LMFDB - Embedded newform 930.2.h.d.371.5

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			371.5
Root			$1.64143 - 0.552909i$ of defining polynomial
Character	$\chi$	$=$	930.371
Dual form			930.2.h.d.371.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.552909 - 1.64143i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.64143 - 0.552909i) q^{6} -2.30718 q^{7} +1.00000i q^{8} +(-2.38858 - 1.81512i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.552909 - 1.64143i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.64143 - 0.552909i) q^{6} -2.30718 q^{7} +1.00000i q^{8} +(-2.38858 - 1.81512i) q^{9} +1.00000 q^{10} -0.334369 q^{11} +(-0.552909 + 1.64143i) q^{12} +1.10582i q^{13} +2.30718i q^{14} +(1.64143 + 0.552909i) q^{15} +1.00000 q^{16} -5.02282 q^{17} +(-1.81512 + 2.38858i) q^{18} -5.08434 q^{19} -1.00000i q^{20} +(-1.27566 + 3.78707i) q^{21} +0.334369i q^{22} +3.61723 q^{23} +(1.64143 + 0.552909i) q^{24} -1.00000 q^{25} +1.10582 q^{26} +(-4.30007 + 2.91709i) q^{27} +2.30718 q^{28} +0.811361 q^{29} +(0.552909 - 1.64143i) q^{30} +(-5.04090 + 2.36418i) q^{31} -1.00000i q^{32} +(-0.184876 + 0.548844i) q^{33} +5.02282i q^{34} -2.30718i q^{35} +(2.38858 + 1.81512i) q^{36} +10.8916i q^{37} +5.08434i q^{38} +(1.81512 + 0.611418i) q^{39} -1.00000 q^{40} -0.369752i q^{41} +(3.78707 + 1.27566i) q^{42} +7.53423i q^{43} +0.334369 q^{44} +(1.81512 - 2.38858i) q^{45} -3.61723i q^{46} -11.3915i q^{47} +(0.552909 - 1.64143i) q^{48} -1.67693 q^{49} +1.00000i q^{50} +(-2.77716 + 8.24460i) q^{51} -1.10582i q^{52} -6.52581 q^{53} +(2.91709 + 4.30007i) q^{54} -0.334369i q^{55} -2.30718i q^{56} +(-2.81118 + 8.34559i) q^{57} -0.811361i q^{58} -3.26050i q^{59} +(-1.64143 - 0.552909i) q^{60} -6.09404i q^{61} +(2.36418 + 5.04090i) q^{62} +(5.51088 + 4.18781i) q^{63} -1.00000 q^{64} -1.10582 q^{65} +(0.548844 + 0.184876i) q^{66} -0.206944 q^{67} +5.02282 q^{68} +(2.00000 - 5.93743i) q^{69} -2.30718 q^{70} -9.40487i q^{71} +(1.81512 - 2.38858i) q^{72} -0.431766i q^{73} +10.8916 q^{74} +(-0.552909 + 1.64143i) q^{75} +5.08434 q^{76} +0.771450 q^{77} +(0.611418 - 1.81512i) q^{78} -8.05113i q^{79} +1.00000i q^{80} +(2.41065 + 8.67115i) q^{81} -0.369752 q^{82} +10.5625 q^{83} +(1.27566 - 3.78707i) q^{84} -5.02282i q^{85} +7.53423 q^{86} +(0.448609 - 1.33179i) q^{87} -0.334369i q^{88} +6.42841 q^{89} +(-2.38858 - 1.81512i) q^{90} -2.55132i q^{91} -3.61723 q^{92} +(1.09348 + 9.58146i) q^{93} -11.3915 q^{94} -5.08434i q^{95} +(-1.64143 - 0.552909i) q^{96} -9.39152 q^{97} +1.67693i q^{98} +(0.798669 + 0.606922i) 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
$3$	0.552909	−	1.64143i	0.319222	−	0.947680i
$3$	0.552909	−	1.64143i	0.319222	−	0.947680i
$4$	−1.00000			−0.500000
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.64143	−	0.552909i	−0.670111	−	0.225724i
$7$	−2.30718			−0.872031			−0.436016	−	0.899939i	$-0.643611\pi$
$7$	−2.30718			−0.872031			−0.436016	+	0.899939i	$0.643611\pi$
$8$			1.00000i			0.353553i
$9$	−2.38858	−	1.81512i	−0.796194	−	0.605041i
$10$	1.00000			0.316228
$11$	−0.334369			−0.100816			−0.0504081	−	0.998729i	$-0.516052\pi$
$11$	−0.334369			−0.100816			−0.0504081	+	0.998729i	$0.516052\pi$
$12$	−0.552909	+	1.64143i	−0.159611	+	0.473840i
$13$			1.10582i			0.306699i	0.988172	+	0.153350i	$0.0490060\pi$
$13$			1.10582i			0.306699i	−0.988172	+	0.153350i	$0.950994\pi$
$14$			2.30718i			0.616619i
$15$	1.64143	+	0.552909i	0.423815	+	0.142761i
$16$	1.00000			0.250000
$17$	−5.02282			−1.21821			−0.609106	−	0.793089i	$-0.708472\pi$
$17$	−5.02282			−1.21821			−0.609106	+	0.793089i	$0.708472\pi$
$18$	−1.81512	+	2.38858i	−0.427829	+	0.562994i
$19$	−5.08434			−1.16643			−0.583214	−	0.812319i	$-0.698205\pi$
$19$	−5.08434			−1.16643			−0.583214	+	0.812319i	$0.698205\pi$
$20$		−	1.00000i		−	0.223607i
$21$	−1.27566	+	3.78707i	−0.278372	+	0.826406i
$22$			0.334369i			0.0712878i
$23$	3.61723			0.754244			0.377122	−	0.926164i	$-0.376914\pi$
$23$	3.61723			0.754244			0.377122	+	0.926164i	$0.376914\pi$
$24$	1.64143	+	0.552909i	0.335055	+	0.112862i
$25$	−1.00000			−0.200000
$26$	1.10582			0.216869
$27$	−4.30007	+	2.91709i	−0.827548	+	0.561394i
$28$	2.30718			0.436016
$29$	0.811361			0.150666			0.0753330	−	0.997158i	$-0.475998\pi$
$29$	0.811361			0.150666			0.0753330	+	0.997158i	$0.475998\pi$
$30$	0.552909	−	1.64143i	0.100947	−	0.299683i
$31$	−5.04090	+	2.36418i	−0.905372	+	0.424619i
$31$	−5.04090	+	2.36418i	−0.905372	+	0.424619i
$32$		−	1.00000i		−	0.176777i
$33$	−0.184876	+	0.548844i	−0.0321828	+	0.0955414i
$34$			5.02282i			0.861406i
$35$		−	2.30718i		−	0.389984i
$36$	2.38858	+	1.81512i	0.398097	+	0.302521i
$37$			10.8916i			1.79057i	0.445496	+	0.895284i	$0.353027\pi$
$37$			10.8916i			1.79057i	−0.445496	+	0.895284i	$0.646973\pi$
$38$			5.08434i			0.824789i
$39$	1.81512	+	0.611418i	0.290652	+	0.0979052i
$40$	−1.00000			−0.158114
$41$		−	0.369752i		−	0.0577456i	−0.999583	−	0.0288728i	$-0.990808\pi$
$41$		−	0.369752i		−	0.0577456i	0.999583	−	0.0288728i	$-0.00919177\pi$
$42$	3.78707	+	1.27566i	0.584358	+	0.196839i
$43$			7.53423i			1.14896i	0.818519	+	0.574480i	$0.194796\pi$
$43$			7.53423i			1.14896i	−0.818519	+	0.574480i	$0.805204\pi$
$44$	0.334369			0.0504081
$45$	1.81512	−	2.38858i	0.270583	−	0.356069i
$46$		−	3.61723i		−	0.533331i
$47$		−	11.3915i		−	1.66162i	−0.556553	−	0.830812i	$-0.687876\pi$
$47$		−	11.3915i		−	1.66162i	0.556553	−	0.830812i	$-0.312124\pi$
$48$	0.552909	−	1.64143i	0.0798056	−	0.236920i
$49$	−1.67693			−0.239561
$50$			1.00000i			0.141421i
$51$	−2.77716	+	8.24460i	−0.388881	+	1.15448i
$52$		−	1.10582i		−	0.153350i
$53$	−6.52581			−0.896388			−0.448194	−	0.893936i	$-0.647933\pi$
$53$	−6.52581			−0.896388			−0.448194	+	0.893936i	$0.647933\pi$
$54$	2.91709	+	4.30007i	0.396966	+	0.585165i
$55$		−	0.334369i		−	0.0450864i
$56$		−	2.30718i		−	0.308310i
$57$	−2.81118	+	8.34559i	−0.372350	+	1.10540i
$58$		−	0.811361i		−	0.106537i
$59$		−	3.26050i		−	0.424480i	−0.977218	−	0.212240i	$-0.931924\pi$
$59$		−	3.26050i		−	0.424480i	0.977218	−	0.212240i	$-0.0680759\pi$
$60$	−1.64143	−	0.552909i	−0.211908	−	0.0713803i
$61$		−	6.09404i		−	0.780262i	−0.920759	−	0.390131i	$-0.872430\pi$
$61$		−	6.09404i		−	0.780262i	0.920759	−	0.390131i	$-0.127570\pi$
$62$	2.36418	+	5.04090i	0.300251	+	0.640195i
$63$	5.51088	+	4.18781i	0.694306	+	0.527615i
$64$	−1.00000			−0.125000
$65$	−1.10582			−0.137160
$66$	0.548844	+	0.184876i	0.0675580	+	0.0227567i
$67$	−0.206944			−0.0252822			−0.0126411	−	0.999920i	$-0.504024\pi$
$67$	−0.206944			−0.0252822			−0.0126411	+	0.999920i	$0.504024\pi$
$68$	5.02282			0.609106
$69$	2.00000	−	5.93743i	0.240772	−	0.714782i
$70$	−2.30718			−0.275761
$71$		−	9.40487i		−	1.11615i	−0.829790	−	0.558076i	$-0.811540\pi$
$71$		−	9.40487i		−	1.11615i	0.829790	−	0.558076i	$-0.188460\pi$
$72$	1.81512	−	2.38858i	0.213914	−	0.281497i
$73$		−	0.431766i		−	0.0505344i	−0.999681	−	0.0252672i	$-0.991956\pi$
$73$		−	0.431766i		−	0.0505344i	0.999681	−	0.0252672i	$-0.00804366\pi$
$74$	10.8916			1.26612
$75$	−0.552909	+	1.64143i	−0.0638445	+	0.189536i
$76$	5.08434			0.583214
$77$	0.771450			0.0879148
$78$	0.611418	−	1.81512i	0.0692294	−	0.205522i
$79$		−	8.05113i		−	0.905823i	−0.891555	−	0.452912i	$-0.850385\pi$
