LMFDB - Embedded newform 930.2.bf.a.377.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(377,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("930.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bf (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			377.5
Character	$\chi$	$=$	930.377
Dual form			930.2.bf.a.893.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.64517 + 0.541693i) q^{3} -1.00000i q^{4} +(-2.17658 - 0.512363i) q^{5} +(0.780273 - 1.54634i) q^{6} +(0.122813 - 0.0329078i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41314 - 1.78235i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.64517 + 0.541693i) q^{3} -1.00000i q^{4} +(-2.17658 - 0.512363i) q^{5} +(0.780273 - 1.54634i) q^{6} +(0.122813 - 0.0329078i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41314 - 1.78235i) q^{9} +(1.90137 - 1.17678i) q^{10} +(-0.268839 + 0.155214i) q^{11} +(0.541693 + 1.64517i) q^{12} +(-0.453387 - 0.121485i) q^{13} +(-0.0635729 + 0.110111i) q^{14} +(3.85837 - 0.336114i) q^{15} -1.00000 q^{16} +(-1.34379 - 5.01511i) q^{17} +(-0.446034 + 2.96666i) q^{18} +(-0.0257776 - 0.0148827i) q^{19} +(-0.512363 + 2.17658i) q^{20} +(-0.184222 + 0.120666i) q^{21} +(0.0803448 - 0.299851i) q^{22} +(3.21861 + 3.21861i) q^{23} +(-1.54634 - 0.780273i) q^{24} +(4.47497 + 2.23040i) q^{25} +(0.406495 - 0.234690i) q^{26} +(-3.00452 + 4.23944i) q^{27} +(-0.0329078 - 0.122813i) q^{28} +7.31810 q^{29} +(-2.49061 + 2.96595i) q^{30} +(1.46005 - 5.37292i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.358206 - 0.400981i) q^{33} +(4.49642 + 2.59601i) q^{34} +(-0.284173 + 0.00870114i) q^{35} +(-1.78235 - 2.41314i) q^{36} +(-11.5505 + 3.09495i) q^{37} +(0.0287512 - 0.00770386i) q^{38} +(0.811703 - 0.0457342i) q^{39} +(-1.17678 - 1.90137i) q^{40} +(-4.71967 + 2.72490i) q^{41} +(0.0449413 - 0.215589i) q^{42} +(2.86792 + 10.7032i) q^{43} +(0.155214 + 0.268839i) q^{44} +(-6.16559 + 2.64302i) q^{45} -4.55180 q^{46} +(-5.57856 + 5.57856i) q^{47} +(1.64517 - 0.541693i) q^{48} +(-6.04818 + 3.49192i) q^{49} +(-4.74141 + 1.58715i) q^{50} +(4.92741 + 7.52276i) q^{51} +(-0.121485 + 0.453387i) q^{52} +(-1.52156 + 5.67855i) q^{53} +(-0.873218 - 5.12225i) q^{54} +(0.664674 - 0.200092i) q^{55} +(0.110111 + 0.0635729i) q^{56} +(0.0504703 + 0.0105210i) q^{57} +(-5.17468 + 5.17468i) q^{58} +(1.91906 - 3.32391i) q^{59} +(-0.336114 - 3.85837i) q^{60} +4.24533 q^{61} +(2.76682 + 4.83164i) q^{62} +(0.237712 - 0.298307i) q^{63} +1.00000i q^{64} +(0.924586 + 0.496719i) q^{65} +(0.0302467 + 0.536826i) q^{66} +(-1.69602 + 6.32965i) q^{67} +(-5.01511 + 1.34379i) q^{68} +(-7.03864 - 3.55164i) q^{69} +(0.194788 - 0.207094i) q^{70} +(-0.897468 + 0.518153i) q^{71} +(2.96666 + 0.446034i) q^{72} +(-6.70705 - 1.79715i) q^{73} +(5.97899 - 10.3559i) q^{74} +(-8.57025 - 1.24531i) q^{75} +(-0.0148827 + 0.0257776i) q^{76} +(-0.0279093 + 0.0279093i) q^{77} +(-0.541622 + 0.606300i) q^{78} +(-8.65613 - 4.99762i) q^{79} +(2.17658 + 0.512363i) q^{80} +(2.64646 - 8.60211i) q^{81} +(1.41051 - 5.26411i) q^{82} +(-0.882080 + 3.29197i) q^{83} +(0.120666 + 0.184222i) q^{84} +(0.355313 + 11.6043i) q^{85} +(-9.59626 - 5.54040i) q^{86} +(-12.0395 + 3.96417i) q^{87} +(-0.299851 - 0.0803448i) q^{88} +7.56862 q^{89} +(2.49083 - 6.22862i) q^{90} -0.0596798 q^{91} +(3.21861 - 3.21861i) q^{92} +(0.508456 + 9.63024i) q^{93} -7.88928i q^{94} +(0.0484816 + 0.0456009i) q^{95} +(-0.780273 + 1.54634i) q^{96} +(-5.23176 - 5.23176i) q^{97} +(1.80755 - 6.74587i) q^{98} +(-0.372099 + 0.853718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) $ 256 * q + 8 * q^3 - 4 * q^7	$ 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) $ 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.64517	+	0.541693i	−0.949837	+	0.312747i
$3$	−1.64517	+	0.541693i	−0.949837	+	0.312747i
$4$		−	1.00000i		−	0.500000i
$5$	−2.17658	−	0.512363i	−0.973394	−	0.229136i
$5$	−2.17658	−	0.512363i	−0.973394	−	0.229136i
$6$	0.780273	−	1.54634i	0.318545	−	0.631292i
$7$	0.122813	−	0.0329078i	0.0464191	−	0.0124380i	−0.235535	−	0.971866i	$-0.575684\pi$
$7$	0.122813	−	0.0329078i	0.0464191	−	0.0124380i	0.281954	+	0.959428i	$0.409017\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.41314	−	1.78235i	0.804379	−	0.594116i
$10$	1.90137	−	1.17678i	0.601265	−	0.372129i
$11$	−0.268839	+	0.155214i	−0.0810580	+	0.0467988i	−0.539981	−	0.841677i	$-0.681569\pi$
$11$	−0.268839	+	0.155214i	−0.0810580	+	0.0467988i	0.458923	+	0.888476i	$0.348235\pi$
$12$	0.541693	+	1.64517i	0.156373	+	0.474918i
$13$	−0.453387	−	0.121485i	−0.125747	−	0.0336938i	0.195397	−	0.980724i	$-0.437401\pi$
$13$	−0.453387	−	0.121485i	−0.125747	−	0.0336938i	−0.321144	+	0.947031i	$0.604067\pi$
$14$	−0.0635729	+	0.110111i	−0.0169906	+	0.0294285i
$15$	3.85837	−	0.336114i	0.996227	−	0.0867843i
$16$	−1.00000			−0.250000
$17$	−1.34379	−	5.01511i	−0.325918	−	1.21634i	−0.913386	−	0.407095i	$-0.866542\pi$
$17$	−1.34379	−	5.01511i	−0.325918	−	1.21634i	0.587468	−	0.809247i	$-0.300125\pi$
$18$	−0.446034	+	2.96666i	−0.105131	+	0.699248i
$19$	−0.0257776	−	0.0148827i	−0.00591379	−	0.00341433i	0.497040	−	0.867728i	$-0.334420\pi$
$19$	−0.0257776	−	0.0148827i	−0.00591379	−	0.00341433i	−0.502954	+	0.864313i	$0.667753\pi$
$20$	−0.512363	+	2.17658i	−0.114568	+	0.486697i
$21$	−0.184222	+	0.120666i	−0.0402006	+	0.0263315i
$22$	0.0803448	−	0.299851i	0.0171296	−	0.0639284i
$23$	3.21861	+	3.21861i	0.671126	+	0.671126i	0.957976	−	0.286850i	$-0.0926080\pi$
$23$	3.21861	+	3.21861i	0.671126	+	0.671126i	−0.286850	+	0.957976i	$0.592608\pi$
$24$	−1.54634	−	0.780273i	−0.315646	−	0.159272i
$25$	4.47497	+	2.23040i	0.894994	+	0.446079i
$26$	0.406495	−	0.234690i	0.0797203	−	0.0460265i
$27$	−3.00452	+	4.23944i	−0.578221	+	0.815880i
$28$	−0.0329078	−	0.122813i	−0.00621898	−	0.0232096i
$29$	7.31810			1.35894			0.679469	−	0.733704i	$-0.262210\pi$
$29$	7.31810			1.35894			0.679469	+	0.733704i	$0.262210\pi$
$30$	−2.49061	+	2.96595i	−0.454721	+	0.541506i
$31$	1.46005	−	5.37292i	0.262232	−	0.965005i
$31$	1.46005	−	5.37292i	0.262232	−	0.965005i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.358206	−	0.400981i	0.0623557	−	0.0698019i
$34$	4.49642	+	2.59601i	0.771130	+	0.445212i
$35$	−0.284173	+	0.00870114i	−0.0480341	+	0.00147076i
$36$	−1.78235	−	2.41314i	−0.297058	−	0.402190i
$37$	−11.5505	+	3.09495i	−1.89889	+	0.508807i	−0.901842	+	0.432065i	$0.857785\pi$
$37$	−11.5505	+	3.09495i	−1.89889	+	0.508807i	−0.997051	+	0.0767419i	$0.975548\pi$
$38$	0.0287512	−	0.00770386i	0.00466406	−	0.00124973i
$39$	0.811703	−	0.0457342i	0.129977	−	0.00732334i
$40$	−1.17678	−	1.90137i	−0.186065	−	0.300633i
$41$	−4.71967	+	2.72490i	−0.737089	+	0.425558i	−0.821010	−	0.570914i	$-0.806589\pi$
$41$	−4.71967	+	2.72490i	−0.737089	+	0.425558i	0.0839212	+	0.996472i	$0.473256\pi$
$42$	0.0449413	−	0.215589i	0.00693459	−	0.0332660i
$43$	2.86792	+	10.7032i	0.437354	+	1.63223i	0.735369	+	0.677667i	$0.237009\pi$
$43$	2.86792	+	10.7032i	0.437354	+	1.63223i	−0.298014	+	0.954561i	$0.596324\pi$
$44$	0.155214	+	0.268839i	0.0233994	+	0.0405290i
$45$	−6.16559	+	2.64302i	−0.919111	+	0.393998i
$46$	−4.55180			−0.671126
$47$	−5.57856	+	5.57856i	−0.813717	+	0.813717i	−0.985189	−	0.171472i	$-0.945148\pi$
$47$	−5.57856	+	5.57856i	−0.813717	+	0.813717i	0.171472	+	0.985189i	$0.445148\pi$
$48$	1.64517	−	0.541693i	0.237459	−	0.0781867i
$49$	−6.04818	+	3.49192i	−0.864025	+	0.498845i
$50$	−4.74141	+	1.58715i	−0.670536	+	0.224457i
$51$	4.92741	+	7.52276i	0.689976	+	1.05340i
$52$	−0.121485	+	0.453387i	−0.0168469	+	0.0628734i
$53$	−1.52156	+	5.67855i	−0.209003	+	0.780009i	0.779189	+	0.626789i	$0.215631\pi$
$53$	−1.52156	+	5.67855i	−0.209003	+	0.780009i	−0.988192	+	0.153220i	$0.951036\pi$
$54$	−0.873218	−	5.12225i	−0.118830	−	0.697051i
$55$	0.664674	−	0.200092i	0.0896247	−	0.0269804i
$56$	0.110111	+	0.0635729i	0.0147143	+	0.00849529i
$57$	0.0504703	+	0.0105210i	0.00668496	+	0.00139354i
$58$	−5.17468	+	5.17468i	−0.679469	+	0.679469i
$59$	1.91906	−	3.32391i	0.249841	−	0.432737i	−0.713641	−	0.700512i	$-0.752955\pi$
$59$	1.91906	−	3.32391i	0.249841	−	0.432737i	0.963481	+	0.267775i	$0.0862884\pi$
$60$	−0.336114	−	3.85837i	−0.0433921	−	0.498114i
$61$	4.24533			0.543559			0.271779	−	0.962360i	$-0.412388\pi$
$61$	4.24533			0.543559			0.271779	+	0.962360i	$0.412388\pi$
$62$	2.76682	+	4.83164i	0.351386	+	0.613618i
$63$	0.237712	−	0.298307i	0.0299490	−	0.0375832i
$64$			1.00000i			0.125000i
$65$	0.924586	+	0.496719i	0.114681	+	0.0616104i
$66$	0.0302467	+	0.536826i	0.00372311	+	0.0660788i
$67$	−1.69602	+	6.32965i	−0.207202	+	0.773290i	0.781565	+	0.623824i	$0.214422\pi$
$67$	−1.69602	+	6.32965i	−0.207202	+	0.773290i	−0.988767	+	0.149465i	$0.952245\pi$
$68$	−5.01511	+	1.34379i	−0.608171	+	0.162959i
$69$	−7.03864	−	3.55164i	−0.847352	−	0.427567i
$70$	0.194788	−	0.207094i	0.0232817	−	0.0247524i
$71$	−0.897468	+	0.518153i	−0.106510	+	0.0614935i	−0.552309	−	0.833640i	$-0.686253\pi$
$71$	−0.897468	+	0.518153i	−0.106510	+	0.0614935i	0.445799	+	0.895133i	$0.352920\pi$
$72$	2.96666	+	0.446034i	0.349624	+	0.0525656i
$73$	−6.70705	−	1.79715i	−0.785001	−	0.210340i	−0.156013	−	0.987755i	$-0.549864\pi$
$73$	−6.70705	−	1.79715i	−0.785001	−	0.210340i	−0.628988	+	0.777415i	$0.716531\pi$
$74$	5.97899	−	10.3559i	0.695043	−	1.20385i
$75$	−8.57025	−	1.24531i	−0.989607	−	0.143796i
$76$	−0.0148827	+	0.0257776i	−0.00170717	+	0.00295690i
