LMFDB - Embedded newform 980.2.o.g.411.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(31,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("980.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.o (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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			411.41
Character	$\chi$	$=$	980.411
Dual form			980.2.o.g.31.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34099 + 0.449173i) q^{2} +(-0.656274 - 1.13670i) q^{3} +(1.59649 + 1.20467i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.369479 - 1.81908i) q^{6} +(1.59976 + 2.33255i) q^{8} +(0.638609 - 1.10610i) q^{9} +O(q^{10})$	\(q+(1.34099 + 0.449173i) q^{2} +(-0.656274 - 1.13670i) q^{3} +(1.59649 + 1.20467i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.369479 - 1.81908i) q^{6} +(1.59976 + 2.33255i) q^{8} +(0.638609 - 1.10610i) q^{9} +(0.936741 + 1.05949i) q^{10} +(-0.769955 + 0.444533i) q^{11} +(0.321617 - 2.60532i) q^{12} -6.39664i q^{13} -1.31255i q^{15} +(1.09754 + 3.84648i) q^{16} +(3.36785 - 1.94443i) q^{17} +(1.35320 - 1.19642i) q^{18} +(-0.471687 + 0.816986i) q^{19} +(0.780262 + 1.84152i) q^{20} +(-1.23217 + 0.250270i) q^{22} +(7.61724 + 4.39781i) q^{23} +(1.60152 - 3.34924i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.87320 - 8.57781i) q^{26} -5.61405 q^{27} -0.497418 q^{29} +(0.589562 - 1.76011i) q^{30} +(2.42987 + 4.20866i) q^{31} +(-0.255955 + 5.65106i) q^{32} +(1.01060 + 0.583472i) q^{33} +(5.38962 - 1.09470i) q^{34} +(2.35202 - 0.996565i) q^{36} +(1.33043 - 2.30437i) q^{37} +(-0.999494 + 0.883697i) q^{38} +(-7.27106 + 4.19795i) q^{39} +(0.219160 + 2.81992i) q^{40} +0.823314i q^{41} -9.92015i q^{43} +(-1.76474 - 0.217850i) q^{44} +(1.10610 - 0.638609i) q^{45} +(8.23923 + 9.31887i) q^{46} +(-3.68744 + 6.38683i) q^{47} +(3.65201 - 3.77192i) q^{48} +(0.281497 + 1.38591i) q^{50} +(-4.42046 - 2.55215i) q^{51} +(7.70585 - 10.2122i) q^{52} +(2.35119 + 4.07237i) q^{53} +(-7.52837 - 2.52168i) q^{54} -0.889067 q^{55} +1.23822 q^{57} +(-0.667031 - 0.223427i) q^{58} +(0.942161 + 1.63187i) q^{59} +(1.58119 - 2.09547i) q^{60} +(-0.502695 - 0.290231i) q^{61} +(1.36800 + 6.73519i) q^{62} +(-2.88154 + 7.46302i) q^{64} +(3.19832 - 5.53966i) q^{65} +(1.09312 + 1.23636i) q^{66} +(-8.07873 + 4.66426i) q^{67} +(7.71911 + 0.952895i) q^{68} -11.5447i q^{69} -14.3163i q^{71} +(3.60165 - 0.279914i) q^{72} +(7.83276 - 4.52225i) q^{73} +(2.81915 - 2.49254i) q^{74} +(0.656274 - 1.13670i) q^{75} +(-1.73724 + 0.736079i) q^{76} +(-11.6360 + 2.36342i) q^{78} +(-12.8891 - 7.44154i) q^{79} +(-0.972745 + 3.87992i) q^{80} +(1.76853 + 3.06319i) q^{81} +(-0.369811 + 1.10405i) q^{82} +4.02691 q^{83} +3.88885 q^{85} +(4.45587 - 13.3028i) q^{86} +(0.326443 + 0.565415i) q^{87} +(-2.26864 - 1.08481i) q^{88} +(-5.21110 - 3.00863i) q^{89} +(1.77011 - 0.359533i) q^{90} +(6.86290 + 16.1973i) q^{92} +(3.18932 - 5.52407i) q^{93} +(-7.81360 + 6.90835i) q^{94} +(-0.816986 + 0.471687i) q^{95} +(6.59154 - 3.41770i) q^{96} +14.5252i q^{97} +1.13553i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 8 q^{2} + 8 q^{4} + 16 q^{8} - 48 q^{9}+O(q^{10}) $ 96 * q - 8 * q^2 + 8 * q^4 + 16 * q^8 - 48 * q^9	$ 96 q - 8 q^{2} + 8 q^{4} + 16 q^{8} - 48 q^{9} + 40 q^{16} - 40 q^{18} - 64 q^{22} + 48 q^{25} + 128 q^{29} - 8 q^{32} - 80 q^{36} - 64 q^{37} + 32 q^{46} - 16 q^{50} + 64 q^{53} + 48 q^{58} - 16 q^{64} + 72 q^{72} - 96 q^{74} - 224 q^{78} - 48 q^{81} - 32 q^{88} - 224 q^{92}+O(q^{100}) $ 96 * q - 8 * q^2 + 8 * q^4 + 16 * q^8 - 48 * q^9 + 40 * q^16 - 40 * q^18 - 64 * q^22 + 48 * q^25 + 128 * q^29 - 8 * q^32 - 80 * q^36 - 64 * q^37 + 32 * q^46 - 16 * q^50 + 64 * q^53 + 48 * q^58 - 16 * q^64 + 72 * q^72 - 96 * q^74 - 224 * q^78 - 48 * q^81 - 32 * q^88 - 224 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.34099	+	0.449173i	0.948220	+	0.317614i
$2$	1.34099	+	0.449173i	0.948220	+	0.317614i
$3$	−0.656274	−	1.13670i	−0.378900	−	0.656274i	0.612002	−	0.790856i	$-0.290364\pi$
$3$	−0.656274	−	1.13670i	−0.378900	−	0.656274i	−0.990902	+	0.134582i	$0.957031\pi$
$4$	1.59649	+	1.20467i	0.798243	+	0.602335i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−0.369479	−	1.81908i	−0.150839	−	0.742636i
$7$		0			0
$7$		0			0
$8$	1.59976	+	2.33255i	0.565600	+	0.824679i
$9$	0.638609	−	1.10610i	0.212870	−	0.368701i
$10$	0.936741	+	1.05949i	0.296224	+	0.335040i
$11$	−0.769955	+	0.444533i	−0.232150	+	0.134032i	−0.611564	−	0.791195i	$-0.709459\pi$
$11$	−0.769955	+	0.444533i	−0.232150	+	0.134032i	0.379413	+	0.925227i	$0.376126\pi$
$12$	0.321617	−	2.60532i	0.0928427	−	0.752091i
$13$		−	6.39664i		−	1.77411i	−0.461664	−	0.887055i	$-0.652747\pi$
$13$		−	6.39664i		−	1.77411i	0.461664	−	0.887055i	$-0.347253\pi$
$14$		0			0
$15$		−	1.31255i		−	0.338898i
$16$	1.09754	+	3.84648i	0.274384	+	0.961620i
$17$	3.36785	−	1.94443i	0.816823	−	0.471593i	−0.0324969	−	0.999472i	$-0.510346\pi$
$17$	3.36785	−	1.94443i	0.816823	−	0.471593i	0.849320	+	0.527879i	$0.177013\pi$
$18$	1.35320	−	1.19642i	0.318952	−	0.281999i
$19$	−0.471687	+	0.816986i	−0.108212	+	0.187429i	−0.915046	−	0.403349i	$-0.867846\pi$
$19$	−0.471687	+	0.816986i	−0.108212	+	0.187429i	0.806834	+	0.590779i	$0.201179\pi$
$20$	0.780262	+	1.84152i	0.174472	+	0.411776i
$21$		0			0
$22$	−1.23217	+	0.250270i	−0.262700	+	0.0533577i
$23$	7.61724	+	4.39781i	1.58830	+	0.917008i	0.993587	+	0.113073i	$0.0360693\pi$
$23$	7.61724	+	4.39781i	1.58830	+	0.917008i	0.594717	+	0.803935i	$0.297264\pi$
$24$	1.60152	−	3.34924i	0.326910	−	0.683660i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	2.87320	−	8.57781i	0.563481	−	1.68225i
$27$	−5.61405			−1.08043
$28$		0			0
$29$	−0.497418			−0.0923682			−0.0461841	−	0.998933i	$-0.514706\pi$
$29$	−0.497418			−0.0923682			−0.0461841	+	0.998933i	$0.514706\pi$
$30$	0.589562	−	1.76011i	0.107639	−	0.321350i
$31$	2.42987	+	4.20866i	0.436418	+	0.755897i	0.997410	−	0.0719234i	$-0.0229137\pi$
$31$	2.42987	+	4.20866i	0.436418	+	0.755897i	−0.560993	+	0.827821i	$0.689580\pi$
$32$	−0.255955	+	5.65106i	−0.0452469	+	0.998976i
$33$	1.01060	+	0.583472i	0.175923	+	0.101569i
$34$	5.38962	−	1.09470i	0.924312	−	0.187740i
$35$		0			0
$36$	2.35202	−	0.996565i	0.392003	−	0.166094i
$37$	1.33043	−	2.30437i	0.218721	−	0.378837i	−0.735696	−	0.677312i	$-0.763145\pi$
$37$	1.33043	−	2.30437i	0.218721	−	0.378837i	0.954417	+	0.298475i	$0.0964780\pi$
$38$	−0.999494	+	0.883697i	−0.162139	+	0.143355i
$39$	−7.27106	+	4.19795i	−1.16430	+	0.672210i
$40$	0.219160	+	2.81992i	0.0346522	+	0.445869i
$41$			0.823314i			0.128580i	0.997931	+	0.0642900i	$0.0204783\pi$
$41$			0.823314i			0.128580i	−0.997931	+	0.0642900i	$0.979522\pi$
$42$		0			0
$43$		−	9.92015i		−	1.51281i	−0.654104	−	0.756404i	$-0.726954\pi$
$43$		−	9.92015i		−	1.51281i	0.654104	−	0.756404i	$-0.273046\pi$
$44$	−1.76474	−	0.217850i	−0.266044	−	0.0328421i
$45$	1.10610	−	0.638609i	0.164888	−	0.0951981i
$46$	8.23923	+	9.31887i	1.21481	+	1.37399i
$47$	−3.68744	+	6.38683i	−0.537868	+	0.931615i	0.461150	+	0.887322i	$0.347437\pi$
$47$	−3.68744	+	6.38683i	−0.537868	+	0.931615i	−0.999019	+	0.0442929i	$0.985897\pi$
$48$	3.65201	−	3.77192i	0.527122	−	0.544429i
$49$		0			0
$50$	0.281497	+	1.38591i	0.0398097	+	0.195998i
$51$	−4.42046	−	2.55215i	−0.618988	−	0.357373i
$52$	7.70585	−	10.2122i	1.06861	−	1.41617i
$53$	2.35119	+	4.07237i	0.322960	+	0.559384i	0.981097	−	0.193514i	$-0.0619886\pi$
$53$	2.35119	+	4.07237i	0.322960	+	0.559384i	−0.658137	+	0.752898i	$0.728655\pi$
$54$	−7.52837	−	2.52168i	−1.02448	−	0.343158i
$55$	−0.889067			−0.119882
$56$		0			0
$57$	1.23822			0.164007
$58$	−0.667031	−	0.223427i	−0.0875854	−	0.0293374i
$59$	0.942161	+	1.63187i	0.122659	+	0.212452i	0.920815	−	0.389999i	$-0.127525\pi$
$59$	0.942161	+	1.63187i	0.122659	+	0.212452i	−0.798156	+	0.602450i	$0.794191\pi$
$60$	1.58119	−	2.09547i	0.204131	−	0.270523i
$61$	−0.502695	−	0.290231i	−0.0643635	−	0.0371603i	0.467473	−	0.884007i	$-0.345165\pi$
$61$	−0.502695	−	0.290231i	−0.0643635	−	0.0371603i	−0.531836	+	0.846847i	$0.678498\pi$
$62$	1.36800	+	6.73519i	0.173737	+	0.855369i
$63$		0			0
$64$	−2.88154	+	7.46302i	−0.360192	+	0.932878i
$65$	3.19832	−	5.53966i	0.396703	−	0.687110i
$66$	1.09312	+	1.23636i	0.134554	+	0.152186i
$67$	−8.07873	+	4.66426i	−0.986975	+	0.569830i	−0.904369	−	0.426752i	$-0.859658\pi$
$67$	−8.07873	+	4.66426i	−0.986975	+	0.569830i	−0.0826060	+	0.996582i	$0.526324\pi$
$68$	7.71911	+	0.952895i	0.936080	+	0.115555i
$69$		−	11.5447i		−	1.38982i
