LMFDB - Embedded newform 414.2.m.a.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(13,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([22, 42]))

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

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

chi := DirichletCharacter("414.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.m (of order $33$, degree $20$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	414.13
Dual form			414.2.m.a.223.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(1.32227 - 1.11875i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.518620 - 0.728300i) q^{5} +(-0.624745 - 1.61545i) q^{6} +(-0.945394 - 3.89697i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.496807 - 2.95858i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(1.32227 - 1.11875i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.518620 - 0.728300i) q^{5} +(-0.624745 - 1.61545i) q^{6} +(-0.945394 - 3.89697i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.496807 - 2.95858i) q^{9} +(-0.857868 + 0.251893i) q^{10} +(0.237462 + 0.0457670i) q^{11} +(-1.73094 + 0.0620208i) q^{12} +(-1.47689 + 6.08781i) q^{13} +(-3.99184 - 0.381175i) q^{14} +(-1.50054 - 0.382806i) q^{15} +(0.235759 + 0.971812i) q^{16} +(0.903107 + 6.28124i) q^{17} +(-2.63337 - 1.43714i) q^{18} +(0.398527 - 2.77182i) q^{19} +(-0.0425423 + 0.893072i) q^{20} +(-5.60979 - 4.09519i) q^{21} +(0.120916 - 0.209432i) q^{22} +(1.94182 - 4.38513i) q^{23} +(-0.507525 + 1.65602i) q^{24} +(1.37389 - 3.96958i) q^{25} +(5.26994 + 3.38679i) q^{26} +(-2.65299 - 4.46785i) q^{27} +(-1.66581 + 3.64763i) q^{28} +(4.89713 - 3.85115i) q^{29} +(-0.852530 + 1.29281i) q^{30} +(0.0101300 + 0.212655i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(0.365191 - 0.205143i) q^{33} +(6.23116 + 1.20096i) q^{34} +(-2.34786 + 2.70957i) q^{35} +(-2.21939 + 2.01849i) q^{36} +(-3.98016 - 8.71533i) q^{37} +(-2.48903 - 1.28318i) q^{38} +(4.85788 + 9.70200i) q^{39} +(0.830040 + 0.332298i) q^{40} +(6.12334 + 8.59902i) q^{41} +(-5.70474 + 3.96185i) q^{42} +(0.0362295 - 0.760551i) q^{43} +(-0.158366 - 0.182764i) q^{44} +(-2.41239 + 1.17255i) q^{45} +(-3.50884 - 3.26926i) q^{46} +(0.622078 + 1.07747i) q^{47} +(1.39895 + 1.02124i) q^{48} +(-8.07073 + 4.16075i) q^{49} +(-3.30190 - 2.59665i) q^{50} +(8.22128 + 7.29516i) q^{51} +(4.92415 - 3.87239i) q^{52} +(10.3251 + 3.03173i) q^{53} +(-5.08983 + 1.04579i) q^{54} +(-0.0898203 - 0.196679i) q^{55} +(2.90217 + 2.76722i) q^{56} +(-2.57401 - 4.11095i) q^{57} +(-2.03764 - 5.88738i) q^{58} +(-0.636660 + 2.62435i) q^{59} +(0.942870 + 1.22848i) q^{60} +(-3.20672 - 1.65318i) q^{61} +(0.204272 + 0.0599797i) q^{62} +(-11.9992 + 0.860981i) q^{63} +(0.415415 - 0.909632i) q^{64} +(5.19969 - 2.08164i) q^{65} +(-0.0744184 - 0.412201i) q^{66} +(14.2758 - 2.75143i) q^{67} +(3.17292 - 5.49565i) q^{68} +(-2.33824 - 7.97074i) q^{69} +(1.79264 + 3.10494i) q^{70} +(2.60048 + 3.00111i) q^{71} +(1.18159 + 2.75751i) q^{72} +(-2.16121 + 15.0315i) q^{73} +(-9.53777 + 0.910747i) q^{74} +(-2.62431 - 6.78590i) q^{75} +(-2.02669 + 1.93244i) q^{76} +(-0.0461424 - 0.968648i) q^{77} +(10.7573 - 1.41748i) q^{78} +(-8.08815 - 7.71203i) q^{79} +(0.585501 - 0.675704i) q^{80} +(-8.50637 - 2.93968i) q^{81} +(10.1288 - 2.97409i) q^{82} +(-3.31066 + 4.64918i) q^{83} +(1.87811 + 6.68678i) q^{84} +(4.10626 - 3.91531i) q^{85} +(-0.706872 - 0.282989i) q^{86} +(2.16688 - 10.5709i) q^{87} +(-0.224509 + 0.0898798i) q^{88} +(4.94391 + 3.17726i) q^{89} +(0.319050 + 2.66321i) q^{90} +25.1202 q^{91} +(-4.23708 + 2.24659i) q^{92} +(0.251301 + 0.269854i) q^{93} +(1.22167 - 0.235458i) q^{94} +(-2.22540 + 1.14727i) q^{95} +(1.42263 - 0.987992i) q^{96} +(9.66885 - 0.923263i) q^{97} +(1.29223 + 8.98769i) q^{98} +(0.253378 - 0.679811i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) $ 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	1.32227	−	1.11875i	0.763414	−	0.645909i
$3$	1.32227	−	1.11875i	0.763414	−	0.645909i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−0.518620	−	0.728300i	−0.231934	−	0.325706i	0.682164	−	0.731199i	$-0.261039\pi$
$5$	−0.518620	−	0.728300i	−0.231934	−	0.325706i	−0.914098	+	0.405494i	$0.867100\pi$
$6$	−0.624745	−	1.61545i	−0.255051	−	0.659507i
$7$	−0.945394	−	3.89697i	−0.357325	−	1.47291i	−0.812735	−	0.582633i	$-0.802023\pi$
$7$	−0.945394	−	3.89697i	−0.357325	−	1.47291i	0.455410	−	0.890282i	$-0.349493\pi$
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	0.496807	−	2.95858i	0.165602	−	0.986193i
$10$	−0.857868	+	0.251893i	−0.271282	+	0.0796555i
$11$	0.237462	+	0.0457670i	0.0715974	+	0.0137993i	0.224924	−	0.974376i	$-0.427787\pi$
$11$	0.237462	+	0.0457670i	0.0715974	+	0.0137993i	−0.153327	+	0.988176i	$0.548999\pi$
$12$	−1.73094	+	0.0620208i	−0.499679	+	0.0179039i
$13$	−1.47689	+	6.08781i	−0.409615	+	1.68845i	0.276543	+	0.961002i	$0.410811\pi$
$13$	−1.47689	+	6.08781i	−0.409615	+	1.68845i	−0.686158	+	0.727453i	$0.740704\pi$
$14$	−3.99184	−	0.381175i	−1.06687	−	0.101873i
$15$	−1.50054	−	0.382806i	−0.387438	−	0.0988400i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	0.903107	+	6.28124i	0.219036	+	1.52343i	0.741610	+	0.670832i	$0.234063\pi$
$17$	0.903107	+	6.28124i	0.219036	+	1.52343i	−0.522574	+	0.852594i	$0.675028\pi$
$18$	−2.63337	−	1.43714i	−0.620691	−	0.338737i
$19$	0.398527	−	2.77182i	0.0914285	−	0.635899i	−0.891652	−	0.452722i	$-0.850453\pi$
$19$	0.398527	−	2.77182i	0.0914285	−	0.635899i	0.983080	−	0.183177i	$-0.0586380\pi$
$20$	−0.0425423	+	0.893072i	−0.00951274	+	0.199697i
$21$	−5.60979	−	4.09519i	−1.22416	−	0.893644i
$22$	0.120916	−	0.209432i	0.0257794	−	0.0446512i
$23$	1.94182	−	4.38513i	0.404898	−	0.914362i
$23$	1.94182	−	4.38513i	0.404898	−	0.914362i
$24$	−0.507525	+	1.65602i	−0.103598	+	0.338035i
$25$	1.37389	−	3.96958i	0.274777	−	0.793916i
$26$	5.26994	+	3.38679i	1.03352	+	0.664203i
$27$	−2.65299	−	4.46785i	−0.510568	−	0.859837i
$28$	−1.66581	+	3.64763i	−0.314809	+	0.689336i
$29$	4.89713	−	3.85115i	0.909374	−	0.715140i	−0.0495590	−	0.998771i	$-0.515782\pi$
$29$	4.89713	−	3.85115i	0.909374	−	0.715140i	0.958933	+	0.283631i	$0.0915392\pi$
$30$	−0.852530	+	1.29281i	−0.155650	+	0.236033i
$31$	0.0101300	+	0.212655i	0.00181940	+	0.0381939i	0.999594	−	0.0284763i	$-0.00906550\pi$
$31$	0.0101300	+	0.212655i	0.00181940	+	0.0381939i	−0.997775	+	0.0666702i	$0.978762\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	0.365191	−	0.205143i	0.0635715	−	0.0357109i
$34$	6.23116	+	1.20096i	1.06863	+	0.205962i
$35$	−2.34786	+	2.70957i	−0.396861	+	0.458002i
$36$	−2.21939	+	2.01849i	−0.369898	+	0.336416i
$37$	−3.98016	−	8.71533i	−0.654334	−	1.43279i	−0.887709	−	0.460404i	$-0.847704\pi$
$37$	−3.98016	−	8.71533i	−0.654334	−	1.43279i	0.233376	−	0.972387i	$-0.425023\pi$
$38$	−2.48903	−	1.28318i	−0.403773	−	0.208160i
$39$	4.85788	+	9.70200i	0.777883	+	1.55356i
$40$	0.830040	+	0.332298i	0.131241	+	0.0525409i
$41$	6.12334	+	8.59902i	0.956305	+	1.34294i	0.939304	+	0.343086i	$0.111472\pi$
$41$	6.12334	+	8.59902i	0.956305	+	1.34294i	0.0170006	+	0.999855i	$0.494588\pi$
$42$	−5.70474	+	3.96185i	−0.880261	+	0.611327i
$43$	0.0362295	−	0.760551i	0.00552495	−	0.115983i	−0.994420	−	0.105493i	$-0.966358\pi$
$43$	0.0362295	−	0.760551i	0.00552495	−	0.115983i	0.999945	−	0.0104898i	$-0.00333908\pi$
$44$	−0.158366	−	0.182764i	−0.0238746	−	0.0275528i
$45$	−2.41239	+	1.17255i	−0.359617	+	0.174794i
$46$	−3.50884	−	3.26926i	−0.517350	−	0.482026i
$47$	0.622078	+	1.07747i	0.0907394	+	0.157165i	0.907822	−	0.419355i	$-0.137744\pi$
$47$	0.622078	+	1.07747i	0.0907394	+	0.157165i	−0.817083	+	0.576520i	$0.804410\pi$
$48$	1.39895	+	1.02124i	0.201921	+	0.147404i
$49$	−8.07073	+	4.16075i	−1.15296	+	0.594393i
$50$	−3.30190	−	2.59665i	−0.466960	−	0.367221i
$51$	8.22128	+	7.29516i	1.15121	+	1.02153i
$52$	4.92415	−	3.87239i	0.682856	−	0.537004i
$53$	10.3251	+	3.03173i	1.41827	+	0.416441i	0.898916	−	0.438121i	$-0.144356\pi$
$53$	10.3251	+	3.03173i	1.41827	+	0.416441i	0.519350	+	0.854561i	$0.326174\pi$
$54$	−5.08983	+	1.04579i	−0.692638	+	0.142314i
$55$	−0.0898203	−	0.196679i	−0.0121114	−	0.0265202i
$56$	2.90217	+	2.76722i	0.387819	+	0.369785i
$57$	−2.57401	−	4.11095i	−0.340935	−	0.544509i
$58$	−2.03764	−	5.88738i	−0.267555	−	0.773051i
$59$	−0.636660	+	2.62435i	−0.0828861	+	0.341661i	−0.998122	−	0.0612573i	$-0.980489\pi$
$59$	−0.636660	+	2.62435i	−0.0828861	+	0.341661i	0.915236	+	0.402918i	$0.132004\pi$
$60$	0.942870	+	1.22848i	0.121724	+	0.158596i
$61$	−3.20672	−	1.65318i	−0.410579	−	0.211668i	0.240548	−	0.970637i	$-0.422673\pi$
$61$	−3.20672	−	1.65318i	−0.410579	−	0.211668i	−0.651127	+	0.758969i	$0.725703\pi$
$62$	0.204272	+	0.0599797i	0.0259426	+	0.00761742i
$63$	−11.9992	+	0.860981i	−1.51175	+	0.108473i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	5.19969	−	2.08164i	0.644943	−	0.258196i
$66$	−0.0744184	−	0.412201i	−0.00916027	−	0.0507385i
$67$	14.2758	−	2.75143i	1.74407	−	0.336141i	0.785037	−	0.619449i	$-0.212644\pi$
$67$	14.2758	−	2.75143i	1.74407	−	0.336141i	0.959029	+	0.283307i	$0.0914317\pi$
$68$	3.17292	−	5.49565i	0.384773	−	0.666446i
$69$	−2.33824	−	7.97074i	−0.281490	−	0.959564i
$70$	1.79264	+	3.10494i	0.214262	+	0.371112i
$71$	2.60048	+	3.00111i	0.308620	+	0.356166i	0.888778	−	0.458337i	$-0.151555\pi$
$71$	2.60048	+	3.00111i	0.308620	+	0.356166i	−0.580159	+	0.814504i	$0.697009\pi$
$72$	1.18159	+	2.75751i	0.139251	+	0.324975i
$73$	−2.16121	+	15.0315i	−0.252950	+	1.75931i	0.327347	+	0.944904i	$0.393845\pi$
$73$	−2.16121	+	15.0315i	−0.252950	+	1.75931i	−0.580297	+	0.814405i	$0.697064\pi$
$74$	−9.53777	+	0.910747i	−1.10874	+	0.105872i
$75$	−2.62431	−	6.78590i	−0.303029	−	0.783568i
$76$	−2.02669	+	1.93244i	−0.232477	+	0.221667i
$77$	−0.0461424	−	0.968648i	−0.00525841	−	0.110388i
