LMFDB - Embedded newform 392.3.k.l.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} + \cdots + 4 $ x^12 - 3x^11 - 4x^10 + 3x^9 + 86x^8 - 163x^7 + 155x^6 - 166x^5 + 164x^4 - 116x^3 + 60x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.3
Root			$0.378279 + 0.358951i$ of defining polynomial
Character	$\chi$	$=$	392.67
Dual form			392.3.k.l.275.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104798 - 1.99725i) q^{2} +(-1.99052 + 3.44767i) q^{3} +(-3.97803 - 0.418616i) q^{4} +(1.63031 - 0.941260i) q^{5} +(6.67727 + 4.33687i) q^{6} +(-1.25297 + 7.90127i) q^{8} +(-3.42430 - 5.93106i) q^{9} +O(q^{10})$	\(q+(0.104798 - 1.99725i) q^{2} +(-1.99052 + 3.44767i) q^{3} +(-3.97803 - 0.418616i) q^{4} +(1.63031 - 0.941260i) q^{5} +(6.67727 + 4.33687i) q^{6} +(-1.25297 + 7.90127i) q^{8} +(-3.42430 - 5.93106i) q^{9} +(-1.70908 - 3.35478i) q^{10} +(3.93973 - 6.82381i) q^{11} +(9.36159 - 12.8817i) q^{12} +11.4863i q^{13} +7.49437i q^{15} +(15.6495 + 3.33054i) q^{16} +(-1.44921 + 2.51011i) q^{17} +(-12.2047 + 6.21763i) q^{18} +(-15.0223 - 26.0194i) q^{19} +(-6.87946 + 3.06189i) q^{20} +(-13.2160 - 8.58375i) q^{22} +(-33.3838 + 19.2741i) q^{23} +(-24.7469 - 20.0474i) q^{24} +(-10.7281 + 18.5815i) q^{25} +(22.9411 + 1.20374i) q^{26} -8.56478 q^{27} -27.8701i q^{29} +(14.9681 + 0.785394i) q^{30} +(-19.4709 - 11.2416i) q^{31} +(8.29196 - 30.9070i) q^{32} +(15.6842 + 27.1658i) q^{33} +(4.86145 + 3.15750i) q^{34} +(11.1392 + 25.0274i) q^{36} +(-39.4520 + 22.7776i) q^{37} +(-53.5417 + 27.2766i) q^{38} +(-39.6011 - 22.8637i) q^{39} +(5.39442 + 14.0609i) q^{40} +40.6313 q^{41} -47.2806 q^{43} +(-18.5289 + 25.4961i) q^{44} +(-11.1653 - 6.44632i) q^{45} +(34.9968 + 68.6958i) q^{46} +(-71.5172 + 41.2905i) q^{47} +(-42.6332 + 47.3250i) q^{48} +(35.9878 + 23.3739i) q^{50} +(-5.76936 - 9.99283i) q^{51} +(4.80836 - 45.6930i) q^{52} +(-23.2823 - 13.4420i) q^{53} +(-0.897571 + 17.1060i) q^{54} -14.8332i q^{55} +119.609 q^{57} +(-55.6637 - 2.92073i) q^{58} +(-5.20555 + 9.01627i) q^{59} +(3.13726 - 29.8129i) q^{60} +(19.1932 - 11.0812i) q^{61} +(-24.4927 + 37.7103i) q^{62} +(-60.8601 - 19.8001i) q^{64} +(10.8116 + 18.7263i) q^{65} +(55.9006 - 28.4783i) q^{66} +(29.6549 - 51.3639i) q^{67} +(6.81579 - 9.37864i) q^{68} -153.462i q^{69} +38.2541i q^{71} +(51.1535 - 19.6249i) q^{72} +(6.98890 - 12.1051i) q^{73} +(41.3581 + 81.1826i) q^{74} +(-42.7087 - 73.9737i) q^{75} +(48.8672 + 109.795i) q^{76} +(-49.8147 + 76.6974i) q^{78} +(44.3314 - 25.5948i) q^{79} +(28.6485 - 9.30046i) q^{80} +(47.8670 - 82.9081i) q^{81} +(4.25807 - 81.1509i) q^{82} +89.4458 q^{83} +5.45635i q^{85} +(-4.95491 + 94.4313i) q^{86} +(96.0871 + 55.4759i) q^{87} +(48.9804 + 39.6789i) q^{88} +(52.6288 + 91.1558i) q^{89} +(-14.0450 + 21.6245i) q^{90} +(140.870 - 62.6982i) q^{92} +(77.5144 - 44.7530i) q^{93} +(74.9726 + 147.165i) q^{94} +(-48.9821 - 28.2798i) q^{95} +(90.0520 + 90.1088i) q^{96} -55.3301 q^{97} -53.9633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 6 q^{3} - 4 q^{4} + 56 q^{6} + 8 q^{8} - 40 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 6 * q^3 - 4 * q^4 + 56 * q^6 + 8 * q^8 - 40 * q^9	$ 12 q + 2 q^{2} + 6 q^{3} - 4 q^{4} + 56 q^{6} + 8 q^{8} - 40 q^{9} + 6 q^{10} + 30 q^{11} - 32 q^{12} + 16 q^{16} - 30 q^{17} - 16 q^{18} - 78 q^{19} - 48 q^{20} + 24 q^{22} + 76 q^{24} - 92 q^{25} + 128 q^{26} - 156 q^{27} - 16 q^{30} + 112 q^{32} + 78 q^{33} - 76 q^{34} - 248 q^{36} - 80 q^{38} - 44 q^{40} + 232 q^{41} - 200 q^{43} + 132 q^{44} - 156 q^{46} - 176 q^{48} + 48 q^{50} + 10 q^{51} - 132 q^{52} + 36 q^{54} + 332 q^{57} + 4 q^{58} + 110 q^{59} + 84 q^{60} + 96 q^{62} - 160 q^{64} - 32 q^{65} + 138 q^{66} + 434 q^{67} - 96 q^{68} - 328 q^{72} - 102 q^{73} - 34 q^{74} + 60 q^{75} + 168 q^{76} + 720 q^{78} + 256 q^{80} - 82 q^{81} + 24 q^{82} + 536 q^{83} + 240 q^{86} - 204 q^{88} - 214 q^{89} - 440 q^{90} + 160 q^{92} + 16 q^{94} - 48 q^{96} + 152 q^{97} + 504 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 6 * q^3 - 4 * q^4 + 56 * q^6 + 8 * q^8 - 40 * q^9 + 6 * q^10 + 30 * q^11 - 32 * q^12 + 16 * q^16 - 30 * q^17 - 16 * q^18 - 78 * q^19 - 48 * q^20 + 24 * q^22 + 76 * q^24 - 92 * q^25 + 128 * q^26 - 156 * q^27 - 16 * q^30 + 112 * q^32 + 78 * q^33 - 76 * q^34 - 248 * q^36 - 80 * q^38 - 44 * q^40 + 232 * q^41 - 200 * q^43 + 132 * q^44 - 156 * q^46 - 176 * q^48 + 48 * q^50 + 10 * q^51 - 132 * q^52 + 36 * q^54 + 332 * q^57 + 4 * q^58 + 110 * q^59 + 84 * q^60 + 96 * q^62 - 160 * q^64 - 32 * q^65 + 138 * q^66 + 434 * q^67 - 96 * q^68 - 328 * q^72 - 102 * q^73 - 34 * q^74 + 60 * q^75 + 168 * q^76 + 720 * q^78 + 256 * q^80 - 82 * q^81 + 24 * q^82 + 536 * q^83 + 240 * q^86 - 204 * q^88 - 214 * q^89 - 440 * q^90 + 160 * q^92 + 16 * q^94 - 48 * q^96 + 152 * q^97 + 504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.104798	−	1.99725i	0.0523990	−	0.998626i
$2$	0.104798	−	1.99725i	0.0523990	−	0.998626i
$3$	−1.99052	+	3.44767i	−0.663505	+	1.14922i	0.316183	+	0.948698i	$0.397599\pi$
$3$	−1.99052	+	3.44767i	−0.663505	+	1.14922i	−0.979688	+	0.200526i	$0.935735\pi$
$4$	−3.97803	−	0.418616i	−0.994509	−	0.104654i
$5$	1.63031	−	0.941260i	0.326062	−	0.188252i	−0.328029	−	0.944668i	$-0.606384\pi$
$5$	1.63031	−	0.941260i	0.326062	−	0.188252i	0.654091	+	0.756416i	$0.273051\pi$
$6$	6.67727	+	4.33687i	1.11288	+	0.722812i
$7$		0			0
$7$		0			0
$8$	−1.25297	+	7.90127i	−0.156621	+	0.987659i
$9$	−3.42430	−	5.93106i	−0.380478	−	0.659007i
$10$	−1.70908	−	3.35478i	−0.170908	−	0.335478i
$11$	3.93973	−	6.82381i	0.358157	−	0.620346i	−0.629496	−	0.777004i	$-0.716739\pi$
$11$	3.93973	−	6.82381i	0.358157	−	0.620346i	0.987653	+	0.156658i	$0.0500719\pi$
$12$	9.36159	−	12.8817i	0.780132	−	1.07348i
$13$			11.4863i			0.883564i	0.897122	+	0.441782i	$0.145654\pi$
$13$			11.4863i			0.883564i	−0.897122	+	0.441782i	$0.854346\pi$
$14$		0			0
$15$			7.49437i			0.499625i
$16$	15.6495	+	3.33054i	0.978095	+	0.208159i
$17$	−1.44921	+	2.51011i	−0.0852478	+	0.147654i	−0.905497	−	0.424353i	$-0.860502\pi$
$17$	−1.44921	+	2.51011i	−0.0852478	+	0.147654i	0.820249	+	0.572007i	$0.193835\pi$
$18$	−12.2047	+	6.21763i	−0.678038	+	0.345424i
$19$	−15.0223	−	26.0194i	−0.790649	−	1.36944i	−0.925566	−	0.378587i	$-0.876410\pi$
$19$	−15.0223	−	26.0194i	−0.790649	−	1.36944i	0.134916	−	0.990857i	$-0.456923\pi$
$20$	−6.87946	+	3.06189i	−0.343973	+	0.153095i
$21$		0			0
$22$	−13.2160	−	8.58375i	−0.600727	−	0.390171i
$23$	−33.3838	+	19.2741i	−1.45147	+	0.838006i	−0.998565	−	0.0535530i	$-0.982945\pi$
$23$	−33.3838	+	19.2741i	−1.45147	+	0.838006i	−0.452904	+	0.891559i	$0.649612\pi$
$24$	−24.7469	−	20.0474i	−1.03112	−	0.835310i
$25$	−10.7281	+	18.5815i	−0.429122	+	0.743262i
$26$	22.9411	+	1.20374i	0.882350	+	0.0462978i
$27$	−8.56478			−0.317214
$28$		0			0
$29$		−	27.8701i		−	0.961039i	−0.876984	−	0.480519i	$-0.840448\pi$
$29$		−	27.8701i		−	0.961039i	0.876984	−	0.480519i	$-0.159552\pi$
$30$	14.9681	+	0.785394i	0.498938	+	0.0261798i
$31$	−19.4709	−	11.2416i	−0.628095	−	0.362631i	0.151919	−	0.988393i	$-0.451455\pi$
$31$	−19.4709	−	11.2416i	−0.628095	−	0.362631i	−0.780014	+	0.625762i	$0.784788\pi$
$32$	8.29196	−	30.9070i	0.259124	−	0.965844i
$33$	15.6842	+	27.1658i	0.475278	+	0.823206i
$34$	4.86145	+	3.15750i	0.142984	+	0.0928676i
$35$		0			0
$36$	11.1392	+	25.0274i	0.309421	+	0.695207i
$37$	−39.4520	+	22.7776i	−1.06627	+	0.615611i	−0.927160	−	0.374666i	$-0.877757\pi$
$37$	−39.4520	+	22.7776i	−1.06627	+	0.615611i	−0.139109	+	0.990277i	$0.544424\pi$
$38$	−53.5417	+	27.2766i	−1.40899	+	0.717805i
$39$	−39.6011	−	22.8637i	−1.01541	−	0.586249i
$40$	5.39442	+	14.0609i	0.134860	+	0.351522i
$41$	40.6313			0.991007			0.495503	−	0.868606i	$-0.334984\pi$
$41$	40.6313			0.991007			0.495503	+	0.868606i	$0.334984\pi$
$42$		0			0
$43$	−47.2806			−1.09955			−0.549774	−	0.835313i	$-0.685286\pi$
$43$	−47.2806			−1.09955			−0.549774	+	0.835313i	$0.685286\pi$
$44$	−18.5289	+	25.4961i	−0.421112	+	0.579457i
$45$	−11.1653	−	6.44632i	−0.248119	−	0.143251i
$46$	34.9968	+	68.6958i	0.760799	+	1.49339i
$47$	−71.5172	+	41.2905i	−1.52164	+	0.878520i	−0.521968	+	0.852965i	$0.674802\pi$
$47$	−71.5172	+	41.2905i	−1.52164	+	0.878520i	−0.999673	+	0.0255554i	$0.991865\pi$
$48$	−42.6332	+	47.3250i	−0.888192	+	0.985937i
$49$		0			0
$50$	35.9878	+	23.3739i	0.719755	+	0.467479i
$51$	−5.76936	−	9.99283i	−0.113125	−	0.195938i
$52$	4.80836	−	45.6930i	0.0924685	−	0.878712i
$53$	−23.2823	−	13.4420i	−0.439288	−	0.253623i	0.264007	−	0.964521i	$-0.414956\pi$
$53$	−23.2823	−	13.4420i	−0.439288	−	0.253623i	−0.703296	+	0.710897i	$0.748289\pi$
$54$	−0.897571	+	17.1060i	−0.0166217	+	0.316778i
$55$		−	14.8332i		−	0.269695i
$56$		0			0
$57$	119.609			2.09840
$58$	−55.6637	−	2.92073i	−0.959719	−	0.0503574i
