\pi$
$569$			6.67026i			0.279632i	−0.990178	+	0.139816i	$0.955349\pi$
$570$			7.49141i			0.313781i
$571$			3.86098i			0.161577i	0.996731	+	0.0807886i	$0.0257439\pi$
$571$			3.86098i			0.161577i	−0.996731	+	0.0807886i	$0.974256\pi$
$572$	3.12311			0.130584
$573$	−4.98485			−0.208245
$574$	−14.2462	−	10.4160i	−0.594625	−	0.434754i
$575$	1.56155	+	4.53448i	0.0651213	+	0.189101i
$576$	2.12311			0.0884627
$577$			41.6639i			1.73449i	0.497882	+	0.867245i	$0.334111\pi$
$577$			41.6639i			1.73449i	−0.497882	+	0.867245i	$0.665889\pi$
$578$	−15.7386			−0.654641
$579$		−	18.1379i		−	0.753787i
$580$	−4.00000			−0.166091
$581$	6.24621	−	8.54312i	0.259137	−	0.354428i
$582$		−	11.4677i		−	0.475350i
$583$	0.384472			0.0159232
$584$		−	3.74571i		−	0.154998i
$585$		−	14.1617i		−	0.585513i
$586$	14.4924			0.598676
$587$		−	41.7792i		−	1.72441i	−0.506559	−	0.862205i	$-0.669083\pi$
$587$		−	41.7792i		−	1.72441i	0.506559	−	0.862205i	$-0.330917\pi$
$588$	−6.24621	+	1.98813i	−0.257589	+	0.0819892i
$589$		−	36.2759i		−	1.49472i
$590$			5.61856i			0.231312i
$591$			3.51515i			0.144594i
$592$		−	3.33513i		−	0.137073i
$593$		−	7.49141i		−	0.307635i	−0.988099	−	0.153818i	$-0.950843\pi$
$593$		−	7.49141i		−	0.307635i	0.988099	−	0.153818i	$-0.0491568\pi$
$594$	4.49242			0.184326
$595$	−3.50758	+	4.79741i	−0.143797	+	0.196675i
$596$		−	6.25969i		−	0.256407i
$597$			19.1896i			0.785380i
$598$	−15.1231	+	5.20798i	−0.618430	+	0.212970i
$599$	−20.4924			−0.837298			−0.418649	−	0.908148i	$-0.637496\pi$
$599$	−20.4924			−0.837298			−0.418649	+	0.908148i	$0.637496\pi$
$600$			0.936426i			0.0382294i
$601$		−	2.10341i		−	0.0857999i	−0.999079	−	0.0429000i	$-0.986340\pi$
$601$		−	2.10341i		−	0.0857999i	0.999079	−	0.0429000i	$-0.0136597\pi$
$602$	−2.00000	−	1.46228i	−0.0815139	−	0.0595981i
$603$			16.1498i			0.657671i
$604$	−3.12311			−0.127077
$605$	20.2462			0.823126
$606$	−9.36932			−0.380602
$607$		−	7.19612i		−	0.292081i	−0.989279	−	0.146041i	$-0.953347\pi$
$607$		−	7.19612i		−	0.292081i	0.989279	−	0.146041i	$-0.0466530\pi$
$608$	−4.00000			−0.162221
$609$	−4.00000	−	2.92456i	−0.162088	−	0.118509i
$610$	−24.4924			−0.991669
$611$	20.4924			0.829035
$612$	2.38447			0.0963866
$613$		−	24.1671i		−	0.976099i	−0.872816	−	0.488049i	$-0.837709\pi$
$613$		−	24.1671i		−	0.976099i	0.872816	−	0.488049i	$-0.162291\pi$
$614$			1.98813i			0.0802345i
$615$	12.4924			0.503743
$616$	−2.00000	−	1.46228i	−0.0805823	−	0.0589169i
$617$		−	17.0862i		−	0.687866i	−0.938994	−	0.343933i	$-0.888241\pi$
$617$		−	17.0862i		−	0.687866i	0.938994	−	0.343933i	$-0.111759\pi$
$618$		−	17.9074i		−	0.720340i
$619$	−5.75379			−0.231264			−0.115632	−	0.993292i	$-0.536889\pi$
$619$	−5.75379			−0.231264			−0.115632	+	0.993292i	$0.536889\pi$
$620$			18.1379i			0.728437i
$621$	−21.7538	+	7.49141i	−0.872949	+	0.300620i
$622$			23.2306i			0.931464i
$623$	3.12311	−	4.27156i	0.125125	−	0.171136i
$624$	−3.12311			−0.125024
$625$	−19.0000			−0.760000
$626$	−14.4924			−0.579234
$627$	−3.50758			−0.140079
$628$	10.0000			0.399043
$629$		−	3.74571i		−	0.149351i
$630$	−6.63068	+	9.06897i	−0.264173	+	0.361316i