$70$		0			0
$71$		−	14.3163i		−	1.69903i	−0.527563	−	0.849516i	$-0.676894\pi$
$71$		−	14.3163i		−	1.69903i	0.527563	−	0.849516i	$-0.323106\pi$
$72$	3.60165	−	0.279914i	0.424459	−	0.0329882i
$73$	7.83276	−	4.52225i	0.916756	−	0.529289i	0.0341570	−	0.999416i	$-0.489125\pi$
$73$	7.83276	−	4.52225i	0.916756	−	0.529289i	0.882599	+	0.470127i	$0.155792\pi$
$74$	2.81915	−	2.49254i	0.327720	−	0.289752i
$75$	0.656274	−	1.13670i	0.0757800	−	0.131255i
$76$	−1.73724	+	0.736079i	−0.199275	+	0.0844341i
$77$		0			0
$78$	−11.6360	+	2.36342i	−1.31752	+	0.267605i
$79$	−12.8891	−	7.44154i	−1.45014	−	0.837239i	−0.451652	−	0.892194i	$-0.649165\pi$
$79$	−12.8891	−	7.44154i	−1.45014	−	0.837239i	−0.998489	+	0.0549552i	$0.982498\pi$
$80$	−0.972745	+	3.87992i	−0.108756	+	0.433788i
$81$	1.76853	+	3.06319i	0.196504	+	0.340354i
$82$	−0.369811	+	1.10405i	−0.0408388	+	0.121922i
$83$	4.02691			0.442011			0.221005	−	0.975273i	$-0.429066\pi$
$83$	4.02691			0.442011			0.221005	+	0.975273i	$0.429066\pi$
$84$		0			0
$85$	3.88885			0.421805
$86$	4.45587	−	13.3028i	0.480489	−	1.43448i
$87$	0.326443	+	0.565415i	0.0349983	+	0.0606189i
$88$	−2.26864	−	1.08481i	−0.241837	−	0.115641i
$89$	−5.21110	−	3.00863i	−0.552375	−	0.318914i	0.197704	−	0.980262i	$-0.436651\pi$
$89$	−5.21110	−	3.00863i	−0.552375	−	0.318914i	−0.750079	+	0.661348i	$0.769985\pi$
$90$	1.77011	−	0.359533i	0.186586	−	0.0378981i
$91$		0			0
$92$	6.86290	+	16.1973i	0.715507	+	1.68869i
$93$	3.18932	−	5.52407i	0.330717	−	0.572819i
$94$	−7.81360	+	6.90835i	−0.805911	+	0.712542i
$95$	−0.816986	+	0.471687i	−0.0838210	+	0.0483941i
$96$	6.59154	−	3.41770i	0.672746	−	0.348818i
$97$			14.5252i			1.47481i	0.675451	+	0.737404i	$0.263949\pi$
$97$			14.5252i			1.47481i	−0.675451	+	0.737404i	$0.736051\pi$
$98$		0			0
$99$			1.13553i			0.114125i
$100$	−0.245032	+	1.98493i	−0.0245032	+	0.198493i
$101$	−12.8372	+	7.41157i	−1.27735	+	0.737478i	−0.976360	−	0.216149i	$-0.930650\pi$
$101$	−12.8372	+	7.41157i	−1.27735	+	0.737478i	−0.300990	+	0.953627i	$0.597317\pi$
$102$	−4.78142	−	5.40796i	−0.473431	−	0.535467i
$103$	−9.16327	+	15.8713i	−0.902884	+	1.56384i	−0.0791513	+	0.996863i	$0.525221\pi$
$103$	−9.16327	+	15.8713i	−0.902884	+	1.56384i	−0.823733	+	0.566978i	$0.808112\pi$
$104$	14.9205	−	10.2331i	1.46307	−	1.00344i
$105$		0			0
$106$	1.32371	+	6.51709i	0.128570	+	0.632995i
$107$	7.21079	+	4.16315i	0.697093	+	0.402467i	0.806264	−	0.591556i	$-0.201486\pi$
$107$	7.21079	+	4.16315i	0.697093	+	0.402467i	−0.109171	+	0.994023i	$0.534819\pi$
$108$	−8.96276	−	6.76309i	−0.862442	−	0.650778i
$109$	−0.497407	−	0.861533i	−0.0476429	−	0.0825199i	0.841221	−	0.540692i	$-0.181838\pi$
$109$	−0.497407	−	0.861533i	−0.0476429	−	0.0825199i	−0.888863	+	0.458172i	$0.848504\pi$
$110$	−1.19223	−	0.399345i	−0.113674	−	0.0380761i
$111$	−3.49251			−0.331494
$112$		0			0
$113$	0.363411			0.0341868			0.0170934	−	0.999854i	$-0.494559\pi$
$113$	0.363411			0.0341868			0.0170934	+	0.999854i	$0.494559\pi$
$114$	1.66044	+	0.556177i	0.155515	+	0.0520908i
$115$	4.39781	+	7.61724i	0.410098	+	0.710311i
$116$	−0.794121	−	0.599225i	−0.0737323	−	0.0556366i
$117$	−7.07534	−	4.08495i	−0.654116	−	0.377654i
$118$	0.530432	+	2.61151i	0.0488302	+	0.240409i
$119$		0			0
$120$	3.06158	−	2.09976i	0.279483	−	0.191681i
$121$	−5.10478	+	8.84174i	−0.464071	+	0.803794i
$122$	−0.543743	−	0.614993i	−0.0492282	−	0.0556789i
$123$	0.935861	−	0.540319i	0.0843837	−	0.0487190i
$124$	−1.19079	+	9.64626i	−0.106936	+	0.866260i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			2.46720i			0.218928i	0.993991	+	0.109464i	$0.0349135\pi$
$127$			2.46720i			0.218928i	−0.993991	+	0.109464i	$0.965087\pi$
$128$	−7.21630	+	8.71350i	−0.637836	+	0.770172i
$129$	−11.2762	+	6.51034i	−0.992817	+	0.573203i
$130$	6.77717	−	5.99200i	0.594397	−	0.525533i
$131$	0.141458	−	0.245013i	0.0123593	−	0.0214069i	−0.859780	−	0.510665i	$-0.829399\pi$
$131$	0.141458	−	0.245013i	0.0123593	−	0.0214069i	0.872139	+	0.489258i	$0.162732\pi$
$132$	0.910522	+	2.14895i	0.0792508	+	0.187042i
$133$		0			0
$134$	−12.9285	+	2.62595i	−1.11685	+	0.226848i
$135$	−4.86191	−	2.80703i	−0.418447	−	0.241590i
$136$	9.92321	+	4.74504i	0.850908	+	0.406884i
$137$	−8.30757	−	14.3891i	−0.709764	−	1.22935i	−0.964945	−	0.262454i	$-0.915468\pi$
$137$	−8.30757	−	14.3891i	−0.709764	−	1.22935i	0.255181	−	0.966893i	$-0.417865\pi$
$138$	5.18557	−	15.4813i	0.441425	−	1.31785i
$139$	−18.6029			−1.57788			−0.788938	−	0.614473i	$-0.789369\pi$
$139$	−18.6029			−1.57788			−0.788938	+	0.614473i	$0.789369\pi$
$140$		0			0
$141$	9.67988			0.815193
$142$	6.43050	−	19.1980i	0.539636	−	1.61106i
$143$	2.84352	+	4.92512i	0.237787	+	0.411860i
$144$	4.95550	+	1.24241i	0.412958	+	0.103534i
$145$	−0.430777	−	0.248709i	−0.0357741	−	0.0206542i
$146$	12.5349	−	2.54600i	1.03740	−	0.210709i
$147$		0			0
$148$	4.90003	−	2.07617i	0.402780	−	0.170660i
$149$	−7.83270	+	13.5666i	−0.641680	+	1.11142i	0.343378	+	0.939197i	$0.388429\pi$
$149$	−7.83270	+	13.5666i	−0.641680	+	1.11142i	−0.985058	+	0.172225i	$0.944904\pi$
$150$	1.39063	−	1.22952i	0.113544	−	0.100390i
$151$	10.3815	−	5.99377i	0.844836	−	0.487766i	−0.0140690	−	0.999901i	$-0.504478\pi$
$151$	10.3815	−	5.99377i	0.844836	−	0.487766i	0.858905	+	0.512135i	$0.171145\pi$
$152$	−2.66024	+	0.206749i	−0.215774	+	0.0167696i
$153$		−	4.96691i		−	0.401551i
$154$		0			0
$155$			4.85974i			0.390344i
$156$	−16.6653	−	2.05727i	−1.33429	−	0.164713i
$157$	9.21060	−	5.31774i	0.735086	−	0.424402i	−0.0851942	−	0.996364i	$-0.527151\pi$
$157$	9.21060	−	5.31774i	0.735086	−	0.424402i	0.820280	+	0.571963i	$0.193818\pi$
$158$	−13.9416	−	15.7685i	−1.10913	−	1.25447i
$159$	3.08605	−	5.34519i	0.244739	−	0.423901i
$160$	−3.04719	+	4.76598i	−0.240902	+	0.376784i
$161$		0			0
$162$	0.995674	+	4.90207i	0.0782276	+	0.385143i
$163$	−6.79907	−	3.92545i	−0.532544	−	0.307465i	0.209508	−	0.977807i	$-0.432814\pi$
$163$	−6.79907	−	3.92545i	−0.532544	−	0.307465i	−0.742052	+	0.670342i	$0.766147\pi$
$164$	−0.991822	+	1.31441i	−0.0774483	+	0.102638i
$165$	0.583472	+	1.01060i	0.0454232	+	0.0786753i
$166$	5.40003	+	1.80878i	0.419124	+	0.140389i
$167$	−7.90245			−0.611510			−0.305755	−	0.952110i	$-0.598909\pi$
$167$	−7.90245			−0.611510			−0.305755	+	0.952110i	$0.598909\pi$
$168$		0			0
$169$	−27.9170			−2.14746
$170$	5.21490	+	1.74677i	0.399964	+	0.133971i
$171$	0.602447	+	1.04347i	0.0460702	+	0.0797960i
$172$	11.9505	−	15.8374i	0.911218	−	1.20759i
$173$	−16.1343	−	9.31513i	−1.22667	−	0.708216i	−0.260336	−	0.965518i	$-0.583833\pi$
$173$	−16.1343	−	9.31513i	−1.22667	−	0.708216i	−0.966331	+	0.257302i	$0.917167\pi$
$174$	0.183785	+	0.904843i	0.0139327	+	0.0685960i
$175$		0			0
$176$	−2.55494	−	2.47372i	−0.192586	−	0.186464i
$177$	1.23663	−	2.14191i	0.0929510	−	0.160996i
$178$	−5.63661	−	6.37521i	−0.422482	−	0.477842i
$179$	−17.7698	+	10.2594i	−1.32818	+	0.766825i	−0.985018	−	0.172451i	$-0.944831\pi$
$179$	−17.7698	+	10.2594i	−1.32818	+	0.766825i	−0.343162	+	0.939276i	$0.611498\pi$
$180$	2.53519	+	0.312959i	0.188962	+	0.0233266i
$181$			13.2693i			0.986296i	0.869946	+	0.493148i	$0.164154\pi$
$181$			13.2693i			0.986296i	−0.869946	+	0.493148i	$0.835846\pi$
$182$		0			0
$183$			0.761885i			0.0563202i
$184$	1.92765	+	24.8030i	0.142108	+	1.82850i
$185$	2.30437	−	1.33043i	0.169421	−	0.0978152i
$186$	6.75810	−	5.97514i	0.495528	−	0.438118i
$187$	−1.72873	+	2.99424i	−0.126417	+	0.218961i
$188$	−13.5810	+	5.75434i	−0.990494	+	0.419678i
$189$		0			0
$190$	−1.30744	+	0.265557i	−0.0948513	+	0.0192655i
$191$	17.9278	+	10.3506i	1.29721	+	0.748945i	0.979922	−	0.199383i	$-0.0638939\pi$
$191$	17.9278	+	10.3506i	1.29721	+	0.748945i	0.317290	+	0.948329i	$0.397227\pi$
$192$	10.3743	−	1.62234i	0.748701	−	0.117083i
$193$	8.79742	+	15.2376i	0.633252	+	1.09683i	0.986883	+	0.161440i	$0.0516138\pi$
$193$	8.79742	+	15.2376i	0.633252	+	1.09683i	−0.353630	+	0.935385i	$0.615053\pi$
$194$	−6.52433	+	19.4781i	−0.468419	+	1.39844i
$195$	−8.39590			−0.601243
$196$		0			0
$197$	23.8347			1.69815			0.849075	−	0.528272i	$-0.177160\pi$
$197$	23.8347			1.69815			0.849075	+	0.528272i	$0.177160\pi$
$198$	−0.510051	+	1.52273i	−0.0362477	+	0.108216i
$199$	−9.25434	−	16.0290i	−0.656023	−	1.13626i	−0.981636	−	0.190762i	$-0.938904\pi$
$199$	−9.25434	−	16.0290i	−0.656023	−	1.13626i	0.325614	−	0.945503i	$-0.394429\pi$
$200$	−1.22016	+	2.55171i	−0.0862786	+	0.180433i
$201$	10.6037	+	6.12207i	0.747929	+	0.431817i
$202$	−20.5436	+	4.17267i	−1.44544	+	0.293588i
