LMFDB - Embedded newform 896.2.bi.a.271.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(47,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 20]))

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

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

chi := DirichletCharacter("896.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bi (of order $24$, degree $8$, not 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			271.9
Character	$\chi$	$=$	896.271
Dual form			896.2.bi.a.367.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.788053 + 1.02701i) q^{3} +(1.15943 + 1.51100i) q^{5} +(-0.624522 - 2.57099i) q^{7} +(0.342734 + 1.27910i) q^{9} +O(q^{10})$	\(q+(-0.788053 + 1.02701i) q^{3} +(1.15943 + 1.51100i) q^{5} +(-0.624522 - 2.57099i) q^{7} +(0.342734 + 1.27910i) q^{9} +(-0.664765 - 5.04939i) q^{11} +(-2.64057 - 6.37490i) q^{13} -2.46550 q^{15} +(0.520718 + 0.901911i) q^{17} +(0.185877 - 1.41188i) q^{19} +(3.13259 + 1.38468i) q^{21} +(-3.16081 + 0.846936i) q^{23} +(0.355257 - 1.32584i) q^{25} +(-5.17168 - 2.14218i) q^{27} +(-1.14636 - 2.76757i) q^{29} +(1.53764 + 2.66328i) q^{31} +(5.70964 + 3.29646i) q^{33} +(3.16067 - 3.92453i) q^{35} +(7.90414 - 6.06506i) q^{37} +(8.62799 + 2.31186i) q^{39} +(0.859509 + 0.859509i) q^{41} +(5.93649 + 2.45898i) q^{43} +(-1.53534 + 2.00090i) q^{45} +(1.27846 + 0.738121i) q^{47} +(-6.21995 + 3.21127i) q^{49} +(-1.33663 - 0.175970i) q^{51} +(-8.48833 + 1.11751i) q^{53} +(6.85887 - 6.85887i) q^{55} +(1.30353 + 1.30353i) q^{57} +(1.46984 + 11.1645i) q^{59} +(1.68729 - 12.8162i) q^{61} +(3.07451 - 1.67999i) q^{63} +(6.57090 - 11.3811i) q^{65} +(-7.53594 - 5.78253i) q^{67} +(1.62107 - 3.91361i) q^{69} +(8.22460 - 8.22460i) q^{71} +(0.468243 - 1.74751i) q^{73} +(1.08169 + 1.40968i) q^{75} +(-12.5667 + 4.86255i) q^{77} +(6.23642 - 10.8018i) q^{79} +(2.83516 - 1.63688i) q^{81} +(-5.52119 + 2.28695i) q^{83} +(-0.759049 + 1.83251i) q^{85} +(3.74571 + 1.00366i) q^{87} +(2.58953 + 9.66427i) q^{89} +(-14.7407 + 10.7701i) q^{91} +(-3.94696 - 0.519627i) q^{93} +(2.34886 - 1.35611i) q^{95} +8.78032i q^{97} +(6.23084 - 2.58090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{3} - 12 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 240 * q + 12 * q^3 - 12 * q^5 + 8 * q^7 - 4 * q^9	$ 240 q + 12 q^{3} - 12 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} + 32 q^{15} + 12 q^{19} - 8 q^{21} - 4 q^{23} - 4 q^{25} - 16 q^{29} - 24 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} + 32 q^{43} - 48 q^{45} + 24 q^{47} - 20 q^{51} - 20 q^{53} - 16 q^{57} - 84 q^{59} - 12 q^{61} - 8 q^{65} - 36 q^{67} + 80 q^{71} - 12 q^{73} + 72 q^{75} - 8 q^{77} + 8 q^{79} + 24 q^{85} + 12 q^{87} - 12 q^{89} - 40 q^{91} + 20 q^{93} + 40 q^{99}+O(q^{100}) $ 240 * q + 12 * q^3 - 12 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 + 32 * q^15 + 12 * q^19 - 8 * q^21 - 4 * q^23 - 4 * q^25 - 16 * q^29 - 24 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 + 32 * q^43 - 48 * q^45 + 24 * q^47 - 20 * q^51 - 20 * q^53 - 16 * q^57 - 84 * q^59 - 12 * q^61 - 8 * q^65 - 36 * q^67 + 80 * q^71 - 12 * q^73 + 72 * q^75 - 8 * q^77 + 8 * q^79 + 24 * q^85 + 12 * q^87 - 12 * q^89 - 40 * q^91 + 20 * q^93 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.788053	+	1.02701i	−0.454982	+	0.592945i	−0.963367	−	0.268185i	$-0.913576\pi$
$3$	−0.788053	+	1.02701i	−0.454982	+	0.592945i	0.508385	+	0.861130i	$0.330243\pi$
$4$		0			0
$5$	1.15943	+	1.51100i	0.518513	+	0.675739i	0.977068	−	0.212927i	$-0.0682996\pi$
$5$	1.15943	+	1.51100i	0.518513	+	0.675739i	−0.458555	+	0.888666i	$0.651633\pi$
$6$		0			0
$7$	−0.624522	−	2.57099i	−0.236047	−	0.971742i
$7$	−0.624522	−	2.57099i	−0.236047	−	0.971742i
$8$		0			0
$9$	0.342734	+	1.27910i	0.114245	+	0.426367i
$10$		0			0
$11$	−0.664765	−	5.04939i	−0.200434	−	1.52245i	−0.735434	−	0.677596i	$-0.763022\pi$
$11$	−0.664765	−	5.04939i	−0.200434	−	1.52245i	0.535000	−	0.844852i	$-0.320311\pi$
$12$		0			0
$13$	−2.64057	−	6.37490i	−0.732362	−	1.76808i	−0.634562	−	0.772872i	$-0.718819\pi$
$13$	−2.64057	−	6.37490i	−0.732362	−	1.76808i	−0.0978003	−	0.995206i	$-0.531181\pi$
$14$		0			0
$15$	−2.46550			−0.636590
$16$		0			0
$17$	0.520718	+	0.901911i	0.126293	+	0.218745i	0.922238	−	0.386624i	$-0.126359\pi$
$17$	0.520718	+	0.901911i	0.126293	+	0.218745i	−0.795945	+	0.605369i	$0.793025\pi$
$18$		0			0
$19$	0.185877	−	1.41188i	0.0426432	−	0.323907i	−0.956806	−	0.290726i	$-0.906103\pi$
$19$	0.185877	−	1.41188i	0.0426432	−	0.323907i	0.999449	−	0.0331805i	$-0.0105636\pi$
$20$		0			0
$21$	3.13259	+	1.38468i	0.683586	+	0.302163i
$22$		0			0
$23$	−3.16081	+	0.846936i	−0.659074	+	0.176598i	−0.572828	−	0.819675i	$-0.694154\pi$
$23$	−3.16081	+	0.846936i	−0.659074	+	0.176598i	−0.0862461	+	0.996274i	$0.527487\pi$
$24$		0			0
$25$	0.355257	−	1.32584i	0.0710514	−	0.265168i
$26$		0			0
$27$	−5.17168	−	2.14218i	−0.995290	−	0.412263i
$28$		0			0
$29$	−1.14636	−	2.76757i	−0.212874	−	0.513924i	0.780988	−	0.624546i	$-0.214716\pi$
$29$	−1.14636	−	2.76757i	−0.212874	−	0.513924i	−0.993863	+	0.110621i	$0.964716\pi$
$30$		0			0
$31$	1.53764	+	2.66328i	0.276169	+	0.478339i	0.970429	−	0.241385i	$-0.0776018\pi$
$31$	1.53764	+	2.66328i	0.276169	+	0.478339i	−0.694260	+	0.719724i	$0.744268\pi$
$32$		0			0
$33$	5.70964	+	3.29646i	0.993921	+	0.573841i
$34$		0			0
$35$	3.16067	−	3.92453i	0.534250	−	0.663366i
$36$		0			0
$37$	7.90414	−	6.06506i	1.29943	−	0.997090i	0.300369	−	0.953823i	$-0.402890\pi$
$37$	7.90414	−	6.06506i	1.29943	−	0.997090i	0.999064	−	0.0432669i	$-0.0137766\pi$
$38$		0			0
$39$	8.62799	+	2.31186i	1.38158	+	0.370194i
$40$		0			0
$41$	0.859509	+	0.859509i	0.134233	+	0.134233i	0.771031	−	0.636798i	$-0.219741\pi$
$41$	0.859509	+	0.859509i	0.134233	+	0.134233i	−0.636798	+	0.771031i	$0.719741\pi$
$42$		0			0
$43$	5.93649	+	2.45898i	0.905307	+	0.374990i	0.786258	−	0.617898i	$-0.212016\pi$
$43$	5.93649	+	2.45898i	0.905307	+	0.374990i	0.119049	+	0.992888i	$0.462016\pi$
$44$		0			0
$45$	−1.53534	+	2.00090i	−0.228875	+	0.298276i
$46$		0			0
$47$	1.27846	+	0.738121i	0.186483	+	0.107666i	0.590335	−	0.807158i	$-0.298996\pi$
$47$	1.27846	+	0.738121i	0.186483	+	0.107666i	−0.403852	+	0.914824i	$0.632329\pi$
$48$		0			0
$49$	−6.21995	+	3.21127i	−0.888564	+	0.458753i
$50$		0			0
$51$	−1.33663	−	0.175970i	−0.187165	−	0.0246407i
$52$		0			0
$53$	−8.48833	+	1.11751i	−1.16596	+	0.153502i	−0.688557	−	0.725182i	$-0.741756\pi$
$53$	−8.48833	+	1.11751i	−1.16596	+	0.153502i	−0.477404	+	0.878684i	$0.658422\pi$
$54$		0			0
$55$	6.85887	−	6.85887i	0.924849	−	0.924849i
$56$		0			0
$57$	1.30353	+	1.30353i	0.172657	+	0.172657i
$58$		0			0
$59$	1.46984	+	11.1645i	0.191357	+	1.45350i	0.770066	+	0.637965i	$0.220223\pi$
$59$	1.46984	+	11.1645i	0.191357	+	1.45350i	−0.578709	+	0.815534i	$0.696443\pi$
$60$		0			0
$61$	1.68729	−	12.8162i	0.216035	−	1.64095i	−0.448565	−	0.893750i	$-0.648065\pi$
$61$	1.68729	−	12.8162i	0.216035	−	1.64095i	0.664600	−	0.747199i	$-0.268602\pi$
$62$		0			0
$63$	3.07451	−	1.67999i	0.387352	−	0.211659i
$64$		0			0
