LMFDB - Embedded newform 950.2.q.g.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (of order $12$, degree $4$, 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.2
Character	$\chi$	$=$	950.107
Dual form			950.2.q.g.293.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.186170 - 0.694795i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.359652 + 0.622936i) q^{6} +(-1.01416 - 1.01416i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.15000 + 1.24130i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.186170 - 0.694795i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.359652 + 0.622936i) q^{6} +(-1.01416 - 1.01416i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.15000 + 1.24130i) q^{9} +2.38827 q^{11} +(0.508625 - 0.508625i) q^{12} +(2.90425 - 0.778192i) q^{13} +(0.717117 + 1.24208i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.22959 + 4.58888i) q^{17} +(-1.75546 - 1.75546i) q^{18} +(-3.35250 - 2.78581i) q^{19} +(-0.893436 + 0.515825i) q^{21} +(-2.30689 - 0.618129i) q^{22} +(1.35931 + 5.07300i) q^{23} +(-0.622936 + 0.359652i) q^{24} -3.00670 q^{26} +(2.78859 - 2.78859i) q^{27} +(-0.371207 - 1.38536i) q^{28} +(4.88449 - 8.46019i) q^{29} +10.0965i q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.444623 - 1.65935i) q^{33} +(2.37538 - 4.11428i) q^{34} +(1.24130 + 2.15000i) q^{36} +(2.87570 - 2.87570i) q^{37} +(2.51725 + 3.55857i) q^{38} -2.16273i q^{39} +(6.97985 - 4.02982i) q^{41} +(0.996498 - 0.267011i) q^{42} +(-1.76075 - 0.471793i) q^{43} +(2.06830 + 1.19413i) q^{44} -5.25195i q^{46} +(0.349235 - 0.0935773i) q^{47} +(0.694795 - 0.186170i) q^{48} -4.94297i q^{49} +(2.95942 + 1.70862i) q^{51} +(2.90425 + 0.778192i) q^{52} +(7.08396 - 1.89814i) q^{53} +(-3.41531 + 1.97183i) q^{54} +1.43423i q^{56} +(-2.55970 + 1.81067i) q^{57} +(-6.90772 + 6.90772i) q^{58} +(1.29825 + 2.24864i) q^{59} +(-0.310205 + 0.537291i) q^{61} +(2.61317 - 9.75248i) q^{62} +(-0.921559 - 3.43931i) q^{63} +1.00000i q^{64} +(-0.858945 + 1.48774i) q^{66} +(0.368486 + 1.37521i) q^{67} +(-3.35930 + 3.35930i) q^{68} +3.77775 q^{69} +(-5.38910 + 3.11140i) q^{71} +(-0.642545 - 2.39801i) q^{72} +(-3.21735 - 0.862086i) q^{73} +(-3.52199 + 2.03342i) q^{74} +(-1.51045 - 4.08883i) q^{76} +(-2.42208 - 2.42208i) q^{77} +(-0.559756 + 2.08904i) q^{78} +(-0.0163335 - 0.0282904i) q^{79} +(2.30556 + 3.99334i) q^{81} +(-7.78501 + 2.08599i) q^{82} +(12.0016 - 12.0016i) q^{83} -1.03165 q^{84} +(1.57865 + 0.911434i) q^{86} +(-4.96875 - 4.96875i) q^{87} +(-1.68876 - 1.68876i) q^{88} +(1.11103 - 1.92436i) q^{89} +(-3.73457 - 2.15616i) q^{91} +(-1.35931 + 5.07300i) q^{92} +(7.01500 + 1.87966i) q^{93} -0.361555 q^{94} -0.719304 q^{96} +(9.85916 + 2.64175i) q^{97} +(-1.27934 + 4.77454i) q^{98} +(5.13476 + 2.96456i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) $ 32 * q + 12 * q^3 - 24 * q^7	$ 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) $ 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.186170	−	0.694795i	0.107485	−	0.401140i	−0.891130	−	0.453748i	$-0.850087\pi$
$3$	0.186170	−	0.694795i	0.107485	−	0.401140i	0.998615	+	0.0526080i	$0.0167534\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−0.359652	+	0.622936i	−0.146827	+	0.254312i
$7$	−1.01416	−	1.01416i	−0.383315	−	0.383315i	0.488980	−	0.872295i	$-0.337369\pi$
$7$	−1.01416	−	1.01416i	−0.383315	−	0.383315i	−0.872295	+	0.488980i	$0.837369\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.15000	+	1.24130i	0.716665	+	0.413767i
$10$		0			0
$11$	2.38827			0.720089			0.360045	−	0.932935i	$-0.382761\pi$
$11$	2.38827			0.720089			0.360045	+	0.932935i	$0.382761\pi$
$12$	0.508625	−	0.508625i	0.146827	−	0.146827i
$13$	2.90425	−	0.778192i	0.805494	−	0.215831i	0.167499	−	0.985872i	$-0.446431\pi$
$13$	2.90425	−	0.778192i	0.805494	−	0.215831i	0.637995	+	0.770041i	$0.279764\pi$
$14$	0.717117	+	1.24208i	0.191658	+	0.331961i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.22959	+	4.58888i	−0.298219	+	1.11297i	0.640408	+	0.768035i	$0.278765\pi$
$17$	−1.22959	+	4.58888i	−0.298219	+	1.11297i	−0.938627	+	0.344933i	$0.887902\pi$
$18$	−1.75546	−	1.75546i	−0.413767	−	0.413767i
$19$	−3.35250	−	2.78581i	−0.769117	−	0.639108i
$19$	−3.35250	−	2.78581i	−0.769117	−	0.639108i
$20$		0			0
$21$	−0.893436	+	0.515825i	−0.194964	+	0.112562i
$22$	−2.30689	−	0.618129i	−0.491830	−	0.131785i
$23$	1.35931	+	5.07300i	0.283435	+	1.05779i	0.949975	+	0.312325i	$0.101108\pi$
$23$	1.35931	+	5.07300i	0.283435	+	1.05779i	−0.666541	+	0.745469i	$0.732226\pi$
$24$	−0.622936	+	0.359652i	−0.127156	+	0.0734137i
$25$		0			0
$26$	−3.00670			−0.589663
$27$	2.78859	−	2.78859i	0.536664	−	0.536664i
$28$	−0.371207	−	1.38536i	−0.0701516	−	0.261809i
$29$	4.88449	−	8.46019i	0.907027	−	1.57102i	0.0888552	−	0.996045i	$-0.471679\pi$
$29$	4.88449	−	8.46019i	0.907027	−	1.57102i	0.818172	−	0.574973i	$-0.194988\pi$
$30$		0			0
$31$			10.0965i			1.81339i	0.421791	+	0.906693i	$0.361402\pi$
$31$			10.0965i			1.81339i	−0.421791	+	0.906693i	$0.638598\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.444623	−	1.65935i	0.0773988	−	0.288856i
$34$	2.37538	−	4.11428i	0.407374	−	0.705593i
$35$		0			0
$36$	1.24130	+	2.15000i	0.206883	+	0.358333i
$37$	2.87570	−	2.87570i	0.472762	−	0.472762i	−0.430046	−	0.902807i	$-0.641503\pi$
$37$	2.87570	−	2.87570i	0.472762	−	0.472762i	0.902807	+	0.430046i	$0.141503\pi$
$38$	2.51725	+	3.55857i	0.408352	+	0.577277i
$39$		−	2.16273i		−	0.346314i
$40$		0			0
$41$	6.97985	−	4.02982i	1.09007	−	0.629352i	0.156475	−	0.987682i	$-0.449987\pi$
$41$	6.97985	−	4.02982i	1.09007	−	0.629352i	0.933595	+	0.358330i	$0.116654\pi$
$42$	0.996498	−	0.267011i	0.153763	−	0.0412007i
$43$	−1.76075	−	0.471793i	−0.268513	−	0.0719477i	0.122051	−	0.992524i	$-0.461053\pi$
$43$	−1.76075	−	0.471793i	−0.268513	−	0.0719477i	−0.390563	+	0.920576i	$0.627720\pi$
$44$	2.06830	+	1.19413i	0.311808	+	0.180022i
$45$		0			0
$46$		−	5.25195i		−	0.774358i
$47$	0.349235	−	0.0935773i	0.0509412	−	0.0136496i	−0.233258	−	0.972415i	$-0.574939\pi$
$47$	0.349235	−	0.0935773i	0.0509412	−	0.0136496i	0.284200	+	0.958765i	$0.408272\pi$
$48$	0.694795	−	0.186170i	0.100285	−	0.0268713i
$49$		−	4.94297i		−	0.706139i
$50$		0			0
$51$	2.95942	+	1.70862i	0.414402	+	0.239255i
$52$	2.90425	+	0.778192i	0.402747	+	0.107916i
$53$	7.08396	−	1.89814i	0.973056	−	0.260730i	0.262939	−	0.964813i	$-0.415308\pi$
$53$	7.08396	−	1.89814i	0.973056	−	0.260730i	0.710118	+	0.704083i	$0.248642\pi$
$54$	−3.41531	+	1.97183i	−0.464765	+	0.268332i
$55$		0			0
$56$			1.43423i			0.191658i
$57$	−2.55970	+	1.81067i	−0.339040	+	0.239829i
$58$	−6.90772	+	6.90772i	−0.907027	+	0.907027i
$59$	1.29825	+	2.24864i	0.169018	+	0.292748i	0.938075	−	0.346433i	$-0.112607\pi$
$59$	1.29825	+	2.24864i	0.169018	+	0.292748i	−0.769057	+	0.639180i	$0.779274\pi$
$60$		0			0
$61$	−0.310205	+	0.537291i	−0.0397177	+	0.0687931i	−0.885201	−	0.465209i	$-0.845979\pi$
$61$	−0.310205	+	0.537291i	−0.0397177	+	0.0687931i	0.845483	+	0.534002i	$0.179313\pi$
$62$	2.61317	−	9.75248i	0.331873	−	1.23857i
$63$	−0.921559	−	3.43931i	−0.116106	−	0.433312i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−0.858945	+	1.48774i	−0.105729	+	0.183128i
$67$	0.368486	+	1.37521i	0.0450177	+	0.168008i	0.984775	−	0.173834i	$-0.0556157\pi$
$67$	0.368486	+	1.37521i	0.0450177	+	0.168008i	−0.939757	+	0.341843i	$0.888949\pi$
$68$	−3.35930	+	3.35930i	−0.407374	+	0.407374i
$69$	3.77775			0.454788
$70$		0			0
$71$	−5.38910	+	3.11140i	−0.639568	+	0.369255i	−0.784448	−	0.620194i	$-0.787054\pi$
$71$	−5.38910	+	3.11140i	−0.639568	+	0.369255i	0.144880	+	0.989449i	$0.453720\pi$
$72$	−0.642545	−	2.39801i	−0.0757246	−	0.282608i
$73$	−3.21735	−	0.862086i	−0.376562	−	0.100900i	0.0655734	−	0.997848i	$-0.479112\pi$
$73$	−3.21735	−	0.862086i	−0.376562	−	0.100900i	−0.442136	+	0.896948i	$0.645779\pi$
$74$	−3.52199	+	2.03342i	−0.409424	+	0.236381i
$75$		0			0
$76$	−1.51045	−	4.08883i	−0.173261	−	0.469021i
$77$	−2.42208	−	2.42208i	−0.276021	−	0.276021i
$78$	−0.559756	+	2.08904i	−0.0633799	+	0.236537i
$79$	−0.0163335	−	0.0282904i	−0.00183766	−	0.00318292i	0.865105	−	0.501591i	$-0.167252\pi$
