LMFDB - Embedded newform 196.3.g.j.79.4

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			79.4
Root			$1.40501 - 0.161055i$ of defining polynomial
Character	$\chi$	$=$	196.79
Dual form			196.3.g.j.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.489450 - 1.93919i) q^{2} +(3.93608 - 2.27250i) q^{3} +(-3.52088 - 1.89827i) q^{4} +(0.683969 - 1.18467i) q^{5} +(-2.48028 - 8.74507i) q^{6} +(-5.40439 + 5.89853i) q^{8} +(5.82850 - 10.0953i) q^{9} +O(q^{10})$	\(q+(0.489450 - 1.93919i) q^{2} +(3.93608 - 2.27250i) q^{3} +(-3.52088 - 1.89827i) q^{4} +(0.683969 - 1.18467i) q^{5} +(-2.48028 - 8.74507i) q^{6} +(-5.40439 + 5.89853i) q^{8} +(5.82850 - 10.0953i) q^{9} +(-1.96252 - 1.90618i) q^{10} +(13.2565 - 7.65363i) q^{11} +(-18.1723 + 0.529446i) q^{12} -19.9460 q^{13} -6.21727i q^{15} +(8.79315 + 13.3671i) q^{16} +(-2.36794 - 4.10139i) q^{17} +(-16.7238 - 16.2437i) q^{18} +(11.4977 + 6.63823i) q^{19} +(-4.65699 + 2.87272i) q^{20} +(-8.35343 - 29.4528i) q^{22} +(12.9460 + 7.47437i) q^{23} +(-7.86773 + 35.4985i) q^{24} +(11.5644 + 20.0301i) q^{25} +(-9.76259 + 38.6791i) q^{26} -12.0760i q^{27} +6.20763 q^{29} +(-12.0564 - 3.04305i) q^{30} +(-16.0548 + 9.26926i) q^{31} +(30.2252 - 10.5090i) q^{32} +(34.7857 - 60.2507i) q^{33} +(-9.11234 + 2.58445i) q^{34} +(-39.6849 + 24.4801i) q^{36} +(13.7608 - 23.8344i) q^{37} +(18.5003 - 19.0472i) q^{38} +(-78.5093 + 45.3274i) q^{39} +(3.29137 + 10.4368i) q^{40} +11.1064 q^{41} +27.0248i q^{43} +(-61.2031 + 1.78314i) q^{44} +(-7.97302 - 13.8097i) q^{45} +(20.8306 - 21.4463i) q^{46} +(-26.8235 - 15.4865i) q^{47} +(64.9874 + 32.6317i) q^{48} +(44.5022 - 12.6217i) q^{50} +(-18.6408 - 10.7623i) q^{51} +(70.2276 + 37.8629i) q^{52} +(6.39287 + 11.0728i) q^{53} +(-23.4176 - 5.91061i) q^{54} -20.9394i q^{55} +60.3415 q^{57} +(3.03832 - 12.0377i) q^{58} +(24.9666 - 14.4145i) q^{59} +(-11.8021 + 21.8903i) q^{60} +(3.26208 - 5.65008i) q^{61} +(10.1168 + 35.6701i) q^{62} +(-5.58519 - 63.7558i) q^{64} +(-13.6425 + 23.6295i) q^{65} +(-99.8113 - 96.9457i) q^{66} +(89.0817 - 51.4313i) q^{67} +(0.551682 + 18.9355i) q^{68} +67.9420 q^{69} +45.8085i q^{71} +(28.0476 + 88.9382i) q^{72} +(-35.0499 - 60.7081i) q^{73} +(-39.4841 - 38.3505i) q^{74} +(91.0366 + 52.5600i) q^{75} +(-27.8810 - 45.1982i) q^{76} +(49.4718 + 174.429i) q^{78} +(28.9027 + 16.6870i) q^{79} +(21.8499 - 1.27427i) q^{80} +(25.0137 + 43.3251i) q^{81} +(5.43601 - 21.5373i) q^{82} +159.301i q^{83} -6.47839 q^{85} +(52.4060 + 13.2273i) q^{86} +(24.4337 - 14.1068i) q^{87} +(-26.4980 + 119.557i) q^{88} +(-25.0208 + 43.3374i) q^{89} +(-30.6819 + 8.70202i) q^{90} +(-31.3929 - 50.8913i) q^{92} +(-42.1287 + 72.9691i) q^{93} +(-43.1600 + 44.4358i) q^{94} +(15.7282 - 9.08069i) q^{95} +(95.0871 - 110.051i) q^{96} -89.7343 q^{97} -178.437i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - q^{4} - 4 q^{5} - 12 q^{6} - 26 q^{8} + 10 q^{9}+O(q^{10}) $ 12 * q + q^2 - q^4 - 4 * q^5 - 12 * q^6 - 26 * q^8 + 10 * q^9	$ 12 q + q^{2} - q^{4} - 4 q^{5} - 12 q^{6} - 26 q^{8} + 10 q^{9} - 28 q^{10} + 6 q^{12} - 24 q^{13} - 17 q^{16} - 4 q^{17} - 43 q^{18} + 64 q^{20} + 104 q^{22} + 122 q^{24} + 30 q^{25} - 56 q^{26} - 72 q^{29} + 64 q^{30} + 101 q^{32} + 80 q^{33} - 116 q^{34} - 262 q^{36} - 28 q^{37} - 190 q^{38} + 40 q^{40} + 40 q^{41} - 164 q^{44} + 12 q^{45} - 120 q^{46} + 196 q^{48} + 322 q^{50} + 292 q^{52} - 92 q^{53} - 44 q^{54} + 320 q^{57} + 166 q^{58} + 176 q^{60} - 164 q^{61} - 296 q^{62} - 430 q^{64} + 136 q^{65} - 408 q^{66} + 62 q^{68} + 96 q^{69} - 151 q^{72} - 132 q^{73} - 250 q^{74} + 156 q^{76} + 496 q^{78} + 312 q^{80} + 218 q^{81} - 86 q^{82} - 464 q^{85} + 164 q^{86} + 100 q^{88} + 348 q^{89} - 104 q^{90} - 208 q^{92} - 288 q^{93} - 276 q^{94} + 170 q^{96} - 504 q^{97}+O(q^{100}) $ 12 * q + q^2 - q^4 - 4 * q^5 - 12 * q^6 - 26 * q^8 + 10 * q^9 - 28 * q^10 + 6 * q^12 - 24 * q^13 - 17 * q^16 - 4 * q^17 - 43 * q^18 + 64 * q^20 + 104 * q^22 + 122 * q^24 + 30 * q^25 - 56 * q^26 - 72 * q^29 + 64 * q^30 + 101 * q^32 + 80 * q^33 - 116 * q^34 - 262 * q^36 - 28 * q^37 - 190 * q^38 + 40 * q^40 + 40 * q^41 - 164 * q^44 + 12 * q^45 - 120 * q^46 + 196 * q^48 + 322 * q^50 + 292 * q^52 - 92 * q^53 - 44 * q^54 + 320 * q^57 + 166 * q^58 + 176 * q^60 - 164 * q^61 - 296 * q^62 - 430 * q^64 + 136 * q^65 - 408 * q^66 + 62 * q^68 + 96 * q^69 - 151 * q^72 - 132 * q^73 - 250 * q^74 + 156 * q^76 + 496 * q^78 + 312 * q^80 + 218 * q^81 - 86 * q^82 - 464 * q^85 + 164 * q^86 + 100 * q^88 + 348 * q^89 - 104 * q^90 - 208 * q^92 - 288 * q^93 - 276 * q^94 + 170 * q^96 - 504 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.489450	−	1.93919i	0.244725	−	0.969593i
$2$	0.489450	−	1.93919i	0.244725	−	0.969593i
$3$	3.93608	−	2.27250i	1.31203	−	0.757499i	0.329596	−	0.944122i	$-0.393088\pi$
$3$	3.93608	−	2.27250i	1.31203	−	0.757499i	0.982432	+	0.186623i	$0.0597542\pi$
$4$	−3.52088	−	1.89827i	−0.880219	−	0.474567i
$5$	0.683969	−	1.18467i	0.136794	−	0.236934i	−0.789487	−	0.613767i	$-0.789654\pi$
$5$	0.683969	−	1.18467i	0.136794	−	0.236934i	0.926281	+	0.376833i	$0.122987\pi$
$6$	−2.48028	−	8.74507i	−0.413380	−	1.45751i
$7$		0			0
$7$		0			0
$8$	−5.40439	+	5.89853i	−0.675548	+	0.737316i
$9$	5.82850	−	10.0953i	0.647611	−	1.12169i
$10$	−1.96252	−	1.90618i	−0.196252	−	0.190618i
$11$	13.2565	−	7.65363i	1.20513	−	0.695785i	0.243442	−	0.969915i	$-0.421723\pi$
$11$	13.2565	−	7.65363i	1.20513	−	0.695785i	0.961692	+	0.274131i	$0.0883900\pi$
$12$	−18.1723	+	0.529446i	−1.51436	+	0.0441205i
$13$	−19.9460			−1.53431			−0.767156	−	0.641461i	$-0.778329\pi$
$13$	−19.9460			−1.53431			−0.767156	+	0.641461i	$0.778329\pi$
$14$		0			0
$15$		−	6.21727i		−	0.414485i
$16$	8.79315	+	13.3671i	0.549572	+	0.835446i
$17$	−2.36794	−	4.10139i	−0.139290	−	0.241258i	0.787938	−	0.615755i	$-0.211149\pi$
$17$	−2.36794	−	4.10139i	−0.139290	−	0.241258i	−0.927228	+	0.374497i	$0.877816\pi$
$18$	−16.7238	−	16.2437i	−0.929100	−	0.902425i
$19$	11.4977	+	6.63823i	0.605145	+	0.349380i	0.771063	−	0.636759i	$-0.219725\pi$
$19$	11.4977	+	6.63823i	0.605145	+	0.349380i	−0.165918	+	0.986140i	$0.553059\pi$
$20$	−4.65699	+	2.87272i	−0.232850	+	0.143636i
$21$		0			0
$22$	−8.35343	−	29.4528i	−0.379701	−	1.33877i
$23$	12.9460	+	7.47437i	0.562869	+	0.324973i	0.754296	−	0.656534i	$-0.227978\pi$
$23$	12.9460	+	7.47437i	0.562869	+	0.324973i	−0.191427	+	0.981507i	$0.561312\pi$
$24$	−7.86773	+	35.4985i	−0.327822	+	1.47911i
$25$	11.5644	+	20.0301i	0.462575	+	0.801203i
$26$	−9.76259	+	38.6791i	−0.375484	+	1.48766i
$27$		−	12.0760i		−	0.447260i
$28$		0			0
$29$	6.20763			0.214056			0.107028	−	0.994256i	$-0.465867\pi$
$29$	6.20763			0.214056			0.107028	+	0.994256i	$0.465867\pi$
$30$	−12.0564	−	3.04305i	−0.401882	−	0.101435i
$31$	−16.0548	+	9.26926i	−0.517898	+	0.299008i	−0.736074	−	0.676901i	$-0.763323\pi$
$31$	−16.0548	+	9.26926i	−0.517898	+	0.299008i	0.218176	+	0.975909i	$0.429989\pi$
$32$	30.2252	−	10.5090i	0.944537	−	0.328406i
$33$	34.7857	−	60.2507i	1.05411	−	1.82578i
$34$	−9.11234	+	2.58445i	−0.268010	+	0.0760131i
$35$		0			0
$36$	−39.6849	+	24.4801i	−1.10236	+	0.680003i
$37$	13.7608	−	23.8344i	0.371914	−	0.644173i	−0.617946	−	0.786220i	$-0.712035\pi$
$37$	13.7608	−	23.8344i	0.371914	−	0.644173i	0.989860	+	0.142047i	$0.0453684\pi$
$38$	18.5003	−	19.0472i	0.486851	−	0.501242i
$39$	−78.5093	+	45.3274i	−2.01306	+	1.16224i
$40$	3.29137	+	10.4368i	0.0822842	+	0.260921i
$41$	11.1064			0.270887			0.135443	−	0.990785i	$-0.456754\pi$
$41$	11.1064			0.270887			0.135443	+	0.990785i	$0.456754\pi$
$42$		0			0
$43$			27.0248i			0.628483i	0.949343	+	0.314241i	$0.101750\pi$
$43$			27.0248i			0.628483i	−0.949343	+	0.314241i	$0.898250\pi$
$44$	−61.2031	+	1.78314i	−1.39098	+	0.0405260i
$45$	−7.97302	−	13.8097i	−0.177178	−	0.306882i
$46$	20.8306	−	21.4463i	0.452839	−	0.466225i
$47$	−26.8235	−	15.4865i	−0.570712	−	0.329501i	0.186722	−	0.982413i	$-0.440214\pi$
$47$	−26.8235	−	15.4865i	−0.570712	−	0.329501i	−0.757434	+	0.652912i	$0.773547\pi$
$48$	64.9874	+	32.6317i	1.35390	+	0.679828i
$49$		0			0
$50$	44.5022	−	12.6217i	0.890044	−	0.252435i
$51$	−18.6408	−	10.7623i	−0.365506	−	0.211025i
$52$	70.2276	+	37.8629i	1.35053	+	0.728134i
$53$	6.39287	+	11.0728i	0.120620	+	0.208920i	0.920012	−	0.391889i	$-0.128178\pi$
$53$	6.39287	+	11.0728i	0.120620	+	0.208920i	−0.799392	+	0.600809i	$0.794845\pi$
$54$	−23.4176	−	5.91061i	−0.433660	−	0.109456i
$55$		−	20.9394i		−	0.380716i
$56$		0			0
$57$	60.3415			1.05862
$58$	3.03832	−	12.0377i	0.0523849	−	0.207547i
