LMFDB - Embedded newform 950.2.u.c.549.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			549.2
Root			$0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	950.549
Dual form			950.2.u.c.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(-0.223238 + 0.266044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.266044 + 0.223238i) q^{6} +(3.25519 - 1.87939i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.500000 + 2.83564i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(-0.223238 + 0.266044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.266044 + 0.223238i) q^{6} +(3.25519 - 1.87939i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.500000 + 2.83564i) q^{9} +(2.76604 - 4.79093i) q^{11} +(-0.300767 + 0.173648i) q^{12} +(0.839100 + 1.00000i) q^{13} +(3.53209 - 1.28558i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-4.68647 - 0.826352i) q^{17} +2.87939i q^{18} +(-2.77719 - 3.35965i) q^{19} +(-0.226682 + 1.28558i) q^{21} +(3.55596 - 4.23783i) q^{22} +(1.13052 - 3.10607i) q^{23} +(-0.326352 + 0.118782i) q^{24} +(0.652704 + 1.13052i) q^{26} +(-1.76833 - 1.02094i) q^{27} +(3.70167 - 0.652704i) q^{28} +(1.65270 + 9.37295i) q^{29} +(3.18479 + 5.51622i) q^{31} +(0.642788 + 0.766044i) q^{32} +(0.657115 + 1.80541i) q^{33} +(-4.47178 - 1.62760i) q^{34} +(-0.500000 + 2.83564i) q^{36} -4.00000i q^{37} +(-2.15160 - 3.79086i) q^{38} -0.453363 q^{39} +(6.13429 + 5.14728i) q^{41} +(-0.446476 + 1.22668i) q^{42} +(-2.46669 - 6.77719i) q^{43} +(4.23783 - 3.55596i) q^{44} +(1.65270 - 2.86257i) q^{46} +(12.0266 - 2.12061i) q^{47} +(-0.342020 + 0.0603074i) q^{48} +(3.56418 - 6.17334i) q^{49} +(1.26604 - 1.06234i) q^{51} +(0.446476 + 1.22668i) q^{52} +(-0.601535 + 1.65270i) q^{53} +(-1.56418 - 1.31250i) q^{54} +3.75877 q^{56} +(1.51379 + 0.0111444i) q^{57} +9.51754i q^{58} +(-1.12314 + 6.36965i) q^{59} +(2.10607 + 0.766546i) q^{61} +(2.17853 + 5.98545i) q^{62} +(6.95686 + 8.29086i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.333626 + 1.89209i) q^{66} +(-12.1893 + 2.14930i) q^{67} +(-4.12122 - 2.37939i) q^{68} +(0.573978 + 0.994159i) q^{69} +(5.53209 - 2.01352i) q^{71} +(-0.984808 + 2.70574i) q^{72} +(-0.747243 + 0.890530i) q^{73} +(0.694593 - 3.93923i) q^{74} +(-1.46064 - 4.10689i) q^{76} -20.7939i q^{77} +(-0.446476 - 0.0787257i) q^{78} +(-6.75877 - 5.67128i) q^{79} +(-7.45084 + 2.71188i) q^{81} +(5.14728 + 6.13429i) q^{82} +(-10.5102 + 6.06805i) q^{83} +(-0.652704 + 1.13052i) q^{84} +(-1.25237 - 7.10257i) q^{86} +(-2.86257 - 1.65270i) q^{87} +(4.79093 - 2.76604i) q^{88} +(-8.62314 + 7.23567i) q^{89} +(4.61081 + 1.67820i) q^{91} +(2.12467 - 2.53209i) q^{92} +(-2.17853 - 0.384133i) q^{93} +12.2121 q^{94} -0.347296 q^{96} +(-7.43961 - 1.31180i) q^{97} +(4.58202 - 5.46064i) q^{98} +(14.9684 + 5.44804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^6 + 6 * q^9	$ 12 q + 6 q^{6} + 6 q^{9} + 24 q^{11} + 24 q^{14} - 12 q^{19} + 24 q^{21} - 6 q^{24} + 12 q^{26} + 24 q^{29} + 24 q^{31} - 24 q^{34} - 6 q^{36} + 48 q^{39} + 54 q^{41} + 12 q^{44} + 24 q^{46} + 6 q^{49} + 6 q^{51} + 18 q^{54} - 6 q^{59} - 24 q^{61} + 6 q^{64} + 42 q^{66} - 24 q^{69} + 48 q^{71} - 36 q^{79} - 66 q^{81} - 12 q^{84} - 48 q^{86} - 96 q^{89} + 72 q^{91} + 48 q^{94} + 66 q^{99}+O(q^{100}) $ 12 * q + 6 * q^6 + 6 * q^9 + 24 * q^11 + 24 * q^14 - 12 * q^19 + 24 * q^21 - 6 * q^24 + 12 * q^26 + 24 * q^29 + 24 * q^31 - 24 * q^34 - 6 * q^36 + 48 * q^39 + 54 * q^41 + 12 * q^44 + 24 * q^46 + 6 * q^49 + 6 * q^51 + 18 * q^54 - 6 * q^59 - 24 * q^61 + 6 * q^64 + 42 * q^66 - 24 * q^69 + 48 * q^71 - 36 * q^79 - 66 * q^81 - 12 * q^84 - 48 * q^86 - 96 * q^89 + 72 * q^91 + 48 * q^94 + 66 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	−0.223238	+	0.266044i	−0.128886	+	0.153601i	−0.826628	−	0.562749i	$-0.809744\pi$
$3$	−0.223238	+	0.266044i	−0.128886	+	0.153601i	0.697742	+	0.716349i	$0.254188\pi$
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	−0.266044	+	0.223238i	−0.108612	+	0.0911364i
$7$	3.25519	−	1.87939i	1.23035	−	0.710341i	0.263244	−	0.964729i	$-0.415207\pi$
$7$	3.25519	−	1.87939i	1.23035	−	0.710341i	0.967102	+	0.254388i	$0.0818741\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	0.500000	+	2.83564i	0.166667	+	0.945214i
$10$		0			0
$11$	2.76604	−	4.79093i	0.833994	−	1.44452i	−0.0608533	−	0.998147i	$-0.519382\pi$
$11$	2.76604	−	4.79093i	0.833994	−	1.44452i	0.894847	−	0.446373i	$-0.147284\pi$
$12$	−0.300767	+	0.173648i	−0.0868241	+	0.0501279i
$13$	0.839100	+	1.00000i	0.232724	+	0.277350i	0.869750	−	0.493492i	$-0.164280\pi$
$13$	0.839100	+	1.00000i	0.232724	+	0.277350i	−0.637026	+	0.770843i	$0.719836\pi$
$14$	3.53209	−	1.28558i	0.943990	−	0.343584i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−4.68647	−	0.826352i	−1.13664	−	0.200420i	−0.426503	−	0.904486i	$-0.640255\pi$
$17$	−4.68647	−	0.826352i	−1.13664	−	0.200420i	−0.710134	+	0.704066i	$0.751366\pi$
$18$			2.87939i			0.678678i
$19$	−2.77719	−	3.35965i	−0.637131	−	0.770756i
$19$	−2.77719	−	3.35965i	−0.637131	−	0.770756i
$20$		0			0
$21$	−0.226682	+	1.28558i	−0.0494660	+	0.280536i
$22$	3.55596	−	4.23783i	0.758133	−	0.903508i
$23$	1.13052	−	3.10607i	0.235729	−	0.647660i	−0.764267	−	0.644900i	$-0.776899\pi$
$23$	1.13052	−	3.10607i	0.235729	−	0.647660i	0.999996	−	0.00276015i	$-0.000878584\pi$
$24$	−0.326352	+	0.118782i	−0.0666163	+	0.0242463i
$25$		0			0
$26$	0.652704	+	1.13052i	0.128006	+	0.221712i
$27$	−1.76833	−	1.02094i	−0.340315	−	0.196481i
$28$	3.70167	−	0.652704i	0.699549	−	0.123349i
$29$	1.65270	+	9.37295i	0.306899	+	1.74051i	0.614427	+	0.788974i	$0.289387\pi$
$29$	1.65270	+	9.37295i	0.306899	+	1.74051i	−0.307528	+	0.951539i	$0.599502\pi$
$30$		0			0
$31$	3.18479	+	5.51622i	0.572006	+	0.990743i	0.996360	+	0.0852466i	$0.0271678\pi$
$31$	3.18479	+	5.51622i	0.572006	+	0.990743i	−0.424354	+	0.905496i	$0.639499\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	0.657115	+	1.80541i	0.114389	+	0.314281i
$34$	−4.47178	−	1.62760i	−0.766904	−	0.279130i
$35$		0			0
$36$	−0.500000	+	2.83564i	−0.0833333	+	0.472607i
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	−2.15160	−	3.79086i	−0.349036	−	0.614959i
$39$	−0.453363			−0.0725962
$40$		0			0
$41$	6.13429	+	5.14728i	0.958014	+	0.803870i	0.980629	−	0.195875i	$-0.0627546\pi$
$41$	6.13429	+	5.14728i	0.958014	+	0.803870i	−0.0226145	+	0.999744i	$0.507199\pi$
$42$	−0.446476	+	1.22668i	−0.0688927	+	0.189281i
$43$	−2.46669	−	6.77719i	−0.376167	−	1.03351i	−0.972931	−	0.231095i	$-0.925769\pi$
$43$	−2.46669	−	6.77719i	−0.376167	−	1.03351i	0.596764	−	0.802417i	$-0.296453\pi$
$44$	4.23783	−	3.55596i	0.638876	−	0.536081i
$45$		0			0
$46$	1.65270	−	2.86257i	0.243678	−	0.422062i
$47$	12.0266	−	2.12061i	1.75426	−	0.309323i	0.798178	−	0.602422i	$-0.205797\pi$
$47$	12.0266	−	2.12061i	1.75426	−	0.309323i	0.956082	+	0.293098i	$0.0946863\pi$
$48$	−0.342020	+	0.0603074i	−0.0493664	+	0.00870462i
$49$	3.56418	−	6.17334i	0.509168	−	0.881905i
$50$		0			0
$51$	1.26604	−	1.06234i	0.177282	−	0.148757i
$52$	0.446476	+	1.22668i	0.0619150	+	0.170110i
$53$	−0.601535	+	1.65270i	−0.0826272	+	0.227016i	−0.974126	−	0.226008i	$-0.927433\pi$
$53$	−0.601535	+	1.65270i	−0.0826272	+	0.227016i	0.891498	+	0.453024i	$0.149655\pi$
$54$	−1.56418	−	1.31250i	−0.212858	−	0.178609i
$55$		0			0
$56$	3.75877			0.502287
$57$	1.51379	+	0.0111444i	0.200506	+	0.00147611i
$58$			9.51754i			1.24971i
$59$	−1.12314	+	6.36965i	−0.146221	+	0.829258i	0.820159	+	0.572136i	$0.193885\pi$
$59$	−1.12314	+	6.36965i	−0.146221	+	0.829258i	−0.966379	+	0.257121i	$0.917226\pi$
$60$		0			0
$61$	2.10607	+	0.766546i	0.269654	+	0.0981461i	0.473308	−	0.880897i	$-0.343060\pi$
$61$	2.10607	+	0.766546i	0.269654	+	0.0981461i	−0.203654	+	0.979043i	$0.565282\pi$
$62$	2.17853	+	5.98545i	0.276673	+	0.760153i
$63$	6.95686	+	8.29086i	0.876482	+	1.04455i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	0.333626	+	1.89209i	0.0410665	+	0.232900i
$67$	−12.1893	+	2.14930i	−1.48916	+	0.262579i	−0.858231	−	0.513263i	$-0.828436\pi$
$67$	−12.1893	+	2.14930i	−1.48916	+	0.262579i	−0.630927	+	0.775842i	$0.717325\pi$
$68$	−4.12122	−	2.37939i	−0.499771	−	0.288543i
$69$	0.573978	+	0.994159i	0.0690988	+	0.119683i
$70$		0			0
$71$	5.53209	−	2.01352i	0.656538	−	0.238960i	0.00779714	−	0.999970i	$-0.497518\pi$
$71$	5.53209	−	2.01352i	0.656538	−	0.238960i	0.648741	+	0.761009i	$0.275296\pi$
$72$	−0.984808	+	2.70574i	−0.116061	+	0.318874i