$79$	−0.0163335	−	0.0282904i	−0.00183766	−	0.00318292i	−0.866943	+	0.498408i	$0.833918\pi$
$80$		0			0
$81$	2.30556	+	3.99334i	0.256173	+	0.443705i
$82$	−7.78501	+	2.08599i	−0.859711	+	0.230359i
$83$	12.0016	−	12.0016i	1.31735	−	1.31735i	0.401485	−	0.915865i	$-0.368494\pi$
$83$	12.0016	−	12.0016i	1.31735	−	1.31735i	0.915865	−	0.401485i	$-0.131506\pi$
$84$	−1.03165			−0.112562
$85$		0			0
$86$	1.57865	+	0.911434i	0.170230	+	0.0982824i
$87$	−4.96875	−	4.96875i	−0.532706	−	0.532706i
$88$	−1.68876	−	1.68876i	−0.180022	−	0.180022i
$89$	1.11103	−	1.92436i	0.117769	−	0.203981i	−0.801114	−	0.598511i	$-0.795759\pi$
$89$	1.11103	−	1.92436i	0.117769	−	0.203981i	0.918883	+	0.394530i	$0.129093\pi$
$90$		0			0
$91$	−3.73457	−	2.15616i	−0.391490	−	0.226027i
$92$	−1.35931	+	5.07300i	−0.141717	+	0.528897i
$93$	7.01500	+	1.87966i	0.727421	+	0.194912i
$94$	−0.361555			−0.0372915
$95$		0			0
$96$	−0.719304			−0.0734137
$97$	9.85916	+	2.64175i	1.00105	+	0.268229i	0.721883	−	0.692015i	$-0.243277\pi$
$97$	9.85916	+	2.64175i	1.00105	+	0.268229i	0.279162	+	0.960244i	$0.409943\pi$
$98$	−1.27934	+	4.77454i	−0.129232	+	0.482302i
$99$	5.13476	+	2.96456i	0.516063	+	0.297949i
$100$		0			0
$101$	8.56678	−	14.8381i	0.852427	−	1.47645i	−0.0265848	−	0.999647i	$-0.508463\pi$
$101$	8.56678	−	14.8381i	0.852427	−	1.47645i	0.879012	−	0.476800i	$-0.158203\pi$
$102$	−2.41636	−	2.41636i	−0.239255	−	0.239255i
$103$	−1.78051	−	1.78051i	−0.175438	−	0.175438i	0.613926	−	0.789364i	$-0.289590\pi$
$103$	−1.78051	−	1.78051i	−0.175438	−	0.175438i	−0.789364	+	0.613926i	$0.789590\pi$
$104$	−2.60388	−	1.50335i	−0.255331	−	0.147416i
$105$		0			0
$106$	−7.33385			−0.712327
$107$	4.96199	−	4.96199i	0.479694	−	0.479694i	−0.425340	−	0.905034i	$-0.639845\pi$
$107$	4.96199	−	4.96199i	0.479694	−	0.479694i	0.905034	+	0.425340i	$0.139845\pi$
$108$	3.80928	−	1.02069i	0.366548	−	0.0982163i
$109$	4.61026	+	7.98521i	0.441583	+	0.764844i	0.997807	−	0.0661882i	$-0.0210838\pi$
$109$	4.61026	+	7.98521i	0.441583	+	0.764844i	−0.556224	+	0.831032i	$0.687750\pi$
$110$		0			0
$111$	−1.46265	−	2.53339i	−0.138829	−	0.240458i
$112$	0.371207	−	1.38536i	0.0350758	−	0.130905i
$113$	0.471659	+	0.471659i	0.0443699	+	0.0443699i	0.728944	−	0.684574i	$-0.240012\pi$
$113$	0.471659	+	0.471659i	0.0443699	+	0.0443699i	−0.684574	+	0.728944i	$0.740012\pi$
$114$	2.94111	−	1.08647i	0.275461	−	0.101758i
$115$		0			0
$116$	8.46019	−	4.88449i	0.785509	−	0.453514i
$117$	7.21010	+	1.93194i	0.666574	+	0.178608i
$118$	−0.672024	−	2.50803i	−0.0618648	−	0.230883i
$119$	5.90084	−	3.40685i	0.540929	−	0.312306i
$120$		0			0
$121$	−5.29619			−0.481472
$122$	0.438696	−	0.438696i	0.0397177	−	0.0397177i
$123$	−1.50046	−	5.59979i	−0.135292	−	0.504916i
$124$	−5.04825	+	8.74383i	−0.453347	+	0.785219i
$125$		0			0
$126$			3.56063i			0.317206i
$127$	−2.58532	−	9.64853i	−0.229410	−	0.856169i	−0.980590	−	0.196071i	$-0.937182\pi$
$127$	−2.58532	−	9.64853i	−0.229410	−	0.856169i	0.751180	−	0.660097i	$-0.229485\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−0.655598	+	1.13553i	−0.0577222	+	0.0999778i
$130$		0			0
$131$	−3.29085	−	5.69992i	−0.287523	−	0.498004i	0.685695	−	0.727889i	$-0.259498\pi$
$131$	−3.29085	−	5.69992i	−0.287523	−	0.498004i	−0.973218	+	0.229885i	$0.926165\pi$
$132$	1.21473	−	1.21473i	0.105729	−	0.105729i
$133$	0.574720	+	6.22521i	0.0498345	+	0.539794i
$134$		−	1.42372i		−	0.122991i
$135$		0			0
$136$	4.11428	−	2.37538i	0.352797	−	0.203687i
$137$	−8.71025	+	2.33391i	−0.744167	+	0.199399i	−0.610929	−	0.791685i	$-0.709204\pi$
$137$	−8.71025	+	2.33391i	−0.744167	+	0.199399i	−0.133238	+	0.991084i	$0.542537\pi$
$138$	−3.64903	−	0.977755i	−0.310626	−	0.0832320i
$139$	−4.69540	−	2.71089i	−0.398259	−	0.229935i	0.287474	−	0.957789i	$-0.407185\pi$
$139$	−4.69540	−	2.71089i	−0.398259	−	0.229935i	−0.685732	+	0.727854i	$0.740518\pi$
$140$		0			0
$141$		−	0.260068i		−	0.0219017i
$142$	6.01076	−	1.61058i	0.504412	−	0.135157i
$143$	6.93612	−	1.85853i	0.580028	−	0.155418i
$144$			2.48260i			0.206883i
$145$		0			0
$146$	2.88460	+	1.66542i	0.238731	+	0.137831i
$147$	−3.43435	−	0.920231i	−0.283260	−	0.0758994i
$148$	3.92827	−	1.05258i	0.322902	−	0.0865214i
$149$	−5.72771	+	3.30689i	−0.469232	+	0.270911i	−0.715918	−	0.698184i	$-0.753992\pi$
$149$	−5.72771	+	3.30689i	−0.469232	+	0.270911i	0.246686	+	0.969095i	$0.420658\pi$
$150$		0			0
$151$			17.2548i			1.40418i	0.712091	+	0.702088i	$0.247749\pi$
$151$			17.2548i			1.40418i	−0.712091	+	0.702088i	$0.752251\pi$
$152$	0.400715	+	4.34044i	0.0325023	+	0.352056i
$153$	−8.33979	+	8.33979i	−0.674232	+	0.674232i
$154$	1.71267	+	2.96642i	0.138011	+	0.239041i
$155$		0			0
$156$	1.08137	−	1.87298i	0.0865786	−	0.149959i
$157$	−0.838326	+	3.12868i	−0.0669057	+	0.249696i	−0.991276	−	0.131800i	$-0.957924\pi$
$157$	−0.838326	+	3.12868i	−0.0669057	+	0.249696i	0.924371	+	0.381496i	$0.124591\pi$
$158$	0.00845484	+	0.0315539i	0.000672631	+	0.00251029i
$159$		−	5.27527i		−	0.418356i
$160$		0			0
$161$	3.76627	−	6.52336i	0.296823	−	0.514113i
$162$	−1.19344	−	4.45399i	−0.0937658	−	0.349939i
$163$	−13.0605	+	13.0605i	−1.02297	+	1.02297i	−0.0232448	+	0.999730i	$0.507400\pi$
$163$	−13.0605	+	13.0605i	−1.02297	+	1.02297i	−0.999730	+	0.0232448i	$0.992600\pi$
$164$	8.05964			0.629352
$165$		0			0
$166$	−14.6989	+	8.48644i	−1.14086	+	0.658675i
$167$	5.62051	+	20.9760i	0.434928	+	1.62317i	0.741238	+	0.671243i	$0.234239\pi$
$167$	5.62051	+	20.9760i	0.434928	+	1.62317i	−0.306309	+	0.951932i	$0.599094\pi$
$168$	0.996498	+	0.267011i	0.0768815	+	0.0206003i
$169$	−3.42924	+	1.97987i	−0.263788	+	0.152298i
$170$		0			0
$171$	−3.74985	−	10.1509i	−0.286758	−	0.776262i
$172$	−1.28896	−	1.28896i	−0.0982824	−	0.0982824i
$173$	1.72920	−	6.45347i	0.131469	−	0.490649i	−0.868519	−	0.495657i	$-0.834927\pi$
$173$	1.72920	−	6.45347i	0.131469	−	0.490649i	0.999987	+	0.00500806i	$0.00159412\pi$
$174$	3.51344	+	6.08545i	0.266353	+	0.461337i
$175$		0			0
$176$	1.19413	+	2.06830i	0.0900111	+	0.155904i
$177$	1.80404	−	0.483390i	0.135600	−	0.0363338i
$178$	−1.57123	+	1.57123i	−0.117769	+	0.117769i
$179$	−11.9857			−0.895851			−0.447925	−	0.894071i	$-0.647837\pi$
$179$	−11.9857			−0.895851			−0.447925	+	0.894071i	$0.647837\pi$
$180$		0			0
$181$	−20.6699	−	11.9338i	−1.53638	−	0.887031i	−0.999046	−	0.0436636i	$-0.986097\pi$
$181$	−20.6699	−	11.9338i	−1.53638	−	0.887031i	−0.537337	−	0.843368i	$-0.680570\pi$
$182$	3.04927	+	3.04927i	0.226027	+	0.226027i
$183$	0.315556	+	0.315556i	0.0233266	+	0.0233266i
$184$	2.62598	−	4.54833i	0.193590	−	0.335307i
$185$		0			0
$186$	−6.28948	−	3.63123i	−0.461167	−	0.266255i
$187$	−2.93658	+	10.9595i	−0.214744	+	0.801436i
$188$	0.349235	+	0.0935773i	0.0254706	+	0.00682482i
$189$	−5.65613			−0.411423
$190$		0			0
$191$	16.5623			1.19840			0.599201	−	0.800598i	$-0.295485\pi$
$191$	16.5623			1.19840			0.599201	+	0.800598i	$0.295485\pi$
$192$	0.694795	+	0.186170i	0.0501425	+	0.0134356i
$193$	−2.74324	+	10.2379i	−0.197463	+	0.736941i	0.794153	+	0.607718i	$0.207915\pi$
$193$	−2.74324	+	10.2379i	−0.197463	+	0.736941i	−0.991616	+	0.129223i	$0.958752\pi$
$194$	−8.83948	−	5.10347i	−0.634637	−	0.366408i
$195$		0			0
$196$	2.47149	−	4.28074i	0.176535	−	0.305767i
$197$	17.3356	+	17.3356i	1.23511	+	1.23511i	0.961975	+	0.273139i	$0.0880618\pi$
$197$	17.3356	+	17.3356i	1.23511	+	1.23511i	0.273139	+	0.961975i	$0.411938\pi$
$198$	−4.19251	−	4.19251i	−0.297949	−	0.297949i
$199$	−9.91254	−	5.72301i	−0.702682	−	0.405693i	0.105664	−	0.994402i	$-0.466303\pi$
$199$	−9.91254	−	5.72301i	−0.702682	−	0.405693i	−0.808345	+	0.588709i	$0.799637\pi$
$200$		0			0
$201$	1.02409			0.0722336
$202$	−12.1153	+	12.1153i	−0.852427	+	0.852427i
$203$	−13.5336	+	3.62632i	−0.949872	+	0.254518i
$204$	1.70862	+	2.95942i	0.119627	+	0.207201i
$205$		0			0
$206$	1.25901	+	2.18067i	0.0877192	+	0.151934i
$207$	−3.37461	+	12.5942i	−0.234552	+	0.875360i
$208$	2.12606	+	2.12606i	0.147416	+	0.147416i
$209$	−8.00667	−	6.65325i	−0.553833	−	0.460215i
$210$		0			0
$211$	−6.74675	+	3.89524i	−0.464465	+	0.268159i	−0.713920	−	0.700227i	$-0.753082\pi$
