LMFDB - Embedded newform 765.2.bh.b.739.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(19,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 4, 7]))

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

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

chi := DirichletCharacter("765.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.bh (of order $8$, degree $4$, 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:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			739.4
Character	$\chi$	$=$	765.739
Dual form			765.2.bh.b.559.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.176012 + 0.176012i) q^{2} -1.93804i q^{4} +(-0.0665446 - 2.23508i) q^{5} +(-0.547653 - 1.32215i) q^{7} +(0.693142 - 0.693142i) q^{8} +O(q^{10})$	\(q+(0.176012 + 0.176012i) q^{2} -1.93804i q^{4} +(-0.0665446 - 2.23508i) q^{5} +(-0.547653 - 1.32215i) q^{7} +(0.693142 - 0.693142i) q^{8} +(0.381688 - 0.405113i) q^{10} +(-1.03080 - 2.48857i) q^{11} -0.174664 q^{13} +(0.136321 - 0.329108i) q^{14} -3.63208 q^{16} +(2.27165 + 3.44088i) q^{17} +(-2.69404 + 2.69404i) q^{19} +(-4.33167 + 0.128966i) q^{20} +(0.256585 - 0.619452i) q^{22} +(2.54807 - 1.05544i) q^{23} +(-4.99114 + 0.297464i) q^{25} +(-0.0307430 - 0.0307430i) q^{26} +(-2.56238 + 1.06137i) q^{28} +(-5.94408 - 2.46212i) q^{29} +(-0.188417 + 0.454879i) q^{31} +(-2.02557 - 2.02557i) q^{32} +(-0.205798 + 1.00547i) q^{34} +(-2.91867 + 1.31203i) q^{35} +(5.30576 + 2.19772i) q^{37} -0.948365 q^{38} +(-1.59535 - 1.50310i) q^{40} +(-5.54000 + 2.29474i) q^{41} +(8.00004 - 8.00004i) q^{43} +(-4.82296 + 1.99773i) q^{44} +(0.634261 + 0.262720i) q^{46} +2.65291 q^{47} +(3.50159 - 3.50159i) q^{49} +(-0.930858 - 0.826143i) q^{50} +0.338506i q^{52} +(-8.73501 - 8.73501i) q^{53} +(-5.49356 + 2.46952i) q^{55} +(-1.29604 - 0.536837i) q^{56} +(-0.612867 - 1.47959i) q^{58} +(5.72232 + 5.72232i) q^{59} +(-6.41902 + 2.65884i) q^{61} +(-0.113228 + 0.0469005i) q^{62} +6.55110i q^{64} +(0.0116230 + 0.390388i) q^{65} +12.3901i q^{67} +(6.66855 - 4.40254i) q^{68} +(-0.744653 - 0.282788i) q^{70} +(4.67878 - 11.2956i) q^{71} +(5.99425 - 14.4714i) q^{73} +(0.547052 + 1.32070i) q^{74} +(5.22115 + 5.22115i) q^{76} +(-2.72575 + 2.72575i) q^{77} +(-4.94031 - 11.9270i) q^{79} +(0.241695 + 8.11797i) q^{80} +(-1.37901 - 0.571204i) q^{82} +(6.06390 + 6.06390i) q^{83} +(7.53946 - 5.30628i) q^{85} +2.81621 q^{86} +(-2.43943 - 1.01044i) q^{88} -11.4907i q^{89} +(0.0956555 + 0.230933i) q^{91} +(-2.04549 - 4.93826i) q^{92} +(0.466944 + 0.466944i) q^{94} +(6.20066 + 5.84211i) q^{95} +(0.879757 - 2.12392i) q^{97} +1.23264 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 16 q^{10} + 24 q^{14} + 8 q^{16} - 24 q^{19} + 8 q^{20} + 16 q^{25} + 16 q^{26} - 24 q^{29} - 24 q^{31} + 8 q^{34} - 8 q^{35} + 16 q^{40} + 48 q^{41} - 72 q^{44} - 16 q^{46} + 48 q^{49} - 16 q^{50} - 24 q^{56} + 48 q^{59} + 16 q^{61} - 24 q^{65} + 32 q^{70} - 16 q^{71} + 64 q^{74} - 24 q^{76} - 72 q^{79} + 64 q^{80} - 24 q^{85} - 8 q^{91} - 40 q^{94} + 88 q^{95}+O(q^{100}) $ 24 * q - 16 * q^10 + 24 * q^14 + 8 * q^16 - 24 * q^19 + 8 * q^20 + 16 * q^25 + 16 * q^26 - 24 * q^29 - 24 * q^31 + 8 * q^34 - 8 * q^35 + 16 * q^40 + 48 * q^41 - 72 * q^44 - 16 * q^46 + 48 * q^49 - 16 * q^50 - 24 * q^56 + 48 * q^59 + 16 * q^61 - 24 * q^65 + 32 * q^70 - 16 * q^71 + 64 * q^74 - 24 * q^76 - 72 * q^79 + 64 * q^80 - 24 * q^85 - 8 * q^91 - 40 * q^94 + 88 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	0.176012	+	0.176012i	0.124459	+	0.124459i	0.766593	−	0.642134i	$-0.221951\pi$
$2$	0.176012	+	0.176012i	0.124459	+	0.124459i	−0.642134	+	0.766593i	$0.721951\pi$
$3$		0			0
$3$		0			0
$4$		−	1.93804i		−	0.969020i
$5$	−0.0665446	−	2.23508i	−0.0297596	−	0.999557i
$5$	−0.0665446	−	2.23508i	−0.0297596	−	0.999557i
$6$		0			0
$7$	−0.547653	−	1.32215i	−0.206993	−	0.499726i	0.785954	−	0.618286i	$-0.212172\pi$
$7$	−0.547653	−	1.32215i	−0.206993	−	0.499726i	−0.992947	+	0.118559i	$0.962172\pi$
$8$	0.693142	−	0.693142i	0.245063	−	0.245063i
$9$		0			0
$10$	0.381688	−	0.405113i	0.120700	−	0.128108i
$11$	−1.03080	−	2.48857i	−0.310798	−	0.750333i	−0.999676	−	0.0254558i	$-0.991896\pi$
$11$	−1.03080	−	2.48857i	−0.310798	−	0.750333i	0.688878	−	0.724878i	$-0.258104\pi$
$12$		0			0
$13$	−0.174664			−0.0484432			−0.0242216	−	0.999707i	$-0.507711\pi$
$13$	−0.174664			−0.0484432			−0.0242216	+	0.999707i	$0.507711\pi$
$14$	0.136321	−	0.329108i	0.0364333	−	0.0879578i
$15$		0			0
$16$	−3.63208			−0.908019
$17$	2.27165	+	3.44088i	0.550955	+	0.834535i
$17$	2.27165	+	3.44088i	0.550955	+	0.834535i
$18$		0			0
$19$	−2.69404	+	2.69404i	−0.618055	+	0.618055i	−0.945032	−	0.326978i	$-0.893970\pi$
$19$	−2.69404	+	2.69404i	−0.618055	+	0.618055i	0.326978	+	0.945032i	$0.393970\pi$
$20$	−4.33167	+	0.128966i	−0.968591	+	0.0288377i
$21$		0			0
$22$	0.256585	−	0.619452i	0.0547042	−	0.132068i
$23$	2.54807	−	1.05544i	0.531309	−	0.220075i	−0.100867	−	0.994900i	$-0.532162\pi$
$23$	2.54807	−	1.05544i	0.531309	−	0.220075i	0.632176	+	0.774825i	$0.282162\pi$
$24$		0			0
$25$	−4.99114	+	0.297464i	−0.998229	+	0.0594929i
$26$	−0.0307430	−	0.0307430i	−0.00602920	−	0.00602920i
$27$		0			0
$28$	−2.56238	+	1.06137i	−0.484245	+	0.200581i
$29$	−5.94408	−	2.46212i	−1.10379	−	0.457204i	−0.244994	−	0.969525i	$-0.578786\pi$
$29$	−5.94408	−	2.46212i	−1.10379	−	0.457204i	−0.858794	+	0.512321i	$0.828786\pi$
$30$		0			0
$31$	−0.188417	+	0.454879i	−0.0338407	+	0.0816987i	−0.939896	−	0.341460i	$-0.889079\pi$
$31$	−0.188417	+	0.454879i	−0.0338407	+	0.0816987i	0.906056	+	0.423159i	$0.139079\pi$
$32$	−2.02557	−	2.02557i	−0.358074	−	0.358074i
$33$		0			0
$34$	−0.205798	+	1.00547i	−0.0352941	+	0.172437i
$35$	−2.91867	+	1.31203i	−0.493345	+	0.221773i
$36$		0			0
$37$	5.30576	+	2.19772i	0.872261	+	0.361302i	0.773490	−	0.633808i	$-0.218509\pi$
$37$	5.30576	+	2.19772i	0.872261	+	0.361302i	0.0987704	+	0.995110i	$0.468509\pi$
$38$	−0.948365			−0.153845
$39$		0			0
$40$	−1.59535	−	1.50310i	−0.252247	−	0.237661i
$41$	−5.54000	+	2.29474i	−0.865203	+	0.358379i	−0.770740	−	0.637150i	$-0.780113\pi$
$41$	−5.54000	+	2.29474i	−0.865203	+	0.358379i	−0.0944627	+	0.995528i	$0.530113\pi$
$42$		0			0
$43$	8.00004	−	8.00004i	1.22000	−	1.22000i	0.252363	−	0.967633i	$-0.418792\pi$
$43$	8.00004	−	8.00004i	1.22000	−	1.22000i	0.967633	−	0.252363i	$-0.0812076\pi$
$44$	−4.82296	+	1.99773i	−0.727088	+	0.301170i
$45$		0			0
$46$	0.634261	+	0.262720i	0.0935167	+	0.0387359i
$47$	2.65291			0.386967			0.193483	−	0.981104i	$-0.438021\pi$
$47$	2.65291			0.386967			0.193483	+	0.981104i	$0.438021\pi$
$48$		0			0
$49$	3.50159	−	3.50159i	0.500227	−	0.500227i
$50$	−0.930858	−	0.826143i	−0.131643	−	0.116834i
$51$		0			0
$52$			0.338506i			0.0469424i
$53$	−8.73501	−	8.73501i	−1.19985	−	1.19985i	−0.974212	−	0.225633i	$-0.927555\pi$
$53$	−8.73501	−	8.73501i	−1.19985	−	1.19985i	−0.225633	−	0.974212i	$-0.572445\pi$
$54$		0			0
$55$	−5.49356	+	2.46952i	−0.740752	+	0.332990i
$56$	−1.29604	−	0.536837i	−0.173191	−	0.0717379i
$57$		0			0
$58$	−0.612867	−	1.47959i	−0.0804733	−	0.194280i
$59$	5.72232	+	5.72232i	0.744982	+	0.744982i	0.973532	−	0.228550i	$-0.0733984\pi$
$59$	5.72232	+	5.72232i	0.744982	+	0.744982i	−0.228550	+	0.973532i	$0.573398\pi$
$60$		0			0
$61$	−6.41902	+	2.65884i	−0.821871	+	0.340430i	−0.753679	−	0.657242i	$-0.771723\pi$
$61$	−6.41902	+	2.65884i	−0.821871	+	0.340430i	−0.0681914	+	0.997672i	$0.521723\pi$
$62$	−0.113228	+	0.0469005i	−0.0143799	+	0.00595637i
$63$		0			0
$64$			6.55110i			0.818888i
$65$	0.0116230	+	0.390388i	0.00144165	+	0.0484217i
$66$		0			0
$67$			12.3901i			1.51369i	0.653594	+	0.756845i	$0.273260\pi$
$67$			12.3901i			1.51369i	−0.653594	+	0.756845i	$0.726740\pi$
