LMFDB - Embedded newform 1334.2.c.b.231.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(231,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1334.231");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			231.6
Character	$\chi$	$=$	1334.231
Dual form			1334.2.c.b.231.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -0.549299i q^{3} -1.00000 q^{4} -1.94586 q^{5} -0.549299 q^{6} -0.582420 q^{7} +1.00000i q^{8} +2.69827 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -0.549299i q^{3} -1.00000 q^{4} -1.94586 q^{5} -0.549299 q^{6} -0.582420 q^{7} +1.00000i q^{8} +2.69827 q^{9} +1.94586i q^{10} -2.36050i q^{11} +0.549299i q^{12} +3.89546 q^{13} +0.582420i q^{14} +1.06886i q^{15} +1.00000 q^{16} -2.04541i q^{17} -2.69827i q^{18} -0.971440i q^{19} +1.94586 q^{20} +0.319923i q^{21} -2.36050 q^{22} -1.00000 q^{23} +0.549299 q^{24} -1.21364 q^{25} -3.89546i q^{26} -3.13005i q^{27} +0.582420 q^{28} +(2.07108 + 4.97098i) q^{29} +1.06886 q^{30} -4.32805i q^{31} -1.00000i q^{32} -1.29662 q^{33} -2.04541 q^{34} +1.13331 q^{35} -2.69827 q^{36} -5.44568i q^{37} -0.971440 q^{38} -2.13977i q^{39} -1.94586i q^{40} +4.39652i q^{41} +0.319923 q^{42} -6.37336i q^{43} +2.36050i q^{44} -5.25045 q^{45} +1.00000i q^{46} -8.16767i q^{47} -0.549299i q^{48} -6.66079 q^{49} +1.21364i q^{50} -1.12354 q^{51} -3.89546 q^{52} -9.86858 q^{53} -3.13005 q^{54} +4.59320i q^{55} -0.582420i q^{56} -0.533611 q^{57} +(4.97098 - 2.07108i) q^{58} -11.6202 q^{59} -1.06886i q^{60} -13.1217i q^{61} -4.32805 q^{62} -1.57153 q^{63} -1.00000 q^{64} -7.58000 q^{65} +1.29662i q^{66} +5.23095 q^{67} +2.04541i q^{68} +0.549299i q^{69} -1.13331i q^{70} +0.514617 q^{71} +2.69827i q^{72} +8.57883i q^{73} -5.44568 q^{74} +0.666653i q^{75} +0.971440i q^{76} +1.37481i q^{77} -2.13977 q^{78} -4.04115i q^{79} -1.94586 q^{80} +6.37548 q^{81} +4.39652 q^{82} -10.1207 q^{83} -0.319923i q^{84} +3.98007i q^{85} -6.37336 q^{86} +(2.73055 - 1.13764i) q^{87} +2.36050 q^{88} -3.24166i q^{89} +5.25045i q^{90} -2.26879 q^{91} +1.00000 q^{92} -2.37739 q^{93} -8.16767 q^{94} +1.89028i q^{95} -0.549299 q^{96} -4.44428i q^{97} +6.66079i q^{98} -6.36928i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} - 54 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 - 54 * q^9	$ 28 q - 28 q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} - 54 q^{9} - 2 q^{13} + 28 q^{16} - 2 q^{20} + 6 q^{22} - 28 q^{23} - 2 q^{24} + 38 q^{25} + 8 q^{28} - 2 q^{29} + 2 q^{30} + 30 q^{33} + 12 q^{34} + 56 q^{35} + 54 q^{36} + 12 q^{38} + 16 q^{42} - 52 q^{45} + 76 q^{49} - 60 q^{51} + 2 q^{52} - 22 q^{53} - 14 q^{54} + 72 q^{57} - 18 q^{58} - 12 q^{59} + 14 q^{62} + 24 q^{63} - 28 q^{64} - 42 q^{65} - 16 q^{67} - 4 q^{71} - 32 q^{74} - 34 q^{78} + 2 q^{80} + 116 q^{81} - 68 q^{82} - 48 q^{83} + 46 q^{86} + 12 q^{87} - 6 q^{88} + 96 q^{91} + 28 q^{92} + 70 q^{93} - 10 q^{94} + 2 q^{96}+O(q^{100}) $ 28 * q - 28 * q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 - 54 * q^9 - 2 * q^13 + 28 * q^16 - 2 * q^20 + 6 * q^22 - 28 * q^23 - 2 * q^24 + 38 * q^25 + 8 * q^28 - 2 * q^29 + 2 * q^30 + 30 * q^33 + 12 * q^34 + 56 * q^35 + 54 * q^36 + 12 * q^38 + 16 * q^42 - 52 * q^45 + 76 * q^49 - 60 * q^51 + 2 * q^52 - 22 * q^53 - 14 * q^54 + 72 * q^57 - 18 * q^58 - 12 * q^59 + 14 * q^62 + 24 * q^63 - 28 * q^64 - 42 * q^65 - 16 * q^67 - 4 * q^71 - 32 * q^74 - 34 * q^78 + 2 * q^80 + 116 * q^81 - 68 * q^82 - 48 * q^83 + 46 * q^86 + 12 * q^87 - 6 * q^88 + 96 * q^91 + 28 * q^92 + 70 * q^93 - 10 * q^94 + 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1334\mathbb{Z}\right)^\times$.

$n$	$465$	$553$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	0.549299i		−	0.317138i	−0.987348	−	0.158569i	$-0.949312\pi$
$3$		−	0.549299i		−	0.317138i	0.987348	−	0.158569i	$-0.0506880\pi$
$4$	−1.00000			−0.500000
$5$	−1.94586			−0.870213			−0.435107	−	0.900379i	$-0.643289\pi$
$5$	−1.94586			−0.870213			−0.435107	+	0.900379i	$0.643289\pi$
$6$	−0.549299			−0.224250
$7$	−0.582420			−0.220134			−0.110067	−	0.993924i	$-0.535107\pi$
$7$	−0.582420			−0.220134			−0.110067	+	0.993924i	$0.535107\pi$
$8$			1.00000i			0.353553i
$9$	2.69827			0.899424
$10$			1.94586i			0.615334i
$11$		−	2.36050i		−	0.711719i	−0.934539	−	0.355859i	$-0.884188\pi$
$11$		−	2.36050i		−	0.711719i	0.934539	−	0.355859i	$-0.115812\pi$
$12$			0.549299i			0.158569i
$13$	3.89546			1.08041			0.540203	−	0.841535i	$-0.318347\pi$
$13$	3.89546			1.08041			0.540203	+	0.841535i	$0.318347\pi$
$14$			0.582420i			0.155658i
$15$			1.06886i			0.275977i
$16$	1.00000			0.250000
$17$		−	2.04541i		−	0.496084i	−0.968749	−	0.248042i	$-0.920213\pi$
$17$		−	2.04541i		−	0.496084i	0.968749	−	0.248042i	$-0.0797871\pi$
$18$		−	2.69827i		−	0.635989i
$19$		−	0.971440i		−	0.222864i	−0.993772	−	0.111432i	$-0.964456\pi$
$19$		−	0.971440i		−	0.222864i	0.993772	−	0.111432i	$-0.0355437\pi$
$20$	1.94586			0.435107
$21$			0.319923i			0.0698128i
$22$	−2.36050			−0.503261
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	0.549299			0.112125
$25$	−1.21364			−0.242729
$26$		−	3.89546i		−	0.763962i
$27$		−	3.13005i		−	0.602379i
$28$	0.582420			0.110067
$29$	2.07108	+	4.97098i	0.384589	+	0.923088i
$29$	2.07108	+	4.97098i	0.384589	+	0.923088i
$30$	1.06886			0.195146
$31$		−	4.32805i		−	0.777341i	−0.921377	−	0.388671i	$-0.872934\pi$
$31$		−	4.32805i		−	0.777341i	0.921377	−	0.388671i	$-0.127066\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.29662			−0.225713
$34$	−2.04541			−0.350784
$35$	1.13331			0.191564
$36$	−2.69827			−0.449712
$37$		−	5.44568i		−	0.895265i	−0.894218	−	0.447632i	$-0.852267\pi$
$37$		−	5.44568i		−	0.895265i	0.894218	−	0.447632i	$-0.147733\pi$
$38$	−0.971440			−0.157588
$39$		−	2.13977i		−	0.342638i
$40$		−	1.94586i		−	0.307667i
$41$			4.39652i			0.686622i	0.939222	+	0.343311i	$0.111548\pi$
$41$			4.39652i			0.686622i	−0.939222	+	0.343311i	$0.888452\pi$
$42$	0.319923			0.0493651
$43$		−	6.37336i		−	0.971928i	−0.873979	−	0.485964i	$-0.838469\pi$
$43$		−	6.37336i		−	0.971928i	0.873979	−	0.485964i	$-0.161531\pi$
$44$			2.36050i			0.355859i
$45$	−5.25045			−0.782690
$46$			1.00000i			0.147442i
$47$		−	8.16767i		−	1.19138i	−0.803215	−	0.595689i	$-0.796879\pi$
$47$		−	8.16767i		−	1.19138i	0.803215	−	0.595689i	$-0.203121\pi$
$48$		−	0.549299i		−	0.0792844i
$49$	−6.66079			−0.951541
$50$			1.21364i			0.171635i
$51$	−1.12354			−0.157327
$52$	−3.89546			−0.540203
$53$	−9.86858			−1.35555			−0.677777	−	0.735267i	$-0.737057\pi$
$53$	−9.86858			−1.35555			−0.677777	+	0.735267i	$0.737057\pi$
$54$	−3.13005			−0.425946
$55$			4.59320i			0.619347i
$56$		−	0.582420i		−	0.0778292i
$57$	−0.533611			−0.0706785
$58$	4.97098	−	2.07108i	0.652722	−	0.271946i
