LMFDB - Embedded newform 731.2.f.c.259.13

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:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.13
Character	$\chi$	$=$	731.259
Dual form			731.2.f.c.302.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.607091i q^{2} +(-1.55808 + 1.55808i) q^{3} +1.63144 q^{4} +(1.22244 - 1.22244i) q^{5} +(0.945900 + 0.945900i) q^{6} +(1.59838 + 1.59838i) q^{7} -2.20462i q^{8} -1.85526i q^{9} +O(q^{10})$	\(q-0.607091i q^{2} +(-1.55808 + 1.55808i) q^{3} +1.63144 q^{4} +(1.22244 - 1.22244i) q^{5} +(0.945900 + 0.945900i) q^{6} +(1.59838 + 1.59838i) q^{7} -2.20462i q^{8} -1.85526i q^{9} +(-0.742133 - 0.742133i) q^{10} +(1.81730 + 1.81730i) q^{11} +(-2.54192 + 2.54192i) q^{12} -1.50335 q^{13} +(0.970361 - 0.970361i) q^{14} +3.80933i q^{15} +1.92448 q^{16} +(3.83958 + 1.50254i) q^{17} -1.12631 q^{18} -7.46343i q^{19} +(1.99434 - 1.99434i) q^{20} -4.98082 q^{21} +(1.10327 - 1.10327i) q^{22} +(0.147185 + 0.147185i) q^{23} +(3.43498 + 3.43498i) q^{24} +2.01128i q^{25} +0.912671i q^{26} +(-1.78361 - 1.78361i) q^{27} +(2.60766 + 2.60766i) q^{28} +(-4.87968 + 4.87968i) q^{29} +2.31261 q^{30} +(-0.417963 + 0.417963i) q^{31} -5.57756i q^{32} -5.66302 q^{33} +(0.912177 - 2.33098i) q^{34} +3.90784 q^{35} -3.02674i q^{36} +(0.347027 - 0.347027i) q^{37} -4.53099 q^{38} +(2.34235 - 2.34235i) q^{39} +(-2.69501 - 2.69501i) q^{40} +(8.12865 + 8.12865i) q^{41} +3.02381i q^{42} +1.00000i q^{43} +(2.96482 + 2.96482i) q^{44} +(-2.26794 - 2.26794i) q^{45} +(0.0893546 - 0.0893546i) q^{46} +10.4138 q^{47} +(-2.99850 + 2.99850i) q^{48} -1.89037i q^{49} +1.22103 q^{50} +(-8.32347 + 3.64131i) q^{51} -2.45263 q^{52} +10.1381i q^{53} +(-1.08281 + 1.08281i) q^{54} +4.44308 q^{55} +(3.52381 - 3.52381i) q^{56} +(11.6287 + 11.6287i) q^{57} +(2.96241 + 2.96241i) q^{58} -8.98894i q^{59} +6.21469i q^{60} +(5.20432 + 5.20432i) q^{61} +(0.253742 + 0.253742i) q^{62} +(2.96540 - 2.96540i) q^{63} +0.462864 q^{64} +(-1.83776 + 1.83776i) q^{65} +3.43797i q^{66} -7.46855 q^{67} +(6.26405 + 2.45130i) q^{68} -0.458653 q^{69} -2.37242i q^{70} +(8.98163 - 8.98163i) q^{71} -4.09013 q^{72} +(3.21114 - 3.21114i) q^{73} +(-0.210677 - 0.210677i) q^{74} +(-3.13375 - 3.13375i) q^{75} -12.1761i q^{76} +5.80947i q^{77} +(-1.42202 - 1.42202i) q^{78} +(-6.40181 - 6.40181i) q^{79} +(2.35256 - 2.35256i) q^{80} +11.1238 q^{81} +(4.93483 - 4.93483i) q^{82} +12.2332i q^{83} -8.12591 q^{84} +(6.53042 - 2.85690i) q^{85} +0.607091 q^{86} -15.2059i q^{87} +(4.00645 - 4.00645i) q^{88} +3.26306 q^{89} +(-1.37685 + 1.37685i) q^{90} +(-2.40292 - 2.40292i) q^{91} +(0.240123 + 0.240123i) q^{92} -1.30244i q^{93} -6.32210i q^{94} +(-9.12360 - 9.12360i) q^{95} +(8.69032 + 8.69032i) q^{96} +(-7.87344 + 7.87344i) q^{97} -1.14763 q^{98} +(3.37156 - 3.37156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * 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 $

$2$		−	0.607091i		−	0.429278i	−0.976693	−	0.214639i	$-0.931142\pi$
$2$		−	0.607091i		−	0.429278i	0.976693	−	0.214639i	$-0.0688576\pi$
$3$	−1.55808	+	1.55808i	−0.899561	+	0.899561i	−0.995397	−	0.0958364i	$-0.969447\pi$
$3$	−1.55808	+	1.55808i	−0.899561	+	0.899561i	0.0958364	+	0.995397i	$0.469447\pi$
$4$	1.63144			0.815720
$5$	1.22244	−	1.22244i	0.546692	−	0.546692i	−0.378791	−	0.925482i	$-0.623660\pi$
$5$	1.22244	−	1.22244i	0.546692	−	0.546692i	0.925482	+	0.378791i	$0.123660\pi$
$6$	0.945900	+	0.945900i	0.386162	+	0.386162i
$7$	1.59838	+	1.59838i	0.604130	+	0.604130i	0.941406	−	0.337276i	$-0.109505\pi$
$7$	1.59838	+	1.59838i	0.604130	+	0.604130i	−0.337276	+	0.941406i	$0.609505\pi$
$8$		−	2.20462i		−	0.779449i
$9$		−	1.85526i		−	0.618419i
$10$	−0.742133	−	0.742133i	−0.234683	−	0.234683i
$11$	1.81730	+	1.81730i	0.547937	+	0.547937i	0.925844	−	0.377907i	$-0.123356\pi$
$11$	1.81730	+	1.81730i	0.547937	+	0.547937i	−0.377907	+	0.925844i	$0.623356\pi$
$12$	−2.54192	+	2.54192i	−0.733790	+	0.733790i
$13$	−1.50335			−0.416955			−0.208477	−	0.978027i	$-0.566851\pi$
$13$	−1.50335			−0.416955			−0.208477	+	0.978027i	$0.566851\pi$
$14$	0.970361	−	0.970361i	0.259340	−	0.259340i
$15$			3.80933i			0.983565i
$16$	1.92448			0.481119
$17$	3.83958	+	1.50254i	0.931235	+	0.364419i
$17$	3.83958	+	1.50254i	0.931235	+	0.364419i
$18$	−1.12631			−0.265474
$19$		−	7.46343i		−	1.71223i	−0.516786	−	0.856115i	$-0.672872\pi$
$19$		−	7.46343i		−	1.71223i	0.516786	−	0.856115i	$-0.327128\pi$
$20$	1.99434	−	1.99434i	0.445947	−	0.445947i
$21$	−4.98082			−1.08690
$22$	1.10327	−	1.10327i	0.235217	−	0.235217i
$23$	0.147185	+	0.147185i	0.0306901	+	0.0306901i	0.722285	−	0.691595i	$-0.243092\pi$
$23$	0.147185	+	0.147185i	0.0306901	+	0.0306901i	−0.691595	+	0.722285i	$0.743092\pi$
$24$	3.43498	+	3.43498i	0.701162	+	0.701162i
$25$			2.01128i			0.402256i
$26$			0.912671i			0.178990i
$27$	−1.78361	−	1.78361i	−0.343255	−	0.343255i
$28$	2.60766	+	2.60766i	0.492801	+	0.492801i
$29$	−4.87968	+	4.87968i	−0.906134	+	0.906134i	−0.995958	−	0.0898241i	$-0.971370\pi$
$29$	−4.87968	+	4.87968i	−0.906134	+	0.906134i	0.0898241	+	0.995958i	$0.471370\pi$
$30$	2.31261			0.422223
$31$	−0.417963	+	0.417963i	−0.0750684	+	0.0750684i	−0.743644	−	0.668576i	$-0.766904\pi$
$31$	−0.417963	+	0.417963i	−0.0750684	+	0.0750684i	0.668576	+	0.743644i	$0.266904\pi$
$32$		−	5.57756i		−	0.985983i
$33$	−5.66302			−0.985805
$34$	0.912177	−	2.33098i	0.156437	−	0.399759i
$35$	3.90784			0.660546
$36$		−	3.02674i		−	0.504457i
$37$	0.347027	−	0.347027i	0.0570509	−	0.0570509i	−0.678006	−	0.735057i	$-0.737156\pi$
$37$	0.347027	−	0.347027i	0.0570509	−	0.0570509i	0.735057	+	0.678006i	$0.237156\pi$
$38$	−4.53099			−0.735023
$39$	2.34235	−	2.34235i	0.375076	−	0.375076i
$40$	−2.69501	−	2.69501i	−0.426119	−	0.426119i
$41$	8.12865	+	8.12865i	1.26948	+	1.26948i	0.946356	+	0.323126i	$0.104734\pi$
$41$	8.12865	+	8.12865i	1.26948	+	1.26948i	0.323126	+	0.946356i	$0.395266\pi$
$42$			3.02381i			0.466584i
$43$			1.00000i			0.152499i
$43$			1.00000i			0.152499i
$44$	2.96482	+	2.96482i	0.446963	+	0.446963i
$45$	−2.26794	−	2.26794i	−0.338084	−	0.338084i
$46$	0.0893546	−	0.0893546i	0.0131746	−	0.0131746i
$47$	10.4138			1.51900			0.759501	−	0.650506i	$-0.225443\pi$
$47$	10.4138			1.51900			0.759501	+	0.650506i	$0.225443\pi$
$48$	−2.99850	+	2.99850i	−0.432796	+	0.432796i
$49$		−	1.89037i		−	0.270054i
$50$	1.22103			0.172680
$51$	−8.32347	+	3.64131i	−1.16552	+	0.509886i
$52$	−2.45263			−0.340118
$53$			10.1381i			1.39258i	0.717763	+	0.696288i	$0.245166\pi$
$53$			10.1381i			1.39258i	−0.717763	+	0.696288i	$0.754834\pi$
$54$	−1.08281	+	1.08281i	−0.147352	+	0.147352i
$55$	4.44308			0.599105
$56$	3.52381	−	3.52381i	0.470889	−	0.470889i
$57$	11.6287	+	11.6287i	1.54025	+	1.54025i
$58$	2.96241	+	2.96241i	0.388984	+	0.388984i
$59$		−	8.98894i		−	1.17026i	−0.810940	−	0.585130i	$-0.801043\pi$
$59$		−	8.98894i		−	1.17026i	0.810940	−	0.585130i	$-0.198957\pi$
$60$			6.21469i			0.802314i
$61$	5.20432	+	5.20432i	0.666345	+	0.666345i	0.956868	−	0.290523i	$-0.0938294\pi$
$61$	5.20432	+	5.20432i	0.666345	+	0.666345i	−0.290523	+	0.956868i	$0.593829\pi$
$62$	0.253742	+	0.253742i	0.0322252	+	0.0322252i
$63$	2.96540	−	2.96540i	0.373605	−	0.373605i
$64$	0.462864			0.0578580
$65$	−1.83776	+	1.83776i	−0.227946	+	0.227946i
$66$			3.43797i			0.423185i
$67$	−7.46855			−0.912428			−0.456214	−	0.889870i	$-0.650795\pi$
$67$	−7.46855			−0.912428			−0.456214	+	0.889870i	$0.650795\pi$
$68$	6.26405	+	2.45130i	0.759627	+	0.297264i
$69$	−0.458653			−0.0552153
$70$		−	2.37242i		−	0.283558i
$71$	8.98163	−	8.98163i	1.06592	−	1.06592i	0.0682559	−	0.997668i	$-0.478257\pi$
$71$	8.98163	−	8.98163i	1.06592	−	1.06592i	0.997668	−	0.0682559i	$-0.0217434\pi$
$72$	−4.09013			−0.482026
$73$	3.21114	−	3.21114i	0.375836	−	0.375836i	−0.493761	−	0.869597i	$-0.664378\pi$
$73$	3.21114	−	3.21114i	0.375836	−	0.375836i	0.869597	+	0.493761i	$0.164378\pi$
$74$	−0.210677	−	0.210677i	−0.0244907	−	0.0244907i
