LMFDB - Embedded newform 950.2.bb.c.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			193.1
Character	$\chi$	$=$	950.193
Dual form			950.2.bb.c.507.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0871557 - 0.996195i) q^{2} +(-1.14235 + 2.44977i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(2.54001 + 0.924487i) q^{6} +(-1.86007 - 0.498404i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.76804 - 3.29882i) q^{9} +O(q^{10})$	\(q+(-0.0871557 - 0.996195i) q^{2} +(-1.14235 + 2.44977i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(2.54001 + 0.924487i) q^{6} +(-1.86007 - 0.498404i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.76804 - 3.29882i) q^{9} +(2.06416 - 3.57523i) q^{11} +(0.699593 - 2.61092i) q^{12} +(1.97909 - 0.922865i) q^{13} +(-0.334392 + 1.89643i) q^{14} +(0.939693 - 0.342020i) q^{16} +(2.23346 - 0.195403i) q^{17} +(-3.04502 + 3.04502i) q^{18} +(4.33300 + 0.474447i) q^{19} +(3.34581 - 3.98739i) q^{21} +(-3.74153 - 1.74470i) q^{22} +(-3.10351 + 4.43228i) q^{23} +(-2.66195 - 0.469374i) q^{24} +(-1.09184 - 1.89113i) q^{26} +(3.41066 - 0.913885i) q^{27} +(1.91836 + 0.167835i) q^{28} +(5.15117 - 4.32234i) q^{29} +(-4.36707 + 2.52133i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(6.40049 + 9.14085i) q^{33} +(-0.389318 - 2.20793i) q^{34} +(3.29882 + 2.76804i) q^{36} +(7.78564 + 7.78564i) q^{37} +(0.0949956 - 4.35786i) q^{38} +5.90254i q^{39} +(1.89280 + 5.20044i) q^{41} +(-4.26382 - 2.98556i) q^{42} +(1.70270 - 1.19225i) q^{43} +(-1.41197 + 3.87935i) q^{44} +(4.68590 + 2.70541i) q^{46} +(-0.279626 + 3.19614i) q^{47} +(-0.235584 + 2.69273i) q^{48} +(-2.85073 - 1.64587i) q^{49} +(-2.07269 + 5.69468i) q^{51} +(-1.78877 + 1.25251i) q^{52} +(2.14091 + 1.49908i) q^{53} +(-1.20767 - 3.31804i) q^{54} -1.92569i q^{56} +(-6.11207 + 10.0729i) q^{57} +(-4.75485 - 4.75485i) q^{58} +(1.19639 + 1.00389i) q^{59} +(1.80359 + 10.2287i) q^{61} +(2.89235 + 4.13070i) q^{62} +(3.50460 + 7.51565i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(8.54823 - 7.17281i) q^{66} +(-7.61405 - 0.666143i) q^{67} +(-2.16560 + 0.580271i) q^{68} +(-7.31276 - 12.6661i) q^{69} +(4.33664 + 0.764666i) q^{71} +(2.47000 - 3.52752i) q^{72} +(9.34513 + 4.35771i) q^{73} +(7.07745 - 8.43458i) q^{74} +(-4.34956 + 0.285179i) q^{76} +(-5.62139 + 5.62139i) q^{77} +(5.88008 - 0.514440i) q^{78} +(11.2708 - 4.10225i) q^{79} +(0.585997 - 3.32336i) q^{81} +(5.01568 - 2.33885i) q^{82} +(4.28190 - 15.9803i) q^{83} +(-2.60258 + 4.50780i) q^{84} +(-1.33611 - 1.59231i) q^{86} +(4.70432 + 17.5568i) q^{87} +(3.98765 + 1.06849i) q^{88} +(6.73471 + 2.45124i) q^{89} +(-4.14120 + 0.730206i) q^{91} +(2.28671 - 4.90386i) q^{92} +(-1.18797 - 13.5785i) q^{93} +3.20835 q^{94} +2.70302 q^{96} +(-0.791080 - 9.04209i) q^{97} +(-1.39115 + 2.98333i) q^{98} +(-17.5077 + 3.08708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{6}+O(q^{10}) $ 72 * q + 24 * q^6	$ 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) $ 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$3$	−1.14235	+	2.44977i	−0.659533	+	1.41437i	0.237050	+	0.971498i	$0.423820\pi$
$3$	−1.14235	+	2.44977i	−0.659533	+	1.41437i	−0.896583	+	0.442876i	$0.853958\pi$
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$		0			0
$5$		0			0
$6$	2.54001	+	0.924487i	1.03695	+	0.377420i
$7$	−1.86007	−	0.498404i	−0.703040	−	0.188379i	−0.110448	−	0.993882i	$-0.535229\pi$
$7$	−1.86007	−	0.498404i	−0.703040	−	0.188379i	−0.592592	+	0.805503i	$0.701895\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	−2.76804	−	3.29882i	−0.922681	−	1.09961i
$10$		0			0
$11$	2.06416	−	3.57523i	0.622367	−	1.07797i	−0.366676	−	0.930349i	$-0.619504\pi$
$11$	2.06416	−	3.57523i	0.622367	−	1.07797i	0.989044	−	0.147623i	$-0.0471623\pi$
$12$	0.699593	−	2.61092i	0.201955	−	0.753706i
$13$	1.97909	−	0.922865i	0.548901	−	0.255957i	−0.128325	−	0.991732i	$-0.540960\pi$
$13$	1.97909	−	0.922865i	0.548901	−	0.255957i	0.677225	+	0.735776i	$0.263182\pi$
$14$	−0.334392	+	1.89643i	−0.0893700	+	0.506842i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	2.23346	−	0.195403i	0.541694	−	0.0473921i	0.186974	−	0.982365i	$-0.440132\pi$
$17$	2.23346	−	0.195403i	0.541694	−	0.0473921i	0.354720	+	0.934973i	$0.384576\pi$
$18$	−3.04502	+	3.04502i	−0.717718	+	0.717718i
$19$	4.33300	+	0.474447i	0.994059	+	0.108846i
$19$	4.33300	+	0.474447i	0.994059	+	0.108846i
$20$		0			0
$21$	3.34581	−	3.98739i	0.730117	−	0.870119i
$22$	−3.74153	−	1.74470i	−0.797696	−	0.371972i
$23$	−3.10351	+	4.43228i	−0.647127	+	0.924194i	−0.999934	−	0.0115026i	$-0.996339\pi$
$23$	−3.10351	+	4.43228i	−0.647127	+	0.924194i	0.352806	+	0.935696i	$0.385227\pi$
$24$	−2.66195	−	0.469374i	−0.543369	−	0.0958106i
$25$		0			0
$26$	−1.09184	−	1.89113i	−0.214128	−	0.370880i
$27$	3.41066	−	0.913885i	0.656383	−	0.175877i
$28$	1.91836	+	0.167835i	0.362536	+	0.0317177i
$29$	5.15117	−	4.32234i	0.956548	−	0.802639i	−0.0238400	−	0.999716i	$-0.507589\pi$
$29$	5.15117	−	4.32234i	0.956548	−	0.802639i	0.980388	+	0.197077i	$0.0631448\pi$
$30$		0			0
$31$	−4.36707	+	2.52133i	−0.784349	+	0.452844i	−0.837969	−	0.545717i	$-0.816257\pi$
$31$	−4.36707	+	2.52133i	−0.784349	+	0.452844i	0.0536206	+	0.998561i	$0.482924\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$	6.40049	+	9.14085i	1.11418	+	1.59122i
$34$	−0.389318	−	2.20793i	−0.0667675	−	0.378657i
$35$		0			0
$36$	3.29882	+	2.76804i	0.549804	+	0.461340i
$37$	7.78564	+	7.78564i	1.27995	+	1.27995i	0.940693	+	0.339258i	$0.110176\pi$
$37$	7.78564	+	7.78564i	1.27995	+	1.27995i	0.339258	+	0.940693i	$0.389824\pi$
$38$	0.0949956	−	4.35786i	0.0154103	−	0.706939i
$39$			5.90254i			0.945163i
$40$		0			0
$41$	1.89280	+	5.20044i	0.295606	+	0.812172i	0.995221	+	0.0976510i	$0.0311329\pi$
$41$	1.89280	+	5.20044i	0.295606	+	0.812172i	−0.699614	+	0.714521i	$0.746645\pi$
$42$	−4.26382	−	2.98556i	−0.657922	−	0.460682i
$43$	1.70270	−	1.19225i	0.259660	−	0.181816i	−0.436497	−	0.899706i	$-0.643781\pi$
$43$	1.70270	−	1.19225i	0.259660	−	0.181816i	0.696156	+	0.717890i	$0.254892\pi$
$44$	−1.41197	+	3.87935i	−0.212862	+	0.584834i
$45$		0			0
$46$	4.68590	+	2.70541i	0.690898	+	0.398890i
$47$	−0.279626	+	3.19614i	−0.0407877	+	0.466205i	0.948145	+	0.317839i	$0.102957\pi$
$47$	−0.279626	+	3.19614i	−0.0407877	+	0.466205i	−0.988932	+	0.148366i	$0.952599\pi$
$48$	−0.235584	+	2.69273i	−0.0340036	+	0.388663i
$49$	−2.85073	−	1.64587i	−0.407247	−	0.235124i
$50$		0			0
$51$	−2.07269	+	5.69468i	−0.290235	+	0.797414i
$52$	−1.78877	+	1.25251i	−0.248058	+	0.173692i
$53$	2.14091	+	1.49908i	0.294076	+	0.205914i	0.711298	−	0.702890i	$-0.248107\pi$
$53$	2.14091	+	1.49908i	0.294076	+	0.205914i	−0.417222	+	0.908804i	$0.636996\pi$
$54$	−1.20767	−	3.31804i	−0.164343	−	0.451528i
$55$		0			0
$56$		−	1.92569i		−	0.257331i
$57$	−6.11207	+	10.0729i	−0.809563	+	1.33418i
$58$	−4.75485	−	4.75485i	−0.624342	−	0.624342i
$59$	1.19639	+	1.00389i	0.155756	+	0.130695i	0.717335	−	0.696728i	$-0.245362\pi$
$59$	1.19639	+	1.00389i	0.155756	+	0.130695i	−0.561579	+	0.827423i	$0.689806\pi$
$60$		0			0
$61$	1.80359	+	10.2287i	0.230926	+	1.30965i	0.851025	+	0.525124i	$0.175981\pi$
$61$	1.80359	+	10.2287i	0.230926	+	1.30965i	−0.620099	+	0.784523i	$0.712908\pi$
$62$	2.89235	+	4.13070i	0.367329	+	0.524600i
$63$	3.50460	+	7.51565i	0.441539	+	0.946882i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$		0			0
$66$	8.54823	−	7.17281i	1.05221	−	0.882912i
$67$	−7.61405	−	0.666143i	−0.930204	−	0.0813823i	−0.388028	−	0.921648i	$-0.626844\pi$
$67$	−7.61405	−	0.666143i	−0.930204	−	0.0813823i	−0.542176	+	0.840265i	$0.682399\pi$
$68$	−2.16560	+	0.580271i	−0.262617	+	0.0703681i
$69$	−7.31276	−	12.6661i	−0.880353	−	1.52482i
$70$		0			0
$71$	4.33664	+	0.764666i	0.514664	+	0.0907492i	0.424947	−	0.905218i	$-0.360293\pi$
$71$	4.33664	+	0.764666i	0.514664	+	0.0907492i	0.0897170	+	0.995967i	$0.471404\pi$
$72$	2.47000	−	3.52752i	0.291092	−	0.415723i
$73$	9.34513	+	4.35771i	1.09376	+	0.510031i	0.883889	−	0.467697i	$-0.154916\pi$
$73$	9.34513	+	4.35771i	1.09376	+	0.510031i	0.209876	+	0.977728i	$0.432694\pi$
$74$	7.07745	−	8.43458i	0.822737	−	0.980499i
$75$		0			0
$76$	−4.34956	+	0.285179i	−0.498929	+	0.0327122i
$77$	−5.62139	+	5.62139i	−0.640616	+	0.640616i
$78$	5.88008	−	0.514440i	0.665788	−	0.0582489i
$79$	11.2708	−	4.10225i	1.26807	−	0.461540i	0.381600	−	0.924327i	$-0.375373\pi$