$65$	6.57090	−	11.3811i	0.815020	−	1.41166i
$66$		0			0
$67$	−7.53594	−	5.78253i	−0.920662	−	0.706449i	0.0354746	−	0.999371i	$-0.488706\pi$
$67$	−7.53594	−	5.78253i	−0.920662	−	0.706449i	−0.956136	+	0.292922i	$0.905372\pi$
$68$		0			0
$69$	1.62107	−	3.91361i	0.195154	−	0.471144i
$70$		0			0
$71$	8.22460	−	8.22460i	0.976081	−	0.976081i	−0.0236400	−	0.999721i	$-0.507526\pi$
$71$	8.22460	−	8.22460i	0.976081	−	0.976081i	0.999721	+	0.0236400i	$0.00752554\pi$
$72$		0			0
$73$	0.468243	−	1.74751i	0.0548037	−	0.204530i	−0.933095	−	0.359629i	$-0.882903\pi$
$73$	0.468243	−	1.74751i	0.0548037	−	0.204530i	0.987899	+	0.155099i	$0.0495698\pi$
$74$		0			0
$75$	1.08169	+	1.40968i	0.124903	+	0.162776i
$76$		0			0
$77$	−12.5667	+	4.86255i	−1.43211	+	0.554139i
$78$		0			0
$79$	6.23642	−	10.8018i	0.701652	−	1.21530i	−0.266234	−	0.963909i	$-0.585779\pi$
$79$	6.23642	−	10.8018i	0.701652	−	1.21530i	0.967886	−	0.251389i	$-0.0808874\pi$
$80$		0			0
$81$	2.83516	−	1.63688i	0.315018	−	0.181876i
$82$		0			0
$83$	−5.52119	+	2.28695i	−0.606030	+	0.251026i	−0.664530	−	0.747262i	$-0.731368\pi$
$83$	−5.52119	+	2.28695i	−0.606030	+	0.251026i	0.0585001	+	0.998287i	$0.481368\pi$
$84$		0			0
$85$	−0.759049	+	1.83251i	−0.0823304	+	0.198763i
$86$		0			0
$87$	3.74571	+	1.00366i	0.401583	+	0.107604i
$88$		0			0
$89$	2.58953	+	9.66427i	0.274490	+	1.02441i	0.956182	+	0.292772i	$0.0945777\pi$
$89$	2.58953	+	9.66427i	0.274490	+	1.02441i	−0.681692	+	0.731639i	$0.738756\pi$
$90$		0			0
$91$	−14.7407	+	10.7701i	−1.54524	+	1.12902i
$92$		0			0
$93$	−3.94696	−	0.519627i	−0.409280	−	0.0538828i
$94$		0			0
$95$	2.34886	−	1.35611i	0.240988	−	0.139134i
$96$		0			0
$97$			8.78032i			0.891506i	0.895156	+	0.445753i	$0.147064\pi$
$97$			8.78032i			0.891506i	−0.895156	+	0.445753i	$0.852936\pi$
$98$		0			0
$99$	6.23084	−	2.58090i	0.626223	−	0.259390i
$100$		0			0
$101$	1.79812	−	0.236727i	0.178919	−	0.0235552i	−0.0405341	−	0.999178i	$-0.512906\pi$
$101$	1.79812	−	0.236727i	0.178919	−	0.0235552i	0.219453	+	0.975623i	$0.429573\pi$
$102$		0			0
$103$	−3.33372	+	0.893268i	−0.328481	+	0.0880163i	−0.419291	−	0.907852i	$-0.637721\pi$
$103$	−3.33372	+	0.893268i	−0.328481	+	0.0880163i	0.0908095	+	0.995868i	$0.471055\pi$
$104$		0			0
$105$	1.53976	+	6.33877i	0.150265	+	0.618601i
$106$		0			0
$107$	3.34486	−	2.56660i	0.323360	−	0.248123i	−0.434306	−	0.900765i	$-0.643006\pi$
$107$	3.34486	−	2.56660i	0.323360	−	0.248123i	0.757666	+	0.652643i	$0.226340\pi$
$108$		0			0
$109$	2.89312	+	2.21997i	0.277111	+	0.212635i	0.737961	−	0.674843i	$-0.235789\pi$
$109$	2.89312	+	2.21997i	0.277111	+	0.212635i	−0.460850	+	0.887478i	$0.652455\pi$
$110$		0			0
$111$			12.8972i			1.22415i
$112$		0			0
$113$		−	12.3773i		−	1.16436i	−0.813061	−	0.582178i	$-0.802200\pi$
$113$		−	12.3773i		−	1.16436i	0.813061	−	0.582178i	$-0.197800\pi$
$114$		0			0
$115$	−4.94445	−	3.79401i	−0.461073	−	0.353794i
$116$		0			0
$117$	7.24913	−	5.56245i	0.670182	−	0.514249i
$118$		0			0
$119$	1.99360	−	1.90202i	0.182753	−	0.174358i
$120$		0			0
$121$	−14.4292	+	3.86630i	−1.31175	+	0.351482i
$122$		0			0
$123$	−1.56006	+	0.205386i	−0.140666	+	0.0185190i
$124$		0			0
$125$	11.2132	−	4.64466i	1.00294	−	0.415431i
$126$		0			0
$127$			2.70749i			0.240251i	0.992759	+	0.120126i	$0.0383297\pi$
$127$			2.70749i			0.240251i	−0.992759	+	0.120126i	$0.961670\pi$
$128$		0			0
$129$	−7.20366	+	4.15904i	−0.634247	+	0.366183i
$130$		0			0
$131$	4.67087	+	0.614931i	0.408096	+	0.0537268i	0.331780	−	0.943357i	$-0.392351\pi$
$131$	4.67087	+	0.614931i	0.408096	+	0.0537268i	0.0763159	+	0.997084i	$0.475684\pi$
$132$		0			0
$133$	−3.74600	+	0.403860i	−0.324820	+	0.0350191i
$134$		0			0
$135$	−2.75937	−	10.2981i	−0.237489	−	0.886320i
$136$		0			0
$137$	−2.77832	−	0.744450i	−0.237368	−	0.0636026i	0.138174	−	0.990408i	$-0.455877\pi$
$137$	−2.77832	−	0.744450i	−0.237368	−	0.0636026i	−0.375542	+	0.926805i	$0.622543\pi$
$138$		0			0
$139$	−4.39928	+	10.6208i	−0.373142	+	0.900844i	0.620072	+	0.784545i	$0.287103\pi$
$139$	−4.39928	+	10.6208i	−0.373142	+	0.900844i	−0.993214	+	0.116300i	$0.962897\pi$
$140$		0			0
$141$	−1.76555	+	0.731316i	−0.148686	+	0.0615880i
$142$		0			0
$143$	−30.4340	+	17.5711i	−2.54502	+	1.46937i
$144$		0			0
$145$	2.85266	−	4.94095i	0.236901	−	0.410324i
$146$		0			0
$147$	1.60363	−	8.91860i	0.132266	−	0.735594i
$148$		0			0
$149$	1.60857	+	2.09633i	0.131779	+	0.171738i	0.854582	−	0.519316i	$-0.173813\pi$
$149$	1.60857	+	2.09633i	0.131779	+	0.171738i	−0.722803	+	0.691054i	$0.757147\pi$
$150$		0			0
$151$	−0.341777	+	1.27553i	−0.0278134	+	0.103801i	−0.978437	−	0.206545i	$-0.933778\pi$
$151$	−0.341777	+	1.27553i	−0.0278134	+	0.103801i	0.950624	+	0.310346i	$0.100445\pi$
$152$		0			0
$153$	−0.975167	+	0.975167i	−0.0788376	+	0.0788376i
$154$		0			0
$155$	−2.24142	+	5.41126i	−0.180035	+	0.434643i
$156$		0			0
$157$	−18.9690	−	14.5554i	−1.51389	−	1.16165i	−0.939245	−	0.343247i	$-0.888473\pi$
$157$	−18.9690	−	14.5554i	−1.51389	−	1.16165i	−0.574646	−	0.818402i	$-0.694860\pi$
$158$		0			0
$159$	5.54156	−	9.59826i	0.439474	−	0.761191i
$160$		0			0
$161$	4.15146	+	7.59747i	0.327181	+	0.598764i
$162$		0			0
$163$	−0.732554	+	5.56430i	−0.0573781	+	0.435830i	0.938511	+	0.345249i	$0.112206\pi$
$163$	−0.732554	+	5.56430i	−0.0573781	+	0.435830i	−0.995889	+	0.0905806i	$0.971128\pi$
$164$		0			0
$165$	1.63898	+	12.4493i	0.127594	+	0.969175i
$166$		0			0
$167$	8.02123	+	8.02123i	0.620702	+	0.620702i	0.945711	−	0.325009i	$-0.105367\pi$
$167$	8.02123	+	8.02123i	0.620702	+	0.620702i	−0.325009	+	0.945711i	$0.605367\pi$
$168$		0			0
$169$	−24.4743	+	24.4743i	−1.88264	+	1.88264i
$170$		0			0
$171$	1.86964	−	0.246143i	0.142975	−	0.0188230i
$172$		0			0
$173$	2.40205	+	0.316235i	0.182624	+	0.0240429i	0.221284	−	0.975210i	$-0.428975\pi$
$173$	2.40205	+	0.316235i	0.182624	+	0.0240429i	−0.0386593	+	0.999252i	$0.512309\pi$
$174$		0			0
$175$	−3.63058	−	0.0853472i	−0.274446	−	0.00645164i
$176$		0			0
$177$	−12.6244	−	7.28870i	−0.948908	−	0.547853i
$178$		0			0
$179$	−6.72543	+	8.76475i	−0.502682	+	0.655108i	−0.973918	−	0.226899i	$-0.927141\pi$
$179$	−6.72543	+	8.76475i	−0.502682	+	0.655108i	0.471236	+	0.882007i	$0.343808\pi$
$180$		0			0
$181$	2.76075	+	1.14354i	0.205205	+	0.0849987i	0.482919	−	0.875665i	$-0.339577\pi$
$181$	2.76075	+	1.14354i	0.205205	+	0.0849987i	−0.277714	+	0.960664i	$0.589577\pi$
$182$		0			0
$183$	11.8327	+	11.8327i	0.874700	+	0.874700i
$184$		0			0
$185$	18.3286	+	4.91113i	1.34754	+	0.361074i
$186$		0			0
$187$	4.20794	−	3.22887i	0.307715	−	0.236118i
$188$		0			0
$189$	−2.27769	+	14.6342i	−0.165678	+	1.06448i
$190$		0			0
$191$	−5.51336	−	3.18314i	−0.398933	−	0.230324i	0.287090	−	0.957903i	$-0.407312\pi$
$191$	−5.51336	−	3.18314i	−0.398933	−	0.230324i	−0.686023	+	0.727579i	$0.740645\pi$
$192$		0			0
$193$	−0.647141	−	1.12088i	−0.0465823	−	0.0806828i	0.841794	−	0.539799i	$-0.181500\pi$
$193$	−0.647141	−	1.12088i	−0.0465823	−	0.0806828i	−0.888376	+	0.459116i	$0.848166\pi$
$194$		0			0
$195$	6.51033	+	15.7173i	0.466214	+	1.12554i
$196$		0			0