$78$	10.7573	−	1.41748i	1.21802	−	0.160498i
$79$	−8.08815	−	7.71203i	−0.909987	−	0.867671i	0.0816586	−	0.996660i	$-0.473978\pi$
$79$	−8.08815	−	7.71203i	−0.909987	−	0.867671i	−0.991646	+	0.128989i	$0.958827\pi$
$80$	0.585501	−	0.675704i	0.0654610	−	0.0755460i
$81$	−8.50637	−	2.93968i	−0.945152	−	0.326632i
$82$	10.1288	−	2.97409i	1.11854	−	0.328434i
$83$	−3.31066	+	4.64918i	−0.363392	+	0.510313i	−0.955278	−	0.295709i	$-0.904444\pi$
$83$	−3.31066	+	4.64918i	−0.363392	+	0.510313i	0.591886	+	0.806022i	$0.298384\pi$
$84$	1.87811	+	6.68678i	0.204919	+	0.729588i
$85$	4.10626	−	3.91531i	0.445386	−	0.424675i
$86$	−0.706872	−	0.282989i	−0.0762240	−	0.0305155i
$87$	2.16688	−	10.5709i	0.232314	−	1.13332i
$88$	−0.224509	+	0.0898798i	−0.0239327	+	0.00958122i
$89$	4.94391	+	3.17726i	0.524054	+	0.336789i	0.775774	−	0.631011i	$-0.217360\pi$
$89$	4.94391	+	3.17726i	0.524054	+	0.336789i	−0.251720	+	0.967800i	$0.580996\pi$
$90$	0.319050	+	2.66321i	0.0336308	+	0.280727i
$91$	25.1202			2.63332
$92$	−4.23708	+	2.24659i	−0.441746	+	0.234223i
$93$	0.251301	+	0.269854i	0.0260587	+	0.0279826i
$94$	1.22167	−	0.235458i	0.126006	−	0.0242857i
$95$	−2.22540	+	1.14727i	−0.228321	+	0.117708i
$96$	1.42263	−	0.987992i	0.145196	−	0.100837i
$97$	9.66885	−	0.923263i	0.981723	−	0.0937432i	0.408165	−	0.912908i	$-0.366169\pi$
$97$	9.66885	−	0.923263i	0.981723	−	0.0937432i	0.573558	+	0.819165i	$0.305563\pi$
$98$	1.29223	+	8.98769i	0.130535	+	0.907894i
$99$	0.253378	−	0.679811i	0.0254654	−	0.0683236i
$100$	−3.53378	+	2.27102i	−0.353378	+	0.227102i
$101$	−4.66692	+	6.55377i	−0.464376	+	0.652124i	−0.978658	−	0.205497i	$-0.934119\pi$
$101$	−4.66692	+	6.55377i	−0.464376	+	0.652124i	0.514282	+	0.857621i	$0.328058\pi$
$102$	9.58285	−	5.38310i	0.948844	−	0.533006i
$103$	0.236207	+	0.682475i	0.0232742	+	0.0672463i	0.956040	−	0.293238i	$-0.0947327\pi$
$103$	0.236207	+	0.682475i	0.0232742	+	0.0672463i	−0.932765	+	0.360484i	$0.882612\pi$
$104$	−2.04888	−	5.91986i	−0.200909	−	0.580490i
$105$	−0.0731789	+	6.20946i	−0.00714153	+	0.605981i
$106$	6.24201	−	8.76568i	0.606278	−	0.851398i
$107$	−8.85957	+	5.69370i	−0.856487	+	0.550431i	−0.893592	−	0.448881i	$-0.851823\pi$
$107$	−8.85957	+	5.69370i	−0.856487	+	0.550431i	0.0371048	+	0.999311i	$0.488186\pi$
$108$	−0.676450	+	5.15193i	−0.0650914	+	0.495745i
$109$	−0.386228	−	2.68628i	−0.0369940	−	0.257299i	0.962928	−	0.269757i	$-0.0869434\pi$
$109$	−0.386228	−	2.68628i	−0.0369940	−	0.257299i	−0.999922	+	0.0124583i	$0.996034\pi$
$110$	−0.215239	+	0.0205528i	−0.0205222	+	0.00195964i
$111$	−15.0131	−	7.07124i	−1.42498	−	0.671173i
$112$	3.56423	−	1.83749i	0.336788	−	0.173626i
$113$	−4.86884	+	0.938392i	−0.458022	+	0.0882765i	−0.413043	−	0.910711i	$-0.635534\pi$
$113$	−4.86884	+	0.938392i	−0.458022	+	0.0882765i	−0.0449789	+	0.998988i	$0.514322\pi$
$114$	−4.72673	+	1.08788i	−0.442699	+	0.101889i
$115$	−4.20075	+	0.859986i	−0.391722	+	0.0801942i
$116$	−6.23003			−0.578443
$117$	17.2775	+	7.39395i	1.59731	+	0.683571i
$118$	2.27178	+	1.45998i	0.209134	+	0.134402i
$119$	23.6240	−	9.45762i	2.16561	−	0.866979i
$120$	1.46930	−	0.489217i	0.134128	−	0.0446592i
$121$	−10.1578	−	4.06655i	−0.923432	−	0.369686i
$122$	−2.61107	+	2.48965i	−0.236396	+	0.225403i
$123$	17.7169	+	4.51978i	1.59748	+	0.407535i
$124$	0.123492	−	0.173420i	0.0110899	−	0.0155736i
$125$	−7.89291	+	2.31757i	−0.705963	+	0.207290i
$126$	−3.11091	+	11.6208i	−0.277142	+	1.03526i
$127$	−9.71332	+	11.2098i	−0.861918	+	0.994706i	0.138073	+	0.990422i	$0.455909\pi$
$127$	−9.71332	+	11.2098i	−0.861918	+	0.994706i	−0.999991	+	0.00428426i	$0.998636\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	−0.802960	−	1.04619i	−0.0706967	−	0.0921117i
$130$	−0.266501	−	5.59455i	−0.0233737	−	0.490675i
$131$	6.64444	−	6.33546i	0.580527	−	0.553531i	−0.341883	−	0.939742i	$-0.611065\pi$
$131$	6.64444	−	6.33546i	0.580527	−	0.553531i	0.922411	+	0.386211i	$0.126216\pi$
$132$	−0.413870	−	0.0644923i	−0.0360228	−	0.00561334i
$133$	−11.1785	+	1.06741i	−0.969295	+	0.0925564i
$134$	2.06905	−	14.3905i	0.178739	−	1.24315i
$135$	−1.87804	+	4.24929i	−0.161636	+	0.365720i
$136$	−4.15564	−	4.79586i	−0.356343	−	0.411242i
$137$	4.00729	+	6.94083i	0.342366	+	0.592996i	0.984872	−	0.173286i	$-0.0554383\pi$
$137$	4.00729	+	6.94083i	0.342366	+	0.592996i	−0.642505	+	0.766281i	$0.722105\pi$
$138$	−8.29712	−	0.397339i	−0.706297	−	0.0338237i
$139$	1.22306	−	2.11840i	0.103738	−	0.179680i	−0.809484	−	0.587142i	$-0.800253\pi$
$139$	1.22306	−	2.11840i	0.103738	−	0.179680i	0.913222	+	0.407462i	$0.133586\pi$
$140$	3.52049	−	0.678519i	0.297536	−	0.0573453i
$141$	2.02797	+	0.728761i	0.170786	+	0.0613728i
$142$	3.68658	−	1.47589i	0.309371	−	0.123854i
$143$	−0.629324	+	1.37803i	−0.0526268	+	0.115237i
$144$	2.99231	−	0.214708i	0.249359	−	0.0178924i
$145$	−5.34454	−	1.56930i	−0.443840	−	0.130323i
$146$	13.4980	+	6.95868i	1.11710	+	0.575904i
$147$	−6.01687	+	14.5307i	−0.496263	+	1.19848i
$148$	−2.25884	+	9.31108i	−0.185676	+	0.765366i
$149$	−2.16095	−	6.24364i	−0.177032	−	0.511499i	0.821220	−	0.570612i	$-0.193294\pi$
$149$	−2.16095	−	6.24364i	−0.177032	−	0.511499i	−0.998251	+	0.0591129i	$0.981173\pi$
$150$	−7.27101	+	0.260525i	−0.593675	+	0.0212718i
$151$	14.1529	+	13.4948i	1.15175	+	1.09819i	0.993850	+	0.110733i	$0.0353198\pi$
$151$	14.1529	+	13.4948i	1.15175	+	1.09819i	0.157897	+	0.987456i	$0.449529\pi$
$152$	1.16330	+	2.54726i	0.0943558	+	0.206610i
$153$	19.0322	+	0.448654i	1.53866	+	0.0362715i
$154$	−0.930464	−	0.273209i	−0.0749790	−	0.0220158i
$155$	0.149623	−	0.117665i	0.0120180	−	0.00945105i
$156$	2.17883	−	10.6292i	0.174446	−	0.851019i
$157$	−2.86649	−	2.25423i	−0.228771	−	0.179907i	0.497194	−	0.867640i	$-0.334364\pi$
$157$	−2.86649	−	2.25423i	−0.228771	−	0.179907i	−0.725964	+	0.687732i	$0.758606\pi$
$158$	−9.93325	+	5.12095i	−0.790247	+	0.407401i
$159$	17.0444	−	7.54245i	1.35171	−	0.598155i
$160$	−0.447042	−	0.774300i	−0.0353418	−	0.0612138i
$161$	−18.9245	−	3.42154i	−1.49146	−	0.269655i
$162$	−5.56016	+	7.07705i	−0.436848	+	0.556025i
$163$	9.09407	+	10.4951i	0.712303	+	0.822041i	0.990359	−	0.138524i	$-0.0442357\pi$
$163$	9.09407	+	10.4951i	0.712303	+	0.822041i	−0.278057	+	0.960565i	$0.589690\pi$
$164$	0.502296	−	10.5445i	0.0392227	−	0.823386i
$165$	−0.338801	−	0.159577i	−0.0263756	−	0.0124230i
$166$	3.31066	+	4.64918i	0.256957	+	0.360846i
$167$	15.0857	+	6.03942i	1.16737	+	0.467344i	0.872701	−	0.488255i	$-0.162366\pi$
$167$	15.0857	+	6.03942i	1.16737	+	0.467344i	0.294669	+	0.955599i	$0.404791\pi$
$168$	6.93328	+	0.412214i	0.534914	+	0.0318030i
$169$	−23.3254	−	12.0251i	−1.79426	−	0.925005i
$170$	−2.35695	−	5.16099i	−0.180770	−	0.395830i
$171$	−8.00265	−	2.55613i	−0.611978	−	0.195472i
$172$	−0.498620	+	0.575438i	−0.0380194	+	0.0438767i
$173$	−14.3463	−	2.76503i	−1.09073	−	0.210221i	−0.387988	−	0.921664i	$-0.626830\pi$
$173$	−14.3463	−	2.76503i	−1.09073	−	0.210221i	−0.702744	+	0.711443i	$0.748042\pi$
$174$	−9.28081	−	5.50511i	−0.703576	−	0.417341i
$175$	−16.7682	−	1.60117i	−1.26756	−	0.121037i
$176$	0.0115068	+	0.241558i	0.000867359	+	0.0182081i
$177$	2.09415	+	4.18236i	0.157406	+	0.314366i
$178$	4.61951	−	3.63282i	0.346247	−	0.272291i
$179$	−6.78855	+	14.8648i	−0.507400	+	1.11105i	0.466593	+	0.884472i	$0.345481\pi$
$179$	−6.78855	+	14.8648i	−0.507400	+	1.11105i	−0.973993	+	0.226578i	$0.927246\pi$
$180$	2.62109	+	0.569549i	0.195364	+	0.0424517i
$181$	−16.8697	−	10.8415i	−1.25392	−	0.805843i	−0.266476	−	0.963841i	$-0.585859\pi$
$181$	−16.8697	−	10.8415i	−1.25392	−	0.805843i	−0.987439	+	0.157999i	$0.949496\pi$
$182$	8.21602	−	23.7386i	0.609012	−	1.75962i
$183$	−6.08966	+	1.40156i	−0.450160	+	0.103606i
$184$	0.737215	+	4.73883i	0.0543482	+	0.349351i
$185$	−4.28318	+	7.41869i	−0.314906	+	0.545433i
$186$	0.337205	−	0.149219i	0.0247251	−	0.0109413i
$187$	−0.0730204	+	1.53289i	−0.00533978	+	0.112096i
$188$	0.177062	−	1.23149i	0.0129136	−	0.0898158i
$189$	−14.9029	+	14.5625i	−1.08403	+	1.05926i
$190$	0.356317	+	2.47824i	0.0258500	+	0.179791i
$191$	−0.891081	−	3.67309i	−0.0644763	−	0.265775i	0.930445	−	0.366432i	$-0.119421\pi$
$191$	−0.891081	−	3.67309i	−0.0644763	−	0.265775i	−0.994921	+	0.100657i	$0.967906\pi$
$192$	−0.468357	−	1.66753i	−0.0338008	−	0.120343i
$193$	7.16762	+	0.684425i	0.515937	+	0.0492660i	0.349777	−	0.936833i	$-0.386257\pi$
$193$	7.16762	+	0.684425i	0.515937	+	0.0492660i	0.166159	+	0.986099i	$0.446863\pi$
$194$	2.28989	−	9.43904i	0.164404	−	0.677684i
$195$	4.54658	−	8.56964i	0.325587	−	0.613685i
$196$	8.91602	+	1.71842i	0.636859	+	0.122744i
$197$	5.85438	−	1.71900i	0.417107	−	0.122474i	−0.0664433	−	0.997790i	$-0.521165\pi$
$197$	5.85438	−	1.71900i	0.417107	−	0.122474i	0.483550	+	0.875316i	$0.339347\pi$
$198$	−0.559550	−	0.461787i	−0.0397655	−	0.0328177i
$199$	7.61510	−	4.89392i	0.539820	−	0.346921i	−0.242149	−	0.970239i	$-0.577852\pi$
$199$	7.61510	−	4.89392i	0.539820	−	0.346921i	0.781968	+	0.623318i	$0.214216\pi$
$200$	0.990332	+	4.08220i	0.0700270	+	0.288655i
$201$	15.7983	−	19.6092i	1.11433	−	1.38312i
$202$	4.66692	+	6.55377i	0.328363	+	0.461122i
$203$	−19.6375	−	15.4431i	−1.37828	−	1.08389i
$204$	−1.95279	−	10.8164i	−0.136723	−	0.757303i
$205$	3.08698	−	8.91925i	0.215604	−	0.622947i
$206$	0.722195			0.0503177
$207$	−12.0090	−	7.92359i	−0.834685	−	0.550727i
$208$	−6.26439			−0.434357
$209$	0.221493	−	0.639961i	0.0153210	−	0.0442670i
$210$	5.84401	+	2.10007i	0.403275	+	0.144919i
$211$	−3.86899	−	3.04261i	−0.266353	−	0.209462i	0.476046	−	0.879420i	$-0.342070\pi$
$211$	−3.86899	−	3.04261i	−0.266353	−	0.209462i	−0.742399	+	0.669958i	$0.766312\pi$
$212$	−6.24201	−	8.76568i	−0.428703	−	0.602029i
$213$	6.79602	+	1.05901i	0.465656	+	0.0725619i
$214$	2.48287	+	10.2345i	0.169725	+	0.699618i