$68$	6.66855	−	4.40254i	0.808681	−	0.533886i
$69$		0			0
$70$	−0.744653	−	0.282788i	−0.0890031	−	0.0337996i
$71$	4.67878	−	11.2956i	0.555269	−	1.34054i	−0.358205	−	0.933643i	$-0.616611\pi$
$71$	4.67878	−	11.2956i	0.555269	−	1.34054i	0.913474	−	0.406896i	$-0.133389\pi$
$72$		0			0
$73$	5.99425	−	14.4714i	0.701574	−	1.69375i	−0.0184781	−	0.999829i	$-0.505882\pi$
$73$	5.99425	−	14.4714i	0.701574	−	1.69375i	0.720052	−	0.693920i	$-0.244118\pi$
$74$	0.547052	+	1.32070i	0.0635935	+	0.153528i
$75$		0			0
$76$	5.22115	+	5.22115i	0.598907	+	0.598907i
$77$	−2.72575	+	2.72575i	−0.310628	+	0.310628i
$78$		0			0
$79$	−4.94031	−	11.9270i	−0.555828	−	1.34189i	−0.913042	−	0.407865i	$-0.866273\pi$
$79$	−4.94031	−	11.9270i	−0.555828	−	1.34189i	0.357214	−	0.934022i	$-0.383727\pi$
$80$	0.241695	+	8.11797i	0.0270223	+	0.907617i
$81$		0			0
$82$	−1.37901	−	0.571204i	−0.152286	−	0.0630789i
$83$	6.06390	+	6.06390i	0.665600	+	0.665600i	0.956694	−	0.291094i	$-0.0940194\pi$
$83$	6.06390	+	6.06390i	0.665600	+	0.665600i	−0.291094	+	0.956694i	$0.594019\pi$
$84$		0			0
$85$	7.53946	−	5.30628i	0.817769	−	0.575546i
$86$	2.81621			0.303679
$87$		0			0
$88$	−2.43943	−	1.01044i	−0.260044	−	0.107714i
$89$		−	11.4907i		−	1.21801i	−0.793165	−	0.609006i	$-0.791568\pi$
$89$		−	11.4907i		−	1.21801i	0.793165	−	0.609006i	$-0.208432\pi$
$90$		0			0
$91$	0.0956555	+	0.230933i	0.0100274	+	0.0242083i
$92$	−2.04549	−	4.93826i	−0.213257	−	0.514849i
$93$		0			0
$94$	0.466944	+	0.466944i	0.0481616	+	0.0481616i
$95$	6.20066	+	5.84211i	0.636174	+	0.599388i
$96$		0			0
$97$	0.879757	−	2.12392i	0.0893258	−	0.215651i	−0.872903	−	0.487894i	$-0.837765\pi$
$97$	0.879757	−	2.12392i	0.0893258	−	0.215651i	0.962229	+	0.272242i	$0.0877653\pi$
$98$	1.23264			0.124516
$99$		0			0
$100$	0.576498	+	9.67303i	0.0576498	+	0.967303i
$101$	0.890917			0.0886495			0.0443248	−	0.999017i	$-0.485886\pi$
$101$	0.890917			0.0886495			0.0443248	+	0.999017i	$0.485886\pi$
$102$		0			0
$103$		−	0.367137i		−	0.0361751i	−0.999836	−	0.0180875i	$-0.994242\pi$
$103$		−	0.367137i		−	0.0361751i	0.999836	−	0.0180875i	$-0.00575776\pi$
$104$	−0.121067	+	0.121067i	−0.0118716	+	0.0118716i
$105$		0			0
$106$		−	3.07493i		−	0.298664i
$107$	2.54389	−	6.14149i	0.245927	−	0.593720i	−0.751924	−	0.659250i	$-0.770874\pi$
$107$	2.54389	−	6.14149i	0.245927	−	0.593720i	0.997851	+	0.0655301i	$0.0208738\pi$
$108$		0			0
$109$	8.16665	−	3.38274i	0.782223	−	0.324007i	0.0444107	−	0.999013i	$-0.485859\pi$
$109$	8.16665	−	3.38274i	0.782223	−	0.324007i	0.737812	+	0.675006i	$0.235859\pi$
$110$	−1.40160	−	0.532267i	−0.133637	−	0.0507497i
$111$		0			0
$112$	1.98912	+	4.80216i	0.187954	+	0.453761i
$113$	5.27825	−	2.18632i	0.496536	−	0.205672i	−0.120339	−	0.992733i	$-0.538398\pi$
$113$	5.27825	−	2.18632i	0.496536	−	0.205672i	0.616875	+	0.787061i	$0.288398\pi$
$114$		0			0
$115$	−2.52856	−	5.62490i	−0.235789	−	0.524524i
$116$	−4.77168	+	11.5199i	−0.443040	+	1.06959i
$117$		0			0
$118$			2.01439i			0.185440i
$119$	3.30529	−	4.88787i	0.302995	−	0.448070i
$120$		0			0
$121$	2.64772	−	2.64772i	0.240702	−	0.240702i
$122$	−1.59781	−	0.661835i	−0.144659	−	0.0599197i
$123$		0			0
$124$	0.881574	+	0.365160i	0.0791676	+	0.0327923i
$125$	0.996990	+	11.1358i	0.0891735	+	0.996016i
$126$		0			0
$127$	−11.5590	+	11.5590i	−1.02569	+	1.02569i	−0.0260300	+	0.999661i	$0.508287\pi$
$127$	−11.5590	+	11.5590i	−1.02569	+	1.02569i	−0.999661	+	0.0260300i	$0.991713\pi$
$128$	−5.20422	+	5.20422i	−0.459992	+	0.459992i
$129$		0			0
$130$	−0.0666672	+	0.0707588i	−0.00584710	+	0.00620596i
$131$	8.90518	+	3.68865i	0.778049	+	0.322279i	0.736128	−	0.676842i	$-0.236652\pi$
$131$	8.90518	+	3.68865i	0.778049	+	0.322279i	0.0419214	+	0.999121i	$0.486652\pi$
$132$		0			0
$133$	5.03733	+	2.08653i	0.436791	+	0.180925i
$134$	−2.18080	+	2.18080i	−0.188393	+	0.188393i
$135$		0			0
$136$	3.95959	+	0.810442i	0.339532	+	0.0694949i
$137$			6.60524i			0.564324i	0.959367	+	0.282162i	$0.0910515\pi$
$137$			6.60524i			0.564324i	−0.959367	+	0.282162i	$0.908948\pi$
$138$		0			0
$139$	−1.75923	+	4.24715i	−0.149216	+	0.360239i	−0.980759	−	0.195221i	$-0.937458\pi$
$139$	−1.75923	+	4.24715i	−0.149216	+	0.360239i	0.831544	+	0.555459i	$0.187458\pi$
$140$	2.54277	+	5.65650i	0.214903	+	0.478061i
$141$		0			0
$142$	2.81168	−	1.16464i	0.235951	−	0.0977340i
$143$	0.180044	+	0.434665i	0.0150561	+	0.0363485i
$144$		0			0
$145$	−5.10748	+	13.4493i	−0.424153	+	1.11691i
$146$	3.60220	−	1.49208i	0.298120	−	0.123485i
$147$		0			0
$148$	4.25926	−	10.2828i	0.350109	−	0.845238i
$149$		−	11.6404i		−	0.953619i	−0.879007	−	0.476810i	$-0.841793\pi$
$149$		−	11.6404i		−	0.953619i	0.879007	−	0.476810i	$-0.158207\pi$
$150$		0			0
$151$	0.0974235	−	0.0974235i	0.00792821	−	0.00792821i	−0.703132	−	0.711060i	$-0.748216\pi$
$151$	0.0974235	−	0.0974235i	0.00792821	−	0.00792821i	0.711060	+	0.703132i	$0.248216\pi$
$152$			3.73470i			0.302924i
$153$		0			0
$154$	−0.959530			−0.0773211
$155$	1.02923	+	0.390857i	0.0826696	+	0.0313944i
$156$		0			0
$157$	−9.66489			−0.771343			−0.385671	−	0.922636i	$-0.626030\pi$
$157$	−9.66489			−0.771343			−0.385671	+	0.922636i	$0.626030\pi$
$158$	1.22973	−	2.96884i	0.0978323	−	0.236188i
$159$		0			0
$160$	−4.39252	+	4.66210i	−0.347259	+	0.368572i
$161$	−2.79092	−	2.79092i	−0.219955	−	0.219955i
$162$		0			0
$163$	4.75100	+	11.4699i	0.372127	+	0.898394i	0.993390	+	0.114792i	$0.0366200\pi$
$163$	4.75100	+	11.4699i	0.372127	+	0.898394i	−0.621263	+	0.783602i	$0.713380\pi$
$164$	4.44730	+	10.7367i	0.347276	+	0.838399i
$165$		0			0
$166$			2.13464i			0.165680i
$167$	−3.86872	−	1.60248i	−0.299371	−	0.124003i	0.227942	−	0.973675i	$-0.426800\pi$
$167$	−3.86872	−	1.60248i	−0.299371	−	0.124003i	−0.527313	+	0.849671i	$0.676800\pi$
$168$		0			0
$169$	−12.9695			−0.997653
$170$	2.26100	+	0.393067i	0.173411	+	0.0301468i
$171$		0			0
$172$	−15.5044	−	15.5044i	−1.18220	−	1.18220i
$173$	2.73000	+	1.13080i	0.207558	+	0.0859733i	0.484040	−	0.875046i	$-0.339169\pi$
$173$	2.73000	+	1.13080i	0.207558	+	0.0859733i	−0.276483	+	0.961019i	$0.589169\pi$
$174$		0			0
$175$	3.12671	+	6.43614i	0.236357	+	0.486527i
$176$	3.74395	+	9.03869i	0.282211	+	0.681317i
$177$		0			0
$178$	2.02250	−	2.02250i	0.151593	−	0.151593i
$179$	16.4589	+	16.4589i	1.23019	+	1.23019i	0.963889	+	0.266304i	$0.0858027\pi$
$179$	16.4589	+	16.4589i	1.23019	+	1.23019i	0.266304	+	0.963889i	$0.414197\pi$
$180$		0			0
$181$	4.37037	+	10.5510i	0.324847	+	0.784250i	0.998959	+	0.0456205i	$0.0145265\pi$
$181$	4.37037	+	10.5510i	0.324847	+	0.784250i	−0.674112	+	0.738629i	$0.735474\pi$
$182$	−0.0238104	+	0.0574834i	−0.00176495	+	0.00426096i
$183$		0			0
$184$	1.03460	−	2.49775i	0.0762717	−	0.184136i
$185$	4.55900	−	12.0050i	0.335184	−	0.882627i
$186$		0			0
$187$	6.22126	−	9.20002i	0.454944	−	0.672772i
$188$		−	5.14145i		−	0.374978i
$189$		0			0
$190$	0.0631085	+	2.11967i	0.00457837	+	0.153777i
$191$			3.08201i			0.223007i	0.993764	+	0.111503i	$0.0355666\pi$
$191$			3.08201i			0.223007i	−0.993764	+	0.111503i	$0.964433\pi$
$192$		0			0
$193$	14.7688	−	6.11743i	1.06308	−	0.440343i	0.218537	−	0.975829i	$-0.429872\pi$
$193$	14.7688	−	6.11743i	1.06308	−	0.440343i	0.844544	+	0.535486i	$0.179872\pi$
$194$	0.528683	−	0.218988i	0.0379572	−	0.0157224i
$195$		0			0
$196$	−6.78621	−	6.78621i	−0.484729	−	0.484729i
$197$	4.08460	+	9.86109i	0.291015	+	0.702573i	0.999996	−	0.00265412i	$-0.000844833\pi$
$197$	4.08460	+	9.86109i	0.291015	+	0.702573i	−0.708981	+	0.705228i	$0.750845\pi$
$198$		0			0
$199$	14.6337	+	6.06147i	1.03735	+	0.429686i	0.835362	−	0.549701i	$-0.185258\pi$
$199$	14.6337	+	6.06147i	1.03735	+	0.429686i	0.201993	+	0.979387i	$0.435258\pi$
$200$	−3.25339	+	3.66576i	−0.230049	+	0.259208i
$201$		0			0
