LMFDB - Embedded newform 975.2.bn.d.218.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(218,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.218"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,2,0,0,-12,12,0,0,0,0,12,24,0,0,16,0,0,0,0,0,-20,0,0,0,0, 32,36,0,0,0,0,-30,0,0,-4,84,0,0,0,0,48,-8,0,0,0,0,28,0,0,-16,-28,0,0,0, 0,0,-84,0,0,-32,0,-90,0,0,0,-36,0,0,0,0,-90,0,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(76)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			218.4
Character	$\chi$	$=$	975.218
Dual form			975.2.bn.d.407.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.09662 - 0.561788i) q^{2} +(-0.298187 - 1.70619i) q^{3} +(2.34816 + 1.35571i) q^{4} +(-0.333332 + 3.74475i) q^{6} +(0.403690 - 0.108168i) q^{7} +(-1.09192 - 1.09192i) q^{8} +(-2.82217 + 1.01753i) q^{9} +(-0.255945 - 0.443309i) q^{11} +(1.61291 - 4.41067i) q^{12} +(3.55810 + 0.583017i) q^{13} -0.907153 q^{14} +(-1.03551 - 1.79356i) q^{16} +(-1.84160 + 0.493455i) q^{17} +(6.48865 - 0.547908i) q^{18} +(-1.50433 + 2.60558i) q^{19} +(-0.304931 - 0.656518i) q^{21} +(0.287573 + 1.07324i) q^{22} +(-5.61575 - 1.50474i) q^{23} +(-1.53743 + 2.18862i) q^{24} +(-7.13246 - 3.22126i) q^{26} +(2.57763 + 4.51174i) q^{27} +(1.09458 + 0.293291i) q^{28} +(3.99826 + 6.92519i) q^{29} +3.08801i q^{31} +(1.96282 + 7.32533i) q^{32} +(-0.680051 + 0.568879i) q^{33} +4.13835 q^{34} +(-8.00639 - 1.43673i) q^{36} +(-1.92109 + 7.16959i) q^{37} +(4.61780 - 4.61780i) q^{38} +(-0.0662412 - 6.24465i) q^{39} +(-1.77356 - 3.07189i) q^{41} +(0.270501 + 1.54778i) q^{42} +(-6.98963 + 1.87287i) q^{43} -1.38795i q^{44} +(10.9288 + 6.30972i) q^{46} +(-5.15313 + 5.15313i) q^{47} +(-2.75138 + 2.30160i) q^{48} +(-5.91091 + 3.41267i) q^{49} +(1.39107 + 2.99498i) q^{51} +(7.56460 + 6.19278i) q^{52} +(7.15880 - 7.15880i) q^{53} +(-2.86967 - 10.9075i) q^{54} +(-0.558908 - 0.322686i) q^{56} +(4.89419 + 1.78973i) q^{57} +(-4.49235 - 16.7657i) q^{58} +(1.74290 + 1.00626i) q^{59} +(-5.39613 + 9.34638i) q^{61} +(1.73481 - 6.47438i) q^{62} +(-1.02922 + 0.716035i) q^{63} -12.3191i q^{64} +(1.74540 - 0.810680i) q^{66} +(2.50128 - 9.33491i) q^{67} +(-4.99336 - 1.33797i) q^{68} +(-0.892822 + 10.0302i) q^{69} +(2.93620 - 5.08564i) q^{71} +(4.19264 + 1.97052i) q^{72} +(-2.10205 + 2.10205i) q^{73} +(8.05558 - 13.9527i) q^{74} +(-7.06484 + 4.07889i) q^{76} +(-0.151274 - 0.151274i) q^{77} +(-3.36928 + 13.1299i) q^{78} +14.3974i q^{79} +(6.92928 - 5.74327i) q^{81} +(1.99273 + 7.43696i) q^{82} +(6.15680 + 6.15680i) q^{83} +(0.174021 - 1.95501i) q^{84} +15.7068 q^{86} +(10.6235 - 8.88680i) q^{87} +(-0.204587 + 0.763529i) q^{88} +(10.4966 - 6.06022i) q^{89} +(1.49943 - 0.149516i) q^{91} +(-11.1467 - 11.1467i) q^{92} +(5.26873 - 0.920803i) q^{93} +(13.6991 - 7.90919i) q^{94} +(11.9131 - 5.53326i) q^{96} +(15.6563 - 4.19510i) q^{97} +(14.3101 - 3.83439i) q^{98} +(1.17340 + 0.990663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.09662	−	0.561788i	−1.48253	−	0.397244i	−0.575326	−	0.817924i	$-0.695125\pi$
$2$	−2.09662	−	0.561788i	−1.48253	−	0.397244i	−0.907209	+	0.420680i	$0.861791\pi$
$3$	−0.298187	−	1.70619i	−0.172158	−	0.985069i
$3$	−0.298187	−	1.70619i	−0.172158	−	0.985069i
$4$	2.34816	+	1.35571i	1.17408	+	0.677856i
$5$		0			0
$5$		0			0
$6$	−0.333332	+	3.74475i	−0.136082	+	1.52879i
$7$	0.403690	−	0.108168i	0.152581	−	0.0408838i	−0.181720	−	0.983350i	$-0.558167\pi$
$7$	0.403690	−	0.108168i	0.152581	−	0.0408838i	0.334301	+	0.942466i	$0.391500\pi$
$8$	−1.09192	−	1.09192i	−0.386052	−	0.386052i
$9$	−2.82217	+	1.01753i	−0.940723	+	0.339176i
$10$		0			0
$11$	−0.255945	−	0.443309i	−0.0771702	−	0.133663i	0.824858	−	0.565340i	$-0.191255\pi$
$11$	−0.255945	−	0.443309i	−0.0771702	−	0.133663i	−0.902028	+	0.431678i	$0.857922\pi$
$12$	1.61291	−	4.41067i	0.465608	−	1.27325i
$13$	3.55810	+	0.583017i	0.986840	+	0.161700i
$13$	3.55810	+	0.583017i	0.986840	+	0.161700i
$14$	−0.907153			−0.242447
$15$		0			0
$16$	−1.03551	−	1.79356i	−0.258878	−	0.448390i
$17$	−1.84160	+	0.493455i	−0.446653	+	0.119680i	−0.475133	−	0.879914i	$-0.657600\pi$
$17$	−1.84160	+	0.493455i	−0.446653	+	0.119680i	0.0284797	+	0.999594i	$0.490933\pi$
$18$	6.48865	−	0.547908i	1.52939	−	0.129143i
$19$	−1.50433	+	2.60558i	−0.345118	+	0.597762i	−0.985375	−	0.170399i	$-0.945494\pi$
$19$	−1.50433	+	2.60558i	−0.345118	+	0.597762i	0.640257	+	0.768161i	$0.278828\pi$
$20$		0			0
$21$	−0.304931	−	0.656518i	−0.0665414	−	0.143264i
$22$	0.287573	+	1.07324i	0.0613108	+	0.228815i
$23$	−5.61575	−	1.50474i	−1.17097	−	0.313759i	−0.379628	−	0.925139i	$-0.623948\pi$
$23$	−5.61575	−	1.50474i	−1.17097	−	0.313759i	−0.791337	+	0.611380i	$0.790615\pi$
$24$	−1.53743	+	2.18862i	−0.313826	+	0.446750i
$25$		0			0
$26$	−7.13246	−	3.22126i	−1.39879	−	0.631742i
$27$	2.57763	+	4.51174i	0.496065	+	0.868285i
$28$	1.09458	+	0.293291i	0.206855	+	0.0554267i
$29$	3.99826	+	6.92519i	0.742459	+	1.28598i	0.951373	+	0.308042i	$0.0996738\pi$
$29$	3.99826	+	6.92519i	0.742459	+	1.28598i	−0.208914	+	0.977934i	$0.566993\pi$
$30$		0			0
$31$			3.08801i			0.554622i	0.960780	+	0.277311i	$0.0894433\pi$
$31$			3.08801i			0.554622i	−0.960780	+	0.277311i	$0.910557\pi$
$32$	1.96282	+	7.32533i	0.346980	+	1.29495i
$33$	−0.680051	+	0.568879i	−0.118382	+	0.0990292i
$34$	4.13835			0.709722
$35$		0			0
$36$	−8.00639	−	1.43673i	−1.33440	−	0.239455i
$37$	−1.92109	+	7.16959i	−0.315825	+	1.17867i	0.607395	+	0.794400i	$0.292215\pi$
$37$	−1.92109	+	7.16959i	−0.315825	+	1.17867i	−0.923219	+	0.384273i	$0.874452\pi$
$38$	4.61780	−	4.61780i	0.749107	−	0.749107i
$39$	−0.0662412	−	6.24465i	−0.0106071	−	0.999944i
$40$		0			0
$41$	−1.77356	−	3.07189i	−0.276983	−	0.479749i	0.693650	−	0.720312i	$-0.256001\pi$
$41$	−1.77356	−	3.07189i	−0.276983	−	0.479749i	−0.970634	+	0.240563i	$0.922668\pi$
$42$	0.270501	+	1.54778i	0.0417392	+	0.238827i
$43$	−6.98963	+	1.87287i	−1.06591	+	0.285609i	−0.748811	−	0.662783i	$-0.769375\pi$
$43$	−6.98963	+	1.87287i	−1.06591	+	0.285609i	−0.317098	+	0.948393i	$0.602708\pi$
$44$		−	1.38795i		−	0.209241i
$45$		0			0
$46$	10.9288	+	6.30972i	1.61136	+	0.930318i
$47$	−5.15313	+	5.15313i	−0.751661	+	0.751661i	−0.974789	−	0.223128i	$-0.928373\pi$
$47$	−5.15313	+	5.15313i	−0.751661	+	0.751661i	0.223128	+	0.974789i	$0.428373\pi$
$48$	−2.75138	+	2.30160i	−0.397127	+	0.332207i
$49$	−5.91091	+	3.41267i	−0.844416	+	0.487524i
$50$		0			0
$51$	1.39107	+	2.99498i	0.194789	+	0.419381i
$52$	7.56460	+	6.19278i	1.04902	+	0.858785i
$53$	7.15880	−	7.15880i	0.983337	−	0.983337i	−0.0165265	−	0.999863i	$-0.505261\pi$
$53$	7.15880	−	7.15880i	0.983337	−	0.983337i	0.999863	+	0.0165265i	$0.00526079\pi$
$54$	−2.86967	−	10.9075i	−0.390512	−	1.48432i
$55$		0			0
$56$	−0.558908	−	0.322686i	−0.0746872	−	0.0431207i
$57$	4.89419	+	1.78973i	0.648252	+	0.237055i
$58$	−4.49235	−	16.7657i	−0.589875	−	2.20144i
$59$	1.74290	+	1.00626i	0.226906	+	0.131004i	0.609144	−	0.793060i	$-0.291513\pi$
$59$	1.74290	+	1.00626i	0.226906	+	0.131004i	−0.382238	+	0.924064i	$0.624847\pi$
$60$		0			0
$61$	−5.39613	+	9.34638i	−0.690904	+	1.19668i	0.280638	+	0.959814i	$0.409454\pi$
$61$	−5.39613	+	9.34638i	−0.690904	+	1.19668i	−0.971542	+	0.236867i	$0.923879\pi$
$62$	1.73481	−	6.47438i	0.220320	−	0.822247i
$63$	−1.02922	+	0.716035i	−0.129669	+	0.0902120i
$64$		−	12.3191i		−	1.53988i
$65$		0			0
$66$	1.74540	−	0.810680i	0.214844	−	0.0997879i
$67$	2.50128	−	9.33491i	0.305580	−	1.14044i	−0.626865	−	0.779128i	$-0.715662\pi$
$67$	2.50128	−	9.33491i	0.305580	−	1.14044i	0.932445	−	0.361312i	$-0.117671\pi$
$68$	−4.99336	−	1.33797i	−0.605534	−	0.162252i
$69$	−0.892822	+	10.0302i	−0.107483	+	1.20750i
$70$		0			0
$71$	2.93620	−	5.08564i	0.348463	−	0.603555i	−0.637514	−	0.770439i	$-0.720037\pi$
$71$	2.93620	−	5.08564i	0.348463	−	0.603555i	0.985977	+	0.166884i	$0.0533705\pi$
$72$	4.19264	+	1.97052i	0.494107	+	0.232228i
$73$	−2.10205	+	2.10205i	−0.246026	+	0.246026i	−0.819338	−	0.573311i	$-0.805659\pi$
$73$	−2.10205	+	2.10205i	−0.246026	+	0.246026i	0.573311	+	0.819338i	$0.305659\pi$
$74$	8.05558	−	13.9527i	0.936442	−	1.62196i
$75$		0			0
$76$	−7.06484	+	4.07889i	−0.810393	+	0.467881i
$77$	−0.151274	−	0.151274i	−0.0172393	−	0.0172393i