$215$	−0.572699	+	0.368051i	−0.0390577	+	0.0251009i
$216$	4.64734	+	2.32428i	0.316211	+	0.158147i
$217$	0.819131	−	0.240519i	0.0556062	−	0.0163275i
$218$	−2.66486	−	0.513609i	−0.180487	−	0.0347860i
$219$	13.9588	+	22.2936i	0.943248	+	1.50646i
$220$	−0.0509754	+	0.210123i	−0.00343676	+	0.0141665i
$221$	−39.5728	−	3.77874i	−2.66195	−	0.254186i
$222$	−11.5926	+	11.8746i	−0.778047	+	0.796972i
$223$	2.70759	+	11.1608i	0.181314	+	0.747385i	0.987747	+	0.156061i	$0.0498795\pi$
$223$	2.70759	+	11.1608i	0.181314	+	0.747385i	−0.806434	+	0.591324i	$0.798605\pi$
$224$	−0.570683	−	3.96919i	−0.0381303	−	0.265202i
$225$	−11.0618	−	6.03686i	−0.737451	−	0.402458i
$226$	−0.705661	+	4.90798i	−0.0469398	+	0.326474i
$227$	1.16746	−	24.5080i	0.0774871	−	1.62666i	−0.541113	−	0.840950i	$-0.681997\pi$
$227$	1.16746	−	24.5080i	0.0774871	−	1.62666i	0.618601	−	0.785706i	$-0.287700\pi$
$228$	−0.517917	+	4.82257i	−0.0342999	+	0.319383i
$229$	−5.16132	+	8.93967i	−0.341070	+	0.590750i	−0.984632	−	0.174644i	$-0.944123\pi$
$229$	−5.16132	+	8.93967i	−0.341070	+	0.590750i	0.643562	+	0.765394i	$0.277456\pi$
$230$	−0.561244	+	4.25099i	−0.0370073	+	0.280302i
$231$	−1.14469	−	1.22919i	−0.0753148	−	0.0808750i
$232$	−2.03764	+	5.88738i	−0.133778	+	0.386525i
$233$	−1.97053	−	1.26638i	−0.129094	−	0.0829634i	0.474500	−	0.880255i	$-0.342629\pi$
$233$	−1.97053	−	1.26638i	−0.129094	−	0.0829634i	−0.603594	+	0.797292i	$0.706265\pi$
$234$	12.6382	−	13.9090i	0.826186	−	0.909257i
$235$	0.462100	−	1.01186i	0.0301441	−	0.0660063i
$236$	2.12271	−	1.66932i	0.138177	−	0.108663i
$237$	−19.3225	−	1.14881i	−1.25513	−	0.0746231i
$238$	−1.21081	−	25.4180i	−0.0784850	−	1.64760i
$239$	−10.5800	−	1.01027i	−0.684362	−	0.0653487i	−0.252917	−	0.967488i	$-0.581390\pi$
$239$	−10.5800	−	1.01027i	−0.684362	−	0.0653487i	−0.431445	+	0.902139i	$0.641996\pi$
$240$	0.0182491	−	1.54849i	0.00117797	−	0.0999548i
$241$	−6.93490	−	1.33659i	−0.446716	−	0.0860975i	−0.0390679	−	0.999237i	$-0.512439\pi$
$241$	−6.93490	−	1.33659i	−0.446716	−	0.0860975i	−0.407648	+	0.913139i	$0.633651\pi$
$242$	−7.16517	+	8.26905i	−0.460595	+	0.531554i
$243$	−14.5365	+	5.62942i	−0.932517	+	0.361127i
$244$	1.49873	+	3.28175i	0.0959461	+	0.210093i
$245$	7.21591	+	3.72006i	0.461008	+	0.237666i
$246$	10.0658	−	15.2642i	0.641773	−	0.973208i
$247$	16.2857	+	6.51982i	1.03624	+	0.414846i
$248$	−0.123492	−	0.173420i	−0.00784173	−	0.0110122i
$249$	0.823658	+	9.85127i	0.0521972	+	0.624299i
$250$	−0.391415	+	8.21681i	−0.0247552	+	0.519677i
$251$	−2.00199	−	2.31042i	−0.126364	−	0.145832i	0.689042	−	0.724722i	$-0.258032\pi$
$251$	−2.00199	−	2.31042i	−0.126364	−	0.145832i	−0.815406	+	0.578890i	$0.803486\pi$
$252$	9.96420	+	6.74061i	0.627685	+	0.424618i
$253$	0.661802	−	0.952428i	0.0416071	−	0.0598786i
$254$	7.41633	+	12.8455i	0.465342	+	0.805995i
$255$	1.04935	−	9.77098i	0.0657127	−	0.611882i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	17.0671	+	13.4217i	1.06462	+	0.837226i	0.987154	−	0.159769i	$-0.0510750\pi$
$257$	17.0671	+	13.4217i	1.06462	+	0.837226i	0.0774648	+	0.996995i	$0.475317\pi$
$258$	−1.25127	+	0.416623i	−0.0779007	+	0.0259378i
$259$	−30.2005	+	23.7499i	−1.87657	+	1.47575i
$260$	−5.37402	−	1.57796i	−0.333283	−	0.0978606i
$261$	−8.96099	−	16.4018i	−0.554671	−	1.01525i
$262$	−3.81383	−	8.35112i	−0.235619	−	0.515934i
$263$	5.36352	+	5.11410i	0.330729	+	0.315349i	0.837189	−	0.546914i	$-0.184198\pi$
$263$	5.36352	+	5.11410i	0.330729	+	0.315349i	−0.506460	+	0.862264i	$0.669046\pi$
$264$	−0.196309	+	0.370014i	−0.0120820	+	0.0227728i
$265$	−3.14681	−	9.09211i	−0.193307	−	0.558524i
$266$	−2.64741	+	10.9128i	−0.162323	+	0.669104i
$267$	10.0917	−	1.32979i	0.617605	−	0.0813818i
$268$	−12.9224	−	6.66194i	−0.789359	−	0.406943i
$269$	−20.5266	−	6.02714i	−1.25153	−	0.367481i	−0.412192	−	0.911097i	$-0.635237\pi$
$269$	−20.5266	−	6.02714i	−1.25153	−	0.367481i	−0.839334	+	0.543616i	$0.817055\pi$
$270$	3.40133	+	3.16455i	0.206998	+	0.192589i
$271$	−1.33015	+	2.91262i	−0.0808007	+	0.176929i	−0.945720	−	0.324981i	$-0.894642\pi$
$271$	−1.33015	+	2.91262i	−0.0808007	+	0.176929i	0.864920	+	0.501910i	$0.167369\pi$
$272$	−5.89127	+	2.35851i	−0.357211	+	0.143006i
$273$	33.2158	−	28.1032i	2.01031	−	1.70088i
$274$	7.86975	−	1.51677i	0.475429	−	0.0916314i
$275$	0.507921	−	0.879745i	0.0306288	−	0.0530506i
$276$	−3.08921	+	7.71082i	−0.185948	+	0.464137i
$277$	10.0759	+	17.4520i	0.605402	+	1.04859i	0.991988	+	0.126333i	$0.0403209\pi$
$277$	10.0759	+	17.4520i	0.605402	+	1.04859i	−0.386586	+	0.922253i	$0.626346\pi$
$278$	−1.60186	−	1.84865i	−0.0960734	−	0.110875i
$279$	0.634188	+	0.0756779i	0.0379678	+	0.00453072i
$280$	0.510239	−	3.54879i	0.0304926	−	0.212081i
$281$	11.0009	−	1.05046i	0.656257	−	0.0626649i	0.238385	−	0.971171i	$-0.423382\pi$
$281$	11.0009	−	1.05046i	0.656257	−	0.0626649i	0.417872	+	0.908506i	$0.362776\pi$
$282$	1.35197	−	1.67808i	0.0805084	−	0.0999284i
$283$	−17.6885	+	16.8660i	−1.05147	+	1.00258i	−0.0514824	+	0.998674i	$0.516395\pi$
$283$	−17.6885	+	16.8660i	−1.05147	+	1.00258i	−0.999992	+	0.00390527i	$0.998757\pi$
$284$	−0.188950	−	3.96654i	−0.0112121	−	0.235371i
$285$	−1.65907	+	4.00667i	−0.0982751	+	0.237335i
$286$	1.09641	+	1.04542i	0.0648318	+	0.0618170i
$287$	27.7211	−	31.9919i	1.63633	−	1.88842i
$288$	0.775788	−	2.89796i	0.0457137	−	0.170764i
$289$	−22.3270	+	6.55581i	−1.31336	+	0.385636i
$290$	−3.23102	+	4.53733i	−0.189732	+	0.266441i
$291$	11.7520	−	12.0378i	0.688912	−	0.705669i
$292$	10.9907	−	10.4796i	0.643183	−	0.613273i
$293$	−6.44650	−	2.58079i	−0.376608	−	0.150771i	0.175633	−	0.984456i	$-0.443803\pi$
$293$	−6.44650	−	2.58079i	−0.376608	−	0.150771i	−0.552241	+	0.833685i	$0.686227\pi$
$294$	11.7636	+	10.4385i	0.686070	+	0.608785i
$295$	2.24150	−	0.897360i	0.130505	−	0.0522463i
$296$	8.06018	+	5.17996i	0.468489	+	0.301079i
$297$	−0.425503	−	1.18236i	−0.0246902	−	0.0686076i
$298$	−6.60702			−0.382735
$299$	23.8280	+	18.2978i	1.37801	+	1.05819i
$300$	−2.13192	+	6.95632i	−0.123086	+	0.401623i
$301$	−2.99809	+	0.577835i	−0.172807	+	0.0333059i
$302$	17.3815	−	8.96080i	1.00019	−	0.515636i
$303$	1.16108	+	13.8870i	0.0667023	+	0.797785i
$304$	2.78764	−	0.266188i	0.159882	−	0.0152669i
$305$	0.459060	+	3.19283i	0.0262857	+	0.182821i
$306$	6.64881	−	17.8387i	0.380087	−	1.01977i
$307$	19.8930	−	12.7845i	1.13535	−	0.729648i	0.168684	−	0.985670i	$-0.446048\pi$
$307$	19.8930	−	12.7845i	1.13535	−	0.729648i	0.966671	+	0.256022i	$0.0824119\pi$
$308$	−0.562508	+	0.789932i	−0.0320519	+	0.0450105i
$309$	1.07585	+	0.638162i	0.0612028	+	0.0363038i
$310$	−0.0622563	−	0.179878i	−0.00353592	−	0.0102164i
$311$	−9.84236	−	28.4376i	−0.558109	−	1.61255i	−0.771952	−	0.635681i	$-0.780719\pi$
$311$	−9.84236	−	28.4376i	−0.558109	−	1.61255i	0.213843	−	0.976868i	$-0.431402\pi$
$312$	−9.33201	−	5.53548i	−0.528321	−	0.313385i
$313$	−0.155225	+	0.217983i	−0.00877383	+	0.0123211i	−0.818940	−	0.573880i	$-0.805438\pi$
$313$	−0.155225	+	0.217983i	−0.00877383	+	0.0123211i	0.810166	+	0.586201i	$0.199377\pi$
$314$	−3.06779	+	1.97155i	−0.173125	+	0.111261i
$315$	6.85005	+	8.29246i	0.385957	+	0.467227i
$316$	1.59045	+	11.0618i	0.0894698	+	0.622276i
$317$	3.36310	−	0.321137i	0.188891	−	0.0180369i	−0.000181966	−	1.00000i	$-0.500058\pi$
$317$	3.36310	−	0.321137i	0.188891	−	0.0180369i	0.189073	+	0.981963i	$0.439452\pi$
$318$	−1.55295	−	18.5739i	−0.0870849	−	1.04157i
$319$	1.33914	−	0.690373i	0.0749772	−	0.0386534i
$320$	−0.877927	+	0.169207i	−0.0490776	+	0.00945894i
$321$	−5.34495	+	17.4402i	−0.298326	+	0.973420i
$322$	−9.42295	+	16.7646i	−0.525120	+	0.934253i
$323$	17.7704			0.988771
$324$	4.86926	+	7.56903i	0.270515	+	0.420502i
$325$	22.1370	+	14.2266i	1.22794	+	0.789149i
$326$	12.8923	−	5.16129i	0.714037	−	0.285857i
$327$	−3.51597	−	3.11990i	−0.194433	−	0.172531i
$328$	−9.80026	−	3.92343i	−0.541129	−	0.216635i
$329$	3.61076	−	3.44285i	0.199068	−	0.189811i
$330$	−0.261611	+	0.267975i	−0.0144012	+	0.0147515i
$331$	−3.60630	+	5.06434i	−0.198220	+	0.278362i	−0.901708	−	0.432346i	$-0.857686\pi$
$331$	−3.60630	+	5.06434i	−0.198220	+	0.278362i	0.703487	+	0.710708i	$0.251625\pi$
$332$	5.47629	−	1.60798i	0.300550	−	0.0882495i
$333$	−27.7623	+	7.44577i	−1.52137	+	0.408026i
$334$	10.6413	−	12.2807i	0.582267	−	0.671972i
$335$	−9.40758	−	8.97011i	−0.513991	−	0.490090i
$336$	2.65720	−	6.41714i	0.144962	−	0.350084i
$337$	1.30443	+	27.3834i	0.0710569	+	1.49167i	0.699958	+	0.714184i	$0.253202\pi$
$337$	1.30443	+	27.3834i	0.0710569	+	1.49167i	−0.628901	+	0.777485i	$0.716495\pi$
$338$	−18.9927	+	18.1095i	−1.03307	+	0.985026i
$339$	−5.38811	+	6.68782i	−0.292642	+	0.363232i
$340$	−5.64802	+	0.539321i	−0.306307	+	0.0292488i
$341$	−0.00732707	+	0.0509609i	−0.000396783	+	0.00275969i
$342$	−5.03296	+	6.72648i	−0.272151	+	0.363727i
$343$	5.46236	+	6.30390i	0.294940	+	0.340379i
$344$	0.380707	+	0.659404i	0.0205263	+	0.0355527i
$345$	−4.59243	+	5.83672i	−0.247248	+	0.314238i
$346$	−7.30518	+	12.6529i	−0.392729	+	0.680227i
$347$	4.18280	−	0.806169i	0.224545	−	0.0432774i	−0.0757378	−	0.997128i	$-0.524131\pi$
$347$	4.18280	−	0.806169i	0.224545	−	0.0432774i	0.300282	+	0.953850i	$0.402919\pi$
$348$	−8.23779	+	6.96983i	−0.441592	+	0.373622i
$349$	5.49855	−	2.20129i	0.294331	−	0.117832i	−0.219798	−	0.975545i	$-0.570540\pi$
$349$	5.49855	−	2.20129i	0.294331	−	0.117832i	0.514128	+	0.857713i	$0.328116\pi$
$350$	−6.99744	+	15.3223i	−0.374029	+	0.819009i
$351$	31.1176	−	9.55239i	1.66093	−	0.509869i
$352$	0.232036	+	0.0681319i	0.0123676	+	0.00363144i
$353$	−6.76128	−	3.48568i	−0.359867	−	0.185524i	0.268806	−	0.963194i	$-0.413371\pi$
$353$	−6.76128	−	3.48568i	−0.359867	−	0.185524i	−0.628672	+	0.777670i	$0.716401\pi$
$354$	4.63727	−	0.611052i	0.246468	−	0.0324771i
$355$	0.837049	−	3.45036i	0.0444259	−	0.183126i
