LMFDB - Embedded newform 363.3.h.k.245.1

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			245.1
Root			$2.01333 - 1.92046i$ of defining polynomial
Character	$\chi$	$=$	363.245
Dual form			363.3.h.k.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.55513 - 2.14046i) q^{2} +(-2.99901 - 0.0770245i) q^{3} +(-0.927051 + 2.85317i) q^{4} +(1.66251 - 2.28825i) q^{5} +(4.49900 + 6.53904i) q^{6} +(2.31247 - 7.11706i) q^{7} +(-2.51626 + 0.817582i) q^{8} +(8.98813 + 0.461994i) q^{9} -7.48331 q^{10} +(3.00000 - 8.48528i) q^{12} +(18.1624 - 13.1957i) q^{13} +(-18.8300 + 6.11822i) q^{14} +(-5.16213 + 6.73442i) q^{15} +(15.3713 + 11.1679i) q^{16} +(12.4411 - 17.1237i) q^{17} +(-12.9889 - 19.9572i) q^{18} +(-4.62494 - 14.2341i) q^{19} +(4.98752 + 6.86474i) q^{20} +(-7.48331 + 21.1660i) q^{21} -31.1127i q^{23} +(7.60926 - 2.25812i) q^{24} +(5.25329 + 16.1680i) q^{25} +(-56.4899 - 18.3547i) q^{26} +(-26.9199 - 2.07783i) q^{27} +(18.1624 + 13.1957i) q^{28} +(20.1301 + 6.54066i) q^{29} +(22.4425 + 0.576398i) q^{30} +(-24.2705 + 17.6336i) q^{31} -39.6863i q^{32} -56.0000 q^{34} +(-12.4411 - 17.1237i) q^{35} +(-9.65061 + 25.2164i) q^{36} +(-3.09017 + 9.51057i) q^{37} +(-23.2751 + 32.0354i) q^{38} +(-55.4856 + 38.1752i) q^{39} +(-2.31247 + 7.11706i) q^{40} +(-40.2601 + 13.0813i) q^{41} +(56.9425 - 16.8983i) q^{42} +14.9666 q^{43} +(16.0000 - 19.7990i) q^{45} +(-66.5954 + 48.3844i) q^{46} +(-34.9699 + 11.3624i) q^{47} +(-45.2386 - 34.6767i) q^{48} +(-5.66312 - 4.11450i) q^{49} +(26.4373 - 36.3878i) q^{50} +(-38.6298 + 50.3958i) q^{51} +(20.8122 + 64.0535i) q^{52} +(24.9376 + 34.3237i) q^{53} +(37.4166 + 60.8523i) q^{54} +19.7990i q^{56} +(12.7739 + 43.0445i) q^{57} +(-17.3050 - 53.2592i) q^{58} +(32.2799 + 10.4884i) q^{59} +(-14.4289 - 20.9716i) q^{60} +(-78.7037 - 57.1816i) q^{61} +(75.4878 + 24.5275i) q^{62} +(24.0728 - 62.9007i) q^{63} +(-23.4615 + 17.0458i) q^{64} -63.4980i q^{65} -42.0000 q^{67} +(37.3232 + 51.3710i) q^{68} +(-2.39644 + 93.3073i) q^{69} +(-17.3050 + 53.2592i) q^{70} +(38.2377 - 52.6296i) q^{71} +(-22.9942 + 6.18604i) q^{72} +(-23.1247 + 71.1706i) q^{73} +(25.1626 - 8.17582i) q^{74} +(-14.5093 - 48.8925i) q^{75} +44.8999 q^{76} +(168.000 + 59.3970i) q^{78} +(18.1624 - 13.1957i) q^{79} +(51.1099 - 16.6066i) q^{80} +(80.5731 + 8.30494i) q^{81} +(90.6099 + 65.8319i) q^{82} +(12.4411 - 17.1237i) q^{83} +(-53.4528 - 40.9731i) q^{84} +(-18.4998 - 56.9364i) q^{85} +(-23.2751 - 32.0354i) q^{86} +(-59.8665 - 21.1660i) q^{87} -62.2254i q^{89} +(-67.2610 - 3.45725i) q^{90} +(-51.9149 - 159.777i) q^{91} +(88.7698 + 28.8431i) q^{92} +(74.1457 - 51.0138i) q^{93} +(78.7037 + 57.1816i) q^{94} +(-40.2601 - 13.0813i) q^{95} +(-3.05681 + 119.020i) 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 $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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	−0.995546	−	0.0942755i	$-0.969947\pi$
$2$	−1.55513	−	2.14046i	−0.777567	−	1.07023i	0.217979	−	0.975953i	$-0.430053\pi$
$3$	−2.99901	−	0.0770245i	−0.999670	−	0.0256748i
$3$	−2.99901	−	0.0770245i	−0.999670	−	0.0256748i
$4$	−0.927051	+	2.85317i	−0.231763	+	0.713292i
$5$	1.66251	−	2.28825i	0.332502	−	0.457649i	−0.609731	−	0.792608i	$-0.708723\pi$
$5$	1.66251	−	2.28825i	0.332502	−	0.457649i	0.942233	+	0.334959i	$0.108723\pi$
$6$	4.49900	+	6.53904i	0.749833	+	1.08984i
$7$	2.31247	−	7.11706i	0.330353	−	1.01672i	−0.638613	−	0.769528i	$-0.720491\pi$
$7$	2.31247	−	7.11706i	0.330353	−	1.01672i	0.968966	−	0.247194i	$-0.0795085\pi$
$8$	−2.51626	+	0.817582i	−0.314532	+	0.102198i
$9$	8.98813	+	0.461994i	0.998682	+	0.0513327i
$10$	−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	0.402064	−	0.915612i	$-0.368293\pi$
$13$	18.1624	−	13.1957i	1.39711	−	1.01506i	0.995043	−	0.0994457i	$-0.0317070\pi$
$14$	−18.8300	+	6.11822i	−1.34500	+	0.437016i
$15$	−5.16213	+	6.73442i	−0.344142	+	0.448961i
$16$	15.3713	+	11.1679i	0.960708	+	0.697995i
$17$	12.4411	−	17.1237i	0.731828	−	1.00727i	−0.267220	−	0.963636i	$-0.586105\pi$
$17$	12.4411	−	17.1237i	0.731828	−	1.00727i	0.999047	−	0.0436386i	$-0.0138950\pi$
$18$	−12.9889	−	19.9572i	−0.721604	−	1.10873i
$19$	−4.62494	−	14.2341i	−0.243418	−	0.749164i	−0.995893	−	0.0905424i	$-0.971140\pi$
$19$	−4.62494	−	14.2341i	−0.243418	−	0.749164i	0.752475	−	0.658621i	$-0.228860\pi$
$20$	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	$-0.236445\pi$
$24$	7.60926	−	2.25812i	0.317053	−	0.0940885i
$25$	5.25329	+	16.1680i	0.210132	+	0.646718i
$26$	−56.4899	−	18.3547i	−2.17269	−	0.705949i
$27$	−26.9199	−	2.07783i	−0.997034	−	0.0769568i
$28$	18.1624	+	13.1957i	0.648657	+	0.471277i
$29$	20.1301	+	6.54066i	0.694140	+	0.225540i	0.634776	−	0.772696i	$-0.281093\pi$
$29$	20.1301	+	6.54066i	0.694140	+	0.225540i	0.0593647	+	0.998236i	$0.481093\pi$
$30$	22.4425	+	0.576398i	0.748085	+	0.0192133i
$31$	−24.2705	+	17.6336i	−0.782920	+	0.568824i	−0.905854	−	0.423590i	$-0.860770\pi$
$31$	−24.2705	+	17.6336i	−0.782920	+	0.568824i	0.122934	+	0.992415i	$0.460770\pi$
$32$		−	39.6863i		−	1.24020i
$33$		0			0
$34$	−56.0000			−1.64706
$35$	−12.4411	−	17.1237i	−0.355459	−	0.489247i
$36$	−9.65061	+	25.2164i	−0.268072	+	0.700455i
$37$	−3.09017	+	9.51057i	−0.0835181	+	0.257042i	−0.984092	−	0.177661i	$-0.943147\pi$
$37$	−3.09017	+	9.51057i	−0.0835181	+	0.257042i	0.900574	+	0.434704i	$0.143147\pi$
$38$	−23.2751	+	32.0354i	−0.612503	+	0.843038i
$39$	−55.4856	+	38.1752i	−1.42271	+	0.978852i
$40$	−2.31247	+	7.11706i	−0.0578118	+	0.177926i
$41$	−40.2601	+	13.0813i	−0.981955	+	0.319056i	−0.755632	−	0.654996i	$-0.772670\pi$
$41$	−40.2601	+	13.0813i	−0.981955	+	0.319056i	−0.226322	+	0.974052i	$0.572670\pi$
$42$	56.9425	−	16.8983i	1.35577	−	0.402339i
$43$	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	$-0.727928\pi$
$47$	−34.9699	+	11.3624i	−0.744041	+	0.241754i	−0.0876258	+	0.996153i	$0.527928\pi$
$48$	−45.2386	−	34.6767i	−0.942470	−	0.722431i
$49$	−5.66312	−	4.11450i	−0.115574	−	0.0839693i
$50$	26.4373	−	36.3878i	0.528745	−	0.727756i
$51$	−38.6298	+	50.3958i	−0.757448	+	0.988153i
$52$	20.8122	+	64.0535i	0.400235	+	1.23180i
$53$	24.9376	+	34.3237i	0.470521	+	0.647617i	0.976649	−	0.214842i	$-0.0689236\pi$
$53$	24.9376	+	34.3237i	0.470521	+	0.647617i	−0.506128	+	0.862458i	$0.668924\pi$
$54$	37.4166	+	60.8523i	0.692900	+	1.12689i
$55$		0			0
$56$			19.7990i			0.353553i
$57$	12.7739	+	43.0445i	0.224103	+	0.755166i
$58$	−17.3050	−	53.2592i	−0.298361	−	0.918261i
$59$	32.2799	+	10.4884i	0.547117	+	0.177769i	0.569517	−	0.821980i	$-0.307130\pi$
$59$	32.2799	+	10.4884i	0.547117	+	0.177769i	−0.0223991	+	0.999749i	$0.507130\pi$
$60$	−14.4289	−	20.9716i	−0.240481	−	0.349526i
$61$	−78.7037	−	57.1816i	−1.29022	−	0.937403i	−0.290414	−	0.956901i	$-0.593793\pi$
$61$	−78.7037	−	57.1816i	−1.29022	−	0.937403i	−0.999810	+	0.0194983i	$0.993793\pi$
$62$	75.4878	+	24.5275i	1.21754	+	0.395604i
$63$	24.0728	−	62.9007i	0.382109	−	0.998424i