$211$	−6.74675	+	3.89524i	−0.464465	+	0.268159i	0.249455	+	0.968387i	$0.419749\pi$
$212$	7.08396	+	1.89814i	0.486528	+	0.130365i
$213$	1.15850	+	4.32356i	0.0793788	+	0.296246i
$214$	−6.07718	+	3.50866i	−0.415427	+	0.239847i
$215$		0			0
$216$	−3.94366			−0.268332
$217$	10.2394	−	10.2394i	0.695099	−	0.695099i
$218$	−2.38645	−	8.90634i	−0.161631	−	0.603213i
$219$	−1.19795	+	2.07490i	−0.0809497	+	0.140209i
$220$		0			0
$221$			14.2841i			0.960854i
$222$	0.757124	+	2.82562i	0.0508148	+	0.189643i
$223$	3.10249	−	11.5787i	0.207758	−	0.775365i	−0.780833	−	0.624740i	$-0.785205\pi$
$223$	3.10249	−	11.5787i	0.207758	−	0.775365i	0.988591	−	0.150625i	$-0.0481285\pi$
$224$	−0.717117	+	1.24208i	−0.0479144	+	0.0829902i
$225$		0			0
$226$	−0.333513	−	0.577661i	−0.0221850	−	0.0384255i
$227$	−15.2621	+	15.2621i	−1.01298	+	1.01298i	−0.0130664	+	0.999915i	$0.504159\pi$
$227$	−15.2621	+	15.2621i	−1.01298	+	1.01298i	−0.999915	+	0.0130664i	$0.995841\pi$
$228$	−3.12210	+	0.288236i	−0.206766	+	0.0190889i
$229$			14.2432i			0.941219i	0.882342	+	0.470609i	$0.155966\pi$
$229$			14.2432i			0.941219i	−0.882342	+	0.470609i	$0.844034\pi$
$230$		0			0
$231$	−2.13376	+	1.23193i	−0.140391	+	0.0810549i
$232$	−9.43611	+	2.52840i	−0.619511	+	0.165998i
$233$	−15.7624	−	4.22353i	−1.03263	−	0.276693i	−0.297575	−	0.954699i	$-0.596178\pi$
$233$	−15.7624	−	4.22353i	−1.03263	−	0.276693i	−0.735056	+	0.678006i	$0.762844\pi$
$234$	−6.46440	−	3.73222i	−0.422591	−	0.243983i
$235$		0			0
$236$			2.59650i			0.169018i
$237$	−0.0226968	+	0.00608160i	−0.00147432	+	0.000395042i
$238$	−6.58153	+	1.76352i	−0.426617	+	0.114312i
$239$			11.7603i			0.760711i	0.924840	+	0.380355i	$0.124198\pi$
$239$			11.7603i			0.760711i	−0.924840	+	0.380355i	$0.875802\pi$
$240$		0			0
$241$	11.5318	+	6.65790i	0.742829	+	0.428873i	0.823097	−	0.567901i	$-0.192244\pi$
$241$	11.5318	+	6.65790i	0.742829	+	0.428873i	−0.0802677	+	0.996773i	$0.525578\pi$
$242$	5.11572	+	1.37075i	0.328851	+	0.0881154i
$243$	14.6316	−	3.92053i	0.938619	−	0.251502i
$244$	−0.537291	+	0.310205i	−0.0343965	+	0.0198589i
$245$		0			0
$246$			5.79733i			0.369624i
$247$	−11.9044	−	5.48179i	−0.757459	−	0.348798i
$248$	7.13931	−	7.13931i	0.453347	−	0.453347i
$249$	−6.10433	−	10.5730i	−0.386846	−	0.670037i
$250$		0			0
$251$	−12.9058	+	22.3535i	−0.814606	+	1.41094i	0.0950040	+	0.995477i	$0.469714\pi$
$251$	−12.9058	+	22.3535i	−0.814606	+	1.41094i	−0.909610	+	0.415463i	$0.863620\pi$
$252$	0.921559	−	3.43931i	0.0580528	−	0.216656i
$253$	3.24638	+	12.1157i	0.204098	+	0.761706i
$254$			9.98889i			0.626759i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.83587	−	6.85158i	−0.114519	−	0.427390i	0.884732	−	0.466101i	$-0.154342\pi$
$257$	−1.83587	−	6.85158i	−0.114519	−	0.427390i	−0.999250	+	0.0387109i	$0.987675\pi$
$258$	0.927156	−	0.927156i	0.0577222	−	0.0577222i
$259$	−5.83281			−0.362433
$260$		0			0
$261$	21.0033	−	12.1262i	1.30007	−	0.750596i
$262$	1.70347	+	6.35743i	0.105241	+	0.392764i
$263$	20.1313	+	5.39416i	1.24135	+	0.332618i	0.818988	−	0.573811i	$-0.194535\pi$
$263$	20.1313	+	5.39416i	1.24135	+	0.332618i	0.422359	+	0.906429i	$0.361202\pi$
$264$	−1.48774	+	0.858945i	−0.0915638	+	0.0528644i
$265$		0			0
$266$	1.05607	−	6.16184i	0.0647516	−	0.377807i
$267$	−1.13019	−	1.13019i	−0.0691667	−	0.0691667i
$268$	−0.368486	+	1.37521i	−0.0225088	+	0.0840042i
$269$	10.3374	+	17.9049i	0.630282	+	1.09168i	0.987494	+	0.157657i	$0.0503942\pi$
$269$	10.3374	+	17.9049i	0.630282	+	1.09168i	−0.357212	+	0.934023i	$0.616272\pi$
$270$		0			0
$271$	−12.5983	−	21.8210i	−0.765295	−	1.32553i	−0.940091	−	0.340925i	$-0.889260\pi$
$271$	−12.5983	−	21.8210i	−0.765295	−	1.32553i	0.174796	−	0.984605i	$-0.444073\pi$
$272$	−4.58888	+	1.22959i	−0.278242	+	0.0745547i
$273$	−2.19335	+	2.19335i	−0.132748	+	0.132748i
$274$	9.01752			0.544768
$275$		0			0
$276$	3.27163	+	1.88888i	0.196929	+	0.113697i
$277$	−16.2232	−	16.2232i	−0.974760	−	0.974760i	0.0249288	−	0.999689i	$-0.492064\pi$
$277$	−16.2232	−	16.2232i	−0.974760	−	0.974760i	−0.999689	+	0.0249288i	$0.992064\pi$
$278$	3.83378	+	3.83378i	0.229935	+	0.229935i
$279$	−12.5328	+	21.7074i	−0.750319	+	1.29959i
$280$		0			0
$281$	−4.62150	−	2.66822i	−0.275695	−	0.159173i	0.355778	−	0.934571i	$-0.384216\pi$
$281$	−4.62150	−	2.66822i	−0.275695	−	0.159173i	−0.631473	+	0.775398i	$0.717549\pi$
$282$	−0.0673105	+	0.251206i	−0.00400828	+	0.0149591i
$283$	−31.6725	−	8.48662i	−1.88274	−	0.504477i	−0.999358	−	0.0358135i	$-0.988598\pi$
$283$	−31.6725	−	8.48662i	−1.88274	−	0.504477i	−0.883377	−	0.468664i	$-0.844736\pi$
$284$	−6.22280			−0.369255
$285$		0			0
$286$	−7.18080			−0.424610
$287$	−11.1655	−	2.99179i	−0.659080	−	0.176600i
$288$	0.642545	−	2.39801i	0.0378623	−	0.141304i
$289$	−4.82354	−	2.78487i	−0.283737	−	0.163816i
$290$		0			0
$291$	3.67095	−	6.35827i	0.215195	−	0.372729i
$292$	−2.35526	−	2.35526i	−0.137831	−	0.137831i
$293$	−13.1650	−	13.1650i	−0.769106	−	0.769106i	0.208844	−	0.977949i	$-0.433030\pi$
$293$	−13.1650	−	13.1650i	−0.769106	−	0.769106i	−0.977949	+	0.208844i	$0.933030\pi$
$294$	3.07915	+	1.77775i	0.179580	+	0.103681i
$295$		0			0
$296$	−4.06685			−0.236381
$297$	6.65989	−	6.65989i	0.386446	−	0.386446i
$298$	6.38843	−	1.71177i	0.370072	−	0.0991604i
$299$	7.89553	+	13.6755i	0.456610	+	0.790872i
$300$		0			0
$301$	1.30721	+	2.26415i	0.0753463	+	0.130504i
$302$	4.46587	−	16.6669i	0.256982	−	0.959070i
$303$	−8.71456	−	8.71456i	−0.500638	−	0.500638i
$304$	0.736327	−	4.29626i	0.0422313	−	0.246407i
$305$		0			0
$306$	10.2141	−	5.89712i	0.583902	−	0.337116i
$307$	−18.1679	−	4.86806i	−1.03689	−	0.277835i	−0.300069	−	0.953918i	$-0.597010\pi$
$307$	−18.1679	−	4.86806i	−1.03689	−	0.277835i	−0.736826	+	0.676083i	$0.763676\pi$
$308$	−0.886541	−	3.30862i	−0.0505154	−	0.188526i
$309$	−1.56856	+	0.905610i	−0.0892324	+	0.0515183i
$310$		0			0
$311$	−4.47649			−0.253838			−0.126919	−	0.991913i	$-0.540509\pi$
$311$	−4.47649			−0.253838			−0.126919	+	0.991913i	$0.540509\pi$
$312$	−1.52928	+	1.52928i	−0.0865786	+	0.0865786i
$313$	−3.22806	−	12.0473i	−0.182461	−	0.680953i	−0.995160	−	0.0982696i	$-0.968669\pi$
$313$	−3.22806	−	12.0473i	−0.182461	−	0.680953i	0.812699	−	0.582684i	$-0.197997\pi$
$314$	1.61952	−	2.80509i	0.0913949	−	0.158301i
$315$		0			0
$316$		−	0.0326670i		−	0.00183766i
$317$	1.46541	+	5.46899i	0.0823058	+	0.307169i	0.994790	−	0.101942i	$-0.0325055\pi$
$317$	1.46541	+	5.46899i	0.0823058	+	0.307169i	−0.912485	+	0.409111i	$0.865839\pi$
$318$	−1.36534	+	5.09552i	−0.0765645	+	0.285743i
$319$	11.6655	−	20.2052i	0.653141	−	1.13127i
$320$		0			0
$321$	−2.52379	−	4.37134i	−0.140864	−	0.243984i
$322$	−5.32631	+	5.32631i	−0.296823	+	0.296823i
$323$	16.9059	−	11.9589i	0.940672	−	0.665409i
$324$			4.61111i			0.256173i
$325$		0			0
$326$	15.9957	−	9.23514i	0.885922	−	0.511487i
$327$	6.40637	−	1.71658i	0.354273	−	0.0949272i
$328$	−7.78501	−	2.08599i	−0.429855	−	0.115179i
$329$	−0.449081	−	0.259277i	−0.0247586	−	0.0142944i
$330$		0			0
$331$		−	13.4811i		−	0.740988i	−0.928835	−	0.370494i	$-0.879188\pi$
$331$		−	13.4811i		−	0.740988i	0.928835	−	0.370494i	$-0.120812\pi$
$332$	16.3945	−	4.39290i	0.899767	−	0.241092i
$333$	9.75234	−	2.61313i	0.534425	−	0.143199i
$334$		−	21.7160i		−	1.18825i
$335$		0			0
$336$	−0.893436	−	0.515825i	−0.0487409	−	0.0281406i
$337$	30.9819	+	8.30158i	1.68769	+	0.452216i	0.969793	−	0.243931i	$-0.0784370\pi$
$337$	30.9819	+	8.30158i	1.68769	+	0.452216i	0.717900	+	0.696147i	$0.245104\pi$
$338$	3.82482	−	1.02486i	0.208043	−	0.0557449i
$339$	0.415514	−	0.239897i	0.0225676	−	0.0130294i
$340$		0			0
$341$			24.1131i			1.30580i
$342$	0.994816	+	10.7756i	0.0537935	+	0.582677i
$343$	−12.1120	+	12.1120i	−0.653989	+	0.653989i
$344$	0.911434	+	1.57865i	0.0491412	+	0.0851151i
$345$		0			0
$346$	−3.34056	+	5.78603i	−0.179590	+	0.311059i
$347$	−0.973759	+	3.63412i	−0.0522741	+	0.195090i	−0.987125	−	0.159951i	$-0.948866\pi$
$347$	−0.973759	+	3.63412i	−0.0522741	+	0.195090i	0.934851	+	0.355041i	$0.115533\pi$
$348$	−1.81869	−	6.78744i	−0.0974919	−	0.363845i
$349$			31.2369i			1.67207i	0.548673	+	0.836037i	$0.315133\pi$