$202$	0.156812	+	0.156812i	0.0110333	+	0.0110333i
$203$			9.20737i			0.646230i
$204$		0			0
$205$	5.49759	+	12.2296i	0.383968	+	0.854154i
$206$	0.0646205	−	0.0646205i	0.00450232	−	0.00450232i
$207$		0			0
$208$	0.634394			0.0439873
$209$	9.48133	+	3.92729i	0.655837	+	0.271657i
$210$		0			0
$211$	−4.54512	+	1.88265i	−0.312899	+	0.129607i	−0.533606	−	0.845733i	$-0.679164\pi$
$211$	−4.54512	+	1.88265i	−0.312899	+	0.129607i	0.220707	+	0.975340i	$0.429164\pi$
$212$	−16.9288	+	16.9288i	−1.16267	+	1.16267i
$213$		0			0
$214$	1.52873	−	0.633221i	0.104502	−	0.0432861i
$215$	−18.4131	−	17.3484i	−1.25576	−	1.18315i
$216$		0			0
$217$	0.704606			0.0478318
$218$	2.03283	+	0.842025i	0.137681	+	0.0570292i
$219$		0			0
$220$	4.78603	+	10.6467i	0.322674	+	0.717803i
$221$	−0.396776	−	0.600998i	−0.0266900	−	0.0404275i
$222$		0			0
$223$	−7.10210	−	7.10210i	−0.475592	−	0.475592i	0.428127	−	0.903719i	$-0.359174\pi$
$223$	−7.10210	−	7.10210i	−0.475592	−	0.475592i	−0.903719	+	0.428127i	$0.859174\pi$
$224$	−1.56880	+	3.78743i	−0.104820	+	0.253058i
$225$		0			0
$226$	1.31385	+	0.544216i	0.0873963	+	0.0362007i
$227$	−4.13654	+	1.71341i	−0.274552	+	0.113723i	−0.515711	−	0.856762i	$-0.672472\pi$
$227$	−4.13654	+	1.71341i	−0.274552	+	0.113723i	0.241160	+	0.970485i	$0.422472\pi$
$228$		0			0
$229$	−0.847088	−	0.847088i	−0.0559771	−	0.0559771i	0.678564	−	0.734541i	$-0.262603\pi$
$229$	−0.847088	−	0.847088i	−0.0559771	−	0.0559771i	−0.734541	+	0.678564i	$0.762603\pi$
$230$	0.544992	−	1.43511i	0.0359357	−	0.0946280i
$231$		0			0
$232$	−5.82669	+	2.41349i	−0.382541	+	0.158454i
$233$	9.74096	−	23.5168i	0.638152	−	1.54063i	−0.190987	−	0.981592i	$-0.561169\pi$
$233$	9.74096	−	23.5168i	0.638152	−	1.54063i	0.829139	−	0.559042i	$-0.188831\pi$
$234$		0			0
$235$	−0.176537	−	5.92946i	−0.0115160	−	0.386795i
$236$	11.0901	−	11.0901i	0.721903	−	0.721903i
$237$		0			0
$238$	1.44209	−	0.278553i	0.0934770	−	0.0180559i
$239$	−6.21407			−0.401955			−0.200977	−	0.979596i	$-0.564412\pi$
$239$	−6.21407			−0.401955			−0.200977	+	0.979596i	$0.564412\pi$
$240$		0			0
$241$	10.2576	−	24.7640i	0.660750	−	1.59519i	−0.135880	−	0.990725i	$-0.543386\pi$
$241$	10.2576	−	24.7640i	0.660750	−	1.59519i	0.796631	−	0.604467i	$-0.206614\pi$
$242$	0.932062			0.0599152
$243$		0			0
$244$	5.15294	+	12.4403i	0.329883	+	0.796409i
$245$	−8.05933	−	7.59330i	−0.514892	−	0.485118i
$246$		0			0
$247$	0.470552	−	0.470552i	0.0299405	−	0.0299405i
$248$	0.184696	+	0.445895i	0.0117282	+	0.0283144i
$249$		0			0
$250$	−1.78455	+	2.13552i	−0.112865	+	0.135062i
$251$			10.6052i			0.669394i	0.942326	+	0.334697i	$0.108634\pi$
$251$			10.6052i			0.669394i	−0.942326	+	0.334697i	$0.891366\pi$
$252$		0			0
$253$	−5.25310	−	5.25310i	−0.330260	−	0.330260i
$254$	−4.06903			−0.255313
$255$		0			0
$256$	11.2702			0.704387
$257$	−1.08911	−	1.08911i	−0.0679369	−	0.0679369i	0.672322	−	0.740259i	$-0.265297\pi$
$257$	−1.08911	−	1.08911i	−0.0679369	−	0.0679369i	−0.740259	+	0.672322i	$0.765297\pi$
$258$		0			0
$259$		−	8.21860i		−	0.510679i
$260$	0.756588	−	0.0225258i	0.0469216	−	0.00139699i
$261$		0			0
$262$	0.918172	+	2.21666i	0.0567249	+	0.136946i
$263$	0.301535	−	0.301535i	0.0185935	−	0.0185935i	−0.697749	−	0.716342i	$-0.745815\pi$
$263$	0.301535	−	0.301535i	0.0185935	−	0.0185935i	0.716342	+	0.697749i	$0.245815\pi$
$264$		0			0
$265$	−18.9421	+	20.1047i	−1.16361	+	1.23502i
$266$	0.519375	+	1.25388i	0.0318449	+	0.0768805i
$267$		0			0
$268$	24.0125			1.46680
$269$	6.54570	−	15.8027i	0.399098	−	0.963508i	−0.588782	−	0.808292i	$-0.700392\pi$
$269$	6.54570	−	15.8027i	0.399098	−	0.963508i	0.987880	−	0.155217i	$-0.0496075\pi$
$270$		0			0
$271$	16.0704			0.976208			0.488104	−	0.872785i	$-0.337689\pi$
$271$	16.0704			0.976208			0.488104	+	0.872785i	$0.337689\pi$
$272$	−8.25079	−	12.4975i	−0.500278	−	0.757774i
$273$		0			0
$274$	−1.16260	+	1.16260i	−0.0702353	+	0.0702353i
$275$	5.88514	+	12.1142i	0.354887	+	0.730514i
$276$		0			0
$277$	6.41483	−	15.4868i	0.385430	−	0.930510i	−0.605465	−	0.795872i	$-0.707013\pi$
$277$	6.41483	−	15.4868i	0.385430	−	0.930510i	0.990895	−	0.134638i	$-0.0429871\pi$
$278$	−1.05719	+	0.437904i	−0.0634063	+	0.0262637i
$279$		0			0
$280$	−1.11363	+	2.93247i	−0.0665521	+	0.175249i
$281$	−5.54254	−	5.54254i	−0.330640	−	0.330640i	0.522189	−	0.852830i	$-0.325115\pi$
$281$	−5.54254	−	5.54254i	−0.330640	−	0.330640i	−0.852830	+	0.522189i	$0.825115\pi$
$282$		0			0
$283$	6.07963	−	2.51826i	0.361396	−	0.149695i	−0.194594	−	0.980884i	$-0.562339\pi$
$283$	6.07963	−	2.51826i	0.361396	−	0.149695i	0.555991	+	0.831189i	$0.312339\pi$
$284$	−21.8913	−	9.06767i	−1.29901	−	0.538067i
$285$		0			0
$286$	−0.0448163	+	0.108196i	−0.00265004	+	0.00639777i
$287$	6.06800	+	6.06800i	0.358183	+	0.358183i
$288$		0			0
$289$	−6.67925	+	15.6329i	−0.392897	+	0.919582i
$290$	−3.26622	+	1.46826i	−0.191799	+	0.0862194i
$291$		0			0
$292$	−28.0461	−	11.6171i	−1.64128	−	0.679839i
$293$	−3.15115			−0.184092			−0.0920461	−	0.995755i	$-0.529341\pi$
$293$	−3.15115			−0.184092			−0.0920461	+	0.995755i	$0.529341\pi$
$294$		0			0
$295$	12.4090	−	13.1706i	0.722482	−	0.766823i
$296$	5.20097	−	2.15431i	0.302300	−	0.125217i
$297$		0			0
$298$	2.04885	−	2.04885i	0.118687	−	0.118687i
$299$	−0.445057	+	0.184348i	−0.0257383	+	0.0106611i
$300$		0			0
$301$	−14.9585	−	6.19602i	−0.862195	−	0.357133i
$302$	0.0342954			0.00197348
$303$		0			0
$304$	9.78495	−	9.78495i	0.561205	−	0.561205i
$305$	6.36987	+	14.1701i	0.364738	+	0.811376i
$306$		0			0
$307$			14.9905i			0.855551i	0.903885	+	0.427775i	$0.140703\pi$
$307$			14.9905i			0.855551i	−0.903885	+	0.427775i	$0.859297\pi$
$308$	5.28261	+	5.28261i	0.301005	+	0.301005i
$309$		0			0
$310$	0.112361	+	0.249952i	0.00638167	+	0.0141963i
$311$	−9.26536	−	3.83784i	−0.525390	−	0.217624i	0.104193	−	0.994557i	$-0.466774\pi$
$311$	−9.26536	−	3.83784i	−0.525390	−	0.217624i	−0.629583	+	0.776933i	$0.716774\pi$
$312$		0			0
$313$	−1.35503	−	3.27134i	−0.0765910	−	0.184907i	0.880946	−	0.473216i	$-0.156907\pi$
$313$	−1.35503	−	3.27134i	−0.0765910	−	0.184907i	−0.957537	+	0.288309i	$0.906907\pi$
$314$	−1.70114	−	1.70114i	−0.0960007	−	0.0960007i
$315$		0			0
$316$	−23.1149	+	9.57451i	−1.30032	+	0.538608i
$317$	11.2813	−	4.67288i	0.633623	−	0.262455i	−0.0426686	−	0.999089i	$-0.513586\pi$
$317$	11.2813	−	4.67288i	0.633623	−	0.262455i	0.676292	+	0.736634i	$0.263586\pi$
$318$		0			0
$319$			17.3302i			0.970307i
$320$	14.6422	−	0.435940i	0.818525	−	0.0243698i
$321$		0			0
$322$		−	0.982469i		−	0.0547508i
$323$	−15.3897	−	3.14995i	−0.856308	−	0.175268i
$324$		0			0
$325$	0.871775	−	0.0519564i	0.0483574	−	0.00288203i
$326$	−1.18261	+	2.85508i	−0.0654988	+	0.158128i
$327$		0			0
$328$	−2.24942	+	5.43059i	−0.124204	+	0.299854i
$329$	−1.45288	−	3.50755i	−0.0800996	−	0.193378i
$330$		0			0
$331$	−13.0768	−	13.0768i	−0.718764	−	0.718764i	0.249588	−	0.968352i	$-0.419705\pi$
$331$	−13.0768	−	13.0768i	−0.718764	−	0.718764i	−0.968352	+	0.249588i	$0.919705\pi$
$332$	11.7521	−	11.7521i	0.644979	−	0.644979i
$333$		0			0
$334$	−0.398886	−	0.962996i	−0.0218261	−	0.0526928i
$335$	27.6928	−	0.824493i	1.51302	−	0.0450469i
$336$		0			0
$337$	17.0378	+	7.05727i	0.928106	+	0.384434i	0.794960	−	0.606662i	$-0.207492\pi$
$337$	17.0378	+	7.05727i	0.928106	+	0.384434i	0.133146	+	0.991096i	$0.457492\pi$
$338$	−2.28279	−	2.28279i	−0.124167	−	0.124167i
$339$		0			0
$340$	−10.2838	−	14.6118i	−0.557716	−	0.792434i
$341$	1.32622			0.0718189
$342$		0			0
$343$	−15.8023	−	6.54555i	−0.853247	−	0.353426i
$344$		−	11.0903i		−	0.597951i
$345$		0			0
$346$	0.281477	+	0.679547i	0.0151323	+	0.0365327i
$347$	−1.94225	−	4.68901i	−0.104265	−	0.251719i	0.863134	−	0.504975i	$-0.168498\pi$
