LMFDB - Embedded newform 928.2.k.e.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [928,2,Mod(191,928)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(928, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("928.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 928 = 2^{5} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	928.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.41011730757$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 23x^{8} + 153x^{6} + 273x^{4} + 103x^{2} + 9 $ x^10 + 23x^8 + 153x^6 + 273x^4 + 103x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.1
Root			$3.51266i$ of defining polynomial
Character	$\chi$	$=$	928.191
Dual form			928.2.k.e.447.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.29821 - 2.29821i) q^{3} +2.13467i q^{5} -1.90496i q^{7} +7.56357i q^{9} +O(q^{10})$	\(q+(-2.29821 - 2.29821i) q^{3} +2.13467i q^{5} -1.90496i q^{7} +7.56357i q^{9} +(2.34912 + 2.34912i) q^{11} -2.98570i q^{13} +(4.90592 - 4.90592i) q^{15} +(4.06947 - 4.06947i) q^{17} +(-4.74237 - 4.74237i) q^{19} +(-4.37800 + 4.37800i) q^{21} -1.30853i q^{23} +0.443197 q^{25} +(10.4880 - 10.4880i) q^{27} +(-3.52696 + 4.06947i) q^{29} +(4.59245 + 4.59245i) q^{31} -10.7975i q^{33} +4.06645 q^{35} +(-6.25504 - 6.25504i) q^{37} +(-6.86178 + 6.86178i) q^{39} +(-4.20413 - 4.20413i) q^{41} +(-6.67621 - 6.67621i) q^{43} -16.1457 q^{45} +(-2.90592 + 2.90592i) q^{47} +3.37114 q^{49} -18.7050 q^{51} -0.397237 q^{53} +(-5.01458 + 5.01458i) q^{55} +21.7980i q^{57} +1.57786i q^{59} +(1.28295 - 1.28295i) q^{61} +14.4083 q^{63} +6.37348 q^{65} -2.78459 q^{67} +(-3.00728 + 3.00728i) q^{69} -3.67291 q^{71} +(-9.79561 - 9.79561i) q^{73} +(-1.01856 - 1.01856i) q^{75} +(4.47496 - 4.47496i) q^{77} +(-7.33482 - 7.33482i) q^{79} -25.5168 q^{81} +2.58966i q^{83} +(8.68695 + 8.68695i) q^{85} +(17.4582 - 1.24679i) q^{87} +(8.13165 - 8.13165i) q^{89} -5.68763 q^{91} -21.1088i q^{93} +(10.1234 - 10.1234i) q^{95} +(1.70275 + 1.70275i) q^{97} +(-17.7677 + 17.7677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{3}+O(q^{10}) $ 10 * q - 2 * q^3	$ 10 q - 2 q^{3} - 14 q^{11} + 14 q^{15} + 6 q^{17} - 12 q^{19} - 28 q^{21} + 2 q^{25} - 2 q^{27} - 28 q^{29} + 14 q^{31} + 4 q^{35} + 10 q^{37} + 6 q^{39} + 14 q^{41} - 30 q^{43} - 36 q^{45} + 6 q^{47} - 42 q^{49} - 56 q^{51} + 4 q^{53} - 42 q^{55} - 26 q^{61} + 32 q^{63} - 36 q^{65} - 56 q^{67} + 16 q^{69} - 36 q^{71} - 22 q^{73} + 8 q^{75} + 28 q^{77} - 6 q^{79} - 54 q^{81} - 16 q^{85} + 58 q^{87} + 58 q^{89} + 20 q^{91} + 52 q^{95} + 26 q^{97} - 68 q^{99}+O(q^{100}) $ 10 * q - 2 * q^3 - 14 * q^11 + 14 * q^15 + 6 * q^17 - 12 * q^19 - 28 * q^21 + 2 * q^25 - 2 * q^27 - 28 * q^29 + 14 * q^31 + 4 * q^35 + 10 * q^37 + 6 * q^39 + 14 * q^41 - 30 * q^43 - 36 * q^45 + 6 * q^47 - 42 * q^49 - 56 * q^51 + 4 * q^53 - 42 * q^55 - 26 * q^61 + 32 * q^63 - 36 * q^65 - 56 * q^67 + 16 * q^69 - 36 * q^71 - 22 * q^73 + 8 * q^75 + 28 * q^77 - 6 * q^79 - 54 * q^81 - 16 * q^85 + 58 * q^87 + 58 * q^89 + 20 * q^91 + 52 * q^95 + 26 * q^97 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/928\mathbb{Z}\right)^\times$.

$n$	$321$	$581$	$639$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	−2.29821	−	2.29821i	−1.32687	−	1.32687i	−0.908082	−	0.418791i	$-0.862454\pi$
$3$	−2.29821	−	2.29821i	−1.32687	−	1.32687i	−0.418791	−	0.908082i	$-0.637546\pi$
$4$		0			0
$5$			2.13467i			0.954652i	0.878726	+	0.477326i	$0.158394\pi$
$5$			2.13467i			0.954652i	−0.878726	+	0.477326i	$0.841606\pi$
$6$		0			0
$7$		−	1.90496i		−	0.720006i	−0.932951	−	0.360003i	$-0.882776\pi$
$7$		−	1.90496i		−	0.720006i	0.932951	−	0.360003i	$-0.117224\pi$
$8$		0			0
$9$			7.56357i			2.52119i
$10$		0			0
$11$	2.34912	+	2.34912i	0.708285	+	0.708285i	0.966174	−	0.257889i	$-0.0830270\pi$
$11$	2.34912	+	2.34912i	0.708285	+	0.708285i	−0.257889	+	0.966174i	$0.583027\pi$
$12$		0			0
$13$		−	2.98570i		−	0.828085i	−0.910258	−	0.414042i	$-0.864117\pi$
$13$		−	2.98570i		−	0.828085i	0.910258	−	0.414042i	$-0.135883\pi$
$14$		0			0
$15$	4.90592	−	4.90592i	1.26670	−	1.26670i
$16$		0			0
$17$	4.06947	−	4.06947i	0.986990	−	0.986990i	−0.0129261	−	0.999916i	$-0.504115\pi$
$17$	4.06947	−	4.06947i	0.986990	−	0.986990i	0.999916	+	0.0129261i	$0.00411463\pi$
$18$		0			0
$19$	−4.74237	−	4.74237i	−1.08797	−	1.08797i	−0.995737	−	0.0922380i	$-0.970598\pi$
$19$	−4.74237	−	4.74237i	−1.08797	−	1.08797i	−0.0922380	−	0.995737i	$-0.529402\pi$
$20$		0			0
$21$	−4.37800	+	4.37800i	−0.955357	+	0.955357i
$22$		0			0
$23$		−	1.30853i		−	0.272847i	−0.990651	−	0.136424i	$-0.956439\pi$
$23$		−	1.30853i		−	0.272847i	0.990651	−	0.136424i	$-0.0435609\pi$
$24$		0			0
$25$	0.443197			0.0886395
$26$		0			0
$27$	10.4880	−	10.4880i	2.01843	−	2.01843i
$28$		0			0
$29$	−3.52696	+	4.06947i	−0.654940	+	0.755681i
$29$	−3.52696	+	4.06947i	−0.654940	+	0.755681i
$30$		0			0
$31$	4.59245	+	4.59245i	0.824828	+	0.824828i	0.986796	−	0.161968i	$-0.0517843\pi$
$31$	4.59245	+	4.59245i	0.824828	+	0.824828i	−0.161968	+	0.986796i	$0.551784\pi$
$32$		0			0
$33$		−	10.7975i		−	1.87961i
$34$		0			0
$35$	4.06645			0.687355
$36$		0			0
$37$	−6.25504	−	6.25504i	−1.02832	−	1.02832i	−0.999587	−	0.0287345i	$-0.990852\pi$
$37$	−6.25504	−	6.25504i	−1.02832	−	1.02832i	−0.0287345	−	0.999587i	$-0.509148\pi$
$38$		0			0
$39$	−6.86178	+	6.86178i	−1.09876	+	1.09876i
$40$		0			0
$41$	−4.20413	−	4.20413i	−0.656575	−	0.656575i	0.297993	−	0.954568i	$-0.403683\pi$
$41$	−4.20413	−	4.20413i	−0.656575	−	0.656575i	−0.954568	+	0.297993i	$0.903683\pi$
$42$		0			0
$43$	−6.67621	−	6.67621i	−1.01811	−	1.01811i	−0.999833	−	0.0182794i	$-0.994181\pi$
$43$	−6.67621	−	6.67621i	−1.01811	−	1.01811i	−0.0182794	−	0.999833i	$-0.505819\pi$
$44$		0			0
$45$	−16.1457			−2.40686
$46$		0			0
$47$	−2.90592	+	2.90592i	−0.423872	+	0.423872i	−0.886534	−	0.462663i	$-0.846894\pi$
$47$	−2.90592	+	2.90592i	−0.423872	+	0.423872i	0.462663	+	0.886534i	$0.346894\pi$
$48$		0			0
$49$	3.37114			0.481592
$50$		0			0
$51$	−18.7050			−2.61922
$52$		0			0
$53$	−0.397237			−0.0545647			−0.0272824	−	0.999628i	$-0.508685\pi$
$53$	−0.397237			−0.0545647			−0.0272824	+	0.999628i	$0.508685\pi$
$54$		0			0
$55$	−5.01458	+	5.01458i	−0.676166	+	0.676166i
$56$		0			0
$57$			21.7980i			2.88721i
$58$		0			0
$59$			1.57786i			0.205420i	0.994711	+	0.102710i	$0.0327514\pi$
