LMFDB - Embedded newform 731.2.f.d.259.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.14
Character	$\chi$	$=$	731.259
Dual form			731.2.f.d.302.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.436020i q^{2} +(0.705146 - 0.705146i) q^{3} +1.80989 q^{4} +(2.58895 - 2.58895i) q^{5} +(-0.307458 - 0.307458i) q^{6} +(0.364609 + 0.364609i) q^{7} -1.66119i q^{8} +2.00554i q^{9} +O(q^{10})$	\(q-0.436020i q^{2} +(0.705146 - 0.705146i) q^{3} +1.80989 q^{4} +(2.58895 - 2.58895i) q^{5} +(-0.307458 - 0.307458i) q^{6} +(0.364609 + 0.364609i) q^{7} -1.66119i q^{8} +2.00554i q^{9} +(-1.12884 - 1.12884i) q^{10} +(-1.51050 - 1.51050i) q^{11} +(1.27623 - 1.27623i) q^{12} -1.21191 q^{13} +(0.158977 - 0.158977i) q^{14} -3.65118i q^{15} +2.89546 q^{16} +(1.47966 - 3.84846i) q^{17} +0.874456 q^{18} +7.23228i q^{19} +(4.68571 - 4.68571i) q^{20} +0.514206 q^{21} +(-0.658610 + 0.658610i) q^{22} +(-2.14222 - 2.14222i) q^{23} +(-1.17138 - 1.17138i) q^{24} -8.40534i q^{25} +0.528419i q^{26} +(3.52964 + 3.52964i) q^{27} +(0.659901 + 0.659901i) q^{28} +(-5.43704 + 5.43704i) q^{29} -1.59199 q^{30} +(-4.92858 + 4.92858i) q^{31} -4.58486i q^{32} -2.13025 q^{33} +(-1.67801 - 0.645160i) q^{34} +1.88791 q^{35} +3.62980i q^{36} +(-6.57299 + 6.57299i) q^{37} +3.15342 q^{38} +(-0.854575 + 0.854575i) q^{39} +(-4.30074 - 4.30074i) q^{40} +(7.89609 + 7.89609i) q^{41} -0.224204i q^{42} -1.00000i q^{43} +(-2.73384 - 2.73384i) q^{44} +(5.19224 + 5.19224i) q^{45} +(-0.934054 + 0.934054i) q^{46} -1.87907 q^{47} +(2.04172 - 2.04172i) q^{48} -6.73412i q^{49} -3.66490 q^{50} +(-1.67035 - 3.75710i) q^{51} -2.19342 q^{52} -6.79743i q^{53} +(1.53899 - 1.53899i) q^{54} -7.82123 q^{55} +(0.605685 - 0.605685i) q^{56} +(5.09981 + 5.09981i) q^{57} +(2.37066 + 2.37066i) q^{58} -9.59899i q^{59} -6.60822i q^{60} +(1.09141 + 1.09141i) q^{61} +(2.14896 + 2.14896i) q^{62} +(-0.731238 + 0.731238i) q^{63} +3.79183 q^{64} +(-3.13758 + 3.13758i) q^{65} +0.928832i q^{66} -5.05143 q^{67} +(2.67801 - 6.96527i) q^{68} -3.02116 q^{69} -0.823168i q^{70} +(-3.18616 + 3.18616i) q^{71} +3.33158 q^{72} +(11.6167 - 11.6167i) q^{73} +(2.86596 + 2.86596i) q^{74} +(-5.92699 - 5.92699i) q^{75} +13.0896i q^{76} -1.10149i q^{77} +(0.372612 + 0.372612i) q^{78} +(9.45865 + 9.45865i) q^{79} +(7.49621 - 7.49621i) q^{80} -1.03880 q^{81} +(3.44286 - 3.44286i) q^{82} -0.743322i q^{83} +0.930653 q^{84} +(-6.13271 - 13.7942i) q^{85} -0.436020 q^{86} +7.66781i q^{87} +(-2.50923 + 2.50923i) q^{88} -7.15638 q^{89} +(2.26392 - 2.26392i) q^{90} +(-0.441875 - 0.441875i) q^{91} +(-3.87718 - 3.87718i) q^{92} +6.95074i q^{93} +0.819314i q^{94} +(18.7240 + 18.7240i) q^{95} +(-3.23299 - 3.23299i) q^{96} +(3.65175 - 3.65175i) q^{97} -2.93621 q^{98} +(3.02937 - 3.02937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	$ 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) $ 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		−	0.436020i		−	0.308313i	−0.988046	−	0.154157i	$-0.950734\pi$
$2$		−	0.436020i		−	0.308313i	0.988046	−	0.154157i	$-0.0492660\pi$
$3$	0.705146	−	0.705146i	0.407116	−	0.407116i	−0.473615	−	0.880732i	$-0.657051\pi$
$3$	0.705146	−	0.705146i	0.407116	−	0.407116i	0.880732	+	0.473615i	$0.157051\pi$
$4$	1.80989			0.904943
$5$	2.58895	−	2.58895i	1.15781	−	1.15781i	0.172870	−	0.984945i	$-0.444696\pi$
$5$	2.58895	−	2.58895i	1.15781	−	1.15781i	0.984945	−	0.172870i	$-0.0553039\pi$
$6$	−0.307458	−	0.307458i	−0.125519	−	0.125519i
$7$	0.364609	+	0.364609i	0.137809	+	0.137809i	0.772646	−	0.634837i	$-0.218933\pi$
$7$	0.364609	+	0.364609i	0.137809	+	0.137809i	−0.634837	+	0.772646i	$0.718933\pi$
$8$		−	1.66119i		−	0.587319i
$9$			2.00554i			0.668513i
$10$	−1.12884	−	1.12884i	−0.356969	−	0.356969i
$11$	−1.51050	−	1.51050i	−0.455434	−	0.455434i	0.441720	−	0.897153i	$-0.354369\pi$
$11$	−1.51050	−	1.51050i	−0.455434	−	0.455434i	−0.897153	+	0.441720i	$0.854369\pi$
$12$	1.27623	−	1.27623i	0.368417	−	0.368417i
$13$	−1.21191			−0.336124			−0.168062	−	0.985776i	$-0.553751\pi$
$13$	−1.21191			−0.336124			−0.168062	+	0.985776i	$0.553751\pi$
$14$	0.158977	−	0.158977i	0.0424884	−	0.0424884i
$15$		−	3.65118i		−	0.942730i
$16$	2.89546			0.723865
$17$	1.47966	−	3.84846i	0.358869	−	0.933388i
$17$	1.47966	−	3.84846i	0.358869	−	0.933388i
$18$	0.874456			0.206111
$19$			7.23228i			1.65920i	0.558360	+	0.829599i	$0.311431\pi$
$19$			7.23228i			1.65920i	−0.558360	+	0.829599i	$0.688569\pi$
$20$	4.68571	−	4.68571i	1.04776	−	1.04776i
$21$	0.514206			0.112209
$22$	−0.658610	+	0.658610i	−0.140416	+	0.140416i
$23$	−2.14222	−	2.14222i	−0.446685	−	0.446685i	0.447566	−	0.894251i	$-0.352291\pi$
$23$	−2.14222	−	2.14222i	−0.446685	−	0.446685i	−0.894251	+	0.447566i	$0.852291\pi$
$24$	−1.17138	−	1.17138i	−0.239107	−	0.239107i
$25$		−	8.40534i		−	1.68107i
$26$			0.528419i			0.103631i
$27$	3.52964	+	3.52964i	0.679279	+	0.679279i
$28$	0.659901	+	0.659901i	0.124710	+	0.124710i
$29$	−5.43704	+	5.43704i	−1.00963	+	1.00963i	−0.00967913	+	0.999953i	$0.503081\pi$
$29$	−5.43704	+	5.43704i	−1.00963	+	1.00963i	−0.999953	+	0.00967913i	$0.996919\pi$
$30$	−1.59199			−0.290656
$31$	−4.92858	+	4.92858i	−0.885200	+	0.885200i	−0.994057	−	0.108858i	$-0.965281\pi$
$31$	−4.92858	+	4.92858i	−0.885200	+	0.885200i	0.108858	+	0.994057i	$0.465281\pi$
$32$		−	4.58486i		−	0.810496i
$33$	−2.13025			−0.370829
$34$	−1.67801	−	0.645160i	−0.287776	−	0.110644i
$35$	1.88791			0.319115
$36$			3.62980i			0.604966i
$37$	−6.57299	+	6.57299i	−1.08059	+	1.08059i	−0.0841392	+	0.996454i	$0.526814\pi$
$37$	−6.57299	+	6.57299i	−1.08059	+	1.08059i	−0.996454	+	0.0841392i	$0.973186\pi$
$38$	3.15342			0.511552
$39$	−0.854575	+	0.854575i	−0.136842	+	0.136842i
$40$	−4.30074	−	4.30074i	−0.680006	−	0.680006i
$41$	7.89609	+	7.89609i	1.23316	+	1.23316i	0.962743	+	0.270419i	$0.0871624\pi$
$41$	7.89609	+	7.89609i	1.23316	+	1.23316i	0.270419	+	0.962743i	$0.412838\pi$
$42$		−	0.224204i		−	0.0345954i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	−2.73384	−	2.73384i	−0.412141	−	0.412141i
$45$	5.19224	+	5.19224i	0.774014	+	0.774014i
$46$	−0.934054	+	0.934054i	−0.137719	+	0.137719i
$47$	−1.87907			−0.274091			−0.137045	−	0.990565i	$-0.543761\pi$
$47$	−1.87907			−0.274091			−0.137045	+	0.990565i	$0.543761\pi$
$48$	2.04172	−	2.04172i	0.294697	−	0.294697i
$49$		−	6.73412i		−	0.962017i
$50$	−3.66490			−0.518295
$51$	−1.67035	−	3.75710i	−0.233896	−	0.526099i
$52$	−2.19342			−0.304173
$53$		−	6.79743i		−	0.933699i	−0.884337	−	0.466850i	$-0.845389\pi$
$53$		−	6.79743i		−	0.933699i	0.884337	−	0.466850i	$-0.154611\pi$
$54$	1.53899	−	1.53899i	0.209430	−	0.209430i
$55$	−7.82123			−1.05461
$56$	0.605685	−	0.605685i	0.0809380	−	0.0809380i
$57$	5.09981	+	5.09981i	0.675486	+	0.675486i
$58$	2.37066	+	2.37066i	0.311283	+	0.311283i
$59$		−	9.59899i		−	1.24968i	−0.780752	−	0.624841i	$-0.785164\pi$
$59$		−	9.59899i		−	1.24968i	0.780752	−	0.624841i	$-0.214836\pi$
$60$		−	6.60822i		−	0.853117i
$61$	1.09141	+	1.09141i	0.139741	+	0.139741i	0.773517	−	0.633776i	$-0.218496\pi$
$61$	1.09141	+	1.09141i	0.139741	+	0.139741i	−0.633776	+	0.773517i	$0.718496\pi$
$62$	2.14896	+	2.14896i	0.272919	+	0.272919i
$63$	−0.731238	+	0.731238i	−0.0921273	+	0.0921273i
$64$	3.79183			0.473979
$65$	−3.13758	+	3.13758i	−0.389169	+	0.389169i
$66$			0.928832i			0.114331i
$67$	−5.05143			−0.617131			−0.308565	−	0.951203i	$-0.599849\pi$
$67$	−5.05143			−0.617131			−0.308565	+	0.951203i	$0.599849\pi$
$68$	2.67801	−	6.96527i	0.324756	−	0.844663i
$69$	−3.02116			−0.363705
$70$		−	0.823168i		−	0.0983874i
$71$	−3.18616	+	3.18616i	−0.378128	+	0.378128i	−0.870426	−	0.492299i	$-0.836157\pi$
$71$	−3.18616	+	3.18616i	−0.378128	+	0.378128i	0.492299	+	0.870426i	$0.336157\pi$
$72$	3.33158			0.392630
$73$	11.6167	−	11.6167i	1.35963	−	1.35963i	0.485269	−	0.874365i	$-0.338722\pi$
$73$	11.6167	−	11.6167i	1.35963	−	1.35963i	0.874365	−	0.485269i	$-0.161278\pi$
$74$	2.86596	+	2.86596i	0.333161	+	0.333161i
$75$	−5.92699	−	5.92699i	−0.684390	−	0.684390i
$76$			13.0896i			1.50148i
$77$		−	1.10149i		−	0.125526i
$78$	0.372612	+	0.372612i	0.0421900	+	0.0421900i
$79$	9.45865	+	9.45865i	1.06418	+	1.06418i	0.997794	+	0.0663875i	$0.0211473\pi$
