LMFDB - Embedded newform 882.2.bb.b.151.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(25,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([28, 16]))

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

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

chi := DirichletCharacter("882.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bb (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			151.10
Character	$\chi$	$=$	882.151
Dual form			882.2.bb.b.625.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 0.433884i) q^{2} +(-0.992605 - 1.41941i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.61016 - 2.42188i) q^{5} +(-1.51017 - 0.848172i) q^{6} +(1.78359 + 1.95418i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-1.02947 + 2.81783i) q^{9} +O(q^{10})$	\(q+(0.900969 - 0.433884i) q^{2} +(-0.992605 - 1.41941i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.61016 - 2.42188i) q^{5} +(-1.51017 - 0.848172i) q^{6} +(1.78359 + 1.95418i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-1.02947 + 2.81783i) q^{9} +(-3.40249 - 1.04953i) q^{10} +(-1.01649 - 0.693029i) q^{11} +(-1.72862 - 0.108940i) q^{12} +(-4.30322 - 2.93389i) q^{13} +(2.45484 + 0.986784i) q^{14} +(-0.846785 + 6.10887i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-3.14924 + 0.474672i) q^{17} +(0.295091 + 2.98545i) q^{18} +(0.0971541 + 0.168276i) q^{19} +(-3.52091 + 0.530692i) q^{20} +(1.00339 - 4.47138i) q^{21} +(-1.21652 - 0.183360i) q^{22} +(0.445732 + 1.13571i) q^{23} +(-1.60470 + 0.651869i) q^{24} +(0.573810 + 7.65697i) q^{25} +(-5.15004 - 0.776243i) q^{26} +(5.02153 - 1.33575i) q^{27} +(2.63989 - 0.176055i) q^{28} +(-5.27139 + 0.794534i) q^{29} +(1.88761 + 5.87131i) q^{30} +3.20535 q^{31} +(-0.623490 - 0.781831i) q^{32} +(0.0252750 + 2.13072i) q^{33} +(-2.63142 + 1.79407i) q^{34} +(0.0773235 - 9.42035i) q^{35} +(1.56121 + 2.56176i) q^{36} +(-1.77461 + 4.52163i) q^{37} +(0.160545 + 0.109458i) q^{38} +(0.107000 + 9.02025i) q^{39} +(-2.94197 + 2.00580i) q^{40} +(0.332314 - 0.102505i) q^{41} +(-1.03604 - 4.46393i) q^{42} +(5.92789 + 1.82851i) q^{43} +(-1.17560 + 0.362625i) q^{44} +(9.51153 - 4.86175i) q^{45} +(0.894355 + 0.829841i) q^{46} +(-9.77196 + 4.70593i) q^{47} +(-1.16295 + 1.28357i) q^{48} +(-0.637625 + 6.97090i) q^{49} +(3.83922 + 6.64972i) q^{50} +(3.79971 + 3.99892i) q^{51} +(-4.97682 + 1.53515i) q^{52} +(-3.03978 - 7.74524i) q^{53} +(3.94468 - 3.38223i) q^{54} +(0.974765 + 4.27072i) q^{55} +(2.30207 - 1.30402i) q^{56} +(0.142417 - 0.304933i) q^{57} +(-4.40462 + 3.00302i) q^{58} +(-2.52250 - 11.0518i) q^{59} +(4.24814 + 4.47086i) q^{60} +(2.79797 + 3.50855i) q^{61} +(2.88792 - 1.39075i) q^{62} +(-7.34270 + 3.01409i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(4.12660 + 18.0798i) q^{65} +(0.947257 + 1.90875i) q^{66} -2.05525 q^{67} +(-1.59241 + 2.75813i) q^{68} +(1.16960 - 1.75999i) q^{69} +(-4.01767 - 8.52100i) q^{70} +(5.74715 - 7.20670i) q^{71} +(2.51811 + 1.63069i) q^{72} +(0.755092 - 0.514813i) q^{73} +(0.362995 + 4.84383i) q^{74} +(10.2988 - 8.41482i) q^{75} +(0.192138 + 0.0289601i) q^{76} +(-0.458692 - 3.22248i) q^{77} +(4.01014 + 8.08054i) q^{78} -16.2274 q^{79} +(-1.78034 + 3.08364i) q^{80} +(-6.88038 - 5.80176i) q^{81} +(0.254929 - 0.236539i) q^{82} +(-4.00512 + 2.73065i) q^{83} +(-2.87026 - 3.57234i) q^{84} +(9.36964 + 6.38811i) q^{85} +(6.13421 - 0.924584i) q^{86} +(6.36018 + 6.69362i) q^{87} +(-0.901843 + 0.836788i) q^{88} +(-0.250654 - 3.34475i) q^{89} +(6.46016 - 8.50719i) q^{90} +(-1.94184 - 13.6421i) q^{91} +(1.16584 + 0.359614i) q^{92} +(-3.18164 - 4.54972i) q^{93} +(-6.76240 + 8.47979i) q^{94} +(0.153955 - 0.674523i) q^{95} +(-0.490863 + 1.66104i) q^{96} +(3.80214 - 6.58550i) q^{97} +(2.45008 + 6.55722i) q^{98} +(2.99928 - 2.15084i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9}+O(q^{10}) $ 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9} - 2 q^{10} - 2 q^{12} + 19 q^{13} - 2 q^{14} + q^{15} - 56 q^{16} + 7 q^{17} + 2 q^{18} + 38 q^{19} + 2 q^{20} + 4 q^{21} - 42 q^{23} + 2 q^{24} + 24 q^{25} + 9 q^{26} + 35 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 88 q^{31} + 56 q^{32} + 26 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} + 11 q^{38} - 60 q^{39} - 2 q^{40} + 3 q^{41} - 53 q^{42} + q^{43} + 108 q^{45} - 42 q^{46} + 3 q^{47} - 2 q^{48} + 70 q^{49} + 172 q^{50} + 13 q^{51} + 5 q^{52} - 78 q^{53} + 14 q^{54} + 23 q^{55} - 2 q^{56} - 30 q^{57} + 38 q^{58} - 28 q^{59} + q^{60} - 37 q^{61} - 24 q^{62} + 26 q^{63} - 56 q^{64} - 14 q^{65} + 2 q^{66} - 58 q^{67} - 21 q^{68} + 19 q^{69} + 44 q^{70} + 7 q^{71} + 2 q^{72} - 8 q^{73} + 4 q^{74} + q^{75} - 4 q^{76} - 13 q^{77} + 4 q^{78} + 18 q^{79} - 12 q^{80} - 87 q^{81} - 3 q^{82} + 185 q^{83} - 17 q^{84} - 159 q^{85} - q^{86} - 132 q^{87} + 47 q^{89} + 60 q^{90} + 45 q^{91} - 21 q^{92} + 53 q^{93} + 18 q^{94} + 26 q^{95} + 2 q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9 - 2 * q^10 - 2 * q^12 + 19 * q^13 - 2 * q^14 + q^15 - 56 * q^16 + 7 * q^17 + 2 * q^18 + 38 * q^19 + 2 * q^20 + 4 * q^21 - 42 * q^23 + 2 * q^24 + 24 * q^25 + 9 * q^26 + 35 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 88 * q^31 + 56 * q^32 + 26 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 + 11 * q^38 - 60 * q^39 - 2 * q^40 + 3 * q^41 - 53 * q^42 + q^43 + 108 * q^45 - 42 * q^46 + 3 * q^47 - 2 * q^48 + 70 * q^49 + 172 * q^50 + 13 * q^51 + 5 * q^52 - 78 * q^53 + 14 * q^54 + 23 * q^55 - 2 * q^56 - 30 * q^57 + 38 * q^58 - 28 * q^59 + q^60 - 37 * q^61 - 24 * q^62 + 26 * q^63 - 56 * q^64 - 14 * q^65 + 2 * q^66 - 58 * q^67 - 21 * q^68 + 19 * q^69 + 44 * q^70 + 7 * q^71 + 2 * q^72 - 8 * q^73 + 4 * q^74 + q^75 - 4 * q^76 - 13 * q^77 + 4 * q^78 + 18 * q^79 - 12 * q^80 - 87 * q^81 - 3 * q^82 + 185 * q^83 - 17 * q^84 - 159 * q^85 - q^86 - 132 * q^87 + 47 * q^89 + 60 * q^90 + 45 * q^91 - 21 * q^92 + 53 * q^93 + 18 * q^94 + 26 * q^95 + 2 * q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$3$	−0.992605	−	1.41941i	−0.573081	−	0.819499i
$3$	−0.992605	−	1.41941i	−0.573081	−	0.819499i
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	−2.61016	−	2.42188i	−1.16730	−	1.08310i	−0.995184	−	0.0980196i	$-0.968749\pi$
$5$	−2.61016	−	2.42188i	−1.16730	−	1.08310i	−0.172116	−	0.985077i	$-0.555060\pi$
$6$	−1.51017	−	0.848172i	−0.616523	−	0.346265i
$7$	1.78359	+	1.95418i	0.674133	+	0.738610i
$7$	1.78359	+	1.95418i	0.674133	+	0.738610i
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	−1.02947	+	2.81783i	−0.343157	+	0.939278i
$10$	−3.40249	−	1.04953i	−1.07596	−	0.331890i
$11$	−1.01649	−	0.693029i	−0.306482	−	0.208956i	0.400305	−	0.916382i	$-0.368904\pi$
$11$	−1.01649	−	0.693029i	−0.306482	−	0.208956i	−0.706788	+	0.707426i	$0.749856\pi$
$12$	−1.72862	−	0.108940i	−0.499010	−	0.0314483i
$13$	−4.30322	−	2.93389i	−1.19350	−	0.813714i	−0.207139	−	0.978312i	$-0.566415\pi$
$13$	−4.30322	−	2.93389i	−1.19350	−	0.813714i	−0.986361	+	0.164597i	$0.947368\pi$
$14$	2.45484	+	0.986784i	0.656085	+	0.263729i
$15$	−0.846785	+	6.10887i	−0.218639	+	1.57730i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	−3.14924	+	0.474672i	−0.763804	+	0.115125i	−0.519380	−	0.854544i	$-0.673837\pi$
$17$	−3.14924	+	0.474672i	−0.763804	+	0.115125i	−0.244424	+	0.969668i	$0.578599\pi$
$18$	0.295091	+	2.98545i	0.0695537	+	0.703678i
$19$	0.0971541	+	0.168276i	0.0222887	+	0.0386051i	0.876955	−	0.480573i	$-0.159571\pi$
$19$	0.0971541	+	0.168276i	0.0222887	+	0.0386051i	−0.854666	+	0.519178i	$0.826238\pi$
$20$	−3.52091	+	0.530692i	−0.787299	+	0.118666i
$21$	1.00339	−	4.47138i	0.218957	−	0.975734i
$22$	−1.21652	−	0.183360i	−0.259362	−	0.0390926i
$23$	0.445732	+	1.13571i	0.0929416	+	0.236811i	0.969783	−	0.243968i	$-0.0784491\pi$
$23$	0.445732	+	1.13571i	0.0929416	+	0.236811i	−0.876842	+	0.480779i	$0.840354\pi$
$24$	−1.60470	+	0.651869i	−0.327558	+	0.133062i
$25$	0.573810	+	7.65697i	0.114762	+	1.53139i
$26$	−5.15004	−	0.776243i	−1.01001	−	0.152234i
$27$	5.02153	−	1.33575i	0.966394	−	0.257065i
$28$	2.63989	−	0.176055i	0.498892	−	0.0332713i
$29$	−5.27139	+	0.794534i	−0.978872	+	0.147541i	−0.618941	−	0.785437i	$-0.712438\pi$
$29$	−5.27139	+	0.794534i	−0.978872	+	0.147541i	−0.359931	+	0.932979i	$0.617200\pi$
$30$	1.88761	+	5.87131i	0.344629	+	1.07195i
$31$	3.20535			0.575698			0.287849	−	0.957676i	$-0.407060\pi$
$31$	3.20535			0.575698			0.287849	+	0.957676i	$0.407060\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	0.0252750	+	2.13072i	0.00439981	+	0.370911i
$34$	−2.63142	+	1.79407i	−0.451285	+	0.307681i
$35$	0.0773235	−	9.42035i	0.0130701	−	1.59233i
$36$	1.56121	+	2.56176i	0.260201	+	0.426961i
$37$	−1.77461	+	4.52163i	−0.291744	+	0.743352i	0.707581	+	0.706632i	$0.249786\pi$
$37$	−1.77461	+	4.52163i	−0.291744	+	0.743352i	−0.999326	+	0.0367201i	$0.988309\pi$
$38$	0.160545	+	0.109458i	0.0260438	+	0.0177564i
$39$	0.107000	+	9.02025i	0.0171337	+	1.44440i
$40$	−2.94197	+	2.00580i	−0.465167	+	0.317145i
$41$	0.332314	−	0.102505i	0.0518987	−	0.0160086i	−0.268697	−	0.963225i	$-0.586593\pi$
$41$	0.332314	−	0.102505i	0.0518987	−	0.0160086i	0.320596	+	0.947216i	$0.396117\pi$
$42$	−1.03604	−	4.46393i	−0.159864	−	0.688799i
$43$	5.92789	+	1.82851i	0.903996	+	0.278846i	0.711694	−	0.702490i	$-0.247928\pi$
$43$	5.92789	+	1.82851i	0.903996	+	0.278846i	0.192302	+	0.981336i	$0.438405\pi$
$44$	−1.17560	+	0.362625i	−0.177229	+	0.0546678i
$45$	9.51153	−	4.86175i	1.41790	−	0.724747i
$46$	0.894355	+	0.829841i	0.131866	+	0.122353i
$47$	−9.77196	+	4.70593i	−1.42539	+	0.686430i	−0.978134	−	0.207978i	$-0.933312\pi$
$47$	−9.77196	+	4.70593i	−1.42539	+	0.686430i	−0.447253	+	0.894408i	$0.647598\pi$
$48$	−1.16295	+	1.28357i	−0.167857	+	0.185267i
$49$	−0.637625	+	6.97090i	−0.0910893	+	0.995843i
$50$	3.83922	+	6.64972i	0.542948	+	0.940413i
$51$	3.79971	+	3.99892i	0.532066	+	0.559961i
$52$	−4.97682	+	1.53515i	−0.690161	+	0.212887i
$53$	−3.03978	−	7.74524i	−0.417547	−	1.06389i	−0.972684	−	0.232133i	$-0.925430\pi$
