LMFDB - Embedded newform 196.3.g.j.79.1

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			79.1
Root			$0.0455406 + 1.41348i$ of defining polynomial
Character	$\chi$	$=$	196.79
Dual form			196.3.g.j.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84709 + 0.766985i) q^{2} +(2.58484 - 1.49236i) q^{3} +(2.82347 - 2.83338i) q^{4} +(-3.40268 + 5.89361i) q^{5} +(-3.62981 + 4.73905i) q^{6} +(-3.04204 + 7.39905i) q^{8} +(-0.0457311 + 0.0792086i) q^{9} +O(q^{10})$	\(q+(-1.84709 + 0.766985i) q^{2} +(2.58484 - 1.49236i) q^{3} +(2.82347 - 2.83338i) 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} +(1.76474 - 13.4958i) q^{10} +(-12.4211 + 7.17132i) q^{11} +(3.06981 - 11.5375i) q^{12} -4.62243 q^{13} +20.3121i q^{15} +(-0.0560414 - 15.9999i) q^{16} +(5.80536 + 10.0552i) q^{17} +(0.0237176 - 0.181380i) 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} +(3.17885 + 23.6652i) q^{24} +(-10.6564 - 18.4575i) q^{25} +(8.53804 - 3.54533i) q^{26} +27.1354i q^{27} -42.8321 q^{29} +(-15.5790 - 37.5182i) q^{30} +(1.34219 - 0.774912i) q^{31} +(12.3752 + 29.5102i) 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} +(-44.5068 - 5.81979i) q^{38} +(-11.9483 + 6.89833i) q^{39} +(-33.2561 - 43.1052i) q^{40} +36.6492 q^{41} -27.9894i q^{43} +(-14.7515 + 55.4416i) q^{44} +(-0.311217 - 0.539043i) q^{45} +(1.69347 + 0.221441i) 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} +(-13.0513 + 13.0971i) q^{52} +(-21.7022 - 37.5893i) q^{53} +(-20.8125 - 50.1216i) q^{54} -97.6068i q^{55} +66.9856 q^{57} +(79.1147 - 32.8516i) q^{58} +(46.7636 - 26.9990i) q^{59} +(57.5517 + 57.3505i) 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} +(11.1010 - 84.8947i) q^{66} +(79.6270 - 45.9726i) q^{67} +(44.8813 + 11.9417i) q^{68} -2.54877 q^{69} +16.3585i q^{71} +(-0.446953 - 0.579323i) q^{72} +(4.79364 + 8.30283i) q^{73} +(11.6731 - 89.2702i) 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} +(94.4879 + 54.1122i) q^{80} +(40.0842 + 69.4279i) q^{81} +(-67.6943 + 28.1094i) q^{82} -14.3077i q^{83} -79.0151 q^{85} +(21.4674 + 51.6989i) q^{86} +(-110.714 + 63.9209i) q^{87} +(-15.2755 - 113.720i) 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} +(-83.6359 - 10.9364i) q^{94} +(-132.269 + 76.3658i) q^{95} +(76.0278 + 57.8111i) 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 $

$2$	−1.84709	+	0.766985i	−0.923544	+	0.383492i
$2$	−1.84709	+	0.766985i	−0.923544	+	0.383492i
$3$	2.58484	−	1.49236i	0.861614	−	0.497453i	−0.00293865	−	0.999996i	$-0.500935\pi$
$3$	2.58484	−	1.49236i	0.861614	−	0.497453i	0.864552	+	0.502543i	$0.167602\pi$
$4$	2.82347	−	2.83338i	0.705867	−	0.708344i
$5$	−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
$10$	1.76474	−	13.4958i	0.176474	−	1.34958i
$11$	−12.4211	+	7.17132i	−1.12919	+	0.651938i	−0.943731	−	0.330714i	$-0.892710\pi$
$11$	−12.4211	+	7.17132i	−1.12919	+	0.651938i	−0.185459	+	0.982652i	$0.559377\pi$
$12$	3.06981	−	11.5375i	0.255817	−	0.961455i
$13$	−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
$16$	−0.0560414	−	15.9999i	−0.00350259	−	0.999994i
$17$	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	$0.722401\pi$
$18$	0.0237176	−	0.181380i	0.00131765	−	0.0100767i
$19$	19.4361	+	11.2214i	1.02295	+	0.590601i	0.914957	−	0.403550i	$-0.132224\pi$
$19$	19.4361	+	11.2214i	1.02295	+	0.590601i	0.107994	+	0.994152i	$0.465557\pi$
$20$	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	0.483837	−	0.875158i	$-0.339243\pi$
$23$	−0.739535	−	0.426971i	−0.0321537	−	0.0185639i	−0.515991	+	0.856594i	$0.672576\pi$
$24$	3.17885	+	23.6652i	0.132452	+	0.986050i
$25$	−10.6564	−	18.4575i	−0.426258	−	0.738300i
$26$	8.53804	−	3.54533i	0.328386	−	0.136359i
$27$			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	$0.764459\pi$
$30$	−15.5790	−	37.5182i	−0.519301	−	1.25061i
$31$	1.34219	−	0.774912i	0.0432963	−	0.0249972i	−0.478196	−	0.878253i	$-0.658709\pi$
$31$	1.34219	−	0.774912i	0.0432963	−	0.0249972i	0.521492	+	0.853256i	$0.325376\pi$
$32$	12.3752	+	29.5102i	0.386725	+	0.922195i
$33$	−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	$0.958514\pi$
$38$	−44.5068	−	5.81979i	−1.17123	−	0.153152i
$39$	−11.9483	+	6.89833i	−0.306366	+	0.176880i
$40$	−33.2561	−	43.1052i	−0.831402	−	1.07763i
$41$	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	$-0.894482\pi$
$43$		−	27.9894i		−	0.650916i	0.945557	−	0.325458i	$-0.105518\pi$
$44$	−14.7515	+	55.4416i	−0.335262	+	1.26004i
$45$	−0.311217	−	0.539043i	−0.00691592	−	0.0119787i
$46$	1.69347	+	0.221441i	0.0368145	+	0.00481393i
$47$	36.5237	+	21.0870i	0.777100	+	0.448659i	0.835402	−	0.549640i	$-0.185235\pi$
$47$	36.5237	+	21.0870i	0.777100	+	0.448659i	−0.0583012	+	0.998299i	$0.518568\pi$
$48$	−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
$52$	−13.0513	+	13.0971i	−0.250987	+	0.251867i
$53$	−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	$0.967621\pi$
$54$	−20.8125	−	50.1216i	−0.385416	−	0.928177i
$55$		−	97.6068i		−	1.77467i
$56$		0			0
$57$	66.9856			1.17519
$58$	79.1147	−	32.8516i	1.36405	−	0.566407i
$59$	46.7636	−	26.9990i	0.792603	−	0.457609i	−0.0482754	−	0.998834i	$-0.515373\pi$
$59$	46.7636	−	26.9990i	0.792603	−	0.457609i	0.840878	+	0.541225i	$0.182039\pi$
$60$	57.5517	+	57.3505i	0.959196	+	0.955842i
$61$	−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
$66$	11.1010	−	84.8947i	0.168197	−	1.28628i
$67$	79.6270	−	45.9726i	1.18846	−	0.686159i	0.230505	−	0.973071i	$-0.425962\pi$
$67$	79.6270	−	45.9726i	1.18846	−	0.686159i	0.957957	+	0.286912i	$0.0926288\pi$
$68$	44.8813	+	11.9417i	0.660020	+	0.175613i
$69$	−2.54877			−0.0369387
$70$		0			0
$71$			16.3585i			0.230401i	0.993342	+	0.115201i	$0.0367511\pi$
$71$			16.3585i			0.230401i	−0.993342	+	0.115201i	$0.963249\pi$
$72$	−0.446953	−	0.579323i	−0.00620768	−	0.00804615i
$73$	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	$0.812416\pi$
