LMFDB - Embedded newform 289.3.e.e.224.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,3,Mod(40,289)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("289.40"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([15])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,16,8,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			224.1
Root			$0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.224
Dual form			289.3.e.e.40.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.63099 + 1.08979i) q^{2} +(5.09606 + 1.01367i) q^{3} +(2.90602 - 2.90602i) q^{4} +(2.02560 + 3.03153i) q^{5} +(-14.5124 + 2.88669i) q^{6} +(1.83409 - 2.74491i) q^{7} +(-0.119585 + 0.288703i) q^{8} +(16.6274 + 6.88730i) q^{9} +(-8.63307 - 5.76843i) q^{10} +(-0.474066 - 2.38329i) q^{11} +(17.7550 - 11.8635i) q^{12} +(7.73173 + 7.73173i) q^{13} +(-1.83409 + 9.22059i) q^{14} +(7.24963 + 17.5022i) q^{15} +15.5490i q^{16} -51.2522 q^{18} +(8.45745 - 3.50319i) q^{19} +(14.6961 + 2.92324i) q^{20} +(12.1291 - 12.1291i) q^{21} +(3.84455 + 5.75378i) q^{22} +(3.38849 - 0.674012i) q^{23} +(-0.902059 + 1.35003i) q^{24} +(4.47998 - 10.8156i) q^{25} +(-28.7680 - 11.9161i) q^{26} +(38.8707 + 25.9726i) q^{27} +(-2.64686 - 13.3067i) q^{28} +(-19.9953 + 13.3605i) q^{29} +(-38.1474 - 38.1474i) q^{30} +(5.40360 - 27.1657i) q^{31} +(-17.4235 - 42.0641i) q^{32} -12.6260i q^{33} +12.0364 q^{35} +(68.3342 - 28.3049i) q^{36} +(37.7780 + 7.51452i) q^{37} +(-18.4337 + 18.4337i) q^{38} +(31.5639 + 47.2388i) q^{39} +(-1.11744 + 0.222273i) q^{40} +(-42.7611 + 63.9965i) q^{41} +(-18.6933 + 45.1295i) q^{42} +(-50.0470 - 20.7301i) q^{43} +(-8.30354 - 5.54825i) q^{44} +(12.8015 + 64.3574i) q^{45} +(-8.18054 + 5.46606i) q^{46} +(5.13810 + 5.13810i) q^{47} +(-15.7616 + 79.2388i) q^{48} +(14.5808 + 35.2013i) q^{49} +33.3380i q^{50} +44.9371 q^{52} +(-52.6837 + 21.8223i) q^{53} +(-130.573 - 25.9726i) q^{54} +(6.26475 - 6.26475i) q^{55} +(0.573134 + 0.857755i) q^{56} +(46.6508 - 9.27942i) q^{57} +(38.0474 - 56.9419i) q^{58} +(-8.82213 + 21.2985i) q^{59} +(71.9292 + 29.7940i) q^{60} +(34.4943 + 23.0484i) q^{61} +(15.3882 + 77.3615i) q^{62} +(49.4011 - 33.0088i) q^{63} +(47.7028 + 47.7028i) q^{64} +(-7.77755 + 39.1004i) q^{65} +(13.7596 + 33.2187i) q^{66} +17.3637i q^{67} +17.9512 q^{69} +(-31.6676 + 13.1172i) q^{70} +(50.6009 + 10.0651i) q^{71} +(-3.97676 + 3.97676i) q^{72} +(-34.5368 - 51.6879i) q^{73} +(-107.583 + 21.3995i) q^{74} +(33.7937 - 50.5759i) q^{75} +(14.3972 - 34.7579i) q^{76} +(-7.41140 - 3.06990i) q^{77} +(-134.525 - 89.8865i) q^{78} +(-23.1267 - 116.266i) q^{79} +(-47.1374 + 31.4962i) q^{80} +(57.2255 + 57.2255i) q^{81} +(42.7611 - 214.975i) q^{82} +(-36.0104 - 86.9369i) q^{83} -70.4946i q^{84} +154.264 q^{86} +(-115.441 + 47.8171i) q^{87} +(0.744754 + 0.148141i) q^{88} +(-19.6021 + 19.6021i) q^{89} +(-103.817 - 155.373i) q^{90} +(35.4036 - 7.04221i) q^{91} +(7.88832 - 11.8057i) q^{92} +(55.0742 - 132.961i) q^{93} +(-19.1177 - 7.91883i) q^{94} +(27.7515 + 18.5429i) q^{95} +(-46.1522 - 232.023i) q^{96} +(12.6670 - 8.46379i) q^{97} +(-76.7240 - 76.7240i) q^{98} +(8.53195 - 42.8930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 16 q^{3} + 8 q^{4} + 8 q^{5} - 40 q^{6} + 16 q^{7} - 8 q^{8} + 56 q^{9} - 16 q^{10} + 32 q^{12} - 16 q^{14} + 80 q^{15} - 136 q^{18} + 80 q^{19} + 48 q^{20} + 64 q^{21} + 40 q^{22} + 16 q^{23}+ \cdots + 144 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 16 * q^3 + 8 * q^4 + 8 * q^5 - 40 * q^6 + 16 * q^7 - 8 * q^8 + 56 * q^9 - 16 * q^10 + 32 * q^12 - 16 * q^14 + 80 * q^15 - 136 * q^18 + 80 * q^19 + 48 * q^20 + 64 * q^21 + 40 * q^22 + 16 * q^23 - 88 * q^24 + 136 * q^25 - 40 * q^26 + 64 * q^27 + 40 * q^28 - 144 * q^29 - 168 * q^30 - 88 * q^31 - 16 * q^32 + 80 * q^35 + 72 * q^36 + 24 * q^37 - 8 * q^38 - 96 * q^40 - 144 * q^41 - 88 * q^42 - 48 * q^43 + 112 * q^44 + 8 * q^46 + 80 * q^47 - 40 * q^48 - 72 * q^49 + 240 * q^52 - 88 * q^53 - 256 * q^54 + 8 * q^55 - 64 * q^56 + 200 * q^57 + 144 * q^58 + 40 * q^59 + 96 * q^60 - 88 * q^61 + 24 * q^62 + 216 * q^63 + 120 * q^64 + 160 * q^65 + 120 * q^66 - 208 * q^69 - 96 * q^70 + 48 * q^71 - 24 * q^72 + 224 * q^73 - 104 * q^74 + 272 * q^75 - 192 * q^76 - 120 * q^77 - 232 * q^78 - 136 * q^79 - 80 * q^80 + 224 * q^81 + 144 * q^82 - 504 * q^83 + 288 * q^86 - 216 * q^87 + 112 * q^88 - 288 * q^89 - 344 * q^90 - 16 * q^91 + 48 * q^92 - 248 * q^93 - 72 * q^94 - 144 * q^95 - 80 * q^96 + 208 * q^97 - 16 * q^98 + 144 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{16}\right)$

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 $

$2$	−2.63099	+	1.08979i	−1.31549	+	0.544895i	−0.926482	−	0.376338i	$-0.877183\pi$
$2$	−2.63099	+	1.08979i	−1.31549	+	0.544895i	−0.389011	+	0.921233i	$0.627183\pi$
$3$	5.09606	+	1.01367i	1.69869	+	0.337890i	0.946903	−	0.321519i	$-0.104193\pi$
$3$	5.09606	+	1.01367i	1.69869	+	0.337890i	0.751784	+	0.659409i	$0.229193\pi$
$4$	2.90602	−	2.90602i	0.726505	−	0.726505i
$5$	2.02560	+	3.03153i	0.405121	+	0.606306i	0.976795	−	0.214174i	$-0.0687061\pi$
$5$	2.02560	+	3.03153i	0.405121	+	0.606306i	−0.571675	+	0.820480i	$0.693706\pi$
$6$	−14.5124	+	2.88669i	−2.41873	+	0.481115i
$7$	1.83409	−	2.74491i	0.262013	−	0.392130i	−0.677016	−	0.735968i	$-0.736727\pi$
$7$	1.83409	−	2.74491i	0.262013	−	0.392130i	0.939029	+	0.343838i	$0.111727\pi$
$8$	−0.119585	+	0.288703i	−0.0149481	+	0.0360878i
$9$	16.6274	+	6.88730i	1.84749	+	0.765255i
$10$	−8.63307	−	5.76843i	−0.863307	−	0.576843i
$11$	−0.474066	−	2.38329i	−0.0430969	−	0.216663i	0.953236	−	0.302228i	$-0.0977304\pi$
$11$	−0.474066	−	2.38329i	−0.0430969	−	0.216663i	−0.996333	+	0.0855651i	$0.972730\pi$
$12$	17.7550	−	11.8635i	1.47958	−	0.988626i
$13$	7.73173	+	7.73173i	0.594748	+	0.594748i	0.938910	−	0.344162i	$-0.111837\pi$
$13$	7.73173	+	7.73173i	0.594748	+	0.594748i	−0.344162	+	0.938910i	$0.611837\pi$
$14$	−1.83409	+	9.22059i	−0.131006	+	0.658614i
$15$	7.24963	+	17.5022i	0.483309	+	1.16681i
$16$			15.5490i			0.971815i
$17$		0			0
$17$		0			0
$18$	−51.2522			−2.84734
$19$	8.45745	−	3.50319i	0.445129	−	0.184379i	−0.148849	−	0.988860i	$-0.547557\pi$
$19$	8.45745	−	3.50319i	0.445129	−	0.184379i	0.593978	+	0.804481i	$0.297557\pi$
$20$	14.6961	+	2.92324i	0.734806	+	0.146162i
$21$	12.1291	−	12.1291i	0.577574	−	0.577574i
$22$	3.84455	+	5.75378i	0.174752	+	0.261535i
$23$	3.38849	−	0.674012i	0.147326	−	0.0293049i	−0.120877	−	0.992668i	$-0.538571\pi$
$23$	3.38849	−	0.674012i	0.147326	−	0.0293049i	0.268202	+	0.963363i	$0.413571\pi$
$24$	−0.902059	+	1.35003i	−0.0375858	+	0.0562511i
$25$	4.47998	−	10.8156i	0.179199	−	0.432625i
$26$	−28.7680	−	11.9161i	−1.10646	−	0.458312i
$27$	38.8707	+	25.9726i	1.43966	+	0.961948i
$28$	−2.64686	−	13.3067i	−0.0945307	−	0.475238i
$29$	−19.9953	+	13.3605i	−0.689495	+	0.460706i	−0.850312	−	0.526279i	$-0.823587\pi$
$29$	−19.9953	+	13.3605i	−0.689495	+	0.460706i	0.160818	+	0.986984i	$0.448587\pi$
$30$	−38.1474	−	38.1474i	−1.27158	−	1.27158i
$31$	5.40360	−	27.1657i	0.174310	−	0.876314i	−0.790318	−	0.612697i	$-0.790085\pi$
$31$	5.40360	−	27.1657i	0.174310	−	0.876314i	0.964627	−	0.263617i	$-0.0849155\pi$
$32$	−17.4235	−	42.0641i	−0.544485	−	1.31450i
$33$		−	12.6260i		−	0.382605i
$34$		0			0
$35$	12.0364			0.343897
$36$	68.3342	−	28.3049i	1.89817	−	0.786248i
$37$	37.7780	+	7.51452i	1.02103	+	0.203095i	0.677092	−	0.735898i	$-0.263240\pi$
$37$	37.7780	+	7.51452i	1.02103	+	0.203095i	0.343936	+	0.938993i	$0.388240\pi$
$38$	−18.4337	+	18.4337i	−0.485097	+	0.485097i
$39$	31.5639	+	47.2388i	0.809332	+	1.21125i
$40$	−1.11744	+	0.222273i	−0.0279360	+	0.00555682i
$41$	−42.7611	+	63.9965i	−1.04295	+	1.56089i	−0.234689	+	0.972070i	$0.575407\pi$
$41$	−42.7611	+	63.9965i	−1.04295	+	1.56089i	−0.808264	+	0.588820i	$0.799593\pi$
$42$	−18.6933	+	45.1295i	−0.445078	+	1.07451i
$43$	−50.0470	−	20.7301i	−1.16388	−	0.482096i	−0.284717	−	0.958612i	$-0.591900\pi$
$43$	−50.0470	−	20.7301i	−1.16388	−	0.482096i	−0.879166	+	0.476515i	$0.841900\pi$
$44$	−8.30354	−	5.54825i	−0.188717	−	0.126097i
$45$	12.8015	+	64.3574i	0.284477	+	1.43016i
$46$	−8.18054	+	5.46606i	−0.177838	+	0.118827i
$47$	5.13810	+	5.13810i	0.109321	+	0.109321i	0.759652	−	0.650330i	$-0.225369\pi$
$47$	5.13810	+	5.13810i	0.109321	+	0.109321i	−0.650330	+	0.759652i	$0.725369\pi$
$48$	−15.7616	+	79.2388i	−0.328366	+	1.65081i
$49$	14.5808	+	35.2013i	0.297568	+	0.718394i
$50$			33.3380i			0.666760i
$51$		0			0
$52$	44.9371			0.864175
$53$	−52.6837	+	21.8223i	−0.994033	+	0.411742i	−0.819606	−	0.572928i	$-0.805807\pi$
$53$	−52.6837	+	21.8223i	−0.994033	+	0.411742i	−0.174427	+	0.984670i	$0.555807\pi$
$54$	−130.573	−	25.9726i	−2.41802	−	0.480974i
$55$	6.26475	−	6.26475i	0.113905	−	0.113905i
$56$	0.573134	+	0.857755i	0.0102345	+	0.0153171i
$57$	46.6508	−	9.27942i	0.818435	−	0.162797i
$58$	38.0474	−	56.9419i	0.655989	−	0.981757i
$59$	−8.82213	+	21.2985i	−0.149528	+	0.360992i	−0.980840	−	0.194813i	$-0.937590\pi$
$59$	−8.82213	+	21.2985i	−0.149528	+	0.360992i	0.831313	+	0.555805i	$0.187590\pi$
$60$	71.9292	+	29.7940i	1.19882	+	0.496567i
$61$	34.4943	+	23.0484i	0.565480	+	0.377842i	0.805203	−	0.593000i	$-0.202056\pi$
$61$	34.4943	+	23.0484i	0.565480	+	0.377842i	−0.239722	+	0.970841i	$0.577056\pi$