$59$			1.57786i			0.205420i	−0.994711	+	0.102710i	$0.967249\pi$
$60$		0			0
$61$	1.28295	−	1.28295i	0.164265	−	0.164265i	−0.620188	−	0.784453i	$-0.712944\pi$
$61$	1.28295	−	1.28295i	0.164265	−	0.164265i	0.784453	+	0.620188i	$0.212944\pi$
$62$		0			0
$63$	14.4083			1.81527
$64$		0			0
$65$	6.37348			0.790533
$66$		0			0
$67$	−2.78459			−0.340192			−0.170096	−	0.985428i	$-0.554408\pi$
$67$	−2.78459			−0.340192			−0.170096	+	0.985428i	$0.554408\pi$
$68$		0			0
$69$	−3.00728	+	3.00728i	−0.362034	+	0.362034i
$70$		0			0
$71$	−3.67291			−0.435894			−0.217947	−	0.975961i	$-0.569936\pi$
$71$	−3.67291			−0.435894			−0.217947	+	0.975961i	$0.569936\pi$
$72$		0			0
$73$	−9.79561	−	9.79561i	−1.14649	−	1.14649i	−0.987238	−	0.159252i	$-0.949092\pi$
$73$	−9.79561	−	9.79561i	−1.14649	−	1.14649i	−0.159252	−	0.987238i	$-0.550908\pi$
$74$		0			0
$75$	−1.01856	−	1.01856i	−0.117613	−	0.117613i
$76$		0			0
$77$	4.47496	−	4.47496i	0.509970	−	0.509970i
$78$		0			0
$79$	−7.33482	−	7.33482i	−0.825232	−	0.825232i	0.161621	−	0.986853i	$-0.448328\pi$
$79$	−7.33482	−	7.33482i	−0.825232	−	0.825232i	−0.986853	+	0.161621i	$0.948328\pi$
$80$		0			0
$81$	−25.5168			−2.83520
$82$		0			0
$83$			2.58966i			0.284252i	0.989849	+	0.142126i	$0.0453939\pi$
$83$			2.58966i			0.284252i	−0.989849	+	0.142126i	$0.954606\pi$
$84$		0			0
$85$	8.68695	+	8.68695i	0.942232	+	0.942232i
$86$		0			0
$87$	17.4582	−	1.24679i	1.87172	−	0.133670i
$88$		0			0
$89$	8.13165	−	8.13165i	0.861953	−	0.861953i	−0.129612	−	0.991565i	$-0.541373\pi$
$89$	8.13165	−	8.13165i	0.861953	−	0.861953i	0.991565	+	0.129612i	$0.0413731\pi$
$90$		0			0
$91$	−5.68763			−0.596226
$92$		0			0
$93$		−	21.1088i		−	2.18888i
$94$		0			0
$95$	10.1234	−	10.1234i	1.03864	−	1.03864i
$96$		0			0
$97$	1.70275	+	1.70275i	0.172888	+	0.172888i	0.788247	−	0.615359i	$-0.210989\pi$
$97$	1.70275	+	1.70275i	0.172888	+	0.172888i	−0.615359	+	0.788247i	$0.710989\pi$
$98$		0			0
$99$	−17.7677	+	17.7677i	−1.78572	+	1.78572i
$100$		0			0
$101$	7.89862	−	7.89862i	0.785942	−	0.785942i	−0.194884	−	0.980826i	$-0.562433\pi$
$101$	7.89862	−	7.89862i	0.785942	−	0.785942i	0.980826	+	0.194884i	$0.0624331\pi$
$102$		0			0
$103$		−	18.5021i		−	1.82307i	−0.411226	−	0.911534i	$-0.634899\pi$
$103$		−	18.5021i		−	1.82307i	0.411226	−	0.911534i	$-0.365101\pi$
$104$		0			0
$105$	−9.34556	−	9.34556i	−0.912034	−	0.912034i
$106$		0			0
$107$		−	6.66095i		−	0.643938i	−0.946750	−	0.321969i	$-0.895655\pi$
$107$		−	6.66095i		−	0.643938i	0.946750	−	0.321969i	$-0.104345\pi$
$108$		0			0
$109$			16.3754i			1.56848i	0.620458	+	0.784240i	$0.286947\pi$
$109$			16.3754i			1.56848i	−0.620458	+	0.784240i	$0.713053\pi$
$110$		0			0
$111$			28.7508i			2.72891i
$112$		0			0
$113$	−7.36438	−	7.36438i	−0.692782	−	0.692782i	0.270061	−	0.962843i	$-0.412956\pi$
$113$	−7.36438	−	7.36438i	−0.692782	−	0.692782i	−0.962843	+	0.270061i	$0.912956\pi$
$114$		0			0
$115$	2.79328			0.260474
$116$		0			0
$117$	22.5826			2.08776
$118$		0			0
$119$	−7.75215	−	7.75215i	−0.710639	−	0.710639i
$120$		0			0
$121$			0.0366970i			0.00333609i
$122$		0			0
$123$			19.3240i			1.74238i
$124$		0			0
$125$			11.6194i			1.03927i
$126$		0			0
$127$	7.16935	+	7.16935i	0.636177	+	0.636177i	0.949610	−	0.313433i	$-0.101479\pi$
$127$	7.16935	+	7.16935i	0.636177	+	0.636177i	−0.313433	+	0.949610i	$0.601479\pi$
$128$		0			0
$129$			30.6867i			2.70181i
$130$		0			0
$131$	11.2663	−	11.2663i	0.984343	−	0.984343i	−0.0155367	−	0.999879i	$-0.504946\pi$
$131$	11.2663	−	11.2663i	0.984343	−	0.984343i	0.999879	+	0.0155367i	$0.00494569\pi$
$132$		0			0
$133$	−9.03401	+	9.03401i	−0.783348	+	0.783348i
$134$		0			0
$135$	22.3885	+	22.3885i	1.92689	+	1.92689i
$136$		0			0
$137$	0.0867812	−	0.0867812i	0.00741422	−	0.00741422i	−0.703390	−	0.710804i	$-0.748331\pi$
$137$	0.0867812	−	0.0867812i	0.00741422	−	0.00741422i	0.710804	+	0.703390i	$0.248331\pi$
$138$		0			0
$139$		−	11.2301i		−	0.952528i	−0.879302	−	0.476264i	$-0.841991\pi$
$139$		−	11.2301i		−	0.952528i	0.879302	−	0.476264i	$-0.158009\pi$
$140$		0			0
$141$	13.3568			1.12485
$142$		0			0
$143$	7.01376	−	7.01376i	0.586520	−	0.586520i
$144$		0			0
$145$	−8.68695	−	7.52889i	−0.721412	−	0.625240i
$146$		0			0
$147$	−7.74760	−	7.74760i	−0.639011	−	0.639011i
$148$		0			0
$149$		−	18.1189i		−	1.48436i	−0.670203	−	0.742178i	$-0.733793\pi$
$149$		−	18.1189i		−	1.48436i	0.670203	−	0.742178i	$-0.266207\pi$
$150$		0			0
$151$	−21.9927			−1.78974			−0.894872	−	0.446324i	$-0.852733\pi$
$151$	−21.9927			−1.78974			−0.894872	+	0.446324i	$0.852733\pi$
$152$		0			0
$153$	30.7797	+	30.7797i	2.48839	+	2.48839i
$154$		0			0
$155$	−9.80334	+	9.80334i	−0.787423	+	0.787423i
$156$		0			0
$157$	9.25009	+	9.25009i	0.738238	+	0.738238i	0.972237	−	0.233999i	$-0.0751813\pi$
$157$	9.25009	+	9.25009i	0.738238	+	0.738238i	−0.233999	+	0.972237i	$0.575181\pi$
$158$		0			0
$159$	0.912936	+	0.912936i	0.0724005	+	0.0724005i
$160$		0			0
$161$	−2.49269			−0.196452
$162$		0			0
$163$	1.96316	−	1.96316i	0.153767	−	0.153767i	−0.626031	−	0.779798i	$-0.715322\pi$
$163$	1.96316	−	1.96316i	0.153767	−	0.153767i	0.779798	+	0.626031i	$0.215322\pi$
$164$		0			0
$165$	23.0492			1.79437
$166$		0			0
$167$	−12.2201			−0.945620			−0.472810	−	0.881164i	$-0.656760\pi$
$167$	−12.2201			−0.945620			−0.472810	+	0.881164i	$0.656760\pi$
$168$		0			0
$169$	4.08558			0.314276
$170$		0			0
$171$	35.8693	−	35.8693i	2.74299	−	2.74299i
$172$		0			0
$173$			1.09001i			0.0828718i	0.999141	+	0.0414359i	$0.0131932\pi$
$173$			1.09001i			0.0828718i	−0.999141	+	0.0414359i	$0.986807\pi$
$174$		0			0
$175$		−	0.844272i		−	0.0638209i
$176$		0			0
$177$	3.62627	−	3.62627i	0.272567	−	0.272567i
$178$		0			0
$179$	−1.10564			−0.0826397			−0.0413199	−	0.999146i	$-0.513156\pi$
$179$	−1.10564			−0.0826397			−0.0413199	+	0.999146i	$0.513156\pi$
$180$		0			0
$181$	8.32475			0.618774			0.309387	−	0.950936i	$-0.399876\pi$
$181$	8.32475			0.618774			0.309387	+	0.950936i	$0.399876\pi$
$182$		0			0
$183$	−5.89700			−0.435918
$184$		0			0
$185$	13.3524	−	13.3524i	0.981689	−	0.981689i
$186$		0			0
$187$	19.1193			1.39814
$188$		0			0
$189$	−19.9793	−	19.9793i	−1.45328	−	1.45328i
$190$		0			0
$191$	6.45240	+	6.45240i	0.466880	+	0.466880i	0.900902	−	0.434022i	$-0.142906\pi$
$191$	6.45240	+	6.45240i	0.466880	+	0.466880i	−0.434022	+	0.900902i	$0.642906\pi$
