LMFDB - Embedded newform 288.2.bf.a.203.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			203.26
Character	$\chi$	$=$	288.203
Dual form			288.2.bf.a.227.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.160623 + 1.40506i) q^{2} +(-0.691397 + 1.58807i) q^{3} +(-1.94840 + 0.451372i) q^{4} +(-2.04053 + 1.56576i) q^{5} +(-2.34239 - 0.716375i) q^{6} +(0.949325 + 0.254371i) q^{7} +(-0.947165 - 2.66512i) q^{8} +(-2.04394 - 2.19598i) q^{9} +O(q^{10})$	\(q+(0.160623 + 1.40506i) q^{2} +(-0.691397 + 1.58807i) q^{3} +(-1.94840 + 0.451372i) q^{4} +(-2.04053 + 1.56576i) q^{5} +(-2.34239 - 0.716375i) q^{6} +(0.949325 + 0.254371i) q^{7} +(-0.947165 - 2.66512i) q^{8} +(-2.04394 - 2.19598i) q^{9} +(-2.52774 - 2.61558i) q^{10} +(0.137776 + 1.04651i) q^{11} +(0.630308 - 3.40628i) q^{12} +(1.88367 + 0.247990i) q^{13} +(-0.204923 + 1.37472i) q^{14} +(-1.07571 - 4.32307i) q^{15} +(3.59253 - 1.75891i) q^{16} -4.36111 q^{17} +(2.75718 - 3.22459i) q^{18} +(0.0481525 - 0.0199454i) q^{19} +(3.26904 - 3.97176i) q^{20} +(-1.06032 + 1.33172i) q^{21} +(-1.44829 + 0.361679i) q^{22} +(0.127774 + 0.476858i) q^{23} +(4.88727 + 0.338494i) q^{24} +(0.418091 - 1.56034i) q^{25} +(-0.0458797 + 2.68651i) q^{26} +(4.90054 - 1.72763i) q^{27} +(-1.96448 - 0.0671175i) q^{28} +(-5.29253 + 6.89735i) q^{29} +(5.90140 - 2.20583i) q^{30} +(-4.82535 - 2.78591i) q^{31} +(3.04842 + 4.76520i) q^{32} +(-1.75720 - 0.504759i) q^{33} +(-0.700496 - 6.12763i) q^{34} +(-2.33541 + 0.967360i) q^{35} +(4.97361 + 3.35606i) q^{36} +(-3.37556 + 8.14932i) q^{37} +(0.0357590 + 0.0644535i) q^{38} +(-1.69619 + 2.81995i) q^{39} +(6.10566 + 3.95525i) q^{40} +(-3.50800 + 0.939965i) q^{41} +(-2.04147 - 1.27591i) q^{42} +(11.1568 - 1.46882i) q^{43} +(-0.740811 - 1.97684i) q^{44} +(7.60910 + 1.28065i) q^{45} +(-0.649492 + 0.256125i) q^{46} +(2.36444 - 1.36511i) q^{47} +(0.309406 + 6.92129i) q^{48} +(-5.22566 - 3.01704i) q^{49} +(2.25953 + 0.336817i) q^{50} +(3.01526 - 6.92575i) q^{51} +(-3.78209 + 0.367053i) q^{52} +(-2.72220 + 6.57198i) q^{53} +(3.21457 + 6.60807i) q^{54} +(-1.91973 - 1.91973i) q^{55} +(-0.221238 - 2.77100i) q^{56} +(-0.00161777 + 0.0902598i) q^{57} +(-10.5413 - 6.32845i) q^{58} +(3.61983 + 4.71745i) q^{59} +(4.04724 + 7.93753i) q^{60} +(1.46451 + 1.12376i) q^{61} +(3.13932 - 7.22739i) q^{62} +(-1.38177 - 2.60461i) q^{63} +(-6.20576 + 5.04862i) q^{64} +(-4.23200 + 2.44334i) q^{65} +(0.426971 - 2.55005i) q^{66} +(-15.0179 - 1.97715i) q^{67} +(8.49718 - 1.96848i) q^{68} +(-0.845627 - 0.126785i) q^{69} +(-1.73432 - 3.12602i) q^{70} +(10.6500 + 10.6500i) q^{71} +(-3.91660 + 7.52730i) q^{72} +(6.06304 - 6.06304i) q^{73} +(-11.9925 - 3.43390i) q^{74} +(2.18886 + 1.74277i) q^{75} +(-0.0848175 + 0.0605963i) q^{76} +(-0.135408 + 1.02853i) q^{77} +(-4.23465 - 1.93031i) q^{78} +(7.26957 + 12.5913i) q^{79} +(-4.57665 + 9.21414i) q^{80} +(-0.644623 + 8.97688i) q^{81} +(-1.88418 - 4.77798i) q^{82} +(4.44061 - 5.78711i) q^{83} +(1.46482 - 3.07333i) q^{84} +(8.89899 - 6.82844i) q^{85} +(3.85583 + 15.4401i) q^{86} +(-7.29425 - 13.1737i) q^{87} +(2.65859 - 1.35841i) q^{88} +(3.67849 - 3.67849i) q^{89} +(-0.577197 + 10.8970i) q^{90} +(1.72514 + 0.714576i) q^{91} +(-0.464195 - 0.871437i) q^{92} +(7.76046 - 5.73682i) q^{93} +(2.29785 + 3.10292i) q^{94} +(-0.0670271 + 0.116094i) q^{95} +(-9.67515 + 1.54646i) q^{96} +(2.21031 + 3.82837i) q^{97} +(3.39976 - 7.82699i) q^{98} +(2.01652 - 2.44157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.160623	+	1.40506i	0.113578	+	0.993529i
$2$	0.160623	+	1.40506i	0.113578	+	0.993529i
$3$	−0.691397	+	1.58807i	−0.399178	+	0.916873i
$3$	−0.691397	+	1.58807i	−0.399178	+	0.916873i
$4$	−1.94840	+	0.451372i	−0.974200	+	0.225686i
$5$	−2.04053	+	1.56576i	−0.912555	+	0.700228i	−0.954284	−	0.298901i	$-0.903380\pi$
$5$	−2.04053	+	1.56576i	−0.912555	+	0.700228i	0.0417292	+	0.999129i	$0.486713\pi$
$6$	−2.34239	−	0.716375i	−0.956278	−	0.292459i
$7$	0.949325	+	0.254371i	0.358811	+	0.0961432i	0.433721	−	0.901047i	$-0.357200\pi$
$7$	0.949325	+	0.254371i	0.358811	+	0.0961432i	−0.0749100	+	0.997190i	$0.523867\pi$
$8$	−0.947165	−	2.66512i	−0.334873	−	0.942263i
$9$	−2.04394	−	2.19598i	−0.681313	−	0.731992i
$10$	−2.52774	−	2.61558i	−0.799343	−	0.827119i
$11$	0.137776	+	1.04651i	0.0415411	+	0.315536i	0.999582	+	0.0289051i	$0.00920205\pi$
$11$	0.137776	+	1.04651i	0.0415411	+	0.315536i	−0.958041	+	0.286631i	$0.907465\pi$
$12$	0.630308	−	3.40628i	0.181954	−	0.983307i
$13$	1.88367	+	0.247990i	0.522437	+	0.0687802i	0.387133	−	0.922024i	$-0.373465\pi$
$13$	1.88367	+	0.247990i	0.522437	+	0.0687802i	0.135304	+	0.990804i	$0.456799\pi$
$14$	−0.204923	+	1.37472i	−0.0547680	+	0.367409i
$15$	−1.07571	−	4.32307i	−0.277748	−	1.11621i
$16$	3.59253	−	1.75891i	0.898132	−	0.439727i
$17$	−4.36111			−1.05772			−0.528862	−	0.848708i	$-0.677381\pi$
$17$	−4.36111			−1.05772			−0.528862	+	0.848708i	$0.677381\pi$
$18$	2.75718	−	3.22459i	0.649873	−	0.760043i
$19$	0.0481525	−	0.0199454i	0.0110469	−	0.00457579i	−0.377153	−	0.926151i	$-0.623097\pi$
$19$	0.0481525	−	0.0199454i	0.0110469	−	0.00457579i	0.388200	+	0.921575i	$0.373097\pi$
$20$	3.26904	−	3.97176i	0.730979	−	0.888113i
$21$	−1.06032	+	1.33172i	−0.231381	+	0.290606i
$22$	−1.44829	+	0.361679i	−0.308776	+	0.0771103i
$23$	0.127774	+	0.476858i	0.0266427	+	0.0994318i	0.977967	−	0.208760i	$-0.0669428\pi$
$23$	0.127774	+	0.476858i	0.0266427	+	0.0994318i	−0.951324	+	0.308192i	$0.900276\pi$
$24$	4.88727	+	0.338494i	0.997610	+	0.0690948i
$25$	0.418091	−	1.56034i	0.0836182	−	0.312067i
$26$	−0.0458797	+	2.68651i	−0.00899774	+	0.526869i
$27$	4.90054	−	1.72763i	0.943109	−	0.332482i
$28$	−1.96448	−	0.0671175i	−0.371252	−	0.0126840i
$29$	−5.29253	+	6.89735i	−0.982797	+	1.28081i	−0.0231112	+	0.999733i	$0.507357\pi$
$29$	−5.29253	+	6.89735i	−0.982797	+	1.28081i	−0.959686	+	0.281074i	$0.909310\pi$
$30$	5.90140	−	2.20583i	1.07744	−	0.402728i
$31$	−4.82535	−	2.78591i	−0.866658	−	0.500365i	−0.000421497	−	1.00000i	$-0.500134\pi$
$31$	−4.82535	−	2.78591i	−0.866658	−	0.500365i	−0.866236	+	0.499635i	$0.833467\pi$
$32$	3.04842	+	4.76520i	0.538889	+	0.842377i
$33$	−1.75720	−	0.504759i	−0.305889	−	0.0878673i
$34$	−0.700496	−	6.12763i	−0.120134	−	1.05088i
$35$	−2.33541	+	0.967360i	−0.394757	+	0.163514i
$36$	4.97361	+	3.35606i	0.828936	+	0.559344i
$37$	−3.37556	+	8.14932i	−0.554938	+	1.33974i	0.358791	+	0.933418i	$0.383189\pi$
$37$	−3.37556	+	8.14932i	−0.554938	+	1.33974i	−0.913730	+	0.406322i	$0.866811\pi$
$38$	0.0357590	+	0.0644535i	0.00580087	+	0.0104557i
$39$	−1.69619	+	2.81995i	−0.271608	+	0.451553i
$40$	6.10566	+	3.95525i	0.965389	+	0.625379i
$41$	−3.50800	+	0.939965i	−0.547857	+	0.146798i	−0.522122	−	0.852871i	$-0.674859\pi$
$41$	−3.50800	+	0.939965i	−0.547857	+	0.146798i	−0.0257354	+	0.999669i	$0.508193\pi$
$42$	−2.04147	−	1.27591i	−0.315005	−	0.196877i
$43$	11.1568	−	1.46882i	1.70140	−	0.223993i	0.783663	−	0.621187i	$-0.213349\pi$
$43$	11.1568	−	1.46882i	1.70140	−	0.223993i	0.917735	+	0.397194i	$0.130016\pi$
$44$	−0.740811	−	1.97684i	−0.111681	−	0.298020i
$45$	7.60910	+	1.28065i	1.13430	+	0.190908i
$46$	−0.649492	+	0.256125i	−0.0957624	+	0.0377635i
$47$	2.36444	−	1.36511i	0.344889	−	0.199122i	−0.317543	−	0.948244i	$-0.602858\pi$
$47$	2.36444	−	1.36511i	0.344889	−	0.199122i	0.662432	+	0.749122i	$0.269524\pi$
$48$	0.309406	+	6.92129i	0.0446589	+	0.999002i
$49$	−5.22566	−	3.01704i	−0.746523	−	0.431006i
$50$	2.25953	+	0.336817i	0.319545	+	0.0476331i
$51$	3.01526	−	6.92575i	0.422221	−	0.969799i
$52$	−3.78209	+	0.367053i	−0.524481	+	0.0509011i
$53$	−2.72220	+	6.57198i	−0.373923	+	0.902731i	0.619154	+	0.785270i	$0.287476\pi$
$53$	−2.72220	+	6.57198i	−0.373923	+	0.902731i	−0.993077	+	0.117461i	$0.962524\pi$
$54$	3.21457	+	6.60807i	0.437447	+	0.899244i
$55$	−1.91973	−	1.91973i	−0.258856	−	0.258856i
$56$	−0.221238	−	2.77100i	−0.0295641	−	0.370290i
$57$	−0.00161777	+	0.0902598i	−0.000214279	+	0.0119552i
$58$	−10.5413	−	6.32845i	−1.38414	−	0.830966i
$59$	3.61983	+	4.71745i	0.471261	+	0.614160i	0.967144	−	0.254230i	$-0.0818220\pi$
$59$	3.61983	+	4.71745i	0.471261	+	0.614160i	−0.495883	+	0.868390i	$0.665155\pi$
$60$	4.04724	+	7.93753i	0.522496	+	1.02473i
$61$	1.46451	+	1.12376i	0.187512	+	0.143883i	0.698251	−	0.715853i	$-0.253962\pi$
$61$	1.46451	+	1.12376i	0.187512	+	0.143883i	−0.510740	+	0.859735i	$0.670628\pi$
$62$	3.13932	−	7.22739i	0.398694	−	0.917880i
$63$	−1.38177	−	2.60461i	−0.174087	−	0.328151i
$64$	−6.20576	+	5.04862i	−0.775720	+	0.631078i
$65$	−4.23200	+	2.44334i	−0.524915	+	0.303060i
$66$	0.426971	−	2.55005i	0.0525564	−	0.313889i
$67$	−15.0179	−	1.97715i	−1.83473	−	0.241547i	−0.867860	−	0.496810i	$-0.834505\pi$
$67$	−15.0179	−	1.97715i	−1.83473	−	0.241547i	−0.966872	+	0.255263i	$0.917838\pi$
$68$	8.49718	−	1.96848i	1.03043	−	0.238713i
$69$	−0.845627	−	0.126785i	−0.101802	−	0.0152631i
$70$	−1.73432	−	3.12602i	−0.207291	−	0.373631i
$71$	10.6500	+	10.6500i	1.26392	+	1.26392i	0.949178	+	0.314740i	$0.101917\pi$
$71$	10.6500	+	10.6500i	1.26392	+	1.26392i	0.314740	+	0.949178i	$0.398083\pi$
$72$	−3.91660	+	7.52730i	−0.461576	+	0.887101i
$73$	6.06304	−	6.06304i	0.709625	−	0.709625i	−0.256831	−	0.966456i	$-0.582679\pi$
$73$	6.06304	−	6.06304i	0.709625	−	0.709625i	0.966456	+	0.256831i	$0.0826785\pi$
$74$	−11.9925	−	3.43390i	−1.39410	−	0.399183i
$75$	2.18886	+	1.74277i	0.252748	+	0.201238i
$76$	−0.0848175	+	0.0605963i	−0.00972924	+	0.00695088i