$74$	11.6731	−	89.2702i	0.157745	−	1.20635i
$75$	−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	0.778682	−	0.627418i	$-0.215888\pi$
$79$	49.3484	+	28.4913i	0.624663	+	0.360649i	−0.154019	+	0.988068i	$0.549222\pi$
$80$	94.4879	+	54.1122i	1.18110	+	0.676403i
$81$	40.0842	+	69.4279i	0.494867	+	0.857135i
$82$	−67.6943	+	28.1094i	−0.825541	+	0.342797i
$83$		−	14.3077i		−	0.172381i	−0.996279	−	0.0861907i	$-0.972531\pi$
$83$		−	14.3077i		−	0.172381i	0.996279	−	0.0861907i	$-0.0274694\pi$
$84$		0			0
$85$	−79.0151			−0.929589
$86$	21.4674	+	51.6989i	0.249621	+	0.601150i
$87$	−110.714	+	63.9209i	−1.27258	+	0.734723i
$88$	−15.2755	−	113.720i	−0.173585	−	1.29227i
$89$	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
$94$	−83.6359	−	10.9364i	−0.889744	−	0.116344i
$95$	−132.269	+	76.3658i	−1.39231	+	0.803850i
$96$	76.0278	+	57.8111i	0.791956	+	0.602199i
$97$	−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
$100$	−82.3852	−	21.9205i	−0.823852	−	0.219205i
$101$	−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	$0.877857\pi$
$102$	−68.7244	−	8.98652i	−0.673768	−	0.0881031i
$103$	−138.774	−	80.1213i	−1.34732	−	0.777877i	−0.359453	−	0.933163i	$-0.617037\pi$
$103$	−138.774	−	80.1213i	−1.34732	−	0.777877i	−0.987870	+	0.155286i	$0.950370\pi$
$104$	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	−0.0655750	−	0.997848i	$-0.520888\pi$
$107$	−102.990	−	59.4613i	−0.962524	−	0.555713i	−0.896949	+	0.442134i	$0.854221\pi$
$108$	76.8849	+	76.6161i	0.711897	+	0.709408i
$109$	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	$0.684485\pi$
$110$	74.8629	+	180.288i	0.680572	+	1.63898i
$111$			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	$0.358798\pi$
$114$	−123.728	+	51.3769i	−1.08534	+	0.450674i
$115$	5.03280	−	2.90569i	0.0437635	−	0.0252669i
$116$	−120.935	+	121.360i	−1.04255	+	1.04620i
$117$	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
$122$	4.13603	−	31.6303i	0.0339019	−	0.259265i
$123$	94.7324	−	54.6938i	0.770182	−	0.444665i
$124$	1.59401	−	5.99086i	0.0128549	−	0.0483134i
$125$	−25.0921			−0.200737
$126$		0			0
$127$		−	71.8712i		−	0.565915i	−0.959132	−	0.282958i	$-0.908684\pi$
$127$		−	71.8712i		−	0.565915i	0.959132	−	0.282958i	$-0.0913156\pi$
$128$	118.555	+	48.2577i	0.926208	+	0.377013i
$129$	−41.7702	−	72.3481i	−0.323800	−	0.560838i
$130$	−8.15738	+	62.3835i	−0.0627491	+	0.479873i
$131$	181.724	+	104.919i	1.38721	+	0.800906i	0.993000	−	0.118115i	$-0.0376851\pi$
$131$	181.724	+	104.919i	1.38721	+	0.800906i	0.394209	+	0.919021i	$0.371018\pi$
$132$	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
$136$	−92.0589	+	12.3659i	−0.676904	+	0.0909257i
$137$	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	$0.812215\pi$
$138$	4.70781	−	1.95487i	0.0341146	−	0.0141657i
$139$			134.084i			0.964635i	0.875996	+	0.482318i	$0.160205\pi$
$139$			134.084i			0.964635i	−0.875996	+	0.482318i	$0.839795\pi$
$140$		0			0
$141$	125.877			0.892747
$142$	−12.5467	−	30.2156i	−0.0883571	−	0.212786i
$143$	57.4156	−	33.1489i	0.401508	−	0.231811i
$144$	1.26989	+	0.727254i	0.00881870	+	0.00505038i
$145$	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	$0.144472\pi$
$150$	126.152	+	16.4959i	0.841013	+	0.109972i
$151$	80.6348	−	46.5545i	0.534005	−	0.308308i	−0.208641	−	0.977992i	$-0.566904\pi$
$151$	80.6348	−	46.5545i	0.534005	−	0.308308i	0.742646	+	0.669684i	$0.233571\pi$
$152$	−142.153	+	109.673i	−0.935219	+	0.721530i
$153$	−1.06194			−0.00694080
$154$		0			0
$155$			10.5471i			0.0680458i
$156$	−14.1900	+	53.3311i	−0.0909614	+	0.341866i
$157$	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	$0.663924\pi$
$158$	−113.003	−	14.7765i	−0.715210	−	0.0935222i
$159$	−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	0.373293	−	0.927714i	$-0.378229\pi$
$163$	−39.6880	−	22.9139i	−0.243485	−	0.140576i	−0.616777	+	0.787138i	$0.711562\pi$
$164$	103.478	−	103.841i	0.630963	−	0.633177i
$165$	−145.664	−	252.298i	−0.882814	−	1.52908i
$166$	10.9738	+	26.4275i	0.0661070	+	0.159202i
$167$			15.5845i			0.0933203i	0.998911	+	0.0466602i	$0.0148578\pi$
$167$			15.5845i			0.0933203i	−0.998911	+	0.0466602i	$0.985142\pi$
$168$		0			0
$169$	−147.633			−0.873569
$170$	145.948	−	60.6033i	0.858516	−	0.356490i
$171$	−1.77767	+	1.02634i	−0.0103957	+	0.00600197i
$172$	−79.3045	−	79.0272i	−0.461072	−	0.459460i
$173$	−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
$178$	−25.9669	+	198.582i	−0.145881	+	1.11563i
$179$	38.5433	−	22.2530i	0.215325	−	0.124318i	−0.388458	−	0.921466i	$-0.626992\pi$
$179$	38.5433	−	22.2530i	0.215325	−	0.124318i	0.603784	+	0.797148i	$0.293659\pi$
$180$	−2.40602	−	0.640178i	−0.0133668	−	0.00355654i
$181$	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
$184$	5.40887	−	4.17300i	0.0293961	−	0.0226793i
$185$	−153.172	−	265.301i	−0.827956	−	1.43406i
$186$	−1.19954	+	9.17348i	−0.00644914	+	0.0493198i
$187$	−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	$0.0431659\pi$
$191$	306.232	+	176.803i	1.60331	+	0.925672i	0.612491	+	0.790477i	$0.290167\pi$
$192$	−184.770	−	48.4700i	−0.962345	−	0.252448i
$193$	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	$0.474662\pi$
$194$	126.125	−	52.3723i	0.650131	−	0.269960i
$195$		−	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	$0.521775\pi$
$198$	1.00614	+	2.42303i	0.00508150	+	0.0122375i
$199$	200.537	−	115.780i	1.00772	−	0.581809i	0.0971981	−	0.995265i	$-0.469012\pi$
$199$	200.537	−	115.780i	1.00772	−	0.581809i	0.910524	+	0.413457i	$0.135679\pi$
$200$	168.985	−	22.6991i	0.844927	−	0.113496i
$201$	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
$206$	317.780	+	41.5535i	1.54262	+	0.201716i
$207$	0.0676395	−	0.0390517i	0.000326761	−	0.000188655i
$208$	0.259047	+	73.9585i	0.00124542	+	0.355570i
$209$	−321.890			−1.54014
$210$		0			0
$211$			79.6903i			0.377679i	0.982008	+	0.188840i	$0.0604726\pi$
