LMFDB - Embedded newform 378.2.u.d.337.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			337.5
Character	$\chi$	$=$	378.337
Dual form			378.2.u.d.295.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(1.58642 - 0.695186i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.532238 + 0.446601i) q^{5} +(0.960103 + 1.44160i) q^{6} +(0.939693 + 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.03343 - 2.20571i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(1.58642 - 0.695186i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.532238 + 0.446601i) q^{5} +(0.960103 + 1.44160i) q^{6} +(0.939693 + 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.03343 - 2.20571i) q^{9} +(-0.347394 + 0.601703i) q^{10} +(3.27840 - 2.75090i) q^{11} +(-1.25298 + 1.19585i) q^{12} +(-0.0180917 + 0.102603i) q^{13} +(-0.173648 + 0.984808i) q^{14} +(1.15482 + 0.338490i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-2.97610 + 5.15476i) q^{17} +(2.52530 + 1.61952i) q^{18} +(1.30510 + 2.26050i) q^{19} +(-0.652886 - 0.237631i) q^{20} +(1.72851 - 0.110675i) q^{21} +(3.27840 + 2.75090i) q^{22} +(-7.13166 + 2.59571i) q^{23} +(-1.39526 - 1.02628i) q^{24} +(-0.784416 - 4.44864i) q^{25} -0.104186 q^{26} +(1.69249 - 4.91279i) q^{27} -1.00000 q^{28} +(0.968359 + 5.49184i) q^{29} +(-0.132815 + 1.19606i) q^{30} +(8.93967 - 3.25378i) q^{31} +(0.766044 + 0.642788i) q^{32} +(3.28852 - 6.64318i) q^{33} +(-5.59324 - 2.03577i) q^{34} +(0.347394 + 0.601703i) q^{35} +(-1.15641 + 2.76816i) q^{36} +(0.298330 - 0.516723i) q^{37} +(-1.99953 + 1.67781i) q^{38} +(0.0426272 + 0.175348i) q^{39} +(0.120649 - 0.684232i) q^{40} +(1.05126 - 5.96199i) q^{41} +(0.409146 + 1.68303i) q^{42} +(-6.51964 + 5.47063i) q^{43} +(-2.13982 + 3.70628i) q^{44} +(2.06734 - 0.265829i) q^{45} +(-3.79467 - 6.57257i) q^{46} +(-7.64344 - 2.78199i) q^{47} +(0.768409 - 1.55227i) q^{48} +(0.766044 + 0.642788i) q^{49} +(4.24485 - 1.54500i) q^{50} +(-1.13782 + 10.2465i) q^{51} +(-0.0180917 - 0.102603i) q^{52} -11.7151 q^{53} +(5.13205 + 0.813685i) q^{54} +2.97345 q^{55} +(-0.173648 - 0.984808i) q^{56} +(3.64191 + 2.67881i) q^{57} +(-5.24025 + 1.90730i) q^{58} +(1.40026 + 1.17496i) q^{59} +(-1.20095 + 0.0768954i) q^{60} +(-7.16052 - 2.60622i) q^{61} +(4.75670 + 8.23885i) q^{62} +(2.66520 - 1.37721i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0554516 + 0.0465294i) q^{65} +(7.11330 + 2.08498i) q^{66} +(2.10869 - 11.9590i) q^{67} +(1.03359 - 5.86177i) q^{68} +(-9.50927 + 9.07570i) q^{69} +(-0.532238 + 0.446601i) q^{70} +(-5.59563 + 9.69191i) q^{71} +(-2.92692 - 0.658151i) q^{72} +(-3.38215 - 5.85805i) q^{73} +(0.560677 + 0.204070i) q^{74} +(-4.33704 - 6.51209i) q^{75} +(-1.99953 - 1.67781i) q^{76} +(4.02155 - 1.46373i) q^{77} +(-0.165282 + 0.0724284i) q^{78} +(-0.872941 - 4.95070i) q^{79} +0.694787 q^{80} +(-0.730299 - 8.97032i) q^{81} +6.05396 q^{82} +(1.55014 + 8.79130i) q^{83} +(-1.58642 + 0.695186i) q^{84} +(-3.88611 + 1.41443i) q^{85} +(-6.51964 - 5.47063i) q^{86} +(5.35407 + 8.03915i) q^{87} +(-4.02155 - 1.46373i) q^{88} +(-0.127102 - 0.220147i) q^{89} +(0.620781 + 1.98977i) q^{90} +(-0.0520929 + 0.0902275i) q^{91} +(5.81378 - 4.87834i) q^{92} +(11.9201 - 11.3766i) q^{93} +(1.41245 - 8.01041i) q^{94} +(-0.314917 + 1.78599i) q^{95} +(1.66212 + 0.487185i) q^{96} +(3.58996 - 3.01233i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(0.598715 - 12.8250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9	$ 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{11} + 3 q^{12} - 9 q^{13} + 12 q^{15} - 12 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} + 9 q^{22} - 12 q^{23} - 3 q^{24} + 21 q^{25} + 18 q^{26} + 3 q^{27} - 30 q^{28} - 30 q^{29} - 15 q^{30} + 18 q^{31} + 9 q^{33} + 12 q^{34} + 3 q^{35} - 12 q^{36} + 3 q^{37} - 3 q^{38} + 72 q^{39} + 3 q^{40} + 36 q^{41} - 3 q^{42} - 9 q^{43} - 3 q^{44} - 48 q^{45} - 15 q^{46} + 3 q^{48} + 3 q^{50} - 6 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} + 66 q^{55} - 51 q^{57} - 3 q^{58} - 48 q^{59} + 24 q^{60} + 57 q^{61} - 18 q^{62} - 15 q^{63} - 15 q^{64} + 24 q^{65} + 54 q^{66} + 6 q^{67} - 15 q^{68} - 48 q^{69} - 3 q^{70} - 24 q^{71} - 6 q^{72} - 36 q^{73} - 48 q^{74} - 129 q^{75} - 3 q^{76} + 9 q^{77} + 24 q^{78} - 21 q^{79} + 6 q^{80} + 27 q^{81} - 15 q^{83} + 3 q^{84} - 72 q^{85} - 9 q^{86} + 42 q^{87} - 9 q^{88} - 30 q^{89} - 30 q^{90} + 9 q^{91} + 6 q^{92} + 111 q^{93} - 45 q^{94} + 81 q^{95} - 6 q^{96} - 15 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^11 + 3 * q^12 - 9 * q^13 + 12 * q^15 - 12 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 + 9 * q^22 - 12 * q^23 - 3 * q^24 + 21 * q^25 + 18 * q^26 + 3 * q^27 - 30 * q^28 - 30 * q^29 - 15 * q^30 + 18 * q^31 + 9 * q^33 + 12 * q^34 + 3 * q^35 - 12 * q^36 + 3 * q^37 - 3 * q^38 + 72 * q^39 + 3 * q^40 + 36 * q^41 - 3 * q^42 - 9 * q^43 - 3 * q^44 - 48 * q^45 - 15 * q^46 + 3 * q^48 + 3 * q^50 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 + 66 * q^55 - 51 * q^57 - 3 * q^58 - 48 * q^59 + 24 * q^60 + 57 * q^61 - 18 * q^62 - 15 * q^63 - 15 * q^64 + 24 * q^65 + 54 * q^66 + 6 * q^67 - 15 * q^68 - 48 * q^69 - 3 * q^70 - 24 * q^71 - 6 * q^72 - 36 * q^73 - 48 * q^74 - 129 * q^75 - 3 * q^76 + 9 * q^77 + 24 * q^78 - 21 * q^79 + 6 * q^80 + 27 * q^81 - 15 * q^83 + 3 * q^84 - 72 * q^85 - 9 * q^86 + 42 * q^87 - 9 * q^88 - 30 * q^89 - 30 * q^90 + 9 * q^91 + 6 * q^92 + 111 * q^93 - 45 * q^94 + 81 * q^95 - 6 * q^96 - 15 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	1.58642	−	0.695186i	0.915918	−	0.401366i
$3$	1.58642	−	0.695186i	0.915918	−	0.401366i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.532238	+	0.446601i	0.238024	+	0.199726i	0.753995	−	0.656880i	$-0.228124\pi$
$5$	0.532238	+	0.446601i	0.238024	+	0.199726i	−0.515971	+	0.856606i	$0.672569\pi$
$6$	0.960103	+	1.44160i	0.391960	+	0.588530i
$7$	0.939693	+	0.342020i	0.355170	+	0.129271i
$7$	0.939693	+	0.342020i	0.355170	+	0.129271i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.03343	−	2.20571i	0.677811	−	0.735236i
$10$	−0.347394	+	0.601703i	−0.109856	+	0.190275i
$11$	3.27840	−	2.75090i	0.988475	−	0.829429i	0.00312875	−	0.999995i	$-0.499004\pi$
$11$	3.27840	−	2.75090i	0.988475	−	0.829429i	0.985346	+	0.170566i	$0.0545596\pi$
$12$	−1.25298	+	1.19585i	−0.361703	+	0.345211i
$13$	−0.0180917	+	0.102603i	−0.00501772	+	0.0284569i	−0.987214	−	0.159402i	$-0.949044\pi$
$13$	−0.0180917	+	0.102603i	−0.00501772	+	0.0284569i	0.982196	+	0.187859i	$0.0601546\pi$
$14$	−0.173648	+	0.984808i	−0.0464094	+	0.263201i
$15$	1.15482	+	0.338490i	0.298174	+	0.0873978i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−2.97610	+	5.15476i	−0.721810	+	1.25021i	0.238463	+	0.971151i	$0.423356\pi$
$17$	−2.97610	+	5.15476i	−0.721810	+	1.25021i	−0.960274	+	0.279060i	$0.909977\pi$
$18$	2.52530	+	1.61952i	0.595219	+	0.381725i
$19$	1.30510	+	2.26050i	0.299411	+	0.518595i	0.976001	−	0.217765i	$-0.0698765\pi$
$19$	1.30510	+	2.26050i	0.299411	+	0.518595i	−0.676590	+	0.736360i	$0.736543\pi$
$20$	−0.652886	−	0.237631i	−0.145990	−	0.0531360i
$21$	1.72851	−	0.110675i	0.377192	−	0.0241512i
$22$	3.27840	+	2.75090i	0.698957	+	0.586495i
$23$	−7.13166	+	2.59571i	−1.48705	+	0.541243i	−0.952672	−	0.304001i	$-0.901677\pi$
$23$	−7.13166	+	2.59571i	−1.48705	+	0.541243i	−0.534381	+	0.845244i	$0.679455\pi$
$24$	−1.39526	−	1.02628i	−0.284806	−	0.209489i
$25$	−0.784416	−	4.44864i	−0.156883	−	0.889729i
$26$	−0.104186			−0.0204325
$27$	1.69249	−	4.91279i	0.325721	−	0.945466i
$28$	−1.00000			−0.188982
$29$	0.968359	+	5.49184i	0.179820	+	1.01981i	0.932432	+	0.361345i	$0.117682\pi$
$29$	0.968359	+	5.49184i	0.179820	+	1.01981i	−0.752612	+	0.658464i	$0.771207\pi$
$30$	−0.132815	+	1.19606i	−0.0242486	+	0.218369i
$31$	8.93967	−	3.25378i	1.60561	−	0.584395i	0.625047	−	0.780587i	$-0.285080\pi$
$31$	8.93967	−	3.25378i	1.60561	−	0.584395i	0.980566	+	0.196192i	$0.0628575\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	3.28852	−	6.64318i	0.572458	−	1.15643i
$34$	−5.59324	−	2.03577i	−0.959232	−	0.349132i
$35$	0.347394	+	0.601703i	0.0587202	+	0.101706i
$36$	−1.15641	+	2.76816i	−0.192734	+	0.461360i
$37$	0.298330	−	0.516723i	0.0490451	−	0.0849487i	−0.840461	−	0.541873i	$-0.817716\pi$
$37$	0.298330	−	0.516723i	0.0490451	−	0.0849487i	0.889506	+	0.456924i	$0.151049\pi$
$38$	−1.99953	+	1.67781i	−0.324367	+	0.272176i
$39$	0.0426272	+	0.175348i	0.00682581	+	0.0280782i
$40$	0.120649	−	0.684232i	0.0190762	−	0.108187i
$41$	1.05126	−	5.96199i	0.164179	−	0.931106i	−0.785728	−	0.618573i	$-0.787711\pi$
$41$	1.05126	−	5.96199i	0.164179	−	0.931106i	0.949907	−	0.312534i	$-0.101178\pi$
$42$	0.409146	+	1.68303i	0.0631326	+	0.259698i
$43$	−6.51964	+	5.47063i	−0.994236	+	0.834263i	−0.986176	−	0.165704i	$-0.947010\pi$
$43$	−6.51964	+	5.47063i	−0.994236	+	0.834263i	−0.00806094	+	0.999968i	$0.502566\pi$
$44$	−2.13982	+	3.70628i	−0.322591	+	0.558743i
$45$	2.06734	−	0.265829i	0.308181	−	0.0396275i
$46$	−3.79467	−	6.57257i	−0.559494	−	0.969072i
$47$	−7.64344	−	2.78199i	−1.11491	−	0.405794i	−0.282118	−	0.959380i	$-0.591037\pi$
$47$	−7.64344	−	2.78199i	−1.11491	−	0.405794i	−0.832793	+	0.553585i	$0.813259\pi$
$48$	0.768409	−	1.55227i	0.110910	−	0.224051i
$49$	0.766044	+	0.642788i	0.109435	+	0.0918268i
$50$	4.24485	−	1.54500i	0.600312	−	0.218496i
$51$	−1.13782	+	10.2465i	−0.159327	+	1.43480i
$52$	−0.0180917	−	0.102603i	−0.00250886	−	0.0142285i
$53$	−11.7151			−1.60919			−0.804594	−	0.593825i	$-0.797617\pi$
$53$	−11.7151			−1.60919			−0.804594	+	0.593825i	$0.797617\pi$
$54$	5.13205	+	0.813685i	0.698383	+	0.110729i
$55$	2.97345			0.400939
$56$	−0.173648	−	0.984808i	−0.0232047	−	0.131600i
$57$	3.64191	+	2.67881i	0.482382	+	0.354817i
$58$	−5.24025	+	1.90730i	−0.688079	+	0.250440i
