LMFDB - Embedded newform 196.3.g.j.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,3,Mod(67,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("196.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	196.g (of order $6$, degree $2$, 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:	$5.34061318146$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.1728283481971641.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 4 x^{10} - 6 x^{9} + 6 x^{8} - 8 x^{7} + 9 x^{6} - 16 x^{5} + 24 x^{4} - 48 x^{3} + \cdots + 64 $ x^12 - 2x^11 + 4x^10 - 6x^9 + 6x^8 - 8x^7 + 9x^6 - 16x^5 + 24x^4 - 48x^3 + 64x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.3
Root			$-1.24688 + 0.667301i$ of defining polynomial
Character	$\chi$	$=$	196.79
Dual form			196.3.g.j.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.259316 + 1.98312i) q^{2} +(-2.58484 + 1.49236i) q^{3} +(-3.86551 + 1.02851i) q^{4} +(-3.40268 + 5.89361i) q^{5} +(-3.62981 - 4.73905i) q^{6} +(-3.04204 - 7.39905i) q^{8} +(-0.0457311 + 0.0792086i) q^{9} +O(q^{10})$	\(q+(0.259316 + 1.98312i) q^{2} +(-2.58484 + 1.49236i) q^{3} +(-3.86551 + 1.02851i) q^{4} +(-3.40268 + 5.89361i) q^{5} +(-3.62981 - 4.73905i) q^{6} +(-3.04204 - 7.39905i) q^{8} +(-0.0457311 + 0.0792086i) q^{9} +(-12.5701 - 5.21960i) q^{10} +(12.4211 - 7.17132i) q^{11} +(8.45683 - 8.42726i) q^{12} -4.62243 q^{13} -20.3121i q^{15} +(13.8843 - 7.95142i) q^{16} +(5.80536 + 10.0552i) q^{17} +(-0.168939 - 0.0701501i) q^{18} +(-19.4361 - 11.2214i) q^{19} +(7.09146 - 26.2815i) q^{20} +(17.4426 + 22.7728i) q^{22} +(0.739535 + 0.426971i) q^{23} +(18.9052 + 14.5856i) q^{24} +(-10.6564 - 18.4575i) q^{25} +(-1.19867 - 9.16683i) q^{26} -27.1354i q^{27} -42.8321 q^{29} +(40.2812 - 5.26724i) q^{30} +(-1.34219 + 0.774912i) q^{31} +(19.3690 + 25.4724i) q^{32} +(-21.4044 + 37.0734i) q^{33} +(-18.4352 + 14.1202i) q^{34} +(0.0953074 - 0.353217i) q^{36} +(-22.5075 + 38.9842i) q^{37} +(17.2133 - 41.4539i) q^{38} +(11.9483 - 6.89833i) q^{39} +(53.9582 + 7.24799i) q^{40} +36.6492 q^{41} +27.9894i q^{43} +(-40.6381 + 40.4960i) q^{44} +(-0.311217 - 0.539043i) q^{45} +(-0.654960 + 1.57730i) q^{46} +(-36.5237 - 21.0870i) q^{47} +(-24.0225 + 41.2736i) q^{48} +(33.8400 - 25.9193i) q^{50} +(-30.0119 - 17.3274i) q^{51} +(17.8681 - 4.75421i) q^{52} +(-21.7022 - 37.5893i) q^{53} +(53.8128 - 7.03665i) q^{54} +97.6068i q^{55} +66.9856 q^{57} +(-11.1071 - 84.9412i) q^{58} +(-46.7636 + 26.9990i) q^{59} +(20.8911 + 78.5165i) q^{60} +(-7.97489 + 13.8129i) q^{61} +(-1.88479 - 2.46077i) q^{62} +(-45.4920 + 45.0164i) q^{64} +(15.7287 - 27.2428i) q^{65} +(-79.0715 - 32.8336i) q^{66} +(-79.6270 + 45.9726i) q^{67} +(-32.7825 - 32.8975i) q^{68} -2.54877 q^{69} -16.3585i q^{71} +(0.725185 + 0.0974111i) q^{72} +(4.79364 + 8.30283i) q^{73} +(-83.1468 - 34.5259i) q^{74} +(55.0904 + 31.8065i) q^{75} +(86.6717 + 23.3864i) q^{76} +(16.7786 + 21.9059i) q^{78} +(-49.3484 - 28.4913i) q^{79} +(-0.381382 + 108.885i) q^{80} +(40.0842 + 69.4279i) q^{81} +(9.50373 + 72.6797i) q^{82} +14.3077i q^{83} -79.0151 q^{85} +(-55.5062 + 7.25809i) q^{86} +(110.714 - 63.9209i) q^{87} +(-90.8464 - 70.0888i) q^{88} +(50.0680 - 86.7204i) q^{89} +(0.988282 - 0.756962i) q^{90} +(-3.29782 - 0.889842i) q^{92} +(2.31289 - 4.00605i) q^{93} +(32.3468 - 77.8990i) q^{94} +(132.269 - 76.3658i) q^{95} +(-88.0797 - 36.9364i) q^{96} -68.2834 q^{97} +1.31181i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - q^{4} - 4 q^{5} - 12 q^{6} - 26 q^{8} + 10 q^{9}+O(q^{10}) $ 12 * q + q^2 - q^4 - 4 * q^5 - 12 * q^6 - 26 * q^8 + 10 * q^9	$ 12 q + q^{2} - q^{4} - 4 q^{5} - 12 q^{6} - 26 q^{8} + 10 q^{9} - 28 q^{10} + 6 q^{12} - 24 q^{13} - 17 q^{16} - 4 q^{17} - 43 q^{18} + 64 q^{20} + 104 q^{22} + 122 q^{24} + 30 q^{25} - 56 q^{26} - 72 q^{29} + 64 q^{30} + 101 q^{32} + 80 q^{33} - 116 q^{34} - 262 q^{36} - 28 q^{37} - 190 q^{38} + 40 q^{40} + 40 q^{41} - 164 q^{44} + 12 q^{45} - 120 q^{46} + 196 q^{48} + 322 q^{50} + 292 q^{52} - 92 q^{53} - 44 q^{54} + 320 q^{57} + 166 q^{58} + 176 q^{60} - 164 q^{61} - 296 q^{62} - 430 q^{64} + 136 q^{65} - 408 q^{66} + 62 q^{68} + 96 q^{69} - 151 q^{72} - 132 q^{73} - 250 q^{74} + 156 q^{76} + 496 q^{78} + 312 q^{80} + 218 q^{81} - 86 q^{82} - 464 q^{85} + 164 q^{86} + 100 q^{88} + 348 q^{89} - 104 q^{90} - 208 q^{92} - 288 q^{93} - 276 q^{94} + 170 q^{96} - 504 q^{97}+O(q^{100}) $ 12 * q + q^2 - q^4 - 4 * q^5 - 12 * q^6 - 26 * q^8 + 10 * q^9 - 28 * q^10 + 6 * q^12 - 24 * q^13 - 17 * q^16 - 4 * q^17 - 43 * q^18 + 64 * q^20 + 104 * q^22 + 122 * q^24 + 30 * q^25 - 56 * q^26 - 72 * q^29 + 64 * q^30 + 101 * q^32 + 80 * q^33 - 116 * q^34 - 262 * q^36 - 28 * q^37 - 190 * q^38 + 40 * q^40 + 40 * q^41 - 164 * q^44 + 12 * q^45 - 120 * q^46 + 196 * q^48 + 322 * q^50 + 292 * q^52 - 92 * q^53 - 44 * q^54 + 320 * q^57 + 166 * q^58 + 176 * q^60 - 164 * q^61 - 296 * q^62 - 430 * q^64 + 136 * q^65 - 408 * q^66 + 62 * q^68 + 96 * q^69 - 151 * q^72 - 132 * q^73 - 250 * q^74 + 156 * q^76 + 496 * q^78 + 312 * q^80 + 218 * q^81 - 86 * q^82 - 464 * q^85 + 164 * q^86 + 100 * q^88 + 348 * q^89 - 104 * q^90 - 208 * q^92 - 288 * q^93 - 276 * q^94 + 170 * q^96 - 504 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.259316	+	1.98312i	0.129658	+	0.991559i
$2$	0.259316	+	1.98312i	0.129658	+	0.991559i
$3$	−2.58484	+	1.49236i	−0.861614	+	0.497453i	−0.864552	−	0.502543i	$-0.832398\pi$
$3$	−2.58484	+	1.49236i	−0.861614	+	0.497453i	0.00293865	+	0.999996i	$0.499065\pi$
$4$	−3.86551	+	1.02851i	−0.966378	+	0.257127i
$5$	−3.40268	+	5.89361i	−0.680536	+	1.17872i	0.294282	+	0.955719i	$0.404920\pi$
$5$	−3.40268	+	5.89361i	−0.680536	+	1.17872i	−0.974818	+	0.223004i	$0.928414\pi$
$6$	−3.62981	−	4.73905i	−0.604969	−	0.789842i
$7$		0			0
$7$		0			0
$8$	−3.04204	−	7.39905i	−0.380255	−	0.924882i
$9$	−0.0457311	+	0.0792086i	−0.00508124	+	0.00880096i
$10$	−12.5701	−	5.21960i	−1.25701	−	0.521960i
$11$	12.4211	−	7.17132i	1.12919	−	0.651938i	0.185459	−	0.982652i	$-0.440623\pi$
$11$	12.4211	−	7.17132i	1.12919	−	0.651938i	0.943731	+	0.330714i	$0.107290\pi$
$12$	8.45683	−	8.42726i	0.704736	−	0.702272i
$13$	−4.62243			−0.355572			−0.177786	−	0.984069i	$-0.556893\pi$
$13$	−4.62243			−0.355572			−0.177786	+	0.984069i	$0.556893\pi$
$14$		0			0
$15$		−	20.3121i		−	1.35414i
$16$	13.8843	−	7.95142i	0.867771	−	0.496964i
$17$	5.80536	+	10.0552i	0.341492	+	0.591481i	0.984710	−	0.174202i	$-0.0557346\pi$
$17$	5.80536	+	10.0552i	0.341492	+	0.591481i	−0.643218	+	0.765683i	$0.722401\pi$
$18$	−0.168939	−	0.0701501i	−0.00938549	−	0.00389723i
$19$	−19.4361	−	11.2214i	−1.02295	−	0.590601i	−0.107994	−	0.994152i	$-0.534443\pi$
$19$	−19.4361	−	11.2214i	−1.02295	−	0.590601i	−0.914957	+	0.403550i	$0.867776\pi$
$20$	7.09146	−	26.2815i	0.354573	−	1.31408i
$21$		0			0
$22$	17.4426	+	22.7728i	0.792843	+	1.03513i
$23$	0.739535	+	0.426971i	0.0321537	+	0.0185639i	0.515991	−	0.856594i	$-0.327424\pi$
$23$	0.739535	+	0.426971i	0.0321537	+	0.0185639i	−0.483837	+	0.875158i	$0.660757\pi$
$24$	18.9052	+	14.5856i	0.787718	+	0.607732i
$25$	−10.6564	−	18.4575i	−0.426258	−	0.738300i
$26$	−1.19867	−	9.16683i	−0.0461027	−	0.352570i
$27$		−	27.1354i		−	1.00502i
$28$		0			0
$29$	−42.8321			−1.47697			−0.738485	−	0.674270i	$-0.764459\pi$
$29$	−42.8321			−1.47697			−0.738485	+	0.674270i	$0.764459\pi$
$30$	40.2812	−	5.26724i	1.34271	−	0.175575i
$31$	−1.34219	+	0.774912i	−0.0432963	+	0.0249972i	−0.521492	−	0.853256i	$-0.674624\pi$
$31$	−1.34219	+	0.774912i	−0.0432963	+	0.0249972i	0.478196	+	0.878253i	$0.341291\pi$
$32$	19.3690	+	25.4724i	0.605282	+	0.796011i
$33$	−21.4044	+	37.0734i	−0.648617	+	1.12344i
$34$	−18.4352	+	14.1202i	−0.542211	+	0.415299i
$35$		0			0
$36$	0.0953074	−	0.353217i	0.00264743	−	0.00981157i
$37$	−22.5075	+	38.9842i	−0.608312	+	1.05363i	0.383207	+	0.923663i	$0.374820\pi$
$37$	−22.5075	+	38.9842i	−0.608312	+	1.05363i	−0.991519	+	0.129964i	$0.958514\pi$
$38$	17.2133	−	41.4539i	0.452982	−	1.09089i
$39$	11.9483	−	6.89833i	0.306366	−	0.176880i
$40$	53.9582	+	7.24799i	1.34896	+	0.181200i
$41$	36.6492			0.893883			0.446942	−	0.894563i	$-0.352513\pi$
$41$	36.6492			0.893883			0.446942	+	0.894563i	$0.352513\pi$
$42$		0			0
$43$			27.9894i			0.650916i	0.945557	+	0.325458i	$0.105518\pi$
$43$			27.9894i			0.650916i	−0.945557	+	0.325458i	$0.894482\pi$
$44$	−40.6381	+	40.4960i	−0.923593	+	0.920363i
$45$	−0.311217	−	0.539043i	−0.00691592	−	0.0119787i
$46$	−0.654960	+	1.57730i	−0.0142383	+	0.0342892i
$47$	−36.5237	−	21.0870i	−0.777100	−	0.448659i	0.0583012	−	0.998299i	$-0.481432\pi$
$47$	−36.5237	−	21.0870i	−0.777100	−	0.448659i	−0.835402	+	0.549640i	$0.814765\pi$
$48$	−24.0225	+	41.2736i	−0.500468	+	0.859866i
$49$		0			0
$50$	33.8400	−	25.9193i	0.676800	−	0.518386i
$51$	−30.0119	−	17.3274i	−0.588468	−	0.339752i
$52$	17.8681	−	4.75421i	0.343617	−	0.0914271i
