LMFDB - Embedded newform 950.2.u.b.149.2

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 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.2
Root			$0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	950.149
Dual form			950.2.u.b.899.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(-0.524005 - 1.43969i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.43969 - 0.524005i) q^{6} +(-2.33359 + 1.34730i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.500000 - 0.419550i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(-0.524005 - 1.43969i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.43969 - 0.524005i) q^{6} +(-2.33359 + 1.34730i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.500000 - 0.419550i) q^{9} +(-1.59240 + 2.75811i) q^{11} +(-1.32683 + 0.766044i) q^{12} +(-1.96962 + 5.41147i) q^{13} +(-0.467911 + 2.65366i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-4.18939 + 4.99273i) q^{17} -0.652704i q^{18} +(-2.82635 - 3.31839i) q^{19} +(3.16250 + 2.65366i) q^{21} +(1.08926 + 2.99273i) q^{22} +(0.684040 - 0.120615i) q^{23} +(-0.266044 + 1.50881i) q^{24} +(2.87939 + 4.98724i) q^{26} +(-4.84651 - 2.79813i) q^{27} +(1.73205 + 2.06418i) q^{28} +(2.16250 - 1.81456i) q^{29} +(-1.22668 - 2.12467i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(4.80526 + 0.847296i) q^{33} +(1.13176 + 6.41852i) q^{34} +(-0.500000 - 0.419550i) q^{36} +4.36959i q^{37} +(-4.35878 + 0.0320889i) q^{38} +8.82295 q^{39} +(0.326352 - 0.118782i) q^{41} +(4.06564 - 0.716881i) q^{42} +(5.97205 + 1.05303i) q^{43} +(2.99273 + 1.08926i) q^{44} +(0.347296 - 0.601535i) q^{46} +(-5.06975 - 6.04189i) q^{47} +(0.984808 + 1.17365i) q^{48} +(0.130415 - 0.225885i) q^{49} +(9.38326 + 3.41523i) q^{51} +(5.67128 + 1.00000i) q^{52} +(-8.08737 + 1.42602i) q^{53} +(-5.25877 + 1.91404i) q^{54} +2.69459 q^{56} +(-3.29644 + 5.80793i) q^{57} -2.82295i q^{58} +(-0.439693 - 0.368946i) q^{59} +(0.509800 + 2.89122i) q^{61} +(-2.41609 - 0.426022i) q^{62} +(-0.601535 + 1.65270i) q^{63} +(0.500000 + 0.866025i) q^{64} +(3.73783 - 3.13641i) q^{66} +(3.18701 + 3.79813i) q^{67} +(5.64436 + 3.25877i) q^{68} +(-0.532089 - 0.921605i) q^{69} +(-1.46791 + 8.32494i) q^{71} +(-0.642788 + 0.113341i) q^{72} +(-5.39246 - 14.8157i) q^{73} +(3.34730 + 2.80872i) q^{74} +(-2.77719 + 3.35965i) q^{76} -8.58172i q^{77} +(5.67128 - 6.75877i) q^{78} +(-8.51754 + 3.10013i) q^{79} +(-1.14883 + 6.51536i) q^{81} +(0.118782 - 0.326352i) q^{82} +(7.34013 - 4.23783i) q^{83} +(2.06418 - 3.57526i) q^{84} +(4.64543 - 3.89798i) q^{86} +(-3.74557 - 2.16250i) q^{87} +(2.75811 - 1.59240i) q^{88} +(7.27244 + 2.64695i) q^{89} +(-2.69459 - 15.2818i) q^{91} +(-0.237565 - 0.652704i) q^{92} +(-2.41609 + 2.87939i) q^{93} -7.88713 q^{94} +1.53209 q^{96} +(-0.223238 + 0.266044i) q^{97} +(-0.0892091 - 0.245100i) q^{98} +(0.360967 + 2.04715i) 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} - 12 q^{11} - 24 q^{14} - 36 q^{19} + 48 q^{21} + 6 q^{24} + 12 q^{26} + 36 q^{29} + 12 q^{31} + 24 q^{34} - 6 q^{36} + 24 q^{39} + 6 q^{41} + 30 q^{49} + 42 q^{51} - 18 q^{54} + 24 q^{56} + 6 q^{59} + 12 q^{61} + 6 q^{64} + 6 q^{66} + 12 q^{69} - 36 q^{71} + 36 q^{74} - 12 q^{76} - 12 q^{79} - 66 q^{81} - 12 q^{84} + 24 q^{86} - 24 q^{91} + 24 q^{94} - 42 q^{99}+O(q^{100}) $ 12 * q - 6 * q^6 + 6 * q^9 - 12 * q^11 - 24 * q^14 - 36 * q^19 + 48 * q^21 + 6 * q^24 + 12 * q^26 + 36 * q^29 + 12 * q^31 + 24 * q^34 - 6 * q^36 + 24 * q^39 + 6 * q^41 + 30 * q^49 + 42 * q^51 - 18 * q^54 + 24 * q^56 + 6 * q^59 + 12 * q^61 + 6 * q^64 + 6 * q^66 + 12 * q^69 - 36 * q^71 + 36 * q^74 - 12 * q^76 - 12 * q^79 - 66 * q^81 - 12 * q^84 + 24 * q^86 - 24 * q^91 + 24 * q^94 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	−0.524005	−	1.43969i	−0.302535	−	0.831207i	−0.994058	−	0.108853i	$-0.965282\pi$
$3$	−0.524005	−	1.43969i	−0.302535	−	0.831207i	0.691523	−	0.722354i	$-0.256940\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	−1.43969	−	0.524005i	−0.587752	−	0.213924i
$7$	−2.33359	+	1.34730i	−0.882013	+	0.509230i	−0.871321	−	0.490713i	$-0.836736\pi$
$7$	−2.33359	+	1.34730i	−0.882013	+	0.509230i	−0.0106911	+	0.999943i	$0.503403\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	0.500000	−	0.419550i	0.166667	−	0.139850i
$10$		0			0
$11$	−1.59240	+	2.75811i	−0.480126	+	0.831602i	−0.999740	−	0.0227990i	$-0.992742\pi$
$11$	−1.59240	+	2.75811i	−0.480126	+	0.831602i	0.519615	+	0.854401i	$0.326076\pi$
$12$	−1.32683	+	0.766044i	−0.383022	+	0.221138i
$13$	−1.96962	+	5.41147i	−0.546273	+	1.50087i	0.292432	+	0.956286i	$0.405536\pi$
$13$	−1.96962	+	5.41147i	−0.546273	+	1.50087i	−0.838705	+	0.544586i	$0.816687\pi$
$14$	−0.467911	+	2.65366i	−0.125055	+	0.709219i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−4.18939	+	4.99273i	−1.01608	+	1.21091i	−0.0387350	+	0.999250i	$0.512333\pi$
$17$	−4.18939	+	4.99273i	−1.01608	+	1.21091i	−0.977342	+	0.211664i	$0.932112\pi$
$18$		−	0.652704i		−	0.153844i
$19$	−2.82635	−	3.31839i	−0.648410	−	0.761292i
$19$	−2.82635	−	3.31839i	−0.648410	−	0.761292i
$20$		0			0
$21$	3.16250	+	2.65366i	0.690115	+	0.579075i
$22$	1.08926	+	2.99273i	0.232232	+	0.638051i
$23$	0.684040	−	0.120615i	0.142632	−	0.0251499i	−0.101876	−	0.994797i	$-0.532485\pi$
$23$	0.684040	−	0.120615i	0.142632	−	0.0251499i	0.244508	+	0.969647i	$0.421373\pi$
$24$	−0.266044	+	1.50881i	−0.0543061	+	0.307985i
$25$		0			0
$26$	2.87939	+	4.98724i	0.564694	+	0.978079i
$27$	−4.84651	−	2.79813i	−0.932711	−	0.538501i
$28$	1.73205	+	2.06418i	0.327327	+	0.390093i
$29$	2.16250	−	1.81456i	0.401567	−	0.336955i	−0.419532	−	0.907741i	$-0.637806\pi$
$29$	2.16250	−	1.81456i	0.401567	−	0.336955i	0.821099	+	0.570786i	$0.193361\pi$
$30$		0			0
$31$	−1.22668	−	2.12467i	−0.220319	−	0.381603i	0.734586	−	0.678515i	$-0.237376\pi$
$31$	−1.22668	−	2.12467i	−0.220319	−	0.381603i	−0.954905	+	0.296913i	$0.904043\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	4.80526	+	0.847296i	0.836488	+	0.147495i
$34$	1.13176	+	6.41852i	0.194095	+	1.10077i
$35$		0			0
$36$	−0.500000	−	0.419550i	−0.0833333	−	0.0699250i
$37$			4.36959i			0.718355i	0.933269	+	0.359178i	$0.116943\pi$
$37$			4.36959i			0.718355i	−0.933269	+	0.359178i	$0.883057\pi$
$38$	−4.35878	+	0.0320889i	−0.707088	+	0.00520550i
$39$	8.82295			1.41280
$40$		0			0
$41$	0.326352	−	0.118782i	0.0509676	−	0.0185507i	−0.316411	−	0.948622i	$-0.602478\pi$
$41$	0.326352	−	0.118782i	0.0509676	−	0.0185507i	0.367378	+	0.930072i	$0.380255\pi$
$42$	4.06564	−	0.716881i	0.627341	−	0.110617i
$43$	5.97205	+	1.05303i	0.910729	+	0.160586i	0.609334	−	0.792913i	$-0.291437\pi$
$43$	5.97205	+	1.05303i	0.910729	+	0.160586i	0.301395	+	0.953499i	$0.402548\pi$
$44$	2.99273	+	1.08926i	0.451170	+	0.164213i
$45$		0			0
$46$	0.347296	−	0.601535i	0.0512061	−	0.0886915i
$47$	−5.06975	−	6.04189i	−0.739499	−	0.881300i	0.256870	−	0.966446i	$-0.417309\pi$
$47$	−5.06975	−	6.04189i	−0.739499	−	0.881300i	−0.996368	+	0.0851459i	$0.972864\pi$
$48$	0.984808	+	1.17365i	0.142145	+	0.169402i
$49$	0.130415	−	0.225885i	0.0186307	−	0.0322693i
$50$		0			0
$51$	9.38326	+	3.41523i	1.31392	+	0.478227i
$52$	5.67128	+	1.00000i	0.786465	+	0.138675i
$53$	−8.08737	+	1.42602i	−1.11089	+	0.195879i	−0.698836	−	0.715282i	$-0.746298\pi$
$53$	−8.08737	+	1.42602i	−1.11089	+	0.195879i	−0.412050	+	0.911161i	$0.635187\pi$
$54$	−5.25877	+	1.91404i	−0.715628	+	0.260467i
$55$		0			0
$56$	2.69459			0.360080
$57$	−3.29644	+	5.80793i	−0.436625	+	0.769280i
$58$		−	2.82295i		−	0.370671i
$59$	−0.439693	−	0.368946i	−0.0572431	−	0.0480327i	0.613717	−	0.789526i	$-0.289673\pi$
$59$	−0.439693	−	0.368946i	−0.0572431	−	0.0480327i	−0.670960	+	0.741493i	$0.734118\pi$
$60$		0			0
$61$	0.509800	+	2.89122i	0.0652732	+	0.370183i	0.999894	+	0.0145378i	$0.00462769\pi$
$61$	0.509800	+	2.89122i	0.0652732	+	0.370183i	−0.934621	+	0.355645i	$0.884261\pi$
$62$	−2.41609	−	0.426022i	−0.306844	−	0.0541049i
$63$	−0.601535	+	1.65270i	−0.0757863	+	0.208221i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	3.73783	−	3.13641i	0.460095	−	0.386065i
$67$	3.18701	+	3.79813i	0.389356	+	0.464016i	0.924744	−	0.380590i	$-0.124279\pi$
$67$	3.18701	+	3.79813i	0.389356	+	0.464016i	−0.535388	+	0.844606i	$0.679835\pi$
$68$	5.64436	+	3.25877i	0.684479	+	0.395184i
$69$	−0.532089	−	0.921605i	−0.0640560	−	0.110948i
$70$		0			0
$71$	−1.46791	+	8.32494i	−0.174209	+	0.987988i	0.764844	+	0.644216i	$0.222816\pi$
$71$	−1.46791	+	8.32494i	−0.174209	+	0.987988i	−0.939053	+	0.343773i	$0.888295\pi$
$72$	−0.642788	+	0.113341i	−0.0757532	+	0.0133573i
$73$	−5.39246	−	14.8157i	−0.631140	−	1.73404i	−0.677917	−	0.735138i	$-0.737117\pi$