$78$	−3.36928	+	13.1299i	−0.381496	+	1.48667i
$79$			14.3974i			1.61983i	0.586544	+	0.809917i	$0.300488\pi$
$79$			14.3974i			1.61983i	−0.586544	+	0.809917i	$0.699512\pi$
$80$		0			0
$81$	6.92928	−	5.74327i	0.769920	−	0.638141i
$82$	1.99273	+	7.43696i	0.220060	+	0.821274i
$83$	6.15680	+	6.15680i	0.675796	+	0.675796i	0.959046	−	0.283250i	$-0.0914125\pi$
$83$	6.15680	+	6.15680i	0.675796	+	0.675796i	−0.283250	+	0.959046i	$0.591413\pi$
$84$	0.174021	−	1.95501i	0.0189873	−	0.213309i
$85$		0			0
$86$	15.7068			1.69370
$87$	10.6235	−	8.88680i	1.13896	−	0.952765i
$88$	−0.204587	+	0.763529i	−0.0218090	+	0.0813924i
$89$	10.4966	−	6.06022i	1.11264	−	0.642382i	0.173126	−	0.984900i	$-0.444613\pi$
$89$	10.4966	−	6.06022i	1.11264	−	0.642382i	0.939511	+	0.342518i	$0.111280\pi$
$90$		0			0
$91$	1.49943	−	0.149516i	0.157183	−	0.0156735i
$92$	−11.1467	−	11.1467i	−1.16212	−	1.16212i
$93$	5.26873	−	0.920803i	0.546342	−	0.0954829i
$94$	13.6991	−	7.90919i	1.41296	−	0.815771i
$95$		0			0
$96$	11.9131	−	5.53326i	1.21588	−	0.564735i
$97$	15.6563	−	4.19510i	1.58966	−	0.425948i	0.647761	−	0.761843i	$-0.275705\pi$
$97$	15.6563	−	4.19510i	1.58966	−	0.425948i	0.941899	+	0.335895i	$0.109039\pi$
$98$	14.3101	−	3.83439i	1.44554	−	0.387332i
$99$	1.17340	+	0.990663i	0.117931	+	0.0995654i
$100$		0			0
$101$	−7.56743	+	4.36906i	−0.752987	+	0.434737i	−0.826772	−	0.562537i	$-0.809825\pi$
$101$	−7.56743	+	4.36906i	−0.752987	+	0.434737i	0.0737851	+	0.997274i	$0.476492\pi$
$102$	−1.23400	−	7.06082i	−0.122184	−	0.699125i
$103$	8.04055	+	8.04055i	0.792259	+	0.792259i	0.981861	−	0.189602i	$-0.0607197\pi$
$103$	8.04055	+	8.04055i	0.792259	+	0.792259i	−0.189602	+	0.981861i	$0.560720\pi$
$104$	−3.24855	−	4.52177i	−0.318547	−	0.443396i
$105$		0			0
$106$	−19.0310	+	10.9876i	−1.84846	+	1.06721i
$107$	−3.12349	+	11.6570i	−0.301959	+	1.12693i	0.633572	+	0.773683i	$0.281588\pi$
$107$	−3.12349	+	11.6570i	−0.301959	+	1.12693i	−0.935531	+	0.353243i	$0.885079\pi$
$108$	−0.0639357	+	14.0888i	−0.00615221	+	1.35570i
$109$	14.0991			1.35045			0.675225	−	0.737612i	$-0.264047\pi$
$109$	14.0991			1.35045			0.675225	+	0.737612i	$0.264047\pi$
$110$		0			0
$111$	12.8055	+	1.13986i	1.21545	+	0.108191i
$112$	−0.612032	−	0.612032i	−0.0578316	−	0.0578316i
$113$	0.871189	+	3.25132i	0.0819545	+	0.305859i	0.994720	−	0.102625i	$-0.0327243\pi$
$113$	0.871189	+	3.25132i	0.0819545	+	0.305859i	−0.912766	+	0.408484i	$0.866058\pi$
$114$	−9.25582	−	6.50188i	−0.866887	−	0.608957i
$115$		0			0
$116$			21.6820i			2.01312i
$117$	−10.6348	+	1.97509i	−0.983188	+	0.182597i
$118$	−3.08889	−	3.08889i	−0.284355	−	0.284355i
$119$	−0.690059	+	0.398406i	−0.0632576	+	0.0365218i
$120$		0			0
$121$	5.36898	−	9.29935i	0.488090	−	0.845396i
$122$	16.5643	−	16.5643i	1.49966	−	1.49966i
$123$	−4.71238	+	3.94202i	−0.424901	+	0.355440i
$124$	−4.18645	+	7.25114i	−0.375954	+	0.651172i
$125$		0			0
$126$	2.56014	−	0.923053i	0.228075	−	0.0822321i
$127$	−17.1178	−	4.58670i	−1.51896	−	0.407003i	−0.599559	−	0.800330i	$-0.704657\pi$
$127$	−17.1178	−	4.58670i	−1.51896	−	0.407003i	−0.919399	+	0.393327i	$0.871324\pi$
$128$	−2.99508	+	11.1778i	−0.264730	+	0.987986i
$129$	5.27968	+	11.3672i	0.464850	+	1.00082i
$130$		0			0
$131$		−	3.62886i		−	0.317055i	−0.987355	−	0.158527i	$-0.949325\pi$
$131$		−	3.62886i		−	0.317055i	0.987355	−	0.158527i	$-0.0506746\pi$
$132$	−2.36811	+	0.413869i	−0.206117	+	0.0360226i
$133$	−0.325443	+	1.21457i	−0.0282195	+	0.105317i
$134$	−10.4885	+	18.1666i	−0.906066	+	1.56935i
$135$		0			0
$136$	2.54969	+	1.47206i	0.218634	+	0.126228i
$137$	−0.997998	−	3.72458i	−0.0852647	−	0.318212i	0.910099	−	0.414390i	$-0.136005\pi$
$137$	−0.997998	−	3.72458i	−0.0852647	−	0.318212i	−0.995364	+	0.0961776i	$0.969338\pi$
$138$	7.50677	−	20.5280i	0.639019	−	1.74746i
$139$	−6.82507	−	3.94046i	−0.578895	−	0.334225i	0.181799	−	0.983336i	$-0.441808\pi$
$139$	−6.82507	−	3.94046i	−0.578895	−	0.334225i	−0.760694	+	0.649110i	$0.775141\pi$
$140$		0			0
$141$	10.3288	+	7.25562i	0.869843	+	0.611034i
$142$	−9.01315	+	9.01315i	−0.756367	+	0.756367i
$143$	−0.652221	−	1.72656i	−0.0545414	−	0.144382i
$144$	4.74738	+	4.00807i	0.395615	+	0.334005i
$145$		0			0
$146$	5.58811	−	3.22629i	0.462475	−	0.267010i
$147$	7.58522	+	9.06753i	0.625618	+	0.747877i
$148$	−14.2309	+	14.2309i	−1.16977	+	1.16977i
$149$	4.77688	+	2.75793i	0.391337	+	0.225938i	0.682739	−	0.730662i	$-0.260789\pi$
$149$	4.77688	+	2.75793i	0.391337	+	0.225938i	−0.291402	+	0.956601i	$0.594122\pi$
$150$		0			0
$151$			3.50398i			0.285150i	0.989784	+	0.142575i	$0.0455382\pi$
$151$			3.50398i			0.285150i	−0.989784	+	0.142575i	$0.954462\pi$
$152$	4.48770	−	1.20247i	0.364000	−	0.0975336i
$153$	4.69520	−	3.26649i	0.379584	−	0.264080i
$154$	0.232181	+	0.402149i	0.0187097	+	0.0324061i
$155$		0			0
$156$	8.31040	−	14.7533i	0.665365	−	1.18121i
$157$	−1.27066	+	1.27066i	−0.101409	+	0.101409i	−0.755991	−	0.654582i	$-0.772845\pi$
$157$	−1.27066	+	1.27066i	−0.101409	+	0.101409i	0.654582	+	0.755991i	$0.272845\pi$
$158$	8.08829	−	30.1859i	0.643470	−	2.40146i
$159$	−14.3489	−	10.0796i	−1.13794	−	0.799365i
$160$		0			0
$161$	−2.42979			−0.191494
$162$	−17.7546	+	8.14867i	−1.39493	+	0.640220i
$163$	2.01921	+	7.53579i	0.158157	+	0.590249i	0.998814	+	0.0486817i	$0.0155020\pi$
$163$	2.01921	+	7.53579i	0.158157	+	0.590249i	−0.840658	+	0.541567i	$0.817831\pi$
$164$		−	9.61774i		−	0.751019i
$165$		0			0
$166$	−9.44966	−	16.3673i	−0.733436	−	1.27035i
$167$	−2.20275	−	0.590226i	−0.170454	−	0.0456731i	0.172583	−	0.984995i	$-0.444789\pi$
$167$	−2.20275	−	0.590226i	−0.170454	−	0.0456731i	−0.343037	+	0.939322i	$0.611456\pi$
$168$	−0.383904	+	1.04982i	−0.0296188	+	0.0809957i
$169$	12.3202	+	4.14887i	0.947706	+	0.319144i
$170$		0			0
$171$	1.59423	−	8.88410i	0.121914	−	0.679384i
$172$	−18.9519	−	5.07814i	−1.44507	−	0.387204i
$173$	5.86243	+	21.8789i	0.445713	+	1.66342i	0.714048	+	0.700097i	$0.246860\pi$
$173$	5.86243	+	21.8789i	0.445713	+	1.66342i	−0.268335	+	0.963326i	$0.586474\pi$
$174$	−27.2659	+	12.6641i	−2.06702	+	0.960064i
$175$		0			0
$176$	−0.530068	+	0.918104i	−0.0399554	+	0.0692047i
$177$	1.19716	−	3.27376i	0.0899844	−	0.246071i
$178$	−25.4120	+	6.80911i	−1.90471	+	0.510365i
$179$	−4.89863	−	8.48468i	−0.366141	−	0.634175i	0.622818	−	0.782367i	$-0.285988\pi$
$179$	−4.89863	−	8.48468i	−0.366141	−	0.634175i	−0.988959	+	0.148192i	$0.952655\pi$
$180$		0			0
$181$	1.50768			0.112065			0.0560325	−	0.998429i	$-0.482155\pi$
$181$	1.50768			0.112065			0.0560325	+	0.998429i	$0.482155\pi$
$182$	−3.22774	−	0.528886i	−0.239256	−	0.0392036i
$183$	17.5557	+	6.41986i	1.29776	+	0.474570i
$184$	4.48890	+	7.77499i	0.330926	+	0.573180i
$185$		0			0
$186$	−11.5638	−	1.02933i	−0.847900	−	0.0754743i
$187$	0.690101	+	0.690101i	0.0504652	+	0.0504652i
$188$	−19.0865	+	5.11423i	−1.39203	+	0.372993i
$189$	1.52859	+	1.54253i	0.111189	+	0.112202i
$190$		0			0
$191$	3.89212	+	2.24712i	0.281624	+	0.162596i	0.634158	−	0.773203i	$-0.281347\pi$
$191$	3.89212	+	2.24712i	0.281624	+	0.162596i	−0.352534	+	0.935799i	$0.614680\pi$
$192$	−21.0187	+	3.67339i	−1.51689	+	0.265104i
$193$	15.3024	+	4.10026i	1.10149	+	0.295143i	0.763371	−	0.645960i	$-0.223543\pi$
$193$	15.3024	+	4.10026i	1.10149	+	0.295143i	0.338118	+	0.941104i	$0.390210\pi$
$194$	−35.1822			−2.52593
$195$		0			0
$196$	−18.5064			−1.32188
$197$	−11.8903	−	3.18600i	−0.847150	−	0.226993i	−0.190968	−	0.981596i	$-0.561163\pi$
$197$	−11.8903	−	3.18600i	−0.847150	−	0.226993i	−0.656181	+	0.754603i	$0.727829\pi$
$198$	−1.90363	−	2.73625i	−0.135285	−	0.194457i
$199$	−19.5208	−	11.2703i	−1.38379	−	0.798933i	−0.391187	−	0.920311i	$-0.627935\pi$
$199$	−19.5208	−	11.2703i	−1.38379	−	0.798933i	−0.992606	+	0.121378i	$0.961269\pi$
$200$		0			0
$201$	−16.6730	−	1.48411i	−1.17602	−	0.104681i
$202$	18.3205	−	4.90897i	1.28903	−	0.345394i
$203$	2.36315	+	2.36315i	0.165860	+	0.165860i
$204$	−0.793871	+	8.91858i	−0.0555821	+	0.624426i
$205$		0			0
$206$	−12.3409	−	21.3751i	−0.859832	−	1.48927i
$207$	17.3797	−	1.46756i	1.20797	−	0.102002i
$208$	−2.63878	−	6.98539i	−0.182967	−	0.484349i
$209$	1.54011			0.106531
$210$		0			0
$211$	1.99042	+	3.44751i	0.137026	+	0.237336i	0.926370	−	0.376616i	$-0.122912\pi$
