LMFDB - Embedded newform 547.2.m.a.10.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(10,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(182))

chi = DirichletCharacter(H, H._module([60]))

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

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

chi := DirichletCharacter("547.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.m (of order $91$, degree $72$, 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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$3168$
Relative dimension:	$44$ over $\Q(\zeta_{91})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{91}]$

Embedding invariants

Embedding label			10.5
Character	$\chi$	$=$	547.10
Dual form			547.2.m.a.383.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19472 - 2.01540i) q^{2} +(-0.168315 - 0.737438i) q^{3} +(-1.67460 + 3.06109i) q^{4} +(-1.16754 - 0.0403228i) q^{5} +(-1.28514 + 1.22026i) q^{6} +(4.11811 - 0.572320i) q^{7} +(3.48700 - 0.120429i) q^{8} +(2.18742 - 1.05341i) q^{9} +O(q^{10})$	\(q+(-1.19472 - 2.01540i) q^{2} +(-0.168315 - 0.737438i) q^{3} +(-1.67460 + 3.06109i) q^{4} +(-1.16754 - 0.0403228i) q^{5} +(-1.28514 + 1.22026i) q^{6} +(4.11811 - 0.572320i) q^{7} +(3.48700 - 0.120429i) q^{8} +(2.18742 - 1.05341i) q^{9} +(1.31362 + 2.40123i) q^{10} +(-2.88671 - 0.711509i) q^{11} +(2.53923 + 0.719686i) q^{12} +(-1.16921 - 1.46615i) q^{13} +(-6.07346 - 7.61588i) q^{14} +(0.166779 + 0.867772i) q^{15} +(-0.645115 - 1.00729i) q^{16} +(4.52566 - 3.73869i) q^{17} +(-4.73640 - 3.15000i) q^{18} +(1.51871 - 0.936081i) q^{19} +(2.07859 - 3.50641i) q^{20} +(-1.11519 - 2.94052i) q^{21} +(2.01484 + 6.66793i) q^{22} +(1.38917 - 4.59734i) q^{23} +(-0.675725 - 2.55118i) q^{24} +(-3.62657 - 0.250799i) q^{25} +(-1.55799 + 4.10807i) q^{26} +(-2.55983 - 3.20992i) q^{27} +(-5.14427 + 13.5643i) q^{28} +(-5.74017 + 3.27020i) q^{29} +(1.54965 - 1.37287i) q^{30} +(-1.60855 + 0.578488i) q^{31} +(1.87642 - 3.73031i) q^{32} +(-0.0388168 + 2.24852i) q^{33} +(-12.9419 - 4.65432i) q^{34} +(-4.83111 + 0.502150i) q^{35} +(-0.438486 + 8.45994i) q^{36} +(-0.108818 + 0.694808i) q^{37} +(-3.70101 - 1.94244i) q^{38} +(-0.884395 + 1.10900i) q^{39} -4.07605 q^{40} -0.0552920 q^{41} +(-4.59398 + 5.76067i) q^{42} +(0.528242 - 0.378245i) q^{43} +(7.01208 - 7.64498i) q^{44} +(-2.59637 + 1.14169i) q^{45} +(-10.9252 + 2.69281i) q^{46} +(-1.55622 + 2.25458i) q^{47} +(-0.634231 + 0.645274i) q^{48} +(9.89655 - 2.80495i) q^{49} +(3.82730 + 7.60864i) q^{50} +(-3.51879 - 2.70811i) q^{51} +(6.44597 - 1.12386i) q^{52} +(-0.914578 - 4.75867i) q^{53} +(-3.41099 + 8.99405i) q^{54} +(3.34164 + 0.947112i) q^{55} +(14.2909 - 2.49162i) q^{56} +(-0.945923 - 0.962394i) q^{57} +(13.4487 + 7.66177i) q^{58} +(1.19876 + 9.87268i) q^{59} +(-2.93562 - 0.942648i) q^{60} +(0.0777446 + 0.898548i) q^{61} +(3.08766 + 2.55075i) q^{62} +(8.40516 - 5.58995i) q^{63} +(-12.1465 + 0.840002i) q^{64} +(1.30598 + 1.75892i) q^{65} +(4.57805 - 2.60813i) q^{66} +(12.2606 + 3.47498i) q^{67} +(3.86580 + 20.1143i) q^{68} +(-3.62407 - 0.250626i) q^{69} +(6.78388 + 9.13670i) q^{70} +(-4.90218 - 14.4073i) q^{71} +(7.50068 - 3.93666i) q^{72} +(-0.142075 + 0.739233i) q^{73} +(1.53032 - 0.610792i) q^{74} +(0.425459 + 2.71659i) q^{75} +(0.322204 + 6.21646i) q^{76} +(-12.2950 - 1.27795i) q^{77} +(3.29168 + 0.457466i) q^{78} +(-3.70207 + 2.65085i) q^{79} +(0.712577 + 1.20206i) q^{80} +(2.60497 - 3.26653i) q^{81} +(0.0660586 + 0.111435i) q^{82} +(-13.4985 - 7.08458i) q^{83} +(10.8687 + 1.51049i) q^{84} +(-5.43462 + 4.18257i) q^{85} +(-1.39342 - 0.612720i) q^{86} +(3.37773 + 3.68260i) q^{87} +(-10.1516 - 2.13339i) q^{88} +(0.525098 - 6.06892i) q^{89} +(5.40290 + 3.86872i) q^{90} +(-5.65405 - 5.36858i) q^{91} +(11.7466 + 11.9511i) q^{92} +(0.697343 + 1.08884i) q^{93} +(6.40313 + 0.442814i) q^{94} +(-1.81089 + 1.03167i) q^{95} +(-3.06670 - 0.755873i) q^{96} +(3.87172 + 2.97973i) q^{97} +(-17.4768 - 16.5944i) q^{98} +(-7.06395 + 1.48451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) $ 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99}+O(q^{100}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9 - 91 * q^10 - 61 * q^11 - 31 * q^12 - 72 * q^13 - 21 * q^14 - 46 * q^15 + 24 * q^16 - 91 * q^17 + 9 * q^18 - 89 * q^19 - 108 * q^20 - 81 * q^21 - 50 * q^22 - 86 * q^23 - 33 * q^24 - 15 * q^25 + 137 * q^26 + 163 * q^27 - 47 * q^28 - 12 * q^29 + 29 * q^30 - 53 * q^31 - 122 * q^32 - 21 * q^33 - 80 * q^34 - 75 * q^35 - 8 * q^36 - 49 * q^37 - 47 * q^38 + 128 * q^39 - 246 * q^40 - 686 * q^41 - 466 * q^42 - 9 * q^43 - 43 * q^44 + 156 * q^45 - 91 * q^46 - 72 * q^47 + 21 * q^48 - 8 * q^49 - 84 * q^50 + 93 * q^51 + 4 * q^52 - 32 * q^53 - 71 * q^54 - 34 * q^55 - 263 * q^56 - 61 * q^57 - 36 * q^58 - 23 * q^59 + 87 * q^60 + 38 * q^61 + 26 * q^62 + 133 * q^63 + 343 * q^64 + 143 * q^65 - 65 * q^66 - 50 * q^67 - 213 * q^68 - 140 * q^69 + 372 * q^70 - 75 * q^71 + 147 * q^72 - 18 * q^73 - 85 * q^74 + 97 * q^75 - 47 * q^76 + 11 * q^77 + 55 * q^78 - 37 * q^79 - 142 * q^80 - 532 * q^81 - 94 * q^82 - 279 * q^83 + 395 * q^84 - 75 * q^85 - 147 * q^86 + 84 * q^87 + 345 * q^88 + 8 * q^89 + 278 * q^90 - 38 * q^91 - 78 * q^92 - 83 * q^93 - 540 * q^94 + 35 * q^95 + 123 * q^96 - 735 * q^97 - 90 * q^98 + 351 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{30}{91}\right)$

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 $

$2$	−1.19472	−	2.01540i	−0.844798	−	1.42510i	−0.904310	−	0.426877i	$-0.859614\pi$
$2$	−1.19472	−	2.01540i	−0.844798	−	1.42510i	0.0595123	−	0.998228i	$-0.481045\pi$
$3$	−0.168315	−	0.737438i	−0.0971769	−	0.425760i	0.902814	−	0.430031i	$-0.141498\pi$
$3$	−0.168315	−	0.737438i	−0.0971769	−	0.425760i	−0.999991	+	0.00427139i	$0.998640\pi$
$4$	−1.67460	+	3.06109i	−0.837301	+	1.53055i
$5$	−1.16754	−	0.0403228i	−0.522138	−	0.0180329i	−0.227751	−	0.973719i	$-0.573137\pi$
$5$	−1.16754	−	0.0403228i	−0.522138	−	0.0180329i	−0.294386	+	0.955686i	$0.595115\pi$
$6$	−1.28514	+	1.22026i	−0.524657	+	0.498168i
$7$	4.11811	−	0.572320i	1.55650	−	0.216317i	0.693101	−	0.720840i	$-0.256244\pi$
$7$	4.11811	−	0.572320i	1.55650	−	0.216317i	0.863398	+	0.504524i	$0.168332\pi$
$8$	3.48700	−	0.120429i	1.23284	−	0.0425783i
$9$	2.18742	−	1.05341i	0.729141	−	0.351136i
$10$	1.31362	+	2.40123i	0.415402	+	0.759335i
$11$	−2.88671	−	0.711509i	−0.870374	−	0.214528i	−0.221256	−	0.975216i	$-0.571016\pi$
$11$	−2.88671	−	0.711509i	−0.870374	−	0.214528i	−0.649118	+	0.760688i	$0.724862\pi$
$12$	2.53923	+	0.719686i	0.733012	+	0.207756i
$13$	−1.16921	−	1.46615i	−0.324281	−	0.406636i	0.592791	−	0.805356i	$-0.298026\pi$
$13$	−1.16921	−	1.46615i	−0.324281	−	0.406636i	−0.917073	+	0.398720i	$0.869454\pi$
$14$	−6.07346	−	7.61588i	−1.62320	−	2.03543i
$15$	0.166779	+	0.867772i	0.0430620	+	0.224058i
$16$	−0.645115	−	1.00729i	−0.161279	−	0.251822i
$17$	4.52566	−	3.73869i	1.09763	−	0.906766i	0.101519	−	0.994834i	$-0.467630\pi$
$17$	4.52566	−	3.73869i	1.09763	−	0.906766i	0.996114	+	0.0880677i	$0.0280692\pi$
$18$	−4.73640	−	3.15000i	−1.11638	−	0.742463i
$19$	1.51871	−	0.936081i	0.348415	−	0.214752i	−0.339393	−	0.940645i	$-0.610222\pi$
$19$	1.51871	−	0.936081i	0.348415	−	0.214752i	0.687808	+	0.725893i	$0.258573\pi$
$20$	2.07859	−	3.50641i	0.464787	−	0.784057i
$21$	−1.11519	−	2.94052i	−0.243355	−	0.641674i
$22$	2.01484	+	6.66793i	0.429565	+	1.42161i
$23$	1.38917	−	4.59734i	0.289663	−	0.958611i	−0.683782	−	0.729687i	$-0.739666\pi$
$23$	1.38917	−	4.59734i	0.289663	−	0.958611i	0.973444	−	0.228925i	$-0.0735209\pi$
$24$	−0.675725	−	2.55118i	−0.137932	−	0.520756i
$25$	−3.62657	−	0.250799i	−0.725315	−	0.0501598i
$26$	−1.55799	+	4.10807i	−0.305546	+	0.805659i
$27$	−2.55983	−	3.20992i	−0.492639	−	0.617750i
$28$	−5.14427	+	13.5643i	−0.972176	+	2.56342i
$29$	−5.74017	+	3.27020i	−1.06592	+	0.607260i	−0.923912	−	0.382605i	$-0.875027\pi$
$29$	−5.74017	+	3.27020i	−1.06592	+	0.607260i	−0.142011	+	0.989865i	$0.545357\pi$
$30$	1.54965	−	1.37287i	0.282927	−	0.250651i
$31$	−1.60855	+	0.578488i	−0.288905	+	0.103899i	−0.478854	−	0.877894i	$-0.658948\pi$
$31$	−1.60855	+	0.578488i	−0.288905	+	0.103899i	0.189950	+	0.981794i	$0.439168\pi$
$32$	1.87642	−	3.73031i	0.331707	−	0.659431i
$33$	−0.0388168	+	2.24852i	−0.00675713	+	0.391418i
$34$	−12.9419	−	4.65432i	−2.21951	−	0.798209i
$35$	−4.83111	+	0.502150i	−0.816607	+	0.0848789i
$36$	−0.438486	+	8.45994i	−0.0730809	+	1.40999i
$37$	−0.108818	+	0.694808i	−0.0178895	+	0.114226i	−0.995249	−	0.0973577i	$-0.968961\pi$
$37$	−0.108818	+	0.694808i	−0.0178895	+	0.114226i	0.977360	+	0.211583i	$0.0678620\pi$
$38$	−3.70101	−	1.94244i	−0.600384	−	0.315106i
$39$	−0.884395	+	1.10900i	−0.141617	+	0.177582i
$40$	−4.07605			−0.644480
$41$	−0.0552920			−0.00863515			−0.00431758	−	0.999991i	$-0.501374\pi$
$41$	−0.0552920			−0.00863515			−0.00431758	+	0.999991i	$0.501374\pi$
$42$	−4.59398	+	5.76067i	−0.708867	+	0.888891i
$43$	0.528242	−	0.378245i	0.0805561	−	0.0576818i	−0.541192	−	0.840899i	$-0.682027\pi$
$43$	0.528242	−	0.378245i	0.0805561	−	0.0576818i	0.621749	+	0.783217i	$0.286423\pi$
$44$	7.01208	−	7.64498i	1.05711	−	1.15252i
$45$	−2.59637	+	1.14169i	−0.387044	+	0.170193i
$46$	−10.9252	+	2.69281i	−1.61083	+	0.397033i
$47$	−1.55622	+	2.25458i	−0.226998	+	0.328864i	−0.919889	−	0.392179i	$-0.871721\pi$
$47$	−1.55622	+	2.25458i	−0.226998	+	0.328864i	0.692891	+	0.721043i	$0.256337\pi$
$48$	−0.634231	+	0.645274i	−0.0915434	+	0.0931373i
$49$	9.89655	−	2.80495i	1.41379	−	0.400708i
$50$	3.82730	+	7.60864i	0.541261	+	1.07602i
$51$	−3.51879	−	2.70811i	−0.492729	−	0.379212i
$52$	6.44597	−	1.12386i	0.893896	−	0.155851i
$53$	−0.914578	−	4.75867i	−0.125627	−	0.653654i	−0.988860	−	0.148849i	$-0.952443\pi$
$53$	−0.914578	−	4.75867i	−0.125627	−	0.653654i	0.863233	−	0.504806i	$-0.168436\pi$
$54$	−3.41099	+	8.99405i	−0.464177	+	1.22394i
