LMFDB - Embedded newform 71.2.g.a.15.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, 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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			15.1
Character	$\chi$	$=$	71.15
Dual form			71.2.g.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996141 + 2.33059i) q^{2} +(0.808832 + 0.146781i) q^{3} +(-3.05722 - 3.19760i) q^{4} +(-1.11904 + 3.44404i) q^{5} +(-1.14780 + 1.73884i) q^{6} +(1.50266 - 1.31283i) q^{7} +(5.75184 - 2.15870i) q^{8} +(-2.17604 - 0.816681i) q^{9} +O(q^{10})$	\(q+(-0.996141 + 2.33059i) q^{2} +(0.808832 + 0.146781i) q^{3} +(-3.05722 - 3.19760i) q^{4} +(-1.11904 + 3.44404i) q^{5} +(-1.14780 + 1.73884i) q^{6} +(1.50266 - 1.31283i) q^{7} +(5.75184 - 2.15870i) q^{8} +(-2.17604 - 0.816681i) q^{9} +(-6.91193 - 6.03877i) q^{10} +(2.16318 - 0.597001i) q^{11} +(-2.00343 - 3.03507i) q^{12} +(5.25473 + 1.45021i) q^{13} +(1.56281 + 4.80984i) q^{14} +(-1.41064 + 2.62140i) q^{15} +(-0.301642 + 6.71658i) q^{16} +(-1.37843 + 1.00148i) q^{17} +(4.07099 - 4.25792i) q^{18} +(1.64337 + 3.05389i) q^{19} +(14.4338 - 6.95096i) q^{20} +(1.40810 - 0.841299i) q^{21} +(-0.763473 + 5.63619i) q^{22} +(1.37949 - 6.04393i) q^{23} +(4.96913 - 0.901765i) q^{24} +(-6.56411 - 4.76911i) q^{25} +(-8.61430 + 10.8020i) q^{26} +(-3.75722 - 2.24484i) q^{27} +(-8.79186 - 0.791282i) q^{28} +(-0.550640 - 4.06499i) q^{29} +(-4.70421 - 5.89890i) q^{30} +(0.159891 + 3.56025i) q^{31} +(-4.28274 - 2.06246i) q^{32} +(1.83728 - 0.165358i) q^{33} +(-0.960942 - 4.21016i) q^{34} +(2.83992 + 6.64433i) q^{35} +(4.04121 + 9.45488i) q^{36} +(-1.97955 - 8.67297i) q^{37} +(-8.75439 + 0.787910i) q^{38} +(4.03733 + 1.94428i) q^{39} +(0.998138 + 22.2253i) q^{40} +(-4.28575 - 5.37417i) q^{41} +(0.558058 + 4.11975i) q^{42} +(-3.19361 - 0.287430i) q^{43} +(-8.52229 - 5.09183i) q^{44} +(5.24776 - 6.58048i) q^{45} +(12.7117 + 9.23563i) q^{46} +(-5.09420 + 0.924462i) q^{47} +(-1.22985 + 5.38831i) q^{48} +(-0.405182 + 2.99117i) q^{49} +(17.6536 - 10.5475i) q^{50} +(-1.26191 + 0.607706i) q^{51} +(-11.4277 - 21.2361i) q^{52} +(0.321079 - 0.335822i) q^{53} +(8.97451 - 6.52037i) q^{54} +(-0.364587 + 8.11817i) q^{55} +(5.80903 - 10.7950i) q^{56} +(0.880956 + 2.71130i) q^{57} +(10.0223 + 2.76599i) q^{58} +(4.74200 + 7.18382i) q^{59} +(12.6948 - 3.50355i) q^{60} +(-1.96254 - 1.71462i) q^{61} +(-8.45675 - 3.17387i) q^{62} +(-4.34201 + 1.62958i) q^{63} +(-1.05337 + 0.920302i) q^{64} +(-10.8748 + 16.4747i) q^{65} +(-1.44481 + 4.44667i) q^{66} +(3.07312 + 3.21423i) q^{67} +(7.41649 + 1.34590i) q^{68} +(2.00291 - 4.68604i) q^{69} -18.3142 q^{70} +(8.02102 - 2.58133i) q^{71} -14.2792 q^{72} +(0.333338 - 0.779882i) q^{73} +(22.1850 + 4.02599i) q^{74} +(-4.60925 - 4.82090i) q^{75} +(4.74098 - 14.5913i) q^{76} +(2.46676 - 3.73698i) q^{77} +(-8.55306 + 7.47258i) q^{78} +(-2.75985 + 1.03579i) q^{79} +(-22.7947 - 8.55498i) q^{80} +(2.54150 + 2.22045i) q^{81} +(16.7942 - 4.63490i) q^{82} +(-4.19075 - 6.34871i) q^{83} +(-6.99500 - 1.93050i) q^{84} +(-1.90665 - 5.86806i) q^{85} +(3.85117 - 7.15667i) q^{86} +(0.151289 - 3.36872i) q^{87} +(11.1535 - 8.10352i) q^{88} +(-9.63125 + 10.0735i) q^{89} +(10.1089 + 18.7854i) q^{90} +(9.79995 - 4.71940i) q^{91} +(-23.5435 + 14.0666i) q^{92} +(-0.393254 + 2.90312i) q^{93} +(2.92001 - 12.7934i) q^{94} +(-12.3567 + 2.24242i) q^{95} +(-3.16129 - 2.29681i) q^{96} +(9.09498 - 11.4047i) q^{97} +(-6.56758 - 3.92394i) q^{98} +(-5.19473 - 0.467534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{27}{35}\right)$

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 $

$2$	−0.996141	+	2.33059i	−0.704378	+	1.64797i	0.0559484	+	0.998434i	$0.482182\pi$
$2$	−0.996141	+	2.33059i	−0.704378	+	1.64797i	−0.760327	+	0.649541i	$0.774961\pi$
$3$	0.808832	+	0.146781i	0.466980	+	0.0847443i	0.406946	−	0.913452i	$-0.366594\pi$
$3$	0.808832	+	0.146781i	0.466980	+	0.0847443i	0.0600333	+	0.998196i	$0.480879\pi$
$4$	−3.05722	−	3.19760i	−1.52861	−	1.59880i
$5$	−1.11904	+	3.44404i	−0.500449	+	1.54022i	0.307840	+	0.951438i	$0.400394\pi$
$5$	−1.11904	+	3.44404i	−0.500449	+	1.54022i	−0.808289	+	0.588785i	$0.799606\pi$
$6$	−1.14780	+	1.73884i	−0.468587	+	0.709879i
$7$	1.50266	−	1.31283i	0.567951	−	0.496204i	−0.325392	−	0.945579i	$-0.605496\pi$
$7$	1.50266	−	1.31283i	0.567951	−	0.496204i	0.893343	+	0.449375i	$0.148353\pi$
$8$	5.75184	−	2.15870i	2.03358	−	0.763217i
$9$	−2.17604	−	0.816681i	−0.725346	−	0.272227i
$10$	−6.91193	−	6.03877i	−2.18574	−	1.90963i
$11$	2.16318	−	0.597001i	0.652224	−	0.180002i	0.0757617	−	0.997126i	$-0.475861\pi$
$11$	2.16318	−	0.597001i	0.652224	−	0.180002i	0.576463	+	0.817123i	$0.304433\pi$
$12$	−2.00343	−	3.03507i	−0.578340	−	0.876148i
$13$	5.25473	+	1.45021i	1.45740	+	0.402217i	0.902858	−	0.429939i	$-0.141465\pi$
$13$	5.25473	+	1.45021i	1.45740	+	0.402217i	0.554542	+	0.832156i	$0.312894\pi$
$14$	1.56281	+	4.80984i	0.417679	+	1.28548i
$15$	−1.41064	+	2.62140i	−0.364225	+	0.676843i
$16$	−0.301642	+	6.71658i	−0.0754105	+	1.67915i
$17$	−1.37843	+	1.00148i	−0.334317	+	0.242896i	−0.742260	−	0.670112i	$-0.766246\pi$
$17$	−1.37843	+	1.00148i	−0.334317	+	0.242896i	0.407943	+	0.913007i	$0.366246\pi$
$18$	4.07099	−	4.25792i	0.959542	−	1.00360i
$19$	1.64337	+	3.05389i	0.377015	+	0.700611i	0.996427	−	0.0844548i	$-0.0269149\pi$
$19$	1.64337	+	3.05389i	0.377015	+	0.700611i	−0.619413	+	0.785066i	$0.712629\pi$
$20$	14.4338	−	6.95096i	3.22750	−	1.55428i
$21$	1.40810	−	0.841299i	0.307272	−	0.183587i
$22$	−0.763473	+	5.63619i	−0.162773	+	1.20164i
$23$	1.37949	−	6.04393i	0.287643	−	1.26025i	−0.600107	−	0.799920i	$-0.704875\pi$
$23$	1.37949	−	6.04393i	0.287643	−	1.26025i	0.887750	−	0.460327i	$-0.152268\pi$
$24$	4.96913	−	0.901765i	1.01432	−	0.184072i
$25$	−6.56411	−	4.76911i	−1.31282	−	0.953821i
$26$	−8.61430	+	10.8020i	−1.68940	+	2.11845i
$27$	−3.75722	−	2.24484i	−0.723078	−	0.432019i
$28$	−8.79186	−	0.791282i	−1.66151	−	0.149538i
$29$	−0.550640	−	4.06499i	−0.102251	−	0.754849i	−0.967385	−	0.253309i	$-0.918481\pi$
$29$	−0.550640	−	4.06499i	−0.102251	−	0.754849i	0.865134	−	0.501540i	$-0.167233\pi$
$30$	−4.70421	−	5.89890i	−0.858868	−	1.07699i
$31$	0.159891	+	3.56025i	0.0287173	+	0.639440i	0.960808	+	0.277215i	$0.0894114\pi$
$31$	0.159891	+	3.56025i	0.0287173	+	0.639440i	−0.932091	+	0.362225i	$0.882017\pi$
$32$	−4.28274	−	2.06246i	−0.757089	−	0.364595i
$33$	1.83728	−	0.165358i	0.319830	−	0.0287852i
$34$	−0.960942	−	4.21016i	−0.164800	−	0.722037i
$35$	2.83992	+	6.64433i	0.480034	+	1.12310i
$36$	4.04121	+	9.45488i	0.673535	+	1.57581i
$37$	−1.97955	−	8.67297i	−0.325436	−	1.42583i	−0.827728	−	0.561130i	$-0.810367\pi$
$37$	−1.97955	−	8.67297i	−0.325436	−	1.42583i	0.502292	−	0.864698i	$-0.332490\pi$
$38$	−8.75439	+	0.787910i	−1.42015	+	0.127816i
$39$	4.03733	+	1.94428i	0.646490	+	0.311333i
$40$	0.998138	+	22.2253i	0.157819	+	3.51412i
$41$	−4.28575	−	5.37417i	−0.669322	−	0.839304i	0.325000	−	0.945714i	$-0.394636\pi$
$41$	−4.28575	−	5.37417i	−0.669322	−	0.839304i	−0.994322	+	0.106410i	$0.966064\pi$
$42$	0.558058	+	4.11975i	0.0861102	+	0.635691i
$43$	−3.19361	−	0.287430i	−0.487021	−	0.0438327i	−0.156592	−	0.987663i	$-0.550051\pi$
$43$	−3.19361	−	0.287430i	−0.487021	−	0.0438327i	−0.330429	+	0.943831i	$0.607194\pi$
$44$	−8.52229	−	5.09183i	−1.28478	−	0.767623i
$45$	5.24776	−	6.58048i	0.782289	−	0.980960i
$46$	12.7117	+	9.23563i	1.87425	+	1.36172i
$47$	−5.09420	+	0.924462i	−0.743066	+	0.134847i	−0.536871	−	0.843664i	$-0.680394\pi$
$47$	−5.09420	+	0.924462i	−0.743066	+	0.134847i	−0.206195	+	0.978511i	$0.566108\pi$
$48$	−1.22985	+	5.38831i	−0.177513	+	0.777736i
$49$	−0.405182	+	2.99117i	−0.0578831	+	0.427311i
$50$	17.6536	−	10.5475i	2.49660	−	1.49165i
$51$	−1.26191	+	0.607706i	−0.176703	+	0.0850959i
$52$	−11.4277	−	21.2361i	−1.58473	−	2.94492i
$53$	0.321079	−	0.335822i	0.0441036	−	0.0461287i	−0.700375	−	0.713775i	$-0.746984\pi$
$53$	0.321079	−	0.335822i	0.0441036	−	0.0461287i	0.744479	+	0.667646i	$0.232698\pi$
$54$	8.97451	−	6.52037i	1.22128	−	0.887309i
$55$	−0.364587	+	8.11817i	−0.0491609	+	1.09465i
$56$	5.80903	−	10.7950i	0.776265	−	1.44254i
$57$	0.880956	+	2.71130i	0.116685	+	0.359121i
$58$	10.0223	+	2.76599i	1.31600	+	0.363192i
$59$	4.74200	+	7.18382i	0.617356	+	0.935254i	0.999936	+	0.0113315i	$0.00360702\pi$
$59$	4.74200	+	7.18382i	0.617356	+	0.935254i	−0.382580	+	0.923922i	$0.624964\pi$
$60$	12.6948	−	3.50355i	1.63889	−	0.452306i
$61$	−1.96254	−	1.71462i	−0.251278	−	0.219535i	0.523079	−	0.852285i	$-0.324783\pi$
$61$	−1.96254	−	1.71462i	−0.251278	−	0.219535i	−0.774357	+	0.632749i	$0.781926\pi$
$62$	−8.45675	−	3.17387i	−1.07401	−	0.403082i
$63$	−4.34201	+	1.62958i	−0.547042	+	0.205308i
$64$	−1.05337	+	0.920302i	−0.131671	+	0.115038i
$65$	−10.8748	+	16.4747i	−1.34886	+	2.04343i
$66$	−1.44481	+	4.44667i	−0.177844	+	0.547347i
$67$	3.07312	+	3.21423i	0.375442	+	0.392681i	0.883338	−	0.468737i	$-0.155291\pi$
$67$	3.07312	+	3.21423i	0.375442	+	0.392681i	−0.507896	+	0.861418i	$0.669577\pi$
$68$	7.41649	+	1.34590i	0.899382	+	0.163214i
$69$	2.00291	−	4.68604i	0.241122	−	0.564133i
$70$	−18.3142			−2.18896
$71$	8.02102	−	2.58133i	0.951920	−	0.306347i
$71$	8.02102	−	2.58133i	0.951920	−	0.306347i
$72$	−14.2792			−1.68282
$73$	0.333338	−	0.779882i	0.0390142	−	0.0912783i	−0.898887	−	0.438180i	$-0.855623\pi$