$53$	−21.7022	−	37.5893i	−0.409475	−	0.709232i	0.585356	−	0.810776i	$-0.300955\pi$
$53$	−21.7022	−	37.5893i	−0.409475	−	0.709232i	−0.994831	+	0.101545i	$0.967621\pi$
$54$	53.8128	−	7.03665i	0.996533	−	0.130308i
$55$			97.6068i			1.77467i
$56$		0			0
$57$	66.9856			1.17519
$58$	−11.1071	−	84.9412i	−0.191501	−	1.46450i
$59$	−46.7636	+	26.9990i	−0.792603	+	0.457609i	−0.840878	−	0.541225i	$-0.817961\pi$
$59$	−46.7636	+	26.9990i	−0.792603	+	0.457609i	0.0482754	+	0.998834i	$0.484627\pi$
$60$	20.8911	+	78.5165i	0.348185	+	1.30861i
$61$	−7.97489	+	13.8129i	−0.130736	+	0.226441i	−0.923960	−	0.382488i	$-0.875067\pi$
$61$	−7.97489	+	13.8129i	−0.130736	+	0.226441i	0.793225	+	0.608929i	$0.208401\pi$
$62$	−1.88479	−	2.46077i	−0.0303999	−	0.0396898i
$63$		0			0
$64$	−45.4920	+	45.0164i	−0.710812	+	0.703382i
$65$	15.7287	−	27.2428i	0.241979	−	0.419120i
$66$	−79.0715	−	32.8336i	−1.19805	−	0.497479i
$67$	−79.6270	+	45.9726i	−1.18846	+	0.686159i	−0.957957	−	0.286912i	$-0.907371\pi$
$67$	−79.6270	+	45.9726i	−1.18846	+	0.686159i	−0.230505	+	0.973071i	$0.574038\pi$
$68$	−32.7825	−	32.8975i	−0.482096	−	0.483787i
$69$	−2.54877			−0.0369387
$70$		0			0
$71$		−	16.3585i		−	0.230401i	−0.993342	−	0.115201i	$-0.963249\pi$
$71$		−	16.3585i		−	0.230401i	0.993342	−	0.115201i	$-0.0367511\pi$
$72$	0.725185	+	0.0974111i	0.0100720	+	0.00135293i
$73$	4.79364	+	8.30283i	0.0656663	+	0.113737i	0.896989	−	0.442052i	$-0.145749\pi$
$73$	4.79364	+	8.30283i	0.0656663	+	0.113737i	−0.831323	+	0.555790i	$0.812416\pi$
$74$	−83.1468	−	34.5259i	−1.12361	−	0.466566i
$75$	55.0904	+	31.8065i	0.734539	+	0.424086i
$76$	86.6717	+	23.3864i	1.14042	+	0.307715i
$77$		0			0
$78$	16.7786	+	21.9059i	0.215110	+	0.280845i
$79$	−49.3484	−	28.4913i	−0.624663	−	0.360649i	0.154019	−	0.988068i	$-0.450778\pi$
$79$	−49.3484	−	28.4913i	−0.624663	−	0.360649i	−0.778682	+	0.627418i	$0.784112\pi$
$80$	−0.381382	+	108.885i	−0.00476727	+	1.36106i
$81$	40.0842	+	69.4279i	0.494867	+	0.857135i
$82$	9.50373	+	72.6797i	0.115899	+	0.886338i
$83$			14.3077i			0.172381i	0.996279	+	0.0861907i	$0.0274694\pi$
$83$			14.3077i			0.172381i	−0.996279	+	0.0861907i	$0.972531\pi$
$84$		0			0
$85$	−79.0151			−0.929589
$86$	−55.5062	+	7.25809i	−0.645421	+	0.0843965i
$87$	110.714	−	63.9209i	1.27258	−	0.734723i
$88$	−90.8464	−	70.0888i	−1.03235	−	0.796464i
$89$	50.0680	−	86.7204i	0.562562	−	0.974386i	−0.434710	−	0.900571i	$-0.643149\pi$
$89$	50.0680	−	86.7204i	0.562562	−	0.974386i	0.997272	−	0.0738155i	$-0.0235176\pi$
$90$	0.988282	−	0.756962i	0.0109809	−	0.00841068i
$91$		0			0
$92$	−3.29782	−	0.889842i	−0.0358459	−	0.00967219i
$93$	2.31289	−	4.00605i	0.0248698	−	0.0430758i
$94$	32.3468	−	77.8990i	0.344115	−	0.828713i
$95$	132.269	−	76.3658i	1.39231	−	0.803850i
$96$	−88.0797	−	36.9364i	−0.917497	−	0.384755i
$97$	−68.2834			−0.703952			−0.351976	−	0.936009i	$-0.614490\pi$
$97$	−68.2834			−0.703952			−0.351976	+	0.936009i	$0.614490\pi$
$98$		0			0
$99$			1.31181i			0.0132506i
$100$	60.1763	+	60.3874i	0.601763	+	0.603874i
$101$	−14.0814	−	24.3897i	−0.139420	−	0.241483i	0.787857	−	0.615858i	$-0.211190\pi$
$101$	−14.0814	−	24.3897i	−0.139420	−	0.241483i	−0.927277	+	0.374375i	$0.877857\pi$
$102$	26.5796	−	64.0103i	0.260585	−	0.627552i
$103$	138.774	+	80.1213i	1.34732	+	0.777877i	0.987870	−	0.155286i	$-0.0496299\pi$
$103$	138.774	+	80.1213i	1.34732	+	0.777877i	0.359453	+	0.933163i	$0.382963\pi$
$104$	14.0616	+	34.2016i	0.135208	+	0.328862i
$105$		0			0
$106$	68.9162	−	52.7855i	0.650153	−	0.497976i
$107$	102.990	+	59.4613i	0.962524	+	0.555713i	0.896949	−	0.442134i	$-0.145779\pi$
$107$	102.990	+	59.4613i	0.962524	+	0.555713i	0.0655750	+	0.997848i	$0.479112\pi$
$108$	27.9090	+	104.892i	0.258417	+	0.971225i
$109$	49.1333	+	85.1014i	0.450764	+	0.780747i	0.998434	−	0.0559480i	$-0.0178181\pi$
$109$	49.1333	+	85.1014i	0.450764	+	0.780747i	−0.547669	+	0.836695i	$0.684485\pi$
$110$	−193.566	+	25.3110i	−1.75969	+	0.230100i
$111$		−	134.357i		−	1.21043i
$112$		0			0
$113$	96.9977			0.858387			0.429193	−	0.903213i	$-0.358798\pi$
$113$	96.9977			0.858387			0.429193	+	0.903213i	$0.358798\pi$
$114$	17.3704	+	132.840i	0.152372	+	1.16527i
$115$	−5.03280	+	2.90569i	−0.0437635	+	0.0252669i
$116$	165.568	−	44.0532i	1.42731	−	0.379769i
$117$	0.211389	−	0.366137i	0.00180674	−	0.00312937i
$118$	−65.6686	−	85.7364i	−0.556514	−	0.726579i
$119$		0			0
$120$	−150.290	+	61.7901i	−1.25242	+	0.514918i
$121$	42.3556	−	73.3620i	0.350046	−	0.606298i
$122$	−29.4606	−	12.2332i	−0.241481	−	0.100272i
$123$	−94.7324	+	54.6938i	−0.770182	+	0.444665i
$124$	4.39123	−	4.37588i	0.0354132	−	0.0352894i
$125$	−25.0921			−0.200737
$126$		0			0
$127$			71.8712i			0.565915i	0.959132	+	0.282958i	$0.0913156\pi$
$127$			71.8712i			0.565915i	−0.959132	+	0.282958i	$0.908684\pi$
$128$	−101.070	−	78.5424i	−0.789607	−	0.613613i
$129$	−41.7702	−	72.3481i	−0.323800	−	0.560838i
$130$	58.1044	+	24.1273i	0.446957	+	0.185594i
$131$	−181.724	−	104.919i	−1.38721	−	0.800906i	−0.394209	−	0.919021i	$-0.628982\pi$
$131$	−181.724	−	104.919i	−1.38721	−	0.800906i	−0.993000	+	0.118115i	$0.962315\pi$
$132$	44.6084	−	165.322i	0.337943	−	1.25244i
$133$		0			0
$134$	−111.818	−	145.988i	−0.834460	−	1.08946i
$135$	159.926	+	92.3332i	1.18464	+	0.683950i
$136$	56.7386	−	73.5424i	0.417196	−	0.540753i
$137$	9.08248	+	15.7313i	0.0662954	+	0.114827i	0.897268	−	0.441486i	$-0.145549\pi$
$137$	9.08248	+	15.7313i	0.0662954	+	0.114827i	−0.830972	+	0.556314i	$0.812215\pi$
$138$	−0.660938	−	5.05452i	−0.00478940	−	0.0366269i
$139$		−	134.084i		−	0.964635i	−0.875996	−	0.482318i	$-0.839795\pi$
$139$		−	134.084i		−	0.964635i	0.875996	−	0.482318i	$-0.160205\pi$
$140$		0			0
$141$	125.877			0.892747
$142$	32.4408	−	4.24202i	0.228456	−	0.0298733i
$143$	−57.4156	+	33.1489i	−0.401508	+	0.231811i
$144$	−0.00512567	+	1.46339i	−3.55949e−5	+	0.0101624i
$145$	145.744	−	252.436i	1.00513	−	1.74094i
$146$	−15.2224	+	11.6594i	−0.104263	+	0.0798590i
$147$		0			0
$148$	46.9076	−	173.843i	0.316943	−	1.17461i
$149$	10.3809	−	17.9803i	0.0696706	−	0.120673i	−0.829086	−	0.559122i	$-0.811139\pi$
$149$	10.3809	−	17.9803i	0.0696706	−	0.120673i	0.898756	+	0.438449i	$0.144472\pi$
$150$	−48.7902	+	117.499i	−0.325268	+	0.783325i
$151$	−80.6348	+	46.5545i	−0.534005	+	0.308308i	−0.742646	−	0.669684i	$-0.766429\pi$
$151$	−80.6348	+	46.5545i	−0.534005	+	0.308308i	0.208641	+	0.977992i	$0.433096\pi$
$152$	−23.9026	+	177.945i	−0.157254	+	1.17069i
$153$	−1.06194			−0.00694080
$154$		0			0
$155$		−	10.5471i		−	0.0680458i
$156$	−39.0911	+	38.9544i	−0.250584	+	0.249708i
$157$	79.6687	+	137.990i	0.507444	+	0.878919i	0.999963	+	0.00861697i	$0.00274290\pi$
$157$	79.6687	+	137.990i	0.507444	+	0.878919i	−0.492519	+	0.870302i	$0.663924\pi$
$158$	43.7048	−	105.252i	0.276613	−	0.666151i
$159$	112.193	+	64.7749i	0.705619	+	0.407389i
$160$	−216.031	+	27.4793i	−1.35019	+	0.171746i
$161$		0			0
$162$	−127.289	+	97.4955i	−0.785736	+	0.601824i
$163$	39.6880	+	22.9139i	0.243485	+	0.140576i	0.616777	−	0.787138i	$-0.288438\pi$
$163$	39.6880	+	22.9139i	0.243485	+	0.140576i	−0.373293	+	0.927714i	$0.621771\pi$
$164$	−141.668	+	37.6940i	−0.863829	+	0.229842i
$165$	−145.664	−	252.298i	−0.882814	−	1.52908i
$166$	−28.3738	+	3.71020i	−0.170926	+	0.0223506i
$167$		−	15.5845i		−	0.0933203i	−0.998911	−	0.0466602i	$-0.985142\pi$
$167$		−	15.5845i		−	0.0933203i	0.998911	−	0.0466602i	$-0.0148578\pi$
$168$		0			0
$169$	−147.633			−0.873569
$170$	−20.4899	−	156.696i	−0.120529	−	0.921742i
$171$	1.77767	−	1.02634i	0.0103957	−	0.00600197i
$172$	−28.7873	−	108.193i	−0.167368	−	0.629031i
$173$	−133.011	+	230.381i	−0.768848	+	1.33168i	0.169340	+	0.985558i	$0.445836\pi$
$173$	−133.011	+	230.381i	−0.768848	+	1.33168i	−0.938188	+	0.346126i	$0.887497\pi$
$174$	155.473	+	202.984i	0.893521	+	1.16657i
$175$		0			0
$176$	115.436	−	198.334i	0.655889	−	1.12690i
$177$	80.5842	−	139.576i	0.455278	−	0.788565i
$178$	184.960	+	76.8028i	1.03910	+	0.431476i
$179$	−38.5433	+	22.2530i	−0.215325	+	0.124318i	−0.603784	−	0.797148i	$-0.706341\pi$
$179$	−38.5433	+	22.2530i	−0.215325	+	0.124318i	0.388458	+	0.921466i	$0.373008\pi$
$180$	1.75742	+	1.76359i	0.00976345	+	0.00979771i
$181$	168.111			0.928787			0.464394	−	0.885629i	$-0.346272\pi$
$181$	168.111			0.928787			0.464394	+	0.885629i	$0.346272\pi$
$182$		0			0
$183$		−	47.6056i		−	0.260140i
$184$	0.909483	−	6.77072i	0.00494284	−	0.0367974i
$185$	−153.172	−	265.301i	−0.827956	−	1.43406i
$186$	8.54423	+	3.54791i	0.0459367	+	0.0190748i
$187$	144.218	+	83.2641i	0.771218	+	0.445263i
$188$	162.871	+	43.9470i	0.866335	+	0.233761i
$189$		0			0
$190$	185.742	+	242.503i	0.977589	+	1.27633i
$191$	−306.232	−	176.803i	−1.60331	−	0.925672i	−0.990819	−	0.135194i	$-0.956834\pi$
$191$	−306.232	−	176.803i	−1.60331	−	0.925672i	−0.612491	−	0.790477i	$-0.709833\pi$