$59$	1.40026	+	1.17496i	0.182299	+	0.152967i	0.729370	−	0.684119i	$-0.239813\pi$
$59$	1.40026	+	1.17496i	0.182299	+	0.152967i	−0.547072	+	0.837086i	$0.684258\pi$
$60$	−1.20095	+	0.0768954i	−0.155042	+	0.00992715i
$61$	−7.16052	−	2.60622i	−0.916810	−	0.333692i	−0.159842	−	0.987143i	$-0.551098\pi$
$61$	−7.16052	−	2.60622i	−0.916810	−	0.333692i	−0.756969	+	0.653451i	$0.773321\pi$
$62$	4.75670	+	8.23885i	0.604102	+	1.04633i
$63$	2.66520	−	1.37721i	0.335783	−	0.173512i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.0554516	+	0.0465294i	−0.00687792	+	0.00577126i
$66$	7.11330	+	2.08498i	0.875586	+	0.256644i
$67$	2.10869	−	11.9590i	0.257617	−	1.46102i	−0.531647	−	0.846966i	$-0.678427\pi$
$67$	2.10869	−	11.9590i	0.257617	−	1.46102i	0.789264	−	0.614054i	$-0.210462\pi$
$68$	1.03359	−	5.86177i	0.125341	−	0.710844i
$69$	−9.50927	+	9.07570i	−1.14478	+	1.09259i
$70$	−0.532238	+	0.446601i	−0.0636146	+	0.0533790i
$71$	−5.59563	+	9.69191i	−0.664079	+	1.15022i	0.315455	+	0.948940i	$0.397843\pi$
$71$	−5.59563	+	9.69191i	−0.664079	+	1.15022i	−0.979534	+	0.201278i	$0.935491\pi$
$72$	−2.92692	−	0.658151i	−0.344940	−	0.0775638i
$73$	−3.38215	−	5.85805i	−0.395851	−	0.685633i	0.597359	−	0.801974i	$-0.296217\pi$
$73$	−3.38215	−	5.85805i	−0.395851	−	0.685633i	−0.993209	+	0.116341i	$0.962884\pi$
$74$	0.560677	+	0.204070i	0.0651774	+	0.0237226i
$75$	−4.33704	−	6.51209i	−0.500799	−	0.751951i
$76$	−1.99953	−	1.67781i	−0.229362	−	0.192458i
$77$	4.02155	−	1.46373i	0.458299	−	0.166807i
$78$	−0.165282	+	0.0724284i	−0.0187145	+	0.00820091i
$79$	−0.872941	−	4.95070i	−0.0982136	−	0.556997i	−0.993715	−	0.111938i	$-0.964294\pi$
$79$	−0.872941	−	4.95070i	−0.0982136	−	0.556997i	0.895502	−	0.445058i	$-0.146817\pi$
$80$	0.694787			0.0776796
$81$	−0.730299	−	8.97032i	−0.0811443	−	0.996702i
$82$	6.05396			0.668548
$83$	1.55014	+	8.79130i	0.170150	+	0.964970i	0.943594	+	0.331105i	$0.107421\pi$
$83$	1.55014	+	8.79130i	0.170150	+	0.964970i	−0.773444	+	0.633865i	$0.781467\pi$
$84$	−1.58642	+	0.695186i	−0.173092	+	0.0758510i
$85$	−3.88611	+	1.41443i	−0.421508	+	0.153416i
$86$	−6.51964	−	5.47063i	−0.703031	−	0.589913i
$87$	5.35407	+	8.03915i	0.574016	+	0.861887i
$88$	−4.02155	−	1.46373i	−0.428699	−	0.156034i
$89$	−0.127102	−	0.220147i	−0.0134728	−	0.0233355i	0.859210	−	0.511622i	$-0.170955\pi$
$89$	−0.127102	−	0.220147i	−0.0134728	−	0.0233355i	−0.872683	+	0.488287i	$0.837622\pi$
$90$	0.620781	+	1.98977i	0.0654360	+	0.209740i
$91$	−0.0520929	+	0.0902275i	−0.00546082	+	0.00945841i
$92$	5.81378	−	4.87834i	0.606128	−	0.508602i
$93$	11.9201	−	11.3766i	1.23605	−	1.17970i
$94$	1.41245	−	8.01041i	0.145683	−	0.826211i
$95$	−0.314917	+	1.78599i	−0.0323098	+	0.183238i
$96$	1.66212	+	0.487185i	0.169640	+	0.0497232i
$97$	3.58996	−	3.01233i	0.364505	−	0.305856i	−0.442078	−	0.896977i	$-0.645759\pi$
$97$	3.58996	−	3.01233i	0.364505	−	0.305856i	0.806583	+	0.591120i	$0.201314\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$	0.598715	−	12.8250i	0.0601731	−	1.28896i
$100$	2.25864	+	3.91207i	0.225864	+	0.391207i
$101$	6.06745	+	2.20837i	0.603734	+	0.219741i	0.625759	−	0.780016i	$-0.284789\pi$
$101$	6.06745	+	2.20837i	0.603734	+	0.219741i	−0.0220252	+	0.999757i	$0.507011\pi$
$102$	−10.2884	+	0.658758i	−1.01871	+	0.0652268i
$103$	6.74256	+	5.65768i	0.664364	+	0.557468i	0.911391	−	0.411541i	$-0.135009\pi$
$103$	6.74256	+	5.65768i	0.664364	+	0.557468i	−0.247027	+	0.969009i	$0.579454\pi$
$104$	0.0979026	−	0.0356336i	0.00960014	−	0.00349416i
$105$	0.969407	+	0.713049i	0.0946044	+	0.0695865i
$106$	−2.03430	−	11.5371i	−0.197589	−	1.12058i
$107$	−9.24769			−0.894008			−0.447004	−	0.894532i	$-0.647509\pi$
$107$	−9.24769			−0.894008			−0.447004	+	0.894532i	$0.647509\pi$
$108$	0.0898473	+	5.19538i	0.00864556	+	0.499925i
$109$	−0.878111			−0.0841077			−0.0420539	−	0.999115i	$-0.513390\pi$
$109$	−0.878111			−0.0841077			−0.0420539	+	0.999115i	$0.513390\pi$
$110$	0.516333	+	2.92827i	0.0492305	+	0.279200i
$111$	0.114057	−	1.02713i	0.0108258	−	0.0974911i
$112$	0.939693	−	0.342020i	0.0887926	−	0.0323179i
$113$	−10.0302	−	8.41631i	−0.943558	−	0.791739i	0.0346427	−	0.999400i	$-0.488971\pi$
$113$	−10.0302	−	8.41631i	−0.943558	−	0.791739i	−0.978201	+	0.207660i	$0.933415\pi$
$114$	−2.00570	+	4.05175i	−0.187851	+	0.379481i
$115$	−4.95498	−	1.80347i	−0.462055	−	0.168174i
$116$	−2.78828	−	4.82944i	−0.258885	−	0.448402i
$117$	0.189524	+	0.248541i	0.0175215	+	0.0229776i
$118$	−0.913956	+	1.58302i	−0.0841365	+	0.145729i
$119$	−4.55965	+	3.82600i	−0.417982	+	0.350729i
$120$	−0.284270	−	1.16935i	−0.0259501	−	0.106747i
$121$	1.27030	−	7.20425i	0.115482	−	0.654932i
$122$	1.32321	−	7.50430i	0.119798	−	0.679407i
$123$	−2.47696	−	10.1890i	−0.223340	−	0.918713i
$124$	−7.28769	+	6.11510i	−0.654454	+	0.549152i
$125$	3.30624	−	5.72657i	0.295719	−	0.512200i
$126$	1.81910	+	2.38556i	0.162058	+	0.212522i
$127$	6.88910	+	11.9323i	0.611308	+	1.05882i	0.991020	+	0.133712i	$0.0426899\pi$
$127$	6.88910	+	11.9323i	0.611308	+	1.05882i	−0.379712	+	0.925105i	$0.623977\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−6.53976	+	13.2111i	−0.575794	+	1.16317i
$130$	−0.0554516	−	0.0465294i	−0.00486343	−	0.00408090i
$131$	12.7783	−	4.65091i	1.11644	−	0.406352i	0.283089	−	0.959094i	$-0.408641\pi$
$131$	12.7783	−	4.65091i	1.11644	−	0.406352i	0.833352	+	0.552742i	$0.186418\pi$
$132$	−0.818095	+	7.36728i	−0.0712061	+	0.641240i
$133$	0.453257	+	2.57055i	0.0393024	+	0.222895i
$134$	12.1435			1.04903
$135$	3.09486	−	1.85890i	0.266363	−	0.159989i
$136$	5.95220			0.510397
$137$	−1.11651	−	6.33202i	−0.0953896	−	0.540981i	−0.994627	−	0.103521i	$-0.966989\pi$
$137$	−1.11651	−	6.33202i	−0.0953896	−	0.540981i	0.899238	−	0.437460i	$-0.144122\pi$
$138$	−10.5891	−	7.78883i	−0.901403	−	0.663029i
$139$	−6.19770	+	2.25578i	−0.525682	+	0.191332i	−0.591209	−	0.806518i	$-0.701349\pi$
$139$	−6.19770	+	2.25578i	−0.525682	+	0.191332i	0.0655275	+	0.997851i	$0.479127\pi$
$140$	−0.532238	−	0.446601i	−0.0449823	−	0.0377446i
$141$	−14.0597	+	0.900226i	−1.18404	+	0.0758127i
$142$	−10.5163	−	3.82763i	−0.882512	−	0.321208i
$143$	0.222939	+	0.386142i	0.0186431	+	0.0322908i
$144$	0.139898	−	2.99674i	0.0116582	−	0.249728i
$145$	−1.93726	+	3.35543i	−0.160881	+	0.278654i
$146$	5.18175	−	4.34801i	0.428845	−	0.359844i
$147$	1.66212	+	0.487185i	0.137090	+	0.0401824i
$148$	−0.103609	+	0.587595i	−0.00851660	+	0.0483000i
$149$	−0.374313	+	2.12283i	−0.0306649	+	0.173909i	−0.996294	−	0.0860154i	$-0.972587\pi$
$149$	−0.374313	+	2.12283i	−0.0306649	+	0.173909i	0.965629	+	0.259925i	$0.0836977\pi$
$150$	5.66003	−	5.40197i	0.462140	−	0.441069i
$151$	−9.45350	+	7.93243i	−0.769315	+	0.645532i	−0.940533	−	0.339701i	$-0.889674\pi$
$151$	−9.45350	+	7.93243i	−0.769315	+	0.645532i	0.171219	+	0.985233i	$0.445230\pi$
$152$	1.30510	−	2.26050i	0.105858	−	0.183351i
$153$	5.31819	+	17.0463i	0.429950	+	1.37811i
$154$	2.13982	+	3.70628i	0.172432	+	0.298661i
$155$	6.21117	+	2.26068i	0.498893	+	0.181582i
$156$	−0.100029	−	0.150194i	−0.00800873	−	0.0120251i
$157$	−3.83109	−	3.21467i	−0.305754	−	0.256558i	0.476980	−	0.878914i	$-0.341731\pi$
$157$	−3.83109	−	3.21467i	−0.305754	−	0.256558i	−0.782735	+	0.622356i	$0.786176\pi$
$158$	4.72390	−	1.71936i	0.375813	−	0.136785i
$159$	−18.5850	+	8.14415i	−1.47388	+	0.645873i
$160$	0.120649	+	0.684232i	0.00953810	+	0.0540933i
$161$	−7.58935			−0.598124
$162$	8.70723	−	2.27688i	0.684104	−	0.178889i
$163$	2.09689			0.164241			0.0821207	−	0.996622i	$-0.473831\pi$
$163$	2.09689			0.164241			0.0821207	+	0.996622i	$0.473831\pi$
$164$	1.05126	+	5.96199i	0.0820896	+	0.465553i
$165$	4.71712	−	2.06710i	0.367227	−	0.160923i
$166$	−8.38856	+	3.05319i	−0.651078	+	0.236973i
$167$	14.7678	+	12.3917i	1.14277	+	0.958896i	0.999526	−	0.0307918i	$-0.00980288\pi$
$167$	14.7678	+	12.3917i	1.14277	+	0.958896i	0.143242	+	0.989688i	$0.454247\pi$
$168$	−0.960103	−	1.44160i	−0.0740735	−	0.111222i
$169$	12.2058	+	4.44255i	0.938908	+	0.341735i
$170$	−2.06776	−	3.58146i	−0.158590	−	0.274685i
$171$	7.63985	+	1.71791i	0.584234	+	0.131372i
$172$	4.25540	−	7.37056i	0.324471	−	0.562000i
$173$	19.0074	−	15.9491i	1.44510	−	1.21258i	0.509044	−	0.860741i	$-0.329999\pi$
$173$	19.0074	−	15.9491i	1.44510	−	1.21258i	0.936059	−	0.351844i	$-0.114445\pi$
$174$	−6.98729	+	6.66871i	−0.529705	+	0.505554i
$175$	0.784416	−	4.44864i	0.0592963	−	0.336286i
$176$	0.743153	−	4.21463i	0.0560173	−	0.317690i
$177$	3.03821	+	0.890533i	0.228366	+	0.0669365i
$178$	0.194731	−	0.163399i	0.0145957	−	0.0122473i
$179$	−8.37195	+	14.5006i	−0.625749	+	1.08383i	0.362647	+	0.931927i	$0.381873\pi$
$179$	−8.37195	+	14.5006i	−0.625749	+	1.08383i	−0.988396	+	0.151902i	$0.951460\pi$
$180$	−1.85175	+	0.956870i	−0.138021	+	0.0713209i
$181$	7.63640	+	13.2266i	0.567609	+	0.983128i	0.996802	+	0.0799147i	$0.0254648\pi$
$181$	7.63640	+	13.2266i	0.567609	+	0.983128i	−0.429193	+	0.903213i	$0.641202\pi$
$182$	−0.0979026	−	0.0356336i	−0.00725702	−	0.00264134i
$183$	−13.1714	+	0.843348i	−0.973656	+	0.0623421i
$184$	5.81378	+	4.87834i	0.428597	+	0.359636i
$185$	0.389551	−	0.141785i	0.0286404	−	0.0104242i
$186$	13.2736	+	9.76345i	0.973270	+	0.715891i
$187$	4.42340	+	25.0863i	0.323471	+	1.83449i
$188$	8.13398			0.593232
$189$	3.27070	−	4.03764i	0.237908	−	0.293695i
$190$	−1.81354			−0.131568
$191$	0.318670	+	1.80727i	0.0230581	+	0.130769i	0.994164	−	0.107880i	$-0.0344064\pi$
$191$	0.318670	+	1.80727i	0.0230581	+	0.130769i	−0.971106	+	0.238650i	$0.923295\pi$
$192$	−0.191160	+	1.72147i	−0.0137957	+	0.124236i
$193$	12.1092	−	4.40739i	0.871639	−	0.317251i	0.132808	−	0.991142i	$-0.457600\pi$
$193$	12.1092	−	4.40739i	0.871639	−	0.317251i	0.738831	+	0.673891i	$0.235378\pi$
$194$	3.58996	+	3.01233i	0.257744	+	0.216273i