$55$	3.34164	+	0.947112i	0.450587	+	0.127709i
$56$	14.2909	−	2.49162i	1.90970	−	0.332957i
$57$	−0.945923	−	0.962394i	−0.125291	−	0.127472i
$58$	13.4487	+	7.66177i	1.76590	+	1.00604i
$59$	1.19876	+	9.87268i	0.156065	+	1.28531i	0.834645	+	0.550788i	$0.185673\pi$
$59$	1.19876	+	9.87268i	0.156065	+	1.28531i	−0.678580	+	0.734526i	$0.737404\pi$
$60$	−2.93562	−	0.942648i	−0.378987	−	0.121695i
$61$	0.0777446	+	0.898548i	0.00995417	+	0.115047i	0.999593	−	0.0285329i	$-0.00908355\pi$
$61$	0.0777446	+	0.898548i	0.00995417	+	0.115047i	−0.989639	+	0.143580i	$0.954138\pi$
$62$	3.08766	+	2.55075i	0.392134	+	0.323945i
$63$	8.40516	−	5.58995i	1.05895	−	0.704268i
$64$	−12.1465	+	0.840002i	−1.51831	+	0.105000i
$65$	1.30598	+	1.75892i	0.161987	+	0.218167i
$66$	4.57805	−	2.60813i	0.563520	−	0.321039i
$67$	12.2606	+	3.47498i	1.49787	+	0.424537i	0.920106	−	0.391669i	$-0.128102\pi$
$67$	12.2606	+	3.47498i	1.49787	+	0.424537i	0.577762	+	0.816206i	$0.303926\pi$
$68$	3.86580	+	20.1143i	0.468797	+	2.43922i
$69$	−3.62407	−	0.250626i	−0.436287	−	0.0301718i
$70$	6.78388	+	9.13670i	0.810829	+	1.09205i
$71$	−4.90218	−	14.4073i	−0.581782	−	1.70983i	−0.697531	−	0.716555i	$-0.745718\pi$
$71$	−4.90218	−	14.4073i	−0.581782	−	1.70983i	0.115749	−	0.993278i	$-0.463073\pi$
$72$	7.50068	−	3.93666i	0.883963	−	0.463940i
$73$	−0.142075	+	0.739233i	−0.0166286	+	0.0865207i	−0.989389	−	0.145294i	$-0.953587\pi$
$73$	−0.142075	+	0.739233i	−0.0166286	+	0.0865207i	0.972760	+	0.231815i	$0.0744663\pi$
$74$	1.53032	−	0.610792i	0.177896	−	0.0710032i
$75$	0.425459	+	2.71659i	0.0491278	+	0.313684i
$76$	0.322204	+	6.21646i	0.0369594	+	0.713077i
$77$	−12.2950	−	1.27795i	−1.40114	−	0.145636i
$78$	3.29168	+	0.457466i	0.372709	+	0.0517979i
$79$	−3.70207	+	2.65085i	−0.416516	+	0.298244i	−0.771021	−	0.636810i	$-0.780254\pi$
$79$	−3.70207	+	2.65085i	−0.416516	+	0.298244i	0.354505	+	0.935054i	$0.384649\pi$
$80$	0.712577	+	1.20206i	0.0796686	+	0.134394i
$81$	2.60497	−	3.26653i	0.289441	−	0.362948i
$82$	0.0660586	+	0.111435i	0.00729496	+	0.0123060i
$83$	−13.4985	−	7.08458i	−1.48166	−	0.777634i	−0.486292	−	0.873797i	$-0.661651\pi$
$83$	−13.4985	−	7.08458i	−1.48166	−	0.777634i	−0.995366	+	0.0961628i	$0.969343\pi$
$84$	10.8687	+	1.51049i	1.18587	+	0.164809i
$85$	−5.43462	+	4.18257i	−0.589468	+	0.453663i
$86$	−1.39342	−	0.612720i	−0.150256	−	0.0660713i
$87$	3.37773	+	3.68260i	0.362130	+	0.394816i
$88$	−10.1516	−	2.13339i	−1.08217	−	0.227420i
$89$	0.525098	−	6.06892i	0.0556603	−	0.643305i	−0.915096	−	0.403237i	$-0.867885\pi$
$89$	0.525098	−	6.06892i	0.0556603	−	0.643305i	0.970756	−	0.240068i	$-0.0771698\pi$
$90$	5.40290	+	3.86872i	0.569516	+	0.407799i
$91$	−5.65405	−	5.36858i	−0.592705	−	0.562781i
$92$	11.7466	+	11.9511i	1.22466	+	1.24599i
$93$	0.697343	+	1.08884i	0.0723111	+	0.112907i
$94$	6.40313	+	0.442814i	0.660432	+	0.0456728i
$95$	−1.81089	+	1.03167i	−0.185793	+	0.105847i
$96$	−3.06670	−	0.755873i	−0.312994	−	0.0771460i
$97$	3.87172	+	2.97973i	0.393113	+	0.302546i	0.787401	−	0.616441i	$-0.211426\pi$
$97$	3.87172	+	2.97973i	0.393113	+	0.302546i	−0.394288	+	0.918987i	$0.629009\pi$
$98$	−17.4768	−	16.5944i	−1.76542	−	1.67629i
$99$	−7.06395	+	1.48451i	−0.709954	+	0.149198i
$100$	6.84079	−	10.6813i	0.684079	−	1.06813i
$101$	9.28368	−	12.5035i	0.923760	−	1.24414i	−0.0457148	−	0.998955i	$-0.514557\pi$
$101$	9.28368	−	12.5035i	0.923760	−	1.24414i	0.969475	−	0.245189i	$-0.0788500\pi$
$102$	−1.25395	+	10.3272i	−0.124160	+	1.02255i
$103$	−0.748372	+	1.62519i	−0.0737393	+	0.160135i	−0.941658	−	0.336572i	$-0.890732\pi$
$103$	−0.748372	+	1.62519i	−0.0737393	+	0.160135i	0.867918	+	0.496707i	$0.165458\pi$
$104$	−4.25361	−	4.97164i	−0.417101	−	0.487509i
$105$	1.18346	+	3.47813i	0.115493	+	0.339431i
$106$	−8.49797	+	7.52854i	−0.825396	+	0.731237i
$107$	−6.09266	−	1.50170i	−0.588999	−	0.145175i	−0.0664579	−	0.997789i	$-0.521170\pi$
$107$	−6.09266	−	1.50170i	−0.588999	−	0.145175i	−0.522541	+	0.852614i	$0.675016\pi$
$108$	14.1126	−	2.46053i	1.35798	−	0.236764i
$109$	−2.86141	−	4.46784i	−0.274073	−	0.427942i	0.677427	−	0.735590i	$-0.263095\pi$
$109$	−2.86141	−	4.46784i	−0.274073	−	0.427942i	−0.951500	+	0.307649i	$0.900458\pi$
$110$	−2.08353	−	7.86628i	−0.198657	−	0.750021i
$111$	0.530693	−	0.0367006i	0.0503712	−	0.00348346i
$112$	−3.23315	−	3.77892i	−0.305504	−	0.357074i
$113$	0.823219	+	0.507406i	0.0774419	+	0.0477327i	0.562882	−	0.826537i	$-0.309692\pi$
$113$	0.823219	+	0.507406i	0.0774419	+	0.0477327i	−0.485440	+	0.874270i	$0.661341\pi$
$114$	−0.809493	+	3.05621i	−0.0758159	+	0.286240i
$115$	−1.80729	+	5.31154i	−0.168530	+	0.495303i
$116$	−0.397874	−	23.0475i	−0.0369416	−	2.13990i
$117$	−4.10201	−	1.97542i	−0.379231	−	0.182628i
$118$	18.4652	−	14.2111i	1.69986	−	1.30824i
$119$	16.4974	−	17.9865i	1.51232	−	1.64882i
$120$	0.686062	+	3.00583i	0.0626286	+	0.274394i
$121$	−1.91319	−	1.00412i	−0.173927	−	0.0912837i
$122$	1.71805	−	1.23020i	0.155545	−	0.111377i
$123$	0.00930649	+	0.0407744i	0.000839138	+	0.00367650i
$124$	0.922883	−	5.89267i	0.0828773	−	0.529177i
$125$	10.0339	+	1.04293i	0.897459	+	0.0932827i
$126$	−21.3078	−	10.2613i	−1.89825	−	0.914151i
$127$	−5.31266	−	0.926262i	−0.471422	−	0.0821925i	−0.0689410	−	0.997621i	$-0.521962\pi$
$127$	−5.31266	−	0.926262i	−0.471422	−	0.0821925i	−0.402481	+	0.915428i	$0.631852\pi$
$128$	11.4606	+	16.6035i	1.01298	+	1.46755i
$129$	−0.367844	−	0.325881i	−0.0323868	−	0.0286922i
$130$	1.98465	−	4.73350i	0.174066	−	0.415155i
$131$	−12.2913	+	2.58304i	−1.07389	+	0.225681i	−0.708886	−	0.705323i	$-0.750802\pi$
$131$	−12.2913	+	2.58304i	−1.07389	+	0.225681i	−0.365009	+	0.931004i	$0.618934\pi$
$132$	−6.81794	−	3.88421i	−0.593425	−	0.338077i
$133$	5.71846	−	4.72407i	0.495853	−	0.409629i
$134$	−7.64452	−	28.8616i	−0.660386	−	2.49326i
$135$	2.85925	+	3.85092i	0.246085	+	0.331434i
$136$	15.3307	−	13.5818i	1.31460	−	1.16463i
$137$	8.14063	+	14.8807i	0.695501	+	1.27134i	0.952384	+	0.304900i	$0.0986232\pi$
$137$	8.14063	+	14.8807i	0.695501	+	1.27134i	−0.256883	+	0.966443i	$0.582695\pi$
$138$	3.82465	+	7.60339i	0.325576	+	0.647243i
$139$	17.9071	+	12.8223i	1.51886	+	1.08758i	0.967361	+	0.253402i	$0.0815495\pi$
$139$	17.9071	+	12.8223i	1.51886	+	1.08758i	0.551502	+	0.834174i	$0.314055\pi$
$140$	6.55307	−	15.6294i	0.553835	−	1.32092i
$141$	1.92455	+	0.768137i	0.162076	+	0.0646888i
$142$	−23.1798	+	27.0926i	−1.94520	+	2.27356i
$143$	2.33200	+	5.06424i	0.195011	+	0.423493i
$144$	−2.47222	−	1.52380i	−0.206019	−	0.126983i
$145$	6.83372	−	3.58661i	0.567509	−	0.297852i
$146$	1.65959	−	0.596843i	0.137349	−	0.0493951i
$147$	−3.73422	−	6.82598i	−0.307993	−	0.562997i
$148$	−1.94464	−	1.49663i	−0.159849	−	0.123022i
$149$	12.2128	+	12.4254i	1.00051	+	1.01793i	0.999839	+	0.0179293i	$0.00570738\pi$
$149$	12.2128	+	12.4254i	1.00051	+	1.01793i	0.000668775		1.00000i	$0.499787\pi$
$150$	4.96671	−	4.10304i	0.405530	−	0.335012i
$151$	4.86619	−	16.1042i	0.396005	−	1.31054i	−0.499818	−	0.866130i	$-0.666600\pi$
$151$	4.86619	−	16.1042i	0.396005	−	1.31054i	0.895823	−	0.444411i	$-0.146587\pi$
$152$	5.18299	−	3.44701i	0.420396	−	0.279590i
$153$	5.96117	−	12.9455i	0.481932	−	1.04658i
$154$	12.1135	+	26.3061i	0.976136	+	2.11981i
$155$	1.90137	−	0.610543i	0.152722	−	0.0490400i
$156$	−1.91373	−	4.56434i	−0.153221	−	0.365440i
$157$	10.0658	+	1.75497i	0.803338	+	0.140062i	0.558503	−	0.829503i	$-0.311376\pi$
$157$	10.0658	+	1.75497i	0.803338	+	0.140062i	0.244835	+	0.969565i	$0.421266\pi$
$158$	9.76549	+	4.29412i	0.776900	+	0.341622i
$159$	−3.35529	+	1.47540i	−0.266092	+	0.117007i
$160$	−2.34120	+	4.27960i	−0.185088	+	0.338332i
$161$	3.08961	−	19.7274i	0.243496	−	1.55474i
$162$	−9.69559	−	1.34746i	−0.761757	−	0.105866i
$163$	8.90460	−	9.70832i	0.697462	−	0.760414i	−0.282571	−	0.959246i	$-0.591187\pi$
$163$	8.90460	−	9.70832i	0.697462	−	0.760414i	0.980034	+	0.198832i	$0.0637149\pi$
$164$	0.0925920	−	0.169254i	0.00723022	−	0.0132165i
$165$	0.135987	−	2.62367i	0.0105866	−	0.204252i
$166$	1.84876	+	35.6691i	0.143492	+	2.76846i
$167$	0.157688	+	9.13436i	0.0122023	+	0.706838i	0.941407	+	0.337273i	$0.109504\pi$
$167$	0.157688	+	9.13436i	0.0122023	+	0.706838i	−0.929205	+	0.369566i	$0.879507\pi$
$168$	−4.24280	−	10.1193i	−0.327339	−	0.780720i
$169$	2.11025	−	9.24559i	0.162327	−	0.711199i
$170$	14.9224	+	5.95593i	1.14450	+	0.456799i
$171$	2.33597	−	3.64742i	0.178636	−	0.278925i
$172$	0.273249	+	2.25041i	0.0208350	+	0.171592i
$173$	−5.45713	−	3.62933i	−0.414898	−	0.275933i	0.328864	−	0.944377i	$-0.393334\pi$
$173$	−5.45713	−	3.62933i	−0.414898	−	0.275933i	−0.743762	+	0.668444i	$0.766961\pi$
$174$	3.38646	−	11.2072i	0.256727	−	0.849613i
$175$	−15.0782	+	1.04274i	−1.13980	+	0.0788241i
$176$	1.14556	+	3.36675i	0.0863499	+	0.253779i
$177$	7.07872	−	2.54574i	0.532069	−	0.191349i
$178$	−12.8587	+	6.19241i	−0.963798	+	0.464141i
$179$	−4.74031	+	1.34353i	−0.354308	+	0.100420i	−0.445177	−	0.895442i	$-0.646859\pi$
$179$	−4.74031	+	1.34353i	−0.354308	+	0.100420i	0.0908700	+	0.995863i	$0.471035\pi$
$180$	0.853076	−	9.85960i	0.0635845	−	0.734891i
$181$	−9.45800	−	8.37905i	−0.703007	−	0.622810i	0.233952	−	0.972248i	$-0.424834\pi$
$181$	−9.45800	−	8.37905i	−0.703007	−	0.622810i	−0.936959	+	0.349438i	$0.886373\pi$
$182$	−4.06482	+	17.8092i	−0.301305	+	1.32010i
$183$	0.649538	−	0.208571i	0.0480152	−	0.0154180i
$184$	4.29039	−	16.1982i	0.316292	−	1.19415i
$185$	0.155065	−	0.806825i	0.0114006	−	0.0593189i
$186$	1.36132	−	2.70629i	0.0998166	−	0.198435i
$187$	−15.7244	+	7.57245i	−1.14988	+	0.553753i
$188$	−4.29541	−	8.53925i	−0.313275	−	0.622789i
$189$	−12.3788	−	11.7538i	−0.900422	−	0.854961i
$190$	4.24274	+	2.41710i	0.307801	+	0.175355i
$191$	18.9501	+	12.6030i	1.37118	+	0.911919i	0.999862	−	0.0165868i	$-0.00527999\pi$
$191$	18.9501	+	12.6030i	1.37118	+	0.911919i	0.371317	+	0.928506i	$0.378906\pi$