$211$			79.6903i			0.377679i	−0.982008	+	0.188840i	$0.939527\pi$
$212$	−167.780	−	44.6417i	−0.791415	−	0.210574i
$213$	24.4127	+	42.2841i	0.114614	+	0.198517i
$214$	235.838	+	30.8385i	1.10205	+	0.144105i
$215$	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
$220$	−276.557	−	275.590i	−1.25708	−	1.25268i
$221$	−26.8349	−	46.4794i	−0.121425	−	0.210314i
$222$	−103.050	−	248.170i	−0.464189	−	1.11788i
$223$		−	264.367i		−	1.18550i	−0.805386	−	0.592750i	$-0.798042\pi$
$223$		−	264.367i		−	1.18550i	0.805386	−	0.592750i	$-0.201958\pi$
$224$		0			0
$225$	1.94932			0.00866367
$226$	−179.163	+	74.3958i	−0.792758	+	0.329185i
$227$	−373.538	+	215.662i	−1.64554	+	0.950053i	−0.666726	+	0.745303i	$0.732305\pi$
$227$	−373.538	+	215.662i	−1.64554	+	0.950053i	−0.978814	+	0.204750i	$0.934362\pi$
$228$	189.132	−	189.795i	0.829525	−	0.832435i
$229$	−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	$0.322264\pi$
$234$	−0.109633	+	0.838419i	−0.000468518	+	0.00358299i
$235$	−248.557	+	143.504i	−1.05769	+	0.610657i
$236$	55.5373	−	208.729i	0.235327	−	0.884447i
$237$	170.077			0.717625
$238$		0			0
$239$		−	90.1656i		−	0.377262i	−0.982048	−	0.188631i	$-0.939595\pi$
$239$		−	90.1656i		−	0.377262i	0.982048	−	0.188631i	$-0.0604050\pi$
$240$	324.991	−	1.13832i	1.35413	−	0.00474298i
$241$	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	$0.548569\pi$
$242$	−21.9670	+	167.992i	−0.0907726	+	0.694183i
$243$	−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
$248$	1.65063	+	12.2882i	0.00665575	+	0.0495493i
$249$	−21.3522	−	36.9830i	−0.0857516	−	0.148526i
$250$	46.3473	−	19.2452i	0.185389	−	0.0769810i
$251$		−	319.525i		−	1.27301i	−0.771274	−	0.636503i	$-0.780380\pi$
$251$		−	319.525i		−	1.27301i	0.771274	−	0.636503i	$-0.219620\pi$
$252$		0			0
$253$	12.2478			0.0484101
$254$	55.1241	+	132.753i	0.217024	+	0.522648i
$255$	−204.241	+	117.919i	−0.800947	+	0.462427i
$256$	−255.994	+	1.79331i	−0.999975	+	0.00700513i
$257$	−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
$262$	−416.132	−	54.4142i	−1.58829	−	0.207688i
$263$	−74.5887	+	43.0638i	−0.283607	+	0.163741i	−0.635055	−	0.772467i	$-0.719023\pi$
$263$	−74.5887	+	43.0638i	−0.283607	+	0.163741i	0.351448	+	0.936207i	$0.385689\pi$
$264$	−209.195	−	271.151i	−0.792407	−	1.02709i
$265$	295.382			1.11465
$266$		0			0
$267$		−	298.878i		−	1.11939i
$268$	94.5665	−	355.415i	0.352860	−	1.32618i
$269$	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	$0.666432\pi$
$270$	366.215	+	47.8869i	1.35635	+	0.177359i
$271$	275.671	+	159.159i	1.01724	+	0.587302i	0.913302	−	0.407282i	$-0.133523\pi$
$271$	275.671	+	159.159i	1.01724	+	0.587302i	0.103935	+	0.994584i	$0.466857\pi$
$272$	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
$276$	−7.19638	+	7.22163i	−0.0260739	+	0.0261653i
$277$	−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	$-0.389259\pi$
$278$	−102.841	−	247.665i	−0.369930	−	0.890883i
$279$			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	$0.437381\pi$
$282$	−232.507	+	96.5460i	−0.824491	+	0.342362i
$283$	445.641	−	257.291i	1.57470	−	0.909155i	0.579123	−	0.815240i	$-0.303395\pi$
$283$	445.641	−	257.291i	1.57470	−	0.909155i	0.995580	−	0.0939154i	$-0.0299383\pi$
$284$	46.3497	+	46.1877i	0.163203	+	0.162633i
$285$	−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
$290$	−75.5875	+	578.055i	−0.260647	+	1.99329i
$291$	−176.502	+	101.903i	−0.606535	+	0.350183i
$292$	37.0597	+	9.86059i	0.126917	+	0.0337692i
$293$	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
$296$	−219.977	−	285.126i	−0.743166	−	0.963263i
$297$	−194.597	−	337.052i	−0.655208	−	1.13485i
$298$	−5.38388	+	41.1732i	−0.0180667	+	0.138165i
$299$	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
$304$	178.452	−	311.604i	0.587015	−	1.02501i
$305$	−54.2720	−	94.0018i	−0.177941	−	0.308203i
$306$	1.96150	−	0.814493i	0.00641013	−	0.00266174i
$307$			382.811i			1.24694i	0.781847	+	0.623471i	$0.214278\pi$
$307$			382.811i			1.24694i	−0.781847	+	0.623471i	$0.785722\pi$
$308$		0			0
$309$	−478.279			−1.54783
$310$	−8.08947	−	19.4814i	−0.0260951	−	0.0628433i
$311$	170.064	−	98.1868i	0.546831	−	0.315713i	−0.201012	−	0.979589i	$-0.564423\pi$
$311$	170.064	−	98.1868i	0.546831	−	0.315713i	0.747843	+	0.663876i	$0.231090\pi$
$312$	−14.6940	−	109.391i	−0.0470962	−	0.350611i
$313$	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	$0.222710\pi$
$318$	256.912	+	33.5943i	0.807900	+	0.105642i
$319$	532.022	−	307.163i	1.66778	−	0.962893i
$320$	420.104	−	114.936i	1.31283	−	0.359174i
$321$	−354.951			−1.10577
$322$		0			0
$323$			260.577i			0.806741i
$324$	309.892	+	82.4539i	0.956457	+	0.254487i
$325$	49.2587	+	85.3186i	0.151565	+	0.262519i
$326$	90.8818	+	11.8839i	0.278779	+	0.0364536i
$327$	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	0.648266	−	0.761414i	$-0.275495\pi$
$331$	103.601	+	59.8143i	0.312995	+	0.180708i	−0.335271	+	0.942122i	$0.608828\pi$
$332$	−40.5390	−	40.3972i	−0.122105	−	0.121678i
$333$	−2.05859	−	3.56558i	−0.00618195	−	0.0107075i
$334$	−11.9531	−	28.7859i	−0.0357876	−	0.0861854i
$335$			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	$0.527124\pi$
$338$	272.691	−	113.232i	0.806779	−	0.335007i
$339$	250.724	−	144.755i	0.739598	−	0.427007i
$340$	−223.097	+	223.879i	−0.656167	+	0.658469i
$341$	−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
$346$	68.9836	−	527.552i	0.199375	−	1.52472i
$347$	−232.766	+	134.387i	−0.670794	+	0.387283i	−0.796377	−	0.604800i	$-0.793253\pi$
$347$	−232.766	+	134.387i	−0.670794	+	0.387283i	0.125583	+	0.992083i	$0.459920\pi$
$348$	−131.486	+	494.174i	−0.377834	+	1.42004i
$349$	−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
$352$	−365.341	−	277.803i	−1.03790	−	0.789213i
$353$	−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	$0.981520\pi$