$73$	−5.39246	−	14.8157i	−0.631140	−	1.73404i	0.0467771	−	0.998905i	$-0.485105\pi$
$74$	3.34730	+	2.80872i	0.389115	+	0.326507i
$75$		0			0
$76$	−2.77719	+	3.35965i	−0.318565	+	0.385378i
$77$		−	8.58172i		−	0.977978i
$78$	5.67128	−	6.75877i	0.642146	−	0.765280i
$79$	−8.51754	+	3.10013i	−0.958298	+	0.348792i	−0.773366	−	0.633959i	$-0.781429\pi$
$79$	−8.51754	+	3.10013i	−0.958298	+	0.348792i	−0.184932	+	0.982751i	$0.559206\pi$
$80$		0			0
$81$	−1.14883	+	6.51536i	−0.127648	+	0.723929i
$82$	0.118782	−	0.326352i	0.0131173	−	0.0360395i
$83$	7.34013	−	4.23783i	0.805684	−	0.465162i	−0.0397709	−	0.999209i	$-0.512663\pi$
$83$	7.34013	−	4.23783i	0.805684	−	0.465162i	0.845455	+	0.534047i	$0.179329\pi$
$84$	2.06418	−	3.57526i	0.225220	−	0.390093i
$85$		0			0
$86$	4.64543	−	3.89798i	0.500930	−	0.420330i
$87$	−3.74557	−	2.16250i	−0.401567	−	0.231845i
$88$	2.75811	−	1.59240i	0.294016	−	0.169750i
$89$	7.27244	+	2.64695i	0.770877	+	0.280576i	0.697363	−	0.716718i	$-0.254356\pi$
$89$	7.27244	+	2.64695i	0.770877	+	0.280576i	0.0735139	+	0.997294i	$0.476579\pi$
$90$		0			0
$91$	−2.69459	−	15.2818i	−0.282470	−	1.60197i
$92$	−0.237565	−	0.652704i	−0.0247678	−	0.0680491i
$93$	−2.41609	+	2.87939i	−0.250537	+	0.298578i
$94$	−7.88713			−0.813495
$95$		0			0
$96$	1.53209			0.156368
$97$	−0.223238	+	0.266044i	−0.0226664	+	0.0270127i	−0.777259	−	0.629181i	$-0.783390\pi$
$97$	−0.223238	+	0.266044i	−0.0226664	+	0.0270127i	0.754592	+	0.656194i	$0.227835\pi$
$98$	−0.0892091	−	0.245100i	−0.00901148	−	0.0247588i
$99$	0.360967	+	2.04715i	0.0362785	+	0.205746i
$100$		0			0
$101$	0.347296	+	0.126406i	0.0345573	+	0.0125778i	0.359241	−	0.933245i	$-0.383036\pi$
$101$	0.347296	+	0.126406i	0.0345573	+	0.0125778i	−0.324684	+	0.945823i	$0.605258\pi$
$102$	8.64766	−	4.99273i	0.856245	−	0.494354i
$103$	−7.43199	−	4.29086i	−0.732295	−	0.422791i	0.0869659	−	0.996211i	$-0.472283\pi$
$103$	−7.43199	−	4.29086i	−0.732295	−	0.422791i	−0.819261	+	0.573420i	$0.805616\pi$
$104$	4.41147	−	3.70167i	0.432581	−	0.362978i
$105$		0			0
$106$	−4.10607	+	7.11192i	−0.398816	+	0.690770i
$107$	9.91890	−	5.72668i	0.958897	−	0.553619i	0.0630633	−	0.998010i	$-0.479913\pi$
$107$	9.91890	−	5.72668i	0.958897	−	0.553619i	0.895833	+	0.444390i	$0.146580\pi$
$108$	−1.91404	+	5.25877i	−0.184178	+	0.506025i
$109$	−1.50980	+	8.56250i	−0.144613	+	0.820139i	0.823065	+	0.567948i	$0.192262\pi$
$109$	−1.50980	+	8.56250i	−0.144613	+	0.820139i	−0.967677	+	0.252191i	$0.918849\pi$
$110$		0			0
$111$	6.29086	−	2.28969i	0.597102	−	0.217327i
$112$	1.73205	−	2.06418i	0.163663	−	0.195046i
$113$			2.85978i			0.269026i	0.990912	+	0.134513i	$0.0429470\pi$
$113$			2.85978i			0.269026i	−0.990912	+	0.134513i	$0.957053\pi$
$114$	2.33022	+	6.25849i	0.218245	+	0.586161i
$115$		0			0
$116$	−2.16250	−	1.81456i	−0.200783	−	0.168477i
$117$	1.28558	+	3.53209i	0.118851	+	0.326542i
$118$	−0.565258	+	0.0996702i	−0.0520362	+	0.00917539i
$119$	3.04963	−	17.2953i	0.279559	−	1.58546i
$120$		0			0
$121$	0.428548	+	0.742267i	0.0389589	+	0.0674789i
$122$	2.54250	+	1.46791i	0.230187	+	0.132898i
$123$	−0.342020	−	0.407604i	−0.0308389	−	0.0367524i
$124$	−1.87939	+	1.57699i	−0.168774	+	0.141618i
$125$		0			0
$126$	0.879385	+	1.52314i	0.0783419	+	0.135692i
$127$	−3.32774	+	9.14290i	−0.295290	+	0.811301i	0.699981	+	0.714161i	$0.253192\pi$
$127$	−3.32774	+	9.14290i	−0.295290	+	0.811301i	−0.995271	+	0.0971401i	$0.969030\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	−1.61334	−	9.14971i	−0.142047	−	0.805587i
$130$		0			0
$131$	−4.95471	−	4.15749i	−0.432895	−	0.363242i	0.400148	−	0.916451i	$-0.368959\pi$
$131$	−4.95471	−	4.15749i	−0.432895	−	0.363242i	−0.833043	+	0.553209i	$0.813403\pi$
$132$		−	4.87939i		−	0.424696i
$133$	11.0664	+	3.93582i	0.959578	+	0.341279i
$134$	4.95811			0.428316
$135$		0			0
$136$	6.12449	−	2.22913i	0.525170	−	0.191146i
$137$	−11.4833	+	2.02481i	−0.981084	+	0.172992i	−0.641115	−	0.767445i	$-0.721528\pi$
$137$	−11.4833	+	2.02481i	−0.981084	+	0.172992i	−0.339969	+	0.940437i	$0.610417\pi$
$138$	−1.04801	−	0.184793i	−0.0892126	−	0.0157306i
$139$	−7.76517	−	2.82629i	−0.658633	−	0.239723i	−0.00898688	−	0.999960i	$-0.502861\pi$
$139$	−7.76517	−	2.82629i	−0.658633	−	0.239723i	−0.649646	+	0.760237i	$0.725083\pi$
$140$		0			0
$141$	−6.04189	+	10.4649i	−0.508819	+	0.881300i
$142$	5.43372	+	6.47565i	0.455987	+	0.543425i
$143$	−11.7890	−	14.0496i	−0.985849	−	1.17489i
$144$	−0.326352	+	0.565258i	−0.0271960	+	0.0471048i
$145$		0			0
$146$	−14.8157	−	5.39246i	−1.22615	−	0.446284i
$147$	−0.393544	−	0.0693923i	−0.0324589	−	0.00572338i
$148$	4.30320	−	0.758770i	0.353721	−	0.0623705i
$149$	−15.4611	+	5.62738i	−1.26662	+	0.461013i	−0.885986	−	0.463712i	$-0.846517\pi$
$149$	−15.4611	+	5.62738i	−1.26662	+	0.461013i	−0.380637	+	0.924725i	$0.624295\pi$
$150$		0			0
$151$	4.65539			0.378850			0.189425	−	0.981895i	$-0.439338\pi$
$151$	4.65539			0.378850			0.189425	+	0.981895i	$0.439338\pi$
$152$	0.788496	+	4.28699i	0.0639554	+	0.347721i
$153$			4.25402i			0.343917i
$154$	−6.57398	−	5.51622i	−0.529746	−	0.444510i
$155$		0			0
$156$	−1.53209	−	8.68891i	−0.122665	−	0.695669i
$157$	−8.32494	−	1.46791i	−0.664402	−	0.117152i	−0.168731	−	0.985662i	$-0.553967\pi$
$157$	−8.32494	−	1.46791i	−0.664402	−	0.117152i	−0.495671	+	0.868510i	$0.665078\pi$
$158$	−3.10013	+	8.51754i	−0.246633	+	0.677619i
$159$	6.29086	+	10.8961i	0.498898	+	0.864116i
$160$		0			0
$161$	−1.43376	+	1.20307i	−0.112996	+	0.0948152i
$162$	4.25260	+	5.06805i	0.334116	+	0.398183i
$163$	−14.7654	−	8.52481i	−1.15652	−	0.667715i	−0.206050	−	0.978542i	$-0.566061\pi$
$163$	−14.7654	−	8.52481i	−1.15652	−	0.667715i	−0.950467	+	0.310826i	$0.899394\pi$
$164$	−0.173648	−	0.300767i	−0.0135596	−	0.0234860i
$165$		0			0
$166$	1.47178	−	8.34689i	0.114232	−	0.647844i
$167$	−3.14403	+	0.554378i	−0.243292	+	0.0428990i	−0.293965	−	0.955816i	$-0.594975\pi$
$167$	−3.14403	+	0.554378i	−0.243292	+	0.0428990i	0.0506721	+	0.998715i	$0.483864\pi$
$168$	−1.41198	−	3.87939i	−0.108937	−	0.299301i
$169$	−15.4461	−	12.9608i	−1.18816	−	0.996985i
$170$		0			0
$171$	−2.80541	−	0.473401i	−0.214535	−	0.0362019i
$172$		−	6.06418i		−	0.462389i
$173$	−6.19031	+	7.37733i	−0.470641	+	0.560888i	−0.948185	−	0.317720i	$-0.897083\pi$
$173$	−6.19031	+	7.37733i	−0.470641	+	0.560888i	0.477544	+	0.878608i	$0.341527\pi$
$174$	−4.06418	+	1.47924i	−0.308105	+	0.112141i
$175$		0			0
$176$	0.553033	−	3.13641i	0.0416865	−	0.236416i
$177$	−0.300767	+	0.826352i	−0.0226071	+	0.0621124i
$178$	6.70232	−	3.86959i	0.502360	−	0.290038i
$179$	9.40807	−	16.2953i	0.703192	−	1.21796i	−0.264148	−	0.964482i	$-0.585091\pi$
$179$	9.40807	−	16.2953i	0.703192	−	1.21796i	0.967340	−	0.253482i	$-0.0815760\pi$
$180$		0			0
$181$	2.12836	−	1.78590i	0.158199	−	0.132745i	−0.560252	−	0.828322i	$-0.689296\pi$
$181$	2.12836	−	1.78590i	0.158199	−	0.132745i	0.718451	+	0.695577i	$0.244851\pi$
$182$	−13.4386	−	7.75877i	−0.996134	−	0.575118i
$183$	3.89533	−	2.24897i	0.287951	−	0.166249i
$184$	−0.652704	−	0.237565i	−0.0481180	−	0.0175135i
$185$		0			0
$186$	0.652704	+	3.70167i	0.0478586	+	0.271419i
$187$	−7.09932	−	19.5052i	−0.519154	−	1.42636i
$188$	−5.06975	+	6.04189i	−0.369749	+	0.440650i
$189$	15.0797			1.09688
$190$		0			0
$191$	9.56212			0.691891			0.345945	−	0.938255i	$-0.387558\pi$
$191$	9.56212			0.691891			0.345945	+	0.938255i	$0.387558\pi$
$192$	0.984808	−	1.17365i	0.0710724	−	0.0847008i
$193$	8.09937	+	22.2528i	0.583006	+	1.60179i	0.783017	+	0.622001i	$0.213680\pi$
$193$	8.09937	+	22.2528i	0.583006	+	1.60179i	−0.200011	+	0.979794i	$0.564098\pi$
$194$	0.0603074	+	0.342020i	0.00432982	+	0.0245556i
$195$		0			0
$196$	−0.245100	−	0.0892091i	−0.0175071	−	0.00637208i
$197$	19.8512	−	11.4611i	1.41434	−	0.816570i	0.418547	−	0.908195i	$-0.362540\pi$
$197$	19.8512	−	11.4611i	1.41434	−	0.816570i	0.995794	+	0.0916253i	$0.0292062\pi$
$198$	1.80023	+	1.03936i	0.127937	+	0.0738643i
$199$	−7.72462	+	6.48173i	−0.547584	+	0.459477i	−0.874122	−	0.485707i	$-0.838562\pi$
$199$	−7.72462	+	6.48173i	−0.547584	+	0.459477i	0.326538	+	0.945184i	$0.394118\pi$
$200$		0			0
$201$	3.79813	−	6.57856i	0.267900	−	0.464016i
$202$	0.320070	−	0.184793i	0.0225201	−	0.0130020i
$203$	−2.60164	+	7.14796i	−0.182600	+	0.501688i
$204$	1.73396	−	9.83375i	0.121401	−	0.688500i
$205$		0			0
$206$	−8.06418	+	2.93512i	−0.561858	+	0.204500i
$207$	0.291416	−	0.347296i	0.0202548	−	0.0241388i
$208$		−	5.75877i		−	0.399299i
$209$	13.6532	−	2.51120i	0.944410	−	0.173703i
$210$		0			0
$211$	−17.1288	−	14.3728i	−1.17920	−	0.989464i	−0.999984	−	0.00565322i	$-0.998201\pi$
