LMFDB - Embedded newform 1560.2.w.h.781.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1560,2,Mod(781,1560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1560, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 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("1560.781");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1560.w (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:	$12.4566627153$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			781.1
Character	$\chi$	$=$	1560.781
Dual form			1560.2.w.h.781.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40574 - 0.154586i) q^{2} -1.00000i q^{3} +(1.95221 + 0.434615i) q^{4} +1.00000i q^{5} +(-0.154586 + 1.40574i) q^{6} +2.68192 q^{7} +(-2.67711 - 0.912739i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.40574 - 0.154586i) q^{2} -1.00000i q^{3} +(1.95221 + 0.434615i) q^{4} +1.00000i q^{5} +(-0.154586 + 1.40574i) q^{6} +2.68192 q^{7} +(-2.67711 - 0.912739i) q^{8} -1.00000 q^{9} +(0.154586 - 1.40574i) q^{10} +3.65883i q^{11} +(0.434615 - 1.95221i) q^{12} -1.00000i q^{13} +(-3.77008 - 0.414587i) q^{14} +1.00000 q^{15} +(3.62222 + 1.69692i) q^{16} -2.06298 q^{17} +(1.40574 + 0.154586i) q^{18} +5.41299i q^{19} +(-0.434615 + 1.95221i) q^{20} -2.68192i q^{21} +(0.565604 - 5.14337i) q^{22} -0.461619 q^{23} +(-0.912739 + 2.67711i) q^{24} -1.00000 q^{25} +(-0.154586 + 1.40574i) q^{26} +1.00000i q^{27} +(5.23566 + 1.16560i) q^{28} +3.76763i q^{29} +(-1.40574 - 0.154586i) q^{30} +1.63167 q^{31} +(-4.82958 - 2.94537i) q^{32} +3.65883 q^{33} +(2.90002 + 0.318908i) q^{34} +2.68192i q^{35} +(-1.95221 - 0.434615i) q^{36} +7.44611i q^{37} +(0.836773 - 7.60926i) q^{38} -1.00000 q^{39} +(0.912739 - 2.67711i) q^{40} -4.68586 q^{41} +(-0.414587 + 3.77008i) q^{42} -3.33338i q^{43} +(-1.59018 + 7.14280i) q^{44} -1.00000i q^{45} +(0.648916 + 0.0713598i) q^{46} -3.52987 q^{47} +(1.69692 - 3.62222i) q^{48} +0.192701 q^{49} +(1.40574 + 0.154586i) q^{50} +2.06298i q^{51} +(0.434615 - 1.95221i) q^{52} +5.62294i q^{53} +(0.154586 - 1.40574i) q^{54} -3.65883 q^{55} +(-7.17979 - 2.44789i) q^{56} +5.41299 q^{57} +(0.582422 - 5.29630i) q^{58} +3.65036i q^{59} +(1.95221 + 0.434615i) q^{60} -4.27777i q^{61} +(-2.29370 - 0.252233i) q^{62} -2.68192 q^{63} +(6.33381 + 4.88700i) q^{64} +1.00000 q^{65} +(-5.14337 - 0.565604i) q^{66} -0.885885i q^{67} +(-4.02737 - 0.896604i) q^{68} +0.461619i q^{69} +(0.414587 - 3.77008i) q^{70} -4.89129 q^{71} +(2.67711 + 0.912739i) q^{72} +4.30767 q^{73} +(1.15106 - 10.4673i) q^{74} +1.00000i q^{75} +(-2.35257 + 10.5673i) q^{76} +9.81270i q^{77} +(1.40574 + 0.154586i) q^{78} -15.7644 q^{79} +(-1.69692 + 3.62222i) q^{80} +1.00000 q^{81} +(6.58709 + 0.724368i) q^{82} +3.08546i q^{83} +(1.16560 - 5.23566i) q^{84} -2.06298i q^{85} +(-0.515293 + 4.68586i) q^{86} +3.76763 q^{87} +(3.33956 - 9.79509i) q^{88} +1.90866 q^{89} +(-0.154586 + 1.40574i) q^{90} -2.68192i q^{91} +(-0.901176 - 0.200627i) q^{92} -1.63167i q^{93} +(4.96207 + 0.545668i) q^{94} -5.41299 q^{95} +(-2.94537 + 4.82958i) q^{96} +9.32678 q^{97} +(-0.270887 - 0.0297889i) q^{98} -3.65883i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{2} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 26 q^{9}+O(q^{10}) $ 26 * q - 2 * q^2 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 26 * q^9	$ 26 q - 2 q^{2} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 26 q^{9} + 2 q^{10} + 10 q^{14} + 26 q^{15} + 12 q^{16} + 28 q^{17} + 2 q^{18} + 10 q^{22} - 12 q^{23} - 4 q^{24} - 26 q^{25} - 2 q^{26} - 4 q^{28} - 2 q^{30} - 20 q^{31} + 8 q^{32} - 30 q^{34} + 40 q^{38} - 26 q^{39} + 4 q^{40} + 6 q^{42} + 42 q^{46} + 36 q^{47} - 8 q^{48} + 42 q^{49} + 2 q^{50} + 2 q^{54} + 40 q^{56} - 12 q^{57} - 16 q^{58} - 4 q^{62} + 4 q^{63} - 12 q^{64} + 26 q^{65} + 6 q^{66} - 24 q^{68} - 6 q^{70} - 52 q^{71} - 4 q^{72} - 32 q^{73} - 62 q^{74} - 40 q^{76} + 2 q^{78} + 28 q^{79} + 8 q^{80} + 26 q^{81} - 18 q^{82} - 8 q^{84} + 8 q^{86} - 20 q^{87} - 36 q^{88} - 2 q^{90} + 16 q^{92} + 72 q^{94} + 12 q^{95} - 12 q^{96} + 56 q^{97} - 76 q^{98}+O(q^{100}) $ 26 * q - 2 * q^2 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 26 * q^9 + 2 * q^10 + 10 * q^14 + 26 * q^15 + 12 * q^16 + 28 * q^17 + 2 * q^18 + 10 * q^22 - 12 * q^23 - 4 * q^24 - 26 * q^25 - 2 * q^26 - 4 * q^28 - 2 * q^30 - 20 * q^31 + 8 * q^32 - 30 * q^34 + 40 * q^38 - 26 * q^39 + 4 * q^40 + 6 * q^42 + 42 * q^46 + 36 * q^47 - 8 * q^48 + 42 * q^49 + 2 * q^50 + 2 * q^54 + 40 * q^56 - 12 * q^57 - 16 * q^58 - 4 * q^62 + 4 * q^63 - 12 * q^64 + 26 * q^65 + 6 * q^66 - 24 * q^68 - 6 * q^70 - 52 * q^71 - 4 * q^72 - 32 * q^73 - 62 * q^74 - 40 * q^76 + 2 * q^78 + 28 * q^79 + 8 * q^80 + 26 * q^81 - 18 * q^82 - 8 * q^84 + 8 * q^86 - 20 * q^87 - 36 * q^88 - 2 * q^90 + 16 * q^92 + 72 * q^94 + 12 * q^95 - 12 * q^96 + 56 * q^97 - 76 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times$.

$n$	$391$	$521$	$781$	$937$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$1$	$1$

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 $

$2$	−1.40574	−	0.154586i	−0.994008	−	0.109309i
$2$	−1.40574	−	0.154586i	−0.994008	−	0.109309i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.95221	+	0.434615i	0.976103	+	0.217308i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.154586	+	1.40574i	−0.0631094	+	0.573891i
$7$	2.68192			1.01367			0.506835	−	0.862043i	$-0.330815\pi$
$7$	2.68192			1.01367			0.506835	+	0.862043i	$0.330815\pi$
$8$	−2.67711	−	0.912739i	−0.946501	−	0.322702i
$9$	−1.00000			−0.333333
$10$	0.154586	−	1.40574i	0.0488844	−	0.444534i
$11$			3.65883i			1.10318i	0.834115	+	0.551590i	$0.185979\pi$
$11$			3.65883i			1.10318i	−0.834115	+	0.551590i	$0.814021\pi$
$12$	0.434615	−	1.95221i	0.125463	−	0.563553i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−3.77008	−	0.414587i	−1.00760	−	0.110803i
$15$	1.00000			0.258199
$16$	3.62222	+	1.69692i	0.905555	+	0.424229i
$17$	−2.06298			−0.500347			−0.250174	−	0.968201i	$-0.580488\pi$
$17$	−2.06298			−0.500347			−0.250174	+	0.968201i	$0.580488\pi$
$18$	1.40574	+	0.154586i	0.331336	+	0.0364363i
$19$			5.41299i			1.24183i	0.783879	+	0.620913i	$0.213238\pi$
$19$			5.41299i			1.24183i	−0.783879	+	0.620913i	$0.786762\pi$
$20$	−0.434615	+	1.95221i	−0.0971829	+	0.436527i
$21$		−	2.68192i		−	0.585243i
$22$	0.565604	−	5.14337i	0.120587	−	1.09657i
$23$	−0.461619			−0.0962543			−0.0481271	−	0.998841i	$-0.515325\pi$
$23$	−0.461619			−0.0962543			−0.0481271	+	0.998841i	$0.515325\pi$
$24$	−0.912739	+	2.67711i	−0.186312	+	0.546462i
$25$	−1.00000			−0.200000
$26$	−0.154586	+	1.40574i	−0.0303168	+	0.275688i
$27$			1.00000i			0.192450i
$28$	5.23566	+	1.16560i	0.989447	+	0.220278i
$29$			3.76763i			0.699631i	0.936819	+	0.349815i	$0.113756\pi$
$29$			3.76763i			0.699631i	−0.936819	+	0.349815i	$0.886244\pi$
$30$	−1.40574	−	0.154586i	−0.256652	−	0.0282234i
$31$	1.63167			0.293056			0.146528	−	0.989207i	$-0.453190\pi$
$31$	1.63167			0.293056			0.146528	+	0.989207i	$0.453190\pi$
$32$	−4.82958	−	2.94537i	−0.853757	−	0.520672i
$33$	3.65883			0.636921
$34$	2.90002	+	0.318908i	0.497349	+	0.0546923i
$35$			2.68192i			0.453327i
$36$	−1.95221	−	0.434615i	−0.325368	−	0.0724358i
$37$			7.44611i			1.22413i	0.790807	+	0.612066i	$0.209661\pi$
$37$			7.44611i			1.22413i	−0.790807	+	0.612066i	$0.790339\pi$
$38$	0.836773	−	7.60926i	0.135742	−	1.23438i
$39$	−1.00000			−0.160128
$40$	0.912739	−	2.67711i	0.144317	−	0.423288i
$41$	−4.68586			−0.731808			−0.365904	−	0.930653i	$-0.619240\pi$
$41$	−4.68586			−0.731808			−0.365904	+	0.930653i	$0.619240\pi$
$42$	−0.414587	+	3.77008i	−0.0639722	+	0.581736i
$43$		−	3.33338i		−	0.508335i	−0.967160	−	0.254168i	$-0.918199\pi$
$43$		−	3.33338i		−	0.508335i	0.967160	−	0.254168i	$-0.0818015\pi$
$44$	−1.59018	+	7.14280i	−0.239729	+	1.07682i
$45$		−	1.00000i		−	0.149071i
$46$	0.648916	+	0.0713598i	0.0956775	+	0.0105214i
$47$	−3.52987			−0.514884			−0.257442	−	0.966294i	$-0.582880\pi$
$47$	−3.52987			−0.514884			−0.257442	+	0.966294i	$0.582880\pi$
$48$	1.69692	−	3.62222i	0.244929	−	0.522822i
$49$	0.192701			0.0275287
$50$	1.40574	+	0.154586i	0.198802	+	0.0218618i
$51$			2.06298i			0.288876i
$52$	0.434615	−	1.95221i	0.0602703	−	0.270722i
