LMFDB - Embedded newform 363.3.h.k.323.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.23612624896000000000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - 5 x^{14} + 20 x^{13} + 19 x^{12} + 88 x^{11} - 497 x^{10} + 10 x^{9} + 3711 x^{8} + \cdots + 16 $ x^16 - 2x^15 - 5x^14 + 20x^13 + 19x^12 + 88x^11 - 497x^10 + 10x^9 + 3711x^8 - 3712x^7 + 2758x^6 - 1816x^5 + 1084x^4 - 464x^3 + 184x^2 - 64*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			323.4
Root			$-1.20431 - 2.50824i$ of defining polynomial
Character	$\chi$	$=$	363.323
Dual form			363.3.h.k.245.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.55513 - 2.14046i) q^{2} +(2.38098 + 1.82509i) q^{3} +(-0.927051 - 2.85317i) q^{4} +(-1.66251 - 2.28825i) q^{5} +(7.60926 - 2.25812i) q^{6} +(2.31247 + 7.11706i) q^{7} +(2.51626 + 0.817582i) q^{8} +(2.33810 + 8.69099i) q^{9} -7.48331 q^{10} +(3.00000 - 8.48528i) q^{12} +(18.1624 + 13.1957i) q^{13} +(18.8300 + 6.11822i) q^{14} +(0.217858 - 8.48248i) q^{15} +(15.3713 - 11.1679i) q^{16} +(-12.4411 - 17.1237i) q^{17} +(22.2388 + 8.51104i) q^{18} +(-4.62494 + 14.2341i) q^{19} +(-4.98752 + 6.86474i) q^{20} +(-7.48331 + 21.1660i) q^{21} -31.1127i q^{23} +(4.49900 + 6.53904i) q^{24} +(5.25329 - 16.1680i) q^{25} +(56.4899 - 18.3547i) q^{26} +(-10.2949 + 24.9603i) q^{27} +(18.1624 - 13.1957i) q^{28} +(-20.1301 + 6.54066i) q^{29} +(-17.8176 - 13.6577i) q^{30} +(-24.2705 - 17.6336i) q^{31} -39.6863i q^{32} -56.0000 q^{34} +(12.4411 - 17.1237i) q^{35} +(22.6293 - 14.7280i) q^{36} +(-3.09017 - 9.51057i) q^{37} +(23.2751 + 32.0354i) q^{38} +(19.1608 + 64.5667i) q^{39} +(-2.31247 - 7.11706i) q^{40} +(40.2601 + 13.0813i) q^{41} +(33.6674 + 48.9337i) q^{42} +14.9666 q^{43} +(16.0000 - 19.7990i) q^{45} +(-66.5954 - 48.3844i) q^{46} +(34.9699 + 11.3624i) q^{47} +(56.9812 + 1.46346i) q^{48} +(-5.66312 + 4.11450i) q^{49} +(-26.4373 - 36.3878i) q^{50} +(1.63030 - 63.4771i) q^{51} +(20.8122 - 64.0535i) q^{52} +(-24.9376 + 34.3237i) q^{53} +(37.4166 + 60.8523i) q^{54} +19.7990i q^{56} +(-36.9904 + 25.4502i) q^{57} +(-17.3050 + 53.2592i) q^{58} +(-32.2799 + 10.4884i) q^{59} +(-24.4039 + 7.24211i) q^{60} +(-78.7037 + 57.1816i) q^{61} +(-75.4878 + 24.5275i) q^{62} +(-56.4474 + 36.7381i) q^{63} +(-23.4615 - 17.0458i) q^{64} -63.4980i q^{65} -42.0000 q^{67} +(-37.3232 + 51.3710i) q^{68} +(56.7834 - 74.0786i) q^{69} +(-17.3050 - 53.2592i) q^{70} +(-38.2377 - 52.6296i) q^{71} +(-1.22232 + 23.7804i) q^{72} +(-23.1247 - 71.1706i) q^{73} +(-25.1626 - 8.17582i) q^{74} +(42.0159 - 28.9078i) q^{75} +44.8999 q^{76} +(168.000 + 59.3970i) q^{78} +(18.1624 + 13.1957i) q^{79} +(-51.1099 - 16.6066i) q^{80} +(-70.0665 + 40.6409i) q^{81} +(90.6099 - 65.8319i) q^{82} +(-12.4411 - 17.1237i) q^{83} +(67.3276 + 1.72920i) q^{84} +(-18.4998 + 56.9364i) q^{85} +(23.2751 - 32.0354i) q^{86} +(-59.8665 - 21.1660i) q^{87} -62.2254i q^{89} +(-17.4968 - 65.0374i) q^{90} +(-51.9149 + 159.777i) q^{91} +(-88.7698 + 28.8431i) q^{92} +(-25.6047 - 86.2809i) q^{93} +(78.7037 - 57.1816i) q^{94} +(40.2601 - 13.0813i) q^{95} +(72.4310 - 94.4921i) q^{96} +(-59.8673 - 43.4961i) q^{97} +18.5203i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 12 q^{4} + 28 q^{9} + 48 q^{12} + 32 q^{15} + 76 q^{16} - 68 q^{25} - 92 q^{27} - 120 q^{31} - 896 q^{34} - 84 q^{36} + 40 q^{37} + 224 q^{42} + 256 q^{45} - 76 q^{48} - 28 q^{49} + 224 q^{58}+ \cdots - 296 q^{97}+O(q^{100}) $ 16 * q + 4 * q^3 + 12 * q^4 + 28 * q^9 + 48 * q^12 + 32 * q^15 + 76 * q^16 - 68 * q^25 - 92 * q^27 - 120 * q^31 - 896 * q^34 - 84 * q^36 + 40 * q^37 + 224 * q^42 + 256 * q^45 - 76 * q^48 - 28 * q^49 + 224 * q^58 - 96 * q^60 - 116 * q^64 - 672 * q^67 - 352 * q^69 + 224 * q^70 + 68 * q^75 + 2688 * q^78 - 68 * q^81 + 448 * q^82 + 672 * q^91 + 120 * q^93 - 296 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.55513	−	2.14046i	0.777567	−	1.07023i	−0.217979	−	0.975953i	$-0.569947\pi$
$2$	1.55513	−	2.14046i	0.777567	−	1.07023i	0.995546	−	0.0942755i	$-0.0300535\pi$
$3$	2.38098	+	1.82509i	0.793659	+	0.608363i
$3$	2.38098	+	1.82509i	0.793659	+	0.608363i
$4$	−0.927051	−	2.85317i	−0.231763	−	0.713292i
$5$	−1.66251	−	2.28825i	−0.332502	−	0.457649i	0.609731	−	0.792608i	$-0.291277\pi$
$5$	−1.66251	−	2.28825i	−0.332502	−	0.457649i	−0.942233	+	0.334959i	$0.891277\pi$
$6$	7.60926	−	2.25812i	1.26821	−	0.376354i
$7$	2.31247	+	7.11706i	0.330353	+	1.01672i	0.968966	+	0.247194i	$0.0795085\pi$
$7$	2.31247	+	7.11706i	0.330353	+	1.01672i	−0.638613	+	0.769528i	$0.720491\pi$
$8$	2.51626	+	0.817582i	0.314532	+	0.102198i
$9$	2.33810	+	8.69099i	0.259789	+	0.965665i
$10$	−7.48331			−0.748331
$11$		0			0
$11$		0			0
$12$	3.00000	−	8.48528i	0.250000	−	0.707107i
$13$	18.1624	+	13.1957i	1.39711	+	1.01506i	0.995043	+	0.0994457i	$0.0317070\pi$
$13$	18.1624	+	13.1957i	1.39711	+	1.01506i	0.402064	+	0.915612i	$0.368293\pi$
$14$	18.8300	+	6.11822i	1.34500	+	0.437016i
$15$	0.217858	−	8.48248i	0.0145239	−	0.565499i
$16$	15.3713	−	11.1679i	0.960708	−	0.697995i
$17$	−12.4411	−	17.1237i	−0.731828	−	1.00727i	−0.999047	−	0.0436386i	$-0.986105\pi$
$17$	−12.4411	−	17.1237i	−0.731828	−	1.00727i	0.267220	−	0.963636i	$-0.413895\pi$
$18$	22.2388	+	8.51104i	1.23549	+	0.472835i
$19$	−4.62494	+	14.2341i	−0.243418	+	0.749164i	0.752475	+	0.658621i	$0.228860\pi$
$19$	−4.62494	+	14.2341i	−0.243418	+	0.749164i	−0.995893	+	0.0905424i	$0.971140\pi$
$20$	−4.98752	+	6.86474i	−0.249376	+	0.343237i
$21$	−7.48331	+	21.1660i	−0.356348	+	1.00791i
$22$		0			0
$23$		−	31.1127i		−	1.35273i	−0.736568	−	0.676363i	$-0.763555\pi$
$23$		−	31.1127i		−	1.35273i	0.736568	−	0.676363i	$-0.236445\pi$
$24$	4.49900	+	6.53904i	0.187458	+	0.272460i
$25$	5.25329	−	16.1680i	0.210132	−	0.646718i
$26$	56.4899	−	18.3547i	2.17269	−	0.705949i
$27$	−10.2949	+	24.9603i	−0.381291	+	0.924455i
$28$	18.1624	−	13.1957i	0.648657	−	0.471277i
$29$	−20.1301	+	6.54066i	−0.694140	+	0.225540i	−0.634776	−	0.772696i	$-0.718907\pi$
$29$	−20.1301	+	6.54066i	−0.694140	+	0.225540i	−0.0593647	+	0.998236i	$0.518907\pi$
$30$	−17.8176	−	13.6577i	−0.593920	−	0.455257i
$31$	−24.2705	−	17.6336i	−0.782920	−	0.568824i	0.122934	−	0.992415i	$-0.460770\pi$
$31$	−24.2705	−	17.6336i	−0.782920	−	0.568824i	−0.905854	+	0.423590i	$0.860770\pi$
$32$		−	39.6863i		−	1.24020i
$33$		0			0
$34$	−56.0000			−1.64706
$35$	12.4411	−	17.1237i	0.355459	−	0.489247i
$36$	22.6293	−	14.7280i	0.628592	−	0.409111i
$37$	−3.09017	−	9.51057i	−0.0835181	−	0.257042i	0.900574	−	0.434704i	$-0.143147\pi$
$37$	−3.09017	−	9.51057i	−0.0835181	−	0.257042i	−0.984092	+	0.177661i	$0.943147\pi$
$38$	23.2751	+	32.0354i	0.612503	+	0.843038i
$39$	19.1608	+	64.5667i	0.491303	+	1.65556i
$40$	−2.31247	−	7.11706i	−0.0578118	−	0.177926i
$41$	40.2601	+	13.0813i	0.981955	+	0.319056i	0.755632	−	0.654996i	$-0.227330\pi$
$41$	40.2601	+	13.0813i	0.981955	+	0.319056i	0.226322	+	0.974052i	$0.427330\pi$
$42$	33.6674	+	48.9337i	0.801605	+	1.16509i
$43$	14.9666			0.348061			0.174031	−	0.984740i	$-0.444321\pi$
$43$	14.9666			0.348061			0.174031	+	0.984740i	$0.444321\pi$
$44$		0			0
$45$	16.0000	−	19.7990i	0.355556	−	0.439978i
$46$	−66.5954	−	48.3844i	−1.44773	−	1.05183i
$47$	34.9699	+	11.3624i	0.744041	+	0.241754i	0.656415	−	0.754400i	$-0.272072\pi$
$47$	34.9699	+	11.3624i	0.744041	+	0.241754i	0.0876258	+	0.996153i	$0.472072\pi$
$48$	56.9812	+	1.46346i	1.18711	+	0.0304889i
$49$	−5.66312	+	4.11450i	−0.115574	+	0.0839693i
$50$	−26.4373	−	36.3878i	−0.528745	−	0.727756i
$51$	1.63030	−	63.4771i	0.0319667	−	1.24465i
$52$	20.8122	−	64.0535i	0.400235	−	1.23180i
$53$	−24.9376	+	34.3237i	−0.470521	+	0.647617i	−0.976649	−	0.214842i	$-0.931076\pi$
$53$	−24.9376	+	34.3237i	−0.470521	+	0.647617i	0.506128	+	0.862458i	$0.331076\pi$
$54$	37.4166	+	60.8523i	0.692900	+	1.12689i
$55$		0			0
$56$			19.7990i			0.353553i
$57$	−36.9904	+	25.4502i	−0.648954	+	0.446494i
$58$	−17.3050	+	53.2592i	−0.298361	+	0.918261i
$59$	−32.2799	+	10.4884i	−0.547117	+	0.177769i	−0.569517	−	0.821980i	$-0.692870\pi$
$59$	−32.2799	+	10.4884i	−0.547117	+	0.177769i	0.0223991	+	0.999749i	$0.492870\pi$
$60$	−24.4039	+	7.24211i	−0.406732	+	0.120702i
$61$	−78.7037	+	57.1816i	−1.29022	+	0.937403i	−0.999810	−	0.0194983i	$-0.993793\pi$
$61$	−78.7037	+	57.1816i	−1.29022	+	0.937403i	−0.290414	+	0.956901i	$0.593793\pi$
$62$	−75.4878	+	24.5275i	−1.21754	+	0.395604i
$63$	−56.4474	+	36.7381i	−0.895991	+	0.583144i
$64$	−23.4615	−	17.0458i	−0.366586	−	0.266340i
$65$		−	63.4980i		−	0.976893i
$66$		0			0
$67$	−42.0000			−0.626866			−0.313433	−	0.949610i	$-0.601479\pi$
$67$	−42.0000			−0.626866			−0.313433	+	0.949610i	$0.601479\pi$
$68$	−37.3232	+	51.3710i	−0.548871	+	0.755456i
$69$	56.7834	−	74.0786i	0.822948	−	1.07360i
$70$	−17.3050	−	53.2592i	−0.247214	−	0.760845i
$71$	−38.2377	−	52.6296i	−0.538559	−	0.741263i	0.449846	−	0.893106i	$-0.351479\pi$