$203$		0			0
$204$	−3.98270	−	9.39968i	−0.278845	−	0.658109i
$205$	−0.411657	+	0.713010i	−0.0287514	+	0.0497988i
$206$	−19.4168	+	17.1672i	−1.35283	+	1.19610i
$207$	9.72887	−	5.61696i	0.676203	−	0.390406i
$208$	24.6046	−	7.02055i	1.70602	−	0.486788i
$209$		−	0.838722i		−	0.0580156i
$210$		0			0
$211$		−	8.96174i		−	0.616952i	−0.951232	−	0.308476i	$-0.900181\pi$
$211$		−	8.96174i		−	0.616952i	0.951232	−	0.308476i	$-0.0998189\pi$
$212$	−1.15223	+	9.33389i	−0.0791357	+	0.641055i
$213$	−16.2733	+	9.39542i	−1.11503	+	0.643763i
$214$	7.79959	+	8.82162i	0.533169	+	0.603034i
$215$	4.96007	−	8.59110i	0.338274	−	0.585908i
$216$	−8.98114	−	13.0950i	−0.611089	−	0.891004i
$217$		0			0
$218$	−0.280037	−	1.37873i	−0.0189665	−	0.0933791i
$219$	−10.2809	−	5.93567i	−0.694717	−	0.401095i
$220$	−1.41938	−	1.07103i	−0.0956948	−	0.0722090i
$221$	−12.4378	−	21.5429i	−0.836657	−	1.44913i
$222$	−4.68341	−	1.56874i	−0.314330	−	0.105287i
$223$	16.4225			1.09973			0.549865	−	0.835253i	$-0.314679\pi$
$223$	16.4225			1.09973			0.549865	+	0.835253i	$0.314679\pi$
$224$		0			0
$225$	1.27722			0.0851478
$226$	0.487329	+	0.163234i	0.0324166	+	0.0108582i
$227$	−6.35591	−	11.0088i	−0.421857	−	0.730677i	0.574264	−	0.818670i	$-0.305288\pi$
$227$	−6.35591	−	11.0088i	−0.421857	−	0.730677i	−0.996121	+	0.0879926i	$0.971955\pi$
$228$	1.97681	+	1.49165i	0.130917	+	0.0987871i
$229$	14.9792	+	8.64823i	0.989851	+	0.571491i	0.905230	−	0.424922i	$-0.139699\pi$
$229$	14.9792	+	8.64823i	0.989851	+	0.571491i	0.0846216	+	0.996413i	$0.473032\pi$
$230$	2.47595	+	12.1900i	0.163259	+	0.803784i
$231$		0			0
$232$	−0.795749	−	1.16025i	−0.0522435	−	0.0761742i
$233$	−11.8739	+	20.5662i	−0.777885	+	1.34734i	0.155274	+	0.987872i	$0.450374\pi$
$233$	−11.8739	+	20.5662i	−0.777885	+	1.34734i	−0.933159	+	0.359465i	$0.882959\pi$
$234$	−7.65308	−	8.65592i	−0.500298	−	0.565855i
$235$	−6.38683	+	3.68744i	−0.416631	+	0.240542i
$236$	−0.461720	+	3.74025i	−0.0300554	+	0.243470i
$237$			19.5348i			1.26892i
$238$		0			0
$239$		−	10.2033i		−	0.659997i	−0.943981	−	0.329998i	$-0.892952\pi$
$239$		−	10.2033i		−	0.659997i	0.943981	−	0.329998i	$-0.107048\pi$
$240$	5.04869	−	1.44057i	0.325892	−	0.0929884i
$241$	−2.01649	+	1.16422i	−0.129893	+	0.0749939i	−0.563539	−	0.826090i	$-0.690560\pi$
$241$	−2.01649	+	1.16422i	−0.129893	+	0.0749939i	0.433645	+	0.901084i	$0.357227\pi$
$242$	−10.8169	+	9.56371i	−0.695337	+	0.614779i
$243$	−6.09980	+	10.5652i	−0.391302	+	0.677755i
$244$	−0.452913	−	1.06893i	−0.0289948	−	0.0684314i
$245$		0			0
$246$	1.49767	−	0.304197i	0.0954881	−	0.0193949i
$247$	5.22597	+	3.01721i	0.332520	+	0.191981i
$248$	−5.92968	+	12.4006i	−0.376535	+	0.787441i
$249$	−2.64276	−	4.57739i	−0.167478	−	0.290080i
$250$	−0.449173	+	1.34099i	−0.0284082	+	0.0848114i
$251$	6.54297			0.412988			0.206494	−	0.978448i	$-0.433795\pi$
$251$	6.54297			0.412988			0.206494	+	0.978448i	$0.433795\pi$
$252$		0			0
$253$	−7.81990			−0.491633
$254$	−1.10820	+	3.30848i	−0.0695346	+	0.207592i
$255$	−2.55215	−	4.42046i	−0.159822	−	0.276820i
$256$	−13.5908	+	8.44331i	−0.849427	+	0.527707i
$257$	17.0076	+	9.81936i	1.06091	+	0.612515i	0.925683	−	0.378300i	$-0.123491\pi$
$257$	17.0076	+	9.81936i	1.06091	+	0.612515i	0.135224	+	0.990815i	$0.456825\pi$
$258$	−18.0455	+	3.66528i	−1.12347	+	0.228191i
$259$		0			0
$260$	11.7795	−	4.99106i	0.730536	−	0.309532i
$261$	−0.317655	+	0.550195i	−0.0196624	+	0.0340562i
$262$	0.299747	−	0.265020i	0.0185184	−	0.0163730i
$263$	9.24916	−	5.34000i	0.570328	−	0.329279i	−0.186953	−	0.982369i	$-0.559861\pi$
$263$	9.24916	−	5.34000i	0.570328	−	0.329279i	0.757280	+	0.653090i	$0.226528\pi$
$264$	0.255747	+	3.29069i	0.0157401	+	0.202528i
$265$			4.70237i			0.288864i
$266$		0			0
$267$			7.89794i			0.483346i
$268$	−18.5165	−	2.28579i	−1.13107	−	0.139627i
$269$	5.37695	−	3.10438i	0.327838	−	0.189278i	−0.327043	−	0.945010i	$-0.606052\pi$
$269$	5.37695	−	3.10438i	0.327838	−	0.189278i	0.654881	+	0.755732i	$0.272719\pi$
$270$	−5.25891	−	5.94803i	−0.320047	−	0.361985i
$271$	−8.73865	+	15.1358i	−0.530835	+	0.919433i	0.468517	+	0.883454i	$0.344788\pi$
$271$	−8.73865	+	15.1358i	−0.530835	+	0.919433i	−0.999353	+	0.0359791i	$0.988545\pi$
$272$	11.1755	+	10.8203i	0.677616	+	0.656075i
$273$		0			0
$274$	−4.67712	−	23.0272i	−0.282555	−	1.39112i
$275$	−0.769955	−	0.444533i	−0.0464300	−	0.0268064i
$276$	13.9075	−	18.4309i	0.837136	−	1.10941i
$277$	−5.49655	−	9.52031i	−0.330256	−	0.572020i	0.652306	−	0.757956i	$-0.273802\pi$
$277$	−5.49655	−	9.52031i	−0.330256	−	0.572020i	−0.982562	+	0.185936i	$0.940468\pi$
$278$	−24.9462	−	8.35592i	−1.49617	−	0.501155i
$279$	6.20694			0.371600
$280$		0			0
$281$	−18.5755			−1.10812			−0.554060	−	0.832477i	$-0.686922\pi$
$281$	−18.5755			−1.10812			−0.554060	+	0.832477i	$0.686922\pi$
$282$	12.9806	+	4.34795i	0.772982	+	0.258916i
$283$	−3.79275	−	6.56924i	−0.225456	−	0.390501i	0.731000	−	0.682377i	$-0.239054\pi$
$283$	−3.79275	−	6.56924i	−0.225456	−	0.390501i	−0.956456	+	0.291876i	$0.905720\pi$
$284$	17.2464	−	22.8558i	1.02339	−	1.35624i
$285$	1.07233	+	0.619112i	0.0635195	+	0.0366730i
$286$	1.60089	+	7.88176i	0.0946625	+	0.466058i
$287$		0			0
$288$	6.08720	+	3.89193i	0.358692	+	0.229334i
$289$	−0.938408	+	1.62537i	−0.0552004	+	0.0956100i
$290$	−0.465952	−	0.527009i	−0.0273616	−	0.0309470i
$291$	16.5108	−	9.53250i	0.967879	−	0.558805i
$292$	17.9527	+	2.21619i	1.05060	+	0.129693i
$293$		−	5.40695i		−	0.315878i	−0.987449	−	0.157939i	$-0.949515\pi$
$293$		−	5.40695i		−	0.315878i	0.987449	−	0.157939i	$-0.0504849\pi$
$294$		0			0
$295$			1.88432i			0.109709i
$296$	7.50343	−	0.583153i	0.436128	−	0.0338951i
$297$	4.32257	−	2.49563i	0.250821	−	0.144811i
$298$	−16.5973	+	14.6744i	−0.961457	+	0.850067i
$299$	28.1312	−	48.7248i	1.62687	−	2.81783i
$300$	2.41708	−	1.02413i	0.139550	−	0.0591283i
$301$		0			0
$302$	16.6137	−	3.37446i	0.956012	−	0.194178i
$303$	16.8495	+	9.72804i	0.967976	+	0.558861i
$304$	−3.66021	−	0.917662i	−0.209928	−	0.0526315i
$305$	−0.290231	−	0.502695i	−0.0166186	−	0.0287842i
$306$	2.23100	−	6.66056i	0.127538	−	0.380759i
$307$	5.68826			0.324646			0.162323	−	0.986738i	$-0.448101\pi$
$307$	5.68826			0.324646			0.162323	+	0.986738i	$0.448101\pi$
$308$		0			0
$309$	24.0545			1.36841
$310$	−2.18287	+	6.51684i	−0.123978	+	0.370132i
$311$	−0.0626204	−	0.108462i	−0.00355087	−	0.00615029i	0.864245	−	0.503072i	$-0.167797\pi$
$311$	−0.0626204	−	0.108462i	−0.00355087	−	0.00615029i	−0.867795	+	0.496922i	$0.834464\pi$
$312$	−21.4239	−	10.2444i	−1.21289	−	0.579974i
$313$	10.0924	+	5.82684i	0.570455	+	0.329352i	0.757331	−	0.653031i	$-0.226503\pi$
$313$	10.0924	+	5.82684i	0.570455	+	0.329352i	−0.186876	+	0.982384i	$0.559836\pi$
$314$	14.7399	−	2.99386i	0.831819	−	0.168953i
$315$		0			0
$316$	−11.6127	−	27.4075i	−0.653266	−	1.54179i
$317$	9.24841	−	16.0187i	0.519442	−	0.899701i	−0.480302	−	0.877103i	$-0.659473\pi$
$317$	9.24841	−	16.0187i	0.519442	−	0.899701i	0.999745	−	0.0225977i	$-0.00719367\pi$
$318$	6.53926	−	5.78165i	0.366703	−	0.324219i
$319$	0.382989	−	0.221119i	0.0214433	−	0.0123803i
$320$	−6.22700	+	5.02240i	−0.348100	+	0.280761i
$321$		−	10.9287i		−	0.609979i
$322$		0			0
$323$			3.66864i			0.204129i
$324$	−0.866695	+	7.02084i	−0.0481497	+	0.390047i
$325$	5.53966	−	3.19832i	0.307285	−	0.177411i
$326$	−7.35425	−	8.31793i	−0.407314	−	0.460688i
$327$	−0.652870	+	1.13080i	−0.0361038	+	0.0625336i
$328$	−1.92042	+	1.31710i	−0.106037	+	0.0727249i
$329$		0			0
$330$	0.328491	+	1.61728i	0.0180829	+	0.0890285i
$331$	−5.99633	−	3.46198i	−0.329588	−	0.190288i	0.326070	−	0.945346i	$-0.394275\pi$
$331$	−5.99633	−	3.46198i	−0.329588	−	0.190288i	−0.655658	+	0.755058i	$0.727609\pi$
$332$	6.42891	+	4.85110i	0.352832	+	0.266239i
$333$	−1.69925	−	2.94319i	−0.0931183	−	0.161286i
$334$	−10.5971	−	3.54957i	−0.579846	−	0.194224i
$335$	−9.32852			−0.509671
$336$		0			0
$337$	−15.5483			−0.846970			−0.423485	−	0.905903i	$-0.639193\pi$
$337$	−15.5483			−0.846970			−0.423485	+	0.905903i	$0.639193\pi$
$338$	−37.4364	−	12.5396i	−2.03627	−	0.682064i
$339$	−0.238497	−	0.413089i	−0.0129534	−	0.0224359i
$340$	6.20850	+	4.68479i	0.336703	+	0.254068i
$341$	−3.74178	−	2.16032i	−0.202629	−	0.116988i
$342$	0.339174	+	1.66988i	0.0183404	+	0.0902967i
$343$		0			0
$344$	23.1392	−	15.8699i	1.24758	−	0.855645i
$345$	5.77234	−	9.99799i	0.310773	−	0.538274i
$346$	−17.4517	−	19.7386i	−0.938211	−	1.06115i
$347$	20.2735	−	11.7049i	1.08834	−	0.628353i	0.155205	−	0.987882i	$-0.450396\pi$