$79$		−	8.05113i		−	0.905823i	0.891555	−	0.452912i	$-0.149615\pi$
$80$			1.00000i			0.111803i
$81$	2.41065	+	8.67115i	0.267850	+	0.963461i
$82$	−0.369752			−0.0408323
$83$	10.5625			1.15939			0.579695	−	0.814834i	$-0.303172\pi$
$83$	10.5625			1.15939			0.579695	+	0.814834i	$0.303172\pi$
$84$	1.27566	−	3.78707i	0.139186	−	0.413203i
$85$		−	5.02282i		−	0.544801i
$86$	7.53423			0.812437
$87$	0.448609	−	1.33179i	0.0480960	−	0.142783i
$88$		−	0.334369i		−	0.0356439i
$89$	6.42841			0.681410			0.340705	−	0.940170i	$-0.389334\pi$
$89$	6.42841			0.681410			0.340705	+	0.940170i	$0.389334\pi$
$90$	−2.38858	−	1.81512i	−0.251779	−	0.191331i
$91$		−	2.55132i		−	0.267451i
$92$	−3.61723			−0.377122
$93$	1.09348	+	9.58146i	0.113388	+	0.993551i
$94$	−11.3915			−1.17495
$95$		−	5.08434i		−	0.521643i
$96$	−1.64143	−	0.552909i	−0.167528	−	0.0564311i
$97$	−9.39152			−0.953564			−0.476782	−	0.879021i	$-0.658197\pi$
$97$	−9.39152			−0.953564			−0.476782	+	0.879021i	$0.658197\pi$
$98$			1.67693i			0.169396i
$99$	0.798669	+	0.606922i	0.0802692	+	0.0609979i
$100$	1.00000			0.100000
$101$		−	6.14437i		−	0.611388i	−0.952130	−	0.305694i	$-0.901112\pi$
$101$		−	6.14437i		−	0.611388i	0.952130	−	0.305694i	$-0.0988884\pi$
$102$	8.24460	+	2.77716i	0.816337	+	0.274980i
$103$	−0.853084			−0.0840568			−0.0420284	−	0.999116i	$-0.513382\pi$
$103$	−0.853084			−0.0840568			−0.0420284	+	0.999116i	$0.513382\pi$
$104$	−1.10582			−0.108434
$105$	−3.78707	−	1.27566i	−0.369580	−	0.124492i
$106$			6.52581i			0.633842i
$107$			12.3448i			1.19342i	0.802457	+	0.596710i	$0.203526\pi$
$107$			12.3448i			1.19342i	−0.802457	+	0.596710i	$0.796474\pi$
$108$	4.30007	−	2.91709i	0.413774	−	0.280697i
$109$	−3.70617			−0.354986			−0.177493	−	0.984122i	$-0.556799\pi$
$109$	−3.70617			−0.354986			−0.177493	+	0.984122i	$0.556799\pi$
$110$	−0.334369			−0.0318809
$111$	17.8778	+	6.02207i	1.69688	+	0.571589i
$112$	−2.30718			−0.218008
$113$			12.5076i			1.17662i	0.808635	+	0.588310i	$0.200207\pi$
$113$			12.5076i			1.17662i	−0.808635	+	0.588310i	$0.799793\pi$
$114$	8.34559	+	2.81118i	0.781636	+	0.263291i
$115$			3.61723i			0.337308i
$116$	−0.811361			−0.0753330
$117$	2.00720	−	2.64134i	0.185566	−	0.244192i
$118$	−3.26050			−0.300153
$119$	11.5885			1.06232
$120$	−0.552909	+	1.64143i	−0.0504735	+	0.149841i
$121$	−10.8882			−0.989836
$122$	−6.09404			−0.551728
$123$	−0.606922	−	0.204439i	−0.0547243	−	0.0184337i
$124$	5.04090	−	2.36418i	0.452686	−	0.212310i
$125$		−	1.00000i		−	0.0894427i
$126$	4.18781	−	5.51088i	0.373080	−	0.490949i
$127$			2.58592i			0.229463i	0.993397	+	0.114732i	$0.0366008\pi$
$127$			2.58592i			0.229463i	−0.993397	+	0.114732i	$0.963399\pi$
$128$			1.00000i			0.0883883i
$129$	12.3669	+	4.16575i	1.08885	+	0.366774i
$130$			1.10582i			0.0969867i
$131$		−	7.26050i		−	0.634352i	−0.948367	−	0.317176i	$-0.897265\pi$
$131$		−	7.26050i		−	0.634352i	0.948367	−	0.317176i	$-0.102735\pi$
$132$	0.184876	−	0.548844i	0.0160914	−	0.0477707i
$133$	11.7305			1.01716
$134$			0.206944i			0.0178772i
$135$	−2.91709	−	4.30007i	−0.251063	−	0.370091i
$136$		−	5.02282i		−	0.430703i
$137$	−20.1711			−1.72333			−0.861667	−	0.507475i	$-0.830579\pi$
$137$	−20.1711			−1.72333			−0.861667	+	0.507475i	$0.830579\pi$
$138$	−5.93743	−	2.00000i	−0.505427	−	0.170251i
$139$		−	17.5371i		−	1.48748i	−0.668469	−	0.743740i	$-0.733050\pi$
$139$		−	17.5371i		−	1.48748i	0.668469	−	0.743740i	$-0.266950\pi$
$140$			2.30718i			0.194992i
$141$	−18.6984	−	6.29848i	−1.57469	−	0.530428i
$142$	−9.40487			−0.789239
$143$		−	0.369752i		−	0.0309202i
$144$	−2.38858	−	1.81512i	−0.199049	−	0.151260i
$145$			0.811361i			0.0673799i
$146$	−0.431766			−0.0357332
$147$	−0.927190	+	2.75256i	−0.0764734	+	0.227028i
$148$		−	10.8916i		−	0.895284i
$149$			9.40487i			0.770477i	0.922817	+	0.385238i	$0.125881\pi$
$149$			9.40487i			0.770477i	−0.922817	+	0.385238i	$0.874119\pi$
$150$	1.64143	+	0.552909i	0.134022	+	0.0451449i
$151$		−	21.3397i		−	1.73660i	−0.496038	−	0.868301i	$-0.665212\pi$
$151$		−	21.3397i		−	1.73660i	0.496038	−	0.868301i	$-0.334788\pi$
$152$		−	5.08434i		−	0.412395i
$153$	11.9974	+	9.11704i	0.969934	+	0.737069i
$154$		−	0.771450i		−	0.0621652i
$155$	−2.36418	−	5.04090i	−0.189896	−	0.404895i
$156$	−1.81512	−	0.611418i	−0.145326	−	0.0489526i
$157$	−19.9810			−1.59465			−0.797327	−	0.603547i	$-0.793753\pi$
$157$	−19.9810			−1.59465			−0.797327	+	0.603547i	$0.793753\pi$
$158$	−8.05113			−0.640514
$159$	−3.60818	+	10.7117i	−0.286147	+	0.849489i
$160$	1.00000			0.0790569
$161$	−8.34559			−0.657725
$162$	8.67115	−	2.41065i	0.681270	−	0.189399i
$163$	−10.0869			−0.790066			−0.395033	−	0.918667i	$-0.629267\pi$
$163$	−10.0869			−0.790066			−0.395033	+	0.918667i	$0.629267\pi$
$164$			0.369752i			0.0288728i
$165$	−0.548844	−	0.184876i	−0.0427274	−	0.0143926i
$166$		−	10.5625i		−	0.819812i
$167$	3.61723			0.279910			0.139955	−	0.990158i	$-0.455304\pi$
$167$	3.61723			0.279910			0.139955	+	0.990158i	$0.455304\pi$
$168$	−3.78707	−	1.27566i	−0.292179	−	0.0984194i
$169$	11.7772			0.905936
$170$	−5.02282			−0.385233
$171$	12.1444	+	9.22871i	0.928703	+	0.705737i
$172$		−	7.53423i		−	0.574480i
$173$		−	18.4892i		−	1.40571i	−0.711334	−	0.702854i	$-0.751909\pi$
$173$		−	18.4892i		−	1.40571i	0.711334	−	0.702854i	$-0.248091\pi$
$174$	−1.33179	−	0.448609i	−0.100963	−	0.0340090i
$175$	2.30718			0.174406
$176$	−0.334369			−0.0252040
$177$	−5.35187	−	1.80276i	−0.402272	−	0.135504i
$178$		−	6.42841i		−	0.481830i
$179$	6.71755			0.502094			0.251047	−	0.967975i	$-0.419225\pi$
$179$	6.71755			0.502094			0.251047	+	0.967975i	$0.419225\pi$
$180$	−1.81512	+	2.38858i	−0.135291	+	0.178034i
$181$			4.65385i			0.345918i	0.984929	+	0.172959i	$0.0553328\pi$
$181$			4.65385i			0.345918i	−0.984929	+	0.172959i	$0.944667\pi$
$182$	−2.55132			−0.189117
$183$	−10.0029	−	3.36945i	−0.739438	−	0.249077i
$184$			3.61723i			0.266666i
$185$	−10.8916			−0.800766
$186$	9.58146	−	1.09348i	0.702546	−	0.0801775i
$187$	1.67948			0.122816
$188$			11.3915i			0.830812i
$189$	9.92102	−	6.73025i	0.721648	−	0.489553i
$190$	−5.08434			−0.368857
$191$			8.86405i			0.641380i	0.947184	+	0.320690i	$0.103915\pi$
$191$			8.86405i			0.641380i	−0.947184	+	0.320690i	$0.896085\pi$
$192$	−0.552909	+	1.64143i	−0.0399028	+	0.118460i
$193$	18.5761			1.33714			0.668568	−	0.743651i	$-0.266907\pi$
$193$	18.5761			1.33714			0.668568	+	0.743651i	$0.266907\pi$
$194$			9.39152i			0.674272i
$195$	−0.611418	+	1.81512i	−0.0437845	+	0.129984i
$196$	1.67693			0.119781
$197$	−12.1945			−0.868821			−0.434410	−	0.900715i	$-0.643043\pi$
$197$	−12.1945			−0.868821			−0.434410	+	0.900715i	$0.643043\pi$
$198$	0.606922	−	0.798669i	0.0431321	−	0.0567589i
$199$		−	0.531430i		−	0.0376721i	−0.999823	−	0.0188360i	$-0.994004\pi$
$199$		−	0.531430i		−	0.0376721i	0.999823	−	0.0188360i	$-0.00599605\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−0.114421	+	0.339683i	−0.00807064	+	0.0239594i
$202$	−6.14437			−0.432316
$203$	−1.87195			−0.131385
$204$	2.77716	−	8.24460i	0.194440	−	0.577238i
$205$	0.369752			0.0258246
$206$			0.853084i			0.0594372i
$207$	−8.64005	−	6.56572i	−0.600525	−	0.456349i
$208$			1.10582i			0.0766748i
$209$	1.70005			0.117595
$210$	−1.27566	+	3.78707i	−0.0880289	+	0.261333i
$211$	−26.3131			−1.81147			−0.905733	−	0.423849i	$-0.860679\pi$