$71$	−38.2377	−	52.6296i	−0.538559	−	0.741263i	−0.988405	+	0.151844i	$0.951479\pi$
$72$	−1.22232	+	23.7804i	−0.0169767	+	0.330283i
$73$	−23.1247	−	71.1706i	−0.316777	−	0.974939i	−0.975017	−	0.222131i	$-0.928699\pi$
$73$	−23.1247	−	71.1706i	−0.316777	−	0.974939i	0.658240	−	0.752808i	$-0.271301\pi$
$74$	−25.1626	−	8.17582i	−0.340035	−	0.110484i
$75$	42.0159	−	28.9078i	0.560212	−	0.385438i
$76$	44.8999			0.590788
$77$		0			0
$78$	168.000	+	59.3970i	2.15385	+	0.761500i
$79$	18.1624	+	13.1957i	0.229904	+	0.167035i	0.696773	−	0.717291i	$-0.254618\pi$
$79$	18.1624	+	13.1957i	0.229904	+	0.167035i	−0.466870	+	0.884326i	$0.654618\pi$
$80$	−51.1099	−	16.6066i	−0.638874	−	0.207583i
$81$	−70.0665	+	40.6409i	−0.865019	+	0.501739i
$82$	90.6099	−	65.8319i	1.10500	−	0.802829i
$83$	−12.4411	−	17.1237i	−0.149892	−	0.206309i	0.727467	−	0.686142i	$-0.240697\pi$
$83$	−12.4411	−	17.1237i	−0.149892	−	0.206309i	−0.877360	+	0.479833i	$0.840697\pi$
$84$	67.3276	+	1.72920i	0.801519	+	0.0205857i
$85$	−18.4998	+	56.9364i	−0.217644	+	0.669840i
$86$	23.2751	−	32.0354i	0.270641	−	0.372505i
$87$	−59.8665	−	21.1660i	−0.688121	−	0.243287i
$88$		0			0
$89$		−	62.2254i		−	0.699162i	−0.936906	−	0.349581i	$-0.886324\pi$
$89$		−	62.2254i		−	0.699162i	0.936906	−	0.349581i	$-0.113676\pi$
$90$	−17.4968	−	65.0374i	−0.194408	−	0.722638i
$91$	−51.9149	+	159.777i	−0.570493	+	1.75580i
$92$	−88.7698	+	28.8431i	−0.964889	+	0.313511i
$93$	−25.6047	−	86.2809i	−0.275320	−	0.927752i
$94$	78.7037	−	57.1816i	0.837273	−	0.608315i
$95$	40.2601	−	13.0813i	0.423791	−	0.137698i
$96$	72.4310	−	94.4921i	0.754489	−	0.984293i
$97$	−59.8673	−	43.4961i	−0.617188	−	0.448413i	0.234750	−	0.972056i	$-0.424573\pi$
$97$	−59.8673	−	43.4961i	−0.617188	−	0.448413i	−0.851938	+	0.523642i	$0.824573\pi$
$98$			18.5203i			0.188982i
$99$		0			0
$100$	−51.0000			−0.510000
$101$	87.0875	−	119.866i	0.862252	−	1.18679i	−0.118775	−	0.992921i	$-0.537897\pi$
$101$	87.0875	−	119.866i	0.862252	−	1.18679i	0.981028	−	0.193867i	$-0.0621031\pi$
$102$	−133.335	−	102.205i	−1.30720	−	1.00201i
$103$	10.5066	+	32.3359i	0.102006	+	0.313941i	0.989016	−	0.147808i	$-0.0472219\pi$
$103$	10.5066	+	32.3359i	0.102006	+	0.313941i	−0.887010	+	0.461749i	$0.847222\pi$
$104$	34.9127	+	48.0532i	0.335699	+	0.462050i
$105$	60.8741	−	18.0650i	0.579753	−	0.172048i
$106$	34.6871	+	106.756i	0.327237	+	1.00713i
$107$	40.2601	+	13.0813i	0.376263	+	0.122255i	0.491042	−	0.871136i	$-0.336616\pi$
$107$	40.2601	+	13.0813i	0.376263	+	0.122255i	−0.114779	+	0.993391i	$0.536616\pi$
$108$	80.7598	+	6.23350i	0.747776	+	0.0577176i
$109$	−67.3498			−0.617888			−0.308944	−	0.951080i	$-0.599976\pi$
$109$	−67.3498			−0.617888			−0.308944	+	0.951080i	$0.599976\pi$
$110$		0			0
$111$	10.0000	−	28.2843i	0.0900901	−	0.254813i
$112$	115.028	+	83.5731i	1.02704	+	0.746188i
$113$	−112.980	−	36.7093i	−0.999821	−	0.324861i	−0.237027	−	0.971503i	$-0.576173\pi$
$113$	−112.980	−	36.7093i	−0.999821	−	0.324861i	−0.762794	+	0.646642i	$0.776173\pi$
$114$	−3.05001	+	118.755i	−0.0267545	+	1.04171i
$115$	−71.1935	+	51.7251i	−0.619074	+	0.449783i
$116$	37.3232	+	51.3710i	0.321752	+	0.442853i
$117$	−72.2185	+	188.702i	−0.617252	+	1.61284i
$118$	−27.7497	+	85.4047i	−0.235167	+	0.723768i
$119$	93.1004	−	128.142i	0.782357	−	1.07682i
$120$	7.48331	−	21.1660i	0.0623610	−	0.176383i
$121$		0			0
$122$			257.387i			2.10973i
$123$	71.9839	+	104.625i	0.585235	+	0.850607i
$124$	−27.8115	+	85.5951i	−0.224287	+	0.690283i
$125$	−112.980	+	36.7093i	−0.903838	+	0.293675i
$126$	−9.14702	+	177.956i	−0.0725954	+	1.41235i
$127$	54.4872	−	39.5872i	0.429033	−	0.311711i	−0.352229	−	0.935914i	$-0.614576\pi$
$127$	54.4872	−	39.5872i	0.429033	−	0.311711i	0.781262	+	0.624203i	$0.214576\pi$
$128$	78.0040	−	25.3450i	0.609406	−	0.198008i
$129$	35.6352	+	27.3154i	0.276242	+	0.211747i
$130$	−135.915	−	98.7479i	−1.04550	−	0.759599i
$131$			232.826i			1.77730i	0.458587	+	0.888649i	$0.348356\pi$
$131$			232.826i			1.77730i	−0.458587	+	0.888649i	$0.651644\pi$
$132$		0			0
$133$	−112.000			−0.842105
$134$	−65.3156	+	89.8992i	−0.487430	+	0.670890i
$135$	74.2305	−	17.9395i	0.549856	−	0.132885i
$136$	−17.3050	−	53.2592i	−0.127242	−	0.391612i
$137$	−93.1004	−	128.142i	−0.679565	−	0.935341i	0.320363	−	0.947295i	$-0.396195\pi$
$137$	−93.1004	−	128.142i	−0.679565	−	0.935341i	−0.999929	+	0.0119535i	$0.996195\pi$
$138$	−70.2563	−	236.745i	−0.509104	−	1.71554i
$139$	27.7497	+	85.4047i	0.199638	+	0.614422i	0.999891	+	0.0147598i	$0.00469838\pi$
$139$	27.7497	+	85.4047i	0.199638	+	0.614422i	−0.800253	+	0.599662i	$0.795302\pi$
$140$	−60.3902	−	19.6220i	−0.431359	−	0.140157i
$141$	62.5252	+	90.8769i	0.443441	+	0.644517i
$142$	−172.116			−1.21209
$143$		0			0
$144$	133.000	+	107.480i	0.923611	+	0.746390i
$145$	48.4330	+	35.1887i	0.334021	+	0.242680i
$146$	−188.300	−	61.1822i	−1.28972	−	0.419056i
$147$	−20.9931	−	0.539171i	−0.142810	−	0.00366783i
$148$	−24.2705	+	17.6336i	−0.163990	+	0.119146i
$149$	−12.4411	−	17.1237i	−0.0834971	−	0.114924i	0.765225	−	0.643763i	$-0.222628\pi$
$149$	−12.4411	−	17.1237i	−0.0834971	−	0.114924i	−0.848722	+	0.528839i	$0.822628\pi$
$150$	3.46439	−	134.889i	0.0230959	−	0.899259i
$151$	20.8122	−	64.0535i	0.137829	−	0.424195i	−0.858190	−	0.513332i	$-0.828411\pi$
$151$	20.8122	−	64.0535i	0.137829	−	0.424195i	0.996019	+	0.0891369i	$0.0284109\pi$
$152$	−23.2751	+	32.0354i	−0.153126	+	0.210759i
$153$	119.733	−	148.162i	0.782569	−	0.968380i
$154$		0			0
$155$			84.8528i			0.547438i
$156$	166.457	−	114.526i	1.06703	−	0.734139i
$157$	26.5755	−	81.7909i	0.169270	−	0.520961i	−0.830055	−	0.557681i	$-0.811691\pi$
$157$	26.5755	−	81.7909i	0.169270	−	0.520961i	0.999326	+	0.0367205i	$0.0116911\pi$
$158$	56.4899	−	18.3547i	0.357531	−	0.116169i
$159$	−122.020	+	36.2105i	−0.767419	+	0.227739i
$160$	−90.8119	+	65.9787i	−0.567575	+	0.412367i
$161$	221.431	−	71.9472i	1.37535	−	0.446877i
$162$	−21.9728	+	213.176i	−0.135635	+	1.31590i
$163$	11.3262	+	8.22899i	0.0694861	+	0.0504846i	0.621986	−	0.783028i	$-0.286326\pi$
$163$	11.3262	+	8.22899i	0.0694861	+	0.0504846i	−0.552500	+	0.833513i	$0.686326\pi$
$164$		−	126.996i		−	0.774366i
$165$		0			0
$166$	−56.0000			−0.337349
$167$	−49.7643	+	68.4946i	−0.297990	+	0.410148i	−0.931589	−	0.363514i	$-0.881577\pi$
$167$	−49.7643	+	68.4946i	−0.297990	+	0.410148i	0.633599	+	0.773662i	$0.281577\pi$
$168$	−36.1349	+	47.1409i	−0.215089	+	0.280601i
$169$	103.521	+	318.604i	0.612548	+	1.88523i
$170$	93.1004	+	128.142i	0.547650	+	0.753775i
$171$	−134.522	−	6.91450i	−0.786679	−	0.0404357i
$172$	−13.8748	−	42.7023i	−0.0806676	−	0.248269i
$173$	−181.171	−	58.8659i	−1.04723	−	0.340265i	−0.265649	−	0.964070i	$-0.585586\pi$
$173$	−181.171	−	58.8659i	−1.04723	−	0.340265i	−0.781580	+	0.623804i	$0.785586\pi$
$174$	−138.405	+	95.2258i	−0.795433	+	0.547275i
$175$	127.216			0.726951
$176$		0			0
$177$	−96.0000	−	33.9411i	−0.542373	−	0.191758i
$178$	−133.191	−	96.7688i	−0.748263	−	0.543645i
$179$	301.279	+	97.8916i	1.68312	+	0.546880i	0.985514	−	0.169596i	$-0.0542463\pi$
$179$	301.279	+	97.8916i	1.68312	+	0.546880i	0.697611	+	0.716477i	$0.254246\pi$
$180$	−71.3227	−	27.2960i	−0.396237	−	0.151645i
$181$	211.962	−	154.000i	1.17106	−	0.850827i	0.179927	−	0.983680i	$-0.442414\pi$
$181$	211.962	−	154.000i	1.17106	−	0.850827i	0.991136	+	0.132853i	$0.0424137\pi$
$182$	261.262	+	359.597i	1.43551	+	1.97581i
$183$	−291.753	−	7.49318i	−1.59428	−	0.0409463i
$184$	25.4372	−	78.2876i	0.138246	−	0.425476i
$185$	−16.6251	+	22.8825i	−0.0898653	+	0.123689i
$186$	−224.499	−	79.3725i	−1.20699	−	0.426734i
$187$		0			0
$188$		−	110.309i		−	0.586748i
$189$	−201.450	−	15.5491i	−1.06587	−	0.0822702i
$190$	34.6099	−	106.518i	0.182157	−	0.560623i
$191$	56.4899	−	18.3547i	0.295759	−	0.0960978i	−0.157379	−	0.987538i	$-0.550305\pi$
$191$	56.4899	−	18.3547i	0.295759	−	0.0960978i	0.453138	+	0.891440i	$0.350305\pi$
$192$	−24.7512	−	83.4049i	−0.128913	−	0.434400i
$193$	121.083	−	87.9716i	0.627371	−	0.455812i	−0.228118	−	0.973634i	$-0.573257\pi$
$193$	121.083	−	87.9716i	0.627371	−	0.455812i	0.855488	+	0.517822i	$0.173257\pi$
$194$	−186.203	+	60.5011i	−0.959810	+	0.311861i
$195$	115.890	−	151.187i	0.594305	−	0.775320i
$196$	16.9894	+	12.3435i	0.0866804	+	0.0629770i
$197$			232.826i			1.18186i	0.806723	+	0.590929i	$0.201239\pi$
$197$			232.826i			1.18186i	−0.806723	+	0.590929i	$0.798761\pi$
$198$		0			0
$199$	222.000			1.11558			0.557789	−	0.829983i	$-0.311650\pi$
$199$	222.000			1.11558			0.557789	+	0.829983i	$0.311650\pi$
$200$	26.4373	−	36.3878i	0.132186	−	0.181939i
$201$	−100.001	−	76.6537i	−0.497518	−	0.381362i
$202$	−121.135	−	372.814i	−0.599677	−	1.84561i
$203$	−93.1004	−	128.142i	−0.458623	−	0.631240i
$204$	−182.622	+	54.1950i	−0.895207	+	0.265662i
