LMFDB - Embedded newform 91.2.i.a.34.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(34,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("91.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.i (of order $4$, degree $2$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 35x^{8} + 295x^{4} + 169 $ x^12 + 35x^8 + 295x^4 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.3
Root			$-1.52891 + 1.52891i$ of defining polynomial
Character	$\chi$	$=$	91.34
Dual form			91.2.i.a.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.403032 - 0.403032i) q^{2} -1.23240i q^{3} -1.67513i q^{4} +(-1.03221 + 1.03221i) q^{5} +(-0.496696 + 0.496696i) q^{6} +(-0.450747 - 2.60707i) q^{7} +(-1.48119 + 1.48119i) q^{8} +1.48119 q^{9} +O(q^{10})$	\(q+(-0.403032 - 0.403032i) q^{2} -1.23240i q^{3} -1.67513i q^{4} +(-1.03221 + 1.03221i) q^{5} +(-0.496696 + 0.496696i) q^{6} +(-0.450747 - 2.60707i) q^{7} +(-1.48119 + 1.48119i) q^{8} +1.48119 q^{9} +0.832030 q^{10} +(-0.596968 + 0.596968i) q^{11} -2.06443 q^{12} +(3.59334 - 0.296512i) q^{13} +(-0.869067 + 1.23240i) q^{14} +(1.27210 + 1.27210i) q^{15} -2.15633 q^{16} +7.34804 q^{17} +(-0.596968 - 0.596968i) q^{18} +(-3.59334 + 3.59334i) q^{19} +(1.72909 + 1.72909i) q^{20} +(-3.21295 + 0.555500i) q^{21} +0.481194 q^{22} +4.44358i q^{23} +(1.82542 + 1.82542i) q^{24} +2.86907i q^{25} +(-1.56773 - 1.32873i) q^{26} -5.52262i q^{27} +(-4.36719 + 0.755061i) q^{28} -3.54420 q^{29} -1.02539i q^{30} +(1.27122 - 1.27122i) q^{31} +(3.83146 + 3.83146i) q^{32} +(0.735703 + 0.735703i) q^{33} +(-2.96149 - 2.96149i) q^{34} +(3.15633 + 2.22579i) q^{35} -2.48119i q^{36} +(2.88423 - 2.88423i) q^{37} +2.89646 q^{38} +(-0.365420 - 4.42842i) q^{39} -3.05782i q^{40} +(-1.23240 + 1.23240i) q^{41} +(1.51881 + 1.07104i) q^{42} -8.66291i q^{43} +(1.00000 + 1.00000i) q^{44} +(-1.52891 + 1.52891i) q^{45} +(1.79090 - 1.79090i) q^{46} +(-2.52230 - 2.52230i) q^{47} +2.65745i q^{48} +(-6.59365 + 2.35026i) q^{49} +(1.15633 - 1.15633i) q^{50} -9.05571i q^{51} +(-0.496696 - 6.01931i) q^{52} -9.79384 q^{53} +(-2.22579 + 2.22579i) q^{54} -1.23240i q^{55} +(4.52923 + 3.19394i) q^{56} +(4.42842 + 4.42842i) q^{57} +(1.42842 + 1.42842i) q^{58} +(1.08972 + 1.08972i) q^{59} +(2.13093 - 2.13093i) q^{60} +7.10903i q^{61} -1.02469 q^{62} +(-0.667644 - 3.86158i) q^{63} +1.22425i q^{64} +(-3.40303 + 4.01516i) q^{65} -0.593023i q^{66} +(8.76845 + 8.76845i) q^{67} -12.3089i q^{68} +5.47626 q^{69} +(-0.375035 - 2.16916i) q^{70} +(-1.46604 - 1.46604i) q^{71} +(-2.19394 + 2.19394i) q^{72} +(0.103857 + 0.103857i) q^{73} -2.32487 q^{74} +3.53583 q^{75} +(6.01931 + 6.01931i) q^{76} +(1.82542 + 1.28726i) q^{77} +(-1.63752 + 1.93207i) q^{78} -4.79877 q^{79} +(2.22579 - 2.22579i) q^{80} -2.36248 q^{81} +0.993391 q^{82} +(-12.3165 + 12.3165i) q^{83} +(0.930536 + 5.38211i) q^{84} +(-7.58475 + 7.58475i) q^{85} +(-3.49143 + 3.49143i) q^{86} +4.36786i q^{87} -1.76845i q^{88} +(6.89017 + 6.89017i) q^{89} +1.23240 q^{90} +(-2.39271 - 9.23444i) q^{91} +7.44358 q^{92} +(-1.56665 - 1.56665i) q^{93} +2.03313i q^{94} -7.41819i q^{95} +(4.72188 - 4.72188i) q^{96} +(6.05814 - 6.05814i) q^{97} +(3.60468 + 1.71022i) q^{98} +(-0.884226 + 0.884226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9	$ 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} - 8 q^{11} + 8 q^{14} - 4 q^{15} + 16 q^{16} - 8 q^{18} - 16 q^{22} - 20 q^{28} - 4 q^{29} - 16 q^{32} - 4 q^{35} + 12 q^{37} + 40 q^{39} + 40 q^{42} + 12 q^{44} + 24 q^{46} - 28 q^{50} - 12 q^{53} - 8 q^{57} - 44 q^{58} + 44 q^{60} + 20 q^{63} - 40 q^{65} + 60 q^{67} + 4 q^{70} - 28 q^{72} - 48 q^{74} + 44 q^{78} - 4 q^{79} - 92 q^{81} - 4 q^{84} + 12 q^{85} + 36 q^{86} - 32 q^{91} + 24 q^{92} - 28 q^{93} - 28 q^{98} + 12 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9 - 8 * q^11 + 8 * q^14 - 4 * q^15 + 16 * q^16 - 8 * q^18 - 16 * q^22 - 20 * q^28 - 4 * q^29 - 16 * q^32 - 4 * q^35 + 12 * q^37 + 40 * q^39 + 40 * q^42 + 12 * q^44 + 24 * q^46 - 28 * q^50 - 12 * q^53 - 8 * q^57 - 44 * q^58 + 44 * q^60 + 20 * q^63 - 40 * q^65 + 60 * q^67 + 4 * q^70 - 28 * q^72 - 48 * q^74 + 44 * q^78 - 4 * q^79 - 92 * q^81 - 4 * q^84 + 12 * q^85 + 36 * q^86 - 32 * q^91 + 24 * q^92 - 28 * q^93 - 28 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.403032	−	0.403032i	−0.284986	−	0.284986i	0.550107	−	0.835094i	$-0.314587\pi$
$2$	−0.403032	−	0.403032i	−0.284986	−	0.284986i	−0.835094	+	0.550107i	$0.814587\pi$
$3$		−	1.23240i		−	0.711526i	−0.934576	−	0.355763i	$-0.884221\pi$
$3$		−	1.23240i		−	0.711526i	0.934576	−	0.355763i	$-0.115779\pi$
$4$		−	1.67513i		−	0.837565i
$5$	−1.03221	+	1.03221i	−0.461620	+	0.461620i	−0.899186	−	0.437566i	$-0.855841\pi$
$5$	−1.03221	+	1.03221i	−0.461620	+	0.461620i	0.437566	+	0.899186i	$0.355841\pi$
$6$	−0.496696	+	0.496696i	−0.202775	+	0.202775i
$7$	−0.450747	−	2.60707i	−0.170366	−	0.985381i
$7$	−0.450747	−	2.60707i	−0.170366	−	0.985381i
$8$	−1.48119	+	1.48119i	−0.523681	+	0.523681i
$9$	1.48119			0.493731
$10$	0.832030			0.263111
$11$	−0.596968	+	0.596968i	−0.179993	+	0.179993i	−0.791353	−	0.611360i	$-0.790623\pi$
$11$	−0.596968	+	0.596968i	−0.179993	+	0.179993i	0.611360	+	0.791353i	$0.290623\pi$
$12$	−2.06443			−0.595949
$13$	3.59334	−	0.296512i	0.996613	−	0.0822375i
$13$	3.59334	−	0.296512i	0.996613	−	0.0822375i
$14$	−0.869067	+	1.23240i	−0.232268	+	0.329372i
$15$	1.27210	+	1.27210i	0.328455	+	0.328455i
$16$	−2.15633			−0.539081
$17$	7.34804			1.78216			0.891080	−	0.453845i	$-0.149948\pi$
$17$	7.34804			1.78216			0.891080	+	0.453845i	$0.149948\pi$
$18$	−0.596968	−	0.596968i	−0.140707	−	0.140707i
$19$	−3.59334	+	3.59334i	−0.824368	+	0.824368i	−0.986731	−	0.162363i	$-0.948089\pi$
$19$	−3.59334	+	3.59334i	−0.824368	+	0.824368i	0.162363	+	0.986731i	$0.448089\pi$
$20$	1.72909	+	1.72909i	0.386637	+	0.386637i
$21$	−3.21295	+	0.555500i	−0.701124	+	0.121220i
$22$	0.481194			0.102591
$23$			4.44358i			0.926551i	0.886214	+	0.463276i	$0.153326\pi$
$23$			4.44358i			0.926551i	−0.886214	+	0.463276i	$0.846674\pi$
$24$	1.82542	+	1.82542i	0.372613	+	0.372613i
$25$			2.86907i			0.573813i
$26$	−1.56773	−	1.32873i	−0.307458	−	0.260585i
$27$		−	5.52262i		−	1.06283i
$28$	−4.36719	+	0.755061i	−0.825321	+	0.142693i
$29$	−3.54420			−0.658141			−0.329071	−	0.944305i	$-0.606735\pi$
$29$	−3.54420			−0.658141			−0.329071	+	0.944305i	$0.606735\pi$
$30$		−	1.02539i		−	0.187210i
$31$	1.27122	−	1.27122i	0.228318	−	0.228318i	−0.583672	−	0.811990i	$-0.698384\pi$
$31$	1.27122	−	1.27122i	0.228318	−	0.228318i	0.811990	+	0.583672i	$0.198384\pi$
$32$	3.83146	+	3.83146i	0.677312	+	0.677312i
$33$	0.735703	+	0.735703i	0.128069	+	0.128069i
$34$	−2.96149	−	2.96149i	−0.507892	−	0.507892i
$35$	3.15633	+	2.22579i	0.533516	+	0.376227i
$36$		−	2.48119i		−	0.413532i
$37$	2.88423	−	2.88423i	0.474164	−	0.474164i	−0.429095	−	0.903259i	$-0.641168\pi$
$37$	2.88423	−	2.88423i	0.474164	−	0.474164i	0.903259	+	0.429095i	$0.141168\pi$
$38$	2.89646			0.469868
$39$	−0.365420	−	4.42842i	−0.0585141	−	0.709115i
$40$		−	3.05782i		−	0.483484i
$41$	−1.23240	+	1.23240i	−0.192468	+	0.192468i	−0.796762	−	0.604294i	$-0.793455\pi$
$41$	−1.23240	+	1.23240i	−0.192468	+	0.192468i	0.604294	+	0.796762i	$0.293455\pi$
$42$	1.51881	+	1.07104i	0.234357	+	0.165265i
$43$		−	8.66291i		−	1.32108i	−0.750790	−	0.660541i	$-0.770327\pi$
$43$		−	8.66291i		−	1.32108i	0.750790	−	0.660541i	$-0.229673\pi$
$44$	1.00000	+	1.00000i	0.150756	+	0.150756i
$45$	−1.52891	+	1.52891i	−0.227916	+	0.227916i
$46$	1.79090	−	1.79090i	0.264055	−	0.264055i
$47$	−2.52230	−	2.52230i	−0.367915	−	0.367915i	0.498801	−	0.866717i	$-0.333774\pi$
$47$	−2.52230	−	2.52230i	−0.367915	−	0.367915i	−0.866717	+	0.498801i	$0.833774\pi$
$48$			2.65745i			0.383570i
$49$	−6.59365	+	2.35026i	−0.941951	+	0.335752i
$50$	1.15633	−	1.15633i	0.163529	−	0.163529i
$51$		−	9.05571i		−	1.26805i
$52$	−0.496696	−	6.01931i	−0.0688793	−	0.834728i
$53$	−9.79384			−1.34529			−0.672644	−	0.739966i	$-0.734841\pi$
$53$	−9.79384			−1.34529			−0.672644	+	0.739966i	$0.734841\pi$
$54$	−2.22579	+	2.22579i	−0.302892	+	0.302892i
$55$		−	1.23240i		−	0.166177i
$56$	4.52923	+	3.19394i	0.605243	+	0.426808i
$57$	4.42842	+	4.42842i	0.586559	+	0.586559i
$58$	1.42842	+	1.42842i	0.187561	+	0.187561i
$59$	1.08972	+	1.08972i	0.141869	+	0.141869i	0.774474	−	0.632605i	$-0.218014\pi$
$59$	1.08972	+	1.08972i	0.141869	+	0.141869i	−0.632605	+	0.774474i	$0.718014\pi$
$60$	2.13093	−	2.13093i	0.275102	−	0.275102i
$61$			7.10903i			0.910218i	0.890436	+	0.455109i	$0.150400\pi$