$211$	−26.3131			−1.81147			−0.905733	+	0.423849i	$0.860679\pi$
$212$	6.52581			0.448194
$213$	−15.4374	−	5.20004i	−1.05775	−	0.356301i
$214$	12.3448			0.843876
$215$	−7.53423			−0.513830
$216$	−2.91709	−	4.30007i	−0.198483	−	0.292583i
$217$	11.6302	−	5.45459i	0.789513	−	0.370281i
$218$			3.70617i			0.251013i
$219$	−0.708714	−	0.238728i	−0.0478905	−	0.0161317i
$220$			0.334369i			0.0225432i
$221$		−	5.55433i		−	0.373625i
$222$	6.02207	−	17.8778i	0.404175	−	1.19988i
$223$			6.26063i			0.419243i	0.977783	+	0.209621i	$0.0672232\pi$
$223$			6.26063i			0.419243i	−0.977783	+	0.209621i	$0.932777\pi$
$224$			2.30718i			0.154155i
$225$	2.38858	+	1.81512i	0.159239	+	0.121008i
$226$	12.5076			0.831996
$227$		−	19.6053i		−	1.30125i	−0.759398	−	0.650626i	$-0.774507\pi$
$227$		−	19.6053i		−	1.30125i	0.759398	−	0.650626i	$-0.225493\pi$
$228$	2.81118	−	8.34559i	0.186175	−	0.552700i
$229$			8.06871i			0.533195i	0.963808	+	0.266598i	$0.0858995\pi$
$229$			8.06871i			0.533195i	−0.963808	+	0.266598i	$0.914101\pi$
$230$	3.61723			0.238513
$231$	0.426542	−	1.26628i	0.0280644	−	0.0833151i
$232$			0.811361i			0.0532685i
$233$		−	5.24715i		−	0.343752i	−0.985119	−	0.171876i	$-0.945017\pi$
$233$		−	5.24715i		−	0.343752i	0.985119	−	0.171876i	$-0.0549829\pi$
$234$	−2.64134	−	2.00720i	−0.172670	−	0.131215i
$235$	11.3915			0.743101
$236$			3.26050i			0.212240i
$237$	−13.2154	−	4.45155i	−0.858430	−	0.289159i
$238$		−	11.5885i		−	0.751173i
$239$	−19.6972			−1.27410			−0.637052	−	0.770821i	$-0.719846\pi$
$239$	−19.6972			−1.27410			−0.637052	+	0.770821i	$0.719846\pi$
$240$	1.64143	+	0.552909i	0.105954	+	0.0356902i
$241$			10.9890i			0.707863i	0.935271	+	0.353932i	$0.115155\pi$
$241$			10.9890i			0.707863i	−0.935271	+	0.353932i	$0.884845\pi$
$242$			10.8882i			0.699920i
$243$	15.5659	+	0.837447i	0.998556	+	0.0537223i
$244$			6.09404i			0.390131i
$245$		−	1.67693i		−	0.107135i
$246$	−0.204439	+	0.606922i	−0.0130346	+	0.0386959i
$247$		−	5.62236i		−	0.357742i
$248$	−2.36418	−	5.04090i	−0.150126	−	0.320097i
$249$	5.84013	−	17.3377i	0.370103	−	1.09873i
$250$	−1.00000			−0.0632456
$251$	28.1823			1.77885			0.889426	−	0.457079i	$-0.151104\pi$
$251$	28.1823			1.77885			0.889426	+	0.457079i	$0.151104\pi$
$252$	−5.51088	−	4.18781i	−0.347153	−	0.263807i
$253$	−1.20949			−0.0760400
$254$	2.58592			0.162255
$255$	−8.24460	−	2.77716i	−0.516297	−	0.173913i
$256$	1.00000			0.0625000
$257$			16.4266i			1.02467i	0.858787	+	0.512333i	$0.171219\pi$
$257$			16.4266i			1.02467i	−0.858787	+	0.512333i	$0.828781\pi$
$258$	4.16575	−	12.3669i	0.259348	−	0.769930i
$259$		−	25.1289i		−	1.56143i
$260$	1.10582			0.0685800
$261$	−1.93800	−	1.47272i	−0.119959	−	0.0911592i
$262$	−7.26050			−0.448555
$263$	16.2371			1.00122			0.500610	−	0.865673i	$-0.333109\pi$
$263$	16.2371			1.00122			0.500610	+	0.865673i	$0.333109\pi$
$264$	−0.548844	−	0.184876i	−0.0337790	−	0.0113783i
$265$		−	6.52581i		−	0.400877i
$266$		−	11.7305i		−	0.719242i
$267$	3.55433	−	10.5518i	0.217521	−	0.645759i
$268$	0.206944			0.0126411
$269$	−1.15104			−0.0701804			−0.0350902	−	0.999384i	$-0.511172\pi$
$269$	−1.15104			−0.0701804			−0.0350902	+	0.999384i	$0.511172\pi$
$270$	−4.30007	+	2.91709i	−0.261694	+	0.177528i
$271$		−	2.42877i		−	0.147537i	−0.997275	−	0.0737686i	$-0.976497\pi$
$271$		−	2.42877i		−	0.147537i	0.997275	−	0.0737686i	$-0.0235026\pi$
$272$	−5.02282			−0.304553
$273$	−4.18781	−	1.41065i	−0.253458	−	0.0853764i
$274$			20.1711i			1.21858i
$275$	0.334369			0.0201632
$276$	−2.00000	+	5.93743i	−0.120386	+	0.357391i
$277$			27.3687i			1.64443i	0.569180	+	0.822213i	$0.307261\pi$
$277$			27.3687i			1.64443i	−0.569180	+	0.822213i	$0.692739\pi$
$278$	−17.5371			−1.05181
$279$	16.3319	+	3.50281i	0.977764	+	0.209708i
$280$	2.30718			0.137880
$281$		−	12.9900i		−	0.774917i	−0.921887	−	0.387459i	$-0.873353\pi$
$281$		−	12.9900i		−	0.774917i	0.921887	−	0.387459i	$-0.126647\pi$
$282$	−6.29848	+	18.6984i	−0.375069	+	1.11347i
$283$	−15.6679			−0.931360			−0.465680	−	0.884953i	$-0.654190\pi$
$283$	−15.6679			−0.931360			−0.465680	+	0.884953i	$0.654190\pi$
$284$			9.40487i			0.558076i
$285$	−8.34559	−	2.81118i	−0.494350	−	0.166520i
$286$	−0.369752			−0.0218639
$287$			0.853084i			0.0503559i
$288$	−1.81512	+	2.38858i	−0.106957	+	0.140749i
$289$	8.22871			0.484042
$290$	0.811361			0.0476448
$291$	−5.19266	+	15.4155i	−0.304399	+	0.903674i
$292$			0.431766i			0.0252672i
$293$		−	10.0753i		−	0.588607i	−0.955712	−	0.294303i	$-0.904912\pi$
$293$		−	10.0753i		−	0.588607i	0.955712	−	0.294303i	$-0.0950876\pi$
$294$	2.75256	+	0.927190i	0.160533	+	0.0540748i
$295$	3.26050			0.189833
$296$	−10.8916			−0.633061
$297$	1.43781	−	0.975386i	0.0834303	−	0.0565976i
$298$	9.40487			0.544809
$299$			4.00000i			0.231326i
$300$	0.552909	−	1.64143i	0.0319222	−	0.0947680i
$301$		−	17.3828i		−	1.00193i
$302$	−21.3397			−1.22796
$303$	−10.0855	−	3.39728i	−0.579400	−	0.195169i
$304$	−5.08434			−0.291607
$305$	6.09404			0.348944
$306$	9.11704	−	11.9974i	0.521186	−	0.685847i
$307$	33.3858			1.90543			0.952715	−	0.303866i	$-0.0982774\pi$
$307$	33.3858			1.90543			0.952715	+	0.303866i	$0.0982774\pi$
$308$	−0.771450			−0.0439574
$309$	−0.471678	+	1.40028i	−0.0268328	+	0.0796590i
$310$	−5.04090	+	2.36418i	−0.286304	+	0.134276i
$311$			4.53256i			0.257018i	0.991708	+	0.128509i	$0.0410191\pi$
$311$			4.53256i			0.257018i	−0.991708	+	0.128509i	$0.958981\pi$
$312$	−0.611418	+	1.81512i	−0.0346147	+	0.102761i
$313$		−	2.80055i		−	0.158297i	−0.996863	−	0.0791483i	$-0.974780\pi$
$313$		−	2.80055i		−	0.158297i	0.996863	−	0.0791483i	$-0.0252201\pi$
$314$			19.9810i			1.12759i
$315$	−4.18781	+	5.51088i	−0.235957	+	0.310503i
$316$			8.05113i			0.452912i
$317$		−	3.55433i		−	0.199631i	−0.995006	−	0.0998155i	$-0.968175\pi$
$317$		−	3.55433i		−	0.199631i	0.995006	−	0.0998155i	$-0.0318253\pi$
$318$	10.7117	+	3.60818i	0.600680	+	0.202337i
$319$	−0.271294			−0.0151896
$320$		−	1.00000i		−	0.0559017i
$321$	20.2632	+	6.82558i	1.13098	+	0.380967i
$322$			8.34559i			0.465082i
$323$	25.5377			1.42096
$324$	−2.41065	−	8.67115i	−0.133925	−	0.481730i
$325$		−	1.10582i		−	0.0613398i
$326$			10.0869i			0.558661i
$327$	−2.04918	+	6.08341i	−0.113320	+	0.336413i
$328$	0.369752			0.0204161
$329$			26.2823i			1.44899i
$330$	−0.184876	+	0.548844i	−0.0101771	+	0.0302129i
$331$			12.6796i			0.696934i	0.937321	+	0.348467i	$0.113298\pi$
$331$			12.6796i			0.696934i	−0.937321	+	0.348467i	$0.886702\pi$
$332$	−10.5625			−0.579695
$333$	19.7696	−	26.0155i	1.08337	−	1.42564i
$334$		−	3.61723i		−	0.197926i
$335$		−	0.206944i		−	0.0113065i
$336$	−1.27566	+	3.78707i	−0.0695930	+	0.206602i
$337$		−	28.1201i		−	1.53180i	−0.642961	−	0.765899i	$-0.722294\pi$
$337$		−	28.1201i		−	1.53180i	0.642961	−	0.765899i	$-0.277706\pi$
$338$		−	11.7772i		−	0.640593i
$339$	20.5304	+	6.91560i	1.11506	+	0.375604i
$340$			5.02282i			0.272401i
$341$	1.68552	−	0.790510i	0.0912761	−	0.0428085i
$342$	9.22871	−	12.1444i	0.499032	−	0.656692i
$343$	20.0192			1.08094
$344$	−7.53423			−0.406218
$345$	5.93743	+	2.00000i	0.319660	+	0.107676i
$346$	−18.4892			−0.993986
$347$	−27.3687			−1.46923			−0.734614	−	0.678485i	$-0.762637\pi$
$347$	−27.3687			−1.46923			−0.734614	+	0.678485i	$0.762637\pi$
$348$	−0.448609	+	1.33179i	−0.0240480	+	0.0713916i