$356$	−1.92213	−	5.55362i	−0.101872	−	0.294341i
$357$	20.6567	−	38.9349i	1.09327	−	2.06065i
$358$	11.8270	+	11.2770i	0.625075	+	0.596008i
$359$	−4.66720	−	10.2198i	−0.246326	−	0.539378i	0.745571	−	0.666426i	$-0.232177\pi$
$359$	−4.66720	−	10.2198i	−0.246326	−	0.539378i	−0.991897	+	0.127048i	$0.959450\pi$
$360$	1.39550	−	2.29065i	0.0735492	−	0.120728i
$361$	10.7062	+	3.14363i	0.563485	+	0.165454i
$362$	−15.7628	+	12.3960i	−0.828473	+	0.651518i
$363$	−17.9808	+	5.98688i	−0.943745	+	0.314230i
$364$	−19.7458	−	15.5283i	−1.03496	−	0.813904i
$365$	12.0683	−	6.22165i	0.631685	−	0.325656i
$366$	−0.667255	+	6.21313i	−0.0348780	+	0.324766i
$367$	−10.6249	−	18.4028i	−0.554613	−	0.960617i	−0.997934	−	0.0642544i	$-0.979533\pi$
$367$	−10.6249	−	18.4028i	−0.554613	−	0.960617i	0.443321	−	0.896363i	$-0.353800\pi$
$368$	4.71932	+	0.853251i	0.246011	+	0.0444788i
$369$	28.4830	−	13.8443i	1.48277	−	0.720706i
$370$	5.60978	+	6.47403i	0.291638	+	0.336569i
$371$	2.05324	−	43.1029i	0.106599	−	2.23779i
$372$	−0.0307234	−	0.367464i	−0.00159293	−	0.0190521i
$373$	−5.78384	−	8.12227i	−0.299476	−	0.420555i	0.637229	−	0.770674i	$-0.280080\pi$
$373$	−5.78384	−	8.12227i	−0.299476	−	0.420555i	−0.936705	+	0.350119i	$0.886141\pi$
$374$	1.42470	+	0.570362i	0.0736693	+	0.0294927i
$375$	−7.84380	+	11.8946i	−0.405052	+	0.614236i
$376$	−1.10585	−	0.570105i	−0.0570299	−	0.0294009i
$377$	16.2125	+	35.5005i	0.834988	+	1.82837i
$378$	8.88729	+	18.8462i	0.457113	+	0.969344i
$379$	0.315872	−	0.364536i	0.0162253	−	0.0187250i	−0.747579	−	0.664173i	$-0.768784\pi$
$379$	0.315872	−	0.364536i	0.0162253	−	0.0187250i	0.763804	+	0.645448i	$0.223329\pi$
$380$	2.45848	+	0.473833i	0.126117	+	0.0243071i
$381$	−0.302748	+	25.6891i	−0.0155103	+	1.31609i
$382$	−3.76251	−	0.359276i	−0.192507	−	0.0183822i
$383$	1.20888	+	25.3775i	0.0617708	+	1.29673i	0.790727	+	0.612168i	$0.209703\pi$
$383$	1.20888	+	25.3775i	0.0617708	+	1.29673i	−0.728957	+	0.684560i	$0.759994\pi$
$384$	−1.72900	−	0.102796i	−0.0882325	−	0.00524581i
$385$	−0.681536	+	0.535965i	−0.0347343	+	0.0273153i
$386$	2.99108	−	6.54955i	0.152242	−	0.333363i
$387$	−2.23215	−	0.485035i	−0.113467	−	0.0246557i
$388$	−8.17095	−	5.25115i	−0.414817	−	0.266587i
$389$	−4.70834	+	13.6038i	−0.238722	+	0.689742i	0.760463	+	0.649381i	$0.224972\pi$
$389$	−4.70834	+	13.6038i	−0.238722	+	0.689742i	−0.999185	+	0.0403610i	$0.987149\pi$
$390$	−6.61128	−	7.09937i	−0.334775	−	0.359491i
$391$	29.2977	+	8.23681i	1.48165	+	0.416553i
$392$	4.54006	−	7.86361i	0.229307	−	0.397172i
$393$	1.69797	−	15.8106i	0.0856515	−	0.797542i
$394$	0.290323	−	6.09462i	0.0146262	−	0.307043i
$395$	−1.42200	+	9.89021i	−0.0715484	+	0.497630i
$396$	−0.619400	+	0.377740i	−0.0311260	+	0.0189822i
$397$	−1.34265	−	9.33833i	−0.0673856	−	0.468677i	−0.995375	−	0.0960696i	$-0.969373\pi$
$397$	−1.34265	−	9.33833i	−0.0673856	−	0.468677i	0.927989	−	0.372608i	$-0.121536\pi$
$398$	−2.13411	−	8.79692i	−0.106973	−	0.440950i
$399$	−13.5868	+	13.9173i	−0.680190	+	0.696735i
$400$	4.18159	+	0.399294i	0.209080	+	0.0199647i
$401$	4.91818	−	20.2730i	0.245602	−	1.01239i	−0.706769	−	0.707444i	$-0.749848\pi$
$401$	4.91818	−	20.2730i	0.245602	−	1.01239i	0.952371	−	0.304941i	$-0.0986368\pi$
$402$	−13.3635	−	21.3430i	−0.666513	−	1.06449i
$403$	−1.30956	−	0.252397i	−0.0652339	−	0.0125728i
$404$	7.71972	−	2.26671i	0.384070	−	0.112773i
$405$	2.27060	+	7.71976i	0.112827	+	0.383598i
$406$	−21.0165	+	13.5065i	−1.04303	+	0.670317i
$407$	−0.546260	−	2.25172i	−0.0270771	−	0.111613i
$408$	−10.8602	−	1.69232i	−0.537662	−	0.0837825i
$409$	1.06777	+	1.49947i	0.0527978	+	0.0741441i	0.840131	−	0.542384i	$-0.182478\pi$
$409$	1.06777	+	1.49947i	0.0527978	+	0.0741441i	−0.787333	+	0.616528i	$0.788539\pi$
$410$	−7.41905	−	5.83440i	−0.366401	−	0.288141i
$411$	13.0638	+	4.69452i	0.644389	+	0.231564i
$412$	0.236207	−	0.682475i	0.0116371	−	0.0336231i
$413$	10.8289			0.532855
$414$	−11.4156	+	8.75699i	−0.561044	+	0.430383i
$415$	5.10297			0.250495
$416$	−2.04888	+	5.91986i	−0.100455	+	0.290245i
$417$	−0.752737	−	4.16939i	−0.0368617	−	0.204176i
$418$	−0.532321	−	0.418622i	−0.0260367	−	0.0204755i
$419$	20.2432	+	28.4275i	0.988943	+	1.38878i	0.920334	+	0.391133i	$0.127917\pi$
$419$	20.2432	+	28.4275i	0.988943	+	1.38878i	0.0686090	+	0.997644i	$0.478144\pi$
$420$	3.89595	−	4.83573i	0.190103	−	0.235959i
$421$	−2.82611	−	11.6494i	−0.137736	−	0.567756i	−0.998293	−	0.0584020i	$-0.981399\pi$
$421$	−2.82611	−	11.6494i	−0.137736	−	0.567756i	0.860557	−	0.509354i	$-0.170116\pi$
$422$	−4.14069	+	2.66106i	−0.201566	+	0.129538i
$423$	3.49683	−	1.30517i	0.170022	−	0.0634596i
$424$	−10.3251	+	3.03173i	−0.501433	+	0.147234i
$425$	26.1747	+	5.04476i	1.26966	+	0.244707i
$426$	3.22352	−	6.07588i	0.156180	−	0.294377i
$427$	−3.41077	+	14.0594i	−0.165059	+	0.680382i
$428$	10.4837	+	1.00107i	0.506749	+	0.0483887i
$429$	0.709528	+	2.52618i	0.0342563	+	0.121965i
$430$	0.160497	+	0.661579i	0.00773986	+	0.0319042i
$431$	1.28240	+	8.91931i	0.0617712	+	0.429628i	0.997116	+	0.0758911i	$0.0241801\pi$
$431$	1.28240	+	8.91931i	0.0617712	+	0.429628i	−0.935345	+	0.353737i	$0.884911\pi$
$432$	3.71644	−	3.63154i	0.178807	−	0.174723i
$433$	2.04692	−	14.2366i	0.0983685	−	0.684168i	−0.879646	−	0.475630i	$-0.842220\pi$
$433$	2.04692	−	14.2366i	0.0983685	−	0.684168i	0.978014	−	0.208538i	$-0.0668706\pi$
$434$	0.0406213	−	0.852745i	0.00194988	−	0.0409331i
$435$	−8.82258	+	3.90415i	−0.423011	+	0.187190i
$436$	−1.35695	+	2.35031i	−0.0649862	+	0.112559i
$437$	−11.3809	−	7.12997i	−0.544423	−	0.341073i
$438$	25.6330	−	5.89954i	1.22479	−	0.281891i
$439$	2.00460	−	5.79190i	0.0956742	−	0.276432i	−0.887001	−	0.461767i	$-0.847216\pi$
$439$	2.00460	−	5.79190i	0.0956742	−	0.276432i	0.982675	+	0.185335i	$0.0593369\pi$
$440$	0.181894	+	0.116896i	0.00867147	+	0.00557281i
$441$	8.30031	+	25.9450i	0.395253	+	1.23547i
$442$	−16.5139	+	36.1604i	−0.785487	+	1.71998i
$443$	−30.0218	+	23.6094i	−1.42638	+	1.12172i	−0.453271	+	0.891373i	$0.649743\pi$
$443$	−30.0218	+	23.6094i	−1.42638	+	1.12172i	−0.973109	+	0.230345i	$0.926014\pi$
$444$	7.42994	+	14.8389i	0.352609	+	0.704221i
$445$	−0.250014	−	5.24844i	−0.0118518	−	0.248800i
$446$	11.4326	+	1.09168i	0.541348	+	0.0516924i
$447$	−9.84242	−	5.83824i	−0.465531	−	0.276139i
$448$	−3.93754	−	0.758898i	−0.186031	−	0.0358546i
$449$	6.92357	−	7.99023i	0.326743	−	0.377082i	−0.568482	−	0.822696i	$-0.692469\pi$
$449$	6.92357	−	7.99023i	0.326743	−	0.377082i	0.895225	+	0.445614i	$0.147015\pi$
$450$	−9.32279	+	8.47891i	−0.439481	+	0.399700i
$451$	1.06051	+	2.32218i	0.0499373	+	0.109347i
$452$	4.40724	+	2.27209i	0.207299	+	0.106870i
$453$	33.8112	+	2.01022i	1.58859	+	0.0944485i
$454$	−22.7783	−	9.11904i	−1.06904	−	0.427978i
$455$	−13.0279	−	18.2951i	−0.610755	−	0.857685i
$456$	4.38794	+	2.06674i	0.205484	+	0.0967840i
$457$	−0.977113	+	20.5121i	−0.0457074	+	0.959517i	0.853256	+	0.521493i	$0.174625\pi$
$457$	−0.977113	+	20.5121i	−0.0457074	+	0.959517i	−0.898963	+	0.438024i	$0.855678\pi$
$458$	6.75989	+	7.80133i	0.315869	+	0.364532i
$459$	25.6677	−	20.6990i	1.19807	−	0.966147i
$460$	3.83362	+	1.92074i	0.178744	+	0.0895549i
$461$	1.13784	+	1.97079i	0.0529943	+	0.0917888i	0.891306	−	0.453403i	$-0.149790\pi$
$461$	1.13784	+	1.97079i	0.0529943	+	0.0917888i	−0.838311	+	0.545192i	$0.816457\pi$
$462$	−1.53598	+	0.679698i	−0.0714602	+	0.0316224i
$463$	−6.66286	+	3.43494i	−0.309649	+	0.159635i	−0.606046	−	0.795430i	$-0.707245\pi$
$463$	−6.66286	+	3.43494i	−0.309649	+	0.159635i	0.296397	+	0.955065i	$0.404215\pi$
$464$	4.89713	+	3.85115i	0.227344	+	0.178785i
$465$	0.0662049	−	0.322975i	0.00307018	−	0.0149776i
$466$	−1.84123	+	1.44796i	−0.0852933	+	0.0670754i
$467$	−33.3757	−	9.79998i	−1.54444	−	0.453489i	−0.605008	−	0.796220i	$-0.706830\pi$
$467$	−33.3757	−	9.79998i	−1.54444	−	0.453489i	−0.939434	+	0.342731i	$0.888648\pi$
$468$	−9.01042	−	16.4923i	−0.416507	−	0.762357i
$469$	−24.2185	−	53.0311i	−1.11831	−	2.44875i
$470$	−0.805068	−	0.767631i	−0.0371350	−	0.0354082i
$471$	−6.31219	+	0.226170i	−0.290850	+	0.0104214i
$472$	−0.883237	−	2.55195i	−0.0406543	−	0.117463i
$473$	0.0434113	−	0.178944i	0.00199605	−	0.00822784i
$474$	−7.40541	+	17.8841i	−0.340142	+	0.821443i
$475$	−10.4554	−	5.39015i	−0.479728	−	0.247317i
$476$	−24.4160	−	7.16919i	−1.11911	−	0.328600i
$477$	14.0992	−	29.0415i	0.645559	−	1.32972i
$478$	−4.41508	+	9.66767i	−0.201941	+	0.442189i
$479$	−10.0775	+	4.03443i	−0.460454	+	0.184338i	−0.590280	−	0.807199i	$-0.700983\pi$
$479$	−10.0775	+	4.03443i	−0.460454	+	0.184338i	0.129826	+	0.991537i	$0.458558\pi$
$480$	−1.45736	−	0.523708i	−0.0665190	−	0.0239039i
$481$	58.9355	−	11.3589i	2.68723	−	0.517920i
$482$	−3.53126	+	6.11633i	−0.160845	+	0.278591i
$483$	−28.8511	+	16.6475i	−1.31277	+	0.757488i
$484$	5.47076	+	9.47563i	0.248671	+	0.430711i
$485$	−5.68687	−	6.56300i	−0.258228	−	0.298010i
$486$	0.565381	+	15.5782i	0.0256462	+	0.706642i
$487$	2.10869	−	14.6663i	0.0955539	−	0.664592i	−0.884600	−	0.466351i	$-0.845568\pi$
$487$	2.10869	−	14.6663i	0.0955539	−	0.664592i	0.980153	−	0.198240i	$-0.0635227\pi$
$488$	3.59145	−	0.342941i	0.162577	−	0.0155242i
$489$	23.7662	+	3.70343i	1.07475	+	0.167475i
$490$	5.87556	−	5.60233i	0.265431	−	0.253088i
$491$	0.726853	+	15.2585i	0.0328024	+	0.688608i	0.954053	+	0.299638i	$0.0968659\pi$
$491$	0.726853	+	15.2585i	0.0328024	+	0.688608i	−0.921251	+	0.388970i	$0.872831\pi$
$492$	−11.1324	−	14.5046i	−0.501889	−	0.653919i
$493$	28.6126	+	27.2821i	1.28865	+	1.22872i
$494$	11.4878	−	13.2576i	0.516859	−	0.596488i
$495$	−0.626513	+	0.168029i	−0.0281597	+	0.00755233i
$496$	−0.204272	+	0.0599797i	−0.00917208	+	0.00269317i
$497$	9.23675	−	12.9712i	0.414325	−	0.581838i
$498$	9.57885	+	2.44368i	0.429239	+	0.109504i
$499$	11.1170	−	10.6001i	0.497666	−	0.474524i	−0.399176	−	0.916874i	$-0.630704\pi$