$79$	9.45865	+	9.45865i	1.06418	+	1.06418i	0.0663875	+	0.997794i	$0.478853\pi$
$80$	7.49621	−	7.49621i	0.838101	−	0.838101i
$81$	−1.03880			−0.115422
$82$	3.44286	−	3.44286i	0.380200	−	0.380200i
$83$		−	0.743322i		−	0.0815902i	−0.999168	−	0.0407951i	$-0.987011\pi$
$83$		−	0.743322i		−	0.0815902i	0.999168	−	0.0407951i	$-0.0129891\pi$
$84$	0.930653			0.101543
$85$	−6.13271	−	13.7942i	−0.665186	−	1.49619i
$86$	−0.436020			−0.0470173
$87$			7.66781i			0.822075i
$88$	−2.50923	+	2.50923i	−0.267485	+	0.267485i
$89$	−7.15638			−0.758575			−0.379288	−	0.925279i	$-0.623831\pi$
$89$	−7.15638			−0.758575			−0.379288	+	0.925279i	$0.623831\pi$
$90$	2.26392	−	2.26392i	0.238638	−	0.238638i
$91$	−0.441875	−	0.441875i	−0.0463210	−	0.0463210i
$92$	−3.87718	−	3.87718i	−0.404224	−	0.404224i
$93$			6.95074i			0.720758i
$94$			0.819314i			0.0845058i
$95$	18.7240	+	18.7240i	1.92104	+	1.92104i
$96$	−3.23299	−	3.23299i	−0.329966	−	0.329966i
$97$	3.65175	−	3.65175i	0.370779	−	0.370779i	−0.496982	−	0.867761i	$-0.665558\pi$
$97$	3.65175	−	3.65175i	0.370779	−	0.370779i	0.867761	+	0.496982i	$0.165558\pi$
$98$	−2.93621			−0.296602
$99$	3.02937	−	3.02937i	0.304463	−	0.304463i
$100$		−	15.2127i		−	1.52127i
$101$	0.342167			0.0340469			0.0170235	−	0.999855i	$-0.494581\pi$
$101$	0.342167			0.0340469			0.0170235	+	0.999855i	$0.494581\pi$
$102$	−1.63817	+	0.728307i	−0.162203	+	0.0721131i
$103$	3.48483			0.343371			0.171685	−	0.985152i	$-0.445079\pi$
$103$	3.48483			0.343371			0.171685	+	0.985152i	$0.445079\pi$
$104$			2.01322i			0.197412i
$105$	1.33125	−	1.33125i	0.129917	−	0.129917i
$106$	−2.96382			−0.287872
$107$	−12.6181	+	12.6181i	−1.21983	+	1.21983i	−0.252145	+	0.967689i	$0.581136\pi$
$107$	−12.6181	+	12.6181i	−1.21983	+	1.21983i	−0.967689	+	0.252145i	$0.918864\pi$
$108$	6.38824	+	6.38824i	0.614709	+	0.614709i
$109$	−7.49093	−	7.49093i	−0.717501	−	0.717501i	0.250592	−	0.968093i	$-0.419375\pi$
$109$	−7.49093	−	7.49093i	−0.717501	−	0.717501i	−0.968093	+	0.250592i	$0.919375\pi$
$110$			3.41022i			0.325151i
$111$			9.26984i			0.879854i
$112$	1.05571	+	1.05571i	0.0997554	+	0.0997554i
$113$	0.573374	+	0.573374i	0.0539385	+	0.0539385i	0.733562	−	0.679623i	$-0.237857\pi$
$113$	0.573374	+	0.573374i	0.0539385	+	0.0539385i	−0.679623	+	0.733562i	$0.737857\pi$
$114$	2.22362	−	2.22362i	0.208261	−	0.208261i
$115$	−11.0922			−1.03436
$116$	−9.84042	+	9.84042i	−0.913660	+	0.913660i
$117$		−	2.43054i		−	0.224703i
$118$	−4.18536			−0.385293
$119$	1.94268	−	0.863686i	0.178085	−	0.0791740i
$120$	−6.06529			−0.553683
$121$		−	6.43677i		−	0.585161i
$122$	0.475878	−	0.475878i	0.0430840	−	0.0430840i
$123$	11.1358			1.00408
$124$	−8.92018	+	8.92018i	−0.801055	+	0.801055i
$125$	−8.81626	−	8.81626i	−0.788550	−	0.788550i
$126$	0.318835	+	0.318835i	0.0284040	+	0.0284040i
$127$			5.27795i			0.468342i	0.972195	+	0.234171i	$0.0752376\pi$
$127$			5.27795i			0.468342i	−0.972195	+	0.234171i	$0.924762\pi$
$128$		−	10.8230i		−	0.956630i
$129$	−0.705146	−	0.705146i	−0.0620846	−	0.0620846i
$130$	1.36805	+	1.36805i	0.119986	+	0.119986i
$131$	14.6179	−	14.6179i	1.27717	−	1.27717i	0.334929	−	0.942243i	$-0.391288\pi$
$131$	14.6179	−	14.6179i	1.27717	−	1.27717i	0.942243	−	0.334929i	$-0.108712\pi$
$132$	−3.85551			−0.335579
$133$	−2.63695	+	2.63695i	−0.228653	+	0.228653i
$134$			2.20253i			0.190269i
$135$	18.2761			1.57296
$136$	−6.39301	−	2.45799i	−0.548196	−	0.210771i
$137$	−12.0520			−1.02967			−0.514834	−	0.857290i	$-0.672146\pi$
$137$	−12.0520			−1.02967			−0.514834	+	0.857290i	$0.672146\pi$
$138$			1.31729i			0.112135i
$139$	−14.3175	+	14.3175i	−1.21440	+	1.21440i	−0.244830	+	0.969566i	$0.578732\pi$
$139$	−14.3175	+	14.3175i	−1.21440	+	1.21440i	−0.969566	+	0.244830i	$0.921268\pi$
$140$	3.41690			0.288781
$141$	−1.32502	+	1.32502i	−0.111587	+	0.111587i
$142$	1.38923	+	1.38923i	0.116582	+	0.116582i
$143$	1.83060	+	1.83060i	0.153082	+	0.153082i
$144$			5.80696i			0.483913i
$145$			28.1524i			2.33793i
$146$	−5.06513	−	5.06513i	−0.419193	−	0.419193i
$147$	−4.74854	−	4.74854i	−0.391653	−	0.391653i
$148$	−11.8964	+	11.8964i	−0.977875	+	0.977875i
$149$	22.9400			1.87932			0.939661	−	0.342107i	$-0.111141\pi$
$149$	22.9400			1.87932			0.939661	+	0.342107i	$0.111141\pi$
$150$	−2.58429	+	2.58429i	−0.211006	+	0.211006i
$151$		−	2.34156i		−	0.190553i	−0.995451	−	0.0952767i	$-0.969626\pi$
$151$		−	2.34156i		−	0.190553i	0.995451	−	0.0952767i	$-0.0303736\pi$
$152$	12.0142			0.974478
$153$	7.71823	+	2.96751i	0.623982	+	0.239909i
$154$	−0.480270			−0.0387013
$155$			25.5197i			2.04979i
$156$	−1.54668	+	1.54668i	−0.123834	+	0.123834i
$157$	12.1719			0.971424			0.485712	−	0.874119i	$-0.338560\pi$
$157$	12.1719			0.971424			0.485712	+	0.874119i	$0.338560\pi$
$158$	4.12417	−	4.12417i	0.328101	−	0.328101i
$159$	−4.79318	−	4.79318i	−0.380124	−	0.380124i
$160$	−11.8700	−	11.8700i	−0.938404	−	0.938404i
$161$		−	1.56215i		−	0.123115i
$162$			0.452937i			0.0355861i
$163$	8.21642	+	8.21642i	0.643560	+	0.643560i	0.951429	−	0.307869i	$-0.0996159\pi$
$163$	8.21642	+	8.21642i	0.643560	+	0.643560i	−0.307869	+	0.951429i	$0.599616\pi$
$164$	14.2910	+	14.2910i	1.11594	+	1.11594i
$165$	−5.51511	+	5.51511i	−0.429351	+	0.429351i
$166$	−0.324104			−0.0251553
$167$	−2.39977	+	2.39977i	−0.185700	+	0.185700i	−0.793834	−	0.608134i	$-0.791918\pi$
$167$	−2.39977	+	2.39977i	−0.185700	+	0.185700i	0.608134	+	0.793834i	$0.291918\pi$
$168$		−	0.854192i		−	0.0659024i
$169$	−11.5313			−0.887021
$170$	−6.01456	+	2.67399i	−0.461296	+	0.205085i
$171$	−14.5046			−1.10919
$172$		−	1.80989i		−	0.138003i
$173$	−3.33750	+	3.33750i	−0.253745	+	0.253745i	−0.822504	−	0.568759i	$-0.807424\pi$
$173$	−3.33750	+	3.33750i	−0.253745	+	0.253745i	0.568759	+	0.822504i	$0.307424\pi$
$174$	3.34332			0.253457
$175$	3.06466	−	3.06466i	0.231667	−	0.231667i
$176$	−4.37360	−	4.37360i	−0.329672	−	0.329672i
$177$	−6.76869	−	6.76869i	−0.508766	−	0.508766i
$178$			3.12033i			0.233879i
$179$		−	14.3954i		−	1.07596i	−0.842957	−	0.537980i	$-0.819187\pi$
$179$		−	14.3954i		−	1.07596i	0.842957	−	0.537980i	$-0.180813\pi$
$180$	9.39737	+	9.39737i	0.700438	+	0.700438i
$181$	−5.85117	−	5.85117i	−0.434914	−	0.434914i	0.455382	−	0.890296i	$-0.349503\pi$
$181$	−5.85117	−	5.85117i	−0.434914	−	0.434914i	−0.890296	+	0.455382i	$0.849503\pi$
$182$	−0.192666	+	0.192666i	−0.0142814	+	0.0142814i
$183$	1.53921			0.113782
$184$	−3.55864	+	3.55864i	−0.262346	+	0.262346i
$185$			34.0343i			2.50225i
$186$	3.03067			0.222219
$187$	−8.04813	+	3.57808i	−0.588537	+	0.261655i
$188$	−3.40091			−0.248037
$189$			2.57388i			0.187222i
$190$	8.16405	−	8.16405i	0.592283	−	0.592283i
$191$	3.58731			0.259568			0.129784	−	0.991542i	$-0.458572\pi$
$191$	3.58731			0.259568			0.129784	+	0.991542i	$0.458572\pi$
$192$	2.67379	−	2.67379i	0.192964	−	0.192964i
$193$	−9.08814	−	9.08814i	−0.654179	−	0.654179i	0.299818	−	0.953996i	$-0.403074\pi$
$193$	−9.08814	−	9.08814i	−0.654179	−	0.654179i	−0.953996	+	0.299818i	$0.903074\pi$
$194$	−1.59224	−	1.59224i	−0.114316	−	0.114316i
$195$			4.42491i			0.316874i
$196$		−	12.1880i		−	0.870571i
$197$	16.3367	+	16.3367i	1.16394	+	1.16394i	0.983604	+	0.180340i	$0.0577198\pi$
$197$	16.3367	+	16.3367i	1.16394	+	1.16394i	0.180340	+	0.983604i	$0.442280\pi$
$198$	−1.32087	−	1.32087i	−0.0938699	−	0.0938699i
$199$	−16.2765	+	16.2765i	−1.15381	+	1.15381i	−0.168027	+	0.985782i	$0.553740\pi$
$199$	−16.2765	+	16.2765i	−1.15381	+	1.15381i	−0.985782	+	0.168027i	$0.946260\pi$
$200$	−13.9629			−0.987323
$201$	−3.56200	+	3.56200i	−0.251244	+	0.251244i
$202$		−	0.149192i		−	0.0104971i
$203$	−3.96479			−0.278274
$204$	−3.02314	−	6.79992i	−0.211662	−	0.476090i
$205$	40.8852			2.85555
$206$		−	1.51946i		−	0.105866i
$207$	4.29631	−	4.29631i	0.298614	−	0.298614i
$208$	−3.50905			−0.243309
$209$	10.9244	−	10.9244i	0.755654	−	0.755654i
$210$	−0.580454	−	0.580454i	−0.0400551	−	0.0400551i
$211$	1.07357	+	1.07357i	0.0739076	+	0.0739076i	0.743094	−	0.669187i	$-0.233357\pi$
$211$	1.07357	+	1.07357i	0.0739076	+	0.0739076i	−0.669187	+	0.743094i	$0.733357\pi$
$212$		−	12.3026i		−	0.844945i
$213$			4.49342i			0.307884i
$214$	5.50174	+	5.50174i	0.376091	+	0.376091i
$215$	−2.58895	−	2.58895i	−0.176565	−	0.176565i