$192$	50.4088	−	184.251i	0.262546	−	0.959639i
$193$	174.287	+	301.874i	0.903042	+	1.56411i	0.823525	+	0.567280i	$0.192004\pi$
$193$	174.287	+	301.874i	0.903042	+	1.56411i	0.0795170	+	0.996834i	$0.474662\pi$
$194$	−17.7070	−	135.414i	−0.0912730	−	0.698010i
$195$			93.8912i			0.481493i
$196$		0			0
$197$	−26.9314			−0.136707			−0.0683537	−	0.997661i	$-0.521775\pi$
$197$	−26.9314			−0.136707			−0.0683537	+	0.997661i	$0.521775\pi$
$198$	−2.60147	+	0.340173i	−0.0131387	+	0.00171805i
$199$	−200.537	+	115.780i	−1.00772	+	0.581809i	−0.910524	−	0.413457i	$-0.864321\pi$
$199$	−200.537	+	115.780i	−1.00772	+	0.581809i	−0.0971981	+	0.995265i	$0.530988\pi$
$200$	−104.151	+	134.996i	−0.520754	+	0.674981i
$201$	137.215	−	237.664i	0.682663	−	1.18241i
$202$	44.7162	−	34.2498i	0.221367	−	0.169553i
$203$		0			0
$204$	133.832	+	36.1116i	0.656041	+	0.177018i
$205$	−124.706	+	215.996i	−0.608320	+	1.05364i
$206$	−122.904	+	295.982i	−0.596620	+	1.43681i
$207$	−0.0676395	+	0.0390517i	−0.000326761	+	0.000188655i
$208$	−64.1794	+	36.7549i	−0.308555	+	0.176706i
$209$	−321.890			−1.54014
$210$		0			0
$211$		−	79.6903i		−	0.377679i	−0.982008	−	0.188840i	$-0.939527\pi$
$211$		−	79.6903i		−	0.377679i	0.982008	−	0.188840i	$-0.0604726\pi$
$212$	122.551	+	122.981i	0.578070	+	0.580098i
$213$	24.4127	+	42.2841i	0.114614	+	0.198517i
$214$	−91.2119	+	219.661i	−0.426224	+	1.02645i
$215$	−164.959	−	95.2389i	−0.767249	−	0.442972i
$216$	−200.777	+	82.5471i	−0.929521	+	0.382163i
$217$		0			0
$218$	−156.025	+	119.505i	−0.715711	+	0.548189i
$219$	−24.7816	−	14.3077i	−0.113158	−	0.0653318i
$220$	−100.389	−	377.300i	−0.456315	−	1.71500i
$221$	−26.8349	−	46.4794i	−0.121425	−	0.210314i
$222$	266.446	−	34.8410i	1.20021	−	0.156941i
$223$			264.367i			1.18550i	0.805386	+	0.592750i	$0.201958\pi$
$223$			264.367i			1.18550i	−0.805386	+	0.592750i	$0.798042\pi$
$224$		0			0
$225$	1.94932			0.00866367
$226$	25.1531	+	192.358i	0.111297	+	0.851141i
$227$	373.538	−	215.662i	1.64554	−	0.950053i	0.666726	−	0.745303i	$-0.267695\pi$
$227$	373.538	−	215.662i	1.64554	−	0.950053i	0.978814	−	0.204750i	$-0.0656383\pi$
$228$	−258.933	+	68.8952i	−1.13567	+	0.302172i
$229$	−212.451	+	367.975i	−0.927732	+	1.60688i	−0.140625	+	0.990063i	$0.544911\pi$
$229$	−212.451	+	367.975i	−0.927732	+	1.60688i	−0.787107	+	0.616816i	$0.788422\pi$
$230$	−7.06741	−	9.22714i	−0.0307279	−	0.0401180i
$231$		0			0
$232$	130.297	+	316.917i	0.561626	+	1.36602i
$233$	−109.414	+	189.511i	−0.469588	+	0.813350i	−0.999395	−	0.0347679i	$-0.988931\pi$
$233$	−109.414	+	189.511i	−0.469588	+	0.813350i	0.529808	+	0.848118i	$0.322264\pi$
$234$	0.780908	+	0.324264i	0.00333722	+	0.00138574i
$235$	248.557	−	143.504i	1.05769	−	0.610657i
$236$	152.996	−	152.461i	0.648290	−	0.646023i
$237$	170.077			0.717625
$238$		0			0
$239$			90.1656i			0.377262i	0.982048	+	0.188631i	$0.0604050\pi$
$239$			90.1656i			0.377262i	−0.982048	+	0.188631i	$0.939595\pi$
$240$	−161.510	−	282.020i	−0.672957	−	1.17508i
$241$	187.972	+	325.577i	0.779968	+	1.35094i	0.931960	+	0.362562i	$0.118098\pi$
$241$	187.972	+	325.577i	0.779968	+	1.35094i	−0.151992	+	0.988382i	$0.548569\pi$
$242$	156.469	+	64.9722i	0.646566	+	0.268480i
$243$	4.27710	+	2.46938i	0.0176012	+	0.0101621i
$244$	16.6203	−	61.5962i	0.0681161	−	0.252443i
$245$		0			0
$246$	−133.030	−	173.683i	−0.540772	−	0.706027i
$247$	89.8420	+	51.8703i	0.363733	+	0.210001i
$248$	9.81660	+	7.57360i	0.0395831	+	0.0305387i
$249$	−21.3522	−	36.9830i	−0.0857516	−	0.148526i
$250$	−6.50678	−	49.7605i	−0.0260271	−	0.199042i
$251$			319.525i			1.27301i	0.771274	+	0.636503i	$0.219620\pi$
$251$			319.525i			1.27301i	−0.771274	+	0.636503i	$0.780380\pi$
$252$		0			0
$253$	12.2478			0.0484101
$254$	−142.529	+	18.6374i	−0.561138	+	0.0733754i
$255$	204.241	−	117.919i	0.800947	−	0.462427i
$256$	129.550	−	220.800i	0.506054	−	0.862502i
$257$	−83.7329	+	145.030i	−0.325809	+	0.564318i	−0.981676	−	0.190559i	$-0.938970\pi$
$257$	−83.7329	+	145.030i	−0.325809	+	0.564318i	0.655867	+	0.754877i	$0.272303\pi$
$258$	132.643	−	101.596i	0.514121	−	0.393784i
$259$		0			0
$260$	−32.7798	+	121.484i	−0.126076	+	0.467248i
$261$	1.95876	−	3.39267i	0.00750483	−	0.0129988i
$262$	160.942	−	387.588i	0.614282	−	1.47934i
$263$	74.5887	−	43.0638i	0.283607	−	0.163741i	−0.351448	−	0.936207i	$-0.614311\pi$
$263$	74.5887	−	43.0638i	0.283607	−	0.163741i	0.635055	+	0.772467i	$0.280977\pi$
$264$	339.421	+	45.5931i	1.28569	+	0.172701i
$265$	295.382			1.11465
$266$		0			0
$267$			298.878i			1.11939i
$268$	260.516	−	259.605i	0.972073	−	0.968674i
$269$	134.672	+	233.258i	0.500638	+	0.867130i	1.00000		0.000736768i	$0.000234520\pi$
$269$	134.672	+	233.258i	0.500638	+	0.867130i	−0.499362	+	0.866394i	$0.666432\pi$
$270$	−141.636	+	341.095i	−0.524579	+	1.26332i
$271$	−275.671	−	159.159i	−1.01724	−	0.587302i	−0.103935	−	0.994584i	$-0.533143\pi$
$271$	−275.671	−	159.159i	−1.01724	−	0.587302i	−0.913302	+	0.407282i	$0.866477\pi$
$272$	160.556	+	93.4487i	0.590281	+	0.343561i
$273$		0			0
$274$	−28.8418	+	22.0910i	−0.105262	+	0.0806241i
$275$	−264.729	−	152.842i	−0.962652	−	0.555787i
$276$	9.85231	−	2.62143i	0.0356968	−	0.00949795i
$277$	−178.298	−	308.822i	−0.643677	−	1.11488i	−0.984605	−	0.174792i	$-0.944075\pi$
$277$	−178.298	−	308.822i	−0.643677	−	1.11488i	0.340929	−	0.940089i	$-0.389259\pi$
$278$	265.905	−	34.7702i	0.956492	−	0.125073i
$279$		−	0.141750i		−	0.000508066i
$280$		0			0
$281$	109.846			0.390911			0.195455	−	0.980713i	$-0.437381\pi$
$281$	109.846			0.390911			0.195455	+	0.980713i	$0.437381\pi$
$282$	32.6420	+	249.630i	0.115752	+	0.885211i
$283$	−445.641	+	257.291i	−1.57470	+	0.909155i	−0.579123	+	0.815240i	$0.696605\pi$
$283$	−445.641	+	257.291i	−1.57470	+	0.909155i	−0.995580	+	0.0939154i	$0.970062\pi$
$284$	16.8248	+	63.2339i	0.0592424	+	0.222654i
$285$	−227.930	+	394.787i	−0.799755	+	1.38522i
$286$	−80.6270	−	105.266i	−0.281913	−	0.368063i
$287$		0			0
$288$	−2.90340	+	0.369315i	−0.0100812	+	0.00128234i
$289$	77.0956	−	133.534i	0.266767	−	0.462054i
$290$	538.404	+	223.567i	1.85657	+	0.770920i
$291$	176.502	−	101.903i	0.606535	−	0.350183i
$292$	−27.0694	−	27.1644i	−0.0927034	−	0.0930287i
$293$	133.002			0.453931			0.226965	−	0.973903i	$-0.427120\pi$
$293$	133.002			0.453931			0.226965	+	0.973903i	$0.427120\pi$
$294$		0			0
$295$		−	367.475i		−	1.24568i
$296$	356.915	+	47.9429i	1.20579	+	0.161969i
$297$	−194.597	−	337.052i	−0.655208	−	1.13485i
$298$	38.3489	+	15.9240i	0.128688	+	0.0534363i
$299$	−3.41845	−	1.97364i	−0.0114329	−	0.00660081i
$300$	−245.666	−	66.2873i	−0.818886	−	0.220958i
$301$		0			0
$302$	−113.233	−	147.836i	−0.374944	−	0.489523i
$303$	72.7965	+	42.0291i	0.240252	+	0.138710i
$304$	−359.083	−	1.25773i	−1.18120	−	0.00413726i
$305$	−54.2720	−	94.0018i	−0.177941	−	0.308203i
$306$	−0.275379	−	2.10596i	−0.000899930	−	0.00688221i
$307$		−	382.811i		−	1.24694i	−0.781847	−	0.623471i	$-0.785722\pi$
$307$		−	382.811i		−	1.24694i	0.781847	−	0.623471i	$-0.214278\pi$
$308$		0			0
$309$	−478.279			−1.54783
$310$	20.9161	−	2.73503i	0.0674714	−	0.00882269i
$311$	−170.064	+	98.1868i	−0.546831	+	0.315713i	−0.747843	−	0.663876i	$-0.768910\pi$
$311$	−170.064	+	98.1868i	−0.546831	+	0.315713i	0.201012	+	0.979589i	$0.435577\pi$
$312$	−87.3882	−	67.4208i	−0.280090	−	0.216092i
$313$	213.523	−	369.832i	0.682181	−	1.18157i	−0.292133	−	0.956378i	$-0.594365\pi$
$313$	213.523	−	369.832i	0.682181	−	1.18157i	0.974314	−	0.225194i	$-0.0723017\pi$
$314$	−252.991	+	193.775i	−0.805705	+	0.617119i
$315$		0			0
$316$	220.060	+	59.3782i	0.696393	+	0.187906i
$317$	−55.5247	+	96.1716i	−0.175157	+	0.303381i	−0.940216	−	0.340580i	$-0.889377\pi$
$317$	−55.5247	+	96.1716i	−0.175157	+	0.303381i	0.765059	+	0.643961i	$0.222710\pi$
$318$	−99.3626	+	239.290i	−0.312461	+	0.752484i
$319$	−532.022	+	307.163i	−1.66778	+	0.962893i
$320$	−110.515	−	421.289i	−0.345359	−	1.31653i
$321$	−354.951			−1.10577
$322$		0			0
$323$		−	260.577i		−	0.806741i
$324$	−226.353	−	227.147i	−0.698621	−	0.701072i
$325$	49.2587	+	85.3186i	0.151565	+	0.262519i
$326$	−35.1492	+	84.6479i	−0.107820	+	0.259656i
$327$	−254.004	−	146.649i	−0.776770	−	0.448468i
$328$	−111.488	−	271.170i	−0.339904	−	0.826736i
$329$		0			0
$330$	462.563	−	354.294i	1.40171	−	1.07362i
$331$	−103.601	−	59.8143i	−0.312995	−	0.180708i	0.335271	−	0.942122i	$-0.391172\pi$
$331$	−103.601	−	59.8143i	−0.312995	−	0.180708i	−0.648266	+	0.761414i	$0.724505\pi$
$332$	−14.7155	−	55.3064i	−0.0443239	−	0.166586i
$333$	−2.05859	−	3.56558i	−0.00618195	−	0.0107075i
$334$	30.9059	−	4.04131i	0.0925326	−	0.0120997i
$335$		−	625.721i		−	1.86782i
$336$		0			0
$337$	−57.3636			−0.170218			−0.0851092	−	0.996372i	$-0.527124\pi$
$337$	−57.3636			−0.170218			−0.0851092	+	0.996372i	$0.527124\pi$
$338$	−38.2836	−	292.774i	−0.113265	−	0.866195i
