LMFDB - Embedded newform 357.2.k.b.106.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(64,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("357.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.k (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:	$2.85065935216$
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} + 426 x^{16} + 3072 x^{14} + 13121 x^{12} + 34148 x^{10} + 53608 x^{8} + 48276 x^{6} + \cdots + 4 $ x^20 + 32x^18 + 426x^16 + 3072x^14 + 13121x^12 + 34148x^10 + 53608x^8 + 48276x^6 + 22224x^4 + 3920*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			106.8
Root			$1.71520i$ of defining polynomial
Character	$\chi$	$=$	357.106
Dual form			357.2.k.b.64.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.71520i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.941909 q^{4} +(2.50881 - 2.50881i) q^{5} +(-1.21283 - 1.21283i) q^{6} +(-0.707107 - 0.707107i) q^{7} +1.81484i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.71520i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.941909 q^{4} +(2.50881 - 2.50881i) q^{5} +(-1.21283 - 1.21283i) q^{6} +(-0.707107 - 0.707107i) q^{7} +1.81484i q^{8} -1.00000i q^{9} +(4.30311 + 4.30311i) q^{10} +(1.81437 + 1.81437i) q^{11} +(0.666030 - 0.666030i) q^{12} +3.70620 q^{13} +(1.21283 - 1.21283i) q^{14} +3.54799i q^{15} -4.99663 q^{16} +(3.33822 + 2.41998i) q^{17} +1.71520 q^{18} +6.90985i q^{19} +(-2.36307 + 2.36307i) q^{20} +1.00000 q^{21} +(-3.11200 + 3.11200i) q^{22} +(-5.39938 - 5.39938i) q^{23} +(-1.28328 - 1.28328i) q^{24} -7.58826i q^{25} +6.35687i q^{26} +(0.707107 + 0.707107i) q^{27} +(0.666030 + 0.666030i) q^{28} +(6.87048 - 6.87048i) q^{29} -6.08552 q^{30} +(-0.818937 + 0.818937i) q^{31} -4.94054i q^{32} -2.56590 q^{33} +(-4.15075 + 5.72571i) q^{34} -3.54799 q^{35} +0.941909i q^{36} +(-6.42994 + 6.42994i) q^{37} -11.8518 q^{38} +(-2.62068 + 2.62068i) q^{39} +(4.55308 + 4.55308i) q^{40} +(-6.03201 - 6.03201i) q^{41} +1.71520i q^{42} +1.71992i q^{43} +(-1.70897 - 1.70897i) q^{44} +(-2.50881 - 2.50881i) q^{45} +(9.26101 - 9.26101i) q^{46} -0.699863 q^{47} +(3.53315 - 3.53315i) q^{48} +1.00000i q^{49} +13.0154 q^{50} +(-4.07166 + 0.649291i) q^{51} -3.49090 q^{52} +3.38235i q^{53} +(-1.21283 + 1.21283i) q^{54} +9.10380 q^{55} +(1.28328 - 1.28328i) q^{56} +(-4.88600 - 4.88600i) q^{57} +(11.7842 + 11.7842i) q^{58} -10.9220i q^{59} -3.34189i q^{60} +(3.62531 + 3.62531i) q^{61} +(-1.40464 - 1.40464i) q^{62} +(-0.707107 + 0.707107i) q^{63} -1.51925 q^{64} +(9.29814 - 9.29814i) q^{65} -4.40103i q^{66} -2.86834 q^{67} +(-3.14430 - 2.27940i) q^{68} +7.63588 q^{69} -6.08552i q^{70} +(9.13401 - 9.13401i) q^{71} +1.81484 q^{72} +(1.00706 - 1.00706i) q^{73} +(-11.0286 - 11.0286i) q^{74} +(5.36571 + 5.36571i) q^{75} -6.50846i q^{76} -2.56590i q^{77} +(-4.49498 - 4.49498i) q^{78} +(-7.80162 - 7.80162i) q^{79} +(-12.5356 + 12.5356i) q^{80} -1.00000 q^{81} +(10.3461 - 10.3461i) q^{82} +8.11587i q^{83} -0.941909 q^{84} +(14.4462 - 2.30368i) q^{85} -2.95001 q^{86} +9.71633i q^{87} +(-3.29278 + 3.29278i) q^{88} -11.1085 q^{89} +(4.30311 - 4.30311i) q^{90} +(-2.62068 - 2.62068i) q^{91} +(5.08573 + 5.08573i) q^{92} -1.15815i q^{93} -1.20040i q^{94} +(17.3355 + 17.3355i) q^{95} +(3.49349 + 3.49349i) q^{96} +(1.25205 - 1.25205i) q^{97} -1.71520 q^{98} +(1.81437 - 1.81437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6}+O(q^{10}) $ 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6	$ 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6} + 16 q^{10} + 4 q^{11} - 12 q^{13} + 4 q^{14} + 40 q^{16} + 4 q^{17} + 8 q^{18} - 52 q^{20} + 20 q^{21} - 24 q^{22} - 4 q^{23} + 4 q^{24} - 8 q^{29} + 8 q^{31} - 4 q^{33} - 44 q^{34} + 12 q^{35} + 24 q^{37} - 64 q^{38} - 12 q^{39} - 52 q^{40} - 20 q^{41} + 72 q^{44} - 8 q^{45} + 28 q^{46} - 32 q^{47} + 32 q^{48} + 104 q^{50} + 8 q^{51} + 48 q^{52} - 4 q^{54} - 36 q^{55} - 4 q^{56} - 16 q^{57} - 60 q^{58} + 28 q^{61} + 36 q^{62} - 112 q^{64} - 4 q^{65} + 40 q^{67} - 52 q^{68} + 36 q^{69} + 16 q^{71} - 24 q^{72} - 72 q^{73} - 24 q^{74} - 8 q^{75} + 40 q^{78} - 8 q^{79} + 120 q^{80} - 20 q^{81} + 108 q^{82} - 24 q^{84} + 40 q^{85} - 28 q^{88} - 64 q^{89} + 16 q^{90} - 12 q^{91} - 56 q^{92} + 60 q^{95} + 16 q^{96} + 60 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6 + 16 * q^10 + 4 * q^11 - 12 * q^13 + 4 * q^14 + 40 * q^16 + 4 * q^17 + 8 * q^18 - 52 * q^20 + 20 * q^21 - 24 * q^22 - 4 * q^23 + 4 * q^24 - 8 * q^29 + 8 * q^31 - 4 * q^33 - 44 * q^34 + 12 * q^35 + 24 * q^37 - 64 * q^38 - 12 * q^39 - 52 * q^40 - 20 * q^41 + 72 * q^44 - 8 * q^45 + 28 * q^46 - 32 * q^47 + 32 * q^48 + 104 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^54 - 36 * q^55 - 4 * q^56 - 16 * q^57 - 60 * q^58 + 28 * q^61 + 36 * q^62 - 112 * q^64 - 4 * q^65 + 40 * q^67 - 52 * q^68 + 36 * q^69 + 16 * q^71 - 24 * q^72 - 72 * q^73 - 24 * q^74 - 8 * q^75 + 40 * q^78 - 8 * q^79 + 120 * q^80 - 20 * q^81 + 108 * q^82 - 24 * q^84 + 40 * q^85 - 28 * q^88 - 64 * q^89 + 16 * q^90 - 12 * q^91 - 56 * q^92 + 60 * q^95 + 16 * q^96 + 60 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$			1.71520i			1.21283i	0.795149	+	0.606415i	$0.207393\pi$
$2$			1.71520i			1.21283i	−0.795149	+	0.606415i	$0.792607\pi$
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−0.941909			−0.470955
$5$	2.50881	−	2.50881i	1.12197	−	1.12197i	0.130530	−	0.991444i	$-0.458332\pi$
$5$	2.50881	−	2.50881i	1.12197	−	1.12197i	0.991444	−	0.130530i	$-0.0416679\pi$
$6$	−1.21283	−	1.21283i	−0.495135	−	0.495135i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$			1.81484i			0.641642i
$9$		−	1.00000i		−	0.333333i
$10$	4.30311	+	4.30311i	1.36076	+	1.36076i
$11$	1.81437	+	1.81437i	0.547052	+	0.547052i	0.925587	−	0.378535i	$-0.123572\pi$
$11$	1.81437	+	1.81437i	0.547052	+	0.547052i	−0.378535	+	0.925587i	$0.623572\pi$
$12$	0.666030	−	0.666030i	0.192266	−	0.192266i
$13$	3.70620			1.02791			0.513957	−	0.857816i	$-0.328179\pi$
$13$	3.70620			1.02791			0.513957	+	0.857816i	$0.328179\pi$
$14$	1.21283	−	1.21283i	0.324142	−	0.324142i
$15$			3.54799i			0.916088i
$16$	−4.99663			−1.24916
$17$	3.33822	+	2.41998i	0.809637	+	0.586932i
$17$	3.33822	+	2.41998i	0.809637	+	0.586932i
$18$	1.71520			0.404276
$19$			6.90985i			1.58523i	0.609723	+	0.792615i	$0.291281\pi$
$19$			6.90985i			1.58523i	−0.609723	+	0.792615i	$0.708719\pi$
$20$	−2.36307	+	2.36307i	−0.528399	+	0.528399i
$21$	1.00000			0.218218
$22$	−3.11200	+	3.11200i	−0.663481	+	0.663481i
$23$	−5.39938	−	5.39938i	−1.12585	−	1.12585i	−0.990845	−	0.135004i	$-0.956895\pi$
$23$	−5.39938	−	5.39938i	−1.12585	−	1.12585i	−0.135004	−	0.990845i	$-0.543105\pi$
$24$	−1.28328	−	1.28328i	−0.261949	−	0.261949i
$25$		−	7.58826i		−	1.51765i
$26$			6.35687i			1.24668i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	0.666030	+	0.666030i	0.125868	+	0.125868i
$29$	6.87048	−	6.87048i	1.27582	−	1.27582i	0.332830	−	0.942987i	$-0.391997\pi$
$29$	6.87048	−	6.87048i	1.27582	−	1.27582i	0.942987	−	0.332830i	$-0.108003\pi$
$30$	−6.08552			−1.11106
$31$	−0.818937	+	0.818937i	−0.147086	+	0.147086i	−0.776815	−	0.629729i	$-0.783166\pi$
$31$	−0.818937	+	0.818937i	−0.147086	+	0.147086i	0.629729	+	0.776815i	$0.283166\pi$
$32$		−	4.94054i		−	0.873372i
$33$	−2.56590			−0.446666
$34$	−4.15075	+	5.72571i	−0.711848	+	0.981951i
$35$	−3.54799			−0.599721
$36$			0.941909i			0.156985i
$37$	−6.42994	+	6.42994i	−1.05708	+	1.05708i	−0.0588066	+	0.998269i	$0.518730\pi$
$37$	−6.42994	+	6.42994i	−1.05708	+	1.05708i	−0.998269	+	0.0588066i	$0.981270\pi$
$38$	−11.8518			−1.92261
$39$	−2.62068	+	2.62068i	−0.419644	+	0.419644i
$40$	4.55308	+	4.55308i	0.719905	+	0.719905i
$41$	−6.03201	−	6.03201i	−0.942042	−	0.942042i	0.0563678	−	0.998410i	$-0.482048\pi$
$41$	−6.03201	−	6.03201i	−0.942042	−	0.942042i	−0.998410	+	0.0563678i	$0.982048\pi$
$42$			1.71520i			0.264661i
$43$			1.71992i			0.262286i	0.991363	+	0.131143i	$0.0418647\pi$
$43$			1.71992i			0.262286i	−0.991363	+	0.131143i	$0.958135\pi$
$44$	−1.70897	−	1.70897i	−0.257637	−	0.257637i
$45$	−2.50881	−	2.50881i	−0.373991	−	0.373991i
$46$	9.26101	−	9.26101i	1.36546	−	1.36546i
$47$	−0.699863			−0.102086			−0.0510428	−	0.998696i	$-0.516254\pi$
$47$	−0.699863			−0.102086			−0.0510428	+	0.998696i	$0.516254\pi$
$48$	3.53315	−	3.53315i	0.509966	−	0.509966i
$49$			1.00000i			0.142857i
$50$	13.0154			1.84065
$51$	−4.07166	+	0.649291i	−0.570147	+	0.0909189i
