LMFDB - Embedded newform 119.2.g.a.106.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [119,2,Mod(64,119)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(119, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("119.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	119.g (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:	$0.950219784053$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 32 x^{18} + 432 x^{16} + 3200 x^{14} + 14160 x^{12} + 38162 x^{10} + 61088 x^{8} + 53872 x^{6} + \cdots + 49 $ x^20 + 32x^18 + 432x^16 + 3200x^14 + 14160x^12 + 38162x^10 + 61088x^8 + 53872x^6 + 22464x^4 + 3504*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			106.3
Root			$-1.57229i$ of defining polynomial
Character	$\chi$	$=$	119.106
Dual form			119.2.g.a.64.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.57229i q^{2} +(-1.43847 + 1.43847i) q^{3} -0.472100 q^{4} +(2.40051 - 2.40051i) q^{5} +(2.26170 + 2.26170i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.40230i q^{8} -1.13841i q^{9} +O(q^{10})$	\(q-1.57229i q^{2} +(-1.43847 + 1.43847i) q^{3} -0.472100 q^{4} +(2.40051 - 2.40051i) q^{5} +(2.26170 + 2.26170i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.40230i q^{8} -1.13841i q^{9} +(-3.77429 - 3.77429i) q^{10} +(-3.30263 - 3.30263i) q^{11} +(0.679103 - 0.679103i) q^{12} +3.63777 q^{13} +(1.11178 - 1.11178i) q^{14} +6.90613i q^{15} -4.72132 q^{16} +(1.70860 + 3.75243i) q^{17} -1.78992 q^{18} +6.19754i q^{19} +(-1.13328 + 1.13328i) q^{20} -2.03431 q^{21} +(-5.19270 + 5.19270i) q^{22} +(0.475240 + 0.475240i) q^{23} +(3.45565 + 3.45565i) q^{24} -6.52485i q^{25} -5.71963i q^{26} +(-2.67784 - 2.67784i) q^{27} +(-0.333825 - 0.333825i) q^{28} +(-3.95461 + 3.95461i) q^{29} +10.8584 q^{30} +(-5.41543 + 5.41543i) q^{31} +2.61868i q^{32} +9.50150 q^{33} +(5.89991 - 2.68641i) q^{34} +3.39483 q^{35} +0.537445i q^{36} +(-0.967703 + 0.967703i) q^{37} +9.74433 q^{38} +(-5.23284 + 5.23284i) q^{39} +(-5.76674 - 5.76674i) q^{40} +(0.492170 + 0.492170i) q^{41} +3.19853i q^{42} -6.64216i q^{43} +(1.55917 + 1.55917i) q^{44} +(-2.73277 - 2.73277i) q^{45} +(0.747216 - 0.747216i) q^{46} +4.32592 q^{47} +(6.79150 - 6.79150i) q^{48} +1.00000i q^{49} -10.2590 q^{50} +(-7.85554 - 2.94000i) q^{51} -1.71739 q^{52} +4.07940i q^{53} +(-4.21035 + 4.21035i) q^{54} -15.8560 q^{55} +(1.69869 - 1.69869i) q^{56} +(-8.91500 - 8.91500i) q^{57} +(6.21780 + 6.21780i) q^{58} +2.73239i q^{59} -3.26038i q^{60} +(-8.55455 - 8.55455i) q^{61} +(8.51463 + 8.51463i) q^{62} +(0.804980 - 0.804980i) q^{63} -5.32531 q^{64} +(8.73248 - 8.73248i) q^{65} -14.9391i q^{66} +12.5590 q^{67} +(-0.806627 - 1.77152i) q^{68} -1.36724 q^{69} -5.33766i q^{70} +(3.04461 - 3.04461i) q^{71} -2.73482 q^{72} +(-1.16753 + 1.16753i) q^{73} +(1.52151 + 1.52151i) q^{74} +(9.38583 + 9.38583i) q^{75} -2.92586i q^{76} -4.67063i q^{77} +(8.22754 + 8.22754i) q^{78} +(7.07442 + 7.07442i) q^{79} +(-11.3336 + 11.3336i) q^{80} +11.1193 q^{81} +(0.773834 - 0.773834i) q^{82} -4.69160i q^{83} +0.960397 q^{84} +(13.1092 + 4.90623i) q^{85} -10.4434 q^{86} -11.3772i q^{87} +(-7.93393 + 7.93393i) q^{88} -2.04706 q^{89} +(-4.29671 + 4.29671i) q^{90} +(2.57229 + 2.57229i) q^{91} +(-0.224361 - 0.224361i) q^{92} -15.5799i q^{93} -6.80161i q^{94} +(14.8772 + 14.8772i) q^{95} +(-3.76691 - 3.76691i) q^{96} +(-2.99116 + 2.99116i) q^{97} +1.57229 q^{98} +(-3.75976 + 3.75976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} - 24 q^{4} - 8 q^{5} + 4 q^{6}+O(q^{10}) $ 20 * q - 4 * q^3 - 24 * q^4 - 8 * q^5 + 4 * q^6	$ 20 q - 4 q^{3} - 24 q^{4} - 8 q^{5} + 4 q^{6} + 4 q^{10} - 4 q^{11} + 12 q^{12} + 16 q^{16} - 12 q^{17} - 8 q^{18} + 20 q^{20} - 8 q^{21} - 20 q^{22} + 4 q^{24} + 8 q^{27} + 16 q^{29} - 36 q^{30} + 4 q^{31} - 16 q^{33} + 36 q^{34} + 16 q^{35} - 28 q^{37} + 48 q^{38} + 20 q^{39} - 24 q^{40} - 24 q^{41} - 28 q^{44} + 36 q^{45} + 8 q^{46} + 40 q^{47} - 8 q^{48} - 28 q^{50} - 40 q^{51} - 28 q^{54} - 40 q^{55} + 36 q^{57} + 56 q^{58} - 16 q^{61} - 40 q^{62} + 8 q^{63} + 32 q^{64} + 8 q^{65} - 32 q^{68} - 88 q^{69} - 8 q^{71} + 108 q^{72} + 8 q^{73} + 36 q^{74} + 8 q^{75} - 44 q^{78} - 4 q^{79} - 116 q^{80} + 4 q^{81} - 16 q^{82} - 32 q^{84} + 16 q^{85} + 44 q^{86} + 72 q^{88} + 48 q^{89} + 56 q^{90} + 20 q^{91} - 32 q^{92} + 44 q^{95} + 68 q^{96} - 24 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 - 24 * q^4 - 8 * q^5 + 4 * q^6 + 4 * q^10 - 4 * q^11 + 12 * q^12 + 16 * q^16 - 12 * q^17 - 8 * q^18 + 20 * q^20 - 8 * q^21 - 20 * q^22 + 4 * q^24 + 8 * q^27 + 16 * q^29 - 36 * q^30 + 4 * q^31 - 16 * q^33 + 36 * q^34 + 16 * q^35 - 28 * q^37 + 48 * q^38 + 20 * q^39 - 24 * q^40 - 24 * q^41 - 28 * q^44 + 36 * q^45 + 8 * q^46 + 40 * q^47 - 8 * q^48 - 28 * q^50 - 40 * q^51 - 28 * q^54 - 40 * q^55 + 36 * q^57 + 56 * q^58 - 16 * q^61 - 40 * q^62 + 8 * q^63 + 32 * q^64 + 8 * q^65 - 32 * q^68 - 88 * q^69 - 8 * q^71 + 108 * q^72 + 8 * q^73 + 36 * q^74 + 8 * q^75 - 44 * q^78 - 4 * q^79 - 116 * q^80 + 4 * q^81 - 16 * q^82 - 32 * q^84 + 16 * q^85 + 44 * q^86 + 72 * q^88 + 48 * q^89 + 56 * q^90 + 20 * q^91 - 32 * q^92 + 44 * q^95 + 68 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/119\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.57229i		−	1.11178i	−0.831257	−	0.555889i	$-0.812378\pi$
$2$		−	1.57229i		−	1.11178i	0.831257	−	0.555889i	$-0.187622\pi$
$3$	−1.43847	+	1.43847i	−0.830503	+	0.830503i	−0.987586	−	0.157082i	$-0.949791\pi$
$3$	−1.43847	+	1.43847i	−0.830503	+	0.830503i	0.157082	+	0.987586i	$0.449791\pi$
$4$	−0.472100			−0.236050
$5$	2.40051	−	2.40051i	1.07354	−	1.07354i	0.0764665	−	0.997072i	$-0.475636\pi$
$5$	2.40051	−	2.40051i	1.07354	−	1.07354i	0.997072	−	0.0764665i	$-0.0243638\pi$
$6$	2.26170	+	2.26170i	0.923335	+	0.923335i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		−	2.40230i		−	0.849343i
$9$		−	1.13841i		−	0.379471i
$10$	−3.77429	−	3.77429i	−1.19354	−	1.19354i
$11$	−3.30263	−	3.30263i	−0.995781	−	0.995781i	0.00421022	−	0.999991i	$-0.498660\pi$
$11$	−3.30263	−	3.30263i	−0.995781	−	0.995781i	−0.999991	+	0.00421022i	$0.998660\pi$
$12$	0.679103	−	0.679103i	0.196040	−	0.196040i
$13$	3.63777			1.00894			0.504468	−	0.863430i	$-0.331689\pi$
$13$	3.63777			1.00894			0.504468	+	0.863430i	$0.331689\pi$
$14$	1.11178	−	1.11178i	0.297135	−	0.297135i
$15$			6.90613i			1.78315i
$16$	−4.72132			−1.18033
$17$	1.70860	+	3.75243i	0.414395	+	0.910097i
$17$	1.70860	+	3.75243i	0.414395	+	0.910097i
$18$	−1.78992			−0.421888
$19$			6.19754i			1.42181i	0.703287	+	0.710906i	$0.251715\pi$
$19$			6.19754i			1.42181i	−0.703287	+	0.710906i	$0.748285\pi$
$20$	−1.13328	+	1.13328i	−0.253409	+	0.253409i
$21$	−2.03431			−0.443923
$22$	−5.19270	+	5.19270i	−1.10709	+	1.10709i
$23$	0.475240	+	0.475240i	0.0990945	+	0.0990945i	0.754916	−	0.655822i	$-0.227678\pi$
$23$	0.475240	+	0.475240i	0.0990945	+	0.0990945i	−0.655822	+	0.754916i	$0.727678\pi$
$24$	3.45565	+	3.45565i	0.705382	+	0.705382i
$25$		−	6.52485i		−	1.30497i
$26$		−	5.71963i		−	1.12171i
$27$	−2.67784	−	2.67784i	−0.515351	−	0.515351i
$28$	−0.333825	−	0.333825i	−0.0630870	−	0.0630870i
$29$	−3.95461	+	3.95461i	−0.734353	+	0.734353i	−0.971479	−	0.237126i	$-0.923795\pi$
$29$	−3.95461	+	3.95461i	−0.734353	+	0.734353i	0.237126	+	0.971479i	$0.423795\pi$
$30$	10.8584			1.98247
$31$	−5.41543	+	5.41543i	−0.972640	+	0.972640i	−0.999636	−	0.0269959i	$-0.991406\pi$
$31$	−5.41543	+	5.41543i	−0.972640	+	0.972640i	0.0269959	+	0.999636i	$0.491406\pi$
$32$			2.61868i			0.462922i
$33$	9.50150			1.65400
$34$	5.89991	−	2.68641i	1.01183	−	0.460715i
$35$	3.39483			0.573831
$36$			0.537445i			0.0895742i
$37$	−0.967703	+	0.967703i	−0.159089	+	0.159089i	−0.782163	−	0.623074i	$-0.785884\pi$
$37$	−0.967703	+	0.967703i	−0.159089	+	0.159089i	0.623074	+	0.782163i	$0.285884\pi$
$38$	9.74433			1.58074
$39$	−5.23284	+	5.23284i	−0.837924	+	0.837924i
$40$	−5.76674	−	5.76674i	−0.911802	−	0.911802i
$41$	0.492170	+	0.492170i	0.0768640	+	0.0768640i	0.744494	−	0.667630i	$-0.232691\pi$
$41$	0.492170	+	0.492170i	0.0768640	+	0.0768640i	−0.667630	+	0.744494i	$0.732691\pi$
$42$			3.19853i			0.493543i
$43$		−	6.64216i		−	1.01292i	−0.862264	−	0.506460i	$-0.830954\pi$
$43$		−	6.64216i		−	1.01292i	0.862264	−	0.506460i	$-0.169046\pi$
$44$	1.55917	+	1.55917i	0.235054	+	0.235054i
$45$	−2.73277	−	2.73277i	−0.407377	−	0.407377i
$46$	0.747216	−	0.747216i	0.110171	−	0.110171i
$47$	4.32592			0.631000			0.315500	−	0.948926i	$-0.397828\pi$
$47$	4.32592			0.631000			0.315500	+	0.948926i	$0.397828\pi$