$62$	15.3882	+	77.3615i	0.248196	+	1.24777i
$63$	49.4011	−	33.0088i	0.784145	−	0.523949i
$64$	47.7028	+	47.7028i	0.745356	+	0.745356i
$65$	−7.77755	+	39.1004i	−0.119655	+	0.601544i
$66$	13.7596	+	33.2187i	0.208479	+	0.503314i
$67$			17.3637i			0.259160i	0.991569	+	0.129580i	$0.0413630\pi$
$67$			17.3637i			0.259160i	−0.991569	+	0.129580i	$0.958637\pi$
$68$		0			0
$69$	17.9512			0.260162
$70$	−31.6676	+	13.1172i	−0.452395	+	0.187388i
$71$	50.6009	+	10.0651i	0.712689	+	0.141763i	0.538103	−	0.842879i	$-0.319141\pi$
$71$	50.6009	+	10.0651i	0.712689	+	0.141763i	0.174586	+	0.984642i	$0.444141\pi$
$72$	−3.97676	+	3.97676i	−0.0552328	+	0.0552328i
$73$	−34.5368	−	51.6879i	−0.473106	−	0.708053i	0.515781	−	0.856720i	$-0.327502\pi$
$73$	−34.5368	−	51.6879i	−0.473106	−	0.708053i	−0.988887	+	0.148667i	$0.952502\pi$
$74$	−107.583	+	21.3995i	−1.45382	+	0.289183i
$75$	33.7937	−	50.5759i	0.450583	−	0.674345i
$76$	14.3972	−	34.7579i	0.189437	−	0.457340i
$77$	−7.41140	−	3.06990i	−0.0962520	−	0.0398689i
$78$	−134.525	−	89.8865i	−1.72468	−	1.15239i
$79$	−23.1267	−	116.266i	−0.292743	−	1.47172i	−0.794793	−	0.606881i	$-0.792420\pi$
$79$	−23.1267	−	116.266i	−0.292743	−	1.47172i	0.502049	−	0.864839i	$-0.332580\pi$
$80$	−47.1374	+	31.4962i	−0.589217	+	0.393702i
$81$	57.2255	+	57.2255i	0.706488	+	0.706488i
$82$	42.7611	−	214.975i	0.521477	−	2.62164i
$83$	−36.0104	−	86.9369i	−0.433861	−	1.04743i	−0.978031	−	0.208458i	$-0.933156\pi$
$83$	−36.0104	−	86.9369i	−0.433861	−	1.04743i	0.544171	−	0.838975i	$-0.316844\pi$
$84$		−	70.4946i		−	0.839221i
$85$		0			0
$86$	154.264			1.79377
$87$	−115.441	+	47.8171i	−1.32690	+	0.549621i
$88$	0.744754	+	0.148141i	0.00846311	+	0.00168342i
$89$	−19.6021	+	19.6021i	−0.220248	+	0.220248i	−0.808603	−	0.588355i	$-0.799776\pi$
$89$	−19.6021	+	19.6021i	−0.220248	+	0.220248i	0.588355	+	0.808603i	$0.299776\pi$
$90$	−103.817	−	155.373i	−1.15352	−	1.72636i
$91$	35.4036	−	7.04221i	0.389050	−	0.0773869i
$92$	7.88832	−	11.8057i	0.0857426	−	0.128323i
$93$	55.0742	−	132.961i	0.592195	−	1.42969i
$94$	−19.1177	−	7.91883i	−0.203380	−	0.0842428i
$95$	27.7515	+	18.5429i	0.292121	+	0.195189i
$96$	−46.1522	−	232.023i	−0.480752	−	2.41691i
$97$	12.6670	−	8.46379i	0.130587	−	0.0872555i	−0.488561	−	0.872530i	$-0.662478\pi$
$97$	12.6670	−	8.46379i	0.130587	−	0.0872555i	0.619148	+	0.785274i	$0.287478\pi$
$98$	−76.7240	−	76.7240i	−0.782898	−	0.782898i
$99$	8.53195	−	42.8930i	0.0861813	−	0.433263i
$100$	−18.4115	−	44.4493i	−0.184115	−	0.444493i
$101$		−	132.191i		−	1.30882i	−0.756140	−	0.654410i	$-0.772917\pi$
$101$		−	132.191i		−	1.30882i	0.756140	−	0.654410i	$-0.227083\pi$
$102$		0			0
$103$	−185.135			−1.79743			−0.898713	−	0.438536i	$-0.855497\pi$
$103$	−185.135			−1.79743			−0.898713	+	0.438536i	$0.855497\pi$
$104$	−3.15676	+	1.30757i	−0.0303535	+	0.0125728i
$105$	61.3383	+	12.2009i	0.584174	+	0.116199i
$106$	114.828	−	114.828i	1.08329	−	1.08329i
$107$	20.6116	+	30.8475i	0.192632	+	0.288294i	0.915195	−	0.403010i	$-0.132036\pi$
$107$	20.6116	+	30.8475i	0.192632	+	0.288294i	−0.722563	+	0.691305i	$0.757036\pi$
$108$	188.436	−	37.4823i	1.74478	−	0.347058i
$109$	25.3190	−	37.8925i	0.232284	−	0.347638i	−0.696956	−	0.717114i	$-0.745463\pi$
$109$	25.3190	−	37.8925i	0.232284	−	0.347638i	0.929240	+	0.369476i	$0.120463\pi$
$110$	−9.65521	+	23.3097i	−0.0877747	+	0.211907i
$111$	184.902	+	76.5889i	1.66578	+	0.689990i
$112$	42.6807	+	28.5183i	0.381077	+	0.254628i
$113$	17.0495	+	85.7136i	0.150881	+	0.758528i	0.979928	+	0.199350i	$0.0638830\pi$
$113$	17.0495	+	85.7136i	0.150881	+	0.758528i	−0.829048	+	0.559178i	$0.811117\pi$
$114$	−112.625	+	75.2536i	−0.987938	+	0.660119i
$115$	8.90702	+	8.90702i	0.0774524	+	0.0774524i
$116$	−19.2811	+	96.9326i	−0.166216	+	0.835626i
$117$	75.3079	+	181.809i	0.643657	+	1.55393i
$118$		−	65.6503i		−	0.556359i
$119$		0			0
$120$	−5.91986			−0.0493322
$121$	106.334	−	44.0450i	0.878794	−	0.364008i
$122$	−115.872	−	23.0484i	−0.949770	−	0.188921i
$123$	−282.785	+	282.785i	−2.29906	+	2.29906i
$124$	−63.2412	−	94.6471i	−0.510010	−	0.763283i
$125$	131.261	−	26.1094i	1.05009	−	0.208875i
$126$	−94.0011	+	140.683i	−0.746040	+	1.11653i
$127$	42.3590	−	102.264i	0.333535	−	0.805226i	−0.664771	−	0.747047i	$-0.731471\pi$
$127$	42.3590	−	102.264i	0.333535	−	0.805226i	0.998306	−	0.0581782i	$-0.0185292\pi$
$128$	−9.23501	−	3.82526i	−0.0721485	−	0.0298849i
$129$	−234.029	−	156.373i	−1.81418	−	1.21219i
$130$	−22.1486	−	111.348i	−0.170374	−	0.856527i
$131$	−37.3157	+	24.9335i	−0.284852	+	0.190332i	−0.689785	−	0.724014i	$-0.742295\pi$
$131$	−37.3157	+	24.9335i	−0.284852	+	0.190332i	0.404933	+	0.914347i	$0.367295\pi$
$132$	−36.6913	−	36.6913i	−0.277964	−	0.277964i
$133$	5.89578	−	29.6401i	0.0443292	−	0.222858i
$134$	−18.9228	−	45.6838i	−0.141215	−	0.340924i
$135$			170.448i			1.26258i
$136$		0			0
$137$	61.5009			0.448911			0.224456	−	0.974484i	$-0.427940\pi$
$137$	61.5009			0.448911			0.224456	+	0.974484i	$0.427940\pi$
$138$	−47.2293	+	19.5630i	−0.342241	+	0.141761i
$139$	−85.6793	−	17.0427i	−0.616398	−	0.122609i	−0.122991	−	0.992408i	$-0.539249\pi$
$139$	−85.6793	−	17.0427i	−0.616398	−	0.122609i	−0.493407	+	0.869799i	$0.664249\pi$
$140$	34.9780	−	34.9780i	0.249843	−	0.249843i
$141$	20.9758	+	31.3924i	0.148764	+	0.222641i
$142$	−144.099	+	28.6631i	−1.01478	+	0.201853i
$143$	14.7616	−	22.0923i	0.103228	−	0.154492i
$144$	−107.091	+	258.540i	−0.743686	+	1.79542i
$145$	−81.0053	−	33.5535i	−0.558657	−	0.231403i
$146$	147.195	+	98.3523i	1.00818	+	0.673646i
$147$	38.6224	+	194.168i	0.262738	+	1.32087i
$148$	131.621	−	87.9464i	0.889331	−	0.594232i
$149$	−132.640	−	132.640i	−0.890200	−	0.890200i	0.104342	−	0.994541i	$-0.466726\pi$
$149$	−132.640	−	132.640i	−0.890200	−	0.890200i	−0.994541	+	0.104342i	$0.966726\pi$
$150$	−33.7937	+	169.893i	−0.225292	+	1.13262i
$151$	−82.7215	−	199.707i	−0.547824	−	1.32257i	−0.919093	−	0.394040i	$-0.871077\pi$
$151$	−82.7215	−	199.707i	−0.547824	−	1.32257i	0.371269	−	0.928525i	$-0.378923\pi$
$152$			2.86062i			0.0188198i
$153$		0			0
$154$	22.8448			0.148343
$155$	93.2993	−	38.6458i	0.601931	−	0.249328i
$156$	229.002	+	45.5514i	1.46796	+	0.291996i
$157$	111.042	−	111.042i	0.707276	−	0.707276i	−0.258686	−	0.965961i	$-0.583289\pi$
$157$	111.042	−	111.042i	0.707276	−	0.707276i	0.965961	+	0.258686i	$0.0832895\pi$
$158$	187.552	+	280.691i	1.18703	+	1.77652i
$159$	−290.600	+	57.8040i	−1.82767	+	0.363547i
$160$	92.2254	−	138.025i	0.576409	−	0.862657i
$161$	4.36469	−	10.5373i	0.0271099	−	0.0654490i
$162$	−212.923	−	88.1957i	−1.31434	−	0.544418i
$163$	138.740	+	92.7032i	0.851166	+	0.568731i	0.902861	−	0.429932i	$-0.141462\pi$
$163$	138.740	+	92.7032i	0.851166	+	0.568731i	−0.0516950	+	0.998663i	$0.516462\pi$
$164$	61.7105	+	310.240i	0.376284	+	1.89171i
$165$	38.2760	−	25.5752i	0.231976	−	0.155001i
$166$	189.486	+	189.486i	1.14148	+	1.14148i
$167$	10.5057	−	52.8159i	0.0629086	−	0.316263i	−0.936499	−	0.350669i	$-0.885954\pi$
$167$	10.5057	−	52.8159i	0.0629086	−	0.316263i	0.999408	+	0.0344064i	$0.0109541\pi$
$168$	2.05124	+	4.95214i	0.0122098	+	0.0294770i
$169$		−	49.4408i		−	0.292549i
$170$		0			0
$171$	164.753			0.963468
$172$	−205.680	+	85.1953i	−1.19581	+	0.495321i
$173$	−65.9632	−	13.1209i	−0.381290	−	0.0758433i	0.000724270	−	1.00000i	$-0.499769\pi$
$173$	−65.9632	−	13.1209i	−0.381290	−	0.0758433i	−0.382014	+	0.924156i	$0.624769\pi$
$174$	251.612	−	251.612i	1.44605	−	1.44605i
$175$	−21.4712	−	32.1340i	−0.122693	−	0.183623i
$176$	37.0579	−	7.37127i	0.210556	−	0.0418822i
$177$	−66.5477	+	99.5957i	−0.375976	+	0.562688i
$178$	30.2106	−	72.9349i	0.169723	−	0.409747i
$179$	−231.811	−	96.0193i	−1.29503	−	0.536421i	−0.374552	−	0.927206i	$-0.622203\pi$
$179$	−231.811	−	96.0193i	−1.29503	−	0.536421i	−0.920482	+	0.390785i	$0.872203\pi$
$180$	224.225	+	149.823i	1.24570	+	0.832347i
$181$	3.34168	+	16.7998i	0.0184623	+	0.0928163i	0.988918	−	0.148464i	$-0.0474328\pi$
$181$	3.34168	+	16.7998i	0.0184623	+	0.0928163i	−0.970456	+	0.241280i	$0.922433\pi$
$182$	−85.4718	+	57.1104i	−0.469625	+	0.313793i
$183$	152.422	+	152.422i	0.832905	+	0.832905i
$184$	−0.210622	+	1.05887i	−0.00114468	+	0.00575471i
$185$	53.7428	+	129.747i	0.290502	+	0.701333i
$186$			409.837i			2.20343i
$187$		0			0
$188$	29.8629			0.158845
$189$	142.585	−	59.0606i	0.754417	−	0.312490i
$190$	−93.2217	−	18.5429i	−0.490640	−	0.0975945i
$191$	−79.7646	+	79.7646i	−0.417615	+	0.417615i	−0.884381	−	0.466766i	$-0.845419\pi$
$191$	−79.7646	+	79.7646i	−0.417615	+	0.417615i	0.466766	+	0.884381i	$0.345419\pi$
$192$	194.741	+	291.451i	1.01428	+	1.51798i
$193$	20.0905	−	3.99625i	0.104096	−	0.0207060i	−0.142767	−	0.989756i	$-0.545600\pi$
$193$	20.0905	−	3.99625i	0.104096	−	0.0207060i	0.246863	+	0.969050i	$0.420600\pi$
$194$	−24.1028	+	36.0724i	−0.124241	+	0.185940i
$195$	−79.2697	+	191.374i	−0.406511	+	0.981406i
$196$	144.668	+	59.9234i	0.738101	+	0.305732i
$197$	−34.2801	−	22.9052i	−0.174011	−	0.116270i	0.465515	−	0.885040i	$-0.345869\pi$
$197$	−34.2801	−	22.9052i	−0.174011	−	0.116270i	−0.639526	+	0.768770i	$0.720869\pi$
$198$	24.2969	+	122.149i	0.122712	+	0.616914i
$199$	304.369	−	203.373i	1.52949	−	1.02197i	0.546685	−	0.837338i	$-0.315890\pi$