$75$	−3.13375	−	3.13375i	−0.361854	−	0.361854i
$76$		−	12.1761i		−	1.39670i
$77$			5.80947i			0.662050i
$78$	−1.42202	−	1.42202i	−0.161012	−	0.161012i
$79$	−6.40181	−	6.40181i	−0.720260	−	0.720260i	0.248398	−	0.968658i	$-0.420096\pi$
$79$	−6.40181	−	6.40181i	−0.720260	−	0.720260i	−0.968658	+	0.248398i	$0.920096\pi$
$80$	2.35256	−	2.35256i	0.263024	−	0.263024i
$81$	11.1238			1.23598
$82$	4.93483	−	4.93483i	0.544961	−	0.544961i
$83$			12.2332i			1.34277i	0.741111	+	0.671383i	$0.234299\pi$
$83$			12.2332i			1.34277i	−0.741111	+	0.671383i	$0.765701\pi$
$84$	−8.12591			−0.886609
$85$	6.53042	−	2.85690i	0.708323	−	0.309874i
$86$	0.607091			0.0654643
$87$		−	15.2059i		−	1.63024i
$88$	4.00645	−	4.00645i	0.427089	−	0.427089i
$89$	3.26306			0.345884			0.172942	−	0.984932i	$-0.444673\pi$
$89$	3.26306			0.345884			0.172942	+	0.984932i	$0.444673\pi$
$90$	−1.37685	+	1.37685i	−0.145132	+	0.145132i
$91$	−2.40292	−	2.40292i	−0.251895	−	0.251895i
$92$	0.240123	+	0.240123i	0.0250346	+	0.0250346i
$93$		−	1.30244i		−	0.135057i
$94$		−	6.32210i		−	0.652075i
$95$	−9.12360	−	9.12360i	−0.936062	−	0.936062i
$96$	8.69032	+	8.69032i	0.886952	+	0.886952i
$97$	−7.87344	+	7.87344i	−0.799427	+	0.799427i	−0.983005	−	0.183578i	$-0.941232\pi$
$97$	−7.87344	+	7.87344i	−0.799427	+	0.799427i	0.183578	+	0.983005i	$0.441232\pi$
$98$	−1.14763			−0.115928
$99$	3.37156	−	3.37156i	0.338854	−	0.338854i
$100$			3.28128i			0.328128i
$101$	−12.5950			−1.25325			−0.626623	−	0.779322i	$-0.715563\pi$
$101$	−12.5950			−1.25325			−0.626623	+	0.779322i	$0.715563\pi$
$102$	2.21061	+	5.05311i	0.218883	+	0.500332i
$103$	−18.9499			−1.86719			−0.933594	−	0.358332i	$-0.883345\pi$
$103$	−18.9499			−1.86719			−0.933594	+	0.358332i	$0.883345\pi$
$104$			3.31431i			0.324995i
$105$	−6.08875	+	6.08875i	−0.594201	+	0.594201i
$106$	6.15475			0.597802
$107$	−14.3819	+	14.3819i	−1.39035	+	1.39035i	−0.565821	+	0.824528i	$0.691441\pi$
$107$	−14.3819	+	14.3819i	−1.39035	+	1.39035i	−0.824528	+	0.565821i	$0.808559\pi$
$108$	−2.90985	−	2.90985i	−0.280000	−	0.280000i
$109$	−9.94067	−	9.94067i	−0.952143	−	0.952143i	0.0467628	−	0.998906i	$-0.485110\pi$
$109$	−9.94067	−	9.94067i	−0.952143	−	0.952143i	−0.998906	+	0.0467628i	$0.985110\pi$
$110$		−	2.69736i		−	0.257183i
$111$			1.08140i			0.102642i
$112$	3.07604	+	3.07604i	0.290659	+	0.290659i
$113$	−1.92291	−	1.92291i	−0.180892	−	0.180892i	0.610853	−	0.791744i	$-0.290827\pi$
$113$	−1.92291	−	1.92291i	−0.180892	−	0.180892i	−0.791744	+	0.610853i	$0.790827\pi$
$114$	7.05966	−	7.05966i	0.661198	−	0.661198i
$115$	0.359849			0.0335561
$116$	−7.96090	+	7.96090i	−0.739151	+	0.739151i
$117$			2.78910i			0.257853i
$118$	−5.45711			−0.502367
$119$	3.73548	+	8.53872i	0.342431	+	0.782744i
$120$	8.39811			0.766639
$121$		−	4.39483i		−	0.399530i
$122$	3.15950	−	3.15950i	0.286047	−	0.286047i
$123$	−25.3303			−2.28395
$124$	−0.681882	+	0.681882i	−0.0612348	+	0.0612348i
$125$	8.57087	+	8.57087i	0.766602	+	0.766602i
$126$	−1.80027	−	1.80027i	−0.160381	−	0.160381i
$127$		−	5.82952i		−	0.517286i	−0.965973	−	0.258643i	$-0.916725\pi$
$127$		−	5.82952i		−	0.517286i	0.965973	−	0.258643i	$-0.0832754\pi$
$128$		−	11.4361i		−	1.01082i
$129$	−1.55808	−	1.55808i	−0.137182	−	0.137182i
$130$	1.11569	+	1.11569i	0.0978521	+	0.0978521i
$131$	7.68850	−	7.68850i	0.671748	−	0.671748i	−0.286371	−	0.958119i	$-0.592449\pi$
$131$	7.68850	−	7.68850i	0.671748	−	0.671748i	0.958119	+	0.286371i	$0.0924491\pi$
$132$	−9.23888			−0.804141
$133$	11.9294	−	11.9294i	1.03441	−	1.03441i
$134$			4.53409i			0.391686i
$135$	−4.36071			−0.375310
$136$	3.31252	−	8.46480i	0.284046	−	0.725851i
$137$	−6.95248			−0.593991			−0.296995	−	0.954879i	$-0.595985\pi$
$137$	−6.95248			−0.593991			−0.296995	+	0.954879i	$0.595985\pi$
$138$			0.278444i			0.0237027i
$139$	14.9819	−	14.9819i	1.27075	−	1.27075i	0.325051	−	0.945697i	$-0.394619\pi$
$139$	14.9819	−	14.9819i	1.27075	−	1.27075i	0.945697	−	0.325051i	$-0.105381\pi$
$140$	6.37541			0.538821
$141$	−16.2255	+	16.2255i	−1.36643	+	1.36643i
$142$	−5.45267	−	5.45267i	−0.457578	−	0.457578i
$143$	−2.73204	−	2.73204i	−0.228465	−	0.228465i
$144$		−	3.57040i		−	0.297533i
$145$			11.9302i			0.990752i
$146$	−1.94946	−	1.94946i	−0.161338	−	0.161338i
$147$	2.94536	+	2.94536i	0.242930	+	0.242930i
$148$	0.566154	−	0.566154i	0.0465376	−	0.0465376i
$149$	−9.20545			−0.754140			−0.377070	−	0.926185i	$-0.623068\pi$
$149$	−9.20545			−0.754140			−0.377070	+	0.926185i	$0.623068\pi$
$150$	−1.90247	+	1.90247i	−0.155336	+	0.155336i
$151$		−	11.1087i		−	0.904011i	−0.892015	−	0.452005i	$-0.850709\pi$
$151$		−	11.1087i		−	0.904011i	0.892015	−	0.452005i	$-0.149291\pi$
$152$	−16.4540			−1.33460
$153$	2.78759	−	7.12341i	0.225363	−	0.575893i
$154$	3.52688			0.284204
$155$			1.02187i			0.0820785i
$156$	3.82140	−	3.82140i	0.305957	−	0.305957i
$157$	−6.90506			−0.551084			−0.275542	−	0.961289i	$-0.588857\pi$
$157$	−6.90506			−0.551084			−0.275542	+	0.961289i	$0.588857\pi$
$158$	−3.88648	+	3.88648i	−0.309192	+	0.309192i
$159$	−15.7960	−	15.7960i	−1.25271	−	1.25271i
$160$	−6.81824	−	6.81824i	−0.539029	−	0.539029i
$161$			0.470514i			0.0370817i
$162$		−	6.75316i		−	0.530578i
$163$	−1.47681	−	1.47681i	−0.115673	−	0.115673i	0.646901	−	0.762574i	$-0.276065\pi$
$163$	−1.47681	−	1.47681i	−0.115673	−	0.115673i	−0.762574	+	0.646901i	$0.776065\pi$
$164$	13.2614	+	13.2614i	1.03554	+	1.03554i
$165$	−6.92270	+	6.92270i	−0.538932	+	0.538932i
$166$	7.42666			0.576420
$167$	9.12734	−	9.12734i	0.706295	−	0.706295i	−0.259459	−	0.965754i	$-0.583544\pi$
$167$	9.12734	−	9.12734i	0.706295	−	0.706295i	0.965754	+	0.259459i	$0.0835444\pi$
$168$			10.9808i			0.847186i
$169$	−10.7399			−0.826149
$170$	−1.73440	−	3.96456i	−0.133022	−	0.304068i
$171$	−13.8466			−1.05887
$172$			1.63144i			0.124396i
$173$	6.53749	−	6.53749i	0.497036	−	0.497036i	−0.413478	−	0.910514i	$-0.635686\pi$
$173$	6.53749	−	6.53749i	0.497036	−	0.497036i	0.910514	+	0.413478i	$0.135686\pi$
$174$	−9.23137			−0.699829
$175$	−3.21479	+	3.21479i	−0.243015	+	0.243015i
$176$	3.49736	+	3.49736i	0.263623	+	0.263623i
$177$	14.0055	+	14.0055i	1.05272	+	1.05272i
$178$		−	1.98098i		−	0.148481i
$179$		−	6.94589i		−	0.519160i	−0.965722	−	0.259580i	$-0.916416\pi$
$179$		−	6.94589i		−	0.519160i	0.965722	−	0.259580i	$-0.0835841\pi$
$180$	−3.70001	−	3.70001i	−0.275782	−	0.275782i
$181$	3.12799	+	3.12799i	0.232501	+	0.232501i	0.813736	−	0.581235i	$-0.197430\pi$
$181$	3.12799	+	3.12799i	0.232501	+	0.232501i	−0.581235	+	0.813736i	$0.697430\pi$
$182$	−1.45879	+	1.45879i	−0.108133	+	0.108133i
$183$	−16.2175			−1.19883
$184$	0.324486	−	0.324486i	0.0239214	−	0.0239214i
$185$		−	0.848440i		−	0.0623785i
$186$	−0.790702			−0.0579771
$187$	4.24711	+	9.70824i	0.310580	+	0.709937i
$188$	16.9894			1.23908
$189$		−	5.70176i		−	0.414742i
$190$	−5.53886	+	5.53886i	−0.401831	+	0.401831i
$191$	−25.6125			−1.85325			−0.926627	−	0.375982i	$-0.877306\pi$
$191$	−25.6125			−1.85325			−0.926627	+	0.375982i	$0.877306\pi$
$192$	−0.721182	+	0.721182i	−0.0520468	+	0.0520468i
$193$	−2.56531	−	2.56531i	−0.184655	−	0.184655i	0.608726	−	0.793381i	$-0.291681\pi$
$193$	−2.56531	−	2.56531i	−0.184655	−	0.184655i	−0.793381	+	0.608726i	$0.791681\pi$
$194$	4.77990	+	4.77990i	0.343177	+	0.343177i
$195$		−	5.72676i		−	0.410102i
$196$		−	3.08403i		−	0.220288i
$197$	−13.9179	−	13.9179i	−0.991610	−	0.991610i	0.00835511	−	0.999965i	$-0.497340\pi$
$197$	−13.9179	−	13.9179i	−0.991610	−	0.991610i	−0.999965	+	0.00835511i	$0.997340\pi$
$198$	−2.04684	−	2.04684i	−0.145463	−	0.145463i
$199$	7.18567	−	7.18567i	0.509379	−	0.509379i	−0.404957	−	0.914336i	$-0.632713\pi$
$199$	7.18567	−	7.18567i	0.509379	−	0.509379i	0.914336	+	0.404957i	$0.132713\pi$
$200$	4.43410			0.313538
$201$	11.6366	−	11.6366i	0.820784	−	0.820784i
$202$			7.64630i			0.537991i
$203$	−15.5991			−1.09485
$204$	−13.5792	+	5.94058i	−0.950738	+	0.415924i
$205$	19.8736			1.38803
$206$			11.5043i			0.801543i