$53$	−3.03978	−	7.74524i	−0.417547	−	1.06389i	0.555138	−	0.831759i	$-0.312666\pi$
$54$	3.94468	−	3.38223i	0.536803	−	0.460263i
$55$	0.974765	+	4.27072i	0.131437	+	0.575864i
$56$	2.30207	−	1.30402i	0.307627	−	0.174258i
$57$	0.142417	−	0.304933i	0.0188636	−	0.0403894i
$58$	−4.40462	+	3.00302i	−0.578355	+	0.394316i
$59$	−2.52250	−	11.0518i	−0.328401	−	1.43882i	−0.822178	−	0.569231i	$-0.807241\pi$
$59$	−2.52250	−	11.0518i	−0.328401	−	1.43882i	0.493776	−	0.869589i	$-0.335616\pi$
$60$	4.24814	+	4.47086i	0.548433	+	0.577186i
$61$	2.79797	+	3.50855i	0.358244	+	0.449223i	0.927994	−	0.372594i	$-0.121532\pi$
$61$	2.79797	+	3.50855i	0.358244	+	0.449223i	−0.569751	+	0.821818i	$0.692960\pi$
$62$	2.88792	−	1.39075i	0.366766	−	0.176625i
$63$	−7.34270	+	3.01409i	−0.925094	+	0.379739i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	4.12660	+	18.0798i	0.511841	+	2.24252i
$66$	0.947257	+	1.90875i	0.116599	+	0.234950i
$67$	−2.05525			−0.251088			−0.125544	−	0.992088i	$-0.540068\pi$
$67$	−2.05525			−0.251088			−0.125544	+	0.992088i	$0.540068\pi$
$68$	−1.59241	+	2.75813i	−0.193108	+	0.334473i
$69$	1.16960	−	1.75999i	0.140804	−	0.211877i
$70$	−4.01767	−	8.52100i	−0.480204	−	1.01845i
$71$	5.74715	−	7.20670i	0.682062	−	0.855278i	−0.313481	−	0.949595i	$-0.601495\pi$
$71$	5.74715	−	7.20670i	0.682062	−	0.855278i	0.995542	+	0.0943165i	$0.0300665\pi$
$72$	2.51811	+	1.63069i	0.296762	+	0.192178i
$73$	0.755092	−	0.514813i	0.0883769	−	0.0602543i	−0.518325	−	0.855183i	$-0.673444\pi$
$73$	0.755092	−	0.514813i	0.0883769	−	0.0602543i	0.606702	+	0.794929i	$0.292492\pi$
$74$	0.362995	+	4.84383i	0.0421973	+	0.563083i
$75$	10.2988	−	8.41482i	1.18921	−	0.971659i
$76$	0.192138	+	0.0289601i	0.0220397	+	0.00332195i
$77$	−0.458692	−	3.22248i	−0.0522728	−	0.367235i
$78$	4.01014	+	8.08054i	0.454059	+	0.914941i
$79$	−16.2274			−1.82572			−0.912862	−	0.408269i	$-0.866132\pi$
$79$	−16.2274			−1.82572			−0.912862	+	0.408269i	$0.866132\pi$
$80$	−1.78034	+	3.08364i	−0.199048	+	0.344761i
$81$	−6.88038	−	5.80176i	−0.764487	−	0.644640i
$82$	0.254929	−	0.236539i	0.0281522	−	0.0261214i
$83$	−4.00512	+	2.73065i	−0.439619	+	0.299727i	−0.762829	−	0.646600i	$-0.776190\pi$
$83$	−4.00512	+	2.73065i	−0.439619	+	0.299727i	0.323210	+	0.946327i	$0.395238\pi$
$84$	−2.87026	−	3.57234i	−0.313171	−	0.389774i
$85$	9.36964	+	6.38811i	1.01628	+	0.692888i
$86$	6.13421	−	0.924584i	0.661469	−	0.0997004i
$87$	6.36018	+	6.69362i	0.681883	+	0.717632i
$88$	−0.901843	+	0.836788i	−0.0961368	+	0.0892019i
$89$	−0.250654	−	3.34475i	−0.0265693	−	0.354543i	−0.994605	−	0.103731i	$-0.966922\pi$
$89$	−0.250654	−	3.34475i	−0.0265693	−	0.354543i	0.968036	−	0.250811i	$-0.0806973\pi$
$90$	6.46016	−	8.50719i	0.680961	−	0.896736i
$91$	−1.94184	−	13.6421i	−0.203560	−	1.43008i
$92$	1.16584	+	0.359614i	0.121547	+	0.0374924i
$93$	−3.18164	−	4.54972i	−0.329921	−	0.471784i
$94$	−6.76240	+	8.47979i	−0.697489	+	0.874623i
$95$	0.153955	−	0.674523i	0.0157955	−	0.0692046i
$96$	−0.490863	+	1.66104i	−0.0500985	+	0.169529i
$97$	3.80214	−	6.58550i	0.386049	−	0.668656i	−0.605865	−	0.795567i	$-0.707173\pi$
$97$	3.80214	−	6.58550i	0.386049	−	0.668656i	0.991914	+	0.126911i	$0.0405063\pi$
$98$	2.45008	+	6.55722i	0.247495	+	0.662379i
$99$	2.99928	−	2.15084i	0.301439	−	0.216167i
$100$	6.34422	+	4.32542i	0.634422	+	0.432542i
$101$	6.46063	−	1.99284i	0.642857	−	0.198295i	0.0438489	−	0.999038i	$-0.486038\pi$
$101$	6.46063	−	1.99284i	0.642857	−	0.198295i	0.599008	+	0.800743i	$0.295562\pi$
$102$	5.15849	+	1.95427i	0.510766	+	0.193501i
$103$	−13.8099	−	12.8137i	−1.36073	−	1.26257i	−0.933572	−	0.358389i	$-0.883326\pi$
$103$	−13.8099	−	12.8137i	−1.36073	−	1.26257i	−0.427153	−	0.904179i	$-0.640483\pi$
$104$	−3.81789	+	3.54248i	−0.374375	+	0.347369i
$105$	−13.4481	+	9.24094i	−1.31240	+	0.901823i
$106$	−6.09929	−	5.65931i	−0.592415	−	0.549681i
$107$	0.0480235	+	0.640829i	0.00464261	+	0.0619513i	0.999044	−	0.0437184i	$-0.0139204\pi$
$107$	0.0480235	+	0.640829i	0.00464261	+	0.0619513i	−0.994401	+	0.105670i	$0.966301\pi$
$108$	2.08654	−	4.75882i	0.200777	−	0.457917i
$109$	1.41847	−	18.9282i	0.135865	−	1.81299i	−0.347613	−	0.937638i	$-0.613008\pi$
$109$	1.41847	−	18.9282i	0.135865	−	1.81299i	0.483478	−	0.875356i	$-0.339373\pi$
$110$	2.73123	+	3.42486i	0.260413	+	0.326547i
$111$	8.17956	−	1.96929i	0.776369	−	0.186917i
$112$	1.50830	−	2.17372i	0.142521	−	0.205397i
$113$	−1.10890	−	14.7973i	−0.104317	−	1.39201i	−0.766295	−	0.642489i	$-0.777902\pi$
$113$	−1.10890	−	14.7973i	−0.104317	−	1.39201i	0.661978	−	0.749523i	$-0.269717\pi$
$114$	−0.00399195	−	0.336528i	−0.000373881	−	0.0315187i
$115$	1.58711	−	4.04389i	0.147999	−	0.377094i
$116$	−2.66547	+	4.61672i	−0.247482	+	0.428652i
$117$	12.6973	−	9.10542i	1.17386	−	0.841796i
$118$	−7.06788	−	8.86284i	−0.650651	−	0.815891i
$119$	−6.54455	−	5.30756i	−0.599938	−	0.486544i
$120$	5.76728	+	2.18491i	0.526478	+	0.199454i
$121$	−3.46579	−	8.83070i	−0.315072	−	0.802791i
$122$	4.04319	+	1.94710i	0.366053	+	0.176282i
$123$	−0.475353	−	0.369943i	−0.0428612	−	0.0333567i
$124$	1.99850	−	2.50604i	0.179471	−	0.225049i
$125$	5.94626	−	7.45637i	0.531849	−	0.666918i
$126$	−5.30778	+	5.90148i	−0.472855	+	0.525745i
$127$	−2.60494	−	3.26649i	−0.231151	−	0.289854i	0.652706	−	0.757611i	$-0.273634\pi$
$127$	−2.60494	−	3.26649i	−0.231151	−	0.289854i	−0.883857	+	0.467757i	$0.845062\pi$
$128$	−1.00000			−0.0883883
$129$	−3.28864	−	10.2291i	−0.289549	−	0.900624i
$130$	11.5625	+	14.4989i	1.01410	+	1.27164i
$131$	−4.87258	−	1.50299i	−0.425719	−	0.131317i	0.0744898	−	0.997222i	$-0.476267\pi$
$131$	−4.87258	−	1.50299i	−0.425719	−	0.131317i	−0.500209	+	0.865905i	$0.666743\pi$
$132$	1.68162	+	1.30872i	0.146366	+	0.113910i
$133$	−0.155558	+	0.489991i	−0.0134886	+	0.0424876i
$134$	−1.85171	+	0.891739i	−0.159964	+	0.0770345i
$135$	−16.3420	−	8.67500i	−1.40650	−	0.746625i
$136$	−0.238002	+	3.17591i	−0.0204085	+	0.272332i
$137$	2.67990	−	2.48658i	0.228959	−	0.212443i	−0.557348	−	0.830279i	$-0.688181\pi$
$137$	2.67990	−	2.48658i	0.228959	−	0.212443i	0.786307	+	0.617836i	$0.211991\pi$
$138$	0.290146	−	2.09316i	0.0246988	−	0.178182i
$139$	−17.8570	+	5.50815i	−1.51461	+	0.467196i	−0.937063	−	0.349161i	$-0.886467\pi$
$139$	−17.8570	+	5.50815i	−1.51461	+	0.467196i	−0.577548	+	0.816357i	$0.695990\pi$
$140$	−7.31692	−	5.93395i	−0.618393	−	0.501510i
$141$	16.3794	+	9.19932i	1.37939	+	0.774723i
$142$	2.05114	−	8.98661i	0.172127	−	0.754140i
$143$	2.34090	+	5.96452i	0.195756	+	0.498778i
$144$	2.97626	+	0.376633i	0.248022	+	0.0313861i
$145$	15.6834	+	10.6928i	1.30244	+	0.887988i
$146$	0.456946	−	0.791453i	0.0378171	−	0.0655011i
$147$	10.5275	−	6.01430i	0.868294	−	0.496051i
$148$	2.42870	+	4.20664i	0.199638	+	0.345784i
$149$	−0.863460	+	11.5221i	−0.0707374	+	0.943925i	0.843077	+	0.537793i	$0.180742\pi$
$149$	−0.863460	+	11.5221i	−0.0707374	+	0.943925i	−0.913814	+	0.406132i	$0.866877\pi$
$150$	5.62788	−	12.0500i	0.459514	−	0.983877i
$151$	20.1019	+	3.02987i	1.63587	+	0.246568i	0.901688	−	0.432386i	$-0.142328\pi$
$151$	20.1019	+	3.02987i	1.63587	+	0.246568i	0.734181	+	0.678954i	$0.237566\pi$
$152$	0.185676	−	0.0572733i	0.0150603	−	0.00464548i
$153$	1.90451	−	9.36271i	0.153970	−	0.756930i
$154$	−1.81145	−	2.70433i	−0.145971	−	0.217921i
$155$	−8.36648	−	7.76296i	−0.672012	−	0.623536i
$156$	7.11903	+	5.54038i	0.569978	+	0.443585i
$157$	2.81241	+	12.3220i	0.224455	+	0.983401i	0.954080	+	0.299553i	$0.0968376\pi$
$157$	2.81241	+	12.3220i	0.224455	+	0.983401i	−0.729625	+	0.683848i	$0.760305\pi$
$158$	−14.6204	+	7.04080i	−1.16313	+	0.560136i
$159$	−7.97640	+	12.0027i	−0.632570	+	0.951874i
$160$	−0.266090	+	3.55072i	−0.0210363	+	0.280709i
$161$	−1.42437	+	2.89667i	−0.112256	+	0.228290i
$162$	−8.71630	−	2.24192i	−0.684817	−	0.176142i
$163$	−7.88769	+	7.31870i	−0.617811	+	0.573245i	−0.925738	−	0.378165i	$-0.876555\pi$
$163$	−7.88769	+	7.31870i	−0.617811	+	0.573245i	0.307927	+	0.951410i	$0.400365\pi$
$164$	0.127052	−	0.323724i	0.00992112	−	0.0252786i
$165$	5.09437	−	5.62274i	0.396596	−	0.437730i
$166$	−2.42371	+	4.19798i	−0.188116	+	0.325827i
$167$	2.43387	−	6.20141i	0.188339	−	0.479880i	−0.805250	−	0.592936i	$-0.797969\pi$
$167$	2.43387	−	6.20141i	0.188339	−	0.479880i	0.993589	+	0.113056i	$0.0360640\pi$
$168$	−4.13600	−	1.97321i	−0.319099	−	0.152236i
$169$	5.16060	+	13.1490i	0.396970	+	1.01146i
$170$	11.2134	+	1.69016i	0.860032	+	0.129629i
$171$	−0.574191	+	0.100529i	−0.0439095	+	0.00768765i
$172$	5.12557	−	3.49456i	0.390821	−	0.266457i
$173$	4.54226	−	5.69582i	0.345342	−	0.433045i	−0.578580	−	0.815625i	$-0.696393\pi$
$173$	4.54226	−	5.69582i	0.345342	−	0.433045i	0.923922	+	0.382580i	$0.124964\pi$
$174$	8.63458	+	3.27117i	0.654586	+	0.247987i
$175$	−13.9396	+	14.7782i	−1.05374	+	1.11713i
$176$	−0.449464	+	1.14521i	−0.0338796	+	0.0863238i
$177$	−13.1832	+	14.5505i	−0.990911	+	1.09368i
$178$	−1.67706	−	2.90476i	−0.125701	−	0.217721i
$179$	22.4668	−	3.38632i	1.67924	−	0.253105i	0.760894	−	0.648876i	$-0.224761\pi$
$179$	22.4668	−	3.38632i	1.67924	−	0.253105i	0.918349	+	0.395770i	$0.129522\pi$
$180$	2.12927	−	10.4677i	0.158707	−	0.780214i
$181$	5.14368	+	2.47707i	0.382327	+	0.184119i	0.615168	−	0.788396i	$-0.289088\pi$
$181$	5.14368	+	2.47707i	0.382327	+	0.184119i	−0.232841	+	0.972515i	$0.574802\pi$
$182$	−7.66863	−	11.4486i	−0.568437	−	0.848626i
$183$	2.20280	−	7.45408i	0.162835	−	0.551022i
$184$	1.20642	−	0.181838i	0.0889382	−	0.0134053i
$185$	15.5829	−	7.50431i	1.14567	−	0.551728i
$186$	−4.84061	−	2.71869i	−0.354931	−	0.199344i
$187$	3.53013	+	1.70002i	0.258148	+	0.124318i
$188$	−2.41347	+	10.5741i	−0.176021	+	0.771197i
$189$	11.5666	+	7.43054i	0.841349	+	0.540492i
$190$	−0.153955	−	0.674523i	−0.0111691	−	0.0489350i
$191$	−4.28764	+	18.7854i	−0.310243	+	1.35926i	0.543867	+	0.839171i	$0.316959\pi$
$191$	−4.28764	+	18.7854i	−0.310243	+	1.35926i	−0.854110	+	0.520092i	$0.825898\pi$
$192$	0.278446	+	1.70952i	0.0200951	+	0.123374i