$59$	24.9666	−	14.4145i	0.423163	−	0.244313i	−0.273267	−	0.961938i	$-0.588104\pi$
$59$	24.9666	−	14.4145i	0.423163	−	0.244313i	0.696430	+	0.717625i	$0.254771\pi$
$60$	−11.8021	+	21.8903i	−0.196701	+	0.364838i
$61$	3.26208	−	5.65008i	0.0534767	−	0.0926243i	−0.838048	−	0.545597i	$-0.816303\pi$
$61$	3.26208	−	5.65008i	0.0534767	−	0.0926243i	0.891525	+	0.452972i	$0.149636\pi$
$62$	10.1168	+	35.6701i	0.163174	+	0.575324i
$63$		0			0
$64$	−5.58519	−	63.7558i	−0.0872687	−	0.996185i
$65$	−13.6425	+	23.6295i	−0.209884	+	0.363530i
$66$	−99.8113	−	96.9457i	−1.51229	−	1.46887i
$67$	89.0817	−	51.4313i	1.32958	−	0.767632i	0.344343	−	0.938844i	$-0.388102\pi$
$67$	89.0817	−	51.4313i	1.32958	−	0.767632i	0.985234	+	0.171212i	$0.0547684\pi$
$68$	0.551682	+	18.9355i	0.00811297	+	0.278463i
$69$	67.9420			0.984666
$70$		0			0
$71$			45.8085i			0.645190i	0.946537	+	0.322595i	$0.104555\pi$
$71$			45.8085i			0.645190i	−0.946537	+	0.322595i	$0.895445\pi$
$72$	28.0476	+	88.9382i	0.389551	+	1.23525i
$73$	−35.0499	−	60.7081i	−0.480135	−	0.831618i	0.519605	−	0.854406i	$-0.326079\pi$
$73$	−35.0499	−	60.7081i	−0.480135	−	0.831618i	−0.999740	+	0.0227881i	$0.992746\pi$
$74$	−39.4841	−	38.3505i	−0.533569	−	0.518250i
$75$	91.0366	+	52.5600i	1.21382	+	0.700800i
$76$	−27.8810	−	45.1982i	−0.366856	−	0.594713i
$77$		0			0
$78$	49.4718	+	174.429i	0.634253	+	2.23628i
$79$	28.9027	+	16.6870i	0.365857	+	0.211228i	0.671647	−	0.740871i	$-0.265587\pi$
$79$	28.9027	+	16.6870i	0.365857	+	0.211228i	−0.305790	+	0.952099i	$0.598921\pi$
$80$	21.8499	−	1.27427i	0.273124	−	0.0159283i
$81$	25.0137	+	43.3251i	0.308812	+	0.534877i
$82$	5.43601	−	21.5373i	0.0662927	−	0.262650i
$83$			159.301i			1.91930i	0.281206	+	0.959648i	$0.409266\pi$
$83$			159.301i			1.91930i	−0.281206	+	0.959648i	$0.590734\pi$
$84$		0			0
$85$	−6.47839			−0.0762163
$86$	52.4060	+	13.2273i	0.609372	+	0.153805i
$87$	24.4337	−	14.1068i	0.280848	−	0.162147i
$88$	−26.4980	+	119.557i	−0.301114	+	1.35860i
$89$	−25.0208	+	43.3374i	−0.281133	+	0.486937i	−0.971664	−	0.236366i	$-0.924044\pi$
$89$	−25.0208	+	43.3374i	−0.281133	+	0.486937i	0.690531	+	0.723303i	$0.257377\pi$
$90$	−30.6819	+	8.70202i	−0.340910	+	0.0966891i
$91$		0			0
$92$	−31.3929	−	50.8913i	−0.341227	−	0.553166i
$93$	−42.1287	+	72.9691i	−0.452997	+	0.784614i
$94$	−43.1600	+	44.4358i	−0.459149	+	0.472721i
$95$	15.7282	−	9.08069i	0.165560	−	0.0955862i
$96$	95.0871	−	110.051i	0.990490	−	1.14636i
$97$	−89.7343			−0.925096			−0.462548	−	0.886594i	$-0.653065\pi$
$97$	−89.7343			−0.925096			−0.462548	+	0.886594i	$0.653065\pi$
$98$		0			0
$99$		−	178.437i		−	1.80239i
$100$	−2.69427	−	92.4757i	−0.0269427	−	0.924757i
$101$	81.4407	+	141.059i	0.806343	+	1.39663i	0.915380	+	0.402590i	$0.131890\pi$
$101$	81.4407	+	141.059i	0.806343	+	1.39663i	−0.109037	+	0.994038i	$0.534777\pi$
$102$	−29.9938	+	30.8804i	−0.294057	+	0.302749i
$103$	−74.5832	−	43.0606i	−0.724109	−	0.418064i	0.0921544	−	0.995745i	$-0.470625\pi$
$103$	−74.5832	−	43.0606i	−0.724109	−	0.418064i	−0.816263	+	0.577680i	$0.803958\pi$
$104$	107.796	−	117.652i	1.03650	−	1.13127i
$105$		0			0
$106$	24.6011	−	6.97739i	0.232086	−	0.0658244i
$107$	−88.4607	−	51.0728i	−0.826735	−	0.477316i	0.0259983	−	0.999662i	$-0.491724\pi$
$107$	−88.4607	−	51.0728i	−0.826735	−	0.477316i	−0.852734	+	0.522346i	$0.825057\pi$
$108$	−22.9235	+	42.5182i	−0.212255	+	0.393687i
$109$	−76.0183	−	131.668i	−0.697416	−	1.20796i	−0.969360	−	0.245646i	$-0.921000\pi$
$109$	−76.0183	−	131.668i	−0.697416	−	1.20796i	0.271944	−	0.962313i	$-0.412333\pi$
$110$	−40.6054	−	10.2488i	−0.369140	−	0.0931708i
$111$		−	125.086i		−	1.12690i
$112$		0			0
$113$	−168.112			−1.48772			−0.743860	−	0.668335i	$-0.767007\pi$
$113$	−168.112			−1.48772			−0.743860	+	0.668335i	$0.767007\pi$
$114$	29.5341	−	117.013i	0.259071	−	1.02643i
$115$	17.7093	−	10.2245i	0.153994	−	0.0889085i
$116$	−21.8563	−	11.7837i	−0.188416	−	0.101584i
$117$	−116.255	+	201.360i	−0.993636	+	1.72103i
$118$	−15.7324	−	55.4700i	−0.133326	−	0.470085i
$119$		0			0
$120$	36.6727	+	33.6006i	0.305606	+	0.280005i
$121$	56.6562	−	98.1314i	0.468233	−	0.811004i
$122$	−9.35993	−	9.09120i	−0.0767207	−	0.0745180i
$123$	43.7155	−	25.2392i	0.355411	−	0.205196i
$124$	74.1226	−	2.15955i	0.597763	−	0.0174157i
$125$	65.8372			0.526697
$126$		0			0
$127$			87.8953i			0.692089i	0.938218	+	0.346044i	$0.112475\pi$
$127$			87.8953i			0.692089i	−0.938218	+	0.346044i	$0.887525\pi$
$128$	−126.368	−	20.3746i	−0.987250	−	0.159176i
$129$	61.4137	+	106.372i	0.476075	+	0.824586i
$130$	39.1446	+	38.0207i	0.301112	+	0.292467i
$131$	−121.365	−	70.0703i	−0.926453	−	0.534888i	−0.0407649	−	0.999169i	$-0.512979\pi$
$131$	−121.365	−	70.0703i	−0.926453	−	0.534888i	−0.885688	+	0.464281i	$0.846313\pi$
$132$	−236.848	+	146.103i	−1.79430	+	1.10684i
$133$		0			0
$134$	−56.1338	−	197.919i	−0.418909	−	1.47701i
$135$	−14.3061	−	8.25962i	−0.105971	−	0.0611824i
$136$	36.9894	+	8.19815i	0.271981	+	0.0602805i
$137$	−59.3623	−	102.818i	−0.433301	−	0.750500i	0.563854	−	0.825875i	$-0.309318\pi$
$137$	−59.3623	−	102.818i	−0.433301	−	0.750500i	−0.997155	+	0.0753745i	$0.975985\pi$
$138$	33.2542	−	131.752i	0.240972	−	0.954725i
$139$		−	72.1046i		−	0.518738i	−0.965778	−	0.259369i	$-0.916485\pi$
$139$		−	72.1046i		−	0.518738i	0.965778	−	0.259369i	$-0.0835147\pi$
$140$		0			0
$141$	−140.772			−0.998386
$142$	88.8311	+	22.4210i	0.625571	+	0.157894i
$143$	−264.414	+	152.660i	−1.84905	+	1.06755i
$144$	186.195	−	10.8588i	1.29302	−	0.0754081i
$145$	4.24583	−	7.35399i	0.0292816	−	0.0507172i
$146$	−134.879	+	38.2546i	−0.923832	+	0.262018i
$147$		0			0
$148$	−93.6942	+	57.7963i	−0.633069	+	0.390516i
$149$	−109.150	+	189.053i	−0.732548	+	1.26881i	0.223244	+	0.974763i	$0.428335\pi$
$149$	−109.150	+	189.053i	−0.732548	+	1.26881i	−0.955791	+	0.294047i	$0.904998\pi$
$150$	146.482	−	150.811i	0.976543	−	1.00541i
$151$	−156.704	+	90.4732i	−1.03778	+	0.599160i	−0.919203	−	0.393785i	$-0.871165\pi$
$151$	−156.704	+	90.4732i	−1.03778	+	0.599160i	−0.118573	+	0.992945i	$0.537832\pi$
$152$	−101.294	+	31.9442i	−0.666408	+	0.210159i
$153$	−55.2061			−0.360824
$154$		0			0
$155$			25.3595i			0.163610i
$156$	362.465	−	10.5604i	2.32349	−	0.0676946i
$157$	−95.5404	−	165.481i	−0.608538	−	1.05402i	−0.991482	−	0.130246i	$-0.958423\pi$
$157$	−95.5404	−	165.481i	−0.608538	−	1.05402i	0.382944	−	0.923772i	$-0.374910\pi$
$158$	46.5055	−	47.8802i	0.294339	−	0.303039i
$159$	50.3257	+	29.0556i	0.316514	+	0.182739i
$160$	8.22339	−	42.9947i	0.0513962	−	0.268717i
$161$		0			0
$162$	96.2583	−	27.3008i	0.594187	−	0.168524i
$163$	249.193	+	143.872i	1.52879	+	0.882648i	0.999413	+	0.0342619i	$0.0109080\pi$
$163$	249.193	+	143.872i	1.52879	+	0.882648i	0.529378	+	0.848386i	$0.322425\pi$
$164$	−39.1041	−	21.0828i	−0.238440	−	0.128554i
$165$	−47.5847	−	82.4192i	−0.288392	−	0.499510i
$166$	308.915	+	77.9701i	1.86093	+	0.469700i
$167$		−	124.859i		−	0.747659i	−0.927497	−	0.373829i	$-0.878045\pi$
$167$		−	124.859i		−	0.747659i	0.927497	−	0.373829i	$-0.121955\pi$
$168$		0			0
$169$	228.845			1.35411
$170$	−3.17085	+	12.5628i	−0.0186520	+	0.0738988i
$171$	134.029	−	77.3818i	0.783796	−	0.452525i
$172$	51.3002	−	95.1508i	0.298257	−	0.553203i
$173$	−137.604	+	238.336i	−0.795396	+	1.37767i	0.127191	+	0.991878i	$0.459404\pi$
$173$	−137.604	+	238.336i	−0.795396	+	1.37767i	−0.922587	+	0.385788i	$0.873930\pi$
$174$	−15.3967	−	54.2861i	−0.0884865	−	0.311989i
$175$		0			0
$176$	218.873	+	109.902i	1.24360	+	0.624441i
$177$	65.5137	−	113.473i	0.370134	−	0.641091i
$178$	71.7927	+	69.7315i	0.403330	+	0.391750i
$179$	6.43005	−	3.71239i	0.0359221	−	0.0207396i	−0.481931	−	0.876209i	$-0.660065\pi$
$179$	6.43005	−	3.71239i	0.0359221	−	0.0207396i	0.517853	+	0.855469i	$0.326731\pi$
$180$	1.85755	+	63.7571i	0.0103197	+	0.354206i
$181$	−99.5623			−0.550068			−0.275034	−	0.961435i	$-0.588689\pi$
$181$	−99.5623			−0.550068			−0.275034	+	0.961435i	$0.588689\pi$
$182$		0			0
$183$		−	29.6522i		−	0.162034i
$184$	−114.053	+	35.9678i	−0.619853	+	0.195477i
$185$	−18.8239	−	32.6040i	−0.101751	−	0.176238i
$186$	120.881	+	117.410i	0.649896	+	0.631237i
$187$	−62.7811	−	36.2467i	−0.335728	−	0.193832i
$188$	65.0445	+	105.444i	0.345981	+	0.560874i
$189$		0			0
$190$	−9.91096	−	34.9445i	−0.0521629	−	0.183918i
$191$	−50.4077	−	29.1029i	−0.263915	−	0.152371i	0.362204	−	0.932099i	$-0.382024\pi$
$191$	−50.4077	−	29.1029i	−0.263915	−	0.152371i	−0.626119	+	0.779727i	$0.715358\pi$