$195$	−0.0556227	+	0.112364i	−0.00398323	+	0.00804657i
$196$	−0.939693	−	0.342020i	−0.0671209	−	0.0244300i
$197$	−1.55097	−	2.68636i	−0.110502	−	0.191395i	0.805471	−	0.592635i	$-0.201912\pi$
$197$	−1.55097	−	2.68636i	−0.110502	−	0.191395i	−0.915973	+	0.401240i	$0.868579\pi$
$198$	12.7341	−	1.63741i	0.904973	−	0.116366i
$199$	−10.5394	+	18.2547i	−0.747116	+	1.29404i	0.202084	+	0.979368i	$0.435229\pi$
$199$	−10.5394	+	18.2547i	−0.747116	+	1.29404i	−0.949200	+	0.314674i	$0.898105\pi$
$200$	−3.46043	+	2.90365i	−0.244689	+	0.205319i
$201$	−4.96845	−	20.4378i	−0.350447	−	1.44157i
$202$	−1.12122	+	6.35875i	−0.0788888	+	0.447400i
$203$	−0.968359	+	5.49184i	−0.0679655	+	0.385451i
$204$	−2.43532	−	10.0177i	−0.170506	−	0.701383i
$205$	3.22215	−	2.70370i	0.225045	−	0.188835i
$206$	−4.40089	+	7.62257i	−0.306625	+	0.531090i
$207$	−8.77636	+	21.0086i	−0.610000	+	1.46020i
$208$	0.0520929	+	0.0902275i	0.00361199	+	0.00625615i
$209$	10.4971	+	3.82062i	0.726098	+	0.264278i
$210$	−0.533880	+	1.07850i	−0.0368413	+	0.0744235i
$211$	19.6214	+	16.4643i	1.35079	+	1.13345i	0.978710	+	0.205249i	$0.0658004\pi$
$211$	19.6214	+	16.4643i	1.35079	+	1.13345i	0.372082	+	0.928200i	$0.378644\pi$
$212$	11.0086	−	4.00679i	0.756071	−	0.275187i
$213$	−2.13931	+	19.2654i	−0.146583	+	1.32004i
$214$	−1.60584	−	9.10720i	−0.109773	−	0.622555i
$215$	−5.91319			−0.403276
$216$	−5.10084	+	0.990650i	−0.347068	+	0.0674052i
$217$	9.51340			0.645812
$218$	−0.152482	−	0.864770i	−0.0103274	−	0.0585696i
$219$	−9.43793	−	6.94209i	−0.637756	−	0.469103i
$220$	−2.79412	+	1.01698i	−0.188380	+	0.0685646i
$221$	−0.475050	−	0.398615i	−0.0319553	−	0.0268137i
$222$	1.03133	−	0.0660352i	0.0692186	−	0.00443199i
$223$	10.6669	+	3.88244i	0.714309	+	0.259987i	0.673508	−	0.739180i	$-0.264787\pi$
$223$	10.6669	+	3.88244i	0.714309	+	0.259987i	0.0408014	+	0.999167i	$0.487009\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	−11.4075	−	7.31583i	−0.760498	−	0.487722i
$226$	6.54672	−	11.3393i	0.435482	−	0.754276i
$227$	−4.15383	+	3.48548i	−0.275699	+	0.231339i	−0.770144	−	0.637870i	$-0.779816\pi$
$227$	−4.15383	+	3.48548i	−0.275699	+	0.231339i	0.494445	+	0.869209i	$0.335371\pi$
$228$	−4.33848	−	1.27165i	−0.287323	−	0.0842173i
$229$	2.80901	−	15.9307i	0.185625	−	1.05273i	−0.739526	−	0.673128i	$-0.764950\pi$
$229$	2.80901	−	15.9307i	0.185625	−	1.05273i	0.925150	−	0.379601i	$-0.123939\pi$
$230$	0.915644	−	5.19287i	0.0603758	−	0.342408i
$231$	5.36230	−	5.11781i	0.352813	−	0.336727i
$232$	4.27189	−	3.58454i	0.280463	−	0.235337i
$233$	5.15855	−	8.93486i	0.337948	−	0.585342i	−0.646099	−	0.763254i	$-0.723601\pi$
$233$	5.15855	−	8.93486i	0.337948	−	0.585342i	0.984047	+	0.177911i	$0.0569340\pi$
$234$	−0.211855	+	0.229803i	−0.0138494	+	0.0150227i
$235$	−2.82569	−	4.89425i	−0.184328	−	0.319265i
$236$	−1.71768	−	0.625183i	−0.111811	−	0.0406959i
$237$	−4.82650	−	7.24701i	−0.313515	−	0.470744i
$238$	−4.55965	−	3.82600i	−0.295558	−	0.248003i
$239$	−6.37049	+	2.31867i	−0.412072	+	0.149982i	−0.539734	−	0.841836i	$-0.681475\pi$
$239$	−6.37049	+	2.31867i	−0.412072	+	0.149982i	0.127661	+	0.991818i	$0.459253\pi$
$240$	1.10222	−	0.483006i	0.0711481	−	0.0311779i
$241$	−0.209677	−	1.18914i	−0.0135065	−	0.0765990i	0.977309	−	0.211816i	$-0.0679379\pi$
$241$	−0.209677	−	1.18914i	−0.0135065	−	0.0765990i	−0.990816	+	0.135217i	$0.956827\pi$
$242$	7.31539			0.470251
$243$	−7.39460	−	13.7230i	−0.474364	−	0.880329i
$244$	7.62006			0.487825
$245$	0.120649	+	0.684232i	0.00770795	+	0.0437140i
$246$	9.60411	−	4.20863i	0.612335	−	0.268332i
$247$	−0.255546	+	0.0930110i	−0.0162600	+	0.00591815i
$248$	−7.28769	−	6.11510i	−0.462769	−	0.388309i
$249$	8.57076	+	12.8690i	0.543150	+	0.815541i
$250$	6.21370	+	2.26160i	0.392989	+	0.143036i
$251$	−0.118284	−	0.204874i	−0.00746603	−	0.0129315i	0.862268	−	0.506452i	$-0.169043\pi$
$251$	−0.118284	−	0.204874i	−0.00746603	−	0.0129315i	−0.869734	+	0.493520i	$0.835710\pi$
$252$	−2.03343	+	2.20571i	−0.128094	+	0.138947i
$253$	−16.2399	+	28.1283i	−1.02099	+	1.76841i
$254$	−10.5547	+	8.85645i	−0.662261	+	0.555703i
$255$	−5.18170	+	4.94544i	−0.324491	+	0.309696i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	0.811754	−	4.60368i	0.0506358	−	0.287170i	−0.948966	−	0.315378i	$-0.897869\pi$
$257$	0.811754	−	4.60368i	0.0506358	−	0.287170i	0.999602	+	0.0282076i	$0.00897996\pi$
$258$	−14.1460	−	4.14633i	−0.880690	−	0.258139i
$259$	0.457068	−	0.383526i	0.0284008	−	0.0238311i
$260$	0.0361935	−	0.0626889i	0.00224462	−	0.00388780i
$261$	14.0825	+	9.03137i	0.871684	+	0.559028i
$262$	6.79917	+	11.7765i	0.420054	+	0.727555i
$263$	2.54720	+	0.927105i	0.157067	+	0.0571677i	0.419357	−	0.907821i	$-0.362256\pi$
$263$	2.54720	+	0.927105i	0.157067	+	0.0571677i	−0.262290	+	0.964989i	$0.584478\pi$
$264$	−7.39742	+	0.473649i	−0.455280	+	0.0291511i
$265$	−6.23520	−	5.23196i	−0.383026	−	0.321397i
$266$	−2.45279	+	0.892743i	−0.150390	+	0.0547376i
$267$	−0.354679	−	0.260885i	−0.0217060	−	0.0159659i
$268$	2.10869	+	11.9590i	0.128809	+	0.730510i
$269$	6.05490			0.369174			0.184587	−	0.982816i	$-0.440905\pi$
$269$	6.05490			0.369174			0.184587	+	0.982816i	$0.440905\pi$
$270$	2.36808	+	2.72505i	0.144117	+	0.165841i
$271$	3.47860			0.211310			0.105655	−	0.994403i	$-0.466306\pi$
$271$	3.47860			0.211310			0.105655	+	0.994403i	$0.466306\pi$
$272$	1.03359	+	5.86177i	0.0626705	+	0.355422i
$273$	−0.0199161	+	0.179353i	−0.00120538	+	0.0108549i
$274$	6.04195	−	2.19909i	0.365007	−	0.132852i
$275$	−14.8094	−	12.4266i	−0.893042	−	0.749351i
$276$	5.83172	−	11.7807i	0.351028	−	0.709117i
$277$	−27.8765	−	10.1462i	−1.67494	−	0.609628i	−0.682336	−	0.731039i	$-0.739036\pi$
$277$	−27.8765	−	10.1462i	−1.67494	−	0.609628i	−0.992602	+	0.121411i	$0.961258\pi$
$278$	−3.29772	−	5.71183i	−0.197784	−	0.342573i
$279$	11.0014	−	26.3346i	0.658634	−	1.57661i
$280$	0.347394	−	0.601703i	0.0207607	−	0.0359587i
$281$	21.0300	−	17.6463i	1.25454	−	1.05269i	0.258303	−	0.966064i	$-0.416837\pi$
$281$	21.0300	−	17.6463i	1.25454	−	1.05269i	0.996241	−	0.0866237i	$-0.0276078\pi$
$282$	−3.32799	−	13.6898i	−0.198179	−	0.815213i
$283$	2.84429	−	16.1308i	0.169076	−	0.958875i	−0.775687	−	0.631118i	$-0.782596\pi$
$283$	2.84429	−	16.1308i	0.169076	−	0.958875i	0.944762	−	0.327757i	$-0.106293\pi$
$284$	1.94334	−	11.0212i	0.115316	−	0.653990i
$285$	0.742002	+	3.05224i	0.0439524	+	0.180799i
$286$	−0.341563	+	0.286605i	−0.0201970	+	0.0169473i
$287$	3.02698	−	5.24289i	0.178677	−	0.309478i
$288$	2.97550	−	0.382605i	0.175333	−	0.0225452i
$289$	−9.21434	−	15.9597i	−0.542020	−	0.938806i
$290$	−3.64086	−	1.32516i	−0.213799	−	0.0778163i
$291$	3.60104	−	7.27451i	0.211097	−	0.426439i
$292$	5.18175	+	4.34801i	0.303239	+	0.254448i
$293$	−4.99540	+	1.81818i	−0.291834	+	0.106219i	−0.483789	−	0.875185i	$-0.660740\pi$
$293$	−4.99540	+	1.81818i	−0.291834	+	0.106219i	0.191954	+	0.981404i	$0.438517\pi$
$294$	−0.191160	+	1.72147i	−0.0111486	+	0.100398i
$295$	0.220535	+	1.25072i	0.0128400	+	0.0728195i
$296$	−0.596660			−0.0346802
$297$	−7.96593	−	20.7620i	−0.462230	−	1.20473i
$298$	−2.15558			−0.124869
$299$	−0.137304	−	0.778689i	−0.00794049	−	0.0450328i
$300$	6.30275	+	4.63600i	0.363890	+	0.267660i
$301$	−7.99753	+	2.91086i	−0.460970	+	0.167779i
$302$	−9.45350	−	7.93243i	−0.543988	−	0.456460i
$303$	11.1607	−	0.714610i	0.641168	−	0.0410533i
$304$	2.45279	+	0.892743i	0.140677	+	0.0512023i
$305$	−2.64716	−	4.58502i	−0.151576	−	0.262537i
$306$	−15.8638	+	8.19744i	−0.906873	+	0.468617i
$307$	4.96767	−	8.60425i	0.283520	−	0.491070i	−0.688729	−	0.725018i	$-0.741831\pi$
$307$	4.96767	−	8.60425i	0.283520	−	0.491070i	0.972249	+	0.233948i	$0.0751645\pi$
$308$	−3.27840	+	2.75090i	−0.186804	+	0.156747i
$309$	14.6296	+	4.28810i	0.832252	+	0.243942i
$310$	−1.14778	+	6.50937i	−0.0651894	+	0.369708i
$311$	1.45304	−	8.24058i	0.0823942	−	0.467281i	−0.915494	−	0.402331i	$-0.868200\pi$
$311$	1.45304	−	8.24058i	0.0823942	−	0.467281i	0.997889	−	0.0649497i	$-0.0206887\pi$
$312$	0.130542	−	0.124590i	0.00739050	−	0.00705353i
$313$	−20.8296	+	17.4781i	−1.17736	+	0.987922i	−0.177367	+	0.984145i	$0.556758\pi$
$313$	−20.8296	+	17.4781i	−1.17736	+	0.987922i	−0.999993	+	0.00377754i	$0.998798\pi$
$314$	2.50057	−	4.33111i	0.141115	−	0.244419i
$315$	2.03358	+	0.457275i	0.114579	+	0.0257645i
$316$	2.51353	+	4.35357i	0.141397	+	0.244907i
$317$	−7.49308	−	2.72726i	−0.420853	−	0.153178i	0.122908	−	0.992418i	$-0.460778\pi$
$317$	−7.49308	−	2.72726i	−0.420853	−	0.153178i	−0.543761	+	0.839240i	$0.683000\pi$
$318$	−11.2477	−	16.8884i	−0.630738	−	0.947055i
$319$	18.2822	+	15.3406i	1.02361	+	0.858908i
$320$	−0.652886	+	0.237631i	−0.0364975	+	0.0132840i
$321$	−14.6707	+	6.42886i	−0.818838	+	0.358824i
$322$	−1.31788	−	7.47405i	−0.0734424	−	0.416512i
$323$	−15.5365			−0.864472
$324$	3.75429	+	8.17957i	0.208571	+	0.454420i
$325$	0.470635			0.0261061
$326$	0.364122	+	2.06504i	0.0201668	+	0.114372i
$327$	−1.39305	+	0.610450i	−0.0770358	+	0.0337580i
$328$	−5.68886	+	2.07058i	−0.314115	+	0.114329i
$329$	−6.23099	−	5.22842i	−0.343526	−	0.288252i
$330$	2.85481	+	4.28651i	0.157152	+	0.235965i
$331$	28.7130	+	10.4507i	1.57821	+	0.574420i	0.974813	−	0.223023i	$-0.0715925\pi$
$331$	28.7130	+	10.4507i	1.57821	+	0.574420i	0.603394	+	0.797443i	$0.293815\pi$
$332$	−4.46346	−	7.73094i	−0.244964	−	0.424290i
$333$	−0.533105	−	1.70875i	−0.0292140	−	0.0936389i
$334$	−9.63901	+	16.6952i	−0.527423	+	0.913523i
$335$	6.46321	−	5.42327i	0.353123	−	0.296305i
$336$	1.25298	−	1.19585i	0.0683555	−	0.0652388i
$337$	0.0391008	−	0.221752i	0.00212996	−	0.0120796i	−0.983724	−	0.179685i	$-0.942492\pi$
$337$	0.0391008	−	0.221752i	0.00212996	−	0.0120796i	0.985854	+	0.167605i	$0.0536034\pi$
$338$	−2.25554	+	12.7918i	−0.122685	+	0.695783i