$73$	−0.747243	+	0.890530i	−0.0874582	+	0.104229i	−0.807999	−	0.589184i	$-0.799449\pi$
$73$	−0.747243	+	0.890530i	−0.0874582	+	0.104229i	0.720541	+	0.693413i	$0.243894\pi$
$74$	0.694593	−	3.93923i	0.0807448	−	0.457926i
$75$		0			0
$76$	−1.46064	−	4.10689i	−0.167547	−	0.471093i
$77$		−	20.7939i		−	2.36968i
$78$	−0.446476	−	0.0787257i	−0.0505534	−	0.00891393i
$79$	−6.75877	−	5.67128i	−0.760421	−	0.638069i	0.177815	−	0.984064i	$-0.443097\pi$
$79$	−6.75877	−	5.67128i	−0.760421	−	0.638069i	−0.938236	+	0.345995i	$0.887541\pi$
$80$		0			0
$81$	−7.45084	+	2.71188i	−0.827871	+	0.301320i
$82$	5.14728	+	6.13429i	0.568422	+	0.677418i
$83$	−10.5102	+	6.06805i	−1.15364	+	0.666055i	−0.949772	−	0.312943i	$-0.898685\pi$
$83$	−10.5102	+	6.06805i	−1.15364	+	0.666055i	−0.203869	+	0.978998i	$0.565352\pi$
$84$	−0.652704	+	1.13052i	−0.0712158	+	0.123349i
$85$		0			0
$86$	−1.25237	−	7.10257i	−0.135047	−	0.765889i
$87$	−2.86257	−	1.65270i	−0.306899	−	0.177188i
$88$	4.79093	−	2.76604i	0.510715	−	0.294861i
$89$	−8.62314	+	7.23567i	−0.914051	+	0.766980i	−0.972885	−	0.231288i	$-0.925706\pi$
$89$	−8.62314	+	7.23567i	−0.914051	+	0.766980i	0.0588343	+	0.998268i	$0.481262\pi$
$90$		0			0
$91$	4.61081	+	1.67820i	0.483345	+	0.175923i
$92$	2.12467	−	2.53209i	0.221513	−	0.263989i
$93$	−2.17853	−	0.384133i	−0.225903	−	0.0398327i
$94$	12.2121			1.25959
$95$		0			0
$96$	−0.347296			−0.0354458
$97$	−7.43961	−	1.31180i	−0.755378	−	0.133194i	−0.217319	−	0.976101i	$-0.569731\pi$
$97$	−7.43961	−	1.31180i	−0.755378	−	0.133194i	−0.538059	+	0.842907i	$0.680842\pi$
$98$	4.58202	−	5.46064i	0.462854	−	0.551608i
$99$	14.9684	+	5.44804i	1.50438	+	0.547549i
$100$		0			0
$101$	−12.6040	+	10.5760i	−1.25415	+	1.05235i	−0.257865	+	0.966181i	$0.583019\pi$
$101$	−12.6040	+	10.5760i	−1.25415	+	1.05235i	−0.996280	+	0.0861723i	$0.972536\pi$
$102$	1.43128	−	0.826352i	0.141718	−	0.0818210i
$103$	−6.41263	−	3.70233i	−0.631855	−	0.364802i	0.149615	−	0.988744i	$-0.452197\pi$
$103$	−6.41263	−	3.70233i	−0.631855	−	0.364802i	−0.781470	+	0.623943i	$0.785530\pi$
$104$	0.226682	+	1.28558i	0.0222280	+	0.126061i
$105$		0			0
$106$	−0.879385	+	1.52314i	−0.0854134	+	0.147940i
$107$	−0.264490	+	0.152704i	−0.0255693	+	0.0147624i	−0.512730	−	0.858550i	$-0.671366\pi$
$107$	−0.264490	+	0.152704i	−0.0255693	+	0.0147624i	0.487161	+	0.873312i	$0.338033\pi$
$108$	−1.31250	−	1.56418i	−0.126295	−	0.150513i
$109$	14.4338	−	5.25346i	1.38250	−	0.503190i	0.459567	−	0.888143i	$-0.348004\pi$
$109$	14.4338	−	5.25346i	1.38250	−	0.503190i	0.922936	+	0.384953i	$0.125782\pi$
$110$		0			0
$111$	1.06418	+	0.892951i	0.101007	+	0.0847552i
$112$	3.70167	+	0.652704i	0.349775	+	0.0616747i
$113$		−	8.22668i		−	0.773901i	−0.922100	−	0.386951i	$-0.873528\pi$
$113$		−	8.22668i		−	0.773901i	0.922100	−	0.386951i	$-0.126472\pi$
$114$	1.48886	+	0.273842i	0.139444	+	0.0256476i
$115$		0			0
$116$	−1.65270	+	9.37295i	−0.153450	+	0.870256i
$117$	−2.41609	+	2.87939i	−0.223368	+	0.266199i
$118$	−2.21216	+	6.07785i	−0.203645	+	0.559511i
$119$	−16.8084	+	6.11776i	−1.54082	+	0.560814i
$120$		0			0
$121$	−9.80200	−	16.9776i	−0.891091	−	1.54342i
$122$	1.94096	+	1.12061i	0.175726	+	0.101456i
$123$	−2.73881	+	0.482926i	−0.246950	+	0.0435440i
$124$	1.10607	+	6.27282i	0.0993277	+	0.563316i
$125$		0			0
$126$	5.41147	+	9.37295i	0.482092	+	0.835009i
$127$	0.291416	+	0.347296i	0.0258590	+	0.0308176i	0.778819	−	0.627249i	$-0.215819\pi$
$127$	0.291416	+	0.347296i	0.0258590	+	0.0308176i	−0.752960	+	0.658066i	$0.771375\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	2.35369	+	0.856674i	0.207231	+	0.0754260i
$130$		0			0
$131$	−0.648833	+	3.67972i	−0.0566888	+	0.321498i	−0.999944	−	0.0105701i	$-0.996635\pi$
$131$	−0.648833	+	3.67972i	−0.0566888	+	0.321498i	0.943255	+	0.332068i	$0.107746\pi$
$132$			1.92127i			0.167225i
$133$	−15.3543	−	5.71688i	−1.33139	−	0.495716i
$134$	−12.3773			−1.06924
$135$		0			0
$136$	−3.64543	−	3.05888i	−0.312593	−	0.262297i
$137$	−3.53898	+	9.72328i	−0.302356	+	0.830716i	0.691734	+	0.722153i	$0.256847\pi$
$137$	−3.53898	+	9.72328i	−0.302356	+	0.830716i	−0.994090	+	0.108563i	$0.965375\pi$
$138$	0.392624	+	1.07873i	0.0334224	+	0.0918272i
$139$	−1.50387	+	1.26190i	−0.127557	+	0.107033i	−0.704334	−	0.709868i	$-0.748754\pi$
$139$	−1.50387	+	1.26190i	−0.127557	+	0.107033i	0.576778	+	0.816901i	$0.304310\pi$
$140$		0			0
$141$	−2.12061	+	3.67301i	−0.178588	+	0.309323i
$142$	5.79769	−	1.02229i	0.486531	−	0.0857886i
$143$	7.11192	−	1.25402i	0.594728	−	0.104867i
$144$	−1.43969	+	2.49362i	−0.119974	+	0.207802i
$145$		0			0
$146$	−0.890530	+	0.747243i	−0.0737008	+	0.0618423i
$147$	0.846723	+	2.32635i	0.0698365	+	0.191874i
$148$	1.36808	−	3.75877i	0.112456	−	0.308969i
$149$	−10.4534	−	8.77141i	−0.856373	−	0.718582i	0.104811	−	0.994492i	$-0.466576\pi$
$149$	−10.4534	−	8.77141i	−0.856373	−	0.718582i	−0.961183	+	0.275910i	$0.911021\pi$
$150$		0			0
$151$	−1.63041			−0.132681			−0.0663406	−	0.997797i	$-0.521132\pi$
$151$	−1.63041			−0.132681			−0.0663406	+	0.997797i	$0.521132\pi$
$152$	−0.725293	−	4.29813i	−0.0588290	−	0.348625i
$153$		−	13.7023i		−	1.10777i
$154$	3.61081	−	20.4779i	0.290968	−	1.65016i
$155$		0			0
$156$	−0.426022	−	0.155059i	−0.0341091	−	0.0124147i
$157$	−2.13463	−	5.86484i	−0.170362	−	0.468065i	0.824902	−	0.565276i	$-0.191230\pi$
$157$	−2.13463	−	5.86484i	−0.170362	−	0.468065i	−0.995264	+	0.0972106i	$0.969008\pi$
$158$	−5.67128	−	6.75877i	−0.451183	−	0.537699i
$159$	−0.305407	−	0.528981i	−0.0242204	−	0.0419509i
$160$		0			0
$161$	−2.15745	−	12.2355i	−0.170031	−	0.964294i
$162$	−7.80856	+	1.37686i	−0.613498	+	0.108176i
$163$	3.16333	+	1.82635i	0.247771	+	0.143051i	0.618743	−	0.785593i	$-0.287642\pi$
$163$	3.16333	+	1.82635i	0.247771	+	0.143051i	−0.370972	+	0.928644i	$0.620975\pi$
$164$	4.00387	+	6.93491i	0.312650	+	0.541525i
$165$		0			0
$166$	−11.4042	+	4.15079i	−0.885138	+	0.322164i
$167$	−5.49102	+	15.0865i	−0.424908	+	1.16743i	0.523957	+	0.851745i	$0.324455\pi$
$167$	−5.49102	+	15.0865i	−0.424908	+	1.16743i	−0.948865	+	0.315681i	$0.897767\pi$
$168$	−0.839100	+	1.00000i	−0.0647379	+	0.0771517i
$169$	1.96151	−	11.1243i	0.150886	−	0.855716i
$170$		0			0
$171$	8.13816	−	9.55493i	0.622340	−	0.730684i
$172$		−	7.21213i		−	0.549920i
$173$	0.712694	+	0.125667i	0.0541851	+	0.00955430i	0.200675	−	0.979658i	$-0.435686\pi$
$173$	0.712694	+	0.125667i	0.0541851	+	0.00955430i	−0.146490	+	0.989212i	$0.546798\pi$
$174$	−2.53209	−	2.12467i	−0.191957	−	0.161071i
$175$		0			0
$176$	5.19846	−	1.89209i	0.391849	−	0.142621i
$177$	−1.44388	−	1.72075i	−0.108529	−	0.129340i
$178$	−9.74860	+	5.62836i	−0.730688	+	0.421863i
$179$	2.40760	−	4.17009i	0.179953	−	0.311687i	−0.761911	−	0.647681i	$-0.775739\pi$
$179$	2.40760	−	4.17009i	0.179953	−	0.311687i	0.941864	+	0.335994i	$0.109072\pi$
$180$		0			0
$181$	0.539830	+	3.06153i	0.0401252	+	0.227561i	0.998275	−	0.0587046i	$-0.0186970\pi$
$181$	0.539830	+	3.06153i	0.0401252	+	0.227561i	−0.958150	+	0.286266i	$0.907586\pi$
$182$	4.24935	+	2.45336i	0.314983	+	0.181855i
$183$	−0.674089	+	0.389185i	−0.0498301	+	0.0287694i
$184$	2.53209	−	2.12467i	0.186668	−	0.156633i
$185$		0			0
$186$	−2.07873	−	0.756594i	−0.152420	−	0.0554762i
$187$	−16.9220	+	20.1668i	−1.23746	+	1.47475i
$188$	12.0266	+	2.12061i	0.877130	+	0.154662i
$189$	−7.67499			−0.558274
$190$		0			0
$191$	−10.6655			−0.771728			−0.385864	−	0.922556i	$-0.626097\pi$
$191$	−10.6655			−0.771728			−0.385864	+	0.922556i	$0.626097\pi$
$192$	−0.342020	−	0.0603074i	−0.0246832	−	0.00435231i
$193$	12.0579	−	14.3701i	0.867947	−	1.03438i	−0.131127	−	0.991366i	$-0.541860\pi$
$193$	12.0579	−	14.3701i	0.867947	−	1.03438i	0.999074	−	0.0430135i	$-0.0136958\pi$
$194$	−7.09879	−	2.58375i	−0.509664	−	0.185502i
$195$		0			0
$196$	5.46064	−	4.58202i	0.390046	−	0.327287i
$197$	−9.48411	+	5.47565i	−0.675715	+	0.390124i	−0.798238	−	0.602342i	$-0.794235\pi$
$197$	−9.48411	+	5.47565i	−0.675715	+	0.390124i	0.122524	+	0.992466i	$0.460901\pi$
$198$	13.7949	+	7.96451i	0.980363	+	0.566013i
$199$	1.15570	+	6.55428i	0.0819252	+	0.464621i	0.997978	+	0.0635627i	$0.0202463\pi$
$199$	1.15570	+	6.55428i	0.0819252	+	0.464621i	−0.916053	+	0.401058i	$0.868643\pi$
$200$		0			0
$201$	2.14930	−	3.72270i	0.151600	−	0.262579i
$202$	−14.2490	+	8.22668i	−1.00256	+	0.578827i
$203$	22.9952	+	27.4047i	1.61395	+	1.92343i
$204$	1.55303	−	0.565258i	0.108734	−	0.0395760i
$205$		0			0