$192$		0			0
$193$	−4.99065	+	4.99065i	−0.359235	+	0.359235i	−0.863531	−	0.504296i	$-0.831752\pi$
$193$	−4.99065	+	4.99065i	−0.359235	+	0.359235i	0.504296	+	0.863531i	$0.331752\pi$
$194$		0			0
$195$	−14.6476	−	14.6476i	−1.04894	−	1.04894i
$196$		0			0
$197$	18.5472			1.32143			0.660716	−	0.750636i	$-0.270253\pi$
$197$	18.5472			1.32143			0.660716	+	0.750636i	$0.270253\pi$
$198$		0			0
$199$			23.8266i			1.68902i	0.535540	+	0.844510i	$0.320108\pi$
$199$			23.8266i			1.68902i	−0.535540	+	0.844510i	$0.679892\pi$
$200$		0			0
$201$	6.39958	+	6.39958i	0.451391	+	0.451391i
$202$		0			0
$203$	7.75215	+	6.71871i	0.544095	+	0.471561i
$204$		0			0
$205$	8.97442	−	8.97442i	0.626801	−	0.626801i
$206$		0			0
$207$	9.89716			0.687900
$208$		0			0
$209$		−	22.2808i		−	1.54119i
$210$		0			0
$211$	12.2471	−	12.2471i	0.843122	−	0.843122i	−0.146142	−	0.989264i	$-0.546685\pi$
$211$	12.2471	−	12.2471i	0.843122	−	0.843122i	0.989264	+	0.146142i	$0.0466855\pi$
$212$		0			0
$213$	8.44112	+	8.44112i	0.578376	+	0.578376i
$214$		0			0
$215$	14.2515	−	14.2515i	0.971943	−	0.971943i
$216$		0			0
$217$	8.74841	−	8.74841i	0.593881	−	0.593881i
$218$		0			0
$219$			45.0248i			3.04250i
$220$		0			0
$221$	−12.1502	−	12.1502i	−0.817312	−	0.817312i
$222$		0			0
$223$			23.4641i			1.57127i	0.618688	+	0.785637i	$0.287664\pi$
$223$			23.4641i			1.57127i	−0.618688	+	0.785637i	$0.712336\pi$
$224$		0			0
$225$			3.35215i			0.223477i
$226$		0			0
$227$			8.70676i			0.577888i	0.957346	+	0.288944i	$0.0933041\pi$
$227$			8.70676i			0.577888i	−0.957346	+	0.288944i	$0.906696\pi$
$228$		0			0
$229$	7.31774	+	7.31774i	0.483570	+	0.483570i	0.906270	−	0.422700i	$-0.138918\pi$
$229$	7.31774	+	7.31774i	0.483570	+	0.483570i	−0.422700	+	0.906270i	$0.638918\pi$
$230$		0			0
$231$	−20.5688			−1.35333
$232$		0			0
$233$	−10.6858			−0.700053			−0.350027	−	0.936740i	$-0.613827\pi$
$233$	−10.6858			−0.700053			−0.350027	+	0.936740i	$0.613827\pi$
$234$		0			0
$235$	−6.20317	−	6.20317i	−0.404650	−	0.404650i
$236$		0			0
$237$			33.7140i			2.18996i
$238$		0			0
$239$		−	16.1897i		−	1.04723i	−0.851956	−	0.523614i	$-0.824584\pi$
$239$		−	16.1897i		−	1.04723i	0.851956	−	0.523614i	$-0.175416\pi$
$240$		0			0
$241$		−	10.6957i		−	0.688973i	−0.938791	−	0.344486i	$-0.888053\pi$
$241$		−	10.6957i		−	0.688973i	0.938791	−	0.344486i	$-0.111947\pi$
$242$		0			0
$243$	27.1790	+	27.1790i	1.74353	+	1.74353i
$244$		0			0
$245$			7.19626i			0.459752i
$246$		0			0
$247$	−14.1593	+	14.1593i	−0.900935	+	0.900935i
$248$		0			0
$249$	5.95160	−	5.95160i	0.377167	−	0.377167i
$250$		0			0
$251$	5.05540	+	5.05540i	0.319094	+	0.319094i	0.848419	−	0.529325i	$-0.177555\pi$
$251$	5.05540	+	5.05540i	0.319094	+	0.319094i	−0.529325	+	0.848419i	$0.677555\pi$
$252$		0			0
$253$	3.07389	−	3.07389i	0.193254	−	0.193254i
$254$		0			0
$255$		−	39.9289i		−	2.50045i
$256$		0			0
$257$	−20.1933			−1.25962			−0.629811	−	0.776748i	$-0.716868\pi$
$257$	−20.1933			−1.25962			−0.629811	+	0.776748i	$0.716868\pi$
$258$		0			0
$259$	−11.9156	+	11.9156i	−0.740398	+	0.740398i
$260$		0			0
$261$	−30.7797	−	26.6764i	−1.90521	−	1.65123i
$262$		0			0
$263$	14.8332	+	14.8332i	0.914653	+	0.914653i	0.996634	−	0.0819807i	$-0.0261246\pi$
$263$	14.8332	+	14.8332i	0.914653	+	0.914653i	−0.0819807	+	0.996634i	$0.526125\pi$
$264$		0			0
$265$		−	0.847969i		−	0.0520903i
$266$		0			0
$267$	−37.3765			−2.28741
$268$		0			0
$269$	−16.8676	−	16.8676i	−1.02843	−	1.02843i	−0.999584	−	0.0288508i	$-0.990815\pi$
$269$	−16.8676	−	16.8676i	−1.02843	−	1.02843i	−0.0288508	−	0.999584i	$-0.509185\pi$
$270$		0			0
$271$	7.51789	−	7.51789i	0.456679	−	0.456679i	−0.440885	−	0.897564i	$-0.645335\pi$
$271$	7.51789	−	7.51789i	0.456679	−	0.456679i	0.897564	+	0.440885i	$0.145335\pi$
$272$		0			0
$273$	13.0714	+	13.0714i	0.791117	+	0.791117i
$274$		0			0
$275$	1.04112	+	1.04112i	0.0627820	+	0.0627820i
$276$		0			0
$277$	23.0624			1.38569			0.692844	−	0.721087i	$-0.256357\pi$
$277$	23.0624			1.38569			0.692844	+	0.721087i	$0.256357\pi$
$278$		0			0
$279$	−34.7353	+	34.7353i	−2.07955	+	2.07955i
$280$		0			0
$281$	−5.58816			−0.333362			−0.166681	−	0.986011i	$-0.553305\pi$
$281$	−5.58816			−0.333362			−0.166681	+	0.986011i	$0.553305\pi$
$282$		0			0
$283$	−18.7842			−1.11661			−0.558304	−	0.829637i	$-0.688548\pi$
$283$	−18.7842			−1.11661			−0.558304	+	0.829637i	$0.688548\pi$
$284$		0			0
$285$	−46.5314			−2.75628
$286$		0			0
$287$	−8.00869	+	8.00869i	−0.472738	+	0.472738i
$288$		0			0
$289$		−	16.1211i		−	0.948300i
$290$		0			0
$291$		−	7.82656i		−	0.458801i
$292$		0			0
$293$	−6.63755	+	6.63755i	−0.387770	+	0.387770i	−0.873891	−	0.486122i	$-0.838411\pi$
$293$	−6.63755	+	6.63755i	−0.387770	+	0.387770i	0.486122	+	0.873891i	$0.338411\pi$
$294$		0			0
$295$	−3.36821			−0.196105
$296$		0			0
$297$	49.2753			2.85924
$298$		0			0
$299$	−3.90688			−0.225941
$300$		0			0
$301$	−12.7179	+	12.7179i	−0.733047	+	0.733047i
$302$		0			0
$303$	−36.3054			−2.08569
$304$		0			0
$305$	2.73868	+	2.73868i	0.156816	+	0.156816i
$306$		0			0
$307$	12.7713	+	12.7713i	0.728894	+	0.728894i	0.970399	−	0.241506i	$-0.0776412\pi$
$307$	12.7713	+	12.7713i	0.728894	+	0.728894i	−0.241506	+	0.970399i	$0.577641\pi$
$308$		0			0
$309$	−42.5218	+	42.5218i	−2.41898	+	2.41898i
$310$		0			0
$311$	11.1427	+	11.1427i	0.631843	+	0.631843i	0.948530	−	0.316687i	$-0.102570\pi$
$311$	11.1427	+	11.1427i	0.631843	+	0.631843i	−0.316687	+	0.948530i	$0.602570\pi$
$312$		0			0
$313$	6.03843			0.341312			0.170656	−	0.985331i	$-0.445411\pi$
$313$	6.03843			0.341312			0.170656	+	0.985331i	$0.445411\pi$
$314$		0			0
$315$			30.7568i			1.73295i
$316$		0			0
$317$	1.61004	+	1.61004i	0.0904291	+	0.0904291i	0.750874	−	0.660445i	$-0.229632\pi$
$317$	1.61004	+	1.61004i	0.0904291	+	0.0904291i	−0.660445	+	0.750874i	$0.729632\pi$
$318$		0			0
$319$	−17.8449	+	1.27441i	−0.999122	+	0.0713531i
$320$		0			0
$321$	−15.3083	+	15.3083i	−0.854425	+	0.854425i
$322$		0			0
$323$	−38.5978			−2.14764
$324$		0			0
$325$		−	1.32326i		−	0.0734010i
$326$		0			0
$327$	37.6342	−	37.6342i	2.08117	−	2.08117i
$328$		0			0
$329$	5.53565	+	5.53565i	0.305190	+	0.305190i
$330$		0			0
$331$	−6.98776	+	6.98776i	−0.384082	+	0.384082i	−0.872570	−	0.488488i	$-0.837548\pi$
$331$	−6.98776	+	6.98776i	−0.384082	+	0.384082i	0.488488	+	0.872570i	$0.337548\pi$