$61$			7.10903i			0.910218i	−0.890436	+	0.455109i	$0.849600\pi$
$62$	−1.02469			−0.130135
$63$	−0.667644	−	3.86158i	−0.0841153	−	0.486513i
$64$			1.22425i			0.153032i
$65$	−3.40303	+	4.01516i	−0.422094	+	0.498019i
$66$		−	0.593023i		−	0.0729961i
$67$	8.76845	+	8.76845i	1.07124	+	1.07124i	0.997260	+	0.0739770i	$0.0235691\pi$
$67$	8.76845	+	8.76845i	1.07124	+	1.07124i	0.0739770	+	0.997260i	$0.476431\pi$
$68$		−	12.3089i		−	1.49268i
$69$	5.47626			0.659265
$70$	−0.375035	−	2.16916i	−0.0448253	−	0.259265i
$71$	−1.46604	−	1.46604i	−0.173986	−	0.173986i	0.614742	−	0.788728i	$-0.289260\pi$
$71$	−1.46604	−	1.46604i	−0.173986	−	0.173986i	−0.788728	+	0.614742i	$0.789260\pi$
$72$	−2.19394	+	2.19394i	−0.258558	+	0.258558i
$73$	0.103857	+	0.103857i	0.0121555	+	0.0121555i	0.713158	−	0.701003i	$-0.247264\pi$
$73$	0.103857	+	0.103857i	0.0121555	+	0.0121555i	−0.701003	+	0.713158i	$0.747264\pi$
$74$	−2.32487			−0.270261
$75$	3.53583			0.408283
$76$	6.01931	+	6.01931i	0.690462	+	0.690462i
$77$	1.82542	+	1.28726i	0.208026	+	0.146697i
$78$	−1.63752	+	1.93207i	−0.185413	+	0.218764i
$79$	−4.79877			−0.539904			−0.269952	−	0.962874i	$-0.587008\pi$
$79$	−4.79877			−0.539904			−0.269952	+	0.962874i	$0.587008\pi$
$80$	2.22579	−	2.22579i	0.248851	−	0.248851i
$81$	−2.36248			−0.262498
$82$	0.993391			0.109702
$83$	−12.3165	+	12.3165i	−1.35191	+	1.35191i	−0.468379	+	0.883528i	$0.655162\pi$
$83$	−12.3165	+	12.3165i	−1.35191	+	1.35191i	−0.883528	+	0.468379i	$0.844838\pi$
$84$	0.930536	+	5.38211i	0.101530	+	0.587237i
$85$	−7.58475	+	7.58475i	−0.822682	+	0.822682i
$86$	−3.49143	+	3.49143i	−0.376490	+	0.376490i
$87$			4.36786i			0.468284i
$88$		−	1.76845i		−	0.188518i
$89$	6.89017	+	6.89017i	0.730356	+	0.730356i	0.970690	−	0.240334i	$-0.0772570\pi$
$89$	6.89017	+	6.89017i	0.730356	+	0.730356i	−0.240334	+	0.970690i	$0.577257\pi$
$90$	1.23240			0.129906
$91$	−2.39271	−	9.23444i	−0.250825	−	0.968033i
$92$	7.44358			0.776047
$93$	−1.56665	−	1.56665i	−0.162454	−	0.162454i
$94$			2.03313i			0.209702i
$95$		−	7.41819i		−	0.761090i
$96$	4.72188	−	4.72188i	0.481925	−	0.481925i
$97$	6.05814	−	6.05814i	0.615110	−	0.615110i	−0.329163	−	0.944273i	$-0.606766\pi$
$97$	6.05814	−	6.05814i	0.615110	−	0.615110i	0.944273	+	0.329163i	$0.106766\pi$
$98$	3.60468	+	1.71022i	0.364128	+	0.172758i
$99$	−0.884226	+	0.884226i	−0.0888681	+	0.0888681i
$100$	4.80606			0.480606
$101$	−12.8707			−1.28068			−0.640339	−	0.768092i	$-0.721206\pi$
$101$	−12.8707			−1.28068			−0.640339	+	0.768092i	$0.721206\pi$
$102$	−3.64974	+	3.64974i	−0.361378	+	0.361378i
$103$	6.11564			0.602592			0.301296	−	0.953531i	$-0.402581\pi$
$103$	6.11564			0.602592			0.301296	+	0.953531i	$0.402581\pi$
$104$	−4.88324	+	5.76162i	−0.478841	+	0.564974i
$105$	2.74306	−	3.88985i	0.267695	−	0.379610i
$106$	3.94723	+	3.94723i	0.383389	+	0.383389i
$107$	8.86907			0.857405			0.428703	−	0.903446i	$-0.358971\pi$
$107$	8.86907			0.857405			0.428703	+	0.903446i	$0.358971\pi$
$108$	−9.25111			−0.890188
$109$	−4.59697	−	4.59697i	−0.440310	−	0.440310i	0.451806	−	0.892116i	$-0.350780\pi$
$109$	−4.59697	−	4.59697i	−0.440310	−	0.440310i	−0.892116	+	0.451806i	$0.850780\pi$
$110$	−0.496696	+	0.496696i	−0.0473581	+	0.0473581i
$111$	−3.55452	−	3.55452i	−0.337380	−	0.337380i
$112$	0.971958	+	5.62170i	0.0918414	+	0.531200i
$113$	1.60720			0.151193			0.0755964	−	0.997138i	$-0.475914\pi$
$113$	1.60720			0.151193			0.0755964	+	0.997138i	$0.475914\pi$
$114$		−	3.56959i		−	0.334323i
$115$	−4.58673	−	4.58673i	−0.427715	−	0.427715i
$116$			5.93700i			0.551236i
$117$	5.32243	−	0.439191i	0.492059	−	0.0406032i
$118$		−	0.878382i		−	0.0808617i
$119$	−3.31211	−	19.1569i	−0.303620	−	1.75611i
$120$	−3.76845			−0.344011
$121$			10.2873i			0.935205i
$122$	2.86516	−	2.86516i	0.259400	−	0.259400i
$123$	1.51881	+	1.51881i	0.136946	+	0.136946i
$124$	−2.12946	−	2.12946i	−0.191231	−	0.191231i
$125$	−8.12256	−	8.12256i	−0.726504	−	0.726504i
$126$	−1.28726	+	1.82542i	−0.114678	+	0.162621i
$127$		−	1.54912i		−	0.137462i	−0.997635	−	0.0687312i	$-0.978105\pi$
$127$		−	1.54912i		−	0.137462i	0.997635	−	0.0687312i	$-0.0218951\pi$
$128$	8.15633	−	8.15633i	0.720924	−	0.720924i
$129$	−10.6762			−0.939983
$130$	2.98977	−	0.246707i	0.262220	−	0.0216376i
$131$			5.31490i			0.464365i	0.972672	+	0.232183i	$0.0745867\pi$
$131$			5.31490i			0.464365i	−0.972672	+	0.232183i	$0.925413\pi$
$132$	1.23240	−	1.23240i	0.107267	−	0.107267i
$133$	10.9878	+	7.74841i	0.952761	+	0.671872i
$134$		−	7.06793i		−	0.610576i
$135$	5.70052	+	5.70052i	0.490623	+	0.490623i
$136$	−10.8839	+	10.8839i	−0.933284	+	0.933284i
$137$	12.7157	−	12.7157i	1.08637	−	1.08637i	0.0904753	−	0.995899i	$-0.471161\pi$
$137$	12.7157	−	12.7157i	1.08637	−	1.08637i	0.995899	−	0.0904753i	$-0.0288386\pi$
$138$	−2.20711	−	2.20711i	−0.187882	−	0.187882i
$139$		−	6.94767i		−	0.589294i	−0.955606	−	0.294647i	$-0.904798\pi$
$139$		−	6.94767i		−	0.589294i	0.955606	−	0.294647i	$-0.0952020\pi$
$140$	3.72849	−	5.28726i	0.315115	−	0.446855i
$141$	−3.10848	+	3.10848i	−0.261781	+	0.261781i
$142$			1.18172i			0.0991676i
$143$	−1.96810	+	2.32212i	−0.164581	+	0.194185i
$144$	−3.19394			−0.266161
$145$	3.65837	−	3.65837i	0.303811	−	0.303811i
$146$		−	0.0837150i		−	0.00692831i
$147$	2.89646	+	8.12601i	0.238896	+	0.670222i
$148$	−4.83146	−	4.83146i	−0.397143	−	0.397143i
$149$	−10.9653	−	10.9653i	−0.898315	−	0.898315i	0.0969724	−	0.995287i	$-0.469084\pi$
$149$	−10.9653	−	10.9653i	−0.898315	−	0.898315i	−0.995287	+	0.0969724i	$0.969084\pi$
$150$	−1.42505	−	1.42505i	−0.116355	−	0.116355i
$151$	6.14117	−	6.14117i	0.499761	−	0.499761i	−0.411602	−	0.911363i	$-0.635031\pi$
$151$	6.14117	−	6.14117i	0.499761	−	0.499761i	0.911363	+	0.411602i	$0.135031\pi$
$152$		−	10.6449i		−	0.863413i
$153$	10.8839			0.879909
$154$	−0.216897	−	1.25451i	−0.0174781	−	0.101091i
$155$			2.62435i			0.210793i
$156$	−7.41819	+	0.612127i	−0.593931	+	0.0490094i
$157$			9.69783i			0.773971i	0.922086	+	0.386985i	$0.126484\pi$
$157$			9.69783i			0.773971i	−0.922086	+	0.386985i	$0.873516\pi$
$158$	1.93406	+	1.93406i	0.153865	+	0.153865i
$159$			12.0699i			0.957207i
$160$	−7.90977			−0.625322
$161$	11.5847	−	2.00293i	0.913006	−	0.157853i
$162$	0.952155	+	0.952155i	0.0748083	+	0.0748083i
$163$	−5.41327	+	5.41327i	−0.424000	+	0.424000i	−0.886578	−	0.462579i	$-0.846924\pi$
$163$	−5.41327	+	5.41327i	−0.424000	+	0.424000i	0.462579	+	0.886578i	$0.346924\pi$
$164$	2.06443	+	2.06443i	0.161205	+	0.161205i
$165$	−1.51881			−0.118239
$166$	9.92784			0.770550
$167$	−8.90824	−	8.90824i	−0.689340	−	0.689340i	0.272746	−	0.962086i	$-0.412068\pi$
$167$	−8.90824	−	8.90824i	−0.689340	−	0.689340i	−0.962086	+	0.272746i	$0.912068\pi$
$168$	3.93620	−	5.58181i	0.303685	−	0.430646i
$169$	12.8242	−	2.13093i	0.986474	−	0.163918i
$170$	6.11379			0.468906
$171$	−5.32243	+	5.32243i	−0.407017	+	0.407017i
$172$	−14.5115			−1.10649
$173$	−7.15538			−0.544014			−0.272007	−	0.962295i	$-0.587687\pi$
$173$	−7.15538			−0.544014			−0.272007	+	0.962295i	$0.587687\pi$
$174$	1.76039	−	1.76039i	0.133455	−	0.133455i
$175$	7.47987	−	1.29322i	0.565425	−	0.0977586i
$176$	1.28726	−	1.28726i	0.0970307	−	0.0970307i
$177$	1.34297	−	1.34297i	0.100944	−	0.100944i
$178$		−	5.55391i		−	0.416283i
$179$			13.8119i			1.03235i	0.856482	+	0.516177i	$0.172645\pi$
$179$			13.8119i			1.03235i	−0.856482	+	0.516177i	$0.827355\pi$
$180$	2.56112	+	2.56112i	0.190895	+	0.190895i
$181$	4.56052			0.338981			0.169490	−	0.985532i	$-0.445788\pi$
$181$	4.56052			0.338981			0.169490	+	0.985532i	$0.445788\pi$
$182$	−2.75743	+	4.68611i	−0.204395	+	0.347358i
$183$	8.76116			0.647643
$184$	−6.58181	−	6.58181i	−0.485217	−	0.485217i
$185$			5.95428i			0.437767i
$186$			1.26282i			0.0925945i
$187$	−4.38655	+	4.38655i	−0.320776	+	0.320776i
$188$	−4.22518	+	4.22518i	−0.308153	+	0.308153i
$189$	−14.3979	+	2.48930i	−1.04729	+	0.181070i
$190$	−2.98977	+	2.98977i	−0.216900	+	0.216900i
$191$	3.70545			0.268117			0.134058	−	0.990973i	$-0.457199\pi$
$191$	3.70545			0.268117			0.134058	+	0.990973i	$0.457199\pi$
$192$	1.50877			0.108886
$193$	−17.0508	+	17.0508i	−1.22734	+	1.22734i	−0.262377	+	0.964965i	$0.584506\pi$
$193$	−17.0508	+	17.0508i	−1.22734	+	1.22734i	−0.964965	+	0.262377i	$0.915494\pi$
$194$	−4.88324			−0.350596
$195$	4.94827	+	4.19389i	0.354353	+	0.300331i
$196$	3.93700	+	11.0452i	0.281214	+	0.788945i
$197$	−8.01810	−	8.01810i	−0.571266	−	0.571266i	0.361216	−	0.932482i	$-0.382362\pi$
$197$	−8.01810	−	8.01810i	−0.571266	−	0.571266i	−0.932482	+	0.361216i	$0.882362\pi$
$198$	0.712742			0.0506524