$59$	−5.20555	+	9.01627i	−0.0882296	+	0.152818i	−0.906763	−	0.421641i	$-0.861454\pi$
$59$	−5.20555	+	9.01627i	−0.0882296	+	0.152818i	0.818533	+	0.574459i	$0.194788\pi$
$60$	3.13726	−	29.8129i	0.0522877	−	0.496881i
$61$	19.1932	−	11.0812i	0.314642	−	0.181659i	−0.334360	−	0.942446i	$-0.608520\pi$
$61$	19.1932	−	11.0812i	0.314642	−	0.181659i	0.649002	+	0.760787i	$0.275187\pi$
$62$	−24.4927	+	37.7103i	−0.395044	+	0.608231i
$63$		0			0
$64$	−60.8601	−	19.8001i	−0.950939	−	0.309377i
$65$	10.8116	+	18.7263i	0.166333	+	0.288097i
$66$	55.9006	−	28.4783i	0.846979	−	0.431490i
$67$	29.6549	−	51.3639i	0.442611	−	0.766625i	−0.555271	−	0.831669i	$-0.687386\pi$
$67$	29.6549	−	51.3639i	0.442611	−	0.766625i	0.997882	+	0.0650444i	$0.0207189\pi$
$68$	6.81579	−	9.37864i	0.100232	−	0.137921i
$69$		−	153.462i		−	2.22409i
$70$		0			0
$71$			38.2541i			0.538791i	0.963030	+	0.269395i	$0.0868238\pi$
$71$			38.2541i			0.538791i	−0.963030	+	0.269395i	$0.913176\pi$
$72$	51.1535	−	19.6249i	0.710465	−	0.272568i
$73$	6.98890	−	12.1051i	0.0957383	−	0.165824i	−0.814178	−	0.580615i	$-0.802812\pi$
$73$	6.98890	−	12.1051i	0.0957383	−	0.165824i	0.909917	+	0.414791i	$0.136145\pi$
$74$	41.3581	+	81.1826i	0.558894	+	1.09706i
$75$	−42.7087	−	73.9737i	−0.569450	−	0.986316i
$76$	48.8672	+	109.795i	0.642990	+	1.44467i
$77$		0			0
$78$	−49.8147	+	76.6974i	−0.638651	+	0.983300i
$79$	44.3314	−	25.5948i	0.561157	−	0.323984i	−0.192453	−	0.981306i	$-0.561644\pi$
$79$	44.3314	−	25.5948i	0.561157	−	0.323984i	0.753610	+	0.657322i	$0.228311\pi$
$80$	28.6485	−	9.30046i	0.358106	−	0.116256i
$81$	47.8670	−	82.9081i	0.590951	−	1.02356i
$82$	4.25807	−	81.1509i	0.0519277	−	0.989646i
$83$	89.4458			1.07766			0.538830	−	0.842414i	$-0.318866\pi$
$83$	89.4458			1.07766			0.538830	+	0.842414i	$0.318866\pi$
$84$		0			0
$85$			5.45635i			0.0641923i
$86$	−4.95491	+	94.4313i	−0.0576152	+	1.09804i
$87$	96.0871	+	55.4759i	1.10445	+	0.637654i
$88$	48.9804	+	39.6789i	0.556595	+	0.450896i
$89$	52.6288	+	91.1558i	0.591335	+	1.02422i	0.994053	+	0.108898i	$0.0347323\pi$
$89$	52.6288	+	91.1558i	0.591335	+	1.02422i	−0.402718	+	0.915324i	$0.631934\pi$
$90$	−14.0450	+	21.6245i	−0.156056	+	0.240272i
$91$		0			0
$92$	140.870	−	62.6982i	1.53120	−	0.681502i
$93$	77.5144	−	44.7530i	0.833488	−	0.481215i
$94$	74.9726	+	147.165i	0.797581	+	1.56558i
$95$	−48.9821	−	28.2798i	−0.515601	−	0.297683i
$96$	90.0520	+	90.1088i	0.938042	+	0.938634i
$97$	−55.3301			−0.570413			−0.285206	−	0.958466i	$-0.592062\pi$
$97$	−55.3301			−0.570413			−0.285206	+	0.958466i	$0.592062\pi$
$98$		0			0
$99$	−53.9633			−0.545084
$100$	50.4551	−	69.4271i	0.504551	−	0.694271i
$101$	−27.2216	−	15.7164i	−0.269521	−	0.155608i	0.359149	−	0.933280i	$-0.383067\pi$
$101$	−27.2216	−	15.7164i	−0.269521	−	0.155608i	−0.628670	+	0.777672i	$0.716400\pi$
$102$	−20.5628	+	10.4756i	−0.201596	+	0.102702i
$103$	−69.2701	+	39.9931i	−0.672525	+	0.388283i	−0.797033	−	0.603936i	$-0.793598\pi$
$103$	−69.2701	+	39.9931i	−0.672525	+	0.388283i	0.124508	+	0.992219i	$0.460265\pi$
$104$	−90.7566	−	14.3920i	−0.872660	−	0.138385i
$105$		0			0
$106$	−29.2871	+	45.0919i	−0.276293	+	0.425395i
$107$	−24.3817	−	42.2303i	−0.227866	−	0.394676i	0.729309	−	0.684184i	$-0.239842\pi$
$107$	−24.3817	−	42.2303i	−0.227866	−	0.394676i	−0.957175	+	0.289508i	$0.906508\pi$
$108$	34.0710	+	3.58535i	0.315472	+	0.0331977i
$109$	−99.6528	−	57.5346i	−0.914246	−	0.527840i	−0.0324509	−	0.999473i	$-0.510331\pi$
$109$	−99.6528	−	57.5346i	−0.914246	−	0.527840i	−0.881795	+	0.471633i	$0.843665\pi$
$110$	−29.6257	−	1.55449i	−0.269325	−	0.0141317i
$111$		−	181.357i		−	1.63384i
$112$		0			0
$113$	−55.7570			−0.493425			−0.246712	−	0.969089i	$-0.579350\pi$
$113$	−55.7570			−0.493425			−0.246712	+	0.969089i	$0.579350\pi$
$114$	12.5347	−	238.889i	0.109954	−	2.09552i
$115$	−36.2840	+	62.8457i	−0.315513	+	0.546484i
$116$	−11.6669	+	110.868i	−0.100577	+	0.955762i
$117$	68.1262	−	39.3327i	0.582275	−	0.336177i
$118$	17.4622	+	11.3417i	0.147985	+	0.0961159i
$119$		0			0
$120$	−59.2150	−	9.39023i	−0.493459	−	0.0782519i
$121$	29.4571	+	51.0212i	0.243447	+	0.421663i
$122$	−20.1205	−	39.4949i	−0.164922	−	0.323729i
$123$	−80.8772	+	140.083i	−0.657538	+	1.13889i
$124$	72.7502	+	52.8701i	0.586695	+	0.426372i
$125$			87.4546i			0.699637i
$126$		0			0
$127$		−	35.6964i		−	0.281074i	−0.990075	−	0.140537i	$-0.955117\pi$
$127$		−	35.6964i		−	0.281074i	0.990075	−	0.140537i	$-0.0448828\pi$
$128$	−45.9239	+	119.478i	−0.358780	+	0.933422i
$129$	94.1127	−	163.008i	0.729556	−	1.26363i
$130$	38.5342	−	19.6311i	0.296417	−	0.151008i
$131$	−60.6462	−	105.042i	−0.462948	−	0.801849i	0.536158	−	0.844117i	$-0.319875\pi$
$131$	−60.6462	−	105.042i	−0.462948	−	0.801849i	−0.999106	+	0.0422680i	$0.986542\pi$
$132$	−51.0202	−	114.632i	−0.386516	−	0.868425i
$133$		0			0
$134$	−99.4788	−	64.6112i	−0.742379	−	0.482173i
$135$	−13.9632	+	8.06168i	−0.103431	+	0.0597162i
$136$	−18.0172	−	14.5957i	−0.132480	−	0.107321i
$137$	4.24835	−	7.35836i	0.0310099	−	0.0537107i	−0.850104	−	0.526615i	$-0.823461\pi$
$137$	4.24835	−	7.35836i	0.0310099	−	0.0537107i	0.881114	+	0.472904i	$0.156794\pi$
$138$	−306.502	−	16.0825i	−2.22103	−	0.116540i
$139$	3.05942			0.0220102			0.0110051	−	0.999939i	$-0.496497\pi$
$139$	3.05942			0.0220102			0.0110051	+	0.999939i	$0.496497\pi$
$140$		0			0
$141$		−	328.757i		−	2.33161i
$142$	76.4032	+	4.00895i	0.538050	+	0.0282321i
$143$	78.3806	+	45.2530i	0.548116	+	0.316455i
$144$	−33.8351	−	104.223i	−0.234966	−	0.723771i
$145$	−26.2330	−	45.4370i	−0.180918	−	0.313358i
$146$	−23.4446	−	15.2272i	−0.160579	−	0.104296i
$147$		0			0
$148$	166.476	−	74.0949i	1.12484	−	0.500641i
$149$	27.4740	−	15.8621i	0.184389	−	0.106457i	−0.404964	−	0.914333i	$-0.632716\pi$
$149$	27.4740	−	15.8621i	0.184389	−	0.106457i	0.589353	+	0.807876i	$0.299383\pi$
$150$	−152.220	+	77.5478i	−1.01480	+	0.516986i
$151$	219.621	+	126.798i	1.45444	+	0.839723i	0.998729	−	0.0504039i	$-0.0160509\pi$
$151$	219.621	+	126.798i	1.45444	+	0.839723i	0.455713	+	0.890127i	$0.349384\pi$
$152$	224.409	−	86.0939i	1.47638	−	0.566407i
$153$	19.8502			0.129740
$154$		0			0
$155$	−42.3249			−0.273064
$156$	147.964	+	107.530i	0.948484	+	0.689297i
$157$	42.7187	+	24.6636i	0.272093	+	0.157093i	0.629839	−	0.776726i	$-0.283121\pi$
$157$	42.7187	+	24.6636i	0.272093	+	0.157093i	−0.357745	+	0.933819i	$0.616454\pi$
$158$	−46.4734	−	91.2233i	−0.294135	−	0.577363i
$159$	92.6875	−	53.5132i	0.582940	−	0.336561i
$160$	−15.5731	−	58.1929i	−0.0973317	−	0.363706i
$161$		0			0
$162$	−160.572	−	104.291i	−0.991186	−	0.643773i
$163$	−57.8597	−	100.216i	−0.354967	−	0.614821i	0.632145	−	0.774850i	$-0.282175\pi$
$163$	−57.8597	−	100.216i	−0.354967	−	0.614821i	−0.987112	+	0.160029i	$0.948841\pi$
$164$	−161.633	−	17.0089i	−0.985565	−	0.103713i
$165$	51.1401	+	29.5258i	0.309940	+	0.178944i
$166$	9.37373	−	178.646i	0.0564683	−	1.07618i
$167$			32.3859i			0.193928i	0.995288	+	0.0969639i	$0.0309131\pi$
$167$			32.3859i			0.193928i	−0.995288	+	0.0969639i	$0.969087\pi$
$168$		0			0
$169$	37.0641			0.219314
$170$	10.8977	+	0.571814i	0.0641041	+	0.00336361i
$171$	−102.882	+	178.197i	−0.601649	+	1.04209i
$172$	188.084	+	19.7924i	1.09351	+	0.115072i
$173$	−179.479	+	103.622i	−1.03745	+	0.598973i	−0.919110	−	0.394000i	$-0.871091\pi$
$173$	−179.479	+	103.622i	−1.03745	+	0.598973i	−0.118341	+	0.992973i	$0.537758\pi$
$174$	120.869	−	186.096i	0.694650	−	1.06952i
$175$		0			0
$176$	84.3818	−	93.6679i	0.479442	−	0.532204i
$177$	−20.7234	−	35.8941i	−0.117082	−	0.202791i
$178$	187.577	−	95.5601i	1.05380	−	0.536855i
$179$	−87.0837	+	150.833i	−0.486501	+	0.842644i	−0.999880	−	0.0155178i	$-0.995060\pi$
$179$	−87.0837	+	150.833i	−0.486501	+	0.842644i	0.513379	+	0.858162i	$0.328394\pi$
$180$	41.7176	+	30.3177i	0.231764	+	0.168431i
$181$			204.244i			1.12842i	0.825632	+	0.564209i	$0.190819\pi$
$181$			204.244i			1.12842i	−0.825632	+	0.564209i	$0.809181\pi$
$182$		0			0
$183$			88.2291i			0.482126i
$184$	−110.461	−	287.924i	−0.600333	−	1.56481i
$185$	−42.8793	+	74.2691i	−0.231780	+	0.401455i
$186$	−81.2596	−	159.506i	−0.436880	−	0.857558i
$187$	11.4190	+	19.7783i	0.0610642	+	0.105766i
$188$	301.783	−	134.317i	1.60523	−	0.714450i
$189$		0			0
$190$	−61.6152	+	94.8660i	−0.324291	+	0.499295i
$191$	−258.518	+	149.255i	−1.35350	+	0.781442i	−0.988737	−	0.149660i	$-0.952182\pi$
$191$	−258.518	+	149.255i	−1.35350	+	0.781442i	−0.364759	+	0.931102i	$0.618849\pi$
$192$	189.407	−	170.413i	0.986497	−	0.887570i
$193$	165.381	−	286.448i	0.856896	−	1.48419i	−0.0179791	−	0.999838i	$-0.505723\pi$
$193$	165.381	−	286.448i	0.856896	−	1.48419i	0.874875	−	0.484349i	$-0.160943\pi$
$194$	−5.79847	+	110.508i	−0.0298890	+	0.569629i
$195$	−86.0828			−0.441450
$196$		0			0