$79$	11.2708	−	4.10225i	1.26807	−	0.461540i	0.886469	+	0.462788i	$0.153151\pi$
$80$		0			0
$81$	0.585997	−	3.32336i	0.0651108	−	0.369262i
$82$	5.01568	−	2.33885i	0.553889	−	0.258283i
$83$	4.28190	−	15.9803i	0.470000	−	1.75406i	−0.169756	−	0.985486i	$-0.554298\pi$
$83$	4.28190	−	15.9803i	0.470000	−	1.75406i	0.639756	−	0.768578i	$-0.279035\pi$
$84$	−2.60258	+	4.50780i	−0.283965	+	0.491842i
$85$		0			0
$86$	−1.33611	−	1.59231i	−0.144076	−	0.171704i
$87$	4.70432	+	17.5568i	0.504356	+	1.88228i
$88$	3.98765	+	1.06849i	0.425085	+	0.113901i
$89$	6.73471	+	2.45124i	0.713878	+	0.259830i	0.673325	−	0.739347i	$-0.264866\pi$
$89$	6.73471	+	2.45124i	0.713878	+	0.259830i	0.0405536	+	0.999177i	$0.487088\pi$
$90$		0			0
$91$	−4.14120	+	0.730206i	−0.434116	+	0.0765464i
$92$	2.28671	−	4.90386i	0.238406	−	0.511263i
$93$	−1.18797	−	13.5785i	−0.123186	−	1.40803i
$94$	3.20835			0.330916
$95$		0			0
$96$	2.70302			0.275876
$97$	−0.791080	−	9.04209i	−0.0803220	−	0.918085i	−0.924290	−	0.381691i	$-0.875342\pi$
$97$	−0.791080	−	9.04209i	−0.0803220	−	0.918085i	0.843968	−	0.536394i	$-0.180214\pi$
$98$	−1.39115	+	2.98333i	−0.140527	+	0.301361i
$99$	−17.5077	+	3.08708i	−1.75959	+	0.310264i
$100$		0			0
$101$	8.21555	+	2.99021i	0.817477	+	0.297537i	0.716709	−	0.697372i	$-0.245648\pi$
$101$	8.21555	+	2.99021i	0.817477	+	0.297537i	0.100768	+	0.994910i	$0.467870\pi$
$102$	5.85366	+	1.56848i	0.579598	+	0.155303i
$103$	4.76646	+	17.7887i	0.469653	+	1.75277i	0.640983	+	0.767555i	$0.278527\pi$
$103$	4.76646	+	17.7887i	0.469653	+	1.75277i	−0.171330	+	0.985214i	$0.554807\pi$
$104$	1.40364	+	1.67280i	0.137639	+	0.164031i
$105$		0			0
$106$	1.30678	−	2.26341i	0.126926	−	0.219842i
$107$	−0.0205678	+	0.0767599i	−0.00198836	+	0.00742066i	−0.966913	−	0.255107i	$-0.917889\pi$
$107$	−0.0205678	+	0.0767599i	−0.00198836	+	0.00742066i	0.964925	+	0.262527i	$0.0845560\pi$
$108$	−3.20015	+	1.49226i	−0.307935	+	0.143592i
$109$	3.36750	−	19.0981i	0.322548	−	1.82926i	−0.203824	−	0.979008i	$-0.565337\pi$
$109$	3.36750	−	19.0981i	0.322548	−	1.82926i	0.526372	−	0.850254i	$-0.323552\pi$
$110$		0			0
$111$	−27.9669	+	10.1791i	−2.65450	+	0.966159i
$112$	−1.91836	+	0.167835i	−0.181268	+	0.0158589i
$113$	12.1333	−	12.1333i	1.14140	−	1.14140i	0.153211	−	0.988193i	$-0.451039\pi$
$113$	12.1333	−	12.1333i	1.14140	−	1.14140i	0.988193	−	0.153211i	$-0.0489614\pi$
$114$	10.5672	+	5.21090i	0.989712	+	0.488046i
$115$		0			0
$116$	−4.32234	+	5.15117i	−0.401320	+	0.478274i
$117$	−8.52257	−	3.97414i	−0.787912	−	0.367409i
$118$	0.895795	−	1.27933i	0.0824646	−	0.117772i
$119$	−4.25178	−	0.749704i	−0.389760	−	0.0687253i
$120$		0			0
$121$	−3.02150	−	5.23339i	−0.274682	−	0.475763i
$122$	10.0326	−	2.68822i	0.908305	−	0.243380i
$123$	−14.9021	−	1.30376i	−1.34368	−	0.117556i
$124$	3.86290	−	3.24136i	0.346899	−	0.291082i
$125$		0			0
$126$	7.18160	−	4.14630i	0.639788	−	0.369382i
$127$	−3.44499	−	7.38780i	−0.305693	−	0.655562i	0.692111	−	0.721791i	$-0.256681\pi$
$127$	−3.44499	−	7.38780i	−0.305693	−	0.655562i	−0.997804	+	0.0662294i	$0.978903\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$	0.975649	+	5.53318i	0.0859011	+	0.487170i
$130$		0			0
$131$	9.80867	+	8.23045i	0.856987	+	0.719098i	0.961317	−	0.275445i	$-0.0888252\pi$
$131$	9.80867	+	8.23045i	0.856987	+	0.719098i	−0.104330	+	0.994543i	$0.533270\pi$
$132$	−7.89055	−	7.89055i	−0.686784	−	0.686784i
$133$	−7.82322	−	3.04209i	−0.678359	−	0.263783i
$134$			7.64313i			0.660266i
$135$		0			0
$136$	0.766807	+	2.10678i	0.0657532	+	0.180655i
$137$	−12.5726	−	8.80344i	−1.07415	−	0.752129i	−0.103987	−	0.994579i	$-0.533160\pi$
$137$	−12.5726	−	8.80344i	−1.07415	−	0.752129i	−0.970164	+	0.242450i	$0.922049\pi$
$138$	−11.9805	+	8.38886i	−1.01985	+	0.714107i
$139$	−3.54798	+	9.74799i	−0.300936	+	0.826814i	0.693402	+	0.720551i	$0.256111\pi$
$139$	−3.54798	+	9.74799i	−0.300936	+	0.826814i	−0.994338	+	0.106263i	$0.966111\pi$
$140$		0			0
$141$	−7.51037	−	4.33611i	−0.632487	−	0.365167i
$142$	0.383794	−	4.38678i	0.0322072	−	0.368130i
$143$	0.785704	−	8.98063i	0.0657038	−	0.750998i
$144$	−3.72937	−	2.15315i	−0.310781	−	0.179430i
$145$		0			0
$146$	3.52664	−	9.68937i	0.291867	−	0.801898i
$147$	7.28851	−	5.10347i	0.601146	−	0.420927i
$148$	−9.01932	−	6.31540i	−0.741384	−	0.519122i
$149$	6.98327	+	19.1864i	0.572091	+	1.57181i	0.801193	+	0.598406i	$0.204199\pi$
$149$	6.98327	+	19.1864i	0.572091	+	1.57181i	−0.229102	+	0.973402i	$0.573579\pi$
$150$		0			0
$151$		−	1.84458i		−	0.150110i	−0.997179	−	0.0750548i	$-0.976087\pi$
$151$		−	1.84458i		−	0.150110i	0.997179	−	0.0750548i	$-0.0239132\pi$
$152$	0.663183	+	4.30815i	0.0537912	+	0.349437i
$153$	−6.82692	−	6.82692i	−0.551924	−	0.551924i
$154$	6.08993	+	5.11006i	0.490741	+	0.411780i
$155$		0			0
$156$	−1.02496	−	5.81287i	−0.0820629	−	0.465402i
$157$	−7.24255	−	10.3434i	−0.578019	−	0.825496i	0.418556	−	0.908191i	$-0.362536\pi$
$157$	−7.24255	−	10.3434i	−0.578019	−	0.825496i	−0.996575	+	0.0826948i	$0.973647\pi$
$158$	−5.06896	−	10.8704i	−0.403265	−	0.864805i
$159$	−6.11804	+	3.53225i	−0.485192	+	0.280126i
$160$		0			0
$161$	7.98182	−	6.69754i	0.629055	−	0.527840i
$162$	−3.36178	−	0.294118i	−0.264127	−	0.0231081i
$163$	−8.10685	+	2.17222i	−0.634977	+	0.170142i	−0.561927	−	0.827187i	$-0.689940\pi$
$163$	−8.10685	+	2.17222i	−0.634977	+	0.170142i	−0.0730501	+	0.997328i	$0.523273\pi$
$164$	−2.76709	−	4.79275i	−0.216074	−	0.374251i
$165$		0			0
$166$	−16.2927	−	2.87284i	−1.26456	−	0.222975i
$167$	5.57717	−	7.96503i	0.431575	−	0.616353i	−0.543184	−	0.839614i	$-0.682781\pi$
$167$	5.57717	−	7.96503i	0.431575	−	0.616353i	0.974759	+	0.223261i	$0.0716703\pi$
$168$	4.71748	+	2.19980i	0.363962	+	0.169718i
$169$	−5.29112	+	6.30571i	−0.407009	+	0.485055i
$170$		0			0
$171$	−10.4288	−	15.6071i	−0.797511	−	1.19350i
$172$	−1.46980	+	1.46980i	−0.112072	+	0.112072i
$173$	12.2676	−	1.07328i	0.932692	−	0.0815999i	0.389330	−	0.921098i	$-0.372707\pi$
$173$	12.2676	−	1.07328i	0.932692	−	0.0815999i	0.543362	+	0.839499i	$0.317151\pi$
$174$	17.0800	−	6.21660i	1.29483	−	0.471279i
$175$		0			0
$176$	0.716875	−	4.06560i	0.0540365	−	0.306456i
$177$	−3.82598	+	1.78408i	−0.287578	+	0.134100i
$178$	1.85494	−	6.92273i	0.139034	−	0.518880i
$179$	−11.0449	+	19.1304i	−0.825536	+	1.42987i	0.0759725	+	0.997110i	$0.475794\pi$
$179$	−11.0449	+	19.1304i	−0.825536	+	1.42987i	−0.901509	+	0.432761i	$0.857539\pi$
$180$		0			0
$181$	2.84867	+	3.39491i	0.211740	+	0.252341i	0.861452	−	0.507838i	$-0.169555\pi$
$181$	2.84867	+	3.39491i	0.211740	+	0.252341i	−0.649713	+	0.760180i	$0.725111\pi$
$182$	1.08836	+	4.06180i	0.0806744	+	0.301081i
$183$	−27.1182	−	7.26630i	−2.00463	−	0.537140i
$184$	−5.08450	−	1.85061i	−0.374834	−	0.136429i
$185$		0			0
$186$	−13.4233	+	2.36689i	−0.984245	+	0.173549i
$187$	3.91161	−	8.38848i	0.286045	−	0.613426i
$188$	−0.279626	−	3.19614i	−0.0203938	−	0.233103i
$189$	−6.79956			−0.494595
$190$		0			0
$191$	−8.48463			−0.613927			−0.306963	−	0.951721i	$-0.599313\pi$
$191$	−8.48463			−0.613927			−0.306963	+	0.951721i	$0.599313\pi$
$192$	−0.235584	−	2.69273i	−0.0170018	−	0.194331i
$193$	9.63312	−	20.6583i	0.693407	−	1.48702i	−0.171553	−	0.985175i	$-0.554878\pi$
$193$	9.63312	−	20.6583i	0.693407	−	1.48702i	0.864960	−	0.501841i	$-0.167344\pi$
$194$	−8.93873	+	1.57614i	−0.641764	+	0.113160i
$195$		0			0
$196$	3.09322	+	1.12584i	0.220944	+	0.0804171i
$197$	−8.05453	−	2.15821i	−0.573862	−	0.153766i	−0.0397946	−	0.999208i	$-0.512670\pi$
$197$	−8.05453	−	2.15821i	−0.573862	−	0.153766i	−0.534067	+	0.845442i	$0.679337\pi$
$198$	4.60124	+	17.1720i	0.326996	+	1.22036i
$199$	−3.63062	−	4.32681i	−0.257368	−	0.306719i	0.621852	−	0.783135i	$-0.286380\pi$
$199$	−3.63062	−	4.32681i	−0.257368	−	0.306719i	−0.879220	+	0.476415i	$0.841936\pi$
$200$		0			0
$201$	10.3298	−	17.8917i	0.728605	−	1.26198i
$202$	2.26280	−	8.44490i	0.159210	−	0.594181i
$203$	−11.7358	+	5.47250i	−0.823692	+	0.384094i
$204$	1.05233	−	5.96808i	0.0736781	−	0.417849i
$205$		0			0
$206$	17.3055	−	6.29870i	1.20573	−	0.438851i
$207$	23.2120	−	2.03078i	1.61334	−	0.141149i
$208$	1.54410	−	1.54410i	0.107064	−	0.107064i
$209$	10.6403	−	14.5121i	0.736002	−	1.00383i
$210$		0			0
$211$	−12.6395	+	15.0631i	−0.870138	+	1.03699i	0.128835	+	0.991666i	$0.458876\pi$
$211$	−12.6395	+	15.0631i	−0.870138	+	1.03699i	−0.998972	+	0.0453234i	$0.985568\pi$
