LMFDB - Embedded newform 85.2.m.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(9,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("85.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.m (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:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	85.49
Dual form			85.2.m.a.59.4

$q$-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} +(-1.51856 + 0.629010i) q^{3} +1.93804i q^{4} +(1.62749 + 1.53338i) q^{5} +(-0.156572 + 0.377999i) q^{6} +(0.547653 - 1.32215i) q^{7} +(0.693142 + 0.693142i) q^{8} +(-0.210935 + 0.210935i) q^{9} +(0.556352 - 0.0165642i) q^{10} +(1.03080 - 2.48857i) q^{11} +(-1.21905 - 2.94304i) q^{12} +0.174664 q^{13} +(-0.136321 - 0.329108i) q^{14} +(-3.43597 - 1.30483i) q^{15} -3.63208 q^{16} +(2.27165 - 3.44088i) q^{17} +0.0742541i q^{18} +(-2.69404 - 2.69404i) q^{19} +(-2.97176 + 3.15415i) q^{20} +2.35225i q^{21} +(-0.256585 - 0.619452i) q^{22} +(2.54807 + 1.05544i) q^{23} +(-1.48857 - 0.616588i) q^{24} +(0.297464 + 4.99114i) q^{25} +(0.0307430 - 0.0307430i) q^{26} +(2.07467 - 5.00869i) q^{27} +(2.56238 + 1.06137i) q^{28} +(5.94408 - 2.46212i) q^{29} +(-0.834438 + 0.375105i) q^{30} +(-0.188417 - 0.454879i) q^{31} +(-2.02557 + 2.02557i) q^{32} +4.42745i q^{33} +(-0.205798 - 1.00547i) q^{34} +(2.91867 - 1.31203i) q^{35} +(-0.408800 - 0.408800i) q^{36} +(-5.30576 + 2.19772i) q^{37} -0.948365 q^{38} +(-0.265239 + 0.109866i) q^{39} +(0.0652303 + 2.19094i) q^{40} +(5.54000 + 2.29474i) q^{41} +(0.414025 + 0.414025i) q^{42} +(-8.00004 - 8.00004i) q^{43} +(4.82296 + 1.99773i) q^{44} +(-0.666739 + 0.0198507i) q^{45} +(0.634261 - 0.262720i) q^{46} +2.65291 q^{47} +(5.51554 - 2.28461i) q^{48} +(3.50159 + 3.50159i) q^{49} +(0.930858 + 0.826143i) q^{50} +(-1.28530 + 6.65408i) q^{51} +0.338506i q^{52} +(-8.73501 + 8.73501i) q^{53} +(-0.516423 - 1.24676i) q^{54} +(5.49356 - 2.46952i) q^{55} +(1.29604 - 0.536837i) q^{56} +(5.78565 + 2.39649i) q^{57} +(0.612867 - 1.47959i) q^{58} +(-5.72232 + 5.72232i) q^{59} +(2.52882 - 6.65904i) q^{60} +(-6.41902 - 2.65884i) q^{61} +(-0.113228 - 0.0469005i) q^{62} +(0.163369 + 0.394407i) q^{63} -6.55110i q^{64} +(0.284265 + 0.267828i) q^{65} +(0.779283 + 0.779283i) q^{66} +12.3901i q^{67} +(6.66855 + 4.40254i) q^{68} -4.53329 q^{69} +(0.282788 - 0.744653i) q^{70} +(-4.67878 - 11.2956i) q^{71} -0.292415 q^{72} +(-5.99425 - 14.4714i) q^{73} +(-0.547052 + 1.32070i) q^{74} +(-3.59120 - 7.39227i) q^{75} +(5.22115 - 5.22115i) q^{76} +(-2.72575 - 2.72575i) q^{77} +(-0.0273476 + 0.0660229i) q^{78} +(-4.94031 + 11.9270i) q^{79} +(-5.91118 - 5.56937i) q^{80} +8.01609i q^{81} +(1.37901 - 0.571204i) q^{82} +(6.06390 - 6.06390i) q^{83} -4.55876 q^{84} +(8.97327 - 2.11669i) q^{85} -2.81621 q^{86} +(-7.47777 + 7.47777i) q^{87} +(2.43943 - 1.01044i) q^{88} -11.4907i q^{89} +(-0.113860 + 0.120848i) q^{90} +(0.0956555 - 0.230933i) q^{91} +(-2.04549 + 4.93826i) q^{92} +(0.572247 + 0.572247i) q^{93} +(0.466944 - 0.466944i) q^{94} +(-0.253531 - 8.51552i) q^{95} +(1.80186 - 4.35007i) q^{96} +(-0.879757 - 2.12392i) q^{97} +1.23264 q^{98} +(0.307495 + 0.742359i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{9} - 16 q^{10} - 24 q^{14} - 16 q^{15} + 8 q^{16} - 24 q^{19} - 8 q^{20} + 32 q^{24} + 16 q^{25} - 16 q^{26} + 24 q^{29} - 24 q^{31} + 8 q^{34} + 8 q^{35} + 8 q^{36} - 24 q^{39} + 16 q^{40}+ \cdots - 80 q^{99}+O(q^{100}) $ 24 * q - 8 * q^9 - 16 * q^10 - 24 * q^14 - 16 * q^15 + 8 * q^16 - 24 * q^19 - 8 * q^20 + 32 * q^24 + 16 * q^25 - 16 * q^26 + 24 * q^29 - 24 * q^31 + 8 * q^34 + 8 * q^35 + 8 * q^36 - 24 * q^39 + 16 * q^40 - 48 * q^41 + 72 * q^44 + 48 * q^45 - 16 * q^46 + 48 * q^49 + 16 * q^50 + 32 * q^54 + 24 * q^56 - 48 * q^59 + 8 * q^60 + 16 * q^61 + 24 * q^65 - 96 * q^66 + 32 * q^69 + 32 * q^70 + 16 * q^71 - 64 * q^74 - 24 * q^76 - 72 * q^79 - 64 * q^80 - 96 * q^84 - 24 * q^85 - 8 * q^91 - 40 * q^94 - 88 * q^95 + 96 * q^96 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.176012	−	0.176012i	0.124459	−	0.124459i	−0.642134	−	0.766593i	$-0.721951\pi$
$2$	0.176012	−	0.176012i	0.124459	−	0.124459i	0.766593	+	0.642134i	$0.221951\pi$
$3$	−1.51856	+	0.629010i	−0.876744	+	0.363159i	−0.775233	−	0.631675i	$-0.782368\pi$
$3$	−1.51856	+	0.629010i	−0.876744	+	0.363159i	−0.101511	+	0.994834i	$0.532368\pi$
$4$			1.93804i			0.969020i
$5$	1.62749	+	1.53338i	0.727837	+	0.685750i
$5$	1.62749	+	1.53338i	0.727837	+	0.685750i
$6$	−0.156572	+	0.377999i	−0.0639203	+	0.154317i
$7$	0.547653	−	1.32215i	0.206993	−	0.499726i	−0.785954	−	0.618286i	$-0.787828\pi$
$7$	0.547653	−	1.32215i	0.206993	−	0.499726i	0.992947	+	0.118559i	$0.0378275\pi$
$8$	0.693142	+	0.693142i	0.245063	+	0.245063i
$9$	−0.210935	+	0.210935i	−0.0703116	+	0.0703116i
$10$	0.556352	−	0.0165642i	0.175934	−	0.00523805i
$11$	1.03080	−	2.48857i	0.310798	−	0.750333i	−0.688878	−	0.724878i	$-0.741896\pi$
$11$	1.03080	−	2.48857i	0.310798	−	0.750333i	0.999676	−	0.0254558i	$-0.00810370\pi$
$12$	−1.21905	−	2.94304i	−0.351908	−	0.849582i
$13$	0.174664			0.0484432			0.0242216	−	0.999707i	$-0.492289\pi$
$13$	0.174664			0.0484432			0.0242216	+	0.999707i	$0.492289\pi$
$14$	−0.136321	−	0.329108i	−0.0364333	−	0.0879578i
$15$	−3.43597	−	1.30483i	−0.887163	−	0.336907i
$16$	−3.63208			−0.908019
$17$	2.27165	−	3.44088i	0.550955	−	0.834535i
$17$	2.27165	−	3.44088i	0.550955	−	0.834535i
$18$			0.0742541i			0.0175019i
$19$	−2.69404	−	2.69404i	−0.618055	−	0.618055i	0.326978	−	0.945032i	$-0.393970\pi$
$19$	−2.69404	−	2.69404i	−0.618055	−	0.618055i	−0.945032	+	0.326978i	$0.893970\pi$
$20$	−2.97176	+	3.15415i	−0.664506	+	0.705288i
$21$			2.35225i			0.513304i
$22$	−0.256585	−	0.619452i	−0.0547042	−	0.132068i
$23$	2.54807	+	1.05544i	0.531309	+	0.220075i	0.632176	−	0.774825i	$-0.282162\pi$
$23$	2.54807	+	1.05544i	0.531309	+	0.220075i	−0.100867	+	0.994900i	$0.532162\pi$
$24$	−1.48857	−	0.616588i	−0.303854	−	0.125860i
$25$	0.297464	+	4.99114i	0.0594929	+	0.998229i
$26$	0.0307430	−	0.0307430i	0.00602920	−	0.00602920i
$27$	2.07467	−	5.00869i	0.399270	−	0.963923i
$28$	2.56238	+	1.06137i	0.484245	+	0.200581i
$29$	5.94408	−	2.46212i	1.10379	−	0.457204i	0.244994	−	0.969525i	$-0.421214\pi$
$29$	5.94408	−	2.46212i	1.10379	−	0.457204i	0.858794	+	0.512321i	$0.171214\pi$
$30$	−0.834438	+	0.375105i	−0.152347	+	0.0684845i
$31$	−0.188417	−	0.454879i	−0.0338407	−	0.0816987i	0.906056	−	0.423159i	$-0.139079\pi$
$31$	−0.188417	−	0.454879i	−0.0338407	−	0.0816987i	−0.939896	+	0.341460i	$0.889079\pi$
$32$	−2.02557	+	2.02557i	−0.358074	+	0.358074i
$33$			4.42745i			0.770719i
$34$	−0.205798	−	1.00547i	−0.0352941	−	0.172437i
$35$	2.91867	−	1.31203i	0.493345	−	0.221773i
$36$	−0.408800	−	0.408800i	−0.0681333	−	0.0681333i
$37$	−5.30576	+	2.19772i	−0.872261	+	0.361302i	−0.773490	−	0.633808i	$-0.781491\pi$
$37$	−5.30576	+	2.19772i	−0.872261	+	0.361302i	−0.0987704	+	0.995110i	$0.531491\pi$
$38$	−0.948365			−0.153845
$39$	−0.265239	+	0.109866i	−0.0424723	+	0.0175926i
$40$	0.0652303	+	2.19094i	0.0103138	+	0.346417i
$41$	5.54000	+	2.29474i	0.865203	+	0.358379i	0.770740	−	0.637150i	$-0.219887\pi$
$41$	5.54000	+	2.29474i	0.865203	+	0.358379i	0.0944627	+	0.995528i	$0.469887\pi$
$42$	0.414025	+	0.414025i	0.0638854	+	0.0638854i
$43$	−8.00004	−	8.00004i	−1.22000	−	1.22000i	−0.967633	−	0.252363i	$-0.918792\pi$
$43$	−8.00004	−	8.00004i	−1.22000	−	1.22000i	−0.252363	−	0.967633i	$-0.581208\pi$
$44$	4.82296	+	1.99773i	0.727088	+	0.301170i
$45$	−0.666739	+	0.0198507i	−0.0993916	+	0.00295917i
$46$	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	$0.438021\pi$
$48$	5.51554	−	2.28461i	0.796100	−	0.329756i
$49$	3.50159	+	3.50159i	0.500227	+	0.500227i
$50$	0.930858	+	0.826143i	0.131643	+	0.116834i
$51$	−1.28530	+	6.65408i	−0.179977	+	0.931758i
$52$			0.338506i			0.0469424i
$53$	−8.73501	+	8.73501i	−1.19985	+	1.19985i	−0.225633	+	0.974212i	$0.572445\pi$
$53$	−8.73501	+	8.73501i	−1.19985	+	1.19985i	−0.974212	+	0.225633i	$0.927555\pi$
$54$	−0.516423	−	1.24676i	−0.0702763	−	0.169662i
$55$	5.49356	−	2.46952i	0.740752	−	0.332990i
$56$	1.29604	−	0.536837i	0.173191	−	0.0717379i
$57$	5.78565	+	2.39649i	0.766328	+	0.317423i
$58$	0.612867	−	1.47959i	0.0804733	−	0.194280i
$59$	−5.72232	+	5.72232i	−0.744982	+	0.744982i	−0.973532	−	0.228550i	$-0.926602\pi$
$59$	−5.72232	+	5.72232i	−0.744982	+	0.744982i	0.228550	+	0.973532i	$0.426602\pi$
$60$	2.52882	−	6.65904i	0.326469	−	0.859679i
$61$	−6.41902	−	2.65884i	−0.821871	−	0.340430i	−0.0681914	−	0.997672i	$-0.521723\pi$
$61$	−6.41902	−	2.65884i	−0.821871	−	0.340430i	−0.753679	+	0.657242i	$0.771723\pi$
$62$	−0.113228	−	0.0469005i	−0.0143799	−	0.00595637i
$63$	0.163369	+	0.394407i	0.0205825	+	0.0496906i
$64$		−	6.55110i		−	0.818888i
$65$	0.284265	+	0.267828i	0.0352587	+	0.0332199i
$66$	0.779283	+	0.779283i	0.0959231	+	0.0959231i
$67$			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
$69$	−4.53329			−0.545744
$70$	0.282788	−	0.744653i	0.0337996	−	0.0890031i
$71$	−4.67878	−	11.2956i	−0.555269	−	1.34054i	−0.913474	−	0.406896i	$-0.866611\pi$