$48$	6.79150	−	6.79150i	0.980268	−	0.980268i
$49$			1.00000i			0.142857i
$50$	−10.2590			−1.45084
$51$	−7.85554	−	2.94000i	−1.10000	−	0.411682i
$52$	−1.71739			−0.238159
$53$			4.07940i			0.560349i	0.959949	+	0.280175i	$0.0903924\pi$
$53$			4.07940i			0.560349i	−0.959949	+	0.280175i	$0.909608\pi$
$54$	−4.21035	+	4.21035i	−0.572956	+	0.572956i
$55$	−15.8560			−2.13802
$56$	1.69869	−	1.69869i	0.226996	−	0.226996i
$57$	−8.91500	−	8.91500i	−1.18082	−	1.18082i
$58$	6.21780	+	6.21780i	0.816437	+	0.816437i
$59$			2.73239i			0.355727i	0.984055	+	0.177864i	$0.0569186\pi$
$59$			2.73239i			0.355727i	−0.984055	+	0.177864i	$0.943081\pi$
$60$		−	3.26038i		−	0.420914i
$61$	−8.55455	−	8.55455i	−1.09530	−	1.09530i	−0.994953	−	0.100345i	$-0.968005\pi$
$61$	−8.55455	−	8.55455i	−1.09530	−	1.09530i	−0.100345	−	0.994953i	$-0.531995\pi$
$62$	8.51463	+	8.51463i	1.08136	+	1.08136i
$63$	0.804980	−	0.804980i	0.101418	−	0.101418i
$64$	−5.32531			−0.665664
$65$	8.73248	−	8.73248i	1.08313	−	1.08313i
$66$		−	14.9391i		−	1.83888i
$67$	12.5590			1.53433			0.767165	−	0.641450i	$-0.221667\pi$
$67$	12.5590			1.53433			0.767165	+	0.641450i	$0.221667\pi$
$68$	−0.806627	−	1.77152i	−0.0978179	−	0.214828i
$69$	−1.36724			−0.164597
$70$		−	5.33766i		−	0.637972i
$71$	3.04461	−	3.04461i	0.361328	−	0.361328i	−0.502973	−	0.864302i	$-0.667761\pi$
$71$	3.04461	−	3.04461i	0.361328	−	0.361328i	0.864302	+	0.502973i	$0.167761\pi$
$72$	−2.73482			−0.322301
$73$	−1.16753	+	1.16753i	−0.136649	+	0.136649i	−0.772123	−	0.635474i	$-0.780805\pi$
$73$	−1.16753	+	1.16753i	−0.136649	+	0.136649i	0.635474	+	0.772123i	$0.280805\pi$
$74$	1.52151	+	1.52151i	0.176872	+	0.176872i
$75$	9.38583	+	9.38583i	1.08378	+	1.08378i
$76$		−	2.92586i		−	0.335619i
$77$		−	4.67063i		−	0.532267i
$78$	8.22754	+	8.22754i	0.931586	+	0.931586i
$79$	7.07442	+	7.07442i	0.795935	+	0.795935i	0.982452	−	0.186517i	$-0.0597199\pi$
$79$	7.07442	+	7.07442i	0.795935	+	0.795935i	−0.186517	+	0.982452i	$0.559720\pi$
$80$	−11.3336	+	11.3336i	−1.26713	+	1.26713i
$81$	11.1193			1.23547
$82$	0.773834	−	0.773834i	0.0854557	−	0.0854557i
$83$		−	4.69160i		−	0.514970i	−0.966282	−	0.257485i	$-0.917106\pi$
$83$		−	4.69160i		−	0.514970i	0.966282	−	0.257485i	$-0.0828938\pi$
$84$	0.960397			0.104788
$85$	13.1092	+	4.90623i	1.42189	+	0.532155i
$86$	−10.4434			−1.12614
$87$		−	11.3772i		−	1.21977i
$88$	−7.93393	+	7.93393i	−0.845759	+	0.845759i
$89$	−2.04706			−0.216988			−0.108494	−	0.994097i	$-0.534603\pi$
$89$	−2.04706			−0.216988			−0.108494	+	0.994097i	$0.534603\pi$
$90$	−4.29671	+	4.29671i	−0.452913	+	0.452913i
$91$	2.57229	+	2.57229i	0.269649	+	0.269649i
$92$	−0.224361	−	0.224361i	−0.0233912	−	0.0233912i
$93$		−	15.5799i		−	1.61556i
$94$		−	6.80161i		−	0.701532i
$95$	14.8772	+	14.8772i	1.52637	+	1.52637i
$96$	−3.76691	−	3.76691i	−0.384459	−	0.384459i
$97$	−2.99116	+	2.99116i	−0.303706	+	0.303706i	−0.842462	−	0.538756i	$-0.818895\pi$
$97$	−2.99116	+	2.99116i	−0.303706	+	0.303706i	0.538756	+	0.842462i	$0.318895\pi$
$98$	1.57229			0.158825
$99$	−3.75976	+	3.75976i	−0.377870	+	0.377870i
$100$			3.08038i			0.308038i
$101$	−5.38529			−0.535856			−0.267928	−	0.963439i	$-0.586339\pi$
$101$	−5.38529			−0.535856			−0.267928	+	0.963439i	$0.586339\pi$
$102$	−4.62253	+	12.3512i	−0.457699	+	1.22295i
$103$	−3.96255			−0.390442			−0.195221	−	0.980759i	$-0.562542\pi$
$103$	−3.96255			−0.390442			−0.195221	+	0.980759i	$0.562542\pi$
$104$		−	8.73903i		−	0.856932i
$105$	−4.88337	+	4.88337i	−0.476568	+	0.476568i
$106$	6.41401			0.622984
$107$	8.04673	−	8.04673i	0.777907	−	0.777907i	−0.201568	−	0.979475i	$-0.564604\pi$
$107$	8.04673	−	8.04673i	0.777907	−	0.777907i	0.979475	+	0.201568i	$0.0646035\pi$
$108$	1.26421	+	1.26421i	0.121649	+	0.121649i
$109$	−3.11536	−	3.11536i	−0.298398	−	0.298398i	0.541988	−	0.840386i	$-0.317672\pi$
$109$	−3.11536	−	3.11536i	−0.298398	−	0.298398i	−0.840386	+	0.541988i	$0.817672\pi$
$110$			24.9302i			2.37700i
$111$		−	2.78403i		−	0.264248i
$112$	−3.33848	−	3.33848i	−0.315457	−	0.315457i
$113$	−8.20042	−	8.20042i	−0.771430	−	0.771430i	0.206926	−	0.978357i	$-0.433654\pi$
$113$	−8.20042	−	8.20042i	−0.771430	−	0.771430i	−0.978357	+	0.206926i	$0.933654\pi$
$114$	−14.0170	+	14.0170i	−1.31281	+	1.31281i
$115$	2.28163			0.212764
$116$	1.86697	−	1.86697i	0.173344	−	0.173344i
$117$		−	4.14129i		−	0.382862i
$118$	4.29612			0.395490
$119$	−1.44521	+	3.86153i	−0.132482	+	0.353985i
$120$	16.5906			1.51451
$121$			10.8148i			0.983159i
$122$	−13.4502	+	13.4502i	−1.21773	+	1.21773i
$123$	−1.41595			−0.127672
$124$	2.55662	−	2.55662i	0.229591	−	0.229591i
$125$	−3.66041	−	3.66041i	−0.327397	−	0.327397i
$126$	−1.26566	−	1.26566i	−0.112754	−	0.112754i
$127$		−	5.12889i		−	0.455115i	−0.973765	−	0.227558i	$-0.926926\pi$
$127$		−	5.12889i		−	0.455115i	0.973765	−	0.227558i	$-0.0730740\pi$
$128$			13.6103i			1.20299i
$129$	9.55457	+	9.55457i	0.841233	+	0.841233i
$130$	−13.7300	−	13.7300i	−1.20420	−	1.20420i
$131$	5.90678	−	5.90678i	0.516078	−	0.516078i	−0.400304	−	0.916382i	$-0.631096\pi$
$131$	5.90678	−	5.90678i	0.516078	−	0.516078i	0.916382	+	0.400304i	$0.131096\pi$
$132$	−4.48566			−0.390426
$133$	−4.38232	+	4.38232i	−0.379995	+	0.379995i
$134$		−	19.7465i		−	1.70583i
$135$	−12.8564			−1.10650
$136$	9.01447	−	4.10456i	0.772984	−	0.351964i
$137$	−20.1939			−1.72528			−0.862639	−	0.505821i	$-0.831190\pi$
$137$	−20.1939			−1.72528			−0.862639	+	0.505821i	$0.831190\pi$
$138$			2.14970i			0.182995i
$139$	5.51905	−	5.51905i	0.468120	−	0.468120i	−0.433185	−	0.901305i	$-0.642610\pi$
$139$	5.51905	−	5.51905i	0.468120	−	0.468120i	0.901305	+	0.433185i	$0.142610\pi$
$140$	−1.60270			−0.135453
$141$	−6.22272	+	6.22272i	−0.524048	+	0.524048i
$142$	−4.78701	−	4.78701i	−0.401717	−	0.401717i
$143$	−12.0142	−	12.0142i	−1.00468	−	1.00468i
$144$			5.37482i			0.447902i
$145$			18.9861i			1.57671i
$146$	1.83570	+	1.83570i	0.151923	+	0.151923i
$147$	−1.43847	−	1.43847i	−0.118643	−	0.118643i
$148$	0.456852	−	0.456852i	0.0375530	−	0.0375530i
$149$	0.670580			0.0549361			0.0274680	−	0.999623i	$-0.491256\pi$
$149$	0.670580			0.0549361			0.0274680	+	0.999623i	$0.491256\pi$
$150$	14.7573	−	14.7573i	1.20492	−	1.20492i
$151$		−	11.4237i		−	0.929644i	−0.885404	−	0.464822i	$-0.846118\pi$
$151$		−	11.4237i		−	0.929644i	0.885404	−	0.464822i	$-0.153882\pi$
$152$	14.8884			1.20761
$153$	4.27182	−	1.94509i	0.345356	−	0.157251i
$154$	−7.34359			−0.591763
$155$			25.9995i			2.08833i
$156$	2.47042	−	2.47042i	0.197792	−	0.197792i
$157$	23.3832			1.86618			0.933090	−	0.359642i	$-0.117101\pi$
$157$	23.3832			1.86618			0.933090	+	0.359642i	$0.117101\pi$
$158$	11.1231	−	11.1231i	0.884903	−	0.884903i
$159$	−5.86812	−	5.86812i	−0.465372	−	0.465372i
$160$	6.28617	+	6.28617i	0.496965	+	0.496965i
$161$			0.672091i			0.0529682i
$162$		−	17.4827i		−	1.37357i
$163$	8.53975	+	8.53975i	0.668885	+	0.668885i	0.957458	−	0.288573i	$-0.0931808\pi$
$163$	8.53975	+	8.53975i	0.668885	+	0.668885i	−0.288573	+	0.957458i	$0.593181\pi$
$164$	−0.232353	−	0.232353i	−0.0181437	−	0.0181437i
$165$	22.8084	−	22.8084i	1.77563	−	1.77563i
$166$	−7.37656			−0.572532
$167$	−17.3482	+	17.3482i	−1.34244	+	1.34244i	−0.448823	+	0.893620i	$0.648157\pi$
$167$	−17.3482	+	17.3482i	−1.34244	+	1.34244i	−0.893620	+	0.448823i	$0.851843\pi$
$168$			4.88703i			0.377043i
$169$	0.233365			0.0179511
$170$	7.71402	−	20.6115i	0.591638	−	1.58083i
$171$	7.05537			0.539537
$172$			3.13576i			0.239100i
$173$	2.52101	−	2.52101i	0.191669	−	0.191669i	−0.604748	−	0.796417i	$-0.706726\pi$
$173$	2.52101	−	2.52101i	0.191669	−	0.191669i	0.796417	+	0.604748i	$0.206726\pi$
$174$	−17.8883			−1.35611
$175$	4.61377	−	4.61377i	0.348768	−	0.348768i
$176$	15.5928	+	15.5928i	1.17535	+	1.17535i
$177$	−3.93047	−	3.93047i	−0.295433	−	0.295433i
$178$			3.21857i			0.241242i
$179$		−	3.96115i		−	0.296071i	−0.988982	−	0.148035i	$-0.952705\pi$
$179$		−	3.96115i		−	0.296071i	0.988982	−	0.148035i	$-0.0472949\pi$
$180$	1.29014	+	1.29014i	0.0961614	+	0.0961614i
$181$	−1.36267	−	1.36267i	−0.101287	−	0.101287i	0.654648	−	0.755934i	$-0.272817\pi$
$181$	−1.36267	−	1.36267i	−0.101287	−	0.101287i	−0.755934	+	0.654648i	$0.772817\pi$
$182$	4.04439	−	4.04439i	0.299790	−	0.299790i
$183$	24.6110			1.81930
$184$	1.14167	−	1.14167i	0.0841652	−	0.0841652i
$185$			4.64595i			0.341577i
$186$	−24.4961			−1.79614
$187$	6.75002	−	18.0357i	0.493610	−	1.31890i
$188$	−2.04227			−0.148948
$189$		−	3.78704i		−	0.275467i
$190$	23.3913	−	23.3913i	1.69699	−	1.69699i
$191$	−25.1726			−1.82143			−0.910714	−	0.413038i	$-0.864468\pi$