$216$	5.86339	−	5.86339i	0.398953	−	0.398953i
$217$	−3.59401			−0.243978
$218$	−3.26620	+	3.26620i	−0.221215	+	0.221215i
$219$		−	16.3830i		−	1.10706i
$220$	−14.1555			−0.954366
$221$	−1.79321	+	4.66399i	−0.120625	+	0.313734i
$222$	4.04184			0.271270
$223$		−	6.94366i		−	0.464982i	−0.972599	−	0.232491i	$-0.925312\pi$
$223$		−	6.94366i		−	0.464982i	0.972599	−	0.232491i	$-0.0746876\pi$
$224$	1.67168	−	1.67168i	0.111694	−	0.111694i
$225$	16.8572			1.12382
$226$	0.250003	−	0.250003i	0.0166299	−	0.0166299i
$227$	15.5752	+	15.5752i	1.03376	+	1.03376i	0.999410	+	0.0343516i	$0.0109366\pi$
$227$	15.5752	+	15.5752i	1.03376	+	1.03376i	0.0343516	+	0.999410i	$0.489063\pi$
$228$	9.23008	+	9.23008i	0.611277	+	0.611277i
$229$			21.0944i			1.39396i	0.717090	+	0.696980i	$0.245473\pi$
$229$			21.0944i			1.39396i	−0.717090	+	0.696980i	$0.754527\pi$
$230$			4.83644i			0.318905i
$231$	−0.776708	−	0.776708i	−0.0511037	−	0.0511037i
$232$	9.03194	+	9.03194i	0.592976	+	0.592976i
$233$	−5.58170	+	5.58170i	−0.365669	+	0.365669i	−0.865895	−	0.500226i	$-0.833250\pi$
$233$	−5.58170	+	5.58170i	−0.365669	+	0.365669i	0.500226	+	0.865895i	$0.333250\pi$
$234$	−1.05976			−0.0692789
$235$	−4.86483	+	4.86483i	−0.317346	+	0.317346i
$236$		−	17.3731i		−	1.13089i
$237$	13.3395			0.866491
$238$	−0.376585	−	0.847048i	−0.0244104	−	0.0549060i
$239$	13.4730			0.871493			0.435746	−	0.900069i	$-0.356484\pi$
$239$	13.4730			0.871493			0.435746	+	0.900069i	$0.356484\pi$
$240$		−	10.5718i		−	0.682409i
$241$	6.64921	−	6.64921i	0.428313	−	0.428313i	−0.459740	−	0.888053i	$-0.652057\pi$
$241$	6.64921	−	6.64921i	0.428313	−	0.428313i	0.888053	+	0.459740i	$0.152057\pi$
$242$	−2.80656			−0.180413
$243$	−11.3214	+	11.3214i	−0.726269	+	0.726269i
$244$	1.97533	+	1.97533i	0.126458	+	0.126458i
$245$	−17.4343	−	17.4343i	−1.11384	−	1.11384i
$246$		−	4.85543i		−	0.309571i
$247$		−	8.76489i		−	0.557696i
$248$	8.18731	+	8.18731i	0.519894	+	0.519894i
$249$	−0.524151	−	0.524151i	−0.0332167	−	0.0332167i
$250$	−3.84407	+	3.84407i	−0.243120	+	0.243120i
$251$	3.80637			0.240256			0.120128	−	0.992758i	$-0.461670\pi$
$251$	3.80637			0.240256			0.120128	+	0.992758i	$0.461670\pi$
$252$	−1.32346	+	1.32346i	−0.0833700	+	0.0833700i
$253$			6.47167i			0.406870i
$254$	2.30129			0.144396
$255$	−14.0514	−	5.40249i	−0.879933	−	0.338317i
$256$	2.86460			0.179037
$257$			6.61480i			0.412620i	0.978487	+	0.206310i	$0.0661455\pi$
$257$			6.61480i			0.412620i	−0.978487	+	0.206310i	$0.933854\pi$
$258$	−0.307458	+	0.307458i	−0.0191415	+	0.0191415i
$259$	−4.79315			−0.297832
$260$	−5.67867	+	5.67867i	−0.352176	+	0.352176i
$261$	−10.9042	−	10.9042i	−0.674952	−	0.674952i
$262$	−6.37370	−	6.37370i	−0.393769	−	0.393769i
$263$		−	21.6266i		−	1.33356i	−0.745256	−	0.666778i	$-0.767673\pi$
$263$		−	21.6266i		−	1.33356i	0.745256	−	0.666778i	$-0.232327\pi$
$264$			3.53874i			0.217795i
$265$	−17.5982	−	17.5982i	−1.08105	−	1.08105i
$266$	1.14977	+	1.14977i	0.0704967	+	0.0704967i
$267$	−5.04630	+	5.04630i	−0.308828	+	0.308828i
$268$	−9.14252			−0.558468
$269$	2.30899	−	2.30899i	0.140782	−	0.140782i	−0.633204	−	0.773985i	$-0.718260\pi$
$269$	2.30899	−	2.30899i	0.140782	−	0.140782i	0.773985	+	0.633204i	$0.218260\pi$
$270$		−	7.96876i		−	0.484963i
$271$	−12.3667			−0.751225			−0.375612	−	0.926777i	$-0.622568\pi$
$271$	−12.3667			−0.751225			−0.375612	+	0.926777i	$0.622568\pi$
$272$	4.28429	−	11.1431i	0.259773	−	0.675647i
$273$	−0.623172			−0.0377161
$274$			5.25490i			0.317460i
$275$	−12.6963	+	12.6963i	−0.765615	+	0.765615i
$276$	−5.46796			−0.329132
$277$	19.3891	−	19.3891i	1.16498	−	1.16498i	0.181609	−	0.983371i	$-0.441870\pi$
$277$	19.3891	−	19.3891i	1.16498	−	1.16498i	0.983371	−	0.181609i	$-0.0581305\pi$
$278$	6.24273	+	6.24273i	0.374414	+	0.374414i
$279$	−9.88446	−	9.88446i	−0.591767	−	0.591767i
$280$		−	3.13618i		−	0.187422i
$281$		−	6.09852i		−	0.363807i	−0.983316	−	0.181904i	$-0.941774\pi$
$281$		−	6.09852i		−	0.363807i	0.983316	−	0.181904i	$-0.0582259\pi$
$282$	0.577736	+	0.577736i	0.0344037	+	0.0344037i
$283$	11.3647	+	11.3647i	0.675564	+	0.675564i	0.958993	−	0.283430i	$-0.0914722\pi$
$283$	11.3647	+	11.3647i	0.675564	+	0.675564i	−0.283430	+	0.958993i	$0.591472\pi$
$284$	−5.76659	+	5.76659i	−0.342184	+	0.342184i
$285$	26.4063			1.56418
$286$	0.798178	−	0.798178i	0.0471972	−	0.0471972i
$287$			5.75797i			0.339882i
$288$	9.19510			0.541827
$289$	−12.6212	−	11.3888i	−0.742426	−	0.669929i
$290$	12.2750			0.720815
$291$		−	5.15004i		−	0.301901i
$292$	21.0249	−	21.0249i	1.23039	−	1.23039i
$293$	−31.2415			−1.82515			−0.912574	−	0.408912i	$-0.865908\pi$
$293$	−31.2415			−1.82515			−0.912574	+	0.408912i	$0.865908\pi$
$294$	−2.07046	+	2.07046i	−0.120752	+	0.120752i
$295$	−24.8513	−	24.8513i	−1.44690	−	1.44690i
$296$	10.9190	+	10.9190i	0.634653	+	0.634653i
$297$		−	10.6630i		−	0.618733i
$298$		−	10.0023i		−	0.579419i
$299$	2.59619	+	2.59619i	0.150141	+	0.150141i
$300$	−10.7272	−	10.7272i	−0.619334	−	0.619334i
$301$	0.364609	−	0.364609i	0.0210157	−	0.0210157i
$302$	−1.02097			−0.0587501
$303$	0.241278	−	0.241278i	0.0138610	−	0.0138610i
$304$			20.9408i			1.20104i
$305$	5.65123			0.323588
$306$	1.29389	−	3.36530i	0.0739670	−	0.192382i
$307$	−16.9327			−0.966398			−0.483199	−	0.875510i	$-0.660525\pi$
$307$	−16.9327			−0.966398			−0.483199	+	0.875510i	$0.660525\pi$
$308$		−	1.99356i		−	0.113594i
$309$	2.45732	−	2.45732i	0.139792	−	0.139792i
$310$	11.1271			0.631978
$311$	−16.5180	+	16.5180i	−0.936649	+	0.936649i	−0.998109	−	0.0614608i	$-0.980424\pi$
$311$	−16.5180	+	16.5180i	−0.936649	+	0.936649i	0.0614608	+	0.998109i	$0.480424\pi$
$312$	1.41961	+	1.41961i	0.0803696	+	0.0803696i
$313$	−16.9061	−	16.9061i	−0.955590	−	0.955590i	0.0434649	−	0.999055i	$-0.486160\pi$
$313$	−16.9061	−	16.9061i	−0.955590	−	0.955590i	−0.999055	+	0.0434649i	$0.986160\pi$
$314$		−	5.30720i		−	0.299503i
$315$			3.78628i			0.213333i
$316$	17.1191	+	17.1191i	0.963024	+	0.963024i
$317$	19.1933	+	19.1933i	1.07801	+	1.07801i	0.996688	+	0.0813174i	$0.0259128\pi$
$317$	19.1933	+	19.1933i	1.07801	+	1.07801i	0.0813174	+	0.996688i	$0.474087\pi$
$318$	−2.08993	+	2.08993i	−0.117197	+	0.117197i
$319$	16.4253			0.919641
$320$	9.81686	−	9.81686i	0.548779	−	0.548779i
$321$			17.7952i			0.993229i
$322$	−0.681129			−0.0379578
$323$	27.8331	+	10.7013i	1.54867	+	0.595435i
$324$	−1.88010			−0.104450
$325$			10.1865i			0.565047i
$326$	3.58253	−	3.58253i	0.198418	−	0.198418i
$327$	−10.5644			−0.584213
$328$	13.1169	−	13.1169i	0.724259	−	0.724259i
$329$	−0.685127	−	0.685127i	−0.0377723	−	0.0377723i
$330$	2.40470	+	2.40470i	0.132374	+	0.132374i
$331$			2.06433i			0.113466i	0.998389	+	0.0567329i	$0.0180683\pi$
$331$			2.06433i			0.113466i	−0.998389	+	0.0567329i	$0.981932\pi$
$332$		−	1.34533i		−	0.0738345i
$333$	−13.1824	−	13.1824i	−0.722390	−	0.722390i
$334$	1.04635	+	1.04635i	0.0572536	+	0.0572536i
$335$	−13.0779	+	13.0779i	−0.714523	+	0.714523i
$336$	1.48886			0.0812241
$337$	8.25854	−	8.25854i	0.449871	−	0.449871i	−0.445440	−	0.895312i	$-0.646953\pi$
$337$	8.25854	−	8.25854i	0.449871	−	0.449871i	0.895312	+	0.445440i	$0.146953\pi$
$338$			5.02787i			0.273480i
$339$	0.808625			0.0439185
$340$	−11.0995	−	24.9660i	−0.601955	−	1.35397i
$341$	14.8893			0.806299
$342$			6.32430i			0.341979i
$343$	5.00759	−	5.00759i	0.270384	−	0.270384i
$344$	−1.66119			−0.0895653
$345$	−7.82164	+	7.82164i	−0.421103	+	0.421103i
$346$	1.45522	+	1.45522i	0.0782330	+	0.0782330i
$347$	−7.58750	−	7.58750i	−0.407318	−	0.407318i	0.473484	−	0.880802i	$-0.342996\pi$
$347$	−7.58750	−	7.58750i	−0.407318	−	0.407318i	−0.880802	+	0.473484i	$0.842996\pi$
$348$			13.8779i			0.743931i
$349$		−	14.1282i		−	0.756265i	−0.925752	−	0.378132i	$-0.876566\pi$
$349$		−	14.1282i		−	0.756265i	0.925752	−	0.378132i	$-0.123434\pi$
$350$	−1.33626	−	1.33626i	−0.0714259	−	0.0714259i
$351$	−4.27761	−	4.27761i	−0.228322	−	0.228322i
$352$	−6.92544	+	6.92544i	−0.369127	+	0.369127i
$353$	6.26544			0.333476			0.166738	−	0.986001i	$-0.446677\pi$
$353$	6.26544			0.333476			0.166738	+	0.986001i	$0.446677\pi$
$354$	−2.95129	+	2.95129i	−0.156859	+	0.156859i
$355$			16.4976i			0.875603i
$356$	−12.9522			−0.686467