$339$	−21.7629	−	6.37894i	−1.18200	−	0.346456i
$340$	3.16799	−	2.65826i	0.171808	−	0.144164i
$341$	20.3570	−	35.2594i	1.10239	−	1.90940i
$342$	−0.365163	+	7.82210i	−0.0197458	+	0.422971i
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$	7.99753	+	2.91086i	0.431198	+	0.156943i
$345$	−9.11441	+	0.583586i	−0.490703	+	0.0314192i
$346$	19.0074	+	15.9491i	1.02184	+	0.857427i
$347$	−21.1361	+	7.69291i	−1.13465	+	0.412977i	−0.839977	−	0.542622i	$-0.817431\pi$
$347$	−21.1361	+	7.69291i	−1.13465	+	0.412977i	−0.294668	+	0.955600i	$0.595209\pi$
$348$	−7.78073	−	5.72313i	−0.417091	−	0.306792i
$349$	1.83864	+	10.4275i	0.0984202	+	0.558169i	0.993646	+	0.112555i	$0.0359034\pi$
$349$	1.83864	+	10.4275i	0.0984202	+	0.558169i	−0.895225	+	0.445614i	$0.852985\pi$
$350$	4.51727			0.241458
$351$	0.473446	+	0.262535i	0.0252707	+	0.0140131i
$352$	4.27965			0.228106
$353$	3.75670	+	21.3053i	0.199949	+	1.13397i	0.905193	+	0.425002i	$0.139727\pi$
$353$	3.75670	+	21.3053i	0.199949	+	1.13397i	−0.705244	+	0.708965i	$0.749162\pi$
$354$	−0.349423	+	3.14670i	−0.0185716	+	0.167245i
$355$	−7.30662	+	2.65939i	−0.387795	+	0.141146i
$356$	0.194731	+	0.163399i	0.0103207	+	0.00866013i
$357$	−4.57372	+	9.23943i	−0.242067	+	0.489003i
$358$	−15.7341	−	5.72675i	−0.831574	−	0.302668i
$359$	6.31055	+	10.9302i	0.333058	+	0.576873i	0.983110	−	0.183016i	$-0.0585862\pi$
$359$	6.31055	+	10.9302i	0.333058	+	0.576873i	−0.650052	+	0.759890i	$0.725253\pi$
$360$	−1.26389	−	1.65746i	−0.0666126	−	0.0873556i
$361$	6.09342	−	10.5541i	0.320706	−	0.555479i
$362$	−11.6996	+	9.81716i	−0.614919	+	0.515979i
$363$	−2.99306	−	12.3120i	−0.157095	−	0.646214i
$364$	0.0180917	−	0.102603i	0.000948261	−	0.00537785i
$365$	0.816103	−	4.62835i	0.0427168	−	0.242259i
$366$	−3.11772	−	12.8248i	−0.162966	−	0.670364i
$367$	19.2584	−	16.1598i	1.00528	−	0.843532i	0.0175751	−	0.999846i	$-0.494405\pi$
$367$	19.2584	−	16.1598i	1.00528	−	0.843532i	0.987708	+	0.156313i	$0.0499610\pi$
$368$	−3.79467	+	6.57257i	−0.197811	+	0.342619i
$369$	−11.0127	−	14.4421i	−0.573301	−	0.751825i
$370$	0.207276	+	0.359012i	0.0107758	+	0.0186642i
$371$	−11.0086	−	4.00679i	−0.571536	−	0.208022i
$372$	−7.31018	+	14.7674i	−0.379015	+	0.765653i
$373$	−5.40234	−	4.53310i	−0.279723	−	0.234715i	0.492122	−	0.870526i	$-0.336221\pi$
$373$	−5.40234	−	4.53310i	−0.279723	−	0.234715i	−0.771845	+	0.635811i	$0.780666\pi$
$374$	−23.9371	+	8.71239i	−1.23776	+	0.450507i
$375$	1.26404	−	11.3832i	0.0652747	−	0.587825i
$376$	1.41245	+	8.01041i	0.0728416	+	0.413105i
$377$	−0.580998			−0.0299229
$378$	4.54425	+	2.51988i	0.233731	+	0.129609i
$379$	−33.0837			−1.69939			−0.849697	−	0.527271i	$-0.823215\pi$
$379$	−33.0837			−1.69939			−0.849697	+	0.527271i	$0.823215\pi$
$380$	−0.314917	−	1.78599i	−0.0161549	−	0.0916191i
$381$	19.2241	+	14.1403i	0.984881	+	0.724431i
$382$	−1.72447	+	0.627657i	−0.0882317	+	0.0321137i
$383$	28.7747	+	24.1448i	1.47032	+	1.23374i	0.915841	+	0.401542i	$0.131525\pi$
$383$	28.7747	+	24.1448i	1.47032	+	1.23374i	0.554475	+	0.832200i	$0.312919\pi$
$384$	−1.72851	+	0.110675i	−0.0882077	+	0.00564784i
$385$	2.79412	+	1.01698i	0.142402	+	0.0518300i
$386$	6.44317	+	11.1599i	0.327949	+	0.568024i
$387$	−1.19064	+	25.5046i	−0.0605239	+	1.29647i
$388$	−2.34318	+	4.05851i	−0.118957	+	0.206039i
$389$	2.97849	−	2.49925i	0.151015	−	0.126717i	−0.564150	−	0.825672i	$-0.690796\pi$
$389$	2.97849	−	2.49925i	0.151015	−	0.126717i	0.715165	+	0.698956i	$0.246351\pi$
$390$	−0.120316	−	0.0352659i	−0.00609243	−	0.00178576i
$391$	7.84426	−	44.4870i	0.396701	−	2.24981i
$392$	0.173648	−	0.984808i	0.00877056	−	0.0497403i
$393$	17.0384	−	16.2615i	0.859473	−	0.820286i
$394$	2.37622	−	1.99389i	0.119712	−	0.100451i
$395$	1.74637	−	3.02480i	0.0878695	−	0.152194i
$396$	3.82379	+	12.2563i	0.192153	+	0.615903i
$397$	12.4083	+	21.4918i	0.622756	+	1.07864i	0.988970	+	0.148114i	$0.0473202\pi$
$397$	12.4083	+	21.4918i	0.622756	+	1.07864i	−0.366215	+	0.930530i	$0.619346\pi$
$398$	−19.8075	−	7.20935i	−0.992861	−	0.361372i
$399$	2.50606	+	3.76286i	0.125460	+	0.188379i
$400$	−3.46043	−	2.90365i	−0.173022	−	0.145182i
$401$	6.97294	−	2.53794i	0.348212	−	0.126739i	−0.161992	−	0.986792i	$-0.551792\pi$
$401$	6.97294	−	2.53794i	0.348212	−	0.126739i	0.510204	+	0.860053i	$0.329570\pi$
$402$	19.2646	−	8.44196i	0.960829	−	0.421046i
$403$	0.172113	+	0.976103i	0.00857357	+	0.0486231i
$404$	−6.45685			−0.321240
$405$	3.61746	−	5.10050i	0.179753	−	0.253446i
$406$	−5.57656			−0.276760
$407$	−0.443410	−	2.51470i	−0.0219790	−	0.124649i
$408$	9.44267	−	4.13788i	0.467482	−	0.204856i
$409$	−29.9730	+	10.9093i	−1.48207	+	0.539429i	−0.951348	−	0.308117i	$-0.900301\pi$
$409$	−29.9730	+	10.9093i	−1.48207	+	0.539429i	−0.530721	+	0.847546i	$0.678079\pi$
$410$	3.22215	+	2.70370i	0.159131	+	0.133526i
$411$	−6.17318	−	9.26904i	−0.304500	−	0.457208i
$412$	−8.27098	−	3.01039i	−0.407482	−	0.148311i
$413$	0.913956	+	1.58302i	0.0449729	+	0.0778953i
$414$	−22.2134	−	4.99493i	−1.09173	−	0.245488i
$415$	−3.10115	+	5.37136i	−0.152230	+	0.263670i
$416$	−0.0798109	+	0.0669693i	−0.00391305	+	0.00328344i
$417$	−8.26394	+	7.88715i	−0.404687	+	0.386235i
$418$	−1.93978	+	11.0010i	−0.0948778	+	0.538079i
$419$	4.04106	−	22.9180i	0.197419	−	1.11962i	−0.711513	−	0.702673i	$-0.751990\pi$
$419$	4.04106	−	22.9180i	0.197419	−	1.11962i	0.908932	−	0.416945i	$-0.136899\pi$
$420$	−1.15482	−	0.338490i	−0.0563495	−	0.0165166i
$421$	15.3618	−	12.8901i	0.748691	−	0.628226i	−0.186466	−	0.982461i	$-0.559703\pi$
$421$	15.3618	−	12.8901i	0.748691	−	0.628226i	0.935156	+	0.354235i	$0.115259\pi$
$422$	−12.8069	+	22.1823i	−0.623432	+	1.07982i
$423$	−21.6787	+	11.2022i	−1.05405	+	0.544671i
$424$	5.85753	+	10.1455i	0.284467	+	0.492711i
$425$	25.2662	+	9.19613i	1.22559	+	0.446078i
$426$	−19.3442	+	1.23859i	−0.937230	+	0.0600098i
$427$	−5.83731	−	4.89808i	−0.282487	−	0.237035i
$428$	8.68999	−	3.16290i	0.420046	−	0.152884i
$429$	0.622115	+	0.457598i	0.0300360	+	0.0220930i
$430$	−1.02681	−	5.82335i	−0.0495174	−	0.280827i
$431$	−33.5350			−1.61532			−0.807662	−	0.589646i	$-0.799267\pi$
$431$	−33.5350			−1.61532			−0.807662	+	0.589646i	$0.799267\pi$
$432$	−1.86135	−	4.85133i	−0.0895543	−	0.233410i
$433$	−33.0631			−1.58891			−0.794457	−	0.607321i	$-0.792244\pi$
$433$	−33.0631			−1.58891			−0.794457	+	0.607321i	$0.792244\pi$
$434$	1.65198	+	9.36887i	0.0792978	+	0.449720i
$435$	−0.740652	+	6.66987i	−0.0355115	+	0.319796i
$436$	0.825154	−	0.300331i	0.0395177	−	0.0143833i
$437$	−15.1752	−	12.7335i	−0.725926	−	0.609124i
$438$	5.19775	−	10.5000i	0.248358	−	0.501711i
$439$	25.3395	+	9.22284i	1.20939	+	0.440182i	0.866492	−	0.499191i	$-0.166369\pi$
$439$	25.3395	+	9.22284i	1.20939	+	0.440182i	0.342898	+	0.939373i	$0.388592\pi$
$440$	−1.48672	−	2.57508i	−0.0708767	−	0.122762i
$441$	2.97550	−	0.382605i	0.141691	−	0.0182193i
$442$	0.310067	−	0.537052i	0.0147484	−	0.0255450i
$443$	28.9533	−	24.2947i	1.37561	−	1.15428i	0.404808	−	0.914402i	$-0.367338\pi$
$443$	28.9533	−	24.2947i	1.37561	−	1.15428i	0.970804	−	0.239874i	$-0.0771061\pi$
$444$	0.244121	+	1.00420i	0.0115855	+	0.0476571i
$445$	0.0306693	−	0.173934i	0.00145386	−	0.00824527i
$446$	−1.97117	+	11.1790i	−0.0933374	+	0.529343i
$447$	0.881947	+	3.62791i	0.0417147	+	0.171594i
$448$	−0.766044	+	0.642788i	−0.0361922	+	0.0303689i
$449$	−2.66591	+	4.61749i	−0.125812	+	0.217913i	−0.922050	−	0.387071i	$-0.873487\pi$
$449$	−2.66591	+	4.61749i	−0.125812	+	0.217913i	0.796238	+	0.604983i	$0.206820\pi$
$450$	5.22380	−	12.5045i	0.246252	−	0.589470i
$451$	−12.9544	−	22.4377i	−0.610000	−	1.05655i
$452$	12.3038	+	4.47822i	0.578723	+	0.210638i
$453$	−9.48267	+	19.1561i	−0.445535	+	0.900031i
$454$	−4.15383	−	3.48548i	−0.194949	−	0.163582i
$455$	−0.0680215	+	0.0247578i	−0.00318889	+	0.00116066i
$456$	0.498966	−	4.49339i	0.0233662	−	0.210422i
$457$	−1.10475	−	6.26535i	−0.0516780	−	0.293081i	0.948005	−	0.318255i	$-0.103097\pi$
$457$	−1.10475	−	6.26535i	−0.0516780	−	0.293081i	−0.999683	+	0.0251747i	$0.991986\pi$
$458$	16.1764			0.755876
$459$	20.2872	+	23.3453i	0.946924	+	1.08967i
$460$	5.27298			0.245854
$461$	−1.19479	−	6.77598i	−0.0556468	−	0.315589i	0.944261	−	0.329199i	$-0.106779\pi$
$461$	−1.19479	−	6.77598i	−0.0556468	−	0.315589i	−0.999907	+	0.0136102i	$0.995668\pi$
$462$	5.97121	+	4.39213i	0.277806	+	0.204341i
$463$	−6.23373	+	2.26889i	−0.289706	+	0.105444i	−0.482785	−	0.875739i	$-0.660375\pi$
$463$	−6.23373	+	2.26889i	−0.289706	+	0.105444i	0.193079	+	0.981183i	$0.438153\pi$
$464$	4.27189	+	3.58454i	0.198318	+	0.166408i
$465$	11.4251	−	0.731537i	0.529826	−	0.0339242i
$466$	9.69490	+	3.52865i	0.449107	+	0.163462i
$467$	−8.17686	−	14.1627i	−0.378380	−	0.655373i	0.612447	−	0.790512i	$-0.290185\pi$
$467$	−8.17686	−	14.1627i	−0.378380	−	0.655373i	−0.990827	+	0.135138i	$0.956852\pi$
$468$	−0.263100	−	0.168731i	−0.0121618	−	0.00779960i
$469$	6.07173	−	10.5165i	0.280366	−	0.485609i
$470$	4.32921	−	3.63264i	0.199692	−	0.167561i
$471$	−8.31250	−	2.43648i	−0.383020	−	0.112267i
$472$	0.317414	−	1.80014i	0.0146102	−	0.0828583i
$473$	−6.32482	+	35.8698i	−0.290816	+	1.64930i
$474$	6.29880	−	6.01161i	0.289313	−	0.276122i
$475$	9.03243	−	7.57911i	0.414436	−	0.347753i
$476$	2.97610	−	5.15476i	0.136409	−	0.236268i
$477$	−23.8218	+	25.8400i	−1.09073	+	1.18313i
$478$	−3.38966	−	5.87107i	−0.155040	−	0.268537i
$479$	3.44782	+	1.25490i	0.157535	+	0.0573380i	0.419584	−	0.907717i	$-0.362176\pi$
$479$	3.44782	+	1.25490i	0.157535	+	0.0573380i	−0.262049	+	0.965055i	$0.584398\pi$
$480$	0.667067	+	1.00160i	0.0304473	+	0.0457167i
$481$	0.0476200	+	0.0399579i	0.00217128	+	0.00182192i
$482$	1.13466	−	0.412983i	0.0516824	−	0.0188108i
$483$	−12.0399	+	5.27601i	−0.547833	+	0.240067i
$484$	1.27030	+	7.20425i	0.0577411	+	0.327466i
$485$	3.25602			0.147848
