LMFDB - Embedded newform 1380.2.p.b.91.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(91,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 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("1380.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.p (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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.19
Character	$\chi$	$=$	1380.91
Dual form			1380.2.p.b.91.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.651202 - 1.25536i) q^{2} +1.00000i q^{3} +(-1.15187 + 1.63499i) q^{4} -1.00000i q^{5} +(1.25536 - 0.651202i) q^{6} -2.14037 q^{7} +(2.80261 + 0.381312i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.651202 - 1.25536i) q^{2} +1.00000i q^{3} +(-1.15187 + 1.63499i) q^{4} -1.00000i q^{5} +(1.25536 - 0.651202i) q^{6} -2.14037 q^{7} +(2.80261 + 0.381312i) q^{8} -1.00000 q^{9} +(-1.25536 + 0.651202i) q^{10} +3.55021 q^{11} +(-1.63499 - 1.15187i) q^{12} -4.04464 q^{13} +(1.39382 + 2.68695i) q^{14} +1.00000 q^{15} +(-1.34638 - 3.76660i) q^{16} -0.843658i q^{17} +(0.651202 + 1.25536i) q^{18} +5.13553 q^{19} +(1.63499 + 1.15187i) q^{20} -2.14037i q^{21} +(-2.31190 - 4.45680i) q^{22} +(-2.71512 + 3.95324i) q^{23} +(-0.381312 + 2.80261i) q^{24} -1.00000 q^{25} +(2.63388 + 5.07749i) q^{26} -1.00000i q^{27} +(2.46544 - 3.49949i) q^{28} +0.275665 q^{29} +(-0.651202 - 1.25536i) q^{30} -8.41233i q^{31} +(-3.85169 + 4.14301i) q^{32} +3.55021i q^{33} +(-1.05910 + 0.549392i) q^{34} +2.14037i q^{35} +(1.15187 - 1.63499i) q^{36} +2.63854i q^{37} +(-3.34426 - 6.44695i) q^{38} -4.04464i q^{39} +(0.381312 - 2.80261i) q^{40} +7.36818 q^{41} +(-2.68695 + 1.39382i) q^{42} +11.6118 q^{43} +(-4.08939 + 5.80455i) q^{44} +1.00000i q^{45} +(6.73084 + 0.834108i) q^{46} -10.4234i q^{47} +(3.76660 - 1.34638i) q^{48} -2.41880 q^{49} +(0.651202 + 1.25536i) q^{50} +0.843658 q^{51} +(4.65891 - 6.61294i) q^{52} +5.60182i q^{53} +(-1.25536 + 0.651202i) q^{54} -3.55021i q^{55} +(-5.99863 - 0.816150i) q^{56} +5.13553i q^{57} +(-0.179514 - 0.346060i) q^{58} -2.95080i q^{59} +(-1.15187 + 1.63499i) q^{60} -7.05529i q^{61} +(-10.5605 + 5.47812i) q^{62} +2.14037 q^{63} +(7.70920 + 2.13733i) q^{64} +4.04464i q^{65} +(4.45680 - 2.31190i) q^{66} +2.62970 q^{67} +(1.37937 + 0.971787i) q^{68} +(-3.95324 - 2.71512i) q^{69} +(2.68695 - 1.39382i) q^{70} -2.73387i q^{71} +(-2.80261 - 0.381312i) q^{72} +4.84511 q^{73} +(3.31232 - 1.71822i) q^{74} -1.00000i q^{75} +(-5.91548 + 8.39653i) q^{76} -7.59878 q^{77} +(-5.07749 + 2.63388i) q^{78} +16.2338 q^{79} +(-3.76660 + 1.34638i) q^{80} +1.00000 q^{81} +(-4.79817 - 9.24974i) q^{82} +9.45106 q^{83} +(3.49949 + 2.46544i) q^{84} -0.843658 q^{85} +(-7.56161 - 14.5770i) q^{86} +0.275665i q^{87} +(9.94984 + 1.35374i) q^{88} -16.0179i q^{89} +(1.25536 - 0.651202i) q^{90} +8.65705 q^{91} +(-3.33603 - 8.99283i) q^{92} +8.41233 q^{93} +(-13.0851 + 6.78772i) q^{94} -5.13553i q^{95} +(-4.14301 - 3.85169i) q^{96} +0.845087i q^{97} +(1.57512 + 3.03647i) q^{98} -3.55021 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.651202	−	1.25536i	−0.460469	−	0.887676i
$2$	−0.651202	−	1.25536i	−0.460469	−	0.887676i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.15187	+	1.63499i	−0.575937	+	0.817494i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.25536	−	0.651202i	0.512500	−	0.265852i
$7$	−2.14037			−0.808986			−0.404493	−	0.914541i	$-0.632552\pi$
$7$	−2.14037			−0.808986			−0.404493	+	0.914541i	$0.632552\pi$
$8$	2.80261	+	0.381312i	0.990871	+	0.134814i
$9$	−1.00000			−0.333333
$10$	−1.25536	+	0.651202i	−0.396981	+	0.205928i
$11$	3.55021			1.07043			0.535214	−	0.844716i	$-0.320231\pi$
$11$	3.55021			1.07043			0.535214	+	0.844716i	$0.320231\pi$
$12$	−1.63499	−	1.15187i	−0.471981	−	0.332517i
$13$	−4.04464			−1.12178			−0.560891	−	0.827890i	$-0.689541\pi$
$13$	−4.04464			−1.12178			−0.560891	+	0.827890i	$0.689541\pi$
$14$	1.39382	+	2.68695i	0.372513	+	0.718117i
$15$	1.00000			0.258199
$16$	−1.34638	−	3.76660i	−0.336594	−	0.941650i
$17$		−	0.843658i		−	0.204617i	−0.994753	−	0.102309i	$-0.967377\pi$
$17$		−	0.843658i		−	0.204617i	0.994753	−	0.102309i	$-0.0326229\pi$
$18$	0.651202	+	1.25536i	0.153490	+	0.295892i
$19$	5.13553			1.17817			0.589085	−	0.808071i	$-0.299488\pi$
$19$	5.13553			1.17817			0.589085	+	0.808071i	$0.299488\pi$
$20$	1.63499	+	1.15187i	0.365595	+	0.257567i
$21$		−	2.14037i		−	0.467068i
$22$	−2.31190	−	4.45680i	−0.492899	−	0.950193i
$23$	−2.71512	+	3.95324i	−0.566142	+	0.824308i
$23$	−2.71512	+	3.95324i	−0.566142	+	0.824308i
$24$	−0.381312	+	2.80261i	−0.0778349	+	0.572080i
$25$	−1.00000			−0.200000
$26$	2.63388	+	5.07749i	0.516546	+	0.995778i
$27$		−	1.00000i		−	0.192450i
$28$	2.46544	−	3.49949i	0.465924	−	0.661341i
$29$	0.275665			0.0511898			0.0255949	−	0.999672i	$-0.491852\pi$
$29$	0.275665			0.0511898			0.0255949	+	0.999672i	$0.491852\pi$
$30$	−0.651202	−	1.25536i	−0.118893	−	0.229197i
$31$		−	8.41233i		−	1.51090i	−0.655207	−	0.755450i	$-0.727419\pi$
$31$		−	8.41233i		−	1.51090i	0.655207	−	0.755450i	$-0.272581\pi$
$32$	−3.85169	+	4.14301i	−0.680888	+	0.732387i
$33$			3.55021i			0.618012i
$34$	−1.05910	+	0.549392i	−0.181634	+	0.0942199i
$35$			2.14037i			0.361789i
$36$	1.15187	−	1.63499i	0.191979	−	0.272498i
$37$			2.63854i			0.433773i	0.976197	+	0.216886i	$0.0695901\pi$
$37$			2.63854i			0.433773i	−0.976197	+	0.216886i	$0.930410\pi$
$38$	−3.34426	−	6.44695i	−0.542511	−	1.04583i
$39$		−	4.04464i		−	0.647661i
$40$	0.381312	−	2.80261i	0.0602907	−	0.443131i
$41$	7.36818			1.15072			0.575358	−	0.817901i	$-0.304863\pi$
$41$	7.36818			1.15072			0.575358	+	0.817901i	$0.304863\pi$
$42$	−2.68695	+	1.39382i	−0.414605	+	0.215070i
$43$	11.6118			1.77078			0.885389	−	0.464850i	$-0.153892\pi$
$43$	11.6118			1.77078			0.885389	+	0.464850i	$0.153892\pi$
$44$	−4.08939	+	5.80455i	−0.616499	+	0.875069i
$45$			1.00000i			0.149071i
$46$	6.73084	+	0.834108i	0.992409	+	0.122983i
$47$		−	10.4234i		−	1.52040i	−0.649686	−	0.760202i	$-0.725100\pi$
$47$		−	10.4234i		−	1.52040i	0.649686	−	0.760202i	$-0.274900\pi$
$48$	3.76660	−	1.34638i	0.543662	−	0.194333i
$49$	−2.41880			−0.345542
$50$	0.651202	+	1.25536i	0.0920938	+	0.177535i
$51$	0.843658			0.118136
$52$	4.65891	−	6.61294i	0.646075	−	0.917050i
$53$			5.60182i			0.769470i	0.923027	+	0.384735i	$0.125707\pi$
$53$			5.60182i			0.769470i	−0.923027	+	0.384735i	$0.874293\pi$
$54$	−1.25536	+	0.651202i	−0.170833	+	0.0886173i
$55$		−	3.55021i		−	0.478710i
$56$	−5.99863	−	0.816150i	−0.801600	−	0.109063i
$57$			5.13553i			0.680217i
$58$	−0.179514	−	0.346060i	−0.0235713	−	0.0454399i
$59$		−	2.95080i		−	0.384162i	−0.981379	−	0.192081i	$-0.938476\pi$
$59$		−	2.95080i		−	0.384162i	0.981379	−	0.192081i	$-0.0615236\pi$
$60$	−1.15187	+	1.63499i	−0.148706	+	0.211076i
$61$		−	7.05529i		−	0.903338i	−0.892186	−	0.451669i	$-0.850829\pi$
$61$		−	7.05529i		−	0.903338i	0.892186	−	0.451669i	$-0.149171\pi$
$62$	−10.5605	+	5.47812i	−1.34119	+	0.695722i
$63$	2.14037			0.269662
$64$	7.70920	+	2.13733i	0.963650	+	0.267167i
$65$			4.04464i			0.501676i
$66$	4.45680	−	2.31190i	0.548594	−	0.284575i
$67$	2.62970			0.321269			0.160634	−	0.987014i	$-0.448646\pi$
$67$	2.62970			0.321269			0.160634	+	0.987014i	$0.448646\pi$
$68$	1.37937	+	0.971787i	0.167273	+	0.117847i
$69$	−3.95324	−	2.71512i	−0.475914	−	0.326862i
$70$	2.68695	−	1.39382i	0.321152	−	0.166593i
$71$		−	2.73387i		−	0.324450i	−0.986754	−	0.162225i	$-0.948133\pi$
$71$		−	2.73387i		−	0.324450i	0.986754	−	0.162225i	$-0.0518671\pi$
$72$	−2.80261	−	0.381312i	−0.330290	−	0.0449380i
$73$	4.84511			0.567077			0.283538	−	0.958961i	$-0.408492\pi$
$73$	4.84511			0.567077			0.283538	+	0.958961i	$0.408492\pi$
$74$	3.31232	−	1.71822i	0.385050	−	0.199739i
$75$		−	1.00000i		−	0.115470i