$77$	−0.135408	+	1.02853i	−0.0154312	+	0.117212i
$78$	−4.23465	−	1.93031i	−0.479480	−	0.218564i
$79$	7.26957	+	12.5913i	0.817891	+	1.41663i	0.907233	+	0.420627i	$0.138190\pi$
$79$	7.26957	+	12.5913i	0.817891	+	1.41663i	−0.0893427	+	0.996001i	$0.528477\pi$
$80$	−4.57665	+	9.21414i	−0.511686	+	1.03017i
$81$	−0.644623	+	8.97688i	−0.0716248	+	0.997432i
$82$	−1.88418	−	4.77798i	−0.208073	−	0.527639i
$83$	4.44061	−	5.78711i	0.487420	−	0.635218i	−0.483293	−	0.875458i	$-0.660560\pi$
$83$	4.44061	−	5.78711i	0.487420	−	0.635218i	0.970713	+	0.240240i	$0.0772263\pi$
$84$	1.46482	−	3.07333i	0.159825	−	0.335328i
$85$	8.89899	−	6.82844i	0.965231	−	0.740648i
$86$	3.85583	+	15.4401i	0.415785	+	1.66495i
$87$	−7.29425	−	13.1737i	−0.782026	−	1.41237i
$88$	2.65859	−	1.35841i	0.283407	−	0.144807i
$89$	3.67849	−	3.67849i	0.389919	−	0.389919i	−0.484740	−	0.874659i	$-0.661086\pi$
$89$	3.67849	−	3.67849i	0.389919	−	0.389919i	0.874659	+	0.484740i	$0.161086\pi$
$90$	−0.577197	+	10.8970i	−0.0608419	+	1.14864i
$91$	1.72514	+	0.714576i	0.180844	+	0.0749079i
$92$	−0.464195	−	0.871437i	−0.0483957	−	0.0908536i
$93$	7.76046	−	5.73682i	0.804722	−	0.594880i
$94$	2.29785	+	3.10292i	0.237005	+	0.320041i
$95$	−0.0670271	+	0.116094i	−0.00687684	+	0.0119110i
$96$	−9.67515	+	1.54646i	−0.987466	+	0.157835i
$97$	2.21031	+	3.82837i	0.224423	+	0.388712i	0.956146	−	0.292890i	$-0.0946170\pi$
$97$	2.21031	+	3.82837i	0.224423	+	0.388712i	−0.731723	+	0.681602i	$0.761284\pi$
$98$	3.39976	−	7.82699i	0.343428	−	0.790645i
$99$	2.01652	−	2.44157i	0.202667	−	0.245387i
$100$	−0.110316	+	3.22887i	−0.0110316	+	0.322887i
$101$	1.87263	+	14.2240i	0.186333	+	1.41534i	0.787547	+	0.616254i	$0.211351\pi$
$101$	1.87263	+	14.2240i	0.186333	+	1.41534i	−0.601214	+	0.799088i	$0.705316\pi$
$102$	10.2154	+	3.12419i	1.01148	+	0.309341i
$103$	−0.570981	−	2.13093i	−0.0562605	−	0.209967i	0.932073	−	0.362269i	$-0.117998\pi$
$103$	−0.570981	−	2.13093i	−0.0562605	−	0.209967i	−0.988334	+	0.152302i	$0.951331\pi$
$104$	−1.12322	−	5.25511i	−0.110141	−	0.515306i
$105$	0.0784624	−	4.37763i	0.00765714	−	0.427213i
$106$	−9.67129	−	2.76925i	−0.939359	−	0.268973i
$107$	−7.12875	−	2.95283i	−0.689162	−	0.285460i	0.0104888	−	0.999945i	$-0.496661\pi$
$107$	−7.12875	−	2.95283i	−0.689162	−	0.285460i	−0.699651	+	0.714485i	$0.746661\pi$
$108$	−8.76841	+	5.57808i	−0.843741	+	0.536751i
$109$	1.98604	+	4.79472i	0.190228	+	0.459251i	0.990003	−	0.141049i	$-0.0450477\pi$
$109$	1.98604	+	4.79472i	0.190228	+	0.459251i	−0.799775	+	0.600300i	$0.795048\pi$
$110$	2.38898	−	3.00569i	0.227780	−	0.286581i
$111$	−10.6078	−	10.9950i	−1.00685	−	1.04360i
$112$	3.85789	−	0.755940i	0.364536	−	0.0714296i
$113$	9.47124	−	16.4047i	0.890979	−	1.54322i	0.0522757	−	0.998633i	$-0.483353\pi$
$113$	9.47124	−	16.4047i	0.890979	−	1.54322i	0.838703	−	0.544588i	$-0.183314\pi$
$114$	−0.127080	+	0.0122248i	−0.0119022	+	0.00114496i
$115$	−1.00737	−	0.772983i	−0.0939379	−	0.0720811i
$116$	7.19869	−	15.8277i	0.668381	−	1.46957i
$117$	−3.30554	−	4.64338i	−0.305597	−	0.429281i
$118$	−6.04688	+	5.84381i	−0.556660	+	0.537967i
$119$	−4.14011	−	1.10934i	−0.379523	−	0.101693i
$120$	−10.5026	+	6.96157i	−0.958756	+	0.635502i
$121$	9.54897	−	2.55864i	0.868088	−	0.232604i
$122$	−1.34372	+	2.23823i	−0.121654	+	0.202640i
$123$	0.932689	−	6.22084i	0.0840977	−	0.560914i
$124$	10.6592	+	3.25005i	0.957223	+	0.291863i
$125$	−3.33140	−	8.04272i	−0.297970	−	0.719362i
$126$	3.43770	−	2.35984i	0.306255	−	0.210231i
$127$			3.17879i			0.282072i	0.990004	+	0.141036i	$0.0450433\pi$
$127$			3.17879i			0.282072i	−0.990004	+	0.141036i	$0.954957\pi$
$128$	−8.09042	−	7.90855i	−0.715099	−	0.699024i
$129$	−5.38119	+	18.7333i	−0.473788	+	1.64938i
$130$	−4.11281	−	5.55376i	−0.360717	−	0.487097i
$131$	1.90515	−	14.4711i	0.166454	−	1.26434i	−0.680529	−	0.732721i	$-0.738250\pi$
$131$	1.90515	−	14.4711i	0.166454	−	1.26434i	0.846983	−	0.531621i	$-0.178417\pi$
$132$	3.65156	+	0.190322i	0.317827	+	0.0165654i
$133$	0.0507859	−	0.00668609i	0.00440370	−	0.000579758i
$134$	0.365784	−	21.4187i	0.0315989	−	1.85029i
$135$	−7.29468	+	11.1983i	−0.627826	+	0.963800i
$136$	4.13069	+	11.6229i	0.354203	+	0.996654i
$137$	−2.16012	+	8.06167i	−0.184551	+	0.688755i	0.810175	+	0.586188i	$0.199372\pi$
$137$	−2.16012	+	8.06167i	−0.184551	+	0.688755i	−0.994726	+	0.102567i	$0.967295\pi$
$138$	0.0423128	−	1.20852i	0.00360190	−	0.102876i
$139$	9.50171	+	12.3829i	0.805924	+	1.05030i	0.997627	+	0.0688480i	$0.0219324\pi$
$139$	9.50171	+	12.3829i	0.805924	+	1.05030i	−0.191703	+	0.981453i	$0.561401\pi$
$140$	4.11368	−	2.93895i	0.347670	−	0.248386i
$141$	0.533124	+	4.69873i	0.0448972	+	0.395705i
$142$	−13.2532	+	16.6745i	−1.11219	+	1.39929i
$143$			2.00546i			0.167705i
$144$	−11.2054	−	4.29400i	−0.933785	−	0.357834i
$145$		−	22.3611i		−	1.85699i
$146$	9.49281	+	7.54508i	0.785631	+	0.624435i
$147$	8.40428	−	6.21275i	0.693173	−	0.512419i
$148$	2.89856	−	17.4018i	0.238261	−	1.43042i
$149$	−2.90716	−	3.78868i	−0.238164	−	0.310381i	0.658945	−	0.752191i	$-0.271003\pi$
$149$	−2.90716	−	3.78868i	−0.238164	−	0.310381i	−0.897108	+	0.441810i	$0.854336\pi$
$150$	−2.09712	+	3.35541i	−0.171229	+	0.273968i
$151$	0.795904	−	2.97035i	0.0647698	−	0.241724i	−0.925950	−	0.377647i	$-0.876733\pi$
$151$	0.795904	−	2.97035i	0.0647698	−	0.241724i	0.990719	+	0.135923i	$0.0434000\pi$
$152$	−0.0987653	−	0.109441i	−0.00801092	−	0.00887681i
$153$	8.91384	+	9.57689i	0.720641	+	0.774245i
$154$	−1.46690	−	0.0250513i	−0.118206	−	0.00201869i
$155$	14.2084	−	1.87056i	1.14124	−	0.150247i
$156$	2.03202	−	6.26000i	0.162692	−	0.501201i
$157$	1.95872	−	14.8780i	0.156323	−	1.18739i	−0.715871	−	0.698233i	$-0.753970\pi$
$157$	1.95872	−	14.8780i	0.156323	−	1.18739i	0.872194	−	0.489160i	$-0.162697\pi$
$158$	−16.5239	+	12.2367i	−1.31457	+	0.973496i
$159$	−8.55465	−	8.86690i	−0.678428	−	0.703191i
$160$	−13.6816	−	4.95048i	−1.08162	−	0.391370i
$161$			0.485195i			0.0382388i
$162$	−12.7166	+	0.536163i	−0.999112	+	0.0421249i
$163$	6.58738	+	15.9033i	0.515963	+	1.24565i	0.940364	+	0.340171i	$0.110485\pi$
$163$	6.58738	+	15.9033i	0.515963	+	1.24565i	−0.424400	+	0.905475i	$0.639515\pi$
$164$	6.41071	−	3.41484i	0.500592	−	0.266654i
$165$	4.37595	−	1.72137i	0.340668	−	0.134008i
$166$	8.84452	+	5.30978i	0.686468	+	0.412119i
$167$	0.156824	−	0.0420210i	0.0121354	−	0.00325168i	−0.252746	−	0.967533i	$-0.581334\pi$
$167$	0.156824	−	0.0420210i	0.0121354	−	0.00325168i	0.264882	+	0.964281i	$0.414667\pi$
$168$	4.55351	+	1.56452i	0.351311	+	0.120705i
$169$	−9.07031	−	2.43038i	−0.697716	−	0.186952i
$170$	11.0238	+	11.4068i	0.845484	+	0.874864i
$171$	−0.142220	−	0.0649745i	−0.0108759	−	0.00496872i
$172$	−21.0749	+	7.89772i	−1.60695	+	0.602196i
$173$	−20.8198	−	15.9756i	−1.58290	−	1.21460i	−0.833610	−	0.552353i	$-0.813730\pi$
$173$	−20.8198	−	15.9756i	−1.58290	−	1.21460i	−0.749286	−	0.662246i	$-0.769603\pi$
$174$	17.3383	−	12.3649i	1.31441	−	0.937379i
$175$	0.793808	−	1.37492i	0.0600063	−	0.103934i
$176$	2.33569	+	3.51730i	0.176059	+	0.265126i
$177$	−9.99438	+	2.48691i	−0.751224	+	0.186928i
$178$	5.75936	+	4.57765i	0.431682	+	0.343110i
$179$	−2.47489	−	5.97491i	−0.184982	−	0.446586i	0.803999	−	0.594631i	$-0.202702\pi$
$179$	−2.47489	−	5.97491i	−0.184982	−	0.446586i	−0.988981	+	0.148045i	$0.952702\pi$
$180$	−15.4036	+	0.939309i	−1.14812	+	0.0700120i
$181$	7.08174	+	2.93335i	0.526381	+	0.218034i	0.630017	−	0.776581i	$-0.283048\pi$
$181$	7.08174	+	2.93335i	0.526381	+	0.218034i	−0.103636	+	0.994615i	$0.533048\pi$
$182$	−0.726925	+	2.53870i	−0.0538833	+	0.188181i
$183$	−2.79717	+	1.54878i	−0.206773	+	0.114489i
$184$	1.14986	−	0.792196i	0.0847690	−	0.0584015i
$185$	−5.87191	−	21.9143i	−0.431712	−	1.61117i
$186$	9.30710	+	9.98246i	0.682430	+	0.731950i
$187$	−0.600857	−	4.56396i	−0.0439390	−	0.333750i
$188$	−3.99070	+	3.72702i	−0.291052	+	0.271821i
$189$	5.09166	−	0.393527i	0.370364	−	0.0286249i
$190$	−0.173886	−	0.0755298i	−0.0126150	−	0.00547951i
$191$	3.33741	+	5.78056i	0.241486	+	0.418266i	0.961138	−	0.276069i	$-0.0890318\pi$
$191$	3.33741	+	5.78056i	0.241486	+	0.418266i	−0.719652	+	0.694335i	$0.755698\pi$
$192$	−3.72692	−	13.3458i	−0.268968	−	0.963149i
$193$	−2.53844	+	4.39671i	−0.182721	+	0.316482i	−0.942806	−	0.333341i	$-0.891824\pi$
$193$	−2.53844	+	4.39671i	−0.182721	+	0.316482i	0.760085	+	0.649824i	$0.225157\pi$
$194$	−5.02407	+	3.72055i	−0.360707	+	0.267120i
$195$	−0.954213	−	8.41003i	−0.0683326	−	0.602255i
$196$	11.5435	+	3.51968i	0.824535	+	0.251406i
$197$	4.04397	+	1.67507i	0.288121	+	0.119343i	0.522063	−	0.852907i	$-0.325163\pi$
$197$	4.04397	+	1.67507i	0.288121	+	0.119343i	−0.233942	+	0.972251i	$0.575163\pi$
$198$	3.75445	+	2.44116i	0.266817	+	0.173485i
$199$	−6.65464	+	6.65464i	−0.471735	+	0.471735i	−0.902476	−	0.430741i	$-0.858252\pi$
$199$	−6.65464	+	6.65464i	−0.471735	+	0.471735i	0.430741	+	0.902476i	$0.358252\pi$
$200$	−4.55449	+	0.363632i	−0.322051	+	0.0257127i
$201$	13.5232	−	22.4825i	0.953853	−	1.58580i
$202$	−19.6848	+	4.91587i	−1.38502	+	0.345879i
$203$	−6.77881	+	5.20157i	−0.475779	+	0.365078i
$204$	−2.74884	+	14.8551i	−0.192457	+	1.04007i
$205$	5.68644	−	7.41071i	0.397158	−	0.517586i
$206$	2.90238	−	1.14454i	0.202218	−	0.0797440i
$207$	0.786008	−	1.25526i	0.0546313	−	0.0872464i
$208$	7.20334	−	2.42230i	0.499462	−	0.167956i
$209$	0.0275074	+	0.0476443i	0.00190273	+	0.00329562i
$210$	6.16345	−	0.592906i	0.425319	−	0.0409144i