$347$	20.2735	−	11.7049i	1.08834	−	0.628353i	0.933134	+	0.359529i	$0.117063\pi$
$348$	−0.159978	+	1.29593i	−0.00857572	+	0.0694693i
$349$		−	31.1435i		−	1.66707i	−0.552465	−	0.833536i	$-0.686313\pi$
$349$		−	31.1435i		−	1.66707i	0.552465	−	0.833536i	$-0.313687\pi$
$350$		0			0
$351$			35.9111i			1.91679i
$352$	−2.31501	−	4.46484i	−0.123391	−	0.237977i
$353$	8.85370	−	5.11168i	0.471235	−	0.272068i	−0.245522	−	0.969391i	$-0.578959\pi$
$353$	8.85370	−	5.11168i	0.471235	−	0.272068i	0.716756	+	0.697324i	$0.245626\pi$
$354$	2.62040	−	2.31681i	0.139272	−	0.123137i
$355$	7.15815	−	12.3983i	0.379915	−	0.658032i
$356$	−4.69504	−	11.0809i	−0.248836	−	0.587286i
$357$		0			0
$358$	−28.4374	+	5.77600i	−1.50296	+	0.305271i
$359$	−9.79157	−	5.65316i	−0.516779	−	0.298363i	0.218837	−	0.975761i	$-0.429774\pi$
$359$	−9.79157	−	5.65316i	−0.516779	−	0.298363i	−0.735616	+	0.677399i	$0.763107\pi$
$360$	3.25908	+	1.55841i	0.171769	+	0.0821357i
$361$	9.05502	+	15.6838i	0.476580	+	0.825461i
$362$	−5.96020	+	17.7939i	−0.313261	+	0.935225i
$363$	13.4005			0.703346
$364$		0			0
$365$	9.04450			0.473411
$366$	−0.342219	+	1.02168i	−0.0178881	+	0.0534039i
$367$	11.4577	+	19.8454i	0.598090	+	1.03592i	0.993103	+	0.117246i	$0.0374067\pi$
$367$	11.4577	+	19.8454i	0.598090	+	1.03592i	−0.395013	+	0.918675i	$0.629260\pi$
$368$	−8.55590	+	34.1263i	−0.446007	+	1.77896i
$369$	0.910669	+	0.525775i	0.0474075	+	0.0273708i
$370$	3.68773	−	0.749025i	0.191716	−	0.0389400i
$371$		0			0
$372$	11.7464	−	4.97702i	0.609022	−	0.258046i
$373$	5.60441	−	9.70712i	0.290185	−	0.502616i	−0.683668	−	0.729793i	$-0.739616\pi$
$373$	5.60441	−	9.70712i	0.290185	−	0.502616i	0.973853	+	0.227177i	$0.0729497\pi$
$374$	−3.66313	+	3.23874i	−0.189416	+	0.167471i
$375$	1.13670	−	0.656274i	0.0586989	−	0.0338898i
$376$	−20.7966	+	1.61627i	−1.07250	+	0.0833530i
$377$			3.18181i			0.163871i
$378$		0			0
$379$			24.2647i			1.24639i	0.782065	+	0.623197i	$0.214166\pi$
$379$			24.2647i			1.24639i	−0.782065	+	0.623197i	$0.785834\pi$
$380$	−1.87253	−	0.231157i	−0.0960590	−	0.0118581i
$381$	2.80446	−	1.61916i	0.143677	−	0.0829519i
$382$	19.3917	+	21.9327i	0.992167	+	1.12218i
$383$	4.03102	−	6.98193i	0.205976	−	0.356760i	−0.744468	−	0.667659i	$-0.767297\pi$
$383$	4.03102	−	6.98193i	0.205976	−	0.356760i	0.950443	+	0.310899i	$0.100630\pi$
$384$	14.6405	+	2.48432i	0.747120	+	0.126777i
$385$		0			0
$386$	4.95290	+	24.3850i	0.252096	+	1.24116i
$387$	−10.9727	−	6.33509i	−0.557774	−	0.322031i
$388$	−17.4981	+	23.1893i	−0.888330	+	1.17726i
$389$	−6.98572	−	12.0996i	−0.354190	−	0.613475i	0.632789	−	0.774324i	$-0.281910\pi$
$389$	−6.98572	−	12.0996i	−0.354190	−	0.613475i	−0.986979	+	0.160849i	$0.948577\pi$
$390$	−11.2588	−	3.77122i	−0.570111	−	0.190963i
$391$	34.2049			1.72982
$392$		0			0
$393$	−0.371342			−0.0187317
$394$	31.9620	+	10.7059i	1.61022	+	0.539356i
$395$	−7.44154	−	12.8891i	−0.374425	−	0.648523i
$396$	−1.36794	+	1.81286i	−0.0687416	+	0.0910997i
$397$	−9.84236	−	5.68249i	−0.493974	−	0.285196i	0.232248	−	0.972657i	$-0.425392\pi$
$397$	−9.84236	−	5.68249i	−0.493974	−	0.285196i	−0.726221	+	0.687461i	$0.758725\pi$
$398$	−5.21014	−	25.6514i	−0.261161	−	1.28579i
$399$		0			0
$400$	−2.78238	+	2.87374i	−0.139119	+	0.143687i
$401$	1.88851	−	3.27099i	0.0943076	−	0.163346i	−0.815012	−	0.579444i	$-0.803270\pi$
$401$	1.88851	−	3.27099i	0.0943076	−	0.163346i	0.909319	+	0.416099i	$0.136603\pi$
$402$	11.4696	+	12.9725i	0.572051	+	0.647010i
$403$	26.9213	−	15.5430i	1.34104	−	0.774253i
$404$	−29.4229	−	3.63215i	−1.46385	−	0.180706i
$405$			3.53706i			0.175758i
$406$		0			0
$407$			2.36568i			0.117263i
$408$	−1.11866	−	14.3938i	−0.0553818	−	0.712597i
$409$	−12.1060	+	6.98940i	−0.598603	+	0.345603i	−0.768492	−	0.639860i	$-0.778992\pi$
$409$	−12.1060	+	6.98940i	−0.598603	+	0.345603i	0.169889	+	0.985463i	$0.445659\pi$
$410$	−0.872291	+	0.771232i	−0.0430794	+	0.0380884i
$411$	−10.9041	+	18.8864i	−0.537859	+	0.931599i
$412$	−33.7487	+	14.2995i	−1.66268	+	0.704486i
$413$		0			0
$414$	15.5693	−	3.16232i	0.765188	−	0.155420i
$415$	3.48741	+	2.01346i	0.171190	+	0.0988367i
$416$	36.1478	+	1.63725i	1.77229	+	0.0802730i
$417$	12.2086	+	21.1459i	0.597857	+	1.03552i
$418$	0.376732	−	1.12472i	0.0184266	−	0.0550116i
$419$	6.23483			0.304591			0.152296	−	0.988335i	$-0.451333\pi$
$419$	6.23483			0.304591			0.152296	+	0.988335i	$0.451333\pi$
$420$		0			0
$421$	−9.67347			−0.471456			−0.235728	−	0.971819i	$-0.575747\pi$
$421$	−9.67347			−0.471456			−0.235728	+	0.971819i	$0.575747\pi$
$422$	4.02538	−	12.0176i	0.195952	−	0.585006i
$423$	4.70966	+	8.15737i	0.228991	+	0.396625i
$424$	−5.73767	+	11.9991i	−0.278646	+	0.582726i
$425$	3.36785	+	1.94443i	0.163365	+	0.0943186i
$426$	−26.0425	+	5.28957i	−1.26176	+	0.256280i
$427$		0			0
$428$	6.49670	+	15.3330i	0.314030	+	0.741150i
$429$	3.73226	−	6.46446i	0.180195	−	0.312107i
$430$	10.5103	−	9.29261i	0.506851	−	0.448129i
$431$	−7.34260	+	4.23925i	−0.353680	+	0.204197i	−0.666305	−	0.745679i	$-0.732125\pi$
$431$	−7.34260	+	4.23925i	−0.353680	+	0.204197i	0.312625	+	0.949877i	$0.398792\pi$
$432$	−6.16163	−	21.5943i	−0.296452	−	1.03896i
$433$			24.9330i			1.19820i	0.800674	+	0.599101i	$0.204475\pi$
$433$			24.9330i			1.19820i	−0.800674	+	0.599101i	$0.795525\pi$
$434$		0			0
$435$			0.652885i			0.0313035i
$436$	0.243761	−	1.97464i	0.0116740	−	0.0945680i
$437$	−7.18590	+	4.14878i	−0.343748	+	0.198463i
$438$	−11.1204	−	12.5775i	−0.531352	−	0.600978i
$439$	12.7059	−	22.0072i	0.606418	−	1.05035i	−0.385408	−	0.922746i	$-0.625939\pi$
$439$	12.7059	−	22.0072i	0.606418	−	1.05035i	0.991826	−	0.127600i	$-0.0407275\pi$
$440$	−1.42229	−	2.07379i	−0.0678052	−	0.0988640i
$441$		0			0
$442$	−7.00242	−	34.4755i	−0.333071	−	1.63983i
$443$	20.7750	+	11.9944i	0.987049	+	0.569873i	0.904391	−	0.426705i	$-0.140326\pi$
$443$	20.7750	+	11.9944i	0.987049	+	0.569873i	0.0826584	+	0.996578i	$0.473659\pi$
$444$	−5.57574	−	4.20732i	−0.264613	−	0.199671i
$445$	−3.00863	−	5.21110i	−0.142623	−	0.247030i
$446$	22.0223	+	7.37654i	1.04279	+	0.349289i
$447$	20.5616			0.972530
$448$		0			0
$449$	−17.1281			−0.808326			−0.404163	−	0.914687i	$-0.632437\pi$
$449$	−17.1281			−0.808326			−0.404163	+	0.914687i	$0.632437\pi$
$450$	1.71273	+	0.573692i	0.0807389	+	0.0270441i
$451$	−0.365990	−	0.633914i	−0.0172338	−	0.0298498i
$452$	0.580180	+	0.437790i	0.0272894	+	0.0205919i
$453$	−13.6262	−	7.86712i	−0.640217	−	0.369629i
$454$	−3.57834	−	17.6175i	−0.167940	−	0.826830i
$455$		0			0
$456$	1.98086	+	2.88821i	0.0927623	+	0.135253i
$457$	5.59177	−	9.68522i	0.261572	−	0.453056i	−0.705088	−	0.709120i	$-0.749093\pi$
$457$	5.59177	−	9.68522i	0.261572	−	0.453056i	0.966660	+	0.256064i	$0.0824258\pi$
$458$	16.2023	+	18.3254i	0.757084	+	0.856290i
$459$	−18.9073	+	10.9161i	−0.882516	+	0.509521i
$460$	−2.15521	+	17.4587i	−0.100487	+	0.814018i
$461$		−	25.3723i		−	1.18170i	−0.806780	−	0.590852i	$-0.798792\pi$
$461$		−	25.3723i		−	1.18170i	0.806780	−	0.590852i	$-0.201208\pi$
$462$		0			0
$463$		−	0.0511973i		−	0.00237934i	−0.999999	−	0.00118967i	$-0.999621\pi$
$463$		−	0.0511973i		−	0.00237934i	0.999999	−	0.00118967i	$-0.000378684\pi$
$464$	−0.545935	−	1.91331i	−0.0253444	−	0.0888231i
$465$	5.52407	−	3.18932i	0.256173	−	0.147901i
$466$	−25.1605	+	22.2455i	−1.16554	+	1.03050i
$467$	6.64553	−	11.5104i	0.307518	−	0.532638i	−0.670300	−	0.742090i	$-0.733835\pi$
$467$	6.64553	−	11.5104i	0.307518	−	0.532638i	0.977819	+	0.209452i	$0.0671681\pi$
$468$	−6.37467	−	15.0450i	−0.294669	−	0.695457i
$469$		0			0
$470$	−10.2209	+	2.07601i	−0.471457	+	0.0957591i
$471$	−12.0894	−	6.97979i	−0.557048	−	0.321612i
$472$	−2.29918	+	4.80824i	−0.105828	+	0.221317i
$473$	4.40984	+	7.63806i	0.202765	+	0.351199i
$474$	−8.77450	+	26.1959i	−0.403026	+	1.20322i
$475$	−0.943374			−0.0432850
$476$		0			0
$477$	6.00595			0.274994
$478$	4.58305	−	13.6825i	0.209624	−	0.625822i
$479$	−4.83560	−	8.37550i	−0.220944	−	0.382686i	0.734151	−	0.678986i	$-0.237580\pi$
$479$	−4.83560	−	8.37550i	−0.220944	−	0.382686i	−0.955095	+	0.296300i	$0.904247\pi$
$480$	7.41729	+	0.335953i	0.338551	+	0.0153341i
$481$	−14.7403	−	8.51029i	−0.672098	−	0.388036i
$482$	−3.22701	+	0.655449i	−0.146986	+	0.0298549i
$483$		0			0
$484$	−18.8011	+	7.96614i	−0.854595	+	0.362097i
$485$	−7.26259	+	12.5792i	−0.329777	+	0.571191i
$486$	−12.9253	+	11.4279i	−0.586305	+	0.518378i
$487$	−5.92989	+	3.42363i	−0.268709	+	0.155139i	−0.628301	−	0.777970i	$-0.716249\pi$