$192$	−166.869	−	238.256i	−0.869108	−	1.24092i
$193$	51.9407	+	89.9639i	0.269123	+	0.466134i	0.968636	−	0.248486i	$-0.0799329\pi$
$193$	51.9407	+	89.9639i	0.269123	+	0.466134i	−0.699513	+	0.714620i	$0.746600\pi$
$194$	−43.9205	+	174.011i	−0.226394	+	0.896966i
$195$			124.010i			0.635949i
$196$		0			0
$197$	−181.201			−0.919802			−0.459901	−	0.887970i	$-0.652115\pi$
$197$	−181.201			−0.919802			−0.459901	+	0.887970i	$0.652115\pi$
$198$	−346.022	−	87.3358i	−1.74758	−	0.441090i
$199$	188.723	−	108.960i	0.948359	−	0.547535i	0.0557882	−	0.998443i	$-0.482233\pi$
$199$	188.723	−	108.960i	0.948359	−	0.547535i	0.892571	+	0.450907i	$0.148899\pi$
$200$	−180.646	−	40.0376i	−0.903231	−	0.200188i
$201$	233.755	−	404.876i	1.16296	−	2.01431i
$202$	313.401	−	88.8870i	1.55149	−	0.440035i
$203$		0			0
$204$	45.2023	+	73.2779i	0.221580	+	0.359205i
$205$	7.59640	−	13.1574i	0.0370556	−	0.0641822i
$206$	−120.007	+	123.555i	−0.582560	+	0.599779i
$207$	150.911	−	87.1286i	0.729040	−	0.420911i
$208$	−175.389	−	266.622i	−0.843215	−	1.28183i
$209$	203.226			0.972375
$210$		0			0
$211$			107.401i			0.509007i	0.967072	+	0.254504i	$0.0819121\pi$
$211$			107.401i			0.509007i	−0.967072	+	0.254504i	$0.918088\pi$
$212$	−1.48941	−	51.1213i	−0.00702552	−	0.241138i
$213$	104.100	+	180.306i	0.488731	+	0.846507i
$214$	−142.337	+	146.544i	−0.665125	+	0.684785i
$215$	32.0154	+	18.4841i	0.148909	+	0.0859725i
$216$	71.2307	+	65.2635i	0.329772	+	0.302146i
$217$		0			0
$218$	−292.535	+	82.9689i	−1.34190	+	0.380591i
$219$	−275.918	−	159.301i	−1.25990	−	0.727404i
$220$	−39.7486	+	73.7250i	−0.180675	+	0.335114i
$221$	47.2310	+	81.8065i	0.213715	+	0.370165i
$222$	−242.564	−	61.2232i	−1.09263	−	0.275780i
$223$			349.685i			1.56809i	0.620702	+	0.784047i	$0.286848\pi$
$223$			349.685i			1.56809i	−0.620702	+	0.784047i	$0.713152\pi$
$224$		0			0
$225$	269.612			1.19827
$226$	−82.2826	+	326.001i	−0.364082	+	1.44248i
$227$	−15.8847	+	9.17103i	−0.0699766	+	0.0404010i	−0.534580	−	0.845118i	$-0.679530\pi$
$227$	−15.8847	+	9.17103i	−0.0699766	+	0.0404010i	0.464603	+	0.885519i	$0.346197\pi$
$228$	−212.455	−	114.544i	−0.931820	−	0.502387i
$229$	34.2722	−	59.3612i	0.149660	−	0.259219i	−0.781442	−	0.623978i	$-0.785515\pi$
$229$	34.2722	−	59.3612i	0.149660	−	0.259219i	0.931102	+	0.364759i	$0.118849\pi$
$230$	−11.1593	−	39.3460i	−0.0485188	−	0.171070i
$231$		0			0
$232$	−33.5484	+	36.6159i	−0.144605	+	0.157827i
$233$	−30.7394	+	53.2422i	−0.131929	+	0.228507i	−0.924420	−	0.381376i	$-0.875450\pi$
$233$	−30.7394	+	53.2422i	−0.131929	+	0.228507i	0.792491	+	0.609883i	$0.208784\pi$
$234$	333.574	+	323.997i	1.42553	+	1.38460i
$235$	−36.6928	+	21.1846i	−0.156140	+	0.0901473i
$236$	−115.267	+	3.35828i	−0.488419	+	0.0142300i
$237$	151.684			0.640019
$238$		0			0
$239$		−	204.645i		−	0.856256i	−0.903718	−	0.428128i	$-0.859173\pi$
$239$		−	204.645i		−	0.856256i	0.903718	−	0.428128i	$-0.140827\pi$
$240$	83.1072	−	54.6695i	0.346280	−	0.227789i
$241$	−194.633	−	337.114i	−0.807606	−	1.39881i	−0.914518	−	0.404546i	$-0.867430\pi$
$241$	−194.633	−	337.114i	−0.807606	−	1.39881i	0.106912	−	0.994268i	$-0.465904\pi$
$242$	−162.565	−	157.897i	−0.671755	−	0.652468i
$243$	291.035	+	168.029i	1.19768	+	0.691479i
$244$	−22.2107	+	13.7009i	−0.0910276	+	0.0561514i
$245$		0			0
$246$	−27.5469	−	97.1258i	−0.111979	−	0.394820i
$247$	−229.335	−	132.406i	−0.928480	−	0.536058i
$248$	32.0915	−	144.794i	0.129401	−	0.583849i
$249$	362.012	+	627.024i	1.45386	+	2.51817i
$250$	32.2240	−	127.670i	0.128896	−	0.510682i
$251$		−	115.082i		−	0.458494i	−0.973368	−	0.229247i	$-0.926374\pi$
$251$		−	115.082i		−	0.458494i	0.973368	−	0.229247i	$-0.0736264\pi$
$252$		0			0
$253$	228.824			0.904444
$254$	170.445	+	43.0204i	0.671044	+	0.169371i
$255$	−25.4995	+	14.7221i	−0.0999979	+	0.0577338i
$256$	−101.361	+	235.079i	−0.395941	+	0.918276i
$257$	168.616	−	292.052i	0.656094	−	1.13639i	−0.325524	−	0.945534i	$-0.605541\pi$
$257$	168.616	−	292.052i	0.656094	−	1.13639i	0.981618	−	0.190855i	$-0.0611260\pi$
$258$	236.333	−	67.0289i	0.916020	−	0.259802i
$259$		0			0
$260$	92.8886	−	57.2994i	0.357264	−	0.220382i
$261$	36.1811	−	62.6676i	0.138625	−	0.240106i
$262$	−195.282	+	201.054i	−0.745349	+	0.767381i
$263$	141.793	−	81.8644i	0.539138	−	0.311271i	−0.205592	−	0.978638i	$-0.565912\pi$
$263$	141.793	−	81.8644i	0.539138	−	0.311271i	0.744729	+	0.667367i	$0.232579\pi$
$264$	167.394	+	530.802i	0.634070	+	2.01062i
$265$	17.4901			0.0660004
$266$		0			0
$267$			227.439i			0.851832i
$268$	−411.276	+	11.9825i	−1.53461	+	0.0447107i
$269$	145.392	+	251.826i	0.540490	+	0.936156i	0.998876	+	0.0474028i	$0.0150944\pi$
$269$	145.392	+	251.826i	0.540490	+	0.936156i	−0.458386	+	0.888753i	$0.651572\pi$
$270$	−23.0191	+	23.6995i	−0.0852558	+	0.0877758i
$271$	319.241	+	184.314i	1.17801	+	0.680126i	0.955554	−	0.294817i	$-0.0952586\pi$
$271$	319.241	+	184.314i	1.17801	+	0.680126i	0.222458	+	0.974942i	$0.428592\pi$
$272$	34.0022	−	67.7167i	0.125008	−	0.248958i
$273$		0			0
$274$	−228.439	+	64.7899i	−0.833719	+	0.236460i
$275$	306.606	+	177.019i	1.11493	+	0.643705i
$276$	−239.215	−	128.972i	−0.866722	−	0.467290i
$277$	−127.213	−	220.339i	−0.459252	−	0.795447i	0.539670	−	0.841877i	$-0.318549\pi$
$277$	−127.213	−	220.339i	−0.459252	−	0.795447i	−0.998922	+	0.0464295i	$0.985216\pi$
$278$	−139.824	−	35.2916i	−0.502965	−	0.126948i
$279$			216.103i			0.774564i
$280$		0			0
$281$	146.631			0.521819			0.260909	−	0.965363i	$-0.415978\pi$
$281$	146.631			0.521819			0.260909	+	0.965363i	$0.415978\pi$
$282$	−68.9011	+	272.984i	−0.244330	+	0.968028i
$283$	−165.890	+	95.7768i	−0.586185	+	0.338434i	−0.763588	−	0.645704i	$-0.776564\pi$
$283$	−165.890	+	95.7768i	−0.586185	+	0.338434i	0.177403	+	0.984138i	$0.443231\pi$
$284$	86.9568	−	161.286i	0.306186	−	0.567909i
$285$	41.2717	−	71.4847i	0.144813	−	0.250823i
$286$	166.618	+	587.468i	0.582580	+	2.05408i
$287$		0			0
$288$	70.0762	−	366.382i	0.243320	−	1.27216i
$289$	133.286	−	230.858i	0.461196	−	0.798815i
$290$	−12.1826	−	11.8329i	−0.0420090	−	0.0408029i
$291$	−353.202	+	203.921i	−1.21375	+	0.700760i
$292$	8.16591	+	280.280i	0.0279655	+	0.959863i
$293$	−315.496			−1.07678			−0.538389	−	0.842696i	$-0.680967\pi$
$293$	−315.496			−1.07678			−0.538389	+	0.842696i	$0.680967\pi$
$294$		0			0
$295$		−	39.4362i		−	0.133682i
$296$	66.2192	+	209.979i	0.223713	+	0.709388i
$297$	−92.4254	−	160.086i	−0.311197	−	0.539008i
$298$	313.185	+	304.193i	1.05096	+	1.02078i
$299$	−258.221	−	149.084i	−0.863616	−	0.498609i
$300$	−220.756	−	357.869i	−0.735853	−	1.19290i
$301$		0			0
$302$	98.7454	+	348.161i	0.326972	+	1.15285i
$303$	641.114	+	370.148i	2.11589	+	1.22161i
$304$	12.3673	+	212.063i	0.0406821	+	0.697576i
$305$	−4.46232	−	7.72896i	−0.0146306	−	0.0253409i
$306$	−27.0206	+	107.055i	−0.0883027	+	0.349852i
$307$		−	452.508i		−	1.47397i	−0.675911	−	0.736983i	$-0.736250\pi$
$307$		−	452.508i		−	1.47397i	0.675911	−	0.736983i	$-0.263750\pi$
$308$		0			0
$309$	−391.421			−1.26673
$310$	49.1769	+	12.4122i	0.158635	+	0.0400395i
$311$	413.802	−	238.908i	1.33055	−	0.768194i	0.345167	−	0.938541i	$-0.387822\pi$
$311$	413.802	−	238.908i	1.33055	−	0.768194i	0.985384	+	0.170347i	$0.0544888\pi$
$312$	156.930	−	708.055i	0.502981	−	2.26941i
$313$	104.718	−	181.376i	0.334561	−	0.579477i	−0.648839	−	0.760925i	$-0.724745\pi$
$313$	104.718	−	181.376i	0.334561	−	0.579477i	0.983400	+	0.181449i	$0.0580787\pi$
$314$	−367.660	+	104.276i	−1.17089	+	0.332089i
$315$		0			0
$316$	−70.0865	−	113.618i	−0.221793	−	0.359550i
$317$	−0.874367	+	1.51445i	−0.00275825	+	0.00477744i	−0.867401	−	0.497609i	$-0.834211\pi$
$317$	−0.874367	+	1.51445i	−0.00275825	+	0.00477744i	0.864643	+	0.502387i	$0.167545\pi$
$318$	80.9760	−	83.3696i	0.254642	−	0.262169i
$319$	82.2913	−	47.5109i	0.257967	−	0.148937i
$320$	−79.3497	−	36.9904i	−0.247968	−	0.115595i
$321$	−464.251			−1.44627
$322$		0			0
$323$		−	62.8757i		−	0.194662i
$324$	−5.82770	−	200.025i	−0.0179867	−	0.617361i
$325$	−230.663	−	399.521i	−0.709734	−	1.22930i
$326$	400.961	−	412.813i	1.22994	−	1.26630i
$327$	−598.429	−	345.503i	−1.83006	−	1.05658i
$328$	−60.0230	+	65.5111i	−0.182997	+	0.199729i
$329$		0			0
$330$	−183.116	+	51.9355i	−0.554898	+	0.157380i
$331$	−324.802	−	187.524i	−0.981275	−	0.566539i	−0.0786198	−	0.996905i	$-0.525051\pi$
$331$	−324.802	−	187.524i	−0.981275	−	0.566539i	−0.902655	+	0.430366i	$0.858385\pi$
$332$	302.397	−	560.881i	0.910834	−	1.68940i
$333$	−160.410	−	277.838i	−0.481711	−	0.834347i