$197$	−1.64133	−	0.679859i	−0.116940	−	0.0484380i	0.323446	−	0.946246i	$-0.395158\pi$
$197$	−1.64133	−	0.679859i	−0.116940	−	0.0484380i	−0.440386	+	0.897808i	$0.645158\pi$
$198$		0			0
$199$	−2.39258	+	8.92924i	−0.169606	+	0.632977i	0.827802	+	0.561020i	$0.189591\pi$
$199$	−2.39258	+	8.92924i	−0.169606	+	0.632977i	−0.997408	+	0.0719569i	$0.977076\pi$
$200$		0			0
$201$	11.8774	−	3.18255i	0.837770	−	0.224480i
$202$		0			0
$203$	−6.39945	+	4.67569i	−0.449153	+	0.328169i
$204$		0			0
$205$	−0.302176	+	2.29526i	−0.0211049	+	0.160308i
$206$		0			0
$207$	−2.16663	−	3.75272i	−0.150592	−	0.260832i
$208$		0			0
$209$	−7.25268			−0.501678
$210$		0			0
$211$	−7.65203	−	18.4736i	−0.526788	−	1.27178i	−0.933617	−	0.358274i	$-0.883365\pi$
$211$	−7.65203	−	18.4736i	−0.526788	−	1.27178i	0.406829	−	0.913504i	$-0.366635\pi$
$212$		0			0
$213$	1.96533	+	14.9282i	0.134662	+	1.02286i
$214$		0			0
$215$	3.16744	+	11.8210i	0.216017	+	0.806188i
$216$		0			0
$217$	5.88696	−	5.61653i	0.399633	−	0.381275i
$218$		0			0
$219$	1.42571	+	1.85802i	0.0963403	+	0.125553i
$220$		0			0
$221$	4.37460	−	5.70108i	0.294267	−	0.383496i
$222$		0			0
$223$	−5.44239			−0.364449			−0.182225	−	0.983257i	$-0.558330\pi$
$223$	−5.44239			−0.364449			−0.182225	+	0.983257i	$0.558330\pi$
$224$		0			0
$225$	1.81764			0.121176
$226$		0			0
$227$	−0.130527	+	0.170106i	−0.00866337	+	0.0112903i	−0.797665	−	0.603101i	$-0.793932\pi$
$227$	−0.130527	+	0.170106i	−0.00866337	+	0.0112903i	0.789002	+	0.614391i	$0.210598\pi$
$228$		0			0
$229$	12.9967	+	16.9376i	0.858844	+	1.11927i	0.991756	+	0.128139i	$0.0409003\pi$
$229$	12.9967	+	16.9376i	0.858844	+	1.11927i	−0.132913	+	0.991128i	$0.542433\pi$
$230$		0			0
$231$	4.90937	−	16.7381i	0.323013	−	1.10129i
$232$		0			0
$233$	−1.04716	−	3.90806i	−0.0686017	−	0.256025i	0.923105	−	0.384549i	$-0.125643\pi$
$233$	−1.04716	−	3.90806i	−0.0686017	−	0.256025i	−0.991706	+	0.128523i	$0.958976\pi$
$234$		0			0
$235$	0.366988	+	2.78755i	0.0239397	+	0.181840i
$236$		0			0
$237$	6.17893	+	14.9173i	0.401365	+	0.968980i
$238$		0			0
$239$	2.73300			0.176783			0.0883915	−	0.996086i	$-0.471827\pi$
$239$	2.73300			0.176783			0.0883915	+	0.996086i	$0.471827\pi$
$240$		0			0
$241$	7.50863	+	13.0053i	0.483673	+	0.837747i	0.999824	−	0.0187508i	$-0.00596890\pi$
$241$	7.50863	+	13.0053i	0.483673	+	0.837747i	−0.516151	+	0.856498i	$0.672636\pi$
$242$		0			0
$243$	1.63881	−	12.4480i	0.105130	−	0.798539i
$244$		0			0
$245$	−12.0638	−	5.67508i	−0.770729	−	0.362568i
$246$		0			0
$247$	−9.49140	+	2.54321i	−0.603923	+	0.161821i
$248$		0			0
$249$	2.00227	−	7.47256i	0.126889	−	0.473554i
$250$		0			0
$251$	22.8325	+	9.45753i	1.44117	+	0.596954i	0.960083	−	0.279716i	$-0.0902404\pi$
$251$	22.8325	+	9.45753i	1.44117	+	0.596954i	0.481092	+	0.876670i	$0.340240\pi$
$252$		0			0
$253$	6.37770	+	15.3971i	0.400963	+	0.968010i
$254$		0			0
$255$	−1.28383	−	2.22366i	−0.0803967	−	0.139251i
$256$		0			0
$257$	11.9243	+	6.88450i	0.743818	+	0.429443i	0.823456	−	0.567380i	$-0.192043\pi$
$257$	11.9243	+	6.88450i	0.743818	+	0.429443i	−0.0796379	+	0.996824i	$0.525376\pi$
$258$		0			0
$259$	−20.5295	−	16.5337i	−1.27564	−	1.02735i
$260$		0			0
$261$	3.14710	−	2.41486i	0.194801	−	0.149476i
$262$		0			0
$263$	12.6964	+	3.40199i	0.782894	+	0.209776i	0.628060	−	0.778165i	$-0.283849\pi$
$263$	12.6964	+	3.40199i	0.782894	+	0.209776i	0.154834	+	0.987941i	$0.450516\pi$
$264$		0			0
$265$	−11.5302	−	11.5302i	−0.708293	−	0.708293i
$266$		0			0
$267$	−11.9660	−	4.95648i	−0.732307	−	0.303332i
$268$		0			0
$269$	−4.03019	+	5.25225i	−0.245725	+	0.320235i	−0.899890	−	0.436117i	$-0.856354\pi$
$269$	−4.03019	+	5.25225i	−0.245725	+	0.320235i	0.654165	+	0.756352i	$0.273020\pi$
$270$		0			0
$271$	−20.6375	−	11.9151i	−1.25364	−	0.723789i	−0.281809	−	0.959470i	$-0.590935\pi$
$271$	−20.6375	−	11.9151i	−1.25364	−	0.723789i	−0.971830	+	0.235681i	$0.924268\pi$
$272$		0			0
$273$	0.555403	−	23.6263i	0.0336145	−	1.42993i
$274$		0			0
$275$	−6.93083	−	0.912461i	−0.417945	−	0.0550235i
$276$		0			0
$277$	−9.87702	+	1.30034i	−0.593453	+	0.0781296i	−0.421270	−	0.906935i	$-0.638415\pi$
$277$	−9.87702	+	1.30034i	−0.593453	+	0.0781296i	−0.172183	+	0.985065i	$0.555082\pi$
$278$		0			0
$279$	−2.87960	+	2.87960i	−0.172397	+	0.172397i
$280$		0			0
$281$	−17.1617	−	17.1617i	−1.02378	−	1.02378i	−0.999710	−	0.0240710i	$-0.992337\pi$
$281$	−17.1617	−	17.1617i	−1.02378	−	1.02378i	−0.0240710	−	0.999710i	$-0.507663\pi$
$282$		0			0
$283$	−1.93111	−	14.6682i	−0.114793	−	0.871936i	−0.947843	−	0.318739i	$-0.896741\pi$
$283$	−1.93111	−	14.6682i	−0.114793	−	0.871936i	0.833050	−	0.553198i	$-0.186593\pi$
$284$		0			0
$285$	−0.458281	+	3.48099i	−0.0271462	+	0.206196i
$286$		0			0
$287$	1.67300	−	2.74657i	0.0987543	−	0.162125i
$288$		0			0
$289$	7.95770	−	13.7831i	0.468100	−	0.810773i
$290$		0			0
$291$	−9.01748	−	6.91935i	−0.528614	−	0.405620i
$292$		0			0
$293$	10.4831	−	25.3085i	0.612430	−	1.47854i	−0.247892	−	0.968788i	$-0.579738\pi$
$293$	10.4831	−	25.3085i	0.612430	−	1.47854i	0.860323	−	0.509750i	$-0.170262\pi$
$294$		0			0
$295$	−15.1654	+	15.1654i	−0.882965	+	0.882965i
$296$		0			0
$297$	−7.37875	+	27.5379i	−0.428158	+	1.59791i
$298$		0			0
$299$	13.7455	+	17.9134i	0.794921	+	1.03596i
$300$		0			0
$301$	2.61453	−	16.7983i	0.150699	−	0.968240i
$302$		0			0
$303$	−1.17389	+	2.03324i	−0.0674382	+	0.116806i
$304$		0			0
$305$	21.3216	−	12.3100i	1.22087	−	0.704870i
$306$		0			0
$307$	1.05530	−	0.437118i	0.0602290	−	0.0249477i	−0.352366	−	0.935862i	$-0.614623\pi$
$307$	1.05530	−	0.437118i	0.0602290	−	0.0249477i	0.412595	+	0.910915i	$0.364623\pi$
$308$		0			0
$309$	1.70975	−	4.12771i	0.0972644	−	0.234817i
$310$		0			0
$311$	−7.04619	−	1.88802i	−0.399553	−	0.107060i	0.0534464	−	0.998571i	$-0.482979\pi$
$311$	−7.04619	−	1.88802i	−0.399553	−	0.107060i	−0.452999	+	0.891511i	$0.649646\pi$
$312$		0			0
$313$	1.50768	+	5.62674i	0.0852192	+	0.318042i	0.995356	−	0.0962664i	$-0.0306901\pi$
$313$	1.50768	+	5.62674i	0.0852192	+	0.318042i	−0.910136	+	0.414309i	$0.864023\pi$
$314$		0			0
$315$	6.10314	+	2.69774i	0.343873	+	0.152001i
$316$		0			0
$317$	−20.2421	−	2.66492i	−1.13691	−	0.149677i	−0.461514	−	0.887133i	$-0.652693\pi$
$317$	−20.2421	−	2.66492i	−1.13691	−	0.149677i	−0.675395	+	0.737456i	$0.736027\pi$
$318$		0			0
$319$	−13.2125	+	7.62822i	−0.739756	+	0.427098i
$320$		0			0
$321$			5.45782i			0.304626i
$322$		0			0
$323$	1.37018	−	0.567546i	0.0762387	−	0.0315791i
$324$		0			0
$325$	−9.39016	+	1.23624i	−0.520872	+	0.0685742i
$326$		0			0
$327$	−4.55987	+	1.22181i	−0.252161	+	0.0675664i
$328$		0			0
$329$	1.09927	−	3.74788i	0.0606048	−	0.206628i
$330$		0			0
$331$	21.7550	−	16.6932i	1.19576	−	0.917541i	0.197732	−	0.980256i	$-0.436642\pi$
$331$	21.7550	−	16.6932i	1.19576	−	0.917541i	0.998031	+	0.0627147i	$0.0199758\pi$
$332$		0			0
$333$	10.4668	+	8.03149i	0.573580	+	0.440123i
$334$		0			0
$335$		−	18.0912i		−	0.988429i
$336$		0			0
$337$			16.1002i			0.877036i	0.898722	+	0.438518i	$0.144497\pi$
$337$			16.1002i			0.877036i	−0.898722	+	0.438518i	$0.855503\pi$
$338$		0			0