$349$			31.2369i			1.67207i	−0.548673	+	0.836037i	$0.684867\pi$
$350$		0			0
$351$	5.92870	−	10.2688i	0.316451	−	0.548109i
$352$	−0.618129	−	2.30689i	−0.0329464	−	0.122958i
$353$	−17.2688	+	17.2688i	−0.919124	+	0.919124i	−0.996966	−	0.0778415i	$-0.975197\pi$
$353$	−17.2688	+	17.2688i	−0.919124	+	0.919124i	0.0778415	+	0.996966i	$0.475197\pi$
$354$	−1.86767			−0.0992658
$355$		0			0
$356$	1.92436	−	1.11103i	0.101991	−	0.0588843i
$357$	−1.26851	−	4.73413i	−0.0671364	−	0.250556i
$358$	11.5773	+	3.10212i	0.611878	+	0.163952i
$359$	11.6435	−	6.72238i	0.614521	−	0.354794i	−0.160212	−	0.987083i	$-0.551218\pi$
$359$	11.6435	−	6.72238i	0.614521	−	0.354794i	0.774733	+	0.632289i	$0.217884\pi$
$360$		0			0
$361$	3.47856	+	18.6789i	0.183082	+	0.983098i
$362$	16.8769	+	16.8769i	0.887031	+	0.887031i
$363$	−0.985989	+	3.67976i	−0.0517510	+	0.193137i
$364$	−2.15616	−	3.73457i	−0.113013	−	0.195745i
$365$		0			0
$366$	−0.223132	−	0.386476i	−0.0116633	−	0.0202014i
$367$	1.20298	−	0.322337i	0.0627950	−	0.0168259i	−0.227285	−	0.973828i	$-0.572985\pi$
$367$	1.20298	−	0.322337i	0.0627950	−	0.0168259i	0.290080	+	0.957002i	$0.406318\pi$
$368$	−3.71369	+	3.71369i	−0.193590	+	0.193590i
$369$	20.0089			1.04162
$370$		0			0
$371$	−9.10926	−	5.25923i	−0.472929	−	0.273046i
$372$	5.13534	+	5.13534i	0.266255	+	0.266255i
$373$	20.2015	+	20.2015i	1.04599	+	1.04599i	0.998890	+	0.0471036i	$0.0149991\pi$
$373$	20.2015	+	20.2015i	1.04599	+	1.04599i	0.0471036	+	0.998890i	$0.485001\pi$
$374$	5.67304	−	9.82599i	0.293346	−	0.508090i
$375$		0			0
$376$	−0.313116	−	0.180777i	−0.0161477	−	0.00932288i
$377$	7.60214	−	28.3716i	0.391530	−	1.46121i
$378$	5.46340	+	1.46391i	0.281007	+	0.0752956i
$379$	−6.67007			−0.342618			−0.171309	−	0.985217i	$-0.554800\pi$
$379$	−6.67007			−0.342618			−0.171309	+	0.985217i	$0.554800\pi$
$380$		0			0
$381$	−7.18505			−0.368101
$382$	−15.9979	−	4.28663i	−0.818524	−	0.219323i
$383$	6.20447	−	23.1554i	0.317033	−	1.18319i	−0.605048	−	0.796189i	$-0.706846\pi$
$383$	6.20447	−	23.1554i	0.317033	−	1.18319i	0.922081	−	0.386996i	$-0.126487\pi$
$384$	−0.622936	−	0.359652i	−0.0317891	−	0.0183534i
$385$		0			0
$386$	5.29953	−	9.17906i	0.269739	−	0.467202i
$387$	−3.19998	−	3.19998i	−0.162664	−	0.162664i
$388$	7.21740	+	7.21740i	0.366408	+	0.366408i
$389$	−0.912264	−	0.526696i	−0.0462536	−	0.0267045i	0.476695	−	0.879069i	$-0.341835\pi$
$389$	−0.912264	−	0.526696i	−0.0462536	−	0.0267045i	−0.522948	+	0.852364i	$0.675168\pi$
$390$		0			0
$391$	−24.9508			−1.26182
$392$	−3.49521	+	3.49521i	−0.176535	+	0.176535i
$393$	−4.57293	+	1.22531i	−0.230674	+	0.0618089i
$394$	−12.2582	−	21.2317i	−0.617557	−	1.06964i
$395$		0			0
$396$	2.96456	+	5.13476i	0.148975	+	0.258031i
$397$	−3.38776	+	12.6433i	−0.170027	+	0.634548i	0.827319	+	0.561733i	$0.189865\pi$
$397$	−3.38776	+	12.6433i	−0.170027	+	0.634548i	−0.997345	+	0.0728155i	$0.976802\pi$
$398$	8.09356	+	8.09356i	0.405693	+	0.405693i
$399$	4.43224	+	0.759633i	0.221889	+	0.0380292i
$400$		0			0
$401$	0.812592	−	0.469150i	0.0405789	−	0.0234282i	−0.479573	−	0.877502i	$-0.659209\pi$
$401$	0.812592	−	0.469150i	0.0405789	−	0.0234282i	0.520152	+	0.854074i	$0.325875\pi$
$402$	−0.989193	−	0.265053i	−0.0493364	−	0.0132197i
$403$	7.85702	+	29.3228i	0.391386	+	1.46067i
$404$	14.8381	−	8.56678i	0.738223	−	0.426213i
$405$		0			0
$406$	14.0110			0.695355
$407$	6.86793	−	6.86793i	0.340430	−	0.340430i
$408$	−0.884448	−	3.30080i	−0.0437867	−	0.163414i
$409$	6.72826	−	11.6537i	0.332691	−	0.576238i	−0.650347	−	0.759637i	$-0.725377\pi$
$409$	6.72826	−	11.6537i	0.332691	−	0.576238i	0.983039	+	0.183399i	$0.0587100\pi$
$410$		0			0
$411$			6.48634i			0.319947i
$412$	−0.651710	−	2.43222i	−0.0321075	−	0.119827i
$413$	0.963840	−	3.59710i	0.0474275	−	0.177002i
$414$	6.51926	−	11.2917i	0.320404	−	0.554956i
$415$		0			0
$416$	−1.50335	−	2.60388i	−0.0737078	−	0.127666i
$417$	−2.75765	+	2.75765i	−0.135043	+	0.135043i
$418$	6.01186	+	8.49882i	0.294050	+	0.415691i
$419$		−	31.4227i		−	1.53510i	−0.640989	−	0.767550i	$-0.721476\pi$
$419$		−	31.4227i		−	1.53510i	0.640989	−	0.767550i	$-0.278524\pi$
$420$		0			0
$421$	−13.8219	+	7.98005i	−0.673636	+	0.388924i	−0.797453	−	0.603381i	$-0.793820\pi$
$421$	−13.8219	+	7.98005i	−0.673636	+	0.388924i	0.123817	+	0.992305i	$0.460486\pi$
$422$	7.52502	−	2.01632i	0.366312	−	0.0981531i
$423$	0.867011	+	0.232315i	0.0421555	+	0.0112955i
$424$	−6.35130	−	3.66693i	−0.308447	−	0.178082i
$425$		0			0
$426$		−	4.47608i		−	0.216867i
$427$	0.859494	−	0.230301i	0.0415938	−	0.0111450i
$428$	6.77821	−	1.81622i	0.327637	−	0.0877901i
$429$		−	5.16518i		−	0.249377i
$430$		0			0
$431$	16.0614	+	9.27303i	0.773648	+	0.446666i	0.834174	−	0.551501i	$-0.185945\pi$
$431$	16.0614	+	9.27303i	0.773648	+	0.446666i	−0.0605263	+	0.998167i	$0.519278\pi$
$432$	3.80928	+	1.02069i	0.183274	+	0.0491082i
$433$	−4.93514	+	1.32237i	−0.237168	+	0.0635489i	−0.375445	−	0.926845i	$-0.622510\pi$
$433$	−4.93514	+	1.32237i	−0.237168	+	0.0635489i	0.138277	+	0.990394i	$0.455843\pi$
$434$	−12.5407	+	7.24038i	−0.601973	+	0.347549i
$435$		0			0
$436$			9.22052i			0.441583i
$437$	9.57532	−	20.7940i	0.458049	−	0.994712i
$438$	1.69415	−	1.69415i	0.0809497	−	0.0809497i
$439$	−6.25946	−	10.8417i	−0.298748	−	0.517446i	0.677102	−	0.735889i	$-0.263236\pi$
$439$	−6.25946	−	10.8417i	−0.298748	−	0.517446i	−0.975850	+	0.218443i	$0.929902\pi$
$440$		0			0
$441$	6.13572	−	10.6274i	0.292177	−	0.506065i
$442$	3.69700	−	13.7974i	0.175848	−	0.656276i
$443$	−10.0467	−	37.4948i	−0.477333	−	1.78143i	−0.612350	−	0.790587i	$-0.709776\pi$
$443$	−10.0467	−	37.4948i	−0.477333	−	1.78143i	0.135017	−	0.990843i	$-0.456891\pi$
$444$		−	2.92530i		−	0.138829i
$445$		0			0
$446$	−5.99356	+	10.3811i	−0.283803	+	0.491562i
$447$	1.23129	+	4.59522i	0.0582379	+	0.217347i
$448$	1.01416	−	1.01416i	0.0479144	−	0.0479144i
$449$	−10.8951			−0.514169			−0.257085	−	0.966389i	$-0.582762\pi$
$449$	−10.8951			−0.514169			−0.257085	+	0.966389i	$0.582762\pi$
$450$		0			0
$451$	16.6697	−	9.62428i	0.784947	−	0.453189i
$452$	0.172639	+	0.644298i	0.00812026	+	0.0303052i
$453$	11.9885	+	3.21232i	0.563271	+	0.150928i
$454$	18.6922	−	10.7919i	0.877267	−	0.506491i
$455$		0			0
$456$	3.09032	+	0.529643i	0.144717	+	0.0248028i
$457$	−10.9672	−	10.9672i	−0.513025	−	0.513025i	0.402427	−	0.915452i	$-0.368167\pi$
$457$	−10.9672	−	10.9672i	−0.513025	−	0.513025i	−0.915452	+	0.402427i	$0.868167\pi$
$458$	3.68642	−	13.7579i	0.172255	−	0.642864i
$459$	9.36769	+	16.2253i	0.437246	+	0.757333i
$460$		0			0
$461$	1.58025	+	2.73707i	0.0735995	+	0.127478i	0.900476	−	0.434905i	$-0.143218\pi$
$461$	1.58025	+	2.73707i	0.0735995	+	0.127478i	−0.826877	+	0.562383i	$0.809885\pi$
$462$	2.37990	−	0.637693i	0.110723	−	0.0296682i
$463$	−25.6630	+	25.6630i	−1.19266	+	1.19266i	−0.216344	+	0.976317i	$0.569413\pi$
$463$	−25.6630	+	25.6630i	−1.19266	+	1.19266i	−0.976317	+	0.216344i	$0.930587\pi$
$464$	9.76898			0.453514
$465$		0			0
$466$	14.1322	+	8.15923i	0.654662	+	0.377969i
$467$	−15.1541	−	15.1541i	−0.701248	−	0.701248i	0.263431	−	0.964678i	$-0.415146\pi$
$467$	−15.1541	−	15.1541i	−0.701248	−	0.701248i	−0.964678	+	0.263431i	$0.915146\pi$
$468$	5.27816	+	5.27816i	0.243983	+	0.243983i
$469$	1.02097	−	1.76838i	0.0471442	−	0.0816561i
$470$		0			0
$471$	2.01772	+	1.16493i	0.0929715	+	0.0536771i
$472$	0.672024	−	2.50803i	0.0309324	−	0.115441i
$473$	−4.20515	−	1.12677i	−0.193353	−	0.0518088i
$474$	0.0234975			0.00107928
$475$		0			0
$476$	6.81371			0.312306
$477$	17.5866	+	4.71233i	0.805237	+	0.215763i
$478$	3.04379	−	11.3596i	0.139220	−	0.519575i
$479$	8.65416	+	4.99648i	0.395418	+	0.228295i	0.684505	−	0.729008i	$-0.260018\pi$
$479$	8.65416	+	4.99648i	0.395418	+	0.228295i	−0.289087	+	0.957303i	$0.593352\pi$
$480$		0			0
$481$	6.11390	−	10.5896i	0.278770	−	0.482843i
$482$	−9.41569	−	9.41569i	−0.428873	−	0.428873i
$483$	−3.83123	−	3.83123i	−0.174327	−	0.174327i
$484$	−4.58663	−	2.64809i	−0.208483	−	0.120368i
$485$		0			0
$486$	−15.1478			−0.687117
$487$	3.95427	−	3.95427i	0.179185	−	0.179185i	−0.611815	−	0.791001i	$-0.709560\pi$