$73$	0.333338	−	0.779882i	0.0390142	−	0.0912783i	0.937902	+	0.346901i	$0.112766\pi$
$74$	22.1850	+	4.02599i	2.57896	+	0.468012i
$75$	−4.60925	−	4.82090i	−0.532230	−	0.556669i
$76$	4.74098	−	14.5913i	0.543828	−	1.67373i
$77$	2.46676	−	3.73698i	0.281114	−	0.425869i
$78$	−8.55306	+	7.47258i	−0.968443	+	0.846103i
$79$	−2.75985	+	1.03579i	−0.310508	+	0.116535i	−0.501764	−	0.865005i	$-0.667315\pi$
$79$	−2.75985	+	1.03579i	−0.310508	+	0.116535i	0.191256	+	0.981540i	$0.438744\pi$
$80$	−22.7947	−	8.55498i	−2.54852	−	0.956476i
$81$	2.54150	+	2.22045i	0.282389	+	0.246716i
$82$	16.7942	−	4.63490i	1.85461	−	0.511839i
$83$	−4.19075	−	6.34871i	−0.459995	−	0.696862i	0.528362	−	0.849019i	$-0.322807\pi$
$83$	−4.19075	−	6.34871i	−0.459995	−	0.696862i	−0.988356	+	0.152157i	$0.951378\pi$
$84$	−6.99500	−	1.93050i	−0.763217	−	0.210635i
$85$	−1.90665	−	5.86806i	−0.206805	−	0.636480i
$86$	3.85117	−	7.15667i	0.415282	−	0.771724i
$87$	0.151289	−	3.36872i	0.0162199	−	0.361164i
$88$	11.1535	−	8.10352i	1.18897	−	0.863839i
$89$	−9.63125	+	10.0735i	−1.02091	+	1.06779i	−0.0232288	+	0.999730i	$0.507395\pi$
$89$	−9.63125	+	10.0735i	−1.02091	+	1.06779i	−0.997681	+	0.0680581i	$0.978320\pi$
$90$	10.1089	+	18.7854i	1.06557	+	1.98016i
$91$	9.79995	−	4.71940i	1.02731	−	0.494728i
$92$	−23.5435	+	14.0666i	−2.45458	+	1.46654i
$93$	−0.393254	+	2.90312i	−0.0407785	+	0.301039i
$94$	2.92001	−	12.7934i	0.301176	−	1.31954i
$95$	−12.3567	+	2.24242i	−1.26777	+	0.230067i
$96$	−3.16129	−	2.29681i	−0.322648	−	0.234417i
$97$	9.09498	−	11.4047i	0.923456	−	1.15798i	−0.0636606	−	0.997972i	$-0.520278\pi$
$97$	9.09498	−	11.4047i	0.923456	−	1.15798i	0.987116	−	0.160005i	$-0.0511511\pi$
$98$	−6.56758	−	3.92394i	−0.663425	−	0.396378i
$99$	−5.19473	−	0.467534i	−0.522090	−	0.0469890i
$100$	4.81823	+	35.5696i	0.481823	+	3.55696i
$101$	−1.44524	−	1.81228i	−0.143807	−	0.180328i	0.704711	−	0.709494i	$-0.251076\pi$
$101$	−1.44524	−	1.81228i	−0.143807	−	0.180328i	−0.848519	+	0.529166i	$0.822505\pi$
$102$	−0.159267	−	3.54636i	−0.0157698	−	0.351142i
$103$	10.6955	+	5.15067i	1.05386	+	0.507510i	0.878870	−	0.477061i	$-0.158298\pi$
$103$	10.6955	+	5.15067i	1.05386	+	0.507510i	0.174986	+	0.984571i	$0.444012\pi$
$104$	33.3550	−	3.00200i	3.27072	−	0.294370i
$105$	1.32176	+	5.79100i	0.128990	+	0.565143i
$106$	0.462823	+	1.08283i	0.0449534	+	0.105174i
$107$	4.00186	+	9.36282i	0.386875	+	0.905138i	0.993883	+	0.110442i	$0.0352268\pi$
$107$	4.00186	+	9.36282i	0.386875	+	0.905138i	−0.607008	+	0.794696i	$0.707630\pi$
$108$	4.30856	+	18.8771i	0.414592	+	1.81645i
$109$	−9.01979	+	0.811795i	−0.863939	+	0.0777559i	−0.512739	−	0.858545i	$-0.671369\pi$
$109$	−9.01979	+	0.811795i	−0.863939	+	0.0777559i	−0.351200	+	0.936300i	$0.614226\pi$
$110$	−18.5569	−	8.93654i	−1.76933	−	0.852066i
$111$	−0.328092	−	7.30554i	−0.0311412	−	0.693412i
$112$	8.36448	+	10.4887i	0.790369	+	0.991091i
$113$	0.117504	+	0.867453i	0.0110539	+	0.0816031i	0.995636	−	0.0933179i	$-0.0297473\pi$
$113$	0.117504	+	0.867453i	0.0110539	+	0.0816031i	−0.984582	+	0.174921i	$0.944033\pi$
$114$	−7.19649	−	0.647696i	−0.674013	−	0.0606622i
$115$	19.2719	+	11.5144i	1.79711	+	1.07372i
$116$	−11.3148	+	14.1883i	−1.05055	+	1.31735i
$117$	−10.2501	−	7.44716i	−0.947625	−	0.688490i
$118$	−21.4662	+	3.89555i	−1.97613	+	0.358614i
$119$	−0.756520	+	3.31453i	−0.0693501	+	0.303842i
$120$	−2.45493	+	18.1230i	−0.224104	+	1.65440i
$121$	−5.11998	+	3.05905i	−0.465453	+	0.278095i
$122$	5.95105	−	2.86588i	0.538783	−	0.259464i
$123$	−2.67763	−	4.97587i	−0.241434	−	0.448659i
$124$	10.8954	−	11.3957i	0.978439	−	1.02337i
$125$	9.12211	−	6.62760i	0.815906	−	0.592790i
$126$	0.527366	−	11.7427i	0.0469815	−	1.04613i
$127$	6.70247	−	12.4553i	0.594748	−	1.10523i	−0.388240	−	0.921558i	$-0.626917\pi$
$127$	6.70247	−	12.4553i	0.594748	−	1.10523i	0.982988	−	0.183669i	$-0.0587974\pi$
$128$	−4.03335	−	12.4134i	−0.356501	−	1.09720i
$129$	−2.54091	−	0.701246i	−0.223714	−	0.0617413i
$130$	−27.5628	−	41.7559i	−2.41742	−	3.66223i
$131$	1.55775	−	0.429913i	0.136102	−	0.0375617i	−0.197322	−	0.980339i	$-0.563225\pi$
$131$	1.55775	−	0.429913i	0.136102	−	0.0375617i	0.333424	+	0.942777i	$0.391796\pi$
$132$	−6.14572	−	5.36935i	−0.534916	−	0.467342i
$133$	6.47867	+	2.43149i	0.561772	+	0.210836i
$134$	−10.5523	+	3.96035i	−0.911582	+	0.342122i
$135$	11.9358	−	10.4280i	1.02727	−	0.897498i
$136$	−5.76658	+	8.73599i	−0.494480	+	0.749105i
$137$	−2.54304	+	7.82666i	−0.217266	+	0.668676i	0.781719	+	0.623631i	$0.214343\pi$
$137$	−2.54304	+	7.82666i	−0.217266	+	0.668676i	−0.998985	+	0.0450454i	$0.985657\pi$
$138$	8.92606	+	9.33592i	0.759836	+	0.794727i
$139$	−11.9056	−	2.16055i	−1.00982	−	0.183256i	−0.351657	−	0.936129i	$-0.614382\pi$
$139$	−11.9056	−	2.16055i	−1.00982	−	0.183256i	−0.658165	+	0.752873i	$0.728667\pi$
$140$	12.5636	−	29.3941i	1.06182	−	2.48425i
$141$	−4.25605			−0.358424
$142$	−1.97406	+	21.2651i	−0.165660	+	1.78452i
$143$	12.2327			1.02295
$144$	6.14169	−	14.3692i	0.511808	−	1.19743i
$145$	14.6162	+	2.65245i	1.21381	+	0.220274i
$146$	1.48553	+	1.55375i	0.122944	+	0.128589i
$147$	−0.766773	+	2.35989i	−0.0632424	+	0.194640i
$148$	−21.6808	+	32.8450i	−1.78215	+	2.69984i
$149$	2.49193	−	2.17713i	0.204147	−	0.178358i	−0.549794	−	0.835301i	$-0.685294\pi$
$149$	2.49193	−	2.17713i	0.204147	−	0.178358i	0.753940	+	0.656943i	$0.228151\pi$
$150$	15.8270	−	5.93997i	1.29227	−	0.484996i
$151$	−14.7076	−	5.51985i	−1.19689	−	0.449199i	−0.328222	−	0.944601i	$-0.606449\pi$
$151$	−14.7076	−	5.51985i	−1.19689	−	0.449199i	−0.868664	+	0.495402i	$0.835021\pi$
$152$	16.0448	+	14.0180i	1.30141	+	1.13701i
$153$	3.81740	−	1.05354i	0.308619	−	0.0851733i
$154$	6.25213	+	9.47157i	0.503811	+	0.763241i
$155$	−12.4406	−	3.43338i	−0.999252	−	0.275776i
$156$	−6.12599	−	18.8538i	−0.490471	−	1.50952i
$157$	−1.09971	+	2.04361i	−0.0877666	+	0.163098i	−0.920695	−	0.390283i	$-0.872377\pi$
$157$	−1.09971	+	2.04361i	−0.0877666	+	0.163098i	0.832928	+	0.553381i	$0.186663\pi$
$158$	0.335203	−	7.46387i	0.0266673	−	0.593794i
$159$	0.308991	−	0.224495i	0.0245046	−	0.0178036i
$160$	11.8957	−	12.4420i	0.940442	−	0.983625i
$161$	−5.86177	−	10.8930i	−0.461972	−	0.858488i
$162$	−7.70664	+	3.71132i	−0.605491	+	0.291589i
$163$	2.73000	−	1.63110i	0.213830	−	0.127758i	−0.401991	−	0.915644i	$-0.631682\pi$
$163$	2.73000	−	1.63110i	0.213830	−	0.127758i	0.615821	+	0.787886i	$0.288824\pi$
$164$	−4.08194	+	30.1341i	−0.318746	+	2.35308i
$165$	−1.48649	+	6.51272i	−0.115723	+	0.507015i
$166$	18.9708	−	3.44270i	1.47242	−	0.267205i
$167$	9.57782	+	6.95870i	0.741154	+	0.538480i	0.893072	−	0.449913i	$-0.148545\pi$
$167$	9.57782	+	6.95870i	0.741154	+	0.538480i	−0.151918	+	0.988393i	$0.548545\pi$
$168$	6.28304	−	7.87868i	0.484747	−	0.607854i
$169$	14.3492	+	8.57327i	1.10379	+	0.659482i
$170$	15.5753	+	1.40180i	1.19457	+	0.107513i
$171$	−1.08198	−	7.98750i	−0.0827411	−	0.610819i
$172$	8.84448	+	11.0906i	0.674385	+	0.845653i
$173$	−0.0815718	−	1.81634i	−0.00620179	−	0.138093i	−0.999705	−	0.0242892i	$-0.992268\pi$
$173$	−0.0815718	−	1.81634i	−0.00620179	−	0.138093i	0.993503	−	0.113804i	$-0.0363037\pi$
$174$	7.70039	+	3.70831i	0.583765	+	0.281126i
$175$	−16.1246	+	1.45124i	−1.21891	+	0.109704i
$176$	3.35730	+	14.7093i	0.253066	+	1.10875i
$177$	2.78103	+	6.50655i	0.209035	+	0.489062i
$178$	−13.8831	−	32.4811i	−1.04058	−	2.43456i
$179$	−1.55921	−	6.83135i	−0.116541	−	0.510599i	−0.999178	−	0.0405436i	$-0.987091\pi$
$179$	−1.55921	−	6.83135i	−0.116541	−	0.510599i	0.882637	−	0.470056i	$-0.155766\pi$
$180$	−37.0853	+	3.33774i	−2.76417	+	0.248780i
$181$	−3.28278	−	1.58090i	−0.244007	−	0.117507i	0.307884	−	0.951424i	$-0.400379\pi$
$181$	−3.28278	−	1.58090i	−0.244007	−	0.117507i	−0.551891	+	0.833916i	$0.686093\pi$
$182$	1.23686	+	27.5408i	0.0916822	+	2.04146i
$183$	−1.33569	−	1.67491i	−0.0987374	−	0.123813i
$184$	−5.11245	−	37.7416i	−0.376895	−	2.78235i
$185$	32.0853	+	2.88773i	2.35896	+	0.212310i
$186$	−6.37423	−	3.80843i	−0.467381	−	0.279247i
$187$	−2.38390	+	2.98932i	−0.174328	+	0.218600i
$188$	18.5301	+	13.4629i	1.35145	+	0.981886i
$189$	−8.59291	+	1.55938i	−0.625042	+	0.113428i
$190$	7.08290	−	31.0322i	0.513848	−	2.25131i
$191$	2.47224	−	18.2508i	0.178885	−	1.32058i	−0.649474	−	0.760384i	$-0.725011\pi$
$191$	2.47224	−	18.2508i	0.178885	−	1.32058i	0.828359	−	0.560198i	$-0.189275\pi$
$192$	−0.987084	+	0.589755i	−0.0712366	+	0.0425619i
$193$	−8.90620	+	4.28900i	−0.641082	+	0.308729i	−0.726037	−	0.687656i	$-0.758640\pi$
$193$	−8.90620	+	4.28900i	−0.641082	+	0.308729i	0.0849544	+	0.996385i	$0.472926\pi$
$194$	17.5199	+	32.5574i	1.25785	+	2.33748i
$195$	−11.2141	+	11.7290i	−0.803058	+	0.839933i
$196$	10.8033	−	7.84906i	0.771665	−	0.560647i
$197$	−0.0523800	+	1.16633i	−0.00373192	+	0.0830977i	−0.999995	−	0.00327715i	$-0.998957\pi$
$197$	−0.0523800	+	1.16633i	−0.00373192	+	0.0830977i	0.996263	+	0.0863749i	$0.0275283\pi$
$198$	6.26432	−	11.6410i	0.445186	−	0.827293i
$199$	4.52973	+	13.9411i	0.321104	+	0.988257i	0.973169	+	0.230094i	$0.0739032\pi$
$199$	4.52973	+	13.9411i	0.321104	+	0.988257i	−0.652064	+	0.758164i	$0.726097\pi$
$200$	−48.0508	−	13.2612i	−3.39771	−	0.937707i
$201$	2.01385	+	3.05085i	0.142046	+	0.215191i
$202$	5.66334	−	1.56298i	0.398471	−	0.109971i
$203$	−6.16407	−	5.38538i	−0.432633	−	0.377980i
$204$	5.80115	+	2.17721i	0.406162	+	0.152435i
$205$	23.3048	−	8.74643i	1.62768	−	0.610877i