$197$			327.309i			1.66146i	0.556672	+	0.830732i	$0.312078\pi$
$197$			327.309i			1.66146i	−0.556672	+	0.830732i	$0.687922\pi$
$198$	−5.65524	+	107.778i	−0.0285618	+	0.544335i
$199$	−11.0295	−	6.36789i	−0.0554246	−	0.0319994i	0.472032	−	0.881582i	$-0.343521\pi$
$199$	−11.0295	−	6.36789i	−0.0554246	−	0.0319994i	−0.527456	+	0.849582i	$0.676854\pi$
$200$	−133.376	−	108.047i	−0.666879	−	0.540237i
$201$	118.057	+	204.481i	0.587349	+	1.01732i
$202$	−34.2424	+	52.7214i	−0.169517	+	0.260997i
$203$		0			0
$204$	18.7676	+	42.1670i	0.0919979	+	0.206701i
$205$	66.2416	−	38.2446i	0.323130	−	0.186559i
$206$	72.6170	+	142.541i	0.352510	+	0.691947i
$207$	228.632	+	132.001i	1.10450	+	0.637686i
$208$	−38.2557	+	179.756i	−0.183921	+	0.864210i
$209$	−236.736			−1.13271
$210$		0			0
$211$	120.455			0.570875			0.285437	−	0.958397i	$-0.407861\pi$
$211$	120.455			0.570875			0.285437	+	0.958397i	$0.407861\pi$
$212$	86.9907	+	63.2192i	0.410334	+	0.298204i
$213$	−131.888	−	76.1454i	−0.619191	−	0.357490i
$214$	−86.8997	+	44.2707i	−0.406073	+	0.206873i
$215$	−77.0820	+	44.5033i	−0.358521	+	0.206992i
$216$	10.7314	−	67.6726i	0.0496825	−	0.313299i
$217$		0			0
$218$	−125.354	+	193.002i	−0.575020	+	0.885331i
$219$	27.8230	+	48.1909i	0.127046	+	0.220050i
$220$	−6.20943	+	59.0071i	−0.0282247	+	0.268214i
$221$	−28.8320	−	16.6461i	−0.130461	−	0.0753219i
$222$	−362.215	−	19.0058i	−1.63160	−	0.0856117i
$223$			372.958i			1.67246i	0.548382	+	0.836228i	$0.315244\pi$
$223$			372.958i			1.67246i	−0.548382	+	0.836228i	$0.684756\pi$
$224$		0			0
$225$	146.944			0.653086
$226$	−5.84322	+	111.361i	−0.0258549	+	0.492747i
$227$	36.7128	−	63.5885i	0.161730	−	0.280125i	−0.773759	−	0.633480i	$-0.781626\pi$
$227$	36.7128	−	63.5885i	0.161730	−	0.280125i	0.935489	+	0.353355i	$0.114959\pi$
$228$	−475.808	−	50.0701i	−2.08688	−	0.219606i
$229$	367.587	−	212.226i	1.60518	−	0.926752i	0.614755	−	0.788718i	$-0.289255\pi$
$229$	367.587	−	212.226i	1.60518	−	0.926752i	0.990428	−	0.138034i	$-0.0440783\pi$
$230$	121.716	+	79.0543i	0.529201	+	0.343714i
$231$		0			0
$232$	220.209	+	34.9205i	0.949179	+	0.150519i
$233$	41.7070	+	72.2386i	0.179000	+	0.310037i	0.941538	−	0.336906i	$-0.109380\pi$
$233$	41.7070	+	72.2386i	0.179000	+	0.310037i	−0.762538	+	0.646943i	$0.776047\pi$
$234$	−71.4178	−	140.187i	−0.305204	−	0.599090i
$235$	−77.7301	+	134.632i	−0.330766	+	0.572904i
$236$	24.4822	−	33.6879i	0.103738	−	0.142745i
$237$			203.787i			0.859861i
$238$		0			0
$239$			112.561i			0.470967i	0.971878	+	0.235484i	$0.0756674\pi$
$239$			112.561i			0.470967i	−0.971878	+	0.235484i	$0.924333\pi$
$240$	−24.9603	+	117.283i	−0.104001	+	0.488680i
$241$	140.216	−	242.861i	0.581809	−	1.00772i	−0.413455	−	0.910524i	$-0.635678\pi$
$241$	140.216	−	242.861i	0.581809	−	1.00772i	0.995265	−	0.0971992i	$-0.0309884\pi$
$242$	104.989	−	53.4863i	0.433840	−	0.221018i
$243$	152.019	+	263.304i	0.625591	+	1.08356i
$244$	−80.9899	+	36.0468i	−0.331926	+	0.147733i
$245$		0			0
$246$	271.306	+	176.213i	1.10287	+	0.716311i
$247$	298.868	−	172.552i	1.20999	−	0.698589i
$248$	113.219	−	139.760i	0.456529	−	0.563548i
$249$	−178.043	+	308.380i	−0.715033	+	1.23847i
$250$	174.669	+	9.16506i	0.698675	+	0.0366602i
$251$	32.9560			0.131299			0.0656493	−	0.997843i	$-0.479088\pi$
$251$	32.9560			0.131299			0.0656493	+	0.997843i	$0.479088\pi$
$252$		0			0
$253$			303.740i			1.20055i
$254$	−71.2946	−	3.74090i	−0.280688	−	0.0147280i
$255$	−18.8117	−	10.8609i	−0.0737714	−	0.0425919i
$256$	233.815	+	104.243i	0.913340	+	0.407198i
$257$	−112.109	−	194.179i	−0.436223	−	0.755561i	0.561172	−	0.827700i	$-0.310351\pi$
$257$	−112.109	−	194.179i	−0.436223	−	0.755561i	−0.997395	+	0.0721390i	$0.977017\pi$
$258$	−315.705	−	205.050i	−1.22366	−	0.794767i
$259$		0			0
$260$	−35.1699	−	79.0197i	−0.135269	−	0.303922i
$261$	−165.300	+	95.4357i	−0.633332	+	0.365654i
$262$	−216.152	+	110.118i	−0.825006	+	0.420296i
$263$	−147.190	−	84.9804i	−0.559659	−	0.323119i	0.193350	−	0.981130i	$-0.438065\pi$
$263$	−147.190	−	84.9804i	−0.559659	−	0.323119i	−0.753009	+	0.658011i	$0.771398\pi$
$264$	−234.296	+	89.8870i	−0.887485	+	0.340481i
$265$	−50.6098			−0.190980
$266$		0			0
$267$	−419.034			−1.56942
$268$	−139.470	+	191.913i	−0.520411	+	0.716094i
$269$	−93.9863	−	54.2630i	−0.349391	−	0.201721i	0.315026	−	0.949083i	$-0.397987\pi$
$269$	−93.9863	−	54.2630i	−0.349391	−	0.201721i	−0.664417	+	0.747362i	$0.731320\pi$
$270$	14.6379	+	28.7330i	0.0542144	+	0.106418i
$271$	−16.7690	+	9.68157i	−0.0618781	+	0.0357253i	−0.530620	−	0.847610i	$-0.678041\pi$
$271$	−16.7690	+	9.68157i	−0.0618781	+	0.0357253i	0.468742	+	0.883335i	$0.344707\pi$
$272$	−31.0395	+	34.4554i	−0.114116	+	0.126674i
$273$		0			0
$274$	−14.2513	−	9.25617i	−0.0520120	−	0.0337817i
$275$	84.5313	+	146.412i	0.307386	+	0.532409i
$276$	−64.2416	+	610.477i	−0.232759	+	2.21187i
$277$	112.104	+	64.7231i	0.404707	+	0.233658i	0.688513	−	0.725224i	$-0.258264\pi$
$277$	112.104	+	64.7231i	0.404707	+	0.233658i	−0.283806	+	0.958882i	$0.591597\pi$
$278$	0.320621	−	6.11044i	0.00115331	−	0.0219800i
$279$			153.978i			0.551892i
$280$		0			0
$281$	83.3608			0.296658			0.148329	−	0.988938i	$-0.452611\pi$
$281$	83.3608			0.296658			0.148329	+	0.988938i	$0.452611\pi$
$282$	−656.611	−	34.4531i	−2.32841	−	0.122174i
$283$	14.4646	−	25.0535i	0.0511118	−	0.0885282i	−0.839338	−	0.543611i	$-0.817057\pi$
$283$	14.4646	−	25.0535i	0.0511118	−	0.0885282i	0.890449	+	0.455082i	$0.150390\pi$
$284$	16.0138	−	152.176i	0.0563866	−	0.535832i
$285$	194.999	−	112.583i	0.684208	−	0.395028i
$286$	98.5959	−	151.803i	0.344741	−	0.530781i
$287$		0			0
$288$	−211.706	+	56.6548i	−0.735089	+	0.196718i
$289$	140.300	+	243.006i	0.485466	+	0.840851i
$290$	−93.4982	+	47.6323i	−0.322408	+	0.164249i
$291$	110.135	−	190.760i	0.378472	−	0.655533i
$292$	−32.8695	+	45.2290i	−0.112567	+	0.154894i
$293$		−	214.613i		−	0.732468i	−0.930523	−	0.366234i	$-0.880647\pi$
$293$		−	214.613i		−	0.732468i	0.930523	−	0.366234i	$-0.119353\pi$
$294$		0			0
$295$			19.5991i			0.0664376i
$296$	−130.540	−	340.260i	−0.441013	−	1.14953i
$297$	−33.7429	+	58.4444i	−0.113612	+	0.196783i
$298$	−28.8014	−	56.5347i	−0.0966490	−	0.189714i
$299$	−221.389	−	383.457i	−0.740432	−	1.28247i
$300$	138.930	+	312.148i	0.463101	+	1.04049i
$301$		0			0
$302$	276.264	−	425.350i	0.914780	−	1.40844i
$303$	108.370	−	62.5675i	0.357657	−	0.206493i
$304$	−148.434	−	457.224i	−0.488269	−	1.50403i
$305$	20.8606	−	36.1316i	0.0683953	−	0.118464i
$306$	2.08026	−	39.6458i	0.00679822	−	0.129561i
$307$	120.542			0.392644			0.196322	−	0.980539i	$-0.437100\pi$
$307$	120.542			0.392644			0.196322	+	0.980539i	$0.437100\pi$
$308$		0			0
$309$		−	318.427i		−	1.03051i
$310$	−4.43556	+	84.5335i	−0.0143083	+	0.272689i
$311$	−281.771	−	162.681i	−0.906016	−	0.523089i	−0.0268689	−	0.999639i	$-0.508554\pi$
$311$	−281.771	−	162.681i	−0.906016	−	0.523089i	−0.879147	+	0.476550i	$0.841887\pi$
$312$	230.272	−	284.252i	0.738050	−	0.911063i
$313$	228.378	+	395.562i	0.729642	+	1.26378i	0.957034	+	0.289974i	$0.0936467\pi$
$313$	228.378	+	395.562i	0.729642	+	1.26378i	−0.227392	+	0.973803i	$0.573020\pi$
$314$	53.7363	−	82.7353i	0.171135	−	0.263488i
$315$		0			0
$316$	−187.066	+	83.2590i	−0.591982	+	0.263478i
$317$	104.980	−	60.6102i	0.331167	−	0.191199i	−0.325192	−	0.945648i	$-0.605429\pi$
$317$	104.980	−	60.6102i	0.331167	−	0.191199i	0.656359	+	0.754449i	$0.272096\pi$
$318$	−97.1658	−	190.728i	−0.305553	−	0.599775i
$319$	−190.180	−	109.801i	−0.596177	−	0.344203i
$320$	−117.858	+	25.0049i	−0.368306	+	0.0781402i
$321$	194.128			0.604761
$322$		0			0
$323$	87.0822			0.269604
$324$	−225.123	+	309.774i	−0.694825	+	0.956091i
$325$	−213.434	−	123.226i	−0.656719	−	0.379157i
$326$	−206.220	+	105.058i	−0.632577	+	0.322264i
$327$	396.721	−	229.047i	1.21321	−	0.700449i
$328$	−50.9098	+	321.039i	−0.155213	+	0.978777i
$329$		0			0
$330$	64.3298	−	99.0455i	0.194939	−	0.300138i
$331$	−60.5842	−	104.935i	−0.183034	−	0.317024i	0.759878	−	0.650065i	$-0.225258\pi$
$331$	−60.5842	−	104.935i	−0.183034	−	0.317024i	−0.942912	+	0.333041i	$0.891925\pi$
$332$	−355.819	−	37.4434i	−1.07174	−	0.112781i
$333$	270.191	+	155.995i	0.811384	+	0.468453i
$334$	64.6829	+	3.39398i	0.193661	+	0.0101616i
$335$		−	111.652i		−	0.333290i
$336$		0			0
$337$	−464.021			−1.37692			−0.688459	−	0.725275i	$-0.741713\pi$
$337$	−464.021			−1.37692			−0.688459	+	0.725275i	$0.741713\pi$
$338$	3.88424	−	74.0264i	0.0114918	−	0.219013i
$339$	110.985	−	192.232i	0.327390	−	0.567056i
$340$	2.28411	−	21.7055i	0.00671798	−	0.0638398i
$341$	−153.420	+	88.5773i	−0.449913	+	0.259758i
$342$	345.122	+	224.156i	1.00913	+	0.655427i
$343$		0			0
$344$	59.2412	−	373.577i	0.172213	−	1.08598i
$345$	−144.448	−	250.190i	−0.418688	−	0.725190i