$207$	0.273066	−	0.273066i	0.0189794	−	0.0189794i
$208$	−2.89317			−0.200605
$209$	13.5633	−	13.5633i	0.938194	−	0.938194i
$210$	3.69643	+	3.69643i	0.255078	+	0.255078i
$211$	9.31170	+	9.31170i	0.641044	+	0.641044i	0.950812	−	0.309768i	$-0.100251\pi$
$211$	9.31170	+	9.31170i	0.641044	+	0.641044i	−0.309768	+	0.950812i	$0.600251\pi$
$212$			16.5397i			1.13595i
$213$			27.9883i			1.91773i
$214$	8.73112	+	8.73112i	0.596847	+	0.596847i
$215$	1.22244	+	1.22244i	0.0833697	+	0.0833697i
$216$	−3.93217	+	3.93217i	−0.267550	+	0.267550i
$217$	−1.33613			−0.0907021
$218$	−6.03489	+	6.03489i	−0.408734	+	0.408734i
$219$			10.0065i			0.676175i
$220$	7.24862			0.488702
$221$	−5.77224	−	2.25884i	−0.388283	−	0.151946i
$222$	0.656506			0.0440618
$223$			20.0145i			1.34027i	0.742240	+	0.670134i	$0.233763\pi$
$223$			20.0145i			1.34027i	−0.742240	+	0.670134i	$0.766237\pi$
$224$	8.91506	−	8.91506i	0.595662	−	0.595662i
$225$	3.73144			0.248763
$226$	−1.16738	+	1.16738i	−0.0776530	+	0.0776530i
$227$	−3.41445	−	3.41445i	−0.226625	−	0.226625i	0.584656	−	0.811281i	$-0.301229\pi$
$227$	−3.41445	−	3.41445i	−0.226625	−	0.226625i	−0.811281	+	0.584656i	$0.801229\pi$
$228$	18.9715	+	18.9715i	1.25642	+	1.25642i
$229$		−	26.5552i		−	1.75482i	−0.479741	−	0.877410i	$-0.659270\pi$
$229$		−	26.5552i		−	1.75482i	0.479741	−	0.877410i	$-0.340730\pi$
$230$		−	0.218461i		−	0.0144049i
$231$	−9.05165	−	9.05165i	−0.595555	−	0.595555i
$232$	10.7578	+	10.7578i	0.706285	+	0.706285i
$233$	−9.04512	+	9.04512i	−0.592565	+	0.592565i	−0.938324	−	0.345758i	$-0.887622\pi$
$233$	−9.04512	+	9.04512i	−0.592565	+	0.592565i	0.345758	+	0.938324i	$0.387622\pi$
$234$	1.69324			0.110691
$235$	12.7302	−	12.7302i	0.830426	−	0.830426i
$236$		−	14.6649i		−	0.954605i
$237$	19.9491			1.29583
$238$	5.18379	−	2.26778i	0.336015	−	0.146998i
$239$	13.8793			0.897774			0.448887	−	0.893589i	$-0.351821\pi$
$239$	13.8793			0.897774			0.448887	+	0.893589i	$0.351821\pi$
$240$			7.33097i			0.473212i
$241$	−11.2476	+	11.2476i	−0.724524	+	0.724524i	−0.969523	−	0.244999i	$-0.921212\pi$
$241$	−11.2476	+	11.2476i	−0.724524	+	0.724524i	0.244999	+	0.969523i	$0.421212\pi$
$242$	−2.66806			−0.171510
$243$	−11.9810	+	11.9810i	−0.768581	+	0.768581i
$244$	8.49053	+	8.49053i	0.543551	+	0.543551i
$245$	−2.31087	−	2.31087i	−0.147636	−	0.147636i
$246$			15.3778i			0.980451i
$247$			11.2202i			0.713922i
$248$	0.921448	+	0.921448i	0.0585120	+	0.0585120i
$249$	−19.0603	−	19.0603i	−1.20790	−	1.20790i
$250$	5.20330	−	5.20330i	0.329086	−	0.329086i
$251$	−22.6531			−1.42985			−0.714926	−	0.699200i	$-0.753540\pi$
$251$	−22.6531			−1.42985			−0.714926	+	0.699200i	$0.753540\pi$
$252$	4.83787	−	4.83787i	0.304757	−	0.304757i
$253$			0.534958i			0.0336325i
$254$	−3.53905			−0.222060
$255$	−5.72366	+	14.6262i	−0.358430	+	0.915930i
$256$	−6.01705			−0.376065
$257$		−	19.7829i		−	1.23402i	−0.786953	−	0.617012i	$-0.788343\pi$
$257$		−	19.7829i		−	1.23402i	0.786953	−	0.617012i	$-0.211657\pi$
$258$	−0.945900	+	0.945900i	−0.0588891	+	0.0588891i
$259$	1.10936			0.0689324
$260$	−2.99819	+	2.99819i	−0.185940	+	0.185940i
$261$	9.05305	+	9.05305i	0.560370	+	0.560370i
$262$	−4.66762	−	4.66762i	−0.288367	−	0.288367i
$263$			7.57272i			0.466954i	0.972362	+	0.233477i	$0.0750104\pi$
$263$			7.57272i			0.466954i	−0.972362	+	0.233477i	$0.924990\pi$
$264$			12.4848i			0.768385i
$265$	12.3932	+	12.3932i	0.761310	+	0.761310i
$266$	−7.24223	−	7.24223i	−0.444049	−	0.444049i
$267$	−5.08413	+	5.08413i	−0.311144	+	0.311144i
$268$	−12.1845			−0.744286
$269$	−3.23675	+	3.23675i	−0.197348	+	0.197348i	−0.798862	−	0.601514i	$-0.794564\pi$
$269$	−3.23675	+	3.23675i	−0.197348	+	0.197348i	0.601514	+	0.798862i	$0.294564\pi$
$270$			2.64735i			0.161112i
$271$	−4.40571			−0.267628			−0.133814	−	0.991006i	$-0.542722\pi$
$271$	−4.40571			−0.267628			−0.133814	+	0.991006i	$0.542722\pi$
$272$	7.38919	+	2.89160i	0.448035	+	0.175329i
$273$	7.48792			0.453189
$274$			4.22079i			0.254987i
$275$	−3.65510	+	3.65510i	−0.220411	+	0.220411i
$276$	−0.748265			−0.0450402
$277$	−9.61524	+	9.61524i	−0.577724	+	0.577724i	−0.934276	−	0.356552i	$-0.883952\pi$
$277$	−9.61524	+	9.61524i	−0.577724	+	0.577724i	0.356552	+	0.934276i	$0.383952\pi$
$278$	−9.09537	−	9.09537i	−0.545504	−	0.545504i
$279$	0.775428	+	0.775428i	0.0464237	+	0.0464237i
$280$		−	8.61529i		−	0.514862i
$281$			11.3210i			0.675352i	0.941262	+	0.337676i	$0.109641\pi$
$281$			11.3210i			0.675352i	−0.941262	+	0.337676i	$0.890359\pi$
$282$	9.85037	+	9.85037i	0.586581	+	0.586581i
$283$	−1.96277	−	1.96277i	−0.116674	−	0.116674i	0.646359	−	0.763033i	$-0.276291\pi$
$283$	−1.96277	−	1.96277i	−0.116674	−	0.116674i	−0.763033	+	0.646359i	$0.776291\pi$
$284$	14.6530	−	14.6530i	0.869495	−	0.869495i
$285$	28.4307			1.68409
$286$	−1.65860	+	1.65860i	−0.0980750	+	0.0980750i
$287$			25.9853i			1.53386i
$288$	−10.3478			−0.609751
$289$	12.4848	+	11.5382i	0.734398	+	0.678719i
$290$	7.24274			0.425308
$291$		−	24.5350i		−	1.43827i
$292$	5.23879	−	5.23879i	0.306577	−	0.306577i
$293$	23.9044			1.39651			0.698256	−	0.715848i	$-0.253960\pi$
$293$	23.9044			1.39651			0.698256	+	0.715848i	$0.253960\pi$
$294$	1.78810	−	1.78810i	0.104284	−	0.104284i
$295$	−10.9884	−	10.9884i	−0.639771	−	0.639771i
$296$	−0.765062	−	0.765062i	−0.0444683	−	0.0444683i
$297$		−	6.48270i		−	0.376165i
$298$			5.58855i			0.323736i
$299$	−0.221270	−	0.221270i	−0.0127964	−	0.0127964i
$300$	−5.11252	−	5.11252i	−0.295171	−	0.295171i
$301$	−1.59838	+	1.59838i	−0.0921290	+	0.0921290i
$302$	−6.74398			−0.388072
$303$	19.6240	−	19.6240i	1.12737	−	1.12737i
$304$		−	14.3632i		−	0.823787i
$305$	12.7239			0.728570
$306$	−4.32456	−	1.69232i	−0.247219	−	0.0967436i
$307$	−18.9343			−1.08064			−0.540318	−	0.841461i	$-0.681696\pi$
$307$	−18.9343			−1.08064			−0.540318	+	0.841461i	$0.681696\pi$
$308$			9.47780i			0.540048i
$309$	29.5255	−	29.5255i	1.67965	−	1.67965i
$310$	0.620368			0.0352345
$311$	−11.1072	+	11.1072i	−0.629829	+	0.629829i	−0.948025	−	0.318196i	$-0.896923\pi$
$311$	−11.1072	+	11.1072i	−0.629829	+	0.629829i	0.318196	+	0.948025i	$0.396923\pi$
$312$	−5.16398	−	5.16398i	−0.292353	−	0.292353i
$313$	4.55732	+	4.55732i	0.257595	+	0.257595i	0.824075	−	0.566480i	$-0.191695\pi$
$313$	4.55732	+	4.55732i	0.257595	+	0.257595i	−0.566480	+	0.824075i	$0.691695\pi$
$314$			4.19200i			0.236568i
$315$		−	7.25005i		−	0.408494i
$316$	−10.4442	−	10.4442i	−0.587530	−	0.587530i
$317$	−0.783803	−	0.783803i	−0.0440228	−	0.0440228i	0.684753	−	0.728775i	$-0.259910\pi$
$317$	−0.783803	−	0.783803i	−0.0440228	−	0.0440228i	−0.728775	+	0.684753i	$0.759910\pi$
$318$	−9.58963	+	9.58963i	−0.537760	+	0.537760i
$319$	−17.7357			−0.993008
$320$	0.565824	−	0.565824i	0.0316305	−	0.0316305i
$321$		−	44.8164i		−	2.50141i
$322$	0.285645			0.0159184
$323$	11.2141	−	28.6565i	0.623968	−	1.59449i
$324$	18.1478			1.00821
$325$		−	3.02366i		−	0.167723i
$326$	−0.896557	+	0.896557i	−0.0496557	+	0.0496557i
$327$	30.9768			1.71302
$328$	17.9206	−	17.9206i	0.989497	−	0.989497i
$329$	16.6451	+	16.6451i	0.917675	+	0.917675i
$330$	4.20271	+	4.20271i	0.231352	+	0.231352i
$331$		−	19.7331i		−	1.08463i	−0.840175	−	0.542315i	$-0.817548\pi$
$331$		−	19.7331i		−	1.08463i	0.840175	−	0.542315i	$-0.182452\pi$
$332$			19.9577i			1.09532i
$333$	−0.643824	−	0.643824i	−0.0352814	−	0.0352814i
$334$	−5.54113	−	5.54113i	−0.303197	−	0.303197i
$335$	−9.12985	+	9.12985i	−0.498817	+	0.498817i
$336$	−9.58547			−0.522930
$337$	12.0688	−	12.0688i	0.657427	−	0.657427i	−0.297344	−	0.954771i	$-0.596101\pi$
$337$	12.0688	−	12.0688i	0.657427	−	0.657427i	0.954771	+	0.297344i	$0.0961007\pi$
$338$			6.52012i			0.354648i
$339$	5.99210			0.325446
$340$	10.6540	−	4.66085i	0.577794	−	0.252770i
$341$	−1.51913			−0.0822655
$342$			8.40614i			0.454552i
$343$	14.2102	−	14.2102i	0.767278	−	0.767278i
$344$	2.20462			0.118865
$345$	−0.560675	+	0.560675i	−0.0301858	+	0.0301858i
$346$	−3.96885	−	3.96885i	−0.213367	−	0.213367i