$77$	−0.0279093	+	0.0279093i	−0.00318056	+	0.00318056i
$78$	−0.541622	+	0.606300i	−0.0613266	+	0.0686500i
$79$	−8.65613	−	4.99762i	−0.973891	−	0.562276i	−0.0734706	−	0.997297i	$-0.523408\pi$
$79$	−8.65613	−	4.99762i	−0.973891	−	0.562276i	−0.900420	+	0.435021i	$0.856741\pi$
$80$	2.17658	+	0.512363i	0.243349	+	0.0572840i
$81$	2.64646	−	8.60211i	0.294051	−	0.955790i
$82$	1.41051	−	5.26411i	0.155765	−	0.581323i
$83$	−0.882080	+	3.29197i	−0.0968209	+	0.361340i	−0.997289	−	0.0735811i	$-0.976557\pi$
$83$	−0.882080	+	3.29197i	−0.0968209	+	0.361340i	0.900468	+	0.434922i	$0.143224\pi$
$84$	0.120666	+	0.184222i	0.0131657	+	0.0201003i
$85$	0.355313	+	11.6043i	0.0385391	+	1.25866i
$86$	−9.59626	−	5.54040i	−1.03479	−	0.597437i
$87$	−12.0395	+	3.96417i	−1.29077	+	0.425003i
$88$	−0.299851	−	0.0803448i	−0.0319642	−	0.00856478i
$89$	7.56862			0.802272			0.401136	−	0.916018i	$-0.368615\pi$
$89$	7.56862			0.802272			0.401136	+	0.916018i	$0.368615\pi$
$90$	2.49083	−	6.22862i	0.262557	−	0.656555i
$91$	−0.0596798			−0.00625614
$92$	3.21861	−	3.21861i	0.335563	−	0.335563i
$93$	0.508456	+	9.63024i	0.0527245	+	0.998609i
$94$		−	7.88928i		−	0.813717i
$95$	0.0484816	+	0.0456009i	0.00497411	+	0.00467855i
$96$	−0.780273	+	1.54634i	−0.0796362	+	0.157823i
$97$	−5.23176	−	5.23176i	−0.531204	−	0.531204i	0.389726	−	0.920931i	$-0.372570\pi$
$97$	−5.23176	−	5.23176i	−0.531204	−	0.531204i	−0.920931	+	0.389726i	$0.872570\pi$
$98$	1.80755	−	6.74587i	0.182590	−	0.681435i
$99$	−0.372099	+	0.853718i	−0.0373974	+	0.0858019i
$100$	2.23040	−	4.47497i	0.223040	−	0.447497i
$101$			2.13381i			0.212322i	0.994349	+	0.106161i	$0.0338559\pi$
$101$			2.13381i			0.212322i	−0.994349	+	0.106161i	$0.966144\pi$
$102$	−8.80360	−	1.83519i	−0.871686	−	0.181710i
$103$	15.0391	+	4.02972i	1.48185	+	0.397060i	0.906976	−	0.421183i	$-0.138385\pi$
$103$	15.0391	+	4.02972i	1.48185	+	0.397060i	0.574873	+	0.818243i	$0.305052\pi$
$104$	−0.234690	−	0.406495i	−0.0230133	−	0.0398602i
$105$	0.462799	−	0.168250i	0.0451646	−	0.0164195i
$106$	−2.93943	−	5.09125i	−0.285503	−	0.494506i
$107$	1.51774	+	5.66430i	0.146726	+	0.547589i	0.999673	+	0.0255904i	$0.00814656\pi$
$107$	1.51774	+	5.66430i	0.146726	+	0.547589i	−0.852947	+	0.521998i	$0.825187\pi$
$108$	4.23944	+	3.00452i	0.407940	+	0.289110i
$109$			17.4157i			1.66812i	0.551672	+	0.834061i	$0.313990\pi$
$109$			17.4157i			1.66812i	−0.551672	+	0.834061i	$0.686010\pi$
$110$	−0.328509	+	0.611482i	−0.0313221	+	0.0583026i
$111$	17.3260	−	11.3485i	1.64451	−	1.07716i
$112$	−0.122813	+	0.0329078i	−0.0116048	+	0.00310949i
$113$	−0.250186	+	0.933708i	−0.0235355	+	0.0878358i	−0.976695	−	0.214633i	$-0.931144\pi$
$113$	−0.250186	+	0.933708i	−0.0235355	+	0.0878358i	0.953159	+	0.302469i	$0.0978110\pi$
$114$	−0.0431274	+	0.0282485i	−0.00403925	+	0.00264571i
$115$	−5.35645	−	8.65464i	−0.499491	−	0.807049i
$116$		−	7.31810i		−	0.679469i
$117$	−1.31061	+	0.514935i	−0.121166	+	0.0476057i
$118$	0.993380	+	3.70734i	0.0914480	+	0.341289i
$119$	−0.330072	−	0.571701i	−0.0302576	−	0.0524078i
$120$	2.96595	+	2.49061i	0.270753	+	0.227361i
$121$	−5.45182	+	9.44282i	−0.495620	+	0.858439i
$122$	−3.00190	+	3.00190i	−0.271779	+	0.271779i
$123$	6.28858	−	7.03953i	0.567022	−	0.634733i
$124$	−5.37292	−	1.46005i	−0.482502	−	0.131116i
$125$	−8.59733	−	7.14744i	−0.768969	−	0.639286i
$126$	0.0428470	+	0.379023i	0.00381712	+	0.0337661i
$127$	7.29308	−	1.95418i	0.647156	−	0.173405i	0.0797135	−	0.996818i	$-0.474599\pi$
$127$	7.29308	−	1.95418i	0.647156	−	0.173405i	0.567443	+	0.823413i	$0.307933\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−10.5161	−	16.0551i	−0.925889	−	1.41357i
$130$	−1.00501	+	0.302548i	−0.0881456	+	0.0265352i
$131$	12.2263	+	7.05885i	1.06822	+	0.616735i	0.927693	−	0.373343i	$-0.121789\pi$
$131$	12.2263	+	7.05885i	1.06822	+	0.616735i	0.140522	+	0.990078i	$0.455122\pi$
$132$	−0.400981	−	0.358206i	−0.0349009	−	0.0311778i
$133$	−0.00365560		0.000979514i	−0.000316980		8.49346e-5i
$134$	−3.27647	−	5.67501i	−0.283044	−	0.490246i
$135$	8.71171	−	7.68805i	0.749784	−	0.661682i
$136$	2.59601	−	4.49642i	0.222606	−	0.385565i
$137$	6.70830	+	1.79748i	0.573129	+	0.153569i	0.533731	−	0.845654i	$-0.320789\pi$
$137$	6.70830	+	1.79748i	0.573129	+	0.153569i	0.0393977	+	0.999224i	$0.487456\pi$
$138$	7.48846	−	2.46568i	0.637460	−	0.209892i
$139$			19.6064i			1.66300i	0.555528	+	0.831498i	$0.312516\pi$
$139$			19.6064i			1.66300i	−0.555528	+	0.831498i	$0.687484\pi$
$140$	0.00870114	+	0.284173i	0.000735381	+	0.0240170i
$141$	6.15579	−	12.1995i	0.518411	−	1.02739i
$142$	0.268216	−	1.00100i	0.0225082	−	0.0840016i
$143$	0.140744	−	0.0377123i	0.0117696	−	0.00315366i
$144$	−2.41314	+	1.78235i	−0.201095	+	0.148529i
$145$	−15.9284	−	3.74953i	−1.32278	−	0.311381i
$146$	6.01338	−	3.47183i	0.497671	−	0.287330i
$147$	8.05870	−	9.02104i	0.664671	−	0.744043i
$148$	3.09495	+	11.5505i	0.254403	+	0.949447i
$149$	−10.3687	+	17.9591i	−0.849435	+	1.47126i	0.0322783	+	0.999479i	$0.489724\pi$
$149$	−10.3687	+	17.9591i	−0.849435	+	1.47126i	−0.881713	+	0.471786i	$0.843610\pi$
$150$	6.94065	−	5.17952i	0.566702	−	0.422906i
$151$	7.23616			0.588871			0.294435	−	0.955671i	$-0.404868\pi$
$151$	7.23616			0.588871			0.294435	+	0.955671i	$0.404868\pi$
$152$	−0.00770386	−	0.0287512i	−0.000624866	−	0.00233203i
$153$	−12.1814	−	9.70703i	−0.984811	−	0.784767i
$154$		−	0.0394697i		−	0.00318056i
$155$	−5.93079	+	10.9465i	−0.476372	+	0.879244i
$156$	−0.0457342	−	0.811703i	−0.00366167	−	0.0649883i
$157$	3.84316	+	3.84316i	0.306718	+	0.306718i	0.843635	−	0.536917i	$-0.180411\pi$
$157$	3.84316	+	3.84316i	0.306718	+	0.306718i	−0.536917	+	0.843635i	$0.680411\pi$
$158$	9.65466	−	2.58696i	0.768083	−	0.205807i
$159$	−0.572809	−	10.1664i	−0.0454267	−	0.806246i
$160$	−1.90137	+	1.17678i	−0.150316	+	0.0930323i
$161$	0.501205	+	0.289371i	0.0395005	+	0.0228056i
$162$	4.21128	+	7.95394i	0.330869	+	0.624920i
$163$	1.91955	−	1.91955i	0.150351	−	0.150351i	−0.627924	−	0.778275i	$-0.716095\pi$
$163$	1.91955	−	1.91955i	0.150351	−	0.150351i	0.778275	+	0.627924i	$0.216095\pi$
$164$	2.72490	+	4.71967i	0.212779	+	0.368544i
$165$	−0.985111	+	0.689235i	−0.0766908	+	0.0536568i
$166$	−1.70405	−	2.95150i	−0.132260	−	0.229081i
$167$	0.643660	+	2.40217i	0.0498079	+	0.185886i	0.986348	−	0.164675i	$-0.0526576\pi$
$167$	0.643660	+	2.40217i	0.0498079	+	0.185886i	−0.936540	+	0.350561i	$0.885991\pi$
$168$	−0.215589	−	0.0449413i	−0.0166330	−	0.00346730i
$169$	−11.0675	−	6.38984i	−0.851348	−	0.491526i
$170$	−8.45671	−	7.95422i	−0.648600	−	0.610061i
$171$	−0.0887312	+	0.0100307i	−0.00678544	+	0.000767067i
$172$	10.7032	−	2.86792i	0.816114	−	0.218677i
$173$	4.99721	−	18.6498i	0.379931	−	1.41792i	−0.466074	−	0.884746i	$-0.654332\pi$
$173$	4.99721	−	18.6498i	0.379931	−	1.41792i	0.846005	−	0.533175i	$-0.179001\pi$
$174$	5.71012	−	11.3163i	0.432883	−	0.857886i
$175$	0.622983	+	0.126661i	0.0470931	+	0.00957470i
$176$	0.268839	−	0.155214i	0.0202645	−	0.0116997i
$177$	−1.35663	+	6.50793i	−0.101971	+	0.489166i
$178$	−5.35182	+	5.35182i	−0.401136	+	0.401136i
$179$	0.863001	−	1.49476i	0.0645037	−	0.111724i	−0.831970	−	0.554821i	$-0.812787\pi$
$179$	0.863001	−	1.49476i	0.0645037	−	0.111724i	0.896474	+	0.443097i	$0.146120\pi$
$180$	2.64302	+	6.16559i	0.196999	+	0.459556i
$181$	1.08083	+	1.87205i	0.0803375	+	0.139149i	0.903395	−	0.428810i	$-0.141067\pi$
$181$	1.08083	+	1.87205i	0.0803375	+	0.139149i	−0.823057	+	0.567958i	$0.807734\pi$
$182$	0.0422000	−	0.0422000i	0.00312807	−	0.00312807i
$183$	−6.98427	+	2.29967i	−0.516292	+	0.169996i
$184$			4.55180i			0.335563i
$185$	26.7263	−	0.818336i	1.96496	−	0.0601653i
$186$	−7.16914	−	6.45007i	−0.525667	−	0.472942i
$187$	1.13968	+	1.13968i	0.0833417	+	0.0833417i
$188$	5.57856	+	5.57856i	0.406859	+	0.406859i
$189$	−0.229485	+	0.619532i	−0.0166926	+	0.0450643i
$190$	−0.0665264	+	0.00203698i	−0.00482633	+	0.000147778i
$191$	9.20541	−	5.31475i	0.666080	−	0.384562i	−0.128510	−	0.991708i	$-0.541019\pi$
$191$	9.20541	−	5.31475i	0.666080	−	0.384562i	0.794590	+	0.607147i	$0.207686\pi$
$192$	−0.541693	−	1.64517i	−0.0390933	−	0.118730i
$193$	5.14670	+	19.2077i	0.370467	+	1.38260i	0.859856	+	0.510537i	$0.170553\pi$
$193$	5.14670	+	19.2077i	0.370467	+	1.38260i	−0.489388	+	0.872066i	$0.662780\pi$
$194$	7.39882			0.531204
$195$	−1.79017	−	0.316343i	−0.128197	−	0.0226538i
$196$	3.49192	+	6.04818i	0.249423	+	0.432013i
$197$	−4.27771	−	1.14621i	−0.304774	−	0.0816640i	0.103191	−	0.994662i	$-0.467095\pi$
$197$	−4.27771	−	1.14621i	−0.304774	−	0.0816640i	−0.407965	+	0.912998i	$0.633761\pi$
$198$	−0.340556	−	0.866784i	−0.0242023	−	0.0615996i
$199$	15.7963	−	9.11998i	1.11977	−	0.646498i	0.178426	−	0.983953i	$-0.442900\pi$
$199$	15.7963	−	9.11998i	1.11977	−	0.646498i	0.941342	+	0.337455i	$0.109566\pi$
$200$	1.58715	+	4.74141i	0.112229	+	0.335268i
$201$	−0.638487	−	11.3320i	−0.0450354	−	0.799301i
$202$	−1.50883	−	1.50883i	−0.106161	−	0.106161i
$203$	0.898761	−	0.240822i	0.0630807	−	0.0169024i
$204$	7.52276	−	4.92741i	0.526698	−	0.344988i
$205$	11.6689	−	3.51277i	0.814989	−	0.245343i
$206$	−13.4837	+	7.78482i	−0.939454	+	0.542394i
$207$	13.5036	+	2.03026i	0.938567	+	0.141113i
$208$	0.453387	+	0.121485i	0.0314367	+	0.00842344i
$209$	0.00924004			0.000639147
$210$	−0.208278	+	0.446219i	−0.0143725	+	0.0307920i
$211$	−5.26302	+	9.11582i	−0.362321	+	0.627559i	−0.988342	−	0.152247i	$-0.951349\pi$