$205$	−36.9995	−	113.873i	−0.180486	−	0.555477i
$206$	85.5528	+	27.7978i	0.415305	+	0.134941i
$207$	270.400	−	72.7447i	1.30628	−	0.351424i
$208$	426.549			2.05072
$209$		0			0
$210$	56.0000	−	158.392i	0.266667	−	0.754247i
$211$	−314.815	−	228.726i	−1.49201	−	1.08401i	−0.973430	−	0.228983i	$-0.926460\pi$
$211$	−314.815	−	228.726i	−1.49201	−	1.08401i	−0.518582	−	0.855028i	$-0.673540\pi$
$212$	121.050	+	39.3314i	0.570989	+	0.185526i
$213$	5.01074	−	195.097i	0.0235246	−	0.915949i
$214$	90.6099	−	65.8319i	0.423411	−	0.307626i
$215$	−24.8821	−	34.2473i	−0.115731	−	0.159290i
$216$	−46.3116	+	54.3897i	−0.214406	+	0.251804i
$217$	69.3741	−	213.512i	0.319697	−	0.983925i
$218$	−104.738	+	144.159i	−0.480449	+	0.661282i
$219$	74.8331	−	211.660i	0.341704	−	0.966484i
$220$		0			0
$221$		−	475.176i		−	2.15012i
$222$	−44.9900	−	65.3904i	−0.202657	−	0.294551i
$223$	−14.2148	+	43.7486i	−0.0637434	+	0.196182i	−0.977856	−	0.209278i	$-0.932889\pi$
$223$	−14.2148	+	43.7486i	−0.0637434	+	0.196182i	0.914113	+	0.405460i	$0.132889\pi$
$224$	282.449	−	91.7734i	1.26093	−	0.409703i
$225$	152.798	+	7.85391i	0.679103	+	0.0349062i
$226$	−254.273	+	184.740i	−1.12510	+	0.817436i
$227$	201.301	−	65.4066i	0.886787	−	0.288135i	0.170015	−	0.985442i	$-0.445619\pi$
$227$	201.301	−	65.4066i	0.886787	−	0.288135i	0.716773	+	0.697307i	$0.245619\pi$
$228$	106.906	+	81.9463i	0.468884	+	0.359413i
$229$	−95.4640	−	69.3587i	−0.416873	−	0.302876i	0.359505	−	0.933143i	$-0.382945\pi$
$229$	−95.4640	−	69.3587i	−0.416873	−	0.302876i	−0.776379	+	0.630267i	$0.782945\pi$
$230$			232.826i			1.01229i
$231$		0			0
$232$	−56.0000			−0.241379
$233$	−49.7643	+	68.4946i	−0.213581	+	0.293968i	−0.902343	−	0.431019i	$-0.858154\pi$
$233$	−49.7643	+	68.4946i	−0.213581	+	0.293968i	0.688762	+	0.724987i	$0.258154\pi$
$234$	291.599	+	448.038i	1.24615	+	1.91469i
$235$	−32.1378	−	98.9099i	−0.136756	−	0.420893i
$236$	59.8503	+	82.3768i	0.253603	+	0.349054i
$237$	19.1608	+	64.5667i	0.0808473	+	0.272433i
$238$	−129.498	−	398.555i	−0.544111	−	1.67460i
$239$	40.2601	+	13.0813i	0.168452	+	0.0547335i	0.392029	−	0.919953i	$-0.371773\pi$
$239$	40.2601	+	13.0813i	0.168452	+	0.0547335i	−0.223577	+	0.974686i	$0.571773\pi$
$240$	−91.3829	−	132.820i	−0.380762	−	0.553417i
$241$	−149.666			−0.621022			−0.310511	−	0.950570i	$-0.600500\pi$
$241$	−149.666			−0.621022			−0.310511	+	0.950570i	$0.600500\pi$
$242$		0			0
$243$	−241.000	−	31.1127i	−0.991770	−	0.128036i
$244$	236.111	+	171.545i	0.967668	+	0.703052i
$245$	18.8300	+	6.11822i	0.0768570	+	0.0249723i
$246$	335.889	+	8.62674i	1.36540	+	0.0350681i
$247$	−271.830	+	197.496i	−1.10053	+	0.799578i
$248$	−46.6540	−	64.2137i	−0.188121	−	0.258926i
$249$	1.63030	−	63.4771i	0.00654739	−	0.254928i
$250$	−97.1238	+	298.916i	−0.388495	+	1.19567i
$251$	29.9251	−	41.1884i	0.119224	−	0.164097i	−0.745234	−	0.666803i	$-0.767662\pi$
$251$	29.9251	−	41.1884i	0.119224	−	0.164097i	0.864457	+	0.502706i	$0.167662\pi$
$252$	157.150	+	126.996i	0.623610	+	0.503953i
$253$		0			0
$254$		−	178.191i		−	0.701539i
$255$	−147.962	+	101.801i	−0.580241	+	0.399218i
$256$	102.903	−	316.702i	0.401964	−	1.23712i
$257$	−91.4598	+	29.7171i	−0.355875	+	0.115631i	−0.481498	−	0.876447i	$-0.659907\pi$
$257$	−91.4598	+	29.7171i	−0.355875	+	0.115631i	0.125623	+	0.992078i	$0.459907\pi$
$258$	113.885	−	33.7965i	0.441415	−	0.130994i
$259$	60.5413	−	43.9858i	0.233750	−	0.169829i
$260$	−181.171	+	58.8659i	−0.696810	+	0.226407i
$261$	−103.911	−	159.657i	−0.398126	−	0.611714i
$262$	498.354	+	362.076i	1.90212	+	1.38197i
$263$		−	465.652i		−	1.77054i	−0.465077	−	0.885270i	$-0.653973\pi$
$263$		−	465.652i		−	1.77054i	0.465077	−	0.885270i	$-0.346027\pi$
$264$		0			0
$265$	120.000			0.452830
$266$	−174.175	+	239.731i	−0.654793	+	0.901245i
$267$	113.567	−	148.157i	0.425344	−	0.554896i
$268$	38.9361	+	119.833i	0.145284	+	0.447139i
$269$	217.789	+	299.760i	0.809623	+	1.11435i	0.991381	+	0.131007i	$0.0418210\pi$
$269$	217.789	+	299.760i	0.809623	+	1.11435i	−0.181759	+	0.983343i	$0.558179\pi$
$270$	77.0396	−	186.786i	0.285332	−	0.691799i
$271$	104.061	+	320.267i	0.383990	+	1.18180i	0.937211	+	0.348764i	$0.113399\pi$
$271$	104.061	+	320.267i	0.383990	+	1.18180i	−0.553221	+	0.833035i	$0.686601\pi$
$272$	−382.471	−	124.272i	−1.40614	−	0.456884i
$273$	−415.216	+	285.677i	−1.52094	+	1.04644i
$274$	−419.066			−1.52944
$275$		0			0
$276$	−264.000	−	93.3381i	−0.956522	−	0.338182i
$277$	18.1624	+	13.1957i	0.0655682	+	0.0476381i	0.620087	−	0.784533i	$-0.287097\pi$
$277$	18.1624	+	13.1957i	0.0655682	+	0.0476381i	−0.554518	+	0.832171i	$0.687097\pi$
$278$	225.960	+	73.4187i	0.812804	+	0.264096i
$279$	96.5061	−	252.164i	0.345900	−	0.903813i
$280$	45.3050	−	32.9160i	0.161803	−	0.117557i
$281$	−12.4411	−	17.1237i	−0.0442743	−	0.0609383i	0.786306	−	0.617837i	$-0.211991\pi$
$281$	−12.4411	−	17.1237i	−0.0442743	−	0.0609383i	−0.830580	+	0.556899i	$0.811991\pi$
$282$	291.753	+	7.49318i	1.03459	+	0.0265716i
$283$	−55.4993	+	170.809i	−0.196111	+	0.603567i	0.803851	+	0.594830i	$0.202781\pi$
$283$	−55.4993	+	170.809i	−0.196111	+	0.603567i	−0.999962	+	0.00873607i	$0.997219\pi$
$284$	−114.713	+	157.889i	−0.403919	+	0.555947i
$285$	119.733	+	42.3320i	0.420116	+	0.148533i
$286$		0			0
$287$			316.784i			1.10378i
$288$	344.913	−	92.7906i	1.19761	−	0.322190i
$289$	−49.1337	+	151.218i	−0.170013	+	0.523246i
$290$	150.640	−	48.9458i	0.519447	−	0.168779i
$291$	−63.1583	−	212.826i	−0.217039	−	0.731362i
$292$	−181.624	+	131.957i	−0.622000	+	0.451909i
$293$	−20.1301	+	6.54066i	−0.0687033	+	0.0223231i	−0.343167	−	0.939274i	$-0.611500\pi$
$293$	−20.1301	+	6.54066i	−0.0687033	+	0.0223231i	0.274464	+	0.961597i	$0.411500\pi$
$294$	−33.8011	+	44.0963i	−0.114970	+	0.149987i
$295$	77.6656	+	56.4274i	0.263273	+	0.191279i
$296$		−	26.4575i		−	0.0893835i
$297$		0			0
$298$	−56.0000			−0.187919
$299$	410.555	−	565.081i	1.37309	−	1.88990i
$300$	−121.430	−	93.0795i	−0.404766	−	0.310265i
$301$	34.6099	+	106.518i	0.114983	+	0.353881i
$302$	−104.738	−	144.159i	−0.346815	−	0.477349i
$303$	426.119	−	126.455i	1.40633	−	0.417343i
$304$	87.8739	+	270.448i	0.289059	+	0.889632i
$305$	261.691	+	85.0285i	0.858003	+	0.278782i
$306$	−130.934	−	486.695i	−0.427888	−	1.59051i
$307$	−149.666			−0.487512			−0.243756	−	0.969837i	$-0.578380\pi$
$307$	−149.666			−0.487512			−0.243756	+	0.969837i	$0.578380\pi$
$308$		0			0
$309$	−34.0000	+	96.1665i	−0.110032	+	0.311219i
$310$	181.624	+	131.957i	0.585883	+	0.425669i
$311$	−24.2099	−	7.86629i	−0.0778455	−	0.0252935i	0.269835	−	0.962906i	$-0.413031\pi$
$311$	−24.2099	−	7.86629i	−0.0778455	−	0.0252935i	−0.347681	+	0.937613i	$0.613031\pi$
$312$	−4.57502	+	178.132i	−0.0146635	+	0.570936i
$313$	−321.989	+	233.939i	−1.02872	+	0.747407i	−0.968052	−	0.250751i	$-0.919323\pi$
$313$	−321.989	+	233.939i	−1.02872	+	0.747407i	−0.0606664	+	0.998158i	$0.519323\pi$
$314$	−133.741	−	184.079i	−0.425928	−	0.586240i
$315$	177.910	+	68.0883i	0.564794	+	0.216153i
$316$	20.8122	−	64.0535i	0.0658615	−	0.202701i
$317$	−244.389	+	336.372i	−0.770942	+	1.06111i	0.225282	+	0.974294i	$0.427670\pi$
$317$	−244.389	+	336.372i	−0.770942	+	1.06111i	−0.996224	+	0.0868172i	$0.972330\pi$
$318$	−112.250	+	317.490i	−0.352987	+	0.998397i
$319$		0			0
$320$			82.0244i			0.256326i
$321$	71.9839	+	104.625i	0.224249	+	0.325933i
$322$	190.354	−	585.851i	0.591163	−	1.81941i
$323$	301.279	−	97.8916i	0.932753	−	0.303070i
$324$	180.911	+	162.236i	0.558366	+	0.500727i
$325$	308.761	−	224.328i	0.950033	−	0.690239i
$326$	35.2276	−	11.4461i	0.108060	−	0.0351109i
$327$	−160.358	−	122.919i	−0.490393	−	0.375900i
$328$	90.6099	+	65.8319i	0.276250	+	0.200707i
$329$			275.158i			0.836347i
$330$		0			0
$331$	178.000			0.537764			0.268882	−	0.963173i	$-0.413346\pi$
$331$	178.000			0.537764			0.268882	+	0.963173i	$0.413346\pi$
$332$	−37.3232	+	51.3710i	−0.112419	+	0.154732i
$333$	75.4311	−	49.0933i	0.226520	−	0.147427i
$334$	69.2198	+	213.037i	0.207245	+	0.637834i
$335$	69.8253	+	96.1063i	0.208434	+	0.286885i
$336$	121.352	+	408.923i	0.361166	+	1.21703i
$337$	78.6240	+	241.980i	0.233306	+	0.718041i	0.997342	+	0.0728675i	$0.0232150\pi$
$337$	78.6240	+	241.980i	0.233306	+	0.718041i	−0.764036	+	0.645174i	$0.776785\pi$
$338$	842.947	+	273.890i	2.49393	+	0.810325i
$339$	−202.004	−	293.602i	−0.595883	−	0.866083i
$340$	179.600			0.528234
$341$		0			0
$342$	−224.000	+	277.186i	−0.654971	+	0.810485i
$343$	254.273	+	184.740i	0.741322	+	0.538602i
$344$	37.6599	+	12.2364i	0.109477	+	0.0355711i
$345$	−263.913	−	6.77815i	−0.764965	−	0.0196468i
$346$	−407.745	+	296.244i	−1.17845	+	0.856196i
$347$	−286.145	−	393.844i	−0.824624	−	1.13500i	−0.988900	−	0.148583i	$-0.952529\pi$
$347$	−286.145	−	393.844i	−0.824624	−	1.13500i	0.164276	−	0.986414i	$-0.447471\pi$
$348$	−4.89090	+	190.431i	−0.0140543	+	0.547216i