$76$	−5.91548	+	8.39653i	−0.678552	+	0.963148i
$77$	−7.59878			−0.865961
$78$	−5.07749	+	2.63388i	−0.574913	+	0.298228i
$79$	16.2338			1.82645			0.913223	−	0.407461i	$-0.133586\pi$
$79$	16.2338			1.82645			0.913223	+	0.407461i	$0.133586\pi$
$80$	−3.76660	+	1.34638i	−0.421119	+	0.150530i
$81$	1.00000			0.111111
$82$	−4.79817	−	9.24974i	−0.529869	−	1.02146i
$83$	9.45106			1.03739			0.518694	−	0.854960i	$-0.326418\pi$
$83$	9.45106			1.03739			0.518694	+	0.854960i	$0.326418\pi$
$84$	3.49949	+	2.46544i	0.381826	+	0.269002i
$85$	−0.843658			−0.0915076
$86$	−7.56161	−	14.5770i	−0.815389	−	1.57188i
$87$			0.275665i			0.0295544i
$88$	9.94984	+	1.35374i	1.06066	+	0.144309i
$89$		−	16.0179i		−	1.69789i	−0.528482	−	0.848945i	$-0.677238\pi$
$89$		−	16.0179i		−	1.69789i	0.528482	−	0.848945i	$-0.322762\pi$
$90$	1.25536	−	0.651202i	0.132327	−	0.0686427i
$91$	8.65705			0.907505
$92$	−3.33603	−	8.99283i	−0.347805	−	0.937567i
$93$	8.41233			0.872318
$94$	−13.0851	+	6.78772i	−1.34963	+	0.700099i
$95$		−	5.13553i		−	0.526894i
$96$	−4.14301	−	3.85169i	−0.422844	−	0.393111i
$97$			0.845087i			0.0858056i	0.999079	+	0.0429028i	$0.0136606\pi$
$97$			0.845087i			0.0858056i	−0.999079	+	0.0429028i	$0.986339\pi$
$98$	1.57512	+	3.03647i	0.159112	+	0.306730i
$99$	−3.55021			−0.356810
$100$	1.15187	−	1.63499i	0.115187	−	0.163499i
$101$	7.04680			0.701182			0.350591	−	0.936529i	$-0.385981\pi$
$101$	7.04680			0.701182			0.350591	+	0.936529i	$0.385981\pi$
$102$	−0.549392	−	1.05910i	−0.0543979	−	0.104866i
$103$	13.7768			1.35747			0.678736	−	0.734382i	$-0.262528\pi$
$103$	13.7768			1.35747			0.678736	+	0.734382i	$0.262528\pi$
$104$	−11.3355	−	1.54227i	−1.11154	−	0.151232i
$105$	−2.14037			−0.208879
$106$	7.03232	−	3.64792i	0.683040	−	0.354317i
$107$	−1.44719			−0.139905			−0.0699526	−	0.997550i	$-0.522285\pi$
$107$	−1.44719			−0.139905			−0.0699526	+	0.997550i	$0.522285\pi$
$108$	1.63499	+	1.15187i	0.157327	+	0.110839i
$109$		−	1.02911i		−	0.0985713i	−0.998785	−	0.0492856i	$-0.984306\pi$
$109$		−	1.02911i		−	0.0985713i	0.998785	−	0.0492856i	$-0.0156945\pi$
$110$	−4.45680	+	2.31190i	−0.424939	+	0.220431i
$111$	−2.63854			−0.250439
$112$	2.88175	+	8.06193i	0.272300	+	0.761781i
$113$		−	11.0913i		−	1.04338i	−0.853135	−	0.521689i	$-0.825302\pi$
$113$		−	11.0913i		−	1.04338i	0.853135	−	0.521689i	$-0.174698\pi$
$114$	6.44695	−	3.34426i	0.603812	−	0.313219i
$115$	3.95324	+	2.71512i	0.368642	+	0.253186i
$116$	−0.317532	+	0.450710i	−0.0294821	+	0.0418474i
$117$	4.04464			0.373927
$118$	−3.70433	+	1.92157i	−0.341011	+	0.176894i
$119$			1.80574i			0.165532i
$120$	2.80261	+	0.381312i	0.255842	+	0.0348088i
$121$	1.60399			0.145817
$122$	−8.85696	+	4.59442i	−0.801871	+	0.415959i
$123$			7.36818i			0.664367i
$124$	13.7541	+	9.68994i	1.23515	+	0.870182i
$125$			1.00000i			0.0894427i
$126$	−1.39382	−	2.68695i	−0.124171	−	0.239372i
$127$		−	20.3834i		−	1.80873i	−0.426758	−	0.904366i	$-0.640344\pi$
$127$		−	20.3834i		−	1.80873i	0.426758	−	0.904366i	$-0.359656\pi$
$128$	−2.33712	−	11.0697i	−0.206574	−	0.978431i
$129$			11.6118i			1.02236i
$130$	5.07749	−	2.63388i	0.445326	−	0.231006i
$131$			3.33061i			0.290997i	0.989358	+	0.145498i	$0.0464786\pi$
$131$			3.33061i			0.290997i	−0.989358	+	0.145498i	$0.953521\pi$
$132$	−5.80455	−	4.08939i	−0.505222	−	0.355936i
$133$	−10.9920			−0.953123
$134$	−1.71246	−	3.30123i	−0.147934	−	0.285183i
$135$	−1.00000			−0.0860663
$136$	0.321697	−	2.36444i	0.0275853	−	0.202749i
$137$			21.9555i			1.87579i	0.346924	+	0.937893i	$0.387226\pi$
$137$			21.9555i			1.87579i	−0.346924	+	0.937893i	$0.612774\pi$
$138$	−0.834108	+	6.73084i	−0.0710040	+	0.572968i
$139$		−	15.4357i		−	1.30924i	−0.755960	−	0.654618i	$-0.772830\pi$
$139$		−	15.4357i		−	1.30924i	0.755960	−	0.654618i	$-0.227170\pi$
$140$	−3.49949	−	2.46544i	−0.295761	−	0.208368i
$141$	10.4234			0.877806
$142$	−3.43200	+	1.78030i	−0.288007	+	0.149399i
$143$	−14.3593			−1.20079
$144$	1.34638	+	3.76660i	0.112198	+	0.313883i
$145$		−	0.275665i		−	0.0228928i
$146$	−3.15514	−	6.08237i	−0.261121	−	0.503380i
$147$		−	2.41880i		−	0.199499i
$148$	−4.31398	−	3.03926i	−0.354607	−	0.249826i
$149$		−	1.22216i		−	0.100123i	−0.998746	−	0.0500615i	$-0.984058\pi$
$149$		−	1.22216i		−	0.100123i	0.998746	−	0.0500615i	$-0.0159417\pi$
$150$	−1.25536	+	0.651202i	−0.102500	+	0.0531704i
$151$			9.64939i			0.785256i	0.919697	+	0.392628i	$0.128434\pi$
$151$			9.64939i			0.785256i	−0.919697	+	0.392628i	$0.871566\pi$
$152$	14.3929	+	1.95824i	1.16742	+	0.158834i
$153$			0.843658i			0.0682057i
$154$	4.94834	+	9.53923i	0.398748	+	0.768693i
$155$	−8.41233			−0.675695
$156$	6.61294	+	4.65891i	0.529459	+	0.373012i
$157$		−	15.1421i		−	1.20847i	−0.796807	−	0.604234i	$-0.793479\pi$
$157$		−	15.1421i		−	1.20847i	0.796807	−	0.604234i	$-0.206521\pi$
$158$	−10.5715	−	20.3793i	−0.841021	−	1.62129i
$159$	−5.60182			−0.444254
$160$	4.14301	+	3.85169i	0.327533	+	0.304503i
$161$	5.81138	−	8.46142i	0.458001	−	0.666853i
$162$	−0.651202	−	1.25536i	−0.0511632	−	0.0986306i
$163$		−	6.70557i		−	0.525221i	−0.964902	−	0.262610i	$-0.915417\pi$
$163$		−	6.70557i		−	0.525221i	0.964902	−	0.262610i	$-0.0845833\pi$
$164$	−8.48721	+	12.0469i	−0.662740	+	0.940705i
$165$	3.55021			0.276383
$166$	−6.15454	−	11.8645i	−0.477685	−	0.920865i
$167$			22.2534i			1.72202i	0.508589	+	0.861010i	$0.330167\pi$
$167$			22.2534i			1.72202i	−0.508589	+	0.861010i	$0.669833\pi$
$168$	0.816150	−	5.99863i	0.0629673	−	0.462804i
$169$	3.35912			0.258394
$170$	0.549392	+	1.05910i	0.0421364	+	0.0812291i
$171$	−5.13553			−0.392724
$172$	−13.3753	+	18.9851i	−1.01986	+	1.44760i
$173$	−20.8806			−1.58752			−0.793762	−	0.608228i	$-0.791881\pi$
$173$	−20.8806			−1.58752			−0.793762	+	0.608228i	$0.791881\pi$
$174$	0.346060	−	0.179514i	0.0262348	−	0.0136089i
$175$	2.14037			0.161797
$176$	−4.77992	−	13.3722i	−0.360300	−	1.00797i
$177$	2.95080			0.221796
$178$	−20.1082	+	10.4309i	−1.50718	+	0.781826i
$179$			11.9933i			0.896420i	0.893928	+	0.448210i	$0.147938\pi$
$179$			11.9933i			0.896420i	−0.893928	+	0.448210i	$0.852062\pi$
$180$	−1.63499	−	1.15187i	−0.121865	−	0.0858555i
$181$			11.8382i			0.879927i	0.898016	+	0.439964i	$0.145009\pi$
$181$			11.8382i			0.879927i	−0.898016	+	0.439964i	$0.854991\pi$
$182$	−5.63748	−	10.8677i	−0.417878	−	0.805570i
$183$	7.05529			0.521542
$184$	−9.11684	+	10.0441i	−0.672102	+	0.740459i
$185$	2.63854			0.193989
$186$	−5.47812	−	10.5605i	−0.401675	−	0.774336i
$187$		−	2.99516i		−	0.219028i
$188$	17.0421	+	12.0064i	1.24292	+	0.875657i
$189$			2.14037i			0.155689i
$190$	−6.44695	+	3.34426i	−0.467711	+	0.242618i
$191$	−1.29520			−0.0937173			−0.0468587	−	0.998902i	$-0.514921\pi$
$191$	−1.29520			−0.0937173			−0.0468587	+	0.998902i	$0.514921\pi$
$192$	−2.13733	+	7.70920i	−0.154249	+	0.556364i
$193$	−1.48140			−0.106634			−0.0533169	−	0.998578i	$-0.516979\pi$
$193$	−1.48140			−0.106634			−0.0533169	+	0.998578i	$0.516979\pi$
$194$	1.06089	−	0.550322i	0.0761675	−	0.0395108i
$195$	−4.04464			−0.289643
$196$	2.78615	−	3.95471i	0.199010	−	0.282479i
$197$	−13.9422			−0.993338			−0.496669	−	0.867940i	$-0.665444\pi$
$197$	−13.9422			−0.993338			−0.496669	+	0.867940i	$0.665444\pi$
$198$	2.31190	+	4.45680i	0.164300	+	0.316731i
$199$	−5.33970			−0.378521			−0.189261	−	0.981927i	$-0.560609\pi$
$199$	−5.33970			−0.378521			−0.189261	+	0.981927i	$0.560609\pi$
$200$	−2.80261	−	0.381312i	−0.198174	−	0.0269628i
$201$			2.62970i			0.185485i
$202$	−4.58889	−	8.84629i	−0.322873	−	0.622423i
$203$	−0.590027			−0.0414118
$204$	−0.971787	+	1.37937i	−0.0680387	+	0.0965753i
$205$		−	7.36818i		−	0.514616i
$206$	−8.97150	−	17.2949i	−0.625074	−	1.20500i
$207$	2.71512	−	3.95324i	0.188714	−	0.274769i
$208$	5.44561	+	15.2345i	0.377585	+	1.05633i
$209$	18.2322			1.26115