$211$	−1.44041	+	10.9410i	−0.0991621	+	0.753211i	0.867551	+	0.497348i	$0.165693\pi$
$211$	−1.44041	+	10.9410i	−0.0991621	+	0.753211i	−0.966713	+	0.255863i	$0.917640\pi$
$212$	2.33753	−	14.0336i	0.160542	−	0.963830i
$213$	−24.2763	+	9.54954i	−1.66338	+	0.654324i
$214$	3.00386	−	10.4906i	0.205340	−	0.717125i
$215$	−20.4660	+	20.4660i	−1.39577	+	1.39577i
$216$	−9.24596	−	11.4242i	−0.629108	−	0.777318i
$217$	−3.87217	−	3.87217i	−0.262860	−	0.262860i
$218$	−6.41788	+	3.56065i	−0.434674	+	0.241158i
$219$	5.43657	+	13.8205i	0.367369	+	0.933903i
$220$	4.60690	+	2.87388i	0.310597	+	0.193757i
$221$	−8.21491	−	1.08151i	−0.552594	−	0.0727504i
$222$	13.7449	−	16.6707i	0.922494	−	1.11887i
$223$	8.66946	−	5.00532i	0.580550	−	0.335181i	−0.180802	−	0.983520i	$-0.557869\pi$
$223$	8.66946	−	5.00532i	0.580550	−	0.335181i	0.761352	+	0.648339i	$0.224536\pi$
$224$	1.68181	+	5.29915i	0.112371	+	0.354065i
$225$	−4.28101	+	2.27112i	−0.285401	+	0.151408i
$226$	24.5709	+	10.6727i	1.63443	+	0.709938i
$227$	15.5379	+	11.9227i	1.03129	+	0.791336i	0.978286	−	0.207258i	$-0.0664539\pi$
$227$	15.5379	+	11.9227i	1.03129	+	0.791336i	0.0530034	+	0.998594i	$0.483121\pi$
$228$	−0.0375887	−	0.176592i	−0.00248937	−	0.0116951i
$229$	15.3923	+	20.0597i	1.01715	+	1.32558i	0.944603	+	0.328215i	$0.106447\pi$
$229$	15.3923	+	20.0597i	1.01715	+	1.32558i	0.0725505	+	0.997365i	$0.476886\pi$
$230$	0.924282	−	1.53958i	0.0609454	−	0.101517i
$231$	−1.53976	−	0.926160i	−0.101309	−	0.0609369i
$232$	23.3952	+	7.57230i	1.53597	+	0.497146i
$233$	13.9750	+	13.9750i	0.915535	+	0.915535i	0.996701	−	0.0811657i	$-0.0258643\pi$
$233$	13.9750	+	13.9750i	0.915535	+	0.915535i	−0.0811657	+	0.996701i	$0.525864\pi$
$234$	5.99329	−	5.39032i	0.391794	−	0.352376i
$235$	−2.68729	+	6.48770i	−0.175300	+	0.423211i
$236$	−9.18219	−	7.55759i	−0.597710	−	0.491957i
$237$	−25.0220	+	2.83903i	−1.62535	+	0.184415i
$238$	0.893691	−	5.99530i	0.0579294	−	0.388617i
$239$	−4.87863	−	2.81668i	−0.315573	−	0.182196i	0.333845	−	0.942628i	$-0.391654\pi$
$239$	−4.87863	−	2.81668i	−0.315573	−	0.182196i	−0.649417	+	0.760432i	$0.724987\pi$
$240$	−11.4684	−	13.6387i	−0.740283	−	0.880373i
$241$	−12.5599	+	7.25149i	−0.809057	+	0.467109i	−0.846628	−	0.532185i	$-0.821371\pi$
$241$	−12.5599	+	7.25149i	−0.809057	+	0.467109i	0.0375714	+	0.999294i	$0.488038\pi$
$242$	5.12884	+	13.0059i	0.329694	+	0.836052i
$243$	−13.8102	−	7.23030i	−0.885927	−	0.463824i
$244$	−3.36069	−	1.52849i	−0.215146	−	0.0978518i
$245$	15.3871	−	2.02575i	0.983046	−	0.129420i
$246$	8.89048	+	0.311273i	0.566836	+	0.0198460i
$247$	0.0956499	−	0.0256293i	0.00608606	−	0.00163075i
$248$	−2.85441	+	15.4989i	−0.181255	+	0.984178i
$249$	6.12012	+	11.0532i	0.387847	+	0.700468i
$250$	10.7654	−	5.97268i	0.680865	−	0.377745i
$251$	9.44859	−	22.8109i	0.596390	−	1.43981i	−0.280846	−	0.959753i	$-0.590615\pi$
$251$	9.44859	−	22.8109i	0.596390	−	1.43981i	0.877236	−	0.480060i	$-0.159385\pi$
$252$	3.86789	+	4.45114i	0.243654	+	0.280395i
$253$	−0.481435	+	0.199417i	−0.0302676	+	0.0125372i
$254$	−4.46639	+	0.510588i	−0.280247	+	0.0320371i
$255$	4.69130	+	18.8534i	0.293781	+	1.18065i
$256$	9.81249	−	12.6378i	0.613281	−	0.789865i
$257$	−5.88598	−	3.39827i	−0.367157	−	0.211978i	0.305059	−	0.952334i	$-0.401324\pi$
$257$	−5.88598	−	3.39827i	−0.367157	−	0.211978i	−0.672216	+	0.740355i	$0.734657\pi$
$258$	−27.1859	−	4.55190i	−1.69252	−	0.283389i
$259$	−5.27745	+	6.87771i	−0.327925	+	0.427360i
$260$	7.14277	−	6.67082i	0.442975	−	0.413707i
$261$	25.9640	−	2.47551i	1.60713	−	0.153230i
$262$	20.6387	+	0.352464i	1.27507	+	0.0217753i
$263$	−0.489592	+	1.82718i	−0.0301895	+	0.112669i	−0.979376	−	0.202044i	$-0.935242\pi$
$263$	−0.489592	+	1.82718i	−0.0301895	+	0.112669i	0.949187	+	0.314713i	$0.101908\pi$
$264$	0.319111	+	5.16124i	0.0196399	+	0.317652i
$265$	−4.73538	−	17.6727i	−0.290892	−	1.08562i
$266$	0.0175518	+	0.0702834i	0.00107617	+	0.00430935i
$267$	3.29840	+	8.38500i	0.201859	+	0.513153i
$268$	30.1534	−	2.92640i	1.84191	−	0.178758i
$269$	−27.5977	+	11.4314i	−1.68266	+	0.696982i	−0.999448	−	0.0332349i	$-0.989419\pi$
$269$	−27.5977	+	11.4314i	−1.68266	+	0.696982i	−0.683216	+	0.730217i	$0.739419\pi$
$270$	−16.9061	−	8.45076i	−1.02887	−	0.514297i
$271$	18.2622			1.10935			0.554675	−	0.832067i	$-0.312843\pi$
$271$	18.2622			1.10935			0.554675	+	0.832067i	$0.312843\pi$
$272$	−15.6674	+	7.67078i	−0.949975	+	0.465109i
$273$	−2.32755	+	2.24559i	−0.140870	+	0.135909i
$274$	−11.6741	−	1.74021i	−0.705259	−	0.105130i
$275$	1.69052	+	0.222561i	0.101942	+	0.0134209i
$276$	1.70485	−	0.134665i	0.102620	−	0.00810589i
$277$	1.83109	+	13.9085i	0.110020	+	0.835683i	0.954105	+	0.299473i	$0.0968110\pi$
$277$	1.83109	+	13.9085i	0.110020	+	0.835683i	−0.844085	+	0.536210i	$0.819856\pi$
$278$	−15.8725	+	15.3395i	−0.951969	+	0.920000i
$279$	3.74491	+	16.2906i	0.224202	+	0.975292i
$280$	4.79016	+	5.30792i	0.286267	+	0.317209i
$281$	24.8787	+	6.66624i	1.48414	+	0.397675i	0.907754	−	0.419502i	$-0.137795\pi$
$281$	24.8787	+	6.66624i	1.48414	+	0.397675i	0.576387	+	0.817177i	$0.304462\pi$
$282$	−6.51638	+	1.50380i	−0.388045	+	0.0895500i
$283$	−12.1501	+	9.32311i	−0.722249	+	0.554201i	−0.903163	−	0.429298i	$-0.858761\pi$
$283$	−12.1501	+	9.32311i	−0.722249	+	0.554201i	0.180914	+	0.983499i	$0.442095\pi$
$284$	−25.5575	−	15.9433i	−1.51656	−	0.946060i
$285$	−0.138024	−	0.186711i	−0.00817582	−	0.0110598i
$286$	−2.81780	+	0.322124i	−0.166620	+	0.0190476i
$287$	−3.56933			−0.210691
$288$	4.23349	−	16.4340i	0.249461	−	0.968385i
$289$	2.01926			0.118780
$290$	31.4187	−	3.59172i	1.84497	−	0.210913i
$291$	−7.60792	+	0.863204i	−0.445984	+	0.0506019i
$292$	−9.07654	+	14.5499i	−0.531164	+	0.851469i
$293$	−2.08699	+	1.60140i	−0.121923	+	0.0935550i	−0.667923	−	0.744230i	$-0.732817\pi$
$293$	−2.08699	+	1.60140i	−0.121923	+	0.0935550i	0.546000	+	0.837785i	$0.316150\pi$
$294$	10.0792	+	10.8106i	0.587833	+	0.630488i
$295$	−14.7728	−	3.95835i	−0.860103	−	0.230464i
$296$	24.9161	+	1.27753i	1.44822	+	0.0742549i
$297$	2.48317	+	4.89046i	0.144088	+	0.283773i
$298$	4.85638	−	4.69329i	0.281322	−	0.271875i
$299$	0.122428	+	0.929932i	0.00708019	+	0.0537794i
$300$	−5.05141	−	2.40762i	−0.291643	−	0.139004i
$301$	10.9651	+	1.44358i	0.632016	+	0.0832065i
$302$	4.30137	+	0.641186i	0.247516	+	0.0368961i
$303$	−23.8835	−	6.86058i	−1.37207	−	0.394130i
$304$	0.137907	−	0.156350i	0.00790951	−	0.00896730i
$305$	−4.74792			−0.271865
$306$	−12.0244	+	14.0628i	−0.687386	+	0.803915i
$307$	−22.7523	+	9.42430i	−1.29854	+	0.537873i	−0.921520	−	0.388332i	$-0.873051\pi$
$307$	−22.7523	+	9.42430i	−1.29854	+	0.537873i	−0.377021	+	0.926205i	$0.623051\pi$
$308$	−0.200419	−	2.06511i	−0.0114200	−	0.117670i
$309$	3.77884	+	0.566561i	0.214971	+	0.0322305i
$310$	4.91046	+	19.6632i	0.278895	+	1.11679i
$311$	3.06238	+	11.4290i	0.173652	+	0.648077i	0.996777	+	0.0802175i	$0.0255615\pi$
$311$	3.06238	+	11.4290i	0.173652	+	0.648077i	−0.823126	+	0.567859i	$0.807772\pi$
$312$	9.12208	+	1.84961i	0.516436	+	0.104713i
$313$	0.474120	−	1.76944i	0.0267988	−	0.100015i	−0.951231	−	0.308479i	$-0.900180\pi$
$313$	0.474120	−	1.76944i	0.0267988	−	0.100015i	0.978030	+	0.208465i	$0.0668466\pi$
$314$	21.2191	+	0.362375i	1.19746	+	0.0204500i
$315$	6.89775	+	3.15129i	0.388644	+	0.177555i
$316$	−19.8474	−	21.2515i	−1.11650	−	1.19549i
$317$	16.2281	−	21.1489i	0.911462	−	1.18784i	−0.0702617	−	0.997529i	$-0.522383\pi$
$317$	16.2281	−	21.1489i	0.911462	−	1.18784i	0.981724	−	0.190312i	$-0.0609499\pi$
$318$	11.0845	−	13.4440i	0.621586	−	0.753905i
$319$	−7.94737	−	4.58841i	−0.444967	−	0.256902i
$320$	4.75815	−	20.0186i	0.265989	−	1.11907i
$321$	9.61810	−	9.27939i	0.536830	−	0.517925i
$322$	−0.681730	+	0.0779338i	−0.0379913	+	0.00434308i
$323$	−0.209998	+	0.0869841i	−0.0116846	+	0.00483992i
$324$	−2.79593	−	17.7815i	−0.155329	−	0.987863i
$325$	1.17450	−	2.83548i	0.0651493	−	0.157284i
$326$	−21.2871	+	11.8101i	−1.17898	+	0.654103i
$327$	−8.98750	−	0.161087i	−0.497010	−	0.00890814i
$328$	5.82778	+	8.45895i	0.321785	+	0.467067i
$329$	2.59187	−	0.694489i	0.142894	−	0.0382884i
$330$	3.12151	+	5.87200i	0.171833	+	0.323243i
$331$	2.64671	−	0.348446i	0.145476	−	0.0191523i	−0.0574364	−	0.998349i	$-0.518293\pi$
$331$	2.64671	−	0.348446i	0.145476	−	0.0191523i	0.202913	+	0.979197i	$0.434959\pi$
$332$	−6.03994	+	13.2800i	−0.331485	+	0.728833i
$333$	24.7952	−	9.24407i	1.35877	−	0.506572i
$334$	0.0842318	+	0.213599i	0.00460896	+	0.0116876i
$335$	33.7403	−	19.4800i	1.84343	−	1.06431i
$336$	−1.46685	+	6.64926i	−0.0800231	+	0.362747i
$337$	5.47536	+	3.16120i	0.298262	+	0.172202i	0.641662	−	0.766988i	$-0.278245\pi$
$337$	5.47536	+	3.16120i	0.298262	+	0.172202i	−0.343400	+	0.939189i	$0.611579\pi$
$338$	1.95793	−	13.1347i	0.106497	−	0.714435i
$339$	19.5034	+	26.3831i	1.05928	+	1.43294i
$340$	−14.2566	+	17.3213i	−0.773174	+	0.939378i
$341$	2.25068	−	5.43363i	0.121881	−	0.294247i
$342$	0.0684493	−	0.210265i	0.00370131	−	0.0113698i
$343$	−9.05809	−	9.05809i	−0.489091	−	0.489091i
$344$	−14.4819	−	28.3430i	−0.780813	−	1.52815i
$345$	1.92405	−	1.06534i	0.103587	−	0.0573559i
$346$	19.1025	−	31.8191i	1.02696	−	1.71061i
$347$	−0.141211	−	0.184029i	−0.00758059	−	0.00987922i	0.789548	−	0.613689i	$-0.210315\pi$
$347$	−0.141211	−	0.184029i	−0.00758059	−	0.00987922i	−0.797128	+	0.603810i	$0.793649\pi$
$348$	20.1584	+	22.3753i	1.08060	+	1.19944i
$349$	−7.35665	−	5.64496i	−0.393793	−	0.302168i	0.392819	−	0.919616i	$-0.371500\pi$