$487$	3.95427	−	3.95427i	0.179185	−	0.179185i	0.791001	+	0.611815i	$0.209560\pi$
$488$	0.599271	−	0.160574i	0.0271277	−	0.00726885i
$489$	6.64288	+	11.5058i	0.300401	+	0.520310i
$490$		0			0
$491$	15.2803	+	26.4663i	0.689592	+	1.19441i	0.971970	+	0.235105i	$0.0755435\pi$
$491$	15.2803	+	26.4663i	0.689592	+	1.19441i	−0.282378	+	0.959303i	$0.591123\pi$
$492$	1.50046	−	5.59979i	0.0676459	−	0.252458i
$493$	32.8169	+	32.8169i	1.47800	+	1.47800i
$494$	10.0800	+	8.37609i	0.453520	+	0.376858i
$495$		0			0
$496$	−8.74383	+	5.04825i	−0.392610	+	0.226673i
$497$	8.62084	+	2.30995i	0.386697	+	0.103615i
$498$	3.15983	+	11.7927i	0.141596	+	0.528442i
$499$	23.2626	−	13.4307i	1.04138	−	0.601239i	0.121154	−	0.992634i	$-0.461340\pi$
$499$	23.2626	−	13.4307i	1.04138	−	0.601239i	0.920223	+	0.391394i	$0.128007\pi$
$500$		0			0
$501$	15.6204			0.697868
$502$	18.2515	−	18.2515i	0.814606	−	0.814606i
$503$	6.03190	+	22.5113i	0.268949	+	1.00373i	0.959789	+	0.280723i	$0.0905744\pi$
$503$	6.03190	+	22.5113i	0.268949	+	1.00373i	−0.690840	+	0.723008i	$0.742759\pi$
$504$	−1.78032	+	3.08360i	−0.0793016	+	0.137354i
$505$		0			0
$506$		−	12.5431i		−	0.557607i
$507$	0.737185	+	2.75121i	0.0327395	+	0.122186i
$508$	2.58532	−	9.64853i	0.114705	−	0.428084i
$509$	4.75131	−	8.22951i	0.210598	−	0.364767i	−0.741304	−	0.671170i	$-0.765792\pi$
$509$	4.75131	−	8.22951i	0.210598	−	0.364767i	0.951902	+	0.306403i	$0.0991255\pi$
$510$		0			0
$511$	2.38861	+	4.13719i	0.105666	+	0.183018i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−17.1172	+	1.58028i	−0.755744	+	0.0697713i
$514$			7.09327i			0.312871i
$515$		0			0
$516$	−1.13553	+	0.655598i	−0.0499889	+	0.0288611i
$517$	0.834066	−	0.223487i	0.0366822	−	0.00982896i
$518$	5.63406	+	1.50964i	0.247547	+	0.0663299i
$519$	−4.16191	−	2.40288i	−0.182688	−	0.105475i
$520$		0			0
$521$		−	23.0578i		−	1.01018i	−0.863067	−	0.505090i	$-0.831459\pi$
$521$		−	23.0578i		−	1.01018i	0.863067	−	0.505090i	$-0.168541\pi$
$522$	−23.4261	+	6.27701i	−1.02533	+	0.274737i
$523$	32.3420	−	8.66602i	1.41422	−	0.378939i	0.530789	−	0.847504i	$-0.321896\pi$
$523$	32.3420	−	8.66602i	1.41422	−	0.378939i	0.883429	+	0.468565i	$0.155229\pi$
$524$		−	6.58170i		−	0.287523i
$525$		0			0
$526$	−18.0492	−	10.4207i	−0.786983	−	0.454365i
$527$	−46.3317	−	12.4145i	−2.01824	−	0.540786i
$528$	1.65935	−	0.444623i	0.0722141	−	0.0193497i
$529$	−3.96902	+	2.29151i	−0.172566	+	0.0996311i
$530$		0			0
$531$			6.44608i			0.279736i
$532$	−2.61488	+	5.67855i	−0.113370	+	0.246196i
$533$	17.1353	−	17.1353i	0.742211	−	0.742211i
$534$	0.799167	+	1.38420i	0.0345833	+	0.0599001i
$535$		0			0
$536$	0.711860	−	1.23298i	0.0307477	−	0.0532565i
$537$	−2.23137	+	8.32758i	−0.0962906	+	0.359361i
$538$	−5.35103	−	19.9703i	−0.230699	−	0.860982i
$539$		−	11.8051i		−	0.508483i
$540$		0			0
$541$	6.15206	−	10.6557i	0.264498	−	0.458124i	−0.702934	−	0.711255i	$-0.748127\pi$
$541$	6.15206	−	10.6557i	0.264498	−	0.458124i	0.967432	+	0.253131i	$0.0814605\pi$
$542$	6.52138	+	24.3381i	0.280117	+	1.04541i
$543$	−12.1396	+	12.1396i	−0.520962	+	0.520962i
$544$	4.75076			0.203687
$545$		0			0
$546$	2.68629	−	1.55093i	0.114963	−	0.0663738i
$547$	−9.47712	−	35.3691i	−0.405212	−	1.51227i	−0.803664	−	0.595084i	$-0.797119\pi$
$547$	−9.47712	−	35.3691i	−0.405212	−	1.51227i	0.398451	−	0.917189i	$-0.369548\pi$
$548$	−8.71025	−	2.33391i	−0.372084	−	0.0996995i
$549$	−1.33388	+	0.770116i	−0.0569286	+	0.0328677i
$550$		0			0
$551$	−39.9437	+	14.7556i	−1.70166	+	0.628608i
$552$	−2.67127	−	2.67127i	−0.113697	−	0.113697i
$553$	−0.0121262	+	0.0452557i	−0.000515659	+	0.00192447i
$554$	11.4716	+	19.8693i	0.487380	+	0.844167i
$555$		0			0
$556$	−2.71089	−	4.69540i	−0.114967	−	0.199129i
$557$	15.9320	−	4.26897i	0.675061	−	0.180882i	0.0950272	−	0.995475i	$-0.469706\pi$
$557$	15.9320	−	4.26897i	0.675061	−	0.180882i	0.580033	+	0.814593i	$0.303040\pi$
$558$	17.7241	−	17.7241i	0.750319	−	0.750319i
$559$	−5.48082			−0.231814
$560$		0			0
$561$	7.06788	+	4.08064i	0.298406	+	0.172285i
$562$	3.77344	+	3.77344i	0.159173	+	0.159173i
$563$	−3.10059	−	3.10059i	−0.130674	−	0.130674i	0.638745	−	0.769419i	$-0.279454\pi$
$563$	−3.10059	−	3.10059i	−0.130674	−	0.130674i	−0.769419	+	0.638745i	$0.779454\pi$
$564$	0.130034	−	0.225225i	0.00547542	−	0.00948370i
$565$		0			0
$566$	28.3968	+	16.3949i	1.19361	+	0.689129i
$567$	1.71168	−	6.38807i	0.0718837	−	0.268274i
$568$	6.01076	+	1.61058i	0.252206	+	0.0675784i
$569$	−16.6846			−0.699455			−0.349727	−	0.936851i	$-0.613726\pi$
$569$	−16.6846			−0.699455			−0.349727	+	0.936851i	$0.613726\pi$
$570$		0			0
$571$	−7.93391			−0.332024			−0.166012	−	0.986124i	$-0.553089\pi$
$571$	−7.93391			−0.332024			−0.166012	+	0.986124i	$0.553089\pi$
$572$	6.93612	+	1.85853i	0.290014	+	0.0777090i
$573$	3.08339	−	11.5074i	0.128810	−	0.480727i
$574$	10.0107	+	5.77970i	0.417840	+	0.241240i
$575$		0			0
$576$	−1.24130	+	2.15000i	−0.0517209	+	0.0895832i
$577$	−12.2981	−	12.2981i	−0.511976	−	0.511976i	0.403156	−	0.915131i	$-0.367913\pi$
$577$	−12.2981	−	12.2981i	−0.511976	−	0.511976i	−0.915131	+	0.403156i	$0.867913\pi$
$578$	3.93840	+	3.93840i	0.163816	+	0.163816i
$579$	6.60254	+	3.81198i	0.274392	+	0.158420i
$580$		0			0
$581$	−24.3431			−1.00992
$582$	−5.19151	+	5.19151i	−0.215195	+	0.215195i
$583$	16.9184	−	4.53326i	0.700687	−	0.187749i
$584$	1.66542	+	2.88460i	0.0689157	+	0.119365i
$585$		0			0
$586$	9.30904	+	16.1237i	0.384553	+	0.666065i
$587$	−0.106964	+	0.399196i	−0.00441488	+	0.0164766i	−0.968098	−	0.250571i	$-0.919382\pi$
$587$	−0.106964	+	0.399196i	−0.00441488	+	0.0164766i	0.963683	+	0.267048i	$0.0860482\pi$
$588$	−2.51412	−	2.51412i	−0.103681	−	0.103681i
$589$	28.1269	−	33.8486i	1.15895	−	1.39471i
$590$		0			0
$591$	15.2721	−	8.81734i	0.628209	−	0.362697i
$592$	3.92827	+	1.05258i	0.161451	+	0.0432607i
$593$	−0.915527	−	3.41679i	−0.0375962	−	0.140311i	0.944577	−	0.328291i	$-0.106473\pi$
$593$	−0.915527	−	3.41679i	−0.0375962	−	0.140311i	−0.982173	+	0.187980i	$0.939806\pi$
$594$	−8.15666	+	4.70925i	−0.334672	+	0.193223i
$595$		0			0
$596$	−6.61379			−0.270911
$597$	−5.82173	+	5.82173i	−0.238268	+	0.238268i
$598$	−4.08703	−	15.2530i	−0.167131	−	0.623741i
$599$	−6.17905	+	10.7024i	−0.252469	+	0.437290i	−0.964205	−	0.265158i	$-0.914576\pi$
$599$	−6.17905	+	10.7024i	−0.252469	+	0.437290i	0.711736	+	0.702447i	$0.247909\pi$
$600$		0			0
$601$		−	19.5516i		−	0.797528i	−0.917054	−	0.398764i	$-0.869439\pi$
$601$		−	19.5516i		−	0.797528i	0.917054	−	0.398764i	$-0.130561\pi$
$602$	−0.676661	−	2.52533i	−0.0275787	−	0.102925i
$603$	−0.914803	+	3.41409i	−0.0372537	+	0.139033i
$604$	−8.62740	+	14.9431i	−0.351044	+	0.608026i
$605$		0			0
$606$	6.16212	+	10.6731i	0.250319	+	0.433566i
$607$	−11.0587	+	11.0587i	−0.448860	+	0.448860i	−0.894975	−	0.446115i	$-0.852807\pi$
$607$	−11.0587	+	11.0587i	−0.448860	+	0.448860i	0.446115	+	0.894975i	$0.352807\pi$
$608$	−1.82319	+	3.95929i	−0.0739402	+	0.160570i
$609$			10.0782i			0.408388i
$610$		0			0
$611$	0.941445	−	0.543544i	0.0380868	−	0.0219894i
$612$	−11.3924	+	3.05258i	−0.460509	+	0.123393i
$613$	3.06788	+	0.822036i	0.123911	+	0.0332017i	0.320241	−	0.947336i	$-0.396236\pi$
$613$	3.06788	+	0.822036i	0.123911	+	0.0332017i	−0.196331	+	0.980538i	$0.562903\pi$
$614$	16.2889	+	9.40438i	0.657365	+	0.379530i
$615$		0			0
$616$			3.42533i			0.138011i
$617$	35.6742	−	9.55886i	1.43619	−	0.384825i	0.544990	−	0.838442i	$-0.316533\pi$
$617$	35.6742	−	9.55886i	1.43619	−	0.384825i	0.891197	+	0.453617i	$0.149867\pi$
$618$	1.74950	−	0.468778i	0.0703753	−	0.0188570i
$619$		−	18.5959i		−	0.747433i	−0.927543	−	0.373716i	$-0.878083\pi$
$619$		−	18.5959i		−	0.747433i	0.927543	−	0.373716i	$-0.121917\pi$
$620$		0			0
$621$	17.9370	+	10.3560i	0.719789	+	0.415570i
$622$	4.32396	+	1.15860i	0.173375	+	0.0464556i
$623$	−3.07835	+	0.824843i	−0.123332	+	0.0330466i
$624$	1.87298	−	1.08137i	0.0749793	−	0.0432893i
$625$		0			0
$626$			12.4723i			0.498492i
$627$	−6.11324	+	4.32436i	−0.244139	+	0.172698i
$628$	−2.29035	+	2.29035i	−0.0913949	+	0.0913949i
$629$	9.66032	+	16.7322i	0.385182	+	0.667155i
$630$		0			0