$339$	−250.724	+	144.755i	−0.739598	+	0.427007i
$340$	305.434	−	81.2676i	0.898334	−	0.239022i
$341$	−11.1143	+	19.2505i	−0.0325932	+	0.0564531i
$342$	2.49632	+	3.25918i	0.00729919	+	0.00952976i
$343$		0			0
$344$	207.095	−	85.1449i	0.602020	−	0.247514i
$345$	8.67266	−	15.0215i	0.0251381	−	0.0435405i
$346$	−491.365	−	204.034i	−1.42013	−	0.589694i
$347$	232.766	−	134.387i	0.670794	−	0.387283i	−0.125583	−	0.992083i	$-0.540080\pi$
$347$	232.766	−	134.387i	0.670794	−	0.387283i	0.796377	+	0.604800i	$0.206747\pi$
$348$	−362.224	+	360.958i	−1.04087	+	1.03723i
$349$	−97.0498			−0.278080			−0.139040	−	0.990287i	$-0.544402\pi$
$349$	−97.0498			−0.278080			−0.139040	+	0.990287i	$0.544402\pi$
$350$		0			0
$351$			125.432i			0.357356i
$352$	423.255	+	177.493i	1.20243	+	0.504241i
$353$	−158.464	−	274.468i	−0.448907	−	0.777529i	0.549409	−	0.835554i	$-0.314853\pi$
$353$	−158.464	−	274.468i	−0.448907	−	0.777529i	−0.998315	+	0.0580249i	$0.981520\pi$
$354$	297.692	+	123.614i	0.840939	+	0.349191i
$355$	96.4105	+	55.6627i	0.271579	+	0.156796i
$356$	−104.346	+	386.714i	−0.293106	+	1.08627i
$357$		0			0
$358$	−54.1251	−	70.6653i	−0.151187	−	0.197389i
$359$	511.123	+	295.097i	1.42374	+	0.821997i	0.996616	−	0.0821961i	$-0.0261934\pi$
$359$	511.123	+	295.097i	1.42374	+	0.821997i	0.427124	+	0.904193i	$0.359527\pi$
$360$	−3.04167	+	3.94250i	−0.00844909	+	0.0109514i
$361$	71.3407	+	123.566i	0.197620	+	0.342287i
$362$	43.5937	+	333.383i	0.120425	+	0.920947i
$363$			252.839i			0.696526i
$364$		0			0
$365$	−65.2449			−0.178753
$366$	94.4074	−	12.3449i	0.257944	−	0.0337292i
$367$	152.025	−	87.7718i	0.414238	−	0.239160i	−0.278371	−	0.960474i	$-0.589795\pi$
$367$	152.025	−	87.7718i	0.414238	−	0.239160i	0.692609	+	0.721313i	$0.256461\pi$
$368$	13.6630	+	0.0478560i	0.0371277	+	0.000130044i
$369$	−1.67601	+	2.90293i	−0.00454203	+	0.00786703i
$370$	486.404	−	372.555i	1.31461	−	1.00690i
$371$		0			0
$372$	−4.82026	+	17.8642i	−0.0129577	+	0.0480222i
$373$	−277.008	+	479.792i	−0.742649	+	1.28631i	0.208637	+	0.977993i	$0.433097\pi$
$373$	−277.008	+	479.792i	−0.742649	+	1.28631i	−0.951285	+	0.308312i	$0.900236\pi$
$374$	−127.725	+	307.592i	−0.341510	+	0.822439i
$375$	64.8590	−	37.4464i	0.172957	−	0.0998570i
$376$	−44.9170	+	334.388i	−0.119460	+	0.889331i
$377$	197.989			0.525169
$378$		0			0
$379$		−	749.909i		−	1.97865i	−0.145723	−	0.989325i	$-0.546551\pi$
$379$		−	749.909i		−	1.97865i	0.145723	−	0.989325i	$-0.453449\pi$
$380$	−432.746	+	431.233i	−1.13881	+	1.13482i
$381$	−107.258	−	185.776i	−0.281516	−	0.487600i
$382$	271.211	−	653.143i	0.709976	−	1.70980i
$383$	213.242	+	123.115i	0.556767	+	0.321450i	0.751847	−	0.659338i	$-0.229163\pi$
$383$	213.242	+	123.115i	0.556767	+	0.321450i	−0.195080	+	0.980787i	$0.562497\pi$
$384$	378.463	+	52.1875i	0.985580	+	0.135905i
$385$		0			0
$386$	−553.456	+	423.912i	−1.43382	+	1.09822i
$387$	−2.21700	−	1.27999i	−0.00572868	−	0.00330746i
$388$	263.950	−	70.2300i	0.680284	−	0.181005i
$389$	−149.009	−	258.092i	−0.383058	−	0.663475i	0.608440	−	0.793600i	$-0.291796\pi$
$389$	−149.009	−	258.092i	−0.383058	−	0.663475i	−0.991498	+	0.130125i	$0.958462\pi$
$390$	−186.197	+	24.3475i	−0.477429	+	0.0624294i
$391$			9.91487i			0.0253577i
$392$		0			0
$393$	626.305			1.59365
$394$	−6.98373	−	53.4080i	−0.0177252	−	0.135553i
$395$	335.833	−	193.894i	0.850211	−	0.490870i
$396$	−1.34921	−	5.07081i	−0.00340709	−	0.0128051i
$397$	63.9113	−	110.698i	0.160986	−	0.278835i	−0.774237	−	0.632896i	$-0.781866\pi$
$397$	63.9113	−	110.698i	0.160986	−	0.278835i	0.935222	+	0.354061i	$0.115199\pi$
$398$	−281.608	−	367.664i	−0.707557	−	0.923779i
$399$		0			0
$400$	−294.721	−	171.536i	−0.736803	−	0.428841i
$401$	387.143	−	670.552i	0.965444	−	1.67220i	0.257028	−	0.966404i	$-0.417257\pi$
$401$	387.143	−	670.552i	0.965444	−	1.67220i	0.708416	−	0.705795i	$-0.249410\pi$
$402$	506.898	+	210.484i	1.26094	+	0.523592i
$403$	6.20417	−	3.58198i	0.0153950	−	0.00888828i
$404$	79.5169	+	79.7959i	0.196824	+	0.197515i
$405$	−545.575			−1.34710
$406$		0			0
$407$			645.635i			1.58633i
$408$	−36.9087	+	274.770i	−0.0904625	+	0.673455i
$409$	333.442	+	577.538i	0.815262	+	1.41207i	0.909140	+	0.416491i	$0.136740\pi$
$409$	333.442	+	577.538i	0.815262	+	1.41207i	−0.0938783	+	0.995584i	$0.529926\pi$
$410$	−460.684	−	191.294i	−1.12362	−	0.466572i
$411$	−46.9535	−	27.1086i	−0.114242	−	0.0659577i
$412$	−618.839	−	166.979i	−1.50204	−	0.405290i
$413$		0			0
$414$	−0.0949841	−	0.124010i	−0.000229430	−	0.000299542i
$415$	−84.3238	−	48.6844i	−0.203190	−	0.117312i
$416$	−89.5320	−	117.744i	−0.215221	−	0.283039i
$417$	200.102	+	346.587i	0.479861	+	0.831143i
$418$	−83.4711	−	638.345i	−0.199692	−	1.52714i
$419$		−	95.3634i		−	0.227598i	−0.993504	−	0.113799i	$-0.963698\pi$
$419$		−	95.3634i		−	0.227598i	0.993504	−	0.113799i	$-0.0363019\pi$
$420$		0			0
$421$	−279.158			−0.663083			−0.331541	−	0.943441i	$-0.607569\pi$
$421$	−279.158			−0.663083			−0.331541	+	0.943441i	$0.607569\pi$
$422$	158.035	−	20.6650i	0.374491	−	0.0489691i
$423$	3.34054	−	1.92866i	0.00789726	−	0.00455949i
$424$	−212.106	+	274.924i	−0.500250	+	0.648405i
$425$	123.729	−	214.305i	0.291127	−	0.504247i
$426$	−77.5237	+	59.3782i	−0.181980	+	0.139386i
$427$		0			0
$428$	−459.266	−	123.922i	−1.07305	−	0.289538i
$429$	98.9402	−	171.369i	0.230630	−	0.399463i
$430$	146.094	−	351.829i	0.339752	−	0.818208i
$431$	−146.682	+	84.6868i	−0.340329	+	0.196489i	−0.660418	−	0.750899i	$-0.729621\pi$
$431$	−146.682	+	84.6868i	−0.340329	+	0.196489i	0.320088	+	0.947388i	$0.396287\pi$
$432$	−215.765	−	376.758i	−0.499457	−	0.872125i
$433$	295.214			0.681787			0.340894	−	0.940102i	$-0.389270\pi$
$433$	295.214			0.681787			0.340894	+	0.940102i	$0.389270\pi$
$434$		0			0
$435$			870.010i			2.00002i
$436$	−277.453	−	278.426i	−0.636360	−	0.638593i
$437$	−9.58244	−	16.5973i	−0.0219278	−	0.0379800i
$438$	21.9475	−	52.8550i	0.0501085	−	0.120674i
$439$	282.994	+	163.386i	0.644632	+	0.372179i	0.786397	−	0.617722i	$-0.211944\pi$
$439$	282.994	+	163.386i	0.644632	+	0.372179i	−0.141764	+	0.989900i	$0.545278\pi$
$440$	722.198	−	296.924i	1.64136	−	0.674827i
$441$		0			0
$442$	85.2153	−	65.2696i	0.192795	−	0.147669i
$443$	445.821	+	257.395i	1.00637	+	0.581026i	0.910126	−	0.414332i	$-0.135985\pi$
$443$	445.821	+	257.395i	1.00637	+	0.581026i	0.0962414	+	0.995358i	$0.469318\pi$
$444$	138.188	+	519.359i	0.311233	+	1.16973i
$445$	340.731	+	590.163i	0.765687	+	1.32621i
$446$	−524.270	+	68.5545i	−1.17549	+	0.153710i
$447$			61.9682i			0.138631i
$448$		0			0
$449$	602.217			1.34124			0.670620	−	0.741801i	$-0.266028\pi$
$449$	602.217			1.34124			0.670620	+	0.741801i	$0.266028\pi$
$450$	0.505491	+	3.86574i	0.00112331	+	0.00859053i
$451$	455.223	−	262.823i	1.00936	−	0.582757i
$452$	−374.946	+	99.7629i	−0.829526	+	0.220714i
$453$	138.952	−	240.672i	0.306738	−	0.531285i
$454$	524.548	+	684.845i	1.15539	+	1.50847i
$455$		0			0
$456$	−203.773	−	495.630i	−0.446870	−	1.08691i
$457$	132.317	−	229.180i	0.289534	−	0.501488i	−0.684164	−	0.729328i	$-0.739833\pi$
$457$	132.317	−	229.180i	0.289534	−	0.501488i	0.973699	+	0.227840i	$0.0731662\pi$
$458$	−784.830	−	325.893i	−1.71360	−	0.711556i
$459$	272.852	−	157.531i	0.594448	−	0.343205i
$460$	16.4658	−	16.4082i	0.0357952	−	0.0356701i
$461$	434.788			0.943140			0.471570	−	0.881829i	$-0.343687\pi$
$461$	434.788			0.943140			0.471570	+	0.881829i	$0.343687\pi$
$462$		0			0
$463$			193.258i			0.417403i	0.977979	+	0.208702i	$0.0669237\pi$
$463$			193.258i			0.417403i	−0.977979	+	0.208702i	$0.933076\pi$
$464$	−594.696	+	340.576i	−1.28167	+	0.734001i
$465$	15.7401	+	27.2626i	0.0338496	+	0.0586292i
$466$	−404.194	−	167.838i	−0.867370	−	0.360167i
$467$	567.503	+	327.648i	1.21521	+	0.701602i	0.963890	−	0.266301i	$-0.0858017\pi$
$467$	567.503	+	327.648i	1.21521	+	0.701602i	0.251321	+	0.967904i	$0.419135\pi$
$468$	−0.440552	+	1.63272i	−0.000941351	+	0.00348872i
$469$		0			0
$470$	349.041	+	455.705i	0.742640	+	0.969585i
$471$	−411.862	−	237.789i	−0.874441	−	0.504859i
$472$	342.023	+	263.874i	0.724626	+	0.559055i
$473$	200.721	+	347.659i	0.424357	+	0.735008i
$474$	44.1037	+	337.283i	0.0930458	+	0.711567i
$475$			478.322i			1.00699i
$476$		0			0
$477$	3.96986			0.00832256
$478$	−178.809	+	23.3814i	−0.374077	+	0.0489150i
$479$	−88.9066	+	51.3302i	−0.185609	+	0.107161i	−0.589925	−	0.807458i	$-0.700843\pi$
$479$	−88.9066	+	51.3302i	−0.185609	+	0.107161i	0.404316	+	0.914619i	$0.367509\pi$
$480$	517.396	−	393.425i	1.07791	−	0.819635i
$481$	104.040	−	180.202i	0.216298	−	0.374640i
$482$	−596.914	+	457.198i	−1.23841	+	0.948544i
$483$		0			0
$484$	−88.2725	+	327.145i	−0.182381	+	0.675919i
$485$	232.346	−	402.436i	0.479065	−	0.829764i
$486$	−3.78796	+	9.12234i	−0.00779415	+	0.0187702i
$487$	130.469	−	75.3260i	0.267903	−	0.154674i	−0.360032	−	0.932940i	$-0.617234\pi$