$631$		−	25.3341i		−	1.00853i	−0.863548	−	0.504266i	$-0.831763\pi$
$631$		−	25.3341i		−	1.00853i	0.863548	−	0.504266i	$-0.168237\pi$
$632$		−	12.8147i		−	0.509740i
$633$		−	9.59482i		−	0.381360i
$634$	−24.2462			−0.962940
$635$		0			0
$636$	−0.384472			−0.0152453
$637$	−22.2462	+	7.08084i	−0.881427	+	0.280553i
$638$		−	1.87285i		−	0.0741470i
$639$	−19.8920			−0.786917
$640$	2.00000			0.0790569
$641$			16.2651i			0.642432i	0.947006	+	0.321216i	$0.104092\pi$
$641$			16.2651i			0.642432i	−0.947006	+	0.321216i	$0.895908\pi$
$642$	−18.6307			−0.735294
$643$	−22.7386			−0.896724			−0.448362	−	0.893852i	$-0.647992\pi$
$643$	−22.7386			−0.896724			−0.448362	+	0.893852i	$0.647992\pi$
$644$	12.1231	+	3.74571i	0.477717	+	0.147601i
$645$	1.75379			0.0690554
$646$	−4.49242			−0.176752
$647$		−	21.3578i		−	0.839661i	−0.907602	−	0.419831i	$-0.862089\pi$
$647$		−	21.3578i		−	0.839661i	0.907602	−	0.419831i	$-0.137911\pi$
$648$	1.87689			0.0737314
$649$	−2.63068			−0.103263
$650$			3.33513i			0.130815i
$651$	−13.2614	+	18.1379i	−0.519754	+	0.710882i
$652$	16.4924			0.645893
$653$	−20.7386			−0.811565			−0.405783	−	0.913970i	$-0.633001\pi$
$653$	−20.7386			−0.811565			−0.405783	+	0.913970i	$0.633001\pi$
$654$	5.86174			0.229212
$655$		−	1.87285i		−	0.0731784i
$656$			6.67026i			0.260430i
$657$		−	7.95253i		−	0.310258i
$658$	−13.1231	−	9.59482i	−0.511592	−	0.374045i
$659$			0.115279i			0.00449065i	0.999997	+	0.00224532i	$0.000714709\pi$
$659$			0.115279i			0.00449065i	−0.999997	+	0.00224532i	$0.999285\pi$
$660$	1.75379			0.0682661
$661$	5.50758			0.214220			0.107110	−	0.994247i	$-0.465840\pi$
$661$	5.50758			0.214220			0.107110	+	0.994247i	$0.465840\pi$
$662$	2.24621			0.0873015
$663$	−3.50758			−0.136223
$664$	−4.00000			−0.155230
$665$	12.4924	−	17.0862i	0.484435	−	0.662576i
$666$		−	7.08084i		−	0.274377i
$667$	3.12311	+	9.06897i	0.120927	+	0.351152i
$668$			9.89012i			0.382660i
$669$	−26.2462			−1.01474
$670$			15.2134i			0.587744i
$671$		−	11.4677i		−	0.442705i
$672$	2.00000	+	1.46228i	0.0771517	+	0.0564086i
$673$	−25.1231			−0.968425			−0.484212	−	0.874951i	$-0.660894\pi$
$673$	−25.1231			−0.968425			−0.484212	+	0.874951i	$0.660894\pi$
$674$		−	34.1725i		−	1.31627i
$675$			4.79741i			0.184652i
$676$	1.87689			0.0721882
$677$	14.4924			0.556989			0.278495	−	0.960438i	$-0.410165\pi$
$677$	14.4924			0.556989			0.278495	+	0.960438i	$0.410165\pi$
$678$	12.4924			0.479769
$679$	−19.1231	+	26.1552i	−0.733877	+	1.00374i
$680$	2.24621			0.0861383
$681$			9.59482i			0.367674i
$682$	−8.49242			−0.325192
$683$	24.4924			0.937177			0.468588	−	0.883417i	$-0.344763\pi$
$683$	24.4924			0.937177			0.468588	+	0.883417i	$0.344763\pi$
$684$	−8.49242			−0.324716
$685$			28.3234i			1.08218i
$686$	17.5616	+	5.88148i	0.670503	+	0.224556i
$687$		−	22.7048i		−	0.866242i
$688$			0.936426i			0.0357009i
$689$	−1.36932			−0.0521668
$690$	−8.49242	+	2.92456i	−0.323301	+	0.111336i
$691$		−	9.71010i		−	0.369390i	−0.982796	−	0.184695i	$-0.940870\pi$
$691$		−	9.71010i		−	0.369390i	0.982796	−	0.184695i	$-0.0591297\pi$
$692$		−	13.7511i		−	0.522738i