$211$	−17.1288	−	14.3728i	−1.17920	−	0.989464i	−0.179213	−	0.983810i	$-0.557355\pi$
$212$	2.80872	+	7.71688i	0.192903	+	0.529998i
$213$	12.7545	−	2.24897i	0.873927	−	0.154097i
$214$	1.98886	−	11.2794i	0.135955	−	0.771041i
$215$		0			0
$216$	2.79813	+	4.84651i	0.190389	+	0.329763i
$217$	5.72513	+	3.30541i	0.388647	+	0.224386i
$218$	5.58878	+	6.66044i	0.378520	+	0.451102i
$219$	−18.5043	+	15.5270i	−1.25041	+	1.04922i
$220$		0			0
$221$	−18.7665	−	32.5046i	−1.26237	−	2.18649i
$222$	2.28969	−	6.29086i	0.153674	−	0.422215i
$223$	−9.13538	−	1.61081i	−0.611751	−	0.107868i	−0.140815	−	0.990036i	$-0.544972\pi$
$223$	−9.13538	−	1.61081i	−0.611751	−	0.107868i	−0.470935	+	0.882168i	$0.656083\pi$
$224$	−0.467911	−	2.65366i	−0.0312636	−	0.177305i
$225$		0			0
$226$	2.19072	+	1.83823i	0.145725	+	0.122278i
$227$		−	7.73648i		−	0.513488i	−0.966479	−	0.256744i	$-0.917350\pi$
$227$		−	7.73648i		−	0.513488i	0.966479	−	0.256744i	$-0.0826498\pi$
$228$	6.29212	+	2.23783i	0.416706	+	0.148204i
$229$	23.0351			1.52220			0.761101	−	0.648634i	$-0.224659\pi$
$229$	23.0351			1.52220			0.761101	+	0.648634i	$0.224659\pi$
$230$		0			0
$231$	−12.3550	+	4.49687i	−0.812902	+	0.295872i
$232$	−2.78006	+	0.490200i	−0.182520	+	0.0321832i
$233$	8.27201	+	1.45858i	0.541917	+	0.0955546i	0.437905	−	0.899021i	$-0.355721\pi$
$233$	8.27201	+	1.45858i	0.541917	+	0.0955546i	0.104012	+	0.994576i	$0.466832\pi$
$234$	3.53209	+	1.28558i	0.230900	+	0.0840407i
$235$		0			0
$236$	−0.286989	+	0.497079i	−0.0186814	+	0.0323571i
$237$	8.92647	+	10.6382i	0.579837	+	0.691022i
$238$	−11.2887	−	13.4534i	−0.731739	−	0.872052i
$239$	−7.86484	+	13.6223i	−0.508734	+	0.881153i	0.491215	+	0.871038i	$0.336553\pi$
$239$	−7.86484	+	13.6223i	−0.508734	+	0.881153i	−0.999949	+	0.0101147i	$0.996780\pi$
$240$		0			0
$241$	−16.4474	−	5.98638i	−1.05947	−	0.385616i	−0.247242	−	0.968954i	$-0.579524\pi$
$241$	−16.4474	−	5.98638i	−1.05947	−	0.385616i	−0.812230	+	0.583337i	$0.801747\pi$
$242$	0.844075	+	0.148833i	0.0542592	+	0.00956736i
$243$	−6.55163	+	1.15523i	−0.420288	+	0.0741080i
$244$	2.75877	−	1.00411i	0.176612	−	0.0642816i
$245$		0			0
$246$	−0.532089			−0.0339247
$247$	23.5242	−	8.75877i	1.49681	−	0.557307i
$248$			2.45336i			0.155789i
$249$	−9.94743	−	8.34689i	−0.630393	−	0.528963i
$250$		0			0
$251$	1.48767	+	8.43702i	0.0939011	+	0.532540i	0.995079	+	0.0990893i	$0.0315930\pi$
$251$	1.48767	+	8.43702i	0.0939011	+	0.532540i	−0.901177	+	0.433450i	$0.857296\pi$
$252$	1.73205	+	0.305407i	0.109109	+	0.0192389i
$253$	−0.756594	+	2.07873i	−0.0475667	+	0.130688i
$254$	4.86484	+	8.42615i	0.305247	+	0.528703i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	5.15815	+	6.14724i	0.321756	+	0.383454i	0.902542	−	0.430602i	$-0.141699\pi$
$257$	5.15815	+	6.14724i	0.321756	+	0.383454i	−0.580785	+	0.814057i	$0.697254\pi$
$258$	−8.04612	−	4.64543i	−0.500930	−	0.289212i
$259$	−5.88713	−	10.1968i	−0.365808	−	0.633598i
$260$		0			0
$261$	0.319955	−	1.81456i	0.0198047	−	0.112318i
$262$	−6.36965	+	1.12314i	−0.393518	+	0.0693879i
$263$	2.03871	+	5.60132i	0.125712	+	0.345392i	0.986544	−	0.163499i	$-0.0522779\pi$
$263$	2.03871	+	5.60132i	0.125712	+	0.345392i	−0.860831	+	0.508891i	$0.830056\pi$
$264$	−3.73783	−	3.13641i	−0.230047	−	0.193033i
$265$		0			0
$266$	10.1284	−	5.94745i	0.621009	−	0.364662i
$267$		−	11.8571i		−	0.725643i
$268$	3.18701	−	3.79813i	0.194678	−	0.232008i
$269$	−1.07873	+	0.392624i	−0.0657711	+	0.0239387i	−0.374696	−	0.927148i	$-0.622253\pi$
$269$	−1.07873	+	0.392624i	−0.0657711	+	0.0239387i	0.308925	+	0.951086i	$0.400031\pi$
$270$		0			0
$271$	3.48246	−	19.7500i	0.211544	−	1.19973i	−0.675259	−	0.737581i	$-0.735968\pi$
$271$	3.48246	−	19.7500i	0.211544	−	1.19973i	0.886803	−	0.462147i	$-0.152921\pi$
$272$	2.22913	−	6.12449i	0.135161	−	0.371351i
$273$	−20.5891	+	11.8871i	−1.24611	+	0.719442i
$274$	−5.83022	+	10.0982i	−0.352217	+	0.610057i
$275$		0			0
$276$	−0.815207	+	0.684040i	−0.0490697	+	0.0411744i
$277$	15.0343	+	8.68004i	0.903322	+	0.521533i	0.878277	−	0.478153i	$-0.158694\pi$
$277$	15.0343	+	8.68004i	0.903322	+	0.521533i	0.0250457	+	0.999686i	$0.492027\pi$
$278$	−7.15642	+	4.13176i	−0.429213	+	0.247806i
$279$	−1.50475	−	0.547683i	−0.0900869	−	0.0327889i
$280$		0			0
$281$	0.507274	+	2.87689i	0.0302614	+	0.171621i	0.996193	−	0.0871772i	$-0.0277846\pi$
$281$	0.507274	+	2.87689i	0.0302614	+	0.171621i	−0.965931	+	0.258798i	$0.916674\pi$
$282$	4.13290	+	11.3550i	0.246110	+	0.676183i
$283$	6.09408	−	7.26264i	0.362255	−	0.431719i	−0.553875	−	0.832600i	$-0.686851\pi$
$283$	6.09408	−	7.26264i	0.362255	−	0.431719i	0.916130	+	0.400881i	$0.131296\pi$
$284$	8.45336			0.501615
$285$		0			0
$286$	−18.3405			−1.08450
$287$	−0.601535	+	0.716881i	−0.0355075	+	0.0423162i
$288$	0.223238	+	0.613341i	0.0131544	+	0.0361415i
$289$	−4.42427	−	25.0913i	−0.260251	−	1.47596i
$290$		0			0
$291$	0.500000	+	0.181985i	0.0293105	+	0.0106682i
$292$	−13.6542	+	7.88326i	−0.799052	+	0.461333i
$293$	23.6354	+	13.6459i	1.38079	+	0.797202i	0.992253	−	0.124230i	$-0.0396460\pi$
$293$	23.6354	+	13.6459i	1.38079	+	0.797202i	0.388541	+	0.921432i	$0.372979\pi$
$294$	−0.306123	+	0.256867i	−0.0178534	+	0.0149808i
$295$		0			0
$296$	2.18479	−	3.78417i	0.126988	−	0.219951i
$297$	15.4351	−	8.91147i	0.895637	−	0.517096i
$298$	−5.62738	+	15.4611i	−0.325985	+	0.895638i
$299$	−0.694593	+	3.93923i	−0.0401693	+	0.227812i
$300$		0			0
$301$	−15.3550	+	5.58878i	−0.885050	+	0.322132i
$302$	2.99243	−	3.56624i	0.172195	−	0.205214i
$303$		−	0.566237i		−	0.0325295i
$304$	3.79086	+	2.15160i	0.217421	+	0.123403i
$305$		0			0
$306$	3.25877	+	2.73443i	0.186292	+	0.156317i
$307$	7.29482	+	20.0424i	0.416337	+	1.14388i	0.953761	+	0.300565i	$0.0971753\pi$
$307$	7.29482	+	20.0424i	0.416337	+	1.14388i	−0.537424	+	0.843312i	$0.680602\pi$
$308$	−8.45134	+	1.49020i	−0.481560	+	0.0849120i
$309$	−2.28312	+	12.9482i	−0.129882	+	0.736598i
$310$		0			0
$311$	14.6459	+	25.3674i	0.830493	+	1.43846i	0.897648	+	0.440713i	$0.145274\pi$
$311$	14.6459	+	25.3674i	0.830493	+	1.43846i	−0.0671555	+	0.997743i	$0.521392\pi$
$312$	−7.64090	−	4.41147i	−0.432581	−	0.249751i
$313$	3.57466	+	4.26011i	0.202052	+	0.240796i	0.857550	−	0.514401i	$-0.171986\pi$
$313$	3.57466	+	4.26011i	0.202052	+	0.240796i	−0.655498	+	0.755197i	$0.727541\pi$
$314$	−6.47565	+	5.43372i	−0.365442	+	0.306642i
$315$		0			0
$316$	4.53209	+	7.84981i	0.254950	+	0.441586i
$317$	−1.30082	+	3.57398i	−0.0730614	+	0.200735i	−0.970848	−	0.239696i	$-0.922952\pi$
$317$	−1.30082	+	3.57398i	−0.0730614	+	0.200735i	0.897786	+	0.440431i	$0.145174\pi$
$318$	12.3906	+	2.18479i	0.694829	+	0.122517i
$319$	1.56118	+	8.85392i	0.0874096	+	0.495724i
$320$		0			0
$321$	−13.4422	−	11.2794i	−0.750271	−	0.629553i
$322$			1.87164i			0.104303i
$323$	28.4085	−	0.209141i	1.58069	−	0.0116369i
$324$	6.61587			0.367548
$325$		0			0
$326$	−16.0214	+	5.83132i	−0.887344	+	0.322967i
$327$	13.1185	−	2.31315i	0.725456	−	0.127917i
$328$	−0.342020	−	0.0603074i	−0.0188849	−	0.00332992i
$329$	19.9709	+	7.26881i	1.10103	+	0.400743i
$330$		0			0
$331$	−10.2110	+	17.6859i	−0.561245	+	0.972104i	0.436144	+	0.899877i	$0.356344\pi$
$331$	−10.2110	+	17.6859i	−0.561245	+	0.972104i	−0.997388	+	0.0722272i	$0.976989\pi$
$332$	−5.44804	−	6.49273i	−0.299000	−	0.356335i
$333$	1.83326	+	2.18479i	0.100462	+	0.119726i
$334$	−1.59627	+	2.76481i	−0.0873438	+	0.151284i
$335$		0			0
$336$	−3.87939	−	1.41198i	−0.211638	−	0.0770299i
$337$	−20.0019	−	3.52687i	−1.08957	−	0.192121i	−0.400128	−	0.916459i	$-0.631034\pi$
$337$	−20.0019	−	3.52687i	−1.08957	−	0.192121i	−0.689445	+	0.724338i	$0.742145\pi$
$338$	−19.8571	+	3.50134i	−1.08008	+	0.190448i
$339$	4.11721	−	1.49854i	0.223616	−	0.0813896i
$340$		0			0
$341$	7.81345			0.423122
$342$	−2.16593	+	1.84477i	−0.117120	+	0.0997537i
$343$		−	18.1593i		−	0.980511i
$344$	−4.64543	−	3.89798i	−0.250465	−	0.210165i
$345$		0			0
$346$	1.67230	+	9.48411i	0.0899036	+	0.509869i
$347$	−5.13560	−	0.905544i	−0.275693	−	0.0486122i	0.0340920	−	0.999419i	$-0.489146\pi$
$347$	−5.13560	−	0.905544i	−0.275693	−	0.0486122i	−0.309785	+	0.950807i	$0.600257\pi$
$348$	−1.47924	+	4.06418i	−0.0792956	+	0.217863i
$349$	7.17024	+	12.4192i	0.383814	+	0.664786i	0.991604	−	0.129312i	$-0.0412769\pi$
$349$	7.17024	+	12.4192i	0.383814	+	0.664786i	−0.607790	+	0.794098i	$0.707944\pi$
$350$		0			0
$351$	24.6878	−	20.7155i	1.31774	−	1.10571i
$352$	−2.04715	−	2.43969i	−0.109113	−	0.130036i
$353$	−22.7331	−	13.1250i	−1.20996	−	0.698571i	−0.247209	−	0.968962i	$-0.579514\pi$
$353$	−22.7331	−	13.1250i	−1.20996	−	0.698571i	−0.962750	+	0.270391i	$0.912847\pi$
$354$	0.439693	+	0.761570i	0.0233694	+	0.0404770i
$355$		0			0