$631$	−18.8281	+	32.6113i	−0.749536	+	1.29823i	0.198509	+	0.980099i	$0.436390\pi$
$631$	−18.8281	+	32.6113i	−0.749536	+	1.29823i	−0.948045	+	0.318136i	$0.896943\pi$
$632$	−0.00845484	+	0.0315539i	−0.000336315	+	0.00125515i
$633$	1.45035	+	5.41278i	0.0576462	+	0.215139i
$634$		−	5.66192i		−	0.224864i
$635$		0			0
$636$	2.63764	−	4.56852i	0.104589	−	0.181154i
$637$	−3.84658	−	14.3556i	−0.152407	−	0.568791i
$638$	−16.4975	+	16.4975i	−0.653141	+	0.653141i
$639$	−15.4487			−0.611142
$640$		0			0
$641$	29.8628	−	17.2413i	1.17951	−	0.680990i	0.223609	−	0.974679i	$-0.428216\pi$
$641$	29.8628	−	17.2413i	1.17951	−	0.680990i	0.955901	+	0.293689i	$0.0948829\pi$
$642$	1.30641	+	4.87560i	0.0515600	+	0.192424i
$643$	−29.4620	−	7.89433i	−1.16187	−	0.311322i	−0.374157	−	0.927365i	$-0.622068\pi$
$643$	−29.4620	−	7.89433i	−1.16187	−	0.311322i	−0.787712	+	0.616044i	$0.788734\pi$
$644$	6.52336	−	3.76627i	0.257057	−	0.148412i
$645$		0			0
$646$	−19.4251	+	7.17579i	−0.764269	+	0.282328i
$647$	−9.95134	−	9.95134i	−0.391227	−	0.391227i	0.483897	−	0.875125i	$-0.339221\pi$
$647$	−9.95134	−	9.95134i	−0.391227	−	0.391227i	−0.875125	+	0.483897i	$0.839221\pi$
$648$	1.19344	−	4.45399i	0.0468829	−	0.174969i
$649$	3.10057	+	5.37034i	0.121708	+	0.210804i
$650$		0			0
$651$	−5.20803	−	9.02058i	−0.204119	−	0.353544i
$652$	−17.8409	+	4.78046i	−0.698705	+	0.187217i
$653$	−25.1527	+	25.1527i	−0.984302	+	0.984302i	−0.999879	−	0.0155764i	$-0.995042\pi$
$653$	−25.1527	+	25.1527i	−0.984302	+	0.984302i	0.0155764	+	0.999879i	$0.495042\pi$
$654$	−6.63236			−0.259346
$655$		0			0
$656$	6.97985	+	4.02982i	0.272517	+	0.157338i
$657$	−5.84718	−	5.84718i	−0.228120	−	0.228120i
$658$	0.366673	+	0.366673i	0.0142944	+	0.0142944i
$659$	−5.83576	+	10.1078i	−0.227329	+	0.393745i	−0.957016	−	0.290036i	$-0.906333\pi$
$659$	−5.83576	+	10.1078i	−0.227329	+	0.393745i	0.729687	+	0.683782i	$0.239666\pi$
$660$		0			0
$661$	−3.70480	−	2.13897i	−0.144100	−	0.0831963i	0.426217	−	0.904621i	$-0.359846\pi$
$661$	−3.70480	−	2.13897i	−0.144100	−	0.0831963i	−0.570317	+	0.821425i	$0.693180\pi$
$662$	−3.48916	+	13.0217i	−0.135610	+	0.506104i
$663$	9.92453	+	2.65927i	0.385437	+	0.103277i
$664$	−16.9729			−0.658675
$665$		0			0
$666$	−10.0964			−0.391226
$667$	49.5580	+	13.2790i	1.91890	+	0.514166i
$668$	−5.62051	+	20.9760i	−0.217464	+	0.811587i
$669$	−7.46721	−	4.31119i	−0.288699	−	0.166680i
$670$		0			0
$671$	−0.740853	+	1.28319i	−0.0286003	+	0.0495372i
$672$	0.729487	+	0.729487i	0.0281406	+	0.0281406i
$673$	−28.2136	−	28.2136i	−1.08756	−	1.08756i	−0.995780	−	0.0917757i	$-0.970746\pi$
$673$	−28.2136	−	28.2136i	−1.08756	−	1.08756i	−0.0917757	−	0.995780i	$-0.529254\pi$
$674$	−27.7776	−	16.0374i	−1.06995	−	0.617738i
$675$		0			0
$676$	−3.95975			−0.152298
$677$	−28.7454	+	28.7454i	−1.10477	+	1.10477i	−0.110948	+	0.993826i	$0.535389\pi$
$677$	−28.7454	+	28.7454i	−1.10477	+	1.10477i	−0.993826	+	0.110948i	$0.964611\pi$
$678$	−0.463446	+	0.124180i	−0.0177985	+	0.00476910i
$679$	−7.31958	−	12.6779i	−0.280900	−	0.486532i
$680$		0			0
$681$	7.76268	+	13.4454i	0.297467	+	0.515227i
$682$	6.24094	−	23.2915i	0.238978	−	0.891878i
$683$	26.4931	+	26.4931i	1.01373	+	1.01373i	0.999904	+	0.0138253i	$0.00440088\pi$
$683$	26.4931	+	26.4931i	1.01373	+	1.01373i	0.0138253	+	0.999904i	$0.495599\pi$
$684$	1.82801	−	10.6659i	0.0698956	−	0.407821i
$685$		0			0
$686$	14.8342	−	8.56451i	0.566371	−	0.326994i
$687$	9.89611	+	2.65166i	0.377560	+	0.101167i
$688$	−0.471793	−	1.76075i	−0.0179869	−	0.0671281i
$689$	19.0965	−	11.0254i	0.727518	−	0.420032i
$690$		0			0
$691$	14.6142			0.555951			0.277975	−	0.960588i	$-0.410337\pi$
$691$	14.6142			0.555951			0.277975	+	0.960588i	$0.410337\pi$
$692$	4.72427	−	4.72427i	0.179590	−	0.179590i
$693$	−2.20093	−	8.21398i	−0.0836064	−	0.312023i
$694$	1.88116	−	3.25826i	0.0714078	−	0.123682i
$695$		0			0
$696$			7.02687i			0.266353i
$697$	9.91003	+	36.9847i	0.375369	+	1.40090i
$698$	8.08471	−	30.1725i	0.306011	−	1.14205i
$699$	−5.86897	+	10.1654i	−0.221985	+	0.384489i
$700$		0			0
$701$	−8.12955	−	14.0808i	−0.307049	−	0.531824i	0.670666	−	0.741759i	$-0.266008\pi$
$701$	−8.12955	−	14.0808i	−0.307049	−	0.531824i	−0.977715	+	0.209935i	$0.932675\pi$
$702$	−8.38445	+	8.38445i	−0.316451	+	0.316451i
$703$	−17.6519	+	1.62965i	−0.665755	+	0.0614634i
$704$			2.38827i			0.0900111i
$705$		0			0
$706$	21.1498	−	12.2109i	0.795985	−	0.459562i
$707$	−23.7362	+	6.36010i	−0.892693	+	0.239196i
$708$	1.80404	+	0.483390i	0.0677998	+	0.0181669i
$709$	5.92229	+	3.41924i	0.222416	+	0.128412i	0.607069	−	0.794649i	$-0.292345\pi$
$709$	5.92229	+	3.41924i	0.222416	+	0.128412i	−0.384652	+	0.923062i	$0.625679\pi$
$710$		0			0
$711$		−	0.0810991i		−	0.00304145i
$712$	−2.14634	+	0.575110i	−0.0804375	+	0.0215532i
$713$	−51.2196	+	13.7242i	−1.91819	+	0.513977i
$714$			4.90113i			0.183420i
$715$		0			0
$716$	−10.3799	−	5.99283i	−0.387915	−	0.223963i
$717$	8.17099	+	2.18941i	0.305151	+	0.0817651i
$718$	−12.9866	+	3.47976i	−0.484657	+	0.129864i
$719$	−38.3648	+	22.1499i	−1.43077	+	0.826054i	−0.997179	−	0.0750579i	$-0.976086\pi$
$719$	−38.3648	+	22.1499i	−1.43077	+	0.826054i	−0.433588	+	0.901111i	$0.642752\pi$
$720$		0			0
$721$			3.61142i			0.134496i
$722$	1.47441	−	18.9427i	0.0548719	−	0.704975i
$723$	6.77274	−	6.77274i	0.251881	−	0.251881i
$724$	−11.9338	−	20.6699i	−0.443516	−	0.768192i
$725$		0			0
$726$	1.90479	−	3.29918i	0.0706932	−	0.122444i
$727$	2.48623	−	9.27872i	0.0922090	−	0.344129i	−0.904373	−	0.426744i	$-0.859661\pi$
$727$	2.48623	−	9.27872i	0.0922090	−	0.344129i	0.996582	+	0.0826152i	$0.0263272\pi$
$728$	1.11611	+	4.16538i	0.0413657	+	0.154379i
$729$			2.93749i			0.108796i
$730$		0			0
$731$	4.33000	−	7.49979i	0.160151	−	0.277390i
$732$	0.115502	+	0.431058i	0.00426906	+	0.0159324i
$733$	13.8225	−	13.8225i	0.510547	−	0.510547i	−0.404147	−	0.914694i	$-0.632432\pi$
$733$	13.8225	−	13.8225i	0.510547	−	0.510547i	0.914694	+	0.404147i	$0.132432\pi$
$734$	−1.24542			−0.0459691
$735$		0			0
$736$	4.54833	−	2.62598i	0.167654	−	0.0967948i
$737$	0.880042	+	3.28436i	0.0324168	+	0.120981i
$738$	−19.3271	−	5.17868i	−0.711440	−	0.190630i
$739$	2.25750	−	1.30337i	0.0830433	−	0.0479451i	−0.457903	−	0.889002i	$-0.651399\pi$
$739$	2.25750	−	1.30337i	0.0830433	−	0.0479451i	0.540947	+	0.841057i	$0.318066\pi$
$740$		0			0
$741$	−6.02496	+	7.25057i	−0.221332	+	0.266356i
$742$	7.43768	+	7.43768i	0.273046	+	0.273046i
$743$	7.64152	−	28.5185i	0.280340	−	1.04624i	−0.671838	−	0.740698i	$-0.734495\pi$
$743$	7.64152	−	28.5185i	0.280340	−	1.04624i	0.952178	−	0.305545i	$-0.0988386\pi$
$744$	−3.63123	−	6.28948i	−0.133127	−	0.230583i
$745$		0			0
$746$	−14.2846	−	24.7417i	−0.522997	−	0.905857i
$747$	40.7011	−	10.9058i	1.48918	−	0.399023i
$748$	−8.02289	+	8.02289i	−0.293346	+	0.293346i
$749$	−10.0645			−0.367748
$750$		0			0
$751$	23.6406	+	13.6489i	0.862659	+	0.498056i	0.864902	−	0.501941i	$-0.167381\pi$
$751$	23.6406	+	13.6489i	0.862659	+	0.498056i	−0.00224314	+	0.999997i	$0.500714\pi$
$752$	0.255658	+	0.255658i	0.00932288	+	0.00932288i
$753$	13.1284	+	13.1284i	0.478426	+	0.478426i
$754$	−14.6862	+	25.4373i	−0.534840	+	0.926370i
$755$		0			0
$756$	−4.89835	−	2.82806i	−0.178151	−	0.102856i
$757$	−9.93389	+	37.0738i	−0.361053	+	1.34747i	0.511639	+	0.859200i	$0.329038\pi$
$757$	−9.93389	+	37.0738i	−0.361053	+	1.34747i	−0.872693	+	0.488270i	$0.837628\pi$
$758$	6.44279	+	1.72634i	0.234013	+	0.0627035i
$759$	9.02228			0.327488
$760$		0			0
$761$	−37.8413			−1.37175			−0.685873	−	0.727721i	$-0.740580\pi$
$761$	−37.8413			−1.37175			−0.685873	+	0.727721i	$0.740580\pi$
$762$	6.94023	+	1.85963i	0.251418	+	0.0673672i
$763$	3.42272	−	12.7738i	0.123911	−	0.462442i
$764$	14.3433	+	8.28113i	0.518924	+	0.299601i
$765$		0			0
$766$	−11.9861	+	20.7606i	−0.433076	+	0.750109i
$767$	5.52032	+	5.52032i	0.199327	+	0.199327i
$768$	0.508625	+	0.508625i	0.0183534	+	0.0183534i
$769$	3.75568	+	2.16834i	0.135433	+	0.0781925i	0.566186	−	0.824278i	$-0.308418\pi$
$769$	3.75568	+	2.16834i	0.135433	+	0.0781925i	−0.430752	+	0.902470i	$0.641752\pi$
$770$		0			0
$771$	−5.10222			−0.183752