$349$	−7.35665	−	5.64496i	−0.393793	−	0.302168i	−0.786612	+	0.617448i	$0.788167\pi$
$350$	2.05935	+	0.894506i	0.110077	+	0.0478134i
$351$	9.65946	−	2.03900i	0.515584	−	0.108834i
$352$	−4.56685	+	3.84675i	−0.243414	+	0.205032i
$353$	12.4894	−	7.21076i	0.664744	−	0.383790i	−0.129338	−	0.991601i	$-0.541285\pi$
$353$	12.4894	−	7.21076i	0.664744	−	0.383790i	0.794082	+	0.607810i	$0.207952\pi$
$354$	−5.09959	−	13.6433i	−0.271040	−	0.725132i
$355$	−38.4069	−	5.05636i	−2.03843	−	0.268364i
$356$	−5.50680	+	8.82753i	−0.291860	+	0.467858i
$357$	4.62417	−	5.80779i	0.244737	−	0.307381i
$358$	7.99760	−	4.43708i	0.422686	−	0.234507i
$359$	23.2540	+	23.2540i	1.22730	+	1.22730i	0.964982	+	0.262315i	$0.0844859\pi$
$359$	23.2540	+	23.2540i	1.22730	+	1.22730i	0.262315	+	0.964982i	$0.415514\pi$
$360$	−3.79397	−	21.4922i	−0.199960	−	1.13274i
$361$	−13.4331	+	13.4331i	−0.707006	+	0.707006i
$362$	−2.98405	+	10.4214i	−0.156838	+	0.547739i
$363$	−2.53883	+	16.9335i	−0.133254	+	0.888777i
$364$	−3.68380	−	0.613600i	−0.193084	−	0.0321614i
$365$	−2.87859	+	21.8651i	−0.150672	+	1.14447i
$366$	−2.62543	−	3.68143i	−0.137233	−	0.192431i
$367$	−5.27800	−	9.14177i	−0.275510	−	0.477197i	0.694754	−	0.719247i	$-0.255513\pi$
$367$	−5.27800	−	9.14177i	−0.275510	−	0.477197i	−0.970264	+	0.242051i	$0.922180\pi$
$368$	1.29778	+	1.48838i	0.0676515	+	0.0775874i
$369$	9.23428	+	5.78225i	0.480717	+	0.301012i
$370$	29.8478	−	11.7704i	1.55171	−	0.611911i
$371$	−4.25598	+	5.54650i	−0.220959	+	0.287960i
$372$	−12.5310	+	14.6805i	−0.649704	+	0.761147i
$373$	6.04116	−	4.63555i	0.312800	−	0.240020i	−0.440415	−	0.897794i	$-0.645169\pi$
$373$	6.04116	−	4.63555i	0.312800	−	0.240020i	0.753215	+	0.657775i	$0.228502\pi$
$374$	6.31614	−	1.57732i	0.326600	−	0.0815614i
$375$	15.0757	+	0.270209i	0.778507	+	0.0139535i
$376$	−5.87770	−	5.00854i	−0.303119	−	0.258296i
$377$	−11.6799	+	11.6799i	−0.601544	+	0.601544i
$378$	1.37077	+	7.09090i	0.0705048	+	0.364716i
$379$	−19.6865	−	8.15440i	−1.01123	−	0.418863i	−0.185324	−	0.982678i	$-0.559333\pi$
$379$	−19.6865	−	8.15440i	−1.01123	−	0.418863i	−0.825902	+	0.563814i	$0.809333\pi$
$380$	0.0781939	−	0.256453i	0.00401126	−	0.0131557i
$381$	−5.04814	−	2.19781i	−0.258624	−	0.112597i
$382$	−7.58598	+	5.61776i	−0.388132	+	0.287429i
$383$	8.44625	−	14.6293i	0.431583	−	0.747524i	−0.565426	−	0.824799i	$-0.691288\pi$
$383$	8.44625	−	14.6293i	0.431583	−	0.747524i	0.997010	+	0.0772743i	$0.0246217\pi$
$384$	18.1530	−	7.38021i	0.926368	−	0.376620i
$385$	−1.33412	−	2.31077i	−0.0679931	−	0.117768i
$386$	−6.58539	−	2.86046i	−0.335188	−	0.145593i
$387$	−26.0293	−	21.4979i	−1.32315	−	1.09280i
$388$	−6.03458	−	6.46152i	−0.306360	−	0.328034i
$389$	−1.76481	−	13.4051i	−0.0894796	−	0.679665i	−0.976124	−	0.217214i	$-0.930303\pi$
$389$	−1.76481	−	13.4051i	−0.0894796	−	0.679665i	0.886644	−	0.462452i	$-0.153030\pi$
$390$	11.6634	−	2.69158i	0.590597	−	0.136293i
$391$	−0.557235	−	2.07963i	−0.0281806	−	0.105171i
$392$	−3.09121	+	16.7847i	−0.156130	+	0.847754i
$393$	21.6639	+	13.0308i	1.09280	+	0.657315i
$394$	−1.70402	+	5.95108i	−0.0858471	+	0.299811i
$395$	−34.5487	−	14.3105i	−1.73833	−	0.720041i
$396$	−2.82692	+	5.66735i	−0.142058	+	0.284795i
$397$	−2.00950	−	4.85136i	−0.100854	−	0.243483i	0.865396	−	0.501088i	$-0.167067\pi$
$397$	−2.00950	−	4.85136i	−0.100854	−	0.243483i	−0.966250	+	0.257605i	$0.917067\pi$
$398$	−10.4191	−	8.28130i	−0.522261	−	0.415104i
$399$	−0.0244952	+	0.0852744i	−0.00122630	+	0.00426906i
$400$	−1.24248	−	6.34093i	−0.0621242	−	0.317047i
$401$	1.25430	−	2.17251i	0.0626366	−	0.108490i	−0.833007	−	0.553263i	$-0.813382\pi$
$401$	1.25430	−	2.17251i	0.0626366	−	0.108490i	0.895643	+	0.444773i	$0.146716\pi$
$402$	33.7615	+	15.3897i	1.68387	+	0.767569i
$403$	−8.39850	−	6.44440i	−0.418359	−	0.321018i
$404$	−10.0689	−	26.8688i	−0.500949	−	1.33677i
$405$	−12.7402	−	19.3270i	−0.633068	−	0.960365i
$406$	−8.39736	−	8.68916i	−0.416754	−	0.431236i
$407$	−8.99346	−	2.40979i	−0.445789	−	0.119449i
$408$	−21.3139	−	1.47621i	−1.05520	−	0.0730832i
$409$	−4.97879	+	1.33406i	−0.246185	+	0.0659652i	−0.379802	−	0.925068i	$-0.624008\pi$
$409$	−4.97879	+	1.33406i	−0.246185	+	0.0659652i	0.133616	+	0.991033i	$0.457341\pi$
$410$	11.3259	+	6.79946i	0.559345	+	0.335802i
$411$	−11.3090	−	9.00424i	−0.557832	−	0.444146i
$412$	2.07434	+	3.89418i	0.102196	+	0.191853i
$413$	2.23641	+	5.39917i	0.110047	+	0.265676i
$414$	1.88997	+	0.902766i	0.0928868	+	0.0443685i
$415$			18.7617i			0.920976i
$416$	4.56050	+	9.73207i	0.223597	+	0.477154i
$417$	−26.2343	+	6.52791i	−1.28470	+	0.319673i
$418$	−0.0625248	+	0.0463025i	−0.00305819	+	0.00226473i
$419$	−0.0997947	+	0.758016i	−0.00487529	+	0.0370315i	−0.993710	−	0.111988i	$-0.964278\pi$
$419$	−0.0997947	+	0.758016i	−0.00487529	+	0.0370315i	0.988834	+	0.149019i	$0.0476116\pi$
$420$	1.82307	+	8.56480i	0.0889565	+	0.417919i
$421$	−24.0641	+	3.16811i	−1.17281	+	0.154404i	−0.691654	−	0.722229i	$-0.743118\pi$
$421$	−24.0641	+	3.16811i	−1.17281	+	0.154404i	−0.481160	+	0.876633i	$0.659785\pi$
$422$	−15.6042	−	0.266485i	−0.759600	−	0.0129723i
$423$	−7.83052	−	2.40205i	−0.380733	−	0.116792i
$424$	20.0935	+	1.03026i	0.975827	+	0.0500338i
$425$	−1.82334	+	6.80479i	−0.0884449	+	0.330081i
$426$	−17.3170	−	32.5758i	−0.839013	−	1.57830i
$427$	1.10445	+	1.43934i	0.0534479	+	0.0696546i
$428$	15.2225	+	2.53557i	0.735806	+	0.122561i
$429$	−3.18481	−	1.38657i	−0.153764	−	0.0669442i
$430$	−32.0434	−	25.4687i	−1.54527	−	1.22821i
$431$		−	15.8238i		−	0.762205i	−0.924533	−	0.381102i	$-0.875545\pi$
$431$		−	15.8238i		−	0.762205i	0.924533	−	0.381102i	$-0.124455\pi$
$432$	14.5666	−	14.8261i	0.700835	−	0.713323i
$433$		−	10.2972i		−	0.494853i	−0.968907	−	0.247426i	$-0.920415\pi$
$433$		−	10.2972i		−	0.494853i	0.968907	−	0.247426i	$-0.0795849\pi$
$434$	4.81867	−	6.06260i	0.231304	−	0.291014i
$435$	35.5110	+	15.4604i	1.70262	+	0.741270i
$436$	−6.03380	−	8.44559i	−0.288967	−	0.404471i
$437$	0.0156638	+	0.0204134i	0.000749299	+	0.000976506i
$438$	−18.5454	+	9.85861i	−0.886135	+	0.471063i
$439$	5.04096	−	18.8131i	0.240592	−	0.897902i	−0.734956	−	0.678115i	$-0.762797\pi$
$439$	5.04096	−	18.8131i	0.240592	−	0.897902i	0.975548	−	0.219787i	$-0.0705362\pi$
$440$	−3.29801	+	6.93460i	−0.157226	+	0.330594i
$441$	4.05560	+	17.6421i	0.193124	+	0.840099i
$442$	0.200086	−	11.7162i	0.00951712	−	0.557281i
$443$	−27.1148	+	3.56973i	−1.28826	+	0.169603i	−0.743357	−	0.668895i	$-0.766767\pi$
$443$	−27.1148	+	3.56973i	−1.28826	+	0.169603i	−0.544904	+	0.838498i	$0.683434\pi$
$444$	25.6312	+	16.6347i	1.21640	+	0.789446i
$445$	−1.74646	+	13.2657i	−0.0827903	+	0.628855i
$446$	8.42530	+	11.3772i	0.398950	+	0.538724i
$447$	8.02670	−	1.99729i	0.379650	−	0.0944685i
$448$	−7.17550	+	3.21422i	−0.339011	+	0.151858i
$449$		−	24.0023i		−	1.13274i	−0.824152	−	0.566369i	$-0.808348\pi$
$449$		−	24.0023i		−	1.13274i	0.824152	−	0.566369i	$-0.191652\pi$
$450$	−3.87869	−	5.65030i	−0.182843	−	0.266358i
$451$	−1.46701	−	3.54167i	−0.0690787	−	0.166771i
$452$	−11.0492	+	36.2379i	−0.519709	+	1.70449i
$453$	4.16685	+	3.31765i	0.195776	+	0.155877i
$454$	−14.2564	+	23.7468i	−0.669084	+	1.11449i
$455$	−4.63906	+	1.24303i	−0.217482	+	0.0582742i
$456$	0.242086	−	0.0811793i	0.0113367	−	0.00380157i
$457$	−34.7412	−	9.30888i	−1.62513	−	0.435451i	−0.672624	−	0.739984i	$-0.734833\pi$
$457$	−34.7412	−	9.30888i	−1.62513	−	0.435451i	−0.952502	+	0.304533i	$0.901500\pi$
$458$	−25.7127	+	24.8492i	−1.20148	+	1.16113i
$459$	−21.3718	+	7.53438i	−0.997549	+	0.351675i
$460$	2.31167	+	1.05138i	0.107782	+	0.0490209i
$461$	−22.1490	−	16.9956i	−1.03158	−	0.791562i	−0.0532470	−	0.998581i	$-0.516957\pi$
$461$	−22.1490	−	16.9956i	−1.03158	−	0.791562i	−0.978337	+	0.207019i	$0.933624\pi$
$462$	1.05399	−	2.31222i	0.0490362	−	0.107574i
$463$	16.8782	−	29.2340i	0.784399	−	1.35862i	−0.144959	−	0.989438i	$-0.546305\pi$
$463$	16.8782	−	29.2340i	0.784399	−	1.35862i	0.929358	−	0.369181i	$-0.120362\pi$
$464$	−6.88174	+	34.0880i	−0.319477	+	1.58250i
$465$	−6.85303	+	23.8572i	−0.317801	+	1.10635i
$466$	−17.3911	+	21.8805i	−0.805626	+	1.01360i
$467$	0.0101112	+	0.0244107i	0.000467893	+	0.00112959i	0.924113	−	0.382119i	$-0.124805\pi$
$467$	0.0101112	+	0.0244107i	0.000467893	+	0.00112959i	−0.923645	+	0.383248i	$0.874805\pi$
$468$	8.53640	+	7.55514i	0.394595	+	0.349236i
$469$	−13.7540	−	5.69708i	−0.635099	−	0.263067i
$470$	−9.54726	−	2.73374i	−0.440382	−	0.126098i
$471$	22.2730	+	13.3972i	1.02629	+	0.617310i
$472$	9.14401	−	14.1155i	0.420887	−	0.649718i
$473$	3.07429	+	11.4734i	0.141356	+	0.527547i
$474$	−8.00813	−	34.7014i	−0.367826	−	1.59389i
$475$	−0.0109894	−	0.0834731i	−0.000504230	−	0.00383001i
$476$	8.56731	+	0.292707i	0.392682	+	0.0134162i
$477$	19.9959	−	7.45484i	0.915551	−	0.341334i
$478$	3.17399	−	7.30721i	0.145175	−	0.334224i
$479$	2.14432	+	3.71408i	0.0979767	+	0.169701i	0.910847	−	0.412744i	$-0.135430\pi$
$479$	2.14432	+	3.71408i	0.0979767	+	0.169701i	−0.812870	+	0.582445i	$0.802096\pi$
$480$	17.3211	−	18.3045i	0.790596	−	0.835484i
$481$	−8.37941	+	14.5136i	−0.382068	+	0.661761i
$482$	−12.2062	−	16.4827i	−0.555978	−	0.750768i
$483$	−0.770525	−	0.335463i	−0.0350601	−	0.0152641i
$484$	−17.4503	+	9.29539i	−0.793196	+	0.422518i
$485$	−10.5045	−	4.35111i	−0.476985	−	0.197574i
$486$	7.94078	−	20.5656i	0.360201	−	0.932875i
$487$	21.2634	−	21.2634i	0.963536	−	0.963536i	−0.0358223	−	0.999358i	$-0.511405\pi$