$193$	−5.25430	+	23.0206i	−0.378213	+	1.65706i	0.324726	+	0.945808i	$0.394728\pi$
$193$	−5.25430	+	23.0206i	−0.378213	+	1.65706i	−0.702939	+	0.711250i	$0.748129\pi$
$194$	0.568269	−	7.58302i	0.0407993	−	0.544429i
$195$	21.5666	−	23.8035i	1.54442	−	1.70460i
$196$	5.05252	+	4.84480i	0.360894	+	0.346057i
$197$	−21.9900			−1.56672			−0.783360	−	0.621569i	$-0.786496\pi$
$197$	−21.9900			−1.56672			−0.783360	+	0.621569i	$0.786496\pi$
$198$	1.76905	−	3.23918i	0.125721	−	0.230198i
$199$	−13.0379	−	12.0974i	−0.924235	−	0.857565i	0.0658794	−	0.997828i	$-0.479015\pi$
$199$	−13.0379	−	12.0974i	−0.924235	−	0.857565i	−0.990114	+	0.140263i	$0.955205\pi$
$200$	7.59268	+	1.14441i	0.536883	+	0.0809221i
$201$	2.04005	+	2.91725i	0.143894	+	0.205767i
$202$	4.95617	−	4.59865i	0.348715	−	0.323560i
$203$	−10.9546	−	8.88411i	−0.768866	−	0.623542i
$204$	5.49556	−	0.477449i	0.384766	−	0.0334281i
$205$	−1.11565	−	0.537267i	−0.0779202	−	0.0375244i
$206$	−18.0019	−	5.55285i	−1.25425	−	0.386885i
$207$	−3.65910	+	0.0868220i	−0.254325	+	0.00603455i
$208$	−1.90277	+	4.84819i	−0.131934	+	0.336161i
$209$	0.0178642	−	0.238381i	0.00123569	−	0.0164891i
$210$	−8.10686	+	14.1607i	−0.559426	+	0.977183i
$211$	−2.01462	−	26.8833i	−0.138692	−	1.85072i	−0.440996	−	0.897509i	$-0.645375\pi$
$211$	−2.01462	−	26.8833i	−0.138692	−	1.85072i	0.302303	−	0.953212i	$-0.402244\pi$
$212$	−7.95075	−	2.45248i	−0.546060	−	0.168437i
$213$	−15.9339	−	1.00418i	−1.09178	−	0.0688053i
$214$	0.321313	+	0.556531i	0.0219645	+	0.0380437i
$215$	−11.0443	−	19.1294i	−0.753217	−	1.30461i
$216$	−0.184865	−	5.19286i	−0.0125785	−	0.353330i
$217$	5.71702	+	6.26382i	0.388097	+	0.425216i
$218$	−6.93464	−	17.6692i	−0.469673	−	1.19671i
$219$	−1.48024	−	0.560782i	−0.100025	−	0.0378942i
$220$	3.94674	+	1.90065i	0.266089	+	0.128142i
$221$	14.9445	+	7.19691i	1.00528	+	0.484117i
$222$	6.51508	−	5.32324i	0.437264	−	0.357273i
$223$	4.29067	+	10.9324i	0.287324	+	0.732091i	0.999546	+	0.0301359i	$0.00959400\pi$
$223$	4.29067	+	10.9324i	0.287324	+	0.732091i	−0.712221	+	0.701955i	$0.752311\pi$
$224$	0.415789	−	2.61288i	0.0277811	−	0.174580i
$225$	−22.1668	−	6.26572i	−1.47779	−	0.417715i
$226$	−7.41939	−	12.8508i	−0.493531	−	0.854820i
$227$	−5.48347	−	9.49765i	−0.363951	−	0.630381i	0.624657	−	0.780900i	$-0.285239\pi$
$227$	−5.48347	−	9.49765i	−0.363951	−	0.630381i	−0.988607	+	0.150519i	$0.951906\pi$
$228$	−0.149611	−	0.301469i	−0.00990821	−	0.0199653i
$229$	−6.51049	−	2.00822i	−0.430225	−	0.132707i	0.0720770	−	0.997399i	$-0.477037\pi$
$229$	−6.51049	−	2.00822i	−0.430225	−	0.132707i	−0.502302	+	0.864692i	$0.667513\pi$
$230$	−0.324641	−	4.33204i	−0.0214062	−	0.285646i
$231$	−4.11873	+	3.84972i	−0.270992	+	0.253293i
$232$	−0.398381	+	5.31602i	−0.0261550	+	0.349014i
$233$	−6.03721	+	15.3826i	−0.395511	+	1.00774i	0.584957	+	0.811064i	$0.301111\pi$
$233$	−6.03721	+	15.3826i	−0.395511	+	1.00774i	−0.980468	+	0.196680i	$0.936984\pi$
$234$	7.48914	−	13.7128i	0.489580	−	0.896436i
$235$	36.9036	+	11.3832i	2.40732	+	0.742561i
$236$	−10.2134	−	4.91851i	−0.664835	−	0.320168i
$237$	16.1074	+	23.0334i	1.04629	+	1.49618i
$238$	−8.19930	−	1.94238i	−0.531482	−	0.125906i
$239$	21.5730	−	20.0168i	1.39544	−	1.29478i	0.489099	−	0.872228i	$-0.337326\pi$
$239$	21.5730	−	20.0168i	1.39544	−	1.29478i	0.906340	−	0.422549i	$-0.138865\pi$
$240$	6.14413	−	0.533796i	0.396602	−	0.0344564i
$241$	21.7804	+	3.28287i	1.40300	+	0.211468i	0.806542	−	0.591176i	$-0.201336\pi$
$241$	21.7804	+	3.28287i	1.40300	+	0.211468i	0.596457	+	0.802645i	$0.296574\pi$
$242$	−6.95407	−	6.45243i	−0.447025	−	0.414778i
$243$	−1.40559	+	15.5250i	−0.0901689	+	0.995926i
$244$	4.48760			0.287289
$245$	18.5470	−	16.6509i	1.18492	−	1.06379i
$246$	−0.588791	−	0.127059i	−0.0375399	−	0.00810101i
$247$	0.0756267	−	1.00917i	0.00481201	−	0.0642118i
$248$	0.713257	−	3.12498i	0.0452919	−	0.198437i
$249$	7.85142	+	2.97447i	0.497564	+	0.188500i
$250$	2.12219	−	9.29794i	0.134219	−	0.588054i
$251$	−0.611986	−	2.68129i	−0.0386282	−	0.169241i	0.951934	−	0.306302i	$-0.0990917\pi$
$251$	−0.611986	−	2.68129i	−0.0386282	−	0.169241i	−0.990563	+	0.137060i	$0.956235\pi$
$252$	−2.22159	+	7.62001i	−0.139947	+	0.480015i
$253$	0.333997	−	1.46334i	0.0209982	−	0.0919992i
$254$	−3.76424	−	1.81276i	−0.236190	−	0.113743i
$255$	−0.232976	−	19.6403i	−0.0145895	−	1.22992i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	28.2777	−	4.26217i	1.76391	−	0.265867i	0.814560	−	0.580080i	$-0.196979\pi$
$257$	28.2777	−	4.26217i	1.76391	−	0.265867i	0.949353	+	0.314213i	$0.101741\pi$
$258$	−7.40121	−	7.78924i	−0.460780	−	0.484937i
$259$	−12.0013	+	4.59683i	−0.745721	+	0.285633i
$260$	16.7083	+	8.04627i	1.03620	+	0.499009i
$261$	3.18788	−	15.6719i	0.197325	−	0.970063i
$262$	−5.04216	+	0.759984i	−0.311506	+	0.0469520i
$263$	−5.11670	−	8.86239i	−0.315509	−	0.546478i	0.664036	−	0.747700i	$-0.268842\pi$
$263$	−5.11670	−	8.86239i	−0.315509	−	0.546478i	−0.979546	+	0.201222i	$0.935509\pi$
$264$	2.08292	+	0.449488i	0.128195	+	0.0276641i
$265$	−10.8237	+	27.5783i	−0.664894	+	1.69412i
$266$	0.0724463	+	0.508961i	0.00444197	+	0.0312064i
$267$	−4.49878	+	3.67580i	−0.275321	+	0.224955i
$268$	−1.28143	+	1.60686i	−0.0782756	+	0.0981544i
$269$	−6.01257	+	4.09930i	−0.366593	+	0.249939i	−0.732580	−	0.680681i	$-0.761684\pi$
$269$	−6.01257	+	4.09930i	−0.366593	+	0.249939i	0.365987	+	0.930620i	$0.380731\pi$
$270$	−18.4876	−	0.725363i	−1.12512	−	0.0441442i
$271$	−17.2422	−	2.59885i	−1.04739	−	0.157869i	−0.397272	−	0.917701i	$-0.630043\pi$
$271$	−17.2422	−	2.59885i	−1.04739	−	0.157869i	−0.650120	+	0.759832i	$0.725281\pi$
$272$	1.16354	+	2.96466i	0.0705502	+	0.179759i
$273$	−17.4363	+	16.2975i	−1.05529	+	0.986370i
$274$	1.33562	−	3.40310i	0.0806876	−	0.205589i
$275$	4.72323	−	8.18087i	0.284821	−	0.493325i
$276$	−0.646778	−	2.01177i	−0.0389315	−	0.121094i
$277$	8.59325	−	21.8952i	0.516318	−	1.31556i	−0.400516	−	0.916290i	$-0.631169\pi$
$277$	8.59325	−	21.8952i	0.516318	−	1.31556i	0.916834	−	0.399268i	$-0.130736\pi$
$278$	−13.6987	+	12.7105i	−0.821593	+	0.762327i
$279$	−3.29981	+	9.03214i	−0.197555	+	0.540740i
$280$	−9.16696	−	2.17161i	−0.547831	−	0.129779i
$281$	−0.147847	+	1.97288i	−0.00881979	+	0.117692i	−0.999876	−	0.0157539i	$-0.994985\pi$
$281$	−0.147847	+	1.97288i	−0.00881979	+	0.117692i	0.991056	+	0.133446i	$0.0426042\pi$
$282$	18.7487	+	1.18157i	1.11647	+	0.0703616i
$283$	19.7418	−	9.50714i	1.17353	−	0.565141i	0.257508	−	0.966276i	$-0.417099\pi$
$283$	19.7418	−	9.50714i	1.17353	−	0.565141i	0.916019	+	0.401135i	$0.131384\pi$
$284$	−2.05114	−	8.98661i	−0.121712	−	0.533257i
$285$	−1.11024	+	0.451008i	−0.0657651	+	0.0267154i
$286$	4.69699	+	4.35817i	0.277739	+	0.257704i
$287$	0.793024	+	0.466573i	0.0468107	+	0.0275409i
$288$	2.84494	−	0.952018i	0.167639	−	0.0560982i
$289$	−6.55231	+	2.02112i	−0.385430	+	0.118889i
$290$	18.7697	+	2.82908i	1.10220	+	0.166129i
$291$	−13.1216	+	1.13999i	−0.769200	+	0.0668274i
$292$	0.0682952	−	0.911336i	0.00399667	−	0.0533319i
$293$	4.01247	+	6.94981i	0.234411	+	0.406012i	0.959101	−	0.283063i	$-0.0913505\pi$
$293$	4.01247	+	6.94981i	0.234411	+	0.406012i	−0.724690	+	0.689075i	$0.758017\pi$
$294$	6.87544	−	9.98640i	0.400984	−	0.582419i
$295$	−20.1819	+	34.9561i	−1.17504	+	2.03522i
$296$	4.01338	+	2.73628i	0.233273	+	0.159043i
$297$	−6.03003	−	2.12229i	−0.349898	−	0.123148i
$298$	4.22129	+	10.7557i	0.244533	+	0.623059i
$299$	1.41395	−	6.19493i	0.0817710	−	0.358262i
$300$	−0.157749	−	13.2985i	−0.00910766	−	0.767790i
$301$	6.99968	+	14.8455i	0.403455	+	0.855679i
$302$	19.4258	−	5.99206i	1.11783	−	0.344805i
$303$	−9.24152	−	7.19220i	−0.530911	−	0.413181i
$304$	0.142438	−	0.132163i	0.00816938	−	0.00758008i
$305$	1.19410	−	15.9342i	0.0683742	−	0.912391i
$306$	−2.34643	−	9.26184i	−0.134136	−	0.529464i
$307$	−16.5760	+	7.98257i	−0.946041	+	0.455590i	−0.842297	−	0.539014i	$-0.818797\pi$
$307$	−16.5760	+	7.98257i	−0.946041	+	0.455590i	−0.103745	+	0.994604i	$0.533083\pi$
$308$	−2.80542	−	1.65056i	−0.159854	−	0.0940494i
$309$	−4.48017	+	32.3208i	−0.254868	+	1.83867i
$310$	−10.9062	−	3.36410i	−0.619428	−	0.191068i
$311$	8.28812	+	10.3930i	0.469976	+	0.589331i	0.959165	−	0.282846i	$-0.0912787\pi$
$311$	8.28812	+	10.3930i	0.469976	+	0.589331i	−0.489189	+	0.872178i	$0.662707\pi$
$312$	8.81790	+	1.90288i	0.499215	+	0.107729i
$313$	9.44895			0.534086			0.267043	−	0.963685i	$-0.413953\pi$
$313$	9.44895			0.534086			0.267043	+	0.963685i	$0.413953\pi$
$314$	7.88020	+	9.88146i	0.444706	+	0.557643i
$315$	26.4654	+	9.91587i	1.49116	+	0.558696i
$316$	−10.1176	+	12.6871i	−0.569160	+	0.713704i
$317$	−9.17303	+	11.5026i	−0.515209	+	0.646052i	−0.969584	−	0.244759i	$-0.921291\pi$
$317$	−9.17303	+	11.5026i	−0.515209	+	0.646052i	0.454375	+	0.890810i	$0.349863\pi$
$318$	−1.97872	+	14.2749i	−0.110961	+	0.800495i
$319$	5.90893	+	2.84559i	0.330837	+	0.159323i
$320$	1.30086	+	3.31454i	0.0727204	+	0.185289i
$321$	0.861934	−	0.704256i	0.0481084	−	0.0393077i
$322$	−0.0264944	+	3.22782i	−0.00147648	+	0.179880i
$323$	−0.385838	−	0.483825i	−0.0214686	−	0.0269208i
$324$	−8.82584	+	1.76196i	−0.490325	+	0.0978867i
$325$	19.9955	−	34.6331i	1.10915	−	1.92110i
$326$	−3.93109	+	10.0163i	−0.217723	+	0.554750i
$327$	−28.2750	+	16.7748i	−1.56361	+	0.927651i
$328$	−0.0259884	−	0.346791i	−0.00143497	−	0.0191483i
$329$	−26.6254	−	10.7027i	−1.46790	−	0.590059i
$330$	2.15025	−	7.27628i	0.118368	−	0.400546i
$331$	−8.32697	−	10.4417i	−0.457691	−	0.573927i	0.498418	−	0.866937i	$-0.333915\pi$
$331$	−8.32697	−	10.4417i	−0.457691	−	0.573927i	−0.956109	+	0.293010i	$0.905343\pi$
$332$	−0.362248	+	4.83386i	−0.0198809	+	0.265293i
$333$	−10.9143	−	9.65545i	−0.598100	−	0.529115i
$334$	−0.497846	−	6.64330i	−0.0272409	−	0.363505i
$335$	5.36453	+	4.97756i	0.293096	+	0.271953i
$336$	−4.58255	+	0.0167432i	−0.249998	+	0.000913416i
$337$	22.4124	−	20.7957i	1.22088	−	1.13281i	0.233853	−	0.972272i	$-0.424867\pi$
$337$	22.4124	−	20.7957i	1.22088	−	1.13281i	0.987029	−	0.160541i	$-0.0513239\pi$