$212$	−2.36869	−	1.10454i	−0.162682	−	0.0758601i
$213$	−6.82719	+	9.75024i	−0.467791	+	0.668075i
$214$	0.0782604	+	0.0137994i	0.00534977	+	0.000943310i
$215$		0			0
$216$	1.76549	+	3.05792i	0.120126	+	0.208065i
$217$	9.37969	−	2.51328i	0.636735	−	0.170613i
$218$	−19.3189	−	1.69018i	−1.30844	−	0.114474i
$219$	−21.3507	+	17.9154i	−1.44275	+	1.21061i
$220$		0			0
$221$	4.23989	−	2.44790i	0.285206	−	0.164664i
$222$	12.5779	+	26.9733i	0.844170	+	1.81033i
$223$	2.00605	+	2.86493i	0.134335	+	0.191850i	0.880684	−	0.473705i	$-0.157084\pi$
$223$	2.00605	+	2.86493i	0.134335	+	0.191850i	−0.746349	+	0.665555i	$0.768195\pi$
$224$	0.334392	+	1.89643i	0.0223425	+	0.126711i
$225$		0			0
$226$	−13.1446	−	11.0296i	−0.874367	−	0.733681i
$227$	12.9417	+	12.9417i	0.858971	+	0.858971i	0.991217	−	0.132246i	$-0.0422188\pi$
$227$	12.9417	+	12.9417i	0.858971	+	0.858971i	−0.132246	+	0.991217i	$0.542219\pi$
$228$	4.27008	−	10.9812i	0.282793	−	0.727246i
$229$		−	23.9221i		−	1.58081i	−0.612582	−	0.790407i	$-0.709869\pi$
$229$		−	23.9221i		−	1.58081i	0.612582	−	0.790407i	$-0.290131\pi$
$230$		0			0
$231$	−7.34952	−	20.1926i	−0.483563	−	1.32858i
$232$	5.50828	+	3.85694i	0.361637	+	0.253221i
$233$	−16.2584	+	11.3843i	−1.06513	+	0.745809i	−0.968375	−	0.249500i	$-0.919734\pi$
$233$	−16.2584	+	11.3843i	−1.06513	+	0.745809i	−0.0967508	+	0.995309i	$0.530845\pi$
$234$	−3.21623	+	8.83651i	−0.210251	+	0.577661i
$235$		0			0
$236$	−1.35253	−	0.780886i	−0.0880424	−	0.0508313i
$237$	−2.82563	+	32.2971i	−0.183545	+	2.09792i
$238$	−0.376284	+	4.30095i	−0.0243909	+	0.278789i
$239$	14.1933	+	8.19453i	0.918091	+	0.530060i	0.883026	−	0.469325i	$-0.155503\pi$
$239$	14.1933	+	8.19453i	0.918091	+	0.530060i	0.0350655	+	0.999385i	$0.488836\pi$
$240$		0			0
$241$	−3.09606	+	8.50637i	−0.199435	+	0.547943i	−0.998584	−	0.0531891i	$-0.983061\pi$
$241$	−3.09606	+	8.50637i	−0.199435	+	0.547943i	0.799149	+	0.601132i	$0.205284\pi$
$242$	−4.95014	+	3.46612i	−0.318207	+	0.222811i
$243$	16.1493	+	11.3078i	1.03598	+	0.725398i
$244$	−3.55238	−	9.76009i	−0.227418	−	0.624826i
$245$		0			0
$246$			14.9590i			0.953752i
$247$	9.01325	−	3.05980i	0.573499	−	0.194690i
$248$	−3.56570	−	3.56570i	−0.226422	−	0.226422i
$249$	34.2566	+	28.7447i	2.17092	+	1.82162i
$250$		0			0
$251$	2.94101	+	16.6793i	0.185635	+	1.05279i	0.925137	+	0.379634i	$0.123950\pi$
$251$	2.94101	+	16.6793i	0.185635	+	1.05279i	−0.739502	+	0.673155i	$0.764939\pi$
$252$	−4.75644	−	6.79290i	−0.299627	−	0.427912i
$253$	9.44026	+	20.2447i	0.593504	+	1.27277i
$254$	−7.05944	+	4.07577i	−0.442949	+	0.255737i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	0.378732	+	0.0331348i	0.0236247	+	0.00206689i	0.0989619	−	0.995091i	$-0.468448\pi$
$257$	0.378732	+	0.0331348i	0.0236247	+	0.00206689i	−0.0753373	+	0.997158i	$0.524003\pi$
$258$	5.42709	−	1.45419i	0.337876	−	0.0905336i
$259$	−10.6014	−	18.3622i	−0.658741	−	1.14097i
$260$		0			0
$261$	−28.5173	−	5.02837i	−1.76518	−	0.311248i
$262$	7.34425	−	10.4887i	0.453729	−	0.647992i
$263$	15.6657	+	7.30504i	0.965989	+	0.450448i	0.840598	−	0.541660i	$-0.182204\pi$
$263$	15.6657	+	7.30504i	0.965989	+	0.450448i	0.125391	+	0.992107i	$0.459982\pi$
$264$	−7.17281	+	8.54823i	−0.441456	+	0.526107i
$265$		0			0
$266$	−2.34868	+	8.05858i	−0.144007	+	0.494103i
$267$	−13.6983	+	13.6983i	−0.838324	+	0.838324i
$268$	7.61405	−	0.666143i	0.465102	−	0.0406911i
$269$	8.25382	−	3.00414i	0.503244	−	0.183166i	−0.0779085	−	0.996961i	$-0.524824\pi$
$269$	8.25382	−	3.00414i	0.503244	−	0.183166i	0.581153	+	0.813795i	$0.302602\pi$
$270$		0			0
$271$	2.80993	−	15.9359i	0.170691	−	0.968038i	−0.772309	−	0.635247i	$-0.780898\pi$
$271$	2.80993	−	15.9359i	0.170691	−	0.968038i	0.943000	−	0.332792i	$-0.107991\pi$
$272$	2.03194	−	0.947507i	0.123204	−	0.0574511i
$273$	2.94185	−	10.9791i	0.178049	−	0.664487i
$274$	−7.67416	+	13.2920i	−0.463613	+	0.803002i
$275$		0			0
$276$	9.40111	+	11.2038i	0.565880	+	0.674390i
$277$	1.46612	+	5.47163i	0.0880905	+	0.328758i	0.995881	−	0.0906646i	$-0.0288991\pi$
$277$	1.46612	+	5.47163i	0.0880905	+	0.328758i	−0.907791	+	0.419423i	$0.862232\pi$
$278$	10.0201	+	2.68488i	0.600967	+	0.161029i
$279$	20.4057	+	7.42705i	1.22165	+	0.444646i
$280$		0			0
$281$	−13.6998	+	2.41564i	−0.817259	+	0.144105i	−0.566624	−	0.823977i	$-0.691751\pi$
$281$	−13.6998	+	2.41564i	−0.817259	+	0.144105i	−0.250635	+	0.968082i	$0.580640\pi$
$282$	−3.66504	+	7.85971i	−0.218250	+	0.468039i
$283$	−0.973015	−	11.1216i	−0.0578397	−	0.661111i	−0.968673	−	0.248338i	$-0.920116\pi$
$283$	−0.973015	−	11.1216i	−0.0578397	−	0.661111i	0.910834	−	0.412773i	$-0.135440\pi$
$284$	−4.40354			−0.261302
$285$		0			0
$286$	−9.01494			−0.533065
$287$	−0.928828	−	10.6166i	−0.0548270	−	0.626675i
$288$	−1.81993	+	3.90284i	−0.107240	+	0.229977i
$289$	−11.7916	+	2.07917i	−0.693621	+	0.122304i
$290$		0			0
$291$	23.0547	+	8.39122i	1.35149	+	0.491902i
$292$	−9.95987	−	2.66874i	−0.582857	−	0.156176i
$293$	−5.48705	−	20.4779i	−0.320557	−	1.19633i	−0.918704	−	0.394947i	$-0.870763\pi$
$293$	−5.48705	−	20.4779i	−0.320557	−	1.19633i	0.598147	−	0.801386i	$-0.295904\pi$
$294$	−5.71928	−	6.81597i	−0.333555	−	0.397516i
$295$		0			0
$296$	−5.50528	+	9.53542i	−0.319988	+	0.554235i
$297$	3.77281	−	14.0803i	0.218920	−	0.817022i
$298$	18.5047	−	8.62889i	1.07195	−	0.499858i
$299$	−2.05174	+	11.6360i	−0.118655	+	0.672927i
$300$		0			0
$301$	−3.76137	+	1.36903i	−0.216802	+	0.0789093i
$302$	−1.83756	+	0.160765i	−0.105740	+	0.00925101i
$303$	−16.7103	+	16.7103i	−0.959983	+	0.959983i
$304$	4.23396	−	1.03614i	0.242834	−	0.0594267i
$305$		0			0
$306$	−6.20593	+	7.39594i	−0.354770	+	0.422798i
$307$	−23.9757	−	11.1801i	−1.36837	−	0.638080i	−0.407020	−	0.913419i	$-0.633432\pi$
$307$	−23.9757	−	11.1801i	−1.36837	−	0.638080i	−0.961347	+	0.275340i	$0.911210\pi$
$308$	4.55984	−	6.51213i	0.259821	−	0.371063i
$309$	−49.0230	−	8.64408i	−2.78882	−	0.491744i
$310$		0			0
$311$	6.27752	+	10.8730i	0.355965	+	0.616550i	0.987283	−	0.158975i	$-0.0508188\pi$
$311$	6.27752	+	10.8730i	0.355965	+	0.616550i	−0.631317	+	0.775525i	$0.717485\pi$
$312$	−5.70141	+	1.52769i	−0.322779	+	0.0864884i
$313$	−29.7369	−	2.60164i	−1.68083	−	0.147054i	−0.793618	−	0.608416i	$-0.791805\pi$
$313$	−29.7369	−	2.60164i	−1.68083	−	0.147054i	−0.887212	+	0.461362i	$0.847361\pi$
$314$	−9.67285	+	8.11648i	−0.545870	+	0.458040i
$315$		0			0
$316$	−10.3873	+	5.99709i	−0.584330	+	0.337363i
$317$	8.49232	+	18.2118i	0.476976	+	1.02288i	0.986702	+	0.162541i	$0.0519691\pi$
$317$	8.49232	+	18.2118i	0.476976	+	1.02288i	−0.509726	+	0.860337i	$0.670253\pi$
$318$	4.05204	+	5.78691i	0.227227	+	0.324514i
$319$	−4.82053	−	27.3386i	−0.269898	−	1.53067i
$320$		0			0
$321$	−0.164548	−	0.138073i	−0.00918420	−	0.00770646i
$322$	−7.36771	−	7.36771i	−0.410587	−	0.410587i
$323$	9.77030	+	0.212980i	0.543634	+	0.0118505i
$324$			3.37462i			0.187479i
$325$		0			0
$326$	2.87052	+	7.88668i	0.158983	+	0.436803i
$327$	42.9389	+	30.0662i	2.37453	+	1.66266i
$328$	−4.53334	+	3.17428i	−0.250312	+	0.175270i
$329$	2.11309	−	5.80568i	0.116499	−	0.320077i
$330$		0			0
$331$	−26.1604	−	15.1037i	−1.43791	−	0.830176i	−0.440203	−	0.897898i	$-0.645093\pi$
$331$	−26.1604	−	15.1037i	−1.43791	−	0.830176i	−0.997704	+	0.0677224i	$0.978427\pi$
$332$	−1.44191	+	16.4810i	−0.0791348	+	0.904515i
$333$	4.13248	−	47.2344i	0.226458	−	2.58843i
$334$	−8.42080	−	4.86175i	−0.460766	−	0.266023i
$335$		0			0
$336$	1.78027	−	4.89125i	0.0971217	−	0.266840i
$337$	6.25587	−	4.38041i	0.340779	−	0.238616i	−0.390641	−	0.920543i	$-0.627747\pi$
$337$	6.25587	−	4.38041i	0.340779	−	0.238616i	0.731420	+	0.681927i	$0.238858\pi$
$338$	6.74287	+	4.72141i	0.366764	+	0.256811i
$339$	15.8633	+	43.5842i	0.861578	+	2.36717i
$340$		0			0
$341$			20.8177i			1.12734i
$342$	−14.6388	+	11.7494i	−0.791575	+	0.635334i
$343$	14.0139	+	14.0139i	0.756679	+	0.756679i
$344$	1.59231	+	1.33611i	0.0858518	+	0.0720382i
$345$		0			0
$346$	−2.13839	−	12.1274i	−0.114961	−	0.651974i
$347$	−12.5913	−	17.9822i	−0.675934	−	0.965334i	−0.999815	−	0.0192363i	$-0.993877\pi$
$347$	−12.5913	−	17.9822i	−0.675934	−	0.965334i	0.323881	−	0.946098i	$-0.395012\pi$
$348$	−7.68156	−	16.4731i	−0.411775	−	0.883053i
$349$	14.2855	−	8.24774i	0.764685	−	0.441491i	−0.0662901	−	0.997800i	$-0.521116\pi$
$349$	14.2855	−	8.24774i	0.764685	−	0.441491i	0.830975	+	0.556309i	$0.187783\pi$