$486$	12.2304	−	9.66523i	0.554784	−	0.438424i
$487$	−8.56920			−0.388308			−0.194154	−	0.980971i	$-0.562196\pi$
$487$	−8.56920			−0.388308			−0.194154	+	0.980971i	$0.562196\pi$
$488$	1.32321	+	7.50430i	0.0598989	+	0.339704i
$489$	3.32655	−	1.45773i	0.150432	−	0.0659209i
$490$	−0.652886	+	0.237631i	−0.0294944	+	0.0107351i
$491$	−8.38220	−	7.03350i	−0.378283	−	0.317417i	0.433745	−	0.901036i	$-0.357192\pi$
$491$	−8.38220	−	7.03350i	−0.378283	−	0.317417i	−0.812028	+	0.583618i	$0.801636\pi$
$492$	5.81243	+	8.72738i	0.262044	+	0.393461i
$493$	−31.1910	−	11.3526i	−1.40477	−	0.511295i
$494$	−0.135973	−	0.235512i	−0.00611772	−	0.0105962i
$495$	6.04630	−	6.55855i	0.271761	−	0.294785i
$496$	4.75670	−	8.23885i	0.213582	−	0.369935i
$497$	−8.57300	+	7.19360i	−0.384552	+	0.322677i
$498$	−11.1852	+	10.6752i	−0.501221	+	0.478369i
$499$	7.29445	−	41.3689i	0.326544	−	1.85193i	−0.172047	−	0.985089i	$-0.555038\pi$
$499$	7.29445	−	41.3689i	0.326544	−	1.85193i	0.498592	−	0.866837i	$-0.333851\pi$
$500$	−1.14824	+	6.51202i	−0.0513511	+	0.291226i
$501$	32.0424	+	9.39197i	1.43155	+	0.419602i
$502$	0.181222	−	0.152063i	0.00808833	−	0.00678691i
$503$	16.1211	−	27.9227i	0.718807	−	1.24501i	−0.242666	−	0.970110i	$-0.578022\pi$
$503$	16.1211	−	27.9227i	0.718807	−	1.24501i	0.961473	−	0.274900i	$-0.0886446\pi$
$504$	−2.52530	−	1.61952i	−0.112486	−	0.0721393i
$505$	2.24307	+	3.88511i	0.0998152	+	0.172885i
$506$	−30.5210	−	11.1087i	−1.35682	−	0.493843i
$507$	22.4519	−	1.43757i	0.997123	−	0.0638447i
$508$	−10.5547	−	8.85645i	−0.468289	−	0.392942i
$509$	8.80941	−	3.20636i	0.390470	−	0.142120i	−0.139322	−	0.990247i	$-0.544492\pi$
$509$	8.80941	−	3.20636i	0.390470	−	0.142120i	0.529792	+	0.848128i	$0.322270\pi$
$510$	−5.77010	−	4.24421i	−0.255504	−	0.187937i
$511$	−1.17461	−	6.66153i	−0.0519616	−	0.294689i
$512$	1.00000			0.0441942
$513$	13.3142	−	2.58580i	0.587838	−	0.114166i
$514$	4.67470			0.206192
$515$	1.06192	+	6.02246i	0.0467939	+	0.265381i
$516$	1.62692	−	14.6511i	0.0716211	−	0.644977i
$517$	−32.7112	+	11.9059i	−1.43864	+	0.523622i
$518$	0.457068	+	0.383526i	0.0200824	+	0.0168511i
$519$	19.0660	−	38.5155i	0.836905	−	1.69064i
$520$	0.0680215	+	0.0247578i	0.00298294	+	0.00108570i
$521$	5.18254	+	8.97643i	0.227051	+	0.393264i	0.956933	−	0.290309i	$-0.0937581\pi$
$521$	5.18254	+	8.97643i	0.227051	+	0.393264i	−0.729882	+	0.683574i	$0.760425\pi$
$522$	−6.44876	+	15.4368i	−0.282255	+	0.675651i
$523$	13.9619	−	24.1827i	0.610512	−	1.05744i	−0.380642	−	0.924722i	$-0.624297\pi$
$523$	13.9619	−	24.1827i	0.610512	−	1.05744i	0.991154	−	0.132715i	$-0.0423696\pi$
$524$	−10.4169	+	8.74084i	−0.455066	+	0.381846i
$525$	−1.84822	−	7.60271i	−0.0806631	−	0.331810i
$526$	−0.470703	+	2.66949i	−0.0205236	+	0.116395i
$527$	−9.83294	+	55.7654i	−0.428330	+	2.42918i
$528$	−1.75100	−	7.20279i	−0.0762026	−	0.313461i
$529$	26.5038	−	22.2393i	1.15234	−	0.966926i
$530$	4.06974	−	7.04900i	0.176778	−	0.306189i
$531$	5.43896	−	0.699368i	0.236031	−	0.0303500i
$532$	−1.30510	−	2.26050i	−0.0565834	−	0.0980053i
$533$	0.592698	+	0.215725i	0.0256726	+	0.00934407i
$534$	0.195332	−	0.394593i	0.00845285	−	0.0170757i
$535$	−4.92197	−	4.13002i	−0.212795	−	0.178557i
$536$	−11.4111	+	4.15330i	−0.492885	+	0.179395i
$537$	−3.20076	+	28.8241i	−0.138123	+	1.24385i
$538$	1.05142	+	5.96291i	0.0453300	+	0.257079i
$539$	4.27965			0.184337
$540$	−2.27244	+	2.80530i	−0.0977902	+	0.120721i
$541$	−6.78565			−0.291738			−0.145869	−	0.989304i	$-0.546598\pi$
$541$	−6.78565			−0.291738			−0.145869	+	0.989304i	$0.546598\pi$
$542$	0.604052	+	3.42575i	0.0259463	+	0.147149i
$543$	21.3095	+	15.6742i	0.914477	+	0.672645i
$544$	−5.59324	+	2.03577i	−0.239808	+	0.0872830i
$545$	−0.467364	−	0.392165i	−0.0200197	−	0.0167985i
$546$	−0.180086	+	0.0115307i	−0.00770698	+	0.000493469i
$547$	−0.564924	−	0.205616i	−0.0241544	−	0.00879149i	0.329915	−	0.944011i	$-0.392980\pi$
$547$	−0.564924	−	0.205616i	−0.0241544	−	0.00879149i	−0.354069	+	0.935219i	$0.615202\pi$
$548$	3.21485	+	5.56829i	0.137332	+	0.237865i
$549$	−20.3090	+	10.4945i	−0.866767	+	0.447892i
$550$	9.66616	−	16.7423i	0.412167	−	0.713894i
$551$	−11.1505	+	9.35639i	−0.475028	+	0.398596i
$552$	12.6144	+	3.69742i	0.536906	+	0.157373i
$553$	0.872941	−	4.95070i	0.0371212	−	0.210525i
$554$	5.15138	−	29.2149i	0.218861	−	1.24122i
$555$	0.519423	−	0.495741i	0.0220483	−	0.0210430i
$556$	5.05241	−	4.23947i	0.214270	−	0.179794i
$557$	5.33464	−	9.23986i	0.226036	−	0.391505i	−0.730594	−	0.682812i	$-0.760757\pi$
$557$	5.33464	−	9.23986i	0.226036	−	0.391505i	0.956630	+	0.291307i	$0.0940900\pi$
$558$	27.8449	+	6.26125i	1.17877	+	0.265060i
$559$	−0.443351	−	0.767907i	−0.0187518	−	0.0324790i
$560$	0.652886	+	0.237631i	0.0275895	+	0.0100418i
$561$	24.4570	+	36.7223i	1.03258	+	1.55042i
$562$	21.0300	+	17.6463i	0.887097	+	0.744363i
$563$	29.9974	−	10.9182i	1.26424	−	0.460146i	0.379050	−	0.925376i	$-0.376251\pi$
$563$	29.9974	−	10.9182i	1.26424	−	0.460146i	0.885189	+	0.465231i	$0.154029\pi$
$564$	12.9039	−	5.65463i	0.543351	−	0.238103i
$565$	−1.57971	−	8.95895i	−0.0664587	−	0.376906i
$566$	16.3796			0.688487
$567$	2.38177	−	8.67912i	0.100025	−	0.364489i
$568$	11.1913			0.469575
$569$	4.51106	+	25.5835i	0.189113	+	1.07252i	0.920555	+	0.390612i	$0.127737\pi$
$569$	4.51106	+	25.5835i	0.189113	+	1.07252i	−0.731442	+	0.681904i	$0.761152\pi$
$570$	−2.87702	+	1.26075i	−0.120505	+	0.0528068i
$571$	−1.88526	+	0.686178i	−0.0788956	+	0.0287156i	−0.381166	−	0.924506i	$-0.624478\pi$
$571$	−1.88526	+	0.686178i	−0.0788956	+	0.0287156i	0.302271	+	0.953222i	$0.402255\pi$
$572$	−0.341563	−	0.286605i	−0.0142814	−	0.0119836i
$573$	1.76193	+	2.64554i	0.0736056	+	0.110519i
$574$	5.68886	+	2.07058i	0.237449	+	0.0864242i
$575$	17.1416	+	29.6901i	0.714853	+	1.23816i
$576$	0.893483	+	2.86386i	0.0372285	+	0.119327i
$577$	−3.37436	+	5.84457i	−0.140477	+	0.243313i	−0.927676	−	0.373386i	$-0.878197\pi$
$577$	−3.37436	+	5.84457i	−0.140477	+	0.243313i	0.787200	+	0.616698i	$0.211530\pi$
$578$	14.1172	−	11.8457i	0.587197	−	0.492717i
$579$	16.1463	−	15.4101i	0.671016	−	0.640422i
$580$	0.672804	−	3.81566i	0.0279366	−	0.158437i
$581$	−1.55014	+	8.79130i	−0.0643108	+	0.364725i
$582$	7.78930	+	2.28313i	0.322877	+	0.0946386i
$583$	−38.4067	+	32.2270i	−1.59064	+	1.33471i
$584$	−3.38215	+	5.85805i	−0.139954	+	0.242408i
$585$	−0.0101268	+	0.216924i	−0.000418692	+	0.00896872i
$586$	−2.65800	−	4.60378i	−0.109801	−	0.190181i
$587$	−34.5012	−	12.5574i	−1.42402	−	0.518299i	−0.488806	−	0.872393i	$-0.662567\pi$
$587$	−34.5012	−	12.5574i	−1.42402	−	0.518299i	−0.935210	+	0.354093i	$0.884790\pi$
$588$	−1.72851	+	0.110675i	−0.0712826	+	0.00456415i
$589$	19.0224	+	15.9617i	0.783803	+	0.657689i
$590$	−1.19342	+	0.434369i	−0.0491323	+	0.0178827i
$591$	−4.32800	−	3.18347i	−0.178030	−	0.130950i
$592$	−0.103609	−	0.587595i	−0.00425830	−	0.0241500i
$593$	42.0175			1.72545			0.862727	−	0.505671i	$-0.168755\pi$
$593$	42.0175			1.72545			0.862727	+	0.505671i	$0.168755\pi$
$594$	19.0633	−	11.4502i	0.782176	−	0.469807i
$595$	−4.13551			−0.169539
$596$	−0.374313	−	2.12283i	−0.0153324	−	0.0869546i
$597$	−4.02940	+	36.2864i	−0.164912	+	1.48510i
$598$	0.743017	−	0.270436i	0.0303842	−	0.0110589i
$599$	18.7373	+	15.7225i	0.765587	+	0.642404i	0.939575	−	0.342344i	$-0.111221\pi$
$599$	18.7373	+	15.7225i	0.765587	+	0.642404i	−0.173988	+	0.984748i	$0.555665\pi$
$600$	−3.47111	+	7.01203i	−0.141707	+	0.286265i
$601$	11.8825	+	4.32487i	0.484697	+	0.176415i	0.572798	−	0.819696i	$-0.305858\pi$
$601$	11.8825	+	4.32487i	0.484697	+	0.176415i	−0.0881016	+	0.996111i	$0.528080\pi$
$602$	−4.25540	−	7.37056i	−0.173437	−	0.300402i
$603$	−22.0901	−	28.9689i	−0.899579	−	1.17971i
$604$	6.17033	−	10.6873i	0.251067	−	0.434861i
$605$	3.89353	−	3.26706i	0.158294	−	0.132825i
$606$	2.64179	+	10.8671i	0.107316	+	0.441445i
$607$	−7.14394	+	40.5153i	−0.289964	+	1.64447i	0.397033	+	0.917805i	$0.370040\pi$
$607$	−7.14394	+	40.5153i	−0.289964	+	1.64447i	−0.686996	+	0.726661i	$0.741071\pi$
$608$	−0.453257	+	2.57055i	−0.0183820	+	0.104250i
$609$	2.28163	+	9.38553i	0.0924562	+	0.380321i
$610$	4.05569	−	3.40313i	0.164210	−	0.137789i
$611$	0.423722	−	0.733909i	0.0171420	−	0.0296908i
$612$	−10.8276	−	14.1993i	−0.437681	−	0.573973i
$613$	−4.34656	−	7.52847i	−0.175556	−	0.304072i	0.764797	−	0.644271i	$-0.222839\pi$
$613$	−4.34656	−	7.52847i	−0.175556	−	0.304072i	−0.940354	+	0.340199i	$0.889506\pi$
$614$	9.33616	+	3.39808i	0.376777	+	0.137135i
$615$	3.23209	−	6.52919i	0.130331	−	0.263282i
$616$	−3.27840	−	2.75090i	−0.132091	−	0.110837i
$617$	−26.0006	+	9.46345i	−1.04675	+	0.380984i	−0.807434	−	0.589958i	$-0.799144\pi$
$617$	−26.0006	+	9.46345i	−1.04675	+	0.380984i	−0.239312	+	0.970943i	$0.576922\pi$
$618$	−1.68255	+	15.1520i	−0.0676819	+	0.609503i
$619$	−6.08858	−	34.5300i	−0.244721	−	1.38788i	−0.821141	−	0.570726i	$-0.806662\pi$
$619$	−6.08858	−	34.5300i	−0.244721	−	1.38788i	0.576420	−	0.817153i	$-0.304449\pi$
$620$	−6.60979			−0.265456
$621$	0.681882	+	39.4295i	0.0273630	+	1.58225i
$622$	8.36771			0.335514
$623$	−0.0441420	−	0.250342i	−0.00176851	−	0.0100297i
$624$	0.145366	+	0.106924i	0.00581929	+	0.00428039i
$625$	−16.9070	+	6.15366i	−0.676281	+	0.246146i
$626$	−20.8296	−	17.4781i	−0.832519	−	0.698567i
$627$	19.3088	−	1.23632i	0.771118	−	0.0493739i
$628$	4.69953	+	1.71049i	0.187532	+	0.0682559i
$629$	1.77572	+	3.07564i	0.0708026	+	0.122634i
$630$	−0.0971995	+	2.08209i	−0.00387252	+	0.0829526i
$631$	6.06272	−	10.5009i	0.241353	−	0.418036i	−0.719747	−	0.694237i	$-0.755742\pi$
$631$	6.06272	−	10.5009i	0.241353	−	0.418036i	0.961100	+	0.276201i	$0.0890755\pi$
$632$	−3.85096	+	3.23134i	−0.153183	+	0.128536i
$633$	42.5734	+	12.4787i	1.69214	+	0.495984i
$634$	1.38467	−	7.85283i	0.0549921	−	0.311876i