$191$	−25.1726			−1.82143			−0.910714	+	0.413038i	$0.864468\pi$
$192$	7.66032	−	7.66032i	0.552836	−	0.552836i
$193$	7.95263	+	7.95263i	0.572443	+	0.572443i	0.932810	−	0.360367i	$-0.117349\pi$
$193$	7.95263	+	7.95263i	0.572443	+	0.572443i	−0.360367	+	0.932810i	$0.617349\pi$
$194$	4.70297	+	4.70297i	0.337654	+	0.337654i
$195$			25.1229i			1.79909i
$196$		−	0.472100i		−	0.0337214i
$197$	−16.0035	−	16.0035i	−1.14020	−	1.14020i	−0.988413	−	0.151789i	$-0.951497\pi$
$197$	−16.0035	−	16.0035i	−1.14020	−	1.14020i	−0.151789	−	0.988413i	$-0.548503\pi$
$198$	5.91144	+	5.91144i	0.420108	+	0.420108i
$199$	−3.71192	+	3.71192i	−0.263131	+	0.263131i	−0.826325	−	0.563194i	$-0.809572\pi$
$199$	−3.71192	+	3.71192i	−0.263131	+	0.263131i	0.563194	+	0.826325i	$0.309572\pi$
$200$	−15.6747			−1.10837
$201$	−18.0658	+	18.0658i	−1.27427	+	1.27427i
$202$			8.46724i			0.595753i
$203$	−5.59267			−0.392528
$204$	3.70860	+	1.38797i	0.259654	+	0.0971775i
$205$	2.36291			0.165033
$206$			6.23029i			0.434085i
$207$	0.541021	−	0.541021i	0.0376035	−	0.0376035i
$208$	−17.1751			−1.19088
$209$	20.4682	−	20.4682i	1.41581	−	1.41581i
$210$	7.67808	+	7.67808i	0.529838	+	0.529838i
$211$	−6.87817	−	6.87817i	−0.473513	−	0.473513i	0.429536	−	0.903050i	$-0.358677\pi$
$211$	−6.87817	−	6.87817i	−0.473513	−	0.473513i	−0.903050	+	0.429536i	$0.858677\pi$
$212$		−	1.92589i		−	0.132270i
$213$			8.75918i			0.600169i
$214$	−12.6518	−	12.6518i	−0.864860	−	0.864860i
$215$	−15.9445	−	15.9445i	−1.08741	−	1.08741i
$216$	−6.43299	+	6.43299i	−0.437710	+	0.437710i
$217$	−7.65857			−0.519898
$218$	−4.89826	+	4.89826i	−0.331752	+	0.331752i
$219$		−	3.35892i		−	0.226975i
$220$	7.48560			0.504679
$221$	6.21547	+	13.6505i	0.418098	+	0.918229i
$222$	−4.37731			−0.293786
$223$			17.5438i			1.17482i	0.809289	+	0.587411i	$0.199853\pi$
$223$			17.5438i			1.17482i	−0.809289	+	0.587411i	$0.800147\pi$
$224$	−1.85169	+	1.85169i	−0.123721	+	0.123721i
$225$	−7.42798			−0.495199
$226$	−12.8934	+	12.8934i	−0.857659	+	0.857659i
$227$	−5.89982	−	5.89982i	−0.391585	−	0.391585i	0.483667	−	0.875252i	$-0.339305\pi$
$227$	−5.89982	−	5.89982i	−0.391585	−	0.391585i	−0.875252	+	0.483667i	$0.839305\pi$
$228$	4.20877	+	4.20877i	0.278732	+	0.278732i
$229$		−	15.3443i		−	1.01398i	−0.861952	−	0.506990i	$-0.830758\pi$
$229$		−	15.3443i		−	1.01398i	0.861952	−	0.506990i	$-0.169242\pi$
$230$		−	3.58739i		−	0.236546i
$231$	6.71857	+	6.71857i	0.442050	+	0.442050i
$232$	9.50018	+	9.50018i	0.623717	+	0.623717i
$233$	17.3081	−	17.3081i	1.13389	−	1.13389i	0.144371	−	0.989524i	$-0.453884\pi$
$233$	17.3081	−	17.3081i	1.13389	−	1.13389i	0.989524	−	0.144371i	$-0.0461158\pi$
$234$	−6.51131			−0.425658
$235$	10.3844	−	10.3844i	0.677403	−	0.677403i
$236$		−	1.28996i		−	0.0839694i
$237$	−20.3527			−1.32205
$238$	6.07144	+	2.27229i	0.393553	+	0.147290i
$239$	14.5771			0.942916			0.471458	−	0.881889i	$-0.343728\pi$
$239$	14.5771			0.942916			0.471458	+	0.881889i	$0.343728\pi$
$240$		−	32.6061i		−	2.10471i
$241$	−10.7589	+	10.7589i	−0.693041	+	0.693041i	−0.962900	−	0.269859i	$-0.913023\pi$
$241$	−10.7589	+	10.7589i	−0.693041	+	0.693041i	0.269859	+	0.962900i	$0.413023\pi$
$242$	17.0039			1.09305
$243$	−7.96123	+	7.96123i	−0.510713	+	0.510713i
$244$	4.03860	+	4.03860i	0.258545	+	0.258545i
$245$	2.40051	+	2.40051i	0.153363	+	0.153363i
$246$			2.22628i			0.141942i
$247$			22.5452i			1.43452i
$248$	13.0095	+	13.0095i	0.826104	+	0.826104i
$249$	6.74874	+	6.74874i	0.427684	+	0.427684i
$250$	−5.75524	+	5.75524i	−0.363993	+	0.363993i
$251$	1.54033			0.0972246			0.0486123	−	0.998818i	$-0.484520\pi$
$251$	1.54033			0.0972246			0.0486123	+	0.998818i	$0.484520\pi$
$252$	−0.380031	+	0.380031i	−0.0239397	+	0.0239397i
$253$		−	3.13909i		−	0.197353i
$254$	−8.06411			−0.505987
$255$	−25.9147	+	11.7998i	−1.62284	+	0.738931i
$256$	10.7487			0.671797
$257$			4.02923i			0.251337i	0.992072	+	0.125668i	$0.0401075\pi$
$257$			4.02923i			0.251337i	−0.992072	+	0.125668i	$0.959893\pi$
$258$	15.0226	−	15.0226i	0.935264	−	0.935264i
$259$	−1.36854			−0.0850368
$260$	−4.12260	+	4.12260i	−0.255673	+	0.255673i
$261$	4.50199	+	4.50199i	0.278666	+	0.278666i
$262$	−9.28718	−	9.28718i	−0.573764	−	0.573764i
$263$		−	17.9741i		−	1.10833i	−0.832407	−	0.554164i	$-0.813038\pi$
$263$		−	17.9741i		−	1.10833i	0.832407	−	0.554164i	$-0.186962\pi$
$264$		−	22.8255i		−	1.40481i
$265$	9.79263	+	9.79263i	0.601557	+	0.601557i
$266$	6.89028	+	6.89028i	0.422470	+	0.422470i
$267$	2.94464	−	2.94464i	0.180209	−	0.180209i
$268$	−5.92912			−0.362178
$269$	12.7503	−	12.7503i	0.777400	−	0.777400i	−0.201988	−	0.979388i	$-0.564740\pi$
$269$	12.7503	−	12.7503i	0.777400	−	0.777400i	0.979388	+	0.201988i	$0.0647403\pi$
$270$			20.2139i			1.23018i
$271$	16.7080			1.01494			0.507469	−	0.861670i	$-0.330581\pi$
$271$	16.7080			1.01494			0.507469	+	0.861670i	$0.330581\pi$
$272$	−8.06683	−	17.7164i	−0.489123	−	1.07422i
$273$	−7.40035			−0.447889
$274$			31.7506i			1.91812i
$275$	−21.5492	+	21.5492i	−1.29946	+	1.29946i
$276$	0.645475			0.0388530
$277$	−0.737934	+	0.737934i	−0.0443381	+	0.0443381i	−0.728928	−	0.684590i	$-0.759981\pi$
$277$	−0.737934	+	0.737934i	−0.0443381	+	0.0443381i	0.684590	+	0.728928i	$0.259981\pi$
$278$	−8.67755	−	8.67755i	−0.520445	−	0.520445i
$279$	6.16500	+	6.16500i	0.369089	+	0.369089i
$280$		−	8.15541i		−	0.487379i
$281$			3.53036i			0.210604i	0.994440	+	0.105302i	$0.0335809\pi$
$281$			3.53036i			0.210604i	−0.994440	+	0.105302i	$0.966419\pi$
$282$	9.78393	+	9.78393i	0.582625	+	0.582625i
$283$	−1.28939	−	1.28939i	−0.0766462	−	0.0766462i	0.667744	−	0.744391i	$-0.267260\pi$
$283$	−1.28939	−	1.28939i	−0.0766462	−	0.0766462i	−0.744391	+	0.667744i	$0.767260\pi$
$284$	−1.43736	+	1.43736i	−0.0852915	+	0.0852915i
$285$	−42.8010			−2.53531
$286$	−18.8898	+	18.8898i	−1.11698	+	1.11698i
$287$			0.696033i			0.0410855i
$288$	2.98115			0.175666
$289$	−11.1614	+	12.8228i	−0.656553	+	0.754280i
$290$	29.8517			1.75295
$291$		−	8.60540i		−	0.504458i
$292$	0.551191	−	0.551191i	0.0322560	−	0.0322560i
$293$	14.9585			0.873883			0.436942	−	0.899490i	$-0.356062\pi$
$293$	14.9585			0.873883			0.436942	+	0.899490i	$0.356062\pi$
$294$	−2.26170	+	2.26170i	−0.131905	+	0.131905i
$295$	6.55912	+	6.55912i	0.381887	+	0.381887i
$296$	2.32472	+	2.32472i	0.135121	+	0.135121i
$297$			17.6879i			1.02635i
$298$		−	1.05435i		−	0.0610767i
$299$	1.72882	+	1.72882i	0.0999800	+	0.0999800i
$300$	−4.43105	−	4.43105i	−0.255827	−	0.255827i
$301$	4.69671	−	4.69671i	0.270714	−	0.270714i
$302$	−17.9613			−1.03356
$303$	7.74659	−	7.74659i	0.445030	−	0.445030i
$304$		−	29.2606i		−	1.67821i
$305$	−41.0705			−2.35169
$306$	−3.05825	−	6.71654i	−0.174828	−	0.383959i
$307$	−7.16409			−0.408876			−0.204438	−	0.978879i	$-0.565537\pi$
$307$	−7.16409			−0.408876			−0.204438	+	0.978879i	$0.565537\pi$
$308$			2.20500i			0.125642i
$309$	5.70003	−	5.70003i	0.324263	−	0.324263i
$310$	40.8788			2.32176
$311$	−4.45087	+	4.45087i	−0.252386	+	0.252386i	−0.821948	−	0.569562i	$-0.807113\pi$
$311$	−4.45087	+	4.45087i	−0.252386	+	0.252386i	0.569562	+	0.821948i	$0.307113\pi$
$312$	12.5709	+	12.5709i	0.711685	+	0.711685i
$313$	22.1833	+	22.1833i	1.25387	+	1.25387i	0.953969	+	0.299905i	$0.0969550\pi$
$313$	22.1833	+	22.1833i	1.25387	+	1.25387i	0.299905	+	0.953969i	$0.403045\pi$
$314$		−	36.7652i		−	2.07478i
$315$		−	3.86472i		−	0.217752i
$316$	−3.33983	−	3.33983i	−0.187880	−	0.187880i
$317$	11.7136	+	11.7136i	0.657900	+	0.657900i	0.954883	−	0.296983i	$-0.0959805\pi$
$317$	11.7136	+	11.7136i	0.657900	+	0.657900i	−0.296983	+	0.954883i	$0.595980\pi$
$318$	−9.22639	+	9.22639i	−0.517390	+	0.517390i
$319$	26.1213			1.46251
$320$	−12.7834	+	12.7834i	−0.714616	+	0.714616i
$321$			23.1500i			1.29211i
$322$	1.05672			0.0588889
$323$	−23.2558	+	10.5891i	−1.29399	+	0.589192i
$324$	−5.24940			−0.291633
$325$		−	23.7359i		−	1.31663i
$326$	13.4270	−	13.4270i	0.743651	−	0.743651i
$327$	8.96274			0.495640
$328$	1.18234	−	1.18234i	0.0652839	−	0.0652839i
$329$	3.05889	+	3.05889i	0.168642	+	0.168642i
$330$	−35.8614	−	35.8614i	−1.97411	−	1.97411i
$331$		−	4.73294i		−	0.260146i	−0.991504	−	0.130073i	$-0.958479\pi$
$331$		−	4.73294i		−	0.260146i	0.991504	−	0.130073i	$-0.0415212\pi$
$332$			2.21490i			0.121559i
$333$	1.10165	+	1.10165i	0.0603698	+	0.0603698i
$334$	27.2764	+	27.2764i	1.49250	+	1.49250i
$335$	30.1480	−	30.1480i	1.64716	−	1.64716i
$336$	9.60463			0.523975
$337$	17.0523	−	17.0523i	0.928898	−	0.928898i	−0.0687369	−	0.997635i	$-0.521897\pi$