$772$	−7.49467	+	7.49467i	−0.269739	+	0.269739i
$773$	15.7765	−	4.22729i	0.567440	−	0.152045i	0.0363177	−	0.999340i	$-0.488437\pi$
$773$	15.7765	−	4.22729i	0.567440	−	0.152045i	0.531122	+	0.847295i	$0.321770\pi$
$774$	2.26273	+	3.91916i	0.0813320	+	0.140871i
$775$		0			0
$776$	−5.10347	−	8.83948i	−0.183204	−	0.317319i
$777$	−1.08589	+	4.05261i	−0.0389562	+	0.145386i
$778$	0.744860	+	0.744860i	0.0267045	+	0.0267045i
$779$	−34.6263	−	5.93453i	−1.24061	−	0.212627i
$780$		0			0
$781$	−12.8706	+	7.43084i	−0.460546	+	0.265897i
$782$	24.1006	+	6.45774i	0.861836	+	0.230928i
$783$	−9.97114	−	37.2128i	−0.356340	−	1.32988i
$784$	4.28074	−	2.47149i	0.152884	−	0.0882674i
$785$		0			0
$786$	4.73425			0.168865
$787$	−20.1032	+	20.1032i	−0.716600	+	0.716600i	−0.967907	−	0.251307i	$-0.919140\pi$
$787$	−20.1032	+	20.1032i	−0.716600	+	0.716600i	0.251307	+	0.967907i	$0.419140\pi$
$788$	6.34529	+	23.6809i	0.226041	+	0.843598i
$789$	7.49566	−	12.9829i	0.266853	−	0.462202i
$790$		0			0
$791$		−	0.956671i		−	0.0340153i
$792$	−1.53457	−	5.72708i	−0.0545285	−	0.203503i
$793$	−0.482798	+	1.80183i	−0.0171447	+	0.0639848i
$794$	6.54465	−	11.3357i	0.232261	−	0.402287i
$795$		0			0
$796$	−5.72301	−	9.91254i	−0.202847	−	0.351341i
$797$	−15.3795	+	15.3795i	−0.544770	+	0.544770i	−0.924923	−	0.380154i	$-0.875871\pi$
$797$	−15.3795	+	15.3795i	−0.544770	+	0.544770i	0.380154	+	0.924923i	$0.375871\pi$
$798$	−4.08460	−	1.88090i	−0.144593	−	0.0665830i
$799$			1.71766i			0.0607665i
$800$		0			0
$801$	4.77741	−	2.75824i	0.168801	−	0.0974576i
$802$	−0.906329	+	0.242850i	−0.0320036	+	0.00857533i
$803$	−7.68389	−	2.05889i	−0.271158	−	0.0726567i
$804$	0.886886	+	0.512044i	0.0312780	+	0.0180584i
$805$		0			0
$806$		−	30.3572i		−	1.06929i
$807$	14.3647	−	3.84902i	0.505663	−	0.135492i
$808$	−16.5498	+	4.43449i	−0.582218	+	0.156005i
$809$			33.7129i			1.18528i	0.805466	+	0.592642i	$0.201915\pi$
$809$			33.7129i			1.18528i	−0.805466	+	0.592642i	$0.798085\pi$
$810$		0			0
$811$	−3.19078	−	1.84220i	−0.112043	−	0.0646883i	0.442931	−	0.896556i	$-0.353939\pi$
$811$	−3.19078	−	1.84220i	−0.112043	−	0.0646883i	−0.554974	+	0.831867i	$0.687272\pi$
$812$	−13.5336	−	3.62632i	−0.474936	−	0.127259i
$813$	−17.5065	+	4.69086i	−0.613980	+	0.164516i
$814$	−8.41146	+	4.85636i	−0.294821	+	0.170215i
$815$		0			0
$816$			3.41724i			0.119627i
$817$	4.58861	+	6.48681i	0.160535	+	0.226945i
$818$	−9.51520	+	9.51520i	−0.332691	+	0.332691i
$819$	−5.35288	−	9.27146i	−0.187045	−	0.323971i
$820$		0			0
$821$	10.9004	−	18.8801i	0.380427	−	0.658919i	−0.610696	−	0.791865i	$-0.709110\pi$
$821$	10.9004	−	18.8801i	0.380427	−	0.658919i	0.991123	+	0.132946i	$0.0424437\pi$
$822$	1.67879	−	6.26532i	0.0585545	−	0.218528i
$823$	−12.7952	−	47.7524i	−0.446014	−	1.66455i	−0.713246	−	0.700914i	$-0.752776\pi$
$823$	−12.7952	−	47.7524i	−0.446014	−	1.66455i	0.267232	−	0.963632i	$-0.413891\pi$
$824$			2.51802i			0.0877192i
$825$		0			0
$826$	−1.86200	+	3.22507i	−0.0647871	+	0.112215i
$827$	−0.389735	−	1.45451i	−0.0135524	−	0.0505783i	0.958819	−	0.284019i	$-0.0916680\pi$
$827$	−0.389735	−	1.45451i	−0.0135524	−	0.0505783i	−0.972371	+	0.233441i	$0.925001\pi$
$828$	−9.21962	+	9.21962i	−0.320404	+	0.320404i
$829$	14.5438			0.505127			0.252563	−	0.967580i	$-0.418726\pi$
$829$	14.5438			0.505127			0.252563	+	0.967580i	$0.418726\pi$
$830$		0			0
$831$	−14.2921	+	8.25155i	−0.495787	+	0.286243i
$832$	0.778192	+	2.90425i	0.0269789	+	0.100687i
$833$	22.6827	+	6.07782i	0.785910	+	0.210584i
$834$	3.37742	−	1.94996i	0.116951	−	0.0675215i
$835$		0			0
$836$	−3.60736	−	9.76521i	−0.124763	−	0.337737i
$837$	28.1550	+	28.1550i	0.973179	+	0.973179i
$838$	−8.13280	+	30.3520i	−0.280943	+	1.04849i
$839$	−27.6955	−	47.9700i	−0.956155	−	1.65611i	−0.731702	−	0.681625i	$-0.761274\pi$
$839$	−27.6955	−	47.9700i	−0.956155	−	1.65611i	−0.224454	−	0.974485i	$-0.572060\pi$
$840$		0			0
$841$	−33.2165	−	57.5327i	−1.14540	−	1.98389i
$842$	15.4163	−	4.13078i	0.531280	−	0.142356i
$843$	−2.71425	+	2.71425i	−0.0934837	+	0.0934837i
$844$	−7.79048			−0.268159
$845$		0			0
$846$	−0.777341	−	0.448798i	−0.0267255	−	0.0154300i
$847$	5.37116	+	5.37116i	0.184555	+	0.184555i
$848$	5.18582	+	5.18582i	0.178082	+	0.178082i
$849$	−11.7929	+	20.4259i	−0.404732	+	0.701016i
$850$		0			0
$851$	18.4974	+	10.6795i	0.634081	+	0.366087i
$852$	−1.15850	+	4.32356i	−0.0396894	+	0.148123i
$853$	−3.24887	−	0.870532i	−0.111239	−	0.0298064i	0.202770	−	0.979226i	$-0.435006\pi$
$853$	−3.24887	−	0.870532i	−0.111239	−	0.0298064i	−0.314009	+	0.949420i	$0.601672\pi$
$854$	−0.889814			−0.0304488
$855$		0			0
$856$	−7.01732			−0.239847
$857$	−54.1712	−	14.5151i	−1.85045	−	0.495827i	−0.850889	−	0.525346i	$-0.823936\pi$
$857$	−54.1712	−	14.5151i	−1.85045	−	0.495827i	−0.999564	+	0.0295186i	$0.990603\pi$
$858$	−1.33685	+	4.98918i	−0.0456392	+	0.170328i
$859$	−9.38131	−	5.41630i	−0.320086	−	0.184802i	0.331345	−	0.943510i	$-0.392498\pi$
$859$	−9.38131	−	5.41630i	−0.320086	−	0.184802i	−0.651431	+	0.758708i	$0.725831\pi$
$860$		0			0
$861$	−4.15737	+	7.20077i	−0.141683	+	0.245402i
$862$	−13.1140	−	13.1140i	−0.446666	−	0.446666i
$863$	14.3014	+	14.3014i	0.486824	+	0.486824i	0.907302	−	0.420479i	$-0.138138\pi$
$863$	14.3014	+	14.3014i	0.486824	+	0.486824i	−0.420479	+	0.907302i	$0.638138\pi$
$864$	−3.41531	−	1.97183i	−0.116191	−	0.0670830i
$865$		0			0
$866$	5.10923			0.173619
$867$	−2.83291	+	2.83291i	−0.0962106	+	0.0962106i
$868$	13.9873	−	3.74790i	0.474761	−	0.127212i
$869$	−0.0390087	−	0.0675651i	−0.00132328	−	0.00229199i
$870$		0			0
$871$	2.14035	+	3.70719i	0.0725230	+	0.125613i
$872$	2.38645	−	8.90634i	0.0808153	−	0.301607i
$873$	17.9179	+	17.9179i	0.606430	+	0.606430i
$874$	−14.6309	+	17.6072i	−0.494899	+	0.595572i
$875$		0			0
$876$	−2.07490	+	1.19795i	−0.0701045	+	0.0404748i
$877$	−38.7696	−	10.3883i	−1.30916	−	0.350787i	−0.464251	−	0.885704i	$-0.653676\pi$
$877$	−38.7696	−	10.3883i	−1.30916	−	0.350787i	−0.844905	+	0.534917i	$0.820343\pi$
$878$	3.24013	+	12.0923i	0.109349	+	0.408097i
$879$	−11.5979	+	6.69603i	−0.391186	+	0.225851i
$880$		0			0
$881$	22.6745			0.763922			0.381961	−	0.924178i	$-0.375249\pi$
$881$	22.6745			0.763922			0.381961	+	0.924178i	$0.375249\pi$
$882$	−8.67721	+	8.67721i	−0.292177	+	0.292177i
$883$	2.64511	+	9.87168i	0.0890150	+	0.332209i	0.996044	−	0.0888592i	$-0.0283221\pi$
$883$	2.64511	+	9.87168i	0.0890150	+	0.332209i	−0.907029	+	0.421068i	$0.861655\pi$
$884$	−7.14206	+	12.3704i	−0.240214	+	0.416062i
$885$		0			0
$886$			38.8174i			1.30410i
$887$	8.93508	+	33.3462i	0.300011	+	1.11966i	0.937156	+	0.348911i	$0.113449\pi$
$887$	8.93508	+	33.3462i	0.300011	+	1.11966i	−0.637145	+	0.770744i	$0.719885\pi$
$888$	−0.757124	+	2.82562i	−0.0254074	+	0.0948217i
$889$	−7.16321	+	12.4070i	−0.240246	+	0.416119i
$890$		0			0
$891$	5.50628	+	9.53716i	0.184467	+	0.319507i
$892$	8.47617	−	8.47617i	0.283803	−	0.283803i
$893$	−1.43150	−	0.659183i	−0.0479033	−	0.0220587i
$894$		−	4.75733i		−	0.159109i
$895$		0			0
$896$	−1.24208	+	0.717117i	−0.0414951	+	0.0239572i
$897$	10.9715	−	2.93982i	0.366329	−	0.0981576i
$898$	10.5238	+	2.81985i	0.351184	+	0.0940995i
$899$	85.4184	+	49.3163i	2.84886	+	1.64479i
$900$		0			0
$901$			34.8414i			1.16074i
$902$	−18.5927	+	4.98189i	−0.619068	+	0.165879i
$903$	1.81648	−	0.486725i	0.0604488	−	0.0161972i
$904$		−	0.667026i		−	0.0221850i
$905$		0			0
$906$	−10.7486	−	6.20572i	−0.357099	−	0.206171i
$907$	17.7271	+	4.74996i	0.588618	+	0.157720i	0.540821	−	0.841137i	$-0.318113\pi$
$907$	17.7271	+	4.74996i	0.588618	+	0.157720i	0.0477964	+	0.998857i	$0.484780\pi$
$908$	−20.8484	+	5.58632i	−0.691879	+	0.185388i
$909$	36.8371	−	21.2679i	1.22181	−	0.705412i
$910$		0			0
$911$		−	17.9694i		−	0.595351i	−0.954667	−	0.297676i	$-0.903789\pi$
$911$		−	17.9694i		−	0.595351i	0.954667	−	0.297676i	$-0.0962114\pi$
$912$	−2.84793	−	1.31143i	−0.0943045	−	0.0434257i
$913$	28.6631	−	28.6631i	0.948610	−	0.948610i
$914$	7.75500	+	13.4321i	0.256513	+	0.444293i
$915$		0			0
$916$	−7.12161	+	12.3350i	−0.235305	+	0.407560i
$917$	−2.44317	+	9.11805i	−0.0806807	+	0.301105i