$635$	−1.66232	+	9.42748i	−0.0659671	+	0.374118i
$636$	14.6787	−	14.0094i	0.582048	−	0.555510i
$637$	−0.0798109	+	0.0669693i	−0.00316222	+	0.00265342i
$638$	−11.9329	+	20.6683i	−0.472426	+	0.818266i
$639$	9.99919	+	32.0502i	0.395562	+	1.26789i
$640$	−0.347394	−	0.601703i	−0.0137319	−	0.0237844i
$641$	−11.0893	−	4.03616i	−0.438000	−	0.159419i	0.113602	−	0.993526i	$-0.463761\pi$
$641$	−11.0893	−	4.03616i	−0.438000	−	0.159419i	−0.551602	+	0.834108i	$0.685983\pi$
$642$	−8.87873	−	13.3314i	−0.350416	−	0.526150i
$643$	20.1576	+	16.9143i	0.794939	+	0.667033i	0.946963	−	0.321344i	$-0.104134\pi$
$643$	20.1576	+	16.9143i	0.794939	+	0.667033i	−0.152023	+	0.988377i	$0.548579\pi$
$644$	7.13166	−	2.59571i	0.281027	−	0.102285i
$645$	−9.38078	+	4.11077i	−0.369368	+	0.161861i
$646$	−2.69788	−	15.3004i	−0.106147	−	0.601987i
$647$	−4.39110			−0.172632			−0.0863160	−	0.996268i	$-0.527509\pi$
$647$	−4.39110			−0.172632			−0.0863160	+	0.996268i	$0.527509\pi$
$648$	−7.40338	+	5.11762i	−0.290832	+	0.201039i
$649$	7.82282			0.307073
$650$	0.0817249	+	0.463485i	0.00320552	+	0.0181794i
$651$	15.0922	−	6.61358i	0.591511	−	0.259207i
$652$	−1.97044	+	0.717180i	−0.0771682	+	0.0280869i
$653$	19.9590	+	16.7476i	0.781058	+	0.655385i	0.943515	−	0.331330i	$-0.107497\pi$
$653$	19.9590	+	16.7476i	0.781058	+	0.655385i	−0.162457	+	0.986716i	$0.551942\pi$
$654$	−0.843076	−	1.26588i	−0.0329669	−	0.0494999i
$655$	8.87817	+	3.23139i	0.346899	+	0.126261i
$656$	−3.02698	−	5.24289i	−0.118184	−	0.204700i
$657$	−19.7985	−	4.45193i	−0.772414	−	0.173686i
$658$	4.06699	−	7.04424i	0.158548	−	0.274613i
$659$	−8.90423	+	7.47153i	−0.346859	+	0.291050i	−0.799528	−	0.600629i	$-0.794917\pi$
$659$	−8.90423	+	7.47153i	−0.346859	+	0.291050i	0.452668	+	0.891679i	$0.350472\pi$
$660$	−3.72566	+	3.55579i	−0.145021	+	0.138409i
$661$	3.88885	−	22.0548i	0.151259	−	0.857831i	−0.810868	−	0.585229i	$-0.801005\pi$
$661$	3.88885	−	22.0548i	0.151259	−	0.857831i	0.962127	−	0.272602i	$-0.0878842\pi$
$662$	−5.30594	+	30.0915i	−0.206221	+	1.16954i
$663$	−1.03074	−	0.302120i	−0.0400306	−	0.0117334i
$664$	6.83842	−	5.73811i	0.265382	−	0.222682i
$665$	−0.906769	+	1.57057i	−0.0351630	+	0.0609041i
$666$	1.59022	−	0.821728i	0.0616197	−	0.0318413i
$667$	−21.1612	−	36.6523i	−0.819366	−	1.41918i
$668$	−18.1154	−	6.59347i	−0.700906	−	0.255109i
$669$	19.6212	−	1.25632i	0.758599	−	0.0485723i
$670$	6.46321	+	5.42327i	0.249695	+	0.209519i
$671$	−30.6445	+	11.1537i	−1.18302	+	0.430583i
$672$	1.39526	+	1.02628i	0.0538232	+	0.0395898i
$673$	−7.62422	−	43.2391i	−0.293892	−	1.66674i	−0.671672	−	0.740849i	$-0.734424\pi$
$673$	−7.62422	−	43.2391i	−0.293892	−	1.66674i	0.377780	−	0.925895i	$-0.376688\pi$
$674$	0.225172			0.00867332
$675$	−23.1828	−	3.67564i	−0.892308	−	0.141475i
$676$	−12.9891			−0.499583
$677$	−6.81801	−	38.6668i	−0.262037	−	1.48609i	−0.777341	−	0.629079i	$-0.783432\pi$
$677$	−6.81801	−	38.6668i	−0.262037	−	1.48609i	0.515304	−	0.857008i	$-0.327679\pi$
$678$	2.50294	−	22.5400i	0.0961247	−	0.865642i
$679$	4.40374	−	1.60283i	0.169000	−	0.0615110i
$680$	3.16799	+	2.65826i	0.121487	+	0.101939i
$681$	−4.16665	+	8.41710i	−0.159666	+	0.322544i
$682$	38.2587	+	13.9250i	1.46500	+	0.533216i
$683$	12.5822	+	21.7930i	0.481444	+	0.833885i	0.999773	−	0.0212961i	$-0.00677928\pi$
$683$	12.5822	+	21.7930i	0.481444	+	0.833885i	−0.518330	+	0.855181i	$0.673446\pi$
$684$	−7.76667	+	0.998677i	−0.296966	+	0.0381854i
$685$	2.23364	−	3.86878i	0.0853429	−	0.147818i
$686$	−0.766044	+	0.642788i	−0.0292477	+	0.0245417i
$687$	−6.61853	−	27.2255i	−0.252513	−	1.03872i
$688$	−1.47788	+	8.38149i	−0.0563438	+	0.319541i
$689$	0.211945	−	1.20200i	0.00807446	−	0.0457926i
$690$	−2.15742	−	8.87460i	−0.0821316	−	0.337850i
$691$	−12.7814	+	10.7249i	−0.486228	+	0.407994i	−0.852672	−	0.522446i	$-0.825020\pi$
$691$	−12.7814	+	10.7249i	−0.486228	+	0.407994i	0.366444	+	0.930440i	$0.380575\pi$
$692$	−12.4062	+	21.4881i	−0.471612	+	0.816856i
$693$	4.94901	−	11.8468i	0.187997	−	0.450021i
$694$	−11.2463	−	19.4791i	−0.426903	−	0.739418i
$695$	−4.30608	−	1.56728i	−0.163339	−	0.0594505i
$696$	4.28507	−	8.65633i	0.162425	−	0.328118i
$697$	27.6039	+	23.1625i	1.04557	+	0.877341i
$698$	−9.94976	+	3.62142i	−0.376604	+	0.137073i
$699$	1.97221	−	17.7606i	0.0745958	−	0.671766i
$700$	0.784416	+	4.44864i	0.0296481	+	0.168143i
$701$	2.37882			0.0898467			0.0449233	−	0.998990i	$-0.485696\pi$
$701$	2.37882			0.0898467			0.0449233	+	0.998990i	$0.485696\pi$
$702$	−0.176334	+	0.511842i	−0.00665529	+	0.0193182i
$703$	1.55740			0.0587386
$704$	0.743153	+	4.21463i	0.0280086	+	0.158845i
$705$	−7.88514	−	5.79993i	−0.296971	−	0.218438i
$706$	−20.3293	+	7.39925i	−0.765103	+	0.278475i
$707$	4.94623	+	4.15038i	0.186022	+	0.156091i
$708$	−3.15957	+	0.202304i	−0.118744	+	0.00760304i
$709$	15.7986	+	5.75021i	0.593328	+	0.215954i	0.621193	−	0.783658i	$-0.286648\pi$
$709$	15.7986	+	5.75021i	0.593328	+	0.215954i	−0.0278646	+	0.999612i	$0.508871\pi$
$710$	−3.88777	−	6.73382i	−0.145905	−	0.252716i
$711$	−12.6949	−	8.14146i	−0.476094	−	0.305328i
$712$	−0.127102	+	0.220147i	−0.00476334	+	0.00825035i
$713$	−55.3088	+	46.4096i	−2.07133	+	1.73805i
$714$	−9.89328	−	2.89982i	−0.370247	−	0.108523i
$715$	−0.0537946	+	0.305084i	−0.00201180	+	0.0114095i
$716$	2.90755	−	16.4895i	0.108660	−	0.616242i
$717$	−8.49434	+	8.10704i	−0.317227	+	0.302763i
$718$	−9.66832	+	8.11269i	−0.360819	+	0.302763i
$719$	−8.90616	+	15.4259i	−0.332144	+	0.575290i	−0.982932	−	0.183969i	$-0.941105\pi$
$719$	−8.90616	+	15.4259i	−0.332144	+	0.575290i	0.650788	+	0.759259i	$0.274439\pi$
$720$	1.41280	−	1.53250i	0.0526521	−	0.0571128i
$721$	4.40089	+	7.62257i	0.163898	+	0.283879i
$722$	11.4519	+	4.16814i	0.426195	+	0.155122i
$723$	−1.15931	−	1.74070i	−0.0431150	−	0.0647374i
$724$	−11.6996	−	9.81716i	−0.434814	−	0.364852i
$725$	23.6716	−	8.61577i	0.879142	−	0.319982i
$726$	11.6053	−	5.08555i	0.430711	−	0.188743i
$727$	7.98516	+	45.2861i	0.296153	+	1.67957i	0.662478	+	0.749081i	$0.269505\pi$
$727$	7.98516	+	45.2861i	0.296153	+	1.67957i	−0.366325	+	0.930487i	$0.619384\pi$
$728$	0.104186			0.00386138
$729$	−21.2709	−	16.6297i	−0.787812	−	0.615916i
$730$	4.69975			0.173946
$731$	−8.79666	−	49.8883i	−0.325356	−	1.84519i
$732$	12.0886	−	5.29736i	0.446807	−	0.195796i
$733$	−33.6147	+	12.2348i	−1.24159	+	0.451901i	−0.877551	−	0.479483i	$-0.840824\pi$
$733$	−33.6147	+	12.2348i	−1.24159	+	0.451901i	−0.364037	+	0.931384i	$0.618602\pi$
$734$	19.2584	+	16.1598i	0.710842	+	0.596467i
$735$	0.667067	+	1.00160i	0.0246051	+	0.0369447i
$736$	−7.13166	−	2.59571i	−0.262876	−	0.0956791i
$737$	−25.9848	−	45.0071i	−0.957164	−	1.65786i
$738$	12.3103	−	13.3533i	0.453150	−	0.491541i
$739$	1.43031	−	2.47738i	0.0526149	−	0.0911317i	−0.838518	−	0.544873i	$-0.816578\pi$
$739$	1.43031	−	2.47738i	0.0526149	−	0.0911317i	0.891133	+	0.453742i	$0.149911\pi$
$740$	−0.317565	+	0.266469i	−0.0116739	+	0.00979559i
$741$	−0.340742	+	0.325206i	−0.0125175	+	0.0119467i
$742$	2.03430	−	11.5371i	0.0746815	−	0.423540i
$743$	7.63187	−	43.2825i	0.279986	−	1.58788i	−0.442677	−	0.896681i	$-0.645971\pi$
$743$	7.63187	−	43.2825i	0.279986	−	1.58788i	0.722664	−	0.691200i	$-0.242918\pi$
$744$	−15.8124	−	4.63479i	−0.579712	−	0.169920i
$745$	−1.14728	+	0.962683i	−0.0420331	+	0.0352700i
$746$	3.52613	−	6.10743i	0.129101	−	0.223609i
$747$	22.5432	+	14.4574i	0.824811	+	0.528967i
$748$	−12.7367	−	22.0605i	−0.465698	−	0.806613i
$749$	−8.68999	−	3.16290i	−0.317525	−	0.115570i
$750$	11.4297	−	0.731834i	0.417355	−	0.0267228i
$751$	−40.5972	−	34.0651i	−1.48141	−	1.24305i	−0.904659	−	0.426136i	$-0.859874\pi$
$751$	−40.5972	−	34.0651i	−1.48141	−	1.24305i	−0.576755	−	0.816917i	$-0.695681\pi$
$752$	−7.64344	+	2.78199i	−0.278728	+	0.101449i
$753$	−0.330074	−	0.242786i	−0.0120286	−	0.00884762i
$754$	−0.100889	−	0.572171i	−0.00367417	−	0.0208372i
$755$	−8.57414			−0.312045
$756$	−1.69249	+	4.91279i	−0.0615554	+	0.178676i
$757$	−50.2851			−1.82764			−0.913822	−	0.406115i	$-0.866883\pi$
$757$	−50.2851			−1.82764			−0.913822	+	0.406115i	$0.866883\pi$
$758$	−5.74492	−	32.5811i	−0.208665	−	1.18340i
$759$	−6.20881	+	55.9129i	−0.225366	+	2.02951i
$760$	1.70417	−	0.620266i	0.0618167	−	0.0224994i
$761$	28.5965	+	23.9953i	1.03662	+	0.869830i	0.991624	−	0.129157i	$-0.0412273\pi$
$761$	28.5965	+	23.9953i	1.03662	+	0.869830i	0.0449984	+	0.998987i	$0.485672\pi$
$762$	−10.5873	+	21.3875i	−0.383537	+	0.774788i
$763$	−0.825154	−	0.300331i	−0.0298726	−	0.0108727i
$764$	−0.917573	−	1.58928i	−0.0331966	−	0.0574982i
$765$	−4.78233	+	11.4478i	−0.172905	+	0.413895i
$766$	−18.7813	+	32.5302i	−0.678597	+	1.17536i
$767$	−0.145887	+	0.122414i	−0.00526769	+	0.00442011i
$768$	−0.409146	−	1.68303i	−0.0147638	−	0.0607312i
$769$	−5.67779	+	32.2004i	−0.204746	+	1.16117i	0.693092	+	0.720849i	$0.256248\pi$
$769$	−5.67779	+	32.2004i	−0.204746	+	1.16117i	−0.897838	+	0.440325i	$0.854863\pi$
$770$	−0.516333	+	2.92827i	−0.0186074	+	0.105528i
$771$	−1.91264	−	7.86768i	−0.0688819	−	0.283348i
$772$	−9.87151	+	8.28318i	−0.355283	+	0.298118i
$773$	1.15306	−	1.99717i	0.0414728	−	0.0718330i	−0.844544	−	0.535486i	$-0.820128\pi$
$773$	1.15306	−	1.99717i	0.0414728	−	0.0718330i	0.886017	+	0.463653i	$0.153462\pi$
$774$	−25.3239	+	3.25627i	−0.910248	+	0.117044i
$775$	−21.4873	−	37.2171i	−0.771847	−	1.33688i
$776$	−4.40374	−	1.60283i	−0.158085	−	0.0575382i
$777$	0.458479	−	0.926179i	0.0164478	−	0.0332265i
$778$	2.97849	+	2.49925i	0.106784	+	0.0896024i
$779$	14.8491	−	5.40463i	0.532024	−	0.193641i
$780$	0.0138374	−	0.124612i	0.000495460	−	0.00446182i
$781$	8.31681	+	47.1670i	0.297599	+	1.68777i
$782$	45.1733			1.61539
$783$	28.6192	+	4.53756i	1.02277	+	0.162159i
$784$	1.00000			0.0357143