$346$	188.151	+	369.325i	0.543789	+	1.06741i
$347$	185.593	−	321.457i	0.534851	−	0.926388i	−0.464320	−	0.885667i	$-0.653701\pi$
$347$	185.593	−	321.457i	0.534851	−	0.926388i	0.999171	−	0.0407208i	$-0.0129654\pi$
$348$	−359.015	−	260.909i	−1.03165	−	0.749738i
$349$			207.871i			0.595619i	0.954625	+	0.297809i	$0.0962560\pi$
$349$			207.871i			0.595619i	−0.954625	+	0.297809i	$0.903744\pi$
$350$		0			0
$351$		−	98.3779i		−	0.280279i
$352$	−178.236	−	178.348i	−0.506351	−	0.506670i
$353$	−307.007	+	531.751i	−0.869708	+	1.50638i	−0.00741211	+	0.999973i	$0.502359\pi$
$353$	−307.007	+	531.751i	−0.869708	+	1.50638i	−0.862296	+	0.506405i	$0.830974\pi$
$354$	−73.8613	+	37.6283i	−0.208648	+	0.106295i
$355$	36.0071	+	62.3661i	0.101428	+	0.175679i
$356$	−171.200	−	384.652i	−0.480899	−	1.08048i
$357$		0			0
$358$	292.126	+	189.735i	0.815995	+	0.529986i
$359$	−93.5930	+	54.0359i	−0.260705	+	0.150518i	−0.624656	−	0.780900i	$-0.714761\pi$
$359$	−93.5930	+	54.0359i	−0.260705	+	0.150518i	0.363951	+	0.931418i	$0.381427\pi$
$360$	64.9239	−	80.1434i	0.180344	−	0.222620i
$361$	−270.841	+	469.110i	−0.750252	+	1.29947i
$362$	407.926	+	21.4043i	1.12687	+	0.0591280i
$363$	−234.539			−0.646113
$364$		0			0
$365$		−	26.3135i		−	0.0720917i
$366$	176.216	+	9.24623i	0.481464	+	0.0252629i
$367$	−393.881	−	227.407i	−1.07325	−	0.619639i	−0.144179	−	0.989552i	$-0.546054\pi$
$367$	−393.881	−	227.407i	−1.07325	−	0.619639i	−0.929067	+	0.369913i	$0.879388\pi$
$368$	−586.634	+	190.445i	−1.59411	+	0.517514i
$369$	−139.134	−	240.987i	−0.377056	−	0.653081i
$370$	143.840	+	93.4240i	0.388758	+	0.252497i
$371$		0			0
$372$	−327.089	+	145.580i	−0.879272	+	0.391344i
$373$	235.344	−	135.876i	0.630949	−	0.364279i	−0.150171	−	0.988660i	$-0.547982\pi$
$373$	235.344	−	135.876i	0.630949	−	0.364279i	0.781119	+	0.624382i	$0.214649\pi$
$374$	40.6990	−	20.7339i	0.108821	−	0.0554383i
$375$	−301.515	−	174.080i	−0.804039	−	0.464212i
$376$	−236.638	−	616.812i	−0.629357	−	1.64046i
$377$	320.126			0.849140
$378$		0			0
$379$	268.351			0.708051			0.354026	−	0.935236i	$-0.384813\pi$
$379$	268.351			0.708051			0.354026	+	0.935236i	$0.384813\pi$
$380$	183.014	+	133.003i	0.481616	+	0.350008i
$381$	123.069	+	71.0541i	0.323017	+	0.186494i
$382$	271.008	+	531.967i	0.709446	+	1.39258i
$383$	−283.718	+	163.805i	−0.740779	+	0.427689i	−0.822352	−	0.568979i	$-0.807339\pi$
$383$	−283.718	+	163.805i	−0.740779	+	0.427689i	0.0815738	+	0.996667i	$0.474005\pi$
$384$	−320.509	−	396.153i	−0.834659	−	1.03165i
$385$		0			0
$386$	−554.778	−	360.327i	−1.43725	−	0.933489i
$387$	161.903	+	280.424i	0.418354	+	0.724610i
$388$	220.105	+	23.1620i	0.567281	+	0.0596960i
$389$	−109.380	−	63.1506i	−0.281183	−	0.162341i	0.352776	−	0.935708i	$-0.385238\pi$
$389$	−109.380	−	63.1506i	−0.281183	−	0.162341i	−0.633959	+	0.773367i	$0.718571\pi$
$390$	−9.02130	+	171.929i	−0.0231315	+	0.440844i
$391$		−	111.729i		−	0.285753i
$392$		0			0
$393$	482.869			1.22867
$394$	653.718	+	34.3013i	1.65918	+	0.0870590i
$395$	48.1826	−	83.4548i	0.121981	−	0.211278i
$396$	214.668	+	22.5899i	0.542090	+	0.0570451i
$397$	110.110	−	63.5720i	0.277355	−	0.160131i	−0.354870	−	0.934916i	$-0.615475\pi$
$397$	110.110	−	63.5720i	0.277355	−	0.160131i	0.632225	+	0.774784i	$0.282142\pi$
$398$	−13.8741	+	21.3614i	−0.0348597	+	0.0536718i
$399$		0			0
$400$	−229.775	+	255.062i	−0.574439	+	0.637655i
$401$	−30.0751	−	52.0916i	−0.0750003	−	0.129904i	0.826086	−	0.563544i	$-0.190562\pi$
$401$	−30.0751	−	52.0916i	−0.0750003	−	0.129904i	−0.901086	+	0.433640i	$0.857229\pi$
$402$	420.773	−	214.361i	1.04670	−	0.533236i
$403$	129.124	−	223.650i	0.320408	−	0.554962i
$404$	101.709	+	73.9158i	0.251756	+	0.182960i
$405$		−	180.221i		−	0.444991i
$406$		0			0
$407$			358.950i			0.881941i
$408$	86.1849	−	33.0646i	0.211237	−	0.0810406i
$409$	−34.8873	+	60.4267i	−0.0852991	+	0.147742i	−0.905519	−	0.424306i	$-0.860518\pi$
$409$	−34.8873	+	60.4267i	−0.0852991	+	0.147742i	0.820220	+	0.572049i	$0.193851\pi$
$410$	−69.4421	−	136.309i	−0.169371	−	0.332461i
$411$	16.9128	+	29.2939i	0.0411504	+	0.0712746i
$412$	292.301	−	130.096i	0.709467	−	0.315768i
$413$		0			0
$414$	287.599	−	442.803i	0.694685	−	1.06957i
$415$	145.824	−	84.1918i	0.351384	−	0.202872i
$416$	355.008	+	95.2442i	0.853385	+	0.228952i
$417$	−6.08982	+	10.5479i	−0.0146039	+	0.0252947i
$418$	−24.8094	+	472.821i	−0.0593526	+	1.13115i
$419$	−714.794			−1.70595			−0.852976	−	0.521950i	$-0.825205\pi$
$419$	−714.794			−1.70595			−0.852976	+	0.521950i	$0.825205\pi$
$420$		0			0
$421$		−	303.440i		−	0.720759i	−0.932806	−	0.360380i	$-0.882647\pi$
$421$		−	303.440i		−	0.720759i	0.932806	−	0.360380i	$-0.117353\pi$
$422$	12.6234	−	240.578i	0.0299132	−	0.570090i
$423$	489.793	+	282.782i	1.15790	+	0.668515i
$424$	135.381	−	167.117i	0.319295	−	0.394144i
$425$	−31.0945	−	53.8572i	−0.0731635	−	0.126723i
$426$	−165.903	+	255.433i	−0.389444	+	0.599609i
$427$		0			0
$428$	79.3129	+	178.200i	0.185310	+	0.416356i
$429$	−312.035	+	180.154i	−0.727355	+	0.419939i
$430$	80.8064	+	158.616i	0.187922	+	0.368875i
$431$	373.685	+	215.747i	0.867019	+	0.500574i	0.866357	−	0.499426i	$-0.166456\pi$
$431$	373.685	+	215.747i	0.867019	+	0.500574i	0.000662591		1.00000i	$0.499789\pi$
$432$	−134.035	−	28.5253i	−0.310265	−	0.0660308i
$433$	−194.875			−0.450057			−0.225029	−	0.974352i	$-0.572248\pi$
$433$	−194.875			−0.450057			−0.225029	+	0.974352i	$0.572248\pi$
$434$		0			0
$435$	208.869			0.480159
$436$	372.337	+	270.591i	0.853985	+	0.620621i
$437$	1003.00	+	579.085i	2.29521	+	1.32514i
$438$	99.1652	−	50.5193i	0.226404	−	0.115341i
$439$	264.977	−	152.985i	0.603593	−	0.348485i	−0.166861	−	0.985980i	$-0.553363\pi$
$439$	264.977	−	152.985i	0.603593	−	0.348485i	0.770454	+	0.637496i	$0.220030\pi$
$440$	117.201	+	18.5856i	0.266367	+	0.0422400i
$441$		0			0
$442$	−36.2681	+	55.8402i	−0.0820545	+	0.126335i
$443$	−125.099	−	216.677i	−0.282390	−	0.489113i	0.689583	−	0.724206i	$-0.257794\pi$
$443$	−125.099	−	216.677i	−0.282390	−	0.489113i	−0.971973	+	0.235093i	$0.924460\pi$
$444$	−75.9187	+	721.443i	−0.170988	+	1.62487i
$445$	171.603	+	99.0748i	0.385624	+	0.222640i
$446$	744.891	+	39.0852i	1.67016	+	0.0876350i
$447$			126.295i			0.282539i
$448$		0			0
$449$	−688.681			−1.53381			−0.766905	−	0.641761i	$-0.778204\pi$
$449$	−688.681			−1.53381			−0.766905	+	0.641761i	$0.778204\pi$
$450$	15.3995	−	293.485i	0.0342210	−	0.652189i
$451$	160.076	−	277.260i	0.354936	−	0.614768i
$452$	221.803	+	23.3408i	0.490715	+	0.0516388i
$453$	−874.317	+	504.787i	−1.93006	+	1.11432i
$454$	−123.155	−	79.9887i	−0.271266	−	0.176187i
$455$		0			0
$456$	−149.866	+	945.061i	−0.328654	+	2.07250i
$457$	−402.259	−	696.733i	−0.880217	−	1.52458i	−0.851100	−	0.525004i	$-0.824064\pi$
$457$	−402.259	−	696.733i	−0.880217	−	1.52458i	−0.0291166	−	0.999576i	$-0.509269\pi$
$458$	−385.347	−	756.404i	−0.841369	−	1.65154i
$459$	12.4122	−	21.4985i	0.0270418	−	0.0468378i
$460$	170.647	−	234.813i	0.370972	−	0.510463i
$461$		−	693.657i		−	1.50468i	−0.658776	−	0.752339i	$-0.728926\pi$
$461$		−	693.657i		−	1.50468i	0.658776	−	0.752339i	$-0.271074\pi$
$462$		0			0
$463$		−	321.194i		−	0.693724i	−0.937916	−	0.346862i	$-0.887247\pi$
$463$		−	321.194i		−	0.693724i	0.937916	−	0.346862i	$-0.112753\pi$
$464$	92.8225	−	436.154i	0.200048	−	0.939988i
$465$	84.2484	−	145.922i	0.181179	−	0.313812i
$466$	148.650	−	75.7289i	0.318990	−	0.162508i
$467$	375.937	+	651.142i	0.805005	+	1.39431i	0.916288	+	0.400521i	$0.131171\pi$
$467$	375.937	+	651.142i	0.805005	+	1.39431i	−0.111283	+	0.993789i	$0.535496\pi$
$468$	−287.474	+	127.948i	−0.614260	+	0.273393i
$469$		0			0
$470$	260.749	+	169.356i	0.554785	+	0.360332i
$471$	−170.064	+	98.1867i	−0.361071	+	0.208464i
$472$	−64.7176	−	52.4276i	−0.137114	−	0.111075i
$473$	−186.273	+	322.634i	−0.393811	+	0.682101i
$474$	407.014	+	21.3565i	0.858680	+	0.0450558i
$475$	644.642			1.35714
$476$		0			0
$477$			184.118i			0.385992i
$478$	224.813	+	11.7962i	0.470320	+	0.0246782i
$479$	625.392	+	361.070i	1.30562	+	0.753800i	0.981362	−	0.192169i	$-0.0615523\pi$
$479$	625.392	+	361.070i	1.30562	+	0.753800i	0.324257	+	0.945969i	$0.394886\pi$
$480$	231.629	+	62.1430i	0.482559	+	0.129465i
$481$	−261.631	−	453.158i	−0.543932	−	0.942117i
$482$	−470.361	−	305.498i	−0.975853	−	0.633814i
$483$		0			0
$484$	−95.8230	−	215.295i	−0.197981	−	0.444825i
$485$	−90.2052	+	52.0800i	−0.185990	+	0.107381i
$486$	541.816	−	276.026i	1.11485	−	0.567954i
$487$	−41.4211	−	23.9145i	−0.0850536	−	0.0491057i	0.456870	−	0.889533i	$-0.348970\pi$
$487$	−41.4211	−	23.9145i	−0.0850536	−	0.0491057i	−0.541924	+	0.840428i	$0.682304\pi$
$488$	63.5070	+	165.535i	0.130137	+	0.339211i
$489$	460.682			0.942090
$490$		0			0
$491$	44.4724			0.0905752			0.0452876	−	0.998974i	$-0.485580\pi$