$350$		0			0
$351$	5.90662	−	4.95624i	0.315272	−	0.264545i
$352$	−4.11261	−	0.359807i	−0.219203	−	0.0191778i
$353$	2.13228	−	0.571342i	0.113490	−	0.0304094i	−0.201627	−	0.979462i	$-0.564623\pi$
$353$	2.13228	−	0.571342i	0.113490	−	0.0304094i	0.315117	+	0.949053i	$0.397956\pi$
$354$	2.11075	+	3.65592i	0.112185	+	0.194310i
$355$		0			0
$356$	−7.05805	−	1.24452i	−0.374076	−	0.0659597i
$357$	6.69360	−	9.55946i	0.354263	−	0.505940i
$358$	20.0202	+	9.33557i	1.05810	+	0.493400i
$359$	17.2609	−	20.5708i	0.910997	−	1.08568i	−0.0850073	−	0.996380i	$-0.527091\pi$
$359$	17.2609	−	20.5708i	0.910997	−	1.08568i	0.996004	−	0.0893038i	$-0.0284642\pi$
$360$		0			0
$361$	18.5498	+	4.11156i	0.976305	+	0.216398i
$362$	3.13371	−	3.13371i	0.164704	−	0.164704i
$363$	16.2722	−	1.42363i	0.854068	−	0.0747213i
$364$	3.95149	−	1.43822i	0.207114	−	0.0753835i
$365$		0			0
$366$	−4.87514	+	27.6483i	−0.254828	+	1.44520i
$367$	−1.20270	+	0.560827i	−0.0627803	+	0.0292749i	−0.453755	−	0.891127i	$-0.649916\pi$
$367$	−1.20270	+	0.560827i	−0.0627803	+	0.0292749i	0.390975	+	0.920401i	$0.372138\pi$
$368$	−1.40042	+	5.22644i	−0.0730020	+	0.272447i
$369$	11.9160	−	20.6391i	0.620320	−	1.07443i
$370$		0			0
$371$	−3.23509	−	3.85542i	−0.167957	−	0.200164i
$372$	3.52781	+	13.1660i	0.182908	+	0.682623i
$373$	−13.5915	−	3.64184i	−0.703744	−	0.188568i	−0.110837	−	0.993839i	$-0.535353\pi$
$373$	−13.5915	−	3.64184i	−0.703744	−	0.188568i	−0.592907	+	0.805271i	$0.702020\pi$
$374$	−8.69748	−	3.16562i	−0.449736	−	0.163690i
$375$		0			0
$376$	−3.15961	+	0.557124i	−0.162944	+	0.0287315i
$377$	6.20569	−	13.3081i	0.319609	−	0.685404i
$378$	0.592620	+	6.77368i	0.0304811	+	0.348401i
$379$	−25.6821			−1.31920			−0.659600	−	0.751617i	$-0.729274\pi$
$379$	−25.6821			−1.31920			−0.659600	+	0.751617i	$0.729274\pi$
$380$		0			0
$381$	22.0338			1.12882
$382$	0.739485	+	8.45235i	0.0378353	+	0.432460i
$383$	0.248451	−	0.532805i	0.0126953	−	0.0272251i	−0.899858	−	0.436183i	$-0.856330\pi$
$383$	0.248451	−	0.532805i	0.0126953	−	0.0272251i	0.912553	+	0.408958i	$0.134108\pi$
$384$	−2.66195	+	0.469374i	−0.135842	+	0.0239527i
$385$		0			0
$386$	−21.4193	−	7.79597i	−1.09021	−	0.396805i
$387$	−8.64617	−	2.31673i	−0.439509	−	0.117766i
$388$	2.34920	+	8.76735i	0.119263	+	0.445095i
$389$	18.1795	+	21.6655i	0.921739	+	1.09849i	0.994870	+	0.101164i	$0.0322566\pi$
$389$	18.1795	+	21.6655i	0.921739	+	1.09849i	−0.0731306	+	0.997322i	$0.523299\pi$
$390$		0			0
$391$	−6.06550	+	10.5058i	−0.306746	+	0.531299i
$392$	0.851964	−	3.17957i	0.0430307	−	0.160593i
$393$	−31.3676	+	14.6269i	−1.58228	+	0.737831i
$394$	−1.44799	+	8.21198i	−0.0729489	+	0.413714i
$395$		0			0
$396$	16.7057	−	6.08037i	0.839492	−	0.305550i
$397$	2.20153	−	0.192609i	0.110492	−	0.00966676i	−0.0317758	−	0.999495i	$-0.510116\pi$
$397$	2.20153	−	0.192609i	0.110492	−	0.00966676i	0.142267	+	0.989828i	$0.454561\pi$
$398$	−3.99391	+	3.99391i	−0.200197	+	0.200197i
$399$	16.3892	−	15.6899i	0.820487	−	0.785479i
$400$		0			0
$401$	20.9193	−	24.9307i	1.04466	−	1.24498i	0.0758664	−	0.997118i	$-0.475828\pi$
$401$	20.9193	−	24.9307i	1.04466	−	1.24498i	0.968795	−	0.247862i	$-0.0797278\pi$
$402$	−18.7239	−	8.73109i	−0.933863	−	0.435467i
$403$	−6.31598	+	9.02015i	−0.314621	+	0.449326i
$404$	−8.60998	−	1.51817i	−0.428362	−	0.0755319i
$405$		0			0
$406$	6.47451	+	11.2142i	0.321325	+	0.556551i
$407$	43.9062	−	11.7646i	2.17635	−	0.583151i
$408$	−6.03709	−	0.528177i	−0.298880	−	0.0261487i
$409$	2.10990	−	1.77041i	0.104328	−	0.0875413i	−0.589132	−	0.808037i	$-0.700530\pi$
$409$	2.10990	−	1.77041i	0.104328	−	0.0875413i	0.693459	+	0.720496i	$0.256086\pi$
$410$		0			0
$411$	35.9286	−	20.7434i	1.77223	−	1.02320i
$412$	−7.78301	−	16.6907i	−0.383441	−	0.822293i
$413$	−1.72502	−	2.46358i	−0.0848827	−	0.121225i
$414$	−4.04611	−	22.9466i	−0.198856	−	1.12777i
$415$		0			0
$416$	−1.67280	−	1.40364i	−0.0820157	−	0.0688194i
$417$	−19.8273	−	19.8273i	−0.970947	−	0.970947i
$418$	−15.3843	−	9.33495i	−0.752469	−	0.456587i
$419$		−	21.3800i		−	1.04448i	−0.852798	−	0.522240i	$-0.825096\pi$
$419$		−	21.3800i		−	1.04448i	0.852798	−	0.522240i	$-0.174904\pi$
$420$		0			0
$421$	−8.39922	−	23.0767i	−0.409353	−	1.12469i	−0.957532	−	0.288327i	$-0.906901\pi$
$421$	−8.39922	−	23.0767i	−0.409353	−	1.12469i	0.548179	−	0.836361i	$-0.315321\pi$
$422$	16.1074	+	11.2785i	0.784097	+	0.549031i
$423$	11.3175	−	7.92462i	0.550277	−	0.385308i
$424$	−0.893891	+	2.45595i	−0.0434112	+	0.119271i
$425$		0			0
$426$	10.3082	+	5.95142i	0.499432	+	0.288347i
$427$	1.74321	−	19.9250i	0.0843598	−	0.964237i
$428$	0.00692607	−	0.0791653i	0.000334784	−	0.00382660i
$429$	21.1029	+	12.1838i	1.01886	+	0.588238i
$430$		0			0
$431$	10.0432	−	27.5935i	0.483765	−	1.32913i	−0.422477	−	0.906374i	$-0.638839\pi$
$431$	10.0432	−	27.5935i	0.483765	−	1.32913i	0.906242	−	0.422760i	$-0.138939\pi$
$432$	2.89241	−	2.02529i	0.139161	−	0.0974417i
$433$	12.8200	+	8.97670i	0.616092	+	0.431392i	0.839521	−	0.543328i	$-0.182836\pi$
$433$	12.8200	+	8.97670i	0.616092	+	0.431392i	−0.223428	+	0.974720i	$0.571725\pi$
$434$	−3.32121	−	9.12495i	−0.159423	−	0.438012i
$435$		0			0
$436$			19.3927i			0.928741i
$437$	−15.5504	+	17.7326i	−0.743877	+	0.848266i
$438$	19.7081	+	19.7081i	0.941687	+	0.941687i
$439$	−9.61925	−	8.07151i	−0.459102	−	0.385232i	0.383699	−	0.923458i	$-0.374650\pi$
$439$	−9.61925	−	8.07151i	−0.459102	−	0.385232i	−0.842800	+	0.538226i	$0.819095\pi$
$440$		0			0
$441$	2.46150	+	13.9599i	0.117214	+	0.664756i
$442$	−2.80812	−	4.01041i	−0.133569	−	0.190756i
$443$	12.5012	+	26.8090i	0.593951	+	1.27373i	0.941798	+	0.336181i	$0.109135\pi$
$443$	12.5012	+	26.8090i	0.593951	+	1.27373i	−0.347846	+	0.937552i	$0.613087\pi$
$444$	25.7744	−	14.8809i	1.22320	−	0.706215i
$445$		0			0
$446$	2.67919	−	2.24811i	0.126863	−	0.106451i
$447$	−54.9794	−	4.81008i	−2.60044	−	0.227509i
$448$	1.86007	−	0.498404i	0.0878800	−	0.0235474i
$449$	−3.27073	−	5.66507i	−0.154355	−	0.267351i	0.778469	−	0.627683i	$-0.215997\pi$
$449$	−3.27073	−	5.66507i	−0.154355	−	0.267351i	−0.932824	+	0.360332i	$0.882663\pi$
$450$		0			0
$451$	22.4998	+	3.96732i	1.05947	+	0.186814i
$452$	−9.84204	+	14.0559i	−0.462931	+	0.661133i
$453$	4.51878	+	2.10714i	0.212311	+	0.0990022i
$454$	11.7645	−	14.0204i	0.552136	−	0.658010i
$455$		0			0
$456$	−11.3116	−	3.29676i	−0.529712	−	0.154385i
$457$	−1.89298	+	1.89298i	−0.0885500	+	0.0885500i	−0.749994	−	0.661444i	$-0.769944\pi$
$457$	−1.89298	+	1.89298i	−0.0885500	+	0.0885500i	0.661444	+	0.749994i	$0.269944\pi$
$458$	−23.8310	+	2.08495i	−1.11355	+	0.0974231i
$459$	7.43901	−	2.70758i	0.347223	−	0.126379i
$460$		0			0
$461$	−1.88632	+	10.6979i	−0.0878548	+	0.498249i	0.908849	+	0.417125i	$0.136962\pi$
$461$	−1.88632	+	10.6979i	−0.0878548	+	0.498249i	−0.996704	+	0.0811244i	$0.974149\pi$
$462$	−19.4753	+	9.08146i	−0.906071	+	0.422508i
$463$	−6.34485	+	23.6793i	−0.294870	+	1.10047i	0.646450	+	0.762956i	$0.276253\pi$
$463$	−6.34485	+	23.6793i	−0.294870	+	1.10047i	−0.941320	+	0.337514i	$0.890414\pi$
$464$	3.36219	−	5.82348i	0.156086	−	0.270348i
$465$		0			0
$466$	12.7580	+	15.2044i	0.591002	+	0.704329i
$467$	1.73770	+	6.48520i	0.0804113	+	0.300099i	0.994406	−	0.105628i	$-0.0336851\pi$
$467$	1.73770	+	6.48520i	0.0804113	+	0.300099i	−0.913994	+	0.405727i	$0.867018\pi$
$468$	9.08320	+	2.43384i	0.419871	+	0.112504i
$469$	13.8306	+	5.03394i	0.638640	+	0.232446i
$470$		0			0
$471$	33.6125	−	5.92679i	1.54878	−	0.273092i
$472$	−0.660033	+	1.41545i	−0.0303805	+	0.0651512i
$473$	−0.747900	−	8.54854i	−0.0343885	−	0.393062i
$474$	32.4205			1.48912
$475$		0			0
$476$	4.31737			0.197887
$477$	−0.980921	−	11.2120i	−0.0449133	−	0.513361i
$478$	6.92632	−	14.8535i	0.316802	−	0.679385i
$479$	11.8954	−	2.09747i	0.543513	−	0.0958360i	0.104851	−	0.994488i	$-0.466564\pi$
$479$	11.8954	−	2.09747i	0.543513	−	0.0958360i	0.438662	+	0.898652i	$0.355452\pi$
$480$		0			0
$481$	22.5936	+	8.22339i	1.03018	+	0.374954i
$482$	8.74384	+	2.34290i	0.398271	+	0.106716i
$483$	7.28942	+	27.2045i	0.331680	+	1.23785i
$484$	3.88437	+	4.62921i	0.176562	+	0.210419i
$485$		0			0
$486$	9.85731	−	17.0734i	0.447137	−	0.774463i
$487$	6.02394	−	22.4817i	0.272971	−	1.01874i	−0.684218	−	0.729277i	$-0.739856\pi$
$487$	6.02394	−	22.4817i	0.272971	−	1.01874i	0.957189	−	0.289464i	$-0.0934769\pi$
$488$	−9.41334	+	4.38951i	−0.426122	+	0.198704i