$487$	−5.92989	+	3.42363i	−0.268709	+	0.155139i	0.359592	+	0.933110i	$0.382916\pi$
$488$	−0.127214	−	1.63686i	−0.00575870	−	0.0740972i
$489$			10.3047i			0.465993i
$490$		0			0
$491$			24.0395i			1.08489i	0.840092	+	0.542444i	$0.182501\pi$
$491$			24.0395i			1.08489i	−0.840092	+	0.542444i	$0.817499\pi$
$492$	2.14500	+	0.264791i	0.0967039	+	0.0119377i
$493$	−1.67523	+	0.967193i	−0.0754485	+	0.0435602i
$494$	5.65269	+	6.39341i	0.254327	+	0.287653i
$495$	−0.567766	+	0.983399i	−0.0255192	+	0.0442005i
$496$	−13.5217	+	13.9656i	−0.607140	+	0.627074i
$497$		0			0
$498$	−1.48786	−	7.32527i	−0.0666725	−	0.328253i
$499$	−11.2049	−	6.46915i	−0.501600	−	0.289599i	0.227774	−	0.973714i	$-0.426855\pi$
$499$	−11.2049	−	6.46915i	−0.501600	−	0.289599i	−0.729374	+	0.684115i	$0.760189\pi$
$500$	−1.20467	+	1.59649i	−0.0538745	+	0.0713970i
$501$	5.18617	+	8.98271i	0.231701	+	0.401318i
$502$	8.77403	+	2.93893i	0.391604	+	0.131171i
$503$	32.0665			1.42978			0.714888	−	0.699239i	$-0.246478\pi$
$503$	32.0665			1.42978			0.714888	+	0.699239i	$0.246478\pi$
$504$		0			0
$505$	−14.8231			−0.659621
$506$	−10.4864	−	3.51249i	−0.466176	−	0.156149i
$507$	18.3212	+	31.7333i	0.813674	+	1.40933i
$508$	−2.97216	+	3.93884i	−0.131868	+	0.174758i
$509$	8.15433	+	4.70790i	0.361434	+	0.208674i	0.669710	−	0.742623i	$-0.266419\pi$
$509$	8.15433	+	4.70790i	0.361434	+	0.208674i	−0.308275	+	0.951297i	$0.599752\pi$
$510$	−1.43685	−	7.07414i	−0.0636247	−	0.313248i
$511$		0			0
$512$	−22.0176	+	5.21772i	−0.973050	+	0.230593i
$513$	2.64808	−	4.58660i	0.116915	−	0.202503i
$514$	18.3964	+	20.8070i	0.811430	+	0.917757i
$515$	−15.8713	+	9.16327i	−0.699371	+	0.403782i
$516$	−25.8452	−	3.19048i	−1.13777	−	0.140453i
$517$		−	6.55676i		−	0.288366i
$518$		0			0
$519$			24.4531i			1.07337i
$520$	18.0380	−	1.40189i	0.791021	−	0.0614767i
$521$	29.5858	−	17.0814i	1.29618	−	0.748348i	0.316435	−	0.948614i	$-0.397514\pi$
$521$	29.5858	−	17.0814i	1.29618	−	0.748348i	0.979742	+	0.200266i	$0.0641807\pi$
$522$	−0.673105	+	0.595122i	−0.0294610	+	0.0260478i
$523$	−16.7507	+	29.0130i	−0.732456	+	1.26865i	0.223375	+	0.974733i	$0.428293\pi$
$523$	−16.7507	+	29.0130i	−0.732456	+	1.26865i	−0.955831	+	0.293918i	$0.905041\pi$
$524$	0.520997	−	0.220749i	0.0227598	−	0.00964348i
$525$		0			0
$526$	14.8016	−	3.00639i	0.645380	−	0.131085i
$527$	16.3669	+	9.44941i	0.712952	+	0.411623i
$528$	−1.13514	+	4.52764i	−0.0494006	+	0.197040i
$529$	27.1815	+	47.0798i	1.18181	+	2.04695i
$530$	−2.11218	+	6.30582i	−0.0917473	+	0.273907i
$531$	2.40669			0.104441
$532$		0			0
$533$	5.26644			0.228115
$534$	−3.54754	+	10.5910i	−0.153517	+	0.458318i
$535$	4.16315	+	7.21079i	0.179989	+	0.311750i
$536$	−23.8036	−	11.3823i	−1.02816	−	0.491642i
$537$	23.3238	+	13.4660i	1.00650	+	0.581100i
$538$	8.60482	−	1.74775i	0.370980	−	0.0753509i
$539$		0			0
$540$	−4.38044	−	10.3384i	−0.188504	−	0.444893i
$541$	8.65326	−	14.9879i	0.372033	−	0.644380i	−0.617845	−	0.786300i	$-0.711994\pi$
$541$	8.65326	−	14.9879i	0.372033	−	0.644380i	0.989878	+	0.141920i	$0.0453276\pi$
$542$	−18.5170	+	16.3717i	−0.795373	+	0.703225i
$543$	15.0832	−	8.70827i	0.647280	−	0.373707i
$544$	10.1261	+	19.5296i	0.434151	+	0.837324i
$545$		−	0.994813i		−	0.0426131i
$546$		0			0
$547$			12.8897i			0.551122i	0.961284	+	0.275561i	$0.0888636\pi$
$547$			12.8897i			0.551122i	−0.961284	+	0.275561i	$0.911136\pi$
$548$	4.07125	−	32.9799i	0.173915	−	1.40883i
$549$	−0.642051	+	0.370688i	−0.0274021	+	0.0158206i
$550$	−0.832826	−	0.941956i	−0.0355118	−	0.0401651i
$551$	0.234626	−	0.406383i	0.00999539	−	0.0173125i
$552$	26.9285	−	18.4687i	1.14615	−	0.786081i
$553$		0			0
$554$	−3.09453	−	15.2355i	−0.131474	−	0.647295i
$555$	−3.02460	−	1.74625i	−0.128387	−	0.0741244i
$556$	−29.6993	−	22.4104i	−1.25953	−	0.950411i
$557$	17.5977	+	30.4800i	0.745636	+	1.29148i	0.949897	+	0.312564i	$0.101188\pi$
$557$	17.5977	+	30.4800i	0.745636	+	1.29148i	−0.204260	+	0.978917i	$0.565479\pi$
$558$	8.32342	+	2.78799i	0.352359	+	0.118025i
$559$	−63.4556			−2.68389
$560$		0			0
$561$	4.53807			0.191598
$562$	−24.9094	−	8.34360i	−1.05074	−	0.351954i
$563$	−2.62715	−	4.55035i	−0.110721	−	0.191775i	0.805340	−	0.592813i	$-0.201983\pi$
$563$	−2.62715	−	4.55035i	−0.110721	−	0.191775i	−0.916061	+	0.401038i	$0.868649\pi$
$564$	15.4538	+	11.6611i	0.650722	+	0.491020i
$565$	0.314723	+	0.181705i	0.0132405	+	0.00764440i
$566$	−2.13530	−	10.5129i	−0.0897533	−	0.441888i
$567$		0			0
$568$	33.3934	−	22.9026i	1.40116	−	0.960973i
$569$	7.02532	−	12.1682i	0.294517	−	0.510118i	−0.680356	−	0.732882i	$-0.738175\pi$
$569$	7.02532	−	12.1682i	0.294517	−	0.510118i	0.974872	+	0.222764i	$0.0715080\pi$
$570$	1.15990	+	1.31188i	0.0485827	+	0.0549488i
$571$	−11.4617	+	6.61743i	−0.479659	+	0.276931i	−0.720274	−	0.693689i	$-0.755984\pi$
$571$	−11.4617	+	6.61743i	−0.479659	+	0.276931i	0.240616	+	0.970620i	$0.422651\pi$
$572$	−1.39351	+	11.2884i	−0.0582655	+	0.471992i
$573$		−	27.1714i		−	1.13510i
$574$		0			0
$575$			8.79563i			0.366803i
$576$	6.41469	+	7.95323i	0.267279	+	0.331385i
$577$	8.05094	−	4.64821i	0.335165	−	0.193508i	−0.322967	−	0.946410i	$-0.604680\pi$
$577$	8.05094	−	4.64821i	0.335165	−	0.193508i	0.658132	+	0.752903i	$0.271347\pi$
$578$	−1.98846	+	1.75809i	−0.0827092	+	0.0731269i
$579$	11.5470	−	20.0001i	0.479879	−	0.831174i
$580$	−0.388117	−	0.916005i	−0.0161157	−	0.0380350i
$581$		0			0
$582$	26.4225	−	5.36675i	1.09525	−	0.222459i
$583$	−3.62061	−	2.09036i	−0.149950	−	0.0865739i
$584$	23.0789	+	11.0358i	0.955011	+	0.456663i
$585$	−4.08495	−	7.07534i	−0.168892	−	0.292529i
$586$	2.42866	−	7.25065i	0.100327	−	0.299522i
$587$	−7.75382			−0.320034			−0.160017	−	0.987114i	$-0.551155\pi$
$587$	−7.75382			−0.320034			−0.160017	+	0.987114i	$0.551155\pi$
$588$		0			0
$589$	−4.58455			−0.188903
$590$	−0.846388	+	2.52685i	−0.0348452	+	0.104029i
$591$	−15.6421	−	27.0929i	−0.643429	−	1.11445i
$592$	10.3239	+	2.58834i	0.424311	+	0.106380i
$593$	−2.79212	−	1.61203i	−0.114659	−	0.0661983i	0.441574	−	0.897225i	$-0.354420\pi$
$593$	−2.79212	−	1.61203i	−0.114659	−	0.0661983i	−0.556233	+	0.831027i	$0.687754\pi$
$594$	6.91747	−	1.40503i	0.283827	−	0.0576490i
$595$		0			0
$596$	−28.8481	+	12.2231i	−1.18167	+	0.500679i
$597$	−12.1468	+	21.0388i	−0.497134	+	0.861061i
$598$	59.6095	−	52.7034i	2.43761	−	2.15520i
$599$	15.7055	−	9.06755i	0.641707	−	0.370490i	−0.143565	−	0.989641i	$-0.545856\pi$
$599$	15.7055	−	9.06755i	0.641707	−	0.370490i	0.785272	+	0.619151i	$0.212523\pi$
$600$	3.70129	−	0.287657i	0.151104	−	0.0117436i
$601$			40.6079i			1.65643i	0.560408	+	0.828216i	$0.310644\pi$
$601$			40.6079i			1.65643i	−0.560408	+	0.828216i	$0.689356\pi$
$602$		0			0
$603$			11.9145i			0.485198i
$604$	23.7945	+	2.93734i	0.968184	+	0.119518i
$605$	−8.84174	+	5.10478i	−0.359468	+	0.207539i
$606$	18.2253	+	20.6135i	0.740353	+	0.837366i
$607$	9.03433	−	15.6479i	0.366692	−	0.635129i	−0.622354	−	0.782736i	$-0.713824\pi$
$607$	9.03433	−	15.6479i	0.366692	−	0.635129i	0.989046	+	0.147607i	$0.0471570\pi$
$608$	−4.49611	−	2.87464i	−0.182341	−	0.116582i
$609$		0			0
$610$	−0.163399	−	0.804471i	−0.00661582	−	0.0325721i
$611$	40.8543	+	23.5872i	1.65279	+	0.954237i
$612$	5.98349	−	7.92961i	0.241868	−	0.320535i
$613$	−17.4060	−	30.1480i	−0.703020	−	1.21767i	−0.967401	−	0.253248i	$-0.918501\pi$
$613$	−17.4060	−	30.1480i	−0.703020	−	1.21767i	0.264381	−	0.964418i	$-0.414832\pi$
$614$	7.62787	+	2.55501i	0.307836	+	0.103112i
$615$	1.08064			0.0435756
$616$		0			0
$617$	10.5532			0.424854			0.212427	−	0.977177i	$-0.431863\pi$
$617$	10.5532			0.424854			0.212427	+	0.977177i	$0.431863\pi$
$618$	32.2567	+	10.8046i	1.29756	+	0.434626i
$619$	12.3185	+	21.3363i	0.495123	+	0.857579i	0.999984	−	0.00562191i	$-0.00178952\pi$
$619$	12.3185	+	21.3363i	0.495123	+	0.857579i	−0.504861	+	0.863201i	$0.668456\pi$
$620$	−5.85439	+	7.75851i	−0.235118	+	0.311589i
$621$	−42.7636	−	24.6896i	−1.71604	−	0.990758i
$622$	−0.0352549	−	0.173573i	−0.00141359	−	0.00695964i
$623$		0			0
$624$	−24.1276	−	23.3606i	−0.965877	−	0.935172i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	10.9165	+	12.3469i	0.436310	+	0.493483i
$627$	−0.953376	+	0.550432i	−0.0380742	+	0.0219821i
$628$	21.1107	+	2.60604i	0.842409	+	0.103992i
$629$		−	10.3477i		−	0.412590i
$630$		0			0
$631$		−	18.9068i		−	0.752668i	−0.926484	−	0.376334i	$-0.877185\pi$
$631$		−	18.9068i		−	0.752668i	0.926484	−	0.376334i	$-0.122815\pi$
$632$	−3.26177	−	41.9692i	−0.129746	−	1.66944i
$633$	−10.1868	+	5.88136i	−0.404889	+	0.233763i