$338$	10.3547	+	9.60774i	0.563221	+	0.522592i
$339$	−19.9028	+	16.2619i	−1.08097	+	0.883223i
$340$	10.8363	−	3.34256i	0.587681	−	0.181276i
$341$	−3.25819	−	2.22140i	−0.176441	−	0.120296i
$342$	−0.473710	+	0.339706i	−0.0256153	+	0.0183692i
$343$	−14.7596	+	11.1872i	−0.796946	+	0.604051i
$344$	3.10175	−	5.37239i	0.167235	−	0.289660i
$345$	−7.31532	+	1.76122i	−0.393844	+	0.0948208i
$346$	1.62112	−	7.10257i	0.0871517	−	0.381836i
$347$	−18.7088	+	23.4601i	−1.00434	+	1.25941i	−0.0387761	+	0.999248i	$0.512346\pi$
$347$	−18.7088	+	23.4601i	−1.00434	+	1.25941i	−0.965566	+	0.260158i	$0.916226\pi$
$348$	9.19879	−	0.799182i	0.493107	−	0.0428407i
$349$	18.8791	+	5.82342i	1.01057	+	0.311721i	0.755463	−	0.655191i	$-0.227412\pi$
$349$	18.8791	+	5.82342i	1.01057	+	0.311721i	0.255111	+	0.966912i	$0.417888\pi$
$350$	−6.14716	+	19.3629i	−0.328579	+	1.03499i
$351$	−25.5277	−	8.98458i	−1.36257	−	0.479561i
$352$	0.0919373	+	1.22682i	0.00490027	+	0.0653896i
$353$	−9.70457	+	9.00453i	−0.516522	+	0.479263i	−0.894824	−	0.446420i	$-0.852699\pi$
$353$	−9.70457	+	9.00453i	−0.516522	+	0.479263i	0.378301	+	0.925683i	$0.376508\pi$
$354$	−5.56443	+	18.8295i	−0.295746	+	1.00078i
$355$	−32.4547	+	4.89177i	−1.72252	+	0.259628i
$356$	−2.77131	−	1.88945i	−0.146879	−	0.100140i
$357$	−1.03748	+	14.5577i	−0.0549092	+	0.770477i
$358$	18.7726	−	12.7989i	0.992161	−	0.676444i
$359$	11.5303	−	10.6986i	0.608547	−	0.564649i	−0.314538	−	0.949245i	$-0.601850\pi$
$359$	11.5303	−	10.6986i	0.608547	−	0.564649i	0.923085	+	0.384596i	$0.125659\pi$
$360$	−2.62334	−	10.3549i	−0.138262	−	0.545751i
$361$	9.48112	−	16.4218i	0.499006	−	0.864304i
$362$	5.70906			0.300062
$363$	−9.09425	+	13.6848i	−0.477325	+	0.718265i
$364$	−11.8766	−	6.98753i	−0.622501	−	0.366246i
$365$	−3.21773	−	0.484994i	−0.168424	−	0.0253858i
$366$	−1.24955	−	7.67165i	−0.0653151	−	0.401004i
$367$	0.264176	+	3.52518i	0.0137899	+	0.184013i	0.999845	+	0.0175952i	$0.00560103\pi$
$367$	0.264176	+	3.52518i	0.0137899	+	0.184013i	−0.986055	+	0.166418i	$0.946780\pi$
$368$	1.00805	−	0.687275i	0.0525481	−	0.0358267i
$369$	−0.0532646	+	1.04193i	−0.00277284	+	0.0542407i
$370$	10.7837	−	13.5223i	0.560617	−	0.702991i
$371$	9.71386	−	19.7546i	0.504319	−	1.02561i
$372$	−5.54083	−	0.349191i	−0.287279	−	0.0181047i
$373$	0.620923	−	1.07547i	0.0321502	−	0.0556858i	−0.849503	−	0.527584i	$-0.823098\pi$
$373$	0.620923	−	1.07547i	0.0321502	−	0.0556858i	0.881653	+	0.471899i	$0.156431\pi$
$374$	3.91815			0.202602
$375$	−16.4860	−	1.03897i	−0.851331	−	0.0536521i
$376$	2.41347	+	10.5741i	0.124465	+	0.545319i
$377$	25.0150	+	12.0466i	1.28834	+	0.620432i
$378$	13.6452	+	1.67610i	0.701832	+	0.0862095i
$379$	17.9610	−	8.64957i	0.922595	−	0.444298i	0.0885983	−	0.996067i	$-0.471761\pi$
$379$	17.9610	−	8.64957i	0.922595	−	0.444298i	0.833997	+	0.551769i	$0.186047\pi$
$380$	−0.431373	−	0.540925i	−0.0221290	−	0.0277489i
$381$	−2.05082	+	6.93982i	−0.105067	+	0.355538i
$382$	4.28764	+	18.7854i	0.219375	+	0.961144i
$383$	−2.95490	+	2.01462i	−0.150988	+	0.102942i	−0.636458	−	0.771311i	$-0.719601\pi$
$383$	−2.95490	+	2.01462i	−0.150988	+	0.102942i	0.485469	+	0.874254i	$0.338649\pi$
$384$	0.992605	+	1.41941i	0.0506537	+	0.0724342i
$385$	−6.60718	+	9.52208i	−0.336733	+	0.485290i
$386$	5.25430	+	23.0206i	0.267437	+	1.17172i
$387$	−11.2550	+	14.8214i	−0.572126	+	0.753415i
$388$	−2.77816	−	7.07862i	−0.141039	−	0.359363i
$389$	−17.3761	+	5.35982i	−0.881004	+	0.271754i	−0.702070	−	0.712107i	$-0.747741\pi$
$389$	−17.3761	+	5.35982i	−0.881004	+	0.271754i	−0.178933	+	0.983861i	$0.557265\pi$
$390$	9.10294	−	30.8036i	0.460945	−	1.55980i
$391$	−1.94281	−	3.36504i	−0.0982520	−	0.170177i
$392$	6.65424	+	2.17281i	0.336090	+	0.109743i
$393$	2.70318	+	8.40808i	0.136357	+	0.424131i
$394$	−19.8123	+	9.54108i	−0.998128	+	0.480673i
$395$	42.3561	+	39.3007i	2.13117	+	1.97743i
$396$	0.188430	−	3.68596i	0.00946897	−	0.185227i
$397$	9.54421	−	2.94400i	0.479010	−	0.147755i	−0.0458416	−	0.998949i	$-0.514597\pi$
$397$	9.54421	−	2.94400i	0.479010	−	0.147755i	0.524852	+	0.851194i	$0.324121\pi$
$398$	−16.9957	−	5.24247i	−0.851915	−	0.262781i
$399$	0.849908	−	0.265566i	0.0425486	−	0.0132950i
$400$	7.33731	−	2.26326i	0.366865	−	0.113163i
$401$	−12.8237	+	8.74302i	−0.640383	+	0.436606i	−0.839492	−	0.543372i	$-0.817147\pi$
$401$	−12.8237	+	8.74302i	−0.640383	+	0.436606i	0.199110	+	0.979977i	$0.436195\pi$
$402$	3.10377	+	1.74320i	0.154802	+	0.0869431i
$403$	−13.7933	−	9.40414i	−0.687095	−	0.468453i
$404$	2.47007	−	6.29364i	0.122891	−	0.313120i
$405$	3.90777	+	31.8070i	0.194179	+	1.58050i
$406$	−13.7245	−	3.25126i	−0.681134	−	0.161358i
$407$	4.93749	−	3.36632i	0.244742	−	0.166863i
$408$	4.74417	−	2.81460i	0.234872	−	0.139344i
$409$	−0.468070	−	0.586941i	−0.0231446	−	0.0290224i	0.770125	−	0.637894i	$-0.220194\pi$
$409$	−0.468070	−	0.586941i	−0.0231446	−	0.0290224i	−0.793269	+	0.608871i	$0.791623\pi$
$410$	−1.23827			−0.0611540
$411$	−6.18957	−	1.33569i	−0.305309	−	0.0658847i
$412$	−18.6284	+	2.80778i	−0.917757	+	0.138330i
$413$	17.0981	−	24.6412i	0.841340	−	1.21252i
$414$	−3.25907	+	1.66585i	−0.160174	+	0.0818720i
$415$	17.0673	+	2.57248i	0.837801	+	0.126278i
$416$	0.389210	+	5.19365i	0.0190826	+	0.254639i
$417$	25.5433	+	19.8790i	1.25086	+	0.973481i
$418$	−0.0873345	−	0.222525i	−0.00427167	−	0.0108840i
$419$	37.6660	+	5.67723i	1.84010	+	0.277351i	0.974666	−	0.223665i	$-0.0718023\pi$
$419$	37.6660	+	5.67723i	1.84010	+	0.277351i	0.865438	+	0.501016i	$0.167040\pi$
$420$	−1.15992	+	16.2758i	−0.0565982	+	0.794178i
$421$	7.92283	−	1.19417i	0.386135	−	0.0582005i	0.0468938	−	0.998900i	$-0.485068\pi$
$421$	7.92283	−	1.19417i	0.386135	−	0.0582005i	0.339241	+	0.940699i	$0.389830\pi$
$422$	−13.4793	−	23.3469i	−0.656163	−	1.13651i
$423$	−3.20058	−	32.3804i	−0.155617	−	1.57439i
$424$	−8.22747	+	1.24009i	−0.399561	+	0.0602242i
$425$	−5.44162	−	23.8413i	−0.263957	−	1.15647i
$426$	−14.7917	+	6.00874i	−0.716659	+	0.291125i
$427$	−1.86589	+	11.7255i	−0.0902969	+	0.567439i
$428$	0.530963	+	0.362004i	0.0256651	+	0.0174981i
$429$	6.14253	−	9.24312i	0.296564	−	0.446262i
$430$	−18.2505	−	12.4430i	−0.880118	−	0.600054i
$431$	−3.79222	−	1.16975i	−0.182665	−	0.0563446i	0.202073	−	0.979370i	$-0.435232\pi$
$431$	−3.79222	−	1.16975i	−0.182665	−	0.0563446i	−0.384738	+	0.923026i	$0.625708\pi$
$432$	−2.41966	−	4.59840i	−0.116416	−	0.221241i
$433$	−4.50088	+	19.7196i	−0.216299	+	0.947666i	0.743888	+	0.668305i	$0.232980\pi$
$433$	−4.50088	+	19.7196i	−0.216299	+	0.947666i	−0.960186	+	0.279361i	$0.909877\pi$
$434$	7.86863	+	3.16299i	0.377706	+	0.151828i
$435$	−0.389969	−	32.8750i	−0.0186976	−	1.57624i
$436$	−13.9143	−	12.9106i	−0.666373	−	0.618304i
$437$	−0.147807	+	0.185344i	−0.00707058	+	0.00886623i
$438$	−1.57697	+	0.137005i	−0.0753503	+	0.00654636i
$439$	11.0275	−	5.31054i	0.526312	−	0.253458i	−0.151808	−	0.988410i	$-0.548509\pi$
$439$	11.0275	−	5.31054i	0.526312	−	0.253458i	0.678120	+	0.734952i	$0.262795\pi$
$440$	4.38055			0.208835
$441$	−18.9864	−	8.97306i	−0.904115	−	0.427289i
$442$	16.5872			0.788972
$443$	29.7054	−	14.3054i	1.41135	−	0.679670i	0.435920	−	0.899986i	$-0.356423\pi$
$443$	29.7054	−	14.3054i	1.41135	−	0.679670i	0.975429	+	0.220316i	$0.0707088\pi$
$444$	3.56022	−	7.62287i	0.168960	−	0.361765i
$445$	−7.44632	+	9.33739i	−0.352989	+	0.442635i
$446$	8.60917	+	7.98814i	0.407656	+	0.378250i
$447$	17.2117	−	10.2113i	0.814084	−	0.482976i
$448$	−0.759071	−	2.53452i	−0.0358628	−	0.119745i
$449$	−2.81630	+	12.3390i	−0.132909	+	0.582314i	0.863982	+	0.503523i	$0.167963\pi$
$449$	−2.81630	+	12.3390i	−0.132909	+	0.582314i	−0.996891	+	0.0787912i	$0.974894\pi$
$450$	−22.6902	+	3.97259i	−1.06963	+	0.187270i
$451$	−0.408831	−	0.126108i	−0.0192511	−	0.00593818i
$452$	−12.2604	−	8.35899i	−0.576680	−	0.393174i
$453$	−15.6526	−	31.5404i	−0.735423	−	1.48190i
$454$	−9.06131	−	6.17789i	−0.425268	−	0.289943i
$455$	−27.9710	+	40.3110i	−1.31130	+	1.88981i
$456$	−0.265597	−	0.206701i	−0.0124377	−	0.00967965i
$457$	7.79056	+	34.1327i	0.364427	+	1.59666i	0.741816	+	0.670604i	$0.233965\pi$
$457$	7.79056	+	34.1327i	0.364427	+	1.59666i	−0.377389	+	0.926055i	$0.623178\pi$
$458$	−6.73708	+	1.01545i	−0.314803	+	0.0474489i
$459$	−15.1800	+	6.59019i	−0.708541	+	0.307604i
$460$	−2.17209	−	3.76217i	−0.101274	−	0.175412i
$461$	−39.6738	+	5.97987i	−1.84779	+	0.278510i	−0.977016	−	0.213167i	$-0.931622\pi$
$461$	−39.6738	+	5.97987i	−1.84779	+	0.278510i	−0.870778	+	0.491677i	$0.836384\pi$
$462$	−2.04051	+	5.25552i	−0.0949333	+	0.244509i
$463$	−9.43430	−	1.42199i	−0.438449	−	0.0660855i	−0.0738912	−	0.997266i	$-0.523542\pi$
$463$	−9.43430	−	1.42199i	−0.438449	−	0.0660855i	−0.364558	+	0.931181i	$0.618780\pi$
$464$	1.94761	+	4.96242i	0.0904154	+	0.230375i
$465$	−2.71424	+	19.5810i	−0.125870	+	0.908049i
$466$	1.23490	+	16.4786i	0.0572058	+	0.763359i
$467$	−5.00946	−	0.755055i	−0.231810	−	0.0349398i	0.0321098	−	0.999484i	$-0.489777\pi$
$467$	−5.00946	−	0.755055i	−0.231810	−	0.0349398i	−0.263920	+	0.964545i	$0.585015\pi$
$468$	0.797706	−	15.6043i	0.0368740	−	0.721307i
$469$	−3.66572	−	4.01632i	−0.169267	−	0.185456i
$470$	38.1880	−	5.75591i	1.76148	−	0.265500i
$471$	14.6984	−	16.2228i	0.677265	−	0.747509i
$472$	−11.3360			−0.521782
$473$	−4.75841	−	5.96686i	−0.218792	−	0.274357i
$474$	24.5061	+	13.7636i	1.12560	+	0.632184i
$475$	−1.23273	+	0.840464i	−0.0565617	+	0.0385631i
$476$	−8.23008	+	1.80752i	−0.377225	+	0.0828477i
$477$	24.9542	−	0.592105i	1.14257	−	0.0271106i
$478$	10.7516	−	27.3946i	0.491767	−	1.25300i
$479$	−19.3091	−	13.1647i	−0.882256	−	0.601512i	0.0351860	−	0.999381i	$-0.488798\pi$
$479$	−19.3091	−	13.1647i	−0.882256	−	0.601512i	−0.917442	+	0.397869i	$0.869750\pi$
$480$	5.30407	−	3.14677i	0.242096	−	0.143630i
$481$	20.9025	−	14.2511i	0.953073	−	0.649794i
$482$	21.0479	−	6.49240i	0.958704	−	0.295721i
$483$	5.52542	−	0.853481i	0.251415	−	0.0388347i
$484$	−9.06501	−	2.79618i	−0.412046	−	0.127099i