$349$	−8.77129			−0.469516			−0.234758	−	0.972054i	$-0.575430\pi$
$349$	−8.77129			−0.469516			−0.234758	+	0.972054i	$0.575430\pi$
$350$		−	2.30718i		−	0.123324i
$351$	−3.22577	−	4.75510i	−0.172179	−	0.253808i
$352$			0.334369i			0.0178219i
$353$	−13.0622			−0.695233			−0.347616	−	0.937637i	$-0.613009\pi$
$353$	−13.0622			−0.695233			−0.347616	+	0.937637i	$0.613009\pi$
$354$	−1.80276	+	5.35187i	−0.0958156	+	0.284449i
$355$	9.40487			0.499158
$356$	−6.42841			−0.340705
$357$	6.40741	−	19.0218i	0.339116	−	1.00674i
$358$		−	6.71755i		−	0.355034i
$359$			1.62278i			0.0856470i	0.999083	+	0.0428235i	$0.0136353\pi$
$359$			1.62278i			0.0856470i	−0.999083	+	0.0428235i	$0.986365\pi$
$360$	2.38858	+	1.81512i	0.125889	+	0.0956654i
$361$	6.85054			0.360555
$362$	4.65385			0.244601
$363$	−6.02019	+	17.8722i	−0.315978	+	0.938048i
$364$			2.55132i			0.133726i
$365$	0.431766			0.0225997
$366$	−3.36945	+	10.0029i	−0.176124	+	0.522862i
$367$			6.20207i			0.323745i	0.986812	+	0.161873i	$0.0517534\pi$
$367$			6.20207i			0.323745i	−0.986812	+	0.161873i	$0.948247\pi$
$368$	3.61723			0.188561
$369$	−0.671146	+	0.883183i	−0.0349385	+	0.0459767i
$370$			10.8916i			0.566227i
$371$	15.0562			0.781679
$372$	−1.09348	−	9.58146i	−0.0566941	−	0.496775i
$373$	−23.7538			−1.22993			−0.614963	−	0.788556i	$-0.710829\pi$
$373$	−23.7538			−1.22993			−0.614963	+	0.788556i	$0.710829\pi$
$374$		−	1.67948i		−	0.0868437i
$375$	−1.64143	−	0.552909i	−0.0847631	−	0.0285521i
$376$	11.3915			0.587473
$377$			0.897219i			0.0462091i
$378$	−6.73025	−	9.92102i	−0.346167	−	0.510282i
$379$	12.7320			0.654001			0.327000	−	0.945024i	$-0.393962\pi$
$379$	12.7320			0.654001			0.327000	+	0.945024i	$0.393962\pi$
$380$			5.08434i			0.260821i
$381$	4.24460	+	1.42978i	0.217458	+	0.0732498i
$382$	8.86405			0.453524
$383$	20.0714			1.02560			0.512801	−	0.858507i	$-0.328608\pi$
$383$	20.0714			1.02560			0.512801	+	0.858507i	$0.328608\pi$
$384$	1.64143	+	0.552909i	0.0837639	+	0.0282155i
$385$			0.771450i			0.0393167i
$386$		−	18.5761i		−	0.945498i
$387$	13.6756	−	17.9961i	0.695168	−	0.914794i
$388$	9.39152			0.476782
$389$	3.60778			0.182922			0.0914610	−	0.995809i	$-0.470846\pi$
$389$	3.60778			0.182922			0.0914610	+	0.995809i	$0.470846\pi$
$390$	1.81512	+	0.611418i	0.0919124	+	0.0309603i
$391$	−18.1687			−0.918830
$392$		−	1.67693i		−	0.0846978i
$393$	−11.9176	−	4.01440i	−0.601163	−	0.202500i
$394$			12.1945i			0.614349i
$395$	8.05113			0.405096
$396$	−0.798669	−	0.606922i	−0.0401346	−	0.0304990i
$397$	−11.3282			−0.568544			−0.284272	−	0.958744i	$-0.591752\pi$
$397$	−11.3282			−0.568544			−0.284272	+	0.958744i	$0.591752\pi$
$398$	−0.531430			−0.0266382
$399$	6.48590	−	19.2548i	0.324701	−	0.963944i
$400$	−1.00000			−0.0500000
$401$	19.0295			0.950288			0.475144	−	0.879908i	$-0.342396\pi$
$401$	19.0295			0.950288			0.475144	+	0.879908i	$0.342396\pi$
$402$	0.339683	+	0.114421i	0.0169419	+	0.00570680i
$403$	−2.61436	−	5.57432i	−0.130230	−	0.277677i
$404$			6.14437i			0.305694i
$405$	−8.67115	+	2.41065i	−0.430873	+	0.119786i
$406$			1.87195i			0.0929036i
$407$		−	3.64182i		−	0.180518i
$408$	−8.24460	−	2.77716i	−0.408169	−	0.137490i
$409$		−	8.78798i		−	0.434538i	−0.976112	−	0.217269i	$-0.930285\pi$
$409$		−	8.78798i		−	0.434538i	0.976112	−	0.217269i	$-0.0697149\pi$
$410$		−	0.369752i		−	0.0182607i
$411$	−11.1528	+	33.1094i	−0.550127	+	1.63317i
$412$	0.853084			0.0420284
$413$			7.52254i			0.370160i
$414$	−6.56572	+	8.64005i	−0.322687	+	0.424635i
$415$			10.5625i			0.518495i
$416$	1.10582			0.0542172
$417$	−28.7860	−	9.69645i	−1.40966	−	0.474837i
$418$		−	1.70005i		−	0.0831521i
$419$			19.5225i			0.953739i	0.878974	+	0.476869i	$0.158229\pi$
$419$			19.5225i			0.953739i	−0.878974	+	0.476869i	$0.841771\pi$
$420$	3.78707	+	1.27566i	0.184790	+	0.0622459i
$421$	0.0317842			0.00154907			0.000774535	−	1.00000i	$-0.499753\pi$
$421$	0.0317842			0.00154907			0.000774535		1.00000i	$0.499753\pi$
$422$			26.3131i			1.28090i
$423$	−20.6770	+	27.2096i	−1.00535	+	1.32298i
$424$		−	6.52581i		−	0.316921i
$425$	5.02282			0.243643
$426$	−5.20004	+	15.4374i	−0.251943	+	0.747946i
$427$			14.0600i			0.680413i
$428$		−	12.3448i		−	0.596710i
$429$	−0.606922	−	0.204439i	−0.0293025	−	0.00987043i
$430$			7.53423i			0.363333i
$431$		−	26.2446i		−	1.26416i	−0.774904	−	0.632079i	$-0.782202\pi$
$431$		−	26.2446i		−	1.26416i	0.774904	−	0.632079i	$-0.217798\pi$
$432$	−4.30007	+	2.91709i	−0.206887	+	0.140349i
$433$			17.3574i			0.834144i	0.908873	+	0.417072i	$0.136944\pi$
$433$			17.3574i			0.834144i	−0.908873	+	0.417072i	$0.863056\pi$
$434$	−5.45459	−	11.6302i	−0.261828	−	0.558270i
$435$	1.33179	+	0.448609i	0.0638546	+	0.0215092i
$436$	3.70617			0.177493
$437$	−18.3912			−0.879772
$438$	−0.238728	+	0.708714i	−0.0114069	+	0.0338637i
$439$	−3.71714			−0.177409			−0.0887046	−	0.996058i	$-0.528273\pi$
$439$	−3.71714			−0.177409			−0.0887046	+	0.996058i	$0.528273\pi$
$440$	0.334369			0.0159404
$441$	4.00548	+	3.04384i	0.190737	+	0.144945i
$442$	−5.55433			−0.264192
$443$			13.3464i			0.634106i	0.948408	+	0.317053i	$0.102693\pi$
$443$			13.3464i			0.634106i	−0.948408	+	0.317053i	$0.897307\pi$
$444$	−17.8778	−	6.02207i	−0.848442	−	0.285795i
$445$			6.42841i			0.304736i
$446$	6.26063			0.296450
$447$	15.4374	+	5.20004i	0.730165	+	0.245953i
$448$	2.30718			0.109004
$449$	17.2603			0.814562			0.407281	−	0.913303i	$-0.366477\pi$
$449$	17.2603			0.814562			0.407281	+	0.913303i	$0.366477\pi$
$450$	1.81512	−	2.38858i	0.0855658	−	0.112599i
$451$			0.123634i			0.00582169i
$452$		−	12.5076i		−	0.588310i
$453$	−35.0276	−	11.7989i	−1.64574	−	0.554362i
$454$	−19.6053			−0.920124
$455$	2.55132			0.119608
$456$	−8.34559	−	2.81118i	−0.390818	−	0.131646i
$457$			9.92004i			0.464040i	0.972711	+	0.232020i	$0.0745335\pi$
$457$			9.92004i			0.464040i	−0.972711	+	0.232020i	$0.925467\pi$
$458$	8.06871			0.377026
$459$	21.5985	−	14.6520i	1.00813	−	0.683898i
$460$		−	3.61723i		−	0.168654i
$461$	19.9847			0.930779			0.465389	−	0.885106i	$-0.345914\pi$
$461$	19.9847			0.930779			0.465389	+	0.885106i	$0.345914\pi$
$462$	−1.26628	−	0.426542i	−0.0589127	−	0.0198445i
$463$			35.0707i			1.62987i	0.579550	+	0.814937i	$0.303228\pi$
$463$			35.0707i			1.62987i	−0.579550	+	0.814937i	$0.696772\pi$
$464$	0.811361			0.0376665
$465$	−9.58146	+	1.09348i	−0.444329	+	0.0507087i
$466$	−5.24715			−0.243070
$467$			27.2605i			1.26147i	0.776000	+	0.630733i	$0.217246\pi$
$467$			27.2605i			1.26147i	−0.776000	+	0.630733i	$0.782754\pi$
$468$	−2.00720	+	2.64134i	−0.0927828	+	0.122096i
$469$	0.477456			0.0220468
$470$		−	11.3915i		−	0.525452i
$471$	−11.0477	+	32.7973i	−0.509049	+	1.51122i
$472$	3.26050			0.150076
$473$		−	2.51922i		−	0.115834i
$474$	−4.45155	+	13.2154i	−0.204466	+	0.607002i
$475$	5.08434			0.233286
$476$	−11.5885			−0.531160
$477$	15.5874	+	11.8451i	0.713699	+	0.542352i
$478$			19.6972i			0.900927i
$479$			28.7256i			1.31250i	0.754542	+	0.656252i	$0.227859\pi$
$479$			28.7256i			1.31250i	−0.754542	+	0.656252i	$0.772141\pi$
$480$	0.552909	−	1.64143i	0.0252368	−	0.0749207i
$481$	−12.0441			−0.549165
$482$	10.9890			0.500535
$483$	−4.61436	+	13.6987i	−0.209960	+	0.623312i
$484$	10.8882			0.494918
$485$		−	9.39152i		−	0.426447i
$486$	0.837447	−	15.5659i	0.0379874	−	0.706086i