$499$	11.1170	−	10.6001i	0.497666	−	0.474524i	0.896842	+	0.442350i	$0.145855\pi$
$500$	7.63687	+	3.05734i	0.341531	+	0.136729i
$501$	26.7040	−	8.89139i	1.19305	−	0.397238i
$502$	−2.83813	+	1.13622i	−0.126672	+	0.0507118i
$503$	3.98400	+	2.56036i	0.177638	+	0.114161i	0.626438	−	0.779471i	$-0.284512\pi$
$503$	3.98400	+	2.56036i	0.177638	+	0.114161i	−0.448800	+	0.893632i	$0.648149\pi$
$504$	9.62885	−	7.21154i	0.428903	−	0.321227i
$505$	7.19346			0.320105
$506$	−0.683591	−	0.936912i	−0.0303893	−	0.0416508i
$507$	−44.2955	+	10.1948i	−1.96723	+	0.452767i
$508$	14.5646	−	2.80710i	0.646200	−	0.124545i
$509$	−13.1686	+	6.78888i	−0.583688	+	0.300912i	−0.724665	−	0.689101i	$-0.758006\pi$
$509$	−13.1686	+	6.78888i	−0.583688	+	0.300912i	0.140978	+	0.990013i	$0.454975\pi$
$510$	−8.89037	−	4.18741i	−0.393672	−	0.185422i
$511$	60.6206	−	5.78857i	2.68170	−	0.256071i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	−13.4414	+	5.57305i	−0.593450	+	0.246056i
$514$	18.2657	−	11.7386i	0.805665	−	0.517769i
$515$	0.374545	−	0.525975i	0.0165044	−	0.0231772i
$516$	−0.0155412	+	1.31872i	−0.000684161	+	0.0580532i
$517$	0.0984071	+	0.284329i	0.00432794	+	0.0125048i
$518$	12.5661	+	36.3074i	0.552123	+	1.59525i
$519$	−22.0631	+	12.3938i	−0.968464	+	0.544028i
$520$	−3.24884	+	4.56236i	−0.142471	+	0.200073i
$521$	9.70998	−	6.24023i	0.425402	−	0.273389i	−0.310374	−	0.950615i	$-0.600454\pi$
$521$	9.70998	−	6.24023i	0.425402	−	0.273389i	0.735776	+	0.677225i	$0.236818\pi$
$522$	−18.4306	+	3.10363i	−0.806685	+	0.135842i
$523$	−0.914558	−	6.36089i	−0.0399908	−	0.278142i	0.960007	−	0.279974i	$-0.0903260\pi$
$523$	−0.914558	−	6.36089i	−0.0399908	−	0.278142i	−0.999998	+	0.00183192i	$0.999417\pi$
$524$	−9.13920	+	0.872688i	−0.399248	+	0.0381235i
$525$	−23.9634	+	16.6422i	−1.04585	+	0.726325i
$526$	6.58707	−	3.39587i	0.287210	−	0.148067i
$527$	−1.32659	+	0.255679i	−0.0577870	+	0.0111375i
$528$	0.285458	+	0.306532i	0.0124229	+	0.0133401i
$529$	−15.4587	−	17.0303i	−0.672116	−	0.740446i
$530$	−9.62128			−0.417922
$531$	7.44804	+	3.18740i	0.323217	+	0.138321i
$532$	9.44669	+	6.07102i	0.409566	+	0.263212i
$533$	−61.3927	+	24.5779i	−2.65921	+	1.06459i
$534$	2.04404	−	9.97164i	0.0884541	−	0.431515i
$535$	8.74147	+	3.49956i	0.377927	+	0.151299i
$536$	−10.5220	+	10.0327i	−0.454482	+	0.433348i
$537$	7.65370	+	27.2500i	0.330282	+	1.17593i
$538$	−12.4092	+	17.4263i	−0.535000	+	0.751302i
$539$	−2.10691	+	0.618645i	−0.0907512	+	0.0266469i
$540$	4.10297	−	2.17924i	0.176564	−	0.0937794i
$541$	2.05074	−	2.36668i	0.0881682	−	0.101751i	−0.709951	−	0.704251i	$-0.751283\pi$
$541$	2.05074	−	2.36668i	0.0881682	−	0.101751i	0.798119	+	0.602499i	$0.205828\pi$
$542$	2.31738	+	2.20961i	0.0995399	+	0.0949111i
$543$	−34.4353	+	4.53753i	−1.47776	+	0.194724i
$544$	0.301947	+	6.33865i	0.0129459	+	0.271767i
$545$	−1.75611	+	1.67445i	−0.0752235	+	0.0717254i
$546$	−15.6937	−	40.5806i	−0.671630	−	1.73669i
$547$	1.08996	−	0.104078i	0.0466031	−	0.00445006i	−0.0717284	−	0.997424i	$-0.522851\pi$
$547$	1.08996	−	0.104078i	0.0466031	−	0.00445006i	0.118332	+	0.992974i	$0.462245\pi$
$548$	1.14059	−	7.93301i	0.0487238	−	0.338881i
$549$	−6.48419	+	8.66603i	−0.276738	+	0.369857i
$550$	−0.665235	−	0.767722i	−0.0283657	−	0.0327358i
$551$	−8.72304	−	15.1088i	−0.371614	−	0.643654i
$552$	6.27635	+	5.44127i	0.267139	+	0.231596i
$553$	−22.4070	+	38.8101i	−0.952844	+	1.65037i
$554$	19.7876	−	3.81375i	0.840695	−	0.162031i
$555$	2.63611	+	14.6013i	0.111897	+	0.619792i
$556$	−2.27089	+	0.909128i	−0.0963073	+	0.0385556i
$557$	15.5132	−	33.9692i	0.657317	−	1.43932i	−0.227685	−	0.973735i	$-0.573116\pi$
$557$	15.5132	−	33.9692i	0.657317	−	1.43932i	0.885002	−	0.465588i	$-0.154157\pi$
$558$	0.278938	−	0.574556i	0.0118084	−	0.0243229i
$559$	4.57658	+	1.34381i	0.193569	+	0.0568370i
$560$	−3.18672	−	1.64287i	−0.134664	−	0.0694240i
$561$	1.61836	+	2.10858i	0.0683272	+	0.0890245i
$562$	2.60535	−	10.7394i	0.109900	−	0.453014i
$563$	−2.54942	−	7.36608i	−0.107445	−	0.310443i	0.878443	−	0.477847i	$-0.158583\pi$
$563$	−2.54942	−	7.36608i	−0.107445	−	0.310443i	−0.985888	+	0.167404i	$0.946462\pi$
$564$	−1.14361	−	1.82646i	−0.0481545	−	0.0769077i
$565$	3.20851	+	3.05931i	0.134983	+	0.128706i
$566$	10.1530	+	22.2320i	0.426763	+	0.934481i
$567$	−3.41398	+	35.9282i	−0.143374	+	1.50884i
$568$	−3.81018	−	1.11877i	−0.159872	−	0.0469426i
$569$	−21.3056	+	16.7549i	−0.893179	+	0.702404i	−0.955292	−	0.295665i	$-0.904459\pi$
$569$	−21.3056	+	16.7549i	−0.893179	+	0.702404i	0.0621125	+	0.998069i	$0.480216\pi$
$570$	3.24368	+	2.87828i	0.135863	+	0.120558i
$571$	1.43868	+	1.13139i	0.0602068	+	0.0473472i	0.647809	−	0.761803i	$-0.275686\pi$
$571$	1.43868	+	1.13139i	0.0602068	+	0.0473472i	−0.587602	+	0.809150i	$0.699928\pi$
$572$	1.34652	−	0.694181i	0.0563010	−	0.0290252i
$573$	−5.28751	−	3.85992i	−0.220889	−	0.161251i
$574$	−21.1657	−	36.6600i	−0.883438	−	1.53016i
$575$	−14.7393	−	13.7329i	−0.614670	−	0.572701i
$576$	−2.48484	−	1.68095i	−0.103535	−	0.0700395i
$577$	4.05491	+	4.67962i	0.168808	+	0.194815i	0.833850	−	0.551991i	$-0.186132\pi$
$577$	4.05491	+	4.67962i	0.168808	+	0.194815i	−0.665042	+	0.746806i	$0.731586\pi$
$578$	−1.10721	+	23.2433i	−0.0460540	+	0.966793i
$579$	10.2432	−	7.11376i	0.425695	−	0.295638i
$580$	3.23102	+	4.53733i	0.134161	+	0.188402i
$581$	21.2476	+	8.50624i	0.881497	+	0.352898i
$582$	−7.53205	−	15.0428i	−0.312214	−	0.623544i
$583$	2.31307	+	1.19247i	0.0957976	+	0.0493871i
$584$	−6.30854	−	13.8138i	−0.261049	−	0.571618i
$585$	−3.57546	−	16.4179i	−0.147827	−	0.678795i
$586$	−4.54729	+	5.24785i	−0.187847	+	0.216787i
$587$	−9.54008	−	1.83870i	−0.393761	−	0.0758912i	−0.0114724	−	0.999934i	$-0.503652\pi$
$587$	−9.54008	−	1.83870i	−0.393761	−	0.0758912i	−0.382289	+	0.924043i	$0.624864\pi$
$588$	13.7119	−	7.70256i	0.565469	−	0.317648i
$589$	0.593477	+	0.0566702i	0.0244538	+	0.00233506i
$590$	−0.114884	−	2.41171i	−0.00472970	−	0.0992887i
$591$	5.81795	−	8.82256i	0.239319	−	0.362912i
$592$	7.53130	−	5.92268i	0.309534	−	0.243421i
$593$	−12.0998	+	26.4949i	−0.496880	+	1.08802i	0.480591	+	0.876945i	$0.340422\pi$
$593$	−12.0998	+	26.4949i	−0.496880	+	1.08802i	−0.977471	+	0.211071i	$0.932305\pi$
$594$	−1.25650	+	0.0153883i	−0.0515549	+	0.000631389i
$595$	−19.1399	−	12.3004i	−0.784658	−	0.504269i
$596$	−2.16095	+	6.24364i	−0.0885158	+	0.255750i
$597$	4.59416	−	14.9905i	0.188026	−	0.613519i
$598$	25.0848	−	16.5328i	1.02579	−	0.676078i
$599$	10.1093	−	17.5098i	0.413054	−	0.715430i	−0.582168	−	0.813068i	$-0.697796\pi$
$599$	10.1093	−	17.5098i	0.413054	−	0.715430i	0.995222	+	0.0976384i	$0.0311289\pi$
$600$	5.87644	+	4.28985i	0.239905	+	0.175133i
$601$	1.67711	−	35.2069i	0.0684109	−	1.43612i	−0.660147	−	0.751137i	$-0.729506\pi$
$601$	1.67711	−	35.2069i	0.0684109	−	1.43612i	0.728558	−	0.684985i	$-0.240191\pi$
$602$	−0.434526	+	3.02219i	−0.0177099	+	0.123175i
$603$	−1.04802	−	43.6030i	−0.0426786	−	1.77565i
$604$	−2.78302	−	19.3563i	−0.113240	−	0.787599i
$605$	2.30635	+	9.50689i	0.0937663	+	0.386510i
$606$	13.5029	+	3.44476i	0.548520	+	0.139934i
$607$	36.3069	+	3.46688i	1.47365	+	0.140716i	0.800742	−	0.599010i	$-0.204439\pi$
$607$	36.3069	+	3.46688i	1.47365	+	0.140716i	0.672908	+	0.739726i	$0.265045\pi$
$608$	0.660201	−	2.72139i	0.0267747	−	0.110367i
$609$	−43.2431	+	1.54943i	−1.75230	+	0.0627860i
$610$	3.16737	+	0.610461i	0.128243	+	0.0247168i
$611$	−7.47818	+	2.19579i	−0.302535	+	0.0888322i
$612$	−14.6830	−	12.1176i	−0.593525	−	0.489825i
$613$	0.689914	−	0.443381i	0.0278654	−	0.0179080i	−0.526634	−	0.850092i	$-0.676546\pi$
$613$	0.689914	−	0.443381i	0.0278654	−	0.0179080i	0.554499	+	0.832184i	$0.312910\pi$
$614$	−5.57496	−	22.9803i	−0.224987	−	0.927410i
$615$	−5.89656	−	15.2472i	−0.237772	−	0.614828i
$616$	0.562508	+	0.789932i	0.0226641	+	0.0318273i
$617$	7.64249	+	6.01012i	0.307675	+	0.241958i	0.760043	−	0.649873i	$-0.225178\pi$
$617$	7.64249	+	6.01012i	0.307675	+	0.241958i	−0.452367	+	0.891832i	$0.649420\pi$
$618$	0.954939	−	0.807954i	0.0384133	−	0.0325007i
$619$	−3.37287	+	9.74526i	−0.135567	+	0.391695i	−0.992267	−	0.124119i	$-0.960389\pi$
$619$	−3.37287	+	9.74526i	−0.135567	+	0.391695i	0.856700	+	0.515814i	$0.172511\pi$
$620$	−0.190347			−0.00764451
$621$	−24.7437	+	2.95793i	−0.992930	+	0.118698i
$622$	−30.0927			−1.20661
$623$	7.70773	−	22.2700i	0.308804	−	0.892229i
$624$	−8.28323	+	7.00827i	−0.331595	+	0.280556i
$625$	−10.7282	−	8.43676i	−0.429129	−	0.337471i
$626$	0.155225	+	0.217983i	0.00620403	+	0.00871234i
$627$	−0.423082	−	1.09400i	−0.0168963	−	0.0436900i
$628$	0.859739	+	3.54389i	0.0343073	+	0.141417i
$629$	51.1486	−	32.8712i	2.03943	−	1.31066i
$630$	10.0768	−	3.76111i	0.401470	−	0.149846i
$631$	5.83241	−	1.71255i	0.232185	−	0.0681756i	−0.163570	−	0.986532i	$-0.552301\pi$
$631$	5.83241	−	1.71255i	0.232185	−	0.0681756i	0.395755	+	0.918356i	$0.370483\pi$
$632$	10.9736	+	2.11499i	0.436507	+	0.0841299i
$633$	−8.51978	+	0.305270i	−0.338631	+	0.0121334i
$634$	0.796488	−	3.28317i	0.0316326	−	0.130391i
$635$	13.2016	+	1.26060i	0.523889	+	0.0500254i
$636$	−18.0602	−	4.60738i	−0.716134	−	0.182694i
$637$	−13.4103	−	55.2780i	−0.531335	−	2.19019i
$638$	−0.214414	−	1.49128i	−0.00848874	−	0.0590405i
$639$	10.1710	−	6.20274i	0.402357	−	0.245377i
$640$	−0.127242	+	0.884984i	−0.00502966	+	0.0349821i
$641$	−1.97651	+	41.4920i	−0.0780673	+	1.63883i	0.532185	+	0.846628i	$0.321371\pi$
$641$	−1.97651	+	41.4920i	−0.0780673	+	1.63883i	−0.610253	+	0.792207i	$0.708932\pi$
$642$	14.7329	+	10.7551i	0.581461	+	0.424471i
$643$	17.8129	−	30.8528i	0.702471	−	1.21672i	−0.265125	−	0.964214i	$-0.585413\pi$
$643$	17.8129	−	30.8528i	0.702471	−	1.21672i	0.967596	−	0.252502i	$-0.0812535\pi$
$644$	12.7606	+	14.3878i	0.502838	+	0.566960i