$199$	304.369	−	203.373i	1.52949	−	1.02197i	0.982807	−	0.184636i	$-0.0591105\pi$
$200$	2.58676	+	2.58676i	0.0129338	+	0.0129338i
$201$	−17.6011	+	88.4867i	−0.0875677	+	0.440232i
$202$	144.060	+	347.792i	0.713170	+	1.72174i
$203$			79.3897i			0.391082i
$204$		0			0
$205$	−280.624			−1.36890
$206$	487.088	−	201.758i	2.36450	−	0.979409i
$207$	60.9839	+	12.1305i	0.294608	+	0.0586012i
$208$	−120.221	+	120.221i	−0.577985	+	0.577985i
$209$	−12.3585	−	18.4958i	−0.0591317	−	0.0884969i
$210$	−174.677	+	34.7454i	−0.831794	+	0.165454i
$211$	−178.204	+	266.702i	−0.844570	+	1.26399i	0.118015	+	0.993012i	$0.462347\pi$
$211$	−178.204	+	266.702i	−0.844570	+	1.26399i	−0.962586	+	0.270977i	$0.912653\pi$
$212$	−89.6839	+	216.516i	−0.423037	+	1.02130i
$213$	247.663	+	102.585i	1.16274	+	0.481621i
$214$	−87.8463	−	58.6970i	−0.410497	−	0.274285i
$215$	−38.5313	−	193.710i	−0.179215	−	0.900976i
$216$	−12.1467	+	8.11616i	−0.0562347	+	0.0375748i
$217$	−64.6568	−	64.6568i	−0.297958	−	0.297958i
$218$	−25.3190	+	127.287i	−0.116142	+	0.583885i
$219$	−123.607	−	298.414i	−0.564415	−	1.36262i
$220$		−	36.4110i		−	0.165504i
$221$		0			0
$222$	−569.940			−2.56730
$223$	100.397	−	41.5859i	0.450211	−	0.186484i	−0.146045	−	0.989278i	$-0.546654\pi$
$223$	100.397	−	41.5859i	0.450211	−	0.186484i	0.596256	+	0.802794i	$0.296654\pi$
$224$	−147.418	−	29.3233i	−0.658118	−	0.130908i
$225$	148.981	−	148.981i	0.662137	−	0.662137i
$226$	−138.267	−	206.931i	−0.611800	−	0.915624i
$227$	193.543	−	38.4981i	0.852612	−	0.169595i	0.250609	−	0.968089i	$-0.419369\pi$
$227$	193.543	−	38.4981i	0.852612	−	0.169595i	0.602004	+	0.798493i	$0.294369\pi$
$228$	108.602	−	162.534i	0.476324	−	0.712870i
$229$	−69.3072	+	167.322i	−0.302651	+	0.730665i	0.697253	+	0.716825i	$0.254406\pi$
$229$	−69.3072	+	167.322i	−0.302651	+	0.730665i	−0.999904	+	0.0138399i	$0.995594\pi$
$230$	−33.1410	−	13.7275i	−0.144091	−	0.0596847i
$231$	−34.6571	−	23.1571i	−0.150031	−	0.100247i
$232$	−1.46607	−	7.37041i	−0.00631925	−	0.0317690i
$233$	4.87031	−	3.25423i	0.0209026	−	0.0139667i	−0.545075	−	0.838387i	$-0.683499\pi$
$233$	4.87031	−	3.25423i	0.0209026	−	0.0139667i	0.565978	+	0.824421i	$0.308499\pi$
$234$	−396.268	−	396.268i	−1.69345	−	1.69345i
$235$	−5.16856	+	25.9841i	−0.0219939	+	0.110571i
$236$	36.2566	+	87.5311i	0.153630	+	0.370895i
$237$		−	615.941i		−	2.59891i
$238$		0			0
$239$	68.9414			0.288458			0.144229	−	0.989544i	$-0.453930\pi$
$239$	68.9414			0.288458			0.144229	+	0.989544i	$0.453930\pi$
$240$	−272.142	+	112.725i	−1.13392	+	0.469686i
$241$	303.925	+	60.4544i	1.26110	+	0.250848i	0.779978	−	0.625806i	$-0.215230\pi$
$241$	303.925	+	60.4544i	1.26110	+	0.250848i	0.481120	+	0.876655i	$0.340230\pi$
$242$	−231.764	+	231.764i	−0.957701	+	0.957701i
$243$	−0.136443	−	0.204201i	−0.000561493	−	0.000840334i
$244$	167.220	−	33.2621i	0.685328	−	0.136320i
$245$	−77.1787	+	115.506i	−0.315015	+	0.471454i
$246$	435.826	−	1052.18i	1.77165	−	4.27715i
$247$	92.4764	+	38.3050i	0.374399	+	0.155081i
$248$	7.19663	+	4.80864i	0.0290187	+	0.0193897i
$249$	−95.3861	−	479.538i	−0.383077	−	1.92586i
$250$	−316.892	+	211.740i	−1.26757	+	0.846962i
$251$	−149.892	−	149.892i	−0.597178	−	0.597178i	0.342382	−	0.939561i	$-0.388766\pi$
$251$	−149.892	−	149.892i	−0.597178	−	0.597178i	−0.939561	+	0.342382i	$0.888766\pi$
$252$	47.6365	−	239.485i	0.189034	−	0.950337i
$253$	−3.21274	−	7.75623i	−0.0126986	−	0.0306571i
$254$			315.217i			1.24101i
$255$		0			0
$256$	−241.382			−0.942898
$257$	−223.240	+	92.4689i	−0.868637	+	0.359801i	−0.772079	−	0.635526i	$-0.780783\pi$
$257$	−223.240	+	92.4689i	−0.868637	+	0.359801i	−0.0965575	+	0.995327i	$0.530783\pi$
$258$	786.141	+	156.373i	3.04706	+	0.606097i
$259$	89.9150	−	89.9150i	0.347162	−	0.347162i
$260$	91.0247	+	136.228i	0.350095	+	0.523954i
$261$	−424.488	+	84.4359i	−1.62639	+	0.323509i
$262$	71.0047	−	106.266i	0.271010	−	0.405595i
$263$	−91.5602	+	221.046i	−0.348138	+	0.840479i	0.648702	+	0.761042i	$0.275312\pi$
$263$	−91.5602	+	221.046i	−0.348138	+	0.840479i	−0.996840	+	0.0794365i	$0.974688\pi$
$264$	3.64515	+	1.50987i	0.0138074	+	0.00571920i
$265$	−172.871	−	115.509i	−0.652345	−	0.435883i
$266$	16.7898	+	84.4079i	0.0631194	+	0.317323i
$267$	−119.763	+	80.0234i	−0.448552	+	0.299713i
$268$	50.4594	+	50.4594i	0.188281	+	0.188281i
$269$	−2.21012	+	11.1110i	−0.00821606	+	0.0413049i	−0.984676	−	0.174395i	$-0.944203\pi$
$269$	−2.21012	+	11.1110i	−0.00821606	+	0.0413049i	0.976460	+	0.215700i	$0.0692032\pi$
$270$	−185.753	−	448.446i	−0.687973	−	1.66091i
$271$			352.304i			1.30001i	0.759929	+	0.650007i	$0.225234\pi$
$271$			352.304i			1.30001i	−0.759929	+	0.650007i	$0.774766\pi$
$272$		0			0
$273$	187.557			0.687023
$274$	−161.808	+	67.0230i	−0.590540	+	0.244610i
$275$	−27.9006	−	5.54978i	−0.101457	−	0.0201810i
$276$	52.1665	−	52.1665i	0.189009	−	0.189009i
$277$	51.8121	+	77.5423i	0.187047	+	0.279936i	0.913128	−	0.407674i	$-0.133660\pi$
$277$	51.8121	+	77.5423i	0.187047	+	0.279936i	−0.726080	+	0.687610i	$0.758660\pi$
$278$	243.994	−	48.5334i	0.877677	−	0.174581i
$279$	276.946	−	414.480i	0.992639	−	1.48559i
$280$	−1.43937	+	3.47494i	−0.00514060	+	0.0124105i
$281$	−205.670	−	85.1913i	−0.731922	−	0.303172i	−0.0145802	−	0.999894i	$-0.504641\pi$
$281$	−205.670	−	85.1913i	−0.731922	−	0.303172i	−0.717341	+	0.696722i	$0.754641\pi$
$282$	−89.3981	−	59.7339i	−0.317015	−	0.211822i
$283$	−24.4057	−	122.696i	−0.0862394	−	0.433555i	−0.999648	−	0.0265119i	$-0.991560\pi$
$283$	−24.4057	−	122.696i	−0.0862394	−	0.433555i	0.913409	−	0.407043i	$-0.133440\pi$
$284$	176.297	−	117.798i	0.620763	−	0.414781i
$285$	122.627	+	122.627i	0.430270	+	0.430270i
$286$	−14.7616	+	74.2117i	−0.0516141	+	0.259481i
$287$	97.2369	+	234.751i	0.338804	+	0.817946i
$288$		−	819.418i		−	2.84520i
$289$		0			0
$290$	249.690			0.861000
$291$	73.1311	−	30.2919i	0.251309	−	0.104096i
$292$	−250.570	−	49.8416i	−0.858118	−	0.170690i
$293$	84.7101	−	84.7101i	0.289113	−	0.289113i	−0.547617	−	0.836729i	$-0.684465\pi$
$293$	84.7101	−	84.7101i	0.289113	−	0.289113i	0.836729	+	0.547617i	$0.184465\pi$
$294$	−313.218	−	468.763i	−1.06537	−	1.59443i
$295$	−82.4372	+	16.3978i	−0.279448	+	0.0555857i
$296$	−6.68713	+	10.0080i	−0.0225917	+	0.0338108i
$297$	43.4730	−	104.953i	0.146374	−	0.353378i
$298$	493.523	+	204.424i	1.65612	+	0.685986i
$299$	31.4101	+	20.9876i	0.105051	+	0.0701926i
$300$	−48.7693	−	245.180i	−0.162564	−	0.817266i
$301$	−148.693	+	99.3534i	−0.493996	+	0.330078i
$302$	435.278	+	435.278i	1.44132	+	1.44132i
$303$	133.998	−	673.653i	0.442237	−	2.22328i
$304$	54.4712	+	131.505i	0.179182	+	0.432583i
$305$			151.257i			0.495926i
$306$		0			0
$307$	237.264			0.772846			0.386423	−	0.922322i	$-0.373711\pi$
$307$	237.264			0.772846			0.386423	+	0.922322i	$0.373711\pi$
$308$	−30.4589	+	12.6165i	−0.0988924	+	0.0409626i
$309$	−943.459	−	187.666i	−3.05327	−	0.607332i
$310$	−203.353	+	203.353i	−0.655979	+	0.655979i
$311$	−178.860	−	267.683i	−0.575112	−	0.860716i	0.423875	−	0.905721i	$-0.360670\pi$
$311$	−178.860	−	267.683i	−0.575112	−	0.860716i	−0.998987	+	0.0450046i	$0.985670\pi$
$312$	−17.4125	+	3.46356i	−0.0558093	+	0.0111012i
$313$	−175.035	+	261.959i	−0.559218	+	0.836929i	−0.998100	−	0.0616158i	$-0.980375\pi$
$313$	−175.035	+	261.959i	−0.559218	+	0.836929i	0.438882	+	0.898545i	$0.355375\pi$
$314$	−171.138	+	413.163i	−0.545025	+	1.31581i
$315$	200.134	+	82.8983i	0.635347	+	0.263169i
$316$	−405.078	−	270.664i	−1.28189	−	0.856532i
$317$	62.6351	+	314.888i	0.197587	+	0.993338i	0.944524	+	0.328443i	$0.106524\pi$
$317$	62.6351	+	314.888i	0.197587	+	0.993338i	−0.746937	+	0.664895i	$0.768476\pi$
$318$	701.571	−	468.775i	2.20620	−	1.47413i
$319$	41.3210	+	41.3210i	0.129533	+	0.129533i
$320$	−47.9855	+	241.239i	−0.149955	+	0.753873i
$321$	73.7690	+	178.094i	0.229810	+	0.554811i
$322$			32.4801i			0.100870i
$323$		0			0
$324$	332.597			1.02653
$325$	118.262	−	48.9855i	0.363882	−	0.150725i
$326$	−466.050	−	92.7032i	−1.42960	−	0.284366i
$327$	167.437	−	167.437i	0.512041	−	0.512041i
$328$	−13.3624	−	19.9982i	−0.0407390	−	0.0609702i
$329$	23.5274	−	4.67989i	0.0715118	−	0.0142246i
$330$	−72.8320	+	109.001i	−0.220703	+	0.330305i
$331$	10.2295	−	24.6962i	0.0309049	−	0.0746109i	−0.907674	−	0.419677i	$-0.862143\pi$
$331$	10.2295	−	24.6962i	0.0309049	−	0.0746109i	0.938578	+	0.345066i	$0.112143\pi$
$332$	−357.287	−	147.993i	−1.07617	−	0.445763i
$333$	576.396	+	385.135i	1.73092	+	1.15656i
$334$	29.9178	+	150.407i	0.0895743	+	0.450320i
$335$	−52.6387	+	35.1721i	−0.157130	+	0.104991i
$336$	188.595	+	188.595i	0.561295	+	0.561295i
$337$	−95.4695	+	479.958i	−0.283292	+	1.42421i	0.532778	+	0.846255i	$0.321148\pi$
$337$	−95.4695	+	479.958i	−0.283292	+	1.42421i	−0.816071	+	0.577952i	$0.803852\pi$
$338$	53.8801	+	130.078i	0.159409	+	0.384846i
$339$			454.084i			1.33948i
$340$		0			0
$341$	−67.3056			−0.197377
$342$	−433.463	+	179.546i	−1.26744	+	0.524989i
$343$	282.021	+	56.0975i	0.822219	+	0.163549i
$344$	11.9697	−	11.9697i	0.0347956	−	0.0347956i
$345$	36.3620	+	54.4195i	0.105397	+	0.157738i
$346$	187.847	−	37.3651i	0.542911	−	0.107992i
$347$	134.365	−	201.092i	0.387220	−	0.579516i	−0.585737	−	0.810501i	$-0.699195\pi$
$347$	134.365	−	201.092i	0.387220	−	0.579516i	0.972957	+	0.230985i	$0.0741948\pi$