$487$		−	17.6437i		−	0.799515i	−0.916621	−	0.399757i	$-0.869094\pi$
$487$		−	17.6437i		−	0.799515i	0.916621	−	0.399757i	$-0.130906\pi$
$488$	6.09404			0.275864
$489$	−5.57714	+	16.5569i	−0.252207	+	0.748730i
$490$	−1.67693			−0.0757560
$491$	34.9998			1.57952			0.789759	−	0.613418i	$-0.210206\pi$
$491$	34.9998			1.57952			0.789759	+	0.613418i	$0.210206\pi$
$492$	0.606922	+	0.204439i	0.0273622	+	0.00921684i
$493$	−4.07532			−0.183543
$494$	−5.62236			−0.252962
$495$	−0.606922	+	0.798669i	−0.0272791	+	0.0358975i
$496$	−5.04090	+	2.36418i	−0.226343	+	0.106155i
$497$			21.6987i			0.973320i
$498$	−17.3377	−	5.84013i	−0.776920	−	0.261702i
$499$			1.02600i			0.0459299i	0.999736	+	0.0229649i	$0.00731061\pi$
$499$			1.02600i			0.0459299i	−0.999736	+	0.0229649i	$0.992689\pi$
$500$			1.00000i			0.0447214i
$501$	2.00000	−	5.93743i	0.0893534	−	0.265265i
$502$		−	28.1823i		−	1.25784i
$503$		−	9.66791i		−	0.431071i	−0.976496	−	0.215535i	$-0.930850\pi$
$503$		−	9.66791i		−	0.431071i	0.976496	−	0.215535i	$-0.0691497\pi$
$504$	−4.18781	+	5.51088i	−0.186540	+	0.245474i
$505$	6.14437			0.273421
$506$			1.20949i			0.0537684i
$507$	6.51171	−	19.3314i	0.289195	−	0.858537i
$508$		−	2.58592i		−	0.114732i
$509$	−17.7624			−0.787305			−0.393652	−	0.919259i	$-0.628789\pi$
$509$	−17.7624			−0.787305			−0.393652	+	0.919259i	$0.628789\pi$
$510$	−2.77716	+	8.24460i	−0.122975	+	0.365077i
$511$			0.996162i			0.0440676i
$512$		−	1.00000i		−	0.0441942i
$513$	21.8630	−	14.8315i	0.965276	−	0.654826i
$514$	16.4266			0.724548
$515$		−	0.853084i		−	0.0375914i
$516$	−12.3669	−	4.16575i	−0.544423	−	0.183387i
$517$			3.80898i			0.167519i
$518$	−25.1289			−1.10410
$519$	−30.3487	−	10.2229i	−1.33216	−	0.448734i
$520$		−	1.10582i		−	0.0484934i
$521$			13.6412i			0.597633i	0.954311	+	0.298816i	$0.0965918\pi$
$521$			13.6412i			0.597633i	−0.954311	+	0.298816i	$0.903408\pi$
$522$	−1.47272	+	1.93800i	−0.0644593	+	0.0848241i
$523$			26.7620i			1.17022i	0.810954	+	0.585110i	$0.198949\pi$
$523$			26.7620i			1.17022i	−0.810954	+	0.585110i	$0.801051\pi$
$524$			7.26050i			0.317176i
$525$	1.27566	−	3.78707i	0.0556744	−	0.165281i
$526$		−	16.2371i		−	0.707970i
$527$	25.3195	−	11.8749i	1.10294	−	0.517277i
$528$	−0.184876	+	0.548844i	−0.00804570	+	0.0238854i
$529$	−9.91566			−0.431116
$530$	−6.52581			−0.283463
$531$	−5.91820	+	7.78796i	−0.256828	+	0.337969i
$532$	−11.7305			−0.508581
$533$	0.408879			0.0177105
$534$	−10.5518	−	3.55433i	−0.456620	−	0.153811i
$535$	−12.3448			−0.533714
$536$		−	0.206944i		−	0.00893860i
$537$	3.71420	−	11.0264i	0.160280	−	0.475824i
$538$			1.15104i			0.0496250i
$539$	0.560714			0.0241517
$540$	2.91709	+	4.30007i	0.125532	+	0.185045i
$541$	23.1036			0.993300			0.496650	−	0.867951i	$-0.334563\pi$
$541$	23.1036			0.993300			0.496650	+	0.867951i	$0.334563\pi$
$542$	−2.42877			−0.104325
$543$	7.63897	+	2.57316i	0.327820	+	0.110425i
$544$			5.02282i			0.215352i
$545$		−	3.70617i		−	0.158755i
$546$	−1.41065	+	4.18781i	−0.0603702	+	0.179222i
$547$	19.9566			0.853285			0.426642	−	0.904420i	$-0.359696\pi$
$547$	19.9566			0.853285			0.426642	+	0.904420i	$0.359696\pi$
$548$	20.1711			0.861667
$549$	−11.0614	+	14.5561i	−0.472091	+	0.621240i
$550$		−	0.334369i		−	0.0142576i
$551$	−4.12524			−0.175741
$552$	5.93743	+	2.00000i	0.252714	+	0.0851257i
$553$			18.5754i			0.789906i
$554$	27.3687			1.16278
$555$	−6.02207	+	17.8778i	−0.255623	+	0.758870i
$556$			17.5371i			0.743740i
$557$	−14.3054			−0.606138			−0.303069	−	0.952969i	$-0.598011\pi$
$557$	−14.3054			−0.606138			−0.303069	+	0.952969i	$0.598011\pi$
$558$	3.50281	−	16.3319i	0.148286	−	0.691384i
$559$	−8.33149			−0.352385
$560$		−	2.30718i		−	0.0974961i
$561$	0.928599	−	2.75674i	0.0392055	−	0.116390i
$562$	−12.9900			−0.547949
$563$			16.0753i			0.677494i	0.940878	+	0.338747i	$0.110003\pi$
$563$			16.0753i			0.677494i	−0.940878	+	0.338747i	$0.889997\pi$
$564$	18.6984	+	6.29848i	0.787344	+	0.265214i
$565$	−12.5076			−0.526201
$566$			15.6679i			0.658571i
$567$	−5.56180	−	20.0059i	−0.233574	−	0.840168i
$568$	9.40487			0.394619
$569$	−8.70924			−0.365110			−0.182555	−	0.983196i	$-0.558437\pi$
$569$	−8.70924			−0.365110			−0.182555	+	0.983196i	$0.558437\pi$
$570$	−2.81118	+	8.34559i	−0.117747	+	0.349558i
$571$			30.8380i			1.29053i	0.763959	+	0.645265i	$0.223253\pi$
$571$			30.8380i			1.29053i	−0.763959	+	0.645265i	$0.776747\pi$
$572$			0.369752i			0.0154601i
$573$	14.5497	+	4.90102i	0.607823	+	0.204743i
$574$	0.853084			0.0356070
$575$	−3.61723			−0.150849
$576$	2.38858	+	1.81512i	0.0995243	+	0.0756302i
$577$	12.5767			0.523575			0.261787	−	0.965126i	$-0.415688\pi$
$577$	12.5767			0.523575			0.261787	+	0.965126i	$0.415688\pi$
$578$		−	8.22871i		−	0.342269i
$579$	10.2709	−	30.4914i	0.426844	−	1.26718i
$580$		−	0.811361i		−	0.0336899i
$581$	−24.3697			−1.01102
$582$	15.4155	+	5.19266i	0.638994	+	0.215243i
$583$	2.18203			0.0903704
$584$	0.431766			0.0178666
$585$	2.64134	+	2.00720i	0.109206	+	0.0829874i
$586$	−10.0753			−0.416208
$587$	41.9612			1.73193			0.865963	−	0.500108i	$-0.166706\pi$
$587$	41.9612			1.73193			0.865963	+	0.500108i	$0.166706\pi$
$588$	0.927190	−	2.75256i	0.0382367	−	0.113514i
$589$	25.6296	−	12.0203i	1.05605	−	0.495288i
$590$		−	3.26050i		−	0.134232i
$591$	−6.74244	+	20.0164i	−0.277347	+	0.823364i
$592$			10.8916i			0.447642i
$593$		−	17.8423i		−	0.732695i	−0.930478	−	0.366347i	$-0.880608\pi$
$593$		−	17.8423i		−	0.732695i	0.930478	−	0.366347i	$-0.119392\pi$
$594$	−0.975386	−	1.43781i	−0.0400206	−	0.0589941i
$595$			11.5885i			0.475084i
$596$		−	9.40487i		−	0.385238i
$597$	−0.872305	−	0.293833i	−0.0357011	−	0.0120258i
$598$	4.00000			0.163572
$599$		−	11.9166i		−	0.486900i	−0.969914	−	0.243450i	$-0.921721\pi$
$599$		−	11.9166i		−	0.486900i	0.969914	−	0.243450i	$-0.0782791\pi$
$600$	−1.64143	−	0.552909i	−0.0670111	−	0.0225724i
$601$			38.6692i			1.57735i	0.614811	+	0.788674i	$0.289232\pi$
$601$			38.6692i			1.57735i	−0.614811	+	0.788674i	$0.710768\pi$
$602$	−17.3828			−0.708470
$603$	0.494302	+	0.375628i	0.0201295	+	0.0152968i
$604$			21.3397i			0.868301i
$605$		−	10.8882i		−	0.442668i
$606$	−3.39728	+	10.0855i	−0.138005	+	0.409697i
$607$	25.5469			1.03692			0.518458	−	0.855103i	$-0.326506\pi$
$607$	25.5469			1.03692			0.518458	+	0.855103i	$0.326506\pi$
$608$			5.08434i			0.206197i
$609$	−1.03502	+	3.07268i	−0.0419412	+	0.124511i
$610$		−	6.09404i		−	0.246740i
$611$	12.5970			0.509618
$612$	−11.9974	−	9.11704i	−0.484967	−	0.368534i
$613$		−	3.49749i		−	0.141262i	−0.997502	−	0.0706312i	$-0.977499\pi$
$613$		−	3.49749i		−	0.141262i	0.997502	−	0.0706312i	$-0.0225014\pi$
$614$		−	33.3858i		−	1.34734i
$615$	0.204439	−	0.606922i	0.00824379	−	0.0244735i
$616$			0.771450i			0.0310826i
$617$			16.1879i			0.651701i	0.945421	+	0.325850i	$0.105651\pi$
$617$			16.1879i			0.651701i	−0.945421	+	0.325850i	$0.894349\pi$
$618$	1.40028	+	0.471678i	0.0563274	+	0.0189737i
$619$		−	29.2259i		−	1.17469i	−0.809338	−	0.587344i	$-0.800174\pi$
$619$		−	29.2259i		−	1.17469i	0.809338	−	0.587344i	$-0.199826\pi$
$620$	2.36418	+	5.04090i	0.0949478	+	0.202447i
$621$	−15.5543	+	10.5518i	−0.624174	+	0.423428i
$622$	4.53256			0.181739
$623$	−14.8315			−0.594211
$624$	1.81512	+	0.611418i	0.0726631	+	0.0244763i
$625$	1.00000			0.0400000