$192$	2.66389	+	8.81590i	0.192250	+	0.636233i
$193$	11.4178	+	9.43239i	0.821874	+	0.678958i	0.949811	−	0.312824i	$-0.101275\pi$
$193$	11.4178	+	9.43239i	0.821874	+	0.678958i	−0.127937	+	0.991782i	$0.540836\pi$
$194$	1.37972	−	11.3630i	0.0990581	−	0.815817i
$195$	1.07728	−	1.25913i	0.0771456	−	0.0901682i
$196$	−7.98657	+	34.9914i	−0.570469	+	2.49939i
$197$	8.65942	+	12.5453i	0.616958	+	0.893818i	0.999547	−	0.0301009i	$-0.00958287\pi$
$197$	8.65942	+	12.5453i	0.616958	+	0.893818i	−0.382589	+	0.923919i	$0.624967\pi$
$198$	11.4313	+	12.4631i	0.812391	+	0.885716i
$199$	16.6572	−	4.10563i	1.18080	−	0.291041i	0.400410	−	0.916336i	$-0.368868\pi$
$199$	16.6572	−	4.10563i	1.18080	−	0.291041i	0.780388	+	0.625295i	$0.215021\pi$
$200$	−12.6761	−	0.437790i	−0.896333	−	0.0309564i
$201$	0.498940	−	9.62631i	0.0351925	−	0.678987i
$202$	−36.2910	−	3.77212i	−2.55342	−	0.265405i
$203$	−21.7671	+	16.7522i	−1.52775	+	1.17578i
$204$	14.1824	−	6.23633i	0.992964	−	0.436631i
$205$	0.0645553	+	0.00222953i	0.00450874	+	0.000155717i
$206$	4.16950	−	0.433382i	0.290503	−	0.0301952i
$207$	−1.80416	−	11.5197i	−0.125398	−	0.800673i
$208$	−0.722558	+	2.12357i	−0.0501004	+	0.147243i
$209$	−5.05009	+	1.62162i	−0.349322	+	0.112170i
$210$	5.59592	−	6.54054i	0.386155	−	0.451340i
$211$	−1.71730	+	2.31291i	−0.118224	+	0.159227i	−0.858041	−	0.513581i	$-0.828319\pi$
$211$	−1.71730	+	2.31291i	−0.118224	+	0.159227i	0.739817	+	0.672808i	$0.234912\pi$
$212$	16.0983	+	5.16928i	1.10564	+	0.355027i
$213$	−9.79938	+	6.04003i	−0.671443	+	0.413856i
$214$	4.25251	+	14.0733i	0.290695	+	0.962029i
$215$	−0.631993	+	0.420314i	−0.0431015	+	0.0286652i
$216$	−9.31268	−	10.8847i	−0.633648	−	0.740611i
$217$	−6.29312	+	3.30288i	−0.427205	+	0.224214i
$218$	−5.58590	+	11.1047i	−0.378325	+	0.752107i
$219$	0.569052	−	0.0196532i	0.0384530	−	0.00132804i
$220$	−8.49512	+	8.64303i	−0.572741	+	0.582713i
$221$	−10.7729	−	2.26395i	−0.724665	−	0.152290i
$222$	−0.707998	−	1.02571i	−0.0475177	−	0.0688413i
$223$	−2.07282	−	4.94377i	−0.138806	−	0.331059i	0.837839	−	0.545917i	$-0.183819\pi$
$223$	−2.07282	−	4.94377i	−0.138806	−	0.331059i	−0.976645	+	0.214857i	$0.931071\pi$
$224$	5.59236	−	16.4357i	0.373655	−	1.09816i
$225$	−8.19704	+	3.27165i	−0.546469	+	0.218110i
$226$	0.0391068	−	2.26533i	0.00260135	−	0.150687i
$227$	0.362780	−	0.0125292i	0.0240786	−	0.000831595i	−0.0224743	−	0.999747i	$-0.507154\pi$
$227$	0.362780	−	0.0125292i	0.0240786	−	0.000831595i	0.0465529	+	0.998916i	$0.485176\pi$
$228$	4.53002	−	1.28393i	0.300008	−	0.0850305i
$229$	8.19061	+	5.86485i	0.541251	+	0.387560i	0.819614	−	0.572916i	$-0.194188\pi$
$229$	8.19061	+	5.86485i	0.541251	+	0.387560i	−0.278364	+	0.960476i	$0.589792\pi$
$230$	12.8641	−	2.70342i	0.848233	−	0.178258i
$231$	1.12702	+	9.28188i	0.0741528	+	0.610703i
$232$	−19.6221	+	12.0945i	−1.28826	+	0.794040i
$233$	10.0100	+	26.3943i	0.655780	+	1.72915i	0.683931	+	0.729546i	$0.260269\pi$
$233$	10.0100	+	26.3943i	0.655780	+	1.72915i	−0.0281514	+	0.999604i	$0.508962\pi$
$234$	0.919498	+	10.6273i	0.0601095	+	0.694727i
$235$	1.90785	−	2.56954i	0.124455	−	0.167619i
$236$	−32.2287	−	12.8633i	−2.09791	−	0.837330i
$237$	2.57795	+	2.28387i	0.167456	+	0.148353i
$238$	−55.9598	−	11.7601i	−3.62734	−	0.762293i
$239$	10.1064	−	14.6416i	0.653726	−	0.947085i	−0.346234	−	0.938148i	$-0.612540\pi$
$239$	10.1064	−	14.6416i	0.653726	−	0.947085i	0.999960	−	0.00893720i	$-0.00284484\pi$
$240$	0.766506	−	0.727807i	0.0494778	−	0.0469797i
$241$	8.45714	−	0.879043i	0.544773	−	0.0566241i	0.172955	−	0.984930i	$-0.444669\pi$
$241$	8.45714	−	0.879043i	0.544773	−	0.0566241i	0.371818	+	0.928306i	$0.378735\pi$
$242$	0.262031	+	5.05550i	0.0168440	+	0.324980i
$243$	−13.9445	−	6.71531i	−0.894539	−	0.430787i
$244$	−2.88073	−	1.26673i	−0.184420	−	0.0810939i
$245$	−11.6677	+	2.87582i	−0.745420	+	0.183730i
$246$	0.0710581	−	0.0674705i	0.00453050	−	0.00430176i
$247$	−3.14812	−	1.13217i	−0.200310	−	0.0720380i
$248$	−5.53936	+	2.21090i	−0.351750	+	0.140392i
$249$	−2.95243	+	11.1468i	−0.187102	+	0.706398i
$250$	−9.88581	−	21.4683i	−0.625234	−	1.35778i
$251$	0.782165	−	6.44171i	0.0493698	−	0.406597i	−0.946984	−	0.321280i	$-0.895887\pi$
$251$	0.782165	−	6.44171i	0.0493698	−	0.406597i	0.996354	−	0.0853165i	$-0.0271901\pi$
$252$	3.03606	+	35.0899i	0.191254	+	2.21046i
$253$	−7.28118	+	12.2828i	−0.457764	+	0.772210i
$254$	4.48037	+	11.8138i	0.281124	+	0.741262i
$255$	3.99911	+	3.30371i	0.250434	+	0.206886i
$256$	9.58524	−	20.8156i	0.599078	−	1.30098i
$257$	21.9706	+	13.5420i	1.37049	+	0.844726i	0.996572	−	0.0827359i	$-0.0263658\pi$
$257$	21.9706	+	13.5420i	1.37049	+	0.844726i	0.373918	+	0.927462i	$0.378014\pi$
$258$	−0.217309	+	1.13069i	−0.0135291	+	0.0703937i
$259$	−0.0504703	+	2.92357i	−0.00313607	+	0.181662i
$260$	−7.57122	+	1.05222i	−0.469547	+	0.0652560i
$261$	−9.11133	+	13.2000i	−0.563977	+	0.817062i
$262$	19.8906	+	21.6859i	1.22884	+	1.33976i
$263$	0.0529852	+	0.00923798i	0.00326721	+	0.000569638i	0.173392	−	0.984853i	$-0.444527\pi$
$263$	0.0529852	+	0.00923798i	0.00326721	+	0.000569638i	−0.170125	+	0.985422i	$0.554417\pi$
$264$	0.135435	+	7.84528i	0.00833543	+	0.482843i
$265$	0.875918	+	5.59280i	0.0538072	+	0.343563i
$266$	−16.3529	−	5.88102i	−1.00266	−	0.360589i
$267$	−4.56384	+	0.634266i	−0.279302	+	0.0388165i
$268$	−31.1688	+	31.7115i	−1.90394	+	1.93709i
$269$	−2.36171	+	27.2959i	−0.143996	+	1.66426i	0.475843	+	0.879530i	$0.342143\pi$
$269$	−2.36171	+	27.2959i	−0.143996	+	1.66426i	−0.619838	+	0.784729i	$0.712802\pi$
$270$	4.34512	−	10.3633i	0.264436	−	0.630692i
$271$	−10.9513	+	17.0995i	−0.665245	+	1.03872i	0.330248	+	0.943894i	$0.392868\pi$
$271$	−10.9513	+	17.0995i	−0.665245	+	1.03872i	−0.995494	+	0.0948283i	$0.969770\pi$
$272$	−6.68552	−	2.14677i	−0.405369	−	0.130167i
$273$	−3.00733	+	5.07313i	−0.182012	+	0.307040i
$274$	20.2647	−	34.1850i	1.22424	−	2.06519i
$275$	10.2904	+	3.30432i	0.620535	+	0.199258i
$276$	6.83607	−	10.6739i	0.411483	−	0.642494i
$277$	−6.25755	+	14.9246i	−0.375980	+	0.896731i	0.617899	+	0.786257i	$0.287984\pi$
$277$	−6.25755	+	14.9246i	−0.375980	+	0.896731i	−0.993879	+	0.110474i	$0.964763\pi$
$278$	4.44805	−	51.4092i	0.266776	−	3.08332i
$279$	−2.90920	+	2.95986i	−0.174169	+	0.177202i
$280$	−16.7856	+	2.33281i	−1.00313	+	0.139412i
$281$	25.7298	+	9.25327i	1.53491	+	0.552004i	0.963278	−	0.268505i	$-0.0865295\pi$
$281$	25.7298	+	9.25327i	1.53491	+	0.552004i	0.571634	+	0.820509i	$0.306310\pi$
$282$	−0.751197	−	4.79644i	−0.0447331	−	0.285624i
$283$	−0.525354	−	30.4320i	−0.0312291	−	1.80900i	−0.441743	−	0.897141i	$-0.645640\pi$
$283$	−0.525354	−	30.4320i	−0.0312291	−	1.80900i	0.410514	−	0.911854i	$-0.365349\pi$
$284$	52.3113	+	9.12048i	3.10411	+	0.541201i
$285$	1.06559	+	1.16177i	0.0631202	+	0.0688174i
$286$	7.42038	−	10.7503i	0.438776	−	0.635677i
$287$	−0.227698	+	0.0316447i	−0.0134406	+	0.00186793i
$288$	0.174987	−	10.1364i	0.0103112	−	0.597292i
$289$	3.29525	−	17.1456i	0.193838	−	1.00857i
$290$	−15.3929	−	9.48767i	−0.903900	−	0.557135i
$291$	1.54570	−	3.35669i	0.0906104	−	0.196772i
$292$	−2.02494	−	1.67283i	−0.118501	−	0.0978947i
$293$	8.38720	+	22.1152i	0.489985	+	1.29199i	0.920973	+	0.389627i	$0.127396\pi$
$293$	8.38720	+	22.1152i	0.489985	+	1.29199i	−0.430987	+	0.902358i	$0.641835\pi$
$294$	−9.29572	+	15.6811i	−0.542137	+	0.914541i
$295$	−1.00150	−	11.5750i	−0.0583096	−	0.673925i
$296$	−0.295772	+	2.43590i	−0.0171914	+	0.141584i
$297$	5.10558	+	11.0874i	0.296256	+	0.643358i
$298$	10.4513	−	39.4585i	0.605428	−	2.28577i
$299$	−8.36460	+	3.33853i	−0.483738	+	0.193072i
$300$	−9.02820	−	3.24683i	−0.521243	−	0.187456i
$301$	1.95888	−	1.85998i	0.112908	−	0.107207i
$302$	−38.2702	+	9.43275i	−2.20220	+	0.542794i
$303$	−10.7831	−	4.74161i	−0.619475	−	0.272398i
$304$	−1.92264	−	0.925897i	−0.110271	−	0.0531038i
$305$	−0.0545375	−	1.05222i	−0.00312281	−	0.0602500i
$306$	−33.2122	+	3.45211i	−1.89862	+	0.197344i
$307$	−2.33078	+	2.21310i	−0.133024	+	0.126308i	−0.752173	−	0.658966i	$-0.770994\pi$
$307$	−2.33078	+	2.21310i	−0.133024	+	0.126308i	0.619149	+	0.785274i	$0.287478\pi$
$308$	24.5011	−	35.4960i	1.39608	−	2.02257i
$309$	1.32444	+	0.278334i	0.0753446	+	0.0158338i
$310$	−3.50210	−	3.10259i	−0.198906	−	0.176215i
$311$	−27.2601	−	10.8802i	−1.54578	−	0.616960i	−0.567335	−	0.823487i	$-0.692026\pi$
$311$	−27.2601	−	10.8802i	−1.54578	−	0.616960i	−0.978441	+	0.206527i	$0.933784\pi$
$312$	−2.95033	+	3.97358i	−0.167029	+	0.224959i
$313$	1.90894	+	22.0630i	0.107900	+	1.24707i	0.830977	+	0.556307i	$0.187782\pi$
$313$	1.90894	+	22.0630i	0.107900	+	1.24707i	−0.723077	+	0.690768i	$0.757273\pi$
$314$	−8.48888	−	22.3833i	−0.479055	−	1.26316i
$315$	−10.0387	+	6.18754i	−0.565618	+	0.348629i
$316$	−1.91501	−	15.7715i	−0.107728	−	0.887217i
$317$	17.4399	−	3.66503i	0.979522	−	0.205849i	0.311709	−	0.950178i	$-0.399099\pi$
$317$	17.4399	−	3.66503i	0.979522	−	0.205849i	0.667813	+	0.744329i	$0.267231\pi$
$318$	6.98217	+	4.99956i	0.391541	+	0.280361i
$319$	18.8970	−	5.35591i	1.05803	−	0.299874i
$320$	14.2153	−	0.490951i	0.794661	−	0.0274450i
$321$	−0.0819263	+	4.74572i	−0.00457268	+	0.264880i
$322$	−43.4499	+	17.3420i	−2.42137	+	0.966431i
$323$	3.37343	−	9.91436i	0.187702	−	0.551650i
$324$	5.63686	+	13.4442i	0.313159	+	0.746899i
$325$	3.87253	+	5.61032i	0.214809	+	0.311205i
$326$	−30.2047	−	6.34759i	−1.67288	−	0.351560i
$327$	−2.81314	+	2.86212i	−0.155567	+	0.158276i
$328$	−0.192803	+	0.00665878i	−0.0106458	+	0.000367670i
$329$	−5.11835	+	10.1752i	−0.282184	+	0.560979i
$330$	−5.45021	+	2.86049i	−0.300024	+	0.157465i
$331$	0.496193	+	0.579953i	0.0272732	+	0.0318771i	0.773315	−	0.634023i	$-0.218597\pi$
$331$	0.496193	+	0.579953i	0.0272732	+	0.0318771i	−0.746041	+	0.665900i	$0.768048\pi$
$332$	44.2912	−	29.4564i	2.43080	−	1.61663i
$333$	0.493885	+	1.63447i	0.0270647	+	0.0895682i