$339$	12.7116	+	9.75395i	0.690399	+	0.529762i
$340$		0			0
$341$	12.4257	−	9.53461i	0.672892	−	0.516328i
$342$		0			0
$343$	12.1406	+	13.9859i	0.655532	+	0.755167i
$344$		0			0
$345$	7.79298	−	2.08812i	0.419560	−	0.112421i
$346$		0			0
$347$	16.6462	−	2.19151i	0.893612	−	0.117646i	0.330286	−	0.943881i	$-0.392855\pi$
$347$	16.6462	−	2.19151i	0.893612	−	0.117646i	0.563326	+	0.826235i	$0.309521\pi$
$348$		0			0
$349$	−15.7087	+	6.50674i	−0.840865	+	0.348298i	−0.761195	−	0.648523i	$-0.775387\pi$
$349$	−15.7087	+	6.50674i	−0.840865	+	0.348298i	−0.0796707	+	0.996821i	$0.525387\pi$
$350$		0			0
$351$			38.6255i			2.06168i
$352$		0			0
$353$	12.0664	−	6.96653i	0.642229	−	0.370791i	−0.143244	−	0.989687i	$-0.545753\pi$
$353$	12.0664	−	6.96653i	0.642229	−	0.370791i	0.785473	+	0.618897i	$0.212420\pi$
$354$		0			0
$355$	21.9632	+	2.89151i	1.16569	+	0.153465i
$356$		0			0
$357$	0.382335	+	3.54634i	0.0202353	+	0.187692i
$358$		0			0
$359$	−7.58620	−	28.3121i	−0.400384	−	1.49426i	−0.812412	−	0.583084i	$-0.801846\pi$
$359$	−7.58620	−	28.3121i	−0.400384	−	1.49426i	0.412028	−	0.911171i	$-0.364821\pi$
$360$		0			0
$361$	16.3937	+	4.39269i	0.862829	+	0.231194i
$362$		0			0
$363$	7.40026	−	17.8658i	0.388413	−	0.937711i
$364$		0			0
$365$	3.18337	−	1.31860i	0.166625	−	0.0690185i
$366$		0			0
$367$	10.1024	−	5.83264i	0.527343	−	0.304462i	−0.212591	−	0.977141i	$-0.568190\pi$
$367$	10.1024	−	5.83264i	0.527343	−	0.304462i	0.739934	+	0.672680i	$0.234857\pi$
$368$		0			0
$369$	−0.804816	+	1.39398i	−0.0418970	+	0.0725678i
$370$		0			0
$371$	8.17425	+	21.1255i	0.424386	+	1.09678i
$372$		0			0
$373$	1.58394	+	2.06423i	0.0820134	+	0.106882i	0.832558	−	0.553938i	$-0.186875\pi$
$373$	1.58394	+	2.06423i	0.0820134	+	0.106882i	−0.750545	+	0.660820i	$0.770209\pi$
$374$		0			0
$375$	−4.06648	+	15.1763i	−0.209992	+	0.783702i
$376$		0			0
$377$	−14.6159	+	14.6159i	−0.752757	+	0.752757i
$378$		0			0
$379$	−2.88601	+	6.96745i	−0.148244	+	0.357894i	−0.980506	−	0.196490i	$-0.937046\pi$
$379$	−2.88601	+	6.96745i	−0.148244	+	0.357894i	0.832262	+	0.554383i	$0.187046\pi$
$380$		0			0
$381$	−2.78062	−	2.13365i	−0.142456	−	0.109310i
$382$		0			0
$383$	11.5792	−	20.0558i	0.591670	−	1.02480i	−0.402338	−	0.915491i	$-0.631802\pi$
$383$	11.5792	−	20.0558i	0.591670	−	1.02480i	0.994008	−	0.109311i	$-0.0348644\pi$
$384$		0			0
$385$	−21.9176	−	13.3505i	−1.11702	−	0.680407i
$386$		0			0
$387$	−1.11064	+	8.43615i	−0.0564570	+	0.428834i
$388$		0			0
$389$	3.13990	+	23.8499i	0.159199	+	1.20924i	0.865346	+	0.501174i	$0.167099\pi$
$389$	3.13990	+	23.8499i	0.159199	+	1.20924i	−0.706147	+	0.708065i	$0.749568\pi$
$390$		0			0
$391$	−2.40975	−	2.40975i	−0.121866	−	0.121866i
$392$		0			0
$393$	−4.31243	+	4.31243i	−0.217533	+	0.217533i
$394$		0			0
$395$	23.5522	−	3.10071i	1.18504	−	0.156013i
$396$		0			0
$397$	−13.3525	−	1.75790i	−0.670145	−	0.0882262i	−0.212226	−	0.977221i	$-0.568071\pi$
$397$	−13.3525	−	1.75790i	−0.670145	−	0.0882262i	−0.457918	+	0.888994i	$0.651405\pi$
$398$		0			0
$399$	2.53728	−	4.16545i	0.127023	−	0.208533i
$400$		0			0
$401$	4.45802	+	2.57384i	0.222623	+	0.128531i	0.607164	−	0.794576i	$-0.292307\pi$
$401$	4.45802	+	2.57384i	0.222623	+	0.128531i	−0.384541	+	0.923108i	$0.625640\pi$
$402$		0			0
$403$	12.9179	−	16.8349i	0.643484	−	0.838605i
$404$		0			0
$405$	5.76050	+	2.38608i	0.286241	+	0.118565i
$406$		0			0
$407$	−35.8792	−	35.8792i	−1.77847	−	1.77847i
$408$		0			0
$409$	−1.10573	−	0.296281i	−0.0546751	−	0.0146501i	0.231378	−	0.972864i	$-0.425677\pi$
$409$	−1.10573	−	0.296281i	−0.0546751	−	0.0146501i	−0.286053	+	0.958214i	$0.592343\pi$
$410$		0			0
$411$	2.95402	−	2.26670i	0.145711	−	0.111808i
$412$		0			0
$413$	27.7859	−	10.7514i	1.36726	−	0.529043i
$414$		0			0
$415$	−9.85702	−	5.69095i	−0.483862	−	0.279358i
$416$		0			0
$417$	−7.44080	−	12.8879i	−0.364378	−	0.631121i
$418$		0			0
$419$	10.7109	+	25.8583i	0.523261	+	1.26326i	0.935867	+	0.352353i	$0.114618\pi$
$419$	10.7109	+	25.8583i	0.523261	+	1.26326i	−0.412606	+	0.910909i	$0.635382\pi$
$420$		0			0
$421$	−10.9194	−	4.52297i	−0.532179	−	0.220436i	0.100378	−	0.994949i	$-0.467995\pi$
$421$	−10.9194	−	4.52297i	−0.532179	−	0.220436i	−0.632557	+	0.774514i	$0.717995\pi$
$422$		0			0
$423$	−0.505959	+	1.88826i	−0.0246005	+	0.0918105i
$424$		0			0
$425$	1.38078	−	0.369978i	0.0669775	−	0.0179466i
$426$		0			0
$427$	−34.0041	+	3.66601i	−1.64557	+	0.177411i
$428$		0			0
$429$	5.93791	−	45.1029i	0.286685	−	2.17759i
$430$		0			0
$431$	16.1978	+	28.0554i	0.780219	+	1.35138i	0.931814	+	0.362937i	$0.118226\pi$
$431$	16.1978	+	28.0554i	0.780219	+	1.35138i	−0.151595	+	0.988443i	$0.548441\pi$
$432$		0			0
$433$	23.2185			1.11581			0.557905	−	0.829905i	$-0.311605\pi$
$433$	23.2185			1.11581			0.557905	+	0.829905i	$0.311605\pi$
$434$		0			0
$435$	2.82636	+	6.82344i	0.135514	+	0.327159i
$436$		0			0
$437$	0.608248	+	4.62010i	0.0290964	+	0.221009i
$438$		0			0
$439$	5.31588	+	19.8391i	0.253713	+	0.946870i	0.968802	+	0.247836i	$0.0797195\pi$
$439$	5.31588	+	19.8391i	0.253713	+	0.946870i	−0.715089	+	0.699034i	$0.753614\pi$
$440$		0			0
$441$	−6.23933	−	6.85533i	−0.297111	−	0.326444i
$442$		0			0
$443$	−15.2770	−	19.9093i	−0.725830	−	0.945921i	0.274045	−	0.961717i	$-0.411638\pi$
$443$	−15.2770	−	19.9093i	−0.725830	−	0.945921i	−0.999875	+	0.0157964i	$0.994972\pi$
$444$		0			0
$445$	−11.6003	+	15.1178i	−0.549908	+	0.716654i
$446$		0			0
$447$	−3.42059			−0.161788
$448$		0			0
$449$	20.2136			0.953938			0.476969	−	0.878920i	$-0.341735\pi$
$449$	20.2136			0.953938			0.476969	+	0.878920i	$0.341735\pi$
$450$		0			0
$451$	3.76862	−	4.91136i	0.177457	−	0.231267i
$452$		0			0
$453$	−1.04064	−	1.35619i	−0.0488937	−	0.0637195i
$454$		0			0
$455$	−33.3644	−	9.78594i	−1.56415	−	0.458772i
$456$		0			0
$457$	−5.73442	−	21.4011i	−0.268245	−	1.00110i	−0.960234	−	0.279196i	$-0.909932\pi$
$457$	−5.73442	−	21.4011i	−0.268245	−	1.00110i	0.691989	−	0.721908i	$-0.256734\pi$
$458$		0			0
$459$	−0.760934	−	5.77986i	−0.0355173	−	0.269781i
$460$		0			0
$461$	9.74244	+	23.5203i	0.453751	+	1.09545i	0.970885	+	0.239546i	$0.0769987\pi$
$461$	9.74244	+	23.5203i	0.453751	+	1.09545i	−0.517134	+	0.855904i	$0.673001\pi$
$462$		0			0
$463$	12.3133			0.572248			0.286124	−	0.958193i	$-0.407633\pi$
$463$	12.3133			0.572248			0.286124	+	0.958193i	$0.407633\pi$
$464$		0			0
$465$	−3.79106	−	6.56631i	−0.175806	−	0.304505i
$466$		0			0
$467$	3.77280	−	28.6573i	0.174585	−	1.32610i	−0.649815	−	0.760092i	$-0.725154\pi$
$467$	3.77280	−	28.6573i	0.174585	−	1.32610i	0.824399	−	0.566008i	$-0.191513\pi$
$468$		0			0
$469$	−10.1605	+	22.9861i	−0.469166	+	1.06140i
$470$		0			0
$471$	29.8971	−	8.01092i	1.37759	−	0.369123i
$472$		0			0
$473$	8.46995	−	31.6103i	0.389449	−	1.45344i
$474$		0			0
$475$	−1.80589	−	0.748023i	−0.0828598	−	0.0343216i
$476$		0			0
$477$	−4.33865	−	10.4744i	−0.198653	−	0.479591i
$478$		0			0
$479$	10.5049	+	18.1950i	0.479980	+	0.831350i	0.999736	−	0.0229647i	$-0.00731053\pi$
$479$	10.5049	+	18.1950i	0.479980	+	0.831350i	−0.519756	+	0.854315i	$0.673977\pi$
$480$		0			0
