LMFDB - Embedded newform 930.2.h.d.371.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(371,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("930.371");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.h (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} + 36x^{10} - 142x^{8} + 324x^{6} + 486x^{4} - 2916x^{2} + 6561 $ x^16 - 4x^14 + 6x^12 + 36x^10 - 142x^8 + 324x^6 + 486x^4 - 2916*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			371.7
Root			$1.29725 - 1.14767i$ of defining polynomial
Character	$\chi$	$=$	930.371
Dual form			930.2.h.d.371.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.14767 - 1.29725i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.29725 - 1.14767i) q^{6} +3.69457 q^{7} +1.00000i q^{8} +(-0.365730 - 2.97762i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.14767 - 1.29725i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.29725 - 1.14767i) q^{6} +3.69457 q^{7} +1.00000i q^{8} +(-0.365730 - 2.97762i) q^{9} +1.00000 q^{10} +0.851837 q^{11} +(-1.14767 + 1.29725i) q^{12} +2.29533i q^{13} -3.69457i q^{14} +(1.29725 + 1.14767i) q^{15} +1.00000 q^{16} +1.10532 q^{17} +(-2.97762 + 0.365730i) q^{18} +4.96311 q^{19} -1.00000i q^{20} +(4.24012 - 4.79279i) q^{21} -0.851837i q^{22} +1.74267 q^{23} +(1.29725 + 1.14767i) q^{24} -1.00000 q^{25} +2.29533 q^{26} +(-4.28247 - 2.94287i) q^{27} -3.69457 q^{28} -4.78042 q^{29} +(1.14767 - 1.29725i) q^{30} +(3.77724 - 4.09054i) q^{31} -1.00000i q^{32} +(0.977624 - 1.10505i) q^{33} -1.10532i q^{34} +3.69457i q^{35} +(0.365730 + 2.97762i) q^{36} -2.69958i q^{37} -4.96311i q^{38} +(2.97762 + 2.63427i) q^{39} -1.00000 q^{40} +1.95525i q^{41} +(-4.79279 - 4.24012i) q^{42} -1.65798i q^{43} -0.851837 q^{44} +(2.97762 - 0.365730i) q^{45} -1.74267i q^{46} +4.65767i q^{47} +(1.14767 - 1.29725i) q^{48} +6.64981 q^{49} +1.00000i q^{50} +(1.26854 - 1.43388i) q^{51} -2.29533i q^{52} -13.1166 q^{53} +(-2.94287 + 4.28247i) q^{54} +0.851837i q^{55} +3.69457i q^{56} +(5.69598 - 6.43840i) q^{57} +4.78042i q^{58} -7.91049i q^{59} +(-1.29725 - 1.14767i) q^{60} +3.10148i q^{61} +(-4.09054 - 3.77724i) q^{62} +(-1.35121 - 11.0010i) q^{63} -1.00000 q^{64} -2.29533 q^{65} +(-1.10505 - 0.977624i) q^{66} +10.0758 q^{67} -1.10532 q^{68} +(2.00000 - 2.26068i) q^{69} +3.69457 q^{70} -0.0953391i q^{71} +(2.97762 - 0.365730i) q^{72} -16.2181i q^{73} -2.69958 q^{74} +(-1.14767 + 1.29725i) q^{75} -4.96311 q^{76} +3.14717 q^{77} +(2.63427 - 2.97762i) q^{78} +13.5142i q^{79} +1.00000i q^{80} +(-8.73248 + 2.17801i) q^{81} +1.95525 q^{82} -14.0668 q^{83} +(-4.24012 + 4.79279i) q^{84} +1.10532i q^{85} -1.65798 q^{86} +(-5.48632 + 6.20141i) q^{87} +0.851837i q^{88} -3.95331 q^{89} +(-0.365730 - 2.97762i) q^{90} +8.48025i q^{91} -1.74267 q^{92} +(-0.971456 - 9.59460i) q^{93} +4.65767 q^{94} +4.96311i q^{95} +(-1.29725 - 1.14767i) q^{96} +6.65767 q^{97} -6.64981i q^{98} +(-0.311542 - 2.53645i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 + 4 * q^7 - 8 * q^9	$ 16 q - 16 q^{4} + 4 q^{7} - 8 q^{9} + 16 q^{10} + 16 q^{16} - 8 q^{18} + 20 q^{19} - 16 q^{25} - 4 q^{28} - 8 q^{31} - 24 q^{33} + 8 q^{36} + 8 q^{39} - 16 q^{40} + 8 q^{45} - 28 q^{49} + 16 q^{51} - 4 q^{63} - 16 q^{64} - 44 q^{66} - 24 q^{67} + 32 q^{69} + 4 q^{70} + 8 q^{72} - 20 q^{76} + 40 q^{78} + 8 q^{81} - 48 q^{82} + 16 q^{87} - 8 q^{90} + 12 q^{93} - 40 q^{94} - 8 q^{97}+O(q^{100}) $ 16 * q - 16 * q^4 + 4 * q^7 - 8 * q^9 + 16 * q^10 + 16 * q^16 - 8 * q^18 + 20 * q^19 - 16 * q^25 - 4 * q^28 - 8 * q^31 - 24 * q^33 + 8 * q^36 + 8 * q^39 - 16 * q^40 + 8 * q^45 - 28 * q^49 + 16 * q^51 - 4 * q^63 - 16 * q^64 - 44 * q^66 - 24 * q^67 + 32 * q^69 + 4 * q^70 + 8 * q^72 - 20 * q^76 + 40 * q^78 + 8 * q^81 - 48 * q^82 + 16 * q^87 - 8 * q^90 + 12 * q^93 - 40 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.14767	−	1.29725i	0.662605	−	0.748969i
$3$	1.14767	−	1.29725i	0.662605	−	0.748969i
$4$	−1.00000			−0.500000
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.29725	−	1.14767i	−0.529601	−	0.468532i
$7$	3.69457			1.39641			0.698207	−	0.715896i	$-0.253981\pi$
$7$	3.69457			1.39641			0.698207	+	0.715896i	$0.253981\pi$
$8$			1.00000i			0.353553i
$9$	−0.365730	−	2.97762i	−0.121910	−	0.992541i
$10$	1.00000			0.316228
$11$	0.851837			0.256838			0.128419	−	0.991720i	$-0.459010\pi$
$11$	0.851837			0.256838			0.128419	+	0.991720i	$0.459010\pi$
$12$	−1.14767	+	1.29725i	−0.331302	+	0.374485i
$13$			2.29533i			0.636610i	0.947988	+	0.318305i	$0.103114\pi$
$13$			2.29533i			0.636610i	−0.947988	+	0.318305i	$0.896886\pi$
$14$		−	3.69457i		−	0.987414i
$15$	1.29725	+	1.14767i	0.334949	+	0.296326i
$16$	1.00000			0.250000
$17$	1.10532			0.268080			0.134040	−	0.990976i	$-0.457205\pi$
$17$	1.10532			0.268080			0.134040	+	0.990976i	$0.457205\pi$
$18$	−2.97762	+	0.365730i	−0.701833	+	0.0862033i
$19$	4.96311			1.13861			0.569307	−	0.822125i	$-0.307211\pi$
$19$	4.96311			1.13861			0.569307	+	0.822125i	$0.307211\pi$
$20$		−	1.00000i		−	0.223607i
$21$	4.24012	−	4.79279i	0.925271	−	1.04587i
$22$		−	0.851837i		−	0.181612i
$23$	1.74267			0.363372			0.181686	−	0.983357i	$-0.441845\pi$
$23$	1.74267			0.363372			0.181686	+	0.983357i	$0.441845\pi$
$24$	1.29725	+	1.14767i	0.264801	+	0.234266i
$25$	−1.00000			−0.200000
$26$	2.29533			0.450151
$27$	−4.28247	−	2.94287i	−0.824161	−	0.566356i
$28$	−3.69457			−0.698207
$29$	−4.78042			−0.887701			−0.443851	−	0.896101i	$-0.646388\pi$
$29$	−4.78042			−0.887701			−0.443851	+	0.896101i	$0.646388\pi$
$30$	1.14767	−	1.29725i	0.209534	−	0.236845i
$31$	3.77724	−	4.09054i	0.678412	−	0.734682i
$31$	3.77724	−	4.09054i	0.678412	−	0.734682i
$32$		−	1.00000i		−	0.176777i
$33$	0.977624	−	1.10505i	0.170182	−	0.192364i
$34$		−	1.10532i		−	0.189561i
$35$			3.69457i			0.624496i
$36$	0.365730	+	2.97762i	0.0609549	+	0.496271i
$37$		−	2.69958i		−	0.443808i	−0.975069	−	0.221904i	$-0.928773\pi$
$37$		−	2.69958i		−	0.443808i	0.975069	−	0.221904i	$-0.0712272\pi$
$38$		−	4.96311i		−	0.805122i
$39$	2.97762	+	2.63427i	0.476801	+	0.421821i
$40$	−1.00000			−0.158114
$41$			1.95525i			0.305358i	0.988276	+	0.152679i	$0.0487901\pi$
$41$			1.95525i			0.305358i	−0.988276	+	0.152679i	$0.951210\pi$
$42$	−4.79279	−	4.24012i	−0.739543	−	0.654265i
$43$		−	1.65798i		−	0.252840i	−0.991977	−	0.126420i	$-0.959651\pi$
$43$		−	1.65798i		−	0.252840i	0.991977	−	0.126420i	$-0.0403487\pi$
$44$	−0.851837			−0.128419
$45$	2.97762	−	0.365730i	0.443878	−	0.0545198i
$46$		−	1.74267i		−	0.256942i
$47$			4.65767i			0.679391i	0.940535	+	0.339696i	$0.110324\pi$
$47$			4.65767i			0.679391i	−0.940535	+	0.339696i	$0.889676\pi$
$48$	1.14767	−	1.29725i	0.165651	−	0.187242i
$49$	6.64981			0.949973
$50$			1.00000i			0.141421i
$51$	1.26854	−	1.43388i	0.177631	−	0.200784i
$52$		−	2.29533i		−	0.318305i
$53$	−13.1166			−1.80170			−0.900852	−	0.434127i	$-0.857057\pi$
$53$	−13.1166			−1.80170			−0.900852	+	0.434127i	$0.857057\pi$
$54$	−2.94287	+	4.28247i	−0.400474	+	0.582770i
$55$			0.851837i			0.114862i
$56$			3.69457i			0.493707i
$57$	5.69598	−	6.43840i	0.754451	−	0.852787i
$58$			4.78042i			0.627700i
$59$		−	7.91049i		−	1.02986i	−0.857233	−	0.514929i	$-0.827818\pi$
$59$		−	7.91049i		−	1.02986i	0.857233	−	0.514929i	$-0.172182\pi$
$60$	−1.29725	−	1.14767i	−0.167475	−	0.148163i
$61$			3.10148i			0.397104i	0.980090	+	0.198552i	$0.0636238\pi$
$61$			3.10148i			0.397104i	−0.980090	+	0.198552i	$0.936376\pi$
$62$	−4.09054	−	3.77724i	−0.519499	−	0.479710i
$63$	−1.35121	−	11.0010i	−0.170237	−	1.38600i