$349$	20.8122	−	64.0535i	0.0596339	−	0.183534i	−0.916802	−	0.399342i	$-0.869239\pi$
$349$	20.8122	−	64.0535i	0.0596339	−	0.183534i	0.976436	+	0.215808i	$0.0692385\pi$
$350$	197.838	−	272.301i	0.565253	−	0.778004i
$351$	−516.349	+	317.490i	−1.47108	+	0.904530i
$352$		0			0
$353$			124.451i			0.352552i	0.984341	+	0.176276i	$0.0564051\pi$
$353$			124.451i			0.352552i	−0.984341	+	0.176276i	$0.943595\pi$
$354$	−221.942	+	152.701i	−0.626956	+	0.431359i
$355$	−56.8591	+	174.994i	−0.160167	+	0.492942i
$356$	−177.540	+	57.6861i	−0.498707	+	0.162040i
$357$	455.540	−	135.186i	1.27602	−	0.378672i
$358$	678.062	−	492.641i	1.89403	−	1.37609i
$359$	−241.561	+	78.4879i	−0.672871	+	0.218629i	−0.625472	−	0.780247i	$-0.715093\pi$
$359$	−241.561	+	78.4879i	−0.672871	+	0.218629i	−0.0473997	+	0.998876i	$0.515093\pi$
$360$	56.4474	−	36.7381i	0.156798	−	0.102050i
$361$	110.835	+	80.5266i	0.307023	+	0.223065i
$362$		−	693.187i		−	1.91488i
$363$		0			0
$364$	504.000			1.38462
$365$	−124.411	+	171.237i	−0.340851	+	0.469141i
$366$	−469.754	+	612.832i	−1.28348	+	1.67440i
$367$	−43.8804	−	135.050i	−0.119565	−	0.367984i	0.873307	−	0.487171i	$-0.161971\pi$
$367$	−43.8804	−	135.050i	−0.119565	−	0.367984i	−0.992872	+	0.119187i	$0.961971\pi$
$368$	−347.464	−	478.243i	−0.944196	−	1.29957i
$369$	−19.5572	+	380.486i	−0.0530004	+	1.03113i
$370$	23.1247	+	71.1706i	0.0624992	+	0.192353i
$371$	−301.951	−	98.1099i	−0.813884	−	0.264447i
$372$	−222.437	+	153.041i	−0.597950	+	0.411402i
$373$	426.549			1.14356			0.571781	−	0.820406i	$-0.306253\pi$
$373$	426.549			1.14356			0.571781	+	0.820406i	$0.306253\pi$
$374$		0			0
$375$	−336.000	−	118.794i	−0.896000	−	0.316784i
$376$	78.7037	+	57.1816i	0.209318	+	0.152079i
$377$	−451.919	−	146.837i	−1.19872	−	0.389489i
$378$	−346.564	+	407.015i	−0.916837	+	1.07676i
$379$	283.156	−	205.725i	0.747113	−	0.542810i	−0.147817	−	0.989015i	$-0.547225\pi$
$379$	283.156	−	205.725i	0.747113	−	0.542810i	0.894931	+	0.446205i	$0.147225\pi$
$380$	−74.6464	−	102.742i	−0.196438	−	0.270374i
$381$	201.983	+	5.18759i	0.530139	+	0.0136157i
$382$	48.5619	−	149.458i	0.127125	−	0.391252i
$383$	304.239	−	418.749i	0.794357	−	1.09334i	−0.199194	−	0.979960i	$-0.563832\pi$
$383$	304.239	−	418.749i	0.794357	−	1.09334i	0.993552	−	0.113379i	$-0.0361675\pi$
$384$	231.983	+	82.0183i	0.604122	+	0.213589i
$385$		0			0
$386$		−	395.980i		−	1.02585i
$387$	34.9935	+	130.075i	0.0904226	+	0.336111i
$388$	−68.6018	+	211.135i	−0.176809	+	0.544161i
$389$	−416.949	+	135.475i	−1.07185	+	0.348265i	−0.791207	−	0.611548i	$-0.790547\pi$
$389$	−416.949	+	135.475i	−1.07185	+	0.348265i	−0.280641	+	0.959813i	$0.590547\pi$
$390$	−143.386	−	483.173i	−0.367658	−	1.23891i
$391$	−532.763	+	387.075i	−1.36257	+	0.989962i
$392$	−17.6138	+	5.72307i	−0.0449332	+	0.0145997i
$393$	−424.928	+	554.354i	−1.08124	+	1.41057i
$394$	498.354	+	362.076i	1.26486	+	0.918974i
$395$		−	63.4980i		−	0.160755i
$396$		0			0
$397$	442.000			1.11335			0.556675	−	0.830730i	$-0.312077\pi$
$397$	442.000			1.11335			0.556675	+	0.830730i	$0.312077\pi$
$398$	345.240	−	475.182i	0.867436	−	1.19392i
$399$	−266.669	−	204.410i	−0.668344	−	0.512306i
$400$	−99.8125	−	307.191i	−0.249531	−	0.767978i
$401$	309.226	+	425.614i	0.771138	+	1.06138i	0.996205	+	0.0870374i	$0.0277400\pi$
$401$	309.226	+	425.614i	0.771138	+	1.06138i	−0.225067	+	0.974343i	$0.572260\pi$
$402$	−319.589	+	94.8412i	−0.794998	+	0.235923i
$403$	−208.122	−	640.535i	−0.516433	−	1.58942i
$404$	−422.732	−	137.354i	−1.04637	−	0.339985i
$405$	209.482	+	92.7637i	0.517241	+	0.229046i
$406$	−419.066			−1.03218
$407$		0			0
$408$	56.0000	−	158.392i	0.137255	−	0.388215i
$409$	−181.624	−	131.957i	−0.444068	−	0.322634i	0.343181	−	0.939269i	$-0.388496\pi$
$409$	−181.624	−	131.957i	−0.444068	−	0.322634i	−0.787249	+	0.616635i	$0.788496\pi$
$410$	−301.279	−	97.8916i	−0.734828	−	0.238760i
$411$	12.2001	−	475.019i	0.0296838	−	1.15576i
$412$	82.5197	−	59.9541i	0.200291	−	0.145520i
$413$	−149.293	−	205.484i	−0.361484	−	0.497540i
$414$	264.801	−	691.908i	0.639617	−	1.67127i
$415$	−18.4998	+	56.9364i	−0.0445778	+	0.137196i
$416$	523.690	−	720.797i	1.25887	−	1.73269i
$417$	−89.7998	+	253.992i	−0.215347	+	0.609094i
$418$		0			0
$419$			684.479i			1.63360i	0.576919	+	0.816801i	$0.304255\pi$
$419$			684.479i			1.63360i	−0.576919	+	0.816801i	$0.695745\pi$
$420$	−107.976	−	156.937i	−0.257085	−	0.373659i
$421$	−82.1985	+	252.981i	−0.195246	+	0.600905i	0.804728	+	0.593644i	$0.202311\pi$
$421$	−82.1985	+	252.981i	−0.195246	+	0.600905i	−0.999974	+	0.00726102i	$0.997689\pi$
$422$	−979.158	+	318.148i	−2.32028	+	0.753904i
$423$	−16.9873	+	330.490i	−0.0401592	+	0.781299i
$424$	−90.8119	+	65.9787i	−0.214179	+	0.155610i
$425$	−342.211	+	111.191i	−0.805203	+	0.261626i
$426$	−409.805	−	314.127i	−0.961983	−	0.737388i
$427$	−588.964	−	427.908i	−1.37931	−	1.00213i
$428$		−	126.996i		−	0.296720i
$429$		0			0
$430$	−112.000			−0.260465
$431$	−323.468	+	445.215i	−0.750505	+	1.03298i	0.247440	+	0.968903i	$0.420411\pi$
$431$	−323.468	+	445.215i	−0.750505	+	1.03298i	−0.997945	+	0.0640786i	$0.979589\pi$
$432$	120.509	+	498.645i	0.278956	+	1.15427i
$433$	228.055	+	701.880i	0.526685	+	1.62097i	0.760960	+	0.648799i	$0.224728\pi$
$433$	228.055	+	701.880i	0.526685	+	1.62097i	−0.234275	+	0.972170i	$0.575272\pi$
$434$	−349.127	−	480.532i	−0.804439	−	1.10722i
$435$	51.0955	+	172.178i	0.117461	+	0.395811i
$436$	62.4367	+	192.160i	0.143204	+	0.440735i
$437$	442.862	+	143.894i	1.01341	+	0.329278i
$438$	−336.674	−	489.337i	−0.768662	−	1.11721i
$439$	426.549			0.971638			0.485819	−	0.874060i	$-0.338521\pi$
$439$	426.549			0.971638			0.485819	+	0.874060i	$0.338521\pi$
$440$		0			0
$441$	−49.0000	−	39.5980i	−0.111111	−	0.0897913i
$442$	−1017.09	−	738.962i	−2.30112	−	1.67186i
$443$	−112.980	−	36.7093i	−0.255033	−	0.0828653i	0.178710	−	0.983902i	$-0.442808\pi$
$443$	−112.980	−	36.7093i	−0.255033	−	0.0828653i	−0.433743	+	0.901036i	$0.642808\pi$
$444$	−89.9703	−	2.31073i	−0.202636	−	0.00520436i
$445$	−142.387	+	103.450i	−0.319971	+	0.232472i
$446$	71.5361	+	98.4611i	0.160395	+	0.220765i
$447$	1.63030	−	63.4771i	0.00364721	−	0.142007i
$448$	67.0617	−	206.395i	0.149691	−	0.460702i
$449$	−299.251	+	411.884i	−0.666484	+	0.917337i	−0.999674	−	0.0255229i	$-0.991875\pi$
$449$	−299.251	+	411.884i	−0.666484	+	0.917337i	0.333190	+	0.942860i	$0.391875\pi$
$450$	254.433	−	314.844i	0.565406	−	0.699654i
$451$		0			0
$452$			356.382i			0.788455i
$453$	166.457	−	114.526i	0.367454	−	0.252816i
$454$	173.050	−	532.592i	0.381166	−	1.17311i
$455$	451.919	−	146.837i	0.993229	−	0.322720i
$456$	−113.885	+	33.7965i	−0.249748	+	0.0741152i
$457$	−544.872	+	395.872i	−1.19228	+	0.866242i	−0.993503	−	0.113803i	$-0.963697\pi$
$457$	−544.872	+	395.872i	−1.19228	+	0.866242i	−0.198776	+	0.980045i	$0.563697\pi$
$458$	−296.919	+	96.4747i	−0.648294	+	0.210643i
$459$	555.491	−	134.247i	1.21022	−	0.292477i
$460$	213.580	+	155.175i	0.464305	+	0.337338i
$461$		−	698.478i		−	1.51514i	−0.652755	−	0.757569i	$-0.726387\pi$
$461$		−	698.478i		−	1.51514i	0.652755	−	0.757569i	$-0.273613\pi$
$462$		0			0
$463$	882.000			1.90497			0.952484	−	0.304589i	$-0.0985192\pi$
$463$	882.000			1.90497			0.952484	+	0.304589i	$0.0985192\pi$
$464$	−236.380	+	325.350i	−0.509440	+	0.701184i
$465$	−154.864	+	202.033i	−0.333041	+	0.434479i
$466$	69.2198	+	213.037i	0.148540	+	0.457160i
$467$	−312.551	−	430.190i	−0.669275	−	0.921178i	0.330469	−	0.943817i	$-0.392793\pi$
$467$	−312.551	−	430.190i	−0.669275	−	0.921178i	−0.999744	+	0.0226389i	$0.992793\pi$
$468$	605.349	+	31.1152i	1.29348	+	0.0664856i
$469$	−97.1238	−	298.916i	−0.207087	−	0.637348i
$470$	−261.691	−	85.0285i	−0.556789	−	0.180912i
$471$	212.551	−	146.240i	0.451276	−	0.310487i
$472$	−89.7998			−0.190254
$473$		0			0
$474$	168.000	+	59.3970i	0.354430	+	0.125310i
$475$	205.840	+	149.552i	0.433348	+	0.314846i
$476$	−451.919	−	146.837i	−0.949410	−	0.308482i
$477$	−356.613	−	136.480i	−0.747617	−	0.286122i
$478$	90.6099	−	65.8319i	0.189560	−	0.137724i
$479$	398.114	+	547.957i	0.831136	+	1.14396i	0.987710	+	0.156295i	$0.0499549\pi$
$479$	398.114	+	547.957i	0.831136	+	1.14396i	−0.156574	+	0.987666i	$0.550045\pi$
$480$	−336.638	−	8.64598i	−0.701329	−	0.0180124i
$481$	69.3741	−	213.512i	0.144229	−	0.443891i
$482$	−232.751	+	320.354i	−0.482886	+	0.664636i
$483$	658.532	+	232.826i	1.36342	+	0.482042i
$484$		0			0
$485$			209.304i			0.431554i
$486$	−441.383	+	467.466i	−0.908195	+	0.961864i
$487$	108.156	−	332.870i	0.222086	−	0.683511i	−0.776488	−	0.630132i	$-0.783001\pi$
$487$	108.156	−	332.870i	0.222086	−	0.683511i	0.998574	−	0.0533790i	$-0.0169992\pi$
$488$	−244.789	+	79.5369i	−0.501618	+	0.162985i
$489$	11.9489	+	40.2644i	0.0244353	+	0.0823404i
$490$	42.3789	−	30.7901i	0.0864876	−	0.0628369i