$206$	−5.67230	−	4.75963i	−0.395208	−	0.331619i
$207$	9.37295	+	1.65270i	0.651465	+	0.114871i
$208$			1.30541i			0.0905137i
$209$	−23.7777	+	4.01239i	−1.64473	+	0.277542i
$210$		0			0
$211$	3.50640	−	19.8858i	0.241390	−	1.36899i	−0.587338	−	0.809342i	$-0.699824\pi$
$211$	3.50640	−	19.8858i	0.241390	−	1.36899i	0.828729	−	0.559651i	$-0.189065\pi$
$212$	−1.13052	+	1.34730i	−0.0776441	+	0.0925327i
$213$	−0.699287	+	1.92127i	−0.0479143	+	0.131644i
$214$	−0.286989	+	0.104455i	−0.0196182	+	0.00714043i
$215$		0			0
$216$	−1.02094	−	1.76833i	−0.0694665	−	0.120319i
$217$	20.7342	+	11.9709i	1.40753	+	0.812638i
$218$	15.1267	−	2.66725i	1.02451	−	0.180649i
$219$	−0.0701076	−	0.397600i	−0.00473743	−	0.0268673i
$220$		0			0
$221$	−3.10607	−	5.37987i	−0.208937	−	0.361889i
$222$	0.892951	+	1.06418i	0.0599310	+	0.0714229i
$223$	5.35121	+	14.7023i	0.358344	+	0.984541i	0.979604	+	0.200937i	$0.0643986\pi$
$223$	5.35121	+	14.7023i	0.358344	+	0.984541i	−0.621261	+	0.783604i	$0.713379\pi$
$224$	3.53209	+	1.28558i	0.235998	+	0.0858961i
$225$		0			0
$226$	1.42855	−	8.10170i	0.0950256	−	0.538917i
$227$		−	8.54488i		−	0.567144i	−0.958951	−	0.283572i	$-0.908481\pi$
$227$		−	8.54488i		−	0.567144i	0.958951	−	0.283572i	$-0.0915195\pi$
$228$	1.41868	+	0.528218i	0.0939547	+	0.0349821i
$229$	4.11287			0.271786			0.135893	−	0.990723i	$-0.456610\pi$
$229$	4.11287			0.271786			0.135893	+	0.990723i	$0.456610\pi$
$230$		0			0
$231$	5.53209	+	4.64197i	0.363985	+	0.305419i
$232$	−3.25519	+	8.94356i	−0.213714	+	0.587174i
$233$	0.860130	+	2.36319i	0.0563490	+	0.154818i	0.964673	−	0.263449i	$-0.0848600\pi$
$233$	0.860130	+	2.36319i	0.0563490	+	0.154818i	−0.908324	+	0.418267i	$0.862638\pi$
$234$	−2.87939	+	2.41609i	−0.188231	+	0.157945i
$235$		0			0
$236$	−3.23396	+	5.60138i	−0.210513	+	0.364618i
$237$	3.01763	−	0.532089i	0.196016	−	0.0345629i
$238$	−17.6154	+	3.10607i	−1.14184	+	0.201336i
$239$	−4.65270	+	8.05872i	−0.300958	+	0.521275i	−0.976353	−	0.216181i	$-0.930640\pi$
$239$	−4.65270	+	8.05872i	−0.300958	+	0.521275i	0.675395	+	0.737456i	$0.263973\pi$
$240$		0			0
$241$	−5.45858	+	4.58029i	−0.351618	+	0.295042i	−0.801439	−	0.598076i	$-0.795932\pi$
$241$	−5.45858	+	4.58029i	−0.351618	+	0.295042i	0.449821	+	0.893119i	$0.351488\pi$
$242$	−6.70497	−	18.4217i	−0.431012	−	1.18419i
$243$	3.03693	−	8.34389i	0.194819	−	0.535261i
$244$	1.71688	+	1.44063i	0.109912	+	0.0922272i
$245$		0			0
$246$	−2.78106			−0.177314
$247$	1.02931	−	5.59627i	0.0654933	−	0.356082i
$248$			6.36959i			0.404469i
$249$	0.731896	−	4.15079i	0.0463820	−	0.263046i
$250$		0			0
$251$	−15.5239	−	5.65025i	−0.979862	−	0.356641i	−0.198076	−	0.980187i	$-0.563469\pi$
$251$	−15.5239	−	5.65025i	−0.979862	−	0.356641i	−0.781787	+	0.623546i	$0.785691\pi$
$252$	3.70167	+	10.1702i	0.233183	+	0.640665i
$253$	−11.7539	−	14.0077i	−0.738961	−	0.880659i
$254$	0.226682	+	0.392624i	0.0142233	+	0.0246354i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	8.77812	−	1.54782i	0.547564	−	0.0965503i	0.106979	−	0.994261i	$-0.465882\pi$
$257$	8.77812	−	1.54782i	0.547564	−	0.0965503i	0.440585	+	0.897711i	$0.354771\pi$
$258$	2.16918	+	1.25237i	0.135047	+	0.0779694i
$259$	−7.51754	−	13.0208i	−0.467117	−	0.809071i
$260$		0			0
$261$	−25.7520	+	9.37295i	−1.59401	+	0.580171i
$262$	−1.27795	+	3.51114i	−0.0789521	+	0.216919i
$263$	−6.32667	+	7.53983i	−0.390119	+	0.464926i	−0.924981	−	0.380014i	$-0.875919\pi$
$263$	−6.32667	+	7.53983i	−0.390119	+	0.464926i	0.534862	+	0.844940i	$0.320364\pi$
$264$	−0.333626	+	1.89209i	−0.0205332	+	0.116450i
$265$		0			0
$266$	−14.1284	−	8.29628i	−0.866265	−	0.508678i
$267$		−	3.90941i		−	0.239252i
$268$	−12.1893	−	2.14930i	−0.744579	−	0.131289i
$269$	6.41147	+	5.37987i	0.390914	+	0.328016i	0.816969	−	0.576681i	$-0.195652\pi$
$269$	6.41147	+	5.37987i	0.390914	+	0.328016i	−0.426055	+	0.904697i	$0.640097\pi$
$270$		0			0
$271$	−1.19934	+	0.436524i	−0.0728547	+	0.0265170i	−0.378190	−	0.925728i	$-0.623454\pi$
$271$	−1.19934	+	0.436524i	−0.0728547	+	0.0265170i	0.305336	+	0.952245i	$0.401231\pi$
$272$	−3.05888	−	3.64543i	−0.185472	−	0.221037i
$273$	−1.47578	+	0.852044i	−0.0893185	+	0.0515681i
$274$	−5.17365	+	8.96102i	−0.312552	+	0.541355i
$275$		0			0
$276$	0.199340	+	1.13052i	0.0119989	+	0.0680491i
$277$	6.14296	+	3.54664i	0.369094	+	0.213097i	0.673063	−	0.739585i	$-0.264978\pi$
$277$	6.14296	+	3.54664i	0.369094	+	0.213097i	−0.303968	+	0.952682i	$0.598312\pi$
$278$	−1.70015	+	0.981582i	−0.101968	+	0.0588714i
$279$	−14.0496	+	11.7890i	−0.841129	+	0.705791i
$280$		0			0
$281$	19.4033	+	7.06223i	1.15751	+	0.421297i	0.848206	−	0.529667i	$-0.177683\pi$
$281$	19.4033	+	7.06223i	1.15751	+	0.421297i	0.309300	+	0.950965i	$0.399905\pi$
$282$	−2.72621	+	3.24897i	−0.162343	+	0.193473i
$283$	13.9433	+	2.45858i	0.828842	+	0.146147i	0.571946	−	0.820292i	$-0.306189\pi$
$283$	13.9433	+	2.45858i	0.828842	+	0.146147i	0.256897	+	0.966439i	$0.417300\pi$
$284$	5.88713			0.349337
$285$		0			0
$286$	7.22163			0.427024
$287$	29.6420	+	5.22668i	1.74971	+	0.308521i
$288$	−1.85083	+	2.20574i	−0.109061	+	0.129974i
$289$	5.30541	+	1.93101i	0.312083	+	0.113589i
$290$		0			0
$291$	2.00980	−	1.68642i	0.117817	−	0.0988598i
$292$	−1.00676	+	0.581252i	−0.0589160	+	0.0340152i
$293$	−19.9624	−	11.5253i	−1.16621	−	0.673314i	−0.213429	−	0.976959i	$-0.568463\pi$
$293$	−19.9624	−	11.5253i	−1.16621	−	0.673314i	−0.952785	+	0.303644i	$0.901797\pi$
$294$	0.429892	+	2.43804i	0.0250718	+	0.142189i
$295$		0			0
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	−9.78255	+	5.64796i	−0.567641	+	0.327728i
$298$	−8.77141	−	10.4534i	−0.508114	−	0.605547i
$299$	4.05468	−	1.47578i	0.234488	−	0.0853468i
$300$		0			0
$301$	−20.7665	−	17.4252i	−1.19696	−	1.00437i
$302$	−1.60565	−	0.283119i	−0.0923945	−	0.0162916i
$303$		−	5.71419i		−	0.328272i
$304$	0.0320889	−	4.35878i	0.00184042	−	0.249993i
$305$		0			0
$306$	2.37939	−	13.4942i	0.136020	−	0.771410i
$307$	−2.71686	+	3.23783i	−0.155059	+	0.184792i	−0.837982	−	0.545699i	$-0.816264\pi$
$307$	−2.71686	+	3.23783i	−0.155059	+	0.184792i	0.682922	+	0.730491i	$0.260709\pi$
$308$	7.11192	−	19.5398i	0.405239	−	1.11339i
$309$	2.41653	−	0.879544i	0.137471	−	0.0500355i
$310$		0			0
$311$	4.18479	+	7.24827i	0.237298	+	0.411012i	0.959938	−	0.280213i	$-0.0904049\pi$
$311$	4.18479	+	7.24827i	0.237298	+	0.411012i	−0.722640	+	0.691224i	$0.757072\pi$
$312$	−0.392624	−	0.226682i	−0.0222280	−	0.0128333i
$313$	−18.1564	+	3.20146i	−1.02626	+	0.180957i	−0.661343	−	0.750084i	$-0.730013\pi$
$313$	−18.1564	+	3.20146i	−1.02626	+	0.180957i	−0.364915	+	0.931041i	$0.618902\pi$
$314$	−1.08378	−	6.14641i	−0.0611611	−	0.346862i
$315$		0			0
$316$	−4.41147	−	7.64090i	−0.248165	−	0.429834i
$317$	−19.9490	−	23.7743i	−1.12045	−	1.33530i	−0.935817	−	0.352487i	$-0.885336\pi$
$317$	−19.9490	−	23.7743i	−1.12045	−	1.33530i	−0.184629	−	0.982808i	$-0.559108\pi$
$318$	−0.208911	−	0.573978i	−0.0117151	−	0.0321871i
$319$	49.4766	+	18.0080i	2.77016	+	1.00825i
$320$		0			0
$321$	0.0184183	−	0.104455i	0.00102801	−	0.00583013i
$322$		−	12.4243i		−	0.692377i
$323$	10.2390	+	18.0398i	0.569712	+	1.00376i
$324$	−7.92902			−0.440501
$325$		0			0
$326$	2.79813	+	2.34791i	0.154974	+	0.130039i
$327$	−1.82451	+	5.01279i	−0.100895	+	0.277208i
$328$	2.73881	+	7.52481i	0.151225	+	0.415488i
$329$	35.1634	−	29.5056i	1.93862	−	1.62670i
$330$		0			0
$331$	4.29813	−	7.44459i	0.236247	−	0.409191i	−0.723388	−	0.690442i	$-0.757416\pi$
$331$	4.29813	−	7.44459i	0.236247	−	0.409191i	0.959634	+	0.281251i	$0.0907493\pi$
$332$	−11.9517	+	2.10741i	−0.655936	+	0.115659i
$333$	11.3426	−	2.00000i	0.621569	−	0.109599i
$334$	−8.02734	+	13.9038i	−0.439237	+	0.760780i
$335$		0			0
$336$	−1.00000	+	0.839100i	−0.0545545	+	0.0457766i
$337$	10.9271	+	30.0219i	0.595235	+	1.63540i	0.760643	+	0.649171i	$0.224884\pi$
$337$	10.9271	+	30.0219i	0.595235	+	1.63540i	−0.165407	+	0.986225i	$0.552894\pi$
$338$	3.86343	−	10.6147i	0.210143	−	0.577363i
$339$	2.18866	+	1.83651i	0.118872	+	0.0997453i
$340$		0			0
$341$	35.2371			1.90820
$342$	9.67372	−	7.99660i	0.523095	−	0.432406i
$343$		−	0.482459i		−	0.0260503i
$344$	1.25237	−	7.10257i	0.0675235	−	0.382945i
$345$		0			0
$346$	0.680045	+	0.247516i	0.0365594	+	0.0133065i
$347$	−1.54915	−	4.25624i	−0.0831625	−	0.228487i	0.891141	−	0.453727i	$-0.149906\pi$
$347$	−1.54915	−	4.25624i	−0.0831625	−	0.228487i	−0.974303	+	0.225240i	$0.927684\pi$