$347$	−4.40415	−	4.40415i	−0.236427	−	0.236427i	0.578942	−	0.815369i	$-0.303466\pi$
$347$	−4.40415	−	4.40415i	−0.236427	−	0.236427i	−0.815369	+	0.578942i	$0.803466\pi$
$348$		−	24.8075i		−	1.32982i
$349$			4.04627i			0.216592i	0.994119	+	0.108296i	$0.0345394\pi$
$349$			4.04627i			0.216592i	−0.994119	+	0.108296i	$0.965461\pi$
$350$	1.95167	+	1.95167i	0.104321	+	0.104321i
$351$	2.68139	+	2.68139i	0.143122	+	0.143122i
$352$	10.1361	−	10.1361i	0.540257	−	0.540257i
$353$	22.7174			1.20912			0.604562	−	0.796558i	$-0.293348\pi$
$353$	22.7174			1.20912			0.604562	+	0.796558i	$0.293348\pi$
$354$	8.50263	−	8.50263i	0.451910	−	0.451910i
$355$		−	21.9590i		−	1.16546i
$356$	5.32349			0.282145
$357$	−19.1243	−	7.48386i	−1.01216	−	0.396088i
$358$	−4.21679			−0.222864
$359$			29.0548i			1.53346i	0.641973	+	0.766728i	$0.278116\pi$
$359$			29.0548i			1.53346i	−0.641973	+	0.766728i	$0.721884\pi$
$360$	−4.99993	+	4.99993i	−0.263520	+	0.263520i
$361$	−36.7028			−1.93173
$362$	1.89897	−	1.89897i	0.0998079	−	0.0998079i
$363$	6.84752	+	6.84752i	0.359402	+	0.359402i
$364$	−3.92023	−	3.92023i	−0.205476	−	0.205476i
$365$		−	7.85086i		−	0.410933i
$366$			9.84553i			0.514634i
$367$	10.4191	+	10.4191i	0.543874	+	0.543874i	0.924662	−	0.380788i	$-0.124347\pi$
$367$	10.4191	+	10.4191i	0.543874	+	0.543874i	−0.380788	+	0.924662i	$0.624347\pi$
$368$	0.283254	+	0.283254i	0.0147656	+	0.0147656i
$369$	15.0807	−	15.0807i	0.785072	−	0.785072i
$370$	−0.515080			−0.0267778
$371$	−16.2045	+	16.2045i	−0.841297	+	0.841297i
$372$		−	2.12486i		−	0.110169i
$373$	−20.4342			−1.05804			−0.529021	−	0.848609i	$-0.677441\pi$
$373$	−20.4342			−1.05804			−0.529021	+	0.848609i	$0.677441\pi$
$374$	5.89379	−	2.57838i	0.304760	−	0.133325i
$375$	−26.7083			−1.37921
$376$		−	22.9583i		−	1.18399i
$377$	7.33587	−	7.33587i	0.377817	−	0.377817i
$378$	−3.46149			−0.178040
$379$	5.78134	−	5.78134i	0.296968	−	0.296968i	−0.542857	−	0.839825i	$-0.682658\pi$
$379$	5.78134	−	5.78134i	0.296968	−	0.296968i	0.839825	+	0.542857i	$0.182658\pi$
$380$	−14.8846	−	14.8846i	−0.763564	−	0.763564i
$381$	9.08289	+	9.08289i	0.465331	+	0.465331i
$382$			15.5491i			0.795562i
$383$		−	16.4501i		−	0.840559i	−0.907395	−	0.420279i	$-0.861932\pi$
$383$		−	16.4501i		−	0.840559i	0.907395	−	0.420279i	$-0.138068\pi$
$384$	17.8185	+	17.8185i	0.909295	+	0.909295i
$385$	7.10173	+	7.10173i	0.361938	+	0.361938i
$386$	−1.55737	+	1.55737i	−0.0792683	+	0.0792683i
$387$	1.85526			0.0943080
$388$	−12.8450	+	12.8450i	−0.652108	+	0.652108i
$389$			18.6919i			0.947716i	0.880601	+	0.473858i	$0.157139\pi$
$389$			18.6919i			0.947716i	−0.880601	+	0.473858i	$0.842861\pi$
$390$	−3.47667			−0.176048
$391$	0.343977	+	0.786278i	0.0173957	+	0.0397638i
$392$	−4.16755			−0.210493
$393$			23.9587i			1.20856i
$394$	−8.44944	+	8.44944i	−0.425677	+	0.425677i
$395$	−15.6517			−0.787520
$396$	5.50050	−	5.50050i	0.276410	−	0.276410i
$397$	0.871063	+	0.871063i	0.0437174	+	0.0437174i	0.728628	−	0.684910i	$-0.240159\pi$
$397$	0.871063	+	0.871063i	0.0437174	+	0.0437174i	−0.684910	+	0.728628i	$0.740159\pi$
$398$	−4.36236	−	4.36236i	−0.218665	−	0.218665i
$399$			37.1740i			1.86103i
$400$			3.87067i			0.193533i
$401$	−23.2787	−	23.2787i	−1.16248	−	1.16248i	−0.983930	−	0.178553i	$-0.942858\pi$
$401$	−23.2787	−	23.2787i	−1.16248	−	1.16248i	−0.178553	−	0.983930i	$-0.557142\pi$
$402$	−7.06450	−	7.06450i	−0.352345	−	0.352345i
$403$	0.628345	−	0.628345i	0.0313001	−	0.0313001i
$404$	−20.5479			−1.02230
$405$	13.5982	−	13.5982i	0.675698	−	0.675698i
$406$			9.47010i			0.469993i
$407$	1.26131			0.0625206
$408$	8.02769	+	18.3501i	0.397430	+	0.908463i
$409$	36.2816			1.79401			0.897005	−	0.442020i	$-0.145738\pi$
$409$	36.2816			1.79401			0.897005	+	0.442020i	$0.145738\pi$
$410$		−	12.0651i		−	0.595852i
$411$	10.8326	−	10.8326i	0.534331	−	0.534331i
$412$	−30.9156			−1.52310
$413$	14.3677	−	14.3677i	0.706989	−	0.706989i
$414$	−0.165776	−	0.165776i	−0.00814743	−	0.00814743i
$415$	14.9543	+	14.9543i	0.734079	+	0.734079i
$416$			8.38504i			0.411110i
$417$			46.6861i			2.28623i
$418$	−8.23416	−	8.23416i	−0.402746	−	0.402746i
$419$	−7.44979	−	7.44979i	−0.363946	−	0.363946i	0.501317	−	0.865263i	$-0.332849\pi$
$419$	−7.44979	−	7.44979i	−0.363946	−	0.363946i	−0.865263	+	0.501317i	$0.832849\pi$
$420$	−9.93343	+	9.93343i	−0.484702	+	0.484702i
$421$	−4.25553			−0.207402			−0.103701	−	0.994609i	$-0.533069\pi$
$421$	−4.25553			−0.207402			−0.103701	+	0.994609i	$0.533069\pi$
$422$	5.65305	−	5.65305i	0.275186	−	0.275186i
$423$		−	19.3202i		−	0.939379i
$424$	22.3506			1.08544
$425$	−3.02202	+	7.72248i	−0.146590	+	0.374595i
$426$	16.9914			0.823238
$427$			16.6369i			0.805118i
$428$	−23.4632	+	23.4632i	−1.13414	+	1.13414i
$429$	8.51351			0.411036
$430$	0.742133	−	0.742133i	0.0357888	−	0.0357888i
$431$	11.0502	+	11.0502i	0.532267	+	0.532267i	0.921247	−	0.388979i	$-0.127172\pi$
$431$	11.0502	+	11.0502i	0.532267	+	0.532267i	−0.388979	+	0.921247i	$0.627172\pi$
$432$	−3.43251	−	3.43251i	−0.165147	−	0.165147i
$433$			19.9841i			0.960376i	0.877166	+	0.480188i	$0.159432\pi$
$433$			19.9841i			0.960376i	−0.877166	+	0.480188i	$0.840568\pi$
$434$			0.811150i			0.0389365i
$435$	−18.5883	−	18.5883i	−0.891241	−	0.891241i
$436$	−16.2176	−	16.2176i	−0.776682	−	0.776682i
$437$	1.09850	−	1.09850i	0.0525486	−	0.0525486i
$438$	6.07484			0.290267
$439$	0.748559	−	0.748559i	0.0357268	−	0.0357268i	−0.689018	−	0.724744i	$-0.741958\pi$
$439$	0.748559	−	0.748559i	0.0357268	−	0.0357268i	0.724744	+	0.689018i	$0.241958\pi$
$440$		−	9.79529i		−	0.466972i
$441$	−3.50713			−0.167006
$442$	−1.37132	+	3.50428i	−0.0652272	+	0.166681i
$443$	−11.1441			−0.529472			−0.264736	−	0.964321i	$-0.585285\pi$
$443$	−11.1441			−0.529472			−0.264736	+	0.964321i	$0.585285\pi$
$444$			1.76423i			0.0837268i
$445$	3.98890	−	3.98890i	0.189092	−	0.189092i
$446$	12.1506			0.575348
$447$	14.3429	−	14.3429i	0.678394	−	0.678394i
$448$	0.739832	+	0.739832i	0.0349538	+	0.0349538i
$449$	7.82489	+	7.82489i	0.369280	+	0.369280i	0.867214	−	0.497935i	$-0.165908\pi$
$449$	7.82489	+	7.82489i	0.369280	+	0.369280i	−0.497935	+	0.867214i	$0.665908\pi$
$450$		−	2.26533i		−	0.106788i
$451$			29.5444i			1.39119i
$452$	−3.13711	−	3.13711i	−0.147557	−	0.147557i
$453$	17.3082	+	17.3082i	0.813212	+	0.813212i
$454$	−2.07288	+	2.07288i	−0.0972853	+	0.0972853i
$455$	−5.87486			−0.275418
$456$	25.6367	−	25.6367i	1.20055	−	1.20055i
$457$		−	26.8836i		−	1.25756i	−0.777583	−	0.628780i	$-0.783555\pi$
$457$		−	26.8836i		−	1.25756i	0.777583	−	0.628780i	$-0.216445\pi$
$458$	−16.1215			−0.753306
$459$	−4.16837	−	9.52824i	−0.194563	−	0.444740i
$460$	0.587072			0.0273724
$461$			16.1809i			0.753619i	0.926291	+	0.376810i	$0.122979\pi$
$461$			16.1809i			0.753619i	−0.926291	+	0.376810i	$0.877021\pi$
$462$	−5.49517	+	5.49517i	−0.255659	+	0.255659i
$463$	25.1685			1.16968			0.584839	−	0.811149i	$-0.301158\pi$
$463$	25.1685			1.16968			0.584839	+	0.811149i	$0.301158\pi$
$464$	−9.39083	+	9.39083i	−0.435958	+	0.435958i
$465$	−1.59216	−	1.59216i	−0.0738346	−	0.0738346i
$466$	5.49121	+	5.49121i	0.254375	+	0.254375i
$467$		−	15.6154i		−	0.722594i	−0.932451	−	0.361297i	$-0.882334\pi$
$467$		−	15.6154i		−	0.722594i	0.932451	−	0.361297i	$-0.117666\pi$
$468$			4.55025i			0.210336i
$469$	−11.9376	−	11.9376i	−0.551225	−	0.551225i
$470$	−7.72839	−	7.72839i	−0.356484	−	0.356484i
$471$	10.7587	−	10.7587i	0.495733	−	0.495733i
$472$	−19.8172			−0.912158
$473$	−1.81730	+	1.81730i	−0.0835596	+	0.0835596i
$474$		−	12.1109i		−	0.556274i
$475$	15.0111			0.688755
$476$	6.09421	+	13.9304i	0.279328	+	0.638500i
$477$	18.8088			0.861195
$478$		−	8.42597i		−	0.385395i
$479$	3.25616	−	3.25616i	0.148778	−	0.148778i	−0.628794	−	0.777572i	$-0.716451\pi$
$479$	3.25616	−	3.25616i	0.148778	−	0.148778i	0.777572	+	0.628794i	$0.216451\pi$
$480$	21.2468			0.969779
$481$	−0.521704	+	0.521704i	−0.0237876	+	0.0237876i