$206$	−22.6583	+	19.7959i	−1.57868	+	1.37925i
$207$	−7.93779	+	12.0252i	−0.551714	+	0.835811i
$208$	−11.3255	+	34.8564i	−0.785284	+	2.41685i
$209$	5.37808	+	5.62504i	0.372010	+	0.389092i
$210$	−14.8131	−	2.68818i	−1.02220	−	0.185502i
$211$	−11.1238	+	26.0254i	−0.765793	+	1.79166i	−0.175489	+	0.984481i	$0.556151\pi$
$211$	−11.1238	+	26.0254i	−0.765793	+	1.79166i	−0.590304	+	0.807181i	$0.700992\pi$
$212$	−2.05543			−0.141168
$213$	6.86655	−	0.910523i	0.470488	−	0.0623880i
$214$	−25.8073			−1.76415
$215$	4.56370	−	10.6773i	0.311241	−	0.728186i
$216$	−26.4569	−	4.80122i	−1.80016	−	0.326681i
$217$	4.91427	+	5.13993i	0.333603	+	0.348921i
$218$	7.09302	−	21.8301i	0.480400	−	1.47852i
$219$	0.384087	−	0.581866i	0.0259542	−	0.0393189i
$220$	27.0733	−	23.6532i	1.82528	−	1.59470i
$221$	−8.69562	+	3.26352i	−0.584931	+	0.219528i
$222$	17.3530	+	6.51271i	1.16466	+	0.437104i
$223$	−11.4888	−	10.0375i	−0.769350	−	0.672161i	0.180951	−	0.983492i	$-0.442082\pi$
$223$	−11.4888	−	10.0375i	−0.769350	−	0.672161i	−0.950301	+	0.311331i	$0.899225\pi$
$224$	−9.14316	+	2.52335i	−0.610903	+	0.168598i
$225$	10.3889	+	15.7385i	0.692595	+	1.04924i
$226$	−2.13873	−	0.590251i	−0.142266	−	0.0392629i
$227$	−5.51912	−	16.9861i	−0.366317	−	1.12741i	−0.949152	−	0.314817i	$-0.898057\pi$
$227$	−5.51912	−	16.9861i	−0.366317	−	1.12741i	0.582835	−	0.812590i	$-0.301943\pi$
$228$	5.97639	−	11.1060i	0.395796	−	0.735512i
$229$	−0.815873	+	18.1668i	−0.0539144	+	1.20050i	0.771597	+	0.636112i	$0.219458\pi$
$229$	−0.815873	+	18.1668i	−0.0539144	+	1.20050i	−0.825511	+	0.564386i	$0.809113\pi$
$230$	−46.0328	+	33.4448i	−3.03532	+	2.20529i
$231$	2.54372	−	2.66052i	0.167364	−	0.175049i
$232$	−11.9423	−	22.1925i	−0.784050	−	1.45701i
$233$	−10.0889	+	4.85857i	−0.660948	+	0.318296i	−0.734116	−	0.679024i	$-0.762403\pi$
$233$	−10.0889	+	4.85857i	−0.660948	+	0.318296i	0.0731682	+	0.997320i	$0.476689\pi$
$234$	27.5668	−	16.4704i	1.80210	−	1.07671i
$235$	2.51672	−	18.5792i	0.164173	−	1.21197i
$236$	8.47366	−	37.1255i	0.551588	−	2.41667i
$237$	−2.38429	+	0.432685i	−0.154876	+	0.0281059i
$238$	−6.97120	−	5.06488i	−0.451876	−	0.328307i
$239$	−15.3614	+	19.2625i	−0.993643	+	1.24599i	−0.0244468	+	0.999701i	$0.507782\pi$
$239$	−15.3614	+	19.2625i	−0.993643	+	1.24599i	−0.969197	+	0.246288i	$0.920789\pi$
$240$	−17.1813	−	10.2654i	−1.10905	−	0.662627i
$241$	−2.29287	−	0.206362i	−0.147697	−	0.0132929i	0.0155442	−	0.999879i	$-0.495052\pi$
$241$	−2.29287	−	0.206362i	−0.147697	−	0.0132929i	−0.163241	+	0.986586i	$0.552195\pi$
$242$	−2.02915	−	14.9798i	−0.130439	−	0.962939i
$243$	9.91632	+	12.4347i	0.636133	+	0.797685i
$244$	0.517247	+	11.5174i	0.0331134	+	0.737327i
$245$	−9.84832	−	4.74270i	−0.629186	−	0.303000i
$246$	14.2640	−	1.28378i	0.909439	−	0.0818510i
$247$	4.20667	+	18.4306i	0.267664	+	1.17271i
$248$	8.60519	+	20.1328i	0.546430	+	1.27844i
$249$	−2.45774	−	5.75017i	−0.155753	−	0.364402i
$250$	6.35930	+	27.8619i	0.402197	+	1.76214i
$251$	7.21248	−	0.649135i	0.455248	−	0.0409730i	0.140357	−	0.990101i	$-0.455175\pi$
$251$	7.21248	−	0.649135i	0.455248	−	0.0409730i	0.314891	+	0.949128i	$0.398032\pi$
$252$	18.4852	+	8.90201i	1.16446	+	0.560774i
$253$	−0.624146	−	13.8977i	−0.0392397	−	0.873740i
$254$	22.3515	+	28.0279i	1.40246	+	1.75863i
$255$	−0.680836	−	5.02614i	−0.0426356	−	0.314749i
$256$	30.1620	+	2.71463i	1.88513	+	0.169664i
$257$	−23.0575	−	13.7762i	−1.43829	−	0.859337i	−0.439053	−	0.898461i	$-0.644686\pi$
$257$	−23.0575	−	13.7762i	−1.43829	−	0.859337i	−0.999234	+	0.0391241i	$0.987543\pi$
$258$	4.16542	−	5.22327i	0.259328	−	0.325187i
$259$	−14.3607	−	10.4337i	−0.892333	−	0.648318i
$260$	85.9262	−	15.5933i	5.32892	−	0.967056i
$261$	−2.12158	+	9.29527i	−0.131323	+	0.575363i
$262$	−0.549793	+	4.05874i	−0.0339663	+	0.250750i
$263$	21.5134	−	12.8536i	1.32657	−	0.792590i	0.337685	−	0.941259i	$-0.390356\pi$
$263$	21.5134	−	12.8536i	1.32657	−	0.792590i	0.988887	+	0.148669i	$0.0474990\pi$
$264$	10.2108	−	4.91726i	0.628431	−	0.302636i
$265$	0.797287	+	1.48161i	0.0489769	+	0.0910144i
$266$	−12.1205	+	12.6770i	−0.743153	+	0.777277i
$267$	−9.26867	+	6.73408i	−0.567233	+	0.412119i
$268$	0.882628	−	19.6532i	0.0539151	−	1.20051i
$269$	6.06674	−	11.2739i	0.369896	−	0.687382i	−0.625808	−	0.779977i	$-0.715231\pi$
$269$	6.06674	−	11.2739i	0.369896	−	0.687382i	0.995704	+	0.0925955i	$0.0295164\pi$
$270$	12.4136	+	38.2052i	0.755468	+	2.32509i
$271$	2.32705	+	0.642226i	0.141359	+	0.0390125i	0.336000	−	0.941862i	$-0.390926\pi$
$271$	2.32705	+	0.642226i	0.141359	+	0.0390125i	−0.194642	+	0.980874i	$0.562354\pi$
$272$	−6.31076	−	9.56040i	−0.382646	−	0.579684i
$273$	8.61923	−	2.37876i	0.521660	−	0.143969i
$274$	−15.7075	−	13.7232i	−0.948924	−	0.829050i
$275$	−17.0465	−	6.39767i	−1.02794	−	0.385794i
$276$	−21.1074	+	7.92175i	−1.27052	+	0.476833i
$277$	0.496930	−	0.434154i	0.0298576	−	0.0260858i	−0.642881	−	0.765966i	$-0.722261\pi$
$277$	0.496930	−	0.434154i	0.0298576	−	0.0260858i	0.672738	+	0.739881i	$0.265118\pi$
$278$	16.8950	−	25.5949i	1.01330	−	1.53508i
$279$	2.55966	−	7.87783i	0.153243	−	0.471633i
$280$	30.6779	+	32.0866i	1.83336	+	1.91754i
$281$	1.01017	+	0.183318i	0.0602615	+	0.0109358i	0.208604	−	0.978000i	$-0.433108\pi$
$281$	1.01017	+	0.183318i	0.0602615	+	0.0109358i	−0.148342	+	0.988936i	$0.547394\pi$
$282$	4.23963	−	9.91910i	0.252466	−	0.590674i
$283$	26.1927			1.55699			0.778496	−	0.627649i	$-0.215983\pi$
$283$	26.1927			1.55699			0.778496	+	0.627649i	$0.215983\pi$
$284$	−32.7761	−	17.7563i	−1.94490	−	1.05364i
$285$	−10.3237			−0.611521
$286$	−12.1855	+	28.5094i	−0.720545	+	1.68580i
$287$	−13.4954	−	2.44905i	−0.796608	−	0.144563i
$288$	7.63504	+	7.98563i	0.449899	+	0.470558i
$289$	−4.35620	+	13.4070i	−0.256247	+	0.788648i
$290$	−20.7415	+	31.4221i	−1.21799	+	1.84517i
$291$	9.03032	−	7.88956i	0.529367	−	0.462494i
$292$	−3.51284	+	1.31839i	−0.205573	+	0.0771530i
$293$	7.14827	+	2.68279i	0.417606	+	0.156730i	0.551328	−	0.834289i	$-0.314121\pi$
$293$	7.14827	+	2.68279i	0.417606	+	0.156730i	−0.133721	+	0.991019i	$0.542693\pi$
$294$	−4.73611	−	4.13781i	−0.276215	−	0.241322i
$295$	−30.0479	+	8.29269i	−1.74945	+	0.482819i
$296$	−30.1084	−	45.6123i	−1.75002	−	2.65116i
$297$	−9.46773	−	2.61293i	−0.549374	−	0.151617i
$298$	2.59169	+	7.97639i	0.150132	+	0.462060i
$299$	16.0138	−	29.7587i	0.926103	−	1.72099i
$300$	−1.32382	+	29.4771i	−0.0764306	+	1.70186i
$301$	−5.17625	+	3.76077i	−0.298354	+	0.216767i
$302$	27.5153	−	28.7788i	1.58333	−	1.65603i
$303$	−0.902951	−	1.67796i	−0.0518732	−	0.0963965i
$304$	−21.0074	+	10.1166i	−1.20486	+	0.580229i
$305$	8.10140	−	4.84036i	0.463885	−	0.277158i
$306$	−1.34731	+	9.94626i	−0.0770207	+	0.568590i
$307$	2.75314	−	12.0623i	0.157130	−	0.688431i	−0.833576	−	0.552405i	$-0.813710\pi$
$307$	2.75314	−	12.0623i	0.157130	−	0.688431i	0.990705	−	0.136025i	$-0.0434328\pi$
$308$	−19.4908	+	3.53706i	−1.11059	+	0.201543i
$309$	7.89482	+	5.73592i	0.449121	+	0.326305i
$310$	20.3944	−	25.5737i	1.15832	−	1.45249i
$311$	−3.03136	−	1.81116i	−0.171893	−	0.102701i	0.424376	−	0.905486i	$-0.360494\pi$
$311$	−3.03136	−	1.81116i	−0.171893	−	0.102701i	−0.596269	+	0.802785i	$0.703351\pi$
$312$	27.4192	+	2.46777i	1.55231	+	0.139710i
$313$	−1.73100	−	12.7787i	−0.0978418	−	0.722297i	−0.971717	−	0.236147i	$-0.924115\pi$
$313$	−1.73100	−	12.7787i	−0.0978418	−	0.722297i	0.873875	−	0.486150i	$-0.161599\pi$
$314$	−3.66734	−	4.59870i	−0.206960	−	0.259520i
$315$	−0.753484	−	16.7776i	−0.0424540	−	0.945312i
$316$	11.7495	+	5.65827i	0.660962	+	0.318302i
$317$	26.6902	−	2.40216i	1.49907	−	0.134919i	0.690507	−	0.723326i	$-0.257387\pi$
$317$	26.6902	−	2.40216i	1.49907	−	0.134919i	0.808565	+	0.588407i	$0.200245\pi$
$318$	0.215407	+	0.943761i	0.0120794	+	0.0529235i
$319$	−3.61793	−	8.46458i	−0.202565	−	0.473925i
$320$	−1.99080	−	4.65771i	−0.111289	−	0.260374i
$321$	1.86255	+	8.16036i	0.103957	+	0.455467i
$322$	31.2262	−	2.81041i	1.74017	−	0.156618i
$323$	−5.32369	−	2.56375i	−0.296218	−	0.142651i
$324$	−0.669838	−	14.9151i	−0.0372132	−	0.828617i
$325$	−27.5764	−	34.5797i	−1.52966	−	1.91814i
$326$	1.08196	+	7.98732i	0.0599240	+	0.442377i
$327$	−7.41465	−	0.667331i	−0.410031	−	0.0369035i
$328$	−36.2522	−	21.6597i	−2.00169	−	1.19596i
$329$	−6.44118	+	8.07698i	−0.355114	+	0.445298i
$330$	−13.6977	−	9.95198i	−0.754035	−	0.547838i
$331$	9.91190	−	1.79874i	0.544807	−	0.0988679i	0.100826	−	0.994904i	$-0.467851\pi$
$331$	9.91190	−	1.79874i	0.544807	−	0.0988679i	0.443981	+	0.896036i	$0.353566\pi$
$332$	−7.48861	+	32.8097i	−0.410991	+	1.80067i
$333$	−2.77548	+	20.4894i	−0.152095	+	1.12281i
$334$	−25.7587	+	15.3901i	−1.40945	+	0.842110i
$335$	−14.5089	+	6.98712i	−0.792706	+	0.381747i
$336$	5.22591	+	9.71137i	0.285097	+	0.529799i
$337$	−17.9661	+	18.7910i	−0.978675	+	1.02361i	0.0210410	+	0.999779i	$0.493302\pi$
$337$	−17.9661	+	18.7910i	−0.978675	+	1.02361i	−0.999716	+	0.0238351i	$0.992412\pi$
$338$	−34.2746	+	24.9020i	−1.86429	+	1.35449i
$339$	−0.0322846	+	0.718872i	−0.00175346	+	0.0390437i
$340$	−12.9347	+	24.0366i	−0.701481	+	1.30357i
$341$	2.47135	+	7.60602i	0.133831	+	0.411889i
$342$	19.6934	+	5.43503i	1.06490	+	0.293893i
$343$	11.0128	+	16.6836i	0.594634	+	0.900831i
$344$	−18.9896	+	5.24081i	−1.02385	+	0.282565i
$345$	13.8976	+	12.1420i	0.748222	+	0.653702i
$346$	4.31439	+	1.61922i	0.231943	+	0.0870497i