$354$	−41.7936	+	319.616i	−0.118061	+	0.902870i
$355$	−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	−0.427124	−	0.904193i	$-0.640473\pi$
$359$	−511.123	−	295.097i	−1.42374	−	0.821997i	−0.996616	+	0.0821961i	$0.973807\pi$
$360$	4.93514	−	0.662917i	0.0137087	−	0.00184144i
$361$	71.3407	+	123.566i	0.197620	+	0.342287i
$362$	−310.515	+	128.938i	−0.857776	+	0.356183i
$363$		−	252.839i		−	0.696526i
$364$		0			0
$365$	−65.2449			−0.178753
$366$	−36.5127	−	87.9317i	−0.0997616	−	0.240251i
$367$	−152.025	+	87.7718i	−0.414238	+	0.239160i	−0.692609	−	0.721313i	$-0.743539\pi$
$367$	−152.025	+	87.7718i	−0.414238	+	0.239160i	0.278371	+	0.960474i	$0.410205\pi$
$368$	−6.79004	+	11.8564i	−0.0184512	+	0.0322185i
$369$	−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	$0.900236\pi$
$374$	330.245	+	43.1834i	0.883008	+	0.115464i
$375$	−64.8590	+	37.4464i	−0.172957	+	0.0998570i
$376$	−267.130	+	206.093i	−0.710453	+	0.548121i
$377$	197.989			0.525169
$378$		0			0
$379$			749.909i			1.97865i	0.145723	+	0.989325i	$0.453449\pi$
$379$			749.909i			1.97865i	−0.145723	+	0.989325i	$0.546551\pi$
$380$	−157.086	+	590.386i	−0.413383	+	1.55365i
$381$	−107.258	−	185.776i	−0.281516	−	0.487600i
$382$	−701.243	−	91.6958i	−1.83572	−	0.240041i
$383$	−213.242	−	123.115i	−0.556767	−	0.321450i	0.195080	−	0.980787i	$-0.437503\pi$
$383$	−213.242	−	123.115i	−0.556767	−	0.321450i	−0.751847	+	0.659338i	$0.770837\pi$
$384$	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
$388$	−192.796	+	193.472i	−0.496897	+	0.498640i
$389$	−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	$0.958462\pi$
$390$	72.0131	+	173.425i	0.184649	+	0.444680i
$391$		−	9.91487i		−	0.0253577i
$392$		0			0
$393$	626.305			1.59365
$394$	49.7446	−	20.6559i	0.126255	−	0.0524262i
$395$	−335.833	+	193.894i	−0.850211	+	0.490870i
$396$	−3.71685	−	3.70385i	−0.00938598	−	0.00935317i
$397$	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	$-0.249410\pi$
$402$	−71.1643	+	544.228i	−0.177026	+	1.35380i
$403$	−6.20417	+	3.58198i	−0.0153950	+	0.00888828i
$404$	−108.864	−	28.9657i	−0.269465	−	0.0716973i
$405$	−545.575			−1.34710
$406$		0			0
$407$		−	645.635i		−	1.58633i
$408$	−219.503	+	169.349i	−0.537998	+	0.415071i
$409$	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	$0.529926\pi$
$410$	64.6763	−	494.611i	0.157747	−	1.20637i
$411$	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
$416$	−57.2035	−	136.409i	−0.137508	−	0.327907i
$417$	200.102	+	346.587i	0.479861	+	0.831143i
$418$	594.558	−	246.884i	1.42239	−	0.590632i
$419$			95.3634i			0.227598i	0.993504	+	0.113799i	$0.0363019\pi$
$419$			95.3634i			0.227598i	−0.993504	+	0.113799i	$0.963698\pi$
$420$		0			0
$421$	−279.158			−0.663083			−0.331541	−	0.943441i	$-0.607569\pi$
$421$	−279.158			−0.663083			−0.331541	+	0.943441i	$0.607569\pi$
$422$	−61.1212	−	147.195i	−0.144837	−	0.348803i
$423$	−3.34054	+	1.92866i	−0.00789726	+	0.00455949i
$424$	344.144	−	46.2274i	0.811660	−	0.109027i
$425$	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
$430$	−377.740	−	49.3939i	−0.878465	−	0.114870i
$431$	146.682	−	84.6868i	0.340329	−	0.196489i	−0.320088	−	0.947388i	$-0.603713\pi$
$431$	146.682	−	84.6868i	0.340329	−	0.196489i	0.660418	+	0.750899i	$0.270379\pi$
$432$	434.164	−	1.52071i	1.00501	−	0.00352016i
$433$	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
$436$	379.851	+	101.068i	0.871217	+	0.231807i
$437$	−9.58244	−	16.5973i	−0.0219278	−	0.0379800i
$438$	−56.7475	−	7.42041i	−0.129561	−	0.0169416i
$439$	−282.994	−	163.386i	−0.644632	−	0.372179i	0.141764	−	0.989900i	$-0.454722\pi$
$439$	−282.994	−	163.386i	−0.644632	−	0.372179i	−0.786397	+	0.617722i	$0.788056\pi$
$440$	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	−0.0962414	−	0.995358i	$-0.530682\pi$
$443$	−445.821	−	257.395i	−1.00637	−	0.581026i	−0.910126	+	0.414332i	$0.864015\pi$
$444$	380.685	+	379.354i	0.857398	+	0.854400i
$445$	340.731	+	590.163i	0.765687	+	1.32621i
$446$	202.765	+	488.309i	0.454630	+	1.09486i
$447$		−	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	$0.266028\pi$
$450$	−3.60057	+	1.49510i	−0.00800128	+	0.00332245i
$451$	−455.223	+	262.823i	−1.00936	+	0.582757i
$452$	273.870	−	274.831i	0.605907	−	0.608033i
$453$	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	$0.0731662\pi$
$458$	110.184	−	842.629i	0.240576	−	1.83980i
$459$	−272.852	+	157.531i	−0.594448	+	0.343205i
$460$	5.97705	−	22.4639i	0.0129936	−	0.0488346i
$461$	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	$-0.933076\pi$
$463$		−	193.258i		−	0.417403i	0.977979	−	0.208702i	$-0.0669237\pi$
$464$	2.40037	+	685.310i	0.00517322	+	1.47696i
$465$	15.7401	+	27.2626i	0.0338496	+	0.0586292i
$466$	56.7456	−	433.961i	0.121772	−	0.931248i
$467$	−567.503	−	327.648i	−1.21521	−	0.701602i	−0.251321	−	0.967904i	$-0.580865\pi$
$467$	−567.503	−	327.648i	−1.21521	−	0.701602i	−0.963890	+	0.266301i	$0.914198\pi$
$468$	−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
$472$	57.5100	+	428.138i	0.121843	+	0.907072i
$473$	200.721	+	347.659i	0.424357	+	0.735008i
$474$	−314.147	+	130.446i	−0.662758	+	0.275203i
$475$		−	478.322i		−	1.00699i
$476$		0			0
$477$	3.96986			0.00832256
$478$	69.1556	+	166.544i	0.144677	+	0.348418i
$479$	88.9066	−	51.3302i	0.185609	−	0.107161i	−0.404316	−	0.914619i	$-0.632491\pi$
$479$	88.9066	−	51.3302i	0.185609	−	0.107161i	0.589925	+	0.807458i	$0.299157\pi$
$480$	−599.414	+	251.366i	−1.24878	+	0.523679i
$481$	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
$486$	9.79416	+	1.28070i	0.0201526	+	0.00263519i
$487$	−130.469	+	75.3260i	−0.267903	+	0.154674i	−0.627934	−	0.778267i	$-0.716099\pi$
$487$	−130.469	+	75.3260i	−0.267903	+	0.154674i	0.360032	+	0.932940i	$0.382766\pi$
$488$	−77.9425	−	101.026i	−0.159718	−	0.207021i
$489$	−136.783			−0.279720
$490$		0			0
$491$			118.795i			0.241946i	0.992656	+	0.120973i	$0.0386014\pi$