$348$	−196.515	+	474.430i	−0.564699	+	1.36330i
$349$	36.6909	+	15.1979i	0.105132	+	0.0435470i	0.434629	−	0.900609i	$-0.356879\pi$
$349$	36.6909	+	15.1979i	0.105132	+	0.0435470i	−0.329498	+	0.944156i	$0.606879\pi$
$350$	91.5098	+	61.1449i	0.261457	+	0.174700i
$351$	99.7249	+	501.351i	0.284117	+	1.42835i
$352$	−91.9912	+	61.4665i	−0.261339	+	0.174621i
$353$	451.955	+	451.955i	1.28033	+	1.28033i	0.940482	+	0.339843i	$0.110374\pi$
$353$	451.955	+	451.955i	1.28033	+	1.28033i	0.339843	+	0.940482i	$0.389626\pi$
$354$	66.5477	−	334.558i	0.187988	−	0.945079i
$355$	71.9846	+	173.786i	0.202773	+	0.489538i
$356$			113.928i			0.320022i
$357$		0			0
$358$	714.533			1.99590
$359$	−188.393	+	78.0349i	−0.524771	+	0.217367i	−0.629311	−	0.777153i	$-0.716663\pi$
$359$	−188.393	+	78.0349i	−0.524771	+	0.217367i	0.104540	+	0.994521i	$0.466663\pi$
$360$	−20.1110	−	4.00033i	−0.0558639	−	0.0111120i
$361$	−196.009	+	196.009i	−0.542962	+	0.542962i
$362$	−27.1001	−	40.5582i	−0.0748622	−	0.112039i
$363$	586.532	−	116.668i	1.61579	−	0.321401i
$364$	82.4186	−	123.348i	0.226425	−	0.338869i
$365$	86.7357	−	209.398i	0.237632	−	0.573694i
$366$	−567.127	−	234.912i	−1.54953	−	0.641835i
$367$	−234.454	−	156.657i	−0.638840	−	0.426859i	0.193519	−	0.981097i	$-0.438010\pi$
$367$	−234.454	−	156.657i	−0.638840	−	0.426859i	−0.832359	+	0.554238i	$0.813010\pi$
$368$	10.4802	+	52.6877i	0.0284789	+	0.143173i
$369$	−1151.77	+	769.587i	−3.12133	+	2.08560i
$370$	−282.793	−	282.793i	−0.764306	−	0.764306i
$371$	−36.7264	+	184.636i	−0.0989930	+	0.497672i
$372$	−226.340	−	546.433i	−0.608441	−	1.46891i
$373$		−	340.976i		−	0.914144i	−0.889430	−	0.457072i	$-0.848898\pi$
$373$		−	340.976i		−	0.914144i	0.889430	−	0.457072i	$-0.151102\pi$
$374$		0			0
$375$	695.380			1.85435
$376$	−2.09782	+	0.868946i	−0.00557931	+	0.00231103i
$377$	−257.898	−	51.2991i	−0.684080	−	0.136072i
$378$	−310.775	+	310.775i	−0.822156	+	0.822156i
$379$	198.969	+	297.778i	0.524984	+	0.785695i	0.995304	−	0.0968017i	$-0.0308613\pi$
$379$	198.969	+	297.778i	0.524984	+	0.785695i	−0.470319	+	0.882496i	$0.655861\pi$
$380$	134.532	−	26.7602i	0.354033	−	0.0704215i
$381$	319.526	−	478.204i	0.838650	−	1.25513i
$382$	122.933	−	296.786i	0.321814	−	0.776927i
$383$	−223.470	−	92.5645i	−0.583474	−	0.241683i	0.0713664	−	0.997450i	$-0.477264\pi$
$383$	−223.470	−	92.5645i	−0.583474	−	0.241683i	−0.654840	+	0.755767i	$0.727264\pi$
$384$	−43.1846	−	28.8550i	−0.112460	−	0.0751433i
$385$	−5.70606	−	28.6863i	−0.0148209	−	0.0745099i
$386$	−48.5028	+	32.4085i	−0.125655	+	0.0839599i
$387$	−689.377	−	689.377i	−1.78134	−	1.78134i
$388$	12.2145	−	61.4063i	0.0314806	−	0.158264i
$389$	−256.470	−	619.174i	−0.659307	−	1.59171i	−0.798877	−	0.601495i	$-0.794572\pi$
$389$	−256.470	−	619.174i	−0.659307	−	1.59171i	0.139570	−	0.990212i	$-0.455428\pi$
$390$		−	589.890i		−	1.51254i
$391$		0			0
$392$	−11.9063			−0.0303733
$393$	−215.437	+	89.2370i	−0.548186	+	0.227066i
$394$	115.152	+	22.9052i	0.292265	+	0.0581351i
$395$	305.618	−	305.618i	0.773716	−	0.773716i
$396$	−99.8539	−	149.442i	−0.252156	−	0.377379i
$397$	−439.343	+	87.3907i	−1.10666	+	0.220128i	−0.714407	−	0.699731i	$-0.753303\pi$
$397$	−439.343	+	87.3907i	−1.10666	+	0.220128i	−0.392250	+	0.919858i	$0.628303\pi$
$398$	−579.157	+	866.769i	−1.45517	+	2.17781i
$399$	60.0906	−	145.071i	0.150603	−	0.363588i
$400$	168.173	+	69.6594i	0.420431	+	0.174148i
$401$	115.578	+	77.2270i	0.288225	+	0.192586i	0.691274	−	0.722592i	$-0.257050\pi$
$401$	115.578	+	77.2270i	0.288225	+	0.192586i	−0.403049	+	0.915178i	$0.632050\pi$
$402$	−50.1237	−	251.989i	−0.124686	−	0.626838i
$403$	251.817	−	168.259i	0.624857	−	0.417516i
$404$	−384.149	−	384.149i	−0.950864	−	0.950864i
$405$	−57.5647	+	289.397i	−0.142135	+	0.714561i
$406$	−86.5181	−	208.873i	−0.213099	−	0.514466i
$407$		−	93.5985i		−	0.229972i
$408$		0			0
$409$	−404.559			−0.989142			−0.494571	−	0.869137i	$-0.664675\pi$
$409$	−404.559			−0.989142			−0.494571	+	0.869137i	$0.664675\pi$
$410$	738.319	−	305.822i	1.80078	−	0.745907i
$411$	313.412	+	62.3416i	0.762560	+	0.151683i
$412$	−538.006	+	538.006i	−1.30584	+	1.30584i
$413$	42.2819	+	63.2793i	0.102377	+	0.153219i
$414$	−173.667	+	34.5446i	−0.419487	+	0.0834411i
$415$	190.609	−	285.266i	0.459299	−	0.687389i
$416$	190.514	−	459.942i	0.457967	−	1.10563i
$417$	−419.352	−	173.701i	−1.00564	−	0.416549i
$418$	52.6717	+	35.1941i	0.126009	+	0.0841964i
$419$	50.9740	+	256.264i	0.121656	+	0.611608i	0.992721	+	0.120439i	$0.0384303\pi$
$419$	50.9740	+	256.264i	0.121656	+	0.611608i	−0.871064	+	0.491169i	$0.836570\pi$
$420$	213.706	−	142.794i	0.508825	−	0.339986i
$421$	−429.955	−	429.955i	−1.02127	−	1.02127i	−0.999769	−	0.0215010i	$-0.993156\pi$
$421$	−429.955	−	429.955i	−1.02127	−	1.02127i	−0.0215010	−	0.999769i	$-0.506844\pi$
$422$	178.204	−	895.894i	0.422285	−	2.12297i
$423$	50.0457	+	120.821i	0.118311	+	0.285629i
$424$		−	17.8195i		−	0.0420272i
$425$		0			0
$426$	−763.393			−1.79200
$427$	126.531	−	52.4110i	0.296326	−	0.122742i
$428$	149.541	+	29.7456i	0.349395	+	0.0694991i
$429$	97.6204	−	97.6204i	0.227553	−	0.227553i
$430$	312.479	+	467.657i	0.726694	+	1.08757i
$431$	628.034	−	124.924i	1.45715	−	0.289846i	0.597973	−	0.801516i	$-0.295973\pi$
$431$	628.034	−	124.924i	1.45715	−	0.289846i	0.859182	+	0.511670i	$0.170973\pi$
$432$	−403.849	+	604.403i	−0.934835	+	1.39908i
$433$	−244.632	+	590.594i	−0.564971	+	1.36396i	0.340778	+	0.940144i	$0.389310\pi$
$433$	−244.632	+	590.594i	−0.564971	+	1.36396i	−0.905748	+	0.423816i	$0.860690\pi$
$434$	240.573	+	99.6488i	0.554317	+	0.229605i
$435$	−378.796	−	253.103i	−0.870795	−	0.581847i
$436$	−36.5390	−	183.694i	−0.0838049	−	0.421316i
$437$	26.2968	−	17.5710i	0.0601757	−	0.0402081i
$438$	650.416	+	650.416i	1.48497	+	1.48497i
$439$	−137.567	+	691.596i	−0.313364	+	1.57539i	0.427678	+	0.903931i	$0.359332\pi$
$439$	−137.567	+	691.596i	−0.313364	+	1.57539i	−0.741043	+	0.671458i	$0.765668\pi$
$440$	1.05948	+	2.55782i	0.00240792	+	0.00581322i
$441$			685.729i			1.55494i
$442$		0			0
$443$	−317.185			−0.715994			−0.357997	−	0.933723i	$-0.616540\pi$
$443$	−317.185			−0.715994			−0.357997	+	0.933723i	$0.616540\pi$
$444$	759.898	−	314.760i	1.71148	−	0.708919i
$445$	−99.1303	−	19.7182i	−0.222765	−	0.0443107i
$446$	−218.824	+	218.824i	−0.490636	+	0.490636i
$447$	−541.487	−	810.393i	−1.21138	−	1.81296i
$448$	218.431	−	43.4486i	0.487569	−	0.0969835i
$449$	136.636	−	204.490i	0.304312	−	0.455434i	−0.647523	−	0.762046i	$-0.724195\pi$
$449$	136.636	−	204.490i	0.304312	−	0.455434i	0.951835	+	0.306611i	$0.0991951\pi$
$450$	−229.609	+	554.325i	−0.510242	+	1.23183i
$451$	172.794	+	71.5736i	0.383135	+	0.158700i
$452$	298.632	+	199.539i	0.660689	+	0.441459i
$453$	−219.117	−	1101.57i	−0.483701	−	2.43173i
$454$	−467.254	+	312.209i	−1.02919	+	0.687685i
$455$	93.0622	+	93.0622i	0.204532	+	0.204532i
$456$	−2.89972	+	14.5779i	−0.00635904	+	0.0319690i
$457$	142.406	+	343.798i	0.311610	+	0.752293i	0.999646	+	0.0266163i	$0.00847324\pi$
$457$	142.406	+	343.798i	0.311610	+	0.752293i	−0.688036	+	0.725677i	$0.741527\pi$
$458$		−	515.753i		−	1.12610i
$459$		0			0
$460$	51.7680			0.112539
$461$	−795.940	+	329.689i	−1.72655	+	0.715161i	−0.726957	+	0.686683i	$0.759066\pi$
$461$	−795.940	+	329.689i	−1.72655	+	0.715161i	−0.999594	+	0.0284783i	$0.990934\pi$
$462$	116.419	+	23.1571i	0.251989	+	0.0501237i
$463$	386.172	−	386.172i	0.834065	−	0.834065i	−0.154005	−	0.988070i	$-0.549217\pi$
$463$	386.172	−	386.172i	0.834065	−	0.834065i	0.988070	+	0.154005i	$0.0492172\pi$
$464$	−207.742	−	310.908i	−0.447720	−	0.670061i
$465$	514.633	−	102.367i	1.10674	−	0.220144i
$466$	−9.26727	+	13.8695i	−0.0198869	+	0.0297628i
$467$	154.996	−	374.194i	0.331898	−	0.801272i	−0.666544	−	0.745466i	$-0.732227\pi$
$467$	154.996	−	374.194i	0.331898	−	0.801272i	0.998442	−	0.0558061i	$-0.0177729\pi$
$468$	747.187	+	309.495i	1.59655	+	0.661314i
$469$	47.6619	+	31.8467i	0.101624	+	0.0679033i
$470$	−14.7188	−	73.9964i	−0.0313166	−	0.157439i
$471$	678.438	−	453.318i	1.44042	−	0.962459i
$472$	−5.09394	−	5.09394i	−0.0107922	−	0.0107922i
$473$	−25.6804	+	129.104i	−0.0542926	+	0.272947i
$474$	671.246	+	1620.53i	1.41613	+	3.41884i
$475$		−	107.167i		−	0.225615i
$476$		0			0
$477$	−1026.29			−2.15155
$478$	−181.384	+	75.1317i	−0.379464	+	0.157179i
$479$	−117.948	−	23.4613i	−0.246238	−	0.0489798i	0.0704280	−	0.997517i	$-0.477564\pi$
$479$	−117.948	−	23.4613i	−0.246238	−	0.0489798i	−0.316666	+	0.948537i	$0.602564\pi$
$480$	609.898	−	609.898i	1.27062	−	1.27062i
$481$	233.989	+	350.190i	0.486464	+	0.728045i
$482$	−865.505	+	172.160i	−1.79565	+	0.357178i
$483$	32.9241	−	49.2743i	0.0681657	−	0.102017i
$484$	181.013	−	437.005i	0.373994	−	0.902902i
$485$	51.3164	+	21.2560i	0.105807	+	0.0438267i
$486$	0.581516	+	0.388556i	0.00119653	+	0.000799499i
$487$	158.120	+	794.921i	0.324681	+	1.63228i	0.706265	+	0.707947i	$0.250379\pi$
$487$	158.120	+	794.921i	0.324681	+	1.63228i	−0.381584	+	0.924334i	$0.624621\pi$
$488$	−10.7791	+	7.20237i	−0.0220883	+	0.0147590i
$489$	613.058	+	613.058i	1.25370	+	1.25370i
$490$	77.1787	−	388.004i	0.157508	−	0.791844i
$491$	−57.6444	−	139.166i	−0.117402	−	0.283433i	0.854245	−	0.519871i	$-0.174020\pi$