$210$	1.39382	+	2.68695i	0.0961824	+	0.185417i
$211$		−	2.76105i		−	0.190078i	−0.995474	−	0.0950392i	$-0.969702\pi$
$211$		−	2.76105i		−	0.190078i	0.995474	−	0.0950392i	$-0.0302976\pi$
$212$	−9.15892	−	6.45259i	−0.629037	−	0.443166i
$213$	2.73387			0.187321
$214$	0.942413	+	1.81675i	0.0644220	+	0.124190i
$215$		−	11.6118i		−	0.791916i
$216$	0.381312	−	2.80261i	0.0259450	−	0.190693i
$217$			18.0055i			1.22230i
$218$	−1.29191	+	0.670161i	−0.0874993	+	0.0453890i
$219$			4.84511i			0.327402i
$220$	5.80455	+	4.08939i	0.391343	+	0.275707i
$221$			3.41229i			0.229536i
$222$	1.71822	+	3.31232i	0.115319	+	0.222308i
$223$		−	7.40876i		−	0.496127i	−0.968744	−	0.248063i	$-0.920206\pi$
$223$		−	7.40876i		−	0.496127i	0.968744	−	0.248063i	$-0.0797942\pi$
$224$	8.24405	−	8.86759i	0.550829	−	0.592491i
$225$	1.00000			0.0666667
$226$	−13.9236	+	7.22265i	−0.926182	+	0.480444i
$227$	10.8648			0.721119			0.360560	−	0.932736i	$-0.382586\pi$
$227$	10.8648			0.721119			0.360560	+	0.932736i	$0.382586\pi$
$228$	−8.39653	−	5.91548i	−0.556074	−	0.391762i
$229$		−	12.6365i		−	0.835044i	−0.908667	−	0.417522i	$-0.862899\pi$
$229$		−	12.6365i		−	0.835044i	0.908667	−	0.417522i	$-0.137101\pi$
$230$	0.834108	−	6.73084i	0.0549995	−	0.443819i
$231$		−	7.59878i		−	0.499963i
$232$	0.772582	+	0.105114i	0.0507225	+	0.00690110i
$233$	2.14877			0.140771			0.0703854	−	0.997520i	$-0.477577\pi$
$233$	2.14877			0.140771			0.0703854	+	0.997520i	$0.477577\pi$
$234$	−2.63388	−	5.07749i	−0.172182	−	0.331926i
$235$	−10.4234			−0.679946
$236$	4.82453	+	3.39895i	0.314050	+	0.221253i
$237$			16.2338i			1.05450i
$238$	2.26687	−	1.17590i	0.146939	−	0.0762225i
$239$			15.5046i			1.00291i	0.865183	+	0.501456i	$0.167202\pi$
$239$			15.5046i			1.00291i	−0.865183	+	0.501456i	$0.832798\pi$
$240$	−1.34638	−	3.76660i	−0.0869083	−	0.243133i
$241$		−	12.5601i		−	0.809065i	−0.914524	−	0.404532i	$-0.867434\pi$
$241$		−	12.5601i		−	0.809065i	0.914524	−	0.404532i	$-0.132566\pi$
$242$	−1.04452	−	2.01359i	−0.0671443	−	0.129438i
$243$			1.00000i			0.0641500i
$244$	11.5353	+	8.12680i	0.738474	+	0.520265i
$245$			2.41880i			0.154531i
$246$	9.24974	−	4.79817i	0.589742	−	0.305920i
$247$	−20.7714			−1.32165
$248$	3.20772	−	23.5764i	0.203690	−	1.49711i
$249$			9.45106i			0.598937i
$250$	1.25536	−	0.651202i	0.0793961	−	0.0411856i
$251$	24.6936			1.55865			0.779323	−	0.626622i	$-0.215563\pi$
$251$	24.6936			1.55865			0.779323	+	0.626622i	$0.215563\pi$
$252$	−2.46544	+	3.49949i	−0.155308	+	0.220447i
$253$	−9.63925	+	14.0348i	−0.606015	+	0.882362i
$254$	−25.5885	+	13.2737i	−1.60557	+	0.832865i
$255$		−	0.843658i		−	0.0528319i
$256$	−12.3745	+	10.1425i	−0.773409	+	0.633908i
$257$	−29.0352			−1.81116			−0.905582	−	0.424171i	$-0.860566\pi$
$257$	−29.0352			−1.81116			−0.905582	+	0.424171i	$0.860566\pi$
$258$	14.5770	−	7.56161i	0.907524	−	0.470765i
$259$		−	5.64746i		−	0.350916i
$260$	−6.61294	−	4.65891i	−0.410117	−	0.288933i
$261$	−0.275665			−0.0170633
$262$	4.18113	−	2.16890i	0.258311	−	0.133995i
$263$	−25.0910			−1.54718			−0.773589	−	0.633688i	$-0.781540\pi$
$263$	−25.0910			−1.54718			−0.773589	+	0.633688i	$0.781540\pi$
$264$	−1.35374	+	9.94984i	−0.0833167	+	0.612370i
$265$	5.60182			0.344117
$266$	7.15798	+	13.7989i	0.438884	+	0.846064i
$267$	16.0179			0.980277
$268$	−3.02908	+	4.29953i	−0.185030	+	0.262636i
$269$	15.8583			0.966900			0.483450	−	0.875372i	$-0.339384\pi$
$269$	15.8583			0.966900			0.483450	+	0.875372i	$0.339384\pi$
$270$	0.651202	+	1.25536i	0.0396309	+	0.0763990i
$271$			19.2143i			1.16719i	0.812046	+	0.583594i	$0.198354\pi$
$271$			19.2143i			1.16719i	−0.812046	+	0.583594i	$0.801646\pi$
$272$	−3.17772	+	1.13588i	−0.192678	+	0.0688730i
$273$			8.65705i			0.523948i
$274$	27.5621	−	14.2975i	1.66509	−	0.863741i
$275$	−3.55021			−0.214086
$276$	8.99283	−	3.33603i	0.541305	−	0.200805i
$277$	2.32664			0.139794			0.0698972	−	0.997554i	$-0.477733\pi$
$277$	2.32664			0.139794			0.0698972	+	0.997554i	$0.477733\pi$
$278$	−19.3774	+	10.0517i	−1.16218	+	0.602862i
$279$			8.41233i			0.503633i
$280$	−0.816150	+	5.99863i	−0.0487743	+	0.358487i
$281$			2.44660i			0.145952i	0.997334	+	0.0729758i	$0.0232496\pi$
$281$			2.44660i			0.145952i	−0.997334	+	0.0729758i	$0.976750\pi$
$282$	−6.78772	−	13.0851i	−0.404203	−	0.779207i
$283$	−9.49613			−0.564486			−0.282243	−	0.959343i	$-0.591078\pi$
$283$	−9.49613			−0.564486			−0.282243	+	0.959343i	$0.591078\pi$
$284$	4.46984	+	3.14907i	0.265236	+	0.186863i
$285$	5.13553			0.304202
$286$	9.35081	+	18.0262i	0.552925	+	1.06591i
$287$	−15.7707			−0.930913
$288$	3.85169	−	4.14301i	0.226963	−	0.244129i
$289$	16.2882			0.958132
$290$	−0.346060	+	0.179514i	−0.0203214	+	0.0105414i
$291$	−0.845087			−0.0495399
$292$	−5.58095	+	7.92169i	−0.326600	+	0.463582i
$293$			16.0874i			0.939836i	0.882710	+	0.469918i	$0.155717\pi$
$293$			16.0874i			0.939836i	−0.882710	+	0.469918i	$0.844283\pi$
$294$	−3.03647	+	1.57512i	−0.177090	+	0.0918631i
$295$	−2.95080			−0.171802
$296$	−1.00610	+	7.39478i	−0.0584786	+	0.429813i
$297$		−	3.55021i		−	0.206004i
$298$	−1.53425	+	0.795871i	−0.0888768	+	0.0461036i
$299$	10.9817	−	15.9894i	0.635088	−	0.924693i
$300$	1.63499	+	1.15187i	0.0943961	+	0.0665034i
$301$	−24.8535			−1.43253
$302$	12.1135	−	6.28370i	0.697053	−	0.361586i
$303$			7.04680i			0.404828i
$304$	−6.91436	−	19.3435i	−0.396566	−	1.10942i
$305$	−7.05529			−0.403985
$306$	1.05910	−	0.549392i	0.0605446	−	0.0314066i
$307$			1.09550i			0.0625235i	0.999511	+	0.0312618i	$0.00995255\pi$
$307$			1.09550i			0.0625235i	−0.999511	+	0.0312618i	$0.990047\pi$
$308$	8.75283	−	12.4239i	0.498739	−	0.707918i
$309$			13.7768i			0.783737i
$310$	5.47812	+	10.5605i	0.311136	+	0.599798i
$311$			33.0428i			1.87368i	0.349754	+	0.936842i	$0.386265\pi$
$311$			33.0428i			1.87368i	−0.349754	+	0.936842i	$0.613735\pi$
$312$	1.54227	−	11.3355i	0.0873137	−	0.641748i
$313$			17.6117i			0.995472i	0.867329	+	0.497736i	$0.165835\pi$
$313$			17.6117i			0.995472i	−0.867329	+	0.497736i	$0.834165\pi$
$314$	−19.0088	+	9.86053i	−1.07273	+	0.556462i
$315$		−	2.14037i		−	0.120596i
$316$	−18.6993	+	26.5421i	−1.05192	+	1.49311i
$317$	11.9669			0.672130			0.336065	−	0.941839i	$-0.390904\pi$
$317$	11.9669			0.672130			0.336065	+	0.941839i	$0.390904\pi$
$318$	3.64792	+	7.03232i	0.204565	+	0.394353i
$319$	0.978670			0.0547950
$320$	2.13733	−	7.70920i	0.119481	−	0.430958i
$321$		−	1.44719i		−	0.0807743i
$322$	−14.4065	−	1.78530i	−0.802844	−	0.0994911i
$323$		−	4.33263i		−	0.241074i
$324$	−1.15187	+	1.63499i	−0.0639929	+	0.0908327i
$325$	4.04464			0.224356
$326$	−8.41792	+	4.36668i	−0.466226	+	0.241848i
$327$	1.02911			0.0569101
$328$	20.6501	+	2.80957i	1.14021	+	0.155133i
$329$			22.3099i			1.22999i
$330$	−2.31190	−	4.45680i	−0.127266	−	0.245339i
$331$			5.36132i			0.294685i	0.989086	+	0.147343i	$0.0470720\pi$
$331$			5.36132i			0.294685i	−0.989086	+	0.147343i	$0.952928\pi$
$332$	−10.8864	+	15.4524i	−0.597470	+	0.848059i
$333$		−	2.63854i		−	0.144591i
$334$	27.9361	−	14.4914i	1.52859	−	0.792937i
$335$		−	2.62970i		−	0.143676i
$336$	−8.06193	+	2.88175i	−0.439814	+	0.157212i
$337$		−	18.1283i		−	0.987513i	−0.869600	−	0.493756i	$-0.835623\pi$
$337$		−	18.1283i		−	0.987513i	0.869600	−	0.493756i	$-0.164377\pi$
$338$	−2.18746	−	4.21691i	−0.118982	−	0.229370i
$339$	11.0913			0.602395
$340$	0.971787	−	1.37937i	0.0527026	−	0.0748069i
$341$		−	29.8655i		−	1.61731i
$342$	3.34426	+	6.44695i	0.180837	+	0.348611i
$343$	20.1598			1.08852
$344$	32.5432	+	4.42770i	1.75461	+	0.238726i
$345$	−2.71512	+	3.95324i	−0.146177	+	0.212835i
$346$	13.5975	+	26.2128i	0.731006	+	1.40921i
$347$		−	6.76150i		−	0.362976i	−0.983393	−	0.181488i	$-0.941909\pi$
$347$		−	6.76150i		−	0.362976i	0.983393	−	0.181488i	$-0.0580914\pi$