$211$	−5.26302	+	9.11582i	−0.362321	+	0.627559i	0.626021	+	0.779806i	$0.284682\pi$
$212$	5.67855	+	1.52156i	0.390004	+	0.104501i
$213$	1.19580	−	1.33860i	0.0819350	−	0.0917193i
$214$	−5.07847	−	2.93206i	−0.347157	−	0.200431i
$215$	−0.758308	−	24.7658i	−0.0517162	−	1.68902i
$216$	−5.12225	+	0.873218i	−0.348525	+	0.0594150i
$217$	0.00250257	−	0.707913i	0.000169885	−	0.0480563i
$218$	−12.3148	−	12.3148i	−0.834061	−	0.834061i
$219$	12.0077	−	0.676557i	0.811406	−	0.0457175i
$220$	−0.200092	−	0.664674i	−0.0134902	−	0.0448123i
$221$			2.43703i			0.163933i
$222$	−4.22670	+	20.2760i	−0.283677	+	1.36083i
$223$	4.55822	+	17.0115i	0.305241	+	1.13917i	0.932738	+	0.360555i	$0.117413\pi$
$223$	4.55822	+	17.0115i	0.305241	+	1.13917i	−0.627497	+	0.778619i	$0.715921\pi$
$224$	0.0635729	−	0.110111i	0.00424764	−	0.00735713i
$225$	14.7741	−	2.59371i	0.984937	−	0.172914i
$226$	−0.483323	−	0.837139i	−0.0321501	−	0.0556857i
$227$	−0.920354	−	0.246608i	−0.0610860	−	0.0163680i	0.228147	−	0.973627i	$-0.426733\pi$
$227$	−0.920354	−	0.246608i	−0.0610860	−	0.0163680i	−0.289233	+	0.957259i	$0.593400\pi$
$228$	0.0105210	−	0.0504703i	0.000696768	−	0.00334248i
$229$	−13.5056	−	7.79748i	−0.892477	−	0.515272i	−0.0177249	−	0.999843i	$-0.505642\pi$
$229$	−13.5056	−	7.79748i	−0.892477	−	0.515272i	−0.874752	+	0.484571i	$0.838976\pi$
$230$	9.90733	+	2.33217i	0.653270	+	0.153779i
$231$	0.0307971	−	0.0610336i	0.00202630	−	0.00401572i
$232$	5.17468	+	5.17468i	0.339734	+	0.339734i
$233$	−4.77221	−	4.77221i	−0.312638	−	0.312638i	0.533293	−	0.845931i	$-0.320954\pi$
$233$	−4.77221	−	4.77221i	−0.312638	−	0.312638i	−0.845931	+	0.533293i	$0.820954\pi$
$234$	0.562629	−	1.29086i	0.0367802	−	0.0843859i
$235$	15.0004	−	9.28392i	0.978520	−	0.605616i
$236$	−3.32391	−	1.91906i	−0.216368	−	0.124920i
$237$	16.9479	+	3.53294i	1.10089	+	0.229489i
$238$	0.637650	+	0.170858i	0.0413327	+	0.0110751i
$239$	−4.85211	−	8.40411i	−0.313857	−	0.543617i	0.665337	−	0.746543i	$-0.268288\pi$
$239$	−4.85211	−	8.40411i	−0.313857	−	0.543617i	−0.979194	+	0.202927i	$0.934955\pi$
$240$	−3.85837	+	0.336114i	−0.249057	+	0.0216961i
$241$	6.78860	−	11.7582i	0.437292	−	0.757412i	−0.560188	−	0.828366i	$-0.689271\pi$
$241$	6.78860	−	11.7582i	0.437292	−	0.757412i	0.997480	+	0.0709539i	$0.0226043\pi$
$242$	−2.82207	−	10.5321i	−0.181409	−	0.677029i
$243$	0.305838	+	15.5855i	0.0196195	+	0.999808i
$244$		−	4.24533i		−	0.271779i
$245$	14.9534	−	4.50156i	0.955341	−	0.287594i
$246$	0.531004	+	9.42439i	0.0338556	+	0.600877i
$247$	0.00987921	+	0.00987921i	0.000628599	+	0.000628599i
$248$	4.83164	−	2.76682i	0.306809	−	0.175693i
$249$	−0.332069	−	5.89365i	−0.0210440	−	0.373495i
$250$	11.1332	−	1.02523i	0.704128	−	0.0648414i
$251$	12.8935	+	7.44407i	0.813831	+	0.469865i	0.848284	−	0.529541i	$-0.177636\pi$
$251$	12.8935	+	7.44407i	0.813831	+	0.469865i	−0.0344536	+	0.999406i	$0.510969\pi$
$252$	−0.298307	−	0.237712i	−0.0187916	−	0.0149745i
$253$	−1.36486	−	0.365713i	−0.0858080	−	0.0229922i
$254$	−3.77518	+	6.53880i	−0.236876	+	0.410281i
$255$	−6.87050	−	18.8985i	−0.430248	−	1.18347i
$256$	1.00000			0.0625000
$257$	−14.8220	−	3.97155i	−0.924572	−	0.247738i	−0.235034	−	0.971987i	$-0.575520\pi$
$257$	−14.8220	−	3.97155i	−0.924572	−	0.247738i	−0.689539	+	0.724249i	$0.742187\pi$
$258$	18.7886	+	3.91665i	1.16973	+	0.243840i
$259$	−1.31671	+	0.760203i	−0.0818164	+	0.0472367i
$260$	0.496719	−	0.924586i	0.0308052	−	0.0573404i
$261$	17.6596	−	13.0434i	1.09310	−	0.807367i
$262$	−13.6367	+	3.65393i	−0.842475	+	0.225741i
$263$	−9.52387	−	9.52387i	−0.587267	−	0.587267i	0.349623	−	0.936890i	$-0.386310\pi$
$263$	−9.52387	−	9.52387i	−0.587267	−	0.587267i	−0.936890	+	0.349623i	$0.886310\pi$
$264$	0.536826	−	0.0302467i	0.0330394	−	0.00186156i
$265$	6.22128	−	11.5802i	0.382170	−	0.711366i
$266$	0.00327752	−	0.00189228i	0.000200957	−	0.000116023i
$267$	−12.4516	+	4.09987i	−0.762027	+	0.250908i
$268$	6.32965	+	1.69602i	0.386645	+	0.103601i
$269$	−0.357310	−	0.618879i	−0.0217856	−	0.0377337i	0.854927	−	0.518748i	$-0.173602\pi$
$269$	−0.357310	−	0.618879i	−0.0217856	−	0.0377337i	−0.876713	+	0.481014i	$0.840268\pi$
$270$	−0.723830	+	11.5964i	−0.0440509	+	0.705733i
$271$	−8.69234			−0.528022			−0.264011	−	0.964520i	$-0.585046\pi$
$271$	−8.69234			−0.528022			−0.264011	+	0.964520i	$0.585046\pi$
$272$	1.34379	+	5.01511i	0.0814795	+	0.304086i
$273$	0.0981831	−	0.0323281i	0.00594231	−	0.00195659i
$274$	−6.01450	+	3.47247i	−0.363349	+	0.209780i
$275$	−1.54923	+	0.0949614i	−0.0934224	+	0.00572639i
$276$	−3.55164	+	7.03864i	−0.213784	+	0.423676i
$277$	−18.9961	−	18.9961i	−1.14136	−	1.14136i	−0.988201	−	0.153162i	$-0.951054\pi$
$277$	−18.9961	−	18.9961i	−1.14136	−	1.14136i	−0.153162	−	0.988201i	$-0.548946\pi$
$278$	−13.8638	−	13.8638i	−0.831498	−	0.831498i
$279$	−6.05313	−	15.5679i	−0.362391	−	0.932026i
$280$	−0.207094	−	0.194788i	−0.0123762	−	0.0116408i
$281$			17.8362i			1.06402i	0.846738	+	0.532010i	$0.178563\pi$
$281$			17.8362i			1.06402i	−0.846738	+	0.532010i	$0.821437\pi$
$282$	4.27357	+	12.9792i	0.254487	+	0.772898i
$283$	18.9300	−	18.9300i	1.12527	−	1.12527i	0.134333	−	0.990936i	$-0.457111\pi$
$283$	18.9300	−	18.9300i	1.12527	−	1.12527i	0.990936	−	0.134333i	$-0.0428891\pi$
$284$	0.518153	+	0.897468i	0.0307467	+	0.0532549i
$285$	−0.104462	−	0.0487588i	−0.00618779	−	0.00288822i
$286$	−0.0728545	+	0.126188i	−0.00430798	+	0.00746164i
$287$	−0.489968	+	0.489968i	−0.0289219	+	0.0289219i
$288$	0.446034	−	2.96666i	0.0262828	−	0.174812i
$289$	−8.62309	+	4.97854i	−0.507241	+	0.292856i
$290$	13.9144	−	8.61177i	0.817082	−	0.505701i
$291$	11.4411	+	5.77310i	0.670690	+	0.338425i
$292$	−1.79715	+	6.70705i	−0.105170	+	0.392501i
$293$	−17.8507	+	4.78308i	−1.04285	+	0.279431i	−0.739294	−	0.673383i	$-0.764841\pi$
$293$	−17.8507	+	4.78308i	−1.04285	+	0.279431i	−0.303556	+	0.952814i	$0.598174\pi$
$294$	0.680472	+	12.0772i	0.0396859	+	0.704357i
$295$	−5.88004	+	6.25149i	−0.342349	+	0.363976i
$296$	−10.3559	−	5.97899i	−0.601925	−	0.347522i
$297$	0.149711	−	1.60607i	0.00868713	−	0.0931937i
$298$	−5.36722	−	20.0307i	−0.310915	−	1.16035i
$299$	−1.06826	−	1.85028i	−0.0617792	−	0.107005i
$300$	−1.24531	+	8.57025i	−0.0718980	+	0.494804i
$301$	0.704439	+	1.22012i	0.0406032	+	0.0703268i
$302$	−5.11674	+	5.11674i	−0.294435	+	0.294435i
$303$	−1.15587	−	3.51048i	−0.0664031	−	0.201672i
$304$	0.0257776	+	0.0148827i	0.00147845	+	0.000853583i
$305$	−9.24028	−	2.17515i	−0.529097	−	0.124549i
$306$	15.4775	−	1.74967i	0.884789	−	0.100022i
$307$	−9.73103	+	2.60742i	−0.555379	+	0.148813i	−0.525583	−	0.850743i	$-0.676153\pi$
$307$	−9.73103	+	2.60742i	−0.555379	+	0.148813i	−0.0297965	+	0.999556i	$0.509486\pi$
$308$	0.0279093	+	0.0279093i	0.00159028	+	0.00159028i
$309$	−26.9247	+	1.51703i	−1.53169	+	0.0863010i
$310$	−3.54664	−	11.9340i	−0.201436	−	0.677808i
$311$			26.3081i			1.49179i	0.666062	+	0.745897i	$0.267979\pi$
$311$			26.3081i			1.49179i	−0.666062	+	0.745897i	$0.732021\pi$
$312$	0.606300	+	0.541622i	0.0343250	+	0.0306633i
$313$	8.69271	+	32.4416i	0.491341	+	1.83371i	0.549628	+	0.835409i	$0.314769\pi$
$313$	8.69271	+	32.4416i	0.491341	+	1.83371i	−0.0582876	+	0.998300i	$0.518564\pi$
$314$	−5.43505			−0.306718
$315$	−0.670241	+	0.527493i	−0.0377638	+	0.0297209i
$316$	−4.99762	+	8.65613i	−0.281138	+	0.486945i
$317$	−4.16373	−	15.5392i	−0.233858	−	0.872771i	−0.978660	−	0.205485i	$-0.934123\pi$
$317$	−4.16373	−	15.5392i	−0.233858	−	0.872771i	0.744802	−	0.667286i	$-0.232544\pi$
$318$	7.59375	+	6.78367i	0.425836	+	0.380410i
$319$	−1.96739	+	1.13587i	−0.110153	+	0.0635967i
$320$	0.512363	−	2.17658i	0.0286420	−	0.121674i
$321$	−5.56525	−	8.49656i	−0.310622	−	0.474232i
$322$	−0.559022	+	0.149789i	−0.0311531	+	0.00834744i
$323$	−0.0399986	+	0.149277i	−0.00222558	+	0.00830599i
$324$	−8.60211	−	2.64646i	−0.477895	−	0.147026i
$325$	−1.75793	−	1.55487i	−0.0975125	−	0.0862487i
$326$			2.71466i			0.150351i
$327$	−9.43397	−	28.6517i	−0.521700	−	1.58444i
$328$	−5.26411	−	1.41051i	−0.290662	−	0.0778826i
$329$	−0.501544	+	0.868700i	−0.0276510	+	0.0478930i
$330$	0.209216	−	1.18394i	0.0115170	−	0.0651738i
$331$	8.21772	+	14.2335i	0.451687	+	0.782345i	0.998491	−	0.0549159i	$-0.0174891\pi$
$331$	8.21772	+	14.2335i	0.451687	+	0.782345i	−0.546804	+	0.837261i	$0.684156\pi$
$332$	3.29197	+	0.882080i	0.180670	+	0.0484104i
$333$	−22.3567	+	28.0556i	−1.22514	+	1.53744i
$334$	−2.15373	−	1.24346i	−0.117847	−	0.0680388i
$335$	6.93461	−	12.9080i	0.378878	−	0.705238i
$336$	0.184222	−	0.120666i	0.0100502	−	0.00658286i
$337$	8.97305	+	8.97305i	0.488793	+	0.488793i	0.907925	−	0.419132i	$-0.137666\pi$
$337$	8.97305	+	8.97305i	0.488793	+	0.488793i	−0.419132	+	0.907925i	$0.637666\pi$
$338$	12.3442	−	3.30763i	0.671437	−	0.179911i
$339$	−0.0941854	−	1.67163i	−0.00511545	−	0.0907903i
$340$	11.6043	−	0.355313i	0.629330	−	0.0192695i
$341$	0.441436	+	1.67107i	0.0239051	+	0.0904935i
$342$	0.0556496	−	0.0698352i	0.00300919	−	0.00377625i
$343$	−1.25723	+	1.25723i	−0.0678838	+	0.0678838i
$344$	−5.54040	+	9.59626i	−0.298719	+	0.517396i
$345$	13.5004	+	11.3368i	0.726837	+	0.610351i
$346$	9.65387	+	16.7210i	0.518995	+	0.898926i
$347$	−3.09857	−	11.5640i	−0.166340	−	0.620790i	−0.997865	−	0.0653029i	$-0.979199\pi$
$347$	−3.09857	−	11.5640i	−0.166340	−	0.620790i	0.831525	−	0.555487i	$-0.187468\pi$
$348$	3.96417	+	12.0395i	0.212502	+	0.645384i