$347$	5.48606	−	2.05895i	0.294507	−	0.110530i	−0.199748	−	0.979847i	$-0.564012\pi$
$347$	5.48606	−	2.05895i	0.294507	−	0.110530i	0.494255	+	0.869317i	$0.335441\pi$
$348$	−11.2343	+	9.81514i	−0.602223	+	0.526147i
$349$	1.72202	−	2.60875i	0.0921777	−	0.139643i	−0.785559	−	0.618787i	$-0.787624\pi$
$349$	1.72202	−	2.60875i	0.0921777	−	0.139643i	0.877736	+	0.479144i	$0.159053\pi$
$350$	12.6802	−	39.0256i	0.677784	−	2.08600i
$351$	−16.4877	−	17.2448i	−0.880048	−	0.920458i
$352$	−10.4956	−	1.90468i	−0.559420	−	0.101520i
$353$	−9.00595	+	21.0705i	−0.479338	+	1.12147i	0.489103	+	0.872226i	$0.337324\pi$
$353$	−9.00595	+	21.0705i	−0.479338	+	1.12147i	−0.968441	+	0.249242i	$0.919819\pi$
$354$	−17.9344			−0.953201
$355$	−0.0856258	+	30.5133i	−0.00454455	+	1.61948i
$356$	61.6558			3.26775
$357$	−1.09841	+	2.56986i	−0.0581340	+	0.136011i
$358$	17.4743	+	3.17111i	0.923543	+	0.167598i
$359$	−8.86935	−	9.27661i	−0.468106	−	0.489601i	0.446024	−	0.895021i	$-0.352840\pi$
$359$	−8.86935	−	9.27661i	−0.468106	−	0.489601i	−0.914131	+	0.405420i	$0.867125\pi$
$360$	15.9790	−	49.1782i	0.842166	−	2.59192i
$361$	3.84145	−	5.81955i	0.202182	−	0.306292i
$362$	6.95454	−	6.07600i	0.365522	−	0.319347i
$363$	−4.59022	+	1.72274i	−0.240924	+	0.0904203i
$364$	−45.0513	−	16.9081i	−2.36133	−	0.886223i
$365$	2.31293	+	2.02075i	0.121064	+	0.105771i
$366$	5.23406	−	1.44451i	0.273589	−	0.0755057i
$367$	12.2121	+	18.5005i	0.637465	+	0.965718i	0.999438	+	0.0335294i	$0.0106747\pi$
$367$	12.2121	+	18.5005i	0.637465	+	0.965718i	−0.361973	+	0.932189i	$0.617897\pi$
$368$	40.1784	+	11.0885i	2.09445	+	0.578030i
$369$	4.93699	+	15.1945i	0.257009	+	0.790994i
$370$	−38.6916	+	71.9010i	−2.01148	+	3.73796i
$371$	0.0415934	−	0.926148i	0.00215942	−	0.0480832i
$372$	10.4853	−	7.61799i	0.543636	−	0.394974i
$373$	5.93797	−	6.21063i	0.307456	−	0.321574i	−0.550956	−	0.834534i	$-0.685737\pi$
$373$	5.93797	−	6.21063i	0.307456	−	0.321574i	0.858412	+	0.512960i	$0.171451\pi$
$374$	−4.59216	−	8.53367i	−0.237455	−	0.441266i
$375$	8.35106	−	4.02166i	0.431247	−	0.207678i
$376$	−27.3054	+	16.3142i	−1.40817	+	0.841342i
$377$	3.00163	−	22.1590i	0.154592	−	1.14124i
$378$	4.92547	−	21.5799i	0.253339	−	1.10995i
$379$	31.9218	−	5.79296i	1.63971	−	0.297564i	0.721133	−	0.692796i	$-0.243622\pi$
$379$	31.9218	−	5.79296i	1.63971	−	0.297564i	0.918581	+	0.395232i	$0.129336\pi$
$380$	44.9476	+	32.6563i	2.30576	+	1.67523i
$381$	7.24938	−	9.09044i	0.371397	−	0.465717i
$382$	40.0724	+	23.9421i	2.05028	+	1.22499i
$383$	20.0342	+	1.80311i	1.02370	+	0.0921345i	0.588745	−	0.808319i	$-0.299622\pi$
$383$	20.0342	+	1.80311i	1.02370	+	0.0921345i	0.434953	+	0.900453i	$0.356765\pi$
$384$	−1.44025	−	10.6324i	−0.0734976	−	0.542581i
$385$	10.1099	+	12.6775i	0.515250	+	0.646103i
$386$	−1.12406	−	25.0291i	−0.0572131	−	1.27395i
$387$	6.71469	+	3.23362i	0.341327	+	0.164374i
$388$	−64.2732	+	5.78469i	−3.26298	+	0.293673i
$389$	0.126943	+	0.556173i	0.00643626	+	0.0281991i	0.978044	−	0.208398i	$-0.0668250\pi$
$389$	0.126943	+	0.556173i	0.00643626	+	0.0281991i	−0.971608	+	0.236597i	$0.923968\pi$
$390$	−16.1647	−	37.8192i	−0.818532	−	1.91505i
$391$	4.15138	+	9.71264i	0.209944	+	0.491190i
$392$	4.12651	+	18.0794i	0.208420	+	0.913149i
$393$	1.32307	−	0.119078i	0.0667398	−	0.00600669i
$394$	−2.66606	−	1.28391i	−0.134314	−	0.0646823i
$395$	−0.478927	−	10.6641i	−0.0240974	−	0.536571i
$396$	14.3864	+	18.0400i	0.722946	+	0.906545i
$397$	−4.33150	−	31.9764i	−0.217392	−	1.60485i	−0.690156	−	0.723661i	$-0.742458\pi$
$397$	−4.33150	−	31.9764i	−0.217392	−	1.60485i	0.472764	−	0.881189i	$-0.343256\pi$
$398$	−37.0032	−	3.33035i	−1.85480	−	0.166935i
$399$	4.88326	+	2.91761i	0.244469	+	0.146063i
$400$	34.0121	−	42.6498i	1.70060	−	2.13249i
$401$	−9.36027	−	6.80063i	−0.467429	−	0.339607i	0.329009	−	0.944327i	$-0.393285\pi$
$401$	−9.36027	−	6.80063i	−0.467429	−	0.339607i	−0.796439	+	0.604719i	$0.793285\pi$
$402$	−9.11636	+	1.65438i	−0.454683	+	0.0825128i
$403$	−4.32294	+	18.9400i	−0.215341	+	0.943470i
$404$	−1.37651	+	10.1618i	−0.0684842	+	0.505570i
$405$	−10.4914	+	6.26829i	−0.521320	+	0.311474i
$406$	18.6914	−	9.00130i	0.927638	−	0.446727i
$407$	−9.45990	−	17.5794i	−0.468910	−	0.871381i
$408$	−5.94648	+	6.21953i	−0.294395	+	0.307913i
$409$	−12.1382	+	8.81889i	−0.600193	+	0.436066i	−0.845948	−	0.533266i	$-0.820964\pi$
$409$	−12.1382	+	8.81889i	−0.600193	+	0.436066i	0.245754	+	0.969332i	$0.420964\pi$
$410$	−2.83053	+	63.0265i	−0.139790	+	3.11266i
$411$	−3.20570	+	5.95718i	−0.158125	+	0.293846i
$412$	−16.2286	−	49.9465i	−0.799527	−	2.46069i
$413$	16.5568	+	4.56937i	0.814705	+	0.224844i
$414$	−20.1187	−	30.4785i	−0.988780	−	1.49794i
$415$	26.5549	−	7.32868i	1.30353	−	0.359751i
$416$	−19.5136	−	17.0486i	−0.956735	−	0.835874i
$417$	−9.31253	−	3.49505i	−0.456036	−	0.171153i
$418$	−18.4670	+	6.93077i	−0.903249	+	0.338995i
$419$	−9.69577	+	8.47094i	−0.473669	+	0.413832i	−0.861390	−	0.507945i	$-0.830405\pi$
$419$	−9.69577	+	8.47094i	−0.473669	+	0.413832i	0.387721	+	0.921777i	$0.373263\pi$
$420$	14.4764	−	21.9308i	0.706375	−	1.07011i
$421$	8.21434	−	25.2811i	0.400342	−	1.23213i	−0.524380	−	0.851484i	$-0.675703\pi$
$421$	8.21434	−	25.2811i	0.400342	−	1.23213i	0.924722	−	0.380643i	$-0.124297\pi$
$422$	−49.5736	−	51.8499i	−2.41321	−	2.52402i
$423$	11.8402	+	2.14868i	0.575689	+	0.104472i
$424$	1.12185	−	2.62471i	0.0544821	−	0.127467i
$425$	13.8243			0.670578
$426$	−4.71800	+	16.9101i	−0.228588	+	0.819298i
$427$	−5.20005			−0.251648
$428$	17.7040	−	41.4206i	0.855755	−	2.00214i
$429$	9.89422	+	1.79554i	0.477698	+	0.0866893i
$430$	20.3383	+	21.2722i	0.980800	+	1.02584i
$431$	−12.4375	+	38.2788i	−0.599095	+	1.84382i	−0.0659081	+	0.997826i	$0.520994\pi$
$431$	−12.4375	+	38.2788i	−0.599095	+	1.84382i	−0.533186	+	0.845998i	$0.679006\pi$
$432$	16.2110	−	24.5586i	0.779950	−	1.18157i
$433$	−22.5050	+	19.6620i	−1.08152	+	0.944896i	−0.998664	−	0.0516658i	$-0.983547\pi$
$433$	−22.5050	+	19.6620i	−1.08152	+	0.944896i	−0.0828558	+	0.996562i	$0.526404\pi$
$434$	−16.8744	+	6.33306i	−0.809995	+	0.303996i
$435$	11.4327	+	4.29077i	0.548157	+	0.205727i
$436$	30.1713	+	26.3598i	1.44494	+	1.26241i
$437$	20.7245	−	5.71960i	0.991388	−	0.273606i
$438$	0.973486	+	1.47477i	0.0465150	+	0.0704672i
$439$	−11.4846	−	3.16956i	−0.548132	−	0.151275i	−0.0190081	−	0.999819i	$-0.506051\pi$
$439$	−11.4846	−	3.16956i	−0.548132	−	0.151275i	−0.529124	+	0.848544i	$0.677479\pi$
$440$	15.4277	+	47.4814i	0.735485	+	2.26359i
$441$	3.32453	−	6.17801i	0.158311	−	0.294191i
$442$	1.05614	−	23.5168i	0.0502356	−	1.11858i
$443$	−24.1711	+	17.5613i	−1.14840	+	0.834364i	−0.988268	−	0.152731i	$-0.951193\pi$
$443$	−24.1711	+	17.5613i	−1.14840	+	0.834364i	−0.160135	+	0.987095i	$0.551193\pi$
$444$	−22.3572	+	23.3838i	−1.06102	+	1.10974i
$445$	−23.9158	−	44.4431i	−1.13372	−	2.10680i
$446$	34.8378	−	16.7770i	1.64962	−	0.794414i
$447$	2.33511	−	1.39517i	0.110447	−	0.0659891i
$448$	−0.374653	+	2.76580i	−0.0177007	+	0.130672i
$449$	−3.58737	+	15.7173i	−0.169298	+	0.741745i	0.816982	+	0.576664i	$0.195646\pi$
$449$	−3.58737	+	15.7173i	−0.169298	+	0.741745i	−0.986280	+	0.165081i	$0.947211\pi$
$450$	−47.0289	+	8.53449i	−2.21696	+	0.402320i
$451$	−12.4793	−	9.06671i	−0.587625	−	0.426935i
$452$	2.41453	−	3.02773i	0.113570	−	0.142412i
$453$	−11.0858	−	6.62343i	−0.520854	−	0.311196i
$454$	45.0854	+	4.05776i	2.11596	+	0.190440i
$455$	5.28733	+	39.0326i	0.247874	+	1.82988i
$456$	10.9200	+	13.6933i	0.511377	+	0.641246i
$457$	0.344479	+	7.67041i	0.0161140	+	0.358807i	0.990809	+	0.135268i	$0.0431895\pi$
$457$	0.344479	+	7.67041i	0.0161140	+	0.358807i	−0.974695	+	0.223539i	$0.928239\pi$
$458$	−41.5267	−	19.9982i	−1.94041	−	0.934454i
$459$	7.42722	−	0.668462i	0.346673	−	0.0312011i
$460$	−22.0998	−	96.8258i	−1.03041	−	4.51452i
$461$	15.3448	+	35.9010i	0.714680	+	1.67208i	0.740185	+	0.672403i	$0.234738\pi$
$461$	15.3448	+	35.9010i	0.714680	+	1.67208i	−0.0255050	+	0.999675i	$0.508119\pi$
$462$	3.66667	+	8.57861i	0.170589	+	0.399113i
$463$	7.18045	+	31.4596i	0.333704	+	1.46205i	0.811899	+	0.583798i	$0.198434\pi$
$463$	7.18045	+	31.4596i	0.333704	+	1.46205i	−0.478195	+	0.878254i	$0.658709\pi$
$464$	27.4689	−	2.47225i	1.27521	−	0.114771i
$465$	−9.55839	−	4.60308i	−0.443260	−	0.213463i
$466$	−1.27333	−	28.3530i	−0.0589860	−	1.31343i
$467$	5.51557	+	6.91630i	0.255230	+	0.320048i	0.892895	−	0.450266i	$-0.148671\pi$
$467$	5.51557	+	6.91630i	0.255230	+	0.320048i	−0.637665	+	0.770314i	$0.720099\pi$
$468$	7.52387	+	55.5434i	0.347791	+	2.56750i
$469$	8.83760	+	0.795398i	0.408082	+	0.0367281i
$470$	40.7934	+	24.3729i	1.88166	+	1.12424i
$471$	−1.18945	+	1.49152i	−0.0548068	+	0.0687256i
$472$	42.7830	+	31.0836i	1.96925	+	1.43074i
$473$	−7.07997	+	1.28482i	−0.325537	+	0.0590763i
$474$	1.36668	−	5.98782i	0.0627737	−	0.275030i
$475$	3.77708	−	27.8835i	0.173304	−	1.27938i
$476$	12.9114	−	7.71419i	0.591792	−	0.353580i
$477$	−0.972940	+	0.468543i	−0.0445479	+	0.0214531i
$478$	−29.5909	−	54.9892i	−1.35346	−	2.51515i
$479$	22.0930	−	23.1075i	1.00945	−	1.05581i	0.0110166	−	0.999939i	$-0.496493\pi$
$479$	22.0930	−	23.1075i	1.00945	−	1.05581i	0.998438	−	0.0558676i	$-0.0177925\pi$
$480$	11.4479	−	8.31740i	0.522524	−	0.379636i
$481$	2.17566	−	48.4449i	0.0992017	−	2.20890i
$482$	2.76497	−	5.13817i	0.125941	−	0.234037i
$483$	−3.14230	−	9.67101i	−0.142980	−	0.440046i