$481$	−59.5356	−	34.3729i	−2.71459	−	1.56727i
$482$		0			0
$483$	−11.0742	−	1.72362i	−0.503896	−	0.0784273i
$484$		0			0
$485$	−13.2670	+	10.1802i	−0.602425	+	0.462257i
$486$		0			0
$487$	−8.74932	−	2.34437i	−0.396469	−	0.106234i	0.0550752	−	0.998482i	$-0.482460\pi$
$487$	−8.74932	−	2.34437i	−0.396469	−	0.106234i	−0.451545	+	0.892249i	$0.649127\pi$
$488$		0			0
$489$	−5.13730	−	5.13730i	−0.232317	−	0.232317i
$490$		0			0
$491$	9.93228	+	4.11409i	0.448238	+	0.185666i	0.595372	−	0.803450i	$-0.297005\pi$
$491$	9.93228	+	4.11409i	0.448238	+	0.185666i	−0.147134	+	0.989117i	$0.547005\pi$
$492$		0			0
$493$	1.89917	−	2.47504i	0.0855341	−	0.111470i
$494$		0			0
$495$	11.1240	+	6.42242i	0.499985	+	0.288666i
$496$		0			0
$497$	−26.2818	−	16.0089i	−1.17890	−	0.718097i
$498$		0			0
$499$	9.69348	+	1.27617i	0.433940	+	0.0571293i	0.344332	−	0.938848i	$-0.388105\pi$
$499$	9.69348	+	1.27617i	0.433940	+	0.0571293i	0.0896076	+	0.995977i	$0.471439\pi$
$500$		0			0
$501$	−14.5590	+	1.91673i	−0.650450	+	0.0856334i
$502$		0			0
$503$	21.5342	−	21.5342i	0.960163	−	0.960163i	−0.0390731	−	0.999236i	$-0.512441\pi$
$503$	21.5342	−	21.5342i	0.960163	−	0.960163i	0.999236	+	0.0390731i	$0.0124405\pi$
$504$		0			0
$505$	2.44248	+	2.44248i	0.108689	+	0.108689i
$506$		0			0
$507$	−5.84832	−	44.4224i	−0.259733	−	1.97287i
$508$		0			0
$509$	−1.76046	+	13.3721i	−0.0780312	+	0.592706i	0.907102	+	0.420912i	$0.138290\pi$
$509$	−1.76046	+	13.3721i	−0.0780312	+	0.592706i	−0.985133	+	0.171794i	$0.945044\pi$
$510$		0			0
$511$	−4.78524	−	0.112491i	−0.211687	−	0.00497630i
$512$		0			0
$513$	−3.98579	+	6.90359i	−0.175977	+	0.304801i
$514$		0			0
$515$	−5.21494	−	4.00156i	−0.229798	−	0.176330i
$516$		0			0
$517$	2.87718	−	6.94613i	0.126538	−	0.305491i
$518$		0			0
$519$	−2.21772	+	2.21772i	−0.0973469	+	0.0973469i
$520$		0			0
$521$	7.80395	−	29.1247i	0.341897	−	1.27598i	−0.554298	−	0.832318i	$-0.687013\pi$
$521$	7.80395	−	29.1247i	0.341897	−	1.27598i	0.896195	−	0.443659i	$-0.146320\pi$
$522$		0			0
$523$	0.0340226	+	0.0443391i	0.00148770	+	0.00193881i	0.794097	−	0.607792i	$-0.207944\pi$
$523$	0.0340226	+	0.0443391i	0.00148770	+	0.00193881i	−0.792609	+	0.609730i	$0.791278\pi$
$524$		0			0
$525$	2.94874	−	3.66138i	0.128693	−	0.159796i
$526$		0			0
$527$	−1.60136	+	2.77363i	−0.0697563	+	0.120821i
$528$		0			0
$529$	−10.6452	+	6.14599i	−0.462834	+	0.267217i
$530$		0			0
$531$	−13.7768	+	5.70654i	−0.597863	+	0.247643i
$532$		0			0
$533$	3.20969	−	7.74887i	0.139027	−	0.335641i
$534$		0			0
$535$	7.75626	+	2.07828i	0.335332	+	0.0898520i
$536$		0			0
$537$	−3.70149	−	13.8142i	−0.159731	−	0.596125i
$538$		0			0
$539$	20.3498	+	29.2722i	0.876526	+	1.26084i
$540$		0			0
$541$	30.8782	+	4.06519i	1.32756	+	0.174776i	0.760734	−	0.649063i	$-0.224839\pi$
$541$	30.8782	+	4.06519i	1.32756	+	0.174776i	0.566823	+	0.823840i	$0.308172\pi$
$542$		0			0
$543$	−3.35005	+	1.93415i	−0.143764	+	0.0830023i
$544$		0			0
$545$			6.94540i			0.297508i
$546$		0			0
$547$	34.0676	−	14.1112i	1.45662	−	0.603353i	0.492860	−	0.870109i	$-0.335952\pi$
$547$	34.0676	−	14.1112i	1.45662	−	0.603353i	0.963764	+	0.266755i	$0.0859515\pi$
$548$		0			0
$549$	16.9715	−	2.23435i	0.724328	−	0.0953595i
$550$		0			0
$551$	−4.12055	+	1.10410i	−0.175541	+	0.0470361i
$552$		0			0
$553$	−31.6661	−	9.28780i	−1.34658	−	0.394958i
$554$		0			0
$555$	−19.4877	+	14.9534i	−0.827206	+	0.634737i
$556$		0			0
$557$	8.88642	+	6.81879i	0.376530	+	0.288922i	0.779638	−	0.626231i	$-0.215403\pi$
$557$	8.88642	+	6.81879i	0.376530	+	0.288922i	−0.403108	+	0.915153i	$0.632070\pi$
$558$		0			0
$559$		−	44.3376i		−	1.87528i
$560$		0			0
$561$			6.86612i			0.289888i
$562$		0			0
$563$	2.52674	+	1.93883i	0.106489	+	0.0817121i	0.660634	−	0.750709i	$-0.270288\pi$
$563$	2.52674	+	1.93883i	0.106489	+	0.0817121i	−0.554144	+	0.832421i	$0.686954\pi$
$564$		0			0
$565$	18.7021	−	14.3506i	0.786801	−	0.603734i
$566$		0			0
$567$	−5.97902	−	6.26690i	−0.251095	−	0.263185i
$568$		0			0
$569$	31.5198	−	8.44569i	1.32138	−	0.354062i	0.471883	−	0.881661i	$-0.343574\pi$
$569$	31.5198	−	8.44569i	1.32138	−	0.354062i	0.849493	+	0.527599i	$0.176908\pi$
$570$		0			0
$571$	−28.4516	+	3.74573i	−1.19066	+	0.156754i	−0.699707	−	0.714430i	$-0.746686\pi$
$571$	−28.4516	+	3.74573i	−1.19066	+	0.156754i	−0.490957	+	0.871184i	$0.663353\pi$
$572$		0			0
$573$	7.61394	−	3.15380i	0.318077	−	0.131752i
$574$		0			0
$575$			4.49160i			0.187313i
$576$		0			0
$577$	−8.18229	+	4.72405i	−0.340633	+	0.196665i	−0.660552	−	0.750780i	$-0.729678\pi$
$577$	−8.18229	+	4.72405i	−0.340633	+	0.196665i	0.319919	+	0.947445i	$0.396344\pi$
$578$		0			0
$579$	1.66114	+	0.218693i	0.0690346	+	0.00908857i
$580$		0			0
$581$	9.32783	+	12.7667i	0.386984	+	0.529651i
$582$		0			0
$583$	11.2855	+	42.1180i	0.467397	+	1.74435i
$584$		0			0
$585$	16.8097	+	4.50415i	0.694996	+	0.186223i
$586$		0			0
$587$	1.45514	−	3.51303i	0.0600602	−	0.144998i	−0.891000	−	0.454002i	$-0.849996\pi$
$587$	1.45514	−	3.51303i	0.0600602	−	0.144998i	0.951061	+	0.309004i	$0.0999957\pi$
$588$		0			0
$589$	4.04603	−	1.67592i	0.166714	−	0.0690551i
$590$		0			0
$591$	1.99167	−	1.14989i	0.0819265	−	0.0473003i
$592$		0			0
$593$	−24.2502	+	42.0026i	−0.995837	+	1.72484i	−0.418976	+	0.907997i	$0.637611\pi$
$593$	−24.2502	+	42.0026i	−0.995837	+	1.72484i	−0.576860	+	0.816843i	$0.695722\pi$
$594$		0			0
$595$	5.18539	+	0.807065i	0.212580	+	0.0330864i
$596$		0			0
$597$	−7.28494	−	9.49392i	−0.298153	−	0.388560i
$598$		0			0
$599$	4.20531	−	15.6944i	0.171824	−	0.641257i	−0.825246	−	0.564773i	$-0.808964\pi$
$599$	4.20531	−	15.6944i	0.171824	−	0.641257i	0.997071	−	0.0764845i	$-0.0243696\pi$
$600$		0			0
$601$	−11.9648	+	11.9648i	−0.488053	+	0.488053i	−0.907691	−	0.419638i	$-0.862157\pi$
$601$	−11.9648	+	11.9648i	−0.488053	+	0.488053i	0.419638	+	0.907691i	$0.362157\pi$
$602$		0			0
$603$	4.81362	−	11.6211i	0.196026	−	0.473248i
$604$		0			0
$605$	−22.5716	−	17.3198i	−0.917667	−	0.704151i
$606$		0			0
$607$	1.40684	−	2.43672i	0.0571020	−	0.0989035i	−0.836061	−	0.548636i	$-0.815147\pi$
$607$	1.40684	−	2.43672i	0.0571020	−	0.0989035i	0.893163	+	0.449732i	$0.148481\pi$
$608$		0			0
$609$	0.241120	−	10.2570i	0.00977068	−	0.415634i
$610$		0			0
$611$	1.32958	−	10.0991i	0.0537889	−	0.408567i
$612$		0			0
$613$	0.669238	+	5.08336i	0.0270303	+	0.205315i	0.999631	−	0.0271670i	$-0.00864860\pi$
$613$	0.669238	+	5.08336i	0.0270303	+	0.205315i	−0.972601	+	0.232482i	$0.925315\pi$
$614$		0			0
$615$	−2.11912	−	2.11912i	−0.0854512	−	0.0854512i
$616$		0			0
$617$	6.91032	−	6.91032i	0.278199	−	0.278199i	−0.554191	−	0.832390i	$-0.686972\pi$
$617$	6.91032	−	6.91032i	0.278199	−	0.278199i	0.832390	+	0.554191i	$0.186972\pi$
$618$		0			0
$619$	−16.1936	+	2.13193i	−0.650875	+	0.0856893i	−0.448732	−	0.893667i	$-0.648124\pi$
$619$	−16.1936	+	2.13193i	−0.650875	+	0.0856893i	−0.202143	+	0.979356i	$0.564791\pi$
$620$		0			0
$621$	18.1610	+	2.39094i	0.728775	+	0.0959450i
$622$		0			0
$623$	23.2295	−	12.6932i	0.930670	−	0.508543i
$624$		0			0
$625$	14.0754	+	8.12645i	0.563017	+	0.325058i