$349$		−	16.0895i		−	0.861253i	−0.902530	−	0.430627i	$-0.858293\pi$
$349$		−	16.0895i		−	0.861253i	0.902530	−	0.430627i	$-0.141707\pi$
$350$	−0.530079	+	0.350953i	−0.0283339	+	0.0187592i
$351$	1.87724	−	1.55710i	0.100200	−	0.0831120i
$352$	−0.0803448	+	0.299851i	−0.00428239	+	0.0159821i
$353$	13.8922	−	3.72239i	0.739405	−	0.198123i	0.130592	−	0.991436i	$-0.458312\pi$
$353$	13.8922	−	3.72239i	0.739405	−	0.198123i	0.608814	+	0.793313i	$0.291646\pi$
$354$	−3.64252	−	5.56108i	−0.193598	−	0.295568i
$355$	2.21889	−	0.667970i	0.117766	−	0.0354522i
$356$		−	7.56862i		−	0.401136i
$357$	0.852709	+	0.761745i	0.0451302	+	0.0403158i
$358$	0.446722	+	1.66719i	0.0236100	+	0.0881137i
$359$	11.1522	+	19.3161i	0.588589	+	1.01947i	0.994417	+	0.105517i	$0.0336499\pi$
$359$	11.1522	+	19.3161i	0.588589	+	1.01947i	−0.405828	+	0.913949i	$0.633017\pi$
$360$	−6.22862	−	2.49083i	−0.328277	−	0.131278i
$361$	−9.49956	−	16.4537i	−0.499977	−	0.865985i
$362$	−2.08800	−	0.559479i	−0.109743	−	0.0294056i
$363$	3.85403	−	18.4882i	0.202284	−	0.970380i
$364$			0.0596798i			0.00312807i
$365$	13.6776	+	7.34808i	0.715919	+	0.384616i
$366$	3.31251	−	6.56473i	0.173148	−	0.343144i
$367$	6.04473	−	22.5592i	0.315532	−	1.17758i	−0.607960	−	0.793967i	$-0.708012\pi$
$367$	6.04473	−	22.5592i	0.315532	−	1.17758i	0.923493	−	0.383616i	$-0.125321\pi$
$368$	−3.21861	−	3.21861i	−0.167781	−	0.167781i
$369$	−6.53248	+	14.9877i	−0.340067	+	0.780227i
$370$	−18.3197	+	19.4770i	−0.952396	+	1.01256i
$371$			0.747473i			0.0388069i
$372$	9.63024	−	0.508456i	0.499305	−	0.0263622i
$373$	−3.68726	+	3.68726i	−0.190919	+	0.190919i	−0.796093	−	0.605174i	$-0.793104\pi$
$373$	−3.68726	+	3.68726i	−0.190919	+	0.190919i	0.605174	+	0.796093i	$0.293104\pi$
$374$	−1.61175			−0.0833417
$375$	18.0158	+	7.10160i	0.930329	+	0.366725i
$376$	−7.88928			−0.406859
$377$	−3.31793	−	0.889037i	−0.170882	−	0.0457877i
$378$	−0.275805	−	0.600346i	−0.0141859	−	0.0308785i
$379$	2.93830	+	1.69643i	0.150930	+	0.0871396i	0.573563	−	0.819161i	$-0.305561\pi$
$379$	2.93830	+	1.69643i	0.150930	+	0.0871396i	−0.422633	+	0.906301i	$0.638894\pi$
$380$	0.0456009	−	0.0484816i	0.00233928	−	0.00248705i
$381$	−10.9398	+	7.16555i	−0.560461	+	0.367102i
$382$	−2.75112	+	10.2673i	−0.140759	+	0.525321i
$383$	−0.639713	+	2.38744i	−0.0326878	+	0.121993i	−0.980342	−	0.197306i	$-0.936781\pi$
$383$	−0.639713	+	2.38744i	−0.0326878	+	0.121993i	0.947654	+	0.319299i	$0.103447\pi$
$384$	1.54634	+	0.780273i	0.0789115	+	0.0398181i
$385$	0.0750463	−	0.0464470i	0.00382472	−	0.00236716i
$386$	−17.2212	−	9.94265i	−0.876535	−	0.506068i
$387$	25.9976	+	20.7167i	1.32153	+	1.05309i
$388$	−5.23176	+	5.23176i	−0.265602	+	0.265602i
$389$	−9.28053	+	16.0744i	−0.470542	+	0.815002i	−0.999432	−	0.0336880i	$-0.989275\pi$
$389$	−9.28053	+	16.0744i	−0.470542	+	0.815002i	0.528891	+	0.848690i	$0.322608\pi$
$390$	1.48953	−	1.04215i	0.0754252	−	0.0527714i
$391$	11.8165	−	20.4668i	0.597587	−	1.03505i
$392$	−6.74587	−	1.80755i	−0.340718	−	0.0912950i
$393$	−23.9380	−	4.99008i	−1.20751	−	0.251716i
$394$	3.83529	−	2.21430i	0.193219	−	0.111555i
$395$	16.2801	+	15.3128i	0.819142	+	0.770470i
$396$	0.853718	+	0.372099i	0.0429009	+	0.0186987i
$397$	−17.4856	+	4.68524i	−0.877575	+	0.235146i	−0.669361	−	0.742938i	$-0.733432\pi$
$397$	−17.4856	+	4.68524i	−0.877575	+	0.235146i	−0.208215	+	0.978083i	$0.566765\pi$
$398$	−4.72085	+	17.6184i	−0.236635	+	0.883133i
$399$	0.00654465		0.000368749i	0.000327643		1.84605e-5i
$400$	−4.47497	−	2.23040i	−0.223748	−	0.111520i
$401$			12.1653i			0.607505i	0.952751	+	0.303752i	$0.0982396\pi$
$401$			12.1653i			0.607505i	−0.952751	+	0.303752i	$0.901760\pi$
$402$	8.46444	+	7.56148i	0.422168	+	0.377133i
$403$	−1.31469	+	2.25864i	−0.0654895	+	0.112511i
$404$	2.13381			0.106161
$405$	−10.1676	+	17.3672i	−0.505233	+	0.862983i
$406$	−0.465233	+	0.805807i	−0.0230891	+	0.0399915i
$407$	2.62485	−	2.62485i	0.130109	−	0.130109i
$408$	−1.83519	+	8.80360i	−0.0908552	+	0.435843i
$409$	−19.0446	−	10.9954i	−0.941697	−	0.543689i	−0.0512050	−	0.998688i	$-0.516306\pi$
$409$	−19.0446	−	10.9954i	−0.941697	−	0.543689i	−0.890492	+	0.454999i	$0.849640\pi$
$410$	−5.76723	+	10.7350i	−0.284823	+	0.530166i
$411$	−12.0099	+	0.676683i	−0.592407	+	0.0333783i
$412$	4.02972	−	15.0391i	0.198530	−	0.740924i
$413$	0.126304	−	0.471373i	0.00621502	−	0.0231948i
$414$	−10.9841	+	8.11289i	−0.539840	+	0.398727i
$415$	3.60660	−	6.71327i	0.177041	−	0.329542i
$416$	−0.406495	+	0.234690i	−0.0199301	+	0.0115066i
$417$	−10.6207	−	32.2558i	−0.520096	−	1.57957i
$418$	−0.00653370	+	0.00653370i	−0.000319573	+	0.000319573i
$419$	−5.88410			−0.287457			−0.143729	−	0.989617i	$-0.545909\pi$
$419$	−5.88410			−0.287457			−0.143729	+	0.989617i	$0.545909\pi$
$420$	−0.168250	−	0.462799i	−0.00820974	−	0.0225823i
$421$	−13.7821	−	23.8714i	−0.671700	−	1.16342i	−0.977422	−	0.211298i	$-0.932231\pi$
$421$	−13.7821	−	23.8714i	−0.671700	−	1.16342i	0.305722	−	0.952121i	$-0.401102\pi$
$422$	−2.72434	−	10.1674i	−0.132619	−	0.494940i
$423$	−3.51889	+	23.4048i	−0.171094	+	1.13798i
$424$	−5.09125	+	2.93943i	−0.247253	+	0.142752i
$425$	5.17224	−	25.4396i	0.250891	−	1.23400i
$426$	0.100973	+	1.79209i	0.00489215	+	0.0868272i
$427$	0.521383	−	0.139704i	0.0252315	−	0.00676076i
$428$	5.66430	−	1.51774i	0.273794	−	0.0733630i
$429$	−0.211119	+	0.138283i	−0.0101929	+	0.00667637i
$430$	18.0483	+	16.9759i	0.870366	+	0.818650i
$431$	−25.4145	−	14.6731i	−1.22417	−	0.706777i	−0.258369	−	0.966046i	$-0.583185\pi$
$431$	−25.4145	−	14.6731i	−1.22417	−	0.706777i	−0.965805	+	0.259269i	$0.916518\pi$
$432$	3.00452	−	4.23944i	0.144555	−	0.203970i
$433$	−12.8000	+	12.8000i	−0.615129	+	0.615129i	−0.944278	−	0.329149i	$-0.893238\pi$
$433$	−12.8000	+	12.8000i	−0.615129	+	0.615129i	0.329149	+	0.944278i	$0.393238\pi$
$434$	0.498801	+	0.502340i	0.0239432	+	0.0241131i
$435$	28.2360	−	2.45972i	1.35381	−	0.117934i
$436$	17.4157			0.834061
$437$	−0.0350664	−	0.130870i	−0.00167745	−	0.00626035i
$438$	−8.01234	+	8.96913i	−0.382844	+	0.428562i
$439$	1.65092	−	0.953157i	0.0787939	−	0.0454917i	−0.460085	−	0.887875i	$-0.652181\pi$
$439$	1.65092	−	0.953157i	0.0787939	−	0.0454917i	0.538879	+	0.842383i	$0.318848\pi$
$440$	0.611482	+	0.328509i	0.0291513	+	0.0156611i
$441$	−8.37126	+	19.2064i	−0.398632	+	0.914592i
$442$	−1.72324	−	1.72324i	−0.0819663	−	0.0819663i
$443$	−5.09613	+	19.0190i	−0.242125	+	0.903621i	0.732682	+	0.680571i	$0.238268\pi$
$443$	−5.09613	+	19.0190i	−0.242125	+	0.903621i	−0.974807	+	0.223050i	$0.928399\pi$
$444$	−11.3485	−	17.3260i	−0.538578	−	0.822255i
$445$	−16.4737	−	3.87788i	−0.780927	−	0.183829i
$446$	−15.2521	−	8.80580i	−0.722207	−	0.416966i
$447$	7.32988	−	35.1623i	0.346691	−	1.66312i
$448$	0.0329078	+	0.122813i	0.00155475	+	0.00580239i
$449$	1.34029			0.0632521			0.0316261	−	0.999500i	$-0.489931\pi$
$449$	1.34029			0.0632521			0.0316261	+	0.999500i	$0.489931\pi$
$450$	−8.61281	+	12.2809i	−0.406012	+	0.578925i
$451$	0.845887	−	1.46512i	0.0398313	−	0.0689898i
$452$	0.933708	+	0.250186i	0.0439179	+	0.0117678i
$453$	−11.9047	+	3.91978i	−0.559331	+	0.184167i
$454$	0.825167	−	0.476410i	0.0387270	−	0.0223590i
$455$	0.129898	+	0.0305777i	0.00608969	+	0.00143351i
$456$	0.0282485	+	0.0431274i	0.00132286	+	0.00201962i
$457$	−4.05959	−	4.05959i	−0.189899	−	0.189899i	0.605753	−	0.795653i	$-0.292872\pi$
$457$	−4.05959	−	4.05959i	−0.189899	−	0.189899i	−0.795653	+	0.605753i	$0.792872\pi$
$458$	15.0636	−	4.03627i	0.703874	−	0.188603i
$459$	25.2987	+	9.37107i	1.18084	+	0.437404i
$460$	−8.65464	+	5.35645i	−0.403525	+	0.249746i
$461$			21.7536i			1.01316i	0.862192	+	0.506582i	$0.169091\pi$
$461$			21.7536i			1.01316i	−0.862192	+	0.506582i	$0.830909\pi$
$462$	0.0213805	+	0.0649341i	0.000994709	+	0.00302101i
$463$	12.4900	−	12.4900i	0.580460	−	0.580460i	−0.354570	−	0.935030i	$-0.615373\pi$
$463$	12.4900	−	12.4900i	0.580460	−	0.580460i	0.935030	+	0.354570i	$0.115373\pi$
$464$	−7.31810			−0.339734
$465$	3.82749	−	21.2215i	0.177495	−	0.984122i
$466$	6.74893			0.312638
$467$	−27.5725	+	27.5725i	−1.27590	+	1.27590i	−0.332965	+	0.942939i	$0.608049\pi$
$467$	−27.5725	+	27.5725i	−1.27590	+	1.27590i	−0.942939	+	0.332965i	$0.891951\pi$
$468$	0.514935	+	1.31061i	0.0238029	+	0.0605831i
$469$			0.833178i			0.0384726i
$470$	−4.04218	+	17.1716i	−0.186452	+	0.792068i
$471$	−8.40445	−	4.24082i	−0.387257	−	0.195407i
$472$	3.70734	−	0.993380i	0.170644	−	0.0457240i
$473$	−2.43230	−	2.43230i	−0.111837	−	0.111837i
$474$	−14.4822	+	9.48584i	−0.665188	+	0.435699i
$475$	−0.0821597	−	0.124094i	−0.00376975	−	0.00569382i
$476$	−0.571701	+	0.330072i	−0.0262039	+	0.0151288i
$477$	6.44942	+	16.4151i	0.295299	+	0.751595i
$478$	9.37356	+	2.51164i	0.428737	+	0.114880i
$479$	−11.3367	+	19.6358i	−0.517988	+	0.897181i	0.481794	+	0.876284i	$0.339985\pi$
$479$	−11.3367	+	19.6358i	−0.517988	+	0.897181i	−0.999782	+	0.0208963i	$0.993348\pi$
$480$	2.49061	−	2.96595i	0.113680	−	0.135376i
$481$	5.61284			0.255923
$482$	3.51404	+	13.1146i	0.160060	+	0.597352i
$483$	−0.981316	−	0.204564i	−0.0446514	−	0.00930797i
$484$	9.44282	+	5.45182i	0.429219	+	0.247810i
$485$	8.70676	+	14.0679i	0.395353	+	0.638789i
$486$	−11.2368	−	10.8043i	−0.509714	−	0.490094i
$487$	8.74811	−	32.6484i	0.396415	−	1.47944i	−0.422943	−	0.906156i	$-0.639003\pi$
$487$	8.74811	−	32.6484i	0.396415	−	1.47944i	0.819358	−	0.573283i	$-0.194330\pi$