$491$	−57.6444	−	139.166i	−0.117402	−	0.283433i	−0.971647	+	0.236438i	$0.924020\pi$
$492$			1643.55i			3.34056i
$493$		0			0
$494$	−285.049			−0.577022
$495$	147.314	−	61.0194i	0.297604	−	0.123271i
$496$	422.401	+	84.0208i	0.851615	+	0.169397i
$497$	120.434	−	120.434i	0.242323	−	0.242323i
$498$	773.556	+	1157.71i	1.55333	+	2.32472i
$499$	−808.149	+	160.751i	−1.61954	+	0.322146i	−0.919840	−	0.392294i	$-0.871682\pi$
$499$	−808.149	+	160.751i	−1.61954	+	0.322146i	−0.699697	+	0.714440i	$0.746682\pi$
$500$	305.572	−	457.321i	0.611145	−	0.914642i
$501$	107.076	−	258.504i	0.213724	−	0.515976i
$502$	557.714	+	231.013i	1.11098	+	0.460185i
$503$	562.798	+	376.050i	1.11888	+	0.747614i	0.970449	−	0.241308i	$-0.0775764\pi$
$503$	562.798	+	376.050i	1.11888	+	0.747614i	0.148435	+	0.988922i	$0.452576\pi$
$504$	3.62211	+	18.2096i	0.00718673	+	0.0361301i
$505$	400.740	−	267.766i	0.793545	−	0.530230i
$506$	16.9053	+	16.9053i	0.0334098	+	0.0334098i
$507$	50.1166	−	251.953i	0.0988494	−	0.496949i
$508$	−174.084	−	420.276i	−0.342685	−	0.827315i
$509$		−	340.603i		−	0.669161i	−0.942367	−	0.334581i	$-0.891405\pi$
$509$		−	340.603i		−	0.669161i	0.942367	−	0.334581i	$-0.108595\pi$
$510$		0			0
$511$	−205.222			−0.401609
$512$	672.012	−	278.357i	1.31252	−	0.543665i
$513$	419.735	+	83.4904i	0.818196	+	0.162749i
$514$	486.569	−	486.569i	0.946632	−	0.946632i
$515$	−375.010	−	561.242i	−0.728175	−	1.08979i
$516$	−1134.52	+	225.669i	−2.19867	+	0.437344i
$517$	9.80981	−	14.6814i	0.0189745	−	0.0283973i
$518$	−138.577	+	334.553i	−0.267522	+	0.645856i
$519$	−322.852	−	133.730i	−0.622066	−	0.257668i
$520$	−10.3583	−	6.92120i	−0.0199198	−	0.0133100i
$521$	−87.9243	−	442.025i	−0.168761	−	0.848417i	−0.968681	−	0.248310i	$-0.920125\pi$
$521$	−87.9243	−	442.025i	−0.168761	−	0.848417i	0.799920	−	0.600107i	$-0.204875\pi$
$522$	1024.80	−	684.753i	1.96323	−	1.31179i
$523$	−425.914	−	425.914i	−0.814367	−	0.814367i	0.170918	−	0.985285i	$-0.445327\pi$
$523$	−425.914	−	425.914i	−0.814367	−	0.814367i	−0.985285	+	0.170918i	$0.945327\pi$
$524$	−35.9827	+	180.897i	−0.0686693	+	0.345224i
$525$	−76.8455	−	185.521i	−0.146372	−	0.353374i
$526$		−	681.350i		−	1.29534i
$527$		0			0
$528$	196.321			0.371821
$529$	−477.705	+	197.872i	−0.903033	+	0.374049i
$530$	580.703	+	115.509i	1.09567	+	0.217941i
$531$	−293.378	+	293.378i	−0.552501	+	0.552501i
$532$	−69.0015	−	103.268i	−0.129702	−	0.194113i
$533$	−825.421	+	164.186i	−1.54863	+	0.308042i
$534$	227.887	−	341.057i	0.426755	−	0.638684i
$535$	−51.7641	+	124.970i	−0.0967554	+	0.233588i
$536$	−5.01296	−	2.07643i	−0.00935253	−	0.00387395i
$537$	−1083.99	−	724.300i	−2.01861	−	1.34879i
$538$	−6.29389	−	31.6415i	−0.0116987	−	0.0588132i
$539$	76.9827	−	51.4382i	0.142825	−	0.0954326i
$540$	495.325	+	495.325i	0.917269	+	0.917269i
$541$	95.3109	−	479.160i	0.176175	−	0.885693i	−0.787027	−	0.616918i	$-0.788381\pi$
$541$	95.3109	−	479.160i	0.176175	−	0.885693i	0.963203	−	0.268775i	$-0.0866190\pi$
$542$	−383.937	−	926.906i	−0.708371	−	1.71016i
$543$			88.9999i			0.163904i
$544$		0			0
$545$	166.158			0.304878
$546$	−493.460	+	204.398i	−0.903774	+	0.374355i
$547$	369.427	+	73.4837i	0.675370	+	0.134339i	0.520847	−	0.853650i	$-0.325616\pi$
$547$	369.427	+	73.4837i	0.675370	+	0.134339i	0.154523	+	0.987989i	$0.450616\pi$
$548$	178.723	−	178.723i	0.326136	−	0.326136i
$549$	414.810	+	620.807i	0.755574	+	1.13080i
$550$	79.4543	−	15.8044i	0.144462	−	0.0287353i
$551$	−122.305	+	183.043i	−0.221970	+	0.332201i
$552$	−2.14668	+	5.18255i	−0.00388892	+	0.00938868i
$553$	−361.556	−	149.761i	−0.653808	−	0.270816i
$554$	−220.822	−	147.548i	−0.398595	−	0.266333i
$555$	142.357	+	715.675i	0.256498	+	1.28950i
$556$	−298.512	+	199.459i	−0.536892	+	0.358740i
$557$	−58.1418	−	58.1418i	−0.104384	−	0.104384i	0.652986	−	0.757370i	$-0.273516\pi$
$557$	−58.1418	−	58.1418i	−0.104384	−	0.104384i	−0.757370	+	0.652986i	$0.773516\pi$
$558$	−276.946	+	1392.30i	−0.496320	+	2.49517i
$559$	−226.670	−	547.229i	−0.405492	−	0.978943i
$560$			187.155i			0.334205i
$561$		0			0
$562$	633.956			1.12803
$563$	−226.413	+	93.7832i	−0.402154	+	0.166578i	−0.574587	−	0.818444i	$-0.694837\pi$
$563$	−226.413	+	93.7832i	−0.402154	+	0.166578i	0.172433	+	0.985021i	$0.444837\pi$
$564$	152.183	+	30.2711i	0.269828	+	0.0536721i
$565$	−225.308	+	225.308i	−0.398775	+	0.398775i
$566$	197.924	+	296.214i	0.349689	+	0.523347i
$567$	262.036	−	52.1221i	0.462144	−	0.0919261i
$568$	−8.95692	+	13.4050i	−0.0157692	+	0.0236003i
$569$	−14.5673	+	35.1685i	−0.0256015	+	0.0618076i	−0.936163	−	0.351565i	$-0.885649\pi$
$569$	−14.5673	+	35.1685i	−0.0256015	+	0.0618076i	0.910562	+	0.413373i	$0.135649\pi$
$570$	−456.267	−	188.992i	−0.800469	−	0.331565i
$571$	−47.1646	−	31.5143i	−0.0825999	−	0.0551915i	0.513584	−	0.858039i	$-0.328317\pi$
$571$	−47.1646	−	31.5143i	−0.0825999	−	0.0551915i	−0.596184	+	0.802848i	$0.703317\pi$
$572$	−21.3032	−	107.098i	−0.0372433	−	0.187235i
$573$	−487.340	+	325.630i	−0.850506	+	0.568290i
$574$	−511.658	−	511.658i	−0.891390	−	0.891390i
$575$	7.89050	−	39.6682i	0.0137226	−	0.0689882i
$576$	464.630	+	1121.72i	0.806650	+	1.94743i
$577$			711.158i			1.23251i	0.787547	+	0.616255i	$0.211351\pi$
$577$			711.158i			1.23251i	−0.787547	+	0.616255i	$0.788649\pi$
$578$		0			0
$579$	106.433			0.183823
$580$	−332.910	+	137.896i	−0.573983	+	0.237751i
$581$	−304.680	−	60.6047i	−0.524407	−	0.104311i
$582$	−159.395	+	159.395i	−0.273875	+	0.273875i
$583$	76.9846	+	115.216i	0.132049	+	0.197625i
$584$	19.0525	−	3.78978i	0.0326241	−	0.00648934i
$585$	−398.616	+	596.572i	−0.681396	+	1.01978i
$586$	−130.555	+	315.187i	−0.222790	+	0.537862i
$587$	865.959	+	358.692i	1.47523	+	0.611060i	0.968045	−	0.250778i	$-0.0806864\pi$
$587$	865.959	+	358.692i	1.47523	+	0.611060i	0.507184	+	0.861838i	$0.330686\pi$
$588$	676.494	+	452.019i	1.15050	+	0.768739i
$589$	−49.4661	−	248.683i	−0.0839832	−	0.422212i
$590$	199.021	−	132.982i	0.337324	−	0.225392i
$591$	−151.475	−	151.475i	−0.256303	−	0.256303i
$592$	−116.843	+	587.412i	−0.197371	+	0.992250i
$593$	355.720	+	858.785i	0.599865	+	1.44820i	0.873719	+	0.486432i	$0.161702\pi$
$593$	355.720	+	858.785i	0.599865	+	1.44820i	−0.273853	+	0.961772i	$0.588298\pi$
$594$			323.507i			0.544624i
$595$		0			0
$596$	−770.907			−1.29347
$597$	1757.24	−	727.871i	2.94344	−	1.21921i
$598$	−105.512	−	20.9876i	−0.176441	−	0.0350963i
$599$	278.647	−	278.647i	0.465187	−	0.465187i	−0.435164	−	0.900351i	$-0.643310\pi$
$599$	278.647	−	278.647i	0.465187	−	0.465187i	0.900351	+	0.435164i	$0.143310\pi$
$600$	10.5602	+	15.8044i	0.0176003	+	0.0263407i
$601$	−495.145	+	98.4905i	−0.823869	+	0.163878i	−0.588983	−	0.808145i	$-0.700472\pi$
$601$	−495.145	+	98.4905i	−0.823869	+	0.163878i	−0.234886	+	0.972023i	$0.575472\pi$
$602$	282.935	−	423.442i	0.469991	−	0.703391i
$603$	−119.589	+	288.714i	−0.198324	+	0.478796i
$604$	−820.744	−	339.963i	−1.35885	−	0.562853i
$605$	348.914	+	233.137i	0.576718	+	0.385351i
$606$	381.594	+	1918.40i	0.629692	+	3.16568i
$607$	−256.652	+	171.489i	−0.422820	+	0.282519i	−0.748722	−	0.662884i	$-0.769332\pi$
$607$	−256.652	+	171.489i	−0.422820	+	0.282519i	0.325902	+	0.945404i	$0.394332\pi$
$608$	−294.717	−	294.717i	−0.484732	−	0.484732i
$609$	−80.4749	+	404.575i	−0.132143	+	0.664326i
$610$	−164.839	−	397.956i	−0.270228	−	0.652387i
$611$			79.4528i			0.130037i
$612$		0			0
$613$	116.450			0.189967			0.0949835	−	0.995479i	$-0.469720\pi$
$613$	116.450			0.189967			0.0949835	+	0.995479i	$0.469720\pi$
$614$	−624.237	+	258.568i	−1.01667	+	0.421120i
$615$	−1430.08	−	284.460i	−2.32533	−	0.462537i
$616$	1.77258	−	1.77258i	0.00287756	−	0.00287756i
$617$	353.298	+	528.748i	0.572606	+	0.856966i	0.998865	−	0.0476356i	$-0.0151686\pi$
$617$	353.298	+	528.748i	0.572606	+	0.856966i	−0.426259	+	0.904601i	$0.640169\pi$
$618$	2686.74	−	534.427i	4.34748	−	0.864768i
$619$	−327.199	+	489.688i	−0.528593	+	0.791095i	−0.995654	−	0.0931298i	$-0.970313\pi$
$619$	−327.199	+	489.688i	−0.528593	+	0.791095i	0.467061	+	0.884225i	$0.345313\pi$
$620$	158.824	−	383.435i	0.256168	−	0.618444i
$621$	149.219	+	61.8085i	0.240288	+	0.0995306i
$622$	762.296	+	509.350i	1.22556	+	0.818891i
$623$	17.8539	+	89.7579i	0.0286580	+	0.144074i
$624$	−734.517	+	490.789i	−1.17711	+	0.786520i
$625$	138.086	+	138.086i	0.220938	+	0.220938i
$626$	175.035	−	879.962i	0.279609	−	1.40569i
$627$	−44.2311	−	106.783i	−0.0705441	−	0.170309i
$628$		−	645.382i		−	1.02768i
$629$		0			0
$630$	−616.892			−0.979194
$631$	1001.16	−	414.694i	1.58662	−	0.657201i	0.597179	−	0.802108i	$-0.296288\pi$
$631$	1001.16	−	414.694i	1.58662	−	0.657201i	0.989445	+	0.144906i	$0.0462881\pi$
$632$	36.3319	+	7.22686i	0.0574871	+	0.0114349i
$633$	−1178.49	+	1178.49i	−1.86175	+	1.86175i
$634$	−507.954	−	760.207i	−0.801189	−	1.19906i
$635$	395.818	−	78.7331i	0.623335	−	0.123989i
$636$	−676.510	+	1012.47i	−1.06370	+	1.59193i
$637$	−159.432	+	384.902i	−0.250285	+	0.604242i
$638$	−153.746	−	63.6838i	−0.240982	−	0.0998178i
$639$	772.040	+	515.861i	1.20820	+	0.807294i
$640$	−7.11006	−	35.7447i	−0.0111095	−	0.0558510i
$641$	−462.591	+	309.094i	−0.721671	+	0.482205i	−0.861363	−	0.507990i	$-0.830389\pi$
$641$	−462.591	+	309.094i	−0.721671	+	0.482205i	0.139692	+	0.990195i	$0.455389\pi$