$337$	17.0523	−	17.0523i	0.928898	−	0.928898i	0.997635	+	0.0687369i	$0.0218969\pi$
$338$		−	0.366917i		−	0.0199577i
$339$	23.5922			1.28135
$340$	−6.18886	−	2.31623i	−0.335638	−	0.125615i
$341$	35.7703			1.93707
$342$		−	11.0931i		−	0.599846i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−15.9565			−0.860316
$345$	−3.28207	+	3.28207i	−0.176701	+	0.176701i
$346$	−3.96376	−	3.96376i	−0.213093	−	0.213093i
$347$	−16.1971	−	16.1971i	−0.869505	−	0.869505i	0.122912	−	0.992418i	$-0.460777\pi$
$347$	−16.1971	−	16.1971i	−0.869505	−	0.869505i	−0.992418	+	0.122912i	$0.960777\pi$
$348$			5.37118i			0.287925i
$349$			10.1897i			0.545442i	0.962093	+	0.272721i	$0.0879235\pi$
$349$			10.1897i			0.545442i	−0.962093	+	0.272721i	$0.912076\pi$
$350$	−7.25419	−	7.25419i	−0.387753	−	0.387753i
$351$	−9.74137	−	9.74137i	−0.519956	−	0.519956i
$352$	8.64855	−	8.64855i	0.460969	−	0.460969i
$353$	−16.7999			−0.894167			−0.447084	−	0.894492i	$-0.647537\pi$
$353$	−16.7999			−0.894167			−0.447084	+	0.894492i	$0.647537\pi$
$354$	−6.17985	+	6.17985i	−0.328455	+	0.328455i
$355$		−	14.6172i		−	0.775800i
$356$	0.966416			0.0512199
$357$	−3.47581	−	7.63360i	−0.183959	−	0.404013i
$358$	−6.22809			−0.329165
$359$		−	28.2418i		−	1.49055i	−0.666759	−	0.745273i	$-0.732319\pi$
$359$		−	28.2418i		−	1.49055i	0.666759	−	0.745273i	$-0.267681\pi$
$360$	−6.56494	+	6.56494i	−0.346003	+	0.346003i
$361$	−19.4095			−1.02155
$362$	−2.14252	+	2.14252i	−0.112608	+	0.112608i
$363$	−15.5567	−	15.5567i	−0.816517	−	0.816517i
$364$	−1.21438	−	1.21438i	−0.0636507	−	0.0636507i
$365$			5.60532i			0.293396i
$366$		−	38.6956i		−	2.02265i
$367$	−13.3024	−	13.3024i	−0.694382	−	0.694382i	0.268811	−	0.963193i	$-0.413369\pi$
$367$	−13.3024	−	13.3024i	−0.694382	−	0.694382i	−0.963193	+	0.268811i	$0.913369\pi$
$368$	−2.24376	−	2.24376i	−0.116964	−	0.116964i
$369$	0.560293	−	0.560293i	0.0291677	−	0.0291677i
$370$	7.30479			0.379758
$371$	−2.88457	+	2.88457i	−0.149760	+	0.149760i
$372$			7.35527i			0.381353i
$373$	30.9655			1.60333			0.801666	−	0.597772i	$-0.203947\pi$
$373$	30.9655			1.60333			0.801666	+	0.597772i	$0.203947\pi$
$374$	−28.3574	−	10.6130i	−1.46633	−	0.548785i
$375$	10.5308			0.543809
$376$		−	10.3922i		−	0.535936i
$377$	−14.3860	+	14.3860i	−0.740915	+	0.740915i
$378$	−5.95433			−0.306258
$379$	−8.80375	+	8.80375i	−0.452218	+	0.452218i	−0.896090	−	0.443872i	$-0.853604\pi$
$379$	−8.80375	+	8.80375i	−0.452218	+	0.452218i	0.443872	+	0.896090i	$0.353604\pi$
$380$	−7.02353	−	7.02353i	−0.360300	−	0.360300i
$381$	7.37778	+	7.37778i	0.377975	+	0.377975i
$382$			39.5787i			2.02502i
$383$			29.8457i			1.52505i	0.646961	+	0.762523i	$0.276040\pi$
$383$			29.8457i			1.52505i	−0.646961	+	0.762523i	$0.723960\pi$
$384$	−19.5781	−	19.5781i	−0.999089	−	0.999089i
$385$	−11.2119	−	11.2119i	−0.571409	−	0.571409i
$386$	12.5039	−	12.5039i	0.636429	−	0.636429i
$387$	−7.56153			−0.384374
$388$	1.41212	−	1.41212i	0.0716898	−	0.0716898i
$389$			20.9404i			1.06172i	0.847459	+	0.530861i	$0.178131\pi$
$389$			20.9404i			1.06172i	−0.847459	+	0.530861i	$0.821869\pi$
$390$	39.5005			2.00019
$391$	−0.971311	+	2.59530i	−0.0491213	+	0.131250i
$392$	2.40230			0.121335
$393$			16.9935i			0.857208i
$394$	−25.1622	+	25.1622i	−1.26765	+	1.26765i
$395$	33.9644			1.70893
$396$	1.77498	−	1.77498i	0.0891963	−	0.0891963i
$397$	−20.0540	−	20.0540i	−1.00648	−	1.00648i	−0.999979	−	0.00650493i	$-0.997929\pi$
$397$	−20.0540	−	20.0540i	−1.00648	−	1.00648i	−0.00650493	−	0.999979i	$-0.502071\pi$
$398$	5.83622	+	5.83622i	0.292543	+	0.292543i
$399$		−	12.6077i		−	0.631175i
$400$			30.8059i			1.54030i
$401$	2.31141	+	2.31141i	0.115426	+	0.115426i	0.762461	−	0.647034i	$-0.223991\pi$
$401$	2.31141	+	2.31141i	0.115426	+	0.115426i	−0.647034	+	0.762461i	$0.723991\pi$
$402$	28.4048	+	28.4048i	1.41670	+	1.41670i
$403$	−19.7001	+	19.7001i	−0.981331	+	0.981331i
$404$	2.54239			0.126489
$405$	26.6918	−	26.6918i	1.32633	−	1.32633i
$406$			8.79330i			0.436404i
$407$	6.39193			0.316836
$408$	−7.06277	+	18.8714i	−0.349659	+	0.934273i
$409$	−34.3864			−1.70030			−0.850149	−	0.526542i	$-0.823488\pi$
$409$	−34.3864			−1.70030			−0.850149	+	0.526542i	$0.823488\pi$
$410$		−	3.71518i		−	0.183480i
$411$	29.0483	−	29.0483i	1.43285	−	1.43285i
$412$	1.87072			0.0921638
$413$	−1.93209	+	1.93209i	−0.0950721	+	0.0950721i
$414$	−0.850642	−	0.850642i	−0.0418068	−	0.0418068i
$415$	−11.2622	−	11.2622i	−0.552840	−	0.552840i
$416$			9.52617i			0.467059i
$417$			15.8780i			0.777550i
$418$	−32.1819	−	32.1819i	−1.57407	−	1.57407i
$419$	−12.3869	−	12.3869i	−0.605140	−	0.605140i	0.336532	−	0.941672i	$-0.390746\pi$
$419$	−12.3869	−	12.3869i	−0.605140	−	0.605140i	−0.941672	+	0.336532i	$0.890746\pi$
$420$	2.30544	−	2.30544i	0.112494	−	0.112494i
$421$	−13.1028			−0.638593			−0.319296	−	0.947655i	$-0.603447\pi$
$421$	−13.1028			−0.638593			−0.319296	+	0.947655i	$0.603447\pi$
$422$	−10.8145	+	10.8145i	−0.526441	+	0.526441i
$423$		−	4.92469i		−	0.239447i
$424$	9.79997			0.475929
$425$	24.4840	−	11.1483i	1.18765	−	0.540773i
$426$	13.7720			0.667254
$427$		−	12.0980i		−	0.585461i
$428$	−3.79886	+	3.79886i	−0.183625	+	0.183625i
$429$	34.5643			1.66878
$430$	−25.0695	+	25.0695i	−1.20896	+	1.20896i
$431$	18.5848	+	18.5848i	0.895197	+	0.895197i	0.995007	−	0.0998095i	$-0.0318233\pi$
$431$	18.5848	+	18.5848i	0.895197	+	0.895197i	−0.0998095	+	0.995007i	$0.531823\pi$
$432$	12.6430	+	12.6430i	0.608284	+	0.608284i
$433$		−	0.783681i		−	0.0376613i	−0.999823	−	0.0188307i	$-0.994006\pi$
$433$		−	0.783681i		−	0.0376613i	0.999823	−	0.0188307i	$-0.00599434\pi$
$434$			12.0415i			0.578011i
$435$	−27.3111	−	27.3111i	−1.30947	−	1.30947i
$436$	1.47076	+	1.47076i	0.0704367	+	0.0704367i
$437$	−2.94532	+	2.94532i	−0.140894	+	0.140894i
$438$	−5.28120			−0.252346
$439$	17.7866	−	17.7866i	0.848908	−	0.848908i	−0.141089	−	0.989997i	$-0.545060\pi$
$439$	17.7866	−	17.7866i	0.848908	−	0.848908i	0.989997	+	0.141089i	$0.0450604\pi$
$440$			38.0909i			1.81591i
$441$	1.13841			0.0542102
$442$	21.4625	−	9.77254i	1.02087	−	0.464832i
$443$	−12.1317			−0.576395			−0.288197	−	0.957571i	$-0.593056\pi$
$443$	−12.1317			−0.576395			−0.288197	+	0.957571i	$0.593056\pi$
$444$			1.31434i			0.0623758i
$445$	−4.91397	+	4.91397i	−0.232945	+	0.232945i
$446$	27.5840			1.30614
$447$	−0.964612	+	0.964612i	−0.0456246	+	0.0456246i
$448$	−3.76556	−	3.76556i	−0.177906	−	0.177906i
$449$	26.1661	+	26.1661i	1.23485	+	1.23485i	0.962077	+	0.272777i	$0.0879421\pi$
$449$	26.1661	+	26.1661i	1.23485	+	1.23485i	0.272777	+	0.962077i	$0.412058\pi$
$450$			11.6790i			0.550551i
$451$		−	3.25091i		−	0.153079i
$452$	3.87142	+	3.87142i	0.182096	+	0.182096i
$453$	16.4326	+	16.4326i	0.772073	+	0.772073i
$454$	−9.27624	+	9.27624i	−0.435355	+	0.435355i
$455$	12.3496			0.578958
$456$	−21.4165	+	21.4165i	−1.00292	+	1.00292i
$457$		−	12.7879i		−	0.598192i	−0.954223	−	0.299096i	$-0.903315\pi$
$457$		−	12.7879i		−	0.598192i	0.954223	−	0.299096i	$-0.0966851\pi$
$458$	−24.1257			−1.12732
$459$	5.47306	−	14.6238i	0.255460	−	0.682578i
$460$	−1.07716			−0.0502228
$461$			4.58089i			0.213353i	0.994294	+	0.106677i	$0.0340210\pi$
$461$			4.58089i			0.213353i	−0.994294	+	0.106677i	$0.965979\pi$
$462$	10.5636	−	10.5636i	0.491461	−	0.491461i
$463$	−1.53844			−0.0714973			−0.0357486	−	0.999361i	$-0.511382\pi$
$463$	−1.53844			−0.0714973			−0.0357486	+	0.999361i	$0.511382\pi$
$464$	18.6710	−	18.6710i	0.866779	−	0.866779i
$465$	−37.3996	−	37.3996i	−1.73437	−	1.73437i
$466$	−27.2134	−	27.2134i	−1.26064	−	1.26064i
$467$			11.0027i			0.509143i	0.967054	+	0.254572i	$0.0819345\pi$
$467$			11.0027i			0.509143i	−0.967054	+	0.254572i	$0.918066\pi$
$468$			1.95510i			0.0903746i
$469$	8.88058	+	8.88058i	0.410067	+	0.410067i
$470$	−16.3273	−	16.3273i	−0.753122	−	0.753122i
$471$	−33.6361	+	33.6361i	−1.54987	+	1.54987i
$472$	6.56404			0.302134
$473$	−21.9366	+	21.9366i	−1.00865	+	1.00865i
$474$			32.0004i			1.46983i
$475$	40.4380			1.85542
$476$	0.682282	−	1.82303i	0.0312723	−	0.0835582i
$477$	4.64405			0.212637
$478$		−	22.9195i		−	1.04831i
$479$	16.4487	−	16.4487i	0.751558	−	0.751558i	−0.223212	−	0.974770i	$-0.571654\pi$
$479$	16.4487	−	16.4487i	0.751558	−	0.751558i	0.974770	+	0.223212i	$0.0716542\pi$
$480$	−18.0850			−0.825462
$481$	−3.52028	+	3.52028i	−0.160511	+	0.160511i
$482$	16.9161	+	16.9161i	0.770508	+	0.770508i
$483$	−0.966786	−	0.966786i	−0.0439903	−	0.0439903i
$484$		−	5.10564i		−	0.232075i
$485$			14.3606i			0.652080i
$486$	12.5174	+	12.5174i	0.567800	+	0.567800i