$332$		0			0
$333$	47.3104	−	47.3104i	2.59259	−	2.59259i
$334$		0			0
$335$		−	5.94417i		−	0.324765i
$336$		0			0
$337$	0.317472	+	0.317472i	0.0172938	+	0.0172938i	0.715701	−	0.698407i	$-0.246107\pi$
$337$	0.317472	+	0.317472i	0.0172938	+	0.0172938i	−0.698407	+	0.715701i	$0.746107\pi$
$338$		0			0
$339$			33.8498i			1.83847i
$340$		0			0
$341$			21.5764i			1.16843i
$342$		0			0
$343$		−	19.7566i		−	1.06675i
$344$		0			0
$345$	−6.41954	−	6.41954i	−0.345617	−	0.345617i
$346$		0			0
$347$	25.5992			1.37424			0.687118	−	0.726546i	$-0.258875\pi$
$347$	25.5992			1.37424			0.687118	+	0.726546i	$0.258875\pi$
$348$		0			0
$349$	−26.4704			−1.41693			−0.708465	−	0.705746i	$-0.750612\pi$
$349$	−26.4704			−1.41693			−0.708465	+	0.705746i	$0.750612\pi$
$350$		0			0
$351$	−31.3142	−	31.3142i	−1.67143	−	1.67143i
$352$		0			0
$353$		−	29.2089i		−	1.55463i	−0.629111	−	0.777316i	$-0.716581\pi$
$353$		−	29.2089i		−	1.55463i	0.629111	−	0.777316i	$-0.283419\pi$
$354$		0			0
$355$		−	7.84043i		−	0.416127i
$356$		0			0
$357$			35.6322i			1.88586i
$358$		0			0
$359$	1.88912	+	1.88912i	0.0997040	+	0.0997040i	0.755199	−	0.655495i	$-0.227540\pi$
$359$	1.88912	+	1.88912i	0.0997040	+	0.0997040i	−0.655495	+	0.755199i	$0.727540\pi$
$360$		0			0
$361$			25.9802i			1.36738i
$362$		0			0
$363$	0.0843376	−	0.0843376i	0.00442657	−	0.00442657i
$364$		0			0
$365$	20.9104	−	20.9104i	1.09450	−	1.09450i
$366$		0			0
$367$	10.4526	+	10.4526i	0.545619	+	0.545619i	0.925171	−	0.379551i	$-0.123922\pi$
$367$	10.4526	+	10.4526i	0.545619	+	0.545619i	−0.379551	+	0.925171i	$0.623922\pi$
$368$		0			0
$369$	31.7982	−	31.7982i	1.65535	−	1.65535i
$370$		0			0
$371$			0.756719i			0.0392869i
$372$		0			0
$373$	−20.8335			−1.07872			−0.539358	−	0.842077i	$-0.681333\pi$
$373$	−20.8335			−1.07872			−0.539358	+	0.842077i	$0.681333\pi$
$374$		0			0
$375$	26.7039	−	26.7039i	1.37898	−	1.37898i
$376$		0			0
$377$	12.1502	+	10.5305i	0.625768	+	0.542346i
$378$		0			0
$379$	12.0254	+	12.0254i	0.617705	+	0.617705i	0.944942	−	0.327237i	$-0.106118\pi$
$379$	12.0254	+	12.0254i	0.617705	+	0.617705i	−0.327237	+	0.944942i	$0.606118\pi$
$380$		0			0
$381$		−	32.9534i		−	1.68825i
$382$		0			0
$383$	8.44612			0.431576			0.215788	−	0.976440i	$-0.430768\pi$
$383$	8.44612			0.431576			0.215788	+	0.976440i	$0.430768\pi$
$384$		0			0
$385$	9.55256	+	9.55256i	0.486843	+	0.486843i
$386$		0			0
$387$	50.4959	−	50.4959i	2.56685	−	2.56685i
$388$		0			0
$389$	−20.8376	−	20.8376i	−1.05651	−	1.05651i	−0.998305	−	0.0582030i	$-0.981463\pi$
$389$	−20.8376	−	20.8376i	−1.05651	−	1.05651i	−0.0582030	−	0.998305i	$-0.518537\pi$
$390$		0			0
$391$	−5.32502	−	5.32502i	−0.269298	−	0.269298i
$392$		0			0
$393$	−51.7848			−2.61220
$394$		0			0
$395$	15.6574	−	15.6574i	0.787809	−	0.787809i
$396$		0			0
$397$	−1.20511			−0.0604829			−0.0302414	−	0.999543i	$-0.509628\pi$
$397$	−1.20511			−0.0604829			−0.0302414	+	0.999543i	$0.509628\pi$
$398$		0			0
$399$	41.5242			2.07881
$400$		0			0
$401$	−24.9340			−1.24514			−0.622572	−	0.782563i	$-0.713912\pi$
$401$	−24.9340			−1.24514			−0.622572	+	0.782563i	$0.713912\pi$
$402$		0			0
$403$	13.7117	−	13.7117i	0.683027	−	0.683027i
$404$		0			0
$405$		−	54.4699i		−	2.70663i
$406$		0			0
$407$		−	29.3876i		−	1.45669i
$408$		0			0
$409$	−1.88036	+	1.88036i	−0.0929778	+	0.0929778i	−0.752066	−	0.659088i	$-0.770942\pi$
$409$	−1.88036	+	1.88036i	−0.0929778	+	0.0929778i	0.659088	+	0.752066i	$0.270942\pi$
$410$		0			0
$411$	−0.398883			−0.0196755
$412$		0			0
$413$	3.00576			0.147904
$414$		0			0
$415$	−5.52807			−0.271362
$416$		0			0
$417$	−25.8092	+	25.8092i	−1.26388	+	1.26388i
$418$		0			0
$419$	30.7874			1.50406			0.752031	−	0.659128i	$-0.229075\pi$
$419$	30.7874			1.50406			0.752031	+	0.659128i	$0.229075\pi$
$420$		0			0
$421$	3.75710	+	3.75710i	0.183110	+	0.183110i	0.792709	−	0.609600i	$-0.208670\pi$
$421$	3.75710	+	3.75710i	0.183110	+	0.183110i	−0.609600	+	0.792709i	$0.708670\pi$
$422$		0			0
$423$	−21.9791	−	21.9791i	−1.06866	−	1.06866i
$424$		0			0
$425$	1.80358	−	1.80358i	0.0874863	−	0.0874863i
$426$		0			0
$427$	−2.44397	−	2.44397i	−0.118272	−	0.118272i
$428$		0			0
$429$	−32.2382			−1.55648
$430$		0			0
$431$			15.5267i			0.747895i	0.927450	+	0.373948i	$0.121996\pi$
$431$			15.5267i			0.747895i	−0.927450	+	0.373948i	$0.878004\pi$
$432$		0			0
$433$	11.6652	+	11.6652i	0.560594	+	0.560594i	0.929476	−	0.368882i	$-0.120259\pi$
$433$	11.6652	+	11.6652i	0.560594	+	0.560594i	−0.368882	+	0.929476i	$0.620259\pi$
$434$		0			0
$435$	2.66148	+	37.2675i	0.127608	+	1.78684i
$436$		0			0
$437$	−6.20554	+	6.20554i	−0.296851	+	0.296851i
$438$		0			0
$439$	−9.26726			−0.442302			−0.221151	−	0.975240i	$-0.570981\pi$
$439$	−9.26726			−0.442302			−0.221151	+	0.975240i	$0.570981\pi$
$440$		0			0
$441$			25.4978i			1.21418i
$442$		0			0
$443$	−19.7745	+	19.7745i	−0.939513	+	0.939513i	−0.998272	−	0.0587591i	$-0.981286\pi$
$443$	−19.7745	+	19.7745i	−0.939513	+	0.939513i	0.0587591	+	0.998272i	$0.481286\pi$
$444$		0			0
$445$	17.3584	+	17.3584i	0.822865	+	0.822865i
$446$		0			0
$447$	−41.6410	+	41.6410i	−1.96955	+	1.96955i
$448$		0			0
$449$	23.7792	−	23.7792i	1.12221	−	1.12221i	0.130804	−	0.991408i	$-0.458244\pi$
$449$	23.7792	−	23.7792i	1.12221	−	1.12221i	0.991408	−	0.130804i	$-0.0417557\pi$
$450$		0			0
$451$		−	19.7520i		−	0.930085i
$452$		0			0
$453$	50.5440	+	50.5440i	2.37476	+	2.37476i
$454$		0			0
$455$		−	12.1412i		−	0.569188i
$456$		0			0
$457$		−	23.5481i		−	1.10153i	−0.834660	−	0.550766i	$-0.814336\pi$
$457$		−	23.5481i		−	1.10153i	0.834660	−	0.550766i	$-0.185664\pi$
$458$		0			0
$459$		−	85.3615i		−	3.98433i
$460$		0			0
$461$	−2.93428	−	2.93428i	−0.136663	−	0.136663i	0.635466	−	0.772129i	$-0.280808\pi$
$461$	−2.93428	−	2.93428i	−0.136663	−	0.136663i	−0.772129	+	0.635466i	$0.780808\pi$
$462$		0			0
$463$	−15.1419			−0.703702			−0.351851	−	0.936056i	$-0.614448\pi$
$463$	−15.1419			−0.703702			−0.351851	+	0.936056i	$0.614448\pi$
$464$		0			0
$465$	45.0603			2.08962
$466$		0			0
$467$	−7.79778	−	7.79778i	−0.360838	−	0.360838i	0.503283	−	0.864121i	$-0.332125\pi$
$467$	−7.79778	−	7.79778i	−0.360838	−	0.360838i	−0.864121	+	0.503283i	$0.832125\pi$
$468$		0			0
$469$			5.30452i			0.244940i
$470$		0			0
$471$		−	42.5174i		−	1.95910i
$472$		0			0