$785$	−0.603380	−	3.42194i	−0.0215355	−	0.122134i
$786$	18.9732	+	13.9558i	0.676751	+	0.497785i
$787$	17.3409	−	6.31158i	0.618137	−	0.224983i	−0.0139229	−	0.999903i	$-0.504432\pi$
$787$	17.3409	−	6.31158i	0.618137	−	0.224983i	0.632060	+	0.774920i	$0.282210\pi$
$788$	2.37622	+	1.99389i	0.0846494	+	0.0710293i
$789$	4.68543	−	0.300003i	0.166806	−	0.0106804i
$790$	3.28210	+	1.19459i	0.116772	+	0.0425016i
$791$	−6.54672	−	11.3393i	−0.232775	−	0.403178i
$792$	−11.4061	+	5.89399i	−0.405299	+	0.209434i
$793$	0.396951	−	0.687539i	0.0140961	−	0.0244152i
$794$	−19.0106	+	15.9518i	−0.674663	+	0.566109i
$795$	−13.5288	−	3.96544i	−0.479818	−	0.140640i
$796$	3.66028	−	20.7585i	0.129735	−	0.735765i
$797$	−5.66261	+	32.1143i	−0.200580	+	1.13755i	0.703665	+	0.710532i	$0.251546\pi$
$797$	−5.66261	+	32.1143i	−0.200580	+	1.13755i	−0.904245	+	0.427014i	$0.859566\pi$
$798$	−3.27052	+	3.12141i	−0.115775	+	0.110497i
$799$	37.0881	−	31.1206i	1.31208	−	1.10097i
$800$	2.25864	−	3.91207i	0.0798548	−	0.138313i
$801$	−0.744033	−	0.167304i	−0.0262891	−	0.00591141i
$802$	3.71022	+	6.42629i	0.131013	+	0.226920i
$803$	−27.2030	−	9.90108i	−0.959973	−	0.349402i
$804$	11.6590	+	17.5060i	0.411180	+	0.617388i
$805$	−4.03934	−	3.38941i	−0.142368	−	0.119461i
$806$	−0.931386	+	0.338997i	−0.0328067	+	0.0119407i
$807$	9.60559	−	4.20928i	0.338133	−	0.148174i
$808$	−1.12122	−	6.35875i	−0.0394444	−	0.223700i
$809$	−25.2049			−0.886156			−0.443078	−	0.896483i	$-0.646113\pi$
$809$	−25.2049			−0.886156			−0.443078	+	0.896483i	$0.646113\pi$
$810$	5.65117	+	2.67681i	0.198562	+	0.0940535i
$811$	34.8432			1.22351			0.611754	−	0.791048i	$-0.290464\pi$
$811$	34.8432			1.22351			0.611754	+	0.791048i	$0.290464\pi$
$812$	−0.968359	−	5.49184i	−0.0339827	−	0.192726i
$813$	5.51851	−	2.41827i	0.193542	−	0.0848125i
$814$	2.39950	−	0.873347i	0.0841024	−	0.0306108i
$815$	1.11605	+	0.936474i	0.0390934	+	0.0328033i
$816$	5.71472	+	8.58067i	0.200055	+	0.300384i
$817$	−20.8752	−	7.59795i	−0.730330	−	0.265819i
$818$	−15.9483	−	27.6233i	−0.557619	−	0.965825i
$819$	0.0930882	+	0.298373i	0.00325276	+	0.0104260i
$820$	−2.10311	+	3.64269i	−0.0734437	+	0.127208i
$821$	−26.7632	+	22.4570i	−0.934042	+	0.783754i	−0.976539	−	0.215342i	$-0.930913\pi$
$821$	−26.7632	+	22.4570i	−0.934042	+	0.783754i	0.0424968	+	0.999097i	$0.486469\pi$
$822$	8.05627	−	7.68894i	0.280995	−	0.268183i
$823$	−4.61077	+	26.1490i	−0.160721	+	0.911496i	0.792646	+	0.609683i	$0.208703\pi$
$823$	−4.61077	+	26.1490i	−0.160721	+	0.911496i	−0.953367	+	0.301814i	$0.902408\pi$
$824$	1.52841	−	8.66807i	0.0532448	−	0.301967i
$825$	−32.1327	−	9.41843i	−1.11872	−	0.327908i
$826$	−1.40026	+	1.17496i	−0.0487214	+	0.0408821i
$827$	6.54077	−	11.3289i	0.227445	−	0.393946i	−0.729605	−	0.683869i	$-0.760296\pi$
$827$	6.54077	−	11.3289i	0.227445	−	0.393946i	0.957050	+	0.289922i	$0.0936295\pi$
$828$	1.06174	−	22.7433i	0.0368979	−	0.790384i
$829$	−7.95893	−	13.7853i	−0.276425	−	0.478782i	0.694069	−	0.719909i	$-0.255816\pi$
$829$	−7.95893	−	13.7853i	−0.276425	−	0.478782i	−0.970494	+	0.241127i	$0.922483\pi$
$830$	−5.82826	−	2.12131i	−0.202302	−	0.0736319i
$831$	−51.2773	+	3.28323i	−1.77879	+	0.113894i
$832$	−0.0798109	−	0.0669693i	−0.00276694	−	0.00232174i
$833$	−5.59324	+	2.03577i	−0.193794	+	0.0705353i
$834$	−9.20235	−	6.76880i	−0.318651	−	0.234384i
$835$	2.32586	+	13.1906i	0.0804898	+	0.456481i
$836$	−11.1708			−0.386349
$837$	−0.854753	−	49.4257i	−0.0295446	−	1.70840i
$838$	23.2716			0.803902
$839$	−4.05839	−	23.0163i	−0.140111	−	0.794610i	−0.971163	−	0.238415i	$-0.923372\pi$
$839$	−4.05839	−	23.0163i	−0.140111	−	0.794610i	0.831052	−	0.556195i	$-0.187739\pi$
$840$	0.132815	−	1.19606i	0.00458256	−	0.0412678i
$841$	−1.97147	+	0.717558i	−0.0679819	+	0.0247434i
$842$	15.3618	+	12.8901i	0.529404	+	0.444223i
$843$	21.0949	−	42.6141i	0.726547	−	1.46771i
$844$	−24.0692	−	8.76047i	−0.828496	−	0.301548i
$845$	4.51235	+	7.81561i	0.155229	+	0.268865i
$846$	−14.7965	−	19.4041i	−0.508714	−	0.667126i
$847$	3.65769	−	6.33531i	0.125680	−	0.217684i
$848$	−8.97426	+	7.53030i	−0.308177	+	0.258592i
$849$	−6.70166	−	27.5674i	−0.230000	−	0.946112i
$850$	−4.66900	+	26.4792i	−0.160145	+	0.908229i
$851$	−0.786324	+	4.45947i	−0.0269548	+	0.152869i
$852$	−4.57886	−	18.8352i	−0.156869	−	0.645285i
$853$	−6.27656	+	5.26666i	−0.214905	+	0.180327i	−0.743885	−	0.668307i	$-0.767019\pi$
$853$	−6.27656	+	5.26666i	−0.214905	+	0.180327i	0.528980	+	0.848634i	$0.322575\pi$
$854$	3.81003	−	6.59917i	0.130377	−	0.225819i
$855$	3.29900	+	4.32630i	0.112823	+	0.147956i
$856$	4.62384	+	8.00873i	0.158040	+	0.273733i
$857$	17.7527	+	6.46145i	0.606421	+	0.220719i	0.626936	−	0.779070i	$-0.284309\pi$
$857$	17.7527	+	6.46145i	0.606421	+	0.220719i	−0.0205158	+	0.999790i	$0.506531\pi$
$858$	−0.342617	+	0.692124i	−0.0116967	+	0.0236287i
$859$	−8.88268	−	7.45345i	−0.303073	−	0.254308i	0.478549	−	0.878061i	$-0.341163\pi$
$859$	−8.88268	−	7.45345i	−0.303073	−	0.254308i	−0.781622	+	0.623752i	$0.785607\pi$
$860$	5.55658	−	2.02243i	0.189478	−	0.0689643i
$861$	1.15727	−	10.4217i	0.0394397	−	0.355171i
$862$	−5.82329	−	33.0255i	−0.198342	−	1.12485i
$863$	15.9659			0.543486			0.271743	−	0.962370i	$-0.412400\pi$
$863$	15.9659			0.543486			0.271743	+	0.962370i	$0.412400\pi$
$864$	4.45440	−	2.67550i	0.151542	−	0.0910223i
$865$	17.2393			0.586154
$866$	−5.74135	−	32.5608i	−0.195099	−	1.10646i
$867$	−25.7127	−	18.9131i	−0.873250	−	0.642321i
$868$	−8.93967	+	3.25378i	−0.303432	+	0.110440i
$869$	−16.4807	−	13.8290i	−0.559071	−	0.469116i
$870$	−6.69715	+	0.428812i	−0.227055	+	0.0145381i
$871$	1.18887	+	0.432715i	0.0402835	+	0.0146620i
$872$	0.439055	+	0.760466i	0.0148683	+	0.0257526i
$873$	0.655613	−	14.0438i	0.0221892	−	0.475310i
$874$	9.90488	−	17.1558i	0.335037	−	0.580302i
$875$	5.06545	−	4.25042i	0.171244	−	0.143690i
$876$	11.2431	+	3.29547i	0.379869	+	0.111344i
$877$	−3.83483	+	21.7484i	−0.129493	+	0.734392i	0.849044	+	0.528322i	$0.177179\pi$
$877$	−3.83483	+	21.7484i	−0.129493	+	0.734392i	−0.978537	+	0.206070i	$0.933933\pi$
$878$	−4.68256	+	26.5561i	−0.158029	+	0.896225i
$879$	−6.66081	+	6.35712i	−0.224664	+	0.214420i
$880$	2.27779	−	1.91129i	0.0767843	−	0.0644297i
$881$	18.2040	−	31.5303i	0.613309	−	1.06228i	−0.377370	−	0.926063i	$-0.623171\pi$
$881$	18.2040	−	31.5303i	0.613309	−	1.06228i	0.990679	−	0.136219i	$-0.0434952\pi$
$882$	0.893483	+	2.86386i	0.0300851	+	0.0964311i
$883$	29.1033	+	50.4084i	0.979405	+	1.69638i	0.664558	+	0.747237i	$0.268620\pi$
$883$	29.1033	+	50.4084i	0.979405	+	1.69638i	0.314847	+	0.949142i	$0.398047\pi$
$884$	0.582736	+	0.212098i	0.0195995	+	0.00713364i
$885$	1.21934	+	1.83084i	0.0409877	+	0.0615431i
$886$	28.9533	+	24.2947i	0.972705	+	0.816196i
$887$	−9.59313	+	3.49161i	−0.322106	+	0.117237i	−0.498012	−	0.867170i	$-0.665937\pi$
$887$	−9.59313	+	3.49161i	−0.322106	+	0.117237i	0.175907	+	0.984407i	$0.443714\pi$
$888$	−0.946551	+	0.414790i	−0.0317642	+	0.0139194i
$889$	2.39256	+	13.5689i	0.0802438	+	0.455085i
$890$	0.176617			0.00592023
$891$	−27.0707	−	27.3993i	−0.906903	−	0.917912i
$892$	−11.3515			−0.380076
$893$	−3.68679	−	20.9088i	−0.123374	−	0.699687i
$894$	−3.41965	+	1.49853i	−0.114370	+	0.0501183i
$895$	−10.9319	+	3.97887i	−0.365412	+	0.132999i
$896$	−0.766044	−	0.642788i	−0.0255917	−	0.0214740i
$897$	−0.759155	−	1.13987i	−0.0253474	−	0.0380593i
$898$	−5.01027	−	1.82359i	−0.167195	−	0.0608539i
$899$	26.5260	+	45.9444i	0.884692	+	1.53233i
$900$	13.2217	+	2.97304i	0.440722	+	0.0991015i
$901$	34.8652	−	60.3883i	1.16153	−	2.01183i
$902$	19.8473	−	16.6539i	0.660843	−	0.554513i
$903$	−10.6638	+	10.1776i	−0.354870	+	0.338690i
$904$	−2.27365	+	12.8945i	−0.0756206	+	0.428866i
$905$	−1.84264	+	10.4501i	−0.0612514	+	0.347374i
$906$	−20.5117	−	6.01219i	−0.681455	−	0.199742i
$907$	−19.2226	+	16.1296i	−0.638275	+	0.535576i	−0.903488	−	0.428614i	$-0.859002\pi$
$907$	−19.2226	+	16.1296i	−0.638275	+	0.535576i	0.265213	+	0.964190i	$0.414558\pi$
$908$	2.71122	−	4.69597i	0.0899750	−	0.155841i
$909$	17.2088	−	8.89245i	0.570779	−	0.294944i
$910$	−0.0361935	−	0.0626889i	−0.00119980	−	0.00207812i
$911$	24.2237	+	8.81672i	0.802568	+	0.292111i	0.710550	−	0.703646i	$-0.248446\pi$
$911$	24.2237	+	8.81672i	0.802568	+	0.292111i	0.0920180	+	0.995757i	$0.470668\pi$
$912$	4.51177	−	0.288884i	0.149400	−	0.00956589i
$913$	29.2660	+	24.5571i	0.968564	+	0.812721i
$914$	5.97832	−	2.17593i	0.197745	−	0.0719734i
$915$	−7.38694	−	5.43348i	−0.244205	−	0.179625i
$916$	2.80901	+	15.9307i	0.0928123	+	0.526365i
$917$	13.5983			0.449057
$918$	−19.4678	+	24.0328i	−0.642534	+	0.793202i
$919$	33.1605			1.09387			0.546933	−	0.837177i	$-0.315795\pi$
$919$	33.1605			1.09387			0.546933	+	0.837177i	$0.315795\pi$
$920$	0.915644	+	5.19287i	0.0301879	+	0.171204i
$921$	1.89923	−	17.1034i	0.0625819	−	0.563575i
$922$	6.46556	−	2.35327i	0.212932	−	0.0775009i
$923$	−0.893184	−	0.749470i	−0.0293995	−	0.0246691i
$924$	−3.28852	+	6.64318i	−0.108184	+	0.218545i
$925$	−2.53273	−	0.921838i	−0.0832756	−	0.0303099i
$926$	−3.31690	−	5.74504i	−0.109000	−	0.188794i
$927$	26.1897	−	3.36761i	0.860184	−	0.110607i
$928$	−2.78828	+	4.82944i	−0.0915297	+	0.158534i
$929$	−33.3778	+	28.0073i	−1.09509	+	0.918889i	−0.997085	−	0.0762974i	$-0.975690\pi$
$929$	−33.3778	+	28.0073i	−1.09509	+	0.918889i	−0.0980038	+	0.995186i	$0.531246\pi$
$930$	2.70437	+	11.1245i	0.0886798	+	0.364787i
$931$	−0.453257	+	2.57055i	−0.0148549	+	0.0842464i
$932$	−1.79154	+	10.1604i	−0.0586840	+	0.332813i
$933$	−3.42361	−	14.0831i	−0.112084	−	0.461061i
$934$	12.5277	−	10.5120i	0.409918	−	0.343962i
$935$	−8.84927	+	15.3274i	−0.289402	+	0.501259i
$936$	0.120481	−	0.288403i	0.00393804	−	0.00942675i
$937$	23.3640	+	40.4676i	0.763269	+	1.32202i	0.941157	+	0.337969i	$0.109740\pi$