$491$			118.795i			0.241946i	−0.992656	+	0.120973i	$0.961399\pi$
$492$	112.506	−	422.839i	0.228671	−	0.859428i
$493$	−248.656	−	430.685i	−0.504373	−	0.873600i
$494$	205.730	+	26.9016i	0.416457	+	0.0544566i
$495$	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	0.892566	−	0.450917i	$-0.148903\pi$
$499$	473.223	+	273.215i	0.948343	+	0.547526i	0.0557769	+	0.998443i	$0.482236\pi$
$500$	−70.8467	+	71.0953i	−0.141693	+	0.142191i
$501$	23.2577	+	40.2834i	0.0464225	+	0.0804061i
$502$	245.070	+	590.190i	0.488188	+	1.17568i
$503$		−	520.718i		−	1.03522i	−0.855615	−	0.517612i	$-0.826821\pi$
$503$		−	520.718i		−	1.03522i	0.855615	−	0.517612i	$-0.173179\pi$
$504$		0			0
$505$	191.658			0.379521
$506$	−22.6227	+	9.39385i	−0.0447089	+	0.0185649i
$507$	−381.608	+	220.322i	−0.752679	+	0.434559i
$508$	−203.638	−	202.926i	−0.400863	−	0.399461i
$509$	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
$514$	43.4266	−	332.105i	0.0844875	−	0.646118i
$515$	944.408	−	545.254i	1.83380	−	1.05875i
$516$	−322.926	−	85.9220i	−0.625826	−	0.166515i
$517$	−604.886			−1.16999
$518$		0			0
$519$			793.998i			1.52986i
$520$	153.724	+	199.251i	0.295623	+	0.383175i
$521$	−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	$-0.355404\pi$
$522$	−1.01588	+	7.76891i	−0.00194612	+	0.0148830i
$523$	−124.355	−	71.7965i	−0.237773	−	0.137278i	0.376380	−	0.926465i	$-0.377169\pi$
$523$	−124.355	−	71.7965i	−0.237773	−	0.137278i	−0.614153	+	0.789187i	$0.710502\pi$
$524$	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
$528$	594.371	+	340.390i	1.12570	+	0.644678i
$529$	−264.135	−	457.496i	−0.499311	−	0.864832i
$530$	−545.597	+	226.554i	−1.02943	+	0.427460i
$531$			4.93877i			0.00930088i
$532$		0			0
$533$	−169.409			−0.317840
$534$	229.235	+	552.054i	0.429278	+	1.03381i
$535$	700.884	−	404.656i	1.31006	−	0.756366i
$536$	97.9256	+	729.015i	0.182697	+	1.36010i
$537$	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	$0.886943\pi$
$542$	−631.262	−	82.5449i	−1.16469	−	0.152297i
$543$	434.539	−	250.881i	0.800256	−	0.462028i
$544$	−224.888	+	295.752i	−0.413398	+	0.543662i
$545$	−668.740			−1.22705
$546$		0			0
$547$		−	356.858i		−	0.652391i	−0.945302	−	0.326196i	$-0.894233\pi$
$547$		−	356.858i		−	0.652391i	0.945302	−	0.326196i	$-0.105767\pi$
$548$	70.2168	+	18.6828i	0.128133	+	0.0340927i
$549$	−0.729401	−	1.26336i	−0.00132860	−	0.00230120i
$550$	−606.205	−	79.2685i	−1.10219	−	0.144125i
$551$	−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
$556$	379.911	+	378.583i	0.683294	+	0.680904i
$557$	−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	$0.927526\pi$
$558$	−0.108720	−	0.261825i	−0.000194839	−	0.000469221i
$559$			129.379i			0.231447i
$560$		0			0
$561$	−497.040			−0.885989
$562$	−202.895	+	84.2502i	−0.361023	+	0.149911i
$563$	73.8314	−	42.6266i	0.131139	−	0.0757133i	−0.432995	−	0.901396i	$-0.642543\pi$
$563$	73.8314	−	42.6266i	0.131139	−	0.0757133i	0.564134	+	0.825683i	$0.309210\pi$
$564$	355.411	−	356.658i	0.630161	−	0.632372i
$565$	−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	$0.158624\pi$
$570$	118.212	−	904.025i	0.207389	−	1.58601i
$571$	586.760	−	338.766i	1.02760	−	0.593286i	0.111304	−	0.993786i	$-0.464497\pi$
$571$	586.760	−	338.766i	1.02760	−	0.593286i	0.916296	+	0.400501i	$0.131164\pi$
$572$	68.1879	−	256.275i	0.119210	−	0.448033i
$573$	1055.42			1.84191
$574$		0			0
$575$			18.2000i			0.0316521i
$576$	5.64609	−	1.54470i	0.00980224	−	0.00268178i
$577$	−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	$0.839034\pi$
$578$	−39.9843	+	305.779i	−0.0691769	+	0.529030i
$579$	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
$584$	−76.0155	+	10.2109i	−0.130164	+	0.0174843i
$585$	1.43858	+	2.49169i	0.00245911	+	0.00425930i
$586$	−245.666	+	102.010i	−0.419225	+	0.174079i
$587$			551.489i			0.939504i	0.882798	+	0.469752i	$0.155657\pi$
$587$			551.489i			0.939504i	−0.882798	+	0.469752i	$0.844343\pi$
$588$		0			0
$589$	34.7825			0.0590534
$590$	−281.848	−	678.759i	−0.477708	−	1.15044i
$591$	−69.6133	+	40.1912i	−0.117789	+	0.0680055i
$592$	625.005	+	357.934i	1.05575	+	0.604618i
$593$	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
$598$	−7.82793	−	1.02359i	−0.0130902	−	0.00171170i
$599$	−573.698	+	331.225i	−0.957759	+	0.552963i	−0.895483	−	0.445096i	$-0.853169\pi$
$599$	−573.698	+	331.225i	−0.957759	+	0.552963i	−0.0622766	+	0.998059i	$0.519836\pi$
$600$	402.925	−	310.860i	0.671542	−	0.518101i
$601$	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
$604$	95.7634	−	359.914i	0.158549	−	0.595884i
$605$	288.245	+	499.255i	0.476438	+	0.825215i
$606$	166.697	+	21.7976i	0.275078	+	0.0359697i
$607$	887.606	+	512.459i	1.46228	+	0.844249i	0.999117	−	0.0420222i	$-0.0133800\pi$
$607$	887.606	+	512.459i	1.46228	+	0.844249i	0.463166	+	0.886272i	$0.346713\pi$
$608$	−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
$612$	−2.99836	+	3.00888i	−0.00489928	+	0.00491647i
$613$	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	$0.804957\pi$
$614$	−293.610	−	707.086i	−0.478192	−	1.15161i
$615$			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	$0.479629\pi$
$618$	883.424	−	366.833i	1.42949	−	0.593580i
$619$	620.070	−	357.997i	1.00173	−	0.578348i	0.0929689	−	0.995669i	$-0.470364\pi$
$619$	620.070	−	357.997i	1.00173	−	0.578348i	0.908759	+	0.417321i	$0.137031\pi$
$620$	29.8839	+	29.7794i	0.0481999	+	0.0480313i
$621$	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
$626$	−110.740	+	846.881i	−0.176900	+	1.35284i
$627$	−832.033	+	480.375i	−1.32701	+	0.766148i
$628$	615.920	+	163.880i	0.980765	+	0.260955i
$629$	−522.657			−0.830933
$630$		0			0
$631$		−	849.316i		−	1.34598i	−0.739650	−	0.672992i	$-0.765009\pi$
$631$		−	849.316i		−	1.34598i	0.739650	−	0.672992i	$-0.234991\pi$
$632$	−360.929	+	278.460i	−0.571089	+	0.440601i
$633$	118.927	+	205.987i	0.187878	+	0.325414i