$473$		−	31.3664i		−	1.44223i
$474$		0			0
$475$	−2.10181	−	2.10181i	−0.0964375	−	0.0964375i
$476$		0			0
$477$		−	3.00453i		−	0.137568i
$478$		0			0
$479$	−2.19287	+	2.19287i	−0.100195	+	0.100195i	−0.755427	−	0.655232i	$-0.772571\pi$
$479$	−2.19287	+	2.19287i	−0.100195	+	0.100195i	0.655232	+	0.755427i	$0.272571\pi$
$480$		0			0
$481$	−18.6757	+	18.6757i	−0.851537	+	0.851537i
$482$		0			0
$483$	5.72874	+	5.72874i	0.260667	+	0.260667i
$484$		0			0
$485$	−3.63480	+	3.63480i	−0.165048	+	0.165048i
$486$		0			0
$487$			14.2054i			0.643707i	0.946789	+	0.321854i	$0.104306\pi$
$487$			14.2054i			0.643707i	−0.946789	+	0.321854i	$0.895694\pi$
$488$		0			0
$489$	−9.02352			−0.408058
$490$		0			0
$491$	16.8592	−	16.8592i	0.760845	−	0.760845i	−0.215631	−	0.976475i	$-0.569181\pi$
$491$	16.8592	−	16.8592i	0.760845	−	0.760845i	0.976475	+	0.215631i	$0.0691807\pi$
$492$		0			0
$493$	2.20770	+	30.9134i	0.0994300	+	1.39227i
$494$		0			0
$495$	−37.9281	−	37.9281i	−1.70474	−	1.70474i
$496$		0			0
$497$			6.99673i			0.313846i
$498$		0			0
$499$	13.5638			0.607200			0.303600	−	0.952800i	$-0.401811\pi$
$499$	13.5638			0.607200			0.303600	+	0.952800i	$0.401811\pi$
$500$		0			0
$501$	28.0844	+	28.0844i	1.25472	+	1.25472i
$502$		0			0
$503$	10.3876	−	10.3876i	0.463162	−	0.463162i	−0.436529	−	0.899690i	$-0.643792\pi$
$503$	10.3876	−	10.3876i	0.463162	−	0.463162i	0.899690	+	0.436529i	$0.143792\pi$
$504$		0			0
$505$	16.8609	+	16.8609i	0.750301	+	0.750301i
$506$		0			0
$507$	−9.38954	−	9.38954i	−0.417004	−	0.417004i
$508$		0			0
$509$	30.5084			1.35226			0.676131	−	0.736781i	$-0.263655\pi$
$509$	30.5084			1.35226			0.676131	+	0.736781i	$0.263655\pi$
$510$		0			0
$511$	−18.6602	+	18.6602i	−0.825480	+	0.825480i
$512$		0			0
$513$	−99.4765			−4.39199
$514$		0			0
$515$	39.4958			1.74039
$516$		0			0
$517$	−13.6527			−0.600444
$518$		0			0
$519$	2.50507	−	2.50507i	0.109960	−	0.109960i
$520$		0			0
$521$			42.8384i			1.87679i	0.345570	+	0.938393i	$0.387685\pi$
$521$			42.8384i			1.87679i	−0.345570	+	0.938393i	$0.612315\pi$
$522$		0			0
$523$			5.93677i			0.259597i	0.991540	+	0.129798i	$0.0414330\pi$
$523$			5.93677i			0.259597i	−0.991540	+	0.129798i	$0.958567\pi$
$524$		0			0
$525$	−1.94032	+	1.94032i	−0.0846823	+	0.0846823i
$526$		0			0
$527$	37.3776			1.62819
$528$		0			0
$529$	21.2877			0.925554
$530$		0			0
$531$	−11.9343			−0.517904
$532$		0			0
$533$	−12.5523	+	12.5523i	−0.543700	+	0.543700i
$534$		0			0
$535$	14.2189			0.614737
$536$		0			0
$537$	2.54101	+	2.54101i	0.109652	+	0.109652i
$538$		0			0
$539$	7.91920	+	7.91920i	0.341104	+	0.341104i
$540$		0			0
$541$	−25.9798	+	25.9798i	−1.11696	+	1.11696i	−0.124773	+	0.992185i	$0.539820\pi$
$541$	−25.9798	+	25.9798i	−1.11696	+	1.11696i	−0.992185	+	0.124773i	$0.960180\pi$
$542$		0			0
$543$	−19.1321	−	19.1321i	−0.821035	−	0.821035i
$544$		0			0
$545$	−34.9560			−1.49735
$546$		0			0
$547$		−	7.65904i		−	0.327477i	−0.986504	−	0.163738i	$-0.947645\pi$
$547$		−	7.65904i		−	0.327477i	0.986504	−	0.163738i	$-0.0523553\pi$
$548$		0			0
$549$	9.70369	+	9.70369i	0.414144	+	0.414144i
$550$		0			0
$551$	36.0251	−	2.57276i	1.53472	−	0.109603i
$552$		0			0
$553$	−13.9725	+	13.9725i	−0.594172	+	0.594172i
$554$		0			0
$555$	−61.3734			−2.60516
$556$		0			0
$557$			29.6408i			1.25592i	0.778244	+	0.627961i	$0.216110\pi$
$557$			29.6408i			1.25592i	−0.778244	+	0.627961i	$0.783890\pi$
$558$		0			0
$559$	−19.9332	+	19.9332i	−0.843083	+	0.843083i
$560$		0			0
$561$	−43.9402	−	43.9402i	−1.85516	−	1.85516i
$562$		0			0
$563$	−9.55091	+	9.55091i	−0.402523	+	0.402523i	−0.879121	−	0.476598i	$-0.841870\pi$
$563$	−9.55091	+	9.55091i	−0.402523	+	0.402523i	0.476598	+	0.879121i	$0.341870\pi$
$564$		0			0
$565$	15.7205	−	15.7205i	0.661366	−	0.661366i
$566$		0			0
$567$			48.6085i			2.04136i
$568$		0			0
$569$	−20.5267	−	20.5267i	−0.860524	−	0.860524i	0.130875	−	0.991399i	$-0.458221\pi$
$569$	−20.5267	−	20.5267i	−0.860524	−	0.860524i	−0.991399	+	0.130875i	$0.958221\pi$
$570$		0			0
$571$			29.7450i			1.24479i	0.782703	+	0.622396i	$0.213841\pi$
$571$			29.7450i			1.24479i	−0.782703	+	0.622396i	$0.786159\pi$
$572$		0			0
$573$		−	29.6580i		−	1.23898i
$574$		0			0
$575$		−	0.579937i		−	0.0241851i
$576$		0			0
$577$	7.01571	+	7.01571i	0.292068	+	0.292068i	0.837897	−	0.545829i	$-0.183785\pi$
$577$	7.01571	+	7.01571i	0.292068	+	0.292068i	−0.545829	+	0.837897i	$0.683785\pi$
$578$		0			0
$579$	22.9391			0.953318
$580$		0			0
$581$	4.93319			0.204663
$582$		0			0
$583$	−0.933156	−	0.933156i	−0.0386474	−	0.0386474i
$584$		0			0
$585$			48.2062i			1.99308i
$586$		0			0
$587$		−	6.28185i		−	0.259280i	−0.991561	−	0.129640i	$-0.958618\pi$
$587$		−	6.28185i		−	0.259280i	0.991561	−	0.129640i	$-0.0413821\pi$
$588$		0			0
$589$		−	43.5582i		−	1.79478i
$590$		0			0
$591$	−42.6254	−	42.6254i	−1.75337	−	1.75337i
$592$		0			0
$593$			19.7528i			0.811149i	0.914062	+	0.405575i	$0.132929\pi$
$593$			19.7528i			0.811149i	−0.914062	+	0.405575i	$0.867071\pi$
$594$		0			0
$595$	16.5483	−	16.5483i	0.678413	−	0.678413i
$596$		0			0
$597$	54.7585	−	54.7585i	2.24112	−	2.24112i
$598$		0			0
$599$	15.7186	+	15.7186i	0.642244	+	0.642244i	0.951107	−	0.308862i	$-0.0999482\pi$
$599$	15.7186	+	15.7186i	0.642244	+	0.642244i	−0.308862	+	0.951107i	$0.599948\pi$
$600$		0			0
$601$	20.7768	−	20.7768i	0.847503	−	0.847503i	−0.142318	−	0.989821i	$-0.545455\pi$
$601$	20.7768	−	20.7768i	0.847503	−	0.847503i	0.989821	+	0.142318i	$0.0454555\pi$
$602$		0			0
$603$		−	21.0614i		−	0.857687i
$604$		0			0
$605$	−0.0783359			−0.00318481
$606$		0			0
$607$	6.81893	−	6.81893i	0.276772	−	0.276772i	−0.555047	−	0.831819i	$-0.687300\pi$
$607$	6.81893	−	6.81893i	0.276772	−	0.276772i	0.831819	+	0.555047i	$0.187300\pi$
$608$		0			0
$609$	−2.37508	−	33.2571i	−0.0962432	−	1.34765i
$610$		0			0
$611$	8.67621	+	8.67621i	0.351002	+	0.351002i
$612$		0			0
$613$		−	27.6400i		−	1.11637i	−0.829717	−	0.558185i	$-0.811498\pi$
$613$		−	27.6400i		−	1.11637i	0.829717	−	0.558185i	$-0.188502\pi$
$614$		0			0
$615$	−41.2503			−1.66337
$616$		0			0
$617$	24.6612	+	24.6612i	0.992823	+	0.992823i	0.999974	−	0.00715136i	$-0.00227637\pi$
$617$	24.6612	+	24.6612i	0.992823	+	0.992823i	−0.00715136	+	0.999974i	$0.502276\pi$
$618$		0			0
$619$	13.3962	−	13.3962i	0.538438	−	0.538438i	−0.384632	−	0.923070i	$-0.625672\pi$