$487$	21.2634	−	21.2634i	0.963536	−	0.963536i	0.999358	+	0.0358223i	$0.0114050\pi$
$488$	1.60782	−	4.96749i	0.0727827	−	0.224868i
$489$	−29.8101	−	0.534301i	−1.34806	−	0.0241619i
$490$	5.31784	+	21.2945i	0.240235	+	0.961985i
$491$	29.4392	−	22.5895i	1.32857	−	1.01945i	0.331464	−	0.943468i	$-0.392458\pi$
$491$	29.4392	−	22.5895i	1.32857	−	1.01945i	0.997109	−	0.0759818i	$-0.0242091\pi$
$492$	0.990662	+	12.5417i	0.0446625	+	0.565423i
$493$	23.0813	−	30.0801i	1.03953	−	1.35474i
$494$	0.0513744	+	0.130277i	0.00231144	+	0.00586146i
$495$	−0.291869	+	8.13948i	−0.0131185	+	0.365842i
$496$	−22.2353	−	1.52114i	−0.998396	−	0.0683012i
$497$	7.40124	+	12.8193i	0.331991	+	0.575025i
$498$	−14.5474	+	10.3746i	−0.651884	+	0.464895i
$499$	−2.18367	+	16.5866i	−0.0977545	+	0.742519i	0.870432	+	0.492289i	$0.163840\pi$
$499$	−2.18367	+	16.5866i	−0.0977545	+	0.742519i	−0.968186	+	0.250230i	$0.919494\pi$
$500$	10.1212	+	14.1667i	0.452632	+	0.633555i
$501$	−0.0416957	+	0.278102i	−0.00186283	+	0.0124247i
$502$	33.5684	+	9.61189i	1.49823	+	0.429000i
$503$	−0.717471	+	0.717471i	−0.0319904	+	0.0319904i	−0.722921	−	0.690931i	$-0.757201\pi$
$503$	−0.717471	+	0.717471i	−0.0319904	+	0.0319904i	0.690931	+	0.722921i	$0.257201\pi$
$504$	−5.63285	+	6.14959i	−0.250907	+	0.273924i
$505$	−26.0925	−	26.0925i	−1.16110	−	1.16110i
$506$	−0.357523	−	0.644415i	−0.0158938	−	0.0286478i
$507$	10.1308	−	12.7239i	0.449925	−	0.565090i
$508$	−1.43482	−	6.19355i	−0.0636597	−	0.274794i
$509$	20.6886	+	2.72371i	0.917008	+	0.120726i	0.574234	−	0.818692i	$-0.305300\pi$
$509$	20.6886	+	2.72371i	0.917008	+	0.120726i	0.342774	+	0.939418i	$0.388633\pi$
$510$	−25.7367	+	9.61987i	−1.13964	+	0.425975i
$511$	7.29805	−	4.21353i	0.322847	−	0.186396i
$512$	19.3331	+	11.7572i	0.854409	+	0.519601i
$513$	0.201515	−	0.180933i	0.00889710	−	0.00798838i
$514$	3.82936	−	8.81601i	0.168906	−	0.388857i
$515$	4.50163	+	3.45422i	0.198365	+	0.152211i
$516$	2.02901	−	38.9290i	0.0893223	−	1.71375i
$517$	1.75437	+	2.28634i	0.0771572	+	0.100553i
$518$	−10.5113	−	6.31043i	−0.461840	−	0.277264i
$519$	39.7650	−	22.0178i	1.74549	−	0.966474i
$520$	10.5202	+	8.96454i	0.461342	+	0.393121i
$521$	24.3396	+	24.3396i	1.06634	+	1.06634i	0.997637	+	0.0686992i	$0.0218849\pi$
$521$	24.3396	+	24.3396i	1.06634	+	1.06634i	0.0686992	+	0.997637i	$0.478115\pi$
$522$	7.64868	+	36.0835i	0.334774	+	1.57933i
$523$	−1.63536	+	3.94811i	−0.0715094	+	0.172639i	−0.955593	−	0.294690i	$-0.904784\pi$
$523$	−1.63536	+	3.94811i	−0.0715094	+	0.172639i	0.884084	+	0.467329i	$0.154784\pi$
$524$	2.81983	+	29.0553i	0.123185	+	1.26929i
$525$	1.63463	+	2.21124i	0.0713410	+	0.0965063i
$526$	−2.64595	−	0.394419i	−0.115369	−	0.0171975i
$527$	21.0438	+	12.1497i	0.916684	+	0.529248i
$528$	−7.20060	+	1.27739i	−0.313366	+	0.0555911i
$529$	19.7075	−	11.3781i	0.856849	−	0.494702i
$530$	24.0706	−	9.49215i	1.04556	−	0.412312i
$531$	2.96070	−	17.5912i	0.128483	−	0.763394i
$532$	−0.0959333	+	0.0359505i	−0.00415924	+	0.00155865i
$533$	−6.84103	+	0.900639i	−0.296318	+	0.0390110i
$534$	−11.2516	+	5.98129i	−0.486906	+	0.258836i
$535$	19.1699	−	5.13655i	0.828786	−	0.222073i
$536$	8.95511	+	41.8973i	0.386802	+	1.80969i
$537$	11.1997	+	0.200738i	0.483303	+	0.00866247i
$538$	−20.4946	−	36.9404i	−0.883585	−	1.59261i
$539$	2.43740	−	5.88441i	0.104986	−	0.253460i
$540$	9.15833	−	25.1115i	0.394112	−	1.08063i
$541$	−3.42729	+	1.41963i	−0.147351	+	0.0610346i	−0.455140	−	0.890420i	$-0.650411\pi$
$541$	−3.42729	+	1.41963i	−0.147351	+	0.0610346i	0.307789	+	0.951455i	$0.400411\pi$
$542$	2.93334	+	25.6595i	0.125998	+	1.10217i
$543$	−9.55467	+	9.21819i	−0.410030	+	0.395590i
$544$	−13.2945	−	20.7816i	−0.569996	−	0.891002i
$545$	−11.5600	−	6.67414i	−0.495174	−	0.285889i
$546$	−3.52905	−	2.90966i	−0.151029	−	0.124522i
$547$	14.4812	−	18.8723i	0.619173	−	0.806923i	−0.373515	−	0.927624i	$-0.621848\pi$
$547$	14.4812	−	18.8723i	0.619173	−	0.806923i	0.992689	+	0.120701i	$0.0385144\pi$
$548$	0.569962	−	16.6824i	0.0243476	−	0.712636i
$549$	−0.525624	−	5.51293i	−0.0224331	−	0.235286i
$550$	−0.0411750	+	2.41103i	−0.00175571	+	0.102807i
$551$	−0.117278	+	0.437686i	−0.00499620	+	0.0186461i
$552$	0.463052	+	2.37379i	0.0197088	+	0.101035i
$553$	3.69834	+	13.8024i	0.157269	+	0.586937i
$554$	−19.2482	+	4.80684i	−0.817779	+	0.204223i
$555$	38.8613	+	5.82646i	1.64957	+	0.247319i
$556$	−24.1024	−	19.8380i	−1.02217	−	0.841318i
$557$	9.09220	−	3.76611i	0.385249	−	0.159575i	−0.181649	−	0.983363i	$-0.558143\pi$
$557$	9.09220	−	3.76611i	0.385249	−	0.159575i	0.566898	+	0.823788i	$0.308143\pi$
$558$	−22.2878	+	7.87848i	−0.943516	+	0.333523i
$559$	21.3800			0.904280
$560$	−6.68854	+	7.58304i	−0.282642	+	0.320442i
$561$	7.66333	+	2.20131i	0.323546	+	0.0929393i
$562$	−5.37037	+	36.0269i	−0.226535	+	1.51971i
$563$	−15.9631	−	2.10158i	−0.672763	−	0.0885709i	−0.213598	−	0.976922i	$-0.568518\pi$
$563$	−15.9631	−	2.10158i	−0.672763	−	0.0885709i	−0.459165	+	0.888351i	$0.651851\pi$
$564$	−3.15962	−	8.91437i	−0.133044	−	0.375363i
$565$	6.35934	+	48.3040i	0.267539	+	2.03216i
$566$	−15.0511	−	15.5742i	−0.632647	−	0.654631i
$567$	−2.89542	+	8.35801i	−0.121596	+	0.351003i
$568$	18.2962	−	38.4707i	0.767691	−	1.61420i
$569$	13.9576	+	3.73992i	0.585132	+	0.156786i	0.539227	−	0.842160i	$-0.318716\pi$
$569$	13.9576	+	3.73992i	0.585132	+	0.156786i	0.0459046	+	0.998946i	$0.485383\pi$
$570$	0.240171	−	0.223922i	0.0100597	−	0.00937907i
$571$	10.6514	−	8.17311i	0.445748	−	0.342034i	−0.361372	−	0.932422i	$-0.617692\pi$
$571$	10.6514	−	8.17311i	0.445748	−	0.342034i	0.807120	+	0.590387i	$0.201025\pi$
$572$	−0.905209	−	3.90744i	−0.0378487	−	0.163378i
$573$	−11.4874	+	1.30338i	−0.479893	+	0.0544493i
$574$	−0.573318	−	5.01513i	−0.0239299	−	0.209328i
$575$	0.797480			0.0332572
$576$	23.7708	+	3.30862i	0.990452	+	0.137859i
$577$	6.84675			0.285034			0.142517	−	0.989792i	$-0.454480\pi$
$577$	6.84675			0.285034			0.142517	+	0.989792i	$0.454480\pi$
$578$	0.324340	+	2.83718i	0.0134908	+	0.118011i
$579$	−5.22722	−	7.07110i	−0.217236	−	0.293865i
$580$	10.0932	+	43.5684i	0.419096	+	1.80908i
$581$	5.68765	−	4.36429i	0.235964	−	0.181061i
$582$	−2.43487	−	10.5509i	−0.100928	−	0.437351i
$583$	−7.25273	−	1.94336i	−0.300377	−	0.0804859i
$584$	−21.9014	−	10.4160i	−0.906288	−	0.431019i
$585$	14.0155	+	4.29932i	0.579468	+	0.177755i
$586$	−2.58529	−	2.67513i	−0.106797	−	0.110508i
$587$	−1.66637	−	12.6574i	−0.0687785	−	0.522425i	−0.990805	−	0.135298i	$-0.956801\pi$
$587$	−1.66637	−	12.6574i	−0.0687785	−	0.522425i	0.922026	−	0.387127i	$-0.126532\pi$
$588$	−13.5706	+	15.8984i	−0.559644	+	0.655638i
$589$	−0.287919	−	0.0379052i	−0.0118635	−	0.00156186i
$590$	3.18888	−	21.3925i	0.131284	−	0.880713i
$591$	−5.45611	+	5.26397i	−0.224434	+	0.216531i
$592$	2.20711	+	35.2139i	0.0907116	+	1.44728i
$593$	−12.7737			−0.524553			−0.262277	−	0.964993i	$-0.584473\pi$
$593$	−12.7737			−0.524553			−0.262277	+	0.964993i	$0.584473\pi$
$594$	−6.47255	+	4.27453i	−0.265572	+	0.175386i
$595$	10.1850	−	4.21876i	0.417544	−	0.172952i
$596$	7.37441	+	6.06966i	0.302068	+	0.248623i
$597$	−5.96704	−	15.1690i	−0.244215	−	0.620828i
$598$	−1.28695	+	0.321388i	−0.0526272	+	0.0131425i
$599$	−1.14967	−	4.29061i	−0.0469741	−	0.175310i	0.938453	−	0.345406i	$-0.112259\pi$
$599$	−1.14967	−	4.29061i	−0.0469741	−	0.175310i	−0.985427	+	0.170096i	$0.945592\pi$
$600$	2.57149	−	7.48427i	0.104981	−	0.305544i
$601$	−9.64044	+	35.9786i	−0.393242	+	1.46760i	0.431512	+	0.902107i	$0.357980\pi$
$601$	−9.64044	+	35.9786i	−0.393242	+	1.46760i	−0.824754	+	0.565491i	$0.808687\pi$
$602$	−0.267070	+	15.6385i	−0.0108850	+	0.637377i
$603$	26.3540	+	37.0202i	1.07322	+	1.50758i
$604$	−0.210005	+	6.14669i	−0.00854497	+	0.250105i
$605$	−15.4788	+	20.1724i	−0.629303	+	0.820123i
$606$	5.80330	−	34.6597i	0.235743	−	1.40796i
$607$	−28.1930	−	16.2773i	−1.14432	−	0.660674i	−0.196824	−	0.980439i	$-0.563063\pi$
$607$	−28.1930	−	16.2773i	−1.14432	−	0.660674i	−0.947497	+	0.319765i	$0.896396\pi$
$608$	0.241833	+	0.168654i	0.00980762	+	0.00683984i
$609$	−3.57360	−	14.3616i	−0.144810	−	0.581961i
$610$	−0.762628	−	6.67113i	−0.0308779	−	0.270106i
$611$	4.79237	−	1.98506i	0.193879	−	0.0803071i
$612$	−21.6905	−	14.6362i	−0.876785	−	0.591631i
$613$	5.53671	−	13.3668i	0.223626	−	0.539880i	−0.771752	−	0.635924i	$-0.780619\pi$
$613$	5.53671	−	13.3668i	0.223626	−	0.539880i	0.995377	+	0.0960444i	$0.0306191\pi$
$614$	−16.8963	−	30.4546i	−0.681878	−	1.22905i
$615$	7.83714	+	14.1542i	0.316024	+	0.570753i
$616$	2.86941	−	0.613306i	0.115612	−	0.0247108i
$617$	12.0313	−	3.22379i	0.484364	−	0.129785i	−0.00837016	−	0.999965i	$-0.502664\pi$
$617$	12.0313	−	3.22379i	0.484364	−	0.129785i	0.492734	+	0.870180i	$0.335998\pi$
$618$	−0.189083	+	5.40052i	−0.00760602	+	0.217241i
$619$	40.2861	−	5.30377i	1.61924	−	0.213176i	0.734278	−	0.678849i	$-0.237521\pi$
$619$	40.2861	−	5.30377i	1.61924	−	0.213176i	0.884957	+	0.465672i	$0.154187\pi$
$620$	−26.8392	+	10.0579i	−1.07789	+	0.403933i
$621$	1.44999	+	2.11612i	0.0581863	+	0.0849169i
$622$	−15.5665	+	6.13859i	−0.624160	+	0.246135i
$623$	4.42778	−	2.55638i	0.177395	−	0.102419i
$624$	−1.13359	+	13.1142i	−0.0453801	+	0.524988i
$625$	26.3856	+	15.2337i	1.05542	+	0.609349i
$626$	2.56233	+	0.381954i	0.102411	+	0.0152660i
$627$	−0.0946811	+	0.0107426i	−0.00378120	+	0.000429020i
$628$	2.89913	+	29.8724i	0.115688	+	1.19204i
$629$	14.7212	−	35.5401i	0.586972	−	1.41707i
$630$	−3.31982	+	10.1979i	−0.132265	+	0.406295i