$348$	−2.12467	−	2.53209i	−0.113895	−	0.135734i
$349$	−13.5621	−	23.4903i	−0.725964	−	1.25741i	−0.958576	−	0.284836i	$-0.908061\pi$
$349$	−13.5621	−	23.4903i	−0.725964	−	1.25741i	0.232613	−	0.972569i	$-0.425273\pi$
$350$		0			0
$351$	−0.462859	−	2.62500i	−0.0247056	−	0.140112i
$352$	5.44804	−	0.960637i	0.290382	−	0.0512021i
$353$	17.0797	+	9.86097i	0.909060	+	0.524846i	0.880129	−	0.474735i	$-0.157456\pi$
$353$	17.0797	+	9.86097i	0.909060	+	0.524846i	0.0289317	+	0.999581i	$0.490789\pi$
$354$	−1.12314	−	1.94534i	−0.0596943	−	0.103394i
$355$		0			0
$356$	−10.5778	+	3.85002i	−0.560625	+	0.204051i
$357$	2.12467	−	5.83750i	0.112450	−	0.308953i
$358$	3.09516	−	3.68866i	0.163584	−	0.194952i
$359$	3.78611	−	21.4721i	0.199823	−	1.13325i	−0.705557	−	0.708653i	$-0.749303\pi$
$359$	3.78611	−	21.4721i	0.199823	−	1.13325i	0.905380	−	0.424601i	$-0.139586\pi$
$360$		0			0
$361$	−3.57444	+	18.6607i	−0.188129	+	0.982144i
$362$			3.10876i			0.163393i
$363$	6.70497	+	1.18227i	0.351919	+	0.0620529i
$364$	3.75877	+	3.15398i	0.197013	+	0.165314i
$365$		0			0
$366$	−0.731429	+	0.266219i	−0.0382324	+	0.0139155i
$367$	−2.36224	−	2.81521i	−0.123308	−	0.146953i	0.700859	−	0.713300i	$-0.252800\pi$
$367$	−2.36224	−	2.81521i	−0.123308	−	0.146953i	−0.824166	+	0.566348i	$0.808356\pi$
$368$	2.86257	−	1.65270i	0.149222	−	0.0861531i
$369$	−11.5287	+	19.9683i	−0.600159	+	1.03951i
$370$		0			0
$371$	1.14796	+	6.51038i	0.0595989	+	0.338002i
$372$	−1.91576	−	1.10607i	−0.0993277	−	0.0573469i
$373$	−11.4117	+	6.58853i	−0.590873	+	0.341141i	−0.765443	−	0.643504i	$-0.777480\pi$
$373$	−11.4117	+	6.58853i	−0.590873	+	0.341141i	0.174569	+	0.984645i	$0.444147\pi$
$374$	−20.1668	+	16.9220i	−1.04280	+	0.875015i
$375$		0			0
$376$	11.4757	+	4.17680i	0.591812	+	0.215402i
$377$	−7.98617	+	9.51754i	−0.411308	+	0.490178i
$378$	−7.55839	−	1.33275i	−0.388762	−	0.0685492i
$379$	−11.2918			−0.580020			−0.290010	−	0.957024i	$-0.593659\pi$
$379$	−11.2918			−0.580020			−0.290010	+	0.957024i	$0.593659\pi$
$380$		0			0
$381$	−0.157451			−0.00806648
$382$	−10.5035	−	1.85204i	−0.537404	−	0.0947588i
$383$	16.5101	−	19.6759i	0.843625	−	1.00539i	−0.156219	−	0.987722i	$-0.549931\pi$
$383$	16.5101	−	19.6759i	0.843625	−	1.00539i	0.999844	−	0.0176704i	$-0.00562496\pi$
$384$	−0.326352	−	0.118782i	−0.0166541	−	0.00606159i
$385$		0			0
$386$	14.3701	−	12.0579i	0.731416	−	0.613731i
$387$	17.9843	−	10.3833i	0.914195	−	0.527811i
$388$	−6.54228	−	3.77719i	−0.332134	−	0.191758i
$389$	1.79797	+	10.1968i	0.0911608	+	0.516998i	0.995856	+	0.0909399i	$0.0289871\pi$
$389$	1.79797	+	10.1968i	0.0911608	+	0.516998i	−0.904696	+	0.426058i	$0.859902\pi$
$390$		0			0
$391$	−7.86484	+	13.6223i	−0.397742	+	0.688909i
$392$	6.17334	−	3.56418i	0.311801	−	0.180018i
$393$	−0.834124	−	0.994070i	−0.0420760	−	0.0501442i
$394$	−10.2909	+	3.74557i	−0.518446	+	0.188699i
$395$		0			0
$396$	12.2023	+	10.2390i	0.613190	+	0.514528i
$397$	9.40160	+	1.65776i	0.471853	+	0.0832004i	0.404518	−	0.914530i	$-0.367439\pi$
$397$	9.40160	+	1.65776i	0.471853	+	0.0832004i	0.0673349	+	0.997730i	$0.478550\pi$
$398$			6.65539i			0.333605i
$399$	4.94862	−	2.80872i	0.247741	−	0.140612i
$400$		0			0
$401$	−5.20187	+	29.5013i	−0.259769	+	1.47322i	0.523760	+	0.851866i	$0.324529\pi$
$401$	−5.20187	+	29.5013i	−0.259769	+	1.47322i	−0.783528	+	0.621356i	$0.786582\pi$
$402$	2.76309	−	3.29292i	0.137810	−	0.164236i
$403$	−2.84386	+	7.81345i	−0.141663	+	0.389216i
$404$	−15.4611	+	5.62738i	−0.769219	+	0.279973i
$405$		0			0
$406$	17.8871	+	30.9814i	0.887723	+	1.53758i
$407$	−19.1637	−	11.0642i	−0.949910	−	0.548431i
$408$	1.62760	−	0.286989i	0.0805780	−	0.0142081i
$409$	−4.27110	−	24.2226i	−0.211192	−	1.19773i	−0.887393	−	0.461013i	$-0.847486\pi$
$409$	−4.27110	−	24.2226i	−0.211192	−	1.19773i	0.676201	−	0.736717i	$-0.263625\pi$
$410$		0			0
$411$	−1.79679	−	3.11213i	−0.0886291	−	0.153510i
$412$	−4.75963	−	5.67230i	−0.234490	−	0.279454i
$413$	8.31499	+	22.8452i	0.409154	+	1.12414i
$414$	8.94356	+	3.25519i	0.439552	+	0.159984i
$415$		0			0
$416$	−0.226682	+	1.28558i	−0.0111140	+	0.0630305i
$417$		−	0.681799i		−	0.0333879i
$418$	−24.1132	−	0.177519i	−1.17941	−	0.00868272i
$419$	11.8075			0.576832			0.288416	−	0.957505i	$-0.406871\pi$
$419$	11.8075			0.576832			0.288416	+	0.957505i	$0.406871\pi$
$420$		0			0
$421$	−4.66044	−	3.91058i	−0.227136	−	0.190590i	0.522116	−	0.852874i	$-0.325143\pi$
$421$	−4.66044	−	3.91058i	−0.227136	−	0.190590i	−0.749253	+	0.662284i	$0.769587\pi$
$422$	6.90625	−	18.9748i	0.336191	−	0.923678i
$423$	12.0266	+	33.0428i	0.584753	+	1.60660i
$424$	−1.34730	+	1.13052i	−0.0654305	+	0.0549027i
$425$		0			0
$426$	−1.02229	+	1.77066i	−0.0495300	+	0.0857886i
$427$	8.29628	−	1.46286i	0.401485	−	0.0707927i
$428$	−0.300767	+	0.0530334i	−0.0145381	+	0.00256347i
$429$	−1.25402	+	2.17203i	−0.0605448	+	0.104867i
$430$		0			0
$431$	−9.98545	+	8.37879i	−0.480982	+	0.403592i	−0.850781	−	0.525520i	$-0.823871\pi$
$431$	−9.98545	+	8.37879i	−0.480982	+	0.403592i	0.369799	+	0.929112i	$0.379426\pi$
$432$	−0.698367	−	1.91875i	−0.0336002	−	0.0923158i
$433$	9.06812	−	24.9145i	0.435786	−	1.19731i	−0.506422	−	0.862286i	$-0.669032\pi$
$433$	9.06812	−	24.9145i	0.435786	−	1.19731i	0.942208	−	0.335027i	$-0.108746\pi$
$434$	18.3405	+	15.3895i	0.880372	+	0.738720i
$435$		0			0
$436$	15.3601			0.735615
$437$	−13.5749	+	4.82800i	−0.649378	+	0.230955i
$438$		−	0.403733i		−	0.0192911i
$439$	6.15064	−	34.8820i	0.293554	−	1.66483i	−0.379467	−	0.925205i	$-0.623893\pi$
$439$	6.15064	−	34.8820i	0.293554	−	1.66483i	0.673021	−	0.739623i	$-0.264996\pi$
$440$		0			0
$441$	19.2875	+	7.02006i	0.918450	+	0.334289i
$442$	−2.12467	−	5.83750i	−0.101060	−	0.277661i
$443$	−19.1429	−	22.8136i	−0.909506	−	1.08391i	−0.996150	−	0.0876682i	$-0.972058\pi$
$443$	−19.1429	−	22.8136i	−0.909506	−	1.08391i	0.0866433	−	0.996239i	$-0.472386\pi$
$444$	0.694593	+	1.20307i	0.0329639	+	0.0570952i
$445$		0			0
$446$	2.71688	+	15.4082i	0.128648	+	0.729599i
$447$	4.66717	−	0.822948i	0.220750	−	0.0389241i
$448$	3.25519	+	1.87939i	0.153793	+	0.0887926i
$449$	14.5655	+	25.2282i	0.687389	+	1.19059i	0.972679	+	0.232152i	$0.0745768\pi$
$449$	14.5655	+	25.2282i	0.687389	+	1.19059i	−0.285290	+	0.958441i	$0.592090\pi$
$450$		0			0
$451$	41.6279	−	15.1513i	1.96018	−	0.713448i
$452$	2.81369	−	7.73055i	0.132345	−	0.363615i
$453$	0.363970	−	0.433763i	0.0171008	−	0.0203800i
$454$	1.48380	−	8.41507i	0.0696383	−	0.394939i
$455$		0			0
$456$	1.30541	+	0.766546i	0.0611313	+	0.0358968i
$457$			23.4807i			1.09838i	0.835697	+	0.549191i	$0.185064\pi$
$457$			23.4807i			1.09838i	−0.835697	+	0.549191i	$0.814936\pi$
$458$	4.05039	+	0.714193i	0.189262	+	0.0333721i
$459$	7.44356	+	6.24589i	0.347436	+	0.291533i
$460$		0			0
$461$	4.85204	−	1.76600i	0.225982	−	0.0822508i	−0.226548	−	0.974000i	$-0.572744\pi$
$461$	4.85204	−	1.76600i	0.225982	−	0.0822508i	0.452530	+	0.891749i	$0.350522\pi$
$462$	4.64197	+	5.53209i	0.215964	+	0.257376i
$463$	−21.7582	+	12.5621i	−1.01119	+	0.583811i	−0.911540	−	0.411211i	$-0.865106\pi$
$463$	−21.7582	+	12.5621i	−1.01119	+	0.583811i	−0.0996505	+	0.995022i	$0.531772\pi$
$464$	−4.75877	+	8.24243i	−0.220920	+	0.382645i
$465$		0			0
$466$	0.436700	+	2.47665i	0.0202297	+	0.114728i
$467$	17.8562	+	10.3093i	0.826286	+	0.477056i	0.852579	−	0.522598i	$-0.175037\pi$
$467$	17.8562	+	10.3093i	0.826286	+	0.477056i	−0.0262933	+	0.999654i	$0.508370\pi$
$468$	−3.25519	+	1.87939i	−0.150471	+	0.0868746i
$469$	−35.6391	+	29.9047i	−1.64566	+	1.38087i
$470$		0			0
$471$	2.03684	+	0.741348i	0.0938525	+	0.0341595i
$472$	−4.15749	+	4.95471i	−0.191364	+	0.228059i
$473$	−39.2920	−	6.92824i	−1.80665	−	0.318561i
$474$	3.06418			0.140742
$475$		0			0
$476$	−17.8871			−0.819855
$477$	−4.98724	−	0.879385i	−0.228350	−	0.0402643i
$478$	−5.98140	+	7.12836i	−0.273583	+	0.326043i
$479$	−10.8648	−	3.95448i	−0.496427	−	0.180685i	0.0816592	−	0.996660i	$-0.473978\pi$
$479$	−10.8648	−	3.95448i	−0.496427	−	0.180685i	−0.578086	+	0.815976i	$0.696200\pi$
$480$		0			0
$481$	4.00000	−	3.35640i	0.182384	−	0.153039i
$482$	−6.17101	+	3.56283i	−0.281082	+	0.162283i
$483$	3.73682	+	2.15745i	0.170031	+	0.0981674i
$484$	−3.40420	−	19.3062i	−0.154736	−	0.877554i
$485$		0			0
$486$	4.43969	−	7.68977i	0.201389	−	0.348815i
$487$	4.24935	−	2.45336i	0.192556	−	0.111172i	−0.400622	−	0.916243i	$-0.631206\pi$
$487$	4.24935	−	2.45336i	0.192556	−	0.111172i	0.593179	+	0.805071i	$0.297873\pi$