$693$	−4.24621	−	3.10457i	−0.161300	−	0.117933i
$694$	−16.4924			−0.626044
$695$		−	9.36426i		−	0.355207i
$696$			1.87285i			0.0709903i
$697$			7.49141i			0.283757i
$698$			30.8373i			1.16721i
$699$		−	0.230559i		−	0.00872053i
$700$	1.56155	−	2.13578i	0.0590211	−	0.0807249i
$701$		−	27.9128i		−	1.05425i	−0.849787	−	0.527126i	$-0.823270\pi$
$701$		−	27.9128i		−	1.05425i	0.849787	−	0.527126i	$-0.176730\pi$
$702$	−16.0000			−0.603881
$703$			13.3405i			0.503148i
$704$			0.936426i			0.0352929i
$705$	11.5076			0.433400
$706$		−	26.6811i		−	1.00415i
$707$	21.3693	+	15.6240i	0.803676	+	0.587599i
$708$	2.63068			0.0988671
$709$			27.9128i			1.04829i	0.851630	+	0.524143i	$0.175614\pi$
$709$			27.9128i			1.04829i	−0.851630	+	0.524143i	$0.824386\pi$
$710$	−18.7386			−0.703248
$711$		−	27.2069i		−	1.02034i
$712$	−2.00000			−0.0749532
$713$	41.1231	−	14.1617i	1.54007	−	0.530359i
$714$	2.24621	+	1.64229i	0.0840623	+	0.0614613i
$715$	6.24621			0.233595
$716$	−2.24621			−0.0839449
$717$			22.1142i			0.825870i
$718$		−	11.9935i		−	0.447594i
$719$			28.2586i			1.05387i	0.849906	+	0.526934i	$0.176659\pi$
$719$			28.2586i			1.05387i	−0.849906	+	0.526934i	$0.823341\pi$
$720$	4.24621			0.158247
$721$	−29.8617	+	40.8427i	−1.11211	+	1.52106i
$722$	−3.00000			−0.111648
$723$			3.51515i			0.130730i
$724$	8.24621			0.306468
$725$	2.00000			0.0742781
$726$		−	9.47954i		−	0.351819i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$	7.12311	+	5.20798i	0.264000	+	0.193021i
$729$	−9.49242			−0.351571
$730$		−	7.49141i		−	0.277270i
$731$			1.05171i			0.0388987i
$732$			11.4677i			0.423857i
$733$	−9.50758			−0.351170			−0.175585	−	0.984464i	$-0.556182\pi$
$733$	−9.50758			−0.351170			−0.175585	+	0.984464i	$0.556182\pi$
$734$	−11.1231			−0.410561
$735$	−12.4924	+	3.97626i	−0.460790	+	0.146667i
$736$	−1.56155	−	4.53448i	−0.0575596	−	0.167143i
$737$	−7.12311			−0.262383
$738$			14.1617i			0.521298i
$739$	−28.0000			−1.03000			−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000			−1.03000			−0.514998	+	0.857191i	$0.672207\pi$
$740$		−	6.67026i		−	0.245204i
$741$	12.4924			0.458921
$742$	0.876894	+	0.641132i	0.0321918	+	0.0235367i
$743$			45.9354i			1.68521i	0.538534	+	0.842604i	$0.318978\pi$
$743$			45.9354i			1.68521i	−0.538534	+	0.842604i	$0.681022\pi$
$744$	8.49242			0.311347
$745$		−	12.5194i		−	0.458675i
$746$			36.6865i			1.34319i
$747$	−8.49242			−0.310721
$748$			1.05171i			0.0384542i
$749$	42.4924	+	31.0679i	1.55264	+	1.13520i
$750$			11.2371i			0.410321i
$751$		−	6.96556i		−	0.254177i	−0.991891	−	0.127088i	$-0.959437\pi$
$751$		−	6.96556i		−	0.254177i	0.991891	−	0.127088i	$-0.0405632\pi$
$752$			6.14441i			0.224064i
$753$		−	21.2931i		−	0.775962i
$754$			6.67026i			0.242917i
$755$	−6.24621			−0.227323
$756$	10.2462	+	7.49141i	0.372651	+	0.272460i
$757$		−	37.5076i		−	1.36324i	−0.731708	−	0.681618i	$-0.761276\pi$
$757$		−	37.5076i		−	1.36324i	0.731708	−	0.681618i	$-0.238724\pi$
$758$		−	1.98813i		−	0.0722122i
$759$	−1.36932	−	3.97626i	−0.0497031	−	0.144329i
$760$	−8.00000			−0.290191
$761$		−	33.3513i		−	1.20898i	−0.796611	−	0.604492i	$-0.793376\pi$