$53$			5.62294i			0.772370i	0.922421	+	0.386185i	$0.126207\pi$
$53$			5.62294i			0.772370i	−0.922421	+	0.386185i	$0.873793\pi$
$54$	0.154586	−	1.40574i	0.0210365	−	0.191297i
$55$	−3.65883			−0.493357
$56$	−7.17979	−	2.44789i	−0.959440	−	0.327114i
$57$	5.41299			0.716969
$58$	0.582422	−	5.29630i	0.0764758	−	0.695438i
$59$			3.65036i			0.475237i	0.971359	+	0.237618i	$0.0763668\pi$
$59$			3.65036i			0.475237i	−0.971359	+	0.237618i	$0.923633\pi$
$60$	1.95221	+	0.434615i	0.252029	+	0.0561086i
$61$		−	4.27777i		−	0.547712i	−0.961771	−	0.273856i	$-0.911701\pi$
$61$		−	4.27777i		−	0.547712i	0.961771	−	0.273856i	$-0.0882992\pi$
$62$	−2.29370	−	0.252233i	−0.291300	−	0.0320336i
$63$	−2.68192			−0.337890
$64$	6.33381	+	4.88700i	0.791727	+	0.610875i
$65$	1.00000			0.124035
$66$	−5.14337	−	0.565604i	−0.633105	−	0.0696211i
$67$		−	0.885885i		−	0.108228i	−0.998535	−	0.0541140i	$-0.982767\pi$
$67$		−	0.885885i		−	0.108228i	0.998535	−	0.0541140i	$-0.0172335\pi$
$68$	−4.02737	−	0.896604i	−0.488390	−	0.108729i
$69$			0.461619i			0.0555724i
$70$	0.414587	−	3.77008i	0.0495527	−	0.450611i
$71$	−4.89129			−0.580489			−0.290245	−	0.956952i	$-0.593737\pi$
$71$	−4.89129			−0.580489			−0.290245	+	0.956952i	$0.593737\pi$
$72$	2.67711	+	0.912739i	0.315500	+	0.107567i
$73$	4.30767			0.504175			0.252087	−	0.967704i	$-0.418883\pi$
$73$	4.30767			0.504175			0.252087	+	0.967704i	$0.418883\pi$
$74$	1.15106	−	10.4673i	0.133808	−	1.21680i
$75$			1.00000i			0.115470i
$76$	−2.35257	+	10.5673i	−0.269858	+	1.21215i
$77$			9.81270i			1.11826i
$78$	1.40574	+	0.154586i	0.159169	+	0.0175034i
$79$	−15.7644			−1.77364			−0.886818	−	0.462119i	$-0.847089\pi$
$79$	−15.7644			−1.77364			−0.886818	+	0.462119i	$0.847089\pi$
$80$	−1.69692	+	3.62222i	−0.189721	+	0.404976i
$81$	1.00000			0.111111
$82$	6.58709	+	0.724368i	0.727423	+	0.0799930i
$83$			3.08546i			0.338673i	0.985558	+	0.169336i	$0.0541624\pi$
$83$			3.08546i			0.338673i	−0.985558	+	0.169336i	$0.945838\pi$
$84$	1.16560	−	5.23566i	0.127178	−	0.571258i
$85$		−	2.06298i		−	0.223762i
$86$	−0.515293	+	4.68586i	−0.0555655	+	0.505289i
$87$	3.76763			0.403932
$88$	3.33956	−	9.79509i	0.355998	−	1.04416i
$89$	1.90866			0.202318			0.101159	−	0.994870i	$-0.467745\pi$
$89$	1.90866			0.202318			0.101159	+	0.994870i	$0.467745\pi$
$90$	−0.154586	+	1.40574i	−0.0162948	+	0.148178i
$91$		−	2.68192i		−	0.281142i
$92$	−0.901176	−	0.200627i	−0.0939541	−	0.0209168i
$93$		−	1.63167i		−	0.169196i
$94$	4.96207	+	0.545668i	0.511799	+	0.0562813i
$95$	−5.41299			−0.555362
$96$	−2.94537	+	4.82958i	−0.300610	+	0.492917i
$97$	9.32678			0.946991			0.473496	−	0.880796i	$-0.342992\pi$
$97$	9.32678			0.946991			0.473496	+	0.880796i	$0.342992\pi$
$98$	−0.270887	−	0.0297889i	−0.0273637	−	0.00300913i
$99$		−	3.65883i		−	0.367727i
$100$	−1.95221	−	0.434615i	−0.195221	−	0.0434615i
$101$			10.7969i			1.07433i	0.843478	+	0.537164i	$0.180504\pi$
$101$			10.7969i			1.07433i	−0.843478	+	0.537164i	$0.819496\pi$
$102$	0.318908	−	2.90002i	0.0315766	−	0.287145i
$103$	−10.1628			−1.00137			−0.500687	−	0.865628i	$-0.666919\pi$
$103$	−10.1628			−1.00137			−0.500687	+	0.865628i	$0.666919\pi$
$104$	−0.912739	+	2.67711i	−0.0895014	+	0.262512i
$105$	2.68192			0.261729
$106$	0.869227	−	7.90438i	0.0844268	−	0.767741i
$107$		−	9.13091i		−	0.882718i	−0.897331	−	0.441359i	$-0.854496\pi$
$107$		−	9.13091i		−	0.882718i	0.897331	−	0.441359i	$-0.145504\pi$
$108$	−0.434615	+	1.95221i	−0.0418209	+	0.187851i
$109$			7.57707i			0.725751i	0.931838	+	0.362876i	$0.118205\pi$
$109$			7.57707i			0.725751i	−0.931838	+	0.362876i	$0.881795\pi$
$110$	5.14337	+	0.565604i	0.490401	+	0.0539282i
$111$	7.44611			0.706753
$112$	9.71451	+	4.55100i	0.917935	+	0.430029i
$113$	10.4655			0.984515			0.492258	−	0.870450i	$-0.336172\pi$
$113$	10.4655			0.984515			0.492258	+	0.870450i	$0.336172\pi$
$114$	−7.60926	−	0.836773i	−0.712672	−	0.0783709i
$115$		−	0.461619i		−	0.0430462i
$116$	−1.63747	+	7.35518i	−0.152035	+	0.682912i
$117$			1.00000i			0.0924500i
$118$	0.564295	−	5.13146i	0.0519475	−	0.472389i
$119$	−5.53276			−0.507187
$120$	−2.67711	−	0.912739i	−0.244385	−	0.0833213i
$121$	−2.38706			−0.217006
$122$	−0.661283	+	6.01343i	−0.0598698	+	0.544430i
$123$			4.68586i			0.422510i
$124$	3.18535	+	0.709147i	0.286053	+	0.0636832i
$125$		−	1.00000i		−	0.0894427i
$126$	3.77008	+	0.414587i	0.335866	+	0.0369344i
$127$	15.2502			1.35323			0.676617	−	0.736335i	$-0.263445\pi$
$127$	15.2502			1.35323			0.676617	+	0.736335i	$0.263445\pi$
$128$	−8.14823	−	7.84897i	−0.720209	−	0.693758i
$129$	−3.33338			−0.293487
$130$	−1.40574	−	0.154586i	−0.123291	−	0.0135581i
$131$			1.58278i			0.138288i	0.997607	+	0.0691440i	$0.0220268\pi$
$131$			1.58278i			0.138288i	−0.997607	+	0.0691440i	$0.977973\pi$
$132$	7.14280	+	1.59018i	0.621701	+	0.138408i
$133$			14.5172i			1.25880i
$134$	−0.136945	+	1.24532i	−0.0118303	+	0.107580i
$135$	−1.00000			−0.0860663
$136$	5.52283	+	1.88297i	0.473579	+	0.161463i
$137$	17.0293			1.45492			0.727458	−	0.686152i	$-0.240702\pi$
$137$	17.0293			1.45492			0.727458	+	0.686152i	$0.240702\pi$
$138$	0.0713598	−	0.648916i	0.00607455	−	0.0552394i
$139$			4.60208i			0.390344i	0.980769	+	0.195172i	$0.0625264\pi$
$139$			4.60208i			0.390344i	−0.980769	+	0.195172i	$0.937474\pi$
$140$	−1.16560	+	5.23566i	−0.0985115	+	0.442494i
$141$			3.52987i			0.297268i
$142$	6.87588	+	0.756125i	0.577011	+	0.0634526i
$143$	3.65883			0.305967
$144$	−3.62222	−	1.69692i	−0.301852	−	0.141410i
$145$	−3.76763			−0.312884
$146$	−6.05546	−	0.665905i	−0.501154	−	0.0551107i
$147$		−	0.192701i		−	0.0158937i
$148$	−3.23619	+	14.5363i	−0.266013	+	1.19488i
$149$			15.9180i			1.30406i	0.758195	+	0.652028i	$0.226082\pi$
$149$			15.9180i			1.30406i	−0.758195	+	0.652028i	$0.773918\pi$
$150$	0.154586	−	1.40574i	0.0126219	−	0.114778i
$151$	21.2193			1.72680			0.863402	−	0.504516i	$-0.168329\pi$
$151$	21.2193			1.72680			0.863402	+	0.504516i	$0.168329\pi$
$152$	4.94065	−	14.4912i	0.400740	−	1.17539i
$153$	2.06298			0.166782
$154$	1.51691	−	13.7941i	0.122236	−	1.11156i
$155$			1.63167i			0.131059i
$156$	−1.95221	−	0.434615i	−0.156302	−	0.0347971i
$157$			9.74439i			0.777687i	0.921304	+	0.388843i	$0.127125\pi$
$157$			9.74439i			0.777687i	−0.921304	+	0.388843i	$0.872875\pi$
$158$	22.1607	+	2.43696i	1.76301	+	0.193874i
$159$	5.62294			0.445928
$160$	2.94537	−	4.82958i	0.232852	−	0.381812i
$161$	−1.23803			−0.0975701
$162$	−1.40574	−	0.154586i	−0.110445	−	0.0121454i
$163$		−	3.07725i		−	0.241029i	−0.992712	−	0.120514i	$-0.961546\pi$
$163$		−	3.07725i		−	0.241029i	0.992712	−	0.120514i	$-0.0384544\pi$
$164$	−9.14776	−	2.03654i	−0.714320	−	0.159027i
$165$			3.65883i			0.284840i
$166$	0.476968	−	4.33735i	0.0370199	−	0.336643i
$167$	3.08440			0.238678			0.119339	−	0.992854i	$-0.461922\pi$
$167$	3.08440			0.238678			0.119339	+	0.992854i	$0.461922\pi$
$168$	−2.44789	+	7.17979i	−0.188859	+	0.553933i
$169$	−1.00000			−0.0769231
$170$	−0.318908	+	2.90002i	−0.0244591	+	0.222421i
$171$		−	5.41299i		−	0.413942i
$172$	1.44874	−	6.50744i	0.110465	−	0.496187i
$173$			15.6744i			1.19170i	0.803096	+	0.595850i	$0.203185\pi$
$173$			15.6744i			1.19170i	−0.803096	+	0.595850i	$0.796815\pi$
$174$	−5.29630	−	0.582422i	−0.401512	−	0.0441533i
$175$	−2.68192			−0.202734
$176$	−6.20874	+	13.2531i	−0.468001	+	0.998990i
$177$	3.65036			0.274378
$178$	−2.68308	−	0.295052i	−0.201105	−	0.0221151i
$179$			1.98266i			0.148191i	0.997251	+	0.0740954i	$0.0236069\pi$
$179$			1.98266i			0.148191i	−0.997251	+	0.0740954i	$0.976393\pi$
$180$	0.434615	−	1.95221i	0.0323943	−	0.145509i
$181$			12.4177i			0.923004i	0.887139	+	0.461502i	$0.152689\pi$
$181$			12.4177i			0.923004i	−0.887139	+	0.461502i	$0.847311\pi$
$182$	−0.414587	+	3.77008i	−0.0307313	+	0.279457i
$183$	−4.27777			−0.316222
$184$	1.23580	+	0.421338i	0.0911047	+	0.0310614i
$185$	−7.44611			−0.547449
$186$	−0.252233	+	2.29370i	−0.0184946	+	0.168182i
$187$		−	7.54811i		−	0.551973i
$188$	−6.89103	−	1.53413i	−0.502580	−	0.111888i
$189$			2.68192i			0.195081i
$190$	7.60926	+	0.836773i	0.552034	+	0.0607059i
$191$	12.2350			0.885295			0.442647	−	0.896696i	$-0.354039\pi$
$191$	12.2350			0.885295			0.442647	+	0.896696i	$0.354039\pi$