$71$	−4.67878	−	11.2956i	−0.555269	−	1.34054i	0.358205	−	0.933643i	$-0.383389\pi$
$72$	−0.292415			−0.0344615
$73$	−5.99425	−	14.4714i	−0.701574	−	1.69375i	−0.720052	−	0.693920i	$-0.755882\pi$
$73$	−5.99425	−	14.4714i	−0.701574	−	1.69375i	0.0184781	−	0.999829i	$-0.494118\pi$
$74$	−0.547052	+	1.32070i	−0.0635935	+	0.153528i
$75$	−3.59120	−	7.39227i	−0.414676	−	0.853586i
$76$	5.22115	−	5.22115i	0.598907	−	0.598907i
$77$	−2.72575	−	2.72575i	−0.310628	−	0.310628i
$78$	−0.0273476	+	0.0660229i	−0.00309650	+	0.00747562i
$79$	−4.94031	+	11.9270i	−0.555828	+	1.34189i	0.357214	+	0.934022i	$0.383727\pi$
$79$	−4.94031	+	11.9270i	−0.555828	+	1.34189i	−0.913042	+	0.407865i	$0.866273\pi$
$80$	−5.91118	−	5.56937i	−0.660890	−	0.622674i
$81$			8.01609i			0.890677i
$82$	1.37901	−	0.571204i	0.152286	−	0.0630789i
$83$	6.06390	−	6.06390i	0.665600	−	0.665600i	−0.291094	−	0.956694i	$-0.594019\pi$
$83$	6.06390	−	6.06390i	0.665600	−	0.665600i	0.956694	+	0.291094i	$0.0940194\pi$
$84$	−4.55876			−0.497401
$85$	8.97327	−	2.11669i	0.973288	−	0.229588i
$86$	−2.81621			−0.303679
$87$	−7.47777	+	7.47777i	−0.801702	+	0.801702i
$88$	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	$-0.208432\pi$
$90$	−0.113860	+	0.120848i	−0.0120019	+	0.0127385i
$91$	0.0956555	−	0.230933i	0.0100274	−	0.0242083i
$92$	−2.04549	+	4.93826i	−0.213257	+	0.514849i
$93$	0.572247	+	0.572247i	0.0593393	+	0.0593393i
$94$	0.466944	−	0.466944i	0.0481616	−	0.0481616i
$95$	−0.253531	−	8.51552i	−0.0260117	−	0.873674i
$96$	1.80186	−	4.35007i	0.183901	−	0.443977i
$97$	−0.879757	−	2.12392i	−0.0893258	−	0.215651i	0.872903	−	0.487894i	$-0.162235\pi$
$97$	−0.879757	−	2.12392i	−0.0893258	−	0.215651i	−0.962229	+	0.272242i	$0.912235\pi$
$98$	1.23264			0.124516
$99$	0.307495	+	0.742359i	0.0309044	+	0.0746099i
$100$	−9.67303	+	0.576498i	−0.967303	+	0.0576498i
$101$	−0.890917			−0.0886495			−0.0443248	−	0.999017i	$-0.514114\pi$
$101$	−0.890917			−0.0886495			−0.0443248	+	0.999017i	$0.514114\pi$
$102$	0.944970	+	1.39742i	0.0935660	+	0.138366i
$103$		−	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
$105$	−3.60691	+	3.82827i	−0.351998	+	0.373601i
$106$			3.07493i			0.298664i
$107$	2.54389	+	6.14149i	0.245927	+	0.593720i	0.997851	−	0.0655301i	$-0.0208738\pi$
$107$	2.54389	+	6.14149i	0.245927	+	0.593720i	−0.751924	+	0.659250i	$0.770874\pi$
$108$	9.70705	+	4.02079i	0.934061	+	0.386901i
$109$	8.16665	+	3.38274i	0.782223	+	0.324007i	0.737812	−	0.675006i	$-0.235859\pi$
$109$	8.16665	+	3.38274i	0.782223	+	0.324007i	0.0444107	+	0.999013i	$0.485859\pi$
$110$	0.532267	−	1.40160i	0.0507497	−	0.133637i
$111$	6.67475	−	6.67475i	0.633539	−	0.633539i
$112$	−1.98912	+	4.80216i	−0.187954	+	0.453761i
$113$	5.27825	+	2.18632i	0.496536	+	0.205672i	0.616875	−	0.787061i	$-0.288398\pi$
$113$	5.27825	+	2.18632i	0.496536	+	0.205672i	−0.120339	+	0.992733i	$0.538398\pi$
$114$	1.44015	−	0.596531i	0.134883	−	0.0558703i
$115$	2.52856	+	5.62490i	0.235789	+	0.524524i
$116$	4.77168	+	11.5199i	0.443040	+	1.06959i
$117$	−0.0368428	+	0.0368428i	−0.00340612	+	0.00340612i
$118$			2.01439i			0.185440i
$119$	−3.30529	−	4.88787i	−0.302995	−	0.448070i
$120$	−1.47718	−	3.28605i	−0.134847	−	0.299974i
$121$	2.64772	+	2.64772i	0.240702	+	0.240702i
$122$	−1.59781	+	0.661835i	−0.144659	+	0.0599197i
$123$	−9.85627			−0.888710
$124$	0.881574	−	0.365160i	0.0791676	−	0.0327923i
$125$	−7.16922	+	8.57918i	−0.641235	+	0.767345i
$126$	0.0981752	+	0.0406655i	0.00874614	+	0.00362277i
$127$	11.5590	+	11.5590i	1.02569	+	1.02569i	0.999661	+	0.0260300i	$0.00828653\pi$
$127$	11.5590	+	11.5590i	1.02569	+	1.02569i	0.0260300	+	0.999661i	$0.491713\pi$
$128$	−5.20422	−	5.20422i	−0.459992	−	0.459992i
$129$	17.1807	+	7.11648i	1.51268	+	0.626571i
$130$	0.0971749	−	0.00289317i	0.00852280	−	0.000253748i
$131$	−8.90518	+	3.68865i	−0.778049	+	0.322279i	−0.736128	−	0.676842i	$-0.763348\pi$
$131$	−8.90518	+	3.68865i	−0.778049	+	0.322279i	−0.0419214	+	0.999121i	$0.513348\pi$
$132$	−8.58057			−0.746842
$133$	−5.03733	+	2.08653i	−0.436791	+	0.180925i
$134$	2.18080	+	2.18080i	0.188393	+	0.188393i
$135$	11.0568	−	4.97035i	0.951614	−	0.427779i
$136$	3.95959	−	0.810442i	0.339532	−	0.0694949i
$137$		−	6.60524i		−	0.564324i	−0.959367	−	0.282162i	$-0.908948\pi$
$137$		−	6.60524i		−	0.564324i	0.959367	−	0.282162i	$-0.0910515\pi$
$138$	−0.797913	+	0.797913i	−0.0679229	+	0.0679229i
$139$	−1.75923	−	4.24715i	−0.149216	−	0.360239i	0.831544	−	0.555459i	$-0.187458\pi$
$139$	−1.75923	−	4.24715i	−0.149216	−	0.360239i	−0.980759	+	0.195221i	$0.937458\pi$
$140$	2.54277	+	5.65650i	0.214903	+	0.478061i
$141$	−4.02862	+	1.66871i	−0.339271	+	0.140531i
$142$	−2.81168	−	1.16464i	−0.235951	−	0.0977340i
$143$	0.180044	−	0.434665i	0.0150561	−	0.0363485i
$144$	0.766131	−	0.766131i	0.0638443	−	0.0638443i
$145$	13.4493	+	5.10748i	1.11691	+	0.424153i
$146$	−3.60220	−	1.49208i	−0.298120	−	0.123485i
$147$	−7.51992	−	3.11485i	−0.620232	−	0.256909i
$148$	−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	$-0.158207\pi$
$150$	−1.93322	−	0.669033i	−0.157847	−	0.0546263i
$151$	0.0974235	+	0.0974235i	0.00792821	+	0.00792821i	0.711060	−	0.703132i	$-0.248216\pi$
$151$	0.0974235	+	0.0974235i	0.00792821	+	0.00792821i	−0.703132	+	0.711060i	$0.748216\pi$
$152$		−	3.73470i		−	0.302924i
$153$	0.246631	+	1.20497i	0.0199390	+	0.0974160i
$154$	−0.959530			−0.0773211
$155$	0.390857	−	1.02923i	0.0313944	−	0.0826696i
$156$	−0.212924	−	0.514044i	−0.0170476	−	0.0411565i
$157$	9.66489			0.771343			0.385671	−	0.922636i	$-0.373970\pi$
$157$	9.66489			0.771343			0.385671	+	0.922636i	$0.373970\pi$
$158$	1.22973	+	2.96884i	0.0978323	+	0.236188i
$159$	7.77027	−	18.7591i	0.616222	−	1.48769i
$160$	−6.40259	+	0.190623i	−0.506169	+	0.0150701i
$161$	2.79092	−	2.79092i	0.219955	−	0.219955i
$162$	1.41093	+	1.41093i	0.110853	+	0.110853i
$163$	−4.75100	+	11.4699i	−0.372127	+	0.898394i	0.621263	+	0.783602i	$0.286620\pi$
$163$	−4.75100	+	11.4699i	−0.372127	+	0.898394i	−0.993390	+	0.114792i	$0.963380\pi$
$164$	−4.44730	+	10.7367i	−0.347276	+	0.838399i
$165$	−6.78898	+	7.20564i	−0.528521	+	0.560958i
$166$		−	2.13464i		−	0.165680i
$167$	−3.86872	+	1.60248i	−0.299371	+	0.124003i	−0.527313	−	0.849671i	$-0.676800\pi$
$167$	−3.86872	+	1.60248i	−0.299371	+	0.124003i	0.227942	+	0.973675i	$0.426800\pi$
$168$	−1.63045	+	1.63045i	−0.125792	+	0.125792i
$169$	−12.9695			−0.997653
$170$	1.20684	−	1.95197i	0.0925603	−	0.149709i
$171$	1.13653			0.0869128
$172$	15.5044	−	15.5044i	1.18220	−	1.18220i
$173$	2.73000	−	1.13080i	0.207558	−	0.0859733i	−0.276483	−	0.961019i	$-0.589169\pi$
$173$	2.73000	−	1.13080i	0.207558	−	0.0859733i	0.484040	+	0.875046i	$0.339169\pi$
$174$			2.63235i			0.199558i
$175$	6.76196	+	2.34012i	0.511156	+	0.176897i
$176$	−3.74395	+	9.03869i	−0.282211	+	0.681317i
$177$	5.09032	−	12.2891i	0.382612	−	0.923706i
$178$	−2.02250	−	2.02250i	−0.151593	−	0.151593i
$179$	−16.4589	+	16.4589i	−1.23019	+	1.23019i	−0.266304	+	0.963889i	$0.585803\pi$
$179$	−16.4589	+	16.4589i	−1.23019	+	1.23019i	−0.963889	+	0.266304i	$0.914197\pi$
$180$	−0.0384714	−	1.29217i	−0.00286749	−	0.0963124i
$181$	4.37037	−	10.5510i	0.324847	−	0.784250i	−0.674112	−	0.738629i	$-0.735474\pi$
$181$	4.37037	−	10.5510i	0.324847	−	0.784250i	0.998959	−	0.0456205i	$-0.0145265\pi$
$182$	−0.0238104	−	0.0574834i	−0.00176495	−	0.00426096i
$183$	11.4201			0.844200
$184$	1.03460	+	2.49775i	0.0762717	+	0.184136i
$185$	−12.0050	−	4.55900i	−0.882627	−	0.335184i
$186$	0.201445			0.0147706
$187$	−6.22126	−	9.20002i	−0.454944	−	0.672772i
$188$			5.14145i			0.374978i
$189$	−5.48605	−	5.48605i	−0.399052	−	0.399052i
$190$	−1.54346	−	1.45421i	−0.111974	−	0.105499i
$191$			3.08201i			0.223007i	0.993764	+	0.111503i	$0.0355666\pi$
$191$			3.08201i			0.223007i	−0.993764	+	0.111503i	$0.964433\pi$
$192$	4.12071	+	9.94828i	0.297387	+	0.717955i
$193$	−14.7688	−	6.11743i	−1.06308	−	0.440343i	−0.218537	−	0.975829i	$-0.570128\pi$
$193$	−14.7688	−	6.11743i	−1.06308	−	0.440343i	−0.844544	+	0.535486i	$0.820128\pi$
$194$	−0.528683	−	0.218988i	−0.0379572	−	0.0157224i
$195$	−0.600141	−	0.227908i	−0.0429770	−	0.0163208i
$196$	−6.78621	+	6.78621i	−0.484729	+	0.484729i
$197$	4.08460	−	9.86109i	0.291015	−	0.702573i	−0.708981	−	0.705228i	$-0.750845\pi$
$197$	4.08460	−	9.86109i	0.291015	−	0.702573i	0.999996	+	0.00265412i	$0.000844833\pi$
$198$	0.184787	+	0.0765412i	0.0131322	+	0.00543954i
$199$	14.6337	−	6.06147i	1.03735	−	0.429686i	0.201993	−	0.979387i	$-0.435258\pi$
$199$	14.6337	−	6.06147i	1.03735	−	0.429686i	0.835362	+	0.549701i	$0.185258\pi$
$200$	−3.25339	+	3.66576i	−0.230049	+	0.259208i
$201$	−7.79349	−	18.8152i	−0.549710	−	1.32712i
$202$	−0.156812	+	0.156812i	−0.0110333	+	0.0110333i
$203$		−	9.20737i		−	0.646230i
$204$	−12.8959	−	2.49095i	−0.902892	−	0.174402i
$205$	5.49759	+	12.2296i	0.383968	+	0.854154i
$206$	−0.0646205	−	0.0646205i	−0.00450232	−	0.00450232i
$207$	−0.760106	+	0.314846i	−0.0528310	+	0.0218833i
$208$	−0.634394			−0.0439873