$491$	−241.561	+	78.4879i	−0.491977	+	0.159853i	−0.544490	−	0.838767i	$-0.683277\pi$
$491$	−241.561	+	78.4879i	−0.491977	+	0.159853i	0.0525130	+	0.998620i	$0.483277\pi$
$492$	231.779	−	302.375i	0.471096	−	0.614583i
$493$	362.440	+	263.328i	0.735172	+	0.534133i
$494$			888.972i			1.79954i
$495$		0			0
$496$	−570.000			−1.14919
$497$	286.145	−	393.844i	0.575744	−	0.792443i
$498$	−133.335	−	102.205i	−0.267740	−	0.205231i
$499$	−30.2837	−	93.2035i	−0.0606887	−	0.186781i	0.916116	−	0.400914i	$-0.131307\pi$
$499$	−30.2837	−	93.2035i	−0.0606887	−	0.186781i	−0.976804	+	0.214133i	$0.931307\pi$
$500$	209.476	+	288.319i	0.418952	+	0.576638i
$501$	−243.496	+	72.2600i	−0.486021	+	0.144231i
$502$	−41.6245	−	128.107i	−0.0829173	−	0.255193i
$503$	483.122	+	156.976i	0.960481	+	0.312079i	0.746967	−	0.664861i	$-0.231509\pi$
$503$	483.122	+	156.976i	0.960481	+	0.312079i	0.213514	+	0.976940i	$0.431509\pi$
$504$	−172.073	+	46.2921i	−0.341414	+	0.0918494i
$505$	−419.066			−0.829833
$506$		0			0
$507$	−335.000	+	947.523i	−0.660750	+	1.86888i
$508$	−163.461	−	118.762i	−0.321775	−	0.233783i
$509$	153.330	+	49.8198i	0.301237	+	0.0978779i	0.455736	−	0.890115i	$-0.349376\pi$
$509$	153.330	+	49.8198i	0.301237	+	0.0978779i	−0.154499	+	0.987993i	$0.549376\pi$
$510$	−12.2001	+	475.019i	−0.0239217	+	0.931410i
$511$	453.050	−	329.160i	0.886594	−	0.644148i
$512$	−325.023	−	447.356i	−0.634810	−	0.873742i
$513$	−307.674	−	261.978i	−0.599755	−	0.510678i
$514$	−78.6240	+	241.980i	−0.152965	+	0.470778i
$515$	56.5253	−	77.8004i	0.109758	−	0.151069i
$516$	44.8999	−	126.996i	0.0870153	−	0.246116i
$517$		0			0
$518$		−	197.990i		−	0.382220i
$519$	−323.928	−	470.811i	−0.624138	−	0.907150i
$520$	51.9149	−	159.777i	0.0998363	−	0.307264i
$521$	145.260	−	47.1977i	0.278809	−	0.0905907i	−0.166275	−	0.986079i	$-0.553174\pi$
$521$	145.260	−	47.1977i	0.278809	−	0.0905907i	0.445084	+	0.895489i	$0.353174\pi$
$522$	−503.336	−	25.8717i	−0.964244	−	0.0495626i
$523$	−12.1083	+	8.79716i	−0.0231515	+	0.0168206i	−0.599301	−	0.800524i	$-0.704555\pi$
$523$	−12.1083	+	8.79716i	−0.0231515	+	0.0168206i	0.576149	+	0.817344i	$0.304555\pi$
$524$	664.292	−	215.842i	1.26773	−	0.411912i
$525$	302.899	+	232.181i	0.576951	+	0.442250i
$526$	−996.709	−	724.151i	−1.89488	−	1.37671i
$527$			634.980i			1.20490i
$528$		0			0
$529$	−439.000			−0.829868
$530$	186.616	−	256.855i	0.352106	−	0.484632i
$531$	−166.628	−	256.022i	−0.313801	−	0.482150i
$532$	103.830	+	319.555i	0.195169	+	0.600667i
$533$	558.603	+	768.851i	1.04803	+	1.44250i
$534$	−140.513	−	473.489i	−0.263132	−	0.886684i
$535$	−36.9995	−	113.873i	−0.0691580	−	0.212847i
$536$	−105.683	−	34.3384i	−0.197170	−	0.0640643i
$537$	538.678	+	782.939i	1.00313	+	1.45799i
$538$	980.314			1.82215
$539$		0			0
$540$	−120.000	−	195.161i	−0.222222	−	0.361410i
$541$	417.735	+	303.502i	0.772153	+	0.561002i	0.902614	−	0.430451i	$-0.141646\pi$
$541$	417.735	+	303.502i	0.772153	+	0.561002i	−0.130461	+	0.991453i	$0.541646\pi$
$542$	847.348	+	275.320i	1.56337	+	0.507971i
$543$	785.741	+	20.1804i	1.44704	+	0.0371647i
$544$	−679.574	+	493.740i	−1.24922	+	0.907610i
$545$	111.970	+	154.113i	0.205449	+	0.282776i
$546$	−34.2363	+	1333.02i	−0.0627039	+	2.44143i
$547$	−208.122	+	640.535i	−0.380480	+	1.17100i	0.559227	+	0.829015i	$0.311098\pi$
$547$	−208.122	+	640.535i	−0.380480	+	1.17100i	−0.939707	+	0.341982i	$0.888902\pi$
$548$	−279.301	+	384.425i	−0.509674	+	0.701506i
$549$	−680.982	−	550.316i	−1.24040	−	1.00240i
$550$		0			0
$551$		−	316.784i		−	0.574925i
$552$	203.447	−	139.976i	0.368564	−	0.253579i
$553$	−51.9149	+	159.777i	−0.0938786	+	0.288929i
$554$	56.4899	−	18.3547i	0.101967	−	0.0331312i
$555$	−81.3464	+	24.1404i	−0.146570	+	0.0434962i
$556$	217.949	−	158.349i	0.391994	−	0.284800i
$557$	422.732	−	137.354i	0.758943	−	0.246596i	0.0961183	−	0.995370i	$-0.469357\pi$
$557$	422.732	−	137.354i	0.758943	−	0.246596i	0.662825	+	0.748774i	$0.269357\pi$
$558$	−389.666	−	598.716i	−0.698326	−	1.07297i
$559$	271.830	+	197.496i	0.486279	+	0.353302i
$560$		−	402.154i		−	0.718132i
$561$		0			0
$562$	−56.0000			−0.0996441
$563$	−323.468	+	445.215i	−0.574543	+	0.790791i	−0.993084	−	0.117407i	$-0.962542\pi$
$563$	−323.468	+	445.215i	−0.574543	+	0.790791i	0.418541	+	0.908198i	$0.362542\pi$
$564$	201.323	−	262.642i	0.356956	−	0.465678i
$565$	103.830	+	319.555i	0.183769	+	0.565584i
$566$	279.301	+	384.425i	0.493465	+	0.679197i
$567$	−451.270	−	404.687i	−0.795891	−	0.713733i
$568$	−53.1868	−	163.692i	−0.0936388	−	0.288191i
$569$	−1066.89	−	346.655i	−1.87503	−	0.609235i	−0.989474	−	0.144708i	$-0.953776\pi$
$569$	−1066.89	−	346.655i	−1.87503	−	0.609235i	−0.885559	−	0.464528i	$-0.846224\pi$
$570$	276.811	−	190.452i	0.485633	−	0.334126i
$571$	−808.198			−1.41541			−0.707704	−	0.706509i	$-0.750269\pi$
$571$	−808.198			−1.41541			−0.707704	+	0.706509i	$0.750269\pi$
$572$		0			0
$573$	168.000	+	59.3970i	0.293194	+	0.103660i
$574$	678.062	+	492.641i	1.18129	+	0.858260i
$575$	−503.029	−	163.444i	−0.874833	−	0.284250i
$576$	93.2892	−	243.758i	0.161960	−	0.423192i
$577$	−250.795	+	182.213i	−0.434654	+	0.315795i	−0.783507	−	0.621383i	$-0.786571\pi$
$577$	−250.795	+	182.213i	−0.434654	+	0.315795i	0.348853	+	0.937177i	$0.386571\pi$
$578$	247.266	+	340.333i	0.427796	+	0.588811i
$579$	448.851	+	11.5280i	0.775217	+	0.0199101i
$580$	55.4993	−	170.809i	0.0956885	−	0.294499i
$581$	93.1004	−	128.142i	0.160242	−	0.220554i
$582$	−553.765	−	195.786i	−0.951487	−	0.336401i
$583$		0			0
$584$		−	197.990i		−	0.339024i
$585$	551.861	−	148.465i	0.943352	−	0.253786i
$586$	−17.3050	+	53.2592i	−0.0295306	+	0.0908859i
$587$	914.598	−	297.171i	1.55809	−	0.506254i	0.601792	−	0.798653i	$-0.294454\pi$
$587$	914.598	−	297.171i	1.55809	−	0.506254i	0.956296	+	0.292399i	$0.0944536\pi$
$588$	17.9233	+	60.3966i	0.0304818	+	0.102715i
$589$	363.248	−	263.915i	0.616719	−	0.448073i
$590$	241.561	−	78.4879i	0.409425	−	0.133030i
$591$	−424.928	+	554.354i	−0.718999	+	0.937993i
$592$	−153.713	−	111.679i	−0.259651	−	0.188647i
$593$		−	232.826i		−	0.392624i	−0.980541	−	0.196312i	$-0.937103\pi$
$593$		−	232.826i		−	0.392624i	0.980541	−	0.196312i	$-0.0628966\pi$
$594$		0			0
$595$	−448.000			−0.752941
$596$	−37.3232	+	51.3710i	−0.0626228	+	0.0861929i
$597$	528.577	+	405.170i	0.885388	+	0.678676i
$598$	−571.063	−	1757.55i	−0.954956	−	2.93905i
$599$	−513.715	−	707.068i	−0.857621	−	1.18041i	−0.982132	−	0.188196i	$-0.939736\pi$
$599$	−513.715	−	707.068i	−0.857621	−	1.18041i	0.124511	−	0.992218i	$-0.460264\pi$
$600$	129.357	−	38.3881i	0.215596	−	0.0639802i
$601$	180.373	+	555.130i	0.300121	+	0.923678i	0.981453	+	0.191703i	$0.0614011\pi$
$601$	180.373	+	555.130i	0.300121	+	0.923678i	−0.681332	+	0.731975i	$0.738599\pi$
$602$	281.821	+	91.5692i	0.468141	+	0.152108i
$603$	−98.2003	−	365.021i	−0.162853	−	0.605342i
$604$	−202.049			−0.334519
$605$		0			0
$606$	392.000	−	1108.74i	0.646865	−	1.82961i
$607$	684.117	+	497.040i	1.12705	+	0.818846i	0.985262	−	0.171051i	$-0.0547164\pi$
$607$	684.117	+	497.040i	1.12705	+	0.818846i	0.141783	+	0.989898i	$0.454716\pi$
$608$	564.899	+	183.547i	0.929110	+	0.301886i
$609$	12.2001	−	475.019i	0.0200329	−	0.779999i
$610$	588.964	−	427.908i	0.965515	−	0.701488i
$611$	485.202	+	667.823i	0.794111	+	1.09300i
$612$	−533.730	−	204.265i	−0.872108	−	0.333766i
$613$	−182.685	+	562.247i	−0.298018	+	0.917206i	0.684173	+	0.729320i	$0.260164\pi$
$613$	−182.685	+	562.247i	−0.298018	+	0.917206i	−0.982191	+	0.187886i	$0.939836\pi$
$614$	−232.751	+	320.354i	−0.379073	+	0.521750i
$615$	119.733	−	338.656i	0.194688	−	0.550660i
$616$		0			0
$617$		−	435.578i		−	0.705961i	−0.935631	−	0.352980i	$-0.885168\pi$
$617$		−	435.578i		−	0.705961i	0.935631	−	0.352980i	$-0.114832\pi$
$618$	152.966	+	222.327i	0.247518	+	0.359753i
$619$	−258.956	+	796.985i	−0.418346	+	1.28754i	0.490877	+	0.871229i	$0.336676\pi$
$619$	−258.956	+	796.985i	−0.418346	+	1.28754i	−0.909224	+	0.416308i	$0.863324\pi$
$620$	242.099	−	78.6629i	0.390483	−	0.126876i
$621$	776.582	+	320.301i	1.25053	+	0.515782i
$622$	−54.4872	+	39.5872i	−0.0875999	+	0.0636451i
$623$	442.862	−	143.894i	0.710853	−	0.230970i
$624$	1015.60	+	778.490i	1.62757	+	1.24758i
$625$	−72.0025	−	52.3129i	−0.115204	−	0.0837006i
$626$			1053.01i			1.68212i
$627$		0			0
$628$	−258.000			−0.410828
$629$	−124.411	+	171.237i	−0.197791	+	0.272236i
$630$	422.414	−	274.923i	0.670498	−	0.436385i
$631$	78.4903	+	241.568i	0.124390	+	0.382834i	0.993790	−	0.111276i	$-0.0354938\pi$
$631$	78.4903	+	241.568i	0.124390	+	0.382834i	−0.869399	+	0.494110i	$0.835494\pi$
$632$	34.9127	+	48.0532i	0.0552416	+	0.0760335i
$633$	−332.121	−	1119.16i	−0.524678	−	1.76802i
$634$	339.933	+	1046.21i	0.536172	+	1.65017i
$635$	−181.171	−	58.8659i	−0.285308	−	0.0927022i
$636$	216.433	+	314.574i	0.340304	+	0.494613i