$626$		0			0
$627$	5.71550	−	7.44858i	0.228255	−	0.297468i
$628$		0			0
$629$	9.58598	+	3.97064i	0.382218	+	0.158320i
$630$		0			0
$631$	−32.1040	−	32.1040i	−1.27804	−	1.27804i	−0.941763	−	0.336278i	$-0.890832\pi$
$631$	−32.1040	−	32.1040i	−1.27804	−	1.27804i	−0.336278	−	0.941763i	$-0.609168\pi$
$632$		0			0
$633$	25.0028	+	6.69949i	0.993773	+	0.266281i
$634$		0			0
$635$	−4.09102	+	3.13915i	−0.162347	+	0.124573i
$636$		0			0
$637$	36.8957	+	31.1719i	1.46186	+	1.23508i
$638$		0			0
$639$	13.3389	+	7.70125i	0.527681	+	0.304657i
$640$		0			0
$641$	4.77006	+	8.26198i	0.188406	+	0.326329i	0.944719	−	0.327881i	$-0.106335\pi$
$641$	4.77006	+	8.26198i	0.188406	+	0.326329i	−0.756313	+	0.654210i	$0.773001\pi$
$642$		0			0
$643$	1.30599	+	3.15294i	0.0515033	+	0.124340i	0.947537	−	0.319646i	$-0.103564\pi$
$643$	1.30599	+	3.15294i	0.0515033	+	0.124340i	−0.896034	+	0.443986i	$0.853564\pi$
$644$		0			0
$645$	−14.6364	−	6.06261i	−0.576309	−	0.238715i
$646$		0			0
$647$	−6.07105	+	22.6575i	−0.238678	+	0.890757i	0.737779	+	0.675043i	$0.235875\pi$
$647$	−6.07105	+	22.6575i	−0.238678	+	0.890757i	−0.976456	+	0.215715i	$0.930792\pi$
$648$		0			0
$649$	55.3970	−	14.8436i	2.17452	−	0.582661i
$650$		0			0
$651$	1.12901	+	10.4721i	0.0442492	+	0.410433i
$652$		0			0
$653$	−6.33574	+	48.1248i	−0.247937	+	1.88327i	0.186336	+	0.982486i	$0.440339\pi$
$653$	−6.33574	+	48.1248i	−0.247937	+	1.88327i	−0.434273	+	0.900781i	$0.642995\pi$
$654$		0			0
$655$	4.48638	+	7.77064i	0.175297	+	0.303624i
$656$		0			0
$657$	2.39572			0.0934659
$658$		0			0
$659$	12.9028	+	31.1501i	0.502621	+	1.21343i	0.948051	+	0.318118i	$0.103051\pi$
$659$	12.9028	+	31.1501i	0.502621	+	1.21343i	−0.445430	+	0.895317i	$0.646949\pi$
$660$		0			0
$661$	−4.05812	−	30.8245i	−0.157843	−	1.19893i	−0.868606	−	0.495503i	$-0.834984\pi$
$661$	−4.05812	−	30.8245i	−0.157843	−	1.19893i	0.710763	−	0.703431i	$-0.248350\pi$
$662$		0			0
$663$	2.40766	+	8.98551i	0.0935057	+	0.348968i
$664$		0			0
$665$	−4.95346	−	5.19196i	−0.192087	−	0.201335i
$666$		0			0
$667$	5.96739	+	7.77685i	0.231058	+	0.301121i
$668$		0			0
$669$	4.28889	−	5.58939i	0.165818	−	0.216098i
$670$		0			0
$671$	−65.8357			−2.54156
$672$		0			0
$673$	40.9511			1.57855			0.789274	−	0.614041i	$-0.210457\pi$
$673$	40.9511			1.57855			0.789274	+	0.614041i	$0.210457\pi$
$674$		0			0
$675$	−4.67746	+	6.09578i	−0.180035	+	0.234627i
$676$		0			0
$677$	−10.0454	−	13.0914i	−0.386075	−	0.503142i	0.559373	−	0.828916i	$-0.311042\pi$
$677$	−10.0454	−	13.0914i	−0.386075	−	0.503142i	−0.945448	+	0.325774i	$0.894375\pi$
$678$		0			0
$679$	22.5741	−	5.48350i	0.866314	−	0.210437i
$680$		0			0
$681$	−0.0718385	−	0.268105i	−0.00275286	−	0.0102738i
$682$		0			0
$683$	−0.239358	−	1.81811i	−0.00915880	−	0.0695680i	0.986255	−	0.165230i	$-0.0528366\pi$
$683$	−0.239358	−	1.81811i	−0.00915880	−	0.0695680i	−0.995414	+	0.0956619i	$0.969503\pi$
$684$		0			0
$685$	−2.09641	−	5.06118i	−0.0800996	−	0.193378i
$686$		0			0
$687$	−27.6371			−1.05442
$688$		0			0
$689$	29.5380	+	51.1614i	1.12531	+	1.94909i
$690$		0			0
$691$	−5.74341	+	43.6255i	−0.218490	+	1.65959i	0.433343	+	0.901229i	$0.357334\pi$
$691$	−5.74341	+	43.6255i	−0.218490	+	1.65959i	−0.651832	+	0.758363i	$0.725999\pi$
$692$		0			0
$693$	−10.5268	−	14.4076i	−0.399878	−	0.547299i
$694$		0			0
$695$	−21.1487	+	5.66676i	−0.802214	+	0.214953i
$696$		0			0
$697$	−0.327638	+	1.22276i	−0.0124102	+	0.0463154i
$698$		0			0
$699$	4.83883	+	2.00431i	0.183021	+	0.0758099i
$700$		0			0
$701$	17.7520	+	42.8570i	0.670483	+	1.61869i	0.780792	+	0.624791i	$0.214816\pi$
$701$	17.7520	+	42.8570i	0.670483	+	1.61869i	−0.110309	+	0.993897i	$0.535184\pi$
$702$		0			0
$703$	−7.09392	−	12.2870i	−0.267552	−	0.463414i
$704$		0			0
$705$	−3.15205	−	1.81984i	−0.118713	−	0.0685391i
$706$		0			0
$707$	−1.73158	−	4.47509i	−0.0651229	−	0.168303i
$708$		0			0
$709$	−0.950811	+	0.729583i	−0.0357084	+	0.0274001i	−0.626461	−	0.779452i	$-0.715497\pi$
$709$	−0.950811	+	0.729583i	−0.0357084	+	0.0274001i	0.590753	+	0.806852i	$0.298831\pi$
$710$		0			0
$711$	15.9540	+	4.27487i	0.598323	+	0.160320i
$712$		0			0
$713$	−7.11582	−	7.11582i	−0.266490	−	0.266490i
$714$		0			0
$715$	−61.8359	−	25.6133i	−2.31253	−	0.957882i
$716$		0			0
$717$	−2.15375	+	2.80682i	−0.0804332	+	0.104823i
$718$		0			0
$719$	19.7501	+	11.4027i	0.736554	+	0.425250i	0.820815	−	0.571194i	$-0.193520\pi$
$719$	19.7501	+	11.4027i	0.736554	+	0.425250i	−0.0842609	+	0.996444i	$0.526853\pi$
$720$		0			0
$721$	4.37856	+	8.01309i	0.163066	+	0.298423i
$722$		0			0
$723$	−19.2738	−	2.53744i	−0.716801	−	0.0943686i
$724$		0			0
$725$	−4.07660	+	0.536694i	−0.151401	+	0.0199323i
$726$		0			0
$727$	1.25193	−	1.25193i	0.0464316	−	0.0464316i	−0.683510	−	0.729941i	$-0.739547\pi$
$727$	1.25193	−	1.25193i	0.0464316	−	0.0464316i	0.729941	+	0.683510i	$0.239547\pi$
$728$		0			0
$729$	18.4375	+	18.4375i	0.682869	+	0.682869i
$730$		0			0
$731$	0.873464	+	6.63462i	0.0323062	+	0.245390i
$732$		0			0
$733$	3.22720	−	24.5131i	0.119200	−	0.905410i	−0.822455	−	0.568830i	$-0.807396\pi$
$733$	3.22720	−	24.5131i	0.119200	−	0.905410i	0.941655	−	0.336580i	$-0.109270\pi$
$734$		0			0
$735$	15.3353	−	7.91740i	0.565651	−	0.292038i
$736$		0			0
$737$	−24.1886	+	41.8959i	−0.890999	+	1.54326i
$738$		0			0
$739$	−23.8650	−	18.3122i	−0.877887	−	0.673626i	0.0681536	−	0.997675i	$-0.478289\pi$
$739$	−23.8650	−	18.3122i	−0.877887	−	0.673626i	−0.946040	+	0.324049i	$0.894956\pi$
$740$		0			0
$741$	4.86781	−	11.7519i	0.178824	−	0.431718i
$742$		0			0
$743$	4.91671	−	4.91671i	0.180377	−	0.180377i	−0.611143	−	0.791520i	$-0.709290\pi$
$743$	4.91671	−	4.91671i	0.180377	−	0.180377i	0.791520	+	0.611143i	$0.209290\pi$
$744$		0			0
$745$	−1.30252	+	4.86109i	−0.0477208	+	0.178097i
$746$		0			0
$747$	−4.81755	−	6.27835i	−0.176265	−	0.229713i
$748$		0			0
$749$	−8.68764	−	6.99669i	−0.317439	−	0.255654i
$750$		0			0
$751$	7.80945	−	13.5264i	0.284971	−	0.493584i	−0.687631	−	0.726060i	$-0.741349\pi$
$751$	7.80945	−	13.5264i	0.284971	−	0.493584i	0.972602	+	0.232476i	$0.0746828\pi$
$752$		0			0
$753$	−27.7062	+	15.9962i	−1.00967	+	0.582933i
$754$		0			0
$755$	−2.32359	+	0.962461i	−0.0845640	+	0.0350276i
$756$		0			0
$757$	6.69326	−	16.1590i	0.243271	−	0.587308i	−0.754333	−	0.656492i	$-0.772040\pi$
$757$	6.69326	−	16.1590i	0.243271	−	0.587308i	0.997604	+	0.0691842i	$0.0220396\pi$
$758$		0			0
$759$	−20.8390	−	5.58379i	−0.756407	−	0.202679i
$760$		0			0
$761$	5.17487	+	19.3129i	0.187589	+	0.700092i	0.994061	+	0.108820i	$0.0347073\pi$
$761$	5.17487	+	19.3129i	0.187589	+	0.700092i	−0.806472	+	0.591272i	$0.798626\pi$
$762$		0			0
$763$	3.90070	−	8.82460i	0.141215	−	0.319472i
$764$		0			0
$765$	−2.60411	−	0.342838i	−0.0941519	−	0.0123953i
$766$		0			0
$767$	67.2916	−	38.8508i	2.42976	−	1.40282i
$768$		0			0
$769$			46.5336i			1.67804i	0.544098	+	0.839022i	$0.316872\pi$
$769$			46.5336i			1.67804i	−0.544098	+	0.839022i	$0.683128\pi$
$770$		0			0
$771$	−16.4674	+	6.82104i	−0.593060	+	0.245654i
$772$		0			0
$773$	−28.8332	+	3.79596i	−1.03706	+	0.136531i	−0.629781	−	0.776773i	$-0.716855\pi$