$64$	−1.00000			−0.125000
$65$	−2.29533			−0.284701
$66$	−1.10505	−	0.977624i	−0.136022	−	0.120337i
$67$	10.0758			1.23096			0.615480	−	0.788153i	$-0.288962\pi$
$67$	10.0758			1.23096			0.615480	+	0.788153i	$0.288962\pi$
$68$	−1.10532			−0.134040
$69$	2.00000	−	2.26068i	0.240772	−	0.272154i
$70$	3.69457			0.441585
$71$		−	0.0953391i		−	0.0113147i	−0.999984	−	0.00565733i	$-0.998199\pi$
$71$		−	0.0953391i		−	0.0113147i	0.999984	−	0.00565733i	$-0.00180079\pi$
$72$	2.97762	−	0.365730i	0.350916	−	0.0431017i
$73$		−	16.2181i		−	1.89818i	−0.315002	−	0.949091i	$-0.602005\pi$
$73$		−	16.2181i		−	1.89818i	0.315002	−	0.949091i	$-0.397995\pi$
$74$	−2.69958			−0.313820
$75$	−1.14767	+	1.29725i	−0.132521	+	0.149794i
$76$	−4.96311			−0.569307
$77$	3.14717			0.358653
$78$	2.63427	−	2.97762i	0.298272	−	0.337149i
$79$			13.5142i			1.52046i	0.649654	+	0.760230i	$0.274914\pi$
$79$			13.5142i			1.52046i	−0.649654	+	0.760230i	$0.725086\pi$
$80$			1.00000i			0.111803i
$81$	−8.73248	+	2.17801i	−0.970276	+	0.242001i
$82$	1.95525			0.215921
$83$	−14.0668			−1.54403			−0.772017	−	0.635602i	$-0.780752\pi$
$83$	−14.0668			−1.54403			−0.772017	+	0.635602i	$0.780752\pi$
$84$	−4.24012	+	4.79279i	−0.462635	+	0.522936i
$85$			1.10532i			0.119889i
$86$	−1.65798			−0.178785
$87$	−5.48632	+	6.20141i	−0.588195	+	0.664861i
$88$			0.851837i			0.0908061i
$89$	−3.95331			−0.419051			−0.209525	−	0.977803i	$-0.567192\pi$
$89$	−3.95331			−0.419051			−0.209525	+	0.977803i	$0.567192\pi$
$90$	−0.365730	−	2.97762i	−0.0385513	−	0.313869i
$91$			8.48025i			0.888971i
$92$	−1.74267			−0.181686
$93$	−0.971456	−	9.59460i	−0.100735	−	0.994913i
$94$	4.65767			0.480402
$95$			4.96311i			0.509204i
$96$	−1.29725	−	1.14767i	−0.132400	−	0.117133i
$97$	6.65767			0.675984			0.337992	−	0.941149i	$-0.390252\pi$
$97$	6.65767			0.675984			0.337992	+	0.941149i	$0.390252\pi$
$98$		−	6.64981i		−	0.671732i
$99$	−0.311542	−	2.53645i	−0.0313112	−	0.254923i
$100$	1.00000			0.100000
$101$			7.81516i			0.777637i	0.921314	+	0.388818i	$0.127117\pi$
$101$			7.81516i			0.777637i	−0.921314	+	0.388818i	$0.872883\pi$
$102$	−1.43388	−	1.26854i	−0.141976	−	0.125604i
$103$	−7.22379			−0.711781			−0.355890	−	0.934528i	$-0.615822\pi$
$103$	−7.22379			−0.711781			−0.355890	+	0.934528i	$0.615822\pi$
$104$	−2.29533			−0.225076
$105$	4.79279	+	4.24012i	0.467728	+	0.413794i
$106$			13.1166i			1.27400i
$107$			6.94739i			0.671629i	0.941928	+	0.335815i	$0.109012\pi$
$107$			6.94739i			0.671629i	−0.941928	+	0.335815i	$0.890988\pi$
$108$	4.28247	+	2.94287i	0.412080	+	0.283178i
$109$	−16.4476			−1.57539			−0.787696	−	0.616064i	$-0.788726\pi$
$109$	−16.4476			−1.57539			−0.787696	+	0.616064i	$0.788726\pi$
$110$	0.851837			0.0812195
$111$	−3.50204	−	3.09821i	−0.332399	−	0.294069i
$112$	3.69457			0.349104
$113$			15.0680i			1.41748i	0.705472	+	0.708738i	$0.250735\pi$
$113$			15.0680i			1.41748i	−0.705472	+	0.708738i	$0.749265\pi$
$114$	−6.43840	−	5.69598i	−0.603012	−	0.533478i
$115$			1.74267i			0.162505i
$116$	4.78042			0.443851
$117$	6.83463	−	0.839470i	0.631862	−	0.0776091i
$118$	−7.91049			−0.728220
$119$	4.08369			0.374351
$120$	−1.14767	+	1.29725i	−0.104767	+	0.118422i
$121$	−10.2744			−0.934034
$122$	3.10148			0.280795
$123$	2.53645	+	2.24397i	0.228704	+	0.202332i
$124$	−3.77724	+	4.09054i	−0.339206	+	0.367341i
$125$		−	1.00000i		−	0.0894427i
$126$	−11.0010	+	1.35121i	−0.980049	+	0.120376i
$127$		−	4.18876i		−	0.371693i	−0.982579	−	0.185846i	$-0.940497\pi$
$127$		−	4.18876i		−	0.371693i	0.982579	−	0.185846i	$-0.0595026\pi$
$128$			1.00000i			0.0883883i
$129$	−2.15083	−	1.90281i	−0.189370	−	0.167533i
$130$			2.29533i			0.201314i
$131$		−	11.9105i		−	1.04062i	−0.853976	−	0.520312i	$-0.825816\pi$
$131$		−	11.9105i		−	1.04062i	0.853976	−	0.520312i	$-0.174184\pi$
$132$	−0.977624	+	1.10505i	−0.0850912	+	0.0961821i
$133$	18.3365			1.58998
$134$		−	10.0758i		−	0.870420i
$135$	2.94287	−	4.28247i	0.253282	−	0.368576i
$136$			1.10532i			0.0947807i
$137$	20.2765			1.73234			0.866168	−	0.499754i	$-0.166576\pi$
$137$	20.2765			1.73234			0.866168	+	0.499754i	$0.166576\pi$
$138$	−2.26068	−	2.00000i	−0.192442	−	0.170251i
$139$			13.3657i			1.13367i	0.823832	+	0.566834i	$0.191832\pi$
$139$			13.3657i			1.13367i	−0.823832	+	0.566834i	$0.808168\pi$
$140$		−	3.69457i		−	0.312248i
$141$	6.04218	+	5.34545i	0.508843	+	0.450168i
$142$	−0.0953391			−0.00800068
$143$			1.95525i			0.163506i
$144$	−0.365730	−	2.97762i	−0.0304775	−	0.248135i
$145$		−	4.78042i		−	0.396992i
$146$	−16.2181			−1.34222
$147$	7.63176	−	8.62649i	0.629457	−	0.711501i
$148$			2.69958i			0.221904i
$149$			0.0953391i			0.00781048i	0.999992	+	0.00390524i	$0.00124308\pi$
$149$			0.0953391i			0.00781048i	−0.999992	+	0.00390524i	$0.998757\pi$
$150$	1.29725	+	1.14767i	0.105920	+	0.0937065i
$151$			5.20271i			0.423390i	0.977336	+	0.211695i	$0.0678984\pi$
$151$			5.20271i			0.423390i	−0.977336	+	0.211695i	$0.932102\pi$
$152$			4.96311i			0.402561i
$153$	−0.404249	−	3.29124i	−0.0326816	−	0.266081i
$154$		−	3.14717i		−	0.253606i
$155$	4.09054	+	3.77724i	0.328560	+	0.303395i
$156$	−2.97762	−	2.63427i	−0.238401	−	0.210910i
$157$	11.1442			0.889401			0.444701	−	0.895679i	$-0.353310\pi$
$157$	11.1442			0.889401			0.444701	+	0.895679i	$0.353310\pi$
$158$	13.5142			1.07513
$159$	−15.0535	+	17.0155i	−1.19382	+	1.34942i
$160$	1.00000			0.0790569
$161$	6.43840			0.507417
$162$	2.17801	+	8.73248i	0.171121	+	0.686089i
$163$	−7.62826			−0.597492			−0.298746	−	0.954333i	$-0.596568\pi$
$163$	−7.62826			−0.597492			−0.298746	+	0.954333i	$0.596568\pi$
$164$		−	1.95525i		−	0.152679i
$165$	1.10505	+	0.977624i	0.0860279	+	0.0761079i
$166$			14.0668i			1.09180i
$167$	1.74267			0.134852			0.0674259	−	0.997724i	$-0.478521\pi$
$167$	1.74267			0.134852			0.0674259	+	0.997724i	$0.478521\pi$
$168$	4.79279	+	4.24012i	0.369771	+	0.327133i
$169$	7.73146			0.594728
$170$	1.10532			0.0847744
$171$	−1.81516	−	14.7783i	−0.138808	−	1.13012i
$172$			1.65798i			0.126420i
$173$			0.867767i			0.0659751i	0.999456	+	0.0329875i	$0.0105022\pi$
$173$			0.867767i			0.0659751i	−0.999456	+	0.0329875i	$0.989498\pi$
$174$	6.20141	+	5.48632i	0.470128	+	0.415917i
$175$	−3.69457			−0.279283
$176$	0.851837			0.0642096
$177$	−10.2619	−	9.07860i	−0.771332	−	0.682389i
$178$			3.95331i			0.296313i
$179$	15.3415			1.14668			0.573339	−	0.819318i	$-0.305648\pi$
$179$	15.3415			1.14668			0.573339	+	0.819318i	$0.305648\pi$
$180$	−2.97762	+	0.365730i	−0.221939	+	0.0272599i
$181$		−	4.54497i		−	0.337825i	−0.985631	−	0.168913i	$-0.945974\pi$
$181$		−	4.54497i		−	0.337825i	0.985631	−	0.168913i	$-0.0540255\pi$
$182$	8.48025			0.628598
$183$	4.02340	+	3.55946i	0.297418	+	0.263123i
$184$			1.74267i			0.128471i
$185$	2.69958			0.198477
$186$	−9.59460	+	0.971456i	−0.703510	+	0.0712306i
$187$	0.941555			0.0688533
$188$		−	4.65767i		−	0.339696i
$189$	−15.8218	−	10.8726i	−1.15087	−	0.790867i
$190$	4.96311			0.360062
$191$			2.35972i			0.170743i	0.996349	+	0.0853717i	$0.0272078\pi$
$191$			2.35972i			0.170743i	−0.996349	+	0.0853717i	$0.972792\pi$
$192$	−1.14767	+	1.29725i	−0.0828256	+	0.0936212i
$193$	−3.23951			−0.233185			−0.116592	−	0.993180i	$-0.537197\pi$
$193$	−3.23951			−0.233185			−0.116592	+	0.993180i	$0.537197\pi$
$194$		−	6.65767i		−	0.477993i
$195$	−2.63427	+	2.97762i	−0.188644	+	0.213232i
$196$	−6.64981			−0.474987
$197$	10.3984			0.740856			0.370428	−	0.928861i	$-0.379211\pi$
$197$	10.3984			0.740856			0.370428	+	0.928861i	$0.379211\pi$