$637$	−157.150			−0.246703
$638$		0			0
$639$	368.000	−	455.377i	0.575900	−	0.712640i
$640$	−187.678	−	136.356i	−0.293247	−	0.213056i
$641$	−112.980	−	36.7093i	−0.176255	−	0.0572689i	0.219560	−	0.975599i	$-0.429538\pi$
$641$	−112.980	−	36.7093i	−0.176255	−	0.0572689i	−0.395815	+	0.918330i	$0.629538\pi$
$642$	335.889	+	8.62674i	0.523192	+	0.0134373i
$643$	354.349	−	257.450i	0.551088	−	0.400389i	−0.277099	−	0.960841i	$-0.589373\pi$
$643$	354.349	−	257.450i	0.551088	−	0.400389i	0.828186	+	0.560453i	$0.189373\pi$
$644$	−410.555	−	565.081i	−0.637508	−	0.877455i
$645$	3.26060	−	126.954i	0.00505520	−	0.196828i
$646$	258.997	−	797.110i	0.400924	−	1.23392i
$647$	194.513	−	267.725i	0.300639	−	0.413794i	−0.631794	−	0.775136i	$-0.717681\pi$
$647$	194.513	−	267.725i	0.300639	−	0.413794i	0.932433	+	0.361342i	$0.117681\pi$
$648$	−209.533	+	44.9778i	−0.323353	+	0.0694101i
$649$		0			0
$650$		−	1009.75i		−	1.55346i
$651$	554.856	−	381.752i	0.852313	−	0.586409i
$652$	12.9787	−	39.9444i	0.0199060	−	0.0612644i
$653$	−594.489	+	193.161i	−0.910396	+	0.295806i	−0.726521	−	0.687144i	$-0.758864\pi$
$653$	−594.489	+	193.161i	−0.910396	+	0.295806i	−0.183875	+	0.982950i	$0.558864\pi$
$654$	−512.483	+	152.084i	−0.783612	+	0.232545i
$655$	532.763	−	387.075i	0.813379	−	0.590955i
$656$	764.943	−	248.545i	1.16607	−	0.378880i
$657$	564.474	−	367.381i	0.859170	−	0.559179i
$658$	588.964	+	427.908i	0.895083	+	0.650316i
$659$			465.652i			0.706604i	0.935509	+	0.353302i	$0.114941\pi$
$659$			465.652i			0.706604i	−0.935509	+	0.353302i	$0.885059\pi$
$660$		0			0
$661$	−394.000			−0.596067			−0.298033	−	0.954555i	$-0.596331\pi$
$661$	−394.000			−0.596067			−0.298033	+	0.954555i	$0.596331\pi$
$662$	276.814	−	381.001i	0.418148	−	0.575531i
$663$	867.238	−	1131.38i	1.30805	−	1.70646i
$664$	−17.3050	−	53.2592i	−0.0260617	−	0.0802096i
$665$	186.201	+	256.284i	0.280001	+	0.385389i
$666$	12.2232	−	237.804i	0.0183532	−	0.357063i
$667$	203.497	+	626.301i	0.305094	+	0.938982i
$668$	241.561	+	78.4879i	0.361618	+	0.117497i
$669$	−113.690	+	78.2212i	−0.169940	+	0.116923i
$670$	314.299			0.469103
$671$		0			0
$672$	840.000	+	296.985i	1.25000	+	0.441942i
$673$	−714.387	−	519.033i	−1.06150	−	0.771222i	−0.0871319	−	0.996197i	$-0.527770\pi$
$673$	−714.387	−	519.033i	−1.06150	−	0.771222i	−0.974365	+	0.224974i	$0.927770\pi$
$674$	640.219	+	208.020i	0.949879	+	0.308634i
$675$	349.475	+	297.570i	0.517741	+	0.440845i
$676$	813.062	−	590.724i	1.20275	−	0.873852i
$677$	534.966	+	736.317i	0.790201	+	1.08762i	0.994083	+	0.108623i	$0.0346440\pi$
$677$	534.966	+	736.317i	0.790201	+	1.08762i	−0.203882	+	0.978995i	$0.565356\pi$
$678$	−942.587	−	24.2087i	−1.39025	−	0.0357061i
$679$	171.123	−	526.662i	0.252022	−	0.775644i
$680$	−93.1004	+	128.142i	−0.136912	+	0.188444i
$681$	598.665	+	211.660i	0.879097	+	0.310808i
$682$		0			0
$683$			435.578i			0.637742i	0.947798	+	0.318871i	$0.103304\pi$
$683$			435.578i			0.637742i	−0.947798	+	0.318871i	$0.896696\pi$
$684$	104.981	+	390.224i	0.153480	+	0.570503i
$685$	−138.440	+	426.073i	−0.202102	+	0.622005i
$686$	790.858	−	256.965i	1.15285	−	0.374585i
$687$	−100.712	−	339.372i	−0.146597	−	0.493991i
$688$	230.057	−	167.146i	0.334385	−	0.242945i
$689$	−905.853	+	294.330i	−1.31474	+	0.427184i
$690$	−424.928	+	554.354i	−0.615838	+	0.803411i
$691$	−344.641	−	250.397i	−0.498757	−	0.362368i	0.309785	−	0.950807i	$-0.399743\pi$
$691$	−344.641	−	250.397i	−0.498757	−	0.362368i	−0.808542	+	0.588438i	$0.799743\pi$
$692$			571.482i			0.825841i
$693$		0			0
$694$	−1288.00			−1.85591
$695$	149.293	−	205.484i	0.214810	−	0.295660i
$696$	−133.335	−	102.205i	−0.191573	−	0.146846i
$697$	−276.879	−	852.147i	−0.397244	−	1.22259i
$698$	−104.738	−	144.159i	−0.150054	−	0.206532i
$699$	−243.496	+	72.2600i	−0.348350	+	0.103376i
$700$	−117.936	−	362.970i	−0.168480	−	0.518528i
$701$	261.691	+	85.0285i	0.373311	+	0.121296i	0.489663	−	0.871912i	$-0.337120\pi$
$701$	261.691	+	85.0285i	0.373311	+	0.121296i	−0.116352	+	0.993208i	$0.537120\pi$
$702$	−123.417	+	1598.96i	−0.175808	+	2.27772i
$703$	149.666			0.212897
$704$		0			0
$705$	104.000	−	294.156i	0.147518	−	0.417243i
$706$	266.382	+	193.538i	0.377311	+	0.274133i
$707$	1054.48	+	342.621i	1.49148	+	0.484612i
$708$	−7.84289	+	305.369i	−0.0110775	+	0.431313i
$709$	33.9787	−	24.6870i	0.0479248	−	0.0348194i	−0.563565	−	0.826072i	$-0.690571\pi$
$709$	33.9787	−	24.6870i	0.0479248	−	0.0348194i	0.611490	+	0.791252i	$0.290571\pi$
$710$	286.145	+	393.844i	0.403021	+	0.554710i
$711$	−72.2185	+	188.702i	−0.101573	+	0.265404i
$712$	50.8744	−	156.575i	0.0714528	−	0.219909i
$713$	−548.628	+	755.121i	−0.769464	+	1.05908i
$714$	419.066	−	1185.30i	0.586927	−	1.66008i
$715$		0			0
$716$		−	950.352i		−	1.32731i
$717$	71.9839	+	104.625i	0.100396	+	0.145920i
$718$	−207.659	+	639.110i	−0.289219	+	0.890125i
$719$	411.569	−	133.727i	0.572419	−	0.185990i	−0.00848270	−	0.999964i	$-0.502700\pi$
$719$	411.569	−	133.727i	0.572419	−	0.185990i	0.580901	+	0.813974i	$0.302700\pi$
$720$	24.8276	−	483.023i	0.0344828	−	0.670866i
$721$	−205.840	+	149.552i	−0.285493	+	0.207423i
$722$	344.727	−	112.009i	0.477462	−	0.155137i
$723$	−356.352	−	273.154i	−0.492880	−	0.377807i
$724$	−635.887	−	461.999i	−0.878297	−	0.638120i
$725$			359.822i			0.496306i
$726$		0			0
$727$	1102.00			1.51582			0.757909	−	0.652360i	$-0.226221\pi$
$727$	1102.00			1.51582			0.757909	+	0.652360i	$0.226221\pi$
$728$	−261.262	+	359.597i	−0.358877	+	0.493952i
$729$	−517.032	−	513.925i	−0.709235	−	0.704973i
$730$	173.050	+	532.592i	0.237054	+	0.729578i
$731$	−186.201	−	256.284i	−0.254721	−	0.350593i
$732$	249.091	+	839.368i	0.340288	+	1.14668i
$733$	−150.311	−	462.609i	−0.205062	−	0.631117i	−0.999711	−	0.0240470i	$-0.992345\pi$
$733$	−150.311	−	462.609i	−0.205062	−	0.631117i	0.794649	−	0.607070i	$-0.207655\pi$
$734$	−357.309	−	116.097i	−0.486797	−	0.158170i
$735$	33.6674	+	48.9337i	0.0458060	+	0.0665765i
$736$	−1234.75			−1.67765
$737$		0			0
$738$	784.000	+	633.568i	1.06233	+	0.858493i
$739$	−847.578	−	615.801i	−1.14693	−	0.833290i	−0.158857	−	0.987302i	$-0.550781\pi$
$739$	−847.578	−	615.801i	−1.14693	−	0.833290i	−0.988069	+	0.154011i	$0.950781\pi$
$740$	80.6998	+	26.2210i	0.109054	+	0.0354337i
$741$	−1007.67	−	25.8802i	−1.35988	−	0.0349261i
$742$	−679.574	+	493.740i	−0.915868	+	0.665417i
$743$	−149.293	−	205.484i	−0.200932	−	0.276560i	0.696646	−	0.717416i	$-0.254675\pi$
$743$	−149.293	−	205.484i	−0.200932	−	0.276560i	−0.897578	+	0.440856i	$0.854675\pi$
$744$	6.11363	−	238.039i	0.00821724	−	0.319945i
$745$	−18.4998	+	56.9364i	−0.0248319	+	0.0764248i
$746$	663.341	−	913.010i	0.889197	−	1.22387i
$747$	119.733	−	148.162i	0.160285	−	0.198343i
$748$		0			0
$749$			316.784i			0.422942i
$750$	−776.798	+	534.453i	−1.03573	+	0.712604i
$751$	108.156	−	332.870i	0.144016	−	0.443235i	−0.852867	−	0.522128i	$-0.825138\pi$
$751$	108.156	−	332.870i	0.144016	−	0.443235i	0.996883	+	0.0788925i	$0.0251384\pi$
$752$	664.429	−	215.886i	0.883549	−	0.287082i
$753$	146.424	−	43.4527i	0.194454	−	0.0577060i
$754$	−1017.09	+	738.962i	−1.34893	+	0.980055i
$755$	−181.171	+	58.8659i	−0.239961	+	0.0779681i
$756$	142.391	+	589.187i	0.188347	+	0.779347i
$757$	−237.851	−	172.809i	−0.314202	−	0.228281i	0.419495	−	0.907757i	$-0.362207\pi$
$757$	−237.851	−	172.809i	−0.314202	−	0.228281i	−0.733697	+	0.679476i	$0.762207\pi$
$758$		−	926.013i		−	1.22165i
$759$		0			0
$760$	112.000			0.147368
$761$	−460.320	+	633.576i	−0.604888	+	0.832557i	−0.996145	−	0.0877249i	$-0.972040\pi$
$761$	−460.320	+	633.576i	−0.604888	+	0.832557i	0.391257	+	0.920281i	$0.372040\pi$
$762$	325.214	−	424.268i	0.426790	−	0.556783i
$763$	−155.745	−	479.332i	−0.204121	−	0.628221i
$764$	−104.738	−	144.159i	−0.137092	−	0.188690i
$765$	−538.088	−	27.6580i	−0.703383	−	0.0361542i
$766$	−423.182	−	1302.42i	−0.552457	−	1.70029i
$767$	−724.683	−	235.464i	−0.944827	−	0.306993i
$768$	823.018	−	566.253i	1.07164	−	0.737309i
$769$	838.131			1.08990			0.544949	−	0.838469i	$-0.316549\pi$
$769$	838.131			1.08990			0.544949	+	0.838469i	$0.316549\pi$
$770$		0			0
$771$	−272.000	−	96.1665i	−0.352789	−	0.124730i
$772$	−363.248	−	263.915i	−0.470528	−	0.341859i
$773$	390.049	+	126.735i	0.504591	+	0.163952i	0.550241	−	0.835006i	$-0.314536\pi$
$773$	390.049	+	126.735i	0.504591	+	0.163952i	−0.0456497	+	0.998958i	$0.514536\pi$
$774$	332.839	+	127.382i	0.430025	+	0.164576i
$775$	−412.599	+	299.770i	−0.532385	+	0.386801i
$776$	−115.080	−	158.394i	−0.148299	−	0.204116i
$777$	224.425	+	5.76398i	0.288836	+	0.00741825i
$778$	−358.433	+	1103.14i	−0.460711	+	1.41792i
$779$	−372.402	+	512.567i	−0.478051	+	0.657981i
$780$	−538.799	−	190.494i	−0.690768	−	0.244223i
$781$		0			0
$782$			1742.31i			2.22802i
$783$	43.9794	−	569.788i	0.0561679	−	0.727698i
$784$	−41.0993	+	126.491i	−0.0524225	+	0.161340i