$487$	130.469	−	75.3260i	0.267903	−	0.154674i	0.627934	+	0.778267i	$0.283901\pi$
$488$	126.462	+	16.9872i	0.259144	+	0.0348098i
$489$	−136.783			−0.279720
$490$		0			0
$491$		−	118.795i		−	0.241946i	−0.992656	−	0.120973i	$-0.961399\pi$
$491$		−	118.795i		−	0.241946i	0.992656	−	0.120973i	$-0.0386014\pi$
$492$	309.936	−	308.852i	0.629951	−	0.627749i
$493$	−248.656	−	430.685i	−0.504373	−	0.873600i
$494$	−79.5674	+	191.618i	−0.161068	+	0.387891i
$495$	−7.73130	−	4.46367i	−0.0156188	−	0.00901751i
$496$	−12.4737	+	21.4314i	−0.0251487	+	0.0432085i
$497$		0			0
$498$	67.8047	−	51.9341i	0.136154	−	0.104285i
$499$	−473.223	−	273.215i	−0.948343	−	0.547526i	−0.0557769	−	0.998443i	$-0.517764\pi$
$499$	−473.223	−	273.215i	−0.948343	−	0.547526i	−0.892566	+	0.450917i	$0.851097\pi$
$500$	96.9937	−	25.8074i	0.193987	−	0.0516148i
$501$	23.2577	+	40.2834i	0.0464225	+	0.0804061i
$502$	−633.655	+	82.8578i	−1.26226	+	0.165055i
$503$			520.718i			1.03522i	0.855615	+	0.517612i	$0.173179\pi$
$503$			520.718i			1.03522i	−0.855615	+	0.517612i	$0.826821\pi$
$504$		0			0
$505$	191.658			0.379521
$506$	3.17604	+	24.2888i	0.00627676	+	0.0480015i
$507$	381.608	−	220.322i	0.752679	−	0.434559i
$508$	−73.9201	−	277.819i	−0.145512	−	0.546888i
$509$	300.714	−	520.851i	0.590793	−	1.02328i	−0.403333	−	0.915053i	$-0.632148\pi$
$509$	300.714	−	520.851i	0.590793	−	1.02328i	0.994126	−	0.108230i	$-0.0345183\pi$
$510$	286.810	+	374.456i	0.562372	+	0.734228i
$511$		0			0
$512$	471.468	+	199.656i	0.920835	+	0.389952i
$513$	−304.498	+	527.407i	−0.593564	+	1.02808i
$514$	−309.324	−	128.444i	−0.601798	−	0.249891i
$515$	−944.408	+	545.254i	−1.83380	+	1.05875i
$516$	235.874	+	236.701i	0.457120	+	0.458724i
$517$	−604.886			−1.16999
$518$		0			0
$519$		−	793.998i		−	1.52986i
$520$	−249.418	−	33.5033i	−0.479651	−	0.0644295i
$521$	−291.134	−	504.259i	−0.558798	−	0.967867i	−0.997597	−	0.0692818i	$-0.977929\pi$
$521$	−291.134	−	504.259i	−0.558798	−	0.967867i	0.438799	−	0.898585i	$-0.355404\pi$
$522$	7.23601	+	3.00468i	0.0138621	+	0.00575609i
$523$	124.355	+	71.7965i	0.237773	+	0.137278i	0.614153	−	0.789187i	$-0.289498\pi$
$523$	124.355	+	71.7965i	0.237773	+	0.137278i	−0.376380	+	0.926465i	$0.622831\pi$
$524$	810.367	+	218.659i	1.54650	+	0.417288i
$525$		0			0
$526$	104.743	+	136.751i	0.199130	+	0.259983i
$527$	−15.5837	−	8.99728i	−0.0295707	−	0.0170726i
$528$	−2.39906	+	684.935i	−0.00454367	+	1.29723i
$529$	−264.135	−	457.496i	−0.499311	−	0.864832i
$530$	76.5973	+	585.778i	0.144523	+	1.10524i
$531$		−	4.93877i		−	0.00930088i
$532$		0			0
$533$	−169.409			−0.317840
$534$	−592.710	+	77.5038i	−1.10994	+	0.145138i
$535$	−700.884	+	404.656i	−1.31006	+	0.756366i
$536$	582.382	+	449.313i	1.08653	+	0.838271i
$537$	66.4188	−	115.041i	0.123685	−	0.214229i
$538$	−427.656	+	327.557i	−0.794899	+	0.608842i
$539$		0			0
$540$	−713.160	−	192.430i	−1.32067	−	0.356352i
$541$	−416.548	+	721.483i	−0.769960	+	1.33361i	0.167624	+	0.985851i	$0.446391\pi$
$541$	−416.548	+	721.483i	−0.769960	+	1.33361i	−0.937584	+	0.347759i	$0.886943\pi$
$542$	244.145	−	587.961i	0.450452	−	1.08480i
$543$	−434.539	+	250.881i	−0.800256	+	0.462028i
$544$	−143.685	+	342.635i	−0.264127	+	0.629844i
$545$	−668.740			−1.22705
$546$		0			0
$547$			356.858i			0.652391i	0.945302	+	0.326196i	$0.105767\pi$
$547$			356.858i			0.652391i	−0.945302	+	0.326196i	$0.894233\pi$
$548$	−51.2882	−	51.4681i	−0.0935916	−	0.0939200i
$549$	−0.729401	−	1.26336i	−0.00132860	−	0.00230120i
$550$	234.454	−	564.624i	0.426280	−	1.02659i
$551$	832.489	+	480.638i	1.51087	+	0.872301i
$552$	7.75347	+	18.8585i	0.0140461	+	0.0341640i
$553$		0			0
$554$	566.195	−	433.669i	1.02201	−	0.782796i
$555$	791.850	+	457.175i	1.42676	+	0.823738i
$556$	137.907	+	518.304i	0.248034	+	0.932202i
$557$	−162.430	−	281.336i	−0.291615	−	0.505092i	0.682577	−	0.730814i	$-0.260859\pi$
$557$	−162.430	−	281.336i	−0.291615	−	0.505092i	−0.974192	+	0.225722i	$0.927526\pi$
$558$	0.281108	−	0.0367581i	0.000503777	−	6.58748e-5i
$559$		−	129.379i		−	0.231447i
$560$		0			0
$561$	−497.040			−0.885989
$562$	28.4848	+	217.837i	0.0506847	+	0.387611i
$563$	−73.8314	+	42.6266i	−0.131139	+	0.0757133i	−0.564134	−	0.825683i	$-0.690790\pi$
$563$	−73.8314	+	42.6266i	−0.131139	+	0.0757133i	0.432995	+	0.901396i	$0.357457\pi$
$564$	−486.580	+	129.466i	−0.862731	+	0.229549i
$565$	−330.052	+	571.667i	−0.584163	+	1.01180i
$566$	−625.800	−	817.039i	−1.10565	−	1.44353i
$567$		0			0
$568$	−121.037	+	49.7632i	−0.213094	+	0.0876112i
$569$	14.3756	−	24.8993i	0.0252647	−	0.0437597i	−0.853117	−	0.521720i	$-0.825290\pi$
$569$	14.3756	−	24.8993i	0.0252647	−	0.0437597i	0.878381	+	0.477961i	$0.158624\pi$
$570$	−842.015	−	349.638i	−1.47722	−	0.613400i
$571$	−586.760	+	338.766i	−1.02760	+	0.593286i	−0.916296	−	0.400501i	$-0.868836\pi$
$571$	−586.760	+	338.766i	−1.02760	+	0.593286i	−0.111304	+	0.993786i	$0.535503\pi$
$572$	187.847	−	187.190i	0.328404	−	0.327255i
$573$	1055.42			1.84191
$574$		0			0
$575$		−	18.2000i		−	0.0316521i
$576$	−1.48529	−	5.66201i	−0.00257863	−	0.00982988i
$577$	−10.3338	−	17.8986i	−0.0179095	−	0.0310201i	0.856932	−	0.515430i	$-0.172368\pi$
$577$	−10.3338	−	17.8986i	−0.0179095	−	0.0310201i	−0.874841	+	0.484410i	$0.839034\pi$
$578$	284.805	+	118.262i	0.492742	+	0.204606i
$579$	−901.009	−	520.198i	−1.55615	−	0.898441i
$580$	−303.743	+	1125.69i	−0.523694	+	1.94085i
$581$		0			0
$582$	247.856	+	323.598i	0.425869	+	0.556011i
$583$	−539.129	−	311.266i	−0.924750	−	0.533905i
$584$	46.8506	−	60.7259i	0.0802237	−	0.103983i
$585$	1.43858	+	2.49169i	0.00245911	+	0.00425930i
$586$	34.4895	+	263.758i	0.0588557	+	0.450099i
$587$		−	551.489i		−	0.939504i	−0.882798	−	0.469752i	$-0.844343\pi$
$587$		−	551.489i		−	0.939504i	0.882798	−	0.469752i	$-0.155657\pi$
$588$		0			0
$589$	34.7825			0.0590534
$590$	728.746	−	95.2921i	1.23516	−	0.161512i
$591$	69.6133	−	40.1912i	0.117789	−	0.0680055i
$592$	−2.52271	+	720.237i	−0.00426133	+	1.21662i
$593$	22.9656	−	39.7776i	0.0387279	−	0.0670787i	−0.846012	−	0.533164i	$-0.821003\pi$
$593$	22.9656	−	39.7776i	0.0387279	−	0.0670787i	0.884740	+	0.466086i	$0.154336\pi$
$594$	617.951	−	473.311i	1.04032	−	0.796821i
$595$		0			0
$596$	−21.6347	+	80.1798i	−0.0362998	+	0.134530i
$597$	345.570	−	598.545i	0.578845	−	1.00259i
$598$	3.02751	−	7.29099i	0.00506272	−	0.0121923i
$599$	573.698	−	331.225i	0.957759	−	0.552963i	0.0622766	−	0.998059i	$-0.480164\pi$
$599$	573.698	−	331.225i	0.957759	−	0.552963i	0.895483	+	0.445096i	$0.146831\pi$
$600$	67.7505	−	504.374i	0.112917	−	0.840623i
$601$	840.257			1.39810			0.699049	−	0.715074i	$-0.253607\pi$
$601$	840.257			1.39810			0.699049	+	0.715074i	$0.253607\pi$
$602$		0			0
$603$		−	8.40952i		−	0.0139461i
$604$	263.813	−	262.891i	0.436776	−	0.435249i
$605$	288.245	+	499.255i	0.476438	+	0.825215i
$606$	−64.4713	+	155.263i	−0.106388	+	0.256209i
$607$	−887.606	−	512.459i	−1.46228	−	0.844249i	−0.463166	−	0.886272i	$-0.653287\pi$
$607$	−887.606	−	512.459i	−1.46228	−	0.844249i	−0.999117	+	0.0420222i	$0.986620\pi$
$608$	−90.6218	−	712.431i	−0.149049	−	1.17176i
$609$		0			0
$610$	172.343	−	132.004i	0.282530	−	0.216400i
$611$	168.828	+	97.4732i	0.276315	+	0.159531i
$612$	4.10495	−	1.09222i	0.00670743	−	0.00178467i
$613$	54.5739	+	94.5248i	0.0890276	+	0.154200i	0.907100	−	0.420914i	$-0.138291\pi$
$613$	54.5739	+	94.5248i	0.0890276	+	0.154200i	−0.818073	+	0.575115i	$0.804957\pi$
$614$	759.159	−	99.2690i	1.23642	−	0.161676i
$615$		−	744.422i		−	1.21044i
$616$		0			0
$617$	78.9177			0.127905			0.0639527	−	0.997953i	$-0.479629\pi$
$617$	78.9177			0.127905			0.0639527	+	0.997953i	$0.479629\pi$
$618$	−124.025	−	948.484i	−0.200688	−	1.53476i
$619$	−620.070	+	357.997i	−1.00173	+	0.578348i	−0.908759	−	0.417321i	$-0.862969\pi$
$619$	−620.070	+	357.997i	−1.00173	+	0.578348i	−0.0929689	+	0.995669i	$0.529636\pi$
$620$	10.8478	+	40.7699i	0.0174964	+	0.0657580i
$621$	11.5860	−	20.0676i	0.0186571	−	0.0323150i
$622$	−238.816	−	311.796i	−0.383949	−	0.501281i
$623$		0			0
$624$	111.042	−	190.784i	0.177952	−	0.305744i
$625$	351.791	−	609.321i	0.562866	−	0.974913i
$626$	788.790	+	327.537i	1.26005	+	0.523222i
$627$	832.033	−	480.375i	1.32701	−	0.766148i
$628$	−449.884	−	451.463i	−0.716376	−	0.718890i
$629$	−522.657			−0.830933
$630$		0			0
$631$			849.316i			1.34598i	0.739650	+	0.672992i	$0.234991\pi$
$631$			849.316i			1.34598i	−0.739650	+	0.672992i	$0.765009\pi$
$632$	−60.6889	+	451.803i	−0.0960267	+	0.714878i
$633$	118.927	+	205.987i	0.187878	+	0.325414i
$634$	−205.118	−	85.1732i	−0.323530	−	0.134343i
$635$	−423.581	−	244.555i	−0.667057	−	0.385126i
$636$	−500.306	−	134.996i	−0.786645	−	0.212258i
$637$		0			0
$638$	−747.102	−	975.409i	−1.17101	−	1.52885i
$639$	1.29573	+	0.748092i	0.00202775	+	0.00117072i
$640$	806.806	−	328.411i	1.26064	−	0.513142i