$64$	−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
$69$	−2.39644	+	93.3073i	−0.0347310	+	1.35228i
$70$	−17.3050	+	53.2592i	−0.247214	+	0.760845i
$71$	38.2377	−	52.6296i	0.538559	−	0.741263i	−0.449846	−	0.893106i	$-0.648521\pi$
$71$	38.2377	−	52.6296i	0.538559	−	0.741263i	0.988405	+	0.151844i	$0.0485210\pi$
$72$	−22.9942	+	6.18604i	−0.319364	+	0.0859172i
$73$	−23.1247	+	71.1706i	−0.316777	+	0.974939i	0.658240	+	0.752808i	$0.271301\pi$
$73$	−23.1247	+	71.1706i	−0.316777	+	0.974939i	−0.975017	+	0.222131i	$0.928699\pi$
$74$	25.1626	−	8.17582i	0.340035	−	0.110484i
$75$	−14.5093	−	48.8925i	−0.193458	−	0.651900i
$76$	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	−0.466870	−	0.884326i	$-0.654618\pi$
$79$	18.1624	−	13.1957i	0.229904	−	0.167035i	0.696773	+	0.717291i	$0.254618\pi$
$80$	51.1099	−	16.6066i	0.638874	−	0.207583i
$81$	80.5731	+	8.30494i	0.994730	+	0.102530i
$82$	90.6099	+	65.8319i	1.10500	+	0.802829i
$83$	12.4411	−	17.1237i	0.149892	−	0.206309i	−0.727467	−	0.686142i	$-0.759303\pi$
$83$	12.4411	−	17.1237i	0.149892	−	0.206309i	0.877360	+	0.479833i	$0.159303\pi$
$84$	−53.4528	−	40.9731i	−0.636343	−	0.487775i
$85$	−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	$-0.113676\pi$
$90$	−67.2610	−	3.45725i	−0.747345	−	0.0384139i
$91$	−51.9149	−	159.777i	−0.570493	−	1.75580i
$92$	88.7698	+	28.8431i	0.964889	+	0.313511i
$93$	74.1457	−	51.0138i	0.797266	−	0.548536i
$94$	78.7037	+	57.1816i	0.837273	+	0.608315i
$95$	−40.2601	−	13.0813i	−0.423791	−	0.137698i
$96$	−3.05681	+	119.020i	−0.0318418	+	1.23979i
$97$	−59.8673	+	43.4961i	−0.617188	+	0.448413i	−0.851938	−	0.523642i	$-0.824573\pi$
$97$	−59.8673	+	43.4961i	−0.617188	+	0.448413i	0.234750	+	0.972056i	$0.424573\pi$
$98$			18.5203i			0.188982i
$99$		0			0
$100$	−51.0000			−0.510000
$101$	−87.0875	−	119.866i	−0.862252	−	1.18679i	−0.981028	−	0.193867i	$-0.937897\pi$
$101$	−87.0875	−	119.866i	−0.862252	−	1.18679i	0.118775	−	0.992921i	$-0.462103\pi$
$102$	167.945	+	4.31337i	1.64652	+	0.0422879i
$103$	10.5066	−	32.3359i	0.102006	−	0.313941i	−0.887010	−	0.461749i	$-0.847222\pi$
$103$	10.5066	−	32.3359i	0.102006	−	0.313941i	0.989016	+	0.147808i	$0.0472219\pi$
$104$	−34.9127	+	48.0532i	−0.335699	+	0.462050i
$105$	35.9920	+	52.3123i	0.342781	+	0.498213i
$106$	34.6871	−	106.756i	0.327237	−	1.00713i
$107$	−40.2601	+	13.0813i	−0.376263	+	0.122255i	−0.491042	−	0.871136i	$-0.663384\pi$
$107$	−40.2601	+	13.0813i	−0.376263	+	0.122255i	0.114779	+	0.993391i	$0.463384\pi$
$108$	30.8846	−	74.8809i	0.285968	−	0.693341i
$109$	−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	$-0.423827\pi$
$113$	112.980	−	36.7093i	0.999821	−	0.324861i	0.762794	+	0.646642i	$0.223827\pi$
$114$	72.2698	−	94.2819i	0.633946	−	0.827034i
$115$	−71.1935	−	51.7251i	−0.619074	−	0.449783i
$116$	−37.3232	+	51.3710i	−0.321752	+	0.442853i
$117$	169.342	−	110.214i	1.44737	−	0.942002i
$118$	−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
$123$	121.748	−	36.1300i	0.989823	−	0.293740i
$124$	−27.8115	−	85.5951i	−0.224287	−	0.690283i
$125$	112.980	+	36.7093i	0.903838	+	0.293675i
$126$	−172.073	+	46.2921i	−1.36566	+	0.367398i
$127$	54.4872	+	39.5872i	0.429033	+	0.311711i	0.781262	−	0.624203i	$-0.214576\pi$
$127$	54.4872	+	39.5872i	0.429033	+	0.311711i	−0.352229	+	0.935914i	$0.614576\pi$
$128$	−78.0040	−	25.3450i	−0.609406	−	0.198008i
$129$	−44.8851	−	1.15280i	−0.347946	−	0.00893641i
$130$	−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
$135$	−49.5092	+	58.1450i	−0.366735	+	0.430704i
$136$	−17.3050	+	53.2592i	−0.127242	+	0.391612i
$137$	93.1004	−	128.142i	0.679565	−	0.935341i	−0.320363	−	0.947295i	$-0.603805\pi$
$137$	93.1004	−	128.142i	0.679565	−	0.935341i	0.999929	+	0.0119535i	$0.00380500\pi$
$138$	203.447	−	139.976i	1.47425	−	1.01432i
$139$	27.7497	−	85.4047i	0.199638	−	0.614422i	−0.800253	−	0.599662i	$-0.795302\pi$
$139$	27.7497	−	85.4047i	0.199638	−	0.614422i	0.999891	−	0.0147598i	$-0.00469838\pi$
$140$	60.3902	−	19.6220i	0.431359	−	0.140157i
$141$	105.750	−	31.3825i	0.750003	−	0.222571i
$142$	−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
$147$	16.6668	+	12.7756i	0.113380	+	0.0869090i
$148$	−24.2705	−	17.6336i	−0.163990	−	0.119146i
$149$	12.4411	−	17.1237i	0.0834971	−	0.114924i	−0.765225	−	0.643763i	$-0.777372\pi$
$149$	12.4411	−	17.1237i	0.0834971	−	0.114924i	0.848722	+	0.528839i	$0.177372\pi$
$150$	−82.0884	+	107.091i	−0.547256	+	0.713940i
$151$	20.8122	+	64.0535i	0.137829	+	0.424195i	0.996019	−	0.0891369i	$-0.0284109\pi$
$151$	20.8122	+	64.0535i	0.137829	+	0.424195i	−0.858190	+	0.513332i	$0.828411\pi$
$152$	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
$156$	−57.4825	−	193.700i	−0.368477	−	1.24167i
$157$	26.5755	+	81.7909i	0.169270	+	0.520961i	0.999326	−	0.0367205i	$-0.0116911\pi$
$157$	26.5755	+	81.7909i	0.169270	+	0.520961i	−0.830055	+	0.557681i	$0.811691\pi$
$158$	−56.4899	−	18.3547i	−0.357531	−	0.116169i
$159$	−72.1444	−	104.858i	−0.453739	−	0.659484i
$160$	−90.8119	−	65.9787i	−0.567575	−	0.412367i
$161$	−221.431	−	71.9472i	−1.37535	−	0.446877i
$162$	−107.526	−	185.379i	−0.663738	−	1.14431i
$163$	11.3262	−	8.22899i	0.0694861	−	0.0504846i	−0.552500	−	0.833513i	$-0.686326\pi$
$163$	11.3262	−	8.22899i	0.0694861	−	0.0504846i	0.621986	+	0.783028i	$0.286326\pi$
$164$		−	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	$-0.118423\pi$
$167$	49.7643	+	68.4946i	0.297990	+	0.410148i	−0.633599	+	0.773662i	$0.718423\pi$
$168$	1.52501	−	59.3774i	0.00907742	−	0.353437i
$169$	103.521	−	318.604i	0.612548	−	1.88523i
$170$	−93.1004	+	128.142i	−0.547650	+	0.753775i
$171$	−34.9935	−	130.075i	−0.204641	−	0.760671i
$172$	−13.8748	+	42.7023i	−0.0806676	+	0.248269i
$173$	181.171	−	58.8659i	1.04723	−	0.340265i	0.265649	−	0.964070i	$-0.414414\pi$
$173$	181.171	−	58.8659i	1.04723	−	0.340265i	0.781580	+	0.623804i	$0.214414\pi$
$174$	47.7955	+	161.058i	0.274687	+	0.925619i
$175$	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	$-0.945754\pi$
$179$	−301.279	+	97.8916i	−1.68312	+	0.546880i	−0.697611	+	0.716477i	$0.745754\pi$
$180$	41.6571	+	64.0054i	0.231428	+	0.355585i
$181$	211.962	+	154.000i	1.17106	+	0.850827i	0.991136	−	0.132853i	$-0.0424137\pi$
$181$	211.962	+	154.000i	1.17106	+	0.850827i	0.179927	+	0.983680i	$0.442414\pi$
$182$	−261.262	+	359.597i	−1.43551	+	1.97581i
$183$	231.629	+	177.550i	1.26573	+	0.970220i
$184$	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
$189$	−77.0396	+	186.786i	−0.407617	+	0.988284i
$190$	34.6099	+	106.518i	0.182157	+	0.560623i
$191$	−56.4899	−	18.3547i	−0.295759	−	0.0960978i	0.157379	−	0.987538i	$-0.449695\pi$
$191$	−56.4899	−	18.3547i	−0.295759	−	0.0960978i	−0.453138	+	0.891440i	$0.649695\pi$
$192$	71.6742	−	49.3134i	0.373303	−	0.256840i
$193$	121.083	+	87.9716i	0.627371	+	0.455812i	0.855488	−	0.517822i	$-0.173257\pi$
$193$	121.083	+	87.9716i	0.627371	+	0.455812i	−0.228118	+	0.973634i	$0.573257\pi$
$194$	186.203	+	60.5011i	0.959810	+	0.311861i