$192$	4.88700	−	6.33381i	0.352689	−	0.457104i
$193$	15.8183			1.13862			0.569311	−	0.822122i	$-0.307210\pi$
$193$	15.8183			1.13862			0.569311	+	0.822122i	$0.307210\pi$
$194$	−13.1110	−	1.44179i	−0.941317	−	0.103514i
$195$		−	1.00000i		−	0.0716115i
$196$	0.376192	+	0.0837507i	0.0268709	+	0.00598219i
$197$		−	14.8146i		−	1.05550i	−0.849400	−	0.527749i	$-0.823036\pi$
$197$		−	14.8146i		−	1.05550i	0.849400	−	0.527749i	$-0.176964\pi$
$198$	−0.565604	+	5.14337i	−0.0401957	+	0.365523i
$199$	−19.3825			−1.37399			−0.686994	−	0.726663i	$-0.741070\pi$
$199$	−19.3825			−1.37399			−0.686994	+	0.726663i	$0.741070\pi$
$200$	2.67711	+	0.912739i	0.189300	+	0.0645404i
$201$	−0.885885			−0.0624855
$202$	1.66904	−	15.1776i	0.117433	−	1.06789i
$203$			10.1045i			0.709195i
$204$	−0.896604	+	4.02737i	−0.0627748	+	0.281972i
$205$		−	4.68586i		−	0.327275i
$206$	14.2863	+	1.57103i	0.995374	+	0.109459i
$207$	0.461619			0.0320848
$208$	1.69692	−	3.62222i	0.117660	−	0.251156i
$209$	−19.8052			−1.36996
$210$	−3.77008	−	0.414587i	−0.260160	−	0.0286092i
$211$			2.80637i			0.193198i	0.995323	+	0.0965992i	$0.0307965\pi$
$211$			2.80637i			0.193198i	−0.995323	+	0.0965992i	$0.969203\pi$
$212$	−2.44381	+	10.9771i	−0.167842	+	0.753912i
$213$			4.89129i			0.335146i
$214$	−1.41151	+	12.8357i	−0.0964889	+	0.877429i
$215$	3.33338			0.227334
$216$	0.912739	−	2.67711i	0.0621040	−	0.182154i
$217$	4.37600			0.297062
$218$	1.17131	−	10.6514i	0.0793310	−	0.721403i
$219$		−	4.30767i		−	0.291085i
$220$	−7.14280	−	1.59018i	−0.481567	−	0.107210i
$221$			2.06298i			0.138771i
$222$	−10.4673	−	1.15106i	−0.702518	−	0.0772543i
$223$	5.03056			0.336871			0.168436	−	0.985713i	$-0.446128\pi$
$223$	5.03056			0.336871			0.168436	+	0.985713i	$0.446128\pi$
$224$	−12.9525	−	7.89924i	−0.865428	−	0.527790i
$225$	1.00000			0.0666667
$226$	−14.7118	−	1.61783i	−0.978616	−	0.107616i
$227$		−	15.1822i		−	1.00768i	−0.863797	−	0.503840i	$-0.831920\pi$
$227$		−	15.1822i		−	1.00768i	0.863797	−	0.503840i	$-0.168080\pi$
$228$	10.5673	+	2.35257i	0.699835	+	0.155803i
$229$			18.8791i			1.24757i	0.781597	+	0.623784i	$0.214406\pi$
$229$			18.8791i			1.24757i	−0.781597	+	0.623784i	$0.785594\pi$
$230$	−0.0713598	+	0.648916i	−0.00470533	+	0.0427883i
$231$	9.81270			0.645628
$232$	3.43886	−	10.0863i	0.225772	−	0.662201i
$233$	−15.7620			−1.03260			−0.516301	−	0.856407i	$-0.672691\pi$
$233$	−15.7620			−1.03260			−0.516301	+	0.856407i	$0.672691\pi$
$234$	0.154586	−	1.40574i	0.0101056	−	0.0918961i
$235$		−	3.52987i		−	0.230263i
$236$	−1.58650	+	7.12626i	−0.103273	+	0.463880i
$237$			15.7644i			1.02401i
$238$	7.77762	+	0.855287i	0.504148	+	0.0554400i
$239$	0.698989			0.0452138			0.0226069	−	0.999744i	$-0.492803\pi$
$239$	0.698989			0.0452138			0.0226069	+	0.999744i	$0.492803\pi$
$240$	3.62222	+	1.69692i	0.233813	+	0.109535i
$241$	−11.4199			−0.735621			−0.367810	−	0.929901i	$-0.619892\pi$
$241$	−11.4199			−0.735621			−0.367810	+	0.929901i	$0.619892\pi$
$242$	3.35559	+	0.369006i	0.215705	+	0.0237206i
$243$		−	1.00000i		−	0.0641500i
$244$	1.85918	−	8.35109i	0.119022	−	0.534624i
$245$			0.192701i			0.0123112i
$246$	0.724368	−	6.58709i	0.0461840	−	0.419978i
$247$	5.41299			0.344421
$248$	−4.36815	−	1.48929i	−0.277378	−	0.0945697i
$249$	3.08546			0.195533
$250$	−0.154586	+	1.40574i	−0.00977687	+	0.0889068i
$251$		−	9.47493i		−	0.598053i	−0.954245	−	0.299026i	$-0.903338\pi$
$251$		−	9.47493i		−	0.598053i	0.954245	−	0.299026i	$-0.0966618\pi$
$252$	−5.23566	−	1.16560i	−0.329816	−	0.0734261i
$253$		−	1.68899i		−	0.106186i
$254$	−21.4378	−	2.35746i	−1.34513	−	0.147920i
$255$	−2.06298			−0.129189
$256$	10.2409	+	12.2932i	0.640059	+	0.768326i
$257$	25.6643			1.60090			0.800449	−	0.599401i	$-0.204594\pi$
$257$	25.6643			1.60090			0.800449	+	0.599401i	$0.204594\pi$
$258$	4.68586	+	0.515293i	0.291729	+	0.0320807i
$259$			19.9699i			1.24087i
$260$	1.95221	+	0.434615i	0.121071	+	0.0269537i
$261$		−	3.76763i		−	0.233210i
$262$	0.244675	−	2.22497i	0.0151161	−	0.137459i
$263$	−20.9294			−1.29056			−0.645282	−	0.763944i	$-0.723260\pi$
$263$	−20.9294			−1.29056			−0.645282	+	0.763944i	$0.723260\pi$
$264$	−9.79509	−	3.33956i	−0.602846	−	0.205536i
$265$	−5.62294			−0.345414
$266$	2.24416	−	20.4074i	0.137598	−	1.25126i
$267$		−	1.90866i		−	0.116808i
$268$	0.385019	−	1.72943i	0.0235188	−	0.105642i
$269$		−	7.41190i		−	0.451911i	−0.974138	−	0.225956i	$-0.927450\pi$
$269$		−	7.41190i		−	0.451911i	0.974138	−	0.225956i	$-0.0725504\pi$
$270$	1.40574	+	0.154586i	0.0855506	+	0.00940780i
$271$	22.2288			1.35030			0.675152	−	0.737679i	$-0.264078\pi$
$271$	22.2288			1.35030			0.675152	+	0.737679i	$0.264078\pi$
$272$	−7.47258	−	3.50071i	−0.453092	−	0.212262i
$273$	−2.68192			−0.162317
$274$	−23.9388	−	2.63250i	−1.44620	−	0.159035i
$275$		−	3.65883i		−	0.220636i
$276$	−0.200627	+	0.901176i	−0.0120763	+	0.0542444i
$277$			21.9465i			1.31864i	0.751863	+	0.659319i	$0.229155\pi$
$277$			21.9465i			1.31864i	−0.751863	+	0.659319i	$0.770845\pi$
$278$	0.711417	−	6.46933i	0.0426680	−	0.388005i
$279$	−1.63167			−0.0976853
$280$	2.44789	−	7.17979i	0.146290	−	0.429075i
$281$	22.7782			1.35883			0.679417	−	0.733752i	$-0.262233\pi$
$281$	22.7782			1.35883			0.679417	+	0.733752i	$0.262233\pi$
$282$	0.545668	−	4.96207i	0.0324940	−	0.295487i
$283$		−	24.0010i		−	1.42671i	−0.700801	−	0.713356i	$-0.747174\pi$
$283$		−	24.0010i		−	1.42671i	0.700801	−	0.713356i	$-0.252826\pi$
$284$	−9.54881	−	2.12583i	−0.566618	−	0.126145i
$285$			5.41299i			0.320638i
$286$	−5.14337	−	0.565604i	−0.304134	−	0.0334449i
$287$	−12.5671			−0.741813
$288$	4.82958	+	2.94537i	0.284586	+	0.173557i
$289$	−12.7441			−0.749653
$290$	5.29630	+	0.582422i	0.311009	+	0.0342010i
$291$		−	9.32678i		−	0.546746i
$292$	8.40946	+	1.87218i	0.492127	+	0.109561i
$293$		−	23.4482i		−	1.36986i	−0.728610	−	0.684928i	$-0.759833\pi$
$293$		−	23.4482i		−	1.36986i	0.728610	−	0.684928i	$-0.240167\pi$
$294$	−0.0297889	+	0.270887i	−0.00173732	+	0.0157985i
$295$	−3.65036			−0.212532
$296$	6.79635	−	19.9340i	0.395030	−	1.15864i
$297$	−3.65883			−0.212307
$298$	2.46070	−	22.3766i	0.142545	−	1.29624i
$299$			0.461619i			0.0266961i
$300$	−0.434615	+	1.95221i	−0.0250925	+	0.112711i
$301$		−	8.93985i		−	0.515284i
$302$	−29.8288	−	3.28021i	−1.71646	−	0.188755i
$303$	10.7969			0.620264
$304$	−9.18540	+	19.6071i	−0.526819	+	1.12454i
$305$	4.27777			0.244944
$306$	−2.90002	−	0.318908i	−0.165783	−	0.0182308i
$307$			11.0199i			0.628939i	0.949268	+	0.314470i	$0.101827\pi$
$307$			11.0199i			0.628939i	−0.949268	+	0.314470i	$0.898173\pi$
$308$	−4.26475	+	19.1564i	−0.243007	+	1.09154i
$309$			10.1628i			0.578144i
$310$	0.252233	−	2.29370i	0.0143258	−	0.130273i
$311$	4.43687			0.251592			0.125796	−	0.992056i	$-0.459852\pi$
$311$	4.43687			0.251592			0.125796	+	0.992056i	$0.459852\pi$
$312$	2.67711	+	0.912739i	0.151561	+	0.0516737i
$313$	−19.0588			−1.07727			−0.538633	−	0.842540i	$-0.681059\pi$
$313$	−19.0588			−1.07727			−0.538633	+	0.842540i	$0.681059\pi$
$314$	1.50635	−	13.6981i	0.0850080	−	0.773027i
$315$		−	2.68192i		−	0.151109i
$316$	−30.7754	−	6.85146i	−1.73125	−	0.385424i
$317$			15.2599i			0.857083i	0.903522	+	0.428542i	$0.140972\pi$
$317$			15.2599i			0.857083i	−0.903522	+	0.428542i	$0.859028\pi$
$318$	−7.90438	−	0.869227i	−0.443256	−	0.0487438i
$319$	−13.7851			−0.771818
$320$	−4.88700	+	6.33381i	−0.273192	+	0.354071i
$321$	−9.13091			−0.509638
$322$	1.74034	+	0.191381i	0.0969855	+	0.0106653i
$323$		−	11.1669i		−	0.621344i
$324$	1.95221	+	0.434615i	0.108456	+	0.0241453i
$325$			1.00000i			0.0554700i
$326$	−0.475699	+	4.32581i	−0.0263466	+	0.239584i
$327$	7.57707			0.419013
$328$	12.5445	+	4.27697i	0.692657	+	0.236156i
$329$	−9.46682			−0.521923
$330$	0.565604	−	5.14337i	0.0311355	−	0.283133i
$331$		−	17.8967i		−	0.983691i	−0.870683	−	0.491845i	$-0.836323\pi$
$331$		−	17.8967i		−	0.983691i	0.870683	−	0.491845i	$-0.163677\pi$
$332$	−1.34099	+	6.02345i	−0.0735961	+	0.330580i
$333$		−	7.44611i		−	0.408044i
$334$	−4.33586	−	0.476805i	−0.237248	−	0.0260896i
$335$	0.885885			0.0484011
$336$	4.55100	−	9.71451i	0.248277	−	0.529970i
$337$	−8.47933			−0.461898			−0.230949	−	0.972966i	$-0.574183\pi$