$211$	1.99042	+	3.44751i	0.137026	+	0.237336i	−0.789344	+	0.613952i	$0.789579\pi$
$212$	26.5153	−	7.10476i	1.82108	−	0.487957i
$213$	−9.55261	−	3.49324i	−0.654534	−	0.239353i
$214$	13.0975	−	22.6856i	0.895330	−	1.55076i
$215$		0			0
$216$	2.11190	−	7.74102i	0.143696	−	0.526710i
$217$	0.334025	+	1.24660i	0.0226751	+	0.0846246i
$218$	−29.5605	−	7.92071i	−2.00209	−	0.536458i
$219$	4.21330	+	2.95969i	0.284708	+	0.199997i
$220$		0			0
$221$	−6.84029	+	0.682079i	−0.460128	+	0.0458816i
$222$	−26.2080	−	9.58384i	−1.75896	−	0.643225i
$223$	−13.5539	−	3.63175i	−0.907635	−	0.243200i	−0.225342	−	0.974280i	$-0.572350\pi$
$223$	−13.5539	−	3.63175i	−0.907635	−	0.243200i	−0.682292	+	0.731080i	$0.739017\pi$
$224$	1.58474	+	2.74485i	0.105885	+	0.183398i
$225$		0			0
$226$		−	7.30621i		−	0.486002i
$227$	2.30516	+	8.60297i	0.152999	+	0.570999i	0.999268	+	0.0382445i	$0.0121766\pi$
$227$	2.30516	+	8.60297i	0.152999	+	0.570999i	−0.846270	+	0.532755i	$0.821157\pi$
$228$	9.06600	+	10.8377i	0.600411	+	0.717744i
$229$	−13.9049			−0.918865			−0.459432	−	0.888213i	$-0.651947\pi$
$229$	−13.9049			−0.918865			−0.459432	+	0.888213i	$0.651947\pi$
$230$		0			0
$231$	−0.212995	+	0.303211i	−0.0140140	+	0.0199498i
$232$	3.19597	−	11.9275i	0.209826	−	0.783081i
$233$	−10.6874	+	10.6874i	−0.700154	+	0.700154i	−0.964443	−	0.264289i	$-0.914863\pi$
$233$	−10.6874	+	10.6874i	−0.700154	+	0.700154i	0.264289	+	0.964443i	$0.414863\pi$
$234$	23.4067	+	1.83348i	1.53015	+	0.119859i
$235$		0			0
$236$	2.72840	+	4.72573i	0.177604	+	0.307619i
$237$	24.5647	−	4.29312i	1.59565	−	0.278868i
$238$	1.67061	−	0.447639i	0.108290	−	0.0290161i
$239$		−	2.14533i		−	0.138770i	−0.997590	−	0.0693849i	$-0.977896\pi$
$239$		−	2.14533i		−	0.138770i	0.997590	−	0.0693849i	$-0.0221036\pi$
$240$		0			0
$241$	4.50245	+	2.59949i	0.290028	+	0.167448i	0.637955	−	0.770074i	$-0.279781\pi$
$241$	4.50245	+	2.59949i	0.290028	+	0.167448i	−0.347926	+	0.937522i	$0.613114\pi$
$242$	−16.4810	+	16.4810i	−1.05944	+	1.05944i
$243$	−11.8653	−	10.1101i	−0.761161	−	0.648563i
$244$	−25.3420	+	14.6312i	−1.62236	+	0.936667i
$245$		0			0
$246$	12.0947	−	5.61757i	0.771127	−	0.358163i
$247$	−6.87167	+	8.39388i	−0.437234	+	0.534090i
$248$	3.37185	−	3.37185i	0.214113	−	0.214113i
$249$	8.66879	−	12.3405i	0.549362	−	0.782050i
$250$		0			0
$251$	3.01039	+	1.73805i	0.190014	+	0.109705i	0.591989	−	0.805946i	$-0.298343\pi$
$251$	3.01039	+	1.73805i	0.190014	+	0.109705i	−0.401975	+	0.915651i	$0.631676\pi$
$252$	−3.38751	+	0.286045i	−0.213393	+	0.0180191i
$253$	0.770259	+	2.87464i	0.0484257	+	0.180727i
$254$	33.3128	+	19.2331i	2.09023	+	1.20679i
$255$		0			0
$256$	0.240005	−	0.415700i	0.0150003	−	0.0259813i
$257$	1.03229	−	3.85254i	0.0643922	−	0.240315i	−0.926227	−	0.376966i	$-0.876967\pi$
$257$	1.03229	−	3.85254i	0.0643922	−	0.240315i	0.990619	+	0.136651i	$0.0436339\pi$
$258$	−4.68355	−	26.7987i	−0.291585	−	1.66842i
$259$			3.10209i			0.192755i
$260$		0			0
$261$	−18.3303	−	15.4757i	−1.13462	−	0.957924i
$262$	−2.03865	+	7.60834i	−0.125948	+	0.470045i
$263$	−23.3298	−	6.25119i	−1.43857	−	0.385465i	−0.546540	−	0.837433i	$-0.684055\pi$
$263$	−23.3298	−	6.25119i	−1.43857	−	0.385465i	−0.892034	+	0.451968i	$0.850722\pi$
$264$	1.36373	+	0.121390i	0.0839318	+	0.00747103i
$265$		0			0
$266$	1.36466	−	2.36366i	0.0836727	−	0.144925i
$267$	−13.4698	−	16.1021i	−0.824340	−	0.985434i
$268$	18.5289	−	18.5289i	1.13183	−	1.13183i
$269$	−12.4058	+	21.4875i	−0.756397	+	1.31012i	0.188280	+	0.982115i	$0.439709\pi$
$269$	−12.4058	+	21.4875i	−0.756397	+	1.31012i	−0.944677	+	0.328003i	$0.893625\pi$
$270$		0			0
$271$	18.7408	−	10.8200i	1.13842	−	0.657270i	0.192385	−	0.981320i	$-0.438378\pi$
$271$	18.7408	−	10.8200i	1.13842	−	0.657270i	0.946040	+	0.324050i	$0.105045\pi$
$272$	2.79204	+	2.79204i	0.169292	+	0.169292i
$273$	−0.702215	−	2.51374i	−0.0425000	−	0.152138i
$274$			8.36970i			0.505632i
$275$		0			0
$276$	−15.6946	+	22.3422i	−0.944704	+	1.34484i
$277$	0.115159	+	0.429778i	0.00691921	+	0.0258228i	0.969299	−	0.245885i	$-0.0790784\pi$
$277$	0.115159	+	0.429778i	0.00691921	+	0.0258228i	−0.962380	+	0.271707i	$0.912412\pi$
$278$	12.0959	+	12.0959i	0.725463	+	0.725463i
$279$	−3.14213	−	8.71488i	−0.188114	−	0.521746i
$280$		0			0
$281$	−10.2114			−0.609162			−0.304581	−	0.952486i	$-0.598516\pi$
$281$	−10.2114			−0.609162			−0.304581	+	0.952486i	$0.598516\pi$
$282$	−17.5795	−	21.0149i	−1.04684	−	1.25142i
$283$	2.14169	−	7.99290i	0.127310	−	0.475129i	−0.872601	−	0.488433i	$-0.837568\pi$
$283$	2.14169	−	7.99290i	0.127310	−	0.475129i	0.999911	+	0.0133048i	$0.00423516\pi$
$284$	13.7893	−	7.96128i	0.818247	−	0.472415i
$285$		0			0
$286$	0.397499	+	3.98635i	0.0235046	+	0.235718i
$287$	−1.04825	−	1.04825i	−0.0618762	−	0.0618762i
$288$	−12.9931	−	18.6761i	−0.765627	−	1.10050i
$289$	−11.5744	+	6.68251i	−0.680850	+	0.393089i
$290$		0			0
$291$	−11.8262	−	25.4618i	−0.693262	−	1.49260i
$292$	−7.78573	+	2.08618i	−0.455625	+	0.122084i
$293$	17.1295	−	4.58984i	1.00072	−	0.268141i	0.278971	−	0.960300i	$-0.410007\pi$
$293$	17.1295	−	4.58984i	1.00072	−	0.268141i	0.721745	+	0.692159i	$0.243340\pi$
$294$	−10.8093	−	23.2725i	−0.630411	−	1.35728i
$295$		0			0
$296$	9.92628	−	5.73094i	0.576953	−	0.333104i
$297$	1.34037	−	2.29744i	0.0777760	−	0.133311i
$298$	−8.46593	−	8.46593i	−0.490418	−	0.490418i
$299$	−19.1041	−	8.62808i	−1.10482	−	0.498975i
$300$		0			0
$301$	−2.61906	+	1.51212i	−0.150960	+	0.0871569i
$302$	1.96850	−	7.34652i	0.113274	−	0.422745i
$303$	9.71095	+	11.6087i	0.557879	+	0.666901i
$304$	6.23102			0.357374
$305$		0			0
$306$	−11.6791	+	4.21089i	−0.667651	+	0.240720i
$307$	−18.0565	−	18.0565i	−1.03054	−	1.03054i	−0.999519	−	0.0310201i	$-0.990124\pi$
$307$	−18.0565	−	18.0565i	−1.03054	−	1.03054i	−0.0310201	−	0.999519i	$-0.509876\pi$
$308$	−0.150132	−	0.560302i	−0.00855459	−	0.0319262i
$309$	11.3211	−	16.1163i	0.644036	−	0.916824i
$310$		0			0
$311$			25.9620i			1.47217i	0.676890	+	0.736084i	$0.263327\pi$
$311$			25.9620i			1.47217i	−0.676890	+	0.736084i	$0.736673\pi$
$312$	−6.74632	+	6.89098i	−0.381935	+	0.390125i
$313$	−1.24977	−	1.24977i	−0.0706415	−	0.0706415i	0.670903	−	0.741545i	$-0.265907\pi$
$313$	−1.24977	−	1.24977i	−0.0706415	−	0.0706415i	−0.741545	+	0.670903i	$0.765907\pi$
$314$	3.37793	−	1.95025i	0.190627	−	0.110059i
$315$		0			0
$316$	−19.5187	+	33.8075i	−1.09802	+	1.90182i
$317$	−12.6999	+	12.6999i	−0.713299	+	0.713299i	−0.967224	−	0.253925i	$-0.918278\pi$
$317$	−12.6999	+	12.6999i	−0.713299	+	0.713299i	0.253925	+	0.967224i	$0.418278\pi$
$318$	24.4217	+	29.1942i	1.36950	+	1.63713i
$319$	2.04667	−	3.54493i	0.114591	−	0.198478i
$320$		0			0
$321$	20.8205	+	1.85330i	1.16209	+	0.103441i
$322$	5.09435	+	1.36503i	0.283897	+	0.0760699i
$323$	1.48464	−	5.54076i	0.0826077	−	0.308296i
$324$	24.0573	−	4.09202i	1.33652	−	0.227334i
$325$		0			0
$326$		−	16.9341i		−	0.937891i
$327$	−4.20417	−	24.0558i	−0.232491	−	1.33029i
$328$	−1.41768	+	5.29084i	−0.0782780	+	0.292138i
$329$	−1.52286	+	2.63767i	−0.0839581	+	0.145420i
$330$		0			0
$331$	−7.74634	−	4.47235i	−0.425777	−	0.245823i	0.271769	−	0.962363i	$-0.412391\pi$
$331$	−7.74634	−	4.47235i	−0.425777	−	0.245823i	−0.697546	+	0.716540i	$0.745725\pi$
$332$	6.11032	+	22.8040i	0.335347	+	1.25153i
$333$	−1.87362	−	22.1885i	−0.102674	−	1.21592i
$334$	4.28676	+	2.47496i	0.234561	+	0.135424i
$335$		0			0
$336$	−0.861744	+	1.22674i	−0.0470120	+	0.0669244i
$337$	−1.08661	+	1.08661i	−0.0591915	+	0.0591915i	−0.736083	−	0.676891i	$-0.763327\pi$
$337$	−1.08661	+	1.08661i	−0.0591915	+	0.0591915i	0.676891	+	0.736083i	$0.263327\pi$
$338$	−23.5000	−	15.6199i	−1.27823	−	0.849613i
$339$	5.28759	−	2.45591i	0.287183	−	0.133387i
$340$		0			0
$341$	1.36894	−	0.790359i	0.0741324	−	0.0428004i
$342$	−8.33348	+	17.7310i	−0.450623	+	0.958781i
$343$	−4.08569	+	4.08569i	−0.220606	+	0.220606i
$344$	9.67713	+	5.58709i	0.521756	+	0.301236i
$345$		0			0
$346$		−	49.1652i		−	2.64314i
$347$	34.3656	−	9.20824i	1.84484	−	0.494324i	0.845622	−	0.533782i	$-0.179230\pi$
$347$	34.3656	−	9.20824i	1.84484	−	0.494324i	0.999221	+	0.0394575i	$0.0125630\pi$
$348$	36.9936	−	6.46528i	1.98306	−	0.346576i
$349$	−0.580105	−	1.00477i	−0.0310523	−	0.0537841i	0.850082	−	0.526651i	$-0.176553\pi$