$634$	19.5972	−	17.3267i	0.778303	−	0.688132i
$635$	−1.23360	+	2.13665i	−0.0489538	+	0.0847905i
$636$	11.3660	−	4.81585i	0.450692	−	0.190961i
$637$		0			0
$638$	0.612904	−	0.124489i	0.0242651	−	0.00492856i
$639$	−15.8353	−	9.14251i	−0.626434	−	0.361672i
$640$	−10.6062	+	3.93796i	−0.419249	+	0.155662i
$641$	7.64681	+	13.2447i	0.302031	+	0.523133i	0.976596	−	0.215083i	$-0.0690020\pi$
$641$	7.64681	+	13.2447i	0.302031	+	0.523133i	−0.674565	+	0.738216i	$0.735669\pi$
$642$	4.90887	−	14.6552i	0.193738	−	0.578394i
$643$	13.9558			0.550362			0.275181	−	0.961393i	$-0.411262\pi$
$643$	13.9558			0.550362			0.275181	+	0.961393i	$0.411262\pi$
$644$		0			0
$645$	−13.0207			−0.512688
$646$	−1.64786	+	4.91960i	−0.0648341	+	0.193559i
$647$	−14.1146	−	24.4473i	−0.554904	−	0.961122i	−0.997911	−	0.0646035i	$-0.979422\pi$
$647$	−14.1146	−	24.4473i	−0.554904	−	0.961122i	0.443007	−	0.896518i	$-0.353912\pi$
$648$	−4.31580	+	9.02555i	−0.169541	+	0.354557i
$649$	−1.45084	−	0.837644i	−0.0569506	−	0.0328804i
$650$	8.86520	−	1.80064i	0.347722	−	0.0706268i
$651$		0			0
$652$	−6.12576	−	14.4576i	−0.239903	−	0.566202i
$653$	−12.6553	+	21.9196i	−0.495240	+	0.857781i	−0.999985	−	0.00548743i	$-0.998253\pi$
$653$	−12.6553	+	21.9196i	−0.495240	+	0.857781i	0.504745	+	0.863269i	$0.331587\pi$
$654$	−1.38342	+	1.22314i	−0.0540959	+	0.0478286i
$655$	0.245013	−	0.141458i	0.00957346	−	0.00552724i
$656$	−3.16686	+	0.903617i	−0.123645	+	0.0352803i
$657$		−	11.5518i		−	0.450678i
$658$		0			0
$659$		−	27.5411i		−	1.07285i	−0.843948	−	0.536425i	$-0.819774\pi$
$659$		−	27.5411i		−	1.07285i	0.843948	−	0.536425i	$-0.180226\pi$
$660$	−0.285939	+	2.31630i	−0.0111301	+	0.0901620i
$661$	19.4724	−	11.2424i	0.757390	−	0.437279i	−0.0709679	−	0.997479i	$-0.522609\pi$
$661$	19.4724	−	11.2424i	0.757390	−	0.437279i	0.828358	+	0.560199i	$0.189275\pi$
$662$	−6.48596	−	7.33586i	−0.252084	−	0.285116i
$663$	−16.3252	+	28.2761i	−0.634019	+	1.09815i
$664$	6.44209	+	9.39295i	0.250002	+	0.364517i
$665$		0			0
$666$	−0.956668	−	4.71003i	−0.0370701	−	0.182510i
$667$	−3.78895	−	2.18755i	−0.146709	−	0.0847024i
$668$	−12.6162	−	9.51985i	−0.488134	−	0.368334i
$669$	−10.7776	−	18.6674i	−0.416688	−	0.721725i
$670$	−12.5094	−	4.19012i	−0.483281	−	0.161879i
$671$	0.516070			0.0199227
$672$		0			0
$673$	−11.4276			−0.440501			−0.220251	−	0.975443i	$-0.570688\pi$
$673$	−11.4276			−0.440501			−0.220251	+	0.975443i	$0.570688\pi$
$674$	−20.8501	−	6.98389i	−0.803114	−	0.269009i
$675$	−2.80703	−	4.86191i	−0.108043	−	0.187135i
$676$	−44.5692	−	33.6308i	−1.71420	−	1.29349i
$677$	−39.9384	−	23.0585i	−1.53496	−	0.886209i	−0.999122	−	0.0418868i	$-0.986663\pi$
$677$	−39.9384	−	23.0585i	−1.53496	−	0.886209i	−0.535836	−	0.844322i	$-0.680004\pi$
$678$	−0.134273	−	0.661073i	−0.00515671	−	0.0253884i
$679$		0			0
$680$	6.22123	+	9.07093i	0.238573	+	0.347854i
$681$	−8.34244	+	14.4495i	−0.319683	+	0.553707i
$682$	−4.04732	−	4.57766i	−0.154980	−	0.175288i
$683$	27.9026	−	16.1096i	1.06766	−	0.616416i	0.140122	−	0.990134i	$-0.455250\pi$
$683$	27.9026	−	16.1096i	1.06766	−	0.616416i	0.927542	+	0.373718i	$0.121917\pi$
$684$	−0.295238	+	2.39163i	−0.0112887	+	0.0914464i
$685$		−	16.6151i		−	0.634832i
$686$		0			0
$687$		−	22.7024i		−	0.866152i
$688$	38.1577	−	10.8877i	1.45475	−	0.415091i
$689$	26.0495	−	15.0397i	0.992408	−	0.572967i
$690$	12.2315	−	10.8144i	0.465644	−	0.411697i
$691$	15.5135	−	26.8703i	0.590163	−	1.02219i	−0.404047	−	0.914738i	$-0.632397\pi$
$691$	15.5135	−	26.8703i	0.590163	−	1.02219i	0.994210	−	0.107454i	$-0.0342699\pi$
$692$	−14.5365	−	34.3080i	−0.552595	−	1.30419i
$693$		0			0
$694$	32.4440	−	6.58980i	1.23156	−	0.250146i
$695$	−16.1106	−	9.30144i	−0.611109	−	0.352824i
$696$	−0.796627	+	1.66597i	−0.0301961	+	0.0631485i
$697$	1.60087	+	2.77279i	0.0606374	+	0.105027i
$698$	13.9888	−	41.7630i	0.529485	−	1.58075i
$699$	31.1701			1.17896
$700$		0			0
$701$	31.9213			1.20565			0.602826	−	0.797873i	$-0.294041\pi$
$701$	31.9213			1.20565			0.602826	+	0.797873i	$0.294041\pi$
$702$	−16.1303	+	48.1563i	−0.608799	+	1.81754i
$703$	1.25509	+	2.17389i	0.0473368	+	0.0819897i
$704$	−1.09891	−	7.02713i	−0.0414167	−	0.264845i
$705$	8.38302	+	4.83994i	0.315723	+	0.182283i
$706$	14.1687	−	2.87785i	0.533247	−	0.108309i
$707$		0			0
$708$	4.55456	−	1.92979i	0.171171	−	0.0725261i
$709$	2.49320	−	4.31835i	0.0936342	−	0.162179i	−0.815404	−	0.578893i	$-0.803485\pi$
$709$	2.49320	−	4.31835i	0.0936342	−	0.162179i	0.909038	+	0.416714i	$0.136818\pi$
$710$	15.1680	−	13.4107i	0.569243	−	0.503293i
$711$	−16.4622	+	9.50447i	−0.617381	+	0.356445i
$712$	−1.31874	−	16.9682i	−0.0494218	−	0.635910i
$713$			42.7445i			1.60079i
$714$		0			0
$715$			5.68704i			0.212683i
$716$	−40.7285	−	5.02778i	−1.52210	−	0.187897i
$717$	−11.5981	+	6.69616i	−0.433139	+	0.250073i
$718$	−10.5911	−	11.9789i	−0.395256	−	0.447050i
$719$	8.64963	−	14.9816i	0.322577	−	0.558720i	−0.658442	−	0.752631i	$-0.728784\pi$
$719$	8.64963	−	14.9816i	0.322577	−	0.558720i	0.981019	+	0.193912i	$0.0621176\pi$
$720$	3.67038	+	3.55370i	0.136787	+	0.132439i
$721$		0			0
$722$	5.09793	+	25.0990i	0.189725	+	0.934087i
$723$	2.64673	+	1.52809i	0.0984331	+	0.0568304i
$724$	−15.9851	+	21.1842i	−0.594081	+	0.787304i
$725$	−0.248709	−	0.430777i	−0.00923682	−	0.0159986i
$726$	17.9699	+	6.01917i	0.666927	+	0.223392i
$727$	4.42613			0.164156			0.0820780	−	0.996626i	$-0.473844\pi$
$727$	4.42613			0.164156			0.0820780	+	0.996626i	$0.473844\pi$
$728$		0			0
$729$	26.6237			0.986065
$730$	12.1285	+	4.06255i	0.448897	+	0.150362i
$731$	−19.2890	−	33.4095i	−0.713430	−	1.23570i
$732$	−0.917821	+	1.21634i	−0.0339236	+	0.0449572i
$733$	32.3952	+	18.7034i	1.19655	+	0.690826i	0.959783	−	0.280742i	$-0.0905806\pi$
$733$	32.3952	+	18.7034i	1.19655	+	0.690826i	0.236762	+	0.971568i	$0.423914\pi$
$734$	6.45065	+	31.7589i	0.238098	+	1.17224i
$735$		0			0
$736$	−26.8020	+	41.9198i	−0.987934	+	1.54519i
$737$	4.14684	−	7.18254i	0.152751	−	0.264572i
$738$	0.985030	+	1.11411i	0.0362595	+	0.0410108i
$739$	−36.2776	+	20.9449i	−1.33449	+	0.770469i	−0.985984	−	0.166837i	$-0.946645\pi$
$739$	−36.2776	+	20.9449i	−1.33449	+	0.770469i	−0.348507	+	0.937306i	$0.613311\pi$
$740$	5.28163	+	0.651997i	0.194157	+	0.0239679i
$741$		−	7.92048i		−	0.290966i
$742$		0			0
$743$		−	33.0690i		−	1.21318i	−0.795014	−	0.606591i	$-0.792536\pi$
$743$		−	33.0690i		−	1.21318i	0.795014	−	0.606591i	$-0.207464\pi$
$744$	17.9873	−	1.39794i	0.659446	−	0.0512510i
$745$	−13.5666	+	7.83270i	−0.497043	+	0.286968i
$746$	11.8756	−	10.4998i	0.434797	−	0.384424i
$747$	2.57162	−	4.45418i	0.0940907	−	0.162970i
$748$	−6.36696	+	2.69772i	−0.232799	+	0.0986384i
$749$		0			0
$750$	1.81908	−	0.369479i	0.0664234	−	0.0134915i
$751$	5.95362	+	3.43732i	0.217251	+	0.125430i	0.604677	−	0.796471i	$-0.293302\pi$
$751$	5.95362	+	3.43732i	0.217251	+	0.125430i	−0.387426	+	0.921901i	$0.626636\pi$
$752$	−28.6139	−	7.17387i	−1.04344	−	0.261604i
$753$	−4.29398	−	7.43739i	−0.156481	−	0.271034i
$754$	−1.42918	+	4.26676i	−0.0520478	+	0.155386i
$755$	11.9875			0.436272
$756$		0			0
$757$	18.4550			0.670758			0.335379	−	0.942083i	$-0.391136\pi$
$757$	18.4550			0.670758			0.335379	+	0.942083i	$0.391136\pi$
$758$	−10.8991	+	32.5386i	−0.395871	+	1.18186i
$759$	5.13200	+	8.88888i	0.186280	+	0.322646i
$760$	−2.40721	−	1.15107i	−0.0873188	−	0.0417537i
$761$	35.2440	+	20.3481i	1.27759	+	0.737618i	0.976405	−	0.215946i	$-0.0692837\pi$
$761$	35.2440	+	20.3481i	1.27759	+	0.737618i	0.301187	+	0.953565i	$0.402617\pi$
$762$	4.48803	−	0.911577i	0.162584	−	0.0330229i
$763$		0			0
$764$	16.1524	+	38.1218i	0.584374	+	1.37920i
$765$	2.48346	−	4.30147i	0.0897895	−	0.155520i
$766$	8.54164	−	7.55205i	0.308622	−	0.272866i
$767$	10.4385	−	6.02667i	0.376912	−	0.217610i
$768$	18.5168	+	9.90756i	0.668168	+	0.357508i
$769$			39.5711i			1.42697i	0.700670	+	0.713485i	$0.252885\pi$
$769$			39.5711i			1.42697i	−0.700670	+	0.713485i	$0.747115\pi$
$770$		0			0
$771$		−	25.7768i		−	0.928327i
$772$	−4.31130	+	34.9246i	−0.155167	+	1.25696i
$773$	−12.9250	+	7.46225i	−0.464880	+	0.268399i	−0.714094	−	0.700050i	$-0.753161\pi$
$773$	−12.9250	+	7.46225i	−0.464880	+	0.268399i	0.249214	+	0.968448i	$0.419828\pi$
$774$	−11.8687	−	13.4239i	−0.426611	−	0.482513i
$775$	−2.42987	+	4.20866i	−0.0872835	+	0.151179i
$776$	−33.8807	+	23.2368i	−1.21624	+	0.834153i
$777$		0			0
$778$	−3.93292	−	19.3632i	−0.141002	−	0.694205i
$779$	−0.672635	−	0.388346i	−0.0240997	−	0.0139139i