$645$	−0.345507	+	1.12737i	−0.0136043	+	0.0443901i
$646$	5.81212	−	16.7930i	0.228675	−	0.660713i
$647$	−42.6466	−	27.4073i	−1.67661	−	1.07749i	−0.883528	−	0.468378i	$-0.844839\pi$
$647$	−42.6466	−	27.4073i	−1.67661	−	1.07749i	−0.793082	−	0.609115i	$-0.791525\pi$
$648$	8.74532	−	2.12587i	0.343549	−	0.0835120i
$649$	−0.271291	+	0.594044i	−0.0106491	+	0.0233183i
$650$	20.6844	−	16.2664i	0.811310	−	0.638021i
$651$	0.814034	−	1.23443i	0.0319045	−	0.0483812i
$652$	−0.660772	−	13.8713i	−0.0258778	−	0.543242i
$653$	21.9597	+	2.09690i	0.859351	+	0.0820580i	0.515421	−	0.856937i	$-0.327636\pi$
$653$	21.9597	+	2.09690i	0.859351	+	0.0820580i	0.343930	+	0.938995i	$0.388242\pi$
$654$	−4.09827	+	2.30217i	−0.160255	+	0.0900221i
$655$	−8.06005	−	1.55345i	−0.314932	−	0.0606982i
$656$	−6.91300	+	7.97803i	−0.269907	+	0.311490i
$657$	43.3983	+	13.8619i	1.69313	+	0.540803i
$658$	−2.07253	−	4.53822i	−0.0807958	−	0.176918i
$659$	−30.6659	−	15.8094i	−1.19458	−	0.615846i	−0.257943	−	0.966160i	$-0.583045\pi$
$659$	−30.6659	−	15.8094i	−1.19458	−	0.615846i	−0.936632	+	0.350314i	$0.886075\pi$
$660$	0.167672	+	0.334869i	0.00652661	+	0.0130347i
$661$	−28.4820	−	11.4025i	−1.10782	−	0.443505i	−0.255651	−	0.966769i	$-0.582290\pi$
$661$	−28.4820	−	11.4025i	−1.10782	−	0.443505i	−0.852170	+	0.523264i	$0.824714\pi$
$662$	3.60630	+	5.06434i	0.140163	+	0.196831i
$663$	−56.5535	+	39.2755i	−2.19635	+	1.52533i
$664$	0.271573	−	5.70101i	0.0105391	−	0.221242i
$665$	6.57476	+	7.58768i	0.254958	+	0.294238i
$666$	−2.04392	+	28.6707i	−0.0792001	+	1.11097i
$667$	−7.37841	−	28.9528i	−0.285693	−	1.12106i
$668$	−8.12487	−	14.0727i	−0.314361	−	0.544489i
$669$	16.0663	+	11.7286i	0.621160	+	0.453452i
$670$	−11.5537	+	5.95634i	−0.446358	+	0.230113i
$671$	−0.685813	−	0.539329i	−0.0264755	−	0.0208206i
$672$	−5.19512	−	4.60989i	−0.200406	−	0.177830i
$673$	32.5404	−	25.5900i	1.25434	−	0.986424i	0.254527	−	0.967066i	$-0.418080\pi$
$673$	32.5404	−	25.5900i	1.25434	−	0.986424i	0.999813	−	0.0193582i	$-0.00616228\pi$
$674$	26.3040	+	7.72354i	1.01319	+	0.297500i
$675$	−21.3804	+	4.39295i	−0.822932	+	0.169085i
$676$	10.9016	+	23.8711i	0.419291	+	0.918120i
$677$	−11.9138	−	11.3598i	−0.457884	−	0.436591i	0.425700	−	0.904864i	$-0.360028\pi$
$677$	−11.9138	−	11.3598i	−0.457884	−	0.436591i	−0.883584	+	0.468273i	$0.844876\pi$
$678$	4.55771	+	7.27914i	0.175038	+	0.279554i
$679$	−12.7388	−	36.8063i	−0.488870	−	1.41250i
$680$	−1.33763	+	5.51378i	−0.0512957	+	0.211444i
$681$	−25.8746	−	33.7124i	−0.991517	−	1.29186i
$682$	0.0457617	+	0.0235918i	0.00175230	+	0.000903376i
$683$	−10.2175	−	3.00012i	−0.390960	−	0.114796i	0.0803434	−	0.996767i	$-0.474398\pi$
$683$	−10.2175	−	3.00012i	−0.390960	−	0.114796i	−0.471304	+	0.881971i	$0.656216\pi$
$684$	4.71041	+	6.95617i	0.180107	+	0.265976i
$685$	2.97675	−	6.51817i	0.113736	−	0.249046i
$686$	7.74376	−	3.10013i	0.295658	−	0.118364i
$687$	3.17657	+	17.5949i	0.121194	+	0.671287i
$688$	0.747654	−	0.144098i	0.0285040	−	0.00549370i
$689$	−33.7057	+	58.3799i	−1.28408	+	2.22410i
$690$	4.01367	+	6.24886i	0.152798	+	0.237890i
$691$	−19.2968	−	33.4230i	−0.734083	−	1.27147i	−0.955124	−	0.296205i	$-0.904279\pi$
$691$	−19.2968	−	33.4230i	−0.734083	−	1.27147i	0.221041	−	0.975264i	$-0.429054\pi$
$692$	9.56775	+	11.0418i	0.363711	+	0.419745i
$693$	−2.88874	−	0.344715i	−0.109734	−	0.0130946i
$694$	0.606230	−	4.21642i	0.0230122	−	0.160053i
$695$	−2.17713	+	0.207891i	−0.0825832	+	0.00788574i
$696$	3.89218	+	10.0643i	0.147533	+	0.381487i
$697$	−48.4825	+	46.2280i	−1.83641	+	1.75101i
$698$	−0.281819	−	5.91610i	−0.0106670	−	0.223928i
$699$	−4.02234	+	0.530023i	−0.152139	+	0.0200473i
$700$	12.1909	+	11.6240i	0.460773	+	0.439346i
$701$	7.73732	−	8.92935i	0.292235	−	0.337257i	−0.590579	−	0.806980i	$-0.701101\pi$
$701$	7.73732	−	8.92935i	0.292235	−	0.337257i	0.882814	+	0.469723i	$0.155646\pi$
$702$	1.15054	−	32.5304i	0.0434245	−	1.22778i
$703$	−25.7435	+	7.55898i	−0.970935	+	0.285092i
$704$	0.140276	−	0.196990i	0.00528686	−	0.00742435i
$705$	−0.520992	−	1.85492i	−0.0196217	−	0.0698605i
$706$	−5.50537	+	5.24936i	−0.207198	+	0.197562i
$707$	29.9519	+	11.9909i	1.12646	+	0.450965i
$708$	0.939256	−	4.58208i	0.0352994	−	0.172205i
$709$	30.7467	−	12.3091i	1.15471	−	0.462278i	0.286312	−	0.958137i	$-0.407571\pi$
$709$	30.7467	−	12.3091i	1.15471	−	0.462278i	0.868403	+	0.495858i	$0.165147\pi$
$710$	−2.98682	−	1.91951i	−0.112093	−	0.0720381i
$711$	−26.8349	+	20.0980i	−1.00639	+	0.753735i
$712$	−5.87684			−0.220244
$713$	0.952188	+	0.368516i	0.0356597	+	0.0138010i
$714$	−30.0373	−	32.2549i	−1.12412	−	1.20711i
$715$	1.33000	−	0.256336i	0.0497391	−	0.00958643i
$716$	14.5250	−	7.48815i	0.542825	−	0.279845i
$717$	−15.1199	+	10.5005i	−0.564661	+	0.392148i
$718$	−11.1842	+	1.06796i	−0.417389	+	0.0398559i
$719$	4.05269	+	28.1871i	0.151140	+	1.05120i	0.914313	+	0.405008i	$0.132731\pi$
$719$	4.05269	+	28.1871i	0.151140	+	1.05120i	−0.763173	+	0.646194i	$0.776360\pi$
$720$	−1.70824	−	2.06794i	−0.0636624	−	0.0770677i
$721$	2.43627	−	1.56570i	0.0907316	−	0.0583096i
$722$	6.47239	−	9.08920i	0.240877	−	0.338265i
$723$	−10.6651	+	5.99106i	−0.396641	+	0.222810i
$724$	6.55871	+	18.9502i	0.243753	+	0.704277i
$725$	−8.55934	−	24.7306i	−0.317886	−	0.918471i
$726$	−0.223326	+	18.9499i	−0.00828842	+	0.703299i
$727$	−24.9928	+	35.0975i	−0.926933	+	1.30170i	0.0263607	+	0.999652i	$0.491608\pi$
$727$	−24.9928	+	35.0975i	−0.926933	+	1.30170i	−0.953294	+	0.302043i	$0.902331\pi$
$728$	−21.1325	+	13.5810i	−0.783222	+	0.503346i
$729$	−12.9233	+	23.7063i	−0.478641	+	0.878011i
$730$	−1.93230	−	13.4395i	−0.0715178	−	0.497417i
$731$	4.80993	−	0.459292i	0.177902	−	0.0169875i
$732$	5.65318	+	2.66267i	0.208948	+	0.0984153i
$733$	7.73121	−	3.98572i	0.285559	−	0.147216i	−0.309496	−	0.950901i	$-0.600160\pi$
$733$	7.73121	−	3.98572i	0.285559	−	0.147216i	0.595055	+	0.803685i	$0.297130\pi$
$734$	−20.8657	+	4.02153i	−0.770167	+	0.148437i
$735$	13.7032	−	3.15385i	0.505451	−	0.116332i
$736$	2.34986	−	4.18069i	0.0866170	−	0.154102i
$737$	3.51588			0.129509
$738$	−3.76701	−	31.4445i	−0.138666	−	1.15749i
$739$	−10.4164	−	6.69419i	−0.383172	−	0.246250i	0.334848	−	0.942272i	$-0.391315\pi$
$739$	−10.4164	−	6.69419i	−0.383172	−	0.246250i	−0.718020	+	0.696022i	$0.754951\pi$
$740$	7.95274	−	3.18380i	0.292348	−	0.117039i
$741$	28.8282	−	9.59864i	1.05903	−	0.352615i
$742$	−40.0607	−	16.0379i	−1.47068	−	0.588770i
$743$	13.6433	−	13.0089i	0.500524	−	0.477249i	−0.397246	−	0.917712i	$-0.630034\pi$
$743$	13.6433	−	13.0089i	0.500524	−	0.477249i	0.897771	+	0.440463i	$0.145186\pi$
$744$	−0.357303	−	0.0911521i	−0.0130993	−	0.00334180i
$745$	−3.42653	+	4.81189i	−0.125539	+	0.176294i
$746$	−9.56726	+	2.80920i	−0.350282	+	0.102852i
$747$	12.1102	+	12.1046i	0.443089	+	0.442884i
$748$	1.00497	−	1.15979i	0.0367452	−	0.0424062i
$749$	30.5639	+	29.1427i	1.11678	+	1.06485i
$750$	8.67498	+	11.3028i	0.316765	+	0.412718i
$751$	−1.87205	−	39.2992i	−0.0683121	−	1.43405i	−0.729578	−	0.683897i	$-0.760284\pi$
$751$	−1.87205	−	39.2992i	−0.0683121	−	1.43405i	0.661266	−	0.750151i	$-0.270019\pi$
$752$	−0.900438	+	0.858566i	−0.0328356	+	0.0313087i
$753$	−5.23194	−	0.815280i	−0.190663	−	0.0297105i
$754$	38.8506	−	3.70978i	1.41486	−	0.135102i
$755$	2.48826	−	17.3062i	0.0905570	−	0.629838i
$756$	20.7164	−	2.23450i	0.753449	−	0.0812681i
$757$	28.8372	+	33.2799i	1.04811	+	1.20958i	0.977250	+	0.212092i	$0.0680278\pi$
$757$	28.8372	+	33.2799i	1.04811	+	1.20958i	0.0708564	+	0.997487i	$0.477427\pi$
$758$	−0.241175	−	0.417728i	−0.00875988	−	0.0151726i
$759$	−0.190445	−	1.99976i	−0.00691270	−	0.0725866i
$760$	1.25186	−	2.16829i	0.0454098	−	0.0786521i
$761$	39.2654	−	7.56779i	1.42337	−	0.274332i	0.581296	−	0.813692i	$-0.302546\pi$
$761$	39.2654	−	7.56779i	1.42337	−	0.274332i	0.842075	+	0.539360i	$0.181334\pi$
$762$	24.1772	+	8.68819i	0.875848	+	0.314740i
$763$	−10.1032	+	4.04471i	−0.365760	+	0.146428i
$764$	−1.57011	+	3.43807i	−0.0568047	+	0.124385i
$765$	−9.54373	−	14.0938i	−0.345054	−	0.509564i
$766$	24.3771	+	7.15777i	0.880781	+	0.258621i
$767$	−15.0363	−	7.75173i	−0.542928	−	0.279899i
$768$	−0.662642	+	1.60028i	−0.0239110	+	0.0577452i
$769$	−5.42258	+	22.3522i	−0.195543	+	0.806040i	0.786532	+	0.617550i	$0.211875\pi$
$769$	−5.42258	+	22.3522i	−0.195543	+	0.806040i	−0.982075	+	0.188490i	$0.939641\pi$
$770$	0.283579	+	0.819349i	0.0102195	+	0.0295273i
$771$	37.5830	−	1.34662i	1.35352	−	0.0484975i
$772$	−5.21105	−	4.96872i	−0.187550	−	0.178828i
$773$	21.1118	+	46.2284i	0.759339	+	1.66272i	0.748817	+	0.662777i	$0.230622\pi$
$773$	21.1118	+	46.2284i	0.759339	+	1.66272i	0.0105223	+	0.999945i	$0.496651\pi$
$774$	−1.18842	+	1.95075i	−0.0427170	+	0.0701181i
$775$	0.858067	+	0.251951i	0.0308227	+	0.00905036i
$776$	−7.63480	+	6.00407i	−0.274073	+	0.215534i
$777$	−13.3631	+	65.1907i	−0.479398	+	2.33870i
$778$	11.3157	+	8.89876i	0.405687	+	0.319036i
$779$	26.2753	−	13.5458i	0.941409	−	0.485330i
$780$	−8.87125	+	3.92569i	−0.317642	+	0.140562i
$781$	0.480162	+	0.831664i	0.0171815	+	0.0297593i
$782$	17.3661	−	24.9924i	0.621012	−	0.893725i
$783$	−30.1984	−	11.6626i	−1.07920	−	0.416787i
$784$	−5.94621	−	6.86229i	−0.212365	−	0.245082i
$785$	−0.155138	+	3.25675i	−0.00553712	+	0.116238i
$786$	−14.3857	−	6.77574i	−0.513122	−	0.241683i
$787$	27.8134	+	39.0584i	0.991440	+	1.39228i	0.918711	+	0.394930i	$0.129231\pi$
$787$	27.8134	+	39.0584i	0.991440	+	1.39228i	0.0727284	+	0.997352i	$0.476829\pi$
$788$	−5.66447	−	2.26771i	−0.201788	−	0.0807838i
$789$	12.8134	+	0.761813i	0.456170	+	0.0271213i
$790$	8.88117	+	4.57856i	0.315978	+	0.162898i
$791$	8.25986	+	18.0866i	0.293687	+	0.643084i
$792$	0.154379	+	0.708880i	0.00548561	+	0.0251890i
$793$	14.8002	−	17.0804i	0.525571	−	0.606542i
$794$	−9.26386	−	1.78546i	−0.328762	−	0.0633637i