$356$	1.34389	−	7.62159i	0.0712262	−	0.403944i
$357$	−26.4980	+	4.67230i	−1.40242	+	0.247285i
$358$	−6.43550	−	17.6814i	−0.340127	−	0.934490i
$359$	25.8084	+	21.6558i	1.36212	+	1.14295i	0.975323	+	0.220784i	$0.0708615\pi$
$359$	25.8084	+	21.6558i	1.36212	+	1.14295i	0.386792	+	0.922167i	$0.373583\pi$
$360$		0			0
$361$	−3.02347	+	18.7579i	−0.159130	+	0.987258i
$362$		−	2.77837i		−	0.146028i
$363$	0.844075	−	1.00593i	0.0443025	−	0.0527976i
$364$	−14.5817	+	5.30731i	−0.764290	+	0.278179i
$365$		0			0
$366$	0.781059	−	4.42961i	0.0408266	−	0.231539i
$367$	3.58056	−	9.83750i	0.186903	−	0.513513i	−0.810483	−	0.585762i	$-0.800795\pi$
$367$	3.58056	−	9.83750i	0.186903	−	0.513513i	0.997387	+	0.0722488i	$0.0230176\pi$
$368$	−0.601535	+	0.347296i	−0.0313572	+	0.0181041i
$369$	0.113341	−	0.196312i	0.00590029	−	0.0102196i
$370$		0			0
$371$	16.9513	−	14.2238i	0.880068	−	0.738465i
$372$	3.25519	+	1.87939i	0.168774	+	0.0974416i
$373$	20.7003	−	11.9513i	1.07182	−	0.618815i	0.143141	−	0.989702i	$-0.454280\pi$
$373$	20.7003	−	11.9513i	1.07182	−	0.618815i	0.928678	+	0.370887i	$0.120946\pi$
$374$	−19.5052	−	7.09932i	−1.00859	−	0.367097i
$375$		0			0
$376$	1.36959	+	7.76730i	0.0706310	+	0.400568i
$377$	5.56012	+	15.2763i	0.286361	+	0.786770i
$378$	9.69302	−	11.5517i	0.498555	−	0.594155i
$379$	−17.8135			−0.915016			−0.457508	−	0.889206i	$-0.651258\pi$
$379$	−17.8135			−0.915016			−0.457508	+	0.889206i	$0.651258\pi$
$380$		0			0
$381$	14.9067			0.763695
$382$	6.14641	−	7.32501i	0.314478	−	0.374780i
$383$	−8.57775	−	23.5672i	−0.438302	−	1.20423i	−0.940596	−	0.339529i	$-0.889732\pi$
$383$	−8.57775	−	23.5672i	−0.438302	−	1.20423i	0.502293	−	0.864697i	$-0.332490\pi$
$384$	−0.266044	−	1.50881i	−0.0135765	−	0.0769963i
$385$		0			0
$386$	22.2528	+	8.09937i	1.13264	+	0.412247i
$387$	3.42782	−	1.97906i	0.174246	−	0.100601i
$388$	0.300767	+	0.173648i	0.0152692	+	0.00881565i
$389$	7.21482	−	6.05395i	0.365806	−	0.306948i	−0.441294	−	0.897363i	$-0.645480\pi$
$389$	7.21482	−	6.05395i	0.365806	−	0.306948i	0.807100	+	0.590415i	$0.201036\pi$
$390$		0			0
$391$	−2.26352	+	3.92053i	−0.114471	+	0.198270i
$392$	−0.225885	+	0.130415i	−0.0114089	+	0.00658695i
$393$	−3.38922	+	9.31180i	−0.170964	+	0.469718i
$394$	3.98040	−	22.5740i	0.200530	−	1.13726i
$395$		0			0
$396$	1.95336	−	0.710966i	0.0981602	−	0.0357274i
$397$	4.40441	−	5.24897i	0.221051	−	0.263438i	−0.644110	−	0.764933i	$-0.722772\pi$
$397$	4.40441	−	5.24897i	0.221051	−	0.263438i	0.865161	+	0.501495i	$0.167216\pi$
$398$			10.0838i			0.505454i
$399$	−0.132474	−	17.9946i	−0.00663201	−	0.900857i
$400$		0			0
$401$	3.63634	+	3.05126i	0.181590	+	0.152372i	0.729052	−	0.684458i	$-0.239961\pi$
$401$	3.63634	+	3.05126i	0.181590	+	0.152372i	−0.547461	+	0.836831i	$0.684406\pi$
$402$	−2.59808	−	7.13816i	−0.129580	−	0.356019i
$403$	13.9137	−	2.45336i	0.693091	−	0.122211i
$404$	0.0641778	−	0.363970i	0.00319296	−	0.0181082i
$405$		0			0
$406$	3.80335	+	6.58759i	0.188757	+	0.326937i
$407$	−12.0518	−	6.95811i	−0.597386	−	0.344901i
$408$	−6.41852	−	7.64930i	−0.317764	−	0.378697i
$409$	−24.2781	+	20.3718i	−1.20048	+	1.00732i	−0.200860	+	0.979620i	$0.564373\pi$
$409$	−24.2781	+	20.3718i	−1.20048	+	1.00732i	−0.999616	+	0.0276988i	$0.991182\pi$
$410$		0			0
$411$	8.93242	+	15.4714i	0.440604	+	0.763148i
$412$	−2.93512	+	8.06418i	−0.144603	+	0.397294i
$413$	1.52314	+	0.268571i	0.0749488	+	0.0132155i
$414$	−0.0787257	−	0.446476i	−0.00386916	−	0.0219431i
$415$		0			0
$416$	−4.41147	−	3.70167i	−0.216290	−	0.181489i
$417$			12.6604i			0.619985i
$418$	6.85240	−	12.0731i	0.335162	−	0.590515i
$419$	11.0101			0.537879			0.268939	−	0.963157i	$-0.413327\pi$
$419$	11.0101			0.537879			0.268939	+	0.963157i	$0.413327\pi$
$420$		0			0
$421$	8.14290	−	2.96377i	0.396861	−	0.144446i	−0.135877	−	0.990726i	$-0.543385\pi$
$421$	8.14290	−	2.96377i	0.396861	−	0.144446i	0.532738	+	0.846280i	$0.321163\pi$
$422$	−22.0204	+	3.88279i	−1.07194	+	0.189011i
$423$	−5.06975	−	0.893933i	−0.246500	−	0.0434645i
$424$	7.71688	+	2.80872i	0.374765	+	0.136403i
$425$		0			0
$426$	6.47565	−	11.2162i	0.313746	−	0.543425i
$427$	−5.08499	−	6.06006i	−0.246080	−	0.293267i
$428$	−7.36208	−	8.77379i	−0.355860	−	0.424097i
$429$	−14.0496	+	24.3347i	−0.678323	+	1.17489i
$430$		0			0
$431$	28.0847	+	10.2220i	1.35279	+	0.492376i	0.913818	−	0.406123i	$-0.133120\pi$
$431$	28.0847	+	10.2220i	1.35279	+	0.492376i	0.438975	+	0.898499i	$0.355342\pi$
$432$	5.51125	+	0.971782i	0.265160	+	0.0467549i
$433$	−9.12014	+	1.60813i	−0.438286	+	0.0772816i	−0.388437	−	0.921475i	$-0.626985\pi$
$433$	−9.12014	+	1.60813i	−0.438286	+	0.0772816i	−0.0498486	+	0.998757i	$0.515874\pi$
$434$	6.21213	−	2.26103i	0.298192	−	0.108533i
$435$		0			0
$436$	8.69459			0.416395
$437$	−2.33359	−	1.92902i	−0.111631	−	0.0922773i
$438$			24.1557i			1.15420i
$439$	−15.9813	−	13.4099i	−0.762747	−	0.640021i	0.176093	−	0.984374i	$-0.443654\pi$
$439$	−15.9813	−	13.4099i	−0.762747	−	0.640021i	−0.938840	+	0.344352i	$0.888098\pi$
$440$		0			0
$441$	−0.0295627	−	0.167658i	−0.00140775	−	0.00798372i
$442$	−36.9628	−	6.51754i	−1.75814	−	0.310008i
$443$	8.14966	−	22.3910i	0.387202	−	1.06383i	−0.581054	−	0.813865i	$-0.697359\pi$
$443$	8.14966	−	22.3910i	0.387202	−	1.06383i	0.968255	−	0.249963i	$-0.0804185\pi$
$444$	−3.34730	−	5.79769i	−0.158856	−	0.275146i
$445$		0			0
$446$	−7.10607	+	5.96270i	−0.336482	+	0.282342i
$447$	16.2034	+	19.3105i	0.766395	+	0.913353i
$448$	−2.33359	−	1.34730i	−0.110252	−	0.0636538i
$449$	−1.09105	−	1.88976i	−0.0514899	−	0.0891832i	0.839132	−	0.543928i	$-0.183064\pi$
$449$	−1.09105	−	1.88976i	−0.0514899	−	0.0891832i	−0.890622	+	0.454745i	$0.849730\pi$
$450$		0			0
$451$	−0.192066	+	1.08926i	−0.00904406	+	0.0512914i
$452$	2.81634	−	0.496596i	0.132469	−	0.0233579i
$453$	−2.43945	−	6.70233i	−0.114615	−	0.314903i
$454$	−5.92649	−	4.97291i	−0.278144	−	0.233390i
$455$		0			0
$456$	5.75877	−	3.38160i	0.269679	−	0.158358i
$457$		−	1.78106i		−	0.0833144i	−0.999132	−	0.0416572i	$-0.986736\pi$
$457$		−	1.78106i		−	0.0833144i	0.999132	−	0.0416572i	$-0.0132637\pi$
$458$	14.8067	−	17.6459i	0.691870	−	0.824539i
$459$	34.2743	−	12.4748i	1.59979	−	0.582274i
$460$		0			0
$461$	−2.68954	+	15.2531i	−0.125264	+	0.710410i	0.855886	+	0.517164i	$0.173012\pi$
$461$	−2.68954	+	15.2531i	−0.125264	+	0.710410i	−0.981150	+	0.193245i	$0.938099\pi$
$462$	−4.49687	+	12.3550i	−0.209213	+	0.574808i
$463$	−2.34699	+	1.35504i	−0.109074	+	0.0629739i	−0.553545	−	0.832820i	$-0.686725\pi$
$463$	−2.34699	+	1.35504i	−0.109074	+	0.0629739i	0.444471	+	0.895793i	$0.353392\pi$
$464$	−1.41147	+	2.44474i	−0.0655260	+	0.113494i
$465$		0			0
$466$	6.43448	−	5.39917i	0.298071	−	0.250112i
$467$	11.1834	+	6.45677i	0.517508	+	0.298784i	0.735915	−	0.677074i	$-0.236752\pi$
$467$	11.1834	+	6.45677i	0.517508	+	0.298784i	−0.218406	+	0.975858i	$0.570086\pi$
$468$	3.25519	−	1.87939i	0.150471	−	0.0868746i
$469$	−12.5544	−	4.56942i	−0.579707	−	0.210996i
$470$		0			0
$471$	2.24897	+	12.7545i	0.103627	+	0.587698i
$472$	0.196312	+	0.539363i	0.00903599	+	0.0248262i
$473$	−12.4143	+	14.7947i	−0.570808	+	0.680262i
$474$	13.8871			0.637857
$475$		0			0
$476$	−17.5621			−0.804958
$477$	−3.44540	+	4.10607i	−0.157754	+	0.188004i
$478$	5.37987	+	14.7811i	0.246069	+	0.676070i
$479$	3.22163	+	18.2708i	0.147200	+	0.834813i	0.965574	+	0.260127i	$0.0837645\pi$
$479$	3.22163	+	18.2708i	0.147200	+	0.834813i	−0.818374	+	0.574685i	$0.805124\pi$
$480$		0			0
$481$	−23.6459	−	8.60640i	−1.07816	−	0.392418i
$482$	−15.1580	+	8.75150i	−0.690430	+	0.398620i
$483$	2.48335	+	1.43376i	0.112996	+	0.0652385i
$484$	0.656574	−	0.550931i	0.0298443	−	0.0250423i
$485$		0			0
$486$	−3.32635	+	5.76141i	−0.150886	+	0.261343i
$487$	−35.6573	+	20.5868i	−1.61579	+	0.932876i	−0.627795	+	0.778379i	$0.716042\pi$
$487$	−35.6573	+	20.5868i	−1.61579	+	0.932876i	−0.987993	+	0.154497i	$0.950624\pi$
$488$	1.00411	−	2.75877i	0.0454539	−	0.124884i
$489$	−4.53596	+	25.7247i	−0.205123	+	1.16331i
$490$		0			0
$491$	21.2160	−	7.72199i	0.957465	−	0.348489i	0.184425	−	0.982847i	$-0.440958\pi$
$491$	21.2160	−	7.72199i	0.957465	−	0.348489i	0.773040	+	0.634358i	$0.218735\pi$
$492$	−0.342020	+	0.407604i	−0.0154195	+	0.0183762i
$493$			18.3987i			0.828635i
$494$	8.41147	−	23.6506i	0.378450	−	1.06409i
$495$		0			0
$496$	1.87939	+	1.57699i	0.0843869	+	0.0708090i
$497$	−7.79066	−	21.4047i	−0.349459	−	0.960131i
$498$	−12.7882	+	2.25490i	−0.573052	+	0.101044i
$499$	5.09286	−	28.8831i	0.227988	−	1.29298i	−0.628902	−	0.777484i	$-0.716495\pi$
$499$	5.09286	−	28.8831i	0.227988	−	1.29298i	0.856890	−	0.515499i	$-0.172393\pi$
$500$		0			0