$334$	18.2210	−	11.2309i	0.997010	−	0.614525i
$335$	−14.1745	−	4.55154i	−0.774437	−	0.248677i
$336$	−2.24253	+	3.02029i	−0.122340	+	0.164771i
$337$	−11.7416	+	13.7236i	−0.639604	+	0.747573i	−0.981352	−	0.192219i	$-0.938432\pi$
$337$	−11.7416	+	13.7236i	−0.639604	+	0.747573i	0.341748	+	0.939792i	$0.388981\pi$
$338$	−21.1547	+	6.79294i	−1.15067	+	0.369487i
$339$	0.235620	−	0.692477i	0.0127971	−	0.0376102i
$340$	−3.70239	−	23.6400i	−0.200790	−	1.28206i
$341$	5.05502	−	0.525423i	0.273745	−	0.0284533i
$342$	−10.1419	−	0.350267i	−0.548409	−	0.0189402i
$343$	12.5079	−	5.50002i	0.675362	−	0.296973i
$344$	1.79643	−	1.38256i	0.0968568	−	0.0745424i
$345$	4.22112	+	0.438747i	0.227258	+	0.0236214i
$346$	−0.794792	+	15.3344i	−0.0427283	+	0.824380i
$347$	−6.64896	−	0.229633i	−0.356935	−	0.0123274i	−0.144506	−	0.989504i	$-0.546159\pi$
$347$	−6.64896	−	0.229633i	−0.356935	−	0.0123274i	−0.212429	+	0.977177i	$0.568137\pi$
$348$	−16.9291	+	4.17265i	−0.907496	+	0.223678i
$349$	−9.13647	−	9.96111i	−0.489064	−	0.533206i	0.442507	−	0.896765i	$-0.354089\pi$
$349$	−9.13647	−	9.96111i	−0.489064	−	0.533206i	−0.931571	+	0.363559i	$0.881562\pi$
$350$	20.1158	+	29.1428i	1.07523	+	1.55775i
$351$	−1.71323	+	7.50616i	−0.0914455	+	0.400649i
$352$	−8.07081	+	9.43320i	−0.430176	+	0.502792i
$353$	1.44737	−	11.9202i	0.0770357	−	0.634446i	−0.902142	−	0.431440i	$-0.858006\pi$
$353$	1.44737	−	11.9202i	0.0770357	−	0.634446i	0.979177	−	0.203006i	$-0.0650712\pi$
$354$	−13.5878	−	11.2250i	−0.722184	−	0.596603i
$355$	5.14253	+	17.0187i	0.272937	+	0.903259i
$356$	17.6982	+	11.7704i	0.938003	+	0.623830i
$357$	−16.0407	−	9.13843i	−0.848963	−	0.483657i
$358$	8.37112	+	7.94848i	0.442428	+	0.420090i
$359$	7.91595	+	15.7369i	0.417788	+	0.830560i	0.999848	+	0.0174143i	$0.00554341\pi$
$359$	7.91595	+	15.7369i	0.417788	+	0.830560i	−0.582060	+	0.813146i	$0.697753\pi$
$360$	−8.91604	+	4.29374i	−0.469917	+	0.226300i
$361$	−7.10782	+	14.1303i	−0.374096	+	0.743700i
$362$	−5.58746	+	29.0723i	−0.293670	+	1.52801i
$363$	−0.418457	+	1.57987i	−0.0219633	+	0.0829217i
$364$	25.9020	−	8.31732i	1.35763	−	0.435946i
$365$	0.195685	−	0.857352i	0.0102426	−	0.0448759i
$366$	−1.19637	−	1.05989i	−0.0625354	−	0.0554016i
$367$	1.92049	−	22.1965i	0.100249	−	1.15865i	−0.760403	−	0.649452i	$-0.774998\pi$
$367$	1.92049	−	22.1965i	0.100249	−	1.15865i	0.860652	−	0.509194i	$-0.170056\pi$
$368$	−5.52703	+	1.56651i	−0.288116	+	0.0816600i
$369$	−0.120947	+	0.0582449i	−0.00629624	+	0.00303211i
$370$	−1.81134	+	0.651415i	−0.0941668	+	0.0338654i
$371$	−6.48982	−	19.0733i	−0.336935	−	0.990237i
$372$	−4.50081	+	0.311258i	−0.233356	+	0.0161380i
$373$	6.52633	−	21.5983i	0.337921	−	1.11832i	−0.608005	−	0.793933i	$-0.708030\pi$
$373$	6.52633	−	21.5983i	0.337921	−	1.11832i	0.945926	−	0.324384i	$-0.105157\pi$
$374$	34.0478	+	22.6439i	1.76057	+	1.17089i
$375$	−0.919761	−	7.57492i	−0.0474963	−	0.391167i
$376$	−5.15502	+	8.04912i	−0.265850	+	0.415102i
$377$	11.5061	+	4.59237i	0.592592	+	0.236519i
$378$	−8.89936	+	38.9907i	−0.457734	+	2.00546i
$379$	−1.52363	−	3.63393i	−0.0782636	−	0.186663i	0.878353	−	0.478013i	$-0.158643\pi$
$379$	−1.52363	−	3.63393i	−0.0782636	−	0.186663i	−0.956616	+	0.291350i	$0.905896\pi$
$380$	−0.125520	−	7.27093i	−0.00643902	−	0.372991i
$381$	0.211141	+	4.07366i	0.0108171	+	0.208700i
$382$	2.75994	−	53.2491i	0.141211	−	2.72446i
$383$	−17.8277	+	32.5882i	−0.910954	+	1.66518i	−0.178974	+	0.983854i	$0.557278\pi$
$383$	−17.8277	+	32.5882i	−0.910954	+	1.66518i	−0.731980	+	0.681326i	$0.761403\pi$
$384$	10.3151	−	11.2461i	0.526388	−	0.573899i
$385$	14.3033	+	1.98782i	0.728963	+	0.101309i
$386$	5.36888	−	34.2806i	0.273269	−	1.74484i
$387$	0.757041	−	1.38384i	0.0384826	−	0.0703443i
$388$	−15.6048	+	6.86182i	−0.792215	+	0.348356i
$389$	4.64771	+	2.04371i	0.235648	+	0.103620i	0.517003	−	0.855984i	$-0.327048\pi$
$389$	4.64771	+	2.04371i	0.235648	+	0.103620i	−0.281355	+	0.959604i	$0.590784\pi$
$390$	−3.82471	−	0.666838i	−0.193672	−	0.0337666i
$391$	−10.9011	−	25.9997i	−0.551293	−	1.31486i
$392$	34.1715	−	10.9727i	1.72592	−	0.554205i
$393$	3.97365	+	8.62930i	0.200444	+	0.435290i
$394$	14.9383	−	32.4404i	0.752579	−	1.63432i
$395$	4.42919	−	2.94569i	0.222857	−	0.148214i
$396$	7.28510	−	24.1094i	0.366090	−	1.21154i
$397$	4.14852	−	3.42713i	0.208208	−	0.172003i	−0.526954	−	0.849894i	$-0.676666\pi$
$397$	4.14852	−	3.42713i	0.208208	−	0.172003i	0.735163	+	0.677891i	$0.237106\pi$
$398$	−28.1753	−	28.6659i	−1.41230	−	1.43689i
$399$	−4.44621	−	3.42187i	−0.222589	−	0.171308i
$400$	2.08693	+	3.81481i	0.104346	+	0.190740i
$401$	25.7474	−	9.25958i	1.28576	−	0.462401i	0.395758	−	0.918355i	$-0.370482\pi$
$401$	25.7474	−	9.25958i	1.28576	−	0.462401i	0.890004	+	0.455953i	$0.150702\pi$
$402$	−19.9970	+	10.4952i	−0.997358	+	0.523454i
$403$	2.72889	+	1.68200i	0.135936	+	0.0837863i
$404$	22.7279	+	49.3566i	1.13075	+	2.45558i
$405$	−3.17311	+	3.70875i	−0.157673	+	0.184289i
$406$	59.7681	+	23.8550i	2.96624	+	1.18391i
$407$	0.808486	−	1.92828i	0.0400752	−	0.0955813i
$408$	−12.5962	−	9.01942i	−0.623603	−	0.446528i
$409$	−11.9517	−	23.7598i	−0.590972	−	1.17485i	−0.968538	−	0.248866i	$-0.919942\pi$
$409$	−11.9517	−	23.7598i	−0.590972	−	1.17485i	0.377566	−	0.925983i	$-0.376761\pi$
$410$	−0.0726324	−	0.132769i	−0.00358706	−	0.00655697i
$411$	9.60339	−	8.50786i	0.473700	−	0.419662i
$412$	−3.72163	−	5.01238i	−0.183351	−	0.246942i
$413$	10.5870	+	39.9707i	0.520951	+	1.96683i
$414$	−21.0613	+	17.3990i	−1.03511	+	0.855112i
$415$	15.4743	+	8.81580i	0.759606	+	0.432750i
$416$	−7.66310	+	1.61042i	−0.375714	+	0.0789572i
$417$	6.44162	−	15.3636i	0.315448	−	0.752358i
$418$	9.30167	+	8.24056i	0.454960	+	0.403059i
$419$	−4.22784	−	6.12508i	−0.206543	−	0.299230i	0.705998	−	0.708214i	$-0.250499\pi$
$419$	−4.22784	−	6.12508i	−0.206543	−	0.299230i	−0.912542	+	0.408984i	$0.865883\pi$
$420$	−12.6287	−	2.20181i	−0.616217	−	0.107437i
$421$	5.99466	+	2.88687i	0.292162	+	0.140698i	0.574223	−	0.818699i	$-0.305304\pi$
$421$	5.99466	+	2.88687i	0.292162	+	0.140698i	−0.282062	+	0.959396i	$0.591018\pi$
$422$	6.71314	+	0.697770i	0.326791	+	0.0339669i
$423$	−1.02913	+	6.57104i	−0.0500379	+	0.319495i
$424$	−3.76222	−	16.4833i	−0.182709	−	0.800502i
$425$	−17.3503	+	12.4236i	−0.841613	+	0.602634i
$426$	23.8806	+	12.5335i	1.15702	+	0.607251i
$427$	0.834418	+	3.65582i	0.0403803	+	0.176918i
$428$	14.7996	−	16.1354i	0.715367	−	0.779935i
$429$	3.34205	−	2.57209i	0.161356	−	0.124182i
$430$	1.60216	+	0.771559i	0.0772630	+	0.0372079i
$431$	−0.458435	−	26.5556i	−0.0220821	−	1.27914i	−0.779580	−	0.626302i	$-0.784568\pi$
$431$	−0.458435	−	26.5556i	−0.0220821	−	1.27914i	0.757498	−	0.652837i	$-0.226421\pi$
$432$	−1.58194	+	4.64926i	−0.0761111	+	0.223687i
$433$	0.174118	−	0.657376i	0.00836757	−	0.0315915i	−0.962354	−	0.271801i	$-0.912381\pi$
$433$	0.174118	−	0.657376i	0.00836757	−	0.0315915i	0.970721	+	0.240209i	$0.0772160\pi$
$434$	14.1752	+	8.73713i	0.680430	+	0.419396i
$435$	−3.79512	−	4.43576i	−0.181962	−	0.212678i
$436$	18.4682	−	1.27719i	0.884466	−	0.0611661i
$437$	−2.19374	−	8.28238i	−0.104941	−	0.396200i
$438$	−0.719469	−	1.12339i	−0.0343776	−	0.0536776i
$439$	4.62321	−	0.806058i	0.220654	−	0.0384710i	−0.0603516	−	0.998177i	$-0.519222\pi$
$439$	4.62321	−	0.806058i	0.220654	−	0.0384710i	0.281006	+	0.959706i	$0.409332\pi$
$440$	11.7664	+	2.90015i	0.560939	+	0.138259i
$441$	18.6932	−	16.5607i	0.890151	−	0.788605i
$442$	8.30790	+	24.4166i	0.395166	+	1.16138i
$443$	23.1989	+	27.1150i	1.10221	+	1.28827i	0.954161	+	0.299293i	$0.0967508\pi$
$443$	23.1989	+	27.1150i	1.10221	+	1.28827i	0.148052	+	0.988980i	$0.452700\pi$
$444$	−0.776356	+	1.68596i	−0.0368442	+	0.0800121i
$445$	−0.857787	+	7.06451i	−0.0406630	+	0.334890i
$446$	−7.48724	+	10.0840i	−0.354531	+	0.477491i
$447$	7.10737	−	11.0975i	0.336167	−	0.524896i
$448$	−49.5398	+	10.4109i	−2.34054	+	0.491869i
$449$	20.8337	+	19.7818i	0.983202	+	0.933562i	0.997798	−	0.0663319i	$-0.0211296\pi$
$449$	20.8337	+	19.7818i	0.983202	+	0.933562i	−0.0145956	+	0.999893i	$0.504646\pi$
$450$	16.3869	+	12.6116i	0.772486	+	0.594517i
$451$	0.159612	+	0.0393407i	0.00751582	+	0.00185248i
$452$	−2.93178	+	1.67025i	−0.137899	+	0.0785618i
$453$	−12.6949	−	0.877928i	−0.596459	−	0.0412486i
$454$	−0.458674	−	0.716179i	−0.0215266	−	0.0336120i
$455$	6.38482	+	6.49600i	0.299325	+	0.304537i
$456$	−3.41433	−	3.24195i	−0.159891	−	0.151818i
$457$	−16.8554	−	12.0693i	−0.788463	−	0.564576i	0.114938	−	0.993373i	$-0.463333\pi$
$457$	−16.8554	−	12.0693i	−0.788463	−	0.564576i	−0.903401	+	0.428797i	$0.858938\pi$
$458$	2.03451	−	23.5142i	0.0950664	−	1.09875i
$459$	−23.5858	−	4.95661i	−1.10089	−	0.231355i
$460$	−13.2326	−	14.4270i	−0.616974	−	0.672662i
$461$	−24.5651	−	10.8019i	−1.14411	−	0.503093i	−0.257806	−	0.966197i	$-0.583000\pi$
$461$	−24.5651	−	10.8019i	−1.14411	−	0.503093i	−0.886304	+	0.463104i	$0.846736\pi$
$462$	17.3602	−	13.3607i	0.807671	−	0.621596i
$463$	5.66410	+	0.787176i	0.263233	+	0.0365832i	0.268049	−	0.963405i	$-0.413621\pi$
$463$	5.66410	+	0.787176i	0.263233	+	0.0365832i	−0.00481634	+	0.999988i	$0.501533\pi$
$464$	6.99711	+	3.67236i	0.324833	+	0.170485i
$465$	−0.770268	−	1.29938i	−0.0357203	−	0.0602572i
$466$	41.2359	−	51.7082i	1.91022	−	2.39534i
$467$	−16.8815	−	28.4777i	−0.781184	−	1.31779i	−0.943606	−	0.331071i	$-0.892590\pi$
$467$	−16.8815	−	28.4777i	−0.781184	−	1.31779i	0.162422	−	0.986721i	$-0.448069\pi$
$468$	12.9162	−	9.24858i	0.597051	−	0.427516i
$469$	52.4792	+	7.29338i	2.42326	+	0.336777i
$470$	−7.45802	−	0.775194i	−0.344013	−	0.0357570i
$471$	−0.400045	−	7.71829i	−0.0184331	−	0.355640i
$472$	5.36904	+	34.2817i	0.247130	+	1.57794i
$473$	−1.79400	+	0.716034i	−0.0824883	+	0.0329233i
$474$	1.52297	−	7.92421i	0.0699522	−	0.363971i
$475$	−5.74247	+	3.01388i	−0.263482	+	0.138286i
$476$	27.4316	+	80.6204i	1.25733	+	3.69523i