$641$	−244.045	−	422.698i	−0.380725	−	0.659435i	0.610441	−	0.792062i	$-0.290992\pi$
$641$	−244.045	−	422.698i	−0.380725	−	0.659435i	−0.991166	+	0.132627i	$0.957659\pi$
$642$	−92.0444	−	703.909i	−0.143371	−	1.09643i
$643$			257.106i			0.399854i	0.979811	+	0.199927i	$0.0640705\pi$
$643$			257.106i			0.399854i	−0.979811	+	0.199927i	$0.935930\pi$
$644$		0			0
$645$	568.522			0.881430
$646$	516.756	−	67.5719i	0.799932	−	0.104600i
$647$	605.816	−	349.768i	0.936346	−	0.540600i	0.0475329	−	0.998870i	$-0.484864\pi$
$647$	605.816	−	349.768i	0.936346	−	0.540600i	0.888813	+	0.458270i	$0.151531\pi$
$648$	391.763	−	507.788i	0.604573	−	0.783624i
$649$	−387.236	+	670.713i	−0.596666	+	1.03346i
$650$	−156.423	+	119.810i	−0.240651	+	0.184324i
$651$		0			0
$652$	−176.981	−	47.7544i	−0.271444	−	0.0732429i
$653$	−138.815	+	240.434i	−0.212580	+	0.368199i	−0.952521	−	0.304472i	$-0.901520\pi$
$653$	−138.815	+	240.434i	−0.212580	+	0.368199i	0.739941	+	0.672671i	$0.234853\pi$
$654$	224.955	−	541.748i	0.343968	−	0.828360i
$655$	1236.70	−	714.009i	1.88809	−	1.09009i
$656$	508.850	−	291.413i	0.775686	−	0.444228i
$657$	−0.876874			−0.00133466
$658$		0			0
$659$		−	522.721i		−	0.793204i	−0.917991	−	0.396602i	$-0.870189\pi$
$659$		−	522.721i		−	0.793204i	0.917991	−	0.396602i	$-0.129811\pi$
$660$	822.557	+	825.443i	1.24630	+	1.25067i
$661$	257.961	+	446.802i	0.390259	+	0.675948i	0.992484	−	0.122378i	$-0.0390521\pi$
$661$	257.961	+	446.802i	0.390259	+	0.675948i	−0.602224	+	0.798327i	$0.705719\pi$
$662$	91.7533	−	220.964i	0.138600	−	0.333783i
$663$	138.728	+	80.0945i	0.209243	+	0.120806i
$664$	105.863	−	43.5245i	0.159432	−	0.0655489i
$665$		0			0
$666$	6.53714	−	5.00704i	0.00981553	−	0.00751807i
$667$	−31.6759	−	18.2881i	−0.0474901	−	0.0274184i
$668$	16.0288	+	60.2420i	0.0239952	+	0.0901827i
$669$	−394.530	−	683.346i	−0.589731	−	1.02144i
$670$	1240.88	−	162.259i	1.85206	−	0.242178i
$671$			228.762i			0.340927i
$672$		0			0
$673$	−1231.64			−1.83008			−0.915041	−	0.403361i	$-0.867842\pi$
$673$	−1231.64			−1.83008			−0.915041	+	0.403361i	$0.867842\pi$
$674$	−14.8753	−	113.759i	−0.0220702	−	0.168781i
$675$	−500.853	+	289.167i	−0.742004	+	0.428396i
$676$	570.677	−	151.842i	0.844197	−	0.224618i
$677$	−288.282	+	499.319i	−0.425822	+	0.737546i	−0.996497	−	0.0836304i	$-0.973348\pi$
$677$	−288.282	+	499.319i	−0.425822	+	0.737546i	0.570674	+	0.821176i	$0.306682\pi$
$678$	−352.084	−	459.677i	−0.519297	−	0.677990i
$679$		0			0
$680$	240.367	+	584.637i	0.353481	+	0.859760i
$681$	−643.690	+	1114.90i	−0.945213	+	1.63716i
$682$	−41.0581	−	17.0490i	−0.0602025	−	0.0249985i
$683$	−139.772	+	80.6973i	−0.204644	+	0.118151i	−0.598820	−	0.800884i	$-0.704363\pi$
$683$	−139.772	+	80.6973i	−0.204644	+	0.118151i	0.394176	+	0.919035i	$0.371030\pi$
$684$	−5.81599	+	5.79566i	−0.00850292	+	0.00847318i
$685$	−123.619			−0.180466
$686$		0			0
$687$		−	1268.21i		−	1.84601i
$688$	222.555	+	388.614i	0.323482	+	0.564846i
$689$	100.317	+	173.754i	0.145598	+	0.252183i
$690$	32.0383	+	13.3036i	0.0464324	+	0.0192806i
$691$	−98.4337	−	56.8307i	−0.142451	−	0.0822442i	0.427081	−	0.904214i	$-0.359542\pi$
$691$	−98.4337	−	56.8307i	−0.142451	−	0.0822442i	−0.569532	+	0.821969i	$0.692875\pi$
$692$	277.205	−	1027.34i	0.400585	−	1.48460i
$693$		0			0
$694$	326.865	+	426.753i	0.470988	+	0.614917i
$695$	790.241	+	456.246i	1.13704	+	0.656469i
$696$	−809.752	−	624.731i	−1.16344	−	0.897602i
$697$	212.762	+	368.514i	0.305254	+	0.528715i
$698$	−25.1666	−	192.461i	−0.0360552	−	0.275732i
$699$		−	653.140i		−	0.934391i
$700$		0			0
$701$	331.011			0.472198			0.236099	−	0.971729i	$-0.424131\pi$
$701$	331.011			0.472198			0.236099	+	0.971729i	$0.424131\pi$
$702$	−248.746	+	32.5265i	−0.354339	+	0.0463340i
$703$	874.916	−	505.133i	1.24455	−	0.718539i
$704$	−242.232	+	885.391i	−0.344080	+	1.25766i
$705$	−428.320	+	741.872i	−0.607546	+	1.05230i
$706$	503.210	−	385.427i	0.712761	−	0.545930i
$707$		0			0
$708$	−167.944	+	622.414i	−0.237209	+	0.879116i
$709$	295.675	−	512.125i	0.417032	−	0.722320i	−0.578608	−	0.815606i	$-0.696404\pi$
$709$	295.675	−	512.125i	0.417032	−	0.722320i	0.995639	+	0.0932861i	$0.0297371\pi$
$710$	−85.3848	+	205.628i	−0.120260	+	0.289616i
$711$	4.51351	−	2.60588i	0.00634812	−	0.00366509i
$712$	−793.958	−	106.649i	−1.11511	−	0.149788i
$713$	−1.32346			−0.00185618
$714$		0			0
$715$		−	451.181i		−	0.631022i
$716$	126.102	−	125.661i	0.176120	−	0.175504i
$717$	−134.559	−	233.064i	−0.187670	−	0.325054i
$718$	−452.669	+	1090.14i	−0.630459	+	1.51830i
$719$	−418.810	−	241.800i	−0.582489	−	0.336300i	0.179633	−	0.983734i	$-0.442509\pi$
$719$	−418.810	−	241.800i	−0.582489	−	0.336300i	−0.762122	+	0.647433i	$0.775842\pi$
$720$	−8.60719	−	5.00964i	−0.0119544	−	0.00695784i
$721$		0			0
$722$	−226.545	+	173.519i	−0.313775	+	0.240332i
$723$	−971.756	−	561.044i	−1.34406	−	0.775994i
$724$	−649.833	+	172.903i	−0.897559	+	0.238816i
$725$	456.438	+	790.575i	0.629570	+	1.09045i
$726$	−501.409	+	65.5652i	−0.690646	+	0.0903101i
$727$			659.508i			0.907163i	0.891215	+	0.453582i	$0.149854\pi$
$727$			659.508i			0.907163i	−0.891215	+	0.453582i	$0.850146\pi$
$728$		0			0
$729$	−736.257			−1.00995
$730$	−16.9190	−	129.388i	−0.0231768	−	0.177244i
$731$	−281.438	+	162.488i	−0.385004	+	0.222282i
$732$	48.9627	+	184.020i	0.0668890	+	0.251393i
$733$	105.888	−	183.403i	0.144458	−	0.250209i	−0.784713	−	0.619860i	$-0.787189\pi$
$733$	105.888	−	183.403i	0.144458	−	0.250209i	0.929171	+	0.369651i	$0.120523\pi$
$734$	213.484	+	278.723i	0.290851	+	0.379732i
$735$		0			0
$736$	3.44812	+	27.1077i	0.00468495	+	0.0368311i
$737$	−659.369	+	1142.06i	−0.894666	+	1.54961i
$738$	−6.19148	−	2.57095i	−0.00838953	−	0.00348367i
$739$	213.832	−	123.456i	0.289353	−	0.167058i	−0.348297	−	0.937384i	$-0.613240\pi$
$739$	213.832	−	123.456i	0.289353	−	0.167058i	0.637650	+	0.770326i	$0.279907\pi$
$740$	864.952	+	867.987i	1.16885	+	1.17296i
$741$	−309.636			−0.417863
$742$		0			0
$743$			333.126i			0.448352i	0.974549	+	0.224176i	$0.0719691\pi$
$743$			333.126i			0.448352i	−0.974549	+	0.224176i	$0.928031\pi$
$744$	−36.6769	−	4.92665i	−0.0492969	−	0.00662185i
$745$	70.6459	+	122.362i	0.0948267	+	0.164245i
$746$	−1023.32	−	424.922i	−1.37174	−	0.569600i
$747$	−1.13329	−	0.654305i	−0.00151712	−	0.000875911i
$748$	−643.113	−	173.529i	−0.859776	−	0.231991i
$749$		0			0
$750$	91.0796	+	118.913i	0.121439	+	0.158550i
$751$	528.203	+	304.958i	0.703333	+	0.406069i	0.808588	−	0.588376i	$-0.200232\pi$
$751$	528.203	+	304.958i	0.703333	+	0.406069i	−0.105255	+	0.994445i	$0.533566\pi$
$752$	−674.779	−	2.36349i	−0.897313	−	0.00314293i
$753$	−476.845	−	825.920i	−0.633261	−	1.09684i
$754$	51.3416	+	392.635i	0.0680924	+	0.520736i
$755$		−	633.640i		−	0.839259i
$756$		0			0
$757$	439.344			0.580375			0.290187	−	0.956970i	$-0.406282\pi$
$757$	439.344			0.580375			0.290187	+	0.956970i	$0.406282\pi$
$758$	1487.16	−	194.463i	1.96195	−	0.256548i
$759$	−31.6585	+	18.2781i	−0.0417108	+	0.0240818i
$760$	−967.404	−	746.361i	−1.27290	−	0.982054i
$761$	−230.484	+	399.210i	−0.302870	+	0.524586i	−0.976785	−	0.214223i	$-0.931278\pi$
$761$	−230.484	+	399.210i	−0.302870	+	0.524586i	0.673915	+	0.738809i	$0.264611\pi$
$762$	340.601	−	260.879i	0.446984	−	0.342361i
$763$		0			0
$764$	1365.59	+	368.473i	1.78742	+	0.482294i
$765$	3.61345	−	6.25867i	0.00472346	−	0.00818127i
$766$	−188.855	+	454.809i	−0.246547	+	0.593746i
$767$	216.161	−	124.801i	0.281827	−	0.162713i
$768$	−5.35253	+	764.069i	−0.00696944	+	0.994881i
$769$	−1431.37			−1.86134			−0.930670	−	0.365859i	$-0.880775\pi$
$769$	−1431.37			−1.86134			−0.930670	+	0.365859i	$0.880775\pi$
$770$		0			0
$771$		−	499.838i		−	0.648299i
$772$	−984.188	−	987.641i	−1.27486	−	1.27933i
$773$	122.740	+	212.592i	0.158784	+	0.275022i	0.934430	−	0.356146i	$-0.115909\pi$
$773$	122.740	+	212.592i	0.158784	+	0.275022i	−0.775646	+	0.631168i	$0.782576\pi$
$774$	1.96346	−	4.72849i	0.00253677	−	0.00610916i
$775$	28.6059	+	16.5156i	0.0369108	+	0.0213105i
$776$	207.721	+	505.232i	0.267681	+	0.651073i
$777$		0			0
$778$	473.186	−	362.431i	0.608208	−	0.465849i
$779$	−712.317	−	411.256i	−0.914399	−	0.527929i
$780$	−96.5678	−	362.937i	−0.123805	−	0.465304i
$781$	−117.312	−	203.190i	−0.150207	−	0.260167i
$782$	−19.6624	+	2.57108i	−0.0251437	+	0.00328783i
$783$			1162.27i			1.48438i
$784$		0			0
$785$	−1084.35			−1.38134
$786$	162.411	+	1242.04i	0.206630	+	1.58020i
$787$	−502.289	+	289.997i	−0.638232	+	0.368483i	−0.783933	−	0.620845i	$-0.786790\pi$
$787$	−502.289	+	289.997i	−0.638232	+	0.368483i	0.145701	+	0.989329i	$0.453456\pi$
$788$	104.103	−	27.6991i	0.132111	−	0.0351512i
$789$	−128.533	+	222.626i	−0.162907	+	0.282162i
$790$	471.601	+	615.718i	0.596963	+	0.779389i
$791$		0			0
$792$	9.70615	−	3.99058i	0.0122552	−	0.00503861i
$793$	36.8634	−	63.8493i	0.0464860	−	0.0805161i
$794$	236.100	+	98.0379i	0.297355	+	0.123473i
