LMFDB - Embedded newform 322.2.i.a.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			71.1
Root			$0.142315 - 0.989821i$ of defining polynomial
Character	$\chi$	$=$	322.71
Dual form			322.2.i.a.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 - 0.540641i) q^{2} +(0.130785 + 0.909632i) q^{3} +(0.415415 + 0.909632i) q^{4} +(2.30075 + 0.675560i) q^{5} +(0.381761 - 0.835939i) q^{6} +(0.654861 - 0.755750i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.06815 - 0.607265i) q^{9} +O(q^{10})$	\(q+(-0.841254 - 0.540641i) q^{2} +(0.130785 + 0.909632i) q^{3} +(0.415415 + 0.909632i) q^{4} +(2.30075 + 0.675560i) q^{5} +(0.381761 - 0.835939i) q^{6} +(0.654861 - 0.755750i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.06815 - 0.607265i) q^{9} +(-1.57028 - 1.81219i) q^{10} +(-3.45561 + 2.22078i) q^{11} +(-0.773100 + 0.496841i) q^{12} +(0.442270 + 0.510407i) q^{13} +(-0.959493 + 0.281733i) q^{14} +(-0.313607 + 2.18119i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.52357 - 3.33616i) q^{17} +(-2.06815 - 0.607265i) q^{18} +(1.75667 + 3.84657i) q^{19} +(0.341254 + 2.37347i) q^{20} +(0.773100 + 0.496841i) q^{21} +4.10769 q^{22} +(3.21727 + 3.55657i) q^{23} +0.918986 q^{24} +(0.630785 + 0.405381i) q^{25} +(-0.0961145 - 0.668491i) q^{26} +(1.96815 + 4.30965i) q^{27} +(0.959493 + 0.281733i) q^{28} +(-0.445841 + 0.976256i) q^{29} +(1.44306 - 1.66538i) q^{30} +(0.525092 - 3.65209i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-2.47204 - 2.85288i) q^{33} +(-3.08538 + 1.98285i) q^{34} +(2.01722 - 1.29639i) q^{35} +(1.41153 + 1.62899i) q^{36} +(8.25654 - 2.42434i) q^{37} +(0.601808 - 4.18567i) q^{38} +(-0.406440 + 0.469057i) q^{39} +(0.996114 - 2.18119i) q^{40} +(-4.74788 - 1.39410i) q^{41} +(-0.381761 - 0.835939i) q^{42} +(-0.187094 - 1.30127i) q^{43} +(-3.45561 - 2.22078i) q^{44} +5.16854 q^{45} +(-0.783711 - 4.73136i) q^{46} -2.95001 q^{47} +(-0.773100 - 0.496841i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.311485 - 0.682057i) q^{50} +(3.23394 + 0.949570i) q^{51} +(-0.280557 + 0.614334i) q^{52} +(-7.47107 + 8.62207i) q^{53} +(0.674259 - 4.68958i) q^{54} +(-9.45075 + 2.77499i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(-3.26921 + 2.10100i) q^{57} +(0.902869 - 0.580239i) q^{58} +(-2.85848 - 3.29886i) q^{59} +(-2.11435 + 0.620830i) q^{60} +(0.699730 - 4.86673i) q^{61} +(-2.41621 + 2.78845i) q^{62} +(0.895412 - 1.96068i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.672741 + 1.47310i) q^{65} +(0.537225 + 3.73648i) q^{66} +(2.97001 + 1.90871i) q^{67} +3.66759 q^{68} +(-2.81440 + 3.39168i) q^{69} -2.39788 q^{70} +(-4.59845 - 2.95525i) q^{71} +(-0.306755 - 2.13353i) q^{72} +(-1.85763 - 4.06765i) q^{73} +(-8.25654 - 2.42434i) q^{74} +(-0.286250 + 0.626800i) q^{75} +(-2.76921 + 3.19584i) q^{76} +(-0.584585 + 4.06588i) q^{77} +(0.595510 - 0.174858i) q^{78} +(-7.31964 - 8.44732i) q^{79} +(-2.01722 + 1.29639i) q^{80} +(1.77708 - 1.14206i) q^{81} +(3.24046 + 3.73969i) q^{82} +(-16.4238 + 4.82245i) q^{83} +(-0.130785 + 0.909632i) q^{84} +(5.75913 - 6.64639i) q^{85} +(-0.546126 + 1.19585i) q^{86} +(-0.946343 - 0.277871i) q^{87} +(1.70640 + 3.73648i) q^{88} +(-1.92745 - 13.4057i) q^{89} +(-4.34805 - 2.79432i) q^{90} +0.675365 q^{91} +(-1.89867 + 4.40398i) q^{92} +3.39074 q^{93} +(2.48171 + 1.59490i) q^{94} +(1.44306 + 10.0367i) q^{95} +(0.381761 + 0.835939i) q^{96} +(7.13787 + 2.09587i) q^{97} +(-0.415415 + 0.909632i) q^{98} +(-5.79812 + 6.69139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9}+O(q^{10}) $ 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9	\( 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9} - 5 q^{10} - 11 q^{11} - 3 q^{12} + 10 q^{13} - q^{14} - 7 q^{15} - q^{16} + q^{17} - 16 q^{18} + 3 q^{19} - 6 q^{20} + 3 q^{21} + 12 q^{23} - 8 q^{24} + 2 q^{25} - 10 q^{26} - 9 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} - 5 q^{31} + q^{32} - 11 q^{33} - 12 q^{34} + 6 q^{35} - 6 q^{36} + 27 q^{37} - 3 q^{38} + 8 q^{39} - 5 q^{40} - 12 q^{41} - 3 q^{42} + 38 q^{43} - 11 q^{44} + 8 q^{45} + 10 q^{46} + 2 q^{47} - 3 q^{48} - q^{49} - 13 q^{50} + 36 q^{51} - q^{52} - 16 q^{53} + 9 q^{54} - 11 q^{55} - q^{56} - 13 q^{57} + 9 q^{58} - 5 q^{59} - 7 q^{60} - 26 q^{61} + 5 q^{62} + 6 q^{63} - q^{64} + 5 q^{65} - 11 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 6 q^{70} + q^{71} + 6 q^{72} + 9 q^{73} - 27 q^{74} + 17 q^{75} - 8 q^{76} - 11 q^{77} + 25 q^{78} - 50 q^{79} - 6 q^{80} + 2 q^{81} + 23 q^{82} - 29 q^{83} + 3 q^{84} + 28 q^{85} + 17 q^{86} - 16 q^{87} + 11 q^{88} + 7 q^{89} - 19 q^{90} + 12 q^{91} + 23 q^{92} + 40 q^{93} + 20 q^{94} - 4 q^{95} + 3 q^{96} + 12 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9 - 5 * q^10 - 11 * q^11 - 3 * q^12 + 10 * q^13 - q^14 - 7 * q^15 - q^16 + q^17 - 16 * q^18 + 3 * q^19 - 6 * q^20 + 3 * q^21 + 12 * q^23 - 8 * q^24 + 2 * q^25 - 10 * q^26 - 9 * q^27 + q^28 + 2 * q^29 - 4 * q^30 - 5 * q^31 + q^32 - 11 * q^33 - 12 * q^34 + 6 * q^35 - 6 * q^36 + 27 * q^37 - 3 * q^38 + 8 * q^39 - 5 * q^40 - 12 * q^41 - 3 * q^42 + 38 * q^43 - 11 * q^44 + 8 * q^45 + 10 * q^46 + 2 * q^47 - 3 * q^48 - q^49 - 13 * q^50 + 36 * q^51 - q^52 - 16 * q^53 + 9 * q^54 - 11 * q^55 - q^56 - 13 * q^57 + 9 * q^58 - 5 * q^59 - 7 * q^60 - 26 * q^61 + 5 * q^62 + 6 * q^63 - q^64 + 5 * q^65 - 11 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 6 * q^70 + q^71 + 6 * q^72 + 9 * q^73 - 27 * q^74 + 17 * q^75 - 8 * q^76 - 11 * q^77 + 25 * q^78 - 50 * q^79 - 6 * q^80 + 2 * q^81 + 23 * q^82 - 29 * q^83 + 3 * q^84 + 28 * q^85 + 17 * q^86 - 16 * q^87 + 11 * q^88 + 7 * q^89 - 19 * q^90 + 12 * q^91 + 23 * q^92 + 40 * q^93 + 20 * q^94 - 4 * q^95 + 3 * q^96 + 12 * q^97 + q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$3$	0.130785	+	0.909632i	0.0755089	+	0.525176i	0.992110	+	0.125373i	$0.0400126\pi$
$3$	0.130785	+	0.909632i	0.0755089	+	0.525176i	−0.916601	+	0.399804i	$0.869078\pi$
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	2.30075	+	0.675560i	1.02893	+	0.302120i	0.752274	−	0.658851i	$-0.228957\pi$
$5$	2.30075	+	0.675560i	1.02893	+	0.302120i	0.276651	+	0.960970i	$0.410775\pi$
$6$	0.381761	−	0.835939i	0.155853	−	0.341271i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	2.06815	−	0.607265i	0.689384	−	0.202422i
$10$	−1.57028	−	1.81219i	−0.496565	−	0.573066i
$11$	−3.45561	+	2.22078i	−1.04190	+	0.669592i	−0.945457	−	0.325747i	$-0.894384\pi$
$11$	−3.45561	+	2.22078i	−1.04190	+	0.669592i	−0.0964476	+	0.995338i	$0.530748\pi$
$12$	−0.773100	+	0.496841i	−0.223175	+	0.143426i
$13$	0.442270	+	0.510407i	0.122664	+	0.141561i	0.813760	−	0.581202i	$-0.197417\pi$
$13$	0.442270	+	0.510407i	0.122664	+	0.141561i	−0.691096	+	0.722763i	$0.742872\pi$
$14$	−0.959493	+	0.281733i	−0.256435	+	0.0752962i
$15$	−0.313607	+	2.18119i	−0.0809730	+	0.563180i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	1.52357	−	3.33616i	0.369521	−	0.809138i	−0.629951	−	0.776635i	$-0.716925\pi$
$17$	1.52357	−	3.33616i	0.369521	−	0.809138i	0.999472	−	0.0325028i	$-0.0103478\pi$
$18$	−2.06815	−	0.607265i	−0.487468	−	0.143134i
$19$	1.75667	+	3.84657i	0.403007	+	0.882463i	0.996956	+	0.0779605i	$0.0248408\pi$
$19$	1.75667	+	3.84657i	0.403007	+	0.882463i	−0.593949	+	0.804503i	$0.702432\pi$
$20$	0.341254	+	2.37347i	0.0763066	+	0.530724i
$21$	0.773100	+	0.496841i	0.168704	+	0.108420i
$22$	4.10769			0.875762
$23$	3.21727	+	3.55657i	0.670847	+	0.741596i
$23$	3.21727	+	3.55657i	0.670847	+	0.741596i
$24$	0.918986			0.187587
$25$	0.630785	+	0.405381i	0.126157	+	0.0810762i
$26$	−0.0961145	−	0.668491i	−0.0188496	−	0.131102i
$27$	1.96815	+	4.30965i	0.378771	+	0.829393i
$28$	0.959493	+	0.281733i	0.181327	+	0.0532424i
$29$	−0.445841	+	0.976256i	−0.0827906	+	0.181286i	−0.946500	−	0.322704i	$-0.895408\pi$
$29$	−0.445841	+	0.976256i	−0.0827906	+	0.181286i	0.863709	+	0.503990i	$0.168135\pi$
$30$	1.44306	−	1.66538i	0.263466	−	0.304056i
$31$	0.525092	−	3.65209i	0.0943093	−	0.655935i	−0.886753	−	0.462243i	$-0.847045\pi$
$31$	0.525092	−	3.65209i	0.0943093	−	0.655935i	0.981062	−	0.193692i	$-0.0620463\pi$
$32$	0.959493	−	0.281733i	0.169616	−	0.0498038i
$33$	−2.47204	−	2.85288i	−0.430327	−	0.496624i
$34$	−3.08538	+	1.98285i	−0.529138	+	0.340056i
$35$	2.01722	−	1.29639i	0.340973	−	0.219130i
$36$	1.41153	+	1.62899i	0.235255	+	0.271499i
$37$	8.25654	−	2.42434i	1.35737	−	0.398559i	0.479533	−	0.877524i	$-0.340806\pi$
$37$	8.25654	−	2.42434i	1.35737	−	0.398559i	0.877834	+	0.478965i	$0.158988\pi$
$38$	0.601808	−	4.18567i	0.0976261	−	0.679005i
$39$	−0.406440	+	0.469057i	−0.0650825	+	0.0751092i
$40$	0.996114	−	2.18119i	0.157499	−	0.344876i
$41$	−4.74788	−	1.39410i	−0.741494	−	0.217722i	−0.110896	−	0.993832i	$-0.535372\pi$
$41$	−4.74788	−	1.39410i	−0.741494	−	0.217722i	−0.630598	+	0.776110i	$0.717190\pi$
$42$	−0.381761	−	0.835939i	−0.0589069	−	0.128988i
$43$	−0.187094	−	1.30127i	−0.0285316	−	0.198442i	0.970570	−	0.240819i	$-0.0774160\pi$
$43$	−0.187094	−	1.30127i	−0.0285316	−	0.198442i	−0.999102	+	0.0423771i	$0.986507\pi$
$44$	−3.45561	−	2.22078i	−0.520952	−	0.334796i
$45$	5.16854			0.770481
$46$	−0.783711	−	4.73136i	−0.115552	−	0.697601i
$47$	−2.95001			−0.430303			−0.215152	−	0.976581i	$-0.569025\pi$
$47$	−2.95001			−0.430303			−0.215152	+	0.976581i	$0.569025\pi$
$48$	−0.773100	−	0.496841i	−0.111587	−	0.0717129i
$49$	−0.142315	−	0.989821i	−0.0203307	−	0.141403i
$50$	−0.311485	−	0.682057i	−0.0440506	−	0.0964574i
$51$	3.23394	+	0.949570i	0.452842	+	0.132966i
$52$	−0.280557	+	0.614334i	−0.0389062	+	0.0851928i
$53$	−7.47107	+	8.62207i	−1.02623	+	1.18433i	−0.0435444	+	0.999051i	$0.513865\pi$
$53$	−7.47107	+	8.62207i	−1.02623	+	1.18433i	−0.982686	+	0.185281i	$0.940680\pi$
$54$	0.674259	−	4.68958i	0.0917551	−	0.638170i
$55$	−9.45075	+	2.77499i	−1.27434	+	0.374180i