$337$	−8.47933			−0.461898			−0.230949	+	0.972966i	$0.574183\pi$
$338$	1.40574	+	0.154586i	0.0764621	+	0.00840837i
$339$		−	10.4655i		−	0.568410i
$340$	0.896604	−	4.02737i	0.0486252	−	0.218415i
$341$			5.96999i			0.323293i
$342$	−0.836773	+	7.60926i	−0.0452475	+	0.411462i
$343$	−18.2566			−0.985766
$344$	−3.04250	+	8.92381i	−0.164041	+	0.481139i
$345$	−0.461619			−0.0248527
$346$	2.42303	−	22.0341i	0.130263	−	1.18456i
$347$		−	25.8732i		−	1.38895i	−0.719519	−	0.694473i	$-0.755638\pi$
$347$		−	25.8732i		−	1.38895i	0.719519	−	0.694473i	$-0.244362\pi$
$348$	7.35518	+	1.63747i	0.394279	+	0.0877774i
$349$		−	24.1506i		−	1.29275i	−0.763019	−	0.646376i	$-0.776284\pi$
$349$		−	24.1506i		−	1.29275i	0.763019	−	0.646376i	$-0.223716\pi$
$350$	3.77008	+	0.414587i	0.201519	+	0.0221606i
$351$	1.00000			0.0533761
$352$	10.7766	−	17.6706i	0.574395	−	0.941847i
$353$	−28.4447			−1.51396			−0.756978	−	0.653440i	$-0.773325\pi$
$353$	−28.4447			−1.51396			−0.756978	+	0.653440i	$0.773325\pi$
$354$	−5.13146	−	0.564295i	−0.272734	−	0.0299919i
$355$		−	4.89129i		−	0.259603i
$356$	3.72610	+	0.829533i	0.197483	+	0.0439652i
$357$			5.53276i			0.292825i
$358$	0.306491	−	2.78710i	0.0161985	−	0.147303i
$359$	−17.6342			−0.930699			−0.465349	−	0.885127i	$-0.654071\pi$
$359$	−17.6342			−0.930699			−0.465349	+	0.885127i	$0.654071\pi$
$360$	−0.912739	+	2.67711i	−0.0481056	+	0.141096i
$361$	−10.3005			−0.542132
$362$	1.91961	−	17.4561i	0.100892	−	0.917473i
$363$			2.38706i			0.125288i
$364$	1.16560	−	5.23566i	0.0610942	−	0.274423i
$365$			4.30767i			0.225474i
$366$	6.01343	+	0.661283i	0.314327	+	0.0345658i
$367$	8.57136			0.447422			0.223711	−	0.974656i	$-0.428183\pi$
$367$	8.57136			0.447422			0.223711	+	0.974656i	$0.428183\pi$
$368$	−1.67209	−	0.783329i	−0.0871635	−	0.0408339i
$369$	4.68586			0.243936
$370$	10.4673	+	1.15106i	0.544168	+	0.0598409i
$371$			15.0803i			0.782929i
$372$	0.709147	−	3.18535i	0.0367675	−	0.165153i
$373$		−	11.2923i		−	0.584695i	−0.956312	−	0.292348i	$-0.905564\pi$
$373$		−	11.2923i		−	0.584695i	0.956312	−	0.292348i	$-0.0944364\pi$
$374$	−1.16683	+	10.6107i	−0.0603355	+	0.548665i
$375$	−1.00000			−0.0516398
$376$	9.44983	+	3.22185i	0.487338	+	0.166154i
$377$	3.76763			0.194043
$378$	0.414587	−	3.77008i	0.0213241	−	0.193912i
$379$		−	0.879340i		−	0.0451687i	−0.999745	−	0.0225843i	$-0.992811\pi$
$379$		−	0.879340i		−	0.0451687i	0.999745	−	0.0225843i	$-0.00718943\pi$
$380$	−10.5673	−	2.35257i	−0.542090	−	0.120684i
$381$		−	15.2502i		−	0.781291i
$382$	−17.1992	−	1.89136i	−0.879990	−	0.0967704i
$383$	16.3487			0.835382			0.417691	−	0.908589i	$-0.362839\pi$
$383$	16.3487			0.835382			0.417691	+	0.908589i	$0.362839\pi$
$384$	−7.84897	+	8.14823i	−0.400541	+	0.415813i
$385$	−9.81270			−0.500102
$386$	−22.2363	−	2.44528i	−1.13180	−	0.124461i
$387$			3.33338i			0.169445i
$388$	18.2078	+	4.05356i	0.924361	+	0.205788i
$389$		−	7.34928i		−	0.372623i	−0.982491	−	0.186312i	$-0.940347\pi$
$389$		−	7.34928i		−	0.372623i	0.982491	−	0.186312i	$-0.0596534\pi$
$390$	−0.154586	+	1.40574i	−0.00782776	+	0.0711824i
$391$	0.952313			0.0481605
$392$	−0.515881	−	0.175886i	−0.0260559	−	0.00888357i
$393$	1.58278			0.0798406
$394$	−2.29013	+	20.8255i	−0.115375	+	1.04917i
$395$		−	15.7644i		−	0.793194i
$396$	1.59018	−	7.14280i	0.0799098	−	0.358939i
$397$		−	24.2976i		−	1.21946i	−0.792609	−	0.609731i	$-0.791278\pi$
$397$		−	24.2976i		−	1.21946i	0.792609	−	0.609731i	$-0.208722\pi$
$398$	27.2467	+	2.99626i	1.36575	+	0.150189i
$399$	14.5172			0.726770
$400$	−3.62222	−	1.69692i	−0.181111	−	0.0848458i
$401$	23.4720			1.17213			0.586067	−	0.810263i	$-0.300676\pi$
$401$	23.4720			1.17213			0.586067	+	0.810263i	$0.300676\pi$
$402$	1.24532	+	0.136945i	0.0621111	+	0.00683021i
$403$		−	1.63167i		−	0.0812791i
$404$	−4.69248	+	21.0777i	−0.233460	+	1.04865i
$405$			1.00000i			0.0496904i
$406$	1.56201	−	14.2043i	0.0775212	−	0.704946i
$407$	−27.2441			−1.35044
$408$	1.88297	−	5.52283i	0.0932207	−	0.273421i
$409$	0.0588074			0.00290784			0.00145392	−	0.999999i	$-0.499537\pi$
$409$	0.0588074			0.00290784			0.00145392	+	0.999999i	$0.499537\pi$
$410$	−0.724368	+	6.58709i	−0.0357740	+	0.325313i
$411$		−	17.0293i		−	0.839996i
$412$	−19.8400	−	4.41693i	−0.977445	−	0.217606i
$413$			9.78999i			0.481734i
$414$	−0.648916	−	0.0713598i	−0.0318925	−	0.00350714i
$415$	−3.08546			−0.151459
$416$	−2.94537	+	4.82958i	−0.144408	+	0.236790i
$417$	4.60208			0.225365
$418$	27.8410	+	3.06161i	1.36175	+	0.149748i
$419$		−	30.7636i		−	1.50290i	−0.659791	−	0.751449i	$-0.729355\pi$
$419$		−	30.7636i		−	1.50290i	0.659791	−	0.751449i	$-0.270645\pi$
$420$	5.23566	+	1.16560i	0.255474	+	0.0568756i
$421$		−	19.7742i		−	0.963735i	−0.876244	−	0.481868i	$-0.839959\pi$
$421$		−	19.7742i		−	0.963735i	0.876244	−	0.481868i	$-0.160041\pi$
$422$	0.433825	−	3.94502i	0.0211183	−	0.192041i
$423$	3.52987			0.171628
$424$	5.13227	−	15.0532i	0.249245	−	0.731048i
$425$	2.06298			0.100069
$426$	0.756125	−	6.87588i	0.0366344	−	0.333137i
$427$		−	11.4726i		−	0.555200i
$428$	3.96843	−	17.8254i	0.191821	−	0.861624i
$429$		−	3.65883i		−	0.176650i
$430$	−4.68586	−	0.515293i	−0.225972	−	0.0248496i
$431$	27.4222			1.32088			0.660440	−	0.750878i	$-0.270370\pi$
$431$	27.4222			1.32088			0.660440	+	0.750878i	$0.270370\pi$
$432$	−1.69692	+	3.62222i	−0.0816429	+	0.174274i
$433$	8.99002			0.432033			0.216016	−	0.976390i	$-0.430694\pi$
$433$	8.99002			0.432033			0.216016	+	0.976390i	$0.430694\pi$
$434$	−6.15151	−	0.676468i	−0.295282	−	0.0324715i
$435$			3.76763i			0.180644i
$436$	−3.29311	+	14.7920i	−0.157711	+	0.708408i
$437$		−	2.49874i		−	0.119531i
$438$	−0.665905	+	6.05546i	−0.0318182	+	0.289341i
$439$	36.0850			1.72224			0.861122	−	0.508398i	$-0.169762\pi$
$439$	36.0850			1.72224			0.861122	+	0.508398i	$0.169762\pi$
$440$	9.79509	+	3.33956i	0.466963	+	0.159207i
$441$	−0.192701			−0.00917623
$442$	0.318908	−	2.90002i	0.0151689	−	0.137940i
$443$			8.91100i			0.423375i	0.977337	+	0.211687i	$0.0678958\pi$
$443$			8.91100i			0.423375i	−0.977337	+	0.211687i	$0.932104\pi$
$444$	14.5363	+	3.23619i	0.689864	+	0.153583i
$445$			1.90866i			0.0904793i
$446$	−7.07165	−	0.777654i	−0.334853	−	0.0368230i
$447$	15.9180			0.752897
$448$	16.9868	+	13.1066i	0.802550	+	0.619227i
$449$	33.5911			1.58526			0.792632	−	0.609700i	$-0.208710\pi$
$449$	33.5911			1.58526			0.792632	+	0.609700i	$0.208710\pi$
$450$	−1.40574	−	0.154586i	−0.0662672	−	0.00728725i
$451$		−	17.1448i		−	0.807316i
$452$	20.4309	+	4.54848i	0.960988	+	0.213943i
$453$		−	21.2193i		−	0.996971i
$454$	−2.34696	+	21.3422i	−0.110148	+	1.00164i
$455$	2.68192			0.125730
$456$	−14.4912	−	4.94065i	−0.678611	−	0.231367i
$457$	−38.7184			−1.81117			−0.905586	−	0.424164i	$-0.860568\pi$
$457$	−38.7184			−1.81117			−0.905586	+	0.424164i	$0.860568\pi$
$458$	2.91845	−	26.5391i	0.136370	−	1.24009i
$459$		−	2.06298i		−	0.0962918i
$460$	0.200627	−	0.901176i	0.00935427	−	0.0420175i
$461$			4.05415i			0.188821i	0.995533	+	0.0944103i	$0.0300965\pi$
$461$			4.05415i			0.188821i	−0.995533	+	0.0944103i	$0.969903\pi$
$462$	−13.7941	−	1.51691i	−0.641760	−	0.0705728i
$463$	−14.8658			−0.690875			−0.345437	−	0.938442i	$-0.612269\pi$
$463$	−14.8658			−0.690875			−0.345437	+	0.938442i	$0.612269\pi$
$464$	−6.39335	+	13.6472i	−0.296804	+	0.633554i
$465$	1.63167			0.0756667
$466$	22.1572	+	2.43658i	1.02641	+	0.112872i
$467$			33.8931i			1.56839i	0.620516	+	0.784194i	$0.286923\pi$
$467$			33.8931i			1.56839i	−0.620516	+	0.784194i	$0.713077\pi$
$468$	−0.434615	+	1.95221i	−0.0200901	+	0.0902408i
$469$		−	2.37587i		−	0.109708i
$470$	−0.545668	+	4.96207i	−0.0251698	+	0.228883i
$471$	9.74439			0.448998
$472$	3.33183	−	9.77242i	0.153360	−	0.449812i
$473$	12.1963			0.560785
$474$	2.43696	−	22.1607i	0.111933	−	1.01787i
$475$		−	5.41299i		−	0.248365i
$476$	−10.8011	−	2.40462i	−0.495067	−	0.110216i
$477$		−	5.62294i		−	0.257457i
$478$	−0.982596	−	0.108054i	−0.0449429	−	0.00494227i
$479$	−28.5515			−1.30455			−0.652276	−	0.757981i	$-0.726186\pi$
$479$	−28.5515			−1.30455			−0.652276	+	0.757981i	$0.726186\pi$
$480$	−4.82958	−	2.94537i	−0.220439	−	0.134437i
$481$	7.44611			0.339513
$482$	16.0534	+	1.76536i	0.731213	+	0.0804098i