$477$	−7.01339	−	9.44580i	−0.321121	−	0.432494i
$478$	−41.5830	−	2.87571i	−1.90196	−	0.131532i
$479$	−4.87495	−	25.3650i	−0.222742	−	1.15896i	−0.904203	−	0.427103i	$-0.859534\pi$
$479$	−4.87495	−	25.3650i	−0.222742	−	1.15896i	0.681461	−	0.731855i	$-0.261345\pi$
$480$	3.55000	+	1.00617i	0.162035	+	0.0459250i
$481$	1.14592	−	0.652835i	0.0522495	−	0.0297667i
$482$	−11.8756	−	15.9943i	−0.540918	−	0.728522i
$483$	−15.0678	+	1.04202i	−0.685607	+	0.0474138i
$484$	6.27754	−	4.17496i	0.285343	−	0.189771i
$485$	−4.40021	−	3.63506i	−0.199803	−	0.165060i
$486$	3.12577	+	36.1267i	0.141788	+	1.63874i
$487$	−27.4598	−	8.81754i	−1.24432	−	0.399561i	−0.390731	−	0.920505i	$-0.627778\pi$
$487$	−27.4598	−	8.81754i	−1.24432	−	0.399561i	−0.853591	+	0.520944i	$0.825580\pi$
$488$	0.379307	+	3.12387i	0.0171704	+	0.141411i
$489$	−8.65806	−	4.93253i	−0.391531	−	0.223057i
$490$	19.7356	+	20.0792i	0.891563	+	0.907087i
$491$	−23.2561	+	4.05471i	−1.04953	+	0.182986i	−0.670129	−	0.742244i	$-0.733761\pi$
$491$	−23.2561	+	4.05471i	−1.04953	+	0.182986i	−0.379405	+	0.925231i	$0.623871\pi$
$492$	−0.140399	−	0.0397929i	−0.00632967	−	0.00179400i
$493$	−13.7518	+	36.2605i	−0.619350	+	1.63309i
$494$	1.47937	+	7.69735i	0.0665599	+	0.346320i
$495$	8.30727	−	1.44837i	0.373384	−	0.0650995i
$496$	1.62041	+	1.24709i	0.0727584	+	0.0559959i
$497$	−28.4333	−	56.5253i	−1.27541	−	2.53550i
$498$	25.9926	−	7.36700i	1.16476	−	0.330123i
$499$	−16.0326	+	16.3118i	−0.717719	+	0.730216i	−0.971498	−	0.237046i	$-0.923821\pi$
$499$	−16.0326	+	16.3118i	−0.717719	+	0.730216i	0.253780	+	0.967262i	$0.418326\pi$
$500$	−19.9953	+	28.9682i	−0.894217	+	1.29550i
$501$	6.70949	−	1.65374i	0.299758	−	0.0738836i
$502$	−13.9171	+	6.11969i	−0.621150	+	0.273135i
$503$	24.4841	−	26.6940i	1.09169	−	1.19023i	0.111174	−	0.993801i	$-0.464539\pi$
$503$	24.4841	−	26.6940i	1.09169	−	1.19023i	0.980519	−	0.196426i	$-0.0629337\pi$
$504$	28.6356	−	20.5044i	1.27553	−	0.913338i
$505$	−11.3432	+	14.2239i	−0.504766	+	0.632956i
$506$	33.4537			1.48720
$507$	−7.17324			−0.318575
$508$	11.7320	−	14.7114i	0.520522	−	0.652714i
$509$	9.98964	+	5.24297i	0.442783	+	0.232390i	0.671354	−	0.741137i	$-0.265713\pi$
$509$	9.98964	+	5.24297i	0.442783	+	0.232390i	−0.228571	+	0.973527i	$0.573405\pi$
$510$	1.88046	−	12.0068i	0.0832680	−	0.531672i
$511$	−0.162000	+	3.12556i	−0.00716647	+	0.138266i
$512$	−13.2703	+	1.37933i	−0.586469	+	0.0609582i
$513$	−6.89237	−	2.47872i	−0.304306	−	0.109438i
$514$	1.04371	−	60.4586i	0.0460360	−	2.66671i
$515$	0.939282	−	1.86729i	0.0413897	−	0.0822825i
$516$	1.61354	−	0.580282i	0.0710323	−	0.0255455i
$517$	6.09650	−	5.40103i	0.268124	−	0.237537i
$518$	5.95247	−	3.39114i	0.261537	−	0.148998i
$519$	−1.75789	+	4.63517i	−0.0771627	+	0.203461i
$520$	4.76577	+	5.97608i	0.208993	+	0.262069i
$521$	−1.44092	+	3.79940i	−0.0631280	+	0.166455i	−0.962869	−	0.269970i	$-0.912986\pi$
$521$	−1.44092	+	3.79940i	−0.0631280	+	0.166455i	0.899741	+	0.436425i	$0.143755\pi$
$522$	37.4889	+	2.59258i	1.64084	+	0.113474i
$523$	−7.25399	−	27.3872i	−0.317195	−	1.19756i	−0.917483	−	0.397774i	$-0.869783\pi$
$523$	−7.25399	−	27.3872i	−0.317195	−	1.19756i	0.600289	−	0.799783i	$-0.295052\pi$
$524$	12.6761	−	41.9503i	0.553758	−	1.83261i
$525$	3.30685	+	10.9437i	0.144323	+	0.477622i
$526$	−0.0446845	−	0.117823i	−0.00194834	−	0.00513734i
$527$	−5.11698	+	8.63192i	−0.222899	+	0.376013i
$528$	2.28996	−	1.41146i	0.0996576	−	0.0614257i
$529$	−0.0543874	−	0.0361710i	−0.00236467	−	0.00157265i
$530$	10.2252	−	8.44718i	0.444156	−	0.366922i
$531$	13.0222	+	20.3329i	0.565113	+	0.882375i
$532$	4.88468	+	25.4157i	0.211778	+	1.10191i
$533$	0.0646480	+	0.0810661i	0.00280022	+	0.00351136i
$534$	6.73083	+	8.44019i	0.291271	+	0.365243i
$535$	7.05284	+	1.99897i	0.304921	+	0.0864228i
$536$	43.1711	+	10.6407i	1.86471	+	0.459609i
$537$	1.78864	+	3.26955i	0.0771855	+	0.141091i
$538$	57.8338	−	27.8513i	2.49339	−	1.20075i
$539$	−30.5642	+	1.05559i	−1.31649	+	0.0454673i
$540$	−16.5761	+	2.30369i	−0.713323	+	0.0991351i
$541$	−9.83831	+	9.34159i	−0.422982	+	0.401626i	−0.870121	−	0.492838i	$-0.835959\pi$
$541$	−9.83831	+	9.34159i	−0.422982	+	0.401626i	0.447139	+	0.894465i	$0.352443\pi$
$542$	47.5462	+	1.64209i	2.04229	+	0.0705338i
$543$	−4.58711	+	8.38501i	−0.196852	+	0.359835i
$544$	−5.45443	−	23.8974i	−0.233857	−	1.02459i
$545$	3.16064	+	5.33174i	0.135387	+	0.228387i
$546$	13.8173			0.591327
$547$	14.2868	+	18.5172i	0.610861	+	0.791738i
$547$	14.2868	+	18.5172i	0.610861	+	0.791738i
$548$	−59.1835			−2.52819
$549$	1.11660	+	1.88361i	0.0476552	+	0.0803904i
$550$	−5.63466	−	24.6871i	−0.240263	−	1.05266i
$551$	−5.65646	+	10.3397i	−0.240973	+	0.440488i
$552$	−12.6673	−	0.437487i	−0.539157	−	0.0186207i
$553$	−13.7284	+	13.0353i	−0.583791	+	0.554316i
$554$	37.5551	−	5.21927i	1.59556	−	0.221746i
$555$	−0.621083	+	0.0214502i	−0.0263635	+	0.000910509i
$556$	−69.2377	+	33.3431i	−2.93633	+	1.41406i
$557$	−7.37246	−	13.4765i	−0.312381	−	0.571018i	0.673354	−	0.739320i	$-0.264853\pi$
$557$	−7.37246	−	13.4765i	−0.312381	−	0.571018i	−0.985735	+	0.168302i	$0.946172\pi$
$558$	9.44100	+	2.32700i	0.399669	+	0.0985096i
$559$	−1.17219	−	0.332230i	−0.0495783	−	0.0140518i
$560$	3.62243	+	4.54239i	0.153076	+	0.191951i
$561$	8.23087	+	10.3212i	0.347507	+	0.435761i
$562$	−12.0910	−	62.9110i	−0.510027	−	2.65374i
$563$	2.27184	+	3.54727i	0.0957465	+	0.149500i	0.886650	−	0.462441i	$-0.153026\pi$
$563$	2.27184	+	3.54727i	0.0957465	+	0.149500i	−0.790903	+	0.611941i	$0.790389\pi$
$564$	−5.57419	+	4.60489i	−0.234716	+	0.193901i
$565$	−0.940677	−	0.625608i	−0.0395746	−	0.0263195i
$566$	−60.7051	+	37.4167i	−2.55162	+	1.57274i
$567$	8.85805	−	14.9428i	0.372003	−	0.627539i
$568$	−18.8290	−	49.6479i	−0.790046	−	2.08318i
$569$	−3.28464	−	10.8702i	−0.137699	−	0.455702i	0.860891	−	0.508790i	$-0.169907\pi$
$569$	−3.28464	−	10.8702i	−0.137699	−	0.455702i	−0.998590	+	0.0530875i	$0.983094\pi$
$570$	1.06835	−	3.53559i	0.0447481	−	0.148090i
$571$	10.0329	+	37.8787i	0.419862	+	1.58517i	0.763329	+	0.646009i	$0.223563\pi$
$571$	10.0329	+	37.8787i	0.419862	+	1.58517i	−0.343468	+	0.939165i	$0.611602\pi$
$572$	−19.4073	−	1.34213i	−0.811458	−	0.0561171i
$573$	6.10432	−	16.0958i	0.255012	−	0.672411i
$574$	0.335814	+	0.421097i	0.0140166	+	0.0175762i
$575$	−6.19095	+	16.3242i	−0.258180	+	0.680765i
$576$	−25.6846	+	14.6326i	−1.07019	+	0.609693i
$577$	16.5204	−	14.6358i	0.687755	−	0.609298i	−0.245122	−	0.969492i	$-0.578828\pi$
$577$	16.5204	−	14.6358i	0.687755	−	0.609298i	0.932877	+	0.360194i	$0.117290\pi$
$578$	−38.4922	+	13.8430i	−1.60107	+	0.575795i
$579$	5.03400	−	10.0076i	0.209206	−	0.415900i
$580$	−0.464808	+	26.9248i	−0.0193001	+	1.11799i
$581$	−59.6431	−	21.4496i	−2.47441	−	0.889879i
$582$	−8.61175	+	0.895113i	−0.356969	+	0.0371036i
$583$	−0.745722	+	14.3876i	−0.0308847	+	0.595874i
$584$	−0.406388	+	2.59482i	−0.0168165	+	0.107374i
$585$	4.70958	+	2.47178i	0.194717	+	0.102196i
$586$	34.5507	−	43.3252i	1.42728	−	1.78975i
$587$	25.8798			1.06817			0.534086	−	0.845430i	$-0.320656\pi$
$587$	25.8798			1.06817			0.534086	+	0.845430i	$0.320656\pi$
$588$	27.1483			1.11958
$589$	−1.90141	+	2.38429i	−0.0783461	+	0.0982429i
$590$	−22.1318	+	15.8474i	−0.911154	+	0.652428i
$591$	7.79389	−	8.49735i	0.320598	−	0.349534i
$592$	0.770073	−	0.338620i	0.0316498	−	0.0139172i
$593$	7.62273	−	1.87883i	0.313028	−	0.0771545i	−0.0796719	−	0.996821i	$-0.525387\pi$
$593$	7.62273	−	1.87883i	0.313028	−	0.0771545i	0.392700	+	0.919667i	$0.371541\pi$
$594$	16.2459	−	23.5362i	0.666577	−	0.965703i
$595$	−19.9866	+	20.3346i	−0.819371	+	0.833638i
$596$	−58.4868	+	16.5768i	−2.39571	+	0.679011i
$597$	−5.83132	−	11.5926i	−0.238660	−	0.474454i
$598$	16.7219	+	12.8694i	0.683809	+	0.526269i
$599$	−31.6873	+	5.52469i	−1.29471	+	0.225733i	−0.776824	−	0.629718i	$-0.783171\pi$
$599$	−31.6873	+	5.52469i	−1.29471	+	0.225733i	−0.517885	+	0.855450i	$0.673281\pi$
$600$	1.81073	+	9.42150i	0.0739229	+	0.384631i
$601$	−10.3423	+	27.2703i	−0.421869	+	1.11238i	0.540670	+	0.841235i	$0.318171\pi$
$601$	−10.3423	+	27.2703i	−0.421869	+	1.11238i	−0.962539	+	0.271143i	$0.912598\pi$
$602$	−6.08892	−	1.72577i	−0.248166	−	0.0703370i
$603$	30.4796	−	5.31412i	1.24123	−	0.216408i
$604$	41.1475	+	41.8640i	1.67427	+	1.70342i
$605$	2.19323	+	1.24949i	0.0891675	+	0.0507991i
$606$	3.32663	+	27.3973i	0.135135	+	1.11294i
$607$	−18.4115	−	5.91207i	−0.747300	−	0.239964i	−0.0924450	−	0.995718i	$-0.529468\pi$
$607$	−18.4115	−	5.91207i	−0.747300	−	0.239964i	−0.654855	+	0.755754i	$0.727270\pi$
$608$	−0.642145	−	7.42171i	−0.0260424	−	0.300990i
$609$	16.0175	+	13.2322i	0.649061	+	0.536195i
$610$	−2.05549	+	1.36703i	−0.0832244	+	0.0553494i
$611$	5.12509	−	0.354430i	0.207339	−	0.0143387i
$612$	29.6447	+	39.9262i	1.19831	+	1.61392i
$613$	27.2307	−	15.5134i	1.09984	−	0.626581i	0.166665	−	0.986014i	$-0.446700\pi$
$613$	27.2307	−	15.5134i	1.09984	−	0.626581i	0.933171	+	0.359433i	$0.117030\pi$
$614$	7.24492	+	2.05341i	0.292381	+	0.0828688i
$615$	−0.00922151	−	0.0479808i	−0.000371847	−	0.00193477i
$616$	−43.0265	−	2.97554i	−1.73359	−	0.119888i
$617$	23.8492	+	32.1207i	0.960134	+	1.29313i	0.956070	+	0.293140i	$0.0947002\pi$
$617$	23.8492	+	32.1207i	0.960134	+	1.29313i	0.00406407	+	0.999992i	$0.498706\pi$
$618$	−1.02138	−	3.00181i	−0.0410861	−	0.120750i
$619$	−11.4202	+	5.99378i	−0.459016	+	0.240910i	−0.678349	−	0.734740i	$-0.737304\pi$
$619$	−11.4202	+	5.99378i	−0.459016	+	0.240910i	0.219333	+	0.975650i	$0.429612\pi$
$620$	−1.31511	+	6.84268i	−0.0528160	+	0.274809i
$621$	−18.3131	+	7.30925i	−0.734881	+	0.293310i
$622$	10.6403	+	67.9388i	0.426636	+	2.72410i
$623$	−1.31096	−	25.2930i	−0.0525224	−	1.01334i
$624$	1.68762	+	0.175412i	0.0675587	+	0.00702212i
$625$	6.33028	+	0.879760i	0.253211	+	0.0351904i
$626$	42.1852	−	30.2065i	1.68606	−	1.20729i
$627$	2.04585	+	3.45118i	0.0817034	+	0.137827i