$487$	15.5818	+	15.5818i	0.706079	+	0.706079i	0.965708	−	0.259629i	$-0.0836003\pi$
$487$	15.5818	+	15.5818i	0.706079	+	0.706079i	−0.259629	+	0.965708i	$0.583600\pi$
$488$	−20.5506	+	20.5506i	−0.930283	+	0.930283i
$489$	−24.5684			−1.11102
$490$	3.77429	−	3.77429i	0.170505	−	0.170505i
$491$			19.2671i			0.869512i	0.900548	+	0.434756i	$0.143165\pi$
$491$			19.2671i			0.869512i	−0.900548	+	0.434756i	$0.856835\pi$
$492$	0.668468			0.0301369
$493$	−21.5962	−	8.08256i	−0.972645	−	0.364020i
$494$	35.4476			1.59486
$495$			18.0507i			0.811317i
$496$	25.5680	−	25.5680i	1.14804	−	1.14804i
$497$	4.30572			0.193138
$498$	10.6110	−	10.6110i	0.475490	−	0.475490i
$499$	29.9541	+	29.9541i	1.34093	+	1.34093i	0.895136	+	0.445793i	$0.147078\pi$
$499$	29.9541	+	29.9541i	1.34093	+	1.34093i	0.445793	+	0.895136i	$0.352922\pi$
$500$	1.72808	+	1.72808i	0.0772821	+	0.0772821i
$501$		−	49.9099i		−	2.22981i
$502$		−	2.42184i		−	0.108092i
$503$	−7.89613	−	7.89613i	−0.352071	−	0.352071i	0.508809	−	0.860880i	$-0.330086\pi$
$503$	−7.89613	−	7.89613i	−0.352071	−	0.352071i	−0.860880	+	0.508809i	$0.830086\pi$
$504$	−1.93381	−	1.93381i	−0.0861386	−	0.0861386i
$505$	−12.9274	+	12.9274i	−0.575262	+	0.575262i
$506$	−4.93556			−0.219412
$507$	−0.335689	+	0.335689i	−0.0149085	+	0.0149085i
$508$			2.42135i			0.107430i
$509$	−33.7960			−1.49798			−0.748991	−	0.662580i	$-0.769462\pi$
$509$	−33.7960			−1.49798			−0.748991	+	0.662580i	$0.769462\pi$
$510$	18.5527	+	40.7455i	0.821527	+	1.80424i
$511$	−1.65114			−0.0730420
$512$			10.3205i			0.456104i
$513$	16.5960	−	16.5960i	0.732733	−	0.732733i
$514$	6.33513			0.279430
$515$	−9.51213	+	9.51213i	−0.419154	+	0.419154i
$516$	−4.51071	−	4.51071i	−0.198573	−	0.198573i
$517$	−14.2869	−	14.2869i	−0.628338	−	0.628338i
$518$			2.15174i			0.0945420i
$519$			7.25281i			0.318363i
$520$	−20.9781	−	20.9781i	−0.919950	−	0.919950i
$521$	10.4802	+	10.4802i	0.459145	+	0.459145i	0.898375	−	0.439230i	$-0.144749\pi$
$521$	10.4802	+	10.4802i	0.459145	+	0.459145i	−0.439230	+	0.898375i	$0.644749\pi$
$522$	7.07843	−	7.07843i	0.309815	−	0.309815i
$523$	−2.75940			−0.120660			−0.0603300	−	0.998178i	$-0.519215\pi$
$523$	−2.75940			−0.120660			−0.0603300	+	0.998178i	$0.519215\pi$
$524$	−2.78859	+	2.78859i	−0.121820	+	0.121820i
$525$			13.2736i			0.579306i
$526$	−28.2605			−1.23221
$527$	−29.5738	−	11.0682i	−1.28825	−	0.482139i
$528$	−44.8596			−1.95226
$529$		−	22.5483i		−	0.980361i
$530$	15.3969	−	15.3969i	0.668797	−	0.668797i
$531$	3.11059			0.134988
$532$	2.06889	−	2.06889i	0.0896979	−	0.0896979i
$533$	1.79040	+	1.79040i	0.0775508	+	0.0775508i
$534$	−4.62983	−	4.62983i	−0.200352	−	0.200352i
$535$		−	38.6325i		−	1.67023i
$536$		−	30.1706i		−	1.30317i
$537$	5.69802	+	5.69802i	0.245888	+	0.245888i
$538$	−20.0472	−	20.0472i	−0.864296	−	0.864296i
$539$	3.30263	−	3.30263i	0.142254	−	0.142254i
$540$	6.06948			0.261189
$541$	7.88750	−	7.88750i	0.339110	−	0.339110i	−0.516922	−	0.856032i	$-0.672922\pi$
$541$	7.88750	−	7.88750i	0.339110	−	0.339110i	0.856032	+	0.516922i	$0.172922\pi$
$542$		−	26.2698i		−	1.12839i
$543$	3.92034			0.168238
$544$	−9.82642	+	4.47427i	−0.421304	+	0.191833i
$545$	−14.9569			−0.640683
$546$			11.6355i			0.497954i
$547$	5.17129	−	5.17129i	0.221108	−	0.221108i	−0.587857	−	0.808965i	$-0.700028\pi$
$547$	5.17129	−	5.17129i	0.221108	−	0.221108i	0.808965	+	0.587857i	$0.200028\pi$
$548$	9.53351			0.407252
$549$	−9.73862	+	9.73862i	−0.415634	+	0.415634i
$550$	33.8816	+	33.8816i	1.44472	+	1.44472i
$551$	−24.5089	−	24.5089i	−1.04411	−	1.04411i
$552$			3.28453i			0.139799i
$553$			10.0047i			0.425445i
$554$	1.16025	+	1.16025i	0.0492942	+	0.0492942i
$555$	−6.68308	−	6.68308i	−0.283681	−	0.283681i
$556$	−2.60554	+	2.60554i	−0.110500	+	0.110500i
$557$	15.3543			0.650583			0.325291	−	0.945614i	$-0.394538\pi$
$557$	15.3543			0.650583			0.325291	+	0.945614i	$0.394538\pi$
$558$	9.69318	−	9.69318i	0.410345	−	0.410345i
$559$		−	24.1626i		−	1.02197i
$560$	−16.0281			−0.677310
$561$	16.2342	+	35.6537i	0.685409	+	1.50530i
$562$	5.55076			0.234145
$563$			6.62599i			0.279252i	0.990204	+	0.139626i	$0.0445901\pi$
$563$			6.62599i			0.279252i	−0.990204	+	0.139626i	$0.955410\pi$
$564$	2.93775	−	2.93775i	0.123701	−	0.123701i
$565$	−39.3703			−1.65632
$566$	−2.02730	+	2.02730i	−0.0852136	+	0.0852136i
$567$	7.86250	+	7.86250i	0.330194	+	0.330194i
$568$	−7.31407	−	7.31407i	−0.306892	−	0.306892i
$569$			36.9677i			1.54977i	0.632105	+	0.774883i	$0.282191\pi$
$569$			36.9677i			1.54977i	−0.632105	+	0.774883i	$0.717809\pi$
$570$			67.2956i			2.81870i
$571$	−25.8702	−	25.8702i	−1.08264	−	1.08264i	−0.996263	−	0.0863725i	$-0.972472\pi$
$571$	−25.8702	−	25.8702i	−1.08264	−	1.08264i	−0.0863725	−	0.996263i	$-0.527528\pi$
$572$	5.67191	+	5.67191i	0.237154	+	0.237154i
$573$	36.2102	−	36.2102i	1.51270	−	1.51270i
$574$	1.09437			0.0456780
$575$	3.10087	−	3.10087i	0.129315	−	0.129315i
$576$			6.06241i			0.252600i
$577$	6.70916			0.279306			0.139653	−	0.990200i	$-0.455401\pi$
$577$	6.70916			0.279306			0.139653	+	0.990200i	$0.455401\pi$
$578$	20.1611	+	17.5490i	0.838591	+	0.729941i
$579$	−22.8793			−0.950832
$580$		−	8.96335i		−	0.372183i
$581$	3.31746	−	3.31746i	0.137632	−	0.137632i
$582$	−13.5302			−0.560845
$583$	13.4728	−	13.4728i	0.557985	−	0.557985i
$584$	2.80476	+	2.80476i	0.116062	+	0.116062i
$585$	−9.94118	−	9.94118i	−0.411017	−	0.411017i
$586$		−	23.5191i		−	0.971564i
$587$			0.653601i			0.0269770i	0.999909	+	0.0134885i	$0.00429365\pi$
$587$			0.653601i			0.0269770i	−0.999909	+	0.0134885i	$0.995706\pi$
$588$	0.679103	+	0.679103i	0.0280057	+	0.0280057i
$589$	−33.5623	−	33.5623i	−1.38291	−	1.38291i
$590$	10.3129	−	10.3129i	0.424573	−	0.424573i
$591$	46.0412			1.89388
$592$	4.56883	−	4.56883i	0.187778	−	0.187778i
$593$		−	27.7090i		−	1.13787i	−0.822381	−	0.568937i	$-0.807355\pi$
$593$		−	27.7090i		−	1.13787i	0.822381	−	0.568937i	$-0.192645\pi$
$594$	27.8105			1.14108
$595$	5.80039	+	12.7388i	0.237793	+	0.522241i
$596$	−0.316581			−0.0129677
$597$		−	10.6790i		−	0.437063i
$598$	2.71820	−	2.71820i	0.111155	−	0.111155i
$599$	−7.54536			−0.308295			−0.154148	−	0.988048i	$-0.549263\pi$
$599$	−7.54536			−0.308295			−0.154148	+	0.988048i	$0.549263\pi$
$600$	22.5476	−	22.5476i	0.920503	−	0.920503i
$601$	12.8735	+	12.8735i	0.525119	+	0.525119i	0.919113	−	0.393994i	$-0.128907\pi$
$601$	12.8735	+	12.8735i	0.525119	+	0.525119i	−0.393994	+	0.919113i	$0.628907\pi$
$602$	−7.38460	−	7.38460i	−0.300974	−	0.300974i
$603$		−	14.2974i		−	0.582234i
$604$			5.39311i			0.219442i
$605$	25.9609	+	25.9609i	1.05546	+	1.05546i
$606$	−12.1799	−	12.1799i	−0.494775	−	0.494775i
$607$	−8.64742	+	8.64742i	−0.350988	+	0.350988i	−0.860477	−	0.509489i	$-0.829834\pi$
$607$	−8.64742	+	8.64742i	−0.350988	+	0.350988i	0.509489	+	0.860477i	$0.329834\pi$
$608$	−16.2294			−0.658189
$609$	8.04490	−	8.04490i	0.325996	−	0.325996i
$610$			64.5748i			2.61456i
$611$	15.7367			0.636639
$612$	−2.01672	+	0.918276i	−0.0815212	+	0.0371191i
$613$	−39.4099			−1.59175			−0.795876	−	0.605460i	$-0.792989\pi$
$613$	−39.4099			−1.59175			−0.795876	+	0.605460i	$0.792989\pi$
$614$			11.2640i			0.454580i
$615$	−3.39899	+	3.39899i	−0.137060	+	0.137060i
$616$	−11.2203			−0.452077
$617$	10.4142	−	10.4142i	0.419260	−	0.419260i	−0.465689	−	0.884948i	$-0.654193\pi$
$617$	10.4142	−	10.4142i	0.419260	−	0.419260i	0.884948	+	0.465689i	$0.154193\pi$
$618$	−8.96211	−	8.96211i	−0.360509	−	0.360509i
$619$	26.1584	+	26.1584i	1.05140	+	1.05140i	0.998606	+	0.0527903i	$0.0168115\pi$
$619$	26.1584	+	26.1584i	1.05140	+	1.05140i	0.0527903	+	0.998606i	$0.483188\pi$
$620$		−	12.2744i		−	0.492951i
$621$		−	2.54524i		−	0.102137i
$622$	6.99806	+	6.99806i	0.280597	+	0.280597i
$623$	−1.44749	−	1.44749i	−0.0579924	−	0.0579924i
$624$	24.7059	−	24.7059i	0.989028	−	0.989028i
$625$	15.0506			0.602023
$626$	34.8786	−	34.8786i	1.39403	−	1.39403i
$627$			58.8859i			2.35168i
$628$	−11.0392			−0.440512
$629$	−5.28464	−	1.97782i	−0.210713	−	0.0788609i
$630$	−6.07647			−0.242092
$631$		−	31.7794i		−	1.26512i	−0.774512	−	0.632559i	$-0.782004\pi$
$631$		−	31.7794i		−	1.26512i	0.774512	−	0.632559i	$-0.217996\pi$
$632$	16.9949	−	16.9949i	0.676021	−	0.676021i
$633$	19.7881			0.786508
$634$	18.4171	−	18.4171i	0.731438	−	0.731438i
$635$	−12.3119	−	12.3119i	−0.488584	−	0.488584i
$636$	2.77034	+	2.77034i	0.109851	+	0.109851i
$637$			3.63777i			0.144134i
$638$		−	41.0702i		−	1.62599i
$639$	−3.46602	−	3.46602i	−0.137114	−	0.137114i
$640$	32.6716	+	32.6716i	1.29146	+	1.29146i
$641$	−13.4016	+	13.4016i	−0.529331	+	0.529331i	−0.920373	−	0.391042i	$-0.872115\pi$