$489$	3.93938	−	22.3413i	0.178145	−	1.01031i
$490$		0			0
$491$	21.6048	−	7.86352i	0.975013	−	0.354876i	0.195113	−	0.980781i	$-0.437493\pi$
$491$	21.6048	−	7.86352i	0.975013	−	0.354876i	0.779899	+	0.625905i	$0.215270\pi$
$492$	14.9021	−	1.30376i	0.671838	−	0.0587782i
$493$	10.6603	−	10.6603i	0.480118	−	0.480118i
$494$	−3.83371	−	8.71227i	−0.172487	−	0.391984i
$495$		0			0
$496$	−3.24136	+	3.86290i	−0.145541	+	0.173449i
$497$	−7.68533	−	3.58373i	−0.344734	−	0.160752i
$498$	25.6496	−	36.6315i	1.14939	−	1.64149i
$499$	−39.4109	−	6.94921i	−1.76428	−	0.311089i	−0.804940	−	0.593356i	$-0.797803\pi$
$499$	−39.4109	−	6.94921i	−1.76428	−	0.311089i	−0.959336	+	0.282267i	$0.908914\pi$
$500$		0			0
$501$	13.1414	+	22.7616i	0.587115	+	1.01691i
$502$	16.3595	−	4.38352i	0.730161	−	0.195646i
$503$	−7.74044	−	0.677201i	−0.345129	−	0.0301949i	−0.0867264	−	0.996232i	$-0.527641\pi$
$503$	−7.74044	−	0.677201i	−0.345129	−	0.0301949i	−0.258403	+	0.966037i	$0.583196\pi$
$504$	−6.35250	+	5.33038i	−0.282963	+	0.237434i
$505$		0			0
$506$	19.3449	−	11.1688i	0.859985	−	0.496513i
$507$	−9.40324	−	20.1653i	−0.417613	−	0.895573i
$508$	4.67553	+	6.67735i	0.207443	+	0.296260i
$509$	4.13998	+	23.4790i	0.183501	+	1.04069i	0.927866	+	0.372914i	$0.121641\pi$
$509$	4.13998	+	23.4790i	0.183501	+	1.04069i	−0.744365	+	0.667773i	$0.767248\pi$
$510$		0			0
$511$	−15.2107	−	12.7633i	−0.672881	−	0.564615i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	15.2120	−	2.34168i	0.671626	−	0.103388i
$514$		−	0.380179i		−	0.0167690i
$515$		0			0
$516$	−1.92165	−	5.27970i	−0.0845961	−	0.232426i
$517$	10.8497	+	7.59707i	0.477171	+	0.334119i
$518$	−17.3684	+	12.1615i	−0.763122	+	0.534344i
$519$	−11.3846	+	31.2789i	−0.499728	+	1.37299i
$520$		0			0
$521$	−12.3736	−	7.14391i	−0.542098	−	0.312981i	0.203831	−	0.979006i	$-0.434661\pi$
$521$	−12.3736	−	7.14391i	−0.542098	−	0.312981i	−0.745929	+	0.666026i	$0.767994\pi$
$522$	−2.52379	+	28.8470i	−0.110463	+	1.26260i
$523$	1.47405	−	16.8485i	0.0644558	−	0.736733i	−0.893358	−	0.449345i	$-0.851657\pi$
$523$	1.47405	−	16.8485i	0.0644558	−	0.736733i	0.957814	−	0.287388i	$-0.0927870\pi$
$524$	−11.0889	−	6.40215i	−0.484419	−	0.279679i
$525$		0			0
$526$	5.91188	−	16.2428i	0.257770	−	0.708218i
$527$	−9.26101	+	6.48463i	−0.403416	+	0.282475i
$528$	9.14085	+	6.40049i	0.397804	+	0.278546i
$529$	−2.14682	−	5.89834i	−0.0933400	−	0.256450i
$530$		0			0
$531$		−	6.72547i		−	0.291861i
$532$	8.23262	+	1.63739i	0.356929	+	0.0709897i
$533$	8.54533	+	8.54533i	0.370139	+	0.370139i
$534$	14.8401	+	12.4523i	0.642193	+	0.538864i
$535$		0			0
$536$	−1.32722	−	7.52701i	−0.0573270	−	0.325117i
$537$	−34.2478	−	48.9110i	−1.47790	−	2.11066i
$538$	−3.71208	−	7.96058i	−0.160039	−	0.343205i
$539$	−11.7687	+	6.79466i	−0.506914	+	0.292667i
$540$		0			0
$541$	−11.3997	+	9.56549i	−0.490112	+	0.411253i	−0.854066	−	0.520164i	$-0.825871\pi$
$541$	−11.3997	+	9.56549i	−0.490112	+	0.411253i	0.363955	+	0.931417i	$0.381426\pi$
$542$	−16.1202	−	1.41033i	−0.692421	−	0.0605790i
$543$	−11.5709	+	3.10041i	−0.496554	+	0.133051i
$544$	−1.12100	−	1.94162i	−0.0480623	−	0.0832464i
$545$		0			0
$546$	−11.1937	−	1.97376i	−0.479048	−	0.0844691i
$547$	−1.33205	+	1.90237i	−0.0569545	+	0.0813395i	−0.846619	−	0.532199i	$-0.821366\pi$
$547$	−1.33205	+	1.90237i	−0.0569545	+	0.0813395i	0.789665	+	0.613539i	$0.210255\pi$
$548$	13.9103	+	6.48648i	0.594219	+	0.277089i
$549$	28.7502	−	34.2631i	1.22703	−	1.46232i
$550$		0			0
$551$	24.3707	−	16.2848i	1.03823	−	0.693754i
$552$	10.3418	−	10.3418i	0.440177	−	0.440177i
$553$	−23.0091	+	2.01304i	−0.978448	+	0.0856031i
$554$	5.32303	−	1.93742i	0.226154	−	0.0823132i
$555$		0			0
$556$	1.80136	−	10.2160i	0.0763945	−	0.433255i
$557$	1.94317	−	0.906114i	0.0823347	−	0.0383933i	−0.381015	−	0.924569i	$-0.624425\pi$
$557$	1.94317	−	0.906114i	0.0823347	−	0.0383933i	0.463349	+	0.886176i	$0.346647\pi$
$558$	5.62032	−	20.9753i	0.237927	−	0.887956i
$559$	2.26952	−	3.93093i	0.0959905	−	0.166260i
$560$		0			0
$561$	16.0814	+	19.1651i	0.678957	+	0.809150i
$562$	3.60046	+	13.4371i	0.151876	+	0.566809i
$563$	8.22905	+	2.20497i	0.346813	+	0.0929283i	0.428021	−	0.903769i	$-0.359211\pi$
$563$	8.22905	+	2.20497i	0.346813	+	0.0929283i	−0.0812076	+	0.996697i	$0.525878\pi$
$564$	8.14923	+	2.96608i	0.343144	+	0.124894i
$565$		0			0
$566$	−10.9945	+	1.93862i	−0.462133	+	0.0814865i
$567$	−2.74637	+	5.88961i	−0.115337	+	0.247340i
$568$	0.383794	+	4.38678i	0.0161036	+	0.184065i
$569$	−20.4241			−0.856224			−0.428112	−	0.903726i	$-0.640821\pi$
$569$	−20.4241			−0.856224			−0.428112	+	0.903726i	$0.640821\pi$
$570$		0			0
$571$	4.08844			0.171096			0.0855480	−	0.996334i	$-0.472736\pi$
$571$	4.08844			0.171096			0.0855480	+	0.996334i	$0.472736\pi$
$572$	0.785704	+	8.98063i	0.0328519	+	0.375499i
$573$	9.69238	−	20.7854i	0.404905	−	0.868322i
$574$	−10.4952	+	1.85059i	−0.438061	+	0.0772420i
$575$		0			0
$576$	4.04661	+	1.47284i	0.168609	+	0.0613685i
$577$	19.4187	+	5.20323i	0.808412	+	0.216613i	0.639274	−	0.768979i	$-0.279235\pi$
$577$	19.4187	+	5.20323i	0.808412	+	0.216613i	0.169138	+	0.985592i	$0.445902\pi$
$578$	3.09896	+	11.5655i	0.128900	+	0.481061i
$579$	39.6036	+	47.1978i	1.64587	+	1.96147i
$580$		0			0
$581$	−15.9293	+	27.5903i	−0.660858	+	1.14464i
$582$	6.34994	−	23.6983i	0.263214	−	0.982326i
$583$	9.77871	−	4.55989i	0.404993	−	0.188851i
$584$	−1.79052	+	10.1546i	−0.0740924	+	0.420199i
$585$		0			0
$586$	−19.9218	+	7.25094i	−0.822961	+	0.299533i
$587$	−39.3404	+	3.44184i	−1.62375	+	0.142060i	−0.862382	−	0.506259i	$-0.831028\pi$
$587$	−39.3404	+	3.44184i	−1.62375	+	0.142060i	−0.761369	+	0.648318i	$0.775473\pi$
$588$	−6.29157	+	6.29157i	−0.259460	+	0.259460i
$589$	−20.1188	+	8.85298i	−0.828979	+	0.364781i
$590$		0			0
$591$	14.4882	−	17.2663i	0.595963	−	0.710241i
$592$	9.97895	+	4.65326i	0.410132	+	0.191248i
$593$	−21.5679	+	30.8022i	−0.885689	+	1.26490i	0.0777511	+	0.996973i	$0.475226\pi$
$593$	−21.5679	+	30.8022i	−0.885689	+	1.26490i	−0.963440	+	0.267923i	$0.913663\pi$
$594$	−14.3555	−	2.53127i	−0.589015	−	0.103859i
$595$		0			0
$596$	−10.2089	−	17.6822i	−0.418171	−	0.724293i
$597$	14.7471	−	3.95147i	0.603559	−	0.161723i
$598$	11.7705	+	1.02979i	0.481333	+	0.0421112i
$599$	−0.707860	+	0.593965i	−0.0289224	+	0.0242687i	−0.657134	−	0.753774i	$-0.728232\pi$
$599$	−0.707860	+	0.593965i	−0.0289224	+	0.0242687i	0.628212	+	0.778042i	$0.283787\pi$
$600$		0			0
$601$	0.525630	−	0.303473i	0.0214409	−	0.0123789i	−0.489241	−	0.872149i	$-0.662726\pi$
$601$	0.525630	−	0.303473i	0.0214409	−	0.0123789i	0.510682	+	0.859770i	$0.329393\pi$
$602$	1.69164	+	3.62774i	0.0689461	+	0.147855i
$603$	18.8785	+	26.9613i	0.768793	+	1.09795i
$604$	0.320307	+	1.81655i	0.0130331	+	0.0739145i
$605$		0			0
$606$	18.1031	+	15.1903i	0.735389	+	0.617065i
$607$	11.9618	+	11.9618i	0.485516	+	0.485516i	0.906888	−	0.421372i	$-0.138451\pi$
$607$	11.9618	+	11.9618i	0.485516	+	0.485516i	−0.421372	+	0.906888i	$0.638451\pi$
$608$	−1.40121	−	4.12754i	−0.0568266	−	0.167394i
$609$		−	35.0015i		−	1.41833i
$610$		0			0
$611$	2.39620	+	6.58351i	0.0969399	+	0.266340i
$612$	7.90868	+	5.53772i	0.319690	+	0.223849i
$613$	−7.40948	+	5.18818i	−0.299266	+	0.209548i	−0.713559	−	0.700595i	$-0.752918\pi$
$613$	−7.40948	+	5.18818i	−0.299266	+	0.209548i	0.414293	+	0.910144i	$0.364029\pi$
$614$	−9.04790	+	24.8589i	−0.365143	+	1.00322i
$615$		0			0
$616$	−6.88476	−	3.97492i	−0.277395	−	0.160154i
$617$	−2.51381	+	28.7330i	−0.101202	+	1.15675i	0.760502	+	0.649335i	$0.224953\pi$
$617$	−2.51381	+	28.7330i	−0.101202	+	1.15675i	−0.861704	+	0.507410i	$0.830603\pi$
$618$	−4.33855	+	49.5898i	−0.174522	+	1.99480i
$619$	−38.4200	−	22.1818i	−1.54423	−	0.891562i	−0.998565	−	0.0535599i	$-0.982943\pi$
$619$	−38.4200	−	22.1818i	−1.54423	−	0.891562i	−0.545667	−	0.838002i	$-0.683723\pi$
$620$		0			0
$621$	−6.53446	+	17.9533i	−0.262219	+	0.720440i
$622$	10.2845	−	7.20127i	0.412370	−	0.288745i
$623$	−11.3053	−	7.91608i	−0.452938	−	0.317151i
$624$	2.01879	+	5.54657i	0.0808162	+	0.222041i
$625$		0			0
$626$			29.8505i			1.19307i
$627$	23.3965	+	42.6440i	0.934366	+	1.70304i
$628$	8.92864	+	8.92864i	0.356291	+	0.356291i
$629$	18.9103	+	15.8676i	0.754002	+	0.632682i
$630$		0			0
$631$	4.85690	+	27.5449i	0.193350	+	1.09654i	0.914749	+	0.404023i	$0.132389\pi$