$56$	−0.654861	−	0.755750i	−0.0875094	−	0.100991i
$57$	−3.26921	+	2.10100i	−0.433018	+	0.278284i
$58$	0.902869	−	0.580239i	0.118553	−	0.0761891i
$59$	−2.85848	−	3.29886i	−0.372142	−	0.429475i	0.538529	−	0.842607i	$-0.318980\pi$
$59$	−2.85848	−	3.29886i	−0.372142	−	0.429475i	−0.910671	+	0.413132i	$0.864435\pi$
$60$	−2.11435	+	0.620830i	−0.272962	+	0.0801488i
$61$	0.699730	−	4.86673i	0.0895912	−	0.623121i	−0.894713	−	0.446641i	$-0.852620\pi$
$61$	0.699730	−	4.86673i	0.0895912	−	0.623121i	0.984304	−	0.176479i	$-0.0564709\pi$
$62$	−2.41621	+	2.78845i	−0.306858	+	0.354134i
$63$	0.895412	−	1.96068i	0.112811	−	0.247022i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	0.672741	+	1.47310i	0.0834432	+	0.182715i
$66$	0.537225	+	3.73648i	0.0661279	+	0.459929i
$67$	2.97001	+	1.90871i	0.362845	+	0.233186i	0.709342	−	0.704865i	$-0.248992\pi$
$67$	2.97001	+	1.90871i	0.362845	+	0.233186i	−0.346497	+	0.938051i	$0.612629\pi$
$68$	3.66759			0.444761
$69$	−2.81440	+	3.39168i	−0.338814	+	0.408310i
$70$	−2.39788			−0.286601
$71$	−4.59845	−	2.95525i	−0.545736	−	0.350723i	0.238543	−	0.971132i	$-0.423330\pi$
$71$	−4.59845	−	2.95525i	−0.545736	−	0.350723i	−0.784279	+	0.620409i	$0.786967\pi$
$72$	−0.306755	−	2.13353i	−0.0361514	−	0.251438i
$73$	−1.85763	−	4.06765i	−0.217419	−	0.476082i	0.769224	−	0.638980i	$-0.220643\pi$
$73$	−1.85763	−	4.06765i	−0.217419	−	0.476082i	−0.986643	+	0.162898i	$0.947916\pi$
$74$	−8.25654	−	2.42434i	−0.959803	−	0.281824i
$75$	−0.286250	+	0.626800i	−0.0330533	+	0.0723767i
$76$	−2.76921	+	3.19584i	−0.317651	+	0.366588i
$77$	−0.584585	+	4.06588i	−0.0666196	+	0.463350i
$78$	0.595510	−	0.174858i	0.0674283	−	0.0197987i
$79$	−7.31964	−	8.44732i	−0.823524	−	0.950398i	0.175897	−	0.984409i	$-0.443717\pi$
$79$	−7.31964	−	8.44732i	−0.823524	−	0.950398i	−0.999421	+	0.0340110i	$0.989172\pi$
$80$	−2.01722	+	1.29639i	−0.225532	+	0.144941i
$81$	1.77708	−	1.14206i	0.197454	−	0.126896i
$82$	3.24046	+	3.73969i	0.357849	+	0.412980i
$83$	−16.4238	+	4.82245i	−1.80274	+	0.529333i	−0.997937	−	0.0642052i	$-0.979549\pi$
$83$	−16.4238	+	4.82245i	−1.80274	+	0.529333i	−0.804806	+	0.593538i	$0.797731\pi$
$84$	−0.130785	+	0.909632i	−0.0142699	+	0.0992490i
$85$	5.75913	−	6.64639i	0.624666	−	0.720903i
$86$	−0.546126	+	1.19585i	−0.0588903	+	0.128952i
$87$	−0.946343	−	0.277871i	−0.101459	−	0.0297909i
$88$	1.70640	+	3.73648i	0.181902	+	0.398311i
$89$	−1.92745	−	13.4057i	−0.204310	−	1.42101i	−0.791308	−	0.611417i	$-0.790600\pi$
$89$	−1.92745	−	13.4057i	−0.204310	−	1.42101i	0.586998	−	0.809588i	$-0.300309\pi$
$90$	−4.34805	−	2.79432i	−0.458325	−	0.294548i
$91$	0.675365			0.0707975
$92$	−1.89867	+	4.40398i	−0.197950	+	0.459147i
$93$	3.39074			0.351603
$94$	2.48171	+	1.59490i	0.255969	+	0.164501i
$95$	1.44306	+	10.0367i	0.148055	+	1.02974i
$96$	0.381761	+	0.835939i	0.0389633	+	0.0853177i
$97$	7.13787	+	2.09587i	0.724741	+	0.212803i	0.623238	−	0.782032i	$-0.285817\pi$
$97$	7.13787	+	2.09587i	0.724741	+	0.212803i	0.101503	+	0.994835i	$0.467635\pi$
$98$	−0.415415	+	0.909632i	−0.0419633	+	0.0918867i
$99$	−5.79812	+	6.69139i	−0.582733	+	0.672510i
$100$	−0.106710	+	0.742184i	−0.0106710	+	0.0742184i
$101$	−16.3844	+	4.81091i	−1.63031	+	0.478703i	−0.963764	−	0.266757i	$-0.914048\pi$
$101$	−16.3844	+	4.81091i	−1.63031	+	0.478703i	−0.666550	+	0.745461i	$0.732230\pi$
$102$	−2.20719	−	2.54723i	−0.218544	−	0.252213i
$103$	−1.56061	+	1.00294i	−0.153771	+	0.0988227i	−0.615264	−	0.788321i	$-0.710950\pi$
$103$	−1.56061	+	1.00294i	−0.153771	+	0.0988227i	0.461493	+	0.887144i	$0.347314\pi$
$104$	0.568153	−	0.365130i	0.0557120	−	0.0358039i
$105$	1.44306	+	1.66538i	0.140828	+	0.162525i
$106$	10.9465	−	3.21418i	1.06322	−	0.312189i
$107$	2.24926	−	15.6440i	0.217444	−	1.51236i	−0.529980	−	0.848010i	$-0.677800\pi$
$107$	2.24926	−	15.6440i	0.217444	−	1.51236i	0.747424	−	0.664348i	$-0.231291\pi$
$108$	−3.10260	+	3.58059i	−0.298548	+	0.344542i
$109$	5.63866	−	12.3469i	0.540086	−	1.18262i	−0.421174	−	0.906980i	$-0.638382\pi$
$109$	5.63866	−	12.3469i	0.540086	−	1.18262i	0.961260	−	0.275643i	$-0.0888908\pi$
$110$	9.45075	+	2.77499i	0.901094	+	0.264585i
$111$	3.28509	+	7.19335i	0.311807	+	0.682762i
$112$	0.142315	+	0.989821i	0.0134475	+	0.0935293i
$113$	5.16236	+	3.31765i	0.485634	+	0.312098i	0.760447	−	0.649400i	$-0.224980\pi$
$113$	5.16236	+	3.31765i	0.485634	+	0.312098i	−0.274813	+	0.961498i	$0.588616\pi$
$114$	3.88612			0.363969
$115$	4.99944	+	10.3562i	0.466200	+	0.965723i
$116$	−1.07324			−0.0996481
$117$	1.22463	+	0.787025i	0.113218	+	0.0727605i
$118$	0.621206	+	4.32058i	0.0571867	+	0.397742i
$119$	−1.52357	−	3.33616i	−0.139666	−	0.305825i
$120$	2.11435	+	0.620830i	0.193013	+	0.0566738i
$121$	2.43978	−	5.34236i	0.221798	−	0.485669i
$122$	−3.21980	+	3.71585i	−0.291507	+	0.336417i
$123$	0.647168	−	4.50115i	0.0583532	−	0.405855i
$124$	3.54019	−	1.03949i	0.317919	−	0.0933493i
$125$	−6.67396	−	7.70216i	−0.596937	−	0.688902i
$126$	−1.81329	+	1.16533i	−0.161541	+	0.103816i
$127$	8.50112	−	5.46334i	0.754352	−	0.484793i	−0.106080	−	0.994358i	$-0.533830\pi$
$127$	8.50112	−	5.46334i	0.754352	−	0.484793i	0.860432	+	0.509565i	$0.170194\pi$
$128$	0.654861	+	0.755750i	0.0578821	+	0.0667995i
$129$	1.15921	−	0.340374i	0.102063	−	0.0299683i
$130$	0.230471	−	1.60296i	0.0202136	−	0.140589i
$131$	2.63422	−	3.04005i	0.230153	−	0.265611i	−0.628913	−	0.777476i	$-0.716500\pi$
$131$	2.63422	−	3.04005i	0.230153	−	0.265611i	0.859066	+	0.511865i	$0.171045\pi$
$132$	1.56815	−	3.43378i	0.136490	−	0.298872i
$133$	4.05742	+	1.19136i	0.351823	+	0.103304i
$134$	−1.46661	−	3.21142i	−0.126696	−	0.277425i
$135$	1.61679	+	11.2450i	0.139151	+	0.967818i
$136$	−3.08538	−	1.98285i	−0.264569	−	0.170028i
$137$	−7.56840			−0.646612			−0.323306	−	0.946295i	$-0.604794\pi$
$137$	−7.56840			−0.646612			−0.323306	+	0.946295i	$0.604794\pi$
$138$	4.20130	−	1.33168i	0.357639	−	0.113360i
$139$	−15.7758			−1.33808			−0.669042	−	0.743225i	$-0.733295\pi$
$139$	−15.7758			−1.33808			−0.669042	+	0.743225i	$0.733295\pi$
$140$	2.01722	+	1.29639i	0.170486	+	0.109565i
$141$	−0.385818	−	2.68342i	−0.0324918	−	0.225985i
$142$	2.27074	+	4.97222i	0.190556	+	0.417260i
$143$	−2.66182	−	0.781580i	−0.222592	−	0.0653590i
$144$	−0.895412	+	1.96068i	−0.0746177	+	0.163390i
$145$	−1.68529	+	1.94492i	−0.139955	+	0.161517i
$146$	−0.636396	+	4.42623i	−0.0526685	+	0.366318i
$147$	0.881761	−	0.258908i	0.0727264	−	0.0213544i
$148$	5.63515	+	6.50331i	0.463206	+	0.534569i
$149$	11.3073	−	7.26676i	0.926330	−	0.595316i	0.0118421	−	0.999930i	$-0.496230\pi$
$149$	11.3073	−	7.26676i	0.926330	−	0.595316i	0.914488	+	0.404614i	$0.132594\pi$
$150$	0.579683	−	0.372540i	0.0473309	−	0.0304177i
$151$	10.6288	+	12.2663i	0.864960	+	0.998217i	0.999973	+	0.00737306i	$0.00234694\pi$
$151$	10.6288	+	12.2663i	0.864960	+	0.998217i	−0.135013	+	0.990844i	$0.543108\pi$
$152$	4.05742	−	1.19136i	0.329100	−	0.0966324i
$153$	1.12505	−	7.82490i	0.0909550	−	0.632606i
$154$	2.68996	−	3.10438i	0.216763	−	0.250158i
$155$	3.67531	−	8.04781i	0.295208	−	0.646416i
$156$	−0.595510	−	0.174858i	−0.0476790	−	0.0139998i
$157$	2.14382	+	4.69432i	0.171096	+	0.374648i	0.975683	−	0.219187i	$-0.0703406\pi$
$157$	2.14382	+	4.69432i	0.171096	+	0.374648i	−0.804587	+	0.593835i	$0.797613\pi$
$158$	1.59071	+	11.0636i	0.126550	+	0.880175i
$159$	−8.82002	−	5.66828i	−0.699473	−	0.449524i
$160$	2.39788			0.189569
$161$	4.79474	−	0.102391i	0.377878	−	0.00806951i
$162$	−2.11242			−0.165968
$163$	10.0169	+	6.43748i	0.784585	+	0.504222i	0.870552	−	0.492076i	$-0.163762\pi$
$163$	10.0169	+	6.43748i	0.784585	+	0.504222i	−0.0859671	+	0.996298i	$0.527398\pi$
$164$	−0.704220	−	4.89796i	−0.0549903	−	0.382466i
$165$	−3.76024	−	8.23378i	−0.292734	−	0.640999i
$166$	16.4238	+	4.82245i	1.27473	+	0.374295i
$167$	6.02961	−	13.2030i	0.466585	−	1.02168i	−0.519352	−	0.854561i	$-0.673827\pi$
$167$	6.02961	−	13.2030i	0.466585	−	1.02168i	0.985937	−	0.167118i	$-0.0534462\pi$
$168$	0.601808	−	0.694523i	0.0464305	−	0.0535836i
$169$	1.78518	−	12.4162i	0.137322	−	0.955093i
$170$	−8.43820	+	2.47768i	−0.647181	+	0.190029i
$171$	5.96894	+	6.88853i	0.456457	+	0.526779i
$172$	1.10596	−	0.710754i	0.0843283	−	0.0541945i
$173$	−9.63976	+	6.19510i	−0.732897	+	0.471004i	−0.853102	−	0.521745i	$-0.825281\pi$
$173$	−9.63976	+	6.19510i	−0.732897	+	0.471004i	0.120204	+	0.992749i	$0.461645\pi$
$174$	0.645886	+	0.745392i	0.0489645	+	0.0565080i
$175$	0.719443	−	0.211248i	0.0543848	−	0.0159688i
$176$	0.584585	−	4.06588i	0.0440648	−	0.306477i
$177$	2.62690	−	3.03160i	0.197450	−	0.227869i
$178$	−5.62621	+	12.3197i	−0.421702	+	0.923400i
$179$	9.03335	+	2.65243i	0.675184	+	0.198252i	0.601310	−	0.799016i	$-0.294646\pi$
$179$	9.03335	+	2.65243i	0.675184	+	0.198252i	0.0738738	+	0.997268i	$0.476464\pi$
$180$	2.14709	+	4.70147i	0.160035	+	0.350427i
$181$	2.28347	+	15.8819i	0.169729	+	1.18049i	0.879443	+	0.476004i	$0.157915\pi$
$181$	2.28347	+	15.8819i	0.169729	+	1.18049i	−0.709714	+	0.704490i	$0.751176\pi$
$182$	−0.568153	−	0.365130i	−0.0421143	−	0.0270652i
$183$	4.51845			0.334013
$184$	3.97823	−	2.67837i	0.293279	−	0.197452i
$185$	20.6340			1.51704
$186$	−2.85247	−	1.83317i	−0.209153	−	0.134415i
$187$	2.14402	+	14.9120i	0.156786	+	1.09047i
$188$	−1.22548	−	2.68342i	−0.0893772	−	0.195709i
$189$	4.54589	+	1.33479i	0.330665	+	0.0970919i
$190$	4.21228	−	9.22360i	0.305591	−	0.669150i
$191$	−8.13325	+	9.38627i	−0.588501	+	0.679167i	−0.969410	−	0.245446i	$-0.921066\pi$
$191$	−8.13325	+	9.38627i	−0.588501	+	0.679167i	0.380909	+	0.924613i	$0.375611\pi$
$192$	0.130785	−	0.909632i	0.00943862	−	0.0656470i
$193$	−3.03327	+	0.890647i	−0.218339	+	0.0641102i	−0.389073	−	0.921207i	$-0.627205\pi$
$193$	−3.03327	+	0.890647i	−0.218339	+	0.0641102i	0.170733	+	0.985317i	$0.445386\pi$