$634$	28.7969	−	220.224i	0.0454210	−	0.347357i
$635$	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
$640$	−687.815	+	534.509i	−1.07471	+	0.835171i
$641$	−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	$0.957659\pi$
$642$	655.625	−	272.242i	1.02122	−	0.424052i
$643$		−	257.106i		−	0.399854i	−0.979811	−	0.199927i	$-0.935930\pi$
$643$		−	257.106i		−	0.399854i	0.979811	−	0.199927i	$-0.0640705\pi$
$644$		0			0
$645$	568.522			0.881430
$646$	−199.859	−	481.310i	−0.309379	−	0.745061i
$647$	−605.816	+	349.768i	−0.936346	+	0.540600i	−0.888813	−	0.458270i	$-0.848469\pi$
$647$	−605.816	+	349.768i	−0.936346	+	0.540600i	−0.0475329	+	0.998870i	$0.515136\pi$
$648$	−635.639	+	85.3828i	−0.980924	+	0.131764i
$649$	−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	$0.234853\pi$
$654$	−581.645	−	76.0569i	−0.889365	−	0.116295i
$655$	−1236.70	+	714.009i	−1.88809	+	1.09009i
$656$	−2.05387	−	586.384i	−0.00313090	−	0.893878i
$657$	−0.876874			−0.00133466
$658$		0			0
$659$			522.721i			0.793204i	0.917991	+	0.396602i	$0.129811\pi$
$659$			522.721i			0.793204i	−0.917991	+	0.396602i	$0.870189\pi$
$660$	−1126.13	−	299.634i	−1.70626	−	0.453991i
$661$	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	$0.705719\pi$
$662$	−237.237	−	31.0216i	−0.358365	−	0.0468604i
$663$	−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
$668$	44.1567	+	44.0023i	0.0661029	+	0.0658718i
$669$	−394.530	−	683.346i	−0.589731	−	1.02144i
$670$	−479.918	−	1155.76i	−0.716296	−	1.72502i
$671$		−	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	$0.867842\pi$
$674$	105.956	−	43.9970i	0.157204	−	0.0652774i
$675$	500.853	−	289.167i	0.742004	−	0.428396i
$676$	−416.838	+	418.300i	−0.616624	+	0.618787i
$677$	−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
$682$	5.76422	−	44.0818i	0.00845193	−	0.0646361i
$683$	139.772	−	80.6973i	0.204644	−	0.118151i	−0.394176	−	0.919035i	$-0.628970\pi$
$683$	139.772	−	80.6973i	0.204644	−	0.118151i	0.598820	+	0.800884i	$0.295637\pi$
$684$	−2.11119	+	7.93463i	−0.00308654	+	0.0116003i
$685$	−123.619			−0.180466
$686$		0			0
$687$			1268.21i			1.84601i
$688$	−447.827	+	1.56856i	−0.650912	+	0.00227989i
$689$	100.317	+	173.754i	0.145598	+	0.252183i
$690$	−4.49792	+	34.3978i	−0.00651872	+	0.0498519i
$691$	98.4337	+	56.8307i	0.142451	+	0.0822442i	0.569532	−	0.821969i	$-0.307125\pi$
$691$	98.4337	+	56.8307i	0.142451	+	0.0822442i	−0.427081	+	0.904214i	$0.640458\pi$
$692$	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
$696$	−136.157	−	1013.63i	−0.195628	−	1.45637i
$697$	212.762	+	368.514i	0.305254	+	0.528715i
$698$	179.260	−	74.4357i	0.256819	−	0.106641i
$699$			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	$0.424131\pi$
$702$	96.2042	+	231.684i	0.137043	+	0.330034i
$703$	−874.916	+	505.133i	−1.24455	+	0.718539i
$704$	887.887	+	232.916i	1.26120	+	0.330846i
$705$	−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	$0.0297371\pi$
$710$	220.771	+	28.8684i	0.310945	+	0.0406598i
$711$	−4.51351	+	2.60588i	−0.00634812	+	0.00366509i
$712$	489.340	+	634.263i	0.687275	+	0.890819i
$713$	−1.32346			−0.00185618
$714$		0			0
$715$			451.181i			0.631022i
$716$	45.7747	−	172.038i	0.0639312	−	0.240277i
$717$	−134.559	−	233.064i	−0.187670	−	0.325054i
$718$	1170.42	+	153.047i	1.63012	+	0.213157i
$719$	418.810	+	241.800i	0.582489	+	0.336300i	0.762122	−	0.647433i	$-0.224158\pi$
$719$	418.810	+	241.800i	0.582489	+	0.336300i	−0.179633	+	0.983734i	$0.557491\pi$
$720$	−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
$724$	474.655	−	476.320i	0.655601	−	0.657901i
$725$	456.438	+	790.575i	0.629570	+	1.09045i
$726$	193.924	+	467.016i	0.267112	+	0.643272i
$727$		−	659.508i		−	0.907163i	−0.891215	−	0.453582i	$-0.850146\pi$
$727$		−	659.508i		−	0.907163i	0.891215	−	0.453582i	$-0.149854\pi$
$728$		0			0
$729$	−736.257			−1.00995
$730$	120.513	−	50.0418i	0.165086	−	0.0685504i
$731$	281.438	−	162.488i	0.385004	−	0.222282i
$732$	134.884	+	134.413i	0.184268	+	0.183624i
$733$	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
$738$	0.869232	−	6.64745i	0.00117782	−	0.00900738i
$739$	−213.832	+	123.456i	−0.289353	+	0.167058i	−0.637650	−	0.770326i	$-0.720093\pi$
$739$	−213.832	+	123.456i	−0.289353	+	0.167058i	0.348297	+	0.937384i	$0.386760\pi$
$740$	−1184.17	−	315.077i	−1.60024	−	0.425780i
$741$	−309.636			−0.417863
$742$		0			0
$743$		−	333.126i		−	0.448352i	−0.974549	−	0.224176i	$-0.928031\pi$
$743$		−	333.126i		−	0.448352i	0.974549	−	0.224176i	$-0.0719691\pi$
$744$	22.6050	+	29.2998i	0.0303831	+	0.0393814i
$745$	70.6459	+	122.362i	0.0948267	+	0.164245i
$746$	143.665	−	1098.68i	0.192581	−	1.47276i
$747$	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	0.105255	−	0.994445i	$-0.466434\pi$
$751$	−528.203	−	304.958i	−0.703333	−	0.406069i	−0.808588	+	0.588376i	$0.799768\pi$
$752$	335.343	−	585.558i	0.445935	−	0.778667i
$753$	−476.845	−	825.920i	−0.633261	−	1.09684i
$754$	−365.703	+	151.854i	−0.485017	+	0.201398i
$755$			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	$0.406282\pi$
$758$	−575.168	−	1385.15i	−0.758797	−	1.82737i
$759$	31.6585	−	18.2781i	0.0417108	−	0.0240818i
$760$	−162.666	−	1210.98i	−0.214034	−	1.59339i
$761$	−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
$766$	488.304	+	63.8515i	0.637472	+	0.0833570i
$767$	−216.161	+	124.801i	−0.281827	+	0.162713i
$768$	−659.027	+	386.670i	−0.858108	+	0.503476i
$769$	−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
$772$	1347.42	+	358.511i	1.74536	+	0.464393i
$773$	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	$0.782576\pi$
$774$	−5.07672	−	0.663842i	−0.00655908	−	0.000857676i
$775$	−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
$780$	−266.029	−	265.099i	−0.341063	−	0.339870i
$781$	−117.312	−	203.190i	−0.150207	−	0.260167i
$782$	7.60455	+	18.3136i	0.00972449	+	0.0234190i