$626$	−2.80055			−0.111933
$627$	0.939973	−	2.79051i	0.0375389	−	0.111442i
$628$	19.9810			0.797327
$629$		−	54.7065i		−	2.18129i
$630$	5.51088	+	4.18781i	0.219559	+	0.166847i
$631$			42.2970i			1.68382i	0.539620	+	0.841909i	$0.318568\pi$
$631$			42.2970i			1.68382i	−0.539620	+	0.841909i	$0.681432\pi$
$632$	8.05113			0.320257
$633$	−14.5487	+	43.1910i	−0.578260	+	1.71669i
$634$	−3.55433			−0.141160
$635$	−2.58592			−0.102619
$636$	3.60818	−	10.7117i	0.143074	−	0.424745i
$637$		−	1.85438i		−	0.0734732i
$638$			0.271294i			0.0107406i
$639$	−17.0710	+	22.4643i	−0.675318	+	0.888674i
$640$	−1.00000			−0.0395285
$641$	−38.8487			−1.53443			−0.767215	−	0.641390i	$-0.778358\pi$
$641$	−38.8487			−1.53443			−0.767215	+	0.641390i	$0.778358\pi$
$642$	6.82558	−	20.2632i	0.269384	−	0.799724i
$643$		−	35.6691i		−	1.40665i	−0.710868	−	0.703325i	$-0.751698\pi$
$643$		−	35.6691i		−	1.40665i	0.710868	−	0.703325i	$-0.248302\pi$
$644$	8.34559			0.328862
$645$	−4.16575	+	12.3669i	−0.164026	+	0.486946i
$646$		−	25.5377i		−	1.00477i
$647$	−34.9263			−1.37310			−0.686548	−	0.727084i	$-0.740875\pi$
$647$	−34.9263			−1.37310			−0.686548	+	0.727084i	$0.740875\pi$
$648$	−8.67115	+	2.41065i	−0.340635	+	0.0946993i
$649$			1.09021i			0.0427945i
$650$	−1.10582			−0.0433738
$651$	−2.52284	−	22.1061i	−0.0988780	−	0.866407i
$652$	10.0869			0.395033
$653$			23.4292i			0.916855i	0.888732	+	0.458427i	$0.151587\pi$
$653$			23.4292i			0.916855i	−0.888732	+	0.458427i	$0.848413\pi$
$654$	6.08341	+	2.04918i	0.237880	+	0.0801291i
$655$	7.26050			0.283691
$656$		−	0.369752i		−	0.0144364i
$657$	−0.783710	+	1.03131i	−0.0305754	+	0.0402352i
$658$	26.2823			1.02459
$659$		−	28.7513i		−	1.11999i	−0.828496	−	0.559995i	$-0.810803\pi$
$659$		−	28.7513i		−	1.11999i	0.828496	−	0.559995i	$-0.189197\pi$
$660$	0.548844	+	0.184876i	0.0213637	+	0.00719629i
$661$	28.2440			1.09856			0.549282	−	0.835637i	$-0.314901\pi$
$661$	28.2440			1.09856			0.549282	+	0.835637i	$0.314901\pi$
$662$	12.6796			0.492807
$663$	−9.11704	−	3.07104i	−0.354076	−	0.119269i
$664$			10.5625i			0.409906i
$665$			11.7305i			0.454889i
$666$	−26.0155	−	19.7696i	−1.00808	−	0.766056i
$667$	2.93488			0.113639
$668$	−3.61723			−0.139955
$669$	10.2764	+	3.46156i	0.397308	+	0.133832i
$670$	−0.206944			−0.00799493
$671$			2.03766i			0.0786630i
$672$	3.78707	+	1.27566i	0.146089	+	0.0492097i
$673$			3.02940i			0.116775i	0.998294	+	0.0583873i	$0.0185958\pi$
$673$			3.02940i			0.116775i	−0.998294	+	0.0583873i	$0.981404\pi$
$674$	−28.1201			−1.08314
$675$	4.30007	−	2.91709i	0.165510	−	0.112279i
$676$	−11.7772			−0.452968
$677$	25.1037			0.964814			0.482407	−	0.875947i	$-0.339763\pi$
$677$	25.1037			0.964814			0.482407	+	0.875947i	$0.339763\pi$
$678$	6.91560	−	20.5304i	0.265592	−	0.788466i
$679$	21.6679			0.831538
$680$	5.02282			0.192616
$681$	−32.1808	−	10.8400i	−1.23317	−	0.415389i
$682$	−0.790510	−	1.68552i	−0.0302702	−	0.0645420i
$683$			19.2899i			0.738108i	0.929408	+	0.369054i	$0.120318\pi$
$683$			19.2899i			0.738108i	−0.929408	+	0.369054i	$0.879682\pi$
$684$	−12.1444	−	9.22871i	−0.464352	−	0.352869i
$685$		−	20.1711i		−	0.770698i
$686$		−	20.0192i		−	0.764337i
$687$	13.2442	+	4.46126i	0.505298	+	0.170208i
$688$			7.53423i			0.287240i
$689$		−	7.21636i		−	0.274921i
$690$	2.00000	−	5.93743i	0.0761387	−	0.226034i
$691$	8.14437			0.309826			0.154913	−	0.987928i	$-0.450490\pi$
$691$	8.14437			0.309826			0.154913	+	0.987928i	$0.450490\pi$
$692$			18.4892i			0.702854i
$693$	−1.84267	−	1.40028i	−0.0699973	−	0.0531921i
$694$			27.3687i			1.03890i
$695$	17.5371			0.665222
$696$	1.33179	+	0.448609i	0.0504815	+	0.0170045i
$697$			1.85720i			0.0703464i
$698$			8.77129i			0.331998i
$699$	−8.61283	−	2.90120i	−0.325767	−	0.109733i
$700$	−2.30718			−0.0872031
$701$		−	50.9709i		−	1.92515i	−0.271022	−	0.962573i	$-0.587362\pi$
$701$		−	50.9709i		−	1.92515i	0.271022	−	0.962573i	$-0.412638\pi$
$702$	−4.75510	+	3.22577i	−0.179470	+	0.121749i
$703$		−	55.3766i		−	2.08857i
$704$	0.334369			0.0126020
$705$	6.29848	−	18.6984i	0.237214	−	0.704222i
$706$			13.0622i			0.491604i
$707$			14.1762i			0.533149i
$708$	5.35187	+	1.80276i	0.201136	+	0.0677518i
$709$		−	17.7747i		−	0.667541i	−0.942654	−	0.333771i	$-0.891679\pi$
$709$		−	17.7747i		−	0.667541i	0.942654	−	0.333771i	$-0.108321\pi$
$710$		−	9.40487i		−	0.352958i
$711$	−14.6138	+	19.2308i	−0.548060	+	0.721211i
$712$			6.42841i			0.240915i
$713$	−18.2341	+	8.55178i	−0.682872	+	0.320267i
$714$	−19.0218	−	6.40741i	−0.711872	−	0.239791i
$715$	0.369752			0.0138279
$716$	−6.71755			−0.251047
$717$	−10.8907	+	32.3315i	−0.406722	+	1.20744i
$718$	1.62278			0.0605616
$719$	−22.5211			−0.839896			−0.419948	−	0.907548i	$-0.637952\pi$
$719$	−22.5211			−0.839896			−0.419948	+	0.907548i	$0.637952\pi$
$720$	1.81512	−	2.38858i	0.0676457	−	0.0890172i
$721$	1.96822			0.0733002
$722$		−	6.85054i		−	0.254951i
$723$	18.0377	+	6.07592i	0.670828	+	0.225966i
$724$		−	4.65385i		−	0.172959i
$725$	−0.811361			−0.0301332
$726$	17.8722	+	6.02019i	0.663300	+	0.223430i
$727$	1.72539			0.0639911			0.0319956	−	0.999488i	$-0.489814\pi$
$727$	1.72539			0.0639911			0.0319956	+	0.999488i	$0.489814\pi$
$728$	2.55132			0.0945583
$729$	9.98117	−	25.0874i	0.369673	−	0.929162i
$730$		−	0.431766i		−	0.0159804i
$731$		−	37.8431i		−	1.39968i
$732$	10.0029	+	3.36945i	0.369719	+	0.124539i
$733$	30.4341			1.12411			0.562055	−	0.827100i	$-0.310011\pi$
$733$	30.4341			1.12411			0.562055	+	0.827100i	$0.310011\pi$
$734$	6.20207			0.228922
$735$	−2.75256	−	0.927190i	−0.101530	−	0.0341999i
$736$		−	3.61723i		−	0.133333i
$737$	0.0691956			0.00254885
$738$	0.883183	+	0.671146i	0.0325104	+	0.0247052i
$739$		−	3.10791i		−	0.114326i	−0.998365	−	0.0571631i	$-0.981795\pi$
$739$		−	3.10791i		−	0.114326i	0.998365	−	0.0571631i	$-0.0182055\pi$
$740$	10.8916			0.400383
$741$	−9.22871	−	3.10866i	−0.339025	−	0.114199i
$742$		−	15.0562i		−	0.552730i
$743$	−29.5491			−1.08405			−0.542025	−	0.840362i	$-0.682342\pi$
$743$	−29.5491			−1.08405			−0.542025	+	0.840362i	$0.682342\pi$
$744$	−9.58146	+	1.09348i	−0.351273	+	0.0400888i
$745$	−9.40487			−0.344568
$746$			23.7538i			0.869689i
$747$	−25.2295	−	19.1723i	−0.923099	−	0.701479i
$748$	−1.67948			−0.0614078
$749$		−	28.4817i		−	1.04070i
$750$	−0.552909	+	1.64143i	−0.0201894	+	0.0599365i
$751$	−4.03257			−0.147150			−0.0735752	−	0.997290i	$-0.523441\pi$
$751$	−4.03257			−0.147150			−0.0735752	+	0.997290i	$0.523441\pi$
$752$		−	11.3915i		−	0.415406i
$753$	15.5823	−	46.2593i	0.567850	−	1.68578i
$754$	0.897219			0.0326748
$755$	21.3397			0.776632
$756$	−9.92102	+	6.73025i	−0.360824	+	0.244777i
$757$			53.7307i			1.95287i	0.215801	+	0.976437i	$0.430764\pi$
$757$			53.7307i			1.95287i	−0.215801	+	0.976437i	$0.569236\pi$
$758$		−	12.7320i		−	0.462448i
$759$	−0.668739	+	1.98529i	−0.0242737	+	0.0720616i
$760$	5.08434			0.184428
$761$	−43.6345			−1.58175			−0.790875	−	0.611978i	$-0.790374\pi$
$761$	−43.6345			−1.58175			−0.790875	+	0.611978i	$0.790374\pi$
$762$	1.42978	−	4.24460i	0.0517954	−	0.153766i
$763$	8.55079			0.309559
$764$		−	8.86405i		−	0.320690i
$765$	−9.11704	+	11.9974i	−0.329627	+	0.433767i
$766$		−	20.0714i		−	0.725210i
$767$	3.60552			0.130188
$768$	0.552909	−	1.64143i	0.0199514	−	0.0592300i