$501$	2.44562	+	4.23594i	0.109262	+	0.189248i
$502$	7.41939	+	4.28359i	0.331143	+	0.191186i
$503$	21.6085	+	25.7520i	0.963474	+	1.14822i	0.988905	+	0.148547i	$0.0474595\pi$
$503$	21.6085	+	25.7520i	0.963474	+	1.14822i	−0.0254316	+	0.999677i	$0.508096\pi$
$504$	1.34730	−	1.13052i	0.0600133	−	0.0503572i
$505$		0			0
$506$	1.10607	+	1.91576i	0.0491707	+	0.0851661i
$507$	−10.5657	+	29.0292i	−0.469241	+	1.28923i
$508$	9.58186	+	1.68954i	0.425126	+	0.0749612i
$509$	−0.699645	−	3.96788i	−0.0310112	−	0.175873i	0.965368	−	0.260891i	$-0.0840164\pi$
$509$	−0.699645	−	3.96788i	−0.0310112	−	0.175873i	−0.996379	+	0.0850178i	$0.972905\pi$
$510$		0			0
$511$	32.5449	+	27.3084i	1.43970	+	1.20805i
$512$		−	1.00000i		−	0.0441942i
$513$	4.41263	+	23.9911i	0.194822	+	1.05923i
$514$	8.02465			0.353952
$515$		0			0
$516$	−8.73055	+	3.17766i	−0.384341	+	0.139889i
$517$	24.7372	−	4.36184i	1.08794	−	0.191834i
$518$	−11.5954	−	2.04458i	−0.509472	−	0.0898336i
$519$	13.8648	+	5.04639i	0.608599	+	0.221512i
$520$		0			0
$521$	−2.49479	+	4.32110i	−0.109299	+	0.189311i	−0.915486	−	0.402349i	$-0.868194\pi$
$521$	−2.49479	+	4.32110i	−0.109299	+	0.189311i	0.806188	+	0.591660i	$0.201527\pi$
$522$	−1.18437	−	1.41147i	−0.0518384	−	0.0617785i
$523$	−17.0677	−	20.3405i	−0.746318	−	0.889427i	0.250583	−	0.968095i	$-0.419378\pi$
$523$	−17.0677	−	20.3405i	−0.746318	−	0.889427i	−0.996901	+	0.0786677i	$0.974933\pi$
$524$	−3.23396	+	5.60138i	−0.141276	+	0.244697i
$525$		0			0
$526$	5.60132	+	2.03871i	0.244229	+	0.0888921i
$527$	15.7470	+	2.77662i	0.685949	+	0.120951i
$528$	−4.80526	+	0.847296i	−0.209122	+	0.0368738i
$529$	−21.1596	+	7.70145i	−0.919981	+	0.334846i
$530$		0			0
$531$	−0.374638			−0.0162579
$532$	1.95437	−	11.5817i	0.0847326	−	0.502131i
$533$			2.00000i			0.0866296i
$534$	−9.08306	−	7.62159i	−0.393063	−	0.329819i
$535$		0			0
$536$	−0.860967	−	4.88279i	−0.0371881	−	0.210904i
$537$	−28.3900	−	5.00593i	−1.22512	−	0.216022i
$538$	−0.392624	+	1.07873i	−0.0169272	+	0.0465072i
$539$	0.415345	+	0.719398i	0.0178902	+	0.0309867i
$540$		0			0
$541$	−9.17024	+	7.69475i	−0.394260	+	0.330823i	−0.818270	−	0.574834i	$-0.805067\pi$
$541$	−9.17024	+	7.69475i	−0.394260	+	0.330823i	0.424010	+	0.905657i	$0.360622\pi$
$542$	−12.8909	−	15.3628i	−0.553712	−	0.659888i
$543$	−3.68642	−	2.12836i	−0.158199	−	0.0913365i
$544$	−3.25877	−	5.64436i	−0.139719	−	0.242000i
$545$		0			0
$546$	−4.12836	+	23.4131i	−0.176677	+	1.00199i
$547$	3.14809	−	0.555093i	0.134603	−	0.0237341i	−0.105941	−	0.994372i	$-0.533785\pi$
$547$	3.14809	−	0.555093i	0.134603	−	0.0237341i	0.240543	+	0.970638i	$0.422674\pi$
$548$	3.98811	+	10.9572i	0.170363	+	0.468070i
$549$	1.46791	+	1.23172i	0.0626489	+	0.0525687i
$550$		0			0
$551$	−12.1334	−	2.04746i	−0.516901	−	0.0872249i
$552$			1.06418i			0.0452944i
$553$	15.6996	−	18.7101i	0.667616	−	0.795633i
$554$	16.3131	−	5.93750i	0.693079	−	0.252260i
$555$		0			0
$556$	−1.43494	+	8.13798i	−0.0608552	+	0.345127i
$557$	8.20037	−	22.5303i	0.347461	−	0.954641i	−0.635706	−	0.771931i	$-0.719291\pi$
$557$	8.20037	−	22.5303i	0.347461	−	0.954641i	0.983167	−	0.182710i	$-0.0584868\pi$
$558$	−1.38678	+	0.800660i	−0.0587072	+	0.0338946i
$559$	−17.4611	+	30.2435i	−0.738526	+	1.27916i
$560$		0			0
$561$	−24.3614	+	20.4417i	−1.02854	+	0.863048i
$562$	2.52990	+	1.46064i	0.106717	+	0.0616133i
$563$	−7.58380	+	4.37851i	−0.319619	+	0.184532i	−0.651223	−	0.758887i	$-0.725744\pi$
$563$	−7.58380	+	4.37851i	−0.319619	+	0.184532i	0.331604	+	0.943419i	$0.392410\pi$
$564$	11.3550	+	4.13290i	0.478133	+	0.174026i
$565$		0			0
$566$	−1.64631	−	9.33667i	−0.0691994	−	0.392450i
$567$	−6.09722	−	16.7520i	−0.256059	−	0.703516i
$568$	5.43372	−	6.47565i	0.227994	−	0.271712i
$569$	36.4201			1.52681			0.763406	−	0.645919i	$-0.223526\pi$
$569$	36.4201			1.52681			0.763406	+	0.645919i	$0.223526\pi$
$570$		0			0
$571$	34.2131			1.43177			0.715886	−	0.698217i	$-0.246023\pi$
$571$	34.2131			1.43177			0.715886	+	0.698217i	$0.246023\pi$
$572$	−11.7890	+	14.0496i	−0.492924	+	0.587445i
$573$	−5.01060	−	13.7665i	−0.209321	−	0.575104i
$574$	0.162504	+	0.921605i	0.00678278	+	0.0384670i
$575$		0			0
$576$	0.613341	+	0.223238i	0.0255559	+	0.00930157i
$577$	−13.4319	+	7.75490i	−0.559177	+	0.322841i	−0.752815	−	0.658232i	$-0.771304\pi$
$577$	−13.4319	+	7.75490i	−0.559177	+	0.322841i	0.193638	+	0.981073i	$0.437971\pi$
$578$	−22.0649	−	12.7392i	−0.917778	−	0.529880i
$579$	27.7931	−	23.3212i	1.15504	−	0.969196i
$580$		0			0
$581$	−11.4192	+	19.7787i	−0.473749	+	0.820557i
$582$	0.460802	−	0.266044i	0.0191009	−	0.0110279i
$583$	8.94517	−	24.5767i	0.370471	−	1.01786i
$584$	−2.73783	+	15.5270i	−0.113292	+	0.642511i
$585$		0			0
$586$	25.6459	−	9.33434i	1.05942	−	0.385598i
$587$	−7.44459	+	8.87211i	−0.307271	+	0.366191i	−0.897477	−	0.441061i	$-0.854602\pi$
$587$	−7.44459	+	8.87211i	−0.307271	+	0.366191i	0.590206	+	0.807253i	$0.299047\pi$
$588$			0.399615i			0.0164798i
$589$	−3.58347	+	10.0757i	−0.147654	+	0.415162i
$590$		0			0
$591$	−26.9026	−	22.5740i	−1.10663	−	0.928569i
$592$	−1.49449	−	4.10607i	−0.0614230	−	0.168758i
$593$	45.6880	−	8.05603i	1.87618	−	0.330821i	0.885242	−	0.465131i	$-0.153993\pi$
$593$	45.6880	−	8.05603i	1.87618	−	0.330821i	0.990939	+	0.134310i	$0.0428817\pi$
$594$	3.09492	−	17.5522i	0.126986	−	0.720175i
$595$		0			0
$596$	8.22668	+	14.2490i	0.336978	+	0.583663i
$597$	13.3794	+	7.72462i	0.547584	+	0.316148i
$598$	2.57115	+	3.06418i	0.105142	+	0.125304i
$599$	−19.6355	+	16.4761i	−0.802283	+	0.673196i	−0.948753	−	0.316019i	$-0.897654\pi$
$599$	−19.6355	+	16.4761i	−0.802283	+	0.673196i	0.146469	+	0.989215i	$0.453209\pi$
$600$		0			0
$601$	−3.99613	−	6.92150i	−0.163006	−	0.282334i	0.772940	−	0.634480i	$-0.218786\pi$
$601$	−3.99613	−	6.92150i	−0.163006	−	0.282334i	−0.935945	+	0.352146i	$0.885452\pi$
$602$	−5.58878	+	15.3550i	−0.227782	+	0.625825i
$603$	3.18701	+	0.561956i	0.129785	+	0.0228846i
$604$	−0.808400	−	4.58467i	−0.0328933	−	0.186547i
$605$		0			0
$606$	−0.433763	−	0.363970i	−0.0176204	−	0.0147853i
$607$			26.9905i			1.09551i	0.836639	+	0.547755i	$0.184518\pi$
$607$			26.9905i			1.09551i	−0.836639	+	0.547755i	$0.815482\pi$
$608$	4.08494	−	1.52094i	0.165666	−	0.0616824i
$609$	11.6541			0.472249
$610$		0			0
$611$	42.6810	−	15.5346i	1.72669	−	0.628463i
$612$	4.18939	−	0.738703i	0.169346	−	0.0298603i
$613$	−14.0348	−	2.47472i	−0.566861	−	0.0999529i	−0.117130	−	0.993117i	$-0.537369\pi$
$613$	−14.0348	−	2.47472i	−0.566861	−	0.0999529i	−0.449732	+	0.893164i	$0.648480\pi$
$614$	20.0424	+	7.29482i	0.808844	+	0.294395i
$615$		0			0
$616$	−4.29086	+	7.43199i	−0.172884	+	0.299443i
$617$	19.6438	+	23.4106i	0.790831	+	0.942475i	0.999368	−	0.0355392i	$-0.0113149\pi$
$617$	19.6438	+	23.4106i	0.790831	+	0.942475i	−0.208538	+	0.978014i	$0.566870\pi$
$618$	8.45134	+	10.0719i	0.339963	+	0.405152i
$619$	−14.3375	+	24.8333i	−0.576273	+	0.998133i	0.419629	+	0.907695i	$0.362160\pi$
$619$	−14.3375	+	24.8333i	−0.576273	+	0.998133i	−0.995902	+	0.0904380i	$0.971173\pi$
$620$		0			0
$621$	−3.65270	−	1.32948i	−0.146578	−	0.0533500i
$622$	28.8468	+	5.08647i	1.15665	+	0.203949i
$623$	−20.5371	+	3.62124i	−0.822801	+	0.145082i
$624$	−8.29086	+	3.01763i	−0.331900	+	0.120802i
$625$		0			0
$626$	5.56118			0.222270
$627$	−10.7697	−	18.3405i	−0.430100	−	0.732449i
$628$			8.45336i			0.337326i
$629$	−21.8161	−	18.3059i	−0.869867	−	0.729905i
$630$		0			0
$631$	−0.781059	−	4.42961i	−0.0310935	−	0.176340i	0.965306	−	0.261121i	$-0.0840921\pi$
$631$	−0.781059	−	4.42961i	−0.0310935	−	0.176340i	−0.996400	+	0.0847809i	$0.972981\pi$
$632$	8.92647	+	1.57398i	0.355076	+	0.0626095i
$633$	−11.7168	+	32.1917i	−0.465701	+	1.27950i
$634$	1.90167	+	3.29380i	0.0755251	+	0.130813i
$635$		0			0
$636$	9.63816	−	8.08737i	0.382178	−	0.320685i
$637$	0.965505	+	1.15064i	0.0382547	+	0.0455902i
$638$	7.78601	+	4.49525i	0.308251	+	0.177969i
$639$	2.75877	+	4.77833i	0.109135	+	0.189028i
$640$		0			0
$641$	−2.01573	+	11.4318i	−0.0796165	+	0.451528i	0.918772	+	0.394788i	$0.129182\pi$
$641$	−2.01573	+	11.4318i	−0.0796165	+	0.451528i	−0.998389	+	0.0567403i	$0.981929\pi$
$642$	−17.2810	+	3.04710i	−0.682026	+	0.120260i
$643$	−8.90809	−	24.4748i	−0.351301	−	0.965191i	−0.981953	−	0.189125i	$-0.939435\pi$
$643$	−8.90809	−	24.4748i	−0.351301	−	0.965191i	0.630652	−	0.776066i	$-0.282787\pi$
$644$	1.43376	+	1.20307i	0.0564982	+	0.0474076i
$645$		0			0
$646$	18.1004	−	21.8966i	0.712152	−	0.861511i
$647$			2.31490i			0.0910082i	0.998964	+	0.0455041i	$0.0144894\pi$
$647$			2.31490i			0.0910082i	−0.998964	+	0.0455041i	$0.985511\pi$
$648$	4.25260	−	5.06805i	0.167058	−	0.199092i
$649$	1.71776	−	0.625213i	0.0674279	−	0.0245418i