$631$	4.85690	+	27.5449i	0.193350	+	1.09654i	−0.721399	+	0.692520i	$0.756500\pi$
$632$	6.87958	+	9.82506i	0.273655	+	0.390820i
$633$	−22.4625	−	48.1711i	−0.892806	−	1.91463i
$634$	17.4024	−	10.0473i	0.691137	−	0.399028i
$635$		0			0
$636$	5.41173	−	4.54098i	0.214589	−	0.180062i
$637$	−7.16076	−	0.626485i	−0.283720	−	0.0248222i
$638$	−26.8144	+	7.18491i	−1.06159	+	0.284453i
$639$	−9.48150	−	16.4224i	−0.375082	−	0.649662i
$640$		0			0
$641$	−29.5618	−	5.21255i	−1.16762	−	0.205883i	−0.443966	−	0.896044i	$-0.646429\pi$
$641$	−29.5618	−	5.21255i	−1.16762	−	0.205883i	−0.723656	+	0.690160i	$0.757540\pi$
$642$	−0.123206	+	0.175956i	−0.00486255	+	0.00694444i
$643$	−17.6970	−	8.25222i	−0.697900	−	0.325436i	0.0410874	−	0.999156i	$-0.486918\pi$
$643$	−17.6970	−	8.25222i	−0.697900	−	0.325436i	−0.738987	+	0.673720i	$0.764696\pi$
$644$	−6.69754	+	7.98182i	−0.263920	+	0.314528i
$645$		0			0
$646$	−0.639369	−	9.75169i	−0.0251556	−	0.383675i
$647$	18.5227	−	18.5227i	0.728204	−	0.728204i	−0.242058	−	0.970262i	$-0.577822\pi$
$647$	18.5227	−	18.5227i	0.728204	−	0.728204i	0.970262	+	0.242058i	$0.0778223\pi$
$648$	3.36178	−	0.294118i	0.132063	−	0.0115540i
$649$	6.05866	−	2.20517i	0.237823	−	0.0865605i
$650$		0			0
$651$	−4.55789	+	25.8491i	−0.178638	+	1.01311i
$652$	7.60649	−	3.54696i	0.297893	−	0.138910i
$653$	−4.17605	+	15.5852i	−0.163422	+	0.609897i	0.834815	+	0.550531i	$0.185575\pi$
$653$	−4.17605	+	15.5852i	−0.163422	+	0.609897i	−0.998236	+	0.0593665i	$0.981092\pi$
$654$	26.2094	−	45.3960i	1.02487	−	1.77512i
$655$		0			0
$656$	3.55731	+	4.23943i	0.138890	+	0.165522i
$657$	−11.4924	−	42.8903i	−0.448362	−	1.67331i
$658$	−5.96775	−	1.59905i	−0.232647	−	0.0623376i
$659$	−25.7887	−	9.38632i	−1.00458	−	0.365639i	−0.213234	−	0.977001i	$-0.568400\pi$
$659$	−25.7887	−	9.38632i	−1.00458	−	0.365639i	−0.791351	+	0.611362i	$0.790622\pi$
$660$		0			0
$661$	−40.5445	+	7.14908i	−1.57700	+	0.278067i	−0.892534	−	0.450981i	$-0.851074\pi$
$661$	−40.5445	+	7.14908i	−1.57700	+	0.278067i	−0.684463	+	0.729048i	$0.739963\pi$
$662$	−12.7662	+	27.3773i	−0.496173	+	1.06405i
$663$	1.15337	+	13.1831i	0.0447932	+	0.511989i
$664$	16.5440			0.642032
$665$		0			0
$666$	−47.4149			−1.83729
$667$	3.17110	+	36.2459i	0.122786	+	1.40345i
$668$	−4.10933	+	8.81249i	−0.158995	+	0.340965i
$669$	−9.31001	+	1.64161i	−0.359946	+	0.0634682i
$670$		0			0
$671$	40.2927	+	14.6654i	1.55548	+	0.566150i
$672$	−5.02780	−	1.34720i	−0.193952	−	0.0519692i
$673$	−3.21835	−	12.0110i	−0.124058	−	0.462991i	0.875746	−	0.482772i	$-0.160370\pi$
$673$	−3.21835	−	12.0110i	−0.124058	−	0.462991i	−0.999804	+	0.0197805i	$0.993703\pi$
$674$	−4.90897	−	5.85028i	−0.189087	−	0.225345i
$675$		0			0
$676$	4.11576	−	7.12871i	0.158299	−	0.274181i
$677$	−0.238549	+	0.890275i	−0.00916817	+	0.0342161i	−0.970358	−	0.241670i	$-0.922305\pi$
$677$	−0.238549	+	0.890275i	−0.00916817	+	0.0342161i	0.961190	+	0.275886i	$0.0889714\pi$
$678$	42.0357	−	19.6016i	1.61437	−	0.752794i
$679$	−3.03515	+	17.2132i	−0.116478	+	0.660581i
$680$		0			0
$681$	−46.4881	+	16.9203i	−1.78143	+	0.648386i
$682$	20.7385	−	1.81438i	0.794117	−	0.0694762i
$683$	−1.43038	+	1.43038i	−0.0547319	+	0.0547319i	−0.733943	−	0.679211i	$-0.762322\pi$
$683$	−1.43038	+	1.43038i	−0.0547319	+	0.0547319i	0.679211	+	0.733943i	$0.262322\pi$
$684$	12.9805	+	13.5590i	0.496323	+	0.518443i
$685$		0			0
$686$	12.7392	−	15.1820i	0.486384	−	0.579650i
$687$	58.6035	+	27.3273i	2.23586	+	1.04260i
$688$	1.19225	−	1.70270i	0.0454539	−	0.0649150i
$689$	5.62049	+	0.991044i	0.214124	+	0.0377558i
$690$		0			0
$691$	6.42214	+	11.1235i	0.244310	+	0.423157i	0.961937	−	0.273270i	$-0.0881054\pi$
$691$	6.42214	+	11.1235i	0.244310	+	0.423157i	−0.717628	+	0.696427i	$0.754772\pi$
$692$	−11.8949	+	3.18723i	−0.452176	+	0.121160i
$693$	34.1042	+	2.98373i	1.29551	+	0.113343i
$694$	−16.8164	+	14.1106i	−0.638340	+	0.535631i
$695$		0			0
$696$	−15.7410	+	9.08805i	−0.596660	+	0.344482i
$697$	5.24368	+	11.2451i	0.198619	+	0.425939i
$698$	−9.46142	−	13.5123i	−0.358120	−	0.511448i
$699$	−9.31609	−	52.8342i	−0.352367	−	1.99837i
$700$		0			0
$701$	−0.649360	−	0.544878i	−0.0245260	−	0.0205798i	0.630442	−	0.776236i	$-0.282874\pi$
$701$	−0.649360	−	0.544878i	−0.0245260	−	0.0205798i	−0.654968	+	0.755656i	$0.727318\pi$
$702$	−5.45218	−	5.45218i	−0.205779	−	0.205779i
$703$	30.0413	+	37.4291i	1.13303	+	1.41166i
$704$			4.12832i			0.155592i
$705$		0			0
$706$	−0.755008	−	2.07437i	−0.0284151	−	0.0780698i
$707$	−13.7911	−	9.65667i	−0.518670	−	0.363176i
$708$	3.45805	−	2.42135i	0.129961	−	0.0910000i
$709$	−8.84184	+	24.2928i	−0.332062	+	0.912333i	0.655513	+	0.755184i	$0.272453\pi$
$709$	−8.84184	+	24.2928i	−0.332062	+	0.912333i	−0.987575	+	0.157149i	$0.949770\pi$
$710$		0			0
$711$	−44.7308	−	25.8253i	−1.67754	−	0.968526i
$712$	−0.624639	+	7.13966i	−0.0234094	+	0.267570i
$713$	2.37803	−	27.1810i	0.0890580	−	1.01794i
$714$	−10.1065	−	5.83497i	−0.378225	−	0.218368i
$715$		0			0
$716$	7.55517	−	20.7577i	0.282350	−	0.775750i
$717$	−36.2884	+	25.4094i	−1.35521	+	0.948931i
$718$	−21.9969	−	15.4024i	−0.820917	−	0.574812i
$719$	−1.50829	−	4.14400i	−0.0562498	−	0.154545i	0.908385	−	0.418134i	$-0.137316\pi$
$719$	−1.50829	−	4.14400i	−0.0562498	−	0.154545i	−0.964635	+	0.263589i	$0.915094\pi$
$720$		0			0
$721$		−	35.4638i		−	1.32074i
$722$	2.47919	−	18.8376i	0.0922660	−	0.701061i
$723$	−17.3018	−	17.3018i	−0.643463	−	0.643463i
$724$	−3.39491	−	2.84867i	−0.126171	−	0.105870i
$725$		0			0
$726$	−2.83643	−	16.0862i	−0.105270	−	0.597015i
$727$	−3.32559	−	4.74943i	−0.123339	−	0.176147i	0.752734	−	0.658325i	$-0.228735\pi$
$727$	−3.32559	−	4.74943i	−0.123339	−	0.176147i	−0.876073	+	0.482178i	$0.839846\pi$
$728$	−1.77715	−	3.81110i	−0.0658654	−	0.141249i
$729$	−37.3821	+	21.5825i	−1.38452	+	0.799354i
$730$		0			0
$731$	3.56996	−	2.99555i	0.132040	−	0.110794i
$732$	27.9680	+	2.44688i	1.03373	+	0.0904394i
$733$	28.6373	−	7.67334i	1.05774	−	0.283421i	0.312295	−	0.949985i	$-0.398902\pi$
$733$	28.6373	−	7.67334i	1.05774	−	0.283421i	0.745448	+	0.666564i	$0.232236\pi$
$734$	0.663515	+	1.14924i	0.0244908	+	0.0424193i
$735$		0			0
$736$	5.32861	+	0.939578i	0.196415	+	0.0346333i
$737$	−18.0982	+	25.8469i	−0.666656	+	0.952084i
$738$	−21.5991	−	10.0718i	−0.795072	−	0.370748i
$739$	−8.35850	+	9.96127i	−0.307472	+	0.366431i	−0.897548	−	0.440917i	$-0.854653\pi$
$739$	−8.35850	+	9.96127i	−0.307472	+	0.366431i	0.590076	+	0.807348i	$0.299098\pi$
$740$		0			0
$741$	−2.80044	+	25.5757i	−0.102877	+	0.939547i
$742$	−3.55880	+	3.55880i	−0.130648	+	0.130648i
$743$	39.7542	−	3.47805i	1.45844	−	0.127597i	0.669842	−	0.742504i	$-0.266362\pi$
$743$	39.7542	−	3.47805i	1.45844	−	0.127597i	0.788600	+	0.614907i	$0.210806\pi$
$744$	12.8084	−	4.66187i	0.469578	−	0.170912i
$745$		0			0
$746$	−2.44340	+	13.8572i	−0.0894594	+	0.507349i
$747$	−64.5686	+	30.1089i	−2.36244	+	1.10163i
$748$	−2.39554	+	8.94028i	−0.0875897	+	0.326889i
$749$	0.0765149	−	0.132528i	0.00279579	−	0.00484246i
$750$		0			0
$751$	11.6447	+	13.8776i	0.424920	+	0.506400i	0.935449	−	0.353460i	$-0.114995\pi$
$751$	11.6447	+	13.8776i	0.424920	+	0.506400i	−0.510530	+	0.859860i	$0.670551\pi$
$752$	0.830382	+	3.09903i	0.0302809	+	0.113010i
$753$	−44.2201	−	11.8487i	−1.61147	−	0.431792i
$754$	−13.7984	−	5.02219i	−0.502507	−	0.182897i
$755$		0			0
$756$	6.69626	−	1.18073i	0.243540	−	0.0429428i
$757$	17.0860	−	36.6410i	0.621000	−	1.33174i	−0.304327	−	0.952568i	$-0.598432\pi$
$757$	17.0860	−	36.6410i	0.621000	−	1.33174i	0.925327	−	0.379171i	$-0.123791\pi$
$758$	2.23834	+	25.5844i	0.0813002	+	0.929266i
$759$	−60.3788			−2.19161
$760$		0			0
$761$	7.82239			0.283562			0.141781	−	0.989898i	$-0.454717\pi$
$761$	7.82239			0.283562			0.141781	+	0.989898i	$0.454717\pi$
$762$	−1.92037	−	21.9499i	−0.0695676	−	0.795162i
$763$	−15.7823	+	33.8453i	−0.571359	+	1.22528i
$764$	8.35573	−	1.47334i	0.302300	−	0.0533036i
$765$		0			0
$766$	−0.552432	−	0.201069i	−0.0199602	−	0.00726491i
$767$	3.29421	+	0.882680i	0.118947	+	0.0318717i
$768$	0.699593	+	2.61092i	0.0252444	+	0.0942133i
$769$	4.85436	+	5.78520i	0.175053	+	0.208620i	0.846436	−	0.532491i	$-0.178744\pi$
$769$	4.85436	+	5.78520i	0.175053	+	0.208620i	−0.671383	+	0.741111i	$0.734299\pi$
$770$		0			0
$771$	−0.513815	+	0.889954i	−0.0185046	+	0.0320509i
$772$	−5.89950	+	22.0172i	−0.212327	+	0.792417i
