LMFDB - Embedded newform 91.2.i.a.34.4

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			34.4
Root			$1.52891 - 1.52891i$ of defining polynomial
Character	$\chi$	$=$	91.34
Dual form			91.2.i.a.83.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.403032 - 0.403032i) q^{2} +1.23240i q^{3} -1.67513i q^{4} +(1.03221 - 1.03221i) q^{5} +(0.496696 - 0.496696i) q^{6} +(2.60707 + 0.450747i) q^{7} +(-1.48119 + 1.48119i) q^{8} +1.48119 q^{9} +O(q^{10})$	\(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} +(2.60707 + 0.450747i) 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} +(-0.555500 + 3.21295i) 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} +(0.755061 - 4.36719i) 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} +(3.86158 + 0.667644i) 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} +(-2.16916 - 0.375035i) 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} +(5.38211 + 0.930536i) 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} +(-9.50175 - 0.846661i) 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} +(-1.71022 - 3.60468i) 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	$0.115779\pi$
$3$			1.23240i			0.711526i	−0.934576	+	0.355763i	$0.884221\pi$
$4$		−	1.67513i		−	0.837565i
$5$	1.03221	−	1.03221i	0.461620	−	0.461620i	−0.437566	−	0.899186i	$-0.644159\pi$
$5$	1.03221	−	1.03221i	0.461620	−	0.461620i	0.899186	+	0.437566i	$0.144159\pi$
$6$	0.496696	−	0.496696i	0.202775	−	0.202775i
$7$	2.60707	+	0.450747i	0.985381	+	0.170366i
$7$	2.60707	+	0.450747i	0.985381	+	0.170366i
$8$	−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	$-0.850052\pi$
$17$	−7.34804			−1.78216			−0.891080	+	0.453845i	$0.850052\pi$
$18$	−0.596968	−	0.596968i	−0.140707	−	0.140707i
$19$	3.59334	−	3.59334i	0.824368	−	0.824368i	−0.162363	−	0.986731i	$-0.551911\pi$
$19$	3.59334	−	3.59334i	0.824368	−	0.824368i	0.986731	+	0.162363i	$0.0519115\pi$
$20$	−1.72909	−	1.72909i	−0.386637	−	0.386637i
$21$	−0.555500	+	3.21295i	−0.121220	+	0.701124i
$22$	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
$28$	0.755061	−	4.36719i	0.142693	−	0.825321i
$29$	−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	−0.811990	−	0.583672i	$-0.801616\pi$
$31$	−1.27122	+	1.27122i	−0.228318	+	0.228318i	0.583672	+	0.811990i	$0.301616\pi$
$32$	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	−0.604294	−	0.796762i	$-0.706545\pi$
$41$	1.23240	−	1.23240i	0.192468	−	0.192468i	0.796762	+	0.604294i	$0.206545\pi$
$42$	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	0.866717	−	0.498801i	$-0.166226\pi$
$47$	2.52230	+	2.52230i	0.367915	+	0.367915i	−0.498801	+	0.866717i	$0.666226\pi$
$48$		−	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	0.632605	−	0.774474i	$-0.281986\pi$
$59$	−1.08972	−	1.08972i	−0.141869	−	0.141869i	−0.774474	+	0.632605i	$0.781986\pi$
$60$	2.13093	−	2.13093i	0.275102	−	0.275102i
$61$		−	7.10903i		−	0.910218i	−0.890436	−	0.455109i	$-0.849600\pi$
$61$		−	7.10903i		−	0.910218i	0.890436	−	0.455109i	$-0.150400\pi$
$62$	1.02469			0.130135
$63$	3.86158	+	0.667644i	0.486513	+	0.0841153i
$64$			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
$70$	−2.16916	−	0.375035i	−0.259265	−	0.0448253i
$71$	−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	0.701003	−	0.713158i	$-0.252736\pi$
$73$	−0.103857	−	0.103857i	−0.0121555	−	0.0121555i	−0.713158	+	0.701003i	$0.752736\pi$
$74$	−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	$-0.344838\pi$
$83$	12.3165	−	12.3165i	1.35191	−	1.35191i	0.883528	−	0.468379i	$-0.155162\pi$