$194$	−4.87165	−	5.62218i	−0.349764	−	0.403649i
$195$	−1.25199	+	0.804606i	−0.0896570	+	0.0576190i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	10.8149	+	12.4811i	0.770530	+	0.889239i	0.996388	−	0.0849214i	$-0.0270639\pi$
$197$	10.8149	+	12.4811i	0.770530	+	0.889239i	−0.225858	+	0.974160i	$0.572518\pi$
$198$	8.49533	−	2.49445i	0.603737	−	0.177273i
$199$	0.298639	−	2.07708i	0.0211700	−	0.147240i	−0.976495	−	0.215541i	$-0.930849\pi$
$199$	0.298639	−	2.07708i	0.0211700	−	0.147240i	0.997665	+	0.0683004i	$0.0217576\pi$
$200$	0.491025	−	0.566673i	0.0347207	−	0.0400698i
$201$	−1.34779	+	2.95125i	−0.0950659	+	0.208165i
$202$	16.3844	+	4.81091i	1.15281	+	0.338494i
$203$	0.445841	+	0.976256i	0.0312919	+	0.0685197i
$204$	0.479667	+	3.33616i	0.0335834	+	0.233578i
$205$	−9.98187	−	6.41496i	−0.697164	−	0.448040i
$206$	1.85510			0.129251
$207$	8.81358	+	5.40180i	0.612586	+	0.375451i
$208$	−0.675365			−0.0468282
$209$	−14.6128	−	9.39105i	−1.01079	−	0.649592i
$210$	−0.313607	−	2.18119i	−0.0216410	−	0.150516i
$211$	−9.82295	−	21.5093i	−0.676240	−	1.48076i	−0.866579	−	0.499040i	$-0.833686\pi$
$211$	−9.82295	−	21.5093i	−0.676240	−	1.48076i	0.190339	−	0.981718i	$-0.439041\pi$
$212$	−10.9465	−	3.21418i	−0.751809	−	0.220751i
$213$	2.08678	−	4.56940i	0.142984	−	0.313090i
$214$	−10.3500	+	11.9445i	−0.707509	+	0.816508i
$215$	0.448629	−	3.12029i	0.0305963	−	0.212802i
$216$	4.54589	−	1.33479i	0.309308	−	0.0908211i
$217$	−2.41621	−	2.78845i	−0.164023	−	0.189292i
$218$	−11.4188	+	7.33842i	−0.773379	+	0.497021i
$219$	3.45711	−	2.22175i	0.233610	−	0.150132i
$220$	−6.45020	−	7.44393i	−0.434873	−	0.501870i
$221$	2.37663	−	0.697842i	0.159869	−	0.0469419i
$222$	1.12542	−	7.82748i	0.0755334	−	0.525346i
$223$	−7.96383	+	9.19075i	−0.533298	+	0.615458i	−0.956910	−	0.290385i	$-0.906217\pi$
$223$	−7.96383	+	9.19075i	−0.533298	+	0.615458i	0.423612	+	0.905844i	$0.360762\pi$
$224$	0.415415	−	0.909632i	0.0277561	−	0.0607773i
$225$	1.55073	+	0.455337i	0.103382	+	0.0303558i
$226$	−2.54920	−	5.58197i	−0.169570	−	0.371307i
$227$	1.23312	+	8.57654i	0.0818451	+	0.569245i	0.988940	+	0.148318i	$0.0473860\pi$
$227$	1.23312	+	8.57654i	0.0818451	+	0.569245i	−0.907095	+	0.420927i	$0.861705\pi$
$228$	−3.26921	−	2.10100i	−0.216509	−	0.139142i
$229$	−20.9606			−1.38512			−0.692558	−	0.721362i	$-0.743516\pi$
$229$	−20.9606			−1.38512			−0.692558	+	0.721362i	$0.743516\pi$
$230$	1.39320	−	11.4151i	0.0918649	−	0.752690i
$231$	−3.77491			−0.248371
$232$	0.902869	+	0.580239i	0.0592763	+	0.0380945i
$233$	2.98504	+	20.7614i	0.195556	+	1.36012i	0.816988	+	0.576655i	$0.195642\pi$
$233$	2.98504	+	20.7614i	0.195556	+	1.36012i	−0.621431	+	0.783469i	$0.713448\pi$
$234$	−0.604730	−	1.32417i	−0.0395325	−	0.0865640i
$235$	−6.78723	−	1.99291i	−0.442750	−	0.130003i
$236$	1.81329	−	3.97056i	0.118035	−	0.258461i
$237$	6.72665	−	7.76297i	0.436943	−	0.504259i
$238$	−0.521953	+	3.63026i	−0.0338332	+	0.235315i
$239$	−27.5160	+	8.07943i	−1.77986	+	0.522615i	−0.995248	−	0.0973681i	$-0.968958\pi$
$239$	−27.5160	+	8.07943i	−1.77986	+	0.522615i	−0.784615	+	0.619983i	$0.787139\pi$
$240$	−1.44306	−	1.66538i	−0.0931492	−	0.107500i
$241$	5.04396	−	3.24156i	0.324910	−	0.208807i	−0.368009	−	0.929822i	$-0.619961\pi$
$241$	5.04396	−	3.24156i	0.324910	−	0.208807i	0.692919	+	0.721015i	$0.256324\pi$
$242$	−4.94077	+	3.17524i	−0.317605	+	0.204112i
$243$	10.5791	+	12.2089i	0.678648	+	0.783201i
$244$	4.71761	−	1.38522i	0.302014	−	0.0886793i
$245$	0.341254	−	2.37347i	0.0218019	−	0.151635i
$246$	−2.97794	+	3.43672i	−0.189866	+	0.219118i
$247$	−1.18639	+	2.59784i	−0.0754884	+	0.165296i
$248$	−3.54019	−	1.03949i	−0.224802	−	0.0660079i
$249$	−6.53465	−	14.3089i	−0.414116	−	0.906788i
$250$	1.45039	+	10.0877i	0.0917307	+	0.638001i
$251$	18.1802	+	11.6837i	1.14752	+	0.737469i	0.969145	−	0.246493i	$-0.0792782\pi$
$251$	18.1802	+	11.6837i	1.14752	+	0.737469i	0.178380	+	0.983962i	$0.442915\pi$
$252$	2.15546			0.135782
$253$	−19.0160	−	5.14525i	−1.19552	−	0.323479i
$254$	−10.1053			−0.634063
$255$	6.79898	+	4.36944i	0.425769	+	0.273625i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−0.600210	−	1.31428i	−0.0374401	−	0.0819824i	0.889988	−	0.455984i	$-0.150713\pi$
$257$	−0.600210	−	1.31428i	−0.0374401	−	0.0819824i	−0.927428	+	0.374002i	$0.877985\pi$
$258$	−1.15921	−	0.340374i	−0.0721691	−	0.0211908i
$259$	3.57469	−	7.82748i	0.222120	−	0.486376i
$260$	−1.06051	+	1.22389i	−0.0657700	+	0.0759026i
$261$	−0.329222	+	2.28979i	−0.0203783	+	0.141734i
$262$	−3.85963	+	1.13329i	−0.238449	+	0.0700148i
$263$	−0.729441	−	0.841819i	−0.0449792	−	0.0519088i	0.732814	−	0.680429i	$-0.238206\pi$
$263$	−0.729441	−	0.841819i	−0.0449792	−	0.0519088i	−0.777793	+	0.628520i	$0.783661\pi$
$264$	−3.17565	+	2.04087i	−0.195448	+	0.125607i
$265$	−23.0138	+	14.7900i	−1.41372	+	0.908545i
$266$	−2.76921	−	3.19584i	−0.169791	−	0.195950i
$267$	11.9422	−	3.50655i	0.730851	−	0.214597i
$268$	−0.502437	+	3.49453i	−0.0306912	+	0.213462i
$269$	−9.27793	+	10.7073i	−0.565686	+	0.652836i	−0.964465	−	0.264211i	$-0.914888\pi$
$269$	−9.27793	+	10.7073i	−0.565686	+	0.652836i	0.398779	+	0.917047i	$0.369434\pi$
$270$	4.71939	−	10.3340i	0.287213	−	0.628909i
$271$	−28.6766	−	8.42020i	−1.74198	−	0.511490i	−0.752804	−	0.658245i	$-0.771299\pi$
$271$	−28.6766	−	8.42020i	−1.74198	−	0.511490i	−0.989173	+	0.146755i	$0.953117\pi$
$272$	1.52357	+	3.33616i	0.0923802	+	0.202284i
$273$	0.0883279	+	0.614334i	0.00534585	+	0.0371812i
$274$	6.36694	+	4.09178i	0.384641	+	0.247194i
$275$	−3.08001			−0.185732
$276$	−4.25432	−	1.15111i	−0.256080	−	0.0692889i
$277$	−8.64999			−0.519727			−0.259864	−	0.965645i	$-0.583678\pi$
$277$	−8.64999			−0.519727			−0.259864	+	0.965645i	$0.583678\pi$
$278$	13.2714	+	8.52903i	0.795967	+	0.511537i
$279$	−1.13182	−	7.87196i	−0.0677601	−	0.471282i
$280$	−0.996114	−	2.18119i	−0.0595292	−	0.130351i
$281$	27.6375	+	8.11509i	1.64871	+	0.484106i	0.968522	−	0.248929i	$-0.0800787\pi$
$281$	27.6375	+	8.11509i	1.64871	+	0.484106i	0.680191	+	0.733035i	$0.261897\pi$
$282$	−1.12620	+	2.46603i	−0.0670641	+	0.146850i
$283$	7.05901	−	8.14653i	0.419615	−	0.484261i	−0.506105	−	0.862472i	$-0.668915\pi$
$283$	7.05901	−	8.14653i	0.419615	−	0.484261i	0.925719	+	0.378211i	$0.123461\pi$
$284$	0.777920	−	5.41055i	0.0461611	−	0.321057i
$285$	−8.94098	+	2.62531i	−0.529618	+	0.155510i
$286$	1.81671	+	2.09659i	0.107424	+	0.123974i
$287$	−4.16279	+	2.67527i	−0.245722	+	0.157916i
$288$	1.81329	−	1.16533i	0.106849	−	0.0686679i
$289$	2.32394	+	2.68197i	0.136702	+	0.157763i
$290$	2.46926	−	0.725040i	0.145000	−	0.0425758i
$291$	−0.972940	+	6.76694i	−0.0570347	+	0.396685i
$292$	2.92837	−	3.37952i	0.171370	−	0.197772i
$293$	13.6363	−	29.8594i	0.796644	−	1.74441i	0.140074	−	0.990141i	$-0.455266\pi$
$293$	13.6363	−	29.8594i	0.796644	−	1.74441i	0.656570	−	0.754265i	$-0.272007\pi$
$294$	−0.881761	−	0.258908i	−0.0514253	−	0.0150998i
$295$	−4.34805	−	9.52091i	−0.253153	−	0.554329i
$296$	−1.22463	−	8.51752i	−0.0711804	−	0.495071i
$297$	−16.3720	−	10.5216i	−0.949998	−	0.610527i
$298$	−13.4410			−0.778617
$299$	−0.392397	+	3.21508i	−0.0226929	+	0.185933i
$300$	−0.689070			−0.0397835
$301$	−1.10596	−	0.710754i	−0.0637462	−	0.0409672i
$302$	−2.30986	−	16.0654i	−0.132918	−	0.924462i
$303$	−6.51900	−	14.2746i	−0.374507	−	0.820056i
$304$	−4.05742	−	1.19136i	−0.232709	−	0.0683294i
$305$	4.89767	−	10.7244i	0.280440	−	0.614077i
$306$	−5.17692	+	5.97448i	−0.295945	+	0.341538i
$307$	−0.0650272	+	0.452274i	−0.00371130	+	0.0258126i	−0.991593	−	0.129396i	$-0.958696\pi$
$307$	−0.0650272	+	0.452274i	−0.00371130	+	0.0258126i	0.987882	+	0.155209i	$0.0496051\pi$
$308$	−3.94130	+	1.15727i	−0.224576	+	0.0659416i
$309$	−1.11641	−	1.28841i	−0.0635105	−	0.0732950i
$310$	−7.44284	+	4.78323i	−0.422725	+	0.271669i
$311$	−26.1401	+	16.7992i	−1.48227	+	0.952595i	−0.485334	+	0.874329i	$0.661302\pi$
$311$	−26.1401	+	16.7992i	−1.48227	+	0.952595i	−0.996933	+	0.0782659i	$0.975062\pi$
$312$	0.406440	+	0.469057i	0.0230101	+	0.0265551i
$313$	19.1893	−	5.63449i	1.08464	−	0.318480i	0.309909	−	0.950766i	$-0.399702\pi$
$313$	19.1893	−	5.63449i	1.08464	−	0.318480i	0.774735	+	0.632286i	$0.217883\pi$
$314$	0.734441	−	5.10815i	0.0414469	−	0.288270i
$315$	3.38467	−	3.90612i	0.190705	−	0.220085i
$316$	4.64326	−	10.1673i	0.261204	−	0.571957i
$317$	−3.02502	−	0.888227i	−0.169902	−	0.0498878i	0.195675	−	0.980669i	$-0.437310\pi$
$317$	−3.02502	−	0.888227i	−0.169902	−	0.0498878i	−0.365577	+	0.930781i	$0.619128\pi$
$318$	4.35537	+	9.53692i	0.244237	+	0.534804i
$319$	−0.627402	−	4.36367i	−0.0351277	−	0.244319i
$320$	−2.01722	−	1.29639i	−0.112766	−	0.0724704i
$321$	14.5244			0.810674
$322$	−4.08895	−	2.50609i	−0.227868	−	0.139659i
$323$	15.5092			0.862954
$324$	1.77708	+	1.14206i	0.0987269	+	0.0634479i
$325$	0.0720682	+	0.501245i	0.00399762	+	0.0278041i
$326$	−4.94640	−	10.8311i	−0.273956	−	0.599880i
$327$	11.9686	+	3.51431i	0.661867	+	0.194342i
$328$	−2.05561	+	4.50115i	−0.113502	+	0.248535i
$329$	−1.93185	+	2.22947i	−0.106506	+	0.122915i
$330$	−1.28820	+	8.95963i	−0.0709131	+	0.493212i
$331$	1.65132	−	0.484872i	0.0907649	−	0.0266510i	−0.236035	−	0.971745i	$-0.575848\pi$
$331$	1.65132	−	0.484872i	0.0907649	−	0.0266510i	0.326800	+	0.945094i	$0.394030\pi$
$332$	−11.2093	−	12.9363i	−0.615192	−	0.709970i
$333$	15.6036	−	10.0278i	0.855071	−	0.549521i
$334$	−12.2105	+	7.84722i	−0.668130	+	0.429381i
$335$	5.54380	+	6.39789i	0.302890	+	0.349554i
$336$	−0.881761	+	0.258908i	−0.0481040	+	0.0141246i
$337$	−4.67997	+	32.5499i	−0.254934	+	1.77311i	0.312724	+	0.949844i	$0.398758\pi$
$337$	−4.67997	+	32.5499i	−0.254934	+	1.77311i	−0.567659	+	0.823264i	$0.692151\pi$
$338$	−8.21450	+	9.48003i	−0.446810	+	0.515646i
$339$	−2.34268	+	5.12975i	−0.127237	+	0.278610i