$348$	−0.450710	−	0.317532i	−0.0241606	−	0.0170215i
$349$	35.9054			1.92197			0.960987	−	0.276593i	$-0.0892055\pi$
$349$	35.9054			1.92197			0.960987	+	0.276593i	$0.0892055\pi$
$350$	−1.39382	−	2.68695i	−0.0745026	−	0.143623i
$351$			4.04464i			0.215887i
$352$	−13.6743	+	14.7085i	−0.728842	+	0.783968i
$353$	19.5489			1.04048			0.520240	−	0.854020i	$-0.325842\pi$
$353$	19.5489			1.04048			0.520240	+	0.854020i	$0.325842\pi$
$354$	−1.92157	−	3.70433i	−0.102130	−	0.196883i
$355$	−2.73387			−0.145099
$356$	26.1890	+	18.4505i	1.38802	+	0.977877i
$357$	−1.80574			−0.0955701
$358$	15.0559	−	7.81004i	0.795730	−	0.412774i
$359$	−28.3999			−1.49889			−0.749446	−	0.662065i	$-0.769680\pi$
$359$	−28.3999			−1.49889			−0.749446	+	0.662065i	$0.769680\pi$
$360$	−0.381312	+	2.80261i	−0.0200969	+	0.147710i
$361$	7.37365			0.388087
$362$	14.8613	−	7.70906i	0.781090	−	0.405179i
$363$			1.60399i			0.0841876i
$364$	−9.97182	+	14.1542i	−0.522665	+	0.741880i
$365$		−	4.84511i		−	0.253604i
$366$	−4.59442	−	8.85696i	−0.240154	−	0.462961i
$367$	17.3687			0.906639			0.453319	−	0.891348i	$-0.350240\pi$
$367$	17.3687			0.906639			0.453319	+	0.891348i	$0.350240\pi$
$368$	18.5459	+	4.90422i	0.966769	+	0.255650i
$369$	−7.36818			−0.383572
$370$	−1.71822	−	3.31232i	−0.0893260	−	0.172199i
$371$		−	11.9900i		−	0.622490i
$372$	−9.68994	+	13.7541i	−0.502400	+	0.713115i
$373$		−	16.4101i		−	0.849683i	−0.905268	−	0.424841i	$-0.860330\pi$
$373$		−	16.4101i		−	0.849683i	0.905268	−	0.424841i	$-0.139670\pi$
$374$	−3.76002	+	1.95046i	−0.194426	+	0.100856i
$375$	−1.00000			−0.0516398
$376$	3.97455	−	29.2126i	0.204972	−	1.50652i
$377$	−1.11497			−0.0574237
$378$	2.68695	−	1.39382i	0.138202	−	0.0716901i
$379$	−19.6429			−1.00899			−0.504493	−	0.863416i	$-0.668321\pi$
$379$	−19.6429			−1.00899			−0.504493	+	0.863416i	$0.668321\pi$
$380$	8.39653	+	5.91548i	0.430733	+	0.303458i
$381$	20.3834			1.04427
$382$	0.843436	+	1.62594i	0.0431539	+	0.0831906i
$383$	18.4931			0.944955			0.472477	−	0.881343i	$-0.343360\pi$
$383$	18.4931			0.944955			0.472477	+	0.881343i	$0.343360\pi$
$384$	11.0697	−	2.33712i	0.564897	−	0.119266i
$385$			7.59878i			0.387270i
$386$	0.964692	+	1.85970i	0.0491015	+	0.0946562i
$387$	−11.6118			−0.590260
$388$	−1.38171	−	0.973433i	−0.0701456	−	0.0494186i
$389$		−	18.5928i		−	0.942690i	−0.881949	−	0.471345i	$-0.843769\pi$
$389$		−	18.5928i		−	0.942690i	0.881949	−	0.471345i	$-0.156231\pi$
$390$	2.63388	+	5.07749i	0.133372	+	0.257109i
$391$	3.33518	+	2.29064i	0.168668	+	0.115842i
$392$	−6.77893	−	0.922315i	−0.342388	−	0.0465839i
$393$	−3.33061			−0.168007
$394$	9.07916	+	17.5025i	0.457401	+	0.881762i
$395$		−	16.2338i		−	0.816811i
$396$	4.08939	−	5.80455i	0.205500	−	0.291690i
$397$	−17.8628			−0.896510			−0.448255	−	0.893906i	$-0.647954\pi$
$397$	−17.8628			−0.896510			−0.448255	+	0.893906i	$0.647954\pi$
$398$	3.47722	+	6.70326i	0.174297	+	0.336004i
$399$		−	10.9920i		−	0.550286i
$400$	1.34638	+	3.76660i	0.0673189	+	0.188330i
$401$			10.8994i			0.544288i	0.962257	+	0.272144i	$0.0877327\pi$
$401$			10.8994i			0.544288i	−0.962257	+	0.272144i	$0.912267\pi$
$402$	3.30123	−	1.71246i	0.164650	−	0.0854100i
$403$			34.0249i			1.69490i
$404$	−8.11701	+	11.5214i	−0.403837	+	0.573213i
$405$		−	1.00000i		−	0.0496904i
$406$	0.384227	+	0.740698i	0.0190688	+	0.0367602i
$407$			9.36736i			0.464323i
$408$	2.36444	+	0.321697i	0.117057	+	0.0159264i
$409$	9.59039			0.474214			0.237107	−	0.971483i	$-0.423801\pi$
$409$	9.59039			0.474214			0.237107	+	0.971483i	$0.423801\pi$
$410$	−9.24974	+	4.79817i	−0.456812	+	0.236965i
$411$	−21.9555			−1.08299
$412$	−15.8692	+	22.5250i	−0.781818	+	1.10973i
$413$			6.31582i			0.310781i
$414$	−6.73084	−	0.834108i	−0.330803	−	0.0409942i
$415$		−	9.45106i		−	0.463934i
$416$	15.5787	−	16.7570i	0.763808	−	0.821578i
$417$	15.4357			0.755887
$418$	−11.8728	−	22.8880i	−0.580719	−	1.11949i
$419$	−3.49424			−0.170705			−0.0853525	−	0.996351i	$-0.527202\pi$
$419$	−3.49424			−0.170705			−0.0853525	+	0.996351i	$0.527202\pi$
$420$	2.46544	−	3.49949i	0.120301	−	0.170758i
$421$			19.9196i			0.970823i	0.874286	+	0.485411i	$0.161330\pi$
$421$			19.9196i			0.970823i	−0.874286	+	0.485411i	$0.838670\pi$
$422$	−3.46612	+	1.79800i	−0.168728	+	0.0875252i
$423$			10.4234i			0.506802i
$424$	−2.13604	+	15.6997i	−0.103735	+	0.762445i
$425$			0.843658i			0.0409234i
$426$	−1.78030	−	3.43200i	−0.0862557	−	0.166281i
$427$			15.1010i			0.730787i
$428$	1.66698	−	2.36614i	0.0805765	−	0.114372i
$429$		−	14.3593i		−	0.693275i
$430$	−14.5770	+	7.56161i	−0.702965	+	0.364653i
$431$	1.01045			0.0486715			0.0243358	−	0.999704i	$-0.492253\pi$
$431$	1.01045			0.0486715			0.0243358	+	0.999704i	$0.492253\pi$
$432$	−3.76660	+	1.34638i	−0.181221	+	0.0647776i
$433$		−	24.4879i		−	1.17682i	−0.808564	−	0.588408i	$-0.799755\pi$
$433$		−	24.4879i		−	1.17682i	0.808564	−	0.588408i	$-0.200245\pi$
$434$	22.6035	−	11.7252i	1.08500	−	0.562829i
$435$	0.275665			0.0132171
$436$	1.68259	+	1.18541i	0.0805815	+	0.0567708i
$437$	−13.9436	+	20.3020i	−0.667012	+	0.971175i
$438$	6.08237	−	3.15514i	0.290627	−	0.150758i
$439$		−	3.96239i		−	0.189115i	−0.995519	−	0.0945573i	$-0.969856\pi$
$439$		−	3.96239i		−	0.189115i	0.995519	−	0.0945573i	$-0.0301436\pi$
$440$	1.35374	−	9.94984i	0.0645368	−	0.474340i
$441$	2.41880			0.115181
$442$	4.28367	−	2.22209i	0.203753	−	0.105694i
$443$			3.21788i			0.152886i	0.997074	+	0.0764431i	$0.0243563\pi$
$443$			3.21788i			0.152886i	−0.997074	+	0.0764431i	$0.975644\pi$
$444$	3.03926	−	4.31398i	0.144237	−	0.204732i
$445$	−16.0179			−0.759319
$446$	−9.30068	+	4.82459i	−0.440400	+	0.228451i
$447$	1.22216			0.0578061
$448$	−16.5006	−	4.57469i	−0.779579	−	0.216134i
$449$	3.13859			0.148119			0.0740596	−	0.997254i	$-0.476404\pi$
$449$	3.13859			0.148119			0.0740596	+	0.997254i	$0.476404\pi$
$450$	−0.651202	−	1.25536i	−0.0306979	−	0.0591784i
$451$	26.1586			1.23176
$452$	18.1341	+	12.7757i	0.852956	+	0.600920i
$453$	−9.64939			−0.453368
$454$	−7.07515	−	13.6392i	−0.332053	−	0.640120i
$455$		−	8.65705i		−	0.405849i
$456$	−1.95824	+	14.3929i	−0.0917028	+	0.674008i
$457$			4.45089i			0.208204i	0.994567	+	0.104102i	$0.0331968\pi$
$457$			4.45089i			0.208204i	−0.994567	+	0.104102i	$0.966803\pi$
$458$	−15.8634	+	8.22892i	−0.741248	+	0.384512i
$459$	−0.843658			−0.0393786
$460$	−8.99283	+	3.33603i	−0.419293	+	0.155543i
$461$	18.0299			0.839738			0.419869	−	0.907585i	$-0.362076\pi$
$461$	18.0299			0.839738			0.419869	+	0.907585i	$0.362076\pi$
$462$	−9.53923	+	4.94834i	−0.443805	+	0.230217i
$463$			34.3361i			1.59573i	0.602835	+	0.797866i	$0.294038\pi$
$463$			34.3361i			1.59573i	−0.602835	+	0.797866i	$0.705962\pi$
$464$	−0.371150	−	1.03832i	−0.0172302	−	0.0482028i
$465$		−	8.41233i		−	0.390112i
$466$	−1.39929	−	2.69749i	−0.0648206	−	0.124959i
$467$	−36.9009			−1.70757			−0.853786	−	0.520624i	$-0.825699\pi$
$467$	−36.9009			−1.70757			−0.853786	+	0.520624i	$0.825699\pi$
$468$	−4.65891	+	6.61294i	−0.215358	+	0.305683i
$469$	−5.62854			−0.259902
$470$	6.78772	+	13.0851i	0.313094	+	0.603571i
$471$	15.1421			0.697709
$472$	1.12517	−	8.26993i	0.0517903	−	0.380654i
$473$	41.2242			1.89549
$474$	20.3793	−	10.5715i	0.936053	−	0.485564i
$475$	−5.13553			−0.235634
$476$	−2.95237	−	2.07999i	−0.135322	−	0.0953361i
$477$		−	5.60182i		−	0.256490i
$478$	19.4639	−	10.0966i	0.890260	−	0.461810i
$479$	−36.3522			−1.66098			−0.830488	−	0.557037i	$-0.811938\pi$
$479$	−36.3522			−1.66098			−0.830488	+	0.557037i	$0.811938\pi$
$480$	−3.85169	+	4.14301i	−0.175805	+	0.189102i
$481$		−	10.6719i		−	0.486598i
$482$	−15.7674	+	8.17913i	−0.718187	+	0.372549i
$483$	8.46142	+	5.81138i	0.385008	+	0.264427i
$484$	−1.84759	+	2.62250i	−0.0839814	+	0.119205i
$485$	0.845087			0.0383734
$486$	1.25536	−	0.651202i	0.0569444	−	0.0295391i