$195$	−4.89090	+	190.431i	−0.0250815	+	0.976571i
$196$	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
$201$	125.958	+	3.23503i	0.626659	+	0.0160947i
$202$	−121.135	+	372.814i	−0.599677	+	1.84561i
$203$	93.1004	−	128.142i	0.458623	−	0.631240i
$204$	−107.976	−	156.937i	−0.529294	−	0.769299i
$205$	−36.9995	+	113.873i	−0.180486	+	0.555477i
$206$	−85.5528	+	27.7978i	−0.415305	+	0.134941i
$207$	14.3739	−	279.645i	0.0694391	−	1.35094i
$208$	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	−0.518582	+	0.855028i	$0.673540\pi$
$211$	−314.815	+	228.726i	−1.49201	+	1.08401i	−0.973430	+	0.228983i	$0.926460\pi$
$212$	−121.050	+	39.3314i	−0.570989	+	0.185526i
$213$	−118.729	+	154.892i	−0.557413	+	0.727191i
$214$	90.6099	+	65.8319i	0.423411	+	0.307626i
$215$	24.8821	−	34.2473i	0.115731	−	0.159290i
$216$	69.4363	−	16.7809i	0.321464	−	0.0776893i
$217$	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
$222$	−76.0926	+	22.5812i	−0.342760	+	0.101717i
$223$	−14.2148	−	43.7486i	−0.0637434	−	0.196182i	0.914113	−	0.405460i	$-0.132889\pi$
$223$	−14.2148	−	43.7486i	−0.0637434	−	0.196182i	−0.977856	+	0.209278i	$0.932889\pi$
$224$	−282.449	−	91.7734i	−1.26093	−	0.409703i
$225$	39.7478	+	147.747i	0.176657	+	0.656652i
$226$	−254.273	−	184.740i	−1.12510	−	0.817436i
$227$	−201.301	−	65.4066i	−0.886787	−	0.288135i	−0.170015	−	0.985442i	$-0.554381\pi$
$227$	−201.301	−	65.4066i	−0.886787	−	0.288135i	−0.716773	+	0.697307i	$0.754381\pi$
$228$	−134.655	−	3.45839i	−0.590593	−	0.0151684i
$229$	−95.4640	+	69.3587i	−0.416873	+	0.302876i	−0.776379	−	0.630267i	$-0.782945\pi$
$229$	−95.4640	+	69.3587i	−0.416873	+	0.302876i	0.359505	+	0.933143i	$0.382945\pi$
$230$			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	$-0.141846\pi$
$233$	49.7643	+	68.4946i	0.213581	+	0.293968i	−0.688762	+	0.724987i	$0.741846\pi$
$234$	−499.259	−	191.072i	−2.13358	−	0.816548i
$235$	−32.1378	+	98.9099i	−0.136756	+	0.420893i
$236$	−59.8503	+	82.3768i	−0.253603	+	0.349054i
$237$	−55.4856	+	38.1752i	−0.234116	+	0.161077i
$238$	−129.498	+	398.555i	−0.544111	+	1.67460i
$239$	−40.2601	+	13.0813i	−0.168452	+	0.0547335i	−0.392029	−	0.919953i	$-0.628227\pi$
$239$	−40.2601	+	13.0813i	−0.168452	+	0.0547335i	0.223577	+	0.974686i	$0.428227\pi$
$240$	−154.558	+	45.8667i	−0.643993	+	0.191111i
$241$	−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
$246$	−266.669	−	204.410i	−1.08402	−	0.830935i
$247$	−271.830	−	197.496i	−1.10053	−	0.799578i
$248$	46.6540	−	64.2137i	0.188121	−	0.258926i
$249$	−38.6298	+	50.3958i	−0.155140	+	0.202393i
$250$	−97.1238	−	298.916i	−0.388495	−	1.19567i
$251$	−29.9251	−	41.1884i	−0.119224	−	0.164097i	0.745234	−	0.666803i	$-0.232338\pi$
$251$	−29.9251	−	41.1884i	−0.119224	−	0.164097i	−0.864457	+	0.502706i	$0.832338\pi$
$252$	157.150	+	126.996i	0.623610	+	0.503953i
$253$		0			0
$254$		−	178.191i		−	0.701539i
$255$	51.0955	+	172.178i	0.200375	+	0.675208i
$256$	102.903	+	316.702i	0.401964	+	1.23712i
$257$	91.4598	+	29.7171i	0.355875	+	0.115631i	0.481498	−	0.876447i	$-0.340093\pi$
$257$	91.4598	+	29.7171i	0.355875	+	0.115631i	−0.125623	+	0.992078i	$0.540093\pi$
$258$	67.3348	+	97.8674i	0.260988	+	0.379331i
$259$	60.5413	+	43.9858i	0.233750	+	0.169829i
$260$	181.171	+	58.8659i	0.696810	+	0.226407i
$261$	177.910	+	68.0883i	0.681648	+	0.260875i
$262$	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
$267$	−4.79288	+	186.615i	−0.0179509	+	0.698931i
$268$	38.9361	−	119.833i	0.145284	−	0.447139i
$269$	−217.789	+	299.760i	−0.809623	+	1.11435i	0.181759	+	0.983343i	$0.441821\pi$
$269$	−217.789	+	299.760i	−0.809623	+	1.11435i	−0.991381	+	0.131007i	$0.958179\pi$
$270$	201.450	+	15.5491i	0.746112	+	0.0575892i
$271$	104.061	−	320.267i	0.383990	−	1.18180i	−0.553221	−	0.833035i	$-0.686601\pi$
$271$	104.061	−	320.267i	0.383990	−	1.18180i	0.937211	−	0.348764i	$-0.113399\pi$
$272$	382.471	−	124.272i	1.40614	−	0.456884i
$273$	143.386	+	483.173i	0.525225	+	1.76987i
$274$	−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	−0.554518	−	0.832171i	$-0.687097\pi$
$277$	18.1624	−	13.1957i	0.0655682	−	0.0476381i	0.620087	+	0.784533i	$0.287097\pi$
$278$	−225.960	+	73.4187i	−0.812804	+	0.264096i
$279$	−226.293	+	147.280i	−0.811087	+	0.527885i
$280$	45.3050	+	32.9160i	0.161803	+	0.117557i
$281$	12.4411	−	17.1237i	0.0442743	−	0.0609383i	−0.786306	−	0.617837i	$-0.788009\pi$
$281$	12.4411	−	17.1237i	0.0442743	−	0.0609383i	0.830580	+	0.556899i	$0.188009\pi$
$282$	−231.629	−	177.550i	−0.821379	−	0.629611i
$283$	−55.4993	−	170.809i	−0.196111	−	0.603567i	−0.999962	−	0.00873607i	$-0.997219\pi$
$283$	−55.4993	−	170.809i	−0.196111	−	0.603567i	0.803851	−	0.594830i	$-0.202781\pi$
$284$	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
$288$	18.3348	−	356.706i	0.0636626	−	1.23856i
$289$	−49.1337	−	151.218i	−0.170013	−	0.523246i
$290$	−150.640	−	48.9458i	−0.519447	−	0.168779i
$291$	182.893	−	125.834i	0.628498	−	0.432419i
$292$	−181.624	−	131.957i	−0.622000	−	0.451909i
$293$	20.1301	+	6.54066i	0.0687033	+	0.0223231i	0.343167	−	0.939274i	$-0.388500\pi$
$293$	20.1301	+	6.54066i	0.0687033	+	0.0223231i	−0.274464	+	0.961597i	$0.588500\pi$
$294$	1.42651	−	55.5425i	0.00485209	−	0.188920i
$295$	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
$300$	152.950	+	3.92825i	0.509832	+	0.0130942i
$301$	34.6099	−	106.518i	0.114983	−	0.353881i
$302$	104.738	−	144.159i	0.346815	−	0.477349i
$303$	251.944	+	366.186i	0.831497	+	1.20854i
$304$	87.8739	−	270.448i	0.289059	−	0.889632i
$305$	−261.691	+	85.0285i	−0.858003	+	0.278782i
$306$	−503.336	−	25.8717i	−1.64489	−	0.0845480i
$307$	−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	$-0.586969\pi$
$311$	24.2099	−	7.86629i	0.0778455	−	0.0252935i	0.347681	+	0.937613i	$0.386969\pi$
$312$	108.405	−	141.423i	0.347451	−	0.453278i
$313$	−321.989	−	233.939i	−1.02872	−	0.747407i	−0.0606664	−	0.998158i	$-0.519323\pi$
$313$	−321.989	−	233.939i	−1.02872	−	0.747407i	−0.968052	+	0.250751i	$0.919323\pi$
$314$	133.741	−	184.079i	0.425928	−	0.586240i
$315$	−103.911	−	159.657i	−0.329876	−	0.506849i
$316$	20.8122	+	64.0535i	0.0658615	+	0.202701i
$317$	244.389	+	336.372i	0.770942	+	1.06111i	0.996224	+	0.0868172i	$0.0276696\pi$
$317$	244.389	+	336.372i	0.770942	+	1.06111i	−0.225282	+	0.974294i	$0.572330\pi$
$318$	−112.250	+	317.490i	−0.352987	+	0.998397i
$319$		0			0
$320$			82.0244i			0.256326i
$321$	121.748	−	36.1300i	0.379278	−	0.112554i
$322$	190.354	+	585.851i	0.591163	+	1.81941i
$323$	−301.279	−	97.8916i	−0.932753	−	0.303070i
$324$	−98.3908	+	222.190i	−0.303675	+	0.685771i
$325$	308.761	+	224.328i	0.950033	+	0.690239i
$326$	−35.2276	−	11.4461i	−0.108060	−	0.0351109i
$327$	201.983	+	5.18759i	0.617685	+	0.0158642i
$328$	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
$333$	−32.1687	+	84.0546i	−0.0966027	+	0.252416i
$334$	69.2198	−	213.037i	0.207245	−	0.637834i
$335$	−69.8253	+	96.1063i	−0.208434	+	0.286885i
$336$	−351.409	+	241.777i	−1.04586	+	0.719573i