$340$	8.43820	+	2.47768i	0.457626	+	0.134371i
$341$	6.29600	+	13.7863i	0.340948	+	0.746571i
$342$	−1.29718	−	9.02205i	−0.0701432	−	0.487857i
$343$	−0.841254	−	0.540641i	−0.0454234	−	0.0291919i
$344$	−1.31465			−0.0708813
$345$	−8.76650	+	5.90209i	−0.471972	+	0.317758i
$346$	11.4588			0.616029
$347$	16.4679	+	10.5833i	0.884045	+	0.568141i	0.902019	−	0.431697i	$-0.142085\pi$
$347$	16.4679	+	10.5833i	0.884045	+	0.568141i	−0.0179736	+	0.999838i	$0.505721\pi$
$348$	−0.140364	−	0.976256i	−0.00752432	−	0.0523328i
$349$	−3.11700	−	6.82528i	−0.166849	−	0.365349i	0.807676	−	0.589627i	$-0.200725\pi$
$349$	−3.11700	−	6.82528i	−0.166849	−	0.365349i	−0.974525	+	0.224278i	$0.927998\pi$
$350$	−0.719443	−	0.211248i	−0.0384559	−	0.0112917i
$351$	−1.32922	+	2.91059i	−0.0709486	+	0.155356i
$352$	−2.68996	+	3.10438i	−0.143376	+	0.165464i
$353$	0.229590	−	1.59683i	0.0122198	−	0.0849909i	−0.982799	−	0.184679i	$-0.940875\pi$
$353$	0.229590	−	1.59683i	0.0122198	−	0.0849909i	0.995019	+	0.0996882i	$0.0317845\pi$
$354$	−3.84890	+	1.13014i	−0.204567	+	0.0600662i
$355$	−8.58343	−	9.90580i	−0.455561	−	0.525745i
$356$	11.3936	−	7.32222i	0.603859	−	0.388077i
$357$	2.83542	−	1.82221i	0.150066	−	0.0964417i
$358$	−6.16532	−	7.11516i	−0.325847	−	0.376048i
$359$	3.51990	−	1.03354i	0.185773	−	0.0545480i	−0.187523	−	0.982260i	$-0.560046\pi$
$359$	3.51990	−	1.03354i	0.185773	−	0.0545480i	0.373296	+	0.927712i	$0.378228\pi$
$360$	0.735560	−	5.11593i	0.0387674	−	0.269633i
$361$	0.732156	−	0.844953i	0.0385345	−	0.0444712i
$362$	6.66543	−	14.5953i	0.350327	−	0.767110i
$363$	5.17867	+	1.52059i	0.271810	+	0.0798105i
$364$	0.280557	+	0.614334i	0.0147052	+	0.0321998i
$365$	−1.52600	−	10.6136i	−0.0798745	−	0.555539i
$366$	−3.80116	−	2.44286i	−0.198690	−	0.127690i
$367$	15.1579			0.791238			0.395619	−	0.918415i	$-0.370530\pi$
$367$	15.1579			0.791238			0.395619	+	0.918415i	$0.370530\pi$
$368$	−4.79474	+	0.102391i	−0.249943	+	0.00533748i
$369$	−10.6659			−0.555246
$370$	−17.3584	−	11.1556i	−0.902421	−	0.579951i
$371$	1.62362	+	11.2925i	0.0842940	+	0.586278i
$372$	1.40856	+	3.08432i	0.0730306	+	0.159915i
$373$	27.4879	+	8.07116i	1.42327	+	0.417909i	0.900608	−	0.434632i	$-0.143122\pi$
$373$	27.4879	+	8.07116i	1.42327	+	0.417909i	0.522660	+	0.852542i	$0.324940\pi$
$374$	6.25836	−	13.7039i	0.323612	−	0.708612i
$375$	6.13328	−	7.07818i	0.316721	−	0.365516i
$376$	−0.419830	+	2.91998i	−0.0216511	+	0.150587i
$377$	−0.695470	+	0.204208i	−0.0358185	+	0.0105173i
$378$	−3.10260	−	3.58059i	−0.159580	−	0.184166i
$379$	−11.4489	+	7.35778i	−0.588092	+	0.377944i	−0.800585	−	0.599219i	$-0.795478\pi$
$379$	−11.4489	+	7.35778i	−0.588092	+	0.377944i	0.212493	+	0.977163i	$0.431842\pi$
$380$	−8.53025	+	5.48206i	−0.437592	+	0.281224i
$381$	6.08145	+	7.01836i	0.311562	+	0.359562i
$382$	11.9167	−	3.49907i	0.609713	−	0.179028i
$383$	3.49223	−	24.2890i	0.178445	−	1.24111i	−0.681918	−	0.731429i	$-0.738854\pi$
$383$	3.49223	−	24.2890i	0.178445	−	1.24111i	0.860363	−	0.509682i	$-0.170237\pi$
$384$	−0.601808	+	0.694523i	−0.0307109	+	0.0354422i
$385$	−4.09173	+	8.95963i	−0.208534	+	0.456625i
$386$	3.03327	+	0.890647i	0.154389	+	0.0453328i
$387$	−1.17716	−	2.57761i	−0.0598382	−	0.131027i
$388$	1.05871	+	7.36349i	0.0537479	+	0.373825i
$389$	17.9965	+	11.5656i	0.912457	+	0.586401i	0.910460	−	0.413597i	$-0.135728\pi$
$389$	17.9965	+	11.5656i	0.912457	+	0.586401i	0.00199737	+	0.999998i	$0.499364\pi$
$390$	1.48825			0.0753602
$391$	16.7670	−	5.31463i	0.847945	−	0.268772i
$392$	−1.00000			−0.0505076
$393$	3.10985	+	1.99858i	0.156871	+	0.100815i
$394$	−2.35030	−	16.3467i	−0.118407	−	0.823536i
$395$	−11.1340	−	24.3800i	−0.560211	−	1.22669i
$396$	−8.49533	−	2.49445i	−0.426906	−	0.125351i
$397$	−12.8266	+	28.0864i	−0.643749	+	1.40961i	0.253171	+	0.967421i	$0.418526\pi$
$397$	−12.8266	+	28.0864i	−0.643749	+	1.40961i	−0.896920	+	0.442192i	$0.854201\pi$
$398$	−1.37419	+	1.58590i	−0.0688817	+	0.0794938i
$399$	−0.553053	+	3.84657i	−0.0276873	+	0.192569i
$400$	−0.719443	+	0.211248i	−0.0359722	+	0.0105624i
$401$	1.60534	+	1.85266i	0.0801670	+	0.0925176i	0.794416	−	0.607374i	$-0.207777\pi$
$401$	1.60534	+	1.85266i	0.0801670	+	0.0925176i	−0.714249	+	0.699892i	$0.753232\pi$
$402$	2.72940	−	1.75408i	0.136130	−	0.0874855i
$403$	2.09629	−	1.34720i	0.104423	−	0.0671089i
$404$	−11.1825	−	12.9053i	−0.556350	−	0.642062i
$405$	4.86015	−	1.42707i	0.241503	−	0.0709116i
$406$	0.152738	−	1.06232i	0.00758028	−	0.0527220i
$407$	−23.1474	+	26.7136i	−1.14738	+	1.32414i
$408$	1.40014	−	3.06588i	0.0693174	−	0.151784i
$409$	7.67363	+	2.25318i	0.379436	+	0.111413i	0.465888	−	0.884843i	$-0.345735\pi$
$409$	7.67363	+	2.25318i	0.379436	+	0.111413i	−0.0864521	+	0.996256i	$0.527553\pi$
$410$	4.92909	+	10.7932i	0.243431	+	0.533039i
$411$	−0.989835	−	6.88445i	−0.0488250	−	0.339585i
$412$	−1.56061	−	1.00294i	−0.0768856	−	0.0494114i
$413$	−4.36501			−0.214788
$414$	−4.49402	−	9.30926i	−0.220869	−	0.457525i
$415$	−41.0448			−2.01481
$416$	0.568153	+	0.365130i	0.0278560	+	0.0179020i
$417$	−2.06324	−	14.3501i	−0.101037	−	0.702730i
$418$	7.21585	+	15.8005i	0.352939	+	0.772828i
$419$	32.9986	+	9.68926i	1.61209	+	0.473351i	0.958876	−	0.283825i	$-0.0916036\pi$
$419$	32.9986	+	9.68926i	1.61209	+	0.473351i	0.653210	+	0.757177i	$0.273422\pi$
$420$	−0.915415	+	2.00448i	−0.0446677	+	0.0978086i
$421$	−18.4149	+	21.2519i	−0.897487	+	1.03576i	0.101675	+	0.994818i	$0.467580\pi$
$421$	−18.4149	+	21.2519i	−0.897487	+	1.03576i	−0.999162	+	0.0409377i	$0.986965\pi$
$422$	−3.36519	+	23.4054i	−0.163815	+	1.13936i
$423$	−6.10108	+	1.79144i	−0.296644	+	0.0871027i
$424$	7.47107	+	8.62207i	0.362827	+	0.418725i
$425$	2.31346	−	1.48677i	0.112220	−	0.0721191i
$426$	−4.22591	+	2.71583i	−0.204746	+	0.131582i
$427$	−3.21980	−	3.71585i	−0.155817	−	0.179823i
$428$	15.1646	−	4.45273i	0.733009	−	0.215231i
$429$	0.362823	−	2.52349i	0.0175173	−	0.121835i
$430$	−2.06437	+	2.38240i	−0.0995525	+	0.114890i
$431$	7.49930	−	16.4212i	0.361229	−	0.790980i	−0.638542	−	0.769587i	$-0.720462\pi$
$431$	7.49930	−	16.4212i	0.361229	−	0.790980i	0.999771	−	0.0213939i	$-0.00681039\pi$
$432$	−4.54589	−	1.33479i	−0.218714	−	0.0642202i
$433$	0.0695992	+	0.152401i	0.00334473	+	0.00732393i	0.911297	−	0.411750i	$-0.135082\pi$
$433$	0.0695992	+	0.152401i	0.00334473	+	0.00732393i	−0.907952	+	0.419074i	$0.862355\pi$
$434$	0.525092	+	3.65209i	0.0252052	+	0.175306i
$435$	−1.98958	−	1.27862i	−0.0953929	−	0.0613053i
$436$	13.5736			0.650056
$437$	−8.02891	+	18.6232i	−0.384075	+	0.890866i
$438$	−4.10948			−0.196358
$439$	−16.0057	−	10.2862i	−0.763910	−	0.490935i	0.0997482	−	0.995013i	$-0.468196\pi$
$439$	−16.0057	−	10.2862i	−0.763910	−	0.490935i	−0.863659	+	0.504077i	$0.831833\pi$
$440$	1.40176	+	9.74948i	0.0668264	+	0.464788i
$441$	−0.895412	−	1.96068i	−0.0426387	−	0.0933657i
$442$	−2.37663	−	0.697842i	−0.113045	−	0.0331929i
$443$	−2.91621	+	6.38561i	−0.138553	+	0.303389i	−0.966171	−	0.257903i	$-0.916968\pi$
$443$	−2.91621	+	6.38561i	−0.138553	+	0.303389i	0.827618	+	0.561292i	$0.189696\pi$
$444$	−5.17862	+	5.97645i	−0.245766	+	0.283630i
$445$	4.62180	−	32.1453i	0.219094	−	1.52383i
$446$	11.6685	−	3.42618i	0.552519	−	0.162234i
$447$	8.08890	+	9.33509i	0.382592	+	0.441535i
$448$	−0.841254	+	0.540641i	−0.0397455	+	0.0255429i
$449$	3.45620	−	2.22117i	0.163108	−	0.104823i	−0.456540	−	0.889703i	$-0.650912\pi$
$449$	3.45620	−	2.22117i	0.163108	−	0.104823i	0.619648	+	0.784879i	$0.287275\pi$
$450$	−1.05839	−	1.22144i	−0.0498929	−	0.0575794i
$451$	19.5028	−	5.72654i	0.918352	−	0.269652i
$452$	−0.873317	+	6.07405i	−0.0410774	+	0.285699i
$453$	−9.76772	+	11.2726i	−0.458928	+	0.529631i
$454$	3.59946	−	7.88172i	0.168931	−	0.369908i
$455$	1.55384	+	0.456250i	0.0728453	+	0.0213893i
$456$	1.61435	+	3.53494i	0.0755990	+	0.165539i
$457$	3.85457	+	26.8091i	0.180309	+	1.25408i	0.856032	+	0.516922i	$0.172922\pi$
$457$	3.85457	+	26.8091i	0.180309	+	1.25408i	−0.675723	+	0.737155i	$0.736169\pi$
$458$	17.6332	+	11.3322i	0.823945	+	0.529517i
$459$	17.3763			0.811057
$460$	−7.34351	+	8.84978i	−0.342393	+	0.412623i
$461$	5.49557			0.255954			0.127977	−	0.991777i	$-0.459152\pi$
$461$	5.49557			0.255954			0.127977	+	0.991777i	$0.459152\pi$
$462$	3.17565	+	2.04087i	0.147745	+	0.0949498i
$463$	−1.35784	−	9.44399i	−0.0631042	−	0.438899i	−0.996740	−	0.0806765i	$-0.974292\pi$
$463$	−1.35784	−	9.44399i	−0.0631042	−	0.438899i	0.933636	−	0.358223i	$-0.116617\pi$
$464$	−0.445841	−	0.976256i	−0.0206977	−	0.0453215i
$465$	7.80122	+	2.29065i	0.361773	+	0.106226i
$466$	8.71328	−	19.0794i	0.403635	−	0.883837i
$467$	23.7538	−	27.4133i	1.09919	−	1.26854i	0.138672	−	0.990338i	$-0.455717\pi$
$467$	23.7538	−	27.4133i	1.09919	−	1.26854i	0.960523	−	0.278200i	$-0.0897378\pi$
$468$	−0.207171	+	1.44091i	−0.00957650	+	0.0666060i
$469$	3.38745	−	0.994646i	0.156418	−	0.0459285i
$470$	4.63233	+	5.34600i	0.213674	+	0.246592i
$471$	−3.98972	+	2.56404i	−0.183837	+	0.118145i
$472$	−3.67208	+	2.35990i	−0.169021	+	0.108623i
$473$	3.53636	+	4.08118i	0.162602	+	0.187653i
$474$	−9.85579	+	2.89392i	−0.452692	+	0.132922i
$475$	−0.451245	+	3.13848i	−0.0207045	+	0.144003i
$476$	2.40176	−	2.77178i	0.110085	−	0.127044i
$477$	−10.2154	+	22.3687i	−0.467733	+	1.02419i
$478$	27.5160	+	8.07943i	1.25855	+	0.369545i
$479$	−8.74127	−	19.1407i	−0.399399	−	0.874561i	−0.997331	−	0.0730145i	$-0.976738\pi$
$479$	−8.74127	−	19.1407i	−0.399399	−	0.874561i	0.597932	−	0.801547i	$-0.295989\pi$
$480$	0.313607	+	2.18119i	0.0143141	+	0.0995571i
$481$	4.88902	+	3.14198i	0.222920	+	0.143262i
$482$	−5.99577			−0.273100
$483$	0.720219	+	4.34806i	0.0327711	+	0.197843i
$484$	5.87310			0.266959
$485$	15.0065	+	9.64412i	0.681412	+	0.437917i
$486$	−2.29905	−	15.9903i	−0.104287	−	0.725333i
$487$	1.81333	+	3.97065i	0.0821700	+	0.179927i	0.946257	−	0.323415i	$-0.104831\pi$