$334$	−242.125	−	61.1123i	−0.724924	−	0.182971i
$335$		−	140.710i		−	0.420029i
$336$		0			0
$337$	254.740			0.755906			0.377953	−	0.925825i	$-0.376628\pi$
$337$	254.740			0.755906			0.377953	+	0.925825i	$0.376628\pi$
$338$	112.008	−	443.772i	0.331385	−	1.31294i
$339$	−661.704	+	382.035i	−1.95193	+	1.12695i
$340$	22.8096	+	12.2977i	0.0670871	+	0.0361698i
$341$	−141.887	+	245.756i	−0.416091	+	0.720691i
$342$	−84.4570	−	297.782i	−0.246950	−	0.870707i
$343$		0			0
$344$	−159.406	−	146.052i	−0.463390	−	0.424570i
$345$	46.4702	−	80.4887i	0.134696	−	0.233301i
$346$	394.828	+	383.492i	1.14112	+	1.10836i
$347$	−442.904	+	255.711i	−1.27638	+	0.736919i	−0.976181	−	0.216957i	$-0.930387\pi$
$347$	−442.904	+	255.711i	−1.27638	+	0.736919i	−0.300200	+	0.953876i	$0.597053\pi$
$348$	−112.807	+	3.28661i	−0.324157	+	0.00944427i
$349$	383.129			1.09779			0.548895	−	0.835891i	$-0.315049\pi$
$349$	383.129			1.09779			0.548895	+	0.835891i	$0.315049\pi$
$350$		0			0
$351$			240.869i			0.686236i
$352$	320.247	−	370.645i	0.909794	−	1.05297i
$353$	108.692	+	188.260i	0.307909	+	0.533315i	0.977905	−	0.209050i	$-0.0670373\pi$
$353$	108.692	+	188.260i	0.307909	+	0.533315i	−0.669995	+	0.742365i	$0.733704\pi$
$354$	−187.980	−	182.583i	−0.531016	−	0.515770i
$355$	54.2679	+	31.3316i	0.152867	+	0.0882580i
$356$	170.361	−	105.089i	0.478543	−	0.295195i
$357$		0			0
$358$	−4.05183	−	14.2861i	−0.0113180	−	0.0399053i
$359$	−418.376	−	241.550i	−1.16539	−	0.672840i	−0.212803	−	0.977095i	$-0.568259\pi$
$359$	−418.376	−	241.550i	−1.16539	−	0.672840i	−0.952591	+	0.304255i	$0.901593\pi$
$360$	124.546	+	27.6038i	0.345961	+	0.0766772i
$361$	−92.3678	−	159.986i	−0.255867	−	0.443174i
$362$	−48.7308	+	193.070i	−0.134615	+	0.533342i
$363$		−	515.005i		−	1.41875i
$364$		0			0
$365$	−95.8921			−0.262718
$366$	−57.5012	−	14.5133i	−0.157107	−	0.0396538i
$367$	407.850	−	235.472i	1.11131	−	0.641614i	0.172140	−	0.985073i	$-0.444932\pi$
$367$	407.850	−	235.472i	1.11131	−	0.641614i	0.939168	+	0.343459i	$0.111599\pi$
$368$	13.9251	+	238.774i	0.0378400	+	0.648843i
$369$	64.7333	−	112.121i	0.175429	−	0.303852i
$370$	−72.4386	+	20.5451i	−0.195780	+	0.0555272i
$371$		0			0
$372$	286.845	−	176.944i	0.771089	−	0.475655i
$373$	89.7674	−	155.482i	0.240663	−	0.416841i	−0.720240	−	0.693725i	$-0.755968\pi$
$373$	89.7674	−	155.482i	0.240663	−	0.416841i	0.960903	+	0.276884i	$0.0893017\pi$
$374$	−101.017	+	104.003i	−0.270099	+	0.278083i
$375$	259.140	−	149.615i	0.691041	−	0.398973i
$376$	236.312	−	74.5236i	0.628490	−	0.198201i
$377$	−123.818			−0.328429
$378$		0			0
$379$			87.8468i			0.231786i	0.993262	+	0.115893i	$0.0369729\pi$
$379$			87.8468i			0.231786i	−0.993262	+	0.115893i	$0.963027\pi$
$380$	−72.6147	+	2.11562i	−0.191091	+	0.00556742i
$381$	199.742	+	345.963i	0.524257	+	0.908040i
$382$	−81.1080	+	83.5055i	−0.212325	+	0.218601i
$383$	566.021	+	326.792i	1.47786	+	0.853243i	0.999687	−	0.0250220i	$-0.00796558\pi$
$383$	566.021	+	326.792i	1.47786	+	0.853243i	0.478174	+	0.878265i	$0.341299\pi$
$384$	−543.696	+	206.975i	−1.41588	+	0.538998i
$385$		0			0
$386$	199.879	−	56.6898i	0.517822	−	0.146865i
$387$	272.822	+	157.514i	0.704966	+	0.407012i
$388$	315.944	+	170.340i	0.814287	+	0.439020i
$389$	84.4304	+	146.238i	0.217045	+	0.375933i	0.953903	−	0.300114i	$-0.0970249\pi$
$389$	84.4304	+	146.238i	0.217045	+	0.375933i	−0.736858	+	0.676047i	$0.763692\pi$
$390$	240.478	+	60.6967i	0.616611	+	0.155633i
$391$		−	70.7954i		−	0.181062i
$392$		0			0
$393$	−636.939			−1.62071
$394$	−88.6888	+	351.382i	−0.225099	+	0.891833i
$395$	39.5371	−	22.8267i	0.100094	−	0.0577892i
$396$	−338.721	+	628.254i	−0.855355	+	1.58650i
$397$	−345.761	+	598.875i	−0.870934	+	1.50850i	−0.00990149	+	0.999951i	$0.503152\pi$
$397$	−345.761	+	598.875i	−0.870934	+	1.50850i	−0.861032	+	0.508550i	$0.830182\pi$
$398$	−118.922	−	419.300i	−0.298799	−	1.05352i
$399$		0			0
$400$	−166.058	+	330.710i	−0.415144	+	0.826775i
$401$	199.917	−	346.266i	0.498546	−	0.863506i	−0.501453	−	0.865185i	$-0.667201\pi$
$401$	199.917	−	346.266i	0.498546	−	0.863506i	0.999999	+	0.00167866i	$0.000534334\pi$
$402$	−670.718	−	651.461i	−1.66845	−	1.62055i
$403$	320.230	−	184.885i	0.794616	−	0.458772i
$404$	−18.9740	−	651.249i	−0.0469655	−	1.61200i
$405$	68.4345			0.168974
$406$		0			0
$407$		−	421.281i		−	1.03509i
$408$	164.224	−	51.7897i	0.402509	−	0.126936i
$409$	55.5394	+	96.1970i	0.135793	+	0.235201i	0.925900	−	0.377768i	$-0.123308\pi$
$409$	55.5394	+	96.1970i	0.135793	+	0.235201i	−0.790107	+	0.612969i	$0.789975\pi$
$410$	−21.7965	−	21.1707i	−0.0531622	−	0.0516359i
$411$	−467.310	−	269.801i	−1.13701	−	0.656451i
$412$	180.858	+	293.190i	0.438975	+	0.711626i
$413$		0			0
$414$	−95.0951	−	335.290i	−0.229698	−	0.809879i
$415$	188.720	+	108.957i	0.454746	+	0.262548i
$416$	−602.873	+	209.613i	−1.44921	+	0.503878i
$417$	−163.858	−	283.810i	−0.392944	−	0.680599i
$418$	99.4691	−	394.093i	0.237964	−	0.942807i
$419$			641.986i			1.53219i	0.642729	+	0.766094i	$0.277802\pi$
$419$			641.986i			1.53219i	−0.642729	+	0.766094i	$0.722198\pi$
$420$		0			0
$421$	151.970			0.360975			0.180487	−	0.983577i	$-0.442233\pi$
$421$	151.970			0.360975			0.180487	+	0.983577i	$0.442233\pi$
$422$	208.270	+	52.5672i	0.493530	+	0.124567i
$423$	−312.681	+	180.526i	−0.739198	+	0.426776i
$424$	−99.8626	−	22.1331i	−0.235525	−	0.0522006i
$425$	54.7674	−	94.8600i	0.128865	−	0.223200i
$426$	400.598	−	113.618i	0.940372	−	0.266709i
$427$		0			0
$428$	214.509	+	347.743i	0.501190	+	0.812484i
$429$	−693.838	+	1201.76i	−1.61734	+	2.80131i
$430$	51.5140	−	53.0367i	0.119800	−	0.123341i
$431$	398.245	−	229.927i	0.924002	−	0.533473i	0.0390927	−	0.999236i	$-0.487553\pi$
$431$	398.245	−	229.927i	0.924002	−	0.533473i	0.884910	+	0.465763i	$0.154220\pi$
$432$	161.422	−	106.186i	0.373662	−	0.245802i
$433$	−534.370			−1.23411			−0.617056	−	0.786919i	$-0.711675\pi$
$433$	−534.370			−1.23411			−0.617056	+	0.786919i	$0.711675\pi$
$434$		0			0
$435$		−	38.5945i		−	0.0887231i
$436$	17.7107	+	607.888i	0.0406210	+	1.39424i
$437$	99.2331	+	171.877i	0.227078	+	0.393311i
$438$	−443.963	+	457.086i	−1.01361	+	1.04358i
$439$	174.295	+	100.629i	0.397028	+	0.229224i	0.685201	−	0.728354i	$-0.259714\pi$
$439$	174.295	+	100.629i	0.397028	+	0.229224i	−0.288173	+	0.957578i	$0.593048\pi$
$440$	123.512	+	113.165i	0.280708	+	0.257192i
$441$		0			0
$442$	181.755	−	51.5495i	0.411211	−	0.116628i
$443$	−63.6467	−	36.7464i	−0.143672	−	0.0829490i	0.426441	−	0.904515i	$-0.359767\pi$
$443$	−63.6467	−	36.7464i	−0.143672	−	0.0829490i	−0.570113	+	0.821566i	$0.693101\pi$
$444$	−237.446	+	440.411i	−0.534789	+	0.991917i
$445$	34.2270	+	59.2828i	0.0769145	+	0.133220i
$446$	678.104	+	171.153i	1.52041	+	0.383752i
$447$			992.169i			2.21962i
$448$		0			0
$449$	−41.4382			−0.0922899			−0.0461450	−	0.998935i	$-0.514694\pi$
$449$	−41.4382			−0.0922899			−0.0461450	+	0.998935i	$0.514694\pi$
$450$	131.961	−	522.827i	0.293248	−	1.16184i
$451$	147.231	−	85.0040i	0.326455	−	0.188479i
$452$	591.903	+	319.122i	1.30952	+	0.706023i
$453$	−411.200	+	712.220i	−0.907727	+	1.57223i
$454$	10.0096	+	35.2921i	0.0220475	+	0.0777359i
$455$		0			0
$456$	−326.109	+	355.926i	−0.715150	+	0.780539i
$457$	−135.103	+	234.004i	−0.295629	+	0.512045i	−0.975131	−	0.221629i	$-0.928863\pi$
$457$	−135.103	+	234.004i	−0.295629	+	0.512045i	0.679502	+	0.733674i	$0.262196\pi$
$458$	−98.3378	−	95.5144i	−0.214711	−	0.208547i
$459$	−49.5285	+	28.5953i	−0.107905	+	0.0622991i
$460$	−81.7611	+	2.38210i	−0.177742	+	0.00517847i
$461$	735.133			1.59465			0.797324	−	0.603552i	$-0.206248\pi$
$461$	735.133			1.59465			0.797324	+	0.603552i	$0.206248\pi$
$462$		0			0
$463$		−	742.356i		−	1.60336i	−0.597753	−	0.801681i	$-0.703940\pi$
$463$		−	742.356i		−	1.60336i	0.597753	−	0.801681i	$-0.296060\pi$
$464$	54.5846	+	82.9783i	0.117639	+	0.178832i
$465$	57.6295	+	99.8173i	0.123934	+	0.214661i
$466$	88.2011	+	85.6688i	0.189273	+	0.183839i
$467$	348.274	+	201.076i	0.745769	+	0.430570i	0.824163	−	0.566352i	$-0.191646\pi$
$467$	348.274	+	201.076i	0.745769	+	0.430570i	−0.0783941	+	0.996922i	$0.524979\pi$
$468$	791.557	−	488.281i	1.69136	−	1.04334i
$469$		0			0
$470$	23.1216	+	81.5230i	0.0491949	+	0.173453i
$471$	−752.110	−	434.231i	−1.59684	−	0.921934i
$472$	−49.9051	+	225.168i	−0.105731	+	0.477050i
$473$	206.838	+	358.253i	0.437289	+	0.757406i
$474$	74.2420	−	294.144i	0.156629	−	0.620557i
$475$			307.068i			0.646459i
$476$		0			0
$477$	149.043			0.312460
$478$	−396.845	−	100.164i	−0.830220	−	0.209547i