$337$	78.6240	−	241.980i	0.233306	−	0.718041i	−0.764036	−	0.645174i	$-0.776785\pi$
$337$	78.6240	−	241.980i	0.233306	−	0.718041i	0.997342	−	0.0728675i	$-0.0232150\pi$
$338$	−842.947	+	273.890i	−2.49393	+	0.810325i
$339$	−341.655	+	101.390i	−1.00783	+	0.299084i
$340$	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
$345$	209.526	+	160.608i	0.607322	+	0.465530i
$346$	−407.745	−	296.244i	−1.17845	−	0.856196i
$347$	286.145	−	393.844i	0.824624	−	1.13500i	−0.164276	−	0.986414i	$-0.552529\pi$
$347$	286.145	−	393.844i	0.824624	−	1.13500i	0.988900	−	0.148583i	$-0.0474713\pi$
$348$	115.890	−	151.187i	0.333016	−	0.434446i
$349$	20.8122	+	64.0535i	0.0596339	+	0.183534i	0.976436	−	0.215808i	$-0.0692385\pi$
$349$	20.8122	+	64.0535i	0.0596339	+	0.183534i	−0.916802	+	0.399342i	$0.869239\pi$
$350$	−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	$0.943595\pi$
$354$	76.6433	+	258.267i	0.216506	+	0.729568i
$355$	−56.8591	−	174.994i	−0.160167	−	0.492942i
$356$	177.540	+	57.6861i	0.498707	+	0.162040i
$357$	269.339	+	391.470i	0.754451	+	1.09655i
$358$	678.062	+	492.641i	1.89403	+	1.37609i
$359$	241.561	+	78.4879i	0.672871	+	0.218629i	0.625472	−	0.780247i	$-0.284907\pi$
$359$	241.561	+	78.4879i	0.672871	+	0.218629i	0.0473997	+	0.998876i	$0.484907\pi$
$360$	−24.0728	+	62.9007i	−0.0668690	+	0.174724i
$361$	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
$366$	19.8251	−	771.906i	0.0541669	−	2.10903i
$367$	−43.8804	+	135.050i	−0.119565	+	0.367984i	−0.992872	−	0.119187i	$-0.961971\pi$
$367$	−43.8804	+	135.050i	−0.119565	+	0.367984i	0.873307	+	0.487171i	$0.161971\pi$
$368$	347.464	−	478.243i	0.944196	−	1.29957i
$369$	−367.907	+	98.9766i	−0.997038	+	0.268229i
$370$	23.1247	−	71.1706i	0.0624992	−	0.192353i
$371$	301.951	−	98.1099i	0.813884	−	0.264447i
$372$	76.8142	+	258.843i	0.206490	+	0.695814i
$373$	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
$378$	519.614	−	125.577i	1.37464	−	0.332213i
$379$	283.156	+	205.725i	0.747113	+	0.542810i	0.894931	−	0.446205i	$-0.147225\pi$
$379$	283.156	+	205.725i	0.747113	+	0.542810i	−0.147817	+	0.989015i	$0.547225\pi$
$380$	74.6464	−	102.742i	0.196438	−	0.270374i
$381$	−160.358	−	122.919i	−0.420888	−	0.322623i
$382$	48.5619	+	149.458i	0.127125	+	0.391252i
$383$	−304.239	−	418.749i	−0.794357	−	1.09334i	−0.993552	−	0.113379i	$-0.963832\pi$
$383$	−304.239	−	418.749i	−0.794357	−	1.09334i	0.199194	−	0.979960i	$-0.436168\pi$
$384$	231.983	+	82.0183i	0.604122	+	0.213589i
$385$		0			0
$386$		−	395.980i		−	1.02585i
$387$	134.522	+	6.91450i	0.347602	+	0.0178669i
$388$	−68.6018	−	211.135i	−0.176809	−	0.544161i
$389$	416.949	+	135.475i	1.07185	+	0.348265i	0.791207	−	0.611548i	$-0.209453\pi$
$389$	416.949	+	135.475i	1.07185	+	0.348265i	0.280641	+	0.959813i	$0.409453\pi$
$390$	415.216	−	285.677i	1.06466	−	0.732506i
$391$	−532.763	−	387.075i	−1.36257	−	0.989962i
$392$	17.6138	+	5.72307i	0.0449332	+	0.0145997i
$393$	17.9333	−	698.248i	0.0456318	−	1.77671i
$394$	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
$399$	335.889	+	8.62674i	0.841828	+	0.0216209i
$400$	−99.8125	+	307.191i	−0.249531	+	0.767978i
$401$	−309.226	+	425.614i	−0.771138	+	1.06138i	0.225067	+	0.974343i	$0.427740\pi$
$401$	−309.226	+	425.614i	−0.771138	+	1.06138i	−0.996205	+	0.0870374i	$0.972260\pi$
$402$	−188.958	−	274.640i	−0.470044	−	0.683183i
$403$	−208.122	+	640.535i	−0.516433	+	1.58942i
$404$	422.732	−	137.354i	1.04637	−	0.339985i
$405$	152.957	−	170.564i	0.377672	−	0.421146i
$406$	−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	−0.787249	−	0.616635i	$-0.788496\pi$
$409$	−181.624	+	131.957i	−0.444068	+	0.322634i	0.343181	+	0.939269i	$0.388496\pi$
$410$	301.279	−	97.8916i	0.734828	−	0.238760i
$411$	−289.079	+	377.128i	−0.703356	+	0.917585i
$412$	82.5197	+	59.9541i	0.200291	+	0.145520i
$413$	149.293	−	205.484i	0.361484	−	0.497540i
$414$	−620.922	+	404.119i	−1.49981	+	0.976132i
$415$	−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	$0.695745\pi$
$420$	−182.622	+	54.1950i	−0.434815	+	0.129036i
$421$	−82.1985	−	252.981i	−0.195246	−	0.600905i	−0.999974	−	0.00726102i	$-0.997689\pi$
$421$	−82.1985	−	252.981i	−0.195246	−	0.600905i	0.804728	−	0.593644i	$-0.202311\pi$
$422$	979.158	+	318.148i	2.32028	+	0.753904i
$423$	−319.564	+	85.9710i	−0.755470	+	0.203241i
$424$	−90.8119	−	65.9787i	−0.214179	−	0.155610i
$425$	342.211	+	111.191i	0.805203	+	0.261626i
$426$	516.179	+	13.2572i	1.21169	+	0.0311201i
$427$	−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	0.997945	+	0.0640786i	$0.0204108\pi$
$431$	323.468	+	445.215i	0.750505	+	1.03298i	−0.247440	+	0.968903i	$0.579589\pi$
$432$	−390.590	−	332.579i	−0.904143	−	0.769858i
$433$	228.055	−	701.880i	0.526685	−	1.62097i	−0.234275	−	0.972170i	$-0.575272\pi$
$433$	228.055	−	701.880i	0.526685	−	1.62097i	0.760960	−	0.648799i	$-0.224728\pi$
$434$	349.127	−	480.532i	0.804439	−	1.10722i
$435$	−147.962	+	101.801i	−0.340142	+	0.234024i
$436$	62.4367	−	192.160i	0.143204	−	0.440735i
$437$	−442.862	+	143.894i	−1.01341	+	0.329278i
$438$	−569.425	+	168.983i	−1.30006	+	0.385805i
$439$	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	$-0.557192\pi$
$443$	112.980	−	36.7093i	0.255033	−	0.0828653i	0.433743	+	0.901036i	$0.357192\pi$
$444$	71.4293	+	54.7527i	0.160877	+	0.123317i
$445$	−142.387	−	103.450i	−0.319971	−	0.232472i
$446$	−71.5361	+	98.4611i	−0.160395	+	0.220765i
$447$	−38.6298	+	50.3958i	−0.0864202	+	0.112742i
$448$	67.0617	+	206.395i	0.149691	+	0.460702i
$449$	299.251	+	411.884i	0.666484	+	0.917337i	0.999674	−	0.0255229i	$-0.00812508\pi$
$449$	299.251	+	411.884i	0.666484	+	0.917337i	−0.333190	+	0.942860i	$0.608125\pi$
$450$	254.433	−	314.844i	0.565406	−	0.699654i
$451$		0			0
$452$			356.382i			0.788455i
$453$	−57.4825	−	193.700i	−0.126893	−	0.427594i
$454$	173.050	+	532.592i	0.381166	+	1.17311i
$455$	−451.919	−	146.837i	−0.993229	−	0.322720i
$456$	−67.3348	−	97.8674i	−0.147664	−	0.214621i
$457$	−544.872	−	395.872i	−1.19228	−	0.866242i	−0.198776	−	0.980045i	$-0.563697\pi$
$457$	−544.872	−	395.872i	−1.19228	−	0.866242i	−0.993503	+	0.113803i	$0.963697\pi$
$458$	296.919	+	96.4747i	0.648294	+	0.210643i
$459$	−370.493	+	435.117i	−0.807174	+	0.947968i
$460$	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
$465$	6.53574	−	254.475i	0.0140554	−	0.547257i
$466$	69.2198	−	213.037i	0.148540	−	0.457160i
$467$	312.551	−	430.190i	0.669275	−	0.921178i	−0.330469	−	0.943817i	$-0.607207\pi$
$467$	312.551	−	430.190i	0.669275	−	0.921178i	0.999744	+	0.0226389i	$0.00720679\pi$
$468$	157.471	+	585.337i	0.336476	+	1.25072i
$469$	−97.1238	+	298.916i	−0.207087	+	0.637348i
$470$	261.691	−	85.0285i	0.556789	−	0.180912i
$471$	−73.4002	−	247.339i	−0.155839	−	0.525135i
$472$	−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
$477$	208.285	+	320.027i	0.436657	+	0.670916i
$478$	90.6099	+	65.8319i	0.189560	+	0.137724i
$479$	−398.114	+	547.957i	−0.831136	+	1.14396i	0.156574	+	0.987666i	$0.449955\pi$