$773$	−16.0480	+	7.48331i	−0.577207	+	0.269156i	−0.689222	−	0.724551i	$-0.742047\pi$
$773$	−16.0480	+	7.48331i	−0.577207	+	0.269156i	0.112015	+	0.993707i	$0.464270\pi$
$774$	−1.55435	+	8.81518i	−0.0558701	+	0.316855i
$775$		0			0
$776$	8.52924	−	3.10439i	0.306182	−	0.111441i
$777$	57.0937	−	4.99505i	2.04822	−	0.179196i
$778$	19.9986	−	19.9986i	0.716986	−	0.716986i
$779$	5.73419	+	23.4315i	0.205449	+	0.839522i
$780$		0			0
$781$	11.6854	−	13.9261i	0.418135	−	0.498314i
$782$	10.9944	+	5.12678i	0.393160	+	0.183333i
$783$	13.6188	−	19.4496i	0.486696	−	0.695074i
$784$	−3.24173	−	0.571604i	−0.115776	−	0.0204144i
$785$		0			0
$786$	17.3051	+	29.9734i	0.617254	+	1.06912i
$787$	49.6584	−	13.3059i	1.77013	−	0.474305i	0.781402	−	0.624028i	$-0.214505\pi$
$787$	49.6584	−	13.3059i	1.77013	−	0.474305i	0.988728	+	0.149723i	$0.0478384\pi$
$788$	8.30693	+	0.726763i	0.295922	+	0.0258898i
$789$	−35.7913	+	30.0324i	−1.27420	+	1.06918i
$790$		0			0
$791$	−28.6161	+	16.5215i	−1.01747	+	0.587436i
$792$	−7.51323	−	16.1122i	−0.266971	−	0.572521i
$793$	13.0092	+	18.5790i	0.461969	+	0.659760i
$794$	−0.383752	−	2.17637i	−0.0136188	−	0.0772363i
$795$		0			0
$796$	4.32681	+	3.63062i	0.153360	+	0.128684i
$797$	−14.1266	−	14.1266i	−0.500391	−	0.500391i	0.411168	−	0.911560i	$-0.365121\pi$
$797$	−14.1266	−	14.1266i	−0.500391	−	0.500391i	−0.911560	+	0.411168i	$0.865121\pi$
$798$	−17.0586	−	14.9594i	−0.603870	−	0.529557i
$799$			7.19310i			0.254474i
$800$		0			0
$801$	−10.5558	−	29.0018i	−0.372970	−	1.02473i
$802$	−26.6591	−	18.6669i	−0.941364	−	0.659150i
$803$	34.8696	−	24.4160i	1.23052	−	0.861621i
$804$	−7.06597	+	19.4136i	−0.249198	+	0.684665i
$805$		0			0
$806$	9.53630	+	5.50578i	0.335902	+	0.193933i
$807$	−2.06925	+	23.6517i	−0.0728412	+	0.832579i
$808$	−0.761985	+	8.70953i	−0.0268066	+	0.306400i
$809$	36.6900	+	21.1830i	1.28995	+	0.744754i	0.978645	−	0.205555i	$-0.0659001\pi$
$809$	36.6900	+	21.1830i	1.28995	+	0.744754i	0.311307	+	0.950310i	$0.399233\pi$
$810$		0			0
$811$	−7.55893	+	20.7680i	−0.265430	+	0.729262i	0.733349	+	0.679853i	$0.237956\pi$
$811$	−7.55893	+	20.7680i	−0.265430	+	0.729262i	−0.998779	+	0.0494098i	$0.984266\pi$
$812$	10.6072	−	7.42726i	0.372241	−	0.260646i
$813$	35.8294	+	25.0880i	1.25659	+	0.879875i
$814$	−15.5465	−	42.7138i	−0.544906	−	1.49712i
$815$		0			0
$816$			6.06015i			0.212148i
$817$	7.94347	−	4.35816i	0.277907	−	0.152473i
$818$	−1.94757	−	1.94757i	−0.0680950	−	0.0680950i
$819$	13.8718	+	11.6399i	0.484722	+	0.406730i
$820$		0			0
$821$	−3.37315	−	19.1301i	−0.117724	−	0.667645i	−0.985366	−	0.170455i	$-0.945476\pi$
$821$	−3.37315	−	19.1301i	−0.117724	−	0.667645i	0.867642	−	0.497190i	$-0.165635\pi$
$822$	−23.7959	−	33.9840i	−0.829976	−	1.18533i
$823$	−9.22373	−	19.7804i	−0.321519	−	0.689500i	0.677418	−	0.735598i	$-0.263099\pi$
$823$	−9.22373	−	19.7804i	−0.321519	−	0.689500i	−0.998937	+	0.0460986i	$0.985321\pi$
$824$	−15.9489	+	9.20809i	−0.555605	+	0.320779i
$825$		0			0
$826$	−2.30386	+	1.93317i	−0.0801617	+	0.0672636i
$827$	−0.567217	−	0.0496250i	−0.0197241	−	0.00172563i	0.0772894	−	0.997009i	$-0.475373\pi$
$827$	−0.567217	−	0.0496250i	−0.0197241	−	0.00172563i	−0.0970135	+	0.995283i	$0.530929\pi$
$828$	−22.5067	+	6.03065i	−0.782161	+	0.209579i
$829$	7.11756	+	12.3280i	0.247203	+	0.428168i	0.962749	−	0.270398i	$-0.0871552\pi$
$829$	7.11756	+	12.3280i	0.247203	+	0.428168i	−0.715546	+	0.698566i	$0.753822\pi$
$830$		0			0
$831$	−15.0790	−	2.65884i	−0.523086	−	0.0922341i
$832$	−1.25251	+	1.78877i	−0.0434230	+	0.0620144i
$833$	−6.68860	−	3.11894i	−0.231746	−	0.108065i
$834$	−18.0238	+	21.4799i	−0.624113	+	0.743788i
$835$		0			0
$836$	−7.95860	+	16.1393i	−0.275254	+	0.558190i
$837$	−12.5904	+	12.5904i	−0.435188	+	0.435188i
$838$	−21.2986	+	1.86339i	−0.735749	+	0.0643697i
$839$	1.42379	−	0.518216i	0.0491546	−	0.0178908i	−0.317326	−	0.948317i	$-0.602785\pi$
$839$	1.42379	−	0.518216i	0.0491546	−	0.0178908i	0.366480	+	0.930426i	$0.380563\pi$
$840$		0			0
$841$	2.81609	−	15.9708i	0.0971065	−	0.550718i
$842$	−22.2568	+	10.3785i	−0.767020	+	0.357667i
$843$	9.73210	−	36.3207i	0.335191	−	1.25095i
$844$	9.83177	−	17.0291i	0.338423	−	0.586167i
$845$		0			0
$846$	−8.88085	−	10.5838i	−0.305330	−	0.363878i
$847$	3.01186	+	11.2404i	0.103489	+	0.386225i
$848$	2.52451	+	0.676440i	0.0866919	+	0.0232290i
$849$	28.3569	+	10.3211i	0.973205	+	0.354218i
$850$		0			0
$851$	−58.6710	+	10.3453i	−2.01121	+	0.354631i
$852$	5.03036	−	10.7876i	0.172337	−	0.369578i
$853$	1.83559	+	20.9809i	0.0628495	+	0.718373i	0.960612	+	0.277893i	$0.0896361\pi$
$853$	1.83559	+	20.9809i	0.0628495	+	0.718373i	−0.897763	+	0.440480i	$0.854808\pi$
$854$	−20.0011			−0.684423
$855$		0			0
$856$	−0.0794677			−0.00271615
$857$	3.16034	+	36.1229i	0.107955	+	1.23393i	0.836126	+	0.548538i	$0.184815\pi$
$857$	3.16034	+	36.1229i	0.107955	+	1.23393i	−0.728171	+	0.685396i	$0.759629\pi$
$858$	10.2982	−	22.0845i	0.351574	−	0.753952i
$859$	28.6638	−	5.05421i	0.977997	−	0.172447i	0.338270	−	0.941049i	$-0.390158\pi$
$859$	28.6638	−	5.05421i	0.977997	−	0.172447i	0.639727	+	0.768602i	$0.279047\pi$
$860$		0			0
$861$	27.0691	+	9.85235i	0.922513	+	0.335767i
$862$	−28.3639	−	7.60007i	−0.966077	−	0.258860i
$863$	−1.65512	−	6.17698i	−0.0563408	−	0.210267i	0.932017	−	0.362415i	$-0.118048\pi$
$863$	−1.65512	−	6.17698i	−0.0563408	−	0.210267i	−0.988358	+	0.152148i	$0.951381\pi$
$864$	−2.26967	−	2.70489i	−0.0772158	−	0.0920221i
$865$		0			0
$866$	7.82520	−	13.5536i	0.265911	−	0.460571i
$867$	8.37655	−	31.2617i	0.284483	−	1.06170i
$868$	−8.80077	+	4.10386i	−0.298717	+	0.139294i
$869$	8.59833	−	48.7635i	0.291678	−	1.65419i
$870$		0			0
$871$	−15.6836	+	5.70838i	−0.531420	+	0.193421i
$872$	19.3189	−	1.69018i	0.654220	−	0.0572368i
$873$	−27.6385	+	27.6385i	−0.935422	+	0.935422i
$874$	19.0204	+	13.9457i	0.643376	+	0.471722i
$875$		0			0
$876$	17.9154	−	21.3507i	0.605305	−	0.721374i
$877$	27.4515	+	12.8009i	0.926972	+	0.432254i	0.826660	−	0.562702i	$-0.190238\pi$
$877$	27.4515	+	12.8009i	0.926972	+	0.432254i	0.100312	+	0.994956i	$0.468016\pi$
$878$	−7.20242	+	10.2861i	−0.243070	+	0.347140i
$879$	56.4343	+	9.95088i	1.90348	+	0.335635i
$880$		0			0
$881$	−25.4317	−	44.0490i	−0.856815	−	1.48405i	−0.874951	−	0.484211i	$-0.839107\pi$
$881$	−25.4317	−	44.0490i	−0.856815	−	1.48405i	0.0181362	−	0.999836i	$-0.494227\pi$
$882$	13.6922	−	3.66882i	0.461041	−	0.123536i
$883$	−24.0775	−	2.10651i	−0.810272	−	0.0708896i	−0.325513	−	0.945538i	$-0.605537\pi$
$883$	−24.0775	−	2.10651i	−0.810272	−	0.0708896i	−0.484759	+	0.874648i	$0.661093\pi$
$884$	−3.75040	+	3.14696i	−0.126140	+	0.105844i
$885$		0			0
$886$	25.6174	−	14.7902i	0.860633	−	0.496887i
$887$	−6.44718	−	13.8260i	−0.216475	−	0.464232i	0.767842	−	0.640639i	$-0.221330\pi$
$887$	−6.44718	−	13.8260i	−0.216475	−	0.464232i	−0.984317	+	0.176407i	$0.943553\pi$
$888$	−17.0706	−	24.3794i	−0.572853	−	0.818119i
$889$	2.72581	+	15.4588i	0.0914207	+	0.518472i
$890$		0			0
$891$	−10.6722	−	8.95501i	−0.357531	−	0.300004i
$892$	−2.47306	−	2.47306i	−0.0828042	−	0.0828042i
$893$	−2.72802	+	13.7162i	−0.0912897	+	0.458996i
$894$			55.1894i			1.84581i
$895$		0			0
$896$	−0.658623	−	1.80955i	−0.0220031	−	0.0604529i
$897$	−26.1617	−	18.3186i	−0.873513	−	0.611641i
$898$	−5.35845	+	3.75202i	−0.178814	+	0.125207i
$899$	−11.5975	+	31.8638i	−0.386797	+	1.06272i
$900$		0			0
$901$	5.07455	+	2.92980i	0.169058	+	0.0976056i
$902$	1.99124	−	22.7599i	0.0663009	−	0.757823i
$903$	0.942985	−	10.7784i	0.0313806	−	0.358682i
$904$	14.8602	+	8.57954i	0.494243	+	0.285351i
$905$		0			0
$906$	1.70529	−	4.68524i	0.0566544	−	0.155657i
$907$	−1.65031	+	1.15556i	−0.0547978	+	0.0383698i	−0.600654	−	0.799509i	$-0.705093\pi$
$907$	−1.65031	+	1.15556i	−0.0547978	+	0.0383698i	0.545857	+	0.837879i	$0.316204\pi$
$908$	−14.9924	−	10.4978i	−0.497540	−	0.348381i
$909$	−12.8768	−	35.3787i	−0.427096	−	1.17344i
$910$		0			0
$911$		−	49.3348i		−	1.63454i	−0.576258	−	0.817268i	$-0.695488\pi$
$911$		−	49.3348i		−	1.63454i	0.576258	−	0.817268i	$-0.304512\pi$
$912$	−2.29834	+	11.5558i	−0.0761057	+	0.382652i
$913$	−48.2946	−	48.2946i	−1.59832	−	1.59832i
$914$	2.05076	+	1.72080i	0.0678333	+	0.0569189i
$915$		0			0
$916$	4.15402	+	23.5586i	0.137253	+	0.778399i
$917$	−14.1427	−	20.1979i	−0.467033	−	0.666993i
$918$	−3.34563	−	7.17473i	−0.110422	−	0.236801i
$919$	0.794027	−	0.458432i	0.0261925	−	0.0151223i	−0.486847	−	0.873488i	$-0.661853\pi$