$780$	−13.4039	−	10.1143i	−0.479938	−	0.362150i
$781$	6.36407	+	11.0229i	0.227724	+	0.394430i
$782$	45.8683	+	15.3639i	1.64025	+	0.549413i
$783$	2.79253			0.0997969
$784$		0			0
$785$	10.6355			0.379597
$786$	−0.497964	−	0.166797i	−0.0177618	−	0.00594945i
$787$	−14.6145	−	25.3131i	−0.520952	−	0.902315i	−0.999703	−	0.0243647i	$-0.992244\pi$
$787$	−14.6145	−	25.3131i	−0.520952	−	0.902315i	0.478751	−	0.877951i	$-0.341090\pi$
$788$	38.0517	+	28.7129i	1.35554	+	1.02286i
$789$	−12.1400	−	7.00901i	−0.432194	−	0.249528i
$790$	−4.18955	−	20.6267i	−0.149057	−	0.733865i
$791$		0			0
$792$	−2.64868	+	1.81658i	−0.0941167	+	0.0645493i
$793$	−1.85651	+	3.21556i	−0.0659264	+	0.114188i
$794$	−10.6460	−	12.0411i	−0.377814	−	0.427321i
$795$	5.34519	−	3.08605i	0.189574	−	0.109451i
$796$	4.53522	−	36.7385i	0.160747	−	1.30216i
$797$		−	32.2478i		−	1.14228i	−0.820854	−	0.571138i	$-0.806502\pi$
$797$		−	32.2478i		−	1.14228i	0.820854	−	0.571138i	$-0.193498\pi$
$798$		0			0
$799$			28.6798i			1.01462i
$800$	−5.02194	+	2.60387i	−0.177552	+	0.0920606i
$801$	−6.65570	+	3.84267i	−0.235168	+	0.135774i
$802$	4.00171	−	3.53809i	0.141305	−	0.124934i
$803$	−4.02058	+	6.96385i	−0.141883	+	0.245749i
$804$	9.55364	+	22.5478i	0.336931	+	0.795199i
$805$		0			0
$806$	43.0826	−	8.75063i	1.51752	−	0.308228i
$807$	−7.05750	−	4.07465i	−0.248436	−	0.143435i
$808$	−37.8243	−	18.0867i	−1.33065	−	0.636286i
$809$	−9.03143	−	15.6429i	−0.317528	−	0.549975i	0.662443	−	0.749112i	$-0.269519\pi$
$809$	−9.03143	−	15.6429i	−0.317528	−	0.549975i	−0.979972	+	0.199137i	$0.936186\pi$
$810$	−1.58876	+	4.74315i	−0.0558232	+	0.166657i
$811$	−26.8176			−0.941692			−0.470846	−	0.882215i	$-0.656051\pi$
$811$	−26.8176			−0.941692			−0.470846	+	0.882215i	$0.656051\pi$
$812$		0			0
$813$	22.9398			0.804534
$814$	−1.06260	+	3.17235i	−0.0372442	+	0.111191i
$815$	−3.92545	−	6.79907i	−0.137502	−	0.238161i
$816$	4.96519	−	19.8043i	0.173816	−	0.693289i
$817$	8.10462	+	4.67920i	0.283545	+	0.163705i
$818$	−19.3734	+	3.93499i	−0.677375	+	0.137584i
$819$		0			0
$820$	−1.51615	+	0.642401i	−0.0529462	+	0.0224336i
$821$	−4.09094	+	7.08571i	−0.142775	+	0.247293i	−0.928540	−	0.371231i	$-0.878936\pi$
$821$	−4.09094	+	7.08571i	−0.142775	+	0.247293i	0.785766	+	0.618524i	$0.212269\pi$
$822$	−23.1055	+	20.4286i	−0.805897	+	0.712530i
$823$	−29.7686	+	17.1869i	−1.03767	+	0.599097i	−0.919172	−	0.393857i	$-0.871140\pi$
$823$	−29.7686	+	17.1869i	−1.03767	+	0.599097i	−0.118495	+	0.992955i	$0.537807\pi$
$824$	−51.6795	+	4.01644i	−1.80034	+	0.139919i
$825$			1.16694i			0.0406277i
$826$		0			0
$827$		−	41.6060i		−	1.44678i	−0.690439	−	0.723391i	$-0.742582\pi$
$827$		−	41.6060i		−	1.44678i	0.690439	−	0.723391i	$-0.257418\pi$
$828$	22.2986	+	2.75267i	0.774930	+	0.0956620i
$829$	−2.96337	+	1.71090i	−0.102922	+	0.0594222i	−0.550578	−	0.834784i	$-0.685592\pi$
$829$	−2.96337	+	1.71090i	−0.102922	+	0.0594222i	0.447655	+	0.894206i	$0.352259\pi$
$830$	3.77217	+	4.26647i	0.130934	+	0.148091i
$831$	−7.21449	+	12.4959i	−0.250268	+	0.433477i
$832$	47.7383	+	18.4322i	1.65503	+	0.639021i
$833$		0			0
$834$	6.87337	+	33.8401i	0.238005	+	1.17179i
$835$	−6.84372	−	3.95122i	−0.236837	−	0.136738i
$836$	1.01038	−	1.33901i	0.0349449	−	0.0463106i
$837$	−13.6414	−	23.6276i	−0.471517	−	0.816691i
$838$	8.36081	+	2.80052i	0.288820	+	0.0967423i
$839$	−42.9230			−1.48187			−0.740933	−	0.671579i	$-0.765616\pi$
$839$	−42.9230			−1.48187			−0.740933	+	0.671579i	$0.765616\pi$
$840$		0			0
$841$	−28.7526			−0.991468
$842$	−12.9720	−	4.34506i	−0.447044	−	0.149741i
$843$	12.1906	+	21.1147i	0.419866	+	0.727230i
$844$	10.7959	−	14.3073i	0.371612	−	0.492477i
$845$	−24.1769	−	13.9585i	−0.831710	−	0.480188i
$846$	2.65151	+	13.0544i	0.0911609	+	0.448818i
$847$		0			0
$848$	−13.0838	+	13.5134i	−0.449299	+	0.464051i
$849$	−4.97817	+	8.62244i	−0.170850	+	0.295921i
$850$	3.64285	+	4.12020i	0.124949	+	0.141322i
$851$	20.2684	−	11.7020i	0.694792	−	0.401139i
$852$	−37.2985	−	4.60436i	−1.27783	−	0.157743i
$853$			31.3541i			1.07355i	0.843727	+	0.536773i	$0.180357\pi$
$853$			31.3541i			1.07355i	−0.843727	+	0.536773i	$0.819643\pi$
$854$		0			0
$855$			1.20489i			0.0412065i
$856$	1.82479	+	23.4795i	0.0623700	+	0.802514i
$857$	−30.2447	+	17.4618i	−1.03314	+	0.596484i	−0.917883	−	0.396852i	$-0.870103\pi$
$857$	−30.2447	+	17.4618i	−1.03314	+	0.596484i	−0.115257	+	0.993336i	$0.536769\pi$
$858$	7.90857	−	6.99232i	0.269994	−	0.238714i
$859$	−21.1548	+	36.6412i	−0.721793	+	1.25018i	0.238488	+	0.971145i	$0.423348\pi$
$859$	−21.1548	+	36.6412i	−0.721793	+	1.25018i	−0.960281	+	0.279036i	$0.909985\pi$
$860$	18.2681	−	7.74032i	0.622938	−	0.263943i
$861$		0			0
$862$	−11.7505	+	2.38667i	−0.400223	+	0.0812905i
$863$	21.0827	+	12.1721i	0.717665	+	0.414344i	0.813893	−	0.581015i	$-0.197344\pi$
$863$	21.0827	+	12.1721i	0.717665	+	0.414344i	−0.0962279	+	0.995359i	$0.530678\pi$
$864$	1.43695	−	31.7254i	0.0488859	−	1.07932i
$865$	−9.31513	−	16.1343i	−0.316724	−	0.548582i
$866$	−11.1992	+	33.4347i	−0.380565	+	1.13616i
$867$	2.46341			0.0836618
$868$		0			0
$869$	13.2321			0.448867
$870$	−0.293259	+	0.875510i	−0.00994240	+	0.0296826i
$871$	29.8356	+	51.6768i	1.01094	+	1.75100i
$872$	1.21384	−	2.53847i	0.0411056	−	0.0859634i
$873$	16.0663	+	9.27591i	0.543763	+	0.313942i
$874$	−11.4997	+	2.33574i	−0.388984	+	0.0790077i
$875$		0			0
$876$	−9.26276	−	21.8613i	−0.312960	−	0.738624i
$877$	−21.2613	+	36.8256i	−0.717942	+	1.24351i	0.243871	+	0.969808i	$0.421583\pi$
$877$	−21.2613	+	36.8256i	−0.717942	+	1.24351i	−0.961814	+	0.273705i	$0.911751\pi$
$878$	26.9234	−	23.8042i	0.908622	−	0.803353i
$879$	−6.14608	+	3.54844i	−0.207302	+	0.119686i
$880$	−0.975784	−	3.41978i	−0.0328937	−	0.115281i
$881$		−	30.5097i		−	1.02790i	−0.857820	−	0.513950i	$-0.828182\pi$
$881$		−	30.5097i		−	1.02790i	0.857820	−	0.513950i	$-0.171818\pi$
$882$		0			0
$883$		−	12.7488i		−	0.429030i	−0.976721	−	0.214515i	$-0.931183\pi$
$883$		−	12.7488i		−	0.429030i	0.976721	−	0.214515i	$-0.0688170\pi$
$884$	6.09533	−	49.3764i	0.205008	−	1.66071i
$885$	2.14191	−	1.23663i	0.0719995	−	0.0415689i
$886$	22.4714	+	25.4160i	0.754941	+	0.853866i
$887$	4.75891	−	8.24267i	0.159788	−	0.276762i	−0.775004	−	0.631956i	$-0.782252\pi$
$887$	4.75891	−	8.24267i	0.159788	−	0.276762i	0.934792	+	0.355195i	$0.115585\pi$
$888$	−5.58718	−	8.14644i	−0.187493	−	0.273377i
$889$		0			0
$890$	−1.69384	−	8.33940i	−0.0567777	−	0.279537i
$891$	−2.72338	−	1.57234i	−0.0912366	−	0.0526755i
$892$	26.2183	+	19.7837i	0.877852	+	0.662407i
$893$	−3.47863	−	6.02517i	−0.116408	−	0.201625i
$894$	27.5728	+	9.23572i	0.922173	+	0.308889i
$895$	−20.5188			−0.685869
$896$		0			0
$897$	−73.8472			−2.46569
$898$	−22.9686	−	7.69350i	−0.766471	−	0.256735i
$899$	−1.20866	−	2.09346i	−0.0403111	−	0.0698209i
$900$	2.03906	+	1.53863i	0.0679687	+	0.0512875i
$901$	15.8369	+	9.14342i	0.527603	+	0.304611i
$902$	−0.206051	−	1.01446i	−0.00686074	−	0.0337779i
$903$		0			0
$904$	0.581370	+	0.847672i	0.0193361	+	0.0281932i
$905$	−6.63463	+	11.4915i	−0.220542	+	0.381991i
$906$	−14.7389	−	16.6702i	−0.489667	−	0.553832i
$907$	1.34001	−	0.773654i	0.0444942	−	0.0256887i	−0.477588	−	0.878584i	$-0.658489\pi$
$907$	1.34001	−	0.773654i	0.0444942	−	0.0256887i	0.522082	+	0.852895i	$0.325155\pi$
$908$	3.11481	−	25.2321i	0.103368	−	0.837357i
$909$			18.9324i			0.627947i
$910$		0			0
$911$		−	19.9439i		−	0.660769i	−0.943846	−	0.330385i	$-0.892822\pi$
$911$		−	19.9439i		−	0.660769i	0.943846	−	0.330385i	$-0.107178\pi$
$912$	1.35900	+	4.76280i	0.0450009	+	0.157712i
$913$	−3.10054	+	1.79010i	−0.102613	+	0.0592436i
$914$	11.8488	−	10.4761i	0.391924	−	0.346518i
$915$	−0.380943	+	0.659812i	−0.0125936	+	0.0218127i
$916$	13.4958	+	31.8517i	0.445913	+	1.05241i
$917$		0			0
$918$	−30.2576	+	6.14571i	−0.998650	+	0.202839i
$919$	−9.06367	−	5.23291i	−0.298983	−	0.172618i	0.343003	−	0.939334i	$-0.388556\pi$
$919$	−9.06367	−	5.23291i	−0.298983	−	0.172618i	−0.641986	+	0.766716i	$0.721889\pi$
$920$	−10.7321	+	22.4439i	−0.353827	+	0.739952i
$921$	−3.73306	−	6.46584i	−0.123008	−	0.213057i
$922$	11.3965	−	34.0238i	0.375325	−	1.12052i
$923$	−91.5762			−3.01427
$924$		0			0
$925$	2.66086			0.0874886
$926$	0.0229965	−	0.0686548i	0.000755710	−	0.00225614i
$927$	11.7035	+	20.2710i	0.384393	+	0.665788i
$928$	0.127317	−	2.81094i	0.00417938	−	0.0922736i
$929$	27.7313	+	16.0107i	0.909836	+	0.525294i	0.880378	−	0.474272i	$-0.157289\pi$
$929$	27.7313	+	16.0107i	0.909836	+	0.525294i	0.0294574	+	0.999566i	$0.490622\pi$