$479$	−398.114	+	547.957i	−0.831136	+	1.14396i	−0.987710	+	0.156295i	$0.950045\pi$
$480$	267.264	+	204.866i	0.556800	+	0.426804i
$481$	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
$486$	308.192	+	564.235i	0.634139	+	1.16098i
$487$	108.156	+	332.870i	0.222086	+	0.683511i	0.998574	+	0.0533790i	$0.0169992\pi$
$487$	108.156	+	332.870i	0.222086	+	0.683511i	−0.776488	+	0.630132i	$0.783001\pi$
$488$	244.789	+	79.5369i	0.501618	+	0.162985i
$489$	−34.6013	+	23.8064i	−0.0707594	+	0.0486839i
$490$	42.3789	+	30.7901i	0.0864876	+	0.0628369i
$491$	241.561	+	78.4879i	0.491977	+	0.159853i	0.544490	−	0.838767i	$-0.316723\pi$
$491$	241.561	+	78.4879i	0.491977	+	0.159853i	−0.0525130	+	0.998620i	$0.516723\pi$
$492$	−9.78180	+	380.863i	−0.0198817	+	0.774111i
$493$	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
$498$	167.945	+	4.31337i	0.337238	+	0.00866139i
$499$	−30.2837	+	93.2035i	−0.0606887	+	0.186781i	−0.976804	−	0.214133i	$-0.931307\pi$
$499$	−30.2837	+	93.2035i	−0.0606887	+	0.186781i	0.916116	+	0.400914i	$0.131307\pi$
$500$	−209.476	+	288.319i	−0.418952	+	0.576638i
$501$	−143.968	−	209.249i	−0.287361	−	0.417663i
$502$	−41.6245	+	128.107i	−0.0829173	+	0.255193i
$503$	−483.122	+	156.976i	−0.960481	+	0.312079i	−0.746967	−	0.664861i	$-0.768491\pi$
$503$	−483.122	+	156.976i	−0.960481	+	0.312079i	−0.213514	+	0.976940i	$0.568491\pi$
$504$	−9.14702	+	177.956i	−0.0181489	+	0.353087i
$505$	−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	$-0.650624\pi$
$509$	−153.330	+	49.8198i	−0.301237	+	0.0978779i	0.154499	+	0.987993i	$0.450624\pi$
$510$	289.079	−	377.128i	0.566822	−	0.739466i
$511$	453.050	+	329.160i	0.886594	+	0.644148i
$512$	325.023	−	447.356i	0.634810	−	0.873742i
$513$	94.9270	+	392.791i	0.185043	+	0.765675i
$514$	−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
$519$	−547.867	+	162.585i	−1.05562	+	0.313266i
$520$	51.9149	+	159.777i	0.0998363	+	0.307264i
$521$	−145.260	−	47.1977i	−0.278809	−	0.0905907i	0.166275	−	0.986079i	$-0.446826\pi$
$521$	−145.260	−	47.1977i	−0.278809	−	0.0905907i	−0.445084	+	0.895489i	$0.646826\pi$
$522$	−130.934	−	486.695i	−0.250831	−	0.932367i
$523$	−12.1083	−	8.79716i	−0.0231515	−	0.0168206i	0.576149	−	0.817344i	$-0.304555\pi$
$523$	−12.1083	−	8.79716i	−0.0231515	−	0.0168206i	−0.599301	+	0.800524i	$0.704555\pi$
$524$	−664.292	−	215.842i	−1.26773	−	0.411912i
$525$	−381.523	−	9.79877i	−0.726711	−	0.0186643i
$526$	−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
$531$	285.291	+	109.184i	0.537271	+	0.205620i
$532$	103.830	−	319.555i	0.195169	−	0.600667i
$533$	−558.603	+	768.851i	−1.04803	+	1.44250i
$534$	406.894	−	279.952i	0.761974	−	0.524254i
$535$	−36.9995	+	113.873i	−0.0691580	+	0.212847i
$536$	105.683	−	34.3384i	0.197170	−	0.0640643i
$537$	911.080	−	270.372i	1.69661	−	0.503486i
$538$	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	−0.130461	−	0.991453i	$-0.541646\pi$
$541$	417.735	−	303.502i	0.772153	−	0.561002i	0.902614	+	0.430451i	$0.141646\pi$
$542$	−847.348	+	275.320i	−1.56337	+	0.507971i
$543$	−623.816	−	478.173i	−1.14883	−	0.880614i
$544$	−679.574	−	493.740i	−1.24922	−	0.907610i
$545$	−111.970	+	154.113i	−0.205449	+	0.282776i
$546$	811.227	−	1058.31i	1.48576	−	1.93830i
$547$	−208.122	−	640.535i	−0.380480	−	1.17100i	−0.939707	−	0.341982i	$-0.888902\pi$
$547$	−208.122	−	640.535i	−0.380480	−	1.17100i	0.559227	−	0.829015i	$-0.311098\pi$
$548$	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
$552$	−70.2563	−	236.745i	−0.127276	−	0.428885i
$553$	−51.9149	−	159.777i	−0.0938786	−	0.288929i
$554$	−56.4899	−	18.3547i	−0.101967	−	0.0331312i
$555$	−48.0963	−	69.9053i	−0.0866600	−	0.125955i
$556$	217.949	+	158.349i	0.391994	+	0.284800i
$557$	−422.732	−	137.354i	−0.758943	−	0.246596i	−0.0961183	−	0.995370i	$-0.530643\pi$
$557$	−422.732	−	137.354i	−0.758943	−	0.246596i	−0.662825	+	0.748774i	$0.730643\pi$
$558$	667.163	+	255.331i	1.19563	+	0.457583i
$559$	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	$-0.0374583\pi$
$563$	323.468	+	445.215i	0.574543	+	0.790791i	−0.418541	+	0.908198i	$0.637458\pi$
$564$	−8.49647	+	330.817i	−0.0150647	+	0.586555i
$565$	103.830	−	319.555i	0.183769	−	0.565584i
$566$	−279.301	+	384.425i	−0.493465	+	0.679197i
$567$	245.430	−	554.238i	0.432857	−	0.977493i
$568$	−53.1868	+	163.692i	−0.0936388	+	0.288191i
$569$	1066.89	−	346.655i	1.87503	−	0.609235i	0.885559	−	0.464528i	$-0.153776\pi$
$569$	1066.89	−	346.655i	1.87503	−	0.609235i	0.989474	−	0.144708i	$-0.0462241\pi$
$570$	−95.5910	−	322.115i	−0.167703	−	0.565115i
$571$	−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
$576$	−218.750	+	142.371i	−0.379774	+	0.247171i
$577$	−250.795	−	182.213i	−0.434654	−	0.315795i	0.348853	−	0.937177i	$-0.386571\pi$
$577$	−250.795	−	182.213i	−0.434654	−	0.315795i	−0.783507	+	0.621383i	$0.786571\pi$
$578$	−247.266	+	340.333i	−0.427796	+	0.588811i
$579$	−356.352	−	273.154i	−0.615461	−	0.471769i
$580$	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
$585$	29.3357	−	570.729i	0.0501466	−	0.975605i
$586$	−17.3050	−	53.2592i	−0.0295306	−	0.0908859i
$587$	−914.598	−	297.171i	−1.55809	−	0.506254i	−0.601792	−	0.798653i	$-0.705546\pi$
$587$	−914.598	−	297.171i	−1.55809	−	0.506254i	−0.956296	+	0.292399i	$0.905546\pi$
$588$	−51.9020	+	35.7097i	−0.0882687	+	0.0607307i
$589$	363.248	+	263.915i	0.616719	+	0.448073i
$590$	−241.561	−	78.4879i	−0.409425	−	0.133030i
$591$	17.9333	−	698.248i	0.0303440	−	1.18147i
$592$	−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
$597$	−665.780	−	17.0994i	−1.11521	−	0.0286423i
$598$	−571.063	+	1757.55i	−0.954956	+	2.93905i
$599$	513.715	−	707.068i	0.857621	−	1.18041i	−0.124511	−	0.992218i	$-0.539736\pi$
$599$	513.715	−	707.068i	0.857621	−	1.18041i	0.982132	−	0.188196i	$-0.0602639\pi$
$600$	76.4829	+	111.164i	0.127472	+	0.185273i
$601$	180.373	−	555.130i	0.300121	−	0.923678i	−0.681332	−	0.731975i	$-0.738599\pi$
$601$	180.373	−	555.130i	0.300121	−	0.923678i	0.981453	−	0.191703i	$-0.0614011\pi$
$602$	−281.821	+	91.5692i	−0.468141	+	0.152108i
$603$	−377.502	−	19.4038i	−0.626039	−	0.0321787i
$604$	−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	0.141783	−	0.989898i	$-0.454716\pi$
$607$	684.117	−	497.040i	1.12705	−	0.818846i	0.985262	+	0.171051i	$0.0547164\pi$
$608$	−564.899	+	183.547i	−0.929110	+	0.301886i
$609$	−289.079	+	377.128i	−0.474679	+	0.619257i
$610$	588.964	+	427.908i	0.965515	+	0.701488i
$611$	−485.202	+	667.823i	−0.794111	+	1.09300i
$612$	311.733	+	478.972i	0.509367	+	0.782635i
$613$	−182.685	−	562.247i	−0.298018	−	0.917206i	−0.982191	−	0.187886i	$-0.939836\pi$
$613$	−182.685	−	562.247i	−0.298018	−	0.917206i	0.684173	−	0.729320i	$-0.260164\pi$
$614$	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	$-0.114832\pi$
$618$	258.715	−	76.7762i	0.418633	−	0.124233i
$619$	−258.956	−	796.985i	−0.418346	−	1.28754i	−0.909224	−	0.416308i	$-0.863324\pi$
$619$	−258.956	−	796.985i	−0.418346	−	1.28754i	0.490877	−	0.871229i	$-0.336676\pi$