$198$	−2.53645	+	0.311542i	−0.180258	+	0.0221403i
$199$			10.8460i			0.768853i	0.923156	+	0.384426i	$0.125601\pi$
$199$			10.8460i			0.768853i	−0.923156	+	0.384426i	$0.874399\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	11.5637	−	13.0709i	0.815640	−	0.921951i
$202$	7.81516			0.549872
$203$	−17.6616			−1.23960
$204$	−1.26854	+	1.43388i	−0.0888156	+	0.100392i
$205$	−1.95525			−0.136560
$206$			7.22379i			0.503305i
$207$	−0.637346	−	5.18901i	−0.0442986	−	0.360661i
$208$			2.29533i			0.159153i
$209$	4.22776			0.292440
$210$	4.24012	−	4.79279i	0.292596	−	0.330734i
$211$	7.74137			0.532938			0.266469	−	0.963844i	$-0.414143\pi$
$211$	7.74137			0.532938			0.266469	+	0.963844i	$0.414143\pi$
$212$	13.1166			0.900852
$213$	−0.123679	−	0.109417i	−0.00847434	−	0.00749715i
$214$	6.94739			0.474914
$215$	1.65798			0.113074
$216$	2.94287	−	4.28247i	0.200237	−	0.291385i
$217$	13.9552	−	15.1128i	0.947344	−	1.02592i
$218$			16.4476i			1.11397i
$219$	−21.0389	−	18.6129i	−1.42168	−	1.25774i
$220$		−	0.851837i		−	0.0574308i
$221$			2.53708i			0.170663i
$222$	−3.09821	+	3.50204i	−0.207938	+	0.235041i
$223$			22.5514i			1.51015i	0.655636	+	0.755077i	$0.272400\pi$
$223$			22.5514i			1.51015i	−0.655636	+	0.755077i	$0.727600\pi$
$224$		−	3.69457i		−	0.246854i
$225$	0.365730	+	2.97762i	0.0243820	+	0.198508i
$226$	15.0680			1.00231
$227$		−	18.8579i		−	1.25164i	−0.779967	−	0.625821i	$-0.784764\pi$
$227$		−	18.8579i		−	1.25164i	0.779967	−	0.625821i	$-0.215236\pi$
$228$	−5.69598	+	6.43840i	−0.377226	+	0.426394i
$229$			19.4109i			1.28271i	0.767244	+	0.641355i	$0.221627\pi$
$229$			19.4109i			1.28271i	−0.767244	+	0.641355i	$0.778373\pi$
$230$	1.74267			0.114908
$231$	3.61189	−	4.08267i	0.237645	−	0.268620i
$232$		−	4.78042i		−	0.313850i
$233$		−	3.15748i		−	0.206854i	−0.994637	−	0.103427i	$-0.967019\pi$
$233$		−	3.15748i		−	0.206854i	0.994637	−	0.103427i	$-0.0329808\pi$
$234$	−0.839470	−	6.83463i	−0.0548779	−	0.446794i
$235$	−4.65767			−0.303833
$236$			7.91049i			0.514929i
$237$	17.5313	+	15.5097i	1.13878	+	1.00746i
$238$		−	4.08369i		−	0.264706i
$239$	−15.5670			−1.00695			−0.503474	−	0.864010i	$-0.667945\pi$
$239$	−15.5670			−1.00695			−0.503474	+	0.864010i	$0.667945\pi$
$240$	1.29725	+	1.14767i	0.0837373	+	0.0740815i
$241$			14.3703i			0.925674i	0.886443	+	0.462837i	$0.153169\pi$
$241$			14.3703i			0.925674i	−0.886443	+	0.462837i	$0.846831\pi$
$242$			10.2744i			0.660462i
$243$	−7.19654	+	13.8279i	−0.461658	+	0.887058i
$244$		−	3.10148i		−	0.198552i
$245$			6.64981i			0.424841i
$246$	2.24397	−	2.53645i	0.143070	−	0.161718i
$247$			11.3920i			0.724853i
$248$	4.09054	+	3.77724i	0.259749	+	0.239855i
$249$	−16.1440	+	18.2482i	−1.02308	+	1.15643i
$250$	−1.00000			−0.0632456
$251$	−25.8630			−1.63246			−0.816230	−	0.577727i	$-0.803940\pi$
$251$	−25.8630			−1.63246			−0.816230	+	0.577727i	$0.803940\pi$
$252$	1.35121	+	11.0010i	0.0851184	+	0.692999i
$253$	1.48447			0.0933278
$254$	−4.18876			−0.262826
$255$	1.43388	+	1.26854i	0.0897933	+	0.0794391i
$256$	1.00000			0.0625000
$257$		−	6.60709i		−	0.412139i	−0.978537	−	0.206069i	$-0.933933\pi$
$257$		−	6.60709i		−	0.412139i	0.978537	−	0.206069i	$-0.0660672\pi$
$258$	−1.90281	+	2.15083i	−0.118464	+	0.133905i
$259$		−	9.97377i		−	0.619740i
$260$	2.29533			0.142350
$261$	1.74834	+	14.2343i	0.108220	+	0.881080i
$262$	−11.9105			−0.735833
$263$	11.7578			0.725016			0.362508	−	0.931981i	$-0.381921\pi$
$263$	11.7578			0.725016			0.362508	+	0.931981i	$0.381921\pi$
$264$	1.10505	+	0.977624i	0.0680110	+	0.0601686i
$265$		−	13.1166i		−	0.805746i
$266$		−	18.3365i		−	1.12428i
$267$	−4.53708	+	5.12845i	−0.277665	+	0.313856i
$268$	−10.0758			−0.615480
$269$	17.8513			1.08841			0.544207	−	0.838951i	$-0.316831\pi$
$269$	17.8513			1.08841			0.544207	+	0.838951i	$0.316831\pi$
$270$	−4.28247	−	2.94287i	−0.260623	−	0.179097i
$271$			2.12218i			0.128914i	0.997920	+	0.0644568i	$0.0205315\pi$
$271$			2.12218i			0.128914i	−0.997920	+	0.0644568i	$0.979469\pi$
$272$	1.10532			0.0670201
$273$	11.0010	+	9.73248i	0.665812	+	0.589037i
$274$		−	20.2765i		−	1.22495i
$275$	−0.851837			−0.0513677
$276$	−2.00000	+	2.26068i	−0.120386	+	0.136077i
$277$			23.0514i			1.38502i	0.721407	+	0.692511i	$0.243496\pi$
$277$			23.0514i			1.38502i	−0.721407	+	0.692511i	$0.756504\pi$
$278$	13.3657			0.801624
$279$	−13.5615	−	9.75116i	−0.811907	−	0.583787i
$280$	−3.69457			−0.220793
$281$			29.3912i			1.75333i	0.481101	+	0.876665i	$0.340237\pi$
$281$			29.3912i			1.75333i	−0.481101	+	0.876665i	$0.659763\pi$
$282$	5.34545	−	6.04218i	0.318317	−	0.359806i
$283$	−18.5972			−1.10549			−0.552744	−	0.833351i	$-0.686419\pi$
$283$	−18.5972			−1.10549			−0.552744	+	0.833351i	$0.686419\pi$
$284$			0.0953391i			0.00565733i
$285$	6.43840	+	5.69598i	0.381378	+	0.337401i
$286$	1.95525			0.115616
$287$			7.22379i			0.426407i
$288$	−2.97762	+	0.365730i	−0.175458	+	0.0215508i
$289$	−15.7783			−0.928133
$290$	−4.78042			−0.280716
$291$	7.64078	−	8.63668i	0.447910	−	0.506291i
$292$			16.2181i			0.949091i
$293$		−	11.2839i		−	0.659213i	−0.944118	−	0.329606i	$-0.893084\pi$
$293$		−	11.2839i		−	0.659213i	0.944118	−	0.329606i	$-0.106916\pi$
$294$	−8.62649	−	7.63176i	−0.503107	−	0.445093i
$295$	7.91049			0.460567
$296$	2.69958			0.156910
$297$	−3.64796	−	2.50685i	−0.211676	−	0.145462i
$298$	0.0953391			0.00552284
$299$			4.00000i			0.231326i
$300$	1.14767	−	1.29725i	0.0662605	−	0.0748969i
$301$		−	6.12553i		−	0.353070i
$302$	5.20271			0.299382
$303$	10.1382	+	8.96918i	0.582426	+	0.515266i
$304$	4.96311			0.284654
$305$	−3.10148			−0.177590
$306$	−3.29124	+	0.404249i	−0.188147	+	0.0231094i
$307$	−7.04883			−0.402298			−0.201149	−	0.979561i	$-0.564468\pi$
$307$	−7.04883			−0.402298			−0.201149	+	0.979561i	$0.564468\pi$
$308$	−3.14717			−0.179326
$309$	−8.29049	+	9.37108i	−0.471629	+	0.533102i
$310$	3.77724	−	4.09054i	0.214533	−	0.232327i
$311$			10.1653i			0.576424i	0.957567	+	0.288212i	$0.0930607\pi$
$311$			10.1653i			0.576424i	−0.957567	+	0.288212i	$0.906939\pi$
$312$	−2.63427	+	2.97762i	−0.149136	+	0.168575i
$313$		−	18.7422i		−	1.05937i	−0.848195	−	0.529685i	$-0.822310\pi$
$313$		−	18.7422i		−	1.05937i	0.848195	−	0.529685i	$-0.177690\pi$
$314$		−	11.1442i		−	0.628902i
$315$	11.0010	−	1.35121i	0.619838	−	0.0761322i
$316$		−	13.5142i		−	0.760230i
$317$			4.53708i			0.254828i	0.991850	+	0.127414i	$0.0406677\pi$
$317$			4.53708i			0.254828i	−0.991850	+	0.127414i	$0.959332\pi$
$318$	17.0155	+	15.0535i	0.954184	+	0.844156i
$319$	−4.07214			−0.227996
$320$		−	1.00000i		−	0.0559017i
$321$	9.01252	+	7.97327i	0.503030	+	0.445025i
$322$		−	6.43840i		−	0.358798i
$323$	5.48584			0.305240
$324$	8.73248	−	2.17801i	0.485138	−	0.121001i
$325$		−	2.29533i		−	0.127322i
$326$			7.62826i			0.422490i
$327$	−18.8763	+	21.3367i	−1.04386	+	1.17992i
$328$	−1.95525			−0.107960
$329$			17.2081i			0.948712i
$330$	0.977624	−	1.10505i	0.0538164	−	0.0608309i
$331$		−	9.12137i		−	0.501356i	−0.968071	−	0.250678i	$-0.919346\pi$
$331$		−	9.12137i		−	0.501356i	0.968071	−	0.250678i	$-0.0806535\pi$
$332$	14.0668			0.772017
$333$	−8.03833	+	0.987316i	−0.440498	+	0.0541046i
$334$		−	1.74267i		−	0.0953546i
$335$			10.0758i			0.550502i
$336$	4.24012	−	4.79279i	0.231318	−	0.261468i
$337$		−	22.9172i		−	1.24838i	−0.781272	−	0.624190i	$-0.785429\pi$
$337$		−	22.9172i		−	1.24838i	0.781272	−	0.624190i	$-0.214571\pi$
$338$		−	7.73146i		−	0.420536i
$339$	19.5470	+	17.2930i	1.06165	+	0.939226i
$340$		−	1.10532i		−	0.0599446i
$341$	3.21759	−	3.48447i	0.174242	−	0.188695i