$84$	5.38211	+	0.930536i	0.587237	+	0.101530i
$85$	−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	0.240334	−	0.970690i	$-0.422743\pi$
$89$	−6.89017	−	6.89017i	−0.730356	−	0.730356i	−0.970690	+	0.240334i	$0.922743\pi$
$90$	−1.23240			−0.129906
$91$	−9.50175	−	0.846661i	−0.996054	−	0.0887541i
$92$	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	−0.944273	−	0.329163i	$-0.893234\pi$
$97$	−6.05814	+	6.05814i	−0.615110	+	0.615110i	0.329163	+	0.944273i	$0.393234\pi$
$98$	−1.71022	−	3.60468i	−0.172758	−	0.364128i
$99$	−0.884226	+	0.884226i	−0.0888681	+	0.0888681i
$100$	4.80606			0.480606
$101$	12.8707			1.28068			0.640339	−	0.768092i	$-0.278794\pi$
$101$	12.8707			1.28068			0.640339	+	0.768092i	$0.278794\pi$
$102$	−3.64974	+	3.64974i	−0.361378	+	0.361378i
$103$	−6.11564			−0.602592			−0.301296	−	0.953531i	$-0.597419\pi$
$103$	−6.11564			−0.602592			−0.301296	+	0.953531i	$0.597419\pi$
$104$	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
$112$	−5.62170	−	0.971958i	−0.531200	−	0.0918414i
$113$	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
$119$	−19.1569	−	3.31211i	−1.75611	−	0.303620i
$120$	−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	$-0.925413\pi$
$131$		−	5.31490i		−	0.464365i	0.972672	−	0.232183i	$-0.0745867\pi$
$132$	−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	$0.0952020\pi$
$139$			6.94767i			0.589294i	−0.955606	+	0.294647i	$0.904798\pi$
$140$	−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
$154$	1.25451	+	0.216897i	0.101091	+	0.0174781i
$155$			2.62435i			0.210793i
$156$	−7.41819	+	0.612127i	−0.593931	+	0.0490094i
$157$		−	9.69783i		−	0.773971i	−0.922086	−	0.386985i	$-0.873516\pi$
$157$		−	9.69783i		−	0.773971i	0.922086	−	0.386985i	$-0.126484\pi$
$158$	1.93406	+	1.93406i	0.153865	+	0.153865i
$159$		−	12.0699i		−	0.957207i
$160$	7.90977			0.625322
$161$	−2.00293	+	11.5847i	−0.157853	+	0.913006i
$162$	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	0.962086	−	0.272746i	$-0.0879318\pi$
$167$	8.90824	+	8.90824i	0.689340	+	0.689340i	−0.272746	+	0.962086i	$0.587932\pi$
$168$	−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	$-0.412313\pi$
$173$	7.15538			0.544014			0.272007	+	0.962295i	$0.412313\pi$
$174$	−1.76039	+	1.76039i	−0.133455	+	0.133455i
$175$	−1.29322	+	7.47987i	−0.0977586	+	0.565425i
$176$	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	$-0.554212\pi$
$181$	−4.56052			−0.338981			−0.169490	+	0.985532i	$0.554212\pi$
$182$	3.48827	+	4.17074i	0.258568	+	0.309156i
$183$	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
$189$	−2.48930	+	14.3979i	−0.181070	+	1.04729i
$190$	−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	$-0.551852\pi$
$199$	−4.57558			−0.324354			−0.162177	+	0.986762i	$0.551852\pi$
$200$	−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
$203$	−9.23998	−	1.59754i	−0.648520	−	0.112125i
$204$	−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
$210$	0.462193	−	2.67327i	0.0318943	−	0.184473i
$211$	−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	−0.604923	−	0.796284i	$-0.706796\pi$
$223$	2.85764	−	2.85764i	0.191361	−	0.191361i	0.796284	+	0.604923i	$0.206796\pi$
$224$	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	$0.623896\pi$
$227$	−19.6570	+	19.6570i	−1.30468	+	1.30468i	−0.925201	+	0.379477i	$0.876104\pi$
$228$	7.41819	−	7.41819i	0.491282	−	0.491282i
$229$	−13.2060	−	13.2060i	−0.872676	−	0.872676i	0.120087	−	0.992763i	$-0.461683\pi$
$229$	−13.2060	−	13.2060i	−0.872676	−	0.872676i	−0.992763	+	0.120087i	$0.961683\pi$