$199$	4.57558			0.324354			0.162177	−	0.986762i	$-0.448148\pi$
$199$	4.57558			0.324354			0.162177	+	0.986762i	$0.448148\pi$
$200$	−4.24965	−	4.24965i	−0.300495	−	0.300495i
$201$	10.8062	−	10.8062i	0.762212	−	0.762212i
$202$	5.18728	+	5.18728i	0.364976	+	0.364976i
$203$	1.59754	+	9.23998i	0.112125	+	0.648520i
$204$	−15.1695			−1.06208
$205$		−	2.54420i		−	0.177695i
$206$	−2.46480	−	2.46480i	−0.171731	−	0.171731i
$207$			6.58181i			0.457467i
$208$	−7.74841	+	0.639375i	−0.537255	+	0.0443327i
$209$		−	4.29022i		−	0.296761i
$210$	−2.67327	+	0.462193i	−0.184473	+	0.0318943i
$211$	−0.594028			−0.0408946			−0.0204473	−	0.999791i	$-0.506509\pi$
$211$	−0.594028			−0.0408946			−0.0204473	+	0.999791i	$0.506509\pi$
$212$			16.4060i			1.12677i
$213$	−1.80674	+	1.80674i	−0.123796	+	0.123796i
$214$	−3.57452	−	3.57452i	−0.244349	−	0.244349i
$215$	8.94198	+	8.94198i	0.609838	+	0.609838i
$216$	8.18007	+	8.18007i	0.556583	+	0.556583i
$217$	−3.88717	−	2.74117i	−0.263878	−	0.186083i
$218$			3.70545i			0.250965i
$219$	0.127993	−	0.127993i	0.00864895	−	0.00864895i
$220$	−2.06443			−0.139184
$221$	26.4040	−	2.17878i	1.77612	−	0.146560i
$222$			2.86516i			0.192297i
$223$	−2.85764	+	2.85764i	−0.191361	+	0.191361i	−0.796284	−	0.604923i	$-0.793204\pi$
$223$	−2.85764	+	2.85764i	−0.191361	+	0.191361i	0.604923	+	0.796284i	$0.293204\pi$
$224$	8.26187	−	11.7159i	0.552019	−	0.782802i
$225$			4.24965i			0.283310i
$226$	−0.647754	−	0.647754i	−0.0430879	−	0.0430879i
$227$	19.6570	−	19.6570i	1.30468	−	1.30468i	0.379477	−	0.925201i	$-0.376104\pi$
$227$	19.6570	−	19.6570i	1.30468	−	1.30468i	0.925201	−	0.379477i	$-0.123896\pi$
$228$	7.41819	−	7.41819i	0.491282	−	0.491282i
$229$	13.2060	+	13.2060i	0.872676	+	0.872676i	0.992763	−	0.120087i	$-0.0383174\pi$
$229$	13.2060	+	13.2060i	0.872676	+	0.872676i	−0.120087	+	0.992763i	$0.538317\pi$
$230$			3.69720i			0.243786i
$231$	1.58641	−	2.24965i	0.104378	−	0.148016i
$232$	5.24965	−	5.24965i	0.344656	−	0.344656i
$233$		−	16.2243i		−	1.06289i	−0.847094	−	0.531443i	$-0.821650\pi$
$233$		−	16.2243i		−	1.06289i	0.847094	−	0.531443i	$-0.178350\pi$
$234$	−2.32212	−	1.96810i	−0.151802	−	0.128659i
$235$	5.20711			0.339674
$236$	1.82542	−	1.82542i	0.118825	−	0.118825i
$237$			5.91400i			0.384155i
$238$	−6.38594	+	9.05571i	−0.413939	+	0.586994i
$239$	−0.843675	−	0.843675i	−0.0545728	−	0.0545728i	0.679294	−	0.733867i	$-0.262286\pi$
$239$	−0.843675	−	0.843675i	−0.0545728	−	0.0545728i	−0.733867	+	0.679294i	$0.762286\pi$
$240$	−2.74306	−	2.74306i	−0.177064	−	0.177064i
$241$	−15.2966	−	15.2966i	−0.985342	−	0.985342i	0.0145517	−	0.999894i	$-0.495368\pi$
$241$	−15.2966	−	15.2966i	−0.985342	−	0.985342i	−0.999894	+	0.0145517i	$0.995368\pi$
$242$	4.14609	−	4.14609i	0.266521	−	0.266521i
$243$		−	13.6563i		−	0.876054i
$244$	11.9086			0.762367
$245$	4.38009	−	9.23204i	0.279834	−	0.589813i
$246$		−	1.22425i		−	0.0780556i
$247$	−11.8466	+	13.9775i	−0.753782	+	0.889370i
$248$			3.76585i			0.239132i
$249$	15.1788	+	15.1788i	0.961916	+	0.961916i
$250$			6.54730i			0.414088i
$251$	−27.4367			−1.73179			−0.865893	−	0.500229i	$-0.833249\pi$
$251$	−27.4367			−1.73179			−0.865893	+	0.500229i	$0.833249\pi$
$252$	−6.46865	+	1.11839i	−0.407487	+	0.0704521i
$253$	−2.65268	−	2.65268i	−0.166772	−	0.166772i
$254$	−0.624346	+	0.624346i	−0.0391749	+	0.0391749i
$255$	9.34743	+	9.34743i	0.585359	+	0.585359i
$256$	−4.12601			−0.257876
$257$	−20.5727			−1.28329			−0.641645	−	0.767002i	$-0.721748\pi$
$257$	−20.5727			−1.28329			−0.641645	+	0.767002i	$0.721748\pi$
$258$	4.30283	+	4.30283i	0.267883	+	0.267883i
$259$	−8.81944	−	6.21933i	−0.548014	−	0.386450i
$260$	6.72592	+	5.70052i	0.417124	+	0.353531i
$261$	−5.24965			−0.324945
$262$	2.14207	−	2.14207i	0.132338	−	0.132338i
$263$	−23.8568			−1.47108			−0.735538	−	0.677483i	$-0.763071\pi$
$263$	−23.8568			−1.47108			−0.735538	+	0.677483i	$0.763071\pi$
$264$	−2.17944			−0.134135
$265$	10.1093	−	10.1093i	0.621012	−	0.621012i
$266$	−1.30557	−	7.55128i	−0.0800497	−	0.462999i
$267$	8.49143	−	8.49143i	0.519667	−	0.519667i
$268$	14.6883	−	14.6883i	0.897231	−	0.897231i
$269$			1.10840i			0.0675803i	0.999429	+	0.0337902i	$0.0107578\pi$
$269$			1.10840i			0.0675803i	−0.999429	+	0.0337902i	$0.989242\pi$
$270$		−	4.59498i		−	0.279642i
$271$	−20.8894	−	20.8894i	−1.26894	−	1.26894i	−0.946637	−	0.322301i	$-0.895544\pi$
$271$	−20.8894	−	20.8894i	−1.26894	−	1.26894i	−0.322301	−	0.946637i	$-0.604456\pi$
$272$	−15.8448			−0.960730
$273$	−11.3805	+	2.94878i	−0.688780	+	0.178468i
$274$	−10.2496			−0.619204
$275$	−1.71274	−	1.71274i	−0.103282	−	0.103282i
$276$		−	9.17346i		−	0.552177i
$277$		−	25.8265i		−	1.55177i	−0.630877	−	0.775883i	$-0.717305\pi$
$277$		−	25.8265i		−	1.55177i	0.630877	−	0.775883i	$-0.282695\pi$
$278$	−2.80013	+	2.80013i	−0.167941	+	0.167941i
$279$	1.88293	−	1.88293i	0.112728	−	0.112728i
$280$	−7.97196	+	1.37830i	−0.476416	+	0.0823694i
$281$	12.0782	−	12.0782i	0.720523	−	0.720523i	−0.248189	−	0.968712i	$-0.579835\pi$
$281$	12.0782	−	12.0782i	0.720523	−	0.720523i	0.968712	+	0.248189i	$0.0798354\pi$
$282$	2.50563			0.149208
$283$	15.3667			0.913458			0.456729	−	0.889606i	$-0.349021\pi$
$283$	15.3667			0.913458			0.456729	+	0.889606i	$0.349021\pi$
$284$	−2.45580	+	2.45580i	−0.145725	+	0.145725i
$285$	−9.14217			−0.541535
$286$	1.72909	−	0.142680i	0.102243	−	0.00843683i
$287$	3.76845	+	2.65745i	0.222445	+	0.156864i
$288$	5.67513	+	5.67513i	0.334410	+	0.334410i
$289$	36.9937			2.17610
$290$	−2.94888			−0.173164
$291$	−7.46604	−	7.46604i	−0.437667	−	0.437667i
$292$	0.173973	−	0.173973i	0.0101810	−	0.0101810i
$293$	9.78662	+	9.78662i	0.571741	+	0.571741i	0.932615	−	0.360874i	$-0.117522\pi$
$293$	9.78662	+	9.78662i	0.571741	+	0.571741i	−0.360874	+	0.932615i	$0.617522\pi$
$294$	2.10767	−	4.44240i	0.122922	−	0.259086i
$295$	−2.24965			−0.130979
$296$			8.54420i			0.496621i
$297$	3.29683	+	3.29683i	0.191301	+	0.191301i
$298$			8.83875i			0.512015i
$299$	1.31757	+	15.9673i	0.0761972	+	0.923413i
$300$		−	5.92298i		−	0.341964i
$301$	−22.5848	+	3.90478i	−1.30177	+	0.225068i
$302$	−4.95017			−0.284850
$303$			15.8618i			0.911235i
$304$	7.74841	−	7.74841i	0.444402	−	0.444402i
$305$	−7.33804	−	7.33804i	−0.420175	−	0.420175i
$306$	−4.38655	−	4.38655i	−0.250762	−	0.250762i
$307$	8.14125	+	8.14125i	0.464645	+	0.464645i	0.900175	−	0.435529i	$-0.143439\pi$
$307$	8.14125	+	8.14125i	0.464645	+	0.464645i	−0.435529	+	0.900175i	$0.643439\pi$
$308$	2.15633	−	3.05782i	0.122868	−	0.174235i
$309$		−	7.53690i		−	0.428759i
$310$	1.05769	−	1.05769i	0.0600730	−	0.0600730i
$311$	32.4813			1.84184			0.920922	−	0.389747i	$-0.127438\pi$
$311$	32.4813			1.84184			0.920922	+	0.389747i	$0.127438\pi$
$312$	7.10062	+	6.01810i	0.401993	+	0.340708i
$313$		−	19.7346i		−	1.11547i	−0.830020	−	0.557733i	$-0.811671\pi$
$313$		−	19.7346i		−	1.11547i	0.830020	−	0.557733i	$-0.188329\pi$
$314$	3.90853	−	3.90853i	0.220571	−	0.220571i
$315$	4.67513	+	3.29683i	0.263414	+	0.185755i
$316$			8.03857i			0.452205i
$317$	−8.11871	−	8.11871i	−0.455992	−	0.455992i	0.441345	−	0.897337i	$-0.354501\pi$
$317$	−8.11871	−	8.11871i	−0.455992	−	0.455992i	−0.897337	+	0.441345i	$0.854501\pi$
$318$	4.86456	−	4.86456i	0.272791	−	0.272791i
$319$	2.11577	−	2.11577i	0.118461	−	0.118461i
$320$	−1.26369	−	1.26369i	−0.0706425	−	0.0706425i
$321$		−	10.9302i		−	0.610066i
$322$	−5.47626	−	3.86177i	−0.305180	−	0.215208i
$323$	−26.4040	+	26.4040i	−1.46916	+	1.46916i
$324$			3.95746i			0.219859i
$325$	0.850712	+	10.3095i	0.0471890	+	0.571870i
$326$	4.36344			0.241668
$327$	−5.66530	+	5.66530i	−0.313292	+	0.313292i
$328$		−	3.65084i		−	0.201584i
$329$	−5.43890	+	7.71274i	−0.299856	+	0.425217i
$330$	0.612127	+	0.612127i	0.0336965	+	0.0336965i
$331$	−0.806063	−	0.806063i	−0.0443053	−	0.0443053i	0.684607	−	0.728912i	$-0.259974\pi$
$331$	−0.806063	−	0.806063i	−0.0443053	−	0.0443053i	−0.728912	+	0.684607i	$0.759974\pi$
$332$	20.6317	+	20.6317i	1.13231	+	1.13231i
$333$	4.27210	−	4.27210i	0.234110	−	0.234110i
$334$			7.18061i			0.392905i
$335$	−18.1018			−0.989009
$336$	6.92817	−	1.19784i	0.377963	−	0.0653475i
$337$			26.6058i			1.44931i	0.689112	+	0.724655i	$0.258001\pi$
$337$			26.6058i			1.44931i	−0.689112	+	0.724655i	$0.741999\pi$
$338$	−6.02738	−	4.30971i	−0.327846	−	0.234417i
$339$		−	1.98071i		−	0.107578i
$340$	12.7054	+	12.7054i	0.689050	+	0.689050i
$341$			1.51776i			0.0821912i
$342$	4.29022			0.231988
$343$	9.09937	+	16.1308i	0.491320	+	0.870979i
$344$	12.8315	+	12.8315i	0.691826	+	0.691826i
$345$	−5.65268	+	5.65268i	−0.304330	+	0.304330i
$346$	2.88385	+	2.88385i	0.155037	+	0.155037i