$628$	−22.2283	+	27.8734i	−0.887007	+	1.11227i
$629$	2.10520	+	3.55130i	0.0839398	+	0.141600i
$630$	24.4639	+	12.8396i	0.974665	+	0.511543i
$631$	0.174827	+	0.0242968i	0.00695974	+	0.000967240i	0.141133	−	0.989991i	$-0.454926\pi$
$631$	0.174827	+	0.0242968i	0.00695974	+	0.000967240i	−0.134173	+	0.990958i	$0.542838\pi$
$632$	−12.5899	+	9.68936i	−0.500798	+	0.385422i
$633$	1.99467	+	0.877107i	0.0792812	+	0.0348619i
$634$	−28.2224	−	30.7697i	−1.12085	−	1.22202i
$635$	6.16537	+	1.29567i	0.244665	+	0.0514169i
$636$	1.10243	−	12.7416i	0.0437142	−	0.505236i
$637$	−15.6836	−	11.2302i	−0.621408	−	0.444957i
$638$	−33.3710	−	31.6861i	−1.32117	−	1.25447i
$639$	−25.8999	−	26.3509i	−1.02458	−	1.04242i
$640$	−12.7111	−	19.8473i	−0.502451	−	0.784532i
$641$	−23.5228	−	1.62674i	−0.929094	−	0.0642524i	−0.403492	−	0.914983i	$-0.632204\pi$
$641$	−23.5228	−	1.62674i	−0.929094	−	0.0642524i	−0.525602	+	0.850731i	$0.676160\pi$
$642$	9.66240	−	5.50471i	0.381345	−	0.217253i
$643$	11.9187	+	2.93771i	0.470030	+	0.115852i	0.467214	−	0.884144i	$-0.345258\pi$
$643$	11.9187	+	2.93771i	0.470030	+	0.115852i	0.00281533	+	0.999996i	$0.499104\pi$
$644$	55.2135	+	42.4931i	2.17572	+	1.67446i
$645$	0.416330	+	0.395310i	0.0163930	+	0.0155653i
$646$	−24.0117	+	5.04612i	−0.944729	+	0.198537i
$647$	−22.8391	+	35.6613i	−0.897899	+	1.40199i	0.0176758	+	0.999844i	$0.494373\pi$
$647$	−22.8391	+	35.6613i	−0.897899	+	1.40199i	−0.915575	+	0.402147i	$0.868264\pi$
$648$	8.69014	−	11.7041i	0.341381	−	0.459780i
$649$	3.56403	−	29.3525i	0.139901	−	1.15218i
$650$	6.68045	−	14.5075i	0.262029	−	0.569030i
$651$	3.49490	+	4.08486i	0.136976	+	0.160098i
$652$	14.8064	+	43.5154i	0.579863	+	1.70419i
$653$	−22.0975	+	19.5767i	−0.864744	+	0.766096i	−0.973672	−	0.227954i	$-0.926797\pi$
$653$	−22.0975	+	19.5767i	−0.864744	+	0.766096i	0.108928	+	0.994050i	$0.465258\pi$
$654$	9.12924	+	2.25016i	0.356982	+	0.0879881i
$655$	14.4547	−	2.52017i	0.564791	−	0.0984713i
$656$	0.0356697	+	0.0556950i	0.00139267	+	0.00217453i
$657$	0.467937	+	1.76668i	0.0182559	+	0.0689247i
$658$	26.6222	−	1.84108i	1.03784	−	0.0717729i
$659$	9.12172	+	10.6615i	0.355332	+	0.415314i	0.908585	−	0.417699i	$-0.137163\pi$
$659$	9.12172	+	10.6615i	0.355332	+	0.415314i	−0.553254	+	0.833013i	$0.686614\pi$
$660$	7.80356	+	4.80986i	0.303753	+	0.187224i
$661$	−1.70552	+	6.43915i	−0.0663372	+	0.250454i	−0.991689	−	0.128655i	$-0.958934\pi$
$661$	−1.70552	+	6.43915i	−0.0663372	+	0.250454i	0.925352	+	0.379108i	$0.123769\pi$
$662$	0.576024	−	1.69291i	0.0223878	−	0.0657969i
$663$	0.143724	+	8.32542i	0.00558176	+	0.323333i
$664$	−47.9226	−	23.0783i	−1.85976	−	0.895612i
$665$	−6.86699	+	5.28494i	−0.266290	+	0.204941i
$666$	2.70405	−	2.94811i	0.104780	−	0.114237i
$667$	7.06011	+	30.9324i	0.273369	+	1.19771i
$668$	−28.2252	−	14.8137i	−1.09207	−	0.573160i
$669$	−3.29684	+	2.36069i	−0.127463	+	0.0912694i
$670$	7.76147	+	34.0052i	0.299852	+	1.31374i
$671$	0.414899	−	2.64916i	0.0160170	−	0.102270i
$672$	−13.0616	−	1.35763i	−0.503862	−	0.0523719i
$673$	22.9157	+	11.0356i	0.883335	+	0.425391i	0.819841	−	0.572591i	$-0.194062\pi$
$673$	22.9157	+	11.0356i	0.883335	+	0.425391i	0.0634932	+	0.997982i	$0.479776\pi$
$674$	41.6865	+	7.26805i	1.60570	+	0.279955i
$675$	8.47836	+	12.2830i	0.326332	+	0.472774i
$676$	24.7678	+	21.9423i	0.952607	+	0.843937i
$677$	−3.42478	+	8.16826i	−0.131625	+	0.313932i	−0.974576	−	0.224059i	$-0.928069\pi$
$677$	−3.42478	+	8.16826i	−0.131625	+	0.313932i	0.842951	+	0.537991i	$0.180816\pi$
$678$	−1.67712	+	0.352450i	−0.0644094	+	0.0135358i
$679$	17.6495	+	10.0550i	0.677326	+	0.385875i
$680$	−18.4468	+	15.2391i	−0.707403	+	0.584392i
$681$	−0.0703011	−	0.265419i	−0.00269394	−	0.0101709i
$682$	−7.09829	−	9.56016i	−0.271808	−	0.366077i
$683$	12.0913	−	10.7120i	0.462662	−	0.409883i	−0.399328	−	0.916808i	$-0.630756\pi$
$683$	12.0913	−	10.7120i	0.462662	−	0.409883i	0.861990	+	0.506925i	$0.169218\pi$
$684$	7.25326	+	13.2586i	0.277335	+	0.506956i
$685$	−8.90444	−	17.7020i	−0.340221	−	0.676358i
$686$	−26.0282	−	18.6374i	−0.993762	−	0.711579i
$687$	2.94636	−	7.02721i	0.112411	−	0.268105i
$688$	−0.721779	−	0.288081i	−0.0275176	−	0.0109830i
$689$	−5.90757	+	6.90480i	−0.225061	+	0.263052i
$690$	−4.15883	−	9.03144i	−0.158324	−	0.343821i
$691$	28.3320	+	17.4629i	1.07780	+	0.664322i	0.945082	−	0.326832i	$-0.105981\pi$
$691$	28.3320	+	17.4629i	1.07780	+	0.664322i	0.132718	+	0.991154i	$0.457629\pi$
$692$	20.2482	−	10.6271i	0.769723	−	0.403982i
$693$	−28.2405	+	10.1562i	−1.07277	+	0.385802i
$694$	7.48088	+	13.6747i	0.283970	+	0.519084i
$695$	−20.3902	−	15.6926i	−0.773443	−	0.595254i
$696$	12.2216	+	12.4344i	0.463259	+	0.471326i
$697$	−0.250233	+	0.206720i	−0.00947824	+	0.00783006i
$698$	−9.16008	+	30.3144i	−0.346714	+	1.14742i
$699$	17.7793	−	11.8244i	0.672476	−	0.447238i
$700$	22.0580	−	47.9018i	0.833714	−	1.81052i
$701$	3.82809	+	8.31320i	0.144585	+	0.313985i	0.966946	−	0.254980i	$-0.0820690\pi$
$701$	3.82809	+	8.31320i	0.144585	+	0.313985i	−0.822361	+	0.568966i	$0.807344\pi$
$702$	17.1748	−	5.51494i	0.648220	−	0.208148i
$703$	0.485135	+	1.15707i	0.0182972	+	0.0436397i
$704$	35.6610	+	6.21750i	1.34402	+	0.234331i
$705$	−2.21600	−	0.974430i	−0.0834594	−	0.0366991i
$706$	−25.7531	+	11.3243i	−0.969232	+	0.426195i
$707$	31.0752	−	56.8040i	1.16870	−	2.13633i
$708$	−4.06131	+	25.9317i	−0.152633	+	0.974574i
$709$	17.6127	+	2.44775i	0.661458	+	0.0919271i	0.460482	−	0.887669i	$-0.347677\pi$
$709$	17.6127	+	2.44775i	0.661458	+	0.0919271i	0.200976	+	0.979596i	$0.435589\pi$
$710$	28.1556	−	30.6969i	1.05666	−	1.15203i
$711$	−5.30557	+	9.69832i	−0.198974	+	0.363715i
$712$	1.10014	−	21.2256i	0.0412294	−	0.795462i
$713$	0.424945	+	8.19868i	0.0159143	+	0.307043i
$714$	0.746570	+	43.2463i	0.0279397	+	1.61845i
$715$	−2.51848	−	6.00671i	−0.0941859	−	0.224638i
$716$	3.82546	−	16.7604i	0.142964	−	0.626366i
$717$	−12.4983	−	4.98841i	−0.466758	−	0.186295i
$718$	22.2587	−	34.7550i	0.830688	−	1.29705i
$719$	0.329264	+	2.71173i	0.0122795	+	0.101130i	0.997560	−	0.0698150i	$-0.0222409\pi$
$719$	0.329264	+	2.71173i	0.0122795	+	0.101130i	−0.985280	+	0.170945i	$0.945318\pi$
$720$	2.82496	+	1.87878i	0.105280	+	0.0700179i
$721$	−2.15175	+	7.12101i	−0.0801353	+	0.265200i
$722$	36.9701	−	2.55670i	1.37589	−	0.0951506i
$723$	−2.07171	−	6.08866i	−0.0770476	−	0.226440i
$724$	41.4874	−	14.9202i	1.54187	−	0.554506i
$725$	21.6373	−	10.4200i	0.803590	−	0.386989i
$726$	3.68401	−	1.04415i	0.136727	−	0.0387520i
$727$	0.290964	−	3.36287i	0.0107912	−	0.124722i	−0.988929	−	0.148392i	$-0.952590\pi$
$727$	0.290964	−	3.36287i	0.0107912	−	0.124722i	0.999720	+	0.0236704i	$0.00753521\pi$
$728$	−20.3622	−	18.0393i	−0.754673	−	0.668582i
$729$	0.184055	−	0.806396i	0.00681684	−	0.0298665i
$730$	−1.96170	+	0.629916i	−0.0726057	+	0.0233142i
$731$	0.976500	−	3.68674i	0.0361172	−	0.136359i
$732$	−0.449262	+	2.33757i	−0.0166052	+	0.0863990i
$733$	13.8338	−	27.5014i	0.510962	−	1.01579i	−0.479441	−	0.877574i	$-0.659160\pi$
$733$	13.8338	−	27.5014i	0.510962	−	1.01579i	0.990402	−	0.138214i	$-0.0441363\pi$
$734$	−47.0292	+	22.6481i	−1.73588	+	0.835956i
$735$	4.08459	+	8.12014i	0.150662	+	0.299516i
$736$	−14.5428	−	13.8086i	−0.536055	−	0.508990i
$737$	−32.9202	−	18.7548i	−1.21263	−	0.690840i
$738$	0.261885	+	0.174170i	0.00964012	+	0.00641128i
$739$	−7.55773	−	25.0116i	−0.278015	−	0.920066i	−0.978473	−	0.206373i	$-0.933834\pi$
$739$	−7.55773	−	25.0116i	−0.278015	−	0.920066i	0.700458	−	0.713694i	$-0.252979\pi$
$740$	2.21009	+	1.82578i	0.0812446	+	0.0671170i
$741$	−0.305025	+	2.51210i	−0.0112054	+	0.0922845i
$742$	−30.6868	+	35.8669i	−1.12655	+	1.31672i
$743$	−10.0396	+	43.9863i	−0.368316	+	1.61370i	0.363088	+	0.931755i	$0.381723\pi$
$743$	−10.0396	+	43.9863i	−0.368316	+	1.61370i	−0.731404	+	0.681944i	$0.761135\pi$
$744$	2.56276	+	3.71280i	0.0939555	+	0.136118i
$745$	−13.7578	−	14.9996i	−0.504047	−	0.549541i
$746$	−51.3264	+	12.6508i	−1.87919	+	0.463179i
$747$	−36.9899	−	1.27751i	−1.35339	−	0.0467417i
$748$	3.15207	−	60.8146i	0.115251	−	2.22360i
$749$	−25.9497	−	2.69723i	−0.948181	−	0.0985547i
$750$	−14.1676	+	10.9036i	−0.517329	+	0.398144i
$751$	−38.7407	+	17.0352i	−1.41367	+	0.621624i	−0.962615	−	0.270874i	$-0.912687\pi$
$751$	−38.7407	+	17.0352i	−1.41367	+	0.621624i	−0.451052	+	0.892498i	$0.648951\pi$
$752$	3.27495	+	0.113106i	0.119425	+	0.00412456i
$753$	−4.88201	+	0.507440i	−0.177910	+	0.0184922i
$754$	−4.49110	−	28.6760i	−0.163556	−	1.04432i
$755$	−6.33081	+	18.6060i	−0.230402	+	0.677142i
$756$	56.7088	−	18.2096i	2.06248	−	0.662277i
$757$	7.01068	−	8.19412i	0.254807	−	0.297820i	−0.617707	−	0.786408i	$-0.711938\pi$
$757$	7.01068	−	8.19412i	0.254807	−	0.297820i	0.872515	+	0.488588i	$0.162488\pi$
$758$	−5.50352	+	7.41228i	−0.199897	+	0.269226i
$759$	10.2833	+	3.30204i	0.373260	+	0.119857i
$760$	−6.19032	+	3.81551i	−0.224546	+	0.138403i
$761$	14.8564	+	49.1658i	0.538544	+	1.78226i	0.618872	+	0.785492i	$0.287590\pi$
$761$	14.8564	+	49.1658i	0.538544	+	1.78226i	−0.0803286	+	0.996768i	$0.525597\pi$
$762$	7.95781	−	5.29244i	0.288281	−	0.191725i
$763$	−14.3406	−	16.7614i	−0.519166	−	0.606804i
$764$	−70.3127	+	36.9030i	−2.54382	+	1.33510i
$765$	−7.48187	+	14.8739i	−0.270507	+	0.537767i
$766$	86.9776	−	3.00392i	3.14263	−	0.108536i
$767$	13.0732	−	13.3008i	0.472045	−	0.480265i
$768$	−16.9636	−	3.56493i	−0.612120	−	0.128638i
$769$	−19.8787	−	28.7993i	−0.716846	−	1.03853i	−0.996910	−	0.0785493i	$-0.974971\pi$
$769$	−19.8787	−	28.7993i	−0.716846	−	1.03853i	0.280064	−	0.959981i	$-0.409644\pi$
$770$	−13.0822	−	31.2018i	−0.471451	−	1.12443i
$771$	6.28838	−	18.4813i	0.226471	−	0.665587i
$772$	−47.9938	+	19.1556i	−1.72733	+	0.689424i
$773$	0.306864	−	17.7756i	0.0110371	−	0.639344i	−0.941852	−	0.336027i	$-0.890917\pi$
$773$	0.306864	−	17.7756i	0.0110371	−	0.639344i	0.952890	−	0.303317i	$-0.0980943\pi$