$491$	44.4724			0.0905752			0.0452876	+	0.998974i	$0.485580\pi$
$492$	380.373	−	523.400i	0.773117	−	1.06382i
$493$	69.9571	+	40.3898i	0.141901	+	0.0819265i
$494$	−313.308	−	614.998i	−0.634227	−	1.24494i
$495$	−87.9769	+	50.7935i	−0.177731	+	0.102613i
$496$	−267.271	−	240.774i	−0.538852	−	0.485431i
$497$		0			0
$498$	597.254	+	387.915i	1.19931	+	0.778945i
$499$	250.786	+	434.374i	0.502577	+	0.870489i	0.999996	+	0.00297862i	$0.000948124\pi$
$499$	250.786	+	434.374i	0.502577	+	0.870489i	−0.497418	+	0.867511i	$0.665719\pi$
$500$	36.6099	−	347.897i	0.0732197	−	0.695795i
$501$	−111.656	−	64.4647i	−0.222867	−	0.128672i
$502$	3.45372	−	65.8214i	0.00687991	−	0.131118i
$503$		−	462.733i		−	0.919946i	−0.887933	−	0.459973i	$-0.847859\pi$
$503$		−	462.733i		−	0.919946i	0.887933	−	0.459973i	$-0.152141\pi$
$504$		0			0
$505$	−59.1729			−0.117174
$506$	606.645	+	31.8313i	1.19890	+	0.0629076i
$507$	−73.7767	+	127.785i	−0.145516	+	0.252041i
$508$	−14.9431	+	142.001i	−0.0294155	+	0.279530i
$509$	−408.751	+	235.992i	−0.803046	+	0.463639i	−0.844535	−	0.535500i	$-0.820123\pi$
$509$	−408.751	+	235.992i	−0.803046	+	0.463639i	0.0414889	+	0.999139i	$0.486790\pi$
$510$	−23.6635	+	36.4335i	−0.0463989	+	0.0714382i
$511$		0			0
$512$	232.702	−	456.063i	0.454496	−	0.890749i
$513$	128.663	+	222.851i	0.250805	+	0.434407i
$514$	−399.573	+	203.561i	−0.777380	+	0.396033i
$515$	−75.2878	+	130.402i	−0.146190	+	0.253208i
$516$	−442.621	+	609.055i	−0.857794	+	1.18034i
$517$			650.693i			1.25859i
$518$		0			0
$519$		−	825.047i		−	1.58969i
$520$	−161.508	+	61.9621i	−0.310593	+	0.119158i
$521$	−45.3709	+	78.5848i	−0.0870843	+	0.150834i	−0.906277	−	0.422683i	$-0.861088\pi$
$521$	−45.3709	+	78.5848i	−0.0870843	+	0.150834i	0.819193	+	0.573518i	$0.194422\pi$
$522$	173.286	+	340.146i	0.331966	+	0.651621i
$523$	−180.256	−	312.213i	−0.344658	−	0.596965i	0.640634	−	0.767847i	$-0.278672\pi$
$523$	−180.256	−	312.213i	−0.344658	−	0.596965i	−0.985292	+	0.170882i	$0.945338\pi$
$524$	197.280	+	443.249i	0.376489	+	0.845896i
$525$		0			0
$526$	−185.152	+	285.070i	−0.352001	+	0.541959i
$527$	56.4351	−	32.5828i	0.107087	−	0.0618270i
$528$	154.973	+	477.368i	0.293510	+	0.904107i
$529$	478.485	−	828.760i	0.904509	−	1.56665i
$530$	−5.30380	+	101.081i	−0.0100072	+	0.190718i
$531$	71.3014			0.134278
$532$		0			0
$533$			466.705i			0.875618i
$534$	−43.9139	+	836.917i	−0.0822357	+	1.56726i
$535$	−79.4994	−	45.8990i	−0.148597	−	0.0857925i
$536$	368.683	+	298.669i	0.687841	+	0.557218i
$537$	−346.683	−	600.472i	−0.645592	−	1.11820i
$538$	−118.226	+	182.028i	−0.219752	+	0.338341i
$539$		0			0
$540$	58.9210	−	26.2244i	0.109113	−	0.0485637i
$541$	−485.969	+	280.574i	−0.898278	+	0.518621i	−0.876641	−	0.481145i	$-0.840221\pi$
$541$	−485.969	+	280.574i	−0.898278	+	0.518621i	−0.0216371	+	0.999766i	$0.506888\pi$
$542$	17.5792	+	34.5065i	0.0324339	+	0.0636651i
$543$	−704.166	−	406.550i	−1.29681	−	0.748712i
$544$	65.5632	+	65.6046i	0.120521	+	0.120597i
$545$	−216.620			−0.397468
$546$		0			0
$547$	1043.62			1.90790			0.953952	−	0.299960i	$-0.0969733\pi$
$547$	1043.62			1.90790			0.953952	+	0.299960i	$0.0969733\pi$
$548$	−19.9804	+	27.4934i	−0.0364606	+	0.0501704i
$549$	−131.447	−	75.8907i	−0.239429	−	0.138234i
$550$	301.281	−	153.487i	0.547784	−	0.279067i
$551$	−725.165	+	418.674i	−1.31609	+	0.759845i
$552$	1212.54	+	192.283i	2.19664	+	0.348339i
$553$		0			0
$554$	141.017	−	217.117i	0.254543	−	0.391907i
$555$	−170.704	−	295.667i	−0.307574	−	0.532734i
$556$	−12.1705	−	1.28072i	−0.0218894	−	0.00230346i
$557$	42.1273	+	24.3222i	0.0756324	+	0.0436664i	0.537339	−	0.843366i	$-0.319429\pi$
$557$	42.1273	+	24.3222i	0.0756324	+	0.0436664i	−0.461707	+	0.887033i	$0.652763\pi$
$558$	307.533	+	16.1366i	0.551134	+	0.0289186i
$559$		−	543.081i		−	0.971522i
$560$		0			0
$561$	−90.9189			−0.162066
$562$	8.73604	−	166.493i	0.0155446	−	0.296250i
$563$	363.015	−	628.761i	0.644787	−	1.11680i	−0.339563	−	0.940583i	$-0.610279\pi$
$563$	363.015	−	628.761i	0.644787	−	1.11680i	0.984351	−	0.176221i	$-0.0563874\pi$
$564$	−137.623	+	1307.81i	−0.244012	+	2.31881i
$565$	−90.9012	+	52.4818i	−0.160887	+	0.0928882i
$566$	−48.5223	−	31.5151i	−0.0857284	−	0.0556804i
$567$		0			0
$568$	−302.256	−	47.9313i	−0.532141	−	0.0843861i
$569$	240.696	+	416.898i	0.423016	+	0.732685i	0.996233	−	0.0867185i	$-0.0276381\pi$
$569$	240.696	+	416.898i	0.423016	+	0.732685i	−0.573217	+	0.819404i	$0.694305\pi$
$570$	−204.421	−	401.261i	−0.358633	−	0.703967i
$571$	−55.0633	+	95.3724i	−0.0964331	+	0.167027i	−0.910206	−	0.414156i	$-0.864077\pi$
$571$	−55.0633	+	95.3724i	−0.0964331	+	0.167027i	0.813773	+	0.581183i	$0.197410\pi$
$572$	−292.857	−	212.829i	−0.511988	−	0.372080i
$573$		−	1188.38i		−	2.07396i
$574$		0			0
$575$		−	827.097i		−	1.43843i
$576$	90.9676	+	428.767i	0.157930	+	0.744387i
$577$	−101.168	+	175.228i	−0.175335	+	0.303688i	−0.940277	−	0.340410i	$-0.889434\pi$
$577$	−101.168	+	175.228i	−0.175335	+	0.303688i	0.764942	+	0.644099i	$0.222767\pi$
$578$	500.047	−	254.747i	0.865134	−	0.440739i
$579$	658.386	+	1140.36i	1.13711	+	1.96953i
$580$	85.3353	+	191.731i	0.147130	+	0.330571i
$581$		0			0
$582$	−369.454	−	239.959i	−0.634800	−	0.412301i
$583$	−183.452	+	105.916i	−0.314669	+	0.181674i
$584$	86.8890	+	70.3886i	0.148783	+	0.120528i
$585$	74.0445	−	128.249i	0.126572	−	0.219229i
$586$	−428.637	−	22.4910i	−0.731462	−	0.0383806i
$587$	568.689			0.968805			0.484403	−	0.874845i	$-0.339037\pi$
$587$	568.689			0.968805			0.484403	+	0.874845i	$0.339037\pi$
$588$		0			0
$589$			675.497i			1.14685i
$590$	39.1443	+	2.05394i	0.0663463	+	0.00348126i
$591$	−1128.45	−	651.513i	−1.90940	−	1.10239i
$592$	−693.266	+	225.062i	−1.17106	+	0.380173i
$593$	−342.686	−	593.550i	−0.577886	−	1.00093i	−0.995721	−	0.0924054i	$-0.970544\pi$
$593$	−342.686	−	593.550i	−0.577886	−	1.00093i	0.417835	−	0.908523i	$-0.362789\pi$
$594$	113.192	+	73.5179i	0.190559	+	0.123768i
$595$		0			0
$596$	−115.932	+	51.5989i	−0.194518	+	0.0865754i
$597$	43.9088	−	25.3507i	0.0735491	−	0.0424636i
$598$	−789.062	+	401.985i	−1.31950	+	0.672215i
$599$	318.077	+	183.642i	0.531013	+	0.306580i	0.741429	−	0.671032i	$-0.234149\pi$
$599$	318.077	+	183.642i	0.531013	+	0.306580i	−0.210416	+	0.977612i	$0.567482\pi$
$600$	637.999	−	244.766i	1.06333	−	0.407944i
$601$	−412.344			−0.686097			−0.343049	−	0.939318i	$-0.611460\pi$
$601$	−412.344			−0.686097			−0.343049	+	0.939318i	$0.611460\pi$
$602$		0			0
$603$	−406.190			−0.673615
$604$	−820.579	−	596.344i	−1.35858	−	0.987325i
$605$	96.0484	+	55.4535i	0.158758	+	0.0916588i
$606$	−113.606	−	222.999i	−0.187469	−	0.367986i
$607$	1010.46	−	583.389i	1.66468	−	0.961102i	0.694241	−	0.719743i	$-0.255740\pi$
$607$	1010.46	−	583.389i	1.66468	−	0.961102i	0.970436	−	0.241359i	$-0.0775930\pi$
$608$	−928.748	+	248.543i	−1.52755	+	0.408788i
$609$		0			0
$610$	−69.9777	−	45.4503i	−0.114718	−	0.0745087i
$611$	−474.276	−	821.470i	−0.776229	−	1.34447i
$612$	−78.9647	−	8.30959i	−0.129027	−	0.0135778i
$613$	−373.900	−	215.871i	−0.609951	−	0.352155i	0.162995	−	0.986627i	$-0.447885\pi$
$613$	−373.900	−	215.871i	−0.609951	−	0.352155i	−0.772946	+	0.634471i	$0.781218\pi$
$614$	12.6325	−	240.752i	0.0205741	−	0.392105i
$615$			304.506i			0.495131i
$616$		0			0
$617$	−333.751			−0.540926			−0.270463	−	0.962730i	$-0.587177\pi$
$617$	−333.751			−0.540926			−0.270463	+	0.962730i	$0.587177\pi$
$618$	−635.980	−	33.3705i	−1.02909	−	0.0539976i
$619$	−488.158	+	845.514i	−0.788624	+	1.36594i	0.138187	+	0.990406i	$0.455873\pi$
$619$	−488.158	+	845.514i	−0.788624	+	1.36594i	−0.926810	+	0.375530i	$0.877461\pi$
$620$	168.370	+	17.7179i	0.271564	+	0.0285772i
$621$	285.925	−	165.079i	0.460426	−	0.265827i
$622$	−354.443	+	545.719i	−0.569844	+	0.877362i
$623$		0			0
$624$	−543.590	−	489.699i	−0.871138	−	0.784775i
$625$	−185.884	−	321.961i	−0.297414	−	0.515137i
$626$	813.971	−	414.674i	1.30027	−	0.662419i
$627$	471.226	−	816.187i	0.751556	−	1.30173i
$628$	−159.612	−	115.996i	−0.254159	−	0.184706i
$629$		−	132.038i		−	0.209918i
$630$		0			0
$631$		−	639.885i		−	1.01408i	−0.861922	−	0.507040i	$-0.830739\pi$
$631$		−	639.885i		−	1.01408i	0.861922	−	0.507040i	$-0.169261\pi$
$632$	146.685	+	382.344i	0.232097	+	0.604975i
$633$	−239.767	+	415.288i	−0.378778	+	0.656063i
$634$	−110.052	−	216.023i	−0.173584	−	0.340731i
$635$	−33.5995	−	58.1961i	−0.0529127	−	0.0916474i
$636$	−391.116	+	174.077i	−0.614962	+	0.273706i
$637$		0			0
$638$	−239.230	+	368.332i	−0.374969	+	0.577322i
$639$	226.888	−	130.994i	0.355067	−	0.204998i
$640$	37.5898	+	238.013i	0.0587340	+	0.371895i
$641$	−10.4295	+	18.0645i	−0.0162707	+	0.0281817i	−0.874046	−	0.485843i	$-0.838513\pi$
$641$	−10.4295	+	18.0645i	−0.0162707	+	0.0281817i	0.857775	+	0.514025i	$0.171846\pi$