$761$		−	33.3513i		−	1.20898i	0.796611	−	0.604492i	$-0.206624\pi$
$762$		0			0
$763$	−13.3693	−	9.77484i	−0.484002	−	0.353873i
$764$		−	5.32326i		−	0.192589i
$765$	4.76894			0.172422
$766$	−27.1231			−0.979998
$767$	9.36932			0.338306
$768$		−	0.936426i		−	0.0337904i
$769$	−27.3693			−0.986963			−0.493481	−	0.869756i	$-0.664276\pi$
$769$	−27.3693			−0.986963			−0.493481	+	0.869756i	$0.664276\pi$
$770$	−4.00000	−	2.92456i	−0.144150	−	0.105394i
$771$	19.5076			0.702548
$772$	19.3693			0.697117
$773$	−52.2462			−1.87917			−0.939583	−	0.342322i	$-0.888787\pi$
$773$	−52.2462			−1.87917			−0.939583	+	0.342322i	$0.888787\pi$
$774$			1.98813i			0.0714619i
$775$		−	9.06897i		−	0.325767i
$776$	12.2462			0.439613
$777$	4.87689	−	6.67026i	0.174958	−	0.239294i
$778$			23.3459i			0.836992i
$779$		−	26.6811i		−	0.955948i
$780$	−6.24621			−0.223650
$781$		−	8.77368i		−	0.313947i
$782$	−1.75379	−	5.09271i	−0.0627154	−	0.182115i
$783$			9.59482i			0.342891i
$784$	−2.12311	−	6.67026i	−0.0758252	−	0.238224i
$785$	20.0000			0.713831
$786$	−0.876894			−0.0312778
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$	−3.75379			−0.133723
$789$	−5.75379			−0.204840
$790$		−	25.6294i		−	0.911851i
$791$	−28.4924	−	20.8319i	−1.01307	−	0.740698i
$792$			1.98813i			0.0706452i
$793$			40.8427i			1.45037i
$794$		−	19.6002i		−	0.695586i
$795$	−0.768944			−0.0272716
$796$	−20.4924			−0.726335
$797$	−34.4924			−1.22178			−0.610892	−	0.791714i	$-0.709189\pi$
$797$	−34.4924			−1.22178			−0.610892	+	0.791714i	$0.709189\pi$
$798$	−8.00000	−	5.84912i	−0.283197	−	0.207056i
$799$			6.90082i			0.244134i
$800$	−1.00000			−0.0353553
$801$	−4.24621			−0.150032
$802$			2.92456i			0.103270i
$803$	3.50758			0.123780
$804$	7.12311			0.251213
$805$	24.2462	+	7.49141i	0.854567	+	0.264038i
$806$	30.2462			1.06538
$807$	16.3845			0.576761
$808$		−	10.0054i		−	0.351989i
$809$	14.8769			0.523044			0.261522	−	0.965198i	$-0.415776\pi$
$809$	14.8769			0.523044			0.261522	+	0.965198i	$0.415776\pi$
$810$	3.75379			0.131895
$811$			47.3977i			1.66436i	0.554506	+	0.832179i	$0.312907\pi$
$811$			47.3977i			1.66436i	−0.554506	+	0.832179i	$0.687093\pi$
$812$	3.12311	−	4.27156i	0.109600	−	0.149902i
$813$	−4.00000			−0.140286
$814$	3.12311			0.109465
$815$	32.9848			1.15541
$816$		−	1.05171i		−	0.0368171i
$817$		−	3.74571i		−	0.131046i
$818$		−	6.67026i		−	0.233220i
$819$	15.1231	+	11.0571i	0.528444	+	0.386366i
$820$			13.3405i			0.465871i
$821$	37.2311			1.29937			0.649686	−	0.760202i	$-0.274900\pi$
$821$	37.2311			1.29937			0.649686	+	0.760202i	$0.274900\pi$
$822$	13.2614			0.462543
$823$	36.4924			1.27205			0.636023	−	0.771670i	$-0.280578\pi$
$823$	36.4924			1.27205			0.636023	+	0.771670i	$0.280578\pi$
$824$	19.1231			0.666185
$825$	−0.876894			−0.0305295
$826$	−6.00000	−	4.38684i	−0.208767	−	0.152638i
$827$			3.86098i			0.134260i	0.997744	+	0.0671298i	$0.0213842\pi$
$827$			3.86098i			0.134260i	−0.997744	+	0.0671298i	$0.978616\pi$
$828$	−3.31534	−	9.62719i	−0.115216	−	0.334568i
$829$			41.2533i			1.43279i	0.697697	+	0.716393i	$0.254208\pi$
$829$			41.2533i			1.43279i	−0.697697	+	0.716393i	$0.745792\pi$