$357$	0.760847	−	1.97890i	0.0402683	−	0.104734i
$358$	−6.27668			−0.331733
$359$			6.23738i			0.329196i	0.986361	+	0.164598i	$0.0526327\pi$
$359$			6.23738i			0.329196i	−0.986361	+	0.164598i	$0.947367\pi$
$360$	8.62529	−	8.62529i	0.454593	−	0.454593i
$361$	−33.3058			−1.75294
$362$	−2.55123	+	2.55123i	−0.134090	+	0.134090i
$363$	−4.53886	−	4.53886i	−0.238228	−	0.238228i
$364$	−0.799743	−	0.799743i	−0.0419179	−	0.0419179i
$365$		−	60.1502i		−	3.14841i
$366$		−	0.671127i		−	0.0350804i
$367$	−18.5544	−	18.5544i	−0.968533	−	0.968533i	0.0309865	−	0.999520i	$-0.490135\pi$
$367$	−18.5544	−	18.5544i	−0.968533	−	0.968533i	−0.999520	+	0.0309865i	$0.990135\pi$
$368$	−6.20273	−	6.20273i	−0.323339	−	0.323339i
$369$	−15.8359	+	15.8359i	−0.824384	+	0.824384i
$370$	14.8397			0.771477
$371$	2.47841	−	2.47841i	0.128673	−	0.128673i
$372$			12.5801i			0.652245i
$373$	12.2908			0.636393			0.318196	−	0.948025i	$-0.396923\pi$
$373$	12.2908			0.636393			0.318196	+	0.948025i	$0.396923\pi$
$374$	1.56011	+	3.50915i	0.0806716	+	0.181454i
$375$	−12.4335			−0.642063
$376$			3.12149i			0.160979i
$377$	6.58921	−	6.58921i	0.339362	−	0.339362i
$378$	1.12226			0.0577229
$379$	17.8110	−	17.8110i	0.914890	−	0.914890i	−0.0817616	−	0.996652i	$-0.526055\pi$
$379$	17.8110	−	17.8110i	0.914890	−	0.914890i	0.996652	+	0.0817616i	$0.0260546\pi$
$380$	33.8883	+	33.8883i	1.73843	+	1.73843i
$381$	3.72172	+	3.72172i	0.190670	+	0.190670i
$382$		−	1.56414i		−	0.0800283i
$383$		−	8.60494i		−	0.439692i	−0.975535	−	0.219846i	$-0.929444\pi$
$383$		−	8.60494i		−	0.439692i	0.975535	−	0.219846i	$-0.0705555\pi$
$384$	−7.63182	−	7.63182i	−0.389459	−	0.389459i
$385$	−2.85169	−	2.85169i	−0.145336	−	0.145336i
$386$	−3.96262	+	3.96262i	−0.201692	+	0.201692i
$387$	2.00554			0.101947
$388$	6.60926	−	6.60926i	0.335534	−	0.335534i
$389$			1.15404i			0.0585122i	0.999572	+	0.0292561i	$0.00931384\pi$
$389$			1.15404i			0.0585122i	−0.999572	+	0.0292561i	$0.990686\pi$
$390$	1.92935			0.0976965
$391$	−11.4140	+	5.07450i	−0.577231	+	0.256629i
$392$	−11.1866			−0.565011
$393$		−	20.6155i		−	1.03992i
$394$	7.12315	−	7.12315i	0.358859	−	0.358859i
$395$	48.9760			2.46425
$396$	5.48281	−	5.48281i	0.275522	−	0.275522i
$397$	12.8349	+	12.8349i	0.644166	+	0.644166i	0.951577	−	0.307411i	$-0.0994627\pi$
$397$	12.8349	+	12.8349i	0.644166	+	0.644166i	−0.307411	+	0.951577i	$0.599463\pi$
$398$	7.09688	+	7.09688i	0.355734	+	0.355734i
$399$			3.71888i			0.186177i
$400$		−	24.3373i		−	1.21687i
$401$	−7.09427	−	7.09427i	−0.354271	−	0.354271i	0.507425	−	0.861696i	$-0.330597\pi$
$401$	−7.09427	−	7.09427i	−0.354271	−	0.354271i	−0.861696	+	0.507425i	$0.830597\pi$
$402$	1.55310	+	1.55310i	0.0774618	+	0.0774618i
$403$	5.97301	−	5.97301i	0.297537	−	0.297537i
$404$	0.619284			0.0308105
$405$	−2.68940	+	2.68940i	−0.133637	+	0.133637i
$406$			1.72873i			0.0857953i
$407$	19.8570			0.984277
$408$	−6.24125	+	2.77477i	−0.308988	+	0.137371i
$409$	−30.8847			−1.52715			−0.763574	−	0.645720i	$-0.776557\pi$
$409$	−30.8847			−1.52715			−0.763574	+	0.645720i	$0.776557\pi$
$410$		−	17.8268i		−	0.880402i
$411$	−8.49839	+	8.49839i	−0.419195	+	0.419195i
$412$	6.30715			0.310731
$413$	3.49988	−	3.49988i	0.172218	−	0.172218i
$414$	−1.87328	−	1.87328i	−0.0920667	−	0.0920667i
$415$	−1.92443	−	1.92443i	−0.0944663	−	0.0944663i
$416$			5.55645i			0.272427i
$417$			20.1919i			0.988801i
$418$	−4.76325	−	4.76325i	−0.232978	−	0.232978i
$419$	1.47914	+	1.47914i	0.0722607	+	0.0722607i	0.742313	−	0.670053i	$-0.233729\pi$
$419$	1.47914	+	1.47914i	0.0722607	+	0.0722607i	−0.670053	+	0.742313i	$0.733729\pi$
$420$	2.40942	−	2.40942i	0.117567	−	0.117567i
$421$	33.1612			1.61618			0.808088	−	0.589062i	$-0.200502\pi$
$421$	33.1612			1.61618			0.808088	+	0.589062i	$0.200502\pi$
$422$	0.468098	−	0.468098i	0.0227867	−	0.0227867i
$423$		−	3.76855i		−	0.183233i
$424$	−11.2918			−0.548379
$425$	−32.3476	−	12.4370i	−1.56909	−	0.603284i
$426$	1.95922			0.0949246
$427$			0.795878i			0.0385152i
$428$	−22.8373	+	22.8373i	−1.10388	+	1.10388i
$429$	2.58168			0.124644
$430$	−1.12884	+	1.12884i	−0.0544373	+	0.0544373i
$431$	15.7571	+	15.7571i	0.758992	+	0.758992i	0.976139	−	0.217147i	$-0.0696749\pi$
$431$	15.7571	+	15.7571i	0.758992	+	0.758992i	−0.217147	+	0.976139i	$0.569675\pi$
$432$	10.2199	+	10.2199i	0.491706	+	0.491706i
$433$		−	32.3054i		−	1.55250i	−0.630426	−	0.776249i	$-0.717120\pi$
$433$		−	32.3054i		−	1.55250i	0.630426	−	0.776249i	$-0.282880\pi$
$434$			1.56706i			0.0752215i
$435$	19.8516	+	19.8516i	0.951811	+	0.951811i
$436$	−13.5577	−	13.5577i	−0.649298	−	0.649298i
$437$	15.4932	−	15.4932i	0.741138	−	0.741138i
$438$	−7.14331			−0.341320
$439$	−10.6233	+	10.6233i	−0.507024	+	0.507024i	−0.913612	−	0.406588i	$-0.866719\pi$
$439$	−10.6233	+	10.6233i	−0.507024	+	0.507024i	0.406588	+	0.913612i	$0.366719\pi$
$440$			12.9925i			0.619395i
$441$	13.5055			0.643121
$442$	2.03360	+	0.781878i	0.0967283	+	0.0371902i
$443$	−16.9675			−0.806151			−0.403076	−	0.915167i	$-0.632059\pi$
$443$	−16.9675			−0.806151			−0.403076	+	0.915167i	$0.632059\pi$
$444$			16.7774i			0.796218i
$445$	−18.5275	+	18.5275i	−0.878289	+	0.878289i
$446$	−3.02758			−0.143360
$447$	16.1761	−	16.1761i	0.765103	−	0.765103i
$448$	1.38254	+	1.38254i	0.0653187	+	0.0653187i
$449$	−14.9707	−	14.9707i	−0.706510	−	0.706510i	0.259290	−	0.965800i	$-0.416512\pi$
$449$	−14.9707	−	14.9707i	−0.706510	−	0.706510i	−0.965800	+	0.259290i	$0.916512\pi$
$450$		−	7.35010i		−	0.346487i
$451$		−	23.8541i		−	1.12325i
$452$	1.03774	+	1.03774i	0.0488113	+	0.0488113i
$453$	−1.65114	−	1.65114i	−0.0775774	−	0.0775774i
$454$	6.79110	−	6.79110i	0.318722	−	0.318722i
$455$	−2.28798			−0.107262
$456$	8.47175	−	8.47175i	0.396726	−	0.396726i
$457$			3.63769i			0.170164i	0.996374	+	0.0850819i	$0.0271152\pi$
$457$			3.63769i			0.170164i	−0.996374	+	0.0850819i	$0.972885\pi$
$458$	9.19761			0.429776
$459$	18.8063	−	8.36100i	0.877803	−	0.390258i
$460$	−20.0757			−0.936033
$461$		−	17.7009i		−	0.824414i	−0.911090	−	0.412207i	$-0.864758\pi$
$461$		−	17.7009i		−	0.824414i	0.911090	−	0.412207i	$-0.135242\pi$
$462$	−0.338661	+	0.338661i	−0.0157559	+	0.0157559i
$463$	18.3867			0.854502			0.427251	−	0.904133i	$-0.359482\pi$
$463$	18.3867			0.854502			0.427251	+	0.904133i	$0.359482\pi$
$464$	−15.7427	+	15.7427i	−0.730838	+	0.730838i
$465$	17.9951	+	17.9951i	0.834504	+	0.834504i
$466$	2.43373	+	2.43373i	0.112741	+	0.112741i
$467$		−	20.0726i		−	0.928851i	−0.885612	−	0.464426i	$-0.846261\pi$
$467$		−	20.0726i		−	0.928851i	0.885612	−	0.464426i	$-0.153739\pi$
$468$		−	4.39900i		−	0.203344i
$469$	−1.84180	−	1.84180i	−0.0850464	−	0.0850464i
$470$	2.12116	+	2.12116i	0.0978420	+	0.0978420i
$471$	8.58297	−	8.58297i	0.395483	−	0.395483i
$472$	−15.9457			−0.733962
$473$	−1.51050	+	1.51050i	−0.0694530	+	0.0694530i
$474$		−	5.81628i		−	0.267150i
$475$	60.7897			2.78922
$476$	3.51603	−	1.56317i	0.161157	−	0.0716480i
$477$	13.6325			0.624190
$478$		−	5.87448i		−	0.268693i
$479$	9.47133	−	9.47133i	0.432756	−	0.432756i	−0.456809	−	0.889565i	$-0.651008\pi$
$479$	9.47133	−	9.47133i	0.432756	−	0.432756i	0.889565	+	0.456809i	$0.151008\pi$
$480$	−16.7401			−0.764079
$481$	7.96589	−	7.96589i	0.363213	−	0.363213i
$482$	−2.89919	−	2.89919i	−0.132055	−	0.132055i
$483$	−1.10154	−	1.10154i	−0.0501220	−	0.0501220i
$484$		−	11.6498i		−	0.529537i
$485$		−	18.9084i		−	0.858587i
$486$	4.93637	+	4.93637i	0.223918	+	0.223918i
$487$	15.9401	+	15.9401i	0.722314	+	0.722314i	0.969076	−	0.246762i	$-0.0793665\pi$
$487$	15.9401	+	15.9401i	0.722314	+	0.722314i	−0.246762	+	0.969076i	$0.579367\pi$
$488$	1.81304	−	1.81304i	0.0820725	−	0.0820725i
$489$	11.5875			0.524007
$490$	−7.60172	+	7.60172i	−0.343411	+	0.343411i
$491$			12.8990i			0.582125i	0.956704	+	0.291062i	$0.0940087\pi$
$491$			12.8990i			0.582125i	−0.956704	+	0.291062i	$0.905991\pi$
$492$	20.1545			0.908636
$493$	12.8793	+	28.9691i	0.580052	+	1.30470i
$494$	−3.82167			−0.171945
$495$		−	15.6858i		−	0.705023i
$496$	−14.2705	+	14.2705i	−0.640765	+	0.640765i
$497$	−2.32341			−0.104219
$498$	−0.228540	+	0.228540i	−0.0102411	+	0.0102411i
$499$	−12.8505	−	12.8505i	−0.575266	−	0.575266i	0.358329	−	0.933595i	$-0.383347\pi$