$52$	−3.49090			−0.484101
$53$			3.38235i			0.464602i	0.972644	+	0.232301i	$0.0746255\pi$
$53$			3.38235i			0.464602i	−0.972644	+	0.232301i	$0.925375\pi$
$54$	−1.21283	+	1.21283i	−0.165045	+	0.165045i
$55$	9.10380			1.22756
$56$	1.28328	−	1.28328i	0.171486	−	0.171486i
$57$	−4.88600	−	4.88600i	−0.647167	−	0.647167i
$58$	11.7842	+	11.7842i	1.54735	+	1.54735i
$59$		−	10.9220i		−	1.42193i	−0.703228	−	0.710965i	$-0.748259\pi$
$59$		−	10.9220i		−	1.42193i	0.703228	−	0.710965i	$-0.251741\pi$
$60$		−	3.34189i		−	0.431436i
$61$	3.62531	+	3.62531i	0.464173	+	0.464173i	0.900021	−	0.435847i	$-0.143551\pi$
$61$	3.62531	+	3.62531i	0.464173	+	0.464173i	−0.435847	+	0.900021i	$0.643551\pi$
$62$	−1.40464	−	1.40464i	−0.178390	−	0.178390i
$63$	−0.707107	+	0.707107i	−0.0890871	+	0.0890871i
$64$	−1.51925			−0.189906
$65$	9.29814	−	9.29814i	1.15329	−	1.15329i
$66$		−	4.40103i		−	0.541730i
$67$	−2.86834			−0.350423			−0.175212	−	0.984531i	$-0.556061\pi$
$67$	−2.86834			−0.350423			−0.175212	+	0.984531i	$0.556061\pi$
$68$	−3.14430	−	2.27940i	−0.381302	−	0.276418i
$69$	7.63588			0.919252
$70$		−	6.08552i		−	0.727359i
$71$	9.13401	−	9.13401i	1.08401	−	1.08401i	0.0878766	−	0.996131i	$-0.471992\pi$
$71$	9.13401	−	9.13401i	1.08401	−	1.08401i	0.996131	−	0.0878766i	$-0.0280081\pi$
$72$	1.81484			0.213881
$73$	1.00706	−	1.00706i	0.117867	−	0.117867i	−0.645713	−	0.763580i	$-0.723440\pi$
$73$	1.00706	−	1.00706i	0.117867	−	0.117867i	0.763580	+	0.645713i	$0.223440\pi$
$74$	−11.0286	−	11.0286i	−1.28205	−	1.28205i
$75$	5.36571	+	5.36571i	0.619579	+	0.619579i
$76$		−	6.50846i		−	0.746571i
$77$		−	2.56590i		−	0.292412i
$78$	−4.49498	−	4.49498i	−0.508957	−	0.508957i
$79$	−7.80162	−	7.80162i	−0.877751	−	0.877751i	0.115551	−	0.993302i	$-0.463137\pi$
$79$	−7.80162	−	7.80162i	−0.877751	−	0.877751i	−0.993302	+	0.115551i	$0.963137\pi$
$80$	−12.5356	+	12.5356i	−1.40152	+	1.40152i
$81$	−1.00000			−0.111111
$82$	10.3461	−	10.3461i	1.14254	−	1.14254i
$83$			8.11587i			0.890832i	0.895324	+	0.445416i	$0.146944\pi$
$83$			8.11587i			0.890832i	−0.895324	+	0.445416i	$0.853056\pi$
$84$	−0.941909			−0.102771
$85$	14.4462	−	2.30368i	1.56691	−	0.249869i
$86$	−2.95001			−0.318108
$87$			9.71633i			1.04170i
$88$	−3.29278	+	3.29278i	−0.351011	+	0.351011i
$89$	−11.1085			−1.17750			−0.588752	−	0.808314i	$-0.700381\pi$
$89$	−11.1085			−1.17750			−0.588752	+	0.808314i	$0.700381\pi$
$90$	4.30311	−	4.30311i	0.453588	−	0.453588i
$91$	−2.62068	−	2.62068i	−0.274722	−	0.274722i
$92$	5.08573	+	5.08573i	0.530224	+	0.530224i
$93$		−	1.15815i		−	0.120095i
$94$		−	1.20040i		−	0.123812i
$95$	17.3355	+	17.3355i	1.77859	+	1.77859i
$96$	3.49349	+	3.49349i	0.356552	+	0.356552i
$97$	1.25205	−	1.25205i	0.127127	−	0.127127i	−0.640681	−	0.767808i	$-0.721348\pi$
$97$	1.25205	−	1.25205i	0.127127	−	0.127127i	0.767808	+	0.640681i	$0.221348\pi$
$98$	−1.71520			−0.173261
$99$	1.81437	−	1.81437i	0.182351	−	0.182351i
$100$			7.14746i			0.714746i
$101$	9.90253			0.985339			0.492669	−	0.870217i	$-0.336021\pi$
$101$	9.90253			0.985339			0.492669	+	0.870217i	$0.336021\pi$
$102$	−1.11366	−	6.98371i	−0.110269	−	0.691490i
$103$	−5.57897			−0.549712			−0.274856	−	0.961485i	$-0.588630\pi$
$103$	−5.57897			−0.549712			−0.274856	+	0.961485i	$0.588630\pi$
$104$			6.72614i			0.659552i
$105$	2.50881	−	2.50881i	0.244835	−	0.244835i
$106$	−5.80141			−0.563483
$107$	−3.97950	+	3.97950i	−0.384713	+	0.384713i	−0.872797	−	0.488084i	$-0.837696\pi$
$107$	−3.97950	+	3.97950i	−0.384713	+	0.384713i	0.488084	+	0.872797i	$0.337696\pi$
$108$	−0.666030	−	0.666030i	−0.0640888	−	0.0640888i
$109$	−11.4638	−	11.4638i	−1.09803	−	1.09803i	−0.994641	−	0.103390i	$-0.967031\pi$
$109$	−11.4638	−	11.4638i	−1.09803	−	1.09803i	−0.103390	−	0.994641i	$-0.532969\pi$
$110$			15.6148i			1.48882i
$111$		−	9.09331i		−	0.863099i
$112$	3.53315	+	3.53315i	0.333851	+	0.333851i
$113$	6.84563	+	6.84563i	0.643983	+	0.643983i	0.951532	−	0.307549i	$-0.0995089\pi$
$113$	6.84563	+	6.84563i	0.643983	+	0.643983i	−0.307549	+	0.951532i	$0.599509\pi$
$114$	8.38047	−	8.38047i	0.784903	−	0.784903i
$115$	−27.0920			−2.52635
$116$	−6.47137	+	6.47137i	−0.600852	+	0.600852i
$117$		−	3.70620i		−	0.342638i
$118$	18.7335			1.72456
$119$	−0.649291	−	4.07166i	−0.0595204	−	0.373249i
$120$	−6.43903			−0.587800
$121$		−	4.41615i		−	0.401468i
$122$	−6.21813	+	6.21813i	−0.562963	+	0.562963i
$123$	8.53056			0.769174
$124$	0.771365	−	0.771365i	0.0692706	−	0.0692706i
$125$	−6.49347	−	6.49347i	−0.580793	−	0.580793i
$126$	−1.21283	−	1.21283i	−0.108047	−	0.108047i
$127$			1.97182i			0.174971i	0.996166	+	0.0874855i	$0.0278831\pi$
$127$			1.97182i			0.174971i	−0.996166	+	0.0874855i	$0.972117\pi$
$128$		−	12.4869i		−	1.10369i
$129$	−1.21617	−	1.21617i	−0.107078	−	0.107078i
$130$	15.9482	+	15.9482i	1.39875	+	1.39875i
$131$	−6.05141	+	6.05141i	−0.528714	+	0.528714i	−0.920189	−	0.391475i	$-0.871965\pi$
$131$	−6.05141	+	6.05141i	−0.528714	+	0.528714i	0.391475	+	0.920189i	$0.371965\pi$
$132$	2.41685			0.210360
$133$	4.88600	−	4.88600i	0.423670	−	0.423670i
$134$		−	4.91977i		−	0.425004i
$135$	3.54799			0.305363
$136$	−4.39187	+	6.05832i	−0.376600	+	0.519497i
$137$	−18.7573			−1.60254			−0.801270	−	0.598303i	$-0.795842\pi$
$137$	−18.7573			−1.60254			−0.801270	+	0.598303i	$0.795842\pi$
$138$			13.0971i			1.11490i
$139$	−4.56390	+	4.56390i	−0.387105	+	0.387105i	−0.873654	−	0.486548i	$-0.838256\pi$
$139$	−4.56390	+	4.56390i	−0.387105	+	0.387105i	0.486548	+	0.873654i	$0.338256\pi$
$140$	3.34189			0.282441
$141$	0.494878	−	0.494878i	0.0416762	−	0.0416762i
$142$	15.6667	+	15.6667i	1.31472	+	1.31472i
$143$	6.72440	+	6.72440i	0.562322	+	0.562322i
$144$			4.99663i			0.416385i
$145$		−	34.4735i		−	2.86287i
$146$	1.72731	+	1.72731i	0.142953	+	0.142953i
$147$	−0.707107	−	0.707107i	−0.0583212	−	0.0583212i
$148$	6.05642	−	6.05642i	0.497835	−	0.497835i
$149$	−15.4004			−1.26165			−0.630824	−	0.775926i	$-0.717283\pi$
$149$	−15.4004			−1.26165			−0.630824	+	0.775926i	$0.717283\pi$
$150$	−9.20327	+	9.20327i	−0.751444	+	0.751444i
$151$		−	10.0010i		−	0.813872i	−0.913457	−	0.406936i	$-0.866597\pi$
$151$		−	10.0010i		−	0.813872i	0.913457	−	0.406936i	$-0.133403\pi$
$152$	−12.5403			−1.01715
$153$	2.41998	−	3.33822i	0.195644	−	0.269879i
$154$	4.40103			0.354645
$155$			4.10912i			0.330052i
$156$	2.46844	−	2.46844i	0.197633	−	0.197633i
$157$	−7.69824			−0.614387			−0.307193	−	0.951647i	$-0.599390\pi$
$157$	−7.69824			−0.614387			−0.307193	+	0.951647i	$0.599390\pi$
$158$	13.3813	−	13.3813i	1.06456	−	1.06456i
$159$	−2.39169	−	2.39169i	−0.189673	−	0.189673i
$160$	−12.3949	−	12.3949i	−0.979901	−	0.979901i
$161$			7.63588i			0.601791i
$162$		−	1.71520i		−	0.134759i
$163$	4.17446	+	4.17446i	0.326969	+	0.326969i	0.851433	−	0.524464i	$-0.175734\pi$
$163$	4.17446	+	4.17446i	0.326969	+	0.326969i	−0.524464	+	0.851433i	$0.675734\pi$
$164$	5.68161	+	5.68161i	0.443659	+	0.443659i
$165$	−6.43736	+	6.43736i	−0.501148	+	0.501148i
$166$	−13.9203			−1.08043
$167$	−2.28192	+	2.28192i	−0.176580	+	0.176580i	−0.789863	−	0.613283i	$-0.789848\pi$
$167$	−2.28192	+	2.28192i	−0.176580	+	0.176580i	0.613283	+	0.789863i	$0.289848\pi$
$168$			1.81484i			0.140018i
$169$	0.735888			0.0566068
$170$	3.95127	+	24.7782i	0.303049	+	1.90040i
$171$	6.90985			0.528410
$172$		−	1.62001i		−	0.123525i
$173$	15.8344	−	15.8344i	1.20387	−	1.20387i	0.230891	−	0.972980i	$-0.425836\pi$
$173$	15.8344	−	15.8344i	1.20387	−	1.20387i	0.972980	−	0.230891i	$-0.0741641\pi$
$174$	−16.6654			−1.26340
$175$	−5.36571	+	5.36571i	−0.405610	+	0.405610i
$176$	−9.06571	−	9.06571i	−0.683354	−	0.683354i
$177$	7.72305	+	7.72305i	0.580500	+	0.580500i
$178$		−	19.0534i		−	1.42811i
$179$		−	14.0892i		−	1.05308i	−0.850152	−	0.526538i	$-0.823490\pi$
$179$		−	14.0892i		−	1.05308i	0.850152	−	0.526538i	$-0.176510\pi$
$180$	2.36307	+	2.36307i	0.176133	+	0.176133i
$181$	14.7689	+	14.7689i	1.09776	+	1.09776i	0.994672	+	0.103090i	$0.0328731\pi$
$181$	14.7689	+	14.7689i	1.09776	+	1.09776i	0.103090	+	0.994672i	$0.467127\pi$
$182$	4.49498	−	4.49498i	0.333190	−	0.333190i
$183$	−5.12696			−0.378996
$184$	9.79899	−	9.79899i	0.722391	−	0.722391i
$185$			32.2630i			2.37202i
$186$	1.98646			0.145654
$187$	1.66602	+	10.4475i	0.121831	+	0.763995i
$188$	0.659207			0.0480776
$189$		−	1.00000i		−	0.0727393i
$190$	−29.7339	+	29.7339i	−2.15712	+	2.15712i
$191$	4.70406			0.340373			0.170187	−	0.985412i	$-0.445563\pi$