$342$	−14.7783	+	1.81516i	−0.799117	+	0.0981523i
$343$	−1.29379			−0.0698582
$344$	1.65798			0.0893925
$345$	2.26068	+	2.00000i	0.121711	+	0.107676i
$346$	0.867767			0.0466514
$347$	−23.0514			−1.23746			−0.618731	−	0.785603i	$-0.712353\pi$
$347$	−23.0514			−1.23746			−0.618731	+	0.785603i	$0.712353\pi$
$348$	5.48632	−	6.20141i	0.294098	−	0.332431i
$349$	−32.7783			−1.75458			−0.877290	−	0.479961i	$-0.840651\pi$
$349$	−32.7783			−1.75458			−0.877290	+	0.479961i	$0.840651\pi$
$350$			3.69457i			0.197483i
$351$	6.75486	−	9.82967i	0.360548	−	0.524669i
$352$		−	0.851837i		−	0.0454031i
$353$	−1.79505			−0.0955410			−0.0477705	−	0.998858i	$-0.515212\pi$
$353$	−1.79505			−0.0955410			−0.0477705	+	0.998858i	$0.515212\pi$
$354$	−9.07860	+	10.2619i	−0.482522	+	0.545414i
$355$	0.0953391			0.00506007
$356$	3.95331			0.209525
$357$	4.68671	−	5.29758i	0.248047	−	0.280377i
$358$		−	15.3415i		−	0.810824i
$359$		−	30.8446i		−	1.62791i	−0.580925	−	0.813957i	$-0.697309\pi$
$359$		−	30.8446i		−	1.62791i	0.580925	−	0.813957i	$-0.302691\pi$
$360$	0.365730	+	2.97762i	0.0192756	+	0.156935i
$361$	5.63242			0.296443
$362$	−4.54497			−0.238878
$363$	−11.7915	+	13.3285i	−0.618895	+	0.699563i
$364$		−	8.48025i		−	0.444486i
$365$	16.2181			0.848893
$366$	3.55946	−	4.02340i	0.186056	−	0.210307i
$367$		−	10.4697i		−	0.546514i	−0.961941	−	0.273257i	$-0.911899\pi$
$367$		−	10.4697i		−	0.546514i	0.961941	−	0.273257i	$-0.0881010\pi$
$368$	1.74267			0.0908429
$369$	5.82199	−	0.715092i	0.303081	−	0.0372262i
$370$		−	2.69958i		−	0.140344i
$371$	−48.4601			−2.51592
$372$	0.971456	+	9.59460i	0.0503677	+	0.497457i
$373$	29.4127			1.52293			0.761467	−	0.648204i	$-0.224480\pi$
$373$	29.4127			1.52293			0.761467	+	0.648204i	$0.224480\pi$
$374$		−	0.941555i		−	0.0486867i
$375$	−1.29725	−	1.14767i	−0.0669898	−	0.0592652i
$376$	−4.65767			−0.240201
$377$		−	10.9726i		−	0.565120i
$378$	−10.8726	+	15.8218i	−0.559228	+	0.813788i
$379$	−26.7103			−1.37202			−0.686008	−	0.727594i	$-0.740639\pi$
$379$	−26.7103			−1.37202			−0.686008	+	0.727594i	$0.740639\pi$
$380$		−	4.96311i		−	0.254602i
$381$	−5.43388	−	4.80730i	−0.278386	−	0.246285i
$382$	2.35972			0.120734
$383$	6.78761			0.346831			0.173415	−	0.984849i	$-0.444520\pi$
$383$	6.78761			0.346831			0.173415	+	0.984849i	$0.444520\pi$
$384$	1.29725	+	1.14767i	0.0662002	+	0.0585665i
$385$			3.14717i			0.160394i
$386$			3.23951i			0.164886i
$387$	−4.93685	+	0.606374i	−0.250954	+	0.0308237i
$388$	−6.65767			−0.337992
$389$	−25.9768			−1.31708			−0.658538	−	0.752548i	$-0.728825\pi$
$389$	−25.9768			−1.31708			−0.658538	+	0.752548i	$0.728825\pi$
$390$	2.97762	+	2.63427i	0.150778	+	0.133391i
$391$	1.92621			0.0974127
$392$			6.64981i			0.335866i
$393$	−15.4509	−	13.6693i	−0.779396	−	0.689523i
$394$		−	10.3984i		−	0.523864i
$395$	−13.5142			−0.679971
$396$	0.311542	+	2.53645i	0.0156556	+	0.127461i
$397$	−34.8325			−1.74820			−0.874098	−	0.485750i	$-0.838546\pi$
$397$	−34.8325			−1.74820			−0.874098	+	0.485750i	$0.838546\pi$
$398$	10.8460			0.543661
$399$	21.0442	−	23.7871i	1.05353	−	1.19084i
$400$	−1.00000			−0.0500000
$401$	25.2943			1.26314			0.631569	−	0.775320i	$-0.282411\pi$
$401$	25.2943			1.26314			0.631569	+	0.775320i	$0.282411\pi$
$402$	−13.0709	−	11.5637i	−0.651918	−	0.576744i
$403$	9.38913	+	8.67001i	0.467706	+	0.431884i
$404$		−	7.81516i		−	0.388818i
$405$	−2.17801	−	8.73248i	−0.108226	−	0.433921i
$406$			17.6616i			0.876529i
$407$		−	2.29960i		−	0.113987i
$408$	1.43388	+	1.26854i	0.0709878	+	0.0628021i
$409$			14.6585i			0.724815i	0.932020	+	0.362407i	$0.118045\pi$
$409$			14.6585i			0.724815i	−0.932020	+	0.362407i	$0.881955\pi$
$410$			1.95525i			0.0965628i
$411$	23.2706	−	26.3037i	1.14785	−	1.29747i
$412$	7.22379			0.355890
$413$		−	29.2258i		−	1.43811i
$414$	−5.18901	+	0.637346i	−0.255026	+	0.0313238i
$415$		−	14.0668i		−	0.690513i
$416$	2.29533			0.112538
$417$	17.3387	+	15.3394i	0.849082	+	0.751173i
$418$		−	4.22776i		−	0.206786i
$419$		−	17.2258i		−	0.841537i	−0.907168	−	0.420769i	$-0.861760\pi$
$419$		−	17.2258i		−	0.841537i	0.907168	−	0.420769i	$-0.138240\pi$
$420$	−4.79279	−	4.24012i	−0.233864	−	0.206897i
$421$	28.6888			1.39820			0.699102	−	0.715022i	$-0.253583\pi$
$421$	28.6888			1.39820			0.699102	+	0.715022i	$0.253583\pi$
$422$		−	7.74137i		−	0.376844i
$423$	13.8688	−	1.70345i	0.674324	−	0.0828245i
$424$		−	13.1166i		−	0.636998i
$425$	−1.10532			−0.0536160
$426$	−0.109417	+	0.123679i	−0.00530129	+	0.00599226i
$427$			11.4586i			0.554521i
$428$		−	6.94739i		−	0.335815i
$429$	2.53645	+	2.24397i	0.122461	+	0.108340i
$430$		−	1.65798i		−	0.0799551i
$431$		−	16.5661i		−	0.797962i	−0.916959	−	0.398981i	$-0.869364\pi$
$431$		−	16.5661i		−	0.797962i	0.916959	−	0.398981i	$-0.130636\pi$
$432$	−4.28247	−	2.94287i	−0.206040	−	0.141589i
$433$			15.0633i			0.723895i	0.932198	+	0.361948i	$0.117888\pi$
$433$			15.0633i			0.723895i	−0.932198	+	0.361948i	$0.882112\pi$
$434$	−15.1128	−	13.9552i	−0.725435	−	0.669873i
$435$	−6.20141	−	5.48632i	−0.297335	−	0.263049i
$436$	16.4476			0.787696
$437$	8.64905			0.413740
$438$	−18.6129	+	21.0389i	−0.889360	+	1.00528i
$439$	−3.58351			−0.171032			−0.0855158	−	0.996337i	$-0.527254\pi$
$439$	−3.58351			−0.171032			−0.0855158	+	0.996337i	$0.527254\pi$
$440$	−0.851837			−0.0406097
$441$	−2.43203	−	19.8006i	−0.115811	−	0.942887i
$442$	2.53708			0.120677
$443$		−	38.0994i		−	1.81016i	−0.425243	−	0.905079i	$-0.639811\pi$
$443$		−	38.0994i		−	1.81016i	0.425243	−	0.905079i	$-0.360189\pi$
$444$	3.50204	+	3.09821i	0.166199	+	0.147035i
$445$		−	3.95331i		−	0.187405i
$446$	22.5514			1.06784
$447$	0.123679	+	0.109417i	0.00584981	+	0.00517526i
$448$	−3.69457			−0.174552
$449$	12.4836			0.589137			0.294569	−	0.955630i	$-0.404824\pi$
$449$	12.4836			0.589137			0.294569	+	0.955630i	$0.404824\pi$
$450$	2.97762	−	0.365730i	0.140367	−	0.0172407i
$451$			1.66555i			0.0784278i
$452$		−	15.0680i		−	0.708738i
$453$	6.74923	+	5.97096i	0.317106	+	0.280540i
$454$	−18.8579			−0.885044
$455$	−8.48025			−0.397560
$456$	6.43840	+	5.69598i	0.301506	+	0.266739i
$457$		−	27.7675i		−	1.29891i	−0.760401	−	0.649454i	$-0.774997\pi$
$457$		−	27.7675i		−	1.29891i	0.760401	−	0.649454i	$-0.225003\pi$
$458$	19.4109			0.907013
$459$	−4.73351	−	3.25282i	−0.220941	−	0.151829i
$460$		−	1.74267i		−	0.0812523i
$461$	−34.7204			−1.61709			−0.808546	−	0.588433i	$-0.799745\pi$
$461$	−34.7204			−1.61709			−0.808546	+	0.588433i	$0.799745\pi$
$462$	−4.08267	−	3.61189i	−0.189943	−	0.168041i
$463$		−	5.11133i		−	0.237544i	−0.992922	−	0.118772i	$-0.962104\pi$
$463$		−	5.11133i		−	0.237544i	0.992922	−	0.118772i	$-0.0378957\pi$
$464$	−4.78042			−0.221925
$465$	9.59460	−	0.971456i	0.444939	−	0.0450502i
$466$	−3.15748			−0.146268
$467$			31.9105i			1.47664i	0.674450	+	0.738321i	$0.264381\pi$
$467$			31.9105i			1.47664i	−0.674450	+	0.738321i	$0.735619\pi$
$468$	−6.83463	+	0.839470i	−0.315931	+	0.0388045i
$469$	37.2258			1.71893
$470$			4.65767i			0.214842i
$471$	12.7898	−	14.4568i	0.589322	−	0.666134i
$472$	7.91049			0.364110
$473$		−	1.41233i		−	0.0649391i
$474$	15.5097	−	17.5313i	0.712385	−	0.805238i
$475$	−4.96311			−0.227723
$476$	−4.08369			−0.187176
$477$	4.79713	+	39.0563i	0.219645	+	1.78826i
$478$			15.5670i			0.712020i
$479$			8.12807i			0.371381i	0.982608	+	0.185691i	$0.0594522\pi$
$479$			8.12807i			0.371381i	−0.982608	+	0.185691i	$0.940548\pi$
$480$	1.14767	−	1.29725i	0.0523835	−	0.0592112i
$481$	6.19643			0.282533
$482$	14.3703			0.654551