$209$	−9.48133	+	3.92729i	−0.655837	+	0.271657i
$210$	0.0389631	+	1.30868i	0.00268871	+	0.0903076i
$211$	−4.54512	−	1.88265i	−0.312899	−	0.129607i	0.220707	−	0.975340i	$-0.429164\pi$
$211$	−4.54512	−	1.88265i	−0.312899	−	0.129607i	−0.533606	+	0.845733i	$0.679164\pi$
$212$	−16.9288	−	16.9288i	−1.16267	−	1.16267i
$213$	14.2101	+	14.2101i	0.973658	+	0.973658i
$214$	1.52873	+	0.633221i	0.104502	+	0.0432861i
$215$	−0.752870	−	25.2872i	−0.0513453	−	1.72457i
$216$	4.90977	−	2.03370i	0.334068	−	0.138375i
$217$	−0.704606			−0.0478318
$218$	2.03283	−	0.842025i	0.137681	−	0.0570292i
$219$	18.2053	+	18.2053i	1.23020	+	1.23020i
$220$	4.78603	+	10.6467i	0.322674	+	0.717803i
$221$	0.396776	−	0.600998i	0.0266900	−	0.0404275i
$222$		−	2.34967i		−	0.157700i
$223$	7.10210	−	7.10210i	0.475592	−	0.475592i	−0.428127	−	0.903719i	$-0.640826\pi$
$223$	7.10210	−	7.10210i	0.475592	−	0.475592i	0.903719	+	0.428127i	$0.140826\pi$
$224$	1.56880	+	3.78743i	0.104820	+	0.253058i
$225$	−1.11555	−	0.990060i	−0.0743701	−	0.0660040i
$226$	1.31385	−	0.544216i	0.0873963	−	0.0362007i
$227$	−4.13654	−	1.71341i	−0.274552	−	0.113723i	0.241160	−	0.970485i	$-0.422472\pi$
$227$	−4.13654	−	1.71341i	−0.274552	−	0.113723i	−0.515711	+	0.856762i	$0.672472\pi$
$228$	−4.64450	+	11.2128i	−0.307589	+	0.742587i
$229$	−0.847088	+	0.847088i	−0.0559771	+	0.0559771i	−0.734541	−	0.678564i	$-0.762603\pi$
$229$	−0.847088	+	0.847088i	−0.0559771	+	0.0559771i	0.678564	+	0.734541i	$0.262603\pi$
$230$	1.43511	+	0.544992i	0.0946280	+	0.0359357i
$231$	5.85376	+	2.42471i	0.385149	+	0.159534i
$232$	5.82669	+	2.41349i	0.382541	+	0.158454i
$233$	9.74096	+	23.5168i	0.638152	+	1.54063i	0.829139	+	0.559042i	$0.188831\pi$
$233$	9.74096	+	23.5168i	0.638152	+	1.54063i	−0.190987	+	0.981592i	$0.561169\pi$
$234$			0.0129695i			0.000847845i
$235$	4.31759	+	4.06793i	0.281649	+	0.265363i
$236$	−11.0901	−	11.0901i	−0.721903	−	0.721903i
$237$		−	21.2194i		−	1.37835i
$238$	−1.44209	−	0.278553i	−0.0934770	−	0.0180559i
$239$	6.21407			0.401955			0.200977	−	0.979596i	$-0.435588\pi$
$239$	6.21407			0.401955			0.200977	+	0.979596i	$0.435588\pi$
$240$	12.4797	+	4.73926i	0.805561	+	0.305918i
$241$	10.2576	+	24.7640i	0.660750	+	1.59519i	0.796631	+	0.604467i	$0.206614\pi$
$241$	10.2576	+	24.7640i	0.660750	+	1.59519i	−0.135880	+	0.990725i	$0.543386\pi$
$242$	0.932062			0.0599152
$243$	1.18180	+	2.85312i	0.0758126	+	0.183028i
$244$	5.15294	−	12.4403i	0.329883	−	0.796409i
$245$	0.329528	+	11.0681i	0.0210528	+	0.707114i
$246$	−1.73482	+	1.73482i	−0.110608	+	0.110608i
$247$	−0.470552	−	0.470552i	−0.0299405	−	0.0299405i
$248$	0.184696	−	0.445895i	0.0117282	−	0.0283144i
$249$	−5.39417	+	13.0227i	−0.341842	+	0.825279i
$250$	0.248169	+	2.77191i	0.0156956	+	0.175311i
$251$			10.6052i			0.669394i	0.942326	+	0.334697i	$0.108634\pi$
$251$			10.6052i			0.669394i	−0.942326	+	0.334697i	$0.891366\pi$
$252$	−0.764376	+	0.316615i	−0.0481512	+	0.0199449i
$253$	5.25310	−	5.25310i	0.330260	−	0.330260i
$254$	4.06903			0.255313
$255$	−12.2951	+	8.85862i	−0.769947	+	0.554748i
$256$	11.2702			0.704387
$257$	−1.08911	+	1.08911i	−0.0679369	+	0.0679369i	−0.740259	−	0.672322i	$-0.765297\pi$
$257$	−1.08911	+	1.08911i	−0.0679369	+	0.0679369i	0.672322	+	0.740259i	$0.265297\pi$
$258$	4.27659	−	1.77142i	0.266249	−	0.110284i
$259$			8.21860i			0.510679i
$260$	−0.519061	+	0.550917i	−0.0321908	+	0.0341664i
$261$	−0.734467	+	1.77316i	−0.0454624	+	0.109756i
$262$	−0.918172	+	2.21666i	−0.0567249	+	0.136946i
$263$	0.301535	+	0.301535i	0.0185935	+	0.0185935i	0.716342	−	0.697749i	$-0.245815\pi$
$263$	0.301535	+	0.301535i	0.0185935	+	0.0185935i	−0.697749	+	0.716342i	$0.745815\pi$
$264$	−3.06885	+	3.06885i	−0.188875	+	0.188875i
$265$	−27.6103	+	0.822036i	−1.69609	+	0.0504973i
$266$	−0.519375	+	1.25388i	−0.0318449	+	0.0768805i
$267$	7.22777	+	17.4494i	0.442333	+	1.06789i
$268$	−24.0125			−1.46680
$269$	−6.54570	−	15.8027i	−0.399098	−	0.963508i	−0.987880	−	0.155217i	$-0.950392\pi$
$269$	−6.54570	−	15.8027i	−0.399098	−	0.963508i	0.588782	−	0.808292i	$-0.299608\pi$
$270$	1.07128	−	2.82096i	0.0651961	−	0.171678i
$271$	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
$273$			0.410855i			0.0248661i
$274$	−1.16260	−	1.16260i	−0.0702353	−	0.0702353i
$275$	12.7275	+	4.40461i	0.767495	+	0.265608i
$276$		−	8.78570i		−	0.528837i
$277$	−6.41483	−	15.4868i	−0.385430	−	0.930510i	−0.990895	−	0.134638i	$-0.957013\pi$
$277$	−6.41483	−	15.4868i	−0.385430	−	0.930510i	0.605465	−	0.795872i	$-0.292987\pi$
$278$	−1.05719	−	0.437904i	−0.0634063	−	0.0262637i
$279$	0.135694	+	0.0562061i	0.00812376	+	0.00336497i
$280$	2.93247	+	1.11363i	0.175249	+	0.0665521i
$281$	5.54254	−	5.54254i	0.330640	−	0.330640i	−0.522189	−	0.852830i	$-0.674885\pi$
$281$	5.54254	−	5.54254i	0.330640	−	0.330640i	0.852830	+	0.522189i	$0.174885\pi$
$282$	−0.415372	+	1.00280i	−0.0247350	+	0.0597157i
$283$	−6.07963	−	2.51826i	−0.361396	−	0.149695i	0.194594	−	0.980884i	$-0.437661\pi$
$283$	−6.07963	−	2.51826i	−0.361396	−	0.149695i	−0.555991	+	0.831189i	$0.687661\pi$
$284$	21.8913	−	9.06767i	1.29901	−	0.538067i
$285$	5.74135	+	12.7719i	0.340088	+	0.756542i
$286$	−0.0448163	−	0.108196i	−0.00265004	−	0.00639777i
$287$	6.06800	−	6.06800i	0.358183	−	0.358183i
$288$		−	0.854527i		−	0.0503535i
$289$	−6.67925	−	15.6329i	−0.392897	−	0.919582i
$290$	3.26622	−	1.46826i	0.191799	−	0.0862194i
$291$	2.67194	+	2.67194i	0.156632	+	0.156632i
$292$	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	$0.529341\pi$
$294$	−1.87185	+	0.775344i	−0.109168	+	0.0452190i
$295$	−18.0875	+	0.538517i	−1.05310	+	0.0313537i
$296$	−5.20097	−	2.15431i	−0.302300	−	0.125217i
$297$	−10.3259	−	10.3259i	−0.599171	−	0.599171i
$298$	−2.04885	−	2.04885i	−0.118687	−	0.118687i
$299$	0.445057	+	0.184348i	0.0257383	+	0.0106611i
$300$	14.3265	−	6.95989i	0.827141	−	0.401829i
$301$	−14.9585	+	6.19602i	−0.862195	+	0.357133i
$302$	0.0342954			0.00197348
$303$	1.35292	−	0.560396i	0.0777229	−	0.0321939i
$304$	9.78495	+	9.78495i	0.561205	+	0.561205i
$305$	−6.36987	−	14.1701i	−0.364738	−	0.811376i
$306$	0.255499	+	0.168679i	0.0146059	+	0.00964273i
$307$			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
$309$	0.230933	+	0.557521i	0.0131373	+	0.0317163i
$310$	−0.112361	−	0.249952i	−0.00638167	−	0.0141963i
$311$	9.26536	−	3.83784i	0.525390	−	0.217624i	−0.104193	−	0.994557i	$-0.533226\pi$
$311$	9.26536	−	3.83784i	0.525390	−	0.217624i	0.629583	+	0.776933i	$0.283226\pi$
$312$	−0.260001	−	0.107696i	−0.0147196	−	0.00609708i
$313$	1.35503	−	3.27134i	0.0765910	−	0.184907i	−0.880946	−	0.473216i	$-0.843093\pi$
$313$	1.35503	−	3.27134i	0.0765910	−	0.184907i	0.957537	+	0.288309i	$0.0930930\pi$
$314$	1.70114	−	1.70114i	0.0960007	−	0.0960007i
$315$	−0.338896	+	0.892401i	−0.0190946	+	0.0502811i
$316$	−23.1149	−	9.57451i	−1.30032	−	0.538608i
$317$	11.2813	+	4.67288i	0.633623	+	0.262455i	0.676292	−	0.736634i	$-0.263586\pi$
$317$	11.2813	+	4.67288i	0.633623	+	0.262455i	−0.0426686	+	0.999089i	$0.513586\pi$
$318$	−1.93416	−	4.66948i	−0.108462	−	0.261851i
$319$		−	17.3302i		−	0.970307i
$320$	10.0454	−	10.6619i	0.561553	−	0.596017i
$321$	−7.72612	−	7.72612i	−0.431230	−	0.431230i
$322$		−	0.982469i		−	0.0547508i
$323$	−15.3897	+	3.14995i	−0.856308	+	0.175268i
$324$	−15.5355			−0.863084
$325$	0.0519564	+	0.871775i	0.00288203	+	0.0483574i
$326$	1.18261	+	2.85508i	0.0654988	+	0.158128i
$327$	−14.5294			−0.803475
$328$	2.24942	+	5.43059i	0.124204	+	0.299854i
$329$	1.45288	−	3.50755i	0.0800996	−	0.193378i
$330$	0.0733369	+	2.46322i	0.00403707	+	0.135596i
$331$	−13.0768	+	13.0768i	−0.718764	+	0.718764i	−0.968352	−	0.249588i	$-0.919705\pi$
$331$	−13.0768	+	13.0768i	−0.718764	+	0.718764i	0.249588	+	0.968352i	$0.419705\pi$
$332$	11.7521	+	11.7521i	0.644979	+	0.644979i
$333$	0.655594	−	1.58274i	0.0359263	−	0.0867338i
$334$	−0.398886	+	0.962996i	−0.0218261	+	0.0526928i
$335$	−18.9988	+	20.1648i	−1.03801	+	1.10172i
$336$		−	8.54356i		−	0.466090i
$337$	−17.0378	+	7.05727i	−0.928106	+	0.384434i	−0.794960	−	0.606662i	$-0.792508\pi$
$337$	−17.0378	+	7.05727i	−0.928106	+	0.384434i	−0.133146	+	0.991096i	$0.542508\pi$
$338$	−2.28279	+	2.28279i	−0.124167	+	0.124167i
$339$	−9.39059			−0.510027
$340$	4.10224	+	17.3906i	0.222475	+	0.943135i
$341$	−1.32622			−0.0718189
$342$	0.200043	−	0.200043i	0.0108171	−	0.0108171i
$343$	15.8023	−	6.54555i	0.853247	−	0.353426i
$344$		−	11.0903i		−	0.597951i
$345$	−7.37790	−	6.95128i	−0.397213	−	0.374244i
$346$	0.281477	−	0.679547i	0.0151323	−	0.0365327i
$347$	−1.94225	+	4.68901i	−0.104265	+	0.251719i	−0.967399	−	0.253256i	$-0.918498\pi$
$347$	−1.94225	+	4.68901i	−0.104265	+	0.251719i	0.863134	+	0.504975i	$0.168498\pi$
$348$	−14.4922	−	14.4922i	−0.776865	−	0.776865i
$349$	−17.2978	+	17.2978i	−0.925928	+	0.925928i	−0.997440	−	0.0715119i	$-0.977218\pi$
$349$	−17.2978	+	17.2978i	−0.925928	+	0.925928i	0.0715119	+	0.997440i	$0.477218\pi$
$350$	1.60207	−	0.778296i	0.0856345	−	0.0416017i
$351$	0.362371	−	0.874840i	0.0193419	−	0.0466955i