$485$	−25.8735	+	7.98091i	−1.17485	+	0.362394i
$486$	5.46963	+	14.5974i	0.248107	+	0.662150i
$487$	2.92469	+	2.71371i	0.132530	+	0.122970i	0.743653	−	0.668566i	$-0.233091\pi$
$487$	2.92469	+	2.71371i	0.132530	+	0.122970i	−0.611123	+	0.791536i	$0.709282\pi$
$488$	4.04319	−	1.94710i	0.183026	−	0.0881409i
$489$	18.2176	+	3.93131i	0.823830	+	0.177780i
$490$	9.48567	−	23.0492i	0.428519	−	1.04126i
$491$	−4.09879	−	7.09931i	−0.184976	−	0.320387i	0.758593	−	0.651565i	$-0.225887\pi$
$491$	−4.09879	−	7.09931i	−0.184976	−	0.320387i	−0.943568	+	0.331178i	$0.892554\pi$
$492$	−0.585611	+	0.140990i	−0.0264014	+	0.00635633i
$493$	16.2237	−	5.00436i	0.730681	−	0.225385i
$494$	−0.369724	−	0.942042i	−0.0166347	−	0.0423845i
$495$	−13.0377	−	1.64986i	−0.586000	−	0.0741557i
$496$	−0.713257	−	3.12498i	−0.0320262	−	0.140316i
$497$	24.3337	−	1.62283i	1.09152	−	0.0727938i
$498$	8.36446	−	0.726696i	0.374820	−	0.0325640i
$499$	20.9538	−	14.2861i	0.938022	−	0.639532i	0.00524465	−	0.999986i	$-0.498331\pi$
$499$	20.9538	−	14.2861i	0.938022	−	0.639532i	0.932777	+	0.360454i	$0.117378\pi$
$500$	−2.12219	−	9.29794i	−0.0949074	−	0.415817i
$501$	−11.2182	+	2.70088i	−0.501194	+	0.120666i
$502$	−1.71475	−	2.15023i	−0.0765329	−	0.0959692i
$503$	−0.300006	+	0.144476i	−0.0133766	+	0.00644184i	−0.440560	−	0.897723i	$-0.645220\pi$
$503$	−0.300006	+	0.144476i	−0.0133766	+	0.00644184i	0.427183	+	0.904165i	$0.359506\pi$
$504$	1.30461	+	7.82930i	0.0581121	+	0.348745i
$505$	−21.6897	−	10.4452i	−0.965179	−	0.464806i
$506$	−0.333997	−	1.46334i	−0.0148480	−	0.0650532i
$507$	13.5414	−	20.3768i	0.601396	−	0.904965i
$508$	−4.17799			−0.185369
$509$	6.87566	−	11.9090i	0.304758	−	0.527857i	−0.672449	−	0.740143i	$-0.734758\pi$
$509$	6.87566	−	11.9090i	0.304758	−	0.527857i	0.977208	+	0.212286i	$0.0680910\pi$
$510$	−8.73149	−	17.5942i	−0.386637	−	0.779083i
$511$	2.35281	+	0.557370i	0.104082	+	0.0246566i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	0.712637	+	0.715229i	0.0314637	+	0.0315781i
$514$	23.6280	−	16.1093i	1.04219	−	0.710551i
$515$	5.01283	+	66.8915i	0.220892	+	2.94759i
$516$	−10.0479	−	3.80659i	−0.442334	−	0.167576i
$517$	13.1944	+	1.98874i	0.580290	+	0.0874646i
$518$	−8.81826	+	9.34875i	−0.387452	+	0.410760i
$519$	−12.5934	−	0.793654i	−0.552789	−	0.0348375i
$520$	18.5448			0.813242
$521$	−18.0493	+	31.2623i	−0.790754	+	1.36963i	0.134746	+	0.990880i	$0.456978\pi$
$521$	−18.0493	+	31.2623i	−0.790754	+	1.36963i	−0.925500	+	0.378747i	$0.876355\pi$
$522$	−3.92758	−	15.5030i	−0.171906	−	0.678549i
$523$	−25.7918	+	23.9313i	−1.12780	+	1.04644i	−0.129301	+	0.991605i	$0.541273\pi$
$523$	−25.7918	+	23.9313i	−1.12780	+	1.04644i	−0.998495	+	0.0548362i	$0.982536\pi$
$524$	−4.21309	+	2.87243i	−0.184050	+	0.125483i
$525$	34.8129	+	5.11719i	1.51936	+	0.223333i
$526$	−8.45523	−	5.76468i	−0.368666	−	0.251352i
$527$	−10.0944	+	1.52149i	−0.439720	+	0.0662771i
$528$	2.07167	−	0.498771i	0.0901580	−	0.0217062i
$529$	15.7690	−	14.6315i	0.685610	−	0.636154i
$530$	2.21398	+	29.5434i	0.0961689	+	1.28329i
$531$	33.7389	+	4.26951i	1.46415	+	0.185281i
$532$	0.286102	+	0.427125i	0.0124041	+	0.0185182i
$533$	−1.73076	−	0.533868i	−0.0749675	−	0.0231244i
$534$	−2.45839	+	5.26373i	−0.106385	+	0.227784i
$535$	1.42666	−	1.78898i	0.0616799	−	0.0773442i
$536$	−0.457336	+	2.00372i	−0.0197539	+	0.0865475i
$537$	−27.1072	−	28.5283i	−1.16976	−	1.23109i
$538$	−3.63852	+	6.30210i	−0.156868	+	0.271703i
$539$	5.47917	−	6.64394i	0.236005	−	0.286175i
$540$	−16.9715	+	7.36794i	−0.730336	+	0.317066i
$541$	9.05499	+	6.17359i	0.389304	+	0.265423i	0.742116	−	0.670271i	$-0.233822\pi$
$541$	9.05499	+	6.17359i	0.389304	+	0.265423i	−0.352812	+	0.935694i	$0.614774\pi$
$542$	−16.6623	+	5.13965i	−0.715708	+	0.220767i
$543$	−1.58966	−	9.75977i	−0.0682189	−	0.418832i
$544$	2.33464	+	2.16622i	0.100097	+	0.0928761i
$545$	−49.5443	+	45.9704i	−2.12224	+	1.96915i
$546$	−8.63837	+	22.2489i	−0.369688	+	0.952164i
$547$	−29.0714	−	26.9743i	−1.24300	−	1.15334i	−0.982178	−	0.187953i	$-0.939815\pi$
$547$	−29.0714	−	26.9743i	−1.24300	−	1.15334i	−0.260826	−	0.965386i	$-0.583995\pi$
$548$	−0.273199	−	3.64559i	−0.0116705	−	0.155732i
$549$	−12.7669	+	4.27228i	−0.544879	+	0.182336i
$550$	0.705935	−	9.42005i	0.0301012	−	0.401672i
$551$	−0.645838	−	0.809855i	−0.0275136	−	0.0345010i
$552$	−1.45560	−	1.53191i	−0.0619544	−	0.0652025i
$553$	−28.9430	−	31.7112i	−1.23078	−	1.34850i
$554$	−1.75774	−	23.4554i	−0.0746792	−	0.996524i
$555$	−26.1193	−	14.6697i	−1.10870	−	0.622695i
$556$	−6.82721	+	17.3954i	−0.289538	+	0.737731i
$557$	−7.00026	+	12.1248i	−0.296610	+	0.513744i	−0.975358	−	0.220627i	$-0.929190\pi$
$557$	−7.00026	+	12.1248i	−0.296610	+	0.513744i	0.678748	+	0.734371i	$0.262523\pi$
$558$	0.945870	+	9.56941i	0.0400419	+	0.405106i
$559$	−20.1444	−	25.2603i	−0.852018	−	1.06840i
$560$	−9.20137	+	2.02084i	−0.388829	+	0.0853961i
$561$	−1.09099	−	6.69816i	−0.0460616	−	0.282796i
$562$	0.722794	+	1.84165i	0.0304892	+	0.0776852i
$563$	−12.8817	−	6.20352i	−0.542901	−	0.261447i	0.142272	−	0.989828i	$-0.454559\pi$
$563$	−12.8817	−	6.20352i	−0.542901	−	0.261447i	−0.685173	+	0.728380i	$0.740273\pi$
$564$	17.4047	−	7.07021i	0.732869	−	0.297709i
$565$	−32.9428	+	41.3090i	−1.38591	+	1.73788i
$566$	13.6617	−	17.1313i	0.574246	−	0.720081i
$567$	−0.934099	−	23.7934i	−0.0392285	−	0.999230i
$568$	−5.74715	−	7.20670i	−0.241145	−	0.302386i
$569$	47.0150			1.97097			0.985486	−	0.169757i	$-0.0542981\pi$
$569$	47.0150			1.97097			0.985486	+	0.169757i	$0.0542981\pi$
$570$	−0.804610	+	0.888061i	−0.0337014	+	0.0371968i
$571$	2.22738	+	2.79305i	0.0932130	+	0.116885i	0.826251	−	0.563303i	$-0.190470\pi$
$571$	2.22738	+	2.79305i	0.0932130	+	0.116885i	−0.733038	+	0.680188i	$0.761898\pi$
$572$	6.12278	+	1.88863i	0.256006	+	0.0789674i
$573$	30.9202	−	12.5605i	1.29171	−	0.524724i
$574$	0.916928	+	0.0762875i	0.0382718	+	0.00318418i
$575$	−8.44030	+	4.06464i	−0.351985	+	0.169507i
$576$	2.15013	−	2.09211i	0.0895889	−	0.0871713i
$577$	2.97246	−	39.6648i	0.123745	−	1.65127i	−0.497364	−	0.867542i	$-0.665699\pi$
$577$	2.97246	−	39.6648i	0.123745	−	1.65127i	0.621109	−	0.783724i	$-0.286682\pi$
$578$	−5.02650	+	4.66391i	−0.209075	+	0.193993i
$579$	37.8912	−	15.3923i	1.57470	−	0.639683i
$580$	18.1384	−	5.59497i	0.753157	−	0.232318i
$581$	−12.4797	−	2.95637i	−0.517743	−	0.122651i
$582$	−11.3275	+	6.72033i	−0.469540	+	0.278567i
$583$	−2.27778	+	9.97960i	−0.0943359	+	0.413313i
$584$	−0.333882	−	0.850717i	−0.0138161	−	0.0352029i
$585$	−55.1941	−	6.98457i	−2.28200	−	0.288776i
$586$	6.63052	+	4.52061i	0.273904	+	0.186745i
$587$	−10.2143	+	17.6917i	−0.421590	+	0.730216i	−0.996095	−	0.0882851i	$-0.971861\pi$
$587$	−10.2143	+	17.6917i	−0.421590	+	0.730216i	0.574505	+	0.818501i	$0.305195\pi$
$588$	1.86162	−	11.9806i	0.0767721	−	0.494071i
$589$	0.311413	+	0.539383i	0.0128315	+	0.0222249i
$590$	−3.01640	+	40.2510i	−0.124183	+	1.65711i
$591$	21.8273	+	31.2128i	0.897857	+	1.28392i
$592$	4.80315	+	0.723959i	0.197408	+	0.0297545i
$593$	−26.3740	+	8.13532i	−1.08305	+	0.334077i	−0.784381	−	0.620279i	$-0.787019\pi$
$593$	−26.3740	+	8.13532i	−1.08305	+	0.334077i	−0.298671	+	0.954356i	$0.596543\pi$
$594$	−6.35370	+	0.704214i	−0.260696	+	0.0288942i
$595$	4.22807	+	29.7037i	0.173334	+	1.21773i
$596$	8.46996	+	7.85897i	0.346943	+	0.321916i
$597$	−4.22975	+	30.5142i	−0.173112	+	1.24886i
$598$	−1.41395	−	6.19493i	−0.0578208	−	0.253330i
$599$	−23.5889	+	11.3598i	−0.963818	+	0.464150i	−0.848510	−	0.529180i	$-0.822500\pi$
$599$	−23.5889	+	11.3598i	−0.963818	+	0.464150i	−0.115308	+	0.993330i	$0.536785\pi$
$600$	−5.91213	−	11.9131i	−0.241362	−	0.486350i
$601$	−0.674208	+	8.99668i	−0.0275015	+	0.366982i	0.966426	+	0.256945i	$0.0827160\pi$
$601$	−0.674208	+	8.99668i	−0.0275015	+	0.366982i	−0.993927	+	0.110037i	$0.964903\pi$
$602$	12.7477	+	10.3383i	0.519558	+	0.421356i
$603$	2.11582	−	5.79135i	0.0861628	−	0.235842i
$604$	14.9022	−	13.8272i	0.606361	−	0.562621i
$605$	−12.3406	+	31.4433i	−0.501716	+	1.27835i
$606$	−11.4469	−	2.47021i	−0.464999	−	0.100345i
$607$	0.724104	−	1.25419i	0.0293905	−	0.0509058i	−0.850956	−	0.525237i	$-0.823977\pi$
$607$	0.724104	−	1.25419i	0.0293905	−	0.0509058i	0.880347	+	0.474331i	$0.157310\pi$
$608$	0.0709888	−	0.180876i	0.00287897	−	0.00733551i
$609$	−1.73659	+	24.3676i	−0.0703702	+	0.987425i
$610$	−5.83775	−	14.8743i	−0.236364	−	0.602244i
$611$	55.8576	+	8.41918i	2.25976	+	0.340603i
$612$	−6.13262	−	7.32656i	−0.247896	−	0.296159i
$613$	−17.7449	+	12.0983i	−0.716711	+	0.488645i	−0.865934	−	0.500158i	$-0.833275\pi$
$613$	−17.7449	+	12.0983i	−0.716711	+	0.488645i	0.149223	+	0.988804i	$0.452323\pi$
$614$	−11.4709	+	14.3841i	−0.462929	+	0.580495i
$615$	0.344792	+	2.11686i	0.0139034	+	0.0853600i
$616$	−3.24375	−	0.269877i	−0.130694	−	0.0108736i
$617$	4.98539	−	12.7026i	0.200704	−	0.511386i	−0.794716	−	0.606981i	$-0.792380\pi$
$617$	4.98539	−	12.7026i	0.200704	−	0.511386i	0.995420	+	0.0955955i	$0.0304755\pi$
$618$	9.98698	+	31.0639i	0.401735	+	1.24957i
$619$	10.1504	+	17.5810i	0.407980	+	0.706642i	0.994663	−	0.103175i	$-0.0329001\pi$
$619$	10.1504	+	17.5810i	0.407980	+	0.706642i	−0.586683	+	0.809816i	$0.699567\pi$
$620$	−11.2857	+	1.70105i	−0.453246	+	0.0683159i
$621$	3.75528	+	5.10760i	0.150694	+	0.204961i
$622$	11.9767	+	5.76766i	0.480221	+	0.231262i
$623$	6.08917	−	6.45548i	0.243957	−	0.258633i
$624$	8.77028	−	2.11151i	0.351092	−	0.0845281i
$625$	4.38426	−	0.660821i	0.175371	−	0.0264329i
$626$	8.51321	−	4.09975i	0.340256	−	0.163859i
$627$	−0.356093	+	0.211261i	−0.0142210	+	0.00843696i
$628$	11.3872	+	5.48380i	0.454400	+	0.218827i
$629$	3.44239	−	15.0821i	0.137257	−	0.601362i
$630$	28.1468	−	2.54902i	1.12140	−	0.101555i
$631$	1.78499	+	7.82054i	0.0710592	+	0.311331i	0.997950	−	0.0640009i	$-0.0203860\pi$
$631$	1.78499	+	7.82054i	0.0710592	+	0.311331i	−0.926891	+	0.375331i	$0.877529\pi$
$632$	−3.61093	+	15.8205i	−0.143635	+	0.629307i
$633$	−36.1588	+	29.5441i	−1.43718	+	1.17427i