$642$	20.3442	−	387.723i	0.0316889	−	0.603931i
$643$	69.1348			0.107519			0.0537596	−	0.998554i	$-0.482880\pi$
$643$	69.1348			0.107519			0.0537596	+	0.998554i	$0.482880\pi$
$644$		0			0
$645$		−	354.338i		−	0.549362i
$646$	9.12604	−	173.925i	0.0141270	−	0.269234i
$647$	−310.868	−	179.480i	−0.480476	−	0.277403i	0.240139	−	0.970739i	$-0.422807\pi$
$647$	−310.868	−	179.480i	−0.480476	−	0.277403i	−0.720615	+	0.693336i	$0.756140\pi$
$648$	595.104	+	482.092i	0.918370	+	0.743969i
$649$	41.0169	+	71.0433i	0.0632001	+	0.109466i
$650$	−268.481	+	413.367i	−0.413048	+	0.635950i
$651$		0			0
$652$	188.216	+	422.883i	0.288675	+	0.648594i
$653$	32.1227	−	18.5460i	0.0491925	−	0.0284013i	−0.475202	−	0.879877i	$-0.657625\pi$
$653$	32.1227	−	18.5460i	0.0491925	−	0.0284013i	0.524395	+	0.851475i	$0.324292\pi$
$654$	−415.889	−	816.355i	−0.635916	−	1.24825i
$655$	−197.744	−	114.168i	−0.301900	−	0.174302i
$656$	635.860	+	135.324i	0.969299	+	0.206287i
$657$	−95.7284			−0.145705
$658$		0			0
$659$	197.302			0.299396			0.149698	−	0.988732i	$-0.452170\pi$
$659$	197.302			0.299396			0.149698	+	0.988732i	$0.452170\pi$
$660$	−191.077	−	138.863i	−0.289511	−	0.210398i
$661$	−938.626	−	541.916i	−1.42001	−	0.819843i	−0.423710	−	0.905798i	$-0.639272\pi$
$661$	−938.626	−	541.916i	−1.42001	−	0.819843i	−0.996299	+	0.0859554i	$0.972606\pi$
$662$	−215.931	+	110.005i	−0.326179	+	0.166171i
$663$	114.781	−	66.2688i	0.173124	−	0.0999530i
$664$	−112.073	+	706.735i	−0.168785	+	1.06436i
$665$		0			0
$666$	339.876	−	523.291i	0.510325	−	0.785723i
$667$	537.173	+	930.411i	0.805357	+	1.39492i
$668$	13.5573	−	128.832i	0.0202953	−	0.192863i
$669$	−1285.84	−	742.378i	−1.92203	−	1.10968i
$670$	−222.997	−	11.7009i	−0.332832	−	0.0174640i
$671$		−	174.628i		−	0.260250i
$672$		0			0
$673$	−286.066			−0.425061			−0.212530	−	0.977154i	$-0.568170\pi$
$673$	−286.066			−0.425061			−0.212530	+	0.977154i	$0.568170\pi$
$674$	−48.6285	+	926.768i	−0.0721491	+	1.37503i
$675$	91.8834	−	159.147i	0.136124	−	0.235773i
$676$	−147.442	−	15.5156i	−0.218110	−	0.0229521i
$677$	−433.324	+	250.180i	−0.640065	+	0.369542i	−0.784640	−	0.619952i	$-0.787152\pi$
$677$	−433.324	+	250.180i	−0.640065	+	0.369542i	0.144575	+	0.989494i	$0.453819\pi$
$678$	−372.305	−	241.811i	−0.549122	−	0.356653i
$679$		0			0
$680$	−43.1121	−	6.83664i	−0.0634001	−	0.0100539i
$681$	146.155	+	253.148i	0.214618	+	0.371729i
$682$	160.833	+	315.702i	0.235826	+	0.462906i
$683$	−473.225	+	819.650i	−0.692862	+	1.20007i	0.278034	+	0.960571i	$0.410317\pi$
$683$	−473.225	+	819.650i	−0.692862	+	1.20007i	−0.970896	+	0.239501i	$0.923016\pi$
$684$	483.864	−	665.805i	0.707404	−	0.973399i
$685$		−	15.9952i		−	0.0233507i
$686$		0			0
$687$			1689.76i			2.45962i
$688$	−739.919	−	157.470i	−1.07546	−	0.228880i
$689$	154.400	−	267.428i	0.224092	−	0.388140i
$690$	−514.831	+	262.279i	−0.746132	+	0.380114i
$691$	151.632	+	262.634i	0.219439	+	0.380079i	0.954636	−	0.297774i	$-0.0962441\pi$
$691$	151.632	+	262.634i	0.219439	+	0.380079i	−0.735198	+	0.677853i	$0.762911\pi$
$692$	757.352	−	337.080i	1.09444	−	0.487111i
$693$		0			0
$694$	−622.580	−	404.364i	−0.897090	−	0.582658i
$695$	4.98781	−	2.87971i	0.00717670	−	0.00414347i
$696$	−558.725	+	689.700i	−0.802765	+	0.990949i
$697$	−58.8834	+	101.989i	−0.0844812	+	0.146326i
$698$	415.171	+	21.7844i	0.594801	+	0.0312098i
$699$	−332.074			−0.475069
$700$		0			0
$701$			390.864i			0.557580i	0.960352	+	0.278790i	$0.0899333\pi$
$701$			390.864i			0.557580i	−0.960352	+	0.278790i	$0.910067\pi$
$702$	−196.486	−	10.3098i	−0.279894	−	0.0146863i
$703$	1185.32	+	684.345i	1.68609	+	0.973464i
$704$	−374.885	+	337.291i	−0.532507	+	0.479106i
$705$	−309.446	−	535.976i	−0.438930	−	0.760250i
$706$	1029.87	+	668.897i	1.45874	+	0.947446i
$707$		0			0
$708$	67.4128	+	151.463i	0.0952158	+	0.213931i
$709$	832.393	−	480.582i	1.17404	−	0.677831i	0.219410	−	0.975633i	$-0.429587\pi$
$709$	832.393	−	480.582i	1.17404	−	0.677831i	0.954628	+	0.297801i	$0.0962533\pi$
$710$	128.334	−	65.3794i	0.180753	−	0.0920837i
$711$	−303.608	−	175.288i	−0.427016	−	0.246538i
$712$	−786.189	+	301.619i	−1.10420	+	0.423622i
$713$	866.685			1.21555
$714$		0			0
$715$	170.379			0.238293
$716$	409.563	−	563.566i	0.572016	−	0.787103i
$717$	−388.074	−	224.055i	−0.541247	−	0.312489i
$718$	98.1151	+	192.592i	0.136650	+	0.268234i
$719$	454.773	−	262.563i	0.632507	−	0.365178i	−0.149215	−	0.988805i	$-0.547675\pi$
$719$	454.773	−	262.563i	0.632507	−	0.365178i	0.781722	+	0.623627i	$0.214341\pi$
$720$	−153.263	−	138.068i	−0.212865	−	0.191762i
$721$		0			0
$722$	908.548	+	590.100i	1.25838	+	0.817312i
$723$	558.204	+	966.838i	0.772067	+	1.33726i
$724$	85.4997	−	812.489i	0.118093	−	1.12222i
$725$	517.870	+	298.992i	0.714304	+	0.412403i
$726$	−24.5792	+	468.434i	−0.0338557	+	0.645226i
$727$		−	108.633i		−	0.149426i	−0.997205	−	0.0747131i	$-0.976196\pi$
$727$		−	108.633i		−	0.149426i	0.997205	−	0.0747131i	$-0.0238041\pi$
$728$		0			0
$729$	−348.775			−0.478429
$730$	−52.5547	−	2.75760i	−0.0719927	−	0.00377753i
$731$	68.5197	−	118.680i	0.0937341	−	0.162352i
$732$	36.9341	−	350.979i	0.0504564	−	0.479479i
$733$	−34.8609	+	20.1270i	−0.0475593	+	0.0274584i	−0.523591	−	0.851970i	$-0.675408\pi$
$733$	−34.8609	+	20.1270i	−0.0475593	+	0.0274584i	0.476032	+	0.879428i	$0.342075\pi$
$734$	−495.468	+	762.849i	−0.675025	+	1.03930i
$735$		0			0
$736$	318.889	+	1191.61i	0.433273	+	1.61904i
$737$	−233.665	−	404.719i	−0.317049	−	0.549144i
$738$	−495.892	+	252.630i	−0.671941	+	0.342318i
$739$	−498.602	+	863.603i	−0.674698	+	1.16861i	0.301859	+	0.953352i	$0.402393\pi$
$739$	−498.602	+	863.603i	−0.674698	+	1.16861i	−0.976557	+	0.215258i	$0.930941\pi$
$740$	201.665	−	277.495i	0.272521	−	0.374993i
$741$			1373.87i			1.85407i
$742$		0			0
$743$			476.575i			0.641420i	0.947177	+	0.320710i	$0.103922\pi$
$743$			476.575i			0.641420i	−0.947177	+	0.320710i	$0.896078\pi$
$744$	256.482	+	668.536i	0.344734	+	0.898570i
$745$	29.8607	−	51.7203i	0.0400815	−	0.0694232i
$746$	−246.715	−	484.281i	−0.330717	−	0.649170i
$747$	−306.289	−	530.509i	−0.410026	−	0.710186i
$748$	−37.1457	−	83.4590i	−0.0496600	−	0.111576i
$749$		0			0
$750$	−379.279	+	583.958i	−0.505706	+	0.778611i
$751$	−457.691	+	264.248i	−0.609442	+	0.351862i	−0.772747	−	0.634714i	$-0.781118\pi$
$751$	−457.691	+	264.248i	−0.609442	+	0.351862i	0.163305	+	0.986576i	$0.447785\pi$
$752$	−1256.73	+	407.985i	−1.67118	+	0.542534i
$753$	−65.5993	+	113.621i	−0.0871173	+	0.150892i
$754$	33.5485	−	639.372i	0.0444940	−	0.847973i
$755$	477.400			0.632318
$756$		0			0
$757$		−	455.964i		−	0.602331i	−0.953572	−	0.301165i	$-0.902624\pi$
$757$		−	455.964i		−	0.602331i	0.953572	−	0.301165i	$-0.0973756\pi$
$758$	28.1227	−	535.965i	0.0371011	−	0.707078i
$759$	−1047.19	−	604.598i	−1.37970	−	0.796572i
$760$	284.820	−	351.587i	0.374763	−	0.462615i
$761$	238.325	+	412.791i	0.313174	+	0.542433i	0.979048	−	0.203632i	$-0.0652745\pi$
$761$	238.325	+	412.791i	0.313174	+	0.542433i	−0.665874	+	0.746064i	$0.731941\pi$
$762$	154.810	−	238.354i	0.203163	−	0.312801i
$763$		0			0
$764$	1090.87	−	485.523i	1.42784	−	0.635502i
$765$	32.3619	−	18.6842i	0.0423032	−	0.0244238i
$766$	297.426	+	583.823i	0.388285	+	0.762171i
$767$	−103.564	−	59.7927i	−0.135025	−	0.0779565i
$768$	−824.807	+	598.622i	−1.07397	+	0.779455i
$769$	568.246			0.738941			0.369471	−	0.929242i	$-0.379539\pi$
$769$	568.246			0.738941			0.369471	+	0.929242i	$0.379539\pi$
$770$		0			0
$771$	892.621			1.15774
$772$	−777.803	+	1070.27i	−1.00752	+	1.38636i
$773$	1036.66	+	598.515i	1.34108	+	0.774275i	0.986967	−	0.160925i	$-0.0514478\pi$
$773$	1036.66	+	598.515i	1.34108	+	0.774275i	0.354118	+	0.935201i	$0.384781\pi$
$774$	577.045	−	293.973i	0.745536	−	0.379810i
$775$	417.771	−	241.200i	0.539059	−	0.311226i
$776$	69.3270	−	437.178i	0.0893389	−	0.563373i
$777$		0			0
$778$	−137.590	+	211.842i	−0.176852	+	0.272290i
$779$	−610.377	−	1057.20i	−0.783539	−	1.35713i
$780$	342.440	+	36.0356i	0.439026	+	0.0461995i
$781$	261.039	+	150.711i	0.334237	+	0.192972i
$782$	−223.152	−	11.7090i	−0.285360	−	0.0149731i
$783$			238.701i			0.304855i
$784$		0			0
$785$	92.8596			0.118292
$786$	50.6036	−	964.411i	0.0643812	−	1.22699i
$787$	226.134	−	391.676i	0.287337	−	0.497682i	−0.685836	−	0.727756i	$-0.740563\pi$
$787$	226.134	−	391.676i	0.287337	−	0.497682i	0.973173	+	0.230074i	$0.0738967\pi$
$788$	137.017	−	1302.04i	0.173879	−	1.65234i
$789$	585.969	−	338.309i	0.742673	−	0.428783i
$790$	−161.631	−	104.979i	−0.204596	−	0.132885i
$791$		0			0
$792$	67.6144	−	426.378i	0.0853717	−	0.538356i
$793$	127.282	+	220.459i	0.160507	+	0.278007i
$794$	−115.430	−	226.580i	−0.145378	−	0.285365i
$795$	100.740	−	174.486i	0.126716	−	0.219479i
$796$	41.2100	+	29.9488i	0.0517714	+	0.0376241i