$347$	−20.2071			−1.08477			−0.542387	−	0.840129i	$-0.682479\pi$
$347$	−20.2071			−1.08477			−0.542387	+	0.840129i	$0.682479\pi$
$348$	7.31674			0.392219
$349$	2.31459	+	2.31459i	0.123897	+	0.123897i	0.766336	−	0.642439i	$-0.222078\pi$
$349$	2.31459	+	2.31459i	0.123897	+	0.123897i	−0.642439	+	0.766336i	$0.722078\pi$
$350$	−3.53583	−	2.49341i	−0.188998	−	0.133279i
$351$	−1.63752	−	19.8446i	−0.0874043	−	1.05923i
$352$	−4.57452			−0.243822
$353$	10.7412	−	10.7412i	0.571696	−	0.571696i	−0.360906	−	0.932602i	$-0.617533\pi$
$353$	10.7412	−	10.7412i	0.571696	−	0.571696i	0.932602	+	0.360906i	$0.117533\pi$
$354$	−1.08252			−0.0575351
$355$	3.02653			0.160631
$356$	11.5419	−	11.5419i	0.611721	−	0.611721i
$357$	−23.6089	+	4.08184i	−1.24952	+	0.216034i
$358$	5.56665	−	5.56665i	0.294207	−	0.294207i
$359$	−16.9726	+	16.9726i	−0.895781	+	0.895781i	−0.995060	−	0.0992789i	$-0.968346\pi$
$359$	−16.9726	+	16.9726i	−0.895781	+	0.895781i	0.0992789	+	0.995060i	$0.468346\pi$
$360$		−	4.52923i		−	0.238711i
$361$		−	6.82416i		−	0.359166i
$362$	−1.83803	−	1.83803i	−0.0966049	−	0.0966049i
$363$	12.6780			0.665422
$364$	−15.4689	+	4.00811i	−0.810791	+	0.210082i
$365$	−0.214405			−0.0112225
$366$	−3.53102	−	3.53102i	−0.184570	−	0.184570i
$367$			9.79778i			0.511440i	0.966751	+	0.255720i	$0.0823125\pi$
$367$			9.79778i			0.511440i	−0.966751	+	0.255720i	$0.917688\pi$
$368$		−	9.58181i		−	0.499486i
$369$	−1.82542	+	1.82542i	−0.0950276	+	0.0950276i
$370$	2.39976	−	2.39976i	0.124758	−	0.124758i
$371$	4.41455	+	25.5333i	0.229192	+	1.32562i
$372$	−2.62435	+	2.62435i	−0.136066	+	0.136066i
$373$	−5.96731			−0.308976			−0.154488	−	0.987995i	$-0.549373\pi$
$373$	−5.96731			−0.308976			−0.154488	+	0.987995i	$0.549373\pi$
$374$	3.53583			0.182834
$375$	−10.0102	+	10.0102i	−0.516926	+	0.516926i
$376$	7.47204			0.385341
$377$	−12.7355	+	1.05090i	−0.655912	+	0.0541239i
$378$	6.80606	+	4.79953i	0.350066	+	0.246861i
$379$	2.14117	+	2.14117i	0.109984	+	0.109984i	0.759957	−	0.649973i	$-0.225220\pi$
$379$	2.14117	+	2.14117i	0.109984	+	0.109984i	−0.649973	+	0.759957i	$0.725220\pi$
$380$	−12.4264			−0.637463
$381$	−1.90914			−0.0978080
$382$	−1.49341	−	1.49341i	−0.0764097	−	0.0764097i
$383$	−2.91152	+	2.91152i	−0.148772	+	0.148772i	−0.777569	−	0.628798i	$-0.783547\pi$
$383$	−2.91152	+	2.91152i	−0.148772	+	0.148772i	0.628798	+	0.777569i	$0.283547\pi$
$384$	−10.0518	−	10.0518i	−0.512956	−	0.512956i
$385$	−3.21295	+	0.555500i	−0.163747	+	0.0283109i
$386$	13.7440			0.699552
$387$		−	12.8315i		−	0.652260i
$388$	−10.1482	−	10.1482i	−0.515195	−	0.515195i
$389$			17.4436i			0.884425i	0.896910	+	0.442212i	$0.145806\pi$
$389$			17.4436i			0.884425i	−0.896910	+	0.442212i	$0.854194\pi$
$390$	−0.304041	−	3.68458i	−0.0153957	−	0.186576i
$391$			32.6516i			1.65126i
$392$	6.28529	−	13.2477i	0.317455	−	0.669109i
$393$	6.55008			0.330408
$394$			6.46310i			0.325606i
$395$	4.95336	−	4.95336i	0.249230	−	0.249230i
$396$	1.48119	+	1.48119i	0.0744328	+	0.0744328i
$397$	−10.1870	−	10.1870i	−0.511270	−	0.511270i	0.403645	−	0.914916i	$-0.367743\pi$
$397$	−10.1870	−	10.1870i	−0.511270	−	0.511270i	−0.914916	+	0.403645i	$0.867743\pi$
$398$	−1.84410	−	1.84410i	−0.0924365	−	0.0924365i
$399$	9.54912	−	13.5413i	0.478054	−	0.677914i
$400$		−	6.18664i		−	0.309332i
$401$	15.5950	−	15.5950i	0.778776	−	0.778776i	−0.200846	−	0.979623i	$-0.564369\pi$
$401$	15.5950	−	15.5950i	0.778776	−	0.778776i	0.979623	+	0.200846i	$0.0643692\pi$
$402$	−8.71050			−0.434440
$403$	4.19100	−	4.94486i	0.208768	−	0.246321i
$404$			21.5600i			1.07265i
$405$	2.43859	−	2.43859i	0.121174	−	0.121174i
$406$	3.08015	−	4.36786i	0.152865	−	0.216773i
$407$			3.44358i			0.170692i
$408$	13.4133	+	13.4133i	0.664056	+	0.664056i
$409$	−1.79921	+	1.79921i	−0.0889652	+	0.0889652i	−0.750189	−	0.661224i	$-0.770037\pi$
$409$	−1.79921	+	1.79921i	−0.0889652	+	0.0889652i	0.661224	+	0.750189i	$0.270037\pi$
$410$	−1.02539	+	1.02539i	−0.0506405	+	0.0506405i
$411$	−15.6708	−	15.6708i	−0.772983	−	0.772983i
$412$		−	10.2445i		−	0.504710i
$413$	2.34979	−	3.33216i	0.115626	−	0.163965i
$414$	2.65268	−	2.65268i	0.130372	−	0.130372i
$415$		−	25.4264i		−	1.24813i
$416$	14.9038	+	12.6316i	0.730718	+	0.619317i
$417$	−8.56230			−0.419297
$418$	−1.72909	+	1.72909i	−0.0845728	+	0.0845728i
$419$		−	16.5064i		−	0.806392i	−0.915114	−	0.403196i	$-0.867899\pi$
$419$		−	16.5064i		−	0.806392i	0.915114	−	0.403196i	$-0.132101\pi$
$420$	−6.51601	−	4.59498i	−0.317949	−	0.224212i
$421$	−8.53492	−	8.53492i	−0.415967	−	0.415967i	0.467844	−	0.883811i	$-0.345031\pi$
$421$	−8.53492	−	8.53492i	−0.415967	−	0.415967i	−0.883811	+	0.467844i	$0.845031\pi$
$422$	0.239412	+	0.239412i	0.0116544	+	0.0116544i
$423$	−3.73602	−	3.73602i	−0.181651	−	0.181651i
$424$	14.5066	−	14.5066i	0.704502	−	0.704502i
$425$			21.0820i			1.02263i
$426$	1.45635			0.0705602
$427$	18.5338	−	3.20438i	0.896911	−	0.155071i
$428$		−	14.8568i		−	0.718133i
$429$	2.86177	+	2.42548i	0.138168	+	0.117103i
$430$		−	7.20780i		−	0.347591i
$431$	24.2071	+	24.2071i	1.16602	+	1.16602i	0.983135	+	0.182880i	$0.0585421\pi$
$431$	24.2071	+	24.2071i	1.16602	+	1.16602i	0.182880	+	0.983135i	$0.441458\pi$
$432$			11.9086i			0.572951i
$433$	35.8708			1.72384			0.861920	−	0.507044i	$-0.169262\pi$
$433$	35.8708			1.72384			0.861920	+	0.507044i	$0.169262\pi$
$434$	0.461874	+	2.67143i	0.0221707	+	0.128233i
$435$	−4.50857	−	4.50857i	−0.216169	−	0.216169i
$436$	−7.70052	+	7.70052i	−0.368788	+	0.368788i
$437$	−15.9673	−	15.9673i	−0.763819	−	0.763819i
$438$	−0.103170			−0.00492967
$439$	−10.5299			−0.502563			−0.251281	−	0.967914i	$-0.580852\pi$
$439$	−10.5299			−0.502563			−0.251281	+	0.967914i	$0.580852\pi$
$440$	1.82542	+	1.82542i	0.0870236	+	0.0870236i
$441$	−9.76648	+	3.48119i	−0.465071	+	0.165771i
$442$	−11.5198	−	9.76353i	−0.547939	−	0.464404i
$443$	12.8618			0.611081			0.305541	−	0.952179i	$-0.401163\pi$
$443$	12.8618			0.611081			0.305541	+	0.952179i	$0.401163\pi$
$444$	−5.95428	+	5.95428i	−0.282578	+	0.282578i
$445$	−14.2243			−0.674294
$446$	2.30344			0.109071
$447$	−13.5137	+	13.5137i	−0.639174	+	0.639174i
$448$	3.19172	−	0.551829i	0.150795	−	0.0260715i
$449$	9.65069	−	9.65069i	0.455444	−	0.455444i	−0.441712	−	0.897157i	$-0.645629\pi$
$449$	9.65069	−	9.65069i	0.455444	−	0.455444i	0.897157	+	0.441712i	$0.145629\pi$
$450$	1.71274	−	1.71274i	0.0807394	−	0.0807394i
$451$		−	1.47141i		−	0.0692858i
$452$		−	2.69227i		−	0.126634i
$453$	−7.56836	−	7.56836i	−0.355593	−	0.355593i
$454$	−15.8448			−0.743631
$455$	12.0017	+	7.06213i	0.562649	+	0.331078i
$456$	−13.1187			−0.614340
$457$	−22.1217	−	22.1217i	−1.03481	−	1.03481i	−0.999372	−	0.0354353i	$-0.988718\pi$
$457$	−22.1217	−	22.1217i	−1.03481	−	1.03481i	−0.0354353	−	0.999372i	$-0.511282\pi$
$458$		−	10.6449i		−	0.497402i
$459$		−	40.5804i		−	1.89413i
$460$	−7.68337	+	7.68337i	−0.358239	+	0.358239i
$461$	−0.593023	+	0.593023i	−0.0276198	+	0.0276198i	−0.720782	−	0.693162i	$-0.756217\pi$
$461$	−0.593023	+	0.593023i	−0.0276198	+	0.0276198i	0.693162	+	0.720782i	$0.256217\pi$
$462$	−1.54605	+	0.267304i	−0.0719289	+	0.0124361i
$463$	2.47096	−	2.47096i	0.114835	−	0.114835i	−0.647354	−	0.762189i	$-0.724124\pi$
$463$	2.47096	−	2.47096i	0.114835	−	0.114835i	0.762189	+	0.647354i	$0.224124\pi$
$464$	7.64244			0.354792
$465$	3.23424			0.149984
$466$	−6.53889	+	6.53889i	−0.302908	+	0.302908i
$467$	13.3860			0.619432			0.309716	−	0.950829i	$-0.399766\pi$
$467$	13.3860			0.619432			0.309716	+	0.950829i	$0.399766\pi$
$468$	−0.735703	−	8.91577i	−0.0340079	−	0.412132i
$469$	18.9076	−	26.8123i	0.873073	−	1.23808i
$470$	−2.09863	−	2.09863i	−0.0968026	−	0.0968026i
$471$	11.9516			0.550700
$472$	−3.22817			−0.148589
$473$	5.17148	+	5.17148i	0.237785	+	0.237785i
$474$	2.38353	−	2.38353i	0.109479	−	0.109479i
$475$	−10.3095	−	10.3095i	−0.473034	−	0.473034i
$476$	−32.0903	+	5.54821i	−1.47085	+	0.254302i
$477$	−14.5066			−0.664211
$478$			0.680055i			0.0311050i
$479$	8.85827	+	8.85827i	0.404745	+	0.404745i	0.879901	−	0.475157i	$-0.157609\pi$
$479$	8.85827	+	8.85827i	0.404745	+	0.404745i	−0.475157	+	0.879901i	$0.657609\pi$
$480$			9.74798i			0.444933i
$481$	9.50879	−	11.2192i	0.433564	−	0.511552i
$482$			12.3301i			0.561619i
$483$	−2.46841	−	14.2770i	−0.112317	−	0.649627i
$484$	17.2325			0.783296
$485$			12.5066i			0.567895i
$486$	−5.50394	+	5.50394i	−0.249664	+	0.249664i
$487$	17.9805	+	17.9805i	0.814774	+	0.814774i	0.985345	−	0.170572i	$-0.0545614\pi$
$487$	17.9805	+	17.9805i	0.814774	+	0.814774i	−0.170572	+	0.985345i	$0.554561\pi$