$479$	−308.947	+	178.371i	−0.644984	+	0.372381i	−0.786532	−	0.617550i	$-0.788125\pi$
$479$	−308.947	+	178.371i	−0.644984	+	0.372381i	0.141548	+	0.989931i	$0.454792\pi$
$480$	−65.3374	−	187.918i	−0.136120	−	0.391496i
$481$	−274.474	+	475.402i	−0.570631	+	0.988362i
$482$	−748.990	+	212.429i	−1.55392	+	0.440724i
$483$		0			0
$484$	−385.759	+	237.960i	−0.797024	+	0.491653i
$485$	−61.3755	+	106.305i	−0.126547	+	0.219187i
$486$	468.287	−	482.130i	0.963554	−	0.992036i
$487$	104.896	−	60.5616i	0.215392	−	0.124356i	−0.388423	−	0.921481i	$-0.626980\pi$
$487$	104.896	−	60.5616i	0.215392	−	0.124356i	0.603815	+	0.797125i	$0.293647\pi$
$488$	15.6976	+	49.7767i	0.0321673	+	0.102001i
$489$	1307.79			2.67442
$490$		0			0
$491$			18.4535i			0.0375835i	0.999823	+	0.0187917i	$0.00598195\pi$
$491$			18.4535i			0.0375835i	−0.999823	+	0.0187917i	$0.994018\pi$
$492$	−201.828	+	5.88022i	−0.410219	+	0.0119517i
$493$	−14.6993	−	25.4599i	−0.0298160	−	0.0516428i
$494$	−369.008	+	379.916i	−0.746981	+	0.769061i
$495$	−211.388	−	122.045i	−0.427047	−	0.246556i
$496$	−265.076	−	133.101i	−0.534427	−	0.268349i
$497$		0			0
$498$	1393.10	−	395.112i	2.79739	−	0.793398i
$499$	129.533	+	74.7857i	0.259585	+	0.149871i	0.624145	−	0.781308i	$-0.285447\pi$
$499$	129.533	+	74.7857i	0.259585	+	0.149871i	−0.364560	+	0.931180i	$0.618781\pi$
$500$	−231.805	−	124.977i	−0.463609	−	0.249953i
$501$	−283.742	−	491.455i	−0.566351	−	0.980949i
$502$	−223.166	−	56.3269i	−0.444553	−	0.112205i
$503$		−	651.239i		−	1.29471i	−0.762189	−	0.647354i	$-0.775875\pi$
$503$		−	651.239i		−	1.29471i	0.762189	−	0.647354i	$-0.224125\pi$
$504$		0			0
$505$	222.812			0.441211
$506$	111.998	−	443.733i	0.221340	−	0.876942i
$507$	900.752	−	520.049i	1.77663	−	1.02574i
$508$	166.849	−	309.469i	0.328443	−	0.609190i
$509$	408.986	−	708.385i	0.803509	−	1.39172i	−0.113784	−	0.993506i	$-0.536297\pi$
$509$	408.986	−	708.385i	0.803509	−	1.39172i	0.917293	−	0.398213i	$-0.130369\pi$
$510$	16.0682	+	56.6539i	0.0315063	+	0.111086i
$511$		0			0
$512$	406.250	+	311.617i	0.793457	+	0.608627i
$513$	80.1634	−	138.847i	0.156264	−	0.270657i
$514$	−483.813	−	469.923i	−0.941271	−	0.914247i
$515$	−102.025	+	58.9043i	−0.198107	+	0.114377i
$516$	−14.3082	−	491.101i	−0.0277290	−	0.951747i
$517$	−474.113			−0.917046
$518$		0			0
$519$			1250.82i			2.41005i
$520$	−65.6498	−	208.173i	−0.126250	−	0.400333i
$521$	−86.8015	−	150.345i	−0.166606	−	0.288569i	0.770619	−	0.637297i	$-0.219947\pi$
$521$	−86.8015	−	150.345i	−0.166606	−	0.288569i	−0.937224	+	0.348727i	$0.886614\pi$
$522$	−103.815	−	100.835i	−0.198880	−	0.193170i
$523$	−589.442	−	340.315i	−1.12704	−	0.650697i	−0.183852	−	0.982954i	$-0.558857\pi$
$523$	−589.442	−	340.315i	−1.12704	−	0.650697i	−0.943189	+	0.332256i	$0.892190\pi$
$524$	294.300	+	477.093i	0.561642	+	0.910483i
$525$		0			0
$526$	−89.3494	−	315.032i	−0.169866	−	0.598920i
$527$	76.0337	+	43.8981i	0.144276	+	0.0832980i
$528$	1111.26	−	64.8075i	2.10465	−	0.122742i
$529$	−152.768	−	264.601i	−0.288786	−	0.500192i
$530$	8.56053	−	33.9165i	0.0161519	−	0.0639935i
$531$		−	336.059i		−	0.632879i
$532$		0			0
$533$	−221.528			−0.415624
$534$	441.047	+	111.320i	0.825930	+	0.208465i
$535$	−121.009	+	69.8644i	−0.226185	+	0.130588i
$536$	−178.063	+	803.405i	−0.332207	+	1.49889i
$537$	16.8728	−	29.2246i	0.0314205	−	0.0544219i
$538$	559.499	−	158.685i	1.03996	−	0.294954i
$539$		0			0
$540$	34.6910	+	56.2379i	0.0642426	+	0.104144i
$541$	156.595	−	271.230i	0.289454	−	0.501350i	−0.684225	−	0.729271i	$-0.739859\pi$
$541$	156.595	−	271.230i	0.289454	−	0.501350i	0.973680	+	0.227921i	$0.0731928\pi$
$542$	513.672	−	528.855i	0.947734	−	0.975748i
$543$	−391.885	+	226.255i	−0.721704	+	0.416676i
$544$	−114.673	−	99.0805i	−0.210796	−	0.182133i
$545$	−207.977			−0.381609
$546$		0			0
$547$			352.784i			0.644944i	0.946579	+	0.322472i	$0.104514\pi$
$547$			352.784i			0.644944i	−0.946579	+	0.322472i	$0.895486\pi$
$548$	13.8302	+	474.697i	0.0252376	+	0.866235i
$549$	−38.0260	−	65.8630i	−0.0692641	−	0.119969i
$550$	493.341	−	507.923i	0.896983	−	0.923497i
$551$	71.3738	+	41.2077i	0.129535	+	0.0747871i
$552$	−367.185	+	400.757i	−0.665190	+	0.726010i
$553$		0			0
$554$	−489.542	+	138.844i	−0.883650	+	0.250621i
$555$	−148.185	−	85.5547i	−0.267000	−	0.154153i
$556$	−136.874	+	253.872i	−0.246176	+	0.456604i
$557$	67.9624	+	117.714i	0.122015	+	0.211336i	0.920562	−	0.390596i	$-0.127731\pi$
$557$	67.9624	+	117.714i	0.122015	+	0.211336i	−0.798547	+	0.601932i	$0.794398\pi$
$558$	419.064	+	105.772i	0.751011	+	0.189555i
$559$		−	539.037i		−	0.964288i
$560$		0			0
$561$	−329.482			−0.587312
$562$	71.7686	−	284.345i	0.127702	−	0.505952i
$563$	−138.878	+	80.1815i	−0.246676	+	0.142418i	−0.618241	−	0.785989i	$-0.712154\pi$
$563$	−138.878	+	80.1815i	−0.246676	+	0.142418i	0.371565	+	0.928407i	$0.378821\pi$
$564$	495.643	+	267.224i	0.878799	+	0.473801i
$565$	−114.984	+	199.158i	−0.203511	+	0.352491i
$566$	104.534	+	368.570i	0.184689	+	0.651184i
$567$		0			0
$568$	−270.203	−	247.567i	−0.475709	−	0.435857i
$569$	−305.648	+	529.399i	−0.537168	+	0.930402i	0.461887	+	0.886939i	$0.347172\pi$
$569$	−305.648	+	529.399i	−0.537168	+	0.930402i	−0.999055	+	0.0434633i	$0.986161\pi$
$570$	−118.422	−	115.022i	−0.207757	−	0.201792i
$571$	−248.507	+	143.476i	−0.435214	+	0.251271i	−0.701566	−	0.712605i	$-0.747515\pi$
$571$	−248.507	+	143.476i	−0.435214	+	0.251271i	0.266351	+	0.963876i	$0.414182\pi$
$572$	1220.76	−	35.5666i	2.13420	−	0.0621795i
$573$	−264.545			−0.461685
$574$		0			0
$575$			345.746i			0.601297i
$576$	−676.184	−	315.217i	−1.17393	−	0.547251i
$577$	−265.214	−	459.364i	−0.459643	−	0.796125i	0.539299	−	0.842114i	$-0.318689\pi$
$577$	−265.214	−	459.364i	−0.459643	−	0.796125i	−0.998942	+	0.0459893i	$0.985356\pi$
$578$	−382.439	−	371.459i	−0.661659	−	0.642663i
$579$	408.886	+	236.070i	0.706193	+	0.407721i
$580$	−28.9089	+	17.8328i	−0.0498429	+	0.0307462i
$581$		0			0
$582$	222.566	+	784.733i	0.382416	+	1.34834i
$583$	169.494	+	97.8573i	0.290727	+	0.167851i
$584$	547.511	+	121.348i	0.937520	+	0.207787i
$585$	159.030	+	275.449i	0.271847	+	0.470852i
$586$	−154.420	+	611.805i	−0.263515	+	1.04404i
$587$			10.9359i			0.0186301i	0.999957	+	0.00931506i	$0.00296512\pi$
$587$			10.9359i			0.0186301i	−0.999957	+	0.00931506i	$0.997035\pi$
$588$		0			0
$589$	−246.126			−0.417871
$590$	−76.4741	−	19.3021i	−0.129617	−	0.0327154i
$591$	−713.222	+	411.779i	−1.20681	+	0.696749i
$592$	439.599	−	25.6371i	0.742566	−	0.0433058i
$593$	59.7297	−	103.455i	0.100725	−	0.174460i	−0.811259	−	0.584687i	$-0.801217\pi$
$593$	59.7297	−	103.455i	0.100725	−	0.174460i	0.911983	+	0.410227i	$0.134551\pi$
$594$	−355.673	+	100.876i	−0.598776	+	0.169825i
$595$		0			0
$596$	743.175	−	458.436i	1.24694	−	0.769188i
$597$	495.221	−	857.747i	0.829515	−	1.43676i
$598$	−415.488	+	427.769i	−0.694796	+	0.715334i
$599$	−883.647	+	510.174i	−1.47520	+	0.851710i	−0.999609	−	0.0279546i	$-0.991101\pi$
$599$	−883.647	+	510.174i	−1.47520	+	0.851710i	−0.475595	+	0.879664i	$0.657767\pi$
$600$	−802.024	+	252.927i	−1.33671	+	0.421545i
$601$	109.785			0.182671			0.0913356	−	0.995820i	$-0.470886\pi$
$601$	109.785			0.182671			0.0913356	+	0.995820i	$0.470886\pi$
$602$		0			0
$603$		−	1199.07i		−	1.98851i
$604$	723.479	−	21.0784i	1.19781	−	0.0348981i
$605$	−77.5022	−	134.238i	−0.128103	−	0.221881i
$606$	1031.58	−	1062.07i	1.70227	−	1.75259i
$607$	−562.533	−	324.779i	−0.926743	−	0.535055i	−0.0409629	−	0.999161i	$-0.513043\pi$
$607$	−562.533	−	324.779i	−0.926743	−	0.535055i	−0.885780	+	0.464105i	$0.846376\pi$
$608$	417.283	+	79.8117i	0.686320	+	0.131269i
$609$		0			0
$610$	−17.1720	+	4.87032i	−0.0281508	+	0.00798413i
$611$	535.022	+	308.895i	0.875650	+	0.505557i
$612$	194.374	+	104.796i	0.317604	+	0.171235i
$613$	−401.074	−	694.681i	−0.654281	−	1.13325i	−0.982074	−	0.188498i	$-0.939638\pi$
$613$	−401.074	−	694.681i	−0.654281	−	1.13325i	0.327793	−	0.944750i	$-0.393695\pi$
$614$	−877.496	−	221.480i	−1.42915	−	0.360716i
$615$		−	69.0513i		−	0.112278i
$616$		0			0
$617$	1151.11			1.86565			0.932825	−	0.360329i	$-0.117336\pi$
$617$	1151.11			1.86565			0.932825	+	0.360329i	$0.117336\pi$
$618$	−191.581	+	759.037i	−0.310001	+	1.22822i
$619$	−193.842	+	111.914i	−0.313153	+	0.180799i	−0.648336	−	0.761354i	$-0.724535\pi$
$619$	−193.842	+	111.914i	−0.313153	+	0.180799i	0.335184	+	0.942153i	$0.391202\pi$
$620$	48.1392	−	89.2879i	0.0776439	−	0.144013i
$621$	90.2606	−	156.336i	0.145347	−	0.251749i
$622$	−260.752	−	919.371i	−0.419216	−	1.47809i