$830$	−8.00000			−0.277684
$831$			9.36426i			0.324843i
$832$		−	3.33513i		−	0.115625i
$833$	−2.38447	−	7.49141i	−0.0826171	−	0.259562i
$834$	−4.38447			−0.151822
$835$			19.7802i			0.684523i
$836$		−	3.74571i		−	0.129548i
$837$	43.5076			1.50384
$838$	24.4924			0.846077
$839$	−37.8617			−1.30713			−0.653566	−	0.756869i	$-0.726728\pi$
$839$	−37.8617			−1.30713			−0.653566	+	0.756869i	$0.726728\pi$
$840$	4.00000	+	2.92456i	0.138013	+	0.100907i
$841$	−25.0000			−0.862069
$842$		−	19.6002i		−	0.675468i
$843$	16.0000			0.551069
$844$	10.2462			0.352689
$845$	3.75379			0.129134
$846$			13.0452i			0.448504i
$847$	−15.8078	+	21.6207i	−0.543161	+	0.742897i
$848$		−	0.410574i		−	0.0140992i
$849$		−	18.7285i		−	0.642761i
$850$	−1.12311			−0.0385222
$851$	−15.1231	+	5.20798i	−0.518413	+	0.178527i
$852$			8.77368i			0.300581i
$853$		−	27.9128i		−	0.955715i	−0.878437	−	0.477858i	$-0.841413\pi$
$853$		−	27.9128i		−	0.955715i	0.878437	−	0.477858i	$-0.158587\pi$
$854$	19.1231	−	26.1552i	0.654379	−	0.895013i
$855$	−16.9848			−0.580869
$856$		−	19.8955i		−	0.680015i
$857$		−	27.5022i		−	0.939457i	−0.882811	−	0.469729i	$-0.844352\pi$
$857$		−	27.5022i		−	0.939457i	0.882811	−	0.469729i	$-0.155648\pi$
$858$		−	2.92456i		−	0.0998428i
$859$		−	44.7037i		−	1.52527i	−0.646828	−	0.762636i	$-0.723905\pi$
$859$		−	44.7037i		−	1.52527i	0.646828	−	0.762636i	$-0.276095\pi$
$860$			1.87285i			0.0638637i
$861$	−9.75379	+	13.3405i	−0.332408	+	0.454644i
$862$			24.2824i			0.827060i
$863$	−32.0000			−1.08929			−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000			−1.08929			−0.544646	+	0.838666i	$0.683336\pi$
$864$		−	4.79741i		−	0.163211i
$865$		−	27.5022i		−	0.935103i
$866$	13.6155			0.462674
$867$			14.7381i			0.500531i
$868$	−19.3693	−	14.1617i	−0.657437	−	0.480679i
$869$	12.0000			0.407072
$870$			3.74571i			0.126991i
$871$	25.3693			0.859607
$872$			6.25969i			0.211980i
$873$	26.0000			0.879967
$874$	6.24621	+	18.1379i	0.211281	+	0.613525i
$875$	18.7386	−	25.6294i	0.633481	−	0.866430i
$876$	−3.50758			−0.118510
$877$	−30.4924			−1.02966			−0.514828	−	0.857294i	$-0.672144\pi$
$877$	−30.4924			−1.02966			−0.514828	+	0.857294i	$0.672144\pi$
$878$			18.6638i			0.629872i
$879$		−	13.5711i		−	0.457741i
$880$			1.87285i			0.0631339i
$881$	23.3693			0.787332			0.393666	−	0.919253i	$-0.371207\pi$
$881$	23.3693			0.787332			0.393666	+	0.919253i	$0.371207\pi$
$882$	−4.50758	−	14.1617i	−0.151778	−	0.476848i
$883$	−12.0000			−0.403832			−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000			−0.403832			−0.201916	+	0.979403i	$0.564717\pi$
$884$		−	3.74571i		−	0.125982i
$885$	5.26137			0.176859
$886$	40.4924			1.36037
$887$			2.39871i			0.0805407i	0.999189	+	0.0402703i	$0.0128219\pi$
$887$			2.39871i			0.0805407i	−0.999189	+	0.0402703i	$0.987178\pi$
$888$	−3.12311			−0.104805
$889$		0			0
$890$	−4.00000			−0.134080
$891$			1.75757i			0.0588809i
$892$		−	28.0281i		−	0.938449i
$893$		−	24.5776i		−	0.822460i
$894$	−5.86174			−0.196046
$895$	−4.49242			−0.150165
$896$	−1.56155	+	2.13578i	−0.0521678	+	0.0713514i