$352$	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	$0.345486\pi$
$354$	−1.26707	−	3.05899i	−0.0673442	−	0.162583i
$355$	9.70578	−	25.5579i	0.515130	−	1.35647i
$356$	22.2695			1.18028
$357$	8.09381	+	5.34349i	0.428370	+	0.282807i
$358$			5.79391i			0.306218i
$359$	−1.42687	−	1.42687i	−0.0753076	−	0.0753076i	0.668450	−	0.743757i	$-0.266958\pi$
$359$	−1.42687	−	1.42687i	−0.0753076	−	0.0753076i	−0.743757	+	0.668450i	$0.766958\pi$
$360$	−0.475904	−	0.448385i	−0.0250823	−	0.0236320i
$361$		−	4.48433i		−	0.236017i
$362$	−1.08786	−	2.62634i	−0.0571769	−	0.138037i
$363$	−5.68619	−	2.35530i	−0.298447	−	0.123621i
$364$	0.447557	+	0.185384i	0.0234584	+	0.00971677i
$365$	12.4346	−	32.7436i	0.650858	−	1.71388i
$366$	2.01008	−	2.01008i	0.105069	−	0.105069i
$367$	−12.4008	+	29.9381i	−0.647315	+	1.56276i	0.169294	+	0.985566i	$0.445851\pi$
$367$	−12.4008	+	29.9381i	−0.647315	+	1.56276i	−0.816609	+	0.577191i	$0.804149\pi$
$368$	−9.25478	−	3.83345i	−0.482439	−	0.199833i
$369$	−1.65262	+	0.684538i	−0.0860320	+	0.0356356i
$370$	−2.91546	+	1.31059i	−0.151568	+	0.0681343i
$371$	6.76525	+	16.3328i	0.351234	+	0.847955i
$372$	−1.10904	+	1.10904i	−0.0575009	+	0.0575009i
$373$		−	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
$375$	5.49054	−	17.5375i	0.283530	−	0.905635i
$376$	1.83884	+	1.83884i	0.0948311	+	0.0948311i
$377$	1.03822	−	0.430044i	0.0534710	−	0.0221484i
$378$	−1.93122			−0.0993313
$379$	15.3385	−	6.35343i	0.787887	−	0.326354i	0.0477935	−	0.998857i	$-0.484781\pi$
$379$	15.3385	−	6.35343i	0.787887	−	0.326354i	0.740094	+	0.672504i	$0.234781\pi$
$380$	16.5034	−	0.491353i	0.846607	−	0.0252059i
$381$	−24.8237	−	10.2823i	−1.27176	−	0.526779i
$382$	0.542471	+	0.542471i	0.0277552	+	0.0277552i
$383$	16.4274	+	16.4274i	0.839401	+	0.839401i	0.988780	−	0.149379i	$-0.0477274\pi$
$383$	16.4274	+	16.4274i	0.839401	+	0.839401i	−0.149379	+	0.988780i	$0.547727\pi$
$384$	11.1764	+	4.62944i	0.570346	+	0.236245i
$385$	−0.256516	−	8.61577i	−0.0130732	−	0.439100i
$386$	−3.67622	+	1.52274i	−0.187115	+	0.0775055i
$387$	3.37498			0.171560
$388$	4.11624	−	1.70500i	0.208971	−	0.0865584i
$389$	25.9259	+	25.9259i	1.31450	+	1.31450i	0.918064	+	0.396433i	$0.129752\pi$
$389$	25.9259	+	25.9259i	1.31450	+	1.31450i	0.396433	+	0.918064i	$0.370248\pi$
$390$	−0.145747	+	0.0655174i	−0.00738016	+	0.00331760i
$391$	9.41996	−	6.36999i	0.476388	−	0.322144i
$392$			4.85419i			0.245174i
$393$	11.2029	−	11.2029i	0.565112	−	0.565112i
$394$	−1.01673	−	2.45461i	−0.0512222	−	0.123661i
$395$	−26.3289	+	11.8356i	−1.32475	+	0.595516i
$396$	−1.43872	+	0.595938i	−0.0722984	+	0.0299470i
$397$	−9.06522	−	3.75494i	−0.454970	−	0.188455i	0.143416	−	0.989662i	$-0.454191\pi$
$397$	−9.06522	−	3.75494i	−0.454970	−	0.188455i	−0.598386	+	0.801208i	$0.704191\pi$
$398$	1.50881	−	3.64259i	0.0756299	−	0.182587i
$399$	6.33706	−	6.33706i	0.317250	−	0.317250i
$400$	−1.08041	−	18.1282i	−0.0540207	−	0.906411i
$401$	19.8539	+	8.22376i	0.991457	+	0.410675i	0.818657	−	0.574282i	$-0.194719\pi$
$401$	19.8539	+	8.22376i	0.991457	+	0.410675i	0.172799	+	0.984957i	$0.444719\pi$
$402$	−4.68344	−	1.93994i	−0.233589	−	0.0967556i
$403$	−0.0329097	−	0.0794512i	−0.00163935	−	0.00395774i
$404$		−	1.72663i		−	0.0859032i
$405$	−12.2918	+	13.0461i	−0.610782	+	0.648267i
$406$	−1.62061	−	1.62061i	−0.0804293	−	0.0804293i
$407$			15.4692i			0.766779i
$408$	−5.50311	+	3.72133i	−0.272445	+	0.184233i
$409$	−31.2735			−1.54638			−0.773189	−	0.634176i	$-0.781339\pi$
$409$	−31.2735			−1.54638			−0.773189	+	0.634176i	$0.781339\pi$
$410$	3.12020	+	1.18492i	0.154096	+	0.0585190i
$411$	4.15476	+	10.0305i	0.204939	+	0.494767i
$412$	0.711526			0.0350544
$413$	4.43193	+	10.6996i	0.218081	+	0.526494i
$414$	−0.0783710	+	0.189204i	−0.00385173	+	0.00929889i
$415$	19.1673	−	0.570663i	0.940883	−	0.0280128i
$416$	−0.353795	+	0.353795i	−0.0173462	+	0.0173462i
$417$	5.34300	+	5.34300i	0.261648	+	0.261648i
$418$	−0.977576	+	2.36008i	−0.0478148	+	0.115435i
$419$	−7.78615	+	18.7974i	−0.380378	+	0.918314i	0.611514	+	0.791234i	$0.290561\pi$
$419$	−7.78615	+	18.7974i	−0.380378	+	0.918314i	−0.991892	+	0.127081i	$0.959439\pi$
$420$	−7.41935	−	6.99033i	−0.362027	−	0.341093i
$421$		−	1.80862i		−	0.0881467i	−0.999028	−	0.0440733i	$-0.985966\pi$
$421$		−	1.80862i		−	0.0881467i	0.999028	−	0.0440733i	$-0.0140335\pi$
$422$	−1.13136	+	0.468626i	−0.0550740	+	0.0228124i
$423$	−0.559591	+	0.559591i	−0.0272083	+	0.0272083i
$424$	−12.1092			−0.588075
$425$	17.8496	+	10.3146i	0.865835	+	0.500330i
$426$	5.00228			0.242361
$427$	−7.03079	+	7.03079i	−0.340244	+	0.340244i
$428$	−11.9024	+	4.93016i	−0.575327	+	0.238308i
$429$			0.773317i			0.0373361i
$430$	−4.58335	−	4.31833i	−0.221029	−	0.208248i
$431$	6.37695	−	15.3953i	0.307167	−	0.741566i	−0.692628	−	0.721295i	$-0.743547\pi$
$431$	6.37695	−	15.3953i	0.307167	−	0.741566i	0.999795	−	0.0202708i	$-0.00645283\pi$
$432$	−7.53536	+	18.1920i	−0.362545	+	0.875261i
$433$	11.5388	+	11.5388i	0.554519	+	0.554519i	0.927742	−	0.373222i	$-0.121747\pi$
$433$	11.5388	+	11.5388i	0.554519	+	0.554519i	−0.373222	+	0.927742i	$0.621747\pi$
$434$	−0.124019	+	0.124019i	−0.00595311	+	0.00595311i
$435$	−23.6363	+	0.703720i	−1.13328	+	0.0337408i
$436$	−6.55588	+	15.8273i	−0.313970	+	0.757990i
$437$	−4.02118	−	9.70800i	−0.192359	−	0.464396i
$438$	6.40870			0.306220
$439$	9.19489	+	22.1984i	0.438848	+	1.05947i	0.976347	+	0.216209i	$0.0693692\pi$
$439$	9.19489	+	22.1984i	0.438848	+	1.05947i	−0.537499	+	0.843264i	$0.680631\pi$
$440$	5.51955	+	2.09609i	0.263134	+	0.0999271i
$441$	−1.47721			−0.0703434
$442$	−0.0359457	−	0.175620i	−0.00170976	−	0.00835340i
$443$		−	21.2757i		−	1.01084i	−0.862874	−	0.505419i	$-0.831338\pi$
$443$		−	21.2757i		−	1.01084i	0.862874	−	0.505419i	$-0.168662\pi$
$444$	12.9359	+	12.9359i	0.613912	+	0.613912i
$445$	17.6197	−	18.7010i	0.835253	−	0.886515i
$446$		−	2.50011i		−	0.118384i
$447$	7.32193	+	17.6767i	0.346316	+	0.836080i
$448$	−8.66156	−	3.58773i	−0.409220	−	0.169504i
$449$	26.9783	+	11.1748i	1.27318	+	0.527370i	0.913931	−	0.405870i	$-0.133031\pi$
$449$	26.9783	+	11.1748i	1.27318	+	0.527370i	0.359253	+	0.933240i	$0.383031\pi$
$450$	−0.370613	+	0.0220879i	−0.0174709	+	0.00104124i
$451$	11.4213	−	11.4213i	0.537807	−	0.537807i
$452$	−4.23718	+	10.2295i	−0.199300	+	0.481153i
$453$	−0.209224	−	0.0866636i	−0.00983022	−	0.00407181i
$454$	−1.02966	+	0.426500i	−0.0483244	+	0.0200166i
$455$	0.509787	−	0.229165i	0.0238992	−	0.0107434i
$456$	2.34916	+	5.67138i	0.110010	+	0.265587i
$457$	0.734055	−	0.734055i	0.0343376	−	0.0343376i	−0.689729	−	0.724067i	$-0.742271\pi$
$457$	0.734055	−	0.734055i	0.0343376	−	0.0343376i	0.724067	+	0.689729i	$0.242271\pi$
$458$			0.298195i			0.0139337i
$459$	−12.5214	−	18.5167i	−0.584448	−	0.864283i
$460$	−10.9013	+	4.90045i	−0.508274	+	0.228485i
$461$	0.0496372	+	0.0496372i	0.00231183	+	0.00231183i	0.708262	−	0.705950i	$-0.249480\pi$
$461$	0.0496372	+	0.0496372i	0.00231183	+	0.00231183i	−0.705950	+	0.708262i	$0.749480\pi$
$462$	1.45711	−	0.603554i	0.0677908	−	0.0280799i
$463$	40.0649			1.86197			0.930987	−	0.365051i	$-0.118949\pi$
$463$	40.0649			1.86197			0.930987	+	0.365051i	$0.118949\pi$
$464$	−21.5894	+	8.94260i	−1.00226	+	0.415150i
$465$	0.0538532	+	1.80880i	0.00249738	+	0.0838812i
$466$	5.85376	+	2.42471i	0.271170	+	0.112322i
$467$	16.0563	+	16.0563i	0.742997	+	0.742997i	0.973154	−	0.230156i	$-0.0739238\pi$
$467$	16.0563	+	16.0563i	0.742997	+	0.742997i	−0.230156	+	0.973154i	$0.573924\pi$
$468$	−0.0714028	−	0.0714028i	−0.00330059	−	0.00330059i
$469$	16.3816	+	6.78547i	0.756431	+	0.313324i
$470$	1.47595	−	0.0439433i	0.0680806	−	0.00202695i
$471$	−14.6768	+	6.07932i	−0.676270	+	0.280120i
$472$	−7.93276			−0.365135
$473$	−28.1552	+	11.6622i	−1.29458	+	0.536231i
$474$	−3.73486	−	3.73486i	−0.171548	−	0.171548i
$475$	12.6449	−	14.2477i	0.580190	−	0.653730i
$476$	9.47288	−	6.40578i	0.434189	−	0.293608i
$477$		−	3.68503i		−	0.168726i
$478$	1.09375	−	1.09375i	0.0500270	−	0.0500270i
$479$	−8.90144	−	21.4900i	−0.406717	−	0.981902i	−0.985995	−	0.166772i	$-0.946665\pi$
$479$	−8.90144	−	21.4900i	−0.406717	−	0.981902i	0.579278	−	0.815130i	$-0.303335\pi$
$480$	9.60284	−	4.31676i	0.438308	−	0.197032i
$481$	−0.926726	+	0.383863i	−0.0422551	+	0.0175026i
$482$	6.16422	+	2.55331i	0.280773	+	0.116300i
$483$	−2.48267	+	5.99370i	−0.112965	+	0.272723i
$484$	−5.13139	+	5.13139i	−0.233245	+	0.233245i
$485$	1.82499	−	4.80567i	0.0828685	−	0.218214i
$486$	0.710195	+	0.294172i	0.0322151	+	0.0133439i
$487$	−15.6248	−	6.47199i	−0.708026	−	0.293274i	−0.000538564	−	1.00000i	$-0.500171\pi$
$487$	−15.6248	−	6.47199i	−0.708026	−	0.293274i	−0.707488	+	0.706726i	$0.750171\pi$
$488$	−2.60633	−	6.29224i	−0.117983	−	0.284837i
$489$		−	20.4063i		−	0.922803i
$490$	2.00611	+	1.89011i	0.0906270	+	0.0853866i
$491$	−14.8915	−	14.8915i	−0.672045	−	0.672045i	0.286142	−	0.958187i	$-0.407627\pi$
$491$	−14.8915	−	14.8915i	−0.672045	−	0.672045i	−0.958187	+	0.286142i	$0.907627\pi$
$492$		−	19.1018i		−	0.861177i
$493$	5.03100	−	26.0459i	0.226585	−	1.17305i