$59$	−11.6202			−1.51282			−0.756408	−	0.654101i	$-0.773047\pi$
$59$	−11.6202			−1.51282			−0.756408	+	0.654101i	$0.773047\pi$
$60$		−	1.06886i		−	0.137989i
$61$		−	13.1217i		−	1.68007i	−0.542535	−	0.840033i	$-0.682535\pi$
$61$		−	13.1217i		−	1.68007i	0.542535	−	0.840033i	$-0.317465\pi$
$62$	−4.32805			−0.549663
$63$	−1.57153			−0.197994
$64$	−1.00000			−0.125000
$65$	−7.58000			−0.940184
$66$			1.29662i			0.159603i
$67$	5.23095			0.639062			0.319531	−	0.947576i	$-0.396475\pi$
$67$	5.23095			0.639062			0.319531	+	0.947576i	$0.396475\pi$
$68$			2.04541i			0.248042i
$69$			0.549299i			0.0661278i
$70$		−	1.13331i		−	0.135456i
$71$	0.514617			0.0610739			0.0305369	−	0.999534i	$-0.490278\pi$
$71$	0.514617			0.0610739			0.0305369	+	0.999534i	$0.490278\pi$
$72$			2.69827i			0.317994i
$73$			8.57883i			1.00408i	0.864846	+	0.502038i	$0.167416\pi$
$73$			8.57883i			1.00408i	−0.864846	+	0.502038i	$0.832584\pi$
$74$	−5.44568			−0.633048
$75$			0.666653i			0.0769784i
$76$			0.971440i			0.111432i
$77$			1.37481i			0.156674i
$78$	−2.13977			−0.242281
$79$		−	4.04115i		−	0.454665i	−0.973817	−	0.227332i	$-0.927000\pi$
$79$		−	4.04115i		−	0.454665i	0.973817	−	0.227332i	$-0.0730003\pi$
$80$	−1.94586			−0.217553
$81$	6.37548			0.708387
$82$	4.39652			0.485515
$83$	−10.1207			−1.11089			−0.555446	−	0.831553i	$-0.687452\pi$
$83$	−10.1207			−1.11089			−0.555446	+	0.831553i	$0.687452\pi$
$84$		−	0.319923i		−	0.0349064i
$85$			3.98007i			0.431699i
$86$	−6.37336			−0.687257
$87$	2.73055	−	1.13764i	0.292746	−	0.121968i
$88$	2.36050			0.251631
$89$		−	3.24166i		−	0.343615i	−0.985131	−	0.171807i	$-0.945039\pi$
$89$		−	3.24166i		−	0.343615i	0.985131	−	0.171807i	$-0.0549607\pi$
$90$			5.25045i			0.553446i
$91$	−2.26879			−0.237834
$92$	1.00000			0.104257
$93$	−2.37739			−0.246524
$94$	−8.16767			−0.842431
$95$			1.89028i			0.193939i
$96$	−0.549299			−0.0560626
$97$		−	4.44428i		−	0.451249i	−0.974214	−	0.225624i	$-0.927558\pi$
$97$		−	4.44428i		−	0.451249i	0.974214	−	0.225624i	$-0.0724422\pi$
$98$			6.66079i			0.672841i
$99$		−	6.36928i		−	0.640137i
$100$	1.21364			0.121364
$101$		−	0.280601i		−	0.0279209i	−0.999903	−	0.0139604i	$-0.995556\pi$
$101$		−	0.280601i		−	0.0279209i	0.999903	−	0.0139604i	$-0.00444389\pi$
$102$			1.12354i			0.111247i
$103$	15.5450			1.53169			0.765845	−	0.643025i	$-0.222321\pi$
$103$	15.5450			1.53169			0.765845	+	0.643025i	$0.222321\pi$
$104$			3.89546i			0.381981i
$105$		−	0.622523i		−	0.0607521i
$106$			9.86858i			0.958522i
$107$	0.762010			0.0736663			0.0368331	−	0.999321i	$-0.488273\pi$
$107$	0.762010			0.0736663			0.0368331	+	0.999321i	$0.488273\pi$
$108$			3.13005i			0.301189i
$109$	−2.37550			−0.227531			−0.113766	−	0.993508i	$-0.536291\pi$
$109$	−2.37550			−0.227531			−0.113766	+	0.993508i	$0.536291\pi$
$110$	4.59320			0.437945
$111$	−2.99131			−0.283922
$112$	−0.582420			−0.0550335
$113$		−	14.3608i		−	1.35095i	−0.737383	−	0.675475i	$-0.763939\pi$
$113$		−	14.3608i		−	1.35095i	0.737383	−	0.675475i	$-0.236061\pi$
$114$			0.533611i			0.0499772i
$115$	1.94586			0.181452
$116$	−2.07108	−	4.97098i	−0.192295	−	0.461544i
$117$	10.5110			0.971743
$118$			11.6202i			1.06972i
$119$			1.19129i			0.109205i
$120$	−1.06886			−0.0975728
$121$	5.42802			0.493456
$122$	−13.1217			−1.18799
$123$	2.41501			0.217754
$124$			4.32805i			0.388671i
$125$	12.0909			1.08144
$126$			1.57153i			0.140003i
$127$		−	8.86745i		−	0.786859i	−0.919355	−	0.393430i	$-0.871289\pi$
$127$		−	8.86745i		−	0.786859i	0.919355	−	0.393430i	$-0.128711\pi$
$128$			1.00000i			0.0883883i
$129$	−3.50088			−0.308235
$130$			7.58000i			0.664810i
$131$			15.2635i			1.33358i	0.745245	+	0.666791i	$0.232332\pi$
$131$			15.2635i			1.33358i	−0.745245	+	0.666791i	$0.767668\pi$
$132$	1.29662			0.112856
$133$			0.565786i			0.0490599i
$134$		−	5.23095i		−	0.451885i
$135$			6.09063i			0.524198i
$136$	2.04541			0.175392
$137$			12.2410i			1.04582i	0.852389	+	0.522909i	$0.175153\pi$
$137$			12.2410i			1.04582i	−0.852389	+	0.522909i	$0.824847\pi$
$138$	0.549299			0.0467594
$139$	−13.9894			−1.18657			−0.593283	−	0.804994i	$-0.702168\pi$
$139$	−13.9894			−1.18657			−0.593283	+	0.804994i	$0.702168\pi$
$140$	−1.13331			−0.0957818
$141$	−4.48649			−0.377831
$142$		−	0.514617i		−	0.0431857i
$143$		−	9.19525i		−	0.768945i
$144$	2.69827			0.224856
$145$	−4.03002	−	9.67281i	−0.334675	−	0.803283i
$146$	8.57883			0.709989
$147$			3.65876i			0.301770i
$148$			5.44568i			0.447632i
$149$	11.1254			0.911428			0.455714	−	0.890126i	$-0.349384\pi$
$149$	11.1254			0.911428			0.455714	+	0.890126i	$0.349384\pi$
$150$	0.666653			0.0544320
$151$	9.19486			0.748267			0.374134	−	0.927375i	$-0.377940\pi$
$151$	9.19486			0.748267			0.374134	+	0.927375i	$0.377940\pi$
$152$	0.971440			0.0787942
$153$		−	5.51906i		−	0.446190i
$154$	1.37481			0.110785
$155$			8.42177i			0.676453i
$156$			2.13977i			0.171319i
$157$			4.31362i			0.344264i	0.985074	+	0.172132i	$0.0550656\pi$
$157$			4.31362i			0.344264i	−0.985074	+	0.172132i	$0.944934\pi$
$158$	−4.04115			−0.321496
$159$			5.42080i			0.429897i
$160$			1.94586i			0.153833i
$161$	0.582420			0.0459011
$162$		−	6.37548i		−	0.500905i
$163$		−	16.7155i		−	1.30926i	−0.755950	−	0.654629i	$-0.772825\pi$
$163$		−	16.7155i		−	1.30926i	0.755950	−	0.654629i	$-0.227175\pi$
$164$		−	4.39652i		−	0.343311i
$165$	2.52304			0.196418
$166$			10.1207i			0.785519i
$167$	−11.2441			−0.870094			−0.435047	−	0.900408i	$-0.643268\pi$
$167$	−11.2441			−0.870094			−0.435047	+	0.900408i	$0.643268\pi$
$168$	−0.319923			−0.0246826
$169$	2.17460			0.167277
$170$	3.98007			0.305257
$171$		−	2.62121i		−	0.200449i
$172$			6.37336i			0.485964i
$173$	15.1926			1.15507			0.577536	−	0.816365i	$-0.304014\pi$
$173$	15.1926			1.15507			0.577536	+	0.816365i	$0.304014\pi$
$174$	−1.13764	−	2.73055i	−0.0862442	−	0.207003i
$175$	0.706850			0.0534329
$176$		−	2.36050i		−	0.177930i
$177$			6.38293i			0.479771i
$178$	−3.24166			−0.242972
$179$	12.4053			0.927218			0.463609	−	0.886040i	$-0.346554\pi$
$179$	12.4053			0.927218			0.463609	+	0.886040i	$0.346554\pi$
$180$	5.25045			0.391345
$181$	4.15674			0.308968			0.154484	−	0.987995i	$-0.450628\pi$
$181$	4.15674			0.308968			0.154484	+	0.987995i	$0.450628\pi$
$182$			2.26879i			0.168174i
$183$	−7.20775			−0.532812
$184$		−	1.00000i		−	0.0737210i
$185$			10.5965i			0.779071i
$186$			2.37739i			0.174319i
$187$	−4.82819			−0.353072
$188$			8.16767i			0.595689i
$189$			1.82301i			0.132604i
$190$	1.89028			0.137135
$191$		−	8.35670i		−	0.604670i	−0.953202	−	0.302335i	$-0.902234\pi$
$191$		−	8.35670i		−	0.604670i	0.953202	−	0.302335i	$-0.0977661\pi$
$192$			0.549299i			0.0396422i