$483$	7.38913	−	8.35224i	0.336217	−	0.380040i
$484$	10.2744			0.467017
$485$			6.65767i			0.302309i
$486$	13.8279	+	7.19654i	0.627245	+	0.326442i
$487$		−	16.9334i		−	0.767326i	−0.923473	−	0.383663i	$-0.874662\pi$
$487$		−	16.9334i		−	0.767326i	0.923473	−	0.383663i	$-0.125338\pi$
$488$	−3.10148			−0.140397
$489$	−8.75469	+	9.89578i	−0.395901	+	0.447503i
$490$	6.64981			0.300408
$491$	−23.0954			−1.04228			−0.521140	−	0.853471i	$-0.674493\pi$
$491$	−23.0954			−1.04228			−0.521140	+	0.853471i	$0.674493\pi$
$492$	−2.53645	−	2.24397i	−0.114352	−	0.101166i
$493$	−5.28391			−0.237975
$494$	11.3920			0.512549
$495$	2.53645	−	0.311542i	0.114005	−	0.0140028i
$496$	3.77724	−	4.09054i	0.169603	−	0.183670i
$497$		−	0.352236i		−	0.0158000i
$498$	18.2482	+	16.1440i	0.817722	+	0.723430i
$499$			18.1505i			0.812528i	0.913756	+	0.406264i	$0.133169\pi$
$499$			18.1505i			0.812528i	−0.913756	+	0.406264i	$0.866831\pi$
$500$			1.00000i			0.0447214i
$501$	2.00000	−	2.26068i	0.0893534	−	0.101000i
$502$			25.8630i			1.15432i
$503$		−	12.5972i		−	0.561681i	−0.959754	−	0.280841i	$-0.909387\pi$
$503$		−	12.5972i		−	0.561681i	0.959754	−	0.280841i	$-0.0906133\pi$
$504$	11.0010	−	1.35121i	0.490025	−	0.0601878i
$505$	−7.81516			−0.347770
$506$		−	1.48447i		−	0.0659927i
$507$	8.87313	−	10.0297i	0.394069	−	0.445433i
$508$			4.18876i			0.185846i
$509$	14.8730			0.659232			0.329616	−	0.944115i	$-0.393081\pi$
$509$	14.8730			0.659232			0.329616	+	0.944115i	$0.393081\pi$
$510$	1.26854	−	1.43388i	0.0561719	−	0.0634934i
$511$		−	59.9187i		−	2.65065i
$512$		−	1.00000i		−	0.0441942i
$513$	−21.2543	−	14.6058i	−0.938402	−	0.644861i
$514$	−6.60709			−0.291426
$515$		−	7.22379i		−	0.318318i
$516$	2.15083	+	1.90281i	0.0946848	+	0.0837666i
$517$			3.96758i			0.174494i
$518$	−9.97377			−0.438222
$519$	1.12571	+	0.995906i	0.0494133	+	0.0437154i
$520$		−	2.29533i		−	0.100657i
$521$			3.09118i			0.135427i	0.997705	+	0.0677135i	$0.0215704\pi$
$521$			3.09118i			0.135427i	−0.997705	+	0.0677135i	$0.978430\pi$
$522$	14.2343	−	1.74834i	0.623018	−	0.0765228i
$523$		−	38.5154i		−	1.68416i	−0.539351	−	0.842081i	$-0.681330\pi$
$523$		−	38.5154i		−	1.68416i	0.539351	−	0.842081i	$-0.318670\pi$
$524$			11.9105i			0.520312i
$525$	−4.24012	+	4.79279i	−0.185054	+	0.209174i
$526$		−	11.7578i		−	0.512664i
$527$	4.17507	−	4.52136i	0.181869	−	0.196954i
$528$	0.977624	−	1.10505i	0.0425456	−	0.0480910i
$529$	−19.9631			−0.867961
$530$	−13.1166			−0.569749
$531$	−23.5545	+	2.89310i	−1.02218	+	0.125550i
$532$	−18.3365			−0.794989
$533$	−4.48794			−0.194394
$534$	5.12845	+	4.53708i	0.221930	+	0.196339i
$535$	−6.94739			−0.300362
$536$			10.0758i			0.435210i
$537$	17.6069	−	19.9018i	0.759794	−	0.858826i
$538$		−	17.8513i		−	0.769625i
$539$	5.66456			0.243990
$540$	−2.94287	+	4.28247i	−0.126641	+	0.184288i
$541$	−8.25690			−0.354992			−0.177496	−	0.984122i	$-0.556800\pi$
$541$	−8.25690			−0.354992			−0.177496	+	0.984122i	$0.556800\pi$
$542$	2.12218			0.0911556
$543$	−5.89598	−	5.21610i	−0.253021	−	0.223844i
$544$		−	1.10532i		−	0.0473903i
$545$		−	16.4476i		−	0.704537i
$546$	9.73248	−	11.0010i	0.416512	−	0.470800i
$547$	−5.03311			−0.215200			−0.107600	−	0.994194i	$-0.534317\pi$
$547$	−5.03311			−0.215200			−0.107600	+	0.994194i	$0.534317\pi$
$548$	−20.2765			−0.866168
$549$	9.23503	−	1.13430i	0.394142	−	0.0484108i
$550$			0.851837i			0.0363224i
$551$	−23.7257			−1.01075
$552$	2.26068	+	2.00000i	0.0962210	+	0.0851257i
$553$			49.9289i			2.12319i
$554$	23.0514			0.979359
$555$	3.09821	−	3.50204i	0.131512	−	0.148653i
$556$		−	13.3657i		−	0.566834i
$557$	−13.2327			−0.560688			−0.280344	−	0.959900i	$-0.590449\pi$
$557$	−13.2327			−0.560688			−0.280344	+	0.959900i	$0.590449\pi$
$558$	−9.75116	+	13.5615i	−0.412799	+	0.574105i
$559$	3.80562			0.160961
$560$			3.69457i			0.156124i
$561$	1.08059	−	1.22143i	0.0456225	−	0.0515690i
$562$	29.3912			1.23979
$563$			17.2839i			0.728430i	0.931315	+	0.364215i	$0.118663\pi$
$563$			17.2839i			0.728430i	−0.931315	+	0.364215i	$0.881337\pi$
$564$	−6.04218	−	5.34545i	−0.254422	−	0.225084i
$565$	−15.0680			−0.633915
$566$			18.5972i			0.781699i
$567$	−32.2627	+	8.04680i	−1.35491	+	0.337934i
$568$	0.0953391			0.00400034
$569$	−9.22032			−0.386536			−0.193268	−	0.981146i	$-0.561909\pi$
$569$	−9.22032			−0.386536			−0.193268	+	0.981146i	$0.561909\pi$
$570$	5.69598	−	6.43840i	0.238578	−	0.269675i
$571$			40.0899i			1.67771i	0.544356	+	0.838854i	$0.316774\pi$
$571$			40.0899i			1.67771i	−0.544356	+	0.838854i	$0.683226\pi$
$572$		−	1.95525i		−	0.0817530i
$573$	3.06115	+	2.70817i	0.127882	+	0.113135i
$574$	7.22379			0.301515
$575$	−1.74267			−0.0726743
$576$	0.365730	+	2.97762i	0.0152387	+	0.124068i
$577$	−0.0310839			−0.00129404			−0.000647019	−	1.00000i	$-0.500206\pi$
$577$	−0.0310839			−0.00129404			−0.000647019		1.00000i	$0.500206\pi$
$578$			15.7783i			0.656289i
$579$	−3.71787	+	4.20246i	−0.154509	+	0.174648i
$580$			4.78042i			0.198496i
$581$	−51.9708			−2.15611
$582$	−8.63668	−	7.64078i	−0.358002	−	0.316720i
$583$	−11.1732			−0.462747
$584$	16.2181			0.671109
$585$	0.839470	+	6.83463i	0.0347078	+	0.282577i
$586$	−11.2839			−0.466134
$587$	31.6876			1.30789			0.653944	−	0.756543i	$-0.273113\pi$
$587$	31.6876			1.30789			0.653944	+	0.756543i	$0.273113\pi$
$588$	−7.63176	+	8.62649i	−0.314728	+	0.355750i
$589$	18.7468	−	20.3018i	0.772449	−	0.836520i
$590$		−	7.91049i		−	0.325670i
$591$	11.9339	−	13.4894i	0.490895	−	0.554879i
$592$		−	2.69958i		−	0.110952i
$593$		−	25.0621i		−	1.02918i	−0.857437	−	0.514589i	$-0.827944\pi$
$593$		−	25.0621i		−	1.02918i	0.857437	−	0.514589i	$-0.172056\pi$
$594$	−2.50685	+	3.64796i	−0.102857	+	0.149678i
$595$			4.08369i			0.167415i
$596$		−	0.0953391i		−	0.00390524i
$597$	14.0700	+	12.4476i	0.575847	+	0.509445i
$598$	4.00000			0.163572
$599$			33.2921i			1.36028i	0.733082	+	0.680140i	$0.238081\pi$
$599$			33.2921i			1.36028i	−0.733082	+	0.680140i	$0.761919\pi$
$600$	−1.29725	−	1.14767i	−0.0529601	−	0.0468532i
$601$			15.8639i			0.647100i	0.946211	+	0.323550i	$0.104876\pi$
$601$			15.8639i			0.647100i	−0.946211	+	0.323550i	$0.895124\pi$
$602$	−6.12553			−0.249658
$603$	−3.68503	−	30.0020i	−0.150066	−	1.22178i
$604$		−	5.20271i		−	0.211695i
$605$		−	10.2744i		−	0.417713i
$606$	8.96918	−	10.1382i	0.364348	−	0.411838i
$607$	−17.3369			−0.703683			−0.351841	−	0.936060i	$-0.614444\pi$
$607$	−17.3369			−0.703683			−0.351841	+	0.936060i	$0.614444\pi$
$608$		−	4.96311i		−	0.201281i
$609$	−20.2696	+	22.9115i	−0.821364	+	0.928422i
$610$			3.10148i			0.125575i
$611$	−10.6909			−0.432507
$612$	0.404249	+	3.29124i	0.0163408	+	0.133040i
$613$		−	25.5254i		−	1.03096i	−0.856901	−	0.515481i	$-0.827613\pi$
$613$		−	25.5254i		−	1.03096i	0.856901	−	0.515481i	$-0.172387\pi$
$614$			7.04883i			0.284468i
$615$	−2.24397	+	2.53645i	−0.0904856	+	0.102280i
$616$			3.14717i			0.126803i
$617$		−	25.2200i		−	1.01532i	−0.861558	−	0.507660i	$-0.830511\pi$
$617$		−	25.2200i		−	1.01532i	0.861558	−	0.507660i	$-0.169489\pi$
$618$	9.37108	+	8.29049i	0.376960	+	0.333492i
$619$		−	25.2126i		−	1.01338i	−0.862129	−	0.506689i	$-0.830869\pi$
$619$		−	25.2126i		−	1.01338i	0.862129	−	0.506689i	$-0.169131\pi$
$620$	−4.09054	−	3.77724i	−0.164280	−	0.151697i
$621$	−7.46292	−	5.12845i	−0.299477	−	0.205798i
$622$	10.1653			0.407593
$623$	−14.6058			−0.585168
$624$	2.97762	+	2.63427i	0.119200	+	0.105455i
$625$	1.00000			0.0400000
$626$	−18.7422			−0.749087
$627$	4.85205	−	5.48447i	0.193772	−	0.219029i
$628$	−11.1442			−0.444701