$783$		−	1162.27i		−	1.48438i
$784$		0			0
$785$	−1084.35			−1.38134
$786$	−1156.84	+	480.366i	−1.47181	+	0.611153i
$787$	502.289	−	289.997i	0.638232	−	0.368483i	−0.145701	−	0.989329i	$-0.546544\pi$
$787$	502.289	−	289.997i	0.638232	−	0.368483i	0.783933	+	0.620845i	$0.213210\pi$
$788$	−76.0399	+	76.3067i	−0.0964973	+	0.0968359i
$789$	−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
$794$	−33.1464	+	253.487i	−0.0417461	+	0.319253i
$795$	763.516	−	440.816i	0.960397	−	0.554486i
$796$	238.161	−	895.097i	0.299197	−	1.12449i
$797$	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
$800$	412.810	−	542.890i	0.516013	−	0.678612i
$801$	4.57933	+	7.93164i	0.00571702	+	0.00990217i
$802$	−200.785	+	1535.50i	−0.250355	+	1.91459i
$803$	−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
$808$	223.297	−	29.9946i	0.276358	−	0.0371220i
$809$	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	$0.691471\pi$
$810$	1007.73	−	418.448i	1.24411	−	0.516602i
$811$		−	482.271i		−	0.594662i	−0.954774	−	0.297331i	$-0.903903\pi$
$811$		−	482.271i		−	0.594662i	0.954774	−	0.297331i	$-0.0960965\pi$
$812$		0			0
$813$	950.089			1.16862
$814$	495.192	+	1192.54i	0.608344	+	1.46504i
$815$	270.091	−	155.937i	0.331400	−	0.191334i
$816$	275.554	−	481.158i	0.337689	−	0.589654i
$817$	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	$0.0910629\pi$
$822$	−107.519	−	14.0594i	−0.130802	−	0.0171039i
$823$	306.907	−	177.193i	0.372913	−	0.215301i	−0.301817	−	0.953366i	$-0.597593\pi$
$823$	306.907	−	177.193i	0.372913	−	0.215301i	0.674730	+	0.738064i	$0.264260\pi$
$824$	1014.98	−	783.066i	1.23177	−	0.950322i
$825$	912.377			1.10591
$826$		0			0
$827$		−	1260.47i		−	1.52414i	−0.647493	−	0.762072i	$-0.724182\pi$
$827$		−	1260.47i		−	1.52414i	0.647493	−	0.762072i	$-0.275818\pi$
$828$	0.0803300	−	0.301909i	9.70169e−5	−	0.000364625i
$829$	−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	$-0.503026\pi$
$830$	−193.094	−	25.2493i	−0.232643	−	0.0304208i
$831$	−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
$836$	−908.845	+	912.034i	−1.08714	+	1.09095i
$837$	21.0276	+	36.4208i	0.0251226	+	0.0435135i
$838$	−73.1423	−	176.145i	−0.0872819	−	0.210196i
$839$		−	44.6511i		−	0.0532194i	−0.999646	−	0.0266097i	$-0.991529\pi$
$839$		−	44.6511i		−	0.0532194i	0.999646	−	0.0266097i	$-0.00847114\pi$
$840$		0			0
$841$	993.593			1.18144
$842$	515.629	−	214.110i	0.612386	−	0.254287i
$843$	283.934	−	163.930i	0.336814	−	0.194460i
$844$	225.793	+	225.003i	0.267527	+	0.266591i
$845$	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
$850$	−64.1698	+	490.738i	−0.0754939	+	0.577339i
$851$	33.2902	−	19.2201i	0.0391189	−	0.0225853i
$852$	188.735	+	50.2174i	0.221520	+	0.0589406i
$853$	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
$856$	753.258	−	581.145i	0.879974	−	0.678908i
$857$	−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	$0.861809\pi$
$858$	−51.3135	+	392.420i	−0.0598060	+	0.457366i
$859$	−118.348	−	68.3281i	−0.137774	−	0.0795437i	0.429529	−	0.903053i	$-0.358680\pi$
$859$	−118.348	−	68.3281i	−0.137774	−	0.0795437i	−0.567303	+	0.823509i	$0.692013\pi$
$860$	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	0.999344	−	0.0362164i	$-0.0115306\pi$
$863$	1266.58	+	731.262i	1.46765	+	0.847349i	0.468308	+	0.883565i	$0.344864\pi$
$864$	−800.774	+	335.806i	−0.926821	+	0.388665i
$865$	−905.185	−	1567.83i	−1.04646	−	1.81252i
$866$	−545.286	+	226.424i	−0.629661	+	0.261460i
$867$		−	460.217i		−	0.530816i
$868$		0			0
$869$	−817.281			−0.940484
$870$	667.284	+	1606.98i	0.766993	+	1.84711i
$871$	−368.070	+	212.505i	−0.422584	+	0.243979i
$872$	−779.135	+	104.658i	−0.893504	+	0.120021i
$873$	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	$0.172091\pi$
$878$	648.029	+	84.7374i	0.738074	+	0.0965118i
$879$	343.788	−	198.486i	0.391113	−	0.225809i
$880$	−1561.70	+	5.47002i	−1.77466	+	0.00621593i
$881$	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	$-0.699307\pi$
$883$		−	1430.98i		−	1.62059i	0.586022	−	0.810295i	$-0.300693\pi$
$884$	−207.461	−	55.1998i	−0.234684	−	0.0624432i
$885$	548.405	+	949.865i	0.619666	+	1.07329i
$886$	1020.89	+	133.493i	1.15224	+	0.150669i
$887$	1028.15	+	593.605i	1.15914	+	0.669228i	0.951097	−	0.308892i	$-0.0999582\pi$
$887$	1028.15	+	593.605i	1.15914	+	0.669228i	0.208040	+	0.978120i	$0.433292\pi$
$888$	−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
$892$	−749.050	−	746.431i	−0.839743	−	0.836806i
$893$	473.252	+	819.696i	0.529957	+	0.917913i
$894$	47.5287	+	114.461i	0.0531641	+	0.128032i
$895$			302.879i			0.338412i
$896$		0			0
$897$	11.7815			0.0131344
$898$	−1112.35	+	461.891i	−1.23869	+	0.514355i
$899$	−57.4887	+	33.1911i	−0.0639474	+	0.0369201i
$900$	5.50386	−	5.52317i	0.00611540	−	0.00613686i
$901$	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
$906$	−72.0650	+	551.117i	−0.0795419	+	0.608297i
$907$	708.980	−	409.330i	0.781676	−	0.451301i	−0.0553481	−	0.998467i	$-0.517627\pi$
$907$	708.980	−	409.330i	0.781676	−	0.451301i	0.837024	+	0.547166i	$0.184294\pi$
$908$	−443.620	+	1667.29i	−0.488569	+	1.83622i
$909$	2.57584			0.00283370
$910$		0			0
$911$		−	774.905i		−	0.850610i	−0.905050	−	0.425305i	$-0.860167\pi$
$911$		−	774.905i		−	0.850610i	0.905050	−	0.425305i	$-0.139833\pi$
$912$	−3.75396	−	1071.76i	−0.00411619	−	1.17518i
$913$	102.605	+	177.717i	0.112382	+	0.194651i
$914$	−68.6239	+	524.801i	−0.0750809	+	0.574181i
$915$	−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	$-0.959282\pi$
$919$	−1468.77	−	847.993i	−1.59822	−	0.922734i	−0.606393	−	0.795165i	$-0.707384\pi$
$920$	6.18936	+	46.0772i	0.00672756	+	0.0500839i
$921$	571.291	+	989.506i	0.620295	+	1.07438i
$922$	−803.091	+	333.475i	−0.871032	+	0.361687i
$923$		−	75.6160i		−	0.0819241i
$924$		0			0
$925$	959.401			1.03719
$926$	148.226	+	356.964i	0.160071	+	0.385490i