$634$	−3.27382	+	14.3435i	−0.130020	+	0.569654i
$635$	−1.11172	+	14.8349i	−0.0441174	+	0.588705i
$636$	4.41087	+	13.7198i	0.174902	+	0.544023i
$637$	23.1957	−	28.1266i	0.919047	−	1.11442i
$638$	6.55842			0.259650
$639$	14.3908	+	23.6136i	0.569290	+	0.934140i
$640$	2.61016	+	2.42188i	0.103176	+	0.0957331i
$641$	29.3338	+	4.42136i	1.15861	+	0.174633i	0.700094	−	0.714051i	$-0.253141\pi$
$641$	29.3338	+	4.42136i	1.15861	+	0.174633i	0.458521	+	0.888684i	$0.348380\pi$
$642$	0.471010	−	1.00849i	0.0185893	−	0.0398020i
$643$	26.0531	−	24.1738i	1.02744	−	0.953321i	0.0285068	−	0.999594i	$-0.490925\pi$
$643$	26.0531	−	24.1738i	1.02744	−	0.953321i	0.998929	+	0.0462727i	$0.0147343\pi$
$644$	1.37663	+	2.91966i	0.0542468	+	0.115051i
$645$	−16.1898	+	34.6644i	−0.637473	+	1.36491i
$646$	−0.557552	−	0.268503i	−0.0219366	−	0.0105641i
$647$	−16.6267	−	5.12865i	−0.653662	−	0.201628i	−0.0498524	−	0.998757i	$-0.515875\pi$
$647$	−16.6267	−	5.12865i	−0.653662	−	0.201628i	−0.603810	+	0.797129i	$0.706351\pi$
$648$	−7.18732	+	5.41686i	−0.282345	+	0.212794i
$649$	−5.09512	+	12.9822i	−0.200001	+	0.509594i
$650$	2.98852	−	39.8791i	0.117220	−	1.56419i
$651$	3.21621	−	14.3323i	0.126053	−	0.561728i
$652$	0.804101	+	10.7300i	0.0314910	+	0.420218i
$653$	−27.0075	−	8.33070i	−1.05688	−	0.326005i	−0.282859	−	0.959161i	$-0.591283\pi$
$653$	−27.0075	−	8.33070i	−1.05688	−	0.326005i	−0.774024	+	0.633156i	$0.781759\pi$
$654$	−18.1965	+	27.3817i	−0.711540	+	1.07071i
$655$	9.07816	+	15.7238i	0.354713	+	0.614381i
$656$	−0.173882	−	0.301172i	−0.00678895	−	0.0117588i
$657$	0.673313	+	2.65771i	0.0262684	+	0.103687i
$658$	−28.6324	+	1.90951i	−1.11621	+	0.0744403i
$659$	14.9362	+	38.0568i	0.581832	+	1.48248i	0.854020	+	0.520240i	$0.174158\pi$
$659$	14.9362	+	38.0568i	0.581832	+	1.48248i	−0.272188	+	0.962244i	$0.587747\pi$
$660$	−1.21975	−	7.48866i	−0.0474786	−	0.291496i
$661$	−21.8386	−	10.5169i	−0.849424	−	0.409061i	−0.0420605	−	0.999115i	$-0.513392\pi$
$661$	−21.8386	−	10.5169i	−0.849424	−	0.409061i	−0.807364	+	0.590054i	$0.799107\pi$
$662$	−12.0328	−	5.79470i	−0.467669	−	0.225217i
$663$	−4.61863	−	28.3562i	−0.179373	−	1.10126i
$664$	1.77096	+	4.51233i	0.0687266	+	0.175112i
$665$	1.59273	−	0.902214i	0.0617634	−	0.0349864i
$666$	−14.0228	−	3.96372i	−0.543372	−	0.153591i
$667$	−3.25199	−	5.63260i	−0.125917	−	0.218095i
$668$	−3.33096	−	5.76940i	−0.128879	−	0.223225i
$669$	11.2587	−	16.9418i	0.435288	−	0.655009i
$670$	6.99296	+	2.15704i	0.270161	+	0.0833338i
$671$	−0.412578	−	5.50547i	−0.0159274	−	0.212536i
$672$	−4.12147	+	2.00338i	−0.158989	+	0.0772819i
$673$	0.886604	−	11.8309i	0.0341761	−	0.456048i	−0.953695	−	0.300774i	$-0.902755\pi$
$673$	0.886604	−	11.8309i	0.0341761	−	0.456048i	0.987871	−	0.155274i	$-0.0496260\pi$
$674$	11.1700	−	28.4606i	0.430252	−	1.09626i
$675$	13.1092	+	37.6832i	0.504574	+	1.45043i
$676$	13.4979	+	4.16355i	0.519150	+	0.160136i
$677$	−43.3600	−	20.8811i	−1.66646	−	0.802525i	−0.998286	−	0.0585207i	$-0.981362\pi$
$677$	−43.3600	−	20.8811i	−1.66646	−	0.802525i	−0.668175	−	0.744005i	$-0.732924\pi$
$678$	−10.8760	+	23.2869i	−0.417691	+	0.894329i
$679$	19.6507	−	4.31576i	0.754124	−	0.165624i
$680$	8.31289	−	7.71323i	0.318785	−	0.295789i
$681$	−8.03817	+	17.2107i	−0.308023	+	0.659516i
$682$	−3.89936	−	0.587734i	−0.149314	−	0.0225055i
$683$	−8.87793	−	8.23752i	−0.339705	−	0.315200i	0.491810	−	0.870702i	$-0.336335\pi$
$683$	−8.87793	−	8.23752i	−0.339705	−	0.315200i	−0.831515	+	0.555503i	$0.812526\pi$
$684$	−0.279405	+	0.511599i	−0.0106833	+	0.0195615i
$685$	−13.0172			−0.497360
$686$	−8.44404	+	16.4833i	−0.322395	+	0.629334i
$687$	3.61185	+	11.2344i	0.137801	+	0.428621i
$688$	0.463588	−	6.18615i	0.0176741	−	0.235845i
$689$	−9.64281	+	42.2479i	−0.367362	+	1.60952i
$690$	−5.82671	+	4.76080i	−0.221819	+	0.181241i
$691$	3.85711	−	16.8991i	0.146732	−	0.642873i	−0.847049	−	0.531515i	$-0.821623\pi$
$691$	3.85711	−	16.8991i	0.146732	−	0.642873i	0.993780	−	0.111358i	$-0.0355200\pi$
$692$	−1.62112	−	7.10257i	−0.0616255	−	0.269999i
$693$	9.55261	+	2.02493i	0.362874	+	0.0769206i
$694$	−6.67710	+	29.2543i	−0.253459	+	1.11048i
$695$	59.9497	+	28.8703i	2.27402	+	1.09511i
$696$	7.94107	−	4.71125i	0.301006	−	0.178579i
$697$	−0.997880	+	0.480554i	−0.0377974	+	0.0182023i
$698$	19.5361	−	2.94460i	0.739454	−	0.111455i
$699$	27.8268	−	6.69950i	1.05250	−	0.253398i
$700$	2.86284	+	20.1125i	0.108205	+	0.760181i
$701$	37.0718	+	17.8528i	1.40018	+	0.674292i	0.973198	−	0.229968i	$-0.0738620\pi$
$701$	37.0718	+	17.8528i	1.40018	+	0.674292i	0.426983	+	0.904259i	$0.359576\pi$
$702$	−26.8979	+	2.98124i	−1.01520	+	0.112520i
$703$	−0.933292	+	0.140671i	−0.0351998	+	0.00530551i
$704$	0.615129	+	1.06543i	0.0231835	+	0.0401551i
$705$	−20.4731	−	63.6805i	−0.771063	−	2.39835i
$706$	−4.83660	+	12.3235i	−0.182028	+	0.463799i
$707$	15.4175	+	9.07082i	0.579834	+	0.341143i
$708$	3.15646	+	19.3792i	0.118627	+	0.728313i
$709$	14.3399	−	17.9817i	0.538547	−	0.675317i	−0.435884	−	0.900003i	$-0.643564\pi$
$709$	14.3399	−	17.9817i	0.538547	−	0.675317i	0.974431	+	0.224686i	$0.0721356\pi$
$710$	−27.1183	+	18.4889i	−1.01773	+	0.693877i
$711$	16.7056	−	45.7261i	0.626510	−	1.71486i
$712$	−3.31666	−	0.499907i	−0.124297	−	0.0187348i
$713$	1.42873	+	3.64034i	0.0535062	+	0.136332i
$714$	5.38163	+	13.5662i	0.201402	+	0.507703i
$715$	8.33520	−	21.2377i	0.311719	−	0.794246i
$716$	11.3603	−	19.6765i	0.424553	−	0.735347i
$717$	−49.8255	−	10.7522i	−1.86077	−	0.401548i
$718$	5.74652	−	14.6419i	0.214458	−	0.546431i
$719$	12.5168	−	11.6139i	0.466797	−	0.433124i	−0.411377	−	0.911465i	$-0.634952\pi$
$719$	12.5168	−	11.6139i	0.466797	−	0.433124i	0.878174	+	0.478341i	$0.158762\pi$
$720$	−6.85638	−	8.19122i	−0.255522	−	0.305269i
$721$	0.409103	−	49.8412i	0.0152358	−	1.85618i
$722$	1.41705	−	18.9092i	0.0527372	−	0.703728i
$723$	−16.9596	−	34.1740i	−0.630734	−	1.27095i
$724$	5.14368	−	2.47707i	0.191164	−	0.0920595i
$725$	−9.10850	−	39.9069i	−0.338281	−	1.48211i
$726$	−2.25603	+	16.2754i	−0.0837291	+	0.604038i
$727$	22.6905	+	21.0537i	0.841545	+	0.780840i	0.977735	−	0.209843i	$-0.0672953\pi$
$727$	22.6905	+	21.0537i	0.841545	+	0.780840i	−0.136190	+	0.990683i	$0.543486\pi$
$728$	−13.7322	−	1.14250i	−0.508948	−	0.0423440i
$729$	23.4315	−	13.4150i	0.867835	−	0.496853i
$730$	−3.10950	+	0.959155i	−0.115088	+	0.0354999i
$731$	−19.5363	−	2.94463i	−0.722577	−	0.108911i
$732$	−4.45441	−	6.36976i	−0.164640	−	0.235433i
$733$	−2.69768	+	35.9980i	−0.0996410	+	1.32962i	0.693446	+	0.720509i	$0.256092\pi$
$733$	−2.69768	+	35.9980i	−0.0996410	+	1.32962i	−0.793087	+	0.609108i	$0.791527\pi$
$734$	1.76753	+	3.06146i	0.0652409	+	0.113001i
$735$	−42.0444	−	9.79802i	−1.55083	−	0.361405i
$736$	0.610022	−	1.05659i	0.0224857	−	0.0389464i
$737$	2.08913	+	1.42435i	0.0769542	+	0.0524665i
$738$	0.404087	+	0.961858i	0.0148746	+	0.0354065i
$739$	3.40366	+	8.67238i	0.125206	+	0.319019i	0.979708	−	0.200428i	$-0.0642333\pi$
$739$	3.40366	+	8.67238i	0.125206	+	0.319019i	−0.854503	+	0.519447i	$0.826138\pi$
$740$	3.84865	−	16.8620i	0.141479	−	0.619861i
$741$	−1.50749	+	0.894360i	−0.0553792	+	0.0328551i
$742$	0.180685	−	22.0130i	0.00663317	−	0.808122i
$743$	13.9699	−	4.30914i	0.512505	−	0.158087i	−0.0277063	−	0.999616i	$-0.508820\pi$
$743$	13.9699	−	4.30914i	0.512505	−	0.158087i	0.540212	+	0.841529i	$0.318344\pi$
$744$	−5.14363	+	2.08947i	−0.188575	+	0.0766036i
$745$	30.1588	−	27.9833i	1.10493	−	1.02523i
$746$	0.0928033	−	1.23837i	0.00339777	−	0.0453401i
$747$	−3.57135	−	14.0969i	−0.130669	−	0.515778i
$748$	3.53013	−	1.70002i	0.129074	−	0.0621589i
$749$	−1.16664	+	1.23682i	−0.0426281	+	0.0451925i
$750$	−15.3041	+	6.21691i	−0.558828	+	0.227010i
$751$	−10.1213	−	3.12201i	−0.369332	−	0.113924i	0.104533	−	0.994521i	$-0.466665\pi$
$751$	−10.1213	−	3.12201i	−0.369332	−	0.113924i	−0.473865	+	0.880598i	$0.657141\pi$
$752$	6.76240	+	8.47979i	0.246600	+	0.309226i
$753$	−3.19839	+	3.53012i	−0.116556	+	0.128645i
$754$	27.7646			1.01113
$755$	−45.1312	−	56.5928i	−1.64249	−	2.05962i
$756$	13.0211	−	4.41030i	0.473573	−	0.160401i
$757$	−1.75766	+	2.20404i	−0.0638833	+	0.0801072i	−0.812746	−	0.582617i	$-0.802029\pi$
$757$	−1.75766	+	2.20404i	−0.0638833	+	0.0801072i	0.748863	+	0.662725i	$0.230600\pi$
$758$	12.4294	−	15.5860i	0.451456	−	0.566108i
$759$	−2.40861	+	0.978435i	−0.0874269	+	0.0355149i
$760$	−0.623353	−	0.300191i	−0.0226114	−	0.0108891i
$761$	12.6192	+	32.1532i	0.457445	+	1.16555i	0.954600	+	0.297890i	$0.0962827\pi$
$761$	12.6192	+	32.1532i	0.457445	+	1.16555i	−0.497155	+	0.867662i	$0.665622\pi$
$762$	1.16334	+	7.14238i	0.0421435	+	0.258741i
$763$	39.5191	−	30.9882i	1.43069	−	1.12185i
$764$	12.0137	+	15.0647i	0.434641	+	0.545022i
$765$	−27.6464	+	19.8257i	−0.999558	+	0.716800i
$766$	−1.78816	+	3.09719i	−0.0646090	+	0.111906i
$767$	−21.5698	+	54.9590i	−0.778842	+	1.98446i
$768$	1.51017	+	0.848172i	0.0544934	+	0.0306058i
$769$	−0.754109	−	10.0629i	−0.0271939	−	0.362877i	−0.994156	−	0.107956i	$-0.965570\pi$
$769$	−0.754109	−	10.0629i	−0.0271939	−	0.362877i	0.966962	−	0.254921i	$-0.0820495\pi$
$770$	−1.82139	+	11.4458i	−0.0656382	+	0.412480i
$771$	−34.1183	−	35.9070i	−1.22874	−	1.29316i
$772$	14.7222	+	18.4611i	0.529864	+	0.664429i
$773$	2.86698	−	38.2572i	0.103118	−	1.37602i	−0.670285	−	0.742103i	$-0.733828\pi$
$773$	2.86698	−	38.2572i	0.103118	−	1.37602i	0.773404	−	0.633914i	$-0.218553\pi$
$774$	−3.70967	+	18.2370i	−0.133341	+	0.655516i
$775$	1.83926	+	24.5432i	0.0660682	+	0.881619i
$776$	−5.57433	−	5.17222i	−0.200107	−	0.185672i
$777$	18.4373	+	12.4719i	0.661435	+	0.447427i
$778$	−13.3298	+	12.3682i	−0.477896	+	0.443423i
$779$	0.0495348	+	0.0459615i	0.00177477	+	0.00164674i
$780$	−5.16371	−	31.7027i	−0.184890	−	1.13514i
$781$	−10.8364	+	3.34257i	−0.387755	+	0.119607i
$782$	−3.21045	−	2.18884i	−0.114805	−	0.0782729i
$783$	−25.4091	+	11.0310i	−0.908049	+	0.394217i
$784$	6.93801	−	0.929533i	0.247786	−	0.0331976i
$785$	22.5015	−	38.9737i	0.803112	−	1.39103i