$482$	6.82834	+	6.82834i	0.311022	+	0.311022i
$483$	−0.733100	−	0.733100i	−0.0333572	−	0.0333572i
$484$		−	7.16991i		−	0.325905i
$485$			19.2496i			0.874080i
$486$	7.27355	+	7.27355i	0.329935	+	0.329935i
$487$	8.37042	+	8.37042i	0.379300	+	0.379300i	0.870850	−	0.491550i	$-0.163569\pi$
$487$	8.37042	+	8.37042i	0.379300	+	0.379300i	−0.491550	+	0.870850i	$0.663569\pi$
$488$	11.4735	−	11.4735i	0.519382	−	0.519382i
$489$	4.60198			0.208109
$490$	−1.40291	+	1.40291i	−0.0633770	+	0.0633770i
$491$			2.22261i			0.100305i	0.998742	+	0.0501525i	$0.0159707\pi$
$491$			2.22261i			0.100305i	−0.998742	+	0.0501525i	$0.984029\pi$
$492$	−41.3248			−1.86307
$493$	−26.0678	+	11.4040i	−1.17404	+	0.513611i
$494$	6.81166			0.306471
$495$		−	8.24306i		−	0.370498i
$496$	−0.804360	+	0.804360i	−0.0361168	+	0.0361168i
$497$	28.7121			1.28791
$498$	−11.5714	+	11.5714i	−0.518525	+	0.518525i
$499$	−3.96839	−	3.96839i	−0.177650	−	0.177650i	0.612681	−	0.790330i	$-0.290091\pi$
$499$	−3.96839	−	3.96839i	−0.177650	−	0.177650i	−0.790330	+	0.612681i	$0.790091\pi$
$500$	13.9829	+	13.9829i	0.625333	+	0.625333i
$501$			28.4423i			1.27071i
$502$			13.7525i			0.613805i
$503$	9.19229	+	9.19229i	0.409864	+	0.409864i	0.881691	−	0.471827i	$-0.156405\pi$
$503$	9.19229	+	9.19229i	0.409864	+	0.409864i	−0.471827	+	0.881691i	$0.656405\pi$
$504$	−6.53757	−	6.53757i	−0.291207	−	0.291207i
$505$	−15.3966	+	15.3966i	−0.685139	+	0.685139i
$506$	0.324768			0.0144377
$507$	16.7337	−	16.7337i	0.743171	−	0.743171i
$508$		−	9.51052i		−	0.421961i
$509$	28.7469			1.27418			0.637092	−	0.770788i	$-0.280137\pi$
$509$	28.7469			1.27418			0.637092	+	0.770788i	$0.280137\pi$
$510$	8.87946	+	3.47478i	0.393189	+	0.153866i
$511$	10.2652			0.454108
$512$		−	19.2194i		−	0.849384i
$513$	−13.3118	+	13.3118i	−0.587732	+	0.587732i
$514$	−12.0100			−0.529740
$515$	−23.1651	+	23.1651i	−1.02078	+	1.02078i
$516$	−2.54192	−	2.54192i	−0.111902	−	0.111902i
$517$	18.9249	+	18.9249i	0.832317	+	0.832317i
$518$		−	0.673484i		−	0.0295912i
$519$			20.3719i			0.894228i
$520$	4.05155	+	4.05155i	0.177672	+	0.177672i
$521$	3.31281	+	3.31281i	0.145137	+	0.145137i	0.775942	−	0.630805i	$-0.217275\pi$
$521$	3.31281	+	3.31281i	0.145137	+	0.145137i	−0.630805	+	0.775942i	$0.717275\pi$
$522$	5.49603	−	5.49603i	0.240555	−	0.240555i
$523$	7.38069			0.322735			0.161367	−	0.986894i	$-0.448410\pi$
$523$	7.38069			0.322735			0.161367	+	0.986894i	$0.448410\pi$
$524$	12.5433	−	12.5433i	0.547958	−	0.547958i
$525$		−	10.0178i		−	0.437214i
$526$	4.59733			0.200453
$527$	−2.23281	+	0.976798i	−0.0972626	+	0.0425500i
$528$	−10.8984			−0.474290
$529$		−	22.9567i		−	0.998116i
$530$	7.52382	−	7.52382i	0.326814	−	0.326814i
$531$	−16.6768			−0.723711
$532$	19.4621	−	19.4621i	0.843788	−	0.843788i
$533$	−12.2202	−	12.2202i	−0.529316	−	0.529316i
$534$	3.08653	+	3.08653i	0.133567	+	0.133567i
$535$			35.1620i			1.52018i
$536$			16.4653i			0.711192i
$537$	10.8223	+	10.8223i	0.467016	+	0.467016i
$538$	1.96500	+	1.96500i	0.0847173	+	0.0847173i
$539$	3.43538	−	3.43538i	0.147972	−	0.147972i
$540$	−7.11423			−0.306148
$541$	−26.6404	+	26.6404i	−1.14536	+	1.14536i	−0.157906	+	0.987454i	$0.550474\pi$
$541$	−26.6404	+	26.6404i	−1.14536	+	1.14536i	−0.987454	+	0.157906i	$0.949526\pi$
$542$			2.67467i			0.114887i
$543$	−9.74734			−0.418298
$544$	8.38050	−	21.4155i	0.359311	−	0.918182i
$545$	−24.3037			−1.04106
$546$		−	4.54585i		−	0.194544i
$547$	−1.65411	+	1.65411i	−0.0707245	+	0.0707245i	−0.741584	−	0.670860i	$-0.765925\pi$
$547$	−1.65411	+	1.65411i	−0.0707245	+	0.0707245i	0.670860	+	0.741584i	$0.265925\pi$
$548$	−11.3426			−0.484530
$549$	9.65534	−	9.65534i	0.412080	−	0.412080i
$550$	2.21898	+	2.21898i	0.0946177	+	0.0946177i
$551$	36.4192	+	36.4192i	1.55151	+	1.55151i
$552$			1.01115i			0.0430375i
$553$		−	20.4650i		−	0.870261i
$554$	5.83733	+	5.83733i	0.248004	+	0.248004i
$555$	1.32194	+	1.32194i	0.0561133	+	0.0561133i
$556$	24.4421	−	24.4421i	1.03657	−	1.03657i
$557$	5.34923			0.226654			0.113327	−	0.993558i	$-0.463849\pi$
$557$	5.34923			0.226654			0.113327	+	0.993558i	$0.463849\pi$
$558$	0.470756	−	0.470756i	0.0199287	−	0.0199287i
$559$		−	1.50335i		−	0.0635850i
$560$	7.52056			0.317801
$561$	−21.7436	−	8.50890i	−0.918016	−	0.359246i
$562$	6.87286			0.289914
$563$			10.2392i			0.431530i	0.976445	+	0.215765i	$0.0692245\pi$
$563$			10.2392i			0.431530i	−0.976445	+	0.215765i	$0.930775\pi$
$564$	−26.4709	+	26.4709i	−1.11463	+	1.11463i
$565$	−4.70128			−0.197784
$566$	−1.19158	+	1.19158i	−0.0500858	+	0.0500858i
$567$	17.7800	+	17.7800i	0.746691	+	0.746691i
$568$	−19.8010	−	19.8010i	−0.830834	−	0.830834i
$569$			18.7248i			0.784984i	0.919755	+	0.392492i	$0.128387\pi$
$569$			18.7248i			0.784984i	−0.919755	+	0.392492i	$0.871613\pi$
$570$		−	17.2600i		−	0.722943i
$571$	−13.9725	−	13.9725i	−0.584731	−	0.584731i	0.351469	−	0.936200i	$-0.385682\pi$
$571$	−13.9725	−	13.9725i	−0.584731	−	0.584731i	−0.936200	+	0.351469i	$0.885682\pi$
$572$	−4.45716	−	4.45716i	−0.186363	−	0.186363i
$573$	39.9064	−	39.9064i	1.66711	−	1.66711i
$574$	15.7755			0.658455
$575$	−0.296030	+	0.296030i	−0.0123453	+	0.0123453i
$576$		−	0.858732i		−	0.0357805i
$577$	−36.6979			−1.52775			−0.763877	−	0.645361i	$-0.776707\pi$
$577$	−36.6979			−1.52775			−0.763877	+	0.645361i	$0.776707\pi$
$578$	7.00476	−	7.57939i	0.291359	−	0.315261i
$579$	7.99393			0.332216
$580$			19.4635i			0.808176i
$581$	−19.5532	+	19.5532i	−0.811205	+	0.811205i
$582$	−14.8950			−0.617416
$583$	−18.4240	+	18.4240i	−0.763043	+	0.763043i
$584$	−7.07934	−	7.07934i	−0.292945	−	0.292945i
$585$	3.40951	+	3.40951i	0.140966	+	0.140966i
$586$		−	14.5122i		−	0.599492i
$587$		−	35.7865i		−	1.47707i	−0.674216	−	0.738534i	$-0.735518\pi$
$587$		−	35.7865i		−	1.47707i	0.674216	−	0.738534i	$-0.264482\pi$
$588$	4.80519	+	4.80519i	0.198163	+	0.198163i
$589$	3.11944	+	3.11944i	0.128534	+	0.128534i
$590$	−6.67098	+	6.67098i	−0.274640	+	0.274640i
$591$	43.3706			1.78403
$592$	0.667846	−	0.667846i	0.0274483	−	0.0274483i
$593$		−	8.84364i		−	0.363165i	−0.983376	−	0.181582i	$-0.941878\pi$
$593$		−	8.84364i		−	0.363165i	0.983376	−	0.181582i	$-0.0581219\pi$
$594$	−3.93559			−0.161479
$595$	15.0045	+	5.87168i	0.615124	+	0.240715i
$596$	−15.0181			−0.615167
$597$			22.3918i			0.916435i
$598$	−0.134331	+	0.134331i	−0.00549322	+	0.00549322i
$599$	−12.5087			−0.511091			−0.255545	−	0.966797i	$-0.582255\pi$
$599$	−12.5087			−0.511091			−0.255545	+	0.966797i	$0.582255\pi$
$600$	−6.90871	+	6.90871i	−0.282047	+	0.282047i
$601$	6.90770	+	6.90770i	0.281771	+	0.281771i	0.833815	−	0.552044i	$-0.186152\pi$
$601$	6.90770	+	6.90770i	0.281771	+	0.281771i	−0.552044	+	0.833815i	$0.686152\pi$
$602$	0.970361	+	0.970361i	0.0395490	+	0.0395490i
$603$			13.8561i			0.564263i
$604$		−	18.1231i		−	0.737420i
$605$	−5.37242	−	5.37242i	−0.218420	−	0.218420i
$606$	−11.9136	−	11.9136i	−0.483956	−	0.483956i
$607$	4.23962	−	4.23962i	0.172081	−	0.172081i	−0.615812	−	0.787893i	$-0.711172\pi$
$607$	4.23962	−	4.23962i	0.172081	−	0.172081i	0.787893	+	0.615812i	$0.211172\pi$
$608$	−41.6278			−1.68823
$609$	24.3048	−	24.3048i	0.984880	−	0.984880i
$610$		−	7.72459i		−	0.312759i
$611$	−15.6555			−0.633355
$612$	4.54779	−	11.6214i	0.183833	−	0.469768i
$613$	−19.8738			−0.802697			−0.401348	−	0.915926i	$-0.631458\pi$
$613$	−19.8738			−0.802697			−0.401348	+	0.915926i	$0.631458\pi$
$614$			11.4948i			0.463893i
$615$	−30.9647	+	30.9647i	−1.24862	+	1.24862i
$616$	12.8076			0.516035
$617$	−12.5652	+	12.5652i	−0.505856	+	0.505856i	−0.913252	−	0.407395i	$-0.866437\pi$
$617$	−12.5652	+	12.5652i	−0.505856	+	0.505856i	0.407395	+	0.913252i	$0.366437\pi$
$618$	−17.9247	−	17.9247i	−0.721037	−	0.721037i
$619$	14.3199	+	14.3199i	0.575564	+	0.575564i	0.933678	−	0.358114i	$-0.116580\pi$
$619$	14.3199	+	14.3199i	0.575564	+	0.575564i	−0.358114	+	0.933678i	$0.616580\pi$
$620$			1.66712i			0.0669531i
$621$		−	0.525040i		−	0.0210691i
$622$	6.74306	+	6.74306i	0.270372	+	0.270372i