$619$	13.3962	−	13.3962i	0.538438	−	0.538438i	0.923070	+	0.384632i	$0.125672\pi$
$620$		0			0
$621$	−13.7239	−	13.7239i	−0.550722	−	0.550722i
$622$		0			0
$623$	−15.4904	−	15.4904i	−0.620611	−	0.620611i
$624$		0			0
$625$	−22.5876			−0.903504
$626$		0			0
$627$	−51.2060	+	51.2060i	−2.04497	+	2.04497i
$628$		0			0
$629$	−50.9093			−2.02989
$630$		0			0
$631$	24.4058			0.971581			0.485790	−	0.874075i	$-0.338532\pi$
$631$	24.4058			0.971581			0.485790	+	0.874075i	$0.338532\pi$
$632$		0			0
$633$	−56.2927			−2.23743
$634$		0			0
$635$	−15.3042	+	15.3042i	−0.607327	+	0.607327i
$636$		0			0
$637$		−	10.0652i		−	0.398799i
$638$		0			0
$639$		−	27.7803i		−	1.09897i
$640$		0			0
$641$	4.14268	−	4.14268i	0.163626	−	0.163626i	−0.620545	−	0.784171i	$-0.713089\pi$
$641$	4.14268	−	4.14268i	0.163626	−	0.163626i	0.784171	+	0.620545i	$0.213089\pi$
$642$		0			0
$643$	−14.3371			−0.565402			−0.282701	−	0.959208i	$-0.591230\pi$
$643$	−14.3371			−0.565402			−0.282701	+	0.959208i	$0.591230\pi$
$644$		0			0
$645$	−65.5059			−2.57929
$646$		0			0
$647$	5.37925			0.211480			0.105740	−	0.994394i	$-0.466279\pi$
$647$	5.37925			0.211480			0.105740	+	0.994394i	$0.466279\pi$
$648$		0			0
$649$	−3.70659	+	3.70659i	−0.145496	+	0.145496i
$650$		0			0
$651$	−40.2114			−1.57601
$652$		0			0
$653$	16.6552	+	16.6552i	0.651770	+	0.651770i	0.953419	−	0.301649i	$-0.0975370\pi$
$653$	16.6552	+	16.6552i	0.651770	+	0.651770i	−0.301649	+	0.953419i	$0.597537\pi$
$654$		0			0
$655$	24.0498	+	24.0498i	0.939705	+	0.939705i
$656$		0			0
$657$	74.0898	−	74.0898i	2.89052	−	2.89052i
$658$		0			0
$659$	30.0901	+	30.0901i	1.17215	+	1.17215i	0.981697	+	0.190448i	$0.0609942\pi$
$659$	30.0901	+	30.0901i	1.17215	+	1.17215i	0.190448	+	0.981697i	$0.439006\pi$
$660$		0			0
$661$	12.1670			0.473242			0.236621	−	0.971602i	$-0.423960\pi$
$661$	12.1670			0.473242			0.236621	+	0.971602i	$0.423960\pi$
$662$		0			0
$663$			55.8475i			2.16894i
$664$		0			0
$665$	−19.2846	−	19.2846i	−0.747825	−	0.747825i
$666$		0			0
$667$	5.32502	+	4.61514i	0.206186	+	0.178699i
$668$		0			0
$669$	53.9255	−	53.9255i	2.08488	−	2.08488i
$670$		0			0
$671$	6.02761			0.232693
$672$		0			0
$673$			34.6914i			1.33725i	0.743598	+	0.668627i	$0.233118\pi$
$673$			34.6914i			1.33725i	−0.743598	+	0.668627i	$0.766882\pi$
$674$		0			0
$675$	4.64827	−	4.64827i	0.178912	−	0.178912i
$676$		0			0
$677$	−16.8412	−	16.8412i	−0.647258	−	0.647258i	0.305071	−	0.952330i	$-0.401320\pi$
$677$	−16.8412	−	16.8412i	−0.647258	−	0.647258i	−0.952330	+	0.305071i	$0.901320\pi$
$678$		0			0
$679$	3.24366	−	3.24366i	0.124480	−	0.124480i
$680$		0			0
$681$	20.0100	−	20.0100i	0.766785	−	0.766785i
$682$		0			0
$683$			16.8600i			0.645130i	0.946547	+	0.322565i	$0.104545\pi$
$683$			16.8600i			0.645130i	−0.946547	+	0.322565i	$0.895455\pi$
$684$		0			0
$685$	0.185249	+	0.185249i	0.00707800	+	0.00707800i
$686$		0			0
$687$		−	33.6354i		−	1.28327i
$688$		0			0
$689$			1.18603i			0.0451842i
$690$		0			0
$691$		−	23.1648i		−	0.881229i	−0.897696	−	0.440615i	$-0.854761\pi$
$691$		−	23.1648i		−	0.881229i	0.897696	−	0.440615i	$-0.145239\pi$
$692$		0			0
$693$	33.8467	+	33.8467i	1.28573	+	1.28573i
$694$		0			0
$695$	23.9726			0.909333
$696$		0			0
$697$	−34.2171			−1.29607
$698$		0			0
$699$	24.5584	+	24.5584i	0.928882	+	0.928882i
$700$		0			0
$701$			13.1681i			0.497353i	0.968587	+	0.248676i	$0.0799956\pi$
$701$			13.1681i			0.497353i	−0.968587	+	0.248676i	$0.920004\pi$
$702$		0			0
$703$			59.3274i			2.23758i
$704$		0			0
$705$			28.5124i			1.07384i
$706$		0			0
$707$	−15.0465	−	15.0465i	−0.565883	−	0.565883i
$708$		0			0
$709$			35.9736i			1.35102i	0.737352	+	0.675509i	$0.236076\pi$
$709$			35.9736i			1.35102i	−0.737352	+	0.675509i	$0.763924\pi$
$710$		0			0
$711$	55.4774	−	55.4774i	2.08056	−	2.08056i
$712$		0			0
$713$	6.00935	−	6.00935i	0.225052	−	0.225052i
$714$		0			0
$715$	14.9720	+	14.9720i	0.559923	+	0.559923i
$716$		0			0
$717$	−37.2075	+	37.2075i	−1.38954	+	1.38954i
$718$		0			0
$719$			32.3490i			1.20641i	0.797585	+	0.603206i	$0.206110\pi$
$719$			32.3490i			1.20641i	−0.797585	+	0.603206i	$0.793890\pi$
$720$		0			0
$721$	−35.2457			−1.31262
$722$		0			0
$723$	−24.5811	+	24.5811i	−0.914180	+	0.914180i
$724$		0			0
$725$	−1.56314	+	1.80358i	−0.0580535	+	0.0669831i
$726$		0			0
$727$	−18.8456	−	18.8456i	−0.698945	−	0.698945i	0.265238	−	0.964183i	$-0.414549\pi$
$727$	−18.8456	−	18.8456i	−0.698945	−	0.698945i	−0.964183	+	0.265238i	$0.914549\pi$
$728$		0			0
$729$		−	48.3757i		−	1.79169i
$730$		0			0
$731$	−54.3372			−2.00973
$732$		0			0
$733$	−9.60069	−	9.60069i	−0.354610	−	0.354610i	0.507212	−	0.861821i	$-0.330676\pi$
$733$	−9.60069	−	9.60069i	−0.354610	−	0.354610i	−0.861821	+	0.507212i	$0.830676\pi$
$734$		0			0
$735$	16.5385	−	16.5385i	0.610033	−	0.610033i
$736$		0			0
$737$	−6.54132	−	6.54132i	−0.240953	−	0.240953i
$738$		0			0
$739$	−23.8355	−	23.8355i	−0.876804	−	0.876804i	0.116398	−	0.993203i	$-0.462865\pi$
$739$	−23.8355	−	23.8355i	−0.876804	−	0.876804i	−0.993203	+	0.116398i	$0.962865\pi$
$740$		0			0
$741$	65.0822			2.39086
$742$		0			0
$743$	−4.12930	+	4.12930i	−0.151489	+	0.151489i	−0.778783	−	0.627294i	$-0.784163\pi$
$743$	−4.12930	+	4.12930i	−0.151489	+	0.151489i	0.627294	+	0.778783i	$0.284163\pi$
$744$		0			0
$745$	38.6778			1.41704
$746$		0			0
$747$	−19.5871			−0.716654
$748$		0			0
$749$	−12.6888			−0.463639
$750$		0			0
$751$	−18.0363	+	18.0363i	−0.658154	+	0.658154i	−0.954943	−	0.296789i	$-0.904084\pi$
$751$	−18.0363	+	18.0363i	−0.658154	+	0.658154i	0.296789	+	0.954943i	$0.404084\pi$
$752$		0			0
$753$		−	23.2368i		−	0.846795i
$754$		0			0
$755$		−	46.9472i		−	1.70858i
$756$		0			0
$757$	4.72189	−	4.72189i	0.171620	−	0.171620i	−0.616071	−	0.787691i	$-0.711277\pi$
$757$	4.72189	−	4.72189i	0.171620	−	0.171620i	0.787691	+	0.616071i	$0.211277\pi$
$758$		0			0
$759$	−14.1289			−0.512847
$760$		0			0
$761$	−15.7390			−0.570539			−0.285269	−	0.958447i	$-0.592083\pi$
$761$	−15.7390			−0.570539			−0.285269	+	0.958447i	$0.592083\pi$
$762$		0			0
$763$	31.1944			1.12931
$764$		0			0
$765$	−65.7043	+	65.7043i	−2.37555	+	2.37555i
$766$		0			0
$767$	4.71103			0.170106
$768$		0			0
$769$	−21.7146	−	21.7146i	−0.783050	−	0.783050i	0.197295	−	0.980344i	$-0.436784\pi$