$786$	6.08361	+	6.40255i	0.216995	+	0.228371i
$787$	1.91752	−	8.40122i	0.0683523	−	0.299471i	−0.929184	−	0.369616i	$-0.879489\pi$
$787$	1.91752	−	8.40122i	0.0683523	−	0.299471i	0.997537	+	0.0701453i	$0.0223463\pi$
$788$	−13.7105	+	17.1924i	−0.488417	+	0.612455i
$789$	−7.50053	+	16.0596i	−0.267026	+	0.571736i
$790$	55.2135	+	17.0311i	1.96441	+	0.605939i
$791$	26.9387	−	28.5593i	0.957831	−	1.01545i
$792$	−1.42951	−	3.40269i	−0.0507954	−	0.120909i
$793$	−1.74662	−	23.3070i	−0.0620242	−	0.827656i
$794$	7.32168	−	6.79353i	0.259837	−	0.241093i
$795$	49.8887	−	12.0111i	1.76937	−	0.425989i
$796$	−17.5872	+	2.65084i	−0.623361	+	0.0939566i
$797$	−20.3002	−	13.8404i	−0.719069	−	0.490253i	0.147656	−	0.989039i	$-0.452827\pi$
$797$	−20.3002	−	13.8404i	−0.719069	−	0.490253i	−0.866725	+	0.498786i	$0.833779\pi$
$798$	0.650516	−	0.608028i	0.0230280	−	0.0215240i
$799$	28.5405	−	19.4586i	1.00969	−	0.688395i
$800$	5.62869	−	5.22266i	0.199004	−	0.184649i
$801$	9.68299	+	2.73702i	0.342132	+	0.0967078i
$802$	−7.76026	+	13.4412i	−0.274024	+	0.474624i
$803$	−1.12432			−0.0396765
$804$	3.55275	+	0.223899i	0.125296	+	0.00789631i
$805$	10.7332	−	4.11114i	0.378297	−	0.144899i
$806$	−16.5077	−	2.48813i	−0.581458	−	0.0876406i
$807$	11.7867	+	4.46534i	0.414912	+	0.157187i
$808$	−0.505250	−	6.74210i	−0.0177746	−	0.237186i
$809$	−10.5942	+	7.22297i	−0.372471	+	0.253946i	−0.735059	−	0.678003i	$-0.762846\pi$
$809$	−10.5942	+	7.22297i	−0.372471	+	0.253946i	0.362588	+	0.931949i	$0.381893\pi$
$810$	17.3213	+	26.9616i	0.608608	+	0.947333i
$811$	9.53511	−	11.9567i	0.334823	−	0.419855i	−0.585709	−	0.810521i	$-0.699184\pi$
$811$	9.53511	−	11.9567i	0.334823	−	0.419855i	0.920532	+	0.390666i	$0.127755\pi$
$812$	−13.7760	+	3.02554i	−0.483443	+	0.106176i
$813$	13.4259	+	27.0535i	0.470867	+	0.948808i
$814$	2.98793	−	5.17525i	0.104727	−	0.181392i
$815$	38.3131			1.34205
$816$	3.05314	−	4.59429i	0.106881	−	0.160832i
$817$	0.268225	+	1.17517i	0.00938399	+	0.0411140i
$818$	−0.676380	−	0.325728i	−0.0236491	−	0.0113888i
$819$	40.4403	+	8.57238i	1.41310	+	0.299543i
$820$	−1.11565	+	0.537267i	−0.0389601	+	0.0187622i
$821$	−12.0781	−	15.1454i	−0.421528	−	0.528579i	0.525043	−	0.851076i	$-0.324049\pi$
$821$	−12.0781	−	15.1454i	−0.421528	−	0.528579i	−0.946571	+	0.322497i	$0.895478\pi$
$822$	−6.15614	+	1.48214i	−0.214720	+	0.0516955i
$823$	−5.49017	−	24.0540i	−0.191375	−	0.838471i	−0.975873	−	0.218339i	$-0.929936\pi$
$823$	−5.49017	−	24.0540i	−0.191375	−	0.838471i	0.784498	−	0.620132i	$-0.212921\pi$
$824$	−15.5654	+	10.6123i	−0.542246	+	0.369697i
$825$	−16.3003	+	1.41616i	−0.567505	+	0.0493043i
$826$	4.71338	−	29.6196i	0.164000	−	1.03060i
$827$	−0.486340	−	2.13080i	−0.0169117	−	0.0740951i	0.965768	−	0.259408i	$-0.0835273\pi$
$827$	−0.486340	−	2.13080i	−0.0169117	−	0.0740951i	−0.982680	+	0.185313i	$0.940670\pi$
$828$	−2.21353	+	2.91493i	−0.0769256	+	0.101301i
$829$	−3.87743	−	9.87954i	−0.134669	−	0.343131i	0.847592	−	0.530648i	$-0.178051\pi$
$829$	−3.87743	−	9.87954i	−0.134669	−	0.343131i	−0.982261	+	0.187517i	$0.939956\pi$
$830$	16.4933	−	5.08750i	0.572490	−	0.176590i
$831$	−39.6081	+	9.53595i	−1.37399	+	0.330798i
$832$	2.60410	+	4.51044i	0.0902811	+	0.156371i
$833$	−1.30086	−	22.2557i	−0.0450720	−	0.771115i
$834$	31.6389	+	6.82758i	1.09557	+	0.236420i
$835$	−21.3719	+	10.2921i	−0.739604	+	0.356174i
$836$	−0.175235	−	0.162595i	−0.00606065	−	0.00562346i
$837$	16.0958	−	4.28155i	0.556351	−	0.147992i
$838$	36.3991	−	11.2276i	1.25739	−	0.387853i
$839$	−18.3280	−	5.65344i	−0.632753	−	0.195178i	−0.0382453	−	0.999268i	$-0.512177\pi$
$839$	−18.3280	−	5.65344i	−0.632753	−	0.195178i	−0.594508	+	0.804090i	$0.702653\pi$
$840$	6.01676	+	15.1673i	0.207598	+	0.523320i
$841$	−0.555352	+	0.171303i	−0.0191501	+	0.00590701i
$842$	6.62009	−	4.51350i	0.228143	−	0.155546i
$843$	2.94708	−	1.74843i	0.101503	−	0.0602192i
$844$	−22.2743	−	15.1864i	−0.766713	−	0.522736i
$845$	18.3753	−	46.8194i	0.632128	−	1.61064i
$846$	−16.9329	−	27.7850i	−0.582166	−	0.955269i
$847$	11.0752	−	22.5231i	0.380549	−	0.773903i
$848$	−6.87464	+	4.68705i	−0.236076	+	0.160954i
$849$	−33.0904	−	18.5849i	−1.13566	−	0.637833i
$850$	−15.2471	−	19.1192i	−0.522970	−	0.655784i
$851$	−5.92625			−0.203149
$852$	−10.7198	+	11.8316i	−0.367253	+	0.405343i
$853$	5.48788	−	0.827165i	0.187901	−	0.0283216i	−0.0544173	−	0.998518i	$-0.517330\pi$
$853$	5.48788	−	0.827165i	0.187901	−	0.0283216i	0.242319	+	0.970197i	$0.422092\pi$
$854$	3.40641	+	11.3739i	0.116565	+	0.389208i
$855$	1.74220	+	1.12822i	0.0595820	+	0.0385844i
$856$	0.635449	+	0.0957785i	0.0217192	+	0.00327364i
$857$	−0.755958	−	10.0876i	−0.0258230	−	0.344585i	−0.995119	−	0.0986860i	$-0.968536\pi$
$857$	−0.755958	−	10.0876i	−0.0258230	−	0.344585i	0.969296	−	0.245899i	$-0.0790830\pi$
$858$	1.52379	−	10.9929i	0.0520213	−	0.375292i
$859$	4.43780	+	11.3073i	0.151416	+	0.385801i	0.986375	−	0.164510i	$-0.0526043\pi$
$859$	4.43780	+	11.3073i	0.151416	+	0.385801i	−0.834960	+	0.550311i	$0.814509\pi$
$860$	−21.8420	−	3.29215i	−0.744805	−	0.112261i
$861$	−0.124899	−	1.58875i	−0.00425656	−	0.0541445i
$862$	−3.92421	+	0.591479i	−0.133659	+	0.0201459i
$863$	10.0885	+	17.4739i	0.343418	+	0.594817i	0.985065	−	0.172183i	$-0.0550819\pi$
$863$	10.0885	+	17.4739i	0.343418	+	0.594817i	−0.641647	+	0.767000i	$0.721749\pi$
$864$	−4.17521	−	3.09316i	−0.142043	−	0.105232i
$865$	−25.6506	+	3.86621i	−0.872147	+	0.131455i
$866$	4.50088	+	19.7196i	0.152946	+	0.670101i
$867$	9.37266	+	7.29427i	0.318312	+	0.247726i
$868$	8.46176	−	0.564319i	0.287211	−	0.0191542i
$869$	16.4949	+	11.2460i	0.559552	+	0.381496i
$870$	−14.6153	−	29.4502i	−0.495505	−	0.998454i
$871$	8.84419	+	6.02987i	0.299674	+	0.204314i
$872$	−18.1380	−	5.59483i	−0.614230	−	0.189465i
$873$	14.6427	+	17.4934i	0.495579	+	0.592061i
$874$	−0.0527518	+	0.231121i	−0.00178436	+	0.00781778i
$875$	25.1768	−	1.67905i	0.851130	−	0.0567623i
$876$	−1.36135	+	0.807657i	−0.0459958	+	0.0272882i
$877$	−14.8606	−	13.7886i	−0.501806	−	0.465608i	0.388188	−	0.921580i	$-0.373101\pi$
$877$	−14.8606	−	13.7886i	−0.501806	−	0.465608i	−0.889994	+	0.455972i	$0.849292\pi$
$878$	7.63124	−	9.56927i	0.257542	−	0.322947i
$879$	5.88185	−	12.5938i	0.198390	−	0.424777i
$880$	3.94674	−	1.90065i	0.133045	−	0.0640709i
$881$	40.8639			1.37674			0.688370	−	0.725360i	$-0.258327\pi$
$881$	40.8639			1.37674			0.688370	+	0.725360i	$0.258327\pi$
$882$	−20.9994	+	0.153453i	−0.707088	+	0.00516703i
$883$	−32.0625			−1.07899			−0.539495	−	0.841989i	$-0.681385\pi$
$883$	−32.0625			−1.07899			−0.539495	+	0.841989i	$0.681385\pi$
$884$	14.9445	−	7.19691i	0.502639	−	0.242058i
$885$	69.6499	−	6.05112i	2.34126	−	0.203406i
$886$	20.5568	−	25.7774i	0.690619	−	0.866009i
$887$	−14.0032	−	12.9931i	−0.470182	−	0.436265i	0.409155	−	0.912465i	$-0.365824\pi$
$887$	−14.0032	−	12.9931i	−0.470182	−	0.436265i	−0.879337	+	0.476199i	$0.842014\pi$
$888$	−0.0997927	−	8.41268i	−0.00334882	−	0.282311i
$889$	1.73716	−	10.9166i	0.0582626	−	0.366130i
$890$	−2.65756	+	11.6435i	−0.0890816	+	0.390292i
$891$	2.97303	+	10.6657i	0.0996003	+	0.357315i
$892$	11.2225	+	3.46169i	0.375758	+	0.115906i
$893$	−1.74128	−	1.18718i	−0.0582697	−	0.0397276i
$894$	11.0767	−	16.6679i	0.370459	−	0.557457i
$895$	−66.8431	−	45.5729i	−2.23432	−	1.52333i
$896$	−1.78359	−	1.95418i	−0.0595855	−	0.0652845i
$897$	−10.1967	+	4.14213i	−0.340457	+	0.138302i
$898$	2.81630	+	12.3390i	0.0939812	+	0.411758i
$899$	−16.8966	+	2.54676i	−0.563534	+	0.0849391i
$900$	−18.7195	+	13.4241i	−0.623983	+	0.447469i
$901$	13.2495	+	22.9488i	0.441404	+	0.764534i
$902$	−0.423060	+	0.0637661i	−0.0140864	+	0.00212318i
$903$	14.1240	−	24.6711i	0.470016	−	0.821004i
$904$	−14.6731	−	2.21161i	−0.488018	−	0.0735569i
$905$	−7.42670	−	18.9229i	−0.246872	−	0.629019i
$906$	−27.7874	−	21.6255i	−0.923173	−	0.718459i
$907$	−2.57706	−	34.3885i	−0.0855698	−	1.14185i	−0.860379	−	0.509655i	$-0.829773\pi$
$907$	−2.57706	−	34.3885i	−0.0855698	−	1.14185i	0.774809	−	0.632195i	$-0.217846\pi$
$908$	−10.8444	−	1.63454i	−0.359886	−	0.0542440i
$909$	−1.03554	+	20.2566i	−0.0343466	+	0.671868i
$910$	−7.71071	+	48.4552i	−0.255607	+	1.60627i
$911$	40.4737	−	6.10042i	1.34095	−	0.202116i	0.560927	−	0.827865i	$-0.310445\pi$
$911$	40.4737	−	6.10042i	1.34095	−	0.202116i	0.780024	+	0.625749i	$0.215207\pi$
$912$	−0.328979	−	0.0709927i	−0.0108936	−	0.00235080i
$913$	5.96357			0.197365
$914$	21.8287	+	27.3723i	0.722028	+	0.905394i
$915$	−23.8025	+	14.1215i	−0.786887	+	0.466841i
$916$	−5.62931	+	3.83800i	−0.185998	+	0.126811i
$917$	−5.75356	−	12.2026i	−0.189999	−	0.402965i
$918$	−10.8173	+	12.5239i	−0.357025	+	0.413350i
$919$	15.6001	−	39.7485i	0.514601	−	1.31118i	−0.403552	−	0.914957i	$-0.632224\pi$
$919$	15.6001	−	39.7485i	0.514601	−	1.31118i	0.918153	−	0.396226i	$-0.129680\pi$
$920$	−3.58933	−	2.44717i	−0.118337	−	0.0806807i
$921$	27.7840	+	15.6046i	0.915513	+	0.514190i
$922$	−33.1503	+	22.6015i	−1.09175	+	0.744341i
$923$	−45.8749	+	14.1505i	−1.50999	+	0.465771i
$924$	0.441848	+	5.62041i	0.0145357	+	0.184898i
$925$	−35.6403	−	10.9936i	−1.17185	−	0.361466i
$926$	−9.11699	+	2.81222i	−0.299603	+	0.0924152i
$927$	50.3236	−	25.7226i	1.65285	−	0.844840i
$928$	3.90785	+	3.62595i	0.128281	+	0.119028i
$929$	43.0118	−	20.7134i	1.41117	−	0.679584i	0.435778	−	0.900054i	$-0.356473\pi$
$929$	43.0118	−	20.7134i	1.41117	−	0.679584i	0.975394	+	0.220470i	$0.0707591\pi$
$930$	6.05045	+	18.8196i	0.198402	+	0.617118i
$931$	−1.23498	+	0.569955i	−0.0404749	+	0.0186795i
$932$	8.26243	+	14.3109i	0.270645	+	0.468770i
$933$	6.52510	−	22.0804i	0.213622	−	0.722879i
$934$	−4.84097	+	1.49324i	−0.158402	+	0.0488604i
$935$	−5.09697	−	12.9869i	−0.166689	−	0.424716i
$936$	−6.05172	−	14.4051i	−0.197807	−	0.470844i
$937$	10.2577	+	44.9420i	0.335105	+	1.46819i	0.809104	+	0.587665i	$0.199953\pi$
$937$	10.2577	+	44.9420i	0.335105	+	1.46819i	−0.473999	+	0.880525i	$0.657190\pi$
$938$	−5.04531	−	2.02809i	−0.164735	−	0.0662193i