$773$	−28.8332	+	3.79596i	−1.03706	+	0.136531i	−0.407278	+	0.913304i	$0.633522\pi$
$774$		0			0
$775$	4.07733	−	1.09252i	0.146462	−	0.0392444i
$776$		0			0
$777$	33.1586	−	8.05459i	1.18956	−	0.288957i
$778$		0			0
$779$	1.37328	−	1.05376i	0.0492030	−	0.0377548i
$780$		0			0
$781$	−46.9966	−	36.0618i	−1.68167	−	1.29039i
$782$		0			0
$783$			16.7687i			0.599264i
$784$		0			0
$785$		−	45.5381i		−	1.62532i
$786$		0			0
$787$	8.08180	+	6.20139i	0.288085	+	0.221056i	0.742686	−	0.669640i	$-0.233551\pi$
$787$	8.08180	+	6.20139i	0.288085	+	0.221056i	−0.454601	+	0.890695i	$0.650218\pi$
$788$		0			0
$789$	−13.4993	+	10.3584i	−0.480589	+	0.368769i
$790$		0			0
$791$	−31.8218	+	7.72988i	−1.13145	+	0.274843i
$792$		0			0
$793$	−86.1575	+	23.0858i	−3.05954	+	0.819802i
$794$		0			0
$795$	20.9280	−	2.75522i	0.742239	−	0.0977177i
$796$		0			0
$797$	−29.1949	+	12.0929i	−1.03414	+	0.428353i	−0.834204	−	0.551457i	$-0.814072\pi$
$797$	−29.1949	+	12.0929i	−1.03414	+	0.428353i	−0.199932	+	0.979810i	$0.564072\pi$
$798$		0			0
$799$			1.53741i			0.0543898i
$800$		0			0
$801$	−11.4741	+	6.62455i	−0.405416	+	0.234067i
$802$		0			0
$803$	−9.13511	−	1.20266i	−0.322371	−	0.0424409i
$804$		0			0
$805$	−6.66644	+	15.0816i	−0.234961	+	0.531555i
$806$		0			0
$807$	−2.21811	−	8.27810i	−0.0780811	−	0.291403i
$808$		0			0
$809$	17.4026	+	4.66300i	0.611841	+	0.163942i	0.551416	−	0.834230i	$-0.314088\pi$
$809$	17.4026	+	4.66300i	0.611841	+	0.163942i	0.0604253	+	0.998173i	$0.480754\pi$
$810$		0			0
$811$	3.00766	−	7.26114i	0.105613	−	0.254973i	−0.862235	−	0.506509i	$-0.830936\pi$
$811$	3.00766	−	7.26114i	0.105613	−	0.254973i	0.967848	+	0.251536i	$0.0809357\pi$
$812$		0			0
$813$	28.5004	−	11.8052i	0.999551	−	0.414028i
$814$		0			0
$815$	−9.25699	+	5.34453i	−0.324258	+	0.187211i
$816$		0			0
$817$	4.57523	−	7.92453i	0.160067	−	0.277244i
$818$		0			0
$819$	−18.8282	−	15.1635i	−0.657911	−	0.529857i
$820$		0			0
$821$	27.1989	+	35.4463i	0.949250	+	1.23709i	0.971429	+	0.237332i	$0.0762730\pi$
$821$	27.1989	+	35.4463i	0.949250	+	1.23709i	−0.0221790	+	0.999754i	$0.507060\pi$
$822$		0			0
$823$	−5.71956	+	21.3457i	−0.199371	+	0.744064i	0.791720	+	0.610884i	$0.209186\pi$
$823$	−5.71956	+	21.3457i	−0.199371	+	0.744064i	−0.991092	+	0.133180i	$0.957481\pi$
$824$		0			0
$825$	6.39897	−	6.39897i	0.222783	−	0.222783i
$826$		0			0
$827$	−10.4914	+	25.3284i	−0.364821	+	0.880755i	0.629760	+	0.776790i	$0.283153\pi$
$827$	−10.4914	+	25.3284i	−0.364821	+	0.880755i	−0.994581	+	0.103965i	$0.966847\pi$
$828$		0			0
$829$	15.2197	+	11.6785i	0.528601	+	0.405610i	0.838287	−	0.545229i	$-0.183557\pi$
$829$	15.2197	+	11.6785i	0.528601	+	0.405610i	−0.309686	+	0.950839i	$0.600224\pi$
$830$		0			0
$831$	6.44816	−	11.1685i	0.223684	−	0.387432i
$832$		0			0
$833$	−6.13512	−	3.93767i	−0.212569	−	0.136432i
$834$		0			0
$835$	−2.82001	+	21.4201i	−0.0975905	+	0.741274i
$836$		0			0
$837$	−2.24698	−	17.0675i	−0.0776670	−	0.589940i
$838$		0			0
$839$	−6.91976	−	6.91976i	−0.238897	−	0.238897i	0.577497	−	0.816393i	$-0.304030\pi$
$839$	−6.91976	−	6.91976i	−0.238897	−	0.238897i	−0.816393	+	0.577497i	$0.804030\pi$
$840$		0			0
$841$	14.1608	−	14.1608i	0.488304	−	0.488304i
$842$		0			0
$843$	31.1496	−	4.10092i	1.07285	−	0.141243i
$844$		0			0
$845$	−65.3569	−	8.60440i	−2.24835	−	0.296000i
$846$		0			0
$847$	18.9516	+	34.6827i	0.651183	+	1.19171i
$848$		0			0
$849$	16.5863	+	9.57608i	0.569239	+	0.328650i
$850$		0			0
$851$	−19.8468	+	25.8648i	−0.680338	+	0.886634i
$852$		0			0
$853$	33.0362	+	13.6840i	1.13114	+	0.468532i	0.868167	−	0.496271i	$-0.165298\pi$
$853$	33.0362	+	13.6840i	1.13114	+	0.468532i	0.262970	+	0.964804i	$0.415298\pi$
$854$		0			0
$855$	2.53964	+	2.53964i	0.0868538	+	0.0868538i
$856$		0			0
$857$	−45.0972	−	12.0838i	−1.54049	−	0.412774i	−0.614068	−	0.789253i	$-0.710468\pi$
$857$	−45.0972	−	12.0838i	−1.54049	−	0.412774i	−0.926425	+	0.376480i	$0.877134\pi$
$858$		0			0
$859$	30.9777	−	23.7700i	1.05695	−	0.811023i	0.0744347	−	0.997226i	$-0.476285\pi$
$859$	30.9777	−	23.7700i	1.05695	−	0.811023i	0.982511	+	0.186203i	$0.0596181\pi$
$860$		0			0
$861$	1.50234	+	3.88263i	0.0511995	+	0.132320i
$862$		0			0
$863$	14.2685	+	8.23794i	0.485706	+	0.280423i	0.722792	−	0.691066i	$-0.242859\pi$
$863$	14.2685	+	8.23794i	0.485706	+	0.280423i	−0.237085	+	0.971489i	$0.576192\pi$
$864$		0			0
$865$	2.30717	+	3.99614i	0.0784462	+	0.135873i
$866$		0			0
$867$	7.88434	+	19.0345i	0.267766	+	0.646445i
$868$		0			0
$869$	−58.6882	−	24.3095i	−1.99086	−	0.824642i
$870$		0			0
$871$	−16.9639	+	63.3100i	−0.574799	+	2.14518i
$872$		0			0
$873$	−11.2309	+	3.00931i	−0.380109	+	0.101850i
$874$		0			0
$875$	−18.9443	−	25.9283i	−0.640433	−	0.876537i
$876$		0			0
$877$	2.96458	−	22.5182i	0.100107	−	0.760385i	−0.865598	−	0.500740i	$-0.833061\pi$
$877$	2.96458	−	22.5182i	0.100107	−	0.760385i	0.965704	−	0.259645i	$-0.0836055\pi$
$878$		0			0
$879$	17.7308	+	30.7107i	0.598046	+	1.03585i
$880$		0			0
$881$	−22.7253			−0.765636			−0.382818	−	0.923824i	$-0.625046\pi$
$881$	−22.7253			−0.765636			−0.382818	+	0.923824i	$0.625046\pi$
$882$		0			0
$883$	17.4587	+	42.1489i	0.587530	+	1.41842i	0.885856	+	0.463960i	$0.153572\pi$
$883$	17.4587	+	42.1489i	0.587530	+	1.41842i	−0.298326	+	0.954464i	$0.596428\pi$
$884$		0			0
$885$	−3.62389	−	27.5262i	−0.121816	−	0.925283i
$886$		0			0
$887$	−0.763209	−	2.84834i	−0.0256261	−	0.0956377i	0.951928	−	0.306321i	$-0.0990979\pi$
$887$	−0.763209	−	2.84834i	−0.0256261	−	0.0956377i	−0.977554	+	0.210683i	$0.932431\pi$
$888$		0			0
$889$	6.96093	−	1.69089i	0.233462	−	0.0567106i
$890$		0			0
$891$	−10.1500	−	13.2277i	−0.340037	−	0.443144i
$892$		0			0
$893$	1.27977	−	1.66783i	0.0428260	−	0.0558119i
$894$		0			0
$895$	−21.0412			−0.703329
$896$		0			0
$897$	−29.2294			−0.975942
$898$		0			0
$899$	5.60810	−	7.30861i	0.187040	−	0.243756i
$900$		0			0
$901$	−5.42792	−	7.07381i	−0.180830	−	0.235663i
$902$		0			0
$903$	15.1917	+	15.9231i	0.505547	+	0.529888i
$904$		0			0
$905$	1.47301	+	5.49735i	0.0489645	+	0.182738i
$906$		0			0
$907$	5.55893	+	42.2242i	0.184581	+	1.40203i	0.793389	+	0.608715i	$0.208315\pi$
$907$	5.55893	+	42.2242i	0.184581	+	1.40203i	−0.608808	+	0.793318i	$0.708352\pi$
$908$		0			0
$909$	0.919074	+	2.21884i	0.0304837	+	0.0735943i
$910$		0			0
$911$	22.9192			0.759346			0.379673	−	0.925121i	$-0.376036\pi$
$911$	22.9192			0.759346			0.379673	+	0.925121i	$0.376036\pi$
$912$		0			0
$913$	15.2180	+	26.3584i	0.503643	+	0.872335i
$914$		0			0
$915$	−4.16001	+	31.5984i	−0.137526	+	1.04461i
$916$		0			0
$917$	−1.33608	−	12.3928i	−0.0441212	−	0.409246i
$918$		0			0
$919$	6.56055	−	1.75789i	0.216413	−	0.0579876i	−0.148984	−	0.988840i	$-0.547600\pi$
$919$	6.56055	−	1.75789i	0.216413	−	0.0579876i	0.365396	+	0.930852i	$0.380933\pi$
$920$		0			0
$921$	−0.382705	+	1.42827i	−0.0126105	+	0.0470632i
$922$		0			0
$923$	−74.1486	−	30.7134i	−2.44063	−	1.01094i
$924$		0			0
$925$	−5.23328	−	12.6343i	−0.172069	−	0.415412i
$926$		0			0
$927$	−2.28516	−	3.95801i	−0.0750545	−	0.129998i