$494$	−0.165646			−0.00745275
$495$	−0.637875	+	1.67969i	−0.0286704	+	0.0754965i
$496$	0.684345	+	1.65216i	0.0307280	+	0.0741840i
$497$	−17.4968			−0.784840
$498$	1.34271	+	3.24159i	0.0601682	+	0.145259i
$499$	8.62028	−	20.8112i	0.385897	−	0.931637i	−0.604903	−	0.796299i	$-0.706788\pi$
$499$	8.62028	−	20.8112i	0.385897	−	0.931637i	0.990800	−	0.135338i	$-0.0432120\pi$
$500$	−16.6268	−	13.8942i	−0.743572	−	0.621369i
$501$	4.86693	−	4.86693i	0.217438	−	0.217438i
$502$	1.86664	+	1.86664i	0.0833122	+	0.0833122i
$503$	11.1063	−	26.8129i	0.495204	−	1.19553i	−0.456835	−	0.889551i	$-0.651017\pi$
$503$	11.1063	−	26.8129i	0.495204	−	1.19553i	0.952039	−	0.305977i	$-0.0989829\pi$
$504$	−0.160142	+	0.386618i	−0.00713330	+	0.0172213i
$505$	−1.44996	−	1.36612i	−0.0645224	−	0.0607915i
$506$		−	1.84922i		−	0.0822077i
$507$	19.6950	−	8.15794i	0.874686	−	0.362307i
$508$	−22.4017	+	22.4017i	−0.993915	+	0.993915i
$509$	−4.38401			−0.194318			−0.0971589	−	0.995269i	$-0.530976\pi$
$509$	−4.38401			−0.194318			−0.0971589	+	0.995269i	$0.530976\pi$
$510$	−0.604857	+	3.72330i	−0.0267835	+	0.164871i
$511$	−22.4162			−0.991633
$512$	12.3921	−	12.3921i	0.547660	−	0.547660i
$513$	−19.0828	+	7.90437i	−0.842528	+	0.348987i
$514$			0.383393i			0.0169107i
$515$	0.562962	−	0.597513i	0.0248071	−	0.0263295i
$516$	−13.7920	+	33.2969i	−0.607160	+	1.46581i
$517$	2.73462	−	6.60196i	0.120269	−	0.290354i
$518$	1.44657	+	1.44657i	0.0635587	+	0.0635587i
$519$	−3.43439	+	3.43439i	−0.150753	+	0.150753i
$520$	0.0113934	+	0.382678i	0.000499634	+	0.0167816i
$521$	−1.22242	+	2.95118i	−0.0535551	+	0.129294i	−0.948393	−	0.317099i	$-0.897291\pi$
$521$	−1.22242	+	2.95118i	−0.0535551	+	0.129294i	0.894837	+	0.446392i	$0.147291\pi$
$522$	0.182822	+	0.441372i	0.00800192	+	0.0193183i
$523$	−34.0520			−1.48899			−0.744494	−	0.667629i	$-0.767309\pi$
$523$	−34.0520			−1.48899			−0.744494	+	0.667629i	$0.767309\pi$
$524$	−7.14875	−	17.2586i	−0.312294	−	0.753945i
$525$	−11.7404	+	0.699712i	−0.512395	+	0.0305379i
$526$	0.106148			0.00462825
$527$	−1.99320	−	0.385004i	−0.0868251	−	0.0167710i
$528$		−	16.0808i		−	0.699828i
$529$	−10.8848	−	10.8848i	−0.473251	−	0.473251i
$530$	−4.71505	+	5.00443i	−0.204809	+	0.217378i
$531$		−	2.41407i		−	0.104762i
$532$	−4.04377	−	9.76254i	−0.175320	−	0.423260i
$533$	0.967641	+	0.400810i	0.0419132	+	0.0173610i
$534$	4.34347	+	1.79913i	0.187961	+	0.0778558i
$535$	−5.27710	+	13.8960i	−0.228149	+	0.600776i
$536$	−8.58809	+	8.58809i	−0.370949	+	0.370949i
$537$	14.6411	−	35.3467i	0.631808	−	1.52532i
$538$	−3.93359	−	1.62934i	−0.169589	−	0.0702460i
$539$	12.3234	−	5.10452i	0.530806	−	0.219867i
$540$	9.63273	+	21.4284i	0.414527	+	0.922133i
$541$	−10.3587	−	25.0081i	−0.445355	−	1.07518i	−0.974042	−	0.226366i	$-0.927315\pi$
$541$	−10.3587	−	25.0081i	−0.445355	−	1.07518i	0.528687	−	0.848817i	$-0.322685\pi$
$542$	2.82859	−	2.82859i	0.121498	−	0.121498i
$543$			18.7714i			0.805557i
$544$	2.36836	+	11.5711i	0.101543	+	0.496108i
$545$	8.10412	+	18.0280i	0.347143	+	0.772234i
$546$	0.0723153	+	0.0723153i	0.00309481	+	0.00309481i
$547$	−12.5020	+	5.17849i	−0.534546	+	0.221416i	−0.633593	−	0.773667i	$-0.718421\pi$
$547$	−12.5020	+	5.17849i	−0.534546	+	0.221416i	0.0990470	+	0.995083i	$0.468421\pi$
$548$	12.8012			0.546841
$549$	1.91484	−	0.793151i	0.0817232	−	0.0338509i
$550$	3.01545	−	1.46492i	0.128579	−	0.0624644i
$551$	−22.6466	−	9.38053i	−0.964778	−	0.399624i
$552$	−3.14221	−	3.14221i	−0.133742	−	0.133742i
$553$	13.0637	+	13.0637i	0.555524	+	0.555524i
$554$	−3.85494	−	1.59677i	−0.163781	−	0.0678402i
$555$	21.0981	−	0.628149i	0.895563	−	0.0266634i
$556$	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	$0.276212\pi$
$558$	0.0337766	−	0.0139907i	0.00142988	−	0.000592275i
$559$	−1.39732	−	1.39732i	−0.0591005	−	0.0591005i
$560$	−10.6008	+	4.76539i	−0.447967	+	0.201375i
$561$	15.2343	+	10.0576i	0.643192	+	0.424632i
$562$		−	1.95111i		−	0.0823024i
$563$	5.73355	−	5.73355i	0.241640	−	0.241640i	−0.575888	−	0.817529i	$-0.695344\pi$
$563$	5.73355	−	5.73355i	0.241640	−	0.241640i	0.817529	+	0.575888i	$0.195344\pi$
$564$	−3.23402	−	7.80762i	−0.136177	−	0.328760i
$565$	5.23784	+	11.6518i	0.220358	+	0.490196i
$566$	−1.51333	+	0.626842i	−0.0636101	+	0.0263481i
$567$	10.5985	+	4.39004i	0.445095	+	0.184364i
$568$	4.58638	−	11.0725i	0.192440	−	0.464592i
$569$	−2.71124	+	2.71124i	−0.113661	+	0.113661i	−0.761650	−	0.647989i	$-0.775610\pi$
$569$	−2.71124	+	2.71124i	−0.113661	+	0.113661i	0.647989	+	0.761650i	$0.275610\pi$
$570$	3.25855	+	1.23746i	0.136486	+	0.0518315i
$571$	6.06730	+	2.51316i	0.253909	+	0.105172i	0.506007	−	0.862529i	$-0.331121\pi$
$571$	6.06730	+	2.51316i	0.253909	+	0.105172i	−0.252099	+	0.967701i	$0.581121\pi$
$572$	0.842398	+	0.348933i	0.0352224	+	0.0145896i
$573$	−1.93862	−	4.68023i	−0.0809869	−	0.195520i
$574$		−	2.13608i		−	0.0891583i
$575$	−4.50991	+	13.0317i	−0.188076	+	0.543461i
$576$	1.38186	+	1.38186i	0.0575773	+	0.0575773i
$577$			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
$579$	26.2753			1.09196
$580$	−9.89850	+	26.0653i	−0.411013	+	1.08230i
$581$	−4.69649	−	11.3383i	−0.194843	−	0.470393i
$582$	0.940585			0.0389885
$583$	12.7337	+	30.7418i	0.527374	+	1.27319i
$584$	5.87587	−	14.1856i	0.243145	−	0.587004i
$585$	−0.116456	+	0.00346721i	−0.00481484	+	0.000143351i
$586$	−0.554640	+	0.554640i	−0.0229120	+	0.0229120i
$587$	−26.0085	−	26.0085i	−1.07348	−	1.07348i	−0.997077	−	0.0764077i	$-0.975655\pi$
$587$	−26.0085	−	26.0085i	−1.07348	−	1.07348i	−0.0764077	−	0.997077i	$-0.524345\pi$
$588$	6.03671	−	14.5739i	0.248950	−	0.601017i
$589$	−0.717858	+	1.73306i	−0.0295788	+	0.0714096i
$590$	−3.08884	+	3.27841i	−0.127165	+	0.134970i
$591$			17.5440i			0.721662i
$592$	19.2709	−	7.98227i	0.792030	−	0.328069i
$593$	−19.1275	+	19.1275i	−0.785474	+	0.785474i	−0.980749	−	0.195275i	$-0.937440\pi$
$593$	−19.1275	+	19.1275i	−0.785474	+	0.785474i	0.195275	+	0.980749i	$0.437440\pi$
$594$	−3.63497			−0.149145
$595$	2.11565	−	13.0232i	0.0867332	−	0.533901i
$596$	22.5596			0.924076
$597$	−18.4095	+	18.4095i	−0.753450	+	0.753450i
$598$	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	$-0.0808344\pi$
$600$	2.63468	−	7.61310i	0.107560	−	0.310804i
$601$	−3.08883	+	7.45710i	−0.125996	+	0.304181i	−0.974273	−	0.225372i	$-0.927640\pi$
$601$	−3.08883	+	7.45710i	−0.125996	+	0.304181i	0.848277	+	0.529553i	$0.177640\pi$
$602$	−1.54230	+	3.72345i	−0.0628596	+	0.151757i
$603$	−2.61350	−	2.61350i	−0.106430	−	0.106430i
$604$	−0.188811	+	0.188811i	−0.00768260	+	0.00768260i
$605$	0.249173	+	8.36913i	0.0101303	+	0.340254i
$606$	0.139493	−	0.336765i	0.00566651	−	0.0136802i
$607$	−9.22388	−	22.2684i	−0.374386	−	0.903847i	−0.992996	−	0.118149i	$-0.962304\pi$
$607$	−9.22388	−	22.2684i	−0.374386	−	0.903847i	0.618610	−	0.785698i	$-0.287696\pi$
$608$	10.9139			0.442619
$609$	5.79153	+	13.9820i	0.234685	+	0.566579i
$610$	−3.61527	−	1.37293i	−0.146378	−	0.0555882i
$611$	0.463369			0.0187459
$612$	−2.33528	+	0.477981i	−0.0943980	+	0.0193212i
$613$			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
$615$	−16.0410	−	15.1134i	−0.646836	−	0.609433i
$616$		−	3.77867i		−	0.152247i
$617$	−9.87155	−	23.8320i	−0.397414	−	0.959442i	−0.988277	−	0.152670i	$-0.951213\pi$
$617$	−9.87155	−	23.8320i	−0.397414	−	0.959442i	0.590863	−	0.806772i	$-0.298787\pi$
$618$	0.138777	+	0.0574834i	0.00558244	+	0.00231232i
$619$	−3.48155	−	1.44210i	−0.139935	−	0.0579630i	0.311617	−	0.950208i	$-0.399129\pi$
$619$	−3.48155	−	1.44210i	−0.139935	−	0.0579630i	−0.451552	+	0.892245i	$0.649129\pi$
$620$	1.99468	+	0.757496i	0.0801085	+	0.0304218i
$621$	10.5728	−	10.5728i	0.424272	−	0.424272i
$622$	0.955308	−	2.30632i	0.0383044	−	0.0924749i
$623$	−15.1925	−	6.29293i	−0.608673	−	0.252121i
$624$	0.963369	−	0.399041i	0.0385656	−	0.0159744i
$625$	−24.8230	+	2.96938i	−0.992921	+	0.118775i
$626$	−0.337293	−	0.814297i	−0.0134809	−	0.0325459i
$627$	11.9277	−	11.9277i	0.476347	−	0.476347i
$628$			18.7309i			0.747446i
$629$	−4.49073	+	23.2489i	−0.179057	+	0.926994i
$630$	0.0974235	+	0.216723i	0.00388145	+	0.00863445i
$631$	13.6572	+	13.6572i	0.543685	+	0.543685i	0.924607	−	0.380922i	$-0.124393\pi$
$631$	13.6572	+	13.6572i	0.543685	+	0.543685i	−0.380922	+	0.924607i	$0.624393\pi$
$632$	−11.6914	+	4.84274i	−0.465059	+	0.192634i
$633$	8.08627			0.321400
$634$	2.80813	−	1.16317i	0.111525	−	0.0461952i
$635$	1.08779	+	36.5364i	0.0431677	+	1.44990i
$636$	36.3558	+	15.0591i	1.44160	+	0.597131i
$637$	0.611602	+	0.611602i	0.0242326	+	0.0242326i
$638$	−3.05033	−	3.05033i	−0.120764	−	0.120764i
$639$	3.36955	+	1.39571i	0.133297	+	0.0552136i
$640$	−0.489760	−	16.4499i	−0.0193594	−	0.650239i
$641$	19.0839	−	7.90483i	0.753770	−	0.312222i	0.0274914	−	0.999622i	$-0.491248\pi$
$641$	19.0839	−	7.90483i	0.753770	−	0.312222i	0.726279	+	0.687400i	$0.241248\pi$
$642$	−2.71978			−0.107341
$643$	26.8106	−	11.1053i	1.05731	−	0.437951i	0.214813	−	0.976655i	$-0.431086\pi$
$643$	26.8106	−	11.1053i	1.05731	−	0.437951i	0.842495	+	0.538704i	$0.181086\pi$