$191$	4.70406			0.340373			0.170187	+	0.985412i	$0.445563\pi$
$192$	1.07427	−	1.07427i	0.0775287	−	0.0775287i
$193$	3.60875	+	3.60875i	0.259763	+	0.259763i	0.824958	−	0.565194i	$-0.191199\pi$
$193$	3.60875	+	3.60875i	0.259763	+	0.259763i	−0.565194	+	0.824958i	$0.691199\pi$
$194$	2.14752	+	2.14752i	0.154183	+	0.154183i
$195$			13.1496i			0.941660i
$196$		−	0.941909i		−	0.0672792i
$197$	−9.53476	−	9.53476i	−0.679323	−	0.679323i	0.280524	−	0.959847i	$-0.409492\pi$
$197$	−9.53476	−	9.53476i	−0.679323	−	0.679323i	−0.959847	+	0.280524i	$0.909492\pi$
$198$	3.11200	+	3.11200i	0.221160	+	0.221160i
$199$	−2.96534	+	2.96534i	−0.210208	+	0.210208i	−0.804356	−	0.594148i	$-0.797489\pi$
$199$	−2.96534	+	2.96534i	−0.210208	+	0.210208i	0.594148	+	0.804356i	$0.297489\pi$
$200$	13.7715			0.973789
$201$	2.02822	−	2.02822i	0.143060	−	0.143060i
$202$			16.9848i			1.19505i
$203$	−9.71633			−0.681953
$204$	3.83514	−	0.611573i	0.268513	−	0.0428187i
$205$	−30.2664			−2.11389
$206$		−	9.56904i		−	0.666707i
$207$	−5.39938	+	5.39938i	−0.375283	+	0.375283i
$208$	−18.5185			−1.28403
$209$	−12.5370	+	12.5370i	−0.867203	+	0.867203i
$210$	4.30311	+	4.30311i	0.296943	+	0.296943i
$211$	−12.6378	−	12.6378i	−0.870022	−	0.870022i	0.122453	−	0.992474i	$-0.460924\pi$
$211$	−12.6378	−	12.6378i	−0.870022	−	0.870022i	−0.992474	+	0.122453i	$0.960924\pi$
$212$		−	3.18587i		−	0.218807i
$213$			12.9174i			0.885089i
$214$	−6.82564	−	6.82564i	−0.466591	−	0.466591i
$215$	4.31497	+	4.31497i	0.294278	+	0.294278i
$216$	−1.28328	+	1.28328i	−0.0873164	+	0.0873164i
$217$	1.15815			0.0786205
$218$	19.6627	−	19.6627i	1.33172	−	1.33172i
$219$			1.42420i			0.0962382i
$220$	−8.57496			−0.578124
$221$	12.3721	+	8.96892i	0.832237	+	0.603315i
$222$	15.5968			1.04679
$223$			1.60272i			0.107326i	0.998559	+	0.0536632i	$0.0170897\pi$
$223$			1.60272i			0.107326i	−0.998559	+	0.0536632i	$0.982910\pi$
$224$	−3.49349	+	3.49349i	−0.233418	+	0.233418i
$225$	−7.58826			−0.505884
$226$	−11.7416	+	11.7416i	−0.781041	+	0.781041i
$227$	8.30778	+	8.30778i	0.551407	+	0.551407i	0.926847	−	0.375440i	$-0.122508\pi$
$227$	8.30778	+	8.30778i	0.551407	+	0.551407i	−0.375440	+	0.926847i	$0.622508\pi$
$228$	4.60217	+	4.60217i	0.304786	+	0.304786i
$229$			1.47791i			0.0976633i	0.998807	+	0.0488317i	$0.0155498\pi$
$229$			1.47791i			0.0976633i	−0.998807	+	0.0488317i	$0.984450\pi$
$230$		−	46.4683i		−	3.06403i
$231$	1.81437	+	1.81437i	0.119377	+	0.119377i
$232$	12.4688	+	12.4688i	0.818617	+	0.818617i
$233$	−9.73346	+	9.73346i	−0.637660	+	0.637660i	−0.949978	−	0.312318i	$-0.898895\pi$
$233$	−9.73346	+	9.73346i	−0.637660	+	0.637660i	0.312318	+	0.949978i	$0.398895\pi$
$234$	6.35687			0.415561
$235$	−1.75582	+	1.75582i	−0.114537	+	0.114537i
$236$			10.2876i			0.669664i
$237$	11.0332			0.716681
$238$	6.98371	−	1.11366i	0.452687	−	0.0721881i
$239$	13.6486			0.882852			0.441426	−	0.897298i	$-0.354473\pi$
$239$	13.6486			0.882852			0.441426	+	0.897298i	$0.354473\pi$
$240$		−	17.7280i		−	1.14434i
$241$	12.2558	−	12.2558i	0.789465	−	0.789465i	−0.191941	−	0.981406i	$-0.561478\pi$
$241$	12.2558	−	12.2558i	0.789465	−	0.789465i	0.981406	+	0.191941i	$0.0614783\pi$
$242$	7.57458			0.486912
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−3.41471	−	3.41471i	−0.218605	−	0.218605i
$245$	2.50881	+	2.50881i	0.160282	+	0.160282i
$246$			14.6316i			0.932877i
$247$			25.6093i			1.62948i
$248$	−1.48624	−	1.48624i	−0.0943762	−	0.0943762i
$249$	−5.73879	−	5.73879i	−0.363681	−	0.363681i
$250$	11.1376	−	11.1376i	0.704403	−	0.704403i
$251$	16.8092			1.06099			0.530493	−	0.847690i	$-0.322007\pi$
$251$	16.8092			1.06099			0.530493	+	0.847690i	$0.322007\pi$
$252$	0.666030	−	0.666030i	0.0419560	−	0.0419560i
$253$		−	19.5929i		−	1.23180i
$254$	−3.38207			−0.212210
$255$	−8.58608	+	11.8440i	−0.537681	+	0.741698i
$256$	18.3790			1.14869
$257$		−	6.87575i		−	0.428897i	−0.976735	−	0.214449i	$-0.931205\pi$
$257$		−	6.87575i		−	0.428897i	0.976735	−	0.214449i	$-0.0687955\pi$
$258$	2.08597	−	2.08597i	0.129867	−	0.129867i
$259$	9.09331			0.565031
$260$	−8.75801	+	8.75801i	−0.543149	+	0.543149i
$261$	−6.87048	−	6.87048i	−0.425272	−	0.425272i
$262$	−10.3794	−	10.3794i	−0.641240	−	0.641240i
$263$		−	0.998666i		−	0.0615804i	−0.999526	−	0.0307902i	$-0.990198\pi$
$263$		−	0.998666i		−	0.0615804i	0.999526	−	0.0307902i	$-0.00980237\pi$
$264$		−	4.65669i		−	0.286600i
$265$	8.48569	+	8.48569i	0.521272	+	0.521272i
$266$	8.38047	+	8.38047i	0.513840	+	0.513840i
$267$	7.85493	−	7.85493i	0.480714	−	0.480714i
$268$	2.70172			0.165034
$269$	−1.72281	+	1.72281i	−0.105041	+	0.105041i	−0.757674	−	0.652633i	$-0.773664\pi$
$269$	−1.72281	+	1.72281i	−0.105041	+	0.105041i	0.652633	+	0.757674i	$0.273664\pi$
$270$			6.08552i			0.370353i
$271$	11.8042			0.717056			0.358528	−	0.933519i	$-0.383279\pi$
$271$	11.8042			0.717056			0.358528	+	0.933519i	$0.383279\pi$
$272$	−16.6798	−	12.0917i	−1.01136	−	0.733169i
$273$	3.70620			0.224309
$274$		−	32.1724i		−	1.94361i
$275$	13.7679	−	13.7679i	0.830235	−	0.830235i
$276$	−7.19230			−0.432926
$277$	−9.09657	+	9.09657i	−0.546560	+	0.546560i	−0.925444	−	0.378884i	$-0.876308\pi$
$277$	−9.09657	+	9.09657i	−0.546560	+	0.546560i	0.378884	+	0.925444i	$0.376308\pi$
$278$	−7.82801	−	7.82801i	−0.469493	−	0.469493i
$279$	0.818937	+	0.818937i	0.0490285	+	0.0490285i
$280$		−	6.43903i		−	0.384806i
$281$			17.9398i			1.07020i	0.844790	+	0.535098i	$0.179725\pi$
$281$			17.9398i			1.07020i	−0.844790	+	0.535098i	$0.820275\pi$
$282$	0.848814	+	0.848814i	0.0505462	+	0.0505462i
$283$	13.4859	+	13.4859i	0.801652	+	0.801652i	0.983354	−	0.181702i	$-0.0581606\pi$
$283$	13.4859	+	13.4859i	0.801652	+	0.801652i	−0.181702	+	0.983354i	$0.558161\pi$
$284$	−8.60341	+	8.60341i	−0.510519	+	0.510519i
$285$	−24.5161			−1.45221
$286$	−11.5337	+	11.5337i	−0.682001	+	0.682001i
$287$			8.53056i			0.503543i
$288$	−4.94054			−0.291124
$289$	5.28739	+	16.1568i	0.311023	+	0.950402i
$290$	59.1289			3.47217
$291$			1.77067i			0.103799i
$292$	−0.948558	+	0.948558i	−0.0555102	+	0.0555102i
$293$	16.9285			0.988974			0.494487	−	0.869185i	$-0.335356\pi$
$293$	16.9285			0.988974			0.494487	+	0.869185i	$0.335356\pi$
$294$	1.21283	−	1.21283i	0.0707336	−	0.0707336i
$295$	−27.4014	−	27.4014i	−1.59537	−	1.59537i
$296$	−11.6693	−	11.6693i	−0.678264	−	0.678264i
$297$			2.56590i			0.148889i
$298$		−	26.4147i		−	1.53016i
$299$	−20.0112	−	20.0112i	−1.15728	−	1.15728i
$300$	−5.05402	−	5.05402i	−0.291794	−	0.291794i
$301$	1.21617	−	1.21617i	0.0700989	−	0.0700989i
$302$	17.1537			0.987087
$303$	−7.00215	+	7.00215i	−0.402263	+	0.402263i
$304$		−	34.5260i		−	1.98020i
$305$	18.1904			1.04158
$306$	5.72571	+	4.15075i	0.327317	+	0.237283i
$307$	−21.9034			−1.25010			−0.625048	−	0.780587i	$-0.714921\pi$
$307$	−21.9034			−1.25010			−0.625048	+	0.780587i	$0.714921\pi$
$308$			2.41685i			0.137713i
$309$	3.94492	−	3.94492i	0.224419	−	0.224419i
$310$	−7.04796			−0.400297
$311$	19.2492	−	19.2492i	1.09152	−	1.09152i	0.0961569	−	0.995366i	$-0.469345\pi$
$311$	19.2492	−	19.2492i	1.09152	−	1.09152i	0.995366	−	0.0961569i	$-0.0306551\pi$
$312$	−4.75610	−	4.75610i	−0.269261	−	0.269261i
$313$	5.09144	+	5.09144i	0.287785	+	0.287785i	0.836204	−	0.548419i	$-0.184770\pi$
$313$	5.09144	+	5.09144i	0.287785	+	0.287785i	−0.548419	+	0.836204i	$0.684770\pi$
$314$		−	13.2040i		−	0.745146i
$315$			3.54799i			0.199907i
$316$	7.34842	+	7.34842i	0.413381	+	0.413381i
$317$	−13.1297	−	13.1297i	−0.737435	−	0.737435i	0.234646	−	0.972081i	$-0.424607\pi$
$317$	−13.1297	−	13.1297i	−0.737435	−	0.737435i	−0.972081	+	0.234646i	$0.924607\pi$
$318$	4.10222	−	4.10222i	0.230041	−	0.230041i
$319$	24.9311			1.39588
$320$	−3.81150	+	3.81150i	−0.213069	+	0.213069i
$321$		−	5.62786i		−	0.314117i
$322$	−13.0971			−0.729870
$323$	−16.7217	+	23.0666i	−0.930421	+	1.28346i
$324$	0.941909			0.0523283
$325$		−	28.1236i		−	1.56002i
$326$	−7.16003	+	7.16003i	−0.396557	+	0.396557i
$327$	16.2122			0.896539
$328$	10.9471	−	10.9471i	0.604454	−	0.604454i
$329$	0.494878	+	0.494878i	0.0272835	+	0.0272835i
$330$	−11.0414	−	11.0414i	−0.607807	−	0.607807i
$331$			8.06322i			0.443194i	0.975138	+	0.221597i	$0.0711270\pi$
$331$			8.06322i			0.443194i	−0.975138	+	0.221597i	$0.928873\pi$
$332$		−	7.64441i		−	0.419542i
$333$	6.42994	+	6.42994i	0.352359	+	0.352359i
$334$	−3.91394	−	3.91394i	−0.214161	−	0.214161i
$335$	−7.19612	+	7.19612i	−0.393166	+	0.393166i