$642$	−388.171	−	388.171i	−0.604627	−	0.604627i
$643$	21.1993	−	106.576i	0.0329694	−	0.165748i	−0.960793	−	0.277267i	$-0.910571\pi$
$643$	21.1993	−	106.576i	0.0329694	−	0.165748i	0.993762	+	0.111518i	$0.0355714\pi$
$644$	−17.9377	−	43.3054i	−0.0278536	−	0.0672445i
$645$		−	1026.22i		−	1.59103i
$646$		0			0
$647$	1175.55			1.81693			0.908463	−	0.417966i	$-0.137257\pi$
$647$	1175.55			1.81693			0.908463	+	0.417966i	$0.137257\pi$
$648$	−23.3644	+	9.67787i	−0.0360562	+	0.0149350i
$649$	54.9428	+	10.9288i	0.0846577	+	0.0168395i
$650$	−257.760	+	257.760i	−0.396555	+	0.396555i
$651$	−263.954	−	395.036i	−0.405460	−	0.606814i
$652$	672.579	−	133.784i	1.03156	−	0.205191i
$653$	378.122	−	565.900i	0.579054	−	0.866616i	−0.420111	−	0.907473i	$-0.638009\pi$
$653$	378.122	−	565.900i	0.579054	−	0.866616i	0.999165	+	0.0408570i	$0.0130088\pi$
$654$	−258.054	+	622.997i	−0.394578	+	0.952596i
$655$	−151.173	−	62.6181i	−0.230799	−	0.0956001i
$656$	−995.084	−	664.894i	−1.51690	−	1.01356i
$657$	−218.267	−	1097.30i	−0.332217	−	1.67017i
$658$	−56.8001	+	37.9526i	−0.0863223	+	0.0576787i
$659$	542.829	+	542.829i	0.823716	+	0.823716i	0.986639	−	0.162923i	$-0.0520921\pi$
$659$	542.829	+	542.829i	0.823716	+	0.823716i	−0.162923	+	0.986639i	$0.552092\pi$
$660$	36.9087	−	185.553i	0.0559223	−	0.281140i
$661$	35.1050	+	84.7509i	0.0531089	+	0.128216i	0.948207	−	0.317653i	$-0.102895\pi$
$661$	35.1050	+	84.7509i	0.0531089	+	0.128216i	−0.895098	+	0.445869i	$0.852895\pi$
$662$			76.1234i			0.114990i
$663$		0			0
$664$	29.4052			0.0442849
$665$	101.797	−	42.1659i	0.153079	−	0.0634073i
$666$	−1936.21	−	385.135i	−2.90722	−	0.578282i
$667$	−58.7489	+	58.7489i	−0.0880793	+	0.0880793i
$668$	−122.954	−	184.014i	−0.184063	−	0.275470i
$669$	553.784	−	110.155i	0.827779	−	0.164656i
$670$	100.162	−	149.902i	0.149495	−	0.223735i
$671$	38.5784	−	93.1365i	0.0574939	−	0.138803i
$672$	−721.529	−	298.867i	−1.07370	−	0.444743i
$673$	−141.118	−	94.2920i	−0.209685	−	0.140107i	0.446293	−	0.894887i	$-0.352744\pi$
$673$	−141.118	−	94.2920i	−0.209685	−	0.140107i	−0.655978	+	0.754780i	$0.727744\pi$
$674$	−271.874	−	1366.80i	−0.403374	−	2.02790i
$675$	455.050	−	304.055i	0.674149	−	0.450452i
$676$	−143.676	−	143.676i	−0.212538	−	0.212538i
$677$	88.7111	−	445.981i	0.131036	−	0.658761i	−0.858305	−	0.513140i	$-0.828482\pi$
$677$	88.7111	−	445.981i	0.131036	−	0.658761i	0.989341	−	0.145621i	$-0.0465179\pi$
$678$	−494.857	−	1194.69i	−0.729877	−	1.76208i
$679$		−	50.2930i		−	0.0740692i
$680$		0			0
$681$	1025.33			1.50563
$682$	177.080	−	73.3490i	0.259648	−	0.107550i
$683$	1316.98	+	261.964i	1.92823	+	0.383548i	0.999931	+	0.0117083i	$0.00372694\pi$
$683$	1316.98	+	261.964i	1.92823	+	0.383548i	0.928297	+	0.371840i	$0.121273\pi$
$684$	478.775	−	478.775i	0.699964	−	0.699964i
$685$	124.576	+	186.442i	0.181863	+	0.272178i
$686$	−803.128	+	159.752i	−1.17074	+	0.232875i
$687$	−522.803	+	782.430i	−0.760995	+	1.13891i
$688$	322.334	−	778.182i	0.468508	−	1.13108i
$689$	−576.061	−	238.612i	−0.836082	−	0.346317i
$690$	−154.974	−	103.550i	−0.224600	−	0.150073i
$691$	38.2589	+	192.341i	0.0553675	+	0.278351i	0.998544	−	0.0539406i	$-0.0171782\pi$
$691$	38.2589	+	192.341i	0.0553675	+	0.278351i	−0.943177	+	0.332292i	$0.892178\pi$
$692$	−229.820	+	153.561i	−0.332109	+	0.221908i
$693$	−102.089	−	102.089i	−0.147315	−	0.147315i
$694$	−134.365	+	675.501i	−0.193610	+	0.973344i
$695$	−121.887	−	294.261i	−0.175377	−	0.423397i
$696$		−	39.0462i		−	0.0561008i
$697$		0			0
$698$	−113.096			−0.162028
$699$	28.1181	−	11.6469i	0.0402262	−	0.0166622i
$700$	−155.778	−	30.9861i	−0.222540	−	0.0442659i
$701$	164.717	−	164.717i	0.234975	−	0.234975i	−0.579791	−	0.814766i	$-0.696866\pi$
$701$	164.717	−	164.717i	0.234975	−	0.234975i	0.814766	+	0.579791i	$0.196866\pi$
$702$	−808.742	−	1210.37i	−1.15205	−	1.72417i
$703$	345.831	−	68.7900i	0.491936	−	0.0978521i
$704$	91.0754	−	136.304i	0.129369	−	0.193614i
$705$	−52.6786	+	127.177i	−0.0747214	+	0.180393i
$706$	−1681.62	−	696.551i	−2.38190	−	0.986616i
$707$	−362.852	−	242.450i	−0.513227	−	0.342928i
$708$	96.0381	+	482.816i	0.135647	+	0.681944i
$709$	625.370	−	417.859i	0.882046	−	0.589364i	−0.0299558	−	0.999551i	$-0.509537\pi$
$709$	625.370	−	417.859i	0.882046	−	0.589364i	0.912001	+	0.410187i	$0.134537\pi$
$710$	−378.781	−	378.781i	−0.533494	−	0.533494i
$711$	416.220	−	2092.48i	0.585401	−	2.94301i
$712$	−3.31506	−	8.00327i	−0.00465599	−	0.0112406i
$713$		−	95.6929i		−	0.134212i
$714$		0			0
$715$	96.8747			0.135489
$716$	−952.681	+	394.613i	−1.33056	+	0.551136i
$717$	351.330	+	69.8838i	0.490000	+	0.0974670i
$718$	410.618	−	410.618i	0.571891	−	0.571891i
$719$	297.051	+	444.568i	0.413144	+	0.618314i	0.978429	−	0.206582i	$-0.0662339\pi$
$719$	297.051	+	444.568i	0.413144	+	0.618314i	−0.565285	+	0.824896i	$0.691234\pi$
$720$	−1000.70	+	199.051i	−1.38985	+	0.276459i
$721$	−339.554	+	508.179i	−0.470949	+	0.704825i
$722$	302.089	−	729.307i	0.418406	−	1.01012i
$723$	1487.54	+	616.159i	2.05745	+	0.852225i
$724$	58.5314	+	39.1094i	0.0808444	+	0.0540185i
$725$	54.9231	+	276.117i	0.0757559	+	0.380851i
$726$	−1416.01	+	946.150i	−1.95043	+	1.30324i
$727$	883.793	+	883.793i	1.21567	+	1.21567i	0.969133	+	0.246538i	$0.0792932\pi$
$727$	883.793	+	883.793i	1.21567	+	1.21567i	0.246538	+	0.969133i	$0.420707\pi$
$728$	−2.20062	+	11.0632i	−0.00302282	+	0.0151968i
$729$	−279.220	−	674.098i	−0.383018	−	0.924688i
$730$			645.448i			0.884175i
$731$		0			0
$732$	885.881			1.21022
$733$	−602.864	+	249.714i	−0.822460	+	0.340674i	−0.753914	−	0.656974i	$-0.771836\pi$
$733$	−602.864	+	249.714i	−0.822460	+	0.340674i	−0.0685469	+	0.997648i	$0.521836\pi$
$734$	787.569	+	156.657i	1.07298	+	0.213429i
$735$	−510.393	+	510.393i	−0.694412	+	0.694412i
$736$	−87.3911	−	130.790i	−0.118738	−	0.177704i
$737$	41.3829	−	8.23157i	0.0561504	−	0.0111690i
$738$	2191.60	−	3279.96i	2.96965	−	4.44439i
$739$	294.324	−	710.562i	0.398274	−	0.961518i	−0.589802	−	0.807548i	$-0.700794\pi$
$739$	294.324	−	710.562i	0.398274	−	0.961518i	0.988075	−	0.153970i	$-0.0492060\pi$
$740$	533.224	+	220.869i	0.720573	+	0.298471i
$741$	432.437	+	288.945i	0.583586	+	0.389940i
$742$	−104.588	−	525.799i	−0.140954	−	0.708624i
$743$	56.1076	−	37.4899i	0.0755150	−	0.0504575i	−0.517240	−	0.855841i	$-0.673040\pi$
$743$	56.1076	−	37.4899i	0.0755150	−	0.0504575i	0.592755	+	0.805383i	$0.298040\pi$
$744$	31.8001	+	31.8001i	0.0427421	+	0.0427421i
$745$	133.426	−	670.777i	0.179095	−	0.900372i
$746$	371.592	+	897.102i	0.498113	+	1.20255i
$747$		−	1693.55i		−	2.26713i
$748$		0			0
$749$	122.477			0.163521
$750$	−1829.54	+	757.818i	−2.43938	+	1.01042i
$751$	−273.988	−	54.4996i	−0.364831	−	0.0725694i	0.00927083	−	0.999957i	$-0.497049\pi$
$751$	−273.988	−	54.4996i	−0.364831	−	0.0725694i	−0.374102	+	0.927388i	$0.622049\pi$
$752$	−79.8926	+	79.8926i	−0.106240	+	0.106240i
$753$	−611.917	−	915.799i	−0.812639	−	1.21620i
$754$	734.431	−	146.087i	0.974047	−	0.193750i
$755$	437.858	−	655.301i	0.579944	−	0.867948i
$756$	242.723	−	585.985i	0.321062	−	0.775113i
$757$	537.150	+	222.495i	0.709577	+	0.293917i	0.708130	−	0.706082i	$-0.249539\pi$
$757$	537.150	+	222.495i	0.709577	+	0.293917i	0.00144764	+	0.999999i	$0.499539\pi$
$758$	−848.001	−	566.616i	−1.11873	−	0.747514i
$759$	−8.51005	−	42.7829i	−0.0112122	−	0.0563675i
$760$	−8.67204	+	5.79447i	−0.0114106	+	0.00762431i
$761$	64.7670	+	64.7670i	0.0851078	+	0.0851078i	0.748379	−	0.663271i	$-0.230832\pi$
$761$	64.7670	+	64.7670i	0.0851078	+	0.0851078i	−0.663271	+	0.748379i	$0.730832\pi$
$762$	−319.526	+	1606.36i	−0.419325	+	2.10809i
$763$	−57.5742	−	138.996i	−0.0754577	−	0.182171i
$764$			463.595i			0.606799i
$765$		0			0
$766$	688.823			0.899247
$767$	−232.884	+	96.4639i	−0.303630	+	0.125768i
$768$	−1230.10	−	244.681i	−1.60169	−	0.318596i
$769$	8.68658	−	8.68658i	0.0112959	−	0.0112959i	−0.701436	−	0.712732i	$-0.747457\pi$
$769$	8.68658	−	8.68658i	0.0112959	−	0.0112959i	0.712732	+	0.701436i	$0.247457\pi$
$770$	46.2746	+	69.2548i	0.0600969	+	0.0899414i
$771$	−1231.38	+	244.936i	−1.59712	+	0.317686i
$772$	46.7702	−	69.9966i	0.0605832	−	0.0906691i
$773$	−106.339	+	256.725i	−0.137567	+	0.332115i	−0.977617	−	0.210393i	$-0.932526\pi$
$773$	−106.339	+	256.725i	−0.137567	+	0.332115i	0.840050	+	0.542509i	$0.182526\pi$
$774$	2565.02	+	1062.46i	3.31397	+	1.37269i
$775$	−269.607	−	180.145i	−0.347879	−	0.232446i
$776$	0.928746	+	4.66912i	0.00119684	+	0.00601691i
$777$	549.356	−	367.068i	0.707022	−	0.472417i
$778$	1349.54	+	1349.54i	1.73463	+	1.73463i
$779$	−137.458	+	691.048i	−0.176454	+	0.887096i
$780$	325.777	+	786.496i	0.417663	+	1.00833i
$781$		−	125.368i		−	0.160523i
$782$		0			0
$783$	−1124.24			−1.43581
$784$	−547.346	+	226.718i	−0.698145	+	0.289181i
$785$	561.556	+	111.700i	0.715357	+	0.142293i
$786$	469.563	−	469.563i	0.597408	−	0.597408i
$787$	73.6228	+	110.184i	0.0935486	+	0.140005i	0.875292	−	0.483595i	$-0.160669\pi$
$787$	73.6228	+	110.184i	0.0935486	+	0.140005i	−0.781743	+	0.623600i	$0.785669\pi$
$788$	−166.182	+	33.0556i	−0.210890	+	0.0419487i
$789$	−690.664	+	1033.65i	−0.875366	+	1.31008i
$790$	−471.017	+	1137.14i	−0.596224	+	1.43941i
$791$	266.546	+	110.407i	0.336974	+	0.139579i
$792$	11.3630	+	7.59254i	0.0143473	+	0.00958654i