$644$	5.40890	+	5.40890i	0.213141	+	0.213141i
$645$	17.0492	+	37.9266i	0.671310	+	1.49336i
$646$	−2.15435	+	3.26321i	−0.0847618	+	0.128389i
$647$		−	41.2848i		−	1.62307i	−0.584302	−	0.811536i	$-0.698632\pi$
$647$		−	41.2848i		−	1.62307i	0.584302	−	0.811536i	$-0.301368\pi$
$648$	−5.55629	+	5.55629i	−0.218272	+	0.218272i
$649$	8.34184	+	20.1390i	0.327446	+	0.790524i
$650$	0.162588	+	0.144298i	0.00637721	+	0.00565983i
$651$	1.06999	−	0.443205i	0.0419362	−	0.0173706i
$652$	−22.2292	−	9.20763i	−0.870562	−	0.360598i
$653$	9.39804	−	22.6889i	0.367774	−	0.887884i	−0.626341	−	0.779549i	$-0.715448\pi$
$653$	9.39804	−	22.6889i	0.367774	−	0.887884i	0.994114	−	0.108335i	$-0.0345519\pi$
$654$	−2.55734	+	2.55734i	−0.0999999	+	0.0999999i
$655$	−20.1492	−	7.65182i	−0.787296	−	0.298981i
$656$	−20.1217	−	8.33468i	−0.785621	−	0.325415i
$657$	4.31692	+	1.78813i	0.168419	+	0.0697614i
$658$	−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	$0.887949\pi$
$660$	−13.9648	−	13.1573i	−0.543579	−	0.512147i
$661$	10.0305	+	10.0305i	0.390141	+	0.390141i	0.874738	−	0.484597i	$-0.161034\pi$
$661$	10.0305	+	10.0305i	0.390141	+	0.390141i	−0.484597	+	0.874738i	$0.661034\pi$
$662$			4.60333i			0.178914i
$663$	−0.224495	+	1.16223i	−0.00871867	+	0.0451373i
$664$	8.40629			0.326227
$665$	−11.3977	−	4.32835i	−0.441982	−	0.167846i
$666$	−0.163189	−	0.393974i	−0.00632346	−	0.0152662i
$667$	17.7445			0.687072
$668$	−3.10566	−	7.49773i	−0.120162	−	0.290096i
$669$	−6.31771	+	15.2523i	−0.244257	+	0.589688i
$670$	0.205231	+	6.89325i	0.00792878	+	0.266309i
$671$	−13.2335	+	13.2335i	−0.510872	+	0.510872i
$672$	−4.76466	−	4.76466i	−0.183801	−	0.183801i
$673$	0.124393	−	0.300312i	0.00479501	−	0.0115762i	−0.921464	−	0.388464i	$-0.873006\pi$
$673$	0.124393	−	0.300312i	0.00479501	−	0.0115762i	0.926259	+	0.376888i	$0.123006\pi$
$674$	−1.75668	+	4.24101i	−0.0676650	+	0.163358i
$675$	25.6162	+	8.86506i	0.985970	+	0.341216i
$676$		−	25.1354i		−	0.966746i
$677$	15.9805	−	6.61933i	0.614180	−	0.254402i	−0.0538347	−	0.998550i	$-0.517144\pi$
$677$	15.9805	−	6.61933i	0.614180	−	0.254402i	0.668014	+	0.744148i	$0.267144\pi$
$678$	−1.65286	+	1.65286i	−0.0634775	+	0.0634775i
$679$	−3.28995			−0.126257
$680$	7.68692	+	4.75258i	0.294780	+	0.182253i
$681$	7.35936			0.282011
$682$	−0.233431	+	0.233431i	−0.00893852	+	0.00893852i
$683$	−31.8570	+	13.1956i	−1.21898	+	0.504916i	−0.897084	−	0.441860i	$-0.854319\pi$
$683$	−31.8570	+	13.1956i	−1.21898	+	0.504916i	−0.321891	+	0.946777i	$0.604319\pi$
$684$			2.20264i			0.0842202i
$685$	10.1284	−	10.7500i	0.386985	−	0.410736i
$686$	1.62931	−	3.93350i	0.0622072	−	0.150182i
$687$	0.753531	−	1.81919i	0.0287490	−	0.0694062i
$688$	29.0568	+	29.0568i	1.10778	+	1.10778i
$689$	−1.52569	+	1.52569i	−0.0581243	+	0.0581243i
$690$	−2.52211	+	0.0750902i	−0.0960149	+	0.00285863i
$691$	16.1221	−	38.9223i	0.613315	−	1.48067i	−0.246022	−	0.969264i	$-0.579124\pi$
$691$	16.1221	−	38.9223i	0.613315	−	1.48067i	0.859337	−	0.511409i	$-0.170876\pi$
$692$	2.19154	+	5.29084i	0.0833098	+	0.201128i
$693$	1.14991			0.0436815
$694$	0.483462	+	1.16718i	0.0183520	+	0.0443056i
$695$	3.64938	−	9.60978i	0.138429	−	0.364520i
$696$	−10.3663			−0.392934
$697$	20.4808	−	13.8496i	0.775767	−	0.524591i
$698$			6.08922i			0.230481i
$699$	−29.5846	−	29.5846i	−1.11899	−	1.11899i
$700$	−4.53525	+	13.1049i	−0.171416	+	0.495320i
$701$			29.6266i			1.11898i	0.828836	+	0.559491i	$0.189003\pi$
$701$			29.6266i			1.11898i	−0.828836	+	0.559491i	$0.810997\pi$
$702$	−0.0902007	−	0.217764i	−0.00340441	−	0.00821897i
$703$	20.2146	+	8.37317i	0.762409	+	0.315800i
$704$	−16.3029	−	6.75289i	−0.614439	−	0.254509i
$705$	−9.11531	−	3.46161i	−0.343303	−	0.130372i
$706$	3.08593	−	3.08593i	0.116140	−	0.116140i
$707$	−0.487914	+	1.17793i	−0.0183499	+	0.0443005i
$708$	23.8168	+	9.86523i	0.895089	+	0.370758i
$709$	15.0352	−	6.22777i	0.564657	−	0.233889i	−0.0820483	−	0.996628i	$-0.526146\pi$
$709$	15.0352	−	6.22777i	0.564657	−	0.233889i	0.646706	+	0.762740i	$0.276146\pi$
$710$	−2.79015	−	6.20682i	−0.104713	−	0.232938i
$711$	−1.47373	−	3.55789i	−0.0552691	−	0.133431i
$712$	7.96469	−	7.96469i	0.298489	−	0.298489i
$713$		−	1.35793i		−	0.0508547i
$714$	2.36512	−	0.484090i	0.0885125	−	0.0181166i
$715$	0.959530	−	0.431337i	0.0358844	−	0.0161311i
$716$	−31.8979	−	31.8979i	−1.19208	−	1.19208i
$717$	−9.43647	+	3.90871i	−0.352411	+	0.145974i
$718$	−0.502294			−0.0187454
$719$	−29.0292	+	12.0243i	−1.08261	+	0.448430i	−0.851423	−	0.524480i	$-0.824260\pi$
$719$	−29.0292	+	12.0243i	−1.08261	+	0.448430i	−0.231184	+	0.972910i	$0.574260\pi$
$720$	2.42165	−	0.0720992i	0.0902495	−	0.00268698i
$721$	−0.485411	−	0.201064i	−0.0180776	−	0.00748800i
$722$	−0.789295	−	0.789295i	−0.0293745	−	0.0293745i
$723$	−31.1537	−	31.1537i	−1.15862	−	1.15862i
$724$	20.4483	+	8.46994i	0.759953	+	0.314783i
$725$	14.0569	+	28.9354i	0.522062	+	1.07463i
$726$	−1.41540	+	0.586276i	−0.0525303	+	0.0217588i
$727$	−21.6544			−0.803118			−0.401559	−	0.915833i	$-0.631532\pi$
$727$	−21.6544			−0.803118			−0.401559	+	0.915833i	$0.631532\pi$
$728$	0.226372	−	0.0937664i	0.00838991	−	0.00347521i
$729$	−20.5940	−	20.5940i	−0.762740	−	0.762740i
$730$	−3.57462	−	7.95190i	−0.132303	−	0.294313i
$731$	−45.7004	+	9.35389i	−1.69029	+	0.345966i
$732$			22.1327i			0.818047i
$733$	−22.2422	+	22.2422i	−0.821534	+	0.821534i	−0.986328	−	0.164794i	$-0.947304\pi$
$733$	−22.2422	+	22.2422i	−0.821534	+	0.821534i	0.164794	+	0.986328i	$0.447304\pi$
$734$	3.08678	+	7.45215i	0.113935	+	0.275064i
$735$	−7.46235	−	16.6003i	−0.275253	−	0.612312i
$736$	−7.29917	+	3.02342i	−0.269051	+	0.111445i
$737$	30.8337	+	12.7717i	1.13577	+	0.470452i
$738$	−0.170394	+	0.411368i	−0.00627229	+	0.0151426i
$739$	−9.68961	+	9.68961i	−0.356438	+	0.356438i	−0.862498	−	0.506060i	$-0.831101\pi$
$739$	−9.68961	+	9.68961i	−0.356438	+	0.356438i	0.506060	+	0.862498i	$0.331101\pi$
$740$	8.83552	−	23.2662i	0.324800	−	0.855283i
$741$	1.01055	+	0.418582i	0.0371233	+	0.0153770i
$742$	4.06552	+	1.68400i	0.149250	+	0.0618214i
$743$	−6.20770	−	14.9867i	−0.227738	−	0.549809i	0.768163	−	0.640254i	$-0.221171\pi$
$743$	−6.20770	−	14.9867i	−0.227738	−	0.549809i	−0.995901	+	0.0904453i	$0.971171\pi$
$744$			0.793297i			0.0290837i
$745$	17.8492	−	18.9447i	0.653945	−	0.694079i
$746$	−3.62775	−	3.62775i	−0.132821	−	0.132821i
$747$			2.55818i			0.0935988i
$748$	17.8300	−	12.0570i	0.651929	−	0.440849i
$749$	9.51315			0.347603
$750$	−2.12042	−	4.05322i	−0.0774267	−	0.148003i
$751$	−4.26568	−	10.2983i	−0.155657	−	0.375789i	0.826743	−	0.562580i	$-0.190191\pi$
$751$	−4.26568	−	10.2983i	−0.155657	−	0.375789i	−0.982400	+	0.186791i	$0.940191\pi$
$752$	−9.63558			−0.351373
$753$	−6.67077	−	16.1047i	−0.243096	−	0.586887i
$754$	0.107046	−	0.258432i	0.00389838	−	0.00941153i
$755$	0.00916835	+	0.307944i	0.000333671	+	0.0112072i
$756$	10.6322	−	10.6322i	0.386689	−	0.386689i
$757$	−14.0667	−	14.0667i	−0.511262	−	0.511262i	0.403651	−	0.914913i	$-0.367741\pi$
$757$	−14.0667	−	14.0667i	−0.511262	−	0.511262i	−0.914913	+	0.403651i	$0.867741\pi$
$758$	1.58149	−	3.81804i	0.0574421	−	0.138678i
$759$	−4.67292	+	11.2814i	−0.169616	+	0.409490i
$760$	5.72673	−	6.07820i	0.207730	−	0.220479i
$761$			45.4255i			1.64667i	0.567553	+	0.823337i	$0.307890\pi$
$761$			45.4255i			1.64667i	−0.567553	+	0.823337i	$0.692110\pi$
$762$	−6.17908	+	2.55946i	−0.223844	+	0.0927194i
$763$	8.94498	−	8.94498i	0.323830	−	0.323830i
$764$	−5.97306			−0.216098
$765$	−1.44629	+	2.33926i	−0.0522908	+	0.0845761i
$766$	5.78284			0.208942
$767$	−0.999485	+	0.999485i	−0.0360893	+	0.0360893i
$768$	−17.1145	+	7.08907i	−0.617567	+	0.255805i
$769$			5.98158i			0.215701i	0.994167	+	0.107851i	$0.0343968\pi$
$769$			5.98158i			0.215701i	−0.994167	+	0.107851i	$0.965603\pi$
$770$	−1.56163	−	1.47133i	−0.0562771	−	0.0530230i
$771$	0.968824	−	2.33895i	0.0348913	−	0.0842352i
$772$	11.8558	−	28.6225i	0.426701	−	1.03015i
$773$	−9.29889	−	9.29889i	−0.334458	−	0.334458i	0.519819	−	0.854277i	$-0.325999\pi$
$773$	−9.29889	−	9.29889i	−0.334458	−	0.334458i	−0.854277	+	0.519819i	$0.825999\pi$
$774$	0.594036	−	0.594036i	0.0213522	−	0.0213522i
$775$	2.21432	−	1.07573i	0.0795407	−	0.0386413i
$776$	0.862382	−	2.08197i	0.0309577	−	0.0747385i
$777$	−5.16958	−	12.4805i	−0.185458	−	0.447735i
$778$	9.12654			0.327202
$779$	−8.74284	−	21.1071i	−0.313245	−	0.756240i
$780$	0.441695	−	1.16310i	0.0158152	−	0.0416456i
$781$	−32.9328			−1.17843
$782$	0.536831	−	2.77922i	0.0191970	−	0.0993847i
$783$		−	34.8802i		−	1.24652i
$784$	−12.7180	−	12.7180i	−0.454215	−	0.454215i
$785$	15.7295	+	14.8200i	0.561412	+	0.528948i
$786$		−	3.94369i		−	0.140667i
$787$	−9.83375	−	23.7408i	−0.350535	−	0.846267i	−0.996554	−	0.0829458i	$-0.973567\pi$
$787$	−9.83375	−	23.7408i	−0.350535	−	0.846267i	0.646019	−	0.763322i	$-0.276433\pi$
$788$	19.1112	+	7.91611i	0.680808	+	0.282000i
$789$	−0.647570	−	0.268232i	−0.0230541	−	0.00954932i
$790$	−2.55099	+	6.71742i	−0.0907601	+	0.238995i
$791$	5.78130	−	5.78130i	0.205560	−	0.205560i