$347$	−1.94225	−	4.68901i	−0.104265	−	0.251719i	−0.967399	+	0.253256i	$0.918498\pi$
$348$		0			0
$349$	−17.2978	−	17.2978i	−0.925928	−	0.925928i	0.0715119	−	0.997440i	$-0.477218\pi$
$349$	−17.2978	−	17.2978i	−0.925928	−	0.925928i	−0.997440	+	0.0715119i	$0.977218\pi$
$350$	−0.582500	+	1.68318i	−0.0311359	+	0.0899695i
$351$		0			0
$352$	−2.95282	+	7.12875i	−0.157386	+	0.379964i
$353$	17.5325			0.933161			0.466580	−	0.884479i	$-0.345486\pi$
$353$	17.5325			0.933161			0.466580	+	0.884479i	$0.345486\pi$
$354$		0			0
$355$	−25.5579	−	9.70578i	−1.35647	−	0.515130i
$356$	−22.2695			−1.18028
$357$		0			0
$358$			5.79391i			0.306218i
$359$	1.42687	−	1.42687i	0.0753076	−	0.0753076i	−0.668450	−	0.743757i	$-0.733042\pi$
$359$	1.42687	−	1.42687i	0.0753076	−	0.0753076i	0.743757	+	0.668450i	$0.233042\pi$
$360$		0			0
$361$			4.48433i			0.236017i
$362$	−1.08786	+	2.62634i	−0.0571769	+	0.138037i
$363$		0			0
$364$	0.447557	−	0.185384i	0.0234584	−	0.00971677i
$365$	−32.7436	−	12.4346i	−1.71388	−	0.650858i
$366$		0			0
$367$	12.4008	+	29.9381i	0.647315	+	1.56276i	0.816609	+	0.577191i	$0.195851\pi$
$367$	12.4008	+	29.9381i	0.647315	+	1.56276i	−0.169294	+	0.985566i	$0.554149\pi$
$368$	−9.25478	+	3.83345i	−0.482439	+	0.199833i
$369$		0			0
$370$	2.91546	−	1.31059i	0.151568	−	0.0681343i
$371$	−6.76525	+	16.3328i	−0.351234	+	0.847955i
$372$		0			0
$373$		−	20.6108i		−	1.06719i	−0.845741	−	0.533593i	$-0.820841\pi$
$373$		−	20.6108i		−	1.06719i	0.845741	−	0.533593i	$-0.179159\pi$
$374$	2.71433	−	0.524297i	0.140355	−	0.0271107i
$375$		0			0
$376$	1.83884	−	1.83884i	0.0948311	−	0.0948311i
$377$	1.03822	+	0.430044i	0.0534710	+	0.0221484i
$378$		0			0
$379$	15.3385	+	6.35343i	0.787887	+	0.326354i	0.740094	−	0.672504i	$-0.234781\pi$
$379$	15.3385	+	6.35343i	0.787887	+	0.326354i	0.0477935	+	0.998857i	$0.484781\pi$
$380$	11.3222	−	12.0171i	0.580819	−	0.616465i
$381$		0			0
$382$	−0.542471	+	0.542471i	−0.0277552	+	0.0277552i
$383$	16.4274	−	16.4274i	0.839401	−	0.839401i	−0.149379	−	0.988780i	$-0.547727\pi$
$383$	16.4274	−	16.4274i	0.839401	−	0.839401i	0.988780	+	0.149379i	$0.0477274\pi$
$384$		0			0
$385$	6.27365	+	5.91088i	0.319735	+	0.301246i
$386$	3.67622	+	1.52274i	0.187115	+	0.0775055i
$387$		0			0
$388$	−4.11624	−	1.70500i	−0.208971	−	0.0865584i
$389$	−25.9259	+	25.9259i	−1.31450	+	1.31450i	−0.396433	+	0.918064i	$0.629752\pi$
$389$	−25.9259	+	25.9259i	−1.31450	+	1.31450i	−0.918064	+	0.396433i	$0.870248\pi$
$390$		0			0
$391$	9.41996	+	6.36999i	0.476388	+	0.322144i
$392$		−	4.85419i		−	0.245174i
$393$		0			0
$394$	−1.01673	+	2.45461i	−0.0512222	+	0.123661i
$395$	−26.3289	+	11.8356i	−1.32475	+	0.595516i
$396$		0			0
$397$	9.06522	−	3.75494i	0.454970	−	0.188455i	−0.143416	−	0.989662i	$-0.545809\pi$
$397$	9.06522	−	3.75494i	0.454970	−	0.188455i	0.598386	+	0.801208i	$0.295809\pi$
$398$	1.50881	+	3.64259i	0.0756299	+	0.182587i
$399$		0			0
$400$	18.1282	−	1.08041i	0.906411	−	0.0540207i
$401$	−19.8539	+	8.22376i	−0.991457	+	0.410675i	−0.818657	−	0.574282i	$-0.805281\pi$
$401$	−19.8539	+	8.22376i	−0.991457	+	0.410675i	−0.172799	+	0.984957i	$0.555281\pi$
$402$		0			0
$403$	0.0329097	−	0.0794512i	0.00163935	−	0.00395774i
$404$		−	1.72663i		−	0.0859032i
$405$		0			0
$406$	−1.62061	+	1.62061i	−0.0804293	+	0.0804293i
$407$		−	15.4692i		−	0.766779i
$408$		0			0
$409$	−31.2735			−1.54638			−0.773189	−	0.634176i	$-0.781339\pi$
$409$	−31.2735			−1.54638			−0.773189	+	0.634176i	$0.781339\pi$
$410$	−1.18492	+	3.12020i	−0.0585190	+	0.154096i
$411$		0			0
$412$	−0.711526			−0.0350544
$413$	4.43193	−	10.6996i	0.218081	−	0.526494i
$414$		0			0
$415$	13.1498	−	13.9568i	0.645497	−	0.685113i
$416$	0.353795	+	0.353795i	0.0173462	+	0.0173462i
$417$		0			0
$418$	0.977576	+	2.36008i	0.0478148	+	0.115435i
$419$	7.78615	+	18.7974i	0.380378	+	0.918314i	0.991892	+	0.127081i	$0.0405608\pi$
$419$	7.78615	+	18.7974i	0.380378	+	0.918314i	−0.611514	+	0.791234i	$0.709439\pi$
$420$		0			0
$421$			1.80862i			0.0881467i	0.999028	+	0.0440733i	$0.0140335\pi$
$421$			1.80862i			0.0881467i	−0.999028	+	0.0440733i	$0.985966\pi$
$422$	−1.13136	−	0.468626i	−0.0550740	−	0.0228124i
$423$		0			0
$424$	−12.1092			−0.588075
$425$	−12.3616	−	16.4982i	−0.599628	−	0.800279i
$426$		0			0
$427$	7.03079	+	7.03079i	0.340244	+	0.340244i
$428$	−11.9024	−	4.93016i	−0.575327	−	0.238308i
$429$		0			0
$430$	−0.187403	−	6.29444i	−0.00903738	−	0.303545i
$431$	−6.37695	−	15.3953i	−0.307167	−	0.741566i	−0.999795	−	0.0202708i	$-0.993547\pi$
$431$	−6.37695	−	15.3953i	−0.307167	−	0.741566i	0.692628	−	0.721295i	$-0.256453\pi$
$432$		0			0
$433$	−11.5388	+	11.5388i	−0.554519	+	0.554519i	−0.927742	−	0.373222i	$-0.878253\pi$
$433$	−11.5388	+	11.5388i	−0.554519	+	0.554519i	0.373222	+	0.927742i	$0.378253\pi$
$434$	0.124019	+	0.124019i	0.00595311	+	0.00595311i
$435$		0			0
$436$	−6.55588	−	15.8273i	−0.313970	−	0.757990i
$437$	−4.02118	+	9.70800i	−0.192359	+	0.464396i
$438$		0			0
$439$	9.19489	−	22.1984i	0.438848	−	1.05947i	−0.537499	−	0.843264i	$-0.680631\pi$
$439$	9.19489	−	22.1984i	0.438848	−	1.05947i	0.976347	−	0.216209i	$-0.0693692\pi$
$440$	−2.09609	+	5.51955i	−0.0999271	+	0.263134i
$441$		0			0
$442$	0.0359457	−	0.175620i	0.00170976	−	0.00835340i
$443$			21.2757i			1.01084i	0.862874	+	0.505419i	$0.168662\pi$
$443$			21.2757i			1.01084i	−0.862874	+	0.505419i	$0.831338\pi$
$444$		0			0
$445$	−25.6826	+	0.764644i	−1.21747	+	0.0362476i
$446$		−	2.50011i		−	0.118384i
$447$		0			0
$448$	8.66156	−	3.58773i	0.409220	−	0.169504i
$449$	−26.9783	+	11.1748i	−1.27318	+	0.527370i	−0.913931	−	0.405870i	$-0.866969\pi$
$449$	−26.9783	+	11.1748i	−1.27318	+	0.527370i	−0.359253	+	0.933240i	$0.616969\pi$
$450$		0			0
$451$	11.4213	+	11.4213i	0.537807	+	0.537807i
$452$	−4.23718	−	10.2295i	−0.199300	−	0.481153i
$453$		0			0
$454$	−1.02966	−	0.426500i	−0.0483244	−	0.0200166i
$455$	0.509787	−	0.229165i	0.0238992	−	0.0107434i
$456$		0			0
$457$	−0.734055	−	0.734055i	−0.0343376	−	0.0343376i	0.689729	−	0.724067i	$-0.257729\pi$
$457$	−0.734055	−	0.734055i	−0.0343376	−	0.0343376i	−0.724067	+	0.689729i	$0.757729\pi$
$458$		−	0.298195i		−	0.0139337i
$459$		0			0
$460$	−10.9013	+	4.90045i	−0.508274	+	0.228485i
$461$	−0.0496372	+	0.0496372i	−0.00231183	+	0.00231183i	−0.708262	−	0.705950i	$-0.750520\pi$
$461$	−0.0496372	+	0.0496372i	−0.00231183	+	0.00231183i	0.705950	+	0.708262i	$0.250520\pi$
$462$		0			0
$463$	−40.0649			−1.86197			−0.930987	−	0.365051i	$-0.881051\pi$
$463$	−40.0649			−1.86197			−0.930987	+	0.365051i	$0.881051\pi$
$464$	21.5894	+	8.94260i	1.00226	+	0.415150i
$465$		0			0
$466$	5.85376	−	2.42471i	0.271170	−	0.112322i
$467$	16.0563	−	16.0563i	0.742997	−	0.742997i	−0.230156	−	0.973154i	$-0.573924\pi$
$467$	16.0563	−	16.0563i	0.742997	−	0.742997i	0.973154	+	0.230156i	$0.0739238\pi$
$468$		0			0
$469$	16.3816	−	6.78547i	0.756431	−	0.313324i
$470$	1.01258	−	1.07473i	0.0467070	−	0.0495735i
$471$		0			0
$472$	7.93276			0.365135
$473$	−28.1552	−	11.6622i	−1.29458	−	0.536231i
$474$		0			0
$475$	12.6449	−	14.2477i	0.580190	−	0.653730i
$476$	−9.47288	−	6.40578i	−0.434189	−	0.293608i
$477$		0			0
$478$	−1.09375	−	1.09375i	−0.0500270	−	0.0500270i
$479$	8.90144	−	21.4900i	0.406717	−	0.981902i	−0.579278	−	0.815130i	$-0.696665\pi$
$479$	8.90144	−	21.4900i	0.406717	−	0.981902i	0.985995	−	0.166772i	$-0.0533345\pi$
$480$		0			0
$481$	−0.926726	−	0.383863i	−0.0422551	−	0.0175026i
$482$	6.16422	−	2.55331i	0.280773	−	0.116300i
$483$		0			0
$484$	−5.13139	−	5.13139i	−0.233245	−	0.233245i
$485$	−4.80567	−	1.82499i	−0.218214	−	0.0828685i
$486$		0			0
$487$	15.6248	−	6.47199i	0.708026	−	0.293274i	0.000538564	−	1.00000i	$-0.499829\pi$
$487$	15.6248	−	6.47199i	0.708026	−	0.293274i	0.707488	+	0.706726i	$0.249829\pi$