$897$	4.87689	+	14.1617i	0.162835	+	0.472845i
$898$	6.87689			0.229485
$899$		−	18.1379i		−	0.604934i
$900$	−2.12311			−0.0707702
$901$		−	0.461117i		−	0.0153620i
$902$	−6.24621			−0.207976
$903$	−1.36932	+	1.87285i	−0.0455680	+	0.0623246i
$904$			13.3405i			0.443699i
$905$	16.4924			0.548227
$906$			2.92456i			0.0971619i
$907$		−	46.5766i		−	1.54655i	−0.634071	−	0.773275i	$-0.718617\pi$
$907$		−	46.5766i		−	1.54655i	0.634071	−	0.773275i	$-0.281383\pi$
$908$	−10.2462			−0.340032
$909$		−	21.2425i		−	0.704570i
$910$	14.2462	+	10.4160i	0.472257	+	0.345286i
$911$			24.2824i			0.804510i	0.915528	+	0.402255i	$0.131774\pi$
$911$			24.2824i			0.804510i	−0.915528	+	0.402255i	$0.868226\pi$
$912$			3.74571i			0.124033i
$913$		−	3.74571i		−	0.123965i
$914$			25.8599i			0.855370i
$915$			22.9354i			0.758219i
$916$	24.2462			0.801117
$917$	2.00000	+	1.46228i	0.0660458	+	0.0482887i
$918$		−	5.38800i		−	0.177830i
$919$		−	35.7500i		−	1.17928i	−0.807665	−	0.589642i	$-0.799269\pi$
$919$		−	35.7500i		−	1.17928i	0.807665	−	0.589642i	$-0.200731\pi$
$920$	−3.12311	−	9.06897i	−0.102966	−	0.298995i
$921$	1.86174			0.0613464
$922$		−	24.1671i		−	0.795900i
$923$			31.2479i			1.02854i
$924$	−1.36932	+	1.87285i	−0.0450472	+	0.0616123i
$925$			3.33513i			0.109658i
$926$	33.3693			1.09658
$927$	40.6004			1.33349
$928$	−2.00000			−0.0656532
$929$			42.9461i			1.40902i	0.709695	+	0.704509i	$0.248833\pi$
$929$			42.9461i			1.40902i	−0.709695	+	0.704509i	$0.751167\pi$
$930$	16.9848			0.556955
$931$	8.49242	+	26.6811i	0.278328	+	0.874436i
$932$	0.246211			0.00806492
$933$	21.7538			0.712187
$934$	40.4924			1.32495
$935$			2.10341i			0.0687889i
$936$		−	7.08084i		−	0.231444i
$937$	−18.0000			−0.588034			−0.294017	−	0.955800i	$-0.594992\pi$
$937$	−18.0000			−0.588034			−0.294017	+	0.955800i	$0.594992\pi$
$938$	−16.2462	−	11.8782i	−0.530458	−	0.387839i
$939$			13.5711i			0.442876i
$940$			12.2888i			0.400817i
$941$	−40.7386			−1.32804			−0.664021	−	0.747714i	$-0.731151\pi$
$941$	−40.7386			−1.32804			−0.664021	+	0.747714i	$0.731151\pi$
$942$		−	9.36426i		−	0.305104i
$943$	30.2462	−	10.4160i	0.984952	−	0.339191i
$944$			2.80928i			0.0914342i
$945$	20.4924	+	14.9828i	0.666619	+	0.487391i
$946$	−0.876894			−0.0285103
$947$	12.9848			0.421951			0.210975	−	0.977491i	$-0.432336\pi$
$947$	12.9848			0.421951			0.210975	+	0.977491i	$0.432336\pi$
$948$	−12.0000			−0.389742
$949$	−12.4924			−0.405521
$950$	4.00000			0.129777
$951$			22.7048i			0.736253i
$952$	−1.75379	+	2.39871i	−0.0568406	+	0.0777425i
$953$			48.3341i			1.56570i	0.622213	+	0.782848i	$0.286234\pi$
$953$			48.3341i			1.56570i	−0.622213	+	0.782848i	$0.713766\pi$
$954$		−	0.871691i		−	0.0282220i
$955$		−	10.6465i		−	0.344514i
$956$	−23.6155			−0.763781
$957$	−1.75379			−0.0566919
$958$	4.87689			0.157565
$959$	−30.2462	−	22.1142i	−0.976701	−	0.714105i
$960$		−	1.87285i		−	0.0604461i
$961$	−51.2462			−1.65310
$962$	−11.1231			−0.358623
$963$		−	42.2403i		−	1.36117i
$964$	−3.75379			−0.120901
$965$	38.7386			1.24704
$966$	3.50758	−	11.3524i	0.112854	−	0.365257i
$967$	5.86174			0.188501			0.0942504	−	0.995549i	$-0.469955\pi$