$230$		−	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	0.999894	−	0.0145517i	$-0.00463211\pi$
$241$	15.2966	+	15.2966i	0.985342	+	0.985342i	−0.0145517	+	0.999894i	$0.504632\pi$
$242$	4.14609	−	4.14609i	0.266521	−	0.266521i
$243$			13.6563i			0.876054i
$244$	−11.9086			−0.762367
$245$	9.23204	−	4.38009i	0.589813	−	0.279834i
$246$		−	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	$-0.166751\pi$
$251$	27.4367			1.73179			0.865893	+	0.500229i	$0.166751\pi$
$252$	1.11839	−	6.46865i	0.0704521	−	0.407487i
$253$	−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	$-0.278252\pi$
$257$	20.5727			1.28329			0.641645	+	0.767002i	$0.278252\pi$
$258$	−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
$266$	−7.55128	−	1.30557i	−0.462999	−	0.0800497i
$267$	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	$-0.989242\pi$
$269$		−	1.10840i		−	0.0675803i	0.999429	−	0.0337902i	$-0.0107578\pi$
$270$		−	4.59498i		−	0.279642i
$271$	20.8894	+	20.8894i	1.26894	+	1.26894i	0.946637	+	0.322301i	$0.104456\pi$
$271$	20.8894	+	20.8894i	1.26894	+	1.26894i	0.322301	+	0.946637i	$0.395544\pi$
$272$	15.8448			0.960730
$273$	1.04342	−	11.7099i	0.0631508	−	0.708718i
$274$	−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
$280$	−1.37830	+	7.97196i	−0.0823694	+	0.476416i
$281$	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	$-0.650979\pi$
$283$	−15.3667			−0.913458			−0.456729	+	0.889606i	$0.650979\pi$
$284$	−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	0.360874	−	0.932615i	$-0.382478\pi$
$293$	−9.78662	−	9.78662i	−0.571741	−	0.571741i	−0.932615	+	0.360874i	$0.882478\pi$
$294$	4.44240	−	2.10767i	0.259086	−	0.122922i
$295$	−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
$301$	3.90478	−	22.5848i	0.225068	−	1.30177i
$302$	−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	0.435529	−	0.900175i	$-0.356561\pi$
$307$	−8.14125	−	8.14125i	−0.464645	−	0.464645i	−0.900175	+	0.435529i	$0.856561\pi$
$308$	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	$-0.872562\pi$
$311$	−32.4813			−1.84184			−0.920922	+	0.389747i	$0.872562\pi$
$312$	7.10062	+	6.01810i	0.401993	+	0.340708i
$313$			19.7346i			1.11547i	0.830020	+	0.557733i	$0.188329\pi$
$313$			19.7346i			1.11547i	−0.830020	+	0.557733i	$0.811671\pi$
$314$	−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
$336$	1.19784	−	6.92817i	0.0653475	−	0.377963i
$337$			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
$343$	16.1308	+	9.09937i	0.870979	+	0.491320i
$344$	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	0.642439	−	0.766336i	$-0.277922\pi$
$349$	−2.31459	−	2.31459i	−0.123897	−	0.123897i	−0.766336	+	0.642439i	$0.777922\pi$
$350$	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	−0.932602	−	0.360906i	$-0.882467\pi$
$353$	−10.7412	+	10.7412i	−0.571696	+	0.571696i	0.360906	+	0.932602i	$0.382467\pi$
$354$	−1.08252			−0.0575351
$355$	−3.02653			−0.160631
$356$	−11.5419	+	11.5419i	−0.611721	+	0.611721i
$357$	4.08184	−	23.6089i	0.216034	−	1.24952i
$358$	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
$364$	−1.41827	+	15.9167i	−0.0743374	+	0.834260i
$365$	−0.214405			−0.0112225
$366$	−3.53102	−	3.53102i	−0.184570	−	0.184570i
$367$		−	9.79778i		−	0.511440i	−0.966751	−	0.255720i	$-0.917688\pi$
$367$		−	9.79778i		−	0.511440i	0.966751	−	0.255720i	$-0.0823125\pi$
$368$		−	9.58181i		−	0.499486i
$369$	1.82542	−	1.82542i	0.0950276	−	0.0950276i
$370$	−2.39976	+	2.39976i	−0.124758	+	0.124758i
$371$	−25.5333	−	4.41455i	−1.32562	−	0.229192i