$488$	3.00190	+	3.00190i	0.135890	+	0.135890i
$489$	−2.11817	+	4.19779i	−0.0957871	+	0.189831i
$490$	−7.39060	+	13.7568i	−0.333873	+	0.621467i
$491$	−26.8359	+	15.4937i	−1.21109	+	0.699220i	−0.962996	−	0.269517i	$-0.913136\pi$
$491$	−26.8359	+	15.4937i	−1.21109	+	0.699220i	−0.248090	+	0.968737i	$0.579803\pi$
$492$	−7.03953	−	6.28858i	−0.317366	−	0.283511i
$493$	−9.83402	−	36.7011i	−0.442902	−	1.65293i
$494$	−0.0139713			−0.000628599
$495$	1.24732	−	1.66753i	0.0560627	−	0.0749500i
$496$	−1.46005	+	5.37292i	−0.0655580	+	0.241251i
$497$	−0.0931698	+	0.0931698i	−0.00417924	+	0.00417924i
$498$	4.40225	+	3.93263i	0.197269	+	0.176225i
$499$	4.71159	+	2.72024i	0.210920	+	0.121775i	0.601739	−	0.798693i	$-0.294475\pi$
$499$	4.71159	+	2.72024i	0.210920	+	0.121775i	−0.390819	+	0.920468i	$0.627808\pi$
$500$	−7.14744	+	8.59733i	−0.319643	+	0.384484i
$501$	−2.36017	−	3.60330i	−0.105444	−	0.160984i
$502$	−14.3808	+	3.85333i	−0.641848	+	0.171983i
$503$	−24.0041	+	6.43189i	−1.07029	+	0.286784i	−0.750613	−	0.660742i	$-0.770242\pi$
$503$	−24.0041	+	6.43189i	−1.07029	+	0.286784i	−0.319679	+	0.947526i	$0.603575\pi$
$504$	0.379023	−	0.0428470i	0.0168830	−	0.00190856i
$505$	1.09329	−	4.64441i	0.0486507	−	0.206673i
$506$	1.22370	−	0.706504i	0.0544001	−	0.0314079i
$507$	21.6692	+	4.51714i	0.962365	+	0.200613i
$508$	−1.95418	−	7.29308i	−0.0867025	−	0.323578i
$509$	11.3434	+	19.6473i	0.502786	+	0.870850i	0.999995	+	0.00321960i	$0.00102483\pi$
$509$	11.3434	+	19.6473i	0.502786	+	0.870850i	−0.497209	+	0.867631i	$0.665642\pi$
$510$	18.2214	+	8.50506i	0.806858	+	0.376610i
$511$	−0.882856			−0.0390553
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.140544	−	0.0645672i	0.00620516	−	0.00285071i
$514$	13.2891	−	7.67244i	0.586155	−	0.338417i
$515$	−30.6691	−	16.4765i	−1.35144	−	0.726041i
$516$	−16.0551	+	10.5161i	−0.706785	+	0.462945i
$517$	0.633863	−	2.36561i	0.0278772	−	0.104039i
$518$	0.393510	−	1.46860i	0.0172898	−	0.0645266i
$519$	1.88126	+	33.3890i	0.0825780	+	1.46562i
$520$	0.302548	+	1.00501i	0.0132676	+	0.0440728i
$521$	10.0588	+	5.80743i	0.440682	+	0.254428i	0.703887	−	0.710312i	$-0.251446\pi$
$521$	10.0588	+	5.80743i	0.440682	+	0.254428i	−0.263205	+	0.964740i	$0.584779\pi$
$522$	−3.26412	+	21.7103i	−0.142867	+	0.950234i
$523$	23.7164	−	23.7164i	1.03705	−	1.03705i	0.0377587	−	0.999287i	$-0.487978\pi$
$523$	23.7164	−	23.7164i	1.03705	−	1.03705i	0.999287	−	0.0377587i	$-0.0120218\pi$
$524$	7.05885	−	12.2263i	0.308367	−	0.534108i
$525$	−1.09352	+	0.129087i	−0.0477252	+	0.00563382i
$526$	13.4688			0.587267
$527$	−28.9078	−	0.102193i	−1.25924	−	0.00445159i
$528$	−0.358206	+	0.400981i	−0.0155889	+	0.0174505i
$529$		−	2.28114i		−	0.0991801i
$530$	3.78933	+	12.5875i	0.164598	+	0.546768i
$531$	−1.29341	−	11.4415i	−0.0561294	−	0.496519i
$532$	−0.000979514		0.00365560i	−4.24673e−5		0.000158490i
$533$	2.47087	−	0.662067i	0.107025	−	0.0286773i
$534$	5.90559	−	11.7037i	0.255560	−	0.506468i
$535$	−0.401307	−	13.1064i	−0.0173500	−	0.566640i
$536$	−5.67501	+	3.27647i	−0.245123	+	0.141522i
$537$	−0.610077	+	2.92661i	−0.0263268	+	0.126293i
$538$	0.690270	+	0.184957i	0.0297596	+	0.00797407i
$539$	1.08399	−	1.87753i	0.0466908	−	0.0808708i
$540$	−7.68805	−	8.71171i	−0.330841	−	0.374892i
$541$	9.73878	−	16.8681i	0.418703	−	0.725214i	−0.577107	−	0.816669i	$-0.695818\pi$
$541$	9.73878	−	16.8681i	0.418703	−	0.725214i	0.995809	+	0.0914545i	$0.0291516\pi$
$542$	6.14641	−	6.14641i	0.264011	−	0.264011i
$543$	−2.79222	−	2.49436i	−0.119826	−	0.107043i
$544$	−4.49642	−	2.59601i	−0.192783	−	0.111303i
$545$	8.92317	−	37.9066i	0.382227	−	1.62374i
$546$	−0.0465665	+	0.0922853i	−0.00199286	+	0.00394945i
$547$	−5.33452	+	19.9087i	−0.228088	+	0.851234i	0.753056	+	0.657956i	$0.228579\pi$
$547$	−5.33452	+	19.9087i	−0.228088	+	0.851234i	−0.981144	+	0.193278i	$0.938088\pi$
$548$	1.79748	−	6.70830i	0.0767847	−	0.286564i
$549$	10.2446	−	7.56666i	0.437227	−	0.322937i
$550$	1.02833	−	1.16262i	0.0438480	−	0.0495744i
$551$	−0.188643	−	0.108913i	−0.00803648	−	0.00463986i
$552$	−2.46568	−	7.48846i	−0.104946	−	0.318730i
$553$	−1.22755	−	0.328921i	−0.0522007	−	0.0139871i
$554$	26.8645			1.14136
$555$	−43.5259	+	15.8238i	−1.84757	+	0.671681i
$556$	19.6064			0.831498
$557$	21.0589	−	21.0589i	0.892293	−	0.892293i	−0.102445	−	0.994739i	$-0.532667\pi$
$557$	21.0589	−	21.0589i	0.892293	−	0.892293i	0.994739	+	0.102445i	$0.0326667\pi$
$558$	15.2884	+	6.72796i	0.647209	+	0.284817i
$559$		−	5.20111i		−	0.219984i
$560$	0.284173	−	0.00870114i	0.0120085	−	0.000367690i
$561$	−2.49232	−	1.25761i	−0.105226	−	0.0530961i
$562$	−12.6121	−	12.6121i	−0.532010	−	0.532010i
$563$	1.55232	−	5.79335i	0.0654227	−	0.244161i	−0.925469	−	0.378824i	$-0.876329\pi$
$563$	1.55232	−	5.79335i	0.0654227	−	0.244161i	0.990891	+	0.134663i	$0.0429953\pi$
$564$	−12.1995	−	6.15579i	−0.513693	−	0.259205i
$565$	1.02295	−	1.90410i	0.0430357	−	0.0801061i
$566$			26.7710i			1.12527i
$567$	0.0419448	−	1.14354i	0.00176152	−	0.0480243i
$568$	−1.00100	−	0.268216i	−0.0420008	−	0.0112541i
$569$	13.1287	+	22.7396i	0.550385	+	0.953295i	0.998247	+	0.0591921i	$0.0188524\pi$
$569$	13.1287	+	22.7396i	0.550385	+	0.953295i	−0.447861	+	0.894103i	$0.647814\pi$
$570$	0.108343	−	0.0393880i	0.00453801	−	0.00164978i
$571$	14.5357	+	25.1766i	0.608301	+	1.05361i	0.991520	+	0.129951i	$0.0414820\pi$
$571$	14.5357	+	25.1766i	0.608301	+	1.05361i	−0.383219	+	0.923657i	$0.625185\pi$
$572$	−0.0377123	−	0.140744i	−0.00157683	−	0.00588481i
$573$	−12.2655	+	13.7301i	−0.512397	+	0.573585i
$574$		−	0.692920i		−	0.0289219i
$575$	7.22439	+	21.5819i	0.301278	+	0.900029i
$576$	1.78235	+	2.41314i	0.0742646	+	0.100547i
$577$	30.9246	−	8.28623i	1.28741	−	0.344960i	0.450734	−	0.892658i	$-0.351162\pi$
$577$	30.9246	−	8.28623i	1.28741	−	0.344960i	0.836676	+	0.547698i	$0.184496\pi$
$578$	2.57708	−	9.61781i	0.107193	−	0.400048i
$579$	−18.8719	−	28.8120i	−0.784288	−	1.19738i
$580$	−3.74953	+	15.9284i	−0.155691	+	0.661391i
$581$			0.433325i			0.0179774i
$582$	−12.1723	+	4.00789i	−0.504557	+	0.166132i
$583$	−0.472336	−	1.76278i	−0.0195622	−	0.0730070i
$584$	−3.47183	−	6.01338i	−0.143665	−	0.248835i
$585$	3.11648	−	0.449285i	0.128851	−	0.0185756i
$586$	9.24021	−	16.0045i	0.381709	−	0.661140i
$587$	−3.54217	+	3.54217i	−0.146201	+	0.146201i	−0.776419	−	0.630218i	$-0.782966\pi$
$587$	−3.54217	+	3.54217i	−0.146201	+	0.146201i	0.630218	+	0.776419i	$0.282966\pi$
$588$	−9.02104	−	8.05870i	−0.372021	−	0.332335i
$589$	−0.117600	+	0.116772i	−0.00484563	+	0.00481149i
$590$	−0.262660	−	8.57829i	−0.0108135	−	0.353162i
$591$	7.65843	−	0.431503i	0.315026	−	0.0177497i
$592$	11.5505	−	3.09495i	0.474723	−	0.127202i
$593$	20.1708	+	20.1708i	0.828314	+	0.828314i	0.987284	−	0.158969i	$-0.0508171\pi$
$593$	20.1708	+	20.1708i	0.828314	+	0.828314i	−0.158969	+	0.987284i	$0.550817\pi$
$594$	1.02980	+	1.24153i	0.0422533	+	0.0509404i
$595$	0.425508	+	1.41347i	0.0174441	+	0.0579465i
$596$	17.9591	+	10.3687i	0.735632	+	0.424717i
$597$	−21.0472	+	23.5606i	−0.861406	+	0.964271i
$598$	2.06372	+	0.552973i	0.0843920	+	0.0226128i
$599$	15.8938	+	27.5288i	0.649402	+	1.12480i	0.983266	+	0.182176i	$0.0583141\pi$
$599$	15.8938	+	27.5288i	0.649402	+	1.12480i	−0.333864	+	0.942621i	$0.608353\pi$
$600$	−5.17952	−	6.94065i	−0.211453	−	0.283351i
$601$	−17.3867	+	30.1146i	−0.709217	+	1.22840i	0.255932	+	0.966695i	$0.417618\pi$
$601$	−17.3867	+	30.1146i	−0.709217	+	1.22840i	−0.965148	+	0.261704i	$0.915715\pi$
$602$	−1.36087	−	0.364645i	−0.0554650	−	0.0148618i
$603$	7.18891	+	18.2972i	0.292755	+	0.745120i
$604$		−	7.23616i		−	0.294435i
$605$	16.7045	−	17.7597i	0.679133	−	0.722035i
$606$	3.29961	+	1.66496i	0.134037	+	0.0676342i
$607$	−7.93223	+	29.6035i	−0.321959	+	1.20157i	0.595374	+	0.803449i	$0.297004\pi$
$607$	−7.93223	+	29.6035i	−0.321959	+	1.20157i	−0.917333	+	0.398120i	$0.869663\pi$
$608$	−0.0287512	+	0.00770386i	−0.00116602	+	0.000312433i
$609$	−1.34816	+	0.883045i	−0.0546302	+	0.0357828i
$610$	8.07193	−	4.99580i	0.326823	−	0.202274i
$611$	3.20696	−	1.85154i	0.129740	−	0.0749052i
$612$	−9.70703	+	12.1814i	−0.392383	+	0.492405i
$613$	−1.78800	−	6.67292i	−0.0722167	−	0.269517i	0.920371	−	0.391046i	$-0.127887\pi$
$613$	−1.78800	−	6.67292i	−0.0722167	−	0.269517i	−0.992588	+	0.121530i	$0.961220\pi$
$614$	5.03715	−	8.72460i	0.203283	−	0.352096i
$615$	−17.2944	+	12.1000i	−0.697376	+	0.487920i
$616$	−0.0394697			−0.00159028
$617$	−8.55497	−	31.9276i	−0.344410	−	1.28536i	−0.893300	−	0.449461i	$-0.851616\pi$
$617$	−8.55497	−	31.9276i	−0.344410	−	1.28536i	0.548890	−	0.835895i	$-0.315051\pi$
$618$	17.9659	−	20.1113i	0.722696	−	0.808997i
$619$		−	33.2095i		−	1.33480i	−0.744698	−	0.667402i	$-0.767406\pi$
$619$		−	33.2095i		−	1.33480i	0.744698	−	0.667402i	$-0.232594\pi$
$620$	10.9465	+	5.93079i	0.439622	+	0.238186i
$621$	−23.3155	+	3.97471i	−0.935617	+	0.159500i
$622$	−18.6026	−	18.6026i	−0.745897	−	0.745897i
$623$	0.929528	−	0.249066i	0.0372408	−	0.00997863i
$624$	−0.811703	+	0.0457342i	−0.0324941	+	0.00183083i
$625$	15.0507	+	19.9619i	0.602027	+	0.798476i
$626$	−29.0864	−	16.7930i	−1.16252	−	0.671184i
$627$	−0.0152014	+	0.00500527i	−0.000607085	+	0.000199891i
$628$	3.84316	−	3.84316i	0.153359	−	0.153359i
$629$	31.0430	+	53.7681i	1.23777	+	2.14388i
$630$	0.100938	−	0.846926i	0.00402146	−	0.0337423i
$631$	−17.5203	−	30.3460i	−0.697472	−	1.20806i	−0.969340	−	0.245722i	$-0.920975\pi$