$623$	5.21561	+	5.21561i	0.208959	+	0.208959i
$624$	4.50780	−	4.50780i	0.180456	−	0.180456i
$625$	10.8983			0.435934
$626$	2.76671	−	2.76671i	0.110580	−	0.110580i
$627$			42.2656i			1.68792i
$628$	−11.2652			−0.449530
$629$	1.85386	−	0.811018i	0.0739183	−	0.0323374i
$630$	−4.40144			−0.175358
$631$		−	39.7304i		−	1.58164i	−0.612047	−	0.790822i	$-0.709654\pi$
$631$		−	39.7304i		−	1.58164i	0.612047	−	0.790822i	$-0.290346\pi$
$632$	−14.1135	+	14.1135i	−0.561406	+	0.561406i
$633$	−29.0168			−1.15332
$634$	−0.475840	+	0.475840i	−0.0188980	+	0.0188980i
$635$	−7.12624	−	7.12624i	−0.282796	−	0.282796i
$636$	−25.7703	−	25.7703i	−1.02186	−	1.02186i
$637$			2.84190i			0.112600i
$638$			10.7672i			0.426277i
$639$	−16.6632	−	16.6632i	−0.659187	−	0.659187i
$640$	−13.9800	−	13.9800i	−0.552607	−	0.552607i
$641$	11.8463	−	11.8463i	0.467900	−	0.467900i	−0.433334	−	0.901234i	$-0.642663\pi$
$641$	11.8463	−	11.8463i	0.467900	−	0.467900i	0.901234	+	0.433334i	$0.142663\pi$
$642$	−27.2076			−1.07380
$643$	−31.8191	+	31.8191i	−1.25482	+	1.25482i	−0.301293	+	0.953532i	$0.597418\pi$
$643$	−31.8191	+	31.8191i	−1.25482	+	1.25482i	−0.953532	+	0.301293i	$0.902582\pi$
$644$			0.767615i			0.0302483i
$645$	−3.80933			−0.149992
$646$	−17.3971	−	6.80797i	−0.684479	−	0.267856i
$647$	−17.1699			−0.675017			−0.337509	−	0.941322i	$-0.609584\pi$
$647$	−17.1699			−0.675017			−0.337509	+	0.941322i	$0.609584\pi$
$648$		−	24.5237i		−	0.963381i
$649$	16.3356	−	16.3356i	0.641229	−	0.641229i
$650$	−1.83564			−0.0719997
$651$	2.08180	−	2.08180i	0.0815921	−	0.0815921i
$652$	−2.40932	−	2.40932i	−0.0943564	−	0.0943564i
$653$	13.5509	+	13.5509i	0.530288	+	0.530288i	0.920658	−	0.390370i	$-0.127653\pi$
$653$	13.5509	+	13.5509i	0.530288	+	0.530288i	−0.390370	+	0.920658i	$0.627653\pi$
$654$		−	18.8057i		−	0.735363i
$655$		−	18.7975i		−	0.734478i
$656$	15.6434	+	15.6434i	0.610773	+	0.610773i
$657$	−5.95750	−	5.95750i	−0.232424	−	0.232424i
$658$	10.1051	−	10.1051i	0.393938	−	0.393938i
$659$	23.2177			0.904434			0.452217	−	0.891908i	$-0.350633\pi$
$659$	23.2177			0.904434			0.452217	+	0.891908i	$0.350633\pi$
$660$	−11.2940	+	11.2940i	−0.439617	+	0.439617i
$661$			6.11486i			0.237841i	0.992904	+	0.118920i	$0.0379433\pi$
$661$			6.11486i			0.237841i	−0.992904	+	0.118920i	$0.962057\pi$
$662$	−11.9798			−0.465608
$663$	12.5131	−	5.47417i	0.485969	−	0.212599i
$664$	26.9695			1.04662
$665$		−	29.1659i		−	1.13101i
$666$	−0.390860	+	0.390860i	−0.0151455	+	0.0151455i
$667$	−1.43643			−0.0556187
$668$	14.8907	−	14.8907i	0.576139	−	0.576139i
$669$	−31.1842	−	31.1842i	−1.20565	−	1.20565i
$670$	5.54265	+	5.54265i	0.214131	+	0.214131i
$671$			18.9156i			0.730230i
$672$			27.7808i			1.07167i
$673$	16.4537	+	16.4537i	0.634245	+	0.634245i	0.949130	−	0.314885i	$-0.101966\pi$
$673$	16.4537	+	16.4537i	0.634245	+	0.634245i	−0.314885	+	0.949130i	$0.601966\pi$
$674$	−7.32684	−	7.32684i	−0.282219	−	0.282219i
$675$	3.58734	−	3.58734i	0.138077	−	0.138077i
$676$	−17.5216			−0.673906
$677$	−3.67608	+	3.67608i	−0.141283	+	0.141283i	−0.774211	−	0.632928i	$-0.781853\pi$
$677$	−3.67608	+	3.67608i	−0.141283	+	0.141283i	0.632928	+	0.774211i	$0.281853\pi$
$678$		−	3.63775i		−	0.139707i
$679$	−25.1695			−0.965915
$680$	−6.29836	−	14.3971i	−0.241531	−	0.552102i
$681$	10.6400			0.407726
$682$			0.922250i			0.0353148i
$683$	24.0534	−	24.0534i	0.920377	−	0.920377i	−0.0766784	−	0.997056i	$-0.524431\pi$
$683$	24.0534	−	24.0534i	0.920377	−	0.920377i	0.997056	+	0.0766784i	$0.0244315\pi$
$684$	−22.5899			−0.863745
$685$	−8.49899	+	8.49899i	−0.324730	+	0.324730i
$686$	−8.62688	−	8.62688i	−0.329376	−	0.329376i
$687$	41.3753	+	41.3753i	1.57857	+	1.57857i
$688$			1.92448i			0.0733700i
$689$		−	15.2411i		−	0.580641i
$690$	0.340381	+	0.340381i	0.0129581	+	0.0129581i
$691$	−4.11944	−	4.11944i	−0.156711	−	0.156711i	0.624397	−	0.781107i	$-0.285345\pi$
$691$	−4.11944	−	4.11944i	−0.156711	−	0.156711i	−0.781107	+	0.624397i	$0.785345\pi$
$692$	10.6655	−	10.6655i	0.405442	−	0.405442i
$693$	10.7781			0.409424
$694$	−2.67372	+	2.67372i	−0.101493	+	0.101493i
$695$		−	36.6289i		−	1.38941i
$696$	−33.5232			−1.27069
$697$	18.9970	+	43.4242i	0.719563	+	1.64481i
$698$	2.45646			0.0929783
$699$		−	28.1861i		−	1.06610i
$700$	−5.24473	+	5.24473i	−0.198232	+	0.198232i
$701$	42.7894			1.61613			0.808067	−	0.589090i	$-0.200514\pi$
$701$	42.7894			1.61613			0.808067	+	0.589090i	$0.200514\pi$
$702$	1.62785	−	1.62785i	0.0614391	−	0.0614391i
$703$	−2.59001	−	2.59001i	−0.0976842	−	0.0976842i
$704$	0.841164	+	0.841164i	0.0317026	+	0.0317026i
$705$			39.6694i			1.49404i
$706$		−	13.7915i		−	0.519051i
$707$	−20.1315	−	20.1315i	−0.757124	−	0.757124i
$708$	22.8492	+	22.8492i	0.858725	+	0.858725i
$709$	−6.02606	+	6.02606i	−0.226314	+	0.226314i	−0.811151	−	0.584837i	$-0.801158\pi$
$709$	−6.02606	+	6.02606i	−0.226314	+	0.226314i	0.584837	+	0.811151i	$0.301158\pi$
$710$	−13.3311			−0.500308
$711$	−11.8770	+	11.8770i	−0.445422	+	0.445422i
$712$		−	7.19380i		−	0.269599i
$713$	−0.123036			−0.00460772
$714$	−4.54339	+	11.6102i	−0.170032	+	0.434500i
$715$	−6.67951			−0.249800
$716$		−	11.3318i		−	0.423489i
$717$	−21.6250	+	21.6250i	−0.807602	+	0.807602i
$718$	17.6389			0.658279
$719$	−3.55688	+	3.55688i	−0.132649	+	0.132649i	−0.770314	−	0.637665i	$-0.779901\pi$
$719$	−3.55688	+	3.55688i	−0.132649	+	0.132649i	0.637665	+	0.770314i	$0.279901\pi$
$720$	−4.36460	−	4.36460i	−0.162659	−	0.162659i
$721$	−30.2891	−	30.2891i	−1.12802	−	1.12802i
$722$			22.2820i			0.829249i
$723$		−	35.0495i		−	1.30351i
$724$	5.10312	+	5.10312i	0.189656	+	0.189656i
$725$	−9.81440	−	9.81440i	−0.364498	−	0.364498i
$726$	4.15707	−	4.15707i	0.154283	−	0.154283i
$727$	−53.1278			−1.97040			−0.985200	−	0.171409i	$-0.945168\pi$
$727$	−53.1278			−1.97040			−0.985200	+	0.171409i	$0.945168\pi$
$728$	−5.29752	+	5.29752i	−0.196339	+	0.196339i
$729$		−	3.96342i		−	0.146793i
$730$	−4.76619			−0.176405
$731$	−1.50254	+	3.83958i	−0.0555733	+	0.142012i
$732$	−26.4579			−0.977914
$733$		−	30.2797i		−	1.11841i	−0.829030	−	0.559204i	$-0.811107\pi$
$733$		−	30.2797i		−	1.11841i	0.829030	−	0.559204i	$-0.188893\pi$
$734$	6.32537	−	6.32537i	0.233474	−	0.233474i
$735$	7.20106			0.265615
$736$	0.820933	−	0.820933i	0.0302600	−	0.0302600i
$737$	−13.5726	−	13.5726i	−0.499953	−	0.499953i
$738$	−9.15538	−	9.15538i	−0.337014	−	0.337014i
$739$		−	27.7513i		−	1.02085i	−0.859923	−	0.510424i	$-0.829489\pi$
$739$		−	27.7513i		−	1.02085i	0.859923	−	0.510424i	$-0.170511\pi$
$740$		−	1.38418i		−	0.0508834i
$741$	−17.4820	−	17.4820i	−0.642216	−	0.642216i
$742$	9.83762	+	9.83762i	0.361150	+	0.361150i
$743$	−29.0195	+	29.0195i	−1.06462	+	1.06462i	−0.0668600	+	0.997762i	$0.521298\pi$
$743$	−29.0195	+	29.0195i	−1.06462	+	1.06462i	−0.997762	+	0.0668600i	$0.978702\pi$
$744$	−2.87139			−0.105270
$745$	−11.2531	+	11.2531i	−0.412282	+	0.412282i
$746$			12.4054i			0.454195i
$747$	22.6957			0.830392
$748$	6.92891	+	15.8384i	0.253346	+	0.579110i
$749$	−45.9754			−1.67990
$750$			16.2144i			0.592065i
$751$	−30.6501	+	30.6501i	−1.11844	+	1.11844i	−0.126468	+	0.991971i	$0.540364\pi$
$751$	−30.6501	+	30.6501i	−1.11844	+	1.11844i	−0.991971	+	0.126468i	$0.959636\pi$
$752$	20.0410			0.730821
$753$	35.2955	−	35.2955i	1.28624	−	1.28624i
$754$	−4.45354	−	4.45354i	−0.162188	−	0.162188i
$755$	−13.5797	−	13.5797i	−0.494215	−	0.494215i
$756$		−	9.30208i		−	0.338313i
$757$		−	8.87956i		−	0.322733i	−0.986895	−	0.161367i	$-0.948410\pi$
$757$		−	8.87956i		−	0.322733i	0.986895	−	0.161367i	$-0.0515901\pi$
$758$	−3.50980	−	3.50980i	−0.127482	−	0.127482i
$759$	−0.833510	−	0.833510i	−0.0302545	−	0.0302545i
$760$	−20.1140	+	20.1140i	−0.729613	+	0.729613i
$761$	5.86303			0.212535			0.106267	−	0.994338i	$-0.466110\pi$
$761$	5.86303			0.212535			0.106267	+	0.994338i	$0.466110\pi$
$762$	5.51414	−	5.51414i	0.199756	−	0.199756i
$763$		−	31.7779i		−	1.15044i
$764$	−41.7852			−1.51174