$336$	−4.99663			−0.272588
$337$	−18.8066	+	18.8066i	−1.02446	+	1.02446i	−0.0247668	+	0.999693i	$0.507884\pi$
$337$	−18.8066	+	18.8066i	−1.02446	+	1.02446i	−0.999693	+	0.0247668i	$0.992116\pi$
$338$			1.26220i			0.0686544i
$339$	−9.68119			−0.525810
$340$	−13.6070	+	2.16986i	−0.737945	+	0.117677i
$341$	−2.97171			−0.160927
$342$			11.8518i			0.640871i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−3.12138			−0.168294
$345$	19.1570	−	19.1570i	1.03138	−	1.03138i
$346$	27.1592	+	27.1592i	1.46009	+	1.46009i
$347$	14.0310	+	14.0310i	0.753225	+	0.753225i	0.975080	−	0.221854i	$-0.0712109\pi$
$347$	14.0310	+	14.0310i	0.753225	+	0.753225i	−0.221854	+	0.975080i	$0.571211\pi$
$348$		−	9.15190i		−	0.490593i
$349$			10.8244i			0.579418i	0.957115	+	0.289709i	$0.0935585\pi$
$349$			10.8244i			0.579418i	−0.957115	+	0.289709i	$0.906441\pi$
$350$	−9.20327	−	9.20327i	−0.491935	−	0.491935i
$351$	2.62068	+	2.62068i	0.139881	+	0.139881i
$352$	8.96394	−	8.96394i	0.477780	−	0.477780i
$353$	−25.1471			−1.33845			−0.669224	−	0.743061i	$-0.733373\pi$
$353$	−25.1471			−1.33845			−0.669224	+	0.743061i	$0.733373\pi$
$354$	−13.2466	+	13.2466i	−0.704048	+	0.704048i
$355$		−	45.8310i		−	2.43246i
$356$	10.4632			0.554551
$357$	3.33822	+	2.41998i	0.176677	+	0.128079i
$358$	24.1658			1.27720
$359$			20.1240i			1.06210i	0.847340	+	0.531051i	$0.178203\pi$
$359$			20.1240i			1.06210i	−0.847340	+	0.531051i	$0.821797\pi$
$360$	4.55308	−	4.55308i	0.239968	−	0.239968i
$361$	−28.7461			−1.51295
$362$	−25.3316	+	25.3316i	−1.33140	+	1.33140i
$363$	3.12269	+	3.12269i	0.163899	+	0.163899i
$364$	2.46844	+	2.46844i	0.129381	+	0.129381i
$365$		−	5.05304i		−	0.264488i
$366$		−	8.79376i		−	0.459657i
$367$	19.3902	+	19.3902i	1.01216	+	1.01216i	0.999925	+	0.0122356i	$0.00389481\pi$
$367$	19.3902	+	19.3902i	1.01216	+	1.01216i	0.0122356	+	0.999925i	$0.496105\pi$
$368$	26.9787	+	26.9787i	1.40636	+	1.40636i
$369$	−6.03201	+	6.03201i	−0.314014	+	0.314014i
$370$	−55.3375			−2.87686
$371$	2.39169	−	2.39169i	0.124170	−	0.124170i
$372$			1.09087i			0.0565592i
$373$	9.01770			0.466919			0.233460	−	0.972367i	$-0.424995\pi$
$373$	9.01770			0.466919			0.233460	+	0.972367i	$0.424995\pi$
$374$	−17.9195	+	2.85755i	−0.926596	+	0.147760i
$375$	9.18315			0.474216
$376$		−	1.27014i		−	0.0655023i
$377$	25.4634	−	25.4634i	1.31143	−	1.31143i
$378$	1.71520			0.0882203
$379$	−2.83907	+	2.83907i	−0.145833	+	0.145833i	−0.776254	−	0.630421i	$-0.782882\pi$
$379$	−2.83907	+	2.83907i	−0.145833	+	0.145833i	0.630421	+	0.776254i	$0.282882\pi$
$380$	−16.3285	−	16.3285i	−0.837634	−	0.837634i
$381$	−1.39429	−	1.39429i	−0.0714316	−	0.0714316i
$382$			8.06839i			0.412815i
$383$		−	7.39041i		−	0.377632i	−0.982012	−	0.188816i	$-0.939535\pi$
$383$		−	7.39041i		−	0.377632i	0.982012	−	0.188816i	$-0.0604651\pi$
$384$	8.82956	+	8.82956i	0.450582	+	0.450582i
$385$	−6.43736	−	6.43736i	−0.328078	−	0.328078i
$386$	−6.18972	+	6.18972i	−0.315048	+	0.315048i
$387$	1.71992			0.0874287
$388$	−1.17932	+	1.17932i	−0.0598710	+	0.0598710i
$389$			16.1413i			0.818397i	0.912445	+	0.409199i	$0.134192\pi$
$389$			16.1413i			0.818397i	−0.912445	+	0.409199i	$0.865808\pi$
$390$	−22.5541			−1.14207
$391$	−4.95791	−	31.0907i	−0.250732	−	1.57232i
$392$	−1.81484			−0.0916631
$393$		−	8.55799i		−	0.431693i
$394$	16.3540	−	16.3540i	0.823903	−	0.823903i
$395$	−39.1456			−1.96963
$396$	−1.70897	+	1.70897i	−0.0858789	+	0.0858789i
$397$	4.74649	+	4.74649i	0.238220	+	0.238220i	0.816113	−	0.577893i	$-0.196125\pi$
$397$	4.74649	+	4.74649i	0.238220	+	0.238220i	−0.577893	+	0.816113i	$0.696125\pi$
$398$	−5.08616	−	5.08616i	−0.254946	−	0.254946i
$399$			6.90985i			0.345925i
$400$			37.9157i			1.89579i
$401$	1.40149	+	1.40149i	0.0699868	+	0.0699868i	0.741234	−	0.671247i	$-0.234241\pi$
$401$	1.40149	+	1.40149i	0.0699868	+	0.0699868i	−0.671247	+	0.741234i	$0.734241\pi$
$402$	3.47881	+	3.47881i	0.173507	+	0.173507i
$403$	−3.03514	+	3.03514i	−0.151191	+	0.151191i
$404$	−9.32729			−0.464050
$405$	−2.50881	+	2.50881i	−0.124664	+	0.124664i
$406$		−	16.6654i		−	0.827092i
$407$	−23.3325			−1.15655
$408$	−1.17836	−	7.38940i	−0.0583374	−	0.365830i
$409$	−15.3390			−0.758464			−0.379232	−	0.925302i	$-0.623812\pi$
$409$	−15.3390			−0.758464			−0.379232	+	0.925302i	$0.623812\pi$
$410$		−	51.9129i		−	2.56379i
$411$	13.2634	−	13.2634i	0.654234	−	0.654234i
$412$	5.25488			0.258889
$413$	−7.72305	+	7.72305i	−0.380027	+	0.380027i
$414$	−9.26101	−	9.26101i	−0.455154	−	0.455154i
$415$	20.3612	+	20.3612i	0.999491	+	0.999491i
$416$		−	18.3106i		−	0.897751i
$417$		−	6.45433i		−	0.316070i
$418$	−21.5035	−	21.5035i	−1.05177	−	1.05177i
$419$	−0.188870	−	0.188870i	−0.00922690	−	0.00922690i	0.702478	−	0.711705i	$-0.252077\pi$
$419$	−0.188870	−	0.188870i	−0.00922690	−	0.00922690i	−0.711705	+	0.702478i	$0.752077\pi$
$420$	−2.36307	+	2.36307i	−0.115306	+	0.115306i
$421$	16.4415			0.801309			0.400655	−	0.916229i	$-0.368783\pi$
$421$	16.4415			0.801309			0.400655	+	0.916229i	$0.368783\pi$
$422$	21.6763	−	21.6763i	1.05519	−	1.05519i
$423$			0.699863i			0.0340285i
$424$	−6.13842			−0.298108
$425$	18.3635	−	25.3313i	0.890758	−	1.22875i
$426$	−22.1560			−1.07346
$427$		−	5.12696i		−	0.248111i
$428$	3.74833	−	3.74833i	0.181182	−	0.181182i
$429$	−9.50973			−0.459134
$430$	−7.40103	+	7.40103i	−0.356909	+	0.356909i
$431$	−1.52988	−	1.52988i	−0.0736917	−	0.0736917i	0.669300	−	0.742992i	$-0.266594\pi$
$431$	−1.52988	−	1.52988i	−0.0736917	−	0.0736917i	−0.742992	+	0.669300i	$0.766594\pi$
$432$	−3.53315	−	3.53315i	−0.169989	−	0.169989i
$433$			5.65283i			0.271658i	0.990732	+	0.135829i	$0.0433697\pi$
$433$			5.65283i			0.271658i	−0.990732	+	0.135829i	$0.956630\pi$
$434$			1.98646i			0.0953532i
$435$	24.3764	+	24.3764i	1.16876	+	1.16876i
$436$	10.7978	+	10.7978i	0.517123	+	0.517123i
$437$	37.3089	−	37.3089i	1.78473	−	1.78473i
$438$	−2.44278			−0.116721
$439$	1.35600	−	1.35600i	0.0647184	−	0.0647184i	−0.674007	−	0.738725i	$-0.735428\pi$
$439$	1.35600	−	1.35600i	0.0647184	−	0.0647184i	0.738725	+	0.674007i	$0.235428\pi$
$440$			16.5219i			0.787652i
$441$	1.00000			0.0476190
$442$	−15.3835	+	21.2206i	−0.731718	+	1.00936i
$443$	28.4710			1.35270			0.676348	−	0.736582i	$-0.263562\pi$
$443$	28.4710			1.35270			0.676348	+	0.736582i	$0.263562\pi$
$444$			8.56508i			0.406480i
$445$	−27.8692	+	27.8692i	−1.32113	+	1.32113i
$446$	−2.74899			−0.130169
$447$	10.8897	−	10.8897i	0.515066	−	0.515066i
$448$	1.07427	+	1.07427i	0.0507544	+	0.0507544i
$449$	9.23165	+	9.23165i	0.435669	+	0.435669i	0.890551	−	0.454883i	$-0.150319\pi$
$449$	9.23165	+	9.23165i	0.435669	+	0.435669i	−0.454883	+	0.890551i	$0.650319\pi$
$450$		−	13.0154i		−	0.613551i
$451$		−	21.8886i		−	1.03069i
$452$	−6.44797	−	6.44797i	−0.303287	−	0.303287i
$453$	7.07179	+	7.07179i	0.332262	+	0.332262i
$454$	−14.2495	+	14.2495i	−0.668763	+	0.668763i
$455$	−13.1496			−0.616461
$456$	8.86730	−	8.86730i	0.415249	−	0.415249i
$457$		−	8.80710i		−	0.411979i	−0.978554	−	0.205989i	$-0.933959\pi$
$457$		−	8.80710i		−	0.411979i	0.978554	−	0.205989i	$-0.0660412\pi$
$458$	−2.53492			−0.118449
$459$	0.649291	+	4.07166i	0.0303063	+	0.190049i
$460$	25.5183			1.18979
$461$			8.14899i			0.379536i	0.981829	+	0.189768i	$0.0607736\pi$
$461$			8.14899i			0.379536i	−0.981829	+	0.189768i	$0.939226\pi$
$462$	−3.11200	+	3.11200i	−0.144783	+	0.144783i
$463$	0.328011			0.0152440			0.00762199	−	0.999971i	$-0.497574\pi$
$463$	0.328011			0.0152440			0.00762199	+	0.999971i	$0.497574\pi$
$464$	−34.3292	+	34.3292i	−1.59369	+	1.59369i
$465$	−2.90559	−	2.90559i	−0.134743	−	0.134743i
$466$	−16.6948	−	16.6948i	−0.773373	−	0.773373i
$467$			23.0220i			1.06533i	0.846326	+	0.532666i	$0.178810\pi$
$467$			23.0220i			1.06533i	−0.846326	+	0.532666i	$0.821190\pi$
$468$			3.49090i			0.161367i
$469$	2.02822	+	2.02822i	0.0936546	+	0.0936546i
$470$	−3.01159	−	3.01159i	−0.138914	−	0.138914i
$471$	5.44348	−	5.44348i	0.250822	−	0.250822i
$472$	19.8217			0.912369
$473$	−3.12057	+	3.12057i	−0.143484	+	0.143484i
$474$			18.9241i			0.869211i
$475$	52.4338			2.40583
$476$	0.611573	+	3.83514i	0.0280314	+	0.175783i
$477$	3.38235			0.154867
$478$			23.4100i			1.07075i
$479$	−19.5440	+	19.5440i	−0.892986	+	0.892986i	−0.994803	−	0.101817i	$-0.967534\pi$
$479$	−19.5440	+	19.5440i	−0.892986	+	0.892986i	0.101817	+	0.994803i	$0.467534\pi$
$480$	17.5290			0.800085
$481$	−23.8306	+	23.8306i	−1.08658	+	1.08658i