$631$	−17.5203	−	30.3460i	−0.697472	−	1.20806i	0.271869	−	0.962334i	$-0.412358\pi$
$632$	−2.58696	−	9.65466i	−0.102904	−	0.384042i
$633$	3.72056	−	17.8480i	0.147879	−	0.709393i
$634$	13.9321	+	8.04371i	0.553315	+	0.319456i
$635$	−16.8752	+	0.516703i	−0.669672	+	0.0205048i
$636$	−10.1664	+	0.572809i	−0.403123	+	0.0227134i
$637$	3.16638	−	0.848428i	0.125456	−	0.0336160i
$638$	0.587972	−	2.19434i	0.0232780	−	0.0868747i
$639$	−1.24218	+	2.84998i	−0.0491400	+	0.112743i
$640$	1.17678	+	1.90137i	0.0465162	+	0.0751581i
$641$	14.1470	−	8.16775i	0.558771	−	0.322607i	−0.193881	−	0.981025i	$-0.562108\pi$
$641$	14.1470	−	8.16775i	0.558771	−	0.322607i	0.752652	+	0.658418i	$0.228774\pi$
$642$	9.94320	+	2.07274i	0.392427	+	0.0818047i
$643$	15.2931	−	15.2931i	0.603102	−	0.603102i	−0.338033	−	0.941134i	$-0.609761\pi$
$643$	15.2931	−	15.2931i	0.603102	−	0.603102i	0.941134	+	0.338033i	$0.109761\pi$
$644$	0.289371	−	0.501205i	0.0114028	−	0.0197503i
$645$	14.6630	+	40.3331i	0.577356	+	1.58811i
$646$	−0.0772714	−	0.133838i	−0.00304020	−	0.00526579i
$647$	−4.28266	+	4.28266i	−0.168369	+	0.168369i	−0.786262	−	0.617893i	$-0.787986\pi$
$647$	−4.28266	+	4.28266i	−0.168369	+	0.168369i	0.617893	+	0.786262i	$0.287986\pi$
$648$	7.95394	−	4.21128i	0.312460	−	0.165435i
$649$			1.19146i			0.0467690i
$650$	2.34251	−	0.143586i	0.0918806	−	0.00563189i
$651$	0.379355	+	1.16599i	0.0148681	+	0.0456988i
$652$	−1.91955	−	1.91955i	−0.0751755	−	0.0751755i
$653$	11.4673	+	11.4673i	0.448751	+	0.448751i	0.894939	−	0.446188i	$-0.147219\pi$
$653$	11.4673	+	11.4673i	0.448751	+	0.448751i	−0.446188	+	0.894939i	$0.647219\pi$
$654$	26.9306	+	13.5890i	1.05307	+	0.531372i
$655$	−22.9947	−	21.6284i	−0.898479	−	0.845093i
$656$	4.71967	−	2.72490i	0.184272	−	0.106390i
$657$	−19.3882	+	7.61754i	−0.756405	+	0.297189i
$658$	−0.259619	−	0.968909i	−0.0101210	−	0.0377720i
$659$	−17.9252			−0.698265			−0.349133	−	0.937073i	$-0.613524\pi$
$659$	−17.9252			−0.698265			−0.349133	+	0.937073i	$0.613524\pi$
$660$	0.689235	+	0.985111i	0.0268284	+	0.0383454i
$661$	20.3264	+	35.2063i	0.790604	+	1.36937i	0.925593	+	0.378519i	$0.123567\pi$
$661$	20.3264	+	35.2063i	0.790604	+	1.36937i	−0.134989	+	0.990847i	$0.543100\pi$
$662$	−15.8754	−	4.25381i	−0.617016	−	0.165329i
$663$	−1.32012	−	4.00932i	−0.0512694	−	0.155709i
$664$	−2.95150	+	1.70405i	−0.114540	+	0.0661299i
$665$	0.00745482	+	0.00400498i	0.000289085	+	0.000155306i
$666$	−4.02974	−	35.6469i	−0.156149	−	1.38129i
$667$	23.5541	+	23.5541i	0.912018	+	0.912018i
$668$	2.40217	−	0.643660i	0.0929428	−	0.0249039i
$669$	−16.7140	−	25.5176i	−0.646202	−	0.986566i
$670$	4.22381	+	14.0308i	0.163180	+	0.542058i
$671$	−1.14131	+	0.658935i	−0.0440598	+	0.0254379i
$672$	−0.0449413	+	0.215589i	−0.00173365	+	0.00831651i
$673$	−9.80842	−	2.62816i	−0.378087	−	0.101308i	0.0647704	−	0.997900i	$-0.479369\pi$
$673$	−9.80842	−	2.62816i	−0.378087	−	0.101308i	−0.442857	+	0.896592i	$0.646035\pi$
$674$	−12.6898			−0.488793
$675$	−22.9008	+	12.2701i	−0.881451	+	0.472276i
$676$	−6.38984	+	11.0675i	−0.245763	+	0.425674i
$677$	−27.5779	−	7.38947i	−1.05990	−	0.284001i	−0.313566	−	0.949567i	$-0.601524\pi$
$677$	−27.5779	−	7.38947i	−1.05990	−	0.284001i	−0.746339	+	0.665566i	$0.768190\pi$
$678$	1.24862	+	1.11542i	0.0479529	+	0.0428374i
$679$	−0.814695	−	0.470364i	−0.0312651	−	0.0180509i
$680$	−7.95422	+	8.45671i	−0.305030	+	0.324300i
$681$	1.64772	−	0.0928384i	0.0631408	−	0.00355758i
$682$	−1.49377	−	0.869482i	−0.0571993	−	0.0332942i
$683$	0.633770	+	0.633770i	0.0242505	+	0.0242505i	0.719128	−	0.694878i	$-0.244541\pi$
$683$	0.633770	+	0.633770i	0.0242505	+	0.0242505i	−0.694878	+	0.719128i	$0.744541\pi$
$684$	0.0100307	+	0.0887312i	0.000383533	+	0.00339272i
$685$	−13.6802	−	7.34945i	−0.522692	−	0.280808i
$686$		−	1.77799i		−	0.0678838i
$687$	26.4428	+	5.51223i	1.00886	+	0.210305i
$688$	−2.86792	−	10.7032i	−0.109339	−	0.408057i
$689$	1.37971	−	2.38973i	0.0525629	−	0.0910416i
$690$	−17.5625	+	1.52992i	−0.668594	+	0.0582432i
$691$	−10.8905	−	18.8629i	−0.414294	−	0.717578i	0.581060	−	0.813861i	$-0.302638\pi$
$691$	−10.8905	−	18.8629i	−0.414294	−	0.717578i	−0.995354	+	0.0962823i	$0.969305\pi$
$692$	−18.6498	−	4.99721i	−0.708961	−	0.189965i
$693$	−0.0176048	+	0.117093i	−0.000668752	+	0.00444799i
$694$	10.3680	+	5.98598i	0.393565	+	0.227225i
$695$	10.0456	−	42.6749i	0.381052	−	1.61875i
$696$	−11.3163	−	5.71012i	−0.428943	−	0.216441i
$697$	20.0079	+	20.0079i	0.757855	+	0.757855i
$698$	11.3770	+	11.3770i	0.430627	+	0.430627i
$699$	10.4361	+	5.26600i	0.394731	+	0.199178i
$700$	0.126661	−	0.622983i	0.00478735	−	0.0235466i
$701$	−11.1437	−	6.43382i	−0.420892	−	0.243002i	0.274567	−	0.961568i	$-0.411465\pi$
$701$	−11.1437	−	6.43382i	−0.420892	−	0.243002i	−0.695459	+	0.718566i	$0.744799\pi$
$702$	−0.226370	+	2.42844i	−0.00854377	+	0.0916557i
$703$	0.343806	+	0.0921226i	0.0129669	+	0.00347447i
$704$	−0.155214	−	0.268839i	−0.00584986	−	0.0101322i
$705$	−19.6491	+	23.3992i	−0.740029	+	0.881265i
$706$	−7.19111	+	12.4554i	−0.270641	+	0.468764i
$707$	0.0702190	+	0.262061i	0.00264086	+	0.00985581i
$708$	6.50793	+	1.35663i	0.244583	+	0.0509854i
$709$			12.3853i			0.465140i	0.972580	+	0.232570i	$0.0747135\pi$
$709$			12.3853i			0.465140i	−0.972580	+	0.232570i	$0.925286\pi$
$710$	−1.09667	+	2.04132i	−0.0411571	+	0.0766093i
$711$	−29.7959	+	3.36831i	−1.11743	+	0.126321i
$712$	5.35182	+	5.35182i	0.200568	+	0.200568i
$713$	21.9926	−	12.5940i	0.823630	−	0.471649i
$714$	−1.14159	+	0.0643213i	−0.0427230	+	0.00240717i
$715$	−0.325663	+	0.00997150i	−0.0121791	+	0.000372913i
$716$	−1.49476	−	0.863001i	−0.0558619	−	0.0322519i
$717$	12.5350	+	11.1978i	0.468127	+	0.418189i
$718$	−21.5444	−	5.77279i	−0.804028	−	0.215439i
$719$	8.75370	−	15.1619i	0.326458	−	0.565442i	−0.655348	−	0.755327i	$-0.727478\pi$
$719$	8.75370	−	15.1619i	0.326458	−	0.565442i	0.981806	+	0.189885i	$0.0608115\pi$
$720$	6.16559	−	2.64302i	0.229778	−	0.0984994i
$721$	1.97961			0.0737247
$722$	18.3517	+	4.91733i	0.682981	+	0.183004i
$723$	−4.79903	+	23.0215i	−0.178478	+	0.856179i
$724$	1.87205	−	1.08083i	0.0695743	−	0.0401687i
$725$	32.7483	+	16.3223i	1.21624	+	0.606194i
$726$	10.3479	+	15.7984i	0.384048	+	0.586332i
$727$	−23.2027	+	6.21713i	−0.860539	+	0.230581i	−0.661992	−	0.749511i	$-0.730289\pi$
$727$	−23.2027	+	6.21713i	−0.860539	+	0.230581i	−0.198547	+	0.980091i	$0.563622\pi$
$728$	−0.0422000	−	0.0422000i	−0.00156403	−	0.00156403i
$729$	−8.94569	−	25.4750i	−0.331322	−	0.943518i
$730$	−14.8674	+	4.47566i	−0.550268	+	0.165652i
$731$	49.8240	−	28.7659i	1.84281	−	1.06395i
$732$	2.29967	+	6.98427i	0.0849981	+	0.258146i
$733$	17.9299	+	4.80431i	0.662257	+	0.177451i	0.574264	−	0.818670i	$-0.305288\pi$
$733$	17.9299	+	4.80431i	0.662257	+	0.177451i	0.0879925	+	0.996121i	$0.471955\pi$
$734$	11.6775	+	20.2261i	0.431025	+	0.746558i
$735$	−22.1624	+	15.5060i	−0.817474	+	0.571947i
$736$	4.55180			0.167781
$737$	−0.526494	−	1.96490i	−0.0193937	−	0.0723781i
$738$	−5.97872	−	15.2170i	−0.220080	−	0.560147i
$739$	−5.56601	+	3.21354i	−0.204749	+	0.118212i	−0.598869	−	0.800847i	$-0.704383\pi$
$739$	−5.56601	+	3.21354i	−0.204749	+	0.118212i	0.394120	+	0.919059i	$0.371050\pi$
$740$	−0.818336	−	26.7263i	−0.0300826	−	0.982479i
$741$	−0.0216044	−	0.0109014i	−0.000793659	−	0.000400474i
$742$	−0.528543	−	0.528543i	−0.0194034	−	0.0194034i
$743$	−29.9189	−	29.9189i	−1.09762	−	1.09762i	−0.994689	−	0.102928i	$-0.967179\pi$
$743$	−29.9189	−	29.9189i	−1.09762	−	1.09762i	−0.102928	−	0.994689i	$-0.532821\pi$
$744$	−6.45007	+	7.16914i	−0.236471	+	0.262833i
$745$	31.7698	−	33.7768i	1.16395	−	1.23748i
$746$		−	5.21457i		−	0.190919i
$747$	3.73886	+	9.51614i	0.136798	+	0.348178i
$748$	1.13968	−	1.13968i	0.0416708	−	0.0416708i
$749$	0.372799	+	0.645706i	0.0136218	+	0.0235936i
$750$	−17.7606	+	7.71747i	−0.648527	+	0.281802i
$751$	−20.6150	+	35.7063i	−0.752253	+	1.30294i	0.194475	+	0.980908i	$0.437700\pi$
$751$	−20.6150	+	35.7063i	−0.752253	+	1.30294i	−0.946728	+	0.322034i	$0.895634\pi$
$752$	5.57856	−	5.57856i	0.203429	−	0.203429i
$753$	−25.2443	−	5.26240i	−0.919955	−	0.191772i
$754$	2.97478	−	1.71749i	0.108335	−	0.0625472i
$755$	−15.7501	−	3.70754i	−0.573203	−	0.134931i
$756$	0.619532	+	0.229485i	0.0225322	+	0.00834630i
$757$	10.3761	−	38.7242i	0.377126	−	1.40746i	−0.473086	−	0.881016i	$-0.656860\pi$
$757$	10.3761	−	38.7242i	0.377126	−	1.40746i	0.850213	−	0.526439i	$-0.176473\pi$
$758$	−3.27724	+	0.878135i	−0.119035	+	0.0318953i
$759$	2.44352	−	0.137677i	0.0886943	−	0.00499735i
$760$	0.00203698	+	0.0665264i	7.38890e−5	+	0.00241317i
$761$	−46.1591	−	26.6500i	−1.67327	−	0.966060i	−0.965791	−	0.259321i	$-0.916501\pi$
$761$	−46.1591	−	26.6500i	−1.67327	−	0.966060i	−0.707474	−	0.706740i	$-0.750165\pi$
$762$	2.66877	−	12.8024i	0.0966792	−	0.463782i
$763$	0.573112	+	2.13888i	0.0207480	+	0.0774327i
$764$	−5.31475	−	9.20541i	−0.192281	−	0.333040i
$765$	21.5403	+	27.3694i	0.778791	+	0.989543i
$766$	−1.23583	−	2.14052i	−0.0446524	−	0.0773402i
$767$	−1.27388	+	1.27388i	−0.0459972	+	0.0459972i
$768$	−1.64517	+	0.541693i	−0.0593648	+	0.0195467i
$769$	5.93147	+	3.42454i	0.213894	+	0.123492i	0.603120	−	0.797651i	$-0.293924\pi$
$769$	5.93147	+	3.42454i	0.213894	+	0.123492i	−0.389226	+	0.921142i	$0.627257\pi$
$770$	−0.0202228	+	0.0859088i	−0.000728780	+	0.00309594i
$771$	26.5360	−	1.49513i	0.955672	−	0.0538460i