$620$	−242.099	−	78.6629i	−0.390483	−	0.126876i
$621$	−64.6470	+	837.552i	−0.104101	+	1.34871i
$622$	−54.4872	−	39.5872i	−0.0875999	−	0.0636451i
$623$	−442.862	−	143.894i	−0.710853	−	0.230970i
$624$	−1279.22	−	32.8547i	−2.05004	−	0.0526518i
$625$	−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
$630$	−180.145	+	470.706i	−0.285944	+	0.747152i
$631$	78.4903	−	241.568i	0.124390	−	0.382834i	−0.869399	−	0.494110i	$-0.835494\pi$
$631$	78.4903	−	241.568i	0.124390	−	0.382834i	0.993790	+	0.111276i	$0.0354938\pi$
$632$	−34.9127	+	48.0532i	−0.0552416	+	0.0760335i
$633$	961.750	−	661.704i	1.51935	−	1.04535i
$634$	339.933	−	1046.21i	0.536172	−	1.65017i
$635$	181.171	−	58.8659i	0.285308	−	0.0927022i
$636$	366.059	−	108.632i	0.575564	−	0.170804i
$637$	−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	$-0.570462\pi$
$641$	112.980	−	36.7093i	0.176255	−	0.0572689i	0.395815	+	0.918330i	$0.370462\pi$
$642$	−266.669	−	204.410i	−0.415373	−	0.318396i
$643$	354.349	+	257.450i	0.551088	+	0.400389i	0.828186	−	0.560453i	$-0.189373\pi$
$643$	354.349	+	257.450i	0.551088	+	0.400389i	−0.277099	+	0.960841i	$0.589373\pi$
$644$	410.555	−	565.081i	0.637508	−	0.877455i
$645$	−77.2597	+	100.792i	−0.119782	+	0.156266i
$646$	258.997	+	797.110i	0.400924	+	1.23392i
$647$	−194.513	−	267.725i	−0.300639	−	0.413794i	0.631794	−	0.775136i	$-0.282319\pi$
$647$	−194.513	−	267.725i	−0.300639	−	0.413794i	−0.932433	+	0.361342i	$0.882319\pi$
$648$	−209.533	+	44.9778i	−0.323353	+	0.0694101i
$649$		0			0
$650$		−	1009.75i		−	1.55346i
$651$	−191.608	−	645.667i	−0.294329	−	0.991808i
$652$	12.9787	+	39.9444i	0.0199060	+	0.0612644i
$653$	594.489	+	193.161i	0.910396	+	0.295806i	0.726521	−	0.687144i	$-0.241136\pi$
$653$	594.489	+	193.161i	0.910396	+	0.295806i	0.183875	+	0.982950i	$0.441136\pi$
$654$	−303.007	−	440.403i	−0.463313	−	0.673399i
$655$	532.763	+	387.075i	0.813379	+	0.590955i
$656$	−764.943	−	248.545i	−1.16607	−	0.378880i
$657$	−240.728	+	629.007i	−0.366406	+	0.957393i
$658$	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
$663$	−36.6002	+	1425.06i	−0.0552039	+	2.14941i
$664$	−17.3050	+	53.2592i	−0.0260617	+	0.0802096i
$665$	−186.201	+	256.284i	−0.280001	+	0.385389i
$666$	229.942	−	61.8604i	0.345258	−	0.0928835i
$667$	203.497	−	626.301i	0.305094	−	0.938982i
$668$	−241.561	+	78.4879i	−0.361618	+	0.117497i
$669$	39.2606	+	132.297i	0.0586855	+	0.197754i
$670$	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	−0.974365	−	0.224974i	$-0.927770\pi$
$673$	−714.387	+	519.033i	−1.06150	+	0.771222i	−0.0871319	+	0.996197i	$0.527770\pi$
$674$	−640.219	+	208.020i	−0.949879	+	0.308634i
$675$	−107.824	−	446.156i	−0.159739	−	0.660972i
$676$	813.062	+	590.724i	1.20275	+	0.873852i
$677$	−534.966	+	736.317i	−0.790201	+	1.08762i	0.203882	+	0.978995i	$0.434644\pi$
$677$	−534.966	+	736.317i	−0.790201	+	1.08762i	−0.994083	+	0.108623i	$0.965356\pi$
$678$	748.339	+	573.624i	1.10375	+	0.846053i
$679$	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	$0.896696\pi$
$684$	403.566	+	20.7435i	0.590009	+	0.0303268i
$685$	−138.440	−	426.073i	−0.202102	−	0.622005i
$686$	−790.858	−	256.965i	−1.15285	−	0.374585i
$687$	291.640	−	200.654i	0.424512	−	0.292073i
$688$	230.057	+	167.146i	0.334385	+	0.242945i
$689$	905.853	+	294.330i	1.31474	+	0.427184i
$690$	17.9333	−	698.248i	0.0259903	−	1.01195i
$691$	−344.641	+	250.397i	−0.498757	+	0.362368i	−0.808542	−	0.588438i	$-0.799743\pi$
$691$	−344.641	+	250.397i	−0.498757	+	0.362368i	0.309785	+	0.950807i	$0.399743\pi$
$692$			571.482i			0.825841i
$693$		0			0
$694$	−1288.00			−1.85591
$695$	−149.293	−	205.484i	−0.214810	−	0.295660i
$696$	167.945	+	4.31337i	0.241300	+	0.00619737i
$697$	−276.879	+	852.147i	−0.397244	+	1.22259i
$698$	104.738	−	144.159i	0.150054	−	0.206532i
$699$	−143.968	−	209.249i	−0.205963	−	0.299355i
$700$	−117.936	+	362.970i	−0.168480	+	0.518528i
$701$	−261.691	+	85.0285i	−0.373311	+	0.121296i	−0.489663	−	0.871912i	$-0.662880\pi$
$701$	−261.691	+	85.0285i	−0.373311	+	0.121296i	0.116352	+	0.993208i	$0.462880\pi$
$702$	1482.57	+	611.483i	2.11192	+	0.871058i
$703$	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
$708$	185.837	−	242.439i	0.262481	−	0.342428i
$709$	33.9787	+	24.6870i	0.0479248	+	0.0348194i	0.611490	−	0.791252i	$-0.290571\pi$
$709$	33.9787	+	24.6870i	0.0479248	+	0.0348194i	−0.563565	+	0.826072i	$0.690571\pi$
$710$	−286.145	+	393.844i	−0.403021	+	0.554710i
$711$	169.342	−	110.214i	0.238175	−	0.155013i
$712$	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
$717$	121.748	−	36.1300i	0.169802	−	0.0503905i
$718$	−207.659	−	639.110i	−0.289219	−	0.890125i
$719$	−411.569	−	133.727i	−0.572419	−	0.185990i	0.00848270	−	0.999964i	$-0.497300\pi$
$719$	−411.569	−	133.727i	−0.572419	−	0.185990i	−0.580901	+	0.813974i	$0.697300\pi$
$720$	467.055	−	125.650i	0.648687	−	0.174514i
$721$	−205.840	−	149.552i	−0.285493	−	0.207423i
$722$	−344.727	−	112.009i	−0.477462	−	0.155137i
$723$	448.851	+	11.5280i	0.620817	+	0.0159446i
$724$	−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
$729$	720.365	+	111.870i	0.988155	+	0.153457i
$730$	173.050	−	532.592i	0.237054	−	0.729578i
$731$	186.201	−	256.284i	0.254721	−	0.350593i
$732$	−721.313	+	496.278i	−0.985400	+	0.677976i
$733$	−150.311	+	462.609i	−0.205062	+	0.631117i	0.794649	+	0.607070i	$0.207655\pi$
$733$	−150.311	+	462.609i	−0.205062	+	0.631117i	−0.999711	+	0.0240470i	$0.992345\pi$
$734$	357.309	−	116.097i	0.486797	−	0.158170i
$735$	56.9425	−	16.8983i	0.0774728	−	0.0229908i
$736$	−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	−0.988069	−	0.154011i	$-0.950781\pi$
$739$	−847.578	+	615.801i	−1.14693	+	0.833290i	−0.158857	+	0.987302i	$0.550781\pi$
$740$	−80.6998	+	26.2210i	−0.109054	+	0.0354337i
$741$	800.008	+	613.230i	1.07963	+	0.827571i
$742$	−679.574	−	493.740i	−0.915868	−	0.665417i
$743$	149.293	−	205.484i	0.200932	−	0.276560i	−0.696646	−	0.717416i	$-0.745325\pi$
$743$	149.293	−	205.484i	0.200932	−	0.276560i	0.897578	+	0.440856i	$0.145325\pi$
$744$	−144.862	+	188.984i	−0.194707	+	0.254011i
$745$	−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
$750$	268.251	+	903.934i	0.357669	+	1.20525i
$751$	108.156	+	332.870i	0.144016	+	0.443235i	0.996883	−	0.0788925i	$-0.0251384\pi$
$751$	108.156	+	332.870i	0.144016	+	0.443235i	−0.852867	+	0.522128i	$0.825138\pi$
$752$	−664.429	−	215.886i	−0.883549	−	0.287082i
$753$	86.5733	+	125.829i	0.114971	+	0.167104i
$754$	−1017.09	−	738.962i	−1.34893	−	0.980055i
$755$	181.171	+	58.8659i	0.239961	+	0.0779681i
$756$	−461.512	−	392.967i	−0.610465	−	0.519798i
$757$	−237.851	+	172.809i	−0.314202	+	0.228281i	−0.733697	−	0.679476i	$-0.762207\pi$
$757$	−237.851	+	172.809i	−0.314202	+	0.228281i	0.419495	+	0.907757i	$0.362207\pi$
$758$		−	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	$-0.0279597\pi$
$761$	460.320	+	633.576i	0.604888	+	0.832557i	−0.391257	+	0.920281i	$0.627960\pi$
$762$	−13.7251	+	534.397i	−0.0180119	+	0.701308i