$774$	−3.69344	+	0.127559i	−0.132758	+	0.00458502i
$775$	5.97862	−	1.69450i	0.214758	−	0.0608684i
$776$	13.8595	+	9.92405i	0.497528	+	0.356253i
$777$	2.16445	−	0.454864i	0.0776491	−	0.0163181i
$778$	−1.43383	−	11.8087i	−0.0514054	−	0.423361i
$779$	−0.0839722	+	0.0517578i	−0.00300862	+	0.00185441i
$780$	2.05030	+	5.40620i	0.0734125	+	0.193573i
$781$	3.90022	+	45.0776i	0.139561	+	1.61300i
$782$	−39.3760	+	53.0325i	−1.40808	+	1.89644i
$783$	25.1909	+	10.0544i	0.900250	+	0.359314i
$784$	−9.20981	−	8.15918i	−0.328922	−	0.291399i
$785$	−11.6814	−	2.45487i	−0.416927	−	0.0876182i
$786$	12.6441	−	18.3181i	0.451000	−	0.653386i
$787$	31.2107	−	29.6349i	1.11254	−	1.05637i	0.114523	−	0.993421i	$-0.463466\pi$
$787$	31.2107	−	29.6349i	1.11254	−	1.05637i	0.998017	−	0.0629486i	$-0.0200504\pi$
$788$	−52.9035	+	5.49884i	−1.88461	+	0.195888i
$789$	−0.00210579	−	0.0406282i	−7.49683e−5	−	0.00144640i
$790$	−11.2284	−	5.40731i	−0.399488	−	0.192384i
$791$	3.68050	+	1.61841i	0.130864	+	0.0575439i
$792$	−24.4532	+	6.02718i	−0.868907	+	0.214166i
$793$	1.22650	−	1.16458i	0.0435544	−	0.0413554i
$794$	−11.8634	−	4.26646i	−0.421016	−	0.151411i
$795$	3.97691	−	1.58729i	0.141046	−	0.0562954i
$796$	−15.3265	+	57.8646i	−0.543233	+	2.05096i
$797$	−8.03059	−	17.4395i	−0.284458	−	0.617739i	0.711967	−	0.702212i	$-0.247804\pi$
$797$	−8.03059	−	17.4395i	−0.284458	−	0.617739i	−0.996426	+	0.0844738i	$0.973079\pi$
$798$	−1.58445	+	13.0491i	−0.0560888	+	0.461933i
$799$	1.38623	+	16.0217i	0.0490414	+	0.566806i
$800$	−7.74052	+	13.0576i	−0.273669	+	0.461657i
$801$	−5.24443	−	13.8284i	−0.185303	−	0.488604i
$802$	−49.4228	−	40.8286i	−1.74518	−	1.44171i
$803$	0.936099	−	2.03286i	0.0330342	−	0.0717381i
$804$	28.6315	+	17.6475i	1.00975	+	0.622381i
$805$	−4.40270	+	22.9078i	−0.155175	+	0.807395i
$806$	0.129635	−	7.50933i	0.00456620	−	0.264505i
$807$	20.5265	−	2.85271i	0.722568	−	0.100420i
$808$	30.8664	−	44.7177i	1.08588	−	1.57316i
$809$	−23.6132	−	25.7445i	−0.830197	−	0.905130i	0.166524	−	0.986037i	$-0.446746\pi$
$809$	−23.6132	−	25.7445i	−0.830197	−	0.905130i	−0.996722	+	0.0809076i	$0.974218\pi$
$810$	11.2656	+	1.96416i	0.395833	+	0.0690135i
$811$	−0.775635	−	44.9299i	−0.0272362	−	1.57770i	−0.627959	−	0.778246i	$-0.716110\pi$
$811$	−0.775635	−	44.9299i	−0.0272362	−	1.57770i	0.600723	−	0.799457i	$-0.294879\pi$
$812$	−14.8290	−	94.6843i	−0.520397	−	3.32277i
$813$	14.4531	+	5.19781i	0.506893	+	0.182295i
$814$	−4.85218	+	0.674339i	−0.170069	+	0.0236356i
$815$	−10.7879	+	10.9757i	−0.377884	+	0.384464i
$816$	−0.457832	+	5.29149i	−0.0160273	+	0.185239i
$817$	0.448175	−	1.06892i	0.0156797	−	0.0373968i
$818$	−33.6067	+	52.4739i	−1.17503	+	1.83471i
$819$	−18.0231	−	5.78734i	−0.629778	−	0.202226i
$820$	−0.114929	+	0.193876i	−0.00401350	+	0.00677045i
$821$	−12.9124	+	21.7822i	−0.450647	+	0.760205i	−0.997004	−	0.0773477i	$-0.975355\pi$
$821$	−12.9124	+	21.7822i	−0.450647	+	0.760205i	0.546357	+	0.837552i	$0.316014\pi$
$822$	−28.6202	−	9.19014i	−0.998243	−	0.320543i
$823$	−16.6628	+	26.0175i	−0.580828	+	0.906913i	−1.00000		0.000994611i	$-0.999683\pi$
$823$	−16.6628	+	26.0175i	−0.580828	+	0.906913i	0.419171	+	0.907907i	$0.362321\pi$
$824$	−2.41385	+	5.75715i	−0.0840905	+	0.200560i
$825$	0.704700	−	8.14470i	0.0245345	−	0.283562i
$826$	67.9085	−	69.0910i	2.36284	−	2.40398i
$827$	−15.8558	+	2.20358i	−0.551359	+	0.0766259i	−0.407894	−	0.913029i	$-0.633737\pi$
$827$	−15.8558	+	2.20358i	−0.551359	+	0.0766259i	−0.143465	+	0.989655i	$0.545825\pi$
$828$	38.2841	+	13.7682i	1.33046	+	0.478477i
$829$	−3.19063	−	20.3724i	−0.110815	−	0.707562i	−0.977849	−	0.209312i	$-0.932877\pi$
$829$	−3.19063	−	20.3724i	−0.110815	−	0.707562i	0.867034	−	0.498250i	$-0.166024\pi$
$830$	−0.720212	−	41.7195i	−0.0249989	−	1.44810i
$831$	12.0592	+	2.10252i	0.418329	+	0.0729356i
$832$	15.4334	+	16.8264i	0.535056	+	0.583350i
$833$	34.3016	−	49.6944i	1.18848	−	1.72181i
$834$	−38.6598	+	5.37280i	−1.33868	+	0.186045i
$835$	0.184217	−	10.6710i	0.00637508	−	0.369287i
$836$	3.49296	−	18.1743i	0.120807	−	0.628573i
$837$	5.97452	+	3.68250i	0.206510	+	0.127286i
$838$	−7.29340	+	15.8386i	−0.251946	+	0.547135i
$839$	−21.4119	−	17.6886i	−0.739220	−	0.610677i	0.189317	−	0.981916i	$-0.439373\pi$
$839$	−21.4119	−	17.6886i	−0.739220	−	0.610677i	−0.928537	+	0.371239i	$0.878933\pi$
$840$	4.54558	+	11.9857i	0.156837	+	0.413546i
$841$	7.46733	−	12.5968i	0.257494	−	0.434372i
$842$	−1.34375	−	15.5307i	−0.0463087	−	0.535222i
$843$	2.49299	−	20.5316i	0.0858631	−	0.707146i
$844$	−4.20422	−	9.13003i	−0.144715	−	0.314268i
$845$	−2.83659	+	10.7095i	−0.0975818	+	0.368417i
$846$	14.4728	−	5.77648i	0.497586	−	0.198599i
$847$	−8.45341	−	3.04012i	−0.290463	−	0.104460i
$848$	−4.20336	+	3.99113i	−0.144344	+	0.137056i
$849$	−22.3533	+	5.50959i	−0.767163	+	0.189089i
$850$	45.7674	+	20.1250i	1.56981	+	0.690283i
$851$	3.04310	+	1.46548i	0.104316	+	0.0502360i
$852$	−2.07901	−	40.1115i	−0.0712257	−	1.37420i
$853$	24.1751	−	2.51278i	0.827738	−	0.0860358i	0.319860	−	0.947465i	$-0.396364\pi$
$853$	24.1751	−	2.51278i	0.827738	−	0.0860358i	0.507878	+	0.861429i	$0.330430\pi$
$854$	6.37105	−	6.04939i	0.218013	−	0.207006i
$855$	−2.87441	+	4.16430i	−0.0983026	+	0.142416i
$856$	−21.4259	−	4.50271i	−0.732323	−	0.153899i
$857$	−20.7122	−	18.3495i	−0.707517	−	0.626805i	0.230630	−	0.973041i	$-0.425921\pi$
$857$	−20.7122	−	18.3495i	−0.707517	−	0.626805i	−0.938147	+	0.346236i	$0.887460\pi$
$858$	−9.17662	−	3.66263i	−0.313285	−	0.125040i
$859$	19.1002	−	25.7246i	0.651690	−	0.877712i	−0.346488	−	0.938054i	$-0.612626\pi$
$859$	19.1002	−	25.7246i	0.651690	−	0.877712i	0.998178	+	0.0603424i	$0.0192193\pi$
$860$	−0.228285	−	2.63845i	−0.00778445	−	0.0899703i
$861$	0.0616612	+	0.162587i	0.00210141	+	0.00554095i
$862$	−52.9726	+	32.6506i	−1.80425	+	1.11208i
$863$	−0.864566	−	7.12035i	−0.0294302	−	0.242379i	−0.999999	−	0.00155458i	$-0.999505\pi$
$863$	−0.864566	−	7.12035i	−0.0294302	−	0.242379i	0.970569	−	0.240825i	$-0.0774179\pi$
$864$	−16.7773	+	3.52578i	−0.570775	+	0.119950i
$865$	6.22505	+	4.45742i	0.211658	+	0.151557i
$866$	−1.53290	+	0.434465i	−0.0520900	+	0.0147637i
$867$	−13.1985	+	0.455832i	−0.448244	+	0.0154809i
$868$	0.428039	−	24.7948i	0.0145286	−	0.841592i
$869$	12.5729	−	5.01817i	0.426506	−	0.170230i
$870$	−4.40571	+	12.9482i	−0.149368	+	0.438985i
$871$	−9.24039	−	22.0388i	−0.313099	−	0.746756i
$872$	−10.5158	−	15.2348i	−0.356110	−	0.515914i
$873$	11.6079	+	2.43944i	0.392869	+	0.0825624i
$874$	−14.0714	+	14.3164i	−0.475973	+	0.484260i
$875$	41.9176	−	1.44770i	1.41707	−	0.0489410i
$876$	−0.892776	+	1.77483i	−0.0301641	+	0.0599660i
$877$	11.3143	−	5.93820i	0.382056	−	0.200519i	−0.262751	−	0.964864i	$-0.584630\pi$
$877$	11.3143	−	5.93820i	0.382056	−	0.200519i	0.644808	+	0.764345i	$0.276938\pi$
$878$	−7.14800	−	8.35462i	−0.241233	−	0.281955i
$879$	14.8969	−	9.90737i	0.502460	−	0.334167i
$880$	−1.20172	−	3.97700i	−0.0405101	−	0.134065i
$881$	16.6492	−	10.2620i	0.560926	−	0.345737i	−0.214947	−	0.976626i	$-0.568958\pi$
$881$	16.6492	−	10.2620i	0.560926	−	0.345737i	0.775873	+	0.630889i	$0.217310\pi$
$882$	−55.7097	−	17.8888i	−1.87584	−	0.602346i
$883$	−2.24710	+	3.02646i	−0.0756211	+	0.101848i	−0.839080	−	0.544008i	$-0.816906\pi$
$883$	−2.24710	+	3.02646i	−0.0756211	+	0.101848i	0.763459	+	0.645856i	$0.223500\pi$
$884$	24.9705	−	29.1857i	0.839850	−	0.981621i
$885$	−8.36731	+	2.68680i	−0.281264	+	0.0903159i
$886$	26.9313	−	79.1501i	0.904776	−	2.65910i
$887$	1.19372	+	7.62199i	0.0400813	+	0.255922i	0.999676	−	0.0254652i	$-0.00810672\pi$
$887$	1.19372	+	7.62199i	0.0400813	+	0.255922i	−0.959594	+	0.281387i	$0.909206\pi$
$888$	1.84611	−	0.191886i	0.0619513	−	0.00643927i
$889$	−22.4082	−	0.773907i	−0.751548	−	0.0259560i
$890$	15.2626	−	6.71135i	0.511605	−	0.224965i
$891$	−9.84394	+	7.57605i	−0.329785	+	0.253807i
$892$	18.6045	+	1.93377i	0.622924	+	0.0647473i
$893$	−0.252975	+	4.88079i	−0.00846549	+	0.163329i
$894$	−30.8573	−	1.06571i	−1.03202	−	0.0356427i
$895$	5.58866	−	1.37748i	0.186808	−	0.0460441i
$896$	56.6983	+	61.8159i	1.89416	+	2.06512i
$897$	3.86985	+	5.60645i	0.129211	+	0.187194i
$898$	14.9778	−	65.6220i	0.499816	−	2.18984i
$899$	7.34161	−	8.58091i	0.244856	−	0.286189i
$900$	3.71195	−	30.5706i	0.123732	−	1.01902i
$901$	−21.9303	−	18.1168i	−0.730604	−	0.603559i
$902$	−0.111404	−	0.368683i	−0.00370936	−	0.0122758i
$903$	−1.70133	−	1.13149i	−0.0566167	−	0.0376536i
$904$	2.93167	+	1.67018i	0.0975059	+	0.0555495i
$905$	10.7047	+	10.1642i	0.355835	+	0.337870i
$906$	13.3975	+	26.6342i	0.445103	+	0.884862i
$907$	30.7059	−	14.7872i	1.01957	−	0.491000i	0.152036	−	0.988375i	$-0.451417\pi$
$907$	30.7059	−	14.7872i	1.01957	−	0.491000i	0.867536	+	0.497375i	$0.165703\pi$
$908$	−0.569160	+	1.13149i	−0.0188882	+	0.0375497i
$909$	7.13606	−	37.1299i	0.236688	−	1.23152i
$910$	5.46394	−	20.6289i	0.181128	−	0.683842i
$911$	−9.41973	+	3.02474i	−0.312090	+	0.100214i	−0.457643	−	0.889136i	$-0.651306\pi$
$911$	−9.41973	+	3.02474i	−0.312090	+	0.100214i	0.145553	+	0.989350i	$0.453504\pi$
$912$	−0.359181	+	1.57367i	−0.0118937	+	0.0521095i
$913$	33.9256	+	30.0554i	1.12277	+	0.994690i
$914$	−4.18681	+	48.3899i	−0.138487	+	1.60059i
$915$	−0.766768	+	0.217323i	−0.0253486	+	0.00718448i
$916$	−31.6689	+	15.2509i	−1.04637	+	0.503905i
$917$	−49.1385	+	17.6718i	−1.62270	+	0.583574i
$918$	18.1890	+	53.4567i	0.600326	+	1.76433i
$919$	6.62443	−	0.458119i	0.218520	−	0.0151119i	0.0406838	−	0.999172i	$-0.487046\pi$
$919$	6.62443	−	0.458119i	0.218520	−	0.0151119i	0.177836	+	0.984060i	$0.443090\pi$
$920$	−5.66234	+	18.7390i	−0.186682	+	0.617806i
$921$	2.02433	+	1.34630i	0.0667039	+	0.0443622i
$922$	7.57840	+	62.4138i	0.249581	+	2.05549i
$923$	−15.3915	+	24.0325i	−0.506618	+	0.791040i
$924$	−30.3000	−	12.0935i	−0.996798	−	0.397848i
$925$	0.568892	−	2.49248i	0.0187051	−	0.0819522i