$484$	25.4345	+	7.01948i	1.15611	+	0.319067i
$485$	29.1008	+	44.0859i	1.32140	+	2.00184i
$486$	−38.8582	+	10.7242i	−1.76264	+	0.486458i
$487$	13.7911	+	12.0489i	0.624934	+	0.545989i	0.911097	−	0.412192i	$-0.135237\pi$
$487$	13.7911	+	12.0489i	0.624934	+	0.545989i	−0.286162	+	0.958181i	$0.592380\pi$
$488$	−14.9896	−	5.62569i	−0.678548	−	0.254663i
$489$	2.44753	−	0.918574i	0.110681	−	0.0415393i
$490$	20.8636	−	18.2280i	0.942521	−	0.823456i
$491$	−0.216672	+	0.328243i	−0.00977825	+	0.0148134i	−0.839430	−	0.543469i	$-0.817111\pi$
$491$	−0.216672	+	0.328243i	−0.00977825	+	0.0148134i	0.829651	+	0.558282i	$0.188539\pi$
$492$	−7.72474	+	23.7743i	−0.348258	+	1.07183i
$493$	4.83004	+	5.05182i	0.217534	+	0.227523i
$494$	−47.1446	−	8.55548i	−2.12114	−	0.384929i
$495$	7.42331	−	17.3677i	0.333653	−	0.780620i
$496$	−23.9609			−1.07588
$497$	8.66400	−	14.4091i	0.388633	−	0.646337i
$498$	15.8495			0.710235
$499$	11.9644	−	27.9921i	0.535599	−	1.25310i	−0.405230	−	0.914215i	$-0.632808\pi$
$499$	11.9644	−	27.9921i	0.535599	−	1.25310i	0.940829	−	0.338882i	$-0.110049\pi$
$500$	−49.0807	−	8.90683i	−2.19495	−	0.398326i
$501$	6.72545	+	7.03427i	0.300471	+	0.314268i
$502$	−5.67178	+	17.4559i	−0.253144	+	0.779097i
$503$	16.6233	−	25.1832i	0.741197	−	1.12286i	−0.246902	−	0.969041i	$-0.579412\pi$
$503$	16.6233	−	25.1832i	0.741197	−	1.12286i	0.988098	−	0.153824i	$-0.0491590\pi$
$504$	−21.4568	+	18.7462i	−0.955760	+	0.835022i
$505$	7.85885	−	2.94948i	0.349714	−	0.131250i
$506$	33.0115	+	12.3894i	1.46754	+	0.550777i
$507$	10.3477	+	9.04054i	0.459559	+	0.401504i
$508$	−60.3179	+	16.6467i	−2.67617	+	0.738577i
$509$	17.1143	+	25.9271i	0.758578	+	1.14920i	0.984557	+	0.175064i	$0.0560133\pi$
$509$	17.1143	+	25.9271i	0.758578	+	1.14920i	−0.225979	+	0.974132i	$0.572558\pi$
$510$	12.3921	+	3.41999i	0.548730	+	0.151440i
$511$	−0.522962	−	1.60951i	−0.0231345	−	0.0712007i
$512$	−24.0022	+	44.6036i	−1.06076	+	1.97122i
$513$	0.680982	−	15.1632i	0.0300661	−	0.669474i
$514$	55.0752	−	40.0145i	2.42926	−	1.76496i
$515$	−29.7078	+	31.0719i	−1.30908	+	1.36919i
$516$	5.52581	+	10.2687i	0.243260	+	0.452053i
$517$	−10.4678	+	5.04102i	−0.460373	+	0.221704i
$518$	38.6220	−	23.0756i	1.69695	−	1.01388i
$519$	0.200627	−	1.48108i	0.00880653	−	0.0650124i
$520$	−26.9864	+	118.235i	−1.18343	+	5.18496i
$521$	−15.3081	+	2.77801i	−0.670660	+	0.121707i	−0.503198	−	0.864171i	$-0.667843\pi$
$521$	−15.3081	+	2.77801i	−0.670660	+	0.121707i	−0.167463	+	0.985878i	$0.553557\pi$
$522$	−19.5500	−	14.2039i	−0.855682	−	0.621690i
$523$	−26.8294	+	33.6430i	−1.17317	+	1.47111i	−0.321590	+	0.946879i	$0.604217\pi$
$523$	−26.8294	+	33.6430i	−1.17317	+	1.47111i	−0.851578	+	0.524228i	$0.824354\pi$
$524$	−6.13708	−	3.66674i	−0.268100	−	0.160182i
$525$	−13.2552	−	1.19299i	−0.578502	−	0.0520662i
$526$	8.52619	+	62.9429i	0.371760	+	2.74444i
$527$	−3.78594	−	4.74741i	−0.164918	−	0.206801i
$528$	0.556441	+	12.3901i	0.0242160	+	0.539211i
$529$	−13.9038	−	6.69573i	−0.604514	−	0.291119i
$530$	−4.24723	+	0.382257i	−0.184488	+	0.0166042i
$531$	−4.45188	−	19.5050i	−0.193195	−	0.846444i
$532$	−12.0318	−	28.1498i	−0.521644	−	1.22045i
$533$	−14.7268	−	34.4550i	−0.637888	−	1.49241i
$534$	−6.46147	−	28.3095i	−0.279615	−	1.22507i
$535$	−36.7242	+	3.30524i	−1.58773	+	0.142898i
$536$	24.6147	+	11.8538i	1.06319	+	0.512007i
$537$	−0.258425	−	5.75428i	−0.0111519	−	0.248316i
$538$	20.2315	+	25.3695i	0.872241	+	1.09376i
$539$	0.909250	+	6.71235i	0.0391642	+	0.289121i
$540$	−69.8348	−	6.28525i	−3.00521	−	0.270474i
$541$	−12.4417	−	7.43357i	−0.534910	−	0.319594i	0.219916	−	0.975519i	$-0.429422\pi$
$541$	−12.4417	−	7.43357i	−0.534910	−	0.319594i	−0.754826	+	0.655925i	$0.772279\pi$
$542$	−3.81484	+	4.78366i	−0.163861	+	0.205476i
$543$	−2.42317	−	1.76054i	−0.103988	−	0.0755518i
$544$	7.96896	−	1.44615i	0.341666	−	0.0620033i
$545$	7.29762	−	31.9730i	0.312596	−	1.36957i
$546$	−3.04207	+	22.4575i	−0.130189	+	0.961091i
$547$	−6.25476	+	3.73705i	−0.267434	+	0.159785i	−0.640356	−	0.768078i	$-0.721213\pi$
$547$	−6.25476	+	3.73705i	−0.267434	+	0.159785i	0.372922	+	0.927863i	$0.378356\pi$
$548$	32.8011	−	15.7962i	1.40119	−	0.674780i
$549$	2.87027	+	5.33386i	0.122500	+	0.227644i
$550$	31.8911	−	33.3555i	1.35984	−	1.42228i
$551$	11.5091	−	8.36187i	0.490305	−	0.356228i
$552$	1.40466	−	31.2771i	0.0597861	−	1.33124i
$553$	−2.78729	+	5.17966i	−0.118528	+	0.220262i
$554$	0.516823	+	1.59062i	0.0219577	+	0.0675789i
$555$	25.5278	+	7.04522i	1.08359	+	0.299053i
$556$	29.4895	+	44.6747i	1.25063	+	1.89463i
$557$	16.8156	−	4.64081i	0.712500	−	0.196637i	0.109048	−	0.994037i	$-0.465220\pi$
$557$	16.8156	−	4.64081i	0.712500	−	0.196637i	0.603452	+	0.797399i	$0.293791\pi$
$558$	15.8102	+	13.8129i	0.669299	+	0.584749i
$559$	−16.3647	−	6.14179i	−0.692154	−	0.259770i
$560$	−45.4838	+	17.0704i	−1.92204	+	0.721354i
$561$	−2.36695	+	2.06794i	−0.0999328	+	0.0873087i
$562$	−1.43351	+	2.17167i	−0.0604689	+	0.0916064i
$563$	2.96338	−	9.12035i	0.124892	−	0.384377i	−0.868990	−	0.494830i	$-0.835230\pi$
$563$	2.96338	−	9.12035i	0.124892	−	0.384377i	0.993881	+	0.110453i	$0.0352303\pi$
$564$	13.0117	+	13.6091i	0.547890	+	0.573048i
$565$	−3.11904	−	0.566022i	−0.131219	−	0.0238127i
$566$	−26.0916	+	61.0443i	−1.09671	+	2.56588i
$567$	6.73408			0.282805
$568$	40.5633	−	32.1624i	1.70200	−	1.34950i
$569$	−45.5501			−1.90956			−0.954779	−	0.297317i	$-0.903908\pi$
$569$	−45.5501			−1.90956			−0.954779	+	0.297317i	$0.903908\pi$
$570$	10.2838	−	24.0602i	0.430742	−	1.00777i
$571$	2.16527	+	0.392938i	0.0906136	+	0.0164439i	0.223674	−	0.974664i	$-0.428195\pi$
$571$	2.16527	+	0.392938i	0.0906136	+	0.0164439i	−0.133061	+	0.991108i	$0.542481\pi$
$572$	−37.3981	−	39.1153i	−1.56369	−	1.63549i
$573$	4.67851	−	14.3990i	0.195447	−	0.601525i
$574$	19.1511	−	29.0126i	0.799350	−	1.21096i
$575$	−37.8793	+	33.0941i	−1.57967	+	1.38012i
$576$	3.04377	−	1.14235i	0.126824	−	0.0475977i
$577$	−14.8272	−	5.56474i	−0.617265	−	0.231663i	0.0231014	−	0.999733i	$-0.492646\pi$
$577$	−14.8272	−	5.56474i	−0.617265	−	0.231663i	−0.640366	+	0.768070i	$0.721217\pi$
$578$	−26.9068	−	23.5078i	−1.11918	−	0.977795i
$579$	−7.83317	+	2.16182i	−0.325535	+	0.0898421i
$580$	−36.2034	−	54.8458i	−1.50326	−	2.27735i
$581$	−14.6321	−	4.03819i	−0.607040	−	0.167532i
$582$	9.39183	+	28.9051i	0.389304	+	1.19815i
$583$	0.494066	−	0.918129i	0.0204621	−	0.0380250i
$584$	0.233772	−	5.20534i	0.00967355	−	0.215398i
$585$	37.1186	−	26.9683i	1.53467	−	1.11500i
$586$	−13.3732	+	13.9872i	−0.552441	+	0.577807i
$587$	8.54919	+	15.8871i	0.352863	+	0.655729i	0.993716	−	0.111935i	$-0.0357048\pi$
$587$	8.54919	+	15.8871i	0.352863	+	0.655729i	−0.640853	+	0.767664i	$0.721419\pi$
$588$	9.89016	−	4.76285i	0.407863	−	0.196417i
$589$	−10.6099	+	6.33910i	−0.437172	+	0.261198i
$590$	10.6051	−	78.2899i	0.436605	−	3.22314i
$591$	−0.213563	+	0.935679i	−0.00878479	+	0.0384887i
$592$	58.8499	−	10.6797i	2.41871	−	0.438932i
$593$	3.20378	+	2.32768i	0.131563	+	0.0955864i	0.651621	−	0.758545i	$-0.274089\pi$
$593$	3.20378	+	2.32768i	0.131563	+	0.0955864i	−0.520057	+	0.854131i	$0.674089\pi$
$594$	15.5209	−	19.4625i	0.636828	−	0.798558i
$595$	−10.5688	−	6.31457i	−0.433279	−	0.258872i
$596$	−14.5800	−	1.31222i	−0.597219	−	0.0537506i
$597$	1.61750	+	11.9409i	0.0662000	+	0.488708i
$598$	53.4032	+	66.9655i	2.18382	+	2.73842i
$599$	−1.73441	−	38.6197i	−0.0708662	−	1.57796i	−0.648212	−	0.761460i	$-0.724483\pi$
$599$	−1.73441	−	38.6197i	−0.0708662	−	1.57796i	0.577346	−	0.816499i	$-0.304088\pi$
$600$	−36.9186	−	17.7790i	−1.50719	−	0.725826i
$601$	−31.4516	+	2.83070i	−1.28294	+	0.115467i	−0.710041	−	0.704160i	$-0.751324\pi$
$601$	−31.4516	+	2.83070i	−1.28294	+	0.115467i	−0.572898	+	0.819627i	$0.694181\pi$
$602$	−3.60852	−	15.8100i	−0.147072	−	0.644366i
$603$	−4.06223	−	9.50406i	−0.165427	−	0.387035i
$604$	27.3140	+	63.9043i	1.11139	+	2.60023i
$605$	−4.80604	−	21.0566i	−0.195393	−	0.856074i
$606$	4.81011	−	0.432918i	0.195397	−	0.0175861i
$607$	2.89836	+	1.39578i	0.117641	+	0.0566528i	0.491778	−	0.870720i	$-0.336347\pi$
$607$	2.89836	+	1.39578i	0.117641	+	0.0566528i	−0.374138	+	0.927373i	$0.622061\pi$
$608$	−0.739597	−	16.4684i	−0.0299946	−	0.667882i
$609$	−4.19522	−	5.26064i	−0.169999	−	0.213172i
$610$	3.21075	+	23.7027i	0.129999	+	0.959695i
$611$	−28.1093	−	2.52989i	−1.13718	−	0.102348i
$612$	−15.0394	−	8.98563i	−0.607932	−	0.363223i
$613$	28.3576	−	35.5593i	1.14535	−	1.43623i	0.263529	−	0.964652i	$-0.415114\pi$
$613$	28.3576	−	35.5593i	1.14535	−	1.43623i	0.881825	−	0.471577i	$-0.156315\pi$
$614$	25.3697	+	18.4322i	1.02384	+	0.743861i
$615$	20.1335	−	3.65369i	0.811860	−	0.147331i
$616$	6.12139	−	26.8196i	0.246638	−	1.08059i
$617$	6.62595	−	48.9147i	0.266751	−	1.96923i	0.0215151	−	0.999769i	$-0.493151\pi$
$617$	6.62595	−	48.9147i	0.266751	−	1.96923i	0.245236	−	0.969464i	$-0.421135\pi$
$618$	−21.2324	+	12.6858i	−0.854094	+	0.510297i
$619$	27.0275	−	13.0157i	1.08633	−	0.523147i	0.196992	−	0.980405i	$-0.436883\pi$
$619$	27.0275	−	13.0157i	1.08633	−	0.523147i	0.889334	+	0.457258i	$0.151169\pi$
$620$	27.0550	+	50.2766i	1.08656	+	2.01916i
$621$	−18.7507	+	19.6117i	−0.752439	+	0.786989i
$622$	7.24072	−	5.26069i	0.290327	−	0.210935i
$623$	−1.24766	+	27.7812i	−0.0499863	+	1.11303i
$624$	−14.2767	+	26.5306i	−0.571526	+	1.06207i
$625$	0.0814229	+	0.250594i	0.00325692	+	0.0100238i