$372$	−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	−0.628798	−	0.777569i	$-0.716453\pi$
$383$	2.91152	−	2.91152i	0.148772	−	0.148772i	0.777569	+	0.628798i	$0.216453\pi$
$384$	10.0518	+	10.0518i	0.512956	+	0.512956i
$385$	−0.555500	+	3.21295i	−0.0283109	+	0.163747i
$386$	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
$392$	−13.2477	+	6.28529i	−0.669109	+	0.317455i
$393$	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	0.914916	−	0.403645i	$-0.132257\pi$
$397$	10.1870	+	10.1870i	0.511270	+	0.511270i	−0.403645	+	0.914916i	$0.632257\pi$
$398$	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	−0.661224	−	0.750189i	$-0.729963\pi$
$409$	1.79921	−	1.79921i	0.0889652	−	0.0889652i	0.750189	+	0.661224i	$0.229963\pi$
$410$	−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	$0.132101\pi$
$419$			16.5064i			0.806392i	−0.915114	+	0.403196i	$0.867899\pi$
$420$	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
$427$	3.20438	−	18.5338i	0.155071	−	0.896911i
$428$		−	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	$-0.830738\pi$
$433$	−35.8708			−1.72384			−0.861920	+	0.507044i	$0.830738\pi$
$434$	2.67143	+	0.461874i	0.128233	+	0.0221707i
$435$	−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	$-0.419148\pi$
$439$	10.5299			0.502563			0.251281	+	0.967914i	$0.419148\pi$
$440$	−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
$448$	−0.551829	+	3.19172i	−0.0260715	+	0.150795i
$449$	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
$455$	−10.6818	+	8.93390i	−0.500769	+	0.418828i
$456$	−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	−0.693162	−	0.720782i	$-0.743783\pi$
$461$	0.593023	−	0.593023i	0.0276198	−	0.0276198i	0.720782	+	0.693162i	$0.243783\pi$
$462$	−0.267304	+	1.54605i	−0.0124361	+	0.0719289i
$463$	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	$-0.600234\pi$
$467$	−13.3860			−0.619432			−0.309716	+	0.950829i	$0.600234\pi$
$468$	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
$476$	−5.54821	+	32.0903i	−0.254302	+	1.47085i
$477$	−14.5066			−0.664211
$478$			0.680055i			0.0311050i
$479$	−8.85827	−	8.85827i	−0.404745	−	0.404745i	0.475157	−	0.879901i	$-0.342391\pi$
$479$	−8.85827	−	8.85827i	−0.404745	−	0.404745i	−0.879901	+	0.475157i	$0.842391\pi$
$480$			9.74798i			0.444933i
$481$	−9.50879	+	11.2192i	−0.433564	+	0.511552i
$482$		−	12.3301i		−	0.561619i
$483$	−14.2770	−	2.46841i	−0.649627	−	0.112317i
$484$	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	$-0.748974\pi$
$503$		−	31.8196i		−	1.41877i	0.704824	−	0.709383i	$-0.251026\pi$
$504$	−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	−0.941220	−	0.337795i	$-0.890319\pi$
$509$	−13.6139	+	13.6139i	−0.603425	+	0.603425i	0.337795	+	0.941220i	$0.390319\pi$
$510$			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
$518$	−6.06110	−	1.04793i	−0.266310	−	0.0460433i
$519$			8.81828i			0.387080i
$520$	−0.906679	−	10.9878i	−0.0397605	−	0.481846i
$521$			21.6750i			0.949601i	0.880094	+	0.474800i	$0.157480\pi$
$521$			21.6750i			0.949601i	−0.880094	+	0.474800i	$0.842520\pi$
$522$	2.11577	+	2.11577i	0.0926049	+	0.0926049i
$523$			8.77309i			0.383620i	0.981432	+	0.191810i	$0.0614358\pi$
$523$			8.77309i			0.383620i	−0.981432	+	0.191810i	$0.938564\pi$
$524$	−8.90316			−0.388936
$525$	−9.21818	−	1.59377i	−0.402314	−	0.0695577i
$526$	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
$539$	−5.33923	+	2.53317i	−0.229977	+	0.109111i
$540$	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
$546$	−5.14001	+	4.29894i	−0.219972	+	0.183978i