$488$	1.44063	+	1.71688i	0.0652145	+	0.0777196i
$489$	−1.19207	+	0.433877i	−0.0539071	+	0.0196206i
$490$		0			0
$491$	9.80793	+	8.22983i	0.442626	+	0.371407i	0.836691	−	0.547675i	$-0.184487\pi$
$491$	9.80793	+	8.22983i	0.442626	+	0.371407i	−0.394065	+	0.919083i	$0.628932\pi$
$492$	−2.73881	−	0.482926i	−0.123475	−	0.0217720i
$493$		−	45.2918i		−	2.03984i
$494$	1.98545	−	5.33251i	0.0893297	−	0.239921i
$495$		0			0
$496$	−1.10607	+	6.27282i	−0.0496639	+	0.281658i
$497$	14.2238	−	16.9513i	0.638026	−	0.760370i
$498$	1.44155	−	3.96064i	0.0645976	−	0.177480i
$499$	3.86571	−	1.40701i	0.173053	−	0.0629862i	−0.254041	−	0.967194i	$-0.581760\pi$
$499$	3.86571	−	1.40701i	0.173053	−	0.0629862i	0.427094	+	0.904207i	$0.359537\pi$
$500$		0			0
$501$	−2.78787	−	4.82873i	−0.124553	−	0.215732i
$502$	−14.3069	−	8.26011i	−0.638550	−	0.368667i
$503$	19.7401	−	3.48070i	0.880166	−	0.155197i	0.284737	−	0.958606i	$-0.408094\pi$
$503$	19.7401	−	3.48070i	0.880166	−	0.155197i	0.595428	+	0.803409i	$0.296982\pi$
$504$	1.87939	+	10.6585i	0.0837145	+	0.474768i
$505$		0			0
$506$	−9.14290	−	15.8360i	−0.406452	−	0.703995i
$507$	2.52167	+	3.00521i	0.111991	+	0.133466i
$508$	0.155059	+	0.426022i	0.00687965	+	0.0189017i
$509$	11.3824	+	4.14285i	0.504515	+	0.183628i	0.581724	−	0.813387i	$-0.302379\pi$
$509$	11.3824	+	4.14285i	0.504515	+	0.183628i	−0.0772086	+	0.997015i	$0.524601\pi$
$510$		0			0
$511$	−0.758770	+	4.30320i	−0.0335660	+	0.190362i
$512$			1.00000i			0.0441942i
$513$	1.48097	+	8.77631i	0.0653863	+	0.387484i
$514$	8.91353			0.393159
$515$		0			0
$516$	1.91875	+	1.61002i	0.0844682	+	0.0708772i
$517$	23.1064	−	63.4843i	1.01622	−	2.79204i
$518$	−5.14230	−	14.1284i	−0.225940	−	0.620764i
$519$	−0.192533	+	0.161555i	−0.00845127	+	0.00709146i
$520$		0			0
$521$	−12.6202	+	21.8588i	−0.552901	+	0.957653i	0.445162	+	0.895450i	$0.353146\pi$
$521$	−12.6202	+	21.8588i	−0.552901	+	0.957653i	−0.998064	+	0.0622031i	$0.980187\pi$
$522$	−26.9883	+	4.75877i	−1.18125	+	0.208286i
$523$	18.9109	−	3.33450i	0.826916	−	0.145808i	0.255855	−	0.966715i	$-0.417643\pi$
$523$	18.9109	−	3.33450i	0.826916	−	0.145808i	0.571061	+	0.820908i	$0.306532\pi$
$524$	−1.86824	+	3.23589i	−0.0816145	+	0.141360i
$525$		0			0
$526$	−7.53983	+	6.32667i	−0.328752	+	0.275856i
$527$	−10.3671	−	28.4834i	−0.451598	−	1.24076i
$528$	−0.657115	+	1.80541i	−0.0285972	+	0.0785703i
$529$	9.24944	+	7.76120i	0.402149	+	0.337443i
$530$		0			0
$531$	−18.6236			−0.808196
$532$	−12.4731	−	10.6236i	−0.540777	−	0.460592i
$533$			10.4534i			0.452785i
$534$	0.678863	−	3.85002i	0.0293773	−	0.166607i
$535$		0			0
$536$	−11.6309	−	4.23329i	−0.502378	−	0.182850i
$537$	0.571962	+	1.57145i	0.0246820	+	0.0678131i
$538$	5.37987	+	6.41147i	0.231942	+	0.276418i
$539$	−19.7173	−	34.1514i	−0.849286	−	1.47101i
$540$		0			0
$541$	−0.0273411	−	0.155059i	−0.00117549	−	0.00666652i	0.984214	−	0.176980i	$-0.0566329\pi$
$541$	−0.0273411	−	0.155059i	−0.00117549	−	0.00666652i	−0.985390	+	0.170314i	$0.945522\pi$
$542$	−1.25692	+	0.221629i	−0.0539894	+	0.00951979i
$543$	−0.935012	−	0.539830i	−0.0401252	−	0.0231663i
$544$	−2.37939	−	4.12122i	−0.102015	−	0.176696i
$545$		0			0
$546$	−1.60132	+	0.582832i	−0.0685301	+	0.0249429i
$547$	11.7571	−	32.3025i	0.502699	−	1.38115i	−0.385930	−	0.922528i	$-0.626120\pi$
$547$	11.7571	−	32.3025i	0.502699	−	1.38115i	0.888629	−	0.458626i	$-0.151658\pi$
$548$	−6.65111	+	7.92649i	−0.284122	+	0.338603i
$549$	−1.12061	+	6.35532i	−0.0478267	+	0.271239i
$550$		0			0
$551$	26.8999	−	31.5829i	1.14598	−	1.34548i
$552$			1.14796i			0.0488602i
$553$	−32.6596	−	5.75877i	−1.38883	−	0.244888i
$554$	5.43376	+	4.55947i	0.230858	+	0.193713i
$555$		0			0
$556$	−1.84477	+	0.671441i	−0.0782357	+	0.0284755i
$557$	8.51515	+	10.1480i	0.360798	+	0.429983i	0.915656	−	0.401963i	$-0.131672\pi$
$557$	8.51515	+	10.1480i	0.360798	+	0.429983i	−0.554858	+	0.831945i	$0.687227\pi$
$558$	−15.8833	+	9.17024i	−0.672395	+	0.388207i
$559$	4.70739	−	8.15343i	0.199101	−	0.344853i
$560$		0			0
$561$	−1.58765	−	9.00400i	−0.0670306	−	0.380149i
$562$	17.8822	+	10.3243i	0.754315	+	0.435504i
$563$	−33.1912	+	19.1630i	−1.39884	+	0.807623i	−0.994272	−	0.106883i	$-0.965913\pi$
$563$	−33.1912	+	19.1630i	−1.39884	+	0.807623i	−0.404572	+	0.914506i	$0.632580\pi$
$564$	−3.24897	+	2.72621i	−0.136806	+	0.114794i
$565$		0			0
$566$	13.3045	+	4.84245i	0.559231	+	0.203543i
$567$	−19.1572	+	22.8307i	−0.804528	+	0.958799i
$568$	5.79769	+	1.02229i	0.243266	+	0.0428943i
$569$	32.1634			1.34836			0.674181	−	0.738566i	$-0.264497\pi$
$569$	32.1634			1.34836			0.674181	+	0.738566i	$0.264497\pi$
$570$		0			0
$571$	16.2635			0.680607			0.340304	−	0.940316i	$-0.389470\pi$
$571$	16.2635			0.680607			0.340304	+	0.940316i	$0.389470\pi$
$572$	7.11192	+	1.25402i	0.297364	+	0.0524333i
$573$	2.38094	−	2.83750i	0.0994653	−	0.118538i
$574$	28.2841	+	10.2946i	1.18055	+	0.429686i
$575$		0			0
$576$	−2.20574	+	1.85083i	−0.0919057	+	0.0771180i
$577$	18.1570	−	10.4829i	0.755884	−	0.436410i	−0.0719319	−	0.997410i	$-0.522916\pi$
$577$	18.1570	−	10.4829i	0.755884	−	0.436410i	0.827816	+	0.561000i	$0.189583\pi$
$578$	4.88949	+	2.82295i	0.203376	+	0.117419i
$579$	1.13129	+	6.41588i	0.0470149	+	0.266635i
$580$		0			0
$581$	−22.8084	+	39.5053i	−0.946252	+	1.63896i
$582$	2.27211	−	1.31180i	0.0941820	−	0.0543760i
$583$	6.25411	+	7.45336i	0.259019	+	0.308687i
$584$	−1.09240	+	0.397600i	−0.0452037	+	0.0164528i
$585$		0			0
$586$	−17.6578	−	14.8166i	−0.729435	−	0.612069i
$587$	34.7463	+	6.12671i	1.43413	+	0.252876i	0.836092	−	0.548590i	$-0.184835\pi$
$587$	34.7463	+	6.12671i	1.43413	+	0.252876i	0.598041	+	0.801466i	$0.295946\pi$
$588$			2.47565i			0.102094i
$589$	9.68779	−	26.0194i	0.399178	−	1.07211i
$590$		0			0
$591$	0.660444	−	3.74557i	0.0271671	−	0.154072i
$592$	2.57115	−	3.06418i	0.105674	−	0.125937i
$593$	5.53990	−	15.2208i	0.227496	−	0.625041i	−0.772453	−	0.635072i	$-0.780971\pi$
$593$	5.53990	−	15.2208i	0.227496	−	0.625041i	0.999950	+	0.0100303i	$0.00319279\pi$
$594$	−10.6147	+	3.86343i	−0.435526	+	0.158518i
$595$		0			0
$596$	−6.82295	−	11.8177i	−0.279479	−	0.484072i
$597$	−2.00173	−	1.15570i	−0.0819252	−	0.0472995i
$598$	4.24935	−	0.749275i	0.173769	−	0.0306401i
$599$	2.70502	+	15.3409i	0.110524	+	0.626814i	0.988869	+	0.148787i	$0.0475368\pi$
$599$	2.70502	+	15.3409i	0.110524	+	0.626814i	−0.878345	+	0.478027i	$0.841352\pi$
$600$		0			0
$601$	10.9089	+	18.8949i	0.444985	+	0.770737i	0.998051	−	0.0624004i	$-0.0198756\pi$
$601$	10.9089	+	18.8949i	0.444985	+	0.770737i	−0.553066	+	0.833137i	$0.686542\pi$
$602$	−17.4252	−	20.7665i	−0.710197	−	0.846380i
$603$	−12.1893	−	33.4898i	−0.496386	−	1.36381i
$604$	−1.53209	−	0.557635i	−0.0623398	−	0.0226898i
$605$		0			0
$606$	0.992259	−	5.62738i	0.0403078	−	0.228597i
$607$			32.2722i			1.30989i	0.755677	+	0.654944i	$0.227308\pi$
$607$			32.2722i			1.30989i	−0.755677	+	0.654944i	$0.772692\pi$
$608$	0.788496	−	4.28699i	0.0319777	−	0.173860i
$609$	−12.4243			−0.503457
$610$		0			0
$611$	12.2121	+	10.2472i	0.494050	+	0.414557i
$612$	4.68647	−	12.8760i	0.189439	−	0.520481i
$613$	12.6515	+	34.7597i	0.510989	+	1.40393i	0.880208	+	0.474589i	$0.157403\pi$
$613$	12.6515	+	34.7597i	0.510989	+	1.40393i	−0.369219	+	0.929343i	$0.620375\pi$
$614$	−3.23783	+	2.71686i	−0.130668	+	0.109643i
$615$		0			0
$616$	10.3969	−	18.0080i	0.418904	−	0.725563i
$617$	−2.57207	+	0.453525i	−0.103548	+	0.0182582i	−0.225182	−	0.974317i	$-0.572298\pi$
$617$	−2.57207	+	0.453525i	−0.103548	+	0.0182582i	0.121634	+	0.992575i	$0.461187\pi$
$618$	2.53255	−	0.446556i	0.101874	−	0.0179631i
$619$	4.61381	−	7.99135i	0.185445	−	0.321199i	−0.758282	−	0.651927i	$-0.773961\pi$
$619$	4.61381	−	7.99135i	0.185445	−	0.321199i	0.943726	+	0.330728i	$0.107294\pi$
$620$		0			0
$621$	−5.17024	+	4.33835i	−0.207475	+	0.174092i
$622$	2.86257	+	7.86484i	0.114778	+	0.315351i
$623$	−14.4713	+	39.7597i	−0.579782	+	1.59294i
$624$	−0.347296	−	0.291416i	−0.0139030	−	0.0116660i
$625$		0			0
$626$	−18.4365			−0.736869
$627$	4.24060	−	7.22163i	0.169353	−	0.288404i
$628$		−	6.24123i		−	0.249052i
$629$	−3.30541	+	18.7459i	−0.131795	+	0.747448i
$630$		0			0
$631$	26.1925	+	9.53330i	1.04271	+	0.379515i	0.805906	−	0.592043i	$-0.201679\pi$
$631$	26.1925	+	9.53330i	1.04271	+	0.379515i	0.236802	+	0.971558i	$0.423901\pi$
$632$	−3.01763	−	8.29086i	−0.120035	−	0.329793i
$633$	4.50774	+	5.37211i	0.179166	+	0.213522i