$193$			19.4994i			1.40359i	0.712377	+	0.701797i	$0.247619\pi$
$193$			19.4994i			1.40359i	−0.712377	+	0.701797i	$0.752381\pi$
$194$	−4.44428			−0.319081
$195$			4.16369i			0.298168i
$196$	6.66079			0.475770
$197$	4.49356			0.320153			0.160076	−	0.987105i	$-0.448826\pi$
$197$	4.49356			0.320153			0.160076	+	0.987105i	$0.448826\pi$
$198$	−6.36928			−0.452645
$199$	1.03197			0.0731542			0.0365771	−	0.999331i	$-0.488355\pi$
$199$	1.03197			0.0731542			0.0365771	+	0.999331i	$0.488355\pi$
$200$		−	1.21364i		−	0.0858176i
$201$		−	2.87335i		−	0.202671i
$202$	−0.280601			−0.0197430
$203$	−1.20624	−	2.89520i	−0.0846612	−	0.203203i
$204$	1.12354			0.0786635
$205$		−	8.55500i		−	0.597507i
$206$		−	15.5450i		−	1.08307i
$207$	−2.69827			−0.187543
$208$	3.89546			0.270102
$209$	−2.29309			−0.158616
$210$	−0.622523			−0.0429582
$211$		−	15.0676i		−	1.03730i	−0.854988	−	0.518648i	$-0.826436\pi$
$211$		−	15.0676i		−	1.03730i	0.854988	−	0.518648i	$-0.173564\pi$
$212$	9.86858			0.677777
$213$		−	0.282679i		−	0.0193688i
$214$		−	0.762010i		−	0.0520899i
$215$			12.4016i			0.845785i
$216$	3.13005			0.212973
$217$			2.52075i			0.171119i
$218$			2.37550i			0.160889i
$219$	4.71234			0.318430
$220$		−	4.59320i		−	0.309674i
$221$		−	7.96780i		−	0.535972i
$222$			2.99131i			0.200763i
$223$	20.7233			1.38773			0.693866	−	0.720104i	$-0.255906\pi$
$223$	20.7233			1.38773			0.693866	+	0.720104i	$0.255906\pi$
$224$			0.582420i			0.0389146i
$225$	−3.27474			−0.218316
$226$	−14.3608			−0.955266
$227$	−10.4266			−0.692037			−0.346018	−	0.938228i	$-0.612467\pi$
$227$	−10.4266			−0.692037			−0.346018	+	0.938228i	$0.612467\pi$
$228$	0.533611			0.0353392
$229$		−	6.17037i		−	0.407750i	−0.978997	−	0.203875i	$-0.934646\pi$
$229$		−	6.17037i		−	0.407750i	0.978997	−	0.203875i	$-0.0653536\pi$
$230$		−	1.94586i		−	0.128306i
$231$	0.755179			0.0496871
$232$	−4.97098	+	2.07108i	−0.326361	+	0.135973i
$233$	−22.6863			−1.48623			−0.743115	−	0.669163i	$-0.766653\pi$
$233$	−22.6863			−1.48623			−0.743115	+	0.669163i	$0.766653\pi$
$234$		−	10.5110i		−	0.687126i
$235$			15.8931i			1.03675i
$236$	11.6202			0.756408
$237$	−2.21980			−0.144191
$238$	1.19129			0.0772196
$239$	7.62876			0.493464			0.246732	−	0.969084i	$-0.420643\pi$
$239$	7.62876			0.493464			0.246732	+	0.969084i	$0.420643\pi$
$240$			1.06886i			0.0689944i
$241$	−17.0008			−1.09512			−0.547559	−	0.836767i	$-0.684443\pi$
$241$	−17.0008			−1.09512			−0.547559	+	0.836767i	$0.684443\pi$
$242$		−	5.42802i		−	0.348926i
$243$		−	12.8922i		−	0.827035i
$244$			13.1217i			0.840033i
$245$	12.9609			0.828044
$246$		−	2.41501i		−	0.153975i
$247$		−	3.78420i		−	0.240783i
$248$	4.32805			0.274832
$249$			5.55929i			0.352306i
$250$		−	12.0909i		−	0.764693i
$251$		−	16.2150i		−	1.02348i	−0.859140	−	0.511741i	$-0.829001\pi$
$251$		−	16.2150i		−	1.02348i	0.859140	−	0.511741i	$-0.170999\pi$
$252$	1.57153			0.0989969
$253$			2.36050i			0.148404i
$254$	−8.86745			−0.556393
$255$	2.18625			0.136908
$256$	1.00000			0.0625000
$257$	−9.85651			−0.614832			−0.307416	−	0.951575i	$-0.599464\pi$
$257$	−9.85651			−0.614832			−0.307416	+	0.951575i	$0.599464\pi$
$258$			3.50088i			0.217955i
$259$			3.17168i			0.197078i
$260$	7.58000			0.470092
$261$	5.58833	+	13.4131i	0.345909	+	0.830247i
$262$	15.2635			0.942984
$263$			27.6032i			1.70208i	0.525098	+	0.851042i	$0.324029\pi$
$263$			27.6032i			1.70208i	−0.525098	+	0.851042i	$0.675971\pi$
$264$		−	1.29662i		−	0.0798016i
$265$	19.2028			1.17962
$266$	0.565786			0.0346906
$267$	−1.78064			−0.108973
$268$	−5.23095			−0.319531
$269$		−	2.91052i		−	0.177458i	−0.996056	−	0.0887288i	$-0.971720\pi$
$269$		−	2.91052i		−	0.177458i	0.996056	−	0.0887288i	$-0.0282804\pi$
$270$	6.09063			0.370664
$271$			2.07515i			0.126056i	0.998012	+	0.0630282i	$0.0200758\pi$
$271$			2.07515i			0.126056i	−0.998012	+	0.0630282i	$0.979924\pi$
$272$		−	2.04541i		−	0.124021i
$273$			1.24625i			0.0754262i
$274$	12.2410			0.739505
$275$			2.86481i			0.172755i
$276$		−	0.549299i		−	0.0330639i
$277$	−20.3851			−1.22482			−0.612410	−	0.790541i	$-0.709800\pi$
$277$	−20.3851			−1.22482			−0.612410	+	0.790541i	$0.709800\pi$
$278$			13.9894i			0.839028i
$279$		−	11.6783i		−	0.699159i
$280$			1.13331i			0.0677280i
$281$	−8.17401			−0.487620			−0.243810	−	0.969823i	$-0.578397\pi$
$281$	−8.17401			−0.487620			−0.243810	+	0.969823i	$0.578397\pi$
$282$			4.48649i			0.267167i
$283$	19.9485			1.18581			0.592906	−	0.805271i	$-0.297980\pi$
$283$	19.9485			1.18581			0.592906	+	0.805271i	$0.297980\pi$
$284$	−0.514617			−0.0305369
$285$	1.03833			0.0615053
$286$	−9.19525			−0.543726
$287$		−	2.56062i		−	0.151149i
$288$		−	2.69827i		−	0.158997i
$289$	12.8163			0.753901
$290$	−9.67281	+	4.03002i	−0.568007	+	0.236651i
$291$	−2.44124			−0.143108
$292$		−	8.57883i		−	0.502038i
$293$		−	18.5393i		−	1.08308i	−0.840675	−	0.541540i	$-0.817842\pi$
$293$		−	18.5393i		−	1.08308i	0.840675	−	0.541540i	$-0.182158\pi$
$294$	3.65876			0.213383
$295$	22.6111			1.31647
$296$	5.44568			0.316524
$297$	−7.38850			−0.428724
$298$		−	11.1254i		−	0.644477i
$299$	−3.89546			−0.225280
$300$		−	0.666653i		−	0.0384892i
$301$			3.71197i			0.213955i
$302$		−	9.19486i		−	0.529105i
$303$	−0.154134			−0.00885476
$304$		−	0.971440i		−	0.0557159i
$305$			25.5330i			1.46202i
$306$	−5.51906			−0.315504
$307$		−	8.10315i		−	0.462471i	−0.972898	−	0.231236i	$-0.925723\pi$
$307$		−	8.10315i		−	0.462471i	0.972898	−	0.231236i	$-0.0742768\pi$
$308$		−	1.37481i		−	0.0783368i
$309$		−	8.53883i		−	0.485757i
$310$	8.42177			0.478324
$311$			7.78752i			0.441590i	0.975320	+	0.220795i	$0.0708651\pi$
$311$			7.78752i			0.441590i	−0.975320	+	0.220795i	$0.929135\pi$
$312$	2.13977			0.121141
$313$	27.6267			1.56155			0.780776	−	0.624811i	$-0.214824\pi$
$313$	27.6267			1.56155			0.780776	+	0.624811i	$0.214824\pi$
$314$	4.31362			0.243432
$315$	3.05797			0.172297
$316$			4.04115i			0.227332i
$317$		−	3.58878i		−	0.201566i	−0.994908	−	0.100783i	$-0.967865\pi$
$317$		−	3.58878i		−	0.201566i	0.994908	−	0.100783i	$-0.0321348\pi$
$318$	5.42080			0.303983
$319$	11.7340	−	4.88879i	0.656979	−	0.273719i
$320$	1.94586			0.108777
$321$		−	0.418571i		−	0.0233624i
$322$		−	0.582420i		−	0.0324570i
$323$	−1.98699			−0.110559
$324$	−6.37548			−0.354193
$325$	−4.72770			−0.262246
$326$	−16.7155			−0.925786
$327$			1.30486i			0.0721587i
$328$	−4.39652			−0.242757
$329$			4.75702i			0.262263i
$330$		−	2.52304i		−	0.138889i
$331$			14.2482i			0.783153i	0.920146	+	0.391576i	$0.128070\pi$
$331$			14.2482i			0.783153i	−0.920146	+	0.391576i	$0.871930\pi$
$332$	10.1207			0.555446
$333$		−	14.6939i		−	0.805222i
$334$			11.2441i			0.615249i
$335$	−10.1787			−0.556120
$336$			0.319923i			0.0174532i