$488$	−2.60633	+	6.29224i	−0.117983	+	0.284837i
$489$		0			0
$490$	−0.0820256	−	2.75505i	−0.00370554	−	0.124460i
$491$	14.8915	−	14.8915i	0.672045	−	0.672045i	−0.286142	−	0.958187i	$-0.592373\pi$
$491$	14.8915	−	14.8915i	0.672045	−	0.672045i	0.958187	+	0.286142i	$0.0923729\pi$
$492$		0			0
$493$	−5.03100	−	26.0459i	−0.226585	−	1.17305i
$494$	0.165646			0.00745275
$495$		0			0
$496$	0.684345	−	1.65216i	0.0307280	−	0.0741840i
$497$	−17.4968			−0.784840
$498$		0			0
$499$	8.62028	+	20.8112i	0.385897	+	0.931637i	0.990800	+	0.135338i	$0.0432120\pi$
$499$	8.62028	+	20.8112i	0.385897	+	0.931637i	−0.604903	+	0.796299i	$0.706788\pi$
$500$	21.5816	−	1.93221i	0.965159	−	0.0864109i
$501$		0			0
$502$	−1.86664	+	1.86664i	−0.0833122	+	0.0833122i
$503$	11.1063	+	26.8129i	0.495204	+	1.19553i	0.952039	+	0.305977i	$0.0989829\pi$
$503$	11.1063	+	26.8129i	0.495204	+	1.19553i	−0.456835	+	0.889551i	$0.651017\pi$
$504$		0			0
$505$	−0.0592857	−	1.99127i	−0.00263818	−	0.0886103i
$506$		−	1.84922i		−	0.0822077i
$507$		0			0
$508$	22.4017	+	22.4017i	0.993915	+	0.993915i
$509$	4.38401			0.194318			0.0971589	−	0.995269i	$-0.469024\pi$
$509$	4.38401			0.194318			0.0971589	+	0.995269i	$0.469024\pi$
$510$		0			0
$511$	−22.4162			−0.991633
$512$	12.3921	+	12.3921i	0.547660	+	0.547660i
$513$		0			0
$514$		−	0.383393i		−	0.0169107i
$515$	−0.820579	+	0.0244310i	−0.0361590	+	0.00107656i
$516$		0			0
$517$	−2.73462	−	6.60196i	−0.120269	−	0.290354i
$518$	1.44657	−	1.44657i	0.0635587	−	0.0635587i
$519$		0			0
$520$	0.278651	+	0.262538i	0.0122197	+	0.0115131i
$521$	1.22242	+	2.95118i	0.0535551	+	0.129294i	0.948393	−	0.317099i	$-0.102709\pi$
$521$	1.22242	+	2.95118i	0.0535551	+	0.129294i	−0.894837	+	0.446392i	$0.852709\pi$
$522$		0			0
$523$	34.0520			1.48899			0.744494	−	0.667629i	$-0.232691\pi$
$523$	34.0520			1.48899			0.744494	+	0.667629i	$0.232691\pi$
$524$	7.14875	−	17.2586i	0.312294	−	0.753945i
$525$		0			0
$526$	0.106148			0.00462825
$527$	−1.99320	+	0.385004i	−0.0868251	+	0.0167710i
$528$		0			0
$529$	−10.8848	+	10.8848i	−0.473251	+	0.473251i
$530$	−6.87271	+	0.204620i	−0.298531	+	0.00888812i
$531$		0			0
$532$	4.04377	−	9.76254i	0.175320	−	0.423260i
$533$	0.967641	−	0.400810i	0.0419132	−	0.0173610i
$534$		0			0
$535$	−13.8960	−	5.27710i	−0.600776	−	0.228149i
$536$	8.58809	+	8.58809i	0.370949	+	0.370949i
$537$		0			0
$538$	3.93359	−	1.62934i	0.169589	−	0.0702460i
$539$	−12.3234	−	5.10452i	−0.530806	−	0.219867i
$540$		0			0
$541$	−10.3587	+	25.0081i	−0.445355	+	1.07518i	0.528687	+	0.848817i	$0.322685\pi$
$541$	−10.3587	+	25.0081i	−0.445355	+	1.07518i	−0.974042	+	0.226366i	$0.927315\pi$
$542$	2.82859	+	2.82859i	0.121498	+	0.121498i
$543$		0			0
$544$	2.36836	−	11.5711i	0.101543	−	0.496108i
$545$	−8.10412	−	18.0280i	−0.347143	−	0.772234i
$546$		0			0
$547$	12.5020	+	5.17849i	0.534546	+	0.221416i	0.633593	−	0.773667i	$-0.281579\pi$
$547$	12.5020	+	5.17849i	0.534546	+	0.221416i	−0.0990470	+	0.995083i	$0.531579\pi$
$548$	12.8012			0.546841
$549$		0			0
$550$	−1.09639	+	3.16810i	−0.0467502	+	0.135088i
$551$	22.6466	−	9.38053i	0.964778	−	0.399624i
$552$		0			0
$553$	−13.0637	+	13.0637i	−0.555524	+	0.555524i
$554$	3.85494	−	1.59677i	0.163781	−	0.0678402i
$555$		0			0
$556$	8.23114	+	3.40945i	0.349078	+	0.144593i
$557$	30.5182			1.29310			0.646548	−	0.762873i	$-0.276212\pi$
$557$	30.5182			1.29310			0.646548	+	0.762873i	$0.276212\pi$
$558$		0			0
$559$	−1.39732	+	1.39732i	−0.0591005	+	0.0591005i
$560$	10.6008	−	4.76539i	0.447967	−	0.201375i
$561$		0			0
$562$		−	1.95111i		−	0.0823024i
$563$	5.73355	+	5.73355i	0.241640	+	0.241640i	0.817529	−	0.575888i	$-0.195344\pi$
$563$	5.73355	+	5.73355i	0.241640	+	0.241640i	−0.575888	+	0.817529i	$0.695344\pi$
$564$		0			0
$565$	−5.23784	−	11.6518i	−0.220358	−	0.490196i
$566$	1.51333	+	0.626842i	0.0636101	+	0.0263481i
$567$		0			0
$568$	−4.58638	−	11.0725i	−0.192440	−	0.464592i
$569$	2.71124	+	2.71124i	0.113661	+	0.113661i	0.761650	−	0.647989i	$-0.224390\pi$
$569$	2.71124	+	2.71124i	0.113661	+	0.113661i	−0.647989	+	0.761650i	$0.724390\pi$
$570$		0			0
$571$	6.06730	−	2.51316i	0.253909	−	0.105172i	−0.252099	−	0.967701i	$-0.581121\pi$
$571$	6.06730	−	2.51316i	0.253909	−	0.105172i	0.506007	+	0.862529i	$0.331121\pi$
$572$	0.842398	−	0.348933i	0.0352224	−	0.0145896i
$573$		0			0
$574$			2.13608i			0.0891583i
$575$	−12.4038	+	6.02583i	−0.517275	+	0.251295i
$576$		0			0
$577$			23.2880i			0.969493i	0.874655	+	0.484746i	$0.161088\pi$
$577$			23.2880i			0.969493i	−0.874655	+	0.484746i	$0.838912\pi$
$578$	−3.92720	+	1.57595i	−0.163350	+	0.0655508i
$579$		0			0
$580$	26.0653	+	9.89850i	1.08230	+	0.411013i
$581$	4.69649	−	11.3383i	0.194843	−	0.470393i
$582$		0			0
$583$	−12.7337	+	30.7418i	−0.527374	+	1.27319i
$584$	−5.87587	−	14.1856i	−0.243145	−	0.587004i
$585$		0			0
$586$	−0.554640	−	0.554640i	−0.0229120	−	0.0229120i
$587$	−26.0085	+	26.0085i	−1.07348	+	1.07348i	−0.0764077	+	0.997077i	$0.524345\pi$
$587$	−26.0085	+	26.0085i	−1.07348	+	1.07348i	−0.997077	+	0.0764077i	$0.975655\pi$
$588$		0			0
$589$	−0.717858	−	1.73306i	−0.0295788	−	0.0714096i
$590$	4.50232	−	0.134047i	0.185358	−	0.00551862i
$591$		0			0
$592$	−19.2709	−	7.98227i	−0.792030	−	0.328069i
$593$	−19.1275	−	19.1275i	−0.785474	−	0.785474i	0.195275	−	0.980749i	$-0.437440\pi$
$593$	−19.1275	−	19.1275i	−0.785474	−	0.785474i	−0.980749	+	0.195275i	$0.937440\pi$
$594$		0			0
$595$	−11.1447	−	7.06231i	−0.456889	−	0.289527i
$596$	−22.5596			−0.924076
$597$		0			0
$598$	−0.110783	−	0.0458877i	−0.00453025	−	0.00187649i
$599$		−	12.2973i		−	0.502456i	−0.967928	−	0.251228i	$-0.919166\pi$
$599$		−	12.2973i		−	0.502456i	0.967928	−	0.251228i	$-0.0808344\pi$
$600$		0			0
$601$	−3.08883	−	7.45710i	−0.125996	−	0.304181i	0.848277	−	0.529553i	$-0.177640\pi$
$601$	−3.08883	−	7.45710i	−0.125996	−	0.304181i	−0.974273	+	0.225372i	$0.927640\pi$
$602$	−1.54230	−	3.72345i	−0.0628596	−	0.151757i
$603$		0			0
$604$	−0.188811	−	0.188811i	−0.00768260	−	0.00768260i
$605$	−6.09406	−	5.74168i	−0.247759	−	0.233432i
$606$		0			0
$607$	9.22388	−	22.2684i	0.374386	−	0.903847i	−0.618610	−	0.785698i	$-0.712304\pi$
$607$	9.22388	−	22.2684i	0.374386	−	0.903847i	0.992996	−	0.118149i	$-0.0376960\pi$
$608$	10.9139			0.442619
$609$		0			0
$610$	−1.37293	+	3.61527i	−0.0555882	+	0.146378i
$611$	−0.463369			−0.0187459
$612$		0			0
$613$			39.8359i			1.60896i	0.593983	+	0.804478i	$0.297555\pi$
$613$			39.8359i			1.60896i	−0.593983	+	0.804478i	$0.702445\pi$
$614$	−2.63850	+	2.63850i	−0.106481	+	0.106481i
$615$		0			0
$616$			3.77867i			0.152247i
$617$	−9.87155	+	23.8320i	−0.397414	+	0.959442i	0.590863	+	0.806772i	$0.298787\pi$
$617$	−9.87155	+	23.8320i	−0.397414	+	0.959442i	−0.988277	+	0.152670i	$0.951213\pi$
$618$		0			0
$619$	−3.48155	+	1.44210i	−0.139935	+	0.0579630i	−0.451552	−	0.892245i	$-0.649129\pi$
$619$	−3.48155	+	1.44210i	−0.139935	+	0.0579630i	0.311617	+	0.950208i	$0.399129\pi$
$620$	0.757496	−	1.99468i	0.0304218	−	0.0801085i
$621$		0			0
$622$	−0.955308	−	2.30632i	−0.0383044	−	0.0924749i
$623$	−15.1925	+	6.29293i	−0.608673	+	0.252121i
$624$		0			0
$625$	24.8230	−	2.96938i	0.992921	−	0.118775i
$626$	0.337293	−	0.814297i	0.0134809	−	0.0325459i
$627$		0			0
$628$			18.7309i			0.747446i
$629$	4.49073	+	23.2489i	0.179057	+	0.926994i
$630$		0			0
$631$	13.6572	−	13.6572i	0.543685	−	0.543685i	−0.380922	−	0.924607i	$-0.624393\pi$
$631$	13.6572	−	13.6572i	0.543685	−	0.543685i	0.924607	+	0.380922i	$0.124393\pi$
$632$	−11.6914	−	4.84274i	−0.465059	−	0.192634i
$633$		0			0
$634$	2.80813	+	1.16317i	0.111525	+	0.0461952i
$635$	26.6043	+	25.0660i	1.05576	+	0.994713i
$636$		0			0
$637$	−0.611602	+	0.611602i	−0.0242326	+	0.0242326i
$638$	−3.05033	+	3.05033i	−0.120764	+	0.120764i