$482$	21.0211	+	21.0211i	0.957486	+	0.957486i
$483$	−5.39938	−	5.39938i	−0.245680	−	0.245680i
$484$			4.15961i			0.189073i
$485$		−	6.28234i		−	0.285266i
$486$	1.21283	+	1.21283i	0.0550150	+	0.0550150i
$487$	−1.54988	−	1.54988i	−0.0702319	−	0.0702319i	0.671118	−	0.741350i	$-0.265814\pi$
$487$	−1.54988	−	1.54988i	−0.0702319	−	0.0702319i	−0.741350	+	0.671118i	$0.765814\pi$
$488$	−6.57934	+	6.57934i	−0.297833	+	0.297833i
$489$	−5.90357			−0.266969
$490$	−4.30311	+	4.30311i	−0.194395	+	0.194395i
$491$		−	8.04025i		−	0.362851i	−0.983405	−	0.181426i	$-0.941929\pi$
$491$		−	8.04025i		−	0.362851i	0.983405	−	0.181426i	$-0.0580712\pi$
$492$	−8.03501			−0.362246
$493$	39.5616	−	6.30873i	1.78176	−	0.284131i
$494$	−43.9250			−1.97628
$495$		−	9.10380i		−	0.409186i
$496$	4.09192	−	4.09192i	0.183733	−	0.183733i
$497$	−12.9174			−0.579427
$498$	9.84316	−	9.84316i	0.441083	−	0.441083i
$499$	8.08881	+	8.08881i	0.362105	+	0.362105i	0.864587	−	0.502482i	$-0.167580\pi$
$499$	8.08881	+	8.08881i	0.362105	+	0.362105i	−0.502482	+	0.864587i	$0.667580\pi$
$500$	6.11626	+	6.11626i	0.273527	+	0.273527i
$501$		−	3.22712i		−	0.144177i
$502$			28.8311i			1.28679i
$503$	5.61907	+	5.61907i	0.250542	+	0.250542i	0.821193	−	0.570651i	$-0.193309\pi$
$503$	5.61907	+	5.61907i	0.250542	+	0.250542i	−0.570651	+	0.821193i	$0.693309\pi$
$504$	−1.28328	−	1.28328i	−0.0571620	−	0.0571620i
$505$	24.8436	−	24.8436i	1.10552	−	1.10552i
$506$	33.6057			1.49396
$507$	−0.520352	+	0.520352i	−0.0231096	+	0.0231096i
$508$		−	1.85728i		−	0.0824034i
$509$	23.7079			1.05083			0.525417	−	0.850845i	$-0.323909\pi$
$509$	23.7079			1.05083			0.525417	+	0.850845i	$0.323909\pi$
$510$	−20.3148	−	14.7268i	−0.899554	−	0.652115i
$511$	−1.42420			−0.0630027
$512$			6.54989i			0.289467i
$513$	−4.88600	+	4.88600i	−0.215722	+	0.215722i
$514$	11.7933			0.520179
$515$	−13.9966	+	13.9966i	−0.616763	+	0.616763i
$516$	1.14552	+	1.14552i	0.0504288	+	0.0504288i
$517$	−1.26981	−	1.26981i	−0.0558461	−	0.0558461i
$518$			15.5968i			0.685286i
$519$			22.3933i			0.982956i
$520$	16.8746	+	16.8746i	0.740001	+	0.740001i
$521$	−5.55277	−	5.55277i	−0.243271	−	0.243271i	0.574931	−	0.818202i	$-0.305029\pi$
$521$	−5.55277	−	5.55277i	−0.243271	−	0.243271i	−0.818202	+	0.574931i	$0.805029\pi$
$522$	11.7842	−	11.7842i	0.515783	−	0.515783i
$523$	−7.79018			−0.340641			−0.170320	−	0.985389i	$-0.554480\pi$
$523$	−7.79018			−0.340641			−0.170320	+	0.985389i	$0.554480\pi$
$524$	5.69988	−	5.69988i	0.249000	−	0.249000i
$525$		−	7.58826i		−	0.331179i
$526$	1.71291			0.0746865
$527$	−4.71560	+	0.751978i	−0.205415	+	0.0327567i
$528$	12.8208			0.557956
$529$			35.3066i			1.53507i
$530$	−14.5546	+	14.5546i	−0.632213	+	0.632213i
$531$	−10.9220			−0.473977
$532$	−4.60217	+	4.60217i	−0.199530	+	0.199530i
$533$	−22.3558	−	22.3558i	−0.968338	−	0.968338i
$534$	13.4728	+	13.4728i	0.583024	+	0.583024i
$535$			19.9676i			0.863276i
$536$		−	5.20557i		−	0.224846i
$537$	9.96257	+	9.96257i	0.429916	+	0.429916i
$538$	−2.95496	−	2.95496i	−0.127397	−	0.127397i
$539$	−1.81437	+	1.81437i	−0.0781503	+	0.0781503i
$540$	−3.34189			−0.143812
$541$	9.70894	−	9.70894i	0.417420	−	0.417420i	−0.466894	−	0.884313i	$-0.654627\pi$
$541$	9.70894	−	9.70894i	0.417420	−	0.417420i	0.884313	+	0.466894i	$0.154627\pi$
$542$			20.2466i			0.869666i
$543$	−20.8864			−0.896319
$544$	11.9560	−	16.4926i	0.512609	−	0.707114i
$545$	−57.5209			−2.46393
$546$			6.35687i			0.272049i
$547$	14.8748	−	14.8748i	0.636002	−	0.636002i	−0.313564	−	0.949567i	$-0.601523\pi$
$547$	14.8748	−	14.8748i	0.636002	−	0.636002i	0.949567	+	0.313564i	$0.101523\pi$
$548$	17.6676			0.754724
$549$	3.62531	−	3.62531i	0.154724	−	0.154724i
$550$	23.6147	+	23.6147i	1.00693	+	1.00693i
$551$	47.4740	+	47.4740i	2.02246	+	2.02246i
$552$			13.8579i			0.589830i
$553$			11.0332i			0.469178i
$554$	−15.6024	−	15.6024i	−0.662884	−	0.662884i
$555$	−22.8134	−	22.8134i	−0.968375	−	0.968375i
$556$	4.29878	−	4.29878i	0.182309	−	0.182309i
$557$	−18.9903			−0.804645			−0.402323	−	0.915498i	$-0.631797\pi$
$557$	−18.9903			−0.804645			−0.402323	+	0.915498i	$0.631797\pi$
$558$	−1.40464	+	1.40464i	−0.0594632	+	0.0594632i
$559$			6.37438i			0.269607i
$560$	17.7280			0.749145
$561$	−8.56554	−	6.20943i	−0.361637	−	0.262162i
$562$	−30.7703			−1.29797
$563$		−	17.8871i		−	0.753851i	−0.926244	−	0.376925i	$-0.876981\pi$
$563$		−	17.8871i		−	0.753851i	0.926244	−	0.376925i	$-0.123019\pi$
$564$	−0.466130	+	0.466130i	−0.0196276	+	0.0196276i
$565$	34.3488			1.44506
$566$	−23.1310	+	23.1310i	−0.972266	+	0.972266i
$567$	0.707107	+	0.707107i	0.0296957	+	0.0296957i
$568$	16.5767	+	16.5767i	0.695545	+	0.695545i
$569$		−	17.6081i		−	0.738170i	−0.929396	−	0.369085i	$-0.879671\pi$
$569$		−	17.6081i		−	0.738170i	0.929396	−	0.369085i	$-0.120329\pi$
$570$		−	42.0500i		−	1.76128i
$571$	−11.5255	−	11.5255i	−0.482328	−	0.482328i	0.423546	−	0.905875i	$-0.360785\pi$
$571$	−11.5255	−	11.5255i	−0.482328	−	0.482328i	−0.905875	+	0.423546i	$0.860785\pi$
$572$	−6.33377	−	6.33377i	−0.264828	−	0.264828i
$573$	−3.32627	+	3.32627i	−0.138957	+	0.138957i
$574$	−14.6316			−0.610711
$575$	−40.9719	+	40.9719i	−1.70865	+	1.70865i
$576$			1.51925i			0.0633019i
$577$	18.0748			0.752464			0.376232	−	0.926526i	$-0.377220\pi$
$577$	18.0748			0.752464			0.376232	+	0.926526i	$0.377220\pi$
$578$	−27.7122	+	9.06892i	−1.15268	+	0.377217i
$579$	−5.10354			−0.212096
$580$			32.4709i			1.34828i
$581$	5.73879	−	5.73879i	0.238085	−	0.238085i
$582$	−3.03706			−0.125890
$583$	−6.13683	+	6.13683i	−0.254162	+	0.254162i
$584$	1.82765	+	1.82765i	0.0756286	+	0.0756286i
$585$	−9.29814	−	9.29814i	−0.384431	−	0.384431i
$586$			29.0358i			1.19946i
$587$			5.40978i			0.223286i	0.993748	+	0.111643i	$0.0356113\pi$
$587$			5.40978i			0.223286i	−0.993748	+	0.111643i	$0.964389\pi$
$588$	0.666030	+	0.666030i	0.0274666	+	0.0274666i
$589$	−5.65874	−	5.65874i	−0.233164	−	0.233164i
$590$	46.9988	−	46.9988i	1.93491	−	1.93491i
$591$	13.4842			0.554665
$592$	32.1280	−	32.1280i	1.32045	−	1.32045i
$593$			8.20619i			0.336988i	0.985703	+	0.168494i	$0.0538904\pi$
$593$			8.20619i			0.336988i	−0.985703	+	0.168494i	$0.946110\pi$
$594$	−4.40103			−0.180577
$595$	−11.8440	−	8.58608i	−0.485556	−	0.351995i
$596$	14.5058			0.594179
$597$		−	4.19363i		−	0.171634i
$598$	34.3231	−	34.3231i	1.40358	−	1.40358i
$599$	−16.5369			−0.675681			−0.337840	−	0.941203i	$-0.609696\pi$
$599$	−16.5369			−0.675681			−0.337840	+	0.941203i	$0.609696\pi$
$600$	−9.73789	+	9.73789i	−0.397548	+	0.397548i
$601$	21.8842	+	21.8842i	0.892673	+	0.892673i	0.994774	−	0.102101i	$-0.0325564\pi$
$601$	21.8842	+	21.8842i	0.892673	+	0.892673i	−0.102101	+	0.994774i	$0.532556\pi$
$602$	2.08597	+	2.08597i	0.0850180	+	0.0850180i
$603$			2.86834i			0.116808i
$604$			9.42006i			0.383297i
$605$	−11.0793	−	11.0793i	−0.450437	−	0.450437i
$606$	−12.0101	−	12.0101i	−0.487876	−	0.487876i
$607$	−6.89084	+	6.89084i	−0.279691	+	0.279691i	−0.832986	−	0.553295i	$-0.813370\pi$
$607$	−6.89084	+	6.89084i	−0.279691	+	0.279691i	0.553295	+	0.832986i	$0.313370\pi$
$608$	34.1384			1.38449
$609$	6.87048	−	6.87048i	0.278406	−	0.278406i
$610$			31.2002i			1.26326i
$611$	−2.59383			−0.104935
$612$	−2.27940	+	3.14430i	−0.0921394	+	0.127101i
$613$	41.7672			1.68696			0.843480	−	0.537160i	$-0.180503\pi$
$613$	41.7672			1.68696			0.843480	+	0.537160i	$0.180503\pi$
$614$		−	37.5688i		−	1.51615i
$615$	21.4016	−	21.4016i	0.862994	−	0.862994i
$616$	4.65669			0.187623
$617$	27.4160	−	27.4160i	1.10373	−	1.10373i	0.109769	−	0.993957i	$-0.464989\pi$
$617$	27.4160	−	27.4160i	1.10373	−	1.10373i	0.993957	−	0.109769i	$-0.0350113\pi$
$618$	6.76633	+	6.76633i	0.272182	+	0.272182i
$619$	−31.4963	−	31.4963i	−1.26594	−	1.26594i	−0.948166	−	0.317777i	$-0.897064\pi$
$619$	−31.4963	−	31.4963i	−1.26594	−	1.26594i	−0.317777	−	0.948166i	$-0.602936\pi$
$620$		−	3.87042i		−	0.155440i
$621$		−	7.63588i		−	0.306417i
$622$	33.0163	+	33.0163i	1.32383	+	1.32383i
$623$	7.85493	+	7.85493i	0.314701	+	0.314701i
$624$	13.0945	−	13.0945i	0.524201	−	0.524201i
$625$	5.35957			0.214383
$626$	−8.73283	+	8.73283i	−0.349034	+	0.349034i
$627$		−	17.7300i		−	0.708068i
$628$	7.25105			0.289348
$629$	−37.0249	+	5.90421i	−1.47628	+	0.235416i
$630$	−6.08552			−0.242453
$631$			7.99744i			0.318373i	0.987249	+	0.159186i	$0.0508871\pi$
$631$			7.99744i			0.318373i	−0.987249	+	0.159186i	$0.949113\pi$
$632$	14.1587	−	14.1587i	0.563202	−	0.563202i