$487$	1.81333	+	3.97065i	0.0821700	+	0.179927i	−0.864087	+	0.503342i	$0.832104\pi$
$488$	−4.71761	−	1.38522i	−0.213556	−	0.0627058i
$489$	−4.54567	+	9.95364i	−0.205562	+	0.450119i
$490$	−1.57028	+	1.81219i	−0.0709378	+	0.0818666i
$491$	1.57170	−	10.9314i	0.0709300	−	0.493329i	−0.923129	−	0.384490i	$-0.874377\pi$
$491$	1.57170	−	10.9314i	0.0709300	−	0.493329i	0.994059	−	0.108840i	$-0.0347135\pi$
$492$	4.36324	−	1.28116i	0.196710	−	0.0577592i
$493$	2.57767	+	2.97479i	0.116093	+	0.133978i
$494$	2.40255	−	1.54403i	0.108096	−	0.0694691i
$495$	−17.8604	+	11.4782i	−0.802767	+	0.515907i
$496$	2.41621	+	2.78845i	0.108491	+	0.125205i
$497$	−5.24477	+	1.54000i	−0.235260	+	0.0690786i
$498$	−2.23867	+	15.5703i	−0.100317	+	0.697721i
$499$	14.8251	−	17.1091i	0.663665	−	0.765910i	−0.319707	−	0.947517i	$-0.603584\pi$
$499$	14.8251	−	17.1091i	0.663665	−	0.765910i	0.983371	+	0.181607i	$0.0581298\pi$
$500$	4.23367	−	9.27044i	0.189335	−	0.414587i
$501$	12.7985	+	3.75797i	0.571793	+	0.167894i
$502$	−8.97747	−	19.6579i	−0.400684	−	0.877376i
$503$	2.92029	+	20.3111i	0.130209	+	0.905626i	0.945279	+	0.326263i	$0.105789\pi$
$503$	2.92029	+	20.3111i	0.130209	+	0.905626i	−0.815070	+	0.579363i	$0.803301\pi$
$504$	−1.81329	−	1.16533i	−0.0807705	−	0.0519080i
$505$	−40.9465			−1.82210
$506$	13.2155	+	14.6093i	0.587502	+	0.649462i
$507$	11.5277			0.511961
$508$	8.50112	+	5.46334i	0.377176	+	0.242396i
$509$	−0.0354042	−	0.246242i	−0.00156927	−	0.0109145i	0.989022	−	0.147770i	$-0.0472095\pi$
$509$	−0.0354042	−	0.246242i	−0.00156927	−	0.0109145i	−0.990591	+	0.136855i	$0.956300\pi$
$510$	−3.35737	−	7.35162i	−0.148667	−	0.325535i
$511$	−4.29061	−	1.25984i	−0.189806	−	0.0557319i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	−13.1200	+	15.1413i	−0.579261	+	0.668503i
$514$	−0.205623	+	1.43014i	−0.00906964	+	0.0630807i
$515$	−4.26811	+	1.25323i	−0.188075	+	0.0552239i
$516$	0.791167	+	0.913056i	0.0348292	+	0.0401950i
$517$	10.1941	−	6.55134i	0.448335	−	0.288128i
$518$	−7.23908	+	4.65227i	−0.318067	+	0.204409i
$519$	−6.89600	−	7.95840i	−0.302701	−	0.349335i
$520$	1.55384	−	0.456250i	0.0681406	−	0.0200079i
$521$	−1.16240	+	8.08467i	−0.0509257	+	0.354196i	0.948387	+	0.317116i	$0.102715\pi$
$521$	−1.16240	+	8.08467i	−0.0509257	+	0.354196i	−0.999312	+	0.0370794i	$0.988195\pi$
$522$	1.51491	−	1.74830i	0.0663060	−	0.0765212i
$523$	15.7967	−	34.5899i	0.690741	−	1.51251i	−0.160107	−	0.987100i	$-0.551184\pi$
$523$	15.7967	−	34.5899i	0.690741	−	1.51251i	0.850848	−	0.525412i	$-0.176089\pi$
$524$	3.85963	+	1.13329i	0.168609	+	0.0495079i
$525$	0.286250	+	0.626800i	0.0124930	+	0.0273558i
$526$	0.158523	+	1.10255i	0.00691191	+	0.0480734i
$527$	−11.3840	−	7.31602i	−0.495893	−	0.318691i
$528$	3.77491			0.164282
$529$	−2.29838	+	22.8849i	−0.0999295	+	0.994995i
$530$	27.3565			1.18829
$531$	−7.91505	−	5.08669i	−0.343484	−	0.220744i
$532$	0.601808	+	4.18567i	0.0260917	+	0.181472i
$533$	−1.38829	−	3.03992i	−0.0601333	−	0.131674i
$534$	−11.9422	−	3.50655i	−0.516790	−	0.151743i
$535$	15.7434	−	34.4733i	0.680647	−	1.49041i
$536$	2.31196	−	2.66815i	0.0998615	−	0.115246i
$537$	−1.23131	+	8.56392i	−0.0531348	+	0.369560i
$538$	13.5939	−	3.99153i	0.586075	−	0.172087i
$539$	2.68996	+	3.10438i	0.115865	+	0.133715i
$540$	−9.55720	+	6.14204i	−0.411276	+	0.264311i
$541$	0.448568	−	0.288277i	0.0192854	−	0.0123940i	−0.530963	−	0.847395i	$-0.678170\pi$
$541$	0.448568	−	0.288277i	0.0192854	−	0.0123940i	0.550248	+	0.835001i	$0.314533\pi$
$542$	19.5719	+	22.5872i	0.840687	+	0.970205i
$543$	−14.1481	+	4.15424i	−0.607151	+	0.178276i
$544$	0.521953	−	3.63026i	0.0223786	−	0.155646i
$545$	21.3142	−	24.5979i	0.913001	−	1.05366i
$546$	0.257828	−	0.564564i	0.0110340	−	0.0241611i
$547$	3.79053	+	1.11300i	0.162071	+	0.0475884i	0.361762	−	0.932271i	$-0.382175\pi$
$547$	3.79053	+	1.11300i	0.162071	+	0.0475884i	−0.199690	+	0.979859i	$0.563994\pi$
$548$	−3.14402	−	6.88445i	−0.134306	−	0.294089i
$549$	−1.50824	−	10.4901i	−0.0643702	−	0.447705i
$550$	2.59107	+	1.66518i	0.110484	+	0.0710035i
$551$	−4.53843			−0.193344
$552$	2.95662	+	3.26844i	0.125842	+	0.139114i
$553$	−11.1774			−0.475312
$554$	7.27683	+	4.67653i	0.309163	+	0.198687i
$555$	2.69862	+	18.7693i	0.114550	+	0.796714i
$556$	−6.55349	−	14.3501i	−0.277930	−	0.608582i
$557$	−33.7997	−	9.92449i	−1.43214	−	0.420514i	−0.528546	−	0.848905i	$-0.677263\pi$
$557$	−33.7997	−	9.92449i	−1.43214	−	0.420514i	−0.903594	+	0.428390i	$0.859081\pi$
$558$	−3.30376	+	7.23422i	−0.139859	+	0.306249i
$559$	0.581431	−	0.671007i	0.0245919	−	0.0283806i
$560$	−0.341254	+	2.37347i	−0.0144206	+	0.100297i
$561$	−13.2840	+	3.90054i	−0.560852	+	0.164681i
$562$	−18.8628	−	21.7688i	−0.795678	−	0.918261i
$563$	25.6392	−	16.4773i	1.08057	−	0.694437i	0.125878	−	0.992046i	$-0.459825\pi$
$563$	25.6392	−	16.4773i	1.08057	−	0.694437i	0.954688	+	0.297609i	$0.0961890\pi$
$564$	2.28065	−	1.46569i	0.0960329	−	0.0617166i
$565$	9.63601	+	11.1206i	0.405390	+	0.467845i
$566$	−10.3428	+	3.03691i	−0.434739	+	0.127651i
$567$	0.300629	−	2.09092i	0.0126252	−	0.0878105i
$568$	−3.57959	+	4.13107i	−0.150196	+	0.173336i
$569$	−8.58956	+	18.8085i	−0.360093	+	0.788494i	0.639709	+	0.768617i	$0.279055\pi$
$569$	−8.58956	+	18.8085i	−0.360093	+	0.788494i	−0.999802	+	0.0198772i	$0.993672\pi$
$570$	8.94098	+	2.62531i	0.374497	+	0.109962i
$571$	11.2615	+	24.6592i	0.471278	+	1.03196i	0.984770	+	0.173861i	$0.0556243\pi$
$571$	11.2615	+	24.6592i	0.471278	+	1.03196i	−0.513492	+	0.858094i	$0.671648\pi$
$572$	−0.394808	−	2.74595i	−0.0165078	−	0.114814i
$573$	−9.60176	−	6.17068i	−0.401119	−	0.257784i
$574$	4.94832			0.206539
$575$	0.587639	+	3.54765i	0.0245062	+	0.147947i
$576$	−2.15546			−0.0898110
$577$	−36.4651	−	23.4347i	−1.51806	−	0.975600i	−0.992149	−	0.125063i	$-0.960087\pi$
$577$	−36.4651	−	23.4347i	−1.51806	−	0.975600i	−0.525915	−	0.850537i	$-0.676277\pi$
$578$	−0.505041	−	3.51264i	−0.0210069	−	0.146106i
$579$	−1.20687	−	2.64267i	−0.0501557	−	0.109826i
$580$	−2.46926	−	0.725040i	−0.102530	−	0.0301056i
$581$	−7.11071	+	15.5703i	−0.295002	+	0.645964i
$582$	4.47697	−	5.16670i	0.185577	−	0.214167i
$583$	6.66932	−	46.3861i	0.276215	−	1.92112i
$584$	−4.29061	+	1.25984i	−0.177547	+	0.0521324i
$585$	2.28589	+	2.63806i	0.0945100	+	0.109070i
$586$	−27.6148	+	17.7470i	−1.14076	+	0.733121i
$587$	22.1344	−	14.2249i	0.913582	−	0.587124i	0.00279353	−	0.999996i	$-0.499111\pi$
$587$	22.1344	−	14.2249i	0.913582	−	0.587124i	0.910789	+	0.412872i	$0.135474\pi$
$588$	0.601808	+	0.694523i	0.0248181	+	0.0286417i
$589$	14.9704	−	4.39572i	0.616846	−	0.181122i
$590$	−1.48958	+	10.3602i	−0.0613249	+	0.426524i
$591$	−9.93874	+	11.4699i	−0.408825	+	0.471810i
$592$	−3.57469	+	7.82748i	−0.146919	+	0.321708i
$593$	21.7270	+	6.37963i	0.892223	+	0.261980i	0.695540	−	0.718487i	$-0.255165\pi$
$593$	21.7270	+	6.37963i	0.892223	+	0.261980i	0.196682	+	0.980467i	$0.436983\pi$
$594$	8.08456	+	17.7027i	0.331713	+	0.726351i
$595$	−1.25158	−	8.70493i	−0.0513097	−	0.356867i
$596$	11.3073	+	7.26676i	0.463165	+	0.297658i
$597$	1.92844			0.0789257
$598$	2.06831	−	2.49255i	0.0845794	−	0.101928i
$599$	−36.1551			−1.47726			−0.738628	−	0.674114i	$-0.764526\pi$
$599$	−36.1551			−1.47726			−0.738628	+	0.674114i	$0.764526\pi$
$600$	0.579683	+	0.372540i	0.0236655	+	0.0152089i
$601$	−3.70877	−	25.7951i	−0.151284	−	1.05220i	−0.914071	−	0.405554i	$-0.867079\pi$
$601$	−3.70877	−	25.7951i	−0.151284	−	1.05220i	0.762787	−	0.646650i	$-0.223830\pi$
$602$	0.546126	+	1.19585i	0.0222584	+	0.0487392i
$603$	7.30154	+	2.14392i	0.297342	+	0.0873074i
$604$	−6.74245	+	14.7639i	−0.274346	+	0.600735i
$605$	9.22239	−	10.6432i	0.374943	−	0.432708i
$606$	−2.23331	+	15.5330i	−0.0907220	+	0.630986i
$607$	17.8489	−	5.24092i	0.724465	−	0.212722i	0.101349	−	0.994851i	$-0.467684\pi$
$607$	17.8489	−	5.24092i	0.724465	−	0.212722i	0.623117	+	0.782129i	$0.285866\pi$
$608$	2.76921	+	3.19584i	0.112306	+	0.129609i
$609$	−0.829724	+	0.533231i	−0.0336221	+	0.0216076i
$610$	−9.91823	+	6.37406i	−0.401577	+	0.258078i
$611$	−1.30470	−	1.50571i	−0.0527826	−	0.0609144i
$612$	7.58515	−	2.22720i	0.306611	−	0.0900292i
$613$	−5.51733	+	38.3739i	−0.222843	+	1.54991i	0.504365	+	0.863490i	$0.331727\pi$
$613$	−5.51733	+	38.3739i	−0.222843	+	1.54991i	−0.727208	+	0.686417i	$0.759183\pi$
$614$	0.299222	−	0.345321i	0.0120756	−	0.0139360i
$615$	4.52977	−	9.91881i	0.182658	−	0.399965i
$616$	3.94130	+	1.15727i	0.158799	+	0.0466277i
$617$	−10.8681	−	23.7979i	−0.437534	−	0.958065i	−0.992044	−	0.125889i	$-0.959822\pi$
$617$	−10.8681	−	23.7979i	−0.437534	−	0.958065i	0.554511	−	0.832177i	$-0.312906\pi$
$618$	0.242620	+	1.68746i	0.00975959	+	0.0678794i
$619$	14.7943	+	9.50772i	0.594633	+	0.382148i	0.803067	−	0.595889i	$-0.203200\pi$
$619$	14.7943	+	9.50772i	0.594633	+	0.382148i	−0.208434	+	0.978037i	$0.566836\pi$
$620$	8.84733			0.355317
$621$	−8.99551	+	20.8652i	−0.360977	+	0.837291i
$622$	31.0727			1.24590
$623$	−11.3936	−	7.32222i	−0.456475	−	0.293359i
$624$	−0.0883279	−	0.614334i	−0.00353594	−	0.0245930i
$625$	−11.7092	−	25.6397i	−0.468370	−	1.02559i
$626$	−19.1893	−	5.63449i	−0.766959	−	0.225199i
$627$	6.63126	−	14.5204i	0.264827	−	0.579890i
$628$	−3.37953	+	3.90018i	−0.134858	+	0.155634i
$629$	4.49146	−	31.2388i	0.179086	−	1.24557i
$630$	−4.95918	+	1.45615i	−0.197578	+	0.0580142i
$631$	−0.719679	−	0.830553i	−0.0286500	−	0.0330638i	0.741244	−	0.671236i	$-0.234236\pi$
$631$	−0.719679	−	0.830553i	−0.0286500	−	0.0330638i	−0.769894	+	0.638172i	$0.779691\pi$
$632$	−9.40303	+	6.04296i	−0.374032	+	0.240376i
$633$	18.2808	−	11.7484i	0.726597	−	0.466956i
$634$	2.06460	+	2.38267i	0.0819957	+	0.0946281i
$635$	23.2497	−	6.82674i	0.922637	−	0.270911i
$636$	1.49208	−	10.3777i	0.0591649	−	0.411501i