$769$	−21.7146	−	21.7146i	−0.783050	−	0.783050i	−0.980344	+	0.197295i	$0.936784\pi$
$770$		0			0
$771$	46.4085	+	46.4085i	1.67136	+	1.67136i
$772$		0			0
$773$	28.6858	−	28.6858i	1.03176	−	1.03176i	0.0322764	−	0.999479i	$-0.489724\pi$
$773$	28.6858	−	28.6858i	1.03176	−	1.03176i	0.999479	−	0.0322764i	$-0.0102757\pi$
$774$		0			0
$775$	2.03536	+	2.03536i	0.0731123	+	0.0731123i
$776$		0			0
$777$	54.7690			1.96483
$778$		0			0
$779$			39.8751i			1.42867i
$780$		0			0
$781$	−8.62809	−	8.62809i	−0.308737	−	0.308737i
$782$		0			0
$783$	5.68981	+	79.6717i	0.203337	+	2.84723i
$784$		0			0
$785$	−19.7459	+	19.7459i	−0.704760	+	0.704760i
$786$		0			0
$787$	23.5274			0.838663			0.419331	−	0.907833i	$-0.362265\pi$
$787$	23.5274			0.838663			0.419331	+	0.907833i	$0.362265\pi$
$788$		0			0
$789$		−	68.1796i		−	2.42726i
$790$		0			0
$791$	−14.0288	+	14.0288i	−0.498807	+	0.498807i
$792$		0			0
$793$	−3.83051	−	3.83051i	−0.136026	−	0.136026i
$794$		0			0
$795$	−1.94881	+	1.94881i	−0.0691173	+	0.0691173i
$796$		0			0
$797$	16.3369	−	16.3369i	0.578682	−	0.578682i	−0.355858	−	0.934540i	$-0.615811\pi$
$797$	16.3369	−	16.3369i	0.578682	−	0.578682i	0.934540	+	0.355858i	$0.115811\pi$
$798$		0			0
$799$			23.6511i			0.836715i
$800$		0			0
$801$	61.5043	+	61.5043i	2.17315	+	2.17315i
$802$		0			0
$803$		−	46.0221i		−	1.62408i
$804$		0			0
$805$		−	5.32107i		−	0.187543i
$806$		0			0
$807$			77.5306i			2.72921i
$808$		0			0
$809$	27.9059	+	27.9059i	0.981121	+	0.981121i	0.999825	−	0.0187041i	$-0.00595405\pi$
$809$	27.9059	+	27.9059i	0.981121	+	0.981121i	−0.0187041	+	0.999825i	$0.505954\pi$
$810$		0			0
$811$	−16.3493			−0.574102			−0.287051	−	0.957915i	$-0.592675\pi$
$811$	−16.3493			−0.574102			−0.287051	+	0.957915i	$0.592675\pi$
$812$		0			0
$813$	−34.5554			−1.21191
$814$		0			0
$815$	4.19069	+	4.19069i	0.146794	+	0.146794i
$816$		0			0
$817$			63.3221i			2.21536i
$818$		0			0
$819$		−	43.0188i		−	1.50320i
$820$		0			0
$821$			28.0677i			0.979570i	0.871843	+	0.489785i	$0.162925\pi$
$821$			28.0677i			0.979570i	−0.871843	+	0.489785i	$0.837075\pi$
$822$		0			0
$823$	−34.2131	−	34.2131i	−1.19259	−	1.19259i	−0.976337	−	0.216257i	$-0.930615\pi$
$823$	−34.2131	−	34.2131i	−1.19259	−	1.19259i	−0.216257	−	0.976337i	$-0.569385\pi$
$824$		0			0
$825$		−	4.78544i		−	0.166608i
$826$		0			0
$827$	1.15392	−	1.15392i	0.0401259	−	0.0401259i	−0.686759	−	0.726885i	$-0.740967\pi$
$827$	1.15392	−	1.15392i	0.0401259	−	0.0401259i	0.726885	+	0.686759i	$0.240967\pi$
$828$		0			0
$829$	−30.0776	+	30.0776i	−1.04464	+	1.04464i	−0.0456840	+	0.998956i	$0.514547\pi$
$829$	−30.0776	+	30.0776i	−1.04464	+	1.04464i	−0.998956	+	0.0456840i	$0.985453\pi$
$830$		0			0
$831$	−53.0024	−	53.0024i	−1.83863	−	1.83863i
$832$		0			0
$833$	13.7187	−	13.7187i	0.475326	−	0.475326i
$834$		0			0
$835$		−	26.0858i		−	0.902738i
$836$		0			0
$837$	96.3316			3.32971
$838$		0			0
$839$	10.2078	−	10.2078i	0.352414	−	0.352414i	−0.508593	−	0.861007i	$-0.669834\pi$
$839$	10.2078	−	10.2078i	0.352414	−	0.352414i	0.861007	+	0.508593i	$0.169834\pi$
$840$		0			0
$841$	−4.12110	−	28.7057i	−0.142107	−	0.989851i
$842$		0			0
$843$	12.8428	+	12.8428i	0.442329	+	0.442329i
$844$		0			0
$845$			8.72136i			0.300024i
$846$		0			0
$847$	0.0699062			0.00240201
$848$		0			0
$849$	43.1702	+	43.1702i	1.48160	+	1.48160i
$850$		0			0
$851$	−8.18490	+	8.18490i	−0.280575	+	0.280575i
$852$		0			0
$853$	−6.67775	−	6.67775i	−0.228642	−	0.228642i	0.583483	−	0.812125i	$-0.301689\pi$
$853$	−6.67775	−	6.67775i	−0.228642	−	0.228642i	−0.812125	+	0.583483i	$0.801689\pi$
$854$		0			0
$855$	76.5689	+	76.5689i	2.61860	+	2.61860i
$856$		0			0
$857$	−11.6635			−0.398416			−0.199208	−	0.979957i	$-0.563837\pi$
$857$	−11.6635			−0.398416			−0.199208	+	0.979957i	$0.563837\pi$
$858$		0			0
$859$	−2.74766	+	2.74766i	−0.0937488	+	0.0937488i	−0.752426	−	0.658677i	$-0.771116\pi$
$859$	−2.74766	+	2.74766i	−0.0937488	+	0.0937488i	0.658677	+	0.752426i	$0.271116\pi$
$860$		0			0
$861$	36.8113			1.25453
$862$		0			0
$863$	−3.44819			−0.117378			−0.0586889	−	0.998276i	$-0.518692\pi$
$863$	−3.44819			−0.117378			−0.0586889	+	0.998276i	$0.518692\pi$
$864$		0			0
$865$	−2.32681			−0.0791138
$866$		0			0
$867$	−37.0497	+	37.0497i	−1.25827	+	1.25827i
$868$		0			0
$869$		−	34.4607i		−	1.16900i
$870$		0			0
$871$			8.31395i			0.281707i
$872$		0			0
$873$	−12.8789	+	12.8789i	−0.435883	+	0.435883i
$874$		0			0
$875$	22.1345			0.748282
$876$		0			0
$877$	−34.8707			−1.17750			−0.588750	−	0.808315i	$-0.700380\pi$
$877$	−34.8707			−1.17750			−0.588750	+	0.808315i	$0.700380\pi$
$878$		0			0
$879$	30.5090			1.02904
$880$		0			0
$881$	29.0380	−	29.0380i	0.978314	−	0.978314i	−0.0214555	−	0.999770i	$-0.506830\pi$
$881$	29.0380	−	29.0380i	0.978314	−	0.978314i	0.999770	+	0.0214555i	$0.00683002\pi$
$882$		0			0
$883$	33.5732			1.12983			0.564915	−	0.825149i	$-0.308909\pi$
$883$	33.5732			1.12983			0.564915	+	0.825149i	$0.308909\pi$
$884$		0			0
$885$	7.74087	+	7.74087i	0.260207	+	0.260207i
$886$		0			0
$887$	−24.2296	−	24.2296i	−0.813552	−	0.813552i	0.171613	−	0.985165i	$-0.445102\pi$
$887$	−24.2296	−	24.2296i	−0.813552	−	0.813552i	−0.985165	+	0.171613i	$0.945102\pi$
$888$		0			0
$889$	13.6573	−	13.6573i	0.458051	−	0.458051i
$890$		0			0
$891$	−59.9420	−	59.9420i	−2.00813	−	2.00813i
$892$		0			0
$893$	27.5619			0.922324
$894$		0			0
$895$		−	2.36018i		−	0.0788922i
$896$		0			0
$897$	8.97885	+	8.97885i	0.299795	+	0.299795i
$898$		0			0
$899$	−34.8862	+	2.49142i	−1.16352	+	0.0830936i
$900$		0			0
$901$	−1.61654	+	1.61654i	−0.0538548	+	0.0538548i
$902$		0			0
$903$	58.4568			1.94532
$904$		0			0
$905$			17.7706i			0.590714i
$906$		0			0
$907$	13.9134	−	13.9134i	0.461987	−	0.461987i	−0.437320	−	0.899306i	$-0.644072\pi$
$907$	13.9134	−	13.9134i	0.461987	−	0.461987i	0.899306	+	0.437320i	$0.144072\pi$
$908$		0			0
$909$	59.7417	+	59.7417i	1.98151	+	1.98151i
$910$		0			0
$911$	5.27772	−	5.27772i	0.174859	−	0.174859i	−0.614252	−	0.789110i	$-0.710542\pi$
$911$	5.27772	−	5.27772i	0.174859	−	0.174859i	0.789110	+	0.614252i	$0.210542\pi$
$912$		0			0
$913$	−6.08342	+	6.08342i	−0.201332	+	0.201332i
$914$		0			0
$915$		−	12.5881i		−	0.416150i
$916$		0			0
$917$	−21.4618	−	21.4618i	−0.708732	−	0.708732i
$918$		0			0
$919$		−	41.5984i		−	1.37220i	−0.727506	−	0.686102i	$-0.759320\pi$