$499$	−12.8505	−	12.8505i	−0.575266	−	0.575266i	−0.933595	+	0.358329i	$0.883347\pi$
$500$	−15.9564	−	15.9564i	−0.713593	−	0.713593i
$501$			3.38437i			0.151203i
$502$		−	1.65965i		−	0.0740739i
$503$	−2.68633	−	2.68633i	−0.119778	−	0.119778i	0.644677	−	0.764455i	$-0.276992\pi$
$503$	−2.68633	−	2.68633i	−0.119778	−	0.119778i	−0.764455	+	0.644677i	$0.776992\pi$
$504$	1.21472	+	1.21472i	0.0541081	+	0.0541081i
$505$	0.885854	−	0.885854i	0.0394200	−	0.0394200i
$506$	2.82178			0.125443
$507$	−8.13123	+	8.13123i	−0.361121	+	0.361121i
$508$			9.55248i			0.423823i
$509$	2.30069			0.101976			0.0509882	−	0.998699i	$-0.483763\pi$
$509$	2.30069			0.101976			0.0509882	+	0.998699i	$0.483763\pi$
$510$	−2.35560	+	6.12670i	−0.104308	+	0.271295i
$511$	8.47112			0.374740
$512$		−	22.8951i		−	1.01183i
$513$	−25.5273	+	25.5273i	−1.12706	+	1.12706i
$514$	2.88419			0.127216
$515$	9.02207	−	9.02207i	0.397560	−	0.397560i
$516$	−1.27623	−	1.27623i	−0.0561831	−	0.0561831i
$517$	2.83834	+	2.83834i	0.124830	+	0.124830i
$518$			2.08991i			0.0918254i
$519$			4.70685i			0.206608i
$520$	5.21212	+	5.21212i	0.228566	+	0.228566i
$521$	−21.5712	−	21.5712i	−0.945051	−	0.945051i	0.0535158	−	0.998567i	$-0.482957\pi$
$521$	−21.5712	−	21.5712i	−0.945051	−	0.945051i	−0.998567	+	0.0535158i	$0.982957\pi$
$522$	−4.75445	+	4.75445i	−0.208096	+	0.208096i
$523$	−4.21292			−0.184218			−0.0921091	−	0.995749i	$-0.529361\pi$
$523$	−4.21292			−0.184218			−0.0921091	+	0.995749i	$0.529361\pi$
$524$	26.4567	−	26.4567i	1.15577	−	1.15577i
$525$		−	4.32207i		−	0.188631i
$526$	−9.42966			−0.411153
$527$	11.6748	+	26.2600i	0.508564	+	1.14391i
$528$	−6.16805			−0.268430
$529$		−	13.8217i		−	0.600946i
$530$	−7.67319	+	7.67319i	−0.333302	+	0.333302i
$531$	19.2511			0.835429
$532$	−4.77259	+	4.77259i	−0.206918	+	0.206918i
$533$	−9.56937	−	9.56937i	−0.414495	−	0.414495i
$534$	2.20029	+	2.20029i	0.0952158	+	0.0952158i
$535$			65.3351i			2.82468i
$536$			8.39138i			0.362452i
$537$	−10.1508	−	10.1508i	−0.438041	−	0.438041i
$538$	−1.00677	−	1.00677i	−0.0434048	−	0.0434048i
$539$	−10.1719	+	10.1719i	−0.438135	+	0.438135i
$540$	33.0777			1.42344
$541$	−28.4094	+	28.4094i	−1.22141	+	1.22141i	−0.254285	+	0.967129i	$0.581840\pi$
$541$	−28.4094	+	28.4094i	−1.22141	+	1.22141i	−0.967129	+	0.254285i	$0.918160\pi$
$542$			5.39214i			0.231612i
$543$	−8.25186			−0.354121
$544$	−17.6446	−	6.78401i	−0.756507	−	0.290862i
$545$	−38.7873			−1.66147
$546$			0.271716i			0.0116284i
$547$	−2.61015	+	2.61015i	−0.111602	+	0.111602i	−0.760703	−	0.649101i	$-0.775145\pi$
$547$	−2.61015	+	2.61015i	−0.111602	+	0.111602i	0.649101	+	0.760703i	$0.275145\pi$
$548$	−21.8127			−0.931791
$549$	−2.18887	+	2.18887i	−0.0934186	+	0.0934186i
$550$	5.53584	+	5.53584i	0.236049	+	0.236049i
$551$	−39.3221	−	39.3221i	−1.67518	−	1.67518i
$552$			5.01872i			0.213611i
$553$			6.89742i			0.293308i
$554$	−8.45406	−	8.45406i	−0.359178	−	0.359178i
$555$	23.9992	+	23.9992i	1.01871	+	1.01871i
$556$	−25.9131	+	25.9131i	−1.09896	+	1.09896i
$557$	9.80539			0.415468			0.207734	−	0.978185i	$-0.433391\pi$
$557$	9.80539			0.415468			0.207734	+	0.978185i	$0.433391\pi$
$558$	−4.30983	+	4.30983i	−0.182450	+	0.182450i
$559$			1.21191i			0.0512584i
$560$	5.46637			0.230996
$561$	−3.15204	+	8.19817i	−0.133079	+	0.346127i
$562$	−2.65908			−0.112167
$563$			14.7530i			0.621767i	0.950448	+	0.310883i	$0.100625\pi$
$563$			14.7530i			0.621767i	−0.950448	+	0.310883i	$0.899375\pi$
$564$	−2.39814	+	2.39814i	−0.100980	+	0.100980i
$565$	2.96888			0.124902
$566$	4.95526	−	4.95526i	0.208285	−	0.208285i
$567$	−0.378755	−	0.378755i	−0.0159062	−	0.0159062i
$568$	5.29281	+	5.29281i	0.222081	+	0.222081i
$569$		−	32.5818i		−	1.36590i	−0.730465	−	0.682951i	$-0.760696\pi$
$569$		−	32.5818i		−	1.36590i	0.730465	−	0.682951i	$-0.239304\pi$
$570$		−	11.5137i		−	0.482256i
$571$	−18.8354	−	18.8354i	−0.788239	−	0.788239i	0.192967	−	0.981205i	$-0.438189\pi$
$571$	−18.8354	−	18.8354i	−0.788239	−	0.788239i	−0.981205	+	0.192967i	$0.938189\pi$
$572$	3.31317	+	3.31317i	0.138531	+	0.138531i
$573$	2.52957	−	2.52957i	0.105674	−	0.105674i
$574$	2.51059			0.104790
$575$	−18.0061	+	18.0061i	−0.750907	+	0.750907i
$576$			7.60466i			0.316861i
$577$	14.6498			0.609879			0.304940	−	0.952372i	$-0.401364\pi$
$577$	14.6498			0.609879			0.304940	+	0.952372i	$0.401364\pi$
$578$	−4.96574	+	5.50312i	−0.206548	+	0.228899i
$579$	−12.8169			−0.532654
$580$			50.9527i			2.11570i
$581$	0.271022	−	0.271022i	0.0112439	−	0.0112439i
$582$	−2.24552			−0.0930799
$583$	−10.2675	+	10.2675i	−0.425238	+	0.425238i
$584$	−19.2976	−	19.2976i	−0.798538	−	0.798538i
$585$	−6.29254	−	6.29254i	−0.260165	−	0.260165i
$586$			13.6219i			0.562717i
$587$		−	17.9669i		−	0.741572i	−0.928718	−	0.370786i	$-0.879088\pi$
$587$		−	17.9669i		−	0.741572i	0.928718	−	0.370786i	$-0.120912\pi$
$588$	−8.59431	−	8.59431i	−0.354424	−	0.354424i
$589$	−35.6449	−	35.6449i	−1.46872	−	1.46872i
$590$	−10.8357	+	10.8357i	−0.446098	+	0.446098i
$591$	23.0396			0.947721
$592$	−19.0318	+	19.0318i	−0.782204	+	0.782204i
$593$		−	9.81839i		−	0.403193i	−0.979469	−	0.201596i	$-0.935387\pi$
$593$		−	9.81839i		−	0.403193i	0.979469	−	0.201596i	$-0.0646129\pi$
$594$	−4.64930			−0.190763
$595$	2.79346	−	7.26554i	0.114521	−	0.297858i
$596$	41.5189			1.70068
$597$			22.9546i			0.939469i
$598$	1.13199	−	1.13199i	0.0462906	−	0.0462906i
$599$	−32.8635			−1.34277			−0.671383	−	0.741111i	$-0.734299\pi$
$599$	−32.8635			−1.34277			−0.671383	+	0.741111i	$0.734299\pi$
$600$	−9.84585	+	9.84585i	−0.401955	+	0.401955i
$601$	−0.389217	−	0.389217i	−0.0158765	−	0.0158765i	0.699124	−	0.715000i	$-0.253574\pi$
$601$	−0.389217	−	0.389217i	−0.0158765	−	0.0158765i	−0.715000	+	0.699124i	$0.753574\pi$
$602$	−0.158977	−	0.158977i	−0.00647942	−	0.00647942i
$603$		−	10.1308i		−	0.412560i
$604$		−	4.23796i		−	0.172440i
$605$	−16.6645	−	16.6645i	−0.677507	−	0.677507i
$606$	−0.105202	−	0.105202i	−0.00427354	−	0.00427354i
$607$	8.84017	−	8.84017i	0.358811	−	0.358811i	−0.504563	−	0.863375i	$-0.668346\pi$
$607$	8.84017	−	8.84017i	0.358811	−	0.358811i	0.863375	+	0.504563i	$0.168346\pi$
$608$	33.1589			1.34477
$609$	−2.79575	+	2.79575i	−0.113290	+	0.113290i
$610$		−	2.46405i		−	0.0997665i
$611$	2.27727			0.0921285
$612$	13.9691	+	5.37085i	0.564668	+	0.217104i
$613$	6.45835			0.260850			0.130425	−	0.991458i	$-0.458366\pi$
$613$	6.45835			0.260850			0.130425	+	0.991458i	$0.458366\pi$
$614$			7.38299i			0.297953i
$615$	28.8300	−	28.8300i	1.16254	−	1.16254i
$616$	−1.82978			−0.0737238
$617$	26.1805	−	26.1805i	1.05399	−	1.05399i	0.0555308	−	0.998457i	$-0.482315\pi$
$617$	26.1805	−	26.1805i	1.05399	−	1.05399i	0.998457	−	0.0555308i	$-0.0176851\pi$
$618$	−1.07144	−	1.07144i	−0.0430997	−	0.0430997i
$619$	9.99745	+	9.99745i	0.401831	+	0.401831i	0.878878	−	0.477047i	$-0.158293\pi$
$619$	9.99745	+	9.99745i	0.401831	+	0.401831i	−0.477047	+	0.878878i	$0.658293\pi$
$620$			46.1878i			1.85495i
$621$		−	15.1225i		−	0.606847i
$622$	7.20218	+	7.20218i	0.288781	+	0.288781i
$623$	−2.60928	−	2.60928i	−0.104539	−	0.104539i
$624$	−2.47439	+	2.47439i	−0.0990548	+	0.0990548i
$625$	−3.62304			−0.144922
$626$	−7.37141	+	7.37141i	−0.294621	+	0.294621i
$627$		−	15.4065i		−	0.615278i
$628$	22.0298			0.879084
$629$	15.5701	+	35.0216i	0.620821	+	1.39640i
$630$	1.65089			0.0657732
$631$			48.5029i			1.93087i	0.260641	+	0.965436i	$0.416066\pi$
$631$			48.5029i			1.93087i	−0.260641	+	0.965436i	$0.583934\pi$
$632$	15.7126	−	15.7126i	0.625014	−	0.625014i
$633$	1.51405			0.0601780
$634$	8.36869	−	8.36869i	0.332363	−	0.332363i
$635$	13.6643	+	13.6643i	0.542253	+	0.542253i
$636$	−8.67512	−	8.67512i	−0.343991	−	0.343991i
$637$			8.16117i			0.323357i
$638$		−	7.16177i		−	0.283537i
$639$	−6.38996	−	6.38996i	−0.252783	−	0.252783i
$640$	−28.0203	−	28.0203i	−1.10760	−	1.10760i
$641$	−23.1297	+	23.1297i	−0.913570	+	0.913570i	−0.996551	−	0.0829813i	$-0.973556\pi$
$641$	−23.1297	+	23.1297i	−0.913570	+	0.913570i	0.0829813	+	0.996551i	$0.473556\pi$
$642$	7.75906			0.306225
$643$	−23.7416	+	23.7416i	−0.936276	+	0.936276i	−0.998088	−	0.0618121i	$-0.980312\pi$
$643$	−23.7416	+	23.7416i	−0.936276	+	0.936276i	0.0618121	+	0.998088i	$0.480312\pi$