$488$	−10.5299	−	10.5299i	−0.476664	−	0.476664i
$489$	6.67130	+	6.67130i	0.301687	+	0.301687i
$490$	−5.48612	+	1.95549i	−0.247838	+	0.0883400i
$491$			19.4944i			0.879769i	0.898054	+	0.439884i	$0.144981\pi$
$491$			19.4944i			0.879769i	−0.898054	+	0.439884i	$0.855019\pi$
$492$	2.54420	−	2.54420i	0.114701	−	0.114701i
$493$	−26.0429			−1.17291
$494$	10.4080	−	0.858833i	0.468276	−	0.0386407i
$495$		−	1.82542i		−	0.0820466i
$496$	−2.74117	+	2.74117i	−0.123082	+	0.123082i
$497$	−3.16125	+	4.48287i	−0.141801	+	0.201084i
$498$		−	12.2351i		−	0.548266i
$499$	10.2150	+	10.2150i	0.457285	+	0.457285i	0.897763	−	0.440478i	$-0.145191\pi$
$499$	10.2150	+	10.2150i	0.457285	+	0.457285i	−0.440478	+	0.897763i	$0.645191\pi$
$500$	−13.6064	+	13.6064i	−0.608495	+	0.608495i
$501$	−10.9785	+	10.9785i	−0.490483	+	0.490483i
$502$	11.0578	+	11.0578i	0.493536	+	0.493536i
$503$			31.8196i			1.41877i	0.704824	+	0.709383i	$0.251026\pi$
$503$			31.8196i			1.41877i	−0.704824	+	0.709383i	$0.748974\pi$
$504$	6.70866	+	4.73084i	0.298828	+	0.210728i
$505$	13.2853	−	13.2853i	0.591187	−	0.591187i
$506$			2.13823i			0.0950558i
$507$	−2.62616	−	15.8045i	−0.116632	−	0.701901i
$508$	−2.59498			−0.115134
$509$	13.6139	−	13.6139i	0.603425	−	0.603425i	−0.337795	−	0.941220i	$-0.609681\pi$
$509$	13.6139	−	13.6139i	0.603425	−	0.603425i	0.941220	+	0.337795i	$0.109681\pi$
$510$		−	7.53462i		−	0.333639i
$511$	0.223949	−	0.317575i	0.00990691	−	0.0140487i
$512$	−14.6497	−	14.6497i	−0.647433	−	0.647433i
$513$	19.8446	+	19.8446i	0.876162	+	0.876162i
$514$	8.29145	+	8.29145i	0.365720	+	0.365720i
$515$	−6.31265	+	6.31265i	−0.278169	+	0.278169i
$516$			17.8840i			0.787298i
$517$	3.01147			0.132444
$518$	1.04793	+	6.06110i	0.0460433	+	0.266310i
$519$			8.81828i			0.387080i
$520$	−0.906679	−	10.9878i	−0.0397605	−	0.481846i
$521$		−	21.6750i		−	0.949601i	−0.880094	−	0.474800i	$-0.842520\pi$
$521$		−	21.6750i		−	0.949601i	0.880094	−	0.474800i	$-0.157480\pi$
$522$	2.11577	+	2.11577i	0.0926049	+	0.0926049i
$523$		−	8.77309i		−	0.383620i	−0.981432	−	0.191810i	$-0.938564\pi$
$523$		−	8.77309i		−	0.383620i	0.981432	−	0.191810i	$-0.0614358\pi$
$524$	8.90316			0.388936
$525$	−1.59377	−	9.21818i	−0.0695577	−	0.402314i
$526$	9.61507	+	9.61507i	0.419237	+	0.419237i
$527$	9.34098	−	9.34098i	0.406900	−	0.406900i
$528$	−1.58641	−	1.58641i	−0.0690398	−	0.0690398i
$529$	3.25457			0.141503
$530$	−8.14877			−0.353960
$531$	1.61409	+	1.61409i	0.0700453	+	0.0700453i
$532$	12.9796	−	18.4060i	0.562737	−	0.798000i
$533$	−4.06300	+	4.79384i	−0.175988	+	0.207644i
$534$	−6.84463			−0.296196
$535$	−9.15478	+	9.15478i	−0.395796	+	0.395796i
$536$	−25.9756			−1.12197
$537$	17.0218			0.734546
$538$	0.446720	−	0.446720i	0.0192595	−	0.0192595i
$539$	2.53317	−	5.33923i	0.109111	−	0.229977i
$540$	9.54912	−	9.54912i	0.410929	−	0.410929i
$541$	−23.2853	+	23.2853i	−1.00111	+	1.00111i	−0.00111270	+	0.999999i	$0.500354\pi$
$541$	−23.2853	+	23.2853i	−1.00111	+	1.00111i	−0.999999	+	0.00111270i	$0.999646\pi$
$542$			16.8382i			0.723260i
$543$		−	5.62038i		−	0.241193i
$544$	28.1537	+	28.1537i	1.20708	+	1.20708i
$545$	9.49011			0.406512
$546$	5.77516	+	3.39826i	0.247154	+	0.145432i
$547$	−15.1744			−0.648812			−0.324406	−	0.945918i	$-0.605164\pi$
$547$	−15.1744			−0.648812			−0.324406	+	0.945918i	$0.605164\pi$
$548$	−21.3004	−	21.3004i	−0.909909	−	0.909909i
$549$			10.5299i			0.449403i
$550$			1.38058i			0.0588681i
$551$	12.7355	−	12.7355i	0.542551	−	0.542551i
$552$	−8.11141	+	8.11141i	−0.345245	+	0.345245i
$553$	2.16303	+	12.5107i	0.0919815	+	0.532011i
$554$	−10.4089	+	10.4089i	−0.442232	+	0.442232i
$555$	7.33804			0.311483
$556$	−11.6383			−0.493572
$557$	8.45676	−	8.45676i	0.358324	−	0.358324i	−0.504871	−	0.863195i	$-0.668460\pi$
$557$	8.45676	−	8.45676i	0.358324	−	0.358324i	0.863195	+	0.504871i	$0.168460\pi$
$558$	−1.51776			−0.0642518
$559$	−2.56865	−	31.1288i	−0.108642	−	1.31661i
$560$	−6.80606	−	4.79953i	−0.287609	−	0.202817i
$561$	5.40597	+	5.40597i	0.228240	+	0.228240i
$562$	−9.73577			−0.410678
$563$	−6.34858			−0.267561			−0.133780	−	0.991011i	$-0.542712\pi$
$563$	−6.34858			−0.267561			−0.133780	+	0.991011i	$0.542712\pi$
$564$	5.20711	+	5.20711i	0.219259	+	0.219259i
$565$	−1.65898	+	1.65898i	−0.0697937	+	0.0697937i
$566$	−6.19329	−	6.19329i	−0.260323	−	0.260323i
$567$	1.06488	+	6.15916i	0.0447208	+	0.258660i
$568$	4.34297			0.182227
$569$			36.6140i			1.53494i	0.641085	+	0.767470i	$0.278485\pi$
$569$			36.6140i			1.53494i	−0.641085	+	0.767470i	$0.721515\pi$
$570$	3.68458	+	3.68458i	0.154330	+	0.154330i
$571$		−	18.8070i		−	0.787049i	−0.919314	−	0.393525i	$-0.871256\pi$
$571$		−	18.8070i		−	0.787049i	0.919314	−	0.393525i	$-0.128744\pi$
$572$	3.88985	+	3.29683i	0.162643	+	0.137847i
$573$		−	4.56659i		−	0.190772i
$574$	−0.447768	−	2.58984i	−0.0186895	−	0.108098i
$575$	−12.7489			−0.531668
$576$			1.81336i			0.0755566i
$577$	−31.3416	+	31.3416i	−1.30477	+	1.30477i	−0.379627	+	0.925140i	$0.623948\pi$
$577$	−31.3416	+	31.3416i	−1.30477	+	1.30477i	−0.925140	+	0.379627i	$0.876052\pi$
$578$	−14.9096	−	14.9096i	−0.620158	−	0.620158i
$579$	21.0134	+	21.0134i	0.873285	+	0.873285i
$580$	−6.12825	−	6.12825i	−0.254462	−	0.254462i
$581$	37.6615	+	26.5583i	1.56246	+	1.10182i
$582$			6.01810i			0.249458i
$583$	5.84661	−	5.84661i	0.242142	−	0.242142i
$584$	−0.307664			−0.0127312
$585$	−5.04055	+	5.94723i	−0.208401	+	0.245888i
$586$		−	7.88864i		−	0.325877i
$587$	−3.36694	+	3.36694i	−0.138969	+	0.138969i	−0.773169	−	0.634200i	$-0.781329\pi$
$587$	−3.36694	+	3.36694i	−0.138969	+	0.138969i	0.634200	+	0.773169i	$0.281329\pi$
$588$	13.6121	−	4.85195i	0.561355	−	0.200091i
$589$			9.13586i			0.376436i
$590$	0.906679	+	0.906679i	0.0373274	+	0.0373274i
$591$	−9.88149	+	9.88149i	−0.406470	+	0.406470i
$592$	−6.21933	+	6.21933i	−0.255613	+	0.255613i
$593$	−10.6837	−	10.6837i	−0.438726	−	0.438726i	0.452857	−	0.891583i	$-0.350405\pi$
$593$	−10.6837	−	10.6837i	−0.438726	−	0.438726i	−0.891583	+	0.452857i	$0.850405\pi$
$594$		−	2.65745i		−	0.109037i
$595$	23.1928	+	16.3552i	0.950812	+	0.670497i
$596$	−18.3684	+	18.3684i	−0.752397	+	0.752397i
$597$		−	5.63893i		−	0.230786i
$598$	5.90430	−	6.96635i	0.241445	−	0.284875i
$599$	−12.8437			−0.524778			−0.262389	−	0.964962i	$-0.584510\pi$
$599$	−12.8437			−0.524778			−0.262389	+	0.964962i	$0.584510\pi$
$600$	−5.23726	+	5.23726i	−0.213810	+	0.213810i
$601$			19.5732i			0.798409i	0.916862	+	0.399205i	$0.130714\pi$
$601$			19.5732i			0.798409i	−0.916862	+	0.399205i	$0.869286\pi$
$602$	10.6762	+	7.52865i	0.435128	+	0.306845i
$603$	12.9878	+	12.9878i	0.528903	+	0.528903i
$604$	−10.2873	−	10.2873i	−0.418583	−	0.418583i
$605$	−10.6187	−	10.6187i	−0.431710	−	0.431710i
$606$	6.39280	−	6.39280i	0.259690	−	0.259690i
$607$		−	41.9804i		−	1.70393i	−0.523598	−	0.851965i	$-0.675411\pi$
$607$		−	41.9804i		−	1.70393i	0.523598	−	0.851965i	$-0.324589\pi$
$608$	−27.5354			−1.11671
$609$	11.3873	−	1.96880i	0.461438	−	0.0797799i
$610$			5.91493i			0.239488i
$611$	−9.81137	−	8.31559i	−0.396926	−	0.336413i
$612$		−	18.2319i		−	0.736981i
$613$	20.4993	+	20.4993i	0.827959	+	0.827959i	0.987234	−	0.159276i	$-0.0509158\pi$
$613$	20.4993	+	20.4993i	0.827959	+	0.827959i	−0.159276	+	0.987234i	$0.550916\pi$
$614$		−	6.56236i		−	0.264835i
$615$	−3.13547			−0.126434
$616$	−4.61048	+	0.797125i	−0.185762	+	0.0321171i
$617$	8.21440	+	8.21440i	0.330699	+	0.330699i	0.852852	−	0.522153i	$-0.174871\pi$
$617$	8.21440	+	8.21440i	0.330699	+	0.330699i	−0.522153	+	0.852852i	$0.674871\pi$
$618$	−3.03761	+	3.03761i	−0.122191	+	0.122191i
$619$	−26.6973	−	26.6973i	−1.07306	−	1.07306i	−0.997112	−	0.0759445i	$-0.975803\pi$
$619$	−26.6973	−	26.6973i	−1.07306	−	1.07306i	−0.0759445	−	0.997112i	$-0.524197\pi$
$620$	4.39612			0.176553
$621$	24.5402			0.984764
$622$	−13.0910	−	13.0910i	−0.524900	−	0.524900i
$623$	14.8574	−	21.0689i	0.595251	−	0.844107i
$624$	0.787965	+	9.54912i	0.0315438	+	0.382271i
$625$	2.42311			0.0969246
$626$	−7.95367	+	7.95367i	−0.317893	+	0.317893i
$627$	−5.28726			−0.211153
$628$	16.2451			0.648251
$629$	21.1934	−	21.1934i	0.845036	−	0.845036i
$630$	−0.555500	−	3.21295i	−0.0221317	−	0.128007i
$631$	5.13093	−	5.13093i	0.204259	−	0.204259i	−0.597563	−	0.801822i	$-0.703864\pi$
$631$	5.13093	−	5.13093i	0.204259	−	0.204259i	0.801822	+	0.597563i	$0.203864\pi$
$632$	7.10791	−	7.10791i	0.282737	−	0.282737i
$633$			0.732080i			0.0290976i
$634$			6.54420i			0.259903i
$635$	1.59903	+	1.59903i	0.0634554	+	0.0634554i
$636$	20.2187			0.801723
$637$	−22.9963	+	10.4004i	−0.911149	+	0.412078i