$483$			1.23803i			0.0563322i
$484$	−4.66004	−	1.03745i	−0.211820	−	0.0471570i
$485$			9.32678i			0.423507i
$486$	−0.154586	+	1.40574i	−0.00701216	+	0.0637656i
$487$	−35.2074			−1.59540			−0.797701	−	0.603054i	$-0.793951\pi$
$487$	−35.2074			−1.59540			−0.797701	+	0.603054i	$0.793951\pi$
$488$	−3.90449	+	11.4521i	−0.176748	+	0.518410i
$489$	−3.07725			−0.139158
$490$	0.0297889	−	0.270887i	0.00134572	−	0.0122374i
$491$		−	34.9061i		−	1.57529i	−0.616130	−	0.787644i	$-0.711301\pi$
$491$		−	34.9061i		−	1.57529i	0.616130	−	0.787644i	$-0.288699\pi$
$492$	−2.03654	+	9.14776i	−0.0918145	+	0.412413i
$493$		−	7.77255i		−	0.350058i
$494$	−7.60926	−	0.836773i	−0.342357	−	0.0376482i
$495$	3.65883			0.164452
$496$	5.91025	+	2.76880i	0.265378	+	0.124323i
$497$	−13.1181			−0.588425
$498$	−4.33735	−	0.476968i	−0.194361	−	0.0213734i
$499$			8.09657i			0.362452i	0.983441	+	0.181226i	$0.0580066\pi$
$499$			8.09657i			0.362452i	−0.983441	+	0.181226i	$0.941993\pi$
$500$	0.434615	−	1.95221i	0.0194366	−	0.0873053i
$501$		−	3.08440i		−	0.137801i
$502$	−1.46469	+	13.3193i	−0.0653724	+	0.594469i
$503$	−22.2160			−0.990561			−0.495281	−	0.868733i	$-0.664935\pi$
$503$	−22.2160			−0.990561			−0.495281	+	0.868733i	$0.664935\pi$
$504$	7.17979	+	2.44789i	0.319813	+	0.109038i
$505$	−10.7969			−0.480454
$506$	−0.261094	+	2.37428i	−0.0116070	+	0.105549i
$507$			1.00000i			0.0444116i
$508$	29.7715	+	6.62796i	1.32090	+	0.294068i
$509$		−	21.2238i		−	0.940729i	−0.882472	−	0.470365i	$-0.844122\pi$
$509$		−	21.2238i		−	0.940729i	0.882472	−	0.470365i	$-0.155878\pi$
$510$	2.90002	+	0.318908i	0.128415	+	0.0141215i
$511$	11.5528			0.511067
$512$	−12.4957	−	18.8642i	−0.552239	−	0.833686i
$513$	−5.41299			−0.238990
$514$	−36.0774	−	3.96735i	−1.59131	−	0.174992i
$515$		−	10.1628i		−	0.447828i
$516$	−6.50744	−	1.44874i	−0.286474	−	0.0637770i
$517$		−	12.9152i		−	0.568009i
$518$	3.08706	−	28.0724i	0.135638	−	1.23343i
$519$	15.6744			0.688028
$520$	−2.67711	−	0.912739i	−0.117399	−	0.0400263i
$521$	−14.9661			−0.655677			−0.327839	−	0.944734i	$-0.606320\pi$
$521$	−14.9661			−0.655677			−0.327839	+	0.944734i	$0.606320\pi$
$522$	−0.582422	+	5.29630i	−0.0254919	+	0.231813i
$523$			6.37281i			0.278663i	0.990246	+	0.139332i	$0.0444954\pi$
$523$			6.37281i			0.278663i	−0.990246	+	0.139332i	$0.955505\pi$
$524$	−0.687899	+	3.08991i	−0.0300510	+	0.134983i
$525$			2.68192i			0.117049i
$526$	29.4213	+	3.23540i	1.28283	+	0.141070i
$527$	−3.36610			−0.146630
$528$	13.2531	+	6.20874i	0.576767	+	0.270201i
$529$	−22.7869			−0.990735
$530$	7.90438	+	0.869227i	0.343344	+	0.0377568i
$531$		−	3.65036i		−	0.158412i
$532$	−6.30940	+	28.3406i	−0.273547	+	1.22872i
$533$			4.68586i			0.202967i
$534$	−0.295052	+	2.68308i	−0.0127682	+	0.116108i
$535$	9.13091			0.394764
$536$	−0.808582	+	2.37161i	−0.0349254	+	0.102438i
$537$	1.98266			0.0855580
$538$	−1.14577	+	10.4192i	−0.0493979	+	0.449203i
$539$			0.705061i			0.0303691i
$540$	−1.95221	−	0.434615i	−0.0840096	−	0.0187029i
$541$		−	5.20872i		−	0.223940i	−0.993712	−	0.111970i	$-0.964284\pi$
$541$		−	5.20872i		−	0.223940i	0.993712	−	0.111970i	$-0.0357161\pi$
$542$	−31.2479	−	3.43626i	−1.34221	−	0.147600i
$543$	12.4177			0.532896
$544$	9.96334	+	6.07624i	0.427175	+	0.260517i
$545$	−7.57707			−0.324566
$546$	3.77008	+	0.414587i	0.161345	+	0.0177427i
$547$		−	1.14923i		−	0.0491374i	−0.999698	−	0.0245687i	$-0.992179\pi$
$547$		−	1.14923i		−	0.0491374i	0.999698	−	0.0245687i	$-0.00782124\pi$
$548$	33.2448	+	7.40121i	1.42015	+	0.316164i
$549$			4.27777i			0.182571i
$550$	−0.565604	+	5.14337i	−0.0241174	+	0.219314i
$551$	−20.3941			−0.868820
$552$	0.421338	−	1.23580i	0.0179333	−	0.0525993i
$553$	−42.2789			−1.79788
$554$	3.39262	−	30.8511i	0.144139	−	1.31074i
$555$			7.44611i			0.316070i
$556$	−2.00013	+	8.98422i	−0.0848246	+	0.381016i
$557$		−	17.5537i		−	0.743775i	−0.928278	−	0.371887i	$-0.878711\pi$
$557$		−	17.5537i		−	0.743775i	0.928278	−	0.371887i	$-0.121289\pi$
$558$	2.29370	+	0.252233i	0.0970999	+	0.0106779i
$559$	−3.33338			−0.140987
$560$	−4.55100	+	9.71451i	−0.192315	+	0.410513i
$561$	−7.54811			−0.318682
$562$	−32.0202	−	3.52119i	−1.35069	−	0.148533i
$563$		−	2.46277i		−	0.103794i	−0.998652	−	0.0518968i	$-0.983473\pi$
$563$		−	2.46277i		−	0.103794i	0.998652	−	0.0518968i	$-0.0165267\pi$
$564$	−1.53413	+	6.89103i	−0.0645986	+	0.290165i
$565$			10.4655i			0.440289i
$566$	−3.71022	+	33.7392i	−0.155952	+	1.41816i
$567$	2.68192			0.112630
$568$	13.0945	+	4.46447i	0.549434	+	0.187325i
$569$	28.3229			1.18736			0.593678	−	0.804702i	$-0.297675\pi$
$569$	28.3229			1.18736			0.593678	+	0.804702i	$0.297675\pi$
$570$	0.836773	−	7.60926i	0.0350486	−	0.318717i
$571$			19.6004i			0.820250i	0.912029	+	0.410125i	$0.134515\pi$
$571$			19.6004i			0.820250i	−0.912029	+	0.410125i	$0.865485\pi$
$572$	7.14280	+	1.59018i	0.298655	+	0.0664889i
$573$		−	12.2350i		−	0.511125i
$574$	17.6661	+	1.94270i	0.737367	+	0.0810866i
$575$	0.461619			0.0192509
$576$	−6.33381	−	4.88700i	−0.263909	−	0.203625i
$577$	19.5513			0.813932			0.406966	−	0.913443i	$-0.366587\pi$
$577$	19.5513			0.813932			0.406966	+	0.913443i	$0.366587\pi$
$578$	17.9149	+	1.97006i	0.745161	+	0.0819436i
$579$		−	15.8183i		−	0.657384i
$580$	−7.35518	−	1.63747i	−0.305407	−	0.0679921i
$581$			8.27495i			0.343303i
$582$	−1.44179	+	13.1110i	−0.0597641	+	0.543470i
$583$	−20.5734			−0.852062
$584$	−11.5321	−	3.93178i	−0.477202	−	0.162698i
$585$	−1.00000			−0.0413449
$586$	−3.62476	+	32.9620i	−0.149737	+	1.36165i
$587$		−	28.7078i		−	1.18490i	−0.805609	−	0.592448i	$-0.798162\pi$
$587$		−	28.7078i		−	1.18490i	0.805609	−	0.592448i	$-0.201838\pi$
$588$	0.0837507	−	0.376192i	0.00345382	−	0.0155139i
$589$			8.83220i			0.363924i
$590$	5.13146	+	0.564295i	0.211259	+	0.0232316i
$591$	−14.8146			−0.609392
$592$	−12.6354	+	26.9714i	−0.519313	+	1.10852i
$593$	44.9129			1.84435			0.922175	−	0.386772i	$-0.126410\pi$
$593$	44.9129			1.84435			0.922175	+	0.386772i	$0.126410\pi$
$594$	5.14337	+	0.565604i	0.211035	+	0.0232070i
$595$		−	5.53276i		−	0.226821i
$596$	−6.91822	+	31.0753i	−0.283381	+	1.27289i
$597$			19.3825i			0.793272i
$598$	0.0713598	−	0.648916i	0.00291812	−	0.0265362i
$599$	−12.4455			−0.508511			−0.254255	−	0.967137i	$-0.581830\pi$
$599$	−12.4455			−0.508511			−0.254255	+	0.967137i	$0.581830\pi$
$600$	0.912739	−	2.67711i	0.0372624	−	0.109292i
$601$	−35.2686			−1.43864			−0.719319	−	0.694680i	$-0.755546\pi$
$601$	−35.2686			−1.43864			−0.719319	+	0.694680i	$0.755546\pi$
$602$	−1.38198	+	12.5671i	−0.0563251	+	0.512197i
$603$			0.885885i			0.0360760i
$604$	41.4245	+	9.22224i	1.68554	+	0.375248i
$605$		−	2.38706i		−	0.0970479i
$606$	−15.1776	−	1.66904i	−0.616547	−	0.0678002i
$607$	−32.5475			−1.32106			−0.660531	−	0.750799i	$-0.729669\pi$
$607$	−32.5475			−1.32106			−0.660531	+	0.750799i	$0.729669\pi$
$608$	15.9433	−	26.1425i	0.646584	−	1.06022i
$609$	10.1045			0.409454
$610$	−6.01343	−	0.661283i	−0.243477	−	0.0267746i
$611$			3.52987i			0.142803i
$612$	4.02737	+	0.896604i	0.162797	+	0.0362431i
$613$			39.2979i			1.58723i	0.608421	+	0.793614i	$0.291803\pi$
$613$			39.2979i			1.58723i	−0.608421	+	0.793614i	$0.708197\pi$
$614$	1.70352	−	15.4911i	0.0687486	−	0.625171i
$615$	−4.68586			−0.188952
$616$	8.95644	−	26.2697i	0.360865	−	1.05843i
$617$	38.1569			1.53614			0.768070	−	0.640366i	$-0.221217\pi$
$617$	38.1569			1.53614			0.768070	+	0.640366i	$0.221217\pi$
$618$	1.57103	−	14.2863i	0.0631962	−	0.574680i
$619$			38.6267i			1.55254i	0.630402	+	0.776269i	$0.282890\pi$
$619$			38.6267i			1.55254i	−0.630402	+	0.776269i	$0.717110\pi$
$620$	−0.709147	+	3.18535i	−0.0284800	+	0.127927i
$621$		−	0.461619i		−	0.0185241i
$622$	−6.23708	−	0.685877i	−0.250084	−	0.0275012i
$623$	5.11888			0.205084
$624$	−3.62222	−	1.69692i	−0.145005	−	0.0679310i
$625$	1.00000			0.0400000
$626$	26.7917	+	2.94622i	1.07081	+	0.117755i
$627$			19.8052i			0.790945i
$628$	−4.23506	+	19.0231i	−0.168997	+	0.759103i
$629$		−	15.3612i		−	0.612491i
$630$	−0.414587	+	3.77008i	−0.0165176	+	0.150204i
$631$	1.36308			0.0542633			0.0271317	−	0.999632i	$-0.491363\pi$
$631$	1.36308			0.0542633			0.0271317	+	0.999632i	$0.491363\pi$
$632$	42.2031	+	14.3888i	1.67875	+	0.572356i