$637$	0.442270	−	0.510407i	0.0175234	−	0.0202231i
$638$	−1.83138	+	4.01015i	−0.0725049	+	0.158764i
$639$	−11.3049	−	3.31942i	−0.447216	−	0.131314i
$640$	0.996114	+	2.18119i	0.0393749	+	0.0862189i
$641$	1.70824	+	11.8811i	0.0674714	+	0.469274i	0.995345	+	0.0963786i	$0.0307260\pi$
$641$	1.70824	+	11.8811i	0.0674714	+	0.469274i	−0.927873	+	0.372896i	$0.878365\pi$
$642$	−12.2187	−	7.85249i	−0.482234	−	0.309913i
$643$	13.9886			0.551656			0.275828	−	0.961207i	$-0.411048\pi$
$643$	13.9886			0.551656			0.275828	+	0.961207i	$0.411048\pi$
$644$	2.08494	+	4.31891i	0.0821583	+	0.170189i
$645$	2.89699			0.114069
$646$	−13.0472	−	8.38490i	−0.513333	−	0.329899i
$647$	2.01007	+	13.9804i	0.0790241	+	0.549625i	0.990419	+	0.138093i	$0.0440971\pi$
$647$	2.01007	+	13.9804i	0.0790241	+	0.549625i	−0.911395	+	0.411532i	$0.864994\pi$
$648$	−0.877532	−	1.92153i	−0.0344727	−	0.0754847i
$649$	17.2038	+	5.05150i	0.675309	+	0.198289i
$650$	0.210366	−	0.460637i	0.00825123	−	0.0180677i
$651$	2.22046	−	2.56255i	0.0870267	−	0.100434i
$652$	−1.69456	+	11.7859i	−0.0663641	+	0.461573i
$653$	−2.79318	+	0.820151i	−0.109306	+	0.0320950i	−0.335928	−	0.941888i	$-0.609050\pi$
$653$	−2.79318	+	0.820151i	−0.109306	+	0.0320950i	0.226622	+	0.973983i	$0.427232\pi$
$654$	−8.16867	−	9.42715i	−0.319420	−	0.368631i
$655$	8.11442	−	5.21482i	0.317057	−	0.203760i
$656$	4.16279	−	2.67527i	0.162530	−	0.104452i
$657$	−6.31201	−	7.28444i	−0.246255	−	0.284193i
$658$	2.83052	−	0.831114i	0.110345	−	0.0324002i
$659$	3.60422	−	25.0679i	0.140401	−	0.976508i	−0.790819	−	0.612050i	$-0.790345\pi$
$659$	3.60422	−	25.0679i	0.140401	−	0.976508i	0.931220	−	0.364458i	$-0.118746\pi$
$660$	5.92765	−	6.84087i	0.230733	−	0.266280i
$661$	−8.38900	+	18.3693i	−0.326294	+	0.714485i	−0.999693	−	0.0247950i	$-0.992107\pi$
$661$	−8.38900	+	18.3693i	−0.326294	+	0.714485i	0.673398	+	0.739280i	$0.264834\pi$
$662$	−1.65132	−	0.484872i	−0.0641805	−	0.0188451i
$663$	0.945608	+	2.07059i	0.0367244	+	0.0804151i
$664$	2.43602	+	16.9429i	0.0945360	+	0.657512i
$665$	8.53025	+	5.48206i	0.330789	+	0.212585i
$666$	−18.5480			−0.718721
$667$	−4.90651	+	1.55521i	−0.189981	+	0.0602180i
$668$	14.5147			0.561589
$669$	−9.40176	−	6.04214i	−0.363493	−	0.233603i
$670$	−1.20478	−	8.37945i	−0.0465448	−	0.323726i
$671$	8.38996	+	18.3715i	0.323891	+	0.709222i
$672$	0.881761	+	0.258908i	0.0340147	+	0.00998760i
$673$	−18.3813	+	40.2494i	−0.708546	+	1.55150i	0.120746	+	0.992683i	$0.461471\pi$
$673$	−18.3813	+	40.2494i	−0.708546	+	1.55150i	−0.829292	+	0.558816i	$0.811256\pi$
$674$	21.5349	−	24.8526i	0.829492	−	0.957285i
$675$	−0.505570	+	3.51632i	−0.0194594	+	0.135343i
$676$	12.0358	−	3.53402i	0.462914	−	0.135924i
$677$	−9.81771	−	11.3302i	−0.377325	−	0.435457i	0.535044	−	0.844824i	$-0.320295\pi$
$677$	−9.81771	−	11.3302i	−0.377325	−	0.435457i	−0.912370	+	0.409367i	$0.865749\pi$
$678$	4.74414	−	3.04887i	0.182198	−	0.117091i
$679$	6.25826	−	4.02194i	0.240170	−	0.154348i
$680$	−5.75913	−	6.64639i	−0.220853	−	0.254878i
$681$	−7.64022	+	2.24337i	−0.292774	+	0.0859662i
$682$	2.15691	−	15.0017i	0.0825925	−	0.574443i
$683$	−17.5745	+	20.2820i	−0.672469	+	0.776071i	−0.984761	−	0.173916i	$-0.944358\pi$
$683$	−17.5745	+	20.2820i	−0.672469	+	0.776071i	0.312291	+	0.949986i	$0.398903\pi$
$684$	−3.78644	+	8.29114i	−0.144778	+	0.317020i
$685$	−17.4130	−	5.11291i	−0.665315	−	0.195354i
$686$	0.415415	+	0.909632i	0.0158606	+	0.0347299i
$687$	−2.74134	−	19.0664i	−0.104589	−	0.727430i
$688$	1.10596	+	0.710754i	0.0421641	+	0.0270972i
$689$	−7.70499			−0.293537
$690$	10.5658	−	0.225629i	0.402232	−	0.00858957i
$691$	−21.7685			−0.828113			−0.414056	−	0.910251i	$-0.635888\pi$
$691$	−21.7685			−0.828113			−0.414056	+	0.910251i	$0.635888\pi$
$692$	−9.63976	−	6.19510i	−0.366449	−	0.235502i
$693$	1.26005	+	8.76386i	0.0478654	+	0.332911i
$694$	−8.13194	−	17.8065i	−0.308684	−	0.675925i
$695$	−36.2961	−	10.6575i	−1.37679	−	0.404261i
$696$	−0.409722	+	0.897165i	−0.0155305	+	0.0340070i
$697$	−11.8847	+	13.7157i	−0.450165	+	0.519518i
$698$	−1.06784	+	7.42697i	−0.0404182	+	0.281115i
$699$	−18.4948	+	5.43057i	−0.699539	+	0.205403i
$700$	0.491025	+	0.566673i	0.0185590	+	0.0214182i
$701$	32.3169	−	20.7688i	1.22059	−	0.784428i	0.238193	−	0.971218i	$-0.423445\pi$
$701$	32.3169	−	20.7688i	1.22059	−	0.784428i	0.982400	+	0.186790i	$0.0598084\pi$
$702$	2.69180	−	1.72991i	0.101595	−	0.0652914i
$703$	23.8294	+	27.5006i	0.898742	+	1.03720i
$704$	3.94130	−	1.15727i	0.148543	−	0.0436162i
$705$	0.925145	−	6.43452i	0.0348430	−	0.242338i
$706$	−1.05646	+	1.21922i	−0.0397603	+	0.0458858i
$707$	−7.09369	+	15.5330i	−0.266786	+	0.584179i
$708$	3.84890	+	1.13014i	0.144650	+	0.0424732i
$709$	−3.72238	−	8.15087i	−0.139797	−	0.306113i	0.826764	−	0.562548i	$-0.190179\pi$
$709$	−3.72238	−	8.15087i	−0.139797	−	0.306113i	−0.966561	+	0.256436i	$0.917452\pi$
$710$	1.86536	+	12.9738i	0.0700056	+	0.486900i
$711$	−20.2679	−	13.0254i	−0.760106	−	0.488490i
$712$	−13.5436			−0.507568
$713$	14.6783	−	9.88224i	0.549706	−	0.370093i
$714$	−3.37047			−0.126137
$715$	−5.59616	−	3.59643i	−0.209284	−	0.134499i
$716$	1.33985	+	9.31888i	0.0500726	+	0.348263i
$717$	−10.9480	−	23.9728i	−0.408861	−	0.895280i
$718$	−3.51990	−	1.03354i	−0.131362	−	0.0385713i
$719$	−21.0969	+	46.1958i	−0.786783	+	1.72281i	−0.101144	+	0.994872i	$0.532250\pi$
$719$	−21.0969	+	46.1958i	−0.786783	+	1.72281i	−0.685639	+	0.727942i	$0.740477\pi$
$720$	−3.38467	+	3.90612i	−0.126139	+	0.145573i
$721$	−0.264008	+	1.83622i	−0.00983217	+	0.0683842i
$722$	−1.07275	+	0.314986i	−0.0399234	+	0.0117226i
$723$	3.60830	+	4.16420i	0.134194	+	0.154868i
$724$	−13.4981	+	8.67471i	−0.501653	+	0.322393i
$725$	−0.676986	+	0.435072i	−0.0251426	+	0.0161582i
$726$	−3.53448	−	4.07901i	−0.131177	−	0.151386i
$727$	−20.7806	+	6.10174i	−0.770710	+	0.226301i	−0.643367	−	0.765558i	$-0.722463\pi$
$727$	−20.7806	+	6.10174i	−0.770710	+	0.226301i	−0.127343	+	0.991859i	$0.540645\pi$
$728$	0.0961145	−	0.668491i	0.00356224	−	0.0247759i
$729$	−5.57199	+	6.43042i	−0.206370	+	0.238164i
$730$	−4.45437	+	9.75372i	−0.164864	+	0.361001i
$731$	−4.62630	−	1.35840i	−0.171110	−	0.0502424i
$732$	1.87703	+	4.11012i	0.0693770	+	0.151915i
$733$	−0.545340	−	3.79292i	−0.0201426	−	0.140095i	0.977268	−	0.212005i	$-0.0679995\pi$
$733$	−0.545340	−	3.79292i	−0.0201426	−	0.140095i	−0.997411	+	0.0719106i	$0.977090\pi$
$734$	−12.7517	−	8.19500i	−0.470673	−	0.302483i
$735$	2.20362			0.0812816
$736$	4.08895	+	2.50609i	0.150721	+	0.0923759i
$737$	−14.5020			−0.534189
$738$	8.97276	+	5.76644i	0.330292	+	0.212266i
$739$	−4.64568	−	32.3114i	−0.170894	−	1.18859i	−0.877001	−	0.480488i	$-0.840459\pi$
$739$	−4.64568	−	32.3114i	−0.170894	−	1.18859i	0.706107	−	0.708105i	$-0.250450\pi$
$740$	8.57167	+	18.7693i	0.315101	+	0.689975i
$741$	−2.51824	−	0.739422i	−0.0925098	−	0.0271633i
$742$	4.73932	−	10.3777i	0.173986	−	0.380976i
$743$	1.56805	−	1.80962i	0.0575260	−	0.0663886i	−0.726257	−	0.687423i	$-0.758742\pi$
$743$	1.56805	−	1.80962i	0.0575260	−	0.0663886i	0.783783	+	0.621034i	$0.213287\pi$
$744$	0.482552	−	3.35622i	0.0176912	−	0.123045i
$745$	30.9244	−	9.08021i	1.13298	−	0.332673i
$746$	−18.7607	−	21.6510i	−0.686877	−	0.792698i
$747$	−31.0384	+	19.9471i	−1.13563	+	0.729828i
$748$	−12.6738	+	8.14493i	−0.463399	+	0.297808i
$749$	−10.3500	−	11.9445i	−0.378179	−	0.436442i
$750$	−8.98639	+	2.63864i	−0.328137	+	0.0963496i
$751$	−0.712854	+	4.95801i	−0.0260124	+	0.180920i	−0.998685	−	0.0512591i	$-0.983677\pi$
$751$	−0.712854	+	4.95801i	−0.0260124	+	0.180920i	0.972673	+	0.232179i	$0.0745856\pi$
$752$	1.93185	−	2.22947i	0.0704472	−	0.0813004i
$753$	−8.25017	+	18.0654i	−0.300653	+	0.658338i
$754$	0.695470	+	0.204208i	0.0253275	+	0.00743683i
$755$	16.1676	+	35.4020i	0.588398	+	1.28841i
$756$	0.674259	+	4.68958i	0.0245226	+	0.170558i
$757$	23.2587	+	14.9475i	0.845352	+	0.543275i	0.890122	−	0.455722i	$-0.150619\pi$
$757$	23.2587	+	14.9475i	0.845352	+	0.543275i	−0.0447696	+	0.998997i	$0.514255\pi$
$758$	13.6094			0.494315
$759$	2.19327	−	17.9705i	0.0796108	−	0.652287i
$760$	10.1399			0.367814
$761$	−19.8203	−	12.7377i	−0.718486	−	0.461743i	0.129624	−	0.991563i	$-0.458623\pi$
$761$	−19.8203	−	12.7377i	−0.718486	−	0.461743i	−0.848110	+	0.529820i	$0.822259\pi$
$762$	−1.32162	−	9.19210i	−0.0478774	−	0.332995i
$763$	−5.63866	−	12.3469i	−0.204133	−	0.446989i
$764$	−11.9167	−	3.49907i	−0.431132	−	0.126592i
$765$	7.87465	−	17.2431i	0.284709	−	0.623425i
$766$	−16.0695	+	18.5452i	−0.580614	+	0.670065i
$767$	0.419541	−	2.91797i	0.0151488	−	0.105362i
$768$	0.881761	−	0.258908i	0.0318178	−	0.00934255i
$769$	−3.77584	−	4.35755i	−0.136160	−	0.157137i	0.683574	−	0.729881i	$-0.260424\pi$
$769$	−3.77584	−	4.35755i	−0.136160	−	0.157137i	−0.819735	+	0.572744i	$0.805879\pi$
$770$	8.28612	−	5.32517i	0.298611	−	0.191906i
$771$	1.11701	−	0.717859i	0.0402281	−	0.0258531i
$772$	−2.07023	−	2.38917i	−0.0745091	−	0.0859880i
$773$	−32.9279	+	9.66849i	−1.18433	+	0.347751i	−0.813843	−	0.581085i	$-0.802628\pi$
$773$	−32.9279	+	9.66849i	−1.18433	+	0.347751i	−0.370490	+	0.928836i	$0.620810\pi$
$774$	−0.403275	+	2.80484i	−0.0144954	+	0.100818i
$775$	1.81171	−	2.09082i	0.0650785	−	0.0751046i
$776$	3.09036	−	6.76694i	0.110937	−	0.242919i
$777$	7.58765	+	2.22793i	0.272205	+	0.0799267i
$778$	−8.88674	−	19.4593i	−0.318605	−	0.697648i
$779$	−2.97794	−	20.7120i	−0.106696	−	0.742085i
$780$	−1.25199	−	0.804606i	−0.0448285	−	0.0288095i
$781$	22.4534			0.803446
$782$	−16.9786	−	4.59399i	−0.607155	−	0.164281i
$783$	−5.08481			−0.181716
$784$	0.841254	+	0.540641i	0.0300448	+	0.0193086i
$785$	1.76110	+	12.2487i	0.0628564	+	0.437176i
$786$	−1.53566	−	3.36262i	−0.0547751	−	0.119941i
$787$	−30.8626	−	9.06207i	−1.10013	−	0.323028i	−0.319227	−	0.947678i	$-0.603423\pi$