$763$	−155.745	+	479.332i	−0.204121	+	0.628221i
$764$	104.738	−	144.159i	0.137092	−	0.188690i
$765$	−139.974	−	520.299i	−0.182973	−	0.680130i
$766$	−423.182	+	1302.42i	−0.552457	+	1.70029i
$767$	724.683	−	235.464i	0.944827	−	0.306993i
$768$	−284.212	−	957.718i	−0.370068	−	1.24703i
$769$	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	$-0.685464\pi$
$773$	−390.049	+	126.735i	−0.504591	+	0.163952i	0.0456497	+	0.998958i	$0.485464\pi$
$774$	−194.400	−	298.692i	−0.251162	−	0.385907i
$775$	−412.599	−	299.770i	−0.532385	−	0.386801i
$776$	115.080	−	158.394i	0.148299	−	0.204116i
$777$	−178.176	−	136.577i	−0.229313	−	0.175775i
$778$	−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
$783$	−528.310	−	217.901i	−0.674725	−	0.278290i
$784$	−41.0993	−	126.491i	−0.0524225	−	0.161340i
$785$	231.339	+	75.1668i	0.294700	+	0.0957538i
$786$	−1522.46	+	1047.48i	−1.93697	+	1.33268i
$787$	254.273	+	184.740i	0.323092	+	0.234740i	0.737494	−	0.675354i	$-0.236009\pi$
$787$	254.273	+	184.740i	0.323092	+	0.234740i	−0.414402	+	0.910094i	$0.636009\pi$
$788$	−664.292	−	215.842i	−0.843011	−	0.273911i
$789$	−35.8666	+	1396.50i	−0.0454583	+	1.76996i
$790$	−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
$795$	−359.881	−	9.24294i	−0.452681	−	0.0116263i
$796$	−205.805	+	633.404i	−0.258549	+	0.795733i
$797$	−144.638	+	199.077i	−0.181478	+	0.249783i	−0.890058	−	0.455847i	$-0.849336\pi$
$797$	−144.638	+	199.077i	−0.181478	+	0.249783i	0.708580	+	0.705631i	$0.249336\pi$
$798$	−503.887	−	732.372i	−0.631438	−	0.917760i
$799$	−240.497	+	740.174i	−0.300998	+	0.926375i
$800$	641.646	−	208.483i	0.802058	−	0.260604i
$801$	28.7478	−	559.290i	0.0358899	−	0.698240i
$802$	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
$807$	676.239	−	882.209i	0.837967	−	1.09320i
$808$	317.135	+	230.412i	0.392493	+	0.285163i
$809$	149.293	−	205.484i	0.184540	−	0.253997i	−0.706717	−	0.707497i	$-0.749824\pi$
$809$	149.293	−	205.484i	0.184540	−	0.253997i	0.891257	+	0.453499i	$0.149824\pi$
$810$	−602.954	−	62.1485i	−0.744388	−	0.0767265i
$811$	300.621	+	925.217i	0.370680	+	1.14084i	0.946347	+	0.323151i	$0.104742\pi$
$811$	300.621	+	925.217i	0.370680	+	1.14084i	−0.575668	+	0.817684i	$0.695258\pi$
$812$	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
$816$	−1156.61	+	343.235i	−1.41741	+	0.420631i
$817$	−69.2198	−	213.037i	−0.0847244	−	0.260755i
$818$	564.899	+	183.547i	0.690585	+	0.224385i
$819$	−392.801	−	1460.09i	−0.479611	−	1.78277i
$820$	−290.598	−	211.132i	−0.354388	−	0.257478i
$821$	462.992	+	150.435i	0.563936	+	0.183234i	0.577092	−	0.816679i	$-0.304188\pi$
$821$	462.992	+	150.435i	0.563936	+	0.183234i	−0.0131553	+	0.999913i	$0.504188\pi$
$822$	1256.78	+	32.2783i	1.52893	+	0.0392680i
$823$	−842.996	+	612.472i	−1.02430	+	0.744195i	−0.967159	−	0.254172i	$-0.918197\pi$
$823$	−842.996	+	612.472i	−1.02430	+	0.744195i	−0.0571370	+	0.998366i	$0.518197\pi$
$824$			89.9555i			0.109169i
$825$		0			0
$826$	−672.000			−0.813559
$827$	734.023	+	1010.30i	0.887573	+	1.22164i	0.974265	+	0.225405i	$0.0723704\pi$
$827$	734.023	+	1010.30i	0.887573	+	1.22164i	−0.0866920	+	0.996235i	$0.527630\pi$
$828$	784.550	+	300.256i	0.947524	+	0.362629i
$829$	364.022	−	1120.34i	0.439110	−	1.35144i	−0.449706	−	0.893177i	$-0.648471\pi$
$829$	364.022	−	1120.34i	0.439110	−	1.35144i	0.888816	−	0.458264i	$-0.151529\pi$
$830$	−93.1004	+	128.142i	−0.112169	+	0.154388i
$831$	−55.4856	+	38.1752i	−0.0667697	+	0.0459389i
$832$	−201.185	+	619.184i	−0.241809	+	0.744211i
$833$	−140.911	+	45.7846i	−0.169160	+	0.0549635i
$834$	683.310	−	202.779i	0.819317	−	0.243140i
$835$	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	$-0.391772\pi$
$839$	971.088	−	315.526i	1.15743	−	0.376073i	0.823939	+	0.566678i	$0.191772\pi$
$840$	−133.335	−	102.205i	−0.158732	−	0.121673i
$841$	−317.944	−	231.000i	−0.378054	−	0.274673i
$842$	−413.666	+	569.362i	−0.491289	+	0.676202i
$843$	−38.6298	+	50.3958i	−0.0458243	+	0.0597815i
$844$	−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
$849$	153.287	+	516.534i	0.180550	+	0.608403i
$850$	−294.184	−	905.406i	−0.346099	−	1.06518i
$851$	295.899	+	96.1435i	0.347708	+	0.112977i
$852$	−331.864	−	482.346i	−0.389512	−	0.566134i
$853$	−478.276	−	347.488i	−0.560699	−	0.407372i	0.271016	−	0.962575i	$-0.412640\pi$
$853$	−478.276	−	347.488i	−0.560699	−	0.407372i	−0.831715	+	0.555203i	$0.812640\pi$
$854$	1831.84	+	595.200i	2.14501	+	0.696955i
$855$	−355.820	−	136.177i	−0.416164	−	0.159271i
$856$	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
$861$	24.4001	−	950.038i	0.0283393	−	1.10341i
$862$	449.929	−	1384.74i	0.521959	−	1.60642i
$863$	−290.939	+	400.443i	−0.337125	+	0.464013i	−0.943599	−	0.331091i	$-0.892583\pi$
$863$	−290.939	+	400.443i	−0.337125	+	0.464013i	0.606474	+	0.795103i	$0.292583\pi$
$864$	−82.4614	+	1068.35i	−0.0954415	+	1.23652i
$865$	166.498	−	512.428i	0.192483	−	0.592402i
$866$	−1857.00	+	603.376i	−2.14434	+	0.696739i
$867$	135.705	+	457.289i	0.156523	+	0.527438i
$868$	−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
$873$	−558.190	+	363.291i	−0.639393	+	0.416140i
$874$	996.709	+	724.151i	1.14040	+	0.828549i
$875$	522.525	−	719.194i	0.597171	−	0.821936i
$876$	534.528	+	409.731i	0.610192	+	0.467730i
$877$	−30.0621	−	92.5217i	−0.0342784	−	0.105498i	0.932453	−	0.361290i	$-0.117664\pi$
$877$	−30.0621	−	92.5217i	−0.0342784	−	0.105498i	−0.966732	+	0.255792i	$0.917664\pi$
$878$	−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	$-0.321932\pi$
$882$	−8.55626	+	166.463i	−0.00970097	+	0.188733i
$883$	26.5755	+	81.7909i	0.0300968	+	0.0926284i	0.964977	−	0.262336i	$-0.0844929\pi$
$883$	26.5755	+	81.7909i	0.0300968	+	0.0926284i	−0.934880	+	0.354965i	$0.884493\pi$
$884$	1355.76	+	440.512i	1.53366	+	0.498317i
$885$	−237.266	+	163.244i	−0.268098	+	0.184457i
$886$	−254.273	−	184.740i	−0.286990	−	0.208511i
$887$	241.561	+	78.4879i	0.272335	+	0.0884869i	0.442001	−	0.897015i	$-0.354269\pi$
$887$	241.561	+	78.4879i	0.272335	+	0.0884869i	−0.169666	+	0.985502i	$0.554269\pi$
$888$	−2.03788	+	79.3464i	−0.00229491	+	0.0893540i
$889$	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
$894$	167.945	+	4.31337i	0.187858	+	0.00482480i
$895$	−276.879	+	852.147i	−0.309362	+	0.952119i
$896$	−360.764	+	496.549i	−0.402639	+	0.554184i
$897$	1187.73	+	1726.31i	1.32412	+	1.92453i
$898$	416.245	−	1281.07i	0.463524	−	1.42658i
$899$	−603.902	+	196.220i	−0.671749	+	0.218264i
$900$	−458.395	−	23.5617i	−0.509328	−	0.0261797i
$901$	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
$906$	−325.214	+	424.268i	−0.358956	+	0.468287i
$907$	781.510	+	567.801i	0.861643	+	0.626020i	0.928332	−	0.371753i	$-0.121243\pi$
$907$	781.510	+	567.801i	0.861643	+	0.626020i	−0.0666883	+	0.997774i	$0.521243\pi$
$908$	373.232	−	513.710i	0.411049	−	0.565760i
$909$	−727.377	−	1117.60i	−0.800194	−	1.22949i
$910$	388.495	+	1195.67i	0.426918	+	1.31392i