$792$	−0.301422	+	0.727698i	−0.0107106	+	0.0258576i
$793$	−1.12117	−	0.464405i	−0.0398140	−	0.0164915i
$794$	−2.25650	+	0.934673i	−0.0800802	+	0.0331703i
$795$	41.4109	−	18.6155i	1.46869	−	0.660222i
$796$	11.7474	+	28.3607i	0.416375	+	1.00522i
$797$	−35.6691	+	35.6691i	−1.26347	+	1.26347i	−0.314064	+	0.949402i	$0.601691\pi$
$797$	−35.6691	+	35.6691i	−1.26347	+	1.26347i	−0.949402	+	0.314064i	$0.898309\pi$
$798$		−	2.23080i		−	0.0789693i
$799$	6.02647	−	9.12834i	0.213201	−	0.322937i
$800$	−10.7125	−	9.50739i	−0.378743	−	0.336137i
$801$	2.42379	+	2.42379i	0.0856404	+	0.0856404i
$802$	4.94200	−	2.04704i	0.174508	−	0.0722836i
$803$	−42.1920			−1.48892
$804$	36.4645	−	15.1041i	1.28600	−	0.532680i
$805$	8.82174	−	0.262648i	0.310926	−	0.00925713i
$806$	−0.0197769	−	0.00819184i	−0.000696610	−	0.000288545i
$807$	19.8801	+	19.8801i	0.699814	+	0.699814i
$808$	−0.617532	−	0.617532i	−0.0217247	−	0.0217247i
$809$	−8.50125	−	3.52133i	−0.298888	−	0.123803i	0.228200	−	0.973614i	$-0.426716\pi$
$809$	−8.50125	−	3.52133i	−0.298888	−	0.123803i	−0.527088	+	0.849811i	$0.676716\pi$
$810$	0.132780	+	4.45977i	0.00466541	+	0.156700i
$811$	9.89831	−	4.10002i	0.347577	−	0.143971i	−0.202064	−	0.979372i	$-0.564765\pi$
$811$	9.89831	−	4.10002i	0.347577	−	0.143971i	0.549640	+	0.835401i	$0.314765\pi$
$812$	17.8442			0.626210
$813$	−24.4040	+	10.1085i	−0.855885	+	0.354519i
$814$	2.72276	+	2.72276i	0.0954327	+	0.0954327i
$815$	−25.3200	+	11.3821i	−0.886922	+	0.398698i
$816$	4.66829	−	24.1681i	0.163423	−	0.846054i
$817$			43.1048i			1.50805i
$818$	−5.50452	+	5.50452i	−0.192461	+	0.192461i
$819$	0.0285347	+	0.0688888i	0.000997083	+	0.00240717i
$820$	−23.7015	+	10.6545i	−0.827692	+	0.372073i
$821$	26.0334	−	10.7834i	0.908572	−	0.376343i	0.121062	−	0.992645i	$-0.461370\pi$
$821$	26.0334	−	10.7834i	0.908572	−	0.376343i	0.787510	+	0.616302i	$0.211370\pi$
$822$	2.49677	+	1.03420i	0.0870849	+	0.0360718i
$823$	−13.5250	+	32.6522i	−0.471452	+	1.13819i	0.492070	+	0.870556i	$0.336240\pi$
$823$	−13.5250	+	32.6522i	−0.471452	+	1.13819i	−0.963522	+	0.267630i	$0.913760\pi$
$824$	0.254478	−	0.254478i	0.00886516	−	0.00886516i
$825$	−22.0980	+	1.31701i	−0.769354	+	0.0458523i
$826$	2.66333	+	1.10319i	0.0926692	+	0.0383848i
$827$	36.2562	+	15.0178i	1.26075	+	0.522221i	0.910140	−	0.414300i	$-0.135974\pi$
$827$	36.2562	+	15.0178i	1.26075	+	0.522221i	0.350612	+	0.936521i	$0.385974\pi$
$828$	−0.610184	−	1.47312i	−0.0212054	−	0.0511943i
$829$		−	17.4130i		−	0.604779i	−0.953184	−	0.302389i	$-0.902216\pi$
$829$		−	17.4130i		−	0.604779i	0.953184	−	0.302389i	$-0.0977843\pi$
$830$	3.27322	−	3.47411i	0.113615	−	0.120588i
$831$	19.4827	+	19.4827i	0.675846	+	0.675846i
$832$		−	1.14424i		−	0.0396695i
$833$	20.0029	−	4.09416i	0.693059	−	0.141854i
$834$	1.88086			0.0651290
$835$	−8.75353	−	3.32422i	−0.302928	−	0.115039i
$836$	−7.61125	−	18.3752i	−0.263241	−	0.635519i
$837$	−2.66925			−0.0922629
$838$	1.93812	+	4.67903i	0.0669511	+	0.161634i
$839$	−10.2960	+	24.8566i	−0.355456	+	0.858147i	0.640471	+	0.767982i	$0.278739\pi$
$839$	−10.2960	+	24.8566i	−0.355456	+	0.858147i	−0.995927	+	0.0901643i	$0.971261\pi$
$840$	−5.15364	+	0.153438i	−0.177817	+	0.00529412i
$841$	8.76397	−	8.76397i	0.302206	−	0.302206i
$842$	−0.318338	−	0.318338i	−0.0109707	−	0.0109707i
$843$	−4.93039	+	11.9030i	−0.169812	+	0.409962i
$844$	3.64865	−	8.80862i	0.125592	−	0.303205i
$845$	−21.1078	−	19.8872i	−0.726129	−	0.684141i
$846$			0.196989i			0.00677263i
$847$	4.95073	−	2.05066i	0.170109	−	0.0704615i
$848$	31.7262	−	31.7262i	1.08948	−	1.08948i
$849$	10.8163			0.371215
$850$	4.95724	−	1.32626i	0.170032	−	0.0454904i
$851$	−15.8390			−0.542954
$852$	−27.5397	+	27.5397i	−0.943494	+	0.943494i
$853$	15.1019	−	6.25540i	0.517078	−	0.214181i	−0.108855	−	0.994058i	$-0.534718\pi$
$853$	15.1019	−	6.25540i	0.517078	−	0.214181i	0.625933	+	0.779877i	$0.284718\pi$
$854$			2.47501i			0.0846930i
$855$	1.84970	+	1.74274i	0.0632583	+	0.0596005i
$856$	−2.49365	+	6.02020i	−0.0852311	+	0.205766i
$857$	−1.47991	+	3.57282i	−0.0505527	+	0.122045i	−0.947138	−	0.320825i	$-0.896040\pi$
$857$	−1.47991	+	3.57282i	−0.0505527	+	0.122045i	0.896586	+	0.442870i	$0.146040\pi$
$858$	0.136113	+	0.136113i	0.00464682	+	0.00464682i
$859$	27.6000	−	27.6000i	0.941701	−	0.941701i	−0.0566905	−	0.998392i	$-0.518055\pi$
$859$	27.6000	−	27.6000i	0.941701	−	0.941701i	0.998392	+	0.0566905i	$0.0180548\pi$
$860$	49.0075	−	1.45909i	1.67114	−	0.0497546i
$861$	−5.39782	+	13.0315i	−0.183957	+	0.444112i
$862$	−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	$0.622914\pi$
$864$	5.94308	+	14.3479i	0.202188	+	0.488124i
$865$	6.17700	+	2.34576i	0.210024	+	0.0797583i
$866$	4.06193			0.138030
$867$	19.9761	+	19.5383i	0.678425	+	0.663554i
$868$		−	1.36556i		−	0.0463500i
$869$	24.5886	+	24.5886i	0.834112	+	0.834112i
$870$	−4.03641	+	4.28414i	−0.136847	+	0.145246i
$871$			2.16411i			0.0733280i
$872$	3.31593	+	8.00536i	0.112292	+	0.271096i
$873$	0.633580	+	0.262437i	0.0214434	+	0.00888216i
$874$	−2.41650	−	1.00095i	−0.0817393	−	0.0338575i
$875$	7.41673	+	14.1772i	0.250731	+	0.479277i
$876$	−35.2826	+	35.2826i	−1.19209	+	1.19209i
$877$	−7.55317	+	18.2350i	−0.255052	+	0.615751i	−0.998598	−	0.0529342i	$-0.983143\pi$
$877$	−7.55317	+	18.2350i	−0.255052	+	0.615751i	0.743546	+	0.668685i	$0.233143\pi$
$878$	5.52560	+	2.28878i	0.186480	+	0.0772425i
$879$	4.78523	−	1.98211i	0.161402	−	0.0668548i
$880$	−19.9530	+	8.96949i	−0.672617	+	0.302362i
$881$	4.37489	+	10.5619i	0.147394	+	0.355840i	0.980283	−	0.197600i	$-0.0633147\pi$
$881$	4.37489	+	10.5619i	0.147394	+	0.355840i	−0.832889	+	0.553440i	$0.813315\pi$
$882$	−0.260007	+	0.260007i	−0.00875489	+	0.00875489i
$883$			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
$885$	27.1284	−	12.1950i	0.911911	−	0.409931i
$886$	−3.74477	−	3.74477i	−0.125808	−	0.125808i
$887$	−28.2772	+	11.7128i	−0.949455	+	0.393277i	−0.803026	−	0.595944i	$-0.796778\pi$
$887$	−28.2772	+	11.7128i	−0.949455	+	0.393277i	−0.146429	+	0.989221i	$0.546778\pi$
$888$	9.25310			0.310514
$889$	21.6130	−	8.95239i	0.724876	−	0.300254i
$890$	−0.190334	−	6.39288i	−0.00638001	−	0.214290i
$891$	19.9486	+	8.26300i	0.668305	+	0.276821i
$892$	13.7642	+	13.7642i	0.460858	+	0.460858i
$893$	−7.14704	−	7.14704i	−0.239167	−	0.239167i
$894$	4.40006	+	1.82256i	0.147160	+	0.0609557i
$895$	−52.0245	+	1.54891i	−1.73899	+	0.0517745i
$896$	−9.73087	+	4.03066i	−0.325086	+	0.134655i
$897$	−0.791804			−0.0264376
$898$	6.71539	−	2.78161i	0.224096	−	0.0928234i
$899$	−2.23993	−	2.23993i	−0.0747059	−	0.0747059i
$900$	1.91878	−	2.16198i	0.0639592	−	0.0720661i
$901$	10.2132	+	49.8989i	0.340252	+	1.66237i
$902$		−	4.02056i		−	0.133870i
$903$	18.8181	−	18.8181i	0.626228	−	0.626228i
$904$	2.14315	+	5.17401i	0.0712799	+	0.172085i
$905$	23.2915	−	10.4702i	0.774235	−	0.348042i
$906$	−0.0520798	+	0.0215722i	−0.00173024	+	0.000716687i
$907$	−0.707707	−	0.293142i	−0.0234990	−	0.00973362i	0.370903	−	0.928672i	$-0.379048\pi$
$907$	−0.707707	−	0.293142i	−0.0234990	−	0.00973362i	−0.394402	+	0.918938i	$0.629048\pi$
$908$	3.32066	−	8.01678i	0.110200	−	0.266046i
$909$	0.187925	−	0.187925i	0.00623309	−	0.00623309i
$910$	0.0493929	−	0.130064i	0.00163736	−	0.00431159i
$911$	7.79323	+	3.22806i	0.258201	+	0.106951i	0.508029	−	0.861340i	$-0.330374\pi$
$911$	7.79323	+	3.22806i	0.258201	+	0.106951i	−0.249828	+	0.968290i	$0.580374\pi$
$912$	−21.0139	−	8.70425i	−0.695840	−	0.288226i
$913$	−8.83979	−	21.3412i	−0.292555	−	0.706289i
$914$		−	0.258405i		−	0.00854727i
$915$	18.5862	+	17.5115i	0.614440	+	0.578911i
$916$	−1.64169	−	1.64169i	−0.0542430	−	0.0542430i
$917$			13.7941i			0.455522i
$918$	−5.46306	−	1.05524i	−0.180308	−	0.0348281i
$919$	−13.0143			−0.429302			−0.214651	−	0.976691i	$-0.568861\pi$
$919$	−13.0143			−0.429302			−0.214651	+	0.976691i	$0.568861\pi$
$920$	−2.14620	+	5.65150i	−0.0707581	+	0.186324i
$921$	−9.42915	−	22.7640i	−0.310701	−	0.750099i
$922$	0.0174735			0.000575458
$923$	−0.817217	−	1.97294i	−0.0268990	−	0.0649400i
$924$	−4.69918	+	11.3448i	−0.154592	+	0.373217i
$925$	−12.5474	−	25.8280i	−0.412556	−	0.849221i
$926$	7.05190	−	7.05190i	0.231740	−	0.231740i
$927$	0.0774419	+	0.0774419i	0.00254353	+	0.00254353i
$928$	−7.05297	+	17.0274i	−0.231525	+	0.558951i
$929$	9.89198	−	23.8814i	0.324545	−	0.783522i	−0.674433	−	0.738336i	$-0.735612\pi$
$929$	9.89198	−	23.8814i	0.324545	−	0.783522i	0.998979	−	0.0451859i	$-0.0143880\pi$
$930$	0.327850	+	0.308892i	0.0107506	+	0.0101290i
$931$		−	18.8668i		−	0.618335i
$932$	−45.5764	+	18.8784i	−1.49291	+	0.618382i
$933$	−11.6560	+	11.6560i	−0.381601	+	0.381601i
$934$	5.65220			0.184946
$935$	3.98211	−	24.5125i	0.130229	−	0.801646i
$936$	−0.0510746			−0.00166942
$937$	0.615699	−	0.615699i	0.0201140	−	0.0201140i	−0.696978	−	0.717092i	$-0.745473\pi$
$937$	0.615699	−	0.615699i	0.0201140	−	0.0201140i	0.717092	+	0.696978i	$0.245473\pi$
$938$	4.07768	−	1.68903i	0.133141	−	0.0551488i
$939$			5.82007i			0.189931i
$940$	−7.88381	+	8.36767i	−0.257142	+	0.272923i