$787$	−30.8626	−	9.06207i	−1.10013	−	0.323028i	−0.780905	+	0.624650i	$0.785242\pi$
$788$	−6.86050	+	15.0224i	−0.244395	+	0.535151i
$789$	0.670346	−	0.773620i	0.0238649	−	0.0275416i
$790$	−3.81433	+	26.5292i	−0.135708	+	0.943868i
$791$	5.88794	−	1.72885i	0.209351	−	0.0614710i
$792$	5.79812	+	6.69139i	0.206027	+	0.237768i
$793$	2.79348	−	1.79526i	0.0991994	−	0.0637516i
$794$	25.9751	−	16.6932i	0.921820	−	0.592418i
$795$	−16.4634	−	18.9997i	−0.583895	−	0.673851i
$796$	2.01344	−	0.591199i	0.0713645	−	0.0209545i
$797$	6.87192	−	47.7952i	0.243416	−	1.69299i	−0.391311	−	0.920258i	$-0.627978\pi$
$797$	6.87192	−	47.7952i	0.243416	−	1.69299i	0.634727	−	0.772736i	$-0.281112\pi$
$798$	2.54487	−	2.93694i	0.0900874	−	0.103966i
$799$	−4.49456	+	9.84171i	−0.159006	+	0.348175i
$800$	0.719443	+	0.211248i	0.0254362	+	0.00746873i
$801$	−12.1271	−	26.5546i	−0.428490	−	0.938262i
$802$	−0.348874	−	2.42647i	−0.0123192	−	0.0856818i
$803$	15.4526	+	9.93079i	0.545311	+	0.350450i
$804$	−3.24445			−0.114423
$805$	11.1006	+	3.00356i	0.391246	+	0.105862i
$806$	−2.49186			−0.0877720
$807$	−10.9531	−	7.03915i	−0.385568	−	0.247790i
$808$	2.43019	+	16.9023i	0.0854938	+	0.594622i
$809$	−2.01537	−	4.41305i	−0.0708568	−	0.155155i	0.870890	−	0.491479i	$-0.163543\pi$
$809$	−2.01537	−	4.41305i	−0.0708568	−	0.155155i	−0.941746	+	0.336324i	$0.890816\pi$
$810$	−4.86015	−	1.42707i	−0.170768	−	0.0501421i
$811$	−8.41550	+	18.4274i	−0.295508	+	0.647073i	−0.997904	−	0.0647139i	$-0.979387\pi$
$811$	−8.41550	+	18.4274i	−0.295508	+	0.647073i	0.702396	+	0.711787i	$0.252114\pi$
$812$	−0.702824	+	0.811103i	−0.0246643	+	0.0284641i
$813$	3.90881	−	27.1863i	0.137088	−	0.953467i
$814$	33.9153	−	9.95843i	1.18873	−	0.349043i
$815$	18.6975	+	21.5780i	0.654944	+	0.755846i
$816$	−2.83542	+	1.82221i	−0.0992595	+	0.0637902i
$817$	4.67676	−	3.00557i	0.163619	−	0.105152i
$818$	−5.23730	−	6.04417i	−0.183118	−	0.211329i
$819$	1.39676	−	0.410125i	0.0488067	−	0.0143309i
$820$	1.68863	−	11.7447i	0.0589696	−	0.410143i
$821$	−33.4002	+	38.5459i	−1.16567	+	1.34526i	−0.238270	+	0.971199i	$0.576580\pi$
$821$	−33.4002	+	38.5459i	−1.16567	+	1.34526i	−0.927404	+	0.374061i	$0.877965\pi$
$822$	−2.88931	+	6.32672i	−0.100776	+	0.220670i
$823$	−16.8308	−	4.94197i	−0.586686	−	0.172266i	−0.0250998	−	0.999685i	$-0.507990\pi$
$823$	−16.8308	−	4.94197i	−0.586686	−	0.172266i	−0.561586	+	0.827419i	$0.689809\pi$
$824$	0.770635	+	1.68746i	0.0268464	+	0.0587853i
$825$	−0.402820	−	2.80168i	−0.0140244	−	0.0975418i
$826$	3.67208	+	2.35990i	0.127768	+	0.0821116i
$827$	11.7022			0.406927			0.203463	−	0.979083i	$-0.434780\pi$
$827$	11.7022			0.406927			0.203463	+	0.979083i	$0.434780\pi$
$828$	−1.25236	+	10.2611i	−0.0435224	+	0.356598i
$829$	−46.0517			−1.59944			−0.799720	−	0.600373i	$-0.795019\pi$
$829$	−46.0517			−1.59944			−0.799720	+	0.600373i	$0.795019\pi$
$830$	34.5291	+	22.1905i	1.19852	+	0.770243i
$831$	−1.13129	−	7.86830i	−0.0392441	−	0.272948i
$832$	−0.280557	−	0.614334i	−0.00972656	−	0.0212982i
$833$	−3.51903	−	1.03328i	−0.121927	−	0.0358010i
$834$	−6.02257	+	13.1876i	−0.208544	+	0.456649i
$835$	22.7920	−	26.3034i	0.788751	−	0.910267i
$836$	2.47204	−	17.1934i	0.0854973	−	0.594646i
$837$	16.7727	−	4.92492i	0.579750	−	0.170230i
$838$	−22.5218	−	25.9915i	−0.778001	−	0.897862i
$839$	3.59474	−	2.31020i	0.124104	−	0.0797570i	−0.477116	−	0.878840i	$-0.658318\pi$
$839$	3.59474	−	2.31020i	0.124104	−	0.0797570i	0.601220	+	0.799083i	$0.294681\pi$
$840$	1.85380	−	1.19136i	0.0639622	−	0.0411060i
$841$	18.2367	+	21.0462i	0.628850	+	0.725732i
$842$	26.9813	−	7.92241i	0.929835	−	0.273024i
$843$	−3.76717	+	26.2013i	−0.129748	+	0.902419i
$844$	15.4849	−	17.8705i	0.533013	−	0.615129i
$845$	12.4951	−	27.3605i	0.429846	−	0.941231i
$846$	6.10108	+	1.79144i	0.209759	+	0.0615909i
$847$	−2.43978	−	5.34236i	−0.0838317	−	0.183566i
$848$	−1.62362	−	11.2925i	−0.0557553	−	0.387786i
$849$	8.33356	+	5.35566i	0.286007	+	0.183806i
$850$	−2.75002			−0.0943249
$851$	35.1858	+	21.5652i	1.20615	+	0.739246i
$852$	5.02335			0.172097
$853$	−26.1624	−	16.8136i	−0.895785	−	0.575686i	0.00975236	−	0.999952i	$-0.496896\pi$
$853$	−26.1624	−	16.8136i	−0.895785	−	0.575686i	−0.905537	+	0.424266i	$0.860532\pi$
$854$	0.699730	+	4.86673i	0.0239443	+	0.166536i
$855$	9.07941	+	19.8811i	0.310509	+	0.679921i
$856$	−15.1646	−	4.45273i	−0.518316	−	0.152191i
$857$	0.0896135	−	0.196226i	0.00306114	−	0.00670296i	−0.908095	−	0.418764i	$-0.862464\pi$
$857$	0.0896135	−	0.196226i	0.00306114	−	0.00670296i	0.911156	+	0.412061i	$0.135191\pi$
$858$	−1.66953	+	1.92674i	−0.0569968	+	0.0657778i
$859$	−2.69856	+	18.7689i	−0.0920736	+	0.640386i	0.890565	+	0.454856i	$0.150309\pi$
$859$	−2.69856	+	18.7689i	−0.0920736	+	0.640386i	−0.982639	+	0.185530i	$0.940600\pi$
$860$	3.02468	−	0.888126i	0.103141	−	0.0302848i
$861$	−2.97794	−	3.43672i	−0.101488	−	0.117123i
$862$	−15.1868	+	9.75995i	−0.517264	+	0.332425i
$863$	28.5483	−	18.3469i	0.971797	−	0.624536i	0.0445583	−	0.999007i	$-0.485812\pi$
$863$	28.5483	−	18.3469i	0.971797	−	0.624536i	0.927239	+	0.374471i	$0.122176\pi$
$864$	3.10260	+	3.58059i	0.105553	+	0.121814i
$865$	−26.3638	+	7.74111i	−0.896396	+	0.263206i
$866$	0.0238436	−	0.165836i	0.000810240	−	0.00563534i
$867$	−2.13567	+	2.46469i	−0.0725311	+	0.0837054i
$868$	1.53274	−	3.35622i	0.0520244	−	0.113918i
$869$	44.0535	+	12.9353i	1.49441	+	0.438799i
$870$	0.982462	+	2.15129i	0.0333086	+	0.0729356i
$871$	0.339329	+	2.36008i	0.0114977	+	0.0799683i
$872$	−11.4188	−	7.33842i	−0.386690	−	0.248510i
$873$	16.0350			0.542701
$874$	16.8228	−	11.3260i	0.569039	−	0.383109i
$875$	−10.1914			−0.344533
$876$	3.45711	+	2.22175i	0.116805	+	0.0750660i
$877$	5.57559	+	38.7791i	0.188274	+	1.30948i	0.836474	+	0.548007i	$0.184613\pi$
$877$	5.57559	+	38.7791i	0.188274	+	1.30948i	−0.648200	+	0.761471i	$0.724478\pi$
$878$	7.90369	+	17.3067i	0.266737	+	0.584072i
$879$	28.9445	+	8.49888i	0.976275	+	0.286660i
$880$	4.09173	−	8.95963i	0.137932	−	0.302029i
$881$	−18.1606	+	20.9585i	−0.611847	+	0.706109i	−0.974137	−	0.225957i	$-0.927449\pi$
$881$	−18.1606	+	20.9585i	−0.611847	+	0.706109i	0.362291	+	0.932065i	$0.381995\pi$
$882$	−0.306755	+	2.13353i	−0.0103290	+	0.0718395i
$883$	−18.4602	+	5.42039i	−0.621234	+	0.182411i	−0.577178	−	0.816618i	$-0.695846\pi$
$883$	−18.4602	+	5.42039i	−0.621234	+	0.182411i	−0.0440557	+	0.999029i	$0.514028\pi$
$884$	1.62207	+	1.87197i	0.0545560	+	0.0629610i
$885$	8.09186	−	5.20032i	0.272005	−	0.174807i
$886$	5.90559	−	3.79529i	0.198402	−	0.127505i
$887$	3.66478	+	4.22938i	0.123051	+	0.142009i	0.813932	−	0.580960i	$-0.197323\pi$
$887$	3.66478	+	4.22938i	0.123051	+	0.142009i	−0.690881	+	0.722968i	$0.742777\pi$
$888$	7.58765	−	2.22793i	0.254625	−	0.0747646i
$889$	1.43813	−	10.0024i	0.0482335	−	0.335471i
$890$	−21.2672	+	24.5436i	−0.712877	+	0.822704i
$891$	−3.60463	+	7.89304i	−0.120760	+	0.264427i
$892$	−11.6685	−	3.42618i	−0.390690	−	0.114717i
$893$	−5.18219	−	11.3474i	−0.173415	−	0.379727i
$894$	−1.75789	−	12.2264i	−0.0587925	−	0.408911i
$895$	18.9916	+	12.2051i	0.634818	+	0.407973i
$896$	1.00000			0.0334077
$897$	−2.97586	+	0.0635488i	−0.0993611	+	0.00212183i
$898$	−4.10839			−0.137099
$899$	3.33127	+	2.14088i	0.111104	+	0.0714023i
$900$	0.230010	+	1.59975i	0.00766698	+	0.0533250i
$901$	17.3819	+	38.0610i	0.579075	+	1.26800i
$902$	−19.5028	−	5.72654i	−0.649373	−	0.190673i
$903$	0.501882	−	1.09897i	0.0167016	−	0.0365714i
$904$	4.01856	−	4.63767i	0.133655	−	0.154246i
$905$	−5.47549	+	38.0829i	−0.182012	+	1.26592i
$906$	14.3115	−	4.20225i	0.475469	−	0.139610i
$907$	3.30168	+	3.81034i	0.109630	+	0.126520i	0.807912	−	0.589302i	$-0.200597\pi$
$907$	3.30168	+	3.81034i	0.109630	+	0.126520i	−0.698282	+	0.715823i	$0.746052\pi$
$908$	−7.28924	+	4.68451i	−0.241902	+	0.155461i
$909$	−30.9641	+	19.8994i	−1.02701	+	0.660021i
$910$	−1.06051	−	1.22389i	−0.0351556	−	0.0405717i
$911$	52.9931	−	15.5602i	1.75574	−	0.515531i	0.764159	−	0.645028i	$-0.223154\pi$
$911$	52.9931	−	15.5602i	1.75574	−	0.515531i	0.991580	+	0.129497i	$0.0413362\pi$
$912$	0.553053	−	3.84657i	0.0183134	−	0.127373i
$913$	46.0445	−	53.1381i	1.52385	−	1.75862i
$914$	11.2514	−	24.6372i	0.372164	−	0.814926i
$915$	10.3958	+	3.05248i	0.343675	+	0.100912i
$916$	−8.70735	−	19.0664i	−0.287699	−	0.629973i
$917$	−0.572471	−	3.98162i	−0.0189047	−	0.131485i
$918$	−14.6179	−	9.39435i	−0.482462	−	0.310060i
$919$	29.0339			0.957741			0.478871	−	0.877885i	$-0.341046\pi$
$919$	29.0339			0.957741			0.478871	+	0.877885i	$0.341046\pi$
$920$	10.9623	−	3.47471i	0.361417	−	0.114558i
$921$	−0.419907			−0.0138364
$922$	−4.62317	−	2.97113i	−0.152256	−	0.0978490i
$923$	−0.525380	−	3.65410i	−0.0172931	−	0.120276i
$924$	−1.56815	−	3.43378i	−0.0515885	−	0.112963i
$925$	6.19089	+	1.81781i	0.203555	+	0.0597692i
$926$	−3.96352	+	8.67889i	−0.130249	+	0.285206i
$927$	−2.61852	+	3.02194i	−0.0860036	+	0.0992535i
$928$	−0.152738	+	1.06232i	−0.00501388	+	0.0348723i
$929$	52.6616	−	15.4628i	1.72777	−	0.507320i	0.741289	−	0.671186i	$-0.234215\pi$
$929$	52.6616	−	15.4628i	1.72777	−	0.507320i	0.986483	+	0.163866i	$0.0523966\pi$
$930$	−5.32439	−	6.14467i	−0.174594	−	0.201492i
$931$	3.55742	−	2.28621i	0.116590	−	0.0749276i
$932$	−17.6452	+	11.3399i	−0.577988	+	0.371450i
$933$	−18.6998	−	21.5807i	−0.612205	−	0.706522i
$934$	−34.8037	+	10.2193i	−1.13881	+	0.334386i
$935$	−5.14110	+	35.7571i	−0.168132	+	1.16938i
$936$	0.953298	−	1.10016i	0.0311595	−	0.0359600i
$937$	−20.8002	+	45.5461i	−0.679514	+	1.48793i	0.183644	+	0.982993i	$0.441211\pi$
$937$	−20.8002	+	45.5461i	−0.679514	+	1.48793i	−0.863158	+	0.504934i	$0.831517\pi$
$938$	−3.38745	−	0.994646i	−0.110604	−	0.0324763i
$939$	7.63499	+	16.7183i	0.249158	+	0.545581i
$940$	−1.00670	−	7.00176i	−0.0328350	−	0.228372i
$941$	12.8400	+	8.25176i	0.418572	+	0.269000i	0.732929	−	0.680305i	$-0.238153\pi$