$626$	31.5063	+	8.69519i	1.25925	+	0.347530i
$627$	3.52432	+	5.33911i	0.140748	+	0.213224i
$628$	9.89671	−	2.73132i	0.394922	−	0.108991i
$629$	11.4145	+	9.97256i	0.455126	+	0.397632i
$630$	39.8523	+	14.9568i	1.58775	+	0.595894i
$631$	32.7844	−	12.3042i	1.30513	−	0.489823i	0.400606	−	0.916250i	$-0.368800\pi$
$631$	32.7844	−	12.3042i	1.30513	−	0.489823i	0.904522	+	0.426428i	$0.140228\pi$
$632$	−13.6383	+	11.9154i	−0.542501	+	0.473969i
$633$	−12.8173	+	19.4174i	−0.509443	+	0.771773i
$634$	−20.9888	+	64.5968i	−0.833571	+	2.56547i
$635$	35.3962	+	37.0215i	1.40466	+	1.46915i
$636$	−1.66250	−	0.301699i	−0.0659224	−	0.0119632i
$637$	−6.46696	+	15.1302i	−0.256230	+	0.599481i
$638$	23.3314			0.923700
$639$	−19.5622	−	0.933551i	−0.773868	−	0.0369307i
$640$	47.2657			1.86834
$641$	−5.33980	+	12.4931i	−0.210909	+	0.493447i	−0.991264	−	0.131890i	$-0.957895\pi$
$641$	−5.33980	+	12.4931i	−0.210909	+	0.493447i	0.780355	+	0.625337i	$0.215038\pi$
$642$	−20.8738	−	3.78803i	−0.823823	−	0.149502i
$643$	−14.3009	−	14.9575i	−0.563971	−	0.589867i	0.377898	−	0.925847i	$-0.376647\pi$
$643$	−14.3009	−	14.9575i	−0.563971	−	0.589867i	−0.941869	+	0.335980i	$0.890933\pi$
$644$	−16.9107	+	52.0459i	−0.666376	+	2.05089i
$645$	5.25849	−	7.96628i	0.207053	−	0.313672i
$646$	11.2782	−	9.85346i	0.443735	−	0.387679i
$647$	−13.8230	+	5.18787i	−0.543439	+	0.203956i	−0.607971	−	0.793960i	$-0.708016\pi$
$647$	−13.8230	+	5.18787i	−0.543439	+	0.203956i	0.0645315	+	0.997916i	$0.479445\pi$
$648$	19.4116	+	7.28530i	0.762560	+	0.286194i
$649$	14.5466	+	12.7089i	0.571002	+	0.498870i
$650$	108.061	−	29.8230i	4.23850	−	1.16975i
$651$	3.22038	+	4.87866i	0.126217	+	0.191210i
$652$	−13.5618	−	3.74283i	−0.531122	−	0.146580i
$653$	10.9790	+	33.7898i	0.429641	+	1.32230i	0.898480	+	0.439014i	$0.144672\pi$
$653$	10.9790	+	33.7898i	0.429641	+	1.32230i	−0.468839	+	0.883283i	$0.655328\pi$
$654$	8.94131	−	16.6157i	0.349633	−	0.649727i
$655$	−0.262547	+	5.84606i	−0.0102586	+	0.228425i
$656$	37.3888	−	27.1645i	1.45979	−	1.06060i
$657$	−1.36227	+	1.42482i	−0.0531473	+	0.0555877i
$658$	−12.4078	−	23.0576i	−0.483706	−	0.898877i
$659$	9.29847	−	4.47791i	0.362217	−	0.174434i	−0.243919	−	0.969796i	$-0.578433\pi$
$659$	9.29847	−	4.47791i	0.362217	−	0.174434i	0.606136	+	0.795361i	$0.292719\pi$
$660$	25.3696	−	15.1576i	0.987510	−	0.590010i
$661$	−3.39558	+	25.0672i	−0.132073	+	0.974999i	0.796707	+	0.604366i	$0.206574\pi$
$661$	−3.39558	+	25.0672i	−0.132073	+	0.974999i	−0.928779	+	0.370633i	$0.879141\pi$
$662$	−5.68152	+	24.8924i	−0.220818	+	0.967469i
$663$	−7.51232	+	1.36329i	−0.291754	+	0.0529456i
$664$	−37.8095	−	27.4702i	−1.46729	−	1.06605i
$665$	−15.6240	+	19.5919i	−0.605873	+	0.759741i
$666$	−44.9876	−	26.8788i	−1.74323	−	1.04153i
$667$	−25.3281	−	2.27957i	−0.980708	−	0.0882653i
$668$	−7.03037	−	51.9003i	−0.272013	−	2.00808i
$669$	−7.81923	−	9.80501i	−0.302309	−	0.379083i
$670$	−1.83118	−	40.7744i	−0.0707447	−	1.57525i
$671$	−5.26898	−	2.53740i	−0.203407	−	0.0979554i
$672$	−7.76566	+	0.698922i	−0.299567	+	0.0269615i
$673$	6.99117	+	30.6303i	0.269490	+	1.18071i	0.910608	+	0.413270i	$0.135613\pi$
$673$	6.99117	+	30.6303i	0.269490	+	1.18071i	−0.641119	+	0.767442i	$0.721529\pi$
$674$	−25.8974	−	60.5901i	−0.997532	−	2.33384i
$675$	13.9570	+	32.6540i	0.537204	+	1.25685i
$676$	−16.4549	−	72.0934i	−0.632879	−	2.77282i
$677$	−19.6334	+	1.76704i	−0.754573	+	0.0679128i	−0.460245	−	0.887792i	$-0.652239\pi$
$677$	−19.6334	+	1.76704i	−0.754573	+	0.0679128i	−0.294328	+	0.955705i	$0.595096\pi$
$678$	−1.64323	−	0.791340i	−0.0631080	−	0.0303912i
$679$	−1.30588	−	29.0776i	−0.0501150	−	1.11590i
$680$	−23.6341	−	29.6363i	−0.906327	−	1.13650i
$681$	−1.97080	−	14.5490i	−0.0755212	−	0.557520i
$682$	−20.1883	−	1.81698i	−0.773050	−	0.0695758i
$683$	25.8537	+	15.4469i	0.989264	+	0.591058i	0.913832	−	0.406093i	$-0.133109\pi$
$683$	25.8537	+	15.4469i	0.989264	+	0.591058i	0.0754325	+	0.997151i	$0.475966\pi$
$684$	−22.2330	+	27.8793i	−0.850099	+	1.06599i
$685$	−24.1096	−	17.5167i	−0.921181	−	0.669277i
$686$	−49.8529	+	9.04698i	−1.90339	+	0.345415i
$687$	−3.32646	+	14.5742i	−0.126912	+	0.556039i
$688$	2.89388	−	21.3635i	0.110328	−	0.814474i
$689$	2.17420	−	1.29902i	0.0828303	−	0.0494888i
$690$	−42.1419	+	20.2945i	−1.60432	+	0.772598i
$691$	22.5374	+	41.8815i	0.857364	+	1.59325i	0.803966	+	0.594676i	$0.202720\pi$
$691$	22.5374	+	41.8815i	0.857364	+	1.59325i	0.0533983	+	0.998573i	$0.482995\pi$
$692$	−5.55853	+	5.81377i	−0.211304	+	0.221006i
$693$	−8.41970	+	6.11727i	−0.319838	+	0.232376i
$694$	−0.666319	+	14.8367i	−0.0252931	+	0.563195i
$695$	20.7639	−	38.5858i	0.787619	−	1.46364i
$696$	−6.40187	−	19.7029i	−0.242662	−	0.746837i
$697$	11.2897	+	3.11577i	0.427629	+	0.118018i
$698$	4.36455	+	6.61201i	0.165201	+	0.250268i
$699$	−8.87341	+	2.44890i	−0.335623	+	0.0926261i
$700$	53.9371	+	47.1234i	2.03863	+	1.78110i
$701$	−39.7817	−	14.9303i	−1.50253	−	0.563911i	−0.541588	−	0.840644i	$-0.682177\pi$
$701$	−39.7817	−	14.9303i	−1.50253	−	0.563911i	−0.960947	+	0.276734i	$0.910748\pi$
$702$	56.6146	−	21.2478i	2.13678	−	0.801947i
$703$	23.2332	−	20.2982i	0.876257	−	0.765562i
$704$	−1.72921	+	2.61965i	−0.0651722	+	0.0987316i
$705$	4.76268	−	14.6580i	0.179373	−	0.552053i
$706$	−40.1354	−	41.9783i	−1.51052	−	1.57988i
$707$	−4.55092	−	0.825871i	−0.171155	−	0.0310601i
$708$	12.3031	−	28.7846i	0.462379	−	1.08179i
$709$	−14.2324			−0.534509			−0.267254	−	0.963626i	$-0.586116\pi$
$709$	−14.2324			−0.534509			−0.267254	+	0.963626i	$0.586116\pi$
$710$	−71.0288	−	30.5952i	−2.66566	−	1.14822i
$711$	6.85146			0.256950
$712$	−33.6517	+	78.7322i	−1.26115	+	2.95061i
$713$	21.7385	+	3.94495i	0.814113	+	0.147740i
$714$	−4.89511	−	5.11988i	−0.183195	−	0.191607i
$715$	−13.6889	+	42.1300i	−0.511935	+	1.57557i
$716$	−17.0771	+	25.8707i	−0.638200	+	0.966832i
$717$	−15.2521	+	13.3254i	−0.569602	+	0.497646i
$718$	30.4551	−	11.4300i	1.13657	−	0.426563i
$719$	35.4413	+	13.3013i	1.32174	+	0.496056i	0.909759	−	0.415137i	$-0.136266\pi$
$719$	35.4413	+	13.3013i	1.32174	+	0.496056i	0.411979	+	0.911194i	$0.364838\pi$
$720$	42.6154	+	37.2319i	1.58818	+	1.38755i
$721$	22.8336	−	6.30167i	0.850367	−	0.234686i
$722$	9.73634	+	14.7499i	0.362349	+	0.548936i
$723$	−1.82426	−	0.503463i	−0.0678448	−	0.0187240i
$724$	4.98107	+	15.3302i	0.185120	+	0.569741i
$725$	−15.7719	+	29.3091i	−0.585753	+	1.08851i
$726$	0.557514	−	12.4140i	0.0206913	−	0.460727i
$727$	−3.13634	+	2.27869i	−0.116321	+	0.0845118i	−0.644425	−	0.764668i	$-0.722903\pi$
$727$	−3.13634	+	2.27869i	−0.116321	+	0.0845118i	0.528104	+	0.849180i	$0.322903\pi$
$728$	46.1799	−	48.3004i	1.71154	−	1.79013i
$729$	1.39776	+	2.59747i	0.0517687	+	0.0962024i
$730$	−7.01354	+	3.37754i	−0.259583	+	0.125008i
$731$	4.69001	−	2.80215i	0.173466	−	0.103641i
$732$	−1.27218	+	9.39158i	−0.0470210	+	0.347123i
$733$	2.55997	−	11.2159i	0.0945545	−	0.414270i	−0.905392	−	0.424576i	$-0.860423\pi$
$733$	2.55997	−	11.2159i	0.0945545	−	0.414270i	0.999947	+	0.0103055i	$0.00328041\pi$
$734$	−55.2820	+	10.0322i	−2.04050	+	0.370295i
$735$	−7.26950	−	5.28160i	−0.268140	−	0.194815i
$736$	−18.3733	+	23.0395i	−0.677251	+	0.849245i
$737$	8.56663	+	5.11832i	0.315556	+	0.188536i
$738$	−40.3300	−	3.62977i	−1.48457	−	0.133614i
$739$	−4.48804	−	33.1320i	−0.165095	−	1.21878i	−0.863972	−	0.503539i	$-0.832031\pi$
$739$	−4.48804	−	33.1320i	−0.165095	−	1.21878i	0.698877	−	0.715242i	$-0.253683\pi$
$740$	−88.8580	−	111.424i	−3.26648	−	4.09604i
$741$	0.697217	+	15.5247i	0.0256129	+	0.570315i
$742$	2.11704	+	1.01951i	0.0777189	+	0.0374274i
$743$	−27.5881	+	2.48297i	−1.01211	+	0.0910915i	−0.583261	−	0.812285i	$-0.698223\pi$
$743$	−27.5881	+	2.48297i	−1.01211	+	0.0910915i	−0.428849	+	0.903376i	$0.641081\pi$
$744$	4.00503	+	17.5472i	0.146832	+	0.643311i
$745$	4.70958	+	11.0186i	0.172546	+	0.403690i
$746$	8.55936	+	20.0256i	0.313380	+	0.733190i
$747$	3.93436	+	17.2376i	0.143951	+	0.630689i
$748$	16.8467	−	1.51623i	0.615978	−	0.0554390i
$749$	18.3052	+	8.81534i	0.668859	+	0.322106i
$750$	1.05400	+	23.4690i	0.0384865	+	0.856968i
$751$	0.343558	+	0.430808i	0.0125366	+	0.0157204i	0.788060	−	0.615598i	$-0.211086\pi$
$751$	0.343558	+	0.430808i	0.0125366	+	0.0157204i	−0.775524	+	0.631318i	$0.782514\pi$
$752$	−4.67260	−	34.4945i	−0.170392	−	1.25788i
$753$	5.92897	+	0.533617i	0.216064	+	0.0194461i
$754$	48.6533	+	29.0690i	1.77185	+	1.05863i
$755$	35.4689	−	44.4766i	1.29085	−	1.61867i
$756$	31.2567	+	22.7093i	1.13680	+	0.825930i
$757$	−16.7582	+	3.04117i	−0.609089	+	0.110533i	−0.474333	−	0.880345i	$-0.657311\pi$
$757$	−16.7582	+	3.04117i	−0.609089	+	0.110533i	−0.134756	+	0.990879i	$0.543025\pi$
$758$	−18.2977	+	80.1672i	−0.664601	+	2.91181i
$759$	1.53509	−	11.3325i	0.0557204	−	0.411344i
$760$	−66.2333	+	39.5725i	−2.40253	+	1.43545i
$761$	35.5148	−	17.1030i	1.28741	−	0.619985i	0.340127	−	0.940379i	$-0.389530\pi$
$761$	35.5148	−	17.1030i	1.28741	−	0.619985i	0.947284	+	0.320395i	$0.103816\pi$
$762$	13.9647	+	25.9507i	0.505886	+	0.940094i
$763$	−12.4879	+	13.0613i	−0.452092	+	0.472851i
$764$	−65.9169	+	47.8914i	−2.38479	+	1.73265i
$765$	−0.643393	+	14.3262i	−0.0232619	+	0.517967i
$766$	−24.1592	+	44.8952i	−0.872906	+	1.62213i
$767$	14.4998	+	44.6259i	0.523559	+	1.61135i
$768$	23.9976	+	6.62290i	0.865937	+	0.238983i
$769$	−14.4608	−	21.9071i	−0.521469	−	0.789992i	0.474446	−	0.880284i	$-0.342648\pi$