$633$	2.80637			0.111543
$634$	2.35897	−	21.4515i	0.0936867	−	0.851948i
$635$			15.2502i			0.605185i
$636$	10.9771	+	2.44381i	0.435272	+	0.0969035i
$637$		−	0.192701i		−	0.00763509i
$638$	19.3783	+	2.13099i	0.767193	+	0.0843665i
$639$	4.89129			0.193496
$640$	7.84897	−	8.14823i	0.310258	−	0.322087i
$641$	36.3057			1.43399			0.716995	−	0.697078i	$-0.245517\pi$
$641$	36.3057			1.43399			0.716995	+	0.697078i	$0.245517\pi$
$642$	12.8357	+	1.41151i	0.506584	+	0.0557079i
$643$		−	10.6297i		−	0.419195i	−0.977788	−	0.209598i	$-0.932785\pi$
$643$		−	10.6297i		−	0.419195i	0.977788	−	0.209598i	$-0.0672154\pi$
$644$	−2.41688	−	0.538065i	−0.0952385	−	0.0212027i
$645$		−	3.33338i		−	0.131252i
$646$	−1.72625	+	15.6978i	−0.0679183	+	0.617621i
$647$	−25.7943			−1.01408			−0.507040	−	0.861923i	$-0.669260\pi$
$647$	−25.7943			−1.01408			−0.507040	+	0.861923i	$0.669260\pi$
$648$	−2.67711	−	0.912739i	−0.105167	−	0.0358558i
$649$	−13.3561			−0.524272
$650$	0.154586	−	1.40574i	0.00606336	−	0.0551376i
$651$		−	4.37600i		−	0.171509i
$652$	1.33742	−	6.00743i	0.0523774	−	0.235269i
$653$			9.66428i			0.378192i	0.981959	+	0.189096i	$0.0605558\pi$
$653$			9.66428i			0.378192i	−0.981959	+	0.189096i	$0.939444\pi$
$654$	−10.6514	−	1.17131i	−0.416502	−	0.0458018i
$655$	−1.58278			−0.0618443
$656$	−16.9732	−	7.95151i	−0.662692	−	0.310454i
$657$	−4.30767			−0.168058
$658$	13.3079	+	1.46344i	0.518795	+	0.0570507i
$659$		−	19.8849i		−	0.774604i	−0.921953	−	0.387302i	$-0.873407\pi$
$659$		−	19.8849i		−	0.774604i	0.921953	−	0.387302i	$-0.126593\pi$
$660$	−1.59018	+	7.14280i	−0.0618978	+	0.278033i
$661$			43.8601i			1.70596i	0.521944	+	0.852980i	$0.325207\pi$
$661$			43.8601i			1.70596i	−0.521944	+	0.852980i	$0.674793\pi$
$662$	−2.76658	+	25.1581i	−0.107526	+	0.977796i
$663$	2.06298			0.0801197
$664$	2.81622	−	8.26010i	0.109290	−	0.320554i
$665$	−14.5172			−0.562954
$666$	−1.15106	+	10.4673i	−0.0446028	+	0.405599i
$667$		−	1.73921i		−	0.0673424i
$668$	6.02138	+	1.34053i	0.232974	+	0.0518665i
$669$		−	5.03056i		−	0.194493i
$670$	−1.24532	−	0.136945i	−0.0481110	−	0.00529066i
$671$	15.6517			0.604225
$672$	−7.89924	+	12.9525i	−0.304720	+	0.499655i
$673$	−15.5596			−0.599778			−0.299889	−	0.953974i	$-0.596950\pi$
$673$	−15.5596			−0.599778			−0.299889	+	0.953974i	$0.596950\pi$
$674$	11.9197	+	1.31079i	0.459131	+	0.0504896i
$675$		−	1.00000i		−	0.0384900i
$676$	−1.95221	−	0.434615i	−0.0750849	−	0.0167160i
$677$			11.0104i			0.423165i	0.977360	+	0.211583i	$0.0678617\pi$
$677$			11.0104i			0.423165i	−0.977360	+	0.211583i	$0.932138\pi$
$678$	−1.61783	+	14.7118i	−0.0621322	+	0.565004i
$679$	25.0137			0.959938
$680$	−1.88297	+	5.52283i	−0.0722085	+	0.211791i
$681$	−15.1822			−0.581784
$682$	0.922877	−	8.39225i	0.0353388	−	0.321356i
$683$			43.8155i			1.67656i	0.545244	+	0.838278i	$0.316437\pi$
$683$			43.8155i			1.67656i	−0.545244	+	0.838278i	$0.683563\pi$
$684$	2.35257	−	10.5673i	0.0899527	−	0.404050i
$685$			17.0293i			0.650658i
$686$	25.6641	+	2.82222i	0.979859	+	0.107753i
$687$	18.8791			0.720284
$688$	5.65646	−	12.0742i	0.215651	−	0.460325i
$689$	5.62294			0.214217
$690$	0.648916	+	0.0713598i	0.0247038	+	0.00271662i
$691$		−	9.19588i		−	0.349828i	−0.984584	−	0.174914i	$-0.944035\pi$
$691$		−	9.19588i		−	0.349828i	0.984584	−	0.174914i	$-0.0559647\pi$
$692$	−6.81231	+	30.5996i	−0.258965	+	1.16322i
$693$		−	9.81270i		−	0.372754i
$694$	−3.99963	+	36.3710i	−0.151824	+	1.38062i
$695$	−4.60208			−0.174567
$696$	−10.0863	−	3.43886i	−0.382322	−	0.130350i
$697$	9.66685			0.366158
$698$	−3.73334	+	33.9494i	−0.141309	+	1.28501i
$699$			15.7620i			0.596173i
$700$	−5.23566	−	1.16560i	−0.197889	−	0.0440557i
$701$		−	42.3439i		−	1.59931i	−0.600461	−	0.799654i	$-0.705016\pi$
$701$		−	42.3439i		−	1.59931i	0.600461	−	0.799654i	$-0.294984\pi$
$702$	−1.40574	−	0.154586i	−0.0530562	−	0.00583447i
$703$	−40.3057			−1.52016
$704$	−17.8807	+	23.1744i	−0.673905	+	0.873417i
$705$	−3.52987			−0.132942
$706$	39.9858	+	4.39714i	1.50488	+	0.165489i
$707$			28.9563i			1.08901i
$708$	7.12626	+	1.58650i	0.267821	+	0.0596244i
$709$			35.4195i			1.33021i	0.746752	+	0.665103i	$0.231612\pi$
$709$			35.4195i			1.33021i	−0.746752	+	0.665103i	$0.768388\pi$
$710$	−0.756125	+	6.87588i	−0.0283769	+	0.258047i
$711$	15.7644			0.591212
$712$	−5.10969	−	1.74211i	−0.191494	−	0.0652884i
$713$	−0.753208			−0.0282079
$714$	0.855287	−	7.77762i	0.0320083	−	0.291070i
$715$			3.65883i			0.136833i
$716$	−0.861693	+	3.87056i	−0.0322030	+	0.144649i
$717$		−	0.698989i		−	0.0261042i
$718$	24.7891	+	2.72600i	0.925122	+	0.101734i
$719$	−26.0594			−0.971852			−0.485926	−	0.874000i	$-0.661517\pi$
$719$	−26.0594			−0.971852			−0.485926	+	0.874000i	$0.661517\pi$
$720$	1.69692	−	3.62222i	0.0632403	−	0.134992i
$721$	−27.2559			−1.01506
$722$	14.4798	+	1.59231i	0.538883	+	0.0592598i
$723$			11.4199i			0.424711i
$724$	−5.39694	+	24.2420i	−0.200576	+	0.900947i
$725$		−	3.76763i		−	0.139926i
$726$	0.369006	−	3.35559i	0.0136951	−	0.124538i
$727$	−21.4753			−0.796474			−0.398237	−	0.917283i	$-0.630378\pi$
$727$	−21.4753			−0.796474			−0.398237	+	0.917283i	$0.630378\pi$
$728$	−2.44789	+	7.17979i	−0.0907250	+	0.266101i
$729$	−1.00000			−0.0370370
$730$	0.665905	−	6.05546i	0.0246463	−	0.224123i
$731$			6.87670i			0.254344i
$732$	−8.35109	−	1.85918i	−0.308665	−	0.0687174i
$733$			32.1006i			1.18566i	0.805327	+	0.592831i	$0.201990\pi$
$733$			32.1006i			1.18566i	−0.805327	+	0.592831i	$0.798010\pi$
$734$	−12.0491	−	1.32501i	−0.444741	−	0.0489071i
$735$	0.192701			0.00710788
$736$	2.22943	+	1.35964i	0.0821777	+	0.0501169i
$737$	3.24131			0.119395
$738$	−6.58709	−	0.724368i	−0.242474	−	0.0266643i
$739$			42.2219i			1.55316i	0.630021	+	0.776578i	$0.283046\pi$
$739$			42.2219i			1.55316i	−0.630021	+	0.776578i	$0.716954\pi$
$740$	−14.5363	−	3.23619i	−0.534366	−	0.118965i
$741$		−	5.41299i		−	0.198851i
$742$	2.33120	−	21.1989i	0.0855809	−	0.778237i
$743$	16.3941			0.601442			0.300721	−	0.953712i	$-0.402773\pi$
$743$	16.3941			0.601442			0.300721	+	0.953712i	$0.402773\pi$
$744$	−1.48929	+	4.36815i	−0.0545998	+	0.160144i
$745$	−15.9180			−0.583192
$746$	−1.74564	+	15.8741i	−0.0639123	+	0.581191i
$747$		−	3.08546i		−	0.112891i
$748$	3.28052	−	14.7355i	0.119948	−	0.538782i
$749$		−	24.4884i		−	0.894786i
$750$	1.40574	+	0.154586i	0.0513303	+	0.00564468i
$751$	34.5359			1.26023			0.630117	−	0.776500i	$-0.283007\pi$
$751$	34.5359			1.26023			0.630117	+	0.776500i	$0.283007\pi$
$752$	−12.7859	−	5.98989i	−0.466256	−	0.218429i
$753$	−9.47493			−0.345286
$754$	−5.29630	−	0.582422i	−0.192880	−	0.0212106i
$755$			21.2193i			0.772250i
$756$	−1.16560	+	5.23566i	−0.0423926	+	0.190419i
$757$			22.5707i			0.820345i	0.912008	+	0.410172i	$0.134531\pi$
$757$			22.5707i			0.820345i	−0.912008	+	0.410172i	$0.865469\pi$
$758$	−0.135934	+	1.23612i	−0.00493733	+	0.0448980i
$759$	−1.68899			−0.0613064
$760$	14.4912	+	4.94065i	0.525650	+	0.179216i
$761$	42.1665			1.52854			0.764268	−	0.644899i	$-0.223101\pi$
$761$	42.1665			1.52854			0.764268	+	0.644899i	$0.223101\pi$
$762$	−2.35746	+	21.4378i	−0.0854019	+	0.776609i
$763$			20.3211i			0.735673i
$764$	23.8853	+	5.31752i	0.864139	+	0.192381i
$765$			2.06298i			0.0745873i
$766$	−22.9821	−	2.52729i	−0.830376	−	0.0913146i
$767$	3.65036			0.131807
$768$	12.2932	−	10.2409i	0.443593	−	0.369538i
$769$	19.3667			0.698381			0.349190	−	0.937052i	$-0.386457\pi$
$769$	19.3667			0.698381			0.349190	+	0.937052i	$0.386457\pi$
$770$	13.7941	+	1.51691i	0.497105	+	0.0546655i
$771$		−	25.6643i		−	0.924279i
$772$	30.8805	+	6.87485i	1.11141	+	0.247431i
$773$			7.55570i			0.271760i	0.990725	+	0.135880i	$0.0433861\pi$
$773$			7.55570i			0.271760i	−0.990725	+	0.135880i	$0.956614\pi$
$774$	0.515293	−	4.68586i	0.0185218	−	0.168430i
$775$	−1.63167			−0.0586112
$776$	−24.9688	−	8.51292i	−0.896328	−	0.305596i
$777$	19.9699			0.716415
$778$	−1.13609	+	10.3312i	−0.0407310	+	0.370390i
$779$		−	25.3645i		−	0.908778i
$780$	0.434615	−	1.95221i	0.0155617	−	0.0699002i
$781$		−	17.8964i		−	0.640384i
$782$	−1.33870	−	0.147214i	−0.0478720	−	0.00526437i
$783$	−3.76763			−0.134644
$784$	0.698005	+	0.326997i	0.0249288	+	0.0116785i
$785$	−9.74439			−0.347792