$633$	17.8725			0.710370
$634$	22.5200	−	22.5200i	0.894383	−	0.894383i
$635$	4.94693	+	4.94693i	0.196313	+	0.196313i
$636$	2.25275	+	2.25275i	0.0893274	+	0.0893274i
$637$			3.70620i			0.146845i
$638$			42.7619i			1.69296i
$639$	−9.13401	−	9.13401i	−0.361336	−	0.361336i
$640$	−31.3272	−	31.3272i	−1.23832	−	1.23832i
$641$	−27.5919	+	27.5919i	−1.08982	+	1.08982i	−0.0942694	+	0.995547i	$0.530051\pi$
$641$	−27.5919	+	27.5919i	−1.08982	+	1.08982i	−0.995547	+	0.0942694i	$0.969949\pi$
$642$	9.65291			0.380970
$643$	−4.16724	+	4.16724i	−0.164340	+	0.164340i	−0.784486	−	0.620146i	$-0.787073\pi$
$643$	−4.16724	+	4.16724i	−0.164340	+	0.164340i	0.620146	+	0.784486i	$0.287073\pi$
$644$		−	7.19230i		−	0.283416i
$645$	−6.10228			−0.240277
$646$	−39.5638	−	28.6811i	−1.55662	−	1.12844i
$647$	−27.4242			−1.07816			−0.539079	−	0.842255i	$-0.681228\pi$
$647$	−27.4242			−1.07816			−0.539079	+	0.842255i	$0.681228\pi$
$648$		−	1.81484i		−	0.0712935i
$649$	19.8166	−	19.8166i	0.777870	−	0.777870i
$650$	48.2376			1.89203
$651$	−0.818937	+	0.818937i	−0.0320967	+	0.0320967i
$652$	−3.93196	−	3.93196i	−0.153987	−	0.153987i
$653$	−15.1507	−	15.1507i	−0.592891	−	0.592891i	0.345520	−	0.938411i	$-0.387702\pi$
$653$	−15.1507	−	15.1507i	−0.592891	−	0.592891i	−0.938411	+	0.345520i	$0.887702\pi$
$654$			27.8072i			1.08735i
$655$			30.3637i			1.18641i
$656$	30.1397	+	30.1397i	1.17676	+	1.17676i
$657$	−1.00706	−	1.00706i	−0.0392891	−	0.0392891i
$658$	−0.848814	+	0.848814i	−0.0330902	+	0.0330902i
$659$	10.2775			0.400356			0.200178	−	0.979760i	$-0.435848\pi$
$659$	10.2775			0.400356			0.200178	+	0.979760i	$0.435848\pi$
$660$	6.06341	−	6.06341i	0.236018	−	0.236018i
$661$			5.90247i			0.229580i	0.993390	+	0.114790i	$0.0366195\pi$
$661$			5.90247i			0.229580i	−0.993390	+	0.114790i	$0.963381\pi$
$662$	−13.8300			−0.537519
$663$	−15.0904	+	2.40640i	−0.586062	+	0.0934568i
$664$	−14.7290			−0.571595
$665$		−	24.5161i		−	0.950695i
$666$	−11.0286	+	11.0286i	−0.427351	+	0.427351i
$667$	−74.1927			−2.87275
$668$	2.14936	−	2.14936i	0.0831612	−	0.0831612i
$669$	−1.13330	−	1.13330i	−0.0438158	−	0.0438158i
$670$	−12.3428	−	12.3428i	−0.476843	−	0.476843i
$671$			13.1553i			0.507854i
$672$		−	4.94054i		−	0.190585i
$673$	2.65833	+	2.65833i	0.102471	+	0.102471i	0.756484	−	0.654013i	$-0.226916\pi$
$673$	2.65833	+	2.65833i	0.102471	+	0.102471i	−0.654013	+	0.756484i	$0.726916\pi$
$674$	−32.2570	−	32.2570i	−1.24250	−	1.24250i
$675$	5.36571	−	5.36571i	0.206526	−	0.206526i
$676$	−0.693140			−0.0266592
$677$	13.4750	−	13.4750i	0.517885	−	0.517885i	−0.399046	−	0.916931i	$-0.630659\pi$
$677$	13.4750	−	13.4750i	0.517885	−	0.517885i	0.916931	+	0.399046i	$0.130659\pi$
$678$		−	16.6052i		−	0.637718i
$679$	−1.77067			−0.0679522
$680$	4.18080	+	26.2175i	0.160327	+	1.00540i
$681$	−11.7490			−0.450222
$682$		−	5.09707i		−	0.195177i
$683$	27.5713	−	27.5713i	1.05499	−	1.05499i	0.0565907	−	0.998397i	$-0.481977\pi$
$683$	27.5713	−	27.5713i	1.05499	−	1.05499i	0.998397	−	0.0565907i	$-0.0180230\pi$
$684$	−6.50846			−0.248857
$685$	−47.0584	+	47.0584i	−1.79801	+	1.79801i
$686$	1.21283	+	1.21283i	0.0463060	+	0.0463060i
$687$	−1.04504	−	1.04504i	−0.0398709	−	0.0398709i
$688$		−	8.59382i		−	0.327636i
$689$			12.5357i			0.477571i
$690$	32.8580	+	32.8580i	1.25088	+	1.25088i
$691$	−10.7045	−	10.7045i	−0.407218	−	0.407218i	0.473549	−	0.880767i	$-0.342973\pi$
$691$	−10.7045	−	10.7045i	−0.407218	−	0.407218i	−0.880767	+	0.473549i	$0.842973\pi$
$692$	−14.9146	+	14.9146i	−0.566969	+	0.566969i
$693$	−2.56590			−0.0974705
$694$	−24.0660	+	24.0660i	−0.913534	+	0.913534i
$695$			22.8999i			0.868644i
$696$	−17.6336			−0.668398
$697$	−5.53881	−	34.7335i	−0.209798	−	1.31563i
$698$	−18.5660			−0.702735
$699$		−	13.7652i		−	0.520647i
$700$	5.05402	−	5.05402i	0.191024	−	0.191024i
$701$	−4.53361			−0.171232			−0.0856160	−	0.996328i	$-0.527286\pi$
$701$	−4.53361			−0.171232			−0.0856160	+	0.996328i	$0.527286\pi$
$702$	−4.49498	+	4.49498i	−0.169652	+	0.169652i
$703$	−44.4300	−	44.4300i	−1.67571	−	1.67571i
$704$	−2.75647	−	2.75647i	−0.103888	−	0.103888i
$705$		−	2.48311i		−	0.0935193i
$706$		−	43.1324i		−	1.62331i
$707$	−7.00215	−	7.00215i	−0.263343	−	0.263343i
$708$	−7.27442	−	7.27442i	−0.273389	−	0.273389i
$709$	28.5897	−	28.5897i	1.07371	−	1.07371i	0.0766494	−	0.997058i	$-0.475578\pi$
$709$	28.5897	−	28.5897i	1.07371	−	1.07371i	0.997058	−	0.0766494i	$-0.0244222\pi$
$710$	78.6093			2.95016
$711$	−7.80162	+	7.80162i	−0.292584	+	0.292584i
$712$		−	20.1602i		−	0.755535i
$713$	8.84351			0.331192
$714$	−4.15075	+	5.72571i	−0.155338	+	0.214279i
$715$	33.7405			1.26182
$716$			13.2707i			0.495951i
$717$	−9.65099	+	9.65099i	−0.360423	+	0.360423i
$718$	−34.5166			−1.28815
$719$	33.6094	−	33.6094i	1.25342	−	1.25342i	0.299244	−	0.954177i	$-0.403265\pi$
$719$	33.6094	−	33.6094i	1.25342	−	1.25342i	0.954177	−	0.299244i	$-0.0967345\pi$
$720$	12.5356	+	12.5356i	0.467174	+	0.467174i
$721$	3.94492	+	3.94492i	0.146917	+	0.146917i
$722$		−	49.3053i		−	1.83495i
$723$			17.3323i			0.644596i
$724$	−13.9109	−	13.9109i	−0.516996	−	0.516996i
$725$	−52.1350	−	52.1350i	−1.93625	−	1.93625i
$726$	−5.35603	+	5.35603i	−0.198781	+	0.198781i
$727$	−12.1751			−0.451549			−0.225774	−	0.974180i	$-0.572491\pi$
$727$	−12.1751			−0.451549			−0.225774	+	0.974180i	$0.572491\pi$
$728$	4.75610	−	4.75610i	0.176273	−	0.176273i
$729$			1.00000i			0.0370370i
$730$	8.66697			0.320779
$731$	−4.16218	+	5.74148i	−0.153944	+	0.212356i
$732$	4.82913			0.178490
$733$			16.4228i			0.606589i	0.952897	+	0.303294i	$0.0980865\pi$
$733$			16.4228i			0.606589i	−0.952897	+	0.303294i	$0.901913\pi$
$734$	−33.2581	+	33.2581i	−1.22758	+	1.22758i
$735$	−3.54799			−0.130870
$736$	−26.6758	+	26.6758i	−0.983284	+	0.983284i
$737$	−5.20422	−	5.20422i	−0.191700	−	0.191700i
$738$	−10.3461	−	10.3461i	−0.380845	−	0.380845i
$739$			14.0884i			0.518249i	0.965844	+	0.259125i	$0.0834340\pi$
$739$			14.0884i			0.518249i	−0.965844	+	0.259125i	$0.916566\pi$
$740$		−	30.3888i		−	1.11712i
$741$	−18.1085	−	18.1085i	−0.665232	−	0.665232i
$742$	4.10222	+	4.10222i	0.150597	+	0.150597i
$743$	−37.0522	+	37.0522i	−1.35931	+	1.35931i	−0.484551	+	0.874763i	$0.661017\pi$
$743$	−37.0522	+	37.0522i	−1.35931	+	1.35931i	−0.874763	+	0.484551i	$0.838983\pi$
$744$	2.10186			0.0770578
$745$	−38.6366	+	38.6366i	−1.41554	+	1.41554i
$746$			15.4672i			0.566293i
$747$	8.11587			0.296944
$748$	−1.56924	−	9.84058i	−0.0573770	−	0.359807i
$749$	5.62786			0.205638
$750$			15.7509i			0.575143i
$751$	−13.5973	+	13.5973i	−0.496174	+	0.496174i	−0.910245	−	0.414071i	$-0.864107\pi$
$751$	−13.5973	+	13.5973i	−0.496174	+	0.496174i	0.414071	+	0.910245i	$0.364107\pi$
$752$	3.49695			0.127521
$753$	−11.8859	+	11.8859i	−0.433145	+	0.433145i
$754$	43.6747	+	43.6747i	1.59054	+	1.59054i
$755$	−25.0907	−	25.0907i	−0.913143	−	0.913143i
$756$			0.941909i			0.0342569i
$757$			28.7663i			1.04553i	0.852477	+	0.522764i	$0.175099\pi$
$757$			28.7663i			1.04553i	−0.852477	+	0.522764i	$0.824901\pi$
$758$	−4.86957	−	4.86957i	−0.176871	−	0.176871i
$759$	13.8543	+	13.8543i	0.502878	+	0.502878i
$760$	−31.4611	+	31.4611i	−1.14122	+	1.14122i
$761$	39.8043			1.44291			0.721453	−	0.692463i	$-0.243475\pi$
$761$	39.8043			1.44291			0.721453	+	0.692463i	$0.243475\pi$
$762$	2.39148	−	2.39148i	0.0866344	−	0.0866344i
$763$			16.2122i			0.586922i
$764$	−4.43079			−0.160300
$765$	−2.30368	−	14.4462i	−0.0832898	−	0.522305i
$766$	12.6760			0.458004
$767$		−	40.4793i		−	1.46162i
$768$	−12.9959	+	12.9959i	−0.468950	+	0.468950i
$769$	−1.97929			−0.0713750			−0.0356875	−	0.999363i	$-0.511362\pi$
$769$	−1.97929			−0.0713750			−0.0356875	+	0.999363i	$0.511362\pi$
$770$	11.0414	−	11.0414i	0.397903	−	0.397903i
$771$	4.86189	+	4.86189i	0.175097	+	0.175097i
$772$	−3.39911	−	3.39911i	−0.122337	−	0.122337i
$773$			30.2810i			1.08913i	0.838718	+	0.544565i	$0.183305\pi$
$773$			30.2810i			1.08913i	−0.838718	+	0.544565i	$0.816695\pi$
$774$			2.95001i			0.106036i
$775$	6.21431	+	6.21431i	0.223225	+	0.223225i
$776$	2.27227	+	2.27227i	0.0815699	+	0.0815699i
$777$	−6.42994	+	6.42994i	−0.230673	+	0.230673i
$778$	−27.6856			−0.992576
$779$	41.6803	−	41.6803i	1.49335	−	1.49335i
$780$		−	12.3857i		−	0.443479i
$781$	33.1449			1.18602
$782$	53.3268	−	8.50380i	1.90696	−	0.304095i
$783$	9.71633			0.347233
$784$		−	4.99663i		−	0.178451i
$785$	−19.3134	+	19.3134i	−0.689326	+	0.689326i