$337$			22.1750i			1.20795i	0.797003	+	0.603976i	$0.206418\pi$
$337$			22.1750i			1.20795i	−0.797003	+	0.603976i	$0.793582\pi$
$338$		−	2.17460i		−	0.118283i
$339$	−7.88837			−0.428437
$340$		−	3.98007i		−	0.215850i
$341$	−10.2164			−0.553248
$342$	−2.62121			−0.141739
$343$	7.95632			0.429601
$344$	6.37336			0.343628
$345$		−	1.06886i		−	0.0575453i
$346$		−	15.1926i		−	0.816759i
$347$	20.0079			1.07408			0.537041	−	0.843556i	$-0.319542\pi$
$347$	20.0079			1.07408			0.537041	+	0.843556i	$0.319542\pi$
$348$	−2.73055	+	1.13764i	−0.146373	+	0.0609839i
$349$	−17.7463			−0.949936			−0.474968	−	0.880003i	$-0.657540\pi$
$349$	−17.7463			−0.949936			−0.474968	+	0.880003i	$0.657540\pi$
$350$		−	0.706850i		−	0.0377827i
$351$		−	12.1930i		−	0.650814i
$352$	−2.36050			−0.125815
$353$	5.13924			0.273534			0.136767	−	0.990603i	$-0.456329\pi$
$353$	5.13924			0.273534			0.136767	+	0.990603i	$0.456329\pi$
$354$	6.38293			0.339249
$355$	−1.00137			−0.0531473
$356$			3.24166i			0.171807i
$357$	0.654372			0.0346330
$358$		−	12.4053i		−	0.655642i
$359$			18.2335i			0.962325i	0.876631	+	0.481162i	$0.159785\pi$
$359$			18.2335i			0.962325i	−0.876631	+	0.481162i	$0.840215\pi$
$360$		−	5.25045i		−	0.276723i
$361$	18.0563			0.950332
$362$		−	4.15674i		−	0.218473i
$363$		−	2.98160i		−	0.156494i
$364$	2.26879			0.118917
$365$		−	16.6932i		−	0.873760i
$366$			7.20775i			0.376755i
$367$		−	33.9714i		−	1.77329i	−0.462446	−	0.886647i	$-0.653028\pi$
$367$		−	33.9714i		−	1.77329i	0.462446	−	0.886647i	$-0.346972\pi$
$368$	−1.00000			−0.0521286
$369$			11.8630i			0.617564i
$370$	10.5965			0.550887
$371$	5.74766			0.298404
$372$	2.37739			0.123262
$373$	24.7264			1.28028			0.640141	−	0.768257i	$-0.278876\pi$
$373$	24.7264			1.28028			0.640141	+	0.768257i	$0.278876\pi$
$374$			4.82819i			0.249660i
$375$		−	6.64149i		−	0.342965i
$376$	8.16767			0.421216
$377$	8.06779	+	19.3642i	0.415513	+	0.997310i
$378$	1.82301			0.0937653
$379$		−	7.93125i		−	0.407401i	−0.979033	−	0.203700i	$-0.934703\pi$
$379$		−	7.93125i		−	0.407401i	0.979033	−	0.203700i	$-0.0652968\pi$
$380$		−	1.89028i		−	0.0969694i
$381$	−4.87088			−0.249543
$382$	−8.35670			−0.427566
$383$	23.1623			1.18354			0.591769	−	0.806107i	$-0.298430\pi$
$383$	23.1623			1.18354			0.591769	+	0.806107i	$0.298430\pi$
$384$	0.549299			0.0280313
$385$		−	2.67517i		−	0.136339i
$386$	19.4994			0.992491
$387$		−	17.1970i		−	0.874175i
$388$			4.44428i			0.225624i
$389$		−	9.89322i		−	0.501606i	−0.968038	−	0.250803i	$-0.919305\pi$
$389$		−	9.89322i		−	0.501606i	0.968038	−	0.250803i	$-0.0806947\pi$
$390$	4.16369			0.210836
$391$			2.04541i			0.103441i
$392$		−	6.66079i		−	0.336421i
$393$	8.38424			0.422929
$394$		−	4.49356i		−	0.226382i
$395$			7.86349i			0.395655i
$396$			6.36928i			0.320068i
$397$	27.8326			1.39688			0.698439	−	0.715670i	$-0.253879\pi$
$397$	27.8326			1.39688			0.698439	+	0.715670i	$0.253879\pi$
$398$		−	1.03197i		−	0.0517278i
$399$	0.310786			0.0155587
$400$	−1.21364			−0.0606822
$401$	−21.4700			−1.07216			−0.536079	−	0.844168i	$-0.680095\pi$
$401$	−21.4700			−1.07216			−0.536079	+	0.844168i	$0.680095\pi$
$402$	−2.87335			−0.143310
$403$		−	16.8598i		−	0.839844i
$404$			0.280601i			0.0139604i
$405$	−12.4058			−0.616447
$406$	−2.89520	+	1.20624i	−0.143686	+	0.0598645i
$407$	−12.8546			−0.637177
$408$		−	1.12354i		−	0.0556235i
$409$			30.9091i			1.52836i	0.645004	+	0.764179i	$0.276856\pi$
$409$			30.9091i			1.52836i	−0.645004	+	0.764179i	$0.723144\pi$
$410$	−8.55500			−0.422502
$411$	6.72395			0.331668
$412$	−15.5450			−0.765845
$413$	6.76781			0.333022
$414$			2.69827i			0.132613i
$415$	19.6934			0.966713
$416$		−	3.89546i		−	0.190991i
$417$			7.68436i			0.376305i
$418$			2.29309i			0.112159i
$419$	16.5069			0.806413			0.403206	−	0.915109i	$-0.367896\pi$
$419$	16.5069			0.806413			0.403206	+	0.915109i	$0.367896\pi$
$420$			0.622523i			0.0303760i
$421$			36.9148i			1.79912i	0.436801	+	0.899558i	$0.356111\pi$
$421$			36.9148i			1.79912i	−0.436801	+	0.899558i	$0.643889\pi$
$422$	−15.0676			−0.733479
$423$		−	22.0386i		−	1.07155i
$424$		−	9.86858i		−	0.479261i
$425$			2.48240i			0.120414i
$426$	−0.282679			−0.0136958
$427$			7.64236i			0.369840i
$428$	−0.762010			−0.0368331
$429$	−5.05094			−0.243862
$430$	12.4016			0.598060
$431$	−16.2070			−0.780662			−0.390331	−	0.920675i	$-0.627639\pi$
$431$	−16.2070			−0.780662			−0.390331	+	0.920675i	$0.627639\pi$
$432$		−	3.13005i		−	0.150595i
$433$			35.3414i			1.69840i	0.528071	+	0.849200i	$0.322916\pi$
$433$			35.3414i			1.69840i	−0.528071	+	0.849200i	$0.677084\pi$
$434$	2.52075			0.121000
$435$	−5.31326	+	2.21368i	−0.254751	+	0.106138i
$436$	2.37550			0.113766
$437$			0.971440i			0.0464703i
$438$		−	4.71234i		−	0.225164i
$439$	−9.53450			−0.455057			−0.227529	−	0.973771i	$-0.573065\pi$
$439$	−9.53450			−0.455057			−0.227529	+	0.973771i	$0.573065\pi$
$440$	−4.59320			−0.218972
$441$	−17.9726			−0.855838
$442$	−7.96780			−0.378990
$443$			3.90950i			0.185746i	0.995678	+	0.0928729i	$0.0296050\pi$
$443$			3.90950i			0.185746i	−0.995678	+	0.0928729i	$0.970395\pi$
$444$	2.99131			0.141961
$445$			6.30780i			0.299018i
$446$		−	20.7233i		−	0.981275i
$447$		−	6.11116i		−	0.289048i
$448$	0.582420			0.0275168
$449$			42.3078i			1.99663i	0.0580321	+	0.998315i	$0.481517\pi$
$449$			42.3078i			1.99663i	−0.0580321	+	0.998315i	$0.518483\pi$
$450$			3.27474i			0.154373i
$451$	10.3780			0.488682
$452$			14.3608i			0.675475i
$453$		−	5.05073i		−	0.237304i
$454$			10.4266i			0.489344i
$455$	4.41475			0.206967
$456$		−	0.533611i		−	0.0249886i
$457$	9.79939			0.458396			0.229198	−	0.973380i	$-0.426390\pi$
$457$	9.79939			0.458396			0.229198	+	0.973380i	$0.426390\pi$
$458$	−6.17037			−0.288323
$459$	−6.40223			−0.298831
$460$	−1.94586			−0.0907260
$461$		−	16.5522i		−	0.770915i	−0.922726	−	0.385458i	$-0.874044\pi$
$461$		−	16.5522i		−	0.770915i	0.922726	−	0.385458i	$-0.125956\pi$
$462$		−	0.755179i		−	0.0351341i
$463$	−32.5054			−1.51065			−0.755327	−	0.655348i	$-0.772522\pi$
$463$	−32.5054			−1.51065			−0.755327	+	0.655348i	$0.772522\pi$
$464$	2.07108	+	4.97098i	0.0961473	+	0.230772i
$465$	4.62607			0.214529
$466$			22.6863i			1.05092i
$467$		−	11.2645i		−	0.521258i	−0.965439	−	0.260629i	$-0.916070\pi$
$467$		−	11.2645i		−	0.521258i	0.965439	−	0.260629i	$-0.0839300\pi$
$468$	−10.5110			−0.485871
$469$	−3.04661			−0.140679
$470$	15.8931			0.733095
$471$	2.36947			0.109179
$472$		−	11.6202i		−	0.534861i
$473$	−15.0443			−0.691740
$474$			2.21980i			0.101959i
$475$			1.17898i			0.0540954i
$476$		−	1.19129i		−	0.0546025i
$477$	−26.6281			−1.21922
$478$		−	7.62876i		−	0.348932i
$479$			17.4124i			0.795592i	0.917474	+	0.397796i	$0.130225\pi$