$769$	−37.6995			−1.35948			−0.679739	−	0.733454i	$-0.737907\pi$
$769$	−37.6995			−1.35948			−0.679739	+	0.733454i	$0.737907\pi$
$770$	0.771450			0.0278011
$771$	26.9632	+	9.08244i	0.971055	+	0.327096i
$772$	−18.5761			−0.668568
$773$	37.2120			1.33842			0.669211	−	0.743073i	$-0.266632\pi$
$773$	37.2120			1.33842			0.669211	+	0.743073i	$0.266632\pi$
$774$	−17.9961	−	13.6756i	−0.646857	−	0.491558i
$775$	5.04090	−	2.36418i	0.181074	−	0.0849239i
$776$		−	9.39152i		−	0.337136i
$777$	−41.2472	−	13.8940i	−1.47974	−	0.498444i
$778$		−	3.60778i		−	0.129345i
$779$			1.87995i			0.0673560i
$780$	0.611418	−	1.81512i	0.0218923	−	0.0649919i
$781$			3.14470i			0.112526i
$782$			18.1687i			0.649711i
$783$	−3.48891	+	2.36681i	−0.124683	+	0.0845830i
$784$	−1.67693			−0.0598904
$785$		−	19.9810i		−	0.713151i
$786$	−4.01440	+	11.9176i	−0.143189	+	0.425086i
$787$		−	31.7431i		−	1.13152i	−0.824570	−	0.565760i	$-0.808583\pi$
$787$		−	31.7431i		−	1.13152i	0.824570	−	0.565760i	$-0.191417\pi$
$788$	12.1945			0.434410
$789$	8.97763	−	26.6520i	0.319612	−	0.948837i
$790$		−	8.05113i		−	0.286446i
$791$		−	28.8574i		−	1.02605i
$792$	−0.606922	+	0.798669i	−0.0215660	+	0.0283795i
$793$	6.73891			0.239306
$794$			11.3282i			0.402021i
$795$	−10.7117	−	3.60818i	−0.379903	−	0.127969i
$796$			0.531430i			0.0188360i
$797$	26.7890			0.948915			0.474457	−	0.880278i	$-0.342644\pi$
$797$	26.7890			0.948915			0.474457	+	0.880278i	$0.342644\pi$
$798$	−19.2548	−	6.48590i	−0.681611	−	0.229598i
$799$			57.2175i			2.02421i
$800$			1.00000i			0.0353553i
$801$	−15.3548	−	11.6684i	−0.542535	−	0.412281i
$802$		−	19.0295i		−	0.671955i
$803$			0.144369i			0.00509469i
$804$	0.114421	−	0.339683i	0.00403532	−	0.0119797i
$805$		−	8.34559i		−	0.294143i
$806$	−5.57432	+	2.61436i	−0.196347	+	0.0920868i
$807$	−0.636423	+	1.88936i	−0.0224032	+	0.0665086i
$808$	6.14437			0.216158
$809$	−19.0904			−0.671184			−0.335592	−	0.942007i	$-0.608936\pi$
$809$	−19.0904			−0.671184			−0.335592	+	0.942007i	$0.608936\pi$
$810$	2.41065	+	8.67115i	0.0847016	+	0.304673i
$811$	2.99098			0.105027			0.0525137	−	0.998620i	$-0.483277\pi$
$811$	2.99098			0.105027			0.0525137	+	0.998620i	$0.483277\pi$
$812$	1.87195			0.0656927
$813$	−3.98665	−	1.34289i	−0.139818	−	0.0470972i
$814$	−3.64182			−0.127646
$815$		−	10.0869i		−	0.353328i
$816$	−2.77716	+	8.24460i	−0.0972202	+	0.288619i
$817$		−	38.3066i		−	1.34018i
$818$	−8.78798			−0.307265
$819$	−4.63096	+	6.09404i	−0.161819	+	0.212943i
$820$	−0.369752			−0.0129123
$821$	18.2171			0.635780			0.317890	−	0.948128i	$-0.397026\pi$
$821$	18.2171			0.635780			0.317890	+	0.948128i	$0.397026\pi$
$822$	33.1094	+	11.1528i	1.15482	+	0.388998i
$823$		−	1.08880i		−	0.0379530i	−0.999820	−	0.0189765i	$-0.993959\pi$
$823$		−	1.08880i		−	0.0379530i	0.999820	−	0.0189765i	$-0.00604077\pi$
$824$		−	0.853084i		−	0.0297186i
$825$	0.184876	−	0.548844i	0.00643656	−	0.0191083i
$826$	7.52254			0.261743
$827$	−26.7839			−0.931368			−0.465684	−	0.884951i	$-0.654192\pi$
$827$	−26.7839			−0.931368			−0.465684	+	0.884951i	$0.654192\pi$
$828$	8.64005	+	6.56572i	0.300262	+	0.228174i
$829$		−	35.0654i		−	1.21787i	−0.793220	−	0.608936i	$-0.791597\pi$
$829$		−	35.0654i		−	1.21787i	0.793220	−	0.608936i	$-0.208403\pi$
$830$	10.5625			0.366631
$831$	44.9238	+	15.1324i	1.55839	+	0.524937i
$832$		−	1.10582i		−	0.0383374i
$833$	8.42292			0.291837
$834$	−9.69645	+	28.7860i	−0.335761	+	0.996777i
$835$			3.61723i			0.125179i
$836$	−1.70005			−0.0587974
$837$	14.7797	−	24.8709i	0.510860	−	0.859664i
$838$	19.5225			0.674395
$839$		−	32.0186i		−	1.10541i	−0.833378	−	0.552703i	$-0.813596\pi$
$839$		−	32.0186i		−	1.10541i	0.833378	−	0.552703i	$-0.186404\pi$
$840$	1.27566	−	3.78707i	0.0440145	−	0.130666i
$841$	−28.3417			−0.977300
$842$		−	0.0317842i		−	0.00109536i
$843$	−21.3221	−	7.18229i	−0.734374	−	0.247371i
$844$	26.3131			0.905733
$845$			11.7772i			0.405147i
$846$	27.2096	+	20.6770i	0.935485	+	0.710891i
$847$	25.1210			0.863168
$848$	−6.52581			−0.224097
$849$	−8.66294	+	25.7178i	−0.297311	+	0.882632i
$850$		−	5.02282i		−	0.172281i
$851$			39.3974i			1.35053i
$852$	15.4374	+	5.20004i	0.528877	+	0.178150i
$853$	−43.7307			−1.49731			−0.748655	−	0.662960i	$-0.769300\pi$
$853$	−43.7307			−1.49731			−0.748655	+	0.662960i	$0.769300\pi$
$854$	14.0600			0.481125
$855$	−9.22871	+	12.1444i	−0.315615	+	0.415329i
$856$	−12.3448			−0.421938
$857$			48.5445i			1.65825i	0.559064	+	0.829124i	$0.311160\pi$
$857$			48.5445i			1.65825i	−0.559064	+	0.829124i	$0.688840\pi$
$858$	−0.204439	+	0.606922i	−0.00697945	+	0.0207200i
$859$		−	18.2017i		−	0.621036i	−0.950568	−	0.310518i	$-0.899498\pi$
$859$		−	18.2017i		−	0.621036i	0.950568	−	0.310518i	$-0.100502\pi$
$860$	7.53423			0.256915
$861$	1.40028	+	0.471678i	0.0477213	+	0.0160747i
$862$	−26.2446			−0.893895
$863$	−56.3529			−1.91828			−0.959138	−	0.282939i	$-0.908691\pi$
$863$	−56.3529			−1.91828			−0.959138	+	0.282939i	$0.908691\pi$
$864$	2.91709	+	4.30007i	0.0992414	+	0.146291i
$865$	18.4892			0.628652
$866$	17.3574			0.589829
$867$	4.54973	−	13.5069i	0.154517	−	0.458717i
$868$	−11.6302	+	5.45459i	−0.394756	+	0.185141i
$869$			2.69205i			0.0913216i
$870$	0.448609	−	1.33179i	0.0152093	−	0.0451520i
$871$		−	0.228842i		−	0.00775402i
$872$		−	3.70617i		−	0.125507i
$873$	22.4324	+	17.0468i	0.759222	+	0.576946i
$874$			18.3912i			0.622093i
$875$			2.30718i			0.0779969i
$876$	0.708714	+	0.238728i	0.0239452	+	0.00806586i
$877$	−38.5443			−1.30155			−0.650774	−	0.759271i	$-0.725556\pi$
$877$	−38.5443			−1.30155			−0.650774	+	0.759271i	$0.725556\pi$
$878$			3.71714i			0.125447i
$879$	−16.5379	−	5.57074i	−0.557811	−	0.187896i
$880$		−	0.334369i		−	0.0112716i
$881$	14.0489			0.473318			0.236659	−	0.971593i	$-0.423948\pi$
$881$	14.0489			0.473318			0.236659	+	0.971593i	$0.423948\pi$
$882$	3.04384	−	4.00548i	0.102491	−	0.134872i
$883$		−	27.0407i		−	0.909993i	−0.890493	−	0.454996i	$-0.849641\pi$
$883$		−	27.0407i		−	0.909993i	0.890493	−	0.454996i	$-0.150359\pi$
$884$			5.55433i			0.186812i
$885$	1.80276	−	5.35187i	0.0605991	−	0.179901i
$886$	13.3464			0.448381
$887$		−	23.4668i		−	0.787939i	−0.919123	−	0.393970i	$-0.871101\pi$
$887$		−	23.4668i		−	0.787939i	0.919123	−	0.393970i	$-0.128899\pi$
$888$	−6.02207	+	17.8778i	−0.202087	+	0.599939i
$889$		−	5.96618i		−	0.200099i
$890$	6.42841			0.215481
$891$	−0.806047	−	2.89937i	−0.0270036	−	0.0971324i
$892$		−	6.26063i		−	0.209621i
$893$			57.9184i			1.93816i
$894$	5.20004	−	15.4374i	0.173915	−	0.516305i
$895$			6.71755i			0.224543i
$896$		−	2.30718i		−	0.0770774i
$897$	6.56572	+	2.21164i	0.219223	+	0.0738444i
$898$		−	17.2603i		−	0.575982i
$899$	−4.08999	+	1.91820i	−0.136409	+	0.0639757i
$900$	−2.38858	−	1.81512i	−0.0796194	−	0.0605041i
$901$	32.7779			1.09199
$902$	0.123634			0.00411655
$903$	−28.5327	−	9.61112i	−0.949507	−	0.319838i
$904$	−12.5076			−0.415998
$905$	−4.65385			−0.154699
$906$	−11.7989	+	35.0276i	−0.391993	+	1.16372i
$907$	−12.1454			−0.403280			−0.201640	−	0.979460i	$-0.564627\pi$
$907$	−12.1454			−0.403280			−0.201640	+	0.979460i	$0.564627\pi$
$908$			19.6053i			0.650626i
$909$	−11.1528	+	14.6763i	−0.369915	+	0.486783i
$910$		−	2.55132i		−	0.0845755i
$911$	−45.2852			−1.50037			−0.750183	−	0.661231i	$-0.770034\pi$
$911$	−45.2852			−1.50037			−0.750183	+	0.661231i	$0.770034\pi$