$765$	−5.30027	−	12.1156i	−0.191632	−	0.438040i
$766$	−9.98669			−0.360834
$767$			13.5135i			0.487945i
$768$	9.37507	−	9.37507i	0.338294	−	0.338294i
$769$	4.06930			0.146743			0.0733713	−	0.997305i	$-0.476624\pi$
$769$	4.06930			0.146743			0.0733713	+	0.997305i	$0.476624\pi$
$770$	4.31140	−	4.31140i	0.155372	−	0.155372i
$771$	30.8235	+	30.8235i	1.11008	+	1.11008i
$772$	−4.18514	−	4.18514i	−0.150627	−	0.150627i
$773$			32.6218i			1.17332i	0.809832	+	0.586662i	$0.199558\pi$
$773$			32.6218i			1.17332i	−0.809832	+	0.586662i	$0.800442\pi$
$774$		−	1.12631i		−	0.0404844i
$775$	−0.840641	−	0.840641i	−0.0301967	−	0.0301967i
$776$	17.3579	+	17.3579i	0.623112	+	0.623112i
$777$	−1.72848	+	1.72848i	−0.0620088	+	0.0620088i
$778$	11.3477			0.406834
$779$	60.6677	−	60.6677i	2.17364	−	2.17364i
$780$		−	9.34287i		−	0.334528i
$781$	32.6447			1.16812
$782$	0.477343	−	0.208826i	0.0170697	−	0.00746759i
$783$	17.4069			0.622071
$784$		−	3.63798i		−	0.129928i
$785$	−8.44102	+	8.44102i	−0.301273	+	0.301273i
$786$	14.5451			0.518807
$787$	−21.4707	+	21.4707i	−0.765349	+	0.765349i	−0.977284	−	0.211935i	$-0.932024\pi$
$787$	−21.4707	+	21.4707i	−0.765349	+	0.765349i	0.211935	+	0.977284i	$0.432024\pi$
$788$	−22.7062	−	22.7062i	−0.808876	−	0.808876i
$789$	−11.7989	−	11.7989i	−0.420053	−	0.420053i
$790$			9.50198i			0.338065i
$791$		−	6.14706i		−	0.218564i
$792$	−7.43299	−	7.43299i	−0.264120	−	0.264120i
$793$	−7.82392	−	7.82392i	−0.277835	−	0.277835i
$794$	0.528815	−	0.528815i	0.0187669	−	0.0187669i
$795$	−38.6194			−1.36969
$796$	11.7230	−	11.7230i	0.415511	−	0.415511i
$797$			15.5555i			0.551002i	0.961301	+	0.275501i	$0.0888438\pi$
$797$			15.5555i			0.551002i	−0.961301	+	0.275501i	$0.911156\pi$
$798$	22.5680			0.798899
$799$	39.9844	+	15.6471i	1.41455	+	0.553553i
$800$	11.2180			0.396618
$801$		−	6.05382i		−	0.213901i
$802$	−14.1323	+	14.1323i	−0.499029	+	0.499029i
$803$	11.6712			0.411869
$804$	18.9845	−	18.9845i	0.669530	−	0.669530i
$805$	0.575175	+	0.575175i	0.0202723	+	0.0202723i
$806$	−0.381463	−	0.381463i	−0.0134365	−	0.0134365i
$807$		−	10.0863i		−	0.355053i
$808$			27.7671i			0.976842i
$809$	−23.6810	−	23.6810i	−0.832580	−	0.832580i	0.155289	−	0.987869i	$-0.450369\pi$
$809$	−23.6810	−	23.6810i	−0.832580	−	0.832580i	−0.987869	+	0.155289i	$0.950369\pi$
$810$	−8.25533	−	8.25533i	−0.290063	−	0.290063i
$811$	32.9461	−	32.9461i	1.15690	−	1.15690i	0.171756	−	0.985140i	$-0.445056\pi$
$811$	32.9461	−	32.9461i	1.15690	−	1.15690i	0.985140	−	0.171756i	$-0.0549441\pi$
$812$	−25.4491			−0.893087
$813$	6.86447	−	6.86447i	0.240747	−	0.240747i
$814$		−	0.765728i		−	0.0268387i
$815$	−3.61062			−0.126474
$816$	−16.0183	+	7.00762i	−0.560754	+	0.245316i
$817$	7.46343			0.261112
$818$		−	22.0262i		−	0.770130i
$819$	−4.45804	+	4.45804i	−0.155777	+	0.155777i
$820$	32.4226			1.13224
$821$	−13.6435	+	13.6435i	−0.476160	+	0.476160i	−0.903901	−	0.427741i	$-0.859310\pi$
$821$	−13.6435	+	13.6435i	−0.476160	+	0.476160i	0.427741	+	0.903901i	$0.359310\pi$
$822$	−6.57635	−	6.57635i	−0.229377	−	0.229377i
$823$	−20.5462	−	20.5462i	−0.716196	−	0.716196i	0.251628	−	0.967824i	$-0.419034\pi$
$823$	−20.5462	−	20.5462i	−0.716196	−	0.716196i	−0.967824	+	0.251628i	$0.919034\pi$
$824$			41.7772i			1.45538i
$825$		−	11.3899i		−	0.396546i
$826$	−8.72252	−	8.72252i	−0.303495	−	0.303495i
$827$	13.1202	+	13.1202i	0.456234	+	0.456234i	0.897417	−	0.441183i	$-0.145441\pi$
$827$	13.1202	+	13.1202i	0.456234	+	0.456234i	−0.441183	+	0.897417i	$0.645441\pi$
$828$	0.445490	−	0.445490i	0.0154818	−	0.0154818i
$829$	−28.5865			−0.992852			−0.496426	−	0.868079i	$-0.665355\pi$
$829$	−28.5865			−0.992852			−0.496426	+	0.868079i	$0.665355\pi$
$830$	9.07864	−	9.07864i	0.315124	−	0.315124i
$831$		−	29.9627i		−	1.03939i
$832$	−0.695848			−0.0241242
$833$	2.84036	−	7.25825i	0.0984126	−	0.251483i
$834$	28.3427			0.981428
$835$		−	22.3152i		−	0.772251i
$836$	22.1277	−	22.1277i	0.765303	−	0.765303i
$837$	1.49096			0.0515352
$838$	−4.52270	+	4.52270i	−0.156234	+	0.156234i
$839$	−9.67736	−	9.67736i	−0.334099	−	0.334099i	0.520042	−	0.854141i	$-0.325916\pi$
$839$	−9.67736	−	9.67736i	−0.334099	−	0.334099i	−0.854141	+	0.520042i	$0.825916\pi$
$840$	13.4234	+	13.4234i	0.463150	+	0.463150i
$841$		−	18.6225i		−	0.642156i
$842$			2.58350i			0.0890332i
$843$	−17.6390	−	17.6390i	−0.607520	−	0.607520i
$844$	15.1915	+	15.1915i	0.522913	+	0.522913i
$845$	−13.1289	+	13.1289i	−0.451649	+	0.451649i
$846$	−11.7291			−0.403255
$847$	7.02460	−	7.02460i	0.241368	−	0.241368i
$848$			19.5105i			0.669995i
$849$	6.11632			0.209911
$850$	4.68825	+	1.83464i	0.160806	+	0.0629278i
$851$	0.102154			0.00350180
$852$			45.6612i			1.56433i
$853$	11.1947	−	11.1947i	0.383299	−	0.383299i	−0.488990	−	0.872289i	$-0.662635\pi$
$853$	11.1947	−	11.1947i	0.383299	−	0.383299i	0.872289	+	0.488990i	$0.162635\pi$
$854$	10.1001			0.345620
$855$	−16.9266	+	16.9266i	−0.578878	+	0.578878i
$856$	31.7065	+	31.7065i	1.08371	+	1.08371i
$857$	−9.34007	−	9.34007i	−0.319051	−	0.319051i	0.529352	−	0.848402i	$-0.322435\pi$
$857$	−9.34007	−	9.34007i	−0.319051	−	0.319051i	−0.848402	+	0.529352i	$0.822435\pi$
$858$		−	5.16848i		−	0.176449i
$859$			9.67939i			0.330256i	0.986272	+	0.165128i	$0.0528038\pi$
$859$			9.67939i			0.330256i	−0.986272	+	0.165128i	$0.947196\pi$
$860$	1.99434	+	1.99434i	0.0680064	+	0.0680064i
$861$	−40.4873	−	40.4873i	−1.37980	−	1.37980i
$862$	6.70845	−	6.70845i	0.228491	−	0.228491i
$863$	10.7080			0.364504			0.182252	−	0.983252i	$-0.441661\pi$
$863$	10.7080			0.364504			0.182252	+	0.983252i	$0.441661\pi$
$864$	−9.94819	+	9.94819i	−0.338444	+	0.338444i
$865$		−	15.9834i		−	0.543451i
$866$	12.1322			0.412269
$867$	−37.4299	+	1.47479i	−1.27118	+	0.0500864i
$868$	−2.17981			−0.0739875
$869$		−	23.2680i		−	0.789314i
$870$	−11.2848	+	11.2848i	−0.382591	+	0.382591i
$871$	11.2278			0.380441
$872$	−21.9153	+	21.9153i	−0.742147	+	0.742147i
$873$	14.6072	+	14.6072i	0.494380	+	0.494380i
$874$	−0.666892	−	0.666892i	−0.0225580	−	0.0225580i
$875$			27.3990i			0.926255i
$876$			16.3250i			0.551569i
$877$	15.9602	+	15.9602i	0.538939	+	0.538939i	0.923217	−	0.384278i	$-0.125550\pi$
$877$	15.9602	+	15.9602i	0.538939	+	0.538939i	−0.384278	+	0.923217i	$0.625550\pi$
$878$	−0.454444	−	0.454444i	−0.0153367	−	0.0153367i
$879$	−37.2451	+	37.2451i	−1.25625	+	1.25625i
$880$	8.55061			0.288241
$881$	−1.89806	+	1.89806i	−0.0639474	+	0.0639474i	−0.738357	−	0.674410i	$-0.764398\pi$
$881$	−1.89806	+	1.89806i	−0.0639474	+	0.0639474i	0.674410	+	0.738357i	$0.264398\pi$
$882$			2.12915i			0.0716921i
$883$	27.3168			0.919283			0.459641	−	0.888105i	$-0.347978\pi$
$883$	27.3168			0.919283			0.459641	+	0.888105i	$0.347978\pi$
$884$	−9.41706	−	3.68516i	−0.316730	−	0.123945i
$885$	34.2418			1.15103
$886$			6.76548i			0.227291i
$887$	−4.24992	+	4.24992i	−0.142698	+	0.142698i	−0.774847	−	0.632149i	$-0.782173\pi$
$887$	−4.24992	+	4.24992i	−0.142698	+	0.142698i	0.632149	+	0.774847i	$0.282173\pi$
$888$	2.38406			0.0800039
$889$	9.31778	−	9.31778i	0.312508	−	0.312508i
$890$	−2.42163	−	2.42163i	−0.0811731	−	0.0811731i
$891$	20.2153	+	20.2153i	0.677237	+	0.677237i
$892$			32.6524i			1.09328i
$893$		−	77.7224i		−	2.60088i
$894$	−8.70743	−	8.70743i	−0.291220	−	0.291220i
$895$	−8.49093	−	8.49093i	−0.283820	−	0.283820i
$896$	18.2793	−	18.2793i	0.610667	−	0.610667i
$897$	0.689516			0.0230223
$898$	4.75042	−	4.75042i	0.158524	−	0.158524i
$899$		−	4.07905i		−	0.136044i
$900$	6.08762			0.202921
$901$	−15.2329	+	38.9261i	−0.507481	+	1.29682i
$902$	17.9362			0.597209
$903$		−	4.98082i		−	0.165751i
$904$	−4.23927	+	4.23927i	−0.140996	+	0.140996i
$905$	7.64755			0.254213
$906$	10.5077	−	10.5077i	0.349094	−	0.349094i
$907$	33.5266	+	33.5266i	1.11323	+	1.11323i	0.992711	+	0.120521i	$0.0384565\pi$
$907$	33.5266	+	33.5266i	1.11323	+	1.11323i	0.120521	+	0.992711i	$0.461543\pi$
$908$	−5.57047	−	5.57047i	−0.184863	−	0.184863i
$909$			23.3669i			0.775031i