$650$		0			0
$651$	1.75877	−	9.97448i	0.0689316	−	0.390931i
$652$	−5.83132	+	16.0214i	−0.228372	+	0.627447i
$653$	2.86257	−	1.65270i	0.112021	−	0.0646753i	−0.442943	−	0.896550i	$-0.646066\pi$
$653$	2.86257	−	1.65270i	0.112021	−	0.0646753i	0.554964	+	0.831875i	$0.312732\pi$
$654$	6.66044	−	11.5362i	0.260444	−	0.451102i
$655$		0			0
$656$	−0.266044	+	0.223238i	−0.0103873	+	0.00871597i
$657$	−8.91215	−	5.14543i	−0.347696	−	0.200742i
$658$	18.4053	−	10.6263i	0.717513	−	0.414256i
$659$	−12.9201	−	4.70253i	−0.503295	−	0.183185i	0.0778802	−	0.996963i	$-0.475185\pi$
$659$	−12.9201	−	4.70253i	−0.503295	−	0.183185i	−0.581176	+	0.813778i	$0.697407\pi$
$660$		0			0
$661$	−0.579030	−	3.28384i	−0.0225217	−	0.127727i	0.971474	−	0.237146i	$-0.0762120\pi$
$661$	−0.579030	−	3.28384i	−0.0225217	−	0.127727i	−0.993996	+	0.109419i	$0.965101\pi$
$662$	6.98470	+	19.1903i	0.271468	+	0.745853i
$663$	−36.9628	+	44.0506i	−1.43552	+	1.71078i
$664$	−8.47565			−0.328919
$665$		0			0
$666$	2.85204			0.110514
$667$	1.26038	−	1.50206i	0.0488020	−	0.0581600i
$668$	1.09191	+	3.00000i	0.0422473	+	0.116073i
$669$	2.46791	+	13.9962i	0.0954150	+	0.541125i
$670$		0			0
$671$	−8.78611	−	3.19788i	−0.339184	−	0.123453i
$672$	−3.57526	+	2.06418i	−0.137919	+	0.0796274i
$673$	−33.7585	−	19.4905i	−1.30130	−	0.751304i	−0.320670	−	0.947191i	$-0.603908\pi$
$673$	−33.7585	−	19.4905i	−1.30130	−	0.751304i	−0.980626	+	0.195887i	$0.937241\pi$
$674$	−15.5587	+	13.0553i	−0.599299	+	0.502872i
$675$		0			0
$676$	−10.0817	+	17.4620i	−0.387758	+	0.671617i
$677$	37.7481	−	21.7939i	1.45078	−	0.837606i	0.452250	−	0.891891i	$-0.350621\pi$
$677$	37.7481	−	21.7939i	1.45078	−	0.837606i	0.998525	+	0.0542853i	$0.0172880\pi$
$678$	1.49854	−	4.11721i	0.0575512	−	0.158121i
$679$	0.162504	−	0.921605i	0.00623632	−	0.0353680i
$680$		0			0
$681$	−11.1382	+	4.05396i	−0.426815	+	0.155348i
$682$	5.02239	−	5.98545i	0.192317	−	0.229195i
$683$			32.9317i			1.26010i	0.776556	+	0.630048i	$0.216965\pi$
$683$			32.9317i			1.26010i	−0.776556	+	0.630048i	$0.783035\pi$
$684$	0.0209445	+	2.84499i	0.000800834	+	0.108781i
$685$		0			0
$686$	−13.9108	−	11.6726i	−0.531119	−	0.445661i
$687$	−12.0705	−	33.1634i	−0.460518	−	1.26526i
$688$	−5.97205	+	1.05303i	−0.227682	+	0.0401465i
$689$	8.21213	−	46.5733i	0.312857	−	1.77430i
$690$		0			0
$691$	−17.1604	−	29.7228i	−0.652814	−	1.13071i	−0.982437	−	0.186594i	$-0.940255\pi$
$691$	−17.1604	−	29.7228i	−0.652814	−	1.13071i	0.329623	−	0.944113i	$-0.393078\pi$
$692$	8.34018	+	4.81521i	0.317046	+	0.183047i
$693$	−3.60046	−	4.29086i	−0.136770	−	0.162996i
$694$	−3.99479	+	3.35202i	−0.151640	+	0.127241i
$695$		0			0
$696$	2.16250	+	3.74557i	0.0819695	+	0.141975i
$697$	−0.774169	+	2.12701i	−0.0293237	+	0.0805663i
$698$	14.1226	+	2.49020i	0.534549	+	0.0942555i
$699$	−2.23467	−	12.6734i	−0.0845230	−	0.479354i
$700$		0			0
$701$	4.94356	+	4.14814i	0.186716	+	0.156673i	0.731354	−	0.681998i	$-0.238889\pi$
$701$	4.94356	+	4.14814i	0.186716	+	0.156673i	−0.544638	+	0.838671i	$0.683333\pi$
$702$		−	32.2276i		−	1.21635i
$703$	14.5000	−	12.3500i	0.546878	−	0.465788i
$704$	−3.18479			−0.120031
$705$		0			0
$706$	−24.6668	+	8.97800i	−0.928349	+	0.337891i
$707$	−0.980752	+	0.172933i	−0.0368850	+	0.00650381i
$708$	0.866025	+	0.152704i	0.0325472	+	0.00573895i
$709$	−3.17530	−	1.15571i	−0.119251	−	0.0434037i	0.281706	−	0.959501i	$-0.409100\pi$
$709$	−3.17530	−	1.15571i	−0.119251	−	0.0434037i	−0.400956	+	0.916097i	$0.631322\pi$
$710$		0			0
$711$	−2.95811	+	5.12360i	−0.110938	+	0.192150i
$712$	−4.97464	−	5.92855i	−0.186433	−	0.222182i
$713$	−1.09537	−	1.30541i	−0.0410218	−	0.0488879i
$714$	−13.4534	+	23.3019i	−0.503479	+	0.872052i
$715$		0			0
$716$	−17.6814	−	6.43550i	−0.660785	−	0.240506i
$717$	23.7331	+	4.18479i	0.886330	+	0.156284i
$718$	33.1786	−	5.85029i	1.23822	−	0.218331i
$719$	−29.3209	+	10.6719i	−1.09348	+	0.397996i	−0.824911	−	0.565263i	$-0.808775\pi$
$719$	−29.3209	+	10.6719i	−1.09348	+	0.397996i	−0.268574	+	0.963259i	$0.586552\pi$
$720$		0			0
$721$	23.1242			0.861192
$722$	12.4259	+	14.3735i	0.462445	+	0.534925i
$723$			26.8161i			0.997303i
$724$	−2.12836	−	1.78590i	−0.0790997	−	0.0663725i
$725$		0			0
$726$	−0.228026	−	1.29320i	−0.00846283	−	0.0479951i
$727$	25.2715	+	4.45605i	0.937269	+	0.165266i	0.621361	−	0.783524i	$-0.286580\pi$
$727$	25.2715	+	4.45605i	0.937269	+	0.165266i	0.315908	+	0.948790i	$0.397691\pi$
$728$	−5.30731	+	14.5817i	−0.196702	+	0.540434i
$729$	15.0201	+	26.0155i	0.556299	+	0.963538i
$730$		0			0
$731$	−30.2768	+	25.4052i	−1.11983	+	0.939647i
$732$	−2.89122	−	3.44562i	−0.106863	−	0.127354i
$733$	20.6751	+	11.9368i	0.763651	+	0.440894i	0.830605	−	0.556862i	$-0.187995\pi$
$733$	20.6751	+	11.9368i	0.763651	+	0.440894i	−0.0669540	+	0.997756i	$0.521328\pi$
$734$	−5.23442	−	9.06629i	−0.193206	−	0.334643i
$735$		0			0
$736$	−0.120615	+	0.684040i	−0.00444592	+	0.0252141i
$737$	−15.5507	+	2.74200i	−0.572816	+	0.101003i
$738$	−0.0775297	−	0.213011i	−0.00285391	−	0.00784104i
$739$	35.1924	+	29.5299i	1.29457	+	1.08628i	0.991056	+	0.133449i	$0.0426052\pi$
$739$	35.1924	+	29.5299i	1.29457	+	1.08628i	0.303517	+	0.952826i	$0.401839\pi$
$740$		0			0
$741$	−24.9368	−	29.2780i	−0.916075	−	1.07555i
$742$		−	22.1284i		−	0.812357i
$743$	32.7895	−	39.0770i	1.20293	−	1.43360i	0.331232	−	0.943549i	$-0.392536\pi$
$743$	32.7895	−	39.0770i	1.20293	−	1.43360i	0.871697	−	0.490046i	$-0.163020\pi$
$744$	3.53209	−	1.28558i	0.129493	−	0.0471315i
$745$		0			0
$746$	4.15064	−	23.5395i	0.151966	−	0.861841i
$747$	1.89209	−	5.19846i	0.0692278	−	0.190202i
$748$	−17.9761	+	10.3785i	−0.657271	+	0.379476i
$749$	−15.4311	+	26.7274i	−0.563839	+	0.976598i
$750$		0			0
$751$	−27.8607	+	23.3779i	−1.01665	+	0.853072i	−0.989203	−	0.146551i	$-0.953183\pi$
$751$	−27.8607	+	23.3779i	−1.01665	+	0.853072i	−0.0274489	+	0.999623i	$0.508738\pi$
$752$	6.83045	+	3.94356i	0.249081	+	0.143807i
$753$	11.3672	−	6.56283i	0.414242	−	0.239163i
$754$	15.2763	+	5.56012i	0.556330	+	0.202488i
$755$		0			0
$756$	−2.61856	−	14.8506i	−0.0952359	−	0.540110i
$757$	−1.98486	−	5.45336i	−0.0721410	−	0.198206i	0.898382	−	0.439216i	$-0.144744\pi$
$757$	−1.98486	−	5.45336i	−0.0721410	−	0.198206i	−0.970523	+	0.241010i	$0.922521\pi$
$758$	−11.4503	+	13.6459i	−0.415892	+	0.495641i
$759$	3.38919			0.123020
$760$		0			0
$761$	22.6355			0.820535			0.410268	−	0.911965i	$-0.365435\pi$
$761$	22.6355			0.820535			0.410268	+	0.911965i	$0.365435\pi$
$762$	9.58186	−	11.4192i	0.347114	−	0.413675i
$763$	−8.01298	−	22.0155i	−0.290089	−	0.797014i
$764$	−1.66044	−	9.41685i	−0.0600728	−	0.340690i
$765$		0			0
$766$	−23.5672	−	8.57775i	−0.851516	−	0.309927i
$767$	2.86257	−	1.65270i	0.103361	−	0.0596757i
$768$	−1.32683	−	0.766044i	−0.0478778	−	0.0276422i
$769$	−8.35188	+	7.00806i	−0.301177	+	0.252717i	−0.780834	−	0.624739i	$-0.785205\pi$
$769$	−8.35188	+	7.00806i	−0.301177	+	0.252717i	0.479657	+	0.877456i	$0.340761\pi$
$770$		0			0
$771$	6.14724	−	10.6473i	0.221387	−	0.383454i
$772$	20.5083	−	11.8405i	0.738111	−	0.426149i
$773$	−1.79585	+	4.93407i	−0.0645924	+	0.177466i	−0.967790	−	0.251759i	$-0.918991\pi$
$773$	−1.79585	+	4.93407i	−0.0645924	+	0.177466i	0.903198	+	0.429225i	$0.141213\pi$
$774$	0.687319	−	3.89798i	0.0247052	−	0.140110i
$775$		0			0
$776$	0.326352	−	0.118782i	0.0117153	−	0.00426404i
$777$	−11.5954	+	13.8188i	−0.415982	+	0.495748i
$778$		−	9.41828i		−	0.337662i
$779$	−1.31655	−	0.747243i	−0.0471704	−	0.0267728i
$780$		0			0
$781$	−20.6236	−	17.3053i	−0.737971	−	0.619231i
$782$	1.54834	+	4.25402i	0.0553684	+	0.152124i
$783$	−15.5580	+	2.74329i	−0.555996	+	0.0980371i
$784$	−0.0452926	+	0.256867i	−0.00161759	+	0.00917383i
$785$		0			0
$786$	4.95471	+	8.58180i	0.176729	+	0.306103i
$787$	−2.06758	−	1.19372i	−0.0737011	−	0.0425514i	0.462697	−	0.886517i	$-0.346882\pi$
$787$	−2.06758	−	1.19372i	−0.0737011	−	0.0425514i	−0.536398	+	0.843965i	$0.680215\pi$
$788$	−14.7341	−	17.5594i	−0.524881	−	0.625529i
$789$	6.99588	−	5.87024i	0.249060	−	0.208986i
$790$		0			0
$791$	−3.85298	−	6.67355i	−0.136996	−	0.237284i
$792$	0.710966	−	1.95336i	0.0252631	−	0.0694097i
$793$	−16.6499	−	2.93582i	−0.591254	−	0.104254i
$794$	−1.18984	−	6.74795i	−0.0422260	−	0.239476i
$795$		0			0
$796$	7.72462	+	6.48173i	0.273792	+	0.229739i
$797$		−	31.0951i		−	1.10145i	−0.834688	−	0.550723i	$-0.814352\pi$
$797$		−	31.0951i		−	1.10145i	0.834688	−	0.550723i	$-0.185648\pi$
$798$	−13.8698	−	11.4652i	−0.490986	−	0.405864i
$799$	51.4047			1.81857
$800$		0			0
$801$	4.74675	−	1.72768i	0.167718	−	0.0610444i
$802$	4.67479	−	0.824292i	0.165073	−	0.0291068i