$967$	5.86174			0.188501			0.0942504	+	0.995549i	$0.469955\pi$
$968$	10.1231			0.325369
$969$			4.20682i			0.135143i
$970$	24.4924			0.786404
$971$	−43.2311			−1.38735			−0.693675	−	0.720288i	$-0.744010\pi$
$971$	−43.2311			−1.38735			−0.693675	+	0.720288i	$0.744010\pi$
$972$		−	16.1498i		−	0.518005i
$973$	10.0000	+	7.31140i	0.320585	+	0.234393i
$974$	−4.49242			−0.143947
$975$	3.12311			0.100019
$976$	−12.2462			−0.391992
$977$		−	17.9074i		−	0.572908i	−0.958094	−	0.286454i	$-0.907523\pi$
$977$		−	17.9074i		−	0.572908i	0.958094	−	0.286454i	$-0.0924765\pi$
$978$		−	15.4439i		−	0.493843i
$979$		−	1.87285i		−	0.0598566i
$980$	−4.24621	−	13.3405i	−0.135640	−	0.426148i
$981$			13.2900i			0.424317i
$982$	14.7386			0.470329
$983$	−11.5076			−0.367035			−0.183517	−	0.983016i	$-0.558748\pi$
$983$	−11.5076			−0.367035			−0.183517	+	0.983016i	$0.558748\pi$
$984$	6.24621			0.199122
$985$	−7.50758			−0.239211
$986$	−2.24621			−0.0715339
$987$	−8.98485	+	12.2888i	−0.285991	+	0.391158i
$988$			13.3405i			0.424419i
$989$	4.24621	−	1.46228i	0.135022	−	0.0464978i
$990$			3.97626i			0.126374i
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$			9.06897i			0.287940i
$993$		−	2.10341i		−	0.0667497i
$994$	14.6307	−	20.0108i	0.464057	−	0.634704i
$995$	−40.9848			−1.29931
$996$			3.74571i			0.118687i
$997$		−	10.0054i		−	0.316874i	−0.987369	−	0.158437i	$-0.949355\pi$
$997$		−	10.0054i		−	0.316874i	0.987369	−	0.158437i	$-0.0506455\pi$
$998$	7.50758			0.237648
$999$	−16.0000			−0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.c.d.321.2	yes	4
3.2	odd	2		2898.2.g.a.2575.2		4
4.3	odd	2		2576.2.f.e.321.3		4
7.6	odd	2		322.2.c.c.321.3	yes	4
21.20	even	2		2898.2.g.b.2575.4		4
23.22	odd	2		322.2.c.c.321.2	✓	4
28.27	even	2		2576.2.f.b.321.2		4
69.68	even	2		2898.2.g.b.2575.3		4
92.91	even	2		2576.2.f.b.321.3		4
161.160	even	2	inner	322.2.c.d.321.3	yes	4
483.482	odd	2		2898.2.g.a.2575.1		4
644.643	odd	2		2576.2.f.e.321.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.c.c.321.2	✓	4	23.22	odd	2
322.2.c.c.321.3	yes	4	7.6	odd	2
322.2.c.d.321.2	yes	4	1.1	even	1	trivial
322.2.c.d.321.3	yes	4	161.160	even	2	inner
2576.2.f.b.321.2		4	28.27	even	2
2576.2.f.b.321.3		4	92.91	even	2
2576.2.f.e.321.2		4	644.643	odd	2
2576.2.f.e.321.3		4	4.3	odd	2
2898.2.g.a.2575.1		4	483.482	odd	2
2898.2.g.a.2575.2		4	3.2	odd	2
2898.2.g.b.2575.3		4	69.68	even	2
2898.2.g.b.2575.4		4	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.936426i q^{3} +1.00000 q^{4} +2.00000 q^{5} -0.936426i q^{6} +(-1.56155 + 2.13578i) q^{7} +1.00000 q^{8} +2.12311 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.936426i q^{3} +1.00000 q^{4} +2.00000 q^{5} -0.936426i q^{6} +(-1.56155 + 2.13578i) q^{7} +1.00000 q^{8} +2.12311 q^{9} +2.00000 q^{10} +0.936426i q^{11} -0.936426i q^{12} -3.33513i q^{13} +(-1.56155 + 2.13578i) q^{14} -1.87285i q^{15} +1.00000 q^{16} +1.12311 q^{17} +2.12311 q^{18} -4.00000 q^{19} +2.00000 q^{20} +(2.00000 + 1.46228i) q^{21} +0.936426i q^{22} +(-1.56155 - 4.53448i) q^{23} -0.936426i q^{24} -1.00000 q^{25} -3.33513i q^{26} -4.79741i q^{27} +(-1.56155 + 