$623$		0			0
$624$	−1296.24	−	650.874i	−2.07731	−	1.04307i
$625$	−244.079	+	422.757i	−0.390526	+	0.676411i
$626$	−300.468	−	291.841i	−0.479981	−	0.466200i
$627$	799.915	−	461.831i	1.27578	−	0.736573i
$628$	22.2590	+	763.999i	0.0354443	+	1.21656i
$629$	−130.339			−0.207216
$630$		0			0
$631$		−	385.557i		−	0.611026i	−0.952188	−	0.305513i	$-0.901172\pi$
$631$		−	385.557i		−	0.611026i	0.952188	−	0.305513i	$-0.0988279\pi$
$632$	−254.630	+	80.3003i	−0.402895	+	0.127058i
$633$	244.068	+	422.737i	0.385573	+	0.667832i
$634$	2.50883	+	2.43680i	0.00395715	+	0.00384354i
$635$	104.127	+	60.1177i	0.163979	+	0.0946735i
$636$	−122.035	−	197.833i	−0.191880	−	0.311058i
$637$		0			0
$638$	−51.8550	−	182.832i	−0.0812774	−	0.286571i
$639$	462.448	+	266.995i	0.723706	+	0.417832i
$640$	−110.569	+	135.769i	−0.172764	+	0.212139i
$641$	144.930	+	251.027i	0.226100	+	0.391617i	0.956649	−	0.291243i	$-0.0940689\pi$
$641$	144.930	+	251.027i	0.226100	+	0.391617i	−0.730549	+	0.682861i	$0.760736\pi$
$642$	−227.228	+	900.269i	−0.353937	+	1.40229i
$643$			525.629i			0.817463i	0.912655	+	0.408731i	$0.134029\pi$
$643$			525.629i			0.817463i	−0.912655	+	0.408731i	$0.865971\pi$
$644$		0			0
$645$	168.020			0.260497
$646$	−121.928	−	30.7745i	−0.188742	−	0.0476385i
$647$	82.7956	−	47.8021i	0.127969	−	0.0738827i	−0.434649	−	0.900600i	$-0.643128\pi$
$647$	82.7956	−	47.8021i	0.127969	−	0.0738827i	0.562618	+	0.826717i	$0.309794\pi$
$648$	−390.738	−	86.6013i	−0.602991	−	0.133644i
$649$	220.646	−	382.170i	0.339979	−	0.588860i
$650$	−887.643	+	251.754i	−1.36560	+	0.387313i
$651$		0			0
$652$	−604.271	−	979.589i	−0.926796	−	1.50244i
$653$	313.754	−	543.438i	0.480481	−	0.832217i	−0.519268	−	0.854611i	$-0.673796\pi$
$653$	313.754	−	543.438i	0.480481	−	0.832217i	0.999749	+	0.0223940i	$0.00712884\pi$
$654$	−962.895	+	991.357i	−1.47232	+	1.51584i
$655$	−166.020	+	95.8518i	−0.253466	+	0.146339i
$656$	97.6599	+	148.460i	0.148872	+	0.226311i
$657$	−817.152			−1.24376
$658$		0			0
$659$			220.070i			0.333945i	0.985962	+	0.166972i	$0.0533991\pi$
$659$			220.070i			0.333945i	−0.985962	+	0.166972i	$0.946601\pi$
$660$	11.0863	+	380.516i	0.0167974	+	0.576540i
$661$	371.855	+	644.071i	0.562564	+	0.974389i	0.997272	+	0.0738178i	$0.0235183\pi$
$661$	371.855	+	644.071i	0.562564	+	0.974389i	−0.434708	+	0.900572i	$0.643148\pi$
$662$	−522.619	+	538.067i	−0.789455	+	0.812790i
$663$	371.810	+	214.665i	0.560800	+	0.323778i
$664$	−939.644	−	860.927i	−1.41513	−	1.29658i
$665$		0			0
$666$	−617.291	+	175.076i	−0.926863	+	0.262877i
$667$	80.3639	+	46.3981i	0.120486	+	0.0695624i
$668$	−237.016	+	439.613i	−0.354814	+	0.658104i
$669$	794.658	+	1376.39i	1.18783	+	2.05738i
$670$	−272.862	−	68.8704i	−0.407257	−	0.102792i
$671$		−	99.8669i		−	0.148833i
$672$		0			0
$673$	−1017.05			−1.51122			−0.755610	−	0.655022i	$-0.772659\pi$
$673$	−1017.05			−1.51122			−0.755610	+	0.655022i	$0.772659\pi$
$674$	124.683	−	493.989i	0.184989	−	0.732921i
$675$	241.884	−	139.652i	0.358346	−	0.206891i
$676$	−805.734	−	434.409i	−1.19191	−	0.642616i
$677$	430.952	−	746.432i	0.636562	−	1.10256i	−0.349620	−	0.936892i	$-0.613689\pi$
$677$	430.952	−	746.432i	0.636562	−	1.10256i	0.986182	−	0.165666i	$-0.0529774\pi$
$678$	416.966	+	1470.15i	0.614993	+	2.16837i
$679$		0			0
$680$	35.0117	−	38.2129i	0.0514878	−	0.0561955i
$681$	−41.6823	+	72.1958i	−0.0612075	+	0.106014i
$682$	407.119	+	395.430i	0.596948	+	0.579810i
$683$	550.611	−	317.895i	0.806165	−	0.465440i	−0.0394574	−	0.999221i	$-0.512563\pi$
$683$	550.611	−	317.895i	0.806165	−	0.465440i	0.845622	+	0.533782i	$0.179230\pi$
$684$	−618.792	+	18.0284i	−0.904666	+	0.0263573i
$685$	−162.408			−0.237092
$686$		0			0
$687$		−	311.534i		−	0.453470i
$688$	−361.244	+	237.633i	−0.525063	+	0.345397i
$689$	−127.512	−	220.858i	−0.185069	−	0.320549i
$690$	−133.338	−	129.510i	−0.193243	−	0.187695i
$691$	186.005	+	107.390i	0.269182	+	0.155412i	0.628516	−	0.777797i	$-0.283663\pi$
$691$	186.005	+	107.390i	0.269182	+	0.155412i	−0.359334	+	0.933209i	$0.616996\pi$
$692$	936.911	−	577.944i	1.35392	−	0.835180i
$693$		0			0
$694$	279.091	+	984.031i	0.402149	+	1.41791i
$695$	−85.4202	−	49.3174i	−0.122907	−	0.0709602i
$696$	−48.8399	+	220.362i	−0.0701723	+	0.316612i
$697$	−26.2992	−	45.5515i	−0.0377319	−	0.0653536i
$698$	187.522	−	742.957i	0.268657	−	1.06441i
$699$			279.421i			0.399744i
$700$		0			0
$701$	−271.746			−0.387655			−0.193828	−	0.981036i	$-0.562090\pi$
$701$	−271.746			−0.387655			−0.193828	+	0.981036i	$0.562090\pi$
$702$	467.089	+	117.893i	0.665369	+	0.167939i
$703$	316.437	−	182.695i	0.450123	−	0.259879i
$704$	−562.004	−	802.431i	−0.798301	−	1.13982i
$705$	−96.2840	+	166.769i	−0.136573	+	0.236552i
$706$	418.271	−	118.630i	0.592451	−	0.168031i
$707$		0			0
$708$	−446.068	+	275.162i	−0.630040	+	0.388647i
$709$	308.447	−	534.246i	0.435045	−	0.753520i	−0.562254	−	0.826964i	$-0.690066\pi$
$709$	308.447	−	534.246i	0.435045	−	0.753520i	0.997299	+	0.0734445i	$0.0233992\pi$
$710$	87.3192	−	89.9003i	0.122985	−	0.126620i
$711$	336.918	−	194.520i	0.473865	−	0.273586i
$712$	−120.404	−	381.798i	−0.169107	−	0.536233i
$713$	−277.127			−0.388678
$714$		0			0
$715$			417.658i			0.584137i
$716$	−29.6865	+	0.864913i	−0.0414617	+	0.00120798i
$717$	−465.056	−	805.500i	−0.648613	−	1.12343i
$718$	−673.184	+	693.083i	−0.937582	+	0.965296i
$719$	−47.9283	−	27.6714i	−0.0666596	−	0.0384859i	0.466300	−	0.884627i	$-0.345587\pi$
$719$	−47.9283	−	27.6714i	−0.0666596	−	0.0384859i	−0.532959	+	0.846141i	$0.678920\pi$
$720$	114.488	−	228.007i	0.159011	−	0.316677i
$721$		0			0
$722$	−355.451	+	100.813i	−0.492315	+	0.139631i
$723$	−1532.18	−	884.606i	−2.11920	−	1.22352i
$724$	350.547	+	188.996i	0.484180	+	0.261044i
$725$	71.7873	+	124.339i	0.0990170	+	0.171503i
$726$	−998.689	−	252.069i	−1.37560	−	0.347202i
$727$		−	1046.07i		−	1.43888i	−0.694554	−	0.719440i	$-0.744398\pi$
$727$		−	1046.07i		−	1.43888i	0.694554	−	0.719440i	$-0.255602\pi$
$728$		0			0
$729$	1077.14			1.47756
$730$	−46.9344	+	185.953i	−0.0642937	+	0.254729i
$731$	110.839	−	63.9929i	0.151627	−	0.0875417i
$732$	−56.2879	+	104.402i	−0.0768961	+	0.142626i
$733$	425.664	−	737.272i	0.580715	−	1.00583i	−0.414680	−	0.909967i	$-0.636106\pi$
$733$	425.664	−	737.272i	0.580715	−	1.00583i	0.995395	−	0.0958604i	$-0.0305603\pi$
$734$	−257.002	−	906.148i	−0.350139	−	1.23453i
$735$		0			0
$736$	469.843	+	89.8646i	0.638373	+	0.122099i
$737$	787.273	−	1363.60i	1.06821	−	1.85020i
$738$	−185.740	−	180.408i	−0.251681	−	0.244455i
$739$	683.801	−	394.793i	0.925306	−	0.534226i	0.0399819	−	0.999200i	$-0.487270\pi$
$739$	683.801	−	394.793i	0.925306	−	0.534226i	0.885324	+	0.464975i	$0.153937\pi$
$740$	4.38560	+	150.528i	0.00592648	+	0.203416i
$741$	−1203.57			−1.62426
$742$		0			0
$743$			892.788i			1.20160i	0.799400	+	0.600799i	$0.205151\pi$
$743$			892.788i			1.20160i	−0.799400	+	0.600799i	$0.794849\pi$
$744$	−202.730	−	642.851i	−0.272487	−	0.864047i
$745$	149.310	+	258.612i	0.200416	+	0.347131i
$746$	−257.571	−	250.176i	−0.345270	−	0.335357i
$747$	1608.19	+	928.488i	2.15286	+	1.24296i
$748$	152.239	+	246.795i	0.203527	+	0.329940i
$749$		0			0
$750$	−163.294	−	575.750i	−0.217726	−	0.767667i
$751$	351.789	+	203.106i	0.468428	+	0.270447i	0.715581	−	0.698529i	$-0.246162\pi$
$751$	351.789	+	203.106i	0.468428	+	0.270447i	−0.247153	+	0.968976i	$0.579495\pi$
$752$	−28.8522	−	494.728i	−0.0383672	−	0.657884i
$753$	−261.524	−	452.973i	−0.347309	−	0.601557i
$754$	−60.6026	+	240.105i	−0.0803747	+	0.318442i
$755$			247.524i			0.327846i
$756$		0			0
$757$	89.9062			0.118766			0.0593832	−	0.998235i	$-0.481087\pi$
$757$	89.9062			0.118766			0.0593832	+	0.998235i	$0.481087\pi$
$758$	170.351	+	42.9966i	0.224738	+	0.0567237i
$759$	900.671	−	520.003i	1.18666	−	0.685116i
$760$	−31.4387	+	141.849i	−0.0413667	+	0.186643i
$761$	−130.875	+	226.683i	−0.171978	+	0.297875i	−0.939111	−	0.343613i	$-0.888349\pi$
$761$	−130.875	+	226.683i	−0.171978	+	0.297875i	0.767133	+	0.641488i	$0.221683\pi$
$762$	768.650	−	218.005i	1.00873	−	0.286096i
$763$		0			0
$764$	122.234	+	198.155i	0.159992	+	0.259365i
$765$	−37.7593	+	65.4009i	−0.0493585	+	0.0854914i
$766$	910.749	−	937.670i	1.18897	−	1.22411i
$767$	−497.985	+	287.512i	−0.649263	+	0.374852i
$768$	135.251	+	1155.63i	0.176108	+	1.50473i
$769$	753.905			0.980370			0.490185	−	0.871618i	$-0.336929\pi$
$769$	753.905			0.980370			0.490185	+	0.871618i	$0.336929\pi$
$770$		0			0
$771$		−	1532.72i		−	1.98796i