$641$	−13.4016	+	13.4016i	−0.529331	+	0.529331i	0.391042	+	0.920373i	$0.372115\pi$
$642$	36.3986			1.43654
$643$	−19.0600	+	19.0600i	−0.751652	+	0.751652i	−0.974787	−	0.223135i	$-0.928371\pi$
$643$	−19.0600	+	19.0600i	−0.751652	+	0.751652i	0.223135	+	0.974787i	$0.428371\pi$
$644$		−	0.317294i		−	0.0125031i
$645$	45.8716			1.80619
$646$	16.6491	+	36.5649i	0.655051	+	1.43863i
$647$	0.816139			0.0320858			0.0160429	−	0.999871i	$-0.494893\pi$
$647$	0.816139			0.0320858			0.0160429	+	0.999871i	$0.494893\pi$
$648$		−	26.7118i		−	1.04934i
$649$	9.02408	−	9.02408i	0.354226	−	0.354226i
$650$	−37.3198			−1.46380
$651$	11.0167	−	11.0167i	0.431777	−	0.431777i
$652$	−4.03161	−	4.03161i	−0.157890	−	0.157890i
$653$	18.7492	+	18.7492i	0.733712	+	0.733712i	0.971353	−	0.237641i	$-0.0763743\pi$
$653$	18.7492	+	18.7492i	0.733712	+	0.733712i	−0.237641	+	0.971353i	$0.576374\pi$
$654$		−	14.0920i		−	0.551042i
$655$		−	28.3585i		−	1.10806i
$656$	−2.32369	−	2.32369i	−0.0907249	−	0.0907249i
$657$	1.32913	+	1.32913i	0.0518544	+	0.0518544i
$658$	4.80946	−	4.80946i	0.187492	−	0.187492i
$659$	−15.6995			−0.611566			−0.305783	−	0.952101i	$-0.598918\pi$
$659$	−15.6995			−0.611566			−0.305783	+	0.952101i	$0.598918\pi$
$660$	−10.7678	+	10.7678i	−0.419138	+	0.419138i
$661$			15.5120i			0.603348i	0.953411	+	0.301674i	$0.0975454\pi$
$661$			15.5120i			0.603348i	−0.953411	+	0.301674i	$0.902455\pi$
$662$	−7.44156			−0.289224
$663$	−28.5766	−	10.6950i	−1.10982	−	0.415361i
$664$	−11.2707			−0.437386
$665$			21.0396i			0.815880i
$666$	1.73211	−	1.73211i	0.0671179	−	0.0671179i
$667$	−3.75878			−0.145541
$668$	8.19008	−	8.19008i	0.316884	−	0.316884i
$669$	−25.2364	−	25.2364i	−0.975694	−	0.975694i
$670$	−47.4015	−	47.4015i	−1.83128	−	1.83128i
$671$			56.5050i			2.18135i
$672$		−	5.32721i		−	0.205502i
$673$	25.7151	+	25.7151i	0.991243	+	0.991243i	0.999962	−	0.00871919i	$-0.00277544\pi$
$673$	25.7151	+	25.7151i	0.991243	+	0.991243i	−0.00871919	+	0.999962i	$0.502775\pi$
$674$	−26.8112	−	26.8112i	−1.03273	−	1.03273i
$675$	−17.4725	+	17.4725i	−0.672518	+	0.672518i
$676$	−0.110171			−0.00423736
$677$	−20.2679	+	20.2679i	−0.778959	+	0.778959i	−0.979654	−	0.200695i	$-0.935680\pi$
$677$	−20.2679	+	20.2679i	−0.778959	+	0.778959i	0.200695	+	0.979654i	$0.435680\pi$
$678$		−	37.0938i		−	1.42458i
$679$	−4.23013			−0.162338
$680$	11.7863	−	31.4923i	0.451982	−	1.20768i
$681$	16.9735			0.650425
$682$		−	56.2414i		−	2.15359i
$683$	13.9866	−	13.9866i	0.535181	−	0.535181i	−0.386929	−	0.922110i	$-0.626464\pi$
$683$	13.9866	−	13.9866i	0.535181	−	0.535181i	0.922110	+	0.386929i	$0.126464\pi$
$684$	−3.33084			−0.127358
$685$	−48.4754	+	48.4754i	−1.85215	+	1.85215i
$686$	1.11178	+	1.11178i	0.0424479	+	0.0424479i
$687$	22.0724	+	22.0724i	0.842114	+	0.842114i
$688$			31.3598i			1.19558i
$689$			14.8399i			0.565356i
$690$	5.16037	+	5.16037i	0.196452	+	0.196452i
$691$	26.6547	+	26.6547i	1.01399	+	1.01399i	0.999901	+	0.0140930i	$0.00448608\pi$
$691$	26.6547	+	26.6547i	1.01399	+	1.01399i	0.0140930	+	0.999901i	$0.495514\pi$
$692$	−1.19017	+	1.19017i	−0.0452434	+	0.0452434i
$693$	−5.31711			−0.201980
$694$	−25.4665	+	25.4665i	−0.966697	+	0.966697i
$695$		−	26.4970i		−	1.00509i
$696$	−27.3315			−1.03600
$697$	−1.00591	+	2.68775i	−0.0381016	+	0.101806i
$698$	16.0212			0.606410
$699$			49.7946i			1.88341i
$700$	−2.17816	+	2.17816i	−0.0823267	+	0.0823267i
$701$	12.4612			0.470652			0.235326	−	0.971916i	$-0.424384\pi$
$701$	12.4612			0.470652			0.235326	+	0.971916i	$0.424384\pi$
$702$	−15.3163	+	15.3163i	−0.578076	+	0.578076i
$703$	−5.99737	−	5.99737i	−0.226195	−	0.226195i
$704$	17.5875	+	17.5875i	0.662855	+	0.662855i
$705$			29.8754i			1.12517i
$706$			26.4143i			0.994116i
$707$	−3.80797	−	3.80797i	−0.143214	−	0.143214i
$708$	1.85558	+	1.85558i	0.0697368	+	0.0697368i
$709$	−10.2099	+	10.2099i	−0.383439	+	0.383439i	−0.872340	−	0.488900i	$-0.837398\pi$
$709$	−10.2099	+	10.2099i	−0.383439	+	0.383439i	0.488900	+	0.872340i	$0.337398\pi$
$710$	−22.9825			−0.862517
$711$	8.05362	−	8.05362i	0.302034	−	0.302034i
$712$			4.91766i			0.184297i
$713$	−5.14726			−0.192766
$714$	−12.0022	+	5.46499i	−0.449172	+	0.204522i
$715$	−57.6804			−2.15712
$716$			1.87006i			0.0698874i
$717$	−20.9688	+	20.9688i	−0.783095	+	0.783095i
$718$	−44.4044			−1.65716
$719$	−6.54115	+	6.54115i	−0.243944	+	0.243944i	−0.818479	−	0.574536i	$-0.805183\pi$
$719$	−6.54115	+	6.54115i	−0.243944	+	0.243944i	0.574536	+	0.818479i	$0.305183\pi$
$720$	12.9023	+	12.9023i	0.480840	+	0.480840i
$721$	−2.80195	−	2.80195i	−0.104350	−	0.104350i
$722$			30.5173i			1.13574i
$723$		−	30.9528i		−	1.15115i
$724$	0.643317	+	0.643317i	0.0239087	+	0.0239087i
$725$	25.8033	+	25.8033i	0.958309	+	0.958309i
$726$	−24.4597	+	24.4597i	−0.907785	+	0.907785i
$727$	33.0618			1.22619			0.613096	−	0.790008i	$-0.289924\pi$
$727$	33.0618			1.22619			0.613096	+	0.790008i	$0.289924\pi$
$728$	6.17943	−	6.17943i	0.229025	−	0.229025i
$729$			10.4537i			0.387175i
$730$	8.81320			0.326191
$731$	24.9242	−	11.3488i	0.921855	−	0.419749i
$732$	−11.6188			−0.429445
$733$		−	1.81758i		−	0.0671338i	−0.999436	−	0.0335669i	$-0.989313\pi$
$733$		−	1.81758i		−	0.0671338i	0.999436	−	0.0335669i	$-0.0106867\pi$
$734$	−20.9153	+	20.9153i	−0.771998	+	0.771998i
$735$	−6.90613			−0.254736
$736$	−1.24450	+	1.24450i	−0.0458730	+	0.0458730i
$737$	−41.4779	−	41.4779i	−1.52786	−	1.52786i
$738$	−0.880943	−	0.880943i	−0.0324280	−	0.0324280i
$739$			30.1602i			1.10946i	0.832031	+	0.554730i	$0.187178\pi$
$739$			30.1602i			1.10946i	−0.832031	+	0.554730i	$0.812822\pi$
$740$		−	2.19335i		−	0.0806292i
$741$	−32.4307	−	32.4307i	−1.19137	−	1.19137i
$742$	4.53539	+	4.53539i	0.166499	+	0.166499i
$743$	28.0426	−	28.0426i	1.02878	−	1.02878i	0.0292082	−	0.999573i	$-0.490701\pi$
$743$	28.0426	−	28.0426i	1.02878	−	1.02878i	0.999573	−	0.0292082i	$-0.00929860\pi$
$744$	−37.4277			−1.37216
$745$	1.60973	−	1.60973i	0.0589760	−	0.0589760i
$746$		−	48.6867i		−	1.78255i
$747$	−5.34098			−0.195416
$748$	−3.18668	+	8.51467i	−0.116517	+	0.311327i
$749$	11.3798			0.415809
$750$		−	16.5575i		−	0.604595i
$751$	−29.5789	+	29.5789i	−1.07935	+	1.07935i	−0.0827803	+	0.996568i	$0.526380\pi$
$751$	−29.5789	+	29.5789i	−1.07935	+	1.07935i	−0.996568	+	0.0827803i	$0.973620\pi$
$752$	−20.4241			−0.744789
$753$	−2.21572	+	2.21572i	−0.0807454	+	0.0807454i
$754$	22.6189	+	22.6189i	0.823733	+	0.823733i
$755$	−27.4226	−	27.4226i	−0.998009	−	0.998009i
$756$			1.78786i			0.0650239i
$757$		−	29.9024i		−	1.08682i	−0.839467	−	0.543411i	$-0.817133\pi$
$757$		−	29.9024i		−	1.08682i	0.839467	−	0.543411i	$-0.182867\pi$
$758$	13.8421	+	13.8421i	0.502766	+	0.502766i
$759$	4.51550	+	4.51550i	0.163902	+	0.163902i
$760$	35.7396	−	35.7396i	1.29641	−	1.29641i
$761$	−29.8807			−1.08318			−0.541588	−	0.840644i	$-0.682177\pi$
$761$	−29.8807			−1.08318			−0.541588	+	0.840644i	$0.682177\pi$
$762$	11.6000	−	11.6000i	0.420224	−	0.420224i
$763$		−	4.40579i		−	0.159500i
$764$	11.8840			0.429948
$765$	5.58532	−	14.9237i	0.201938	−	0.539568i
$766$	46.9262			1.69551
$767$			9.93981i			0.358906i
$768$	−15.4618	+	15.4618i	−0.557929	+	0.557929i
$769$	35.8821			1.29394			0.646971	−	0.762514i	$-0.276035\pi$
$769$	35.8821			1.29394			0.646971	+	0.762514i	$0.276035\pi$
$770$	−17.6283	+	17.6283i	−0.635280	+	0.635280i
$771$	−5.79594	−	5.79594i	−0.208736	−	0.208736i
$772$	−3.75444	−	3.75444i	−0.135125	−	0.135125i
$773$		−	13.1964i		−	0.474642i	−0.971431	−	0.237321i	$-0.923731\pi$
$773$		−	13.1964i		−	0.474642i	0.971431	−	0.237321i	$-0.0762692\pi$
$774$			11.8889i			0.427338i
$775$	35.3349	+	35.3349i	1.26927	+	1.26927i
$776$	7.18567	+	7.18567i	0.257950	+	0.257950i
$777$	1.96861	−	1.96861i	0.0706234	−	0.0706234i
$778$	32.9245			1.18040
$779$	−3.05024	+	3.05024i	−0.109286	+	0.109286i
$780$		−	11.8605i		−	0.424675i
$781$	−20.1104			−0.719608
$782$	4.08056	+	1.52718i	0.145921	+	0.0546120i
$783$	21.1797			0.756899
$784$		−	4.72132i		−	0.168619i
$785$	56.1314	−	56.1314i	2.00342	−	2.00342i
$786$	26.7187			0.953025
$787$	20.2916	−	20.2916i	0.723318	−	0.723318i	−0.245962	−	0.969280i	$-0.579104\pi$
$787$	20.2916	−	20.2916i	0.723318	−	0.723318i	0.969280	+	0.245962i	$0.0791038\pi$
$788$	7.55525	+	7.55525i	0.269144	+	0.269144i
$789$	25.8552	+	25.8552i	0.920470	+	0.920470i
$790$		−	53.4019i		−	1.89995i
$791$		−	11.5971i		−	0.412347i
$792$	9.03209	+	9.03209i	0.320941	+	0.320941i
$793$	−31.1195	−	31.1195i	−1.10508	−	1.10508i
$794$	−31.5308	+	31.5308i	−1.11899	+	1.11899i