$547$	−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
$553$	−12.5107	−	2.16303i	−0.532011	−	0.0919815i
$554$	−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	$-0.457288\pi$
$563$	6.34858			0.267561			0.133780	+	0.991011i	$0.457288\pi$
$564$	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
$567$	−6.15916	−	1.06488i	−0.258660	−	0.0447208i
$568$	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
$574$	−2.58984	−	0.447768i	−0.108098	−	0.0186895i
$575$	−12.7489			−0.531668
$576$			1.81336i			0.0755566i
$577$	31.3416	−	31.3416i	1.30477	−	1.30477i	0.379627	−	0.925140i	$-0.376052\pi$
$577$	31.3416	−	31.3416i	1.30477	−	1.30477i	0.925140	−	0.379627i	$-0.123948\pi$
$578$	−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	−0.634200	−	0.773169i	$-0.718671\pi$
$587$	3.36694	−	3.36694i	0.138969	−	0.138969i	0.773169	+	0.634200i	$0.218671\pi$
$588$	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	0.891583	−	0.452857i	$-0.149595\pi$
$593$	10.6837	+	10.6837i	0.438726	+	0.438726i	−0.452857	+	0.891583i	$0.649595\pi$
$594$			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	$-0.869286\pi$
$601$		−	19.5732i		−	0.798409i	0.916862	−	0.399205i	$-0.130714\pi$
$602$	−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	$0.324589\pi$
$607$			41.9804i			1.70393i	−0.523598	+	0.851965i	$0.675411\pi$
$608$	27.5354			1.11671
$609$	1.96880	−	11.3873i	0.0797799	−	0.461438i
$610$			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
$616$	0.797125	−	4.61048i	0.0321171	−	0.185762i
$617$	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	$0.0241972\pi$
$619$	26.6973	+	26.6973i	1.07306	+	1.07306i	0.0759445	+	0.997112i	$0.475803\pi$
$620$	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
$630$	−3.21295	−	0.555500i	−0.128007	−	0.0221317i
$631$	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
$637$	−24.3901	−	6.49019i	−0.966371	−	0.257151i
$638$	−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	$-0.462085\pi$
$643$	28.1910	−	28.1910i	1.11175	−	1.11175i	0.992914	−	0.118832i	$-0.0379150\pi$
$644$	19.4060	+	3.35517i	0.764702	+	0.132212i
$645$	11.0201	−	11.0201i	0.433915	−	0.433915i
$646$	21.2833			0.837380
$647$	11.1139			0.436932			0.218466	−	0.975845i	$-0.429895\pi$
$647$	11.1139			0.436932			0.218466	+	0.975845i	$0.429895\pi$
$648$	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
$658$	0.916430	−	5.30053i	0.0357262	−	0.206636i
$659$	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	0.125134	−	0.992140i	$-0.460064\pi$
$661$	−22.2906	−	22.2906i	−0.867006	−	0.867006i	−0.992140	+	0.125134i	$0.960064\pi$
$662$			0.649738i			0.0252528i
$663$	2.68512	+	32.5402i	0.104282	+	1.26376i
$664$			36.4861i			1.41594i
$665$	3.34373	−	19.3398i	0.129664	−	0.749964i
$666$	−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	$0.0878905\pi$
$677$			14.1868i			0.545242i	−0.962122	+	0.272621i	$0.912110\pi$
$678$	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	−0.328475	−	0.944513i	$-0.606535\pi$
$691$	16.1937	−	16.1937i	0.616037	−	0.616037i	0.944513	+	0.328475i	$0.106535\pi$
$692$		−	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
$700$	12.5298	+	2.16632i	0.473580	+	0.0818792i
$701$		−	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
$707$	33.5547	+	5.80141i	1.26196	+	0.218185i
$708$	−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	$-0.535655\pi$
$719$	−5.99456			−0.223559			−0.111780	+	0.993733i	$0.535655\pi$
$720$	−3.29683	+	3.29683i	−0.122865	+	0.122865i
$721$	−15.9439	−	2.75661i	−0.593782	−	0.102661i