$786$	14.6787			0.523570
$787$	37.6231	−	37.6231i	1.34112	−	1.34112i	0.446167	−	0.894950i	$-0.352789\pi$
$787$	37.6231	−	37.6231i	1.34112	−	1.34112i	0.894950	−	0.446167i	$-0.147211\pi$
$788$	8.98088	+	8.98088i	0.319930	+	0.319930i
$789$	0.706163	+	0.706163i	0.0251401	+	0.0251401i
$790$		−	67.1425i		−	2.38882i
$791$		−	9.68119i		−	0.344223i
$792$	3.29278	+	3.29278i	0.117004	+	0.117004i
$793$	13.4361	+	13.4361i	0.477130	+	0.477130i
$794$	−8.14118	+	8.14118i	−0.288920	+	0.288920i
$795$	−12.0006			−0.425616
$796$	2.79309	−	2.79309i	0.0989983	−	0.0989983i
$797$		−	39.2847i		−	1.39154i	−0.718266	−	0.695768i	$-0.755064\pi$
$797$		−	39.2847i		−	1.39154i	0.718266	−	0.695768i	$-0.244936\pi$
$798$	−11.8518			−0.419548
$799$	−2.33629	−	1.69365i	−0.0826522	−	0.0599172i
$800$	−37.4901			−1.32547
$801$			11.1085i			0.392501i
$802$	−2.40383	+	2.40383i	−0.0848821	+	0.0848821i
$803$	3.65435			0.128959
$804$	−1.91040	+	1.91040i	−0.0673747	+	0.0673747i
$805$	19.1570	+	19.1570i	0.675195	+	0.675195i
$806$	−5.20588	−	5.20588i	−0.183369	−	0.183369i
$807$		−	2.43642i		−	0.0857660i
$808$			17.9715i			0.632234i
$809$	32.7701	+	32.7701i	1.15214	+	1.15214i	0.986123	+	0.166014i	$0.0530896\pi$
$809$	32.7701	+	32.7701i	1.15214	+	1.15214i	0.166014	+	0.986123i	$0.446910\pi$
$810$	−4.30311	−	4.30311i	−0.151196	−	0.151196i
$811$	32.4710	−	32.4710i	1.14021	−	1.14021i	0.151802	−	0.988411i	$-0.451492\pi$
$811$	32.4710	−	32.4710i	1.14021	−	1.14021i	0.988411	−	0.151802i	$-0.0485075\pi$
$812$	9.15190			0.321169
$813$	−8.34685	+	8.34685i	−0.292737	+	0.292737i
$814$		−	40.0200i		−	1.40270i
$815$	20.9458			0.733701
$816$	20.3446	−	3.24426i	0.712202	−	0.113572i
$817$	−11.8844			−0.415784
$818$		−	26.3094i		−	0.919887i
$819$	−2.62068	+	2.62068i	−0.0915738	+	0.0915738i
$820$	28.5082			0.995549
$821$	−25.0935	+	25.0935i	−0.875768	+	0.875768i	−0.993094	−	0.117325i	$-0.962568\pi$
$821$	−25.0935	+	25.0935i	−0.875768	+	0.875768i	0.117325	+	0.993094i	$0.462568\pi$
$822$	22.7493	+	22.7493i	0.793475	+	0.793475i
$823$	−7.45205	−	7.45205i	−0.259762	−	0.259762i	0.565195	−	0.824957i	$-0.308801\pi$
$823$	−7.45205	−	7.45205i	−0.259762	−	0.259762i	−0.824957	+	0.565195i	$0.808801\pi$
$824$		−	10.1249i		−	0.352718i
$825$			19.4707i			0.677884i
$826$	−13.2466	−	13.2466i	−0.460907	−	0.460907i
$827$	−39.0403	−	39.0403i	−1.35757	−	1.35757i	−0.876909	−	0.480656i	$-0.840399\pi$
$827$	−39.0403	−	39.0403i	−1.35757	−	1.35757i	−0.480656	−	0.876909i	$-0.659601\pi$
$828$	5.08573	−	5.08573i	0.176741	−	0.176741i
$829$	37.2823			1.29487			0.647435	−	0.762121i	$-0.275842\pi$
$829$	37.2823			1.29487			0.647435	+	0.762121i	$0.275842\pi$
$830$	−34.9235	+	34.9235i	−1.21221	+	1.21221i
$831$		−	12.8645i		−	0.446264i
$832$	−5.63062			−0.195207
$833$	−2.41998	+	3.33822i	−0.0838474	+	0.115662i
$834$	11.0705			0.383339
$835$			11.4498i			0.396237i
$836$	11.8087	−	11.8087i	0.408413	−	0.408413i
$837$	−1.15815			−0.0400316
$838$	0.323950	−	0.323950i	0.0111907	−	0.0111907i
$839$	16.4347	+	16.4347i	0.567387	+	0.567387i	0.931396	−	0.364008i	$-0.118592\pi$
$839$	16.4347	+	16.4347i	0.567387	+	0.567387i	−0.364008	+	0.931396i	$0.618592\pi$
$840$	4.55308	+	4.55308i	0.157096	+	0.157096i
$841$		−	65.4071i		−	2.25542i
$842$			28.2004i			0.971851i
$843$	−12.6853	−	12.6853i	−0.436906	−	0.436906i
$844$	11.9037	+	11.9037i	0.409741	+	0.409741i
$845$	1.84620	−	1.84620i	0.0635114	−	0.0635114i
$846$	−1.20040			−0.0412708
$847$	−3.12269	+	3.12269i	−0.107297	+	0.107297i
$848$		−	16.9004i		−	0.580361i
$849$	−19.0719			−0.654546
$850$	43.4482	+	31.4970i	1.49026	+	1.08034i
$851$	69.4354			2.38022
$852$		−	12.1671i		−	0.416837i
$853$	−9.97344	+	9.97344i	−0.341484	+	0.341484i	−0.856925	−	0.515441i	$-0.827628\pi$
$853$	−9.97344	+	9.97344i	−0.341484	+	0.341484i	0.515441	+	0.856925i	$0.327628\pi$
$854$	8.79376			0.300916
$855$	17.3355	−	17.3355i	0.592862	−	0.592862i
$856$	−7.22214	−	7.22214i	−0.246848	−	0.246848i
$857$	−25.6259	−	25.6259i	−0.875362	−	0.875362i	0.117688	−	0.993051i	$-0.462452\pi$
$857$	−25.6259	−	25.6259i	−0.875362	−	0.875362i	−0.993051	+	0.117688i	$0.962452\pi$
$858$		−	16.3111i		−	0.556851i
$859$		−	35.1436i		−	1.19908i	−0.800343	−	0.599542i	$-0.795349\pi$
$859$		−	35.1436i		−	1.19908i	0.800343	−	0.599542i	$-0.204651\pi$
$860$	−4.06431	−	4.06431i	−0.138592	−	0.138592i
$861$	−6.03201	−	6.03201i	−0.205570	−	0.205570i
$862$	2.62405	−	2.62405i	0.0893754	−	0.0893754i
$863$	18.5693			0.632106			0.316053	−	0.948742i	$-0.397642\pi$
$863$	18.5693			0.632106			0.316053	+	0.948742i	$0.397642\pi$
$864$	3.49349	−	3.49349i	0.118851	−	0.118851i
$865$		−	79.4513i		−	2.70142i
$866$	−9.69573			−0.329474
$867$	−15.1634	−	7.68587i	−0.514975	−	0.261026i
$868$	−1.09087			−0.0370267
$869$		−	28.3100i		−	0.960351i
$870$	−41.8104	+	41.8104i	−1.41751	+	1.41751i
$871$	−10.6306			−0.360205
$872$	20.8049	−	20.8049i	0.704542	−	0.704542i
$873$	−1.25205	−	1.25205i	−0.0423756	−	0.0423756i
$874$	63.9923	+	63.9923i	2.16457	+	2.16457i
$875$			9.18315i			0.310447i
$876$		−	1.34146i		−	0.0453239i
$877$	−12.7084	−	12.7084i	−0.429133	−	0.429133i	0.459200	−	0.888333i	$-0.348136\pi$
$877$	−12.7084	−	12.7084i	−0.429133	−	0.429133i	−0.888333	+	0.459200i	$0.848136\pi$
$878$	2.32581	+	2.32581i	0.0784924	+	0.0784924i
$879$	−11.9703	+	11.9703i	−0.403747	+	0.403747i
$880$	−45.4883			−1.53341
$881$	24.4657	−	24.4657i	0.824269	−	0.824269i	−0.162448	−	0.986717i	$-0.551939\pi$
$881$	24.4657	−	24.4657i	0.824269	−	0.824269i	0.986717	+	0.162448i	$0.0519390\pi$
$882$			1.71520i			0.0577538i
$883$	20.3212			0.683863			0.341931	−	0.939725i	$-0.388919\pi$
$883$	20.3212			0.683863			0.341931	+	0.939725i	$0.388919\pi$
$884$	−11.6534	−	8.44791i	−0.391946	−	0.284134i
$885$	38.7514			1.30261
$886$			48.8334i			1.64059i
$887$	13.5104	−	13.5104i	0.453634	−	0.453634i	−0.442925	−	0.896559i	$-0.646059\pi$
$887$	13.5104	−	13.5104i	0.453634	−	0.453634i	0.896559	+	0.442925i	$0.146059\pi$
$888$	16.5029			0.553800
$889$	1.39429	−	1.39429i	0.0467630	−	0.0467630i
$890$	−47.8013	−	47.8013i	−1.60230	−	1.60230i
$891$	−1.81437	−	1.81437i	−0.0607836	−	0.0607836i
$892$		−	1.50962i		−	0.0505459i
$893$		−	4.83595i		−	0.161829i
$894$	18.6780	+	18.6780i	0.624687	+	0.624687i
$895$	−35.3471	−	35.3471i	−1.18152	−	1.18152i
$896$	−8.82956	+	8.82956i	−0.294975	+	0.294975i
$897$	28.3001			0.944911
$898$	−15.8341	+	15.8341i	−0.528392	+	0.528392i
$899$			11.2530i			0.375308i
$900$	7.14746			0.238249
$901$	−8.18523	+	11.2910i	−0.272690	+	0.376159i
$902$	37.5433			1.25005
$903$			1.71992i			0.0572355i
$904$	−12.4237	+	12.4237i	−0.413206	+	0.413206i
$905$	74.1047			2.46332
$906$	−12.1295	+	12.1295i	−0.402977	+	0.402977i
$907$	−41.1761	−	41.1761i	−1.36723	−	1.36723i	−0.864364	−	0.502867i	$-0.832278\pi$
$907$	−41.1761	−	41.1761i	−1.36723	−	1.36723i	−0.502867	−	0.864364i	$-0.667722\pi$
$908$	−7.82518	−	7.82518i	−0.259688	−	0.259688i
$909$		−	9.90253i		−	0.328446i
$910$		−	22.5541i		−	0.747662i
$911$	1.65907	+	1.65907i	0.0549673	+	0.0549673i	0.734056	−	0.679089i	$-0.237625\pi$
$911$	1.65907	+	1.65907i	0.0549673	+	0.0549673i	−0.679089	+	0.734056i	$0.737625\pi$
$912$	24.4135	+	24.4135i	0.808413	+	0.808413i
$913$	−14.7252	+	14.7252i	−0.487332	+	0.487332i
$914$	15.1059			0.499660
$915$	−12.8626	+	12.8626i	−0.425224	+	0.425224i
$916$		−	1.39206i		−	0.0459950i
$917$	8.55799			0.282610
$918$	−6.98371	+	1.11366i	−0.230497	+	0.0367564i
$919$	−0.903634			−0.0298081			−0.0149041	−	0.999889i	$-0.504744\pi$
$919$	−0.903634			−0.0298081			−0.0149041	+	0.999889i	$0.504744\pi$
$920$		−	49.1676i		−	1.62101i
$921$	15.4881	−	15.4881i	0.510349	−	0.510349i
$922$	−13.9771			−0.460313
$923$	33.8524	−	33.8524i	1.11427	−	1.11427i
$924$	−1.70897	−	1.70897i	−0.0562209	−	0.0562209i
$925$	48.7921	+	48.7921i	1.60427	+	1.60427i
$926$			0.562605i			0.0184883i
$927$			5.57897i			0.183237i
$928$	−33.9439	−	33.9439i	−1.11426	−	1.11426i
$929$	19.7422	+	19.7422i	0.647721	+	0.647721i	0.952442	−	0.304721i	$-0.0985631\pi$
$929$	19.7422	+	19.7422i	0.647721	+	0.647721i	−0.304721	+	0.952442i	$0.598563\pi$
$930$	4.98366	−	4.98366i	0.163421	−	0.163421i
$931$	−6.90985			−0.226461
$932$	9.16804	−	9.16804i	0.300309	−	0.300309i
$933$			27.2225i			0.891225i
$934$	−39.4873			−1.29206
$935$	30.3905	+	22.0310i	0.993875	+	0.720492i
$936$	6.72614			0.219851
$937$			36.6825i			1.19836i	0.800613	+	0.599182i	$0.204507\pi$
$937$			36.6825i			1.19836i	−0.800613	+	0.599182i	$0.795493\pi$