$479$			17.4124i			0.795592i	−0.917474	+	0.397796i	$0.869775\pi$
$480$	1.06886			0.0487864
$481$		−	21.2134i		−	0.967250i
$482$			17.0008i			0.774365i
$483$		−	0.319923i		−	0.0145570i
$484$	−5.42802			−0.246728
$485$			8.64794i			0.392683i
$486$	−12.8922			−0.584802
$487$	24.9805			1.13197			0.565987	−	0.824414i	$-0.308495\pi$
$487$	24.9805			1.13197			0.565987	+	0.824414i	$0.308495\pi$
$488$	13.1217			0.593993
$489$	−9.18180			−0.415215
$490$		−	12.9609i		−	0.585515i
$491$		−	7.29013i		−	0.328999i	−0.986377	−	0.164500i	$-0.947399\pi$
$491$		−	7.29013i		−	0.328999i	0.986377	−	0.164500i	$-0.0526009\pi$
$492$	−2.41501			−0.108877
$493$	10.1677	−	4.23620i	0.457929	−	0.190789i
$494$	−3.78420			−0.170259
$495$			12.3937i			0.557056i
$496$		−	4.32805i		−	0.194335i
$497$	−0.299724			−0.0134444
$498$	5.55929			0.249118
$499$	26.9510			1.20649			0.603247	−	0.797555i	$-0.293873\pi$
$499$	26.9510			1.20649			0.603247	+	0.797555i	$0.293873\pi$
$500$	−12.0909			−0.540720
$501$			6.17637i			0.275940i
$502$	−16.2150			−0.723711
$503$		−	24.7282i		−	1.10258i	−0.834315	−	0.551288i	$-0.814137\pi$
$503$		−	24.7282i		−	1.10258i	0.834315	−	0.551288i	$-0.185863\pi$
$504$		−	1.57153i		−	0.0700014i
$505$			0.546010i			0.0242971i
$506$	2.36050			0.104937
$507$		−	1.19451i		−	0.0530499i
$508$			8.86745i			0.393430i
$509$	−28.4920			−1.26289			−0.631443	−	0.775422i	$-0.717537\pi$
$509$	−28.4920			−1.26289			−0.631443	+	0.775422i	$0.717537\pi$
$510$		−	2.18625i		−	0.0968086i
$511$		−	4.99648i		−	0.221031i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.04066			−0.134248
$514$			9.85651i			0.434752i
$515$	−30.2483			−1.33290
$516$	3.50088			0.154118
$517$	−19.2798			−0.847926
$518$	3.17168			0.139355
$519$		−	8.34527i		−	0.366317i
$520$		−	7.58000i		−	0.332405i
$521$	−38.6325			−1.69252			−0.846261	−	0.532769i	$-0.821151\pi$
$521$	−38.6325			−1.69252			−0.846261	+	0.532769i	$0.821151\pi$
$522$	13.4131	−	5.58833i	0.587073	−	0.244594i
$523$	12.2280			0.534693			0.267347	−	0.963600i	$-0.413853\pi$
$523$	12.2280			0.534693			0.267347	+	0.963600i	$0.413853\pi$
$524$		−	15.2635i		−	0.666791i
$525$		−	0.388272i		−	0.0169456i
$526$	27.6032			1.20356
$527$	−8.85263			−0.385627
$528$	−1.29662			−0.0564282
$529$	1.00000			0.0434783
$530$		−	19.2028i		−	0.834118i
$531$	−31.3543			−1.36066
$532$		−	0.565786i		−	0.0245299i
$533$			17.1265i			0.741830i
$534$			1.78064i			0.0770557i
$535$	−1.48276			−0.0641054
$536$			5.23095i			0.225942i
$537$		−	6.81423i		−	0.294056i
$538$	−2.91052			−0.125481
$539$			15.7228i			0.677230i
$540$		−	6.09063i		−	0.262099i
$541$			7.08135i			0.304451i	0.988346	+	0.152225i	$0.0486440\pi$
$541$			7.08135i			0.304451i	−0.988346	+	0.152225i	$0.951356\pi$
$542$	2.07515			0.0891353
$543$		−	2.28329i		−	0.0979855i
$544$	−2.04541			−0.0876961
$545$	4.62237			0.198001
$546$	1.24625			0.0533344
$547$	28.4255			1.21539			0.607694	−	0.794171i	$-0.292095\pi$
$547$	28.4255			1.21539			0.607694	+	0.794171i	$0.292095\pi$
$548$		−	12.2410i		−	0.522909i
$549$		−	35.4060i		−	1.51109i
$550$	2.86481			0.122156
$551$	4.82901	−	2.01193i	0.205723	−	0.0857109i
$552$	−0.549299			−0.0233797
$553$			2.35364i			0.100087i
$554$			20.3851i			0.866078i
$555$	5.82065			0.247073
$556$	13.9894			0.593283
$557$	30.2200			1.28046			0.640232	−	0.768182i	$-0.278838\pi$
$557$	30.2200			1.28046			0.640232	+	0.768182i	$0.278838\pi$
$558$	−11.6783			−0.494380
$559$		−	24.8272i		−	1.05008i
$560$	1.13331			0.0478909
$561$			2.65212i			0.111973i
$562$			8.17401i			0.344800i
$563$		−	27.1743i		−	1.14526i	−0.819814	−	0.572629i	$-0.805923\pi$
$563$		−	27.1743i		−	1.14526i	0.819814	−	0.572629i	$-0.194077\pi$
$564$	4.48649			0.188915
$565$			27.9440i			1.17561i
$566$		−	19.9485i		−	0.838496i
$567$	−3.71321			−0.155940
$568$			0.514617i			0.0215929i
$569$			22.6635i			0.950102i	0.879958	+	0.475051i	$0.157570\pi$
$569$			22.6635i			0.950102i	−0.879958	+	0.475051i	$0.842430\pi$
$570$		−	1.03833i		−	0.0434908i
$571$	−18.8992			−0.790905			−0.395452	−	0.918486i	$-0.629412\pi$
$571$	−18.8992			−0.790905			−0.395452	+	0.918486i	$0.629412\pi$
$572$			9.19525i			0.384473i
$573$	−4.59032			−0.191764
$574$	−2.56062			−0.106878
$575$	1.21364			0.0506124
$576$	−2.69827			−0.112428
$577$			14.4341i			0.600898i	0.953798	+	0.300449i	$0.0971366\pi$
$577$			14.4341i			0.600898i	−0.953798	+	0.300449i	$0.902863\pi$
$578$		−	12.8163i		−	0.533088i
$579$	10.7110			0.445133
$580$	4.03002	+	9.67281i	0.167337	+	0.401642i
$581$	5.89450			0.244545
$582$			2.44124i			0.101193i
$583$			23.2948i			0.964774i
$584$	−8.57883			−0.354994
$585$	−20.4529			−0.845624
$586$	−18.5393			−0.765853
$587$	−18.6207			−0.768559			−0.384279	−	0.923217i	$-0.625550\pi$
$587$	−18.6207			−0.768559			−0.384279	+	0.923217i	$0.625550\pi$
$588$		−	3.65876i		−	0.150885i
$589$	−4.20444			−0.173241
$590$		−	22.6111i		−	0.930886i
$591$		−	2.46830i		−	0.101532i
$592$		−	5.44568i		−	0.223816i
$593$	10.6660			0.438002			0.219001	−	0.975725i	$-0.429720\pi$
$593$	10.6660			0.438002			0.219001	+	0.975725i	$0.429720\pi$
$594$			7.38850i			0.303154i
$595$		−	2.31807i		−	0.0950317i
$596$	−11.1254			−0.455714
$597$		−	0.566858i		−	0.0231999i
$598$			3.89546i			0.159297i
$599$			16.3664i			0.668712i	0.942447	+	0.334356i	$0.108519\pi$
$599$			16.3664i			0.668712i	−0.942447	+	0.334356i	$0.891481\pi$
$600$	−0.666653			−0.0272160
$601$			19.7966i			0.807518i	0.914865	+	0.403759i	$0.132297\pi$
$601$			19.7966i			0.807518i	−0.914865	+	0.403759i	$0.867703\pi$
$602$	3.71197			0.151289
$603$	14.1145			0.574787
$604$	−9.19486			−0.374134
$605$	−10.5621			−0.429412
$606$			0.154134i			0.00626126i
$607$		−	14.5010i		−	0.588577i	−0.955717	−	0.294288i	$-0.904917\pi$
$607$		−	14.5010i		−	0.588577i	0.955717	−	0.294288i	$-0.0950826\pi$
$608$	−0.971440			−0.0393971
$609$	−1.59033	+	0.662584i	−0.0644434	+	0.0268493i
$610$	25.5330			1.03380
$611$		−	31.8168i		−	1.28717i
$612$			5.51906i			0.223095i
$613$	44.0279			1.77827			0.889134	−	0.457647i	$-0.151308\pi$
$613$	44.0279			1.77827			0.889134	+	0.457647i	$0.151308\pi$
$614$	−8.10315			−0.327016
$615$	−4.69925			−0.189492
$616$	−1.37481			−0.0553925
$617$			6.03060i			0.242783i	0.992605	+	0.121391i	$0.0387356\pi$
$617$			6.03060i			0.242783i	−0.992605	+	0.121391i	$0.961264\pi$
$618$	−8.53883			−0.343482
$619$		−	34.8961i		−	1.40259i	−0.712870	−	0.701296i	$-0.752605\pi$
$619$		−	34.8961i		−	1.40259i	0.712870	−	0.701296i	$-0.247395\pi$
$620$		−	8.42177i		−	0.338226i
$621$			3.13005i			0.125605i
$622$	7.78752			0.312251
$623$			1.88801i			0.0756413i
$624$		−	2.13977i		−	0.0856594i
$625$	−17.4589			−0.698354
$626$		−	27.6267i		−	1.10418i
$627$			1.25959i			0.0503032i