$644$		−	2.82731i		−	0.111412i
$645$	−3.65118			−0.143765
$646$	4.66598	−	12.1358i	0.183580	−	0.477477i
$647$	−23.6908			−0.931381			−0.465690	−	0.884948i	$-0.654194\pi$
$647$	−23.6908			−0.931381			−0.465690	+	0.884948i	$0.654194\pi$
$648$			1.72564i			0.0677895i
$649$	−14.4993	+	14.4993i	−0.569147	+	0.569147i
$650$	4.44154			0.174211
$651$	−2.53430	+	2.53430i	−0.0993272	+	0.0993272i
$652$	14.8708	+	14.8708i	0.582385	+	0.582385i
$653$	2.40158	+	2.40158i	0.0939811	+	0.0939811i	0.752534	−	0.658553i	$-0.228831\pi$
$653$	2.40158	+	2.40158i	0.0939811	+	0.0939811i	−0.658553	+	0.752534i	$0.728831\pi$
$654$			4.60630i			0.180120i
$655$		−	75.6901i		−	2.95746i
$656$	22.8628	+	22.8628i	0.892643	+	0.892643i
$657$	23.2978	+	23.2978i	0.908933	+	0.908933i
$658$	−0.298729	+	0.298729i	−0.0116457	+	0.0116457i
$659$	40.6418			1.58318			0.791590	−	0.611053i	$-0.209254\pi$
$659$	40.6418			1.58318			0.791590	+	0.611053i	$0.209254\pi$
$660$	−9.98172	+	9.98172i	−0.388538	+	0.388538i
$661$			34.2477i			1.33208i	0.745915	+	0.666041i	$0.232012\pi$
$661$			34.2477i			1.33208i	−0.745915	+	0.666041i	$0.767988\pi$
$662$	0.900090			0.0349830
$663$	2.02432	+	4.55327i	0.0786180	+	0.176835i
$664$	−1.23480			−0.0479195
$665$			13.6539i			0.529475i
$666$	−5.74779	+	5.74779i	−0.222722	+	0.222722i
$667$	23.2947			0.901975
$668$	−4.34331	+	4.34331i	−0.168048	+	0.168048i
$669$	−4.89630	−	4.89630i	−0.189302	−	0.189302i
$670$	5.70224	+	5.70224i	0.220297	+	0.220297i
$671$		−	3.29716i		−	0.127285i
$672$		−	2.35756i		−	0.0909448i
$673$	−12.8298	−	12.8298i	−0.494554	−	0.494554i	0.415183	−	0.909738i	$-0.363717\pi$
$673$	−12.8298	−	12.8298i	−0.494554	−	0.494554i	−0.909738	+	0.415183i	$0.863717\pi$
$674$	−3.60089	−	3.60089i	−0.138701	−	0.138701i
$675$	29.6678	−	29.6678i	1.14191	−	1.14191i
$676$	−20.8703			−0.802703
$677$	16.4768	−	16.4768i	0.633257	−	0.633257i	−0.315627	−	0.948883i	$-0.602215\pi$
$677$	16.4768	−	16.4768i	0.633257	−	0.633257i	0.948883	+	0.315627i	$0.102215\pi$
$678$		−	0.352577i		−	0.0135406i
$679$	2.66293			0.102194
$680$	−22.9148	+	10.1876i	−0.878743	+	0.390676i
$681$	21.9656			0.841722
$682$		−	6.49203i		−	0.248593i
$683$	13.1518	−	13.1518i	0.503240	−	0.503240i	−0.409203	−	0.912443i	$-0.634193\pi$
$683$	13.1518	−	13.1518i	0.503240	−	0.503240i	0.912443	+	0.409203i	$0.134193\pi$
$684$	−26.2517			−1.00376
$685$	−31.2019	+	31.2019i	−1.19216	+	1.19216i
$686$	−2.18341	−	2.18341i	−0.0833630	−	0.0833630i
$687$	14.8747	+	14.8747i	0.567504	+	0.567504i
$688$		−	2.89546i		−	0.110388i
$689$			8.23790i			0.313839i
$690$	3.41040	+	3.41040i	0.129832	+	0.129832i
$691$	13.5265	+	13.5265i	0.514572	+	0.514572i	0.915924	−	0.401352i	$-0.131459\pi$
$691$	13.5265	+	13.5265i	0.514572	+	0.514572i	−0.401352	+	0.915924i	$0.631459\pi$
$692$	−6.04049	+	6.04049i	−0.229625	+	0.229625i
$693$	2.20907			0.0839157
$694$	−3.30830	+	3.30830i	−0.125581	+	0.125581i
$695$			74.1347i			2.81209i
$696$	12.7377			0.482820
$697$	42.0713	−	18.7043i	1.59356	−	0.708474i
$698$	−6.16018			−0.233166
$699$			7.87182i			0.297740i
$700$	5.54669	−	5.54669i	0.209645	−	0.209645i
$701$	−12.1042			−0.457167			−0.228584	−	0.973524i	$-0.573409\pi$
$701$	−12.1042			−0.457167			−0.228584	+	0.973524i	$0.573409\pi$
$702$	−1.86513	+	1.86513i	−0.0703946	+	0.0703946i
$703$	−47.5377	−	47.5377i	−1.79292	−	1.79292i
$704$	−5.72757	−	5.72757i	−0.215866	−	0.215866i
$705$			6.86083i			0.258394i
$706$		−	2.73186i		−	0.102815i
$707$	0.124757	+	0.124757i	0.00469198	+	0.00469198i
$708$	−12.2506	−	12.2506i	−0.460404	−	0.460404i
$709$	11.7340	−	11.7340i	0.440681	−	0.440681i	−0.451560	−	0.892241i	$-0.649132\pi$
$709$	11.7340	−	11.7340i	0.440681	−	0.440681i	0.892241	+	0.451560i	$0.149132\pi$
$710$	7.19330			0.269960
$711$	−18.9697	+	18.9697i	−0.711419	+	0.711419i
$712$			11.8881i			0.445525i
$713$	21.1163			0.790810
$714$	−0.862840	−	0.331745i	−0.0322910	−	0.0124152i
$715$	9.47865			0.354481
$716$		−	26.0540i		−	0.973683i
$717$	9.50040	−	9.50040i	0.354799	−	0.354799i
$718$	2.71962			0.101495
$719$	0.567075	−	0.567075i	0.0211483	−	0.0211483i	−0.696454	−	0.717602i	$-0.745240\pi$
$719$	0.567075	−	0.567075i	0.0211483	−	0.0211483i	0.717602	+	0.696454i	$0.245240\pi$
$720$	15.0339	+	15.0339i	0.560281	+	0.560281i
$721$	1.27060	+	1.27060i	0.0473197	+	0.0473197i
$722$			14.5220i			0.540453i
$723$		−	9.37733i		−	0.348747i
$724$	−10.5900	−	10.5900i	−0.393573	−	0.393573i
$725$	45.7001	+	45.7001i	1.69726	+	1.69726i
$726$	−1.97904	+	1.97904i	−0.0734489	+	0.0734489i
$727$	−21.7403			−0.806302			−0.403151	−	0.915133i	$-0.632085\pi$
$727$	−21.7403			−0.806302			−0.403151	+	0.915133i	$0.632085\pi$
$728$	−0.734037	+	0.734037i	−0.0272052	+	0.0272052i
$729$			12.8501i			0.475930i
$730$	−26.2267			−0.970695
$731$	−3.84846	−	1.47966i	−0.142340	−	0.0547271i
$732$	2.78579			0.102966
$733$			5.15333i			0.190343i	0.995461	+	0.0951713i	$0.0303399\pi$
$733$			5.15333i			0.190343i	−0.995461	+	0.0951713i	$0.969660\pi$
$734$	−8.09011	+	8.09011i	−0.298611	+	0.298611i
$735$	−24.5875			−0.906923
$736$	−9.82179	+	9.82179i	−0.362036	+	0.362036i
$737$	7.63020	+	7.63020i	0.281062	+	0.281062i
$738$	6.90478	+	6.90478i	0.254168	+	0.254168i
$739$			24.1841i			0.889626i	0.895623	+	0.444813i	$0.146730\pi$
$739$			24.1841i			0.889626i	−0.895623	+	0.444813i	$0.853270\pi$
$740$			61.5982i			2.26440i
$741$	−6.18052	−	6.18052i	−0.227047	−	0.227047i
$742$	−1.08064	−	1.08064i	−0.0396714	−	0.0396714i
$743$	−19.0097	+	19.0097i	−0.697398	+	0.697398i	−0.963849	−	0.266450i	$-0.914149\pi$
$743$	−19.0097	+	19.0097i	−0.697398	+	0.697398i	0.266450	+	0.963849i	$0.414149\pi$
$744$	11.5465			0.423315
$745$	59.3907	−	59.3907i	2.17591	−	2.17591i
$746$		−	5.35903i		−	0.196208i
$747$	1.49076			0.0545441
$748$	−14.5662	+	6.47591i	−0.532593	+	0.236783i
$749$	−9.20133			−0.336209
$750$			5.42126i			0.197956i
$751$	18.1702	−	18.1702i	0.663039	−	0.663039i	−0.293056	−	0.956095i	$-0.594672\pi$
$751$	18.1702	−	18.1702i	0.663039	−	0.663039i	0.956095	+	0.293056i	$0.0946722\pi$
$752$	−5.44078			−0.198405
$753$	2.68404	−	2.68404i	0.0978120	−	0.0978120i
$754$	−2.87303	−	2.87303i	−0.104630	−	0.104630i
$755$	−6.06219	−	6.06219i	−0.220626	−	0.220626i
$756$			4.65842i			0.169425i
$757$		−	27.8883i		−	1.01362i	−0.862059	−	0.506808i	$-0.830825\pi$
$757$		−	27.8883i		−	1.01362i	0.862059	−	0.506808i	$-0.169175\pi$
$758$	−7.76597	−	7.76597i	−0.282073	−	0.282073i
$759$	4.56347	+	4.56347i	0.165644	+	0.165644i
$760$	31.1041	−	31.1041i	1.12826	−	1.12826i
$761$	−19.8197			−0.718464			−0.359232	−	0.933248i	$-0.616961\pi$
$761$	−19.8197			−0.718464			−0.359232	+	0.933248i	$0.616961\pi$
$762$	1.62275	−	1.62275i	0.0587859	−	0.0587859i
$763$		−	5.46253i		−	0.197757i
$764$	6.49262			0.234895
$765$	27.6648	−	12.2994i	1.00022	−	0.444685i
$766$	−3.75193			−0.135563
$767$			11.6331i			0.420048i
$768$	2.01996	−	2.01996i	0.0728890	−	0.0728890i
$769$	26.9838			0.973060			0.486530	−	0.873664i	$-0.338263\pi$
$769$	26.9838			0.973060			0.486530	+	0.873664i	$0.338263\pi$
$770$	−1.24340	+	1.24340i	−0.0448089	+	0.0448089i
$771$	4.66440	+	4.66440i	0.167984	+	0.167984i
$772$	−16.4485	−	16.4485i	−0.591995	−	0.591995i
$773$		−	17.0223i		−	0.612251i	−0.951991	−	0.306125i	$-0.900967\pi$
$773$		−	17.0223i		−	0.612251i	0.951991	−	0.306125i	$-0.0990326\pi$
$774$		−	0.874456i		−	0.0314317i
$775$	41.4264	+	41.4264i	1.48808	+	1.48808i
$776$	−6.06625	−	6.06625i	−0.217766	−	0.217766i
$777$	−3.37987	+	3.37987i	−0.121252	+	0.121252i
$778$	0.503186			0.0180401
$779$	−57.1067	+	57.1067i	−2.04606	+	2.04606i
$780$			8.00858i			0.286753i
$781$	9.62540			0.344424
$782$	2.21259	+	4.97674i	0.0791219	+	0.177968i
$783$	−38.3815			−1.37164
$784$		−	19.4984i		−	0.696371i
$785$	31.5125	−	31.5125i	1.12473	−	1.12473i
$786$	−8.98879			−0.320619
$787$	11.6416	−	11.6416i	0.414979	−	0.414979i	−0.468490	−	0.883469i	$-0.655202\pi$
$787$	11.6416	−	11.6416i	0.414979	−	0.414979i	0.883469	+	0.468490i	$0.155202\pi$
$788$	29.5676	+	29.5676i	1.05330	+	1.05330i
$789$	−15.2499	−	15.2499i	−0.542912	−	0.542912i
$790$		−	21.3545i		−	0.759760i
$791$			0.418115i			0.0148665i
$792$	−5.03235	−	5.03235i	−0.178817	−	0.178817i
$793$	−1.32270	−	1.32270i	−0.0469703	−	0.0469703i