$629$		−	2.98391i		−	0.118976i
$630$	−1.35121	−	11.0010i	−0.0538336	−	0.438291i
$631$		−	6.83161i		−	0.271962i	−0.990711	−	0.135981i	$-0.956581\pi$
$631$		−	6.83161i		−	0.271962i	0.990711	−	0.135981i	$-0.0434187\pi$
$632$	−13.5142			−0.537564
$633$	8.88450	−	10.0425i	0.353127	−	0.399154i
$634$	4.53708			0.180191
$635$	4.18876			0.166226
$636$	15.0535	−	17.0155i	0.596909	−	0.674710i
$637$			15.2635i			0.604762i
$638$			4.07214i			0.161217i
$639$	−0.283884	+	0.0348683i	−0.0112303	+	0.00137937i
$640$	−1.00000			−0.0395285
$641$	27.0554			1.06862			0.534312	−	0.845287i	$-0.320571\pi$
$641$	27.0554			1.06862			0.534312	+	0.845287i	$0.320571\pi$
$642$	7.97327	−	9.01252i	0.314680	−	0.355696i
$643$		−	36.7596i		−	1.44966i	−0.688929	−	0.724829i	$-0.741919\pi$
$643$		−	36.7596i		−	1.44966i	0.688929	−	0.724829i	$-0.258081\pi$
$644$	−6.43840			−0.253709
$645$	1.90281	−	2.15083i	0.0749231	−	0.0846887i
$646$		−	5.48584i		−	0.215837i
$647$	11.4357			0.449582			0.224791	−	0.974407i	$-0.427830\pi$
$647$	11.4357			0.449582			0.224791	+	0.974407i	$0.427830\pi$
$648$	−2.17801	−	8.73248i	−0.0855603	−	0.343044i
$649$		−	6.73845i		−	0.264507i
$650$	−2.29533			−0.0900303
$651$	−3.58911	−	35.4479i	−0.140668	−	1.38931i
$652$	7.62826			0.298746
$653$			7.98428i			0.312449i	0.987722	+	0.156225i	$0.0499324\pi$
$653$			7.98428i			0.312449i	−0.987722	+	0.156225i	$0.950068\pi$
$654$	21.3367	+	18.8763i	0.834330	+	0.738122i
$655$	11.9105			0.465382
$656$			1.95525i			0.0763396i
$657$	−48.2913	+	5.93143i	−1.88402	+	0.231407i
$658$	17.2081			0.670840
$659$			32.0041i			1.24670i	0.781942	+	0.623351i	$0.214229\pi$
$659$			32.0041i			1.24670i	−0.781942	+	0.623351i	$0.785771\pi$
$660$	−1.10505	−	0.977624i	−0.0430139	−	0.0380539i
$661$	9.35769			0.363972			0.181986	−	0.983301i	$-0.441747\pi$
$661$	9.35769			0.363972			0.181986	+	0.983301i	$0.441747\pi$
$662$	−9.12137			−0.354512
$663$	3.29124	+	2.91172i	0.127821	+	0.113082i
$664$		−	14.0668i		−	0.545898i
$665$			18.3365i			0.711060i
$666$	0.987316	+	8.03833i	0.0382577	+	0.311479i
$667$	−8.33069			−0.322565
$668$	−1.74267			−0.0674259
$669$	29.2549	+	25.8815i	1.13106	+	1.00064i
$670$	10.0758			0.389264
$671$			2.64195i			0.101991i
$672$	−4.79279	−	4.24012i	−0.184886	−	0.163566i
$673$		−	4.38521i		−	0.169038i	−0.996422	−	0.0845188i	$-0.973065\pi$
$673$		−	4.38521i		−	0.169038i	0.996422	−	0.0845188i	$-0.0269353\pi$
$674$	−22.9172			−0.882739
$675$	4.28247	+	2.94287i	0.164832	+	0.113271i
$676$	−7.73146			−0.297364
$677$	33.4017			1.28373			0.641867	−	0.766816i	$-0.278160\pi$
$677$	33.4017			1.28373			0.641867	+	0.766816i	$0.278160\pi$
$678$	17.2930	−	19.5470i	0.664133	−	0.750697i
$679$	24.5972			0.943954
$680$	−1.10532			−0.0423872
$681$	−24.4634	−	21.6425i	−0.937441	−	0.829344i
$682$	−3.48447	−	3.21759i	−0.133427	−	0.123208i
$683$			32.9822i			1.26203i	0.775772	+	0.631014i	$0.217361\pi$
$683$			32.9822i			1.26203i	−0.775772	+	0.631014i	$0.782639\pi$
$684$	1.81516	+	14.7783i	0.0694042	+	0.565061i
$685$			20.2765i			0.774724i
$686$			1.29379i			0.0493972i
$687$	25.1809	+	22.2772i	0.960711	+	0.849930i
$688$		−	1.65798i		−	0.0632101i
$689$		−	30.1069i		−	1.14698i
$690$	2.00000	−	2.26068i	0.0761387	−	0.0860627i
$691$	−5.81516			−0.221219			−0.110609	−	0.993864i	$-0.535280\pi$
$691$	−5.81516			−0.221219			−0.110609	+	0.993864i	$0.535280\pi$
$692$		−	0.867767i		−	0.0329875i
$693$	−1.15101	−	9.37108i	−0.0437233	−	0.355978i
$694$			23.0514i			0.875018i
$695$	−13.3657			−0.506991
$696$	−6.20141	−	5.48632i	−0.235064	−	0.207958i
$697$			2.16118i			0.0818605i
$698$			32.7783i			1.24068i
$699$	−4.09605	−	3.62373i	−0.154927	−	0.137062i
$700$	3.69457			0.139641
$701$			22.5353i			0.851148i	0.904924	+	0.425574i	$0.139928\pi$
$701$			22.5353i			0.851148i	−0.904924	+	0.425574i	$0.860072\pi$
$702$	−9.82967	−	6.75486i	−0.370997	−	0.254946i
$703$		−	13.3983i		−	0.505326i
$704$	−0.851837			−0.0321048
$705$	−5.34545	+	6.04218i	−0.201321	+	0.227562i
$706$			1.79505i			0.0675577i
$707$			28.8736i			1.08590i
$708$	10.2619	+	9.07860i	0.385666	+	0.341195i
$709$		−	30.2712i		−	1.13686i	−0.822732	−	0.568429i	$-0.807551\pi$
$709$		−	30.2712i		−	1.13686i	0.822732	−	0.568429i	$-0.192449\pi$
$710$		−	0.0953391i		−	0.00357801i
$711$	40.2401	−	4.94253i	1.50912	−	0.185359i
$712$		−	3.95331i		−	0.148157i
$713$	6.58247	−	7.12845i	0.246516	−	0.266963i
$714$	−5.29758	−	4.68671i	−0.198257	−	0.175396i
$715$	−1.95525			−0.0731221
$716$	−15.3415			−0.573339
$717$	−17.8657	+	20.1944i	−0.667208	+	0.754173i
$718$	−30.8446			−1.15111
$719$	−1.48014			−0.0551998			−0.0275999	−	0.999619i	$-0.508786\pi$
$719$	−1.48014			−0.0551998			−0.0275999	+	0.999619i	$0.508786\pi$
$720$	2.97762	−	0.365730i	0.110969	−	0.0136299i
$721$	−26.6888			−0.993941
$722$		−	5.63242i		−	0.209617i
$723$	18.6420	+	16.4923i	0.693302	+	0.613356i
$724$			4.54497i			0.168913i
$725$	4.78042			0.177540
$726$	13.3285	+	11.7915i	0.494666	+	0.437625i
$727$	−6.84622			−0.253912			−0.126956	−	0.991908i	$-0.540521\pi$
$727$	−6.84622			−0.253912			−0.126956	+	0.991908i	$0.540521\pi$
$728$	−8.48025			−0.314299
$729$	9.67902	+	25.2055i	0.358482	+	0.933537i
$730$		−	16.2181i		−	0.600258i
$731$		−	1.83261i		−	0.0677815i
$732$	−4.02340	−	3.55946i	−0.148709	−	0.131561i
$733$	42.1927			1.55842			0.779212	−	0.626760i	$-0.215620\pi$
$733$	42.1927			1.55842			0.779212	+	0.626760i	$0.215620\pi$
$734$	−10.4697			−0.386444
$735$	8.62649	+	7.63176i	0.318193	+	0.281502i
$736$		−	1.74267i		−	0.0642356i
$737$	8.58297			0.316158
$738$	−0.715092	−	5.82199i	−0.0263229	−	0.214310i
$739$			42.7542i			1.57274i	0.617756	+	0.786370i	$0.288042\pi$
$739$			42.7542i			1.57274i	−0.617756	+	0.786370i	$0.711958\pi$
$740$	−2.69958			−0.0992385
$741$	14.7783	+	13.0742i	0.542893	+	0.480291i
$742$			48.4601i			1.77903i
$743$	12.7598			0.468112			0.234056	−	0.972223i	$-0.424800\pi$
$743$	12.7598			0.468112			0.234056	+	0.972223i	$0.424800\pi$
$744$	9.59460	−	0.971456i	0.351755	−	0.0356153i
$745$	−0.0953391			−0.00349295
$746$		−	29.4127i		−	1.07688i
$747$	5.14465	+	41.8857i	0.188233	+	1.53252i
$748$	−0.941555			−0.0344267
$749$			25.6676i			0.937873i
$750$	−1.14767	+	1.29725i	−0.0419068	+	0.0473690i
$751$	10.5408			0.384639			0.192319	−	0.981332i	$-0.438399\pi$
$751$	10.5408			0.384639			0.192319	+	0.981332i	$0.438399\pi$
$752$			4.65767i			0.169848i
$753$	−29.6821	+	33.5509i	−1.08168	+	1.22266i
$754$	−10.9726			−0.399600
$755$	−5.20271			−0.189346
$756$	15.8218	+	10.8726i	0.575435	+	0.395434i
$757$		−	44.8153i		−	1.62884i	−0.580275	−	0.814421i	$-0.697055\pi$
$757$		−	44.8153i		−	1.62884i	0.580275	−	0.814421i	$-0.302945\pi$
$758$			26.7103i			0.970162i
$759$	1.70367	−	1.92573i	0.0618394	−	0.0698997i
$760$	−4.96311			−0.180031
$761$	10.2390			0.371162			0.185581	−	0.982629i	$-0.440583\pi$
$761$	10.2390			0.371162			0.185581	+	0.982629i	$0.440583\pi$
$762$	−4.80730	+	5.43388i	−0.174150	+	0.196849i
$763$	−60.7666			−2.19990
$764$		−	2.35972i		−	0.0853717i
$765$	3.29124	−	0.404249i	0.118995	−	0.0146157i
$766$		−	6.78761i		−	0.245246i
$767$	18.1572			0.655618
$768$	1.14767	−	1.29725i	0.0414128	−	0.0468106i
$769$	27.5818			0.994624			0.497312	−	0.867572i	$-0.334320\pi$
$769$	27.5818			0.994624			0.497312	+	0.867572i	$0.334320\pi$
$770$	3.14717			0.113416
$771$	−8.57106	−	7.58272i	−0.308679	−	0.273085i
$772$	3.23951			0.116592
$773$	43.0540			1.54854			0.774272	−	0.632853i	$-0.218116\pi$
$773$	43.0540			1.54854			0.774272	+	0.632853i	$0.218116\pi$