$795$	−14.3327	−	8.50176i	−0.508329	−	0.301526i
$796$	−9.01109	−	0.860455i	−0.319390	−	0.0304980i
$797$	1.17388	+	24.6428i	0.0415810	+	0.872894i	0.919262	+	0.393647i	$0.128787\pi$
$797$	1.17388	+	24.6428i	0.0415810	+	0.872894i	−0.877680	+	0.479246i	$0.840910\pi$
$798$	8.70804	+	17.3914i	0.308261	+	0.615650i
$799$	−6.20606	+	4.88050i	−0.219554	+	0.172660i
$800$	1.74500	−	3.82101i	0.0616950	−	0.135093i
$801$	11.8563	−	13.0485i	0.418923	−	0.461045i
$802$	−17.5494	−	11.2783i	−0.619692	−	0.398252i
$803$	−1.20115	+	3.47050i	−0.0423877	+	0.122471i
$804$	−24.5399	+	5.64796i	−0.865456	+	0.199188i
$805$	7.32270	+	15.5572i	0.258091	+	0.548318i
$806$	−0.666831	+	1.15499i	−0.0234881	+	0.0406826i
$807$	−33.8845	+	14.9945i	−1.19279	+	0.527832i
$808$	0.382826	−	8.03651i	0.0134678	−	0.282723i
$809$	−1.47382	+	10.2506i	−0.0518168	+	0.360394i	0.947372	+	0.320133i	$0.103728\pi$
$809$	−1.47382	+	10.2506i	−0.0518168	+	0.360394i	−0.999189	+	0.0402601i	$0.987181\pi$
$810$	8.03782	+	0.379168i	0.282420	+	0.0133226i
$811$	−2.05088	−	14.2642i	−0.0720161	−	0.500883i	−0.993623	−	0.112757i	$-0.964032\pi$
$811$	−2.05088	−	14.2642i	−0.0720161	−	0.500883i	0.921606	−	0.388126i	$-0.126877\pi$
$812$	5.88983	+	24.2782i	0.206692	+	0.851998i
$813$	1.49967	+	5.33937i	0.0525956	+	0.187260i
$814$	−2.30654	−	0.220248i	−0.0808441	−	0.00771967i
$815$	2.92723	−	12.0662i	0.102536	−	0.422660i
$816$	−5.15129	+	9.70944i	−0.180331	+	0.339898i
$817$	−2.09367	−	0.403522i	−0.0732483	−	0.0141175i
$818$	1.76624	−	0.518614i	0.0617550	−	0.0181329i
$819$	12.4799	−	74.3201i	0.436083	−	2.59696i
$820$	−7.94005	+	5.10276i	−0.277278	+	0.178196i
$821$	0.0649347	+	0.267665i	0.00226624	+	0.00934156i	0.972933	−	0.231085i	$-0.0742277\pi$
$821$	0.0649347	+	0.267665i	0.00226624	+	0.00934156i	−0.970667	+	0.240427i	$0.922713\pi$
$822$	8.70907	−	10.8099i	0.303764	−	0.377037i
$823$	30.2817	+	42.5247i	1.05555	+	1.48232i	0.865737	+	0.500500i	$0.166850\pi$
$823$	30.2817	+	42.5247i	1.05555	+	1.48232i	0.189818	+	0.981819i	$0.439210\pi$
$824$	−0.567684	−	0.446431i	−0.0197762	−	0.0155522i
$825$	−0.312603	−	1.73150i	−0.0108834	−	0.0602830i
$826$	3.54178	−	10.2333i	0.123234	−	0.356062i
$827$	−8.32128			−0.289359			−0.144680	−	0.989479i	$-0.546215\pi$
$827$	−8.32128			−0.289359			−0.144680	+	0.989479i	$0.546215\pi$
$828$	4.54170	+	13.6518i	0.157835	+	0.474435i
$829$	12.2298			0.424757			0.212379	−	0.977187i	$-0.431879\pi$
$829$	12.2298			0.424757			0.212379	+	0.977187i	$0.431879\pi$
$830$	1.66902	−	4.82231i	0.0579325	−	0.167385i
$831$	32.8474	+	11.8039i	1.13946	+	0.409471i
$832$	4.92415	+	3.87239i	0.170714	+	0.134251i
$833$	−33.4234	−	46.9366i	−1.15805	−	1.62626i
$834$	−4.18627	−	0.652336i	−0.144959	−	0.0225885i
$835$	−3.42526	−	14.1191i	−0.118536	−	0.488612i
$836$	−0.569703	+	0.366126i	−0.0197036	+	0.0126627i
$837$	0.923233	−	0.609429i	0.0319116	−	0.0210650i
$838$	33.4849	−	9.83207i	1.15672	−	0.339643i
$839$	15.0375	+	2.89823i	0.519151	+	0.100058i	0.442094	−	0.896969i	$-0.354236\pi$
$839$	15.0375	+	2.89823i	0.519151	+	0.100058i	0.0770566	+	0.997027i	$0.475448\pi$
$840$	−3.29552	−	5.26329i	−0.113706	−	0.181601i
$841$	2.31355	−	9.53660i	0.0797777	−	0.328848i
$842$	−11.9330	−	1.13946i	−0.411238	−	0.0392685i
$843$	13.3710	−	13.6962i	0.460520	−	0.471722i
$844$	1.16042	+	4.78331i	0.0399432	+	0.164648i
$845$	3.33915	+	23.2243i	0.114870	+	0.798940i
$846$	−0.0896858	−	3.73139i	−0.00308346	−	0.128288i
$847$	−6.24414	+	43.4289i	−0.214551	+	1.49224i
$848$	−0.512031	+	10.7488i	−0.0175832	+	0.369117i
$849$	−4.52028	+	42.0904i	−0.155135	+	1.44454i
$850$	13.3282	−	23.0851i	0.457153	−	0.791813i
$851$	−45.9466	+	0.529888i	−1.57503	+	0.0181643i
$852$	−4.68740	−	5.03346i	−0.160588	−	0.172443i
$853$	−4.62021	+	13.3492i	−0.158193	+	0.457069i	−0.996047	−	0.0888254i	$-0.971689\pi$
$853$	−4.62021	+	13.3492i	−0.158193	+	0.457069i	0.837854	+	0.545894i	$0.183810\pi$
$854$	12.1706	+	7.82156i	0.416469	+	0.267648i
$855$	2.28870	+	7.15399i	0.0782720	+	0.244661i
$856$	4.37490	−	9.57969i	0.149531	−	0.327427i
$857$	−18.0405	+	14.1872i	−0.616252	+	0.484626i	−0.876813	−	0.480832i	$-0.840335\pi$
$857$	−18.0405	+	14.1872i	−0.616252	+	0.484626i	0.260561	+	0.965457i	$0.416092\pi$
$858$	2.61931	+	0.155729i	0.0894217	+	0.00531651i
$859$	−1.24817	−	26.2023i	−0.0425870	−	0.894011i	−0.914558	−	0.404454i	$-0.867462\pi$
$859$	−1.24817	−	26.2023i	−0.0425870	−	0.894011i	0.871971	−	0.489557i	$-0.162841\pi$
$860$	0.677686	+	0.0647111i	0.0231089	+	0.00220663i
$861$	0.864022	−	73.3150i	0.0294458	−	2.49857i
$862$	8.84819	+	1.70535i	0.301371	+	0.0580844i
$863$	8.89097	−	10.2607i	0.302652	−	0.349279i	−0.583969	−	0.811776i	$-0.698501\pi$
$863$	8.89097	−	10.2607i	0.302652	−	0.349279i	0.886621	+	0.462497i	$0.153046\pi$
$864$	−2.21628	−	4.69980i	−0.0753994	−	0.159890i
$865$	5.42653	+	11.8824i	0.184507	+	0.404015i
$866$	−12.7841	−	6.59068i	−0.434422	−	0.223960i
$867$	−22.1881	+	33.6469i	−0.753548	+	1.14271i
$868$	−0.792559	−	0.317293i	−0.0269012	−	0.0107696i
$869$	−1.56767	−	2.20148i	−0.0531795	−	0.0746801i
$870$	0.803842	+	9.61427i	0.0272528	+	0.325954i
$871$	−4.33353	+	90.9719i	−0.146836	+	3.08246i
$872$	1.77723	+	2.05103i	0.0601845	+	0.0694566i
$873$	2.07201	−	29.0647i	0.0701268	−	0.983692i
$874$	−10.4602	+	8.42298i	−0.353820	+	0.284912i
$875$	16.4934	+	28.5674i	0.557578	+	0.965754i
$876$	2.80866	−	26.1527i	0.0948957	−	0.883619i
$877$	−14.9454	+	7.70487i	−0.504669	+	0.260175i	−0.691708	−	0.722178i	$-0.743141\pi$
$877$	−14.9454	+	7.70487i	−0.504669	+	0.260175i	0.187039	+	0.982353i	$0.440111\pi$
$878$	−4.81771	−	3.78869i	−0.162590	−	0.127862i
$879$	−11.4113	+	3.79950i	−0.384893	+	0.128154i
$880$	0.169959	−	0.133657i	0.00572931	−	0.00450558i
$881$	3.61690	+	1.06202i	0.121857	+	0.0357803i	0.342092	−	0.939666i	$-0.388864\pi$
$881$	3.61690	+	1.06202i	0.121857	+	0.0357803i	−0.220236	+	0.975447i	$0.570683\pi$
$882$	27.2328	+	0.641969i	0.916975	+	0.0216162i
$883$	6.09040	+	13.3361i	0.204958	+	0.448796i	0.983998	−	0.178178i	$-0.0570204\pi$
$883$	6.09040	+	13.3361i	0.204958	+	0.448796i	−0.779040	+	0.626974i	$0.784293\pi$
$884$	28.7705	+	27.4326i	0.967655	+	0.922657i
$885$	1.95995	−	3.69422i	0.0658830	−	0.124180i
$886$	12.4918	+	36.0925i	0.419669	+	1.21255i
$887$	−6.09627	+	25.1292i	−0.204693	+	0.843755i	0.773117	+	0.634263i	$0.218696\pi$
$887$	−6.09627	+	25.1292i	−0.204693	+	0.843755i	−0.977810	+	0.209492i	$0.932819\pi$
$888$	16.4528	−	2.16799i	0.552121	−	0.0727529i
$889$	52.8670	+	27.2548i	1.77310	+	0.914098i
$890$	−5.04155	−	1.48033i	−0.168993	−	0.0496209i
$891$	−1.88539	−	1.08737i	−0.0631631	−	0.0364284i
$892$	4.77086	−	10.4467i	0.159740	−	0.349782i
$893$	3.23447	−	1.29489i	0.108237	−	0.0433317i
$894$	−8.73628	+	7.39159i	−0.292185	+	0.247212i
$895$	14.3467	−	2.76511i	0.479559	−	0.0924273i
$896$	−2.00500	+	3.47276i	−0.0669824	+	0.116017i
$897$	51.9776	−	2.46285i	1.73548	−	0.0822323i
$898$	−5.28629	−	9.15613i	−0.176406	−	0.305544i
$899$	0.868572	+	1.00239i	0.0289685	+	0.0334314i
$900$	4.96339	+	11.5832i	0.165446	+	0.386107i
$901$	−9.71836	+	67.5927i	−0.323766	+	2.25184i
$902$	2.54132	−	0.242667i	0.0846168	−	0.00807993i
$903$	−3.31784	+	4.11817i	−0.110411	+	0.137044i
$904$	3.58860	−	3.42172i	0.119355	−	0.113805i
$905$	0.853103	+	17.9088i	0.0283581	+	0.595310i
$906$	12.9582	−	31.2942i	0.430508	−	1.03968i
$907$	−18.6377	−	17.7710i	−0.618855	−	0.590077i	0.314400	−	0.949290i	$-0.398197\pi$
$907$	−18.6377	−	17.7710i	−0.618855	−	0.590077i	−0.933255	+	0.359213i	$0.883045\pi$
$908$	−16.0675	+	18.5429i	−0.533220	+	0.615369i
$909$	17.0713	+	17.0634i	0.566218	+	0.565957i
$910$	−21.5498	+	6.32760i	−0.714370	+	0.209758i
$911$	−25.4068	+	35.6789i	−0.841765	+	1.18209i	0.139650	+	0.990201i	$0.455402\pi$
$911$	−25.4068	+	35.6789i	−0.841765	+	1.18209i	−0.981416	+	0.191893i	$0.938537\pi$
$912$	3.38823	−	3.47064i	0.112195	−	0.114924i
$913$	−0.998934	+	0.952482i	−0.0330599	+	0.0315225i
$914$	19.0644	+	7.63224i	0.630594	+	0.252452i
$915$	4.17897	+	3.70822i	0.138153	+	0.122590i
$916$	9.58321	−	3.83654i	0.316638	−	0.126763i
$917$	−30.9707	−	19.9036i	−1.02274	−	0.657276i
$918$	−11.1655	−	31.0260i	−0.368516	−	1.02401i
$919$	5.92357			0.195401			0.0977003	−	0.995216i	$-0.468851\pi$
$919$	5.92357			0.195401			0.0977003	+	0.995216i	$0.468851\pi$
$920$	3.06896	−	2.99457i	0.101180	−	0.0987279i
$921$	12.0014	−	39.1598i	0.395459	−	1.29036i
$922$	2.23455	−	0.430674i	0.0735909	−	0.0141835i
$923$	−22.1108	+	11.3989i	−0.727786	+	0.375200i
$924$	0.139946	+	1.67381i	0.00460388	+	0.0550643i
$925$	−40.0645	+	3.82569i	−1.31731	+	0.125788i
$926$	1.06682	+	7.41987i	0.0350578	+	0.243832i
$927$	2.13650	−	0.359778i	0.0701720	−	0.0118167i
$928$	5.24103	−	3.36821i	0.172045	−	0.110567i
$929$	18.4978	−	25.9765i	0.606893	−	0.852262i	−0.390777	−	0.920485i	$-0.627794\pi$
$929$	18.4978	−	25.9765i	0.606893	−	0.852262i	0.997670	+	0.0682236i	$0.0217331\pi$
$930$	−0.283558	−	0.168198i	−0.00929823	−	0.00551544i
$931$	8.31644	+	24.0288i	0.272560	+	0.787511i
$932$	0.766115	+	2.21354i	0.0250949	+	0.0725070i
$933$	−44.8288	−	26.5912i	−1.46763	−	0.870555i
$934$	−20.1771	+	28.3348i	−0.660215	+	0.927142i
$935$	1.15427	−	0.741805i	0.0377487	−	0.0242596i
$936$	−18.5323	+	3.12075i	−0.605746	+	0.102005i
$937$	3.09351	+	21.5158i	0.101061	+	0.702891i	0.975859	+	0.218404i	$0.0700849\pi$
$937$	3.09351	+	21.5158i	0.101061	+	0.702891i	−0.874798	+	0.484488i	$0.839006\pi$
$938$	−58.0355	+	5.54172i	−1.89493	+	0.180944i
$939$	0.0386183	+	0.461890i	0.00126026	+	0.0150732i
$940$	−0.988724	+	0.509723i	−0.0322486	+	0.0166253i
$941$	20.9037	−	4.02886i	0.681442	−	0.131337i	0.163228	−	0.986588i	$-0.447809\pi$
$941$	20.9037	−	4.02886i	0.681442	−	0.131337i	0.518214	+	0.855251i	$0.326597\pi$
$942$	−1.85079	+	6.03900i	−0.0603018	+	0.196761i