$797$			1047.47i			1.31426i	0.753777	+	0.657130i	$0.228230\pi$
$797$			1047.47i			1.31426i	−0.753777	+	0.657130i	$0.771770\pi$
$798$		0			0
$799$		−	239.355i		−	0.299568i
$800$	485.343	+	485.650i	0.606679	+	0.607062i
$801$	360.434	−	624.290i	0.449980	−	0.779388i
$802$	−107.192	+	54.6085i	−0.133656	+	0.0680904i
$803$	−55.0687	−	95.3818i	−0.0685787	−	0.118782i
$804$	−384.037	−	862.854i	−0.477658	−	1.07320i
$805$		0			0
$806$	−433.153	−	281.332i	−0.537411	−	0.349047i
$807$	374.162	−	216.023i	0.463646	−	0.267686i
$808$	158.288	−	195.393i	0.195900	−	0.241823i
$809$	149.332	−	258.651i	0.184589	−	0.319717i	−0.758849	−	0.651267i	$-0.774238\pi$
$809$	149.332	−	258.651i	0.184589	−	0.319717i	0.943438	+	0.331549i	$0.107571\pi$
$810$	−359.947	−	18.8868i	−0.444380	−	0.0233171i
$811$	−633.054			−0.780584			−0.390292	−	0.920691i	$-0.627626\pi$
$811$	−633.054			−0.780584			−0.390292	+	0.920691i	$0.627626\pi$
$812$		0			0
$813$		−	77.0852i		−	0.0948158i
$814$	716.914	+	37.6172i	0.880730	+	0.0462128i
$815$	−188.658	−	108.922i	−0.231483	−	0.133647i
$816$	−57.0063	−	175.598i	−0.0698606	−	0.215194i
$817$	710.265	+	1230.21i	0.869357	+	1.50577i
$818$	117.031	+	76.0114i	0.143070	+	0.0929235i
$819$		0			0
$820$	−279.521	+	124.409i	−0.340879	+	0.151718i
$821$	−1083.83	+	625.749i	−1.32013	+	0.762178i	−0.983749	−	0.179547i	$-0.942537\pi$
$821$	−1083.83	+	625.749i	−1.32013	+	0.762178i	−0.336382	+	0.941725i	$0.609203\pi$
$822$	60.2797	−	30.7092i	0.0733329	−	0.0373592i
$823$	1062.45	+	613.409i	1.29095	+	0.745332i	0.978823	−	0.204707i	$-0.0656241\pi$
$823$	1062.45	+	613.409i	1.29095	+	0.745332i	0.312130	+	0.950039i	$0.398957\pi$
$824$	−229.203	−	597.432i	−0.278159	−	0.725039i
$825$	−673.043			−0.815810
$826$		0			0
$827$	−1438.26			−1.73913			−0.869566	−	0.493816i	$-0.835602\pi$
$827$	−1438.26			−1.73913			−0.869566	+	0.493816i	$0.835602\pi$
$828$	−854.250	−	620.813i	−1.03170	−	0.749775i
$829$	−542.554	−	313.244i	−0.654468	−	0.377858i	0.135698	−	0.990750i	$-0.456672\pi$
$829$	−542.554	−	313.244i	−0.654468	−	0.377858i	−0.790166	+	0.612893i	$0.790006\pi$
$830$	−152.870	−	300.071i	−0.184181	−	0.361532i
$831$	−446.289	+	257.665i	−0.537050	+	0.310066i
$832$	227.431	−	699.060i	0.273354	−	0.840216i
$833$		0			0
$834$	20.4286	+	13.2683i	0.0244947	+	0.0159092i
$835$	30.4836	+	52.7991i	0.0365073	+	0.0632325i
$836$	941.743	+	99.1013i	1.12649	+	0.118542i
$837$	166.764	+	96.2814i	0.199240	+	0.115032i
$838$	−74.9089	+	1427.62i	−0.0893901	+	1.70361i
$839$			1062.37i			1.26624i	0.774055	+	0.633118i	$0.218225\pi$
$839$			1062.37i			1.26624i	−0.774055	+	0.633118i	$0.781775\pi$
$840$		0			0
$841$	64.2558			0.0764041
$842$	−606.046	−	31.7998i	−0.719769	−	0.0377670i
$843$	−165.931	+	287.401i	−0.196834	+	0.340926i
$844$	−479.172	−	50.4242i	−0.567740	−	0.0597443i
$845$	60.4260	−	34.8870i	0.0715101	−	0.0412864i
$846$	616.116	−	948.605i	0.728270	−	1.12128i
$847$		0			0
$848$	−319.588	−	287.904i	−0.376872	−	0.339509i
$849$	57.5842	+	99.7387i	0.0678259	+	0.117478i
$850$	−110.825	+	56.4594i	−0.130383	+	0.0664228i
$851$	878.037	−	1520.80i	1.03177	−	1.78708i
$852$	492.778	+	358.119i	0.578378	+	0.420328i
$853$		−	698.388i		−	0.818743i	−0.912368	−	0.409372i	$-0.865748\pi$
$853$		−	698.388i		−	0.818743i	0.912368	−	0.409372i	$-0.134252\pi$
$854$		0			0
$855$			387.355i			0.453047i
$856$	364.223	−	139.733i	0.425494	−	0.163239i
$857$	−365.162	+	632.479i	−0.426094	+	0.738016i	−0.996522	−	0.0833317i	$-0.973444\pi$
$857$	−365.162	+	632.479i	−0.426094	+	0.738016i	0.570428	+	0.821347i	$0.306777\pi$
$858$	327.112	+	642.093i	0.381249	+	0.748360i
$859$	−483.130	−	836.805i	−0.562433	−	0.974162i	−0.997283	−	0.0736593i	$-0.976532\pi$
$859$	−483.130	−	836.805i	−0.562433	−	0.974162i	0.434851	−	0.900502i	$-0.356801\pi$
$860$	325.265	−	144.768i	0.378215	−	0.168335i
$861$		0			0
$862$	470.063	−	723.734i	0.545317	−	0.839598i
$863$	−255.023	+	147.237i	−0.295507	+	0.170611i	−0.640423	−	0.768023i	$-0.721241\pi$
$863$	−255.023	+	147.237i	−0.295507	+	0.170611i	0.344916	+	0.938634i	$0.387907\pi$
$864$	−71.0188	+	264.712i	−0.0821977	+	0.306379i
$865$	−195.071	+	337.873i	−0.225516	+	0.390605i
$866$	−20.4225	+	389.214i	−0.0235825	+	0.449439i
$867$	−1117.07			−1.28844
$868$		0			0
$869$		−	403.346i		−	0.464149i
$870$	21.8890	−	417.164i	0.0251598	−	0.479499i
$871$	589.983	+	340.627i	0.677362	+	0.391075i
$872$	579.458	−	715.294i	0.664516	−	0.820292i
$873$	189.467	+	328.166i	0.217030	+	0.375906i
$874$	1261.69	−	1942.57i	1.44358	−	2.22262i
$875$		0			0
$876$	−90.5075	−	203.352i	−0.103319	−	0.232137i
$877$	−818.300	+	472.446i	−0.933067	+	0.538706i	−0.887780	−	0.460268i	$-0.847753\pi$
$877$	−818.300	+	472.446i	−0.933067	+	0.538706i	−0.0452867	+	0.998974i	$0.514420\pi$
$878$	−277.780	−	545.259i	−0.316378	−	0.621024i
$879$	739.916	+	427.191i	0.841770	+	0.485996i
$880$	49.4026	−	232.133i	0.0561393	−	0.263788i
$881$	−744.098			−0.844606			−0.422303	−	0.906455i	$-0.638778\pi$
$881$	−744.098			−0.844606			−0.422303	+	0.906455i	$0.638778\pi$
$882$		0			0
$883$	23.9032			0.0270704			0.0135352	−	0.999908i	$-0.495691\pi$
$883$	23.9032			0.0270704			0.0135352	+	0.999908i	$0.495691\pi$
$884$	107.726	+	78.2885i	0.121862	+	0.0885616i
$885$	−67.5713	−	39.0123i	−0.0763517	−	0.0440817i
$886$	−445.869	+	227.146i	−0.503238	+	0.256373i
$887$	−820.397	+	473.656i	−0.924912	+	0.533998i	−0.885199	−	0.465213i	$-0.845978\pi$
$887$	−820.397	+	473.656i	−0.924912	+	0.533998i	−0.0397129	+	0.999211i	$0.512644\pi$
$888$	1432.95	+	227.235i	1.61368	+	0.255895i
$889$		0			0
$890$	215.861	−	332.351i	0.242541	−	0.373428i
$891$	−377.166	−	653.271i	−0.423307	−	0.733189i
$892$	156.126	−	1483.64i	0.175029	−	1.66327i
$893$	2148.71	+	1240.56i	2.40617	+	1.38920i
$894$	252.243	+	13.2354i	0.282151	+	0.0148048i
$895$			327.874i			0.366339i
$896$		0			0
$897$	1762.71			1.96512
$898$	−72.1723	+	1375.47i	−0.0803700	+	1.53170i
$899$	−313.304	+	542.658i	−0.348502	+	0.603624i
$900$	−584.550	−	61.5133i	−0.649500	−	0.0683481i
$901$	67.4820	−	38.9607i	0.0748968	−	0.0432417i
$902$	−536.983	−	348.769i	−0.595325	−	0.386662i
$903$		0			0
$904$	69.8619	−	440.551i	0.0772809	−	0.487335i
$905$	192.247	+	332.981i	0.212427	+	0.367935i
$906$	916.561	+	1799.13i	1.01166	+	1.98580i
$907$	−275.512	+	477.200i	−0.303761	+	0.526130i	−0.976985	−	0.213309i	$-0.931576\pi$
$907$	−275.512	+	477.200i	−0.303761	+	0.526130i	0.673223	+	0.739439i	$0.264909\pi$
$908$	−172.664	+	237.589i	−0.190159	+	0.261661i
$909$			215.271i			0.236822i
$910$		0			0
$911$			827.652i			0.908509i	0.890872	+	0.454254i	$0.150094\pi$
$911$			827.652i			0.908509i	−0.890872	+	0.454254i	$0.849906\pi$
$912$	1871.82	+	398.361i	2.05243	+	0.436800i
$913$	352.392	−	610.361i	0.385972	−	0.668523i
$914$	−1433.71	+	730.397i	−1.56861	+	0.799121i
$915$	83.0466	+	143.841i	0.0907613	+	0.157203i
$916$	−1551.11	+	690.366i	−1.69336	+	0.753675i
$917$		0			0
$918$	−41.6372	−	27.0433i	−0.0453565	−	0.0294589i
$919$	−309.165	+	178.497i	−0.336415	+	0.194229i	−0.658685	−	0.752418i	$-0.728887\pi$
$919$	−309.165	+	178.497i	−0.336415	+	0.194229i	0.322271	+	0.946648i	$0.395554\pi$
$920$	−451.098	−	365.433i	−0.490324	−	0.397210i
$921$	−239.940	+	415.588i	−0.260521	+	0.451236i
$922$	−1385.41	−	72.6938i	−1.50261	−	0.0788435i
$923$	−439.400			−0.476056
$924$		0			0
$925$		−	977.438i		−	1.05669i
$926$	−641.506	−	33.6605i	−0.692771	−	0.0363504i
$927$	474.403	+	273.897i	0.511762	+	0.295466i
$928$	−861.382	−	231.098i	−0.928214	−	0.249028i
$929$	484.873	+	839.824i	0.521930	+	0.904009i	0.999675	+	0.0255102i	$0.00812102\pi$
$929$	484.873	+	839.824i	0.521930	+	0.904009i	−0.477745	+	0.878499i	$0.658546\pi$
$930$	−282.615	−	183.558i	−0.303887	−	0.197374i
$931$		0			0
$932$	−135.672	−	304.827i	−0.145570	−	0.327068i
$933$	1121.74	−	647.636i	1.20229	−	0.694144i
$934$	1339.89	−	682.603i	1.43458	−	0.730839i
$935$	37.2331	+	21.4965i	0.0398215	+	0.0229909i
$936$	225.418	+	587.566i	0.240831	+	0.627742i
$937$	−1287.55			−1.37412			−0.687061	−	0.726600i	$-0.741099\pi$
$937$	−1287.55			−1.37412			−0.687061	+	0.726600i	$0.741099\pi$
$938$		0			0
$939$	−1818.36			−1.93649
$940$	365.572	−	503.034i	0.388907	−	0.535142i
$941$	395.597	+	228.398i	0.420400	+	0.242718i	0.695249	−	0.718769i	$-0.255294\pi$
$941$	395.597	+	228.398i	0.420400	+	0.242718i	−0.274848	+	0.961488i	$0.588628\pi$
$942$	178.281	+	349.951i	0.189258	+	0.371498i
$943$	−1356.43	+	783.133i	−1.43842	+	0.830470i
$944$	−111.493	+	123.763i	−0.118107	+	0.131105i
$945$		0			0
$946$	624.860	+	405.845i	0.660529	+	0.429012i
$947$	573.925	+	994.067i	0.606045	+	1.04970i	0.991885	+	0.127135i	$0.0405782\pi$
$947$	573.925	+	994.067i	0.606045	+	1.04970i	−0.385840	+	0.922566i	$0.626088\pi$
$948$	85.3085	−	810.672i	0.0899878	−	0.855139i
$949$	139.044	+	80.2768i	0.146516	+	0.0845910i