$772$	−12.1011	−	415.349i	−0.0156751	−	0.538017i
$773$	−231.765	−	401.428i	−0.299825	−	0.519312i	0.676271	−	0.736653i	$-0.263595\pi$
$773$	−231.765	−	401.428i	−0.299825	−	0.519312i	−0.976096	+	0.217341i	$0.930262\pi$
$774$	438.981	−	451.957i	0.567159	−	0.583923i
$775$	−371.328	−	214.386i	−0.479133	−	0.276627i
$776$	484.959	−	529.300i	0.624947	−	0.682088i
$777$		0			0
$778$	324.907	−	92.1501i	0.417618	−	0.118445i
$779$	127.698	+	73.7265i	0.163926	+	0.0946425i
$780$	235.404	−	436.624i	0.301800	−	0.559775i
$781$	350.601	+	607.259i	0.448913	+	0.777541i
$782$	−137.285	−	34.6508i	−0.175557	−	0.0443105i
$783$		−	74.9634i		−	0.0957388i
$784$		0			0
$785$	−261.387			−0.332977
$786$	−311.750	+	1235.14i	−0.396628	+	1.57143i
$787$	−535.915	+	309.411i	−0.680959	+	0.393152i	−0.800216	−	0.599711i	$-0.795282\pi$
$787$	−535.915	+	309.411i	−0.680959	+	0.393152i	0.119257	+	0.992863i	$0.461949\pi$
$788$	637.986	+	343.968i	0.809628	+	0.436508i
$789$	372.073	−	644.450i	0.471576	−	0.816793i
$790$	−24.9139	−	87.8423i	−0.0315365	−	0.111193i
$791$		0			0
$792$	1052.51	+	964.341i	1.32893	+	1.21760i
$793$	−65.0655	+	112.697i	−0.0820498	+	0.142114i
$794$	992.097	+	963.613i	1.24949	+	1.21362i
$795$	68.8425	−	39.7462i	0.0865943	−	0.0499952i
$796$	−871.307	+	25.3854i	−1.09461	+	0.0318912i
$797$	441.998			0.554577			0.277289	−	0.960787i	$-0.410564\pi$
$797$	441.998			0.554577			0.277289	+	0.960787i	$0.410564\pi$
$798$		0			0
$799$			146.685i			0.183585i
$800$	560.031	+	483.883i	0.700039	+	0.604853i
$801$	291.668	+	505.183i	0.364129	+	0.630691i
$802$	−573.625	−	557.155i	−0.715243	−	0.694708i
$803$	−929.276	−	536.518i	−1.15725	−	0.668141i
$804$	−1591.59	+	981.788i	−1.97958	+	1.22113i
$805$		0			0
$806$	−201.790	−	711.478i	−0.250359	−	0.882727i
$807$	1144.55	+	660.805i	1.41828	+	0.818842i
$808$	−1272.18	−	281.960i	−1.57448	−	0.348960i
$809$	−155.723	−	269.721i	−0.192489	−	0.333400i	0.753586	−	0.657350i	$-0.228323\pi$
$809$	−155.723	−	269.721i	−0.192489	−	0.333400i	−0.946074	+	0.323949i	$0.894989\pi$
$810$	33.4953	−	132.707i	0.0413522	−	0.163836i
$811$			965.110i			1.19002i	0.803717	+	0.595012i	$0.202853\pi$
$811$			965.110i			1.19002i	−0.803717	+	0.595012i	$0.797147\pi$
$812$		0			0
$813$	1675.41			2.06078
$814$	−816.941	−	206.196i	−1.00361	−	0.253312i
$815$	340.881	−	196.807i	0.418258	−	0.241482i
$816$	−20.0506	−	343.808i	−0.0245719	−	0.421334i
$817$	−179.397	+	310.724i	−0.219580	+	0.380323i
$818$	213.728	−	60.6175i	0.261281	−	0.0741045i
$819$		0			0
$820$	−51.7222	+	31.9054i	−0.0630759	+	0.0389091i
$821$	−732.403	+	1268.56i	−0.892087	+	1.54514i	−0.0547173	+	0.998502i	$0.517426\pi$
$821$	−732.403	+	1268.56i	−0.892087	+	1.54514i	−0.837369	+	0.546637i	$0.815908\pi$
$822$	−751.920	+	774.146i	−0.914744	+	0.941783i
$823$	−837.584	+	483.579i	−1.01772	+	0.587581i	−0.913443	−	0.406967i	$-0.866586\pi$
$823$	−837.584	+	483.579i	−1.01772	+	0.587581i	−0.104278	+	0.994548i	$0.533253\pi$
$824$	657.071	−	207.215i	0.797416	−	0.251474i
$825$	1609.10			1.95043
$826$		0			0
$827$			1298.46i			1.57009i	0.619441	+	0.785043i	$0.287359\pi$
$827$			1298.46i			1.57009i	−0.619441	+	0.785043i	$0.712641\pi$
$828$	−696.734	+	20.2992i	−0.841466	+	0.0245160i
$829$	−385.699	−	668.050i	−0.465258	−	0.805850i	0.533955	−	0.845513i	$-0.320705\pi$
$829$	−385.699	−	668.050i	−0.465258	−	0.805850i	−0.999213	+	0.0396627i	$0.987372\pi$
$830$	303.657	−	312.633i	0.365852	−	0.376666i
$831$	−1001.44	−	578.181i	−1.20510	−	0.695766i
$832$	111.403	+	1271.68i	0.133897	+	1.52846i
$833$		0			0
$834$	−630.560	+	178.840i	−0.756067	+	0.214436i
$835$	−147.917	−	85.3997i	−0.177146	−	0.102275i
$836$	−715.535	−	385.778i	−0.855903	−	0.461457i
$837$	111.936	+	193.878i	0.133734	+	0.231635i
$838$	1244.93	+	314.220i	1.48560	+	0.374965i
$839$			1088.04i			1.29683i	0.761287	+	0.648415i	$0.224568\pi$
$839$			1088.04i			1.29683i	−0.761287	+	0.648415i	$0.775432\pi$
$840$		0			0
$841$	−802.465			−0.954180
$842$	74.3819	−	294.699i	0.0883395	−	0.349998i
$843$	577.152	−	333.219i	0.684641	−	0.395277i
$844$	203.875	−	378.144i	0.241558	−	0.448038i
$845$	156.523	−	271.105i	0.185234	−	0.320835i
$846$	197.032	+	694.705i	0.232899	+	0.821164i
$847$		0			0
$848$	−91.7978	+	182.819i	−0.108252	+	0.215588i
$849$	−435.305	+	753.971i	−0.512727	+	0.888070i
$850$	−157.145	−	152.633i	−0.184877	−	0.179569i
$851$	356.294	−	205.707i	0.418677	−	0.241723i
$852$	−24.2531	−	832.445i	−0.0284661	−	0.977048i
$853$	−126.051			−0.147774			−0.0738870	−	0.997267i	$-0.523540\pi$
$853$	−126.051			−0.147774			−0.0738870	+	0.997267i	$0.523540\pi$
$854$		0			0
$855$		−	211.707i		−	0.247611i
$856$	779.330	−	245.770i	0.910432	−	0.287115i
$857$	−567.965	−	983.744i	−0.662736	−	1.14789i	−0.979894	−	0.199520i	$-0.936062\pi$
$857$	−567.965	−	983.744i	−0.662736	−	1.14789i	0.317158	−	0.948373i	$-0.397271\pi$
$858$	1990.84	+	1933.68i	2.32033	+	2.25371i
$859$	511.436	+	295.278i	0.595385	+	0.343746i	0.767224	−	0.641379i	$-0.221637\pi$
$859$	511.436	+	295.278i	0.595385	+	0.343746i	−0.171839	+	0.985125i	$0.554971\pi$
$860$	−77.6345	−	125.854i	−0.0902727	−	0.146342i
$861$		0			0
$862$	−250.950	−	884.809i	−0.291125	−	1.02646i
$863$	−252.937	−	146.033i	−0.293090	−	0.169216i	0.346244	−	0.938144i	$-0.387457\pi$
$863$	−252.937	−	146.033i	−0.293090	−	0.169216i	−0.639335	+	0.768929i	$0.720790\pi$
$864$	−126.907	−	365.000i	−0.146883	−	0.422453i
$865$	188.233	+	326.029i	0.217611	+	0.376913i
$866$	−261.548	+	1036.24i	−0.302018	+	1.19659i
$867$		−	1211.57i		−	1.39742i
$868$		0			0
$869$	510.864			0.587876
$870$	−74.8419	−	18.8901i	−0.0860252	−	0.0217128i
$871$	−1776.83	+	1025.85i	−2.03998	+	1.17779i
$872$	1187.48	+	263.187i	1.36179	+	0.301820i
$873$	−523.016	+	905.890i	−0.599102	+	1.03768i
$874$	381.871	−	108.306i	0.436923	−	0.123920i
$875$		0			0
$876$	669.077	+	1084.65i	0.763787	+	1.23818i
$877$	−543.614	+	941.567i	−0.619856	+	1.07362i	0.369655	+	0.929169i	$0.379476\pi$
$877$	−543.614	+	941.567i	−0.619856	+	1.07362i	−0.989512	+	0.144454i	$0.953858\pi$
$878$	280.448	−	288.738i	0.319417	−	0.328859i
$879$	−1241.82	+	716.964i	−1.41276	+	0.815659i
$880$	279.900	−	184.123i	0.318068	−	0.209231i
$881$	−1217.53			−1.38198			−0.690991	−	0.722863i	$-0.742826\pi$
$881$	−1217.53			−1.38198			−0.690991	+	0.722863i	$0.742826\pi$
$882$		0			0
$883$			1141.10i			1.29230i	0.763212	+	0.646148i	$0.223621\pi$
$883$			1141.10i			1.29230i	−0.763212	+	0.646148i	$0.776379\pi$
$884$	−11.0039	−	377.688i	−0.0124478	−	0.427249i
$885$	−89.6187	−	155.224i	−0.101264	−	0.175395i
$886$	−102.410	+	105.437i	−0.115587	+	0.119004i
$887$	319.146	+	184.259i	0.359804	+	0.207733i	0.668995	−	0.743267i	$-0.266725\pi$
$887$	319.146	+	184.259i	0.359804	+	0.207733i	−0.309191	+	0.951000i	$0.600058\pi$
$888$	737.821	+	676.011i	0.830879	+	0.761274i
$889$		0			0
$890$	131.713	−	37.3564i	0.147992	−	0.0419735i
$891$	663.188	+	382.892i	0.744319	+	0.429733i
$892$	663.796	−	1231.20i	0.744166	−	1.38027i
$893$	−205.606	−	356.121i	−0.230242	−	0.398791i
$894$	1924.00	+	485.617i	2.15212	+	0.543196i
$895$		−	10.1566i		−	0.0113482i
$896$		0			0
$897$	−1355.17			−1.51078
$898$	−20.2819	+	80.3563i	−0.0225857	+	0.0894836i
$899$	−99.6624	+	57.5401i	−0.110859	+	0.0640046i
$900$	−949.269	−	511.795i	−1.05474	−	0.568661i
$901$	30.2758	−	52.4393i	0.0336025	−	0.0582012i
$902$	−92.7761	−	327.114i	−0.102856	−	0.362654i
$903$		0			0
$904$	908.544	−	991.615i	1.00503	−	1.09692i
$905$	−68.0975	+	117.948i	−0.0752459	+	0.130330i
$906$	1179.86	+	1145.99i	1.30228	+	1.26489i
$907$	−295.769	+	170.763i	−0.326096	+	0.188272i	−0.654107	−	0.756402i	$-0.726955\pi$
$907$	−295.769	+	170.763i	−0.326096	+	0.188272i	0.328010	+	0.944674i	$0.393622\pi$
$908$	73.3371	−	2.13666i	0.0807677	−	0.00235316i
$909$	1898.71			2.08879
$910$		0			0
$911$		−	536.979i		−	0.589439i	−0.955584	−	0.294719i	$-0.904774\pi$
$911$		−	536.979i		−	0.589439i	0.955584	−	0.294719i	$-0.0952262\pi$
$912$	530.592	+	806.593i	0.581789	+	0.884422i
$913$	1219.24	+	2111.78i	1.33542	+	2.31301i
$914$	387.652	+	376.522i	0.424127	+	0.411950i
$915$	−35.1281	−	20.2812i	−0.0383914	−	0.0221653i
$916$	−233.352	+	143.946i	−0.254751	+	0.157146i
$917$		0			0
$918$	31.2098	+	110.041i	0.0339976	+	0.119870i
$919$	−855.098	−	493.691i	−0.930466	−	0.537205i	−0.0435072	−	0.999053i	$-0.513853\pi$
$919$	−855.098	−	493.691i	−0.930466	−	0.537205i	−0.886959	+	0.461848i	$0.847186\pi$
$920$	−35.3986	+	159.716i	−0.0384768	+	0.173604i
$921$	−1028.32	−	1781.11i	−1.11653	−	1.93388i
$922$	359.811	−	1425.56i	0.390250	−	1.54616i