$793$	88.4969	+	444.904i	0.111598	+	0.561039i
$794$	1060.67	−	708.715i	1.33585	−	0.892589i
$795$	−763.875	−	763.875i	−0.960850	−	0.960850i
$796$	293.497	−	1475.51i	0.368714	−	1.85365i
$797$	471.097	+	1137.33i	0.591087	+	1.42701i	0.882453	+	0.470400i	$0.155890\pi$
$797$	471.097	+	1137.33i	0.591087	+	1.42701i	−0.291366	+	0.956612i	$0.594110\pi$
$798$			447.167i			0.560360i
$799$		0			0
$800$	−533.007			−0.666259
$801$	−460.937	+	190.926i	−0.575452	+	0.238360i
$802$	−388.246	−	77.2270i	−0.484098	−	0.0962930i
$803$	−106.815	+	106.815i	−0.133020	+	0.133020i
$804$	205.995	+	308.293i	0.256213	+	0.383449i
$805$	40.7852	−	8.11269i	0.0506649	−	0.0100779i
$806$	−479.161	+	717.115i	−0.594492	+	0.889721i
$807$	−22.5258	+	54.3821i	−0.0279130	+	0.0673880i
$808$	38.1638	+	15.8080i	0.0472325	+	0.0195643i
$809$	−1311.89	−	876.574i	−1.62161	−	1.08353i	−0.933892	−	0.357555i	$-0.883611\pi$
$809$	−1311.89	−	876.574i	−1.62161	−	1.08353i	−0.687722	−	0.725974i	$-0.741389\pi$
$810$	−163.930	−	824.133i	−0.202383	−	1.01745i
$811$	500.179	−	334.209i	0.616744	−	0.412095i	−0.207576	−	0.978219i	$-0.566558\pi$
$811$	500.179	−	334.209i	0.616744	−	0.412095i	0.824320	+	0.566124i	$0.191558\pi$
$812$	230.708	+	230.708i	0.284123	+	0.284123i
$813$	−357.119	+	1795.36i	−0.439261	+	2.20832i
$814$	102.003	+	246.256i	0.125310	+	0.302526i
$815$			608.375i			0.746472i
$816$		0			0
$817$	−495.892			−0.606966
$818$	1064.39	−	440.884i	1.30121	−	0.538978i
$819$	637.171	+	126.741i	0.777987	+	0.154751i
$820$	−815.500	+	815.500i	−0.994512	+	0.994512i
$821$	−436.732	−	653.616i	−0.531952	−	0.796122i	0.464017	−	0.885827i	$-0.346408\pi$
$821$	−436.732	−	653.616i	−0.531952	−	0.796122i	−0.995968	+	0.0897043i	$0.971408\pi$
$822$	−892.522	+	177.534i	−1.08579	+	0.215978i
$823$	155.881	−	233.293i	0.189406	−	0.283466i	−0.724598	−	0.689172i	$-0.757974\pi$
$823$	155.881	−	233.293i	0.189406	−	0.283466i	0.914004	+	0.405706i	$0.132974\pi$
$824$	22.1393	−	53.4489i	0.0268681	−	0.0648652i
$825$	−136.558	−	56.5640i	−0.165524	−	0.0685625i
$826$	−180.204	−	120.409i	−0.218165	−	0.145773i
$827$	−288.440	−	1450.09i	−0.348779	−	1.75343i	−0.614059	−	0.789260i	$-0.710464\pi$
$827$	−288.440	−	1450.09i	−0.348779	−	1.75343i	0.265280	−	0.964171i	$-0.414536\pi$
$828$	212.472	−	141.969i	0.256608	−	0.171460i
$829$	331.030	+	331.030i	0.399312	+	0.399312i	0.877990	−	0.478678i	$-0.158884\pi$
$829$	331.030	+	331.030i	0.399312	+	0.399312i	−0.478678	+	0.877990i	$0.658884\pi$
$830$	−190.609	+	958.256i	−0.229649	+	1.15453i
$831$	185.435	+	447.681i	0.223147	+	0.538725i
$832$			737.650i			0.886598i
$833$		0			0
$834$	1292.61			1.54989
$835$	181.394	−	75.1357i	0.217238	−	0.0899828i
$836$	−89.6634	−	17.8352i	−0.107253	−	0.0213339i
$837$	915.607	−	915.607i	1.09392	−	1.09392i
$838$	−413.386	−	618.676i	−0.493300	−	0.738276i
$839$	207.442	−	41.2627i	0.247249	−	0.0491809i	−0.0699099	−	0.997553i	$-0.522271\pi$
$839$	207.442	−	41.2627i	0.247249	−	0.0491809i	0.317159	+	0.948372i	$0.397271\pi$
$840$	−10.8576	+	16.2495i	−0.0129257	+	0.0193446i
$841$	−100.525	+	242.689i	−0.119530	+	0.288572i
$842$	1599.76	+	662.644i	1.89996	+	0.786988i
$843$	−961.751	−	642.622i	−1.14087	−	0.762303i
$844$	257.175	+	1292.91i	0.304710	+	1.53188i
$845$	149.881	−	100.147i	0.177374	−	0.118518i
$846$	−263.339	−	263.339i	−0.311276	−	0.311276i
$847$	74.1266	−	372.660i	0.0875167	−	0.439976i
$848$	−339.316	−	819.181i	−0.400137	−	0.966016i
$849$		−	650.006i		−	0.765613i
$850$		0			0
$851$	133.075			0.156375
$852$	1017.83	−	421.598i	1.19463	−	0.494833i
$853$	−981.657	−	195.264i	−1.15083	−	0.228914i	−0.417428	−	0.908710i	$-0.637068\pi$
$853$	−981.657	−	195.264i	−1.15083	−	0.228914i	−0.733401	+	0.679796i	$0.762068\pi$
$854$	−275.785	+	275.785i	−0.322933	+	0.322933i
$855$	333.724	+	499.454i	0.390321	+	0.584156i
$856$	−11.3706	+	2.26175i	−0.0132834	+	0.00264223i
$857$	−413.523	+	618.882i	−0.482524	+	0.722149i	−0.990240	−	0.139376i	$-0.955490\pi$
$857$	−413.523	+	618.882i	−0.482524	+	0.722149i	0.507715	+	0.861525i	$0.330490\pi$
$858$	−150.452	+	363.224i	−0.175352	+	0.423338i
$859$	−903.157	−	374.100i	−1.05141	−	0.435506i	−0.211012	−	0.977483i	$-0.567676\pi$
$859$	−903.157	−	374.100i	−1.05141	−	0.435506i	−0.840393	+	0.541977i	$0.817676\pi$
$860$	−674.897	−	450.952i	−0.784765	−	0.524363i
$861$	257.566	+	1294.87i	0.299147	+	1.50391i
$862$	−1516.21	+	1013.10i	−1.75894	+	1.17529i
$863$	−799.269	−	799.269i	−0.926152	−	0.926152i	0.0713024	−	0.997455i	$-0.477284\pi$
$863$	−799.269	−	799.269i	−0.926152	−	0.926152i	−0.997455	+	0.0713024i	$0.977284\pi$
$864$	415.249	−	2087.60i	0.480612	−	2.41620i
$865$	−93.8388	−	226.547i	−0.108484	−	0.261904i
$866$		−	1820.44i		−	2.10213i
$867$		0			0
$868$	−375.788			−0.432935
$869$	−266.132	+	110.236i	−0.306251	+	0.126853i
$870$	1272.44	+	253.103i	1.46257	+	0.290923i
$871$	−134.252	+	134.252i	−0.154135	+	0.154135i
$872$	7.91191	+	11.8410i	0.00907329	+	0.0135791i
$873$	268.911	−	53.4898i	0.308031	−	0.0612712i
$874$	−50.0378	+	74.8869i	−0.0572515	+	0.0856830i
$875$	169.076	−	408.186i	0.193230	−	0.466499i
$876$	−1226.40	−	507.991i	−1.40000	−	0.579899i
$877$	1119.07	+	747.740i	1.27602	+	0.852611i	0.994272	−	0.106877i	$-0.0340851\pi$
$877$	1119.07	+	747.740i	1.27602	+	0.852611i	0.281750	+	0.959488i	$0.409085\pi$
$878$	−391.758	−	1969.50i	−0.446193	−	2.24316i
$879$	517.556	−	345.820i	0.588801	−	0.393424i
$880$	97.4109	+	97.4109i	0.110694	+	0.110694i
$881$	206.693	−	1039.11i	0.234611	−	1.17947i	−0.666373	−	0.745619i	$-0.732154\pi$
$881$	206.693	−	1039.11i	0.234611	−	1.17947i	0.900984	−	0.433852i	$-0.142846\pi$
$882$	−747.300	−	1804.14i	−0.847279	−	2.04551i
$883$			658.553i			0.745813i	0.927869	+	0.372907i	$0.121639\pi$
$883$			658.553i			0.745813i	−0.927869	+	0.372907i	$0.878361\pi$
$884$		0			0
$885$	−436.727			−0.493477
$886$	834.510	−	345.665i	0.941885	−	0.390142i
$887$	654.269	+	130.142i	0.737620	+	0.146722i	0.549582	−	0.835440i	$-0.314787\pi$
$887$	654.269	+	130.142i	0.737620	+	0.146722i	0.188038	+	0.982162i	$0.439787\pi$
$888$	−44.2228	+	44.2228i	−0.0498005	+	0.0498005i
$889$	−203.014	−	303.832i	−0.228362	−	0.341769i
$890$	282.299	−	56.1528i	0.317190	−	0.0630930i
$891$	109.256	−	163.514i	0.122622	−	0.183517i
$892$	170.907	−	412.605i	0.191599	−	0.462562i
$893$	61.4550	+	25.4555i	0.0688186	+	0.0285056i
$894$	2307.80	+	1542.03i	2.58144	+	1.72486i
$895$	−178.472	−	897.239i	−0.199410	−	1.00250i
$896$	−27.4378	+	18.3334i	−0.0306226	+	0.0204614i
$897$	138.794	+	138.794i	0.154731	+	0.154731i
$898$	−136.636	+	686.915i	−0.152156	+	0.764939i
$899$	254.900	+	615.383i	0.283537	+	0.684519i
$900$		−	865.883i		−	0.962092i
$901$		0			0
$902$	−532.619			−0.590487
$903$	−858.460	+	355.586i	−0.950676	+	0.393783i
$904$	−26.7846	−	5.32779i	−0.0296290	−	0.00589357i
$905$	−44.1600	+	44.1600i	−0.0487956	+	0.0487956i
$906$	1776.98	+	2659.43i	1.96134	+	2.93536i
$907$	176.970	−	35.2015i	0.195116	−	0.0388109i	−0.0965649	−	0.995327i	$-0.530786\pi$
$907$	176.970	−	35.2015i	0.195116	−	0.0388109i	0.291681	+	0.956516i	$0.405786\pi$
$908$	450.563	−	674.316i	0.496215	−	0.742638i
$909$	910.437	−	2197.99i	1.00158	−	2.41803i
$910$	−346.264	−	143.427i	−0.380510	−	0.157612i
$911$	1373.95	+	918.042i	1.50817	+	1.00773i	0.988135	+	0.153588i	$0.0490829\pi$
$911$	1373.95	+	918.042i	1.50817	+	1.00773i	0.520040	+	0.854142i	$0.325917\pi$
$912$	144.286	+	725.375i	0.158208	+	0.795367i
$913$	−190.125	+	127.037i	−0.208242	+	0.139143i
$914$	−749.335	−	749.335i	−0.819842	−	0.819842i
$915$	−153.325	+	770.817i	−0.167568	+	0.842423i
$916$	284.834	+	687.650i	0.310954	+	0.750709i
$917$			148.158i			0.161569i
$918$		0			0
$919$	−630.155			−0.685697			−0.342848	−	0.939391i	$-0.611392\pi$
$919$	−630.155			−0.685697			−0.342848	+	0.939391i	$0.611392\pi$
$920$	−3.63662	+	1.50634i	−0.00395285	+	0.00163732i
$921$	1209.11	+	240.507i	1.31282	+	0.261137i
$922$	1734.82	−	1734.82i	1.88158	−	1.88158i
$923$	313.411	+	469.053i	0.339557	+	0.508183i
$924$	−168.009	+	33.4191i	−0.181828	+	0.0361679i
$925$	250.519	−	374.928i	0.270832	−	0.405328i
$926$	−595.167	+	1436.86i	−0.642729	+	1.55169i
$927$	−3078.31	−	1275.08i	−3.32073	−	1.37549i
$928$	910.385	+	608.300i	0.981018	+	0.655496i
$929$	305.811	+	1537.42i	0.329183	+	1.65492i	0.691140	+	0.722721i	$0.257109\pi$
$929$	305.811	+	1537.42i	0.329183	+	1.65492i	−0.361956	+	0.932195i	$0.617891\pi$
$930$	−1242.43	+	830.168i	−1.33595	+	0.892654i
$931$	246.634	+	246.634i	0.264913	+	0.264913i
$932$	4.69633	−	23.6101i	0.00503899	−	0.0253327i
$933$	−640.139	−	1545.43i	−0.686109	−	1.65641i
$934$			1153.41i			1.23492i
$935$		0			0
$936$	−61.4945			−0.0656992
$937$	704.857	−	291.961i	0.752248	−	0.311591i	0.0265897	−	0.999646i	$-0.491535\pi$
$937$	704.857	−	291.961i	0.752248	−	0.311591i	0.725659	+	0.688055i	$0.241535\pi$
$938$	−160.104	−	31.8467i	−0.170686	−	0.0339517i
$939$	−1157.53	+	1157.53i	−1.23273	+	1.23273i
$940$	60.4903	+	90.5302i	0.0643514	+	0.0963087i
$941$	1158.57	−	230.453i	1.23121	−	0.244902i	0.463728	−	0.885977i	$-0.346511\pi$
$941$	1158.57	−	230.453i	1.23121	−	0.244902i	0.767478	+	0.641075i	$0.221511\pi$
$942$	−1290.94	+	1932.03i	−1.37043	+	2.05099i
$943$	−101.761	+	245.673i	−0.107912	+	0.260523i
$944$	−331.171	−	137.176i	−0.350817	−	0.145313i