$786$	−2.22497	−	0.244675i	−0.0793622	−	0.00872728i
$787$		−	49.1811i		−	1.75312i	−0.481296	−	0.876558i	$-0.659834\pi$
$787$		−	49.1811i		−	1.75312i	0.481296	−	0.876558i	$-0.340166\pi$
$788$	6.43866	−	28.9212i	0.229368	−	1.03027i
$789$			20.9294i			0.745108i
$790$	−2.43696	+	22.1607i	−0.0867031	+	0.788441i
$791$	28.0678			0.997974
$792$	−3.33956	+	9.79509i	−0.118666	+	0.348053i
$793$	−4.27777			−0.151908
$794$	−3.75607	+	34.1561i	−0.133298	+	1.21215i
$795$			5.62294i			0.199425i
$796$	−37.8386	−	8.42392i	−1.34115	−	0.298578i
$797$		−	7.14045i		−	0.252928i	−0.991971	−	0.126464i	$-0.959637\pi$
$797$		−	7.14045i		−	0.252928i	0.991971	−	0.126464i	$-0.0403628\pi$
$798$	−20.4074	−	2.24416i	−0.722415	−	0.0794424i
$799$	7.28206			0.257621
$800$	4.82958	+	2.94537i	0.170751	+	0.104134i
$801$	−1.90866			−0.0674393
$802$	−32.9955	−	3.62843i	−1.16511	−	0.128124i
$803$			15.7610i			0.556195i
$804$	−1.72943	−	0.385019i	−0.0609923	−	0.0135786i
$805$		−	1.23803i		−	0.0436347i
$806$	−0.252233	+	2.29370i	−0.00888451	+	0.0807920i
$807$	−7.41190			−0.260911
$808$	9.85472	−	28.9044i	0.346688	−	1.01685i
$809$	25.5132			0.896995			0.448498	−	0.893784i	$-0.351959\pi$
$809$	25.5132			0.896995			0.448498	+	0.893784i	$0.351959\pi$
$810$	0.154586	−	1.40574i	0.00543160	−	0.0493926i
$811$		−	39.8927i		−	1.40082i	−0.713739	−	0.700411i	$-0.753000\pi$
$811$		−	39.8927i		−	1.40082i	0.713739	−	0.700411i	$-0.247000\pi$
$812$	−4.39156	+	19.7260i	−0.154113	+	0.692248i
$813$		−	22.2288i		−	0.779598i
$814$	38.2980	+	4.21155i	1.34235	+	0.147615i
$815$	3.07725			0.107791
$816$	−3.50071	+	7.47258i	−0.122549	+	0.261593i
$817$	18.0435			0.631264
$818$	−0.0826679	−	0.00909080i	−0.00289042	−	0.000317852i
$819$			2.68192i			0.0937139i
$820$	2.03654	−	9.14776i	0.0711192	−	0.319454i
$821$			42.3623i			1.47845i	0.673456	+	0.739227i	$0.264809\pi$
$821$			42.3623i			1.47845i	−0.673456	+	0.739227i	$0.735191\pi$
$822$	−2.63250	+	23.9388i	−0.0918189	+	0.834962i
$823$	45.2288			1.57658			0.788289	−	0.615305i	$-0.210967\pi$
$823$	45.2288			1.57658			0.788289	+	0.615305i	$0.210967\pi$
$824$	27.2070	+	9.27603i	0.947802	+	0.323146i
$825$	−3.65883			−0.127384
$826$	1.51339	−	13.7622i	0.0526577	−	0.478847i
$827$		−	35.6657i		−	1.24022i	−0.784515	−	0.620109i	$-0.787088\pi$
$827$		−	35.6657i		−	1.24022i	0.784515	−	0.620109i	$-0.212912\pi$
$828$	0.901176	+	0.200627i	0.0313180	+	0.00697226i
$829$		−	28.6512i		−	0.995097i	−0.867436	−	0.497548i	$-0.834234\pi$
$829$		−	28.6512i		−	0.995097i	0.867436	−	0.497548i	$-0.165766\pi$
$830$	4.33735	+	0.476968i	0.150551	+	0.0165558i
$831$	21.9465			0.761316
$832$	4.88700	−	6.33381i	0.169426	−	0.219586i
$833$	−0.397539			−0.0137739
$834$	−6.46933	−	0.711417i	−0.224015	−	0.0246344i
$835$			3.08440i			0.106740i
$836$	−38.6639	−	8.60766i	−1.33722	−	0.297702i
$837$			1.63167i			0.0563986i
$838$	−4.75561	+	43.2455i	−0.164280	+	1.49389i
$839$	−25.3537			−0.875307			−0.437654	−	0.899144i	$-0.644190\pi$
$839$	−25.3537			−0.875307			−0.437654	+	0.899144i	$0.644190\pi$
$840$	−7.17979	−	2.44789i	−0.247726	−	0.0844604i
$841$	14.8050			0.510517
$842$	−3.05681	+	27.7974i	−0.105345	+	0.957960i
$843$		−	22.7782i		−	0.784524i
$844$	−1.21969	+	5.47861i	−0.0419835	+	0.188582i
$845$		−	1.00000i		−	0.0344010i
$846$	−4.96207	−	0.545668i	−0.170600	−	0.0187604i
$847$	−6.40191			−0.219972
$848$	−9.54165	+	20.3675i	−0.327662	+	0.699423i
$849$	−24.0010			−0.823713
$850$	−2.90002	−	0.318908i	−0.0994698	−	0.0109385i
$851$		−	3.43727i		−	0.117828i
$852$	−2.12583	+	9.54881i	−0.0728297	+	0.327137i
$853$			25.6225i			0.877299i	0.898658	+	0.438650i	$0.144543\pi$
$853$			25.6225i			0.877299i	−0.898658	+	0.438650i	$0.855457\pi$
$854$	−1.77351	+	16.1275i	−0.0606882	+	0.551873i
$855$	5.41299			0.185121
$856$	−8.33414	+	24.4444i	−0.284855	+	0.835494i
$857$	20.7763			0.709706			0.354853	−	0.934922i	$-0.384531\pi$
$857$	20.7763			0.709706			0.354853	+	0.934922i	$0.384531\pi$
$858$	−0.565604	+	5.14337i	−0.0193094	+	0.175592i
$859$		−	0.646354i		−	0.0220533i	−0.999939	−	0.0110267i	$-0.996490\pi$
$859$		−	0.646354i		−	0.0220533i	0.999939	−	0.0110267i	$-0.00350997\pi$
$860$	6.50744	+	1.44874i	0.221902	+	0.0494015i
$861$			12.5671i			0.428286i
$862$	−38.5485	−	4.23909i	−1.31297	−	0.144384i
$863$	−1.29317			−0.0440201			−0.0220101	−	0.999758i	$-0.507007\pi$
$863$	−1.29317			−0.0440201			−0.0220101	+	0.999758i	$0.507007\pi$
$864$	2.94537	−	4.82958i	0.100203	−	0.164306i
$865$	−15.6744			−0.532944
$866$	−12.6376	−	1.38973i	−0.429444	−	0.0472250i
$867$			12.7441i			0.432812i
$868$	8.54285	+	1.90188i	0.289963	+	0.0645538i
$869$		−	57.6794i		−	1.95664i
$870$	0.582422	−	5.29630i	0.0197460	−	0.179561i
$871$	−0.885885			−0.0300171
$872$	6.91589	−	20.2846i	0.234201	−	0.686924i
$873$	−9.32678			−0.315664
$874$	−0.386270	+	3.51258i	−0.0130658	+	0.118815i
$875$		−	2.68192i		−	0.0906655i
$876$	1.87218	−	8.40946i	0.0632551	−	0.284129i
$877$		−	51.3563i		−	1.73418i	−0.498151	−	0.867090i	$-0.665987\pi$
$877$		−	51.3563i		−	1.73418i	0.498151	−	0.867090i	$-0.334013\pi$
$878$	−50.7261	−	5.57824i	−1.71192	−	0.188256i
$879$	−23.4482			−0.790887
$880$	−13.2531	−	6.20874i	−0.446762	−	0.209296i
$881$	8.99343			0.302996			0.151498	−	0.988458i	$-0.451590\pi$
$881$	8.99343			0.302996			0.151498	+	0.988458i	$0.451590\pi$
$882$	0.270887	+	0.0297889i	0.00912125	+	0.00100304i
$883$		−	59.2011i		−	1.99227i	−0.0878087	−	0.996137i	$-0.527986\pi$
$883$		−	59.2011i		−	1.99227i	0.0878087	−	0.996137i	$-0.472014\pi$
$884$	−0.896604	+	4.02737i	−0.0301560	+	0.135455i
$885$			3.65036i			0.122706i
$886$	1.37752	−	12.5266i	0.0462786	−	0.420838i
$887$	17.6505			0.592646			0.296323	−	0.955088i	$-0.404240\pi$
$887$	17.6505			0.592646			0.296323	+	0.955088i	$0.404240\pi$
$888$	−19.9340	−	6.79635i	−0.668942	−	0.228071i
$889$	40.8998			1.37173
$890$	0.295052	−	2.68308i	0.00989018	−	0.0899371i
$891$			3.65883i			0.122576i
$892$	9.82069	+	2.18636i	0.328821	+	0.0732046i
$893$		−	19.1071i		−	0.639396i
$894$	−22.3766	−	2.46070i	−0.748386	−	0.0822982i
$895$	−1.98266			−0.0662729
$896$	−21.8529	−	21.0503i	−0.730055	−	0.703242i
$897$	0.461619			0.0154130
$898$	−47.2204	−	5.19272i	−1.57577	−	0.173283i
$899$			6.14751i			0.205031i
$900$	1.95221	+	0.434615i	0.0650735	+	0.0144872i
$901$		−	11.6000i		−	0.386453i
$902$	−2.65034	+	24.1011i	−0.0882467	+	0.802478i
$903$	−8.93985			−0.297500
$904$	−28.0174	−	9.55231i	−0.931844	−	0.317705i
$905$	−12.4177			−0.412780
$906$	−3.28021	+	29.8288i	−0.108978	+	0.990997i
$907$		−	49.1464i		−	1.63188i	−0.578136	−	0.815940i	$-0.696220\pi$
$907$		−	49.1464i		−	1.63188i	0.578136	−	0.815940i	$-0.303780\pi$
$908$	6.59842	−	29.6388i	0.218976	−	0.983599i
$909$		−	10.7969i		−	0.358109i
$910$	−3.77008	−	0.414587i	−0.124977	−	0.0137434i
$911$	−4.55660			−0.150967			−0.0754835	−	0.997147i	$-0.524050\pi$
$911$	−4.55660			−0.150967			−0.0754835	+	0.997147i	$0.524050\pi$
$912$	19.6071	+	9.18540i	0.649254	+	0.304159i
$913$	−11.2892			−0.373617
$914$	54.4280	+	5.98532i	1.80032	+	0.197977i
$915$		−	4.27777i		−	0.141419i
$916$	−8.20516	+	36.8560i	−0.271106	+	1.21776i
$917$			4.24489i			0.140178i
$918$	−0.318908	+	2.90002i	−0.0105255	+	0.0957148i
$919$	26.7052			0.880925			0.440462	−	0.897771i	$-0.354815\pi$
$919$	26.7052			0.880925			0.440462	+	0.897771i	$0.354815\pi$
$920$	−0.421338	+	1.23580i	−0.0138911	+	0.0407433i
$921$	11.0199			0.363118
$922$	0.626714	−	5.69908i	0.0206397	−	0.187689i
$923$			4.89129i			0.160999i
$924$	19.1564	+	4.26475i	0.630200	+	0.140300i
$925$		−	7.44611i		−	0.244826i
$926$	20.8975	+	2.29805i	0.686735	+	0.0755186i
$927$	10.1628			0.333792
$928$	11.0970	−	18.1960i	0.364278	−	0.597314i
$929$	−32.3021			−1.05980			−0.529899	−	0.848061i	$-0.677770\pi$
$929$	−32.3021			−1.05980			−0.529899	+	0.848061i	$0.677770\pi$
$930$	−2.29370	−	0.252233i	−0.0752133	−	0.00827103i
$931$			1.04309i			0.0341859i
$932$	−30.7706	−	6.85039i	−1.00793	−	0.224392i
$933$		−	4.43687i		−	0.145257i
$934$	5.23940	−	47.6449i	0.171438	−	1.55899i
$935$	7.54811			0.246850
$936$	0.912739	−	2.67711i	0.0298338	−	0.0875040i
$937$	−22.9706			−0.750415			−0.375208	−	0.926941i	$-0.622429\pi$
$937$	−22.9706			−0.750415			−0.375208	+	0.926941i	$0.622429\pi$