$631$	15.1745	+	15.1745i	0.604088	+	0.604088i	0.941395	−	0.337307i	$-0.109516\pi$
$631$	15.1745	+	15.1745i	0.604088	+	0.604088i	−0.337307	+	0.941395i	$0.609516\pi$
$632$	26.6718	−	31.3003i	1.06095	−	1.24506i
$633$	−16.3792	−	9.85207i	−0.651016	−	0.391585i
$634$	32.3221	+	19.4045i	1.28368	+	0.770652i
$635$	−4.97721	−	6.48643i	−0.197515	−	0.257406i
$636$	20.6702	+	13.4149i	0.819625	+	0.531937i
$637$	−9.09525	−	6.97903i	−0.360367	−	0.276519i
$638$	5.17047	−	11.9036i	0.204701	−	0.471266i
$639$	1.61919	−	45.1549i	0.0640540	−	1.78630i
$640$	28.8916	+	3.47004i	1.14204	+	0.137165i
$641$	26.3543	−	15.2157i	1.04093	−	0.600983i	0.120835	−	0.992673i	$-0.461443\pi$
$641$	26.3543	−	15.2157i	1.04093	−	0.600983i	0.920097	+	0.391690i	$0.128109\pi$
$642$	14.5830	+	12.0235i	0.575545	+	0.474531i
$643$	34.5592	+	4.54981i	1.36288	+	0.179427i	0.776249	−	0.630426i	$-0.217120\pi$
$643$	34.5592	+	4.54981i	1.36288	+	0.179427i	0.586633	+	0.809853i	$0.300453\pi$
$644$	−0.219004	−	0.945355i	−0.00862995	−	0.0372522i
$645$	−18.3514	−	46.6517i	−0.722584	−	1.83691i
$646$	−0.155949	−	0.281089i	−0.00613572	−	0.0110593i
$647$	0.701049	+	0.701049i	0.0275611	+	0.0275611i	0.720753	−	0.693192i	$-0.243796\pi$
$647$	0.701049	+	0.701049i	0.0275611	+	0.0275611i	−0.693192	+	0.720753i	$0.743796\pi$
$648$	24.5351	−	6.78459i	0.963828	−	0.266524i
$649$	−4.43815	+	4.43815i	−0.174213	+	0.174213i
$650$	4.17268	+	1.19479i	0.163666	+	0.0468637i
$651$	8.82648	−	3.47207i	0.345937	−	0.136081i
$652$	−20.0132	−	28.0127i	−0.783776	−	1.09706i
$653$	−5.32531	+	40.4497i	−0.208395	+	1.58292i	0.492924	+	0.870073i	$0.335928\pi$
$653$	−5.32531	+	40.4497i	−0.208395	+	1.58292i	−0.701319	+	0.712847i	$0.747405\pi$
$654$	−1.21727	−	12.6539i	−0.0475989	−	0.494806i
$655$	18.7706	+	32.5117i	0.733430	+	1.27034i
$656$	−10.9493	+	9.54709i	−0.427497	+	0.372751i
$657$	−25.7068	−	0.921805i	−1.00292	−	0.0359630i
$658$	1.39211	+	3.53018i	0.0542703	+	0.137621i
$659$	−17.4306	+	22.7160i	−0.678999	+	0.884888i	−0.998022	−	0.0628584i	$-0.979978\pi$
$659$	−17.4306	+	22.7160i	−0.678999	+	0.884888i	0.319024	+	0.947747i	$0.396645\pi$
$660$	−7.74913	+	5.32910i	−0.301635	+	0.207435i
$661$	−25.1459	+	19.2951i	−0.978061	+	0.750493i	−0.968385	−	0.249460i	$-0.919747\pi$
$661$	−25.1459	+	19.2951i	−0.978061	+	0.750493i	−0.00967629	+	0.999953i	$0.503080\pi$
$662$	0.914711	+	3.66282i	0.0355512	+	0.142360i
$663$	7.39728	−	12.2981i	0.287287	−	0.477619i
$664$	−19.6293	−	6.35341i	−0.761766	−	0.246560i
$665$	−0.0931616	+	0.0931616i	−0.00361265	+	0.00361265i
$666$	16.9712	+	33.3539i	0.657620	+	1.29244i
$667$	−3.96531	−	1.64248i	−0.153537	−	0.0635972i
$668$	−0.286590	+	0.152660i	−0.0110885	+	0.00590659i
$669$	1.95476	+	17.2284i	0.0755752	+	0.666088i
$670$	32.7901	+	44.2783i	1.26679	+	1.71062i
$671$	−0.974256	+	1.68746i	−0.0376107	+	0.0651437i
$672$	−9.57823	−	0.992986i	−0.369488	−	0.0383053i
$673$	17.3691	+	30.0842i	0.669531	+	1.15966i	0.978035	+	0.208439i	$0.0668382\pi$
$673$	17.3691	+	30.0842i	0.669531	+	1.15966i	−0.308504	+	0.951223i	$0.599828\pi$
$674$	−3.56221	+	8.20099i	−0.137211	+	0.315890i
$675$	−0.646811	−	8.36880i	−0.0248958	−	0.322115i
$676$	18.7696	+	0.641273i	0.721907	+	0.0246643i
$677$	0.922328	+	7.00578i	0.0354480	+	0.269254i	0.999986	+	0.00530975i	$0.00169015\pi$
$677$	0.922328	+	7.00578i	0.0354480	+	0.269254i	−0.964538	+	0.263944i	$0.914977\pi$
$678$	−33.9373	+	31.6412i	−1.30335	+	1.21517i
$679$	1.12448	+	4.19660i	0.0431534	+	0.161051i
$680$	−26.6274	−	17.2493i	−1.02112	−	0.661479i
$681$	−29.6770	+	16.4321i	−1.13722	+	0.629678i
$682$	7.99610	+	2.28958i	0.306186	+	0.0876726i
$683$	−17.9428	−	7.43214i	−0.686561	−	0.284383i	0.0120054	−	0.999928i	$-0.496178\pi$
$683$	−17.9428	−	7.43214i	−0.686561	−	0.284383i	−0.698567	+	0.715545i	$0.746178\pi$
$684$	0.306430	+	0.0624020i	0.0117166	+	0.00238600i
$685$	−8.21482	−	19.8323i	−0.313872	−	0.757755i
$686$	11.2722	−	14.1821i	0.430376	−	0.541476i
$687$	−42.4984	+	10.5749i	−1.62141	+	0.403458i
$688$	37.4976	−	24.9006i	1.42958	−	0.949325i
$689$	−6.75753	+	11.7044i	−0.257442	+	0.445902i
$690$	1.80591	+	2.53229i	0.0687500	+	0.0964025i
$691$	−26.5781	−	20.3941i	−1.01108	−	0.775828i	−0.0363766	−	0.999338i	$-0.511582\pi$
$691$	−26.5781	−	20.3941i	−1.01108	−	0.775828i	−0.974701	+	0.223511i	$0.928248\pi$
$692$	47.7761	+	21.7293i	1.81618	+	0.826025i
$693$	2.53539	−	1.80490i	0.0963116	−	0.0685624i
$694$	0.235891	−	0.227969i	0.00895430	−	0.00865360i
$695$	−38.7771	−	10.3903i	−1.47090	−	0.394127i
$696$	−28.2007	+	31.9178i	−1.06895	+	1.20984i
$697$	15.2988	−	4.09929i	0.579482	−	0.155272i
$698$	6.74987	−	11.2433i	0.255486	−	0.425564i
$699$	−31.8556	+	12.5310i	−1.20489	+	0.473968i
$700$	−0.926058	+	3.03719i	−0.0350017	+	0.114795i
$701$	3.78906	+	9.14760i	0.143111	+	0.345500i	0.979141	−	0.203184i	$-0.0651290\pi$
$701$	3.78906	+	9.14760i	0.143111	+	0.345500i	−0.836030	+	0.548684i	$0.815129\pi$
$702$	4.41646	+	13.2446i	0.166689	+	0.499886i
$703$			0.459737i			0.0173393i
$704$	−6.13846	−	5.79884i	−0.231352	−	0.218552i
$705$	−8.44494	−	8.75319i	−0.318055	−	0.329664i
$706$	12.1377	+	16.3902i	0.456807	+	0.616852i
$707$	−1.84044	+	13.9796i	−0.0692170	+	0.525755i
$708$	18.3505	−	9.35668i	0.689655	−	0.351646i
$709$	−44.9333	+	5.91558i	−1.68751	+	0.222164i	−0.912294	−	0.409536i	$-0.865691\pi$
$709$	−44.9333	+	5.91558i	−1.68751	+	0.222164i	−0.775213	+	0.631700i	$0.782357\pi$
$710$	0.935456	−	54.7762i	0.0351070	−	2.05572i
$711$	12.7916	−	41.6996i	0.479721	−	1.56386i
$712$	−13.2878	−	6.31949i	−0.497980	−	0.236833i
$713$	0.711934	−	2.65697i	0.0266621	−	0.0995044i
$714$	8.90306	+	5.56438i	0.333189	+	0.208242i
$715$	−3.14006	−	4.09221i	−0.117432	−	0.153040i
$716$	7.51898	+	10.5244i	0.280998	+	0.393316i
$717$	7.84616	−	5.80017i	0.293020	−	0.216611i
$718$	−28.9381	+	36.4084i	−1.07996	+	1.35875i
$719$			23.1837i			0.864608i	0.901728	+	0.432304i	$0.142299\pi$
$719$			23.1837i			0.864608i	−0.901728	+	0.432304i	$0.857701\pi$
$720$	29.5884	−	8.78291i	1.10270	−	0.327320i
$721$		−	2.16819i		−	0.0807475i
$722$	−21.0320	−	16.7167i	−0.782731	−	0.622130i
$723$	−2.83196	−	24.9597i	−0.105322	−	0.928263i
$724$	−15.1221	−	2.51884i	−0.562008	−	0.0936121i
$725$	8.54944	+	11.1418i	0.317518	+	0.413798i
$726$	−24.2004	−	0.847303i	−0.898161	−	0.0314464i
$727$	4.03213	−	15.0481i	0.149543	−	0.558104i	−0.849968	−	0.526835i	$-0.823379\pi$
$727$	4.03213	−	15.0481i	0.149543	−	0.558104i	0.999511	−	0.0312687i	$-0.00995475\pi$
$728$	0.270442	−	5.27453i	0.0100232	−	0.195487i
$729$	21.0306	−	16.9326i	0.778911	−	0.627135i
$730$	−31.1842	−	0.532556i	−1.15418	−	0.0197108i
$731$	−48.6560	+	6.40569i	−1.79961	+	0.236923i
$732$	4.75093	−	4.28022i	0.175599	−	0.158201i
$733$	0.808918	−	6.14434i	0.0298781	−	0.226947i	−0.969991	−	0.243142i	$-0.921822\pi$
$733$	0.808918	−	6.14434i	0.0298781	−	0.226947i	0.999869	+	0.0161952i	$0.00515532\pi$
$734$	11.9970	−	8.88431i	0.442817	−	0.327926i
$735$	−7.42157	+	25.8364i	−0.273749	+	0.952990i
$736$	−1.88282	+	2.06253i	−0.0694016	+	0.0760259i
$737$		−	15.9889i		−	0.588958i
$738$	−6.64118	+	13.9035i	−0.244465	+	0.511795i
$739$	15.6959	+	37.8932i	0.577382	+	1.39392i	0.895154	+	0.445757i	$0.147065\pi$
$739$	15.6959	+	37.8932i	0.577382	+	1.39392i	−0.317772	+	0.948167i	$0.602935\pi$
$740$	21.3323	+	40.0474i	0.784192	+	1.47217i
$741$	−0.0254309	+	0.169619i	−0.000934228	+	0.00623110i
$742$	−8.47678	−	5.08902i	−0.311193	−	0.186824i
$743$	−28.2851	+	7.57896i	−1.03768	+	0.278045i	−0.737151	−	0.675728i	$-0.763829\pi$
$743$	−28.2851	+	7.57896i	−1.03768	+	0.278045i	−0.300527	+	0.953773i	$0.597163\pi$
$744$	−22.6398	−	15.2489i	−0.830014	−	0.559051i
$745$	11.8643	+	3.17903i	0.434675	+	0.116471i
$746$	7.48359	+	7.74363i	0.273994	+	0.283515i
$747$	−21.7847	+	2.07704i	−0.797060	+	0.0759949i
$748$	3.23076	+	8.62122i	0.118128	+	0.315223i
$749$	−6.01639	−	4.61654i	−0.219834	−	0.168685i
$750$	2.04186	+	21.2257i	0.0745580	+	0.775054i
$751$	−10.8009	+	18.7077i	−0.394131	+	0.682654i	−0.992990	−	0.118200i	$-0.962288\pi$
$751$	−10.8009	+	18.7077i	−0.394131	+	0.682654i	0.598859	+	0.800854i	$0.295621\pi$
$752$	6.09321	−	9.06303i	0.222197	−	0.330495i
$753$	29.6926	+	30.7765i	1.08206	+	1.12156i
$754$	−18.2870	−	14.5349i	−0.665974	−	0.529329i
$755$	3.02678	+	7.30731i	0.110156	+	0.265940i
$756$	−9.74297	+	3.06498i	−0.354349	+	0.111472i
$757$	16.7909	+	6.95501i	0.610275	+	0.252784i	0.666346	−	0.745643i	$-0.267857\pi$
$757$	16.7909	+	6.95501i	0.610275	+	0.252784i	−0.0560710	+	0.998427i	$0.517857\pi$
$758$	8.29533	−	28.9705i	0.301300	−	1.05226i
$759$	0.0161747	−	0.902429i	0.000587103	−	0.0327561i
$760$	0.372892	+	0.0686750i	0.0135262	+	0.00249111i
$761$	−10.5672	−	39.4374i	−0.383061	−	1.42960i	−0.841201	−	0.540723i	$-0.818151\pi$
$761$	−10.5672	−	39.4374i	−0.383061	−	1.42960i	0.458139	−	0.888880i	$-0.348516\pi$
$762$	2.27720	−	7.44597i	0.0824944	−	0.269739i
$763$	0.665759	+	5.05694i	0.0241021	+	0.183074i
$764$	−9.11178	−	9.75642i	−0.329653	−	0.352975i
$765$	−33.1841	−	5.58506i	−1.19977	−	0.201928i
$766$	21.9118	+	9.51770i	0.791706	+	0.343888i
$767$	5.64869	+	9.78382i	0.203962	+	0.353273i
$768$	13.2855	+	24.3207i	0.479397	+	0.877598i
$769$	−24.9239	+	43.1695i	−0.898780	+	1.55673i	−0.0697240	+	0.997566i	$0.522212\pi$
$769$	−24.9239	+	43.1695i	−0.898780	+	1.55673i	−0.829056	+	0.559166i	$0.811121\pi$
$770$	3.03248	−	2.24569i	0.109283	−	0.0809290i
$771$	9.46625	−	6.99780i	0.340919	−	0.252019i