$772$	19.2077	−	5.14670i	0.691301	−	0.185234i
$773$	−15.6194	−	15.6194i	−0.561792	−	0.561792i	0.368024	−	0.929816i	$-0.380034\pi$
$773$	−15.6194	−	15.6194i	−0.561792	−	0.561792i	−0.929816	+	0.368024i	$0.880034\pi$
$774$	−33.0320	+	3.73414i	−1.18731	+	0.134221i
$775$	18.5174	−	20.7872i	0.665165	−	0.746697i
$776$		−	7.39882i		−	0.265602i
$777$	1.75441	−	1.96391i	0.0629391	−	0.0704550i
$778$	−4.80396	−	17.9286i	−0.172230	−	0.642772i
$779$	0.162216			0.00581199
$780$	−0.316343	+	1.79017i	−0.0113269	+	0.0640983i
$781$	0.160849	−	0.278599i	0.00575565	−	0.00996907i
$782$	6.11668	+	22.8278i	0.218732	+	0.816319i
$783$	−21.9874	+	31.0247i	−0.785766	+	1.10873i
$784$	6.04818	−	3.49192i	0.216006	−	0.124711i
$785$	−6.39584	−	10.3340i	−0.228277	−	0.368837i
$786$	20.4552	−	13.3982i	0.729614	−	0.477898i
$787$	−12.8359	+	3.43938i	−0.457552	+	0.122601i	−0.480231	−	0.877142i	$-0.659447\pi$
$787$	−12.8359	+	3.43938i	−0.457552	+	0.122601i	0.0226788	+	0.999743i	$0.492780\pi$
$788$	−1.14621	+	4.27771i	−0.0408320	+	0.152387i
$789$	20.8273	+	10.5093i	0.741473	+	0.374142i
$790$	−22.3396	+	0.684018i	−0.794806	+	0.0243363i
$791$			0.122905i			0.00436999i
$792$	−0.866784	+	0.340556i	−0.0307998	+	0.0121011i
$793$	−1.92478	−	0.515742i	−0.0683508	−	0.0183145i
$794$	9.05119	−	15.6771i	0.321215	−	0.556360i
$795$	−3.96211	+	22.4214i	−0.140522	+	0.795204i
$796$	−9.11998	−	15.7963i	−0.323249	−	0.559884i
$797$	−10.4028	−	2.78742i	−0.368486	−	0.0987356i	0.0698240	−	0.997559i	$-0.477756\pi$
$797$	−10.4028	−	2.78742i	−0.368486	−	0.0987356i	−0.438310	+	0.898824i	$0.644423\pi$
$798$	−0.00436702	+	0.00488851i	−0.000154591	+	0.000173052i
$799$	35.4735	+	20.4807i	1.25496	+	0.724554i
$800$	4.74141	−	1.58715i	0.167634	−	0.0561143i
$801$	18.2641	−	13.4899i	0.645331	−	0.476643i
$802$	−8.60215	−	8.60215i	−0.303752	−	0.303752i
$803$	2.08206	−	0.557886i	0.0734743	−	0.0196874i
$804$	−11.3320	+	0.638487i	−0.399650	+	0.0225177i
$805$	−0.942648	−	0.886637i	−0.0332240	−	0.0312499i
$806$	−0.667470	−	2.52673i	−0.0235106	−	0.0890001i
$807$	0.923076	+	0.824606i	0.0324938	+	0.0290275i
$808$	−1.50883	+	1.50883i	−0.0530806	+	0.0530806i
$809$	23.8257	−	41.2673i	0.837667	−	1.45088i	−0.0541726	−	0.998532i	$-0.517252\pi$
$809$	23.8257	−	41.2673i	0.837667	−	1.45088i	0.891840	−	0.452351i	$-0.149415\pi$
$810$	−5.09086	−	19.4701i	−0.178875	−	0.684108i
$811$	6.04894	+	10.4771i	0.212407	+	0.367900i	0.952467	−	0.304641i	$-0.0985364\pi$
$811$	6.04894	+	10.4771i	0.212407	+	0.367900i	−0.740060	+	0.672541i	$0.765203\pi$
$812$	−0.240822	−	0.898761i	−0.00845121	−	0.0315403i
$813$	14.3003	−	4.70858i	0.501535	−	0.165137i
$814$			3.71210i			0.130109i
$815$	−5.16156	+	3.19454i	−0.180802	+	0.111900i
$816$	−4.92741	−	7.52276i	−0.172494	−	0.263349i
$817$	0.0853650	−	0.318587i	0.00298654	−	0.0111459i
$818$	21.2415	−	5.69165i	0.742693	−	0.199004i
$819$	−0.144015	+	0.106370i	−0.00503231	+	0.00371687i
$820$	−3.51277	−	11.6689i	−0.122671	−	0.407494i
$821$		−	41.4399i		−	1.44626i	−0.690710	−	0.723132i	$-0.742702\pi$
$821$		−	41.4399i		−	1.44626i	0.690710	−	0.723132i	$-0.257298\pi$
$822$	8.01383	−	8.97080i	0.279514	−	0.312893i
$823$	−4.95784	−	18.5029i	−0.172819	−	0.644970i	−0.996913	−	0.0785166i	$-0.974982\pi$
$823$	−4.95784	−	18.5029i	−0.172819	−	0.644970i	0.824093	−	0.566454i	$-0.191685\pi$
$824$	7.78482	+	13.4837i	0.271197	+	0.469727i
$825$	2.49731	−	0.995437i	0.0869451	−	0.0346567i
$826$	0.244001	+	0.422622i	0.00848987	+	0.0147049i
$827$	33.4676	+	8.96762i	1.16378	+	0.311835i	0.788476	−	0.615066i	$-0.210870\pi$
$827$	33.4676	+	8.96762i	1.16378	+	0.311835i	0.375307	+	0.926900i	$0.377537\pi$
$828$	2.03026	−	13.5036i	0.0705563	−	0.469283i
$829$		−	0.159635i		−	0.00554436i	−0.999996	−	0.00277218i	$-0.999118\pi$
$829$		−	0.159635i		−	0.00554436i	0.999996	−	0.00277218i	$-0.000882413\pi$
$830$	2.19675	+	7.29725i	0.0762503	+	0.253291i
$831$	41.5417	+	20.9616i	1.44107	+	0.727151i
$832$	0.121485	−	0.453387i	0.00421172	−	0.0157184i
$833$	25.6398	+	25.6398i	0.888368	+	0.888368i
$834$	30.3183	+	15.2984i	1.04984	+	0.529739i
$835$	−0.170190	−	5.55830i	−0.00588967	−	0.192353i
$836$		−	0.00924004i		−	0.000319573i
$837$	18.3914	+	22.3328i	0.635701	+	0.771936i
$838$	4.16069	−	4.16069i	0.143729	−	0.143729i
$839$	7.54445			0.260463			0.130232	−	0.991484i	$-0.458428\pi$
$839$	7.54445			0.260463			0.130232	+	0.991484i	$0.458428\pi$
$840$	0.446219	+	0.208278i	0.0153960	+	0.00718627i
$841$	24.5546			0.846712
$842$	26.6250	+	7.13416i	0.917559	+	0.245859i
$843$	−9.66176	−	29.3435i	−0.332769	−	1.01064i
$844$	9.11582	+	5.26302i	0.313779	+	0.181161i
$845$	20.8154	+	19.5786i	0.716072	+	0.673523i
$846$	−14.0615	−	19.0379i	−0.483443	−	0.654537i
$847$	−0.358814	+	1.33911i	−0.0123290	+	0.0460125i
$848$	1.52156	−	5.67855i	0.0522507	−	0.195002i
$849$	−20.8887	+	41.3971i	−0.716897	+	1.42075i
$850$	14.3312	+	21.6459i	0.491557	+	0.742447i
$851$	−47.1380	−	27.2151i	−1.61587	−	0.932923i
$852$	−1.33860	−	1.19580i	−0.0458597	−	0.0409675i
$853$	20.1916	−	20.1916i	0.691346	−	0.691346i	−0.271182	−	0.962528i	$-0.587415\pi$
$853$	20.1916	−	20.1916i	0.691346	−	0.691346i	0.962528	+	0.271182i	$0.0874146\pi$
$854$	−0.269888	+	0.467459i	−0.00923537	+	0.0159961i
$855$	0.198269	+	0.0236300i	0.00678067	+	0.000808130i
$856$	−2.93206	+	5.07847i	−0.100216	+	0.173579i
$857$	−4.93231	−	1.32161i	−0.168484	−	0.0451453i	0.173591	−	0.984818i	$-0.444463\pi$
$857$	−4.93231	−	1.32161i	−0.168484	−	0.0451453i	−0.342075	+	0.939673i	$0.611130\pi$
$858$	0.0515027	−	0.247064i	0.00175827	−	0.00843464i
$859$	−44.2023	+	25.5202i	−1.50816	+	0.870738i	−0.508208	+	0.861234i	$0.669692\pi$
$859$	−44.2023	+	25.5202i	−1.50816	+	0.870738i	−0.999955	+	0.00950373i	$0.996975\pi$
$860$	−24.7658	+	0.758308i	−0.844508	+	0.0258581i
$861$	0.540666	−	1.07149i	0.0184259	−	0.0365163i
$862$	28.3462	−	7.59534i	0.965476	−	0.258698i
$863$	2.37008	−	8.84525i	0.0806784	−	0.301096i	−0.913782	−	0.406204i	$-0.866852\pi$
$863$	2.37008	−	8.84525i	0.0806784	−	0.301096i	0.994461	+	0.105108i	$0.0335189\pi$
$864$	0.873218	+	5.12225i	0.0297075	+	0.174263i
$865$	−20.4323	+	38.0324i	−0.694719	+	1.29314i
$866$		−	18.1019i		−	0.615129i
$867$	11.4896	−	12.8616i	0.390206	−	0.436803i
$868$	−0.707913	−	0.00250257i	−0.0240281	−	8.49427e-5i
$869$	3.10281			0.105255
$870$	−18.2266	+	21.7051i	−0.617938	+	0.735873i
$871$	1.53791	−	2.66374i	0.0521101	−	0.0902573i
$872$	−12.3148	+	12.3148i	−0.417031	+	0.417031i
$873$	−21.9498	−	3.30013i	−0.742887	−	0.111692i
$874$	0.117335	+	0.0677431i	0.00396890	+	0.00229145i
$875$	−1.29107	−	0.594882i	−0.0436463	−	0.0201107i
$876$	−0.676557	−	12.0077i	−0.0228587	−	0.405703i
$877$	−13.7792	+	51.4245i	−0.465289	+	1.73648i	0.190639	+	0.981660i	$0.438944\pi$
$877$	−13.7792	+	51.4245i	−0.465289	+	1.73648i	−0.655929	+	0.754823i	$0.727723\pi$
$878$	−0.493390	+	1.84136i	−0.0166511	+	0.0621428i
$879$	26.7764	−	17.5386i	0.903146	−	0.591561i
$880$	−0.664674	+	0.200092i	−0.0224062	+	0.00674511i
$881$	19.0935	−	11.0236i	0.643276	−	0.371396i	−0.142599	−	0.989780i	$-0.545546\pi$
$881$	19.0935	−	11.0236i	0.643276	−	0.371396i	0.785875	+	0.618385i	$0.212213\pi$
$882$	−7.66163	−	19.5004i	−0.257980	−	0.656612i
$883$	14.9523	−	14.9523i	0.503186	−	0.503186i	−0.409240	−	0.912427i	$-0.634206\pi$
$883$	14.9523	−	14.9523i	0.503186	−	0.503186i	0.912427	+	0.409240i	$0.134206\pi$
$884$	2.43703			0.0819663
$885$	6.28724	−	13.4699i	0.211343	−	0.452786i
$886$	−9.84497	−	17.0520i	−0.330748	−	0.572873i
$887$	−3.87859	−	14.4751i	−0.130230	−	0.486026i	0.869742	−	0.493507i	$-0.164285\pi$
$887$	−3.87859	−	14.4751i	−0.130230	−	0.486026i	−0.999972	+	0.00748101i	$0.997619\pi$
$888$	20.2760	+	4.22670i	0.680417	+	0.141839i
$889$	0.831381	−	0.479998i	0.0278836	−	0.0160986i
$890$	14.3907	−	8.90657i	0.482378	−	0.298549i
$891$	0.623698	+	2.72335i	0.0208947	+	0.0912356i
$892$	17.0115	−	4.55822i	0.569587	−	0.152620i
$893$	0.226826	−	0.0607779i	0.00759045	−	0.00203386i
$894$	19.6805	+	30.0465i	0.658214	+	1.00491i
$895$	−2.64425	+	2.81129i	−0.0883875	+	0.0939711i
$896$	−0.110111	−	0.0635729i	−0.00367857	−	0.00212382i
$897$	2.75975	+	2.46535i	0.0921455	+	0.0823158i
$898$	−0.947727	+	0.947727i	−0.0316261	+	0.0316261i
$899$	10.6848	−	39.3196i	0.356357	−	1.31138i
$900$	−2.59371	−	14.7741i	−0.0864568	−	0.492468i
$901$	30.5232			1.01688
$902$	0.437863	+	1.63413i	0.0145793	+	0.0544105i
$903$	−1.81985	−	1.62572i	−0.0605609	−	0.0541005i
$904$	−0.837139	+	0.483323i	−0.0278428	+	0.0160751i
$905$	−1.39334	−	4.62844i	−0.0463161	−	0.153855i
$906$	5.64618	−	11.1896i	0.187582	−	0.371749i
$907$	31.6847	+	31.6847i	1.05207	+	1.05207i	0.998568	+	0.0535063i	$0.0170397\pi$
$907$	31.6847	+	31.6847i	1.05207	+	1.05207i	0.0535063	+	0.998568i	$0.482960\pi$
$908$	−0.246608	+	0.920354i	−0.00818398	+	0.0305430i
$909$	3.80320	+	5.14918i	0.126144	+	0.170788i
$910$	−0.113473	+	0.0702297i	−0.00376160	+	0.00232809i
$911$	45.8794	+	26.4885i	1.52005	+	0.877602i	0.999721	+	0.0236375i	$0.00752474\pi$
$911$	45.8794	+	26.4885i	1.52005	+	0.877602i	0.520331	+	0.853965i	$0.325809\pi$
$912$	−0.0504703	−	0.0105210i	−0.00167124	−	0.000348384i
$913$	−0.273823	−	1.02192i	−0.00906221	−	0.0338206i
$914$	5.74112			0.189899
$915$	16.3801	−	1.42691i	0.541508	−	0.0471723i
$916$	−7.79748	+	13.5056i	−0.257636	+	0.446238i
$917$	1.73384	+	0.464582i	0.0572565	+	0.0153418i
$918$	−24.5152	+	11.2625i	−0.809123	+	0.371719i