$349$	−0.580105	−	1.00477i	−0.0310523	−	0.0537841i	−0.881134	+	0.472867i	$0.843219\pi$
$350$		0			0
$351$	6.54104	+	17.5560i	0.349135	+	0.937072i
$352$	2.74501	−	2.74501i	0.146310	−	0.146310i
$353$	−8.13026	+	30.3425i	−0.432730	+	1.61497i	0.313710	+	0.949519i	$0.398428\pi$
$353$	−8.13026	+	30.3425i	−0.432730	+	1.61497i	−0.746440	+	0.665452i	$0.768239\pi$
$354$	−4.34916	+	6.19129i	−0.231155	+	0.329063i
$355$		0			0
$356$	32.8636			1.74177
$357$	0.885523	+	1.05857i	0.0468668	+	0.0560256i
$358$	5.50399	+	20.5412i	0.290895	+	1.08563i
$359$			18.5415i			0.978582i	0.872120	+	0.489291i	$0.162744\pi$
$359$			18.5415i			0.978582i	−0.872120	+	0.489291i	$0.837256\pi$
$360$		0			0
$361$	4.97396	+	8.61515i	0.261787	+	0.453429i
$362$	−3.16104	−	0.846997i	−0.166140	−	0.0445172i
$363$	−17.4674	−	6.38756i	−0.916802	−	0.335260i
$364$	3.72362	+	1.68171i	0.195171	+	0.0881458i
$365$		0			0
$366$	−33.2012	−	23.3226i	−1.73545	−	1.21909i
$367$	−5.91325	−	1.58445i	−0.308669	−	0.0827076i	0.101159	−	0.994870i	$-0.467745\pi$
$367$	−5.91325	−	1.58445i	−0.308669	−	0.0827076i	−0.409828	+	0.912163i	$0.634411\pi$
$368$	3.11634	+	11.6304i	0.162451	+	0.606274i
$369$	8.13101	+	6.86475i	0.423284	+	0.357365i
$370$		0			0
$371$	2.11558	−	3.66429i	0.109835	−	0.190241i
$372$	13.6202	+	4.98068i	0.706173	+	0.258236i
$373$	25.0927	−	6.72356i	1.29925	−	0.348133i	0.458083	−	0.888909i	$-0.348536\pi$
$373$	25.0927	−	6.72356i	1.29925	−	0.348133i	0.841167	+	0.540776i	$0.181869\pi$
$374$	−1.05919	−	1.83457i	−0.0547694	−	0.0948634i
$375$		0			0
$376$	11.2536			0.580360
$377$	10.1887	+	26.9716i	0.524746	+	1.38911i
$378$	−2.33830	−	4.09284i	−0.120269	−	0.210513i
$379$	10.9047	+	18.8876i	0.560139	+	0.970189i	0.997484	+	0.0708954i	$0.0225857\pi$
$379$	10.9047	+	18.8876i	0.560139	+	0.970189i	−0.437345	+	0.899294i	$0.644081\pi$
$380$		0			0
$381$	−2.72148	+	30.5739i	−0.139425	+	1.56635i
$382$	−6.89790	−	6.89790i	−0.352927	−	0.352927i
$383$	−11.4935	+	3.07967i	−0.587290	+	0.157364i	−0.540215	−	0.841527i	$-0.681657\pi$
$383$	−11.4935	+	3.07967i	−0.587290	+	0.157364i	−0.0470758	+	0.998891i	$0.514990\pi$
$384$	19.9645	+	1.77710i	1.01881	+	0.0906874i
$385$		0			0
$386$	−29.7798	−	17.1934i	−1.51575	−	0.875120i
$387$	17.8202	−	12.3977i	0.905853	−	0.630210i
$388$	42.4510	+	11.3747i	2.15512	+	0.577463i
$389$	−18.6519			−0.945690			−0.472845	−	0.881146i	$-0.656773\pi$
$389$	−18.6519			−0.945690			−0.472845	+	0.881146i	$0.656773\pi$
$390$		0			0
$391$	11.0845			0.560566
$392$	10.1806	+	2.72788i	0.514198	+	0.137779i
$393$	−6.19152	+	1.08208i	−0.312321	+	0.0545836i
$394$	23.1396	+	13.3597i	1.16576	+	0.673050i
$395$		0			0
$396$	1.41228	+	3.91703i	0.0709696	+	0.196838i
$397$	16.8034	−	4.50246i	0.843340	−	0.225972i	0.188815	−	0.982013i	$-0.439535\pi$
$397$	16.8034	−	4.50246i	0.843340	−	0.225972i	0.654525	+	0.756041i	$0.272869\pi$
$398$	34.5962	+	34.5962i	1.73415	+	1.73415i
$399$	2.16933	+	0.193099i	0.108602	+	0.00966703i
$400$		0			0
$401$	−2.63268	−	4.55994i	−0.131470	−	0.227712i	0.792774	−	0.609516i	$-0.208636\pi$
$401$	−2.63268	−	4.55994i	−0.131470	−	0.227712i	−0.924243	+	0.381804i	$0.875303\pi$
$402$	34.1232	+	12.4783i	1.70191	+	0.622361i
$403$	−1.80036	+	10.9874i	−0.0896824	+	0.547324i
$404$	−23.6927			−1.17876
$405$		0			0
$406$	−3.62704	−	6.28221i	−0.180007	−	0.311781i
$407$	3.67004	−	0.983383i	0.181917	−	0.0487445i
$408$	1.75134	−	4.78921i	0.0867041	−	0.237101i
$409$	4.97625	−	8.61911i	0.246060	−	0.426188i	−0.716369	−	0.697721i	$-0.754197\pi$
$409$	4.97625	−	8.61911i	0.246060	−	0.426188i	0.962429	+	0.271534i	$0.0875308\pi$
$410$		0			0
$411$	−6.05725	+	2.81340i	−0.298782	+	0.138775i
$412$	7.97985	+	29.7812i	0.393139	+	1.46721i
$413$	0.812435	+	0.217691i	0.0399773	+	0.0107119i
$414$	−37.2631	−	6.68679i	−1.83138	−	0.328638i
$415$		0			0
$416$	2.71311	+	27.2086i	0.133021	+	1.33401i
$417$	−4.68802	+	12.8199i	−0.229573	+	0.627791i
$418$	−3.22902	−	0.865213i	−0.157936	−	0.0423189i
$419$	−8.67323	−	15.0225i	−0.423715	−	0.733896i	0.572584	−	0.819846i	$-0.305941\pi$
$419$	−8.67323	−	15.0225i	−0.423715	−	0.733896i	−0.996299	+	0.0859496i	$0.972608\pi$
$420$		0			0
$421$			9.95497i			0.485175i	0.970129	+	0.242588i	$0.0779962\pi$
$421$			9.95497i			0.485175i	−0.970129	+	0.242588i	$0.922004\pi$
$422$	−2.23639	−	8.34631i	−0.108866	−	0.406292i
$423$	9.29955	−	19.7864i	0.452160	−	0.962050i
$424$	−15.6337			−0.759238
$425$		0			0
$426$	18.0657	+	12.6905i	0.875288	+	0.614859i
$427$	−1.16738	+	4.35673i	−0.0564936	+	0.210837i
$428$	−23.1380	+	23.1380i	−1.11842	+	1.11842i
$429$	−2.75136	+	1.62765i	−0.132837	+	0.0785837i
$430$		0			0
$431$	6.30631	+	10.9229i	0.303764	+	0.526135i	0.976985	−	0.213306i	$-0.0684231\pi$
$431$	6.30631	+	10.9229i	0.303764	+	0.526135i	−0.673221	+	0.739441i	$0.735090\pi$
$432$	5.42291	−	9.29509i	0.260910	−	0.447210i
$433$	−21.8390	+	5.85174i	−1.04952	+	0.281217i	−0.742052	−	0.670343i	$-0.766147\pi$
$433$	−21.8390	+	5.85174i	−1.04952	+	0.281217i	−0.307464	+	0.951560i	$0.599480\pi$
$434$		−	2.80129i		−	0.134466i
$435$		0			0
$436$	33.1070	+	19.1143i	1.58554	+	0.915411i
$437$	12.3687	−	12.3687i	0.591674	−	0.591674i
$438$	−7.17097	−	8.57233i	−0.342642	−	0.409602i
$439$	10.2958	−	5.94428i	0.491391	−	0.283705i	−0.233760	−	0.972294i	$-0.575103\pi$
$439$	10.2958	−	5.94428i	0.491391	−	0.283705i	0.725152	+	0.688589i	$0.241770\pi$
$440$		0			0
$441$	13.2091	−	15.6456i	0.629005	−	0.745030i
$442$	14.7247	+	2.41273i	0.700382	+	0.114762i
$443$	14.0199	−	14.0199i	0.666105	−	0.666105i	−0.290707	−	0.956812i	$-0.593891\pi$
$443$	14.0199	−	14.0199i	0.666105	−	0.666105i	0.956812	+	0.290707i	$0.0938906\pi$
$444$	28.5241	+	20.0372i	1.35370	+	0.950923i
$445$		0			0
$446$	26.3771	+	15.2288i	1.24899	+	0.721105i
$447$	3.28115	−	8.97264i	0.155193	−	0.424391i
$448$	−1.33254	−	4.97309i	−0.0629564	−	0.234956i
$449$	−3.69387	−	2.13266i	−0.174324	−	0.100646i	0.410299	−	0.911951i	$-0.365424\pi$
$449$	−3.69387	−	2.13266i	−0.174324	−	0.100646i	−0.584623	+	0.811305i	$0.698758\pi$
$450$		0			0
$451$	−0.907865	+	1.57247i	−0.0427497	+	0.0740447i
$452$	−2.36216	+	8.81571i	−0.111107	+	0.414656i
$453$	5.97846	−	1.04484i	0.280893	−	0.0490910i
$454$		−	19.3322i		−	0.907304i
$455$		0			0
$456$	−3.38982	−	7.29830i	−0.158743	−	0.341774i
$457$	−6.74076	+	25.1569i	−0.315320	+	1.17679i	0.608372	+	0.793652i	$0.291823\pi$
$457$	−6.74076	+	25.1569i	−0.315320	+	1.17679i	−0.923692	+	0.383137i	$0.874844\pi$
$458$	29.1534	+	7.81163i	1.36225	+	0.365014i
$459$	−6.97330	−	7.03688i	−0.325486	−	0.328453i
$460$		0			0
$461$	−6.68465	+	11.5782i	−0.311335	+	0.539249i	−0.978652	−	0.205526i	$-0.934110\pi$
$461$	−6.68465	+	11.5782i	−0.311335	+	0.539249i	0.667316	+	0.744774i	$0.267443\pi$
$462$	0.616910	−	0.516061i	0.0287012	−	0.0240093i
$463$	−3.79477	+	3.79477i	−0.176358	+	0.176358i	−0.789766	−	0.613408i	$-0.789798\pi$
$463$	−3.79477	+	3.79477i	−0.176358	+	0.176358i	0.613408	+	0.789766i	$0.289798\pi$
$464$	8.28050	−	14.3422i	0.384412	−	0.665822i
$465$		0			0
$466$	28.4115	−	16.4034i	1.31614	−	0.759871i
$467$	−15.8650	−	15.8650i	−0.734143	−	0.734143i	0.237294	−	0.971438i	$-0.423739\pi$
$467$	−15.8650	−	15.8650i	−0.734143	−	0.734143i	−0.971438	+	0.237294i	$0.923739\pi$
$468$	−27.6499	−	9.77990i	−1.27812	−	0.452076i
$469$		−	4.03897i		−	0.186502i
$470$		0			0
$471$	2.54688	+	1.78909i	0.117354	+	0.0824369i
$472$	−0.804345	−	3.00186i	−0.0370230	−	0.138172i
$473$	2.61922	+	2.61922i	0.120432	+	0.120432i
$474$	−53.9147	−	4.79912i	−2.47638	−	0.220431i
$475$		0			0
$476$	−2.16050			−0.0990261
$477$	−12.9191	+	27.4876i	−0.591524	+	1.25857i
$478$	−1.20522	+	4.49794i	−0.0551254	+	0.205731i
$479$	17.3730	−	10.0303i	0.793793	−	0.458297i	−0.0475029	−	0.998871i	$-0.515126\pi$
$479$	17.3730	−	10.0303i	0.793793	−	0.458297i	0.841296	+	0.540574i	$0.181793\pi$
$480$		0			0
$481$	−11.0154	+	24.3901i	−0.502260	+	1.11209i
$482$	−7.97957	−	7.97957i	−0.363460	−	0.363460i
$483$	0.724531	+	4.14568i	0.0329673	+	0.188635i
$484$	25.2145	−	14.5576i	1.14611	−	0.661709i
$485$		0			0
$486$	19.1974	+	27.8628i	0.870810	+	1.26388i
$487$	27.5972	−	7.39466i	1.25055	−	0.335084i	0.428001	−	0.903778i	$-0.359218\pi$
$487$	27.5972	−	7.39466i	1.25055	−	0.335084i	0.822549	+	0.568694i	$0.192551\pi$