$795$	−763.516	+	440.816i	−0.960397	+	0.554486i
$796$	656.096	−	653.802i	0.824241	−	0.821359i
$797$	1348.22			1.69162			0.845810	−	0.533484i	$-0.179118\pi$
$797$	1348.22			1.69162			0.845810	+	0.533484i	$0.179118\pi$
$798$		0			0
$799$		−	489.670i		−	0.612853i
$800$	263.751	−	628.949i	0.329689	−	0.786186i
$801$	4.57933	+	7.93164i	0.00571702	+	0.00990217i
$802$	1430.18	+	593.866i	1.78326	+	0.740481i
$803$	119.084	+	68.7534i	0.148299	+	0.0856207i
$804$	−285.968	+	1059.82i	−0.355682	+	1.31818i
$805$		0			0
$806$	8.71232	+	11.3747i	0.0108093	+	0.0141126i
$807$	−696.209	−	401.957i	−0.862713	−	0.498088i
$808$	−137.625	+	178.384i	−0.170328	+	0.220772i
$809$	348.732	+	604.022i	0.431066	+	0.746628i	0.996965	−	0.0778461i	$-0.0248043\pi$
$809$	348.732	+	604.022i	0.431066	+	0.746628i	−0.565899	+	0.824474i	$0.691471\pi$
$810$	−141.476	−	1081.94i	−0.174662	−	1.33573i
$811$			482.271i			0.594662i	0.954774	+	0.297331i	$0.0960965\pi$
$811$			482.271i			0.594662i	−0.954774	+	0.297331i	$0.903903\pi$
$812$		0			0
$813$	950.089			1.16862
$814$	−1280.37	+	167.423i	−1.57294	+	0.205680i
$815$	−270.091	+	155.937i	−0.331400	+	0.191334i
$816$	−554.472	−	1.94210i	−0.679500	−	0.00238002i
$817$	314.081	−	544.004i	0.384432	−	0.665855i
$818$	−1058.86	+	811.020i	−1.29445	+	0.991467i
$819$		0			0
$820$	259.897	−	963.197i	0.316947	−	1.17463i
$821$	193.173	−	334.585i	0.235289	−	0.407533i	−0.724067	−	0.689729i	$-0.757730\pi$
$821$	193.173	−	334.585i	0.235289	−	0.407533i	0.959357	+	0.282196i	$0.0910629\pi$
$822$	41.5838	−	100.144i	0.0505886	−	0.121830i
$823$	−306.907	+	177.193i	−0.372913	+	0.215301i	−0.674730	−	0.738064i	$-0.735740\pi$
$823$	−306.907	+	177.193i	−0.372913	+	0.215301i	0.301817	+	0.953366i	$0.402407\pi$
$824$	170.665	−	1270.53i	0.207118	−	1.54191i
$825$	912.377			1.10591
$826$		0			0
$827$			1260.47i			1.52414i	0.647493	+	0.762072i	$0.275818\pi$
$827$			1260.47i			1.52414i	−0.647493	+	0.762072i	$0.724182\pi$
$828$	0.221296	−	0.220522i	0.000267266	−	0.000266332i
$829$	−721.843	−	1250.27i	−0.870739	−	1.50816i	−0.861234	−	0.508209i	$-0.830308\pi$
$829$	−721.843	−	1250.27i	−0.870739	−	1.50816i	−0.00950526	−	0.999955i	$-0.503026\pi$
$830$	74.6803	−	179.849i	0.0899763	−	0.216685i
$831$	921.746	+	532.170i	1.10920	+	0.640398i
$832$	210.284	−	208.086i	0.252745	−	0.250103i
$833$		0			0
$834$	−635.432	+	486.701i	−0.761909	+	0.583574i
$835$	91.8490	+	53.0290i	0.109999	+	0.0635078i
$836$	1244.27	−	331.066i	1.48836	−	0.396012i
$837$	21.0276	+	36.4208i	0.0251226	+	0.0435135i
$838$	189.117	−	24.7293i	0.225676	−	0.0295099i
$839$			44.6511i			0.0532194i	0.999646	+	0.0266097i	$0.00847114\pi$
$839$			44.6511i			0.0532194i	−0.999646	+	0.0266097i	$0.991529\pi$
$840$		0			0
$841$	993.593			1.18144
$842$	−72.3901	−	553.603i	−0.0859740	−	0.657485i
$843$	−283.934	+	163.930i	−0.336814	+	0.194460i
$844$	81.9621	+	308.044i	0.0971115	+	0.364981i
$845$	502.348	−	870.092i	0.594495	−	1.02970i
$846$	4.69102	+	6.12455i	0.00554494	+	0.00723942i
$847$		0			0
$848$	−600.208	−	349.339i	−0.707793	−	0.411957i
$849$	767.941	−	1330.11i	0.904524	−	1.56668i
$850$	457.077	+	189.796i	0.537737	+	0.223290i
$851$	−33.2902	+	19.2201i	−0.0391189	+	0.0225853i
$852$	−137.857	−	138.341i	−0.161804	−	0.162372i
$853$	118.167			0.138531			0.0692655	−	0.997598i	$-0.477934\pi$
$853$	118.167			0.138531			0.0692655	+	0.997598i	$0.477934\pi$
$854$		0			0
$855$			13.9692i			0.0163382i
$856$	126.658	−	942.913i	0.147964	−	1.10153i
$857$	−76.5651	−	132.615i	−0.0893408	−	0.154743i	0.817892	−	0.575372i	$-0.195143\pi$
$857$	−76.5651	−	132.615i	−0.0893408	−	0.154743i	−0.907233	+	0.420629i	$0.861809\pi$
$858$	365.503	+	151.771i	0.425994	+	0.176890i
$859$	118.348	+	68.3281i	0.137774	+	0.0795437i	0.567303	−	0.823509i	$-0.307987\pi$
$859$	118.348	+	68.3281i	0.137774	+	0.0795437i	−0.429529	+	0.903053i	$0.641320\pi$
$860$	735.603	+	198.486i	0.855353	+	0.230797i
$861$		0			0
$862$	−205.981	−	268.927i	−0.238957	−	0.311980i
$863$	−1266.58	−	731.262i	−1.46765	−	0.847349i	−0.468308	−	0.883565i	$-0.655136\pi$
$863$	−1266.58	−	731.262i	−1.46765	−	0.847349i	−0.999344	+	0.0362164i	$0.988469\pi$
$864$	691.204	−	525.587i	0.800004	−	0.608319i
$865$	−905.185	−	1567.83i	−1.04646	−	1.81252i
$866$	76.5537	+	585.444i	0.0883992	+	0.676032i
$867$			460.217i			0.530816i
$868$		0			0
$869$	−817.281			−0.940484
$870$	−1725.33	+	225.607i	−1.98314	+	0.259319i
$871$	368.070	−	212.505i	0.422584	−	0.243979i
$872$	480.204	−	622.422i	0.550693	−	0.713787i
$873$	3.12267	−	5.40863i	0.00357695	−	0.00619545i
$874$	30.4295	−	23.3070i	0.0348163	−	0.0266671i
$875$		0			0
$876$	110.509	+	29.8183i	0.126152	+	0.0340392i
$877$	−14.9440	+	25.8838i	−0.0170399	+	0.0295140i	−0.874420	−	0.485170i	$-0.838758\pi$
$877$	−14.9440	+	25.8838i	−0.0170399	+	0.0295140i	0.857380	+	0.514684i	$0.172091\pi$
$878$	−250.630	+	603.578i	−0.285455	+	0.687447i
$879$	−343.788	+	198.486i	−0.391113	+	0.225809i
$880$	776.112	+	1355.21i	0.881946	+	1.54001i
$881$	497.832			0.565076			0.282538	−	0.959256i	$-0.408824\pi$
$881$	497.832			0.565076			0.282538	+	0.959256i	$0.408824\pi$
$882$		0			0
$883$			1430.98i			1.62059i	0.586022	+	0.810295i	$0.300693\pi$
$883$			1430.98i			1.62059i	−0.586022	+	0.810295i	$0.699307\pi$
$884$	151.535	+	152.067i	0.171420	+	0.172021i
$885$	548.405	+	949.865i	0.619666	+	1.07329i
$886$	−394.836	+	950.862i	−0.445638	+	1.07321i
$887$	−1028.15	−	593.605i	−1.15914	−	0.669228i	−0.208040	−	0.978120i	$-0.566708\pi$
$887$	−1028.15	−	593.605i	−1.15914	−	0.669228i	−0.951097	+	0.308892i	$0.900042\pi$
$888$	−994.117	+	408.720i	−1.11950	+	0.460271i
$889$		0			0
$890$	−1082.01	+	828.748i	−1.21574	+	0.931178i
$891$	995.780	+	574.914i	1.11760	+	0.645245i
$892$	−271.903	−	1021.91i	−0.304824	−	1.14564i
$893$	473.252	+	819.696i	0.529957	+	0.917913i
$894$	−122.890	+	16.0693i	−0.137461	+	0.0179747i
$895$		−	302.879i		−	0.338412i
$896$		0			0
$897$	11.7815			0.0131344
$898$	156.164	+	1194.27i	0.173902	+	1.32992i
$899$	57.4887	−	33.1911i	0.0639474	−	0.0369201i
$900$	−7.53514	+	2.00490i	−0.00837237	+	0.00222766i
$901$	251.978	−	436.438i	0.279665	−	0.484393i
$902$	639.256	+	834.607i	0.708709	+	0.925285i
$903$		0			0
$904$	−295.071	−	717.691i	−0.326406	−	0.793906i
$905$	−572.026	+	990.778i	−0.632073	+	1.09478i
$906$	513.314	+	213.148i	0.566571	+	0.235263i
$907$	−708.980	+	409.330i	−0.781676	+	0.451301i	−0.837024	−	0.547166i	$-0.815706\pi$
$907$	−708.980	+	409.330i	−0.781676	+	0.451301i	0.0553481	+	0.998467i	$0.482373\pi$
$908$	−1222.10	+	1217.83i	−1.34593	+	1.34122i
$909$	2.57584			0.00283370
$910$		0			0
$911$			774.905i			0.850610i	0.905050	+	0.425305i	$0.139833\pi$
$911$			774.905i			0.850610i	−0.905050	+	0.425305i	$0.860167\pi$
$912$	930.050	−	532.630i	1.01979	−	0.584024i
$913$	102.605	+	177.717i	0.112382	+	0.194651i
$914$	488.803	+	202.970i	0.534795	+	0.222068i
$915$	280.569	+	161.986i	0.306633	+	0.177034i
$916$	442.765	−	1640.92i	0.483367	−	1.79140i
$917$		0			0
$918$	383.157	+	500.247i	0.417383	+	0.544931i
$919$	1468.77	+	847.993i	1.59822	+	0.922734i	0.991830	+	0.127569i	$0.0407175\pi$
$919$	1468.77	+	847.993i	1.59822	+	0.922734i	0.606393	+	0.795165i	$0.292616\pi$
$920$	36.8093	+	28.3987i	0.0400101	+	0.0308682i
$921$	571.291	+	989.506i	0.620295	+	1.07438i
$922$	112.747	+	862.235i	0.122286	+	0.935179i
$923$			75.6160i			0.0819241i
$924$		0			0
$925$	959.401			1.03719
$926$	−383.253	+	50.1148i	−0.413880	+	0.0541196i
$927$	−12.6926	+	7.32808i	−0.0136921	+	0.00790515i
$928$	−829.617	−	1091.04i	−0.893984	−	1.17568i
$929$	−586.655	+	1016.12i	−0.631491	+	1.09378i	0.355756	+	0.934579i	$0.384224\pi$
$929$	−586.655	+	1016.12i	−0.631491	+	1.09378i	−0.987247	+	0.159196i	$0.949110\pi$
$930$	−49.9833	+	38.2840i	−0.0537455	+	0.0411656i
$931$		0			0
$932$	228.028	−	845.088i	0.244665	−	0.906747i
$933$	293.060	−	507.594i	0.314105	−	0.544046i
$934$	−502.602	+	1210.39i	−0.538118	+	1.29592i
$935$	−981.453	+	566.642i	−1.04968	+	0.606034i
$936$	−3.35212	−	0.450276i	−0.00358132	−	0.000481064i
$937$	315.505			0.336719			0.168359	−	0.985726i	$-0.446153\pi$
$937$	315.505			0.336719			0.168359	+	0.985726i	$0.446153\pi$
$938$		0			0
$939$			1274.61i			1.35741i
$940$	−813.204	+	810.361i	−0.865111	+	0.862086i
$941$	−211.752	−	366.766i	−0.225029	−	0.389762i	0.731299	−	0.682057i	$-0.238914\pi$
$941$	−211.752	−	366.766i	−0.225029	−	0.389762i	−0.956328	+	0.292295i	$0.905581\pi$
$942$	364.760	−	878.433i	0.387219	−	0.932519i
$943$	27.1034	+	15.6481i	0.0287417	+	0.0165940i
$944$	−434.601	+	746.699i	−0.460383	+	0.790995i
$945$		0			0
$946$	−637.398	+	488.206i	−0.673782	+	0.516074i
$947$	993.572	+	573.639i	1.04918	+	0.605743i	0.922419	−	0.386190i	$-0.126209\pi$
$947$	993.572	+	573.639i	1.04918	+	0.605743i	0.126759	+	0.991934i	$0.459542\pi$
$948$	−657.434	+	174.926i	−0.693496	+	0.184521i