$919$	0.794027	−	0.458432i	0.0261925	−	0.0151223i	0.513039	+	0.858365i	$0.328520\pi$
$920$		0			0
$921$	54.7771	−	45.9634i	1.80497	−	1.51455i
$922$	10.8216	+	0.946764i	0.356389	+	0.0311800i
$923$	9.28828	−	2.48879i	0.305727	−	0.0819194i
$924$	10.7443	+	18.6096i	0.353461	+	0.612212i
$925$		0			0
$926$	24.1422	+	4.25692i	0.793361	+	0.139891i
$927$	45.4879	−	64.9635i	1.49402	−	2.13368i
$928$	−6.09435	−	2.84184i	−0.200057	−	0.0932881i
$929$	8.29183	−	9.88181i	0.272046	−	0.324212i	−0.612673	−	0.790336i	$-0.709906\pi$
$929$	8.29183	−	9.88181i	0.272046	−	0.324212i	0.884719	+	0.466125i	$0.154350\pi$
$930$		0			0
$931$	−11.5713	−	8.48407i	−0.379235	−	0.278054i
$932$	14.0346	−	14.0346i	0.459718	−	0.459718i
$933$	−33.8073	+	2.95776i	−1.10680	+	0.0968327i
$934$	6.30907	−	2.29631i	0.206439	−	0.0751377i
$935$		0			0
$936$	1.63292	−	9.26076i	0.0533737	−	0.302697i
$937$	−22.8809	+	10.6695i	−0.747486	+	0.348559i	−0.758753	−	0.651378i	$-0.774191\pi$
$937$	−22.8809	+	10.6695i	−0.747486	+	0.348559i	0.0112672	+	0.999937i	$0.496413\pi$
$938$	3.80937	−	14.2168i	0.124380	−	0.464193i
$939$	40.3432	−	69.8766i	1.31655	−	2.28034i
$940$		0			0
$941$	−28.7594	−	34.2741i	−0.937529	−	1.11730i	−0.992914	−	0.118839i	$-0.962083\pi$
$941$	−28.7594	−	34.2741i	−0.937529	−	1.11730i	0.0553842	−	0.998465i	$-0.482362\pi$
$942$	−8.83376	−	32.9680i	−0.287819	−	1.07416i
$943$	−28.9241	−	7.75019i	−0.941899	−	0.252381i
$944$	1.46759	+	0.534157i	0.0477658	+	0.0173853i
$945$		0			0
$946$	−8.45082	+	1.49011i	−0.274760	+	0.0484476i
$947$	−14.3749	+	30.8270i	−0.467120	+	1.00174i	0.521769	+	0.853087i	$0.325272\pi$
$947$	−14.3749	+	30.8270i	−0.467120	+	1.00174i	−0.988889	+	0.148656i	$0.952505\pi$
$948$	−2.82563	−	32.2971i	−0.0917723	−	1.04896i
$949$	22.5164			0.730914
$950$		0			0
$951$	−54.3159			−1.76131
$952$	−0.376284	−	4.30095i	−0.0121954	−	0.139394i
$953$	−25.6448	+	54.9955i	−0.830717	+	1.78148i	−0.248095	+	0.968736i	$0.579805\pi$
$953$	−25.6448	+	54.9955i	−0.830717	+	1.78148i	−0.582622	+	0.812743i	$0.697973\pi$
$954$	−11.0838	+	1.95438i	−0.358852	+	0.0632753i
$955$		0			0
$956$	−15.4007	−	5.60539i	−0.498094	−	0.181291i
$957$	72.4799	+	19.4209i	2.34294	+	0.627790i
$958$	−3.12624	−	11.6673i	−0.101004	−	0.376953i
$959$	18.9983	+	22.6413i	0.613486	+	0.731124i
$960$		0			0
$961$	−2.78581	+	4.82516i	−0.0898648	+	0.155650i
$962$	6.22293	−	23.2243i	0.200635	−	0.748782i
$963$	0.310150	−	0.144625i	0.00999445	−	0.00466049i
$964$	1.57191	−	8.91476i	0.0506279	−	0.287125i
$965$		0			0
$966$	26.4657	−	9.63271i	0.851518	−	0.309927i
$967$	−12.5422	+	1.09730i	−0.403329	+	0.0352867i	−0.287016	−	0.957926i	$-0.592663\pi$
$967$	−12.5422	+	1.09730i	−0.403329	+	0.0352867i	−0.116313	+	0.993213i	$0.537108\pi$
$968$	4.27305	−	4.27305i	0.137341	−	0.137341i
$969$	−11.6828	+	23.6917i	−0.375306	+	0.761086i
$970$		0			0
$971$	−7.78750	+	9.28078i	−0.249913	+	0.297834i	−0.876387	−	0.481608i	$-0.840053\pi$
$971$	−7.78750	+	9.28078i	−0.249913	+	0.297834i	0.626474	+	0.779442i	$0.284497\pi$
$972$	−17.8675	−	8.33176i	−0.573101	−	0.267241i
$973$	11.4579	−	16.3636i	0.367324	−	0.524593i
$974$	−22.9211	−	4.04161i	−0.734440	−	0.129502i
$975$		0			0
$976$	5.19324	+	8.99495i	0.166231	+	0.287921i
$977$	−11.5699	+	3.10016i	−0.370155	+	0.0991828i	−0.439101	−	0.898438i	$-0.644703\pi$
$977$	−11.5699	+	3.10016i	−0.370155	+	0.0991828i	0.0689459	+	0.997620i	$0.478036\pi$
$978$	−22.5996	−	1.97721i	−0.722657	−	0.0632243i
$979$	22.6652	−	19.0184i	0.724384	−	0.607831i
$980$		0			0
$981$	−72.3225	+	41.7554i	−2.30908	+	1.33315i
$982$	−9.71658	−	20.8373i	−0.310069	−	0.664944i
$983$	−25.9196	−	37.0170i	−0.826707	−	1.18066i	−0.981262	−	0.192676i	$-0.938283\pi$
$983$	−25.9196	−	37.0170i	−0.826707	−	1.18066i	0.154555	−	0.987984i	$-0.450605\pi$
$984$	−2.59761	−	14.7318i	−0.0828086	−	0.469631i
$985$		0			0
$986$	−11.5489	−	9.69067i	−0.367792	−	0.308614i
$987$	11.8087	+	11.8087i	0.375874	+	0.375874i
$988$	−8.34499	+	4.57845i	−0.265489	+	0.145660i
$989$			11.2470i			0.357634i
$990$		0			0
$991$	−2.53877	−	6.97520i	−0.0806466	−	0.221575i	0.892816	−	0.450422i	$-0.148727\pi$
$991$	−2.53877	−	6.97520i	−0.0806466	−	0.221575i	−0.973462	+	0.228848i	$0.926504\pi$
$992$	4.13070	+	2.89235i	0.131150	+	0.0918322i
$993$	66.8848	−	46.8333i	2.12253	−	1.48621i
$994$	−2.90027	+	7.96843i	−0.0919910	+	0.252743i
$995$		0			0
$996$	−38.7276	−	22.3594i	−1.22713	−	0.708484i
$997$	−0.438430	+	5.01128i	−0.0138852	+	0.158709i	−0.999972	−	0.00752434i	$-0.997605\pi$
$997$	−0.438430	+	5.01128i	−0.0138852	+	0.158709i	0.986086	+	0.166233i	$0.0531605\pi$
$998$	−3.48788	+	39.8666i	−0.110407	+	1.26196i
$999$	33.6694	+	19.4390i	1.06525	+	0.615024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.c.193.1	✓	72
5.2	odd	4	inner	950.2.bb.c.307.6	yes	72
5.3	odd	4	inner	950.2.bb.c.307.1	yes	72
5.4	even	2	inner	950.2.bb.c.193.6	yes	72
19.13	odd	18	inner	950.2.bb.c.393.6	yes	72
95.13	even	36	inner	950.2.bb.c.507.6	yes	72
95.32	even	36	inner	950.2.bb.c.507.1	yes	72
95.89	odd	18	inner	950.2.bb.c.393.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.c.193.1	✓	72	1.1	even	1	trivial
950.2.bb.c.193.6	yes	72	5.4	even	2	inner
950.2.bb.c.307.1	yes	72	5.3	odd	4	inner
950.2.bb.c.307.6	yes	72	5.2	odd	4	inner
950.2.bb.c.393.1	yes	72	95.89	odd	18	inner
950.2.bb.c.393.6	yes	72	19.13	odd	18	inner
950.2.bb.c.507.1	yes	72	95.32	even	36	inner
950.2.bb.c.507.6	yes	72	95.13	even	36	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-1.14235 + 2.44977i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(2.54001 + 0.924487i) q^{6} +(-1.86007 - 0.498404i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.76804 - 3.29882i) q^{9} +O(q^{10})\)	\(q+(-0.0871557 - 0.996195i) q^{2} +(-1.14235 + 2.44977i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(2.54001 + 0.924487i) q^{6} +(-1.86007 - 0.498404i) q^{7} +(0.258819 + 0.965926i) q^{8} +(-2.76804 - 3.29882i) q^{9} +(2.06416 - 3.57523i) q^{11} +(0.699593 - 2.61092i) q^{12} +(1.97909 - 0.922865i) q^{13} +(-0.334392 + 1.89643i) q^{14} +(0.939693 - 0.342020i) q^{16} +(2.23346 - 0.195403i) q^{17} +(-3.04502 + 3.04502i) q^{18} +(4.33300 + 0.474447i) q^{19} +(3.34581 - 3.98739i) q^{21} +(-3.74153 - 1.74470i) q^{22} +(-3.10351 + 4.43228i) q^{23} +(-2.66195 - 0.469374i) q^{24} +(-1.09184 - 1.89113i) q^{26} +(3.41066 - 0.913885i) q^{27} +(1.91836 + 0.167835i) q^{28} +(5.15117 - 4.32234i) q^{29} +(-4.36707 + 2.52133i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(6.40049 + 9.14085i) q^{33} +(-0.389318 - 2.20793i) q^{34} +(3.29882 + 2.76804i) q^{36} +(7.78564 + 7.78564i) q^{37} +(0.0949956 - 4.35786i) q^{38} +5.90254i q^{39} +(1.89280 + 5.20044i) q^{41} +(-4.26382 - 2.98556i) q^{42} +(1.70270 - 1.19225i) q^{43} +(-1.41197 + 3.87935i) q^{44} +(4.68590 + 2.70541i) q^{46} +(-0.279626 + 3.19614i) q^{47} +(-0.235584 + 2.69273i) q^{48} +(-2.85073 - 1.64587i) q^{49} +(-2.07269 + 5.69468i) q^{51} +(-1.78877 + 1.25251i) q^{52} +(2.14091 + 1.49908i) q^{53} +(-1.20767 - 3.31804i) q^{54} -1.92569i q^{56} +(-6.11207 + 10.0729i) q^{57} +(-4.75485 - 4.75485i) q^{58} +(1.19639 + 1.00389i) q^{59} +(1.80359 + 10.2287i) q^{61} +(2.89235 + 4.13070i) q^{62} +(3.50460 + 7.51565i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(8.54823 - 7.17281i) q^{66} +(-7.61405 - 0.666143i) q^{67} +(-2.16560 + 0.580271i) q^{68} +(-7.31276 - 12.6661i) q^{69} +(4.33664 + 0.764666i) q^{71} +(2.47000 - 3.52752i) q^{72} +(9.34513 + 4.35771i) q^{73} +(7.07745 - 8.43458i) q^{74} +(-4.34956 + 0.285179i) q^{76} +(-5.62139 + 5.62139i) q^{77} +(5.88008 - 0.514440i) q^{78} +(11.2708 - 4.10225i) q^{79} +(0.585997 - 3.32336i) q^{81} +(5.01568 - 2.33885i) q^{82} +(4.28190 - 15.9803i) q^{83} +(-2.60258 + 4.50780i) q^{84} +(-1.33611 - 1.59231i) q^{86} +(4.70432 + 17.5568i) q^{87} +(3.98765 + 1.06849i) q^{88} +(6.73471 + 2.45124i) q^{89} +(-4.14120 + 0.730206i) q^{91} +(2.28671 - 4.90386i) q^{92} +(-1.18797 - 13.5785i) q^{93} +3.20835 q^{94} +2.70302 q^{96} +(-0.791080 - 9.04209i) q^{97} +(-1.39115 + 2.98333i) q^{98} +(-17.5077 + 3.08708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{6}+O(q^{10}) \) 72 * q + 24 * q^6	\( 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) \) 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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