$488$	16.0976	−	4.31335i	0.728705	−	0.195256i
$489$	12.2554	−	5.69223i	0.554208	−	0.257411i
$490$		0			0
$491$	25.1585	−	14.5253i	1.13539	−	0.655516i	0.190103	−	0.981764i	$-0.439118\pi$
$491$	25.1585	−	14.5253i	1.13539	−	0.655516i	0.945284	+	0.326248i	$0.105785\pi$
$492$	−16.4097	+	2.86788i	−0.739806	+	0.129294i
$493$	−10.7805	−	10.7805i	−0.485528	−	0.485528i
$494$	19.1229	−	13.7384i	0.860379	−	0.618118i
$495$		0			0
$496$	5.53852	−	3.19767i	0.248687	−	0.143580i
$497$	0.635208	−	2.37063i	0.0284930	−	0.106337i
$498$	−25.1079	+	21.0034i	−1.12511	+	0.941186i
$499$	−20.0887			−0.899294			−0.449647	−	0.893206i	$-0.648450\pi$
$499$	−20.0887			−0.899294			−0.449647	+	0.893206i	$0.648450\pi$
$500$		0			0
$501$	−0.350205	+	3.93431i	−0.0156460	+	0.175772i
$502$	−5.33523	−	5.33523i	−0.238123	−	0.238123i
$503$	2.45860	+	9.17562i	0.109624	+	0.409121i	0.998829	−	0.0483882i	$-0.0154085\pi$
$503$	2.45860	+	9.17562i	0.109624	+	0.409121i	−0.889205	+	0.457509i	$0.848742\pi$
$504$	1.90567	+	0.341970i	0.0848855	+	0.0152325i
$505$		0			0
$506$		−	6.45976i		−	0.287171i
$507$	3.40504	−	22.2577i	0.151223	−	0.988500i
$508$	−33.9771	−	33.9771i	−1.50749	−	1.50749i
$509$	−35.0026	+	20.2088i	−1.55146	+	0.895738i	−0.553441	+	0.832888i	$0.686686\pi$
$509$	−35.0026	+	20.2088i	−1.55146	+	0.895738i	−0.998023	+	0.0628499i	$0.979981\pi$
$510$		0			0
$511$	−0.621201	+	1.07595i	−0.0274803	+	0.0475973i
$512$	15.6287	−	15.6287i	0.690696	−	0.690696i
$513$	−15.6333	−	0.0709447i	−0.690229	−	0.00313228i
$514$	−4.32863	+	7.49740i	−0.190927	+	0.330696i
$515$		0			0
$516$	−3.01307	+	33.8497i	−0.132643	+	1.49015i
$517$	3.60335	+	0.965514i	0.158475	+	0.0424632i
$518$	1.74272	−	6.50391i	0.0765707	−	0.285766i
$519$	35.5815	−	16.5264i	1.56185	−	0.725430i
$520$		0			0
$521$		−	3.29710i		−	0.144448i	−0.997388	−	0.0722242i	$-0.976990\pi$
$521$		−	3.29710i		−	0.144448i	0.997388	−	0.0722242i	$-0.0230097\pi$
$522$	29.7377	+	42.7445i	1.30158	+	1.87088i
$523$	−2.08910	+	7.79663i	−0.0913500	+	0.340923i	−0.996441	−	0.0842956i	$-0.973136\pi$
$523$	−2.08910	+	7.79663i	−0.0913500	+	0.340923i	0.905091	+	0.425218i	$0.139803\pi$
$524$	4.91969	−	8.52115i	0.214918	−	0.372248i
$525$		0			0
$526$	45.4018	+	26.2127i	1.97961	+	1.14293i
$527$	−1.52379	−	5.68687i	−0.0663774	−	0.247724i
$528$	1.72452	+	0.630630i	0.0750501	+	0.0274446i
$529$	9.35384	+	5.40044i	0.406689	+	0.234802i
$530$		0			0
$531$	−5.94264	−	1.06640i	−0.257889	−	0.0462776i
$532$	−2.41080	+	2.41080i	−0.104521	+	0.104521i
$533$	−4.51953	−	11.9641i	−0.195763	−	0.518224i
$534$	19.1952	+	41.3272i	0.830655	+	1.78840i
$535$		0			0
$536$	−12.9242	+	7.46177i	−0.558239	+	0.322299i
$537$	−13.0158	+	10.8880i	−0.561672	+	0.469853i
$538$	38.0818	−	38.0818i	1.64182	−	1.64182i
$539$	3.02573	+	1.74691i	0.130328	+	0.0752447i
$540$		0			0
$541$		−	20.9027i		−	0.898677i	−0.893362	−	0.449338i	$-0.851660\pi$
$541$		−	20.9027i		−	0.898677i	0.893362	−	0.449338i	$-0.148340\pi$
$542$	−45.3710	+	12.1571i	−1.94885	+	0.522193i
$543$	−0.449571	−	2.57239i	−0.0192929	−	0.110392i
$544$	−7.22944	−	12.5218i	−0.309960	−	0.536866i
$545$		0			0
$546$	0.0600909	+	5.66485i	0.00257165	+	0.242433i
$547$	4.29605	−	4.29605i	0.183686	−	0.183686i	−0.609274	−	0.792960i	$-0.708539\pi$
$547$	4.29605	−	4.29605i	0.183686	−	0.183686i	0.792960	+	0.609274i	$0.208539\pi$
$548$	2.70600	−	10.0989i	0.115594	−	0.431404i
$549$	5.71861	−	31.8678i	0.244064	−	1.36008i
$550$		0			0
$551$	−24.0589			−1.02494
$552$	11.9271	−	9.97731i	0.507651	−	0.424663i
$553$	1.55735	+	5.81209i	0.0662251	+	0.247155i
$554$		−	0.965776i		−	0.0410319i
$555$		0			0
$556$	−10.6843	−	18.5057i	−0.453113	−	0.784815i
$557$	−18.7339	−	5.01972i	−0.793779	−	0.212692i	−0.160928	−	0.986966i	$-0.551449\pi$
$557$	−18.7339	−	5.01972i	−0.793779	−	0.212692i	−0.632851	+	0.774274i	$0.718115\pi$
$558$	1.69194	+	20.0370i	0.0716257	+	0.848234i
$559$	−25.9617	+	2.58877i	−1.09806	+	0.109493i
$560$		0			0
$561$	0.971664	−	1.38322i	0.0410237	−	0.0583997i
$562$	21.4095	+	5.73665i	0.903104	+	0.241986i
$563$	−10.7184	−	40.0016i	−0.451727	−	1.68587i	−0.697536	−	0.716550i	$-0.745720\pi$
$563$	−10.7184	−	40.0016i	−0.451727	−	1.68587i	0.245809	−	0.969318i	$-0.420946\pi$
$564$	14.4172	+	31.0403i	0.607074	+	1.30703i
$565$		0			0
$566$	−8.98063	+	15.5549i	−0.377484	+	0.653822i
$567$	2.17604	−	3.06803i	0.0913851	−	0.128845i
$568$	−8.75920	+	2.34702i	−0.367528	+	0.0984788i
$569$	−8.79437	−	15.2323i	−0.368679	−	0.638571i	0.620680	−	0.784064i	$-0.286857\pi$
$569$	−8.79437	−	15.2323i	−0.368679	−	0.638571i	−0.989359	+	0.145493i	$0.953523\pi$
$570$		0			0
$571$	−28.6479			−1.19888			−0.599439	−	0.800420i	$-0.704610\pi$
$571$	−28.6479			−1.19888			−0.599439	+	0.800420i	$0.704610\pi$
$572$	0.809199	−	4.93847i	0.0338343	−	0.206488i
$573$	2.67343	−	7.31076i	0.111684	−	0.305411i
$574$	1.60889	+	2.78668i	0.0671537	+	0.116314i
$575$		0			0
$576$	12.5350	+	34.7665i	0.522292	+	1.44861i
$577$	7.73617	+	7.73617i	0.322061	+	0.322061i	0.849557	−	0.527496i	$-0.176869\pi$
$577$	7.73617	+	7.73617i	0.322061	+	0.322061i	−0.527496	+	0.849557i	$0.676869\pi$
$578$	28.0214	−	7.50830i	1.16554	−	0.312304i
$579$	2.43285	−	27.3314i	0.101106	−	1.13585i
$580$		0			0
$581$	3.15141	+	1.81947i	0.130743	+	0.0754842i
$582$	10.4909	+	60.0275i	0.434860	+	2.48822i
$583$	−5.00582	−	1.34131i	−0.207320	−	0.0555512i
$584$	4.59053			0.189958
$585$		0			0
$586$	−38.4926			−1.59011
$587$	−27.6328	−	7.40419i	−1.14053	−	0.305604i	−0.361365	−	0.932425i	$-0.617689\pi$
$587$	−27.6328	−	7.40419i	−1.14053	−	0.305604i	−0.779163	+	0.626821i	$0.784356\pi$
$588$	5.51836	+	31.5754i	0.227573	+	1.30215i
$589$	−8.04606	−	4.64539i	−0.331532	−	0.191410i
$590$		0			0
$591$	−1.89039	+	21.2372i	−0.0777601	+	0.873580i
$592$	14.8484	−	3.97861i	0.610265	−	0.163520i
$593$	−0.767325	−	0.767325i	−0.0315103	−	0.0315103i	0.691176	−	0.722686i	$-0.257093\pi$
$593$	−0.767325	−	0.767325i	−0.0315103	−	0.0315103i	−0.722686	+	0.691176i	$0.757093\pi$
$594$	−4.10092	+	4.06387i	−0.168263	+	0.166742i
$595$		0			0
$596$	7.47792	+	12.9521i	0.306308	+	0.530540i
$597$	−13.4085	+	36.6669i	−0.548773	+	1.50068i
$598$	35.2070	+	28.8223i	1.43972	+	1.17863i
$599$	28.3284			1.15747			0.578734	−	0.815516i	$-0.303547\pi$
$599$	28.3284			1.15747			0.578734	+	0.815516i	$0.303547\pi$
$600$		0			0
$601$	8.57196	+	14.8471i	0.349658	+	0.605625i	0.986189	−	0.165626i	$-0.0529646\pi$
$601$	8.57196	+	14.8471i	0.349658	+	0.605625i	−0.636531	+	0.771251i	$0.719631\pi$
$602$	6.34067	−	1.69898i	0.258426	−	0.0692451i
$603$	2.43948	+	28.8898i	0.0993435	+	1.17648i
$604$	−4.75039	+	8.22792i	−0.193291	+	0.334789i
$605$		0			0
$606$	−13.8386	−	29.7945i	−0.562153	−	1.21032i
$607$	−2.05233	−	7.65942i	−0.0833017	−	0.310886i	0.911685	−	0.410889i	$-0.134782\pi$
$607$	−2.05233	−	7.65942i	−0.0833017	−	0.310886i	−0.994987	+	0.100003i	$0.968115\pi$
$608$	−22.0395	−	5.90546i	−0.893819	−	0.239498i
$609$	3.32732	−	4.73664i	0.134830	−	0.191938i
$610$		0			0
$611$	−21.3397	+	15.3310i	−0.863313	+	0.620226i
$612$	15.4535	−	1.30491i	0.624671	−	0.0527479i
$613$	36.5885	+	9.80387i	1.47780	+	0.395975i	0.905597	−	0.424139i	$-0.139423\pi$
$613$	36.5885	+	9.80387i	1.47780	+	0.395975i	0.572200	+	0.820114i	$0.306090\pi$
$614$	27.7137	+	48.0016i	1.11843	+	1.93719i
$615$		0			0
$616$			0.330359i			0.0133105i
$617$	−0.539359	−	2.01292i	−0.0217138	−	0.0810369i	0.954219	−	0.299110i	$-0.0966896\pi$
$617$	−0.539359	−	2.01292i	−0.0217138	−	0.0810369i	−0.975933	+	0.218073i	$0.930023\pi$
$618$	−32.7900	+	27.4297i	−1.31901	+	1.10338i
$619$	−30.7890			−1.23751			−0.618757	−	0.785583i	$-0.712363\pi$
$619$	−30.7890			−1.23751			−0.618757	+	0.785583i	$0.712363\pi$
$620$		0			0
$621$	−7.68634	−	29.2155i	−0.308442	−	1.17238i
$622$	14.5851	−	54.4324i	0.584810	−	2.18254i
$623$	3.58185	−	3.58185i	0.143504	−	0.143504i
$624$	−11.1315	+	6.58521i	−0.445619	+	0.263620i
$625$		0			0
$626$	1.91820	+	3.32241i	0.0766665	+	0.132790i
$627$	−0.459239	−	2.62771i	−0.0183403	−	0.104941i
$628$	−4.70636	+	1.26106i	−0.187804	+	0.0503219i
$629$		−	14.1515i		−	0.564256i
$630$		0			0
$631$	−25.0094	−	14.4392i	−0.995608	−	0.574815i	−0.0886624	−	0.996062i	$-0.528259\pi$
$631$	−25.0094	−	14.4392i	−0.995608	−	0.574815i	−0.906946	+	0.421247i	$0.861593\pi$