$487$			4.53486i			0.205494i	0.994708	+	0.102747i	$0.0327632\pi$
$487$			4.53486i			0.205494i	−0.994708	+	0.102747i	$0.967237\pi$
$488$	2.69027	−	19.7732i	0.121783	−	0.895091i
$489$	6.70557			0.303236
$490$	3.03647	−	1.57512i	0.137174	−	0.0711569i
$491$			13.4429i			0.606670i	0.952884	+	0.303335i	$0.0981001\pi$
$491$			13.4429i			0.606670i	−0.952884	+	0.303335i	$0.901900\pi$
$492$	−12.0469	−	8.48721i	−0.543116	−	0.382633i
$493$		−	0.232567i		−	0.0104743i
$494$	13.5263	+	26.0756i	0.608579	+	1.17320i
$495$			3.55021i			0.159570i
$496$	−31.6859	+	11.3262i	−1.42274	+	0.508560i
$497$			5.85150i			0.262476i
$498$	11.8645	−	6.15454i	0.531661	−	0.275792i
$499$		−	25.2907i		−	1.13217i	−0.824347	−	0.566084i	$-0.808458\pi$
$499$		−	25.2907i		−	1.13217i	0.824347	−	0.566084i	$-0.191542\pi$
$500$	−1.63499	−	1.15187i	−0.0731189	−	0.0515133i
$501$	−22.2534			−0.994208
$502$	−16.0805	−	30.9994i	−0.717708	−	1.38357i
$503$	37.8035			1.68557			0.842787	−	0.538247i	$-0.180913\pi$
$503$	37.8035			1.68557			0.842787	+	0.538247i	$0.180913\pi$
$504$	5.99863	+	0.816150i	0.267200	+	0.0363542i
$505$		−	7.04680i		−	0.313578i
$506$	23.8959	+	2.96126i	1.06230	+	0.131644i
$507$			3.35912i			0.149184i
$508$	33.3266	+	23.4791i	1.47863	+	1.04171i
$509$	−10.9894			−0.487096			−0.243548	−	0.969889i	$-0.578311\pi$
$509$	−10.9894			−0.487096			−0.243548	+	0.969889i	$0.578311\pi$
$510$	−1.05910	+	0.549392i	−0.0468976	+	0.0243275i
$511$	−10.3703			−0.458757
$512$	20.7909	+	8.92971i	0.918835	+	0.394641i
$513$		−	5.13553i		−	0.226739i
$514$	18.9078	+	36.4497i	0.833985	+	1.60773i
$515$		−	13.7768i		−	0.607080i
$516$	−18.9851	−	13.3753i	−0.835773	−	0.588814i
$517$		−	37.0052i		−	1.62748i
$518$	−7.08961	+	3.67763i	−0.311500	+	0.161586i
$519$		−	20.8806i		−	0.916558i
$520$	−1.54227	+	11.3355i	−0.0676329	+	0.497096i
$521$			28.5407i			1.25039i	0.780469	+	0.625195i	$0.214981\pi$
$521$			28.5407i			1.25039i	−0.780469	+	0.625195i	$0.785019\pi$
$522$	0.179514	+	0.346060i	0.00785710	+	0.0151466i
$523$	−14.6277			−0.639625			−0.319813	−	0.947481i	$-0.603620\pi$
$523$	−14.6277			−0.639625			−0.319813	+	0.947481i	$0.603620\pi$
$524$	−5.44551	−	3.83644i	−0.237888	−	0.167596i
$525$			2.14037i			0.0934136i
$526$	16.3393	+	31.4983i	0.712427	+	1.37339i
$527$	−7.09713			−0.309156
$528$	13.3722	−	4.77992i	0.581951	−	0.208019i
$529$	−8.25622	−	21.4671i	−0.358966	−	0.933351i
$530$	−3.64792	−	7.03232i	−0.158455	−	0.305465i
$531$			2.95080i			0.128054i
$532$	12.6613	−	17.9717i	0.548938	−	0.779173i
$533$	−29.8017			−1.29085
$534$	−10.4309	−	20.1082i	−0.451387	−	0.870168i
$535$			1.44719i			0.0625675i
$536$	7.37001	+	1.00273i	0.318336	+	0.0433115i
$537$	−11.9933			−0.517548
$538$	−10.3270	−	19.9080i	−0.445227	−	0.858294i
$539$	−8.58724			−0.369878
$540$	1.15187	−	1.63499i	0.0495687	−	0.0703587i
$541$	−41.9847			−1.80506			−0.902532	−	0.430623i	$-0.858294\pi$
$541$	−41.9847			−1.80506			−0.902532	+	0.430623i	$0.858294\pi$
$542$	24.1210	−	12.5124i	1.03608	−	0.537453i
$543$	−11.8382			−0.508026
$544$	3.49528	+	3.24951i	0.149859	+	0.139321i
$545$	−1.02911			−0.0440824
$546$	10.8677	−	5.63748i	0.465096	−	0.241262i
$547$		−	33.7583i		−	1.44340i	−0.692206	−	0.721700i	$-0.743361\pi$
$547$		−	33.7583i		−	1.44340i	0.692206	−	0.721700i	$-0.256639\pi$
$548$	−35.8970	−	25.2900i	−1.53344	−	1.08033i
$549$			7.05529i			0.301113i
$550$	2.31190	+	4.45680i	0.0985798	+	0.190039i
$551$	1.41569			0.0603103
$552$	−10.0441	−	9.11684i	−0.427504	−	0.388038i
$553$	−34.7464			−1.47757
$554$	−1.51511	−	2.92078i	−0.0643710	−	0.124092i
$555$			2.63854i			0.112000i
$556$	25.2371	+	17.7799i	1.07029	+	0.754037i
$557$		−	16.9360i		−	0.717602i	−0.933414	−	0.358801i	$-0.883186\pi$
$557$		−	16.9360i		−	0.717602i	0.933414	−	0.358801i	$-0.116814\pi$
$558$	10.5605	−	5.47812i	0.447063	−	0.231907i
$559$	−46.9655			−1.98643
$560$	8.06193	−	2.88175i	0.340679	−	0.121776i
$561$	2.99516			0.126456
$562$	3.07137	−	1.59323i	0.129558	−	0.0672062i
$563$	−1.63299			−0.0688224			−0.0344112	−	0.999408i	$-0.510956\pi$
$563$	−1.63299			−0.0688224			−0.0344112	+	0.999408i	$0.510956\pi$
$564$	−12.0064	+	17.0421i	−0.505561	+	0.717602i
$565$	−11.0913			−0.466613
$566$	6.18389	+	11.9211i	0.259928	+	0.501081i
$567$	−2.14037			−0.0898873
$568$	1.04246	−	7.66195i	0.0437404	−	0.321488i
$569$		−	13.7080i		−	0.574669i	−0.957830	−	0.287334i	$-0.907231\pi$
$569$		−	13.7080i		−	0.574669i	0.957830	−	0.287334i	$-0.0927691\pi$
$570$	−3.34426	−	6.44695i	−0.140076	−	0.270033i
$571$	−47.0402			−1.96857			−0.984285	−	0.176585i	$-0.943495\pi$
$571$	−47.0402			−1.96857			−0.984285	+	0.176585i	$0.943495\pi$
$572$	16.5401	−	23.4773i	0.691577	−	0.981637i
$573$		−	1.29520i		−	0.0541077i
$574$	10.2699	+	19.7979i	0.428657	+	0.826349i
$575$	2.71512	−	3.95324i	0.113228	−	0.164862i
$576$	−7.70920	−	2.13733i	−0.321217	−	0.0890555i
$577$	−3.09943			−0.129031			−0.0645154	−	0.997917i	$-0.520550\pi$
$577$	−3.09943			−0.129031			−0.0645154	+	0.997917i	$0.520550\pi$
$578$	−10.6069	−	20.4477i	−0.441190	−	0.850510i
$579$		−	1.48140i		−	0.0615650i
$580$	0.450710	+	0.317532i	0.0187147	+	0.0131848i
$581$	−20.2288			−0.839232
$582$	0.550322	+	1.06089i	0.0228116	+	0.0439753i
$583$			19.8877i			0.823662i
$584$	13.5789	+	1.84749i	0.561900	+	0.0764499i
$585$		−	4.04464i		−	0.167225i
$586$	20.1955	−	10.4761i	0.834270	−	0.432766i
$587$		−	21.9788i		−	0.907160i	−0.891215	−	0.453580i	$-0.850147\pi$
$587$		−	21.9788i		−	0.907160i	0.891215	−	0.453580i	$-0.149853\pi$
$588$	3.95471	+	2.78615i	0.163089	+	0.114899i
$589$		−	43.2018i		−	1.78010i
$590$	1.92157	+	3.70433i	0.0791096	+	0.152505i
$591$		−	13.9422i		−	0.573504i
$592$	9.93831	−	3.55247i	0.408462	−	0.146005i
$593$	−31.2493			−1.28326			−0.641628	−	0.767016i	$-0.721741\pi$
$593$	−31.2493			−1.28326			−0.641628	+	0.767016i	$0.721741\pi$
$594$	−4.45680	+	2.31190i	−0.182865	+	0.0948585i
$595$	1.80574			0.0740283
$596$	1.99821	+	1.40777i	0.0818500	+	0.0576645i
$597$		−	5.33970i		−	0.218539i
$598$	−27.2238	−	3.37367i	−1.11327	−	0.137960i
$599$			19.4722i			0.795614i	0.917469	+	0.397807i	$0.130229\pi$
$599$			19.4722i			0.795614i	−0.917469	+	0.397807i	$0.869771\pi$
$600$	0.381312	−	2.80261i	0.0155670	−	0.114416i
$601$	−27.7862			−1.13342			−0.566711	−	0.823917i	$-0.691784\pi$
$601$	−27.7862			−1.13342			−0.566711	+	0.823917i	$0.691784\pi$
$602$	16.1847	+	31.2002i	0.659638	+	1.27163i
$603$	−2.62970			−0.107090
$604$	−15.7766	−	11.1149i	−0.641943	−	0.452258i
$605$		−	1.60399i		−	0.0652114i
$606$	8.84629	−	4.58889i	0.359356	−	0.186411i
$607$		−	28.1233i		−	1.14149i	−0.821127	−	0.570745i	$-0.806654\pi$
$607$		−	28.1233i		−	1.14149i	0.821127	−	0.570745i	$-0.193346\pi$
$608$	−19.7804	+	21.2765i	−0.802203	+	0.862877i
$609$		−	0.590027i		−	0.0239091i
$610$	4.59442	+	8.85696i	0.186023	+	0.358608i
$611$			42.1588i			1.70556i
$612$	−1.37937	−	0.971787i	−0.0557578	−	0.0392822i
$613$		−	23.6788i		−	0.956378i	−0.878257	−	0.478189i	$-0.841293\pi$
$613$		−	23.6788i		−	0.956378i	0.878257	−	0.478189i	$-0.158707\pi$
$614$	1.37525	−	0.713391i	0.0555006	−	0.0287901i
$615$	7.36818			0.297114
$616$	−21.2964	−	2.89750i	−0.858056	−	0.116744i
$617$			0.878056i			0.0353492i	0.999844	+	0.0176746i	$0.00562629\pi$
$617$			0.878056i			0.0353492i	−0.999844	+	0.0176746i	$0.994374\pi$
$618$	17.2949	−	8.97150i	0.695705	−	0.360887i
$619$	4.28788			0.172344			0.0861722	−	0.996280i	$-0.472536\pi$
$619$	4.28788			0.172344			0.0861722	+	0.996280i	$0.472536\pi$
$620$	9.68994	−	13.7541i	0.389157	−	0.552377i
$621$	3.95324	+	2.71512i	0.158638	+	0.108954i
$622$	41.4807	−	21.5175i	1.66322	−	0.862773i
$623$			34.2842i			1.37357i
$624$	−15.2345	+	5.44561i	−0.609870	+	0.217999i
$625$	1.00000			0.0400000
$626$	22.1091	−	11.4688i	0.883656	−	0.458384i