$628$		−	4.31362i		−	0.172132i
$629$	−11.1386			−0.444127
$630$		−	3.05797i		−	0.121832i
$631$	−21.2098			−0.844348			−0.422174	−	0.906515i	$-0.638733\pi$
$631$	−21.2098			−0.844348			−0.422174	+	0.906515i	$0.638733\pi$
$632$	4.04115			0.160748
$633$	−8.27661			−0.328966
$634$	−3.58878			−0.142529
$635$			17.2548i			0.684735i
$636$		−	5.42080i		−	0.214949i
$637$	−25.9468			−1.02805
$638$	−4.88879	−	11.7340i	−0.193549	−	0.464554i
$639$	1.38858			0.0549313
$640$		−	1.94586i		−	0.0769167i
$641$			29.2173i			1.15402i	0.816739	+	0.577008i	$0.195780\pi$
$641$			29.2173i			1.15402i	−0.816739	+	0.577008i	$0.804220\pi$
$642$	−0.418571			−0.0165197
$643$	−2.43118			−0.0958764			−0.0479382	−	0.998850i	$-0.515265\pi$
$643$	−2.43118			−0.0958764			−0.0479382	+	0.998850i	$0.515265\pi$
$644$	−0.582420			−0.0229506
$645$	6.81220			0.268230
$646$			1.98699i			0.0781771i
$647$	−41.2831			−1.62301			−0.811504	−	0.584347i	$-0.801351\pi$
$647$	−41.2831			−1.62301			−0.811504	+	0.584347i	$0.801351\pi$
$648$			6.37548i			0.250452i
$649$			27.4294i			1.07670i
$650$			4.72770i			0.185436i
$651$	1.38464			0.0542684
$652$			16.7155i			0.654629i
$653$			16.6120i			0.650078i	0.945701	+	0.325039i	$0.105377\pi$
$653$			16.6120i			0.650078i	−0.945701	+	0.325039i	$0.894623\pi$
$654$	1.30486			0.0510239
$655$		−	29.7006i		−	1.16050i
$656$			4.39652i			0.171655i
$657$			23.1480i			0.903089i
$658$	4.75702			0.185448
$659$			43.3522i			1.68876i	0.535744	+	0.844381i	$0.320031\pi$
$659$			43.3522i			1.68876i	−0.535744	+	0.844381i	$0.679969\pi$
$660$	−2.52304			−0.0982092
$661$	−17.5744			−0.683567			−0.341783	−	0.939779i	$-0.611031\pi$
$661$	−17.5744			−0.683567			−0.341783	+	0.939779i	$0.611031\pi$
$662$	14.2482			0.553772
$663$	−4.37670			−0.169977
$664$		−	10.1207i		−	0.392760i
$665$		−	1.10094i		−	0.0426926i
$666$	−14.6939			−0.569378
$667$	−2.07108	−	4.97098i	−0.0801924	−	0.192477i
$668$	11.2441			0.435047
$669$		−	11.3833i		−	0.440102i
$670$			10.1787i			0.393236i
$671$	−30.9739			−1.19573
$672$	0.319923			0.0123413
$673$	−0.202892			−0.00782092			−0.00391046	−	0.999992i	$-0.501245\pi$
$673$	−0.202892			−0.00782092			−0.00391046	+	0.999992i	$0.501245\pi$
$674$	22.1750			0.854151
$675$			3.79877i			0.146215i
$676$	−2.17460			−0.0836386
$677$		−	34.7674i		−	1.33622i	−0.744063	−	0.668110i	$-0.767104\pi$
$677$		−	34.7674i		−	1.33622i	0.744063	−	0.668110i	$-0.232896\pi$
$678$			7.88837i			0.302951i
$679$			2.58844i			0.0993352i
$680$	−3.98007			−0.152629
$681$			5.72731i			0.219471i
$682$			10.2164i			0.391206i
$683$	−23.5896			−0.902630			−0.451315	−	0.892365i	$-0.649045\pi$
$683$	−23.5896			−0.902630			−0.451315	+	0.892365i	$0.649045\pi$
$684$			2.62121i			0.100224i
$685$		−	23.8192i		−	0.910084i
$686$		−	7.95632i		−	0.303774i
$687$	−3.38938			−0.129313
$688$		−	6.37336i		−	0.242982i
$689$	−38.4427			−1.46455
$690$	−1.06886			−0.0406907
$691$	−32.1984			−1.22489			−0.612443	−	0.790515i	$-0.709813\pi$
$691$	−32.1984			−1.22489			−0.612443	+	0.790515i	$0.709813\pi$
$692$	−15.1926			−0.577536
$693$			3.70960i			0.140916i
$694$		−	20.0079i		−	0.759490i
$695$	27.2214			1.03257
$696$	1.13764	+	2.73055i	0.0431221	+	0.103501i
$697$	8.99268			0.340622
$698$			17.7463i			0.671706i
$699$			12.4616i			0.471340i
$700$	−0.706850			−0.0267164
$701$	22.0752			0.833769			0.416884	−	0.908960i	$-0.363122\pi$
$701$	22.0752			0.833769			0.416884	+	0.908960i	$0.363122\pi$
$702$	−12.1930			−0.460195
$703$	−5.29015			−0.199522
$704$			2.36050i			0.0889649i
$705$	8.73007			0.328793
$706$		−	5.13924i		−	0.193418i
$707$			0.163428i			0.00614634i
$708$		−	6.38293i		−	0.239885i
$709$	−11.7663			−0.441894			−0.220947	−	0.975286i	$-0.570915\pi$
$709$	−11.7663			−0.441894			−0.220947	+	0.975286i	$0.570915\pi$
$710$			1.00137i			0.0375808i
$711$		−	10.9041i		−	0.408936i
$712$	3.24166			0.121486
$713$			4.32805i			0.162087i
$714$		−	0.654372i		−	0.0244893i
$715$			17.8926i			0.669147i
$716$	−12.4053			−0.463609
$717$		−	4.19047i		−	0.156496i
$718$	18.2335			0.680466
$719$	52.7262			1.96636			0.983178	−	0.182652i	$-0.0584683\pi$
$719$	52.7262			1.96636			0.983178	+	0.182652i	$0.0584683\pi$
$720$	−5.25045			−0.195673
$721$	−9.05370			−0.337177
$722$		−	18.0563i		−	0.671986i
$723$			9.33852i			0.347303i
$724$	−4.15674			−0.154484
$725$	−2.51355	−	6.03300i	−0.0933509	−	0.224060i
$726$	−2.98160			−0.110658
$727$		−	35.4242i		−	1.31381i	−0.753972	−	0.656906i	$-0.771865\pi$
$727$		−	35.4242i		−	1.31381i	0.753972	−	0.656906i	$-0.228135\pi$
$728$		−	2.26879i		−	0.0840871i
$729$	12.0448			0.446103
$730$	−16.6932			−0.617842
$731$	−13.0361			−0.482158
$732$	7.20775			0.266406
$733$			21.2931i			0.786479i	0.919436	+	0.393240i	$0.128646\pi$
$733$			21.2931i			0.786479i	−0.919436	+	0.393240i	$0.871354\pi$
$734$	−33.9714			−1.25391
$735$		−	7.11942i		−	0.262604i
$736$			1.00000i			0.0368605i
$737$		−	12.3477i		−	0.454832i
$738$	11.8630			0.436684
$739$		−	14.5407i		−	0.534888i	−0.963573	−	0.267444i	$-0.913821\pi$
$739$		−	14.5407i		−	0.534888i	0.963573	−	0.267444i	$-0.0861791\pi$
$740$		−	10.5965i		−	0.389536i
$741$	−2.07866			−0.0763614
$742$		−	5.74766i		−	0.211003i
$743$			47.8261i			1.75457i	0.479970	+	0.877285i	$0.340647\pi$
$743$			47.8261i			1.75457i	−0.479970	+	0.877285i	$0.659353\pi$
$744$		−	2.37739i		−	0.0871595i
$745$	−21.6484			−0.793137
$746$		−	24.7264i		−	0.905296i
$747$	−27.3084			−0.999163
$748$	4.82819			0.176536
$749$	−0.443810			−0.0162165
$750$	−6.64149			−0.242513
$751$		−	3.84342i		−	0.140248i	−0.997538	−	0.0701242i	$-0.977660\pi$
$751$		−	3.84342i		−	0.140248i	0.997538	−	0.0701242i	$-0.0223396\pi$
$752$		−	8.16767i		−	0.297844i
$753$	−8.90688			−0.324585
$754$	19.3642	−	8.06779i	0.705204	−	0.293812i
$755$	−17.8919			−0.651152
$756$		−	1.82301i		−	0.0663021i
$757$		−	15.3487i		−	0.557860i	−0.960311	−	0.278930i	$-0.910020\pi$
$757$		−	15.3487i		−	0.557860i	0.960311	−	0.278930i	$-0.0899797\pi$
$758$	−7.93125			−0.288076
$759$	1.29662			0.0470644
$760$	−1.89028			−0.0685677
$761$	−24.0201			−0.870728			−0.435364	−	0.900255i	$-0.643380\pi$
$761$	−24.0201			−0.870728			−0.435364	+	0.900255i	$0.643380\pi$
$762$			4.87088i			0.176453i
$763$	1.38354			0.0500874
$764$			8.35670i			0.302335i
$765$			10.7393i			0.388280i
$766$		−	23.1623i		−	0.836888i
$767$	−45.2658			−1.63445
$768$		−	0.549299i		−	0.0198211i
$769$			17.1663i			0.619032i	0.950894	+	0.309516i	$0.100167\pi$
$769$			17.1663i			0.619032i	−0.950894	+	0.309516i	$0.899833\pi$
$770$	−2.67517			−0.0964066
$771$			5.41417i			0.194986i
$772$		−	19.4994i		−	0.701797i
$773$			12.7192i			0.457477i	0.973488	+	0.228739i	$0.0734601\pi$
$773$			12.7192i			0.457477i	−0.973488	+	0.228739i	$0.926540\pi$