$939$	−9.37908	−	13.4120i	−0.306075	−	0.437683i
$940$	31.9088	−	21.7550i	1.04075	−	0.709571i
$941$	−1.55281	−	6.80332i	−0.0506203	−	0.221782i	0.943291	−	0.331968i	$-0.107713\pi$
$941$	−1.55281	−	6.80332i	−0.0506203	−	0.221782i	−0.993911	+	0.110186i	$0.964855\pi$
$942$	6.20395	−	20.9937i	0.202136	−	0.684010i
$943$	0.264539	+	0.331721i	0.00861456	+	0.0108023i
$944$	−10.2134	+	4.91851i	−0.332417	+	0.160084i
$945$	−12.1950	−	47.4079i	−0.396702	−	1.54218i
$946$	−6.87611	−	3.31136i	−0.223562	−	0.107662i
$947$	9.85243	+	43.1663i	0.320161	+	1.40272i	0.837266	+	0.546795i	$0.184152\pi$
$947$	9.85243	+	43.1663i	0.320161	+	1.40272i	−0.517105	+	0.855922i	$0.672990\pi$
$948$	28.0510	+	1.76781i	0.911054	+	0.0574159i
$949$	−4.75974			−0.154508
$950$	−0.745992	+	1.29210i	−0.0242032	+	0.0419211i
$951$	25.4322	+	1.60277i	0.824695	+	0.0519735i
$952$	−6.63079	+	5.19942i	−0.214905	+	0.168514i
$953$	−4.09462	+	5.13449i	−0.132638	+	0.166322i	−0.843715	−	0.536791i	$-0.819636\pi$
$953$	−4.09462	+	5.13449i	−0.132638	+	0.166322i	0.711077	+	0.703114i	$0.248208\pi$
$954$	22.2260	−	11.3607i	0.719595	−	0.367816i
$955$	56.6873	−	38.6488i	1.83436	−	1.25064i
$956$	−2.19923	−	29.3467i	−0.0711282	−	0.949139i
$957$	−1.82616	−	11.2118i	−0.0590315	−	0.362425i
$958$	−23.1089	−	3.48310i	−0.746614	−	0.112534i
$959$	9.63906	+	0.801959i	0.311261	+	0.0258966i
$960$	3.41347	−	5.13649i	0.110169	−	0.165780i
$961$	−20.7257			−0.668572
$962$	12.6492	−	21.9091i	0.407826	−	0.706376i
$963$	−1.85519	−	0.524393i	−0.0597826	−	0.0168983i
$964$	16.1465	−	14.9818i	0.520044	−	0.482531i
$965$	69.4676	−	47.3622i	2.23624	−	1.52464i
$966$	4.60792	−	3.16635i	0.148257	−	0.101876i
$967$	−16.9346	−	11.5458i	−0.544579	−	0.371288i	0.259562	−	0.965727i	$-0.416422\pi$
$967$	−16.9346	−	11.5458i	−0.544579	−	0.371288i	−0.804141	+	0.594439i	$0.797374\pi$
$968$	−9.38051	+	1.41388i	−0.301501	+	0.0454440i
$969$	−0.303764	+	1.02791i	−0.00975830	+	0.0330213i
$970$	−19.8484	+	18.4166i	−0.637294	+	0.591322i
$971$	2.92938	+	39.0899i	0.0940084	+	1.25446i	0.822247	+	0.569131i	$0.192720\pi$
$971$	2.92938	+	39.0899i	0.0940084	+	1.25446i	−0.728238	+	0.685324i	$0.759661\pi$
$972$	11.2615	+	10.7786i	0.361214	+	0.345723i
$973$	−42.6134	−	25.0715i	−1.36612	−	0.803755i
$974$	3.81249	+	1.17600i	0.122160	+	0.0376814i
$975$	−69.0063	+	5.99521i	−2.20997	+	0.192000i
$976$	2.79797	−	3.50855i	0.0895609	−	0.112306i
$977$	11.3969	−	49.9329i	0.364618	−	1.59750i	−0.376695	−	0.926337i	$-0.622940\pi$
$977$	11.3969	−	49.9329i	0.364618	−	1.59750i	0.741313	−	0.671159i	$-0.234203\pi$
$978$	18.1192	−	4.36234i	0.579390	−	0.139492i
$979$	−2.06322	+	3.57360i	−0.0659408	+	0.114213i
$980$	−1.45438	−	24.8823i	−0.0464584	−	0.794836i
$981$	51.8763	+	23.4831i	1.65628	+	0.749757i
$982$	−6.77316	−	4.61786i	−0.216140	−	0.147362i
$983$	3.01090	−	0.928741i	0.0960329	−	0.0296222i	−0.246366	−	0.969177i	$-0.579237\pi$
$983$	3.01090	−	0.928741i	0.0960329	−	0.0296222i	0.342399	+	0.939555i	$0.388760\pi$
$984$	−0.466444	+	0.381115i	−0.0148697	+	0.0121495i
$985$	57.3974	+	53.2570i	1.82883	+	1.69691i
$986$	12.4458	−	11.5480i	0.396354	−	0.367763i
$987$	11.2369	+	48.4160i	0.357674	+	1.54110i
$988$	−0.741847	−	0.688333i	−0.0236013	−	0.0218988i
$989$	0.565598	+	7.54738i	0.0179850	+	0.239993i
$990$	−12.4624	+	4.17037i	−0.396081	+	0.132543i
$991$	3.52819	−	47.0804i	0.112077	−	1.49556i	−0.603691	−	0.797218i	$-0.706304\pi$
$991$	3.52819	−	47.0804i	0.112077	−	1.49556i	0.715768	−	0.698339i	$-0.246077\pi$
$992$	−1.99850	−	2.50604i	−0.0634525	−	0.0795669i
$993$	−6.55568	+	22.1839i	−0.208038	+	0.703984i
$994$	21.2198	−	12.0201i	0.673052	−	0.381255i
$995$	4.73263	+	63.1526i	0.150034	+	2.00207i
$996$	7.22082	−	4.28393i	0.228800	−	0.135742i
$997$	10.0458	−	25.5964i	0.318155	−	0.810646i	−0.678920	−	0.734213i	$-0.737552\pi$
$997$	10.0458	−	25.5964i	0.318155	−	0.810646i	0.997075	−	0.0764334i	$-0.0243533\pi$
$998$	12.6802	−	21.9628i	0.401386	−	0.695221i
$999$	−2.87148	+	25.0760i	−0.0908497	+	0.793368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bb.b.151.10	yes	336
9.4	even	3		882.2.y.a.445.5	yes	336
49.37	even	21		882.2.y.a.331.5	✓	336
441.184	even	21	inner	882.2.bb.b.625.10	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.y.a.331.5	✓	336	49.37	even	21
882.2.y.a.445.5	yes	336	9.4	even	3
882.2.bb.b.151.10	yes	336	1.1	even	1	trivial
882.2.bb.b.625.10	yes	336	441.184	even	21	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(-0.992605 - 1.41941i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.61016 - 2.42188i) q^{5} +(-1.51017 - 0.848172i) q^{6} +(1.78359 + 1.95418i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-1.02947 + 2.81783i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 0.433884i) q^{2} +(-0.992605 - 1.41941i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.61016 - 2.42188i) q^{5} +(-1.51017 - 0.848172i) q^{6} +(1.78359 + 1.95418i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-1.02947 + 2.81783i) q^{9} +(-3.40249 - 1.04953i) q^{10} +(-1.01649 - 0.693029i) q^{11} +(-1.72862 - 0.108940i) q^{12} +(-4.30322 - 2.93389i) q^{13} +(2.45484 + 0.986784i) q^{14} +(-0.846785 + 6.10887i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-3.14924 + 0.474672i) q^{17} +(0.295091 + 2.98545i) q^{18} +(0.0971541 + 0.168276i) q^{19} +(-3.52091 + 0.530692i) q^{20} +(1.00339 - 4.47138i) q^{21} +(-1.21652 - 0.183360i) q^{22} +(0.445732 + 1.13571i) q^{23} +(-1.60470 + 0.651869i) q^{24} +(0.573810 + 7.65697i) q^{25} +(-5.15004 - 0.776243i) q^{26} +(5.02153 - 1.33575i) q^{27} +(2.63989 - 0.176055i) q^{28} +(-5.27139 + 0.794534i) q^{29} +(1.88761 + 5.87131i) q^{30} +3.20535 q^{31} +(-0.623490 - 0.781831i) q^{32} +(0.0252750 + 2.13072i) q^{33} +(-2.63142 + 1.79407i) q^{34} +(0.0773235 - 9.42035i) q^{35} +(1.56121 + 2.56176i) q^{36} +(-1.77461 + 4.52163i) q^{37} +(0.160545 + 0.109458i) q^{38} +(0.107000 + 9.02025i) q^{39} +(-2.94197 + 2.00580i) q^{40} +(0.332314 - 0.102505i) q^{41} +(-1.03604 - 4.46393i) q^{42} +(5.92789 + 1.82851i) q^{43} +(-1.17560 + 0.362625i) q^{44} +(9.51153 - 4.86175i) q^{45} +(0.894355 + 0.829841i) q^{46} +(-9.77196 + 4.70593i) q^{47} +(-1.16295 + 1.28357i) q^{48} +(-0.637625 + 6.97090i) q^{49} +(3.83922 + 6.64972i) q^{50} +(3.79971 + 3.99892i) q^{51} +(-4.97682 + 1.53515i) q^{52} +(-3.03978 - 7.74524i) q^{53} +(3.94468 - 3.38223i) q^{54} +(0.974765 + 4.27072i) q^{55} +(2.30207 - 1.30402i) q^{56} +(0.142417 - 0.304933i) q^{57} +(-4.40462 + 3.00302i) q^{58} +(-2.52250 - 11.0518i) q^{59} +(4.24814 + 4.47086i) q^{60} +(2.79797 + 3.50855i) q^{61} +(2.88792 - 1.39075i) q^{62} +(-7.34270 + 3.01409i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(4.12660 + 18.0798i) q^{65} +(0.947257 + 1.90875i) q^{66} -2.05525 q^{67} +(-1.59241 + 2.75813i) q^{68} +(1.16960 - 1.75999i) q^{69} +(-4.01767 - 8.52100i) q^{70} +(5.74715 - 7.20670i) q^{71} +(2.51811 + 1.63069i) q^{72} +(0.755092 - 0.514813i) q^{73} +(0.362995 + 4.84383i) q^{74} +(10.2988 - 8.41482i) q^{75} +(0.192138 + 0.0289601i) q^{76} +(-0.458692 - 3.22248i) q^{77} +(4.01014 + 8.08054i) q^{78} -16.2274 q^{79} +(-1.78034 + 3.08364i) q^{80} +(-6.88038 - 5.80176i) q^{81} +(0.254929 - 0.236539i) q^{82} +(-4.00512 + 2.73065i) q^{83} +(-2.87026 - 3.57234i) q^{84} +(9.36964 + 6.38811i) q^{85} +(6.13421 - 0.924584i) q^{86} +(6.36018 + 6.69362i) q^{87} +(-0.901843 + 0.836788i) q^{88} +(-0.250654 - 3.34475i) q^{89} +(6.46016 - 8.50719i) q^{90} +(-1.94184 - 13.6421i) q^{91} +(1.16584 + 0.359614i) q^{92} +(-3.18164 - 4.54972i) q^{93} +(-6.76240 + 8.47979i) q^{94} +(0.153955 - 0.674523i) q^{95} +(-0.490863 + 1.66104i) q^{96} +(3.80214 - 6.58550i) q^{97} +(2.45008 + 6.55722i) q^{98} +(2.99928 - 2.15084i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9}+O(q^{10}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9} - 2 q^{10} - 2 q^{12} + 19 q^{13} - 2 q^{14} + q^{15} - 56 q^{16} + 7 q^{17} + 2 q^{18} + 38 q^{19} + 2 q^{20} + 4 q^{21} - 42 q^{23} + 2 q^{24} + 24 q^{25} + 9 q^{26} + 35 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 88 q^{31} + 56 q^{32} + 26 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} + 11 q^{38} - 60 q^{39} - 2 q^{40} + 3 q^{41} - 53 q^{42} + q^{43} + 108 q^{45} - 42 q^{46} + 3 q^{47} - 2 q^{48} + 70 q^{49} + 172 q^{50} + 13 q^{51} + 5 q^{52} - 78 q^{53} + 14 q^{54} + 23 q^{55} - 2 q^{56} - 30 q^{57} + 38 q^{58} - 28 q^{59} + q^{60} - 37 q^{61} - 24 q^{62} + 26 q^{63} - 56 q^{64} - 14 q^{65} + 2 q^{66} - 58 q^{67} - 21 q^{68} + 19 q^{69} + 44 q^{70} + 7 q^{71} + 2 q^{72} - 8 q^{73} + 4 q^{74} + q^{75} - 4 q^{76} - 13 q^{77} + 4 q^{78} + 18 q^{79} - 12 q^{80} - 87 q^{81} - 3 q^{82} + 185 q^{83} - 17 q^{84} - 159 q^{85} - q^{86} - 132 q^{87} + 47 q^{89} + 60 q^{90} + 45 q^{91} - 21 q^{92} + 53 q^{93} + 18 q^{94} + 26 q^{95} + 2 q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9 - 2 * q^10 - 2 * q^12 + 19 * q^13 - 2 * q^14 + q^15 - 56 * q^16 + 7 * q^17 + 2 * q^18 + 38 * q^19 + 2 * q^20 + 4 * q^21 - 42 * q^23 + 2 * q^24 + 24 * q^25 + 9 * q^26 + 35 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 88 * q^31 + 56 * q^32 + 26 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 + 11 * q^38 - 60 * q^39 - 2 * q^40 + 3 * q^41 - 53 * q^42 + q^43 + 108 * q^45 - 42 * q^46 + 3 * q^47 - 2 * q^48 + 70 * q^49 + 172 * q^50 + 13 * q^51 + 5 * q^52 - 78 * q^53 + 14 * q^54 + 23 * q^55 - 2 * q^56 - 30 * q^57 + 38 * q^58 - 28 * q^59 + q^60 - 37 * q^61 - 24 * q^62 + 26 * q^63 - 56 * q^64 - 14 * q^65 + 2 * q^66 - 58 * q^67 - 21 * q^68 + 19 * q^69 + 44 * q^70 + 7 * q^71 + 2 * q^72 - 8 * q^73 + 4 * q^74 + q^75 - 4 * q^76 - 13 * q^77 + 4 * q^78 + 18 * q^79 - 12 * q^80 - 87 * q^81 - 3 * q^82 + 185 * q^83 - 17 * q^84 - 159 * q^85 - q^86 - 132 * q^87 + 47 * q^89 + 60 * q^90 + 45 * q^91 - 21 * q^92 + 53 * q^93 + 18 * q^94 + 26 * q^95 + 2 * q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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