$949$	−22.1583	−	38.3793i	−0.0233491	−	0.0404418i
$950$	−948.569	+	124.037i	−0.998493	+	0.130565i
$951$		−	331.451i		−	0.348529i
$952$		0			0
$953$	736.494			0.772816			0.386408	−	0.922328i	$-0.373716\pi$
$953$	736.494			0.772816			0.386408	+	0.922328i	$0.373716\pi$
$954$	1.02945	+	7.87270i	0.00107909	+	0.00825230i
$955$	2084.02	−	1203.21i	2.18222	−	1.25991i
$956$	−92.7361	−	348.536i	−0.0970042	−	0.364577i
$957$	916.794	−	1587.93i	0.957988	−	1.65928i
$958$	−124.849	−	163.001i	−0.130322	−	0.170148i
$959$		0			0
$960$	914.377	+	924.036i	0.952476	+	0.962538i
$961$	−479.299	+	830.170i	−0.498750	+	0.863861i
$962$	384.341	+	159.593i	0.399522	+	0.165898i
$963$	−9.41970	+	5.43847i	−0.00978162	+	0.00564742i
$964$	−1061.47	−	1065.19i	−1.10111	−	1.10497i
$965$	−2372.17			−2.45821
$966$		0			0
$967$		−	1147.66i		−	1.18682i	−0.804899	−	0.593411i	$-0.797781\pi$
$967$		−	1147.66i		−	1.18682i	0.804899	−	0.593411i	$-0.202219\pi$
$968$	−671.657	−	90.2209i	−0.693860	−	0.0932034i
$969$	388.875	+	673.551i	0.401316	+	0.695099i
$970$	858.329	+	356.412i	0.884875	+	0.367435i
$971$	960.111	+	554.321i	0.988786	+	0.570876i	0.904911	−	0.425600i	$-0.139937\pi$
$971$	960.111	+	554.321i	0.988786	+	0.570876i	0.0838750	+	0.996476i	$0.473270\pi$
$972$	−19.0730	−	5.14640i	−0.0196224	−	0.00529465i
$973$		0			0
$974$	183.213	+	239.201i	0.188104	+	0.245586i
$975$	−254.652	−	147.023i	−0.261181	−	0.150793i
$976$	−0.893847	+	255.195i	−0.000915827	+	0.261470i
$977$	−389.513	−	674.657i	−0.398683	−	0.690539i	0.594881	−	0.803814i	$-0.297199\pi$
$977$	−389.513	−	674.657i	−0.398683	−	0.690539i	−0.993564	+	0.113275i	$0.963866\pi$
$978$	−35.4700	−	271.256i	−0.0362679	−	0.277358i
$979$		−	1436.21i		−	1.46702i
$980$		0			0
$981$	−8.98769			−0.00916176
$982$	235.585	−	30.8055i	0.239903	−	0.0313702i
$983$	−68.9305	+	39.7970i	−0.0701225	+	0.0404853i	−0.534651	−	0.845073i	$-0.679557\pi$
$983$	−68.9305	+	39.7970i	−0.0701225	+	0.0404853i	0.464529	+	0.885558i	$0.346224\pi$
$984$	692.862	+	534.549i	0.704128	+	0.543241i
$985$	91.6387	−	158.723i	0.0930343	−	0.161140i
$986$	789.618	−	604.797i	0.800830	−	0.613385i
$987$		0			0
$988$	−400.634	−	108.102i	−0.405500	−	0.109415i
$989$	−11.9506	+	20.6991i	−0.0120836	+	0.0209293i
$990$	6.84713	−	16.4896i	0.00691629	−	0.0166561i
$991$	557.931	−	322.122i	0.562998	−	0.325047i	−0.191350	−	0.981522i	$-0.561286\pi$
$991$	557.931	−	322.122i	0.562998	−	0.325047i	0.754348	+	0.656475i	$0.227953\pi$
$992$	−45.7357	−	19.1794i	−0.0461045	−	0.0193340i
$993$	357.057			0.359574
$994$		0			0
$995$		−	1575.85i		−	1.58377i
$996$	120.574	+	120.997i	0.121059	+	0.121483i
$997$	−869.997	−	1506.88i	−0.872615	−	1.51141i	−0.859282	−	0.511502i	$-0.829089\pi$
$997$	−869.997	−	1506.88i	−0.872615	−	1.51141i	−0.0133331	−	0.999911i	$-0.504244\pi$
$998$	419.104	−	1009.31i	0.419944	−	1.01133i
$999$	1057.85	+	610.752i	1.05891	+	0.611363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.3.g.j.79.3		12
4.3	odd	2	inner	196.3.g.j.79.1		12
7.2	even	3		196.3.c.g.99.5		6
7.3	odd	6		196.3.g.k.67.1		12
7.4	even	3	inner	196.3.g.j.67.1		12
7.5	odd	6		28.3.c.a.15.5	✓	6
7.6	odd	2		196.3.g.k.79.3		12
21.5	even	6		252.3.g.a.127.2		6
28.3	even	6		196.3.g.k.67.3		12
28.11	odd	6	inner	196.3.g.j.67.3		12
28.19	even	6		28.3.c.a.15.6	yes	6
28.23	odd	6		196.3.c.g.99.6		6
28.27	even	2		196.3.g.k.79.1		12
56.5	odd	6		448.3.d.d.127.2		6
56.19	even	6		448.3.d.d.127.5		6
84.47	odd	6		252.3.g.a.127.1		6
112.5	odd	12		1792.3.g.g.127.9		12
112.19	even	12		1792.3.g.g.127.10		12
112.61	odd	12		1792.3.g.g.127.4		12
112.75	even	12		1792.3.g.g.127.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.3.c.a.15.5	✓	6	7.5	odd	6
28.3.c.a.15.6	yes	6	28.19	even	6
196.3.c.g.99.5		6	7.2	even	3
196.3.c.g.99.6		6	28.23	odd	6
196.3.g.j.67.1		12	7.4	even	3	inner
196.3.g.j.67.3		12	28.11	odd	6	inner
196.3.g.j.79.1		12	4.3	odd	2	inner
196.3.g.j.79.3		12	1.1	even	1	trivial
196.3.g.k.67.1		12	7.3	odd	6
196.3.g.k.67.3		12	28.3	even	6
196.3.g.k.79.1		12	28.27	even	2
196.3.g.k.79.3		12	7.6	odd	2
252.3.g.a.127.1		6	84.47	odd	6
252.3.g.a.127.2		6	21.5	even	6
448.3.d.d.127.2		6	56.5	odd	6
448.3.d.d.127.5		6	56.19	even	6
1792.3.g.g.127.3		12	112.75	even	12
1792.3.g.g.127.4		12	112.61	odd	12
1792.3.g.g.127.9		12	112.5	odd	12
1792.3.g.g.127.10		12	112.19	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	196.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.259316 + 1.98312i) q^{2} +(-2.58484 + 1.49236i) q^{3} +(-3.86551 + 1.02851i) q^{4} +(-3.40268 + 5.89361i) q^{5} +(-3.62981 - 4.73905i) q^{6} +(-3.04204 - 7.39905i) q^{8} +(-0.0457311 + 0.0792086i) q^{9} +O(q^{10})\)	\(q+(0.259316 + 1.98312i) q^{2} +(-2.58484 + 1.49236i) q^{3} +(-3.86551 + 1.02851i) q^{4} +(-3.40268 + 5.89361i) q^{5} +(-3.62981 - 4.73905i) q^{6} +(-3.04204 - 7.39905i) q^{8} +(-0.0457311 + 0.0792086i) q^{9} +(-12.5701 - 5.21960i) q^{10} +(12.4211 - 7.17132i) q^{11} +(8.45683 - 8.42726i) q^{12} -4.62243 q^{13} -20.3121i q^{15} +(13.8843 - 7.95142i) q^{16} +(5.80536 + 10.0552i) q^{17} +(-0.168939 - 0.0701501i) q^{18} +(-19.4361 - 11.2214i) q^{19} +(7.09146 - 26.2815i) q^{20} +(17.4426 + 22.7728i) q^{22} +(0.739535 + 0.426971i) q^{23} +(18.9052 + 14.5856i) q^{24} +(-10.6564 - 18.4575i) q^{25} +(-1.19867 - 9.16683i) q^{26} -27.1354i q^{27} -42.8321 q^{29} +(40.2812 - 5.26724i) q^{30} +(-1.34219 + 0.774912i) q^{31} +(19.3690 + 25.4724i) q^{32} +(-21.4044 + 37.0734i) q^{33} +(-18.4352 + 14.1202i) q^{34} +(0.0953074 - 0.353217i) q^{36} +(-22.5075 + 38.9842i) q^{37} +(17.2133 - 41.4539i) q^{38} +(11.9483 - 6.89833i) q^{39} +(53.9582 + 7.24799i) q^{40} +36.6492 q^{41} +27.9894i q^{43} +(-40.6381 + 40.4960i) q^{44} +(-0.311217 - 0.539043i) q^{45} +(-0.654960 + 1.57730i) q^{46} +(-36.5237 - 21.0870i) q^{47} +(-24.0225 + 41.2736i) q^{48} +(33.8400 - 25.9193i) q^{50} +(-30.0119 - 17.3274i) q^{51} +(17.8681 - 4.75421i) q^{52} +(-21.7022 - 37.5893i) q^{53} +(53.8128 - 7.03665i) q^{54} +97.6068i q^{55} +66.9856 q^{57} +(-11.1071 - 84.9412i) q^{58} +(-46.7636 + 26.9990i) q^{59} +(20.8911 + 78.5165i) q^{60} +(-7.97489 + 13.8129i) q^{61} +(-1.88479 - 2.46077i) q^{62} +(-45.4920 + 45.0164i) q^{64} +(15.7287 - 27.2428i) q^{65} +(-79.0715 - 32.8336i) q^{66} +(-79.6270 + 45.9726i) q^{67} +(-32.7825 - 32.8975i) q^{68} -2.54877 q^{69} -16.3585i q^{71} +(0.725185 + 0.0974111i) q^{72} +(4.79364 + 8.30283i) q^{73} +(-83.1468 - 34.5259i) q^{74} +(55.0904 + 31.8065i) q^{75} +(86.6717 + 23.3864i) q^{76} +(16.7786 + 21.9059i) q^{78} +(-49.3484 - 28.4913i) q^{79} +(-0.381382 + 108.885i) q^{80} +(40.0842 + 69.4279i) q^{81} +(9.50373 + 72.6797i) q^{82} +14.3077i q^{83} -79.0151 q^{85} +(-55.5062 + 7.25809i) q^{86} +(110.714 - 63.9209i) q^{87} +(-90.8464 - 70.0888i) q^{88} +(50.0680 - 86.7204i) q^{89} +(0.988282 - 0.756962i) q^{90} +(-3.29782 - 0.889842i) q^{92} +(2.31289 - 4.00605i) q^{93} +(32.3468 - 77.8990i) q^{94} +(132.269 - 76.3658i) q^{95} +(-88.0797 - 36.9364i) q^{96} -68.2834 q^{97} +1.31181i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - q^{4} - 4 q^{5} - 12 q^{6} - 26 q^{8} + 10 q^{9}+O(q^{10}) \) 12 * q + q^2 - q^4 - 4 * q^5 - 12 * q^6 - 26 * q^8 + 10 * q^9	\( 12 q + q^{2} - q^{4} - 4 q^{5} - 12 q^{6} - 26 q^{8} + 10 q^{9} - 28 q^{10} + 6 q^{12} - 24 q^{13} - 17 q^{16} - 4 q^{17} - 43 q^{18} + 64 q^{20} + 104 q^{22} + 122 q^{24} + 30 q^{25} - 56 q^{26} - 72 q^{29} + 64 q^{30} + 101 q^{32} + 80 q^{33} - 116 q^{34} - 262 q^{36} - 28 q^{37} - 190 q^{38} + 40 q^{40} + 40 q^{41} - 164 q^{44} + 12 q^{45} - 120 q^{46} + 196 q^{48} + 322 q^{50} + 292 q^{52} - 92 q^{53} - 44 q^{54} + 320 q^{57} + 166 q^{58} + 176 q^{60} - 164 q^{61} - 296 q^{62} - 430 q^{64} + 136 q^{65} - 408 q^{66} + 62 q^{68} + 96 q^{69} - 151 q^{72} - 132 q^{73} - 250 q^{74} + 156 q^{76} + 496 q^{78} + 312 q^{80} + 218 q^{81} - 86 q^{82} - 464 q^{85} + 164 q^{86} + 100 q^{88} + 348 q^{89} - 104 q^{90} - 208 q^{92} - 288 q^{93} - 276 q^{94} + 170 q^{96} - 504 q^{97}+O(q^{100}) \) 12 * q + q^2 - q^4 - 4 * q^5 - 12 * q^6 - 26 * q^8 + 10 * q^9 - 28 * q^10 + 6 * q^12 - 24 * q^13 - 17 * q^16 - 4 * q^17 - 43 * q^18 + 64 * q^20 + 104 * q^22 + 122 * q^24 + 30 * q^25 - 56 * q^26 - 72 * q^29 + 64 * q^30 + 101 * q^32 + 80 * q^33 - 116 * q^34 - 262 * q^36 - 28 * q^37 - 190 * q^38 + 40 * q^40 + 40 * q^41 - 164 * q^44 + 12 * q^45 - 120 * q^46 + 196 * q^48 + 322 * q^50 + 292 * q^52 - 92 * q^53 - 44 * q^54 + 320 * q^57 + 166 * q^58 + 176 * q^60 - 164 * q^61 - 296 * q^62 - 430 * q^64 + 136 * q^65 - 408 * q^66 + 62 * q^68 + 96 * q^69 - 151 * q^72 - 132 * q^73 - 250 * q^74 + 156 * q^76 + 496 * q^78 + 312 * q^80 + 218 * q^81 - 86 * q^82 - 464 * q^85 + 164 * q^86 + 100 * q^88 + 348 * q^89 - 104 * q^90 - 208 * q^92 - 288 * q^93 - 276 * q^94 + 170 * q^96 - 504 * q^97

Introduction

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