$938$	−3.47881	+	3.47881i	−0.113587	+	0.113587i
$939$	−7.20038			−0.234976
$940$	1.65383	−	1.65383i	0.0539419	−	0.0539419i
$941$	−23.5785	−	23.5785i	−0.768636	−	0.768636i	0.209230	−	0.977866i	$-0.432904\pi$
$941$	−23.5785	−	23.5785i	−0.768636	−	0.768636i	−0.977866	+	0.209230i	$0.932904\pi$
$942$	9.33666	+	9.33666i	0.304205	+	0.304205i
$943$			65.1383i			2.12119i
$944$			54.5734i			1.77621i
$945$	−2.50881	−	2.50881i	−0.0816116	−	0.0816116i
$946$	−5.35241	−	5.35241i	−0.174022	−	0.174022i
$947$	−13.9732	+	13.9732i	−0.454068	+	0.454068i	−0.896702	−	0.442634i	$-0.854044\pi$
$947$	−13.9732	+	13.9732i	−0.454068	+	0.454068i	0.442634	+	0.896702i	$0.354044\pi$
$948$	−10.3922			−0.337524
$949$	3.73236	−	3.73236i	0.121157	−	0.121157i
$950$			89.9344i			2.91786i
$951$	18.5681			0.602113
$952$	7.38940	−	1.17836i	0.239492	−	0.0381908i
$953$	36.5884			1.18521			0.592607	−	0.805491i	$-0.298099\pi$
$953$	36.5884			1.18521			0.592607	+	0.805491i	$0.298099\pi$
$954$			5.80141i			0.187828i
$955$	11.8016	−	11.8016i	0.381890	−	0.381890i
$956$	−12.8557			−0.415783
$957$	−17.6290	+	17.6290i	−0.569864	+	0.569864i
$958$	−33.5218	−	33.5218i	−1.08304	−	1.08304i
$959$	13.2634	+	13.2634i	0.428297	+	0.428297i
$960$		−	5.39027i		−	0.173970i
$961$			29.6587i			0.956732i
$962$	−40.8743	−	40.8743i	−1.31784	−	1.31784i
$963$	3.97950	+	3.97950i	0.128238	+	0.128238i
$964$	−11.5438	+	11.5438i	−0.371802	+	0.371802i
$965$	18.1073			0.582895
$966$	9.26101	−	9.26101i	0.297968	−	0.297968i
$967$		−	29.3184i		−	0.942815i	−0.881915	−	0.471408i	$-0.843746\pi$
$967$		−	29.3184i		−	0.942815i	0.881915	−	0.471408i	$-0.156254\pi$
$968$	8.01459			0.257599
$969$	−4.48651	−	28.1346i	−0.144127	−	0.903813i
$970$	10.7755			0.345979
$971$			30.8608i			0.990370i	0.868788	+	0.495185i	$0.164900\pi$
$971$			30.8608i			0.990370i	−0.868788	+	0.495185i	$0.835100\pi$
$972$	−0.666030	+	0.666030i	−0.0213629	+	0.0213629i
$973$	6.45433			0.206916
$974$	2.65836	−	2.65836i	0.0851793	−	0.0851793i
$975$	19.8864	+	19.8864i	0.636874	+	0.636874i
$976$	−18.1143	−	18.1143i	−0.579825	−	0.579825i
$977$			54.9490i			1.75797i	0.476847	+	0.878987i	$0.341780\pi$
$977$			54.9490i			1.75797i	−0.476847	+	0.878987i	$0.658220\pi$
$978$		−	10.1258i		−	0.323788i
$979$	−20.1550	−	20.1550i	−0.644156	−	0.644156i
$980$	−2.36307	−	2.36307i	−0.0754856	−	0.0754856i
$981$	−11.4638	+	11.4638i	−0.366010	+	0.366010i
$982$	13.7906			0.440077
$983$	−8.91428	+	8.91428i	−0.284321	+	0.284321i	−0.834830	−	0.550508i	$-0.814434\pi$
$983$	−8.91428	+	8.91428i	−0.284321	+	0.284321i	0.550508	+	0.834830i	$0.314434\pi$
$984$			15.4816i			0.493534i
$985$	−47.8418			−1.52437
$986$	10.8207	+	67.8560i	0.344602	+	2.16098i
$987$	−0.699863			−0.0222769
$988$		−	24.1216i		−	0.767411i
$989$	9.28653	−	9.28653i	0.295294	−	0.295294i
$990$	15.6148			0.496272
$991$	6.73346	−	6.73346i	0.213895	−	0.213895i	−0.592024	−	0.805920i	$-0.701671\pi$
$991$	6.73346	−	6.73346i	0.213895	−	0.213895i	0.805920	+	0.592024i	$0.201671\pi$
$992$	4.04599	+	4.04599i	0.128460	+	0.128460i
$993$	−5.70156	−	5.70156i	−0.180933	−	0.180933i
$994$		−	22.1560i		−	0.702746i
$995$			14.8790i			0.471695i
$996$	5.40542	+	5.40542i	0.171277	+	0.171277i
$997$	39.9524	+	39.9524i	1.26531	+	1.26531i	0.948485	+	0.316821i	$0.102615\pi$
$997$	39.9524	+	39.9524i	1.26531	+	1.26531i	0.316821	+	0.948485i	$0.397385\pi$
$998$	−13.8739	+	13.8739i	−0.439172	+	0.439172i
$999$	−9.09331			−0.287700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.k.b.106.8	yes	20
3.2	odd	2		1071.2.n.b.820.3		20
17.8	even	8		6069.2.a.be.1.8		10
17.9	even	8		6069.2.a.bd.1.8		10
17.13	even	4	inner	357.2.k.b.64.3	✓	20
51.47	odd	4		1071.2.n.b.64.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.k.b.64.3	✓	20	17.13	even	4	inner
357.2.k.b.106.8	yes	20	1.1	even	1	trivial
1071.2.n.b.64.8		20	51.47	odd	4
1071.2.n.b.820.3		20	3.2	odd	2
6069.2.a.bd.1.8		10	17.9	even	8
6069.2.a.be.1.8		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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.71520i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.941909 q^{4} +(2.50881 - 2.50881i) q^{5} +(-1.21283 - 1.21283i) q^{6} +(-0.707107 - 0.707107i) q^{7} +1.81484i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.71520i q^{2} +(-0.707107 + 0.707107i) q^{3} -0.941909 q^{4} +(2.50881 - 2.50881i) q^{5} +(-1.21283 - 1.21283i) q^{6} +(-0.707107 - 0.707107i) q^{7} +1.81484i q^{8} -1.00000i q^{9} +(4.30311 + 4.30311i) q^{10} +(1.81437 + 1.81437i) q^{11} +(0.666030 - 0.666030i) q^{12} +3.70620 q^{13} +(1.21283 - 1.21283i) q^{14} +3.54799i q^{15} -4.99663 q^{16} +(3.33822 + 2.41998i) q^{17} +1.71520 q^{18} +6.90985i q^{19} +(-2.36307 + 2.36307i) q^{20} +1.00000 q^{21} +(-3.11200 + 3.11200i) q^{22} +(-5.39938 - 5.39938i) q^{23} +(-1.28328 - 1.28328i) q^{24} -7.58826i q^{25} +6.35687i q^{26} +(0.707107 + 0.707107i) q^{27} +(0.666030 + 0.666030i) q^{28} +(6.87048 - 6.87048i) q^{29} -6.08552 q^{30} +(-0.818937 + 0.818937i) q^{31} -4.94054i q^{32} -2.56590 q^{33} +(-4.15075 + 5.72571i) q^{34} -3.54799 q^{35} +0.941909i q^{36} +(-6.42994 + 6.42994i) q^{37} -11.8518 q^{38} +(-2.62068 + 2.62068i) q^{39} +(4.55308 + 4.55308i) q^{40} +(-6.03201 - 6.03201i) q^{41} +1.71520i q^{42} +1.71992i q^{43} +(-1.70897 - 1.70897i) q^{44} +(-2.50881 - 2.50881i) q^{45} +(9.26101 - 9.26101i) q^{46} -0.699863 q^{47} +(3.53315 - 3.53315i) q^{48} +1.00000i q^{49} +13.0154 q^{50} +(-4.07166 + 0.649291i) q^{51} -3.49090 q^{52} +3.38235i q^{53} +(-1.21283 + 1.21283i) q^{54} +9.10380 q^{55} +(1.28328 - 1.28328i) q^{56} +(-4.88600 - 4.88600i) q^{57} +(11.7842 + 11.7842i) q^{58} -10.9220i q^{59} -3.34189i q^{60} +(3.62531 + 3.62531i) q^{61} +(-1.40464 - 1.40464i) q^{62} +(-0.707107 + 0.707107i) q^{63} -1.51925 q^{64} +(9.29814 - 9.29814i) q^{65} -4.40103i q^{66} -2.86834 q^{67} +(-3.14430 - 2.27940i) q^{68} +7.63588 q^{69} -6.08552i q^{70} +(9.13401 - 9.13401i) q^{71} +1.81484 q^{72} +(1.00706 - 1.00706i) q^{73} +(-11.0286 - 11.0286i) q^{74} +(5.36571 + 5.36571i) q^{75} -6.50846i q^{76} -2.56590i q^{77} +(-4.49498 - 4.49498i) q^{78} +(-7.80162 - 7.80162i) q^{79} +(-12.5356 + 12.5356i) q^{80} -1.00000 q^{81} +(10.3461 - 10.3461i) q^{82} +8.11587i q^{83} -0.941909 q^{84} +(14.4462 - 2.30368i) q^{85} -2.95001 q^{86} +9.71633i q^{87} +(-3.29278 + 3.29278i) q^{88} -11.1085 q^{89} +(4.30311 - 4.30311i) q^{90} +(-2.62068 - 2.62068i) q^{91} +(5.08573 + 5.08573i) q^{92} -1.15815i q^{93} -1.20040i q^{94} +(17.3355 + 17.3355i) q^{95} +(3.49349 + 3.49349i) q^{96} +(1.25205 - 1.25205i) q^{97} -1.71520 q^{98} +(1.81437 - 1.81437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6}+O(q^{10}) \) 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6	\( 20 q - 24 q^{4} + 8 q^{5} - 4 q^{6} + 16 q^{10} + 4 q^{11} - 12 q^{13} + 4 q^{14} + 40 q^{16} + 4 q^{17} + 8 q^{18} - 52 q^{20} + 20 q^{21} - 24 q^{22} - 4 q^{23} + 4 q^{24} - 8 q^{29} + 8 q^{31} - 4 q^{33} - 44 q^{34} + 12 q^{35} + 24 q^{37} - 64 q^{38} - 12 q^{39} - 52 q^{40} - 20 q^{41} + 72 q^{44} - 8 q^{45} + 28 q^{46} - 32 q^{47} + 32 q^{48} + 104 q^{50} + 8 q^{51} + 48 q^{52} - 4 q^{54} - 36 q^{55} - 4 q^{56} - 16 q^{57} - 60 q^{58} + 28 q^{61} + 36 q^{62} - 112 q^{64} - 4 q^{65} + 40 q^{67} - 52 q^{68} + 36 q^{69} + 16 q^{71} - 24 q^{72} - 72 q^{73} - 24 q^{74} - 8 q^{75} + 40 q^{78} - 8 q^{79} + 120 q^{80} - 20 q^{81} + 108 q^{82} - 24 q^{84} + 40 q^{85} - 28 q^{88} - 64 q^{89} + 16 q^{90} - 12 q^{91} - 56 q^{92} + 60 q^{95} + 16 q^{96} + 60 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 24 * q^4 + 8 * q^5 - 4 * q^6 + 16 * q^10 + 4 * q^11 - 12 * q^13 + 4 * q^14 + 40 * q^16 + 4 * q^17 + 8 * q^18 - 52 * q^20 + 20 * q^21 - 24 * q^22 - 4 * q^23 + 4 * q^24 - 8 * q^29 + 8 * q^31 - 4 * q^33 - 44 * q^34 + 12 * q^35 + 24 * q^37 - 64 * q^38 - 12 * q^39 - 52 * q^40 - 20 * q^41 + 72 * q^44 - 8 * q^45 + 28 * q^46 - 32 * q^47 + 32 * q^48 + 104 * q^50 + 8 * q^51 + 48 * q^52 - 4 * q^54 - 36 * q^55 - 4 * q^56 - 16 * q^57 - 60 * q^58 + 28 * q^61 + 36 * q^62 - 112 * q^64 - 4 * q^65 + 40 * q^67 - 52 * q^68 + 36 * q^69 + 16 * q^71 - 24 * q^72 - 72 * q^73 - 24 * q^74 - 8 * q^75 + 40 * q^78 - 8 * q^79 + 120 * q^80 - 20 * q^81 + 108 * q^82 - 24 * q^84 + 40 * q^85 - 28 * q^88 - 64 * q^89 + 16 * q^90 - 12 * q^91 - 56 * q^92 + 60 * q^95 + 16 * q^96 + 60 * q^97 - 8 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more