$769$	−14.4608	−	21.9071i	−0.521469	−	0.789992i	−0.995915	+	0.0902927i	$0.971220\pi$
$770$	−39.6169	+	10.9336i	−1.42769	+	0.394018i
$771$	−16.6276	−	14.5271i	−0.598827	−	0.523180i
$772$	40.9427	+	15.3661i	1.47356	+	0.553036i
$773$	−36.6688	+	13.7620i	−1.31888	+	0.494986i	−0.908865	−	0.417091i	$-0.863050\pi$
$773$	−36.6688	+	13.7620i	−1.31888	+	0.494986i	−0.410020	+	0.912077i	$0.634478\pi$
$774$	−14.2250	+	12.4280i	−0.511308	+	0.446716i
$775$	15.9297	−	24.1324i	0.572211	−	0.866862i
$776$	27.6935	−	85.2317i	0.994137	−	3.05964i
$777$	−10.0840	−	10.5470i	−0.361760	−	0.378372i
$778$	−1.42266	−	0.258175i	−0.0510050	−	0.00925604i
$779$	9.36904	−	21.9200i	0.335681	−	0.785364i
$780$	71.7887			2.57045
$781$	15.8099	−	10.3724i	0.565722	−	0.371155i
$782$	−26.7715			−0.957348
$783$	−7.05635	+	16.5092i	−0.252173	+	0.589989i
$784$	−19.9682	−	3.62370i	−0.713151	−	0.129418i
$785$	−5.80766	−	6.07434i	−0.207284	−	0.216802i
$786$	−1.04044	+	3.20214i	−0.0371112	+	0.114217i
$787$	2.07104	−	3.13750i	0.0738248	−	0.111840i	−0.795785	−	0.605579i	$-0.792942\pi$
$787$	2.07104	−	3.13750i	0.0738248	−	0.111840i	0.869610	+	0.493739i	$0.164370\pi$
$788$	3.88960	−	3.39824i	0.138561	−	0.121057i
$789$	19.2874	−	7.23868i	0.686650	−	0.257704i
$790$	25.3308	+	9.50681i	0.901230	+	0.338237i
$791$	1.31539	+	1.14922i	0.0467699	+	0.0408616i
$792$	−30.8885	+	8.52470i	−1.09758	+	0.302912i
$793$	−7.82607	−	11.8560i	−0.277912	−	0.421019i
$794$	78.8386	+	21.7581i	2.79788	+	0.772165i
$795$	0.427399	+	1.31540i	0.0151583	+	0.0466524i
$796$	30.7296	−	57.1052i	1.08918	−	2.02404i
$797$	0.940047	−	20.9318i	0.0332982	−	0.741441i	−0.911011	−	0.412382i	$-0.864697\pi$
$797$	0.940047	−	20.9318i	0.0332982	−	0.741441i	0.944309	−	0.329059i	$-0.106732\pi$
$798$	−11.6642	+	8.47452i	−0.412907	+	0.299995i
$799$	6.09615	−	6.37607i	0.215666	−	0.225569i
$800$	18.2763	+	33.9631i	0.646165	+	1.20078i
$801$	29.1848	−	14.0547i	1.03119	−	0.496597i
$802$	25.1736	−	15.0405i	0.888911	−	0.531100i
$803$	0.255480	−	1.88603i	0.00901571	−	0.0665566i
$804$	3.59863	−	15.7666i	0.126914	−	0.556046i
$805$	44.0755	−	7.99852i	1.55346	−	0.281911i
$806$	−39.8352	−	28.9419i	−1.40313	−	1.01944i
$807$	6.56178	−	8.22821i	0.230986	−	0.289647i
$808$	−12.2250	−	7.30409i	−0.430073	−	0.256957i
$809$	30.2129	+	2.71921i	1.06223	+	0.0956023i	0.606945	−	0.794744i	$-0.292395\pi$
$809$	30.2129	+	2.71921i	1.06223	+	0.0956023i	0.455284	+	0.890346i	$0.349538\pi$
$810$	−4.15794	−	30.6951i	−0.146095	−	1.07852i
$811$	−16.3738	−	20.5321i	−0.574961	−	0.720978i	0.406283	−	0.913747i	$-0.366825\pi$
$811$	−16.3738	−	20.5321i	−0.574961	−	0.720978i	−0.981244	+	0.192769i	$0.938253\pi$
$812$	1.62460	+	36.1745i	0.0570123	+	1.26948i
$813$	1.78793	+	0.861022i	0.0627055	+	0.0301974i
$814$	50.3938	−	4.53553i	1.76630	−	0.158970i
$815$	2.56261	+	11.2275i	0.0897642	+	0.393283i
$816$	−3.70106	−	8.65906i	−0.129563	−	0.303128i
$817$	−4.37050	−	10.2253i	−0.152905	−	0.357738i
$818$	−8.46188	−	37.0739i	−0.295863	−	1.29626i
$819$	−25.1793	+	2.26618i	−0.879837	+	0.0791867i
$820$	−99.2154	−	47.7796i	−3.46475	−	1.66854i
$821$	0.820681	+	18.2739i	0.0286420	+	0.637763i	0.961053	+	0.276364i	$0.0891295\pi$
$821$	0.820681	+	18.2739i	0.0286420	+	0.637763i	−0.932411	+	0.361399i	$0.882299\pi$
$822$	−10.6904	−	13.4054i	−0.372871	−	0.467565i
$823$	0.331399	+	2.44649i	0.0115519	+	0.0852792i	0.995808	−	0.0914693i	$-0.0291563\pi$
$823$	0.331399	+	2.44649i	0.0115519	+	0.0852792i	−0.984256	+	0.176749i	$0.943442\pi$
$824$	72.6374	+	6.53749i	2.53044	+	0.227744i
$825$	−12.8487	−	7.67676i	−0.447335	−	0.267270i
$826$	−27.1422	+	34.0352i	−0.944398	+	1.18424i
$827$	12.3131	+	8.94600i	0.428169	+	0.311083i	0.780916	−	0.624636i	$-0.214752\pi$
$827$	12.3131	+	8.94600i	0.428169	+	0.311083i	−0.352747	+	0.935719i	$0.614752\pi$
$828$	62.7194	−	11.3819i	2.17965	−	0.395548i
$829$	1.18413	−	5.18802i	0.0411266	−	0.180187i	−0.950193	−	0.311662i	$-0.899114\pi$
$829$	1.18413	−	5.18802i	0.0411266	−	0.180187i	0.991319	+	0.131475i	$0.0419713\pi$
$830$	−9.37227	+	69.1888i	−0.325316	+	2.40158i
$831$	0.465659	−	0.278218i	0.0161535	−	0.00965128i
$832$	−6.86981	+	3.30833i	−0.238168	+	0.114696i
$833$	−2.43710	−	4.52889i	−0.0844406	−	0.156917i
$834$	17.4221	−	18.2221i	0.603278	−	0.630980i
$835$	−34.6840	+	25.1994i	−1.20029	+	0.872061i
$836$	1.54463	−	34.3939i	0.0534222	−	1.18954i
$837$	7.39144	−	13.7356i	0.255485	−	0.474771i
$838$	−10.0839	−	31.0351i	−0.348343	−	1.07209i
$839$	−33.4307	−	9.22629i	−1.15416	−	0.318527i	−0.363980	−	0.931407i	$-0.618582\pi$
$839$	−33.4307	−	9.22629i	−1.15416	−	0.318527i	−0.790176	+	0.612880i	$0.790011\pi$
$840$	20.1036	+	30.4556i	0.693639	+	1.05082i
$841$	11.7340	−	3.23838i	0.404621	−	0.111668i
$842$	50.7373	+	44.3278i	1.74852	+	1.52764i
$843$	0.790148	+	0.296547i	0.0272141	+	0.0102136i
$844$	117.227	−	43.9959i	4.03511	−	1.51440i
$845$	−45.5840	+	39.8256i	−1.56814	+	1.37004i
$846$	−16.8022	+	25.4542i	−0.577670	+	0.875133i
$847$	−3.67757	+	11.3184i	−0.126363	+	0.388904i
$848$	2.15873	+	2.25785i	0.0741309	+	0.0775349i
$849$	21.1855	+	3.84460i	0.727084	+	0.131946i
$850$	−13.7710	+	32.2188i	−0.472341	+	1.10510i
$851$	−55.1496			−1.89050
$852$	−23.9040	−	19.1728i	−0.818939	−	0.656850i
$853$	24.1979			0.828520			0.414260	−	0.910158i	$-0.364040\pi$
$853$	24.1979			0.828520			0.414260	+	0.910158i	$0.364040\pi$
$854$	5.17998	−	12.1192i	0.177255	−	0.414709i
$855$	28.7201	+	5.21193i	0.982206	+	0.178244i
$856$	43.2296	+	45.2147i	1.47756	+	1.54541i
$857$	6.13806	−	18.8910i	0.209672	−	0.645305i	−0.789817	−	0.613343i	$-0.789824\pi$
$857$	6.13806	−	18.8910i	0.209672	−	0.645305i	0.999489	−	0.0319619i	$-0.0101755\pi$
$858$	−14.0407	+	21.2708i	−0.479342	+	0.726171i
$859$	32.0423	−	27.9945i	1.09327	−	0.955159i	0.0940844	−	0.995564i	$-0.470008\pi$
$859$	32.0423	−	27.9945i	1.09327	−	0.955159i	0.999183	+	0.0404049i	$0.0128648\pi$
$860$	−48.0939	+	18.0500i	−1.63999	+	0.615498i
$861$	−10.5560	−	3.96175i	−0.359749	−	0.135016i
$862$	−76.8225	−	67.1178i	−2.61659	−	2.28604i
$863$	−32.7398	+	9.03562i	−1.11448	+	0.307576i	−0.774321	−	0.632793i	$-0.781908\pi$
$863$	−32.7398	+	9.03562i	−1.11448	+	0.307576i	−0.340156	+	0.940369i	$0.610480\pi$
$864$	11.4613	+	17.3632i	0.389922	+	0.590707i
$865$	6.34682	+	1.75161i	0.215799	+	0.0595566i
$866$	−23.4059	−	72.0360i	−0.795365	−	2.44788i
$867$	−5.49134	+	10.2046i	−0.186496	+	0.346567i
$868$	1.41142	−	31.4278i	0.0479068	−	1.06673i
$869$	−5.35170	+	3.88824i	−0.181544	+	0.131899i
$870$	−21.3886	+	22.3707i	−0.725142	+	0.758439i
$871$	11.4871	+	21.3466i	0.389226	+	0.723302i
$872$	−50.1280	+	24.1404i	−1.69755	+	0.817496i
$873$	−29.1051	+	17.3895i	−0.985058	+	0.588545i
$874$	−7.31451	+	53.9979i	−0.247417	+	1.82650i
$875$	5.00648	−	21.9348i	0.169250	−	0.741532i
$876$	−3.03481	+	0.550737i	−0.102537	+	0.0186077i
$877$	35.7598	+	25.9810i	1.20752	+	0.877317i	0.995003	−	0.0998403i	$-0.0318332\pi$
$877$	35.7598	+	25.9810i	1.20752	+	0.877317i	0.212519	+	0.977157i	$0.431833\pi$
$878$	18.8273	−	23.6086i	0.635390	−	0.796753i
$879$	5.38797	+	3.21916i	0.181732	+	0.108580i
$880$	−54.4163	−	4.89756i	−1.83437	−	0.165097i
$881$	−0.706117	−	5.21276i	−0.0237897	−	0.175622i	0.975157	−	0.221516i	$-0.0711006\pi$
$881$	−0.706117	−	5.21276i	−0.0237897	−	0.175622i	−0.998946	+	0.0458940i	$0.985386\pi$
$882$	11.0867	+	13.9023i	0.373308	+	0.468114i
$883$	−0.122605	−	2.73000i	−0.00412597	−	0.0918720i	−0.999999	−	0.00111860i	$-0.999644\pi$
$883$	−0.122605	−	2.73000i	−0.00412597	−	0.0918720i	0.995873	−	0.0907534i	$-0.0289275\pi$
$884$	37.0198	+	17.8278i	1.24511	+	0.599614i
$885$	−25.5209	+	2.29692i	−0.857876	+	0.0772102i
$886$	−16.8504	−	73.8264i	−0.566100	−	2.48025i
$887$	−2.41880	−	5.65906i	−0.0812154	−	0.190013i	0.873999	−	0.485928i	$-0.161518\pi$
$887$	−2.41880	−	5.65906i	−0.0812154	−	0.190013i	−0.955214	+	0.295915i	$0.904375\pi$
$888$	−17.6576	−	41.3121i	−0.592551	−	1.38634i
$889$	−6.28017	−	27.5152i	−0.210630	−	0.922831i
$890$	127.402	−	11.4664i	4.27053	−	0.384354i
$891$	6.82335	+	3.28595i	0.228591	+	0.110084i
$892$	3.02800	+	67.4236i	0.101385	+	2.25751i
$893$	−11.1949	−	14.0379i	−0.374622	−	0.469761i
$894$	0.925454	+	6.83197i	0.0309518	+	0.228495i
$895$	25.2723	+	2.27455i	0.844760	+	0.0760297i
$896$	−22.3574	−	13.3580i	−0.746910	−	0.446258i
$897$	17.3205	−	21.7192i	0.578315	−	0.725185i
$898$	−33.0570	−	24.0173i	−1.10313	−	0.801469i
$899$	14.3843	−	2.61037i	0.479744	−	0.0870608i
$900$	18.5644	−	81.3358i	0.618812	−	2.71119i
$901$	−0.106263	+	0.784461i	−0.00354012	+	0.0261342i
$902$	33.5619	−	20.0523i	1.11749	−	0.667668i
$903$	−4.73873	+	2.28205i	−0.157695	+	0.0759420i
$904$	2.54844	+	4.73580i	0.0847599	+	0.157510i
$905$	9.11825	−	9.53694i	0.303101	−	0.317019i
$906$	26.4795	−	19.2385i	0.879721	−	0.639155i
$907$	0.180043	−	4.00898i	0.00597825	−	0.133116i	−0.993784	−	0.111323i	$-0.964491\pi$
$907$	0.180043	−	4.00898i	0.00597825	−	0.133116i	0.999763	−	0.0217928i	$-0.00693743\pi$
$908$	−37.4416	+	69.5782i	−1.24254	+	2.30903i
$909$	1.66485	+	5.12389i	0.0552197	+	0.169949i
$910$	−96.2359	−	26.5594i	−3.19019	−	0.880437i
$911$	9.87144	+	14.9546i	0.327056	+	0.495468i	0.960485	−	0.278333i	$-0.0897818\pi$
$911$	9.87144	+	14.9546i	0.327056	+	0.495468i	−0.633429	+	0.773801i	$0.718353\pi$
$912$	−18.4764	+	5.09917i	−0.611815	+	0.168850i
$913$	−12.8555	−	11.2316i	−0.425457	−	0.371710i