$930$	8.84026	−	1.79557i	0.289883	−	0.0588791i
$931$		0			0
$932$	−43.7320	+	18.5295i	−1.43249	+	0.606954i
$933$	−0.0821922	+	0.142361i	−0.00269085	+	0.00466069i
$934$	14.0817	−	12.4503i	0.460768	−	0.407386i
$935$	−2.99424	+	1.72873i	−0.0979221	+	0.0565354i
$936$	−1.79051	−	23.0385i	−0.0585247	−	0.753037i
$937$		−	47.3389i		−	1.54649i	−0.634106	−	0.773247i	$-0.718632\pi$
$937$		−	47.3389i		−	1.54649i	0.634106	−	0.773247i	$-0.281368\pi$
$938$		0			0
$939$		−	15.2960i		−	0.499167i
$940$	−14.6386	−	1.80708i	−0.477460	−	0.0589405i
$941$	4.51106	−	2.60446i	0.147056	−	0.0849030i	−0.424667	−	0.905350i	$-0.639609\pi$
$941$	4.51106	−	2.60446i	0.147056	−	0.0849030i	0.571723	+	0.820447i	$0.306275\pi$
$942$	−13.0765	−	14.7900i	−0.426056	−	0.481885i
$943$	−3.62078	+	6.27138i	−0.117909	+	0.204224i
$944$	−5.24290	+	5.41504i	−0.170642	+	0.176245i
$945$		0			0
$946$	2.48271	+	12.2233i	0.0807200	+	0.397414i
$947$	−0.543682	−	0.313895i	−0.0176673	−	0.0102002i	0.491140	−	0.871080i	$-0.336580\pi$
$947$	−0.543682	−	0.313895i	−0.0176673	−	0.0102002i	−0.508808	+	0.860880i	$0.669914\pi$
$948$	−23.5330	+	31.1870i	−0.764315	+	1.01291i
$949$	−28.9272	−	50.1034i	−0.939017	−	1.62642i
$950$	−1.26505	−	0.423739i	−0.0410437	−	0.0137479i
$951$	−24.2780			−0.787267
$952$		0			0
$953$	−4.46691			−0.144697			−0.0723487	−	0.997379i	$-0.523049\pi$
$953$	−4.46691			−0.144697			−0.0723487	+	0.997379i	$0.523049\pi$
$954$	8.05390	+	2.69771i	0.260754	+	0.0873417i
$955$	10.3506	+	17.9278i	0.334939	+	0.580131i
$956$	12.2916	−	16.2894i	0.397539	−	0.526838i
$957$	−0.502692	−	0.290229i	−0.0162497	−	0.00938178i
$958$	−2.72242	−	13.4034i	−0.0879572	−	0.433046i
$959$		0			0
$960$	9.79558	+	3.78216i	0.316151	+	0.122069i
$961$	3.69146	−	6.39380i	0.119079	−	0.206252i
$962$	−15.9439	−	18.0331i	−0.514051	−	0.581411i
$963$	9.20974	−	5.31725i	0.296780	−	0.171346i
$964$	−4.62179	−	0.570542i	−0.148858	−	0.0183759i
$965$			17.5948i			0.566398i
$966$		0			0
$967$			1.90732i			0.0613352i	0.999530	+	0.0306676i	$0.00976333\pi$
$967$			1.90732i			0.0613352i	−0.999530	+	0.0306676i	$0.990237\pi$
$968$	−28.7902	+	2.23752i	−0.925351	+	0.0719167i
$969$	4.17015	−	2.40764i	0.133964	−	0.0773444i
$970$	−15.3893	+	13.6063i	−0.494120	+	0.436873i
$971$	−24.4798	+	42.4002i	−0.785593	+	1.36069i	0.143052	+	0.989715i	$0.454308\pi$
$971$	−24.4798	+	42.4002i	−0.785593	+	1.36069i	−0.928644	+	0.370971i	$0.879025\pi$
$972$	−22.4658	+	9.51888i	−0.720590	+	0.305318i
$973$		0			0
$974$	−9.48971	+	1.92748i	−0.304070	+	0.0617605i
$975$	−7.27106	−	4.19795i	−0.232860	−	0.134442i
$976$	0.564642	−	2.25215i	0.0180738	−	0.0720895i
$977$	−3.15593	−	5.46623i	−0.100967	−	0.174880i	0.811116	−	0.584885i	$-0.198860\pi$
$977$	−3.15593	−	5.46623i	−0.100967	−	0.174880i	−0.912083	+	0.410005i	$0.865527\pi$
$978$	−4.62859	+	13.8184i	−0.148006	+	0.441864i
$979$	5.34974			0.170978
$980$		0			0
$981$	−1.27059			−0.0405669
$982$	−10.7979	+	32.2367i	−0.344576	+	1.02871i
$983$	−10.7447	−	18.6103i	−0.342702	−	0.593577i	0.642232	−	0.766511i	$-0.278009\pi$
$983$	−10.7447	−	18.6103i	−0.342702	−	0.593577i	−0.984933	+	0.172934i	$0.944675\pi$
$984$	2.75747	+	1.31856i	0.0879050	+	0.0420341i
$985$	20.6414	+	11.9173i	0.657691	+	0.379718i
$986$	−2.68089	+	0.544524i	−0.0853771	+	0.0173412i
$987$		0			0
$988$	4.70844	+	11.1125i	0.149795	+	0.353536i
$989$	43.6270	−	75.5641i	1.38726	−	2.40280i
$990$	−1.20308	+	1.06370i	−0.0382365	+	0.0338066i
$991$	5.03965	−	2.90964i	0.160090	−	0.0924279i	−0.417815	−	0.908532i	$-0.637204\pi$
$991$	5.03965	−	2.90964i	0.160090	−	0.0924279i	0.577905	+	0.816104i	$0.303871\pi$
$992$	−24.4053	+	12.6541i	−0.774870	+	0.401769i
$993$			9.08804i			0.288400i
$994$		0			0
$995$		−	18.5087i		−	0.586765i
$996$	1.29512	−	10.4914i	0.0410375	−	0.332433i
$997$	−21.5362	+	12.4339i	−0.682059	+	0.393787i	−0.800630	−	0.599159i	$-0.795502\pi$
$997$	−21.5362	+	12.4339i	−0.682059	+	0.393787i	0.118572	+	0.992946i	$0.462169\pi$
$998$	−12.1198	−	13.7080i	−0.383647	−	0.433918i
$999$	−7.46911	+	12.9369i	−0.236312	+	0.409305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.o.g.411.41		96
4.3	odd	2	inner	980.2.o.g.411.14		96
7.2	even	3		980.2.g.b.391.18	yes	48
7.3	odd	6	inner	980.2.o.g.31.14		96
7.4	even	3	inner	980.2.o.g.31.13		96
7.5	odd	6		980.2.g.b.391.17	✓	48
7.6	odd	2	inner	980.2.o.g.411.42		96
28.3	even	6	inner	980.2.o.g.31.41		96
28.11	odd	6	inner	980.2.o.g.31.42		96
28.19	even	6		980.2.g.b.391.20	yes	48
28.23	odd	6		980.2.g.b.391.19	yes	48
28.27	even	2	inner	980.2.o.g.411.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.g.b.391.17	✓	48	7.5	odd	6
980.2.g.b.391.18	yes	48	7.2	even	3
980.2.g.b.391.19	yes	48	28.23	odd	6
980.2.g.b.391.20	yes	48	28.19	even	6
980.2.o.g.31.13		96	7.4	even	3	inner
980.2.o.g.31.14		96	7.3	odd	6	inner
980.2.o.g.31.41		96	28.3	even	6	inner
980.2.o.g.31.42		96	28.11	odd	6	inner
980.2.o.g.411.13		96	28.27	even	2	inner
980.2.o.g.411.14		96	4.3	odd	2	inner
980.2.o.g.411.41		96	1.1	even	1	trivial
980.2.o.g.411.42		96	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.34099 + 0.449173i) q^{2} +(-0.656274 - 1.13670i) q^{3} +(1.59649 + 1.20467i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.369479 - 1.81908i) q^{6} +(1.59976 + 2.33255i) q^{8} +(0.638609 - 1.10610i) q^{9} +O(q^{10})\)	\(q+(1.34099 + 0.449173i) q^{2} +(-0.656274 - 1.13670i) q^{3} +(1.59649 + 1.20467i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-0.369479 - 1.81908i) q^{6} +(1.59976 + 2.33255i) q^{8} +(0.638609 - 1.10610i) q^{9} +(0.936741 + 1.05949i) q^{10} +(-0.769955 + 0.444533i) q^{11} +(0.321617 - 2.60532i) q^{12} -6.39664i q^{13} -1.31255i q^{15} +(1.09754 + 3.84648i) q^{16} +(3.36785 - 1.94443i) q^{17} +(1.35320 - 1.19642i) q^{18} +(-0.471687 + 0.816986i) q^{19} +(0.780262 + 1.84152i) q^{20} +(-1.23217 + 0.250270i) q^{22} +(7.61724 + 4.39781i) q^{23} +(1.60152 - 3.34924i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.87320 - 8.57781i) q^{26} -5.61405 q^{27} -0.497418 q^{29} +(0.589562 - 1.76011i) q^{30} +(2.42987 + 4.20866i) q^{31} +(-0.255955 + 5.65106i) q^{32} +(1.01060 + 0.583472i) q^{33} +(5.38962 - 1.09470i) q^{34} +(2.35202 - 0.996565i) q^{36} +(1.33043 - 2.30437i) q^{37} +(-0.999494 + 0.883697i) q^{38} +(-7.27106 + 4.19795i) q^{39} +(0.219160 + 2.81992i) q^{40} +0.823314i q^{41} -9.92015i q^{43} +(-1.76474 - 0.217850i) q^{44} +(1.10610 - 0.638609i) q^{45} +(8.23923 + 9.31887i) q^{46} +(-3.68744 + 6.38683i) q^{47} +(3.65201 - 3.77192i) q^{48} +(0.281497 + 1.38591i) q^{50} +(-4.42046 - 2.55215i) q^{51} +(7.70585 - 10.2122i) q^{52} +(2.35119 + 4.07237i) q^{53} +(-7.52837 - 2.52168i) q^{54} -0.889067 q^{55} +1.23822 q^{57} +(-0.667031 - 0.223427i) q^{58} +(0.942161 + 1.63187i) q^{59} +(1.58119 - 2.09547i) q^{60} +(-0.502695 - 0.290231i) q^{61} +(1.36800 + 6.73519i) q^{62} +(-2.88154 + 7.46302i) q^{64} +(3.19832 - 5.53966i) q^{65} +(1.09312 + 1.23636i) q^{66} +(-8.07873 + 4.66426i) q^{67} +(7.71911 + 0.952895i) q^{68} -11.5447i q^{69} -14.3163i q^{71} +(3.60165 - 0.279914i) q^{72} +(7.83276 - 4.52225i) q^{73} +(2.81915 - 2.49254i) q^{74} +(0.656274 - 1.13670i) q^{75} +(-1.73724 + 0.736079i) q^{76} +(-11.6360 + 2.36342i) q^{78} +(-12.8891 - 7.44154i) q^{79} +(-0.972745 + 3.87992i) q^{80} +(1.76853 + 3.06319i) q^{81} +(-0.369811 + 1.10405i) q^{82} +4.02691 q^{83} +3.88885 q^{85} +(4.45587 - 13.3028i) q^{86} +(0.326443 + 0.565415i) q^{87} +(-2.26864 - 1.08481i) q^{88} +(-5.21110 - 3.00863i) q^{89} +(1.77011 - 0.359533i) q^{90} +(6.86290 + 16.1973i) q^{92} +(3.18932 - 5.52407i) q^{93} +(-7.81360 + 6.90835i) q^{94} +(-0.816986 + 0.471687i) q^{95} +(6.59154 - 3.41770i) q^{96} +14.5252i q^{97} +1.13553i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{2} + 8 q^{4} + 16 q^{8} - 48 q^{9}+O(q^{10}) \) 96 * q - 8 * q^2 + 8 * q^4 + 16 * q^8 - 48 * q^9	\( 96 q - 8 q^{2} + 8 q^{4} + 16 q^{8} - 48 q^{9} + 40 q^{16} - 40 q^{18} - 64 q^{22} + 48 q^{25} + 128 q^{29} - 8 q^{32} - 80 q^{36} - 64 q^{37} + 32 q^{46} - 16 q^{50} + 64 q^{53} + 48 q^{58} - 16 q^{64} + 72 q^{72} - 96 q^{74} - 224 q^{78} - 48 q^{81} - 32 q^{88} - 224 q^{92}+O(q^{100}) \) 96 * q - 8 * q^2 + 8 * q^4 + 16 * q^8 - 48 * q^9 + 40 * q^16 - 40 * q^18 - 64 * q^22 + 48 * q^25 + 128 * q^29 - 8 * q^32 - 80 * q^36 - 64 * q^37 + 32 * q^46 - 16 * q^50 + 64 * q^53 + 48 * q^58 - 16 * q^64 + 72 * q^72 - 96 * q^74 - 224 * q^78 - 48 * q^81 - 32 * q^88 - 224 * q^92

Introduction

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