$638$	−1.70545			−0.0675193
$639$	−2.17148	−	2.17148i	−0.0859026	−	0.0859026i
$640$			16.8382i			0.665586i
$641$		−	16.3357i		−	0.645220i	−0.946532	−	0.322610i	$-0.895440\pi$
$641$		−	16.3357i		−	0.645220i	0.946532	−	0.322610i	$-0.104560\pi$
$642$	−4.40523	+	4.40523i	−0.173860	+	0.173860i
$643$	−28.1910	+	28.1910i	−1.11175	+	1.11175i	−0.118832	+	0.992914i	$0.537915\pi$
$643$	−28.1910	+	28.1910i	−1.11175	+	1.11175i	−0.992914	+	0.118832i	$0.962085\pi$
$644$	−3.35517	−	19.4060i	−0.132212	−	0.764702i
$645$	11.0201	−	11.0201i	0.433915	−	0.433915i
$646$	21.2833			0.837380
$647$	−11.1139			−0.436932			−0.218466	−	0.975845i	$-0.570105\pi$
$647$	−11.1139			−0.436932			−0.218466	+	0.975845i	$0.570105\pi$
$648$	3.49929	−	3.49929i	0.137465	−	0.137465i
$649$	−1.30105			−0.0510709
$650$	3.81220	−	4.49793i	0.149527	−	0.176423i
$651$	−3.37821	+	4.79054i	−0.132402	+	0.187756i
$652$	9.06793	+	9.06793i	0.355127	+	0.355127i
$653$	4.95651			0.193963			0.0969816	−	0.995286i	$-0.469081\pi$
$653$	4.95651			0.193963			0.0969816	+	0.995286i	$0.469081\pi$
$654$	4.56659			0.178568
$655$	−5.48612	−	5.48612i	−0.214360	−	0.214360i
$656$	2.65745	−	2.65745i	0.103756	−	0.103756i
$657$	0.153832	+	0.153832i	0.00600155	+	0.00600155i
$658$	5.30053	−	0.916430i	0.206636	−	0.0357262i
$659$	26.1514			1.01871			0.509357	−	0.860555i	$-0.329883\pi$
$659$	26.1514			1.01871			0.509357	+	0.860555i	$0.329883\pi$
$660$			2.54420i			0.0990328i
$661$	22.2906	+	22.2906i	0.867006	+	0.867006i	0.992140	−	0.125134i	$-0.0399361\pi$
$661$	22.2906	+	22.2906i	0.867006	+	0.867006i	−0.125134	+	0.992140i	$0.539936\pi$
$662$			0.649738i			0.0252528i
$663$	−2.68512	−	32.5402i	−0.104282	−	1.26376i
$664$		−	36.4861i		−	1.41594i
$665$	−19.3398	+	3.34373i	−0.749964	+	0.129664i
$666$	−3.44358			−0.133436
$667$		−	15.7489i		−	0.609801i
$668$	−14.9225	+	14.9225i	−0.577368	+	0.577368i
$669$	3.52175	+	3.52175i	0.136159	+	0.136159i
$670$	7.29562	+	7.29562i	0.281854	+	0.281854i
$671$	−4.24387	−	4.24387i	−0.163833	−	0.163833i
$672$	−14.4387	−	10.1819i	−0.556983	−	0.392776i
$673$			1.38550i			0.0534072i	0.999643	+	0.0267036i	$0.00850104\pi$
$673$			1.38550i			0.0534072i	−0.999643	+	0.0267036i	$0.991499\pi$
$674$	10.7230	−	10.7230i	0.413034	−	0.413034i
$675$	15.8448			0.609865
$676$	−3.56959	−	21.4821i	−0.137292	−	0.826237i
$677$		−	14.1868i		−	0.545242i	−0.962122	−	0.272621i	$-0.912110\pi$
$677$		−	14.1868i		−	0.545242i	0.962122	−	0.272621i	$-0.0878905\pi$
$678$	−0.798290	+	0.798290i	−0.0306582	+	0.0306582i
$679$	−18.5247	−	13.0633i	−0.710912	−	0.501324i
$680$		−	22.4690i		−	0.861646i
$681$	−24.2252	−	24.2252i	−0.928312	−	0.928312i
$682$	0.611704	−	0.611704i	0.0234234	−	0.0234234i
$683$	27.2882	−	27.2882i	1.04415	−	1.04415i	0.0451754	−	0.998979i	$-0.485615\pi$
$683$	27.2882	−	27.2882i	1.04415	−	1.04415i	0.998979	−	0.0451754i	$-0.0143847\pi$
$684$	8.91577	+	8.91577i	0.340903	+	0.340903i
$685$			26.2506i			1.00298i
$686$	2.83387	−	10.1685i	0.108198	−	0.388237i
$687$	16.2750	−	16.2750i	0.620931	−	0.620931i
$688$			18.6801i			0.712170i
$689$	−35.1926	+	2.90399i	−1.34073	+	0.110633i
$690$	4.55642			0.173460
$691$	−16.1937	+	16.1937i	−0.616037	+	0.616037i	−0.944513	−	0.328475i	$-0.893465\pi$
$691$	−16.1937	+	16.1937i	−0.616037	+	0.616037i	0.328475	+	0.944513i	$0.393465\pi$
$692$			11.9862i			0.455647i
$693$	2.70380	+	1.90668i	0.102709	+	0.0724287i
$694$	8.14411	+	8.14411i	0.309146	+	0.309146i
$695$	7.17148	+	7.17148i	0.272030	+	0.272030i
$696$	−6.46966	−	6.46966i	−0.245232	−	0.245232i
$697$	−9.05571	+	9.05571i	−0.343009	+	0.343009i
$698$		−	1.86570i		−	0.0706180i
$699$	−19.9947			−0.756271
$700$	−2.16632	−	12.5298i	−0.0818792	−	0.473580i
$701$		−	15.2981i		−	0.577800i	−0.957359	−	0.288900i	$-0.906711\pi$
$701$		−	15.2981i		−	0.577800i	0.957359	−	0.288900i	$-0.0932895\pi$
$702$	−7.33804	+	8.65799i	−0.276957	+	0.326775i
$703$			20.7280i			0.781771i
$704$	−0.730841	−	0.730841i	−0.0275446	−	0.0275446i
$705$		−	6.41723i		−	0.241687i
$706$	−8.65808			−0.325851
$707$	5.80141	+	33.5547i	0.218185	+	1.26196i
$708$	−2.24965	−	2.24965i	−0.0845469	−	0.0845469i
$709$	−2.74107	+	2.74107i	−0.102943	+	0.102943i	−0.756703	−	0.653759i	$-0.773191\pi$
$709$	−2.74107	+	2.74107i	−0.102943	+	0.102943i	0.653759	+	0.756703i	$0.273191\pi$
$710$	−1.21979	−	1.21979i	−0.0457778	−	0.0457778i
$711$	−7.10791			−0.266567
$712$	−20.4113			−0.764948
$713$	5.64878	+	5.64878i	0.211548	+	0.211548i
$714$	11.1602	+	7.87002i	0.417662	+	0.294528i
$715$	−0.365420	−	4.42842i	−0.0136659	−	0.165614i
$716$	23.1368			0.864663
$717$	−1.03974	+	1.03974i	−0.0388299	+	0.0388299i
$718$	13.6810			0.510571
$719$	5.99456			0.223559			0.111780	−	0.993733i	$-0.464345\pi$
$719$	5.99456			0.223559			0.111780	+	0.993733i	$0.464345\pi$
$720$	3.29683	−	3.29683i	0.122865	−	0.122865i
$721$	−2.75661	−	15.9439i	−0.102661	−	0.593782i
$722$	−2.75035	+	2.75035i	−0.102358	+	0.102358i
$723$	−18.8515	+	18.8515i	−0.701096	+	0.701096i
$724$		−	7.63947i		−	0.283919i
$725$		−	10.1685i		−	0.377650i
$726$	−5.10964	−	5.10964i	−0.189636	−	0.189636i
$727$	−14.6184			−0.542168			−0.271084	−	0.962556i	$-0.587382\pi$
$727$	−14.6184			−0.542168			−0.271084	+	0.962556i	$0.587382\pi$
$728$	17.2221	+	10.1339i	0.638293	+	0.375588i
$729$	−23.9175			−0.885833
$730$	0.0864119	+	0.0864119i	0.00319825	+	0.00319825i
$731$		−	63.6554i		−	2.35438i
$732$		−	14.6761i		−	0.542444i
$733$	28.0685	−	28.0685i	1.03673	−	1.03673i	0.0374350	−	0.999299i	$-0.488081\pi$
$733$	28.0685	−	28.0685i	1.03673	−	1.03673i	0.999299	−	0.0374350i	$-0.0119187\pi$
$734$	3.94881	−	3.94881i	0.145753	−	0.145753i
$735$	−11.3775	−	5.39802i	−0.419667	−	0.199109i
$736$	−17.0254	+	17.0254i	−0.627564	+	0.627564i
$737$	−10.4690			−0.385630
$738$	1.47141			0.0541632
$739$	−16.6028	+	16.6028i	−0.610746	+	0.610746i	−0.943140	−	0.332395i	$-0.892143\pi$
$739$	−16.6028	+	16.6028i	−0.610746	+	0.610746i	0.332395	+	0.943140i	$0.392143\pi$
$740$	9.97420			0.366659
$741$	17.2259	+	14.5997i	0.632809	+	0.536335i
$742$	8.51151	−	12.0699i	0.312467	−	0.443101i
$743$	−2.87636	−	2.87636i	−0.105523	−	0.105523i	0.652374	−	0.757897i	$-0.273773\pi$
$743$	−2.87636	−	2.87636i	−0.105523	−	0.105523i	−0.757897	+	0.652374i	$0.773773\pi$
$744$	4.64103			0.170148
$745$	22.6371			0.829361
$746$	2.40502	+	2.40502i	0.0880539	+	0.0880539i
$747$	−18.2431	+	18.2431i	−0.667479	+	0.667479i
$748$	7.34804	+	7.34804i	0.268671	+	0.268671i
$749$	−3.99771	−	23.1223i	−0.146073	−	0.844871i
$750$	8.06888			0.294634
$751$		−	45.9438i		−	1.67651i	−0.545275	−	0.838257i	$-0.683575\pi$
$751$		−	45.9438i		−	1.67651i	0.545275	−	0.838257i	$-0.316425\pi$
$752$	5.43890	+	5.43890i	0.198336	+	0.198336i
$753$			33.8129i			1.23221i
$754$	5.55636	+	4.70927i	0.202351	+	0.171501i
$755$			12.6780i			0.461400i
$756$	4.16991	+	24.1183i	0.151658	+	0.877174i
$757$	−24.7889			−0.900969			−0.450484	−	0.892784i	$-0.648749\pi$
$757$	−24.7889			−0.900969			−0.450484	+	0.892784i	$0.648749\pi$
$758$		−	1.72592i		−	0.0626881i
$759$	−3.26916	+	3.26916i	−0.118663	+	0.118663i
$760$	10.9878	+	10.9878i	0.398569	+	0.398569i
$761$	−10.8450	−	10.8450i	−0.393133	−	0.393133i	0.482670	−	0.875802i	$-0.339667\pi$
$761$	−10.8450	−	10.8450i	−0.393133	−	0.393133i	−0.875802	+	0.482670i	$0.839667\pi$
$762$	0.769443	+	0.769443i	0.0278740	+	0.0278740i
$763$	−9.91256	+	14.0567i	−0.358859	+	0.508887i
$764$		−	6.20711i		−	0.224565i
$765$	−11.2345	+	11.2345i	−0.406184	+	0.406184i
$766$	2.34687			0.0847958
$767$	4.23884	+	3.59261i	0.153056	+	0.129722i
$768$			5.08489i			0.183485i
$769$	4.63670	−	4.63670i	0.167204	−	0.167204i	−0.618545	−	0.785749i	$-0.712278\pi$
$769$	4.63670	−	4.63670i	0.167204	−	0.167204i	0.785749	+	0.618545i	$0.212278\pi$
$770$	1.51881	+	1.07104i	0.0547340	+	0.0385975i
$771$			25.3538i			0.913094i
$772$	28.5623	+	28.5623i	1.02798	+	1.02798i
$773$	5.68398	−	5.68398i	0.204438	−	0.204438i	−0.597460	−	0.801899i	$-0.703823\pi$
$773$	5.68398	−	5.68398i	0.204438	−	0.204438i	0.801899	+	0.597460i	$0.203823\pi$
$774$	−5.17148	+	5.17148i	−0.185885	+	0.185885i
$775$	3.64722	+	3.64722i	0.131012	+	0.131012i
$776$			17.9466i			0.644244i
$777$	−7.66469	+	10.8691i	−0.274969	+	0.389926i
$778$	7.03032	−	7.03032i	0.252049	−	0.252049i
$779$		−	8.85685i		−	0.317330i
$780$	7.02532	−	8.28901i	0.251547	−	0.296794i
$781$	1.75035			0.0626326
$782$	13.1596	−	13.1596i	0.470588	−	0.470588i
$783$			19.5732i			0.699491i
$784$	14.2181	−	5.06793i	0.507788	−	0.180997i
$785$	−10.0102	−	10.0102i	−0.357281	−	0.357281i
$786$	−2.63989	−	2.63989i	−0.0941617	−	0.0941617i