$803$	49.4502	+	8.71941i	1.74506	+	0.307701i
$804$	−7.13816	−	2.59808i	−0.251743	−	0.0916271i
$805$		0			0
$806$	7.06418	−	12.2355i	0.248825	−	0.430978i
$807$	1.13052	+	1.34730i	0.0397960	+	0.0474271i
$808$	−0.237565	−	0.283119i	−0.00835750	−	0.00996008i
$809$	11.1518	−	19.3155i	0.392077	−	0.679098i	−0.600646	−	0.799515i	$-0.705090\pi$
$809$	11.1518	−	19.3155i	0.392077	−	0.679098i	0.992723	+	0.120417i	$0.0384232\pi$
$810$		0			0
$811$	−3.11886	−	1.13517i	−0.109518	−	0.0398613i	0.286680	−	0.958026i	$-0.407448\pi$
$811$	−3.11886	−	1.13517i	−0.109518	−	0.0398613i	−0.396198	+	0.918165i	$0.629671\pi$
$812$	7.49113	+	1.32089i	0.262887	+	0.0463541i
$813$	−30.2588	+	5.33544i	−1.06122	+	0.187122i
$814$	−13.0770	+	4.75963i	−0.458348	+	0.166825i
$815$		0			0
$816$	−9.98545			−0.349561
$817$	−13.3847	−	22.7939i	−0.468273	−	0.797456i
$818$			31.6928i			1.10811i
$819$	−7.75877	−	6.51038i	−0.271113	−	0.227491i
$820$		0			0
$821$	−0.318201	−	1.80460i	−0.0111053	−	0.0629811i	0.978752	−	0.205050i	$-0.0657357\pi$
$821$	−0.318201	−	1.80460i	−0.0111053	−	0.0629811i	−0.989857	+	0.142069i	$0.954625\pi$
$822$	17.5934	+	3.10220i	0.613641	+	0.108202i
$823$	−11.7100	+	32.1729i	−0.408185	+	1.12148i	0.549959	+	0.835191i	$0.314643\pi$
$823$	−11.7100	+	32.1729i	−0.408185	+	1.12148i	−0.958144	+	0.286287i	$0.907579\pi$
$824$	4.29086	+	7.43199i	0.149479	+	0.258906i
$825$		0			0
$826$	1.18479	−	0.994159i	0.0412242	−	0.0345912i
$827$	12.7695	+	15.2181i	0.444038	+	0.529184i	0.940918	−	0.338636i	$-0.109965\pi$
$827$	12.7695	+	15.2181i	0.444038	+	0.529184i	−0.496880	+	0.867820i	$0.665521\pi$
$828$	−0.392624	−	0.226682i	−0.0136446	−	0.00787773i
$829$	−17.8675	−	30.9475i	−0.620565	−	1.07485i	−0.989381	−	0.145347i	$-0.953570\pi$
$829$	−17.8675	−	30.9475i	−0.620565	−	1.07485i	0.368816	−	0.929502i	$-0.379763\pi$
$830$		0			0
$831$	4.61856	−	26.1931i	0.160216	−	0.908630i
$832$	−5.67128	+	1.00000i	−0.196616	+	0.0346688i
$833$	0.581424	+	1.59745i	0.0201451	+	0.0553483i
$834$	9.69846	+	8.13798i	0.335830	+	0.281795i
$835$		0			0
$836$	−4.84389	−	13.0097i	−0.167530	−	0.449949i
$837$			13.7297i			0.474567i
$838$	7.07716	−	8.43423i	0.244476	−	0.291356i
$839$	−51.1147	+	18.6042i	−1.76468	+	0.642290i	−0.999998	−	0.00212143i	$-0.999325\pi$
$839$	−51.1147	+	18.6042i	−1.76468	+	0.642290i	−0.764679	+	0.644411i	$0.777103\pi$
$840$		0			0
$841$	−3.65199	+	20.7115i	−0.125931	+	0.714188i
$842$	2.96377	−	8.14290i	0.102138	−	0.280623i
$843$	3.87603	−	2.23783i	0.133498	−	0.0770748i
$844$	−11.1800	+	19.3644i	−0.384833	+	0.666550i
$845$		0			0
$846$	−3.94356	+	3.30904i	−0.135582	+	0.113767i
$847$	−2.00011	−	1.15476i	−0.0687245	−	0.0396781i
$848$	7.11192	−	4.10607i	0.244224	−	0.141003i
$849$	−13.6493	−	4.96794i	−0.468443	−	0.170499i
$850$		0			0
$851$	0.527036	+	2.98897i	0.0180666	+	0.102461i
$852$	−4.42961	−	12.1702i	−0.151756	−	0.416946i
$853$	−10.2694	+	12.2385i	−0.351616	+	0.419040i	−0.912643	−	0.408758i	$-0.865962\pi$
$853$	−10.2694	+	12.2385i	−0.351616	+	0.419040i	0.561027	+	0.827798i	$0.310406\pi$
$854$	−7.91085			−0.270704
$855$		0			0
$856$	−11.4534			−0.391468
$857$	−16.7218	+	19.9283i	−0.571207	+	0.680738i	−0.971878	−	0.235484i	$-0.924332\pi$
$857$	−16.7218	+	19.9283i	−0.571207	+	0.680738i	0.400671	+	0.916222i	$0.368777\pi$
$858$	9.61051	+	26.4047i	0.328097	+	0.901440i
$859$	−9.25031	−	52.4611i	−0.315617	−	1.78995i	−0.568740	−	0.822517i	$-0.692569\pi$
$859$	−9.25031	−	52.4611i	−0.315617	−	1.78995i	0.253124	−	0.967434i	$-0.418542\pi$
$860$		0			0
$861$	1.34730	+	0.490376i	0.0459157	+	0.0167120i
$862$	25.8830	−	14.9436i	0.881579	−	0.508980i
$863$	−2.79876	−	1.61587i	−0.0952710	−	0.0550048i	0.451608	−	0.892217i	$-0.350851\pi$
$863$	−2.79876	−	1.61587i	−0.0952710	−	0.0550048i	−0.546879	+	0.837212i	$0.684184\pi$
$864$	4.28699	−	3.59721i	0.145846	−	0.122380i
$865$		0			0
$866$	−4.63041	+	8.02011i	−0.157348	+	0.272535i
$867$	−33.8054	+	19.5175i	−1.14809	+	0.662850i
$868$	2.26103	−	6.21213i	0.0767444	−	0.210854i
$869$	5.01279	−	28.4290i	0.170047	−	0.964387i
$870$		0			0
$871$	−26.8307	+	9.76557i	−0.909123	+	0.330894i
$872$	5.58878	−	6.66044i	0.189260	−	0.225551i
$873$			0.226682i			0.00767201i
$874$	−2.97771	+	0.547683i	−0.100723	+	0.0185257i
$875$		0			0
$876$	18.5043	+	15.5270i	0.625204	+	0.524608i
$877$	4.00995	+	11.0172i	0.135406	+	0.372026i	0.988801	−	0.149239i	$-0.0476825\pi$
$877$	4.00995	+	11.0172i	0.135406	+	0.372026i	−0.853395	+	0.521265i	$0.825460\pi$
$878$	−20.5452	+	3.62267i	−0.693367	+	0.122259i
$879$	7.26083	−	41.1782i	0.244902	−	1.38891i
$880$		0			0
$881$	−13.5236	−	23.4236i	−0.455623	−	0.789162i	0.543101	−	0.839667i	$-0.317250\pi$
$881$	−13.5236	−	23.4236i	−0.455623	−	0.789162i	−0.998724	+	0.0505056i	$0.983917\pi$
$882$	−0.147436	−	0.0851223i	−0.00496443	−	0.00286622i
$883$	9.30823	+	11.0931i	0.313247	+	0.373313i	0.899579	−	0.436758i	$-0.143873\pi$
$883$	9.30823	+	11.0931i	0.313247	+	0.373313i	−0.586333	+	0.810070i	$0.699429\pi$
$884$	−28.7520	+	24.1258i	−0.967033	+	0.811437i
$885$		0			0
$886$	−11.9140	−	20.6357i	−0.400259	−	0.693268i
$887$	3.96443	−	10.8922i	0.133112	−	0.365724i	−0.855172	−	0.518344i	$-0.826549\pi$
$887$	3.96443	−	10.8922i	0.133112	−	0.365724i	0.988285	+	0.152620i	$0.0487711\pi$
$888$	−6.59289	−	1.16250i	−0.221243	−	0.0390111i
$889$	−4.55262	−	25.8192i	−0.152690	−	0.865948i
$890$		0			0
$891$	−16.1407	−	13.5436i	−0.540733	−	0.453729i
$892$			9.27631i			0.310594i
$893$	−5.72048	+	33.8999i	−0.191428	+	1.13442i
$894$	25.2080			0.843082
$895$		0			0
$896$	−2.53209	+	0.921605i	−0.0845912	+	0.0307887i
$897$	6.03525	−	1.06418i	0.201511	−	0.0355319i
$898$	−2.14895	−	0.378918i	−0.0717115	−	0.0126447i
$899$	−6.50805	−	2.36873i	−0.217055	−	0.0790017i
$900$		0			0
$901$	26.7615	−	46.3522i	0.891553	−	1.54422i
$902$	0.710966	+	0.847296i	0.0236726	+	0.0282119i
$903$	16.0922	+	19.1780i	0.535516	+	0.638203i
$904$	1.42989	−	2.47665i	0.0475575	−	0.0823720i
$905$		0			0
$906$	−6.70233	−	2.43945i	−0.222670	−	0.0810453i
$907$	−41.3409	−	7.28952i	−1.37270	−	0.242044i	−0.561823	−	0.827258i	$-0.689900\pi$
$907$	−41.3409	−	7.28952i	−1.37270	−	0.242044i	−0.810879	+	0.585213i	$0.801011\pi$
$908$	−7.61895	+	1.34343i	−0.252844	+	0.0445832i
$909$	0.226682	−	0.0825054i	0.00751855	−	0.00273653i
$910$		0			0
$911$	−44.8675			−1.48653			−0.743264	−	0.668999i	$-0.766723\pi$
$911$	−44.8675			−1.48653			−0.743264	+	0.668999i	$0.766723\pi$
$912$	1.11121	−	6.58512i	0.0367959	−	0.218055i
$913$			26.9932i			0.893344i
$914$	−1.36437	−	1.14484i	−0.0451294	−	0.0378680i
$915$		0			0
$916$	−4.00000	−	22.6851i	−0.132164	−	0.749538i
$917$	17.1636	+	3.02641i	0.566792	+	0.0999408i
$918$	12.4748	−	34.2743i	0.411730	−	1.13122i
$919$	−16.2635	−	28.1692i	−0.536484	−	0.929217i	−0.999090	−	0.0426535i	$-0.986419\pi$
$919$	−16.2635	−	28.1692i	−0.536484	−	0.929217i	0.462606	−	0.886564i	$-0.346914\pi$
$920$		0			0
$921$	25.0323	−	21.0046i	0.824843	−	0.692125i
$922$	9.95578	+	11.8648i	0.327876	+	0.390748i
$923$	−42.1590	−	24.3405i	−1.38768	−	0.801177i
$924$	6.57398	+	11.3865i	0.216268	+	0.374587i
$925$		0			0
$926$	−0.470599	+	2.66890i	−0.0154649	+	0.0877056i
$927$	−5.51622	+	0.972659i	−0.181177	+	0.0319463i
$928$	0.965505	+	2.65270i	0.0316943	+	0.0870793i
$929$	−9.07011	−	7.61072i	−0.297581	−	0.249700i	0.481756	−	0.876305i	$-0.339999\pi$
$929$	−9.07011	−	7.61072i	−0.297581	−	0.249700i	−0.779336	+	0.626606i	$0.784444\pi$
$930$		0			0
$931$	−1.11817	+	0.205663i	−0.0366467	+	0.00674034i
$932$		−	8.39961i		−	0.275139i
$933$	28.8468	−	34.3783i	0.944401	−	1.12549i
$934$	12.1348	−	4.41669i	0.397061	−	0.144518i
$935$		0			0
$936$	0.652704	−	3.70167i	0.0213343	−	0.120993i
$937$	0.261243	−	0.717759i	0.00853443	−	0.0234482i	−0.935352	−	0.353718i	$-0.884917\pi$
$937$	0.261243	−	0.717759i	0.00853443	−	0.0234482i	0.943887	+	0.330269i	$0.107140\pi$
$938$	−11.5702	+	6.68004i	−0.377780	+	0.218111i
$939$	4.26011	−	7.37874i	0.139024	−	0.240796i
$940$		0			0
$941$	−16.4652	+	13.8160i	−0.536751	+	0.450388i	−0.870425	−	0.492301i	$-0.836156\pi$
$941$	−16.4652	+	13.8160i	−0.536751	+	0.450388i	0.333674	+	0.942688i	$0.391711\pi$
$942$	11.2162	+	6.47565i	0.365442	+	0.210988i
$943$	0.208911	−	0.120615i	0.00680307	−	0.00392776i
$944$	0.539363	+	0.196312i	0.0175548	+	0.00638941i
$945$		0			0
$946$	3.35369	+	19.0197i	0.109038	+	0.618385i
$947$	10.8369	+	29.7743i	0.352153	+	0.967533i	0.981677	+	0.190552i	$0.0610278\pi$
$947$	10.8369	+	29.7743i	0.352153	+	0.967533i	−0.629524	+	0.776981i	$0.716750\pi$
$948$	8.92647	−	10.6382i	0.289918	−	0.345511i
$949$	90.7957			2.94735
$950$		0			0
$951$	5.82707			0.188956
$952$	−11.2887	+	13.4534i	−0.365869	+	0.436026i