$912$	−2.81118	+	8.34559i	−0.0930875	+	0.276350i
$913$	−3.53179			−0.116885
$914$	9.92004			0.328126
$915$	3.36945	−	10.0029i	0.111391	−	0.330687i
$916$		−	8.06871i		−	0.266598i
$917$			16.7513i			0.553175i
$918$	−14.6520	−	21.5985i	−0.483589	−	0.712856i
$919$	−49.6681			−1.63840			−0.819200	−	0.573509i	$-0.805582\pi$
$919$	−49.6681			−1.63840			−0.819200	+	0.573509i	$0.805582\pi$
$920$	−3.61723			−0.119256
$921$	18.4593	−	54.8005i	0.608256	−	1.80574i
$922$		−	19.9847i		−	0.658160i
$923$	10.4001			0.342323
$924$	−0.426542	+	1.26628i	−0.0140322	+	0.0416576i
$925$		−	10.8916i		−	0.358114i
$926$	35.0707			1.15249
$927$	2.03766	+	1.54845i	0.0669255	+	0.0508579i
$928$		−	0.811361i		−	0.0266342i
$929$	−8.91467			−0.292481			−0.146240	−	0.989249i	$-0.546717\pi$
$929$	−8.91467			−0.292481			−0.146240	+	0.989249i	$0.546717\pi$
$930$	1.09348	+	9.58146i	0.0358565	+	0.314188i
$931$	8.52609			0.279431
$932$			5.24715i			0.171876i
$933$	7.43988	+	2.50610i	0.243571	+	0.0820459i
$934$	27.2605			0.891991
$935$			1.67948i			0.0549248i
$936$	2.64134	+	2.00720i	0.0863349	+	0.0656073i
$937$	17.3372			0.566382			0.283191	−	0.959064i	$-0.408607\pi$
$937$	17.3372			0.566382			0.283191	+	0.959064i	$0.408607\pi$
$938$		−	0.477456i		−	0.0155895i
$939$	−4.59691	−	1.54845i	−0.150015	−	0.0505318i
$940$	−11.3915			−0.371550
$941$	39.8950			1.30054			0.650271	−	0.759703i	$-0.274656\pi$
$941$	39.8950			1.30054			0.650271	+	0.759703i	$0.274656\pi$
$942$	32.7973	+	11.0477i	1.06860	+	0.359952i
$943$		−	1.33748i		−	0.0435543i
$944$		−	3.26050i		−	0.106120i
$945$	6.73025	+	9.92102i	0.218935	+	0.322731i
$946$	−2.51922			−0.0819068
$947$	23.2831			0.756600			0.378300	−	0.925683i	$-0.376509\pi$
$947$	23.2831			0.756600			0.378300	+	0.925683i	$0.376509\pi$
$948$	13.2154	+	4.45155i	0.429215	+	0.144580i
$949$	0.477456			0.0154989
$950$		−	5.08434i		−	0.164958i
$951$	−5.83418	−	1.96522i	−0.189186	−	0.0637267i
$952$			11.5885i			0.375587i
$953$	−11.7163			−0.379528			−0.189764	−	0.981830i	$-0.560772\pi$
$953$	−11.7163			−0.379528			−0.189764	+	0.981830i	$0.560772\pi$
$954$	11.8451	−	15.5874i	0.383501	−	0.504662i
$955$	−8.86405			−0.286834
$956$	19.6972			0.637052
$957$	−0.150001	+	0.445311i	−0.00484885	+	0.0143948i
$958$	28.7256			0.928081
$959$	46.5383			1.50280
$960$	−1.64143	−	0.552909i	−0.0529769	−	0.0178451i
$961$	19.8213	−	23.8352i	0.639397	−	0.768877i
$962$			12.0441i			0.388318i
$963$	22.4074	−	29.4867i	0.722069	−	0.950194i
$964$		−	10.9890i		−	0.353932i
$965$			18.5761i			0.597986i
$966$	13.6987	+	4.61436i	0.440748	+	0.148464i
$967$			5.53549i			0.178009i	0.996031	+	0.0890047i	$0.0283686\pi$
$967$			5.53549i			0.178009i	−0.996031	+	0.0890047i	$0.971631\pi$
$968$		−	10.8882i		−	0.349960i
$969$	14.1201	−	41.9184i	0.453601	−	1.34661i
$970$	−9.39152			−0.301544
$971$		−	0.792885i		−	0.0254449i	−0.999919	−	0.0127224i	$-0.995950\pi$
$971$		−	0.792885i		−	0.0254449i	0.999919	−	0.0127224i	$-0.00404979\pi$
$972$	−15.5659	−	0.837447i	−0.499278	−	0.0268611i
$973$			40.4613i			1.29713i
$974$	−17.6437			−0.565342
$975$	−1.81512	−	0.611418i	−0.0581305	−	0.0195810i
$976$		−	6.09404i		−	0.195065i
$977$			10.4639i			0.334770i	0.985892	+	0.167385i	$0.0535323\pi$
$977$			10.4639i			0.334770i	−0.985892	+	0.167385i	$0.946468\pi$
$978$	16.5569	+	5.57714i	0.529432	+	0.178337i
$979$	−2.14946			−0.0686971
$980$			1.67693i			0.0535676i
$981$	8.85249	+	6.72715i	0.282638	+	0.214781i
$982$		−	34.9998i		−	1.11689i
$983$	−52.2547			−1.66667			−0.833333	−	0.552771i	$-0.813570\pi$
$983$	−52.2547			−1.66667			−0.833333	+	0.552771i	$0.813570\pi$
$984$	0.204439	−	0.606922i	0.00651729	−	0.0193480i
$985$		−	12.1945i		−	0.388548i
$986$			4.07532i			0.129785i
$987$	43.1405	+	14.5317i	1.37318	+	0.462550i
$988$			5.62236i			0.178871i
$989$			27.2530i			0.866596i
$990$	0.798669	+	0.606922i	0.0253834	+	0.0192892i
$991$		−	42.7827i		−	1.35904i	−0.733658	−	0.679519i	$-0.762189\pi$
$991$		−	42.7827i		−	1.35904i	0.733658	−	0.679519i	$-0.237811\pi$
$992$	2.36418	+	5.04090i	0.0750628	+	0.160049i
$993$	20.8127	+	7.01067i	0.660470	+	0.222477i
$994$	21.6987			0.688241
$995$	0.531430			0.0168475
$996$	−5.84013	+	17.3377i	−0.185052	+	0.549365i
$997$	16.0986			0.509849			0.254925	−	0.966961i	$-0.417949\pi$
$997$	16.0986			0.509849			0.254925	+	0.966961i	$0.417949\pi$
$998$	1.02600			0.0324773
$999$	−31.7718	−	46.8346i	−1.00521	−	1.48178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.h.d.371.5	yes	16
3.2	odd	2	inner	930.2.h.d.371.12	yes	16
31.30	odd	2	inner	930.2.h.d.371.4	✓	16
93.92	even	2	inner	930.2.h.d.371.13	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.h.d.371.4	✓	16	31.30	odd	2	inner
930.2.h.d.371.5	yes	16	1.1	even	1	trivial
930.2.h.d.371.12	yes	16	3.2	odd	2	inner
930.2.h.d.371.13	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.552909 - 1.64143i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.64143 - 0.552909i) q^{6} -2.30718 q^{7} +1.00000i q^{8} +(-2.38858 - 1.81512i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.552909 - 1.64143i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-1.64143 - 0.552909i) q^{6} -2.30718 q^{7} +1.00000i q^{8} +(-2.38858 - 1.81512i) q^{9} +1.00000 q^{10} -0.334369 q^{11} +(-0.552909 + 1.64143i) q^{12} +1.10582i q^{13} +2.30718i q^{14} +(1.64143 + 0.552909i) q^{15} +1.00000 q^{16} -5.02282 q^{17} +(-1.81512 + 2.38858i) q^{18} -5.08434 q^{19} -1.00000i q^{20} +(-1.27566 + 3.78707i) q^{21} +0.334369i q^{22} +3.61723 q^{23} +(1.64143 + 0.552909i) q^{24} -1.00000 q^{25} +1.10582 q^{26} +(-4.30007 + 2.91709i) q^{27} +2.30718 q^{28} +0.811361 q^{29} +(0.552909 - 1.64143i) q^{30} +(-5.04090 + 2.36418i) q^{31} -1.00000i q^{32} +(-0.184876 + 0.548844i) q^{33} +5.02282i q^{34} -2.30718i q^{35} +(2.38858 + 1.81512i) q^{36} +10.8916i q^{37} +5.08434i q^{38} +(1.81512 + 0.611418i) q^{39} -1.00000 q^{40} -0.369752i q^{41} +(3.78707 + 1.27566i) q^{42} +7.53423i q^{43} +0.334369 q^{44} +(1.81512 - 2.38858i) q^{45} -3.61723i q^{46} -11.3915i q^{47} +(0.552909 - 1.64143i) q^{48} -1.67693 q^{49} +1.00000i q^{50} +(-2.77716 + 8.24460i) q^{51} -1.10582i q^{52} -6.52581 q^{53} +(2.91709 + 4.30007i) q^{54} -0.334369i q^{55} -2.30718i q^{56} +(-2.81118 + 8.34559i) q^{57} -0.811361i q^{58} -3.26050i q^{59} +(-1.64143 - 0.552909i) q^{60} -6.09404i q^{61} +(2.36418 + 5.04090i) q^{62} +(5.51088 + 4.18781i) q^{63} -1.00000 q^{64} -1.10582 q^{65} +(0.548844 + 0.184876i) q^{66} -0.206944 q^{67} +5.02282 q^{68} +(2.00000 - 5.93743i) q^{69} -2.30718 q^{70} -9.40487i q^{71} +(1.81512 - 2.38858i) q^{72} -0.431766i q^{73} +10.8916 q^{74} +(-0.552909 + 1.64143i) q^{75} +5.08434 q^{76} +0.771450 q^{77} +(0.611418 - 1.81512i) q^{78} -8.05113i q^{79} +1.00000i q^{80} +(2.41065 + 8.67115i) q^{81} -0.369752 q^{82} +10.5625 q^{83} +(1.27566 - 3.78707i) q^{84} -5.02282i q^{85} +7.53423 q^{86} +(0.448609 - 1.33179i) q^{87} -0.334369i q^{88} +6.42841 q^{89} +(-2.38858 - 1.81512i) q^{90} -2.55132i q^{91} -3.61723 q^{92} +(1.09348 + 9.58146i) q^{93} -11.3915 q^{94} -5.08434i q^{95} +(-1.64143 - 0.552909i) q^{96} -9.39152 q^{97} +1.67693i q^{98} +(0.798669 + 0.606922i) 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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