$639$		0			0
$640$	11.9781	+	11.2855i	0.473478	+	0.446099i
$641$	−19.0839	−	7.90483i	−0.753770	−	0.312222i	−0.0274914	−	0.999622i	$-0.508752\pi$
$641$	−19.0839	−	7.90483i	−0.753770	−	0.312222i	−0.726279	+	0.687400i	$0.758752\pi$
$642$		0			0
$643$	−26.8106	−	11.1053i	−1.05731	−	0.437951i	−0.214813	−	0.976655i	$-0.568914\pi$
$643$	−26.8106	−	11.1053i	−1.05731	−	0.437951i	−0.842495	+	0.538704i	$0.818914\pi$
$644$	−5.40890	+	5.40890i	−0.213141	+	0.213141i
$645$		0			0
$646$	−2.15435	−	3.26321i	−0.0847618	−	0.128389i
$647$			41.2848i			1.62307i	0.584302	+	0.811536i	$0.301368\pi$
$647$			41.2848i			1.62307i	−0.584302	+	0.811536i	$0.698632\pi$
$648$		0			0
$649$	8.34184	−	20.1390i	0.327446	−	0.790524i
$650$	0.162588	+	0.144298i	0.00637721	+	0.00565983i
$651$		0			0
$652$	22.2292	−	9.20763i	0.870562	−	0.360598i
$653$	9.39804	+	22.6889i	0.367774	+	0.887884i	0.994114	+	0.108335i	$0.0345519\pi$
$653$	9.39804	+	22.6889i	0.367774	+	0.887884i	−0.626341	+	0.779549i	$0.715448\pi$
$654$		0			0
$655$	7.65182	−	20.1492i	0.298981	−	0.787296i
$656$	20.1217	−	8.33468i	0.785621	−	0.325415i
$657$		0			0
$658$	0.361647	−	0.873094i	0.0140985	−	0.0340368i
$659$			17.7024i			0.689588i	0.938678	+	0.344794i	$0.112051\pi$
$659$			17.7024i			0.689588i	−0.938678	+	0.344794i	$0.887949\pi$
$660$		0			0
$661$	10.0305	−	10.0305i	0.390141	−	0.390141i	−0.484597	−	0.874738i	$-0.661034\pi$
$661$	10.0305	−	10.0305i	0.390141	−	0.390141i	0.874738	+	0.484597i	$0.161034\pi$
$662$		−	4.60333i		−	0.178914i
$663$		0			0
$664$	8.40629			0.326227
$665$	4.32835	−	11.3977i	0.167846	−	0.441982i
$666$		0			0
$667$	−17.7445			−0.687072
$668$	−3.10566	+	7.49773i	−0.120162	+	0.290096i
$669$		0			0
$670$	5.01938	+	4.72914i	0.193916	+	0.182703i
$671$	13.2335	+	13.2335i	0.510872	+	0.510872i
$672$		0			0
$673$	−0.124393	−	0.300312i	−0.00479501	−	0.0115762i	0.921464	−	0.388464i	$-0.126994\pi$
$673$	−0.124393	−	0.300312i	−0.00479501	−	0.0115762i	−0.926259	+	0.376888i	$0.876994\pi$
$674$	1.75668	+	4.24101i	0.0676650	+	0.163358i
$675$		0			0
$676$			25.1354i			0.966746i
$677$	15.9805	+	6.61933i	0.614180	+	0.254402i	0.668014	−	0.744148i	$-0.267144\pi$
$677$	15.9805	+	6.61933i	0.614180	+	0.254402i	−0.0538347	+	0.998550i	$0.517144\pi$
$678$		0			0
$679$	−3.28995			−0.126257
$680$	1.54791	−	8.90392i	0.0593597	−	0.341450i
$681$		0			0
$682$	0.233431	+	0.233431i	0.00893852	+	0.00893852i
$683$	−31.8570	−	13.1956i	−1.21898	−	0.504916i	−0.321891	−	0.946777i	$-0.604319\pi$
$683$	−31.8570	−	13.1956i	−1.21898	−	0.504916i	−0.897084	+	0.441860i	$0.854319\pi$
$684$		0			0
$685$	14.7632	−	0.439543i	0.564074	−	0.0167941i
$686$	−1.62931	−	3.93350i	−0.0622072	−	0.150182i
$687$		0			0
$688$	−29.0568	+	29.0568i	−1.10778	+	1.10778i
$689$	1.52569	+	1.52569i	0.0581243	+	0.0581243i
$690$		0			0
$691$	16.1221	+	38.9223i	0.613315	+	1.48067i	0.859337	+	0.511409i	$0.170876\pi$
$691$	16.1221	+	38.9223i	0.613315	+	1.48067i	−0.246022	+	0.969264i	$0.579124\pi$
$692$	2.19154	−	5.29084i	0.0833098	−	0.201128i
$693$		0			0
$694$	0.483462	−	1.16718i	0.0183520	−	0.0443056i
$695$	9.60978	+	3.64938i	0.364520	+	0.138429i
$696$		0			0
$697$	−20.4808	−	13.8496i	−0.775767	−	0.524591i
$698$		−	6.08922i		−	0.230481i
$699$		0			0
$700$	12.4735	−	6.05969i	0.471454	−	0.229035i
$701$			29.6266i			1.11898i	0.828836	+	0.559491i	$0.189003\pi$
$701$			29.6266i			1.11898i	−0.828836	+	0.559491i	$0.810997\pi$
$702$		0			0
$703$	−20.2146	+	8.37317i	−0.762409	+	0.315800i
$704$	16.3029	−	6.75289i	0.614439	−	0.254509i
$705$		0			0
$706$	3.08593	+	3.08593i	0.116140	+	0.116140i
$707$	−0.487914	−	1.17793i	−0.0183499	−	0.0443005i
$708$		0			0
$709$	15.0352	+	6.22777i	0.564657	+	0.233889i	0.646706	−	0.762740i	$-0.276146\pi$
$709$	15.0352	+	6.22777i	0.564657	+	0.233889i	−0.0820483	+	0.996628i	$0.526146\pi$
$710$	−2.79015	−	6.20682i	−0.104713	−	0.232938i
$711$		0			0
$712$	−7.96469	−	7.96469i	−0.298489	−	0.298489i
$713$			1.35793i			0.0508547i
$714$		0			0
$715$	0.959530	−	0.431337i	0.0358844	−	0.0161311i
$716$	31.8979	−	31.8979i	1.19208	−	1.19208i
$717$		0			0
$718$	0.502294			0.0187454
$719$	29.0292	+	12.0243i	1.08261	+	0.448430i	0.851423	−	0.524480i	$-0.175740\pi$
$719$	29.0292	+	12.0243i	1.08261	+	0.448430i	0.231184	+	0.972910i	$0.425740\pi$
$720$		0			0
$721$	−0.485411	+	0.201064i	−0.0180776	+	0.00748800i
$722$	−0.789295	+	0.789295i	−0.0293745	+	0.0293745i
$723$		0			0
$724$	20.4483	−	8.46994i	0.759953	−	0.314783i
$725$	30.4002	+	10.5206i	1.12903	+	0.390727i
$726$		0			0
$727$	21.6544			0.803118			0.401559	−	0.915833i	$-0.368468\pi$
$727$	21.6544			0.803118			0.401559	+	0.915833i	$0.368468\pi$
$728$	0.226372	+	0.0937664i	0.00838991	+	0.00347521i
$729$		0			0
$730$	−3.57462	−	7.95190i	−0.132303	−	0.294313i
$731$	45.7004	+	9.35389i	1.69029	+	0.345966i
$732$		0			0
$733$	22.2422	+	22.2422i	0.821534	+	0.821534i	0.986328	−	0.164794i	$-0.0526959\pi$
$733$	22.2422	+	22.2422i	0.821534	+	0.821534i	−0.164794	+	0.986328i	$0.552696\pi$
$734$	−3.08678	+	7.45215i	−0.113935	+	0.275064i
$735$		0			0
$736$	−7.29917	−	3.02342i	−0.269051	−	0.111445i
$737$	30.8337	−	12.7717i	1.13577	−	0.470452i
$738$		0			0
$739$	−9.68961	−	9.68961i	−0.356438	−	0.356438i	0.506060	−	0.862498i	$-0.331101\pi$
$739$	−9.68961	−	9.68961i	−0.356438	−	0.356438i	−0.862498	+	0.506060i	$0.831101\pi$
$740$	−23.2662	−	8.83552i	−0.855283	−	0.324800i
$741$		0			0
$742$	−4.06552	+	1.68400i	−0.149250	+	0.0618214i
$743$	−6.20770	+	14.9867i	−0.227738	+	0.549809i	−0.995901	−	0.0904453i	$-0.971171\pi$
$743$	−6.20770	+	14.9867i	−0.227738	+	0.549809i	0.768163	+	0.640254i	$0.221171\pi$
$744$		0			0
$745$	−26.0172	+	0.774605i	−0.953197	+	0.0283793i
$746$	3.62775	−	3.62775i	0.132821	−	0.132821i
$747$		0			0
$748$	−17.8300	−	12.0570i	−0.651929	−	0.440849i
$749$	−9.51315			−0.347603
$750$		0			0
$751$	−4.26568	+	10.2983i	−0.155657	+	0.375789i	−0.982400	−	0.186791i	$-0.940191\pi$
$751$	−4.26568	+	10.2983i	−0.155657	+	0.375789i	0.826743	+	0.562580i	$0.190191\pi$
$752$	−9.63558			−0.351373
$753$		0			0
$754$	0.107046	+	0.258432i	0.00389838	+	0.00941153i
$755$	−0.224232	−	0.211266i	−0.00816064	−	0.00768876i
$756$		0			0
$757$	14.0667	−	14.0667i	0.511262	−	0.511262i	−0.403651	−	0.914913i	$-0.632259\pi$
$757$	14.0667	−	14.0667i	0.511262	−	0.511262i	0.914913	+	0.403651i	$0.132259\pi$
$758$	1.58149	+	3.81804i	0.0574421	+	0.138678i
$759$		0			0
$760$	8.34734	−	0.248524i	0.302790	−	0.00901491i
$761$			45.4255i			1.64667i	0.567553	+	0.823337i	$0.307890\pi$
$761$			45.4255i			1.64667i	−0.567553	+	0.823337i	$0.692110\pi$
$762$		0			0
$763$	−8.94498	−	8.94498i	−0.323830	−	0.323830i
$764$	5.97306			0.216098
$765$		0			0
$766$	5.78284			0.208942
$767$	−0.999485	−	0.999485i	−0.0360893	−	0.0360893i
$768$		0			0
$769$		−	5.98158i		−	0.215701i	−0.994167	−	0.107851i	$-0.965603\pi$
$769$		−	5.98158i		−	0.215701i	0.994167	−	0.107851i	$-0.0343968\pi$
$770$	0.0638515	+	2.14462i	0.00230105	+	0.0772868i
$771$		0			0
$772$	−11.8558	−	28.6225i	−0.426701	−	1.03015i
$773$	−9.29889	+	9.29889i	−0.334458	+	0.334458i	−0.854277	−	0.519819i	$-0.825999\pi$
$773$	−9.29889	+	9.29889i	−0.334458	+	0.334458i	0.519819	+	0.854277i	$0.325999\pi$
$774$		0			0
$775$	0.805106	−	2.32641i	0.0289203	−	0.0835673i
$776$	−0.862382	−	2.08197i	−0.0309577	−	0.0747385i
$777$		0			0
$778$	−9.12654			−0.327202
$779$	8.74284	−	21.1071i	0.313245	−	0.756240i
$780$		0			0
$781$	−32.9328			−1.17843
$782$	0.536831	+	2.77922i	0.0191970	+	0.0993847i
$783$		0			0
$784$	−12.7180	+	12.7180i	−0.454215	+	0.454215i
$785$	0.643146	+	21.6018i	0.0229549	+	0.771001i
$786$		0			0
$787$	9.83375	−	23.7408i	0.350535	−	0.846267i	−0.646019	−	0.763322i	$-0.723567\pi$