$950$	67.5571	−	1287.51i	0.0711128	−	1.35528i
$951$			482.582i			0.507447i
$952$		0			0
$953$	873.170			0.916232			0.458116	−	0.888892i	$-0.348524\pi$
$953$	873.170			0.916232			0.458116	+	0.888892i	$0.348524\pi$
$954$	367.731	+	19.2952i	0.385462	+	0.0202256i
$955$	−280.976	+	486.665i	−0.294216	+	0.509597i
$956$	47.1199	−	447.772i	0.0492886	−	0.468381i
$957$	757.114	−	437.120i	0.791133	−	0.456761i
$958$	786.688	−	1211.23i	0.821177	−	1.26433i
$959$		0			0
$960$	148.389	−	456.108i	0.154572	−	0.475113i
$961$	−227.755	−	394.483i	−0.236998	−	0.410492i
$962$	−932.490	+	475.053i	−0.969324	+	0.493818i
$963$	−166.980	+	289.219i	−0.173396	+	0.300331i
$964$	−659.450	+	907.414i	−0.684077	+	0.941301i
$965$		−	622.666i		−	0.645249i
$966$		0			0
$967$		−	449.047i		−	0.464372i	−0.972671	−	0.232186i	$-0.925412\pi$
$967$		−	449.047i		−	0.464372i	0.972671	−	0.232186i	$-0.0745878\pi$
$968$	−440.041	+	168.820i	−0.454588	+	0.174401i
$969$	−173.339	+	300.231i	−0.178884	+	0.309836i
$970$	94.5635	+	185.620i	0.0974882	+	0.191361i
$971$	−618.929	−	1072.02i	−0.637414	−	1.10403i	−0.985998	−	0.166756i	$-0.946671\pi$
$971$	−618.929	−	1072.02i	−0.637414	−	1.10403i	0.348584	−	0.937278i	$-0.386663\pi$
$972$	−494.512	−	1111.07i	−0.508757	−	1.14308i
$973$		0			0
$974$	−52.1041	+	80.2222i	−0.0534950	+	0.0823636i
$975$	849.687	−	490.567i	0.871473	−	0.503145i
$976$	337.271	−	109.492i	0.345564	−	0.112184i
$977$	−853.445	+	1478.21i	−0.873536	+	1.51301i	−0.0152219	+	0.999884i	$0.504845\pi$
$977$	−853.445	+	1478.21i	−0.873536	+	1.51301i	−0.858314	+	0.513125i	$0.828488\pi$
$978$	48.2785	−	920.098i	0.0493645	−	0.940796i
$979$	829.373			0.847164
$980$		0			0
$981$			788.063i			0.803326i
$982$	4.66062	−	88.8226i	0.00474604	−	0.0904508i
$983$	997.793	+	576.076i	1.01505	+	0.586039i	0.912666	−	0.408706i	$-0.134020\pi$
$983$	997.793	+	576.076i	1.01505	+	0.586039i	0.102383	+	0.994745i	$0.467353\pi$
$984$	−1005.50	−	814.553i	−1.02185	−	0.827798i
$985$	308.082	+	533.614i	0.312774	+	0.541741i
$986$	87.9999	−	135.489i	0.0892494	−	0.137413i
$987$		0			0
$988$	−1261.14	+	561.305i	−1.27646	+	0.568123i
$989$	1578.41	−	911.293i	1.59596	−	0.921429i
$990$	92.2276	+	181.035i	0.0931592	+	0.182864i
$991$	−357.511	−	206.409i	−0.360758	−	0.208283i	0.308655	−	0.951174i	$-0.400121\pi$
$991$	−357.511	−	206.409i	−0.360758	−	0.208283i	−0.669413	+	0.742890i	$0.733454\pi$
$992$	−508.895	+	508.574i	−0.512999	+	0.512676i
$993$	482.375			0.485776
$994$		0			0
$995$	−23.9753			−0.0240958
$996$	837.355	−	1152.21i	0.840718	−	1.15684i
$997$	−260.805	−	150.576i	−0.261590	−	0.151029i	0.363470	−	0.931606i	$-0.381592\pi$
$997$	−260.805	−	150.576i	−0.261590	−	0.151029i	−0.625060	+	0.780577i	$0.714925\pi$
$998$	893.837	−	455.362i	0.895628	−	0.456274i
$999$	337.897	−	195.085i	0.338235	−	0.195280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.l.67.3		12
7.2	even	3	inner	392.3.k.l.275.1		12
7.3	odd	6		392.3.g.j.99.6		6
7.4	even	3		392.3.g.i.99.6		6
7.5	odd	6		56.3.k.d.51.1	yes	12
7.6	odd	2		56.3.k.d.11.3	yes	12
8.3	odd	2	inner	392.3.k.l.67.1		12
28.3	even	6		1568.3.g.j.687.5		6
28.11	odd	6		1568.3.g.l.687.2		6
28.19	even	6		224.3.o.d.79.2		12
28.27	even	2		224.3.o.d.207.1		12
56.3	even	6		392.3.g.j.99.5		6
56.5	odd	6		224.3.o.d.79.1		12
56.11	odd	6		392.3.g.i.99.5		6
56.13	odd	2		224.3.o.d.207.2		12
56.19	even	6		56.3.k.d.51.3	yes	12
56.27	even	2		56.3.k.d.11.1	✓	12
56.45	odd	6		1568.3.g.j.687.6		6
56.51	odd	6	inner	392.3.k.l.275.3		12
56.53	even	6		1568.3.g.l.687.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.1	✓	12	56.27	even	2
56.3.k.d.11.3	yes	12	7.6	odd	2
56.3.k.d.51.1	yes	12	7.5	odd	6
56.3.k.d.51.3	yes	12	56.19	even	6
224.3.o.d.79.1		12	56.5	odd	6
224.3.o.d.79.2		12	28.19	even	6
224.3.o.d.207.1		12	28.27	even	2
224.3.o.d.207.2		12	56.13	odd	2
392.3.g.i.99.5		6	56.11	odd	6
392.3.g.i.99.6		6	7.4	even	3
392.3.g.j.99.5		6	56.3	even	6
392.3.g.j.99.6		6	7.3	odd	6
392.3.k.l.67.1		12	8.3	odd	2	inner
392.3.k.l.67.3		12	1.1	even	1	trivial
392.3.k.l.275.1		12	7.2	even	3	inner
392.3.k.l.275.3		12	56.51	odd	6	inner
1568.3.g.j.687.5		6	28.3	even	6
1568.3.g.j.687.6		6	56.45	odd	6
1568.3.g.l.687.1		6	56.53	even	6
1568.3.g.l.687.2		6	28.11	odd	6

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.104798 - 1.99725i) q^{2} +(-1.99052 + 3.44767i) q^{3} +(-3.97803 - 0.418616i) q^{4} +(1.63031 - 0.941260i) q^{5} +(6.67727 + 4.33687i) q^{6} +(-1.25297 + 7.90127i) q^{8} +(-3.42430 - 5.93106i) q^{9} +O(q^{10})\)	\(q+(0.104798 - 1.99725i) q^{2} +(-1.99052 + 3.44767i) q^{3} +(-3.97803 - 0.418616i) q^{4} +(1.63031 - 0.941260i) q^{5} +(6.67727 + 4.33687i) q^{6} +(-1.25297 + 7.90127i) q^{8} +(-3.42430 - 5.93106i) q^{9} +(-1.70908 - 3.35478i) q^{10} +(3.93973 - 6.82381i) q^{11} +(9.36159 - 12.8817i) q^{12} +11.4863i q^{13} +7.49437i q^{15} +(15.6495 + 3.33054i) q^{16} +(-1.44921 + 2.51011i) q^{17} +(-12.2047 + 6.21763i) q^{18} +(-15.0223 - 26.0194i) q^{19} +(-6.87946 + 3.06189i) q^{20} +(-13.2160 - 8.58375i) q^{22} +(-33.3838 + 19.2741i) q^{23} +(-24.7469 - 20.0474i) q^{24} +(-10.7281 + 18.5815i) q^{25} +(22.9411 + 1.20374i) q^{26} -8.56478 q^{27} -27.8701i q^{29} +(14.9681 + 0.785394i) q^{30} +(-19.4709 - 11.2416i) q^{31} +(8.29196 - 30.9070i) q^{32} +(15.6842 + 27.1658i) q^{33} +(4.86145 + 3.15750i) q^{34} +(11.1392 + 25.0274i) q^{36} +(-39.4520 + 22.7776i) q^{37} +(-53.5417 + 27.2766i) q^{38} +(-39.6011 - 22.8637i) q^{39} +(5.39442 + 14.0609i) q^{40} +40.6313 q^{41} -47.2806 q^{43} +(-18.5289 + 25.4961i) q^{44} +(-11.1653 - 6.44632i) q^{45} +(34.9968 + 68.6958i) q^{46} +(-71.5172 + 41.2905i) q^{47} +(-42.6332 + 47.3250i) q^{48} +(35.9878 + 23.3739i) q^{50} +(-5.76936 - 9.99283i) q^{51} +(4.80836 - 45.6930i) q^{52} +(-23.2823 - 13.4420i) q^{53} +(-0.897571 + 17.1060i) q^{54} -14.8332i q^{55} +119.609 q^{57} +(-55.6637 - 2.92073i) q^{58} +(-5.20555 + 9.01627i) q^{59} +(3.13726 - 29.8129i) q^{60} +(19.1932 - 11.0812i) q^{61} +(-24.4927 + 37.7103i) q^{62} +(-60.8601 - 19.8001i) q^{64} +(10.8116 + 18.7263i) q^{65} +(55.9006 - 28.4783i) q^{66} +(29.6549 - 51.3639i) q^{67} +(6.81579 - 9.37864i) q^{68} -153.462i q^{69} +38.2541i q^{71} +(51.1535 - 19.6249i) q^{72} +(6.98890 - 12.1051i) q^{73} +(41.3581 + 81.1826i) q^{74} +(-42.7087 - 73.9737i) q^{75} +(48.8672 + 109.795i) q^{76} +(-49.8147 + 76.6974i) q^{78} +(44.3314 - 25.5948i) q^{79} +(28.6485 - 9.30046i) q^{80} +(47.8670 - 82.9081i) q^{81} +(4.25807 - 81.1509i) q^{82} +89.4458 q^{83} +5.45635i q^{85} +(-4.95491 + 94.4313i) q^{86} +(96.0871 + 55.4759i) q^{87} +(48.9804 + 39.6789i) q^{88} +(52.6288 + 91.1558i) q^{89} +(-14.0450 + 21.6245i) q^{90} +(140.870 - 62.6982i) q^{92} +(77.5144 - 44.7530i) q^{93} +(74.9726 + 147.165i) q^{94} +(-48.9821 - 28.2798i) q^{95} +(90.0520 + 90.1088i) q^{96} -55.3301 q^{97} -53.9633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 6 q^{3} - 4 q^{4} + 56 q^{6} + 8 q^{8} - 40 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 6 * q^3 - 4 * q^4 + 56 * q^6 + 8 * q^8 - 40 * q^9	\( 12 q + 2 q^{2} + 6 q^{3} - 4 q^{4} + 56 q^{6} + 8 q^{8} - 40 q^{9} + 6 q^{10} + 30 q^{11} - 32 q^{12} + 16 q^{16} - 30 q^{17} - 16 q^{18} - 78 q^{19} - 48 q^{20} + 24 q^{22} + 76 q^{24} - 92 q^{25} + 128 q^{26} - 156 q^{27} - 16 q^{30} + 112 q^{32} + 78 q^{33} - 76 q^{34} - 248 q^{36} - 80 q^{38} - 44 q^{40} + 232 q^{41} - 200 q^{43} + 132 q^{44} - 156 q^{46} - 176 q^{48} + 48 q^{50} + 10 q^{51} - 132 q^{52} + 36 q^{54} + 332 q^{57} + 4 q^{58} + 110 q^{59} + 84 q^{60} + 96 q^{62} - 160 q^{64} - 32 q^{65} + 138 q^{66} + 434 q^{67} - 96 q^{68} - 328 q^{72} - 102 q^{73} - 34 q^{74} + 60 q^{75} + 168 q^{76} + 720 q^{78} + 256 q^{80} - 82 q^{81} + 24 q^{82} + 536 q^{83} + 240 q^{86} - 204 q^{88} - 214 q^{89} - 440 q^{90} + 160 q^{92} + 16 q^{94} - 48 q^{96} + 152 q^{97} + 504 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 6 * q^3 - 4 * q^4 + 56 * q^6 + 8 * q^8 - 40 * q^9 + 6 * q^10 + 30 * q^11 - 32 * q^12 + 16 * q^16 - 30 * q^17 - 16 * q^18 - 78 * q^19 - 48 * q^20 + 24 * q^22 + 76 * q^24 - 92 * q^25 + 128 * q^26 - 156 * q^27 - 16 * q^30 + 112 * q^32 + 78 * q^33 - 76 * q^34 - 248 * q^36 - 80 * q^38 - 44 * q^40 + 232 * q^41 - 200 * q^43 + 132 * q^44 - 156 * q^46 - 176 * q^48 + 48 * q^50 + 10 * q^51 - 132 * q^52 + 36 * q^54 + 332 * q^57 + 4 * q^58 + 110 * q^59 + 84 * q^60 + 96 * q^62 - 160 * q^64 - 32 * q^65 + 138 * q^66 + 434 * q^67 - 96 * q^68 - 328 * q^72 - 102 * q^73 - 34 * q^74 + 60 * q^75 + 168 * q^76 + 720 * q^78 + 256 * q^80 - 82 * q^81 + 24 * q^82 + 536 * q^83 + 240 * q^86 - 204 * q^88 - 214 * q^89 - 440 * q^90 + 160 * q^92 + 16 * q^94 - 48 * q^96 + 152 * q^97 + 504 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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