$785$	−231.339	+	75.1668i	−0.294700	+	0.0957538i
$786$	525.750	+	1771.64i	0.668894	+	2.25399i
$787$	254.273	−	184.740i	0.323092	−	0.234740i	−0.414402	−	0.910094i	$-0.636009\pi$
$787$	254.273	−	184.740i	0.323092	−	0.234740i	0.737494	+	0.675354i	$0.236009\pi$
$788$	664.292	−	215.842i	0.843011	−	0.273911i
$789$	849.857	−	1108.71i	1.07713	−	1.40521i
$790$	−135.915	−	98.7479i	−0.172044	−	0.124997i
$791$		−	888.972i		−	1.12386i
$792$		0			0
$793$	−2184.00			−2.75410
$794$	687.369	−	946.082i	0.865704	−	1.19154i
$795$	285.717	+	219.011i	0.359393	+	0.275485i
$796$	−205.805	−	633.404i	−0.258549	−	0.795733i
$797$	144.638	+	199.077i	0.181478	+	0.249783i	0.890058	−	0.455847i	$-0.150664\pi$
$797$	144.638	+	199.077i	0.181478	+	0.249783i	−0.708580	+	0.705631i	$0.750664\pi$
$798$	−852.237	+	252.910i	−1.06797	+	0.316930i
$799$	−240.497	−	740.174i	−0.300998	−	0.926375i
$800$	−641.646	−	208.483i	−0.802058	−	0.260604i
$801$	540.800	−	145.489i	0.675156	−	0.181635i
$802$	1391.90			1.73553
$803$		0			0
$804$	−126.000	+	356.382i	−0.156716	+	0.443261i
$805$	−532.763	−	387.075i	−0.661818	−	0.480839i
$806$	−1694.70	−	550.640i	−2.10260	−	0.683176i
$807$	−28.5394	+	1111.21i	−0.0353648	+	1.37696i
$808$	317.135	−	230.412i	0.392493	−	0.285163i
$809$	−149.293	−	205.484i	−0.184540	−	0.253997i	0.706717	−	0.707497i	$-0.250176\pi$
$809$	−149.293	−	205.484i	−0.184540	−	0.253997i	−0.891257	+	0.453499i	$0.850176\pi$
$810$	524.330	−	304.128i	0.647321	−	0.375467i
$811$	300.621	−	925.217i	0.370680	−	1.14084i	−0.575668	−	0.817684i	$-0.695258\pi$
$811$	300.621	−	925.217i	0.370680	−	1.14084i	0.946347	−	0.323151i	$-0.104742\pi$
$812$	−279.301	+	384.425i	−0.343967	+	0.473430i
$813$	−336.749	+	952.470i	−0.414206	+	1.17155i
$814$		0			0
$815$		−	39.5980i		−	0.0485865i
$816$	−683.847	−	993.934i	−0.838048	−	1.21806i
$817$	−69.2198	+	213.037i	−0.0847244	+	0.260755i
$818$	−564.899	+	183.547i	−0.690585	+	0.224385i
$819$	−1510.01	−	77.6151i	−1.84372	−	0.0947681i
$820$	−290.598	+	211.132i	−0.354388	+	0.257478i
$821$	−462.992	+	150.435i	−0.563936	+	0.183234i	−0.577092	−	0.816679i	$-0.695812\pi$
$821$	−462.992	+	150.435i	−0.563936	+	0.183234i	0.0131553	+	0.999913i	$0.495812\pi$
$822$	−997.786	−	764.832i	−1.21385	−	0.930452i
$823$	−842.996	−	612.472i	−1.02430	−	0.744195i	−0.0571370	−	0.998366i	$-0.518197\pi$
$823$	−842.996	−	612.472i	−1.02430	−	0.744195i	−0.967159	+	0.254172i	$0.918197\pi$
$824$			89.9555i			0.109169i
$825$		0			0
$826$	−672.000			−0.813559
$827$	−734.023	+	1010.30i	−0.887573	+	1.22164i	0.0866920	+	0.996235i	$0.472370\pi$
$827$	−734.023	+	1010.30i	−0.887573	+	1.22164i	−0.974265	+	0.225405i	$0.927630\pi$
$828$	−458.228	−	704.059i	−0.553415	−	0.850313i
$829$	364.022	+	1120.34i	0.439110	+	1.35144i	0.888816	+	0.458264i	$0.151529\pi$
$829$	364.022	+	1120.34i	0.439110	+	1.35144i	−0.449706	+	0.893177i	$0.648471\pi$
$830$	93.1004	+	128.142i	0.112169	+	0.154388i
$831$	19.1608	+	64.5667i	0.0230575	+	0.0776976i
$832$	−201.185	−	619.184i	−0.241809	−	0.744211i
$833$	140.911	+	45.7846i	0.169160	+	0.0549635i
$834$	404.009	+	587.204i	0.484423	+	0.704082i
$835$	239.466			0.286786
$836$		0			0
$837$	690.000	−	424.264i	0.824373	−	0.506887i
$838$	1465.10	+	1064.46i	1.74833	+	1.27023i
$839$	−971.088	−	315.526i	−1.15743	−	0.376073i	−0.333496	−	0.942752i	$-0.608228\pi$
$839$	−971.088	−	315.526i	−1.15743	−	0.376073i	−0.823939	+	0.566678i	$0.808228\pi$
$840$	167.945	+	4.31337i	0.199934	+	0.00513496i
$841$	−317.944	+	231.000i	−0.378054	+	0.274673i
$842$	413.666	+	569.362i	0.491289	+	0.676202i
$843$	1.63030	−	63.4771i	0.00193393	−	0.0752991i
$844$	−360.746	+	1110.26i	−0.427424	+	1.31547i
$845$	556.940	−	766.562i	0.659101	−	0.907174i
$846$	680.982	+	550.316i	0.804943	+	0.650492i
$847$		0			0
$848$			806.102i			0.950592i
$849$	−443.885	+	305.402i	−0.522832	+	0.359720i
$850$	−294.184	+	905.406i	−0.346099	+	1.06518i
$851$	−295.899	+	96.1435i	−0.347708	+	0.112977i
$852$	−561.290	+	166.569i	−0.658792	+	0.195503i
$853$	−478.276	+	347.488i	−0.560699	+	0.407372i	−0.831715	−	0.555203i	$-0.812640\pi$
$853$	−478.276	+	347.488i	−0.560699	+	0.407372i	0.271016	+	0.962575i	$0.412640\pi$
$854$	−1831.84	+	595.200i	−2.14501	+	0.696955i
$855$	207.822	+	319.315i	0.243067	+	0.373468i
$856$	90.6099	+	65.8319i	0.105853	+	0.0769065i
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$	706.000			0.821886			0.410943	−	0.911661i	$-0.365200\pi$
$859$	706.000			0.821886			0.410943	+	0.911661i	$0.365200\pi$
$860$	−74.6464	+	102.742i	−0.0867982	+	0.119467i
$861$	−578.159	+	754.255i	−0.671497	+	0.876022i
$862$	449.929	+	1384.74i	0.521959	+	1.60642i
$863$	290.939	+	400.443i	0.337125	+	0.464013i	0.943599	−	0.331091i	$-0.107417\pi$
$863$	290.939	+	400.443i	0.337125	+	0.464013i	−0.606474	+	0.795103i	$0.707417\pi$
$864$	990.581	+	408.564i	1.14651	+	0.472875i
$865$	166.498	+	512.428i	0.192483	+	0.592402i
$866$	1857.00	+	603.376i	2.14434	+	0.696739i
$867$	−392.972	+	270.373i	−0.453255	+	0.311849i
$868$	−673.498			−0.775920
$869$		0			0
$870$	448.000	+	158.392i	0.514943	+	0.182060i
$871$	−762.820	−	554.221i	−0.875798	−	0.636305i
$872$	−169.470	−	55.0640i	−0.194346	−	0.0631468i
$873$	238.048	−	622.004i	0.272678	−	0.712490i
$874$	996.709	−	724.151i	1.14040	−	0.828549i
$875$	−522.525	−	719.194i	−0.597171	−	0.821936i
$876$	−673.276	−	17.2920i	−0.768580	−	0.0197397i
$877$	−30.0621	+	92.5217i	−0.0342784	+	0.105498i	−0.966732	−	0.255792i	$-0.917664\pi$
$877$	−30.0621	+	92.5217i	−0.0342784	+	0.105498i	0.932453	+	0.361290i	$0.117664\pi$
$878$	663.341	−	913.010i	0.755513	−	1.03987i
$879$	−59.8665	−	21.1660i	−0.0681075	−	0.0240796i
$880$		0			0
$881$		−	1493.41i		−	1.69513i	−0.530692	−	0.847565i	$-0.678068\pi$
$881$		−	1493.41i		−	1.69513i	0.530692	−	0.847565i	$-0.321932\pi$
$882$	−160.959	+	43.3023i	−0.182494	+	0.0490956i
$883$	26.5755	−	81.7909i	0.0300968	−	0.0926284i	−0.934880	−	0.354965i	$-0.884493\pi$
$883$	26.5755	−	81.7909i	0.0300968	−	0.0926284i	0.964977	+	0.262336i	$0.0844929\pi$
$884$	−1355.76	+	440.512i	−1.53366	+	0.498317i
$885$	81.9351	+	276.099i	0.0925820	+	0.311976i
$886$	−254.273	+	184.740i	−0.286990	+	0.208511i
$887$	−241.561	+	78.4879i	−0.272335	+	0.0884869i	−0.442001	−	0.897015i	$-0.645731\pi$
$887$	−241.561	+	78.4879i	−0.272335	+	0.0884869i	0.169666	+	0.985502i	$0.445731\pi$
$888$	48.2873	−	62.9947i	0.0543776	−	0.0709400i
$889$	407.745	+	296.244i	0.458655	+	0.333233i
$890$			465.652i			0.523205i
$891$		0			0
$892$	138.000			0.154709
$893$	−323.468	+	445.215i	−0.362226	+	0.498561i
$894$	−133.335	−	102.205i	−0.149144	−	0.114323i
$895$	−276.879	−	852.147i	−0.309362	−	0.952119i
$896$	360.764	+	496.549i	0.402639	+	0.554184i
$897$	2008.85	−	596.145i	2.23952	−	0.664598i
$898$	416.245	+	1281.07i	0.463524	+	1.42658i
$899$	603.902	+	196.220i	0.671749	+	0.218264i
$900$	−119.243	−	443.240i	−0.132493	−	0.492489i
$901$	897.998			0.996668
$902$		0			0
$903$	−112.000	+	316.784i	−0.124031	+	0.350813i
$904$	−254.273	−	184.740i	−0.281276	−	0.204359i
$905$	−704.778	−	228.996i	−0.778761	−	0.253035i
$906$	13.7251	−	534.397i	0.0151491	−	0.589842i
$907$	781.510	−	567.801i	0.861643	−	0.626020i	−0.0666883	−	0.997774i	$-0.521243\pi$
$907$	781.510	−	567.801i	0.861643	−	0.626020i	0.928332	+	0.371753i	$0.121243\pi$
$908$	−373.232	−	513.710i	−0.411049	−	0.565760i
$909$	1245.37	+	476.618i	1.37004	+	0.524332i
$910$	388.495	−	1195.67i	0.426918	−	1.31392i
$911$	852.866	−	1173.87i	0.936187	−	1.28855i	−0.0212096	−	0.999775i	$-0.506752\pi$
$911$	852.866	−	1173.87i	0.936187	−	1.28855i	0.957397	−	0.288776i	$-0.0932483\pi$
$912$	−284.366	+	804.308i	−0.311805	+	0.881917i
$913$		0			0
$914$			1781.91i			1.94957i
$915$	467.896	+	680.060i	0.511361	+	0.743235i
$916$	−109.392	+	336.674i	−0.119424	+	0.367548i
$917$	−1657.04	+	538.404i	−1.80702	+	0.587136i
$918$	576.512	−	1397.78i	0.628008	−	1.52263i
$919$	320.869	−	233.125i	0.349150	−	0.253672i	−0.399362	−	0.916793i	$-0.630768\pi$
$919$	320.869	−	233.125i	0.349150	−	0.253672i	0.748512	+	0.663121i	$0.230768\pi$
$920$	−221.431	+	71.9472i	−0.240686	+	0.0782035i
$921$	−356.352	−	273.154i	−0.386919	−	0.296584i
$922$	−1495.06	−	1086.23i	−1.62154	−	1.17812i
$923$		−	1460.45i		−	1.58229i
$924$		0			0
$925$	−170.000			−0.183784
$926$	1371.63	−	1887.88i	1.48124	−	2.03875i
$927$	−256.466	+	166.917i	−0.276662	+	0.180062i
$928$	259.574	+	798.887i	0.279714	+	0.860870i
$929$	−897.754	−	1235.65i	−0.966366	−	1.33009i	−0.943861	−	0.330342i	$-0.892836\pi$
$929$	−897.754	−	1235.65i	−0.966366	−	1.33009i	−0.0225050	−	0.999747i	$-0.507164\pi$
$930$	191.608	+	645.667i	0.206030	+	0.694266i
$931$	−32.3746	−	99.6388i	−0.0347740	−	0.107023i
$932$	241.561	+	78.4879i	0.259185	+	0.0842145i
$933$	−43.2867	−	62.9147i	−0.0463951	−	0.0674327i
$934$	−1406.86			−1.50628
$935$		0			0