$632$	15.7208	−	15.7208i	0.625340	−	0.625340i
$633$	5.28858	−	4.42403i	0.210202	−	0.175840i
$634$	33.7616	−	19.4923i	1.34084	−	0.774137i
$635$		0			0
$636$	−20.0286	−	43.1216i	−0.794185	−	1.70988i
$637$	−23.0213	+	8.69645i	−0.912136	+	0.344566i
$638$	−6.28259	+	6.28259i	−0.248730	+	0.248730i
$639$	−3.11167	+	17.3402i	−0.123096	+	0.685968i
$640$		0			0
$641$	−36.8548	−	21.2782i	−1.45568	−	0.840437i	−0.456885	−	0.889526i	$-0.651035\pi$
$641$	−36.8548	−	21.2782i	−1.45568	−	0.840437i	−0.998794	+	0.0490894i	$0.984368\pi$
$642$	−42.6115	−	15.5824i	−1.68174	−	0.614986i
$643$	−11.0203	−	41.1282i	−0.434597	−	1.62194i	−0.742029	−	0.670368i	$-0.766136\pi$
$643$	−11.0203	−	41.1282i	−0.434597	−	1.62194i	0.307432	−	0.951570i	$-0.400530\pi$
$644$	−5.70554	−	3.29409i	−0.224830	−	0.129806i
$645$		0			0
$646$	−6.22546	+	10.7828i	−0.244938	+	0.424244i
$647$	0.566681	−	2.11488i	0.0222785	−	0.0831446i	−0.953892	−	0.300152i	$-0.902963\pi$
$647$	0.566681	−	2.11488i	0.0222785	−	0.0831446i	0.976170	+	0.217007i	$0.0696294\pi$
$648$	−13.8374	−	1.29503i	−0.543584	−	0.0508735i
$649$		−	1.03019i		−	0.0404385i
$650$		0			0
$651$	2.02733	−	0.941629i	0.0794574	−	0.0369054i
$652$	−5.47493	+	20.4327i	−0.214415	+	0.800207i
$653$	20.0829	+	5.38119i	0.785904	+	0.210582i	0.629386	−	0.777093i	$-0.283306\pi$
$653$	20.0829	+	5.38119i	0.785904	+	0.210582i	0.156518	+	0.987675i	$0.449973\pi$
$654$	−4.69969	+	52.7977i	−0.183772	+	2.06455i
$655$		0			0
$656$	−3.67308	+	6.36196i	−0.143410	+	0.248393i
$657$	3.79345	−	8.07123i	0.147996	−	0.314889i
$658$	4.67468	−	4.67468i	0.182238	−	0.182238i
$659$	−6.20566	+	10.7485i	−0.241738	+	0.418703i	−0.961210	−	0.275819i	$-0.911051\pi$
$659$	−6.20566	+	10.7485i	−0.241738	+	0.418703i	0.719471	+	0.694522i	$0.244384\pi$
$660$		0			0
$661$	6.32611	−	3.65238i	0.246057	−	0.142061i	−0.371900	−	0.928273i	$-0.621294\pi$
$661$	6.32611	−	3.65238i	0.246057	−	0.142061i	0.617957	+	0.786212i	$0.287960\pi$
$662$	13.7286	+	13.7286i	0.533578	+	0.533578i
$663$	3.20344	+	11.4674i	0.124411	+	0.445359i
$664$		−	13.4454i		−	0.521785i
$665$		0			0
$666$	−8.53698	+	47.5736i	−0.330801	+	1.84344i
$667$	−12.0327	−	44.9065i	−0.465906	−	1.73879i
$668$	−4.37225	−	4.37225i	−0.169167	−	0.169167i
$669$	−2.15487	+	24.2084i	−0.0833120	+	0.935952i
$670$		0			0
$671$	5.52445			0.213269
$672$	4.21069	−	3.52234i	0.162431	−	0.135877i
$673$	0.383129	−	1.42986i	0.0147685	−	0.0551169i	−0.958148	−	0.286272i	$-0.907584\pi$
$673$	0.383129	−	1.42986i	0.0147685	−	0.0551169i	0.972917	+	0.231155i	$0.0742505\pi$
$674$	2.88866	−	1.66777i	0.111267	−	0.0642400i
$675$		0			0
$676$	23.3051	+	26.4448i	0.896351	+	1.01711i
$677$	13.3487	+	13.3487i	0.513033	+	0.513033i	0.915455	−	0.402421i	$-0.131831\pi$
$677$	13.3487	+	13.3487i	0.513033	+	0.513033i	−0.402421	+	0.915455i	$0.631831\pi$
$678$	−12.4658	+	2.17862i	−0.478746	+	0.0836693i
$679$	5.86653	−	3.38704i	0.225137	−	0.129983i
$680$		0			0
$681$	13.9909	−	6.49834i	0.536134	−	0.249017i
$682$	−3.31417	+	0.888028i	−0.126906	+	0.0340044i
$683$	10.7061	−	2.86868i	0.409656	−	0.109767i	−0.0481050	−	0.998842i	$-0.515318\pi$
$683$	10.7061	−	2.86868i	0.409656	−	0.109767i	0.457761	+	0.889075i	$0.348652\pi$
$684$	15.7878	−	18.7000i	0.603662	−	0.715012i
$685$		0			0
$686$	10.8614	−	6.27085i	0.414691	−	0.239422i
$687$	4.14627	+	23.7245i	0.158190	+	0.905145i
$688$	10.5969	+	10.5969i	0.404005	+	0.404005i
$689$	29.6454	−	21.2980i	1.12940	−	0.811391i
$690$		0			0
$691$	7.29352	−	4.21092i	0.277459	−	0.160191i	−0.354814	−	0.934937i	$-0.615456\pi$
$691$	7.29352	−	4.21092i	0.277459	−	0.160191i	0.632272	+	0.774746i	$0.282122\pi$
$692$	−15.8956	+	59.3230i	−0.604258	+	2.25512i
$693$	0.580848	+	0.272996i	0.0220646	+	0.0103703i
$694$	−77.2248			−2.93141
$695$		0			0
$696$	−21.3036	−	1.89630i	−0.807512	−	0.0718792i
$697$	4.78202	+	4.78202i	0.181132	+	0.181132i
$698$	0.651792	+	2.43252i	0.0246707	+	0.0920722i
$699$	21.4216	+	15.0479i	0.810238	+	0.569163i
$700$		0			0
$701$		−	9.61731i		−	0.363241i	−0.983369	−	0.181620i	$-0.941866\pi$
$701$		−	9.61731i		−	0.363241i	0.983369	−	0.181620i	$-0.0581342\pi$
$702$	−3.85131	−	40.4831i	−0.145358	−	1.52793i
$703$	−15.7910	−	15.7910i	−0.595569	−	0.595569i
$704$	−5.46116	+	3.15300i	−0.205825	+	0.118833i
$705$		0			0
$706$	34.0922	−	59.0493i	1.28308	−	2.22235i
$707$	−2.58230	+	2.58230i	−0.0971174	+	0.0971174i
$708$	7.24942	−	6.06432i	0.272450	−	0.227911i
$709$	15.7072	−	27.2057i	0.589896	−	1.02173i	−0.404349	−	0.914605i	$-0.632502\pi$
$709$	15.7072	−	27.2057i	0.589896	−	1.02173i	0.994246	−	0.107125i	$-0.0341647\pi$
$710$		0			0
$711$	−14.6498	−	40.6319i	−0.549409	−	1.52382i
$712$	−18.0787	−	4.84417i	−0.677528	−	0.181543i
$713$	4.64664	−	17.3415i	0.174018	−	0.649443i
$714$	−1.26191	−	2.71690i	−0.0472259	−	0.101677i
$715$		0			0
$716$		−	26.5646i		−	0.992764i
$717$	−3.66034	+	0.639709i	−0.136698	+	0.0238904i
$718$	10.4164	−	38.8745i	0.388736	−	1.45078i
$719$	−6.02748	+	10.4399i	−0.224787	+	0.389342i	−0.956256	−	0.292533i	$-0.905502\pi$
$719$	−6.02748	+	10.4399i	−0.224787	+	0.389342i	0.731469	+	0.681875i	$0.238835\pi$
$720$		0			0
$721$	4.11563	+	2.37616i	0.153274	+	0.0884927i
$722$	−5.58862	−	20.8570i	−0.207987	−	0.776218i
$723$	3.09265	−	8.45717i	0.115017	−	0.314526i
$724$	3.54028	+	2.04398i	0.131573	+	0.0759640i
$725$		0			0
$726$	33.0341	+	23.2053i	1.22601	+	0.861229i
$727$	1.96600	−	1.96600i	0.0729151	−	0.0729151i	−0.669709	−	0.742624i	$-0.733581\pi$
$727$	1.96600	−	1.96600i	0.0729151	−	0.0729151i	0.742624	+	0.669709i	$0.233581\pi$
$728$	−1.80052	−	1.47400i	−0.0667317	−	0.0546301i
$729$	−13.7117	+	23.2592i	−0.507839	+	0.861452i
$730$		0			0
$731$	11.9479	−	6.89814i	0.441910	−	0.255137i
$732$	32.5203	+	38.8754i	1.20198	+	1.43688i
$733$	29.6853	−	29.6853i	1.09645	−	1.09645i	0.101628	−	0.994822i	$-0.467595\pi$
$733$	29.6853	−	29.6853i	1.09645	−	1.09645i	0.994822	−	0.101628i	$-0.0324051\pi$
$734$	11.5077	+	6.64398i	0.424757	+	0.245234i
$735$		0			0
$736$		−	44.0907i		−	1.62521i
$737$	−4.77844	+	1.28038i	−0.176016	+	0.0471634i
$738$	−13.1911	−	18.9607i	−0.485572	−	0.697953i
$739$	16.6414	+	28.8238i	0.612164	+	1.06030i	0.990875	+	0.134784i	$0.0430340\pi$
$739$	16.6414	+	28.8238i	0.612164	+	1.06030i	−0.378711	+	0.925515i	$0.623633\pi$
$740$		0			0
$741$	16.3706	+	9.22144i	0.601389	+	0.338758i
$742$	−6.49413	+	6.49413i	−0.238407	+	0.238407i
$743$	−0.258881	+	0.966155i	−0.00949741	+	0.0354448i	−0.970512	−	0.241053i	$-0.922507\pi$
$743$	−0.258881	+	0.966155i	−0.00949741	+	0.0354448i	0.961015	+	0.276498i	$0.0891739\pi$
$744$	−6.75847	−	4.74758i	−0.247777	−	0.174055i
$745$		0			0
$746$	−56.3871			−2.06448
$747$	−23.6402	−	11.1108i	−0.864951	−	0.406524i
$748$	0.684891	+	2.55605i	0.0250421	+	0.0934584i
$749$			5.04369i			0.184292i
$750$		0			0
$751$	−8.71518	−	15.0951i	−0.318022	−	0.550829i	0.662054	−	0.749456i	$-0.269685\pi$
$751$	−8.71518	−	15.0951i	−0.318022	−	0.550829i	−0.980075	+	0.198627i	$0.936352\pi$
$752$	14.5786	+	3.90632i	0.531626	+	0.142449i
$753$	2.06778	−	5.65456i	0.0753542	−	0.206063i
$754$	−6.20956	−	62.2731i	−0.226139	−	2.26785i
$755$		0			0
$756$	1.49816	+	5.69444i	0.0544874	+	0.207105i
$757$	−15.6903	−	4.20419i	−0.570272	−	0.152804i	−0.0378509	−	0.999283i	$-0.512051\pi$
$757$	−15.6903	−	4.20419i	−0.570272	−	0.152804i	−0.532422	+	0.846479i	$0.678718\pi$
$758$	−12.2523	−	45.7262i	−0.445024	−	1.66085i
$759$	4.67501	−	2.17139i	0.169692	−	0.0788164i
$760$		0			0
$761$	7.90134	−	13.6855i	0.286423	−	0.496100i	−0.686530	−	0.727101i	$-0.740867\pi$
$761$	7.90134	−	13.6855i	0.286423	−	0.496100i	0.972953	+	0.231002i	$0.0742003\pi$
$762$	22.8819	−	62.5730i	0.828925	−	2.26678i
$763$	5.69167	−	1.52508i	0.206052	−	0.0552116i
$764$	6.09289	+	10.5532i	0.220433	+	0.381801i
$765$		0			0
$766$	25.8276			0.933190
$767$	5.61473	+	4.59652i	0.202736	+	0.165971i
$768$	−0.780830	−	0.285537i	−0.0281758	−	0.0103034i
$769$	8.96855	+	15.5340i	0.323414	+	0.560170i	0.981190	−	0.193044i	$-0.0618360\pi$
$769$	8.96855	+	15.5340i	0.323414	+	0.560170i	−0.657776	+	0.753214i	$0.728503\pi$
$770$		0			0
$771$	−6.88099	−	0.612498i	−0.247813	−	0.0220586i
$772$	30.3737	+	30.3737i	1.09317	+	1.09317i