2.13578i) q^{28} -2.00000 q^{29} -1.87285i q^{30} +9.06897i q^{31} +1.00000 q^{32} +0.876894 q^{33} +1.12311 q^{34} +(-3.12311 + 4.27156i) q^{35} +2.12311 q^{36} -3.33513i q^{37} -4.00000 q^{38} -3.12311 q^{39} +2.00000 q^{40} +6.67026i q^{41} +(2.00000 + 1.46228i) q^{42} +0.936426i q^{43} +0.936426i q^{44} +4.24621 q^{45} +(-1.56155 - 4.53448i) q^{46} +6.14441i q^{47} -0.936426i q^{48} +(-2.12311 - 6.67026i) q^{49} -1.00000 q^{50} -1.05171i q^{51} -3.33513i q^{52} -0.410574i q^{53} -4.79741i q^{54} +1.87285i q^{55} +(-1.56155 + 2.13578i) q^{56} +3.74571i q^{57} -2.00000 q^{58} +2.80928i q^{59} -1.87285i q^{60} -12.2462 q^{61} +9.06897i q^{62} +(-3.31534 + 4.53448i) q^{63} +1.00000 q^{64} -6.67026i q^{65} +0.876894 q^{66} +7.60669i q^{67} +1.12311 q^{68} +(-4.24621 + 1.46228i) q^{69} +(-3.12311 + 4.27156i) q^{70} -9.36932 q^{71} +2.12311 q^{72} -3.74571i q^{73} -3.33513i q^{74} +0.936426i q^{75} -4.00000 q^{76} +(-2.00000 - 1.46228i) q^{77} -3.12311 q^{78} -12.8147i q^{79} +2.00000 q^{80} +1.87689 q^{81} +6.67026i q^{82} -4.00000 q^{83} +(2.00000 + 1.46228i) q^{84} +2.24621 q^{85} +0.936426i q^{86} +1.87285i q^{87} +0.936426i q^{88} -2.00000 q^{89} +4.24621 q^{90} +(7.12311 + 5.20798i) q^{91} +(-1.56155 - 4.53448i) q^{92} +8.49242 q^{93} +6.14441i q^{94} -8.00000 q^{95} -0.936426i q^{96} +12.2462 q^{97} +(-2.12311 - 6.67026i) q^{98} +1.98813i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 8 q^{5} + 2 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 8 * q^5 + 2 * q^7 + 4 * q^8 - 8 * q^9	\( 4 q + 4 q^{2} + 4 q^{4} + 8 q^{5} + 2 q^{7} + 4 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{14} + 4 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{19} + 8 q^{20} + 8 q^{21} + 2 q^{23} - 4 q^{25} + 2 q^{28} - 8 q^{29} + 4 q^{32} + 20 q^{33} - 12 q^{34} + 4 q^{35} - 8 q^{36} - 16 q^{38} + 4 q^{39} + 8 q^{40} + 8 q^{42} - 16 q^{45} + 2 q^{46} + 8 q^{49} - 4 q^{50} + 2 q^{56} - 8 q^{58} - 16 q^{61} - 38 q^{63} + 4 q^{64} + 20 q^{66} - 12 q^{68} + 16 q^{69} + 4 q^{70} + 12 q^{71} - 8 q^{72} - 16 q^{76} - 8 q^{77} + 4 q^{78} + 8 q^{80} + 24 q^{81} - 16 q^{83} + 8 q^{84} - 24 q^{85} - 8 q^{89} - 16 q^{90} + 12 q^{91} + 2 q^{92} - 32 q^{93} - 32 q^{95} + 16 q^{97} + 8 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 8 * q^5 + 2 * q^7 + 4 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^14 + 4 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^19 + 8 * q^20 + 8 * q^21 + 2 * q^23 - 4 * q^25 + 2 * q^28 - 8 * q^29 + 4 * q^32 + 20 * q^33 - 12 * q^34 + 4 * q^35 - 8 * q^36 - 16 * q^38 + 4 * q^39 + 8 * q^40 + 8 * q^42 - 16 * q^45 + 2 * q^46 + 8 * q^49 - 4 * q^50 + 2 * q^56 - 8 * q^58 - 16 * q^61 - 38 * q^63 + 4 * q^64 + 20 * q^66 - 12 * q^68 + 16 * q^69 + 4 * q^70 + 12 * q^71 - 8 * q^72 - 16 * q^76 - 8 * q^77 + 4 * q^78 + 8 * q^80 + 24 * q^81 - 16 * q^83 + 8 * q^84 - 24 * q^85 - 8 * q^89 - 16 * q^90 + 12 * q^91 + 2 * q^92 - 32 * q^93 - 32 * q^95 + 16 * q^97 + 8 * q^98

Introduction

L-functions

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Database

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