$936$	−336.000	+	415.779i	−0.358974	+	0.444208i
$937$	1017.09	+	738.962i	1.08548	+	0.788647i	0.978630	−	0.205629i	$-0.0659239\pi$
$937$	1017.09	+	738.962i	1.08548	+	0.788647i	0.106849	+	0.994275i	$0.465924\pi$
$938$	−790.858	−	256.965i	−0.843132	−	0.273950i
$939$	−1193.61	−	30.6557i	−1.27115	−	0.0326472i
$940$	−252.413	+	183.389i	−0.268525	+	0.195095i
$941$	−286.145	−	393.844i	−0.304086	−	0.418538i	0.629440	−	0.777049i	$-0.283284\pi$
$941$	−286.145	−	393.844i	−0.304086	−	0.418538i	−0.933525	+	0.358511i	$0.883284\pi$
$942$	17.5257	−	682.379i	0.0186048	−	0.724394i
$943$	406.995	−	1252.60i	0.431596	−	1.32832i
$944$	−379.052	+	521.720i	−0.401538	+	0.552669i
$945$	299.333	+	486.818i	0.316754	+	0.515152i
$946$		0			0
$947$		−	435.578i		−	0.459955i	−0.973196	−	0.229978i	$-0.926135\pi$
$947$		−	435.578i		−	0.459955i	0.973196	−	0.229978i	$-0.0738653\pi$
$948$	166.457	−	114.526i	0.175587	−	0.120808i
$949$	519.149	−	1597.77i	0.547048	−	1.68364i
$950$	640.219	−	208.020i	0.673914	−	0.218968i
$951$	−1195.79	+	354.863i	−1.25741	+	0.373148i
$952$	339.031	−	246.321i	0.356125	−	0.258740i
$953$	1529.89	−	497.090i	1.60534	−	0.521605i	0.636917	−	0.770932i	$-0.280209\pi$
$953$	1529.89	−	497.090i	1.60534	−	0.521605i	0.968419	+	0.249327i	$0.0802094\pi$
$954$	−846.712	+	551.071i	−0.887538	+	0.577643i
$955$	−135.915	−	98.7479i	−0.142319	−	0.103401i
$956$		−	126.996i		−	0.132841i
$957$		0			0
$958$	1792.00			1.87056
$959$	696.700	−	958.925i	0.726486	−	0.999922i
$960$	−149.702	+	195.298i	−0.155939	+	0.203436i
$961$	−18.8500	−	58.0144i	−0.0196150	−	0.0603688i
$962$	−349.127	−	480.532i	−0.362917	−	0.499513i
$963$	−19.5572	+	380.486i	−0.0203086	+	0.395105i
$964$	138.748	+	427.023i	0.143930	+	0.442970i
$965$	−402.601	−	130.813i	−0.417204	−	0.135558i
$966$	1522.46	−	1047.48i	1.57604	−	1.08435i
$967$	−1055.15			−1.09116			−0.545578	−	0.838060i	$-0.683690\pi$
$967$	−1055.15			−1.09116			−0.545578	+	0.838060i	$0.683690\pi$
$968$		0			0
$969$	896.000	+	316.784i	0.924665	+	0.326918i
$970$	448.006	+	325.495i	0.461861	+	0.335562i
$971$	242.099	+	78.6629i	0.249330	+	0.0810122i	0.431016	−	0.902344i	$-0.358155\pi$
$971$	242.099	+	78.6629i	0.249330	+	0.0810122i	−0.181686	+	0.983357i	$0.558155\pi$
$972$	134.649	+	716.457i	0.138528	+	0.737096i
$973$	−543.659	+	394.992i	−0.558746	+	0.405952i
$974$	−544.297	−	749.160i	−0.558826	−	0.769158i
$975$	1144.57	+	29.3963i	1.17392	+	0.0301501i
$976$	−571.180	+	1757.91i	−0.585226	+	1.80114i
$977$	−847.879	+	1167.01i	−0.867839	+	1.19448i	0.111804	+	0.993730i	$0.464337\pi$
$977$	−847.879	+	1167.01i	−0.867839	+	1.19448i	−0.979643	+	0.200748i	$0.935663\pi$
$978$	104.766	+	37.0405i	0.107123	+	0.0378737i
$979$		0			0
$980$		−	59.3970i		−	0.0606092i
$981$	−157.471	−	585.337i	−0.160521	−	0.596673i
$982$	−207.659	+	639.110i	−0.211466	+	0.650825i
$983$	−653.669	+	212.390i	−0.664973	+	0.216063i	−0.622005	−	0.783014i	$-0.713682\pi$
$983$	−653.669	+	212.390i	−0.664973	+	0.216063i	−0.0429685	+	0.999076i	$0.513682\pi$
$984$	95.5910	+	322.115i	0.0971453	+	0.327353i
$985$	532.763	−	387.075i	0.540876	−	0.392970i
$986$	1127.28	−	366.277i	1.14329	−	0.371477i
$987$	−502.188	+	655.145i	−0.508802	+	0.663774i
$988$	815.489	+	592.488i	0.825394	+	0.599684i
$989$		−	465.652i		−	0.470831i
$990$		0			0
$991$	574.000			0.579213			0.289606	−	0.957146i	$-0.406476\pi$
$991$	574.000			0.579213			0.289606	+	0.957146i	$0.406476\pi$
$992$	−699.810	+	963.206i	−0.705454	+	0.970974i
$993$	423.814	+	324.866i	0.426802	+	0.327156i
$994$	−398.014	−	1224.96i	−0.400416	−	1.23235i
$995$	−369.077	−	507.991i	−0.370931	−	0.510543i
$996$	−182.622	+	54.1950i	−0.183356	+	0.0544126i
$997$	409.307	+	1259.72i	0.410539	+	1.26351i	0.916181	+	0.400766i	$0.131256\pi$
$997$	409.307	+	1259.72i	0.410539	+	1.26351i	−0.505642	+	0.862744i	$0.668744\pi$
$998$	−246.593	−	80.1230i	−0.247088	−	0.0802836i
$999$	269.199	+	20.7783i	0.269469	+	0.0207991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.k.323.4		16
3.2	odd	2	inner	363.3.h.k.323.1		16
11.2	odd	10	inner	363.3.h.k.269.4		16
11.3	even	5	inner	363.3.h.k.245.1		16
11.4	even	5	inner	363.3.h.k.251.3		16
11.5	even	5		363.3.b.i.122.4	yes	4
11.6	odd	10		363.3.b.i.122.2	yes	4
11.7	odd	10	inner	363.3.h.k.251.1		16
11.8	odd	10	inner	363.3.h.k.245.3		16
11.9	even	5	inner	363.3.h.k.269.2		16
11.10	odd	2	inner	363.3.h.k.323.2		16
33.2	even	10	inner	363.3.h.k.269.1		16
33.5	odd	10		363.3.b.i.122.1	✓	4
33.8	even	10	inner	363.3.h.k.245.2		16
33.14	odd	10	inner	363.3.h.k.245.4		16
33.17	even	10		363.3.b.i.122.3	yes	4
33.20	odd	10	inner	363.3.h.k.269.3		16
33.26	odd	10	inner	363.3.h.k.251.2		16
33.29	even	10	inner	363.3.h.k.251.4		16
33.32	even	2	inner	363.3.h.k.323.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.i.122.1	✓	4	33.5	odd	10
363.3.b.i.122.2	yes	4	11.6	odd	10
363.3.b.i.122.3	yes	4	33.17	even	10
363.3.b.i.122.4	yes	4	11.5	even	5
363.3.h.k.245.1		16	11.3	even	5	inner
363.3.h.k.245.2		16	33.8	even	10	inner
363.3.h.k.245.3		16	11.8	odd	10	inner
363.3.h.k.245.4		16	33.14	odd	10	inner
363.3.h.k.251.1		16	11.7	odd	10	inner
363.3.h.k.251.2		16	33.26	odd	10	inner
363.3.h.k.251.3		16	11.4	even	5	inner
363.3.h.k.251.4		16	33.29	even	10	inner
363.3.h.k.269.1		16	33.2	even	10	inner
363.3.h.k.269.2		16	11.9	even	5	inner
363.3.h.k.269.3		16	33.20	odd	10	inner
363.3.h.k.269.4		16	11.2	odd	10	inner
363.3.h.k.323.1		16	3.2	odd	2	inner
363.3.h.k.323.2		16	11.10	odd	2	inner
363.3.h.k.323.3		16	33.32	even	2	inner
363.3.h.k.323.4		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.55513 - 2.14046i) q^{2} +(2.38098 + 1.82509i) q^{3} +(-0.927051 - 2.85317i) q^{4} +(-1.66251 - 2.28825i) q^{5} +(7.60926 - 2.25812i) q^{6} +(2.31247 + 7.11706i) q^{7} +(2.51626 + 0.817582i) q^{8} +(2.33810 + 8.69099i) q^{9} -7.48331 q^{10} +(3.00000 - 8.48528i) q^{12} +(18.1624 + 13.1957i) q^{13} +(18.8300 + 6.11822i) q^{14} +(0.217858 - 8.48248i) q^{15} +(15.3713 - 11.1679i) q^{16} +(-12.4411 - 17.1237i) q^{17} +(22.2388 + 8.51104i) q^{18} +(-4.62494 + 14.2341i) q^{19} +(-4.98752 + 6.86474i) q^{20} +(-7.48331 + 21.1660i) q^{21} -31.1127i q^{23} +(4.49900 + 6.53904i) q^{24} +(5.25329 - 16.1680i) q^{25} +(56.4899 - 18.3547i) q^{26} +(-10.2949 + 24.9603i) q^{27} +(18.1624 - 13.1957i) q^{28} +(-20.1301 + 6.54066i) q^{29} +(-17.8176 - 13.6577i) q^{30} +(-24.2705 - 17.6336i) q^{31} -39.6863i q^{32} -56.0000 q^{34} +(12.4411 - 17.1237i) q^{35} +(22.6293 - 14.7280i) q^{36} +(-3.09017 - 9.51057i) q^{37} +(23.2751 + 32.0354i) q^{38} +(19.1608 + 64.5667i) q^{39} +(-2.31247 - 7.11706i) q^{40} +(40.2601 + 13.0813i) q^{41} +(33.6674 + 48.9337i) q^{42} +14.9666 q^{43} +(16.0000 - 19.7990i) q^{45} +(-66.5954 - 48.3844i) q^{46} +(34.9699 + 11.3624i) q^{47} +(56.9812 + 1.46346i) q^{48} +(-5.66312 + 4.11450i) q^{49} +(-26.4373 - 36.3878i) q^{50} +(1.63030 - 63.4771i) q^{51} +(20.8122 - 64.0535i) q^{52} +(-24.9376 + 34.3237i) q^{53} +(37.4166 + 60.8523i) q^{54} +19.7990i q^{56} +(-36.9904 + 25.4502i) q^{57} +(-17.3050 + 53.2592i) q^{58} +(-32.2799 + 10.4884i) q^{59} +(-24.4039 + 7.24211i) q^{60} +(-78.7037 + 57.1816i) q^{61} +(-75.4878 + 24.5275i) q^{62} +(-56.4474 + 36.7381i) q^{63} +(-23.4615 - 17.0458i) q^{64} -63.4980i q^{65} -42.0000 q^{67} +(-37.3232 + 51.3710i) q^{68} +(56.7834 - 74.0786i) q^{69} +(-17.3050 - 53.2592i) q^{70} +(-38.2377 - 52.6296i) q^{71} +(-1.22232 + 23.7804i) q^{72} +(-23.1247 - 71.1706i) q^{73} +(-25.1626 - 8.17582i) q^{74} +(42.0159 - 28.9078i) q^{75} +44.8999 q^{76} +(168.000 + 59.3970i) q^{78} +(18.1624 + 13.1957i) q^{79} +(-51.1099 - 16.6066i) q^{80} +(-70.0665 + 40.6409i) q^{81} +(90.6099 - 65.8319i) q^{82} +(-12.4411 - 17.1237i) q^{83} +(67.3276 + 1.72920i) q^{84} +(-18.4998 + 56.9364i) q^{85} +(23.2751 - 32.0354i) q^{86} +(-59.8665 - 21.1660i) q^{87} -62.2254i q^{89} +(-17.4968 - 65.0374i) q^{90} +(-51.9149 + 159.777i) q^{91} +(-88.7698 + 28.8431i) q^{92} +(-25.6047 - 86.2809i) q^{93} +(78.7037 - 57.1816i) q^{94} +(40.2601 - 13.0813i) q^{95} +(72.4310 - 94.4921i) q^{96} +(-59.8673 - 43.4961i) q^{97} +18.5203i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 12 q^{4} + 28 q^{9} + 48 q^{12} + 32 q^{15} + 76 q^{16} - 68 q^{25} - 92 q^{27} - 120 q^{31} - 896 q^{34} - 84 q^{36} + 40 q^{37} + 224 q^{42} + 256 q^{45} - 76 q^{48} - 28 q^{49} + 224 q^{58}+ \cdots - 296 q^{97}+O(q^{100}) \) 16 * q + 4 * q^3 + 12 * q^4 + 28 * q^9 + 48 * q^12 + 32 * q^15 + 76 * q^16 - 68 * q^25 - 92 * q^27 - 120 * q^31 - 896 * q^34 - 84 * q^36 + 40 * q^37 + 224 * q^42 + 256 * q^45 - 76 * q^48 - 28 * q^49 + 224 * q^58 - 96 * q^60 - 116 * q^64 - 672 * q^67 - 352 * q^69 + 224 * q^70 + 68 * q^75 + 2688 * q^78 - 68 * q^81 + 448 * q^82 + 672 * q^91 + 120 * q^93 - 296 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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