$923$		−	913.698i		−	0.989922i
$924$		0			0
$925$	636.540			0.688152
$926$	−1439.57	−	363.346i	−1.55461	−	0.392383i
$927$	−869.416	+	501.957i	−0.937881	+	0.541486i
$928$	187.627	−	65.2360i	0.202184	−	0.0702974i
$929$	−642.835	+	1113.42i	−0.691965	+	1.19852i	0.279229	+	0.960225i	$0.409921\pi$
$929$	−642.835	+	1113.42i	−0.691965	+	1.19852i	−0.971193	+	0.238293i	$0.923412\pi$
$930$	221.771	−	62.8987i	0.238463	−	0.0676331i
$931$		0			0
$932$	209.298	−	129.108i	0.224568	−	0.138527i
$933$	1085.84	−	1880.73i	1.16381	−	2.01578i
$934$	560.387	−	576.951i	0.599986	−	0.617721i
$935$	−85.8806	+	49.5832i	−0.0918509	+	0.0530302i
$936$	−559.440	−	1773.96i	−0.597692	−	1.89526i
$937$	887.657			0.947339			0.473670	−	0.880703i	$-0.342929\pi$
$937$	887.657			0.947339			0.473670	+	0.880703i	$0.342929\pi$
$938$		0			0
$939$		−	951.882i		−	1.01372i
$940$	169.405	−	4.93559i	0.180218	−	0.00525063i
$941$	190.263	+	329.545i	0.202192	+	0.350207i	0.949235	−	0.314569i	$-0.101860\pi$
$941$	190.263	+	329.545i	0.202192	+	0.350207i	−0.747042	+	0.664777i	$0.768527\pi$
$942$	−1210.17	+	1245.95i	−1.28469	+	1.32266i
$943$	143.783	+	83.0130i	0.152474	+	0.0880307i
$944$	412.215	+	206.983i	0.436669	+	0.219262i
$945$		0			0
$946$	795.956	−	225.749i	0.841391	−	0.238636i
$947$	−314.513	−	181.584i	−0.332116	−	0.191747i	0.324664	−	0.945829i	$-0.394749\pi$
$947$	−314.513	−	181.584i	−0.332116	−	0.191747i	−0.656780	+	0.754082i	$0.728082\pi$
$948$	−534.062	−	287.938i	−0.563357	−	0.303732i
$949$	699.106	+	1210.89i	0.736677	+	1.27596i
$950$	595.461	+	150.294i	0.626801	+	0.158205i
$951$			7.94799i			0.00835750i
$952$		0			0
$953$	−679.479			−0.712990			−0.356495	−	0.934297i	$-0.616028\pi$
$953$	−679.479			−0.712990			−0.356495	+	0.934297i	$0.616028\pi$
$954$	72.9492	−	289.022i	0.0764667	−	0.302958i
$955$	−68.9547	+	39.8110i	−0.0722038	+	0.0416869i
$956$	−388.472	+	720.531i	−0.406351	+	0.753693i
$957$	215.937	−	374.014i	0.225639	−	0.390819i
$958$	194.680	+	686.409i	0.203215	+	0.716502i
$959$		0			0
$960$	−396.387	+	34.7247i	−0.412904	+	0.0361716i
$961$	−308.662	+	534.618i	−0.321188	+	0.556314i
$962$	787.552	+	764.941i	0.818661	+	0.795157i
$963$	−1031.19	+	595.355i	−1.07081	+	0.618230i
$964$	45.3456	+	1556.40i	0.0470390	+	1.61453i
$965$	142.103			0.147257
$966$		0			0
$967$		−	209.525i		−	0.216675i	−0.994114	−	0.108337i	$-0.965447\pi$
$967$		−	209.525i		−	0.216675i	0.994114	−	0.108337i	$-0.0345527\pi$
$968$	272.639	+	864.528i	0.281651	+	0.893108i
$969$	−142.885	−	247.484i	−0.147456	−	0.255401i
$970$	176.106	+	171.050i	0.181552	+	0.176340i
$971$	−466.673	−	269.434i	−0.480610	−	0.277481i	0.240060	−	0.970758i	$-0.422833\pi$
$971$	−466.673	−	269.434i	−0.480610	−	0.277481i	−0.720671	+	0.693277i	$0.756166\pi$
$972$	−705.735	−	1144.07i	−0.726065	−	1.17703i
$973$		0			0
$974$	−66.0989	−	233.054i	−0.0678633	−	0.239275i
$975$	−1815.82	−	1048.36i	−1.86238	−	1.07525i
$976$	104.209	−	6.07741i	0.106772	−	0.00622685i
$977$	−514.148	−	890.531i	−0.526252	−	0.911495i	−0.999532	−	0.0305831i	$-0.990264\pi$
$977$	−514.148	−	890.531i	−0.526252	−	0.911495i	0.473280	−	0.880912i	$-0.343070\pi$
$978$	640.099	−	2536.05i	0.654498	−	2.59310i
$979$			766.001i			0.782432i
$980$		0			0
$981$	−1772.29			−1.80661
$982$	35.7847	+	9.03206i	0.0364407	+	0.00919762i
$983$	450.748	−	260.240i	0.458543	−	0.264740i	−0.252888	−	0.967496i	$-0.581380\pi$
$983$	450.748	−	260.240i	0.458543	−	0.264740i	0.711432	+	0.702755i	$0.248047\pi$
$984$	−87.3817	+	394.259i	−0.0888026	+	0.400670i
$985$	−123.936	+	214.663i	−0.125823	+	0.217932i
$986$	−56.5660	+	16.0433i	−0.0573692	+	0.0162711i
$987$		0			0
$988$	556.116	+	901.525i	0.562871	+	0.912475i
$989$	−201.993	+	349.862i	−0.204240	+	0.353753i
$990$	−340.132	+	350.186i	−0.343568	+	0.353724i
$991$	1601.28	−	924.499i	1.61582	−	0.932895i	0.627837	−	0.778345i	$-0.283941\pi$
$991$	1601.28	−	924.499i	1.61582	−	0.932895i	0.987985	−	0.154550i	$-0.0493927\pi$
$992$	−387.849	+	448.885i	−0.390977	+	0.452505i
$993$	−1704.60			−1.71661
$994$		0			0
$995$		−	298.100i		−	0.299598i
$996$	−84.3416	−	2894.87i	−0.0846803	−	2.90650i
$997$	505.115	+	874.885i	0.506635	+	0.877518i	0.999971	+	0.00767845i	$0.00244415\pi$
$997$	505.115	+	874.885i	0.506635	+	0.877518i	−0.493336	+	0.869839i	$0.664223\pi$
$998$	208.423	−	214.584i	0.208841	−	0.215014i
$999$	−287.825	−	166.176i	−0.288113	−	0.166342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.3.g.j.79.4		12
4.3	odd	2	inner	196.3.g.j.79.5		12
7.2	even	3		196.3.c.g.99.2		6
7.3	odd	6		196.3.g.k.67.5		12
7.4	even	3	inner	196.3.g.j.67.5		12
7.5	odd	6		28.3.c.a.15.2	yes	6
7.6	odd	2		196.3.g.k.79.4		12
21.5	even	6		252.3.g.a.127.5		6
28.3	even	6		196.3.g.k.67.4		12
28.11	odd	6	inner	196.3.g.j.67.4		12
28.19	even	6		28.3.c.a.15.1	✓	6
28.23	odd	6		196.3.c.g.99.1		6
28.27	even	2		196.3.g.k.79.5		12
56.5	odd	6		448.3.d.d.127.6		6
56.19	even	6		448.3.d.d.127.1		6
84.47	odd	6		252.3.g.a.127.6		6
112.5	odd	12		1792.3.g.g.127.2		12
112.19	even	12		1792.3.g.g.127.1		12
112.61	odd	12		1792.3.g.g.127.11		12
112.75	even	12		1792.3.g.g.127.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.3.c.a.15.1	✓	6	28.19	even	6
28.3.c.a.15.2	yes	6	7.5	odd	6
196.3.c.g.99.1		6	28.23	odd	6
196.3.c.g.99.2		6	7.2	even	3
196.3.g.j.67.4		12	28.11	odd	6	inner
196.3.g.j.67.5		12	7.4	even	3	inner
196.3.g.j.79.4		12	1.1	even	1	trivial
196.3.g.j.79.5		12	4.3	odd	2	inner
196.3.g.k.67.4		12	28.3	even	6
196.3.g.k.67.5		12	7.3	odd	6
196.3.g.k.79.4		12	7.6	odd	2
196.3.g.k.79.5		12	28.27	even	2
252.3.g.a.127.5		6	21.5	even	6
252.3.g.a.127.6		6	84.47	odd	6
448.3.d.d.127.1		6	56.19	even	6
448.3.d.d.127.6		6	56.5	odd	6
1792.3.g.g.127.1		12	112.19	even	12
1792.3.g.g.127.2		12	112.5	odd	12
1792.3.g.g.127.11		12	112.61	odd	12
1792.3.g.g.127.12		12	112.75	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.489450 - 1.93919i) q^{2} +(3.93608 - 2.27250i) q^{3} +(-3.52088 - 1.89827i) q^{4} +(0.683969 - 1.18467i) q^{5} +(-2.48028 - 8.74507i) q^{6} +(-5.40439 + 5.89853i) q^{8} +(5.82850 - 10.0953i) q^{9} +O(q^{10})\)	\(q+(0.489450 - 1.93919i) q^{2} +(3.93608 - 2.27250i) q^{3} +(-3.52088 - 1.89827i) q^{4} +(0.683969 - 1.18467i) q^{5} +(-2.48028 - 8.74507i) q^{6} +(-5.40439 + 5.89853i) q^{8} +(5.82850 - 10.0953i) q^{9} +(-1.96252 - 1.90618i) q^{10} +(13.2565 - 7.65363i) q^{11} +(-18.1723 + 0.529446i) q^{12} -19.9460 q^{13} -6.21727i q^{15} +(8.79315 + 13.3671i) q^{16} +(-2.36794 - 4.10139i) q^{17} +(-16.7238 - 16.2437i) q^{18} +(11.4977 + 6.63823i) q^{19} +(-4.65699 + 2.87272i) q^{20} +(-8.35343 - 29.4528i) q^{22} +(12.9460 + 7.47437i) q^{23} +(-7.86773 + 35.4985i) q^{24} +(11.5644 + 20.0301i) q^{25} +(-9.76259 + 38.6791i) q^{26} -12.0760i q^{27} +6.20763 q^{29} +(-12.0564 - 3.04305i) q^{30} +(-16.0548 + 9.26926i) q^{31} +(30.2252 - 10.5090i) q^{32} +(34.7857 - 60.2507i) q^{33} +(-9.11234 + 2.58445i) q^{34} +(-39.6849 + 24.4801i) q^{36} +(13.7608 - 23.8344i) q^{37} +(18.5003 - 19.0472i) q^{38} +(-78.5093 + 45.3274i) q^{39} +(3.29137 + 10.4368i) q^{40} +11.1064 q^{41} +27.0248i q^{43} +(-61.2031 + 1.78314i) q^{44} +(-7.97302 - 13.8097i) q^{45} +(20.8306 - 21.4463i) q^{46} +(-26.8235 - 15.4865i) q^{47} +(64.9874 + 32.6317i) q^{48} +(44.5022 - 12.6217i) q^{50} +(-18.6408 - 10.7623i) q^{51} +(70.2276 + 37.8629i) q^{52} +(6.39287 + 11.0728i) q^{53} +(-23.4176 - 5.91061i) q^{54} -20.9394i q^{55} +60.3415 q^{57} +(3.03832 - 12.0377i) q^{58} +(24.9666 - 14.4145i) q^{59} +(-11.8021 + 21.8903i) q^{60} +(3.26208 - 5.65008i) q^{61} +(10.1168 + 35.6701i) q^{62} +(-5.58519 - 63.7558i) q^{64} +(-13.6425 + 23.6295i) q^{65} +(-99.8113 - 96.9457i) q^{66} +(89.0817 - 51.4313i) q^{67} +(0.551682 + 18.9355i) q^{68} +67.9420 q^{69} +45.8085i q^{71} +(28.0476 + 88.9382i) q^{72} +(-35.0499 - 60.7081i) q^{73} +(-39.4841 - 38.3505i) q^{74} +(91.0366 + 52.5600i) q^{75} +(-27.8810 - 45.1982i) q^{76} +(49.4718 + 174.429i) q^{78} +(28.9027 + 16.6870i) q^{79} +(21.8499 - 1.27427i) q^{80} +(25.0137 + 43.3251i) q^{81} +(5.43601 - 21.5373i) q^{82} +159.301i q^{83} -6.47839 q^{85} +(52.4060 + 13.2273i) q^{86} +(24.4337 - 14.1068i) q^{87} +(-26.4980 + 119.557i) q^{88} +(-25.0208 + 43.3374i) q^{89} +(-30.6819 + 8.70202i) q^{90} +(-31.3929 - 50.8913i) q^{92} +(-42.1287 + 72.9691i) q^{93} +(-43.1600 + 44.4358i) q^{94} +(15.7282 - 9.08069i) q^{95} +(95.0871 - 110.051i) q^{96} -89.7343 q^{97} -178.437i 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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