$928$		0			0
$929$	2.88857	+	1.66772i	0.0947709	+	0.0547160i	0.546636	−	0.837370i	$-0.315908\pi$
$929$	2.88857	+	1.66772i	0.0947709	+	0.0547160i	−0.451866	+	0.892086i	$0.649241\pi$
$930$		0			0
$931$	3.37778	+	9.37870i	0.110702	+	0.307375i
$932$		0			0
$933$	7.49179	−	5.74865i	0.245270	−	0.188202i
$934$		0			0
$935$	9.75762	+	2.61455i	0.319108	+	0.0855048i
$936$		0			0
$937$	−30.7306	−	30.7306i	−1.00392	−	1.00392i	−0.999992	−	0.00393267i	$-0.998748\pi$
$937$	−30.7306	−	30.7306i	−1.00392	−	1.00392i	−0.00393267	−	0.999992i	$-0.501252\pi$
$938$		0			0
$939$	−6.96685	−	2.88577i	−0.227355	−	0.0941734i
$940$		0			0
$941$	0.0171643	−	0.0223689i	0.000559540	−	0.000729207i	−0.793073	−	0.609126i	$-0.791520\pi$
$941$	0.0171643	−	0.0223689i	0.000559540	−	0.000729207i	0.793633	+	0.608397i	$0.208187\pi$
$942$		0			0
$943$	−3.44469	−	1.98879i	−0.112175	−	0.0647640i
$944$		0			0
$945$	−24.7530	+	13.5257i	−0.805215	+	0.439991i
$946$		0			0
$947$	15.5110	+	2.04206i	0.504040	+	0.0663581i	0.378259	−	0.925700i	$-0.376523\pi$
$947$	15.5110	+	2.04206i	0.504040	+	0.0663581i	0.125781	+	0.992058i	$0.459856\pi$
$948$		0			0
$949$	−12.3766	+	1.62941i	−0.401761	+	0.0528929i
$950$		0			0
$951$	18.6887	−	18.6887i	0.606024	−	0.606024i
$952$		0			0
$953$	41.4334	+	41.4334i	1.34216	+	1.34216i	0.893908	+	0.448251i	$0.147953\pi$
$953$	41.4334	+	41.4334i	1.34216	+	1.34216i	0.448251	+	0.893908i	$0.352047\pi$
$954$		0			0
$955$	−1.58264	−	12.0213i	−0.0512129	−	0.389000i
$956$		0			0
$957$	2.57786	−	19.5808i	0.0833303	−	0.632956i
$958$		0			0
$959$	−0.178847	+	7.60796i	−0.00577527	+	0.245674i
$960$		0			0
$961$	10.7713	−	18.6565i	0.347462	−	0.601821i
$962$		0			0
$963$	4.42934	+	3.39875i	0.142734	+	0.109523i
$964$		0			0
$965$	0.943335	−	2.27741i	0.0303670	−	0.0733125i
$966$		0			0
$967$	42.0180	−	42.0180i	1.35121	−	1.35121i	0.466898	−	0.884311i	$-0.345372\pi$
$967$	42.0180	−	42.0180i	1.35121	−	1.35121i	0.884311	−	0.466898i	$-0.154628\pi$
$968$		0			0
$969$	−0.496896	+	1.85444i	−0.0159626	+	0.0595733i
$970$		0			0
$971$	17.2773	+	22.5162i	0.554455	+	0.722579i	0.983541	−	0.180684i	$-0.0578311\pi$
$971$	17.2773	+	22.5162i	0.554455	+	0.722579i	−0.429087	+	0.903263i	$0.641164\pi$
$972$		0			0
$973$	30.0534	+	4.67757i	0.963467	+	0.149956i
$974$		0			0
$975$	6.13031	−	10.6180i	0.196327	−	0.340049i
$976$		0			0
$977$	22.2372	−	12.8387i	0.711431	−	0.410745i	−0.100159	−	0.994971i	$-0.531935\pi$
$977$	22.2372	−	12.8387i	0.711431	−	0.410745i	0.811591	+	0.584226i	$0.198602\pi$
$978$		0			0
$979$	47.0772	−	19.5000i	1.50460	−	0.623224i
$980$		0			0
$981$	−1.84800	+	4.46146i	−0.0590020	+	0.142443i
$982$		0			0
$983$	−5.74279	−	1.53877i	−0.183166	−	0.0490793i	0.166070	−	0.986114i	$-0.446892\pi$
$983$	−5.74279	−	1.53877i	−0.183166	−	0.0490793i	−0.349236	+	0.937035i	$0.613559\pi$
$984$		0			0
$985$	−0.875735	−	3.26829i	−0.0279032	−	0.104136i
$986$		0			0
$987$	2.98283	+	4.08249i	0.0949446	+	0.129947i
$988$		0			0
$989$	−20.8467	−	2.74452i	−0.662887	−	0.0872707i
$990$		0			0
$991$	−17.8271	+	10.2925i	−0.566296	+	0.326951i	−0.755669	−	0.654954i	$-0.772688\pi$
$991$	−17.8271	+	10.2925i	−0.566296	+	0.326951i	0.189373	+	0.981905i	$0.439355\pi$
$992$		0			0
$993$			35.4977i			1.12649i
$994$		0			0
$995$	−16.2661	+	6.73764i	−0.515670	+	0.213598i
$996$		0			0
$997$	−52.9240	+	6.96758i	−1.67612	+	0.220665i	−0.907801	−	0.419401i	$-0.862240\pi$
$997$	−52.9240	+	6.96758i	−1.67612	+	0.220665i	−0.768319	+	0.640067i	$0.778907\pi$
$998$		0			0
$999$	−53.8701	+	14.4345i	−1.70438	+	0.456686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bi.a.271.9		240
4.3	odd	2		224.2.be.a.187.2	yes	240
7.3	odd	6	inner	896.2.bi.a.143.9		240
28.3	even	6		224.2.be.a.59.21	yes	240
32.13	even	8		224.2.be.a.19.21	✓	240
32.19	odd	8	inner	896.2.bi.a.495.9		240
224.45	odd	24		224.2.be.a.115.2	yes	240
224.115	even	24	inner	896.2.bi.a.367.9		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.19.21	✓	240	32.13	even	8
224.2.be.a.59.21	yes	240	28.3	even	6
224.2.be.a.115.2	yes	240	224.45	odd	24
224.2.be.a.187.2	yes	240	4.3	odd	2
896.2.bi.a.143.9		240	7.3	odd	6	inner
896.2.bi.a.271.9		240	1.1	even	1	trivial
896.2.bi.a.367.9		240	224.115	even	24	inner
896.2.bi.a.495.9		240	32.19	odd	8	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bi (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.788053 + 1.02701i) q^{3} +(1.15943 + 1.51100i) q^{5} +(-0.624522 - 2.57099i) q^{7} +(0.342734 + 1.27910i) q^{9} +O(q^{10})\)	\(q+(-0.788053 + 1.02701i) q^{3} +(1.15943 + 1.51100i) q^{5} +(-0.624522 - 2.57099i) q^{7} +(0.342734 + 1.27910i) q^{9} +(-0.664765 - 5.04939i) q^{11} +(-2.64057 - 6.37490i) q^{13} -2.46550 q^{15} +(0.520718 + 0.901911i) q^{17} +(0.185877 - 1.41188i) q^{19} +(3.13259 + 1.38468i) q^{21} +(-3.16081 + 0.846936i) q^{23} +(0.355257 - 1.32584i) q^{25} +(-5.17168 - 2.14218i) q^{27} +(-1.14636 - 2.76757i) q^{29} +(1.53764 + 2.66328i) q^{31} +(5.70964 + 3.29646i) q^{33} +(3.16067 - 3.92453i) q^{35} +(7.90414 - 6.06506i) q^{37} +(8.62799 + 2.31186i) q^{39} +(0.859509 + 0.859509i) q^{41} +(5.93649 + 2.45898i) q^{43} +(-1.53534 + 2.00090i) q^{45} +(1.27846 + 0.738121i) q^{47} +(-6.21995 + 3.21127i) q^{49} +(-1.33663 - 0.175970i) q^{51} +(-8.48833 + 1.11751i) q^{53} +(6.85887 - 6.85887i) q^{55} +(1.30353 + 1.30353i) q^{57} +(1.46984 + 11.1645i) q^{59} +(1.68729 - 12.8162i) q^{61} +(3.07451 - 1.67999i) q^{63} +(6.57090 - 11.3811i) q^{65} +(-7.53594 - 5.78253i) q^{67} +(1.62107 - 3.91361i) q^{69} +(8.22460 - 8.22460i) q^{71} +(0.468243 - 1.74751i) q^{73} +(1.08169 + 1.40968i) q^{75} +(-12.5667 + 4.86255i) q^{77} +(6.23642 - 10.8018i) q^{79} +(2.83516 - 1.63688i) q^{81} +(-5.52119 + 2.28695i) q^{83} +(-0.759049 + 1.83251i) q^{85} +(3.74571 + 1.00366i) q^{87} +(2.58953 + 9.66427i) q^{89} +(-14.7407 + 10.7701i) q^{91} +(-3.94696 - 0.519627i) q^{93} +(2.34886 - 1.35611i) q^{95} +8.78032i q^{97} +(6.23084 - 2.58090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{3} - 12 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 240 * q + 12 * q^3 - 12 * q^5 + 8 * q^7 - 4 * q^9	\( 240 q + 12 q^{3} - 12 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} + 32 q^{15} + 12 q^{19} - 8 q^{21} - 4 q^{23} - 4 q^{25} - 16 q^{29} - 24 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} + 32 q^{43} - 48 q^{45} + 24 q^{47} - 20 q^{51} - 20 q^{53} - 16 q^{57} - 84 q^{59} - 12 q^{61} - 8 q^{65} - 36 q^{67} + 80 q^{71} - 12 q^{73} + 72 q^{75} - 8 q^{77} + 8 q^{79} + 24 q^{85} + 12 q^{87} - 12 q^{89} - 40 q^{91} + 20 q^{93} + 40 q^{99}+O(q^{100}) \) 240 * q + 12 * q^3 - 12 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 + 32 * q^15 + 12 * q^19 - 8 * q^21 - 4 * q^23 - 4 * q^25 - 16 * q^29 - 24 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 + 32 * q^43 - 48 * q^45 + 24 * q^47 - 20 * q^51 - 20 * q^53 - 16 * q^57 - 84 * q^59 - 12 * q^61 - 8 * q^65 - 36 * q^67 + 80 * q^71 - 12 * q^73 + 72 * q^75 - 8 * q^77 + 8 * q^79 + 24 * q^85 + 12 * q^87 - 12 * q^89 - 40 * q^91 + 20 * q^93 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more