$774$	0.606374	+	4.93685i	0.0217957	+	0.177452i
$775$	−3.77724	+	4.09054i	−0.135682	+	0.146936i
$776$			6.65767i			0.238996i
$777$	−12.9385	−	11.4466i	−0.464166	−	0.410643i
$778$			25.9768i			0.931313i
$779$			9.70410i			0.347685i
$780$	2.63427	−	2.97762i	0.0943220	−	0.106616i
$781$		−	0.0812133i		−	0.00290604i
$782$		−	1.92621i		−	0.0688812i
$783$	20.4720	+	14.0682i	0.731609	+	0.502755i
$784$	6.64981			0.237493
$785$			11.1442i			0.397752i
$786$	−13.6693	+	15.4509i	−0.487566	+	0.551116i
$787$			41.0942i			1.46485i	0.680847	+	0.732426i	$0.261612\pi$
$787$			41.0942i			1.46485i	−0.680847	+	0.732426i	$0.738388\pi$
$788$	−10.3984			−0.370428
$789$	13.4940	−	15.2528i	0.480399	−	0.543015i
$790$			13.5142i			0.480812i
$791$			55.6696i			1.97938i
$792$	2.53645	−	0.311542i	0.0901288	−	0.0110702i
$793$	−7.11892			−0.252800
$794$			34.8325i			1.23616i
$795$	−17.0155	−	15.0535i	−0.603479	−	0.533891i
$796$		−	10.8460i		−	0.384426i
$797$	22.1291			0.783853			0.391927	−	0.919996i	$-0.371809\pi$
$797$	22.1291			0.783853			0.391927	+	0.919996i	$0.371809\pi$
$798$	−23.7871	−	21.0442i	−0.842054	−	0.744956i
$799$			5.14823i			0.182131i
$800$			1.00000i			0.0353553i
$801$	1.44584	+	11.7715i	0.0510864	+	0.415925i
$802$		−	25.2943i		−	0.893174i
$803$		−	13.8152i		−	0.487526i
$804$	−11.5637	+	13.0709i	−0.407820	+	0.460975i
$805$			6.43840i			0.226924i
$806$	8.67001	−	9.38913i	0.305388	−	0.330718i
$807$	20.4873	−	23.1577i	0.721189	−	0.815189i
$808$	−7.81516			−0.274936
$809$	45.9998			1.61727			0.808633	−	0.588314i	$-0.200208\pi$
$809$	45.9998			1.61727			0.808633	+	0.588314i	$0.200208\pi$
$810$	−8.73248	+	2.17801i	−0.306828	+	0.0765275i
$811$	14.2470			0.500280			0.250140	−	0.968210i	$-0.419523\pi$
$811$	14.2470			0.500280			0.250140	+	0.968210i	$0.419523\pi$
$812$	17.6616			0.619800
$813$	2.75301	+	2.43556i	0.0965523	+	0.0854187i
$814$	−2.29960			−0.0806010
$815$		−	7.62826i		−	0.267206i
$816$	1.26854	−	1.43388i	0.0444078	−	0.0501960i
$817$		−	8.22875i		−	0.287888i
$818$	14.6585			0.512521
$819$	25.2510	−	3.10148i	0.882341	−	0.108374i
$820$	1.95525			0.0682802
$821$	22.0511			0.769590			0.384795	−	0.923002i	$-0.374272\pi$
$821$	22.0511			0.769590			0.384795	+	0.923002i	$0.374272\pi$
$822$	−26.3037	−	23.2706i	−0.917447	−	0.811655i
$823$		−	30.9289i		−	1.07811i	−0.842269	−	0.539057i	$-0.818781\pi$
$823$		−	30.9289i		−	1.07811i	0.842269	−	0.539057i	$-0.181219\pi$
$824$		−	7.22379i		−	0.251653i
$825$	−0.977624	+	1.10505i	−0.0340365	+	0.0384728i
$826$	−29.2258			−1.01690
$827$	−48.8384			−1.69828			−0.849139	−	0.528170i	$-0.822879\pi$
$827$	−48.8384			−1.69828			−0.849139	+	0.528170i	$0.822879\pi$
$828$	0.637346	+	5.18901i	0.0221493	+	0.180331i
$829$		−	7.10774i		−	0.246862i	−0.992353	−	0.123431i	$-0.960610\pi$
$829$		−	7.10774i		−	0.246862i	0.992353	−	0.123431i	$-0.0393898\pi$
$830$	−14.0668			−0.488266
$831$	29.9035	+	26.4553i	1.03734	+	0.917723i
$832$		−	2.29533i		−	0.0795763i
$833$	7.35019			0.254669
$834$	15.3394	−	17.3387i	0.531160	−	0.600392i
$835$			1.74267i			0.0603075i
$836$	−4.22776			−0.146220
$837$	−28.2138	+	6.40166i	−0.975212	+	0.221274i
$838$	−17.2258			−0.595057
$839$		−	1.49779i		−	0.0517093i	−0.999666	−	0.0258547i	$-0.991769\pi$
$839$		−	1.49779i		−	0.0517093i	0.999666	−	0.0258547i	$-0.00823072\pi$
$840$	−4.24012	+	4.79279i	−0.146298	+	0.165367i
$841$	−6.14760			−0.211986
$842$		−	28.6888i		−	0.988680i
$843$	38.1278	+	33.7312i	1.31319	+	1.16177i
$844$	−7.74137			−0.266469
$845$			7.73146i			0.265970i
$846$	−1.70345	−	13.8688i	−0.0585658	−	0.476819i
$847$	−37.9593			−1.30430
$848$	−13.1166			−0.450426
$849$	−21.3434	+	24.1253i	−0.732502	+	0.827977i
$850$			1.10532i			0.0379123i
$851$		−	4.70447i		−	0.161267i
$852$	0.123679	+	0.109417i	0.00423717	+	0.00374858i
$853$	2.10144			0.0719519			0.0359760	−	0.999353i	$-0.488546\pi$
$853$	2.10144			0.0719519			0.0359760	+	0.999353i	$0.488546\pi$
$854$	11.4586			0.392106
$855$	14.7783	−	1.81516i	0.505406	−	0.0620770i
$856$	−6.94739			−0.237457
$857$		−	54.3662i		−	1.85711i	−0.371189	−	0.928557i	$-0.621050\pi$
$857$		−	54.3662i		−	1.85711i	0.371189	−	0.928557i	$-0.378950\pi$
$858$	2.24397	−	2.53645i	0.0766078	−	0.0865930i
$859$			55.0079i			1.87685i	0.345487	+	0.938423i	$0.387714\pi$
$859$			55.0079i			1.87685i	−0.345487	+	0.938423i	$0.612286\pi$
$860$	−1.65798			−0.0565368
$861$	9.37108	+	8.29049i	0.319366	+	0.282539i
$862$	−16.5661			−0.564244
$863$	35.3115			1.20202			0.601009	−	0.799242i	$-0.294765\pi$
$863$	35.3115			1.20202			0.601009	+	0.799242i	$0.294765\pi$
$864$	−2.94287	+	4.28247i	−0.100118	+	0.145692i
$865$	−0.867767			−0.0295050
$866$	15.0633			0.511871
$867$	−18.1082	+	20.4684i	−0.614985	+	0.695143i
$868$	−13.9552	+	15.1128i	−0.473672	+	0.512960i
$869$			11.5119i			0.390513i
$870$	−5.48632	+	6.20141i	−0.186004	+	0.210248i
$871$			23.1274i			0.783641i
$872$		−	16.4476i		−	0.556985i
$873$	−2.43491	−	19.8240i	−0.0824091	−	0.670942i
$874$		−	8.64905i		−	0.292558i
$875$		−	3.69457i		−	0.124899i
$876$	21.0389	+	18.6129i	0.710840	+	0.628872i
$877$	11.9283			0.402789			0.201394	−	0.979510i	$-0.435453\pi$
$877$	11.9283			0.402789			0.201394	+	0.979510i	$0.435453\pi$
$878$			3.58351i			0.120938i
$879$	−14.6381	−	12.9501i	−0.493730	−	0.436798i
$880$			0.851837i			0.0287154i
$881$	−25.6619			−0.864572			−0.432286	−	0.901736i	$-0.642293\pi$
$881$	−25.6619			−0.864572			−0.432286	+	0.901736i	$0.642293\pi$
$882$	−19.8006	+	2.43203i	−0.666722	+	0.0818908i
$883$		−	19.7078i		−	0.663219i	−0.943417	−	0.331609i	$-0.892408\pi$
$883$		−	19.7078i		−	0.663219i	0.943417	−	0.331609i	$-0.107592\pi$
$884$		−	2.53708i		−	0.0853313i
$885$	9.07860	−	10.2619i	0.305174	−	0.344950i
$886$	−38.0994			−1.27998
$887$		−	8.62624i		−	0.289641i	−0.989458	−	0.144820i	$-0.953740\pi$
$887$		−	8.62624i		−	0.289641i	0.989458	−	0.144820i	$-0.0462604\pi$
$888$	3.09821	−	3.50204i	0.103969	−	0.117521i
$889$		−	15.4757i		−	0.519037i
$890$	−3.95331			−0.132515
$891$	−7.43865	+	1.85531i	−0.249204	+	0.0621552i
$892$		−	22.5514i		−	0.755077i
$893$			23.1165i			0.773565i
$894$	0.109417	−	0.123679i	0.00365946	−	0.00413644i
$895$			15.3415i			0.512810i
$896$			3.69457i			0.123427i
$897$	5.18901	+	4.59066i	0.173256	+	0.153278i
$898$		−	12.4836i		−	0.416583i
$899$	−18.0568	+	19.5545i	−0.602227	+	0.652178i
$900$	−0.365730	−	2.97762i	−0.0121910	−	0.0992541i
$901$	−14.4981			−0.483001
$902$	1.66555			0.0554568
$903$	−7.94636	−	7.03006i	−0.264438	−	0.233946i
$904$	−15.0680			−0.501153
$905$	4.54497			0.151080
$906$	5.97096	−	6.74923i	0.198372	−	0.224228i
$907$	−51.8230			−1.72076			−0.860378	−	0.509657i	$-0.829772\pi$
$907$	−51.8230			−1.72076			−0.860378	+	0.509657i	$0.829772\pi$
$908$			18.8579i			0.625821i
$909$	23.2706	−	2.85823i	0.771837	−	0.0948016i
$910$			8.48025i			0.281117i
$911$	25.8031			0.854894			0.427447	−	0.904040i	$-0.359413\pi$
$911$	25.8031			0.854894			0.427447	+	0.904040i	$0.359413\pi$
$912$	5.69598	−	6.43840i	0.188613	−	0.213197i
$913$	−11.9826			−0.396567
$914$	−27.7675			−0.918467
$915$	−3.55946	+	4.02340i	−0.117672	+	0.133010i
$916$		−	19.4109i		−	0.641355i
$917$		−	44.0041i		−	1.45314i
$918$	−3.25282	+	4.73351i	−0.107359	+	0.156229i
$919$	−0.159243			−0.00525293			−0.00262646	−	0.999997i	$-0.500836\pi$
$919$	−0.159243			−0.00525293			−0.00262646	+	0.999997i	$0.500836\pi$
$920$	−1.74267			−0.0574541
$921$	−8.08969	+	9.14411i	−0.266564	+	0.301309i
$922$			34.7204i			1.14346i
$923$	0.218835			0.00720303
$924$	−3.61189	+	4.08267i	−0.118823	+	0.134310i