$773$	15.7622	−	4.22347i	0.566927	−	0.151908i	0.0360399	−	0.999350i	$-0.488526\pi$
$773$	15.7622	−	4.22347i	0.566927	−	0.151908i	0.530887	+	0.847443i	$0.321859\pi$
$774$	−44.3271	+	15.9821i	−1.59331	+	0.574463i
$775$		0			0
$776$	−21.6762	−	12.5147i	−0.778129	−	0.449253i
$777$	5.29276	−	0.925004i	0.189877	−	0.0331843i
$778$	39.1060	+	10.4784i	1.40202	+	0.375670i
$779$	10.6721			0.382367
$780$		0			0
$781$	−3.00602			−0.107564
$782$	−23.2400	−	6.22713i	−0.831059	−	0.222682i
$783$	−20.9387	+	35.8897i	−0.748287	+	1.28259i
$784$	12.2416	+	7.06771i	0.437201	+	0.252418i
$785$		0			0
$786$	13.5892	+	1.20961i	0.484710	+	0.0431455i
$787$	7.64525	−	2.04854i	0.272524	−	0.0730225i	−0.119969	−	0.992778i	$-0.538280\pi$
$787$	7.64525	−	2.04854i	0.272524	−	0.0730225i	0.392493	+	0.919755i	$0.371613\pi$
$788$	−23.6011	−	23.6011i	−0.840754	−	0.840754i
$789$	−3.70909	+	41.6690i	−0.132047	+	1.48346i
$790$		0			0
$791$	0.703381	+	1.21829i	0.0250093	+	0.0433174i
$792$	−0.199532	−	2.36298i	−0.00709007	−	0.0839648i
$793$	−24.6491	+	30.1093i	−0.875315	+	1.06921i
$794$	−37.7598			−1.34005
$795$		0			0
$796$	−30.5587	−	52.9292i	−1.08312	−	1.87603i
$797$	6.26020	−	1.67742i	0.221748	−	0.0594171i	−0.146234	−	0.989250i	$-0.546715\pi$
$797$	6.26020	−	1.67742i	0.221748	−	0.0594171i	0.367982	+	0.929833i	$0.380049\pi$
$798$	−4.43978	−	1.62356i	−0.157167	−	0.0574733i
$799$	6.94716	−	12.0328i	0.245773	−	0.425691i
$800$		0			0
$801$	−23.4568	+	27.7835i	−0.828804	+	0.981683i
$802$	2.95802	+	11.0395i	0.104451	+	0.389817i
$803$	1.46987	+	0.393850i	0.0518705	+	0.0138986i
$804$	−37.1388	−	26.0887i	−1.30979	−	0.920078i
$805$		0			0
$806$	9.94729	−	22.0251i	0.350378	−	0.775801i
$807$	40.3611	+	14.7594i	1.42078	+	0.519556i
$808$	13.0337	+	3.49236i	0.458523	+	0.122861i
$809$	7.98528	+	13.8309i	0.280748	+	0.486269i	0.971569	−	0.236756i	$-0.0760843\pi$
$809$	7.98528	+	13.8309i	0.280748	+	0.486269i	−0.690821	+	0.723025i	$0.742751\pi$
$810$		0			0
$811$			8.00665i			0.281151i	0.990070	+	0.140576i	$0.0448953\pi$
$811$			8.00665i			0.281151i	−0.990070	+	0.140576i	$0.955105\pi$
$812$	2.34531	+	8.75280i	0.0823041	+	0.307163i
$813$	−24.0493	−	28.7490i	−0.843445	−	1.00827i
$814$	−8.24713			−0.289062
$815$		0			0
$816$	3.93120	−	5.59630i	0.137619	−	0.195910i
$817$	5.63483	−	21.0295i	0.197138	−	0.735728i
$818$	−15.2754	+	15.2754i	−0.534092	+	0.534092i
$819$	−4.07952	+	1.94768i	−0.142550	+	0.0680573i
$820$		0			0
$821$	−25.1045	−	43.4822i	−0.876152	−	1.51754i	−0.855530	−	0.517753i	$-0.826769\pi$
$821$	−25.1045	−	43.4822i	−0.876152	−	1.51754i	−0.0206220	−	0.999787i	$-0.506565\pi$
$822$	14.2803	−	2.49573i	0.498082	−	0.0870487i
$823$	−47.1413	+	12.6315i	−1.64324	+	0.440306i	−0.957710	−	0.287735i	$-0.907098\pi$
$823$	−47.1413	+	12.6315i	−1.64324	+	0.440306i	−0.685534	+	0.728041i	$0.740431\pi$
$824$		−	17.5593i		−	0.611706i
$825$		0			0
$826$	−1.58107	−	0.912833i	−0.0550126	−	0.0317615i
$827$	−30.0940	+	30.0940i	−1.04647	+	1.04647i	−0.0476050	+	0.998866i	$0.515159\pi$
$827$	−30.0940	+	30.0940i	−1.04647	+	1.04647i	−0.998866	+	0.0476050i	$0.984841\pi$
$828$	42.8000	+	20.1158i	1.48740	+	0.699073i
$829$	9.32181	−	5.38195i	0.323760	−	0.186923i	−0.329307	−	0.944223i	$-0.606815\pi$
$829$	9.32181	−	5.38195i	0.323760	−	0.186923i	0.653067	+	0.757300i	$0.273482\pi$
$830$		0			0
$831$	0.698944	−	0.324637i	0.0242461	−	0.0112615i
$832$	7.18224	−	43.8325i	0.248999	−	1.51962i
$833$	9.20153	−	9.20153i	0.318814	−	0.318814i
$834$	17.0310	−	24.2447i	0.589737	−	0.839526i
$835$		0			0
$836$	3.61642	+	2.08794i	0.125076	+	0.0722129i
$837$	−13.9323	+	7.95974i	−0.481571	+	0.275129i
$838$	9.74504	+	36.3690i	0.336637	+	1.25635i
$839$	24.9640	+	14.4130i	0.861854	+	0.497592i	0.864633	−	0.502405i	$-0.167551\pi$
$839$	24.9640	+	14.4130i	0.861854	+	0.497592i	−0.00277877	+	0.999996i	$0.500885\pi$
$840$		0			0
$841$	−17.4722	+	30.2628i	−0.602490	+	1.04354i
$842$	5.59258	−	20.8718i	0.192733	−	0.719289i
$843$	3.04491	+	17.4226i	0.104872	+	0.600067i
$844$			10.7937i			0.371536i
$845$		0			0
$846$	−30.6134	+	36.2603i	−1.05251	+	1.24666i
$847$	1.16151	−	4.33481i	0.0399099	−	0.148946i
$848$	−20.2528	−	5.42671i	−0.695482	−	0.186354i
$849$	−14.2760	−	1.27075i	−0.489952	−	0.0436122i
$850$		0			0
$851$	21.5767	−	37.3719i	0.739639	−	1.28109i
$852$	−17.6953	−	21.1533i	−0.606230	−	0.724700i
$853$	−18.6086	+	18.6086i	−0.637146	+	0.637146i	−0.949851	−	0.312704i	$-0.898765\pi$
$853$	−18.6086	+	18.6086i	−0.637146	+	0.637146i	0.312704	+	0.949851i	$0.398765\pi$
$854$	4.89512	−	8.47859i	0.167507	−	0.290131i
$855$		0			0
$856$	16.1391	−	9.31793i	0.551624	−	0.318480i
$857$	−4.26135	−	4.26135i	−0.145565	−	0.145565i	0.630569	−	0.776134i	$-0.282822\pi$
$857$	−4.26135	−	4.26135i	−0.145565	−	0.145565i	−0.776134	+	0.630569i	$0.782822\pi$
$858$	6.68294	−	1.86689i	0.228152	−	0.0637345i
$859$		−	29.4002i		−	1.00312i	−0.865122	−	0.501561i	$-0.832759\pi$
$859$		−	29.4002i		−	1.00312i	0.865122	−	0.501561i	$-0.167241\pi$
$860$		0			0
$861$	−1.47594	+	2.10109i	−0.0502999	+	0.0716049i
$862$	−7.08562	−	26.4439i	−0.241337	−	0.900683i
$863$	−23.1832	−	23.1832i	−0.789164	−	0.789164i	0.192193	−	0.981357i	$-0.438440\pi$
$863$	−23.1832	−	23.1832i	−0.789164	−	0.789164i	−0.981357	+	0.192193i	$0.938440\pi$
$864$	−27.9906	+	27.7377i	−0.952260	+	0.943656i
$865$		0			0
$866$	49.0756			1.66766
$867$	14.8530	+	17.7556i	0.504433	+	0.603011i
$868$	−0.905684	+	3.38006i	−0.0307409	+	0.114727i
$869$	6.38250	−	3.68494i	0.216512	−	0.125003i
$870$		0			0
$871$	14.3422	−	31.7563i	0.485968	−	1.07602i
$872$	−15.3951	−	15.3951i	−0.521343	−	0.521343i
$873$	−39.9162	+	27.7700i	−1.35096	+	0.939874i
$874$	−32.8810	+	18.9839i	−1.11222	+	0.642139i
$875$		0			0
$876$	5.88102	+	12.6619i	0.198701	+	0.427805i
$877$	−43.6039	+	11.6836i	−1.47240	+	0.394529i	−0.903754	−	0.428053i	$-0.859200\pi$
$877$	−43.6039	+	11.6836i	−1.47240	+	0.394529i	−0.568647	+	0.822582i	$0.692533\pi$
$878$	−24.9258	+	6.67885i	−0.841205	+	0.225400i
$879$	−12.9389	−	27.8576i	−0.436419	−	0.939612i
$880$		0			0
$881$	−12.6778	+	7.31952i	−0.427125	+	0.246601i	−0.698121	−	0.715980i	$-0.745980\pi$
$881$	−12.6778	+	7.31952i	−0.427125	+	0.246601i	0.270996	+	0.962580i	$0.412647\pi$
$882$	−36.4840	+	25.3823i	−1.22848	+	0.854665i
$883$	−8.31854	−	8.31854i	−0.279941	−	0.279941i	0.553144	−	0.833086i	$-0.313428\pi$
$883$	−8.31854	−	8.31854i	−0.279941	−	0.279941i	−0.833086	+	0.553144i	$0.813428\pi$
$884$	−16.9868	−	7.67183i	−0.571329	−	0.258032i
$885$		0			0
$886$	−37.2706	+	21.5182i	−1.25213	+	0.722917i
$887$	13.7391	−	51.2751i	0.461314	−	1.72165i	−0.207515	−	0.978232i	$-0.566538\pi$
$887$	13.7391	−	51.2751i	0.461314	−	1.72165i	0.668829	−	0.743416i	$-0.266796\pi$
$888$	−12.7380	−	15.2272i	−0.427458	−	0.510992i
$889$	−7.40642			−0.248403
$890$		0			0
$891$	−4.31956	−	1.60185i	−0.144711	−	0.0536641i
$892$	−26.9031	−	26.9031i	−0.900782	−	0.900782i
$893$	−5.67488	−	21.1789i	−0.189903	−	0.708726i
$894$	−11.9201	+	16.9689i	−0.398666	+	0.567525i
$895$		0			0
$896$			4.83633i			0.161571i
$897$	−9.02455	+	35.1681i	−0.301321	+	1.17423i
$898$	6.54654	+	6.54654i	0.218461	+	0.218461i
$899$	−21.3850	+	12.3467i	−0.713231	+	0.411784i
$900$		0			0
$901$	−9.65110	+	16.7162i	−0.321525	+	0.556897i
$902$	2.78684	−	2.78684i	0.0927918	−	0.0927918i
$903$	3.36093	+	4.01772i	0.111845	+	0.133701i
$904$	2.59891	−	4.50145i	0.0864385	−	0.149716i
$905$		0			0
$906$	−13.1215	−	1.16799i	−0.435934	−	0.0388039i
$907$	−16.3128	−	4.37099i	−0.541657	−	0.145136i	−0.0223908	−	0.999749i	$-0.507128\pi$
$907$	−16.3128	−	4.37099i	−0.541657	−	0.145136i	−0.519266	+	0.854613i	$0.673794\pi$
$908$	−6.25027	+	23.3263i	−0.207422	+	0.774111i
$909$	16.9109	−	20.0303i	0.560900	−	0.664362i
$910$		0			0
$911$			52.3968i			1.73598i	0.496579	+	0.867992i	$0.334589\pi$
$911$			52.3968i			1.73598i	−0.496579	+	0.867992i	$0.665411\pi$
$912$	−1.85801	−	10.6313i	−0.0615248	−	0.352038i
$913$	1.15357	−	4.30517i	0.0381775	−	0.142480i
$914$	28.2656	−	48.9575i	0.934945	−	1.61937i
$915$		0			0
$916$	−32.6511	−	18.8511i	−1.07882	−	0.622858i
$917$	−0.392528	−	1.46493i	−0.0129624	−	0.0483764i
$918$	10.6671	+	18.6712i	0.352068	+	0.616241i
$919$	12.0636	+	6.96489i	0.397940	+	0.229751i	0.685595	−	0.727983i	$-0.259542\pi$