$910$			3.56658i			0.118231i
$911$	12.0818	+	12.0818i	0.400288	+	0.400288i	0.878334	−	0.478047i	$-0.158655\pi$
$911$	12.0818	+	12.0818i	0.400288	+	0.400288i	−0.478047	+	0.878334i	$0.658655\pi$
$912$	22.3791	+	22.3791i	0.741046	+	0.741046i
$913$	−22.2314	+	22.2314i	−0.735751	+	0.735751i
$914$	−16.3208			−0.539843
$915$	−19.8250	+	19.8250i	−0.655393	+	0.655393i
$916$		−	43.3233i		−	1.43144i
$917$	24.5783			0.811646
$918$	−5.78451	+	2.53058i	−0.190917	+	0.0835216i
$919$	36.3930			1.20049			0.600247	−	0.799815i	$-0.295069\pi$
$919$	36.3930			1.20049			0.600247	+	0.799815i	$0.295069\pi$
$920$		−	0.793329i		−	0.0261553i
$921$	29.5012	−	29.5012i	0.972097	−	0.972097i
$922$	9.82328			0.323512
$923$	−13.5025	+	13.5025i	−0.444442	+	0.444442i
$924$	−14.7672	−	14.7672i	−0.485806	−	0.485806i
$925$	0.697969	+	0.697969i	0.0229491	+	0.0229491i
$926$		−	15.2796i		−	0.502118i
$927$			35.1569i			1.15470i
$928$	27.2167	+	27.2167i	0.893433	+	0.893433i
$929$	2.70956	+	2.70956i	0.0888979	+	0.0888979i	0.750157	−	0.661259i	$-0.229978\pi$
$929$	2.70956	+	2.70956i	0.0888979	+	0.0888979i	−0.661259	+	0.750157i	$0.729978\pi$
$930$	−0.966586	+	0.966586i	−0.0316956	+	0.0316956i
$931$	−14.1087			−0.462393
$932$	−14.7566	+	14.7566i	−0.483367	+	0.483367i
$933$		−	34.6118i		−	1.13314i
$934$	−9.47997			−0.310194
$935$	17.0596	+	6.67590i	0.557908	+	0.218325i
$936$	6.14890			0.200983
$937$		−	25.2846i		−	0.826012i	−0.910728	−	0.413006i	$-0.864479\pi$
$937$		−	25.2846i		−	0.826012i	0.910728	−	0.413006i	$-0.135521\pi$
$938$	−7.24719	+	7.24719i	−0.236629	+	0.236629i
$939$	−14.2014			−0.463445
$940$	20.7685	−	20.7685i	0.677395	−	0.677395i
$941$	12.5315	+	12.5315i	0.408514	+	0.408514i	0.881220	−	0.472706i	$-0.156723\pi$
$941$	12.5315	+	12.5315i	0.408514	+	0.408514i	−0.472706	+	0.881220i	$0.656723\pi$
$942$	−6.53149	−	6.53149i	−0.212807	−	0.212807i
$943$			2.39283i			0.0779212i
$944$		−	17.2990i		−	0.563035i
$945$	−6.97006	−	6.97006i	−0.226736	−	0.226736i
$946$	1.10327	+	1.10327i	0.0358703	+	0.0358703i
$947$	9.01903	−	9.01903i	0.293079	−	0.293079i	−0.545216	−	0.838295i	$-0.683553\pi$
$947$	9.01903	−	9.01903i	0.293079	−	0.293079i	0.838295	+	0.545216i	$0.183553\pi$
$948$	32.5458			1.05704
$949$	−4.82748	+	4.82748i	−0.156707	+	0.156707i
$950$		−	9.11308i		−	0.295667i
$951$	2.44246			0.0792023
$952$	18.8246	−	8.23530i	0.610109	−	0.266908i
$953$	52.5237			1.70141			0.850704	−	0.525645i	$-0.176176\pi$
$953$	52.5237			1.70141			0.850704	+	0.525645i	$0.176176\pi$
$954$		−	11.4186i		−	0.369692i
$955$	−31.3097	+	31.3097i	−1.01316	+	1.01316i
$956$	22.6432			0.732332
$957$	27.6337	−	27.6337i	0.893271	−	0.893271i
$958$	−1.97679	−	1.97679i	−0.0638671	−	0.0638671i
$959$	−11.1127	−	11.1127i	−0.358848	−	0.358848i
$960$			1.76320i			0.0569071i
$961$			30.6506i			0.988729i
$962$	0.316722	+	0.316722i	0.0102115	+	0.0102115i
$963$	26.6821	+	26.6821i	0.859818	+	0.859818i
$964$	−18.3498	+	18.3498i	−0.591009	+	0.591009i
$965$	−6.27186			−0.201898
$966$	−0.445059	+	0.445059i	−0.0143195	+	0.0143195i
$967$			6.36944i			0.204827i	0.994742	+	0.102414i	$0.0326565\pi$
$967$			6.36944i			0.204827i	−0.994742	+	0.102414i	$0.967343\pi$
$968$	−9.68892			−0.311414
$969$	27.1767	+	62.1217i	0.873041	+	1.99564i
$970$	11.6863			0.375224
$971$		−	31.3843i		−	1.00717i	−0.863946	−	0.503585i	$-0.832014\pi$
$971$		−	31.3843i		−	1.00717i	0.863946	−	0.503585i	$-0.167986\pi$
$972$	−19.5463	+	19.5463i	−0.626947	+	0.626947i
$973$	47.8934			1.53539
$974$	5.08161	−	5.08161i	0.162825	−	0.162825i
$975$	4.71112	+	4.71112i	0.150877	+	0.150877i
$976$	10.0156	+	10.0156i	0.320591	+	0.320591i
$977$			9.01200i			0.288319i	0.989554	+	0.144160i	$0.0460479\pi$
$977$			9.01200i			0.288319i	−0.989554	+	0.144160i	$0.953952\pi$
$978$		−	2.79382i		−	0.0893367i
$979$	5.92997	+	5.92997i	0.189523	+	0.189523i
$980$	−3.77005	−	3.77005i	−0.120430	−	0.120430i
$981$	−18.4425	+	18.4425i	−0.588823	+	0.588823i
$982$	1.34933			0.0430587
$983$	−9.97574	+	9.97574i	−0.318177	+	0.318177i	−0.848066	−	0.529890i	$-0.822233\pi$
$983$	−9.97574	+	9.97574i	−0.318177	+	0.318177i	0.529890	+	0.848066i	$0.322233\pi$
$984$			55.8435i			1.78023i
$985$	−34.0276			−1.08421
$986$	6.92328	+	15.8255i	0.220482	+	0.503988i
$987$	−51.8690			−1.65101
$988$			18.3050i			0.582360i
$989$	−0.147185	+	0.147185i	−0.00468020	+	0.00468020i
$990$	−5.00429			−0.159047
$991$	−41.0161	+	41.0161i	−1.30292	+	1.30292i	−0.376503	+	0.926415i	$0.622874\pi$
$991$	−41.0161	+	41.0161i	−1.30292	+	1.30292i	−0.926415	+	0.376503i	$0.877126\pi$
$992$	2.33122	+	2.33122i	0.0740162	+	0.0740162i
$993$	30.7459	+	30.7459i	0.975691	+	0.975691i
$994$		−	17.4309i		−	0.552873i
$995$		−	17.5681i		−	0.556947i
$996$	−31.0958	−	31.0958i	−0.985308	−	0.985308i
$997$	−26.9766	−	26.9766i	−0.854357	−	0.854357i	0.136309	−	0.990666i	$-0.456476\pi$
$997$	−26.9766	−	26.9766i	−0.854357	−	0.854357i	−0.990666	+	0.136309i	$0.956476\pi$
$998$	−2.40918	+	2.40918i	−0.0762612	+	0.0762612i
$999$	−1.23792			−0.0391661

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.c.259.13	✓	56
17.13	even	4	inner	731.2.f.c.302.16	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.c.259.13	✓	56	1.1	even	1	trivial
731.2.f.c.302.16	yes	56	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)

\(f(q)\)	\(=\)	\(q-0.607091i q^{2} +(-1.55808 + 1.55808i) q^{3} +1.63144 q^{4} +(1.22244 - 1.22244i) q^{5} +(0.945900 + 0.945900i) q^{6} +(1.59838 + 1.59838i) q^{7} -2.20462i q^{8} -1.85526i q^{9} +O(q^{10})\)	\(q-0.607091i q^{2} +(-1.55808 + 1.55808i) q^{3} +1.63144 q^{4} +(1.22244 - 1.22244i) q^{5} +(0.945900 + 0.945900i) q^{6} +(1.59838 + 1.59838i) q^{7} -2.20462i q^{8} -1.85526i q^{9} +(-0.742133 - 0.742133i) q^{10} +(1.81730 + 1.81730i) q^{11} +(-2.54192 + 2.54192i) q^{12} -1.50335 q^{13} +(0.970361 - 0.970361i) q^{14} +3.80933i q^{15} +1.92448 q^{16} +(3.83958 + 1.50254i) q^{17} -1.12631 q^{18} -7.46343i q^{19} +(1.99434 - 1.99434i) q^{20} -4.98082 q^{21} +(1.10327 - 1.10327i) q^{22} +(0.147185 + 0.147185i) q^{23} +(3.43498 + 3.43498i) q^{24} +2.01128i q^{25} +0.912671i q^{26} +(-1.78361 - 1.78361i) q^{27} +(2.60766 + 2.60766i) q^{28} +(-4.87968 + 4.87968i) q^{29} +2.31261 q^{30} +(-0.417963 + 0.417963i) q^{31} -5.57756i q^{32} -5.66302 q^{33} +(0.912177 - 2.33098i) q^{34} +3.90784 q^{35} -3.02674i q^{36} +(0.347027 - 0.347027i) q^{37} -4.53099 q^{38} +(2.34235 - 2.34235i) q^{39} +(-2.69501 - 2.69501i) q^{40} +(8.12865 + 8.12865i) q^{41} +3.02381i q^{42} +1.00000i q^{43} +(2.96482 + 2.96482i) q^{44} +(-2.26794 - 2.26794i) q^{45} +(0.0893546 - 0.0893546i) q^{46} +10.4138 q^{47} +(-2.99850 + 2.99850i) q^{48} -1.89037i q^{49} +1.22103 q^{50} +(-8.32347 + 3.64131i) q^{51} -2.45263 q^{52} +10.1381i q^{53} +(-1.08281 + 1.08281i) q^{54} +4.44308 q^{55} +(3.52381 - 3.52381i) q^{56} +(11.6287 + 11.6287i) q^{57} +(2.96241 + 2.96241i) q^{58} -8.98894i q^{59} +6.21469i q^{60} +(5.20432 + 5.20432i) q^{61} +(0.253742 + 0.253742i) q^{62} +(2.96540 - 2.96540i) q^{63} +0.462864 q^{64} +(-1.83776 + 1.83776i) q^{65} +3.43797i q^{66} -7.46855 q^{67} +(6.26405 + 2.45130i) q^{68} -0.458653 q^{69} -2.37242i q^{70} +(8.98163 - 8.98163i) q^{71} -4.09013 q^{72} +(3.21114 - 3.21114i) q^{73} +(-0.210677 - 0.210677i) q^{74} +(-3.13375 - 3.13375i) q^{75} -12.1761i q^{76} +5.80947i q^{77} +(-1.42202 - 1.42202i) q^{78} +(-6.40181 - 6.40181i) q^{79} +(2.35256 - 2.35256i) q^{80} +11.1238 q^{81} +(4.93483 - 4.93483i) q^{82} +12.2332i q^{83} -8.12591 q^{84} +(6.53042 - 2.85690i) q^{85} +0.607091 q^{86} -15.2059i q^{87} +(4.00645 - 4.00645i) q^{88} +3.26306 q^{89} +(-1.37685 + 1.37685i) q^{90} +(-2.40292 - 2.40292i) q^{91} +(0.240123 + 0.240123i) q^{92} -1.30244i q^{93} -6.32210i q^{94} +(-9.12360 - 9.12360i) q^{95} +(8.69032 + 8.69032i) q^{96} +(-7.87344 + 7.87344i) q^{97} -1.14763 q^{98} +(3.37156 - 3.37156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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