$927$	12.6926	−	7.32808i	0.0136921	−	0.00790515i
$928$	−530.056	−	1263.99i	−0.571181	−	1.36206i
$929$	−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
$934$	1299.53	+	169.929i	1.39136	+	0.181937i
$935$	981.453	−	566.642i	1.04968	−	0.606034i
$936$	2.06601	+	2.67788i	0.00220728	+	0.00286098i
$937$	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
$940$	−295.191	+	1109.44i	−0.314033	+	1.18025i
$941$	−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	$0.905581\pi$
$942$	−943.125	−	123.325i	−1.00119	−	0.130918i
$943$	−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	−0.126759	−	0.991934i	$-0.540458\pi$
$947$	−993.572	−	573.639i	−1.04918	−	0.605743i	−0.922419	+	0.386190i	$0.873791\pi$
$948$	480.207	−	481.892i	0.506548	−	0.508325i
$949$	−22.1583	−	38.3793i	−0.0233491	−	0.0404418i
$950$	366.866	+	883.503i	0.386174	+	0.930003i
$951$			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	$0.373716\pi$
$954$	−7.33268	+	3.04482i	−0.00768625	+	0.00319164i
$955$	−2084.02	+	1203.21i	−2.18222	+	1.25991i
$956$	−255.473	−	254.580i	−0.267231	−	0.266297i
$957$	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
$962$	−53.9582	+	412.645i	−0.0560897	+	0.428945i
$963$	9.41970	−	5.43847i	0.00978162	−	0.00564742i
$964$	1453.22	+	386.662i	1.50749	+	0.401101i
$965$	−2372.17			−2.45821
$966$		0			0
$967$			1147.66i			1.18682i	0.804899	+	0.593411i	$0.202219\pi$
$967$			1147.66i			1.18682i	−0.804899	+	0.593411i	$0.797781\pi$
$968$	413.962	+	536.561i	0.427647	+	0.554299i
$969$	388.875	+	673.551i	0.401316	+	0.695099i
$970$	−120.502	+	921.540i	−0.124229	+	0.950042i
$971$	−960.111	−	554.321i	−0.988786	−	0.570876i	−0.0838750	−	0.996476i	$-0.526730\pi$
$971$	−960.111	−	554.321i	−0.988786	−	0.570876i	−0.904911	+	0.425600i	$0.860063\pi$
$972$	−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
$976$	221.452	+	126.823i	0.226898	+	0.129942i
$977$	−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	$0.963866\pi$
$978$	252.650	−	104.910i	0.258333	−	0.107270i
$979$			1436.21i			1.46702i
$980$		0			0
$981$	−8.98769			−0.00916176
$982$	−91.1142	−	219.426i	−0.0927843	−	0.223448i
$983$	68.9305	−	39.7970i	0.0701225	−	0.0404853i	−0.464529	−	0.885558i	$-0.653776\pi$
$983$	68.9305	−	39.7970i	0.0701225	−	0.0404853i	0.534651	+	0.845073i	$0.320443\pi$
$984$	116.502	+	867.311i	0.118397	+	0.881414i
$985$	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
$990$	−17.7039	−	2.31500i	−0.0178828	−	0.00233838i
$991$	−557.931	+	322.122i	−0.562998	+	0.325047i	−0.754348	−	0.656475i	$-0.772047\pi$
$991$	−557.931	+	322.122i	−0.562998	+	0.325047i	0.191350	+	0.981522i	$0.438714\pi$
$992$	39.4777	+	30.0186i	0.0397960	+	0.0302607i
$993$	357.057			0.359574
$994$		0			0
$995$			1575.85i			1.58377i
$996$	−165.074	−	43.9217i	−0.165737	−	0.0440981i
$997$	−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	$-0.504244\pi$
$998$	−1083.64	−	141.698i	−1.08581	−	0.141982i
$999$	−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.79.1		12
4.3	odd	2	inner	196.3.g.j.79.3		12
7.2	even	3		196.3.c.g.99.6		6
7.3	odd	6		196.3.g.k.67.3		12
7.4	even	3	inner	196.3.g.j.67.3		12
7.5	odd	6		28.3.c.a.15.6	yes	6
7.6	odd	2		196.3.g.k.79.1		12
21.5	even	6		252.3.g.a.127.1		6
28.3	even	6		196.3.g.k.67.1		12
28.11	odd	6	inner	196.3.g.j.67.1		12
28.19	even	6		28.3.c.a.15.5	✓	6
28.23	odd	6		196.3.c.g.99.5		6
28.27	even	2		196.3.g.k.79.3		12
56.5	odd	6		448.3.d.d.127.5		6
56.19	even	6		448.3.d.d.127.2		6
84.47	odd	6		252.3.g.a.127.2		6
112.5	odd	12		1792.3.g.g.127.3		12
112.19	even	12		1792.3.g.g.127.4		12
112.61	odd	12		1792.3.g.g.127.10		12
112.75	even	12		1792.3.g.g.127.9		12

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

\(f(q)\)	\(=\)	\(q+(-1.84709 + 0.766985i) q^{2} +(2.58484 - 1.49236i) q^{3} +(2.82347 - 2.83338i) q^{4} +(-3.40268 + 5.89361i) q^{5} +(-3.62981 + 4.73905i) q^{6} +(-3.04204 + 7.39905i) q^{8} +(-0.0457311 + 0.0792086i) q^{9} +O(q^{10})\)	\(q+(-1.84709 + 0.766985i) q^{2} +(2.58484 - 1.49236i) q^{3} +(2.82347 - 2.83338i) 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} +(1.76474 - 13.4958i) q^{10} +(-12.4211 + 7.17132i) q^{11} +(3.06981 - 11.5375i) q^{12} -4.62243 q^{13} +20.3121i q^{15} +(-0.0560414 - 15.9999i) q^{16} +(5.80536 + 10.0552i) q^{17} +(0.0237176 - 0.181380i) 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} +(3.17885 + 23.6652i) q^{24} +(-10.6564 - 18.4575i) q^{25} +(8.53804 - 3.54533i) q^{26} +27.1354i q^{27} -42.8321 q^{29} +(-15.5790 - 37.5182i) q^{30} +(1.34219 - 0.774912i) q^{31} +(12.3752 + 29.5102i) 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} +(-44.5068 - 5.81979i) q^{38} +(-11.9483 + 6.89833i) q^{39} +(-33.2561 - 43.1052i) q^{40} +36.6492 q^{41} -27.9894i q^{43} +(-14.7515 + 55.4416i) q^{44} +(-0.311217 - 0.539043i) q^{45} +(1.69347 + 0.221441i) 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} +(-13.0513 + 13.0971i) q^{52} +(-21.7022 - 37.5893i) q^{53} +(-20.8125 - 50.1216i) q^{54} -97.6068i q^{55} +66.9856 q^{57} +(79.1147 - 32.8516i) q^{58} +(46.7636 - 26.9990i) q^{59} +(57.5517 + 57.3505i) 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} +(11.1010 - 84.8947i) q^{66} +(79.6270 - 45.9726i) q^{67} +(44.8813 + 11.9417i) q^{68} -2.54877 q^{69} +16.3585i q^{71} +(-0.446953 - 0.579323i) q^{72} +(4.79364 + 8.30283i) q^{73} +(11.6731 - 89.2702i) 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} +(94.4879 + 54.1122i) q^{80} +(40.0842 + 69.4279i) q^{81} +(-67.6943 + 28.1094i) q^{82} -14.3077i q^{83} -79.0151 q^{85} +(21.4674 + 51.6989i) q^{86} +(-110.714 + 63.9209i) q^{87} +(-15.2755 - 113.720i) 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} +(-83.6359 - 10.9364i) q^{94} +(-132.269 + 76.3658i) q^{95} +(76.0278 + 57.8111i) 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

L-functions

Modular forms

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