$941$	20.4139	−	49.2834i	0.665473	−	1.60659i	−0.123627	−	0.992329i	$-0.539453\pi$
$941$	20.4139	−	49.2834i	0.665473	−	1.60659i	0.789100	−	0.614265i	$-0.210547\pi$
$942$	−1.51325	+	3.65332i	−0.0493045	+	0.119032i
$943$	11.6943	+	11.6943i	0.380820	+	0.380820i
$944$	20.7839	−	20.7839i	0.676458	−	0.676458i
$945$	−0.516283	−	17.3407i	−0.0167947	−	0.564094i
$946$	−2.90295	+	7.00834i	−0.0943830	+	0.227861i
$947$	5.21997	+	12.6021i	0.169626	+	0.409514i	0.985717	−	0.168409i	$-0.0538631\pi$
$947$	5.21997	+	12.6021i	0.169626	+	0.409514i	−0.816091	+	0.577924i	$0.803863\pi$
$948$	41.1240			1.33564
$949$	−1.04698	−	2.52764i	−0.0339865	−	0.0820506i
$950$	−0.282105	−	4.73343i	−0.00915269	−	0.153573i
$951$	−20.0707			−0.650838
$952$	1.09695	−	5.67902i	0.0355525	−	0.184058i
$953$		−	10.3660i		−	0.335788i	−0.985805	−	0.167894i	$-0.946303\pi$
$953$		−	10.3660i		−	0.335788i	0.985805	−	0.167894i	$-0.0536967\pi$
$954$	−0.648610	−	0.648610i	−0.0209995	−	0.0209995i
$955$	−4.72591	+	5.01595i	−0.152927	+	0.162312i
$956$			12.0431i			0.389502i
$957$	10.9009	+	26.3171i	0.352376	+	0.850711i
$958$	−5.34925	−	2.21573i	−0.172827	−	0.0715871i
$959$	−8.73313	−	3.61738i	−0.282007	−	0.116811i
$960$	−8.54811	+	22.5094i	−0.275889	+	0.726487i
$961$	21.7489	−	21.7489i	0.701577	−	0.701577i
$962$	−0.0955505	+	0.230679i	−0.00308067	+	0.00743740i
$963$	−1.83205	−	0.758859i	−0.0590369	−	0.0244539i
$964$	−47.9937	+	19.8796i	−1.54577	+	0.640280i
$965$	−14.6557	−	32.6023i	−0.471784	−	1.04951i
$966$	0.617983	+	1.49194i	0.0198833	+	0.0480025i
$967$	−10.1327	+	10.1327i	−0.325847	+	0.325847i	−0.851005	−	0.525158i	$-0.824006\pi$
$967$	−10.1327	+	10.1327i	−0.325847	+	0.325847i	0.525158	+	0.851005i	$0.324006\pi$
$968$			3.67050i			0.117974i
$969$	21.3890	−	14.4637i	0.687113	−	0.464641i
$970$	−0.524635	−	1.16708i	−0.0168450	−	0.0374725i
$971$	21.0309	+	21.0309i	0.674913	+	0.674913i	0.958845	−	0.283931i	$-0.0916388\pi$
$971$	21.0309	+	21.0309i	0.674913	+	0.674913i	−0.283931	+	0.958845i	$0.591639\pi$
$972$	−5.52946	+	2.29038i	−0.177358	+	0.0734639i
$973$	−6.57882			−0.210907
$974$	−3.88929	+	1.61100i	−0.124621	+	0.0516197i
$975$	−0.627255	−	1.29117i	−0.0200882	−	0.0413504i
$976$	23.3144	+	9.65712i	0.746274	+	0.309117i
$977$	−26.2437	−	26.2437i	−0.839611	−	0.839611i	0.149196	−	0.988808i	$-0.452331\pi$
$977$	−26.2437	−	26.2437i	−0.839611	−	0.839611i	−0.988808	+	0.149196i	$0.952331\pi$
$978$	−3.59174	−	3.59174i	−0.114851	−	0.114851i
$979$	−28.5955	−	11.8446i	−0.913916	−	0.378556i
$980$	−21.4504	+	0.638638i	−0.685207	+	0.0204006i
$981$	−2.43617	+	1.00909i	−0.0777808	+	0.0322179i
$982$	−5.24217			−0.167284
$983$	42.9257	−	17.7804i	1.36912	−	0.567107i	0.427568	−	0.903983i	$-0.359371\pi$
$983$	42.9257	−	17.7804i	1.36912	−	0.567107i	0.941549	+	0.336877i	$0.109371\pi$
$984$	−6.83179	−	6.83179i	−0.217790	−	0.217790i
$985$	21.7685	−	9.78559i	0.693602	−	0.311795i
$986$	−3.69887	−	5.46991i	−0.117796	−	0.174197i
$987$			6.24032i			0.198631i
$988$	0.911949	−	0.911949i	0.0290130	−	0.0290130i
$989$	−11.9411	−	28.8283i	−0.379703	−	0.916685i
$990$	0.183372	+	0.407919i	0.00582795	+	0.0129645i
$991$	−40.9290	+	16.9534i	−1.30015	+	0.538541i	−0.921996	−	0.387200i	$-0.873442\pi$
$991$	−40.9290	+	16.9534i	−1.30015	+	0.538541i	−0.378158	+	0.925741i	$0.623442\pi$
$992$	1.30304	+	0.539738i	0.0413717	+	0.0171367i
$993$	11.6325	−	28.0833i	0.369146	−	0.891198i
$994$	−3.07965	+	3.07965i	−0.0976806	+	0.0976806i
$995$	33.1108	+	12.5741i	1.04968	+	0.398625i
$996$	−25.2385	−	10.4541i	−0.799712	−	0.331252i
$997$	22.7561	+	9.42589i	0.720693	+	0.298521i	0.712721	−	0.701447i	$-0.247462\pi$
$997$	22.7561	+	9.42589i	0.720693	+	0.298521i	0.00797178	+	0.999968i	$0.497462\pi$
$998$	−2.14575	−	5.18029i	−0.0679224	−	0.163979i
$999$			31.1344i			0.985050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.m.a.49.4	yes	24
3.2	odd	2		765.2.bh.b.559.3		24
5.2	odd	4		425.2.m.e.151.4		24
5.3	odd	4		425.2.m.e.151.3		24
5.4	even	2	inner	85.2.m.a.49.3	✓	24
15.14	odd	2		765.2.bh.b.559.4		24
17.5	odd	16		1445.2.b.i.579.13		24
17.8	even	8	inner	85.2.m.a.59.3	yes	24
17.12	odd	16		1445.2.b.i.579.14		24
51.8	odd	8		765.2.bh.b.739.4		24
85.8	odd	8		425.2.m.e.76.3		24
85.12	even	16		7225.2.a.by.1.12		24
85.22	even	16		7225.2.a.by.1.11		24
85.29	odd	16		1445.2.b.i.579.11		24
85.39	odd	16		1445.2.b.i.579.12		24
85.42	odd	8		425.2.m.e.76.4		24
85.59	even	8	inner	85.2.m.a.59.4	yes	24
85.63	even	16		7225.2.a.by.1.13		24
85.73	even	16		7225.2.a.by.1.14		24
255.59	odd	8		765.2.bh.b.739.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.49.3	✓	24	5.4	even	2	inner
85.2.m.a.49.4	yes	24	1.1	even	1	trivial
85.2.m.a.59.3	yes	24	17.8	even	8	inner
85.2.m.a.59.4	yes	24	85.59	even	8	inner
425.2.m.e.76.3		24	85.8	odd	8
425.2.m.e.76.4		24	85.42	odd	8
425.2.m.e.151.3		24	5.3	odd	4
425.2.m.e.151.4		24	5.2	odd	4
765.2.bh.b.559.3		24	3.2	odd	2
765.2.bh.b.559.4		24	15.14	odd	2
765.2.bh.b.739.3		24	255.59	odd	8
765.2.bh.b.739.4		24	51.8	odd	8
1445.2.b.i.579.11		24	85.29	odd	16
1445.2.b.i.579.12		24	85.39	odd	16
1445.2.b.i.579.13		24	17.5	odd	16
1445.2.b.i.579.14		24	17.12	odd	16
7225.2.a.by.1.11		24	85.22	even	16
7225.2.a.by.1.12		24	85.12	even	16
7225.2.a.by.1.13		24	85.63	even	16
7225.2.a.by.1.14		24	85.73	even	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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.176012 - 0.176012i) q^{2} +(-1.51856 + 0.629010i) q^{3} +1.93804i q^{4} +(1.62749 + 1.53338i) q^{5} +(-0.156572 + 0.377999i) q^{6} +(0.547653 - 1.32215i) q^{7} +(0.693142 + 0.693142i) q^{8} +(-0.210935 + 0.210935i) q^{9} +(0.556352 - 0.0165642i) q^{10} +(1.03080 - 2.48857i) q^{11} +(-1.21905 - 2.94304i) q^{12} +0.174664 q^{13} +(-0.136321 - 0.329108i) q^{14} +(-3.43597 - 1.30483i) q^{15} -3.63208 q^{16} +(2.27165 - 3.44088i) q^{17} +0.0742541i q^{18} +(-2.69404 - 2.69404i) q^{19} +(-2.97176 + 3.15415i) q^{20} +2.35225i q^{21} +(-0.256585 - 0.619452i) q^{22} +(2.54807 + 1.05544i) q^{23} +(-1.48857 - 0.616588i) q^{24} +(0.297464 + 4.99114i) q^{25} +(0.0307430 - 0.0307430i) q^{26} +(2.07467 - 5.00869i) q^{27} +(2.56238 + 1.06137i) q^{28} +(5.94408 - 2.46212i) q^{29} +(-0.834438 + 0.375105i) q^{30} +(-0.188417 - 0.454879i) q^{31} +(-2.02557 + 2.02557i) q^{32} +4.42745i q^{33} +(-0.205798 - 1.00547i) q^{34} +(2.91867 - 1.31203i) q^{35} +(-0.408800 - 0.408800i) q^{36} +(-5.30576 + 2.19772i) q^{37} -0.948365 q^{38} +(-0.265239 + 0.109866i) q^{39} +(0.0652303 + 2.19094i) q^{40} +(5.54000 + 2.29474i) q^{41} +(0.414025 + 0.414025i) q^{42} +(-8.00004 - 8.00004i) q^{43} +(4.82296 + 1.99773i) q^{44} +(-0.666739 + 0.0198507i) q^{45} +(0.634261 - 0.262720i) q^{46} +2.65291 q^{47} +(5.51554 - 2.28461i) q^{48} +(3.50159 + 3.50159i) q^{49} +(0.930858 + 0.826143i) q^{50} +(-1.28530 + 6.65408i) q^{51} +0.338506i q^{52} +(-8.73501 + 8.73501i) q^{53} +(-0.516423 - 1.24676i) q^{54} +(5.49356 - 2.46952i) q^{55} +(1.29604 - 0.536837i) q^{56} +(5.78565 + 2.39649i) q^{57} +(0.612867 - 1.47959i) q^{58} +(-5.72232 + 5.72232i) q^{59} +(2.52882 - 6.65904i) q^{60} +(-6.41902 - 2.65884i) q^{61} +(-0.113228 - 0.0469005i) q^{62} +(0.163369 + 0.394407i) q^{63} -6.55110i q^{64} +(0.284265 + 0.267828i) q^{65} +(0.779283 + 0.779283i) q^{66} +12.3901i q^{67} +(6.66855 + 4.40254i) q^{68} -4.53329 q^{69} +(0.282788 - 0.744653i) q^{70} +(-4.67878 - 11.2956i) q^{71} -0.292415 q^{72} +(-5.99425 - 14.4714i) q^{73} +(-0.547052 + 1.32070i) q^{74} +(-3.59120 - 7.39227i) q^{75} +(5.22115 - 5.22115i) q^{76} +(-2.72575 - 2.72575i) q^{77} +(-0.0273476 + 0.0660229i) q^{78} +(-4.94031 + 11.9270i) q^{79} +(-5.91118 - 5.56937i) q^{80} +8.01609i q^{81} +(1.37901 - 0.571204i) q^{82} +(6.06390 - 6.06390i) q^{83} -4.55876 q^{84} +(8.97327 - 2.11669i) q^{85} -2.81621 q^{86} +(-7.47777 + 7.47777i) q^{87} +(2.43943 - 1.01044i) q^{88} -11.4907i q^{89} +(-0.113860 + 0.120848i) q^{90} +(0.0956555 - 0.230933i) q^{91} +(-2.04549 + 4.93826i) q^{92} +(0.572247 + 0.572247i) q^{93} +(0.466944 - 0.466944i) q^{94} +(-0.253531 - 8.51552i) q^{95} +(1.80186 - 4.35007i) q^{96} +(-0.879757 - 2.12392i) q^{97} +1.23264 q^{98} +(0.307495 + 0.742359i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{9} - 16 q^{10} - 24 q^{14} - 16 q^{15} + 8 q^{16} - 24 q^{19} - 8 q^{20} + 32 q^{24} + 16 q^{25} - 16 q^{26} + 24 q^{29} - 24 q^{31} + 8 q^{34} + 8 q^{35} + 8 q^{36} - 24 q^{39} + 16 q^{40}+ \cdots - 80 q^{99}+O(q^{100}) \) 24 * q - 8 * q^9 - 16 * q^10 - 24 * q^14 - 16 * q^15 + 8 * q^16 - 24 * q^19 - 8 * q^20 + 32 * q^24 + 16 * q^25 - 16 * q^26 + 24 * q^29 - 24 * q^31 + 8 * q^34 + 8 * q^35 + 8 * q^36 - 24 * q^39 + 16 * q^40 - 48 * q^41 + 72 * q^44 + 48 * q^45 - 16 * q^46 + 48 * q^49 + 16 * q^50 + 32 * q^54 + 24 * q^56 - 48 * q^59 + 8 * q^60 + 16 * q^61 + 24 * q^65 - 96 * q^66 + 32 * q^69 + 32 * q^70 + 16 * q^71 - 64 * q^74 - 24 * q^76 - 72 * q^79 - 64 * q^80 - 96 * q^84 - 24 * q^85 - 8 * q^91 - 40 * q^94 - 88 * q^95 + 96 * q^96 - 80 * q^99

Introduction

L-functions

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