$914$	−18.2197	−	6.83797i	−0.602655	−	0.226180i
$915$	7.26315	−	2.72591i	0.240112	−	0.0901157i
$916$	60.5845	−	52.9311i	2.00177	−	1.74889i
$917$	1.77637	−	2.69108i	0.0586608	−	0.0888674i
$918$	−5.84065	+	17.9757i	−0.192770	+	0.593286i
$919$	−12.3027	−	12.8676i	−0.405828	−	0.424463i	0.488020	−	0.872832i	$-0.337719\pi$
$919$	−12.3027	−	12.8676i	−0.405828	−	0.424463i	−0.893848	+	0.448370i	$0.852005\pi$
$920$	135.705	+	24.6268i	4.47406	+	0.811922i
$921$	3.99734	−	9.35225i	0.131717	−	0.308167i
$922$	−98.9561			−3.25895
$923$	45.8918	−	1.93198i	1.51055	−	0.0635918i
$924$	−16.2840			−0.535703
$925$	−28.3683	+	66.3711i	−0.932746	+	2.18227i
$926$	−80.4721	−	14.6035i	−2.64448	−	0.479902i
$927$	−19.0673	−	19.9428i	−0.626253	−	0.655009i
$928$	−6.02562	+	18.5450i	−0.197801	+	0.608768i
$929$	8.30656	−	12.5839i	0.272529	−	0.412864i	−0.672375	−	0.740211i	$-0.734726\pi$
$929$	8.30656	−	12.5839i	0.272529	−	0.412864i	0.944904	+	0.327346i	$0.106154\pi$
$930$	20.2494	−	17.6914i	0.664004	−	0.580123i
$931$	−9.80059	+	3.67822i	−0.321201	+	0.120549i
$932$	46.3798	+	17.4066i	1.51922	+	0.570174i
$933$	−2.18602	−	1.90987i	−0.0715671	−	0.0625263i
$934$	−21.6133	+	5.96490i	−0.707210	+	0.195177i
$935$	−7.62766	−	11.5554i	−0.249451	−	0.377903i
$936$	−75.0334	−	20.7079i	−2.45254	−	0.676859i
$937$	3.79918	+	11.6927i	0.124114	+	0.381983i	0.993739	−	0.111730i	$-0.0356393\pi$
$937$	3.79918	+	11.6927i	0.124114	+	0.381983i	−0.869625	+	0.493713i	$0.835639\pi$
$938$	−10.6572	+	19.8045i	−0.347971	+	0.646639i
$939$	0.475595	−	10.5899i	0.0155205	−	0.345590i
$940$	−67.1029	+	48.7531i	−2.18866	+	1.59015i
$941$	−5.43407	+	5.68360i	−0.177146	+	0.185280i	−0.805406	−	0.592723i	$-0.798053\pi$
$941$	−5.43407	+	5.68360i	−0.177146	+	0.185280i	0.628261	+	0.778003i	$0.283767\pi$
$942$	−2.29126	−	4.25788i	−0.0746533	−	0.138729i
$943$	−38.3932	+	18.4892i	−1.25026	+	0.602091i
$944$	−49.6811	+	29.6831i	−1.61698	+	0.966102i
$945$	4.24521	−	31.3394i	0.138097	−	1.01947i
$946$	4.05825	−	17.7803i	0.131945	−	0.578089i
$947$	27.4712	−	4.98528i	0.892692	−	0.162000i	0.287219	−	0.957865i	$-0.407269\pi$
$947$	27.4712	−	4.98528i	0.892692	−	0.162000i	0.605474	+	0.795865i	$0.292984\pi$
$948$	8.67286	+	6.30120i	0.281681	+	0.204653i
$949$	2.88260	−	3.61466i	0.0935730	−	0.117337i
$950$	61.2224	+	36.5787i	1.98632	+	1.18677i
$951$	21.9405	+	1.97468i	0.711470	+	0.0640334i
$952$	2.80370	+	20.6978i	0.0908685	+	0.670818i
$953$	26.9323	+	33.7720i	0.872421	+	1.09398i	0.994835	+	0.101503i	$0.0323650\pi$
$953$	26.9323	+	33.7720i	0.872421	+	1.09398i	−0.122414	+	0.992479i	$0.539064\pi$
$954$	−0.122796	−	2.73426i	−0.00397566	−	0.0885248i
$955$	60.0900	+	28.9378i	1.94447	+	0.936406i
$956$	108.557	−	9.77030i	3.51098	−	0.315994i
$957$	−1.68386	−	7.37747i	−0.0544315	−	0.238480i
$958$	31.8462	+	74.5080i	1.02891	+	2.40724i
$959$	6.45378	+	15.0994i	0.208403	+	0.487584i
$960$	−0.926559	−	4.05952i	−0.0299046	−	0.131020i
$961$	18.2254	−	1.64031i	0.587915	−	0.0529133i
$962$	110.738	+	53.3285i	3.57033	+	1.71938i
$963$	−1.06177	−	23.6421i	−0.0342150	−	0.761857i
$964$	6.34994	+	7.96257i	0.204518	+	0.256457i
$965$	−4.80513	−	35.4729i	−0.154683	−	1.14191i
$966$	25.6693	+	2.31028i	0.825896	+	0.0743320i
$967$	−30.3907	−	18.1576i	−0.977299	−	0.583909i	−0.0669527	−	0.997756i	$-0.521328\pi$
$967$	−30.3907	−	18.1576i	−0.977299	−	0.583909i	−0.910346	+	0.413847i	$0.864185\pi$
$968$	−22.8458	+	28.6477i	−0.734291	+	0.920771i
$969$	−3.92966	−	2.85507i	−0.126239	−	0.0917179i
$970$	−131.735	+	23.9063i	−4.22974	+	0.767585i
$971$	0.280594	−	1.22936i	0.00900468	−	0.0394521i	−0.970226	−	0.242201i	$-0.922131\pi$
$971$	0.280594	−	1.22936i	0.00900468	−	0.0394521i	0.979231	+	0.202749i	$0.0649877\pi$
$972$	9.44475	−	69.7240i	0.302941	−	2.23640i
$973$	−20.7265	+	12.3835i	−0.664462	+	0.396997i
$974$	−41.8190	+	20.1389i	−1.33997	+	0.645294i
$975$	−17.2290	−	32.0169i	−0.551771	−	1.02536i
$976$	12.1084	−	12.6644i	0.387580	−	0.405377i
$977$	47.2693	−	34.3431i	1.51228	−	1.09873i	0.547124	−	0.837052i	$-0.315723\pi$
$977$	47.2693	−	34.3431i	1.51228	−	1.09873i	0.965154	−	0.261682i	$-0.0842773\pi$
$978$	−0.297269	+	6.61921i	−0.00950562	+	0.211659i
$979$	−14.8203	+	27.5407i	−0.473658	+	0.880204i
$980$	14.9432	+	45.9905i	0.477343	+	1.46911i
$981$	20.2904	+	5.59979i	0.647822	+	0.178788i
$982$	−0.549165	−	0.831949i	−0.0175245	−	0.0265486i
$983$	16.5094	−	4.55630i	0.526568	−	0.145323i	0.00736214	−	0.999973i	$-0.497657\pi$
$983$	16.5094	−	4.55630i	0.526568	−	0.145323i	0.519205	+	0.854649i	$0.326228\pi$
$984$	−26.1427	−	22.8402i	−0.833400	−	0.728119i
$985$	−3.95828	−	1.48557i	−0.126121	−	0.0473342i
$986$	−16.5851	+	6.22450i	−0.528178	+	0.198228i
$987$	−6.39539	+	5.58748i	−0.203567	+	0.177851i
$988$	46.0730	−	69.7976i	1.46578	−	2.22056i
$989$	−6.14276	+	18.9055i	−0.195328	+	0.601159i
$990$	33.0823	+	34.6014i	1.05142	+	1.09970i
$991$	−39.8730	−	7.23588i	−1.26661	−	0.229855i	−0.496649	−	0.867951i	$-0.665437\pi$
$991$	−39.8730	−	7.23588i	−1.26661	−	0.229855i	−0.769957	+	0.638096i	$0.779722\pi$
$992$	6.65810	−	15.5774i	0.211395	−	0.494583i
$993$	8.28109			0.262792
$994$	24.9511	+	34.5457i	0.791401	+	1.09572i
$995$	−53.0827			−1.68283
$996$	−10.8729	+	25.4384i	−0.344521	+	0.806047i
$997$	−2.31669	−	0.420417i	−0.0733703	−	0.0133147i	0.141748	−	0.989903i	$-0.454728\pi$
$997$	−2.31669	−	0.420417i	−0.0733703	−	0.0133147i	−0.215118	+	0.976588i	$0.569014\pi$
$998$	53.3197	+	55.7681i	1.68781	+	1.76531i
$999$	−12.0318	+	37.0301i	−0.380669	+	1.17158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.15.1	✓	120
3.2	odd	2		639.2.v.a.370.5		120
71.19	even	35	inner	71.2.g.a.19.1	yes	120
71.27	even	35		5041.2.a.s.1.57		60
71.44	odd	70		5041.2.a.t.1.57		60
213.161	odd	70		639.2.v.a.19.5		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.15.1	✓	120	1.1	even	1	trivial
71.2.g.a.19.1	yes	120	71.19	even	35	inner
639.2.v.a.19.5		120	213.161	odd	70
639.2.v.a.370.5		120	3.2	odd	2
5041.2.a.s.1.57		60	71.27	even	35
5041.2.a.t.1.57		60	71.44	odd	70

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.996141 + 2.33059i) q^{2} +(0.808832 + 0.146781i) q^{3} +(-3.05722 - 3.19760i) q^{4} +(-1.11904 + 3.44404i) q^{5} +(-1.14780 + 1.73884i) q^{6} +(1.50266 - 1.31283i) q^{7} +(5.75184 - 2.15870i) q^{8} +(-2.17604 - 0.816681i) q^{9} +O(q^{10})\)	\(q+(-0.996141 + 2.33059i) q^{2} +(0.808832 + 0.146781i) q^{3} +(-3.05722 - 3.19760i) q^{4} +(-1.11904 + 3.44404i) q^{5} +(-1.14780 + 1.73884i) q^{6} +(1.50266 - 1.31283i) q^{7} +(5.75184 - 2.15870i) q^{8} +(-2.17604 - 0.816681i) q^{9} +(-6.91193 - 6.03877i) q^{10} +(2.16318 - 0.597001i) q^{11} +(-2.00343 - 3.03507i) q^{12} +(5.25473 + 1.45021i) q^{13} +(1.56281 + 4.80984i) q^{14} +(-1.41064 + 2.62140i) q^{15} +(-0.301642 + 6.71658i) q^{16} +(-1.37843 + 1.00148i) q^{17} +(4.07099 - 4.25792i) q^{18} +(1.64337 + 3.05389i) q^{19} +(14.4338 - 6.95096i) q^{20} +(1.40810 - 0.841299i) q^{21} +(-0.763473 + 5.63619i) q^{22} +(1.37949 - 6.04393i) q^{23} +(4.96913 - 0.901765i) q^{24} +(-6.56411 - 4.76911i) q^{25} +(-8.61430 + 10.8020i) q^{26} +(-3.75722 - 2.24484i) q^{27} +(-8.79186 - 0.791282i) q^{28} +(-0.550640 - 4.06499i) q^{29} +(-4.70421 - 5.89890i) q^{30} +(0.159891 + 3.56025i) q^{31} +(-4.28274 - 2.06246i) q^{32} +(1.83728 - 0.165358i) q^{33} +(-0.960942 - 4.21016i) q^{34} +(2.83992 + 6.64433i) q^{35} +(4.04121 + 9.45488i) q^{36} +(-1.97955 - 8.67297i) q^{37} +(-8.75439 + 0.787910i) q^{38} +(4.03733 + 1.94428i) q^{39} +(0.998138 + 22.2253i) q^{40} +(-4.28575 - 5.37417i) q^{41} +(0.558058 + 4.11975i) q^{42} +(-3.19361 - 0.287430i) q^{43} +(-8.52229 - 5.09183i) q^{44} +(5.24776 - 6.58048i) q^{45} +(12.7117 + 9.23563i) q^{46} +(-5.09420 + 0.924462i) q^{47} +(-1.22985 + 5.38831i) q^{48} +(-0.405182 + 2.99117i) q^{49} +(17.6536 - 10.5475i) q^{50} +(-1.26191 + 0.607706i) q^{51} +(-11.4277 - 21.2361i) q^{52} +(0.321079 - 0.335822i) q^{53} +(8.97451 - 6.52037i) q^{54} +(-0.364587 + 8.11817i) q^{55} +(5.80903 - 10.7950i) q^{56} +(0.880956 + 2.71130i) q^{57} +(10.0223 + 2.76599i) q^{58} +(4.74200 + 7.18382i) q^{59} +(12.6948 - 3.50355i) q^{60} +(-1.96254 - 1.71462i) q^{61} +(-8.45675 - 3.17387i) q^{62} +(-4.34201 + 1.62958i) q^{63} +(-1.05337 + 0.920302i) q^{64} +(-10.8748 + 16.4747i) q^{65} +(-1.44481 + 4.44667i) q^{66} +(3.07312 + 3.21423i) q^{67} +(7.41649 + 1.34590i) q^{68} +(2.00291 - 4.68604i) q^{69} -18.3142 q^{70} +(8.02102 - 2.58133i) q^{71} -14.2792 q^{72} +(0.333338 - 0.779882i) q^{73} +(22.1850 + 4.02599i) q^{74} +(-4.60925 - 4.82090i) q^{75} +(4.74098 - 14.5913i) q^{76} +(2.46676 - 3.73698i) q^{77} +(-8.55306 + 7.47258i) q^{78} +(-2.75985 + 1.03579i) q^{79} +(-22.7947 - 8.55498i) q^{80} +(2.54150 + 2.22045i) q^{81} +(16.7942 - 4.63490i) q^{82} +(-4.19075 - 6.34871i) q^{83} +(-6.99500 - 1.93050i) q^{84} +(-1.90665 - 5.86806i) q^{85} +(3.85117 - 7.15667i) q^{86} +(0.151289 - 3.36872i) q^{87} +(11.1535 - 8.10352i) q^{88} +(-9.63125 + 10.0735i) q^{89} +(10.1089 + 18.7854i) q^{90} +(9.79995 - 4.71940i) q^{91} +(-23.5435 + 14.0666i) q^{92} +(-0.393254 + 2.90312i) q^{93} +(2.92001 - 12.7934i) q^{94} +(-12.3567 + 2.24242i) q^{95} +(-3.16129 - 2.29681i) q^{96} +(9.09498 - 11.4047i) q^{97} +(-6.56758 - 3.92394i) q^{98} +(-5.19473 - 0.467534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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