$938$	−0.367277	+	3.33986i	−0.0119920	+	0.109050i
$939$			19.0588i			0.621960i
$940$	1.53413	−	6.89103i	0.0500379	−	0.224760i
$941$			15.7011i			0.511841i	0.966698	+	0.255920i	$0.0823785\pi$
$941$			15.7011i			0.511841i	−0.966698	+	0.255920i	$0.917622\pi$
$942$	−13.6981	−	1.50635i	−0.446307	−	0.0490794i
$943$	2.16308			0.0704396
$944$	−6.19436	+	13.2224i	−0.201609	+	0.430353i
$945$	−2.68192			−0.0872429
$946$	−17.1448	−	1.88537i	−0.557425	−	0.0612987i
$947$			24.9752i			0.811585i	0.913965	+	0.405792i	$0.133004\pi$
$947$			24.9752i			0.811585i	−0.913965	+	0.405792i	$0.866996\pi$
$948$	−6.85146	+	30.7754i	−0.222525	+	0.999539i
$949$		−	4.30767i		−	0.139833i
$950$	−0.836773	+	7.60926i	−0.0271485	+	0.246877i
$951$	15.2599			0.494837
$952$	14.8118	+	5.04997i	0.480053	+	0.163670i
$953$	−8.31371			−0.269308			−0.134654	−	0.990893i	$-0.542992\pi$
$953$	−8.31371			−0.269308			−0.134654	+	0.990893i	$0.542992\pi$
$954$	−0.869227	+	7.90438i	−0.0281423	+	0.255914i
$955$			12.2350i			0.395916i
$956$	1.36457	+	0.303791i	0.0441334	+	0.00982531i
$957$			13.7851i			0.445610i
$958$	40.1360	+	4.41366i	1.29674	+	0.142599i
$959$	45.6714			1.47481
$960$	6.33381	+	4.88700i	0.204423	+	0.157727i
$961$	−28.3377			−0.914118
$962$	−10.4673	−	1.15106i	−0.337479	−	0.0371118i
$963$			9.13091i			0.294239i
$964$	−22.2940	−	4.96326i	−0.718042	−	0.159856i
$965$			15.8183i			0.509208i
$966$	0.191381	−	1.74034i	0.00615760	−	0.0559946i
$967$	−10.6898			−0.343761			−0.171881	−	0.985118i	$-0.554984\pi$
$967$	−10.6898			−0.343761			−0.171881	+	0.985118i	$0.554984\pi$
$968$	6.39042	+	2.17876i	0.205396	+	0.0700282i
$969$	−11.1669			−0.358733
$970$	1.44179	−	13.1110i	0.0462931	−	0.420970i
$971$			41.5427i			1.33317i	0.745430	+	0.666584i	$0.232244\pi$
$971$			41.5427i			1.33317i	−0.745430	+	0.666584i	$0.767756\pi$
$972$	0.434615	−	1.95221i	0.0139403	−	0.0626170i
$973$			12.3424i			0.395680i
$974$	49.4925	+	5.44257i	1.58584	+	0.174391i
$975$	1.00000			0.0320256
$976$	7.25902	−	15.4950i	0.232356	−	0.495984i
$977$	24.5483			0.785371			0.392685	−	0.919673i	$-0.371546\pi$
$977$	24.5483			0.785371			0.392685	+	0.919673i	$0.371546\pi$
$978$	4.32581	+	0.475699i	0.138324	+	0.0152112i
$979$			6.98348i			0.223193i
$980$	−0.0837507	+	0.376192i	−0.00267532	+	0.0120170i
$981$		−	7.57707i		−	0.241917i
$982$	−5.39599	+	49.0688i	−0.172193	+	1.56585i
$983$	−17.6254			−0.562162			−0.281081	−	0.959684i	$-0.590693\pi$
$983$	−17.6254			−0.562162			−0.281081	+	0.959684i	$0.590693\pi$
$984$	4.27697	−	12.5445i	0.136345	−	0.399906i
$985$	14.8146			0.472033
$986$	−1.20153	+	10.9262i	−0.0382644	+	0.347961i
$987$			9.46682i			0.301332i
$988$	10.5673	+	2.35257i	0.336190	+	0.0748452i
$989$			1.53875i			0.0489294i
$990$	−5.14337	−	0.565604i	−0.163467	−	0.0179761i
$991$	−16.6848			−0.530009			−0.265005	−	0.964247i	$-0.585373\pi$
$991$	−16.6848			−0.530009			−0.265005	+	0.964247i	$0.585373\pi$
$992$	−7.88026	−	4.80585i	−0.250198	−	0.152586i
$993$	−17.8967			−0.567934
$994$	18.4406	+	2.02787i	0.584899	+	0.0643200i
$995$		−	19.3825i		−	0.614466i
$996$	6.02345	+	1.34099i	0.190860	+	0.0424907i
$997$		−	50.1226i		−	1.58740i	−0.608311	−	0.793699i	$-0.708152\pi$
$997$		−	50.1226i		−	1.58740i	0.608311	−	0.793699i	$-0.291848\pi$
$998$	1.25162	−	11.3817i	0.0396192	−	0.360280i
$999$	−7.44611			−0.235584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1560.2.w.h.781.1	✓	26
4.3	odd	2		6240.2.w.h.3121.4		26
8.3	odd	2		6240.2.w.h.3121.3		26
8.5	even	2	inner	1560.2.w.h.781.2	yes	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.2.w.h.781.1	✓	26	1.1	even	1	trivial
1560.2.w.h.781.2	yes	26	8.5	even	2	inner
6240.2.w.h.3121.3		26	8.3	odd	2
6240.2.w.h.3121.4		26	4.3	odd	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:	\( N \)	\(=\)	\( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1560.w (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40574 - 0.154586i) q^{2} -1.00000i q^{3} +(1.95221 + 0.434615i) q^{4} +1.00000i q^{5} +(-0.154586 + 1.40574i) q^{6} +2.68192 q^{7} +(-2.67711 - 0.912739i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.40574 - 0.154586i) q^{2} -1.00000i q^{3} +(1.95221 + 0.434615i) q^{4} +1.00000i q^{5} +(-0.154586 + 1.40574i) q^{6} +2.68192 q^{7} +(-2.67711 - 0.912739i) q^{8} -1.00000 q^{9} +(0.154586 - 1.40574i) q^{10} +3.65883i q^{11} +(0.434615 - 1.95221i) q^{12} -1.00000i q^{13} +(-3.77008 - 0.414587i) q^{14} +1.00000 q^{15} +(3.62222 + 1.69692i) q^{16} -2.06298 q^{17} +(1.40574 + 0.154586i) q^{18} +5.41299i q^{19} +(-0.434615 + 1.95221i) q^{20} -2.68192i q^{21} +(0.565604 - 5.14337i) q^{22} -0.461619 q^{23} +(-0.912739 + 2.67711i) q^{24} -1.00000 q^{25} +(-0.154586 + 1.40574i) q^{26} +1.00000i q^{27} +(5.23566 + 1.16560i) q^{28} +3.76763i q^{29} +(-1.40574 - 0.154586i) q^{30} +1.63167 q^{31} +(-4.82958 - 2.94537i) q^{32} +3.65883 q^{33} +(2.90002 + 0.318908i) q^{34} +2.68192i q^{35} +(-1.95221 - 0.434615i) q^{36} +7.44611i q^{37} +(0.836773 - 7.60926i) q^{38} -1.00000 q^{39} +(0.912739 - 2.67711i) q^{40} -4.68586 q^{41} +(-0.414587 + 3.77008i) q^{42} -3.33338i q^{43} +(-1.59018 + 7.14280i) q^{44} -1.00000i q^{45} +(0.648916 + 0.0713598i) q^{46} -3.52987 q^{47} +(1.69692 - 3.62222i) q^{48} +0.192701 q^{49} +(1.40574 + 0.154586i) q^{50} +2.06298i q^{51} +(0.434615 - 1.95221i) q^{52} +5.62294i q^{53} +(0.154586 - 1.40574i) q^{54} -3.65883 q^{55} +(-7.17979 - 2.44789i) q^{56} +5.41299 q^{57} +(0.582422 - 5.29630i) q^{58} +3.65036i q^{59} +(1.95221 + 0.434615i) q^{60} -4.27777i q^{61} +(-2.29370 - 0.252233i) q^{62} -2.68192 q^{63} +(6.33381 + 4.88700i) q^{64} +1.00000 q^{65} +(-5.14337 - 0.565604i) q^{66} -0.885885i q^{67} +(-4.02737 - 0.896604i) q^{68} +0.461619i q^{69} +(0.414587 - 3.77008i) q^{70} -4.89129 q^{71} +(2.67711 + 0.912739i) q^{72} +4.30767 q^{73} +(1.15106 - 10.4673i) q^{74} +1.00000i q^{75} +(-2.35257 + 10.5673i) q^{76} +9.81270i q^{77} +(1.40574 + 0.154586i) q^{78} -15.7644 q^{79} +(-1.69692 + 3.62222i) q^{80} +1.00000 q^{81} +(6.58709 + 0.724368i) q^{82} +3.08546i q^{83} +(1.16560 - 5.23566i) q^{84} -2.06298i q^{85} +(-0.515293 + 4.68586i) q^{86} +3.76763 q^{87} +(3.33956 - 9.79509i) q^{88} +1.90866 q^{89} +(-0.154586 + 1.40574i) q^{90} -2.68192i q^{91} +(-0.901176 - 0.200627i) q^{92} -1.63167i q^{93} +(4.96207 + 0.545668i) q^{94} -5.41299 q^{95} +(-2.94537 + 4.82958i) q^{96} +9.32678 q^{97} +(-0.270887 - 0.0297889i) q^{98} -3.65883i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{2} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 26 q^{9}+O(q^{10}) \) 26 * q - 2 * q^2 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 26 * q^9	\( 26 q - 2 q^{2} - 2 q^{6} - 4 q^{7} + 4 q^{8} - 26 q^{9} + 2 q^{10} + 10 q^{14} + 26 q^{15} + 12 q^{16} + 28 q^{17} + 2 q^{18} + 10 q^{22} - 12 q^{23} - 4 q^{24} - 26 q^{25} - 2 q^{26} - 4 q^{28} - 2 q^{30} - 20 q^{31} + 8 q^{32} - 30 q^{34} + 40 q^{38} - 26 q^{39} + 4 q^{40} + 6 q^{42} + 42 q^{46} + 36 q^{47} - 8 q^{48} + 42 q^{49} + 2 q^{50} + 2 q^{54} + 40 q^{56} - 12 q^{57} - 16 q^{58} - 4 q^{62} + 4 q^{63} - 12 q^{64} + 26 q^{65} + 6 q^{66} - 24 q^{68} - 6 q^{70} - 52 q^{71} - 4 q^{72} - 32 q^{73} - 62 q^{74} - 40 q^{76} + 2 q^{78} + 28 q^{79} + 8 q^{80} + 26 q^{81} - 18 q^{82} - 8 q^{84} + 8 q^{86} - 20 q^{87} - 36 q^{88} - 2 q^{90} + 16 q^{92} + 72 q^{94} + 12 q^{95} - 12 q^{96} + 56 q^{97} - 76 q^{98}+O(q^{100}) \) 26 * q - 2 * q^2 - 2 * q^6 - 4 * q^7 + 4 * q^8 - 26 * q^9 + 2 * q^10 + 10 * q^14 + 26 * q^15 + 12 * q^16 + 28 * q^17 + 2 * q^18 + 10 * q^22 - 12 * q^23 - 4 * q^24 - 26 * q^25 - 2 * q^26 - 4 * q^28 - 2 * q^30 - 20 * q^31 + 8 * q^32 - 30 * q^34 + 40 * q^38 - 26 * q^39 + 4 * q^40 + 6 * q^42 + 42 * q^46 + 36 * q^47 - 8 * q^48 + 42 * q^49 + 2 * q^50 + 2 * q^54 + 40 * q^56 - 12 * q^57 - 16 * q^58 - 4 * q^62 + 4 * q^63 - 12 * q^64 + 26 * q^65 + 6 * q^66 - 24 * q^68 - 6 * q^70 - 52 * q^71 - 4 * q^72 - 32 * q^73 - 62 * q^74 - 40 * q^76 + 2 * q^78 + 28 * q^79 + 8 * q^80 + 26 * q^81 - 18 * q^82 - 8 * q^84 + 8 * q^86 - 20 * q^87 - 36 * q^88 - 2 * q^90 + 16 * q^92 + 72 * q^94 + 12 * q^95 - 12 * q^96 + 56 * q^97 - 76 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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