$772$	2.96135	−	9.71234i	0.106581	−	0.349555i
$773$	19.8497	+	8.22201i	0.713943	+	0.295725i	0.709935	−	0.704267i	$-0.248724\pi$
$773$	19.8497	+	8.22201i	0.713943	+	0.295725i	0.00400811	+	0.999992i	$0.498724\pi$
$774$	26.0250	−	40.0259i	0.935448	−	1.43870i
$775$	−6.36440	+	6.36440i	−0.228616	+	0.228616i
$776$	8.10954	−	9.51684i	0.291116	−	0.341635i
$777$	−7.27348	−	13.1362i	−0.260935	−	0.471259i
$778$	18.5515	−	4.63285i	0.665104	−	0.166096i
$779$	−0.150171	+	0.115230i	−0.00538043	+	0.00412855i
$780$	5.65524	+	15.9554i	0.202490	+	0.571295i
$781$	−9.67803	+	12.6127i	−0.346307	+	0.451316i
$782$	2.83250	−	1.11699i	0.101290	−	0.0399434i
$783$	−14.0202	+	42.9443i	−0.501040	+	1.53470i
$784$	−24.0800	−	1.64734i	−0.860001	−	0.0588334i
$785$	19.2985	+	33.4259i	0.688792	+	1.19302i
$786$	−14.8293	+	32.5321i	−0.528944	+	1.16038i
$787$	4.20545	−	31.9436i	0.149908	−	1.13867i	−0.736725	−	0.676192i	$-0.763629\pi$
$787$	4.20545	−	31.9436i	0.149908	−	1.13867i	0.886633	−	0.462473i	$-0.153038\pi$
$788$	−8.63534	−	1.43836i	−0.307621	−	0.0512396i
$789$	−2.56319	−	2.04082i	−0.0912521	−	0.0726550i
$790$	14.5579	−	50.8417i	0.517946	−	1.80887i
$791$	13.1642	−	13.1642i	0.468063	−	0.468063i
$792$	−8.41705	−	3.06170i	−0.299087	−	0.108793i
$793$	2.47998	+	2.47998i	0.0880667	+	0.0880667i
$794$	6.49369	−	3.60271i	0.230452	−	0.127855i
$795$	31.3395	+	4.69872i	1.11150	+	0.166646i
$796$	9.96219	−	15.9696i	0.353100	−	0.566028i
$797$	9.19149	+	1.21008i	0.325579	+	0.0428633i	0.291544	−	0.956557i	$-0.405831\pi$
$797$	9.19149	+	1.21008i	0.325579	+	0.0428633i	0.0340350	+	0.999421i	$0.489164\pi$
$798$	−0.123750	−	0.0207203i	−0.00438071	−	0.000733490i
$799$	−10.3116	+	5.95339i	−0.364797	+	0.210616i
$800$	8.70983	−	2.76427i	0.307939	−	0.0977317i
$801$	−15.5965	−	0.559265i	−0.551074	−	0.0197607i
$802$	3.25398	+	1.41341i	0.114902	+	0.0499093i
$803$	7.18040	+	5.50972i	0.253391	+	0.194434i
$804$	−16.2006	+	49.9090i	−0.571352	+	1.76015i
$805$	−0.759698	−	0.990058i	−0.0267759	−	0.0348950i
$806$	7.70578	−	12.8355i	0.271425	−	0.452112i
$807$	0.927194	−	51.7308i	0.0326388	−	1.82101i
$808$	36.1351	−	18.4633i	1.27123	−	0.649535i
$809$	3.71928	+	3.71928i	0.130763	+	0.130763i	0.769459	−	0.638696i	$-0.220526\pi$
$809$	3.71928	+	3.71928i	0.130763	+	0.130763i	−0.638696	+	0.769459i	$0.720526\pi$
$810$	25.1092	−	21.0052i	0.882248	−	0.738048i
$811$	17.4419	−	42.1084i	0.612467	−	1.47863i	−0.247814	−	0.968808i	$-0.579712\pi$
$811$	17.4419	−	42.1084i	0.612467	−	1.47863i	0.860281	−	0.509820i	$-0.170288\pi$
$812$	10.8600	−	13.1945i	0.381111	−	0.463036i
$813$	−12.6264	+	29.0017i	−0.442828	+	1.01713i
$814$	1.94134	−	13.0234i	0.0680441	−	0.456471i
$815$	−38.3426	−	22.1371i	−1.34308	−	0.775428i
$816$	−1.34935	−	30.1845i	−0.0472367	−	1.05667i
$817$	0.507932	−	0.293255i	0.0177703	−	0.0102597i
$818$	−2.67415	−	6.78123i	−0.0934996	−	0.237100i
$819$	−1.95689	−	5.24891i	−0.0683792	−	0.183412i
$820$	−7.73447	+	17.0057i	−0.270099	+	0.593866i
$821$	−4.89903	+	0.644970i	−0.170977	+	0.0225096i	−0.215529	−	0.976497i	$-0.569148\pi$
$821$	−4.89903	+	0.644970i	−0.170977	+	0.0225096i	0.0445514	+	0.999007i	$0.485814\pi$
$822$	10.8350	−	17.3361i	0.377915	−	0.604668i
$823$	2.36068	−	0.632543i	0.0822882	−	0.0220490i	−0.217440	−	0.976074i	$-0.569771\pi$
$823$	2.36068	−	0.632543i	0.0822882	−	0.0220490i	0.299728	+	0.954025i	$0.403104\pi$
$824$	−5.13838	+	3.54008i	−0.179004	+	0.123324i
$825$	−1.52226	+	2.53079i	−0.0529984	+	0.0881106i
$826$	−7.22695	+	4.00953i	−0.251458	+	0.139509i
$827$	−5.49528	+	13.2668i	−0.191090	+	0.461331i	−0.990166	−	0.139899i	$-0.955322\pi$
$827$	−5.49528	+	13.2668i	−0.191090	+	0.461331i	0.799076	+	0.601230i	$0.205322\pi$
$828$	−0.964869	+	2.80053i	−0.0335315	+	0.0973250i
$829$	−24.4885	+	10.1435i	−0.850521	+	0.352297i	−0.764993	−	0.644038i	$-0.777258\pi$
$829$	−24.4885	+	10.1435i	−0.850521	+	0.352297i	−0.0855278	+	0.996336i	$0.527258\pi$
$830$	−26.3614	+	3.01357i	−0.915017	+	0.104603i
$831$	−23.3538	−	6.70842i	−0.810133	−	0.232712i
$832$	−12.9416	+	7.97099i	−0.448671	+	0.276344i
$833$	22.7897	+	13.1576i	0.789616	+	0.455885i
$834$	−13.3860	−	35.8123i	−0.463518	−	1.24008i
$835$	−0.254211	+	0.331294i	−0.00879734	+	0.0114649i
$836$	−0.0751008	−	0.0804140i	−0.00259742	−	0.00278118i
$837$	−28.4598	−	5.31608i	−0.983715	−	0.183751i
$838$	−1.08109	−	0.0184626i	−0.0373456	−	0.000637780i
$839$	3.65275	−	13.6322i	0.126107	−	0.470637i	−0.873770	−	0.486340i	$-0.838332\pi$
$839$	3.65275	−	13.6322i	0.126107	−	0.470637i	0.999877	+	0.0157023i	$0.00499841\pi$
$840$	−11.7412	+	3.93723i	−0.405112	+	0.135847i
$841$	−12.0569	−	44.9970i	−0.415756	−	1.55162i
$842$	−8.31665	−	33.3028i	−0.286611	−	1.14769i
$843$	−27.7876	+	34.9002i	−0.957055	+	1.20203i
$844$	−2.13197	−	21.9677i	−0.0733855	−	0.756158i
$845$	22.3137	−	9.24262i	0.767613	−	0.317956i
$846$	2.11727	−	11.3882i	0.0727931	−	0.391534i
$847$	9.71592			0.333843
$848$	1.77991	+	28.3981i	0.0611225	+	0.975195i
$849$	−6.40521	−	25.7412i	−0.219826	−	0.883436i
$850$	−9.85403	−	1.46890i	−0.337990	−	0.0503827i
$851$	−4.31738	−	0.568394i	−0.147998	−	0.0194843i
$852$	42.9895	−	29.5639i	1.47279	−	1.01284i
$853$	1.04770	+	7.95806i	0.0358725	+	0.272479i	0.999976	+	0.00695138i	$0.00221271\pi$
$853$	1.04770	+	7.95806i	0.0358725	+	0.272479i	−0.964103	+	0.265527i	$0.914454\pi$
$854$	−1.84497	+	1.78301i	−0.0631334	+	0.0610133i
$855$	0.391940	−	0.0900999i	0.0134041	−	0.00308135i
$856$	−1.11754	+	21.7958i	−0.0381968	+	0.744965i
$857$	−9.15245	−	2.45239i	−0.312642	−	0.0837721i	0.0990864	−	0.995079i	$-0.468408\pi$
$857$	−9.15245	−	2.45239i	−0.312642	−	0.0837721i	−0.411728	+	0.911307i	$0.635075\pi$
$858$	1.43666	−	4.69758i	0.0490468	−	0.160373i
$859$	15.0368	−	11.5381i	0.513048	−	0.393676i	−0.319536	−	0.947574i	$-0.603527\pi$
$859$	15.0368	−	11.5381i	0.513048	−	0.393676i	0.832584	+	0.553898i	$0.186860\pi$
$860$	30.6382	−	49.1138i	1.04476	−	1.67477i
$861$	2.46783	−	5.66835i	0.0841033	−	0.193177i
$862$	22.2334	−	2.54167i	0.757272	−	0.0865696i
$863$	16.9645			0.577478			0.288739	−	0.957408i	$-0.406764\pi$
$863$	16.9645			0.577478			0.288739	+	0.957408i	$0.406764\pi$
$864$	23.1714	+	18.0855i	0.788307	+	0.615282i
$865$	67.4973			2.29498
$866$	14.4682	−	1.65398i	0.491651	−	0.0562044i
$867$	−1.39611	+	3.20672i	−0.0474143	+	0.108906i
$868$	9.29232	+	5.79674i	0.315402	+	0.196754i
$869$	−12.1754	+	9.34249i	−0.413021	+	0.316922i
$870$	−16.0189	+	52.3785i	−0.543093	+	1.77580i
$871$	−27.7986	−	7.44860i	−0.941918	−	0.252386i
$872$	10.8974	−	9.83443i	0.369033	−	0.333036i
$873$	3.88926	−	12.6787i	0.131632	−	0.429110i
$874$	−0.0261661	+	0.0252874i	−0.000885083	+	0.000855360i
$875$	−1.11675	−	8.48256i	−0.0377531	−	0.286763i
$876$	−16.8308	−	24.4740i	−0.568660	−	0.826898i
$877$	34.4988	+	4.54186i	1.16494	+	0.153368i	0.688096	−	0.725619i	$-0.258447\pi$
$877$	34.4988	+	4.54186i	1.16494	+	0.153368i	0.476846	+	0.878987i	$0.341780\pi$
$878$	27.2433	+	4.06104i	0.919417	+	0.137053i
$879$	−1.10020	−	4.42149i	−0.0371089	−	0.149133i
$880$	−10.2733	−	3.52005i	−0.346312	−	0.118661i
$881$	−32.9062			−1.10864			−0.554320	−	0.832304i	$-0.687022\pi$
$881$	−32.9062			−1.10864			−0.554320	+	0.832304i	$0.687022\pi$
$882$	−24.1368	+	8.53210i	−0.812728	+	0.287291i
$883$	20.3345	−	8.42283i	0.684311	−	0.283451i	−0.0133169	−	0.999911i	$-0.504239\pi$
$883$	20.3345	−	8.42283i	0.684311	−	0.283451i	0.697628	+	0.716461i	$0.254239\pi$
$884$	16.4941	−	1.60076i	0.554756	−	0.0538394i
$885$	16.5000	−	20.7234i	0.554641	−	0.696610i
$886$	−9.37095	−	37.5245i	−0.314823	−	1.26066i
$887$	−3.16540	−	11.8134i	−0.106284	−	0.396656i	0.892204	−	0.451633i	$-0.149158\pi$
$887$	−3.16540	−	11.8134i	−0.106284	−	0.396656i	−0.998488	+	0.0549764i	$0.982492\pi$
$888$	−19.2558	+	38.6853i	−0.646181	+	1.29819i
$889$	−0.808591	+	3.01770i	−0.0271193	+	0.101211i
$890$	−18.9197	−	0.323106i	−0.634188	−	0.0108305i
$891$	−9.48326	+	0.562194i	−0.317701	+	0.0188342i
$892$	−14.6323	+	13.6655i	−0.489926	+	0.457555i
$893$	0.0866260	−	0.112893i	0.00289883	−	0.00377783i
$894$	4.09559	+	10.9572i	0.136977	+	0.366463i
$895$	14.4054	+	8.31694i	0.481518	+	0.278005i
$896$	−5.66873	−	9.56575i	−0.189379	−	0.319569i
$897$	−1.56145	−	0.448529i	−0.0521351	−	0.0149759i
$898$	33.7247	−	3.85533i	1.12541	−	0.128654i
$899$	44.7537	−	18.5376i	1.49262	−	0.618263i
$900$	7.31601	−	6.35737i	0.243867	−	0.211912i
$901$	11.8718	−	28.6611i	0.395508	−	0.954840i
$902$	4.74063	−	2.63011i	0.157846	−	0.0875731i
$903$	−9.87372	+	16.4152i	−0.328577	+	0.546264i
$904$	−52.6913	−	9.70409i	−1.75249	−	0.322753i
$905$	−19.0434	+	5.10268i	−0.633026	+	0.169619i
$906$	−3.99221	+	6.38757i	−0.132632	+	0.212213i
$907$	−27.4775	+	3.61748i	−0.912374	+	0.120116i	−0.572075	−	0.820201i	$-0.693862\pi$
$907$	−27.4775	+	3.61748i	−0.912374	+	0.120116i	−0.340299	+	0.940317i	$0.610528\pi$
$908$	−35.6557	−	16.2168i	−1.18328	−	0.538172i
$909$	27.4081	−	33.1853i	0.909068	−	1.10069i
$910$	−2.49168	−	6.31850i	−0.0825983	−	0.209456i
$911$	−22.7451	+	13.1319i	−0.753579	+	0.435079i	−0.826985	−	0.562223i	$-0.809946\pi$
$911$	−22.7451	+	13.1319i	−0.753579	+	0.435079i	0.0734069	+	0.997302i	$0.476613\pi$
$912$	0.152947	+	0.327106i	0.00506457	+	0.0108316i
$913$	6.66811	+	3.84983i	0.220682	+	0.127411i
$914$	7.49930	−	50.3088i	0.248055	−	1.66407i
$915$	3.28270	−	7.54004i	0.108523	−	0.249266i
$916$	−39.0448	−	32.1366i	−1.29008	−	1.06182i
$917$	5.48962	−	13.2531i	0.181283	−	0.437657i
$918$	−14.0191	−	28.8185i	−0.462698	−	0.951152i