$774$	−17.1970			−0.618135
$775$			5.25271i			0.188683i
$776$	4.44428			0.159541
$777$	1.74220			0.0625010
$778$	−9.89322			−0.354689
$779$	4.27096			0.153023
$780$		−	4.16369i		−	0.149084i
$781$		−	1.21476i		−	0.0434674i
$782$	2.04541			0.0731436
$783$	15.5594	−	6.48258i	0.556049	−	0.231668i
$784$	−6.66079			−0.237885
$785$		−	8.39368i		−	0.299583i
$786$		−	8.38424i		−	0.299056i
$787$	3.48239			0.124134			0.0620668	−	0.998072i	$-0.480231\pi$
$787$	3.48239			0.124134			0.0620668	+	0.998072i	$0.480231\pi$
$788$	−4.49356			−0.160076
$789$	15.1624			0.539795
$790$	7.86349			0.279770
$791$			8.36402i			0.297390i
$792$	6.36928			0.226323
$793$		−	51.1152i		−	1.81515i
$794$		−	27.8326i		−	0.987741i
$795$		−	10.5481i		−	0.374102i
$796$	−1.03197			−0.0365771
$797$			2.61765i			0.0927219i	0.998925	+	0.0463610i	$0.0147624\pi$
$797$			2.61765i			0.0927219i	−0.998925	+	0.0463610i	$0.985238\pi$
$798$		−	0.310786i		−	0.0110017i
$799$	−16.7062			−0.591023
$800$			1.21364i			0.0429088i
$801$		−	8.74687i		−	0.309055i
$802$			21.4700i			0.758131i
$803$	20.2504			0.714620
$804$			2.87335i			0.101335i
$805$	−1.13331			−0.0399438
$806$	−16.8598			−0.593860
$807$	−1.59875			−0.0562785
$808$	0.280601			0.00987152
$809$		−	9.83061i		−	0.345626i	−0.984955	−	0.172813i	$-0.944714\pi$
$809$		−	9.83061i		−	0.345626i	0.984955	−	0.172813i	$-0.0552856\pi$
$810$			12.4058i			0.435894i
$811$	41.4972			1.45716			0.728581	−	0.684959i	$-0.240180\pi$
$811$	41.4972			1.45716			0.728581	+	0.684959i	$0.240180\pi$
$812$	1.20624	+	2.89520i	0.0423306	+	0.101602i
$813$	1.13988			0.0399772
$814$			12.8546i			0.450552i
$815$			32.5260i			1.13933i
$816$	−1.12354			−0.0393317
$817$	−6.19133			−0.216607
$818$	30.9091			1.08071
$819$	−6.12182			−0.213914
$820$			8.55500i			0.298754i
$821$	24.7404			0.863445			0.431722	−	0.902006i	$-0.357906\pi$
$821$	24.7404			0.863445			0.431722	+	0.902006i	$0.357906\pi$
$822$		−	6.72395i		−	0.234525i
$823$			31.0431i			1.08209i	0.840992	+	0.541047i	$0.181972\pi$
$823$			31.0431i			1.08209i	−0.840992	+	0.541047i	$0.818028\pi$
$824$			15.5450i			0.541534i
$825$	1.57364			0.0547870
$826$		−	6.76781i		−	0.235482i
$827$			11.2272i			0.390407i	0.980763	+	0.195204i	$0.0625367\pi$
$827$			11.2272i			0.390407i	−0.980763	+	0.195204i	$0.937463\pi$
$828$	2.69827			0.0937714
$829$			12.7979i			0.444489i	0.974991	+	0.222244i	$0.0713383\pi$
$829$			12.7979i			0.444489i	−0.974991	+	0.222244i	$0.928662\pi$
$830$		−	19.6934i		−	0.683570i
$831$			11.1975i			0.388436i
$832$	−3.89546			−0.135051
$833$			13.6240i			0.472044i
$834$	7.68436			0.266088
$835$	21.8794			0.757167
$836$	2.29309			0.0793081
$837$	−13.5470			−0.468254
$838$		−	16.5069i		−	0.570220i
$839$		−	20.5984i		−	0.711136i	−0.934650	−	0.355568i	$-0.884287\pi$
$839$		−	20.5984i		−	0.711136i	0.934650	−	0.355568i	$-0.115713\pi$
$840$	0.622523			0.0214791
$841$	−20.4213	+	20.5906i	−0.704182	+	0.710019i
$842$	36.9148			1.27217
$843$			4.48997i			0.154643i
$844$			15.0676i			0.518648i
$845$	−4.23146			−0.145567
$846$	−22.0386			−0.757702
$847$	−3.16139			−0.108627
$848$	−9.86858			−0.338889
$849$		−	10.9577i		−	0.376066i
$850$	2.48240			0.0851454
$851$			5.44568i			0.186676i
$852$			0.282679i			0.00968441i
$853$		−	33.4850i		−	1.14651i	−0.819379	−	0.573253i	$-0.805681\pi$
$853$		−	33.4850i		−	1.14651i	0.819379	−	0.573253i	$-0.194319\pi$
$854$	7.64236			0.261516
$855$			5.10049i			0.174433i
$856$			0.762010i			0.0260450i
$857$	3.80312			0.129912			0.0649561	−	0.997888i	$-0.479309\pi$
$857$	3.80312			0.129912			0.0649561	+	0.997888i	$0.479309\pi$
$858$			5.05094i			0.172436i
$859$			17.6474i			0.602121i	0.953605	+	0.301060i	$0.0973406\pi$
$859$			17.6474i			0.602121i	−0.953605	+	0.301060i	$0.902659\pi$
$860$		−	12.4016i		−	0.422892i
$861$	−1.40655			−0.0479350
$862$			16.2070i			0.552012i
$863$	26.3834			0.898101			0.449050	−	0.893506i	$-0.351762\pi$
$863$	26.3834			0.898101			0.449050	+	0.893506i	$0.351762\pi$
$864$	−3.13005			−0.106487
$865$	−29.5626			−1.00516
$866$	35.3414			1.20095
$867$		−	7.03998i		−	0.239090i
$868$		−	2.52075i		−	0.0855597i
$869$	−9.53914			−0.323593
$870$	2.21368	+	5.31326i	0.0750509	+	0.180136i
$871$	20.3769			0.690446
$872$		−	2.37550i		−	0.0804444i
$873$		−	11.9919i		−	0.405864i
$874$	0.971440			0.0328594
$875$	−7.04196			−0.238062
$876$	−4.71234			−0.159215
$877$	−50.5744			−1.70778			−0.853888	−	0.520457i	$-0.825761\pi$
$877$	−50.5744			−1.70778			−0.853888	+	0.520457i	$0.825761\pi$
$878$			9.53450i			0.321774i
$879$	−10.1836			−0.343485
$880$			4.59320i			0.154837i
$881$		−	37.3020i		−	1.25674i	−0.777916	−	0.628368i	$-0.783723\pi$
$881$		−	37.3020i		−	1.25674i	0.777916	−	0.628368i	$-0.216277\pi$
$882$			17.9726i			0.605169i
$883$	45.9348			1.54583			0.772914	−	0.634511i	$-0.218798\pi$
$883$	45.9348			1.54583			0.772914	+	0.634511i	$0.218798\pi$
$884$			7.96780i			0.267986i
$885$		−	12.4203i		−	0.417503i
$886$	3.90950			0.131342
$887$		−	34.1371i		−	1.14621i	−0.819481	−	0.573106i	$-0.805738\pi$
$887$		−	34.1371i		−	1.14621i	0.819481	−	0.573106i	$-0.194262\pi$
$888$		−	2.99131i		−	0.100382i
$889$			5.16458i			0.173215i
$890$	6.30780			0.211438
$891$		−	15.0493i		−	0.504172i
$892$	−20.7233			−0.693866
$893$	−7.93440			−0.265515
$894$	−6.11116			−0.204388
$895$	−24.1390			−0.806878
$896$		−	0.582420i		−	0.0194573i
$897$			2.13977i			0.0714449i
$898$	42.3078			1.41183
$899$	21.5147	−	8.96373i	0.717554	−	0.298957i
$900$	3.27474			0.109158
$901$			20.1853i			0.672469i
$902$		−	10.3780i		−	0.345550i
$903$	2.03898			0.0678531
$904$	14.3608			0.477633
$905$	−8.08842			−0.268868
$906$	−5.05073			−0.167799
$907$		−	6.78078i		−	0.225152i	−0.993643	−	0.112576i	$-0.964090\pi$
$907$		−	6.78078i		−	0.225152i	0.993643	−	0.112576i	$-0.0359102\pi$
$908$	10.4266			0.346018
$909$		−	0.757138i		−	0.0251127i
$910$		−	4.41475i		−	0.146347i
$911$		−	13.6002i		−	0.450595i	−0.974290	−	0.225298i	$-0.927665\pi$
$911$		−	13.6002i		−	0.450595i	0.974290	−	0.225298i	$-0.0723354\pi$
$912$	−0.533611			−0.0176696
$913$			23.8900i			0.790643i
$914$		−	9.79939i		−	0.324135i
$915$	14.0253			0.463660
$916$			6.17037i			0.203875i
$917$		−	8.88979i		−	0.293567i
$918$			6.40223i			0.211305i
$919$	23.2694			0.767588			0.383794	−	0.923419i	$-0.374617\pi$
$919$	23.2694			0.767588			0.383794	+	0.923419i	$0.374617\pi$
$920$			1.94586i			0.0641530i
$921$	−4.45105			−0.146667
$922$	−16.5522			−0.545119
$923$	2.00467			0.0659846
$924$	−0.755179			−0.0248436
$925$			6.60912i			0.217306i
$926$			32.5054i			1.06819i
$927$	41.9445			1.37764
$928$	4.97098	−	2.07108i	0.163180	−	0.0679864i
$929$	−20.7751			−0.681608			−0.340804	−	0.940134i	$-0.610699\pi$