$634$	−15.5175	−	26.8772i	−0.616280	−	1.06743i
$635$		0			0
$636$	−0.106067	−	0.601535i	−0.00420582	−	0.0238524i
$637$	9.16404	−	1.61587i	0.363092	−	0.0640230i
$638$	45.5979	+	26.3259i	1.80524	+	1.04225i
$639$	8.47565	+	14.6803i	0.335292	+	0.580742i
$640$		0			0
$641$	28.7866	−	10.4775i	1.13700	−	0.413835i	0.296172	−	0.955135i	$-0.404290\pi$
$641$	28.7866	−	10.4775i	1.13700	−	0.413835i	0.840830	+	0.541300i	$0.182068\pi$
$642$	0.0362770	−	0.0996702i	0.00143174	−	0.00393367i
$643$	−19.0264	+	22.6748i	−0.750330	+	0.894208i	−0.997195	−	0.0748417i	$-0.976155\pi$
$643$	−19.0264	+	22.6748i	−0.750330	+	0.894208i	0.246866	+	0.969050i	$0.420599\pi$
$644$	2.15745	−	12.2355i	0.0850155	−	0.482147i
$645$		0			0
$646$	6.95084	+	19.5437i	0.273477	+	0.768938i
$647$			30.4635i			1.19764i	0.800883	+	0.598821i	$0.204364\pi$
$647$			30.4635i			1.19764i	−0.800883	+	0.598821i	$0.795636\pi$
$648$	−7.80856	−	1.37686i	−0.306749	−	0.0540881i
$649$	27.4099	+	22.9996i	1.07593	+	0.902814i
$650$		0			0
$651$	−7.81345	+	2.84386i	−0.306233	+	0.111460i
$652$	2.34791	+	2.79813i	0.0919514	+	0.109583i
$653$	34.5567	−	19.9513i	1.35231	−	0.780755i	0.363735	−	0.931503i	$-0.381501\pi$
$653$	34.5567	−	19.9513i	1.35231	−	0.780755i	0.988572	+	0.150748i	$0.0481681\pi$
$654$	−2.66725	+	4.61982i	−0.104298	+	0.180649i
$655$		0			0
$656$	1.39053	+	7.88609i	0.0542911	+	0.307900i
$657$	−2.89884	−	1.67365i	−0.113095	−	0.0652952i
$658$	39.7528	−	22.9513i	1.54973	−	0.894735i
$659$	−32.3214	+	27.1208i	−1.25906	+	1.05648i	−0.263280	+	0.964719i	$0.584804\pi$
$659$	−32.3214	+	27.1208i	−1.25906	+	1.05648i	−0.995781	+	0.0917584i	$0.970751\pi$
$660$		0			0
$661$	−15.6186	−	5.68469i	−0.607491	−	0.221109i	0.0199139	−	0.999802i	$-0.493661\pi$
$661$	−15.6186	−	5.68469i	−0.607491	−	0.221109i	−0.627405	+	0.778693i	$0.715883\pi$
$662$	5.52557	−	6.58512i	0.214758	−	0.255938i
$663$	2.12467	+	0.374638i	0.0825155	+	0.0145497i
$664$	−12.1361			−0.470972
$665$		0			0
$666$	11.5175			0.446296
$667$	30.9814	+	5.46286i	1.19961	+	0.211523i
$668$	−10.3198	+	12.2986i	−0.399283	+	0.475847i
$669$	−5.10607	−	1.85846i	−0.197412	−	0.0718521i
$670$		0			0
$671$	9.49794	−	7.96972i	0.366664	−	0.307668i
$672$	−1.13052	+	0.652704i	−0.0436106	+	0.0251786i
$673$	20.1543	+	11.6361i	0.776892	+	0.448539i	0.835328	−	0.549753i	$-0.185278\pi$
$673$	20.1543	+	11.6361i	0.776892	+	0.448539i	−0.0584360	+	0.998291i	$0.518611\pi$
$674$	5.54782	+	31.4632i	0.213694	+	1.21192i
$675$		0			0
$676$	5.64796	−	9.78255i	0.217229	−	0.376252i
$677$	−27.4921	+	15.8726i	−1.05661	+	0.610033i	−0.924492	−	0.381202i	$-0.875510\pi$
$677$	−27.4921	+	15.8726i	−1.05661	+	0.610033i	−0.132116	+	0.991234i	$0.542177\pi$
$678$	1.83651	+	2.18866i	0.0705306	+	0.0840551i
$679$	−26.6827	+	9.71172i	−1.02399	+	0.372702i
$680$		0			0
$681$	2.27332	+	1.90754i	0.0871138	+	0.0730971i
$682$	34.7018	+	6.11886i	1.32880	+	0.234303i
$683$			6.87702i			0.263142i	0.991307	+	0.131571i	$0.0420021\pi$
$683$			6.87702i			0.263142i	−0.991307	+	0.131571i	$0.957998\pi$
$684$	10.9153	−	6.19529i	0.417359	−	0.236883i
$685$		0			0
$686$	0.0837781	−	0.475129i	0.00319866	−	0.0181405i
$687$	−0.918149	+	1.09421i	−0.0350296	+	0.0417466i
$688$	2.46669	−	6.77719i	0.0940419	−	0.258378i
$689$	−2.15745	+	0.785248i	−0.0821924	+	0.0299156i
$690$		0			0
$691$	−8.83544	−	15.3034i	−0.336116	−	0.582170i	0.647583	−	0.761995i	$-0.275780\pi$
$691$	−8.83544	−	15.3034i	−0.336116	−	0.582170i	−0.983699	+	0.179825i	$0.942447\pi$
$692$	0.626733	+	0.361844i	0.0238248	+	0.0137553i
$693$	58.9639	−	10.3969i	2.23985	−	0.394947i
$694$	−0.786522	−	4.46059i	−0.0298560	−	0.169322i
$695$		0			0
$696$	−1.65270	−	2.86257i	−0.0626456	−	0.108505i
$697$	−24.4947	−	29.1917i	−0.927803	−	1.10571i
$698$	−9.27704	−	25.4884i	−0.351141	−	0.964752i
$699$	−0.820727	−	0.298720i	−0.0310427	−	0.0112986i
$700$		0			0
$701$	8.21987	−	46.6172i	0.310460	−	1.76071i	−0.286157	−	0.958183i	$-0.592378\pi$
$701$	8.21987	−	46.6172i	0.310460	−	1.76071i	0.596618	−	0.802526i	$-0.296511\pi$
$702$		−	2.66550i		−	0.100603i
$703$	−13.4386	+	11.1088i	−0.506846	+	0.418975i
$704$	5.53209			0.208498
$705$		0			0
$706$	15.1079	+	12.6770i	0.568592	+	0.477106i
$707$	−21.1520	+	58.1147i	−0.795504	+	2.18563i
$708$	−0.768274	−	2.11081i	−0.0288735	−	0.0793293i
$709$	12.3892	−	10.3958i	0.465286	−	0.390421i	−0.379786	−	0.925074i	$-0.624002\pi$
$709$	12.3892	−	10.3958i	0.465286	−	0.390421i	0.845071	+	0.534653i	$0.179558\pi$
$710$		0			0
$711$	12.7023	−	22.0011i	0.476375	−	0.825105i
$712$	−11.0857	+	1.95471i	−0.415454	+	0.0732558i
$713$	20.7342	−	3.65600i	0.776502	−	0.136918i
$714$	3.10607	−	5.37987i	0.116242	−	0.201336i
$715$		0			0
$716$	3.68866	−	3.09516i	0.137852	−	0.115671i
$717$	−1.10532	−	3.03684i	−0.0412789	−	0.113413i
$718$	7.45718	−	20.4884i	0.278300	−	0.764622i
$719$	11.0942	+	9.30915i	0.413744	+	0.347173i	0.825777	−	0.563996i	$-0.190737\pi$
$719$	11.0942	+	9.30915i	0.413744	+	0.347173i	−0.412033	+	0.911169i	$0.635181\pi$
$720$		0			0
$721$	−27.8324			−1.03653
$722$	−6.76055	+	17.7565i	−0.251601	+	0.660830i
$723$		−	2.47472i		−	0.0920358i
$724$	−0.539830	+	3.06153i	−0.0200626	+	0.113781i
$725$		0			0
$726$	6.39780	+	2.32861i	0.237445	+	0.0864228i
$727$	4.16684	+	11.4483i	0.154540	+	0.424594i	0.992667	−	0.120880i	$-0.0385717\pi$
$727$	4.16684	+	11.4483i	0.154540	+	0.424594i	−0.838127	+	0.545475i	$0.816349\pi$
$728$	3.15398	+	3.75877i	0.116894	+	0.139309i
$729$	−10.3516	−	17.9296i	−0.383394	−	0.664058i
$730$		0			0
$731$	5.95976	+	33.7995i	0.220430	+	1.25012i
$732$	−0.766546	+	0.135163i	−0.0283323	+	0.00499576i
$733$	−41.8436	−	24.1584i	−1.54553	−	0.892310i	−0.998475	−	0.0552118i	$-0.982417\pi$
$733$	−41.8436	−	24.1584i	−1.54553	−	0.892310i	−0.547052	−	0.837099i	$-0.684250\pi$
$734$	−1.83750	−	3.18264i	−0.0678232	−	0.117473i
$735$		0			0
$736$	3.10607	−	1.13052i	0.114491	−	0.0416714i
$737$	−23.4190	+	64.3431i	−0.862649	+	2.37011i
$738$	−14.8210	+	17.6630i	−0.545568	+	0.650183i
$739$	8.71317	−	49.4149i	0.320519	−	1.81776i	−0.218934	−	0.975740i	$-0.570258\pi$
$739$	8.71317	−	49.4149i	0.320519	−	1.81776i	0.539453	−	0.842015i	$-0.318631\pi$
$740$		0			0
$741$	1.25908	+	1.52314i	0.0462533	+	0.0559539i
$742$			6.61081i			0.242691i
$743$	−0.242860	−	0.0428227i	−0.00890966	−	0.00157101i	0.169192	−	0.985583i	$-0.445884\pi$
$743$	−0.242860	−	0.0428227i	−0.00890966	−	0.00157101i	−0.178101	+	0.984012i	$0.556995\pi$
$744$	−1.69459	−	1.42193i	−0.0621268	−	0.0521306i
$745$		0			0
$746$	−12.3824	+	4.50682i	−0.453351	+	0.165006i
$747$	−22.4619	−	26.7690i	−0.821838	−	0.979428i
$748$	−22.7989	+	13.1630i	−0.833612	+	0.481286i
$749$	−0.573978	+	0.994159i	−0.0209727	+	0.0363258i
$750$		0			0
$751$	−4.00681	−	22.7237i	−0.146210	−	0.829201i	−0.966387	−	0.257091i	$-0.917236\pi$
$751$	−4.00681	−	22.7237i	−0.146210	−	0.829201i	0.820177	−	0.572110i	$-0.193875\pi$
$752$	10.5760	+	6.10607i	0.385668	+	0.222665i
$753$	4.96875	−	2.86871i	0.181071	−	0.104542i
$754$	−9.51754	+	7.98617i	−0.346608	+	0.290839i
$755$		0			0
$756$	−7.21213	−	2.62500i	−0.262303	−	0.0954704i
$757$	27.7549	−	33.0770i	1.00877	−	1.20220i	0.0295145	−	0.999564i	$-0.490604\pi$
$757$	27.7549	−	33.0770i	1.00877	−	1.20220i	0.979254	−	0.202639i	$-0.0649517\pi$
$758$	−11.1202	−	1.96080i	−0.403905	−	0.0712194i
$759$	6.35059			0.230512
$760$		0			0
$761$	−26.2499			−0.951558			−0.475779	−	0.879565i	$-0.657834\pi$
$761$	−26.2499			−0.951558			−0.475779	+	0.879565i	$0.657834\pi$
$762$	−0.155059	−	0.0273411i	−0.00561721	−	0.000990465i
$763$	37.1114	−	44.2276i	1.34352	−	1.60115i
$764$	−10.0223	−	3.64781i	−0.362594	−	0.131973i
$765$		0			0
$766$	19.6759	−	16.5101i	0.710920	−	0.596533i
$767$	−7.31208	+	4.22163i	−0.264024	+	0.152434i
$768$	−0.300767	−	0.173648i	−0.0108530	−	0.00626599i
$769$	1.61422	+	9.15469i	0.0582102	+	0.330126i	0.999981	−	0.00612844i	$-0.00195076\pi$
$769$	1.61422	+	9.15469i	0.0582102	+	0.330126i	−0.941771	+	0.336255i	$0.890840\pi$
$770$		0			0
$771$	−1.54782	+	2.68090i	−0.0557433	+	0.0965503i
$772$	16.2456	−	9.37939i	0.584691	−	0.337571i
$773$	18.9075	+	22.5330i	0.680054	+	0.810456i	0.990115	−	0.140260i	$-0.0447939\pi$
$773$	18.9075	+	22.5330i	0.680054	+	0.810456i	−0.310061	+	0.950717i	$0.600349\pi$
$774$	19.5141	−	7.10257i	0.701421	−	0.255296i
$775$		0			0
$776$	−5.78699	−	4.85586i	−0.207741	−	0.174315i
$777$	5.14230	+	0.906726i	0.184479	+	0.0325286i
$778$			10.3541i			0.371213i