$919$	12.0636	+	6.96489i	0.397940	+	0.229751i	−0.287655	+	0.957734i	$0.592876\pi$
$920$		0			0
$921$	−25.4236	+	36.1920i	−0.837736	+	1.19257i
$922$	20.5197	−	20.5197i	0.675779	−	0.675779i
$923$	13.4123	−	16.3834i	0.441472	−	0.539266i
$924$	−0.911214	+	0.423229i	−0.0299767	+	0.0139232i
$925$		0			0
$926$	10.0880	−	5.82433i	0.331514	−	0.191400i
$927$	−30.8733	−	14.5103i	−1.01401	−	0.476581i
$928$	−42.8815	+	42.8815i	−1.40765	+	1.40765i
$929$	0.125289	+	0.0723356i	0.00411060	+	0.00237325i	0.502054	−	0.864836i	$-0.332578\pi$
$929$	0.125289	+	0.0723356i	0.00411060	+	0.00237325i	−0.497943	+	0.867210i	$0.665911\pi$
$930$		0			0
$931$		−	20.5352i		−	0.673013i
$932$	−39.5848	+	10.6067i	−1.29664	+	0.347434i
$933$	44.2961	−	7.74152i	1.45019	−	0.253446i
$934$	24.3501	+	42.1756i	0.796759	+	1.38003i
$935$		0			0
$936$	13.7690	+	9.45570i	0.450053	+	0.309069i
$937$	−35.9634	+	35.9634i	−1.17487	+	1.17487i	−0.193841	+	0.981033i	$0.562095\pi$
$937$	−35.9634	+	35.9634i	−1.17487	+	1.17487i	−0.981033	+	0.193841i	$0.937905\pi$
$938$	−2.26904	+	8.46819i	−0.0740869	+	0.276496i
$939$	−1.75969	+	2.50502i	−0.0574252	+	0.0817482i
$940$		0			0
$941$	28.4119			0.926201			0.463101	−	0.886306i	$-0.346737\pi$
$941$	28.4119			0.926201			0.463101	+	0.886306i	$0.346737\pi$
$942$	−4.33474	−	5.18185i	−0.141234	−	0.168834i
$943$	5.33747	+	19.9197i	0.173812	+	0.648675i
$944$		−	4.16798i		−	0.135656i
$945$		0			0
$946$	−4.02006	−	6.96295i	−0.130704	−	0.226385i
$947$	49.3529	+	13.2241i	1.60375	+	0.429725i	0.946174	−	0.323659i	$-0.104913\pi$
$947$	49.3529	+	13.2241i	1.60375	+	0.429725i	0.657581	+	0.753384i	$0.271580\pi$
$948$	63.5022	+	23.2217i	2.06246	+	0.754207i
$949$	−8.70484	+	6.25377i	−0.282571	+	0.203006i
$950$		0			0
$951$	25.4554	+	17.8815i	0.825449	+	0.579849i
$952$	1.18852	+	0.318462i	0.0385200	+	0.0103214i
$953$	3.42531	+	12.7834i	0.110957	+	0.414095i	0.998953	−	0.0457555i	$-0.0145695\pi$
$953$	3.42531	+	12.7834i	0.110957	+	0.414095i	−0.887996	+	0.459851i	$0.847903\pi$
$954$	42.5286	−	50.3733i	1.37691	−	1.63090i
$955$		0			0
$956$	2.90845	−	5.03758i	0.0940659	−	0.162927i
$957$	−6.65862	−	2.43495i	−0.215243	−	0.0787108i
$958$	−42.0595	+	11.2698i	−1.35888	+	0.364111i
$959$	−0.805764	−	1.39562i	−0.0260195	−	0.0450671i
$960$		0			0
$961$	21.4642			0.692394
$962$	36.7972	−	44.9485i	1.18639	−	1.44920i
$963$	−3.04632	−	36.0763i	−0.0981663	−	1.16254i
$964$	7.04833	+	12.2081i	0.227011	+	0.393195i
$965$		0			0
$966$	0.809926	−	9.09895i	0.0260589	−	0.292754i
$967$	11.1974	+	11.1974i	0.360084	+	0.360084i	0.863844	−	0.503760i	$-0.168050\pi$
$967$	11.1974	+	11.1974i	0.360084	+	0.360084i	−0.503760	+	0.863844i	$0.668050\pi$
$968$	−16.0166	+	4.29165i	−0.514794	+	0.137939i
$969$	−9.89629	−	0.880900i	−0.317915	−	0.0282986i
$970$		0			0
$971$	28.5582	+	16.4881i	0.916478	+	0.529129i	0.882510	−	0.470294i	$-0.155852\pi$
$971$	28.5582	+	16.4881i	0.916478	+	0.529129i	0.0339681	+	0.999423i	$0.489186\pi$
$972$	−14.1553	−	39.8261i	−0.454033	−	1.27742i
$973$	−3.18145	−	0.852466i	−0.101993	−	0.0273288i
$974$	−62.0152			−1.98710
$975$		0			0
$976$	22.3510			0.715439
$977$	−18.7761	−	5.03105i	−0.600701	−	0.160957i	−0.0543619	−	0.998521i	$-0.517312\pi$
$977$	−18.7761	−	5.03105i	−0.600701	−	0.160957i	−0.546339	+	0.837564i	$0.683979\pi$
$978$	−28.8927	+	5.04952i	−0.923887	+	0.161466i
$979$	−5.37310	−	3.10216i	−0.171725	−	0.0991455i
$980$		0			0
$981$	−39.7901	+	14.3462i	−1.27040	+	0.458040i
$982$	−60.9079	+	16.3202i	−1.94365	+	0.520799i
$983$	33.5020	+	33.5020i	1.06855	+	1.06855i	0.997471	+	0.0710772i	$0.0226437\pi$
$983$	33.5020	+	33.5020i	1.06855	+	1.06855i	0.0710772	+	0.997471i	$0.477356\pi$
$984$	9.44991	+	0.841166i	0.301252	+	0.0268154i
$985$		0			0
$986$	16.5462	+	28.6589i	0.526939	+	0.912685i
$987$	4.95447	+	1.81177i	0.157702	+	0.0576693i
$988$	−27.5155	+	10.3942i	−0.875385	+	0.330683i
$989$	42.0702			1.33775
$990$		0			0
$991$	27.1809	+	47.0787i	0.863431	+	1.49551i	0.868597	+	0.495519i	$0.165022\pi$
$991$	27.1809	+	47.0787i	0.863431	+	1.49551i	−0.00516644	+	0.999987i	$0.501645\pi$
$992$	−22.6207	+	6.06119i	−0.718207	+	0.192443i
$993$	−5.32082	+	14.5503i	−0.168851	+	0.461741i
$994$	−2.66358	+	4.61346i	−0.0844837	+	0.146330i
$995$		0			0
$996$	37.0860	−	17.2252i	1.17511	−	0.545802i
$997$	4.05645	+	15.1389i	0.128469	+	0.479453i	0.999940	−	0.0109949i	$-0.00349985\pi$
$997$	4.05645	+	15.1389i	0.128469	+	0.479453i	−0.871471	+	0.490448i	$0.836833\pi$
$998$	42.1184	+	11.2856i	1.33323	+	0.357239i
$999$	−37.2992	+	9.81309i	−1.18009	+	0.310472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.218.4		96
3.2	odd	2	inner	975.2.bn.d.218.21		96
5.2	odd	4	inner	975.2.bn.d.257.21		96
5.3	odd	4		195.2.bf.a.62.4	yes	96
5.4	even	2		195.2.bf.a.23.21	yes	96
13.4	even	6	inner	975.2.bn.d.368.4		96
15.2	even	4	inner	975.2.bn.d.257.4		96
15.8	even	4		195.2.bf.a.62.21	yes	96
15.14	odd	2		195.2.bf.a.23.4	yes	96
39.17	odd	6	inner	975.2.bn.d.368.21		96
65.4	even	6		195.2.bf.a.173.21	yes	96
65.17	odd	12	inner	975.2.bn.d.407.21		96
65.43	odd	12		195.2.bf.a.17.4	✓	96
195.17	even	12	inner	975.2.bn.d.407.4		96
195.134	odd	6		195.2.bf.a.173.4	yes	96
195.173	even	12		195.2.bf.a.17.21	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.4	✓	96	65.43	odd	12
195.2.bf.a.17.21	yes	96	195.173	even	12
195.2.bf.a.23.4	yes	96	15.14	odd	2
195.2.bf.a.23.21	yes	96	5.4	even	2
195.2.bf.a.62.4	yes	96	5.3	odd	4
195.2.bf.a.62.21	yes	96	15.8	even	4
195.2.bf.a.173.4	yes	96	195.134	odd	6
195.2.bf.a.173.21	yes	96	65.4	even	6
975.2.bn.d.218.4		96	1.1	even	1	trivial
975.2.bn.d.218.21		96	3.2	odd	2	inner
975.2.bn.d.257.4		96	15.2	even	4	inner
975.2.bn.d.257.21		96	5.2	odd	4	inner
975.2.bn.d.368.4		96	13.4	even	6	inner
975.2.bn.d.368.21		96	39.17	odd	6	inner
975.2.bn.d.407.4		96	195.17	even	12	inner
975.2.bn.d.407.21		96	65.17	odd	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.09662 - 0.561788i) q^{2} +(-0.298187 - 1.70619i) q^{3} +(2.34816 + 1.35571i) q^{4} +(-0.333332 + 3.74475i) q^{6} +(0.403690 - 0.108168i) q^{7} +(-1.09192 - 1.09192i) q^{8} +(-2.82217 + 1.01753i) q^{9} +(-0.255945 - 0.443309i) q^{11} +(1.61291 - 4.41067i) q^{12} +(3.55810 + 0.583017i) q^{13} -0.907153 q^{14} +(-1.03551 - 1.79356i) q^{16} +(-1.84160 + 0.493455i) q^{17} +(6.48865 - 0.547908i) q^{18} +(-1.50433 + 2.60558i) q^{19} +(-0.304931 - 0.656518i) q^{21} +(0.287573 + 1.07324i) q^{22} +(-5.61575 - 1.50474i) q^{23} +(-1.53743 + 2.18862i) q^{24} +(-7.13246 - 3.22126i) q^{26} +(2.57763 + 4.51174i) q^{27} +(1.09458 + 0.293291i) q^{28} +(3.99826 + 6.92519i) q^{29} +3.08801i q^{31} +(1.96282 + 7.32533i) q^{32} +(-0.680051 + 0.568879i) q^{33} +4.13835 q^{34} +(-8.00639 - 1.43673i) q^{36} +(-1.92109 + 7.16959i) q^{37} +(4.61780 - 4.61780i) q^{38} +(-0.0662412 - 6.24465i) q^{39} +(-1.77356 - 3.07189i) q^{41} +(0.270501 + 1.54778i) q^{42} +(-6.98963 + 1.87287i) q^{43} -1.38795i q^{44} +(10.9288 + 6.30972i) q^{46} +(-5.15313 + 5.15313i) q^{47} +(-2.75138 + 2.30160i) q^{48} +(-5.91091 + 3.41267i) q^{49} +(1.39107 + 2.99498i) q^{51} +(7.56460 + 6.19278i) q^{52} +(7.15880 - 7.15880i) q^{53} +(-2.86967 - 10.9075i) q^{54} +(-0.558908 - 0.322686i) q^{56} +(4.89419 + 1.78973i) q^{57} +(-4.49235 - 16.7657i) q^{58} +(1.74290 + 1.00626i) q^{59} +(-5.39613 + 9.34638i) q^{61} +(1.73481 - 6.47438i) q^{62} +(-1.02922 + 0.716035i) q^{63} -12.3191i q^{64} +(1.74540 - 0.810680i) q^{66} +(2.50128 - 9.33491i) q^{67} +(-4.99336 - 1.33797i) q^{68} +(-0.892822 + 10.0302i) q^{69} +(2.93620 - 5.08564i) q^{71} +(4.19264 + 1.97052i) q^{72} +(-2.10205 + 2.10205i) q^{73} +(8.05558 - 13.9527i) q^{74} +(-7.06484 + 4.07889i) q^{76} +(-0.151274 - 0.151274i) q^{77} +(-3.36928 + 13.1299i) q^{78} +14.3974i q^{79} +(6.92928 - 5.74327i) q^{81} +(1.99273 + 7.43696i) q^{82} +(6.15680 + 6.15680i) q^{83} +(0.174021 - 1.95501i) q^{84} +15.7068 q^{86} +(10.6235 - 8.88680i) q^{87} +(-0.204587 + 0.763529i) q^{88} +(10.4966 - 6.06022i) q^{89} +(1.49943 - 0.149516i) q^{91} +(-11.1467 - 11.1467i) q^{92} +(5.26873 - 0.920803i) q^{93} +(13.6991 - 7.90919i) q^{94} +(11.9131 - 5.53326i) q^{96} +(15.6563 - 4.19510i) q^{97} +(14.3101 - 3.83439i) q^{98} +(1.17340 + 0.990663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more