$929$	−20.7751			−0.681608			−0.340804	+	0.940134i	$0.610699\pi$
$930$		−	4.62607i		−	0.151695i
$931$			6.47055i			0.212064i
$932$	22.6863			0.743115
$933$	4.27767			0.140045
$934$	−11.2645			−0.368585
$935$	9.39497			0.307248
$936$			10.5110i			0.343563i
$937$	−32.9001			−1.07480			−0.537400	−	0.843327i	$-0.680593\pi$
$937$	−32.9001			−1.07480			−0.537400	+	0.843327i	$0.680593\pi$
$938$			3.04661i			0.0994753i
$939$		−	15.1753i		−	0.495227i
$940$		−	15.8931i		−	0.518376i
$941$	18.0683			0.589009			0.294504	−	0.955650i	$-0.404845\pi$
$941$	18.0683			0.589009			0.294504	+	0.955650i	$0.404845\pi$
$942$		−	2.36947i		−	0.0772014i
$943$		−	4.39652i		−	0.143171i
$944$	−11.6202			−0.378204
$945$		−	3.54731i		−	0.115394i
$946$			15.0443i			0.489134i
$947$		−	40.1916i		−	1.30605i	−0.757336	−	0.653025i	$-0.773500\pi$
$947$		−	40.1916i		−	1.30605i	0.757336	−	0.653025i	$-0.226500\pi$
$948$	2.21980			0.0720956
$949$			33.4185i			1.08481i
$950$	1.17898			0.0382512
$951$	−1.97131			−0.0639242
$952$	−1.19129			−0.0386098
$953$	35.5901			1.15288			0.576438	−	0.817141i	$-0.304442\pi$
$953$	35.5901			1.15288			0.576438	+	0.817141i	$0.304442\pi$
$954$			26.6281i			0.862117i
$955$			16.2609i			0.526192i
$956$	−7.62876			−0.246732
$957$	−2.68540	−	6.44548i	−0.0868068	−	0.208353i
$958$	17.4124			0.562569
$959$		−	7.12939i		−	0.230220i
$960$		−	1.06886i		−	0.0344972i
$961$	12.2680			0.395741
$962$	−21.2134			−0.683949
$963$	2.05611			0.0662572
$964$	17.0008			0.547559
$965$		−	37.9430i		−	1.22143i
$966$	−0.319923			−0.0102933
$967$			37.5382i			1.20715i	0.797308	+	0.603573i	$0.206257\pi$
$967$			37.5382i			1.20715i	−0.797308	+	0.603573i	$0.793743\pi$
$968$			5.42802i			0.174463i
$969$			1.09145i			0.0350625i
$970$	8.64794			0.277669
$971$			27.5219i			0.883220i	0.897207	+	0.441610i	$0.145592\pi$
$971$			27.5219i			0.883220i	−0.897207	+	0.441610i	$0.854408\pi$
$972$			12.8922i			0.413518i
$973$	8.14771			0.261204
$974$		−	24.9805i		−	0.800427i
$975$			2.59692i			0.0831680i
$976$		−	13.1217i		−	0.420017i
$977$	41.2970			1.32121			0.660605	−	0.750734i	$-0.270300\pi$
$977$	41.2970			1.32121			0.660605	+	0.750734i	$0.270300\pi$
$978$			9.18180i			0.293602i
$979$	−7.65194			−0.244557
$980$	−12.9609			−0.414022
$981$	−6.40973			−0.204647
$982$	−7.29013			−0.232638
$983$		−	41.6394i		−	1.32809i	−0.747692	−	0.664046i	$-0.768838\pi$
$983$		−	41.6394i		−	1.32809i	0.747692	−	0.664046i	$-0.231162\pi$
$984$			2.41501i			0.0769875i
$985$	−8.74381			−0.278601
$986$	−4.23620	−	10.1677i	−0.134908	−	0.323805i
$987$	2.61302			0.0831734
$988$			3.78420i			0.120392i
$989$			6.37336i			0.202661i
$990$	12.3937			0.393898
$991$	−10.1288			−0.321753			−0.160877	−	0.986975i	$-0.551432\pi$
$991$	−10.1288			−0.321753			−0.160877	+	0.986975i	$0.551432\pi$
$992$	−4.32805			−0.137416
$993$	7.82652			0.248367
$994$			0.299724i			0.00950665i
$995$	−2.00806			−0.0636597
$996$		−	5.55929i		−	0.176153i
$997$		−	42.8652i		−	1.35755i	−0.734344	−	0.678777i	$-0.762510\pi$
$997$		−	42.8652i		−	1.35755i	0.734344	−	0.678777i	$-0.237490\pi$
$998$		−	26.9510i		−	0.853120i
$999$	−17.0453			−0.539289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.c.b.231.6	✓	28
29.28	even	2	inner	1334.2.c.b.231.23	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.c.b.231.6	✓	28	1.1	even	1	trivial
1334.2.c.b.231.23	yes	28	29.28	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -0.549299i q^{3} -1.00000 q^{4} -1.94586 q^{5} -0.549299 q^{6} -0.582420 q^{7} +1.00000i q^{8} +2.69827 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -0.549299i q^{3} -1.00000 q^{4} -1.94586 q^{5} -0.549299 q^{6} -0.582420 q^{7} +1.00000i q^{8} +2.69827 q^{9} +1.94586i q^{10} -2.36050i q^{11} +0.549299i q^{12} +3.89546 q^{13} +0.582420i q^{14} +1.06886i q^{15} +1.00000 q^{16} -2.04541i q^{17} -2.69827i q^{18} -0.971440i q^{19} +1.94586 q^{20} +0.319923i q^{21} -2.36050 q^{22} -1.00000 q^{23} +0.549299 q^{24} -1.21364 q^{25} -3.89546i q^{26} -3.13005i q^{27} +0.582420 q^{28} +(2.07108 + 4.97098i) q^{29} +1.06886 q^{30} -4.32805i q^{31} -1.00000i q^{32} -1.29662 q^{33} -2.04541 q^{34} +1.13331 q^{35} -2.69827 q^{36} -5.44568i q^{37} -0.971440 q^{38} -2.13977i q^{39} -1.94586i q^{40} +4.39652i q^{41} +0.319923 q^{42} -6.37336i q^{43} +2.36050i q^{44} -5.25045 q^{45} +1.00000i q^{46} -8.16767i q^{47} -0.549299i q^{48} -6.66079 q^{49} +1.21364i q^{50} -1.12354 q^{51} -3.89546 q^{52} -9.86858 q^{53} -3.13005 q^{54} +4.59320i q^{55} -0.582420i q^{56} -0.533611 q^{57} +(4.97098 - 2.07108i) q^{58} -11.6202 q^{59} -1.06886i q^{60} -13.1217i q^{61} -4.32805 q^{62} -1.57153 q^{63} -1.00000 q^{64} -7.58000 q^{65} +1.29662i q^{66} +5.23095 q^{67} +2.04541i q^{68} +0.549299i q^{69} -1.13331i q^{70} +0.514617 q^{71} +2.69827i q^{72} +8.57883i q^{73} -5.44568 q^{74} +0.666653i q^{75} +0.971440i q^{76} +1.37481i q^{77} -2.13977 q^{78} -4.04115i q^{79} -1.94586 q^{80} +6.37548 q^{81} +4.39652 q^{82} -10.1207 q^{83} -0.319923i q^{84} +3.98007i q^{85} -6.37336 q^{86} +(2.73055 - 1.13764i) q^{87} +2.36050 q^{88} -3.24166i q^{89} +5.25045i q^{90} -2.26879 q^{91} +1.00000 q^{92} -2.37739 q^{93} -8.16767 q^{94} +1.89028i q^{95} -0.549299 q^{96} -4.44428i q^{97} +6.66079i q^{98} -6.36928i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} - 54 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 - 54 * q^9	\( 28 q - 28 q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} - 54 q^{9} - 2 q^{13} + 28 q^{16} - 2 q^{20} + 6 q^{22} - 28 q^{23} - 2 q^{24} + 38 q^{25} + 8 q^{28} - 2 q^{29} + 2 q^{30} + 30 q^{33} + 12 q^{34} + 56 q^{35} + 54 q^{36} + 12 q^{38} + 16 q^{42} - 52 q^{45} + 76 q^{49} - 60 q^{51} + 2 q^{52} - 22 q^{53} - 14 q^{54} + 72 q^{57} - 18 q^{58} - 12 q^{59} + 14 q^{62} + 24 q^{63} - 28 q^{64} - 42 q^{65} - 16 q^{67} - 4 q^{71} - 32 q^{74} - 34 q^{78} + 2 q^{80} + 116 q^{81} - 68 q^{82} - 48 q^{83} + 46 q^{86} + 12 q^{87} - 6 q^{88} + 96 q^{91} + 28 q^{92} + 70 q^{93} - 10 q^{94} + 2 q^{96}+O(q^{100}) \) 28 * q - 28 * q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 - 54 * q^9 - 2 * q^13 + 28 * q^16 - 2 * q^20 + 6 * q^22 - 28 * q^23 - 2 * q^24 + 38 * q^25 + 8 * q^28 - 2 * q^29 + 2 * q^30 + 30 * q^33 + 12 * q^34 + 56 * q^35 + 54 * q^36 + 12 * q^38 + 16 * q^42 - 52 * q^45 + 76 * q^49 - 60 * q^51 + 2 * q^52 - 22 * q^53 - 14 * q^54 + 72 * q^57 - 18 * q^58 - 12 * q^59 + 14 * q^62 + 24 * q^63 - 28 * q^64 - 42 * q^65 - 16 * q^67 - 4 * q^71 - 32 * q^74 - 34 * q^78 + 2 * q^80 + 116 * q^81 - 68 * q^82 - 48 * q^83 + 46 * q^86 + 12 * q^87 - 6 * q^88 + 96 * q^91 + 28 * q^92 + 70 * q^93 - 10 * q^94 + 2 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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