$787$	9.83375	−	23.7408i	0.350535	−	0.846267i	0.996554	−	0.0829458i	$-0.0264328\pi$
$788$	19.1112	−	7.91611i	0.680808	−	0.282000i
$789$		0			0
$790$	−6.71742	−	2.55099i	−0.238995	−	0.0907601i
$791$	−5.78130	−	5.78130i	−0.205560	−	0.205560i
$792$		0			0
$793$	1.12117	−	0.464405i	0.0398140	−	0.0164915i
$794$	2.25650	+	0.934673i	0.0800802	+	0.0331703i
$795$		0			0
$796$	11.7474	−	28.3607i	0.416375	−	1.00522i
$797$	−35.6691	−	35.6691i	−1.26347	−	1.26347i	−0.949402	−	0.314064i	$-0.898309\pi$
$797$	−35.6691	−	35.6691i	−1.26347	−	1.26347i	−0.314064	−	0.949402i	$-0.601691\pi$
$798$		0			0
$799$	6.02647	+	9.12834i	0.213201	+	0.322937i
$800$	10.7125	+	9.50739i	0.378743	+	0.336137i
$801$		0			0
$802$	−4.94200	−	2.04704i	−0.174508	−	0.0722836i
$803$	−42.1920			−1.48892
$804$		0			0
$805$	−6.05219	+	6.42363i	−0.213312	+	0.226403i
$806$	0.0197769	−	0.00819184i	0.000696610	−	0.000288545i
$807$		0			0
$808$	0.617532	−	0.617532i	0.0217247	−	0.0217247i
$809$	8.50125	−	3.52133i	0.298888	−	0.123803i	−0.228200	−	0.973614i	$-0.573284\pi$
$809$	8.50125	−	3.52133i	0.298888	−	0.123803i	0.527088	+	0.849811i	$0.323284\pi$
$810$		0			0
$811$	9.89831	+	4.10002i	0.347577	+	0.143971i	0.549640	−	0.835401i	$-0.314765\pi$
$811$	9.89831	+	4.10002i	0.347577	+	0.143971i	−0.202064	+	0.979372i	$0.564765\pi$
$812$	17.8442			0.626210
$813$		0			0
$814$	2.72276	−	2.72276i	0.0954327	−	0.0954327i
$815$	25.3200	−	11.3821i	0.886922	−	0.398698i
$816$		0			0
$817$			43.1048i			1.50805i
$818$	−5.50452	−	5.50452i	−0.192461	−	0.192461i
$819$		0			0
$820$	23.7015	−	10.6545i	0.827692	−	0.372073i
$821$	−26.0334	−	10.7834i	−0.908572	−	0.376343i	−0.121062	−	0.992645i	$-0.538630\pi$
$821$	−26.0334	−	10.7834i	−0.908572	−	0.376343i	−0.787510	+	0.616302i	$0.788630\pi$
$822$		0			0
$823$	13.5250	+	32.6522i	0.471452	+	1.13819i	0.963522	+	0.267630i	$0.0862404\pi$
$823$	13.5250	+	32.6522i	0.471452	+	1.13819i	−0.492070	+	0.870556i	$0.663760\pi$
$824$	−0.254478	−	0.254478i	−0.00886516	−	0.00886516i
$825$		0			0
$826$	2.66333	−	1.10319i	0.0926692	−	0.0383848i
$827$	36.2562	−	15.0178i	1.26075	−	0.522221i	0.350612	−	0.936521i	$-0.385974\pi$
$827$	36.2562	−	15.0178i	1.26075	−	0.522221i	0.910140	+	0.414300i	$0.135974\pi$
$828$		0			0
$829$			17.4130i			0.604779i	0.953184	+	0.302389i	$0.0977843\pi$
$829$			17.4130i			0.604779i	−0.953184	+	0.302389i	$0.902216\pi$
$830$	4.77108	−	0.142049i	0.165607	−	0.00493058i
$831$		0			0
$832$		−	1.14424i		−	0.0396695i
$833$	20.0029	+	4.09416i	0.693059	+	0.141854i
$834$		0			0
$835$	−3.32422	+	8.75353i	−0.115039	+	0.302928i
$836$	7.61125	−	18.3752i	0.263241	−	0.635519i
$837$		0			0
$838$	−1.93812	+	4.67903i	−0.0669511	+	0.161634i
$839$	10.2960	+	24.8566i	0.355456	+	0.858147i	0.995927	+	0.0901643i	$0.0287392\pi$
$839$	10.2960	+	24.8566i	0.355456	+	0.858147i	−0.640471	+	0.767982i	$0.721261\pi$
$840$		0			0
$841$	8.76397	+	8.76397i	0.302206	+	0.302206i
$842$	−0.318338	+	0.318338i	−0.0109707	+	0.0109707i
$843$		0			0
$844$	3.64865	+	8.80862i	0.125592	+	0.303205i
$845$	0.863049	+	28.9878i	0.0296898	+	0.997211i
$846$		0			0
$847$	−4.95073	−	2.05066i	−0.170109	−	0.0704615i
$848$	31.7262	+	31.7262i	1.08948	+	1.08948i
$849$		0			0
$850$	0.728077	−	5.07967i	0.0249728	−	0.174231i
$851$	15.8390			0.542954
$852$		0			0
$853$	−15.1019	−	6.25540i	−0.517078	−	0.214181i	0.108855	−	0.994058i	$-0.465282\pi$
$853$	−15.1019	−	6.25540i	−0.517078	−	0.214181i	−0.625933	+	0.779877i	$0.715282\pi$
$854$			2.47501i			0.0846930i
$855$		0			0
$856$	−2.49365	−	6.02020i	−0.0852311	−	0.205766i
$857$	−1.47991	−	3.57282i	−0.0505527	−	0.122045i	0.896586	−	0.442870i	$-0.146040\pi$
$857$	−1.47991	−	3.57282i	−0.0505527	−	0.122045i	−0.947138	+	0.320825i	$0.896040\pi$
$858$		0			0
$859$	27.6000	+	27.6000i	0.941701	+	0.941701i	0.998392	−	0.0566905i	$-0.0180548\pi$
$859$	27.6000	+	27.6000i	0.941701	+	0.941701i	−0.0566905	+	0.998392i	$0.518055\pi$
$860$	−33.6218	+	35.6853i	−1.14649	+	1.21686i
$861$		0			0
$862$	1.58734	−	3.83218i	0.0540650	−	0.130524i
$863$	−22.1279			−0.753243			−0.376621	−	0.926367i	$-0.622914\pi$
$863$	−22.1279			−0.753243			−0.376621	+	0.926367i	$0.622914\pi$
$864$		0			0
$865$	2.34576	−	6.17700i	0.0797583	−	0.210024i
$866$	−4.06193			−0.138030
$867$		0			0
$868$		−	1.36556i		−	0.0463500i
$869$	−24.5886	+	24.5886i	−0.834112	+	0.834112i
$870$		0			0
$871$		−	2.16411i		−	0.0733280i
$872$	3.31593	−	8.00536i	0.112292	−	0.271096i
$873$		0			0
$874$	−2.41650	+	1.00095i	−0.0817393	+	0.0338575i
$875$	14.1772	−	7.41673i	0.479277	−	0.250731i
$876$		0			0
$877$	7.55317	+	18.2350i	0.255052	+	0.615751i	0.998598	−	0.0529342i	$-0.0168574\pi$
$877$	7.55317	+	18.2350i	0.255052	+	0.615751i	−0.743546	+	0.668685i	$0.766857\pi$
$878$	5.52560	−	2.28878i	0.186480	−	0.0772425i
$879$		0			0
$880$	19.9530	−	8.96949i	0.672617	−	0.302362i
$881$	−4.37489	+	10.5619i	−0.147394	+	0.355840i	−0.980283	−	0.197600i	$-0.936685\pi$
$881$	−4.37489	+	10.5619i	−0.147394	+	0.355840i	0.832889	+	0.553440i	$0.186685\pi$
$882$		0			0
$883$			13.2658i			0.446431i	0.974769	+	0.223216i	$0.0716554\pi$
$883$			13.2658i			0.446431i	−0.974769	+	0.223216i	$0.928345\pi$
$884$	−1.16476	+	0.768967i	−0.0391751	+	0.0258631i
$885$		0			0
$886$	−3.74477	+	3.74477i	−0.125808	+	0.125808i
$887$	−28.2772	−	11.7128i	−0.949455	−	0.393277i	−0.146429	−	0.989221i	$-0.546778\pi$
$887$	−28.2772	−	11.7128i	−0.949455	−	0.393277i	−0.803026	+	0.595944i	$0.796778\pi$
$888$		0			0
$889$	21.6130	+	8.95239i	0.724876	+	0.300254i
$890$	−4.65504	−	4.38586i	−0.156037	−	0.147014i
$891$		0			0
$892$	−13.7642	+	13.7642i	−0.460858	+	0.460858i
$893$	−7.14704	+	7.14704i	−0.239167	+	0.239167i
$894$		0			0
$895$	35.6916	−	37.8821i	1.19304	−	1.26626i
$896$	9.73087	+	4.03066i	0.325086	+	0.134655i
$897$		0			0
$898$	−6.71539	−	2.78161i	−0.224096	−	0.0928234i
$899$	2.23993	−	2.23993i	0.0747059	−	0.0747059i
$900$		0			0
$901$	10.2132	−	49.8989i	0.340252	−	1.66237i
$902$			4.02056i			0.133870i
$903$		0			0
$904$	2.14315	−	5.17401i	0.0712799	−	0.172085i
$905$	23.2915	−	10.4702i	0.774235	−	0.348042i
$906$		0			0
$907$	0.707707	−	0.293142i	0.0234990	−	0.00973362i	−0.370903	−	0.928672i	$-0.620952\pi$
$907$	0.707707	−	0.293142i	0.0234990	−	0.00973362i	0.394402	+	0.918938i	$0.370952\pi$
$908$	3.32066	+	8.01678i	0.110200	+	0.266046i
$909$		0			0
$910$	0.130064	+	0.0493929i	0.00431159	+	0.00163736i
$911$	−7.79323	+	3.22806i	−0.258201	+	0.106951i	−0.508029	−	0.861340i	$-0.669626\pi$
$911$	−7.79323	+	3.22806i	−0.258201	+	0.106951i	0.249828	+	0.968290i	$0.419626\pi$
$912$		0			0
$913$	8.83979	−	21.3412i	0.292555	−	0.706289i
$914$		−	0.258405i		−	0.00854727i
$915$		0			0
$916$	−1.64169	+	1.64169i	−0.0542430	+	0.0542430i
$917$		−	13.7941i		−	0.455522i
$918$		0			0
$919$	−13.0143			−0.429302			−0.214651	−	0.976691i	$-0.568861\pi$
$919$	−13.0143			−0.429302			−0.214651	+	0.976691i	$0.568861\pi$
$920$	−5.65150	−	2.14620i	−0.186324	−	0.0707581i
$921$		0			0
$922$	−0.0174735			−0.000575458
$923$	−0.817217	+	1.97294i	−0.0268990	+	0.0649400i
$924$		0			0
$925$	−27.1355	−	9.39084i	−0.892211	−	0.308769i
$926$	−7.05190	−	7.05190i	−0.231740	−	0.231740i
$927$		0			0
$928$	7.05297	+	17.0274i	0.231525	+	0.558951i
$929$	−9.89198	−	23.8814i	−0.324545	−	0.783522i	−0.998979	−	0.0451859i	$-0.985612\pi$
$929$	−9.89198	−	23.8814i	−0.324545	−	0.783522i	0.674433	−	0.738336i	$-0.264388\pi$
$930$		0			0
$931$			18.8668i			0.618335i
$932$	−45.5764	−	18.8784i	−1.49291	−	0.618382i
$933$		0			0
$934$	5.65220			0.184946
$935$	−20.9767	−	13.2928i	−0.686013	−	0.434721i
$936$		0			0
$937$	−0.615699	−	0.615699i	−0.0201140	−	0.0201140i	0.696978	−	0.717092i	$-0.254527\pi$
$937$	−0.615699	−	0.615699i	−0.0201140	−	0.0201140i	−0.717092	+	0.696978i	$0.754527\pi$
$938$	4.07768	+	1.68903i	0.133141	+	0.0551488i