$795$	−28.1729			−0.999189
$796$	1.75240	−	1.75240i	0.0621121	−	0.0621121i
$797$		−	10.8120i		−	0.382980i	−0.981495	−	0.191490i	$-0.938668\pi$
$797$		−	10.8120i		−	0.382980i	0.981495	−	0.191490i	$-0.0613320\pi$
$798$	−19.8230			−0.701726
$799$	7.39125	+	16.2327i	0.261484	+	0.574272i
$800$	17.0865			0.604100
$801$			2.33040i			0.0823406i
$802$	3.63421	−	3.63421i	0.128328	−	0.128328i
$803$	7.71184			0.272145
$804$	8.52888	−	8.52888i	0.300790	−	0.300790i
$805$	1.61336	+	1.61336i	0.0568634	+	0.0568634i
$806$	30.9743	+	30.9743i	1.09102	+	1.09102i
$807$			36.6820i			1.29127i
$808$			12.9371i			0.455125i
$809$	36.0543	+	36.0543i	1.26760	+	1.26760i	0.947324	+	0.320276i	$0.103776\pi$
$809$	36.0543	+	36.0543i	1.26760	+	1.26760i	0.320276	+	0.947324i	$0.396224\pi$
$810$	−41.9673	−	41.9673i	−1.47458	−	1.47458i
$811$	10.8591	−	10.8591i	0.381315	−	0.381315i	−0.490261	−	0.871576i	$-0.663098\pi$
$811$	10.8591	−	10.8591i	0.381315	−	0.381315i	0.871576	+	0.490261i	$0.163098\pi$
$812$	2.64030			0.0926562
$813$	−24.0340	+	24.0340i	−0.842910	+	0.842910i
$814$		−	10.0500i		−	0.352251i
$815$	40.9994			1.43615
$816$	37.0885	+	13.8807i	1.29836	+	0.485921i
$817$	41.1650			1.44018
$818$			54.0654i			1.89035i
$819$	2.92833	−	2.92833i	0.102324	−	0.102324i
$820$	−1.11553			−0.0389560
$821$	9.85365	−	9.85365i	0.343895	−	0.343895i	−0.513935	−	0.857829i	$-0.671813\pi$
$821$	9.85365	−	9.85365i	0.343895	−	0.343895i	0.857829	+	0.513935i	$0.171813\pi$
$822$	−45.6724	−	45.6724i	−1.59301	−	1.59301i
$823$	8.67935	+	8.67935i	0.302543	+	0.302543i	0.842008	−	0.539465i	$-0.181373\pi$
$823$	8.67935	+	8.67935i	0.302543	+	0.302543i	−0.539465	+	0.842008i	$0.681373\pi$
$824$			9.51926i			0.331619i
$825$		−	61.9959i		−	2.15842i
$826$	3.03781	+	3.03781i	0.105699	+	0.105699i
$827$	11.8528	+	11.8528i	0.412162	+	0.412162i	0.882491	−	0.470329i	$-0.155865\pi$
$827$	11.8528	+	11.8528i	0.412162	+	0.412162i	−0.470329	+	0.882491i	$0.655865\pi$
$828$	−0.255416	+	0.255416i	−0.00887631	+	0.00887631i
$829$	−43.4266			−1.50827			−0.754134	−	0.656721i	$-0.771943\pi$
$829$	−43.4266			−1.50827			−0.754134	+	0.656721i	$0.771943\pi$
$830$	−17.7075	+	17.7075i	−0.614635	+	0.614635i
$831$		−	2.12300i		−	0.0736459i
$832$	−19.3722			−0.671612
$833$	−3.75243	+	1.70860i	−0.130014	+	0.0591993i
$834$	24.9649			0.864463
$835$			83.2889i			2.88233i
$836$	−9.66303	+	9.66303i	−0.334203	+	0.334203i
$837$	29.0033			1.00250
$838$	−19.4758	+	19.4758i	−0.672781	+	0.672781i
$839$	4.20215	+	4.20215i	0.145074	+	0.145074i	0.775914	−	0.630839i	$-0.217289\pi$
$839$	4.20215	+	4.20215i	0.145074	+	0.145074i	−0.630839	+	0.775914i	$0.717289\pi$
$840$	11.7313	+	11.7313i	0.404770	+	0.404770i
$841$		−	2.27792i		−	0.0785488i
$842$			20.6015i			0.709973i
$843$	−5.07834	−	5.07834i	−0.174907	−	0.174907i
$844$	3.24718	+	3.24718i	0.111773	+	0.111773i
$845$	0.560193	−	0.560193i	0.0192712	−	0.0192712i
$846$	−7.74305			−0.266211
$847$	−7.64718	+	7.64718i	−0.262760	+	0.262760i
$848$		−	19.2602i		−	0.661397i
$849$	3.70950			0.127310
$850$	−17.5284	−	38.4960i	−0.601220	−	1.32040i
$851$	−0.919783			−0.0315297
$852$		−	4.13521i		−	0.141670i
$853$	−9.18348	+	9.18348i	−0.314436	+	0.314436i	−0.846625	−	0.532189i	$-0.821370\pi$
$853$	−9.18348	+	9.18348i	−0.314436	+	0.314436i	0.532189	+	0.846625i	$0.321370\pi$
$854$	−19.0215			−0.650903
$855$	16.9364	−	16.9364i	0.579214	−	0.579214i
$856$	−19.3307	−	19.3307i	−0.660710	−	0.660710i
$857$	−20.3600	−	20.3600i	−0.695483	−	0.695483i	0.267950	−	0.963433i	$-0.413654\pi$
$857$	−20.3600	−	20.3600i	−0.695483	−	0.695483i	−0.963433	+	0.267950i	$0.913654\pi$
$858$		−	54.3451i		−	1.85531i
$859$		−	8.24733i		−	0.281395i	−0.990053	−	0.140698i	$-0.955065\pi$
$859$		−	8.24733i		−	0.281395i	0.990053	−	0.140698i	$-0.0449345\pi$
$860$	7.52741	+	7.52741i	0.256683	+	0.256683i
$861$	−1.00123	−	1.00123i	−0.0341217	−	0.0341217i
$862$	29.2207	−	29.2207i	0.995260	−	0.995260i
$863$	−35.6828			−1.21466			−0.607329	−	0.794450i	$-0.707759\pi$
$863$	−35.6828			−1.21466			−0.607329	+	0.794450i	$0.707759\pi$
$864$	7.01242	−	7.01242i	0.238567	−	0.238567i
$865$		−	12.1034i		−	0.411527i
$866$	−1.23218			−0.0418710
$867$	−2.38981	−	34.5006i	−0.0811621	−	1.17170i
$868$	3.61561			0.122722
$869$		−	46.7284i		−	1.58515i
$870$	−42.9409	+	42.9409i	−1.45583	+	1.45583i
$871$	45.6869			1.54804
$872$	−7.48405	+	7.48405i	−0.253442	+	0.253442i
$873$	3.40518	+	3.40518i	0.115248	+	0.115248i
$874$	4.63090	+	4.63090i	0.156643	+	0.156643i
$875$		−	5.17661i		−	0.175001i
$876$			1.58575i			0.0535774i
$877$	−9.95149	−	9.95149i	−0.336038	−	0.336038i	0.518836	−	0.854874i	$-0.326366\pi$
$877$	−9.95149	−	9.95149i	−0.336038	−	0.336038i	−0.854874	+	0.518836i	$0.826366\pi$
$878$	−27.9657	−	27.9657i	−0.943797	−	0.943797i
$879$	−21.5174	+	21.5174i	−0.725763	+	0.725763i
$880$	74.8611			2.52357
$881$	10.4454	−	10.4454i	0.351914	−	0.351914i	−0.508907	−	0.860821i	$-0.669950\pi$
$881$	10.4454	−	10.4454i	0.351914	−	0.351914i	0.860821	+	0.508907i	$0.169950\pi$
$882$		−	1.78992i		−	0.0602697i
$883$	4.72305			0.158943			0.0794717	−	0.996837i	$-0.474677\pi$
$883$	4.72305			0.158943			0.0794717	+	0.996837i	$0.474677\pi$
$884$	−2.93432	−	6.44438i	−0.0986920	−	0.216748i
$885$	−18.8703			−0.634317
$886$			19.0746i			0.640823i
$887$	−31.9047	+	31.9047i	−1.07126	+	1.07126i	−0.0739977	+	0.997258i	$0.523576\pi$
$887$	−31.9047	+	31.9047i	−1.07126	+	1.07126i	−0.997258	+	0.0739977i	$0.976424\pi$
$888$	−6.68809			−0.224437
$889$	3.62667	−	3.62667i	0.121635	−	0.121635i
$890$	7.72620	+	7.72620i	0.258983	+	0.258983i
$891$	−36.7228	−	36.7228i	−1.23026	−	1.23026i
$892$		−	8.28245i		−	0.277317i
$893$			26.8101i			0.897164i
$894$	1.51665	+	1.51665i	0.0507244	+	0.0507244i
$895$	−9.50877	−	9.50877i	−0.317843	−	0.317843i
$896$	−9.62394	+	9.62394i	−0.321513	+	0.321513i
$897$	−4.97371			−0.166067
$898$	41.1407	−	41.1407i	1.37288	−	1.37288i
$899$		−	42.8318i		−	1.42852i
$900$	3.50675			0.116892
$901$	−15.3077	+	6.97005i	−0.509972	+	0.232206i
$902$	−5.11138			−0.170190
$903$			13.5122i			0.449658i
$904$	−19.6999	+	19.6999i	−0.655209	+	0.655209i
$905$	−6.54220			−0.217470
$906$	25.8369	−	25.8369i	0.858373	−	0.858373i
$907$	23.9495	+	23.9495i	0.795231	+	0.795231i	0.982339	−	0.187108i	$-0.0599114\pi$
$907$	23.9495	+	23.9495i	0.795231	+	0.795231i	−0.187108	+	0.982339i	$0.559911\pi$
$908$	2.78530	+	2.78530i	0.0924336	+	0.0924336i
$909$			6.13069i			0.203342i
$910$		−	19.4172i		−	0.643673i
$911$	7.16704	+	7.16704i	0.237455	+	0.237455i	0.815795	−	0.578341i	$-0.196300\pi$
$911$	7.16704	+	7.16704i	0.237455	+	0.237455i	−0.578341	+	0.815795i	$0.696300\pi$
$912$	42.0906	+	42.0906i	1.39376	+	1.39376i
$913$	−15.4946	+	15.4946i	−0.512797	+	0.512797i
$914$	−20.1063			−0.665057
$915$	59.0788	−	59.0788i	1.95309	−	1.95309i
$916$			7.24404i			0.239350i
$917$	8.35345			0.275855
$918$	−22.9928	−	8.60524i	−0.758876	−	0.284015i
$919$	−7.90071			−0.260620			−0.130310	−	0.991473i	$-0.541597\pi$
$919$	−7.90071			−0.260620			−0.130310	+	0.991473i	$0.541597\pi$
$920$		−	5.48118i		−	0.180709i
$921$	10.3054	−	10.3054i	0.339573	−	0.339573i
$922$	7.20249			0.237201
$923$	11.0756	−	11.0756i	0.364557	−	0.364557i
$924$	−3.17184	−	3.17184i	−0.104346	−	0.104346i
$925$	6.31412	+	6.31412i	0.207607	+	0.207607i
$926$			2.41887i			0.0794891i
$927$			4.51103i			0.148162i
$928$	−10.3559	−	10.3559i	−0.339948	−	0.339948i
$929$	−6.47675	−	6.47675i	−0.212495	−	0.212495i	0.592831	−	0.805327i	$-0.298010\pi$
$929$	−6.47675	−	6.47675i	−0.212495	−	0.212495i	−0.805327	+	0.592831i	$0.798010\pi$
$930$	−58.8031	+	58.8031i	−1.92823	+	1.92823i
$931$	−6.19754			−0.203116
$932$	−8.17117	+	8.17117i	−0.267656	+	0.267656i
$933$		−	12.8049i		−	0.419214i
$934$	17.2994			0.566054
$935$	−27.0914	−	59.4984i	−0.885985	−	1.94580i
$936$	−9.94863			−0.325181
$937$		−	53.4400i		−	1.74581i	−0.487891	−	0.872905i	$-0.662234\pi$
$937$		−	53.4400i		−	1.74581i	0.487891	−	0.872905i	$-0.337766\pi$
$938$	13.9629	−	13.9629i	0.455903	−	0.455903i
$939$	−63.8202			−2.08269
$940$	−4.90247	+	4.90247i	−0.159901	+	0.159901i
$941$	35.4583	+	35.4583i	1.15591	+	1.15591i	0.985347	+	0.170562i	$0.0545582\pi$
$941$	35.4583	+	35.4583i	1.15591	+	1.15591i	0.170562	+	0.985347i	$0.445442\pi$
$942$	52.8857	+	52.8857i	1.72311	+	1.72311i
$943$			0.467798i			0.0152336i
$944$		−	12.9005i		−	0.419876i
$945$	−9.09081	−	9.09081i	−0.295724	−	0.295724i
$946$	34.4907	+	34.4907i	1.12139	+	1.12139i
$947$	−10.3757	+	10.3757i	−0.337165	+	0.337165i	−0.855299	−	0.518135i	$-0.826627\pi$