$794$	5.59628	−	5.59628i	0.198605	−	0.198605i
$795$	−24.8186			−0.880227
$796$	−29.4586	+	29.4586i	−1.04413	+	1.04413i
$797$		−	38.8807i		−	1.37723i	−0.725130	−	0.688613i	$-0.758220\pi$
$797$		−	38.8807i		−	1.37723i	0.725130	−	0.688613i	$-0.241780\pi$
$798$	1.62151			0.0574007
$799$	−2.78038	+	7.23153i	−0.0983628	+	0.255833i
$800$	−38.5373			−1.36250
$801$		−	14.3524i		−	0.507117i
$802$	−3.09325	+	3.09325i	−0.109226	+	0.109226i
$803$	−35.0941			−1.23845
$804$	−6.44681	+	6.44681i	−0.227361	+	0.227361i
$805$	−4.04433	−	4.04433i	−0.142544	−	0.142544i
$806$	−2.60436	−	2.60436i	−0.0917345	−	0.0917345i
$807$		−	3.25635i		−	0.114629i
$808$		−	0.568404i		−	0.0199964i
$809$	5.08065	+	5.08065i	0.178626	+	0.178626i	0.790757	−	0.612130i	$-0.209687\pi$
$809$	5.08065	+	5.08065i	0.178626	+	0.178626i	−0.612130	+	0.790757i	$0.709687\pi$
$810$	1.17263	+	1.17263i	0.0412021	+	0.0412021i
$811$	−23.7828	+	23.7828i	−0.835129	+	0.835129i	−0.988213	−	0.153085i	$-0.951079\pi$
$811$	−23.7828	+	23.7828i	−0.835129	+	0.835129i	0.153085	+	0.988213i	$0.451079\pi$
$812$	−7.17581			−0.251822
$813$	−8.72034	+	8.72034i	−0.305836	+	0.305836i
$814$		−	8.65807i		−	0.303465i
$815$	42.5438			1.49024
$816$	−4.83643	−	10.8785i	−0.169309	−	0.380825i
$817$	7.23228			0.253025
$818$			13.4664i			0.470840i
$819$	0.886196	−	0.886196i	0.0309662	−	0.0309662i
$820$	73.9975			2.58411
$821$	23.9356	−	23.9356i	0.835359	−	0.835359i	−0.152885	−	0.988244i	$-0.548856\pi$
$821$	23.9356	−	23.9356i	0.835359	−	0.835359i	0.988244	+	0.152885i	$0.0488563\pi$
$822$	3.70547	+	3.70547i	0.129243	+	0.129243i
$823$	15.9373	+	15.9373i	0.555540	+	0.555540i	0.928034	−	0.372494i	$-0.121497\pi$
$823$	15.9373	+	15.9373i	0.555540	+	0.555540i	−0.372494	+	0.928034i	$0.621497\pi$
$824$		−	5.78897i		−	0.201668i
$825$			17.9055i			0.623388i
$826$	−1.52602	−	1.52602i	−0.0530970	−	0.0530970i
$827$	10.5649	+	10.5649i	0.367379	+	0.367379i	0.866521	−	0.499141i	$-0.166351\pi$
$827$	10.5649	+	10.5649i	0.367379	+	0.367379i	−0.499141	+	0.866521i	$0.666351\pi$
$828$	7.77584	−	7.77584i	0.270229	−	0.270229i
$829$	−18.9297			−0.657455			−0.328727	−	0.944425i	$-0.606620\pi$
$829$	−18.9297			−0.657455			−0.328727	+	0.944425i	$0.606620\pi$
$830$	−0.839089	+	0.839089i	−0.0291252	+	0.0291252i
$831$		−	27.3443i		−	0.948564i
$832$	−4.59537			−0.159316
$833$	−25.9160	−	9.96418i	−0.897935	−	0.345239i
$834$	8.80408			0.304860
$835$			12.4258i			0.430011i
$836$	19.7719	−	19.7719i	0.683824	−	0.683824i
$837$	−34.7922			−1.20259
$838$	0.644935	−	0.644935i	0.0222789	−	0.0222789i
$839$	−15.1140	−	15.1140i	−0.521794	−	0.521794i	0.396319	−	0.918113i	$-0.370288\pi$
$839$	−15.1140	−	15.1140i	−0.521794	−	0.521794i	−0.918113	+	0.396319i	$0.870288\pi$
$840$	−2.21146	−	2.21146i	−0.0763027	−	0.0763027i
$841$		−	30.1227i		−	1.03871i
$842$		−	14.4589i		−	0.498288i
$843$	−4.30035	−	4.30035i	−0.148112	−	0.148112i
$844$	1.94304	+	1.94304i	0.0668822	+	0.0668822i
$845$	−29.8539	+	29.8539i	−1.02701	+	1.02701i
$846$	−1.64317			−0.0564932
$847$	2.34690	−	2.34690i	0.0806406	−	0.0806406i
$848$		−	19.6817i		−	0.675872i
$849$	16.0276			0.550066
$850$	−5.42279	+	14.1042i	−0.186000	+	0.483770i
$851$	28.1616			0.965369
$852$			8.13257i			0.278617i
$853$	−16.5484	+	16.5484i	−0.566607	+	0.566607i	−0.931176	−	0.364569i	$-0.881216\pi$
$853$	−16.5484	+	16.5484i	−0.566607	+	0.566607i	0.364569	+	0.931176i	$0.381216\pi$
$854$	0.347019			0.0118747
$855$	−37.5517	+	37.5517i	−1.28424	+	1.28424i
$856$	20.9610	+	20.9610i	0.716432	+	0.716432i
$857$	−18.2196	−	18.2196i	−0.622368	−	0.622368i	0.323768	−	0.946136i	$-0.395050\pi$
$857$	−18.2196	−	18.2196i	−0.622368	−	0.622368i	−0.946136	+	0.323768i	$0.895050\pi$
$858$		−	1.12566i		−	0.0384295i
$859$		−	4.94140i		−	0.168598i	−0.996440	−	0.0842992i	$-0.973135\pi$
$859$		−	4.94140i		−	0.168598i	0.996440	−	0.0842992i	$-0.0268652\pi$
$860$	−4.68571	−	4.68571i	−0.159781	−	0.159781i
$861$	4.06021	+	4.06021i	0.138372	+	0.138372i
$862$	6.87042	−	6.87042i	0.234007	−	0.234007i
$863$	−36.0878			−1.22844			−0.614221	−	0.789134i	$-0.710530\pi$
$863$	−36.0878			−1.22844			−0.614221	+	0.789134i	$0.710530\pi$
$864$	16.1829	−	16.1829i	0.550552	−	0.550552i
$865$			17.2812i			0.587580i
$866$	−14.0858			−0.478655
$867$	−16.9306	+	0.869056i	−0.574992	+	0.0295147i
$868$	−6.50476			−0.220786
$869$		−	28.5746i		−	0.969328i
$870$	8.65570	−	8.65570i	0.293456	−	0.293456i
$871$	6.12190			0.207433
$872$	−12.4439	+	12.4439i	−0.421402	+	0.421402i
$873$	7.32373	+	7.32373i	0.247871	+	0.247871i
$874$	−6.75533	−	6.75533i	−0.228503	−	0.228503i
$875$		−	6.42898i		−	0.217339i
$876$		−	29.6513i		−	1.00182i
$877$	−4.07556	−	4.07556i	−0.137622	−	0.137622i	0.634940	−	0.772562i	$-0.281025\pi$
$877$	−4.07556	−	4.07556i	−0.137622	−	0.137622i	−0.772562	+	0.634940i	$0.781025\pi$
$878$	4.63199	+	4.63199i	0.156322	+	0.156322i
$879$	−22.0298	+	22.0298i	−0.743047	+	0.743047i
$880$	−22.6461			−0.763399
$881$	−12.6506	+	12.6506i	−0.426211	+	0.426211i	−0.887335	−	0.461125i	$-0.847446\pi$
$881$	−12.6506	+	12.6506i	−0.426211	+	0.426211i	0.461125	+	0.887335i	$0.347446\pi$
$882$		−	5.88869i		−	0.198282i
$883$	−42.2358			−1.42135			−0.710673	−	0.703522i	$-0.751610\pi$
$883$	−42.2358			−1.42135			−0.710673	+	0.703522i	$0.751610\pi$
$884$	−3.24551	+	8.44130i	−0.109158	+	0.283912i
$885$	−35.0476			−1.17811
$886$			7.39819i			0.248547i
$887$	−6.30271	+	6.30271i	−0.211624	+	0.211624i	−0.804957	−	0.593333i	$-0.797812\pi$
$887$	−6.30271	+	6.30271i	−0.211624	+	0.211624i	0.593333	+	0.804957i	$0.297812\pi$
$888$	15.3989			0.516755
$889$	−1.92439	+	1.92439i	−0.0645419	+	0.0645419i
$890$	8.07838	+	8.07838i	0.270788	+	0.270788i
$891$	1.56911	+	1.56911i	0.0525670	+	0.0525670i
$892$		−	12.5672i		−	0.420782i
$893$		−	13.5900i		−	0.454771i
$894$	−7.05310	−	7.05310i	−0.235891	−	0.235891i
$895$	−37.2689	−	37.2689i	−1.24576	−	1.24576i
$896$	3.94618	−	3.94618i	0.131832	−	0.131832i
$897$	3.66138			0.122250
$898$	−6.52752	+	6.52752i	−0.217826	+	0.217826i
$899$		−	53.5938i		−	1.78745i
$900$	30.5097			1.01699
$901$	−26.1596	−	10.0579i	−0.871504	−	0.335076i
$902$	−10.4009			−0.346312
$903$		−	0.514206i		−	0.0171117i
$904$	0.952483	−	0.952483i	0.0316791	−	0.0316791i
$905$	−30.2968			−1.00710
$906$	−0.719932	+	0.719932i	−0.0239181	+	0.0239181i
$907$	−22.4149	−	22.4149i	−0.744274	−	0.744274i	0.229123	−	0.973397i	$-0.426414\pi$
$907$	−22.4149	−	22.4149i	−0.744274	−	0.744274i	−0.973397	+	0.229123i	$0.926414\pi$
$908$	28.1893	+	28.1893i	0.935495	+	0.935495i
$909$			0.686229i			0.0227608i
$910$			0.997608i			0.0330704i
$911$	29.1584	+	29.1584i	0.966061	+	0.966061i	0.999443	−	0.0333818i	$-0.0106277\pi$
$911$	29.1584	+	29.1584i	0.966061	+	0.966061i	−0.0333818	+	0.999443i	$0.510628\pi$
$912$	14.7663	+	14.7663i	0.488961	+	0.488961i
$913$	−1.12279	+	1.12279i	−0.0371589	+	0.0371589i
$914$	1.58611			0.0524637
$915$	3.98494	−	3.98494i	0.131738	−	0.131738i
$916$			38.1786i			1.26145i
$917$	10.6596			0.352012
$918$	−3.64557	−	8.19993i	−0.120322	−	0.270638i
$919$	48.9413			1.61443			0.807213	−	0.590261i	$-0.200975\pi$
$919$	48.9413			1.61443			0.807213	+	0.590261i	$0.200975\pi$
$920$			18.4263i			0.607497i
$921$	−11.9400	+	11.9400i	−0.393436	+	0.393436i
$922$	−7.71796			−0.254177
$923$	3.86135	−	3.86135i	0.127098	−	0.127098i
$924$	−1.40575	−	1.40575i	−0.0462459	−	0.0462459i
$925$	55.2482	+	55.2482i	1.81655	+	1.81655i
$926$		−	8.01698i		−	0.263454i
$927$			6.98897i			0.229548i
$928$	24.9280	+	24.9280i	0.818303	+	0.818303i
$929$	−34.2491	−	34.2491i	−1.12368	−	1.12368i	−0.991184	−	0.132493i	$-0.957702\pi$
$929$	−34.2491	−	34.2491i	−1.12368	−	1.12368i	−0.132493	−	0.991184i	$-0.542298\pi$
$930$	7.84625	−	7.84625i	0.257289	−	0.257289i
$931$	48.7030			1.59618
$932$	−10.1022	+	10.1022i	−0.330910	+	0.330910i
$933$			23.2952i			0.762650i
$934$	−8.75208			−0.286377
$935$	−11.5727	+	30.0997i	−0.378469	+	0.984365i
$936$	−4.03758			−0.131972
$937$			14.6405i			0.478286i	0.970984	+	0.239143i	$0.0768664\pi$
$937$			14.6405i			0.478286i	−0.970984	+	0.239143i	$0.923134\pi$
$938$	−0.803062	+	0.803062i	−0.0262209	+	0.0262209i
$939$	−23.8426			−0.778073
$940$	−8.80478	+	8.80478i	−0.287180	+	0.287180i