$943$	49.5982	−	10.1538i	1.61514	−	0.330655i
$944$	−2.70047			−0.0878928
$945$	18.3348	+	3.30141i	0.596431	+	0.107395i
$946$	−0.154903	−	0.0995504i	−0.00503635	−	0.00323666i
$947$	24.8164	−	9.93498i	0.806424	−	0.322843i	0.0684343	−	0.997656i	$-0.478200\pi$
$947$	24.8164	−	9.93498i	0.806424	−	0.322843i	0.737989	+	0.674812i	$0.235775\pi$
$948$	14.4784	+	12.8474i	0.470237	+	0.417265i
$949$	−88.3173	−	35.3569i	−2.86690	−	1.14773i
$950$	−8.51333	+	8.11745i	−0.276209	+	0.263365i
$951$	4.08766	−	4.18709i	0.132552	−	0.135776i
$952$	−14.7606	+	20.7284i	−0.478394	+	0.671810i
$953$	44.9362	−	13.1945i	1.45563	−	0.427411i	0.544229	−	0.838937i	$-0.316822\pi$
$953$	44.9362	−	13.1945i	1.45563	−	0.427411i	0.911398	+	0.411526i	$0.135004\pi$
$954$	−22.8329	−	22.8223i	−0.739242	−	0.738900i
$955$	−2.21298	+	2.55391i	−0.0716102	+	0.0826426i
$956$	7.69192	+	7.33424i	0.248775	+	0.237206i
$957$	0.998349	−	2.41102i	0.0322720	−	0.0779371i
$958$	0.516507	+	10.8428i	0.0166876	+	0.350315i
$959$	23.2597	−	22.1781i	0.751096	−	0.716168i
$960$	−0.971559	+	1.20592i	−0.0313569	+	0.0389208i
$961$	30.8145	−	2.94243i	0.994016	−	0.0949171i
$962$	8.54175	−	59.4092i	0.275397	−	1.91543i
$963$	12.4438	+	29.0404i	0.400995	+	0.935814i
$964$	4.62497	+	5.33750i	0.148960	+	0.171909i
$965$	−3.21880	−	5.57513i	−0.103617	−	0.179470i
$966$	6.29563	+	32.7092i	0.202558	+	1.05240i
$967$	−2.49095	+	4.31445i	−0.0801035	+	0.138743i	−0.903294	−	0.429022i	$-0.858858\pi$
$967$	−2.49095	+	4.31445i	−0.0801035	+	0.138743i	0.823191	+	0.567765i	$0.192192\pi$
$968$	10.7438	−	2.07070i	0.345318	−	0.0665547i
$969$	23.4973	−	19.8806i	0.754842	−	0.638656i
$970$	−8.06203	+	3.22755i	−0.258856	+	0.103630i
$971$	−4.00125	+	8.76151i	−0.128406	+	0.281170i	−0.962906	−	0.269839i	$-0.913030\pi$
$971$	−4.00125	+	8.76151i	−0.128406	+	0.281170i	0.834499	+	0.551009i	$0.185757\pi$
$972$	14.9063	+	4.56084i	0.478121	+	0.146289i
$973$	−9.41159	−	2.76349i	−0.301722	−	0.0885935i
$974$	−13.1699	−	6.78958i	−0.421992	−	0.217552i
$975$	45.1871	−	5.95430i	1.44714	−	0.190690i
$976$	0.850567	−	3.50608i	0.0272260	−	0.112227i
$977$	−7.92855	−	22.9080i	−0.253657	−	0.732893i	−0.997887	−	0.0649702i	$-0.979305\pi$
$977$	−7.92855	−	22.9080i	−0.253657	−	0.732893i	0.744230	−	0.667923i	$-0.232816\pi$
$978$	11.2729	−	21.2478i	0.360468	−	0.679431i
$979$	1.02858	+	0.980745i	0.0328734	+	0.0313447i
$980$	−3.37250	−	7.38475i	−0.107731	−	0.235897i
$981$	−8.13944	−	0.191874i	−0.259872	−	0.00612608i
$982$	14.6571	+	4.30370i	0.467725	+	0.137337i
$983$	−13.1418	+	10.3348i	−0.419158	+	0.329630i	−0.805361	−	0.592784i	$-0.798029\pi$
$983$	−13.1418	+	10.3348i	−0.419158	+	0.329630i	0.386203	+	0.922414i	$0.373786\pi$
$984$	−17.3479	+	5.77617i	−0.553032	+	0.184138i
$985$	−4.28814	−	3.37223i	−0.136632	−	0.107448i
$986$	35.1399	−	18.1159i	1.11908	−	0.576926i
$987$	0.922723	−	8.59192i	0.0293706	−	0.273484i
$988$	−8.77116	−	15.1921i	−0.279048	−	0.483325i
$989$	−3.26476	−	1.63573i	−0.103813	−	0.0520130i
$990$	−0.0461251	+	0.647012i	−0.00146595	+	0.0205634i
$991$	−36.0047	−	41.5516i	−1.14373	−	1.31993i	−0.940107	−	0.340880i	$-0.889275\pi$
$991$	−36.0047	−	41.5516i	−1.14373	−	1.31993i	−0.203619	−	0.979050i	$-0.565270\pi$
$992$	−0.0101300	+	0.212655i	−0.000321627	+	0.00675179i
$993$	0.897210	+	10.7310i	0.0284721	+	0.340537i
$994$	−9.23675	−	12.9712i	−0.292972	−	0.411421i
$995$	−7.51359	−	3.00799i	−0.238197	−	0.0953596i
$996$	5.44221	−	8.25277i	0.172443	−	0.261499i
$997$	−35.4210	−	18.2608i	−1.12179	−	0.578325i	−0.205430	−	0.978672i	$-0.565859\pi$
$997$	−35.4210	−	18.2608i	−1.12179	−	0.578325i	−0.916364	+	0.400347i	$0.868890\pi$
$998$	−6.38104	−	13.9725i	−0.201988	−	0.442293i
$999$	−28.3794	+	40.9044i	−0.897885	+	1.29416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.m.a.13.10	✓	240
9.7	even	3	inner	414.2.m.a.151.5	yes	240
23.16	even	11	inner	414.2.m.a.85.5	yes	240
207.16	even	33	inner	414.2.m.a.223.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.m.a.13.10	✓	240	1.1	even	1	trivial
414.2.m.a.85.5	yes	240	23.16	even	11	inner
414.2.m.a.151.5	yes	240	9.7	even	3	inner
414.2.m.a.223.10	yes	240	207.16	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(1.32227 - 1.11875i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.518620 - 0.728300i) q^{5} +(-0.624745 - 1.61545i) q^{6} +(-0.945394 - 3.89697i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.496807 - 2.95858i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(1.32227 - 1.11875i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.518620 - 0.728300i) q^{5} +(-0.624745 - 1.61545i) q^{6} +(-0.945394 - 3.89697i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.496807 - 2.95858i) q^{9} +(-0.857868 + 0.251893i) q^{10} +(0.237462 + 0.0457670i) q^{11} +(-1.73094 + 0.0620208i) q^{12} +(-1.47689 + 6.08781i) q^{13} +(-3.99184 - 0.381175i) q^{14} +(-1.50054 - 0.382806i) q^{15} +(0.235759 + 0.971812i) q^{16} +(0.903107 + 6.28124i) q^{17} +(-2.63337 - 1.43714i) q^{18} +(0.398527 - 2.77182i) q^{19} +(-0.0425423 + 0.893072i) q^{20} +(-5.60979 - 4.09519i) q^{21} +(0.120916 - 0.209432i) q^{22} +(1.94182 - 4.38513i) q^{23} +(-0.507525 + 1.65602i) q^{24} +(1.37389 - 3.96958i) q^{25} +(5.26994 + 3.38679i) q^{26} +(-2.65299 - 4.46785i) q^{27} +(-1.66581 + 3.64763i) q^{28} +(4.89713 - 3.85115i) q^{29} +(-0.852530 + 1.29281i) q^{30} +(0.0101300 + 0.212655i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(0.365191 - 0.205143i) q^{33} +(6.23116 + 1.20096i) q^{34} +(-2.34786 + 2.70957i) q^{35} +(-2.21939 + 2.01849i) q^{36} +(-3.98016 - 8.71533i) q^{37} +(-2.48903 - 1.28318i) q^{38} +(4.85788 + 9.70200i) q^{39} +(0.830040 + 0.332298i) q^{40} +(6.12334 + 8.59902i) q^{41} +(-5.70474 + 3.96185i) q^{42} +(0.0362295 - 0.760551i) q^{43} +(-0.158366 - 0.182764i) q^{44} +(-2.41239 + 1.17255i) q^{45} +(-3.50884 - 3.26926i) q^{46} +(0.622078 + 1.07747i) q^{47} +(1.39895 + 1.02124i) q^{48} +(-8.07073 + 4.16075i) q^{49} +(-3.30190 - 2.59665i) q^{50} +(8.22128 + 7.29516i) q^{51} +(4.92415 - 3.87239i) q^{52} +(10.3251 + 3.03173i) q^{53} +(-5.08983 + 1.04579i) q^{54} +(-0.0898203 - 0.196679i) q^{55} +(2.90217 + 2.76722i) q^{56} +(-2.57401 - 4.11095i) q^{57} +(-2.03764 - 5.88738i) q^{58} +(-0.636660 + 2.62435i) q^{59} +(0.942870 + 1.22848i) q^{60} +(-3.20672 - 1.65318i) q^{61} +(0.204272 + 0.0599797i) q^{62} +(-11.9992 + 0.860981i) q^{63} +(0.415415 - 0.909632i) q^{64} +(5.19969 - 2.08164i) q^{65} +(-0.0744184 - 0.412201i) q^{66} +(14.2758 - 2.75143i) q^{67} +(3.17292 - 5.49565i) q^{68} +(-2.33824 - 7.97074i) q^{69} +(1.79264 + 3.10494i) q^{70} +(2.60048 + 3.00111i) q^{71} +(1.18159 + 2.75751i) q^{72} +(-2.16121 + 15.0315i) q^{73} +(-9.53777 + 0.910747i) q^{74} +(-2.62431 - 6.78590i) q^{75} +(-2.02669 + 1.93244i) q^{76} +(-0.0461424 - 0.968648i) q^{77} +(10.7573 - 1.41748i) q^{78} +(-8.08815 - 7.71203i) q^{79} +(0.585501 - 0.675704i) q^{80} +(-8.50637 - 2.93968i) q^{81} +(10.1288 - 2.97409i) q^{82} +(-3.31066 + 4.64918i) q^{83} +(1.87811 + 6.68678i) q^{84} +(4.10626 - 3.91531i) q^{85} +(-0.706872 - 0.282989i) q^{86} +(2.16688 - 10.5709i) q^{87} +(-0.224509 + 0.0898798i) q^{88} +(4.94391 + 3.17726i) q^{89} +(0.319050 + 2.66321i) q^{90} +25.1202 q^{91} +(-4.23708 + 2.24659i) q^{92} +(0.251301 + 0.269854i) q^{93} +(1.22167 - 0.235458i) q^{94} +(-2.22540 + 1.14727i) q^{95} +(1.42263 - 0.987992i) q^{96} +(9.66885 - 0.923263i) q^{97} +(1.29223 + 8.98769i) q^{98} +(0.253378 - 0.679811i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9}+O(q^{10}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9	\( 240 q - 12 q^{2} + 12 q^{4} - 13 q^{7} + 24 q^{8} - 36 q^{9} + 2 q^{11} + 11 q^{12} + 4 q^{13} + 2 q^{14} + 6 q^{15} + 12 q^{16} - 8 q^{17} - 18 q^{18} + 12 q^{19} - 29 q^{21} + 20 q^{22} + 10 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} - 8 q^{29} - 18 q^{30} - 12 q^{32} + 50 q^{33} - 4 q^{34} - 12 q^{35} - 4 q^{36} + 92 q^{37} + 6 q^{38} + 44 q^{39} + 2 q^{41} + 42 q^{42} - 14 q^{43} - 4 q^{44} - 2 q^{45} - 44 q^{46} + 10 q^{47} - 22 q^{48} + 43 q^{49} - 43 q^{50} - 90 q^{51} - 18 q^{52} + 16 q^{53} - 29 q^{54} - 8 q^{55} + 13 q^{56} + 7 q^{57} + 8 q^{58} - 84 q^{59} + 9 q^{60} - 53 q^{61} - 66 q^{62} + 11 q^{63} - 24 q^{64} + 79 q^{65} - 110 q^{66} + 46 q^{67} - 40 q^{68} - 55 q^{69} - 6 q^{70} - 14 q^{71} - 19 q^{72} + 16 q^{73} + 46 q^{74} - 44 q^{75} - 6 q^{76} - 96 q^{77} + 20 q^{78} + 20 q^{79} - 22 q^{80} - 56 q^{81} + 26 q^{82} + 57 q^{83} + 5 q^{84} - 2 q^{85} - 8 q^{86} - 198 q^{87} - 2 q^{88} + 60 q^{89} - 22 q^{90} - 252 q^{91} - 218 q^{93} - 10 q^{94} + 6 q^{95} - q^{97} + 20 q^{98} + 84 q^{99}+O(q^{100}) \) 240 * q - 12 * q^2 + 12 * q^4 - 13 * q^7 + 24 * q^8 - 36 * q^9 + 2 * q^11 + 11 * q^12 + 4 * q^13 + 2 * q^14 + 6 * q^15 + 12 * q^16 - 8 * q^17 - 18 * q^18 + 12 * q^19 - 29 * q^21 + 20 * q^22 + 10 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 - 8 * q^29 - 18 * q^30 - 12 * q^32 + 50 * q^33 - 4 * q^34 - 12 * q^35 - 4 * q^36 + 92 * q^37 + 6 * q^38 + 44 * q^39 + 2 * q^41 + 42 * q^42 - 14 * q^43 - 4 * q^44 - 2 * q^45 - 44 * q^46 + 10 * q^47 - 22 * q^48 + 43 * q^49 - 43 * q^50 - 90 * q^51 - 18 * q^52 + 16 * q^53 - 29 * q^54 - 8 * q^55 + 13 * q^56 + 7 * q^57 + 8 * q^58 - 84 * q^59 + 9 * q^60 - 53 * q^61 - 66 * q^62 + 11 * q^63 - 24 * q^64 + 79 * q^65 - 110 * q^66 + 46 * q^67 - 40 * q^68 - 55 * q^69 - 6 * q^70 - 14 * q^71 - 19 * q^72 + 16 * q^73 + 46 * q^74 - 44 * q^75 - 6 * q^76 - 96 * q^77 + 20 * q^78 + 20 * q^79 - 22 * q^80 - 56 * q^81 + 26 * q^82 + 57 * q^83 + 5 * q^84 - 2 * q^85 - 8 * q^86 - 198 * q^87 - 2 * q^88 + 60 * q^89 - 22 * q^90 - 252 * q^91 - 218 * q^93 - 10 * q^94 + 6 * q^95 - q^97 + 20 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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