$722$	−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	$-0.412618\pi$
$727$	14.6184			0.542168			0.271084	+	0.962556i	$0.412618\pi$
$728$	15.3280	−	12.8199i	0.568093	−	0.475136i
$729$	−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	$0.511919\pi$
$733$	−28.0685	+	28.0685i	−1.03673	+	1.03673i	−0.999299	+	0.0374350i	$0.988081\pi$
$734$	−3.94881	+	3.94881i	−0.145753	+	0.145753i
$735$	5.39802	+	11.3775i	0.199109	+	0.419667i
$736$	−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
$749$	23.1223	+	3.99771i	0.844871	+	0.146073i
$750$	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
$756$	24.1183	+	4.16991i	0.877174	+	0.151658i
$757$	−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	0.875802	−	0.482670i	$-0.160333\pi$
$761$	10.8450	+	10.8450i	0.393133	+	0.393133i	−0.482670	+	0.875802i	$0.660333\pi$
$762$	−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	−0.785749	−	0.618545i	$-0.787722\pi$
$769$	−4.63670	+	4.63670i	−0.167204	+	0.167204i	0.618545	+	0.785749i	$0.287722\pi$
$770$	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	−0.801899	−	0.597460i	$-0.796177\pi$
$773$	−5.68398	+	5.68398i	−0.204438	+	0.204438i	0.597460	+	0.801899i	$0.296177\pi$
$774$	−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	0.535781	−	0.844357i	$-0.320017\pi$
$787$	−8.65662	−	8.65662i	−0.308575	−	0.308575i	−0.844357	+	0.535781i	$0.820017\pi$
$788$	−13.4314	+	13.4314i	−0.478473	+	0.478473i
$789$		−	29.4011i		−	1.04671i
$790$	3.99272			0.142055
$791$	4.19009	+	0.724442i	0.148983	+	0.0257582i
$792$		−	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	$-0.665919\pi$
$797$	−28.1163			−0.995931			−0.497966	+	0.867197i	$0.665919\pi$
$798$	1.60898	−	9.30618i	0.0569574	−	0.329435i
$799$	−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	−0.713295	−	0.700864i	$-0.752798\pi$
$811$	−0.354016	+	0.354016i	−0.0124312	+	0.0124312i	0.700864	+	0.713295i	$0.252798\pi$
$812$	−2.67608	+	15.4782i	−0.0939122	+	0.543178i
$813$	−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
$819$	−14.0739	−	1.25407i	−0.491783	−	0.0438207i
$820$	−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
$826$	−0.395928	+	2.29001i	−0.0137761	+	0.0796795i
$827$	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	$-0.612109\pi$
$829$	−19.8647			−0.689929			−0.344964	+	0.938616i	$0.612109\pi$
$830$	−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	0.369698	−	0.929152i	$-0.379461\pi$
$839$	−16.2048	−	16.2048i	−0.559453	−	0.559453i	−0.929152	+	0.369698i	$0.879461\pi$
$840$	−9.82463	−	1.69862i	−0.338982	−	0.0586079i
$841$	−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
$847$	−4.63695	+	26.8196i	−0.159328	+	0.921533i
$848$	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	0.460452	−	0.887684i	$-0.347687\pi$
$853$	−12.4778	−	12.4778i	−0.427232	−	0.427232i	−0.887684	+	0.460452i	$0.847687\pi$
$854$	−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	$-0.345902\pi$
$857$	27.2501			0.930845			0.465422	+	0.885089i	$0.345902\pi$
$858$	−0.175838	−	2.13093i	−0.00600302	−	0.0727488i
$859$		−	22.7834i		−	0.777361i	−0.921373	−	0.388680i	$-0.872931\pi$
$859$		−	22.7834i		−	0.777361i	0.921373	−	0.388680i	$-0.127069\pi$
$860$	−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	$-0.572366\pi$
$881$	−13.3800			−0.450782			−0.225391	+	0.974268i	$0.572366\pi$
$882$	−2.53317	−	5.33923i	−0.0852963	−	0.179781i
$883$			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	$0.117088\pi$
$887$			21.4198i			0.719206i	−0.933105	+	0.359603i	$0.882912\pi$
$888$	−10.5299			−0.353359