$627$			18.2322i			0.728124i
$628$	24.7571	+	17.4417i	0.987916	+	0.696001i
$629$	2.22602			0.0887574
$630$	−2.68695	+	1.39382i	−0.107051	+	0.0555309i
$631$	39.9346			1.58977			0.794886	−	0.606759i	$-0.207531\pi$
$631$	39.9346			1.58977			0.794886	+	0.606759i	$0.207531\pi$
$632$	45.4969	+	6.19014i	1.80977	+	0.246230i
$633$	2.76105			0.109742
$634$	−7.79289	−	15.0228i	−0.309495	−	0.596633i
$635$	−20.3834			−0.808890
$636$	6.45259	−	9.15892i	0.255862	−	0.363175i
$637$	9.78316			0.387623
$638$	−0.637311	−	1.22859i	−0.0252314	−	0.0486402i
$639$			2.73387i			0.108150i
$640$	−11.0697	+	2.33712i	−0.437568	+	0.0923827i
$641$			20.1012i			0.793951i	0.917829	+	0.396976i	$0.129940\pi$
$641$			20.1012i			0.793951i	−0.917829	+	0.396976i	$0.870060\pi$
$642$	−1.81675	+	0.942413i	−0.0717014	+	0.0371941i
$643$	16.2281			0.639976			0.319988	−	0.947422i	$-0.396321\pi$
$643$	16.2281			0.639976			0.319988	+	0.947422i	$0.396321\pi$
$644$	7.14035	+	19.2480i	0.281369	+	0.758478i
$645$	11.6118			0.457213
$646$	−5.43902	+	2.82142i	−0.213996	+	0.111007i
$647$		−	14.3994i		−	0.566100i	−0.959105	−	0.283050i	$-0.908654\pi$
$647$		−	14.3994i		−	0.566100i	0.959105	−	0.283050i	$-0.0913462\pi$
$648$	2.80261	+	0.381312i	0.110097	+	0.0149793i
$649$		−	10.4760i		−	0.411217i
$650$	−2.63388	−	5.07749i	−0.103309	−	0.199156i
$651$	−18.0055			−0.705693
$652$	10.9635	+	7.72396i	0.429365	+	0.302494i
$653$	−8.13213			−0.318235			−0.159118	−	0.987260i	$-0.550865\pi$
$653$	−8.13213			−0.318235			−0.159118	+	0.987260i	$0.550865\pi$
$654$	−0.670161	−	1.29191i	−0.0262054	−	0.0505178i
$655$	3.33061			0.130138
$656$	−9.92035	−	27.7530i	−0.387325	−	1.08357i
$657$	−4.84511			−0.189026
$658$	28.0070	−	14.5283i	1.09183	−	0.566370i
$659$	50.0704			1.95046			0.975232	−	0.221183i	$-0.0709919\pi$
$659$	50.0704			1.95046			0.975232	+	0.221183i	$0.0709919\pi$
$660$	−4.08939	+	5.80455i	−0.159179	+	0.225942i
$661$			34.2686i			1.33290i	0.745552	+	0.666448i	$0.232186\pi$
$661$			34.2686i			1.33290i	−0.745552	+	0.666448i	$0.767814\pi$
$662$	6.73041	−	3.49130i	0.261585	−	0.135693i
$663$	−3.41229			−0.132523
$664$	26.4876	+	3.60380i	1.02792	+	0.139854i
$665$			10.9920i			0.426250i
$666$	−3.31232	+	1.71822i	−0.128350	+	0.0665796i
$667$	−0.748465	+	1.08977i	−0.0289807	+	0.0421961i
$668$	−36.3841	−	25.6331i	−1.40774	−	0.991774i
$669$	7.40876			0.286439
$670$	−3.30123	+	1.71246i	−0.127538	+	0.0661583i
$671$		−	25.0478i		−	0.966959i
$672$	8.86759	+	8.24405i	0.342075	+	0.318021i
$673$	−15.3372			−0.591205			−0.295602	−	0.955311i	$-0.595520\pi$
$673$	−15.3372			−0.591205			−0.295602	+	0.955311i	$0.595520\pi$
$674$	−22.7576	+	11.8052i	−0.876591	+	0.454719i
$675$			1.00000i			0.0384900i
$676$	−3.86928	+	5.49212i	−0.148818	+	0.211236i
$677$		−	22.2137i		−	0.853742i	−0.904312	−	0.426871i	$-0.859616\pi$
$677$		−	22.2137i		−	0.853742i	0.904312	−	0.426871i	$-0.140384\pi$
$678$	−7.22265	−	13.9236i	−0.277384	−	0.534731i
$679$		−	1.80880i		−	0.0694155i
$680$	−2.36444	−	0.321697i	−0.0906722	−	0.0123365i
$681$			10.8648i			0.416338i
$682$	−37.4921	+	19.4485i	−1.43565	+	0.744721i
$683$			5.94111i			0.227330i	0.993519	+	0.113665i	$0.0362591\pi$
$683$			5.94111i			0.227330i	−0.993519	+	0.113665i	$0.963741\pi$
$684$	5.91548	−	8.39653i	0.226184	−	0.321049i
$685$	21.9555			0.838877
$686$	−13.1281	−	25.3078i	−0.501232	−	0.966257i
$687$	12.6365			0.482113
$688$	−15.6338	−	43.7369i	−0.596034	−	1.66745i
$689$		−	22.6574i		−	0.863177i
$690$	6.73084	+	0.834108i	0.256239	+	0.0317539i
$691$		−	0.937628i		−	0.0356690i	−0.999841	−	0.0178345i	$-0.994323\pi$
$691$		−	0.937628i		−	0.0356690i	0.999841	−	0.0178345i	$-0.00567721\pi$
$692$	24.0518	−	34.1396i	0.914313	−	1.29779i
$693$	7.59878			0.288654
$694$	−8.48814	+	4.40310i	−0.322205	+	0.167139i
$695$	−15.4357			−0.585508
$696$	−0.105114	+	0.772582i	−0.00398435	+	0.0292846i
$697$		−	6.21623i		−	0.235456i
$698$	−23.3817	−	45.0744i	−0.885010	−	1.70609i
$699$			2.14877i			0.0812741i
$700$	−2.46544	+	3.49949i	−0.0931849	+	0.132268i
$701$		−	36.2643i		−	1.36968i	−0.728692	−	0.684842i	$-0.759871\pi$
$701$		−	36.2643i		−	1.36968i	0.728692	−	0.684842i	$-0.240129\pi$
$702$	5.07749	−	2.63388i	0.191638	−	0.0994093i
$703$			13.5503i			0.511058i
$704$	27.3693	+	7.58798i	1.03152	+	0.285983i
$705$		−	10.4234i		−	0.392567i
$706$	−12.7302	−	24.5409i	−0.479109	−	0.923610i
$707$	−15.0828			−0.567246
$708$	−3.39895	+	4.82453i	−0.127740	+	0.181317i
$709$		−	45.9613i		−	1.72611i	−0.505107	−	0.863057i	$-0.668547\pi$
$709$		−	45.9613i		−	1.72611i	0.505107	−	0.863057i	$-0.331453\pi$
$710$	1.78030	+	3.43200i	0.0668134	+	0.128801i
$711$	−16.2338			−0.608815
$712$	6.10779	−	44.8917i	0.228899	−	1.68239i
$713$	33.2560	+	22.8405i	1.24545	+	0.855384i
$714$	1.17590	+	2.26687i	0.0440071	+	0.0848353i
$715$			14.3593i			0.537008i
$716$	−19.6089	−	13.8147i	−0.732818	−	0.516281i
$717$	−15.5046			−0.579031
$718$	18.4941	+	35.6522i	0.690193	+	1.33053i
$719$		−	26.7657i		−	0.998193i	−0.866546	−	0.499097i	$-0.833665\pi$
$719$		−	26.7657i		−	0.998193i	0.866546	−	0.499097i	$-0.166335\pi$
$720$	3.76660	−	1.34638i	0.140373	−	0.0501765i
$721$	−29.4876			−1.09818
$722$	−4.80173	−	9.25660i	−0.178702	−	0.344495i
$723$	12.5601			0.467114
$724$	−19.3553	−	13.6361i	−0.719336	−	0.506782i
$725$	−0.275665			−0.0102380
$726$	2.01359	−	1.04452i	0.0747313	−	0.0387658i
$727$	11.7279			0.434963			0.217482	−	0.976064i	$-0.430216\pi$
$727$	11.7279			0.434963			0.217482	+	0.976064i	$0.430216\pi$
$728$	24.2623	+	3.30103i	0.899220	+	0.122344i
$729$	−1.00000			−0.0370370
$730$	−6.08237	+	3.15514i	−0.225118	+	0.116777i
$731$		−	9.79637i		−	0.362332i
$732$	−8.12680	+	11.5353i	−0.300375	+	0.426358i
$733$			10.5869i			0.391036i	0.980700	+	0.195518i	$0.0626389\pi$
$733$			10.5869i			0.391036i	−0.980700	+	0.195518i	$0.937361\pi$
$734$	−11.3105	−	21.8040i	−0.417479	−	0.804801i
$735$	−2.41880			−0.0892187
$736$	−5.92050	−	26.4754i	−0.218233	−	0.975897i
$737$	9.33598			0.343895
$738$	4.79817	+	9.24974i	0.176623	+	0.340488i
$739$			0.174301i			0.00641178i	0.999995	+	0.00320589i	$0.00102047\pi$
$739$			0.174301i			0.00641178i	−0.999995	+	0.00320589i	$0.998980\pi$
$740$	−3.03926	+	4.31398i	−0.111725	+	0.158585i
$741$		−	20.7714i		−	0.763055i
$742$	−15.0518	+	7.80791i	−0.552569	+	0.286637i
$743$	−14.7068			−0.539540			−0.269770	−	0.962925i	$-0.586948\pi$
$743$	−14.7068			−0.539540			−0.269770	+	0.962925i	$0.586948\pi$
$744$	23.5764	+	3.20772i	0.864355	+	0.117601i
$745$	−1.22216			−0.0447764
$746$	−20.6006	+	10.6863i	−0.754243	+	0.391253i
$747$	−9.45106			−0.345796
$748$	4.89706	+	3.45005i	0.179054	+	0.126146i
$749$	3.09753			0.113181
$750$	0.651202	+	1.25536i	0.0237785	+	0.0458394i
$751$	26.8301			0.979043			0.489522	−	0.871991i	$-0.337171\pi$
$751$	26.8301			0.979043			0.489522	+	0.871991i	$0.337171\pi$
$752$	−39.2607	+	14.0338i	−1.43169	+	0.511760i
$753$			24.6936i			0.899885i
$754$	0.726069	+	1.39969i	0.0264419	+	0.0509737i
$755$	9.64939			0.351177
$756$	−3.49949	−	2.46544i	−0.127275	−	0.0896672i
$757$		−	54.6358i		−	1.98577i	−0.119070	−	0.992886i	$-0.537991\pi$
$757$		−	54.6358i		−	1.98577i	0.119070	−	0.992886i	$-0.462009\pi$
$758$	12.7915	+	24.6589i	0.464607	+	0.895653i
$759$	−14.0348	−	9.63925i	−0.509432	−	0.349883i
$760$	1.95824	−	14.3929i	0.0710327	−	0.522084i
$761$	31.9653			1.15874			0.579370	−	0.815064i	$-0.303299\pi$
$761$	31.9653			1.15874			0.579370	+	0.815064i	$0.303299\pi$
$762$	−13.2737	−	25.5885i	−0.480855	−	0.926975i
$763$			2.20269i			0.0797427i
$764$	1.49190	−	2.11764i	0.0539752	−	0.0766134i
$765$	0.843658			0.0305025
$766$	−12.0428	−	23.2156i	−0.435122	−	0.838813i
$767$			11.9349i			0.430945i
$768$	−10.1425	−	12.3745i	−0.365987	−	0.446528i
$769$		−	4.34029i		−	0.156515i	−0.996933	−	0.0782574i	$-0.975064\pi$