$779$	0.256959	−	34.9040i	0.00920653	−	1.25057i
$780$		0			0
$781$	5.65539	−	32.0733i	0.202366	−	1.14767i
$782$	−10.1108	+	12.0496i	−0.361563	+	0.430894i
$783$	6.64674	−	18.2618i	0.237535	−	0.652622i
$784$	6.69846	−	2.43804i	0.239231	−	0.0870729i
$785$		0			0
$786$	−0.648833	−	1.12381i	−0.0231431	−	0.0400851i
$787$	−45.0341	−	26.0005i	−1.60529	−	0.926817i	−0.990404	−	0.138203i	$-0.955867\pi$
$787$	−45.0341	−	26.0005i	−1.60529	−	0.926817i	−0.614889	−	0.788613i	$-0.710799\pi$
$788$	−10.7849	+	1.90167i	−0.384197	+	0.0677443i
$789$	−0.593578	−	3.36635i	−0.0211319	−	0.119845i
$790$		0			0
$791$	−15.4611	−	26.7794i	−0.549734	−	0.952166i
$792$	10.2390	+	12.2023i	0.363826	+	0.433591i
$793$	1.00065	+	2.74928i	0.0355343	+	0.0976296i
$794$	8.97090	+	3.26514i	0.318365	+	0.115876i
$795$		0			0
$796$	−1.15570	+	6.55428i	−0.0409626	+	0.232310i
$797$		−	32.4296i		−	1.14872i	−0.818604	−	0.574358i	$-0.805252\pi$
$797$		−	32.4296i		−	1.14872i	0.818604	−	0.574358i	$-0.194748\pi$
$798$	5.36116	−	1.90673i	0.189783	−	0.0674974i
$799$	−58.1147			−2.05595
$800$		0			0
$801$	−24.8293	−	20.8343i	−0.877302	−	0.736144i
$802$	−10.2457	+	28.1498i	−0.361787	+	0.994003i
$803$	2.19956	+	6.04323i	0.0776207	+	0.213261i
$804$	3.29292	−	2.76309i	0.116132	−	0.0974466i
$805$		0			0
$806$	−4.15745	+	7.20092i	−0.146440	+	0.253641i
$807$	−2.86257	+	0.504748i	−0.100767	+	0.0177680i
$808$	−16.2034	+	2.85710i	−0.570034	+	0.100512i
$809$	15.6190	−	27.0529i	0.549136	−	0.951131i	−0.449198	−	0.893432i	$-0.648290\pi$
$809$	15.6190	−	27.0529i	0.549136	−	0.951131i	0.998334	−	0.0576987i	$-0.0183763\pi$
$810$		0			0
$811$	−17.1480	+	14.3888i	−0.602146	+	0.505261i	−0.892135	−	0.451769i	$-0.850793\pi$
$811$	−17.1480	+	14.3888i	−0.602146	+	0.505261i	0.289989	+	0.957030i	$0.406349\pi$
$812$	12.2355	+	33.6168i	0.429382	+	1.17972i
$813$	0.151603	−	0.416527i	0.00531696	−	0.0146082i
$814$	−16.9513	−	14.2238i	−0.594143	−	0.498545i
$815$		0			0
$816$	1.65270			0.0578562
$817$	−15.9185	+	27.1088i	−0.556917	+	0.948415i
$818$		−	24.5963i		−	0.859988i
$819$	−2.45336	+	13.9137i	−0.0857274	+	0.486185i
$820$		0			0
$821$	16.9949	+	6.18566i	0.593128	+	0.215881i	0.621105	−	0.783728i	$-0.286684\pi$
$821$	16.9949	+	6.18566i	0.593128	+	0.215881i	−0.0279768	+	0.999609i	$0.508906\pi$
$822$	−1.22908	−	3.37686i	−0.0428690	−	0.117781i
$823$	−34.0716	−	40.6049i	−1.18766	−	1.41540i	−0.887063	−	0.461648i	$-0.847258\pi$
$823$	−34.0716	−	40.6049i	−1.18766	−	1.41540i	−0.300598	−	0.953751i	$-0.597186\pi$
$824$	−3.70233	−	6.41263i	−0.128977	−	0.223395i
$825$		0			0
$826$	4.22163	+	23.9420i	0.146889	+	0.833050i
$827$	−6.89863	+	1.21641i	−0.239889	+	0.0422989i	−0.292300	−	0.956327i	$-0.594421\pi$
$827$	−6.89863	+	1.21641i	−0.239889	+	0.0422989i	0.0524110	+	0.998626i	$0.483309\pi$
$828$	8.24243	+	4.75877i	0.286444	+	0.165379i
$829$	5.49020	+	9.50931i	0.190683	+	0.330272i	0.945477	−	0.325690i	$-0.105597\pi$
$829$	5.49020	+	9.50931i	0.190683	+	0.330272i	−0.754794	+	0.655962i	$0.772263\pi$
$830$		0			0
$831$	−2.31490	+	0.842556i	−0.0803031	+	0.0292279i
$832$	−0.446476	+	1.22668i	−0.0154788	+	0.0425275i
$833$	−21.8048	+	25.9859i	−0.755491	+	0.900359i
$834$	0.118393	−	0.671441i	0.00409962	−	0.0232501i
$835$		0			0
$836$	−23.7160	−	4.36203i	−0.820235	−	0.150864i
$837$		−	13.0060i		−	0.449553i
$838$	11.6281	+	2.05035i	0.401686	+	0.0708280i
$839$	10.1284	+	8.49870i	0.349670	+	0.293408i	0.800657	−	0.599122i	$-0.204484\pi$
$839$	10.1284	+	8.49870i	0.349670	+	0.293408i	−0.450988	+	0.892530i	$0.648928\pi$
$840$		0			0
$841$	−57.8696	+	21.0628i	−1.99550	+	0.726304i
$842$	−3.91058	−	4.66044i	−0.134767	−	0.160610i
$843$	−6.21042	+	3.58559i	−0.213898	+	0.123494i
$844$	10.0963	−	17.4872i	0.347528	−	0.601936i
$845$		0			0
$846$	6.10607	+	34.6292i	0.209931	+	1.19058i
$847$	−63.8148	−	36.8435i	−2.19270	−	1.26596i
$848$	−1.52314	+	0.879385i	−0.0523048	+	0.0301982i
$849$	−3.76676	+	3.16069i	−0.129275	+	0.108474i
$850$		0			0
$851$	−12.4243	−	4.52206i	−0.425898	−	0.155014i
$852$	−1.31423	+	1.56624i	−0.0450247	+	0.0536584i
$853$	−13.6896	−	2.41384i	−0.468721	−	0.0826482i	−0.0657013	−	0.997839i	$-0.520928\pi$
$853$	−13.6896	−	2.41384i	−0.468721	−	0.0826482i	−0.403020	+	0.915191i	$0.632040\pi$
$854$	8.42427			0.288272
$855$		0			0
$856$	−0.305407			−0.0104386
$857$	−10.4124	−	1.83599i	−0.355681	−	0.0627162i	−0.00704736	−	0.999975i	$-0.502243\pi$
$857$	−10.4124	−	1.83599i	−0.355681	−	0.0627162i	−0.348634	+	0.937259i	$0.613354\pi$
$858$	−1.61214	+	1.92127i	−0.0550376	+	0.0655912i
$859$	26.7606	+	9.74006i	0.913059	+	0.332326i	0.755474	−	0.655179i	$-0.227407\pi$
$859$	26.7606	+	9.74006i	0.913059	+	0.332326i	0.157586	+	0.987505i	$0.449629\pi$
$860$		0			0
$861$	−8.00774	+	6.71929i	−0.272903	+	0.228993i
$862$	−11.2887	+	6.51754i	−0.384495	+	0.221988i
$863$	12.3467	+	7.12836i	0.420286	+	0.242652i	0.695200	−	0.718817i	$-0.255316\pi$
$863$	12.3467	+	7.12836i	0.420286	+	0.242652i	−0.274914	+	0.961469i	$0.588649\pi$
$864$	−0.354570	−	2.01087i	−0.0120627	−	0.0684111i
$865$		0			0
$866$	13.2567	−	22.9613i	0.450481	−	0.780257i
$867$	−1.69810	+	0.980400i	−0.0576706	+	0.0332961i
$868$	15.3895	+	18.3405i	0.522354	+	0.622517i
$869$	−45.8658	+	16.6938i	−1.55589	+	0.566298i
$870$		0			0
$871$	−12.3773	−	10.3858i	−0.419390	−	0.351910i
$872$	15.1267	+	2.66725i	0.512256	+	0.0903245i
$873$		−	21.7520i		−	0.736192i
$874$	−14.2071	+	2.39739i	−0.480562	+	0.0810929i
$875$		0			0
$876$	0.0701076	−	0.397600i	0.00236871	−	0.0134336i
$877$	28.0142	−	33.3860i	0.945972	−	1.12737i	−0.0457492	−	0.998953i	$-0.514568\pi$
$877$	28.0142	−	33.3860i	0.945972	−	1.12737i	0.991721	−	0.128412i	$-0.0409880\pi$
$878$	12.1144	−	33.2841i	0.408841	−	1.12328i
$879$	7.52259	−	2.73800i	0.253731	−	0.0923505i
$880$		0			0
$881$	−20.3075	−	35.1737i	−0.684178	−	1.18503i	−0.973694	−	0.227858i	$-0.926828\pi$
$881$	−20.3075	−	35.1737i	−0.684178	−	1.18503i	0.289517	−	0.957173i	$-0.406505\pi$
$882$	17.7754	+	10.2626i	0.598529	+	0.345561i
$883$	17.4966	−	3.08512i	0.588807	−	0.103823i	0.128696	−	0.991684i	$-0.458921\pi$
$883$	17.4966	−	3.08512i	0.588807	−	0.103823i	0.460111	+	0.887861i	$0.347810\pi$
$884$	−1.07873	−	6.11776i	−0.0362815	−	0.205762i
$885$		0			0
$886$	−14.8905	−	25.7912i	−0.500257	−	0.866471i
$887$	13.8060	+	16.4534i	0.463560	+	0.552450i	0.946290	−	0.323320i	$-0.104799\pi$
$887$	13.8060	+	16.4534i	0.463560	+	0.552450i	−0.482729	+	0.875770i	$0.660354\pi$
$888$	0.475129	+	1.30541i	0.0159443	+	0.0438066i
$889$	1.60132	+	0.582832i	0.0537065	+	0.0195476i
$890$		0			0
$891$	−7.61691	+	43.1976i	−0.255176	+	1.44717i
$892$			15.6459i			0.523863i
$893$	−40.5247	−	34.5158i	−1.35611	−	1.15503i
$894$	4.73917			0.158502
$895$		0			0
$896$	2.87939	+	2.41609i	0.0961935	+	0.0807159i
$897$	−0.512534	+	1.40818i	−0.0171130	+	0.0470176i
$898$	9.96340	+	27.3742i	0.332483	+	0.913490i
$899$	−46.4397	+	38.9676i	−1.54885	+	1.29964i
$900$		0			0
$901$	4.18479	−	7.24827i	0.139416	−	0.241475i
$902$	43.6265	−	7.69253i	1.45260	−	0.256133i
$903$	9.27174	−	1.63486i	0.308544	−	0.0544047i
$904$	4.11334	−	7.12452i	0.136808	−	0.236958i
$905$		0			0
$906$	0.433763	−	0.363970i	0.0144108	−	0.0120921i
$907$	16.4646	+	45.2362i	0.546699	+	1.50204i	0.838140	+	0.545455i	$0.183643\pi$
$907$	16.4646	+	45.2362i	0.546699	+	1.50204i	−0.291440	+	0.956589i	$0.594134\pi$
$908$	2.92252	−	8.02956i	0.0969873	−	0.266470i
$909$	−36.2918	−	30.4524i	−1.20372	−	1.01004i
$910$		0			0
$911$	11.8527			0.392696			0.196348	−	0.980534i	$-0.437092\pi$
$911$	11.8527			0.392696			0.196348	+	0.980534i	$0.437092\pi$
$912$	1.15247	+	0.981582i	0.0381620	+	0.0325034i
$913$			67.1380i			2.22194i
$914$	−4.07738	+	23.1240i	−0.134868	+	0.764873i
$915$		0			0
$916$	3.86484	+	1.40669i	0.127698	+	0.0464782i
$917$	4.80353	+	13.1976i	0.158626	+	0.435823i
$918$	6.24589	+	7.44356i	0.206145	+	0.245674i
$919$	10.2686	+	17.7857i	0.338729	+	0.586696i	0.984194	−	0.177094i	$-0.0566697\pi$
$919$	10.2686	+	17.7857i	0.338729	+	0.586696i	−0.645465	+	0.763790i	$0.723336\pi$
$920$		0			0
$921$	−0.254900	−	1.44561i	−0.00839924	−	0.0476345i
$922$	5.08499	−	0.896622i	0.167465	−	0.0295287i
$923$	6.65549	+	3.84255i	0.219068	+	0.126479i
$924$	3.61081	+	6.25411i	0.118787	+	0.205745i
$925$		0			0
$926$	−23.6091	+	8.59300i	−0.775842	+	0.282383i
$927$	7.29217	−	20.0351i	0.239506	−	0.658038i
$928$	−6.11776	+	7.29086i	−0.200825	+	0.239334i
$929$	3.65523	−	20.7298i	0.119924	−	0.680124i	−0.864270	−	0.503029i	$-0.832219\pi$