$939$		0			0
$940$	−11.4915	+	0.342135i	−0.374812	+	0.0111592i
$941$	−20.4139	−	49.2834i	−0.665473	−	1.60659i	−0.789100	−	0.614265i	$-0.789453\pi$
$941$	−20.4139	−	49.2834i	−0.665473	−	1.60659i	0.123627	−	0.992329i	$-0.460547\pi$
$942$		0			0
$943$	−11.6943	+	11.6943i	−0.380820	+	0.380820i
$944$	−20.7839	−	20.7839i	−0.676458	−	0.676458i
$945$		0			0
$946$	−2.90295	−	7.00834i	−0.0943830	−	0.227861i
$947$	5.21997	−	12.6021i	0.169626	−	0.409514i	−0.816091	−	0.577924i	$-0.803863\pi$
$947$	5.21997	−	12.6021i	0.169626	−	0.409514i	0.985717	+	0.168409i	$0.0538631\pi$
$948$		0			0
$949$	−1.04698	+	2.52764i	−0.0339865	+	0.0820506i
$950$	4.73343	−	0.282105i	0.153573	−	0.00915269i
$951$		0			0
$952$	−1.09695	−	5.67902i	−0.0355525	−	0.184058i
$953$			10.3660i			0.335788i	0.985805	+	0.167894i	$0.0536967\pi$
$953$			10.3660i			0.335788i	−0.985805	+	0.167894i	$0.946303\pi$
$954$		0			0
$955$	6.88853	−	0.205091i	0.222908	−	0.00663659i
$956$			12.0431i			0.389502i
$957$		0			0
$958$	5.34925	−	2.21573i	0.172827	−	0.0715871i
$959$	8.73313	−	3.61738i	0.282007	−	0.116811i
$960$		0			0
$961$	21.7489	+	21.7489i	0.701577	+	0.701577i
$962$	−0.0955505	−	0.230679i	−0.00308067	−	0.00743740i
$963$		0			0
$964$	−47.9937	−	19.8796i	−1.54577	−	0.640280i
$965$	−14.6557	−	32.6023i	−0.471784	−	1.04951i
$966$		0			0
$967$	10.1327	+	10.1327i	0.325847	+	0.325847i	0.851005	−	0.525158i	$-0.175994\pi$
$967$	10.1327	+	10.1327i	0.325847	+	0.325847i	−0.525158	+	0.851005i	$0.675994\pi$
$968$		−	3.67050i		−	0.117974i
$969$		0			0
$970$	−0.524635	−	1.16708i	−0.0168450	−	0.0374725i
$971$	−21.0309	+	21.0309i	−0.674913	+	0.674913i	−0.958845	−	0.283931i	$-0.908361\pi$
$971$	−21.0309	+	21.0309i	−0.674913	+	0.674913i	0.283931	+	0.958845i	$0.408361\pi$
$972$		0			0
$973$	6.57882			0.210907
$974$	3.88929	+	1.61100i	0.124621	+	0.0516197i
$975$		0			0
$976$	23.3144	−	9.65712i	0.746274	−	0.309117i
$977$	−26.2437	+	26.2437i	−0.839611	+	0.839611i	−0.988808	−	0.149196i	$-0.952331\pi$
$977$	−26.2437	+	26.2437i	−0.839611	+	0.839611i	0.149196	+	0.988808i	$0.452331\pi$
$978$		0			0
$979$	−28.5955	+	11.8446i	−0.913916	+	0.378556i
$980$	−14.7161	+	15.6193i	−0.470089	+	0.498940i
$981$		0			0
$982$	5.24217			0.167284
$983$	42.9257	+	17.7804i	1.36912	+	0.567107i	0.941549	−	0.336877i	$-0.109371\pi$
$983$	42.9257	+	17.7804i	1.36912	+	0.567107i	0.427568	+	0.903983i	$0.359371\pi$
$984$		0			0
$985$	21.7685	−	9.78559i	0.693602	−	0.311795i
$986$	3.69887	−	5.46991i	0.117796	−	0.174197i
$987$		0			0
$988$	−0.911949	−	0.911949i	−0.0290130	−	0.0290130i
$989$	11.9411	−	28.8283i	0.379703	−	0.916685i
$990$		0			0
$991$	−40.9290	−	16.9534i	−1.30015	−	0.538541i	−0.378158	−	0.925741i	$-0.623442\pi$
$991$	−40.9290	−	16.9534i	−1.30015	−	0.538541i	−0.921996	+	0.387200i	$0.873442\pi$
$992$	1.30304	−	0.539738i	0.0413717	−	0.0171367i
$993$		0			0
$994$	−3.07965	−	3.07965i	−0.0976806	−	0.0976806i
$995$	12.5741	−	33.1108i	0.398625	−	1.04968i
$996$		0			0
$997$	−22.7561	+	9.42589i	−0.720693	+	0.298521i	−0.712721	−	0.701447i	$-0.752538\pi$
$997$	−22.7561	+	9.42589i	−0.720693	+	0.298521i	−0.00797178	+	0.999968i	$0.502538\pi$
$998$	−2.14575	+	5.18029i	−0.0679224	+	0.163979i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.bh.b.739.4		24
3.2	odd	2		85.2.m.a.59.3	yes	24
5.4	even	2	inner	765.2.bh.b.739.3		24
15.2	even	4		425.2.m.e.76.4		24
15.8	even	4		425.2.m.e.76.3		24
15.14	odd	2		85.2.m.a.59.4	yes	24
17.15	even	8	inner	765.2.bh.b.559.3		24
51.32	odd	8		85.2.m.a.49.4	yes	24
51.41	even	16		1445.2.b.i.579.13		24
51.44	even	16		1445.2.b.i.579.14		24
85.49	even	8	inner	765.2.bh.b.559.4		24
255.32	even	8		425.2.m.e.151.4		24
255.44	even	16		1445.2.b.i.579.11		24
255.83	even	8		425.2.m.e.151.3		24
255.92	odd	16		7225.2.a.by.1.11		24
255.134	odd	8		85.2.m.a.49.3	✓	24
255.143	odd	16		7225.2.a.by.1.14		24
255.194	even	16		1445.2.b.i.579.12		24
255.197	odd	16		7225.2.a.by.1.12		24
255.248	odd	16		7225.2.a.by.1.13		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.49.3	✓	24	255.134	odd	8
85.2.m.a.49.4	yes	24	51.32	odd	8
85.2.m.a.59.3	yes	24	3.2	odd	2
85.2.m.a.59.4	yes	24	15.14	odd	2
425.2.m.e.76.3		24	15.8	even	4
425.2.m.e.76.4		24	15.2	even	4
425.2.m.e.151.3		24	255.83	even	8
425.2.m.e.151.4		24	255.32	even	8
765.2.bh.b.559.3		24	17.15	even	8	inner
765.2.bh.b.559.4		24	85.49	even	8	inner
765.2.bh.b.739.3		24	5.4	even	2	inner
765.2.bh.b.739.4		24	1.1	even	1	trivial
1445.2.b.i.579.11		24	255.44	even	16
1445.2.b.i.579.12		24	255.194	even	16
1445.2.b.i.579.13		24	51.41	even	16
1445.2.b.i.579.14		24	51.44	even	16
7225.2.a.by.1.11		24	255.92	odd	16
7225.2.a.by.1.12		24	255.197	odd	16
7225.2.a.by.1.13		24	255.248	odd	16
7225.2.a.by.1.14		24	255.143	odd	16

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.bh (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.176012 + 0.176012i) q^{2} -1.93804i q^{4} +(-0.0665446 - 2.23508i) q^{5} +(-0.547653 - 1.32215i) q^{7} +(0.693142 - 0.693142i) q^{8} +O(q^{10})\)	\(q+(0.176012 + 0.176012i) q^{2} -1.93804i q^{4} +(-0.0665446 - 2.23508i) q^{5} +(-0.547653 - 1.32215i) q^{7} +(0.693142 - 0.693142i) q^{8} +(0.381688 - 0.405113i) q^{10} +(-1.03080 - 2.48857i) q^{11} -0.174664 q^{13} +(0.136321 - 0.329108i) q^{14} -3.63208 q^{16} +(2.27165 + 3.44088i) q^{17} +(-2.69404 + 2.69404i) q^{19} +(-4.33167 + 0.128966i) q^{20} +(0.256585 - 0.619452i) q^{22} +(2.54807 - 1.05544i) q^{23} +(-4.99114 + 0.297464i) q^{25} +(-0.0307430 - 0.0307430i) q^{26} +(-2.56238 + 1.06137i) q^{28} +(-5.94408 - 2.46212i) q^{29} +(-0.188417 + 0.454879i) q^{31} +(-2.02557 - 2.02557i) q^{32} +(-0.205798 + 1.00547i) q^{34} +(-2.91867 + 1.31203i) q^{35} +(5.30576 + 2.19772i) q^{37} -0.948365 q^{38} +(-1.59535 - 1.50310i) q^{40} +(-5.54000 + 2.29474i) q^{41} +(8.00004 - 8.00004i) q^{43} +(-4.82296 + 1.99773i) q^{44} +(0.634261 + 0.262720i) q^{46} +2.65291 q^{47} +(3.50159 - 3.50159i) q^{49} +(-0.930858 - 0.826143i) q^{50} +0.338506i q^{52} +(-8.73501 - 8.73501i) q^{53} +(-5.49356 + 2.46952i) q^{55} +(-1.29604 - 0.536837i) q^{56} +(-0.612867 - 1.47959i) q^{58} +(5.72232 + 5.72232i) q^{59} +(-6.41902 + 2.65884i) q^{61} +(-0.113228 + 0.0469005i) q^{62} +6.55110i q^{64} +(0.0116230 + 0.390388i) q^{65} +12.3901i q^{67} +(6.66855 - 4.40254i) q^{68} +(-0.744653 - 0.282788i) q^{70} +(4.67878 - 11.2956i) q^{71} +(5.99425 - 14.4714i) q^{73} +(0.547052 + 1.32070i) q^{74} +(5.22115 + 5.22115i) q^{76} +(-2.72575 + 2.72575i) q^{77} +(-4.94031 - 11.9270i) q^{79} +(0.241695 + 8.11797i) q^{80} +(-1.37901 - 0.571204i) q^{82} +(6.06390 + 6.06390i) q^{83} +(7.53946 - 5.30628i) q^{85} +2.81621 q^{86} +(-2.43943 - 1.01044i) q^{88} -11.4907i q^{89} +(0.0956555 + 0.230933i) q^{91} +(-2.04549 - 4.93826i) q^{92} +(0.466944 + 0.466944i) q^{94} +(6.20066 + 5.84211i) q^{95} +(0.879757 - 2.12392i) q^{97} +1.23264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 16 q^{10} + 24 q^{14} + 8 q^{16} - 24 q^{19} + 8 q^{20} + 16 q^{25} + 16 q^{26} - 24 q^{29} - 24 q^{31} + 8 q^{34} - 8 q^{35} + 16 q^{40} + 48 q^{41} - 72 q^{44} - 16 q^{46} + 48 q^{49} - 16 q^{50} - 24 q^{56} + 48 q^{59} + 16 q^{61} - 24 q^{65} + 32 q^{70} - 16 q^{71} + 64 q^{74} - 24 q^{76} - 72 q^{79} + 64 q^{80} - 24 q^{85} - 8 q^{91} - 40 q^{94} + 88 q^{95}+O(q^{100}) \) 24 * q - 16 * q^10 + 24 * q^14 + 8 * q^16 - 24 * q^19 + 8 * q^20 + 16 * q^25 + 16 * q^26 - 24 * q^29 - 24 * q^31 + 8 * q^34 - 8 * q^35 + 16 * q^40 + 48 * q^41 - 72 * q^44 - 16 * q^46 + 48 * q^49 - 16 * q^50 - 24 * q^56 + 48 * q^59 + 16 * q^61 - 24 * q^65 + 32 * q^70 - 16 * q^71 + 64 * q^74 - 24 * q^76 - 72 * q^79 + 64 * q^80 - 24 * q^85 - 8 * q^91 - 40 * q^94 + 88 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more