$769$		−	4.34029i		−	0.156515i	0.996933	−	0.0782574i	$-0.0249356\pi$
$770$	9.53923	−	4.94834i	0.343770	−	0.178326i
$771$		−	29.0352i		−	1.04568i
$772$	1.70639	−	2.42208i	0.0614142	−	0.0871725i
$773$			0.809691i			0.0291226i	0.999894	+	0.0145613i	$0.00463516\pi$
$773$			0.809691i			0.0291226i	−0.999894	+	0.0145613i	$0.995365\pi$
$774$	7.56161	+	14.5770i	0.271796	+	0.523959i
$775$			8.41233i			0.302180i
$776$	−0.322241	+	2.36845i	−0.0115678	+	0.0850222i
$777$	5.64746			0.202601
$778$	−23.3407	+	12.1076i	−0.836803	+	0.434080i
$779$	37.8395			1.35574
$780$	4.65891	−	6.61294i	0.166816	−	0.236781i
$781$		−	9.70580i		−	0.347301i
$782$	0.703702	−	5.67853i	0.0251643	−	0.203064i
$783$		−	0.275665i		−	0.00985148i
$784$	3.25661	+	9.11064i	0.116308	+	0.325380i
$785$	−15.1421			−0.540443
$786$	2.16890	+	4.18113i	0.0773621	+	0.149136i
$787$	−30.8746			−1.10056			−0.550280	−	0.834980i	$-0.685479\pi$
$787$	−30.8746			−1.10056			−0.550280	+	0.834980i	$0.685479\pi$
$788$	16.0596	−	22.7953i	0.572100	−	0.812048i
$789$		−	25.0910i		−	0.893263i
$790$	−20.3793	+	10.5715i	−0.725063	+	0.376116i
$791$			23.7395i			0.844078i
$792$	−9.94984	−	1.35374i	−0.353552	−	0.0481029i
$793$			28.5361i			1.01335i
$794$	11.6323	+	22.4243i	0.412815	+	0.795810i
$795$			5.60182i			0.198676i
$796$	6.15065	−	8.73034i	0.218004	−	0.309439i
$797$			39.2460i			1.39016i	0.718931	+	0.695082i	$0.244632\pi$
$797$			39.2460i			1.39016i	−0.718931	+	0.695082i	$0.755368\pi$
$798$	−13.7989	+	7.15798i	−0.488475	+	0.253390i
$799$	−8.79376			−0.311101
$800$	3.85169	−	4.14301i	0.136178	−	0.146477i
$801$			16.0179i			0.565963i
$802$	13.6826	−	7.09768i	0.483151	−	0.250628i
$803$	17.2011			0.607015
$804$	−4.29953	−	3.02908i	−0.151633	−	0.106827i
$805$	−8.46142	−	5.81138i	−0.298226	−	0.204824i
$806$	42.7135	−	22.1570i	1.50452	−	0.780448i
$807$			15.8583i			0.558240i
$808$	19.7494	+	2.68702i	0.694781	+	0.0945292i
$809$	41.1210			1.44574			0.722869	−	0.690985i	$-0.242823\pi$
$809$	41.1210			1.44574			0.722869	+	0.690985i	$0.242823\pi$
$810$	−1.25536	+	0.651202i	−0.0441090	+	0.0228809i
$811$			25.9894i			0.912610i	0.889823	+	0.456305i	$0.150827\pi$
$811$			25.9894i			0.912610i	−0.889823	+	0.456305i	$0.849173\pi$
$812$	0.679636	−	0.964688i	0.0238506	−	0.0338539i
$813$	−19.2143			−0.673876
$814$	11.7594	−	6.10004i	0.412168	−	0.213806i
$815$	−6.70557			−0.234886
$816$	−1.13588	−	3.17772i	−0.0397638	−	0.111243i
$817$	59.6326			2.08628
$818$	−6.24528	−	12.0394i	−0.218361	−	0.420949i
$819$	−8.65705			−0.302502
$820$	12.0469	+	8.48721i	0.420696	+	0.296386i
$821$	−27.7229			−0.967537			−0.483769	−	0.875196i	$-0.660732\pi$
$821$	−27.7229			−0.967537			−0.483769	+	0.875196i	$0.660732\pi$
$822$	14.2975	+	27.5621i	0.498681	+	0.961340i
$823$		−	1.31299i		−	0.0457679i	−0.999738	−	0.0228840i	$-0.992715\pi$
$823$		−	1.31299i		−	0.0457679i	0.999738	−	0.0228840i	$-0.00728483\pi$
$824$	38.6111	+	5.25327i	1.34508	+	0.183006i
$825$		−	3.55021i		−	0.123602i
$826$	7.92865	−	4.11287i	0.275873	−	0.143105i
$827$	41.1400			1.43058			0.715288	−	0.698830i	$-0.246295\pi$
$827$	41.1400			1.43058			0.715288	+	0.698830i	$0.246295\pi$
$828$	3.33603	+	8.99283i	0.115935	+	0.312522i
$829$	−43.5731			−1.51336			−0.756678	−	0.653788i	$-0.773179\pi$
$829$	−43.5731			−1.51336			−0.756678	+	0.653788i	$0.773179\pi$
$830$	−11.8645	+	6.15454i	−0.411823	+	0.213627i
$831$			2.32664i			0.0807104i
$832$	−31.1810	−	8.64474i	−1.08101	−	0.299702i
$833$			2.04064i			0.0707039i
$834$	−10.0517	−	19.3774i	−0.348063	−	0.670983i
$835$	22.2534			0.770110
$836$	−21.0012	+	29.8094i	−0.726341	+	1.03098i
$837$	−8.41233			−0.290773
$838$	2.27546	+	4.38654i	0.0786043	+	0.151531i
$839$	24.5721			0.848323			0.424162	−	0.905586i	$-0.360569\pi$
$839$	24.5721			0.848323			0.424162	+	0.905586i	$0.360569\pi$
$840$	−5.99863	−	0.816150i	−0.206972	−	0.0281598i
$841$	−28.9240			−0.997380
$842$	25.0064	−	12.9717i	0.861776	−	0.447034i
$843$	−2.44660			−0.0842652
$844$	4.51428	+	3.18038i	0.155388	+	0.109473i
$845$		−	3.35912i		−	0.115557i
$846$	13.0851	−	6.78772i	0.449876	−	0.233366i
$847$	−3.43314			−0.117964
$848$	21.0998	−	7.54217i	0.724571	−	0.258999i
$849$		−	9.49613i		−	0.325906i
$850$	1.05910	−	0.549392i	0.0363267	−	0.0188440i
$851$	−10.4308	−	7.16395i	−0.357562	−	0.245577i
$852$	−3.14907	+	4.46984i	−0.107885	+	0.153134i
$853$	18.2241			0.623982			0.311991	−	0.950085i	$-0.399004\pi$
$853$	18.2241			0.623982			0.311991	+	0.950085i	$0.399004\pi$
$854$	18.9572	−	9.83378i	0.648702	−	0.336505i
$855$			5.13553i			0.175631i
$856$	−4.05590	−	0.551830i	−0.138628	−	0.0188612i
$857$	−36.4555			−1.24529			−0.622647	−	0.782503i	$-0.713943\pi$
$857$	−36.4555			−1.24529			−0.622647	+	0.782503i	$0.713943\pi$
$858$	−18.0262	+	9.35081i	−0.615403	+	0.319232i
$859$			8.31770i			0.283796i	0.989881	+	0.141898i	$0.0453205\pi$
$859$			8.31770i			0.283796i	−0.989881	+	0.141898i	$0.954679\pi$
$860$	18.9851	+	13.3753i	0.647387	+	0.456094i
$861$		−	15.7707i		−	0.537463i
$862$	−0.658005	−	1.26848i	−0.0224117	−	0.0432045i
$863$			6.91833i			0.235503i	0.993043	+	0.117751i	$0.0375686\pi$
$863$			6.91833i			0.235503i	−0.993043	+	0.117751i	$0.962431\pi$
$864$	4.14301	+	3.85169i	0.140948	+	0.131037i
$865$			20.8806i			0.709963i
$866$	−30.7413	+	15.9466i	−1.04463	+	0.541887i
$867$			16.2882i			0.553178i
$868$	−29.4389	−	20.7401i	−0.999220	−	0.703965i
$869$	57.6334			1.95508
$870$	−0.179514	−	0.346060i	−0.00608609	−	0.0117325i
$871$	−10.6362			−0.360394
$872$	0.392413	−	2.88420i	0.0132888	−	0.0976714i
$873$		−	0.845087i		−	0.0286019i
$874$	34.5664	+	4.28358i	1.16923	+	0.144894i
$875$		−	2.14037i		−	0.0723579i
$876$	−7.92169	−	5.58095i	−0.267649	−	0.188563i
$877$	16.8420			0.568714			0.284357	−	0.958718i	$-0.408220\pi$
$877$	16.8420			0.568714			0.284357	+	0.958718i	$0.408220\pi$
$878$	−4.97424	+	2.58032i	−0.167872	+	0.0870814i
$879$	−16.0874			−0.542615
$880$	−13.3722	+	4.77992i	−0.450777	+	0.161131i
$881$			40.7543i			1.37305i	0.727107	+	0.686524i	$0.240864\pi$
$881$			40.7543i			1.37305i	−0.727107	+	0.686524i	$0.759136\pi$
$882$	−1.57512	−	3.03647i	−0.0530372	−	0.102243i
$883$		−	31.2055i		−	1.05015i	−0.851056	−	0.525075i	$-0.824037\pi$
$883$		−	31.2055i		−	1.05015i	0.851056	−	0.525075i	$-0.175963\pi$
$884$	−5.57906	−	3.93053i	−0.187644	−	0.132198i
$885$		−	2.95080i		−	0.0991901i
$886$	4.03961	−	2.09549i	0.135713	−	0.0703993i
$887$		−	1.74524i		−	0.0585996i	−0.999571	−	0.0292998i	$-0.990672\pi$
$887$		−	1.74524i		−	0.0585996i	0.999571	−	0.0292998i	$-0.00932774\pi$
$888$	−7.39478	−	1.00610i	−0.248153	−	0.0337627i
$889$			43.6281i			1.46324i
$890$	10.4309	+	20.1082i	0.349643	+	0.674029i
$891$	3.55021			0.118937
$892$	12.1132	+	8.53395i	0.405581	+	0.285738i
$893$		−	53.5295i		−	1.79130i
$894$	−0.795871	−	1.53425i	−0.0266179	−	0.0513130i
$895$	11.9933			0.400891
$896$	5.00231	+	23.6933i	0.167115	+	0.791537i
$897$	15.9894	+	10.9817i	0.533872	+	0.366668i
$898$	−2.04385	−	3.94007i	−0.0682043	−	0.131482i
$899$		−	2.31899i		−	0.0773426i
$900$	−1.15187	+	1.63499i	−0.0383958	+	0.0544996i
$901$	4.72603			0.157447
$902$	−17.0345	−	32.8385i	−0.567187	−	1.09340i
$903$		−	24.8535i		−	0.827074i
$904$	4.22923	−	31.0845i	0.140662	−	1.03385i
$905$	11.8382			0.393515
$906$	6.28370	+	12.1135i	0.208762	+	0.402444i
$907$	58.1153			1.92969			0.964844	−	0.262824i	$-0.0846539\pi$
$907$	58.1153			1.92969			0.964844	+	0.262824i	$0.0846539\pi$
$908$	−12.5148	+	17.7638i	−0.415319	+	0.589511i
$909$	−7.04680			−0.233727
$910$	−10.8677	+	5.63748i	−0.360262	+	0.186881i
$911$	34.1132			1.13022			0.565110	−	0.825015i	$-0.308834\pi$
$911$	34.1132			1.13022			0.565110	+	0.825015i	$0.308834\pi$
$912$	19.3435	−	6.91436i	0.640526	−	0.228957i
$913$	33.5532			1.11045
$914$	5.58748	−	2.89843i	0.184818	−	0.0958715i