$919$		−	41.5984i		−	1.37220i	0.727506	−	0.686102i	$-0.240680\pi$
$920$		0			0
$921$		−	58.7021i		−	1.93430i
$922$		0			0
$923$			10.9662i			0.360957i
$924$		0			0
$925$	−2.77222	−	2.77222i	−0.0911499	−	0.0911499i
$926$		0			0
$927$	139.942			4.59630
$928$		0			0
$929$	27.0177			0.886420			0.443210	−	0.896418i	$-0.353840\pi$
$929$	27.0177			0.886420			0.443210	+	0.896418i	$0.353840\pi$
$930$		0			0
$931$	−15.9872	−	15.9872i	−0.523960	−	0.523960i
$932$		0			0
$933$		−	51.2165i		−	1.67675i
$934$		0			0
$935$			40.8133i			1.33474i
$936$		0			0
$937$		−	22.8127i		−	0.745258i	−0.927980	−	0.372629i	$-0.878456\pi$
$937$		−	22.8127i		−	0.745258i	0.927980	−	0.372629i	$-0.121544\pi$
$938$		0			0
$939$	−13.8776	−	13.8776i	−0.452878	−	0.452878i
$940$		0			0
$941$		−	8.97740i		−	0.292655i	−0.989236	−	0.146327i	$-0.953255\pi$
$941$		−	8.97740i		−	0.292655i	0.989236	−	0.146327i	$-0.0467453\pi$
$942$		0			0
$943$	−5.50124	+	5.50124i	−0.179145	+	0.179145i
$944$		0			0
$945$	42.6491	−	42.6491i	1.38738	−	1.38738i
$946$		0			0
$947$	13.3286	+	13.3286i	0.433122	+	0.433122i	0.889689	−	0.456567i	$-0.150921\pi$
$947$	13.3286	+	13.3286i	0.433122	+	0.433122i	−0.456567	+	0.889689i	$0.650921\pi$
$948$		0			0
$949$	−29.2468	+	29.2468i	−0.949391	+	0.949391i
$950$		0			0
$951$		−	7.40045i		−	0.239976i
$952$		0			0
$953$	20.4873			0.663647			0.331824	−	0.943341i	$-0.392336\pi$
$953$	20.4873			0.663647			0.331824	+	0.943341i	$0.392336\pi$
$954$		0			0
$955$	−13.7737	+	13.7737i	−0.445708	+	0.445708i
$956$		0			0
$957$	43.9402	+	38.0825i	1.42039	+	1.23103i
$958$		0			0
$959$	−0.165314	−	0.165314i	−0.00533828	−	0.00533828i
$960$		0			0
$961$			11.1811i			0.360681i
$962$		0			0
$963$	50.3805			1.62349
$964$		0			0
$965$	−10.6534	−	10.6534i	−0.342944	−	0.342944i
$966$		0			0
$967$	−6.37578	+	6.37578i	−0.205031	+	0.205031i	−0.802152	−	0.597120i	$-0.796311\pi$
$967$	−6.37578	+	6.37578i	−0.205031	+	0.205031i	0.597120	+	0.802152i	$0.296311\pi$
$968$		0			0
$969$	88.7061	+	88.7061i	2.84965	+	2.84965i
$970$		0			0
$971$	19.9261	+	19.9261i	0.639458	+	0.639458i	0.950422	−	0.310964i	$-0.100652\pi$
$971$	19.9261	+	19.9261i	0.639458	+	0.639458i	−0.310964	+	0.950422i	$0.600652\pi$
$972$		0			0
$973$	−21.3929			−0.685826
$974$		0			0
$975$	−3.04112	+	3.04112i	−0.0973939	+	0.0973939i
$976$		0			0
$977$	−5.95286			−0.190449			−0.0952245	−	0.995456i	$-0.530357\pi$
$977$	−5.95286			−0.190449			−0.0952245	+	0.995456i	$0.530357\pi$
$978$		0			0
$979$	38.2044			1.22102
$980$		0			0
$981$	−123.856			−3.95443
$982$		0			0
$983$	26.2561	−	26.2561i	0.837438	−	0.837438i	−0.151083	−	0.988521i	$-0.548276\pi$
$983$	26.2561	−	26.2561i	0.837438	−	0.837438i	0.988521	+	0.151083i	$0.0482760\pi$
$984$		0			0
$985$			39.5921i			1.26151i
$986$		0			0
$987$		−	25.4442i		−	0.809898i
$988$		0			0
$989$	−8.73602	+	8.73602i	−0.277789	+	0.277789i
$990$		0			0
$991$	−6.07378			−0.192940			−0.0964700	−	0.995336i	$-0.530755\pi$
$991$	−6.07378			−0.192940			−0.0964700	+	0.995336i	$0.530755\pi$
$992$		0			0
$993$	32.1187			1.01926
$994$		0			0
$995$	−50.8618			−1.61243
$996$		0			0
$997$	19.4264	−	19.4264i	0.615240	−	0.615240i	−0.329067	−	0.944307i	$-0.606734\pi$
$997$	19.4264	−	19.4264i	0.615240	−	0.615240i	0.944307	+	0.329067i	$0.106734\pi$
$998$		0			0
$999$	−131.206			−4.15118

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	928.2.k.e.191.1	✓	10
4.3	odd	2		928.2.k.f.191.5	yes	10
29.12	odd	4		928.2.k.f.447.5	yes	10
116.99	even	4	inner	928.2.k.e.447.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
928.2.k.e.191.1	✓	10	1.1	even	1	trivial
928.2.k.e.447.1	yes	10	116.99	even	4	inner
928.2.k.f.191.5	yes	10	4.3	odd	2
928.2.k.f.447.5	yes	10	29.12	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 928 = 2^{5} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	928.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.29821 - 2.29821i) q^{3} +2.13467i q^{5} -1.90496i q^{7} +7.56357i q^{9} +O(q^{10})\)	\(q+(-2.29821 - 2.29821i) q^{3} +2.13467i q^{5} -1.90496i q^{7} +7.56357i q^{9} +(2.34912 + 2.34912i) q^{11} -2.98570i q^{13} +(4.90592 - 4.90592i) q^{15} +(4.06947 - 4.06947i) q^{17} +(-4.74237 - 4.74237i) q^{19} +(-4.37800 + 4.37800i) q^{21} -1.30853i q^{23} +0.443197 q^{25} +(10.4880 - 10.4880i) q^{27} +(-3.52696 + 4.06947i) q^{29} +(4.59245 + 4.59245i) q^{31} -10.7975i q^{33} +4.06645 q^{35} +(-6.25504 - 6.25504i) q^{37} +(-6.86178 + 6.86178i) q^{39} +(-4.20413 - 4.20413i) q^{41} +(-6.67621 - 6.67621i) q^{43} -16.1457 q^{45} +(-2.90592 + 2.90592i) q^{47} +3.37114 q^{49} -18.7050 q^{51} -0.397237 q^{53} +(-5.01458 + 5.01458i) q^{55} +21.7980i q^{57} +1.57786i q^{59} +(1.28295 - 1.28295i) q^{61} +14.4083 q^{63} +6.37348 q^{65} -2.78459 q^{67} +(-3.00728 + 3.00728i) q^{69} -3.67291 q^{71} +(-9.79561 - 9.79561i) q^{73} +(-1.01856 - 1.01856i) q^{75} +(4.47496 - 4.47496i) q^{77} +(-7.33482 - 7.33482i) q^{79} -25.5168 q^{81} +2.58966i q^{83} +(8.68695 + 8.68695i) q^{85} +(17.4582 - 1.24679i) q^{87} +(8.13165 - 8.13165i) q^{89} -5.68763 q^{91} -21.1088i q^{93} +(10.1234 - 10.1234i) q^{95} +(1.70275 + 1.70275i) q^{97} +(-17.7677 + 17.7677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{3}+O(q^{10}) \) 10 * q - 2 * q^3	\( 10 q - 2 q^{3} - 14 q^{11} + 14 q^{15} + 6 q^{17} - 12 q^{19} - 28 q^{21} + 2 q^{25} - 2 q^{27} - 28 q^{29} + 14 q^{31} + 4 q^{35} + 10 q^{37} + 6 q^{39} + 14 q^{41} - 30 q^{43} - 36 q^{45} + 6 q^{47} - 42 q^{49} - 56 q^{51} + 4 q^{53} - 42 q^{55} - 26 q^{61} + 32 q^{63} - 36 q^{65} - 56 q^{67} + 16 q^{69} - 36 q^{71} - 22 q^{73} + 8 q^{75} + 28 q^{77} - 6 q^{79} - 54 q^{81} - 16 q^{85} + 58 q^{87} + 58 q^{89} + 20 q^{91} + 52 q^{95} + 26 q^{97} - 68 q^{99}+O(q^{100}) \) 10 * q - 2 * q^3 - 14 * q^11 + 14 * q^15 + 6 * q^17 - 12 * q^19 - 28 * q^21 + 2 * q^25 - 2 * q^27 - 28 * q^29 + 14 * q^31 + 4 * q^35 + 10 * q^37 + 6 * q^39 + 14 * q^41 - 30 * q^43 - 36 * q^45 + 6 * q^47 - 42 * q^49 - 56 * q^51 + 4 * q^53 - 42 * q^55 - 26 * q^61 + 32 * q^63 - 36 * q^65 - 56 * q^67 + 16 * q^69 - 36 * q^71 - 22 * q^73 + 8 * q^75 + 28 * q^77 - 6 * q^79 - 54 * q^81 - 16 * q^85 + 58 * q^87 + 58 * q^89 + 20 * q^91 + 52 * q^95 + 26 * q^97 - 68 * q^99

Introduction

L-functions

Modular forms

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Database

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