$787$	8.65662	+	8.65662i	0.308575	+	0.308575i	0.844357	−	0.535781i	$-0.179983\pi$
$787$	8.65662	+	8.65662i	0.308575	+	0.308575i	−0.535781	+	0.844357i	$0.679983\pi$
$788$	−13.4314	+	13.4314i	−0.478473	+	0.478473i
$789$			29.4011i			1.04671i
$790$	−3.99272			−0.142055
$791$	−0.724442	−	4.19009i	−0.0257582	−	0.148983i
$792$		−	2.61942i		−	0.0930771i
$793$	2.10791	+	25.5452i	0.0748541	+	0.907135i
$794$			8.21136i			0.291410i
$795$	−12.4587	−	12.4587i	−0.441866	−	0.441866i
$796$		−	7.66469i		−	0.271668i
$797$	28.1163			0.995931			0.497966	−	0.867197i	$-0.334081\pi$
$797$	28.1163			0.995931			0.497966	+	0.867197i	$0.334081\pi$
$798$	−9.30618	+	1.60898i	−0.329435	+	0.0569574i
$799$	−18.5340	−	18.5340i	−0.655685	−	0.655685i
$800$	−10.9927	+	10.9927i	−0.388651	+	0.388651i
$801$	10.2057	+	10.2057i	0.360600	+	0.360600i
$802$	−12.5705			−0.443881
$803$	−0.123998			−0.00437580
$804$	−18.1018	−	18.1018i	−0.638403	−	0.638403i
$805$	−9.89048	+	14.0254i	−0.348594	+	0.494330i
$806$	−3.68204	+	0.303831i	−0.129694	+	0.0107020i
$807$	1.36599			0.0480851
$808$	19.0639	−	19.0639i	0.670667	−	0.670667i
$809$	0.687350			0.0241659			0.0120830	−	0.999927i	$-0.496154\pi$
$809$	0.687350			0.0241659			0.0120830	+	0.999927i	$0.496154\pi$
$810$	−1.96566			−0.0690661
$811$	0.354016	−	0.354016i	0.0124312	−	0.0124312i	−0.700864	−	0.713295i	$-0.747202\pi$
$811$	0.354016	−	0.354016i	0.0124312	−	0.0124312i	0.713295	+	0.700864i	$0.247202\pi$
$812$	15.4782	−	2.67608i	0.543178	−	0.0939122i
$813$	−25.7440	+	25.7440i	−0.902882	+	0.902882i
$814$	1.38787	−	1.38787i	0.0486449	−	0.0486449i
$815$		−	11.1753i		−	0.391454i
$816$			19.5271i			0.683584i
$817$	31.1288	+	31.1288i	1.08906	+	1.08906i
$818$	1.45028			0.0507078
$819$	−3.54408	−	13.6780i	−0.123840	−	0.477948i
$820$	−4.26187			−0.148831
$821$	20.8773	+	20.8773i	0.728623	+	0.728623i	0.970346	−	0.241722i	$-0.0777122\pi$
$821$	20.8773	+	20.8773i	0.728623	+	0.728623i	−0.241722	+	0.970346i	$0.577712\pi$
$822$			12.6316i			0.440579i
$823$			10.3611i			0.361164i	0.983560	+	0.180582i	$0.0577981\pi$
$823$			10.3611i			0.361164i	−0.983560	+	0.180582i	$0.942202\pi$
$824$	−9.05845	+	9.05845i	−0.315566	+	0.315566i
$825$	−2.11078	+	2.11078i	−0.0734880	+	0.0734880i
$826$	−2.29001	+	0.395928i	−0.0796795	+	0.0137761i
$827$	33.3235	−	33.3235i	1.15877	−	1.15877i	0.174030	−	0.984740i	$-0.444321\pi$
$827$	33.3235	−	33.3235i	1.15877	−	1.15877i	0.984740	−	0.174030i	$-0.0556789\pi$
$828$	11.0254			0.383159
$829$	19.8647			0.689929			0.344964	−	0.938616i	$-0.387891\pi$
$829$	19.8647			0.689929			0.344964	+	0.938616i	$0.387891\pi$
$830$	−10.2477	+	10.2477i	−0.355702	+	0.355702i
$831$	−31.8286			−1.10412
$832$	0.363005	+	4.39916i	0.0125849	+	0.152513i
$833$	−48.4504	+	17.2698i	−1.67871	+	0.598364i
$834$	3.45088	+	3.45088i	0.119494	+	0.119494i
$835$	18.3904			0.636427
$836$	−7.18668			−0.248556
$837$	−7.02047	−	7.02047i	−0.242663	−	0.242663i
$838$	−6.65262	+	6.65262i	−0.229811	+	0.229811i
$839$	16.2048	+	16.2048i	0.559453	+	0.559453i	0.929152	−	0.369698i	$-0.120539\pi$
$839$	16.2048	+	16.2048i	0.559453	+	0.559453i	−0.369698	+	0.929152i	$0.620539\pi$
$840$	1.69862	+	9.82463i	0.0586079	+	0.338982i
$841$	−16.4387			−0.566850
$842$			6.87969i			0.237090i
$843$	−14.8851	−	14.8851i	−0.512670	−	0.512670i
$844$			0.995075i			0.0342519i
$845$	−11.0377	+	15.4369i	−0.379709	+	0.531044i
$846$			3.01147i			0.103536i
$847$	26.8196	−	4.63695i	0.921533	−	0.159328i
$848$	21.1187			0.725220
$849$		−	18.9380i		−	0.649949i
$850$	8.49672	−	8.49672i	0.291435	−	0.291435i
$851$	12.8163	+	12.8163i	0.439337	+	0.439337i
$852$	3.02653	+	3.02653i	0.103687	+	0.103687i
$853$	12.4778	+	12.4778i	0.427232	+	0.427232i	0.887684	−	0.460452i	$-0.152313\pi$
$853$	12.4778	+	12.4778i	0.427232	+	0.427232i	−0.460452	+	0.887684i	$0.652313\pi$
$854$	−8.76116	−	6.17823i	−0.299801	−	0.211415i
$855$		−	10.9878i		−	0.375774i
$856$	−13.1368	+	13.1368i	−0.449007	+	0.449007i
$857$	−27.2501			−0.930845			−0.465422	−	0.885089i	$-0.654098\pi$
$857$	−27.2501			−0.930845			−0.465422	+	0.885089i	$0.654098\pi$
$858$	−0.175838	−	2.13093i	−0.00600302	−	0.0727488i
$859$			22.7834i			0.777361i	0.921373	+	0.388680i	$0.127069\pi$
$859$			22.7834i			0.777361i	−0.921373	+	0.388680i	$0.872931\pi$
$860$	14.9790	−	14.9790i	0.510779	−	0.510779i
$861$	3.27504	−	4.64423i	0.111613	−	0.158275i
$862$		−	19.5125i		−	0.664597i
$863$	−21.1187	−	21.1187i	−0.718889	−	0.718889i	0.249488	−	0.968378i	$-0.419738\pi$
$863$	−21.1187	−	21.1187i	−0.718889	−	0.718889i	−0.968378	+	0.249488i	$0.919738\pi$
$864$	21.1597	−	21.1597i	0.719866	−	0.719866i
$865$	7.38589	−	7.38589i	0.251128	−	0.251128i
$866$	−14.4571	−	14.4571i	−0.491271	−	0.491271i
$867$		−	45.5909i		−	1.54835i
$868$	−4.59181	+	6.51151i	−0.155856	+	0.221015i
$869$	2.86471	−	2.86471i	0.0971787	−	0.0971787i
$870$			3.63419i			0.123211i
$871$	34.1080	+	28.9081i	1.15570	+	0.979513i
$872$	13.6180			0.461164
$873$	8.97328	−	8.97328i	0.303699	−	0.303699i
$874$			12.8707i			0.435356i
$875$	−17.5149	+	24.8373i	−0.592111	+	0.839655i
$876$	−0.214405	−	0.214405i	−0.00724406	−	0.00724406i
$877$	14.0455	+	14.0455i	0.474282	+	0.474282i	0.903297	−	0.429015i	$-0.141139\pi$
$877$	14.0455	+	14.0455i	0.474282	+	0.474282i	−0.429015	+	0.903297i	$0.641139\pi$
$878$	4.24387	+	4.24387i	0.143224	+	0.143224i
$879$	12.0610	−	12.0610i	0.406808	−	0.406808i
$880$			2.65745i			0.0895827i
$881$	13.3800			0.450782			0.225391	−	0.974268i	$-0.427634\pi$
$881$	13.3800			0.450782			0.225391	+	0.974268i	$0.427634\pi$
$882$	5.33923	+	2.53317i	0.179781	+	0.0852963i
$883$			1.63893i			0.0551545i	0.999620	+	0.0275773i	$0.00877923\pi$
$883$			1.63893i			0.0551545i	−0.999620	+	0.0275773i	$0.991221\pi$
$884$	−3.64974	−	44.2301i	−0.122754	−	1.48762i
$885$			2.77246i			0.0931952i
$886$	−5.18370	−	5.18370i	−0.174150	−	0.174150i
$887$		−	21.4198i		−	0.719206i	−0.933105	−	0.359603i	$-0.882912\pi$
$887$		−	21.4198i		−	0.719206i	0.933105	−	0.359603i	$-0.117088\pi$
$888$	10.5299			0.353359
$889$	−4.03868	+	0.698263i	−0.135453	+	0.0234190i
$890$	5.73283	+	5.73283i	0.192165	+	0.192165i
$891$	1.41033	−	1.41033i	0.0472477	−	0.0472477i
$892$	4.78691	+	4.78691i	0.160278	+	0.160278i
$893$	18.1270			0.606596
$894$	10.8929			0.364312
$895$	−14.2569	−	14.2569i	−0.476555	−	0.476555i
$896$	−24.9406	−	17.5877i	−0.833206	−	0.587563i
$897$	19.6781	−	1.62378i	0.657032	−	0.0542163i
$898$	−7.77907			−0.259591
$899$	−4.50546	+	4.50546i	−0.150266	+	0.150266i
$900$	7.11871			0.237290
$901$	−71.9655			−2.39752
$902$	−0.593023	+	0.593023i	−0.0197455	+	0.0197455i
$903$	4.81225	+	27.8335i	0.160142	+	0.926242i
$904$	−2.38058	+	2.38058i	−0.0791769	+	0.0791769i
$905$	−4.70743	+	4.70743i	−0.156480	+	0.156480i
$906$			6.10058i			0.202678i
$907$		−	2.59991i		−	0.0863285i	−0.999068	−	0.0431643i	$-0.986256\pi$
$907$		−	2.59991i		−	0.0863285i	0.999068	−	0.0431643i	$-0.0137439\pi$
$908$	−32.9280	−	32.9280i	−1.09275	−	1.09275i
$909$	−19.0639			−0.632311
$910$	−1.99081	−	7.68333i	−0.0659947	−	0.254700i
$911$	41.2579			1.36694			0.683468	−	0.729981i	$-0.260471\pi$
$911$	41.2579			1.36694			0.683468	+	0.729981i	$0.260471\pi$
$912$	−9.54912	−	9.54912i	−0.316203	−	0.316203i
$913$		−	14.7051i		−	0.486667i
$914$			17.8315i			0.589812i
$915$	−9.04339	+	9.04339i	−0.298965	+	0.298965i
$916$	22.1218	−	22.1218i	0.730924	−	0.730924i
$917$	13.8563	−	2.39568i	0.457577	−	0.0791123i
$918$	−16.3552	+	16.3552i	−0.539802	+	0.539802i
$919$	−48.3039			−1.59340			−0.796700	−	0.604375i	$-0.793423\pi$
$919$	−48.3039			−1.59340			−0.796700	+	0.604375i	$0.793423\pi$
$920$	13.5877			0.447972
$921$	10.0333	−	10.0333i	0.330607	−	0.330607i
$922$	0.478014			0.0157426
$923$	−5.70266	−	4.83327i	−0.187705	−	0.159089i
$924$	−3.76845	−	2.65745i	−0.123973	−	0.0874237i
$925$	8.27504	+	8.27504i	0.272082	+	0.272082i
$926$	−1.99175			−0.0654530
$927$	9.05845			0.297519
$928$	−13.5794	−	13.5794i	−0.445767	−	0.445767i
$929$	−19.1804	+	19.1804i	−0.629289	+	0.629289i	−0.947889	−	0.318600i	$-0.896787\pi$
$929$	−19.1804	+	19.1804i	−0.629289	+	0.629289i	0.318600	+	0.947889i	$0.396787\pi$
$930$	−1.30350	−	1.30350i	−0.0427435	−	0.0427435i
$931$	15.2479	−	32.1385i	0.499731	−	1.05330i
$932$	−27.1777			−0.890237
$933$		−	40.0299i		−	1.31052i
$934$	−5.39500	−	5.39500i	−0.176530	−	0.176530i
$935$		−	9.05571i		−	0.296153i
$936$	−7.23303	+	8.53408i	−0.236419	+	0.278945i
$937$		−	2.66644i		−	0.0871088i	−0.999051	−	0.0435544i	$-0.986132\pi$
$937$		−	2.66644i		−	0.0871088i	0.999051	−	0.0435544i	$-0.0138682\pi$
$938$	−18.4266	+	3.18585i	−0.601650	+	0.104022i
$939$	−24.3209			−0.793683