$915$		−	7.05529i		−	0.233241i
$916$	20.6606	+	14.5557i	0.682644	+	0.480932i
$917$		−	7.12876i		−	0.235412i
$918$	0.549392	+	1.05910i	0.0181326	+	0.0349554i
$919$	−24.4239			−0.805669			−0.402834	−	0.915273i	$-0.631975\pi$
$919$	−24.4239			−0.805669			−0.402834	+	0.915273i	$0.631975\pi$
$920$	10.0441	+	9.11684i	0.331143	+	0.300573i
$921$	−1.09550			−0.0360980
$922$	−11.7411	−	22.6341i	−0.386673	−	0.745415i
$923$			11.0575i			0.363962i
$924$	12.4239	+	8.75283i	0.408717	+	0.287947i
$925$		−	2.63854i		−	0.0867545i
$926$	43.1042	−	22.3597i	1.41649	−	0.734785i
$927$	−13.7768			−0.452491
$928$	−1.06178	+	1.14208i	−0.0348545	+	0.0374907i
$929$	30.3665			0.996294			0.498147	−	0.867093i	$-0.334014\pi$
$929$	30.3665			0.996294			0.498147	+	0.867093i	$0.334014\pi$
$930$	−10.5605	+	5.47812i	−0.346293	+	0.179635i
$931$	−12.4218			−0.407108
$932$	−2.47512	+	3.51322i	−0.0810751	+	0.115079i
$933$	−33.0428			−1.08177
$934$	24.0300	+	46.3241i	0.786284	+	1.51577i
$935$	−2.99516			−0.0979523
$936$	11.3355	+	1.54227i	0.370514	+	0.0504106i
$937$			29.6010i			0.967022i	0.875338	+	0.483511i	$0.160639\pi$
$937$			29.6010i			0.967022i	−0.875338	+	0.483511i	$0.839361\pi$
$938$	3.66532	+	7.06586i	0.119677	+	0.230709i
$939$	−17.6117			−0.574736
$940$	12.0064	−	17.0421i	0.391606	−	0.555852i
$941$		−	15.9140i		−	0.518783i	−0.965772	−	0.259391i	$-0.916478\pi$
$941$		−	15.9140i		−	0.518783i	0.965772	−	0.259391i	$-0.0835219\pi$
$942$	−9.86053	−	19.0088i	−0.321274	−	0.619340i
$943$	−20.0055	+	29.1282i	−0.651469	+	0.948545i
$944$	−11.1145	+	3.97289i	−0.361746	+	0.129307i
$945$	2.14037			0.0696264
$946$	−26.8453	−	51.7514i	−0.872816	−	1.68258i
$947$		−	19.8116i		−	0.643789i	−0.946776	−	0.321894i	$-0.895680\pi$
$947$		−	19.8116i		−	0.643789i	0.946776	−	0.321894i	$-0.104320\pi$
$948$	−26.5421	−	18.6993i	−0.862047	−	0.607324i
$949$	−19.5967			−0.636136
$950$	3.34426	+	6.44695i	0.108502	+	0.209167i
$951$			11.9669i			0.388054i
$952$	−0.688551	+	5.06079i	−0.0223161	+	0.164021i
$953$		−	27.1642i		−	0.879934i	−0.898014	−	0.439967i	$-0.854990\pi$
$953$		−	27.1642i		−	0.879934i	0.898014	−	0.439967i	$-0.145010\pi$
$954$	−7.03232	+	3.64792i	−0.227680	+	0.118106i
$955$			1.29520i			0.0419117i
$956$	−25.3499	−	17.8594i	−0.819875	−	0.577613i
$957$			0.978670i			0.0316359i
$958$	23.6726	+	45.6352i	0.764828	+	1.47441i
$959$		−	46.9930i		−	1.51748i
$960$	7.70920	+	2.13733i	0.248813	+	0.0689821i
$961$	−39.7673			−1.28282
$962$	−13.3972	+	6.94958i	−0.431941	+	0.224063i
$963$	1.44719			0.0466351
$964$	20.5356	+	14.4676i	0.661406	+	0.465970i
$965$			1.48140i			0.0476880i
$966$	1.78530	−	14.4065i	0.0574412	−	0.463522i
$967$			40.9044i			1.31540i	0.753281	+	0.657698i	$0.228470\pi$
$967$			40.9044i			1.31540i	−0.753281	+	0.657698i	$0.771530\pi$
$968$	4.49535	+	0.611620i	0.144486	+	0.0196582i
$969$	4.33263			0.139184
$970$	−0.550322	−	1.06089i	−0.0176698	−	0.0340632i
$971$	−31.1852			−1.00078			−0.500390	−	0.865800i	$-0.666810\pi$
$971$	−31.1852			−1.00078			−0.500390	+	0.865800i	$0.666810\pi$
$972$	−1.63499	−	1.15187i	−0.0524423	−	0.0369463i
$973$			33.0381i			1.05915i
$974$	5.69290	−	2.95311i	0.182412	−	0.0946237i
$975$			4.04464i			0.129532i
$976$	−26.5745	+	9.49909i	−0.850628	+	0.304058i
$977$			43.9246i			1.40527i	0.711549	+	0.702637i	$0.247994\pi$
$977$			43.9246i			1.40527i	−0.711549	+	0.702637i	$0.752006\pi$
$978$	−4.36668	−	8.41792i	−0.139631	−	0.269175i
$979$		−	56.8668i		−	1.81747i
$980$	−3.95471	−	2.78615i	−0.126328	−	0.0890002i
$981$			1.02911i			0.0328571i
$982$	16.8757	−	8.75404i	0.538526	−	0.279353i
$983$	37.6723			1.20156			0.600780	−	0.799414i	$-0.294857\pi$
$983$	37.6723			1.20156			0.600780	+	0.799414i	$0.294857\pi$
$984$	−2.80957	+	20.6501i	−0.0895659	+	0.658302i
$985$			13.9422i			0.444234i
$986$	−0.291957	+	0.151448i	−0.00929779	+	0.00482309i
$987$	−22.3099			−0.710132
$988$	23.9260	−	33.9610i	0.761187	−	1.08044i
$989$	−31.5274	+	45.9041i	−1.00251	+	1.45967i
$990$	4.45680	−	2.31190i	0.141646	−	0.0734771i
$991$			8.15713i			0.259120i	0.991572	+	0.129560i	$0.0413565\pi$
$991$			8.15713i			0.259120i	−0.991572	+	0.129560i	$0.958644\pi$
$992$	34.8523	+	32.4017i	1.10656	+	1.02875i
$993$	−5.36132			−0.170136
$994$	7.34576	−	3.81051i	0.232993	−	0.120862i
$995$			5.33970i			0.169280i
$996$	−15.4524	−	10.8864i	−0.489627	−	0.344949i
$997$	53.7457			1.70214			0.851071	−	0.525051i	$-0.175954\pi$
$997$	53.7457			1.70214			0.851071	+	0.525051i	$0.175954\pi$
$998$	−31.7490	+	16.4694i	−1.00500	+	0.521329i
$999$	2.63854			0.0834796

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.p.b.91.19	yes	48
4.3	odd	2		1380.2.p.a.91.20	yes	48
23.22	odd	2		1380.2.p.a.91.19	✓	48
92.91	even	2	inner	1380.2.p.b.91.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.p.a.91.19	✓	48	23.22	odd	2
1380.2.p.a.91.20	yes	48	4.3	odd	2
1380.2.p.b.91.19	yes	48	1.1	even	1	trivial
1380.2.p.b.91.20	yes	48	92.91	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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.651202 - 1.25536i) q^{2} +1.00000i q^{3} +(-1.15187 + 1.63499i) q^{4} -1.00000i q^{5} +(1.25536 - 0.651202i) q^{6} -2.14037 q^{7} +(2.80261 + 0.381312i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.651202 - 1.25536i) q^{2} +1.00000i q^{3} +(-1.15187 + 1.63499i) q^{4} -1.00000i q^{5} +(1.25536 - 0.651202i) q^{6} -2.14037 q^{7} +(2.80261 + 0.381312i) q^{8} -1.00000 q^{9} +(-1.25536 + 0.651202i) q^{10} +3.55021 q^{11} +(-1.63499 - 1.15187i) q^{12} -4.04464 q^{13} +(1.39382 + 2.68695i) q^{14} +1.00000 q^{15} +(-1.34638 - 3.76660i) q^{16} -0.843658i q^{17} +(0.651202 + 1.25536i) q^{18} +5.13553 q^{19} +(1.63499 + 1.15187i) q^{20} -2.14037i q^{21} +(-2.31190 - 4.45680i) q^{22} +(-2.71512 + 3.95324i) q^{23} +(-0.381312 + 2.80261i) q^{24} -1.00000 q^{25} +(2.63388 + 5.07749i) q^{26} -1.00000i q^{27} +(2.46544 - 3.49949i) q^{28} +0.275665 q^{29} +(-0.651202 - 1.25536i) q^{30} -8.41233i q^{31} +(-3.85169 + 4.14301i) q^{32} +3.55021i q^{33} +(-1.05910 + 0.549392i) q^{34} +2.14037i q^{35} +(1.15187 - 1.63499i) q^{36} +2.63854i q^{37} +(-3.34426 - 6.44695i) q^{38} -4.04464i q^{39} +(0.381312 - 2.80261i) q^{40} +7.36818 q^{41} +(-2.68695 + 1.39382i) q^{42} +11.6118 q^{43} +(-4.08939 + 5.80455i) q^{44} +1.00000i q^{45} +(6.73084 + 0.834108i) q^{46} -10.4234i q^{47} +(3.76660 - 1.34638i) q^{48} -2.41880 q^{49} +(0.651202 + 1.25536i) q^{50} +0.843658 q^{51} +(4.65891 - 6.61294i) q^{52} +5.60182i q^{53} +(-1.25536 + 0.651202i) q^{54} -3.55021i q^{55} +(-5.99863 - 0.816150i) q^{56} +5.13553i q^{57} +(-0.179514 - 0.346060i) q^{58} -2.95080i q^{59} +(-1.15187 + 1.63499i) q^{60} -7.05529i q^{61} +(-10.5605 + 5.47812i) q^{62} +2.14037 q^{63} +(7.70920 + 2.13733i) q^{64} +4.04464i q^{65} +(4.45680 - 2.31190i) q^{66} +2.62970 q^{67} +(1.37937 + 0.971787i) q^{68} +(-3.95324 - 2.71512i) q^{69} +(2.68695 - 1.39382i) q^{70} -2.73387i q^{71} +(-2.80261 - 0.381312i) q^{72} +4.84511 q^{73} +(3.31232 - 1.71822i) q^{74} -1.00000i q^{75} +(-5.91548 + 8.39653i) q^{76} -7.59878 q^{77} +(-5.07749 + 2.63388i) q^{78} +16.2338 q^{79} +(-3.76660 + 1.34638i) q^{80} +1.00000 q^{81} +(-4.79817 - 9.24974i) q^{82} +9.45106 q^{83} +(3.49949 + 2.46544i) q^{84} -0.843658 q^{85} +(-7.56161 - 14.5770i) q^{86} +0.275665i q^{87} +(9.94984 + 1.35374i) q^{88} -16.0179i q^{89} +(1.25536 - 0.651202i) q^{90} +8.65705 q^{91} +(-3.33603 - 8.99283i) q^{92} +8.41233 q^{93} +(-13.0851 + 6.78772i) q^{94} -5.13553i q^{95} +(-4.14301 - 3.85169i) q^{96} +0.845087i q^{97} +(1.57512 + 3.03647i) q^{98} -3.55021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Introduction

L-functions

Modular forms

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Database

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