$918$	−4.84907	−	18.0970i	−0.160043	−	0.597290i
$919$			37.9480i			1.25179i	0.779908	+	0.625895i	$0.215266\pi$
$919$			37.9480i			1.25179i	−0.779908	+	0.625895i	$0.784734\pi$
$920$		0			0
$921$	−6.76461	+	11.7166i	−0.222901	+	0.386077i
$922$	−0.817997	−	3.05281i	−0.0269393	−	0.100539i
$923$	−13.2300	+	13.2300i	−0.435472	+	0.435472i
$924$	−2.46386			−0.0810549
$925$		0			0
$926$	31.4306	−	18.1465i	1.03287	−	0.596331i
$927$	−1.61794	−	6.03822i	−0.0531400	−	0.198321i
$928$	−9.43611	−	2.52840i	−0.309756	−	0.0829988i
$929$	−48.7534	+	28.1478i	−1.59955	+	0.923498i	−0.607972	+	0.793958i	$0.708017\pi$
$929$	−48.7534	+	28.1478i	−1.59955	+	0.923498i	−0.991574	+	0.129540i	$0.958650\pi$
$930$		0			0
$931$	−13.7702	+	16.5713i	−0.451299	+	0.543104i
$932$	−11.5389	−	11.5389i	−0.377969	−	0.377969i
$933$	−0.833386	+	3.11024i	−0.0272838	+	0.101825i
$934$	10.7156	+	18.5599i	0.350624	+	0.607298i
$935$		0			0
$936$	−3.73222	−	6.46440i	−0.121991	−	0.211295i
$937$	38.7515	−	10.3834i	1.26596	−	0.339212i	0.437477	−	0.899230i	$-0.355872\pi$
$937$	38.7515	−	10.3834i	1.26596	−	0.339212i	0.828481	+	0.560017i	$0.189206\pi$
$938$	−1.44387	+	1.44387i	−0.0471442	+	0.0471442i
$939$	−8.97136			−0.292769
$940$		0			0
$941$	6.03359	+	3.48349i	0.196689	+	0.113559i	0.595110	−	0.803644i	$-0.297108\pi$
$941$	6.03359	+	3.48349i	0.196689	+	0.113559i	−0.398421	+	0.917203i	$0.630442\pi$
$942$	−1.64746	−	1.64746i	−0.0536771	−	0.0536771i
$943$	29.9310	+	29.9310i	0.974688	+	0.974688i
$944$	−1.29825	+	2.24864i	−0.0422545	+	0.0731869i
$945$		0			0
$946$	3.77023	+	2.17675i	0.122581	+	0.0707721i
$947$	4.33802	−	16.1897i	0.140967	−	0.526095i	−0.858935	−	0.512084i	$-0.828873\pi$
$947$	4.33802	−	16.1897i	0.140967	−	0.526095i	0.999902	−	0.0140106i	$-0.00445985\pi$
$948$	−0.0226968	−	0.00608160i	−0.000737159	−	0.000197521i
$949$	−10.0149			−0.325096
$950$		0			0
$951$	4.07264			0.132064
$952$	−6.58153	−	1.76352i	−0.213309	−	0.0571559i
$953$	6.50740	−	24.2860i	0.210795	−	0.786699i	−0.776809	−	0.629736i	$-0.783163\pi$
$953$	6.50740	−	24.2860i	0.210795	−	0.786699i	0.987604	−	0.156963i	$-0.0501704\pi$
$954$	−15.7678	−	9.10352i	−0.510500	−	0.294737i
$955$		0			0
$956$	−5.88015	+	10.1847i	−0.190178	+	0.329397i
$957$	−11.8667	−	11.8667i	−0.383596	−	0.383596i
$958$	−7.06609	−	7.06609i	−0.228295	−	0.228295i
$959$	11.2005	+	6.46662i	0.361683	+	0.208818i
$960$		0			0
$961$	−70.9395			−2.28837
$962$	−8.64636	+	8.64636i	−0.278770	+	0.278770i
$963$	16.8276	−	4.50894i	0.542262	−	0.145299i
$964$	6.65790	+	11.5318i	0.214436	+	0.371415i
$965$		0			0
$966$	2.70909	+	4.69228i	0.0871636	+	0.150972i
$967$	−6.83495	+	25.5084i	−0.219797	+	0.820295i	0.764625	+	0.644475i	$0.222924\pi$
$967$	−6.83495	+	25.5084i	−0.219797	+	0.820295i	−0.984422	+	0.175819i	$0.943743\pi$
$968$	3.74497	+	3.74497i	0.120368	+	0.120368i
$969$	−5.16158	−	13.9725i	−0.165814	−	0.448862i
$970$		0			0
$971$	−6.03518	+	3.48441i	−0.193678	+	0.111820i	−0.593703	−	0.804684i	$-0.702335\pi$
$971$	−6.03518	+	3.48441i	−0.193678	+	0.111820i	0.400025	+	0.916504i	$0.369001\pi$
$972$	14.6316	+	3.92053i	0.469309	+	0.125751i
$973$	2.01260	+	7.51114i	0.0645211	+	0.240796i
$974$	−4.84298	+	2.79609i	−0.155179	+	0.0895926i
$975$		0			0
$976$	−0.620411			−0.0198589
$977$	−8.36612	+	8.36612i	−0.267656	+	0.267656i	−0.828155	−	0.560499i	$-0.810609\pi$
$977$	−8.36612	+	8.36612i	−0.267656	+	0.267656i	0.560499	+	0.828155i	$0.310609\pi$
$978$	−3.43861	−	12.8331i	−0.109955	−	0.410356i
$979$	2.65343	−	4.59587i	0.0848039	−	0.146885i
$980$		0			0
$981$			22.8909i			0.730850i
$982$	−7.90969	−	29.5194i	−0.252408	−	0.942000i
$983$	1.60946	−	6.00658i	0.0513338	−	0.191580i	−0.935497	−	0.353333i	$-0.885048\pi$
$983$	1.60946	−	6.00658i	0.0513338	−	0.191580i	0.986831	+	0.161753i	$0.0517148\pi$
$984$	−2.89867	+	5.02064i	−0.0924061	+	0.160052i
$985$		0			0
$986$	−23.2051	−	40.1923i	−0.739000	−	1.27999i
$987$	−0.263750	+	0.263750i	−0.00839524	+	0.00839524i
$988$	−7.56862	−	10.6996i	−0.240790	−	0.340399i
$989$		−	9.57362i		−	0.304423i
$990$		0			0
$991$	45.1901	−	26.0905i	1.43551	−	0.828793i	0.437978	−	0.898986i	$-0.355695\pi$
$991$	45.1901	−	26.0905i	1.43551	−	0.828793i	0.997533	+	0.0701930i	$0.0223615\pi$
$992$	9.75248	−	2.61317i	0.309641	−	0.0829682i
$993$	−9.36659	−	2.50977i	−0.297240	−	0.0796451i
$994$	−7.72923	−	4.46247i	−0.245156	−	0.141541i
$995$		0			0
$996$		−	12.2087i		−	0.386846i
$997$	−27.0771	+	7.25528i	−0.857539	+	0.229777i	−0.660692	−	0.750657i	$-0.729737\pi$
$997$	−27.0771	+	7.25528i	−0.857539	+	0.229777i	−0.196847	+	0.980434i	$0.563070\pi$
$998$	−25.9461	+	6.95223i	−0.821308	+	0.220069i
$999$		−	16.0383i		−	0.507428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.g.107.2		32
5.2	odd	4		190.2.m.b.183.7	yes	32
5.3	odd	4	inner	950.2.q.g.943.2		32
5.4	even	2		190.2.m.b.107.7	yes	32
19.8	odd	6	inner	950.2.q.g.407.2		32
95.8	even	12	inner	950.2.q.g.293.2		32
95.27	even	12		190.2.m.b.103.7	yes	32
95.84	odd	6		190.2.m.b.27.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.m.b.27.7	✓	32	95.84	odd	6
190.2.m.b.103.7	yes	32	95.27	even	12
190.2.m.b.107.7	yes	32	5.4	even	2
190.2.m.b.183.7	yes	32	5.2	odd	4
950.2.q.g.107.2		32	1.1	even	1	trivial
950.2.q.g.293.2		32	95.8	even	12	inner
950.2.q.g.407.2		32	19.8	odd	6	inner
950.2.q.g.943.2		32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.186170 - 0.694795i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.359652 + 0.622936i) q^{6} +(-1.01416 - 1.01416i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.15000 + 1.24130i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.186170 - 0.694795i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.359652 + 0.622936i) q^{6} +(-1.01416 - 1.01416i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.15000 + 1.24130i) q^{9} +2.38827 q^{11} +(0.508625 - 0.508625i) q^{12} +(2.90425 - 0.778192i) q^{13} +(0.717117 + 1.24208i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.22959 + 4.58888i) q^{17} +(-1.75546 - 1.75546i) q^{18} +(-3.35250 - 2.78581i) q^{19} +(-0.893436 + 0.515825i) q^{21} +(-2.30689 - 0.618129i) q^{22} +(1.35931 + 5.07300i) q^{23} +(-0.622936 + 0.359652i) q^{24} -3.00670 q^{26} +(2.78859 - 2.78859i) q^{27} +(-0.371207 - 1.38536i) q^{28} +(4.88449 - 8.46019i) q^{29} +10.0965i q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.444623 - 1.65935i) q^{33} +(2.37538 - 4.11428i) q^{34} +(1.24130 + 2.15000i) q^{36} +(2.87570 - 2.87570i) q^{37} +(2.51725 + 3.55857i) q^{38} -2.16273i q^{39} +(6.97985 - 4.02982i) q^{41} +(0.996498 - 0.267011i) q^{42} +(-1.76075 - 0.471793i) q^{43} +(2.06830 + 1.19413i) q^{44} -5.25195i q^{46} +(0.349235 - 0.0935773i) q^{47} +(0.694795 - 0.186170i) q^{48} -4.94297i q^{49} +(2.95942 + 1.70862i) q^{51} +(2.90425 + 0.778192i) q^{52} +(7.08396 - 1.89814i) q^{53} +(-3.41531 + 1.97183i) q^{54} +1.43423i q^{56} +(-2.55970 + 1.81067i) q^{57} +(-6.90772 + 6.90772i) q^{58} +(1.29825 + 2.24864i) q^{59} +(-0.310205 + 0.537291i) q^{61} +(2.61317 - 9.75248i) q^{62} +(-0.921559 - 3.43931i) q^{63} +1.00000i q^{64} +(-0.858945 + 1.48774i) q^{66} +(0.368486 + 1.37521i) q^{67} +(-3.35930 + 3.35930i) q^{68} +3.77775 q^{69} +(-5.38910 + 3.11140i) q^{71} +(-0.642545 - 2.39801i) q^{72} +(-3.21735 - 0.862086i) q^{73} +(-3.52199 + 2.03342i) q^{74} +(-1.51045 - 4.08883i) q^{76} +(-2.42208 - 2.42208i) q^{77} +(-0.559756 + 2.08904i) q^{78} +(-0.0163335 - 0.0282904i) q^{79} +(2.30556 + 3.99334i) q^{81} +(-7.78501 + 2.08599i) q^{82} +(12.0016 - 12.0016i) q^{83} -1.03165 q^{84} +(1.57865 + 0.911434i) q^{86} +(-4.96875 - 4.96875i) q^{87} +(-1.68876 - 1.68876i) q^{88} +(1.11103 - 1.92436i) q^{89} +(-3.73457 - 2.15616i) q^{91} +(-1.35931 + 5.07300i) q^{92} +(7.01500 + 1.87966i) q^{93} -0.361555 q^{94} -0.719304 q^{96} +(9.85916 + 2.64175i) q^{97} +(-1.27934 + 4.77454i) q^{98} +(5.13476 + 2.96456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) \) 32 * q + 12 * q^3 - 24 * q^7	\( 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) \) 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

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