$929$	3.65523	−	20.7298i	0.119924	−	0.680124i	0.984194	−	0.177095i	$-0.0566700\pi$
$930$		0			0
$931$	−30.6386	+	5.17015i	−1.00414	+	0.169445i
$932$			2.51485i			0.0823767i
$933$	−2.86257	−	0.504748i	−0.0937162	−	0.0165247i
$934$	15.7947	+	13.2534i	0.516819	+	0.433663i
$935$		0			0
$936$	−3.53209	+	1.28558i	−0.115450	+	0.0420203i
$937$	13.7817	+	16.4244i	0.450230	+	0.536563i	0.942645	−	0.333798i	$-0.108330\pi$
$937$	13.7817	+	16.4244i	0.450230	+	0.536563i	−0.492415	+	0.870360i	$0.663886\pi$
$938$	−40.2906	+	23.2618i	−1.31553	+	0.759524i
$939$	3.20146	−	5.54508i	0.104476	−	0.180957i
$940$		0			0
$941$	4.12836	+	23.4131i	0.134581	+	0.763244i	0.975151	+	0.221542i	$0.0711089\pi$
$941$	4.12836	+	23.4131i	0.134581	+	0.763244i	−0.840570	+	0.541702i	$0.817780\pi$
$942$	1.87716	+	1.08378i	0.0611611	+	0.0353114i
$943$	22.9227	−	13.2344i	0.746466	−	0.430972i
$944$	−4.95471	+	4.15749i	−0.161262	+	0.135315i
$945$		0			0
$946$	−37.4920	−	13.6460i	−1.21897	−	0.443669i
$947$	26.0919	−	31.0951i	0.847874	−	1.01046i	−0.151883	−	0.988398i	$-0.548534\pi$
$947$	26.0919	−	31.0951i	0.847874	−	1.01046i	0.999757	−	0.0220579i	$-0.00702180\pi$
$948$	3.01763	+	0.532089i	0.0980079	+	0.0172814i
$949$	−1.51754			−0.0492615
$950$		0			0
$951$	10.7784			0.349513
$952$	−17.6154	−	3.10607i	−0.570918	−	0.100668i
$953$	−39.3157	+	46.8546i	−1.27356	+	1.51777i	−0.532294	+	0.846560i	$0.678670\pi$
$953$	−39.3157	+	46.8546i	−1.27356	+	1.51777i	−0.741267	+	0.671210i	$0.765775\pi$
$954$	−4.75877	−	1.73205i	−0.154071	−	0.0560772i
$955$		0			0
$956$	−7.12836	+	5.98140i	−0.230547	+	0.193452i
$957$	−15.8360	+	9.14290i	−0.511904	+	0.295548i
$958$	−10.0131	−	5.78106i	−0.323508	−	0.186778i
$959$	6.75372	+	38.3022i	0.218089	+	1.23684i
$960$		0			0
$961$	−4.78581	+	8.28926i	−0.154381	+	0.267396i
$962$	4.52206	−	2.61081i	0.145797	−	0.0841760i
$963$	−0.565258	−	0.673648i	−0.0182152	−	0.0217080i
$964$	−6.69594	+	2.43712i	−0.215662	+	0.0784944i
$965$		0			0
$966$	3.30541	+	2.77357i	0.106350	+	0.0892380i
$967$	−45.6078	−	8.04189i	−1.46665	−	0.258610i	−0.617419	−	0.786634i	$-0.711822\pi$
$967$	−45.6078	−	8.04189i	−1.46665	−	0.258610i	−0.849229	+	0.528024i	$0.822933\pi$
$968$		−	19.6040i		−	0.630097i
$969$	−7.08512	−	1.30315i	−0.227607	−	0.0418632i
$970$		0			0
$971$	2.82951	−	16.0469i	0.0908032	−	0.514971i	−0.905150	−	0.425093i	$-0.860241\pi$
$971$	2.82951	−	16.0469i	0.0908032	−	0.514971i	0.995953	−	0.0898774i	$-0.0286475\pi$
$972$	5.70756	−	6.80200i	0.183070	−	0.218174i
$973$	−2.52379	+	6.93407i	−0.0809091	+	0.222296i
$974$	4.61081	−	1.67820i	0.147740	−	0.0537730i
$975$		0			0
$976$	1.12061	+	1.94096i	0.0358700	+	0.0621287i
$977$	−6.59349	−	3.80675i	−0.210944	−	0.121789i	0.390806	−	0.920473i	$-0.372196\pi$
$977$	−6.59349	−	3.80675i	−0.210944	−	0.121789i	−0.601750	+	0.798684i	$0.705530\pi$
$978$	−1.24930	+	0.220285i	−0.0399482	+	0.00704394i
$979$	10.8136	+	61.3271i	0.345605	+	1.96002i
$980$		0			0
$981$	22.1138	+	38.3022i	0.706040	+	1.22290i
$982$	8.22983	+	9.80793i	0.262625	+	0.312984i
$983$	2.64025	+	7.25402i	0.0842108	+	0.231367i	0.974650	−	0.223735i	$-0.0718249\pi$
$983$	2.64025	+	7.25402i	0.0842108	+	0.231367i	−0.890439	+	0.455102i	$0.849603\pi$
$984$	−2.61334	−	0.951178i	−0.0833103	−	0.0303225i
$985$		0			0
$986$	7.86484	−	44.6037i	0.250467	−	1.42047i
$987$			15.9418i			0.507433i
$988$	2.88127	−	4.90673i	0.0916654	−	0.156104i
$989$	−23.8390			−0.758037
$990$		0			0
$991$	−44.9341	−	37.7042i	−1.42738	−	1.19771i	−0.947243	−	0.320518i	$-0.896143\pi$
$991$	−44.9341	−	37.7042i	−1.42738	−	1.19771i	−0.480135	−	0.877195i	$-0.659412\pi$
$992$	−2.17853	+	5.98545i	−0.0691683	+	0.190038i
$993$	1.02108	+	2.80541i	0.0324031	+	0.0890269i
$994$	16.9513	−	14.2238i	0.537663	−	0.451153i
$995$		0			0
$996$	2.10741	−	3.65014i	0.0667759	−	0.115659i
$997$	−59.5601	+	10.5021i	−1.88629	+	0.332604i	−0.993118	−	0.117115i	$-0.962635\pi$
$997$	−59.5601	+	10.5021i	−1.88629	+	0.332604i	−0.893170	+	0.449719i	$0.851524\pi$
$998$	4.05131	−	0.714355i	0.128242	−	0.0226125i
$999$	−4.08378	+	7.07331i	−0.129205	+	0.223790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.c.549.2		12
5.2	odd	4		950.2.l.c.701.1		6
5.3	odd	4		190.2.k.a.131.1	✓	6
5.4	even	2	inner	950.2.u.c.549.1		12
19.9	even	9	inner	950.2.u.c.199.1		12
95.3	even	36		3610.2.a.w.1.2		3
95.9	even	18	inner	950.2.u.c.199.2		12
95.28	odd	36		190.2.k.a.161.1	yes	6
95.47	odd	36		950.2.l.c.351.1		6
95.73	odd	36		3610.2.a.x.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.a.131.1	✓	6	5.3	odd	4
190.2.k.a.161.1	yes	6	95.28	odd	36
950.2.l.c.351.1		6	95.47	odd	36
950.2.l.c.701.1		6	5.2	odd	4
950.2.u.c.199.1		12	19.9	even	9	inner
950.2.u.c.199.2		12	95.9	even	18	inner
950.2.u.c.549.1		12	5.4	even	2	inner
950.2.u.c.549.2		12	1.1	even	1	trivial
3610.2.a.w.1.2		3	95.3	even	36
3610.2.a.x.1.2		3	95.73	odd	36

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.223238 + 0.266044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.266044 + 0.223238i) q^{6} +(3.25519 - 1.87939i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.500000 + 2.83564i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.223238 + 0.266044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-0.266044 + 0.223238i) q^{6} +(3.25519 - 1.87939i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.500000 + 2.83564i) q^{9} +(2.76604 - 4.79093i) q^{11} +(-0.300767 + 0.173648i) q^{12} +(0.839100 + 1.00000i) q^{13} +(3.53209 - 1.28558i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-4.68647 - 0.826352i) q^{17} +2.87939i q^{18} +(-2.77719 - 3.35965i) q^{19} +(-0.226682 + 1.28558i) q^{21} +(3.55596 - 4.23783i) q^{22} +(1.13052 - 3.10607i) q^{23} +(-0.326352 + 0.118782i) q^{24} +(0.652704 + 1.13052i) q^{26} +(-1.76833 - 1.02094i) q^{27} +(3.70167 - 0.652704i) q^{28} +(1.65270 + 9.37295i) q^{29} +(3.18479 + 5.51622i) q^{31} +(0.642788 + 0.766044i) q^{32} +(0.657115 + 1.80541i) q^{33} +(-4.47178 - 1.62760i) q^{34} +(-0.500000 + 2.83564i) q^{36} -4.00000i q^{37} +(-2.15160 - 3.79086i) q^{38} -0.453363 q^{39} +(6.13429 + 5.14728i) q^{41} +(-0.446476 + 1.22668i) q^{42} +(-2.46669 - 6.77719i) q^{43} +(4.23783 - 3.55596i) q^{44} +(1.65270 - 2.86257i) q^{46} +(12.0266 - 2.12061i) q^{47} +(-0.342020 + 0.0603074i) q^{48} +(3.56418 - 6.17334i) q^{49} +(1.26604 - 1.06234i) q^{51} +(0.446476 + 1.22668i) q^{52} +(-0.601535 + 1.65270i) q^{53} +(-1.56418 - 1.31250i) q^{54} +3.75877 q^{56} +(1.51379 + 0.0111444i) q^{57} +9.51754i q^{58} +(-1.12314 + 6.36965i) q^{59} +(2.10607 + 0.766546i) q^{61} +(2.17853 + 5.98545i) q^{62} +(6.95686 + 8.29086i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.333626 + 1.89209i) q^{66} +(-12.1893 + 2.14930i) q^{67} +(-4.12122 - 2.37939i) q^{68} +(0.573978 + 0.994159i) q^{69} +(5.53209 - 2.01352i) q^{71} +(-0.984808 + 2.70574i) q^{72} +(-0.747243 + 0.890530i) q^{73} +(0.694593 - 3.93923i) q^{74} +(-1.46064 - 4.10689i) q^{76} -20.7939i q^{77} +(-0.446476 - 0.0787257i) q^{78} +(-6.75877 - 5.67128i) q^{79} +(-7.45084 + 2.71188i) q^{81} +(5.14728 + 6.13429i) q^{82} +(-10.5102 + 6.06805i) q^{83} +(-0.652704 + 1.13052i) q^{84} +(-1.25237 - 7.10257i) q^{86} +(-2.86257 - 1.65270i) q^{87} +(4.79093 - 2.76604i) q^{88} +(-8.62314 + 7.23567i) q^{89} +(4.61081 + 1.67820i) q^{91} +(2.12467 - 2.53209i) q^{92} +(-2.17853 - 0.384133i) q^{93} +12.2121 q^{94} -0.347296 q^{96} +(-7.43961 - 1.31180i) q^{97} +(4.58202 - 5.46064i) q^{98} +(14.9684 + 5.44804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^6 + 6 * q^9	\( 12 q + 6 q^{6} + 6 q^{9} + 24 q^{11} + 24 q^{14} - 12 q^{19} + 24 q^{21} - 6 q^{24} + 12 q^{26} + 24 q^{29} + 24 q^{31} - 24 q^{34} - 6 q^{36} + 48 q^{39} + 54 q^{41} + 12 q^{44} + 24 q^{46} + 6 q^{49} + 6 q^{51} + 18 q^{54} - 6 q^{59} - 24 q^{61} + 6 q^{64} + 42 q^{66} - 24 q^{69} + 48 q^{71} - 36 q^{79} - 66 q^{81} - 12 q^{84} - 48 q^{86} - 96 q^{89} + 72 q^{91} + 48 q^{94} + 66 q^{99}+O(q^{100}) \) 12 * q + 6 * q^6 + 6 * q^9 + 24 * q^11 + 24 * q^14 - 12 * q^19 + 24 * q^21 - 6 * q^24 + 12 * q^26 + 24 * q^29 + 24 * q^31 - 24 * q^34 - 6 * q^36 + 48 * q^39 + 54 * q^41 + 12 * q^44 + 24 * q^46 + 6 * q^49 + 6 * q^51 + 18 * q^54 - 6 * q^59 - 24 * q^61 + 6 * q^64 + 42 * q^66 - 24 * q^69 + 48 * q^71 - 36 * q^79 - 66 * q^81 - 12 * q^84 - 48 * q^86 - 96 * q^89 + 72 * q^91 + 48 * q^94 + 66 * q^99

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