$937$	23.3640	+	40.4676i	0.763269	+	1.32202i	−0.177888	+	0.984051i	$0.556927\pi$
$938$	11.4111	+	4.15330i	0.372586	+	0.135610i
$939$	−20.8939	+	42.2080i	−0.681847	+	1.37741i
$940$	4.32921	+	3.63264i	0.141203	+	0.118484i
$941$	−9.43866	+	3.43539i	−0.307691	+	0.111991i	−0.491251	−	0.871018i	$-0.663460\pi$
$941$	−9.43866	+	3.43539i	−0.307691	+	0.111991i	0.183560	+	0.983009i	$0.441238\pi$
$942$	0.956014	−	8.60930i	0.0311486	−	0.280506i
$943$	7.97838	+	45.2476i	0.259812	+	1.47347i
$944$	1.82791			0.0594935
$945$	3.54400	−	0.688291i	0.115286	−	0.0223901i
$946$	−36.4232			−1.18422
$947$	0.981306	+	5.56526i	0.0318882	+	0.180847i	0.996592	−	0.0824913i	$-0.0262877\pi$
$947$	0.981306	+	5.56526i	0.0318882	+	0.180847i	−0.964704	+	0.263338i	$0.915177\pi$
$948$	7.01405	+	5.15920i	0.227806	+	0.167563i
$949$	0.662242	−	0.241036i	0.0214973	−	0.00782437i
$950$	9.03243	+	7.57911i	0.293051	+	0.245899i
$951$	−13.7831	+	0.882517i	−0.446947	+	0.0286176i
$952$	5.59324	+	2.03577i	0.181278	+	0.0659798i
$953$	29.7083	+	51.4563i	0.962346	+	1.66683i	0.716582	+	0.697502i	$0.245705\pi$
$953$	29.7083	+	51.4563i	0.962346	+	1.66683i	0.245764	+	0.969330i	$0.420961\pi$
$954$	−29.5841	−	18.9728i	−0.957820	−	0.614268i
$955$	−0.637518	+	1.10421i	−0.0206296	+	0.0357315i
$956$	5.19327	−	4.35767i	0.167962	−	0.140937i
$957$	39.6677	+	11.6270i	1.28228	+	0.375848i
$958$	−0.637131	+	3.61335i	−0.0205848	+	0.116742i
$959$	1.11651	−	6.33202i	0.0360539	−	0.204472i
$960$	−0.870552	+	0.830860i	−0.0280969	+	0.0268159i
$961$	45.5833	−	38.2490i	1.47043	−	1.23384i
$962$	−0.0310817	+	0.0538351i	−0.00100212	+	0.00173571i
$963$	−18.8046	+	20.3977i	−0.605968	+	0.657307i
$964$	0.603740	+	1.04571i	0.0194452	+	0.0336800i
$965$	8.41332	+	3.06220i	0.270834	+	0.0985756i
$966$	−7.28655	−	10.9408i	−0.234441	−	0.352014i
$967$	16.2910	+	13.6698i	0.523882	+	0.439590i	0.865983	−	0.500074i	$-0.166694\pi$
$967$	16.2910	+	13.6698i	0.523882	+	0.439590i	−0.342100	+	0.939663i	$0.611138\pi$
$968$	−6.87422	+	2.50201i	−0.220946	+	0.0804176i
$969$	−24.6473	+	10.8007i	−0.791785	+	0.346969i
$970$	0.565403	+	3.20656i	0.0181540	+	0.102956i
$971$	−43.0069			−1.38016			−0.690079	−	0.723734i	$-0.742424\pi$
$971$	−43.0069			−1.38016			−0.690079	+	0.723734i	$0.742424\pi$
$972$	11.6422	+	10.3663i	0.373423	+	0.332498i
$973$	−6.59545			−0.211440
$974$	−1.48803	−	8.43902i	−0.0476794	−	0.270404i
$975$	0.746623	−	0.327179i	0.0239111	−	0.0104781i
$976$	−7.16052	+	2.60622i	−0.229203	+	0.0834229i
$977$	−44.5644	−	37.3940i	−1.42574	−	1.19634i	−0.948177	−	0.317744i	$-0.897075\pi$
$977$	−44.5644	−	37.3940i	−1.42574	−	1.19634i	−0.477566	−	0.878596i	$-0.658481\pi$
$978$	2.01323	+	3.02288i	0.0643761	+	0.0966610i
$979$	−1.02229	−	0.372084i	−0.0326726	−	0.0118919i
$980$	−0.347394	−	0.601703i	−0.0110971	−	0.0192207i
$981$	−1.78558	+	1.93686i	−0.0570092	+	0.0618390i
$982$	5.47109	−	9.47621i	0.174590	−	0.302398i
$983$	24.3743	−	20.4524i	0.777419	−	0.652332i	−0.165178	−	0.986264i	$-0.552820\pi$
$983$	24.3743	−	20.4524i	0.777419	−	0.652332i	0.942597	+	0.333932i	$0.108376\pi$
$984$	−7.58547	+	7.23962i	−0.241816	+	0.230791i
$985$	0.374244	−	2.12244i	0.0119244	−	0.0676267i
$986$	5.76387	−	32.6885i	0.183559	−	1.04101i
$987$	−13.5197	−	3.96276i	−0.430336	−	0.126136i
$988$	0.208323	−	0.174804i	0.00662763	−	0.00556124i
$989$	32.2957	−	55.9378i	1.02694	−	1.77872i
$990$	7.50884	+	4.81556i	0.238647	+	0.153049i
$991$	−6.66072	−	11.5367i	−0.211585	−	0.366476i	0.740626	−	0.671918i	$-0.234529\pi$
$991$	−6.66072	−	11.5367i	−0.211585	−	0.366476i	−0.952211	+	0.305442i	$0.901196\pi$
$992$	8.93967	+	3.25378i	0.283835	+	0.103307i
$993$	52.8159	−	3.38174i	1.67606	−	0.107316i
$994$	−8.57300	−	7.19360i	−0.271919	−	0.228167i
$995$	−13.7620	+	5.00896i	−0.436285	+	0.158795i
$996$	−12.4553	−	9.16155i	−0.394663	−	0.290295i
$997$	−3.70284	−	20.9998i	−0.117270	−	0.665071i	−0.985601	−	0.169087i	$-0.945918\pi$
$997$	−3.70284	−	20.9998i	−0.117270	−	0.665071i	0.868331	−	0.495985i	$-0.165193\pi$
$998$	42.0071			1.32971
$999$	−2.03363	−	2.34018i	−0.0643411	−	0.0740401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.d.337.5	yes	30
27.25	even	9	inner	378.2.u.d.295.5	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.d.295.5	✓	30	27.25	even	9	inner
378.2.u.d.337.5	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.58642 - 0.695186i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.532238 + 0.446601i) q^{5} +(0.960103 + 1.44160i) q^{6} +(0.939693 + 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.03343 - 2.20571i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(1.58642 - 0.695186i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.532238 + 0.446601i) q^{5} +(0.960103 + 1.44160i) q^{6} +(0.939693 + 0.342020i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.03343 - 2.20571i) q^{9} +(-0.347394 + 0.601703i) q^{10} +(3.27840 - 2.75090i) q^{11} +(-1.25298 + 1.19585i) q^{12} +(-0.0180917 + 0.102603i) q^{13} +(-0.173648 + 0.984808i) q^{14} +(1.15482 + 0.338490i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-2.97610 + 5.15476i) q^{17} +(2.52530 + 1.61952i) q^{18} +(1.30510 + 2.26050i) q^{19} +(-0.652886 - 0.237631i) q^{20} +(1.72851 - 0.110675i) q^{21} +(3.27840 + 2.75090i) q^{22} +(-7.13166 + 2.59571i) q^{23} +(-1.39526 - 1.02628i) q^{24} +(-0.784416 - 4.44864i) q^{25} -0.104186 q^{26} +(1.69249 - 4.91279i) q^{27} -1.00000 q^{28} +(0.968359 + 5.49184i) q^{29} +(-0.132815 + 1.19606i) q^{30} +(8.93967 - 3.25378i) q^{31} +(0.766044 + 0.642788i) q^{32} +(3.28852 - 6.64318i) q^{33} +(-5.59324 - 2.03577i) q^{34} +(0.347394 + 0.601703i) q^{35} +(-1.15641 + 2.76816i) q^{36} +(0.298330 - 0.516723i) q^{37} +(-1.99953 + 1.67781i) q^{38} +(0.0426272 + 0.175348i) q^{39} +(0.120649 - 0.684232i) q^{40} +(1.05126 - 5.96199i) q^{41} +(0.409146 + 1.68303i) q^{42} +(-6.51964 + 5.47063i) q^{43} +(-2.13982 + 3.70628i) q^{44} +(2.06734 - 0.265829i) q^{45} +(-3.79467 - 6.57257i) q^{46} +(-7.64344 - 2.78199i) q^{47} +(0.768409 - 1.55227i) q^{48} +(0.766044 + 0.642788i) q^{49} +(4.24485 - 1.54500i) q^{50} +(-1.13782 + 10.2465i) q^{51} +(-0.0180917 - 0.102603i) q^{52} -11.7151 q^{53} +(5.13205 + 0.813685i) q^{54} +2.97345 q^{55} +(-0.173648 - 0.984808i) q^{56} +(3.64191 + 2.67881i) q^{57} +(-5.24025 + 1.90730i) q^{58} +(1.40026 + 1.17496i) q^{59} +(-1.20095 + 0.0768954i) q^{60} +(-7.16052 - 2.60622i) q^{61} +(4.75670 + 8.23885i) q^{62} +(2.66520 - 1.37721i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0554516 + 0.0465294i) q^{65} +(7.11330 + 2.08498i) q^{66} +(2.10869 - 11.9590i) q^{67} +(1.03359 - 5.86177i) q^{68} +(-9.50927 + 9.07570i) q^{69} +(-0.532238 + 0.446601i) q^{70} +(-5.59563 + 9.69191i) q^{71} +(-2.92692 - 0.658151i) q^{72} +(-3.38215 - 5.85805i) q^{73} +(0.560677 + 0.204070i) q^{74} +(-4.33704 - 6.51209i) q^{75} +(-1.99953 - 1.67781i) q^{76} +(4.02155 - 1.46373i) q^{77} +(-0.165282 + 0.0724284i) q^{78} +(-0.872941 - 4.95070i) q^{79} +0.694787 q^{80} +(-0.730299 - 8.97032i) q^{81} +6.05396 q^{82} +(1.55014 + 8.79130i) q^{83} +(-1.58642 + 0.695186i) q^{84} +(-3.88611 + 1.41443i) q^{85} +(-6.51964 - 5.47063i) q^{86} +(5.35407 + 8.03915i) q^{87} +(-4.02155 - 1.46373i) q^{88} +(-0.127102 - 0.220147i) q^{89} +(0.620781 + 1.98977i) q^{90} +(-0.0520929 + 0.0902275i) q^{91} +(5.81378 - 4.87834i) q^{92} +(11.9201 - 11.3766i) q^{93} +(1.41245 - 8.01041i) q^{94} +(-0.314917 + 1.78599i) q^{95} +(1.66212 + 0.487185i) q^{96} +(3.58996 - 3.01233i) q^{97} +(-0.500000 + 0.866025i) q^{98} +(0.598715 - 12.8250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9	\( 30 q - 3 q^{3} + 3 q^{5} - 6 q^{6} - 15 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{11} + 3 q^{12} - 9 q^{13} + 12 q^{15} - 12 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} + 9 q^{22} - 12 q^{23} - 3 q^{24} + 21 q^{25} + 18 q^{26} + 3 q^{27} - 30 q^{28} - 30 q^{29} - 15 q^{30} + 18 q^{31} + 9 q^{33} + 12 q^{34} + 3 q^{35} - 12 q^{36} + 3 q^{37} - 3 q^{38} + 72 q^{39} + 3 q^{40} + 36 q^{41} - 3 q^{42} - 9 q^{43} - 3 q^{44} - 48 q^{45} - 15 q^{46} + 3 q^{48} + 3 q^{50} - 6 q^{51} - 9 q^{52} + 6 q^{53} + 45 q^{54} + 66 q^{55} - 51 q^{57} - 3 q^{58} - 48 q^{59} + 24 q^{60} + 57 q^{61} - 18 q^{62} - 15 q^{63} - 15 q^{64} + 24 q^{65} + 54 q^{66} + 6 q^{67} - 15 q^{68} - 48 q^{69} - 3 q^{70} - 24 q^{71} - 6 q^{72} - 36 q^{73} - 48 q^{74} - 129 q^{75} - 3 q^{76} + 9 q^{77} + 24 q^{78} - 21 q^{79} + 6 q^{80} + 27 q^{81} - 15 q^{83} + 3 q^{84} - 72 q^{85} - 9 q^{86} + 42 q^{87} - 9 q^{88} - 30 q^{89} - 30 q^{90} + 9 q^{91} + 6 q^{92} + 111 q^{93} - 45 q^{94} + 81 q^{95} - 6 q^{96} - 15 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 3 * q^5 - 6 * q^6 - 15 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^11 + 3 * q^12 - 9 * q^13 + 12 * q^15 - 12 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 + 9 * q^22 - 12 * q^23 - 3 * q^24 + 21 * q^25 + 18 * q^26 + 3 * q^27 - 30 * q^28 - 30 * q^29 - 15 * q^30 + 18 * q^31 + 9 * q^33 + 12 * q^34 + 3 * q^35 - 12 * q^36 + 3 * q^37 - 3 * q^38 + 72 * q^39 + 3 * q^40 + 36 * q^41 - 3 * q^42 - 9 * q^43 - 3 * q^44 - 48 * q^45 - 15 * q^46 + 3 * q^48 + 3 * q^50 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 45 * q^54 + 66 * q^55 - 51 * q^57 - 3 * q^58 - 48 * q^59 + 24 * q^60 + 57 * q^61 - 18 * q^62 - 15 * q^63 - 15 * q^64 + 24 * q^65 + 54 * q^66 + 6 * q^67 - 15 * q^68 - 48 * q^69 - 3 * q^70 - 24 * q^71 - 6 * q^72 - 36 * q^73 - 48 * q^74 - 129 * q^75 - 3 * q^76 + 9 * q^77 + 24 * q^78 - 21 * q^79 + 6 * q^80 + 27 * q^81 - 15 * q^83 + 3 * q^84 - 72 * q^85 - 9 * q^86 + 42 * q^87 - 9 * q^88 - 30 * q^89 - 30 * q^90 + 9 * q^91 + 6 * q^92 + 111 * q^93 - 45 * q^94 + 81 * q^95 - 6 * q^96 - 15 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more