$911$	−852.866	−	1173.87i	−0.936187	−	1.28855i	−0.957397	−	0.288776i	$-0.906752\pi$
$911$	−852.866	−	1173.87i	−0.936187	−	1.28855i	0.0212096	−	0.999775i	$-0.493248\pi$
$912$	−284.366	+	804.308i	−0.311805	+	0.881917i
$913$		0			0
$914$			1781.91i			1.94957i
$915$	791.363	−	234.845i	0.864878	−	0.256661i
$916$	−109.392	−	336.674i	−0.119424	−	0.367548i
$917$	1657.04	+	538.404i	1.80702	+	0.587136i
$918$	1507.52	+	116.359i	1.64217	+	0.126752i
$919$	320.869	+	233.125i	0.349150	+	0.253672i	0.748512	−	0.663121i	$-0.230768\pi$
$919$	320.869	+	233.125i	0.349150	+	0.253672i	−0.399362	+	0.916793i	$0.630768\pi$
$920$	221.431	+	71.9472i	0.240686	+	0.0782035i
$921$	448.851	+	11.5280i	0.487352	+	0.0125168i
$922$	−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
$927$	109.374	−	285.786i	0.117987	−	0.308291i
$928$	259.574	−	798.887i	0.279714	−	0.860870i
$929$	897.754	−	1235.65i	0.966366	−	1.33009i	0.0225050	−	0.999747i	$-0.492836\pi$
$929$	897.754	−	1235.65i	0.966366	−	1.33009i	0.943861	−	0.330342i	$-0.107164\pi$
$930$	−554.856	+	381.752i	−0.596619	+	0.410486i
$931$	−32.3746	+	99.6388i	−0.0347740	+	0.107023i
$932$	−241.561	+	78.4879i	−0.259185	+	0.0842145i
$933$	−73.2118	+	21.7263i	−0.0784692	+	0.0232865i
$934$	−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	0.106849	−	0.994275i	$-0.465924\pi$
$937$	1017.09	−	738.962i	1.08548	−	0.788647i	0.978630	+	0.205629i	$0.0659239\pi$
$938$	790.858	−	256.965i	0.843132	−	0.273950i
$939$	947.629	+	726.385i	1.00919	+	0.773573i
$940$	−252.413	−	183.389i	−0.268525	−	0.195095i
$941$	286.145	−	393.844i	0.304086	−	0.418538i	−0.629440	−	0.777049i	$-0.716716\pi$
$941$	286.145	−	393.844i	0.304086	−	0.418538i	0.933525	+	0.358511i	$0.116716\pi$
$942$	−415.271	+	541.755i	−0.440840	+	0.575111i
$943$	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	$-0.0738653\pi$
$948$	−57.4825	−	193.700i	−0.0606355	−	0.204325i
$949$	519.149	+	1597.77i	0.547048	+	1.68364i
$950$	−640.219	−	208.020i	−0.673914	−	0.218968i
$951$	−707.015	−	1027.61i	−0.743444	−	1.08055i
$952$	339.031	+	246.321i	0.356125	+	0.258740i
$953$	−1529.89	−	497.090i	−1.60534	−	0.521605i	−0.636917	−	0.770932i	$-0.719791\pi$
$953$	−1529.89	−	497.090i	−1.60534	−	0.521605i	−0.968419	+	0.249327i	$0.919791\pi$
$954$	361.093	−	943.511i	0.378504	−	0.989005i
$955$	−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
$960$	6.31788	−	245.992i	0.00658113	−	0.256242i
$961$	−18.8500	+	58.0144i	−0.0196150	+	0.0603688i
$962$	349.127	−	480.532i	0.362917	−	0.499513i
$963$	−367.907	+	98.9766i	−0.382043	+	0.102779i
$964$	138.748	−	427.023i	0.143930	−	0.442970i
$965$	402.601	−	130.813i	0.417204	−	0.135558i
$966$	−525.750	−	1771.64i	−0.544255	−	1.83399i
$967$	−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	$-0.641845\pi$
$971$	−242.099	+	78.6629i	−0.249330	+	0.0810122i	0.181686	+	0.983357i	$0.441845\pi$
$972$	312.189	−	658.771i	0.321182	−	0.677748i
$973$	−543.659	−	394.992i	−0.558746	−	0.405952i
$974$	544.297	−	749.160i	0.558826	−	0.769158i
$975$	−908.698	−	696.543i	−0.931998	−	0.714403i
$976$	−571.180	−	1757.91i	−0.585226	−	1.80114i
$977$	847.879	+	1167.01i	0.867839	+	1.19448i	0.979643	+	0.200748i	$0.0643372\pi$
$977$	847.879	+	1167.01i	0.867839	+	1.19448i	−0.111804	+	0.993730i	$0.535663\pi$
$978$	104.766	+	37.0405i	0.107123	+	0.0378737i
$979$		0			0
$980$		−	59.3970i		−	0.0606092i
$981$	−605.349	−	31.1152i	−0.617074	−	0.0317179i
$982$	−207.659	−	639.110i	−0.211466	−	0.650825i
$983$	653.669	+	212.390i	0.664973	+	0.216063i	0.622005	−	0.783014i	$-0.286318\pi$
$983$	653.669	+	212.390i	0.664973	+	0.216063i	0.0429685	+	0.999076i	$0.486318\pi$
$984$	−276.811	+	190.452i	−0.281312	+	0.193548i
$985$	532.763	+	387.075i	0.540876	+	0.392970i
$986$	−1127.28	−	366.277i	−1.14329	−	0.371477i
$987$	21.1939	−	825.202i	0.0214731	−	0.836071i
$988$	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
$993$	−533.824	−	13.7104i	−0.537587	−	0.0138070i
$994$	−398.014	+	1224.96i	−0.400416	+	1.23235i
$995$	369.077	−	507.991i	0.370931	−	0.510543i
$996$	−107.976	−	156.937i	−0.108410	−	0.157567i
$997$	409.307	−	1259.72i	0.410539	−	1.26351i	−0.505642	−	0.862744i	$-0.668744\pi$
$997$	409.307	−	1259.72i	0.410539	−	1.26351i	0.916181	−	0.400766i	$-0.131256\pi$
$998$	246.593	−	80.1230i	0.247088	−	0.0802836i
$999$	102.949	−	249.603i	0.103052	−	0.249853i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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} +(-2.99901 - 0.0770245i) q^{3} +(-0.927051 + 2.85317i) q^{4} +(1.66251 - 2.28825i) q^{5} +(4.49900 + 6.53904i) q^{6} +(2.31247 - 7.11706i) q^{7} +(-2.51626 + 0.817582i) q^{8} +(8.98813 + 0.461994i) q^{9} -7.48331 q^{10} +(3.00000 - 8.48528i) q^{12} +(18.1624 - 13.1957i) q^{13} +(-18.8300 + 6.11822i) q^{14} +(-5.16213 + 6.73442i) q^{15} +(15.3713 + 11.1679i) q^{16} +(12.4411 - 17.1237i) q^{17} +(-12.9889 - 19.9572i) q^{18} +(-4.62494 - 14.2341i) q^{19} +(4.98752 + 6.86474i) q^{20} +(-7.48331 + 21.1660i) q^{21} -31.1127i q^{23} +(7.60926 - 2.25812i) q^{24} +(5.25329 + 16.1680i) q^{25} +(-56.4899 - 18.3547i) q^{26} +(-26.9199 - 2.07783i) q^{27} +(18.1624 + 13.1957i) q^{28} +(20.1301 + 6.54066i) q^{29} +(22.4425 + 0.576398i) q^{30} +(-24.2705 + 17.6336i) q^{31} -39.6863i q^{32} -56.0000 q^{34} +(-12.4411 - 17.1237i) q^{35} +(-9.65061 + 25.2164i) q^{36} +(-3.09017 + 9.51057i) q^{37} +(-23.2751 + 32.0354i) q^{38} +(-55.4856 + 38.1752i) q^{39} +(-2.31247 + 7.11706i) q^{40} +(-40.2601 + 13.0813i) q^{41} +(56.9425 - 16.8983i) q^{42} +14.9666 q^{43} +(16.0000 - 19.7990i) q^{45} +(-66.5954 + 48.3844i) q^{46} +(-34.9699 + 11.3624i) q^{47} +(-45.2386 - 34.6767i) q^{48} +(-5.66312 - 4.11450i) q^{49} +(26.4373 - 36.3878i) q^{50} +(-38.6298 + 50.3958i) q^{51} +(20.8122 + 64.0535i) q^{52} +(24.9376 + 34.3237i) q^{53} +(37.4166 + 60.8523i) q^{54} +19.7990i q^{56} +(12.7739 + 43.0445i) q^{57} +(-17.3050 - 53.2592i) q^{58} +(32.2799 + 10.4884i) q^{59} +(-14.4289 - 20.9716i) q^{60} +(-78.7037 - 57.1816i) q^{61} +(75.4878 + 24.5275i) q^{62} +(24.0728 - 62.9007i) q^{63} +(-23.4615 + 17.0458i) q^{64} -63.4980i q^{65} -42.0000 q^{67} +(37.3232 + 51.3710i) q^{68} +(-2.39644 + 93.3073i) q^{69} +(-17.3050 + 53.2592i) q^{70} +(38.2377 - 52.6296i) q^{71} +(-22.9942 + 6.18604i) q^{72} +(-23.1247 + 71.1706i) q^{73} +(25.1626 - 8.17582i) q^{74} +(-14.5093 - 48.8925i) q^{75} +44.8999 q^{76} +(168.000 + 59.3970i) q^{78} +(18.1624 - 13.1957i) q^{79} +(51.1099 - 16.6066i) q^{80} +(80.5731 + 8.30494i) q^{81} +(90.6099 + 65.8319i) q^{82} +(12.4411 - 17.1237i) q^{83} +(-53.4528 - 40.9731i) q^{84} +(-18.4998 - 56.9364i) q^{85} +(-23.2751 - 32.0354i) q^{86} +(-59.8665 - 21.1660i) q^{87} -62.2254i q^{89} +(-67.2610 - 3.45725i) q^{90} +(-51.9149 - 159.777i) q^{91} +(88.7698 + 28.8431i) q^{92} +(74.1457 - 51.0138i) q^{93} +(78.7037 + 57.1816i) q^{94} +(-40.2601 - 13.0813i) q^{95} +(-3.05681 + 119.020i) 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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