$926$	−5.18056	−	12.3559i	−0.170244	−	0.406040i
$927$	0.0749795	+	4.34331i	0.00246265	+	0.142653i
$928$	1.42788	+	27.5488i	0.0468724	+	0.904335i
$929$	2.18517	−	42.1597i	0.0716932	−	1.38321i	−0.684570	−	0.728947i	$-0.740010\pi$
$929$	2.18517	−	42.1597i	0.0716932	−	1.38321i	0.756263	−	0.654268i	$-0.227023\pi$
$930$	−1.69851	+	3.10480i	−0.0556964	+	0.101810i
$931$	12.4043	−	13.5239i	0.406534	−	0.443227i
$932$	−97.5583	−	13.5583i	−3.19563	−	0.444117i
$933$	−3.43519	+	21.9339i	−0.112463	+	0.718084i
$934$	−37.2253	+	68.0461i	−1.21805	+	2.22654i
$935$	18.6641	−	8.20705i	0.610381	−	0.268399i
$936$	−14.5416	−	6.39429i	−0.475307	−	0.209004i
$937$	46.3086	+	8.07391i	1.51284	+	0.263763i	0.866456	−	0.499253i	$-0.166392\pi$
$937$	46.3086	+	8.07391i	1.51284	+	0.263763i	0.646379	+	0.763016i	$0.276282\pi$
$938$	−47.9991	−	114.480i	−1.56723	−	3.73791i
$939$	15.9488	−	5.12127i	0.520469	−	0.167126i
$940$	4.67072	+	10.1431i	0.152342	+	0.330831i
$941$	14.5428	−	31.5816i	0.474081	−	1.02953i	−0.511337	−	0.859380i	$-0.670850\pi$
$941$	14.5428	−	31.5816i	0.474081	−	1.02953i	0.985418	−	0.170149i	$-0.0544250\pi$
$942$	−15.0775	+	10.0275i	−0.491252	+	0.326713i
$943$	−0.0768101	+	0.254196i	−0.00250128	+	0.00827775i
$944$	9.17132	−	7.57651i	0.298501	−	0.246595i
$945$	13.9787	+	14.2221i	0.454727	+	0.462644i
$946$	3.58643	+	2.76017i	0.116605	+	0.0897410i
$947$	12.6049	+	23.0412i	0.409606	+	0.748739i	0.998218	−	0.0596762i	$-0.0190068\pi$
$947$	12.6049	+	23.0412i	0.409606	+	0.748739i	−0.588612	+	0.808416i	$0.700325\pi$
$948$	−11.3082	+	4.06679i	−0.367273	+	0.132083i
$949$	1.24994	−	0.656019i	0.0405747	−	0.0212953i
$950$	12.9348	+	7.97262i	0.419662	+	0.258666i
$951$	−5.63814	−	12.2440i	−0.182829	−	0.397037i
$952$	55.3604	−	64.7056i	1.79424	−	2.09712i
$953$	8.93944	+	3.56796i	0.289577	+	0.115578i	0.510947	−	0.859612i	$-0.329295\pi$
$953$	8.93944	+	3.56796i	0.289577	+	0.115578i	−0.221370	+	0.975190i	$0.571053\pi$
$954$	−10.6580	+	25.4199i	−0.345066	+	0.823000i
$955$	−21.6167	−	15.4785i	−0.699500	−	0.500874i
$956$	27.8951	+	55.4553i	0.902193	+	1.79355i
$957$	−7.13030	−	13.0339i	−0.230490	−	0.421325i
$958$	−45.2965	+	40.1292i	−1.46346	+	1.29652i
$959$	42.0405	+	56.6213i	1.35756	+	1.82840i
$960$	−2.75470	−	10.4003i	−0.0889077	−	0.335668i
$961$	−21.6468	+	17.8826i	−0.698282	+	0.576858i
$962$	−2.68478	−	1.52953i	−0.0865609	−	0.0493141i
$963$	−14.9091	+	3.13318i	−0.480440	+	0.100965i
$964$	−11.4715	+	27.3602i	−0.369473	+	0.881211i
$965$	−12.9504	−	11.4730i	−0.416888	−	0.369330i
$966$	20.1019	+	29.1226i	0.646768	+	0.937006i
$967$	−17.9155	−	3.12358i	−0.576125	−	0.100447i	−0.123810	−	0.992306i	$-0.539511\pi$
$967$	−17.9155	−	3.12358i	−0.576125	−	0.100447i	−0.452315	+	0.891858i	$0.649402\pi$
$968$	−6.79223	−	3.27096i	−0.218310	−	0.105133i
$969$	−7.87902	−	0.818953i	−0.253111	−	0.0263086i
$970$	−2.06906	+	13.2111i	−0.0664335	+	0.424183i
$971$	13.8059	+	60.4876i	0.443053	+	1.94114i	0.313599	+	0.949555i	$0.398465\pi$
$971$	13.8059	+	60.4876i	0.443053	+	1.94114i	0.129454	+	0.991585i	$0.458678\pi$
$972$	43.9077	−	31.4399i	1.40834	−	1.00844i
$973$	81.0820	+	42.5551i	2.59937	+	1.36425i
$974$	15.0360	+	65.8770i	0.481785	+	2.11084i
$975$	3.48546	−	3.80005i	0.111624	−	0.121699i
$976$	0.854944	−	0.657978i	0.0273661	−	0.0210614i
$977$	28.8353	+	13.8864i	0.922524	+	0.444264i	0.833971	−	0.551808i	$-0.186062\pi$
$977$	28.8353	+	13.8864i	0.922524	+	0.444264i	0.0885522	+	0.996072i	$0.471776\pi$
$978$	0.402966	+	23.3425i	0.0128854	+	0.746411i
$979$	−5.83390	+	17.1456i	−0.186452	+	0.547975i
$980$	10.7356	−	40.5317i	0.342935	−	1.29474i
$981$	−10.9656	−	6.75882i	−0.350104	−	0.215793i
$982$	35.9565	+	42.0262i	1.14742	+	1.34111i
$983$	−32.7022	+	2.26155i	−1.04304	+	0.0721322i	−0.580332	−	0.814380i	$-0.697077\pi$
$983$	−32.7022	+	2.26155i	−1.04304	+	0.0721322i	−0.462705	+	0.886512i	$0.653121\pi$
$984$	0.0373622	+	0.141059i	0.00119106	+	0.00449681i
$985$	−9.60431	−	14.9963i	−0.306019	−	0.477821i
$986$	89.5092	−	15.6059i	2.85055	−	0.496994i
$987$	8.36511	+	2.06181i	0.266264	+	0.0656283i
$988$	8.73751	−	7.74076i	0.277977	−	0.246266i
$989$	−1.00510	−	2.95395i	−0.0319604	−	0.0939302i
$990$	−12.8440	−	15.0121i	−0.408208	−	0.477115i
$991$	−19.0780	+	41.4305i	−0.606034	+	1.31608i	0.323108	+	0.946362i	$0.395272\pi$
$991$	−19.0780	+	41.4305i	−0.606034	+	1.31608i	−0.929143	+	0.369721i	$0.879453\pi$
$992$	−0.860382	+	7.08588i	−0.0273171	+	0.224977i
$993$	0.344162	−	0.463527i	0.0109217	−	0.0147096i
$994$	−79.9511	+	124.837i	−2.53590	+	3.95958i
$995$	−19.6134	+	4.12181i	−0.621788	+	0.130670i
$996$	−29.1772	−	27.7041i	−0.924515	−	0.877837i
$997$	−11.9104	−	9.16638i	−0.377205	−	0.290302i	0.403776	−	0.914858i	$-0.367698\pi$
$997$	−11.9104	−	9.16638i	−0.377205	−	0.290302i	−0.780980	+	0.624556i	$0.785280\pi$
$998$	52.0294	+	12.8241i	1.64696	+	0.405939i
$999$	2.50883	−	1.42929i	0.0793759	−	0.0452208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.m.a.10.5	✓	3168
547.383	even	91	inner	547.2.m.a.383.5	yes	3168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.m.a.10.5	✓	3168	1.1	even	1	trivial
547.2.m.a.383.5	yes	3168	547.383	even	91	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.m (of order \(91\), degree \(72\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19472 - 2.01540i) q^{2} +(-0.168315 - 0.737438i) q^{3} +(-1.67460 + 3.06109i) q^{4} +(-1.16754 - 0.0403228i) q^{5} +(-1.28514 + 1.22026i) q^{6} +(4.11811 - 0.572320i) q^{7} +(3.48700 - 0.120429i) q^{8} +(2.18742 - 1.05341i) q^{9} +O(q^{10})\)	\(q+(-1.19472 - 2.01540i) q^{2} +(-0.168315 - 0.737438i) q^{3} +(-1.67460 + 3.06109i) q^{4} +(-1.16754 - 0.0403228i) q^{5} +(-1.28514 + 1.22026i) q^{6} +(4.11811 - 0.572320i) q^{7} +(3.48700 - 0.120429i) q^{8} +(2.18742 - 1.05341i) q^{9} +(1.31362 + 2.40123i) q^{10} +(-2.88671 - 0.711509i) q^{11} +(2.53923 + 0.719686i) q^{12} +(-1.16921 - 1.46615i) q^{13} +(-6.07346 - 7.61588i) q^{14} +(0.166779 + 0.867772i) q^{15} +(-0.645115 - 1.00729i) q^{16} +(4.52566 - 3.73869i) q^{17} +(-4.73640 - 3.15000i) q^{18} +(1.51871 - 0.936081i) q^{19} +(2.07859 - 3.50641i) q^{20} +(-1.11519 - 2.94052i) q^{21} +(2.01484 + 6.66793i) q^{22} +(1.38917 - 4.59734i) q^{23} +(-0.675725 - 2.55118i) q^{24} +(-3.62657 - 0.250799i) q^{25} +(-1.55799 + 4.10807i) q^{26} +(-2.55983 - 3.20992i) q^{27} +(-5.14427 + 13.5643i) q^{28} +(-5.74017 + 3.27020i) q^{29} +(1.54965 - 1.37287i) q^{30} +(-1.60855 + 0.578488i) q^{31} +(1.87642 - 3.73031i) q^{32} +(-0.0388168 + 2.24852i) q^{33} +(-12.9419 - 4.65432i) q^{34} +(-4.83111 + 0.502150i) q^{35} +(-0.438486 + 8.45994i) q^{36} +(-0.108818 + 0.694808i) q^{37} +(-3.70101 - 1.94244i) q^{38} +(-0.884395 + 1.10900i) q^{39} -4.07605 q^{40} -0.0552920 q^{41} +(-4.59398 + 5.76067i) q^{42} +(0.528242 - 0.378245i) q^{43} +(7.01208 - 7.64498i) q^{44} +(-2.59637 + 1.14169i) q^{45} +(-10.9252 + 2.69281i) q^{46} +(-1.55622 + 2.25458i) q^{47} +(-0.634231 + 0.645274i) q^{48} +(9.89655 - 2.80495i) q^{49} +(3.82730 + 7.60864i) q^{50} +(-3.51879 - 2.70811i) q^{51} +(6.44597 - 1.12386i) q^{52} +(-0.914578 - 4.75867i) q^{53} +(-3.41099 + 8.99405i) q^{54} +(3.34164 + 0.947112i) q^{55} +(14.2909 - 2.49162i) q^{56} +(-0.945923 - 0.962394i) q^{57} +(13.4487 + 7.66177i) q^{58} +(1.19876 + 9.87268i) q^{59} +(-2.93562 - 0.942648i) q^{60} +(0.0777446 + 0.898548i) q^{61} +(3.08766 + 2.55075i) q^{62} +(8.40516 - 5.58995i) q^{63} +(-12.1465 + 0.840002i) q^{64} +(1.30598 + 1.75892i) q^{65} +(4.57805 - 2.60813i) q^{66} +(12.2606 + 3.47498i) q^{67} +(3.86580 + 20.1143i) q^{68} +(-3.62407 - 0.250626i) q^{69} +(6.78388 + 9.13670i) q^{70} +(-4.90218 - 14.4073i) q^{71} +(7.50068 - 3.93666i) q^{72} +(-0.142075 + 0.739233i) q^{73} +(1.53032 - 0.610792i) q^{74} +(0.425459 + 2.71659i) q^{75} +(0.322204 + 6.21646i) q^{76} +(-12.2950 - 1.27795i) q^{77} +(3.29168 + 0.457466i) q^{78} +(-3.70207 + 2.65085i) q^{79} +(0.712577 + 1.20206i) q^{80} +(2.60497 - 3.26653i) q^{81} +(0.0660586 + 0.111435i) q^{82} +(-13.4985 - 7.08458i) q^{83} +(10.8687 + 1.51049i) q^{84} +(-5.43462 + 4.18257i) q^{85} +(-1.39342 - 0.612720i) q^{86} +(3.37773 + 3.68260i) q^{87} +(-10.1516 - 2.13339i) q^{88} +(0.525098 - 6.06892i) q^{89} +(5.40290 + 3.86872i) q^{90} +(-5.65405 - 5.36858i) q^{91} +(11.7466 + 11.9511i) q^{92} +(0.697343 + 1.08884i) q^{93} +(6.40313 + 0.442814i) q^{94} +(-1.81089 + 1.03167i) q^{95} +(-3.06670 - 0.755873i) q^{96} +(3.87172 + 2.97973i) q^{97} +(-17.4768 - 16.5944i) q^{98} +(-7.06395 + 1.48451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99}+O(q^{100}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9 - 91 * q^10 - 61 * q^11 - 31 * q^12 - 72 * q^13 - 21 * q^14 - 46 * q^15 + 24 * q^16 - 91 * q^17 + 9 * q^18 - 89 * q^19 - 108 * q^20 - 81 * q^21 - 50 * q^22 - 86 * q^23 - 33 * q^24 - 15 * q^25 + 137 * q^26 + 163 * q^27 - 47 * q^28 - 12 * q^29 + 29 * q^30 - 53 * q^31 - 122 * q^32 - 21 * q^33 - 80 * q^34 - 75 * q^35 - 8 * q^36 - 49 * q^37 - 47 * q^38 + 128 * q^39 - 246 * q^40 - 686 * q^41 - 466 * q^42 - 9 * q^43 - 43 * q^44 + 156 * q^45 - 91 * q^46 - 72 * q^47 + 21 * q^48 - 8 * q^49 - 84 * q^50 + 93 * q^51 + 4 * q^52 - 32 * q^53 - 71 * q^54 - 34 * q^55 - 263 * q^56 - 61 * q^57 - 36 * q^58 - 23 * q^59 + 87 * q^60 + 38 * q^61 + 26 * q^62 + 133 * q^63 + 343 * q^64 + 143 * q^65 - 65 * q^66 - 50 * q^67 - 213 * q^68 - 140 * q^69 + 372 * q^70 - 75 * q^71 + 147 * q^72 - 18 * q^73 - 85 * q^74 + 97 * q^75 - 47 * q^76 + 11 * q^77 + 55 * q^78 - 37 * q^79 - 142 * q^80 - 532 * q^81 - 94 * q^82 - 279 * q^83 + 395 * q^84 - 75 * q^85 - 147 * q^86 + 84 * q^87 + 345 * q^88 + 8 * q^89 + 278 * q^90 - 38 * q^91 - 78 * q^92 - 83 * q^93 - 540 * q^94 + 35 * q^95 + 123 * q^96 - 735 * q^97 - 90 * q^98 + 351 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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