$940$		−	8.72259i		−	0.284500i
$941$	31.9331	−	31.9331i	1.04099	−	1.04099i	0.0418672	−	0.999123i	$-0.486669\pi$
$941$	31.9331	−	31.9331i	1.04099	−	1.04099i	0.999123	−	0.0418672i	$-0.0133307\pi$
$942$	−4.81687	−	4.81687i	−0.156942	−	0.156942i
$943$	−5.47626	−	5.47626i	−0.178332	−	0.178332i
$944$	−2.34979	−	2.34979i	−0.0764791	−	0.0764791i
$945$	12.2922	−	17.4312i	0.399865	−	0.567036i
$946$		−	4.16854i		−	0.135531i
$947$	−8.43041	+	8.43041i	−0.273951	+	0.273951i	−0.830689	−	0.556737i	$-0.812053\pi$
$947$	−8.43041	+	8.43041i	−0.273951	+	0.273951i	0.556737	+	0.830689i	$0.312053\pi$
$948$	9.90672			0.321755
$949$	0.403987	+	0.342397i	0.0131140	+	0.0111147i
$950$			8.31014i			0.269616i
$951$	−10.0055	+	10.0055i	−0.324450	+	0.324450i
$952$	33.2809	+	23.4692i	1.07864	+	0.760640i
$953$		−	20.8846i		−	0.676519i	−0.941053	−	0.338259i	$-0.890162\pi$
$953$		−	20.8846i		−	0.676519i	0.941053	−	0.338259i	$-0.109838\pi$
$954$	5.84661	+	5.84661i	0.189291	+	0.189291i
$955$	−3.82482	+	3.82482i	−0.123768	+	0.123768i
$956$	−1.41327	+	1.41327i	−0.0457083	+	0.0457083i
$957$	−2.60748	−	2.60748i	−0.0842877	−	0.0842877i
$958$		−	7.14032i		−	0.230693i
$959$	−38.8823	−	27.4191i	−1.25557	−	0.885410i
$960$	−1.55737	+	1.55737i	−0.0502640	+	0.0502640i
$961$			27.7680i			0.895742i
$962$	−8.35404	+	0.689351i	−0.269345	+	0.0222256i
$963$	13.1368			0.423328
$964$	−25.6239	+	25.6239i	−0.825289	+	0.825289i
$965$		−	35.2001i		−	1.13313i
$966$	−4.75924	+	6.74894i	−0.153126	+	0.217144i
$967$	20.9628	+	20.9628i	0.674117	+	0.674117i	0.958663	−	0.284545i	$-0.0918426\pi$
$967$	20.9628	+	20.9628i	0.674117	+	0.674117i	−0.284545	+	0.958663i	$0.591843\pi$
$968$	−15.2374	−	15.2374i	−0.489749	−	0.489749i
$969$	32.5402	+	32.5402i	1.04534	+	1.04534i
$970$	5.04055	−	5.04055i	0.161842	−	0.161842i
$971$			12.7719i			0.409869i	0.978776	+	0.204935i	$0.0656982\pi$
$971$			12.7719i			0.409869i	−0.978776	+	0.204935i	$0.934302\pi$
$972$	−22.8761			−0.733753
$973$	−18.1131	+	3.13164i	−0.580679	+	0.100396i
$974$		−	14.4934i		−	0.464399i
$975$	12.7054	−	1.04842i	0.406900	−	0.0335762i
$976$		−	15.3294i		−	0.490682i
$977$	−27.8222	−	27.8222i	−0.890110	−	0.890110i	0.104423	−	0.994533i	$-0.466701\pi$
$977$	−27.8222	−	27.8222i	−0.890110	−	0.890110i	−0.994533	+	0.104423i	$0.966701\pi$
$978$		−	5.37749i		−	0.171953i
$979$	−8.22642			−0.262918
$980$	−15.4649	−	7.33722i	−0.494007	−	0.234379i
$981$	−6.80900	−	6.80900i	−0.217395	−	0.217395i
$982$	7.85685	−	7.85685i	0.250722	−	0.250722i
$983$	35.8970	+	35.8970i	1.14494	+	1.14494i	0.987535	+	0.157402i	$0.0503119\pi$
$983$	35.8970	+	35.8970i	1.14494	+	1.14494i	0.157402	+	0.987535i	$0.449688\pi$
$984$	−4.49929			−0.143432
$985$	16.5528			0.527416
$986$	10.4961	+	10.4961i	0.334264	+	0.334264i
$987$	9.50517	+	6.70289i	0.302553	+	0.213355i
$988$	23.4142	+	19.8446i	0.744906	+	0.631342i
$989$	38.4944			1.22405
$990$	−0.735703	+	0.735703i	−0.0233822	+	0.0233822i
$991$	−8.69418			−0.276180			−0.138090	−	0.990420i	$-0.544096\pi$
$991$	−8.69418			−0.276180			−0.138090	+	0.990420i	$0.544096\pi$
$992$	9.74126			0.309285
$993$	−0.993391	+	0.993391i	−0.0315243	+	0.0315243i
$994$	3.08082	−	0.532656i	0.0977178	−	0.0168948i
$995$	−4.72298	+	4.72298i	−0.149728	+	0.149728i
$996$	25.4264	−	25.4264i	0.805668	−	0.805668i
$997$		−	26.5673i		−	0.841394i	−0.907201	−	0.420697i	$-0.861786\pi$
$997$		−	26.5673i		−	0.841394i	0.907201	−	0.420697i	$-0.138214\pi$
$998$		−	8.23392i		−	0.260640i
$999$	−15.9285	−	15.9285i	−0.503955	−	0.503955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.i.a.34.3	✓	12
3.2	odd	2		819.2.y.h.307.4		12
7.2	even	3		637.2.bc.a.619.4		24
7.3	odd	6		637.2.bc.a.411.4		24
7.4	even	3		637.2.bc.a.411.3		24
7.5	odd	6		637.2.bc.a.619.3		24
7.6	odd	2	inner	91.2.i.a.34.4	yes	12
13.5	odd	4	inner	91.2.i.a.83.3	yes	12
21.20	even	2		819.2.y.h.307.3		12
39.5	even	4		819.2.y.h.811.3		12
91.5	even	12		637.2.bc.a.31.3		24
91.18	odd	12		637.2.bc.a.460.3		24
91.31	even	12		637.2.bc.a.460.4		24
91.44	odd	12		637.2.bc.a.31.4		24
91.83	even	4	inner	91.2.i.a.83.4	yes	12
273.83	odd	4		819.2.y.h.811.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.3	✓	12	1.1	even	1	trivial
91.2.i.a.34.4	yes	12	7.6	odd	2	inner
91.2.i.a.83.3	yes	12	13.5	odd	4	inner
91.2.i.a.83.4	yes	12	91.83	even	4	inner
637.2.bc.a.31.3		24	91.5	even	12
637.2.bc.a.31.4		24	91.44	odd	12
637.2.bc.a.411.3		24	7.4	even	3
637.2.bc.a.411.4		24	7.3	odd	6
637.2.bc.a.460.3		24	91.18	odd	12
637.2.bc.a.460.4		24	91.31	even	12
637.2.bc.a.619.3		24	7.5	odd	6
637.2.bc.a.619.4		24	7.2	even	3
819.2.y.h.307.3		12	21.20	even	2
819.2.y.h.307.4		12	3.2	odd	2
819.2.y.h.811.3		12	39.5	even	4
819.2.y.h.811.4		12	273.83	odd	4

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.403032 - 0.403032i) q^{2} -1.23240i q^{3} -1.67513i q^{4} +(-1.03221 + 1.03221i) q^{5} +(-0.496696 + 0.496696i) q^{6} +(-0.450747 - 2.60707i) q^{7} +(-1.48119 + 1.48119i) q^{8} +1.48119 q^{9} +O(q^{10})\)	\(q+(-0.403032 - 0.403032i) q^{2} -1.23240i q^{3} -1.67513i q^{4} +(-1.03221 + 1.03221i) q^{5} +(-0.496696 + 0.496696i) q^{6} +(-0.450747 - 2.60707i) q^{7} +(-1.48119 + 1.48119i) q^{8} +1.48119 q^{9} +0.832030 q^{10} +(-0.596968 + 0.596968i) q^{11} -2.06443 q^{12} +(3.59334 - 0.296512i) q^{13} +(-0.869067 + 1.23240i) q^{14} +(1.27210 + 1.27210i) q^{15} -2.15633 q^{16} +7.34804 q^{17} +(-0.596968 - 0.596968i) q^{18} +(-3.59334 + 3.59334i) q^{19} +(1.72909 + 1.72909i) q^{20} +(-3.21295 + 0.555500i) q^{21} +0.481194 q^{22} +4.44358i q^{23} +(1.82542 + 1.82542i) q^{24} +2.86907i q^{25} +(-1.56773 - 1.32873i) q^{26} -5.52262i q^{27} +(-4.36719 + 0.755061i) q^{28} -3.54420 q^{29} -1.02539i q^{30} +(1.27122 - 1.27122i) q^{31} +(3.83146 + 3.83146i) q^{32} +(0.735703 + 0.735703i) q^{33} +(-2.96149 - 2.96149i) q^{34} +(3.15633 + 2.22579i) q^{35} -2.48119i q^{36} +(2.88423 - 2.88423i) q^{37} +2.89646 q^{38} +(-0.365420 - 4.42842i) q^{39} -3.05782i q^{40} +(-1.23240 + 1.23240i) q^{41} +(1.51881 + 1.07104i) q^{42} -8.66291i q^{43} +(1.00000 + 1.00000i) q^{44} +(-1.52891 + 1.52891i) q^{45} +(1.79090 - 1.79090i) q^{46} +(-2.52230 - 2.52230i) q^{47} +2.65745i q^{48} +(-6.59365 + 2.35026i) q^{49} +(1.15633 - 1.15633i) q^{50} -9.05571i q^{51} +(-0.496696 - 6.01931i) q^{52} -9.79384 q^{53} +(-2.22579 + 2.22579i) q^{54} -1.23240i q^{55} +(4.52923 + 3.19394i) q^{56} +(4.42842 + 4.42842i) q^{57} +(1.42842 + 1.42842i) q^{58} +(1.08972 + 1.08972i) q^{59} +(2.13093 - 2.13093i) q^{60} +7.10903i q^{61} -1.02469 q^{62} +(-0.667644 - 3.86158i) q^{63} +1.22425i q^{64} +(-3.40303 + 4.01516i) q^{65} -0.593023i q^{66} +(8.76845 + 8.76845i) q^{67} -12.3089i q^{68} +5.47626 q^{69} +(-0.375035 - 2.16916i) q^{70} +(-1.46604 - 1.46604i) q^{71} +(-2.19394 + 2.19394i) q^{72} +(0.103857 + 0.103857i) q^{73} -2.32487 q^{74} +3.53583 q^{75} +(6.01931 + 6.01931i) q^{76} +(1.82542 + 1.28726i) q^{77} +(-1.63752 + 1.93207i) q^{78} -4.79877 q^{79} +(2.22579 - 2.22579i) q^{80} -2.36248 q^{81} +0.993391 q^{82} +(-12.3165 + 12.3165i) q^{83} +(0.930536 + 5.38211i) q^{84} +(-7.58475 + 7.58475i) q^{85} +(-3.49143 + 3.49143i) q^{86} +4.36786i q^{87} -1.76845i q^{88} +(6.89017 + 6.89017i) q^{89} +1.23240 q^{90} +(-2.39271 - 9.23444i) q^{91} +7.44358 q^{92} +(-1.56665 - 1.56665i) q^{93} +2.03313i q^{94} -7.41819i q^{95} +(4.72188 - 4.72188i) q^{96} +(6.05814 - 6.05814i) q^{97} +(3.60468 + 1.71022i) q^{98} +(-0.884226 + 0.884226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9	\( 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} - 8 q^{11} + 8 q^{14} - 4 q^{15} + 16 q^{16} - 8 q^{18} - 16 q^{22} - 20 q^{28} - 4 q^{29} - 16 q^{32} - 4 q^{35} + 12 q^{37} + 40 q^{39} + 40 q^{42} + 12 q^{44} + 24 q^{46} - 28 q^{50} - 12 q^{53} - 8 q^{57} - 44 q^{58} + 44 q^{60} + 20 q^{63} - 40 q^{65} + 60 q^{67} + 4 q^{70} - 28 q^{72} - 48 q^{74} + 44 q^{78} - 4 q^{79} - 92 q^{81} - 4 q^{84} + 12 q^{85} + 36 q^{86} - 32 q^{91} + 24 q^{92} - 28 q^{93} - 28 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 8 * q^7 + 4 * q^8 - 4 * q^9 - 8 * q^11 + 8 * q^14 - 4 * q^15 + 16 * q^16 - 8 * q^18 - 16 * q^22 - 20 * q^28 - 4 * q^29 - 16 * q^32 - 4 * q^35 + 12 * q^37 + 40 * q^39 + 40 * q^42 + 12 * q^44 + 24 * q^46 - 28 * q^50 - 12 * q^53 - 8 * q^57 - 44 * q^58 + 44 * q^60 + 20 * q^63 - 40 * q^65 + 60 * q^67 + 4 * q^70 - 28 * q^72 - 48 * q^74 + 44 * q^78 - 4 * q^79 - 92 * q^81 - 4 * q^84 + 12 * q^85 + 36 * q^86 - 32 * q^91 + 24 * q^92 - 28 * q^93 - 28 * q^98 + 12 * q^99

Introduction

L-functions

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