$925$			2.69958i			0.0887616i
$926$	−5.11133			−0.167969
$927$	2.64195	+	21.5097i	0.0867731	+	0.706472i
$928$			4.78042i			0.156925i
$929$	−18.9220			−0.620811			−0.310405	−	0.950604i	$-0.600465\pi$
$929$	−18.9220			−0.620811			−0.310405	+	0.950604i	$0.600465\pi$
$930$	−0.971456	−	9.59460i	−0.0318553	−	0.314619i
$931$	33.0037			1.08165
$932$			3.15748i			0.103427i
$933$	13.1870	+	11.6664i	0.431724	+	0.381941i
$934$	31.9105			1.04414
$935$			0.941555i			0.0307921i
$936$	0.839470	+	6.83463i	0.0274389	+	0.223397i
$937$	−10.8267			−0.353693			−0.176847	−	0.984238i	$-0.556590\pi$
$937$	−10.8267			−0.353693			−0.176847	+	0.984238i	$0.556590\pi$
$938$		−	37.2258i		−	1.21547i
$939$	−24.3133	−	21.5097i	−0.793435	−	0.701943i
$940$	4.65767			0.151916
$941$	41.4449			1.35106			0.675532	−	0.737330i	$-0.263914\pi$
$941$	41.4449			1.35106			0.675532	+	0.737330i	$0.263914\pi$
$942$	−14.4568	−	12.7898i	−0.471028	−	0.416713i
$943$			3.40735i			0.110959i
$944$		−	7.91049i		−	0.257465i
$945$	10.8726	−	15.8218i	0.353687	−	0.514685i
$946$	−1.41233			−0.0459189
$947$	−23.0922			−0.750394			−0.375197	−	0.926945i	$-0.622425\pi$
$947$	−23.0922			−0.750394			−0.375197	+	0.926945i	$0.622425\pi$
$948$	−17.5313	−	15.5097i	−0.569389	−	0.503732i
$949$	37.2258			1.20840
$950$			4.96311i			0.161024i
$951$	5.88574	+	5.20705i	0.190858	+	0.168850i
$952$			4.08369i			0.132353i
$953$	−45.6878			−1.47997			−0.739986	−	0.672622i	$-0.765168\pi$
$953$	−45.6878			−1.47997			−0.739986	+	0.672622i	$0.765168\pi$
$954$	39.0563	−	4.79713i	1.26449	−	0.155313i
$955$	−2.35972			−0.0763588
$956$	15.5670			0.503474
$957$	−4.67345	+	5.28259i	−0.151071	+	0.170762i
$958$	8.12807			0.262606
$959$	74.9127			2.41906
$960$	−1.29725	−	1.14767i	−0.0418687	−	0.0370407i
$961$	−2.46497	−	30.9018i	−0.0795151	−	0.996834i
$962$		−	6.19643i		−	0.199781i
$963$	20.6867	−	2.54087i	0.666620	−	0.0818783i
$964$		−	14.3703i		−	0.462837i
$965$		−	3.23951i		−	0.104283i
$966$	−8.35224	−	7.38913i	−0.268729	−	0.237741i
$967$			7.28119i			0.234147i	0.993123	+	0.117074i	$0.0373514\pi$
$967$			7.28119i			0.234147i	−0.993123	+	0.117074i	$0.962649\pi$
$968$		−	10.2744i		−	0.330231i
$969$	6.29590	−	7.11652i	0.202254	−	0.228615i
$970$	6.65767			0.213765
$971$		−	23.1015i		−	0.741364i	−0.928760	−	0.370682i	$-0.879124\pi$
$971$		−	23.1015i		−	0.741364i	0.928760	−	0.370682i	$-0.120876\pi$
$972$	7.19654	−	13.8279i	0.230829	−	0.443529i
$973$			49.3806i			1.58307i
$974$	−16.9334			−0.542581
$975$	−2.97762	−	2.63427i	−0.0953603	−	0.0843642i
$976$			3.10148i			0.0992759i
$977$		−	56.3949i		−	1.80423i	−0.431493	−	0.902116i	$-0.642013\pi$
$977$		−	56.3949i		−	1.80423i	0.431493	−	0.902116i	$-0.357987\pi$
$978$	9.89578	+	8.75469i	0.316432	+	0.279944i
$979$	−3.36758			−0.107628
$980$		−	6.64981i		−	0.212420i
$981$	6.01537	+	48.9747i	0.192056	+	1.56364i
$982$			23.0954i			0.737003i
$983$	−1.60729			−0.0512645			−0.0256322	−	0.999671i	$-0.508160\pi$
$983$	−1.60729			−0.0512645			−0.0256322	+	0.999671i	$0.508160\pi$
$984$	−2.24397	+	2.53645i	−0.0715351	+	0.0808591i
$985$			10.3984i			0.331321i
$986$			5.28391i			0.168274i
$987$	22.3232	+	19.7491i	0.710556	+	0.628621i
$988$		−	11.3920i		−	0.362427i
$989$		−	2.88932i		−	0.0918750i
$990$	−0.311542	−	2.53645i	−0.00990146	−	0.0806137i
$991$		−	56.0041i		−	1.77903i	−0.456907	−	0.889515i	$-0.651043\pi$
$991$		−	56.0041i		−	1.77903i	0.456907	−	0.889515i	$-0.348957\pi$
$992$	−4.09054	−	3.77724i	−0.129875	−	0.119927i
$993$	−11.8327	−	10.4683i	−0.375500	−	0.332201i
$994$	−0.352236			−0.0111723
$995$	−10.8460			−0.343841
$996$	16.1440	−	18.2482i	0.511542	−	0.578217i
$997$	−42.4653			−1.34489			−0.672445	−	0.740147i	$-0.734756\pi$
$997$	−42.4653			−1.34489			−0.672445	+	0.740147i	$0.734756\pi$
$998$	18.1505			0.574544
$999$	−7.94451	+	11.5609i	−0.251353	+	0.365769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.h.d.371.7	yes	16
3.2	odd	2	inner	930.2.h.d.371.10	yes	16
31.30	odd	2	inner	930.2.h.d.371.2	✓	16
93.92	even	2	inner	930.2.h.d.371.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.h.d.371.2	✓	16	31.30	odd	2	inner
930.2.h.d.371.7	yes	16	1.1	even	1	trivial
930.2.h.d.371.10	yes	16	3.2	odd	2	inner
930.2.h.d.371.15	yes	16	93.92	even	2	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.14767 - 1.29725i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.29725 - 1.14767i) q^{6} +3.69457 q^{7} +1.00000i q^{8} +(-0.365730 - 2.97762i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.14767 - 1.29725i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.29725 - 1.14767i) q^{6} +3.69457 q^{7} +1.00000i q^{8} +(-0.365730 - 2.97762i) q^{9} +1.00000 q^{10} +0.851837 q^{11} +(-1.14767 + 1.29725i) q^{12} +2.29533i q^{13} -3.69457i q^{14} +(1.29725 + 1.14767i) q^{15} +1.00000 q^{16} +1.10532 q^{17} +(-2.97762 + 0.365730i) q^{18} +4.96311 q^{19} -1.00000i q^{20} +(4.24012 - 4.79279i) q^{21} -0.851837i q^{22} +1.74267 q^{23} +(1.29725 + 1.14767i) q^{24} -1.00000 q^{25} +2.29533 q^{26} +(-4.28247 - 2.94287i) q^{27} -3.69457 q^{28} -4.78042 q^{29} +(1.14767 - 1.29725i) q^{30} +(3.77724 - 4.09054i) q^{31} -1.00000i q^{32} +(0.977624 - 1.10505i) q^{33} -1.10532i q^{34} +3.69457i q^{35} +(0.365730 + 2.97762i) q^{36} -2.69958i q^{37} -4.96311i q^{38} +(2.97762 + 2.63427i) q^{39} -1.00000 q^{40} +1.95525i q^{41} +(-4.79279 - 4.24012i) q^{42} -1.65798i q^{43} -0.851837 q^{44} +(2.97762 - 0.365730i) q^{45} -1.74267i q^{46} +4.65767i q^{47} +(1.14767 - 1.29725i) q^{48} +6.64981 q^{49} +1.00000i q^{50} +(1.26854 - 1.43388i) q^{51} -2.29533i q^{52} -13.1166 q^{53} +(-2.94287 + 4.28247i) q^{54} +0.851837i q^{55} +3.69457i q^{56} +(5.69598 - 6.43840i) q^{57} +4.78042i q^{58} -7.91049i q^{59} +(-1.29725 - 1.14767i) q^{60} +3.10148i q^{61} +(-4.09054 - 3.77724i) q^{62} +(-1.35121 - 11.0010i) q^{63} -1.00000 q^{64} -2.29533 q^{65} +(-1.10505 - 0.977624i) q^{66} +10.0758 q^{67} -1.10532 q^{68} +(2.00000 - 2.26068i) q^{69} +3.69457 q^{70} -0.0953391i q^{71} +(2.97762 - 0.365730i) q^{72} -16.2181i q^{73} -2.69958 q^{74} +(-1.14767 + 1.29725i) q^{75} -4.96311 q^{76} +3.14717 q^{77} +(2.63427 - 2.97762i) q^{78} +13.5142i q^{79} +1.00000i q^{80} +(-8.73248 + 2.17801i) q^{81} +1.95525 q^{82} -14.0668 q^{83} +(-4.24012 + 4.79279i) q^{84} +1.10532i q^{85} -1.65798 q^{86} +(-5.48632 + 6.20141i) q^{87} +0.851837i q^{88} -3.95331 q^{89} +(-0.365730 - 2.97762i) q^{90} +8.48025i q^{91} -1.74267 q^{92} +(-0.971456 - 9.59460i) q^{93} +4.65767 q^{94} +4.96311i q^{95} +(-1.29725 - 1.14767i) q^{96} +6.65767 q^{97} -6.64981i q^{98} +(-0.311542 - 2.53645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 + 4 * q^7 - 8 * q^9	\( 16 q - 16 q^{4} + 4 q^{7} - 8 q^{9} + 16 q^{10} + 16 q^{16} - 8 q^{18} + 20 q^{19} - 16 q^{25} - 4 q^{28} - 8 q^{31} - 24 q^{33} + 8 q^{36} + 8 q^{39} - 16 q^{40} + 8 q^{45} - 28 q^{49} + 16 q^{51} - 4 q^{63} - 16 q^{64} - 44 q^{66} - 24 q^{67} + 32 q^{69} + 4 q^{70} + 8 q^{72} - 20 q^{76} + 40 q^{78} + 8 q^{81} - 48 q^{82} + 16 q^{87} - 8 q^{90} + 12 q^{93} - 40 q^{94} - 8 q^{97}+O(q^{100}) \) 16 * q - 16 * q^4 + 4 * q^7 - 8 * q^9 + 16 * q^10 + 16 * q^16 - 8 * q^18 + 20 * q^19 - 16 * q^25 - 4 * q^28 - 8 * q^31 - 24 * q^33 + 8 * q^36 + 8 * q^39 - 16 * q^40 + 8 * q^45 - 28 * q^49 + 16 * q^51 - 4 * q^63 - 16 * q^64 - 44 * q^66 - 24 * q^67 + 32 * q^69 + 4 * q^70 + 8 * q^72 - 20 * q^76 + 40 * q^78 + 8 * q^81 - 48 * q^82 + 16 * q^87 - 8 * q^90 + 12 * q^93 - 40 * q^94 - 8 * q^97

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