$941$	12.8400	+	8.25176i	0.418572	+	0.269000i	−0.314357	+	0.949305i	$0.601789\pi$
$942$	4.74259			0.154522
$943$	−10.3170	−	21.3714i	−0.335967	−	0.695948i
$944$	4.36501			0.142069
$945$	9.55720	+	6.14204i	0.310896	+	0.199801i
$946$	−0.768525	−	5.34521i	−0.0249869	−	0.173788i
$947$	9.45577	+	20.7052i	0.307271	+	0.672830i	0.998772	−	0.0495459i	$-0.0157774\pi$
$947$	9.45577	+	20.7052i	0.307271	+	0.672830i	−0.691501	+	0.722376i	$0.743050\pi$
$948$	9.85579	+	2.89392i	0.320101	+	0.0939902i
$949$	1.25458	−	2.74715i	0.0407254	−	0.0891762i
$950$	2.07640	−	2.39629i	0.0673674	−	0.0777461i
$951$	0.412331	−	2.86782i	0.0133707	−	0.0929956i
$952$	−3.51903	+	1.03328i	−0.114052	+	0.0334888i
$953$	5.54017	+	6.39370i	0.179464	+	0.207112i	0.838353	−	0.545128i	$-0.183519\pi$
$953$	5.54017	+	6.39370i	0.179464	+	0.207112i	−0.658889	+	0.752240i	$0.728973\pi$
$954$	20.6872	−	13.2948i	0.669773	−	0.430437i
$955$	−25.0535	+	16.1009i	−0.810713	+	0.521014i
$956$	−18.7799	−	21.6731i	−0.607385	−	0.700959i
$957$	3.88728	−	1.14141i	0.125658	−	0.0368965i
$958$	−2.99462	+	20.8281i	−0.0967519	+	0.672924i
$959$	−4.95624	+	5.71981i	−0.160045	+	0.184702i
$960$	0.915415	−	2.00448i	0.0295449	−	0.0646943i
$961$	16.6822	+	4.89834i	0.538136	+	0.158011i
$962$	−2.41422	−	5.28641i	−0.0778376	−	0.170441i
$963$	−4.84820	−	33.7200i	−0.156231	−	1.08661i
$964$	5.04396	+	3.24156i	0.162455	+	0.104404i
$965$	−7.58046			−0.244024
$966$	1.74485	−	4.04720i	0.0561396	−	0.130216i
$967$	54.4382			1.75061			0.875307	−	0.483567i	$-0.160659\pi$
$967$	54.4382			1.75061			0.875307	+	0.483567i	$0.160659\pi$
$968$	−4.94077	−	3.17524i	−0.158802	−	0.102056i
$969$	2.02837	+	14.1076i	0.0651607	+	0.453203i
$970$	−7.41030	−	16.2263i	−0.237930	−	0.520995i
$971$	42.0836	+	12.3568i	1.35053	+	0.396550i	0.875413	−	0.483375i	$-0.160589\pi$
$971$	42.0836	+	12.3568i	1.35053	+	0.396550i	0.475112	+	0.879925i	$0.342407\pi$
$972$	−6.71090	+	14.6948i	−0.215252	+	0.471337i
$973$	−10.3309	+	11.9225i	−0.331195	+	0.382219i
$974$	0.621220	−	4.32068i	0.0199052	−	0.138444i
$975$	−0.446523	+	0.131111i	−0.0143002	+	0.00419891i
$976$	3.21980	+	3.71585i	0.103063	+	0.118941i
$977$	42.1923	−	27.1153i	1.34985	−	0.867497i	0.352195	−	0.935927i	$-0.385435\pi$
$977$	42.1923	−	27.1153i	1.34985	−	0.867497i	0.997656	+	0.0684299i	$0.0217990\pi$
$978$	9.20540	−	5.91595i	0.294356	−	0.189171i
$979$	36.4318	+	42.0445i	1.16436	+	1.34375i
$980$	2.30075	−	0.675560i	0.0734947	−	0.0215800i
$981$	4.16375	−	28.9595i	0.132938	−	0.924607i
$982$	−7.23219	+	8.34639i	−0.230788	+	0.266344i
$983$	−8.50752	+	18.6289i	−0.271348	+	0.594169i	−0.995425	−	0.0955507i	$-0.969539\pi$
$983$	−8.50752	+	18.6289i	−0.271348	+	0.594169i	0.724077	+	0.689719i	$0.242266\pi$
$984$	−4.36324	−	1.28116i	−0.139095	−	0.0408419i
$985$	16.4506	+	36.0219i	0.524161	+	1.14775i
$986$	−0.560182	−	3.89615i	−0.0178398	−	0.124079i
$987$	−2.28065	−	1.46569i	−0.0725940	−	0.0466533i
$988$	−2.85592			−0.0908590
$989$	4.02613	−	4.85195i	0.128023	−	0.154283i
$990$	21.2308			0.674758
$991$	−23.7375	−	15.2552i	−0.754047	−	0.484596i	0.106282	−	0.994336i	$-0.466105\pi$
$991$	−23.7375	−	15.2552i	−0.754047	−	0.484596i	−0.860329	+	0.509740i	$0.829742\pi$
$992$	−0.525092	−	3.65209i	−0.0166717	−	0.115954i
$993$	0.657024	+	1.43868i	0.0208500	+	0.0456552i
$994$	5.24477	+	1.54000i	0.166354	+	0.0488460i
$995$	2.09029	−	4.57709i	0.0662665	−	0.145104i
$996$	10.3012	−	11.8882i	0.326407	−	0.376693i
$997$	−6.43643	+	44.7664i	−0.203844	+	1.41777i	0.588898	+	0.808208i	$0.299562\pi$
$997$	−6.43643	+	44.7664i	−0.203844	+	1.41777i	−0.792742	+	0.609558i	$0.791347\pi$
$998$	−21.7216	+	6.37804i	−0.687585	+	0.201893i
$999$	26.6982	+	30.8114i	0.844694	+	0.974828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.a.71.1	✓	10
23.9	even	11		7406.2.a.bg.1.1		5
23.12	even	11	inner	322.2.i.a.127.1	yes	10
23.14	odd	22		7406.2.a.bh.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.a.71.1	✓	10	1.1	even	1	trivial
322.2.i.a.127.1	yes	10	23.12	even	11	inner
7406.2.a.bg.1.1		5	23.9	even	11
7406.2.a.bh.1.1		5	23.14	odd	22

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 - 0.540641i) q^{2} +(0.130785 + 0.909632i) q^{3} +(0.415415 + 0.909632i) q^{4} +(2.30075 + 0.675560i) q^{5} +(0.381761 - 0.835939i) q^{6} +(0.654861 - 0.755750i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.06815 - 0.607265i) q^{9} +O(q^{10})\)	\(q+(-0.841254 - 0.540641i) q^{2} +(0.130785 + 0.909632i) q^{3} +(0.415415 + 0.909632i) q^{4} +(2.30075 + 0.675560i) q^{5} +(0.381761 - 0.835939i) q^{6} +(0.654861 - 0.755750i) q^{7} +(0.142315 - 0.989821i) q^{8} +(2.06815 - 0.607265i) q^{9} +(-1.57028 - 1.81219i) q^{10} +(-3.45561 + 2.22078i) q^{11} +(-0.773100 + 0.496841i) q^{12} +(0.442270 + 0.510407i) q^{13} +(-0.959493 + 0.281733i) q^{14} +(-0.313607 + 2.18119i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.52357 - 3.33616i) q^{17} +(-2.06815 - 0.607265i) q^{18} +(1.75667 + 3.84657i) q^{19} +(0.341254 + 2.37347i) q^{20} +(0.773100 + 0.496841i) q^{21} +4.10769 q^{22} +(3.21727 + 3.55657i) q^{23} +0.918986 q^{24} +(0.630785 + 0.405381i) q^{25} +(-0.0961145 - 0.668491i) q^{26} +(1.96815 + 4.30965i) q^{27} +(0.959493 + 0.281733i) q^{28} +(-0.445841 + 0.976256i) q^{29} +(1.44306 - 1.66538i) q^{30} +(0.525092 - 3.65209i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-2.47204 - 2.85288i) q^{33} +(-3.08538 + 1.98285i) q^{34} +(2.01722 - 1.29639i) q^{35} +(1.41153 + 1.62899i) q^{36} +(8.25654 - 2.42434i) q^{37} +(0.601808 - 4.18567i) q^{38} +(-0.406440 + 0.469057i) q^{39} +(0.996114 - 2.18119i) q^{40} +(-4.74788 - 1.39410i) q^{41} +(-0.381761 - 0.835939i) q^{42} +(-0.187094 - 1.30127i) q^{43} +(-3.45561 - 2.22078i) q^{44} +5.16854 q^{45} +(-0.783711 - 4.73136i) q^{46} -2.95001 q^{47} +(-0.773100 - 0.496841i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.311485 - 0.682057i) q^{50} +(3.23394 + 0.949570i) q^{51} +(-0.280557 + 0.614334i) q^{52} +(-7.47107 + 8.62207i) q^{53} +(0.674259 - 4.68958i) q^{54} +(-9.45075 + 2.77499i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(-3.26921 + 2.10100i) q^{57} +(0.902869 - 0.580239i) q^{58} +(-2.85848 - 3.29886i) q^{59} +(-2.11435 + 0.620830i) q^{60} +(0.699730 - 4.86673i) q^{61} +(-2.41621 + 2.78845i) q^{62} +(0.895412 - 1.96068i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.672741 + 1.47310i) q^{65} +(0.537225 + 3.73648i) q^{66} +(2.97001 + 1.90871i) q^{67} +3.66759 q^{68} +(-2.81440 + 3.39168i) q^{69} -2.39788 q^{70} +(-4.59845 - 2.95525i) q^{71} +(-0.306755 - 2.13353i) q^{72} +(-1.85763 - 4.06765i) q^{73} +(-8.25654 - 2.42434i) q^{74} +(-0.286250 + 0.626800i) q^{75} +(-2.76921 + 3.19584i) q^{76} +(-0.584585 + 4.06588i) q^{77} +(0.595510 - 0.174858i) q^{78} +(-7.31964 - 8.44732i) q^{79} +(-2.01722 + 1.29639i) q^{80} +(1.77708 - 1.14206i) q^{81} +(3.24046 + 3.73969i) q^{82} +(-16.4238 + 4.82245i) q^{83} +(-0.130785 + 0.909632i) q^{84} +(5.75913 - 6.64639i) q^{85} +(-0.546126 + 1.19585i) q^{86} +(-0.946343 - 0.277871i) q^{87} +(1.70640 + 3.73648i) q^{88} +(-1.92745 - 13.4057i) q^{89} +(-4.34805 - 2.79432i) q^{90} +0.675365 q^{91} +(-1.89867 + 4.40398i) q^{92} +3.39074 q^{93} +(2.48171 + 1.59490i) q^{94} +(1.44306 + 10.0367i) q^{95} +(0.381761 + 0.835939i) q^{96} +(7.13787 + 2.09587i) q^{97} +(-0.415415 + 0.909632i) q^{98} +(-5.79812 + 6.69139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9}+O(q^{10}) \) 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9	\( 10 q + q^{2} - 3 q^{3} - q^{4} + 5 q^{5} + 3 q^{6} + q^{7} + q^{8} + 16 q^{9} - 5 q^{10} - 11 q^{11} - 3 q^{12} + 10 q^{13} - q^{14} - 7 q^{15} - q^{16} + q^{17} - 16 q^{18} + 3 q^{19} - 6 q^{20} + 3 q^{21} + 12 q^{23} - 8 q^{24} + 2 q^{25} - 10 q^{26} - 9 q^{27} + q^{28} + 2 q^{29} - 4 q^{30} - 5 q^{31} + q^{32} - 11 q^{33} - 12 q^{34} + 6 q^{35} - 6 q^{36} + 27 q^{37} - 3 q^{38} + 8 q^{39} - 5 q^{40} - 12 q^{41} - 3 q^{42} + 38 q^{43} - 11 q^{44} + 8 q^{45} + 10 q^{46} + 2 q^{47} - 3 q^{48} - q^{49} - 13 q^{50} + 36 q^{51} - q^{52} - 16 q^{53} + 9 q^{54} - 11 q^{55} - q^{56} - 13 q^{57} + 9 q^{58} - 5 q^{59} - 7 q^{60} - 26 q^{61} + 5 q^{62} + 6 q^{63} - q^{64} + 5 q^{65} - 11 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 6 q^{70} + q^{71} + 6 q^{72} + 9 q^{73} - 27 q^{74} + 17 q^{75} - 8 q^{76} - 11 q^{77} + 25 q^{78} - 50 q^{79} - 6 q^{80} + 2 q^{81} + 23 q^{82} - 29 q^{83} + 3 q^{84} + 28 q^{85} + 17 q^{86} - 16 q^{87} + 11 q^{88} + 7 q^{89} - 19 q^{90} + 12 q^{91} + 23 q^{92} + 40 q^{93} + 20 q^{94} - 4 q^{95} + 3 q^{96} + 12 q^{97} + q^{98} - 33 q^{99}+O(q^{100}) \) 10 * q + q^2 - 3 * q^3 - q^4 + 5 * q^5 + 3 * q^6 + q^7 + q^8 + 16 * q^9 - 5 * q^10 - 11 * q^11 - 3 * q^12 + 10 * q^13 - q^14 - 7 * q^15 - q^16 + q^17 - 16 * q^18 + 3 * q^19 - 6 * q^20 + 3 * q^21 + 12 * q^23 - 8 * q^24 + 2 * q^25 - 10 * q^26 - 9 * q^27 + q^28 + 2 * q^29 - 4 * q^30 - 5 * q^31 + q^32 - 11 * q^33 - 12 * q^34 + 6 * q^35 - 6 * q^36 + 27 * q^37 - 3 * q^38 + 8 * q^39 - 5 * q^40 - 12 * q^41 - 3 * q^42 + 38 * q^43 - 11 * q^44 + 8 * q^45 + 10 * q^46 + 2 * q^47 - 3 * q^48 - q^49 - 13 * q^50 + 36 * q^51 - q^52 - 16 * q^53 + 9 * q^54 - 11 * q^55 - q^56 - 13 * q^57 + 9 * q^58 - 5 * q^59 - 7 * q^60 - 26 * q^61 + 5 * q^62 + 6 * q^63 - q^64 + 5 * q^65 - 11 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 6 * q^70 + q^71 + 6 * q^72 + 9 * q^73 - 27 * q^74 + 17 * q^75 - 8 * q^76 - 11 * q^77 + 25 * q^78 - 50 * q^79 - 6 * q^80 + 2 * q^81 + 23 * q^82 - 29 * q^83 + 3 * q^84 + 28 * q^85 + 17 * q^86 - 16 * q^87 + 11 * q^88 + 7 * q^89 - 19 * q^90 + 12 * q^91 + 23 * q^92 + 40 * q^93 + 20 * q^94 - 4 * q^95 + 3 * q^96 + 12 * q^97 + q^98 - 33 * q^99

Introduction

L-functions

Modular forms

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