$919$	19.8928	+	19.8928i	0.656203	+	0.656203i	0.954479	−	0.298277i	$-0.0964118\pi$
$919$	19.8928	+	19.8928i	0.656203	+	0.656203i	−0.298277	+	0.954479i	$0.596412\pi$
$920$	−1.10595	+	3.41691i	−0.0364620	+	0.112652i
$921$	0.764403	−	42.6481i	0.0251879	−	1.40530i
$922$	20.3222	−	33.8507i	0.669275	−	1.11481i
$923$	17.4200	+	22.7021i	0.573385	+	0.747250i
$924$	3.41810	+	1.10953i	0.112447	+	0.0365008i
$925$	11.3044	+	8.67416i	0.371686	+	0.285205i
$926$	43.7866	+	19.0193i	1.43892	+	0.625014i
$927$	−3.51242	+	5.60936i	−0.115363	+	0.184235i
$928$	−49.0011	−	4.19394i	−1.60854	−	0.137673i
$929$	−5.26704	+	3.04093i	−0.172806	+	0.0997695i	−0.583908	−	0.811820i	$-0.698477\pi$
$929$	−5.26704	+	3.04093i	−0.172806	+	0.0997695i	0.411102	+	0.911589i	$0.365144\pi$
$930$	−34.6216	−	5.79691i	−1.13529	−	0.190088i
$931$	−0.311805	−	0.0410499i	−0.0102190	−	0.00134536i
$932$	−33.5369	−	20.9210i	−1.09854	−	0.685291i
$933$	−20.2673	−	3.03867i	−0.663522	−	0.0994817i
$934$	−0.0326745	+	0.0181279i	−0.00106914	+	0.000593162i
$935$	8.37213	+	8.37213i	0.273798	+	0.273798i
$936$	−9.24430	+	13.2077i	−0.302159	+	0.431707i
$937$	−33.7193	+	33.7193i	−1.10156	+	1.10156i	−0.107338	+	0.994223i	$0.534233\pi$
$937$	−33.7193	+	33.7193i	−1.10156	+	1.10156i	−0.994223	+	0.107338i	$0.965767\pi$
$938$	5.79554	−	20.2403i	0.189231	−	0.660868i
$939$	2.48219	+	1.97632i	0.0810032	+	0.0644948i
$940$	2.30755	−	13.8536i	0.0752641	−	0.451854i
$941$	1.54883	−	11.7645i	0.0504905	−	0.383513i	−0.947479	−	0.319818i	$-0.896378\pi$
$941$	1.54883	−	11.7645i	0.0504905	−	0.383513i	0.997969	−	0.0636950i	$-0.0202885\pi$
$942$	−15.2463	+	33.4469i	−0.496752	+	1.08976i
$943$	−0.896461	−	1.55272i	−0.0291928	−	0.0505634i
$944$	21.3019	+	10.5806i	0.693317	+	0.344370i
$945$	−9.77355	+	8.77532i	−0.317934	+	0.285461i
$946$	−15.6270	+	6.16246i	−0.508079	+	0.200359i
$947$	−23.3578	+	30.4405i	−0.759027	+	0.989183i	0.240800	+	0.970575i	$0.422590\pi$
$947$	−23.3578	+	30.4405i	−0.759027	+	0.989183i	−0.999827	+	0.0186081i	$0.994077\pi$
$948$	47.4714	−	16.8258i	1.54180	−	0.546476i
$949$	12.9244	−	9.91721i	0.419543	−	0.321926i
$950$	0.115520	−	0.0288486i	0.00374795	−	0.000935972i
$951$	22.3659	+	40.3937i	0.725263	+	1.30986i
$952$	0.964841	+	12.0846i	0.0312707	+	0.391665i
$953$	−14.3982	+	14.3982i	−0.466402	+	0.466402i	−0.900747	−	0.434345i	$-0.856980\pi$
$953$	−14.3982	+	14.3982i	−0.466402	+	0.466402i	0.434345	+	0.900747i	$0.356980\pi$
$954$	13.6863	+	26.8981i	0.443111	+	0.870859i
$955$	−15.8610	−	6.56986i	−0.513251	−	0.212596i
$956$	10.7769	+	3.28594i	0.348550	+	0.106275i
$957$	12.7815	−	9.44857i	0.413168	−	0.305429i
$958$	−4.87408	+	3.60948i	−0.157474	+	0.116617i
$959$	−4.10131	+	7.10367i	−0.132438	+	0.229390i
$960$	28.5012	+	21.3971i	0.919872	+	0.690588i
$961$	0.0226372	+	0.0392087i	0.000730231	+	0.00126480i
$962$	−21.7384	−	9.44237i	−0.700874	−	0.304434i
$963$	8.08640	+	21.6900i	0.260581	+	0.698949i
$964$	21.1987	−	19.7980i	0.682763	−	0.637651i
$965$	−1.70440	−	12.9462i	−0.0548667	−	0.416754i
$966$	0.347582	−	1.13652i	0.0111833	−	0.0365669i
$967$	−8.62936	−	32.2052i	−0.277501	−	1.03565i	−0.954147	−	0.299340i	$-0.903234\pi$
$967$	−8.62936	−	32.2052i	−0.277501	−	1.03565i	0.676645	−	0.736309i	$-0.263433\pi$
$968$	−15.8635	−	23.0257i	−0.509873	−	0.740075i
$969$	0.00705526	−	0.393633i	0.000226648	−	0.0126453i
$970$	4.42631	−	15.4584i	0.142120	−	0.496338i
$971$	−19.9477	−	8.26262i	−0.640153	−	0.265160i	0.0389071	−	0.999243i	$-0.487612\pi$
$971$	−19.9477	−	8.26262i	−0.640153	−	0.265160i	−0.679060	+	0.734083i	$0.737612\pi$
$972$	30.1714	+	7.85396i	0.967749	+	0.251916i
$973$	5.87037	+	14.1723i	0.188195	+	0.454344i
$974$	33.2918	+	26.4610i	1.06674	+	0.847864i
$975$	3.69091	+	3.82563i	0.118204	+	0.122518i
$976$	7.23789	+	1.46120i	0.231679	+	0.0467717i
$977$	10.5771	−	18.3202i	0.338393	−	0.586114i	−0.645738	−	0.763559i	$-0.723450\pi$
$977$	10.5771	−	18.3202i	0.338393	−	0.586114i	0.984131	+	0.177446i	$0.0567834\pi$
$978$	−4.03748	−	41.9709i	−0.129104	−	1.34208i
$979$	4.35640	+	3.34278i	0.139231	+	0.106836i
$980$	−29.0659	+	10.8923i	−0.928475	+	0.347941i
$981$	6.46975	−	14.1614i	0.206563	−	0.452139i
$982$	36.4683	+	37.7355i	1.16375	+	1.20419i
$983$	12.3525	+	3.30985i	0.393985	+	0.105568i	0.450372	−	0.892841i	$-0.351291\pi$
$983$	12.3525	+	3.30985i	0.393985	+	0.105568i	−0.0563870	+	0.998409i	$0.517958\pi$
$984$	−17.4627	+	3.40643i	−0.556691	+	0.108593i
$985$	−10.8746	+	2.91384i	−0.346494	+	0.0928427i
$986$	45.9718	+	27.5991i	1.46404	+	0.878933i
$987$	−0.689113	+	4.59624i	−0.0219347	+	0.146300i
$988$	−0.174796	+	0.0931098i	−0.00556100	+	0.00296222i
$989$	2.12597	+	5.13254i	0.0676018	+	0.163205i
$990$	−11.4834	+	0.897297i	−0.364965	+	0.0285180i
$991$			45.0980i			1.43259i	0.697800	+	0.716293i	$0.254163\pi$
$991$			45.0980i			1.43259i	−0.697800	+	0.716293i	$0.745837\pi$
$992$	−1.43422	−	31.4864i	−0.0455366	−	0.999693i
$993$	−1.27657	+	4.44407i	−0.0405107	+	0.141028i
$994$	−16.8231	+	12.4583i	−0.533597	+	0.395153i
$995$	3.15947	−	23.9986i	0.100162	−	0.760806i
$996$	−16.9135	−	18.7736i	−0.535926	−	0.594864i
$997$	−27.6145	+	3.63552i	−0.874561	+	0.115138i	−0.554425	−	0.832234i	$-0.687062\pi$
$997$	−27.6145	+	3.63552i	−0.874561	+	0.115138i	−0.320135	+	0.947372i	$0.603728\pi$
$998$	−23.6560	−	0.403992i	−0.748817	−	0.0127881i
$999$	−2.46306	+	45.7678i	−0.0779278	+	1.44803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.203.26	yes	368
3.2	odd	2		864.2.bn.a.395.21		368
9.2	odd	6	inner	288.2.bf.a.11.11	✓	368
9.7	even	3		864.2.bn.a.683.36		368
32.3	odd	8	inner	288.2.bf.a.131.11	yes	368
96.35	even	8		864.2.bn.a.611.36		368
288.227	even	24	inner	288.2.bf.a.227.26	yes	368
288.259	odd	24		864.2.bn.a.35.21		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.11	✓	368	9.2	odd	6	inner
288.2.bf.a.131.11	yes	368	32.3	odd	8	inner
288.2.bf.a.203.26	yes	368	1.1	even	1	trivial
288.2.bf.a.227.26	yes	368	288.227	even	24	inner
864.2.bn.a.35.21		368	288.259	odd	24
864.2.bn.a.395.21		368	3.2	odd	2
864.2.bn.a.611.36		368	96.35	even	8
864.2.bn.a.683.36		368	9.7	even	3

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.160623 + 1.40506i) q^{2} +(-0.691397 + 1.58807i) q^{3} +(-1.94840 + 0.451372i) q^{4} +(-2.04053 + 1.56576i) q^{5} +(-2.34239 - 0.716375i) q^{6} +(0.949325 + 0.254371i) q^{7} +(-0.947165 - 2.66512i) q^{8} +(-2.04394 - 2.19598i) q^{9} +O(q^{10})\)	\(q+(0.160623 + 1.40506i) q^{2} +(-0.691397 + 1.58807i) q^{3} +(-1.94840 + 0.451372i) q^{4} +(-2.04053 + 1.56576i) q^{5} +(-2.34239 - 0.716375i) q^{6} +(0.949325 + 0.254371i) q^{7} +(-0.947165 - 2.66512i) q^{8} +(-2.04394 - 2.19598i) q^{9} +(-2.52774 - 2.61558i) q^{10} +(0.137776 + 1.04651i) q^{11} +(0.630308 - 3.40628i) q^{12} +(1.88367 + 0.247990i) q^{13} +(-0.204923 + 1.37472i) q^{14} +(-1.07571 - 4.32307i) q^{15} +(3.59253 - 1.75891i) q^{16} -4.36111 q^{17} +(2.75718 - 3.22459i) q^{18} +(0.0481525 - 0.0199454i) q^{19} +(3.26904 - 3.97176i) q^{20} +(-1.06032 + 1.33172i) q^{21} +(-1.44829 + 0.361679i) q^{22} +(0.127774 + 0.476858i) q^{23} +(4.88727 + 0.338494i) q^{24} +(0.418091 - 1.56034i) q^{25} +(-0.0458797 + 2.68651i) q^{26} +(4.90054 - 1.72763i) q^{27} +(-1.96448 - 0.0671175i) q^{28} +(-5.29253 + 6.89735i) q^{29} +(5.90140 - 2.20583i) q^{30} +(-4.82535 - 2.78591i) q^{31} +(3.04842 + 4.76520i) q^{32} +(-1.75720 - 0.504759i) q^{33} +(-0.700496 - 6.12763i) q^{34} +(-2.33541 + 0.967360i) q^{35} +(4.97361 + 3.35606i) q^{36} +(-3.37556 + 8.14932i) q^{37} +(0.0357590 + 0.0644535i) q^{38} +(-1.69619 + 2.81995i) q^{39} +(6.10566 + 3.95525i) q^{40} +(-3.50800 + 0.939965i) q^{41} +(-2.04147 - 1.27591i) q^{42} +(11.1568 - 1.46882i) q^{43} +(-0.740811 - 1.97684i) q^{44} +(7.60910 + 1.28065i) q^{45} +(-0.649492 + 0.256125i) q^{46} +(2.36444 - 1.36511i) q^{47} +(0.309406 + 6.92129i) q^{48} +(-5.22566 - 3.01704i) q^{49} +(2.25953 + 0.336817i) q^{50} +(3.01526 - 6.92575i) q^{51} +(-3.78209 + 0.367053i) q^{52} +(-2.72220 + 6.57198i) q^{53} +(3.21457 + 6.60807i) q^{54} +(-1.91973 - 1.91973i) q^{55} +(-0.221238 - 2.77100i) q^{56} +(-0.00161777 + 0.0902598i) q^{57} +(-10.5413 - 6.32845i) q^{58} +(3.61983 + 4.71745i) q^{59} +(4.04724 + 7.93753i) q^{60} +(1.46451 + 1.12376i) q^{61} +(3.13932 - 7.22739i) q^{62} +(-1.38177 - 2.60461i) q^{63} +(-6.20576 + 5.04862i) q^{64} +(-4.23200 + 2.44334i) q^{65} +(0.426971 - 2.55005i) q^{66} +(-15.0179 - 1.97715i) q^{67} +(8.49718 - 1.96848i) q^{68} +(-0.845627 - 0.126785i) q^{69} +(-1.73432 - 3.12602i) q^{70} +(10.6500 + 10.6500i) q^{71} +(-3.91660 + 7.52730i) q^{72} +(6.06304 - 6.06304i) q^{73} +(-11.9925 - 3.43390i) q^{74} +(2.18886 + 1.74277i) q^{75} +(-0.0848175 + 0.0605963i) q^{76} +(-0.135408 + 1.02853i) q^{77} +(-4.23465 - 1.93031i) q^{78} +(7.26957 + 12.5913i) q^{79} +(-4.57665 + 9.21414i) q^{80} +(-0.644623 + 8.97688i) q^{81} +(-1.88418 - 4.77798i) q^{82} +(4.44061 - 5.78711i) q^{83} +(1.46482 - 3.07333i) q^{84} +(8.89899 - 6.82844i) q^{85} +(3.85583 + 15.4401i) q^{86} +(-7.29425 - 13.1737i) q^{87} +(2.65859 - 1.35841i) q^{88} +(3.67849 - 3.67849i) q^{89} +(-0.577197 + 10.8970i) q^{90} +(1.72514 + 0.714576i) q^{91} +(-0.464195 - 0.871437i) q^{92} +(7.76046 - 5.73682i) q^{93} +(2.29785 + 3.10292i) q^{94} +(-0.0670271 + 0.116094i) q^{95} +(-9.67515 + 1.54646i) q^{96} +(2.21031 + 3.82837i) q^{97} +(3.39976 - 7.82699i) q^{98} +(2.01652 - 2.44157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more