$889$	0.698263	−	4.03868i	0.0234190	−	0.135453i
$890$	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
$903$	27.8335	+	4.81225i	0.926242	+	0.160142i
$904$	−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
$910$	7.90574	+	0.704447i	0.262073	+	0.0233522i
$911$	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
$917$	2.39568	−	13.8563i	0.0791123	−	0.457577i
$918$	−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	−0.318600	−	0.947889i	$-0.603213\pi$
$929$	19.1804	−	19.1804i	0.629289	−	0.629289i	0.947889	+	0.318600i	$0.103213\pi$
$930$	1.30350	+	1.30350i	0.0427435	+	0.0427435i
$931$	32.1385	−	15.2479i	1.05330	−	0.499731i
$932$	−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	$0.0138682\pi$
$937$			2.66644i			0.0871088i	−0.999051	+	0.0435544i	$0.986132\pi$
$938$	3.18585	−	18.4266i	0.104022	−	0.601650i
$939$	−24.3209			−0.793683
$940$		−	8.72259i		−	0.284500i
$941$	−31.9331	+	31.9331i	−1.04099	+	1.04099i	−0.0418672	+	0.999123i	$0.513331\pi$
$941$	−31.9331	+	31.9331i	−1.04099	+	1.04099i	−0.999123	+	0.0418672i	$0.986669\pi$
$942$	−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	$-0.934302\pi$
$971$		−	12.7719i		−	0.409869i	0.978776	−	0.204935i	$-0.0656982\pi$
$972$	22.8761			0.733753
$973$	−3.13164	+	18.1131i	−0.100396	+	0.580679i
$974$		−	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
$980$	−7.33722	−	15.4649i	−0.234379	−	0.494007i
$981$	−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	$-0.949688\pi$
$983$	−35.8970	−	35.8970i	−1.14494	−	1.14494i	−0.157402	−	0.987535i	$-0.550312\pi$
$984$	−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
$994$	−0.532656	+	3.08082i	−0.0168948	+	0.0977178i
$995$	−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	$0.138214\pi$
$997$			26.5673i			0.841394i	−0.907201	+	0.420697i	$0.861786\pi$
$998$		−	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.34.4	yes	12
3.2	odd	2		819.2.y.h.307.3		12
7.2	even	3		637.2.bc.a.619.3		24
7.3	odd	6		637.2.bc.a.411.3		24
7.4	even	3		637.2.bc.a.411.4		24
7.5	odd	6		637.2.bc.a.619.4		24
7.6	odd	2	inner	91.2.i.a.34.3	✓	12
13.5	odd	4	inner	91.2.i.a.83.4	yes	12
21.20	even	2		819.2.y.h.307.4		12
39.5	even	4		819.2.y.h.811.4		12
91.5	even	12		637.2.bc.a.31.4		24
91.18	odd	12		637.2.bc.a.460.4		24
91.31	even	12		637.2.bc.a.460.3		24
91.44	odd	12		637.2.bc.a.31.3		24
91.83	even	4	inner	91.2.i.a.83.3	yes	12
273.83	odd	4		819.2.y.h.811.3		12

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

\(f(q)\)	\(=\)	\(q+(-0.403032 - 0.403032i) q^{2} +1.23240i q^{3} -1.67513i q^{4} +(1.03221 - 1.03221i) q^{5} +(0.496696 - 0.496696i) q^{6} +(2.60707 + 0.450747i) q^{7} +(-1.48119 + 1.48119i) q^{8} +1.48119 q^{9} +O(q^{10})\)	\(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} +(2.60707 + 0.450747i) 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} +(-0.555500 + 3.21295i) 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} +(0.755061 - 4.36719i) 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} +(3.86158 + 0.667644i) 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} +(-2.16916 - 0.375035i) 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} +(5.38211 + 0.930536i) 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} +(-9.50175 - 0.846661i) 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} +(-1.71022 - 3.60468i) 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

Modular forms

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Database

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