$947$	−10.3757	+	10.3757i	−0.337165	+	0.337165i	0.518135	+	0.855299i	$0.326627\pi$
$948$	9.60853			0.312070
$949$	−4.24720	+	4.24720i	−0.137870	+	0.137870i
$950$		−	63.5803i		−	2.06282i
$951$	−33.6993			−1.09278
$952$	9.27656	+	3.47183i	0.300655	+	0.112523i
$953$	−4.66197			−0.151016			−0.0755080	−	0.997145i	$-0.524058\pi$
$953$	−4.66197			−0.151016			−0.0755080	+	0.997145i	$0.524058\pi$
$954$		−	7.30180i		−	0.236405i
$955$	−60.4270	+	60.4270i	−1.95537	+	1.95537i
$956$	−6.88186			−0.222575
$957$	−37.5747	+	37.5747i	−1.21462	+	1.21462i
$958$	−25.8621	−	25.8621i	−0.835566	−	0.835566i
$959$	−14.2792	−	14.2792i	−0.461100	−	0.461100i
$960$		−	36.7773i		−	1.18698i
$961$		−	27.6537i		−	0.892056i
$962$	5.53490	+	5.53490i	0.178452	+	0.178452i
$963$	−9.16052	−	9.16052i	−0.295194	−	0.295194i
$964$	5.07927	−	5.07927i	0.163592	−	0.163592i
$965$	38.1807			1.22908
$966$	−1.52007	+	1.52007i	−0.0489074	+	0.0489074i
$967$		−	15.2606i		−	0.490748i	−0.969428	−	0.245374i	$-0.921089\pi$
$967$		−	15.2606i		−	0.490748i	0.969428	−	0.245374i	$-0.0789108\pi$
$968$	25.9803			0.835039
$969$	18.2207	−	48.6850i	0.585335	−	1.56399i
$970$	22.5790			0.724968
$971$			18.5971i			0.596810i	0.954439	+	0.298405i	$0.0964546\pi$
$971$			18.5971i			0.596810i	−0.954439	+	0.298405i	$0.903545\pi$
$972$	3.75850	−	3.75850i	0.120554	−	0.120554i
$973$	7.80511			0.250220
$974$	24.4991	−	24.4991i	0.785003	−	0.785003i
$975$	34.1435	+	34.1435i	1.09347	+	1.09347i
$976$	40.3888	+	40.3888i	1.29281	+	1.29281i
$977$		−	21.7450i		−	0.695683i	−0.937553	−	0.347842i	$-0.886915\pi$
$977$		−	21.7450i		−	0.695683i	0.937553	−	0.347842i	$-0.113085\pi$
$978$			38.6287i			1.23521i
$979$	6.76068	+	6.76068i	0.216072	+	0.216072i
$980$	−1.13328	−	1.13328i	−0.0362012	−	0.0362012i
$981$	−3.54657	+	3.54657i	−0.113233	+	0.113233i
$982$	30.2935			0.966704
$983$	−2.52556	+	2.52556i	−0.0805529	+	0.0805529i	−0.746235	−	0.665682i	$-0.768141\pi$
$983$	−2.52556	+	2.52556i	−0.0805529	+	0.0805529i	0.665682	+	0.746235i	$0.268141\pi$
$984$			3.40153i			0.108437i
$985$	−76.8329			−2.44810
$986$	−12.7081	+	33.9556i	−0.404710	+	1.08137i
$987$	−8.80026			−0.280115
$988$		−	10.6436i		−	0.338618i
$989$	3.15662	−	3.15662i	0.100375	−	0.100375i
$990$	28.3809			0.902004
$991$	−0.300053	+	0.300053i	−0.00953151	+	0.00953151i	−0.711856	−	0.702325i	$-0.752145\pi$
$991$	−0.300053	+	0.300053i	−0.00953151	+	0.00953151i	0.702325	+	0.711856i	$0.252145\pi$
$992$	−14.1813	−	14.1813i	−0.450257	−	0.450257i
$993$	6.80821	+	6.80821i	0.216052	+	0.216052i
$994$		−	6.76985i		−	0.214727i
$995$			17.8210i			0.564963i
$996$	−3.18608	−	3.18608i	−0.100955	−	0.100955i
$997$	−26.4732	−	26.4732i	−0.838416	−	0.838416i	0.150234	−	0.988650i	$-0.451997\pi$
$997$	−26.4732	−	26.4732i	−0.838416	−	0.838416i	−0.988650	+	0.150234i	$0.951997\pi$
$998$	47.0966	−	47.0966i	1.49082	−	1.49082i
$999$	5.18271			0.163974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.2.g.a.106.3	yes	20
3.2	odd	2		1071.2.n.c.820.8		20
7.2	even	3		833.2.o.g.361.3		40
7.3	odd	6		833.2.o.f.667.8		40
7.4	even	3		833.2.o.g.667.8		40
7.5	odd	6		833.2.o.f.361.3		40
7.6	odd	2		833.2.g.h.344.3		20
17.8	even	8		2023.2.a.n.1.3		10
17.9	even	8		2023.2.a.m.1.3		10
17.13	even	4	inner	119.2.g.a.64.8	✓	20
51.47	odd	4		1071.2.n.c.64.3		20
119.13	odd	4		833.2.g.h.540.8		20
119.30	even	12		833.2.o.g.557.8		40
119.47	odd	12		833.2.o.f.557.8		40
119.81	even	12		833.2.o.g.30.3		40
119.115	odd	12		833.2.o.f.30.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.g.a.64.8	✓	20	17.13	even	4	inner
119.2.g.a.106.3	yes	20	1.1	even	1	trivial
833.2.g.h.344.3		20	7.6	odd	2
833.2.g.h.540.8		20	119.13	odd	4
833.2.o.f.30.3		40	119.115	odd	12
833.2.o.f.361.3		40	7.5	odd	6
833.2.o.f.557.8		40	119.47	odd	12
833.2.o.f.667.8		40	7.3	odd	6
833.2.o.g.30.3		40	119.81	even	12
833.2.o.g.361.3		40	7.2	even	3
833.2.o.g.557.8		40	119.30	even	12
833.2.o.g.667.8		40	7.4	even	3
1071.2.n.c.64.3		20	51.47	odd	4
1071.2.n.c.820.8		20	3.2	odd	2
2023.2.a.m.1.3		10	17.9	even	8
2023.2.a.n.1.3		10	17.8	even	8

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:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	119.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.57229i q^{2} +(-1.43847 + 1.43847i) q^{3} -0.472100 q^{4} +(2.40051 - 2.40051i) q^{5} +(2.26170 + 2.26170i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.40230i q^{8} -1.13841i q^{9} +O(q^{10})\)	\(q-1.57229i q^{2} +(-1.43847 + 1.43847i) q^{3} -0.472100 q^{4} +(2.40051 - 2.40051i) q^{5} +(2.26170 + 2.26170i) q^{6} +(0.707107 + 0.707107i) q^{7} -2.40230i q^{8} -1.13841i q^{9} +(-3.77429 - 3.77429i) q^{10} +(-3.30263 - 3.30263i) q^{11} +(0.679103 - 0.679103i) q^{12} +3.63777 q^{13} +(1.11178 - 1.11178i) q^{14} +6.90613i q^{15} -4.72132 q^{16} +(1.70860 + 3.75243i) q^{17} -1.78992 q^{18} +6.19754i q^{19} +(-1.13328 + 1.13328i) q^{20} -2.03431 q^{21} +(-5.19270 + 5.19270i) q^{22} +(0.475240 + 0.475240i) q^{23} +(3.45565 + 3.45565i) q^{24} -6.52485i q^{25} -5.71963i q^{26} +(-2.67784 - 2.67784i) q^{27} +(-0.333825 - 0.333825i) q^{28} +(-3.95461 + 3.95461i) q^{29} +10.8584 q^{30} +(-5.41543 + 5.41543i) q^{31} +2.61868i q^{32} +9.50150 q^{33} +(5.89991 - 2.68641i) q^{34} +3.39483 q^{35} +0.537445i q^{36} +(-0.967703 + 0.967703i) q^{37} +9.74433 q^{38} +(-5.23284 + 5.23284i) q^{39} +(-5.76674 - 5.76674i) q^{40} +(0.492170 + 0.492170i) q^{41} +3.19853i q^{42} -6.64216i q^{43} +(1.55917 + 1.55917i) q^{44} +(-2.73277 - 2.73277i) q^{45} +(0.747216 - 0.747216i) q^{46} +4.32592 q^{47} +(6.79150 - 6.79150i) q^{48} +1.00000i q^{49} -10.2590 q^{50} +(-7.85554 - 2.94000i) q^{51} -1.71739 q^{52} +4.07940i q^{53} +(-4.21035 + 4.21035i) q^{54} -15.8560 q^{55} +(1.69869 - 1.69869i) q^{56} +(-8.91500 - 8.91500i) q^{57} +(6.21780 + 6.21780i) q^{58} +2.73239i q^{59} -3.26038i q^{60} +(-8.55455 - 8.55455i) q^{61} +(8.51463 + 8.51463i) q^{62} +(0.804980 - 0.804980i) q^{63} -5.32531 q^{64} +(8.73248 - 8.73248i) q^{65} -14.9391i q^{66} +12.5590 q^{67} +(-0.806627 - 1.77152i) q^{68} -1.36724 q^{69} -5.33766i q^{70} +(3.04461 - 3.04461i) q^{71} -2.73482 q^{72} +(-1.16753 + 1.16753i) q^{73} +(1.52151 + 1.52151i) q^{74} +(9.38583 + 9.38583i) q^{75} -2.92586i q^{76} -4.67063i q^{77} +(8.22754 + 8.22754i) q^{78} +(7.07442 + 7.07442i) q^{79} +(-11.3336 + 11.3336i) q^{80} +11.1193 q^{81} +(0.773834 - 0.773834i) q^{82} -4.69160i q^{83} +0.960397 q^{84} +(13.1092 + 4.90623i) q^{85} -10.4434 q^{86} -11.3772i q^{87} +(-7.93393 + 7.93393i) q^{88} -2.04706 q^{89} +(-4.29671 + 4.29671i) q^{90} +(2.57229 + 2.57229i) q^{91} +(-0.224361 - 0.224361i) q^{92} -15.5799i q^{93} -6.80161i q^{94} +(14.8772 + 14.8772i) q^{95} +(-3.76691 - 3.76691i) q^{96} +(-2.99116 + 2.99116i) q^{97} +1.57229 q^{98} +(-3.75976 + 3.75976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 24 q^{4} - 8 q^{5} + 4 q^{6}+O(q^{10}) \) 20 * q - 4 * q^3 - 24 * q^4 - 8 * q^5 + 4 * q^6	\( 20 q - 4 q^{3} - 24 q^{4} - 8 q^{5} + 4 q^{6} + 4 q^{10} - 4 q^{11} + 12 q^{12} + 16 q^{16} - 12 q^{17} - 8 q^{18} + 20 q^{20} - 8 q^{21} - 20 q^{22} + 4 q^{24} + 8 q^{27} + 16 q^{29} - 36 q^{30} + 4 q^{31} - 16 q^{33} + 36 q^{34} + 16 q^{35} - 28 q^{37} + 48 q^{38} + 20 q^{39} - 24 q^{40} - 24 q^{41} - 28 q^{44} + 36 q^{45} + 8 q^{46} + 40 q^{47} - 8 q^{48} - 28 q^{50} - 40 q^{51} - 28 q^{54} - 40 q^{55} + 36 q^{57} + 56 q^{58} - 16 q^{61} - 40 q^{62} + 8 q^{63} + 32 q^{64} + 8 q^{65} - 32 q^{68} - 88 q^{69} - 8 q^{71} + 108 q^{72} + 8 q^{73} + 36 q^{74} + 8 q^{75} - 44 q^{78} - 4 q^{79} - 116 q^{80} + 4 q^{81} - 16 q^{82} - 32 q^{84} + 16 q^{85} + 44 q^{86} + 72 q^{88} + 48 q^{89} + 56 q^{90} + 20 q^{91} - 32 q^{92} + 44 q^{95} + 68 q^{96} - 24 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 - 24 * q^4 - 8 * q^5 + 4 * q^6 + 4 * q^10 - 4 * q^11 + 12 * q^12 + 16 * q^16 - 12 * q^17 - 8 * q^18 + 20 * q^20 - 8 * q^21 - 20 * q^22 + 4 * q^24 + 8 * q^27 + 16 * q^29 - 36 * q^30 + 4 * q^31 - 16 * q^33 + 36 * q^34 + 16 * q^35 - 28 * q^37 + 48 * q^38 + 20 * q^39 - 24 * q^40 - 24 * q^41 - 28 * q^44 + 36 * q^45 + 8 * q^46 + 40 * q^47 - 8 * q^48 - 28 * q^50 - 40 * q^51 - 28 * q^54 - 40 * q^55 + 36 * q^57 + 56 * q^58 - 16 * q^61 - 40 * q^62 + 8 * q^63 + 32 * q^64 + 8 * q^65 - 32 * q^68 - 88 * q^69 - 8 * q^71 + 108 * q^72 + 8 * q^73 + 36 * q^74 + 8 * q^75 - 44 * q^78 - 4 * q^79 - 116 * q^80 + 4 * q^81 - 16 * q^82 - 32 * q^84 + 16 * q^85 + 44 * q^86 + 72 * q^88 + 48 * q^89 + 56 * q^90 + 20 * q^91 - 32 * q^92 + 44 * q^95 + 68 * q^96 - 24 * q^99

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