$919$	21.7820	−	12.5758i	0.718521	−	0.414838i	−0.0956874	−	0.995411i	$-0.530505\pi$
$919$	21.7820	−	12.5758i	0.718521	−	0.414838i	0.814208	+	0.580573i	$0.197172\pi$
$920$	2.33217	−	9.90733i	0.0768895	−	0.326635i
$921$	14.5967	−	9.56087i	0.480978	−	0.315041i
$922$	−15.3821	−	15.3821i	−0.506582	−	0.506582i
$923$	0.469848	−	0.125895i	0.0154652	−	0.00414389i
$924$	−0.0610336	−	0.0307971i	−0.00200786	−	0.00101315i
$925$	−58.5912	−	11.9124i	−1.92647	−	0.391678i
$926$			17.6635i			0.580460i
$927$	43.4738	−	17.0807i	1.42787	−	0.561004i
$928$	5.17468	−	5.17468i	0.169867	−	0.169867i
$929$	13.0056			0.426698			0.213349	−	0.976976i	$-0.431563\pi$
$929$	13.0056			0.426698			0.213349	+	0.976976i	$0.431563\pi$
$930$	12.2994	+	17.7123i	0.403313	+	0.580809i
$931$	0.207877			0.00681289
$932$	−4.77221	+	4.77221i	−0.156319	+	0.156319i
$933$	−14.2509	−	43.2811i	−0.466553	−	1.41696i
$934$		−	38.9934i		−	1.27590i
$935$	−1.89667	−	3.06453i	−0.0620278	−	0.100221i
$936$	−1.29086	−	0.562629i	−0.0421930	−	0.0183901i
$937$	21.2868	−	5.70378i	0.695409	−	0.186334i	0.106236	−	0.994341i	$-0.466120\pi$
$937$	21.2868	−	5.70378i	0.695409	−	0.186334i	0.589173	+	0.808007i	$0.299454\pi$
$938$	−0.589146	−	0.589146i	−0.0192363	−	0.0192363i
$939$	−31.8743	−	48.6631i	−1.04018	−	1.58806i
$940$	−9.28392	−	15.0004i	−0.302808	−	0.489260i
$941$	48.2820	−	27.8756i	1.57395	−	0.908720i	0.578272	−	0.815844i	$-0.303727\pi$
$941$	48.2820	−	27.8756i	1.57395	−	0.908720i	0.995678	−	0.0928758i	$-0.0296060\pi$
$942$	8.94156	−	2.94413i	0.291332	−	0.0959249i
$943$	−23.9611	−	6.42037i	−0.780282	−	0.209076i
$944$	−1.91906	+	3.32391i	−0.0624601	+	0.108184i
$945$	0.816918	−	1.23088i	0.0265743	−	0.0400405i
$946$	3.43980			0.111837
$947$	10.4761	+	39.0973i	0.340427	+	1.27049i	0.897865	+	0.440272i	$0.145118\pi$
$947$	10.4761	+	39.0973i	0.340427	+	1.27049i	−0.557438	+	0.830219i	$0.688215\pi$
$948$	3.53294	−	16.9479i	0.114745	−	0.550444i
$949$	2.82256	+	1.62961i	0.0916242	+	0.0528993i
$950$	0.145843	+	0.0296520i	0.00473178	+	0.000962039i
$951$	15.2675	+	23.3092i	0.495083	+	0.755851i
$952$	0.170858	−	0.637650i	0.00553753	−	0.0206664i
$953$	42.8872	+	42.8872i	1.38925	+	1.38925i	0.826892	+	0.562361i	$0.190107\pi$
$953$	42.8872	+	42.8872i	1.38925	+	1.38925i	0.562361	+	0.826892i	$0.309893\pi$
$954$	−16.1676	−	7.04678i	−0.523447	−	0.228148i
$955$	−22.7594	+	6.85144i	−0.736476	+	0.221707i
$956$	−8.40411	+	4.85211i	−0.271808	+	0.156929i
$957$	2.62139	−	2.93442i	0.0847374	−	0.0948564i
$958$	−5.86831	−	21.9008i	−0.189597	−	0.707584i
$959$	0.883021			0.0285142
$960$	0.336114	+	3.85837i	0.0108480	+	0.124528i
$961$	−26.7365	−	15.6894i	−0.862469	−	0.506110i
$962$	−3.96888	+	3.96888i	−0.127962	+	0.127962i
$963$	13.7583	+	10.9636i	0.443355	+	0.353296i
$964$	−11.7582	−	6.78860i	−0.378706	−	0.218646i
$965$	−1.36084	−	44.4441i	−0.0438069	−	1.43071i
$966$	0.838543	−	0.549247i	0.0269797	−	0.0176717i
$967$	16.8371	−	4.51148i	0.541443	−	0.145079i	0.0222758	−	0.999752i	$-0.492909\pi$
$967$	16.8371	−	4.51148i	0.541443	−	0.145079i	0.519167	+	0.854673i	$0.326242\pi$
$968$	−10.5321	+	2.82207i	−0.338515	+	0.0907047i
$969$	−0.0150579	−	0.267252i	−0.000483730	−	0.00858538i
$970$	−16.1041	−	3.79088i	−0.517071	−	0.121718i
$971$	15.6626	−	9.04283i	0.502638	−	0.290198i	−0.227164	−	0.973856i	$-0.572945\pi$
$971$	15.6626	−	9.04283i	0.502638	−	0.290198i	0.729802	+	0.683658i	$0.239612\pi$
$972$	15.5855	−	0.305838i	0.499904	−	0.00980975i
$973$	0.645204	+	2.40793i	0.0206843	+	0.0771948i
$974$	16.9000	+	29.2717i	0.541512	+	0.937927i
$975$	3.73435	+	1.60576i	0.119595	+	0.0514255i
$976$	−4.24533			−0.135890
$977$	10.5668	−	10.5668i	0.338062	−	0.338062i	−0.517575	−	0.855638i	$-0.673165\pi$
$977$	10.5668	−	10.5668i	0.338062	−	0.338062i	0.855638	+	0.517575i	$0.173165\pi$
$978$	−1.47051	−	4.46606i	−0.0470218	−	0.142809i
$979$	−2.03474	+	1.17476i	−0.0650306	+	0.0375454i
$980$	−4.50156	−	14.9534i	−0.143797	−	0.477670i
$981$	31.0409	+	42.0265i	0.991059	+	1.34180i
$982$	8.02012	−	29.9315i	0.255932	−	0.955153i
$983$	12.7066	−	47.4216i	0.405277	−	1.51251i	−0.398269	−	0.917269i	$-0.630389\pi$
$983$	12.7066	−	47.4216i	0.405277	−	1.51251i	0.803545	−	0.595244i	$-0.202945\pi$
$984$	9.42439	−	0.531004i	0.300439	−	0.0169278i
$985$	8.72348	+	4.68655i	0.277953	+	0.149326i
$986$	32.9053	+	18.9979i	1.04792	+	0.605016i
$987$	0.354554	−	1.70084i	0.0112856	−	0.0541383i
$988$	0.00987921	−	0.00987921i	0.000314300	−	0.000314300i
$989$	−25.2188	+	43.6802i	−0.801911	+	1.38895i
$990$	0.297138	+	2.06111i	0.00944366	+	0.0655063i
$991$	−52.4916			−1.66745			−0.833726	−	0.552179i	$-0.813797\pi$
$991$	−52.4916			−1.66745			−0.833726	+	0.552179i	$0.813797\pi$
$992$	−2.76682	−	4.83164i	−0.0878466	−	0.153405i
$993$	−21.2297	−	18.9650i	−0.673704	−	0.601836i
$994$		−	0.131762i		−	0.00417924i
$995$	−39.0545	+	11.7569i	−1.23811	+	0.372719i
$996$	−5.89365	+	0.332069i	−0.186747	+	0.0105220i
$997$	9.59005	−	35.7906i	0.303720	−	1.13350i	−0.630322	−	0.776334i	$-0.717077\pi$
$997$	9.59005	−	35.7906i	0.303720	−	1.13350i	0.934042	−	0.357164i	$-0.116256\pi$
$998$	−5.25510	+	1.40810i	−0.166347	+	0.0445726i
$999$	21.5829	−	58.2666i	0.682854	−	1.84347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bf.a.377.5	✓	256
3.2	odd	2	inner	930.2.bf.a.377.62	yes	256
5.3	odd	4	inner	930.2.bf.a.563.44	yes	256
15.8	even	4	inner	930.2.bf.a.563.17	yes	256
31.25	even	3	inner	930.2.bf.a.707.17	yes	256
93.56	odd	6	inner	930.2.bf.a.707.44	yes	256
155.118	odd	12	inner	930.2.bf.a.893.62	yes	256
465.428	even	12	inner	930.2.bf.a.893.5	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bf.a.377.5	✓	256	1.1	even	1	trivial
930.2.bf.a.377.62	yes	256	3.2	odd	2	inner
930.2.bf.a.563.17	yes	256	15.8	even	4	inner
930.2.bf.a.563.44	yes	256	5.3	odd	4	inner
930.2.bf.a.707.17	yes	256	31.25	even	3	inner
930.2.bf.a.707.44	yes	256	93.56	odd	6	inner
930.2.bf.a.893.5	yes	256	465.428	even	12	inner
930.2.bf.a.893.62	yes	256	155.118	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.64517 + 0.541693i) q^{3} -1.00000i q^{4} +(-2.17658 - 0.512363i) q^{5} +(0.780273 - 1.54634i) q^{6} +(0.122813 - 0.0329078i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41314 - 1.78235i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.64517 + 0.541693i) q^{3} -1.00000i q^{4} +(-2.17658 - 0.512363i) q^{5} +(0.780273 - 1.54634i) q^{6} +(0.122813 - 0.0329078i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.41314 - 1.78235i) q^{9} +(1.90137 - 1.17678i) q^{10} +(-0.268839 + 0.155214i) q^{11} +(0.541693 + 1.64517i) q^{12} +(-0.453387 - 0.121485i) q^{13} +(-0.0635729 + 0.110111i) q^{14} +(3.85837 - 0.336114i) q^{15} -1.00000 q^{16} +(-1.34379 - 5.01511i) q^{17} +(-0.446034 + 2.96666i) q^{18} +(-0.0257776 - 0.0148827i) q^{19} +(-0.512363 + 2.17658i) q^{20} +(-0.184222 + 0.120666i) q^{21} +(0.0803448 - 0.299851i) q^{22} +(3.21861 + 3.21861i) q^{23} +(-1.54634 - 0.780273i) q^{24} +(4.47497 + 2.23040i) q^{25} +(0.406495 - 0.234690i) q^{26} +(-3.00452 + 4.23944i) q^{27} +(-0.0329078 - 0.122813i) q^{28} +7.31810 q^{29} +(-2.49061 + 2.96595i) q^{30} +(1.46005 - 5.37292i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.358206 - 0.400981i) q^{33} +(4.49642 + 2.59601i) q^{34} +(-0.284173 + 0.00870114i) q^{35} +(-1.78235 - 2.41314i) q^{36} +(-11.5505 + 3.09495i) q^{37} +(0.0287512 - 0.00770386i) q^{38} +(0.811703 - 0.0457342i) q^{39} +(-1.17678 - 1.90137i) q^{40} +(-4.71967 + 2.72490i) q^{41} +(0.0449413 - 0.215589i) q^{42} +(2.86792 + 10.7032i) q^{43} +(0.155214 + 0.268839i) q^{44} +(-6.16559 + 2.64302i) q^{45} -4.55180 q^{46} +(-5.57856 + 5.57856i) q^{47} +(1.64517 - 0.541693i) q^{48} +(-6.04818 + 3.49192i) q^{49} +(-4.74141 + 1.58715i) q^{50} +(4.92741 + 7.52276i) q^{51} +(-0.121485 + 0.453387i) q^{52} +(-1.52156 + 5.67855i) q^{53} +(-0.873218 - 5.12225i) q^{54} +(0.664674 - 0.200092i) q^{55} +(0.110111 + 0.0635729i) q^{56} +(0.0504703 + 0.0105210i) q^{57} +(-5.17468 + 5.17468i) q^{58} +(1.91906 - 3.32391i) q^{59} +(-0.336114 - 3.85837i) q^{60} +4.24533 q^{61} +(2.76682 + 4.83164i) q^{62} +(0.237712 - 0.298307i) q^{63} +1.00000i q^{64} +(0.924586 + 0.496719i) q^{65} +(0.0302467 + 0.536826i) q^{66} +(-1.69602 + 6.32965i) q^{67} +(-5.01511 + 1.34379i) q^{68} +(-7.03864 - 3.55164i) q^{69} +(0.194788 - 0.207094i) q^{70} +(-0.897468 + 0.518153i) q^{71} +(2.96666 + 0.446034i) q^{72} +(-6.70705 - 1.79715i) q^{73} +(5.97899 - 10.3559i) q^{74} +(-8.57025 - 1.24531i) q^{75} +(-0.0148827 + 0.0257776i) q^{76} +(-0.0279093 + 0.0279093i) q^{77} +(-0.541622 + 0.606300i) q^{78} +(-8.65613 - 4.99762i) q^{79} +(2.17658 + 0.512363i) q^{80} +(2.64646 - 8.60211i) q^{81} +(1.41051 - 5.26411i) q^{82} +(-0.882080 + 3.29197i) q^{83} +(0.120666 + 0.184222i) q^{84} +(0.355313 + 11.6043i) q^{85} +(-9.59626 - 5.54040i) q^{86} +(-12.0395 + 3.96417i) q^{87} +(-0.299851 - 0.0803448i) q^{88} +7.56862 q^{89} +(2.49083 - 6.22862i) q^{90} -0.0596798 q^{91} +(3.21861 - 3.21861i) q^{92} +(0.508456 + 9.63024i) q^{93} -7.88928i q^{94} +(0.0484816 + 0.0456009i) q^{95} +(-0.780273 + 1.54634i) q^{96} +(-5.23176 - 5.23176i) q^{97} +(1.80755 - 6.74587i) q^{98} +(-0.372099 + 0.853718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) \) 256 * q + 8 * q^3 - 4 * q^7	\( 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) \) 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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