$941$	−0.271038	−	0.271038i	−0.00883560	−	0.00883560i	0.702675	−	0.711511i	$-0.251989\pi$
$941$	−0.271038	−	0.271038i	−0.00883560	−	0.00883560i	−0.711511	+	0.702675i	$0.751989\pi$
$942$	−3.74235	−	3.74235i	−0.121932	−	0.121932i
$943$		−	33.8304i		−	1.10167i
$944$		−	27.7935i		−	0.904602i
$945$	6.66364	+	6.66364i	0.216768	+	0.216768i
$946$	0.658610	+	0.658610i	0.0214133	+	0.0214133i
$947$	17.2722	−	17.2722i	0.561272	−	0.561272i	−0.368397	−	0.929669i	$-0.620093\pi$
$947$	17.2722	−	17.2722i	0.561272	−	0.561272i	0.929669	+	0.368397i	$0.120093\pi$
$948$	24.1429			0.784125
$949$	−14.0784	+	14.0784i	−0.457006	+	0.457006i
$950$		−	26.5056i		−	0.859954i
$951$	27.0682			0.877747
$952$	−1.43475	−	3.22716i	−0.0465004	−	0.104593i
$953$	12.0383			0.389958			0.194979	−	0.980807i	$-0.437536\pi$
$953$	12.0383			0.389958			0.194979	+	0.980807i	$0.437536\pi$
$954$		−	5.94406i		−	0.192446i
$955$	9.28736	−	9.28736i	0.300532	−	0.300532i
$956$	24.3845			0.788652
$957$	11.5822	−	11.5822i	0.374401	−	0.374401i
$958$	−4.12969	−	4.12969i	−0.133424	−	0.133424i
$959$	−4.39425	−	4.39425i	−0.141898	−	0.141898i
$960$		−	13.8446i		−	0.446834i
$961$		−	17.5819i		−	0.567157i
$962$	−3.47329	−	3.47329i	−0.111983	−	0.111983i
$963$	−25.3060	−	25.3060i	−0.815475	−	0.815475i
$964$	12.0343	−	12.0343i	0.387599	−	0.387599i
$965$	−47.0575			−1.51484
$966$	−0.480296	+	0.480296i	−0.0154533	+	0.0154533i
$967$			54.2080i			1.74321i	0.490206	+	0.871606i	$0.336921\pi$
$967$			54.2080i			1.74321i	−0.490206	+	0.871606i	$0.663079\pi$
$968$	−10.6927			−0.343676
$969$	27.1724	−	12.0804i	0.872902	−	0.388079i
$970$	−8.24446			−0.264714
$971$		−	41.1031i		−	1.31906i	−0.751678	−	0.659530i	$-0.770755\pi$
$971$		−	41.1031i		−	1.31906i	0.751678	−	0.659530i	$-0.229245\pi$
$972$	−20.4905	+	20.4905i	−0.657232	+	0.657232i
$973$	−10.4406			−0.334710
$974$	6.95020	−	6.95020i	0.222699	−	0.222699i
$975$	7.18300	+	7.18300i	0.230040	+	0.230040i
$976$	3.16014	+	3.16014i	0.101154	+	0.101154i
$977$			32.6592i			1.04486i	0.852682	+	0.522430i	$0.174974\pi$
$977$			32.6592i			1.04486i	−0.852682	+	0.522430i	$0.825026\pi$
$978$		−	5.05241i		−	0.161558i
$979$	10.8097	+	10.8097i	0.345481	+	0.345481i
$980$	−31.5541	−	31.5541i	−1.00796	−	1.00796i
$981$	15.0234	−	15.0234i	0.479659	−	0.479659i
$982$	5.62424			0.179477
$983$	39.5810	−	39.5810i	1.26244	−	1.26244i	0.312529	−	0.949908i	$-0.398824\pi$
$983$	39.5810	−	39.5810i	1.26244	−	1.26244i	0.949908	−	0.312529i	$-0.101176\pi$
$984$		−	18.4986i		−	0.589715i
$985$	84.5901			2.69526
$986$	12.6311	−	5.61562i	0.402257	−	0.178838i
$987$	−0.966229			−0.0307554
$988$		−	15.8634i		−	0.504683i
$989$	−2.14222	+	2.14222i	−0.0681188	+	0.0681188i
$990$	−6.83932			−0.217368
$991$	10.5062	−	10.5062i	0.333739	−	0.333739i	−0.520265	−	0.854005i	$-0.674167\pi$
$991$	10.5062	−	10.5062i	0.333739	−	0.333739i	0.854005	+	0.520265i	$0.174167\pi$
$992$	22.5968	+	22.5968i	0.717451	+	0.717451i
$993$	1.45565	+	1.45565i	0.0461938	+	0.0461938i
$994$			1.01305i			0.0321321i
$995$			84.2781i			2.67179i
$996$	−0.948653	−	0.948653i	−0.0300592	−	0.0300592i
$997$	25.7149	+	25.7149i	0.814399	+	0.814399i	0.985290	−	0.170891i	$-0.0546646\pi$
$997$	25.7149	+	25.7149i	0.814399	+	0.814399i	−0.170891	+	0.985290i	$0.554665\pi$
$998$	−5.60307	+	5.60307i	−0.177362	+	0.177362i
$999$	−46.4005			−1.46805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.d.259.14	✓	68
17.13	even	4	inner	731.2.f.d.302.21	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.d.259.14	✓	68	1.1	even	1	trivial
731.2.f.d.302.21	yes	68	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.436020i q^{2} +(0.705146 - 0.705146i) q^{3} +1.80989 q^{4} +(2.58895 - 2.58895i) q^{5} +(-0.307458 - 0.307458i) q^{6} +(0.364609 + 0.364609i) q^{7} -1.66119i q^{8} +2.00554i q^{9} +O(q^{10})\)	\(q-0.436020i q^{2} +(0.705146 - 0.705146i) q^{3} +1.80989 q^{4} +(2.58895 - 2.58895i) q^{5} +(-0.307458 - 0.307458i) q^{6} +(0.364609 + 0.364609i) q^{7} -1.66119i q^{8} +2.00554i q^{9} +(-1.12884 - 1.12884i) q^{10} +(-1.51050 - 1.51050i) q^{11} +(1.27623 - 1.27623i) q^{12} -1.21191 q^{13} +(0.158977 - 0.158977i) q^{14} -3.65118i q^{15} +2.89546 q^{16} +(1.47966 - 3.84846i) q^{17} +0.874456 q^{18} +7.23228i q^{19} +(4.68571 - 4.68571i) q^{20} +0.514206 q^{21} +(-0.658610 + 0.658610i) q^{22} +(-2.14222 - 2.14222i) q^{23} +(-1.17138 - 1.17138i) q^{24} -8.40534i q^{25} +0.528419i q^{26} +(3.52964 + 3.52964i) q^{27} +(0.659901 + 0.659901i) q^{28} +(-5.43704 + 5.43704i) q^{29} -1.59199 q^{30} +(-4.92858 + 4.92858i) q^{31} -4.58486i q^{32} -2.13025 q^{33} +(-1.67801 - 0.645160i) q^{34} +1.88791 q^{35} +3.62980i q^{36} +(-6.57299 + 6.57299i) q^{37} +3.15342 q^{38} +(-0.854575 + 0.854575i) q^{39} +(-4.30074 - 4.30074i) q^{40} +(7.89609 + 7.89609i) q^{41} -0.224204i q^{42} -1.00000i q^{43} +(-2.73384 - 2.73384i) q^{44} +(5.19224 + 5.19224i) q^{45} +(-0.934054 + 0.934054i) q^{46} -1.87907 q^{47} +(2.04172 - 2.04172i) q^{48} -6.73412i q^{49} -3.66490 q^{50} +(-1.67035 - 3.75710i) q^{51} -2.19342 q^{52} -6.79743i q^{53} +(1.53899 - 1.53899i) q^{54} -7.82123 q^{55} +(0.605685 - 0.605685i) q^{56} +(5.09981 + 5.09981i) q^{57} +(2.37066 + 2.37066i) q^{58} -9.59899i q^{59} -6.60822i q^{60} +(1.09141 + 1.09141i) q^{61} +(2.14896 + 2.14896i) q^{62} +(-0.731238 + 0.731238i) q^{63} +3.79183 q^{64} +(-3.13758 + 3.13758i) q^{65} +0.928832i q^{66} -5.05143 q^{67} +(2.67801 - 6.96527i) q^{68} -3.02116 q^{69} -0.823168i q^{70} +(-3.18616 + 3.18616i) q^{71} +3.33158 q^{72} +(11.6167 - 11.6167i) q^{73} +(2.86596 + 2.86596i) q^{74} +(-5.92699 - 5.92699i) q^{75} +13.0896i q^{76} -1.10149i q^{77} +(0.372612 + 0.372612i) q^{78} +(9.45865 + 9.45865i) q^{79} +(7.49621 - 7.49621i) q^{80} -1.03880 q^{81} +(3.44286 - 3.44286i) q^{82} -0.743322i q^{83} +0.930653 q^{84} +(-6.13271 - 13.7942i) q^{85} -0.436020 q^{86} +7.66781i q^{87} +(-2.50923 + 2.50923i) q^{88} -7.15638 q^{89} +(2.26392 - 2.26392i) q^{90} +(-0.441875 - 0.441875i) q^{91} +(-3.87718 - 3.87718i) q^{92} +6.95074i q^{93} +0.819314i q^{94} +(18.7240 + 18.7240i) q^{95} +(-3.23299 - 3.23299i) q^{96} +(3.65175 - 3.65175i) q^{97} -2.93621 q^{98} +(3.02937 - 3.02937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6}+O(q^{10}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6	\( 68 q - 76 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{10} - 6 q^{11} - 10 q^{12} - 24 q^{13} - 22 q^{14} + 84 q^{16} - 2 q^{17} + 28 q^{18} + 10 q^{20} - 36 q^{21} + 8 q^{22} + 14 q^{23} - 62 q^{24} - 12 q^{27} - 58 q^{28} + 2 q^{29} + 160 q^{30} - 26 q^{31} + 44 q^{33} + 16 q^{34} + 56 q^{35} - 6 q^{37} - 56 q^{38} - 24 q^{39} + 70 q^{40} + 6 q^{41} + 14 q^{44} + 10 q^{45} + 2 q^{46} - 68 q^{47} - 58 q^{48} + 40 q^{50} + 16 q^{51} + 4 q^{52} + 26 q^{54} - 16 q^{55} + 50 q^{56} + 18 q^{57} - 94 q^{58} + 22 q^{61} - 48 q^{62} + 16 q^{63} + 60 q^{64} - 22 q^{65} + 24 q^{67} + 20 q^{68} + 8 q^{69} - 14 q^{71} - 84 q^{72} + 34 q^{73} + 26 q^{74} - 102 q^{75} + 40 q^{78} + 4 q^{79} - 30 q^{80} - 92 q^{81} - 76 q^{82} + 108 q^{84} + 8 q^{85} + 8 q^{86} + 16 q^{88} - 72 q^{89} + 132 q^{90} + 12 q^{91} - 174 q^{92} + 50 q^{95} + 10 q^{96} - 16 q^{97} - 28 q^{98} - 86 q^{99}+O(q^{100}) \) 68 * q - 76 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^10 - 6 * q^11 - 10 * q^12 - 24 * q^13 - 22 * q^14 + 84 * q^16 - 2 * q^17 + 28 * q^18 + 10 * q^20 - 36 * q^21 + 8 * q^22 + 14 * q^23 - 62 * q^24 - 12 * q^27 - 58 * q^28 + 2 * q^29 + 160 * q^30 - 26 * q^31 + 44 * q^33 + 16 * q^34 + 56 * q^35 - 6 * q^37 - 56 * q^38 - 24 * q^39 + 70 * q^40 + 6 * q^41 + 14 * q^44 + 10 * q^45 + 2 * q^46 - 68 * q^47 - 58 * q^48 + 40 * q^50 + 16 * q^51 + 4 * q^52 + 26 * q^54 - 16 * q^55 + 50 * q^56 + 18 * q^57 - 94 * q^58 + 22 * q^61 - 48 * q^62 + 16 * q^63 + 60 * q^64 - 22 * q^65 + 24 * q^67 + 20 * q^68 + 8 * q^69 - 14 * q^71 - 84 * q^72 + 34 * q^73 + 26 * q^74 - 102 * q^75 + 40 * q^78 + 4 * q^79 - 30 * q^80 - 92 * q^81 - 76 * q^82 + 108 * q^84 + 8 * q^85 + 8 * q^86 + 16 * q^88 - 72 * q^89 + 132 * q^90 + 12 * q^91 - 174 * q^92 + 50 * q^95 + 10 * q^96 - 16 * q^97 - 28 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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