$953$	−19.1091	−	52.5017i	−0.619003	−	1.70070i	−0.709414	−	0.704792i	$-0.751040\pi$
$953$	−19.1091	−	52.5017i	−0.619003	−	1.70070i	0.0904104	−	0.995905i	$-0.471182\pi$
$954$	0.930770	+	5.27866i	0.0301348	+	0.170903i
$955$		0			0
$956$	14.7811	+	5.37987i	0.478054	+	0.173997i
$957$	11.9289	−	6.88713i	0.385605	−	0.222629i
$958$	16.0670	+	9.27631i	0.519103	+	0.299704i
$959$	24.0692	−	20.1965i	0.777236	−	0.652178i
$960$		0			0
$961$	12.4905	−	21.6342i	0.402920	−	0.697877i
$962$	−21.7922	+	12.5817i	−0.702608	+	0.405651i
$963$	2.55682	−	7.02481i	0.0823925	−	0.226371i
$964$	−3.03936	+	17.2371i	−0.0978913	+	0.555169i
$965$		0			0
$966$	2.69459	−	0.980752i	0.0866971	−	0.0315552i
$967$	13.8564	−	16.5134i	0.445592	−	0.531036i	−0.495761	−	0.868459i	$-0.665111\pi$
$967$	13.8564	−	16.5134i	0.445592	−	0.531036i	0.941353	+	0.337423i	$0.109555\pi$
$968$		−	0.857097i		−	0.0275481i
$969$	−15.1873	−	40.7900i	−0.487887	−	1.31036i
$970$		0			0
$971$	37.2729	+	31.2757i	1.19614	+	1.00368i	0.999732	+	0.0231632i	$0.00737372\pi$
$971$	37.2729	+	31.2757i	1.19614	+	1.00368i	0.196413	+	0.980521i	$0.437071\pi$
$972$	2.27536	+	6.25150i	0.0729822	+	0.200517i
$973$	21.9285	−	3.86659i	0.702996	−	0.123957i
$974$	−7.14971	+	40.5480i	−0.229092	+	1.29924i
$975$		0			0
$976$	−1.46791	−	2.54250i	−0.0469867	−	0.0813833i
$977$	−43.7760	−	25.2741i	−1.40052	−	0.808590i	−0.406073	−	0.913841i	$-0.633102\pi$
$977$	−43.7760	−	25.2741i	−1.40052	−	0.808590i	−0.994446	+	0.105251i	$0.966435\pi$
$978$	16.7906	+	20.0103i	0.536904	+	0.639858i
$979$	−18.8812	+	15.8432i	−0.603446	+	0.506351i
$980$		0			0
$981$	2.83750	+	4.91469i	0.0905943	+	0.156914i
$982$	7.72199	−	21.2160i	0.246419	−	0.677030i
$983$	−29.6034	−	5.21987i	−0.944201	−	0.166488i	−0.319706	−	0.947517i	$-0.603584\pi$
$983$	−29.6034	−	5.21987i	−0.944201	−	0.166488i	−0.624495	+	0.781029i	$0.714695\pi$
$984$	0.0923963	+	0.524005i	0.00294549	+	0.0167047i
$985$		0			0
$986$	14.0942	+	11.8264i	0.448851	+	0.376631i
$987$		−	32.5609i		−	1.03642i
$988$	−12.7106	−	21.6459i	−0.404379	−	0.688648i
$989$	4.21213			0.133938
$990$		0			0
$991$	−2.58677	+	0.941508i	−0.0821715	+	0.0299080i	−0.382779	−	0.923840i	$-0.625033\pi$
$991$	−2.58677	+	0.941508i	−0.0821715	+	0.0299080i	0.300607	+	0.953748i	$0.402811\pi$
$992$	2.41609	−	0.426022i	0.0767110	−	0.0135262i
$993$	30.8128	+	5.43313i	0.977816	+	0.172415i
$994$	−21.4047	−	7.79066i	−0.678915	−	0.247105i
$995$		0			0
$996$	−6.49273	+	11.2457i	−0.205730	+	0.356335i
$997$	−5.59527	−	6.66819i	−0.177204	−	0.211184i	0.670130	−	0.742244i	$-0.266238\pi$
$997$	−5.59527	−	6.66819i	−0.177204	−	0.211184i	−0.847334	+	0.531060i	$0.821794\pi$
$998$	−18.8521	−	22.4670i	−0.596752	−	0.711182i
$999$	12.2267	−	21.1772i	0.386835	−	0.670018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.b.149.2		12
5.2	odd	4		38.2.e.a.35.1	yes	6
5.3	odd	4		950.2.l.d.301.1		6
5.4	even	2	inner	950.2.u.b.149.1		12
15.2	even	4		342.2.u.c.73.1		6
19.6	even	9	inner	950.2.u.b.899.1		12
20.7	even	4		304.2.u.c.225.1		6
95.2	even	36		722.2.c.l.653.3		6
95.7	odd	12		722.2.e.b.423.1		6
95.12	even	12		722.2.e.l.423.1		6
95.17	odd	36		722.2.c.k.653.1		6
95.22	even	36		722.2.c.l.429.3		6
95.27	even	12		722.2.e.a.245.1		6
95.32	even	36		722.2.e.k.595.1		6
95.37	even	4		722.2.e.k.415.1		6
95.42	odd	36		722.2.e.m.389.1		6
95.44	even	18	inner	950.2.u.b.899.2		12
95.47	odd	36		722.2.e.b.99.1		6
95.52	even	36		722.2.a.k.1.1		3
95.62	odd	36		722.2.a.l.1.3		3
95.63	odd	36		950.2.l.d.101.1		6
95.67	even	36		722.2.e.l.99.1		6
95.72	even	36		722.2.e.a.389.1		6
95.82	odd	36		38.2.e.a.25.1	✓	6
95.87	odd	12		722.2.e.m.245.1		6
95.92	odd	36		722.2.c.k.429.1		6
285.62	even	36		6498.2.a.bl.1.2		3
285.242	odd	36		6498.2.a.bq.1.2		3
285.272	even	36		342.2.u.c.253.1		6
380.147	odd	36		5776.2.a.bo.1.3		3
380.347	even	36		5776.2.a.bn.1.1		3
380.367	even	36		304.2.u.c.177.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.25.1	✓	6	95.82	odd	36
38.2.e.a.35.1	yes	6	5.2	odd	4
304.2.u.c.177.1		6	380.367	even	36
304.2.u.c.225.1		6	20.7	even	4
342.2.u.c.73.1		6	15.2	even	4
342.2.u.c.253.1		6	285.272	even	36
722.2.a.k.1.1		3	95.52	even	36
722.2.a.l.1.3		3	95.62	odd	36
722.2.c.k.429.1		6	95.92	odd	36
722.2.c.k.653.1		6	95.17	odd	36
722.2.c.l.429.3		6	95.22	even	36
722.2.c.l.653.3		6	95.2	even	36
722.2.e.a.245.1		6	95.27	even	12
722.2.e.a.389.1		6	95.72	even	36
722.2.e.b.99.1		6	95.47	odd	36
722.2.e.b.423.1		6	95.7	odd	12
722.2.e.k.415.1		6	95.37	even	4
722.2.e.k.595.1		6	95.32	even	36
722.2.e.l.99.1		6	95.67	even	36
722.2.e.l.423.1		6	95.12	even	12
722.2.e.m.245.1		6	95.87	odd	12
722.2.e.m.389.1		6	95.42	odd	36
950.2.l.d.101.1		6	95.63	odd	36
950.2.l.d.301.1		6	5.3	odd	4
950.2.u.b.149.1		12	5.4	even	2	inner
950.2.u.b.149.2		12	1.1	even	1	trivial
950.2.u.b.899.1		12	19.6	even	9	inner
950.2.u.b.899.2		12	95.44	even	18	inner
5776.2.a.bn.1.1		3	380.347	even	36
5776.2.a.bo.1.3		3	380.147	odd	36
6498.2.a.bl.1.2		3	285.62	even	36
6498.2.a.bq.1.2		3	285.242	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)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(-0.524005 - 1.43969i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.43969 - 0.524005i) q^{6} +(-2.33359 + 1.34730i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.500000 - 0.419550i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(-0.524005 - 1.43969i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.43969 - 0.524005i) q^{6} +(-2.33359 + 1.34730i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.500000 - 0.419550i) q^{9} +(-1.59240 + 2.75811i) q^{11} +(-1.32683 + 0.766044i) q^{12} +(-1.96962 + 5.41147i) q^{13} +(-0.467911 + 2.65366i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-4.18939 + 4.99273i) q^{17} -0.652704i q^{18} +(-2.82635 - 3.31839i) q^{19} +(3.16250 + 2.65366i) q^{21} +(1.08926 + 2.99273i) q^{22} +(0.684040 - 0.120615i) q^{23} +(-0.266044 + 1.50881i) q^{24} +(2.87939 + 4.98724i) q^{26} +(-4.84651 - 2.79813i) q^{27} +(1.73205 + 2.06418i) q^{28} +(2.16250 - 1.81456i) q^{29} +(-1.22668 - 2.12467i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(4.80526 + 0.847296i) q^{33} +(1.13176 + 6.41852i) q^{34} +(-0.500000 - 0.419550i) q^{36} +4.36959i q^{37} +(-4.35878 + 0.0320889i) q^{38} +8.82295 q^{39} +(0.326352 - 0.118782i) q^{41} +(4.06564 - 0.716881i) q^{42} +(5.97205 + 1.05303i) q^{43} +(2.99273 + 1.08926i) q^{44} +(0.347296 - 0.601535i) q^{46} +(-5.06975 - 6.04189i) q^{47} +(0.984808 + 1.17365i) q^{48} +(0.130415 - 0.225885i) q^{49} +(9.38326 + 3.41523i) q^{51} +(5.67128 + 1.00000i) q^{52} +(-8.08737 + 1.42602i) q^{53} +(-5.25877 + 1.91404i) q^{54} +2.69459 q^{56} +(-3.29644 + 5.80793i) q^{57} -2.82295i q^{58} +(-0.439693 - 0.368946i) q^{59} +(0.509800 + 2.89122i) q^{61} +(-2.41609 - 0.426022i) q^{62} +(-0.601535 + 1.65270i) q^{63} +(0.500000 + 0.866025i) q^{64} +(3.73783 - 3.13641i) q^{66} +(3.18701 + 3.79813i) q^{67} +(5.64436 + 3.25877i) q^{68} +(-0.532089 - 0.921605i) q^{69} +(-1.46791 + 8.32494i) q^{71} +(-0.642788 + 0.113341i) q^{72} +(-5.39246 - 14.8157i) q^{73} +(3.34730 + 2.80872i) q^{74} +(-2.77719 + 3.35965i) q^{76} -8.58172i q^{77} +(5.67128 - 6.75877i) q^{78} +(-8.51754 + 3.10013i) q^{79} +(-1.14883 + 6.51536i) q^{81} +(0.118782 - 0.326352i) q^{82} +(7.34013 - 4.23783i) q^{83} +(2.06418 - 3.57526i) q^{84} +(4.64543 - 3.89798i) q^{86} +(-3.74557 - 2.16250i) q^{87} +(2.75811 - 1.59240i) q^{88} +(7.27244 + 2.64695i) q^{89} +(-2.69459 - 15.2818i) q^{91} +(-0.237565 - 0.652704i) q^{92} +(-2.41609 + 2.87939i) q^{93} -7.88713 q^{94} +1.53209 q^{96} +(-0.223238 + 0.266044i) q^{97} +(-0.0892091 - 0.245100i) q^{98} +(0.360967 + 2.04715i) 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	\( 12 q - 6 q^{6} + 6 q^{9} - 12 q^{11} - 24 q^{14} - 36 q^{19} + 48 q^{21} + 6 q^{24} + 12 q^{26} + 36 q^{29} + 12 q^{31} + 24 q^{34} - 6 q^{36} + 24 q^{39} + 6 q^{41} + 30 q^{49} + 42 q^{51} - 18 q^{54} + 24 q^{56} + 6 q^{59} + 12 q^{61} + 6 q^{64} + 6 q^{66} + 12 q^{69} - 36 q^{71} + 36 q^{74} - 12 q^{76} - 12 q^{79} - 66 q^{81} - 12 q^{84} + 24 q^{86} - 24 q^{91} + 24 q^{94} - 42 q^{99}+O(q^{100}) \) 12 * q - 6 * q^6 + 6 * q^9 - 12 * q^11 - 24 * q^14 - 36 * q^19 + 48 * q^21 + 6 * q^24 + 12 * q^26 + 36 * q^29 + 12 * q^31 + 24 * q^34 - 6 * q^36 + 24 * q^39 + 6 * q^41 + 30 * q^49 + 42 * q^51 - 18 * q^54 + 24 * q^56 + 6 * q^59 + 12 * q^61 + 6 * q^64 + 6 * q^66 + 12 * q^69 - 36 * q^71 + 36 * q^74 - 12 * q^76 - 12 * q^79 - 66 * q^81 - 12 * q^84 + 24 * q^86 - 24 * q^91 + 24 * q^94 - 42 * q^99

Introduction

L-functions

Modular forms

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