$945$	467.864	+	312.617i	0.495095	+	0.330812i
$946$	−73.1316	−	367.657i	−0.0773061	−	0.388644i
$947$	−1449.59	+	968.584i	−1.53072	+	1.02279i	−0.548257	+	0.836310i	$0.684709\pi$
$947$	−1449.59	+	968.584i	−1.53072	+	1.02279i	−0.982458	+	0.186482i	$0.940291\pi$
$948$	−1789.94	−	1789.94i	−1.88812	−	1.88812i
$949$	132.608	−	666.665i	0.139734	−	0.702493i
$950$	116.789	+	281.955i	0.122936	+	0.296794i
$951$			1668.18i			1.75413i
$952$		0			0
$953$	−1007.14			−1.05681			−0.528405	−	0.848992i	$-0.677210\pi$
$953$	−1007.14			−1.05681			−0.528405	+	0.848992i	$0.677210\pi$
$954$	2700.16	−	1118.44i	2.83035	−	1.17237i
$955$	−403.380	−	80.2373i	−0.422387	−	0.0840181i
$956$	200.345	−	200.345i	0.209566	−	0.209566i
$957$	168.689	+	252.460i	0.176268	+	0.263804i
$958$	335.888	−	66.8122i	0.350614	−	0.0697414i
$959$	112.798	−	168.814i	0.117621	−	0.176032i
$960$	−489.074	+	1180.73i	−0.509452	+	1.22993i
$961$	179.070	+	74.1731i	0.186337	+	0.0771833i
$962$	−997.256	−	666.345i	−1.03665	−	0.692666i
$963$	130.262	+	654.872i	0.135267	+	0.680034i
$964$	1058.89	−	707.530i	1.09844	−	0.733952i
$965$	52.8101	+	52.8101i	0.0547255	+	0.0547255i
$966$	−32.9241	+	165.520i	−0.0340829	+	0.171346i
$967$	206.749	+	499.135i	0.213804	+	0.516169i	0.994002	−	0.109364i	$-0.0348815\pi$
$967$	206.749	+	499.135i	0.213804	+	0.516169i	−0.780198	+	0.625533i	$0.784882\pi$
$968$			35.9660i			0.0371550i
$969$		0			0
$970$	−158.177			−0.163069
$971$	−370.956	+	153.655i	−0.382035	+	0.158244i	−0.565432	−	0.824795i	$-0.691291\pi$
$971$	−370.956	+	153.655i	−0.382035	+	0.158244i	0.183397	+	0.983039i	$0.441291\pi$
$972$	−0.989918	−	0.196907i	−0.00101843	−	0.000202579i
$973$	−203.924	+	203.924i	−0.209583	+	0.209583i
$974$	−1282.31	−	1919.11i	−1.31654	−	1.97034i
$975$	652.323	−	129.755i	0.669049	−	0.133082i
$976$	−358.380	+	536.353i	−0.367192	+	0.549542i
$977$	364.881	−	880.902i	0.373471	−	0.901639i	−0.619686	−	0.784850i	$-0.712740\pi$
$977$	364.881	−	880.902i	0.373471	−	0.901639i	0.993157	−	0.116789i	$-0.0372601\pi$
$978$	−2281.05	−	944.842i	−2.33236	−	0.966096i
$979$	56.0102	+	37.4248i	0.0572116	+	0.0382276i
$980$	111.380	+	559.946i	0.113653	+	0.571373i
$981$	681.966	−	455.675i	0.695174	−	0.464500i
$982$	303.323	+	303.323i	0.308883	+	0.308883i
$983$	−278.393	+	1399.58i	−0.283208	+	1.42378i	0.533045	+	0.846087i	$0.321048\pi$
$983$	−278.393	+	1399.58i	−0.283208	+	1.42378i	−0.816253	+	0.577695i	$0.803952\pi$
$984$	−47.8240	−	115.457i	−0.0486016	−	0.117335i
$985$		−	150.318i		−	0.152607i
$986$		0			0
$987$	124.641			0.126282
$988$	380.053	−	157.423i	0.384669	−	0.159335i
$989$	−183.556	−	36.5116i	−0.185598	−	0.0369176i
$990$	−321.082	+	321.082i	−0.324326	+	0.324326i
$991$	−156.350	−	233.995i	−0.157770	−	0.236120i	0.744160	−	0.668001i	$-0.232850\pi$
$991$	−156.350	−	233.995i	−0.157770	−	0.236120i	−0.901930	+	0.431881i	$0.857850\pi$
$992$	−1236.85	+	246.025i	−1.24683	+	0.248009i
$993$	77.1640	−	115.484i	0.0777080	−	0.116298i
$994$	−185.613	+	448.110i	−0.186734	+	0.450815i
$995$	1233.06	+	510.751i	1.23926	+	0.513317i
$996$	−1670.74	−	1116.35i	−1.67745	−	1.12084i
$997$	104.917	+	527.453i	0.105233	+	0.529040i	0.997057	+	0.0766590i	$0.0244253\pi$
$997$	104.917	+	527.453i	0.105233	+	0.529040i	−0.891825	+	0.452381i	$0.850575\pi$
$998$	1951.04	−	1303.65i	1.95495	−	1.30626i
$999$	1273.29	+	1273.29i	1.27456	+	1.27456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.e.224.1		8
17.2	even	8		289.3.e.h.131.1		8
17.3	odd	16		289.3.e.h.214.1		8
17.4	even	4		289.3.e.j.65.1		8
17.5	odd	16		17.3.e.b.7.1	yes	8
17.6	odd	16	inner	289.3.e.e.40.1		8
17.7	odd	16		289.3.e.n.249.1		8
17.8	even	8		17.3.e.b.5.1	✓	8
17.9	even	8		289.3.e.g.158.1		8
17.10	odd	16		289.3.e.j.249.1		8
17.11	odd	16		289.3.e.a.40.1		8
17.12	odd	16		289.3.e.g.75.1		8
17.13	even	4		289.3.e.n.65.1		8
17.14	odd	16		289.3.e.f.214.1		8
17.15	even	8		289.3.e.f.131.1		8
17.16	even	2		289.3.e.a.224.1		8
51.5	even	16		153.3.p.a.109.1		8
51.8	odd	8		153.3.p.a.73.1		8
68.39	even	16		272.3.bh.b.177.1		8
68.59	odd	8		272.3.bh.b.209.1		8
85.8	odd	8		425.3.t.d.124.1		8
85.22	even	16		425.3.t.d.24.1		8
85.39	odd	16		425.3.u.a.126.1		8
85.42	odd	8		425.3.t.b.124.1		8
85.59	even	8		425.3.u.a.226.1		8
85.73	even	16		425.3.t.b.24.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.5.1	✓	8	17.8	even	8
17.3.e.b.7.1	yes	8	17.5	odd	16
153.3.p.a.73.1		8	51.8	odd	8
153.3.p.a.109.1		8	51.5	even	16
272.3.bh.b.177.1		8	68.39	even	16
272.3.bh.b.209.1		8	68.59	odd	8
289.3.e.a.40.1		8	17.11	odd	16
289.3.e.a.224.1		8	17.16	even	2
289.3.e.e.40.1		8	17.6	odd	16	inner
289.3.e.e.224.1		8	1.1	even	1	trivial
289.3.e.f.131.1		8	17.15	even	8
289.3.e.f.214.1		8	17.14	odd	16
289.3.e.g.75.1		8	17.12	odd	16
289.3.e.g.158.1		8	17.9	even	8
289.3.e.h.131.1		8	17.2	even	8
289.3.e.h.214.1		8	17.3	odd	16
289.3.e.j.65.1		8	17.4	even	4
289.3.e.j.249.1		8	17.10	odd	16
289.3.e.n.65.1		8	17.13	even	4
289.3.e.n.249.1		8	17.7	odd	16
425.3.t.b.24.1		8	85.73	even	16
425.3.t.b.124.1		8	85.42	odd	8
425.3.t.d.24.1		8	85.22	even	16
425.3.t.d.124.1		8	85.8	odd	8
425.3.u.a.126.1		8	85.39	odd	16
425.3.u.a.226.1		8	85.59	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.63099 + 1.08979i) q^{2} +(5.09606 + 1.01367i) q^{3} +(2.90602 - 2.90602i) q^{4} +(2.02560 + 3.03153i) q^{5} +(-14.5124 + 2.88669i) q^{6} +(1.83409 - 2.74491i) q^{7} +(-0.119585 + 0.288703i) q^{8} +(16.6274 + 6.88730i) q^{9} +(-8.63307 - 5.76843i) q^{10} +(-0.474066 - 2.38329i) q^{11} +(17.7550 - 11.8635i) q^{12} +(7.73173 + 7.73173i) q^{13} +(-1.83409 + 9.22059i) q^{14} +(7.24963 + 17.5022i) q^{15} +15.5490i q^{16} -51.2522 q^{18} +(8.45745 - 3.50319i) q^{19} +(14.6961 + 2.92324i) q^{20} +(12.1291 - 12.1291i) q^{21} +(3.84455 + 5.75378i) q^{22} +(3.38849 - 0.674012i) q^{23} +(-0.902059 + 1.35003i) q^{24} +(4.47998 - 10.8156i) q^{25} +(-28.7680 - 11.9161i) q^{26} +(38.8707 + 25.9726i) q^{27} +(-2.64686 - 13.3067i) q^{28} +(-19.9953 + 13.3605i) q^{29} +(-38.1474 - 38.1474i) q^{30} +(5.40360 - 27.1657i) q^{31} +(-17.4235 - 42.0641i) q^{32} -12.6260i q^{33} +12.0364 q^{35} +(68.3342 - 28.3049i) q^{36} +(37.7780 + 7.51452i) q^{37} +(-18.4337 + 18.4337i) q^{38} +(31.5639 + 47.2388i) q^{39} +(-1.11744 + 0.222273i) q^{40} +(-42.7611 + 63.9965i) q^{41} +(-18.6933 + 45.1295i) q^{42} +(-50.0470 - 20.7301i) q^{43} +(-8.30354 - 5.54825i) q^{44} +(12.8015 + 64.3574i) q^{45} +(-8.18054 + 5.46606i) q^{46} +(5.13810 + 5.13810i) q^{47} +(-15.7616 + 79.2388i) q^{48} +(14.5808 + 35.2013i) q^{49} +33.3380i q^{50} +44.9371 q^{52} +(-52.6837 + 21.8223i) q^{53} +(-130.573 - 25.9726i) q^{54} +(6.26475 - 6.26475i) q^{55} +(0.573134 + 0.857755i) q^{56} +(46.6508 - 9.27942i) q^{57} +(38.0474 - 56.9419i) q^{58} +(-8.82213 + 21.2985i) q^{59} +(71.9292 + 29.7940i) q^{60} +(34.4943 + 23.0484i) q^{61} +(15.3882 + 77.3615i) q^{62} +(49.4011 - 33.0088i) q^{63} +(47.7028 + 47.7028i) q^{64} +(-7.77755 + 39.1004i) q^{65} +(13.7596 + 33.2187i) q^{66} +17.3637i q^{67} +17.9512 q^{69} +(-31.6676 + 13.1172i) q^{70} +(50.6009 + 10.0651i) q^{71} +(-3.97676 + 3.97676i) q^{72} +(-34.5368 - 51.6879i) q^{73} +(-107.583 + 21.3995i) q^{74} +(33.7937 - 50.5759i) q^{75} +(14.3972 - 34.7579i) q^{76} +(-7.41140 - 3.06990i) q^{77} +(-134.525 - 89.8865i) q^{78} +(-23.1267 - 116.266i) q^{79} +(-47.1374 + 31.4962i) q^{80} +(57.2255 + 57.2255i) q^{81} +(42.7611 - 214.975i) q^{82} +(-36.0104 - 86.9369i) q^{83} -70.4946i q^{84} +154.264 q^{86} +(-115.441 + 47.8171i) q^{87} +(0.744754 + 0.148141i) q^{88} +(-19.6021 + 19.6021i) q^{89} +(-103.817 - 155.373i) q^{90} +(35.4036 - 7.04221i) q^{91} +(7.88832 - 11.8057i) q^{92} +(55.0742 - 132.961i) q^{93} +(-19.1177 - 7.91883i) q^{94} +(27.7515 + 18.5429i) q^{95} +(-46.1522 - 232.023i) q^{96} +(12.6670 - 8.46379i) q^{97} +(-76.7240 - 76.7240i) q^{98} +(8.53195 - 42.8930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{3} + 8 q^{4} + 8 q^{5} - 40 q^{6} + 16 q^{7} - 8 q^{8} + 56 q^{9} - 16 q^{10} + 32 q^{12} - 16 q^{14} + 80 q^{15} - 136 q^{18} + 80 q^{19} + 48 q^{20} + 64 q^{21} + 40 q^{22} + 16 q^{23}+ \cdots + 144 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^3 + 8 * q^4 + 8 * q^5 - 40 * q^6 + 16 * q^7 - 8 * q^8 + 56 * q^9 - 16 * q^10 + 32 * q^12 - 16 * q^14 + 80 * q^15 - 136 * q^18 + 80 * q^19 + 48 * q^20 + 64 * q^21 + 40 * q^22 + 16 * q^23 - 88 * q^24 + 136 * q^25 - 40 * q^26 + 64 * q^27 + 40 * q^28 - 144 * q^29 - 168 * q^30 - 88 * q^31 - 16 * q^32 + 80 * q^35 + 72 * q^36 + 24 * q^37 - 8 * q^38 - 96 * q^40 - 144 * q^41 - 88 * q^42 - 48 * q^43 + 112 * q^44 + 8 * q^46 + 80 * q^47 - 40 * q^48 - 72 * q^49 + 240 * q^52 - 88 * q^53 - 256 * q^54 + 8 * q^55 - 64 * q^56 + 200 * q^57 + 144 * q^58 + 40 * q^59 + 96 * q^60 - 88 * q^61 + 24 * q^62 + 216 * q^63 + 120 * q^64 + 160 * q^65 + 120 * q^66 - 208 * q^69 - 96 * q^70 + 48 * q^71 - 24 * q^72 + 224 * q^73 - 104 * q^74 + 272 * q^75 - 192 * q^76 - 120 * q^77 - 232 * q^78 - 136 * q^79 - 80 * q^80 + 224 * q^81 + 144 * q^82 - 504 * q^83 + 288 * q^86 - 216 * q^87 + 112 * q^88 - 288 * q^89 - 344 * q^90 - 16 * q^91 + 48 * q^92 - 248 * q^93 - 72 * q^94 - 144 * q^95 - 80 * q^96 + 208 * q^97 - 16 * q^98 + 144 * q^99

Introduction

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